Subgroups — #72337714

Order 16384.

Only the 539 normal subgroups are shown; non-normal subgroups are omitted.

The subgroup lattice has 430 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#72337713	C₂	1	1	yes	maximal, characteristic, complemented
2	#72337712	C₂	1	1	yes	maximal, characteristic, complemented
3	#72337601	C₂	1	1	yes	maximal, characteristic, complemented
4	#72337550	C₂	1	1	yes	maximal, characteristic, complemented
5	#72334384	C₂	1	1	yes	maximal, characteristic, complemented
6	#72334286	C₂²	1	1	yes	characteristic, complemented
7	#72334245	C₂	1	1	yes	maximal, characteristic, complemented
8	#72333265	C₂²	1	1	yes	characteristic
9	#72333265	C₂²	1	1	yes	characteristic, complemented
10	#72331660	D₄	1	2	yes	complemented
11	#72329062	C₂²	1	1	yes	characteristic
12	#72324904	C₂	1	1	yes	maximal, characteristic, complemented
13	#72323840	C₂	1	1	yes	maximal, characteristic, complemented
14	#72323236	C₂	1	1	yes	maximal, characteristic, complemented
15	#72323230	C₂	1	1	yes	maximal, characteristic, complemented
16	#72323229	C₂²	1	1	yes	characteristic, complemented
17	#72323229	C₂²	1	1	yes	characteristic, complemented
18	#72316428	C₂	1	1	yes	maximal, characteristic, complemented
19	#72314070	C₂²	1	1	yes	characteristic, complemented
20	#72313274	C₂²	1	1	yes	characteristic
21	#72313194	D₄	1	2	yes	complemented
22	#72313173	D₄	1	2	yes	complemented
23	#72313138	D₄	1	1	yes	characteristic, complemented
24	#72311363	C₂	1	1	yes	maximal, characteristic, complemented
25	#72310618	C₂²	1	1	yes	characteristic, complemented
26	#72310510	C₂²	1	1	yes	characteristic, complemented
27	#72310499	C₂	1	1	yes	maximal, characteristic, complemented
28	#72310498	C₂²	1	1	yes	characteristic, complemented
29	#72310485	C₂²	1	1	yes	characteristic, complemented
30	#72310462	C₂²	1	1	yes	characteristic, complemented
31	#72310459	C₂²	1	1	yes	characteristic, complemented
32	#72310162	C₂²	1	1	yes	characteristic
33	#72310091	C₂²	1	1	yes	characteristic
34	#72309929	D₄	1	1	yes	characteristic, complemented
35	#72309776	D₄	1	1	yes	characteristic, complemented
36	#72309729	D₄	1	1	yes	characteristic, complemented
37	#72309645	D₄	1	1	yes	characteristic, complemented
38	#72309472	D₄	1	1	yes	characteristic, complemented
39	#72309421	D₄	1	1	yes	characteristic, complemented
40	#72309383	C₂²	1	1	yes	characteristic
41	#72309378	D₄	1	2	yes	complemented
42	#72309376	D₄	1	2	yes	complemented
43	#72309341	D₄	1	1	yes	characteristic, complemented
44	#72304965	C₂	1	1	yes	maximal, characteristic, complemented
45	#72304657	C₂²	1	1	yes	characteristic, complemented
46	#72304284	C₂²	1	1	yes	characteristic, complemented
47	#72302118	C₂²	1	1	yes	characteristic
48	#72302078	D₄	1	1	yes	characteristic, complemented
49	#72302062	D₄	1	1	yes	characteristic, complemented
50	#72302047	D₄	1	1	yes	characteristic, complemented
