Subgroups — #72313786

Order 8192.

Only the 1352 normal subgroups are shown; non-normal subgroups are omitted.

The subgroup lattice has 751 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#72313692	C₂	1	1	yes	maximal, characteristic, complemented
2	#72313501	C₂	1	2	yes	maximal, complemented
3	#72313398	C₂	1	1	yes	maximal, characteristic, complemented
4	#72313323	C₂	1	2	yes	maximal, complemented
5	#72313274	C₂	1	1	yes	maximal, characteristic, complemented
6	#72313030	C₂	1	2	yes	maximal, complemented
7	#72313018	C₂²	1	2	yes	complemented
8	#72312950	C₂	1	1	yes	maximal, characteristic, complemented
9	#72312813	C₂	1	2	yes	maximal, complemented
10	#72312718	C₂	1	2	yes	maximal, complemented
11	#72312661	C₂	1	2	yes	maximal, complemented
12	#72312643	C₂²	1	2	yes	complemented
13	#72312471	C₂	1	2	yes	maximal, complemented
14	#72312430	C₂²	1	2	yes	complemented
15	#72312388	C₂	1	2	yes	maximal, complemented
16	#72312360	C₂²	1	2	yes	complemented
17	#72312328	C₂²	1	2	yes	complemented
18	#72312279	C₂	1	2	yes	maximal, complemented
19	#72312258	C₂²	1	2	yes	complemented
20	#72312241	C₂²	1	2	yes	complemented
21	#72312226	C₂²	1	2	yes	complemented
22	#72312205	C₂²	1	2	yes	complemented
23	#72312179	C₂²	1	2	yes	complemented
24	#72310458	C₂	1	1	yes	maximal, characteristic, complemented
25	#72310419	C₂²	1	1	yes	characteristic, complemented
26	#72310409	C₂	1	2	yes	maximal, complemented
27	#72310395	C₂²	1	2	yes	complemented
28	#72310388	C₂²	1	2	yes	complemented
29	#72310388	C₂²	1	2	yes	complemented
30	#72310380	C₂²	1	2	yes	complemented
31	#72310377	C₂²	1	2	yes	complemented
32	#72310339	C₂²	1	2	yes	complemented
33	#72310337	C₂²	1	2	yes	complemented
34	#72310337	C₂²	1	2	yes	complemented
35	#72310295	C₂²	1	2	yes	complemented
36	#72309959	C₂	1	2	yes	maximal, complemented
37	#72309929	C₂²	1	2	yes	complemented
38	#72309804	C₂²	1	2	yes	complemented
39	#72309729	C₂²	1	2	yes	complemented
40	#72309645	C₂²	1	2	yes	complemented
41	#72309548	C₂²	1	2	yes	complemented
42	#72309519	C₂²	1	2	yes	complemented
43	#72309519	C₂²	1	2	yes	complemented
44	#72309519	C₂²	1	2	yes	complemented
45	#72309519	C₂²	1	2	yes	complemented
46	#72309519	C₂²	1	2	yes	complemented
47	#72309374	C₂²	1	2	yes	complemented
48	#72309310	C₂²	1	2	yes	complemented
49	#72266956	C₂	1	1	yes	maximal, characteristic, complemented
50	#72266943	C₂²	1	1	yes	characteristic, complemented
51	#72266881	C₂²	1	1	yes	characteristic, complemented
52	#72266839	C₂	1	2	yes	maximal, complemented
53	#72266836	C₂²	1	2	yes	complemented
54	#72266831	C₂²	1	2	yes	—
55	#72266831	C₂²	1	2	yes	complemented
56	#72266831	C₂²	1	2	yes	complemented
57	#72266831	C₂²	1	2	yes	complemented
58	#72266831	C₂²	1	2	yes	complemented
59	#72266830	D₄	1	8	yes	complemented
60	#72266073	C₂³	1	2	yes	complemented
61	#72265785	C₂²	1	1	yes	characteristic, complemented
62	#72264815	C₂²	1	2	yes	complemented
63	#72264815	C₂²	1	2	yes	complemented
64	#72264799	C₂²	1	2	yes	complemented
65	#72264799	C₂²	1	2	yes	complemented
66	#72264793	C₂²	1	2	yes	complemented
67	#72264784	C₂²	1	2	yes	complemented
68	#72262330	C₂²	1	2	yes	complemented
69	#72262328	C₂²	1	2	yes	complemented
70	#72259008	C₂³	1	2	yes	complemented
71	#72258993	C₂²	1	2	yes	complemented
72	#72258757	C₂²	1	2	yes	complemented
73	#72256245	C₂	1	1	yes	maximal, characteristic, complemented
74	#72251547	C₂²	1	2	yes	complemented
75	#72251494	C₂²	1	2	yes	complemented
76	#72251459	C₂²	1	1	yes	characteristic, complemented
77	#72251277	C₂²	1	1	yes	characteristic, complemented
78	#72251212	C₂²	1	2	yes	—
79	#72251212	C₂²	1	2	yes	—
80	#72251108	D₄	1	2	yes	complemented
81	#72251108	D₄	1	2	yes	complemented
82	#72251073	D₄	1	2	yes	complemented
83	#72251073	D₄	1	2	yes	complemented
84	#72251054	D₄	1	2	yes	complemented
85	#72251054	D₄	1	2	yes	complemented
86	#72240471	D₄	1	2	yes	complemented
87	#72240471	D₄	1	2	yes	complemented
88	#72238718	D₄	1	8	yes	complemented
89	#72238614	C₂²	1	1	yes	characteristic, complemented
90	#72238611	D₄	1	2	yes	complemented
91	#72238611	D₄	1	2	yes	complemented
92	#72238598	C₂²	1	1	yes	characteristic, complemented
93	#72238352	C₂²	1	2	yes	complemented
94	#72238347	C₂²	1	2	yes	complemented
95	#72238346	C₂²	1	2	yes	complemented
96	#72238345	C₂²	1	2	yes	complemented
97	#72238344	C₂²	1	2	yes	complemented
98	#72237907	C₂²	1	1	yes	characteristic, complemented
99	#72237903	D₄	1	2	yes	complemented
100	#72237903	D₄	1	2	yes	complemented
101	#72237854	C₂²	1	1	yes	characteristic, complemented
102	#72237628	C₂²	1	1	yes	characteristic
103	#72237627	D₄	1	2	yes	complemented
104	#72237618	D₄	1	1	yes	characteristic, complemented
105	#72237581	C₂²	1	2	yes	complemented
