Subgroups — #72255637

Order 2048.

At least 8657 conjugacy classes of subgroups; only the 946 normal subgroups are shown.

The subgroup lattice has 411 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#72255632	C₂	1	2	yes	maximal, complemented
2	#72255630	C₂	1	1	yes	maximal, characteristic, complemented
3	#72251614	C₂	1	2	yes	maximal, complemented
4	#72251454	C₂	1	2	yes	maximal, complemented
5	#72251429	C₂	1	2	yes	maximal, complemented
6	#72241287	C₂	1	2	yes	maximal, complemented
7	#72241194	C₂	1	2	yes	maximal, complemented
8	#72241194	C₂	1	2	yes	maximal, complemented
9	#72241183	C₂	1	2	yes	maximal, complemented
10	C₂×#251827	C₂	1	2	yes	maximal, complemented
11	#72240426	C₂	1	2	yes	maximal, complemented
12	#72240425	C₂	1	1	yes	maximal, characteristic, complemented
13	#72225783	C₂	1	1	yes	maximal, characteristic, complemented
14	#72225746	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂²×#32898	C₂	1	1	yes	maximal, characteristic, complemented
16	#72219118	C₂	1	1	yes	maximal, characteristic, complemented
17	#72218846	C₂	1	1	yes	maximal, characteristic, complemented
18	#72218846	C₂	1	2	yes	maximal, complemented
19	#72214549	C₂	1	2	yes	maximal, complemented
20	C₂⁴×H(5,𝔽₂)	C₂²	1	1	yes	characteristic
21	C₂×#46996	C₂²	1	1	yes	characteristic, complemented
22	C₂²×#2403	C₂²	1	2	yes	—
23	C₂²×#2403	C₂²	1	1	yes	characteristic
24	C₂×#32898	C₂²	1	2	yes	—
25	C₂×#32898	C₂²	1	2	yes	—
26	C₂×#32898	C₂²	1	2	yes	—
27	C₂×#32898	C₂²	1	2	yes	—
28	C₂×#32898	C₂²	1	2	yes	complemented
29	C₂×#32898	C₂²	1	2	yes	complemented
30	C₂×#20585	C₂²	1	2	yes	complemented
31	C₂×#20585	C₂²	1	2	yes	complemented
32	C₂²×#1781	C₂²	1	1	yes	characteristic
33	C₂²×#1781	C₂²	1	2	yes	—
34	#4414129	C₂²	1	1	yes	characteristic, complemented
35	#4387644	C₂²	1	1	yes	characteristic, complemented
36	#4387614	C₂²	1	1	yes	characteristic, complemented
37	#4387614	C₂²	1	1	yes	characteristic, complemented
38	#4387614	C₂²	1	1	yes	characteristic, complemented
39	#4387584	C₂²	1	1	yes	characteristic, complemented
40	#4387584	C₂²	1	1	yes	characteristic, complemented
41	#612424	C₂²	1	2	yes	—
42	#612424	C₂²	1	1	yes	characteristic
43	#612424	C₂²	1	1	yes	characteristic, complemented
44	#576607	C₂²	1	1	yes	characteristic, complemented
45	#521311	C₂²	1	1	yes	characteristic, complemented
46	#517411	C₂²	1	1	yes	characteristic
47	#517411	C₂²	1	1	yes	characteristic
48	#517411	C₂²	1	1	yes	characteristic, complemented
49	#392125	C₂²	1	2	yes	complemented