51	#72302019	D₄	1	1	yes	characteristic, complemented
52	#72301510	C₂²	1	1	yes	characteristic
53	#72271184	D₄	1	1	yes	characteristic, complemented
54	#72266956	C₂²	1	1	yes	characteristic
55	#72266943	D₄	1	1	yes	characteristic, complemented
56	#72266881	D₄	1	1	yes	characteristic, complemented
57	#72266870	D₄	1	1	yes	characteristic, complemented
58	#72266870	D₄	1	1	yes	characteristic, complemented
59	#72266039	D₄	1	1	yes	characteristic, complemented
60	#72266038	D₄	1	1	yes	characteristic, complemented
61	#72259048	C₂²	1	1	yes	characteristic, complemented
62	#72259029	C₂³	1	1	yes	characteristic
63	#72259029	C₂³	1	1	yes	characteristic
64	#72259021	C₂×D₄	1	2	yes	—
65	#72259008	C₂×D₄	1	1	yes	characteristic
66	#72259008	C₂×D₄	1	1	yes	characteristic, complemented
67	#72258990	C₂²	1	1	yes	characteristic, complemented
68	#72258115	D₄	1	1	yes	characteristic, complemented
69	#72256276	C₂²	1	1	yes	characteristic, complemented
70	#72251459	D₄	1	1	yes	characteristic, complemented
71	#72251277	D₄	1	1	yes	characteristic, complemented
72	#72238419	C₂²	1	1	yes	characteristic
73	#72238360	C₂²	1	1	yes	characteristic, complemented
74	#72238348	C₂²	1	1	yes	characteristic, complemented
75	#72237630	C₂³	1	1	yes	characteristic
76	#72237628	C₂³	1	1	yes	characteristic
77	#72237618	C₂×D₄	1	1	yes	characteristic
78	#72236376	D₄	1	1	yes	characteristic, complemented
79	#72235847	C₂×D₄	1	1	yes	characteristic
80	#72235847	C₂×D₄	1	1	yes	characteristic, complemented
81	#72234688	C₂³	1	1	yes	characteristic
82	#72234668	C₂×D₄	1	1	yes	characteristic
83	#72234665	C₂³	1	1	yes	characteristic
84	#72234665	C₂³	1	1	yes	characteristic
85	#72234665	C₂³	1	1	yes	characteristic
86	#72234663	C₂×D₄	1	1	yes	characteristic
87	#72234663	C₂×D₄	1	1	yes	characteristic
88	#72234663	C₂×D₄	1	1	yes	characteristic, complemented
89	#72234625	C₂×D₄	1	1	yes	characteristic
90	#72234619	#41	1	1	yes	characteristic
91	#72234619	#41	1	1	yes	characteristic
92	#72234591	C₂×D₄	1	1	yes	characteristic
93	#72234591	C₂×D₄	1	1	yes	characteristic
94	#72232884	C₂×D₄	1	1	yes	characteristic
95	#72232884	C₂×D₄	1	1	yes	characteristic
96	#72232884	C₂×D₄	1	1	yes	characteristic, complemented
97	#72232592	C₂×D₄	1	2	yes	—
98	#72232592	C₂×D₄	1	1	yes	characteristic
99	#72226388	C₂	1	1	yes	maximal, characteristic, complemented
100	#72226365	C₂²	1	1	yes	characteristic, complemented
101	#72226360	C₂²	1	1	yes	characteristic, complemented
102	#72226177	C₂²	1	1	yes	characteristic, complemented
103	#72225910	C₂²	1	1	yes	characteristic, complemented
104	#72225883	C₂³	1	1	yes	characteristic
105	#72225838	C₂²	1	1	yes	characteristic, complemented
106	#72225781	C₂³	1	1	yes	characteristic
107	#72225777	C₂×D₄	1	1	yes	characteristic, complemented
108	#72225776	C₂×D₄	1	1	yes	characteristic, complemented
