Subgroups — #72306331

Order 2048.

At least 8007 conjugacy classes of subgroups; only the 1214 normal subgroups are shown.

The subgroup lattice has 662 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#72306326	C₂	1	4	yes	maximal, complemented
2	#72306322	C₂	1	1	yes	maximal, characteristic, complemented
3	#72306317	C₂	1	4	yes	maximal, complemented
4	#72306314	C₂	1	2	yes	maximal, complemented
5	#72306312	C₂	1	2	yes	maximal, complemented
6	#72306308	C₂	1	4	yes	maximal, complemented
7	#72306305	C₂	1	4	yes	maximal, complemented
8	#72306297	C₂	1	4	yes	maximal, complemented
9	#72306293	C₂	1	1	yes	maximal, characteristic
10	#72306291	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×#152674	C₂	1	4	yes	maximal, complemented
12	#10586091	C₄	1	1	yes	characteristic, complemented
13	C₂×#62812	C₂²	1	1	yes	characteristic
14	C₂×#60391	C₄	1	1	yes	characteristic, complemented
15	C₂×#60390	C₂²	1	1	yes	characteristic
16	C₂×#33361	C₂²	1	2	yes	complemented
17	#6437459	C₄	1	2	yes	complemented
18	#6437459	C₂²	1	2	yes	—
19	#6437458	C₄	1	2	yes	complemented
20	#6437458	C₂²	1	2	yes	—
21	#6437453	C₄	1	2	yes	complemented
22	#6437452	C₂²	1	2	yes	—
23	#6437451	C₂²	1	2	yes	—
24	#6437447	C₄	1	2	yes	complemented
25	#6437447	C₂²	1	2	yes	—
26	#6437437	C₄	1	2	yes	complemented
27	C₂×#23909	C₄	1	2	yes	complemented
28	C₂×#23909	C₂²	1	2	yes	—
29	#6371458	C₂²	1	1	yes	characteristic
30	#6371457	C₄	1	1	yes	characteristic, complemented
31	#6370706	C₄	1	1	yes	characteristic, complemented
32	C₂×#17675	C₂²	1	2	yes	complemented
33	C₂×#13569	C₂²	1	8	yes	complemented
34	#493433	C₂²	1	2	yes	—
35	#493432	C₂²	1	2	yes	complemented
36	#493430	C₂²	1	2	yes	complemented
37	#493374	C₂²	1	2	yes	complemented
38	#493371	C₂²	1	2	yes	complemented
39	C₂×#12695	C₂²	1	2	yes	complemented
40	#187843	C₂²	1	2	yes	—
41	#187843	C₂²	1	2	yes	complemented
42	#187829	C₂²	1	2	yes	complemented
43	#187824	C₂²	1	2	yes	complemented
44	#187819	C₂²	1	2	yes	complemented
45	#187819	C₂²	1	2	yes	complemented
46	#152711	C₂²	1	16	yes	complemented
47	#152710	C₂²	1	16	yes	complemented
48	#152674	C₂²	1	16	yes	complemented
49	#152674	C₂²	1	16	yes	complemented
50	#152319	C₂²	1	8	yes	complemented
51	#152318	C₂²	1	8	yes	complemented
52	#152022	C₂²	1	8	yes	complemented
53	#152021	C₂²	1	8	yes	complemented
54	C₂×#7481	C₂²	1	8	yes	complemented
55	C₂×2₋¹⁺⁶	C₂×C₄	1	1	yes	characteristic, complemented
56	C₂²×#585	C₂×C₄	1	1	yes	characteristic
57	C₂²×#585	D₄	1	1	yes	characteristic
58	#62852	C₂×C₄	1	2	yes	complemented
59	#62848	C₂×C₄	1	2	yes	—
60	#62848	C₂×C₄	1	2	yes	complemented
61	#62811	C₂×C₄	1	2	yes	complemented
62	C₂×#3500	C₂×C₄	1	1	yes	characteristic
63	C₂×#3500	C₂×C₄	1	1	yes	characteristic
64	C₂×#3500	D₄	1	1	yes	characteristic
