Subgroups — #72317708

Order 2048.

At least 8463 conjugacy classes of subgroups; only the 1632 normal subgroups are shown.

The subgroup lattice has 687 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#72317695	C₂	1	2	yes	maximal, complemented
2	#72317688	C₂	1	4	yes	maximal, complemented
3	#72317684	C₂	1	8	yes	maximal, complemented
4	#72317678	C₂	1	4	yes	maximal, complemented
5	#72317673	C₂	1	2	yes	maximal, complemented
6	#72317665	C₂	1	1	yes	maximal, characteristic, complemented
7	#72317654	C₂	1	2	yes	maximal, complemented
8	C₂²×D₄×#99	C₂	1	1	yes	maximal, characteristic, complemented
9	#72280530	C₂	1	1	yes	maximal, characteristic, complemented
10	#72280502	C₂	1	2	yes	maximal, complemented
11	C₂²×#13086	C₂	1	1	yes	maximal, characteristic, complemented
12	#72236709	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×#496225	C₂	1	1	yes	maximal, characteristic, complemented
14	#72225665	C₂	1	1	yes	maximal, characteristic
15	C₂³×D₄²	C₂²	1	1	yes	characteristic
16	C₂⁴×#99	C₂²	1	1	yes	characteristic
17	C₂⁴×#99	C₂²	1	1	yes	characteristic, complemented
18	C₂×#34980	C₄	1	1	yes	characteristic, complemented
19	C₂²×#2403	C₄	1	1	yes	characteristic, complemented
20	C₂²×#2403	C₂²	1	1	yes	characteristic
21	C₂³×AΣL(1,𝔽₁₆)	C₂²	1	2	yes	complemented
22	C₂×D₄×#99	C₂²	1	4	yes	—
23	C₂×D₄×#99	C₂²	1	4	yes	complemented
24	C₂²×#1799	C₂²	1	1	yes	characteristic, complemented
25	C₂²×#1783	C₂²	1	1	yes	characteristic
26	C₂²×#1783	C₂²	1	1	yes	characteristic
27	C₂²×#1781	C₂²	1	1	yes	characteristic
28	C₂²×#1781	C₂²	1	1	yes	characteristic, complemented
29	C₂²×C₄×#99	C₂²	1	1	yes	characteristic, complemented
30	#686258	C₄	1	4	yes	complemented
31	#686258	C₂²	1	4	yes	—
32	#663621	C₄	1	2	yes	complemented
33	#663621	C₂²	1	2	yes	—
34	#647656	C₄	1	2	yes	complemented
35	#647656	C₂²	1	2	yes	—
36	#636791	C₄	1	2	yes	complemented
37	#635984	C₄	1	2	yes	complemented
38	#613191	C₂²	1	2	yes	—
39	#612424	C₂²	1	2	yes	—
40	#556752	C₄	1	1	yes	characteristic, complemented
41	#517411	C₄	1	1	yes	characteristic, complemented
42	#517411	C₂²	1	1	yes	characteristic
43	C₂×#13086	C₂²	1	2	yes	—
44	C₂×#13086	C₂²	1	2	yes	—
45	C₂×#13086	C₂²	1	2	yes	—
46	C₂×#13086	C₂²	1	2	yes	—
47	C₂×#13086	C₂²	1	4	yes	complemented
48	C₂×#13086	C₂²	1	8	yes	complemented
49	C₂×#13082	C₂²	1	4	yes	complemented
50	C₂×#12852	C₂²	1	2	yes	complemented
51	C₂×#12687	C₂²	1	2	yes	complemented
52	C₂×#12574	C₂²	1	4	yes	complemented
53	C₂²×#1390	C₂²	1	2	yes	complemented
54	#392249	C₂²	1	2	yes	complemented
55	#392113	C₂²	1	2	yes	complemented
56	#359583	C₂²	1	4	yes	—
57	#359583	C₂²	1	4	yes	complemented
58	#148688	C₂²	1	8	yes	complemented
59	#148572	C₂²	1	8	yes	complemented
60	#147995	C₂²	1	8	yes	complemented
61	#147555	C₂²	1	8	yes	complemented
62	#147500	C₂²	1	8	yes	complemented
63	#147314	C₂²	1	8	yes	complemented
64	#146566	C₂²	1	2	yes	complemented
65	#146566	C₂²	1	2	yes	complemented
66	#146566	C₂²	1	8	yes	complemented
67	#146566	C₂²	1	2	yes	complemented
68	#146566	C₂²	1	4	yes	complemented
69	#146566	C₂²	1	2	yes	complemented
70	#146564	C₂²	1	4	yes	complemented
71	#146459	C₂²	1	4	yes	complemented
72	C₂⁵×D₄	C₂×C₄	1	1	yes	characteristic
73	C₂⁵×D₄	C₂×C₄	1	1	yes	characteristic, complemented
74	C₂⁵×D₄	D₄	1	1	yes	characteristic
75	C₂⁵×D₄	C₂³	1	1	yes	characteristic
76	C₂⁵×D₄	C₂³	1	1	yes	characteristic
77	C₂²×D₄²	C₂×C₄	1	2	yes	—
78	C₂²×D₄²	C₂×C₄	1	2	yes	—
79	C₂²×D₄²	D₄	1	2	yes	—
80	C₂²×D₄²	D₄	1	2	yes	—
81	C₂²×D₄²	D₄	1	2	yes	—
82	C₂²×D₄²	D₄	1	2	yes	—
83	C₂²×D₄²	C₂³	1	2	yes	—
84	C₂²×D₄²	C₂³	1	2	yes	—
85	C₂³×#127	D₄	1	1	yes	characteristic
86	C₂³×#121	C₂×C₄	1	1	yes	characteristic
87	C₂³×#121	D₄	1	1	yes	characteristic
88	C₂³×#121	D₄	1	1	yes	characteristic