109	#72225776	C₂×D₄	1	1	yes	characteristic, complemented
110	#72225776	C₂×D₄	1	1	yes	characteristic, complemented
111	#72225775	C₂²	1	1	yes	characteristic, complemented
112	#72225731	C₂²	1	1	yes	characteristic
113	#72225676	D₄	1	1	yes	characteristic, complemented
114	#72225655	C₂×D₄	1	1	yes	characteristic
115	#72225655	C₂×D₄	1	1	yes	characteristic
116	#72225652	D₄	1	1	yes	characteristic, complemented
117	#72225629	C₂³	1	1	yes	characteristic
118	C₂×#111462	C₂×D₄	1	2	yes	—
119	#72225615	C₂³	1	1	yes	characteristic
120	#72224136	C₂×D₄	1	1	yes	characteristic
121	#72224136	C₂×D₄	1	1	yes	characteristic
122	#72219397	C₂³	1	1	yes	characteristic
123	#72219311	C₂×D₄	1	1	yes	characteristic, complemented
124	#72219310	C₂×D₄	1	1	yes	characteristic, complemented
125	#72219309	C₂³	1	1	yes	characteristic
126	#72219301	C₂×D₄	1	1	yes	characteristic, complemented
127	#72219299	C₂×D₄	1	1	yes	characteristic, complemented
128	#72219291	D₄	1	1	yes	characteristic, complemented
129	#72219257	C₂×D₄	1	1	yes	characteristic
130	#72219254	C₂×D₄	1	1	yes	characteristic
131	#72219227	C₂×D₄	1	1	yes	characteristic
132	C₂×#106076	C₂×D₄	1	2	yes	—
133	#72219225	C₂×D₄	1	1	yes	characteristic
134	C₂²×#15947	C₂×D₄	1	1	yes	characteristic
135	C₂×#72217546	C₂³	1	1	yes	characteristic
136	C₂×#374022	C₂×D₄	1	1	yes	characteristic
137	C₂×#359428	C₂×D₄	1	1	yes	characteristic
138	C₂×#359428	C₂×D₄	1	1	yes	characteristic
139	C₂×#7670203	C₂⁴	1	1	yes	characteristic
140	C₂²×#62817	C₂×D₄	1	1	yes	characteristic
141	#72218799	D₄	1	1	yes	characteristic, complemented
142	#72218375	C₂×D₄	1	1	yes	characteristic
143	#72217947	D₄	1	1	yes	characteristic, complemented
144	#72217875	C₂×D₄	1	1	yes	characteristic
145	#72217789	C₂×D₄	1	1	yes	characteristic
146	C₂³×#2846	C₂×D₄	1	1	yes	characteristic
147	C₂³×#2846	C₂×D₄	1	1	yes	characteristic
148	#72217511	C₂×D₄	1	1	yes	characteristic
149	#72217511	C₂×D₄	1	1	yes	characteristic
150	#72217511	C₂×D₄	1	1	yes	characteristic
151	C₂×#72209716	D₄	1	2	yes	complemented
152	C₂×#115690	C₂×D₄	1	2	yes	—
153	C₂×#6499867	C₂×D₄	1	2	yes	—
154	#72216064	C₂×D₄	1	1	yes	characteristic
155	#72216064	C₂×D₄	1	1	yes	characteristic
156	C₂×#6342371	C₂×D₄	1	1	yes	characteristic
157	C₂⁹	#120	1	1	yes	characteristic, complemented
158	#10586404	#121	1	1	yes	characteristic
159	#10586404	#121	1	1	yes	characteristic
160	C₂×#62817	#120	1	1	yes	characteristic
161	C₂×#62817	#120	1	1	yes	characteristic
162	C₂×#62817	#120	1	2	yes	—
163	C₂×#62817	#120	1	1	yes	characteristic, complemented
164	#10586066	#120	1	1	yes	characteristic
165	#10586066	#120	1	1	yes	characteristic
166	C₂²×#3484	#120	1	1	yes	characteristic
167	C₂²×#3484	C₂²×D₄	1	1	yes	characteristic
168	C₂²×#3484	C₂²×D₄	1	1	yes	characteristic
169	C₂⁴×#120	#120	1	1	yes	characteristic
170	C₂⁴×#120	C₂²×D₄	1	1	yes	characteristic
171	C₂⁴×#120	C₂²×D₄	1	1	yes	characteristic
