Subgroups — #72333265

Order 4096.

Only the 2307 normal subgroups are shown; non-normal subgroups are omitted.

The subgroup lattice has 629 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#72331660	C₂	1	2	yes	maximal, complemented
2	#72331045	C₂	1	2	yes	maximal, complemented
3	#72313223	C₂	1	4	yes	maximal, complemented
4	#72313018	C₂	1	2	yes	maximal, complemented
5	#72310049	C₂	1	2	yes	maximal, complemented
6	#72309382	C₂	1	2	yes	maximal, complemented
7	#72309381	C₂	1	4	yes	maximal, complemented
8	#72309377	C₂²	1	4	yes	complemented
9	#72309373	C₂²	1	4	yes	complemented
10	#72309370	C₂²	1	4	yes	complemented
11	#72309369	C₂²	1	4	yes	complemented
12	#72309368	C₂²	1	4	yes	complemented
13	#72266073	C₂²	1	2	yes	complemented
14	#72266028	C₂²	1	2	yes	complemented
15	#72259092	C₂	1	2	yes	maximal, complemented
16	#72259089	C₂²	1	4	yes	complemented
17	#72259083	C₂²	1	4	yes	complemented
18	#72259029	C₂	1	1	yes	maximal, characteristic, complemented
19	#72259021	C₂²	1	2	yes	complemented
20	#72259008	C₂²	1	1	yes	characteristic, complemented
21	#72259002	C₂²	1	2	yes	complemented
22	#72237423	C₂	1	2	yes	maximal, complemented
23	#72237400	C₂²	1	2	yes	complemented
24	#72237398	C₂²	1	2	yes	complemented
25	#72237398	C₂²	1	2	yes	complemented
26	#72236453	C₂²	1	4	yes	complemented
27	#72236437	C₂²	1	4	yes	complemented
28	#72236437	C₂²	1	4	yes	complemented
29	#72235847	C₂²	1	1	yes	characteristic, complemented
30	#72234665	C₂	1	1	yes	maximal, characteristic, complemented
31	#72234663	C₂²	1	1	yes	characteristic, complemented
32	#72234661	C₂²	1	2	yes	complemented
33	#72234591	C₂²	1	2	yes	complemented
34	#72232884	C₂²	1	1	yes	characteristic, complemented
35	#72232592	C₂²	1	2	yes	complemented
36	C₂×#72217546	C₂	1	1	yes	maximal, characteristic, complemented
37	C₂×#374022	C₂²	1	1	yes	characteristic, complemented
38	C₂×#394167	C₂²	1	2	yes	complemented
39	C₂×#394058	C₂²	1	2	yes	complemented
40	C₂×#359428	C₂²	1	1	yes	characteristic, complemented
41	C₂×#359428	C₂²	1	1	yes	characteristic, complemented
42	C₂×#7670203	C₂²	1	1	yes	characteristic
43	C₂×#364410	C₂²	1	2	yes	complemented
44	#72218799	C₂	1	2	yes	maximal, complemented
45	#72218766	C₂²	1	4	yes	complemented
46	#72218766	C₂²	1	4	yes	complemented
47	#72218744	C₂²	1	4	yes	complemented
48	#72218451	C₂²	1	2	yes	complemented
49	#72218451	C₂²	1	2	yes	complemented
50	#72218375	C₂²	1	2	yes	complemented
51	#72217947	C₂	1	2	yes	maximal, complemented
52	C₂²×#23900	C₂²	1	2	yes	—
53	C₂²×#23900	C₂²	1	2	yes	—
54	C₂²×#23900	C₂²	1	2	yes	complemented
55	#72217875	C₂²	1	2	yes	complemented
56	#72217818	C₂²	1	4	yes	complemented
57	#72217789	C₂²	1	2	yes	complemented
58	C₂³×#2846	C₂²	1	1	yes	characteristic, complemented
59	C₂³×#2846	C₂²	1	1	yes	characteristic, complemented
60	#72217699	C₂²	1	4	yes	complemented
61	#72217699	C₂²	1	4	yes	complemented
62	#72217666	C₂²	1	4	yes	complemented
63	#72217511	C₂²	1	2	yes	—
64	C₂×#72209716	C₂	1	2	yes	maximal, complemented
65	C₂×#115690	C₂²	1	4	yes	complemented
66	C₂×#115690	C₂²	1	4	yes	complemented
67	C₂×#115690	C₂²	1	4	yes	complemented
68	C₂×#115690	C₂²	1	4	yes	complemented
69	C₂×#115690	C₂²	1	2	yes	complemented
70	C₂×#6499867	C₂²	1	2	yes	—
71	C₂×#6499867	C₂²	1	4	yes	—
72	C₂×#6499867	C₂²	1	4	yes	complemented
73	C₂×#6342371	C₂²	1	1	yes	characteristic, complemented
74	C₂×#6342371	C₂²	1	4	yes	complemented
75	C₂⁹	C₂³	1	1	yes	characteristic, complemented