89	C₂³×#121	D₄	1	1	yes	characteristic
90	C₂³×#120	C₂×C₄	1	1	yes	characteristic
91	C₂³×#120	C₂×C₄	1	1	yes	characteristic
92	C₂³×#120	C₂×C₄	1	1	yes	characteristic, complemented
93	C₂³×#120	C₂×C₄	1	2	yes	complemented
94	C₂³×#120	C₂×C₄	1	2	yes	complemented
95	C₂³×#120	D₄	1	1	yes	characteristic
96	C₂³×#120	D₄	1	1	yes	characteristic
97	C₂³×#120	C₂³	1	1	yes	characteristic
98	C₂³×C₄×D₄	D₄	1	1	yes	characteristic
99	C₂³×C₄×D₄	C₂³	1	1	yes	characteristic
100	C₂³×#100	C₂³	1	2	yes	—
101	C₂³×#100	C₂³	1	2	yes	—
102	C₂³×#99	D₄	1	8	yes	complemented
103	C₂³×#99	C₂³	1	1	yes	characteristic
104	C₂³×#99	C₂³	1	4	yes	—
105	C₂³×#99	C₂³	1	2	yes	—
106	C₂³×#99	C₂³	1	2	yes	—
107	C₂³×#99	C₂³	1	1	yes	characteristic
108	C₂³×#99	C₂³	1	1	yes	characteristic
109	C₂³×#99	C₂³	1	1	yes	characteristic
110	C₂×#2849	C₂×C₄	1	2	yes	complemented
111	C₂×#2846	C₂×C₄	1	2	yes	complemented
112	C₂×#2405	C₂×C₄	1	2	yes	complemented
113	C₂×#2410	C₂×C₄	1	4	yes	complemented
114	C₂×#2403	C₂×C₄	1	2	yes	complemented
115	C₂×#2403	C₂×C₄	1	2	yes	complemented
116	C₂×#2403	C₂×C₄	1	2	yes	complemented
117	C₂×#2403	C₂×C₄	1	4	yes	complemented
118	C₂×#2403	C₂³	1	2	yes	—
119	C₂×#2403	C₂³	1	2	yes	—
120	C₂×#2403	C₂³	1	4	yes	—
121	C₂²×#392	C₂×C₄	1	4	yes	complemented
122	C₂×#2308	C₂×C₄	1	2	yes	complemented
123	C₂×#2308	C₂³	1	2	yes	—
124	C₂²×#386	C₂×C₄	1	2	yes	complemented
125	C₂²×#386	C₂×C₄	1	1	yes	characteristic, complemented
126	C₂²×#386	C₂×C₄	1	2	yes	complemented
127	C₂²×#386	C₂³	1	1	yes	characteristic
128	C₂²×#379	C₂×C₄	1	1	yes	characteristic, complemented
129	C₂²×#379	C₂×C₄	1	1	yes	characteristic, complemented
130	C₂²×#379	C₂×C₄	1	1	yes	characteristic, complemented
131	C₂²×AΣL(1,𝔽₁₆)	C₂³	1	4	yes	—
132	C₂²×AΣL(1,𝔽₁₆)	C₂³	1	4	yes	—
133	C₂²×AΣL(1,𝔽₁₆)	C₂³	1	4	yes	—
134	C₂²×AΣL(1,𝔽₁₆)	C₂³	1	4	yes	—
135	C₂×#1799	C₂³	1	4	yes	—
136	C₂×#1783	C₂³	1	2	yes	—
137	C₂×#1783	C₂³	1	2	yes	—
138	C₂×#1783	C₂³	1	2	yes	—
139	C₂×#1783	C₂³	1	2	yes	—
140	C₂×#1783	C₂³	1	8	yes	—
141	C₂×#1781	D₄	1	8	yes	complemented
142	C₂×#1781	C₂³	1	4	yes	—
143	C₂×#1781	C₂³	1	2	yes	—
144	C₂×#1781	C₂³	1	2	yes	—
145	C₂×C₄×#99	C₂³	1	4	yes	—
146	#14913	C₂×C₄	1	4	yes	complemented
147	#14913	C₂×C₄	1	4	yes	complemented
148	#14718	C₂×C₄	1	4	yes	complemented
149	#14718	C₂×C₄	1	4	yes	complemented
150	#14716	C₂×C₄	1	4	yes	complemented
151	#14716	C₂×C₄	1	4	yes	complemented
152	#14715	C₂×C₄	1	4	yes	complemented
153	#14715	C₂×C₄	1	4	yes	complemented
154	#14681	C₂×C₄	1	2	yes	complemented
155	#14679	C₂×C₄	1	2	yes	complemented
156	#14255	C₂×C₄	1	4	yes	complemented
157	#14134	C₂×C₄	1	2	yes	complemented
158	#14134	C₂×C₄	1	2	yes	complemented
159	#14016	C₂×C₄	1	4	yes	complemented
160	#14016	C₂³	1	4	yes	—
161	#13967	C₂×C₄	1	4	yes	complemented
162	#13967	C₂³	1	4	yes	—
163	#13869	C₂×C₄	1	2	yes	complemented
164	#13867	C₂×C₄	1	2	yes	complemented
165	#13867	C₂×C₄	1	2	yes	complemented
166	#13867	C₂×C₄	1	2	yes	complemented
167	#13867	C₂×C₄	1	4	yes	complemented
168	#13867	C₂×C₄	1	2	yes	complemented
169	#13867	C₂×C₄	1	2	yes	complemented
170	#13867	C₂×C₄	1	4	yes	complemented
171	#13867	C₂³	1	2	yes	—
172	#13867	C₂³	1	2	yes	—
173	#13867	C₂³	1	4	yes	—
174	C₂×#1390	C₂³	1	4	yes	—
175	C₂×#1390	C₂³	1	4	yes	—
176	C₂×#1390	C₂³	1	8	yes	—
177	C₂×#1390	C₂³	1	4	yes	—
178	C₂×#1390	C₂³	1	4	yes	—
179	C₂×#1390	C₂³	1	8	yes	—
180	C₂×#1390	C₂³	1	8	yes	—
181	C₂×#1390	C₂³	1	8	yes	—
182	#10762	C₂³	1	8	yes	—
183	C₂⁷	C₂²×C₄	1	1	yes	characteristic
184	C₂⁷	C₂²×C₄	1	1	yes	characteristic
185	C₂⁷	C₂²×C₄	1	1	yes	characteristic, complemented
186	C₂⁷	C₂×D₄	1	1	yes	characteristic
187	C₂⁷	C₂×D₄	1	1	yes	characteristic
188	C₂⁴×D₄	C₂²⋊C₄	1	2	yes	—
189	C₂⁴×D₄	C₂²⋊C₄	1	1	yes	characteristic
190	C₂⁴×D₄	C₂²⋊C₄	1	1	yes	characteristic