106	#72237400	C₂³	1	2	yes	complemented
107	#72237032	C₂²	1	1	yes	characteristic, complemented
108	#72237027	C₂²	1	1	yes	characteristic, complemented
109	#72234953	D₄	1	2	yes	complemented
110	#72234953	D₄	1	2	yes	complemented
111	#72234693	D₄	1	2	yes	complemented
112	#72234693	D₄	1	2	yes	complemented
113	#72234668	C₂³	1	1	yes	characteristic
114	#72234665	C₂²	1	1	yes	characteristic
115	#72234665	C₂²	1	1	yes	characteristic, complemented
116	#72234663	D₄	1	1	yes	characteristic, complemented
117	#72234663	C₂³	1	1	yes	characteristic, complemented
118	#72234661	C₂³	1	2	yes	—
119	#72234661	C₂³	1	2	yes	—
120	#72234661	C₂³	1	2	yes	complemented
121	#72234625	C₂³	1	1	yes	characteristic
122	#72234619	D₄	1	1	yes	characteristic, complemented
123	#72234619	D₄	1	1	yes	characteristic, complemented
124	#72234591	D₄	1	1	yes	characteristic, complemented
125	#72234591	D₄	1	1	yes	characteristic, complemented
126	#72232884	D₄	1	1	yes	characteristic, complemented
127	#72232884	C₂³	1	1	yes	characteristic, complemented
128	#72232592	D₄	1	1	yes	characteristic, complemented
129	#72225738	C₂²	1	1	yes	characteristic
130	#72225736	D₄	1	1	yes	characteristic, complemented
131	#72225735	D₄	1	1	yes	characteristic, complemented
132	#72225734	D₄	1	2	yes	complemented
133	#72225713	D₄	1	1	yes	characteristic, complemented
134	#72225713	C₂³	1	1	yes	characteristic
135	#72225710	C₂²	1	2	yes	complemented
136	#72225710	C₂²	1	2	yes	complemented
137	#72225664	C₂²	1	2	yes	complemented
138	#72225655	D₄	1	1	yes	characteristic, complemented
139	#72225655	D₄	1	1	yes	characteristic, complemented
140	#72225654	D₄	1	2	yes	complemented
141	#72225650	C₂³	1	2	yes	—
142	#72225650	C₂³	1	2	yes	—
143	#72225629	C₂²	1	1	yes	characteristic, complemented
144	#72225619	C₂³	1	2	yes	—
145	#72225619	C₂³	1	2	yes	—
146	#72225617	C₂³	1	2	yes	—
147	#72225617	C₂³	1	2	yes	—
148	C₂×#115348	C₂³	1	2	yes	—
149	C₂×#115348	C₂³	1	2	yes	complemented
150	#72224136	D₄	1	1	yes	characteristic, complemented
151	#72224136	C₂³	1	1	yes	characteristic
152	#72224136	C₂³	1	1	yes	characteristic
153	#72224136	C₂³	1	1	yes	characteristic
154	#72224136	C₂³	1	2	yes	—
155	#72224136	C₂³	1	2	yes	—
156	#72219455	C₂²	1	2	yes	complemented
157	#72219444	C₂²	1	2	yes	complemented
158	#72219418	C₂³	1	2	yes	complemented
159	#72219415	C₂³	1	2	yes	complemented
160	#72219414	C₂³	1	2	yes	complemented
161	#72219414	C₂³	1	2	yes	complemented
162	#72219311	C₂³	1	2	yes	complemented
163	#72219310	C₂³	1	2	yes	complemented
164	#72219309	C₂²	1	1	yes	characteristic, complemented
165	#72219301	C₂³	1	1	yes	characteristic, complemented
166	#72219300	C₂³	1	2	yes	—
167	#72219300	C₂³	1	2	yes	—
168	#72219300	C₂³	1	2	yes	complemented
169	#72219300	C₂³	1	2	yes	complemented
170	#72219299	C₂³	1	1	yes	characteristic, complemented
171	#72219257	C₂³	1	2	yes	complemented
172	#72219256	C₂²	1	2	yes	complemented
173	#72219251	C₂³	1	2	yes	complemented
174	#72219248	C₂³	1	2	yes	complemented
175	#72219247	C₂²	1	1	yes	characteristic, complemented
176	#72219243	C₂³	1	2	yes	—
177	#72219243	C₂³	1	2	yes	complemented
178	#72219243	C₂³	1	2	yes	complemented
179	#72219237	C₂³	1	2	yes	—
180	#72219237	C₂³	1	2	yes	complemented
181	#72219237	C₂³	1	2	yes	complemented
182	#72219229	C₂³	1	2	yes	complemented
183	#72219227	C₂³	1	1	yes	characteristic, complemented
184	C₂²×#8534	C₂³	1	2	yes	complemented
185	C₂²×#8534	C₂³	1	2	yes	complemented
186	C₂×#394058	C₂³	1	2	yes	—
187	C₂×#7670203	C₂³	1	1	yes	characteristic
188	#72218868	C₂²	1	2	yes	complemented
189	#72218518	C₂³	1	1	yes	characteristic, complemented
190	#72218393	C₂²	1	2	yes	complemented
191	#72218381	C₂³	1	2	yes	complemented
192	#72218381	C₂³	1	2	yes	complemented
193	#72218375	C₂³	1	1	yes	characteristic, complemented
194	#72218321	C₂²	1	2	yes	complemented
195	#72218313	C₂³	1	2	yes	complemented
196	#72218313	C₂³	1	2	yes	complemented
197	#72218306	C₂³	1	2	yes	complemented
198	#72218306	C₂³	1	2	yes	complemented
199	#72218291	C₂³	1	1	yes	characteristic, complemented
200	#72218133	C₂²	1	2	yes	complemented
201	#72218133	C₂²	1	2	yes	complemented
202	#72218069	C₂³	1	2	yes	—
203	#72218069	C₂³	1	2	yes	—
204	#72218069	C₂³	1	2	yes	complemented
205	#72218069	C₂³	1	2	yes	complemented
206	#72218069	C₂³	1	2	yes	complemented
207	#72218069	C₂³	1	2	yes	complemented
208	#72218057	C₂³	1	2	yes	—
209	#72218057	C₂³	1	2	yes	—
210	#72218057	C₂³	1	2	yes	complemented
211	#72218057	C₂³	1	2	yes	complemented
212	#72218057	C₂³	1	2	yes	complemented
213	#72218057	C₂³	1	2	yes	complemented
214	C₂²×#23900	C₂³	1	2	yes	complemented
215	#72217789	D₄	1	1	yes	characteristic, complemented
216	#72217699	D₄	1	2	yes	complemented
