Subgroups — C₃²×#3520 #11770569

Order 1152.

3372 conjugacy classes of subgroups.

The subgroup lattice has 693 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×#554	C₂	1	2	yes	maximal, complemented
3	C₃²×#552	C₂	1	2	yes	maximal, complemented
4	C₃²×#551	C₂	1	4	yes	maximal, complemented
5	C₃²×D₄×Q₈	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃²×#548	C₂	1	2	yes	maximal, complemented
7	C₃²×#547	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃²×#547	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃²×#546	C₂	1	2	yes	maximal, complemented
10	C₃²×#542	C₂	1	2	yes	maximal, complemented
11	C₃²×#539	C₂	1	4	yes	maximal, complemented
12	C₃²×#533	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃²×#529	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃²×#525	C₂	1	2	yes	maximal, complemented
15	C₂×C₃²×C₂²⋊Q₈	C₂	1	2	yes	maximal, complemented
16	C₃²×#520	C₂	1	2	yes	maximal, complemented
17	C₂×C₃²×C₄×D₄	C₂	1	1	yes	maximal, characteristic, complemented
18	C₃×#3520	C₃	1	4	yes	maximal, direct product factor
19	C₂×C₃²×#41	C₂²	1	2	yes	—
20	C₂×C₃²×#41	C₂²	1	2	yes	complemented
21	C₂²×C₃²×Q₈	C₂²	1	2	yes	complemented
22	C₂²×C₃²×D₄	C₂²	1	1	yes	characteristic
23	C₂³×C₃²×C₄	C₂²	1	2	yes	—
24	C₃²×C₄⋊Q₈	C₂²	1	2	yes	complemented
25	C₃²×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
26	C₃²×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
27	C₃²×#126	C₂²	1	4	yes	complemented
28	C₃²×#126	C₂²	1	4	yes	complemented
29	C₃²×#126	C₂²	1	2	yes	complemented
30	C₃²×#125	C₂²	1	1	yes	characteristic, complemented
31	C₃²×#125	C₂²	1	4	yes	complemented
32	C₃²×#125	C₂²	1	2	yes	complemented
33	C₃²×#124	C₂²	1	2	yes	—
34	C₃²×#124	C₂²	1	4	yes	complemented
35	C₃²×#124	C₂²	1	1	yes	characteristic, complemented
36	C₃²×#123	C₂²	1	2	yes	—
37	C₃²×#123	C₂²	1	4	yes	—
38	C₃²×#123	C₂²	1	4	yes	complemented
39	C₃²×#123	C₂²	1	4	yes	complemented
40	C₃²×#123	C₂²	1	4	yes	complemented
41	C₃²×C₂²⋊Q₈	C₂²	1	4	yes	—
42	C₃²×C₂²⋊Q₈	C₂²	1	2	yes	—
43	C₃²×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
44	C₃²×C₂²⋊Q₈	C₂²	1	2	yes	—
45	C₃²×C₂²⋊Q₈	C₂²	1	4	yes	complemented
46	C₃²×C₂²⋊Q₈	C₂²	1	2	yes	complemented
47	C₃²×C₂²⋊Q₈	C₂²	1	2	yes	complemented
48	C₃²×C₂²⋊Q₈	C₂²	1	4	yes	complemented
49	C₃²×C₂²⋊Q₈	C₂²	1	2	yes	complemented
50	C₃²×C₂²⋊Q₈	C₂²	1	2	yes	complemented
51	C₃²×C₂²⋊Q₈	C₂²	1	4	yes	complemented
52	C₃²×#121	C₂²	1	1	yes	characteristic
53	C₃²×#121	C₂²	1	4	yes	—
54	C₃²×#121	C₂²	1	2	yes	—
55	C₃²×#121	C₂²	1	2	yes	complemented
56	C₃²×#120	C₂²	1	4	yes	—
57	C₃²×C₄×Q₈	C₂²	1	2	yes	complemented
58	C₃²×C₄×Q₈	C₂²	1	2	yes	complemented
59	C₃²×C₄×Q₈	C₂²	1	1	yes	characteristic, complemented
60	C₃²×C₄×Q₈	C₂²	1	2	yes	complemented
61	C₃²×C₄×D₄	C₂²	1	4	yes	—
62	C₃²×C₄×D₄	C₂²	1	2	yes	—
63	C₃²×C₄×D₄	C₂²	1	2	yes	—
64	C₃²×C₄×D₄	C₂²	1	1	yes	characteristic
65	C₃²×C₄×D₄	C₂²	1	1	yes	characteristic
66	C₃²×C₄×D₄	C₂²	1	2	yes	—
67	C₃²×C₄×D₄	C₂²	1	1	yes	characteristic
68	C₃²×C₄×D₄	C₂²	1	1	yes	characteristic
69	C₃²×C₄×D₄	C₂²	1	2	yes	—
70	C₃²×C₄×D₄	C₂²	1	4	yes	complemented
71	C₃²×C₄×D₄	C₂²	1	4	yes	complemented
72	C₃²×C₄×D₄	C₂²	1	1	yes	characteristic, complemented
73	C₃²×#117	C₂²	1	2	yes	—
74	C₃²×#117	C₂²	1	4	yes	complemented
75	C₃²×#117	C₂²	1	2	yes	complemented
76	C₃²×#117	C₂²	1	2	yes	complemented
77	C₂×C₃²×C₄⋊C₄	C₂²	1	1	yes	characteristic
78	C₂×C₃²×C₄⋊C₄	C₂²	1	2	yes	complemented
79	C₂×C₃²×C₄⋊C₄	C₂²	1	2	yes	complemented
80	C₂×C₃²×C₄⋊C₄	C₂²	1	4	yes	complemented
81	C₂×C₃²×C₂²⋊C₄	C₂²	1	2	yes	—
82	C₂×C₃²×C₂²⋊C₄	C₂²	1	4	yes	—
83	C₂×C₃²×C₄²	C₂²	1	1	yes	characteristic