76	C₂×#62817	C₂³	1	2	yes	—
77	C₂×#62817	C₂³	1	2	yes	—
78	C₂²×#3484	D₄	1	1	yes	characteristic, complemented
79	C₂²×#3484	C₂³	1	1	yes	characteristic
80	C₂²×#3484	C₂³	1	2	yes	—
81	C₂⁴×#120	C₂³	1	1	yes	characteristic
82	C₂⁴×#120	C₂³	1	1	yes	characteristic
83	C₂⁴×#120	C₂³	1	2	yes	—
84	C₂³×B(4,𝔽₂)	D₄	1	4	yes	complemented
85	#7642273	D₄	1	4	yes	complemented
86	#7642244	D₄	1	4	yes	complemented
87	#7641845	C₂³	1	4	yes	—
88	C₂²×#2846	C₂³	1	2	yes	—
89	C₂²×#2846	C₂³	1	1	yes	characteristic
90	C₂²×#2846	C₂³	1	4	yes	—
91	C₂²×#2846	C₂³	1	4	yes	—
92	C₂²×#2846	C₂³	1	2	yes	—
93	C₂²×#2846	C₂³	1	4	yes	—
94	C₂²×#2846	C₂³	1	2	yes	complemented
95	#7630944	D₄	1	4	yes	complemented
96	#7630939	D₄	1	4	yes	complemented
97	C₂×#35390	D₄	1	1	yes	characteristic, complemented
98	C₂×#35348	D₄	1	1	yes	characteristic, complemented
99	C₂×#35348	D₄	1	1	yes	characteristic, complemented
100	C₂×#35346	D₄	1	1	yes	characteristic, complemented
101	C₂×#34981	D₄	1	1	yes	characteristic, complemented
102	C₂×#34981	C₂³	1	1	yes	characteristic
103	C₂×#34980	D₄	1	1	yes	characteristic, complemented
104	C₂×#34980	C₂³	1	1	yes	characteristic
105	#7626202	C₂³	1	2	yes	—
106	C₂×#34198	D₄	1	1	yes	characteristic, complemented
107	C₂×#34198	C₂³	1	1	yes	characteristic
108	C₂³×#379	C₂³	1	2	yes	complemented
109	C₂³×#379	C₂³	1	1	yes	characteristic, complemented
110	C₂³×#379	C₂³	1	1	yes	characteristic, complemented
111	#6499867	D₄	1	16	yes	complemented
112	C₂×#23984	D₄	1	16	yes	complemented
113	C₂×#23900	D₄	1	16	yes	complemented
114	C₂×#23900	D₄	1	8	yes	complemented
115	C₂×#23900	D₄	1	8	yes	complemented
116	C₂²×#2021	D₄	1	8	yes	complemented
117	C₂×#21746	C₂³	1	4	yes	—
118	C₂×#21746	C₂³	1	4	yes	—
119	C₂×#21746	C₂³	1	4	yes	—
120	C₂×#21746	C₂³	1	4	yes	—
121	C₂×#21746	C₂³	1	4	yes	—
122	C₂×#21746	C₂³	1	2	yes	—
123	C₂×#21746	C₂³	1	4	yes	—
124	C₂×#21746	C₂³	1	4	yes	—
125	C₂×#21746	C₂³	1	2	yes	complemented
126	C₂×#21746	C₂³	1	2	yes	complemented
127	C₂²×#1898	C₂³	1	4	yes	—
128	C₂²×#1898	C₂³	1	4	yes	—
129	C₂²×#1898	C₂³	1	2	yes	—
130	C₂²×#1898	C₂³	1	2	yes	—
131	C₂²×#1898	C₂³	1	2	yes	complemented
132	C₂²×#1889	D₄	1	4	yes	complemented
133	C₂²×#1781	C₂³	1	2	yes	—
134	C₂²×#1781	C₂³	1	2	yes	—
135	C₂²×#1781	C₂³	1	2	yes	—
136	C₂×#14679	C₂³	1	4	yes	complemented
137	C₂×#14679	C₂³	1	2	yes	complemented
138	C₂×#14679	C₂³	1	1	yes	characteristic, complemented
139	C₂×#14679	C₂³	1	4	yes	complemented
140	C₂×#14679	C₂³	1	4	yes	complemented
141	#517411	C₂³	1	2	yes	—
142	#516383	C₂³	1	4	yes	—
143	#355913	C₂³	1	4	yes	complemented
144	#355913	C₂³	1	4	yes	complemented
145	C₂×#10735	C₂³	1	4	yes	complemented
146	C₂×#10735	C₂³	1	2	yes	complemented
147	C₂×#10735	C₂³	1	4	yes	complemented
148	C₂×#10725	C₂³	1	4	yes	complemented
149	C₂×#10725	C₂³	1	2	yes	complemented
150	C₂×#8101	C₂³	1	4	yes	complemented
151	C₂×#8101	C₂³	1	4	yes	complemented
152	C₂×#8101	C₂³	1	2	yes	complemented
153	C₂×#8101	C₂³	1	2	yes	complemented
154	C₂⁸	C₂⁴	1	1	yes	characteristic
155	C₂⁸	C₂⁴	1	2	yes	—
156	C₂³×H(5,𝔽₂)	C₂×D₄	1	1	yes	characteristic
157	C₂³×H(5,𝔽₂)	C₂×D₄	1	2	yes	complemented
158	C₂⁵×D₄	C₂×D₄	1	1	yes	characteristic
159	C₂⁵×D₄	C₂×D₄	1	2	yes	—
160	C₂⁵×D₄	C₂⁴	1	1	yes	characteristic
161	#62817	C₂×D₄	1	8	yes	complemented
162	C₂×#3490	C₂×D₄	1	4	yes	—
163	C₂×#3490	C₂×D₄	1	8	yes	—
164	C₂×#3484	C₂×D₄	1	4	yes	—
165	C₂×#3484	C₂×D₄	1	8	yes	—
166	C₂×#3484	C₂×D₄	1	4	yes	—
