Subgroups — #72313223

Order 2048.

At least 15107 conjugacy classes of subgroups; only the 828 normal subgroups are shown.

The subgroup lattice has 647 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#72309373	C₂	1	1	yes	maximal, characteristic, complemented
2	#72309370	C₂	1	1	yes	maximal, characteristic, complemented
3	#72309369	C₂	1	1	yes	maximal, characteristic, complemented
4	#72259089	C₂	1	1	yes	maximal, characteristic, complemented
5	#72259002	C₂	1	1	yes	maximal, characteristic, complemented
6	#72236453	C₂	1	1	yes	maximal, characteristic, complemented
7	#72236437	C₂	1	1	yes	maximal, characteristic, complemented
8	#72232592	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×#394167	C₂	1	1	yes	maximal, characteristic, complemented
10	#72218766	C₂	1	1	yes	maximal, characteristic, complemented
11	#72218744	C₂	1	1	yes	maximal, characteristic, complemented
12	#72217699	C₂	1	1	yes	maximal, characteristic, complemented
13	#72217699	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×#115690	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×#6499867	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#62817	C₂²	1	1	yes	characteristic
17	#7641845	C₂²	1	1	yes	characteristic
18	#7641845	C₂²	1	1	yes	characteristic
19	C₂²×#2846	C₂²	1	1	yes	characteristic
20	C₂²×#2846	C₂²	1	1	yes	characteristic
21	C₂²×#2846	C₂²	1	1	yes	characteristic
22	C₂²×#2846	C₂²	1	1	yes	characteristic, complemented
23	C₂×#34981	C₂²	1	1	yes	characteristic
24	C₂³×#379	C₂²	1	1	yes	characteristic, complemented
25	C₂×#21746	C₂²	1	1	yes	characteristic
26	C₂×#21746	C₂²	1	1	yes	characteristic
27	C₂×#21746	C₂²	1	1	yes	characteristic
28	C₂×#21746	C₂²	1	1	yes	characteristic
29	C₂×#21746	C₂²	1	1	yes	characteristic
30	C₂×#21746	C₂²	1	1	yes	characteristic
31	C₂×#21746	C₂²	1	1	yes	characteristic
32	C₂×#21746	C₂²	1	1	yes	characteristic, complemented
33	C₂×#21746	C₂²	1	1	yes	characteristic, complemented
34	C₂²×#1898	C₂²	1	1	yes	characteristic
35	C₂²×#1898	C₂²	1	1	yes	characteristic
36	C₂²×#1898	C₂²	1	1	yes	characteristic
37	C₂²×#1898	C₂²	1	1	yes	characteristic
38	C₂²×#1898	C₂²	1	1	yes	characteristic, complemented
39	C₂×#14679	C₂²	1	1	yes	characteristic, complemented
40	C₂×#14679	C₂²	1	1	yes	characteristic, complemented
41	#516383	C₂²	1	1	yes	characteristic
42	#355913	C₂²	1	1	yes	characteristic, complemented
43	#355913	C₂²	1	1	yes	characteristic, complemented
44	C₂×#10735	C₂²	1	1	yes	characteristic, complemented
45	C₂×#10735	C₂²	1	1	yes	characteristic, complemented
46	C₂×#10735	C₂²	1	1	yes	characteristic, complemented
47	C₂×#10725	C₂²	1	1	yes	characteristic, complemented
48	C₂×#10725	C₂²	1	1	yes	characteristic, complemented
49	C₂×#8101	C₂²	1	1	yes	characteristic, complemented
50	C₂×#8101	C₂²	1	1	yes	characteristic, complemented
51	C₂⁸	C₂³	1	1	yes	characteristic
52	#62817	D₄	1	4	yes	complemented
53	C₂²×#534	D₄	1	1	yes	characteristic, complemented
54	C₂³×#120	D₄	1	2	yes	complemented
55	C₂³×#120	C₂³	1	1	yes	characteristic
56	C₂³×#120	C₂³	1	1	yes	characteristic
57	C₂³×#120	C₂³	1	1	yes	characteristic
58	C₂³×#120	C₂³	1	1	yes	characteristic
59	C₂⁴×C₂²⋊C₄	C₂³	1	1	yes	characteristic
60	C₂⁴×C₂²⋊C₄	C₂³	1	1	yes	characteristic
61	C₂³×#99	D₄	1	2	yes	complemented
62	C₂³×#99	D₄	1	2	yes	complemented
63	C₂×#2846	D₄	1	4	yes	complemented
64	C₂×#2846	D₄	1	4	yes	complemented