217	#72217511	D₄	1	1	yes	characteristic, complemented
218	#72217511	C₂³	1	1	yes	characteristic
219	#72217511	C₂³	1	1	yes	characteristic
220	#72216064	C₂³	1	1	yes	characteristic
221	#72216064	C₂³	1	1	yes	characteristic
222	#72215858	C₂³	1	2	yes	—
223	#72215179	C₂³	1	2	yes	complemented
224	#72213862	C₂³	1	2	yes	—
225	#72213862	C₂³	1	2	yes	—
226	#72213862	C₂³	1	2	yes	complemented
227	#72213862	C₂³	1	2	yes	complemented
228	#72210555	C₂³	1	2	yes	complemented
229	#72210511	C₂³	1	2	yes	—
230	#72210511	C₂³	1	2	yes	complemented
231	#72210511	C₂³	1	2	yes	complemented
232	#10586404	C₂×D₄	1	1	yes	characteristic
233	#10586404	C₂×D₄	1	1	yes	characteristic
234	#10586404	C₂×D₄	1	1	yes	characteristic, complemented
235	#10586404	C₂×D₄	1	2	yes	complemented
236	#10586404	C₂×D₄	1	2	yes	complemented
237	C₂×#62817	C₂×D₄	1	1	yes	characteristic
238	C₂×#62817	C₂×D₄	1	1	yes	characteristic
239	C₂×#62817	C₂×D₄	1	1	yes	characteristic, complemented
240	#10586066	C₂×D₄	1	1	yes	characteristic
241	#10586066	C₂×D₄	1	1	yes	characteristic
242	C₂²×#3484	C₂×D₄	1	1	yes	characteristic
243	C₂²×#3484	C₂⁴	1	1	yes	characteristic
244	C₂²×#3484	C₂⁴	1	2	yes	—
245	C₂⁴×#120	C₂×D₄	1	1	yes	characteristic
246	C₂⁴×#120	C₂⁴	1	1	yes	characteristic
247	C₂×#60399	C₂×D₄	1	2	yes	—
248	C₂×#60399	C₂×D₄	1	2	yes	—
249	#7642244	C₂×D₄	1	1	yes	characteristic
250	#7642244	C₂×D₄	1	1	yes	characteristic
251	#7642244	C₂×D₄	1	1	yes	characteristic
252	#7642244	C₂×D₄	1	1	yes	characteristic
253	#7641845	C₂×D₄	1	2	yes	—
254	#7641845	C₂×D₄	1	2	yes	—
255	C₂²×#2846	C₂×D₄	1	1	yes	characteristic
256	C₂²×#2846	C₂×D₄	1	2	yes	complemented
257	#7630939	C₂⁴	1	1	yes	characteristic
258	#7630939	C₂⁴	1	1	yes	characteristic
259	#7630939	C₂⁴	1	1	yes	characteristic
260	#7630939	C₂⁴	1	1	yes	characteristic
261	#7630939	C₂⁴	1	2	yes	—
262	C₂×#35390	C₂×D₄	1	1	yes	characteristic
263	C₂×#35348	C₂×D₄	1	1	yes	characteristic
264	C₂×#35348	C₂×D₄	1	1	yes	characteristic
265	C₂×#35346	C₂×D₄	1	1	yes	characteristic
266	C₂×#34981	C₂×D₄	1	1	yes	characteristic
267	C₂×#34981	C₂×D₄	1	1	yes	characteristic
268	C₂×#34980	C₂×D₄	1	1	yes	characteristic
269	C₂×#34980	C₂⁴	1	1	yes	characteristic
270	C₂×#34980	C₂⁴	1	2	yes	—
271	#7626202	C₂×D₄	1	1	yes	characteristic
272	#7626202	C₂×D₄	1	1	yes	characteristic
273	#7626202	C₂×D₄	1	1	yes	characteristic, complemented
274	C₂×#34198	C₂×D₄	1	1	yes	characteristic
275	C₂×#34198	C₂×D₄	1	1	yes	characteristic
276	#6629258	C₂×D₄	1	4	yes	complemented
277	#6628892	C₂×D₄	1	4	yes	complemented
278	#6628892	C₂×D₄	1	4	yes	complemented
279	#6628867	C₂×D₄	1	4	yes	complemented
280	#6499892	C₂×D₄	1	8	yes	—
281	#6440460	C₂×D₄	1	2	yes	—
282	#6440460	C₂×D₄	1	2	yes	—
283	#6440460	C₂×D₄	1	2	yes	—
284	#6440460	C₂×D₄	1	2	yes	—
285	#6440460	C₂×D₄	1	2	yes	complemented
286	#6440460	C₂×D₄	1	2	yes	complemented
287	C₂×#23895	C₂×D₄	1	2	yes	—
288	C₂×#23895	C₂×D₄	1	2	yes	—
289	C₂×#23895	C₂×D₄	1	2	yes	—
290	C₂×#23895	C₂×D₄	1	2	yes	—
291	C₂×#23895	C₂×D₄	1	2	yes	complemented
292	C₂×#23895	C₂×D₄	1	2	yes	complemented
293	#6437621	C₂×D₄	1	2	yes	—
294	#6437621	C₂×D₄	1	2	yes	—
295	#6437621	C₂×D₄	1	2	yes	—
296	#6437621	C₂×D₄	1	2	yes	—
297	#6437621	C₂×D₄	1	2	yes	—
298	#6437621	C₂×D₄	1	2	yes	—
299	#6437621	C₂×D₄	1	2	yes	complemented
300	#6437621	C₂×D₄	1	2	yes	complemented
301	C₂×#23900	C₂×D₄	1	2	yes	complemented
302	C₂×#23900	C₂×D₄	1	2	yes	complemented
303	#6431795	C₂×D₄	1	2	yes	—
304	#6431795	C₂×D₄	1	2	yes	—
305	#6431795	C₂×D₄	1	2	yes	—
306	#6431795	C₂×D₄	1	2	yes	—
307	#6374251	C₂×D₄	1	1	yes	characteristic, complemented
308	#6374210	C₂×D₄	1	1	yes	characteristic
309	#6374210	C₂×D₄	1	1	yes	characteristic
310	#6374210	C₂×D₄	1	1	yes	characteristic
311	#6374210	C₂×D₄	1	1	yes	characteristic
312	#6374210	C₂×D₄	1	2	yes	complemented
313	#6374210	C₂×D₄	1	2	yes	complemented
314	#6374210	C₂×D₄	1	2	yes	complemented
315	#6374210	C₂×D₄	1	2	yes	complemented
316	#6374210	C₂×D₄	1	2	yes	complemented
317	C₂×#21776	C₂×D₄	1	2	yes	complemented
318	C₂×#21776	C₂×D₄	1	2	yes	complemented
319	#6374128	C₂×D₄	1	1	yes	characteristic
320	#6374128	C₂×D₄	1	1	yes	characteristic
321	#6374128	C₂×D₄	1	1	yes	characteristic, complemented
322	#6374128	C₂×D₄	1	2	yes	complemented
323	#6374128	C₂×D₄	1	2	yes	complemented
324	#6374128	C₂×D₄	1	1	yes	characteristic, complemented
325	C₂×#21746	C₂×D₄	1	2	yes	—
326	C₂×#21746	C₂×D₄	1	2	yes	—
327	C₂×#21746	C₂×D₄	1	1	yes	characteristic, complemented
328	C₂×#21746	C₂×D₄	1	2	yes	complemented
329	C₂×#21746	C₂×D₄	1	1	yes	characteristic, complemented
330	#6371558	C₂×D₄	1	2	yes	—
331	#6371558	C₂×D₄	1	2	yes	—
332	#6371504	C₂×D₄	1	1	yes	characteristic
333	#6371504	C₂×D₄	1	1	yes	characteristic
334	#6371504	C₂×D₄	1	1	yes	characteristic