167	C₂×#3484	C₂×D₄	1	4	yes	—
168	C₂²×#534	C₂×D₄	1	1	yes	characteristic
169	C₂²×#534	C₂×D₄	1	1	yes	characteristic
170	C₂²×#534	C₂×D₄	1	1	yes	characteristic
171	C₂²×#534	C₂×D₄	1	1	yes	characteristic
172	C₂²×#534	C₂×D₄	1	1	yes	characteristic
173	C₂²×#534	C₂×D₄	1	4	yes	complemented
174	C₂³×#120	C₂×D₄	1	2	yes	—
175	C₂³×#120	C₂×D₄	1	1	yes	characteristic
176	C₂³×#120	C₂×D₄	1	1	yes	characteristic
177	C₂³×#120	C₂×D₄	1	2	yes	—
178	C₂³×#120	C₂×D₄	1	4	yes	—
179	C₂³×#120	C₂×D₄	1	4	yes	—
180	C₂³×#120	C₂×D₄	1	1	yes	characteristic
181	C₂³×#120	C₂×D₄	1	1	yes	characteristic
182	C₂³×#120	C₂×D₄	1	1	yes	characteristic
183	C₂³×#120	C₂×D₄	1	1	yes	characteristic
184	C₂³×#120	C₂×D₄	1	8	yes	—
185	C₂³×#120	C₂×D₄	1	1	yes	characteristic
186	C₂³×#120	C₂×D₄	1	1	yes	characteristic
187	C₂³×#120	C₂×D₄	1	4	yes	complemented
188	C₂³×#120	C₂×D₄	1	4	yes	complemented
189	C₂³×#120	C₂×D₄	1	8	yes	complemented
190	C₂³×#120	C₂⁴	1	1	yes	characteristic
191	C₂³×#120	C₂⁴	1	1	yes	characteristic
192	C₂³×#120	C₂⁴	1	4	yes	—
193	C₂³×#120	C₂⁴	1	1	yes	characteristic
194	C₂²×#518	C₂×D₄	1	1	yes	characteristic
195	C₂²×#518	C₂×D₄	1	1	yes	characteristic
196	C₂²×#518	C₂×D₄	1	2	yes	complemented
197	C₂⁴×C₂²⋊C₄	C₂×D₄	1	2	yes	—
198	C₂⁴×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
199	C₂⁴×C₂²⋊C₄	C₂⁴	1	2	yes	—
200	C₂⁴×C₂²⋊C₄	C₂⁴	1	1	yes	characteristic
201	C₂³×#99	C₂×D₄	1	8	yes	complemented
202	C₂³×#99	C₂×D₄	1	4	yes	complemented
203	C₂³×#99	C₂×D₄	1	4	yes	complemented
204	C₂×#2846	C₂×D₄	1	16	yes	—
205	C₂×#2846	C₂×D₄	1	8	yes	—
206	C₂×#2846	C₂×D₄	1	8	yes	—
207	C₂×#2846	C₂×D₄	1	16	yes	—
208	C₂×#2846	C₂×D₄	1	8	yes	—
209	C₂×#2846	C₂×D₄	1	8	yes	—
210	C₂×#2846	C₂×D₄	1	16	yes	complemented
211	C₂×#2846	C₂×D₄	1	8	yes	complemented
212	#34992	C₂×D₄	1	8	yes	—
213	#34980	C₂×D₄	1	8	yes	—
214	#34176	C₂×D₄	1	4	yes	—
215	#34171	C₂×D₄	1	4	yes	—
216	C₂×#2315	C₂×D₄	1	1	yes	characteristic
217	C₂×#2315	C₂×D₄	1	1	yes	characteristic
218	C₂×#2308	C₂×D₄	1	1	yes	characteristic
219	C₂×#2308	C₂×D₄	1	1	yes	characteristic
220	C₂×#2308	C₂×D₄	1	1	yes	characteristic
221	C₂×#2308	C₂×D₄	1	1	yes	characteristic
222	C₂×#2308	C₂×D₄	1	1	yes	characteristic
223	C₂²×#379	C₂×D₄	1	8	yes	—
224	C₂²×#379	C₂×D₄	1	1	yes	characteristic
225	C₂²×#379	C₂×D₄	1	1	yes	characteristic
226	C₂²×#379	C₂×D₄	1	8	yes	complemented
227	C₂²×#379	C₂⁴	1	4	yes	—
228	C₂²×#379	C₂⁴	1	4	yes	—
229	C₂²×#379	C₂⁴	1	1	yes	characteristic
230	C₂²×#379	C₂⁴	1	4	yes	—
231	C₂²×#379	C₂⁴	1	2	yes	—
232	C₂²×#379	C₂⁴	1	2	yes	—
233	C₂×#2273	C₂×D₄	1	1	yes	characteristic
234	#21746	C₂×D₄	1	16	yes	complemented
235	#21746	C₂×D₄	1	8	yes	complemented
236	C₂×#1898	C₂×D₄	1	16	yes	—
237	C₂×#1898	C₂×D₄	1	8	yes	—
238	C₂×#1898	C₂×D₄	1	16	yes	complemented
239	C₂×#1898	C₂×D₄	1	8	yes	complemented
240	C₂×#1819	C₂×D₄	1	8	yes	complemented
241	C₂×#1781	C₂×D₄	1	4	yes	complemented
242	C₂×#1781	C₂×D₄	1	4	yes	complemented
243	C₂×#1781	C₂×D₄	1	8	yes	complemented
244	C₂²×#342	C₂×D₄	1	8	yes	complemented
245	C₂⁷	#120	1	1	yes	characteristic, complemented
246	C₂⁷	C₂²×D₄	1	4	yes	—
247	C₂⁷	C₂²×D₄	1	2	yes	—
248	C₂⁷	C₂²×D₄	1	2	yes	—
249	C₂⁷	C₂²×D₄	1	1	yes	characteristic
250	C₂⁷	C₂²×D₄	1	1	yes	characteristic
251	C₂⁷	C₂²×D₄	1	4	yes	—
252	C₂⁷	C₂²×D₄	1	4	yes	—
253	C₂⁷	C₂²×D₄	1	8	yes	—
254	C₂⁷	H(5,𝔽₂)	1	1	yes	characteristic
255	C₂⁷	C₂⁵	1	1	yes	characteristic
256	C₂²×H(5,𝔽₂)	#120	1	4	yes	complemented
257	C₂²×H(5,𝔽₂)	#120	1	2	yes	complemented
258	C₂²×H(5,𝔽₂)	#120	1	2	yes	complemented
