Subgroups — #72312951

Order 2048.

At least 7807 conjugacy classes of subgroups; only the 1492 normal subgroups are shown.

The subgroup lattice has 753 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#72312840	C₂	1	8	yes	maximal, complemented
2	#72312757	C₂	1	8	yes	maximal, complemented
3	#72312383	C₂	1	1	yes	maximal, characteristic, complemented
4	#72312264	C₂	1	1	yes	maximal, characteristic, complemented
5	#72312211	C₂	1	1	yes	maximal, characteristic, complemented
6	#72312178	C₂	1	1	yes	maximal, characteristic, complemented
7	#72312134	C₂	1	1	yes	maximal, characteristic, complemented
8	#72312125	C₂	1	1	yes	maximal, characteristic, complemented
9	#72312073	C₂	1	1	yes	maximal, characteristic, complemented
10	#72302906	C₂	1	1	yes	maximal, characteristic, complemented
11	#72282320	C₂	1	1	yes	maximal, characteristic, complemented
12	#72263904	C₂	1	1	yes	maximal, characteristic, complemented
13	#72257774	C₂	1	1	yes	maximal, characteristic, complemented
14	#72257772	C₂	1	1	yes	maximal, characteristic, complemented
15	#72257705	C₂	1	1	yes	maximal, characteristic, complemented
16	#72257631	C₂	1	1	yes	maximal, characteristic, complemented
17	#72257408	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×#62812	C₂²	1	1	yes	characteristic
19	C₂×#60968	C₂²	1	1	yes	characteristic
20	C₂×#60968	C₂²	1	1	yes	characteristic
21	C₂×#60561	C₂²	1	1	yes	characteristic
22	C₂×#60561	C₂²	1	1	yes	characteristic
23	#7628578	C₂²	1	1	yes	characteristic
24	#7628578	C₂²	1	1	yes	characteristic, complemented
25	#7628157	C₂²	1	1	yes	characteristic
26	#7625999	C₂²	1	1	yes	characteristic
27	#7625999	C₂²	1	1	yes	characteristic
28	#6508792	C₂²	1	4	yes	complemented
29	#6500360	C₂²	1	4	yes	complemented
30	#6385979	C₂²	1	8	yes	—
31	#6375020	C₂²	1	1	yes	characteristic, complemented
32	#6374676	C₂²	1	1	yes	characteristic, complemented
33	#6374247	C₂²	1	1	yes	characteristic
34	#6374247	C₂²	1	1	yes	characteristic
35	#6374247	C₂²	1	1	yes	characteristic, complemented
36	#6370997	C₂²	1	1	yes	characteristic, complemented
37	#6370978	C₂²	1	1	yes	characteristic, complemented
38	#6370937	C₂²	1	1	yes	characteristic
39	#6370937	C₂²	1	1	yes	characteristic
40	#6370937	C₂²	1	1	yes	characteristic, complemented
41	#6347494	C₂²	1	8	yes	—
42	#6346604	C₂²	1	4	yes	—
43	#6346596	C₂²	1	4	yes	—
44	#6343377	C₂²	1	1	yes	characteristic
45	#6343377	C₂²	1	1	yes	characteristic
46	#6343377	C₂²	1	1	yes	characteristic
47	#6343377	C₂²	1	1	yes	characteristic
48	#6343377	C₂²	1	1	yes	characteristic, complemented
49	#6342561	C₂²	1	1	yes	characteristic
50	#6342561	C₂²	1	1	yes	characteristic
51	#234856	C₂²	1	4	yes	complemented
52	#234851	C₂²	1	4	yes	complemented
53	#233546	C₂²	1	4	yes	complemented
54	#233543	C₂²	1	4	yes	complemented
55	#202019	C₂²	1	4	yes	complemented
56	#202016	C₂²	1	4	yes	complemented
57	#199777	C₂²	1	8	yes	complemented
58	#181777	C₂²	1	1	yes	characteristic, complemented
59	#181375	C₂²	1	1	yes	characteristic, complemented
60	#181358	C₂²	1	1	yes	characteristic, complemented
61	#181358	C₂²	1	1	yes	characteristic, complemented
62	#181343	C₂²	1	1	yes	characteristic, complemented
63	#181124	C₂²	1	1	yes	characteristic, complemented
64	#181122	C₂²	1	1	yes	characteristic, complemented
65	#181122	C₂²	1	1	yes	characteristic, complemented
66	#116394	C₂²	1	8	yes	complemented
67	#116360	C₂²	1	8	yes	complemented
68	#115378	C₂²	1	4	yes	complemented
69	#115377	C₂²	1	4	yes	complemented
70	#114648	C₂²	1	4	yes	complemented
71	#114647	C₂²	1	4	yes	complemented
72	#114551	C₂²	1	8	yes	complemented
73	#112305	C₂²	1	8	yes	complemented
74	#107568	C₂²	1	8	yes	complemented
75	C₂×#3497	D₄	1	2	yes	complemented
76	C₂×#3496	D₄	1	2	yes	complemented
77	C₂×#3496	C₂³	1	4	yes	—
78	C₂×#3449	D₄	1	4	yes	complemented
79	C₂²×#532	C₂³	1	1	yes	characteristic
80	C₂²×#532	C₂³	1	1	yes	characteristic