191	C₂⁴×D₄	C₂²⋊C₄	1	1	yes	characteristic
192	C₂⁴×D₄	C₂²⋊C₄	1	2	yes	—
193	C₂⁴×D₄	C₂²⋊C₄	1	2	yes	—
194	C₂⁴×D₄	C₂²⋊C₄	1	1	yes	characteristic
195	C₂⁴×D₄	C₂²⋊C₄	1	1	yes	characteristic
196	C₂⁴×D₄	C₂²⋊C₄	1	2	yes	—
197	C₂⁴×D₄	C₂²⋊C₄	1	1	yes	characteristic
198	C₂⁴×D₄	C₂²⋊C₄	1	1	yes	characteristic
199	C₂⁴×D₄	C₂²⋊C₄	1	1	yes	characteristic
200	C₂⁴×D₄	C₂²⋊C₄	1	1	yes	characteristic
201	C₂⁴×D₄	C₂²×C₄	1	1	yes	characteristic
202	C₂⁴×D₄	C₂²×C₄	1	2	yes	—
203	C₂⁴×D₄	C₂²×C₄	1	1	yes	characteristic
204	C₂⁴×D₄	C₂²×C₄	1	1	yes	characteristic
205	C₂⁴×D₄	C₂²×C₄	1	1	yes	characteristic
206	C₂⁴×D₄	C₂²×C₄	1	2	yes	—
207	C₂⁴×D₄	C₂²×C₄	1	2	yes	—
208	C₂⁴×D₄	C₂²×C₄	1	2	yes	—
209	C₂⁴×D₄	C₂²×C₄	1	2	yes	complemented
210	C₂⁴×D₄	C₂²×C₄	1	4	yes	complemented
211	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
212	C₂⁴×D₄	C₂×D₄	1	2	yes	—
213	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
214	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
215	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
216	C₂⁴×D₄	C₂×D₄	1	4	yes	—
217	C₂⁴×D₄	C₂×D₄	1	4	yes	—
218	C₂⁴×D₄	C₂×D₄	1	2	yes	—
219	C₂⁴×D₄	C₂×D₄	1	2	yes	—
220	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
221	C₂⁴×D₄	C₂×D₄	1	2	yes	—
222	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
223	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
224	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
225	C₂⁴×D₄	#41	1	4	yes	—
226	C₂⁴×D₄	#41	1	4	yes	—
227	C₂⁴×D₄	C₂⁴	1	2	yes	—
228	C₂⁴×D₄	C₂⁴	1	1	yes	characteristic
229	C₂⁴×D₄	C₂⁴	1	1	yes	characteristic
230	C₂⁴×D₄	C₂⁴	1	1	yes	characteristic
231	C₂⁵×C₄	C₂²×C₄	1	1	yes	characteristic
232	C₂⁵×C₄	C₂²×C₄	1	1	yes	characteristic, complemented
233	C₂⁵×C₄	C₂×D₄	1	1	yes	characteristic
234	C₂⁵×C₄	C₂×D₄	1	1	yes	characteristic
235	C₂⁵×C₄	C₂×D₄	1	1	yes	characteristic
236	C₂²×#127	C₂²⋊C₄	1	2	yes	—
237	C₂²×#127	C₂²⋊C₄	1	2	yes	—
238	C₂²×#127	C₂×D₄	1	2	yes	—
239	C₂²×#127	C₂×D₄	1	2	yes	—
240	C₂²×#121	C₂²⋊C₄	1	2	yes	—
241	C₂²×#121	C₂²⋊C₄	1	2	yes	—
242	C₂²×#121	C₂²⋊C₄	1	2	yes	—
243	C₂²×#121	C₂²⋊C₄	1	2	yes	—
244	C₂²×#121	C₂²⋊C₄	1	2	yes	—
245	C₂²×#121	C₂²⋊C₄	1	2	yes	—
246	C₂²×#121	C₂²⋊C₄	1	2	yes	—
247	C₂²×#121	C₂²⋊C₄	1	2	yes	—
248	C₂²×#121	C₂²×C₄	1	2	yes	—
249	C₂²×#121	C₂²×C₄	1	2	yes	—
250	C₂²×#121	C₂×D₄	1	2	yes	—
251	C₂²×#121	C₂×D₄	1	2	yes	—
252	C₂²×#121	C₂×D₄	1	2	yes	—
253	C₂²×#121	C₂×D₄	1	2	yes	—
254	C₂²×#121	C₂×D₄	1	2	yes	—
255	C₂²×#121	C₂×D₄	1	2	yes	—
256	C₂²×#120	C₂²⋊C₄	1	2	yes	—
257	C₂²×#120	C₂²⋊C₄	1	2	yes	—
258	C₂²×#120	C₂²⋊C₄	1	2	yes	—
259	C₂²×#120	C₂²⋊C₄	1	2	yes	—
260	C₂²×#120	C₂²⋊C₄	1	2	yes	—
261	C₂²×#120	C₂²⋊C₄	1	2	yes	—
262	C₂²×#120	C₂²⋊C₄	1	2	yes	—
263	C₂²×#120	C₂²⋊C₄	1	2	yes	—
264	C₂²×#120	C₂²×C₄	1	2	yes	—
265	C₂²×#120	C₂²×C₄	1	2	yes	—
266	C₂²×#120	C₂²×C₄	1	2	yes	—
267	C₂²×#120	C₂²×C₄	1	2	yes	—
268	C₂²×#120	C₂²×C₄	1	2	yes	—
269	C₂²×#120	C₂²×C₄	1	2	yes	complemented
270	C₂²×#120	C₂²×C₄	1	2	yes	complemented
271	C₂²×#120	C₂²×C₄	1	4	yes	complemented
272	C₂²×#120	C₂×D₄	1	2	yes	—
273	C₂²×#120	C₂×D₄	1	2	yes	—
274	C₂²×#120	C₂×D₄	1	2	yes	—
275	C₂²×#120	C₂×D₄	1	2	yes	—
276	C₂²×#120	C₂⁴	1	2	yes	—
277	C₂²×C₄×D₄	C₂²⋊C₄	1	2	yes	—
278	C₂²×C₄×D₄	C₂²⋊C₄	1	2	yes	—
279	C₂²×C₄×D₄	C₂²×C₄	1	2	yes	—
280	C₂²×C₄×D₄	C₂×D₄	1	2	yes	—
281	C₂²×C₄×D₄	C₂×D₄	1	2	yes	—
282	C₂²×C₄×D₄	C₂×D₄	1	2	yes	—
283	C₂²×C₄×D₄	C₂×D₄	1	2	yes	—
284	C₂²×C₄×D₄	C₂⁴	1	2	yes	—
285	C₂³×C₄⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
286	C₂³×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
287	C₂³×C₂²⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
288	C₂³×C₂²⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
289	C₂³×C₂²⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
290	C₂³×C₂²⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
