Subgroups — #72317926

Order 2048.

At least 9817 conjugacy classes of subgroups; only the 1568 normal subgroups are shown.

The subgroup lattice has 694 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#72317824	C₂	1	8	yes	maximal, complemented
2	#72317801	C₂	1	4	yes	maximal, complemented
3	#72317649	C₂	1	4	yes	maximal, complemented
4	#72240134	C₂	1	4	yes	maximal, complemented
5	#72236670	C₂	1	2	yes	maximal, complemented
6	C₂×#496225	C₂	1	2	yes	maximal, complemented
7	C₂×#6385971	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#188087	C₂	1	1	yes	maximal, characteristic, complemented
9	#72232741	C₂	1	4	yes	maximal, complemented
10	#72225665	C₂	1	1	yes	maximal, characteristic
11	C₂³×D₄²	C₂²	1	1	yes	characteristic
12	C₂×#34980	C₄	1	1	yes	characteristic, complemented
13	C₂²×#2403	C₄	1	1	yes	characteristic, complemented
14	C₂²×#2403	C₂²	1	1	yes	characteristic
15	#6385971	C₂²	1	4	yes	—
16	#6385971	C₂²	1	4	yes	complemented
17	C₂×#21793	C₂²	1	2	yes	complemented
18	C₂×#21746	C₂²	1	2	yes	complemented
19	C₂²×#1783	C₂²	1	2	yes	—
20	C₂²×#1781	C₂²	1	2	yes	—
21	#4420586	C₄	1	4	yes	complemented
22	#4420586	C₂²	1	4	yes	—
23	#663621	C₄	1	2	yes	complemented
24	#663621	C₂²	1	2	yes	—
25	#647656	C₄	1	2	yes	complemented
26	#647656	C₂²	1	2	yes	—
27	#618316	C₄	1	2	yes	complemented
28	#618316	C₂²	1	2	yes	—
29	#617710	C₄	1	2	yes	complemented
30	#616960	C₂²	1	2	yes	—
31	#556752	C₄	1	1	yes	characteristic, complemented
32	#517411	C₄	1	1	yes	characteristic, complemented
33	#517411	C₂²	1	1	yes	characteristic
34	#496225	C₂²	1	8	yes	complemented
35	#496225	C₂²	1	8	yes	complemented
36	C₂×#12852	C₂²	1	4	yes	complemented
37	C₂×#12687	C₂²	1	4	yes	complemented
38	#188087	C₂²	1	4	yes	—
39	#188087	C₂²	1	4	yes	complemented
40	C₂×#8549	C₂²	1	2	yes	complemented
41	C₂×#8547	C₂²	1	2	yes	complemented
42	#139848	C₂²	1	16	yes	complemented
43	#139828	C₂²	1	16	yes	complemented
44	#139793	C₂²	1	16	yes	complemented
45	#139716	C₂²	1	16	yes	complemented
46	#128073	C₂²	1	8	yes	complemented
47	#128073	C₂²	1	8	yes	complemented
48	#128033	C₂²	1	8	yes	complemented
49	C₂⁵×D₄	C₂×C₄	1	1	yes	characteristic
50	C₂⁵×D₄	C₂×C₄	1	1	yes	characteristic, complemented
51	C₂⁵×D₄	D₄	1	1	yes	characteristic
52	C₂⁵×D₄	D₄	1	1	yes	characteristic
53	C₂⁵×D₄	C₂³	1	1	yes	characteristic
54	C₂²×D₄²	C₂×C₄	1	2	yes	—
55	C₂²×D₄²	C₂×C₄	1	2	yes	—
56	C₂²×D₄²	D₄	1	2	yes	—
57	C₂²×D₄²	D₄	1	2	yes	—
58	C₂²×D₄²	D₄	1	2	yes	—
59	C₂²×D₄²	D₄	1	2	yes	—
60	C₂²×D₄²	C₂³	1	2	yes	—
61	C₂²×D₄²	C₂³	1	2	yes	—
62	C₂²×#534	C₂×C₄	1	2	yes	complemented
63	C₂³×#127	C₂×C₄	1	1	yes	characteristic
64	C₂³×#121	C₂×C₄	1	1	yes	characteristic
65	C₂³×#121	D₄	1	1	yes	characteristic
66	C₂³×#121	D₄	1	1	yes	characteristic
67	C₂³×#121	C₂³	1	1	yes	characteristic
68	C₂³×#120	C₂×C₄	1	1	yes	characteristic
69	C₂³×#120	C₂×C₄	1	1	yes	characteristic, complemented
70	C₂³×#120	C₂×C₄	1	2	yes	complemented
71	C₂³×#120	D₄	1	1	yes	characteristic
72	C₂³×#120	D₄	1	1	yes	characteristic
73	C₂³×#120	C₂³	1	1	yes	characteristic
74	C₂³×#120	C₂³	1	1	yes	characteristic
75	C₂³×C₄×D₄	D₄	1	1	yes	characteristic
76	C₂³×C₄×D₄	D₄	1	1	yes	characteristic
77	C₂³×#99	D₄	1	4	yes	complemented
78	C₂×#2849	C₂×C₄	1	2	yes	complemented
79	C₂×#2846	C₂×C₄	1	2	yes	complemented
80	C₂×#2403	C₂×C₄	1	2	yes	complemented
81	C₂×#2403	C₂×C₄	1	2	yes	complemented
82	C₂×#2403	C₂×C₄	1	2	yes	complemented
83	C₂×#2403	C₂×C₄	1	2	yes	complemented
84	C₂×#2403	C₂×C₄	1	4	yes	complemented
85	C₂×#2403	C₂³	1	2	yes	—
86	C₂×#2403	C₂³	1	2	yes	—
87	C₂×#2613	C₂×C₄	1	4	yes	complemented
88	C₂×#2308	C₂×C₄	1	2	yes	complemented
89	C₂²×#386	C₂×C₄	1	1	yes	characteristic, complemented