259	C₂⁴×D₄	#120	1	1	yes	characteristic, complemented
260	C₂⁴×D₄	#120	1	2	yes	complemented
261	C₂⁴×D₄	#120	1	1	yes	characteristic, complemented
262	C₂⁴×D₄	#120	1	2	yes	complemented
263	C₂⁴×D₄	C₂²×D₄	1	2	yes	—
264	C₂⁴×D₄	C₂²×D₄	1	1	yes	characteristic
265	C₂⁴×D₄	C₂²×D₄	1	2	yes	—
266	C₂⁴×D₄	C₂²×D₄	1	1	yes	characteristic
267	C₂⁴×D₄	C₂²×D₄	1	1	yes	characteristic
268	C₂⁴×D₄	C₂²×D₄	1	1	yes	characteristic
269	C₂⁴×D₄	C₂²×D₄	1	1	yes	characteristic
270	C₂⁴×D₄	C₂²×D₄	1	2	yes	—
271	C₂⁴×D₄	C₂²×D₄	1	2	yes	—
272	C₂⁴×D₄	C₂²×D₄	1	4	yes	—
273	C₂⁴×D₄	C₂²×D₄	1	2	yes	—
274	C₂⁴×D₄	C₂²×D₄	1	2	yes	—
275	C₂⁴×D₄	C₂²×D₄	1	4	yes	—
276	C₂⁴×D₄	H(5,𝔽₂)	1	1	yes	characteristic
277	C₂⁴×D₄	H(5,𝔽₂)	1	1	yes	characteristic
278	C₂⁴×D₄	H(5,𝔽₂)	1	2	yes	—
279	C₂⁴×D₄	H(5,𝔽₂)	1	4	yes	—
280	C₂⁵×C₄	#120	1	1	yes	characteristic, complemented
281	C₂⁵×C₄	#120	1	2	yes	complemented
282	C₂⁵×C₄	H(5,𝔽₂)	1	1	yes	characteristic
283	C₂×#543	#120	1	4	yes	complemented
284	C₂×#534	#120	1	4	yes	complemented
285	C₂×#534	#120	1	8	yes	complemented
286	C₂×#534	#120	1	4	yes	complemented
287	C₂×#534	#120	1	4	yes	complemented
288	C₂²×#120	#120	1	2	yes	—
289	C₂²×#120	#120	1	4	yes	—
290	C₂²×#120	#120	1	2	yes	—
291	C₂²×#120	#120	1	2	yes	—
292	C₂²×#120	#120	1	2	yes	—
293	C₂²×#120	#120	1	4	yes	—
294	C₂²×#120	#120	1	4	yes	complemented
295	C₂²×#120	#120	1	4	yes	complemented
296	C₂²×#120	#120	1	16	yes	complemented
297	C₂²×#120	#120	1	16	yes	complemented
298	C₂²×#120	C₂²×D₄	1	8	yes	—
299	C₂²×#120	C₂²×D₄	1	4	yes	—
300	C₂²×#120	C₂²×D₄	1	8	yes	—
301	C₂²×#120	C₂²×D₄	1	8	yes	—
302	C₂²×#120	C₂²×D₄	1	4	yes	—
303	C₂²×#120	C₂²×D₄	1	4	yes	—
304	C₂²×#120	C₂²×D₄	1	8	yes	—
305	C₂²×#120	H(5,𝔽₂)	1	4	yes	—
306	C₂²×#120	H(5,𝔽₂)	1	8	yes	—
307	C₂²×#120	H(5,𝔽₂)	1	8	yes	—
308	C₂×#518	#120	1	2	yes	complemented
309	C₂×#518	#120	1	2	yes	complemented
310	C₂×#518	#120	1	8	yes	complemented
311	C₂×#518	#120	1	4	yes	complemented
312	C₂³×C₂²⋊C₄	#120	1	2	yes	complemented
313	C₂³×C₂²⋊C₄	#120	1	2	yes	complemented
314	C₂³×C₂²⋊C₄	#120	1	2	yes	complemented
315	C₂³×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
316	C₂³×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
317	C₂³×C₂²⋊C₄	C₂²×D₄	1	2	yes	—
318	C₂³×C₂²⋊C₄	C₂²×D₄	1	4	yes	—
319	C₂³×C₂²⋊C₄	C₂²×D₄	1	4	yes	—
320	C₂³×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
321	C₂³×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
322	C₂³×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
323	C₂³×C₂²⋊C₄	C₂²×D₄	1	4	yes	—
324	C₂³×C₂²⋊C₄	C₂²×D₄	1	8	yes	—
325	C₂³×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
326	C₂³×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
327	C₂³×C₂²⋊C₄	C₂²×D₄	1	2	yes	—
328	C₂³×C₂²⋊C₄	C₂²×D₄	1	4	yes	—
329	C₂³×C₂²⋊C₄	C₂²×D₄	1	8	yes	—
330	C₂³×C₂²⋊C₄	H(5,𝔽₂)	1	4	yes	—
331	C₂³×C₂²⋊C₄	H(5,𝔽₂)	1	2	yes	—
332	#2846	#120	1	32	yes	complemented
333	C₂×#379	#120	1	4	yes	complemented
334	C₂×#379	#120	1	4	yes	complemented
335	C₂×#379	#120	1	16	yes	complemented
336	C₂×#379	#120	1	16	yes	complemented
337	C₂×#379	C₂²×D₄	1	8	yes	—
338	C₂×#379	C₂²×D₄	1	8	yes	—
339	C₂×#379	C₂²×D₄	1	4	yes	—
340	C₂×#379	C₂²×D₄	1	4	yes	—
341	C₂×#379	C₂²×D₄	1	8	yes	—
342	C₂×#379	C₂²×D₄	1	4	yes	—
343	C₂×#379	C₂²×D₄	1	8	yes	—
344	C₂⁶	C₂×#120	1	1	yes	characteristic
345	C₂⁶	C₂×#120	1	2	yes	—
346	C₂⁶	C₂×#120	1	1	yes	characteristic
347	C₂⁶	C₂×#120	1	2	yes	—
348	C₂⁶	C₂×#120	1	2	yes	—
349	C₂⁶	C₂×#120	1	8	yes	—
