Subgroups — C₃²×#3513 #11770562

Order 1152.

3456 conjugacy classes of subgroups.

The subgroup lattice has 1017 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×#559	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃²×#554	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃²×#553	C₂	1	2	yes	maximal, complemented
4	C₃²×#553	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃²×#552	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃²×#551	C₂	1	2	yes	maximal, complemented
7	C₃²×#551	C₂	1	2	yes	maximal, complemented
8	C₃²×#547	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃²×#546	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃²×#546	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃²×#546	C₂	1	2	yes	maximal, complemented
12	C₃²×D₄²	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃²×#542	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃²×#540	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃²×#539	C₂	1	2	yes	maximal, complemented
16	C₃²×#538	C₂	1	2	yes	maximal, complemented
17	C₃²×#529	C₂	1	1	yes	maximal, characteristic, complemented
18	C₃²×#529	C₂	1	1	yes	maximal, characteristic, complemented
19	C₃²×#525	C₂	1	2	yes	maximal, complemented
20	C₂×C₃²×#123	C₂	1	2	yes	maximal, complemented
21	C₃²×#520	C₂	1	1	yes	maximal, characteristic, complemented
22	C₃²×#518	C₂	1	1	yes	maximal, characteristic, complemented
23	C₂×C₃²×C₄×D₄	C₂	1	1	yes	maximal, characteristic, complemented
24	C₃×#3513	C₃	1	4	yes	maximal, direct product factor
25	C₂×C₃²×#41	C₂²	1	1	yes	characteristic
26	C₂×C₃²×#41	C₂²	1	2	yes	complemented
27	C₂²×C₃²×D₄	C₂²	1	1	yes	characteristic
28	C₂²×C₃²×D₄	C₂²	1	1	yes	characteristic
29	C₂²×C₃²×D₄	C₂²	1	2	yes	—
30	C₂³×C₃²×C₄	C₂²	1	2	yes	complemented
31	C₃²×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
32	C₃²×#127	C₂²	1	1	yes	characteristic
33	C₃²×#126	C₂²	1	1	yes	characteristic, complemented
34	C₃²×#126	C₂²	1	2	yes	complemented
35	C₃²×#126	C₂²	1	2	yes	complemented
36	C₃²×#126	C₂²	1	2	yes	complemented
37	C₃²×#126	C₂²	1	1	yes	characteristic, complemented
38	C₃²×#126	C₂²	1	2	yes	complemented
39	C₃²×#125	C₂²	1	2	yes	complemented
40	C₃²×#125	C₂²	1	1	yes	characteristic, complemented
41	C₃²×#125	C₂²	1	1	yes	characteristic, complemented
42	C₃²×#125	C₂²	1	1	yes	characteristic, complemented
43	C₃²×#124	C₂²	1	2	yes	complemented
44	C₃²×#124	C₂²	1	2	yes	complemented
45	C₃²×#124	C₂²	1	1	yes	characteristic, complemented
46	C₃²×#124	C₂²	1	1	yes	characteristic, complemented
47	C₃²×#124	C₂²	1	1	yes	characteristic, complemented
48	C₃²×#123	C₂²	1	2	yes	—
49	C₃²×#123	C₂²	1	1	yes	characteristic
50	C₃²×#123	C₂²	1	2	yes	complemented
51	C₃²×#123	C₂²	1	2	yes	complemented
52	C₃²×#123	C₂²	1	2	yes	complemented
53	C₃²×#123	C₂²	1	2	yes	complemented
54	C₃²×#123	C₂²	1	2	yes	complemented
55	C₃²×#123	C₂²	1	2	yes	complemented
56	C₃²×#123	C₂²	1	2	yes	complemented
57	C₃²×#123	C₂²	1	2	yes	complemented
58	C₃²×#123	C₂²	1	2	yes	complemented
59	C₃²×#123	C₂²	1	2	yes	complemented
60	C₃²×#123	C₂²	1	2	yes	complemented
61	C₃²×#123	C₂²	1	1	yes	characteristic, complemented
62	C₃²×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
63	C₃²×C₂²⋊Q₈	C₂²	1	2	yes	complemented
64	C₃²×C₂²⋊Q₈	C₂²	1	2	yes	complemented
65	C₃²×C₂²⋊Q₈	C₂²	1	2	yes	complemented
66	C₃²×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
67	C₃²×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
68	C₃²×C₂²⋊Q₈	C₂²	1	2	yes	complemented
69	C₃²×C₂²⋊Q₈	C₂²	1	2	yes	complemented
70	C₃²×#121	C₂²	1	2	yes	—
71	C₃²×#121	C₂²	1	1	yes	characteristic
72	C₃²×#121	C₂²	1	1	yes	characteristic
73	C₃²×#121	C₂²	1	1	yes	characteristic
74	C₃²×#121	C₂²	1	2	yes	complemented
75	C₃²×#121	C₂²	1	2	yes	complemented
76	C₃²×#121	C₂²	1	2	yes	complemented
77	C₃²×#121	C₂²	1	2	yes	complemented
78	C₃²×#121	C₂²	1	1	yes	characteristic, complemented
79	C₃²×#121	C₂²	1	2	yes	complemented
80	C₃²×#121	C₂²	1	1	yes	characteristic, complemented
81	C₃²×#120	C₂²	1	2	yes	—
82	C₃²×#120	C₂²	1	2	yes	—
83	C₃²×#120	C₂²	1	2	yes	complemented
84	C₃²×#120	C₂²	1	2	yes	complemented
85	C₃²×C₄×Q₈	C₂²	1	1	yes	characteristic, complemented
86	C₃²×C₄×Q₈	C₂²	1	1	yes	characteristic, complemented
87	C₃²×C₄×Q₈	C₂²	1	1	yes	characteristic, complemented
88	C₃²×C₄×D₄	C₂²	1	1	yes	characteristic
89	C₃²×C₄×D₄	C₂²	1	1	yes	characteristic
90	C₃²×C₄×D₄	C₂²	1	1	yes	characteristic
91	C₃²×C₄×D₄	C₂²	1	1	yes	characteristic
92	C₃²×C₄×D₄	C₂²	1	1	yes	characteristic
93	C₃²×C₄×D₄	C₂²	1	2	yes	complemented
94	C₃²×C₄×D₄	C₂²	1	2	yes	complemented
95	C₃²×C₄×D₄	C₂²	1	2	yes	complemented
96	C₃²×C₄×D₄	C₂²	1	2	yes	complemented
97	C₃²×C₄×D₄	C₂²	1	2	yes	complemented
98	C₃²×C₄×D₄	C₂²	1	1	yes	characteristic, complemented
99	C₃²×C₄×D₄	C₂²	1	2	yes	complemented
100	C₃²×C₄×D₄	C₂²	1	1	yes	characteristic, complemented
101	C₃²×C₄×D₄	C₂²	1	1	yes	characteristic, complemented
102	C₃²×C₄×D₄	C₂²	1	2	yes	complemented
103	C₃²×C₄×D₄	C₂²	1	1	yes	characteristic, complemented
104	C₃²×C₄×D₄	C₂²	1	2	yes	complemented
105	C₃²×C₄×D₄	C₂²	1	1	yes	characteristic, complemented
106	C₃²×C₄×D₄	C₂²	1	2	yes	complemented
107	C₃²×C₄×D₄	C₂²	1	1	yes	characteristic, complemented
108	C₃²×#117	C₂²	1	2	yes	complemented
109	C₃²×#117	C₂²	1	2	yes	complemented
110	C₃²×#117	C₂²	1	2	yes	complemented
111	C₃²×#117	C₂²	1	1	yes	characteristic, complemented
112	C₃²×#117	C₂²	1	1	yes	characteristic, complemented
113	C₃²×#117	C₂²	1	1	yes	characteristic, complemented
114	C₂×C₃²×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
115	C₂×C₃²×C₄⋊C₄	C₂²	1	2	yes	complemented
116	C₂×C₃²×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
117	C₂×C₃²×C₄⋊C₄	C₂²	1	2	yes	complemented
118	C₂×C₃²×C₂²⋊C₄	C₂²	1	2	yes	complemented
119	C₂×C₃²×C₂²⋊C₄	C₂²	1	2	yes	complemented
120	C₂×C₃²×C₂²⋊C₄	C₂²	1	2	yes	complemented
121	C₂×C₃²×C₂²⋊C₄	C₂²	1	2	yes	complemented