81	C₂²×#532	C₂³	1	1	yes	characteristic
82	C₂²×C₄×#41	C₂³	1	1	yes	characteristic
83	C₂²×C₄×#41	C₂³	1	1	yes	characteristic
84	C₂×#3227	D₄	1	2	yes	complemented
85	C₂×#3205	D₄	1	2	yes	complemented
86	C₂×#3192	C₂³	1	4	yes	—
87	C₂×#3192	C₂³	1	4	yes	—
88	C₂×#3112	D₄	1	2	yes	complemented
89	C₂×#3109	D₄	1	2	yes	complemented
90	C₂×#3109	D₄	1	4	yes	complemented
91	C₂×#3103	D₄	1	2	yes	complemented
92	C₂×#3100	D₄	1	2	yes	complemented
93	C₂×#3094	C₂³	1	2	yes	—
94	C₂×#3094	C₂³	1	2	yes	—
95	C₂×#3006	C₂³	1	2	yes	—
96	C₂×#3006	C₂³	1	2	yes	—
97	C₂×#2920	C₂³	1	1	yes	characteristic
98	C₂×#2920	C₂³	1	1	yes	characteristic
99	C₂×#2920	C₂³	1	1	yes	characteristic
100	C₂×#2920	C₂³	1	1	yes	characteristic
101	#35262	C₂³	1	2	yes	—
102	#35250	C₂³	1	2	yes	—
103	#35076	C₂³	1	4	yes	—
104	#34809	C₂³	1	2	yes	—
105	#34736	C₂³	1	2	yes	—
106	#34365	D₄	1	2	yes	complemented
107	#34364	D₄	1	2	yes	complemented
108	#34363	C₂³	1	4	yes	—
109	#34363	C₂³	1	4	yes	—
110	D₄×#117	D₄	1	4	yes	complemented
111	#34012	C₂³	1	1	yes	characteristic
112	#34012	C₂³	1	1	yes	characteristic
113	#34012	C₂³	1	1	yes	characteristic
114	#34012	C₂³	1	1	yes	characteristic
115	#34012	C₂³	1	1	yes	characteristic
116	#34012	C₂³	1	1	yes	characteristic
117	#21935	C₂³	1	4	yes	—
118	#21794	D₄	1	4	yes	complemented
119	#21793	C₂³	1	4	yes	—
120	#21793	C₂³	1	4	yes	—
121	#21793	C₂³	1	4	yes	—
122	#21767	C₂³	1	4	yes	—
123	#21212	D₄	1	4	yes	complemented
124	#20722	D₄	1	4	yes	—
125	#20722	C₂³	1	4	yes	—
126	#20722	C₂³	1	4	yes	—
127	#20705	C₂³	1	2	yes	—
128	#20701	C₂³	1	2	yes	—
129	#20688	D₄	1	2	yes	—
130	#20688	C₂³	1	2	yes	—
131	#20605	C₂³	1	2	yes	—
132	#20600	C₂³	1	2	yes	—
133	#20584	D₄	1	2	yes	—
134	#20584	C₂³	1	2	yes	—
135	#17589	D₄	1	4	yes	complemented
136	#17583	D₄	1	4	yes	complemented
137	#17577	C₂³	1	4	yes	—
138	#17577	C₂³	1	4	yes	—
139	#17577	C₂³	1	4	yes	—
140	#17577	C₂³	1	4	yes	—
141	#17577	C₂³	1	4	yes	—
142	#17561	D₄	1	4	yes	complemented
143	#17544	D₄	1	4	yes	complemented
144	#17362	C₂³	1	4	yes	—
145	#17362	C₂³	1	4	yes	—
146	#8112	C₂³	1	4	yes	—
147	#8104	C₂³	1	4	yes	—
148	#8104	C₂³	1	4	yes	—
149	#8102	C₂³	1	4	yes	—
150	#8049	C₂³	1	4	yes	—
151	#7946	C₂³	1	4	yes	—
152	#7946	C₂³	1	4	yes	—
153	#7946	C₂³	1	4	yes	—
154	C₂³×#41	C₂×D₄	1	1	yes	characteristic
155	C₂³×#41	C₂⁴	1	1	yes	characteristic
156	C₂×#537	C₂×D₄	1	8	yes	—
157	C₂×#534	C₂×D₄	1	8	yes	—
158	C₂×#532	C₂×D₄	1	2	yes	—
159	C₂×#532	C₂×D₄	1	2	yes	—
160	C₂×#532	C₂×D₄	1	2	yes	—
161	C₂×#532	C₂×D₄	1	2	yes	—
162	C₂×#532	C₂×D₄	1	2	yes	—
163	C₂×#532	C₂×D₄	1	2	yes	—
164	C₂×#532	C₂×D₄	1	2	yes	—
165	C₂×#532	C₂×D₄	1	2	yes	—
166	C₂×#532	C₂×D₄	1	2	yes	—
167	C₂×#532	C₂×D₄	1	2	yes	—
168	C₂×#532	C₂×D₄	1	2	yes	—
169	C₂×#532	C₂×D₄	1	2	yes	—
170	C₂×#532	C₂×D₄	1	2	yes	—
171	C₂×#532	C₂×D₄	1	2	yes	—
172	C₂×#532	#41	1	2	yes	—
173	C₂×#532	#41	1	2	yes	—
174	C₂²×C₄⋊Q₈	C₂×D₄	1	1	yes	characteristic
175	C₂²×C₄⋊Q₈	C₂×D₄	1	1	yes	characteristic
176	C₂²×C₄⋊Q₈	#41	1	1	yes	characteristic
177	C₂²×#127	C₂×D₄	1	1	yes	characteristic
178	C₂²×#127	C₂×D₄	1	1	yes	characteristic
179	C₂²×#127	#41	1	1	yes	characteristic
180	C₂²×#121	C₂⁴	1	2	yes	—
181	C₂²×#121	C₂⁴	1	2	yes	—
182	C₂²×#121	C₂⁴	1	2	yes	—
183	C₂²×C₄×Q₈	C₂×D₄	1	1	yes	characteristic
184	C₂²×C₄×Q₈	C₂×D₄	1	1	yes	characteristic
185	C₂²×C₄×Q₈	C₂×D₄	1	1	yes	characteristic
186	C₂²×C₄×Q₈	#41	1	1	yes	characteristic
187	C₂²×C₄×D₄	C₂×D₄	1	2	yes	—
188	C₂²×C₄×D₄	C₂×D₄	1	1	yes	characteristic
189	C₂²×C₄×D₄	C₂×D₄	1	1	yes	characteristic
190	C₂²×C₄×D₄	C₂×D₄	1	2	yes	—
191	C₂²×C₄×D₄	C₂×D₄	1	2	yes	—
192	C₂²×C₄×D₄	C₂×D₄	1	1	yes	characteristic
193	C₂²×C₄×D₄	#41	1	2	yes	—
194	C₂²×C₄×D₄	#41	1	1	yes	characteristic
195	C₂²×C₄×D₄	C₂⁴	1	2	yes	—
196	C₂²×#117	C₂×D₄	1	2	yes	—
197	C₂²×#117	C₂×D₄	1	1	yes	characteristic
198	C₂²×#117	C₂⁴	1	1	yes	characteristic
199	C₂³×C₄²	#41	1	2	yes	—
200	C₂³×C₄²	C₂⁴	1	1	yes	characteristic
