Subgroups — C₃²×#3521 #11770570

Order 1152.

3126 conjugacy classes of subgroups.

The subgroup lattice has 969 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×#556	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃²×#556	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃²×#554	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃²×#553	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃²×#553	C₂	1	2	yes	maximal, complemented
6	C₃²×#552	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃²×#552	C₂	1	2	yes	maximal, complemented
8	C₃²×#551	C₂	1	2	yes	maximal, complemented
9	C₃²×#551	C₂	1	2	yes	maximal, complemented
10	C₃²×#547	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃²×#546	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃²×#546	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃²×#542	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃²×#541	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	2	yes	maximal, complemented
19	C₃²×#529	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×C₃²×#126	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	C₃²×C₄×#41	C₂	1	1	yes	maximal, characteristic, complemented
24	C₃×#3521	C₃	1	4	yes	maximal, direct product factor
25	C₂×C₃²×#41	C₂²	1	1	yes	characteristic
26	C₂×C₃²×#41	C₂²	1	1	yes	characteristic
27	C₂²×C₃²×D₄	C₂²	1	1	yes	characteristic
28	C₃²×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
29	C₃²×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
30	C₃²×#126	C₂²	1	2	yes	—
31	C₃²×#126	C₂²	1	2	yes	—
32	C₃²×#126	C₂²	1	2	yes	—
33	C₃²×#126	C₂²	1	1	yes	characteristic
34	C₃²×#126	C₂²	1	2	yes	—
35	C₃²×#126	C₂²	1	2	yes	complemented
36	C₃²×#126	C₂²	1	2	yes	complemented
37	C₃²×#126	C₂²	1	2	yes	complemented
38	C₃²×#126	C₂²	1	2	yes	complemented
39	C₃²×#126	C₂²	1	2	yes	complemented
40	C₃²×#126	C₂²	1	2	yes	complemented
41	C₃²×#126	C₂²	1	1	yes	characteristic, complemented
42	C₃²×#125	C₂²	1	1	yes	characteristic, complemented
43	C₃²×#125	C₂²	1	2	yes	complemented
44	C₃²×#125	C₂²	1	2	yes	complemented
45	C₃²×#125	C₂²	1	1	yes	characteristic, complemented
46	C₃²×#125	C₂²	1	1	yes	characteristic, complemented
47	C₃²×#125	C₂²	1	2	yes	complemented
48	C₃²×#124	C₂²	1	1	yes	characteristic
49	C₃²×#124	C₂²	1	2	yes	—
50	C₃²×#124	C₂²	1	1	yes	characteristic
51	C₃²×#124	C₂²	1	1	yes	characteristic
52	C₃²×#124	C₂²	1	2	yes	complemented
53	C₃²×#123	C₂²	1	1	yes	characteristic
54	C₃²×#123	C₂²	1	2	yes	—
55	C₃²×#123	C₂²	1	2	yes	—
56	C₃²×#123	C₂²	1	2	yes	—
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×#123	C₂²	1	2	yes	complemented
63	C₃²×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
64	C₃²×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
65	C₃²×C₂²⋊Q₈	C₂²	1	2	yes	complemented
66	C₃²×C₂²⋊Q₈	C₂²	1	2	yes	complemented
67	C₃²×C₂²⋊Q₈	C₂²	1	2	yes	complemented
68	C₃²×C₂²⋊Q₈	C₂²	1	2	yes	complemented
69	C₃²×C₂²⋊Q₈	C₂²	1	2	yes	complemented
70	C₃²×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
71	C₃²×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
72	C₃²×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
73	C₃²×#121	C₂²	1	1	yes	characteristic
74	C₃²×#121	C₂²	1	2	yes	—
75	C₃²×#121	C₂²	1	2	yes	—
76	C₃²×#121	C₂²	1	1	yes	characteristic
77	C₃²×#121	C₂²	1	1	yes	characteristic
78	C₃²×#121	C₂²	1	2	yes	complemented
79	C₃²×#121	C₂²	1	2	yes	complemented
80	C₃²×#120	C₂²	1	2	yes	—
81	C₃²×#120	C₂²	1	2	yes	—
82	C₃²×C₄×Q₈	C₂²	1	1	yes	characteristic, complemented
83	C₃²×C₄×Q₈	C₂²	1	2	yes	complemented
84	C₃²×C₄×Q₈	C₂²	1	1	yes	characteristic, 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	2	yes	—
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	1	yes	characteristic
94	C₃²×C₄×D₄	C₂²	1	1	yes	characteristic
95	C₃²×C₄×D₄	C₂²	1	1	yes	characteristic
96	C₃²×C₄×D₄	C₂²	1	2	yes	—
97	C₃²×C₄×D₄	C₂²	1	1	yes	characteristic
98	C₃²×C₄×D₄	C₂²	1	2	yes	complemented
99	C₃²×C₄×D₄	C₂²	1	2	yes	complemented
100	C₃²×C₄×D₄	C₂²	1	2	yes	complemented
101	C₃²×C₄×D₄	C₂²	1	2	yes	complemented
102	C₃²×C₄×D₄	C₂²	1	1	yes	characteristic, complemented
103	C₃²×C₄×D₄	C₂²	1	2	yes	complemented
104	C₃²×C₄×D₄	C₂²	1	2	yes	complemented
105	C₃²×#117	C₂²	1	1	yes	characteristic
106	C₃²×#117	C₂²	1	1	yes	characteristic
107	C₃²×#117	C₂²	1	2	yes	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	2	yes	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	2	yes	complemented
117	C₂×C₃²×C₄⋊C₄	C₂²	1	2	yes	complemented
118	C₂×C₃²×C₂²⋊C₄	C₂²	1	2	yes	—
119	C₂×C₃²×C₂²⋊C₄	C₂²	1	2	yes	—
120	C₂×C₃²×C₂²⋊C₄	C₂²	1	2	yes	—
121	C₂×C₃²×C₂²⋊C₄	C₂²	1	2	yes	—
122	C₂×C₃²×C₄²	C₂²	1	2	yes	complemented
123	C₂×C₃²×C₄²	C₂²	1	1	yes	characteristic, complemented
124	C₃×#556	C₂×C₃	1	4	yes	complemented
125	C₃×#556	C₂×C₃	1	4	yes	complemented
126	C₃×#554	C₂×C₃	1	4	yes	complemented
127	C₃×#553	C₂×C₃	1	4	yes	complemented