84	C₃×#556	C₂×C₃	1	4	yes	complemented
85	C₃×#554	C₂×C₃	1	8	yes	complemented
86	C₃×#552	C₂×C₃	1	8	yes	complemented
87	C₃×#551	C₂×C₃	1	16	yes	complemented
88	C₃×D₄×Q₈	C₂×C₃	1	4	yes	complemented
89	C₃×#548	C₂×C₃	1	8	yes	complemented
90	C₃×#547	C₂×C₃	1	4	yes	complemented
91	C₃×#547	C₂×C₃	1	4	yes	complemented
92	C₃×#546	C₂×C₃	1	8	yes	complemented
93	C₃×#542	C₂×C₃	1	8	yes	complemented
94	C₃×#539	C₂×C₃	1	16	yes	complemented
95	C₃×#533	C₂×C₃	1	4	yes	complemented
96	C₃×#529	C₂×C₃	1	4	yes	complemented
97	C₃×#525	C₂×C₃	1	8	yes	complemented
98	C₂×C₃×C₂²⋊Q₈	C₂×C₃	1	8	yes	complemented
99	C₃×#520	C₂×C₃	1	8	yes	complemented
100	C₂×C₃×C₄×D₄	C₂×C₃	1	4	yes	complemented
101	C₂⁴×C₃²	C₂³	1	2	yes	—
102	C₃²×#41	—	2	8	no	—
103	C₃²×#41	—	4	4	no	—
104	C₂×C₃²×Q₈	—	4	4	no	—
105	C₂×C₃²×Q₈	C₂³	1	1	yes	characteristic
106	C₂×C₃²×Q₈	C₂³	1	2	yes	—
107	C₂×C₃²×Q₈	C₂³	1	2	yes	—
108	C₂×C₃²×Q₈	C₂³	1	4	yes	—
109	C₂×C₃²×D₄	—	2	4	no	—
110	C₂×C₃²×D₄	C₂³	1	2	yes	—
111	C₂×C₃²×D₄	C₂³	1	1	yes	characteristic
112	C₂×C₃²×D₄	C₂³	1	4	yes	—
113	C₂×C₃²×D₄	C₂³	1	1	yes	characteristic
114	C₂×C₃²×D₄	C₂³	1	2	yes	—
115	C₂×C₃²×D₄	C₂³	1	4	yes	—
116	C₂×C₃²×D₄	C₂³	1	1	yes	characteristic
117	C₂²×C₃²×C₄	—	4	4	no	—
118	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
119	C₂²×C₃²×C₄	C₂³	1	2	yes	—
120	C₂²×C₃²×C₄	C₂³	1	2	yes	—
121	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
122	C₂²×C₃²×C₄	C₂³	1	4	yes	—
123	C₂²×C₃²×C₄	C₂³	1	2	yes	—
124	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
125	C₂²×C₃²×C₄	C₂³	1	2	yes	—
126	C₂²×C₃²×C₄	C₂³	1	2	yes	—
127	C₂²×C₃²×C₄	C₂³	1	2	yes	—
128	C₂²×C₃²×C₄	C₂³	1	4	yes	—
129	C₂²×C₃²×C₄	C₂³	1	4	yes	—
130	C₃²×C₄⋊C₄	C₂³	1	1	yes	characteristic
131	C₃²×C₄⋊C₄	C₂³	1	2	yes	—
132	C₃²×C₄⋊C₄	C₂³	1	1	yes	characteristic
133	C₃²×C₄⋊C₄	C₂³	1	2	yes	—
134	C₃²×C₄⋊C₄	C₂³	1	4	yes	—
135	C₃²×C₄⋊C₄	C₂³	1	1	yes	characteristic
136	C₃²×C₄⋊C₄	C₂³	1	2	yes	—
137	C₃²×C₄⋊C₄	C₂³	1	2	yes	—
138	C₃²×C₄⋊C₄	C₂³	1	4	yes	—
139	C₃²×C₄⋊C₄	C₂³	1	4	yes	—
140	C₃²×C₄⋊C₄	C₂³	1	4	yes	—
141	C₃²×C₄⋊C₄	C₂³	1	2	yes	—
142	C₃²×C₄⋊C₄	C₂³	1	2	yes	—
143	C₃²×C₄⋊C₄	C₂³	1	2	yes	—
144	C₃²×C₄⋊C₄	C₂³	1	1	yes	characteristic
145	C₃²×C₄⋊C₄	C₂³	1	4	yes	—
146	C₃²×C₄⋊C₄	C₂³	1	2	yes	—
147	C₃²×C₄⋊C₄	C₂³	1	4	yes	—
148	C₃²×C₄⋊C₄	C₂³	1	2	yes	—
149	C₃²×C₂²⋊C₄	C₂³	1	2	yes	—
150	C₃²×C₂²⋊C₄	C₂³	1	4	yes	—
151	C₃²×C₂²⋊C₄	C₂³	1	2	yes	—
152	C₃²×C₂²⋊C₄	C₂³	1	2	yes	—
153	C₃²×C₂²⋊C₄	C₂³	1	2	yes	—
154	C₃²×C₂²⋊C₄	C₂³	1	2	yes	—
155	C₃²×C₂²⋊C₄	C₂³	1	4	yes	—
156	C₃²×C₂²⋊C₄	C₂³	1	4	yes	—
157	C₃²×C₂²⋊C₄	C₂³	1	4	yes	—
158	C₃²×C₂²⋊C₄	C₂³	1	2	yes	—
159	C₃²×C₂²⋊C₄	C₂³	1	2	yes	—
160	C₃²×C₂²⋊C₄	C₂³	1	4	yes	—
161	C₃²×C₂²⋊C₄	C₂³	1	2	yes	—
162	C₃²×C₂²⋊C₄	C₂³	1	4	yes	—
163	C₃²×C₂²⋊C₄	C₂³	1	2	yes	—
164	C₃²×C₄²	C₂³	1	1	yes	characteristic
165	C₃²×C₄²	C₂³	1	1	yes	characteristic
166	C₃²×C₄²	C₂³	1	1	yes	characteristic
167	C₃²×C₄²	C₂³	1	1	yes	characteristic
168	C₃²×C₄²	C₂³	1	4	yes	—
169	C₃²×C₄²	C₂³	1	4	yes	—
170	C₃²×C₄²	C₂³	1	2	yes	—
171	#3520	C₃²	1	1	yes	characteristic, direct product factor, Sylow
172	C₂×C₃×#41	C₂²×C₃	1	8	yes	—
173	C₂×C₃×#41	C₂²×C₃	1	8	yes	complemented
174	C₂²×C₃×Q₈	C₂²×C₃	1	8	yes	complemented
175	C₂²×C₃×D₄	C₂²×C₃	1	4	yes	—
176	C₂³×C₃×C₄	C₂²×C₃	1	8	yes	—
177	C₃×C₄⋊Q₈	C₂²×C₃	1	4	yes	complemented
178	C₃×C₄⋊Q₈	C₂²×C₃	1	4	yes	complemented
179	C₃×C₄⋊Q₈	C₂²×C₃	1	8	yes	complemented
180	C₃×#126	C₂²×C₃	1	8	yes	complemented
181	C₃×#126	C₂²×C₃	1	16	yes	complemented
182	C₃×#126	C₂²×C₃	1	16	yes	complemented
183	C₃×#125	C₂²×C₃	1	4	yes	complemented
184	C₃×#125	C₂²×C₃	1	8	yes	complemented
185	C₃×#125	C₂²×C₃	1	16	yes	complemented
186	C₃×#124	C₂²×C₃	1	8	yes	—
