Subgroups — #72255694

Order 2048.

At least 7838 conjugacy classes of subgroups; only the 1008 normal subgroups are shown.

The subgroup lattice has 403 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#72255689	C₂	1	2	yes	maximal, complemented
2	#72255688	C₂	1	2	yes	maximal, complemented
3	#72251656	C₂	1	2	yes	maximal, complemented
4	#72251581	C₂	1	1	yes	maximal, characteristic, complemented
5	#72251570	C₂	1	1	yes	maximal, characteristic, complemented
6	#72251498	C₂	1	2	yes	maximal, complemented
7	#72251437	C₂	1	4	yes	maximal, complemented
8	#72241299	C₂	1	2	yes	maximal, complemented
9	#72240427	C₂	1	4	yes	maximal, complemented
10	#72240425	C₂	1	2	yes	maximal, complemented
11	#72240106	C₂	1	2	yes	maximal, complemented
12	#72236754	C₂	1	1	yes	maximal, characteristic, complemented
13	#72236724	C₂	1	2	yes	maximal, complemented
14	#72235930	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×#188035	C₂	1	1	yes	maximal, characteristic, complemented
16	#72225737	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂×#245225	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂²×#3484	C₂²	1	1	yes	characteristic, complemented
19	C₂³×D₄²	C₂²	1	1	yes	characteristic
20	C₂×#35527	C₂²	1	1	yes	characteristic, complemented
21	C₂×#35347	C₂²	1	1	yes	characteristic, complemented
22	C₂×#35346	C₂²	1	1	yes	characteristic
23	C₂×#35346	C₂²	1	1	yes	characteristic
24	C₂×#35346	C₂²	1	1	yes	characteristic, complemented
25	C₂×#32898	C₂²	1	2	yes	complemented
26	C₂×#32898	C₂²	1	2	yes	complemented
27	C₂×#21746	C₂²	1	2	yes	complemented
28	C₂²×#1781	C₂²	1	2	yes	complemented
29	C₂²×#1781	C₂²	1	2	yes	complemented
30	#759288	C₂²	1	4	yes	complemented
31	#635984	C₂²	1	2	yes	—
32	#618316	C₂²	1	2	yes	—
33	#618316	C₂²	1	2	yes	complemented
34	#617710	C₂²	1	2	yes	—
35	#616964	C₂²	1	2	yes	complemented
36	#612424	C₂²	1	2	yes	—
37	#612424	C₂²	1	2	yes	complemented
38	#612424	C₂²	1	2	yes	complemented
39	#555905	C₂²	1	1	yes	characteristic, complemented
40	#555894	C₂²	1	1	yes	characteristic
41	#555894	C₂²	1	1	yes	characteristic, complemented
42	#517411	C₂²	1	1	yes	characteristic, complemented
43	#515362	C₂²	1	1	yes	characteristic, complemented
44	#515285	C₂²	1	1	yes	characteristic
45	#405776	C₂²	1	4	yes	complemented
46	#405104	C₂²	1	4	yes	complemented
47	#395370	C₂²	1	4	yes	complemented
48	#393929	C₂²	1	4	yes	complemented
49	#392658	C₂²	1	2	yes	complemented
50	#392603	C₂²	1	2	yes	complemented
51	#392125	C₂²	1	2	yes	complemented
52	#392125	C₂²	1	2	yes	complemented
53	#380244	C₂²	1	2	yes	complemented
