Subgroups — #72310984

Order 2048.

At least 8045 conjugacy classes of subgroups; only the 2704 normal subgroups are shown.

The subgroup lattice has 692 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#72310959	C₂	1	8	yes	maximal, complemented
2	#72310956	C₂	1	4	yes	maximal, complemented
3	C₂×D₄×#386	C₂	1	1	yes	maximal, characteristic, complemented
4	#72278692	C₂	1	1	yes	maximal, characteristic, complemented
5	#72278681	C₂	1	2	yes	maximal, complemented
6	#72278500	C₂	1	1	yes	maximal, characteristic, complemented
7	#72264018	C₂	1	4	yes	maximal, complemented
8	#72240594	C₂	1	2	yes	maximal, complemented
9	#72240377	C₂	1	1	yes	maximal, characteristic, complemented
10	#72240338	C₂	1	1	yes	maximal, characteristic, complemented
11	#72235625	C₂	1	2	yes	maximal, complemented
12	C₂×#10577301	C₂	1	1	yes	maximal, characteristic
13	C₂×#198404	C₂	1	2	yes	maximal, complemented
14	C₂×#185643	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×#62773	C₂²	1	1	yes	characteristic
16	C₂³×D₄²	C₂²	1	1	yes	characteristic
17	C₂⁴×C₄×D₄	C₂²	1	1	yes	characteristic, complemented
18	#10577301	C₄	1	16	yes	complemented
19	C₂×#61571	C₂²	1	4	yes	—
20	C₂×#61560	C₂²	1	2	yes	—
21	C₂×#61559	C₂²	1	2	yes	—
22	C₂×#60750	C₂²	1	2	yes	—
23	C₂²×#3003	C₂²	1	2	yes	—
24	C₂×#60230	C₂²	1	1	yes	characteristic
25	C₂²×D₄×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
26	C₂×#21420	C₂²	1	2	yes	complemented
27	C₂×#20909	C₂²	1	2	yes	complemented
28	C₂×#20722	C₂²	1	1	yes	characteristic
29	C₂×#20598	C₂²	1	2	yes	complemented
30	C₂×#17592	C₂²	1	2	yes	complemented
31	C₂×#17577	C₂²	1	2	yes	complemented
32	C₂×#17362	C₂²	1	1	yes	characteristic
33	#607597	C₂²	1	2	yes	complemented
34	C₂×#14698	C₂²	1	1	yes	characteristic, complemented
35	D₄×#386	C₂²	1	4	yes	—
36	D₄×#386	C₂²	1	4	yes	complemented
37	C₂×#14137	C₂²	1	1	yes	characteristic, complemented
38	C₂×#13872	C₂²	1	1	yes	characteristic
39	C₂×C₄×#386	C₂²	1	1	yes	characteristic
40	#392632	C₂²	1	8	yes	complemented
41	#392629	C₂²	1	8	yes	complemented
42	#363218	C₂²	1	4	yes	complemented
43	#362751	C₂²	1	2	yes	complemented
44	#361664	C₂²	1	2	yes	complemented
45	#353392	C₂²	1	2	yes	complemented
46	#353286	C₂²	1	2	yes	complemented
47	C₂×#9259	C₂²	1	8	yes	complemented
48	C₂×#9255	C₂²	1	8	yes	complemented
49	#185964	C₂²	1	4	yes	complemented
50	#185961	C₂²	1	2	yes	complemented
51	#185958	C₂²	1	2	yes	complemented
52	C₂×#8375	C₂²	1	4	yes	—
53	C₂×#8375	C₂²	1	4	yes	complemented
54	C₂×#7983	C₂²	1	2	yes	complemented
55	C₂×#7929	C₂²	1	2	yes	complemented
56	#114964	C₂²	1	8	yes	complemented
57	#114963	C₂²	1	8	yes	complemented
58	#111445	C₂²	1	8	yes	complemented
59	#111444	C₂²	1	8	yes	complemented
60	#108187	C₂²	1	4	yes	complemented
61	#108186	C₂²	1	4	yes	complemented
62	#106315	C₂²	1	4	yes	complemented
63	#106314	C₂²	1	4	yes	complemented
64	C₂⁵×D₄	D₄	1	1	yes	characteristic
65	C₂⁵×D₄	C₂³	1	1	yes	characteristic
66	C₂³×AGL(1,ℤ/8)	D₄	1	4	yes	—
67	#62773	C₂×C₄	1	8	yes	complemented
68	C₂×#3505	C₂³	1	2	yes	—
69	C₂×#3501	C₂³	1	1	yes	characteristic
70	C₂×#3496	C₂³	1	1	yes	characteristic
71	C₂²×D₄²	C₂×C₄	1	8	yes	—
72	C₂²×D₄²	D₄	1	8	yes	—
73	C₂²×D₄²	D₄	1	2	yes	—
74	C₂²×D₄²	D₄	1	2	yes	—
75	C₂²×D₄²	C₂³	1	2	yes	—
76	C₂²×D₄²	C₂³	1	2	yes	—
77	C₂³×#127	D₄	1	1	yes	characteristic
78	C₂²×#525	C₂³	1	2	yes	—
79	C₂³×#121	D₄	1	1	yes	characteristic
80	C₂³×#121	C₂³	1	1	yes	characteristic
81	C₂³×C₄×D₄	D₄	1	1	yes	characteristic
82	C₂³×C₄×D₄	C₂³	1	4	yes	—