128	C₃×#553	C₂×C₃	1	8	yes	complemented
129	C₃×#552	C₂×C₃	1	4	yes	complemented
130	C₃×#552	C₂×C₃	1	8	yes	complemented
131	C₃×#551	C₂×C₃	1	8	yes	complemented
132	C₃×#551	C₂×C₃	1	8	yes	complemented
133	C₃×#547	C₂×C₃	1	4	yes	complemented
134	C₃×#546	C₂×C₃	1	4	yes	complemented
135	C₃×#546	C₂×C₃	1	4	yes	complemented
136	C₃×#542	C₂×C₃	1	4	yes	complemented
137	C₃×#541	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	8	yes	complemented
142	C₃×#529	C₂×C₃	1	4	yes	complemented
143	C₂×C₃×#126	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	C₃×C₄×#41	C₂×C₃	1	4	yes	complemented
147	C₂⁴×C₃²	C₂³	1	2	yes	—
148	C₃²×#41	—	2	4	no	—
149	C₃²×#41	—	2	4	no	—
150	C₂×C₃²×Q₈	C₂³	1	1	yes	characteristic
151	C₂×C₃²×Q₈	C₂³	1	1	yes	characteristic
152	C₂×C₃²×Q₈	C₂³	1	1	yes	characteristic
153	C₂×C₃²×Q₈	C₂³	1	2	yes	—
154	C₂×C₃²×D₄	—	2	4	no	—
155	C₂×C₃²×D₄	C₂³	1	2	yes	—
156	C₂×C₃²×D₄	C₂³	1	1	yes	characteristic
157	C₂×C₃²×D₄	C₂³	1	2	yes	—
158	C₂×C₃²×D₄	C₂³	1	2	yes	—
159	C₂×C₃²×D₄	C₂³	1	1	yes	characteristic
160	C₂×C₃²×D₄	C₂³	1	1	yes	characteristic
161	C₂×C₃²×D₄	C₂³	1	2	yes	—
162	C₂×C₃²×D₄	C₂³	1	2	yes	—
163	C₂×C₃²×D₄	C₂³	1	1	yes	characteristic
164	C₂×C₃²×D₄	C₂³	1	1	yes	characteristic
165	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
166	C₂²×C₃²×C₄	C₂³	1	2	yes	—
167	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
168	C₂²×C₃²×C₄	C₂³	1	2	yes	—
169	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
170	C₂²×C₃²×C₄	C₂³	1	2	yes	—
171	C₂²×C₃²×C₄	C₂³	1	2	yes	—
172	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
173	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
174	C₂²×C₃²×C₄	C₂³	1	2	yes	—
175	C₂²×C₃²×C₄	C₂³	1	2	yes	—
176	C₂²×C₃²×C₄	C₂³	1	2	yes	—
177	C₂²×C₃²×C₄	C₂³	1	2	yes	—
178	C₂²×C₃²×C₄	C₂³	1	2	yes	—
179	C₃²×C₄⋊C₄	C₂³	1	1	yes	characteristic
180	C₃²×C₄⋊C₄	C₂³	1	2	yes	—
181	C₃²×C₄⋊C₄	C₂³	1	1	yes	characteristic
182	C₃²×C₄⋊C₄	C₂³	1	1	yes	characteristic
183	C₃²×C₄⋊C₄	C₂³	1	1	yes	characteristic
184	C₃²×C₄⋊C₄	C₂³	1	2	yes	—
185	C₃²×C₄⋊C₄	C₂³	1	2	yes	—
186	C₃²×C₄⋊C₄	C₂³	1	1	yes	characteristic
187	C₃²×C₄⋊C₄	C₂³	1	2	yes	—
188	C₃²×C₄⋊C₄	C₂³	1	2	yes	—
189	C₃²×C₄⋊C₄	C₂³	1	2	yes	—
190	C₃²×C₄⋊C₄	C₂³	1	2	yes	—
191	C₃²×C₄⋊C₄	C₂³	1	2	yes	—
192	C₃²×C₄⋊C₄	C₂³	1	2	yes	—
193	C₃²×C₄⋊C₄	C₂³	1	1	yes	characteristic
194	C₃²×C₄⋊C₄	C₂³	1	1	yes	characteristic
195	C₃²×C₄⋊C₄	C₂³	1	1	yes	characteristic
196	C₃²×C₄⋊C₄	C₂³	1	1	yes	characteristic
197	C₃²×C₄⋊C₄	C₂³	1	1	yes	characteristic
198	C₃²×C₄⋊C₄	C₂³	1	1	yes	characteristic
199	C₃²×C₄⋊C₄	C₂³	1	2	yes	—
200	C₃²×C₄⋊C₄	C₂³	1	2	yes	—
201	C₃²×C₄⋊C₄	C₂³	1	2	yes	—
202	C₃²×C₄⋊C₄	C₂³	1	2	yes	—
203	C₃²×C₄⋊C₄	C₂³	1	2	yes	—
204	C₃²×C₄⋊C₄	C₂³	1	1	yes	characteristic
205	C₃²×C₄⋊C₄	C₂³	1	1	yes	characteristic
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×C₂²⋊C₄	C₂³	1	1	yes	characteristic
210	C₃²×C₂²⋊C₄	C₂³	1	1	yes	characteristic
211	C₃²×C₂²⋊C₄	C₂³	1	2	yes	—
212	C₃²×C₂²⋊C₄	C₂³	1	1	yes	characteristic
213	C₃²×C₂²⋊C₄	C₂³	1	1	yes	characteristic
214	C₃²×C₂²⋊C₄	C₂³	1	2	yes	—
215	C₃²×C₂²⋊C₄	C₂³	1	2	yes	—
216	C₃²×C₂²⋊C₄	C₂³	1	2	yes	—
217	C₃²×C₂²⋊C₄	C₂³	1	2	yes	—
218	C₃²×C₂²⋊C₄	C₂³	1	2	yes	—
219	C₃²×C₂²⋊C₄	C₂³	1	2	yes	—
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	1	yes	characteristic
225	C₃²×C₂²⋊C₄	C₂³	1	2	yes	—
226	C₃²×C₂²⋊C₄	C₂³	1	2	yes	—
227	C₃²×C₂²⋊C₄	C₂³	1	1	yes	characteristic
228	C₃²×C₂²⋊C₄	C₂³	1	2	yes	—
229	C₃²×C₂²⋊C₄	C₂³	1	1	yes	characteristic
230	C₃²×C₂²⋊C₄	C₂³	1	2	yes	—
231	C₃²×C₂²⋊C₄	C₂³	1	2	yes	—
232	C₃²×C₂²⋊C₄	C₂³	1	2	yes	—
233	C₃²×C₂²⋊C₄	C₂³	1	1	yes	characteristic
234	C₃²×C₂²⋊C₄	C₂³	1	1	yes	characteristic
235	C₃²×C₂²⋊C₄	C₂³	1	2	yes	—
236	C₃²×C₂²⋊C₄	C₂³	1	1	yes	characteristic
237	C₃²×C₄²	C₂³	1	1	yes	characteristic
238	C₃²×C₄²	C₂³	1	1	yes	characteristic
239	C₃²×C₄²	C₂³	1	1	yes	characteristic
240	C₃²×C₄²	C₂³	1	2	yes	—
241	C₃²×C₄²	C₂³	1	2	yes	—
242	C₃²×C₄²	C₂³	1	1	yes	characteristic
243	C₃²×C₄²	C₂³	1	2	yes	—
244	C₃²×C₄²	C₂³	1	2	yes	—
245	C₃²×C₄²	C₂³	1	1	yes	characteristic
246	C₃²×C₄²	C₂³	1	2	yes	—
247	C₃²×C₄²	C₂³	1	2	yes	—
248	C₃²×C₄²	C₂³	1	1	yes	characteristic
249	#3521	C₃²	1	1	yes	characteristic, direct product factor, Sylow
250	C₂×C₃×#41	C₂²×C₃	1	4	yes	—
251	C₂×C₃×#41	C₂²×C₃	1	4	yes	—
252	C₂²×C₃×D₄	C₂²×C₃	1	4	yes	—
253	C₃×C₄⋊Q₈	C₂²×C₃	1	4	yes	complemented
254	C₃×C₄⋊Q₈	C₂²×C₃	1	4	yes	complemented
255	C₃×#126	C₂²×C₃	1	4	yes	—
256	C₃×#126	C₂²×C₃	1	8	yes	—
257	C₃×#126	C₂²×C₃	1	8	yes	—
258	C₃×#126	C₂²×C₃	1	8	yes	—
259	C₃×#126	C₂²×C₃	1	8	yes	—
260	C₃×#126	C₂²×C₃	1	8	yes	complemented
261	C₃×#126	C₂²×C₃	1	8	yes	complemented
262	C₃×#126	C₂²×C₃	1	8	yes	complemented
263	C₃×#126	C₂²×C₃	1	8	yes	complemented
264	C₃×#126	C₂²×C₃	1	4	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	8	yes	complemented
268	C₃×#125	C₂²×C₃	1	4	yes	complemented
269	C₃×#125	C₂²×C₃	1	4	yes	complemented