187	C₃×#124	C₂²×C₃	1	4	yes	complemented
188	C₃×#124	C₂²×C₃	1	16	yes	complemented
189	C₃×#123	C₂²×C₃	1	8	yes	—
190	C₃×#123	C₂²×C₃	1	16	yes	—
191	C₃×#123	C₂²×C₃	1	16	yes	complemented
192	C₃×#123	C₂²×C₃	1	16	yes	complemented
193	C₃×#123	C₂²×C₃	1	16	yes	complemented
194	C₃×C₂²⋊Q₈	C₂²×C₃	1	4	yes	—
195	C₃×C₂²⋊Q₈	C₂²×C₃	1	8	yes	—
196	C₃×C₂²⋊Q₈	C₂²×C₃	1	16	yes	—
197	C₃×C₂²⋊Q₈	C₂²×C₃	1	8	yes	—
198	C₃×C₂²⋊Q₈	C₂²×C₃	1	16	yes	complemented
199	C₃×C₂²⋊Q₈	C₂²×C₃	1	8	yes	complemented
200	C₃×C₂²⋊Q₈	C₂²×C₃	1	8	yes	complemented
201	C₃×C₂²⋊Q₈	C₂²×C₃	1	8	yes	complemented
202	C₃×C₂²⋊Q₈	C₂²×C₃	1	16	yes	complemented
203	C₃×C₂²⋊Q₈	C₂²×C₃	1	16	yes	complemented
204	C₃×C₂²⋊Q₈	C₂²×C₃	1	8	yes	complemented
205	C₃×#121	C₂²×C₃	1	4	yes	—
206	C₃×#121	C₂²×C₃	1	16	yes	—
207	C₃×#121	C₂²×C₃	1	8	yes	—
208	C₃×#121	C₂²×C₃	1	8	yes	complemented
209	C₃×#120	C₂²×C₃	1	16	yes	—
210	C₃×C₄×Q₈	C₂²×C₃	1	8	yes	complemented
211	C₃×C₄×Q₈	C₂²×C₃	1	8	yes	complemented
212	C₃×C₄×Q₈	C₂²×C₃	1	4	yes	complemented
213	C₃×C₄×Q₈	C₂²×C₃	1	8	yes	complemented
214	C₃×C₄×D₄	C₂²×C₃	1	4	yes	—
215	C₃×C₄×D₄	C₂²×C₃	1	8	yes	—
216	C₃×C₄×D₄	C₂²×C₃	1	4	yes	—
217	C₃×C₄×D₄	C₂²×C₃	1	4	yes	—
218	C₃×C₄×D₄	C₂²×C₃	1	4	yes	—
219	C₃×C₄×D₄	C₂²×C₃	1	8	yes	—
220	C₃×C₄×D₄	C₂²×C₃	1	8	yes	—
221	C₃×C₄×D₄	C₂²×C₃	1	16	yes	—
222	C₃×C₄×D₄	C₂²×C₃	1	8	yes	—
223	C₃×C₄×D₄	C₂²×C₃	1	16	yes	complemented
224	C₃×C₄×D₄	C₂²×C₃	1	16	yes	complemented
225	C₃×C₄×D₄	C₂²×C₃	1	4	yes	complemented
226	C₃×#117	C₂²×C₃	1	8	yes	—
227	C₃×#117	C₂²×C₃	1	8	yes	complemented
228	C₃×#117	C₂²×C₃	1	16	yes	complemented
229	C₃×#117	C₂²×C₃	1	8	yes	complemented
230	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	4	yes	—
231	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	16	yes	complemented
232	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	8	yes	complemented
233	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	8	yes	complemented
234	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	8	yes	—
235	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	16	yes	—
236	C₂×C₃×C₄²	C₂²×C₃	1	4	yes	—
237	C₂³×C₃²	—	2	4	no	—
238	C₂³×C₃²	—	2	4	no	—
239	C₂³×C₃²	—	4	2	no	—
240	C₂³×C₃²	C₂⁴	1	2	yes	—
241	C₂³×C₃²	C₂⁴	1	2	yes	—
242	C₂³×C₃²	C₂⁴	1	2	yes	—
243	C₂³×C₃²	C₂⁴	1	1	yes	characteristic
244	C₃²×Q₈	—	2	4	no	—
245	C₃²×Q₈	—	2	2	no	—
246	C₃²×Q₈	—	2	4	no	—
247	C₃²×Q₈	—	4	4	no	—
248	C₃²×D₄	—	2	4	no	—
249	C₃²×D₄	—	2	8	no	—
250	C₃²×D₄	—	2	4	no	—
251	C₃²×D₄	—	2	2	no	—
252	C₃²×D₄	—	2	2	no	—
253	C₃²×D₄	—	4	4	no	—
254	C₃²×D₄	#41	1	4	yes	complemented
255	C₂×C₃²×C₄	—	2	8	no	—
256	C₂×C₃²×C₄	—	2	2	no	—
257	C₂×C₃²×C₄	—	2	2	no	—
258	C₂×C₃²×C₄	—	2	4	no	—
259	C₂×C₃²×C₄	—	2	2	no	—
260	C₂×C₃²×C₄	—	2	4	no	—
261	C₂×C₃²×C₄	—	2	4	no	—
262	C₂×C₃²×C₄	—	4	2	no	—
263	C₂×C₃²×C₄	—	4	2	no	—
264	C₂×C₃²×C₄	—	4	2	no	—
265	C₂×C₃²×C₄	—	4	4	no	—
266	C₂×C₃²×C₄	—	4	4	no	—
267	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
268	C₂×C₃²×C₄	C₂⁴	1	2	yes	—
269	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
270	C₂×C₃²×C₄	C₂⁴	1	4	yes	—
271	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
272	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
273	C₂×C₃²×C₄	C₂⁴	1	2	yes	—
274	C₂×C₃²×C₄	C₂⁴	1	2	yes	—
275	C₂×C₃²×C₄	C₂⁴	1	4	yes	—
276	C₂×C₃²×C₄	C₂⁴	1	2	yes	—
277	C₂×C₃²×C₄	C₂⁴	1	2	yes	—
278	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
279	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
280	#556	C₂×C₃²	1	1	yes	characteristic, complemented
281	#554	C₂×C₃²	1	2	yes	complemented
282	#552	C₂×C₃²	1	2	yes	complemented
283	#551	C₂×C₃²	1	4	yes	complemented