65	#34992	D₄	1	2	yes	complemented
66	#34992	D₄	1	2	yes	complemented
67	#34980	D₄	1	2	yes	complemented
68	#34980	D₄	1	2	yes	complemented
69	C₂×#2315	D₄	1	1	yes	characteristic, complemented
70	C₂×#2308	D₄	1	1	yes	characteristic, complemented
71	C₂×#2308	D₄	1	1	yes	characteristic, complemented
72	C₂²×#379	D₄	1	2	yes	complemented
73	C₂²×#379	C₂³	1	1	yes	characteristic
74	C₂²×#379	C₂³	1	1	yes	characteristic
75	C₂²×#379	C₂³	1	1	yes	characteristic
76	C₂²×#379	C₂³	1	1	yes	characteristic
77	C₂²×#379	C₂³	1	1	yes	characteristic
78	C₂²×#379	C₂³	1	1	yes	characteristic
79	C₂²×#379	C₂³	1	1	yes	characteristic
80	C₂²×#379	C₂³	1	1	yes	characteristic
81	#21746	D₄	1	4	yes	complemented
82	#21746	D₄	1	4	yes	complemented
83	C₂×#1898	D₄	1	4	yes	complemented
84	C₂×#1898	D₄	1	4	yes	complemented
85	C₂×#1819	D₄	1	2	yes	complemented
86	C₂×#1819	D₄	1	2	yes	complemented
87	C₂×#1819	D₄	1	2	yes	complemented
88	C₂×#1781	D₄	1	2	yes	complemented
89	C₂×#1781	D₄	1	2	yes	complemented
90	C₂×#1781	D₄	1	2	yes	complemented
91	C₂²×#342	D₄	1	2	yes	complemented
92	C₂²×#342	D₄	1	2	yes	complemented
93	C₂⁷	C₂×D₄	1	2	yes	—
94	C₂⁷	C₂×D₄	1	2	yes	—
95	C₂⁷	C₂×D₄	1	2	yes	—
96	C₂⁷	C₂⁴	1	1	yes	characteristic
97	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
98	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
99	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
100	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
101	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
102	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
103	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
104	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
105	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
106	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
107	C₂⁴×D₄	#41	1	1	yes	characteristic
108	C₂⁴×D₄	#41	1	1	yes	characteristic
109	C₂²×#120	C₂×D₄	1	2	yes	—
110	C₂²×#120	C₂×D₄	1	2	yes	—
111	C₂²×#120	C₂×D₄	1	2	yes	—
112	C₂²×#120	C₂×D₄	1	2	yes	—
113	C₂²×#120	C₂×D₄	1	2	yes	—
114	C₂²×#120	C₂×D₄	1	2	yes	—
115	C₂²×#120	C₂×D₄	1	2	yes	—
116	C₂²×#120	C₂×D₄	1	2	yes	—
117	C₂²×#120	C₂×D₄	1	2	yes	—
118	C₂²×#120	C₂×D₄	1	2	yes	—
119	C₂²×#120	C₂×D₄	1	2	yes	—
120	C₂²×#120	#41	1	2	yes	—
121	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
122	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
123	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
124	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
125	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
126	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
127	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
128	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
129	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
130	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
131	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
132	C₂³×C₂²⋊C₄	C₂×D₄	1	2	yes	—
133	C₂³×C₂²⋊C₄	C₂×D₄	1	2	yes	—
134	C₂³×C₂²⋊C₄	C₂×D₄	1	2	yes	—
135	C₂³×C₂²⋊C₄	C₂×D₄	1	2	yes	—
136	C₂³×C₂²⋊C₄	C₂×D₄	1	2	yes	—
137	C₂³×C₂²⋊C₄	C₂×D₄	1	2	yes	—
138	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
139	C₂³×C₂²⋊C₄	C₂×D₄	1	2	yes	—
140	C₂³×C₂²⋊C₄	#41	1	1	yes	characteristic
141	C₂³×C₂²⋊C₄	#41	1	1	yes	characteristic
142	C₂×#379	C₂×D₄	1	2	yes	—
143	C₂×#379	C₂×D₄	1	2	yes	—
144	C₂×#379	C₂×D₄	1	2	yes	—
145	C₂×#379	C₂×D₄	1	2	yes	—