270	C₃×#125	C₂²×C₃	1	8	yes	complemented
271	C₃×#125	C₂²×C₃	1	8	yes	complemented
272	C₃×#125	C₂²×C₃	1	4	yes	complemented
273	C₃×#124	C₂²×C₃	1	4	yes	—
274	C₃×#124	C₂²×C₃	1	4	yes	—
275	C₃×#124	C₂²×C₃	1	8	yes	—
276	C₃×#124	C₂²×C₃	1	4	yes	—
277	C₃×#124	C₂²×C₃	1	8	yes	complemented
278	C₃×#123	C₂²×C₃	1	8	yes	—
279	C₃×#123	C₂²×C₃	1	4	yes	—
280	C₃×#123	C₂²×C₃	1	8	yes	—
281	C₃×#123	C₂²×C₃	1	8	yes	—
282	C₃×#123	C₂²×C₃	1	8	yes	complemented
283	C₃×#123	C₂²×C₃	1	8	yes	complemented
284	C₃×#123	C₂²×C₃	1	4	yes	complemented
285	C₃×#123	C₂²×C₃	1	8	yes	complemented
286	C₃×#123	C₂²×C₃	1	8	yes	complemented
287	C₃×#123	C₂²×C₃	1	8	yes	complemented
288	C₃×C₂²⋊Q₈	C₂²×C₃	1	4	yes	—
289	C₃×C₂²⋊Q₈	C₂²×C₃	1	4	yes	—
290	C₃×C₂²⋊Q₈	C₂²×C₃	1	4	yes	complemented
291	C₃×C₂²⋊Q₈	C₂²×C₃	1	4	yes	complemented
292	C₃×C₂²⋊Q₈	C₂²×C₃	1	8	yes	complemented
293	C₃×C₂²⋊Q₈	C₂²×C₃	1	8	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	4	yes	complemented
297	C₃×C₂²⋊Q₈	C₂²×C₃	1	8	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	8	yes	—
302	C₃×#121	C₂²×C₃	1	4	yes	—
303	C₃×#121	C₂²×C₃	1	8	yes	complemented
304	C₃×#121	C₂²×C₃	1	8	yes	complemented
305	C₃×#120	C₂²×C₃	1	8	yes	—
306	C₃×#120	C₂²×C₃	1	8	yes	—
307	C₃×C₄×Q₈	C₂²×C₃	1	4	yes	complemented
308	C₃×C₄×Q₈	C₂²×C₃	1	4	yes	complemented
309	C₃×C₄×Q₈	C₂²×C₃	1	4	yes	complemented
310	C₃×C₄×Q₈	C₂²×C₃	1	4	yes	complemented
311	C₃×C₄×Q₈	C₂²×C₃	1	8	yes	complemented
312	C₃×C₄×Q₈	C₂²×C₃	1	4	yes	complemented
313	C₃×C₄×D₄	C₂²×C₃	1	4	yes	—
314	C₃×C₄×D₄	C₂²×C₃	1	4	yes	—
315	C₃×C₄×D₄	C₂²×C₃	1	8	yes	—
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	8	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	—
322	C₃×C₄×D₄	C₂²×C₃	1	4	yes	—
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	8	yes	complemented
326	C₃×C₄×D₄	C₂²×C₃	1	8	yes	complemented
327	C₃×C₄×D₄	C₂²×C₃	1	4	yes	complemented
328	C₃×C₄×D₄	C₂²×C₃	1	8	yes	complemented
329	C₃×C₄×D₄	C₂²×C₃	1	8	yes	complemented
330	C₃×#117	C₂²×C₃	1	4	yes	—
331	C₃×#117	C₂²×C₃	1	4	yes	—
332	C₃×#117	C₂²×C₃	1	8	yes	complemented
333	C₃×#117	C₂²×C₃	1	4	yes	complemented
334	C₃×#117	C₂²×C₃	1	4	yes	complemented
335	C₃×#117	C₂²×C₃	1	8	yes	complemented
336	C₃×#117	C₂²×C₃	1	8	yes	complemented
337	C₃×#117	C₂²×C₃	1	8	yes	complemented
338	C₃×#117	C₂²×C₃	1	8	yes	complemented
339	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	8	yes	complemented
340	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	4	yes	complemented
341	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	8	yes	complemented
342	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	8	yes	complemented
343	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	8	yes	—
344	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	8	yes	—
345	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	8	yes	—
346	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	8	yes	—
347	C₂×C₃×C₄²	C₂²×C₃	1	8	yes	complemented
348	C₂×C₃×C₄²	C₂²×C₃	1	4	yes	complemented
349	C₂³×C₃²	—	2	4	no	—
350	C₂³×C₃²	—	4	2	no	—
351	C₂³×C₃²	—	4	2	no	—
352	C₂³×C₃²	C₂⁴	1	1	yes	characteristic
353	C₂³×C₃²	C₂⁴	1	2	yes	—
354	C₂³×C₃²	C₂⁴	1	1	yes	characteristic
355	C₂³×C₃²	C₂⁴	1	1	yes	characteristic
356	C₂³×C₃²	C₂⁴	1	2	yes	—
357	C₃²×Q₈	—	2	2	no	—
358	C₃²×Q₈	—	2	2	no	—
359	C₃²×Q₈	—	4	1	no	—
360	C₃²×Q₈	—	4	2	no	—
361	C₃²×D₄	—	2	4	no	—
362	C₃²×D₄	—	2	4	no	—
363	C₃²×D₄	—	2	4	no	—
364	C₃²×D₄	—	2	2	no	—
365	C₃²×D₄	—	4	2	no	—
366	C₃²×D₄	—	4	1	no	—
367	C₃²×D₄	—	4	1	no	—
368	C₃²×D₄	—	4	2	no	—
369	C₃²×D₄	—	4	1	no	—
370	C₃²×D₄	#41	1	4	yes	—
371	C₂×C₃²×C₄	—	2	4	no	—
372	C₂×C₃²×C₄	—	2	4	no	—
373	C₂×C₃²×C₄	—	2	2	no	—
374	C₂×C₃²×C₄	—	2	2	no	—
375	C₂×C₃²×C₄	—	2	2	no	—
376	C₂×C₃²×C₄	—	4	2	no	—
377	C₂×C₃²×C₄	—	4	1	no	—
378	C₂×C₃²×C₄	—	4	2	no	—
379	C₂×C₃²×C₄	—	4	2	no	—
380	C₂×C₃²×C₄	—	4	2	no	—
381	C₂×C₃²×C₄	—	4	2	no	—
382	C₂×C₃²×C₄	—	4	1	no	—
383	C₂×C₃²×C₄	—	4	2	no	—
384	C₂×C₃²×C₄	—	4	2	no	—
385	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
386	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
387	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
388	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
389	C₂×C₃²×C₄	C₂⁴	1	2	yes	—
390	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
391	C₂×C₃²×C₄	C₂⁴	1	2	yes	—
392	C₂×C₃²×C₄	C₂⁴	1	2	yes	—
393	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
394	C₂×C₃²×C₄	C₂⁴	1	2	yes	—
395	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
396	C₂×C₃²×C₄	C₂⁴	1	2	yes	—
397	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
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	#556	C₂×C₃²	1	1	yes	characteristic, complemented
404	#556	C₂×C₃²	1	1	yes	characteristic, complemented
405	#554	C₂×C₃²	1	1	yes	characteristic, complemented
406	#553	C₂×C₃²	1	1	yes	characteristic, complemented
407	#553	C₂×C₃²	1	2	yes	complemented