284	D₄×Q₈	C₂×C₃²	1	1	yes	characteristic, complemented
285	#548	C₂×C₃²	1	2	yes	complemented
286	#547	C₂×C₃²	1	1	yes	characteristic, complemented
287	#547	C₂×C₃²	1	1	yes	characteristic, complemented
288	#546	C₂×C₃²	1	2	yes	complemented
289	#542	C₂×C₃²	1	2	yes	complemented
290	#539	C₂×C₃²	1	4	yes	complemented
291	#533	C₂×C₃²	1	1	yes	characteristic, complemented
292	#529	C₂×C₃²	1	1	yes	characteristic, complemented
293	#525	C₂×C₃²	1	2	yes	complemented
294	C₂×C₂²⋊Q₈	C₂×C₃²	1	2	yes	complemented
295	#520	C₂×C₃²	1	2	yes	complemented
296	C₂×C₄×D₄	C₂×C₃²	1	1	yes	characteristic, complemented
297	C₂⁴×C₃	C₂³×C₃	1	8	yes	—
298	C₃×#41	—	2	32	no	—
299	C₃×#41	—	4	16	no	—
300	C₂×C₃×Q₈	—	4	16	no	—
301	C₂×C₃×Q₈	C₂³×C₃	1	8	yes	—
302	C₂×C₃×Q₈	C₂³×C₃	1	4	yes	—
303	C₂×C₃×Q₈	C₂³×C₃	1	8	yes	—
304	C₂×C₃×Q₈	C₂³×C₃	1	16	yes	—
305	C₂×C₃×D₄	—	2	16	no	—
306	C₂×C₃×D₄	C₂³×C₃	1	8	yes	—
307	C₂×C₃×D₄	C₂³×C₃	1	8	yes	—
308	C₂×C₃×D₄	C₂³×C₃	1	4	yes	—
309	C₂×C₃×D₄	C₂³×C₃	1	16	yes	—
310	C₂×C₃×D₄	C₂³×C₃	1	4	yes	—
311	C₂×C₃×D₄	C₂³×C₃	1	16	yes	—
312	C₂×C₃×D₄	C₂³×C₃	1	4	yes	—
313	C₂²×C₃×C₄	—	4	16	no	—
314	C₂²×C₃×C₄	C₂³×C₃	1	4	yes	—
315	C₂²×C₃×C₄	C₂³×C₃	1	4	yes	—
316	C₂²×C₃×C₄	C₂³×C₃	1	4	yes	—
317	C₂²×C₃×C₄	C₂³×C₃	1	16	yes	—
318	C₂²×C₃×C₄	C₂³×C₃	1	8	yes	—
319	C₂²×C₃×C₄	C₂³×C₃	1	8	yes	—
320	C₂²×C₃×C₄	C₂³×C₃	1	8	yes	—
321	C₂²×C₃×C₄	C₂³×C₃	1	8	yes	—
322	C₂²×C₃×C₄	C₂³×C₃	1	16	yes	—
323	C₂²×C₃×C₄	C₂³×C₃	1	8	yes	—
324	C₂²×C₃×C₄	C₂³×C₃	1	16	yes	—
325	C₂²×C₃×C₄	C₂³×C₃	1	8	yes	—
326	C₃×C₄⋊C₄	C₂³×C₃	1	4	yes	—
327	C₃×C₄⋊C₄	C₂³×C₃	1	8	yes	—
328	C₃×C₄⋊C₄	C₂³×C₃	1	4	yes	—
329	C₃×C₄⋊C₄	C₂³×C₃	1	8	yes	—
330	C₃×C₄⋊C₄	C₂³×C₃	1	16	yes	—
331	C₃×C₄⋊C₄	C₂³×C₃	1	4	yes	—
332	C₃×C₄⋊C₄	C₂³×C₃	1	8	yes	—
333	C₃×C₄⋊C₄	C₂³×C₃	1	8	yes	—
334	C₃×C₄⋊C₄	C₂³×C₃	1	16	yes	—
335	C₃×C₄⋊C₄	C₂³×C₃	1	16	yes	—
336	C₃×C₄⋊C₄	C₂³×C₃	1	16	yes	—
337	C₃×C₄⋊C₄	C₂³×C₃	1	8	yes	—
338	C₃×C₄⋊C₄	C₂³×C₃	1	8	yes	—
339	C₃×C₄⋊C₄	C₂³×C₃	1	8	yes	—
340	C₃×C₄⋊C₄	C₂³×C₃	1	4	yes	—
341	C₃×C₄⋊C₄	C₂³×C₃	1	16	yes	—
342	C₃×C₄⋊C₄	C₂³×C₃	1	8	yes	—
343	C₃×C₄⋊C₄	C₂³×C₃	1	16	yes	—
344	C₃×C₄⋊C₄	C₂³×C₃	1	8	yes	—
345	C₃×C₂²⋊C₄	C₂³×C₃	1	8	yes	—
346	C₃×C₂²⋊C₄	C₂³×C₃	1	16	yes	—
347	C₃×C₂²⋊C₄	C₂³×C₃	1	8	yes	—
348	C₃×C₂²⋊C₄	C₂³×C₃	1	8	yes	—
349	C₃×C₂²⋊C₄	C₂³×C₃	1	8	yes	—
350	C₃×C₂²⋊C₄	C₂³×C₃	1	8	yes	—
351	C₃×C₂²⋊C₄	C₂³×C₃	1	16	yes	—
352	C₃×C₂²⋊C₄	C₂³×C₃	1	16	yes	—
353	C₃×C₂²⋊C₄	C₂³×C₃	1	16	yes	—
354	C₃×C₂²⋊C₄	C₂³×C₃	1	8	yes	—
355	C₃×C₂²⋊C₄	C₂³×C₃	1	8	yes	—
356	C₃×C₂²⋊C₄	C₂³×C₃	1	16	yes	—
357	C₃×C₂²⋊C₄	C₂³×C₃	1	8	yes	—
358	C₃×C₂²⋊C₄	C₂³×C₃	1	16	yes	—
359	C₃×C₂²⋊C₄	C₂³×C₃	1	8	yes	—
360	C₃×C₄²	C₂³×C₃	1	4	yes	—
361	C₃×C₄²	C₂³×C₃	1	4	yes	—
362	C₃×C₄²	C₂³×C₃	1	4	yes	—
363	C₃×C₄²	C₂³×C₃	1	4	yes	—
364	C₃×C₄²	C₂³×C₃	1	16	yes	—
365	C₃×C₄²	C₂³×C₃	1	16	yes	—
366	C₃×C₄²	C₂³×C₃	1	8	yes	—
367	C₂²×C₃²	—	2	1	no	—
368	C₂²×C₃²	—	2	2	no	—
369	C₂²×C₃²	—	2	1	no	—
370	C₂²×C₃²	—	2	2	no	—
371	C₂²×C₃²	—	2	2	no	—
372	C₂²×C₃²	—	2	2	no	—
373	C₂²×C₃²	—	2	2	no	—
374	C₂²×C₃²	—	2	2	no	—
375	C₂²×C₃²	—	2	2	no	—
376	C₂²×C₃²	—	2	2	no	—
377	C₂²×C₃²	—	4	8	no	—
378	C₂²×C₃²	C₂×#41	1	4	yes	—
379	C₂²×C₃²	2₋¹⁺⁴	1	2	yes	—
380	C₂²×C₃²	C₂⁵	1	1	yes	characteristic
381	C₃²×C₄	—	2	2	no	—
382	C₃²×C₄	—	2	1	no	—
383	C₃²×C₄	—	2	4	no	—
384	C₃²×C₄	—	2	1	no	—
385	C₃²×C₄	—	2	2	no	—
386	C₃²×C₄	—	2	2	no	—
387	C₃²×C₄	—	2	4	no	—
388	C₃²×C₄	—	2	2	no	—
389	C₃²×C₄	—	2	1	no	—
390	C₃²×C₄	—	2	1	no	—
391	C₃²×C₄	—	2	2	no	—
392	C₃²×C₄	C₂×#41	1	2	yes	—
393	C₃²×C₄	H(5,𝔽₂)	1	2	yes	—
394	C₂×#41	C₂²×C₃²	1	2	yes	—
395	C₂×#41	C₂²×C₃²	1	2	yes	complemented
396	C₂²×Q₈	C₂²×C₃²	1	2	yes	complemented
397	C₂²×D₄	C₂²×C₃²	1	1	yes	characteristic