83	C₂³×C₄×D₄	C₂³	1	1	yes	characteristic
84	C₂⁴×C₄⋊C₄	C₂³	1	1	yes	characteristic
85	C₂⁴×C₄²	C₂³	1	1	yes	characteristic
86	#61571	C₂×C₄	1	32	yes	complemented
87	#61560	C₂×C₄	1	16	yes	complemented
88	#61559	C₂×C₄	1	16	yes	complemented
89	#60750	C₂×C₄	1	16	yes	complemented
90	C₂×#3187	C₂³	1	4	yes	—
91	C₂×#3186	C₂³	1	4	yes	—
92	C₂×#3003	C₂×C₄	1	16	yes	—
93	C₂×#3003	D₄	1	16	yes	—
94	C₂²×#450	D₄	1	4	yes	—
95	C₂²×#450	C₂³	1	4	yes	—
96	C₂²×#447	D₄	1	4	yes	—
97	C₂²×#447	C₂³	1	4	yes	—
98	#60230	C₂×C₄	1	8	yes	complemented
99	C₂×#2973	C₂³	1	2	yes	—
100	C₂×#2972	C₂³	1	2	yes	—
101	C₂²×#418	D₄	1	4	yes	—
102	C₂²×#407	C₂³	1	2	yes	—
103	C₂²×#407	C₂³	1	2	yes	—
104	C₂×D₄×C₂²⋊C₄	C₂³	1	4	yes	—
105	C₂²×#386	D₄	1	1	yes	characteristic
106	C₂²×#386	D₄	1	1	yes	characteristic
107	C₂×#2280	C₂³	1	2	yes	—
108	C₂²×#380	C₂³	1	1	yes	characteristic
109	C₂²×C₄×C₂²⋊C₄	C₂³	1	1	yes	characteristic
110	C₂×#1996	C₂³	1	4	yes	complemented
111	C₂×#1964	C₂³	1	4	yes	complemented
112	C₂×#1874	C₂³	1	4	yes	complemented
113	C₂×#1872	C₂³	1	4	yes	complemented
114	C₂×#1799	C₂³	1	2	yes	—
115	C₂×#1799	C₂³	1	2	yes	—
116	C₂×#1786	C₂³	1	8	yes	—
117	C₂×#1520	C₂³	1	4	yes	complemented
118	C₂×#1519	C₂³	1	8	yes	—
119	C₂×#1519	C₂³	1	4	yes	complemented
120	C₂×#1459	C₂³	1	2	yes	—
121	C₂×#1459	C₂³	1	2	yes	—
122	#14702	C₂³	1	4	yes	complemented
123	#14698	C₂³	1	4	yes	—
124	#14698	C₂³	1	4	yes	complemented
125	#14137	C₂³	1	4	yes	—
126	#13872	D₄	1	2	yes	—
127	#13872	D₄	1	2	yes	—
128	#13872	C₂³	1	2	yes	—
129	#13872	C₂³	1	2	yes	—
130	C₂×#1441	D₄	1	2	yes	—
131	C₂×#1439	D₄	1	2	yes	—
132	C₄×#386	D₄	1	2	yes	—
133	C₄×#386	D₄	1	2	yes	—
134	C₄×#386	C₂³	1	2	yes	—
135	C₄×#386	C₂³	1	2	yes	—
136	C₂×C₂²⋊#95	D₄	1	1	yes	characteristic
137	C₂×C₂²⋊#95	D₄	1	1	yes	characteristic
138	#10730	C₂³	1	8	yes	complemented
139	#10712	C₂³	1	8	yes	complemented
140	C₂×#1289	C₂³	1	8	yes	complemented
141	C₂×#1282	C₂³	1	8	yes	complemented
142	C₂³×#41	C₂×D₄	1	2	yes	—
143	C₂⁴×D₄	C₂²⋊C₄	1	8	yes	complemented
144	C₂⁴×D₄	C₂²×C₄	1	4	yes	—
145	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
146	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
147	C₂⁴×D₄	C₂×D₄	1	4	yes	—
148	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
149	C₂⁴×D₄	C₂×D₄	1	2	yes	—
150	C₂⁴×D₄	C₂×D₄	1	2	yes	—
151	C₂⁴×D₄	C₂×D₄	1	8	yes	—
152	C₂⁴×D₄	C₂×D₄	1	2	yes	—
153	C₂⁴×D₄	C₂×D₄	1	4	yes	—
154	C₂⁴×D₄	C₂×D₄	1	4	yes	—
155	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
156	C₂⁴×D₄	C₂⁴	1	2	yes	—
157	C₂⁵×C₄	C₂×D₄	1	1	yes	characteristic
158	C₂⁵×C₄	C₂×D₄	1	1	yes	characteristic
159	C₂⁵×C₄	C₂×D₄	1	1	yes	characteristic
160	C₂⁵×C₄	C₂⁴	1	1	yes	characteristic
161	C₂²×AGL(1,ℤ/8)	C₂²⋊C₄	1	32	yes	complemented
162	C₂³×SD₁₆	C₂×D₄	1	8	yes	—
163	C₂³×D₈	C₂×D₄	1	8	yes	—
164	C₂³×M₁₆	C₂×D₄	1	4	yes	—
165	#3505	C₂²×C₄	1	8	yes	complemented
166	#3501	C₂²×C₄	1	4	yes	complemented
167	#3496	C₂²×C₄	1	4	yes	complemented
168	C₂×D₄²	C₂²⋊C₄	1	16	yes	complemented
169	C₂×D₄²	C₂²⋊C₄	1	16	yes	complemented
170	C₂×D₄²	C₂²×C₄	1	8	yes	—
171	C₂×D₄²	C₂²×C₄	1	8	yes	—
172	C₂×D₄²	C₂×D₄	1	8	yes	—
173	C₂×D₄²	C₂×D₄	1	8	yes	—
174	C₂²×#127	C₂²⋊C₄	1	8	yes	complemented
175	C₂²×#127	C₂×D₄	1	2	yes	—
176	C₂²×#127	C₂×D₄	1	2	yes	—
177	C₂×#525	C₂²×C₄	1	8	yes	—
178	C₂×#525	C₂×D₄	1	8	yes	—
179	C₂²×C₂²⋊Q₈	C₂×D₄	1	2	yes	—
180	C₂²×C₂²⋊Q₈	C₂⁴	1	2	yes	—
181	C₂²×#121	C₂²⋊C₄	1	8	yes	complemented
182	C₂²×#121	C₂²×C₄	1	4	yes	—
183	C₂²×#121	C₂×D₄	1	4	yes	—
184	C₂²×#121	C₂×D₄	1	2	yes	—
185	C₂²×#121	C₂×D₄	1	2	yes	—