122	C₂×C₃²×C₂²⋊C₄	C₂²	1	2	yes	complemented
123	C₂×C₃²×C₄²	C₂²	1	1	yes	characteristic, complemented
124	C₃×#559	C₂×C₃	1	4	yes	complemented
125	C₃×#554	C₂×C₃	1	4	yes	complemented
126	C₃×#553	C₂×C₃	1	4	yes	complemented
127	C₃×#553	C₂×C₃	1	8	yes	complemented
128	C₃×#552	C₂×C₃	1	4	yes	complemented
129	C₃×#551	C₂×C₃	1	8	yes	complemented
130	C₃×#551	C₂×C₃	1	8	yes	complemented
131	C₃×#547	C₂×C₃	1	4	yes	complemented
132	C₃×#546	C₂×C₃	1	4	yes	complemented
133	C₃×#546	C₂×C₃	1	4	yes	complemented
134	C₃×#546	C₂×C₃	1	8	yes	complemented
135	C₃×D₄²	C₂×C₃	1	4	yes	complemented
136	C₃×#542	C₂×C₃	1	4	yes	complemented
137	C₃×#540	C₂×C₃	1	4	yes	complemented
138	C₃×#539	C₂×C₃	1	8	yes	complemented
139	C₃×#538	C₂×C₃	1	8	yes	complemented
140	C₃×#529	C₂×C₃	1	4	yes	complemented
141	C₃×#529	C₂×C₃	1	4	yes	complemented
142	C₃×#525	C₂×C₃	1	8	yes	complemented
143	C₂×C₃×#123	C₂×C₃	1	8	yes	complemented
144	C₃×#520	C₂×C₃	1	4	yes	complemented
145	C₃×#518	C₂×C₃	1	4	yes	complemented
146	C₂×C₃×C₄×D₄	C₂×C₃	1	4	yes	complemented
147	C₂⁴×C₃²	C₂³	1	2	yes	—
148	C₂⁴×C₃²	C₂³	1	2	yes	—
149	C₃²×#41	—	2	4	no	—
150	C₃²×#41	—	4	4	no	—
151	C₂×C₃²×Q₈	C₂³	1	1	yes	characteristic
152	C₂×C₃²×Q₈	C₂³	1	2	yes	—
153	C₂×C₃²×Q₈	C₂³	1	1	yes	characteristic
154	C₂×C₃²×D₄	—	2	4	no	—
155	C₂×C₃²×D₄	—	2	4	no	—
156	C₂×C₃²×D₄	—	4	4	no	—
157	C₂×C₃²×D₄	C₂³	1	1	yes	characteristic
158	C₂×C₃²×D₄	C₂³	1	2	yes	—
159	C₂×C₃²×D₄	C₂³	1	2	yes	—
160	C₂×C₃²×D₄	C₂³	1	2	yes	—
161	C₂×C₃²×D₄	C₂³	1	1	yes	characteristic
162	C₂×C₃²×D₄	C₂³	1	1	yes	characteristic
163	C₂×C₃²×D₄	C₂³	1	2	yes	—
164	C₂×C₃²×D₄	C₂³	1	1	yes	characteristic
165	C₂×C₃²×D₄	C₂³	1	2	yes	—
166	C₂×C₃²×D₄	C₂³	1	2	yes	—
167	C₂×C₃²×D₄	C₂³	1	2	yes	—
168	C₂×C₃²×D₄	C₂³	1	2	yes	—
169	C₂×C₃²×D₄	C₂³	1	1	yes	characteristic
170	C₂×C₃²×D₄	C₂³	1	2	yes	—
171	C₂×C₃²×D₄	C₂³	1	1	yes	characteristic
172	C₂²×C₃²×C₄	—	4	4	no	—
173	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
174	C₂²×C₃²×C₄	C₂³	1	2	yes	—
175	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
176	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
177	C₂²×C₃²×C₄	C₂³	1	2	yes	—
178	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
179	C₂²×C₃²×C₄	C₂³	1	2	yes	—
180	C₂²×C₃²×C₄	C₂³	1	2	yes	—
181	C₂²×C₃²×C₄	C₂³	1	2	yes	—
182	C₂²×C₃²×C₄	C₂³	1	2	yes	—
183	C₂²×C₃²×C₄	C₂³	1	2	yes	—
184	C₂²×C₃²×C₄	C₂³	1	2	yes	—
185	C₂²×C₃²×C₄	C₂³	1	2	yes	—
186	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
187	C₂²×C₃²×C₄	C₂³	1	2	yes	—
188	C₂²×C₃²×C₄	C₂³	1	2	yes	—
189	C₃²×C₄⋊C₄	C₂³	1	1	yes	characteristic
190	C₃²×C₄⋊C₄	C₂³	1	2	yes	—
191	C₃²×C₄⋊C₄	C₂³	1	1	yes	characteristic
192	C₃²×C₄⋊C₄	C₂³	1	1	yes	characteristic
193	C₃²×C₄⋊C₄	C₂³	1	2	yes	—
194	C₃²×C₄⋊C₄	C₂³	1	1	yes	characteristic
195	C₃²×C₄⋊C₄	C₂³	1	1	yes	characteristic
196	C₃²×C₄⋊C₄	C₂³	1	2	yes	—
197	C₃²×C₄⋊C₄	C₂³	1	2	yes	—
198	C₃²×C₄⋊C₄	C₂³	1	2	yes	—
199	C₃²×C₄⋊C₄	C₂³	1	2	yes	—
200	C₃²×C₄⋊C₄	C₂³	1	2	yes	—
201	C₃²×C₄⋊C₄	C₂³	1	1	yes	characteristic
202	C₃²×C₄⋊C₄	C₂³	1	1	yes	characteristic
203	C₃²×C₄⋊C₄	C₂³	1	1	yes	characteristic
204	C₃²×C₄⋊C₄	C₂³	1	1	yes	characteristic
205	C₃²×C₄⋊C₄	C₂³	1	2	yes	—
206	C₃²×C₄⋊C₄	C₂³	1	2	yes	—
207	C₃²×C₄⋊C₄	C₂³	1	2	yes	—
208	C₃²×C₄⋊C₄	C₂³	1	1	yes	characteristic
209	C₃²×C₄⋊C₄	C₂³	1	1	yes	characteristic
210	C₃²×C₄⋊C₄	C₂³	1	2	yes	—
211	C₃²×C₄⋊C₄	C₂³	1	1	yes	characteristic
212	C₃²×C₄⋊C₄	C₂³	1	1	yes	characteristic
213	C₃²×C₄⋊C₄	C₂³	1	1	yes	characteristic
214	C₃²×C₂²⋊C₄	C₂³	1	2	yes	—
215	C₃²×C₂²⋊C₄	C₂³	1	1	yes	characteristic
216	C₃²×C₂²⋊C₄	C₂³	1	2	yes	—
217	C₃²×C₂²⋊C₄	C₂³	1	1	yes	characteristic
218	C₃²×C₂²⋊C₄	C₂³	1	1	yes	characteristic
219	C₃²×C₂²⋊C₄	C₂³	1	1	yes	characteristic
220	C₃²×C₂²⋊C₄	C₂³	1	2	yes	—
221	C₃²×C₂²⋊C₄	C₂³	1	2	yes	—
222	C₃²×C₂²⋊C₄	C₂³	1	2	yes	—
223	C₃²×C₂²⋊C₄	C₂³	1	2	yes	—
224	C₃²×C₂²⋊C₄	C₂³	1	2	yes	—
225	C₃²×C₂²⋊C₄	C₂³	1	2	yes	—
226	C₃²×C₂²⋊C₄	C₂³	1	2	yes	—
227	C₃²×C₂²⋊C₄	C₂³	1	2	yes	—
228	C₃²×C₂²⋊C₄	C₂³	1	2	yes	—
229	C₃²×C₂²⋊C₄	C₂³	1	2	yes	—
230	C₃²×C₂²⋊C₄	C₂³	1	2	yes	—
231	C₃²×C₂²⋊C₄	C₂³	1	2	yes	—
232	C₃²×C₂²⋊C₄	C₂³	1	1	yes	characteristic
233	C₃²×C₂²⋊C₄	C₂³	1	2	yes	—
234	C₃²×C₂²⋊C₄	C₂³	1	1	yes	characteristic
235	C₃²×C₂²⋊C₄	C₂³	1	1	yes	characteristic
236	C₃²×C₂²⋊C₄	C₂³	1	2	yes	—
237	C₃²×C₂²⋊C₄	C₂³	1	1	yes	characteristic
238	C₃²×C₂²⋊C₄	C₂³	1	1	yes	characteristic
239	C₃²×C₂²⋊C₄	C₂³	1	2	yes	—
240	C₃²×C₂²⋊C₄	C₂³	1	2	yes	—
241	C₃²×C₂²⋊C₄	C₂³	1	2	yes	—
242	C₃²×C₂²⋊C₄	C₂³	1	1	yes	characteristic
243	C₃²×C₄²	C₂³	1	1	yes	characteristic
244	C₃²×C₄²	C₂³	1	1	yes	characteristic
245	C₃²×C₄²	C₂³	1	1	yes	characteristic
246	C₃²×C₄²	C₂³	1	1	yes	characteristic
247	C₃²×C₄²	C₂³	1	2	yes	—
248	C₃²×C₄²	C₂³	1	2	yes	—
249	C₃²×C₄²	C₂³	1	2	yes	—
250	C₃²×C₄²	C₂³	1	1	yes	characteristic
251	C₃²×C₄²	C₂³	1	1	yes	characteristic
252	#3513	C₃²	1	1	yes	characteristic, direct product factor, Sylow
253	C₂×C₃×#41	C₂²×C₃	1	4	yes	—
254	C₂×C₃×#41	C₂²×C₃	1	8	yes	complemented
255	C₂²×C₃×D₄	C₂²×C₃	1	4	yes	—
256	C₂²×C₃×D₄	C₂²×C₃	1	4	yes	—
257	C₂²×C₃×D₄	C₂²×C₃	1	8	yes	—
258	C₂³×C₃×C₄	C₂²×C₃	1	8	yes	complemented
259	C₃×C₄⋊Q₈	C₂²×C₃	1	4	yes	complemented
260	C₃×#127	C₂²×C₃	1	4	yes	—
261	C₃×#126	C₂²×C₃	1	8	yes	complemented
262	C₃×#126	C₂²×C₃	1	4	yes	complemented
263	C₃×#126	C₂²×C₃	1	4	yes	complemented
264	C₃×#126	C₂²×C₃	1	8	yes	complemented
265	C₃×#126	C₂²×C₃	1	8	yes	complemented
266	C₃×#126	C₂²×C₃	1	8	yes	complemented
267	C₃×#125	C₂²×C₃	1	4	yes	complemented
268	C₃×#125	C₂²×C₃	1	4	yes	complemented
269	C₃×#125	C₂²×C₃	1	8	yes	complemented
270	C₃×#125	C₂²×C₃	1	4	yes	complemented
271	C₃×#124	C₂²×C₃	1	4	yes	complemented
272	C₃×#124	C₂²×C₃	1	8	yes	complemented
273	C₃×#124	C₂²×C₃	1	4	yes	complemented
274	C₃×#124	C₂²×C₃	1	4	yes	complemented
275	C₃×#124	C₂²×C₃	1	8	yes	complemented
276	C₃×#123	C₂²×C₃	1	4	yes	—
277	C₃×#123	C₂²×C₃	1	8	yes	—
278	C₃×#123	C₂²×C₃	1	8	yes	complemented
279	C₃×#123	C₂²×C₃	1	8	yes	complemented
280	C₃×#123	C₂²×C₃	1	8	yes	complemented