90	C₂²×#386	C₂×C₄	1	2	yes	complemented
91	C₂²×#386	C₂³	1	1	yes	characteristic
92	C₂²×#379	C₂×C₄	1	1	yes	characteristic, complemented
93	C₂²×#379	C₂×C₄	1	1	yes	characteristic, complemented
94	C₂²×#379	C₂×C₄	1	1	yes	characteristic, complemented
95	#21793	C₂³	1	8	yes	—
96	#21746	C₂³	1	8	yes	—
97	C₂×#1783	C₂³	1	4	yes	—
98	C₂×#1783	C₂³	1	4	yes	—
99	C₂×#1783	C₂³	1	4	yes	—
100	C₂×#1781	D₄	1	4	yes	complemented
101	C₂×#1781	D₄	1	4	yes	complemented
102	C₂×#1781	D₄	1	4	yes	complemented
103	C₂×#1781	C₂³	1	4	yes	—
104	C₂×#1781	C₂³	1	4	yes	—
105	C₂×#1781	C₂³	1	4	yes	—
106	#15984	C₂×C₄	1	4	yes	complemented
107	#15984	C₂×C₄	1	4	yes	complemented
108	#15984	C₂×C₄	1	4	yes	complemented
109	#15984	C₂³	1	4	yes	—
110	#15948	C₂×C₄	1	4	yes	complemented
111	#15948	C₂³	1	4	yes	—
112	#15947	C₂×C₄	1	4	yes	complemented
113	#15947	C₂³	1	4	yes	—
114	#15261	C₂×C₄	1	4	yes	complemented
115	#15261	C₂×C₄	1	4	yes	complemented
116	#15258	C₂×C₄	1	4	yes	complemented
117	#15258	C₂×C₄	1	4	yes	complemented
118	#15257	C₂×C₄	1	4	yes	complemented
119	#15257	C₂×C₄	1	4	yes	complemented
120	#15257	C₂×C₄	1	4	yes	complemented
121	#15257	C₂³	1	4	yes	—
122	#14657	C₂×C₄	1	4	yes	complemented
123	#14341	C₂×C₄	1	2	yes	complemented
124	#14335	C₂×C₄	1	2	yes	complemented
125	#14335	C₂×C₄	1	2	yes	complemented
126	#14335	C₂×C₄	1	4	yes	complemented
127	#14335	C₂³	1	2	yes	—
128	#14134	C₂×C₄	1	2	yes	complemented
129	#14134	C₂×C₄	1	2	yes	complemented
130	#13867	C₂×C₄	1	2	yes	complemented
131	#13867	C₂×C₄	1	2	yes	complemented
132	#13867	C₂×C₄	1	2	yes	complemented
133	#13867	C₂×C₄	1	2	yes	complemented
134	#13867	C₂×C₄	1	2	yes	complemented
135	#13867	C₂×C₄	1	2	yes	complemented
136	#13867	C₂³	1	2	yes	—
137	#13867	C₂³	1	2	yes	—
138	#12852	C₂³	1	16	yes	complemented
139	#12687	C₂³	1	16	yes	complemented
140	#8549	C₂³	1	8	yes	—
141	#8547	C₂³	1	8	yes	—
142	#7304	C₂³	1	32	yes	complemented
143	C₂⁷	C₂²⋊C₄	1	1	yes	characteristic
144	C₂⁷	C₂²×C₄	1	1	yes	characteristic
145	C₂⁷	C₂²×C₄	1	1	yes	characteristic, complemented
146	C₂⁷	C₂×D₄	1	1	yes	characteristic
147	C₂⁷	C₂×D₄	1	1	yes	characteristic
148	C₂⁴×D₄	C₂²⋊C₄	1	2	yes	—
149	C₂⁴×D₄	C₂²⋊C₄	1	1	yes	characteristic
150	C₂⁴×D₄	C₂²⋊C₄	1	1	yes	characteristic
151	C₂⁴×D₄	C₂²⋊C₄	1	2	yes	—
152	C₂⁴×D₄	C₂²⋊C₄	1	1	yes	characteristic
153	C₂⁴×D₄	C₂²⋊C₄	1	1	yes	characteristic
154	C₂⁴×D₄	C₂²⋊C₄	1	2	yes	—
155	C₂⁴×D₄	C₂²⋊C₄	1	1	yes	characteristic
156	C₂⁴×D₄	C₂²⋊C₄	1	2	yes	—
157	C₂⁴×D₄	C₂²⋊C₄	1	1	yes	characteristic
158	C₂⁴×D₄	C₂²⋊C₄	1	1	yes	characteristic
159	C₂⁴×D₄	C₂²⋊C₄	1	2	yes	—
160	C₂⁴×D₄	C₂²⋊C₄	1	2	yes	—
161	C₂⁴×D₄	C₂²⋊C₄	1	1	yes	characteristic
162	C₂⁴×D₄	C₂²×C₄	1	2	yes	—
163	C₂⁴×D₄	C₂²×C₄	1	1	yes	characteristic
164	C₂⁴×D₄	C₂²×C₄	1	1	yes	characteristic
165	C₂⁴×D₄	C₂²×C₄	1	2	yes	—
166	C₂⁴×D₄	C₂²×C₄	1	1	yes	characteristic
167	C₂⁴×D₄	C₂²×C₄	1	1	yes	characteristic
168	C₂⁴×D₄	C₂²×C₄	1	1	yes	characteristic
169	C₂⁴×D₄	C₂²×C₄	1	1	yes	characteristic
170	C₂⁴×D₄	C₂²×C₄	1	2	yes	—
171	C₂⁴×D₄	C₂²×C₄	1	2	yes	complemented
172	C₂⁴×D₄	C₂×D₄	1	2	yes	—
173	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
174	C₂⁴×D₄	C₂×D₄	1	2	yes	—
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	2	yes	—
179	C₂⁴×D₄	C₂×D₄	1	2	yes	—
180	C₂⁴×D₄	C₂×D₄	1	2	yes	—
181	C₂⁴×D₄	C₂×D₄	1	2	yes	—
182	C₂⁴×D₄	C₂×D₄	1	2	yes	—
183	C₂⁴×D₄	C₂×D₄	1	2	yes	—
184	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
185	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
186	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
187	C₂⁴×D₄	#41	1	2	yes	—
188	C₂⁴×D₄	#41	1	2	yes	—
189	C₂⁴×D₄	#41	1	2	yes	—
190	C₂⁴×D₄	#41	1	2	yes	—
191	C₂⁴×D₄	C₂⁴	1	1	yes	characteristic
192	C₂⁴×D₄	C₂⁴	1	1	yes	characteristic