146	C₂×#379	C₂×D₄	1	2	yes	—
147	C₂×#379	C₂×D₄	1	2	yes	—
148	C₂×#379	C₂×D₄	1	2	yes	—
149	C₂×#379	C₂×D₄	1	2	yes	—
150	C₂×#379	C₂×D₄	1	2	yes	—
151	C₂×#379	C₂×D₄	1	2	yes	—
152	C₂×#379	C₂×D₄	1	2	yes	—
153	C₂×#379	C₂×D₄	1	2	yes	—
154	C₂×#379	C₂×D₄	1	2	yes	—
155	C₂×#379	C₂×D₄	1	2	yes	—
156	C₂×#379	C₂×D₄	1	2	yes	—
157	C₂×#379	C₂×D₄	1	2	yes	—
158	C₂⁶	#120	1	4	yes	—
159	C₂⁶	#120	1	1	yes	characteristic
160	C₂⁶	#121	1	1	yes	characteristic
161	C₂⁶	#121	1	1	yes	characteristic
162	C₂⁶	#127	1	1	yes	characteristic
163	C₂⁶	C₂²×D₄	1	1	yes	characteristic
164	C₂⁶	C₂²×D₄	1	1	yes	characteristic
165	C₂⁶	C₂²×D₄	1	1	yes	characteristic
166	C₂⁶	C₂²×D₄	1	1	yes	characteristic
167	C₂⁶	C₂²×D₄	1	1	yes	characteristic
168	C₂⁶	C₂²×D₄	1	1	yes	characteristic
169	C₂⁶	C₂²×D₄	1	1	yes	characteristic
170	C₂⁶	C₂²×D₄	1	1	yes	characteristic
171	C₂⁶	C₂²×D₄	1	1	yes	characteristic
172	C₂⁶	C₂²×D₄	1	1	yes	characteristic
173	C₂⁶	C₂²×D₄	1	1	yes	characteristic
174	C₂⁶	C₂²×D₄	1	1	yes	characteristic
175	C₂⁶	C₂²×D₄	1	1	yes	characteristic
176	C₂⁶	C₂²×D₄	1	1	yes	characteristic
177	C₂⁶	C₂²×D₄	1	1	yes	characteristic
178	C₂⁶	C₂²×D₄	1	1	yes	characteristic
179	C₂⁶	C₂×#41	1	1	yes	characteristic
180	C₂⁶	C₂×#41	1	1	yes	characteristic
181	C₂⁶	C₂×#41	1	1	yes	characteristic
182	C₂⁶	H(5,𝔽₂)	1	1	yes	characteristic
183	C₂⁶	H(5,𝔽₂)	1	1	yes	characteristic
184	C₂⁶	H(5,𝔽₂)	1	1	yes	characteristic
185	C₂⁶	H(5,𝔽₂)	1	1	yes	characteristic
186	C₂⁶	H(5,𝔽₂)	1	1	yes	characteristic
187	C₂⁶	H(5,𝔽₂)	1	1	yes	characteristic
188	C₂⁶	H(5,𝔽₂)	1	1	yes	characteristic
189	C₂⁶	H(5,𝔽₂)	1	1	yes	characteristic
190	C₂⁶	H(5,𝔽₂)	1	1	yes	characteristic
191	C₂⁶	H(5,𝔽₂)	1	1	yes	characteristic
192	C₂⁶	H(5,𝔽₂)	1	1	yes	characteristic
193	C₂⁶	H(5,𝔽₂)	1	1	yes	characteristic
194	C₂³×D₄	#120	1	2	yes	—
195	C₂³×D₄	#120	1	2	yes	—
196	C₂³×D₄	#120	1	2	yes	—
197	C₂³×D₄	#120	1	2	yes	—
198	C₂³×D₄	#120	1	2	yes	—
199	C₂³×D₄	#120	1	2	yes	—
200	C₂³×D₄	#120	1	2	yes	—
201	C₂³×D₄	#120	1	2	yes	—
202	C₂³×D₄	#120	1	2	yes	—
203	C₂³×D₄	#121	1	2	yes	—
204	C₂³×D₄	#121	1	2	yes	—
205	C₂³×D₄	#121	1	2	yes	—
206	C₂³×D₄	#121	1	2	yes	—
207	C₂³×D₄	#121	1	2	yes	—
208	C₂³×D₄	#121	1	2	yes	—
209	C₂³×D₄	#121	1	2	yes	—
210	C₂³×D₄	#127	1	2	yes	—
211	C₂³×D₄	#127	1	2	yes	—
212	C₂⁴×C₄	#120	1	1	yes	characteristic
213	C₂⁴×C₄	#120	1	1	yes	characteristic
214	C₂⁴×C₄	#120	1	1	yes	characteristic
215	C₂⁴×C₄	#121	1	1	yes	characteristic
216	C₂⁴×C₄	#121	1	1	yes	characteristic
217	C₂⁴×C₄	#121	1	1	yes	characteristic
218	C₂⁴×C₄	#121	1	1	yes	characteristic
219	C₂⁴×C₄	#121	1	1	yes	characteristic
220	C₂⁴×C₄	#121	1	1	yes	characteristic
221	C₂⁴×C₄	#127	1	1	yes	characteristic
222	C₂⁴×C₄	#127	1	1	yes	characteristic
223	C₂⁴×C₄	#127	1	1	yes	characteristic
224	C₂²×C₂²⋊C₄	#120	1	2	yes	—
225	C₂²×C₂²⋊C₄	#120	1	2	yes	—
226	C₂²×C₂²⋊C₄	#120	1	2	yes	—
227	C₂²×C₂²⋊C₄	#120	1	2	yes	—
228	C₂²×C₂²⋊C₄	#120	1	2	yes	—
229	C₂²×C₂²⋊C₄	#120	1	2	yes	—
230	C₂²×C₂²⋊C₄	#120	1	2	yes	—
231	C₂²×C₂²⋊C₄	#120	1	2	yes	—
232	C₂²×C₂²⋊C₄	#120	1	2	yes	—
233	C₂²×C₂²⋊C₄	#120	1	2	yes	—
234	C₂²×C₂²⋊C₄	#120	1	2	yes	—
235	C₂²×C₂²⋊C₄	#120	1	4	yes	—
236	C₂²×C₂²⋊C₄	#120	1	4	yes	—
237	C₂²×C₂²⋊C₄	#120	1	4	yes	—
238	C₂²×C₂²⋊C₄	#121	1	2	yes	—
239	C₂²×C₂²⋊C₄	#121	1	2	yes	—
240	C₂²×C₂²⋊C₄	#121	1	2	yes	—
241	C₂²×C₂²⋊C₄	#121	1	2	yes	—
242	C₂²×C₂²⋊C₄	#121	1	2	yes	—
243	C₂²×C₂²⋊C₄	#121	1	2	yes	—
244	C₂²×C₂²⋊C₄	#121	1	2	yes	—