398	C₂³×C₄	C₂²×C₃²	1	2	yes	—
399	C₄⋊Q₈	C₂²×C₃²	1	1	yes	characteristic, complemented
400	C₄⋊Q₈	C₂²×C₃²	1	1	yes	characteristic, complemented
401	C₄⋊Q₈	C₂²×C₃²	1	2	yes	complemented
402	#126	C₂²×C₃²	1	2	yes	complemented
403	#126	C₂²×C₃²	1	4	yes	complemented
404	#126	C₂²×C₃²	1	4	yes	complemented
405	#125	C₂²×C₃²	1	1	yes	characteristic, complemented
406	#125	C₂²×C₃²	1	2	yes	complemented
407	#125	C₂²×C₃²	1	4	yes	complemented
408	#124	C₂²×C₃²	1	2	yes	—
409	#124	C₂²×C₃²	1	1	yes	characteristic, complemented
410	#124	C₂²×C₃²	1	4	yes	complemented
411	#123	C₂²×C₃²	1	2	yes	—
412	#123	C₂²×C₃²	1	4	yes	—
413	#123	C₂²×C₃²	1	4	yes	complemented
414	#123	C₂²×C₃²	1	4	yes	complemented
415	#123	C₂²×C₃²	1	4	yes	complemented
416	C₂²⋊Q₈	C₂²×C₃²	1	1	yes	characteristic
417	C₂²⋊Q₈	C₂²×C₃²	1	2	yes	—
418	C₂²⋊Q₈	C₂²×C₃²	1	4	yes	—
419	C₂²⋊Q₈	C₂²×C₃²	1	2	yes	—
420	C₂²⋊Q₈	C₂²×C₃²	1	4	yes	complemented
421	C₂²⋊Q₈	C₂²×C₃²	1	2	yes	complemented
422	C₂²⋊Q₈	C₂²×C₃²	1	2	yes	complemented
423	C₂²⋊Q₈	C₂²×C₃²	1	2	yes	complemented
424	C₂²⋊Q₈	C₂²×C₃²	1	4	yes	complemented
425	C₂²⋊Q₈	C₂²×C₃²	1	4	yes	complemented
426	C₂²⋊Q₈	C₂²×C₃²	1	2	yes	complemented
427	#121	C₂²×C₃²	1	1	yes	characteristic
428	#121	C₂²×C₃²	1	4	yes	—
429	#121	C₂²×C₃²	1	2	yes	—
430	#121	C₂²×C₃²	1	2	yes	complemented
431	#120	C₂²×C₃²	1	4	yes	—
432	C₄×Q₈	C₂²×C₃²	1	2	yes	complemented
433	C₄×Q₈	C₂²×C₃²	1	2	yes	complemented
434	C₄×Q₈	C₂²×C₃²	1	1	yes	characteristic, complemented
435	C₄×Q₈	C₂²×C₃²	1	2	yes	complemented
436	C₄×D₄	C₂²×C₃²	1	1	yes	characteristic
437	C₄×D₄	C₂²×C₃²	1	2	yes	—
438	C₄×D₄	C₂²×C₃²	1	1	yes	characteristic
439	C₄×D₄	C₂²×C₃²	1	1	yes	characteristic
440	C₄×D₄	C₂²×C₃²	1	1	yes	characteristic
441	C₄×D₄	C₂²×C₃²	1	2	yes	—
442	C₄×D₄	C₂²×C₃²	1	2	yes	—
443	C₄×D₄	C₂²×C₃²	1	4	yes	—
444	C₄×D₄	C₂²×C₃²	1	2	yes	—
445	C₄×D₄	C₂²×C₃²	1	4	yes	complemented
446	C₄×D₄	C₂²×C₃²	1	4	yes	complemented
447	C₄×D₄	C₂²×C₃²	1	1	yes	characteristic, complemented
448	#117	C₂²×C₃²	1	2	yes	—
449	#117	C₂²×C₃²	1	2	yes	complemented
450	#117	C₂²×C₃²	1	4	yes	complemented
451	#117	C₂²×C₃²	1	2	yes	complemented
452	C₂×C₄⋊C₄	C₂²×C₃²	1	1	yes	characteristic
453	C₂×C₄⋊C₄	C₂²×C₃²	1	4	yes	complemented
454	C₂×C₄⋊C₄	C₂²×C₃²	1	2	yes	complemented
455	C₂×C₄⋊C₄	C₂²×C₃²	1	2	yes	complemented
456	C₂×C₂²⋊C₄	C₂²×C₃²	1	2	yes	—
457	C₂×C₂²⋊C₄	C₂²×C₃²	1	4	yes	—
458	C₂×C₄²	C₂²×C₃²	1	1	yes	characteristic
459	C₂³×C₃	—	2	16	no	—
460	C₂³×C₃	—	2	16	no	—
461	C₂³×C₃	—	4	8	no	—
462	C₂³×C₃	C₂⁴×C₃	1	8	yes	—
463	C₂³×C₃	C₂⁴×C₃	1	8	yes	—
464	C₂³×C₃	C₂⁴×C₃	1	8	yes	—
465	C₂³×C₃	C₂⁴×C₃	1	4	yes	—
466	C₃×Q₈	—	2	16	no	—
467	C₃×Q₈	—	2	8	no	—
468	C₃×Q₈	—	2	16	no	—
469	C₃×Q₈	—	4	16	no	—
470	C₃×D₄	—	2	16	no	—
471	C₃×D₄	—	2	32	no	—
472	C₃×D₄	—	2	16	no	—
473	C₃×D₄	—	2	8	no	—
474	C₃×D₄	—	2	8	no	—
475	C₃×D₄	—	4	16	no	—
476	C₃×D₄	C₃×#41	1	16	yes	complemented
477	C₂×C₃×C₄	—	2	32	no	—
478	C₂×C₃×C₄	—	2	8	no	—
479	C₂×C₃×C₄	—	2	8	no	—
480	C₂×C₃×C₄	—	2	16	no	—
481	C₂×C₃×C₄	—	2	8	no	—
482	C₂×C₃×C₄	—	2	16	no	—
483	C₂×C₃×C₄	—	2	16	no	—
484	C₂×C₃×C₄	—	4	8	no	—
485	C₂×C₃×C₄	—	4	8	no	—
486	C₂×C₃×C₄	—	4	8	no	—
487	C₂×C₃×C₄	—	4	16	no	—
488	C₂×C₃×C₄	—	4	16	no	—
489	C₂×C₃×C₄	C₂⁴×C₃	1	4	yes	—
490	C₂×C₃×C₄	C₂⁴×C₃	1	8	yes	—
491	C₂×C₃×C₄	C₂⁴×C₃	1	4	yes	—
492	C₂×C₃×C₄	C₂⁴×C₃	1	16	yes	—
493	C₂×C₃×C₄	C₂⁴×C₃	1	4	yes	—
494	C₂×C₃×C₄	C₂⁴×C₃	1	4	yes	—
495	C₂×C₃×C₄	C₂⁴×C₃	1	8	yes	—
496	C₂×C₃×C₄	C₂⁴×C₃	1	8	yes	—
497	C₂×C₃×C₄	C₂⁴×C₃	1	16	yes	—
498	C₂×C₃×C₄	C₂⁴×C₃	1	8	yes	—
499	C₂×C₃×C₄	C₂⁴×C₃	1	8	yes	—
500	C₂×C₃×C₄	C₂⁴×C₃	1	4	yes	—
501	C₂×C₃×C₄	C₂⁴×C₃	1	4	yes	—
502	C₂×C₃²	—	2	2	no	—
503	C₂×C₃²	—	2	4	no	—
