Subgroups — #72312661

Order 4096.

Only the 1055 normal subgroups are shown; non-normal subgroups are omitted.

The subgroup lattice has 608 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#72312643	C₂	1	1	yes	maximal, characteristic, complemented
2	#72312604	C₂	1	2	yes	maximal, complemented
3	#72312569	C₂	1	2	yes	maximal, complemented
4	#72312555	C₂	1	2	yes	maximal, complemented
5	#72312545	C₂	1	2	yes	maximal, complemented
6	#72312531	C₂	1	2	yes	maximal, complemented
7	#72312516	C₂	1	2	yes	maximal, complemented
8	#72312503	C₂	1	2	yes	maximal, complemented
9	#72312489	C₂	1	2	yes	maximal, complemented
10	#72312328	C₂	1	1	yes	maximal, characteristic, complemented
11	#72312312	C₂²	1	2	yes	complemented
12	#72312226	C₂	1	1	yes	maximal, characteristic, complemented
13	#72312218	C₂²	1	2	yes	complemented
14	#72312216	C₂²	1	2	yes	complemented
15	#72312214	C₂²	1	2	yes	complemented
16	#72310377	C₂	1	1	yes	maximal, characteristic, complemented
17	#72310366	C₂²	1	2	yes	complemented
18	#72310358	C₂²	1	2	yes	complemented
19	#72309804	C₂	1	1	yes	maximal, characteristic, complemented
20	#72309800	C₂²	1	2	yes	complemented
21	#72309794	C₂²	1	2	yes	complemented
22	#72309794	C₂²	1	2	yes	complemented
23	#72266836	C₂	1	1	yes	maximal, characteristic, complemented
24	#72266835	C₂²	1	2	yes	—
25	#72266835	C₂²	1	2	yes	complemented
26	#72266834	C₂²	1	2	yes	complemented
27	#72266834	C₂²	1	2	yes	complemented
28	#72266831	C₂	1	1	yes	maximal, characteristic, complemented
29	#72266378	C₂²	1	2	yes	complemented
30	#72264815	C₂	1	1	yes	maximal, characteristic, complemented
31	#72264799	C₂	1	1	yes	maximal, characteristic, complemented
32	#72264770	C₂²	1	2	yes	complemented
33	#72263490	C₂²	1	2	yes	complemented
34	#72260584	C₂²	1	2	yes	complemented
35	#72259136	C₂²	1	2	yes	complemented
36	#72258368	C₂²	1	2	yes	complemented
37	C₂×#139739	C₂²	1	2	yes	complemented
38	C₂×#139742	C₂²	1	2	yes	complemented
39	#72256113	C₂²	1	2	yes	complemented
40	#72256052	C₂²	1	2	yes	complemented
41	#72256025	C₂²	1	2	yes	complemented
42	#72255971	C₂²	1	2	yes	complemented
43	#72255863	C₂²	1	2	yes	complemented
44	#72255830	C₂²	1	2	yes	complemented
45	#72255764	C₂²	1	2	yes	complemented
46	#72251547	C₂	1	1	yes	maximal, characteristic, complemented
47	#72251533	C₂²	1	2	yes	complemented
48	#72251530	C₂²	1	2	yes	complemented
49	#72251528	C₂²	1	2	yes	complemented
50	#72251527	C₂²	1	2	yes	complemented
51	#72251494	C₂	1	1	yes	maximal, characteristic, complemented
52	#72251485	C₂²	1	2	yes	complemented
53	#72251459	C₂	1	1	yes	maximal, characteristic, complemented
54	#72251422	C₂²	1	2	yes	complemented
55	#72251420	C₂²	1	2	yes	—
56	#72251212	C₂	1	1	yes	maximal, characteristic, complemented
57	#72251108	C₂²	1	1	yes	characteristic, complemented
58	#72251073	C₂²	1	1	yes	characteristic, complemented
59	#72251054	C₂²	1	1	yes	characteristic, complemented
60	#72246450	C₂²	1	2	yes	complemented
61	#72246292	C₂²	1	2	yes	complemented
62	#72246288	C₂²	1	2	yes	complemented
63	#72240471	C₂²	1	1	yes	characteristic, complemented
64	#72238611	C₂²	1	1	yes	characteristic, complemented
65	#72238347	C₂	1	1	yes	maximal, characteristic, complemented
66	#72238344	C₂	1	1	yes	maximal, characteristic, complemented
67	#72238343	C₂²	1	2	yes	complemented
68	#72238343	C₂²	1	2	yes	complemented
69	#72238342	C₂²	1	2	yes	—
70	#72238342	C₂²	1	2	yes	complemented
71	#72237903	C₂²	1	1	yes	characteristic, complemented
72	#72237635	C₂²	1	2	yes	complemented
73	#72237634	C₂²	1	2	yes	complemented
74	#72237467	C₂²	1	2	yes	complemented
75	#72237400	C₂²	1	1	yes	characteristic, complemented
76	#72236678	C₂²	1	2	yes	complemented
77	#72236678	C₂²	1	2	yes	complemented
78	#72236674	C₂²	1	2	yes	complemented
79	#72236521	C₂²	1	2	yes	complemented
80	#72235130	C₂²	1	2	yes	complemented