50	#392125	C₂²	1	2	yes	complemented
51	#392111	C₂²	1	2	yes	complemented
52	#392111	C₂²	1	2	yes	complemented
53	#392109	C₂²	1	2	yes	—
54	#392109	C₂²	1	2	yes	—
55	#392109	C₂²	1	1	yes	characteristic
56	#392109	C₂²	1	2	yes	—
57	#392109	C₂²	1	2	yes	complemented
58	#359428	C₂²	1	2	yes	complemented
59	C₂×#10390	C₂²	1	4	yes	complemented
60	C₂×#10336	C₂²	1	4	yes	complemented
61	C₂×#10336	C₂²	1	4	yes	complemented
62	C₂×#9495	C₂²	1	4	yes	complemented
63	C₂×#9495	C₂²	1	4	yes	complemented
64	C₂×#9495	C₂²	1	2	yes	complemented
65	C₂×#9495	C₂²	1	2	yes	complemented
66	C₂×#9495	C₂²	1	4	yes	complemented
67	C₂×#9495	C₂²	1	2	yes	complemented
68	C₂×#8746	C₂²	1	2	yes	complemented
69	#119494	C₂²	1	2	yes	complemented
70	#119484	C₂²	1	2	yes	complemented
71	#119484	C₂²	1	2	yes	complemented
72	#116356	C₂²	1	4	yes	complemented
73	#116356	C₂²	1	4	yes	complemented
74	#116356	C₂²	1	4	yes	complemented
75	#115723	C₂²	1	4	yes	complemented
76	#115133	C₂²	1	4	yes	complemented
77	#115133	C₂²	1	4	yes	complemented
78	#115133	C₂²	1	4	yes	complemented
79	#115133	C₂²	1	2	yes	complemented
80	#115133	C₂²	1	2	yes	complemented
81	#115133	C₂²	1	2	yes	complemented
82	#111458	C₂²	1	4	yes	complemented
83	#111458	C₂²	1	4	yes	complemented
84	#110401	C₂²	1	4	yes	complemented
85	#106542	C₂²	1	2	yes	complemented
86	#105808	C₂²	1	2	yes	complemented
87	C₂²⋊#1304	C₂²	1	2	yes	complemented
88	C₂²⋊#1304	C₂²	1	2	yes	complemented
89	C₂²⋊#1304	C₂²	1	2	yes	complemented
90	C₂²⋊#1304	C₂²	1	2	yes	complemented
91	C₂³×H(5,𝔽₂)	C₂³	1	2	yes	—
92	C₂³×H(5,𝔽₂)	C₂³	1	2	yes	—
93	C₂⁵×D₄	C₂³	1	1	yes	characteristic
94	C₂⁵×D₄	C₂³	1	1	yes	characteristic
95	C₂⁵×D₄	C₂³	1	2	yes	—
96	C₂³×#120	D₄	1	2	yes	complemented
97	C₂³×#120	C₂³	1	1	yes	characteristic
98	C₂×#2840	C₂³	1	1	yes	characteristic, complemented
99	C₂×#2403	D₄	1	2	yes	complemented
100	C₂×#2403	D₄	1	2	yes	complemented
101	C₂×#2403	D₄	1	2	yes	complemented
102	C₂×#2403	D₄	1	2	yes	complemented
103	C₂×#2403	C₂³	1	1	yes	characteristic
104	C₂×#2403	C₂³	1	1	yes	characteristic
105	C₂×#2403	C₂³	1	1	yes	characteristic
106	C₂×#2403	C₂³	1	1	yes	characteristic
107	C₂×#2403	C₂³	1	1	yes	characteristic
108	C₂×#2403	C₂³	1	1	yes	characteristic
109	C₂×#2403	C₂³	1	4	yes	—
110	C₂×#2403	C₂³	1	4	yes	—
111	C₂×#2403	C₂³	1	4	yes	—
112	C₂×#2403	C₂³	1	1	yes	characteristic, complemented
113	C₂×#2403	C₂³	1	1	yes	characteristic, complemented
114	C₂×#2308	D₄	1	2	yes	complemented
115	C₂×#2308	C₂³	1	1	yes	characteristic