281	C₃×#123	C₂²×C₃	1	8	yes	complemented
282	C₃×#123	C₂²×C₃	1	8	yes	complemented
283	C₃×#123	C₂²×C₃	1	8	yes	complemented
284	C₃×#123	C₂²×C₃	1	8	yes	complemented
285	C₃×#123	C₂²×C₃	1	4	yes	complemented
286	C₃×#123	C₂²×C₃	1	8	yes	complemented
287	C₃×#123	C₂²×C₃	1	8	yes	complemented
288	C₃×#123	C₂²×C₃	1	8	yes	complemented
289	C₃×#123	C₂²×C₃	1	8	yes	complemented
290	C₃×C₂²⋊Q₈	C₂²×C₃	1	8	yes	complemented
291	C₃×C₂²⋊Q₈	C₂²×C₃	1	8	yes	complemented
292	C₃×C₂²⋊Q₈	C₂²×C₃	1	4	yes	complemented
293	C₃×C₂²⋊Q₈	C₂²×C₃	1	4	yes	complemented
294	C₃×C₂²⋊Q₈	C₂²×C₃	1	8	yes	complemented
295	C₃×C₂²⋊Q₈	C₂²×C₃	1	8	yes	complemented
296	C₃×C₂²⋊Q₈	C₂²×C₃	1	8	yes	complemented
297	C₃×C₂²⋊Q₈	C₂²×C₃	1	4	yes	complemented
298	C₃×#121	C₂²×C₃	1	4	yes	—
299	C₃×#121	C₂²×C₃	1	4	yes	—
300	C₃×#121	C₂²×C₃	1	8	yes	—
301	C₃×#121	C₂²×C₃	1	4	yes	—
302	C₃×#121	C₂²×C₃	1	8	yes	complemented
303	C₃×#121	C₂²×C₃	1	8	yes	complemented
304	C₃×#121	C₂²×C₃	1	8	yes	complemented
305	C₃×#121	C₂²×C₃	1	8	yes	complemented
306	C₃×#121	C₂²×C₃	1	4	yes	complemented
307	C₃×#121	C₂²×C₃	1	8	yes	complemented
308	C₃×#121	C₂²×C₃	1	4	yes	complemented
309	C₃×#120	C₂²×C₃	1	8	yes	—
310	C₃×#120	C₂²×C₃	1	8	yes	—
311	C₃×#120	C₂²×C₃	1	8	yes	complemented
312	C₃×#120	C₂²×C₃	1	8	yes	complemented
313	C₃×C₄×Q₈	C₂²×C₃	1	4	yes	complemented
314	C₃×C₄×Q₈	C₂²×C₃	1	4	yes	complemented
315	C₃×C₄×Q₈	C₂²×C₃	1	4	yes	complemented
316	C₃×C₄×D₄	C₂²×C₃	1	4	yes	—
317	C₃×C₄×D₄	C₂²×C₃	1	4	yes	—
318	C₃×C₄×D₄	C₂²×C₃	1	4	yes	—
319	C₃×C₄×D₄	C₂²×C₃	1	4	yes	—
320	C₃×C₄×D₄	C₂²×C₃	1	4	yes	—
321	C₃×C₄×D₄	C₂²×C₃	1	4	yes	complemented
322	C₃×C₄×D₄	C₂²×C₃	1	4	yes	complemented
323	C₃×C₄×D₄	C₂²×C₃	1	8	yes	complemented
324	C₃×C₄×D₄	C₂²×C₃	1	8	yes	complemented
325	C₃×C₄×D₄	C₂²×C₃	1	4	yes	complemented
326	C₃×C₄×D₄	C₂²×C₃	1	8	yes	complemented
327	C₃×C₄×D₄	C₂²×C₃	1	8	yes	complemented
328	C₃×C₄×D₄	C₂²×C₃	1	4	yes	complemented
329	C₃×C₄×D₄	C₂²×C₃	1	8	yes	complemented
330	C₃×C₄×D₄	C₂²×C₃	1	8	yes	complemented
331	C₃×C₄×D₄	C₂²×C₃	1	8	yes	complemented
332	C₃×C₄×D₄	C₂²×C₃	1	8	yes	complemented
333	C₃×C₄×D₄	C₂²×C₃	1	4	yes	complemented
334	C₃×C₄×D₄	C₂²×C₃	1	8	yes	complemented
335	C₃×C₄×D₄	C₂²×C₃	1	4	yes	complemented
336	C₃×#117	C₂²×C₃	1	4	yes	complemented
337	C₃×#117	C₂²×C₃	1	4	yes	complemented
338	C₃×#117	C₂²×C₃	1	4	yes	complemented
339	C₃×#117	C₂²×C₃	1	8	yes	complemented
340	C₃×#117	C₂²×C₃	1	8	yes	complemented
341	C₃×#117	C₂²×C₃	1	8	yes	complemented
342	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	4	yes	complemented
343	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	8	yes	complemented
344	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	4	yes	complemented
345	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	8	yes	complemented
346	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	8	yes	complemented
347	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	8	yes	complemented
348	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	8	yes	complemented
349	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	8	yes	complemented
350	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	8	yes	complemented
351	C₂×C₃×C₄²	C₂²×C₃	1	4	yes	complemented
352	C₂³×C₃²	—	2	4	no	—
353	C₂³×C₃²	—	2	4	no	—
354	C₂³×C₃²	—	2	4	no	—
355	C₂³×C₃²	—	4	2	no	—
356	C₂³×C₃²	—	4	2	no	—
357	C₂³×C₃²	—	4	2	no	—
358	C₂³×C₃²	C₂⁴	1	1	yes	characteristic
359	C₂³×C₃²	C₂⁴	1	2	yes	—
360	C₂³×C₃²	C₂⁴	1	2	yes	—
361	C₂³×C₃²	C₂⁴	1	1	yes	characteristic
362	C₂³×C₃²	C₂⁴	1	2	yes	—
363	C₂³×C₃²	C₂⁴	1	1	yes	characteristic
364	C₃²×Q₈	—	2	2	no	—
365	C₃²×Q₈	—	4	1	no	—
366	C₃²×Q₈	—	4	2	no	—
367	C₃²×D₄	—	2	4	no	—
368	C₃²×D₄	—	2	4	no	—
369	C₃²×D₄	—	2	4	no	—
370	C₃²×D₄	—	2	2	no	—
371	C₃²×D₄	—	2	4	no	—
372	C₃²×D₄	—	2	2	no	—
373	C₃²×D₄	—	2	2	no	—
374	C₃²×D₄	—	2	2	no	—
375	C₃²×D₄	—	4	2	no	—
376	C₃²×D₄	—	4	2	no	—
377	C₃²×D₄	—	4	2	no	—
378	C₃²×D₄	—	4	1	no	—
379	C₃²×D₄	—	4	2	no	—
380	C₃²×D₄	—	4	2	no	—
381	C₃²×D₄	#41	1	4	yes	complemented
382	C₂×C₃²×C₄	—	2	4	no	—
383	C₂×C₃²×C₄	—	2	2	no	—
384	C₂×C₃²×C₄	—	2	4	no	—
385	C₂×C₃²×C₄	—	2	2	no	—
386	C₂×C₃²×C₄	—	2	2	no	—
387	C₂×C₃²×C₄	—	2	2	no	—
388	C₂×C₃²×C₄	—	4	2	no	—
389	C₂×C₃²×C₄	—	4	2	no	—
390	C₂×C₃²×C₄	—	4	2	no	—
391	C₂×C₃²×C₄	—	4	2	no	—
392	C₂×C₃²×C₄	—	4	2	no	—
393	C₂×C₃²×C₄	—	4	1	no	—
394	C₂×C₃²×C₄	—	4	2	no	—
395	C₂×C₃²×C₄	—	4	2	no	—
396	C₂×C₃²×C₄	—	4	2	no	—
397	C₂×C₃²×C₄	—	4	2	no	—
398	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
399	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
400	C₂×C₃²×C₄	C₂⁴	1	2	yes	—
401	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
402	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
403	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
404	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
405	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
406	C₂×C₃²×C₄	C₂⁴	1	2	yes	—
407	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
408	C₂×C₃²×C₄	C₂⁴	1	2	yes	—
409	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
410	C₂×C₃²×C₄	C₂⁴	1	2	yes	—
411	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
412	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
413	C₂×C₃²×C₄	C₂⁴	1	2	yes	—
414	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
415	#559	C₂×C₃²	1	1	yes	characteristic, complemented
416	#554	C₂×C₃²	1	1	yes	characteristic, complemented
417	#553	C₂×C₃²	1	1	yes	characteristic, complemented
418	#553	C₂×C₃²	1	2	yes	complemented
419	#552	C₂×C₃²	1	1	yes	characteristic, complemented
420	#551	C₂×C₃²	1	2	yes	complemented
421	#551	C₂×C₃²	1	2	yes	complemented
422	#547	C₂×C₃²	1	1	yes	characteristic, complemented
423	#546	C₂×C₃²	1	1	yes	characteristic, complemented
424	#546	C₂×C₃²	1	1	yes	characteristic, complemented
425	#546	C₂×C₃²	1	2	yes	complemented
426	D₄²	C₂×C₃²	1	1	yes	characteristic, complemented