186	C₂²×#121	C₂×D₄	1	2	yes	—
187	C₂²×#121	C₂×D₄	1	2	yes	—
188	C₂²×#121	C₂⁴	1	2	yes	—
189	C₂²×#121	C₂⁴	1	2	yes	—
190	C₂²×C₄×D₄	C₂²⋊C₄	1	8	yes	complemented
191	C₂²×C₄×D₄	C₂²×C₄	1	4	yes	—
192	C₂²×C₄×D₄	C₂×D₄	1	2	yes	—
193	C₂²×C₄×D₄	C₂×D₄	1	2	yes	—
194	C₂²×C₄×D₄	C₂×D₄	1	1	yes	characteristic
195	C₂²×C₄×D₄	C₂×D₄	1	1	yes	characteristic
196	C₂²×C₄×D₄	C₂×D₄	1	1	yes	characteristic
197	C₂²×C₄×D₄	C₂×D₄	1	1	yes	characteristic
198	C₂²×C₄×D₄	C₂×D₄	1	1	yes	characteristic
199	C₂²×C₄×D₄	C₂×D₄	1	1	yes	characteristic
200	C₂²×C₄×D₄	C₂×D₄	1	4	yes	—
201	C₂²×C₄×D₄	#41	1	4	yes	—
202	C₂²×C₄×D₄	#41	1	4	yes	—
203	C₂²×C₄×D₄	C₂⁴	1	1	yes	characteristic
204	C₂²×C₄×D₄	C₂⁴	1	1	yes	characteristic
205	C₂²×#117	C₂×D₄	1	2	yes	—
206	C₂³×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
207	C₂³×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
208	C₂³×C₄⋊C₄	C₂×D₄	1	2	yes	—
209	C₂³×C₄⋊C₄	C₂×D₄	1	2	yes	—
210	C₂³×C₄⋊C₄	C₂⁴	1	2	yes	—
211	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
212	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
213	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
214	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
215	C₂³×C₄²	C₂×D₄	1	1	yes	characteristic
216	C₂³×C₄²	C₂×D₄	1	2	yes	—
217	C₂³×C₄²	C₂⁴	1	2	yes	—
218	#3187	C₂²×C₄	1	16	yes	complemented
219	#3186	C₂²×C₄	1	16	yes	complemented
220	C₂×#450	C₂²⋊C₄	1	32	yes	complemented
221	C₂×#450	C₂²×C₄	1	16	yes	—
222	C₂×#450	C₂×D₄	1	16	yes	—
223	C₂×#447	C₂²⋊C₄	1	32	yes	complemented
224	C₂×#447	C₂²×C₄	1	16	yes	—
225	C₂×#447	C₂×D₄	1	16	yes	—
226	#2973	C₂²×C₄	1	8	yes	complemented
227	#2972	C₂²×C₄	1	8	yes	complemented
228	C₂×#418	C₂²⋊C₄	1	32	yes	complemented
229	C₂²×#102	C₂×D₄	1	8	yes	—
230	C₂²×#102	C₂×D₄	1	8	yes	—
231	C₂×#407	C₂²×C₄	1	8	yes	—
232	C₂×#407	C₂×D₄	1	8	yes	—
233	C₂²×C₂²⋊C₈	C₂×D₄	1	4	yes	—
234	C₂²×C₂²⋊C₈	C₂⁴	1	4	yes	—
235	C₂²×C₂²⋊C₈	C₂⁴	1	4	yes	—
236	C₂×#386	C₂×D₄	1	2	yes	—
237	C₂×#386	C₂×D₄	1	2	yes	—
238	C₂×#386	C₂×D₄	1	2	yes	—
239	C₂×#386	C₂×D₄	1	2	yes	—
240	C₂×#380	C₂×D₄	1	2	yes	—
241	C₂×#380	C₂⁴	1	4	yes	—
242	C₂×#380	C₂⁴	1	2	yes	—
243	C₂×C₄×C₂²⋊C₄	C₂×D₄	1	2	yes	—
244	C₂×C₄×C₂²⋊C₄	C₂⁴	1	2	yes	—
245	C₂²×#95	C₂×D₄	1	2	yes	—
246	#1441	C₂×D₄	1	4	yes	—
247	#1441	C₂×D₄	1	4	yes	—
248	#1439	C₂×D₄	1	4	yes	—
249	#1439	C₂×D₄	1	4	yes	—
250	C₂²⋊#95	C₂×D₄	1	2	yes	—
251	C₂²⋊#95	C₂×D₄	1	2	yes	—
252	C₂²⋊#95	C₂×D₄	1	2	yes	—
253	C₂²⋊#95	C₂×D₄	1	2	yes	—
254	C₂⁶	#120	1	1	yes	characteristic
255	C₂⁶	C₂²×D₄	1	1	yes	characteristic
256	C₂²×#41	C₂×C₂²⋊C₄	1	8	yes	complemented
257	C₂³×Q₈	C₂²×D₄	1	2	yes	—
258	C₂³×D₄	C₂×C₂²⋊C₄	1	4	yes	—
259	C₂³×D₄	C₂×C₂²⋊C₄	1	16	yes	—
260	C₂³×D₄	C₂×C₂²⋊C₄	1	4	yes	—
261	C₂³×D₄	C₂×C₂²⋊C₄	1	8	yes	—
262	C₂³×D₄	C₂×C₂²⋊C₄	1	8	yes	—
263	C₂³×D₄	C₂×C₂²⋊C₄	1	4	yes	—
264	C₂³×D₄	C₂×C₂²⋊C₄	1	16	yes	—
265	C₂³×D₄	C₂×C₂²⋊C₄	1	8	yes	—
266	C₂³×D₄	C₄×D₄	1	4	yes	—
267	C₂³×D₄	#120	1	2	yes	—
268	C₂³×D₄	#120	1	4	yes	—
269	C₂³×D₄	#120	1	2	yes	—
270	C₂³×D₄	#120	1	1	yes	characteristic
271	C₂³×D₄	#120	1	1	yes	characteristic
272	C₂³×D₄	#120	1	16	yes	—
273	C₂³×D₄	#120	1	8	yes	—
274	C₂³×D₄	#120	1	2	yes	—
275	C₂³×D₄	#120	1	8	yes	—
276	C₂³×D₄	#120	1	2	yes	—
277	C₂³×D₄	#120	1	4	yes	—
278	C₂³×D₄	#120	1	16	yes	—
279	C₂³×D₄	#121	1	4	yes	—
280	C₂³×D₄	C₂³×C₄	1	4	yes	—
281	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
282	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
283	C₂³×D₄	C₂²×D₄	1	2	yes	—
284	C₂³×D₄	C₂²×D₄	1	8	yes	—
285	C₂³×D₄	C₂²×D₄	1	2	yes	—
286	C₂³×D₄	C₂²×D₄	1	2	yes	—