172	#7642244	#121	1	1	yes	characteristic
173	#7642244	#121	1	1	yes	characteristic
174	#7642244	#121	1	1	yes	characteristic
175	#7642244	#121	1	1	yes	characteristic
176	C₂²×#2846	C₂²×D₄	1	1	yes	characteristic
177	#7630939	#120	1	1	yes	characteristic
178	#7630939	#120	1	1	yes	characteristic
179	#7630939	#120	1	1	yes	characteristic
180	#7630939	#120	1	1	yes	characteristic
181	C₂×#35390	H(5,𝔽₂)	1	1	yes	characteristic
182	C₂×#35348	C₂×#41	1	1	yes	characteristic
183	C₂×#35348	H(5,𝔽₂)	1	1	yes	characteristic
184	C₂×#35346	C₂²×D₄	1	1	yes	characteristic
185	C₂×#34981	C₂²×D₄	1	1	yes	characteristic
186	C₂×#34981	H(5,𝔽₂)	1	1	yes	characteristic
187	C₂×#34980	C₂²×D₄	1	1	yes	characteristic
188	C₂×#34980	C₂²×D₄	1	1	yes	characteristic
189	#7626202	#120	1	1	yes	characteristic
190	#7626202	#120	1	1	yes	characteristic
191	#7626202	#120	1	1	yes	characteristic, complemented
192	C₂×#34198	C₂²×D₄	1	1	yes	characteristic
193	C₂×#34198	H(5,𝔽₂)	1	1	yes	characteristic
194	C₂³×#379	#120	1	1	yes	characteristic, complemented
195	C₂³×#379	#120	1	1	yes	characteristic, complemented
196	#6374210	#127	1	1	yes	characteristic
197	#6374210	#127	1	1	yes	characteristic
198	#6374210	#127	1	1	yes	characteristic
199	#6374210	#127	1	1	yes	characteristic
200	#6374128	#121	1	1	yes	characteristic
201	#6374128	#121	1	1	yes	characteristic
202	C₂×#21746	#120	1	2	yes	—
203	C₂×#21746	#120	1	1	yes	characteristic, complemented
204	C₂×#21746	#120	1	1	yes	characteristic, complemented
205	#6371504	#121	1	1	yes	characteristic
206	#6371504	#121	1	1	yes	characteristic
207	#6371504	#121	1	1	yes	characteristic
208	#6371504	#121	1	1	yes	characteristic
209	#6370693	#120	1	1	yes	characteristic
210	#6370693	#120	1	1	yes	characteristic
211	C₂×#14679	#120	1	1	yes	characteristic, complemented
212	#517411	#120	1	1	yes	characteristic
213	C₂²×#1438	#120	1	1	yes	characteristic
214	C₂×#10725	#120	1	2	yes	complemented
215	C₂×#8101	#120	1	2	yes	complemented
216	C₂×#8101	#120	1	2	yes	complemented
217	C₂×#7555	#120	1	2	yes	complemented
218	C₂⁸	B(4,𝔽₂)	1	1	yes	characteristic, complemented
219	C₂⁸	C₂×#120	1	1	yes	characteristic
220	C₂×H(7,𝔽₂)	B(4,𝔽₂)	1	1	yes	characteristic
221	C₂×H(7,𝔽₂)	B(4,𝔽₂)	1	1	yes	characteristic
222	C₂³×H(5,𝔽₂)	B(4,𝔽₂)	1	1	yes	characteristic, complemented
223	C₂³×H(5,𝔽₂)	C₂×#120	1	1	yes	characteristic
224	C₂⁵×D₄	C₂×#120	1	1	yes	characteristic
225	C₂⁵×D₄	C₂×#120	1	1	yes	characteristic
226	#62842	B(4,𝔽₂)	1	1	yes	characteristic
227	#62842	B(4,𝔽₂)	1	1	yes	characteristic
228	#62842	B(4,𝔽₂)	1	1	yes	characteristic
229	#62842	B(4,𝔽₂)	1	1	yes	characteristic
230	#62817	B(4,𝔽₂)	1	4	yes	complemented
231	C₂×#3484	#392	1	1	yes	characteristic
232	C₂×#3484	#392	1	1	yes	characteristic
233	C₂×#3484	#392	1	1	yes	characteristic
234	C₂×#3484	#392	1	1	yes	characteristic
235	C₂×#3532	B(4,𝔽₂)	1	4	yes	—