291	C₂³×C₂²⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
292	C₂³×C₂²⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
293	C₂³×C₂²⋊C₄	C₂²×C₄	1	1	yes	characteristic
294	C₂³×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
295	C₂³×C₂²⋊C₄	C₂²×C₄	1	1	yes	characteristic, complemented
296	C₂³×C₂²⋊C₄	C₂²×C₄	1	1	yes	characteristic, complemented
297	C₂³×C₂²⋊C₄	C₂²×C₄	1	2	yes	complemented
298	C₂³×C₂²⋊C₄	C₂²×C₄	1	2	yes	complemented
299	C₂³×C₂²⋊C₄	C₂²×C₄	1	4	yes	complemented
300	C₂³×C₂²⋊C₄	C₂²×C₄	1	4	yes	complemented
301	C₂³×C₂²⋊C₄	C₂²×C₄	1	2	yes	complemented
302	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
303	C₂³×C₄²	C₂×D₄	1	1	yes	characteristic
304	C₂²×#100	C₂⁴	1	4	yes	—
305	C₂²×#100	C₂⁴	1	4	yes	—
306	C₂²×#99	C₂×D₄	1	4	yes	—
307	C₂²×#99	C₂×D₄	1	8	yes	—
308	C₂²×#99	C₂×D₄	1	8	yes	—
309	C₂²×#99	C₂×D₄	1	4	yes	—
310	C₂²×#99	C₂×D₄	1	4	yes	—
311	C₂²×#99	C₂×D₄	1	4	yes	—
312	C₂²×#99	C₂⁴	1	2	yes	—
313	C₂²×#99	C₂⁴	1	2	yes	—
314	C₂²×#99	C₂⁴	1	2	yes	—
315	C₂²×#99	C₂⁴	1	2	yes	—
316	C₂×#386	C₂²×C₄	1	2	yes	—
317	C₂×#386	C₂²×C₄	1	4	yes	—
318	C₂×#386	C₂²×C₄	1	2	yes	complemented
319	C₂×#386	C₂²×C₄	1	2	yes	complemented
320	C₂×#386	C₂²×C₄	1	4	yes	complemented
321	C₂×#386	C₂²×C₄	1	4	yes	complemented
322	C₂×#386	C₂²×C₄	1	4	yes	complemented
323	C₂×#386	C₂²×C₄	1	4	yes	complemented
324	C₂×#386	C₂²×C₄	1	4	yes	complemented
325	C₂×#386	C₂⁴	1	4	yes	—
326	C₂×#386	C₂⁴	1	2	yes	—
327	C₂×#385	C₂²×C₄	1	4	yes	complemented
328	C₂×#379	C₂²×C₄	1	2	yes	—
329	C₂×#379	C₂²×C₄	1	2	yes	—
330	C₂×#379	C₂²×C₄	1	2	yes	complemented
331	C₂×#379	C₂²×C₄	1	2	yes	complemented
332	C₂×#379	C₂²×C₄	1	4	yes	complemented
333	C₂×#379	C₂²×C₄	1	4	yes	complemented
334	C₂×#379	C₂²×C₄	1	4	yes	complemented
335	C₂²×#95	C₂²×C₄	1	4	yes	complemented
336	#1781	C₂×D₄	1	8	yes	—
337	#1781	C₂×D₄	1	8	yes	—
338	C₂²⋊#95	C₂²×C₄	1	4	yes	complemented
339	C₂²⋊#95	C₂²×C₄	1	4	yes	complemented
340	C₂²⋊#95	C₂²×C₄	1	4	yes	complemented
341	C₂²⋊#95	C₂²×C₄	1	4	yes	complemented
342	C₂⁶	C₂×C₂²⋊C₄	1	2	yes	—
343	C₂⁶	C₂×C₂²⋊C₄	1	1	yes	characteristic
344	C₂⁶	C₂×C₂²⋊C₄	1	1	yes	characteristic
345	C₂⁶	C₂×C₂²⋊C₄	1	1	yes	characteristic
346	C₂⁶	C₂×C₂²⋊C₄	1	1	yes	characteristic
347	C₂⁶	C₂×C₂²⋊C₄	1	1	yes	characteristic
348	C₂⁶	C₂×C₂²⋊C₄	1	1	yes	characteristic
349	C₂⁶	C₂×C₂²⋊C₄	1	1	yes	characteristic
350	C₂⁶	C₂×C₂²⋊C₄	1	1	yes	characteristic
351	C₂⁶	C₂×C₂²⋊C₄	1	2	yes	—
352	C₂⁶	C₂×C₂²⋊C₄	1	1	yes	characteristic
353	C₂⁶	C₂×C₂²⋊C₄	1	1	yes	characteristic
354	C₂⁶	C₄×D₄	1	4	yes	—
355	C₂⁶	C₄×D₄	1	4	yes	—
356	C₂⁶	#120	1	4	yes	—
357	C₂⁶	#123	1	4	yes	—
358	C₂⁶	C₂³×C₄	1	1	yes	characteristic
359	C₂⁶	C₂³×C₄	1	1	yes	characteristic
360	C₂⁶	C₂³×C₄	1	2	yes	—
361	C₂⁶	C₂³×C₄	1	1	yes	characteristic
362	C₂⁶	C₂³×C₄	1	2	yes	—
363	C₂⁶	C₂²×D₄	1	1	yes	characteristic
364	C₂⁶	C₂²×D₄	1	2	yes	—
365	C₂⁶	C₂²×D₄	1	1	yes	characteristic
366	C₂⁶	C₂²×D₄	1	1	yes	characteristic
367	C₂³×D₄	#99	1	1	yes	characteristic
368	C₂³×D₄	#99	1	2	yes	—
369	C₂³×D₄	#99	1	1	yes	characteristic
370	C₂³×D₄	#99	1	2	yes	—
371	C₂³×D₄	#99	1	1	yes	characteristic
372	C₂³×D₄	#99	1	1	yes	characteristic
373	C₂³×D₄	#99	1	8	yes	—
374	C₂³×D₄	C₂×C₂²⋊C₄	1	2	yes	—
375	C₂³×D₄	C₂×C₂²⋊C₄	1	2	yes	—
376	C₂³×D₄	C₂×C₂²⋊C₄	1	2	yes	—
377	C₂³×D₄	C₂×C₂²⋊C₄	1	2	yes	—
378	C₂³×D₄	C₂×C₂²⋊C₄	1	2	yes	—
379	C₂³×D₄	C₂×C₂²⋊C₄	1	2	yes	—
380	C₂³×D₄	C₂×C₂²⋊C₄	1	2	yes	—
381	C₂³×D₄	C₂×C₂²⋊C₄	1	2	yes	—
382	C₂³×D₄	C₂×C₂²⋊C₄	1	2	yes	—
383	C₂³×D₄	C₂×C₂²⋊C₄	1	2	yes	—
384	C₂³×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
385	C₂³×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
386	C₂³×D₄	C₂×C₂²⋊C₄	1	2	yes	—
387	C₂³×D₄	C₂×C₂²⋊C₄	1	2	yes	—
388	C₂³×D₄	C₂×C₂²⋊C₄	1	2	yes	—
389	C₂³×D₄	C₂×C₂²⋊C₄	1	2	yes	—
390	C₂³×D₄	C₂×C₂²⋊C₄	1	2	yes	—