54	#379754	C₂²	1	2	yes	complemented
55	#359428	C₂²	1	4	yes	complemented
56	#359428	C₂²	1	4	yes	complemented
57	C₂×#10336	C₂²	1	4	yes	complemented
58	C₂×#10336	C₂²	1	4	yes	complemented
59	C₂×#9497	C₂²	1	2	yes	complemented
60	C₂×#9495	C₂²	1	2	yes	complemented
61	C₂×#9495	C₂²	1	2	yes	complemented
62	C₂×#9495	C₂²	1	2	yes	complemented
63	C₂×#8546	C₂²	1	2	yes	complemented
64	C₂×#8542	C₂²	1	2	yes	complemented
65	C₂×#8542	C₂²	1	2	yes	complemented
66	C₂×#8541	C₂²	1	1	yes	characteristic
67	C₂×#8541	C₂²	1	1	yes	characteristic
68	#119495	C₂²	1	4	yes	complemented
69	#119494	C₂²	1	4	yes	complemented
70	#116351	C₂²	1	4	yes	complemented
71	#116351	C₂²	1	4	yes	complemented
72	#115134	C₂²	1	4	yes	complemented
73	#115133	C₂²	1	4	yes	complemented
74	#111458	C₂²	1	4	yes	complemented
75	#111458	C₂²	1	4	yes	complemented
76	#111458	C₂²	1	4	yes	complemented
77	#111458	C₂²	1	4	yes	complemented
78	#106543	C₂²	1	2	yes	complemented
79	#106542	C₂²	1	2	yes	complemented
80	#106542	C₂²	1	2	yes	complemented
81	#106542	C₂²	1	2	yes	complemented
82	C₂²⋊#1304	C₂²	1	4	yes	complemented
83	C₂³×H(5,𝔽₂)	C₂³	1	1	yes	characteristic
84	C₂³×H(5,𝔽₂)	C₂³	1	1	yes	characteristic
85	C₂⁵×D₄	D₄	1	1	yes	characteristic, complemented
86	C₂⁵×D₄	D₄	1	1	yes	characteristic, complemented
87	C₂⁵×D₄	C₂³	1	1	yes	characteristic
88	C₂⁵×D₄	C₂³	1	1	yes	characteristic
89	C₂²×#534	C₂³	1	2	yes	—
90	C₂³×#127	C₂³	1	1	yes	characteristic
91	C₂³×#121	D₄	1	1	yes	characteristic, complemented
92	C₂³×#121	D₄	1	1	yes	characteristic, complemented
93	C₂³×#121	C₂³	1	1	yes	characteristic
94	C₂³×#121	C₂³	1	1	yes	characteristic
95	C₂³×#120	D₄	1	1	yes	characteristic, complemented
96	C₂³×#120	D₄	1	1	yes	characteristic, complemented
97	C₂³×#120	C₂³	1	1	yes	characteristic
98	C₂³×#120	C₂³	1	2	yes	—
99	C₂³×#120	C₂³	1	2	yes	—
100	C₂³×#120	C₂³	1	1	yes	characteristic
101	C₂²×#518	C₂³	1	1	yes	characteristic
102	C₂³×C₄×D₄	D₄	1	1	yes	characteristic, complemented
103	C₂³×C₄×D₄	D₄	1	1	yes	characteristic, complemented
104	C₂×#2405	C₂³	1	2	yes	—
105	C₂×#2403	D₄	1	4	yes	complemented
106	C₂×#2403	D₄	1	4	yes	complemented
107	C₂×#2403	C₂³	1	2	yes	—
108	C₂×#2403	C₂³	1	2	yes	—
109	C₂×#2403	C₂³	1	2	yes	—
110	C₂×#2403	C₂³	1	2	yes	—
111	C₂×#2403	C₂³	1	2	yes	—
112	C₂×#2403	C₂³	1	2	yes	—
113	C₂×#2403	C₂³	1	2	yes	—
114	C₂×#2403	C₂³	1	4	yes	—
115	C₂×#2309	C₂³	1	1	yes	characteristic
116	C₂×#2308	C₂³	1	1	yes	characteristic
117	C₂×#2308	C₂³	1	1	yes	characteristic
118	C₂×#2308	C₂³	1	1	yes	characteristic
119	C₂×#2308	C₂³	1	2	yes	—
120	C₂×#2308	C₂³	1	1	yes	characteristic
121	C₂²×#379	C₂³	1	4	yes	—