116	C₂×#2308	C₂³	1	2	yes	—
117	C₂×#2308	C₂³	1	1	yes	characteristic
118	C₂×#2308	C₂³	1	1	yes	characteristic, complemented
119	C₂×#2308	C₂³	1	1	yes	characteristic, complemented
120	C₂×#2308	C₂³	1	1	yes	characteristic, complemented
121	C₂²×#386	D₄	1	2	yes	complemented
122	C₂²×#379	D₄	1	2	yes	complemented
123	C₂²×#379	C₂³	1	2	yes	—
124	C₂²×#379	C₂³	1	1	yes	characteristic
125	#32898	D₄	1	16	yes	complemented
126	C₂×#1781	C₂³	1	4	yes	—
127	C₂×#1781	C₂³	1	2	yes	—
128	C₂×#1781	C₂³	1	2	yes	—
129	C₂×#1781	C₂³	1	4	yes	—
130	C₂×#1781	C₂³	1	4	yes	—
131	C₂×#1781	C₂³	1	4	yes	—
132	C₂×#1781	C₂³	1	4	yes	—
133	C₂×#1781	C₂³	1	4	yes	—
134	C₂×#1781	C₂³	1	4	yes	—
135	C₂×#1781	C₂³	1	2	yes	—
136	C₂×#1781	C₂³	1	4	yes	—
137	C₂×#1781	C₂³	1	2	yes	—
138	C₂×#1781	C₂³	1	4	yes	complemented
139	C₂×#1781	C₂³	1	4	yes	complemented
140	C₂×#1781	C₂³	1	4	yes	complemented
141	#14681	D₄	1	2	yes	complemented
142	#14679	C₂³	1	2	yes	—
143	#14679	C₂³	1	2	yes	—
144	#14679	C₂³	1	1	yes	characteristic
145	#14679	C₂³	1	1	yes	characteristic
146	#14679	C₂³	1	1	yes	characteristic
147	#14673	C₂³	1	1	yes	characteristic, complemented
148	#14673	C₂³	1	1	yes	characteristic, complemented
149	#14673	C₂³	1	1	yes	characteristic, complemented
150	#14338	C₂³	1	1	yes	characteristic, complemented
151	#14335	D₄	1	2	yes	complemented
152	#14335	C₂³	1	1	yes	characteristic
153	#14335	C₂³	1	1	yes	characteristic
154	#14335	C₂³	1	2	yes	—
155	#14335	C₂³	1	1	yes	characteristic, complemented
156	#14335	C₂³	1	1	yes	characteristic, complemented
157	#14335	C₂³	1	1	yes	characteristic, complemented
158	#13867	D₄	1	2	yes	complemented
159	#13867	D₄	1	2	yes	complemented
160	#13867	C₂³	1	1	yes	characteristic
161	#13867	C₂³	1	1	yes	characteristic
162	#13867	C₂³	1	4	yes	—
163	#13867	C₂³	1	1	yes	characteristic, complemented
164	#13867	C₂³	1	1	yes	characteristic, complemented
165	#13775	C₂³	1	1	yes	characteristic, complemented
166	#10725	C₂³	1	4	yes	complemented
167	C₂×#1304	C₂³	1	4	yes	complemented
168	C₂×#1304	C₂³	1	4	yes	complemented
169	C₂×#1304	C₂³	1	4	yes	complemented
170	C₂×#1304	C₂³	1	4	yes	complemented
171	C₂×#1304	C₂³	1	4	yes	complemented
172	C₂×#1304	C₂³	1	4	yes	complemented
173	C₂×#1304	C₂³	1	4	yes	complemented
174	C₂×#1304	C₂³	1	4	yes	complemented
175	C₂⁷	C₂×D₄	1	1	yes	characteristic
176	C₂⁷	C₂×D₄	1	1	yes	characteristic
177	C₂⁷	#41	1	2	yes	complemented
178	C₂⁷	C₂⁴	1	1	yes	characteristic
179	C₂²×H(5,𝔽₂)	C₂×D₄	1	8	yes	—
180	C₂⁴×D₄	C₂×D₄	1	2	yes	—