245	C₂²×C₂²⋊C₄	#127	1	2	yes	—
246	C₂²×C₂²⋊C₄	#127	1	2	yes	—
247	#379	#120	1	4	yes	—
248	#379	#120	1	4	yes	—
249	#379	#120	1	4	yes	—
250	C₂⁵	#392	1	2	yes	—
251	C₂⁵	#392	1	2	yes	—
252	C₂⁵	#392	1	2	yes	—
253	C₂⁵	C₂×#120	1	1	yes	characteristic
254	C₂⁵	C₂×#120	1	1	yes	characteristic
255	C₂⁵	C₂×#120	1	1	yes	characteristic
256	C₂⁵	C₂×#120	1	1	yes	characteristic
257	C₂⁵	C₂×#120	1	1	yes	characteristic
258	C₂⁵	C₂×#120	1	1	yes	characteristic
259	C₂⁵	C₂×#120	1	1	yes	characteristic
260	C₂⁵	C₂×#120	1	1	yes	characteristic
261	C₂⁵	C₂×#120	1	1	yes	characteristic
262	C₂⁵	C₂×#120	1	1	yes	characteristic
263	C₂⁵	C₂×#120	1	1	yes	characteristic
264	C₂⁵	C₂×#120	1	1	yes	characteristic
265	C₂⁵	C₂×#120	1	1	yes	characteristic
266	C₂⁵	C₂×#120	1	1	yes	characteristic
267	C₂⁵	C₂×#120	1	1	yes	characteristic
268	C₂⁵	C₂×#120	1	1	yes	characteristic
269	C₂⁵	C₂×#120	1	1	yes	characteristic
270	C₂⁵	C₂×#120	1	1	yes	characteristic
271	C₂⁵	C₂×#121	1	1	yes	characteristic
272	C₂⁵	C₂×#121	1	1	yes	characteristic
273	C₂⁵	C₂×#121	1	1	yes	characteristic
274	C₂⁵	C₂×#121	1	1	yes	characteristic
275	C₂⁵	C₂×#121	1	1	yes	characteristic
276	C₂⁵	C₂×#121	1	1	yes	characteristic
277	C₂⁵	C₂×#121	1	1	yes	characteristic
278	C₂⁵	C₂×#121	1	1	yes	characteristic
279	C₂⁵	C₂×#121	1	1	yes	characteristic
280	C₂⁵	#525	1	1	yes	characteristic
281	C₂⁵	#525	1	1	yes	characteristic
282	C₂⁵	#525	1	1	yes	characteristic
283	C₂⁵	C₂×#127	1	1	yes	characteristic
284	C₂⁵	C₂×#127	1	1	yes	characteristic
285	C₂⁵	C₂×#127	1	1	yes	characteristic
286	C₂⁵	#534	1	1	yes	characteristic
287	C₂⁵	#534	1	1	yes	characteristic
288	C₂⁵	#534	1	1	yes	characteristic
289	C₂⁵	#534	1	1	yes	characteristic
290	C₂⁵	#534	1	1	yes	characteristic
291	C₂⁵	#534	1	1	yes	characteristic
292	C₂⁵	#534	1	1	yes	characteristic
293	C₂⁵	#534	1	1	yes	characteristic
294	C₂⁵	#534	1	1	yes	characteristic
295	C₂⁵	#534	1	1	yes	characteristic
296	C₂⁵	#534	1	1	yes	characteristic
297	C₂⁵	#534	1	1	yes	characteristic
298	C₂⁵	#534	1	1	yes	characteristic
299	C₂⁵	#534	1	1	yes	characteristic
300	C₂⁵	#534	1	1	yes	characteristic
301	C₂⁵	#534	1	1	yes	characteristic
302	C₂⁵	#534	1	1	yes	characteristic
303	C₂⁵	#534	1	1	yes	characteristic
304	C₂⁵	#534	1	1	yes	characteristic
305	C₂⁵	#534	1	1	yes	characteristic
306	C₂⁵	#534	1	1	yes	characteristic
307	C₂⁵	#535	1	1	yes	characteristic
308	C₂⁵	#535	1	1	yes	characteristic
309	C₂⁵	#535	1	1	yes	characteristic
310	C₂⁵	#535	1	1	yes	characteristic
311	C₂⁵	#535	1	1	yes	characteristic
312	C₂⁵	#535	1	1	yes	characteristic
313	C₂⁵	#535	1	1	yes	characteristic
314	C₂⁵	#535	1	1	yes	characteristic
315	C₂⁵	#535	1	1	yes	characteristic
316	C₂⁵	#535	1	1	yes	characteristic
317	C₂⁵	#535	1	1	yes	characteristic
318	C₂⁵	#535	1	1	yes	characteristic
319	C₂⁵	#535	1	1	yes	characteristic
320	C₂⁵	#535	1	1	yes	characteristic
321	C₂⁵	#535	1	1	yes	characteristic
322	C₂⁵	#538	1	1	yes	characteristic
323	C₂⁵	#538	1	1	yes	characteristic
324	C₂⁵	#538	1	1	yes	characteristic
325	C₂⁵	#538	1	1	yes	characteristic
326	C₂⁵	#538	1	1	yes	characteristic
327	C₂⁵	#538	1	1	yes	characteristic
328	C₂⁵	D₄²	1	1	yes	characteristic
329	C₂⁵	D₄²	1	1	yes	characteristic
330	C₂⁵	D₄²	1	1	yes	characteristic
331	C₂⁵	D₄²	1	1	yes	characteristic
332	C₂⁵	D₄²	1	1	yes	characteristic
333	C₂⁵	D₄²	1	1	yes	characteristic
334	C₂⁵	D₄²	1	1	yes	characteristic
335	C₂⁵	D₄²	1	1	yes	characteristic