391	C₂³×D₄	C₂×C₂²⋊C₄	1	2	yes	—
392	C₂³×D₄	C₂×C₂²⋊C₄	1	2	yes	—
393	C₂³×D₄	C₂×C₂²⋊C₄	1	2	yes	—
394	C₂³×D₄	C₂×C₂²⋊C₄	1	2	yes	—
395	C₂³×D₄	C₂×C₂²⋊C₄	1	2	yes	—
396	C₂³×D₄	C₂×C₂²⋊C₄	1	2	yes	—
397	C₂³×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
398	C₂³×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
399	C₂³×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
400	C₂³×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
401	C₂³×D₄	C₄×D₄	1	4	yes	—
402	C₂³×D₄	C₄×D₄	1	4	yes	—
403	C₂³×D₄	C₄×D₄	1	4	yes	—
404	C₂³×D₄	C₄×D₄	1	4	yes	—
405	C₂³×D₄	C₄×D₄	1	4	yes	—
406	C₂³×D₄	C₄×D₄	1	4	yes	—
407	C₂³×D₄	#120	1	4	yes	—
408	C₂³×D₄	#120	1	4	yes	—
409	C₂³×D₄	#120	1	4	yes	—
410	C₂³×D₄	#121	1	4	yes	—
411	C₂³×D₄	#121	1	4	yes	—
412	C₂³×D₄	#121	1	4	yes	—
413	C₂³×D₄	#121	1	4	yes	—
414	C₂³×D₄	#121	1	4	yes	—
415	C₂³×D₄	#121	1	4	yes	—
416	C₂³×D₄	#123	1	4	yes	—
417	C₂³×D₄	#123	1	4	yes	—
418	C₂³×D₄	#123	1	4	yes	—
419	C₂³×D₄	C₂³×C₄	1	2	yes	—
420	C₂³×D₄	C₂³×C₄	1	1	yes	characteristic
421	C₂³×D₄	C₂³×C₄	1	1	yes	characteristic
422	C₂³×D₄	C₂³×C₄	1	1	yes	characteristic
423	C₂³×D₄	C₂²×D₄	1	2	yes	—
424	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
425	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
426	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
427	C₂³×D₄	C₂²×D₄	1	2	yes	—
428	C₂³×D₄	C₂²×D₄	1	2	yes	—
429	C₂³×D₄	C₂²×D₄	1	2	yes	—
430	C₂³×D₄	C₂²×D₄	1	2	yes	—
431	C₂³×D₄	C₂²×D₄	1	2	yes	—
432	C₂³×D₄	C₂²×D₄	1	2	yes	—
433	C₂³×D₄	C₂²×D₄	1	2	yes	—
434	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
435	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
436	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
437	C₂³×D₄	C₂×#41	1	2	yes	—
438	C₂³×D₄	C₂×#41	1	2	yes	—
439	C₂³×D₄	C₂×#41	1	2	yes	—
440	C₂³×D₄	C₂×#41	1	2	yes	—
441	C₂³×D₄	C₂×#41	1	2	yes	—
442	C₂³×D₄	C₂×#41	1	2	yes	—
443	C₂³×D₄	C₂⁵	1	1	yes	characteristic
444	C₂⁴×C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
445	C₂⁴×C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
446	C₂⁴×C₄	C₂×C₂²⋊C₄	1	2	yes	—
447	C₂⁴×C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
448	C₂⁴×C₄	C₂×C₂²⋊C₄	1	2	yes	—
449	C₂⁴×C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
450	C₂⁴×C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
451	C₂⁴×C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
452	C₂⁴×C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
453	C₂⁴×C₄	C₂×C₂²⋊C₄	1	2	yes	—
454	C₂⁴×C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
455	C₂⁴×C₄	#121	1	4	yes	—
456	C₂⁴×C₄	#121	1	4	yes	—
457	C₂⁴×C₄	C₂³×C₄	1	2	yes	—
458	C₂⁴×C₄	C₂³×C₄	1	2	yes	—
459	C₂⁴×C₄	C₂³×C₄	1	4	yes	—
460	C₂⁴×C₄	C₂²×D₄	1	2	yes	—
461	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
462	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
463	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
464	C₂⁴×C₄	C₂²×D₄	1	2	yes	—
465	C₂²×C₄⋊C₄	C₂×C₂²⋊C₄	1	2	yes	—
466	C₂²×C₄⋊C₄	C₂×C₂²⋊C₄	1	2	yes	—
467	C₂²×C₄⋊C₄	C₂×C₂²⋊C₄	1	2	yes	—
468	C₂²×C₄⋊C₄	C₂²×D₄	1	2	yes	—
469	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	2	yes	—
470	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	2	yes	—
471	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	2	yes	—
472	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	2	yes	—
473	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	2	yes	—
474	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	2	yes	—
475	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	2	yes	—
476	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	2	yes	—
477	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	2	yes	—
478	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	2	yes	—