193	C₂⁴×D₄	C₂⁴	1	1	yes	characteristic
194	C₂⁵×C₄	C₂²⋊C₄	1	1	yes	characteristic
195	C₂⁵×C₄	C₂²⋊C₄	1	1	yes	characteristic
196	C₂⁵×C₄	C₂²×C₄	1	1	yes	characteristic, complemented
197	C₂⁵×C₄	C₂×D₄	1	1	yes	characteristic
198	C₂⁵×C₄	C₂×D₄	1	1	yes	characteristic
199	C₂²×#127	C₂²⋊C₄	1	2	yes	—
200	C₂²×#127	C₂²⋊C₄	1	2	yes	—
201	C₂²×#127	C₂²×C₄	1	2	yes	—
202	C₂²×#127	C₂²×C₄	1	2	yes	—
203	C₂²×#123	C₂²×C₄	1	4	yes	complemented
204	C₂²×#121	C₂²⋊C₄	1	2	yes	—
205	C₂²×#121	C₂²⋊C₄	1	2	yes	—
206	C₂²×#121	C₂²⋊C₄	1	2	yes	—
207	C₂²×#121	C₂²⋊C₄	1	2	yes	—
208	C₂²×#121	C₂²⋊C₄	1	2	yes	—
209	C₂²×#121	C₂²⋊C₄	1	2	yes	—
210	C₂²×#121	C₂²×C₄	1	2	yes	—
211	C₂²×#121	C₂²×C₄	1	2	yes	—
212	C₂²×#121	C₂²×C₄	1	2	yes	—
213	C₂²×#121	C₂×D₄	1	2	yes	—
214	C₂²×#121	C₂×D₄	1	2	yes	—
215	C₂²×#121	C₂×D₄	1	2	yes	—
216	C₂²×#121	C₂×D₄	1	2	yes	—
217	C₂²×#121	C₂×D₄	1	2	yes	—
218	C₂²×#121	C₂×D₄	1	2	yes	—
219	C₂²×#121	C₂⁴	1	2	yes	—
220	C₂²×#120	C₂²⋊C₄	1	2	yes	—
221	C₂²×#120	C₂²⋊C₄	1	2	yes	—
222	C₂²×#120	C₂²⋊C₄	1	2	yes	—
223	C₂²×#120	C₂²⋊C₄	1	2	yes	—
224	C₂²×#120	C₂²⋊C₄	1	2	yes	—
225	C₂²×#120	C₂²⋊C₄	1	2	yes	—
226	C₂²×#120	C₂²×C₄	1	2	yes	—
227	C₂²×#120	C₂²×C₄	1	2	yes	—
228	C₂²×#120	C₂²×C₄	1	2	yes	—
229	C₂²×#120	C₂²×C₄	1	2	yes	—
230	C₂²×#120	C₂²×C₄	1	2	yes	complemented
231	C₂²×#120	C₂²×C₄	1	2	yes	complemented
232	C₂²×#120	C₂²×C₄	1	4	yes	complemented
233	C₂²×#120	C₂²×C₄	1	4	yes	complemented
234	C₂²×#120	C₂²×C₄	1	4	yes	complemented
235	C₂²×#120	C₂×D₄	1	2	yes	—
236	C₂²×#120	C₂×D₄	1	2	yes	—
237	C₂²×#120	C₂×D₄	1	2	yes	—
238	C₂²×#120	C₂×D₄	1	2	yes	—
239	C₂²×#120	C₂×D₄	1	2	yes	—
240	C₂²×#120	C₂×D₄	1	2	yes	—
241	C₂²×#120	C₂⁴	1	2	yes	—
242	C₂²×#120	C₂⁴	1	2	yes	—
243	C₂²×C₄×D₄	C₂²⋊C₄	1	2	yes	—
244	C₂²×C₄×D₄	C₂²⋊C₄	1	2	yes	—
245	C₂²×C₄×D₄	C₂²⋊C₄	1	2	yes	—
246	C₂²×C₄×D₄	C₂²⋊C₄	1	2	yes	—
247	C₂²×C₄×D₄	C₂×D₄	1	2	yes	—
248	C₂²×C₄×D₄	C₂×D₄	1	2	yes	—
249	C₂²×C₄×D₄	C₂×D₄	1	2	yes	—
250	C₂²×C₄×D₄	C₂×D₄	1	2	yes	—
251	C₂³×C₄⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
252	C₂³×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
253	C₂³×C₂²⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
254	C₂³×C₂²⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
255	C₂³×C₂²⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
256	C₂³×C₂²⋊C₄	C₂²×C₄	1	1	yes	characteristic
257	C₂³×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
258	C₂³×C₂²⋊C₄	C₂²×C₄	1	1	yes	characteristic, complemented
259	C₂³×C₂²⋊C₄	C₂²×C₄	1	1	yes	characteristic, complemented
260	C₂³×C₂²⋊C₄	C₂²×C₄	1	2	yes	complemented
261	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
262	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
263	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
264	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
265	C₂³×C₄²	C₂²⋊C₄	1	1	yes	characteristic
266	C₂²×#99	C₂×D₄	1	8	yes	—
267	C₂²×#99	C₂×D₄	1	8	yes	complemented
268	C₂²×#99	C₂×D₄	1	8	yes	complemented
269	C₂×#386	C₂²×C₄	1	2	yes	—
270	C₂×#386	C₂²×C₄	1	2	yes	complemented
271	C₂×#386	C₂²×C₄	1	2	yes	complemented
272	C₂×#386	C₂²×C₄	1	4	yes	complemented
273	C₂×#386	C₂²×C₄	1	4	yes	complemented
274	C₂×#386	C₂⁴	1	2	yes	—
275	C₂×#381	C₂²×C₄	1	4	yes	complemented
276	C₂×#379	C₂²×C₄	1	2	yes	—
277	C₂×#379	C₂²×C₄	1	2	yes	—
278	C₂×#379	C₂²×C₄	1	2	yes	complemented
279	C₂×#379	C₂²×C₄	1	2	yes	complemented
280	C₂×#379	C₂²×C₄	1	4	yes	complemented
281	C₂×#379	C₂²×C₄	1	2	yes	complemented
282	C₂×#379	C₂²×C₄	1	2	yes	complemented
283	#1783	C₂⁴	1	8	yes	—
284	#1781	C₂×D₄	1	8	yes	—
285	#1781	C₂×D₄	1	8	yes	complemented
286	#1781	C₂×D₄	1	8	yes	complemented
287	#1781	C₂⁴	1	8	yes	—
288	#1440	C₂²×C₄	1	4	yes	complemented
289	#1440	C₂²×C₄	1	4	yes	complemented