336	C₂⁵	D₄²	1	1	yes	characteristic
337	C₂⁵	D₄²	1	1	yes	characteristic
338	C₂⁵	D₄²	1	1	yes	characteristic
339	C₂⁵	D₄²	1	1	yes	characteristic
340	C₂⁵	D₄²	1	1	yes	characteristic
341	C₂⁵	D₄²	1	1	yes	characteristic
342	C₂⁵	D₄²	1	1	yes	characteristic
343	C₂⁵	D₄²	1	1	yes	characteristic
344	C₂⁵	D₄²	1	1	yes	characteristic
345	C₂⁵	D₄²	1	1	yes	characteristic
346	C₂⁵	D₄²	1	1	yes	characteristic
347	C₂⁵	D₄²	1	1	yes	characteristic
348	C₂⁵	D₄²	1	1	yes	characteristic
349	C₂⁵	D₄²	1	1	yes	characteristic
350	C₂⁵	D₄²	1	1	yes	characteristic
351	C₂⁵	D₄²	1	1	yes	characteristic
352	C₂⁵	D₄²	1	1	yes	characteristic
353	C₂⁵	D₄²	1	1	yes	characteristic
354	C₂⁵	D₄²	1	1	yes	characteristic
355	C₂⁵	D₄²	1	1	yes	characteristic
356	C₂⁵	D₄²	1	1	yes	characteristic
357	C₂⁵	D₄²	1	1	yes	characteristic
358	C₂⁵	D₄²	1	1	yes	characteristic
359	C₂⁵	D₄²	1	1	yes	characteristic
360	C₂⁵	D₄²	1	1	yes	characteristic
361	C₂⁵	D₄²	1	1	yes	characteristic
362	C₂⁵	D₄²	1	1	yes	characteristic
363	C₂⁵	D₄²	1	1	yes	characteristic
364	C₂⁵	D₄²	1	1	yes	characteristic
365	C₂⁵	D₄²	1	1	yes	characteristic
366	C₂⁵	D₄²	1	1	yes	characteristic
367	C₂⁵	D₄²	1	1	yes	characteristic
368	C₂⁵	D₄²	1	1	yes	characteristic
369	C₂⁵	D₄²	1	1	yes	characteristic
370	C₂⁵	D₄²	1	1	yes	characteristic
371	C₂⁵	D₄²	1	1	yes	characteristic
372	C₂⁵	D₄²	1	1	yes	characteristic
373	C₂⁵	D₄²	1	1	yes	characteristic
374	C₂⁵	D₄²	1	1	yes	characteristic
375	C₂⁵	D₄²	1	1	yes	characteristic
376	C₂⁵	#546	1	1	yes	characteristic
377	C₂⁵	#546	1	1	yes	characteristic
378	C₂⁵	#546	1	1	yes	characteristic
379	C₂⁵	#546	1	1	yes	characteristic
380	C₂⁵	#546	1	1	yes	characteristic
381	C₂⁵	#546	1	1	yes	characteristic
382	C₂⁵	#546	1	1	yes	characteristic
383	C₂⁵	#546	1	1	yes	characteristic
384	C₂⁵	#546	1	1	yes	characteristic
385	C₂⁵	#546	1	1	yes	characteristic
386	C₂⁵	#546	1	1	yes	characteristic
387	C₂⁵	#546	1	1	yes	characteristic
388	C₂⁵	#546	1	1	yes	characteristic
389	C₂⁵	#546	1	1	yes	characteristic
390	C₂⁵	#546	1	1	yes	characteristic
391	C₂⁵	#546	1	1	yes	characteristic
392	C₂⁵	#546	1	1	yes	characteristic
393	C₂⁵	#546	1	1	yes	characteristic
394	C₂⁵	#546	1	1	yes	characteristic
395	C₂⁵	#546	1	1	yes	characteristic
396	C₂⁵	#546	1	1	yes	characteristic
397	C₂⁵	#546	1	1	yes	characteristic
398	C₂⁵	#546	1	1	yes	characteristic
399	C₂⁵	#546	1	1	yes	characteristic
400	C₂⁵	#560	1	1	yes	characteristic
401	C₂⁵	#560	1	1	yes	characteristic
402	C₂⁵	#560	1	1	yes	characteristic
403	C₂⁵	#560	1	1	yes	characteristic
404	C₂⁵	#560	1	1	yes	characteristic
405	C₂⁵	#560	1	1	yes	characteristic
406	C₂⁵	H(3,𝔽₄)	1	1	yes	characteristic
407	C₂⁵	H(3,𝔽₄)	1	1	yes	characteristic
408	C₂³×C₄	#392	1	2	yes	—
409	C₂³×C₄	#392	1	2	yes	—
410	C₂³×C₄	#392	1	2	yes	—
411	C₂³×C₄	#392	1	2	yes	—
412	C₂³×C₄	#392	1	2	yes	—
413	C₂³×C₄	#392	1	2	yes	—
414	C₂³×C₄	#392	1	2	yes	—
415	C₂³×C₄	#392	1	2	yes	—
416	C₂³×C₄	#392	1	2	yes	—
417	C₂×C₂²⋊C₄	B(4,𝔽₂)	1	4	yes	complemented
418	C₂⁴	C₂×#392	1	1	yes	characteristic
419	C₂⁴	C₂×#392	1	1	yes	characteristic
420	C₂⁴	C₂×#392	1	1	yes	characteristic
421	C₂⁴	#2403	1	1	yes	characteristic
422	C₂⁴	#2403	1	1	yes	characteristic
423	C₂⁴	#2403	1	1	yes	characteristic
424	C₂⁴	#2403	1	1	yes	characteristic
425	C₂⁴	#2403	1	1	yes	characteristic
426	C₂⁴	#2403	1	1	yes	characteristic
427	C₂⁴	#2403	1	1	yes	characteristic
428	C₂⁴	#2403	1	1	yes	characteristic
429	C₂⁴	#2403	1	1	yes	characteristic