181	C₂⁴×D₄	C₂×D₄	1	2	yes	—
182	C₂⁴×D₄	C₂×D₄	1	2	yes	—
183	C₂⁴×D₄	C₂×D₄	1	2	yes	—
184	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
185	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
186	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
187	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
188	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
189	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
190	C₂⁴×D₄	#41	1	4	yes	complemented
191	C₂⁴×D₄	C₂⁴	1	1	yes	characteristic
192	C₂⁴×D₄	C₂⁴	1	1	yes	characteristic
193	C₂⁴×D₄	C₂⁴	1	1	yes	characteristic
194	C₂⁴×D₄	C₂⁴	1	1	yes	characteristic
195	C₂⁴×D₄	C₂⁴	1	1	yes	characteristic
196	C₂⁴×D₄	C₂⁴	1	4	yes	—
197	C₂⁵×C₄	C₂×D₄	1	1	yes	characteristic
198	C₂⁵×C₄	C₂×D₄	1	1	yes	characteristic
199	C₂⁵×C₄	#41	1	2	yes	complemented
200	C₂²×#120	C₂×D₄	1	2	yes	—
201	C₂²×#120	C₂×D₄	1	2	yes	—
202	C₂²×#120	C₂×D₄	1	2	yes	—
203	C₂²×#120	C₂×D₄	1	2	yes	—
204	C₂²×#120	C₂×D₄	1	2	yes	complemented
205	C₂²×#120	C₂×D₄	1	2	yes	complemented
206	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
207	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
208	C₂³×C₂²⋊C₄	C₂×D₄	1	2	yes	—
209	C₂³×C₂²⋊C₄	C₂×D₄	1	2	yes	complemented
210	C₂³×C₂²⋊C₄	C₂×D₄	1	2	yes	complemented
211	C₂³×C₂²⋊C₄	C₂⁴	1	1	yes	characteristic
212	#2403	C₂×D₄	1	16	yes	—
213	#2403	C₂×D₄	1	8	yes	—
214	C₂×#386	C₂×D₄	1	2	yes	—
215	C₂×#386	C₂×D₄	1	2	yes	—
216	C₂×#386	C₂×D₄	1	2	yes	—
217	C₂×#386	C₂×D₄	1	2	yes	—
218	C₂×#386	C₂×D₄	1	2	yes	complemented
219	C₂×#386	C₂×D₄	1	2	yes	complemented
220	C₂×#386	C₂×D₄	1	2	yes	complemented
221	C₂×#386	C₂×D₄	1	2	yes	complemented
222	C₂×#386	C₂×D₄	1	2	yes	complemented
223	C₂×#386	C₂×D₄	1	2	yes	complemented
224	C₂×#381	C₂×D₄	1	2	yes	complemented
225	C₂×#381	C₂×D₄	1	2	yes	complemented
226	C₂×#381	C₂×D₄	1	2	yes	complemented
227	C₂×#381	C₂×D₄	1	2	yes	complemented
228	C₂×#379	C₂×D₄	1	2	yes	—
229	C₂×#379	C₂×D₄	1	2	yes	—
230	C₂×#379	C₂×D₄	1	2	yes	—
231	C₂×#379	C₂×D₄	1	2	yes	—
232	C₂×#379	C₂×D₄	1	2	yes	—
233	C₂×#379	C₂×D₄	1	2	yes	—
234	C₂×#379	C₂×D₄	1	2	yes	—
235	C₂×#379	C₂×D₄	1	2	yes	complemented
236	C₂×#379	C₂×D₄	1	2	yes	complemented
237	C₂×#379	C₂⁴	1	4	yes	—
238	C₂×#379	C₂⁴	1	4	yes	—
239	C₂×#379	C₂⁴	1	4	yes	—
240	C₂×#379	C₂⁴	1	1	yes	characteristic
241	C₂×#379	C₂⁴	1	1	yes	characteristic
242	C₂×#379	C₂⁴	1	1	yes	characteristic
243	C₂×#379	C₂⁴	1	1	yes	characteristic
244	C₂×#379	C₂⁴	1	1	yes	characteristic
245	C₂×#379	C₂⁴	1	1	yes	characteristic