287	C₂³×D₄	C₂²×D₄	1	8	yes	—
288	C₂³×D₄	C₂²×D₄	1	2	yes	—
289	C₂³×D₄	C₂²×D₄	1	4	yes	—
290	C₂⁴×C₄	C₂×C₂²⋊C₄	1	4	yes	—
291	C₂⁴×C₄	#120	1	1	yes	characteristic
292	C₂⁴×C₄	#120	1	1	yes	characteristic
293	C₂⁴×C₄	#120	1	1	yes	characteristic
294	C₂⁴×C₄	#120	1	1	yes	characteristic
295	C₂⁴×C₄	#120	1	1	yes	characteristic
296	C₂⁴×C₄	#123	1	4	yes	—
297	C₂⁴×C₄	C₂³×C₄	1	2	yes	—
298	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
299	C₂⁴×C₄	C₂²×D₄	1	2	yes	—
300	C₂⁴×C₄	C₂²×D₄	1	2	yes	—
301	C₂⁴×C₄	C₂²×D₄	1	2	yes	—
302	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
303	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
304	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
305	C₂⁴×C₄	C₂²×D₄	1	2	yes	—
306	C₂⁴×C₄	C₂²×D₄	1	2	yes	—
307	C₂⁴×C₄	C₂²×D₄	1	4	yes	—
308	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
309	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
310	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
311	C₂⁴×C₄	C₂×#41	1	2	yes	—
312	C₂⁴×C₄	C₂×#41	1	2	yes	—
313	C₂⁴×C₄	H(5,𝔽₂)	1	2	yes	—
314	C₂⁴×C₄	H(5,𝔽₂)	1	2	yes	—
315	C₂⁴×C₄	H(5,𝔽₂)	1	4	yes	—
316	C₂⁴×C₄	C₂⁵	1	1	yes	characteristic
317	C₂²×SD₁₆	C₂×C₂²⋊C₄	1	32	yes	complemented
318	C₂²×D₈	C₂×C₂²⋊C₄	1	32	yes	complemented
319	C₂²×M₁₆	C₂×C₂²⋊C₄	1	16	yes	complemented
320	C₂³×C₈	C₂²×D₄	1	8	yes	—
321	C₂×#127	C₂×C₂²⋊C₄	1	8	yes	—
322	C₂×#127	C₂×C₂²⋊C₄	1	8	yes	—
323	C₂×C₂²⋊Q₈	C₂×C₂²⋊C₄	1	8	yes	complemented
324	C₂×C₂²⋊Q₈	C₂³×C₄	1	4	yes	—
325	C₂×C₂²⋊Q₈	C₂²×D₄	1	4	yes	—
326	C₂×#121	C₂×C₂²⋊C₄	1	8	yes	—
327	C₂×#121	C₂×C₂²⋊C₄	1	8	yes	—
328	C₂×#121	C₂×C₂²⋊C₄	1	8	yes	—
329	C₂×#121	C₂×C₂²⋊C₄	1	8	yes	complemented
330	C₂×#121	C₂³×C₄	1	4	yes	—
331	C₂×#121	C₂³×C₄	1	4	yes	—
332	C₂×#121	C₂²×D₄	1	4	yes	—
333	C₂×#121	C₂²×D₄	1	4	yes	—
334	C₂×C₄×D₄	C₂×C₂²⋊C₄	1	8	yes	—
335	C₂×C₄×D₄	C₂×C₂²⋊C₄	1	8	yes	—
336	C₂×C₄×D₄	C₂×C₂²⋊C₄	1	4	yes	—
337	C₂×C₄×D₄	C₂×C₂²⋊C₄	1	4	yes	—
338	C₂×C₄×D₄	C₄×D₄	1	4	yes	—
339	C₂×C₄×D₄	C₄×D₄	1	4	yes	—
340	C₂×C₄×D₄	C₄×D₄	1	4	yes	—
341	C₂×C₄×D₄	C₄×D₄	1	4	yes	—
342	C₂×C₄×D₄	#121	1	4	yes	—
343	C₂×C₄×D₄	#121	1	4	yes	—
344	C₂×C₄×D₄	#121	1	4	yes	—
345	C₂×C₄×D₄	#121	1	4	yes	—
346	C₂×C₄×D₄	#123	1	4	yes	—
347	C₂×C₄×D₄	#123	1	4	yes	—
348	C₂×C₄×D₄	C₂³×C₄	1	2	yes	—
349	C₂×C₄×D₄	C₂³×C₄	1	2	yes	—
350	C₂×C₄×D₄	C₂²×D₄	1	2	yes	—
351	C₂×C₄×D₄	C₂²×D₄	1	2	yes	—
352	C₂×C₄×D₄	C₂×#41	1	2	yes	—
353	C₂×C₄×D₄	C₂×#41	1	2	yes	—
354	C₂×C₄×D₄	C₂×#41	1	2	yes	—
355	C₂×C₄×D₄	C₂×#41	1	2	yes	—
356	C₂×#117	C₂×C₂²⋊C₄	1	8	yes	complemented
357	C₂²×C₄⋊C₄	C₂×C₂²⋊C₄	1	4	yes	—
358	C₂²×C₄⋊C₄	C₄×D₄	1	4	yes	—
359	C₂²×C₄⋊C₄	#120	1	1	yes	characteristic
360	C₂²×C₄⋊C₄	#120	1	1	yes	characteristic
361	C₂²×C₄⋊C₄	#121	1	4	yes	—
362	C₂²×C₄⋊C₄	C₂²×D₄	1	2	yes	—
363	C₂²×C₄⋊C₄	C₂²×D₄	1	2	yes	—
364	C₂²×C₄⋊C₄	C₂²×D₄	1	2	yes	—
365	C₂²×C₄⋊C₄	C₂²×D₄	1	1	yes	characteristic
366	C₂²×C₄⋊C₄	C₂²×D₄	1	1	yes	characteristic
367	C₂²×C₄⋊C₄	C₂²×D₄	1	4	yes	—
368	C₂²×C₂²⋊C₄	C₄×D₄	1	4	yes	—
369	C₂²×C₂²⋊C₄	C₄×D₄	1	4	yes	—
370	C₂²×C₂²⋊C₄	#120	1	1	yes	characteristic
371	C₂²×C₂²⋊C₄	#120	1	1	yes	characteristic
372	C₂²×C₂²⋊C₄	#120	1	1	yes	characteristic
373	C₂²×C₂²⋊C₄	#120	1	1	yes	characteristic
374	C₂²×C₂²⋊C₄	#121	1	4	yes	—
375	C₂²×C₂²⋊C₄	#121	1	4	yes	—
376	C₂²×C₂²⋊C₄	C₂²×D₄	1	2	yes	—
377	C₂²×C₂²⋊C₄	C₂²×D₄	1	2	yes	—
378	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
379	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
380	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
381	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