430	C₂⁴	#2403	1	1	yes	characteristic
431	C₂⁴	#2403	1	1	yes	characteristic
432	C₂⁴	#2403	1	1	yes	characteristic
433	C₂⁴	#2403	1	1	yes	characteristic
434	C₂⁴	#2403	1	1	yes	characteristic
435	C₂⁴	#2403	1	1	yes	characteristic
436	C₂⁴	#2403	1	1	yes	characteristic
437	C₂⁴	#2403	1	1	yes	characteristic
438	C₂⁴	#2403	1	1	yes	characteristic
439	C₂⁴	#2403	1	1	yes	characteristic
440	C₂⁴	#2403	1	1	yes	characteristic
441	C₂⁴	#2403	1	1	yes	characteristic
442	C₂⁴	#2404	1	1	yes	characteristic
443	C₂⁴	#2404	1	1	yes	characteristic
444	C₂⁴	#2404	1	1	yes	characteristic
445	C₂⁴	#2408	1	1	yes	characteristic
446	C₂⁴	#2408	1	1	yes	characteristic
447	C₂⁴	#2408	1	1	yes	characteristic
448	C₂⁴	#2408	1	1	yes	characteristic
449	C₂⁴	#2408	1	1	yes	characteristic
450	C₂⁴	#2408	1	1	yes	characteristic
451	C₂⁴	#2408	1	1	yes	characteristic
452	C₂⁴	#2408	1	1	yes	characteristic
453	C₂⁴	#2408	1	1	yes	characteristic
454	C₂⁴	#2408	1	1	yes	characteristic
455	C₂⁴	#2408	1	1	yes	characteristic
456	C₂⁴	#2408	1	1	yes	characteristic
457	C₂⁴	#2410	1	1	yes	characteristic
458	C₂⁴	#2410	1	1	yes	characteristic
459	C₂⁴	#2410	1	1	yes	characteristic
460	C₂⁴	#2410	1	1	yes	characteristic
461	C₂⁴	#2410	1	1	yes	characteristic
462	C₂⁴	#2410	1	1	yes	characteristic
463	C₂⁴	#2410	1	1	yes	characteristic
464	C₂⁴	#2410	1	1	yes	characteristic
465	C₂⁴	#2410	1	1	yes	characteristic
466	C₂⁴	#2410	1	1	yes	characteristic
467	C₂⁴	#2410	1	1	yes	characteristic
468	C₂⁴	#2410	1	1	yes	characteristic
469	C₂⁴	#2410	1	1	yes	characteristic
470	C₂⁴	#2410	1	1	yes	characteristic
471	C₂⁴	#2410	1	1	yes	characteristic
472	C₂⁴	#2410	1	1	yes	characteristic
473	C₂⁴	#2410	1	1	yes	characteristic
474	C₂⁴	#2410	1	1	yes	characteristic
475	C₂⁴	#2410	1	1	yes	characteristic
476	C₂⁴	#2410	1	1	yes	characteristic
477	C₂⁴	#2410	1	1	yes	characteristic
478	C₂⁴	#2410	1	1	yes	characteristic
479	C₂⁴	#2410	1	1	yes	characteristic
480	C₂⁴	#2410	1	1	yes	characteristic
481	C₂⁴	#2424	1	1	yes	characteristic
482	C₂⁴	#2424	1	1	yes	characteristic
483	C₂⁴	#2424	1	1	yes	characteristic
484	C₂⁴	#2424	1	1	yes	characteristic
485	C₂⁴	#2424	1	1	yes	characteristic
486	C₂⁴	#2424	1	1	yes	characteristic
487	C₂⁴	#2424	1	1	yes	characteristic
488	C₂⁴	#2424	1	1	yes	characteristic
489	C₂⁴	#2424	1	1	yes	characteristic
490	C₂⁴	#2424	1	1	yes	characteristic
491	C₂⁴	#2424	1	1	yes	characteristic
492	C₂⁴	#2424	1	1	yes	characteristic
493	C₂⁴	#2433	1	1	yes	characteristic
494	C₂⁴	#2433	1	1	yes	characteristic
495	C₂⁴	#2433	1	1	yes	characteristic
496	C₂⁴	#2433	1	1	yes	characteristic
497	C₂⁴	#2433	1	1	yes	characteristic
498	C₂⁴	#2433	1	1	yes	characteristic
499	C₂⁴	#2433	1	1	yes	characteristic
500	C₂⁴	#2433	1	1	yes	characteristic
501	C₂⁴	#2433	1	1	yes	characteristic
502	C₂⁴	#2433	1	1	yes	characteristic
503	C₂⁴	#2433	1	1	yes	characteristic
504	C₂⁴	#2433	1	1	yes	characteristic
505	C₂⁴	#2433	1	1	yes	characteristic
506	C₂⁴	#2433	1	1	yes	characteristic
507	C₂⁴	#2433	1	1	yes	characteristic
508	C₂⁴	#2539	1	1	yes	characteristic
509	C₂⁴	#2539	1	1	yes	characteristic
510	C₂⁴	#2539	1	1	yes	characteristic
511	C₂⁴	#2613	1	1	yes	characteristic
512	C₂⁴	#2613	1	1	yes	characteristic
513	C₂⁴	#2613	1	1	yes	characteristic
514	C₂⁴	#2613	1	1	yes	characteristic
515	C₂⁴	#2613	1	1	yes	characteristic
516	C₂⁴	#2613	1	1	yes	characteristic
517	C₂⁴	#2617	1	1	yes	characteristic