479	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	2	yes	—
480	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	2	yes	—
481	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	2	yes	—
482	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	2	yes	—
483	C₂²×C₂²⋊C₄	C₂³×C₄	1	2	yes	—
484	C₂²×C₂²⋊C₄	C₂³×C₄	1	2	yes	—
485	C₂²×C₂²⋊C₄	C₂³×C₄	1	2	yes	—
486	C₂²×C₂²⋊C₄	C₂³×C₄	1	4	yes	—
487	C₂²×C₂²⋊C₄	C₂²×D₄	1	2	yes	—
488	C₂²×C₄²	C₂×C₂²⋊C₄	1	2	yes	—
489	C₂²×C₄²	C₂²×D₄	1	2	yes	—
490	C₂×#99	C₂²×D₄	1	4	yes	—
491	C₂×#99	C₂²×D₄	1	4	yes	—
492	C₂×#99	C₂²×D₄	1	4	yes	—
493	C₂×#99	C₂²×D₄	1	4	yes	—
494	C₂×#99	H(5,𝔽₂)	1	8	yes	—
495	C₂⁵	#386	1	4	yes	—
496	C₂⁵	#386	1	4	yes	—
497	C₂⁵	#386	1	4	yes	—
498	C₂⁵	#386	1	4	yes	—
499	C₂⁵	#386	1	4	yes	—
500	C₂⁵	#386	1	4	yes	—
501	C₂⁵	#386	1	4	yes	—
502	C₂⁵	C₂×#99	1	1	yes	characteristic
503	C₂⁵	C₂×#99	1	1	yes	characteristic
504	C₂⁵	C₂×#99	1	1	yes	characteristic
505	C₂⁵	C₂×#99	1	2	yes	—
506	C₂⁵	C₂×#99	1	1	yes	characteristic
507	C₂⁵	C₂×#99	1	1	yes	characteristic
508	C₂⁵	C₂×#99	1	4	yes	—
509	C₂⁵	C₂×#99	1	1	yes	characteristic
510	C₂⁵	C₂×#99	1	4	yes	—
511	C₂⁵	C₂²×C₂²⋊C₄	1	2	yes	—
512	C₂⁵	C₂²×C₂²⋊C₄	1	1	yes	characteristic
513	C₂⁵	C₂²×C₂²⋊C₄	1	1	yes	characteristic
514	C₂⁵	C₂²×C₂²⋊C₄	1	2	yes	—
515	C₂⁵	C₂²×C₂²⋊C₄	1	2	yes	—
516	C₂⁵	C₂²×C₂²⋊C₄	1	1	yes	characteristic
517	C₂⁵	C₂²×C₂²⋊C₄	1	1	yes	characteristic
518	C₂⁵	C₂²×C₂²⋊C₄	1	1	yes	characteristic
519	C₂⁵	C₂²×C₂²⋊C₄	1	1	yes	characteristic
520	C₂⁵	C₂²×C₂²⋊C₄	1	1	yes	characteristic
521	C₂⁵	C₂²×C₂²⋊C₄	1	1	yes	characteristic
522	C₂⁵	C₂²×C₂²⋊C₄	1	1	yes	characteristic
523	C₂⁵	C₂×C₄×D₄	1	2	yes	—
524	C₂⁵	C₂×C₄×D₄	1	2	yes	—
525	C₂⁵	C₂×C₄×D₄	1	2	yes	—
526	C₂⁵	C₂×C₄×D₄	1	2	yes	—
527	C₂⁵	C₂×C₄×D₄	1	2	yes	—
528	C₂⁵	C₂×C₄×D₄	1	2	yes	—
529	C₂⁵	C₂×#120	1	2	yes	—
530	C₂⁵	C₂×#120	1	2	yes	—
531	C₂⁵	C₂×#120	1	2	yes	—
532	C₂⁵	C₂×#123	1	2	yes	—
533	C₂⁵	C₂×#123	1	2	yes	—
534	C₂⁵	C₂×#123	1	2	yes	—
535	C₂⁵	C₂⁴×C₄	1	1	yes	characteristic
536	C₂⁵	C₂³×D₄	1	1	yes	characteristic
537	C₂²×D₄	#386	1	4	yes	—
538	C₂²×D₄	#386	1	4	yes	—
539	C₂²×D₄	#386	1	4	yes	—
540	C₂²×D₄	#386	1	4	yes	—
541	C₂²×D₄	#386	1	4	yes	—
542	C₂²×D₄	#386	1	4	yes	—
543	C₂²×D₄	C₂×#99	1	2	yes	—
544	C₂²×D₄	C₂×#99	1	2	yes	—
545	C₂²×D₄	C₂×#99	1	2	yes	—
546	C₂²×D₄	C₂×#99	1	2	yes	—
547	C₂²×D₄	C₂×#99	1	2	yes	—
548	C₂²×D₄	C₂×#99	1	2	yes	—
549	C₂²×D₄	C₂×#99	1	2	yes	—
550	C₂²×D₄	C₂×#99	1	2	yes	—
551	C₂²×D₄	C₂×#99	1	8	yes	—
552	C₂²×D₄	C₂×#99	1	8	yes	—
553	C₂²×D₄	C₂×C₄×D₄	1	2	yes	—
554	C₂²×D₄	C₂×C₄×D₄	1	2	yes	—
555	C₂²×D₄	C₂×C₄×D₄	1	2	yes	—
556	C₂²×D₄	C₂×C₄×D₄	1	2	yes	—
557	C₂²×D₄	C₂×C₄×D₄	1	2	yes	—
558	C₂²×D₄	C₂×C₄×D₄	1	2	yes	—
559	C₂²×D₄	C₂×#120	1	2	yes	—
560	C₂²×D₄	C₂×#120	1	2	yes	—
561	C₂²×D₄	C₂×#120	1	2	yes	—
562	C₂²×D₄	C₂×#121	1	2	yes	—
563	C₂²×D₄	C₂×#121	1	2	yes	—
564	C₂²×D₄	C₂×#121	1	2	yes	—
565	C₂²×D₄	C₂×#121	1	2	yes	—
566	C₂²×D₄	C₂×#121	1	2	yes	—
567	C₂²×D₄	C₂×#121	1	2	yes	—
568	C₂²×D₄	C₂×#123	1	2	yes	—
569	C₂²×D₄	C₂×#123	1	2	yes	—
570	C₂²×D₄	C₂×#123	1	2	yes	—
571	C₂²×D₄	C₂³×D₄	1	1	yes	characteristic
572	C₂²×D₄	C₂³×D₄	1	1	yes	characteristic
573	C₂²×D₄	C₂²×#41	1	1	yes	characteristic
574	C₂²×D₄	C₂²×#41	1	1	yes	characteristic
575	C₂²×D₄	C₂×H(5,𝔽₂)	1	4	yes	—
576	C₂²×D₄	#585	1	4	yes	—
577	C₂³×C₄	#386	1	4	yes	—
578	C₂³×C₄	#386	1	4	yes	—
579	C₂³×C₄	#386	1	4	yes	—
580	C₂³×C₄	C₂×#99	1	1	yes	characteristic
581	C₂³×C₄	C₂×#99	1	2	yes	—
582	C₂³×C₄	C₂×#99	1	1	yes	characteristic
583	C₂³×C₄	C₂×#99	1	4	yes	—
584	C₂³×C₄	C₂²×C₂²⋊C₄	1	2	yes	—
585	C₂³×C₄	C₂²×C₂²⋊C₄	1	1	yes	characteristic
586	C₂³×C₄	C₂²×C₂²⋊C₄	1	1	yes	characteristic
587	C₂³×C₄	C₂²×C₂²⋊C₄	1	1	yes	characteristic
588	C₂³×C₄	C₂²×C₂²⋊C₄	1	2	yes	—
589	C₂³×C₄	C₂²×C₂²⋊C₄	1	2	yes	—
590	C₂³×C₄	C₂²×C₂²⋊C₄	1	2	yes	—
591	C₂³×C₄	C₂²×C₂²⋊C₄	1	2	yes	—