201	C₂×#481	C₂×D₄	1	8	yes	—
202	C₂×#481	C₂×D₄	1	4	yes	—
203	C₂×#480	C₂×D₄	1	4	yes	—
204	C₂×#448	C₂×D₄	1	4	yes	—
205	C₂×#447	C₂×D₄	1	4	yes	—
206	C₂×#447	C₂×D₄	1	8	yes	—
207	#2920	C₂×D₄	1	2	yes	—
208	#2920	C₂×D₄	1	2	yes	—
209	#2920	C₂×D₄	1	2	yes	—
210	#2920	C₂×D₄	1	2	yes	—
211	C₂×#432	C₂×D₄	1	2	yes	—
212	C₂×#432	C₂×D₄	1	2	yes	—
213	C₂×#431	C₂×D₄	1	2	yes	—
214	C₂×#431	C₂×D₄	1	2	yes	—
215	C₂×#407	C₂⁴	1	2	yes	—
216	C₂×#407	C₂⁴	1	2	yes	—
217	C₂×#407	C₂⁴	1	2	yes	—
218	C₂×#407	C₂⁴	1	2	yes	—
219	#2344	C₂×D₄	1	8	yes	—
220	D₄×C₂²⋊C₄	C₂×D₄	1	8	yes	—
221	#2285	C₂×D₄	1	2	yes	—
222	#2285	C₂×D₄	1	2	yes	—
223	#2283	C₂×D₄	1	2	yes	—
224	#2283	C₂×D₄	1	2	yes	—
225	#2283	C₂×D₄	1	2	yes	—
226	#2283	C₂×D₄	1	2	yes	—
227	#2283	C₂×D₄	1	2	yes	—
228	#2283	C₂×D₄	1	2	yes	—
229	#2283	C₂×D₄	1	2	yes	—
230	#2280	C₂×D₄	1	2	yes	—
231	#2280	C₂×D₄	1	2	yes	—
232	#2280	C₂×D₄	1	2	yes	—
233	#2280	C₂×D₄	1	2	yes	—
234	#2280	C₂⁴	1	2	yes	—
235	#2280	C₂⁴	1	2	yes	—
236	#2280	C₂⁴	1	2	yes	—
237	#2280	C₂⁴	1	2	yes	—
238	#2280	C₂⁴	1	2	yes	—
239	#2280	C₂⁴	1	2	yes	—
240	C₄×#117	C₂×D₄	1	2	yes	—
241	C₄×#117	C₂×D₄	1	2	yes	—
242	C₄×#117	C₂×D₄	1	2	yes	—
243	#1964	C₂×D₄	1	16	yes	—
244	#1819	C₂×D₄	1	8	yes	—
245	#1781	C₂×D₄	1	8	yes	—
246	#1510	C₂×D₄	1	16	yes	—
247	#1507	C₂×D₄	1	16	yes	—
248	C₂³×Q₈	#121	1	1	yes	characteristic
249	C₂³×Q₈	C₂²×D₄	1	1	yes	characteristic
250	C₂³×D₄	#121	1	1	yes	characteristic
251	C₂³×D₄	C₂²×D₄	1	2	yes	—
252	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
253	C₂³×D₄	C₂²×D₄	1	2	yes	—
254	C₂³×D₄	C₂²×D₄	1	2	yes	—
255	C₂³×D₄	C₂×#41	1	2	yes	—
256	C₂⁴×C₄	#121	1	2	yes	—
257	C₂⁴×C₄	#121	1	2	yes	—
258	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
259	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
260	C₂⁴×C₄	C₂×#41	1	2	yes	—
261	C₂⁴×C₄	C₂⁵	1	1	yes	characteristic
262	#532	#120	1	4	yes	—
263	#532	#120	1	4	yes	—
264	#532	#120	1	4	yes	—
265	#532	#120	1	4	yes	—
266	#532	#120	1	4	yes	—
267	#532	#120	1	4	yes	—
268	#532	#120	1	4	yes	—
269	#532	#120	1	4	yes	—
270	#532	#121	1	4	yes	—
271	#532	#121	1	4	yes	—
272	#532	#121	1	4	yes	—
273	#532	#121	1	4	yes	—
274	#532	#121	1	4	yes	—
275	#532	#121	1	4	yes	—
276	#532	#121	1	4	yes	—
277	#532	#121	1	4	yes	—
278	C₂×C₄⋊Q₈	#120	1	2	yes	—
279	C₂×C₄⋊Q₈	#120	1	2	yes	—
280	C₂×C₄⋊Q₈	#121	1	2	yes	—
281	C₂×C₄⋊Q₈	#121	1	2	yes	—
282	C₂×C₄⋊Q₈	#121	1	2	yes	—
283	C₂×C₄⋊Q₈	#121	1	2	yes	—
284	C₂×C₄⋊Q₈	#127	1	2	yes	—
285	C₂×C₄⋊Q₈	#127	1	2	yes	—
286	C₂×#127	#120	1	2	yes	—
287	C₂×#127	#120	1	2	yes	—
288	C₂×#127	#121	1	2	yes	—
289	C₂×#127	#121	1	2	yes	—
290	C₂×#127	#121	1	2	yes	—
291	C₂×#127	#121	1	2	yes	—
292	C₂×#127	#127	1	2	yes	—
293	C₂×#127	#127	1	2	yes	—
294	C₂×#121	C₂²×D₄	1	4	yes	—
295	C₂×#121	C₂²×D₄	1	4	yes	—
296	C₂×#121	C₂²×D₄	1	4	yes	—
297	C₂×#121	C₂²×D₄	1	4	yes	—
298	C₂×#121	C₂²×D₄	1	4	yes	—
299	C₂×#121	C₂²×D₄	1	4	yes	—
300	C₂×#121	C₂²×D₄	1	4	yes	—
301	C₂×#121	C₂×#41	1	4	yes	—
302	C₂×C₄×D₄	#120	1	4	yes	—
303	C₂×C₄×D₄	#120	1	4	yes	—
304	C₂×C₄×D₄	#121	1	4	yes	—
305	C₂×C₄×D₄	#121	1	4	yes	—
306	C₂×C₄×D₄	#121	1	4	yes	—
307	C₂×C₄×D₄	#121	1	4	yes	—
308	C₂×C₄×D₄	#127	1	4	yes	—
309	C₂×C₄×D₄	#127	1	4	yes	—
310	C₂×#117	#120	1	4	yes	—
311	C₂²×C₄⋊C₄	#121	1	2	yes	—
312	C₂²×C₄⋊C₄	#121	1	1	yes	characteristic
313	C₂²×C₄⋊C₄	#121	1	1	yes	characteristic
314	C₂²×C₄⋊C₄	C₂²×D₄	1	2	yes	—
315	C₂²×C₄⋊C₄	C₂²×D₄	1	1	yes	characteristic
316	C₂²×C₄⋊C₄	C₂²×D₄	1	1	yes	characteristic
317	C₂²×C₄⋊C₄	C₂²×D₄	1	2	yes	—
318	C₂²×C₄⋊C₄	C₂²×D₄	1	2	yes	—
319	C₂²×C₄⋊C₄	C₂×#41	1	2	yes	—
320	C₂²×C₂²⋊C₄	#121	1	2	yes	—
321	C₂²×C₂²⋊C₄	C₂²×D₄	1	2	yes	—
322	C₂²×C₂²⋊C₄	C₂²×D₄	1	2	yes	—
323	C₂²×C₄²	#121	1	2	yes	—
324	C₂²×C₄²	#121	1	2	yes	—
325	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
326	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
327	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
328	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