236	C₂²×#534	C₂×#121	1	1	yes	characteristic
237	C₂²×#534	#534	1	1	yes	characteristic
238	C₂²×#534	D₄²	1	1	yes	characteristic
239	C₂²×#534	D₄²	1	1	yes	characteristic
240	C₂²×#534	D₄²	1	1	yes	characteristic
241	C₂³×#120	C₂×#120	1	1	yes	characteristic
242	C₂³×#120	C₂×#120	1	1	yes	characteristic
243	C₂³×#120	C₂×#120	1	1	yes	characteristic
244	C₂³×#120	C₂×#121	1	1	yes	characteristic
245	C₂³×#120	#534	1	1	yes	characteristic
246	C₂³×#120	D₄²	1	1	yes	characteristic
247	C₂³×#120	D₄²	1	1	yes	characteristic
248	C₂³×#120	D₄²	1	1	yes	characteristic
249	C₂³×#120	D₄²	1	1	yes	characteristic
250	C₂³×#120	D₄²	1	1	yes	characteristic
251	C₂³×#120	#546	1	1	yes	characteristic
252	#62652	B(4,𝔽₂)	1	1	yes	characteristic
253	#62652	B(4,𝔽₂)	1	1	yes	characteristic
254	C₂²×#518	B(4,𝔽₂)	1	1	yes	characteristic, complemented
255	C₂²×#518	C₂×#121	1	1	yes	characteristic
256	C₂²×#518	#534	1	1	yes	characteristic
257	C₂⁴×C₂²⋊C₄	B(4,𝔽₂)	1	1	yes	characteristic, complemented
258	C₂⁴×C₂²⋊C₄	C₂×#120	1	1	yes	characteristic
259	C₂⁴×C₂²⋊C₄	#534	1	1	yes	characteristic
260	#36614	B(4,𝔽₂)	1	2	yes	—
261	C₂×#2846	B(4,𝔽₂)	1	2	yes	—
262	#35222	B(4,𝔽₂)	1	2	yes	—
263	#34980	B(4,𝔽₂)	1	2	yes	—
264	#34171	#392	1	1	yes	characteristic
265	#34171	#392	1	1	yes	characteristic
266	#34171	#392	1	1	yes	characteristic
267	#34171	#392	1	1	yes	characteristic
268	C₂×#2315	#535	1	1	yes	characteristic
269	C₂×#2315	#546	1	1	yes	characteristic
270	C₂×#2308	C₂×#127	1	1	yes	characteristic
271	C₂×#2308	D₄²	1	1	yes	characteristic
272	C₂×#2308	D₄²	1	1	yes	characteristic
273	C₂×#2308	D₄²	1	1	yes	characteristic
274	C₂×#2308	#546	1	1	yes	characteristic
275	C₂²×#379	C₂×#120	1	1	yes	characteristic
276	C₂²×#379	D₄²	1	1	yes	characteristic
277	C₂²×#379	#546	1	1	yes	characteristic
278	C₂×#2273	#535	1	1	yes	characteristic
279	C₂⁷	#2403	1	1	yes	characteristic
280	C₂⁷	#2410	1	1	yes	characteristic
281	C₂⁷	#2846	1	1	yes	characteristic
282	C₂⁷	C₂×B(4,𝔽₂)	1	1	yes	characteristic
283	C₂⁷	C₂×B(4,𝔽₂)	1	1	yes	characteristic
284	C₂²×H(5,𝔽₂)	#2021	1	1	yes	characteristic
285	C₂²×H(5,𝔽₂)	#2021	1	1	yes	characteristic
286	C₂²×H(5,𝔽₂)	#2021	1	1	yes	characteristic
287	C₂²×H(5,𝔽₂)	#2021	1	1	yes	characteristic
288	C₂²×H(5,𝔽₂)	C₂×B(4,𝔽₂)	1	1	yes	characteristic
289	C₂²×H(5,𝔽₂)	C₂×B(4,𝔽₂)	1	1	yes	characteristic
290	C₂²×H(5,𝔽₂)	C₂×B(4,𝔽₂)	1	1	yes	characteristic
291	C₂²×H(5,𝔽₂)	C₂×B(4,𝔽₂)	1	1	yes	characteristic
292	C₂⁴×D₄	C₂×#392	1	1	yes	characteristic
293	C₂⁴×D₄	#2403	1	1	yes	characteristic
294	C₂⁴×D₄	#2403	1	1	yes	characteristic
295	C₂⁴×D₄	#2403	1	1	yes	characteristic
296	C₂⁴×D₄	#2410	1	1	yes	characteristic
297	C₂⁴×D₄	C₂×B(4,𝔽₂)	1	1	yes	characteristic
298	C₂⁴×D₄	C₂×B(4,𝔽₂)	1	1	yes	characteristic
299	C₂⁴×D₄	C₂×B(4,𝔽₂)	1	1	yes	characteristic
300	C₂⁴×D₄	#3026	1	1	yes	characteristic
301	C₂⁵×C₄	C₂×B(4,𝔽₂)	1	1	yes	characteristic
302	C₂⁵×C₄	#3026	1	1	yes	characteristic