518	C₂⁴	#2617	1	1	yes	characteristic
519	C₂⁴	#2617	1	1	yes	characteristic
520	C₂⁴	#2668	1	1	yes	characteristic
521	C₂⁴	#2668	1	1	yes	characteristic
522	C₂⁴	#2668	1	1	yes	characteristic
523	C₂⁴	#2668	1	1	yes	characteristic
524	C₂⁴	#2668	1	1	yes	characteristic
525	C₂⁴	#2668	1	1	yes	characteristic
526	C₂⁴	#2669	1	1	yes	characteristic
527	C₂⁴	#2669	1	1	yes	characteristic
528	C₂⁴	#2669	1	1	yes	characteristic
529	C₂⁴	#2669	1	1	yes	characteristic
530	C₂⁴	#2669	1	1	yes	characteristic
531	C₂⁴	#2669	1	1	yes	characteristic
532	C₂⁴	#2669	1	1	yes	characteristic
533	C₂⁴	#2669	1	1	yes	characteristic
534	C₂⁴	#2669	1	1	yes	characteristic
535	C₂⁴	#2669	1	1	yes	characteristic
536	C₂⁴	#2669	1	1	yes	characteristic
537	C₂⁴	#2669	1	1	yes	characteristic
538	C₂⁴	#2669	1	1	yes	characteristic
539	C₂⁴	#2669	1	1	yes	characteristic
540	C₂⁴	#2669	1	1	yes	characteristic
541	C₂⁴	#2669	1	1	yes	characteristic
542	C₂⁴	#2669	1	1	yes	characteristic
543	C₂⁴	#2669	1	1	yes	characteristic
544	C₂⁴	#2670	1	1	yes	characteristic
545	C₂⁴	#2670	1	1	yes	characteristic
546	C₂⁴	#2670	1	1	yes	characteristic
547	C₂⁴	#2670	1	1	yes	characteristic
548	C₂⁴	#2670	1	1	yes	characteristic
549	C₂⁴	#2670	1	1	yes	characteristic
550	C₂⁴	#2678	1	1	yes	characteristic
551	C₂⁴	#2678	1	1	yes	characteristic
552	C₂⁴	#2678	1	1	yes	characteristic
553	C₂⁴	#2678	1	1	yes	characteristic
554	C₂⁴	#2678	1	1	yes	characteristic
555	C₂⁴	#2678	1	1	yes	characteristic
556	C₂⁴	#2678	1	1	yes	characteristic
557	C₂⁴	#2678	1	1	yes	characteristic
558	C₂⁴	#2678	1	1	yes	characteristic
559	C₂⁴	#2678	1	1	yes	characteristic
560	C₂⁴	#2678	1	1	yes	characteristic
561	C₂⁴	#2678	1	1	yes	characteristic
562	C₂⁴	#2679	1	1	yes	characteristic
563	C₂⁴	#2679	1	1	yes	characteristic
564	C₂⁴	#2679	1	1	yes	characteristic
565	C₂⁴	#2679	1	1	yes	characteristic
566	C₂⁴	#2679	1	1	yes	characteristic
567	C₂⁴	#2679	1	1	yes	characteristic
568	C₂⁴	#2812	1	1	yes	characteristic
569	C₂⁴	#2812	1	1	yes	characteristic
570	C₂⁴	#2846	1	1	yes	characteristic
571	C₂⁴	#2846	1	1	yes	characteristic
572	C₂⁴	#2847	1	1	yes	characteristic
573	C₂⁴	C₂×B(4,𝔽₂)	1	2	yes	—
574	C₂⁴	#3025	1	2	yes	—
575	C₂⁴	#3026	1	2	yes	—
576	C₂⁴	#3027	1	2	yes	—
577	C₂³	#14715	1	1	yes	characteristic
578	C₂³	#14715	1	1	yes	characteristic
579	C₂³	#14715	1	1	yes	characteristic
580	C₂³	#14715	1	1	yes	characteristic
581	C₂³	#14715	1	1	yes	characteristic
582	C₂³	#14715	1	1	yes	characteristic
583	C₂³	#14716	1	1	yes	characteristic
584	C₂³	#14716	1	1	yes	characteristic
585	C₂³	#14716	1	1	yes	characteristic
586	C₂³	#15257	1	1	yes	characteristic
587	C₂³	#15257	1	1	yes	characteristic
588	C₂³	#15257	1	1	yes	characteristic
589	C₂³	#15257	1	1	yes	characteristic
590	C₂³	#15257	1	1	yes	characteristic
591	C₂³	#15257	1	1	yes	characteristic
592	C₂³	#15258	1	1	yes	characteristic
593	C₂³	#15258	1	1	yes	characteristic
594	C₂³	#15258	1	1	yes	characteristic
595	C₂³	#15267	1	1	yes	characteristic
596	C₂³	#15267	1	1	yes	characteristic
597	C₂³	#15267	1	1	yes	characteristic
598	C₂³	#15267	1	1	yes	characteristic
599	C₂³	#15267	1	1	yes	characteristic
600	C₂³	#15267	1	1	yes	characteristic
601	C₂³	#15947	1	1	yes	characteristic
602	C₂³	#16249	1	1	yes	characteristic
603	C₂³	#16249	1	1	yes	characteristic
604	C₂³	#16249	1	1	yes	characteristic
605	C₂³	#16249	1	1	yes	characteristic
606	C₂³	#16249	1	1	yes	characteristic