81	#72234953	C₂²	1	1	yes	characteristic, complemented
82	#72234693	C₂²	1	1	yes	characteristic, complemented
83	#72234661	C₂²	1	1	yes	characteristic
84	#72234661	C₂²	1	1	yes	characteristic, complemented
85	#72234100	C₂²	1	2	yes	—
86	#72234100	C₂²	1	2	yes	complemented
87	#72232884	C₂²	1	1	yes	characteristic, complemented
88	#72225650	C₂²	1	1	yes	characteristic, complemented
89	#72225619	C₂²	1	1	yes	characteristic, complemented
90	#72225617	C₂²	1	1	yes	characteristic, complemented
91	#72224136	C₂²	1	1	yes	characteristic, complemented
92	#72219415	C₂²	1	1	yes	characteristic, complemented
93	#72219414	C₂²	1	1	yes	characteristic, complemented
94	#72219310	C₂²	1	1	yes	characteristic, complemented
95	#72219300	C₂²	1	1	yes	characteristic, complemented
96	#72219299	C₂²	1	1	yes	characteristic, complemented
97	#72219257	C₂²	1	1	yes	characteristic, complemented
98	#72219251	C₂²	1	1	yes	characteristic, complemented
99	#72219243	C₂²	1	1	yes	characteristic, complemented
100	#72219243	C₂²	1	1	yes	characteristic, complemented
101	#72219237	C₂²	1	1	yes	characteristic, complemented
102	C₂²×#8534	C₂²	1	1	yes	characteristic, complemented
103	C₂²×#8534	C₂²	1	1	yes	characteristic, complemented
104	#72219163	C₂²	1	2	yes	complemented
105	#72219159	C₂²	1	2	yes	complemented
106	#72218313	C₂²	1	1	yes	characteristic, complemented
107	#72218306	C₂²	1	1	yes	characteristic, complemented
108	#72218306	C₂²	1	1	yes	characteristic, complemented
109	C₂×#144364	C₂²	1	2	yes	complemented
110	#72218069	C₂²	1	1	yes	characteristic, complemented
111	#72218069	C₂²	1	1	yes	characteristic, complemented
112	C₂×#133839	C₂²	1	2	yes	complemented
113	#72218057	C₂²	1	1	yes	characteristic, complemented
114	#72216064	C₂²	1	1	yes	characteristic
115	#72213862	C₂²	1	1	yes	characteristic
116	#72213862	C₂²	1	1	yes	characteristic, complemented
117	#72210555	C₂²	1	1	yes	characteristic, complemented
118	#72210511	C₂²	1	1	yes	characteristic
119	#72210511	C₂²	1	1	yes	characteristic
120	#72210511	C₂²	1	1	yes	characteristic, complemented
121	#72210511	C₂²	1	1	yes	characteristic, complemented
122	#72210511	C₂²	1	1	yes	characteristic, complemented
123	#10586422	C₂³	1	2	yes	—
124	#10586422	C₂³	1	2	yes	—
125	#10586404	C₂³	1	1	yes	characteristic, complemented
126	#10586066	D₄	1	1	yes	characteristic, complemented
127	C₂²×#3484	C₂³	1	1	yes	characteristic
128	C₂²×#3484	C₂³	1	1	yes	characteristic
129	C₂²×#3484	C₂³	1	1	yes	characteristic
130	C₂×#60399	D₄	1	1	yes	characteristic, complemented
131	C₂×#60399	C₂³	1	1	yes	characteristic
132	#7641845	D₄	1	2	yes	complemented
133	#7630939	C₂³	1	1	yes	characteristic
134	#7630939	C₂³	1	1	yes	characteristic
135	#7630939	C₂³	1	1	yes	characteristic
136	C₂×#34980	C₂³	1	1	yes	characteristic
137	#6628867	D₄	1	2	yes	complemented
138	#6628867	D₄	1	2	yes	complemented
139	#6440460	D₄	1	2	yes	complemented
140	#6440460	C₂³	1	1	yes	characteristic
141	#6440460	C₂³	1	1	yes	characteristic
142	#6440460	C₂³	1	2	yes	—
143	#6440460	C₂³	1	1	yes	characteristic, complemented
144	C₂×#23895	D₄	1	2	yes	complemented
145	C₂×#23895	C₂³	1	1	yes	characteristic
146	C₂×#23895	C₂³	1	1	yes	characteristic
147	C₂×#23895	C₂³	1	2	yes	—
148	C₂×#23895	C₂³	1	1	yes	characteristic, complemented
149	#6437621	D₄	1	2	yes	complemented
150	#6437621	D₄	1	2	yes	complemented
151	#6437621	C₂³	1	1	yes	characteristic
152	#6437621	C₂³	1	2	yes	—
153	#6437621	C₂³	1	1	yes	characteristic
154	#6437621	C₂³	1	1	yes	characteristic, complemented
155	C₂×#23897	C₂³	1	2	yes	—
156	C₂×#23897	C₂³	1	2	yes	—
157	#6437445	C₂³	1	2	yes	—
158	#6437445	C₂³	1	2	yes	—
159	#6437445	C₂³	1	2	yes	—
160	#6431795	D₄	1	1	yes	characteristic, complemented
161	#6431795	D₄	1	1	yes	characteristic, complemented
162	#6431795	C₂³	1	1	yes	characteristic
163	#6431795	C₂³	1	1	yes	characteristic