335	#6371504	C₂×D₄	1	1	yes	characteristic
336	C₂²×#1898	C₂×D₄	1	2	yes	complemented
337	#6370693	C₂×D₄	1	1	yes	characteristic
338	#6370693	C₂×D₄	1	1	yes	characteristic
339	C₂²×#1781	C₂⁴	1	2	yes	—
340	C₂²×#1781	C₂⁴	1	2	yes	—
341	C₂²×#1781	C₂⁴	1	2	yes	—
342	C₂×#14679	C₂×D₄	1	2	yes	complemented
343	C₂²×#1438	C₂⁴	1	2	yes	—
344	#392699	C₂×D₄	1	4	yes	complemented
345	#392696	C₂×D₄	1	4	yes	complemented
346	#392113	C₂⁴	1	2	yes	—
347	#392113	C₂⁴	1	2	yes	—
348	#392109	C₂⁴	1	2	yes	—
349	#392109	C₂⁴	1	2	yes	—
350	#392109	C₂⁴	1	2	yes	—
351	#382707	C₂×D₄	1	2	yes	complemented
352	#382544	C₂×D₄	1	2	yes	complemented
353	#382544	C₂×D₄	1	2	yes	complemented
354	#382434	C₂×D₄	1	2	yes	complemented
355	#382434	C₂×D₄	1	2	yes	complemented
356	#373637	C₂×D₄	1	2	yes	complemented
357	#373637	C₂×D₄	1	2	yes	complemented
358	#359811	C₂×D₄	1	2	yes	complemented
359	#359811	C₂×D₄	1	2	yes	complemented
360	#359549	C₂×D₄	1	2	yes	—
361	#359549	C₂×D₄	1	2	yes	—
362	#359549	C₂×D₄	1	2	yes	—
363	#359549	C₂×D₄	1	2	yes	—
364	#359549	C₂×D₄	1	2	yes	complemented
365	#359549	C₂×D₄	1	2	yes	complemented
366	#359549	C₂×D₄	1	2	yes	complemented
367	#359549	C₂×D₄	1	2	yes	complemented
368	#359501	C₂×D₄	1	2	yes	complemented
369	#359501	C₂×D₄	1	2	yes	complemented
370	#359442	C₂×D₄	1	2	yes	—
371	#359442	C₂×D₄	1	2	yes	—
372	#359442	C₂×D₄	1	2	yes	complemented
373	#359442	C₂×D₄	1	2	yes	complemented
374	#355913	C₂×D₄	1	2	yes	complemented
375	#355096	C₂×D₄	1	2	yes	complemented
376	#355096	C₂×D₄	1	2	yes	complemented
377	C₂×#10735	C₂×D₄	1	2	yes	complemented
378	#147569	C₂×D₄	1	8	yes	complemented
379	#147567	C₂×D₄	1	8	yes	complemented
380	#147567	C₂×D₄	1	8	yes	complemented
381	C₂⁸	C₂²×D₄	1	1	yes	characteristic
382	C₂×H(7,𝔽₂)	#120	1	1	yes	characteristic
383	C₂×H(7,𝔽₂)	#120	1	1	yes	characteristic
384	C₂³×H(5,𝔽₂)	C₂²×D₄	1	1	yes	characteristic
385	C₂³×H(5,𝔽₂)	C₂²×D₄	1	2	yes	complemented
386	C₂⁵×D₄	#120	1	1	yes	characteristic
387	C₂⁵×D₄	C₂⁵	1	1	yes	characteristic
388	#62862	#120	1	4	yes	—
389	#62842	#120	1	1	yes	characteristic
390	#62842	#120	1	1	yes	characteristic
391	#62842	#120	1	1	yes	characteristic
392	#62842	#120	1	1	yes	characteristic
393	C₂×#3484	C₂²×D₄	1	2	yes	—
394	C₂×#3484	C₂²×D₄	1	2	yes	—
395	C₂×#3484	C₂²×D₄	1	1	yes	characteristic
396	C₂×#3484	C₂²×D₄	1	1	yes	characteristic
397	C₂×#3484	C₂²×D₄	1	2	yes	—
398	C₂×#3484	C₂²×D₄	1	2	yes	—
399	C₂×#3484	C₂²×D₄	1	2	yes	—
400	C₂×#3484	C₂²×D₄	1	2	yes	—
401	C₂×#3484	C₂²×D₄	1	2	yes	—
402	C₂×#3484	C₂²×D₄	1	2	yes	—
403	C₂×#3484	C₂²×D₄	1	2	yes	—
404	C₂×#3484	C₂²×D₄	1	1	yes	characteristic
405	C₂×#3484	C₂²×D₄	1	2	yes	—
406	C₂×#3484	C₂²×D₄	1	1	yes	characteristic
407	C₂×#3484	C₂²×D₄	1	2	yes	—
408	C₂²×#534	#120	1	1	yes	characteristic
409	C₂²×#534	C₂²×D₄	1	2	yes	—
410	C₂²×#534	C₂²×D₄	1	2	yes	—
411	C₂²×#534	C₂²×D₄	1	1	yes	characteristic
412	C₂²×#534	C₂²×D₄	1	1	yes	characteristic
413	C₂²×#534	C₂²×D₄	1	1	yes	characteristic
414	C₂²×#534	C₂²×D₄	1	1	yes	characteristic
415	C₂³×#120	#120	1	1	yes	characteristic
416	C₂³×#120	#120	1	1	yes	characteristic
417	C₂³×#120	#120	1	1	yes	characteristic
418	C₂³×#120	#120	1	1	yes	characteristic
419	C₂³×#120	C₂²×D₄	1	2	yes	—
420	C₂³×#120	C₂²×D₄	1	1	yes	characteristic
421	C₂³×#120	C₂²×D₄	1	1	yes	characteristic
422	C₂³×#120	C₂²×D₄	1	1	yes	characteristic
423	C₂³×#120	C₂²×D₄	1	1	yes	characteristic
424	C₂³×#120	C₂²×D₄	1	1	yes	characteristic
425	C₂³×#120	C₂²×D₄	1	1	yes	characteristic
426	C₂³×#120	C₂²×D₄	1	1	yes	characteristic
427	#62652	#120	1	1	yes	characteristic
428	#62652	#120	1	1	yes	characteristic
429	C₂²×#518	#120	1	1	yes	characteristic
430	C₂²×#518	C₂²×D₄	1	1	yes	characteristic
431	C₂²×#518	C₂²×D₄	1	2	yes	complemented
432	C₂⁴×C₂²⋊C₄	#120	1	1	yes	characteristic
433	C₂⁴×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
434	C₂×#3026	#120	1	2	yes	—
435	C₂×#3026	#120	1	2	yes	—
436	C₂×#3026	#120	1	2	yes	—
437	C₂×#3026	#120	1	2	yes	—
438	C₂×#2883	#120	1	2	yes	—
439	C₂×#2883	#120	1	2	yes	—
440	C₂×#2883	#120	1	2	yes	—
441	C₂×#2883	#120	1	2	yes	—
442	C₂×#2883	#120	1	2	yes	—
443	C₂×#2883	#120	1	2	yes	—
444	C₂×#2883	#120	1	2	yes	—
445	C₂×#2883	#120	1	2	yes	—
446	#36614	H(5,𝔽₂)	1	2	yes	—
447	C₂×#2846	H(5,𝔽₂)	1	2	yes	—
448	#35222	C₂²×D₄	1	4	yes	—
449	#35222	H(5,𝔽₂)	1	2	yes	—
450	#34992	#120	1	2	yes	—
451	#34992	#120	1	2	yes	—
452	#34992	#120	1	2	yes	—
453	#34992	#120	1	2	yes	—
454	#34980	#120	1	2	yes	—
455	#34980	#120	1	2	yes	—
456	#34980	#120	1	2	yes	—
457	#34980	#120	1	2	yes	—
458	#34980	C₂²×D₄	1	4	yes	—
459	#34980	C₂²×D₄	1	4	yes	—
460	#34980	H(5,𝔽₂)	1	4	yes	—
461	#34980	H(5,𝔽₂)	1	2	yes	—
462	#34171	C₂²×D₄	1	1	yes	characteristic
463	#34171	C₂²×D₄	1	2	yes	—
464	#34171	C₂²×D₄	1	1	yes	characteristic