427	#542	C₂×C₃²	1	1	yes	characteristic, complemented
428	#540	C₂×C₃²	1	1	yes	characteristic, complemented
429	#539	C₂×C₃²	1	2	yes	complemented
430	#538	C₂×C₃²	1	2	yes	complemented
431	#529	C₂×C₃²	1	1	yes	characteristic, complemented
432	#529	C₂×C₃²	1	1	yes	characteristic, complemented
433	#525	C₂×C₃²	1	2	yes	complemented
434	C₂×#123	C₂×C₃²	1	2	yes	complemented
435	#520	C₂×C₃²	1	1	yes	characteristic, complemented
436	#518	C₂×C₃²	1	1	yes	characteristic, complemented
437	C₂×C₄×D₄	C₂×C₃²	1	1	yes	characteristic, complemented
438	C₂⁴×C₃	C₂³×C₃	1	8	yes	—
439	C₂⁴×C₃	C₂³×C₃	1	8	yes	—
440	C₃×#41	—	2	16	no	—
441	C₃×#41	—	4	16	no	—
442	C₂×C₃×Q₈	C₂³×C₃	1	4	yes	—
443	C₂×C₃×Q₈	C₂³×C₃	1	4	yes	—
444	C₂×C₃×Q₈	C₂³×C₃	1	8	yes	—
445	C₂×C₃×D₄	—	2	16	no	—
446	C₂×C₃×D₄	—	2	16	no	—
447	C₂×C₃×D₄	—	4	16	no	—
448	C₂×C₃×D₄	C₂³×C₃	1	4	yes	—
449	C₂×C₃×D₄	C₂³×C₃	1	8	yes	—
450	C₂×C₃×D₄	C₂³×C₃	1	8	yes	—
451	C₂×C₃×D₄	C₂³×C₃	1	8	yes	—
452	C₂×C₃×D₄	C₂³×C₃	1	4	yes	—
453	C₂×C₃×D₄	C₂³×C₃	1	4	yes	—
454	C₂×C₃×D₄	C₂³×C₃	1	8	yes	—
455	C₂×C₃×D₄	C₂³×C₃	1	4	yes	—
456	C₂×C₃×D₄	C₂³×C₃	1	8	yes	—
457	C₂×C₃×D₄	C₂³×C₃	1	4	yes	—
458	C₂×C₃×D₄	C₂³×C₃	1	8	yes	—
459	C₂×C₃×D₄	C₂³×C₃	1	8	yes	—
460	C₂×C₃×D₄	C₂³×C₃	1	8	yes	—
461	C₂×C₃×D₄	C₂³×C₃	1	8	yes	—
462	C₂×C₃×D₄	C₂³×C₃	1	4	yes	—
463	C₂²×C₃×C₄	—	4	16	no	—
464	C₂²×C₃×C₄	C₂³×C₃	1	4	yes	—
465	C₂²×C₃×C₄	C₂³×C₃	1	4	yes	—
466	C₂²×C₃×C₄	C₂³×C₃	1	8	yes	—
467	C₂²×C₃×C₄	C₂³×C₃	1	8	yes	—
468	C₂²×C₃×C₄	C₂³×C₃	1	4	yes	—
469	C₂²×C₃×C₄	C₂³×C₃	1	4	yes	—
470	C₂²×C₃×C₄	C₂³×C₃	1	4	yes	—
471	C₂²×C₃×C₄	C₂³×C₃	1	8	yes	—
472	C₂²×C₃×C₄	C₂³×C₃	1	8	yes	—
473	C₂²×C₃×C₄	C₂³×C₃	1	8	yes	—
474	C₂²×C₃×C₄	C₂³×C₃	1	8	yes	—
475	C₂²×C₃×C₄	C₂³×C₃	1	8	yes	—
476	C₂²×C₃×C₄	C₂³×C₃	1	8	yes	—
477	C₂²×C₃×C₄	C₂³×C₃	1	8	yes	—
478	C₂²×C₃×C₄	C₂³×C₃	1	8	yes	—
479	C₂²×C₃×C₄	C₂³×C₃	1	8	yes	—
480	C₃×C₄⋊C₄	C₂³×C₃	1	4	yes	—
481	C₃×C₄⋊C₄	C₂³×C₃	1	8	yes	—
482	C₃×C₄⋊C₄	C₂³×C₃	1	4	yes	—
483	C₃×C₄⋊C₄	C₂³×C₃	1	4	yes	—
484	C₃×C₄⋊C₄	C₂³×C₃	1	8	yes	—
485	C₃×C₄⋊C₄	C₂³×C₃	1	4	yes	—
486	C₃×C₄⋊C₄	C₂³×C₃	1	4	yes	—
487	C₃×C₄⋊C₄	C₂³×C₃	1	8	yes	—
488	C₃×C₄⋊C₄	C₂³×C₃	1	8	yes	—
489	C₃×C₄⋊C₄	C₂³×C₃	1	8	yes	—
490	C₃×C₄⋊C₄	C₂³×C₃	1	8	yes	—
491	C₃×C₄⋊C₄	C₂³×C₃	1	8	yes	—
492	C₃×C₄⋊C₄	C₂³×C₃	1	4	yes	—
493	C₃×C₄⋊C₄	C₂³×C₃	1	4	yes	—
494	C₃×C₄⋊C₄	C₂³×C₃	1	4	yes	—
495	C₃×C₄⋊C₄	C₂³×C₃	1	4	yes	—
496	C₃×C₄⋊C₄	C₂³×C₃	1	8	yes	—
497	C₃×C₄⋊C₄	C₂³×C₃	1	8	yes	—
498	C₃×C₄⋊C₄	C₂³×C₃	1	8	yes	—
499	C₃×C₄⋊C₄	C₂³×C₃	1	4	yes	—
500	C₃×C₄⋊C₄	C₂³×C₃	1	4	yes	—
501	C₃×C₄⋊C₄	C₂³×C₃	1	8	yes	—
502	C₃×C₄⋊C₄	C₂³×C₃	1	4	yes	—
503	C₃×C₄⋊C₄	C₂³×C₃	1	4	yes	—
504	C₃×C₄⋊C₄	C₂³×C₃	1	4	yes	—
505	C₃×C₂²⋊C₄	C₂³×C₃	1	8	yes	—
506	C₃×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
507	C₃×C₂²⋊C₄	C₂³×C₃	1	8	yes	—
508	C₃×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
509	C₃×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
510	C₃×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
511	C₃×C₂²⋊C₄	C₂³×C₃	1	8	yes	—
512	C₃×C₂²⋊C₄	C₂³×C₃	1	8	yes	—
513	C₃×C₂²⋊C₄	C₂³×C₃	1	8	yes	—
514	C₃×C₂²⋊C₄	C₂³×C₃	1	8	yes	—
515	C₃×C₂²⋊C₄	C₂³×C₃	1	8	yes	—
516	C₃×C₂²⋊C₄	C₂³×C₃	1	8	yes	—
517	C₃×C₂²⋊C₄	C₂³×C₃	1	8	yes	—
518	C₃×C₂²⋊C₄	C₂³×C₃	1	8	yes	—
519	C₃×C₂²⋊C₄	C₂³×C₃	1	8	yes	—
520	C₃×C₂²⋊C₄	C₂³×C₃	1	8	yes	—
521	C₃×C₂²⋊C₄	C₂³×C₃	1	8	yes	—
522	C₃×C₂²⋊C₄	C₂³×C₃	1	8	yes	—
523	C₃×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
524	C₃×C₂²⋊C₄	C₂³×C₃	1	8	yes	—
525	C₃×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
526	C₃×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
527	C₃×C₂²⋊C₄	C₂³×C₃	1	8	yes	—
528	C₃×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
529	C₃×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
530	C₃×C₂²⋊C₄	C₂³×C₃	1	8	yes	—
531	C₃×C₂²⋊C₄	C₂³×C₃	1	8	yes	—
532	C₃×C₂²⋊C₄	C₂³×C₃	1	8	yes	—
533	C₃×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
534	C₃×C₄²	C₂³×C₃	1	4	yes	—
535	C₃×C₄²	C₂³×C₃	1	4	yes	—
536	C₃×C₄²	C₂³×C₃	1	4	yes	—
537	C₃×C₄²	C₂³×C₃	1	4	yes	—
538	C₃×C₄²	C₂³×C₃	1	8	yes	—
539	C₃×C₄²	C₂³×C₃	1	8	yes	—
540	C₃×C₄²	C₂³×C₃	1	8	yes	—
541	C₃×C₄²	C₂³×C₃	1	4	yes	—
542	C₃×C₄²	C₂³×C₃	1	4	yes	—
543	C₂²×C₃²	—	2	1	no	—
544	C₂²×C₃²	—	2	2	no	—
545	C₂²×C₃²	—	2	1	no	—
546	C₂²×C₃²	—	2	2	no	—
547	C₂²×C₃²	—	2	1	no	—
548	C₂²×C₃²	—	2	1	no	—
549	C₂²×C₃²	—	2	2	no	—
550	C₂²×C₃²	—	2	2	no	—
551	C₂²×C₃²	—	2	1	no	—
552	C₂²×C₃²	—	2	2	no	—
553	C₂²×C₃²	—	2	2	no	—
554	C₂²×C₃²	—	2	1	no	—
555	C₂²×C₃²	—	2	2	no	—
556	C₂²×C₃²	—	2	1	no	—
557	C₂²×C₃²	—	2	2	no	—
558	C₂²×C₃²	—	2	1	no	—
559	C₂²×C₃²	—	4	8	no	—
560	C₂²×C₃²	—	8	4	no	—
561	C₂²×C₃²	C₂×#41	1	4	yes	—
562	C₂²×C₃²	H(5,𝔽₂)	1	2	yes	—
563	C₂²×C₃²	C₂⁵	1	1	yes	characteristic
564	C₃²×C₄	—	2	1	no	—
565	C₃²×C₄	—	2	1	no	—
566	C₃²×C₄	—	2	1	no	—
567	C₃²×C₄	—	2	2	no	—
568	C₃²×C₄	—	2	1	no	—
569	C₃²×C₄	—	2	1	no	—
570	C₃²×C₄	—	2	2	no	—
571	C₃²×C₄	—	2	2	no	—
572	C₃²×C₄	—	2	1	no	—
573	C₃²×C₄	—	2	2	no	—
574	C₃²×C₄	—	2	1	no	—
575	C₃²×C₄	—	2	1	no	—
576	C₃²×C₄	—	2	2	no	—
577	C₃²×C₄	—	2	1	no	—
578	C₃²×C₄	—	2	1	no	—
579	C₃²×C₄	—	2	1	no	—
580	C₃²×C₄	C₂×#41	1	2	yes	—
581	C₂×#41	C₂²×C₃²	1	1	yes	characteristic
582	C₂×#41	C₂²×C₃²	1	2	yes	complemented
583	C₂²×D₄	C₂²×C₃²	1	1	yes	characteristic
584	C₂²×D₄	C₂²×C₃²	1	1	yes	characteristic
585	C₂²×D₄	C₂²×C₃²	1	2	yes	—
586	C₂³×C₄	C₂²×C₃²	1	2	yes	complemented
587	C₄⋊Q₈	C₂²×C₃²	1	1	yes	characteristic, complemented
588	#127	C₂²×C₃²	1	1	yes	characteristic
589	#126	C₂²×C₃²	1	2	yes	complemented
590	#126	C₂²×C₃²	1	1	yes	characteristic, complemented
591	#126	C₂²×C₃²	1	1	yes	characteristic, complemented
592	#126	C₂²×C₃²	1	2	yes	complemented
593	#126	C₂²×C₃²	1	2	yes	complemented
594	#126	C₂²×C₃²	1	2	yes	complemented
595	#125	C₂²×C₃²	1	1	yes	characteristic, complemented
596	#125	C₂²×C₃²	1	1	yes	characteristic, complemented
597	#125	C₂²×C₃²	1	2	yes	complemented
598	#125	C₂²×C₃²	1	1	yes	characteristic, complemented
599	#124	C₂²×C₃²	1	1	yes	characteristic, complemented