350	C₂⁶	C₂×#120	1	8	yes	—
351	C₂⁶	C₂×#120	1	2	yes	—
352	C₂⁶	C₂×#120	1	2	yes	—
353	C₂⁶	C₂×#120	1	1	yes	characteristic
354	C₂⁶	C₂×#120	1	1	yes	characteristic
355	C₂⁶	C₂×#120	1	8	yes	—
356	C₂⁶	#534	1	1	yes	characteristic
357	C₂⁶	#534	1	1	yes	characteristic
358	C₂⁶	#534	1	1	yes	characteristic
359	C₂⁶	D₄²	1	4	yes	—
360	C₂⁶	D₄²	1	2	yes	—
361	C₂⁶	D₄²	1	2	yes	—
362	C₂⁶	C₂³×D₄	1	1	yes	characteristic
363	C₂⁶	C₂³×D₄	1	2	yes	—
364	C₂⁶	C₂³×D₄	1	2	yes	—
365	C₂⁶	C₂³×D₄	1	2	yes	—
366	C₂⁶	C₂³×D₄	1	2	yes	—
367	C₂⁶	C₂³×D₄	1	4	yes	—
368	C₂⁶	C₂×H(5,𝔽₂)	1	4	yes	—
369	C₂⁶	C₂×H(5,𝔽₂)	1	2	yes	—
370	C₂⁶	C₂×H(5,𝔽₂)	1	1	yes	characteristic
371	C₂⁶	C₂×H(5,𝔽₂)	1	1	yes	characteristic
372	C₂⁶	C₂×H(5,𝔽₂)	1	4	yes	—
373	C₂⁶	C₂×H(5,𝔽₂)	1	2	yes	—
374	C₂⁶	C₂×H(5,𝔽₂)	1	4	yes	—
375	C₂³×D₄	C₂×#120	1	2	yes	—
376	C₂³×D₄	C₂×#120	1	4	yes	—
377	C₂³×D₄	C₂×#120	1	1	yes	characteristic
378	C₂³×D₄	C₂×#120	1	1	yes	characteristic
379	C₂³×D₄	C₂×#120	1	1	yes	characteristic
380	C₂³×D₄	C₂×#120	1	1	yes	characteristic
381	C₂³×D₄	C₂×#120	1	2	yes	—
382	C₂³×D₄	C₂×#120	1	2	yes	—
383	C₂³×D₄	C₂×#120	1	2	yes	—
384	C₂³×D₄	C₂×#120	1	8	yes	—
385	C₂³×D₄	C₂×#120	1	8	yes	—
386	C₂³×D₄	C₂×#120	1	2	yes	—
387	C₂³×D₄	#534	1	4	yes	—
388	C₂³×D₄	#534	1	2	yes	—
389	C₂³×D₄	#534	1	8	yes	—
390	C₂³×D₄	D₄²	1	8	yes	—
391	C₂³×D₄	D₄²	1	8	yes	—
392	C₂³×D₄	D₄²	1	8	yes	—
393	C₂³×D₄	D₄²	1	2	yes	—
394	C₂³×D₄	D₄²	1	2	yes	—
395	C₂³×D₄	D₄²	1	2	yes	—
396	C₂³×D₄	D₄²	1	2	yes	—
397	C₂³×D₄	D₄²	1	8	yes	—
398	C₂³×D₄	D₄²	1	8	yes	—
399	C₂³×D₄	D₄²	1	8	yes	—
400	C₂³×D₄	D₄²	1	8	yes	—
401	C₂⁴×C₄	C₂×#120	1	2	yes	—
402	C₂⁴×C₄	C₂×#120	1	1	yes	characteristic
403	C₂⁴×C₄	C₂×#120	1	2	yes	—
404	C₂⁴×C₄	C₂×#120	1	1	yes	characteristic
405	C₂⁴×C₄	#534	1	1	yes	characteristic
406	C₂⁴×C₄	#534	1	1	yes	characteristic
407	C₂⁴×C₄	#534	1	1	yes	characteristic
408	C₂⁴×C₄	#534	1	2	yes	—
409	C₂⁴×C₄	D₄²	1	2	yes	—
410	C₂⁴×C₄	D₄²	1	2	yes	—
411	C₂⁴×C₄	D₄²	1	4	yes	—
412	C₂⁴×C₄	D₄²	1	4	yes	—
413	C₂⁴×C₄	D₄²	1	4	yes	—
414	C₂×#120	B(4,𝔽₂)	1	8	yes	complemented
415	C₂×#120	C₂×#120	1	8	yes	—
416	C₂×#120	#534	1	8	yes	—
417	C₂×#120	#534	1	16	yes	—
418	C₂×#120	D₄²	1	16	yes	—
419	C₂×#120	D₄²	1	8	yes	—
420	C₂×#120	H(3,𝔽₄)	1	8	yes	—
421	C₂²×C₂²⋊C₄	C₂×#120	1	2	yes	—
422	C₂²×C₂²⋊C₄	C₂×#120	1	4	yes	—
423	C₂²×C₂²⋊C₄	C₂×#120	1	2	yes	—
424	C₂²×C₂²⋊C₄	C₂×#120	1	2	yes	—
425	C₂²×C₂²⋊C₄	C₂×#120	1	8	yes	—
426	C₂²×C₂²⋊C₄	C₂×#120	1	2	yes	—
427	C₂²×C₂²⋊C₄	C₂×#120	1	8	yes	—
428	C₂²×C₂²⋊C₄	C₂×#120	1	2	yes	—
429	C₂²×C₂²⋊C₄	C₂×#120	1	2	yes	—
430	C₂²×C₂²⋊C₄	C₂×#120	1	16	yes	—
431	C₂²×C₂²⋊C₄	C₂×#120	1	2	yes	—
432	C₂²×C₂²⋊C₄	#534	1	2	yes	—
433	C₂²×C₂²⋊C₄	#534	1	4	yes	—
434	C₂²×C₂²⋊C₄	#534	1	8	yes	—
435	C₂²×C₂²⋊C₄	D₄²	1	8	yes	—
436	C₂²×C₂²⋊C₄	D₄²	1	8	yes	—
437	C₂²×C₂²⋊C₄	D₄²	1	8	yes	—
438	C₂²×C₂²⋊C₄	D₄²	1	8	yes	—
439	C₂²×C₂²⋊C₄	D₄²	1	8	yes	—
440	C₂²×C₂²⋊C₄	D₄²	1	8	yes	—
441	C₂²×C₂²⋊C₄	D₄²	1	8	yes	—
442	#379	C₂×#120	1	8	yes	—
443	C₂⁵	#2403	1	2	yes	—
444	C₂⁵	#2403	1	4	yes	—
445	C₂⁵	#2403	1	8	yes	—
446	C₂⁵	#2403	1	2	yes	—
447	C₂⁵	#2403	1	1	yes	characteristic
448	C₂⁵	#2403	1	2	yes	—
449	C₂⁵	#2403	1	1	yes	characteristic
450	C₂⁵	#2846	1	4	yes	—
451	C₂⁵	#2846	1	2	yes	—
452	C₂⁵	#2846	1	2	yes	—
453	C₂⁵	C₂×B(4,𝔽₂)	1	4	yes	—
454	C₂⁵	#3026	1	4	yes	—
455	C₂⁵	C₂²×#120	1	1	yes	characteristic
456	C₂⁵	C₂²×#120	1	1	yes	characteristic
457	C₂⁵	C₂²×#120	1	1	yes	characteristic
458	C₂⁵	C₂²×#120	1	4	yes	—
459	C₂⁵	C₂²×#120	1	2	yes	—
460	C₂⁵	C₂²×#120	1	1	yes	characteristic