504	C₂×C₃²	—	4	2	no	—
505	C₂×C₃²	—	4	2	no	—
506	C₂×C₃²	C₂²×#41	1	1	yes	characteristic
507	C₂×C₃²	C₂×H(5,𝔽₂)	1	1	yes	characteristic
508	C₂×C₃²	C₂×2₋¹⁺⁴	1	1	yes	characteristic
509	C₂⁴	C₂³×C₃²	1	2	yes	—
510	#41	—	2	8	no	—
511	#41	—	4	4	no	—
512	C₂×Q₈	—	4	4	no	—
513	C₂×Q₈	C₂³×C₃²	1	2	yes	—
514	C₂×Q₈	C₂³×C₃²	1	1	yes	characteristic
515	C₂×Q₈	C₂³×C₃²	1	2	yes	—
516	C₂×Q₈	C₂³×C₃²	1	4	yes	—
517	C₂×D₄	—	2	4	no	—
518	C₂×D₄	C₂³×C₃²	1	2	yes	—
519	C₂×D₄	C₂³×C₃²	1	2	yes	—
520	C₂×D₄	C₂³×C₃²	1	1	yes	characteristic
521	C₂×D₄	C₂³×C₃²	1	4	yes	—
522	C₂×D₄	C₂³×C₃²	1	1	yes	characteristic
523	C₂×D₄	C₂³×C₃²	1	4	yes	—
524	C₂×D₄	C₂³×C₃²	1	1	yes	characteristic
525	C₂²×C₄	—	4	4	no	—
526	C₂²×C₄	C₂³×C₃²	1	1	yes	characteristic
527	C₂²×C₄	C₂³×C₃²	1	1	yes	characteristic
528	C₂²×C₄	C₂³×C₃²	1	1	yes	characteristic
529	C₂²×C₄	C₂³×C₃²	1	4	yes	—
530	C₂²×C₄	C₂³×C₃²	1	2	yes	—
531	C₂²×C₄	C₂³×C₃²	1	2	yes	—
532	C₂²×C₄	C₂³×C₃²	1	2	yes	—
533	C₂²×C₄	C₂³×C₃²	1	2	yes	—
534	C₂²×C₄	C₂³×C₃²	1	4	yes	—
535	C₂²×C₄	C₂³×C₃²	1	2	yes	—
536	C₂²×C₄	C₂³×C₃²	1	4	yes	—
537	C₂²×C₄	C₂³×C₃²	1	2	yes	—
538	C₄⋊C₄	C₂³×C₃²	1	1	yes	characteristic
539	C₄⋊C₄	C₂³×C₃²	1	2	yes	—
540	C₄⋊C₄	C₂³×C₃²	1	1	yes	characteristic
541	C₄⋊C₄	C₂³×C₃²	1	2	yes	—
542	C₄⋊C₄	C₂³×C₃²	1	4	yes	—
543	C₄⋊C₄	C₂³×C₃²	1	1	yes	characteristic
544	C₄⋊C₄	C₂³×C₃²	1	2	yes	—
545	C₄⋊C₄	C₂³×C₃²	1	2	yes	—
546	C₄⋊C₄	C₂³×C₃²	1	4	yes	—
547	C₄⋊C₄	C₂³×C₃²	1	4	yes	—
548	C₄⋊C₄	C₂³×C₃²	1	4	yes	—
549	C₄⋊C₄	C₂³×C₃²	1	2	yes	—
550	C₄⋊C₄	C₂³×C₃²	1	2	yes	—
551	C₄⋊C₄	C₂³×C₃²	1	2	yes	—
552	C₄⋊C₄	C₂³×C₃²	1	1	yes	characteristic
553	C₄⋊C₄	C₂³×C₃²	1	4	yes	—
554	C₄⋊C₄	C₂³×C₃²	1	2	yes	—
555	C₄⋊C₄	C₂³×C₃²	1	4	yes	—
556	C₄⋊C₄	C₂³×C₃²	1	2	yes	—
557	C₂²⋊C₄	C₂³×C₃²	1	2	yes	—
558	C₂²⋊C₄	C₂³×C₃²	1	4	yes	—
559	C₂²⋊C₄	C₂³×C₃²	1	2	yes	—
560	C₂²⋊C₄	C₂³×C₃²	1	2	yes	—
561	C₂²⋊C₄	C₂³×C₃²	1	2	yes	—
562	C₂²⋊C₄	C₂³×C₃²	1	2	yes	—
563	C₂²⋊C₄	C₂³×C₃²	1	4	yes	—
564	C₂²⋊C₄	C₂³×C₃²	1	4	yes	—
565	C₂²⋊C₄	C₂³×C₃²	1	4	yes	—
566	C₂²⋊C₄	C₂³×C₃²	1	2	yes	—
567	C₂²⋊C₄	C₂³×C₃²	1	2	yes	—
568	C₂²⋊C₄	C₂³×C₃²	1	4	yes	—
569	C₂²⋊C₄	C₂³×C₃²	1	2	yes	—
570	C₂²⋊C₄	C₂³×C₃²	1	4	yes	—
571	C₂²⋊C₄	C₂³×C₃²	1	2	yes	—
572	C₄²	C₂³×C₃²	1	1	yes	characteristic
573	C₄²	C₂³×C₃²	1	1	yes	characteristic
574	C₄²	C₂³×C₃²	1	1	yes	characteristic
575	C₄²	C₂³×C₃²	1	1	yes	characteristic
576	C₄²	C₂³×C₃²	1	4	yes	—
577	C₄²	C₂³×C₃²	1	4	yes	—
578	C₄²	C₂³×C₃²	1	2	yes	—
579	C₂²×C₃	—	2	4	no	—
580	C₂²×C₃	—	2	8	no	—
581	C₂²×C₃	—	2	4	no	—
582	C₂²×C₃	—	2	8	no	—
583	C₂²×C₃	—	2	8	no	—
584	C₂²×C₃	—	2	8	no	—
585	C₂²×C₃	—	2	8	no	—
586	C₂²×C₃	—	2	8	no	—
587	C₂²×C₃	—	2	8	no	—
588	C₂²×C₃	—	2	8	no	—
589	C₂²×C₃	—	4	32	no	—
590	C₂²×C₃	C₂×C₃×#41	1	16	yes	—
591	C₂²×C₃	C₃×2₋¹⁺⁴	1	8	yes	—
592	C₂²×C₃	C₂⁵×C₃	1	4	yes	—
593	C₃×C₄	—	2	8	no	—
594	C₃×C₄	—	2	4	no	—
595	C₃×C₄	—	2	16	no	—
596	C₃×C₄	—	2	4	no	—
597	C₃×C₄	—	2	8	no	—
598	C₃×C₄	—	2	8	no	—
599	C₃×C₄	—	2	16	no	—
600	C₃×C₄	—	2	8	no	—
601	C₃×C₄	—	2	4	no	—
602	C₃×C₄	—	2	4	no	—
603	C₃×C₄	—	2	8	no	—
604	C₃×C₄	C₂×C₃×#41	1	8	yes	—
605	C₃×C₄	C₃×H(5,𝔽₂)	1	8	yes	—
606	C₃²	#3520	1	1	yes	characteristic, direct product factor, Sylow
607	C₂³	—	2	4	no	—
608	C₂³	—	2	4	no	—
609	C₂³	—	4	2	no	—
610	C₂³	C₂⁴×C₃²	1	2	yes	—
611	C₂³	C₂⁴×C₃²	1	2	yes	—
612	C₂³	C₂⁴×C₃²	1	2	yes	—
613	C₂³	C₂⁴×C₃²	1	1	yes	characteristic
614	Q₈	—	2	4	no	—
615	Q₈	—	2	2	no	—
616	Q₈	—	2	4	no	—
617	Q₈	—	4	4	no	—
618	D₄	—	2	4	no	—
619	D₄	—	2	8	no	—
620	D₄	—	2	4	no	—
621	D₄	—	2	2	no	—
622	D₄	—	2	2	no	—
623	D₄	—	4	4	no	—
624	D₄	C₃²×#41	1	4	yes	complemented
625	C₂×C₄	—	2	8	no	—
626	C₂×C₄	—	2	2	no	—
627	C₂×C₄	—	2	2	no	—
628	C₂×C₄	—	2	4	no	—