600	#124	C₂²×C₃²	1	1	yes	characteristic, complemented
601	#124	C₂²×C₃²	1	2	yes	complemented
602	#124	C₂²×C₃²	1	2	yes	complemented
603	#124	C₂²×C₃²	1	1	yes	characteristic, complemented
604	#123	C₂²×C₃²	1	1	yes	characteristic
605	#123	C₂²×C₃²	1	2	yes	—
606	#123	C₂²×C₃²	1	2	yes	complemented
607	#123	C₂²×C₃²	1	2	yes	complemented
608	#123	C₂²×C₃²	1	2	yes	complemented
609	#123	C₂²×C₃²	1	2	yes	complemented
610	#123	C₂²×C₃²	1	2	yes	complemented
611	#123	C₂²×C₃²	1	2	yes	complemented
612	#123	C₂²×C₃²	1	1	yes	characteristic, complemented
613	#123	C₂²×C₃²	1	2	yes	complemented
614	#123	C₂²×C₃²	1	2	yes	complemented
615	#123	C₂²×C₃²	1	2	yes	complemented
616	#123	C₂²×C₃²	1	2	yes	complemented
617	#123	C₂²×C₃²	1	2	yes	complemented
618	C₂²⋊Q₈	C₂²×C₃²	1	2	yes	complemented
619	C₂²⋊Q₈	C₂²×C₃²	1	2	yes	complemented
620	C₂²⋊Q₈	C₂²×C₃²	1	1	yes	characteristic, complemented
621	C₂²⋊Q₈	C₂²×C₃²	1	1	yes	characteristic, complemented
622	C₂²⋊Q₈	C₂²×C₃²	1	2	yes	complemented
623	C₂²⋊Q₈	C₂²×C₃²	1	2	yes	complemented
624	C₂²⋊Q₈	C₂²×C₃²	1	2	yes	complemented
625	C₂²⋊Q₈	C₂²×C₃²	1	1	yes	characteristic, complemented
626	#121	C₂²×C₃²	1	1	yes	characteristic
627	#121	C₂²×C₃²	1	1	yes	characteristic
628	#121	C₂²×C₃²	1	2	yes	—
629	#121	C₂²×C₃²	1	1	yes	characteristic
630	#121	C₂²×C₃²	1	2	yes	complemented
631	#121	C₂²×C₃²	1	2	yes	complemented
632	#121	C₂²×C₃²	1	2	yes	complemented
633	#121	C₂²×C₃²	1	2	yes	complemented
634	#121	C₂²×C₃²	1	1	yes	characteristic, complemented
635	#121	C₂²×C₃²	1	2	yes	complemented
636	#121	C₂²×C₃²	1	1	yes	characteristic, complemented
637	#120	C₂²×C₃²	1	2	yes	—
638	#120	C₂²×C₃²	1	2	yes	—
639	#120	C₂²×C₃²	1	2	yes	complemented
640	#120	C₂²×C₃²	1	2	yes	complemented
641	C₄×Q₈	C₂²×C₃²	1	1	yes	characteristic, complemented
642	C₄×Q₈	C₂²×C₃²	1	1	yes	characteristic, complemented
643	C₄×Q₈	C₂²×C₃²	1	1	yes	characteristic, complemented
644	C₄×D₄	C₂²×C₃²	1	1	yes	characteristic
645	C₄×D₄	C₂²×C₃²	1	1	yes	characteristic
646	C₄×D₄	C₂²×C₃²	1	1	yes	characteristic
647	C₄×D₄	C₂²×C₃²	1	1	yes	characteristic
648	C₄×D₄	C₂²×C₃²	1	1	yes	characteristic
649	C₄×D₄	C₂²×C₃²	1	2	yes	complemented
650	C₄×D₄	C₂²×C₃²	1	1	yes	characteristic, complemented
651	C₄×D₄	C₂²×C₃²	1	2	yes	complemented
652	C₄×D₄	C₂²×C₃²	1	1	yes	characteristic, complemented
653	C₄×D₄	C₂²×C₃²	1	2	yes	complemented
654	C₄×D₄	C₂²×C₃²	1	1	yes	characteristic, complemented
655	C₄×D₄	C₂²×C₃²	1	1	yes	characteristic, complemented
656	C₄×D₄	C₂²×C₃²	1	2	yes	complemented
657	C₄×D₄	C₂²×C₃²	1	2	yes	complemented
658	C₄×D₄	C₂²×C₃²	1	2	yes	complemented
659	C₄×D₄	C₂²×C₃²	1	2	yes	complemented
660	C₄×D₄	C₂²×C₃²	1	2	yes	complemented
661	C₄×D₄	C₂²×C₃²	1	1	yes	characteristic, complemented
662	C₄×D₄	C₂²×C₃²	1	2	yes	complemented
663	C₄×D₄	C₂²×C₃²	1	1	yes	characteristic, complemented
664	#117	C₂²×C₃²	1	1	yes	characteristic, complemented
665	#117	C₂²×C₃²	1	1	yes	characteristic, complemented
666	#117	C₂²×C₃²	1	1	yes	characteristic, complemented
667	#117	C₂²×C₃²	1	2	yes	complemented
668	#117	C₂²×C₃²	1	2	yes	complemented
669	#117	C₂²×C₃²	1	2	yes	complemented
670	C₂×C₄⋊C₄	C₂²×C₃²	1	1	yes	characteristic, complemented
671	C₂×C₄⋊C₄	C₂²×C₃²	1	2	yes	complemented
672	C₂×C₄⋊C₄	C₂²×C₃²	1	1	yes	characteristic, complemented
673	C₂×C₄⋊C₄	C₂²×C₃²	1	2	yes	complemented
674	C₂×C₂²⋊C₄	C₂²×C₃²	1	2	yes	complemented
675	C₂×C₂²⋊C₄	C₂²×C₃²	1	2	yes	complemented
676	C₂×C₂²⋊C₄	C₂²×C₃²	1	2	yes	complemented
677	C₂×C₂²⋊C₄	C₂²×C₃²	1	2	yes	complemented
678	C₂×C₂²⋊C₄	C₂²×C₃²	1	2	yes	complemented
679	C₂×C₄²	C₂²×C₃²	1	1	yes	characteristic, complemented
680	C₂³×C₃	—	2	16	no	—
681	C₂³×C₃	—	2	16	no	—
682	C₂³×C₃	—	2	16	no	—
683	C₂³×C₃	—	4	8	no	—
684	C₂³×C₃	—	4	8	no	—
685	C₂³×C₃	—	4	8	no	—
686	C₂³×C₃	C₂⁴×C₃	1	4	yes	—
687	C₂³×C₃	C₂⁴×C₃	1	8	yes	—
688	C₂³×C₃	C₂⁴×C₃	1	8	yes	—
689	C₂³×C₃	C₂⁴×C₃	1	4	yes	—
690	C₂³×C₃	C₂⁴×C₃	1	8	yes	—
691	C₂³×C₃	C₂⁴×C₃	1	4	yes	—
692	C₃×Q₈	—	2	8	no	—
693	C₃×Q₈	—	4	4	no	—
694	C₃×Q₈	—	4	8	no	—
695	C₃×D₄	—	2	16	no	—
696	C₃×D₄	—	2	16	no	—
697	C₃×D₄	—	2	16	no	—
698	C₃×D₄	—	2	8	no	—
699	C₃×D₄	—	2	16	no	—
700	C₃×D₄	—	2	8	no	—
701	C₃×D₄	—	2	8	no	—
702	C₃×D₄	—	2	8	no	—
703	C₃×D₄	—	4	8	no	—
704	C₃×D₄	—	4	8	no	—
705	C₃×D₄	—	4	8	no	—
706	C₃×D₄	—	4	4	no	—
707	C₃×D₄	—	4	8	no	—
708	C₃×D₄	—	4	8	no	—
709	C₃×D₄	C₃×#41	1	16	yes	complemented
710	C₂×C₃×C₄	—	2	16	no	—
711	C₂×C₃×C₄	—	2	8	no	—
712	C₂×C₃×C₄	—	2	16	no	—
713	C₂×C₃×C₄	—	2	8	no	—
714	C₂×C₃×C₄	—	2	8	no	—
715	C₂×C₃×C₄	—	2	8	no	—
716	C₂×C₃×C₄	—	4	8	no	—
717	C₂×C₃×C₄	—	4	8	no	—
718	C₂×C₃×C₄	—	4	8	no	—
719	C₂×C₃×C₄	—	4	8	no	—
720	C₂×C₃×C₄	—	4	8	no	—
721	C₂×C₃×C₄	—	4	4	no	—
722	C₂×C₃×C₄	—	4	8	no	—
723	C₂×C₃×C₄	—	4	8	no	—
724	C₂×C₃×C₄	—	4	8	no	—
725	C₂×C₃×C₄	—	4	8	no	—
726	C₂×C₃×C₄	C₂⁴×C₃	1	4	yes	—
727	C₂×C₃×C₄	C₂⁴×C₃	1	4	yes	—
728	C₂×C₃×C₄	C₂⁴×C₃	1	8	yes	—
729	C₂×C₃×C₄	C₂⁴×C₃	1	4	yes	—
730	C₂×C₃×C₄	C₂⁴×C₃	1	4	yes	—
731	C₂×C₃×C₄	C₂⁴×C₃	1	4	yes	—
732	C₂×C₃×C₄	C₂⁴×C₃	1	4	yes	—
733	C₂×C₃×C₄	C₂⁴×C₃	1	4	yes	—
734	C₂×C₃×C₄	C₂⁴×C₃	1	8	yes	—
735	C₂×C₃×C₄	C₂⁴×C₃	1	4	yes	—
736	C₂×C₃×C₄	C₂⁴×C₃	1	8	yes	—
737	C₂×C₃×C₄	C₂⁴×C₃	1	4	yes	—
738	C₂×C₃×C₄	C₂⁴×C₃	1	8	yes	—
739	C₂×C₃×C₄	C₂⁴×C₃	1	4	yes	—
740	C₂×C₃×C₄	C₂⁴×C₃	1	4	yes	—
741	C₂×C₃×C₄	C₂⁴×C₃	1	8	yes	—
742	C₂×C₃×C₄	C₂⁴×C₃	1	4	yes	—
743	C₂×C₃²	—	2	2	no	—
744	C₂×C₃²	—	2	4	no	—
745	C₂×C₃²	—	4	1	no	—
746	C₂×C₃²	—	4	2	no	—
747	C₂×C₃²	—	4	2	no	—
748	C₂×C₃²	—	4	1	no	—
749	C₂×C₃²	C₂²×#41	1	1	yes	characteristic
750	C₂×C₃²	C₂×H(5,𝔽₂)	1	1	yes	characteristic
751	C₂×C₃²	#585	1	1	yes	characteristic
752	C₂⁴	C₂³×C₃²	1	2	yes	—
753	C₂⁴	C₂³×C₃²	1	2	yes	—
754	#41	—	2	4	no	—
755	#41	—	4	4	no	—
756	C₂×Q₈	C₂³×C₃²	1	1	yes	characteristic
757	C₂×Q₈	C₂³×C₃²	1	1	yes	characteristic
758	C₂×Q₈	C₂³×C₃²	1	2	yes	—
759	C₂×D₄	—	2	4	no	—
760	C₂×D₄	—	2	4	no	—
761	C₂×D₄	—	4	4	no	—
762	C₂×D₄	C₂³×C₃²	1	1	yes	characteristic
763	C₂×D₄	C₂³×C₃²	1	2	yes	—
764	C₂×D₄	C₂³×C₃²	1	2	yes	—