408	#552	C₂×C₃²	1	1	yes	characteristic, complemented
409	#552	C₂×C₃²	1	2	yes	complemented
410	#551	C₂×C₃²	1	2	yes	complemented
411	#551	C₂×C₃²	1	2	yes	complemented
412	#547	C₂×C₃²	1	1	yes	characteristic, complemented
413	#546	C₂×C₃²	1	1	yes	characteristic, complemented
414	#546	C₂×C₃²	1	1	yes	characteristic, complemented
415	#542	C₂×C₃²	1	1	yes	characteristic, complemented
416	#541	C₂×C₃²	1	1	yes	characteristic, complemented
417	#539	C₂×C₃²	1	2	yes	complemented
418	#538	C₂×C₃²	1	2	yes	complemented
419	#529	C₂×C₃²	1	1	yes	characteristic, complemented
420	#529	C₂×C₃²	1	2	yes	complemented
421	#529	C₂×C₃²	1	1	yes	characteristic, complemented
422	C₂×#126	C₂×C₃²	1	2	yes	complemented
423	#520	C₂×C₃²	1	1	yes	characteristic, complemented
424	#518	C₂×C₃²	1	1	yes	characteristic, complemented
425	C₄×#41	C₂×C₃²	1	1	yes	characteristic, complemented
426	C₂⁴×C₃	C₂³×C₃	1	8	yes	—
427	C₃×#41	—	2	16	no	—
428	C₃×#41	—	2	16	no	—
429	C₂×C₃×Q₈	C₂³×C₃	1	4	yes	—
430	C₂×C₃×Q₈	C₂³×C₃	1	4	yes	—
431	C₂×C₃×Q₈	C₂³×C₃	1	4	yes	—
432	C₂×C₃×Q₈	C₂³×C₃	1	8	yes	—
433	C₂×C₃×D₄	—	2	16	no	—
434	C₂×C₃×D₄	C₂³×C₃	1	8	yes	—
435	C₂×C₃×D₄	C₂³×C₃	1	4	yes	—
436	C₂×C₃×D₄	C₂³×C₃	1	8	yes	—
437	C₂×C₃×D₄	C₂³×C₃	1	8	yes	—
438	C₂×C₃×D₄	C₂³×C₃	1	4	yes	—
439	C₂×C₃×D₄	C₂³×C₃	1	4	yes	—
440	C₂×C₃×D₄	C₂³×C₃	1	8	yes	—
441	C₂×C₃×D₄	C₂³×C₃	1	8	yes	—
442	C₂×C₃×D₄	C₂³×C₃	1	4	yes	—
443	C₂×C₃×D₄	C₂³×C₃	1	4	yes	—
444	C₂²×C₃×C₄	C₂³×C₃	1	8	yes	—
445	C₂²×C₃×C₄	C₂³×C₃	1	4	yes	—
446	C₂²×C₃×C₄	C₂³×C₃	1	8	yes	—
447	C₂²×C₃×C₄	C₂³×C₃	1	4	yes	—
448	C₂²×C₃×C₄	C₂³×C₃	1	4	yes	—
449	C₂²×C₃×C₄	C₂³×C₃	1	8	yes	—
450	C₂²×C₃×C₄	C₂³×C₃	1	8	yes	—
451	C₂²×C₃×C₄	C₂³×C₃	1	4	yes	—
452	C₂²×C₃×C₄	C₂³×C₃	1	4	yes	—
453	C₂²×C₃×C₄	C₂³×C₃	1	8	yes	—
454	C₂²×C₃×C₄	C₂³×C₃	1	8	yes	—
455	C₂²×C₃×C₄	C₂³×C₃	1	8	yes	—
456	C₂²×C₃×C₄	C₂³×C₃	1	8	yes	—
457	C₂²×C₃×C₄	C₂³×C₃	1	8	yes	—
458	C₃×C₄⋊C₄	C₂³×C₃	1	4	yes	—
459	C₃×C₄⋊C₄	C₂³×C₃	1	8	yes	—
460	C₃×C₄⋊C₄	C₂³×C₃	1	4	yes	—
461	C₃×C₄⋊C₄	C₂³×C₃	1	4	yes	—
462	C₃×C₄⋊C₄	C₂³×C₃	1	4	yes	—
463	C₃×C₄⋊C₄	C₂³×C₃	1	8	yes	—
464	C₃×C₄⋊C₄	C₂³×C₃	1	8	yes	—
465	C₃×C₄⋊C₄	C₂³×C₃	1	4	yes	—
466	C₃×C₄⋊C₄	C₂³×C₃	1	8	yes	—
467	C₃×C₄⋊C₄	C₂³×C₃	1	8	yes	—
468	C₃×C₄⋊C₄	C₂³×C₃	1	8	yes	—
469	C₃×C₄⋊C₄	C₂³×C₃	1	8	yes	—
470	C₃×C₄⋊C₄	C₂³×C₃	1	8	yes	—
471	C₃×C₄⋊C₄	C₂³×C₃	1	8	yes	—
472	C₃×C₄⋊C₄	C₂³×C₃	1	4	yes	—
473	C₃×C₄⋊C₄	C₂³×C₃	1	4	yes	—
474	C₃×C₄⋊C₄	C₂³×C₃	1	4	yes	—
475	C₃×C₄⋊C₄	C₂³×C₃	1	4	yes	—
476	C₃×C₄⋊C₄	C₂³×C₃	1	4	yes	—
477	C₃×C₄⋊C₄	C₂³×C₃	1	4	yes	—
478	C₃×C₄⋊C₄	C₂³×C₃	1	8	yes	—
479	C₃×C₄⋊C₄	C₂³×C₃	1	8	yes	—
480	C₃×C₄⋊C₄	C₂³×C₃	1	8	yes	—
481	C₃×C₄⋊C₄	C₂³×C₃	1	8	yes	—
482	C₃×C₄⋊C₄	C₂³×C₃	1	8	yes	—
483	C₃×C₄⋊C₄	C₂³×C₃	1	4	yes	—
484	C₃×C₄⋊C₄	C₂³×C₃	1	4	yes	—
485	C₃×C₄⋊C₄	C₂³×C₃	1	8	yes	—
486	C₃×C₄⋊C₄	C₂³×C₃	1	8	yes	—
487	C₃×C₄⋊C₄	C₂³×C₃	1	4	yes	—
488	C₃×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
489	C₃×C₂²⋊C₄	C₂³×C₃	1	8	yes	—
490	C₃×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
491	C₃×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
492	C₃×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
493	C₃×C₂²⋊C₄	C₂³×C₃	1	8	yes	—
494	C₃×C₂²⋊C₄	C₂³×C₃	1	8	yes	—
495	C₃×C₂²⋊C₄	C₂³×C₃	1	8	yes	—
496	C₃×C₂²⋊C₄	C₂³×C₃	1	8	yes	—
497	C₃×C₂²⋊C₄	C₂³×C₃	1	8	yes	—
498	C₃×C₂²⋊C₄	C₂³×C₃	1	8	yes	—
499	C₃×C₂²⋊C₄	C₂³×C₃	1	8	yes	—
500	C₃×C₂²⋊C₄	C₂³×C₃	1	8	yes	—
501	C₃×C₂²⋊C₄	C₂³×C₃	1	8	yes	—
502	C₃×C₂²⋊C₄	C₂³×C₃	1	8	yes	—
503	C₃×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
504	C₃×C₂²⋊C₄	C₂³×C₃	1	8	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	8	yes	—
510	C₃×C₂²⋊C₄	C₂³×C₃	1	8	yes	—
511	C₃×C₂²⋊C₄	C₂³×C₃	1	8	yes	—
512	C₃×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
513	C₃×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
514	C₃×C₂²⋊C₄	C₂³×C₃	1	8	yes	—
515	C₃×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
516	C₃×C₄²	C₂³×C₃	1	4	yes	—
517	C₃×C₄²	C₂³×C₃	1	4	yes	—
518	C₃×C₄²	C₂³×C₃	1	4	yes	—
519	C₃×C₄²	C₂³×C₃	1	8	yes	—
520	C₃×C₄²	C₂³×C₃	1	8	yes	—
521	C₃×C₄²	C₂³×C₃	1	4	yes	—
522	C₃×C₄²	C₂³×C₃	1	8	yes	—
523	C₃×C₄²	C₂³×C₃	1	8	yes	—
524	C₃×C₄²	C₂³×C₃	1	4	yes	—
525	C₃×C₄²	C₂³×C₃	1	8	yes	—
526	C₃×C₄²	C₂³×C₃	1	8	yes	—
527	C₃×C₄²	C₂³×C₃	1	4	yes	—
528	C₂²×C₃²	—	2	2	no	—
529	C₂²×C₃²	—	2	2	no	—
530	C₂²×C₃²	—	2	1	no	—
531	C₂²×C₃²	—	2	1	no	—
532	C₂²×C₃²	—	2	1	no	—
533	C₂²×C₃²	—	2	2	no	—
534	C₂²×C₃²	—	2	1	no	—
535	C₂²×C₃²	—	2	1	no	—
536	C₂²×C₃²	—	2	1	no	—
537	C₂²×C₃²	—	2	2	no	—
538	C₂²×C₃²	—	2	2	no	—
539	C₂²×C₃²	—	2	1	no	—
540	C₂²×C₃²	—	2	1	no	—
541	C₂²×C₃²	—	2	1	no	—
542	C₂²×C₃²	—	8	4	no	—
543	C₂²×C₃²	C₂×#41	1	4	yes	—
544	C₂²×C₃²	C₂⁵	1	1	yes	characteristic
545	C₃²×C₄	—	2	1	no	—
546	C₃²×C₄	—	2	1	no	—
547	C₃²×C₄	—	2	1	no	—
548	C₃²×C₄	—	2	2	no	—
549	C₃²×C₄	—	2	2	no	—
550	C₃²×C₄	—	2	1	no	—
551	C₃²×C₄	—	2	2	no	—
552	C₃²×C₄	—	2	1	no	—
553	C₃²×C₄	—	2	1	no	—
554	C₃²×C₄	—	2	2	no	—