122	C₂×#1819	C₂³	1	4	yes	—
123	C₂×#1781	C₂³	1	2	yes	—
124	C₂×#1781	C₂³	1	2	yes	—
125	C₂×#1781	C₂³	1	4	yes	—
126	C₂×#1781	C₂³	1	4	yes	—
127	C₂×#1781	C₂³	1	4	yes	—
128	C₂×#1781	C₂³	1	2	yes	—
129	C₂×#1781	C₂³	1	2	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	2	yes	—
134	C₂×#1781	C₂³	1	2	yes	—
135	#14718	D₄	1	8	yes	complemented
136	#14715	D₄	1	8	yes	complemented
137	#14679	C₂³	1	2	yes	—
138	#14679	C₂³	1	2	yes	—
139	#14341	C₂³	1	2	yes	—
140	#14335	C₂³	1	2	yes	—
141	#14127	C₂³	1	4	yes	—
142	#13869	C₂³	1	2	yes	—
143	#13867	D₄	1	4	yes	complemented
144	#13867	D₄	1	4	yes	complemented
145	#13867	C₂³	1	2	yes	—
146	#13867	C₂³	1	2	yes	—
147	#13867	C₂³	1	2	yes	—
148	#13867	C₂³	1	2	yes	—
149	#13867	C₂³	1	2	yes	—
150	#13867	C₂³	1	2	yes	—
151	#13867	C₂³	1	2	yes	—
152	#13867	C₂³	1	4	yes	—
153	#13867	C₂³	1	4	yes	—
154	#10725	C₂³	1	4	yes	—
155	#10725	C₂³	1	4	yes	—
156	#10725	C₂³	1	4	yes	—
157	#10725	C₂³	1	4	yes	—
158	#8541	D₄	1	8	yes	complemented
159	C₂×#1304	C₂³	1	4	yes	—
160	C₂×#1304	C₂³	1	4	yes	—
161	C₂×#1304	C₂³	1	4	yes	—
162	C₂×#1304	C₂³	1	4	yes	—
163	C₂⁷	C₂×D₄	1	1	yes	characteristic
164	C₂⁷	C₂×D₄	1	1	yes	characteristic
165	C₂⁷	C₂×D₄	1	1	yes	characteristic
166	C₂⁷	C₂⁴	1	1	yes	characteristic
167	C₂⁴×D₄	C₂×D₄	1	4	yes	—
168	C₂⁴×D₄	C₂×D₄	1	4	yes	—
169	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
170	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
171	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
172	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
173	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
174	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
175	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
176	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
177	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
178	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
179	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
180	C₂⁴×D₄	C₂×D₄	1	2	yes	complemented
181	C₂⁴×D₄	C₂×D₄	1	4	yes	complemented
182	C₂⁴×D₄	C₂×D₄	1	2	yes	complemented
183	C₂⁴×D₄	C₂⁴	1	2	yes	—
184	C₂⁴×D₄	C₂⁴	1	2	yes	—
185	C₂⁴×D₄	C₂⁴	1	1	yes	characteristic
186	C₂⁴×D₄	C₂⁴	1	1	yes	characteristic
187	C₂⁴×D₄	C₂⁴	1	1	yes	characteristic
188	C₂⁴×D₄	C₂⁴	1	1	yes	characteristic
189	C₂⁴×D₄	C₂⁴	1	1	yes	characteristic
190	C₂⁵×C₄	C₂×D₄	1	1	yes	characteristic
191	C₂⁵×C₄	C₂×D₄	1	1	yes	characteristic
192	C₂⁵×C₄	C₂×D₄	1	1	yes	characteristic
193	C₂⁵×C₄	C₂×D₄	1	1	yes	characteristic
194	C₂²×#120	C₂×D₄	1	4	yes	—
195	C₂²×#120	C₂×D₄	1	4	yes	—
196	C₂²×#120	C₂×D₄	1	8	yes	—