329	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
330	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
331	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
332	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
333	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
334	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
335	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
336	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
337	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
338	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
339	C₂²×C₄²	C₂×#41	1	2	yes	—
340	C₂²×C₄²	C₂×#41	1	1	yes	characteristic
341	C₂²×C₄²	C₂×#41	1	1	yes	characteristic
342	C₂²×C₄²	C₂×#41	1	1	yes	characteristic
343	C₂²×C₄²	C₂×#41	1	1	yes	characteristic
344	C₂²×C₄²	C₂×#41	1	1	yes	characteristic
345	C₂²×C₄²	C₂×#41	1	1	yes	characteristic
346	C₂²×C₄²	H(5,𝔽₂)	1	1	yes	characteristic
347	C₂²×C₄²	H(5,𝔽₂)	1	1	yes	characteristic
348	C₂²×C₄²	H(5,𝔽₂)	1	1	yes	characteristic
349	C₂²×C₄²	H(5,𝔽₂)	1	1	yes	characteristic
350	C₂²×C₄²	H(5,𝔽₂)	1	1	yes	characteristic
351	C₂²×C₄²	H(5,𝔽₂)	1	1	yes	characteristic
352	C₂²×C₄²	H(5,𝔽₂)	1	1	yes	characteristic
353	C₂²×C₄²	H(5,𝔽₂)	1	1	yes	characteristic
354	#407	C₂²×D₄	1	4	yes	—
355	#407	C₂²×D₄	1	4	yes	—
356	C₂×C₂²⋊C₈	C₂²×D₄	1	4	yes	—
357	C₂×C₂²⋊C₈	C₂²×D₄	1	4	yes	—
358	#381	#120	1	4	yes	—
359	#381	C₂²×D₄	1	4	yes	—
360	#380	#120	1	4	yes	—
361	#380	C₂²×D₄	1	4	yes	—
362	#380	C₂²×D₄	1	4	yes	—
363	#379	C₂²×D₄	1	4	yes	—
364	#379	C₂²×D₄	1	4	yes	—
365	C₄×C₂²⋊C₄	#120	1	4	yes	—
366	C₄×C₂²⋊C₄	C₂²×D₄	1	4	yes	—
367	C₄×C₂²⋊C₄	C₂²×D₄	1	4	yes	—
368	C₄×C₂²⋊C₄	C₂²×D₄	1	4	yes	—
369	C₂⁵	C₂×#121	1	2	yes	—
370	C₂⁵	C₂³×D₄	1	1	yes	characteristic
371	C₂²×D₄	C₂×#120	1	4	yes	—
372	C₂²×D₄	C₂×#121	1	4	yes	—
373	C₂²×D₄	C₂×#121	1	4	yes	—
374	C₂²×D₄	C₂×#127	1	4	yes	—
375	C₂³×C₄	C₂×#120	1	1	yes	characteristic
376	C₂³×C₄	C₂×#120	1	1	yes	characteristic
377	C₂³×C₄	C₂×#120	1	1	yes	characteristic
378	C₂³×C₄	C₂×#120	1	1	yes	characteristic
379	C₂³×C₄	C₂×#121	1	2	yes	—
380	C₂³×C₄	C₂×#121	1	2	yes	—
381	C₂³×C₄	C₂×#121	1	2	yes	—
382	C₂³×C₄	C₂×#121	1	1	yes	characteristic
383	C₂³×C₄	C₂×#121	1	1	yes	characteristic
384	C₂³×C₄	C₂×#121	1	1	yes	characteristic
385	C₂³×C₄	C₂×#121	1	1	yes	characteristic
386	C₂³×C₄	#525	1	1	yes	characteristic
387	C₂³×C₄	#525	1	1	yes	characteristic
388	C₂³×C₄	#525	1	1	yes	characteristic
389	C₂³×C₄	#525	1	1	yes	characteristic
390	C₂³×C₄	D₄²	1	1	yes	characteristic
391	C₂³×C₄	D₄²	1	1	yes	characteristic
392	C₂³×C₄	D₄²	1	1	yes	characteristic
393	C₂³×C₄	D₄²	1	1	yes	characteristic
394	C₂³×C₄	D₄²	1	1	yes	characteristic
395	C₂³×C₄	D₄²	1	1	yes	characteristic
396	C₂³×C₄	D₄²	1	1	yes	characteristic
397	C₂³×C₄	D₄²	1	1	yes	characteristic
398	C₂³×C₄	D₄²	1	1	yes	characteristic
399	C₂³×C₄	D₄²	1	1	yes	characteristic
400	C₂³×C₄	D₄²	1	1	yes	characteristic
401	C₂³×C₄	D₄²	1	1	yes	characteristic
402	C₂³×C₄	D₄²	1	1	yes	characteristic
403	C₂³×C₄	D₄²	1	1	yes	characteristic
404	C₂³×C₄	D₄²	1	1	yes	characteristic
405	C₂³×C₄	D₄²	1	1	yes	characteristic
406	C₂³×C₄	C₂³×D₄	1	1	yes	characteristic
407	C₂³×C₄	C₂³×D₄	1	1	yes	characteristic
408	C₂³×C₄	C₂³×D₄	1	1	yes	characteristic
409	C₂³×C₄	C₂³×D₄	1	1	yes	characteristic
410	C₂³×C₄	C₂³×D₄	1	1	yes	characteristic
411	C₂³×C₄	C₂³×D₄	1	1	yes	characteristic
412	C₂³×C₄	C₂³×D₄	1	1	yes	characteristic
413	C₂³×C₄	C₂²×#41	1	1	yes	characteristic
414	C₂³×C₄	C₂²×#41	1	1	yes	characteristic
415	C₂³×C₄	C₂²×#41	1	1	yes	characteristic
416	C₂³×C₄	C₂×H(5,𝔽₂)	1	1	yes	characteristic
417	C₂³×C₄	C₂×H(5,𝔽₂)	1	1	yes	characteristic
418	C₂³×C₄	C₂×H(5,𝔽₂)	1	1	yes	characteristic
419	C₂³×C₄	C₂×H(5,𝔽₂)	1	1	yes	characteristic
420	C₄⋊Q₈	#392	1	4	yes	—
421	C₄⋊Q₈	#392	1	4	yes	—
422	C₄⋊Q₈	#392	1	4	yes	—
423	C₄⋊Q₈	#392	1	4	yes	—
424	#127	#392	1	4	yes	—
425	#127	#392	1	4	yes	—
426	#127	#392	1	4	yes	—