555	C₃²×C₄	—	2	1	no	—
556	C₃²×C₄	—	2	1	no	—
557	C₃²×C₄	—	2	1	no	—
558	C₃²×C₄	—	2	2	no	—
559	C₃²×C₄	—	2	1	no	—
560	C₃²×C₄	—	2	2	no	—
561	C₃²×C₄	—	2	1	no	—
562	C₃²×C₄	C₂×#41	1	2	yes	—
563	C₂×#41	C₂²×C₃²	1	1	yes	characteristic
564	C₂×#41	C₂²×C₃²	1	1	yes	characteristic
565	C₂²×D₄	C₂²×C₃²	1	1	yes	characteristic
566	C₄⋊Q₈	C₂²×C₃²	1	1	yes	characteristic, complemented
567	C₄⋊Q₈	C₂²×C₃²	1	1	yes	characteristic, complemented
568	#126	C₂²×C₃²	1	1	yes	characteristic
569	#126	C₂²×C₃²	1	2	yes	—
570	#126	C₂²×C₃²	1	2	yes	—
571	#126	C₂²×C₃²	1	2	yes	—
572	#126	C₂²×C₃²	1	2	yes	—
573	#126	C₂²×C₃²	1	2	yes	complemented
574	#126	C₂²×C₃²	1	2	yes	complemented
575	#126	C₂²×C₃²	1	2	yes	complemented
576	#126	C₂²×C₃²	1	2	yes	complemented
577	#126	C₂²×C₃²	1	1	yes	characteristic, complemented
578	#126	C₂²×C₃²	1	2	yes	complemented
579	#126	C₂²×C₃²	1	2	yes	complemented
580	#125	C₂²×C₃²	1	2	yes	complemented
581	#125	C₂²×C₃²	1	1	yes	characteristic, complemented
582	#125	C₂²×C₃²	1	1	yes	characteristic, complemented
583	#125	C₂²×C₃²	1	2	yes	complemented
584	#125	C₂²×C₃²	1	2	yes	complemented
585	#125	C₂²×C₃²	1	1	yes	characteristic, complemented
586	#124	C₂²×C₃²	1	1	yes	characteristic
587	#124	C₂²×C₃²	1	1	yes	characteristic
588	#124	C₂²×C₃²	1	2	yes	—
589	#124	C₂²×C₃²	1	1	yes	characteristic
590	#124	C₂²×C₃²	1	2	yes	complemented
591	#123	C₂²×C₃²	1	2	yes	—
592	#123	C₂²×C₃²	1	1	yes	characteristic
593	#123	C₂²×C₃²	1	2	yes	—
594	#123	C₂²×C₃²	1	2	yes	—
595	#123	C₂²×C₃²	1	2	yes	complemented
596	#123	C₂²×C₃²	1	2	yes	complemented
597	#123	C₂²×C₃²	1	1	yes	characteristic, complemented
598	#123	C₂²×C₃²	1	2	yes	complemented
599	#123	C₂²×C₃²	1	2	yes	complemented
600	#123	C₂²×C₃²	1	2	yes	complemented
601	C₂²⋊Q₈	C₂²×C₃²	1	1	yes	characteristic
602	C₂²⋊Q₈	C₂²×C₃²	1	1	yes	characteristic
603	C₂²⋊Q₈	C₂²×C₃²	1	1	yes	characteristic, complemented
604	C₂²⋊Q₈	C₂²×C₃²	1	1	yes	characteristic, complemented
605	C₂²⋊Q₈	C₂²×C₃²	1	2	yes	complemented
606	C₂²⋊Q₈	C₂²×C₃²	1	2	yes	complemented
607	C₂²⋊Q₈	C₂²×C₃²	1	2	yes	complemented
608	C₂²⋊Q₈	C₂²×C₃²	1	2	yes	complemented
609	C₂²⋊Q₈	C₂²×C₃²	1	1	yes	characteristic, complemented
610	C₂²⋊Q₈	C₂²×C₃²	1	2	yes	complemented
611	#121	C₂²×C₃²	1	1	yes	characteristic
612	#121	C₂²×C₃²	1	1	yes	characteristic
613	#121	C₂²×C₃²	1	2	yes	—
614	#121	C₂²×C₃²	1	2	yes	—
615	#121	C₂²×C₃²	1	1	yes	characteristic
616	#121	C₂²×C₃²	1	2	yes	complemented
617	#121	C₂²×C₃²	1	2	yes	complemented
618	#120	C₂²×C₃²	1	2	yes	—
619	#120	C₂²×C₃²	1	2	yes	—
620	C₄×Q₈	C₂²×C₃²	1	1	yes	characteristic, complemented
621	C₄×Q₈	C₂²×C₃²	1	1	yes	characteristic, complemented
622	C₄×Q₈	C₂²×C₃²	1	1	yes	characteristic, complemented
623	C₄×Q₈	C₂²×C₃²	1	1	yes	characteristic, complemented
624	C₄×Q₈	C₂²×C₃²	1	2	yes	complemented
625	C₄×Q₈	C₂²×C₃²	1	1	yes	characteristic, complemented
626	C₄×D₄	C₂²×C₃²	1	1	yes	characteristic
627	C₄×D₄	C₂²×C₃²	1	1	yes	characteristic
628	C₄×D₄	C₂²×C₃²	1	2	yes	—
629	C₄×D₄	C₂²×C₃²	1	1	yes	characteristic
630	C₄×D₄	C₂²×C₃²	1	1	yes	characteristic
631	C₄×D₄	C₂²×C₃²	1	2	yes	—
632	C₄×D₄	C₂²×C₃²	1	1	yes	characteristic
633	C₄×D₄	C₂²×C₃²	1	1	yes	characteristic
634	C₄×D₄	C₂²×C₃²	1	1	yes	characteristic
635	C₄×D₄	C₂²×C₃²	1	1	yes	characteristic
636	C₄×D₄	C₂²×C₃²	1	2	yes	complemented
637	C₄×D₄	C₂²×C₃²	1	2	yes	complemented
638	C₄×D₄	C₂²×C₃²	1	2	yes	complemented
639	C₄×D₄	C₂²×C₃²	1	2	yes	complemented
640	C₄×D₄	C₂²×C₃²	1	1	yes	characteristic, complemented
641	C₄×D₄	C₂²×C₃²	1	2	yes	complemented
642	C₄×D₄	C₂²×C₃²	1	2	yes	complemented
643	#117	C₂²×C₃²	1	1	yes	characteristic
644	#117	C₂²×C₃²	1	1	yes	characteristic
645	#117	C₂²×C₃²	1	2	yes	complemented
646	#117	C₂²×C₃²	1	1	yes	characteristic, complemented
647	#117	C₂²×C₃²	1	1	yes	characteristic, complemented
648	#117	C₂²×C₃²	1	2	yes	complemented
649	#117	C₂²×C₃²	1	2	yes	complemented
650	#117	C₂²×C₃²	1	2	yes	complemented
651	#117	C₂²×C₃²	1	2	yes	complemented
652	C₂×C₄⋊C₄	C₂²×C₃²	1	2	yes	complemented
653	C₂×C₄⋊C₄	C₂²×C₃²	1	1	yes	characteristic, complemented
654	C₂×C₄⋊C₄	C₂²×C₃²	1	2	yes	complemented
655	C₂×C₄⋊C₄	C₂²×C₃²	1	2	yes	complemented
656	C₂×C₂²⋊C₄	C₂²×C₃²	1	2	yes	—
657	C₂×C₂²⋊C₄	C₂²×C₃²	1	2	yes	—
658	C₂×C₂²⋊C₄	C₂²×C₃²	1	2	yes	—
659	C₂×C₂²⋊C₄	C₂²×C₃²	1	2	yes	—
660	C₂×C₄²	C₂²×C₃²	1	2	yes	complemented
661	C₂×C₄²	C₂²×C₃²	1	1	yes	characteristic, complemented
662	C₂³×C₃	—	2	16	no	—
663	C₂³×C₃	—	4	8	no	—
664	C₂³×C₃	—	4	8	no	—
665	C₂³×C₃	C₂⁴×C₃	1	4	yes	—
666	C₂³×C₃	C₂⁴×C₃	1	8	yes	—
667	C₂³×C₃	C₂⁴×C₃	1	4	yes	—
668	C₂³×C₃	C₂⁴×C₃	1	4	yes	—
669	C₂³×C₃	C₂⁴×C₃	1	8	yes	—
670	C₃×Q₈	—	2	8	no	—
671	C₃×Q₈	—	2	8	no	—
672	C₃×Q₈	—	4	4	no	—
673	C₃×Q₈	—	4	8	no	—
674	C₃×D₄	—	2	16	no	—
675	C₃×D₄	—	2	16	no	—
676	C₃×D₄	—	2	16	no	—
677	C₃×D₄	—	2	8	no	—
678	C₃×D₄	—	4	8	no	—
679	C₃×D₄	—	4	4	no	—
680	C₃×D₄	—	4	4	no	—
681	C₃×D₄	—	4	8	no	—
682	C₃×D₄	—	4	4	no	—