197	C₂²×#120	C₂×D₄	1	4	yes	—
198	C₂²×#120	C₂×D₄	1	4	yes	complemented
199	C₂²×#120	#41	1	4	yes	—
200	C₂³×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
201	C₂³×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
202	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
203	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
204	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
205	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
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	1	yes	characteristic
209	C₂³×C₂²⋊C₄	C₂×D₄	1	4	yes	complemented
210	C₂³×C₂²⋊C₄	C₂×D₄	1	2	yes	complemented
211	C₂³×C₂²⋊C₄	C₂×D₄	1	2	yes	complemented
212	C₂³×C₂²⋊C₄	C₂⁴	1	1	yes	characteristic
213	C₂³×C₂²⋊C₄	C₂⁴	1	2	yes	—
214	C₂³×C₂²⋊C₄	C₂⁴	1	2	yes	—
215	C₂³×C₄²	C₂×D₄	1	1	yes	characteristic
216	C₂×#386	C₂×D₄	1	4	yes	—
217	C₂×#386	C₂×D₄	1	4	yes	—
218	C₂×#386	C₂×D₄	1	4	yes	—
219	C₂×#386	C₂×D₄	1	4	yes	—
220	C₂×#386	C₂×D₄	1	8	yes	—
221	C₂×#386	C₂×D₄	1	4	yes	complemented
222	C₂×#386	C₂×D₄	1	4	yes	complemented
223	C₂×#386	C₂×D₄	1	4	yes	complemented
224	C₂×#385	C₂×D₄	1	4	yes	complemented
225	C₂×#379	C₂×D₄	1	4	yes	complemented
226	C₂×#379	C₂×D₄	1	4	yes	complemented
227	C₂×#379	C₂×D₄	1	4	yes	complemented
228	C₂×#379	C₂×D₄	1	8	yes	complemented
229	C₂×#379	C₂⁴	1	4	yes	—
230	C₂×#379	C₂⁴	1	4	yes	—
231	C₂×#379	C₂⁴	1	2	yes	—
232	C₂×#379	C₂⁴	1	2	yes	—
233	C₂×#379	C₂⁴	1	2	yes	—
234	C₂×#379	C₂⁴	1	2	yes	—
235	#1781	C₂×D₄	1	8	yes	—
236	#1781	C₂×D₄	1	8	yes	complemented
237	#1781	C₂×D₄	1	8	yes	complemented
238	C₂²⋊#95	C₂×D₄	1	8	yes	complemented
239	C₂⁶	#120	1	4	yes	—
240	C₂⁶	#121	1	4	yes	complemented
241	C₂⁶	C₂²×D₄	1	1	yes	characteristic
242	C₂⁶	C₂²×D₄	1	1	yes	characteristic
243	C₂⁶	C₂²×D₄	1	2	yes	—
244	C₂⁶	C₂²×D₄	1	2	yes	—
245	C₂⁶	C₂²×D₄	1	2	yes	—
246	C₂⁶	C₂²×D₄	1	1	yes	characteristic
247	C₂⁶	C₂²×D₄	1	1	yes	characteristic
248	C₂⁶	C₂²×D₄	1	1	yes	characteristic
249	C₂⁶	C₂²×D₄	1	1	yes	characteristic
250	C₂⁶	C₂²×D₄	1	1	yes	characteristic
251	C₂⁶	C₂²×D₄	1	4	yes	—
252	C₂⁶	C₂²×D₄	1	2	yes	—
253	C₂⁶	H(5,𝔽₂)	1	2	yes	—
254	C₂⁶	H(5,𝔽₂)	1	2	yes	—
255	C₂⁶	C₂⁵	1	1	yes	characteristic
256	C₂³×D₄	#120	1	2	yes	—
257	C₂³×D₄	#120	1	2	yes	—
258	C₂³×D₄	#120	1	2	yes	—
259	C₂³×D₄	#120	1	2	yes	—
260	C₂³×D₄	#120	1	4	yes	—
261	C₂³×D₄	#120	1	4	yes	—
262	C₂³×D₄	C₂²×D₄	1	4	yes	—
263	C₂³×D₄	C₂²×D₄	1	4	yes	—
264	C₂³×D₄	C₂²×D₄	1	4	yes	—
265	C₂³×D₄	C₂²×D₄	1	2	yes	—
266	C₂³×D₄	C₂²×D₄	1	2	yes	—
267	C₂³×D₄	C₂²×D₄	1	2	yes	—
268	C₂³×D₄	C₂×#41	1	2	yes	—
269	C₂³×D₄	C₂×#41	1	2	yes	—
270	C₂³×D₄	C₂×#41	1	2	yes	—
271	C₂³×D₄	H(5,𝔽₂)	1	4	yes	—