382	C₂²×C₄²	C₂×C₂²⋊C₄	1	4	yes	—
383	C₂²×C₄²	#120	1	1	yes	characteristic
384	C₂²×C₄²	#120	1	1	yes	characteristic
385	C₂²×C₄²	#123	1	4	yes	—
386	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
387	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
388	C₂×#102	C₂×C₂²⋊C₄	1	32	yes	complemented
389	C₂×#102	C₂×C₂²⋊C₄	1	32	yes	complemented
390	C₂×C₂²⋊C₈	C₂×C₂²⋊C₄	1	16	yes	complemented
391	C₂×C₂²⋊C₈	C₂³×C₄	1	8	yes	—
392	C₂×C₂²⋊C₈	C₂²×D₄	1	8	yes	—
393	#386	AGL(1,ℤ/8)	1	8	yes	complemented
394	C₂×#95	C₂²×D₄	1	4	yes	—
395	C₂⁵	#386	1	4	yes	—
396	C₂⁵	C₂×C₄×D₄	1	2	yes	—
397	C₂⁵	C₂×#120	1	1	yes	characteristic
398	C₂⁵	C₂×#120	1	1	yes	characteristic
399	C₂⁵	C₂×#120	1	1	yes	characteristic
400	C₂⁵	C₂×#120	1	1	yes	characteristic
401	C₂⁵	C₂×#121	1	2	yes	—
402	C₂⁵	D₄²	1	2	yes	—
403	C₂⁵	D₄²	1	2	yes	—
404	C₂⁵	D₄²	1	4	yes	—
405	C₂⁵	C₂³×D₄	1	1	yes	characteristic
406	C₂²×Q₈	C₂²×C₂²⋊C₄	1	4	yes	complemented
407	C₂²×D₄	#379	1	8	yes	—
408	C₂²×D₄	#379	1	8	yes	—
409	C₂²×D₄	#379	1	32	yes	—
410	C₂²×D₄	#379	1	8	yes	—
411	C₂²×D₄	#379	1	8	yes	—
412	C₂²×D₄	#386	1	4	yes	—
413	C₂²×D₄	#386	1	4	yes	—
414	C₂²×D₄	B(4,𝔽₂)	1	8	yes	—
415	C₂²×D₄	#458	1	8	yes	—
416	C₂²×D₄	C₂²×C₂²⋊C₄	1	4	yes	—
417	C₂²×D₄	C₂²×C₂²⋊C₄	1	16	yes	—
418	C₂²×D₄	C₂²×C₂²⋊C₄	1	4	yes	—
419	C₂²×D₄	C₂²×C₂²⋊C₄	1	4	yes	—
420	C₂²×D₄	C₂²×C₂²⋊C₄	1	4	yes	complemented
421	C₂²×D₄	C₂×C₄×D₄	1	2	yes	—
422	C₂²×D₄	C₂×C₄×D₄	1	2	yes	—
423	C₂²×D₄	C₂×#120	1	4	yes	—
424	C₂²×D₄	C₂×#120	1	4	yes	—
425	C₂²×D₄	C₂×#120	1	16	yes	—
426	C₂²×D₄	C₂×#120	1	4	yes	—
427	C₂²×D₄	C₂×#120	1	4	yes	—
428	C₂²×D₄	C₂×#121	1	2	yes	—
429	C₂²×D₄	C₂×#121	1	2	yes	—
430	C₂²×D₄	C₂×AGL(1,ℤ/8)	1	4	yes	—
431	C₂²×D₄	#575	1	4	yes	—
432	C₂³×C₄	#386	1	4	yes	—
433	C₂³×C₄	#386	1	4	yes	—
434	C₂³×C₄	#386	1	4	yes	—
435	C₂³×C₄	#386	1	4	yes	—
436	C₂³×C₄	#386	1	4	yes	—
437	C₂³×C₄	C₂²×C₂²⋊C₄	1	2	yes	—
438	C₂³×C₄	C₂²×C₂²⋊C₄	1	4	yes	—
439	C₂³×C₄	C₂²×C₂²⋊C₄	1	2	yes	—
440	C₂³×C₄	C₂²×C₂²⋊C₄	1	2	yes	—
441	C₂³×C₄	C₂²×C₂²⋊C₄	1	2	yes	—
442	C₂³×C₄	C₂²×C₂²⋊C₄	1	4	yes	—
443	C₂³×C₄	C₂×C₄×D₄	1	2	yes	—
444	C₂³×C₄	C₂×C₄×D₄	1	2	yes	—
445	C₂³×C₄	C₂×C₄×D₄	1	2	yes	—
446	C₂³×C₄	#518	1	4	yes	—
447	C₂³×C₄	#518	1	4	yes	—
448	C₂³×C₄	C₂×#120	1	1	yes	characteristic
449	C₂³×C₄	C₂×#120	1	1	yes	characteristic
450	C₂³×C₄	C₂×#120	1	1	yes	characteristic
451	C₂³×C₄	C₂×#120	1	2	yes	—
452	C₂³×C₄	C₂×#120	1	2	yes	—
453	C₂³×C₄	C₂×#120	1	4	yes	—
454	C₂³×C₄	C₂×#120	1	1	yes	characteristic
455	C₂³×C₄	C₂×#120	1	1	yes	characteristic
456	C₂³×C₄	C₂×#120	1	1	yes	characteristic
457	C₂³×C₄	C₂×#120	1	1	yes	characteristic
458	C₂³×C₄	C₂×#120	1	1	yes	characteristic
459	C₂³×C₄	C₂×#120	1	1	yes	characteristic
460	C₂³×C₄	C₂×#120	1	2	yes	—
461	C₂³×C₄	C₂×#120	1	4	yes	—
462	C₂³×C₄	C₂×#120	1	1	yes	characteristic
463	C₂³×C₄	C₂×#121	1	2	yes	—
464	C₂³×C₄	C₂×#121	1	2	yes	—
465	C₂³×C₄	C₂×#121	1	2	yes	—
466	C₂³×C₄	C₂×#123	1	2	yes	—
467	C₂³×C₄	C₂×#123	1	2	yes	—
468	C₂³×C₄	C₂×#123	1	2	yes	—
469	C₂³×C₄	C₂×#123	1	2	yes	—
470	C₂³×C₄	#534	1	1	yes	characteristic
471	C₂³×C₄	#534	1	1	yes	characteristic
472	C₂³×C₄	#534	1	2	yes	—
473	C₂³×C₄	#534	1	2	yes	—
474	C₂³×C₄	#534	1	2	yes	—
475	C₂³×C₄	#534	1	4	yes	—
476	C₂³×C₄	#534	1	4	yes	—
477	C₂³×C₄	D₄²	1	2	yes	—
478	C₂³×C₄	D₄²	1	2	yes	—
479	C₂³×C₄	D₄²	1	2	yes	—
480	C₂³×C₄	D₄²	1	2	yes	—
481	C₂³×C₄	D₄²	1	4	yes	—
482	C₂³×C₄	D₄²	1	2	yes	—
483	C₂³×C₄	D₄²	1	4	yes	—
484	C₂³×C₄	D₄²	1	2	yes	—
485	C₂³×C₄	D₄²	1	4	yes	—
486	C₂³×C₄	#546	1	4	yes	—
487	C₂³×C₄	#546	1	4	yes	—