303	C₂×H(3,𝔽₄)	#2199	1	4	yes	—
304	C₂×#560	#2199	1	4	yes	—
305	C₂×#551	#2196	1	4	yes	—
306	C₂×D₄²	#2196	1	4	yes	—
307	C₂×#535	#2021	1	2	yes	—
308	C₂×#534	#2021	1	2	yes	—
309	C₂×#525	#2021	1	2	yes	—
310	C₂²×#120	#2021	1	2	yes	—
311	C₂²×#120	C₂×B(4,𝔽₂)	1	2	yes	—
312	C₂²×#120	C₂×B(4,𝔽₂)	1	2	yes	—
313	C₂²×#120	#3026	1	2	yes	—
314	C₂²×#120	#3026	1	2	yes	—
315	C₂×#518	#2021	1	1	yes	characteristic
316	C₂×#518	#2021	1	1	yes	characteristic
317	C₂×#518	#2021	1	1	yes	characteristic
318	C₂×#518	#2021	1	1	yes	characteristic
319	C₂³×C₂²⋊C₄	#2408	1	1	yes	characteristic
320	C₂³×C₂²⋊C₄	#2408	1	1	yes	characteristic
321	C₂³×C₂²⋊C₄	#2410	1	1	yes	characteristic
322	C₂³×C₂²⋊C₄	#2410	1	1	yes	characteristic
323	C₂³×C₂²⋊C₄	#2433	1	1	yes	characteristic
324	C₂³×C₂²⋊C₄	#2433	1	1	yes	characteristic
325	C₂³×C₂²⋊C₄	#2613	1	1	yes	characteristic
326	#2280	#2021	1	2	yes	—
327	C₂×#379	#2021	1	2	yes	—
328	C₂⁶	#14715	1	1	yes	characteristic
329	C₂⁶	C₂×#2021	1	1	yes	characteristic
330	C₂⁶	#23895	1	1	yes	characteristic
331	C₂⁶	#23900	1	1	yes	characteristic
332	C₂⁶	#23900	1	1	yes	characteristic
333	C₂⁶	#23900	1	1	yes	characteristic
334	C₂⁶	#23900	1	1	yes	characteristic
335	C₂⁶	#24404	1	1	yes	characteristic
336	C₂⁶	#32898	1	2	yes	—
337	C₂⁶	#32898	1	1	yes	characteristic
338	C₂⁶	#32898	1	1	yes	characteristic
339	C₂⁶	#32898	1	2	yes	—
340	C₂²×#41	#10336	1	2	yes	—
341	C₂³×D₄	#10336	1	2	yes	—
342	C₂³×D₄	C₂×#2021	1	1	yes	characteristic
343	C₂³×D₄	C₂×#2021	1	1	yes	characteristic
344	C₂³×D₄	C₂×#2021	1	1	yes	characteristic
345	C₂³×D₄	#23444	1	1	yes	characteristic
346	C₂³×D₄	#23895	1	1	yes	characteristic
347	C₂³×D₄	#23895	1	1	yes	characteristic
348	C₂³×D₄	#23900	1	1	yes	characteristic
349	C₂³×D₄	#23900	1	1	yes	characteristic
350	C₂³×D₄	#23900	1	1	yes	characteristic
351	C₂³×D₄	#23900	1	1	yes	characteristic
352	C₂³×D₄	#23900	1	1	yes	characteristic
353	C₂³×D₄	#23903	1	1	yes	characteristic
354	C₂⁴×C₄	C₂×#2021	1	1	yes	characteristic
355	C₂⁴×C₄	#23895	1	1	yes	characteristic
356	C₂⁴×C₄	#23900	1	1	yes	characteristic
357	C₂⁴×C₄	#23903	1	1	yes	characteristic
358	C₂⁴×C₄	#24404	1	1	yes	characteristic
359	C₂×#127	#13343	1	4	yes	—
360	C₂×#124	#13343	1	4	yes	—
361	C₂×#123	#13343	1	4	yes	—
362	C₂×#120	#13343	1	4	yes	—
363	C₂×#120	C₂×#2196	1	4	yes	—
364	C₂×#120	C₂×#2199	1	4	yes	—
365	C₂×#117	#10336	1	2	yes	—
366	C₂²×C₂²⋊C₄	#10336	1	2	yes	—
367	C₂²×C₂²⋊C₄	#24404	1	2	yes	—
368	C₂²×C₂²⋊C₄	#29634	1	2	yes	—
369	C₂⁵	#144366	1	2	yes	complemented
370	C₂⁵	C₂×#10336	1	1	yes	characteristic
371	C₂⁵	#233541	1	1	yes	characteristic
372	C₂⁵	#245225	1	1	yes	characteristic
373	C₂⁵	#245225	1	1	yes	characteristic
374	C₂⁵	#245225	1	1	yes	characteristic
375	C₂⁵	#245246	1	1	yes	characteristic
376	C₂⁵	#347042	1	2	yes	—
377	C₂⁵	#347042	1	2	yes	—
378	C₂⁵	#393929	1	1	yes	characteristic
379	C₂⁵	#394058	1	1	yes	characteristic