427	#127	#392	1	4	yes	—
428	#121	C₂×#120	1	8	yes	—
429	#121	C₂×#120	1	8	yes	—
430	#121	C₂×#121	1	8	yes	—
431	#121	C₂×#121	1	8	yes	—
432	C₄×D₄	#392	1	8	yes	—
433	C₄×D₄	#392	1	8	yes	—
434	C₄×D₄	#392	1	8	yes	—
435	C₄×D₄	#392	1	8	yes	—
436	C₂×C₄⋊C₄	C₂×#120	1	4	yes	—
437	C₂×C₄⋊C₄	C₂×#121	1	4	yes	—
438	C₂×C₄⋊C₄	C₂×#121	1	4	yes	—
439	C₂×C₄⋊C₄	C₂×#127	1	4	yes	—
440	C₂×C₂²⋊C₄	C₂×#120	1	8	yes	—
441	C₂×C₄²	C₂×#120	1	1	yes	characteristic
442	C₂×C₄²	C₂×#120	1	1	yes	characteristic
443	C₂×C₄²	C₂×#120	1	1	yes	characteristic
444	C₂×C₄²	C₂×#120	1	1	yes	characteristic
445	C₂×C₄²	C₂×#120	1	1	yes	characteristic
446	C₂×C₄²	C₂×#120	1	1	yes	characteristic
447	C₂×C₄²	C₂×#120	1	1	yes	characteristic
448	C₂×C₄²	C₂×#120	1	1	yes	characteristic
449	C₂×C₄²	C₂×#120	1	1	yes	characteristic
450	C₂×C₄²	C₂×#120	1	1	yes	characteristic
451	C₂×C₄²	C₂×#120	1	1	yes	characteristic
452	C₂×C₄²	C₂×#120	1	1	yes	characteristic
453	C₂×C₄²	C₂×#121	1	1	yes	characteristic
454	C₂×C₄²	C₂×#121	1	1	yes	characteristic
455	C₂×C₄²	C₂×#121	1	1	yes	characteristic
456	C₂×C₄²	C₂×#121	1	1	yes	characteristic
457	C₂×C₄²	C₂×#121	1	1	yes	characteristic
458	C₂×C₄²	C₂×#121	1	1	yes	characteristic
459	C₂×C₄²	C₂×#121	1	1	yes	characteristic
460	C₂×C₄²	C₂×#121	1	1	yes	characteristic
461	C₂×C₄²	C₂×#121	1	1	yes	characteristic
462	C₂×C₄²	C₂×#121	1	1	yes	characteristic
463	C₂×C₄²	C₂×#121	1	1	yes	characteristic
464	C₂×C₄²	C₂×#121	1	1	yes	characteristic
465	C₂×C₄²	C₂×#121	1	1	yes	characteristic
466	C₂×C₄²	C₂×#121	1	1	yes	characteristic
467	C₂×C₄²	C₂×#121	1	1	yes	characteristic
468	C₂×C₄²	C₂×#121	1	1	yes	characteristic
469	C₂×C₄²	#525	1	1	yes	characteristic
470	C₂×C₄²	#525	1	1	yes	characteristic
471	C₂×C₄²	#525	1	1	yes	characteristic
472	C₂×C₄²	#525	1	1	yes	characteristic
473	C₂×C₄²	#525	1	1	yes	characteristic
474	C₂×C₄²	#525	1	1	yes	characteristic
475	C₂×C₄²	#525	1	1	yes	characteristic
476	C₂×C₄²	#525	1	1	yes	characteristic
477	C₂×C₄²	C₂×#127	1	1	yes	characteristic
478	C₂×C₄²	C₂×#127	1	1	yes	characteristic
479	C₂×C₄²	C₂×#127	1	1	yes	characteristic
480	C₂×C₄²	C₂×#127	1	1	yes	characteristic
481	C₂×C₄²	#534	1	1	yes	characteristic
482	C₂×C₄²	#534	1	1	yes	characteristic
483	C₂×C₄²	#534	1	1	yes	characteristic
484	C₂×C₄²	#534	1	1	yes	characteristic
485	C₂×C₄²	#534	1	1	yes	characteristic
486	C₂×C₄²	#534	1	1	yes	characteristic
487	C₂×C₄²	#534	1	1	yes	characteristic
488	C₂×C₄²	#534	1	1	yes	characteristic
489	C₂×C₄²	#534	1	1	yes	characteristic
490	C₂×C₄²	#534	1	1	yes	characteristic
491	C₂×C₄²	#534	1	1	yes	characteristic
492	C₂×C₄²	#534	1	1	yes	characteristic
493	C₂×C₄²	#535	1	1	yes	characteristic
494	C₂×C₄²	#535	1	1	yes	characteristic
495	C₂×C₄²	#535	1	1	yes	characteristic
496	C₂×C₄²	#535	1	1	yes	characteristic
497	C₂×C₄²	#538	1	1	yes	characteristic
498	C₂×C₄²	#538	1	1	yes	characteristic
499	C₂×C₄²	#538	1	1	yes	characteristic
500	C₂×C₄²	#538	1	1	yes	characteristic
501	C₂×C₄²	#538	1	1	yes	characteristic
502	C₂×C₄²	#538	1	1	yes	characteristic
503	C₂×C₄²	#538	1	1	yes	characteristic
504	C₂×C₄²	#538	1	1	yes	characteristic
505	C₂×C₄²	D₄²	1	1	yes	characteristic
506	C₂×C₄²	D₄²	1	1	yes	characteristic
507	C₂×C₄²	D₄²	1	1	yes	characteristic
508	C₂×C₄²	D₄²	1	1	yes	characteristic
509	C₂×C₄²	D₄²	1	1	yes	characteristic
510	C₂×C₄²	D₄²	1	1	yes	characteristic
511	C₂×C₄²	D₄²	1	1	yes	characteristic
512	C₂×C₄²	D₄²	1	1	yes	characteristic
513	C₂×C₄²	D₄²	1	1	yes	characteristic
514	C₂×C₄²	D₄²	1	1	yes	characteristic
515	C₂×C₄²	D₄²	1	1	yes	characteristic
516	C₂×C₄²	D₄²	1	1	yes	characteristic
517	C₂×C₄²	D₄²	1	1	yes	characteristic
518	C₂×C₄²	D₄²	1	1	yes	characteristic
519	C₂×C₄²	D₄²	1	1	yes	characteristic
520	C₂×C₄²	D₄²	1	1	yes	characteristic
521	C₂×C₄²	#546	1	1	yes	characteristic
522	C₂×C₄²	#546	1	1	yes	characteristic
523	C₂×C₄²	#546	1	1	yes	characteristic
524	C₂×C₄²	#546	1	1	yes	characteristic
525	C₂×C₄²	#546	1	1	yes	characteristic