488	C₂³×C₄	#546	1	4	yes	—
489	C₂³×C₄	#546	1	4	yes	—
490	C₂³×C₄	#546	1	4	yes	—
491	C₂³×C₄	#546	1	4	yes	—
492	C₂³×C₄	#546	1	4	yes	—
493	C₂³×C₄	#546	1	4	yes	—
494	C₂³×C₄	C₂×AGL(1,ℤ/8)	1	4	yes	complemented
495	C₂³×C₄	C₂⁴×C₄	1	1	yes	characteristic
496	C₂³×C₄	C₂³×D₄	1	1	yes	characteristic
497	C₂³×C₄	C₂³×D₄	1	2	yes	—
498	C₂³×C₄	C₂³×D₄	1	1	yes	characteristic
499	C₂³×C₄	C₂³×D₄	1	2	yes	—
500	C₂³×C₄	C₂³×D₄	1	1	yes	characteristic
501	C₂³×C₄	C₂²×#41	1	1	yes	characteristic
502	C₂³×C₄	C₂²×#41	1	1	yes	characteristic
503	C₂³×C₄	C₂×H(5,𝔽₂)	1	2	yes	—
504	C₂³×C₄	C₂×H(5,𝔽₂)	1	2	yes	—
505	C₂²×C₈	C₂²×C₂²⋊C₄	1	16	yes	complemented
506	C₂×C₄⋊C₄	#386	1	4	yes	—
507	C₂×C₄⋊C₄	#386	1	4	yes	—
508	C₂×C₄⋊C₄	C₂²×C₂²⋊C₄	1	4	yes	—
509	C₂×C₄⋊C₄	C₂²×C₂²⋊C₄	1	4	yes	complemented
510	C₂×C₄⋊C₄	C₂²×C₂²⋊C₄	1	4	yes	complemented
511	C₂×C₄⋊C₄	C₂×C₄×D₄	1	2	yes	—
512	C₂×C₄⋊C₄	C₂×C₄×D₄	1	2	yes	—
513	C₂×C₄⋊C₄	C₂×#121	1	2	yes	—
514	C₂×C₄⋊C₄	C₂×#121	1	2	yes	—
515	C₂×C₂²⋊C₄	#386	1	4	yes	—
516	C₂×C₂²⋊C₄	#386	1	4	yes	—
517	C₂×C₂²⋊C₄	#386	1	4	yes	—
518	C₂×C₂²⋊C₄	#386	1	4	yes	—
519	C₂×C₂²⋊C₄	C₂×C₄×D₄	1	2	yes	—
520	C₂×C₂²⋊C₄	C₂×C₄×D₄	1	2	yes	—
521	C₂×C₂²⋊C₄	C₂×C₄×D₄	1	2	yes	—
522	C₂×C₂²⋊C₄	C₂×C₄×D₄	1	2	yes	—
523	C₂×C₂²⋊C₄	C₂×#121	1	2	yes	—
524	C₂×C₂²⋊C₄	C₂×#121	1	2	yes	—
525	C₂×C₂²⋊C₄	C₂×#121	1	2	yes	—
526	C₂×C₂²⋊C₄	C₂×#121	1	2	yes	—
527	C₂×C₂²⋊C₄	C₂×AGL(1,ℤ/8)	1	4	yes	complemented
528	C₂×C₄²	#386	1	4	yes	—
529	C₂×C₄²	#386	1	4	yes	—
530	C₂×C₄²	C₂²×C₂²⋊C₄	1	2	yes	—
531	C₂×C₄²	C₂²×C₂²⋊C₄	1	2	yes	—
532	C₂×C₄²	C₂×#123	1	2	yes	—
533	C₂×C₄²	C₂×#123	1	2	yes	—
534	C₂⁴	C₂×#386	1	2	yes	—
535	C₂⁴	C₂×#386	1	2	yes	—
536	C₂⁴	C₂×#386	1	2	yes	—
537	C₂⁴	C₂×#386	1	2	yes	—
538	C₂⁴	D₄×C₂²⋊C₄	1	4	yes	—
539	C₂⁴	D₄×C₂²⋊C₄	1	4	yes	—
540	C₂⁴	#2403	1	2	yes	—
541	C₂⁴	#2403	1	2	yes	—
542	C₂⁴	#2403	1	1	yes	characteristic
543	C₂⁴	#2403	1	1	yes	characteristic
544	C₂⁴	#2403	1	2	yes	—
545	C₂⁴	#2410	1	4	yes	—
546	C₂⁴	#2410	1	4	yes	—
547	C₂⁴	#3003	1	2	yes	—
548	C₂⁴	#3005	1	2	yes	—
549	C₂⁴	C₂²×C₄×D₄	1	1	yes	characteristic
550	C₂⁴	C₂²×#120	1	1	yes	characteristic
551	C₂⁴	C₂²×#121	1	1	yes	characteristic
552	C₂⁴	C₂×D₄²	1	2	yes	—
553	C₂⁴	C₂×D₄²	1	2	yes	—
554	C₂⁴	C₂²×AGL(1,ℤ/8)	1	2	yes	—
555	C₂⁴	C₂×#575	1	2	yes	—
556	C₂⁴	#3585	1	2	yes	—
557	C₂⁴	#3585	1	2	yes	—
558	C₂×D₄	#1790	1	32	yes	complemented
559	C₂×D₄	C₂×#379	1	8	yes	—
560	C₂×D₄	C₂×#379	1	8	yes	—
561	C₂×D₄	C₄×AGL(1,ℤ/8)	1	8	yes	—
562	C₂×D₄	C₂×B(4,𝔽₂)	1	8	yes	—
563	C₂×D₄	C₂×#458	1	8	yes	—
564	C₂×D₄	#3036	1	8	yes	—
565	C₂²×C₄	C₂×#379	1	2	yes	—
566	C₂²×C₄	C₂×#379	1	4	yes	—
567	C₂²×C₄	C₂×#379	1	2	yes	—
568	C₂²×C₄	C₂×#386	1	2	yes	—
569	C₂²×C₄	C₂×#386	1	2	yes	—
570	C₂²×C₄	C₂×#386	1	2	yes	—
571	C₂²×C₄	C₂×#386	1	2	yes	—
572	C₂²×C₄	C₂×#386	1	2	yes	—
573	C₂²×C₄	C₂×#386	1	2	yes	—
574	C₂²×C₄	C₂×#386	1	2	yes	—
575	C₂²×C₄	C₂×#386	1	2	yes	—
576	C₂²×C₄	#2308	1	2	yes	—
577	C₂²×C₄	#2308	1	2	yes	—
578	C₂²×C₄	#2308	1	4	yes	—
579	C₂²×C₄	D₄×C₂²⋊C₄	1	4	yes	—
580	C₂²×C₄	D₄×C₂²⋊C₄	1	4	yes	—
581	C₂²×C₄	D₄×C₂²⋊C₄	1	4	yes	—
582	C₂²×C₄	D₄×C₂²⋊C₄	1	4	yes	—
583	C₂²×C₄	D₄×C₂²⋊C₄	1	4	yes	—
584	C₂²×C₄	D₄×C₂²⋊C₄	1	4	yes	—
585	C₂²×C₄	#2403	1	2	yes	—
586	C₂²×C₄	#2403	1	1	yes	characteristic
587	C₂²×C₄	#2403	1	2	yes	—
588	C₂²×C₄	#2403	1	2	yes	—
589	C₂²×C₄	#2403	1	1	yes	characteristic
590	C₂²×C₄	#2405	1	2	yes	—
591	C₂²×C₄	#2405	1	2	yes	—
592	C₂²×C₄	#2405	1	2	yes	—
593	C₂²×C₄	#2405	1	4	yes	—
594	C₂²×C₄	#2405	1	4	yes	—
595	C₂²×C₄	#2405	1	2	yes	—
596	C₂²×C₄	#2410	1	4	yes	—
597	C₂²×C₄	#2410	1	4	yes	—