380	C₂⁵	#394058	1	1	yes	characteristic
381	C₂⁵	#394064	1	1	yes	characteristic
382	C₂⁵	#394064	1	1	yes	characteristic
383	C₂⁵	#394066	1	1	yes	characteristic
384	C₂⁵	#394066	1	1	yes	characteristic
385	C₂⁵	#511771	1	2	yes	—
386	C₂⁵	#511775	1	2	yes	—
387	C₂⁵	#511790	1	2	yes	—
388	C₂⁵	#511790	1	2	yes	—
389	C₂²×Q₈	#144366	1	2	yes	complemented
390	C₂²×D₄	#144366	1	2	yes	complemented
391	C₂²×D₄	C₂×#13343	1	4	yes	—
392	C₂³×C₄	#144366	1	2	yes	complemented
393	C₂³×C₄	C₂×#10336	1	1	yes	characteristic
394	C₂³×C₄	#233541	1	1	yes	characteristic
395	C₂³×C₄	#245225	1	1	yes	characteristic
396	C₂³×C₄	#245246	1	1	yes	characteristic
397	C₂³×C₄	#245246	1	1	yes	characteristic
398	C₂³×C₄	#245246	1	1	yes	characteristic
399	C₂×C₂²⋊C₄	#144366	1	4	yes	complemented
400	C₂×C₂²⋊C₄	#508062	1	4	yes	—
401	C₂×C₄²	#144366	1	4	yes	complemented
402	C₂⁴	#72209767	1	2	yes	—
403	C₂⁴	#72209767	1	2	yes	—
404	C₂⁴	B(5,𝔽₂)	1	2	yes	—
405	C₂⁴	#72210600	1	1	yes	characteristic
406	C₂⁴	#72210600	1	1	yes	characteristic
407	C₂⁴	#72214549	1	1	yes	characteristic
408	C₂⁴	#72215683	1	2	yes	—
409	C₂⁴	#72215683	1	2	yes	—
410	C₂⁴	C₂×#144366	1	2	yes	—
411	C₂⁴	#72218121	1	2	yes	—
412	C₂⁴	#72219240	1	1	yes	characteristic
413	C₂⁴	#72219249	1	2	yes	—
414	C₂⁴	#72225609	1	1	yes	characteristic
415	C₂⁴	#72225609	1	1	yes	characteristic
416	C₂⁴	#72225610	1	1	yes	characteristic
417	C₂²×C₄	C₂×#144366	1	2	yes	—
418	C₂³	#72218841	1	1	yes	characteristic
419	C₂³	#72219250	1	1	yes	characteristic
420	C₂³	#72225611	1	1	yes	characteristic
421	C₂³	#72255888	1	1	yes	characteristic
422	C₂³	#72258007	1	2	yes	—
423	C₂³	#72258013	1	2	yes	—
424	C₂³	#72258020	1	1	yes	characteristic
425	C₂²	#72258251	1	1	yes	characteristic
426	C₂²	#72258296	1	1	yes	characteristic
427	C₂²	#72258565	1	1	yes	characteristic
428	C₂	#72266691	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂	#72266691
commutator, Frattini, cosocle	C₂×#7670203	C₂⁴
LCS	G ▷ C₂×#7670203 ▷ C₂⁶ ▷ C₂³ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂ ◁ C₂³ ◁ C₂⁶ ◁ C₂×#7670203 ◁ G
LECS	G ▷ C₂×#7670203 ▷ C₂⁶ ▷ C₂³ ▷ C₂ ▷ C₁

Complements

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

N	H ≅ G/N	type
1. #72337713	C₂	semidirect
2. #72337712	C₂	semidirect
3. #72337601	C₂	semidirect
4. #72337550	C₂	semidirect
5. #72334384	C₂	semidirect
6. #72334286	C₂²	semidirect
7. #72334245	C₂	semidirect
9. #72333265	C₂²	semidirect
10. #72331660	D₄	semidirect
12. #72324904	C₂	semidirect
13. #72323840	C₂	semidirect
14. #72323236	C₂	semidirect
15. #72323230	C₂	semidirect
16. #72323229	C₂²	semidirect
17. #72323229	C₂²	semidirect
18. #72316428	C₂	semidirect
19. #72314070	C₂²	semidirect
21. #72313194	D₄	semidirect
22. #72313173	D₄	semidirect
23. #72313138	D₄	semidirect
24. #72311363	C₂	semidirect
25. #72310618	C₂²	semidirect
26. #72310510	C₂²	semidirect