526	C₂×C₄²	#546	1	1	yes	characteristic
527	C₂×C₄²	#546	1	1	yes	characteristic
528	C₂×C₄²	#546	1	1	yes	characteristic
529	C₂×C₄²	#546	1	1	yes	characteristic
530	C₂×C₄²	#546	1	1	yes	characteristic
531	C₂×C₄²	#546	1	1	yes	characteristic
532	C₂×C₄²	#546	1	1	yes	characteristic
533	C₂×C₄²	#546	1	1	yes	characteristic
534	C₂×C₄²	#546	1	1	yes	characteristic
535	C₂×C₄²	#546	1	1	yes	characteristic
536	C₂×C₄²	#546	1	1	yes	characteristic
537	C₂×C₄²	#546	1	1	yes	characteristic
538	C₂×C₄²	#546	1	1	yes	characteristic
539	C₂×C₄²	#546	1	1	yes	characteristic
540	C₂×C₄²	#546	1	1	yes	characteristic
541	C₂×C₄²	#546	1	1	yes	characteristic
542	C₂×C₄²	#546	1	1	yes	characteristic
543	C₂×C₄²	#546	1	1	yes	characteristic
544	C₂×C₄²	#546	1	1	yes	characteristic
545	C₂×C₄²	#546	1	1	yes	characteristic
546	C₂×C₄²	#546	1	1	yes	characteristic
547	C₂×C₄²	#546	1	1	yes	characteristic
548	C₂×C₄²	#546	1	1	yes	characteristic
549	C₂×C₄²	#546	1	1	yes	characteristic
550	C₂×C₄²	#546	1	1	yes	characteristic
551	C₂×C₄²	#546	1	1	yes	characteristic
552	C₂×C₄²	#546	1	1	yes	characteristic
553	C₂⁴	C₂²×#120	1	1	yes	characteristic
554	C₂⁴	C₂²×#121	1	1	yes	characteristic
555	C₂⁴	C₂×#525	1	1	yes	characteristic
556	C₂⁴	C₂×D₄²	1	1	yes	characteristic
557	C₂⁴	C₂×D₄²	1	1	yes	characteristic
558	C₂⁴	C₂×D₄²	1	1	yes	characteristic
559	C₂⁴	C₂×D₄²	1	1	yes	characteristic
560	C₂×D₄	C₂×#392	1	8	yes	—
561	C₂²×C₄	#2403	1	1	yes	characteristic
562	C₂²×C₄	#2403	1	1	yes	characteristic
563	C₂²×C₄	#2403	1	1	yes	characteristic
564	C₂²×C₄	#2403	1	1	yes	characteristic
565	C₂²×C₄	#2403	1	1	yes	characteristic
566	C₂²×C₄	#2403	1	1	yes	characteristic
567	C₂²×C₄	#2403	1	1	yes	characteristic
568	C₂²×C₄	#2403	1	1	yes	characteristic
569	C₂²×C₄	#2410	1	1	yes	characteristic
570	C₂²×C₄	#2410	1	1	yes	characteristic
571	C₂²×C₄	#2410	1	1	yes	characteristic
572	C₂²×C₄	#2410	1	1	yes	characteristic
573	C₂²×C₄	#2410	1	1	yes	characteristic
574	C₂²×C₄	#2410	1	1	yes	characteristic
575	C₂²×C₄	#2410	1	1	yes	characteristic
576	C₂²×C₄	#2410	1	1	yes	characteristic
577	C₂²×C₄	#2410	1	1	yes	characteristic
578	C₂²×C₄	#2410	1	1	yes	characteristic
579	C₂²×C₄	#2410	1	1	yes	characteristic
580	C₂²×C₄	#2410	1	1	yes	characteristic
581	C₂²×C₄	#2410	1	1	yes	characteristic
582	C₂²×C₄	#2410	1	1	yes	characteristic
583	C₂²×C₄	#2410	1	1	yes	characteristic
584	C₂²×C₄	#2410	1	1	yes	characteristic
585	C₂²×C₄	#2424	1	1	yes	characteristic
586	C₂²×C₄	#2424	1	1	yes	characteristic
587	C₂²×C₄	#2424	1	1	yes	characteristic
588	C₂²×C₄	#2424	1	1	yes	characteristic
589	C₂²×C₄	#2424	1	1	yes	characteristic
590	C₂²×C₄	#2424	1	1	yes	characteristic
591	C₂²×C₄	#2424	1	1	yes	characteristic
592	C₂²×C₄	#2424	1	1	yes	characteristic
593	C₂²×C₄	#2424	1	1	yes	characteristic
594	C₂²×C₄	#2424	1	1	yes	characteristic
595	C₂²×C₄	#2424	1	1	yes	characteristic
596	C₂²×C₄	#2424	1	1	yes	characteristic
597	C₂²×C₄	#2424	1	1	yes	characteristic
598	C₂²×C₄	#2424	1	1	yes	characteristic
599	C₂²×C₄	#2424	1	1	yes	characteristic
600	C₂²×C₄	#2424	1	1	yes	characteristic
601	C₂²×C₄	#2433	1	1	yes	characteristic
602	C₂²×C₄	#2433	1	1	yes	characteristic
603	C₂²×C₄	#2433	1	1	yes	characteristic
604	C₂²×C₄	#2433	1	1	yes	characteristic
605	C₂²×C₄	#2433	1	1	yes	characteristic
606	C₂²×C₄	#2433	1	1	yes	characteristic
607	C₂²×C₄	#2433	1	1	yes	characteristic
608	C₂²×C₄	#2433	1	1	yes	characteristic
609	C₂²×C₄	#2847	1	1	yes	characteristic
610	C₂²×C₄	#2847	1	1	yes	characteristic
611	C₂²×C₄	#2847	1	1	yes	characteristic
612	C₂²×C₄	#2847	1	1	yes	characteristic
613	C₂²×C₄	#2847	1	1	yes	characteristic
614	C₂²×C₄	#2847	1	1	yes	characteristic
615	C₂²×C₄	#2847	1	1	yes	characteristic
616	C₂²×C₄	#2847	1	1	yes	characteristic
617	C₂²×C₄	C₂²×#120	1	1	yes	characteristic
618	C₂²×C₄	C₂²×#120	1	1	yes	characteristic
619	C₂²×C₄	C₂²×#120	1	1	yes	characteristic
620	C₂²×C₄	C₂²×#121	1	1	yes	characteristic