592	C₂³×C₄	C₂×#121	1	2	yes	—
593	C₂³×C₄	C₂×#121	1	2	yes	—
594	C₂³×C₄	C₂×#121	1	2	yes	—
595	C₂³×C₄	C₂×#121	1	2	yes	—
596	C₂³×C₄	C₂×#121	1	2	yes	—
597	C₂³×C₄	C₂×#121	1	2	yes	—
598	C₂³×C₄	C₂³×D₄	1	1	yes	characteristic
599	#99	#534	1	8	yes	complemented
600	C₂⁴	#1898	1	4	yes	—
601	C₂⁴	#1898	1	4	yes	—
602	C₂⁴	#1898	1	4	yes	—
603	C₂⁴	#1898	1	4	yes	—
604	C₂⁴	C₂×#386	1	2	yes	—
605	C₂⁴	C₂×#386	1	2	yes	—
606	C₂⁴	C₂×#386	1	2	yes	—
607	C₂⁴	C₂×#386	1	2	yes	—
608	C₂⁴	C₂×#386	1	2	yes	—
609	C₂⁴	C₂×#386	1	2	yes	—
610	C₂⁴	C₂×#386	1	2	yes	—
611	C₂⁴	C₂×#386	1	2	yes	—
612	C₂⁴	C₂×#386	1	2	yes	—
613	C₂⁴	C₂²×#99	1	2	yes	—
614	C₂⁴	C₂²×#99	1	2	yes	—
615	C₂⁴	C₂²×#99	1	1	yes	characteristic
616	C₂⁴	C₂²×#99	1	1	yes	characteristic
617	C₂⁴	C₂²×#99	1	1	yes	characteristic
618	C₂⁴	C₂²×#99	1	1	yes	characteristic
619	C₂⁴	C₂²×#99	1	2	yes	—
620	C₂⁴	C₂²×#99	1	2	yes	—
621	C₂⁴	C₂²×#99	1	1	yes	characteristic
622	C₂⁴	C₂²×#99	1	1	yes	characteristic
623	C₂⁴	C₂²×#99	1	4	yes	—
624	C₂⁴	C₂²×#99	1	2	yes	—
625	C₂⁴	#2883	1	4	yes	—
626	C₂⁴	C₂³×C₂²⋊C₄	1	1	yes	characteristic
627	C₂⁴	C₂²×C₄×D₄	1	1	yes	characteristic
628	C₂⁴	C₂²×C₄×D₄	1	1	yes	characteristic
629	C₂⁴	C₄×H(5,𝔽₂)	1	4	yes	—
630	C₂⁴	C₂²×#120	1	1	yes	characteristic
631	C₂⁴	C₂²×#123	1	1	yes	characteristic
632	C₂⁴	#3484	1	2	yes	—
633	C₂⁴	#3485	1	2	yes	—
634	C₂×D₄	#2121	1	8	yes	—
635	C₂×D₄	C₂×#534	1	2	yes	—
636	C₂×D₄	#3449	1	2	yes	—
637	C₂×D₄	#3459	1	4	yes	—
638	C₂×D₄	#3484	1	2	yes	—
639	C₂×D₄	#3485	1	2	yes	—
640	C₂×D₄	#3505	1	4	yes	—
641	C₂²×C₄	C₂×#386	1	2	yes	—
642	C₂²×C₄	C₂×#386	1	2	yes	—
643	C₂²×C₄	C₂×#386	1	2	yes	—
644	C₂²×C₄	C₂²×#99	1	2	yes	—
645	C₂²×C₄	C₂²×#99	1	2	yes	—
646	C₂²×C₄	C₂²×#99	1	4	yes	—
647	C₂²×C₄	C₂²×#121	1	1	yes	characteristic
648	C₂²×C₄	C₂²×#121	1	1	yes	characteristic
649	C₂²×C₄	#3496	1	4	yes	—
650	C₂³	C₂×#1898	1	2	yes	—
651	C₂³	C₂×#1898	1	2	yes	—
652	C₂³	C₂×#1898	1	2	yes	—
653	C₂³	C₂×#1898	1	2	yes	—
654	C₂³	C₂×#1898	1	2	yes	—
655	C₂³	C₂×#1898	1	2	yes	—
656	C₂³	#20984	1	4	yes	—
657	C₂³	C₂×#2121	1	4	yes	—
658	C₂³	C₂×#2121	1	4	yes	—
659	C₂³	#33348	1	4	yes	—
660	C₂³	C₂²×#386	1	1	yes	characteristic
661	C₂³	C₄×#534	1	2	yes	—
662	C₂³	#34256	1	2	yes	—
663	C₂³	#34264	1	2	yes	—
664	C₂³	#34980	1	1	yes	characteristic
665	C₂³	#34983	1	2	yes	—
666	C₂³	#35088	1	1	yes	characteristic
667	C₂³	C₂³×#99	1	1	yes	characteristic
668	C₂³	C₂³×#99	1	1	yes	characteristic
669	C₂³	C₂×#2883	1	2	yes	—
670	C₂×C₄	C₂×#2121	1	4	yes	—
671	C₂×C₄	#34984	1	2	yes	—
672	C₂×C₄	#35000	1	2	yes	—
673	C₂²	#494695	1	4	yes	—
674	C₂²	#494700	1	4	yes	—
675	C₂²	#516577	1	1	yes	characteristic
676	C₂²	C₂²×#1898	1	1	yes	characteristic
677	C₂²	C₂×#20984	1	1	yes	characteristic
678	C₂²	#6393523	1	2	yes	—
679	C₂²	#6393523	1	2	yes	—
680	C₂²	C₂²×#2121	1	2	yes	—
681	C₂²	C₂×#33348	1	2	yes	—
682	C₂	C₂×#494700	1	1	yes	characteristic
683	C₂	#72240280	1	4	yes	—
684	C₂	C₂×#494695	1	1	yes	characteristic
685	C₂	#72317564	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³	C₂³×#99
commutator	C₂⁵	C₂⁴×C₄
Frattini, cosocle	C₂³×D₄	C₂⁵
prime radical	#72225665	C₂
LCS	G ▷ C₂⁵ ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³ ◁ C₂⁴×D₄ ◁ C₂³×D₄² ◁ G
LECS	G ▷ C₂³×D₄ ▷ C₂² ▷ C₂ ▷ C₁

Complements

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

N	H ≅ G/N	type
1. #72317695	C₂	semidirect
2. #72317688	C₂	semidirect
3. #72317684	C₂	semidirect
4. #72317678	C₂	semidirect
5. #72317673	C₂	semidirect
6. #72317665	C₂	semidirect
7. #72317654	C₂	semidirect
8. C₂²×D₄×#99	C₂	semidirect
9. #72280530	C₂	semidirect
10. #72280502	C₂	semidirect
11. C₂²×#13086	C₂	semidirect
12. #72236709	C₂	semidirect
13. C₂×#496225	C₂	semidirect
17. C₂⁴×#99	C₂²	semidirect
18. C₂×#34980	C₄	semidirect
19. C₂²×#2403	C₄	semidirect