164	#6374210	C₂³	1	1	yes	characteristic, complemented
165	#6374210	C₂³	1	1	yes	characteristic, complemented
166	C₂×#21778	C₂³	1	2	yes	—
167	C₂×#21776	C₂³	1	1	yes	characteristic, complemented
168	#6374128	C₂³	1	1	yes	characteristic, complemented
169	C₂×#21746	D₄	1	2	yes	complemented
170	#6371558	D₄	1	1	yes	characteristic, complemented
171	#6371558	C₂³	1	1	yes	characteristic
172	#6371504	D₄	1	1	yes	characteristic, complemented
173	#6371504	D₄	1	1	yes	characteristic, complemented
174	#6370693	D₄	1	1	yes	characteristic, complemented
175	C₂²×#1781	C₂³	1	1	yes	characteristic
176	C₂²×#1781	C₂³	1	1	yes	characteristic
177	#763514	C₂³	1	2	yes	—
178	#763333	C₂³	1	2	yes	—
179	C₂²×#1438	C₂³	1	1	yes	characteristic
180	#493879	C₂³	1	2	yes	complemented
181	C₂×#12707	C₂³	1	2	yes	complemented
182	C₂×#12705	C₂³	1	2	yes	—
183	C₂×#12705	C₂³	1	2	yes	—
184	C₂×#12705	C₂³	1	2	yes	—
185	C₂×#12705	C₂³	1	2	yes	—
186	C₂×#12705	C₂³	1	2	yes	complemented
187	C₂×#12705	C₂³	1	2	yes	complemented
188	#493370	C₂³	1	2	yes	—
189	#493370	C₂³	1	2	yes	—
190	#493357	C₂³	1	2	yes	complemented
191	#393988	D₄	1	4	yes	complemented
192	#393975	D₄	1	4	yes	complemented
193	#392696	D₄	1	2	yes	complemented
194	#392696	D₄	1	2	yes	complemented
195	#392113	C₂³	1	1	yes	characteristic
196	#392113	C₂³	1	1	yes	characteristic
197	#392113	C₂³	1	1	yes	characteristic
198	#392109	C₂³	1	1	yes	characteristic
199	#392109	C₂³	1	1	yes	characteristic
200	#382544	C₂³	1	1	yes	characteristic, complemented
201	#382436	C₂³	1	2	yes	—
202	#382434	C₂³	1	1	yes	characteristic, complemented
203	#373637	C₂³	1	1	yes	characteristic, complemented
204	#359811	C₂³	1	1	yes	characteristic, complemented
205	#359558	C₂³	1	2	yes	—
206	#359558	C₂³	1	2	yes	—
207	#359549	D₄	1	2	yes	complemented
208	#359549	C₂³	1	1	yes	characteristic
209	#359549	C₂³	1	1	yes	characteristic
210	#359549	C₂³	1	2	yes	—
211	#359549	C₂³	1	1	yes	characteristic, complemented
212	#359549	C₂³	1	1	yes	characteristic, complemented
213	#359509	C₂³	1	2	yes	—
214	#359509	C₂³	1	2	yes	—
215	#359509	C₂³	1	2	yes	—
216	#359442	D₄	1	2	yes	complemented
217	#359442	C₂³	1	1	yes	characteristic, complemented
218	#355096	C₂³	1	1	yes	characteristic, complemented
219	#347057	D₄	1	4	yes	complemented
220	#347056	D₄	1	4	yes	complemented
221	#347047	D₄	1	4	yes	complemented
222	#347045	D₄	1	4	yes	complemented
223	#190147	C₂³	1	2	yes	complemented
224	#188109	C₂³	1	2	yes	complemented
225	#188050	C₂³	1	2	yes	—
226	#188050	C₂³	1	2	yes	—
227	C₂×#8534	C₂³	1	2	yes	—
228	C₂×#8534	C₂³	1	2	yes	—
229	C₂×#8534	C₂³	1	2	yes	—
230	C₂×#8534	C₂³	1	2	yes	—
231	C₂×#8534	C₂³	1	2	yes	complemented
232	C₂×#8453	C₂³	1	2	yes	complemented
233	C₂×#8453	C₂³	1	2	yes	complemented
234	#146479	C₂³	1	2	yes	complemented
235	#146475	C₂³	1	2	yes	complemented
236	#146475	C₂³	1	2	yes	complemented
237	C₂×#7304	C₂³	1	2	yes	complemented
238	C₂×#7304	C₂³	1	2	yes	complemented
239	C₂×#7316	C₂³	1	2	yes	complemented
240	C₂×#7316	C₂³	1	2	yes	complemented
241	C₂×#7314	C₂³	1	2	yes	complemented
242	C₂×#7314	C₂³	1	2	yes	complemented
243	C₂×#7311	C₂³	1	2	yes	complemented
244	C₂×#7311	C₂³	1	2	yes	complemented
245	#108222	C₂³	1	2	yes	complemented
246	#107130	C₂³	1	2	yes	complemented
247	#107130	C₂³	1	2	yes	complemented
248	C₂×H(7,𝔽₂)	C₂×D₄	1	1	yes	characteristic
249	C₂³×H(5,𝔽₂)	C₂×D₄	1	1	yes	characteristic
250	C₂³×H(5,𝔽₂)	C₂×D₄	1	1	yes	characteristic, complemented
251	C₂³×H(5,𝔽₂)	C₂×D₄	1	1	yes	characteristic, complemented
252	C₂⁵×D₄	C₂⁴	1	1	yes	characteristic
253	#62842	C₂×D₄	1	1	yes	characteristic
254	#62842	C₂×D₄	1	1	yes	characteristic
255	#62832	C₂×D₄	1	4	yes	—
256	#62824	C₂×D₄	1	4	yes	—
257	C₂×#3484	C₂×D₄	1	2	yes	—
258	C₂×#3484	C₂×D₄	1	2	yes	—
259	C₂×#3484	C₂×D₄	1	1	yes	characteristic
260	C₂×#3484	C₂×D₄	1	1	yes	characteristic
261	C₂×#3484	C₂×D₄	1	1	yes	characteristic