461	C₂⁵	C₂²×#120	1	2	yes	—
462	C₂⁵	C₂×#534	1	2	yes	—
463	C₂⁵	C₂×#534	1	4	yes	—
464	C₂⁵	C₂×#534	1	4	yes	—
465	C₂⁵	C₂×#534	1	1	yes	characteristic
466	C₂⁵	C₂×#534	1	1	yes	characteristic
467	C₂⁵	C₂×#534	1	1	yes	characteristic
468	C₂⁵	C₂×#534	1	2	yes	—
469	C₂⁵	C₂×D₄²	1	4	yes	—
470	C₂⁵	C₂×D₄²	1	4	yes	—
471	C₂⁵	C₂×D₄²	1	4	yes	—
472	C₂⁵	C₂×D₄²	1	4	yes	—
473	C₂⁵	C₂×D₄²	1	4	yes	—
474	C₂⁵	C₂×D₄²	1	4	yes	—
475	C₂⁵	C₂×D₄²	1	4	yes	—
476	C₂⁵	C₂×D₄²	1	4	yes	—
477	C₂⁵	C₂×D₄²	1	2	yes	—
478	C₂⁵	C₂×D₄²	1	2	yes	—
479	C₂⁵	C₂×D₄²	1	4	yes	—
480	C₂⁵	C₂×D₄²	1	2	yes	—
481	C₂⁵	#3484	1	4	yes	—
482	C₂⁵	#3484	1	4	yes	—
483	C₂⁵	#3484	1	2	yes	—
484	C₂⁵	#3484	1	4	yes	—
485	C₂⁵	#3484	1	2	yes	—
486	C₂⁵	#3484	1	4	yes	—
487	C₂⁵	#3484	1	4	yes	—
488	C₂⁵	#3484	1	2	yes	—
489	C₂⁵	#3484	1	2	yes	—
490	C₂⁵	#3484	1	4	yes	—
491	C₂⁵	#3484	1	2	yes	—
492	C₂⁵	#3484	1	2	yes	—
493	C₂⁵	#3484	1	4	yes	—
494	C₂⁵	#3484	1	4	yes	—
495	C₂⁵	#3484	1	4	yes	—
496	C₂⁵	#3484	1	2	yes	—
497	C₂⁵	#3484	1	2	yes	—
498	C₂⁵	#3484	1	4	yes	—
499	C₂⁵	#3484	1	4	yes	—
500	C₂⁵	C₂×H(3,𝔽₄)	1	2	yes	—
501	C₂⁵	#3532	1	4	yes	—
502	C₂⁵	#3532	1	4	yes	—
503	C₂⁵	#3532	1	4	yes	—
504	C₂⁵	#3532	1	2	yes	—
505	C₂⁵	#3532	1	4	yes	—
506	C₂⁵	#3532	1	4	yes	—
507	C₂⁵	#3532	1	2	yes	—
508	C₂²×D₄	#2403	1	8	yes	—
509	C₂²×D₄	#2403	1	16	yes	—
510	C₂²×D₄	#2679	1	8	yes	—
511	C₂²×D₄	#2679	1	16	yes	—
512	C₂²×D₄	C₂×B(4,𝔽₂)	1	4	yes	—
513	C₂³×C₄	#2403	1	4	yes	—
514	C₂³×C₄	#2403	1	4	yes	—
515	C₂³×C₄	#2403	1	4	yes	—
516	C₂³×C₄	#2403	1	2	yes	—
517	C₂³×C₄	#2403	1	4	yes	—
518	C₂³×C₄	#2403	1	1	yes	characteristic
519	C₂³×C₄	#2403	1	4	yes	—
520	C₂³×C₄	#2403	1	8	yes	—
521	C₂³×C₄	#2403	1	8	yes	—
522	C₂³×C₄	#2403	1	8	yes	—
523	C₂³×C₄	#2403	1	2	yes	—
524	C₂³×C₄	#2403	1	1	yes	characteristic
525	C₂³×C₄	#2403	1	2	yes	—
526	C₂×C₂²⋊C₄	#2403	1	8	yes	—
527	C₂×C₂²⋊C₄	#2403	1	16	yes	—
528	C₂×C₂²⋊C₄	#2679	1	8	yes	—
529	C₂×C₂²⋊C₄	#2679	1	16	yes	—
530	C₂×C₂²⋊C₄	C₂×B(4,𝔽₂)	1	4	yes	—
531	C₂⁴	#15947	1	4	yes	—
532	C₂⁴	#23900	1	2	yes	complemented
533	C₂⁴	#32898	1	4	yes	—
534	C₂⁴	#32898	1	4	yes	—
535	C₂⁴	C₂×#2403	1	1	yes	characteristic
536	C₂⁴	C₂×#2403	1	2	yes	—
537	C₂⁴	C₂×#2403	1	1	yes	characteristic
538	C₂⁴	C₂×#2403	1	1	yes	characteristic
539	C₂⁴	C₂×#2403	1	4	yes	—
540	C₂⁴	C₂×#2403	1	4	yes	—
541	C₂⁴	C₂×#2403	1	2	yes	—
542	C₂⁴	#34980	1	1	yes	characteristic
543	C₂⁴	#34980	1	2	yes	—
544	C₂⁴	#34980	1	1	yes	characteristic
545	C₂⁴	#34980	1	1	yes	characteristic
546	C₂⁴	#34980	1	4	yes	—
547	C₂⁴	#35346	1	2	yes	—
548	C₂⁴	#35346	1	2	yes	—
549	C₂⁴	#35346	1	2	yes	—
550	C₂⁴	D₄×#120	1	4	yes	—
551	C₂⁴	D₄×#120	1	4	yes	—
552	C₂⁴	D₄×#120	1	4	yes	—
553	C₂⁴	D₄×#120	1	4	yes	—
554	C₂⁴	D₄×#120	1	4	yes	—
555	C₂⁴	D₄×#120	1	4	yes	—
556	C₂⁴	D₄×#120	1	2	yes	—
557	C₂⁴	D₄×#120	1	4	yes	—
558	C₂⁴	D₄×#120	1	2	yes	—
559	C₂⁴	C₂×#2846	1	1	yes	characteristic
560	C₂⁴	#36714	1	2	yes	—
561	C₂⁴	#36714	1	2	yes	—
562	C₂⁴	#36714	1	2	yes	—
563	C₂⁴	#37644	1	4	yes	—
564	C₂⁴	#37644	1	4	yes	—
565	C₂⁴	#37644	1	4	yes	—
566	C₂⁴	#37644	1	4	yes	—
567	C₂⁴	#37644	1	4	yes	—
568	C₂⁴	#37644	1	4	yes	—
569	C₂⁴	#37644	1	4	yes	—
570	C₂⁴	#37644	1	4	yes	—
571	C₂⁴	#37644	1	2	yes	—
572	C₂⁴	#37644	1	2	yes	—
573	C₂⁴	#37644	1	4	yes	—
574	C₂⁴	#37644	1	4	yes	—
575	C₂⁴	#37644	1	4	yes	—
576	C₂⁴	#45439	1	4	yes	—
577	C₂⁴	#45439	1	2	yes	—
578	C₂⁴	#45439	1	2	yes	—
579	C₂⁴	C₂×#2679	1	2	yes	—
580	C₂⁴	C₂×#2679	1	4	yes	—
581	C₂⁴	#58990	1	2	yes	—
582	C₂⁴	#58990	1	4	yes	—