621	C₂²×C₄	C₂²×#121	1	1	yes	characteristic
622	C₂²×C₄	C₂²×#121	1	1	yes	characteristic
623	C₂²×C₄	C₂²×#121	1	1	yes	characteristic
624	C₂²×C₄	C₂×#525	1	1	yes	characteristic
625	C₂²×C₄	C₂×#525	1	1	yes	characteristic
626	C₂²×C₄	C₂²×#127	1	1	yes	characteristic
627	C₂²×C₄	C₂×#534	1	1	yes	characteristic
628	C₂²×C₄	C₂×#534	1	1	yes	characteristic
629	C₂²×C₄	C₂×#534	1	1	yes	characteristic
630	C₂²×C₄	C₂×#535	1	1	yes	characteristic
631	C₂²×C₄	C₂×#538	1	1	yes	characteristic
632	C₂²×C₄	C₂×#538	1	1	yes	characteristic
633	C₂²×C₄	C₂×D₄²	1	1	yes	characteristic
634	C₂²×C₄	C₂×D₄²	1	1	yes	characteristic
635	C₂²×C₄	C₂×D₄²	1	1	yes	characteristic
636	C₂²×C₄	C₂×D₄²	1	1	yes	characteristic
637	C₂²×C₄	C₂×#546	1	1	yes	characteristic
638	C₂²×C₄	C₂×#546	1	1	yes	characteristic
639	C₂²×C₄	C₂×#546	1	1	yes	characteristic
640	C₂²×C₄	C₂×#546	1	1	yes	characteristic
641	C₂²×C₄	C₂×#546	1	1	yes	characteristic
642	C₂²×C₄	C₂×#546	1	1	yes	characteristic
643	C₂²×C₄	C₂×#546	1	1	yes	characteristic
644	C₂²×C₄	C₂×#546	1	1	yes	characteristic
645	C₄⋊C₄	C₂×#392	1	8	yes	—
646	C₄²	C₂×#392	1	1	yes	characteristic
647	C₄²	C₂×#392	1	1	yes	characteristic
648	C₄²	C₂×#392	1	1	yes	characteristic
649	C₄²	C₂×#392	1	1	yes	characteristic
650	C₄²	C₂×#392	1	1	yes	characteristic
651	C₄²	C₂×#392	1	1	yes	characteristic
652	C₄²	C₂×#392	1	1	yes	characteristic
653	C₄²	C₂×#392	1	1	yes	characteristic
654	C₄²	#2404	1	1	yes	characteristic
655	C₄²	#2404	1	1	yes	characteristic
656	C₄²	#2404	1	1	yes	characteristic
657	C₄²	#2404	1	1	yes	characteristic
658	C₄²	#2404	1	1	yes	characteristic
659	C₄²	#2404	1	1	yes	characteristic
660	C₄²	#2404	1	1	yes	characteristic
661	C₄²	#2404	1	1	yes	characteristic
662	C₄²	#2410	1	1	yes	characteristic
663	C₄²	#2410	1	1	yes	characteristic
664	C₄²	#2410	1	1	yes	characteristic
665	C₄²	#2410	1	1	yes	characteristic
666	C₄²	#2410	1	1	yes	characteristic
667	C₄²	#2410	1	1	yes	characteristic
668	C₄²	#2410	1	1	yes	characteristic
669	C₄²	#2410	1	1	yes	characteristic
670	C₄²	#2410	1	1	yes	characteristic
671	C₄²	#2410	1	1	yes	characteristic
672	C₄²	#2410	1	1	yes	characteristic
673	C₄²	#2410	1	1	yes	characteristic
674	C₄²	#2410	1	1	yes	characteristic
675	C₄²	#2410	1	1	yes	characteristic
676	C₄²	#2410	1	1	yes	characteristic
677	C₄²	#2410	1	1	yes	characteristic
678	C₄²	#2424	1	1	yes	characteristic
679	C₄²	#2424	1	1	yes	characteristic
680	C₄²	#2424	1	1	yes	characteristic
681	C₄²	#2424	1	1	yes	characteristic
682	C₄²	#2424	1	1	yes	characteristic
683	C₄²	#2424	1	1	yes	characteristic
684	C₄²	#2424	1	1	yes	characteristic
685	C₄²	#2424	1	1	yes	characteristic
686	C₄²	#2424	1	1	yes	characteristic
687	C₄²	#2424	1	1	yes	characteristic
688	C₄²	#2424	1	1	yes	characteristic
689	C₄²	#2424	1	1	yes	characteristic
690	C₄²	#2424	1	1	yes	characteristic
691	C₄²	#2424	1	1	yes	characteristic
692	C₄²	#2424	1	1	yes	characteristic
693	C₄²	#2424	1	1	yes	characteristic
694	C₄²	#2539	1	1	yes	characteristic
695	C₄²	#2539	1	1	yes	characteristic
696	C₄²	#2539	1	1	yes	characteristic
697	C₄²	#2539	1	1	yes	characteristic
698	C₄²	#2539	1	1	yes	characteristic
699	C₄²	#2539	1	1	yes	characteristic
700	C₄²	#2539	1	1	yes	characteristic
701	C₄²	#2539	1	1	yes	characteristic
702	C₄²	#2617	1	1	yes	characteristic
703	C₄²	#2617	1	1	yes	characteristic
704	C₄²	#2617	1	1	yes	characteristic
705	C₄²	#2617	1	1	yes	characteristic
706	C₄²	#2617	1	1	yes	characteristic
707	C₄²	#2617	1	1	yes	characteristic
708	C₄²	#2617	1	1	yes	characteristic
709	C₄²	#2617	1	1	yes	characteristic
710	C₂³	C₂×#2403	1	1	yes	characteristic
711	C₂³	C₂×#2410	1	1	yes	characteristic
712	C₂³	C₂×#2410	1	1	yes	characteristic
713	C₂³	C₂×#2424	1	1	yes	characteristic
714	C₂³	C₂×#2424	1	1	yes	characteristic
715	C₂³	C₂×#2433	1	1	yes	characteristic
716	C₂³	C₂×#2847	1	1	yes	characteristic
717	C₂×C₄	#14716	1	1	yes	characteristic