262	C₂×#3484	C₂×D₄	1	1	yes	characteristic
263	C₂×#3484	C₂×D₄	1	1	yes	characteristic
264	C₂×#3484	C₂×D₄	1	1	yes	characteristic
265	C₂×#3484	C₂×D₄	1	1	yes	characteristic
266	C₂×#3484	C₂×D₄	1	1	yes	characteristic
267	C₂×#3484	C₂×D₄	1	2	yes	complemented
268	C₂×#3484	C₂⁴	1	1	yes	characteristic
269	C₂×#3484	C₂⁴	1	1	yes	characteristic
270	C₂×#3484	C₂⁴	1	1	yes	characteristic
271	C₂×#3484	C₂⁴	1	1	yes	characteristic
272	C₂×#3484	C₂⁴	1	1	yes	characteristic
273	C₂×#3484	C₂⁴	1	2	yes	—
274	C₂²×#535	C₂⁴	1	2	yes	—
275	C₂²×#534	C₂×D₄	1	2	yes	—
276	C₂²×#534	C₂×D₄	1	1	yes	characteristic
277	C₂²×#534	C₂⁴	1	1	yes	characteristic
278	C₂²×#525	C₂×D₄	1	2	yes	complemented
279	C₂³×#120	C₂×D₄	1	2	yes	—
280	C₂³×#120	C₂×D₄	1	1	yes	characteristic
281	#62652	C₂×D₄	1	1	yes	characteristic
282	C₂²×#518	C₂×D₄	1	1	yes	characteristic
283	C₂²×#518	C₂×D₄	1	1	yes	characteristic, complemented
284	C₂²×#518	C₂×D₄	1	1	yes	characteristic, complemented
285	C₂×#3026	C₂×D₄	1	2	yes	—
286	C₂×#3026	C₂×D₄	1	2	yes	—
287	C₂×#3019	C₂×D₄	1	4	yes	—
288	#60359	C₂×D₄	1	4	yes	—
289	C₂×#2883	C₂×D₄	1	1	yes	characteristic
290	C₂×#2883	C₂×D₄	1	1	yes	characteristic
291	C₂×#2883	C₂×D₄	1	1	yes	characteristic
292	C₂×#2883	C₂×D₄	1	1	yes	characteristic
293	C₂×#2883	C₂×D₄	1	1	yes	characteristic
294	C₂×#2883	C₂×D₄	1	1	yes	characteristic
295	C₂×#2883	C₂×D₄	1	1	yes	characteristic
296	C₂×#2883	C₂×D₄	1	1	yes	characteristic
297	#36614	C₂×D₄	1	2	yes	—
298	#35222	C₂×D₄	1	2	yes	—
299	#35222	C₂×D₄	1	2	yes	—
300	#35222	C₂×D₄	1	2	yes	—
301	#34992	C₂×D₄	1	2	yes	—
302	#34992	C₂×D₄	1	2	yes	—
303	#34980	C₂×D₄	1	2	yes	—
304	#34980	C₂×D₄	1	2	yes	—
305	#34171	C₂×D₄	1	1	yes	characteristic
306	#34171	C₂×D₄	1	1	yes	characteristic
307	#34171	C₂×D₄	1	1	yes	characteristic
308	#34171	C₂×D₄	1	1	yes	characteristic
309	#34171	C₂×D₄	1	1	yes	characteristic
310	#34171	C₂×D₄	1	1	yes	characteristic
311	#34171	C₂⁴	1	1	yes	characteristic
312	#34171	C₂⁴	1	1	yes	characteristic
313	#34171	C₂⁴	1	1	yes	characteristic
314	C₂×#2308	C₂×D₄	1	1	yes	characteristic
315	C₂×#2308	C₂⁴	1	1	yes	characteristic
316	C₂²×#379	C₂×D₄	1	1	yes	characteristic
317	C₂²×#379	C₂×D₄	1	2	yes	—
318	#23901	C₂×D₄	1	4	yes	—
319	#23901	C₂×D₄	1	4	yes	complemented
320	#23900	C₂×D₄	1	4	yes	—
321	#23900	C₂×D₄	1	4	yes	complemented
322	C₂×#1913	C₂×D₄	1	2	yes	—
323	C₂×#1913	C₂×D₄	1	2	yes	—
324	C₂×#1913	C₂×D₄	1	2	yes	—
325	C₂×#1913	C₂×D₄	1	2	yes	—
326	C₂×#1911	C₂×D₄	1	4	yes	—
327	C₂×#1898	C₂×D₄	1	2	yes	—
328	C₂×#1898	C₂×D₄	1	2	yes	—
329	C₂×#1898	C₂×D₄	1	2	yes	—
330	C₂×#1898	C₂×D₄	1	2	yes	—
331	#20979	C₂×D₄	1	4	yes	—
332	#20960	C₂×D₄	1	2	yes	—
333	#20960	C₂×D₄	1	2	yes	—
334	#20616	C₂×D₄	1	4	yes	complemented
335	#20605	C₂×D₄	1	4	yes	complemented
336	C₂×#1783	C₂×D₄	1	2	yes	complemented
337	C₂×#1783	C₂×D₄	1	2	yes	complemented
338	C₂×#1783	C₂×D₄	1	2	yes	complemented
339	C₂×#1783	C₂⁴	1	2	yes	—
340	C₂×#1783	C₂⁴	1	2	yes	—
341	C₂×#1783	C₂⁴	1	2	yes	—
342	C₂×#1781	C₂×D₄	1	2	yes	—
343	C₂×#1781	C₂×D₄	1	2	yes	—
344	C₂×#1781	C₂×D₄	1	2	yes	—
345	C₂×#1781	C₂⁴	1	2	yes	—
346	C₂×#1781	C₂⁴	1	1	yes	characteristic
347	C₂×#1781	C₂⁴	1	1	yes	characteristic
348	C₂×#1781	C₂⁴	1	1	yes	characteristic
349	C₂×#1781	C₂⁴	1	1	yes	characteristic
350	C₂×#1781	C₂⁴	1	2	yes	—
351	#20579	C₂×D₄	1	2	yes	complemented
352	#20354	C₂×D₄	1	1	yes	characteristic
353	#20354	C₂×D₄	1	1	yes	characteristic
354	#20354	C₂×D₄	1	1	yes	characteristic
355	#20354	C₂×D₄	1	1	yes	characteristic
356	#15262	C₂×D₄	1	2	yes	complemented
357	#15261	C₂×D₄	1	2	yes	complemented
358	#15259	C₂×D₄	1	2	yes	complemented
359	#15258	C₂×D₄	1	2	yes	complemented
360	C₂×#1438	C₂⁴	1	2	yes	—
361	#10740	C₂×D₄	1	4	yes	complemented
362	#10716	C₂×D₄	1	4	yes	complemented
363	#8546	C₂×D₄	1	4	yes	complemented
364	#8544	C₂×D₄	1	4	yes	complemented
365	#8534	C₂×D₄	1	4	yes	—