290	#1438	C₂²×C₄	1	4	yes	—
291	#1438	C₂²×C₄	1	4	yes	complemented
292	#1438	C₂²×C₄	1	4	yes	complemented
293	#1438	C₂²×C₄	1	4	yes	complemented
294	#1438	C₂²×C₄	1	4	yes	complemented
295	#1438	C₂²×C₄	1	4	yes	complemented
296	#1438	C₂²×C₄	1	4	yes	complemented
297	#1438	C₂²×C₄	1	4	yes	complemented
298	#1438	C₂²×C₄	1	4	yes	complemented
299	#1438	C₂⁴	1	4	yes	—
300	C₂⁶	C₂×C₂²⋊C₄	1	2	yes	—
301	C₂⁶	C₂×C₂²⋊C₄	1	1	yes	characteristic
302	C₂⁶	C₂×C₂²⋊C₄	1	1	yes	characteristic
303	C₂⁶	C₂×C₂²⋊C₄	1	1	yes	characteristic
304	C₂⁶	C₂×C₂²⋊C₄	1	2	yes	—
305	C₂⁶	C₂×C₂²⋊C₄	1	1	yes	characteristic
306	C₂⁶	C₂×C₂²⋊C₄	1	1	yes	characteristic
307	C₂⁶	C₂×C₂²⋊C₄	1	1	yes	characteristic
308	C₂⁶	C₂×C₂²⋊C₄	1	1	yes	characteristic
309	C₂⁶	C₂×C₂²⋊C₄	1	1	yes	characteristic
310	C₂⁶	C₂×C₂²⋊C₄	1	2	yes	—
311	C₂⁶	C₂×C₂²⋊C₄	1	1	yes	characteristic
312	C₂⁶	C₂×C₂²⋊C₄	1	1	yes	characteristic
313	C₂⁶	C₄×D₄	1	2	yes	—
314	C₂⁶	C₄×D₄	1	2	yes	—
315	C₂⁶	C₄×D₄	1	2	yes	—
316	C₂⁶	C₄×D₄	1	2	yes	—
317	C₂⁶	#120	1	2	yes	—
318	C₂⁶	#120	1	2	yes	—
319	C₂⁶	#123	1	2	yes	—
320	C₂⁶	#123	1	2	yes	—
321	C₂⁶	C₂³×C₄	1	1	yes	characteristic
322	C₂⁶	C₂³×C₄	1	1	yes	characteristic
323	C₂⁶	C₂³×C₄	1	1	yes	characteristic
324	C₂⁶	C₂³×C₄	1	2	yes	—
325	C₂⁶	C₂²×D₄	1	2	yes	—
326	C₂⁶	C₂²×D₄	1	1	yes	characteristic
327	C₂⁶	C₂²×D₄	1	1	yes	characteristic
328	C₂⁶	C₂²×D₄	1	1	yes	characteristic
329	C₂³×D₄	#99	1	1	yes	characteristic
330	C₂³×D₄	#99	1	2	yes	—
331	C₂³×D₄	#99	1	1	yes	characteristic
332	C₂³×D₄	#99	1	2	yes	—
333	C₂³×D₄	#99	1	1	yes	characteristic
334	C₂³×D₄	#99	1	1	yes	characteristic
335	C₂³×D₄	#99	1	4	yes	—
336	C₂³×D₄	#99	1	4	yes	—
337	C₂³×D₄	C₂×C₂²⋊C₄	1	2	yes	—
338	C₂³×D₄	C₂×C₂²⋊C₄	1	2	yes	—
339	C₂³×D₄	C₂×C₂²⋊C₄	1	2	yes	—
340	C₂³×D₄	C₂×C₂²⋊C₄	1	2	yes	—
341	C₂³×D₄	C₂×C₂²⋊C₄	1	2	yes	—
342	C₂³×D₄	C₂×C₂²⋊C₄	1	2	yes	—
343	C₂³×D₄	C₂×C₂²⋊C₄	1	2	yes	—
344	C₂³×D₄	C₂×C₂²⋊C₄	1	2	yes	—
345	C₂³×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
346	C₂³×D₄	C₂×C₂²⋊C₄	1	2	yes	—
347	C₂³×D₄	C₂×C₂²⋊C₄	1	2	yes	—
348	C₂³×D₄	C₂×C₂²⋊C₄	1	2	yes	—
349	C₂³×D₄	C₂×C₂²⋊C₄	1	2	yes	—
350	C₂³×D₄	C₂×C₂²⋊C₄	1	2	yes	—
351	C₂³×D₄	C₂×C₂²⋊C₄	1	2	yes	—
352	C₂³×D₄	C₂×C₂²⋊C₄	1	2	yes	—
353	C₂³×D₄	C₂×C₂²⋊C₄	1	2	yes	—
354	C₂³×D₄	C₂×C₂²⋊C₄	1	2	yes	—
355	C₂³×D₄	C₂×C₂²⋊C₄	1	2	yes	—
356	C₂³×D₄	C₂×C₂²⋊C₄	1	2	yes	—
357	C₂³×D₄	C₂×C₂²⋊C₄	1	2	yes	—
358	C₂³×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
359	C₂³×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
360	C₂³×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
361	C₂³×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
362	C₂³×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
363	C₂³×D₄	C₄×D₄	1	2	yes	—
364	C₂³×D₄	C₄×D₄	1	2	yes	—
365	C₂³×D₄	C₄×D₄	1	2	yes	—
366	C₂³×D₄	C₄×D₄	1	2	yes	—
367	C₂³×D₄	C₄×D₄	1	2	yes	—
368	C₂³×D₄	C₄×D₄	1	2	yes	—
369	C₂³×D₄	C₄×D₄	1	2	yes	—
370	C₂³×D₄	C₄×D₄	1	2	yes	—
371	C₂³×D₄	C₄×D₄	1	2	yes	—
372	C₂³×D₄	C₄×D₄	1	2	yes	—
373	C₂³×D₄	C₄×D₄	1	2	yes	—
374	C₂³×D₄	C₄×D₄	1	2	yes	—
375	C₂³×D₄	#120	1	1	yes	characteristic
376	C₂³×D₄	#120	1	1	yes	characteristic
377	C₂³×D₄	#120	1	1	yes	characteristic
378	C₂³×D₄	#120	1	2	yes	—
379	C₂³×D₄	#120	1	1	yes	characteristic
380	C₂³×D₄	#120	1	2	yes	—
381	C₂³×D₄	#120	1	2	yes	—
382	C₂³×D₄	#120	1	2	yes	—
383	C₂³×D₄	#121	1	2	yes	—
384	C₂³×D₄	#121	1	2	yes	—
385	C₂³×D₄	#121	1	2	yes	—
386	C₂³×D₄	#121	1	2	yes	—
387	C₂³×D₄	#121	1	2	yes	—
388	C₂³×D₄	#121	1	2	yes	—
389	C₂³×D₄	#121	1	2	yes	—
390	C₂³×D₄	#121	1	2	yes	—
391	C₂³×D₄	#121	1	2	yes	—
392	C₂³×D₄	#121	1	2	yes	—
393	C₂³×D₄	#121	1	2	yes	—
394	C₂³×D₄	#121	1	2	yes	—
395	C₂³×D₄	#123	1	1	yes	characteristic
396	C₂³×D₄	#123	1	1	yes	characteristic