465	#34171	C₂²×D₄	1	2	yes	—
466	#34171	C₂²×D₄	1	2	yes	—
467	#34171	C₂²×D₄	1	2	yes	—
468	#34171	C₂²×D₄	1	2	yes	—
469	#34171	C₂²×D₄	1	1	yes	characteristic
470	#34171	C₂²×D₄	1	1	yes	characteristic
471	#34171	C₂²×D₄	1	2	yes	—
472	#34171	C₂²×D₄	1	2	yes	—
473	C₂×#2315	#120	1	1	yes	characteristic
474	C₂×#2315	#120	1	1	yes	characteristic
475	C₂×#2308	#120	1	1	yes	characteristic
476	C₂×#2308	#120	1	1	yes	characteristic
477	C₂×#2308	#120	1	1	yes	characteristic
478	C₂×#2308	C₂²×D₄	1	1	yes	characteristic
479	C₂×#2308	C₂²×D₄	1	1	yes	characteristic
480	C₂×#2308	C₂²×D₄	1	2	yes	—
481	C₂×#2308	C₂²×D₄	1	2	yes	—
482	C₂²×#379	#120	1	1	yes	characteristic
483	C₂²×#379	#120	1	1	yes	characteristic
484	C₂²×#379	C₂²×D₄	1	2	yes	—
485	C₂²×#379	C₂²×D₄	1	1	yes	characteristic
486	C₂²×#379	C₂²×D₄	1	2	yes	—
487	C₂²×#379	C₂²×D₄	1	2	yes	—
488	C₂×#2273	#120	1	1	yes	characteristic
489	#21750	#120	1	4	yes	—
490	#21749	#120	1	4	yes	—
491	#21749	#120	1	4	yes	—
492	C₂×#1913	#120	1	2	yes	—
493	C₂×#1913	#120	1	2	yes	—
494	C₂×#1913	#120	1	2	yes	—
495	C₂×#1913	#120	1	2	yes	—
496	C₂×#1913	#120	1	2	yes	—
497	C₂×#1913	#120	1	2	yes	—
498	C₂×#1913	#120	1	2	yes	—
499	C₂×#1913	#120	1	2	yes	—
500	C₂×#1898	#120	1	2	yes	—
501	C₂×#1898	#120	1	2	yes	—
502	C₂×#1898	#120	1	2	yes	—
503	C₂×#1898	#120	1	2	yes	—
504	C₂×#1898	#120	1	2	yes	—
505	C₂×#1898	#120	1	2	yes	—
506	C₂×#1898	#120	1	2	yes	—
507	C₂×#1898	#120	1	2	yes	—
508	#20960	#120	1	2	yes	—
509	#20960	#120	1	2	yes	—
510	#20960	#120	1	2	yes	—
511	#20960	#120	1	2	yes	—
512	C₂×#1783	C₂²×D₄	1	4	yes	complemented
513	C₂×#1781	C₂²×D₄	1	2	yes	—
514	C₂×#1781	C₂²×D₄	1	2	yes	—
515	C₂×#1781	C₂²×D₄	1	2	yes	—
516	C₂×#1781	C₂²×D₄	1	2	yes	—
517	C₂×#1781	C₂²×D₄	1	2	yes	—
518	C₂×#1781	C₂²×D₄	1	2	yes	—
519	C₂×#1781	C₂²×D₄	1	2	yes	—
520	C₂×#1781	C₂²×D₄	1	2	yes	—
521	C₂×#1781	C₂²×D₄	1	2	yes	—
522	C₂×#1781	C₂²×D₄	1	2	yes	—
523	C₂×#1781	C₂²×D₄	1	4	yes	complemented
524	C₂×#1781	C₂²×D₄	1	4	yes	complemented
525	#20354	#120	1	2	yes	—
526	#20354	#120	1	2	yes	—
527	#20354	#120	1	2	yes	—
528	#20354	#120	1	2	yes	—
529	C₂⁷	B(4,𝔽₂)	1	1	yes	characteristic, complemented
530	C₂⁷	C₂×#120	1	1	yes	characteristic
531	C₂⁷	C₂×#120	1	1	yes	characteristic
532	C₂⁷	C₂³×D₄	1	1	yes	characteristic
533	C₂⁷	C₂×H(5,𝔽₂)	1	1	yes	characteristic
534	C₂²×H(5,𝔽₂)	C₂×#120	1	1	yes	characteristic
535	C₂²×H(5,𝔽₂)	C₂×#120	1	1	yes	characteristic
536	C₂²×H(5,𝔽₂)	C₂×#120	1	1	yes	characteristic
537	C₂²×H(5,𝔽₂)	C₂×#120	1	1	yes	characteristic
538	C₂²×H(5,𝔽₂)	C₂×#120	1	1	yes	characteristic
539	C₂²×H(5,𝔽₂)	C₂×#120	1	1	yes	characteristic
540	C₂²×H(5,𝔽₂)	C₂×#120	1	1	yes	characteristic
541	C₂²×H(5,𝔽₂)	C₂×#120	1	2	yes	—
542	C₂²×H(5,𝔽₂)	C₂×#120	1	1	yes	characteristic
543	C₂⁴×D₄	B(4,𝔽₂)	1	1	yes	characteristic, complemented
544	C₂⁴×D₄	B(4,𝔽₂)	1	1	yes	characteristic, complemented
545	C₂⁴×D₄	C₂×#120	1	1	yes	characteristic
546	C₂⁴×D₄	C₂×#120	1	1	yes	characteristic
547	C₂⁴×D₄	C₂×#120	1	2	yes	—
548	C₂⁴×D₄	C₂×#120	1	1	yes	characteristic
549	C₂⁴×D₄	C₂³×D₄	1	1	yes	characteristic
550	C₂⁴×D₄	C₂³×D₄	1	2	yes	—
551	C₂⁴×D₄	C₂³×D₄	1	2	yes	—
552	C₂⁴×D₄	C₂³×D₄	1	1	yes	characteristic
553	C₂⁴×D₄	C₂³×D₄	1	2	yes	—
554	C₂⁴×D₄	C₂×H(5,𝔽₂)	1	1	yes	characteristic
555	C₂⁴×D₄	C₂×H(5,𝔽₂)	1	2	yes	—
556	C₂⁴×D₄	C₂×H(5,𝔽₂)	1	1	yes	characteristic
557	C₂⁵×C₄	B(4,𝔽₂)	1	1	yes	characteristic, complemented
558	C₂⁵×C₄	C₂×H(5,𝔽₂)	1	1	yes	characteristic
559	C₂×#535	C₂×#120	1	2	yes	—
560	C₂×#535	D₄²	1	4	yes	—
561	C₂×#534	B(4,𝔽₂)	1	2	yes	complemented
562	C₂×#534	B(4,𝔽₂)	1	2	yes	complemented
563	C₂×#534	C₂×#120	1	2	yes	—
564	C₂×#534	C₂×#120	1	2	yes	—
565	C₂×#534	C₂×#120	1	2	yes	—
566	C₂×#534	C₂×#120	1	2	yes	—
567	C₂×#534	C₂×#120	1	2	yes	—
568	C₂×#534	C₂×#120	1	2	yes	—
569	C₂×#534	#534	1	2	yes	—
570	C₂×#534	D₄²	1	4	yes	—
571	C₂×#534	D₄²	1	4	yes	—
572	C₂×#525	#534	1	2	yes	—
573	C₂×#525	D₄²	1	4	yes	—
574	C₂²×#120	C₂×#120	1	2	yes	—
575	C₂²×#120	C₂×#120	1	2	yes	—
576	C₂²×#120	C₂×#120	1	2	yes	—
577	C₂²×#120	C₂×#120	1	2	yes	—
578	C₂²×#120	#534	1	2	yes	—
579	C₂²×#120	D₄²	1	4	yes	—
580	C₂²×#120	D₄²	1	4	yes	—
581	C₂×#518	C₂×#120	1	2	yes	—
582	C₂×#518	C₂×#120	1	2	yes	—
583	C₂×#518	C₂×#120	1	1	yes	characteristic
584	C₂×#518	C₂×#120	1	2	yes	—
585	C₂×#518	C₂×#120	1	1	yes	characteristic
586	C₂×#518	C₂×#120	1	2	yes	—
587	C₂×#518	C₂×#120	1	2	yes	—
588	C₂×#518	C₂×#120	1	2	yes	—
589	C₂×#518	C₂×#120	1	1	yes	characteristic
590	C₂×#518	C₂×#120	1	1	yes	characteristic
591	C₂×#518	C₂×#120	1	2	yes	—
592	C₂×#518	C₂×#120	1	2	yes	—
593	C₂×#518	C₂×#120	1	2	yes	—
594	C₂³×C₂²⋊C₄	C₂×#120	1	1	yes	characteristic
595	C₂³×C₂²⋊C₄	C₂×#120	1	1	yes	characteristic
596	C₂³×C₂²⋊C₄	C₂×#120	1	1	yes	characteristic
597	C₂³×C₂²⋊C₄	C₂×#120	1	1	yes	characteristic