366	#8534	C₂×D₄	1	4	yes	—
367	#8534	C₂×D₄	1	4	yes	complemented
368	#8534	C₂×D₄	1	4	yes	complemented
369	C₂⁷	C₂²×D₄	1	1	yes	characteristic
370	C₂⁷	H(5,𝔽₂)	1	1	yes	characteristic
371	C₂²×H(5,𝔽₂)	#120	1	2	yes	—
372	C₂²×H(5,𝔽₂)	C₂²×D₄	1	1	yes	characteristic
373	C₂²×H(5,𝔽₂)	C₂²×D₄	1	1	yes	characteristic
374	C₂²×H(5,𝔽₂)	C₂²×D₄	1	1	yes	characteristic
375	C₂²×H(5,𝔽₂)	C₂²×D₄	1	1	yes	characteristic
376	C₂²×H(5,𝔽₂)	C₂²×D₄	1	1	yes	characteristic
377	C₂²×H(5,𝔽₂)	C₂²×D₄	1	2	yes	—
378	C₂³×#41	C₂²×D₄	1	2	yes	—
379	C₂⁴×D₄	#120	1	2	yes	—
380	C₂⁴×D₄	C₂²×D₄	1	1	yes	characteristic
381	C₂⁴×D₄	C₂²×D₄	1	1	yes	characteristic
382	C₂⁴×D₄	C₂²×D₄	1	1	yes	characteristic
383	C₂⁴×D₄	C₂²×D₄	1	1	yes	characteristic
384	C₂⁴×D₄	C₂²×D₄	1	1	yes	characteristic
385	C₂⁴×D₄	C₂²×D₄	1	1	yes	characteristic
386	C₂⁴×D₄	C₂²×D₄	1	1	yes	characteristic
387	C₂⁴×D₄	C₂²×D₄	1	1	yes	characteristic
388	C₂⁴×D₄	C₂²×D₄	1	1	yes	characteristic
389	C₂⁴×D₄	H(5,𝔽₂)	1	1	yes	characteristic
390	C₂⁴×D₄	H(5,𝔽₂)	1	1	yes	characteristic
391	C₂⁴×D₄	H(5,𝔽₂)	1	1	yes	characteristic
392	C₂⁴×D₄	C₂⁵	1	1	yes	characteristic
393	C₂⁵×C₄	C₂²×D₄	1	1	yes	characteristic
394	#3484	C₂²×D₄	1	4	yes	—
395	#3484	C₂²×D₄	1	4	yes	—
396	#3484	H(5,𝔽₂)	1	4	yes	—
397	#3484	H(5,𝔽₂)	1	4	yes	—
398	C₂×#535	#120	1	2	yes	—
399	C₂×#535	#120	1	2	yes	—
400	C₂×#535	C₂²×D₄	1	2	yes	—
401	C₂×#534	#120	1	2	yes	—
402	C₂×#534	#120	1	2	yes	—
403	C₂×#534	C₂²×D₄	1	2	yes	—
404	C₂×#534	C₂²×D₄	1	2	yes	—
405	C₂²×#127	C₂²×D₄	1	2	yes	—
406	C₂²×#127	H(5,𝔽₂)	1	2	yes	—
407	C₂²×#124	C₂²×D₄	1	2	yes	—
408	C₂²×#124	H(5,𝔽₂)	1	2	yes	—
409	C₂×#525	#120	1	2	yes	—
410	C₂×#525	#120	1	2	yes	—
411	C₂×#525	C₂²×D₄	1	2	yes	—
412	C₂²×#123	C₂²×D₄	1	2	yes	—
413	C₂²×#120	#120	1	2	yes	—
414	C₂²×#120	#120	1	2	yes	—
415	C₂²×#120	C₂²×D₄	1	2	yes	—
416	C₂²×#120	C₂²×D₄	1	2	yes	—
417	C₂²×#120	C₂²×D₄	1	2	yes	—
418	C₂×#518	#120	1	2	yes	—
419	C₂×#518	C₂²×D₄	1	1	yes	characteristic
420	C₂×#518	C₂²×D₄	1	1	yes	characteristic
421	C₂×#518	C₂²×D₄	1	1	yes	characteristic
422	C₂×#518	C₂²×D₄	1	1	yes	characteristic
423	C₂×#518	C₂²×D₄	1	1	yes	characteristic
424	C₂×#518	C₂²×D₄	1	2	yes	—
425	C₂×#518	C₂²×D₄	1	1	yes	characteristic
426	C₂×#518	C₂²×D₄	1	1	yes	characteristic
427	C₂×#518	C₂²×D₄	1	1	yes	characteristic
428	C₂×#518	C₂²×D₄	1	1	yes	characteristic
429	C₂×#518	C₂²×D₄	1	1	yes	characteristic
430	C₂×#518	C₂²×D₄	1	1	yes	characteristic
431	C₂²×#117	C₂²×D₄	1	2	yes	—
432	C₂³×C₂²⋊C₄	#120	1	2	yes	—
433	C₂³×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
434	C₂³×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
435	C₂³×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
436	C₂²×#100	C₂²×D₄	1	4	yes	—
437	C₂²×#99	C₂²×D₄	1	2	yes	—
438	C₂²×#99	C₂²×D₄	1	2	yes	—
439	C₂×#407	C₂²×D₄	1	4	yes	—
440	#2849	#120	1	4	yes	complemented
441	#2846	#120	1	4	yes	complemented
442	#2309	#120	1	2	yes	—
443	#2309	#120	1	2	yes	—
444	#2309	C₂²×D₄	1	2	yes	—
445	#2280	#120	1	2	yes	—
446	#2280	#120	1	2	yes	—
447	#2280	C₂²×D₄	1	2	yes	—
448	C₂×#379	C₂²×D₄	1	2	yes	—
449	C₂×#379	C₂²×D₄	1	2	yes	—
450	#1898	#120	1	8	yes	complemented
451	#1781	C₂²×D₄	1	4	yes	—
452	#1781	C₂²×D₄	1	4	yes	—
453	#1438	C₂²×D₄	1	2	yes	—
454	#1438	C₂²×D₄	1	2	yes	—
455	C₂⁶	B(4,𝔽₂)	1	2	yes	—
456	C₂⁶	C₂×#120	1	1	yes	characteristic
457	C₂⁶	C₂×#120	1	1	yes	characteristic
458	C₂⁶	C₂×#120	1	1	yes	characteristic
459	C₂⁶	#534	1	1	yes	characteristic
460	C₂⁶	#534	1	1	yes	characteristic
461	C₂⁶	D₄²	1	1	yes	characteristic
462	C₂⁶	D₄²	1	1	yes	characteristic
463	C₂⁶	D₄²	1	1	yes	characteristic
464	C₂⁶	D₄²	1	1	yes	characteristic
465	C₂⁶	D₄²	1	1	yes	characteristic
466	C₂⁶	D₄²	1	1	yes	characteristic
467	C₂⁶	D₄²	1	1	yes	characteristic
468	C₂⁶	C₂³×D₄	1	1	yes	characteristic
469	C₂⁶	C₂×H(5,𝔽₂)	1	1	yes	characteristic
470	C₂×H(5,𝔽₂)	D₄²	1	4	yes	—
471	C₂×H(5,𝔽₂)	D₄²	1	4	yes	—
472	C₂²×#41	C₂×#120	1	2	yes	—
473	C₂³×Q₈	D₄²	1	2	yes	—