272	C₂³×D₄	H(5,𝔽₂)	1	4	yes	—
273	C₂³×D₄	H(5,𝔽₂)	1	4	yes	—
274	C₂⁴×C₄	#120	1	4	yes	—
275	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
276	C₂⁴×C₄	C₂²×D₄	1	2	yes	—
277	C₂⁴×C₄	C₂²×D₄	1	2	yes	—
278	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
279	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
280	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
281	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
282	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
283	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
284	C₂⁴×C₄	C₂²×D₄	1	4	yes	—
285	C₂⁴×C₄	C₂²×D₄	1	2	yes	—
286	C₂⁴×C₄	C₂²×D₄	1	2	yes	—
287	C₂²×C₂²⋊C₄	#120	1	4	yes	—
288	C₂²×C₂²⋊C₄	#120	1	4	yes	—
289	C₂²×C₂²⋊C₄	#121	1	4	yes	complemented
290	C₂²×C₂²⋊C₄	#121	1	4	yes	complemented
291	C₂²×C₂²⋊C₄	#121	1	4	yes	complemented
292	C₂²×C₂²⋊C₄	C₂²×D₄	1	4	yes	—
293	C₂²×C₂²⋊C₄	C₂²×D₄	1	4	yes	—
294	C₂²×C₂²⋊C₄	C₂²×D₄	1	4	yes	—
295	C₂²×C₂²⋊C₄	C₂²×D₄	1	4	yes	—
296	C₂²×C₂²⋊C₄	C₂²×D₄	1	4	yes	—
297	#379	C₂²×D₄	1	8	yes	—
298	C₂⁵	C₂×#120	1	2	yes	—
299	C₂⁵	C₂×#120	1	2	yes	—
300	C₂⁵	C₂×#120	1	2	yes	—
301	C₂⁵	C₂×#120	1	2	yes	—
302	C₂⁵	C₂×#120	1	1	yes	characteristic
303	C₂⁵	C₂×#120	1	2	yes	—
304	C₂⁵	C₂×#120	1	1	yes	characteristic
305	C₂⁵	C₂×#120	1	2	yes	—
306	C₂⁵	C₂×#121	1	2	yes	—
307	C₂⁵	C₂×#121	1	2	yes	—
308	C₂⁵	C₂×#121	1	2	yes	—
309	C₂⁵	#534	1	1	yes	characteristic
310	C₂⁵	#534	1	2	yes	—
311	C₂⁵	#534	1	2	yes	—
312	C₂⁵	#534	1	2	yes	—
313	C₂⁵	#534	1	1	yes	characteristic
314	C₂⁵	#534	1	2	yes	—
315	C₂⁵	D₄²	1	4	yes	—
316	C₂⁵	D₄²	1	4	yes	—
317	C₂⁵	D₄²	1	4	yes	—
318	C₂⁵	D₄²	1	4	yes	—
319	C₂⁵	C₂³×D₄	1	1	yes	characteristic
320	C₂⁵	C₂³×D₄	1	2	yes	—
321	C₂⁵	C₂³×D₄	1	2	yes	—
322	C₂⁵	C₂³×D₄	1	1	yes	characteristic
323	C₂⁵	C₂²×#41	1	1	yes	characteristic
324	C₂⁵	C₂×H(5,𝔽₂)	1	2	yes	—
325	C₂⁵	C₂×H(5,𝔽₂)	1	2	yes	—
326	C₂⁵	C₂×H(5,𝔽₂)	1	2	yes	—
327	C₂⁵	C₂×H(5,𝔽₂)	1	2	yes	—
328	C₂²×D₄	B(4,𝔽₂)	1	8	yes	complemented
329	C₂²×D₄	D₄²	1	8	yes	—
330	C₂²×D₄	D₄²	1	8	yes	—
331	C₂²×D₄	#546	1	8	yes	—
332	C₂²×D₄	#546	1	8	yes	—
333	C₂³×C₄	C₂×#120	1	2	yes	—
334	C₂³×C₄	C₂×#120	1	2	yes	—
335	C₂³×C₄	C₂×#120	1	2	yes	—
336	C₂³×C₄	C₂×#120	1	2	yes	—
337	C₂³×C₄	C₂×#120	1	2	yes	—
338	C₂³×C₄	C₂×#121	1	2	yes	—
339	C₂³×C₄	C₂×#121	1	2	yes	—
340	C₂³×C₄	C₂×#121	1	2	yes	—
341	C₂³×C₄	#534	1	2	yes	—
342	C₂³×C₄	#534	1	2	yes	—
343	C₂³×C₄	#534	1	2	yes	—
344	C₂⁴	#2403	1	2	yes	—
345	C₂⁴	#2403	1	2	yes	—
346	C₂⁴	#2403	1	2	yes	—
347	C₂⁴	#2403	1	2	yes	—
348	C₂⁴	#2410	1	4	yes	—
349	C₂⁴	#2410	1	4	yes	—
350	C₂⁴	C₂×B(4,𝔽₂)	1	4	yes	—
351	C₂⁴	C₂×B(4,𝔽₂)	1	4	yes	—