629	C₂×C₄	—	2	2	no	—
630	C₂×C₄	—	2	4	no	—
631	C₂×C₄	—	2	4	no	—
632	C₂×C₄	—	4	2	no	—
633	C₂×C₄	—	4	2	no	—
634	C₂×C₄	—	4	2	no	—
635	C₂×C₄	—	4	4	no	—
636	C₂×C₄	—	4	4	no	—
637	C₂×C₄	C₂⁴×C₃²	1	1	yes	characteristic
638	C₂×C₄	C₂⁴×C₃²	1	2	yes	—
639	C₂×C₄	C₂⁴×C₃²	1	1	yes	characteristic
640	C₂×C₄	C₂⁴×C₃²	1	4	yes	—
641	C₂×C₄	C₂⁴×C₃²	1	1	yes	characteristic
642	C₂×C₄	C₂⁴×C₃²	1	1	yes	characteristic
643	C₂×C₄	C₂⁴×C₃²	1	2	yes	—
644	C₂×C₄	C₂⁴×C₃²	1	2	yes	—
645	C₂×C₄	C₂⁴×C₃²	1	4	yes	—
646	C₂×C₄	C₂⁴×C₃²	1	2	yes	—
647	C₂×C₄	C₂⁴×C₃²	1	2	yes	—
648	C₂×C₄	C₂⁴×C₃²	1	1	yes	characteristic
649	C₂×C₄	C₂⁴×C₃²	1	1	yes	characteristic
650	C₂×C₃	—	2	8	no	—
651	C₂×C₃	—	2	16	no	—
652	C₂×C₃	—	4	8	no	—
653	C₂×C₃	—	4	8	no	—
654	C₂×C₃	C₂²×C₃×#41	1	4	yes	—
655	C₂×C₃	C₂×C₃×H(5,𝔽₂)	1	4	yes	—
656	C₂×C₃	C₂×C₃×2₋¹⁺⁴	1	4	yes	—
657	C₂²	—	2	1	no	—
658	C₂²	—	2	2	no	—
659	C₂²	—	2	1	no	—
660	C₂²	—	2	2	no	—
661	C₂²	—	2	2	no	—
662	C₂²	—	2	2	no	—
663	C₂²	—	2	2	no	—
664	C₂²	—	2	2	no	—
665	C₂²	—	2	2	no	—
666	C₂²	—	2	2	no	—
667	C₂²	—	4	8	no	—
668	C₂²	C₂×C₃²×#41	1	4	yes	—
669	C₂²	C₃²×2₋¹⁺⁴	1	2	yes	—
670	C₂²	C₂⁵×C₃²	1	1	yes	characteristic
671	C₄	—	2	2	no	—
672	C₄	—	2	1	no	—
673	C₄	—	2	4	no	—
674	C₄	—	2	1	no	—
675	C₄	—	2	2	no	—
676	C₄	—	2	2	no	—
677	C₄	—	2	4	no	—
678	C₄	—	2	2	no	—
679	C₄	—	2	1	no	—
680	C₄	—	2	1	no	—
681	C₄	—	2	2	no	—
682	C₄	C₂×C₃²×#41	1	2	yes	—
683	C₄	C₃²×H(5,𝔽₂)	1	2	yes	—
684	C₃	C₃×#3520	1	4	yes	direct product factor
685	C₂	—	2	2	no	—
686	C₂	—	2	4	no	—
687	C₂	—	4	2	no	—
688	C₂	—	4	2	no	—
689	C₂	C₂²×C₃²×#41	1	1	yes	characteristic
690	C₂	C₂×C₃²×H(5,𝔽₂)	1	1	yes	characteristic
691	C₂	C₂×C₃²×2₋¹⁺⁴	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×#554	C₂	semidirect
3. C₃²×#552	C₂	semidirect
4. C₃²×#551	C₂	semidirect
5. C₃²×D₄×Q₈	C₂	semidirect
6. C₃²×#548	C₂	semidirect
7. C₃²×#547	C₂	semidirect
8. C₃²×#547	C₂	semidirect
9. C₃²×#546	C₂	semidirect
10. C₃²×#542	C₂	semidirect
11. C₃²×#539	C₂	semidirect
12. C₃²×#533	C₂	semidirect
13. C₃²×#529	C₂	semidirect
14. C₃²×#525	C₂	semidirect
15. C₂×C₃²×C₂²⋊Q₈	C₂	semidirect
16. C₃²×#520	C₂	semidirect
17. C₂×C₃²×C₄×D₄	C₂	semidirect
18. C₃×#3520	C₃	direct (N × H)
20. C₂×C₃²×#41	C₂²	semidirect
21. C₂²×C₃²×Q₈	C₂²	semidirect
24. C₃²×C₄⋊Q₈	C₂²	semidirect
25. C₃²×C₄⋊Q₈	C₂²	semidirect
26. C₃²×C₄⋊Q₈	C₂²	semidirect
27. C₃²×#126	C₂²	semidirect
28. C₃²×#126	C₂²	semidirect
29. C₃²×#126	C₂²	semidirect
30. C₃²×#125	C₂²	semidirect
31. C₃²×#125	C₂²	semidirect
32. C₃²×#125	C₂²	semidirect
34. C₃²×#124	C₂²	semidirect
35. C₃²×#124	C₂²	semidirect
38. C₃²×#123	C₂²	semidirect
39. C₃²×#123	C₂²	semidirect
40. C₃²×#123	C₂²	semidirect
45. C₃²×C₂²⋊Q₈	C₂²	semidirect
46. C₃²×C₂²⋊Q₈	C₂²	semidirect
47. C₃²×C₂²⋊Q₈	C₂²	semidirect
48. C₃²×C₂²⋊Q₈	C₂²	semidirect
49. C₃²×C₂²⋊Q₈	C₂²	semidirect
50. C₃²×C₂²⋊Q₈	C₂²	semidirect
51. C₃²×C₂²⋊Q₈	C₂²	semidirect
55. C₃²×#121	C₂²	semidirect
57. C₃²×C₄×Q₈	C₂²	semidirect
58. C₃²×C₄×Q₈	C₂²	semidirect
59. C₃²×C₄×Q₈	C₂²	semidirect
60. C₃²×C₄×Q₈	C₂²	semidirect
70. C₃²×C₄×D₄	C₂²	semidirect
71. C₃²×C₄×D₄	C₂²	semidirect
72. C₃²×C₄×D₄	C₂²	semidirect
74. C₃²×#117	C₂²	semidirect
75. C₃²×#117	C₂²	semidirect
76. C₃²×#117	C₂²	semidirect
78. C₂×C₃²×C₄⋊C₄	C₂²	semidirect
79. C₂×C₃²×C₄⋊C₄	C₂²	semidirect
80. C₂×C₃²×C₄⋊C₄	C₂²	semidirect
84. C₃×#556	C₂×C₃	semidirect
85. C₃×#554	C₂×C₃	semidirect
86. C₃×#552	C₂×C₃	semidirect
87. C₃×#551	C₂×C₃	semidirect
88. C₃×D₄×Q₈	C₂×C₃	semidirect
89. C₃×#548	C₂×C₃	semidirect
90. C₃×#547	C₂×C₃	semidirect
91. C₃×#547	C₂×C₃	semidirect
92. C₃×#546	C₂×C₃	semidirect
93. C₃×#542	C₂×C₃	semidirect
94. C₃×#539	C₂×C₃	semidirect