583	C₂⁴	#58990	1	4	yes	—
584	C₂⁴	#58990	1	4	yes	—
585	C₂⁴	#58990	1	4	yes	—
586	C₂⁴	#58990	1	2	yes	—
587	C₂⁴	#58990	1	4	yes	—
588	C₂⁴	C₂²×B(4,𝔽₂)	1	2	yes	—
589	C₂⁴	C₂×#3026	1	2	yes	—
590	C₂⁴	#60399	1	4	yes	—
591	C₂²×C₄	#15947	1	8	yes	—
592	C₂²×C₄	#15947	1	4	yes	—
593	C₂²×C₄	#23900	1	2	yes	complemented
594	C₂³	C₂×#15947	1	1	yes	characteristic
595	C₂³	#612424	1	1	yes	characteristic
596	C₂³	#612424	1	2	yes	—
597	C₂³	#616960	1	2	yes	—
598	C₂³	#616960	1	1	yes	characteristic
599	C₂³	#647656	1	4	yes	—
600	C₂³	#647656	1	2	yes	—
601	C₂³	#647656	1	2	yes	—
602	C₂³	#647656	1	4	yes	—
603	C₂³	#845297	1	2	yes	—
604	C₂³	#845297	1	4	yes	—
605	C₂³	#845297	1	2	yes	—
606	C₂³	#845297	1	4	yes	—
607	C₂³	C₂×#23900	1	1	yes	characteristic
608	C₂³	#6437621	1	1	yes	characteristic
609	C₂³	#6437632	1	2	yes	—
610	C₂³	#6470225	1	2	yes	—
611	C₂³	#6470231	1	2	yes	—
612	C₂³	#6499874	1	8	yes	—
613	C₂³	D₄×B(4,𝔽₂)	1	8	yes	—
614	C₂³	#6573715	1	8	yes	—
615	C₂³	C₂×#32898	1	2	yes	—
616	C₂³	#6628896	1	2	yes	—
617	C₂²	#72214832	1	1	yes	characteristic
618	C₂²	#72216646	1	8	yes	—
619	C₂²	#72216660	1	2	yes	—
620	C₂²	#72218795	1	1	yes	characteristic
621	C₂²	#72225641	1	4	yes	—
622	C₂²	#72225689	1	2	yes	—
623	C₂²	#72225690	1	1	yes	characteristic
624	C₂²	#72225691	1	4	yes	—
625	C₂²	#72225692	1	4	yes	—
626	C₂	#72225711	1	1	yes	characteristic
627	C₂	#72240558	1	2	yes	—

	subgroup	G/H
center, socle	C₂²	#72218795
commutator, Frattini, cosocle	C₂⁷	C₂⁵
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. #72331660	C₂	semidirect
2. #72331045	C₂	semidirect
3. #72313223	C₂	semidirect
4. #72313018	C₂	semidirect
5. #72310049	C₂	semidirect
6. #72309382	C₂	semidirect
7. #72309381	C₂	semidirect
8. #72309377	C₂²	semidirect
9. #72309373	C₂²	semidirect
10. #72309370	C₂²	semidirect
11. #72309369	C₂²	semidirect
12. #72309368	C₂²	semidirect
13. #72266073	C₂²	semidirect
14. #72266028	C₂²	semidirect
15. #72259092	C₂	semidirect
16. #72259089	C₂²	semidirect
17. #72259083	C₂²	semidirect
18. #72259029	C₂	semidirect
19. #72259021	C₂²	semidirect
20. #72259008	C₂²	semidirect
21. #72259002	C₂²	semidirect
22. #72237423	C₂	semidirect
23. #72237400	C₂²	semidirect
24. #72237398	C₂²	semidirect
25. #72237398	C₂²	semidirect
26. #72236453	C₂²	semidirect
27. #72236437	C₂²	semidirect
28. #72236437	C₂²	semidirect
29. #72235847	C₂²	semidirect
30. #72234665	C₂	semidirect
31. #72234663	C₂²	semidirect
32. #72234661	C₂²	semidirect
33. #72234591	C₂²	semidirect
34. #72232884	C₂²	semidirect
35. #72232592	C₂²	semidirect
36. C₂×#72217546	C₂	semidirect
37. C₂×#374022	C₂²	semidirect
38. C₂×#394167	C₂²	semidirect
39. C₂×#394058	C₂²	semidirect
40. C₂×#359428	C₂²	semidirect
41. C₂×#359428	C₂²	semidirect
43. C₂×#364410	C₂²	semidirect
44. #72218799	C₂	semidirect
45. #72218766	C₂²	semidirect
46. #72218766	C₂²	semidirect
47. #72218744	C₂²	semidirect
48. #72218451	C₂²	semidirect
49. #72218451	C₂²	semidirect
50. #72218375	C₂²	semidirect
51. #72217947	C₂	semidirect
54. C₂²×#23900	C₂²	semidirect
55. #72217875	C₂²	semidirect
56. #72217818	C₂²	semidirect
57. #72217789	C₂²	semidirect
58. C₂³×#2846	C₂²	semidirect
59. C₂³×#2846	C₂²	semidirect
60. #72217699	C₂²	semidirect
61. #72217699	C₂²	semidirect
62. #72217666	C₂²	semidirect
64. C₂×#72209716	C₂	semidirect
65. C₂×#115690	C₂²	semidirect
66. C₂×#115690	C₂²	semidirect
67. C₂×#115690	C₂²	semidirect
68. C₂×#115690	C₂²	semidirect
69. C₂×#115690	C₂²	semidirect