65	C₂×#3500	D₄	1	1	yes	characteristic
66	C₂×#3500	D₄	1	1	yes	characteristic
67	C₂×#3500	D₄	1	1	yes	characteristic
68	C₂×#3500	C₂³	1	1	yes	characteristic
69	C₂×#3500	C₂³	1	1	yes	characteristic
70	C₂×#3499	C₂×C₄	1	1	yes	characteristic
71	C₂×#3499	C₂×C₄	1	1	yes	characteristic
72	C₂×#3499	D₄	1	1	yes	characteristic
73	C₂×#3499	C₂³	1	1	yes	characteristic
74	C₂×#3498	D₄	1	1	yes	characteristic
75	C₂×#3498	D₄	1	1	yes	characteristic
76	C₂×#3498	D₄	1	1	yes	characteristic
77	C₂×#3498	C₂³	1	1	yes	characteristic
78	C₂×#3487	C₂×C₄	1	2	yes	complemented
79	C₂×#3487	C₂×C₄	1	2	yes	complemented
80	C₂×#3449	C₂×C₄	1	1	yes	characteristic
81	C₂×#3449	D₄	1	1	yes	characteristic
82	C₂×#3449	D₄	1	1	yes	characteristic
83	C₂×#3449	D₄	1	1	yes	characteristic
84	C₂×#3449	C₂³	1	1	yes	characteristic
85	C₂×#3449	C₂³	1	1	yes	characteristic
86	C₂²×#532	C₂×C₄	1	1	yes	characteristic
87	C₂²×#532	C₂×C₄	1	1	yes	characteristic
88	C₂²×#532	D₄	1	1	yes	characteristic
89	C₂²×#532	D₄	1	1	yes	characteristic
90	C₂²×#532	D₄	1	1	yes	characteristic
91	C₂²×#532	C₂³	1	1	yes	characteristic
92	#62653	C₂×C₄	1	1	yes	characteristic, complemented
93	C₂²×C₄×#41	D₄	1	1	yes	characteristic
94	C₂×#3022	C₂×C₄	1	2	yes	complemented
95	C₂×#3021	C₂³	1	2	yes	—
96	C₂×#3020	C₂×C₄	1	2	yes	—
97	C₂×#3020	C₂×C₄	1	2	yes	complemented
98	C₂×#3020	C₂×C₄	1	2	yes	complemented
99	C₂×#3020	C₂³	1	2	yes	—
100	C₂×#3018	C₂×C₄	1	2	yes	complemented
101	C₂×#3018	C₂×C₄	1	2	yes	complemented
102	C₂²×#456	C₂×C₄	1	2	yes	complemented
103	C₂²×#456	C₂×C₄	1	2	yes	complemented
104	C₂²×#454	C₂×C₄	1	2	yes	complemented
105	C₂²×#454	C₂³	1	2	yes	—
106	C₂×#2889	C₂×C₄	1	1	yes	characteristic, complemented
107	C₂×#2889	C₂×C₄	1	1	yes	characteristic, complemented
108	C₂×#2129	C₂³	1	4	yes	—
109	C₂×#2127	C₂³	1	4	yes	—
110	C₂²×#354	C₂³	1	4	yes	—
111	#23917	C₂×C₄	1	4	yes	complemented
112	#23917	C₂³	1	4	yes	—
113	#23916	C₂×C₄	1	4	yes	complemented
114	#23916	C₂×C₄	1	4	yes	complemented
115	#23915	C₂×C₄	1	4	yes	complemented
116	#23915	C₂³	1	4	yes	—
117	#23911	C₂×C₄	1	4	yes	complemented
118	#23910	C₂×C₄	1	4	yes	—
119	#23909	C₂×C₄	1	4	yes	—
120	#23909	C₂×C₄	1	4	yes	complemented
121	#23909	C₂×C₄	1	4	yes	complemented
122	#23909	C₂×C₄	1	4	yes	complemented
123	#23909	C₂×C₄	1	4	yes	complemented
124	#23909	C₂×C₄	1	4	yes	complemented
125	#23909	C₂³	1	4	yes	—
126	#23909	C₂³	1	4	yes	—
127	#20956	C₂³	1	2	yes	—
128	#20955	C₂×C₄	1	2	yes	complemented
129	#20954	C₂×C₄	1	2	yes	—
130	#20954	C₂×C₄	1	2	yes	complemented
131	#20954	C₂×C₄	1	2	yes	complemented
132	#20954	C₂³	1	2	yes	—
133	#20952	C₂×C₄	1	2	yes	complemented
134	#20952	C₂×C₄	1	2	yes	complemented
135	C₂×#1888	C₂×C₄	1	2	yes	complemented
136	C₂×#1888	C₂³	1	2	yes	—
137	C₂×#1886	C₂×C₄	1	2	yes	complemented
138	C₂×#1886	C₂×C₄	1	2	yes	complemented