246	C₂×#379	C₂⁴	1	1	yes	characteristic
247	C₂×#379	C₂⁴	1	1	yes	characteristic
248	#1781	C₂×D₄	1	8	yes	—
249	#1781	C₂×D₄	1	16	yes	—
250	C₂⁶	#120	1	2	yes	—
251	C₂⁶	#120	1	2	yes	—
252	C₂⁶	C₂²×D₄	1	1	yes	characteristic
253	C₂⁶	C₂²×D₄	1	1	yes	characteristic
254	C₂⁶	C₂²×D₄	1	1	yes	characteristic
255	C₂⁶	C₂²×D₄	1	1	yes	characteristic
256	C₂⁶	C₂²×D₄	1	1	yes	characteristic
257	C₂⁶	C₂²×D₄	1	1	yes	characteristic
258	C₂⁶	C₂²×D₄	1	1	yes	characteristic
259	C₂⁶	C₂²×D₄	1	1	yes	characteristic
260	C₂⁶	C₂²×D₄	1	1	yes	characteristic
261	C₂⁶	C₂²×D₄	1	1	yes	characteristic
262	C₂⁶	C₂²×D₄	1	1	yes	characteristic
263	C₂⁶	C₂×#41	1	4	yes	—
264	C₂⁶	C₂×#41	1	2	yes	—
265	C₂⁶	C₂×#41	1	2	yes	—
266	C₂⁶	H(5,𝔽₂)	1	2	yes	—
267	C₂⁶	H(5,𝔽₂)	1	2	yes	—
268	C₂⁶	C₂⁵	1	1	yes	characteristic
269	C₂³×D₄	#120	1	2	yes	—
270	C₂³×D₄	#120	1	2	yes	—
271	C₂³×D₄	#120	1	2	yes	—
272	C₂³×D₄	#120	1	2	yes	—
273	C₂³×D₄	C₂²×D₄	1	2	yes	—
274	C₂³×D₄	C₂²×D₄	1	2	yes	—
275	C₂³×D₄	C₂²×D₄	1	2	yes	—
276	C₂³×D₄	C₂²×D₄	1	2	yes	—
277	C₂³×D₄	C₂²×D₄	1	4	yes	—
278	C₂³×D₄	C₂²×D₄	1	4	yes	—
279	C₂³×D₄	C₂²×D₄	1	8	yes	—
280	C₂³×D₄	H(5,𝔽₂)	1	4	yes	—
281	C₂³×D₄	H(5,𝔽₂)	1	8	yes	—
282	C₂⁴×C₄	#120	1	2	yes	—
283	C₂⁴×C₄	#120	1	2	yes	—
284	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
285	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
286	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
287	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
288	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
289	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
290	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
291	C₂⁴×C₄	C₂×#41	1	4	yes	—
292	C₂×#120	#120	1	8	yes	complemented
293	C₂²×C₂²⋊C₄	C₂²×D₄	1	2	yes	—
294	C₂²×C₂²⋊C₄	C₂²×D₄	1	2	yes	—
295	C₂²×C₂²⋊C₄	C₂²×D₄	1	2	yes	—
296	C₂²×C₂²⋊C₄	C₂²×D₄	1	2	yes	—
297	C₂²×C₂²⋊C₄	C₂²×D₄	1	2	yes	—
298	C₂²×C₂²⋊C₄	C₂²×D₄	1	2	yes	—
299	C₂²×C₂²⋊C₄	C₂²×D₄	1	2	yes	—
300	C₂²×C₂²⋊C₄	C₂²×D₄	1	2	yes	—
301	#386	#120	1	8	yes	complemented
302	#379	C₂²×D₄	1	8	yes	—
303	#379	C₂²×D₄	1	4	yes	—
304	C₂⁵	B(4,𝔽₂)	1	8	yes	—
305	C₂⁵	C₂×#120	1	1	yes	characteristic
306	C₂⁵	C₂×#120	1	1	yes	characteristic
307	C₂⁵	C₂×#120	1	1	yes	characteristic
308	C₂⁵	C₂×#120	1	2	yes	—
309	C₂⁵	C₂×#120	1	2	yes	—
310	C₂⁵	C₂×#120	1	1	yes	characteristic
311	C₂⁵	C₂×#120	1	2	yes	—
312	C₂⁵	#525	1	1	yes	characteristic
313	C₂⁵	#525	1	2	yes	—
314	C₂⁵	#525	1	1	yes	characteristic
315	C₂⁵	#535	1	1	yes	characteristic
316	C₂⁵	#535	1	1	yes	characteristic
317	C₂⁵	#535	1	2	yes	—