765	C₂×D₄	C₂³×C₃²	1	2	yes	—
766	C₂×D₄	C₂³×C₃²	1	1	yes	characteristic
767	C₂×D₄	C₂³×C₃²	1	1	yes	characteristic
768	C₂×D₄	C₂³×C₃²	1	2	yes	—
769	C₂×D₄	C₂³×C₃²	1	1	yes	characteristic
770	C₂×D₄	C₂³×C₃²	1	2	yes	—
771	C₂×D₄	C₂³×C₃²	1	1	yes	characteristic
772	C₂×D₄	C₂³×C₃²	1	2	yes	—
773	C₂×D₄	C₂³×C₃²	1	2	yes	—
774	C₂×D₄	C₂³×C₃²	1	2	yes	—
775	C₂×D₄	C₂³×C₃²	1	2	yes	—
776	C₂×D₄	C₂³×C₃²	1	1	yes	characteristic
777	C₂²×C₄	—	4	4	no	—
778	C₂²×C₄	C₂³×C₃²	1	1	yes	characteristic
779	C₂²×C₄	C₂³×C₃²	1	1	yes	characteristic
780	C₂²×C₄	C₂³×C₃²	1	2	yes	—
781	C₂²×C₄	C₂³×C₃²	1	2	yes	—
782	C₂²×C₄	C₂³×C₃²	1	1	yes	characteristic
783	C₂²×C₄	C₂³×C₃²	1	1	yes	characteristic
784	C₂²×C₄	C₂³×C₃²	1	1	yes	characteristic
785	C₂²×C₄	C₂³×C₃²	1	2	yes	—
786	C₂²×C₄	C₂³×C₃²	1	2	yes	—
787	C₂²×C₄	C₂³×C₃²	1	2	yes	—
788	C₂²×C₄	C₂³×C₃²	1	2	yes	—
789	C₂²×C₄	C₂³×C₃²	1	2	yes	—
790	C₂²×C₄	C₂³×C₃²	1	2	yes	—
791	C₂²×C₄	C₂³×C₃²	1	2	yes	—
792	C₂²×C₄	C₂³×C₃²	1	2	yes	—
793	C₂²×C₄	C₂³×C₃²	1	2	yes	—
794	C₄⋊C₄	C₂³×C₃²	1	1	yes	characteristic
795	C₄⋊C₄	C₂³×C₃²	1	2	yes	—
796	C₄⋊C₄	C₂³×C₃²	1	1	yes	characteristic
797	C₄⋊C₄	C₂³×C₃²	1	1	yes	characteristic
798	C₄⋊C₄	C₂³×C₃²	1	2	yes	—
799	C₄⋊C₄	C₂³×C₃²	1	1	yes	characteristic
800	C₄⋊C₄	C₂³×C₃²	1	1	yes	characteristic
801	C₄⋊C₄	C₂³×C₃²	1	2	yes	—
802	C₄⋊C₄	C₂³×C₃²	1	2	yes	—
803	C₄⋊C₄	C₂³×C₃²	1	2	yes	—
804	C₄⋊C₄	C₂³×C₃²	1	2	yes	—
805	C₄⋊C₄	C₂³×C₃²	1	2	yes	—
806	C₄⋊C₄	C₂³×C₃²	1	1	yes	characteristic
807	C₄⋊C₄	C₂³×C₃²	1	1	yes	characteristic
808	C₄⋊C₄	C₂³×C₃²	1	1	yes	characteristic
809	C₄⋊C₄	C₂³×C₃²	1	1	yes	characteristic
810	C₄⋊C₄	C₂³×C₃²	1	2	yes	—
811	C₄⋊C₄	C₂³×C₃²	1	2	yes	—
812	C₄⋊C₄	C₂³×C₃²	1	2	yes	—
813	C₄⋊C₄	C₂³×C₃²	1	1	yes	characteristic
814	C₄⋊C₄	C₂³×C₃²	1	1	yes	characteristic
815	C₄⋊C₄	C₂³×C₃²	1	2	yes	—
816	C₄⋊C₄	C₂³×C₃²	1	1	yes	characteristic
817	C₄⋊C₄	C₂³×C₃²	1	1	yes	characteristic
818	C₄⋊C₄	C₂³×C₃²	1	1	yes	characteristic
819	C₂²⋊C₄	C₂³×C₃²	1	2	yes	—
820	C₂²⋊C₄	C₂³×C₃²	1	1	yes	characteristic
821	C₂²⋊C₄	C₂³×C₃²	1	2	yes	—
822	C₂²⋊C₄	C₂³×C₃²	1	1	yes	characteristic
823	C₂²⋊C₄	C₂³×C₃²	1	1	yes	characteristic
824	C₂²⋊C₄	C₂³×C₃²	1	1	yes	characteristic
825	C₂²⋊C₄	C₂³×C₃²	1	2	yes	—
826	C₂²⋊C₄	C₂³×C₃²	1	2	yes	—
827	C₂²⋊C₄	C₂³×C₃²	1	2	yes	—
828	C₂²⋊C₄	C₂³×C₃²	1	2	yes	—
829	C₂²⋊C₄	C₂³×C₃²	1	2	yes	—
830	C₂²⋊C₄	C₂³×C₃²	1	2	yes	—
831	C₂²⋊C₄	C₂³×C₃²	1	2	yes	—
832	C₂²⋊C₄	C₂³×C₃²	1	2	yes	—
833	C₂²⋊C₄	C₂³×C₃²	1	2	yes	—
834	C₂²⋊C₄	C₂³×C₃²	1	2	yes	—
835	C₂²⋊C₄	C₂³×C₃²	1	2	yes	—
836	C₂²⋊C₄	C₂³×C₃²	1	2	yes	—
837	C₂²⋊C₄	C₂³×C₃²	1	1	yes	characteristic
838	C₂²⋊C₄	C₂³×C₃²	1	2	yes	—
839	C₂²⋊C₄	C₂³×C₃²	1	1	yes	characteristic
840	C₂²⋊C₄	C₂³×C₃²	1	1	yes	characteristic
841	C₂²⋊C₄	C₂³×C₃²	1	2	yes	—
842	C₂²⋊C₄	C₂³×C₃²	1	1	yes	characteristic
843	C₂²⋊C₄	C₂³×C₃²	1	1	yes	characteristic
844	C₂²⋊C₄	C₂³×C₃²	1	2	yes	—
845	C₂²⋊C₄	C₂³×C₃²	1	2	yes	—
846	C₂²⋊C₄	C₂³×C₃²	1	2	yes	—
847	C₂²⋊C₄	C₂³×C₃²	1	1	yes	characteristic
848	C₄²	C₂³×C₃²	1	1	yes	characteristic
849	C₄²	C₂³×C₃²	1	1	yes	characteristic
850	C₄²	C₂³×C₃²	1	1	yes	characteristic
851	C₄²	C₂³×C₃²	1	1	yes	characteristic
852	C₄²	C₂³×C₃²	1	2	yes	—
853	C₄²	C₂³×C₃²	1	2	yes	—
854	C₄²	C₂³×C₃²	1	2	yes	—
855	C₄²	C₂³×C₃²	1	1	yes	characteristic
856	C₄²	C₂³×C₃²	1	1	yes	characteristic
857	C₂²×C₃	—	2	4	no	—
858	C₂²×C₃	—	2	8	no	—
859	C₂²×C₃	—	2	4	no	—
860	C₂²×C₃	—	2	8	no	—
861	C₂²×C₃	—	2	4	no	—
862	C₂²×C₃	—	2	4	no	—
863	C₂²×C₃	—	2	8	no	—
864	C₂²×C₃	—	2	8	no	—
865	C₂²×C₃	—	2	4	no	—
866	C₂²×C₃	—	2	8	no	—
867	C₂²×C₃	—	2	8	no	—
868	C₂²×C₃	—	2	4	no	—
869	C₂²×C₃	—	2	8	no	—
870	C₂²×C₃	—	2	4	no	—
871	C₂²×C₃	—	2	8	no	—
872	C₂²×C₃	—	2	4	no	—
873	C₂²×C₃	—	4	32	no	—
874	C₂²×C₃	—	8	16	no	—
875	C₂²×C₃	C₂×C₃×#41	1	16	yes	—
876	C₂²×C₃	C₃×H(5,𝔽₂)	1	8	yes	—
877	C₂²×C₃	C₂⁵×C₃	1	4	yes	—
878	C₃×C₄	—	2	4	no	—
879	C₃×C₄	—	2	4	no	—
880	C₃×C₄	—	2	4	no	—
881	C₃×C₄	—	2	8	no	—
882	C₃×C₄	—	2	4	no	—
883	C₃×C₄	—	2	4	no	—
884	C₃×C₄	—	2	8	no	—
885	C₃×C₄	—	2	8	no	—
886	C₃×C₄	—	2	4	no	—
887	C₃×C₄	—	2	8	no	—
888	C₃×C₄	—	2	4	no	—
889	C₃×C₄	—	2	4	no	—
890	C₃×C₄	—	2	8	no	—
891	C₃×C₄	—	2	4	no	—
892	C₃×C₄	—	2	4	no	—
893	C₃×C₄	—	2	4	no	—
894	C₃×C₄	C₂×C₃×#41	1	8	yes	—
895	C₃²	#3513	1	1	yes	characteristic, direct product factor, Sylow
896	C₂³	—	2	4	no	—
897	C₂³	—	2	4	no	—
898	C₂³	—	2	4	no	—
899	C₂³	—	4	2	no	—
900	C₂³	—	4	2	no	—
901	C₂³	—	4	2	no	—
902	C₂³	C₂⁴×C₃²	1	1	yes	characteristic
903	C₂³	C₂⁴×C₃²	1	2	yes	—
904	C₂³	C₂⁴×C₃²	1	2	yes	—
905	C₂³	C₂⁴×C₃²	1	1	yes	characteristic
906	C₂³	C₂⁴×C₃²	1	2	yes	—
907	C₂³	C₂⁴×C₃²	1	1	yes	characteristic
908	Q₈	—	2	2	no	—
909	Q₈	—	4	2	no	—
910	Q₈	—	4	1	no	—
911	D₄	—	2	4	no	—
912	D₄	—	2	4	no	—
913	D₄	—	2	4	no	—
914	D₄	—	2	2	no	—
915	D₄	—	2	4	no	—
916	D₄	—	2	2	no	—
917	D₄	—	2	2	no	—
918	D₄	—	2	2	no	—
919	D₄	—	4	2	no	—
920	D₄	—	4	2	no	—
921	D₄	—	4	2	no	—
922	D₄	—	4	2	no	—
923	D₄	—	4	1	no	—
924	D₄	—	4	2	no	—
925	D₄	C₃²×#41	1	4	yes	complemented
926	C₂×C₄	—	2	4	no	—
927	C₂×C₄	—	2	2	no	—
928	C₂×C₄	—	2	4	no	—
929	C₂×C₄	—	2	2	no	—
930	C₂×C₄	—	2	2	no	—
931	C₂×C₄	—	2	2	no	—
932	C₂×C₄	—	4	2	no	—
933	C₂×C₄	—	4	2	no	—
934	C₂×C₄	—	4	2	no	—
935	C₂×C₄	—	4	2	no	—
936	C₂×C₄	—	4	2	no	—
937	C₂×C₄	—	4	2	no	—
938	C₂×C₄	—	4	2	no	—
939	C₂×C₄	—	4	2	no	—
940	C₂×C₄	—	4	1	no	—
941	C₂×C₄	—	4	2	no	—
942	C₂×C₄	C₂⁴×C₃²	1	1	yes	characteristic
943	C₂×C₄	C₂⁴×C₃²	1	1	yes	characteristic
944	C₂×C₄	C₂⁴×C₃²	1	2	yes	—
945	C₂×C₄	C₂⁴×C₃²	1	1	yes	characteristic
946	C₂×C₄	C₂⁴×C₃²	1	1	yes	characteristic
947	C₂×C₄	C₂⁴×C₃²	1	1	yes	characteristic
948	C₂×C₄	C₂⁴×C₃²	1	1	yes	characteristic
949	C₂×C₄	C₂⁴×C₃²	1	1	yes	characteristic
950	C₂×C₄	C₂⁴×C₃²	1	2	yes	—
951	C₂×C₄	C₂⁴×C₃²	1	1	yes	characteristic
952	C₂×C₄	C₂⁴×C₃²	1	2	yes	—
953	C₂×C₄	C₂⁴×C₃²	1	1	yes	characteristic
954	C₂×C₄	C₂⁴×C₃²	1	2	yes	—
955	C₂×C₄	C₂⁴×C₃²	1	1	yes	characteristic
956	C₂×C₄	C₂⁴×C₃²	1	1	yes	characteristic
957	C₂×C₄	C₂⁴×C₃²	1	2	yes	—
958	C₂×C₄	C₂⁴×C₃²	1	1	yes	characteristic
959	C₂×C₃	—	2	8	no	—