27. #72310499	C₂	semidirect
28. #72310498	C₂²	semidirect
29. #72310485	C₂²	semidirect
30. #72310462	C₂²	semidirect
31. #72310459	C₂²	semidirect
34. #72309929	D₄	semidirect
35. #72309776	D₄	semidirect
36. #72309729	D₄	semidirect
37. #72309645	D₄	semidirect
38. #72309472	D₄	semidirect
39. #72309421	D₄	semidirect
41. #72309378	D₄	semidirect
42. #72309376	D₄	semidirect
43. #72309341	D₄	semidirect
44. #72304965	C₂	semidirect
45. #72304657	C₂²	semidirect
46. #72304284	C₂²	semidirect
48. #72302078	D₄	semidirect
49. #72302062	D₄	semidirect
50. #72302047	D₄	semidirect
51. #72302019	D₄	semidirect
53. #72271184	D₄	semidirect
55. #72266943	D₄	semidirect
56. #72266881	D₄	semidirect
57. #72266870	D₄	semidirect
58. #72266870	D₄	semidirect
59. #72266039	D₄	semidirect
60. #72266038	D₄	semidirect
61. #72259048	C₂²	semidirect
66. #72259008	C₂×D₄	semidirect
67. #72258990	C₂²	semidirect
68. #72258115	D₄	semidirect
69. #72256276	C₂²	semidirect
70. #72251459	D₄	semidirect
71. #72251277	D₄	semidirect
73. #72238360	C₂²	semidirect
74. #72238348	C₂²	semidirect
78. #72236376	D₄	semidirect
80. #72235847	C₂×D₄	semidirect
88. #72234663	C₂×D₄	semidirect
96. #72232884	C₂×D₄	semidirect
99. #72226388	C₂	semidirect
100. #72226365	C₂²	semidirect
101. #72226360	C₂²	semidirect
102. #72226177	C₂²	semidirect
103. #72225910	C₂²	semidirect
105. #72225838	C₂²	semidirect
107. #72225777	C₂×D₄	semidirect
108. #72225776	C₂×D₄	semidirect
109. #72225776	C₂×D₄	semidirect
110. #72225776	C₂×D₄	semidirect
111. #72225775	C₂²	semidirect
113. #72225676	D₄	semidirect
116. #72225652	D₄	semidirect
123. #72219311	C₂×D₄	semidirect
124. #72219310	C₂×D₄	semidirect
126. #72219301	C₂×D₄	semidirect
127. #72219299	C₂×D₄	semidirect
128. #72219291	D₄	semidirect
141. #72218799	D₄	semidirect
143. #72217947	D₄	semidirect
151. C₂×#72209716	D₄	semidirect
157. C₂⁹	#120	semidirect
163. C₂×#62817	#120	semidirect
191. #7626202	#120	semidirect
194. C₂³×#379	#120	semidirect
195. C₂³×#379	#120	semidirect
203. C₂×#21746	#120	semidirect
204. C₂×#21746	#120	semidirect
211. C₂×#14679	#120	semidirect
214. C₂×#10725	#120	semidirect
215. C₂×#8101	#120	semidirect
216. C₂×#8101	#120	semidirect
217. C₂×#7555	#120	semidirect
218. C₂⁸	B(4,𝔽₂)	semidirect
222. C₂³×H(5,𝔽₂)	B(4,𝔽₂)	semidirect
230. #62817	B(4,𝔽₂)	semidirect
254. C₂²×#518	B(4,𝔽₂)	semidirect
257. C₂⁴×C₂²⋊C₄	B(4,𝔽₂)	semidirect
369. C₂⁵	#144366	semidirect
389. C₂²×Q₈	#144366	semidirect
390. C₂²×D₄	#144366	semidirect
392. C₂³×C₄	#144366	semidirect
399. C₂×C₂²⋊C₄	#144366	semidirect
401. C₂×C₄²	#144366	semidirect

Maximal subgroups

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

subgroup	index
#72337713	2
#72337712	2
#72337601	2
#72337550	2
#72334384	2
#72334245	2
#72324904	2
#72323840	2
#72323236	2
#72323230	2
#72316428	2
#72311363	2
#72310499	2
#72304965	2
#72226388	2