318	C₂⁵	D₄²	1	4	yes	—
319	C₂⁵	#546	1	2	yes	—
320	C₂⁵	#546	1	2	yes	—
321	C₂⁵	#546	1	2	yes	—
322	C₂⁵	#546	1	2	yes	—
323	C₂⁵	#546	1	2	yes	—
324	C₂⁵	#546	1	2	yes	—
325	C₂⁵	#546	1	2	yes	—
326	C₂⁵	#546	1	2	yes	—
327	C₂⁵	#546	1	8	yes	complemented
328	C₂⁵	C₂³×D₄	1	1	yes	characteristic
329	C₂⁵	C₂³×D₄	1	1	yes	characteristic
330	C₂⁵	C₂³×D₄	1	1	yes	characteristic
331	C₂⁵	C₂³×D₄	1	2	yes	—
332	C₂⁵	C₂²×#41	1	2	yes	—
333	C₂⁵	C₂×H(5,𝔽₂)	1	2	yes	—
334	C₂⁵	C₂×H(5,𝔽₂)	1	2	yes	—
335	C₂⁵	C₂×H(5,𝔽₂)	1	4	yes	—
336	C₂²×D₄	B(4,𝔽₂)	1	8	yes	—
337	C₂²×D₄	C₂×#120	1	4	yes	—
338	C₂²×D₄	#534	1	4	yes	—
339	C₂²×D₄	D₄²	1	8	yes	—
340	C₂³×C₄	C₂×#120	1	2	yes	—
341	C₂³×C₄	C₂×#120	1	2	yes	—
342	C₂³×C₄	C₂×#120	1	2	yes	—
343	C₂³×C₄	D₄²	1	4	yes	—
344	C₂³×C₄	#546	1	8	yes	complemented
345	C₂×C₂²⋊C₄	C₂×#120	1	4	yes	—
346	C₂⁴	#2403	1	4	yes	—
347	C₂⁴	#2404	1	1	yes	characteristic
348	C₂⁴	#2404	1	2	yes	—
349	C₂⁴	#2404	1	1	yes	characteristic
350	C₂⁴	#2404	1	2	yes	—
351	C₂⁴	#2404	1	1	yes	characteristic
352	C₂⁴	#2404	1	1	yes	characteristic
353	C₂⁴	C₂×B(4,𝔽₂)	1	4	yes	—
354	C₂⁴	C₂×B(4,𝔽₂)	1	4	yes	—
355	C₂⁴	C₂×B(4,𝔽₂)	1	4	yes	—
356	C₂⁴	C₂×B(4,𝔽₂)	1	4	yes	—
357	C₂⁴	C₂×B(4,𝔽₂)	1	4	yes	—
358	C₂⁴	C₂²×#120	1	1	yes	characteristic
359	C₂⁴	C₂²×#120	1	1	yes	characteristic
360	C₂⁴	C₂×#525	1	1	yes	characteristic
361	C₂⁴	C₂×#534	1	1	yes	characteristic
362	C₂⁴	C₂×#535	1	1	yes	characteristic
363	C₂⁴	C₂×D₄²	1	2	yes	—
364	C₂⁴	C₂×D₄²	1	2	yes	—
365	C₂⁴	C₂×#546	1	2	yes	—
366	C₂⁴	C₂×#546	1	2	yes	—
367	C₂⁴	C₂×#546	1	4	yes	—
368	C₂⁴	#3484	1	2	yes	—
369	C₂⁴	#3484	1	2	yes	—
370	C₂⁴	#3484	1	2	yes	—
371	C₂⁴	#3484	1	4	yes	—
372	C₂⁴	#3490	1	4	yes	—
373	C₂⁴	#3532	1	4	yes	—
374	C₂²×C₄	#2403	1	4	yes	—
375	C₂²×C₄	C₂×B(4,𝔽₂)	1	4	yes	—
376	C₂³	#23900	1	8	yes	—
377	C₂³	#23984	1	4	yes	—
378	C₂³	#23984	1	2	yes	—
379	C₂³	#23984	1	2	yes	—
380	C₂³	#23996	1	2	yes	—
381	C₂³	#23996	1	2	yes	—
382	C₂³	#23996	1	2	yes	—
383	C₂³	C₂×#2403	1	1	yes	characteristic
384	C₂³	C₂×#2404	1	1	yes	characteristic
385	C₂³	#35346	1	1	yes	characteristic
386	C₂³	#36098	1	2	yes	—
387	C₂³	#36152	1	2	yes	—
388	C₂³	#37645	1	2	yes	—
389	C₂³	#37832	1	2	yes	—
390	C₂³	#58991	1	4	yes	—
391	C₂³	C₂²×B(4,𝔽₂)	1	2	yes	—
392	C₂³	C₂²×B(4,𝔽₂)	1	2	yes	—
393	C₂²	#251827	1	4	yes	complemented
394	C₂²	#647657	1	1	yes	characteristic
395	C₂²	C₂×#23900	1	2	yes	—
396	C₂²	C₂×#23996	1	1	yes	characteristic
397	C₂²	C₂×#23996	1	1	yes	characteristic
398	C₂²	C₂×#23996	1	1	yes	characteristic
399	C₂²	#6451863	1	1	yes	characteristic