397	C₂³×D₄	#123	1	1	yes	characteristic
398	C₂³×D₄	#123	1	1	yes	characteristic
399	C₂³×D₄	#123	1	2	yes	—
400	C₂³×D₄	#123	1	2	yes	—
401	C₂³×D₄	#123	1	2	yes	—
402	C₂³×D₄	#123	1	2	yes	—
403	C₂³×D₄	C₂³×C₄	1	2	yes	—
404	C₂³×D₄	C₂³×C₄	1	2	yes	—
405	C₂³×D₄	C₂³×C₄	1	2	yes	—
406	C₂³×D₄	C₂³×C₄	1	1	yes	characteristic
407	C₂³×D₄	C₂³×C₄	1	1	yes	characteristic
408	C₂³×D₄	C₂³×C₄	1	1	yes	characteristic
409	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
410	C₂³×D₄	C₂²×D₄	1	2	yes	—
411	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
412	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
413	C₂³×D₄	C₂²×D₄	1	2	yes	—
414	C₂³×D₄	C₂²×D₄	1	2	yes	—
415	C₂³×D₄	C₂²×D₄	1	2	yes	—
416	C₂³×D₄	C₂²×D₄	1	2	yes	—
417	C₂³×D₄	C₂²×D₄	1	2	yes	—
418	C₂³×D₄	C₂²×D₄	1	2	yes	—
419	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
420	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
421	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
422	C₂³×D₄	C₂×#41	1	2	yes	—
423	C₂³×D₄	C₂×#41	1	2	yes	—
424	C₂³×D₄	C₂×#41	1	2	yes	—
425	C₂³×D₄	C₂×#41	1	2	yes	—
426	C₂³×D₄	C₂×#41	1	2	yes	—
427	C₂³×D₄	C₂×#41	1	2	yes	—
428	C₂³×D₄	C₂⁵	1	1	yes	characteristic
429	C₂⁴×C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
430	C₂⁴×C₄	C₂×C₂²⋊C₄	1	2	yes	—
431	C₂⁴×C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
432	C₂⁴×C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
433	C₂⁴×C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
434	C₂⁴×C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
435	C₂⁴×C₄	C₂×C₂²⋊C₄	1	2	yes	—
436	C₂⁴×C₄	C₂×C₂²⋊C₄	1	2	yes	—
437	C₂⁴×C₄	C₂×C₂²⋊C₄	1	2	yes	—
438	C₂⁴×C₄	C₂×C₂²⋊C₄	1	2	yes	—
439	C₂⁴×C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
440	C₂⁴×C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
441	C₂⁴×C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
442	C₂⁴×C₄	#121	1	2	yes	—
443	C₂⁴×C₄	#121	1	2	yes	—
444	C₂⁴×C₄	#121	1	2	yes	—
445	C₂⁴×C₄	#121	1	2	yes	—
446	C₂⁴×C₄	C₂³×C₄	1	2	yes	—
447	C₂⁴×C₄	C₂²×D₄	1	2	yes	—
448	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
449	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
450	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
451	C₂²×C₄⋊C₄	C₂×C₂²⋊C₄	1	2	yes	—
452	C₂²×C₄⋊C₄	C₂×C₂²⋊C₄	1	2	yes	—
453	C₂²×C₄⋊C₄	C₂×C₂²⋊C₄	1	2	yes	—
454	C₂²×C₄⋊C₄	C₂²×D₄	1	2	yes	—
455	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	2	yes	—
456	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	2	yes	—
457	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	2	yes	—
458	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	2	yes	—
459	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	2	yes	—
460	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	2	yes	—
461	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	2	yes	—
462	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	2	yes	—
463	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	2	yes	—
464	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	2	yes	—
465	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	2	yes	—
466	C₂²×C₂²⋊C₄	C₂³×C₄	1	2	yes	—
467	C₂²×C₂²⋊C₄	C₂³×C₄	1	2	yes	—
468	C₂²×C₂²⋊C₄	C₂³×C₄	1	2	yes	—
469	C₂²×C₂²⋊C₄	C₂³×C₄	1	4	yes	—
470	C₂²×C₂²⋊C₄	C₂³×C₄	1	4	yes	—
471	C₂²×C₂²⋊C₄	C₂²×D₄	1	2	yes	—
472	C₂²×C₂²⋊C₄	C₂²×D₄	1	2	yes	—
473	C₂²×C₂²⋊C₄	C₂²×D₄	1	2	yes	—
474	C₂²×C₂²⋊C₄	C₂²×D₄	1	2	yes	—
475	C₂²×C₄²	C₂×C₂²⋊C₄	1	2	yes	—
476	C₂²×C₄²	C₂×C₂²⋊C₄	1	2	yes	—
477	C₂×#99	C₂²×D₄	1	16	yes	—
478	C₂⁵	#386	1	1	yes	characteristic
479	C₂⁵	#386	1	1	yes	characteristic
480	C₂⁵	#386	1	1	yes	characteristic
481	C₂⁵	#386	1	1	yes	characteristic
482	C₂⁵	#386	1	2	yes	—
483	C₂⁵	#386	1	2	yes	—
484	C₂⁵	#386	1	2	yes	—