683	C₃×D₄	C₃×#41	1	16	yes	—
684	C₂×C₃×C₄	—	2	16	no	—
685	C₂×C₃×C₄	—	2	16	no	—
686	C₂×C₃×C₄	—	2	8	no	—
687	C₂×C₃×C₄	—	2	8	no	—
688	C₂×C₃×C₄	—	2	8	no	—
689	C₂×C₃×C₄	—	4	8	no	—
690	C₂×C₃×C₄	—	4	4	no	—
691	C₂×C₃×C₄	—	4	8	no	—
692	C₂×C₃×C₄	—	4	8	no	—
693	C₂×C₃×C₄	—	4	8	no	—
694	C₂×C₃×C₄	—	4	8	no	—
695	C₂×C₃×C₄	—	4	4	no	—
696	C₂×C₃×C₄	—	4	8	no	—
697	C₂×C₃×C₄	—	4	8	no	—
698	C₂×C₃×C₄	C₂⁴×C₃	1	4	yes	—
699	C₂×C₃×C₄	C₂⁴×C₃	1	4	yes	—
700	C₂×C₃×C₄	C₂⁴×C₃	1	4	yes	—
701	C₂×C₃×C₄	C₂⁴×C₃	1	4	yes	—
702	C₂×C₃×C₄	C₂⁴×C₃	1	8	yes	—
703	C₂×C₃×C₄	C₂⁴×C₃	1	4	yes	—
704	C₂×C₃×C₄	C₂⁴×C₃	1	8	yes	—
705	C₂×C₃×C₄	C₂⁴×C₃	1	8	yes	—
706	C₂×C₃×C₄	C₂⁴×C₃	1	4	yes	—
707	C₂×C₃×C₄	C₂⁴×C₃	1	8	yes	—
708	C₂×C₃×C₄	C₂⁴×C₃	1	4	yes	—
709	C₂×C₃×C₄	C₂⁴×C₃	1	8	yes	—
710	C₂×C₃×C₄	C₂⁴×C₃	1	4	yes	—
711	C₂×C₃×C₄	C₂⁴×C₃	1	4	yes	—
712	C₂×C₃×C₄	C₂⁴×C₃	1	4	yes	—
713	C₂×C₃×C₄	C₂⁴×C₃	1	8	yes	—
714	C₂×C₃×C₄	C₂⁴×C₃	1	4	yes	—
715	C₂×C₃×C₄	C₂⁴×C₃	1	4	yes	—
716	C₂×C₃²	—	2	4	no	—
717	C₂×C₃²	—	4	1	no	—
718	C₂×C₃²	—	4	1	no	—
719	C₂×C₃²	—	4	2	no	—
720	C₂×C₃²	—	4	1	no	—
721	C₂×C₃²	C₂²×#41	1	1	yes	characteristic
722	C₂×C₃²	#585	1	1	yes	characteristic
723	C₂×C₃²	#585	1	1	yes	characteristic
724	C₂⁴	C₂³×C₃²	1	2	yes	—
725	#41	—	2	4	no	—
726	#41	—	2	4	no	—
727	C₂×Q₈	C₂³×C₃²	1	1	yes	characteristic
728	C₂×Q₈	C₂³×C₃²	1	1	yes	characteristic
729	C₂×Q₈	C₂³×C₃²	1	1	yes	characteristic
730	C₂×Q₈	C₂³×C₃²	1	2	yes	—
731	C₂×D₄	—	2	4	no	—
732	C₂×D₄	C₂³×C₃²	1	2	yes	—
733	C₂×D₄	C₂³×C₃²	1	1	yes	characteristic
734	C₂×D₄	C₂³×C₃²	1	2	yes	—
735	C₂×D₄	C₂³×C₃²	1	2	yes	—
736	C₂×D₄	C₂³×C₃²	1	1	yes	characteristic
737	C₂×D₄	C₂³×C₃²	1	1	yes	characteristic
738	C₂×D₄	C₂³×C₃²	1	2	yes	—
739	C₂×D₄	C₂³×C₃²	1	2	yes	—
740	C₂×D₄	C₂³×C₃²	1	1	yes	characteristic
741	C₂×D₄	C₂³×C₃²	1	1	yes	characteristic
742	C₂²×C₄	C₂³×C₃²	1	2	yes	—
743	C₂²×C₄	C₂³×C₃²	1	1	yes	characteristic
744	C₂²×C₄	C₂³×C₃²	1	2	yes	—
745	C₂²×C₄	C₂³×C₃²	1	1	yes	characteristic
746	C₂²×C₄	C₂³×C₃²	1	1	yes	characteristic
747	C₂²×C₄	C₂³×C₃²	1	2	yes	—
748	C₂²×C₄	C₂³×C₃²	1	2	yes	—
749	C₂²×C₄	C₂³×C₃²	1	1	yes	characteristic
750	C₂²×C₄	C₂³×C₃²	1	1	yes	characteristic
751	C₂²×C₄	C₂³×C₃²	1	2	yes	—
752	C₂²×C₄	C₂³×C₃²	1	2	yes	—
753	C₂²×C₄	C₂³×C₃²	1	2	yes	—
754	C₂²×C₄	C₂³×C₃²	1	2	yes	—
755	C₂²×C₄	C₂³×C₃²	1	2	yes	—
756	C₄⋊C₄	C₂³×C₃²	1	1	yes	characteristic
757	C₄⋊C₄	C₂³×C₃²	1	2	yes	—
758	C₄⋊C₄	C₂³×C₃²	1	1	yes	characteristic
759	C₄⋊C₄	C₂³×C₃²	1	1	yes	characteristic
760	C₄⋊C₄	C₂³×C₃²	1	1	yes	characteristic
761	C₄⋊C₄	C₂³×C₃²	1	2	yes	—
762	C₄⋊C₄	C₂³×C₃²	1	2	yes	—
763	C₄⋊C₄	C₂³×C₃²	1	1	yes	characteristic
764	C₄⋊C₄	C₂³×C₃²	1	2	yes	—
765	C₄⋊C₄	C₂³×C₃²	1	2	yes	—
766	C₄⋊C₄	C₂³×C₃²	1	2	yes	—
767	C₄⋊C₄	C₂³×C₃²	1	2	yes	—
768	C₄⋊C₄	C₂³×C₃²	1	2	yes	—
769	C₄⋊C₄	C₂³×C₃²	1	2	yes	—
770	C₄⋊C₄	C₂³×C₃²	1	1	yes	characteristic
771	C₄⋊C₄	C₂³×C₃²	1	1	yes	characteristic
772	C₄⋊C₄	C₂³×C₃²	1	1	yes	characteristic
773	C₄⋊C₄	C₂³×C₃²	1	1	yes	characteristic
774	C₄⋊C₄	C₂³×C₃²	1	1	yes	characteristic
775	C₄⋊C₄	C₂³×C₃²	1	1	yes	characteristic
776	C₄⋊C₄	C₂³×C₃²	1	2	yes	—
777	C₄⋊C₄	C₂³×C₃²	1	2	yes	—
778	C₄⋊C₄	C₂³×C₃²	1	2	yes	—
779	C₄⋊C₄	C₂³×C₃²	1	2	yes	—
780	C₄⋊C₄	C₂³×C₃²	1	2	yes	—
781	C₄⋊C₄	C₂³×C₃²	1	1	yes	characteristic
782	C₄⋊C₄	C₂³×C₃²	1	1	yes	characteristic
783	C₄⋊C₄	C₂³×C₃²	1	2	yes	—
784	C₄⋊C₄	C₂³×C₃²	1	2	yes	—
785	C₄⋊C₄	C₂³×C₃²	1	1	yes	characteristic
786	C₂²⋊C₄	C₂³×C₃²	1	1	yes	characteristic
787	C₂²⋊C₄	C₂³×C₃²	1	2	yes	—
788	C₂²⋊C₄	C₂³×C₃²	1	1	yes	characteristic
789	C₂²⋊C₄	C₂³×C₃²	1	1	yes	characteristic
790	C₂²⋊C₄	C₂³×C₃²	1	1	yes	characteristic
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	C₂²⋊C₄	C₂³×C₃²	1	2	yes	—
795	C₂²⋊C₄	C₂³×C₃²	1	2	yes	—
796	C₂²⋊C₄	C₂³×C₃²	1	2	yes	—
797	C₂²⋊C₄	C₂³×C₃²	1	2	yes	—
798	C₂²⋊C₄	C₂³×C₃²	1	2	yes	—
799	C₂²⋊C₄	C₂³×C₃²	1	2	yes	—
800	C₂²⋊C₄	C₂³×C₃²	1	2	yes	—
801	C₂²⋊C₄	C₂³×C₃²	1	1	yes	characteristic
802	C₂²⋊C₄	C₂³×C₃²	1	2	yes	—
803	C₂²⋊C₄	C₂³×C₃²	1	2	yes	—
804	C₂²⋊C₄	C₂³×C₃²	1	1	yes	characteristic
805	C₂²⋊C₄	C₂³×C₃²	1	2	yes	—
806	C₂²⋊C₄	C₂³×C₃²	1	1	yes	characteristic
807	C₂²⋊C₄	C₂³×C₃²	1	2	yes	—
808	C₂²⋊C₄	C₂³×C₃²	1	2	yes	—
809	C₂²⋊C₄	C₂³×C₃²	1	2	yes	—
810	C₂²⋊C₄	C₂³×C₃²	1	1	yes	characteristic
811	C₂²⋊C₄	C₂³×C₃²	1	1	yes	characteristic
812	C₂²⋊C₄	C₂³×C₃²	1	2	yes	—
813	C₂²⋊C₄	C₂³×C₃²	1	1	yes	characteristic
814	C₄²	C₂³×C₃²	1	1	yes	characteristic
815	C₄²	C₂³×C₃²	1	1	yes	characteristic
816	C₄²	C₂³×C₃²	1	1	yes	characteristic
817	C₄²	C₂³×C₃²	1	2	yes	—
818	C₄²	C₂³×C₃²	1	2	yes	—
819	C₄²	C₂³×C₃²	1	1	yes	characteristic
820	C₄²	C₂³×C₃²	1	2	yes	—
821	C₄²	C₂³×C₃²	1	2	yes	—
822	C₄²	C₂³×C₃²	1	1	yes	characteristic
823	C₄²	C₂³×C₃²	1	2	yes	—
824	C₄²	C₂³×C₃²	1	2	yes	—
825	C₄²	C₂³×C₃²	1	1	yes	characteristic
826	C₂²×C₃	—	2	8	no	—
827	C₂²×C₃	—	2	8	no	—
828	C₂²×C₃	—	2	4	no	—
829	C₂²×C₃	—	2	4	no	—
830	C₂²×C₃	—	2	4	no	—
831	C₂²×C₃	—	2	8	no	—
832	C₂²×C₃	—	2	4	no	—
833	C₂²×C₃	—	2	4	no	—