960	C₂×C₃	—	2	16	no	—
961	C₂×C₃	—	4	8	no	—
962	C₂×C₃	—	4	4	no	—
963	C₂×C₃	—	4	8	no	—
964	C₂×C₃	—	4	4	no	—
965	C₂×C₃	C₂²×C₃×#41	1	4	yes	—
966	C₂×C₃	C₂×C₃×H(5,𝔽₂)	1	4	yes	—
967	C₂×C₃	C₃×#585	1	4	yes	—
968	C₂²	—	2	1	no	—
969	C₂²	—	2	2	no	—
970	C₂²	—	2	1	no	—
971	C₂²	—	2	2	no	—
972	C₂²	—	2	1	no	—
973	C₂²	—	2	1	no	—
974	C₂²	—	2	2	no	—
975	C₂²	—	2	2	no	—
976	C₂²	—	2	1	no	—
977	C₂²	—	2	2	no	—
978	C₂²	—	2	2	no	—
979	C₂²	—	2	1	no	—
980	C₂²	—	2	2	no	—
981	C₂²	—	2	1	no	—
982	C₂²	—	2	2	no	—
983	C₂²	—	2	1	no	—
984	C₂²	—	4	8	no	—
985	C₂²	—	8	4	no	—
986	C₂²	C₂×C₃²×#41	1	4	yes	—
987	C₂²	C₃²×H(5,𝔽₂)	1	2	yes	—
988	C₂²	C₂⁵×C₃²	1	1	yes	characteristic
989	C₄	—	2	1	no	—
990	C₄	—	2	1	no	—
991	C₄	—	2	1	no	—
992	C₄	—	2	2	no	—
993	C₄	—	2	1	no	—
994	C₄	—	2	1	no	—
995	C₄	—	2	2	no	—
996	C₄	—	2	2	no	—
997	C₄	—	2	1	no	—
998	C₄	—	2	2	no	—
999	C₄	—	2	1	no	—
1000	C₄	—	2	1	no	—
1001	C₄	—	2	2	no	—
1002	C₄	—	2	1	no	—
1003	C₄	—	2	1	no	—
1004	C₄	—	2	1	no	—
1005	C₄	C₂×C₃²×#41	1	2	yes	—
1006	C₃	C₃×#3513	1	4	yes	direct product factor
1007	C₂	—	2	2	no	—
1008	C₂	—	2	4	no	—
1009	C₂	—	4	2	no	—
1010	C₂	—	4	1	no	—
1011	C₂	—	4	2	no	—
1012	C₂	—	4	1	no	—
1013	C₂	C₂²×C₃²×#41	1	1	yes	characteristic
1014	C₂	C₂×C₃²×H(5,𝔽₂)	1	1	yes	characteristic
1015	C₂	C₃²×#585	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₃²	C₂⁵
commutator, Frattini, cosocle	C₂²	C₂⁵×C₃²
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₃² ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. C₃²×#559	C₂	semidirect
2. C₃²×#554	C₂	semidirect
3. C₃²×#553	C₂	semidirect
4. C₃²×#553	C₂	semidirect
5. C₃²×#552	C₂	semidirect
6. C₃²×#551	C₂	semidirect
7. C₃²×#551	C₂	semidirect
8. C₃²×#547	C₂	semidirect
9. C₃²×#546	C₂	semidirect
10. C₃²×#546	C₂	semidirect
11. C₃²×#546	C₂	semidirect
12. C₃²×D₄²	C₂	semidirect
13. C₃²×#542	C₂	semidirect
14. C₃²×#540	C₂	semidirect
15. C₃²×#539	C₂	semidirect
16. C₃²×#538	C₂	semidirect
17. C₃²×#529	C₂	semidirect
18. C₃²×#529	C₂	semidirect
19. C₃²×#525	C₂	semidirect
20. C₂×C₃²×#123	C₂	semidirect
21. C₃²×#520	C₂	semidirect
22. C₃²×#518	C₂	semidirect
23. C₂×C₃²×C₄×D₄	C₂	semidirect
24. C₃×#3513	C₃	direct (N × H)
26. C₂×C₃²×#41	C₂²	semidirect
30. C₂³×C₃²×C₄	C₂²	semidirect
31. C₃²×C₄⋊Q₈	C₂²	semidirect
33. C₃²×#126	C₂²	semidirect
34. C₃²×#126	C₂²	semidirect
35. C₃²×#126	C₂²	semidirect
36. C₃²×#126	C₂²	semidirect
37. C₃²×#126	C₂²	semidirect
38. C₃²×#126	C₂²	semidirect
39. C₃²×#125	C₂²	semidirect
40. C₃²×#125	C₂²	semidirect
41. C₃²×#125	C₂²	semidirect
42. C₃²×#125	C₂²	semidirect
43. C₃²×#124	C₂²	semidirect
44. C₃²×#124	C₂²	semidirect
45. C₃²×#124	C₂²	semidirect
46. C₃²×#124	C₂²	semidirect
47. C₃²×#124	C₂²	semidirect
50. C₃²×#123	C₂²	semidirect
51. C₃²×#123	C₂²	semidirect
52. C₃²×#123	C₂²	semidirect
53. C₃²×#123	C₂²	semidirect
54. C₃²×#123	C₂²	semidirect
55. C₃²×#123	C₂²	semidirect
56. C₃²×#123	C₂²	semidirect
57. C₃²×#123	C₂²	semidirect
58. C₃²×#123	C₂²	semidirect
59. C₃²×#123	C₂²	semidirect
60. C₃²×#123	C₂²	semidirect
61. C₃²×#123	C₂²	semidirect
62. C₃²×C₂²⋊Q₈	C₂²	semidirect
63. C₃²×C₂²⋊Q₈	C₂²	semidirect
64. C₃²×C₂²⋊Q₈	C₂²	semidirect
65. C₃²×C₂²⋊Q₈	C₂²	semidirect
66. C₃²×C₂²⋊Q₈	C₂²	semidirect
67. C₃²×C₂²⋊Q₈	C₂²	semidirect
68. C₃²×C₂²⋊Q₈	C₂²	semidirect
69. C₃²×C₂²⋊Q₈	C₂²	semidirect
74. C₃²×#121	C₂²	semidirect
75. C₃²×#121	C₂²	semidirect
76. C₃²×#121	C₂²	semidirect
77. C₃²×#121	C₂²	semidirect
78. C₃²×#121	C₂²	semidirect
79. C₃²×#121	C₂²	semidirect
80. C₃²×#121	C₂²	semidirect
83. C₃²×#120	C₂²	semidirect
84. C₃²×#120	C₂²	semidirect
85. C₃²×C₄×Q₈	C₂²	semidirect
86. C₃²×C₄×Q₈	C₂²	semidirect
87. C₃²×C₄×Q₈	C₂²	semidirect
93. C₃²×C₄×D₄	C₂²	semidirect
94. C₃²×C₄×D₄	C₂²	semidirect
95. C₃²×C₄×D₄	C₂²	semidirect
96. C₃²×C₄×D₄	C₂²	semidirect
97. C₃²×C₄×D₄	C₂²	semidirect
98. C₃²×C₄×D₄	C₂²	semidirect
99. C₃²×C₄×D₄	C₂²	semidirect
100. C₃²×C₄×D₄	C₂²	semidirect
101. C₃²×C₄×D₄	C₂²	semidirect
102. C₃²×C₄×D₄	C₂²	semidirect
103. C₃²×C₄×D₄	C₂²	semidirect
104. C₃²×C₄×D₄	C₂²	semidirect
105. C₃²×C₄×D₄	C₂²	semidirect
106. C₃²×C₄×D₄	C₂²	semidirect
107. C₃²×C₄×D₄	C₂²	semidirect
108. C₃²×#117	C₂²	semidirect
109. C₃²×#117	C₂²	semidirect
110. C₃²×#117	C₂²	semidirect
111. C₃²×#117	C₂²	semidirect
112. C₃²×#117	C₂²	semidirect
113. C₃²×#117	C₂²	semidirect
114. C₂×C₃²×C₄⋊C₄	C₂²	semidirect
115. C₂×C₃²×C₄⋊C₄	C₂²	semidirect
116. C₂×C₃²×C₄⋊C₄	C₂²	semidirect
117. C₂×C₃²×C₄⋊C₄	C₂²	semidirect
118. C₂×C₃²×C₂²⋊C₄	C₂²	semidirect
119. C₂×C₃²×C₂²⋊C₄	C₂²	semidirect
120. C₂×C₃²×C₂²⋊C₄	C₂²	semidirect
121. C₂×C₃²×C₂²⋊C₄	C₂²	semidirect
122. C₂×C₃²×C₂²⋊C₄	C₂²	semidirect
123. C₂×C₃²×C₄²	C₂²	semidirect
124. C₃×#559	C₂×C₃	semidirect
125. C₃×#554	C₂×C₃	semidirect
126. C₃×#553	C₂×C₃	semidirect
127. C₃×#553	C₂×C₃	semidirect
128. C₃×#552	C₂×C₃	semidirect
129. C₃×#551	C₂×C₃	semidirect
130. C₃×#551	C₂×C₃	semidirect
131. C₃×#547	C₂×C₃	semidirect
132. C₃×#546	C₂×C₃	semidirect
133. C₃×#546	C₂×C₃	semidirect
134. C₃×#546	C₂×C₃	semidirect
135. C₃×D₄²	C₂×C₃	semidirect
136. C₃×#542	C₂×C₃	semidirect
137. C₃×#540	C₂×C₃	semidirect
138. C₃×#539	C₂×C₃	semidirect
139. C₃×#538	C₂×C₃	semidirect
140. C₃×#529	C₂×C₃	semidirect
141. C₃×#529	C₂×C₃	semidirect
142. C₃×#525	C₂×C₃	semidirect
143. C₂×C₃×#123	C₂×C₃	semidirect
144. C₃×#520	C₂×C₃	semidirect
145. C₃×#518	C₂×C₃	semidirect
146. C₂×C₃×C₄×D₄	C₂×C₃	semidirect
252. #3513	C₃²	direct (N × H)
254. C₂×C₃×#41	C₂²×C₃	semidirect
258. C₂³×C₃×C₄	C₂²×C₃	semidirect
259. C₃×C₄⋊Q₈	C₂²×C₃	semidirect
261. C₃×#126	C₂²×C₃	semidirect
262. C₃×#126	C₂²×C₃	semidirect
263. C₃×#126	C₂²×C₃	semidirect
264. C₃×#126	C₂²×C₃	semidirect
265. C₃×#126	C₂²×C₃	semidirect
266. C₃×#126	C₂²×C₃	semidirect
267. C₃×#125	C₂²×C₃	semidirect
268. C₃×#125	C₂²×C₃	semidirect
269. C₃×#125	C₂²×C₃	semidirect
270. C₃×#125	C₂²×C₃	semidirect
271. C₃×#124	C₂²×C₃	semidirect
272. C₃×#124	C₂²×C₃	semidirect
273. C₃×#124	C₂²×C₃	semidirect