474	C₂³×D₄	B(4,𝔽₂)	1	2	yes	—
475	C₂³×D₄	B(4,𝔽₂)	1	2	yes	—
476	C₂³×D₄	C₂×#120	1	1	yes	characteristic
477	C₂³×D₄	C₂×#120	1	1	yes	characteristic
478	C₂³×D₄	C₂×#120	1	1	yes	characteristic
479	C₂³×D₄	C₂×#120	1	1	yes	characteristic
480	C₂³×D₄	C₂×#120	1	2	yes	—
481	C₂³×D₄	C₂×#120	1	2	yes	—
482	C₂³×D₄	#534	1	1	yes	characteristic
483	C₂³×D₄	#534	1	1	yes	characteristic
484	C₂³×D₄	D₄²	1	1	yes	characteristic
485	C₂³×D₄	D₄²	1	1	yes	characteristic
486	C₂³×D₄	D₄²	1	1	yes	characteristic
487	C₂³×D₄	D₄²	1	1	yes	characteristic
488	C₂³×D₄	D₄²	1	2	yes	—
489	C₂³×D₄	D₄²	1	1	yes	characteristic
490	C₂³×D₄	D₄²	1	1	yes	characteristic
491	C₂³×D₄	C₂³×D₄	1	1	yes	characteristic
492	C₂³×D₄	C₂³×D₄	1	1	yes	characteristic
493	C₂³×D₄	C₂³×D₄	1	2	yes	—
494	C₂³×D₄	C₂³×D₄	1	1	yes	characteristic
495	C₂³×D₄	C₂×H(5,𝔽₂)	1	2	yes	—
496	C₂³×D₄	C₂×H(5,𝔽₂)	1	1	yes	characteristic
497	C₂³×D₄	C₂×H(5,𝔽₂)	1	2	yes	—
498	C₂³×D₄	C₂×H(5,𝔽₂)	1	2	yes	—
499	C₂⁴×C₄	B(4,𝔽₂)	1	2	yes	—
500	C₂⁴×C₄	C₂×#120	1	1	yes	characteristic
501	C₂⁴×C₄	C₂×#120	1	1	yes	characteristic
502	C₂⁴×C₄	C₂×#120	1	1	yes	characteristic
503	C₂⁴×C₄	D₄²	1	1	yes	characteristic
504	C₂⁴×C₄	D₄²	1	1	yes	characteristic
505	C₂⁴×C₄	D₄²	1	1	yes	characteristic
506	C₂⁴×C₄	C₂³×D₄	1	1	yes	characteristic
507	#534	D₄²	1	8	yes	—
508	C₂×#120	B(4,𝔽₂)	1	8	yes	—
509	C₂×#120	C₂×#120	1	4	yes	—
510	C₂×#120	#534	1	4	yes	—
511	#518	D₄²	1	4	yes	—
512	#518	D₄²	1	4	yes	—
513	C₂×#117	C₂×#120	1	2	yes	—
514	C₂×#117	C₂×#120	1	2	yes	—
515	C₂×#117	C₂×#120	1	2	yes	—
516	C₂²×C₂²⋊C₄	C₂×#120	1	2	yes	—
517	C₂²×C₂²⋊C₄	C₂×#120	1	2	yes	—
518	C₂²×C₂²⋊C₄	C₂×#120	1	2	yes	—
519	C₂²×C₄²	D₄²	1	2	yes	—
520	C₂²×C₄²	D₄²	1	2	yes	—
521	#379	C₂×#120	1	4	yes	—
522	C₂⁵	#2403	1	1	yes	characteristic
523	C₂⁵	#2403	1	1	yes	characteristic
524	C₂⁵	#2403	1	1	yes	characteristic
525	C₂⁵	#2403	1	1	yes	characteristic
526	C₂⁵	#2403	1	1	yes	characteristic
527	C₂⁵	#2403	1	1	yes	characteristic
528	C₂⁵	C₂×B(4,𝔽₂)	1	4	yes	—
529	C₂⁵	C₂×B(4,𝔽₂)	1	2	yes	—
530	C₂⁵	C₂×B(4,𝔽₂)	1	2	yes	—
531	C₂⁵	C₂×B(4,𝔽₂)	1	2	yes	—
532	C₂⁵	C₂×B(4,𝔽₂)	1	2	yes	—
533	C₂⁵	C₂²×#120	1	1	yes	characteristic
534	C₂⁵	C₂²×#120	1	1	yes	characteristic
535	C₂⁵	C₂×#534	1	1	yes	characteristic
536	C₂⁵	C₂×#534	1	1	yes	characteristic
537	C₂⁵	C₂×D₄²	1	1	yes	characteristic
538	C₂⁵	C₂×D₄²	1	1	yes	characteristic
539	C₂⁵	C₂×D₄²	1	1	yes	characteristic
540	C₂⁵	#3484	1	1	yes	characteristic
541	C₂⁵	#3484	1	1	yes	characteristic
542	C₂⁵	#3484	1	2	yes	—
543	C₂⁵	#3532	1	2	yes	—
544	C₂²×Q₈	#3026	1	2	yes	complemented
545	C₂²×D₄	#2403	1	4	yes	—
546	C₂²×D₄	C₂×B(4,𝔽₂)	1	4	yes	—
547	C₂²×D₄	#3026	1	2	yes	complemented
548	C₂²×D₄	C₂×D₄²	1	2	yes	—
549	C₂²×D₄	C₂×D₄²	1	2	yes	—
550	C₂²×D₄	C₂×D₄²	1	2	yes	—
551	C₂²×D₄	#3484	1	2	yes	—
552	C₂²×D₄	#3484	1	2	yes	—
553	C₂²×D₄	#3484	1	2	yes	—
554	C₂²×D₄	#3484	1	2	yes	—
555	C₂²×D₄	#3532	1	2	yes	—
556	C₂³×C₄	#2403	1	1	yes	characteristic
557	C₂³×C₄	#2403	1	1	yes	characteristic
558	C₂³×C₄	C₂×B(4,𝔽₂)	1	2	yes	—
559	C₂³×C₄	C₂×B(4,𝔽₂)	1	2	yes	—
560	C₂³×C₄	C₂²×#120	1	1	yes	characteristic
561	C₂³×C₄	C₂×D₄²	1	1	yes	characteristic
562	C₂³×C₄	C₂×D₄²	1	2	yes	—
563	C₂³×C₄	#3484	1	2	yes	—
564	C₂×C₂²⋊C₄	#2403	1	4	yes	—
565	C₂×C₂²⋊C₄	C₂×B(4,𝔽₂)	1	4	yes	—
566	C₂⁴	#23895	1	2	yes	—
567	C₂⁴	#23900	1	4	yes	—
568	C₂⁴	#23900	1	2	yes	—
569	C₂⁴	#23900	1	2	yes	—
570	C₂⁴	#23900	1	1	yes	characteristic
571	C₂⁴	#23900	1	1	yes	characteristic
572	C₂⁴	#23900	1	2	yes	—
573	C₂⁴	C₂×#2403	1	1	yes	characteristic
574	C₂⁴	C₂×#2403	1	1	yes	characteristic
575	C₂⁴	#35346	1	1	yes	characteristic
576	C₂⁴	D₄×#120	1	1	yes	characteristic
577	C₂⁴	D₄×#120	1	1	yes	characteristic
578	C₂⁴	#37644	1	1	yes	characteristic
579	C₂⁴	#37644	1	2	yes	—
580	C₂⁴	#37644	1	1	yes	characteristic
581	C₂⁴	#58990	1	2	yes	—
582	C₂⁴	C₂²×B(4,𝔽₂)	1	2	yes	—
583	C₂⁴	C₂²×B(4,𝔽₂)	1	2	yes	—
584	C₂²×C₄	#23900	1	4	yes	—