598	C₂³×C₂²⋊C₄	C₂×#120	1	1	yes	characteristic
599	C₂³×C₂²⋊C₄	C₂×#120	1	1	yes	characteristic
600	C₂³×C₂²⋊C₄	C₂×#120	1	1	yes	characteristic
601	C₂³×C₂²⋊C₄	C₂×#120	1	2	yes	—
602	C₂³×C₂²⋊C₄	C₂×#120	1	2	yes	—
603	C₂³×C₂²⋊C₄	C₂×#120	1	2	yes	—
604	C₂²×#99	C₂×#120	1	2	yes	—
605	C₂²×#99	C₂×#120	1	2	yes	—
606	C₂²×#99	C₂×#120	1	2	yes	—
607	C₂²×#99	C₂×#120	1	2	yes	—
608	#2849	B(4,𝔽₂)	1	4	yes	complemented
609	#2846	B(4,𝔽₂)	1	4	yes	complemented
610	#2309	C₂×#120	1	2	yes	—
611	#2309	D₄²	1	4	yes	—
612	#2308	C₂×#120	1	2	yes	—
613	#2308	C₂×#120	1	2	yes	—
614	#2308	#534	1	2	yes	—
615	#2308	D₄²	1	4	yes	—
616	#2308	D₄²	1	4	yes	—
617	#2280	#534	1	2	yes	—
618	#2280	D₄²	1	4	yes	—
619	C₂×#379	C₂×#120	1	2	yes	—
620	C₂×#379	C₂×#120	1	2	yes	—
621	C₂×#379	C₂×#120	1	2	yes	—
622	C₂×#379	C₂×#120	1	2	yes	—
623	C₂×#379	#534	1	2	yes	—
624	C₂×#379	D₄²	1	4	yes	—
625	C₂×#379	D₄²	1	4	yes	—
626	C₂⁶	C₂×B(4,𝔽₂)	1	1	yes	characteristic
627	C₂⁶	C₂×B(4,𝔽₂)	1	1	yes	characteristic
628	C₂⁶	C₂×B(4,𝔽₂)	1	1	yes	characteristic
629	C₂⁶	C₂×B(4,𝔽₂)	1	2	yes	—
630	C₂⁶	C₂×B(4,𝔽₂)	1	1	yes	characteristic
631	C₂⁶	#3026	1	1	yes	characteristic
632	C₂⁶	C₂²×#120	1	1	yes	characteristic
633	C₂⁶	C₂²×#120	1	2	yes	—
634	C₂⁶	C₂×#534	1	1	yes	characteristic
635	C₂⁶	C₂×D₄²	1	2	yes	—
636	C₂⁶	C₂×D₄²	1	2	yes	—
637	C₂⁶	#3484	1	1	yes	characteristic
638	C₂⁶	#3484	1	2	yes	—
639	C₂⁶	#3484	1	1	yes	characteristic
640	C₂⁶	#3484	1	1	yes	characteristic
641	C₂²×#41	#2403	1	2	yes	—
642	C₂³×D₄	#2403	1	2	yes	—
643	C₂³×D₄	#2403	1	2	yes	—
644	C₂³×D₄	#2846	1	1	yes	characteristic
645	C₂³×D₄	#2846	1	1	yes	characteristic
646	C₂³×D₄	#2846	1	1	yes	characteristic
647	C₂³×D₄	#2846	1	1	yes	characteristic
648	C₂³×D₄	C₂×B(4,𝔽₂)	1	2	yes	—
649	C₂³×D₄	C₂×B(4,𝔽₂)	1	1	yes	characteristic
650	C₂³×D₄	C₂×B(4,𝔽₂)	1	1	yes	characteristic
651	C₂³×D₄	#3026	1	1	yes	characteristic
652	C₂³×D₄	#3026	1	1	yes	characteristic
653	C₂³×D₄	C₂²×#120	1	1	yes	characteristic
654	C₂³×D₄	C₂²×#120	1	1	yes	characteristic
655	C₂³×D₄	C₂²×#120	1	1	yes	characteristic
656	C₂³×D₄	C₂²×#120	1	2	yes	—
657	C₂³×D₄	C₂×#534	1	1	yes	characteristic
658	C₂³×D₄	C₂×D₄²	1	2	yes	—
659	C₂³×D₄	C₂×D₄²	1	2	yes	—
660	C₂³×D₄	C₂×D₄²	1	2	yes	—
661	C₂³×D₄	#3484	1	2	yes	—
662	C₂³×D₄	#3484	1	2	yes	—
663	C₂⁴×C₄	C₂×B(4,𝔽₂)	1	1	yes	characteristic
664	C₂⁴×C₄	C₂×B(4,𝔽₂)	1	1	yes	characteristic
665	C₂⁴×C₄	C₂×B(4,𝔽₂)	1	2	yes	—
666	C₂⁴×C₄	#3026	1	1	yes	characteristic
667	C₂⁴×C₄	C₂×#534	1	1	yes	characteristic
668	C₂⁴×C₄	C₂×D₄²	1	2	yes	—
669	C₂⁴×C₄	#3484	1	2	yes	—
670	C₂⁴×C₄	#3484	1	1	yes	characteristic
671	C₂×#120	C₂×B(4,𝔽₂)	1	4	yes	—
672	C₂×#120	#3026	1	4	yes	—
673	C₂×#117	#2403	1	4	yes	—
674	C₂×#117	#2403	1	2	yes	—
675	C₂²×C₂²⋊C₄	#2403	1	2	yes	—
676	C₂²×C₂²⋊C₄	#2403	1	2	yes	—
677	C₂²×C₂²⋊C₄	#2403	1	4	yes	—
678	C₂²×C₂²⋊C₄	#2403	1	2	yes	—
679	C₂²×C₂²⋊C₄	#2403	1	2	yes	—
680	C₂²×C₂²⋊C₄	#2846	1	2	yes	—
681	C₂²×C₂²⋊C₄	#2846	1	2	yes	—
682	C₂²×C₂²⋊C₄	C₂×B(4,𝔽₂)	1	2	yes	—
683	#379	C₂×B(4,𝔽₂)	1	4	yes	—
684	C₂⁵	#23895	1	2	yes	complemented
685	C₂⁵	#23900	1	2	yes	—
686	C₂⁵	#32898	1	1	yes	characteristic
687	C₂⁵	#32898	1	1	yes	characteristic
688	C₂⁵	#32898	1	1	yes	characteristic
689	C₂⁵	#32898	1	1	yes	characteristic
690	C₂⁵	C₂×#2403	1	1	yes	characteristic
691	C₂⁵	C₂×#2403	1	1	yes	characteristic
692	C₂⁵	#34980	1	1	yes	characteristic
693	C₂⁵	#34980	1	1	yes	characteristic
694	C₂⁵	D₄×#120	1	2	yes	—
695	C₂⁵	D₄×#120	1	2	yes	—
696	C₂⁵	D₄×#120	1	2	yes	—
697	C₂⁵	C₂×#2846	1	1	yes	characteristic
698	C₂⁵	C₂²×B(4,𝔽₂)	1	1	yes	characteristic
699	C₂⁵	C₂²×B(4,𝔽₂)	1	1	yes	characteristic
700	C₂⁵	C₂²×B(4,𝔽₂)	1	2	yes	—
701	C₂⁵	C₂×#3026	1	1	yes	characteristic
702	C₂⁵	C₂×#3026	1	1	yes	characteristic
703	C₂⁵	C₂×#3026	1	2	yes	—
704	C₂⁵	#60399	1	2	yes	—
705	C₂⁵	#60399	1	2	yes	—
706	C₂²×Q₈	#23895	1	2	yes	complemented
707	C₂²×D₄	#23895	1	2	yes	complemented
708	C₂²×D₄	#32898	1	4	yes	—
709	C₂³×C₄	#23895	1	2	yes	complemented
710	C₂³×C₄	#23900	1	2	yes	—
711	C₂³×C₄	#32898	1	1	yes	characteristic
712	C₂³×C₄	#32898	1	1	yes	characteristic
713	C₂³×C₄	#32898	1	1	yes	characteristic
714	C₂³×C₄	#32898	1	1	yes	characteristic
715	C₂³×C₄	C₂×#2403	1	1	yes	characteristic
716	C₂³×C₄	#34980	1	1	yes	characteristic
717	C₂³×C₄	D₄×#120	1	2	yes	—
718	C₂×C₂²⋊C₄	#32898	1	4	yes	—
719	C₂⁴	#347042	1	2	yes	—
720	C₂⁴	#612424	1	1	yes	characteristic
721	C₂⁴	C₂×#23900	1	1	yes	characteristic
722	C₂⁴	#6437621	1	1	yes	characteristic
723	C₂⁴	C₂×#23895	1	2	yes	—
724	C₂⁴	#6470225	1	1	yes	characteristic
725	C₂⁴	#6470225	1	1	yes	characteristic
726	C₂⁴	D₄×B(4,𝔽₂)	1	2	yes	—
727	C₂⁴	D₄×B(4,𝔽₂)	1	2	yes	—
728	C₂⁴	#6573715	1	2	yes	—
729	C₂⁴	#6573715	1	2	yes	—
730	C₂⁴	C₂×#32898	1	1	yes	characteristic
731	C₂⁴	C₂×#32898	1	2	yes	—
732	C₂⁴	C₂×#32898	1	1	yes	characteristic