21. C₂³×AΣL(1,𝔽₁₆)	C₂²	semidirect
23. C₂×D₄×#99	C₂²	semidirect
24. C₂²×#1799	C₂²	semidirect
28. C₂²×#1781	C₂²	semidirect
29. C₂²×C₄×#99	C₂²	semidirect
30. #686258	C₄	semidirect
32. #663621	C₄	semidirect
34. #647656	C₄	semidirect
36. #636791	C₄	semidirect
37. #635984	C₄	semidirect
40. #556752	C₄	semidirect
41. #517411	C₄	semidirect
47. C₂×#13086	C₂²	semidirect
48. C₂×#13086	C₂²	semidirect
49. C₂×#13082	C₂²	semidirect
50. C₂×#12852	C₂²	semidirect
51. C₂×#12687	C₂²	semidirect
52. C₂×#12574	C₂²	semidirect
53. C₂²×#1390	C₂²	semidirect
54. #392249	C₂²	semidirect
55. #392113	C₂²	semidirect
57. #359583	C₂²	semidirect
58. #148688	C₂²	semidirect
59. #148572	C₂²	semidirect
60. #147995	C₂²	semidirect
61. #147555	C₂²	semidirect
62. #147500	C₂²	semidirect
63. #147314	C₂²	semidirect
64. #146566	C₂²	semidirect
65. #146566	C₂²	semidirect
66. #146566	C₂²	semidirect
67. #146566	C₂²	semidirect
68. #146566	C₂²	semidirect
69. #146566	C₂²	semidirect
70. #146564	C₂²	semidirect
71. #146459	C₂²	semidirect
73. C₂⁵×D₄	C₂×C₄	semidirect
92. C₂³×#120	C₂×C₄	semidirect
93. C₂³×#120	C₂×C₄	semidirect
94. C₂³×#120	C₂×C₄	semidirect
102. C₂³×#99	D₄	semidirect
110. C₂×#2849	C₂×C₄	semidirect
111. C₂×#2846	C₂×C₄	semidirect
112. C₂×#2405	C₂×C₄	semidirect
113. C₂×#2410	C₂×C₄	semidirect
114. C₂×#2403	C₂×C₄	semidirect
115. C₂×#2403	C₂×C₄	semidirect
116. C₂×#2403	C₂×C₄	semidirect
117. C₂×#2403	C₂×C₄	semidirect
121. C₂²×#392	C₂×C₄	semidirect
122. C₂×#2308	C₂×C₄	semidirect
124. C₂²×#386	C₂×C₄	semidirect
125. C₂²×#386	C₂×C₄	semidirect
126. C₂²×#386	C₂×C₄	semidirect
128. C₂²×#379	C₂×C₄	semidirect
129. C₂²×#379	C₂×C₄	semidirect
130. C₂²×#379	C₂×C₄	semidirect
141. C₂×#1781	D₄	semidirect
146. #14913	C₂×C₄	semidirect
147. #14913	C₂×C₄	semidirect
148. #14718	C₂×C₄	semidirect
149. #14718	C₂×C₄	semidirect
150. #14716	C₂×C₄	semidirect
151. #14716	C₂×C₄	semidirect
152. #14715	C₂×C₄	semidirect
153. #14715	C₂×C₄	semidirect
154. #14681	C₂×C₄	semidirect
155. #14679	C₂×C₄	semidirect
156. #14255	C₂×C₄	semidirect
157. #14134	C₂×C₄	semidirect
158. #14134	C₂×C₄	semidirect
159. #14016	C₂×C₄	semidirect
161. #13967	C₂×C₄	semidirect
163. #13869	C₂×C₄	semidirect
164. #13867	C₂×C₄	semidirect
165. #13867	C₂×C₄	semidirect
166. #13867	C₂×C₄	semidirect
167. #13867	C₂×C₄	semidirect
168. #13867	C₂×C₄	semidirect
169. #13867	C₂×C₄	semidirect
170. #13867	C₂×C₄	semidirect
185. C₂⁷	C₂²×C₄	semidirect
209. C₂⁴×D₄	C₂²×C₄	semidirect
210. C₂⁴×D₄	C₂²×C₄	semidirect
232. C₂⁵×C₄	C₂²×C₄	semidirect
269. C₂²×#120	C₂²×C₄	semidirect
270. C₂²×#120	C₂²×C₄	semidirect
271. C₂²×#120	C₂²×C₄	semidirect
295. C₂³×C₂²⋊C₄	C₂²×C₄	semidirect
296. C₂³×C₂²⋊C₄	C₂²×C₄	semidirect
297. C₂³×C₂²⋊C₄	C₂²×C₄	semidirect
298. C₂³×C₂²⋊C₄	C₂²×C₄	semidirect
299. C₂³×C₂²⋊C₄	C₂²×C₄	semidirect
300. C₂³×C₂²⋊C₄	C₂²×C₄	semidirect
301. C₂³×C₂²⋊C₄	C₂²×C₄	semidirect
318. C₂×#386	C₂²×C₄	semidirect
319. C₂×#386	C₂²×C₄	semidirect
320. C₂×#386	C₂²×C₄	semidirect
321. C₂×#386	C₂²×C₄	semidirect
322. C₂×#386	C₂²×C₄	semidirect
323. C₂×#386	C₂²×C₄	semidirect
324. C₂×#386	C₂²×C₄	semidirect
327. C₂×#385	C₂²×C₄	semidirect
330. C₂×#379	C₂²×C₄	semidirect
331. C₂×#379	C₂²×C₄	semidirect
332. C₂×#379	C₂²×C₄	semidirect
333. C₂×#379	C₂²×C₄	semidirect
334. C₂×#379	C₂²×C₄	semidirect
335. C₂²×#95	C₂²×C₄	semidirect
338. C₂²⋊#95	C₂²×C₄	semidirect
339. C₂²⋊#95	C₂²×C₄	semidirect
340. C₂²⋊#95	C₂²×C₄	semidirect
341. C₂²⋊#95	C₂²×C₄	semidirect
599. #99	#534	semidirect

Maximal subgroups

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

subgroup	index
#72317695	2
#72317688	2
#72317684	2
#72317678	2
#72317673	2
#72317665	2
#72317654	2
C₂²×D₄×#99	2
#72280530	2
#72280502	2
C₂²×#13086	2
#72236709	2
C₂×#496225	2
#72225665	2