585	C₂²×C₄	D₄×#120	1	2	yes	—
586	C₂²×C₄	#58990	1	2	yes	—
587	C₂²×C₄	C₂×#3026	1	2	yes	—
588	C₂²×C₄	#60399	1	2	yes	—
589	C₂³	#647656	1	1	yes	characteristic
590	C₂³	C₂×#23900	1	1	yes	characteristic
591	C₂³	C₂×#23900	1	1	yes	characteristic
592	C₂³	C₂×#23900	1	2	yes	—
593	C₂³	#6437621	1	1	yes	characteristic
594	C₂³	C₂×#23895	1	1	yes	characteristic
595	C₂³	#6437629	1	1	yes	characteristic
596	C₂³	#6437632	1	1	yes	characteristic
597	C₂³	#6499867	1	2	yes	—
598	C₂×C₄	#6573715	1	4	yes	—
599	C₂²	#72217546	1	1	yes	characteristic
600	C₂²	#72225689	1	1	yes	characteristic
601	C₂²	#72233042	1	1	yes	characteristic
602	C₂²	#72233065	1	1	yes	characteristic
603	C₂²	#72233069	1	1	yes	characteristic
604	C₂²	#72236720	1	1	yes	characteristic
605	C₂²	#72237496	1	1	yes	characteristic
606	C₂	#72266019	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂	#72266019
commutator, Frattini, cosocle	C₂⁴×D₄	C₂⁵
LCS	G ▷ C₂⁴×D₄ ▷ C₂³ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂ ◁ C₂⁴ ◁ C₂⁵×D₄ ◁ G
LECS	G ▷ C₂⁴×D₄ ▷ C₂³ ▷ C₂ ▷ C₁

Complements

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

N	H ≅ G/N	type
1. #72312643	C₂	semidirect
2. #72312604	C₂	semidirect
3. #72312569	C₂	semidirect
4. #72312555	C₂	semidirect
5. #72312545	C₂	semidirect
6. #72312531	C₂	semidirect
7. #72312516	C₂	semidirect
8. #72312503	C₂	semidirect
9. #72312489	C₂	semidirect
10. #72312328	C₂	semidirect
11. #72312312	C₂²	semidirect
12. #72312226	C₂	semidirect
13. #72312218	C₂²	semidirect
14. #72312216	C₂²	semidirect
15. #72312214	C₂²	semidirect
16. #72310377	C₂	semidirect
17. #72310366	C₂²	semidirect
18. #72310358	C₂²	semidirect
19. #72309804	C₂	semidirect
20. #72309800	C₂²	semidirect
21. #72309794	C₂²	semidirect
22. #72309794	C₂²	semidirect
23. #72266836	C₂	semidirect
25. #72266835	C₂²	semidirect
26. #72266834	C₂²	semidirect
27. #72266834	C₂²	semidirect
28. #72266831	C₂	semidirect
29. #72266378	C₂²	semidirect
30. #72264815	C₂	semidirect
31. #72264799	C₂	semidirect
32. #72264770	C₂²	semidirect
33. #72263490	C₂²	semidirect
34. #72260584	C₂²	semidirect
35. #72259136	C₂²	semidirect
36. #72258368	C₂²	semidirect
37. C₂×#139739	C₂²	semidirect
38. C₂×#139742	C₂²	semidirect
39. #72256113	C₂²	semidirect
40. #72256052	C₂²	semidirect
41. #72256025	C₂²	semidirect
42. #72255971	C₂²	semidirect
43. #72255863	C₂²	semidirect
44. #72255830	C₂²	semidirect
45. #72255764	C₂²	semidirect
46. #72251547	C₂	semidirect
47. #72251533	C₂²	semidirect
48. #72251530	C₂²	semidirect
49. #72251528	C₂²	semidirect
50. #72251527	C₂²	semidirect
51. #72251494	C₂	semidirect
52. #72251485	C₂²	semidirect
53. #72251459	C₂	semidirect
54. #72251422	C₂²	semidirect
56. #72251212	C₂	semidirect
57. #72251108	C₂²	semidirect
58. #72251073	C₂²	semidirect
59. #72251054	C₂²	semidirect
60. #72246450	C₂²	semidirect
61. #72246292	C₂²	semidirect
62. #72246288	C₂²	semidirect
63. #72240471	C₂²	semidirect
64. #72238611	C₂²	semidirect
65. #72238347	C₂	semidirect
66. #72238344	C₂	semidirect
67. #72238343	C₂²	semidirect
68. #72238343	C₂²	semidirect
70. #72238342	C₂²	semidirect
71. #72237903	C₂²	semidirect
72. #72237635	C₂²	semidirect
73. #72237634	C₂²	semidirect
74. #72237467	C₂²	semidirect
75. #72237400	C₂²	semidirect
76. #72236678	C₂²	semidirect
77. #72236678	C₂²	semidirect
78. #72236674	C₂²	semidirect
79. #72236521	C₂²	semidirect
80. #72235130	C₂²	semidirect
81. #72234953	C₂²	semidirect
82. #72234693	C₂²	semidirect
84. #72234661	C₂²	semidirect
86. #72234100	C₂²	semidirect
87. #72232884	C₂²	semidirect
88. #72225650	C₂²	semidirect
89. #72225619	C₂²	semidirect
90. #72225617	C₂²	semidirect
91. #72224136	C₂²	semidirect
92. #72219415	C₂²	semidirect
93. #72219414	C₂²	semidirect
94. #72219310	C₂²	semidirect
95. #72219300	C₂²	semidirect
96. #72219299	C₂²	semidirect
97. #72219257	C₂²	semidirect