95. C₃×#533	C₂×C₃	semidirect
96. C₃×#529	C₂×C₃	semidirect
97. C₃×#525	C₂×C₃	semidirect
98. C₂×C₃×C₂²⋊Q₈	C₂×C₃	semidirect
99. C₃×#520	C₂×C₃	semidirect
100. C₂×C₃×C₄×D₄	C₂×C₃	semidirect
171. #3520	C₃²	direct (N × H)
173. C₂×C₃×#41	C₂²×C₃	semidirect
174. C₂²×C₃×Q₈	C₂²×C₃	semidirect
177. C₃×C₄⋊Q₈	C₂²×C₃	semidirect
178. C₃×C₄⋊Q₈	C₂²×C₃	semidirect
179. C₃×C₄⋊Q₈	C₂²×C₃	semidirect
180. C₃×#126	C₂²×C₃	semidirect
181. C₃×#126	C₂²×C₃	semidirect
182. C₃×#126	C₂²×C₃	semidirect
183. C₃×#125	C₂²×C₃	semidirect
184. C₃×#125	C₂²×C₃	semidirect
185. C₃×#125	C₂²×C₃	semidirect
187. C₃×#124	C₂²×C₃	semidirect
188. C₃×#124	C₂²×C₃	semidirect
191. C₃×#123	C₂²×C₃	semidirect
192. C₃×#123	C₂²×C₃	semidirect
193. C₃×#123	C₂²×C₃	semidirect
198. C₃×C₂²⋊Q₈	C₂²×C₃	semidirect
199. C₃×C₂²⋊Q₈	C₂²×C₃	semidirect
200. C₃×C₂²⋊Q₈	C₂²×C₃	semidirect
201. C₃×C₂²⋊Q₈	C₂²×C₃	semidirect
202. C₃×C₂²⋊Q₈	C₂²×C₃	semidirect
203. C₃×C₂²⋊Q₈	C₂²×C₃	semidirect
204. C₃×C₂²⋊Q₈	C₂²×C₃	semidirect
208. C₃×#121	C₂²×C₃	semidirect
210. C₃×C₄×Q₈	C₂²×C₃	semidirect
211. C₃×C₄×Q₈	C₂²×C₃	semidirect
212. C₃×C₄×Q₈	C₂²×C₃	semidirect
213. C₃×C₄×Q₈	C₂²×C₃	semidirect
223. C₃×C₄×D₄	C₂²×C₃	semidirect
224. C₃×C₄×D₄	C₂²×C₃	semidirect
225. C₃×C₄×D₄	C₂²×C₃	semidirect
227. C₃×#117	C₂²×C₃	semidirect
228. C₃×#117	C₂²×C₃	semidirect
229. C₃×#117	C₂²×C₃	semidirect
231. C₂×C₃×C₄⋊C₄	C₂²×C₃	semidirect
232. C₂×C₃×C₄⋊C₄	C₂²×C₃	semidirect
233. C₂×C₃×C₄⋊C₄	C₂²×C₃	semidirect
254. C₃²×D₄	#41	semidirect
280. #556	C₂×C₃²	semidirect
281. #554	C₂×C₃²	semidirect
282. #552	C₂×C₃²	semidirect
283. #551	C₂×C₃²	semidirect
284. D₄×Q₈	C₂×C₃²	semidirect
285. #548	C₂×C₃²	semidirect
286. #547	C₂×C₃²	semidirect
287. #547	C₂×C₃²	semidirect
288. #546	C₂×C₃²	semidirect
289. #542	C₂×C₃²	semidirect
290. #539	C₂×C₃²	semidirect
291. #533	C₂×C₃²	semidirect
292. #529	C₂×C₃²	semidirect
293. #525	C₂×C₃²	semidirect
294. C₂×C₂²⋊Q₈	C₂×C₃²	semidirect
295. #520	C₂×C₃²	semidirect
296. C₂×C₄×D₄	C₂×C₃²	semidirect
395. C₂×#41	C₂²×C₃²	semidirect
396. C₂²×Q₈	C₂²×C₃²	semidirect
399. C₄⋊Q₈	C₂²×C₃²	semidirect
400. C₄⋊Q₈	C₂²×C₃²	semidirect
401. C₄⋊Q₈	C₂²×C₃²	semidirect
402. #126	C₂²×C₃²	semidirect
403. #126	C₂²×C₃²	semidirect
404. #126	C₂²×C₃²	semidirect
405. #125	C₂²×C₃²	semidirect
406. #125	C₂²×C₃²	semidirect
407. #125	C₂²×C₃²	semidirect
409. #124	C₂²×C₃²	semidirect
410. #124	C₂²×C₃²	semidirect
413. #123	C₂²×C₃²	semidirect
414. #123	C₂²×C₃²	semidirect
415. #123	C₂²×C₃²	semidirect
420. C₂²⋊Q₈	C₂²×C₃²	semidirect
421. C₂²⋊Q₈	C₂²×C₃²	semidirect
422. C₂²⋊Q₈	C₂²×C₃²	semidirect
423. C₂²⋊Q₈	C₂²×C₃²	semidirect
424. C₂²⋊Q₈	C₂²×C₃²	semidirect
425. C₂²⋊Q₈	C₂²×C₃²	semidirect
426. C₂²⋊Q₈	C₂²×C₃²	semidirect
430. #121	C₂²×C₃²	semidirect
432. C₄×Q₈	C₂²×C₃²	semidirect
433. C₄×Q₈	C₂²×C₃²	semidirect
434. C₄×Q₈	C₂²×C₃²	semidirect
435. C₄×Q₈	C₂²×C₃²	semidirect
445. C₄×D₄	C₂²×C₃²	semidirect
446. C₄×D₄	C₂²×C₃²	semidirect
447. C₄×D₄	C₂²×C₃²	semidirect
449. #117	C₂²×C₃²	semidirect
450. #117	C₂²×C₃²	semidirect
451. #117	C₂²×C₃²	semidirect
453. C₂×C₄⋊C₄	C₂²×C₃²	semidirect
454. C₂×C₄⋊C₄	C₂²×C₃²	semidirect
455. C₂×C₄⋊C₄	C₂²×C₃²	semidirect
476. C₃×D₄	C₃×#41	semidirect
606. C₃²	#3520	direct (N × H)
624. D₄	C₃²×#41	semidirect
684. C₃	C₃×#3520	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×#552	2
C₃²×#551	2
C₃²×D₄×Q₈	2
C₃²×#548	2
C₃²×#547	2
C₃²×#546	2
C₃²×#542	2
C₃²×#539	2
C₃²×#533	2
C₃²×#529	2
C₃²×#525	2
C₂×C₃²×C₂²⋊Q₈	2
C₃²×#520	2
C₂×C₃²×C₄×D₄	2
C₃×#3520	3

Subgroups — C32×#3520 #11770569

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃²×#3520 #11770569