400	C₂²	C₂×#23984	1	1	yes	characteristic
401	C₂²	C₂×#23984	1	1	yes	characteristic
402	C₂²	#6499867	1	2	yes	—
403	C₂	#72217617	1	1	yes	characteristic
404	C₂	#72225632	1	1	yes	characteristic
405	C₂	#72233156	1	1	yes	characteristic
406	C₂	#72234644	1	1	yes	characteristic
407	C₂	#72234955	1	1	yes	characteristic
408	C₂	#72240110	1	1	yes	characteristic
409	C₂	C₂×#251827	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³	C₂×#2404
commutator, Frattini, cosocle	C₂⁶	C₂⁵
LCS	G ▷ C₂⁶ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³ ◁ C₂⁷ ◁ G
LECS	G ▷ C₂⁶ ▷ C₂² ▷ C₁

Complements

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

N	H ≅ G/N	type
1. #72255632	C₂	semidirect
2. #72255630	C₂	semidirect
3. #72251614	C₂	semidirect
4. #72251454	C₂	semidirect
5. #72251429	C₂	semidirect
6. #72241287	C₂	semidirect
7. #72241194	C₂	semidirect
8. #72241194	C₂	semidirect
9. #72241183	C₂	semidirect
10. C₂×#251827	C₂	semidirect
11. #72240426	C₂	semidirect
12. #72240425	C₂	semidirect
13. #72225783	C₂	semidirect
14. #72225746	C₂	semidirect
15. C₂²×#32898	C₂	semidirect
16. #72219118	C₂	semidirect
17. #72218846	C₂	semidirect
18. #72218846	C₂	semidirect
19. #72214549	C₂	semidirect
21. C₂×#46996	C₂²	semidirect
28. C₂×#32898	C₂²	semidirect
29. C₂×#32898	C₂²	semidirect
30. C₂×#20585	C₂²	semidirect
31. C₂×#20585	C₂²	semidirect
34. #4414129	C₂²	semidirect
35. #4387644	C₂²	semidirect
36. #4387614	C₂²	semidirect
37. #4387614	C₂²	semidirect
38. #4387614	C₂²	semidirect
39. #4387584	C₂²	semidirect
40. #4387584	C₂²	semidirect
43. #612424	C₂²	semidirect
44. #576607	C₂²	semidirect
45. #521311	C₂²	semidirect
48. #517411	C₂²	semidirect
49. #392125	C₂²	semidirect
50. #392125	C₂²	semidirect
51. #392111	C₂²	semidirect
52. #392111	C₂²	semidirect
57. #392109	C₂²	semidirect
58. #359428	C₂²	semidirect
59. C₂×#10390	C₂²	semidirect
60. C₂×#10336	C₂²	semidirect
61. C₂×#10336	C₂²	semidirect
62. C₂×#9495	C₂²	semidirect
63. C₂×#9495	C₂²	semidirect
64. C₂×#9495	C₂²	semidirect
65. C₂×#9495	C₂²	semidirect
66. C₂×#9495	C₂²	semidirect
67. C₂×#9495	C₂²	semidirect
68. C₂×#8746	C₂²	semidirect
69. #119494	C₂²	semidirect
70. #119484	C₂²	semidirect
71. #119484	C₂²	semidirect
72. #116356	C₂²	semidirect
73. #116356	C₂²	semidirect
74. #116356	C₂²	semidirect
75. #115723	C₂²	semidirect
76. #115133	C₂²	semidirect
77. #115133	C₂²	semidirect
78. #115133	C₂²	semidirect
79. #115133	C₂²	semidirect
80. #115133	C₂²	semidirect