718	C₂×C₄	#14716	1	1	yes	characteristic
719	C₂×C₄	#14716	1	1	yes	characteristic
720	C₂×C₄	#14716	1	1	yes	characteristic
721	C₂×C₄	#14716	1	1	yes	characteristic
722	C₂×C₄	#14716	1	1	yes	characteristic
723	C₂×C₄	#14716	1	1	yes	characteristic
724	C₂×C₄	#14716	1	1	yes	characteristic
725	C₂×C₄	#14716	1	1	yes	characteristic
726	C₂×C₄	#14716	1	1	yes	characteristic
727	C₂×C₄	#14716	1	1	yes	characteristic
728	C₂×C₄	#14716	1	1	yes	characteristic
729	C₂×C₄	#14716	1	1	yes	characteristic
730	C₂×C₄	#14716	1	1	yes	characteristic
731	C₂×C₄	#14716	1	1	yes	characteristic
732	C₂×C₄	#14716	1	1	yes	characteristic
733	C₂×C₄	#23882	1	4	yes	—
734	C₂×C₄	C₂²×#392	1	1	yes	characteristic
735	C₂×C₄	C₂×#2617	1	1	yes	characteristic
736	C₂×C₄	C₂×#2410	1	1	yes	characteristic
737	C₂×C₄	C₂×#2410	1	1	yes	characteristic
738	C₂×C₄	C₂×#2424	1	1	yes	characteristic
739	C₂×C₄	C₂×#2424	1	1	yes	characteristic
740	C₂×C₄	C₂×#2404	1	1	yes	characteristic
741	C₂×C₄	C₂×#2539	1	1	yes	characteristic
742	C₂²	C₂×#14716	1	1	yes	characteristic
743	C₂²	C₂×#23882	1	2	yes	—
744	C₄	#394249	1	2	yes	—
745	C₄	#394249	1	2	yes	—
746	C₄	#394362	1	2	yes	—
747	C₄	#6451862	1	1	yes	characteristic
748	C₄	#6451862	1	1	yes	characteristic
749	C₂	C₂×#394249	1	1	yes	characteristic
750	C₂	C₂×#394362	1	1	yes	characteristic
751	C₂	#72311802	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²	C₂×#14716
commutator, Frattini, cosocle	C₂⁴×C₄	C₂⁵
LCS	G ▷ C₂⁴×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂² ◁ C₂³×C₄² ◁ G
LECS	G ▷ C₂⁴×C₄ ▷ C₂² ▷ C₁

Complements

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

N	H ≅ G/N	type
1. #72312840	C₂	semidirect
2. #72312757	C₂	semidirect
3. #72312383	C₂	semidirect
4. #72312264	C₂	semidirect
5. #72312211	C₂	semidirect
6. #72312178	C₂	semidirect
7. #72312134	C₂	semidirect
8. #72312125	C₂	semidirect
9. #72312073	C₂	semidirect
10. #72302906	C₂	semidirect
11. #72282320	C₂	semidirect
12. #72263904	C₂	semidirect
13. #72257774	C₂	semidirect
14. #72257772	C₂	semidirect
15. #72257705	C₂	semidirect
16. #72257631	C₂	semidirect
17. #72257408	C₂	semidirect
24. #7628578	C₂²	semidirect
28. #6508792	C₂²	semidirect
29. #6500360	C₂²	semidirect
31. #6375020	C₂²	semidirect
32. #6374676	C₂²	semidirect
35. #6374247	C₂²	semidirect
36. #6370997	C₂²	semidirect
37. #6370978	C₂²	semidirect
40. #6370937	C₂²	semidirect
48. #6343377	C₂²	semidirect
51. #234856	C₂²	semidirect
52. #234851	C₂²	semidirect
53. #233546	C₂²	semidirect
54. #233543	C₂²	semidirect
55. #202019	C₂²	semidirect
56. #202016	C₂²	semidirect
57. #199777	C₂²	semidirect
58. #181777	C₂²	semidirect
59. #181375	C₂²	semidirect
60. #181358	C₂²	semidirect
61. #181358	C₂²	semidirect
62. #181343	C₂²	semidirect
63. #181124	C₂²	semidirect
64. #181122	C₂²	semidirect
65. #181122	C₂²	semidirect
66. #116394	C₂²	semidirect
67. #116360	C₂²	semidirect
68. #115378	C₂²	semidirect
69. #115377	C₂²	semidirect
70. #114648	C₂²	semidirect
71. #114647	C₂²	semidirect
72. #114551	C₂²	semidirect
73. #112305	C₂²	semidirect
74. #107568	C₂²	semidirect
75. C₂×#3497	D₄	semidirect
76. C₂×#3496	D₄	semidirect
78. C₂×#3449	D₄	semidirect
84. C₂×#3227	D₄	semidirect
85. C₂×#3205	D₄	semidirect
88. C₂×#3112	D₄	semidirect
89. C₂×#3109	D₄	semidirect
90. C₂×#3109	D₄	semidirect
91. C₂×#3103	D₄	semidirect
92. C₂×#3100	D₄	semidirect
106. #34365	D₄	semidirect
107. #34364	D₄	semidirect
110. D₄×#117	D₄	semidirect
118. #21794	D₄	semidirect
123. #21212	D₄	semidirect
135. #17589	D₄	semidirect
136. #17583	D₄	semidirect
142. #17561	D₄	semidirect
143. #17544	D₄	semidirect

Maximal subgroups

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

subgroup	index
#72312840	2
#72312757	2
#72312383	2
#72312264	2
#72312211	2
#72312178	2
#72312134	2
#72312125	2
#72312073	2
#72302906	2
#72282320	2
#72263904	2
#72257774	2
#72257772	2
#72257705	2
#72257631	2
#72257408	2