598	C₂²×C₄	#2410	1	4	yes	—
599	C₂²×C₄	#2410	1	4	yes	—
600	C₂²×C₄	#2410	1	4	yes	—
601	C₂²×C₄	#2410	1	4	yes	—
602	C₂²×C₄	#3003	1	2	yes	—
603	C₂²×C₄	#3005	1	2	yes	—
604	C₂²×C₄	C₂×B(4,𝔽₂)	1	4	yes	—
605	C₂²×C₄	C₂×#458	1	4	yes	—
606	C₂²×C₄	C₂³×C₂²⋊C₄	1	2	yes	—
607	C₂²×C₄	C₂³×C₂²⋊C₄	1	1	yes	characteristic
608	C₂²×C₄	C₂²×C₄×D₄	1	1	yes	characteristic
609	C₂²×C₄	C₂×#518	1	2	yes	—
610	C₂²×C₄	C₂²×#120	1	2	yes	—
611	C₂²×C₄	C₂²×#120	1	1	yes	characteristic
612	C₂²×C₄	C₂²×#120	1	1	yes	characteristic
613	C₂²×C₄	C₂²×#121	1	1	yes	characteristic
614	C₂²×C₄	C₂²×#123	1	1	yes	characteristic
615	C₂²×C₄	C₂×#534	1	1	yes	characteristic
616	C₂²×C₄	C₂×#534	1	1	yes	characteristic
617	C₂²×C₄	C₂×#534	1	2	yes	—
618	C₂²×C₄	C₂×D₄²	1	2	yes	—
619	C₂²×C₄	C₂×D₄²	1	2	yes	—
620	C₂²×C₄	C₂×#546	1	2	yes	—
621	C₂²×C₄	C₂×#546	1	2	yes	—
622	C₂²×C₄	C₂×#546	1	2	yes	—
623	C₂²×C₄	C₂×#546	1	2	yes	—
624	C₂³	#13867	1	4	yes	—
625	C₂³	#13867	1	2	yes	—
626	C₂³	#13867	1	2	yes	—
627	C₂³	#20925	1	4	yes	complemented
628	C₂³	#23882	1	2	yes	—
629	C₂³	#23883	1	2	yes	—
630	C₂³	#23900	1	2	yes	—
631	C₂³	#23901	1	2	yes	—
632	C₂³	C₂²×#386	1	1	yes	characteristic
633	C₂³	C₂×D₄×C₂²⋊C₄	1	2	yes	—
634	C₂³	C₂×#2403	1	1	yes	characteristic
635	C₂³	C₂×#2403	1	1	yes	characteristic
636	C₂³	C₂×#2410	1	2	yes	—
637	C₂³	C₂×C₄×AGL(1,ℤ/8)	1	2	yes	—
638	C₂³	#60168	1	2	yes	—
639	C₂³	C₂×#3003	1	1	yes	characteristic
640	C₂³	C₂×#3005	1	1	yes	characteristic
641	C₂³	#60367	1	1	yes	characteristic
642	C₂³	#60367	1	1	yes	characteristic
643	C₂³	C₂×#3036	1	2	yes	—
644	C₂³	#60423	1	2	yes	—
645	C₂³	D₄×AGL(1,ℤ/8)	1	4	yes	—
646	C₂³	D₄×AGL(1,ℤ/8)	1	4	yes	—
647	C₂³	#61066	1	4	yes	—
648	C₂³	#61066	1	4	yes	—
649	D₄	C₂×#1790	1	16	yes	—
650	C₂×C₄	#13867	1	2	yes	—
651	C₂×C₄	#13867	1	4	yes	—
652	C₂×C₄	#13867	1	2	yes	—
653	C₂×C₄	C₂×#1790	1	8	yes	—
654	C₂×C₄	#20925	1	4	yes	complemented
655	C₂×C₄	#23900	1	2	yes	—
656	C₂×C₄	#23901	1	2	yes	—
657	C₂×C₄	#24056	1	8	yes	—
658	C₂×C₄	C₂²×#379	1	1	yes	characteristic
659	C₂×C₄	C₂×#2308	1	1	yes	characteristic
660	C₂×C₄	C₂×D₄×C₂²⋊C₄	1	2	yes	—
661	C₂×C₄	C₂×#2410	1	2	yes	—
662	C₂×C₄	C₂×#2405	1	1	yes	characteristic
663	C₂×C₄	C₂×#2405	1	1	yes	characteristic
664	C₂×C₄	C₂²×B(4,𝔽₂)	1	2	yes	—
665	C₂×C₄	C₂²×#458	1	2	yes	—
666	C₂²	#359552	1	4	yes	—
667	C₂²	#359576	1	4	yes	—
668	C₂²	C₂×#13867	1	1	yes	characteristic
669	C₂²	C₂×#20925	1	1	yes	characteristic
670	C₂²	#6371420	1	1	yes	characteristic
671	C₂²	C₂²⋊C₄×AGL(1,ℤ/8)	1	4	yes	—
672	C₂²	#6437510	1	1	yes	characteristic
673	C₂²	#6437510	1	1	yes	characteristic
674	C₂²	#6437511	1	1	yes	characteristic
675	C₂²	#6437511	1	1	yes	characteristic
676	C₂²	C₂×#23882	1	1	yes	characteristic
677	C₂²	C₂×#23883	1	1	yes	characteristic
678	C₂²	C₂×#23900	1	1	yes	characteristic
679	C₂²	C₂×#23901	1	1	yes	characteristic
680	C₂²	#6437680	1	4	yes	—
681	C₄	#359552	1	4	yes	—
682	C₄	C₂²×#1790	1	2	yes	—
683	C₄	C₂×#24056	1	2	yes	—
684	C₂	#72214295	1	1	yes	characteristic
685	C₂	C₂×#359576	1	1	yes	characteristic
686	C₂	#72240211	1	1	yes	characteristic
687	C₂	C₂×#359552	1	1	yes	characteristic
688	C₂	#72302221	1	1	yes	characteristic
689	C₂	#72310739	1	1	yes	characteristic
690	C₂	#72310936	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³	C₂×#2403
commutator	C₂³×C₄	C₂⁴×C₄
Frattini, cosocle	C₂⁴×C₄	C₂⁵
prime radical	C₂×#10577301	C₂
LCS	G ▷ C₂³×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³ ◁ C₂⁵×C₄ ◁ G
LECS	G ▷ C₂⁴×C₄ ▷ C₂² ▷ C₁

Complements

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