607	C₂³	#16249	1	1	yes	characteristic
608	C₂³	#23895	1	4	yes	—
609	C₂³	#23900	1	1	yes	characteristic
610	C₂³	#23902	1	1	yes	characteristic
611	C₂³	#23903	1	1	yes	characteristic
612	C₂³	#23904	1	1	yes	characteristic
613	C₂³	#23996	1	4	yes	—
614	C₂³	#24260	1	2	yes	—
615	C₂³	#24260	1	2	yes	—
616	C₂³	#24262	1	2	yes	—
617	C₂³	#24262	1	2	yes	—
618	C₂³	#24404	1	2	yes	—
619	C₂³	#24406	1	2	yes	—
620	C₂³	#25771	1	2	yes	—
621	C₂³	#25771	1	2	yes	—
622	C₂³	#25773	1	2	yes	—
623	C₂³	#25773	1	2	yes	—
624	C₂³	#32898	1	2	yes	—
625	C₂³	#32899	1	2	yes	—
626	C₂²	#156684	1	1	yes	characteristic
627	C₂²	#393934	1	2	yes	—
628	C₂²	#393934	1	2	yes	—
629	C₂²	#394064	1	2	yes	—
630	C₂²	#394066	1	1	yes	characteristic
631	C₂²	#394067	1	1	yes	characteristic
632	C₂²	#394273	1	2	yes	—
633	C₂²	#417526	1	1	yes	characteristic
634	C₂²	#417528	1	1	yes	characteristic
635	C₂²	#417532	1	2	yes	—
636	C₂²	#417538	1	2	yes	—
637	C₂²	#417542	1	2	yes	—
638	C₂²	#417821	1	1	yes	characteristic
639	C₂²	#417823	1	1	yes	characteristic
640	C₂²	#417824	1	2	yes	—
641	C₂²	#419061	1	2	yes	—
642	C₂²	#419061	1	2	yes	—
643	C₂	#72225659	1	1	yes	characteristic
644	C₂	#72240549	1	1	yes	characteristic
645	C₂	#72240552	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²	#156684
commutator, Frattini, cosocle	C₂⁷	C₂⁴
LCS	G ▷ C₂⁷ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂² ◁ C₂⁷ ◁ G
LECS	G ▷ C₂⁷ ▷ C₂² ▷ C₁

Complements

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

N	H ≅ G/N	type
1. #72309373	C₂	semidirect
2. #72309370	C₂	semidirect
3. #72309369	C₂	semidirect
4. #72259089	C₂	semidirect
5. #72259002	C₂	semidirect
6. #72236453	C₂	semidirect
7. #72236437	C₂	semidirect
8. #72232592	C₂	semidirect
9. C₂×#394167	C₂	semidirect
10. #72218766	C₂	semidirect
11. #72218744	C₂	semidirect
12. #72217699	C₂	semidirect
13. #72217699	C₂	semidirect
14. C₂×#115690	C₂	semidirect
15. C₂×#6499867	C₂	semidirect
22. C₂²×#2846	C₂²	semidirect
24. C₂³×#379	C₂²	semidirect
32. C₂×#21746	C₂²	semidirect
33. C₂×#21746	C₂²	semidirect
38. C₂²×#1898	C₂²	semidirect
39. C₂×#14679	C₂²	semidirect
40. C₂×#14679	C₂²	semidirect
42. #355913	C₂²	semidirect
43. #355913	C₂²	semidirect
44. C₂×#10735	C₂²	semidirect
45. C₂×#10735	C₂²	semidirect
46. C₂×#10735	C₂²	semidirect
47. C₂×#10725	C₂²	semidirect
48. C₂×#10725	C₂²	semidirect
49. C₂×#8101	C₂²	semidirect
50. C₂×#8101	C₂²	semidirect
52. #62817	D₄	semidirect
53. C₂²×#534	D₄	semidirect
54. C₂³×#120	D₄	semidirect
61. C₂³×#99	D₄	semidirect
62. C₂³×#99	D₄	semidirect
63. C₂×#2846	D₄	semidirect
64. C₂×#2846	D₄	semidirect
65. #34992	D₄	semidirect
66. #34992	D₄	semidirect
67. #34980	D₄	semidirect
68. #34980	D₄	semidirect
69. C₂×#2315	D₄	semidirect
70. C₂×#2308	D₄	semidirect
71. C₂×#2308	D₄	semidirect
72. C₂²×#379	D₄	semidirect
81. #21746	D₄	semidirect
82. #21746	D₄	semidirect
83. C₂×#1898	D₄	semidirect
84. C₂×#1898	D₄	semidirect
85. C₂×#1819	D₄	semidirect
86. C₂×#1819	D₄	semidirect
87. C₂×#1819	D₄	semidirect
88. C₂×#1781	D₄	semidirect
89. C₂×#1781	D₄	semidirect
90. C₂×#1781	D₄	semidirect
91. C₂²×#342	D₄	semidirect
92. C₂²×#342	D₄	semidirect
417. C₂×C₂²⋊C₄	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
#72309373	2
#72309370	2
#72309369	2
#72259089	2
#72259002	2
#72236453	2
#72236437	2
#72232592	2
C₂×#394167	2
#72218766	2
#72218744	2
#72217699	2
C₂×#115690	2
C₂×#6499867	2