485	C₂⁵	#386	1	2	yes	—
486	C₂⁵	#386	1	2	yes	—
487	C₂⁵	#386	1	2	yes	—
488	C₂⁵	#386	1	2	yes	—
489	C₂⁵	#386	1	2	yes	—
490	C₂⁵	#386	1	2	yes	—
491	C₂⁵	#386	1	2	yes	—
492	C₂⁵	#386	1	2	yes	—
493	C₂⁵	#386	1	2	yes	—
494	C₂⁵	C₂×#99	1	1	yes	characteristic
495	C₂⁵	C₂×#99	1	2	yes	—
496	C₂⁵	C₂×#99	1	2	yes	—
497	C₂⁵	C₂×#99	1	1	yes	characteristic
498	C₂⁵	C₂×#99	1	1	yes	characteristic
499	C₂⁵	C₂×#99	1	2	yes	—
500	C₂⁵	C₂×#99	1	1	yes	characteristic
501	C₂⁵	C₂×#99	1	2	yes	—
502	C₂⁵	C₂×#99	1	2	yes	—
503	C₂⁵	C₂×#99	1	1	yes	characteristic
504	C₂⁵	C₂×#99	1	1	yes	characteristic
505	C₂⁵	C₂²×C₂²⋊C₄	1	1	yes	characteristic
506	C₂⁵	C₂²×C₂²⋊C₄	1	2	yes	—
507	C₂⁵	C₂²×C₂²⋊C₄	1	1	yes	characteristic
508	C₂⁵	C₂²×C₂²⋊C₄	1	1	yes	characteristic
509	C₂⁵	C₂²×C₂²⋊C₄	1	1	yes	characteristic
510	C₂⁵	C₂²×C₂²⋊C₄	1	2	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	1	yes	characteristic
515	C₂⁵	C₂²×C₂²⋊C₄	1	1	yes	characteristic
516	C₂⁵	C₂²×C₂²⋊C₄	1	1	yes	characteristic
517	C₂⁵	C₂×C₄×D₄	1	2	yes	—
518	C₂⁵	C₂×C₄×D₄	1	2	yes	—
519	C₂⁵	C₂×C₄×D₄	1	2	yes	—
520	C₂⁵	C₂×C₄×D₄	1	2	yes	—
521	C₂⁵	C₂×C₄×D₄	1	2	yes	—
522	C₂⁵	C₂×C₄×D₄	1	2	yes	—
523	C₂⁵	C₂×#120	1	1	yes	characteristic
524	C₂⁵	C₂×#120	1	2	yes	—
525	C₂⁵	C₂×#120	1	1	yes	characteristic
526	C₂⁵	C₂×#120	1	2	yes	—
527	C₂⁵	C₂×#123	1	1	yes	characteristic
528	C₂⁵	C₂×#123	1	1	yes	characteristic
529	C₂⁵	C₂×#123	1	2	yes	—
530	C₂⁵	C₂×#123	1	2	yes	—
531	C₂⁵	C₂⁴×C₄	1	1	yes	characteristic
532	C₂⁵	C₂³×D₄	1	1	yes	characteristic
533	C₂²×D₄	#386	1	1	yes	characteristic
534	C₂²×D₄	#386	1	1	yes	characteristic
535	C₂²×D₄	#386	1	1	yes	characteristic
536	C₂²×D₄	#386	1	1	yes	characteristic
537	C₂²×D₄	#386	1	1	yes	characteristic
538	C₂²×D₄	#386	1	1	yes	characteristic
539	C₂²×D₄	#386	1	2	yes	—
540	C₂²×D₄	#386	1	2	yes	—
541	C₂²×D₄	#386	1	2	yes	—
542	C₂²×D₄	#386	1	2	yes	—
543	C₂²×D₄	#386	1	1	yes	characteristic
544	C₂²×D₄	#386	1	2	yes	—
545	C₂²×D₄	#386	1	2	yes	—
546	C₂²×D₄	#386	1	2	yes	—
547	C₂²×D₄	#386	1	2	yes	—
548	C₂²×D₄	#386	1	1	yes	characteristic
549	C₂²×D₄	C₂×#99	1	2	yes	—
550	C₂²×D₄	C₂×#99	1	2	yes	—
551	C₂²×D₄	C₂×#99	1	2	yes	—
552	C₂²×D₄	C₂×#99	1	2	yes	—
553	C₂²×D₄	C₂×#99	1	2	yes	—
554	C₂²×D₄	C₂×#99	1	2	yes	—
555	C₂²×D₄	C₂×#99	1	2	yes	—
556	C₂²×D₄	C₂×#99	1	2	yes	—
557	C₂²×D₄	C₂×#99	1	8	yes	—
558	C₂²×D₄	C₂×#99	1	8	yes	—
559	C₂²×D₄	C₂×C₄×D₄	1	2	yes	—
560	C₂²×D₄	C₂×C₄×D₄	1	2	yes	—
561	C₂²×D₄	C₂×C₄×D₄	1	2	yes	—
562	C₂²×D₄	C₂×C₄×D₄	1	2	yes	—
563	C₂²×D₄	C₂×C₄×D₄	1	2	yes	—
564	C₂²×D₄	C₂×C₄×D₄	1	2	yes	—
565	C₂²×D₄	C₂×#120	1	1	yes	characteristic
566	C₂²×D₄	C₂×#120	1	1	yes	characteristic
567	C₂²×D₄	C₂×#120	1	1	yes	characteristic
568	C₂²×D₄	C₂×#120	1	2	yes	—
569	C₂²×D₄	C₂×#120	1	1	yes	characteristic
570	C₂²×D₄	C₂×#121	1	2	yes	—
571	C₂²×D₄	C₂×#121	1	2	yes	—
572	C₂²×D₄	C₂×#121	1	2	yes	—
573	C₂²×D₄	C₂×#121	1	2	yes	—
574	C₂²×D₄	C₂×#121	1	2	yes	—
575	C₂²×D₄	C₂×#121	1	2	yes	—
576	C₂²×D₄	C₂×#123	1	1	yes	characteristic
577	C₂²×D₄	C₂×#123	1	1	yes	characteristic
578	C₂²×D₄	C₂×#123	1	1	yes	characteristic
579	C₂²×D₄	C₂×#123	1	1	yes	characteristic
580	C₂²×D₄	C₂×#123	1	2	yes	—
581	C₂²×D₄	C₂³×D₄	1	2	yes	—
582	C₂²×D₄	C₂²×#41	1	2	yes	—
583	C₂³×C₄	#386	1	1	yes	characteristic
584	C₂³×C₄	#386	1	2	yes	—
585	C₂³×C₄	#386	1	1	yes	characteristic
586	C₂³×C₄	#386	1	1	yes	characteristic
587	C₂³×C₄	#386	1	2	yes	—
588	C₂³×C₄	#386	1	2	yes	—
589	C₂³×C₄	#386	1	1	yes	characteristic
590	C₂³×C₄	#386	1	2	yes	—
591	C₂³×C₄	C₂×#99	1	1	yes	characteristic
592	C₂³×C₄	C₂×#99	1	2	yes	—
593	C₂³×C₄	C₂×#99	1	1	yes	characteristic
594	C₂³×C₄	C₂×#99	1	2	yes	—
595	C₂³×C₄	C₂×#99	1	2	yes	—
596	C₂³×C₄	C₂²×C₂²⋊C₄	1	2	yes	—
597	C₂³×C₄	C₂²×C₂²⋊C₄	1	1	yes	characteristic