834	C₂²×C₃	—	2	4	no	—
835	C₂²×C₃	—	2	8	no	—
836	C₂²×C₃	—	2	8	no	—
837	C₂²×C₃	—	2	4	no	—
838	C₂²×C₃	—	2	4	no	—
839	C₂²×C₃	—	2	4	no	—
840	C₂²×C₃	—	8	16	no	—
841	C₂²×C₃	C₂×C₃×#41	1	16	yes	—
842	C₂²×C₃	C₂⁵×C₃	1	4	yes	—
843	C₃×C₄	—	2	4	no	—
844	C₃×C₄	—	2	4	no	—
845	C₃×C₄	—	2	4	no	—
846	C₃×C₄	—	2	8	no	—
847	C₃×C₄	—	2	8	no	—
848	C₃×C₄	—	2	4	no	—
849	C₃×C₄	—	2	8	no	—
850	C₃×C₄	—	2	4	no	—
851	C₃×C₄	—	2	4	no	—
852	C₃×C₄	—	2	8	no	—
853	C₃×C₄	—	2	4	no	—
854	C₃×C₄	—	2	4	no	—
855	C₃×C₄	—	2	4	no	—
856	C₃×C₄	—	2	8	no	—
857	C₃×C₄	—	2	4	no	—
858	C₃×C₄	—	2	8	no	—
859	C₃×C₄	—	2	4	no	—
860	C₃×C₄	C₂×C₃×#41	1	8	yes	—
861	C₃²	#3521	1	1	yes	characteristic, direct product factor, Sylow
862	C₂³	—	2	4	no	—
863	C₂³	—	4	2	no	—
864	C₂³	—	4	2	no	—
865	C₂³	C₂⁴×C₃²	1	1	yes	characteristic
866	C₂³	C₂⁴×C₃²	1	2	yes	—
867	C₂³	C₂⁴×C₃²	1	1	yes	characteristic
868	C₂³	C₂⁴×C₃²	1	1	yes	characteristic
869	C₂³	C₂⁴×C₃²	1	2	yes	—
870	Q₈	—	2	2	no	—
871	Q₈	—	2	2	no	—
872	Q₈	—	4	1	no	—
873	Q₈	—	4	2	no	—
874	D₄	—	2	4	no	—
875	D₄	—	2	4	no	—
876	D₄	—	2	4	no	—
877	D₄	—	2	2	no	—
878	D₄	—	4	2	no	—
879	D₄	—	4	1	no	—
880	D₄	—	4	1	no	—
881	D₄	—	4	2	no	—
882	D₄	—	4	1	no	—
883	D₄	C₃²×#41	1	4	yes	—
884	C₂×C₄	—	2	4	no	—
885	C₂×C₄	—	2	4	no	—
886	C₂×C₄	—	2	2	no	—
887	C₂×C₄	—	2	2	no	—
888	C₂×C₄	—	2	2	no	—
889	C₂×C₄	—	4	2	no	—
890	C₂×C₄	—	4	1	no	—
891	C₂×C₄	—	4	2	no	—
892	C₂×C₄	—	4	2	no	—
893	C₂×C₄	—	4	2	no	—
894	C₂×C₄	—	4	2	no	—
895	C₂×C₄	—	4	1	no	—
896	C₂×C₄	—	4	2	no	—
897	C₂×C₄	—	4	2	no	—
898	C₂×C₄	C₂⁴×C₃²	1	1	yes	characteristic
899	C₂×C₄	C₂⁴×C₃²	1	1	yes	characteristic
900	C₂×C₄	C₂⁴×C₃²	1	1	yes	characteristic
901	C₂×C₄	C₂⁴×C₃²	1	1	yes	characteristic
902	C₂×C₄	C₂⁴×C₃²	1	2	yes	—
903	C₂×C₄	C₂⁴×C₃²	1	1	yes	characteristic
904	C₂×C₄	C₂⁴×C₃²	1	2	yes	—
905	C₂×C₄	C₂⁴×C₃²	1	2	yes	—
906	C₂×C₄	C₂⁴×C₃²	1	1	yes	characteristic
907	C₂×C₄	C₂⁴×C₃²	1	2	yes	—
908	C₂×C₄	C₂⁴×C₃²	1	1	yes	characteristic
909	C₂×C₄	C₂⁴×C₃²	1	2	yes	—
910	C₂×C₄	C₂⁴×C₃²	1	1	yes	characteristic
911	C₂×C₄	C₂⁴×C₃²	1	1	yes	characteristic
912	C₂×C₄	C₂⁴×C₃²	1	1	yes	characteristic
913	C₂×C₄	C₂⁴×C₃²	1	2	yes	—
914	C₂×C₄	C₂⁴×C₃²	1	1	yes	characteristic
915	C₂×C₄	C₂⁴×C₃²	1	1	yes	characteristic
916	C₂×C₃	—	2	16	no	—
917	C₂×C₃	—	4	4	no	—
918	C₂×C₃	—	4	8	no	—
919	C₂×C₃	—	4	4	no	—
920	C₂×C₃	—	4	4	no	—
921	C₂×C₃	C₂²×C₃×#41	1	4	yes	—
922	C₂×C₃	C₃×#585	1	4	yes	—
923	C₂×C₃	C₃×#585	1	4	yes	—
924	C₂²	—	2	2	no	—
925	C₂²	—	2	2	no	—
926	C₂²	—	2	1	no	—
927	C₂²	—	2	1	no	—
928	C₂²	—	2	1	no	—
929	C₂²	—	2	2	no	—
930	C₂²	—	2	1	no	—
931	C₂²	—	2	1	no	—
932	C₂²	—	2	1	no	—
933	C₂²	—	2	2	no	—
934	C₂²	—	2	2	no	—
935	C₂²	—	2	1	no	—
936	C₂²	—	2	1	no	—
937	C₂²	—	2	1	no	—
938	C₂²	—	8	4	no	—
939	C₂²	C₂×C₃²×#41	1	4	yes	—
940	C₂²	C₂⁵×C₃²	1	1	yes	characteristic
941	C₄	—	2	1	no	—
942	C₄	—	2	1	no	—
943	C₄	—	2	1	no	—
944	C₄	—	2	2	no	—
945	C₄	—	2	2	no	—
946	C₄	—	2	1	no	—
947	C₄	—	2	2	no	—
948	C₄	—	2	1	no	—
949	C₄	—	2	1	no	—
950	C₄	—	2	2	no	—
951	C₄	—	2	1	no	—
952	C₄	—	2	1	no	—
953	C₄	—	2	1	no	—
954	C₄	—	2	2	no	—
955	C₄	—	2	1	no	—
956	C₄	—	2	2	no	—
957	C₄	—	2	1	no	—
958	C₄	C₂×C₃²×#41	1	2	yes	—
959	C₃	C₃×#3521	1	4	yes	direct product factor
960	C₂	—	2	4	no	—
961	C₂	—	4	1	no	—
962	C₂	—	4	2	no	—
963	C₂	—	4	1	no	—
964	C₂	—	4	1	no	—
965	C₂	C₂²×C₃²×#41	1	1	yes	characteristic
966	C₂	C₃²×#585	1	1	yes	characteristic
967	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×#556	C₂	semidirect
2. C₃²×#556	C₂	semidirect
3. C₃²×#554	C₂	semidirect
4. C₃²×#553	C₂	semidirect
5. C₃²×#553	C₂	semidirect
6. C₃²×#552	C₂	semidirect
7. C₃²×#552	C₂	semidirect
8. C₃²×#551	C₂	semidirect
9. C₃²×#551	C₂	semidirect
10. C₃²×#547	C₂	semidirect
11. C₃²×#546	C₂	semidirect
12. C₃²×#546	C₂	semidirect
13. C₃²×#542	C₂	semidirect
14. C₃²×#541	C₂	semidirect
15. C₃²×#539	C₂	semidirect
16. C₃²×#538	C₂	semidirect
17. C₃²×#529	C₂	semidirect
18. C₃²×#529	C₂	semidirect
19. C₃²×#529	C₂	semidirect
20. C₂×C₃²×#126	C₂	semidirect
21. C₃²×#520	C₂	semidirect
22. C₃²×#518	C₂	semidirect
23. C₃²×C₄×#41	C₂	semidirect
24. C₃×#3521	C₃	direct (N × H)
28. C₃²×C₄⋊Q₈	C₂²	semidirect
29. C₃²×C₄⋊Q₈	C₂²	semidirect
35. C₃²×#126	C₂²	semidirect
36. C₃²×#126	C₂²	semidirect
37. C₃²×#126	C₂²	semidirect
38. C₃²×#126	C₂²	semidirect
39. C₃²×#126	C₂²	semidirect
40. C₃²×#126	C₂²	semidirect
41. C₃²×#126	C₂²	semidirect
42. C₃²×#125	C₂²	semidirect
43. C₃²×#125	C₂²	semidirect
44. C₃²×#125	C₂²	semidirect
45. C₃²×#125	C₂²	semidirect
46. C₃²×#125	C₂²	semidirect
47. C₃²×#125	C₂²	semidirect
52. C₃²×#124	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×#123	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
70. C₃²×C₂²⋊Q₈	C₂²	semidirect
71. C₃²×C₂²⋊Q₈	C₂²	semidirect
72. C₃²×C₂²⋊Q₈	C₂²	semidirect
78. C₃²×#121	C₂²	semidirect
79. C₃²×#121	C₂²	semidirect
82. C₃²×C₄×Q₈	C₂²	semidirect
83. C₃²×C₄×Q₈	C₂²	semidirect
84. C₃²×C₄×Q₈	C₂²	semidirect