352	C₂⁴	#3026	1	4	yes	—
353	C₂⁴	C₂²×#120	1	1	yes	characteristic
354	C₂⁴	C₂²×#120	1	1	yes	characteristic
355	C₂⁴	C₂²×#121	1	1	yes	characteristic
356	C₂⁴	C₂×#534	1	1	yes	characteristic
357	C₂⁴	C₂×#534	1	1	yes	characteristic
358	C₂⁴	C₂×#534	1	1	yes	characteristic
359	C₂⁴	C₂×#534	1	1	yes	characteristic
360	C₂⁴	C₂×D₄²	1	4	yes	—
361	C₂⁴	C₂×D₄²	1	2	yes	—
362	C₂⁴	C₂×D₄²	1	2	yes	—
363	C₂⁴	C₂×#546	1	2	yes	—
364	C₂⁴	C₂×#546	1	2	yes	—
365	C₂⁴	#3484	1	4	yes	—
366	C₂⁴	#3484	1	4	yes	—
367	C₂⁴	#3484	1	2	yes	—
368	C₂⁴	#3490	1	2	yes	—
369	C₂⁴	#3532	1	4	yes	—
370	C₂²×C₄	#2410	1	4	yes	—
371	C₂²×C₄	#2410	1	4	yes	—
372	C₂²×C₄	C₂×B(4,𝔽₂)	1	4	yes	—
373	C₂³	#23895	1	4	yes	—
374	C₂³	#23900	1	4	yes	—
375	C₂³	#24404	1	8	yes	—
376	C₂³	C₂×#2403	1	1	yes	characteristic
377	C₂³	C₂×#2410	1	1	yes	characteristic
378	C₂³	C₂×#2410	1	1	yes	characteristic
379	C₂³	#34980	1	1	yes	characteristic
380	C₂³	#34980	1	1	yes	characteristic
381	C₂³	#34981	1	1	yes	characteristic
382	C₂³	#37436	1	1	yes	characteristic
383	C₂³	#58990	1	4	yes	—
384	C₂³	#58991	1	4	yes	—
385	C₂³	C₂²×B(4,𝔽₂)	1	2	yes	—
386	C₂³	C₂×#3026	1	2	yes	—
387	C₂³	#60399	1	4	yes	—
388	C₂²	#759288	1	1	yes	characteristic
389	C₂²	C₂×#23900	1	1	yes	characteristic
390	C₂²	#6437621	1	1	yes	characteristic
391	C₂²	C₂×#23895	1	2	yes	—
392	C₂²	#6437632	1	2	yes	—
393	C₂²	C₂×#24404	1	2	yes	—
394	C₂²	#6437999	1	2	yes	—
395	C₂²	#6470225	1	2	yes	—
396	C₂²	#6470234	1	2	yes	—
397	C₂	#72225619	1	1	yes	characteristic
398	C₂	#72233042	1	2	yes	—
399	C₂	#72251131	1	1	yes	characteristic
400	C₂	#72251347	1	2	yes	—
401	C₂	#72251411	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³	C₂×#2403
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. #72255689	C₂	semidirect
2. #72255688	C₂	semidirect
3. #72251656	C₂	semidirect
4. #72251581	C₂	semidirect
5. #72251570	C₂	semidirect
6. #72251498	C₂	semidirect
7. #72251437	C₂	semidirect
8. #72241299	C₂	semidirect
9. #72240427	C₂	semidirect
10. #72240425	C₂	semidirect
11. #72240106	C₂	semidirect
12. #72236754	C₂	semidirect
13. #72236724	C₂	semidirect
14. #72235930	C₂	semidirect
15. C₂×#188035	C₂	semidirect
16. #72225737	C₂	semidirect
17. C₂×#245225	C₂	semidirect
18. C₂²×#3484	C₂²	semidirect
20. C₂×#35527	C₂²	semidirect
21. C₂×#35347	C₂²	semidirect
24. C₂×#35346	C₂²	semidirect
25. C₂×#32898	C₂²	semidirect
26. C₂×#32898	C₂²	semidirect
27. C₂×#21746	C₂²	semidirect
28. C₂²×#1781	C₂²	semidirect
29. C₂²×#1781	C₂²	semidirect
30. #759288	C₂²	semidirect
33. #618316	C₂²	semidirect
35. #616964	C₂²	semidirect
37. #612424	C₂²	semidirect