733	C₂⁴	#6628896	1	2	yes	—
734	C₂²×C₄	#347042	1	2	yes	—
735	C₂²×C₄	C₂×#23895	1	2	yes	—
736	C₂³	#72213862	1	1	yes	characteristic
737	C₂³	#72213862	1	1	yes	characteristic
738	C₂³	C₂×#347042	1	1	yes	characteristic
739	C₂³	#72214832	1	1	yes	characteristic
740	C₂³	#72216323	1	2	yes	—
741	C₂³	#72225691	1	2	yes	—
742	C₂³	#72225712	1	1	yes	characteristic
743	C₂³	#72234172	1	2	yes	—
744	C₂²	#72225721	1	1	yes	characteristic
745	C₂²	#72234600	1	1	yes	characteristic
746	C₂²	#72258525	1	1	yes	characteristic
747	C₂²	#72265263	1	2	yes	—
748	C₂²	#72265263	1	2	yes	—
749	C₂	#72266145	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂	#72266145
commutator, Frattini, cosocle	C₂⁵×D₄	C₂⁵
LCS	G ▷ C₂⁵×D₄ ▷ C₂⁴ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂ ◁ C₂⁴ ◁ C₂⁵×D₄ ◁ G
LECS	G ▷ C₂⁵×D₄ ▷ C₂⁴ ▷ C₂ ▷ C₁

Complements

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

N	H ≅ G/N	type
1. #72313692	C₂	semidirect
2. #72313501	C₂	semidirect
3. #72313398	C₂	semidirect
4. #72313323	C₂	semidirect
5. #72313274	C₂	semidirect
6. #72313030	C₂	semidirect
7. #72313018	C₂²	semidirect
8. #72312950	C₂	semidirect
9. #72312813	C₂	semidirect
10. #72312718	C₂	semidirect
11. #72312661	C₂	semidirect
12. #72312643	C₂²	semidirect
13. #72312471	C₂	semidirect
14. #72312430	C₂²	semidirect
15. #72312388	C₂	semidirect
16. #72312360	C₂²	semidirect
17. #72312328	C₂²	semidirect
18. #72312279	C₂	semidirect
19. #72312258	C₂²	semidirect
20. #72312241	C₂²	semidirect
21. #72312226	C₂²	semidirect
22. #72312205	C₂²	semidirect
23. #72312179	C₂²	semidirect
24. #72310458	C₂	semidirect
25. #72310419	C₂²	semidirect
26. #72310409	C₂	semidirect
27. #72310395	C₂²	semidirect
28. #72310388	C₂²	semidirect
29. #72310388	C₂²	semidirect
30. #72310380	C₂²	semidirect
31. #72310377	C₂²	semidirect
32. #72310339	C₂²	semidirect
33. #72310337	C₂²	semidirect
34. #72310337	C₂²	semidirect
35. #72310295	C₂²	semidirect
36. #72309959	C₂	semidirect
37. #72309929	C₂²	semidirect
38. #72309804	C₂²	semidirect
39. #72309729	C₂²	semidirect
40. #72309645	C₂²	semidirect
41. #72309548	C₂²	semidirect
42. #72309519	C₂²	semidirect
43. #72309519	C₂²	semidirect
44. #72309519	C₂²	semidirect
45. #72309519	C₂²	semidirect
46. #72309519	C₂²	semidirect
47. #72309374	C₂²	semidirect
48. #72309310	C₂²	semidirect
49. #72266956	C₂	semidirect
50. #72266943	C₂²	semidirect
51. #72266881	C₂²	semidirect
52. #72266839	C₂	semidirect
53. #72266836	C₂²	semidirect
55. #72266831	C₂²	semidirect
56. #72266831	C₂²	semidirect
57. #72266831	C₂²	semidirect
58. #72266831	C₂²	semidirect
59. #72266830	D₄	semidirect
60. #72266073	C₂³	semidirect
61. #72265785	C₂²	semidirect
62. #72264815	C₂²	semidirect
63. #72264815	C₂²	semidirect
64. #72264799	C₂²	semidirect
65. #72264799	C₂²	semidirect
66. #72264793	C₂²	semidirect
67. #72264784	C₂²	semidirect
68. #72262330	C₂²	semidirect
69. #72262328	C₂²	semidirect
70. #72259008	C₂³	semidirect
71. #72258993	C₂²	semidirect
72. #72258757	C₂²	semidirect
73. #72256245	C₂	semidirect
74. #72251547	C₂²	semidirect
75. #72251494	C₂²	semidirect
76. #72251459	C₂²	semidirect
77. #72251277	C₂²	semidirect
80. #72251108	D₄	semidirect
81. #72251108	D₄	semidirect
82. #72251073	D₄	semidirect
83. #72251073	D₄	semidirect
84. #72251054	D₄	semidirect
85. #72251054	D₄	semidirect
86. #72240471	D₄	semidirect
87. #72240471	D₄	semidirect
88. #72238718	D₄	semidirect
89. #72238614	C₂²	semidirect
90. #72238611	D₄	semidirect
91. #72238611	D₄	semidirect
92. #72238598	C₂²	semidirect
93. #72238352	C₂²	semidirect
94. #72238347	C₂²	semidirect
95. #72238346	C₂²	semidirect
96. #72238345	C₂²	semidirect
97. #72238344	C₂²	semidirect
98. #72237907	C₂²	semidirect
99. #72237903	D₄	semidirect
100. #72237903	D₄	semidirect
101. #72237854	C₂²	semidirect
103. #72237627	D₄	semidirect
104. #72237618	D₄	semidirect
105. #72237581	C₂²	semidirect
106. #72237400	C₂³	semidirect
107. #72237032	C₂²	semidirect
108. #72237027	C₂²	semidirect
109. #72234953	D₄	semidirect
110. #72234953	D₄	semidirect
111. #72234693	D₄	semidirect
112. #72234693	D₄	semidirect
115. #72234665	C₂²	semidirect
116. #72234663	D₄	semidirect
117. #72234663	C₂³	semidirect
120. #72234661	C₂³	semidirect
122. #72234619	D₄	semidirect
123. #72234619	D₄	semidirect
124. #72234591	D₄	semidirect
125. #72234591	D₄	semidirect
126. #72232884	D₄	semidirect
127. #72232884	C₂³	semidirect
128. #72232592	D₄	semidirect
130. #72225736	D₄	semidirect
131. #72225735	D₄	semidirect
132. #72225734	D₄	semidirect
133. #72225713	D₄	semidirect
135. #72225710	C₂²	semidirect
136. #72225710	C₂²	semidirect
137. #72225664	C₂²	semidirect
138. #72225655	D₄	semidirect
139. #72225655	D₄	semidirect