85. C₃²×C₄×Q₈	C₂²	semidirect
86. C₃²×C₄×Q₈	C₂²	semidirect
87. C₃²×C₄×Q₈	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
107. C₃²×#117	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
122. C₂×C₃²×C₄²	C₂²	semidirect
123. C₂×C₃²×C₄²	C₂²	semidirect
124. C₃×#556	C₂×C₃	semidirect
125. C₃×#556	C₂×C₃	semidirect
126. C₃×#554	C₂×C₃	semidirect
127. C₃×#553	C₂×C₃	semidirect
128. C₃×#553	C₂×C₃	semidirect
129. C₃×#552	C₂×C₃	semidirect
130. C₃×#552	C₂×C₃	semidirect
131. C₃×#551	C₂×C₃	semidirect
132. C₃×#551	C₂×C₃	semidirect
133. C₃×#547	C₂×C₃	semidirect
134. C₃×#546	C₂×C₃	semidirect
135. C₃×#546	C₂×C₃	semidirect
136. C₃×#542	C₂×C₃	semidirect
137. C₃×#541	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×#529	C₂×C₃	semidirect
143. C₂×C₃×#126	C₂×C₃	semidirect
144. C₃×#520	C₂×C₃	semidirect
145. C₃×#518	C₂×C₃	semidirect
146. C₃×C₄×#41	C₂×C₃	semidirect
249. #3521	C₃²	direct (N × H)
253. C₃×C₄⋊Q₈	C₂²×C₃	semidirect
254. C₃×C₄⋊Q₈	C₂²×C₃	semidirect
260. C₃×#126	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×#125	C₂²×C₃	semidirect
272. C₃×#125	C₂²×C₃	semidirect
277. C₃×#124	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
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
303. C₃×#121	C₂²×C₃	semidirect
304. C₃×#121	C₂²×C₃	semidirect
307. C₃×C₄×Q₈	C₂²×C₃	semidirect
308. C₃×C₄×Q₈	C₂²×C₃	semidirect
309. C₃×C₄×Q₈	C₂²×C₃	semidirect
310. C₃×C₄×Q₈	C₂²×C₃	semidirect
311. C₃×C₄×Q₈	C₂²×C₃	semidirect
312. C₃×C₄×Q₈	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
332. C₃×#117	C₂²×C₃	semidirect
333. C₃×#117	C₂²×C₃	semidirect
334. C₃×#117	C₂²×C₃	semidirect
335. C₃×#117	C₂²×C₃	semidirect
336. C₃×#117	C₂²×C₃	semidirect
337. C₃×#117	C₂²×C₃	semidirect
338. C₃×#117	C₂²×C₃	semidirect
339. C₂×C₃×C₄⋊C₄	C₂²×C₃	semidirect
340. C₂×C₃×C₄⋊C₄	C₂²×C₃	semidirect
341. C₂×C₃×C₄⋊C₄	C₂²×C₃	semidirect
342. C₂×C₃×C₄⋊C₄	C₂²×C₃	semidirect
347. C₂×C₃×C₄²	C₂²×C₃	semidirect
348. C₂×C₃×C₄²	C₂²×C₃	semidirect
403. #556	C₂×C₃²	semidirect
404. #556	C₂×C₃²	semidirect
405. #554	C₂×C₃²	semidirect
406. #553	C₂×C₃²	semidirect
407. #553	C₂×C₃²	semidirect
408. #552	C₂×C₃²	semidirect
409. #552	C₂×C₃²	semidirect
410. #551	C₂×C₃²	semidirect
411. #551	C₂×C₃²	semidirect
412. #547	C₂×C₃²	semidirect
413. #546	C₂×C₃²	semidirect
414. #546	C₂×C₃²	semidirect
415. #542	C₂×C₃²	semidirect
416. #541	C₂×C₃²	semidirect
417. #539	C₂×C₃²	semidirect
418. #538	C₂×C₃²	semidirect
419. #529	C₂×C₃²	semidirect
420. #529	C₂×C₃²	semidirect
421. #529	C₂×C₃²	semidirect
422. C₂×#126	C₂×C₃²	semidirect
423. #520	C₂×C₃²	semidirect
424. #518	C₂×C₃²	semidirect
425. C₄×#41	C₂×C₃²	semidirect
566. C₄⋊Q₈	C₂²×C₃²	semidirect
567. C₄⋊Q₈	C₂²×C₃²	semidirect
573. #126	C₂²×C₃²	semidirect
574. #126	C₂²×C₃²	semidirect
575. #126	C₂²×C₃²	semidirect
576. #126	C₂²×C₃²	semidirect
577. #126	C₂²×C₃²	semidirect
578. #126	C₂²×C₃²	semidirect
579. #126	C₂²×C₃²	semidirect
580. #125	C₂²×C₃²	semidirect
581. #125	C₂²×C₃²	semidirect
582. #125	C₂²×C₃²	semidirect
583. #125	C₂²×C₃²	semidirect
584. #125	C₂²×C₃²	semidirect
585. #125	C₂²×C₃²	semidirect
590. #124	C₂²×C₃²	semidirect
595. #123	C₂²×C₃²	semidirect
596. #123	C₂²×C₃²	semidirect
597. #123	C₂²×C₃²	semidirect
598. #123	C₂²×C₃²	semidirect
599. #123	C₂²×C₃²	semidirect
600. #123	C₂²×C₃²	semidirect
603. C₂²⋊Q₈	C₂²×C₃²	semidirect
604. C₂²⋊Q₈	C₂²×C₃²	semidirect
605. C₂²⋊Q₈	C₂²×C₃²	semidirect
606. C₂²⋊Q₈	C₂²×C₃²	semidirect
607. C₂²⋊Q₈	C₂²×C₃²	semidirect
608. C₂²⋊Q₈	C₂²×C₃²	semidirect
609. C₂²⋊Q₈	C₂²×C₃²	semidirect
610. C₂²⋊Q₈	C₂²×C₃²	semidirect
616. #121	C₂²×C₃²	semidirect
617. #121	C₂²×C₃²	semidirect
620. C₄×Q₈	C₂²×C₃²	semidirect
621. C₄×Q₈	C₂²×C₃²	semidirect
622. C₄×Q₈	C₂²×C₃²	semidirect
623. C₄×Q₈	C₂²×C₃²	semidirect
624. C₄×Q₈	C₂²×C₃²	semidirect
625. C₄×Q₈	C₂²×C₃²	semidirect
636. C₄×D₄	C₂²×C₃²	semidirect
637. C₄×D₄	C₂²×C₃²	semidirect
638. C₄×D₄	C₂²×C₃²	semidirect
639. C₄×D₄	C₂²×C₃²	semidirect
640. C₄×D₄	C₂²×C₃²	semidirect
641. C₄×D₄	C₂²×C₃²	semidirect
642. C₄×D₄	C₂²×C₃²	semidirect
645. #117	C₂²×C₃²	semidirect
646. #117	C₂²×C₃²	semidirect
647. #117	C₂²×C₃²	semidirect
648. #117	C₂²×C₃²	semidirect
649. #117	C₂²×C₃²	semidirect
650. #117	C₂²×C₃²	semidirect
651. #117	C₂²×C₃²	semidirect
652. C₂×C₄⋊C₄	C₂²×C₃²	semidirect
653. C₂×C₄⋊C₄	C₂²×C₃²	semidirect
654. C₂×C₄⋊C₄	C₂²×C₃²	semidirect
655. C₂×C₄⋊C₄	C₂²×C₃²	semidirect
660. C₂×C₄²	C₂²×C₃²	semidirect
661. C₂×C₄²	C₂²×C₃²	semidirect
861. C₃²	#3521	direct (N × H)
959. C₃	C₃×#3521	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×#556	2
C₃²×#554	2
C₃²×#553	2
C₃²×#552	2
C₃²×#551	2
C₃²×#547	2
C₃²×#546	2
C₃²×#542	2
C₃²×#541	2
C₃²×#539	2
C₃²×#538	2
C₃²×#529	2
C₂×C₃²×#126	2
C₃²×#520	2
C₃²×#518	2
C₃²×C₄×#41	2
C₃×#3521	3

Subgroups — C32×#3521 #11770570

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃²×#3521 #11770570