N	H ≅ G/N	type
1. #72310959	C₂	semidirect
2. #72310956	C₂	semidirect
3. C₂×D₄×#386	C₂	semidirect
4. #72278692	C₂	semidirect
5. #72278681	C₂	semidirect
6. #72278500	C₂	semidirect
7. #72264018	C₂	semidirect
8. #72240594	C₂	semidirect
9. #72240377	C₂	semidirect
10. #72240338	C₂	semidirect
11. #72235625	C₂	semidirect
13. C₂×#198404	C₂	semidirect
14. C₂×#185643	C₂	semidirect
17. C₂⁴×C₄×D₄	C₂²	semidirect
18. #10577301	C₄	semidirect
25. C₂²×D₄×C₂²⋊C₄	C₂²	semidirect
26. C₂×#21420	C₂²	semidirect
27. C₂×#20909	C₂²	semidirect
29. C₂×#20598	C₂²	semidirect
30. C₂×#17592	C₂²	semidirect
31. C₂×#17577	C₂²	semidirect
33. #607597	C₂²	semidirect
34. C₂×#14698	C₂²	semidirect
36. D₄×#386	C₂²	semidirect
37. C₂×#14137	C₂²	semidirect
40. #392632	C₂²	semidirect
41. #392629	C₂²	semidirect
42. #363218	C₂²	semidirect
43. #362751	C₂²	semidirect
44. #361664	C₂²	semidirect
45. #353392	C₂²	semidirect
46. #353286	C₂²	semidirect
47. C₂×#9259	C₂²	semidirect
48. C₂×#9255	C₂²	semidirect
49. #185964	C₂²	semidirect
50. #185961	C₂²	semidirect
51. #185958	C₂²	semidirect
53. C₂×#8375	C₂²	semidirect
54. C₂×#7983	C₂²	semidirect
55. C₂×#7929	C₂²	semidirect
56. #114964	C₂²	semidirect
57. #114963	C₂²	semidirect
58. #111445	C₂²	semidirect
59. #111444	C₂²	semidirect
60. #108187	C₂²	semidirect
61. #108186	C₂²	semidirect
62. #106315	C₂²	semidirect
63. #106314	C₂²	semidirect
67. #62773	C₂×C₄	semidirect
86. #61571	C₂×C₄	semidirect
87. #61560	C₂×C₄	semidirect
88. #61559	C₂×C₄	semidirect
89. #60750	C₂×C₄	semidirect
98. #60230	C₂×C₄	semidirect
110. C₂×#1996	C₂³	semidirect
111. C₂×#1964	C₂³	semidirect
112. C₂×#1874	C₂³	semidirect
113. C₂×#1872	C₂³	semidirect
117. C₂×#1520	C₂³	semidirect
119. C₂×#1519	C₂³	semidirect
122. #14702	C₂³	semidirect
124. #14698	C₂³	semidirect
138. #10730	C₂³	semidirect
139. #10712	C₂³	semidirect
140. C₂×#1289	C₂³	semidirect
141. C₂×#1282	C₂³	semidirect
143. C₂⁴×D₄	C₂²⋊C₄	semidirect
161. C₂²×AGL(1,ℤ/8)	C₂²⋊C₄	semidirect
165. #3505	C₂²×C₄	semidirect
166. #3501	C₂²×C₄	semidirect
167. #3496	C₂²×C₄	semidirect
168. C₂×D₄²	C₂²⋊C₄	semidirect
169. C₂×D₄²	C₂²⋊C₄	semidirect
174. C₂²×#127	C₂²⋊C₄	semidirect
181. C₂²×#121	C₂²⋊C₄	semidirect
190. C₂²×C₄×D₄	C₂²⋊C₄	semidirect
218. #3187	C₂²×C₄	semidirect
219. #3186	C₂²×C₄	semidirect
220. C₂×#450	C₂²⋊C₄	semidirect
223. C₂×#447	C₂²⋊C₄	semidirect
226. #2973	C₂²×C₄	semidirect
227. #2972	C₂²×C₄	semidirect
228. C₂×#418	C₂²⋊C₄	semidirect
256. C₂²×#41	C₂×C₂²⋊C₄	semidirect
317. C₂²×SD₁₆	C₂×C₂²⋊C₄	semidirect
318. C₂²×D₈	C₂×C₂²⋊C₄	semidirect
319. C₂²×M₁₆	C₂×C₂²⋊C₄	semidirect
323. C₂×C₂²⋊Q₈	C₂×C₂²⋊C₄	semidirect
329. C₂×#121	C₂×C₂²⋊C₄	semidirect
356. C₂×#117	C₂×C₂²⋊C₄	semidirect
388. C₂×#102	C₂×C₂²⋊C₄	semidirect
389. C₂×#102	C₂×C₂²⋊C₄	semidirect
390. C₂×C₂²⋊C₈	C₂×C₂²⋊C₄	semidirect
393. #386	AGL(1,ℤ/8)	semidirect
406. C₂²×Q₈	C₂²×C₂²⋊C₄	semidirect
420. C₂²×D₄	C₂²×C₂²⋊C₄	semidirect
494. C₂³×C₄	C₂×AGL(1,ℤ/8)	semidirect
505. C₂²×C₈	C₂²×C₂²⋊C₄	semidirect
509. C₂×C₄⋊C₄	C₂²×C₂²⋊C₄	semidirect
510. C₂×C₄⋊C₄	C₂²×C₂²⋊C₄	semidirect
527. C₂×C₂²⋊C₄	C₂×AGL(1,ℤ/8)	semidirect
558. C₂×D₄	#1790	semidirect
627. C₂³	#20925	semidirect
654. C₂×C₄	#20925	semidirect

Maximal subgroups

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

subgroup	index
#72310959	2
#72310956	2
C₂×D₄×#386	2
#72278692	2
#72278681	2
#72278500	2
#72264018	2
#72240594	2
#72240377	2
#72240338	2
#72235625	2
C₂×#10577301	2
C₂×#198404	2
C₂×#185643	2