274. C₃×#124	C₂²×C₃	semidirect
275. C₃×#124	C₂²×C₃	semidirect
278. C₃×#123	C₂²×C₃	semidirect
279. C₃×#123	C₂²×C₃	semidirect
280. C₃×#123	C₂²×C₃	semidirect
281. C₃×#123	C₂²×C₃	semidirect
282. C₃×#123	C₂²×C₃	semidirect
283. C₃×#123	C₂²×C₃	semidirect
284. C₃×#123	C₂²×C₃	semidirect
285. C₃×#123	C₂²×C₃	semidirect
286. C₃×#123	C₂²×C₃	semidirect
287. C₃×#123	C₂²×C₃	semidirect
288. C₃×#123	C₂²×C₃	semidirect
289. C₃×#123	C₂²×C₃	semidirect
290. C₃×C₂²⋊Q₈	C₂²×C₃	semidirect
291. C₃×C₂²⋊Q₈	C₂²×C₃	semidirect
292. C₃×C₂²⋊Q₈	C₂²×C₃	semidirect
293. C₃×C₂²⋊Q₈	C₂²×C₃	semidirect
294. C₃×C₂²⋊Q₈	C₂²×C₃	semidirect
295. C₃×C₂²⋊Q₈	C₂²×C₃	semidirect
296. C₃×C₂²⋊Q₈	C₂²×C₃	semidirect
297. C₃×C₂²⋊Q₈	C₂²×C₃	semidirect
302. C₃×#121	C₂²×C₃	semidirect
303. C₃×#121	C₂²×C₃	semidirect
304. C₃×#121	C₂²×C₃	semidirect
305. C₃×#121	C₂²×C₃	semidirect
306. C₃×#121	C₂²×C₃	semidirect
307. C₃×#121	C₂²×C₃	semidirect
308. C₃×#121	C₂²×C₃	semidirect
311. C₃×#120	C₂²×C₃	semidirect
312. C₃×#120	C₂²×C₃	semidirect
313. C₃×C₄×Q₈	C₂²×C₃	semidirect
314. C₃×C₄×Q₈	C₂²×C₃	semidirect
315. C₃×C₄×Q₈	C₂²×C₃	semidirect
321. C₃×C₄×D₄	C₂²×C₃	semidirect
322. C₃×C₄×D₄	C₂²×C₃	semidirect
323. C₃×C₄×D₄	C₂²×C₃	semidirect
324. C₃×C₄×D₄	C₂²×C₃	semidirect
325. C₃×C₄×D₄	C₂²×C₃	semidirect
326. C₃×C₄×D₄	C₂²×C₃	semidirect
327. C₃×C₄×D₄	C₂²×C₃	semidirect
328. C₃×C₄×D₄	C₂²×C₃	semidirect
329. C₃×C₄×D₄	C₂²×C₃	semidirect
330. C₃×C₄×D₄	C₂²×C₃	semidirect
331. C₃×C₄×D₄	C₂²×C₃	semidirect
332. C₃×C₄×D₄	C₂²×C₃	semidirect
333. C₃×C₄×D₄	C₂²×C₃	semidirect
334. C₃×C₄×D₄	C₂²×C₃	semidirect
335. C₃×C₄×D₄	C₂²×C₃	semidirect
336. C₃×#117	C₂²×C₃	semidirect
337. C₃×#117	C₂²×C₃	semidirect
338. C₃×#117	C₂²×C₃	semidirect
339. C₃×#117	C₂²×C₃	semidirect
340. C₃×#117	C₂²×C₃	semidirect
341. C₃×#117	C₂²×C₃	semidirect
342. C₂×C₃×C₄⋊C₄	C₂²×C₃	semidirect
343. C₂×C₃×C₄⋊C₄	C₂²×C₃	semidirect
344. C₂×C₃×C₄⋊C₄	C₂²×C₃	semidirect
345. C₂×C₃×C₄⋊C₄	C₂²×C₃	semidirect
346. C₂×C₃×C₂²⋊C₄	C₂²×C₃	semidirect
347. C₂×C₃×C₂²⋊C₄	C₂²×C₃	semidirect
348. C₂×C₃×C₂²⋊C₄	C₂²×C₃	semidirect
349. C₂×C₃×C₂²⋊C₄	C₂²×C₃	semidirect
350. C₂×C₃×C₂²⋊C₄	C₂²×C₃	semidirect
351. C₂×C₃×C₄²	C₂²×C₃	semidirect
381. C₃²×D₄	#41	semidirect
415. #559	C₂×C₃²	semidirect
416. #554	C₂×C₃²	semidirect
417. #553	C₂×C₃²	semidirect
418. #553	C₂×C₃²	semidirect
419. #552	C₂×C₃²	semidirect
420. #551	C₂×C₃²	semidirect
421. #551	C₂×C₃²	semidirect
422. #547	C₂×C₃²	semidirect
423. #546	C₂×C₃²	semidirect
424. #546	C₂×C₃²	semidirect
425. #546	C₂×C₃²	semidirect
426. D₄²	C₂×C₃²	semidirect
427. #542	C₂×C₃²	semidirect
428. #540	C₂×C₃²	semidirect
429. #539	C₂×C₃²	semidirect
430. #538	C₂×C₃²	semidirect
431. #529	C₂×C₃²	semidirect
432. #529	C₂×C₃²	semidirect
433. #525	C₂×C₃²	semidirect
434. C₂×#123	C₂×C₃²	semidirect
435. #520	C₂×C₃²	semidirect
436. #518	C₂×C₃²	semidirect
437. C₂×C₄×D₄	C₂×C₃²	semidirect
582. C₂×#41	C₂²×C₃²	semidirect
586. C₂³×C₄	C₂²×C₃²	semidirect
587. C₄⋊Q₈	C₂²×C₃²	semidirect
589. #126	C₂²×C₃²	semidirect
590. #126	C₂²×C₃²	semidirect
591. #126	C₂²×C₃²	semidirect
592. #126	C₂²×C₃²	semidirect
593. #126	C₂²×C₃²	semidirect
594. #126	C₂²×C₃²	semidirect
595. #125	C₂²×C₃²	semidirect
596. #125	C₂²×C₃²	semidirect
597. #125	C₂²×C₃²	semidirect
598. #125	C₂²×C₃²	semidirect
599. #124	C₂²×C₃²	semidirect
600. #124	C₂²×C₃²	semidirect
601. #124	C₂²×C₃²	semidirect
602. #124	C₂²×C₃²	semidirect
603. #124	C₂²×C₃²	semidirect
606. #123	C₂²×C₃²	semidirect
607. #123	C₂²×C₃²	semidirect
608. #123	C₂²×C₃²	semidirect
609. #123	C₂²×C₃²	semidirect
610. #123	C₂²×C₃²	semidirect
611. #123	C₂²×C₃²	semidirect
612. #123	C₂²×C₃²	semidirect
613. #123	C₂²×C₃²	semidirect
614. #123	C₂²×C₃²	semidirect
615. #123	C₂²×C₃²	semidirect
616. #123	C₂²×C₃²	semidirect
617. #123	C₂²×C₃²	semidirect
618. C₂²⋊Q₈	C₂²×C₃²	semidirect
619. C₂²⋊Q₈	C₂²×C₃²	semidirect
620. C₂²⋊Q₈	C₂²×C₃²	semidirect
621. C₂²⋊Q₈	C₂²×C₃²	semidirect
622. C₂²⋊Q₈	C₂²×C₃²	semidirect
623. C₂²⋊Q₈	C₂²×C₃²	semidirect
624. C₂²⋊Q₈	C₂²×C₃²	semidirect
625. C₂²⋊Q₈	C₂²×C₃²	semidirect
630. #121	C₂²×C₃²	semidirect
631. #121	C₂²×C₃²	semidirect
632. #121	C₂²×C₃²	semidirect
633. #121	C₂²×C₃²	semidirect
634. #121	C₂²×C₃²	semidirect
635. #121	C₂²×C₃²	semidirect
636. #121	C₂²×C₃²	semidirect
639. #120	C₂²×C₃²	semidirect
640. #120	C₂²×C₃²	semidirect
641. C₄×Q₈	C₂²×C₃²	semidirect
642. C₄×Q₈	C₂²×C₃²	semidirect
643. C₄×Q₈	C₂²×C₃²	semidirect
649. C₄×D₄	C₂²×C₃²	semidirect
650. C₄×D₄	C₂²×C₃²	semidirect
651. C₄×D₄	C₂²×C₃²	semidirect
652. C₄×D₄	C₂²×C₃²	semidirect
653. C₄×D₄	C₂²×C₃²	semidirect
654. C₄×D₄	C₂²×C₃²	semidirect
655. C₄×D₄	C₂²×C₃²	semidirect
656. C₄×D₄	C₂²×C₃²	semidirect
657. C₄×D₄	C₂²×C₃²	semidirect
658. C₄×D₄	C₂²×C₃²	semidirect
659. C₄×D₄	C₂²×C₃²	semidirect
660. C₄×D₄	C₂²×C₃²	semidirect
661. C₄×D₄	C₂²×C₃²	semidirect
662. C₄×D₄	C₂²×C₃²	semidirect
663. C₄×D₄	C₂²×C₃²	semidirect
664. #117	C₂²×C₃²	semidirect
665. #117	C₂²×C₃²	semidirect
666. #117	C₂²×C₃²	semidirect
667. #117	C₂²×C₃²	semidirect
668. #117	C₂²×C₃²	semidirect
669. #117	C₂²×C₃²	semidirect
670. C₂×C₄⋊C₄	C₂²×C₃²	semidirect
671. C₂×C₄⋊C₄	C₂²×C₃²	semidirect
672. C₂×C₄⋊C₄	C₂²×C₃²	semidirect
673. C₂×C₄⋊C₄	C₂²×C₃²	semidirect
674. C₂×C₂²⋊C₄	C₂²×C₃²	semidirect
675. C₂×C₂²⋊C₄	C₂²×C₃²	semidirect
676. C₂×C₂²⋊C₄	C₂²×C₃²	semidirect
677. C₂×C₂²⋊C₄	C₂²×C₃²	semidirect
678. C₂×C₂²⋊C₄	C₂²×C₃²	semidirect
679. C₂×C₄²	C₂²×C₃²	semidirect
709. C₃×D₄	C₃×#41	semidirect
895. C₃²	#3513	direct (N × H)
925. D₄	C₃²×#41	semidirect
1006. C₃	C₃×#3513	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₃²×#559	2
C₃²×#554	2
C₃²×#553	2
C₃²×#552	2
C₃²×#551	2
C₃²×#547	2
C₃²×#546	2
C₃²×D₄²	2
C₃²×#542	2
C₃²×#540	2
C₃²×#539	2
C₃²×#538	2
C₃²×#529	2
C₃²×#525	2
C₂×C₃²×#123	2
C₃²×#520	2
C₃²×#518	2
C₂×C₃²×C₄×D₄	2
C₃×#3513	3

Subgroups — C32×#3513 #11770562

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃²×#3513 #11770562