81. #115133	C₂²	semidirect
82. #111458	C₂²	semidirect
83. #111458	C₂²	semidirect
84. #110401	C₂²	semidirect
85. #106542	C₂²	semidirect
86. #105808	C₂²	semidirect
87. C₂²⋊#1304	C₂²	semidirect
88. C₂²⋊#1304	C₂²	semidirect
89. C₂²⋊#1304	C₂²	semidirect
90. C₂²⋊#1304	C₂²	semidirect
96. C₂³×#120	D₄	semidirect
98. C₂×#2840	C₂³	semidirect
99. C₂×#2403	D₄	semidirect
100. C₂×#2403	D₄	semidirect
101. C₂×#2403	D₄	semidirect
102. C₂×#2403	D₄	semidirect
112. C₂×#2403	C₂³	semidirect
113. C₂×#2403	C₂³	semidirect
114. C₂×#2308	D₄	semidirect
118. C₂×#2308	C₂³	semidirect
119. C₂×#2308	C₂³	semidirect
120. C₂×#2308	C₂³	semidirect
121. C₂²×#386	D₄	semidirect
122. C₂²×#379	D₄	semidirect
125. #32898	D₄	semidirect
138. C₂×#1781	C₂³	semidirect
139. C₂×#1781	C₂³	semidirect
140. C₂×#1781	C₂³	semidirect
141. #14681	D₄	semidirect
147. #14673	C₂³	semidirect
148. #14673	C₂³	semidirect
149. #14673	C₂³	semidirect
150. #14338	C₂³	semidirect
151. #14335	D₄	semidirect
155. #14335	C₂³	semidirect
156. #14335	C₂³	semidirect
157. #14335	C₂³	semidirect
158. #13867	D₄	semidirect
159. #13867	D₄	semidirect
163. #13867	C₂³	semidirect
164. #13867	C₂³	semidirect
165. #13775	C₂³	semidirect
166. #10725	C₂³	semidirect
167. C₂×#1304	C₂³	semidirect
168. C₂×#1304	C₂³	semidirect
169. C₂×#1304	C₂³	semidirect
170. C₂×#1304	C₂³	semidirect
171. C₂×#1304	C₂³	semidirect
172. C₂×#1304	C₂³	semidirect
173. C₂×#1304	C₂³	semidirect
174. C₂×#1304	C₂³	semidirect
177. C₂⁷	#41	semidirect
190. C₂⁴×D₄	#41	semidirect
199. C₂⁵×C₄	#41	semidirect
204. C₂²×#120	C₂×D₄	semidirect
205. C₂²×#120	C₂×D₄	semidirect
209. C₂³×C₂²⋊C₄	C₂×D₄	semidirect
210. C₂³×C₂²⋊C₄	C₂×D₄	semidirect
218. C₂×#386	C₂×D₄	semidirect
219. C₂×#386	C₂×D₄	semidirect
220. C₂×#386	C₂×D₄	semidirect
221. C₂×#386	C₂×D₄	semidirect
222. C₂×#386	C₂×D₄	semidirect
223. C₂×#386	C₂×D₄	semidirect
224. C₂×#381	C₂×D₄	semidirect
225. C₂×#381	C₂×D₄	semidirect
226. C₂×#381	C₂×D₄	semidirect
227. C₂×#381	C₂×D₄	semidirect
235. C₂×#379	C₂×D₄	semidirect
236. C₂×#379	C₂×D₄	semidirect
292. C₂×#120	#120	semidirect
301. #386	#120	semidirect
327. C₂⁵	#546	semidirect
344. C₂³×C₄	#546	semidirect
393. C₂²	#251827	semidirect

Maximal subgroups

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

subgroup	index
#72255632	2
#72255630	2
#72251614	2
#72251454	2
#72251429	2
#72241287	2
#72241194	2
#72241183	2
C₂×#251827	2
#72240426	2
#72240425	2
#72225783	2
#72225746	2
C₂²×#32898	2
#72219118	2
#72218846	2
#72214549	2