38. #612424	C₂²	semidirect
39. #555905	C₂²	semidirect
41. #555894	C₂²	semidirect
42. #517411	C₂²	semidirect
43. #515362	C₂²	semidirect
45. #405776	C₂²	semidirect
46. #405104	C₂²	semidirect
47. #395370	C₂²	semidirect
48. #393929	C₂²	semidirect
49. #392658	C₂²	semidirect
50. #392603	C₂²	semidirect
51. #392125	C₂²	semidirect
52. #392125	C₂²	semidirect
53. #380244	C₂²	semidirect
54. #379754	C₂²	semidirect
55. #359428	C₂²	semidirect
56. #359428	C₂²	semidirect
57. C₂×#10336	C₂²	semidirect
58. C₂×#10336	C₂²	semidirect
59. C₂×#9497	C₂²	semidirect
60. C₂×#9495	C₂²	semidirect
61. C₂×#9495	C₂²	semidirect
62. C₂×#9495	C₂²	semidirect
63. C₂×#8546	C₂²	semidirect
64. C₂×#8542	C₂²	semidirect
65. C₂×#8542	C₂²	semidirect
68. #119495	C₂²	semidirect
69. #119494	C₂²	semidirect
70. #116351	C₂²	semidirect
71. #116351	C₂²	semidirect
72. #115134	C₂²	semidirect
73. #115133	C₂²	semidirect
74. #111458	C₂²	semidirect
75. #111458	C₂²	semidirect
76. #111458	C₂²	semidirect
77. #111458	C₂²	semidirect
78. #106543	C₂²	semidirect
79. #106542	C₂²	semidirect
80. #106542	C₂²	semidirect
81. #106542	C₂²	semidirect
82. C₂²⋊#1304	C₂²	semidirect
85. C₂⁵×D₄	D₄	semidirect
86. C₂⁵×D₄	D₄	semidirect
91. C₂³×#121	D₄	semidirect
92. C₂³×#121	D₄	semidirect
95. C₂³×#120	D₄	semidirect
96. C₂³×#120	D₄	semidirect
102. C₂³×C₄×D₄	D₄	semidirect
103. C₂³×C₄×D₄	D₄	semidirect
105. C₂×#2403	D₄	semidirect
106. C₂×#2403	D₄	semidirect
135. #14718	D₄	semidirect
136. #14715	D₄	semidirect
143. #13867	D₄	semidirect
144. #13867	D₄	semidirect
158. #8541	D₄	semidirect
180. C₂⁴×D₄	C₂×D₄	semidirect
181. C₂⁴×D₄	C₂×D₄	semidirect
182. C₂⁴×D₄	C₂×D₄	semidirect
198. C₂²×#120	C₂×D₄	semidirect
209. C₂³×C₂²⋊C₄	C₂×D₄	semidirect
210. C₂³×C₂²⋊C₄	C₂×D₄	semidirect
211. C₂³×C₂²⋊C₄	C₂×D₄	semidirect
221. C₂×#386	C₂×D₄	semidirect
222. C₂×#386	C₂×D₄	semidirect
223. C₂×#386	C₂×D₄	semidirect
224. C₂×#385	C₂×D₄	semidirect
225. C₂×#379	C₂×D₄	semidirect
226. C₂×#379	C₂×D₄	semidirect
227. C₂×#379	C₂×D₄	semidirect
228. C₂×#379	C₂×D₄	semidirect
236. #1781	C₂×D₄	semidirect
237. #1781	C₂×D₄	semidirect
238. C₂²⋊#95	C₂×D₄	semidirect
240. C₂⁶	#121	semidirect
289. C₂²×C₂²⋊C₄	#121	semidirect
290. C₂²×C₂²⋊C₄	#121	semidirect
291. C₂²×C₂²⋊C₄	#121	semidirect
328. C₂²×D₄	B(4,𝔽₂)	semidirect

Maximal subgroups

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

subgroup	index
#72255689	2
#72255688	2
#72251656	2
#72251581	2
#72251570	2
#72251498	2
#72251437	2
#72241299	2
#72240427	2
#72240425	2
#72240106	2
#72236754	2
#72236724	2
#72235930	2
C₂×#188035	2
#72225737	2
C₂×#245225	2