598	C₂³×C₄	C₂²×C₂²⋊C₄	1	1	yes	characteristic
599	C₂³×C₄	C₂²×C₂²⋊C₄	1	2	yes	—
600	C₂³×C₄	C₂²×C₂²⋊C₄	1	2	yes	—
601	C₂³×C₄	C₂²×C₂²⋊C₄	1	2	yes	—
602	C₂³×C₄	C₂²×C₂²⋊C₄	1	2	yes	—
603	C₂³×C₄	C₂²×C₂²⋊C₄	1	1	yes	characteristic
604	C₂³×C₄	C₂×#121	1	2	yes	—
605	C₂³×C₄	C₂×#121	1	2	yes	—
606	C₂³×C₄	C₂×#121	1	2	yes	—
607	C₂³×C₄	C₂×#121	1	2	yes	—
608	C₂³×C₄	C₂×#121	1	2	yes	—
609	C₂³×C₄	C₂×#121	1	2	yes	—
610	C₂³×C₄	C₂³×D₄	1	1	yes	characteristic
611	C₂⁴	#1898	1	2	yes	—
612	C₂⁴	#1898	1	2	yes	—
613	C₂⁴	#1898	1	2	yes	—
614	C₂⁴	#1898	1	2	yes	—
615	C₂⁴	#1898	1	2	yes	—
616	C₂⁴	#1898	1	2	yes	—
617	C₂⁴	#1898	1	2	yes	—
618	C₂⁴	#1898	1	2	yes	—
619	C₂⁴	C₂×#386	1	2	yes	—
620	C₂⁴	C₂×#386	1	1	yes	characteristic
621	C₂⁴	C₂×#386	1	1	yes	characteristic
622	C₂⁴	C₂×#386	1	1	yes	characteristic
623	C₂⁴	C₂×#386	1	1	yes	characteristic
624	C₂⁴	C₂×#386	1	1	yes	characteristic
625	C₂⁴	C₂×#386	1	2	yes	—
626	C₂⁴	C₂×#386	1	2	yes	—
627	C₂⁴	C₂×#386	1	2	yes	—
628	C₂⁴	C₂×#386	1	1	yes	characteristic
629	C₂⁴	C₂×#386	1	1	yes	characteristic
630	C₂⁴	C₂×#386	1	1	yes	characteristic
631	C₂⁴	C₂×#386	1	2	yes	—
632	C₂⁴	C₂²×#99	1	2	yes	—
633	C₂⁴	C₂²×#99	1	1	yes	characteristic
634	C₂⁴	C₂²×#99	1	1	yes	characteristic
635	C₂⁴	C₂²×#99	1	2	yes	—
636	C₂⁴	C₂²×#99	1	4	yes	—
637	C₂⁴	C₂²×#99	1	2	yes	—
638	C₂⁴	C₂²×#99	1	1	yes	characteristic
639	C₂⁴	C₂²×#99	1	1	yes	characteristic
640	C₂⁴	C₂²×#99	1	1	yes	characteristic
641	C₂⁴	C₂²×#99	1	2	yes	—
642	C₂⁴	C₂²×#99	1	1	yes	characteristic
643	C₂⁴	C₂²×#99	1	1	yes	characteristic
644	C₂⁴	C₂²×#99	1	1	yes	characteristic
645	C₂⁴	C₂³×C₂²⋊C₄	1	1	yes	characteristic
646	C₂⁴	C₂²×C₄×D₄	1	2	yes	—
647	C₂⁴	C₂²×#120	1	1	yes	characteristic
648	C₂⁴	C₂²×#123	1	1	yes	characteristic
649	C₂×D₄	#1913	1	4	yes	—
650	C₂×D₄	#2121	1	8	yes	—
651	C₂×D₄	#3026	1	4	yes	—
652	C₂²×C₄	C₂×#386	1	1	yes	characteristic
653	C₂²×C₄	C₂×#386	1	1	yes	characteristic
654	C₂²×C₄	C₂×#386	1	2	yes	—
655	C₂²×C₄	C₂×#386	1	1	yes	characteristic
656	C₂²×C₄	C₂×#386	1	1	yes	characteristic
657	C₂²×C₄	C₂²×#99	1	2	yes	—
658	C₂²×C₄	C₂²×#99	1	2	yes	—
659	C₂²×C₄	C₂²×#99	1	4	yes	—
660	C₂²×C₄	C₂²×#121	1	2	yes	—
661	C₂³	#20960	1	2	yes	—
662	C₂³	C₂×#1898	1	2	yes	—
663	C₂³	C₂×#1898	1	2	yes	—
664	C₂³	C₂×#1898	1	2	yes	—
665	C₂³	C₂×#1898	1	1	yes	characteristic
666	C₂³	C₂×#1898	1	1	yes	characteristic
667	C₂³	C₂×#1898	1	2	yes	—
668	C₂³	C₂×#1898	1	1	yes	characteristic
669	C₂³	C₂×#1898	1	1	yes	characteristic
670	C₂³	C₂×#1913	1	2	yes	—
671	C₂³	C₂×#1913	1	2	yes	—
672	C₂³	C₂×#2121	1	4	yes	—
673	C₂³	C₂×#2121	1	4	yes	—
674	C₂³	#33348	1	4	yes	—
675	C₂³	C₂²×#386	1	1	yes	characteristic
676	C₂³	C₂³×#99	1	1	yes	characteristic
677	C₂³	C₂³×#99	1	1	yes	characteristic
678	C₂³	C₂×#3026	1	2	yes	—
679	C₂×C₄	#20960	1	2	yes	—
680	C₂×C₄	C₂×#1913	1	2	yes	—
681	C₂×C₄	C₂×#2121	1	4	yes	—
682	C₂²	#494695	1	4	yes	—
683	C₂²	#494700	1	2	yes	—
684	C₂²	#494700	1	2	yes	—
685	C₂²	C₂×#20960	1	1	yes	characteristic
686	C₂²	C₂²×#1898	1	1	yes	characteristic
687	C₂²	C₂²×#1913	1	1	yes	characteristic
688	C₂²	C₂²×#2121	1	2	yes	—
689	C₂²	C₂×#33348	1	2	yes	—
690	C₂	C₂×#494700	1	1	yes	characteristic
691	C₂	#72238030	1	1	yes	characteristic
692	C₂	C₂×#494695	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²	C₂²×#1898
commutator	C₂⁵	C₂⁴×C₄
Frattini, cosocle	C₂³×D₄	C₂⁵
prime radical	#72225665	C₂
LCS	G ▷ C₂⁵ ▷ C₂³ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂² ◁ C₂⁶ ◁ C₂³×D₄² ◁ G
LECS	G ▷ C₂³×D₄ ▷ C₂³ ▷ C₂ ▷ C₁

Complements

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

N	H ≅ G/N	type
1. #72317824	C₂	semidirect
2. #72317801	C₂	semidirect
3. #72317649	C₂	semidirect
4. #72240134	C₂	semidirect
5. #72236670	C₂	semidirect
6. C₂×#496225	C₂	semidirect