72. C₂×#6499867	C₂²	semidirect
73. C₂×#6342371	C₂²	semidirect
74. C₂×#6342371	C₂²	semidirect
75. C₂⁹	C₂³	semidirect
78. C₂²×#3484	D₄	semidirect
84. C₂³×B(4,𝔽₂)	D₄	semidirect
85. #7642273	D₄	semidirect
86. #7642244	D₄	semidirect
94. C₂²×#2846	C₂³	semidirect
95. #7630944	D₄	semidirect
96. #7630939	D₄	semidirect
97. C₂×#35390	D₄	semidirect
98. C₂×#35348	D₄	semidirect
99. C₂×#35348	D₄	semidirect
100. C₂×#35346	D₄	semidirect
101. C₂×#34981	D₄	semidirect
103. C₂×#34980	D₄	semidirect
106. C₂×#34198	D₄	semidirect
108. C₂³×#379	C₂³	semidirect
109. C₂³×#379	C₂³	semidirect
110. C₂³×#379	C₂³	semidirect
111. #6499867	D₄	semidirect
112. C₂×#23984	D₄	semidirect
113. C₂×#23900	D₄	semidirect
114. C₂×#23900	D₄	semidirect
115. C₂×#23900	D₄	semidirect
116. C₂²×#2021	D₄	semidirect
125. C₂×#21746	C₂³	semidirect
126. C₂×#21746	C₂³	semidirect
131. C₂²×#1898	C₂³	semidirect
132. C₂²×#1889	D₄	semidirect
136. C₂×#14679	C₂³	semidirect
137. C₂×#14679	C₂³	semidirect
138. C₂×#14679	C₂³	semidirect
139. C₂×#14679	C₂³	semidirect
140. C₂×#14679	C₂³	semidirect
143. #355913	C₂³	semidirect
144. #355913	C₂³	semidirect
145. C₂×#10735	C₂³	semidirect
146. C₂×#10735	C₂³	semidirect
147. C₂×#10735	C₂³	semidirect
148. C₂×#10725	C₂³	semidirect
149. C₂×#10725	C₂³	semidirect
150. C₂×#8101	C₂³	semidirect
151. C₂×#8101	C₂³	semidirect
152. C₂×#8101	C₂³	semidirect
153. C₂×#8101	C₂³	semidirect
157. C₂³×H(5,𝔽₂)	C₂×D₄	semidirect
161. #62817	C₂×D₄	semidirect
173. C₂²×#534	C₂×D₄	semidirect
187. C₂³×#120	C₂×D₄	semidirect
188. C₂³×#120	C₂×D₄	semidirect
189. C₂³×#120	C₂×D₄	semidirect
196. C₂²×#518	C₂×D₄	semidirect
201. C₂³×#99	C₂×D₄	semidirect
202. C₂³×#99	C₂×D₄	semidirect
203. C₂³×#99	C₂×D₄	semidirect
210. C₂×#2846	C₂×D₄	semidirect
211. C₂×#2846	C₂×D₄	semidirect
226. C₂²×#379	C₂×D₄	semidirect
234. #21746	C₂×D₄	semidirect
235. #21746	C₂×D₄	semidirect
238. C₂×#1898	C₂×D₄	semidirect
239. C₂×#1898	C₂×D₄	semidirect
240. C₂×#1819	C₂×D₄	semidirect
241. C₂×#1781	C₂×D₄	semidirect
242. C₂×#1781	C₂×D₄	semidirect
243. C₂×#1781	C₂×D₄	semidirect
244. C₂²×#342	C₂×D₄	semidirect
245. C₂⁷	#120	semidirect
256. C₂²×H(5,𝔽₂)	#120	semidirect
257. C₂²×H(5,𝔽₂)	#120	semidirect
258. C₂²×H(5,𝔽₂)	#120	semidirect
259. C₂⁴×D₄	#120	semidirect
260. C₂⁴×D₄	#120	semidirect
261. C₂⁴×D₄	#120	semidirect
262. C₂⁴×D₄	#120	semidirect
280. C₂⁵×C₄	#120	semidirect
281. C₂⁵×C₄	#120	semidirect
283. C₂×#543	#120	semidirect
284. C₂×#534	#120	semidirect
285. C₂×#534	#120	semidirect
286. C₂×#534	#120	semidirect
287. C₂×#534	#120	semidirect
294. C₂²×#120	#120	semidirect
295. C₂²×#120	#120	semidirect
296. C₂²×#120	#120	semidirect
297. C₂²×#120	#120	semidirect
308. C₂×#518	#120	semidirect
309. C₂×#518	#120	semidirect
310. C₂×#518	#120	semidirect
311. C₂×#518	#120	semidirect
312. C₂³×C₂²⋊C₄	#120	semidirect
313. C₂³×C₂²⋊C₄	#120	semidirect
314. C₂³×C₂²⋊C₄	#120	semidirect
332. #2846	#120	semidirect
333. C₂×#379	#120	semidirect
334. C₂×#379	#120	semidirect
335. C₂×#379	#120	semidirect
336. C₂×#379	#120	semidirect
414. C₂×#120	B(4,𝔽₂)	semidirect
532. C₂⁴	#23900	semidirect
593. C₂²×C₄	#23900	semidirect

Maximal subgroups

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

subgroup	index
#72331660	2
#72331045	2
#72313223	2
#72313018	2
#72310049	2
#72309382	2
#72309381	2
#72259092	2
#72259029	2
#72237423	2
#72234665	2
C₂×#72217546	2
#72218799	2
#72217947	2
C₂×#72209716	2