98. #72219251	C₂²	semidirect
99. #72219243	C₂²	semidirect
100. #72219243	C₂²	semidirect
101. #72219237	C₂²	semidirect
102. C₂²×#8534	C₂²	semidirect
103. C₂²×#8534	C₂²	semidirect
104. #72219163	C₂²	semidirect
105. #72219159	C₂²	semidirect
106. #72218313	C₂²	semidirect
107. #72218306	C₂²	semidirect
108. #72218306	C₂²	semidirect
109. C₂×#144364	C₂²	semidirect
110. #72218069	C₂²	semidirect
111. #72218069	C₂²	semidirect
112. C₂×#133839	C₂²	semidirect
113. #72218057	C₂²	semidirect
116. #72213862	C₂²	semidirect
117. #72210555	C₂²	semidirect
120. #72210511	C₂²	semidirect
121. #72210511	C₂²	semidirect
122. #72210511	C₂²	semidirect
125. #10586404	C₂³	semidirect
126. #10586066	D₄	semidirect
130. C₂×#60399	D₄	semidirect
132. #7641845	D₄	semidirect
137. #6628867	D₄	semidirect
138. #6628867	D₄	semidirect
139. #6440460	D₄	semidirect
143. #6440460	C₂³	semidirect
144. C₂×#23895	D₄	semidirect
148. C₂×#23895	C₂³	semidirect
149. #6437621	D₄	semidirect
150. #6437621	D₄	semidirect
154. #6437621	C₂³	semidirect
160. #6431795	D₄	semidirect
161. #6431795	D₄	semidirect
164. #6374210	C₂³	semidirect
165. #6374210	C₂³	semidirect
167. C₂×#21776	C₂³	semidirect
168. #6374128	C₂³	semidirect
169. C₂×#21746	D₄	semidirect
170. #6371558	D₄	semidirect
172. #6371504	D₄	semidirect
173. #6371504	D₄	semidirect
174. #6370693	D₄	semidirect
180. #493879	C₂³	semidirect
181. C₂×#12707	C₂³	semidirect
186. C₂×#12705	C₂³	semidirect
187. C₂×#12705	C₂³	semidirect
190. #493357	C₂³	semidirect
191. #393988	D₄	semidirect
192. #393975	D₄	semidirect
193. #392696	D₄	semidirect
194. #392696	D₄	semidirect
200. #382544	C₂³	semidirect
202. #382434	C₂³	semidirect
203. #373637	C₂³	semidirect
204. #359811	C₂³	semidirect
207. #359549	D₄	semidirect
211. #359549	C₂³	semidirect
212. #359549	C₂³	semidirect
216. #359442	D₄	semidirect
217. #359442	C₂³	semidirect
218. #355096	C₂³	semidirect
219. #347057	D₄	semidirect
220. #347056	D₄	semidirect
221. #347047	D₄	semidirect
222. #347045	D₄	semidirect
223. #190147	C₂³	semidirect
224. #188109	C₂³	semidirect
231. C₂×#8534	C₂³	semidirect
232. C₂×#8453	C₂³	semidirect
233. C₂×#8453	C₂³	semidirect
234. #146479	C₂³	semidirect
235. #146475	C₂³	semidirect
236. #146475	C₂³	semidirect
237. C₂×#7304	C₂³	semidirect
238. C₂×#7304	C₂³	semidirect
239. C₂×#7316	C₂³	semidirect
240. C₂×#7316	C₂³	semidirect
241. C₂×#7314	C₂³	semidirect
242. C₂×#7314	C₂³	semidirect
243. C₂×#7311	C₂³	semidirect
244. C₂×#7311	C₂³	semidirect
245. #108222	C₂³	semidirect
246. #107130	C₂³	semidirect
247. #107130	C₂³	semidirect
250. C₂³×H(5,𝔽₂)	C₂×D₄	semidirect
251. C₂³×H(5,𝔽₂)	C₂×D₄	semidirect
267. C₂×#3484	C₂×D₄	semidirect
278. C₂²×#525	C₂×D₄	semidirect
283. C₂²×#518	C₂×D₄	semidirect
284. C₂²×#518	C₂×D₄	semidirect
319. #23901	C₂×D₄	semidirect
321. #23900	C₂×D₄	semidirect
334. #20616	C₂×D₄	semidirect
335. #20605	C₂×D₄	semidirect
336. C₂×#1783	C₂×D₄	semidirect
337. C₂×#1783	C₂×D₄	semidirect
338. C₂×#1783	C₂×D₄	semidirect
351. #20579	C₂×D₄	semidirect
356. #15262	C₂×D₄	semidirect
357. #15261	C₂×D₄	semidirect
358. #15259	C₂×D₄	semidirect
359. #15258	C₂×D₄	semidirect
361. #10740	C₂×D₄	semidirect
362. #10716	C₂×D₄	semidirect
363. #8546	C₂×D₄	semidirect
364. #8544	C₂×D₄	semidirect
367. #8534	C₂×D₄	semidirect
368. #8534	C₂×D₄	semidirect
440. #2849	#120	semidirect
441. #2846	#120	semidirect
450. #1898	#120	semidirect
544. C₂²×Q₈	#3026	semidirect
547. C₂²×D₄	#3026	semidirect

Maximal subgroups

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

subgroup	index
#72312643	2
#72312604	2
#72312569	2
#72312555	2
#72312545	2
#72312531	2
#72312516	2
#72312503	2
#72312489	2
#72312328	2
#72312226	2
#72310377	2
#72309804	2
#72266836	2
#72266831	2
#72264815	2
#72264799	2
#72251547	2
#72251494	2
#72251459	2
#72251212	2
#72238347	2
#72238344	2