7. C₂×#6385971	C₂	semidirect
8. C₂×#188087	C₂	semidirect
9. #72232741	C₂	semidirect
12. C₂×#34980	C₄	semidirect
13. C₂²×#2403	C₄	semidirect
16. #6385971	C₂²	semidirect
17. C₂×#21793	C₂²	semidirect
18. C₂×#21746	C₂²	semidirect
21. #4420586	C₄	semidirect
23. #663621	C₄	semidirect
25. #647656	C₄	semidirect
27. #618316	C₄	semidirect
29. #617710	C₄	semidirect
31. #556752	C₄	semidirect
32. #517411	C₄	semidirect
34. #496225	C₂²	semidirect
35. #496225	C₂²	semidirect
36. C₂×#12852	C₂²	semidirect
37. C₂×#12687	C₂²	semidirect
39. #188087	C₂²	semidirect
40. C₂×#8549	C₂²	semidirect
41. C₂×#8547	C₂²	semidirect
42. #139848	C₂²	semidirect
43. #139828	C₂²	semidirect
44. #139793	C₂²	semidirect
45. #139716	C₂²	semidirect
46. #128073	C₂²	semidirect
47. #128073	C₂²	semidirect
48. #128033	C₂²	semidirect
50. C₂⁵×D₄	C₂×C₄	semidirect
62. C₂²×#534	C₂×C₄	semidirect
69. C₂³×#120	C₂×C₄	semidirect
70. C₂³×#120	C₂×C₄	semidirect
77. C₂³×#99	D₄	semidirect
78. C₂×#2849	C₂×C₄	semidirect
79. C₂×#2846	C₂×C₄	semidirect
80. C₂×#2403	C₂×C₄	semidirect
81. C₂×#2403	C₂×C₄	semidirect
82. C₂×#2403	C₂×C₄	semidirect
83. C₂×#2403	C₂×C₄	semidirect
84. C₂×#2403	C₂×C₄	semidirect
87. C₂×#2613	C₂×C₄	semidirect
88. C₂×#2308	C₂×C₄	semidirect
89. C₂²×#386	C₂×C₄	semidirect
90. C₂²×#386	C₂×C₄	semidirect
92. C₂²×#379	C₂×C₄	semidirect
93. C₂²×#379	C₂×C₄	semidirect
94. C₂²×#379	C₂×C₄	semidirect
100. C₂×#1781	D₄	semidirect
101. C₂×#1781	D₄	semidirect
102. C₂×#1781	D₄	semidirect
106. #15984	C₂×C₄	semidirect
107. #15984	C₂×C₄	semidirect
108. #15984	C₂×C₄	semidirect
110. #15948	C₂×C₄	semidirect
112. #15947	C₂×C₄	semidirect
114. #15261	C₂×C₄	semidirect
115. #15261	C₂×C₄	semidirect
116. #15258	C₂×C₄	semidirect
117. #15258	C₂×C₄	semidirect
118. #15257	C₂×C₄	semidirect
119. #15257	C₂×C₄	semidirect
120. #15257	C₂×C₄	semidirect
122. #14657	C₂×C₄	semidirect
123. #14341	C₂×C₄	semidirect
124. #14335	C₂×C₄	semidirect
125. #14335	C₂×C₄	semidirect
126. #14335	C₂×C₄	semidirect
128. #14134	C₂×C₄	semidirect
129. #14134	C₂×C₄	semidirect
130. #13867	C₂×C₄	semidirect
131. #13867	C₂×C₄	semidirect
132. #13867	C₂×C₄	semidirect
133. #13867	C₂×C₄	semidirect
134. #13867	C₂×C₄	semidirect
135. #13867	C₂×C₄	semidirect
138. #12852	C₂³	semidirect
139. #12687	C₂³	semidirect
142. #7304	C₂³	semidirect
145. C₂⁷	C₂²×C₄	semidirect
171. C₂⁴×D₄	C₂²×C₄	semidirect
196. C₂⁵×C₄	C₂²×C₄	semidirect
203. C₂²×#123	C₂²×C₄	semidirect
230. C₂²×#120	C₂²×C₄	semidirect
231. C₂²×#120	C₂²×C₄	semidirect
232. C₂²×#120	C₂²×C₄	semidirect
233. C₂²×#120	C₂²×C₄	semidirect
234. C₂²×#120	C₂²×C₄	semidirect
258. C₂³×C₂²⋊C₄	C₂²×C₄	semidirect
259. C₂³×C₂²⋊C₄	C₂²×C₄	semidirect
260. C₂³×C₂²⋊C₄	C₂²×C₄	semidirect
267. C₂²×#99	C₂×D₄	semidirect
268. C₂²×#99	C₂×D₄	semidirect
270. C₂×#386	C₂²×C₄	semidirect
271. C₂×#386	C₂²×C₄	semidirect
272. C₂×#386	C₂²×C₄	semidirect
273. C₂×#386	C₂²×C₄	semidirect
275. C₂×#381	C₂²×C₄	semidirect
278. C₂×#379	C₂²×C₄	semidirect
279. C₂×#379	C₂²×C₄	semidirect
280. C₂×#379	C₂²×C₄	semidirect
281. C₂×#379	C₂²×C₄	semidirect
282. C₂×#379	C₂²×C₄	semidirect
285. #1781	C₂×D₄	semidirect
286. #1781	C₂×D₄	semidirect
288. #1440	C₂²×C₄	semidirect
289. #1440	C₂²×C₄	semidirect
291. #1438	C₂²×C₄	semidirect
292. #1438	C₂²×C₄	semidirect
293. #1438	C₂²×C₄	semidirect
294. #1438	C₂²×C₄	semidirect
295. #1438	C₂²×C₄	semidirect
296. #1438	C₂²×C₄	semidirect
297. #1438	C₂²×C₄	semidirect
298. #1438	C₂²×C₄	semidirect

Maximal subgroups

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

subgroup	index
#72317824	2
#72317801	2
#72317649	2
#72240134	2
#72236670	2
C₂×#496225	2
C₂×#6385971	2
C₂×#188087	2
#72232741	2
#72225665	2