140. #72225654	D₄	semidirect
143. #72225629	C₂²	semidirect
149. C₂×#115348	C₂³	semidirect
150. #72224136	D₄	semidirect
156. #72219455	C₂²	semidirect
157. #72219444	C₂²	semidirect
158. #72219418	C₂³	semidirect
159. #72219415	C₂³	semidirect
160. #72219414	C₂³	semidirect
161. #72219414	C₂³	semidirect
162. #72219311	C₂³	semidirect
163. #72219310	C₂³	semidirect
164. #72219309	C₂²	semidirect
165. #72219301	C₂³	semidirect
168. #72219300	C₂³	semidirect
169. #72219300	C₂³	semidirect
170. #72219299	C₂³	semidirect
171. #72219257	C₂³	semidirect
172. #72219256	C₂²	semidirect
173. #72219251	C₂³	semidirect
174. #72219248	C₂³	semidirect
175. #72219247	C₂²	semidirect
177. #72219243	C₂³	semidirect
178. #72219243	C₂³	semidirect
180. #72219237	C₂³	semidirect
181. #72219237	C₂³	semidirect
182. #72219229	C₂³	semidirect
183. #72219227	C₂³	semidirect
184. C₂²×#8534	C₂³	semidirect
185. C₂²×#8534	C₂³	semidirect
188. #72218868	C₂²	semidirect
189. #72218518	C₂³	semidirect
190. #72218393	C₂²	semidirect
191. #72218381	C₂³	semidirect
192. #72218381	C₂³	semidirect
193. #72218375	C₂³	semidirect
194. #72218321	C₂²	semidirect
195. #72218313	C₂³	semidirect
196. #72218313	C₂³	semidirect
197. #72218306	C₂³	semidirect
198. #72218306	C₂³	semidirect
199. #72218291	C₂³	semidirect
200. #72218133	C₂²	semidirect
201. #72218133	C₂²	semidirect
204. #72218069	C₂³	semidirect
205. #72218069	C₂³	semidirect
206. #72218069	C₂³	semidirect
207. #72218069	C₂³	semidirect
210. #72218057	C₂³	semidirect
211. #72218057	C₂³	semidirect
212. #72218057	C₂³	semidirect
213. #72218057	C₂³	semidirect
214. C₂²×#23900	C₂³	semidirect
215. #72217789	D₄	semidirect
216. #72217699	D₄	semidirect
217. #72217511	D₄	semidirect
223. #72215179	C₂³	semidirect
226. #72213862	C₂³	semidirect
227. #72213862	C₂³	semidirect
228. #72210555	C₂³	semidirect
230. #72210511	C₂³	semidirect
231. #72210511	C₂³	semidirect
234. #10586404	C₂×D₄	semidirect
235. #10586404	C₂×D₄	semidirect
236. #10586404	C₂×D₄	semidirect
239. C₂×#62817	C₂×D₄	semidirect
256. C₂²×#2846	C₂×D₄	semidirect
273. #7626202	C₂×D₄	semidirect
276. #6629258	C₂×D₄	semidirect
277. #6628892	C₂×D₄	semidirect
278. #6628892	C₂×D₄	semidirect
279. #6628867	C₂×D₄	semidirect
285. #6440460	C₂×D₄	semidirect
286. #6440460	C₂×D₄	semidirect
291. C₂×#23895	C₂×D₄	semidirect
292. C₂×#23895	C₂×D₄	semidirect
299. #6437621	C₂×D₄	semidirect
300. #6437621	C₂×D₄	semidirect
301. C₂×#23900	C₂×D₄	semidirect
302. C₂×#23900	C₂×D₄	semidirect
307. #6374251	C₂×D₄	semidirect
312. #6374210	C₂×D₄	semidirect
313. #6374210	C₂×D₄	semidirect
314. #6374210	C₂×D₄	semidirect
315. #6374210	C₂×D₄	semidirect
316. #6374210	C₂×D₄	semidirect
317. C₂×#21776	C₂×D₄	semidirect
318. C₂×#21776	C₂×D₄	semidirect
321. #6374128	C₂×D₄	semidirect
322. #6374128	C₂×D₄	semidirect
323. #6374128	C₂×D₄	semidirect
324. #6374128	C₂×D₄	semidirect
327. C₂×#21746	C₂×D₄	semidirect
328. C₂×#21746	C₂×D₄	semidirect
329. C₂×#21746	C₂×D₄	semidirect
336. C₂²×#1898	C₂×D₄	semidirect
342. C₂×#14679	C₂×D₄	semidirect
344. #392699	C₂×D₄	semidirect
345. #392696	C₂×D₄	semidirect
351. #382707	C₂×D₄	semidirect
352. #382544	C₂×D₄	semidirect
353. #382544	C₂×D₄	semidirect
354. #382434	C₂×D₄	semidirect
355. #382434	C₂×D₄	semidirect
356. #373637	C₂×D₄	semidirect
357. #373637	C₂×D₄	semidirect
358. #359811	C₂×D₄	semidirect
359. #359811	C₂×D₄	semidirect
364. #359549	C₂×D₄	semidirect
365. #359549	C₂×D₄	semidirect
366. #359549	C₂×D₄	semidirect
367. #359549	C₂×D₄	semidirect
368. #359501	C₂×D₄	semidirect
369. #359501	C₂×D₄	semidirect
372. #359442	C₂×D₄	semidirect
373. #359442	C₂×D₄	semidirect
374. #355913	C₂×D₄	semidirect
375. #355096	C₂×D₄	semidirect
376. #355096	C₂×D₄	semidirect
377. C₂×#10735	C₂×D₄	semidirect
378. #147569	C₂×D₄	semidirect
379. #147567	C₂×D₄	semidirect
380. #147567	C₂×D₄	semidirect
385. C₂³×H(5,𝔽₂)	C₂²×D₄	semidirect
431. C₂²×#518	C₂²×D₄	semidirect
512. C₂×#1783	C₂²×D₄	semidirect
523. C₂×#1781	C₂²×D₄	semidirect
524. C₂×#1781	C₂²×D₄	semidirect
529. C₂⁷	B(4,𝔽₂)	semidirect
543. C₂⁴×D₄	B(4,𝔽₂)	semidirect
544. C₂⁴×D₄	B(4,𝔽₂)	semidirect
557. C₂⁵×C₄	B(4,𝔽₂)	semidirect
561. C₂×#534	B(4,𝔽₂)	semidirect
562. C₂×#534	B(4,𝔽₂)	semidirect
608. #2849	B(4,𝔽₂)	semidirect
609. #2846	B(4,𝔽₂)	semidirect
684. C₂⁵	#23895	semidirect
706. C₂²×Q₈	#23895	semidirect
707. C₂²×D₄	#23895	semidirect
709. C₂³×C₄	#23895	semidirect

Maximal subgroups

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

subgroup	index
#72313692	2
#72313501	2
#72313398	2
#72313323	2
#72313274	2
#72313030	2
#72312950	2
#72312813	2
#72312718	2
#72312661	2
#72312471	2
#72312388	2
#72312279	2
#72310458	2
#72310409	2
#72309959	2
#72266956	2
#72266839	2
#72256245	2