139	#20593	C₂×C₄	1	2	yes	—
140	#20593	C₂×C₄	1	2	yes	complemented
141	#20592	C₂×C₄	1	2	yes	complemented
142	#20591	C₂×C₄	1	2	yes	complemented
143	C₂×#1785	C₂×C₄	1	2	yes	complemented
144	C₂×#1785	C₂×C₄	1	2	yes	complemented
145	#17675	C₂³	1	4	yes	—
146	#17675	C₂³	1	4	yes	—
147	C₂×#1533	C₂³	1	4	yes	—
148	#13569	C₂³	1	32	yes	—
149	#12698	C₂³	1	4	yes	—
150	#12696	C₂³	1	4	yes	—
151	#12695	C₂³	1	4	yes	—
152	#12695	C₂³	1	4	yes	—
153	#8524	C₂³	1	4	yes	—
154	#8524	C₂³	1	4	yes	—
155	#8522	C₂³	1	4	yes	—
156	#8522	C₂³	1	4	yes	—
157	#7481	C₂³	1	32	yes	—
158	C₂×#585	C₂²×C₄	1	2	yes	—
159	C₂²×2₋¹⁺⁴	C₂²⋊C₄	1	1	yes	characteristic
160	C₂²×2₋¹⁺⁴	C₂²⋊C₄	1	1	yes	characteristic
161	C₂²×2₋¹⁺⁴	C₂²⋊C₄	1	1	yes	characteristic
162	C₂²×2₋¹⁺⁴	C₂²⋊C₄	1	1	yes	characteristic
163	C₂²×2₋¹⁺⁴	C₂²×C₄	1	1	yes	characteristic
164	C₂²×2₋¹⁺⁴	C₂²×C₄	1	1	yes	characteristic
165	C₂²×2₋¹⁺⁴	C₂²×C₄	1	1	yes	characteristic
166	C₂²×2₋¹⁺⁴	C₂²×C₄	1	2	yes	—
167	C₂²×2₋¹⁺⁴	C₂²×C₄	1	2	yes	—
168	C₂²×2₋¹⁺⁴	C₂×D₄	1	1	yes	characteristic
169	C₂²×H(5,𝔽₂)	C₂²⋊C₄	1	1	yes	characteristic
170	C₂²×H(5,𝔽₂)	C₂²⋊C₄	1	1	yes	characteristic
171	C₂²×H(5,𝔽₂)	C₂²⋊C₄	1	1	yes	characteristic
172	C₂²×H(5,𝔽₂)	C₂²⋊C₄	1	1	yes	characteristic
173	C₂²×H(5,𝔽₂)	C₂²×C₄	1	1	yes	characteristic
174	C₂²×H(5,𝔽₂)	C₂×D₄	1	1	yes	characteristic
175	C₂²×H(5,𝔽₂)	C₂×D₄	1	1	yes	characteristic
176	C₂²×H(5,𝔽₂)	C₂×D₄	1	1	yes	characteristic
177	C₂³×#41	C₂²⋊C₄	1	1	yes	characteristic
178	C₂³×#41	C₂²⋊C₄	1	1	yes	characteristic
179	C₂³×#41	C₂²⋊C₄	1	1	yes	characteristic
180	C₂³×#41	C₂²⋊C₄	1	1	yes	characteristic
181	C₂³×#41	C₂²⋊C₄	1	1	yes	characteristic
182	C₂³×#41	C₂²⋊C₄	1	1	yes	characteristic
183	C₂³×#41	C₂²⋊C₄	1	1	yes	characteristic
184	C₂³×#41	C₂²×C₄	1	1	yes	characteristic
185	C₂³×#41	C₂²×C₄	1	1	yes	characteristic
186	C₂³×#41	C₂²×C₄	1	1	yes	characteristic
187	C₂³×#41	C₂×D₄	1	1	yes	characteristic
188	C₂³×#41	C₂×D₄	1	1	yes	characteristic
189	C₂³×#41	C₂×D₄	1	1	yes	characteristic
190	#3487	C₂²×C₄	1	4	yes	—
191	#3487	C₂²×C₄	1	4	yes	—
192	#3487	C₂²×C₄	1	4	yes	—
193	#3486	C₂²×C₄	1	4	yes	—
194	C₂×#536	C₂²⋊C₄	1	1	yes	characteristic
195	C₂×#536	C₂²⋊C₄	1	1	yes	characteristic
196	C₂×#536	C₂²⋊C₄	1	1	yes	characteristic
197	C₂×#536	C₂²⋊C₄	1	1	yes	characteristic
198	C₂×#536	C₂²⋊C₄	1	1	yes	characteristic
199	C₂×#536	C₂²⋊C₄	1	1	yes	characteristic
200	C₂×#536	C₂²⋊C₄	1	1	yes	characteristic
201	C₂×#536	C₂²⋊C₄	1	1	yes	characteristic
202	C₂×#536	C₂²×C₄	1	1	yes	characteristic
203	C₂×#536	C₂²×C₄	1	1	yes	characteristic
204	C₂×#536	C₂²×C₄	1	1	yes	characteristic
205	C₂×#536	C₂²×C₄	1	1	yes	characteristic
206	C₂×#536	C₂²×C₄	1	1	yes	characteristic
207	C₂×#536	C₂²×C₄	1	1	yes	characteristic
208	C₂×#536	C₂²×C₄	1	1	yes	characteristic
209	C₂×#536	C₂×D₄	1	1	yes	characteristic
210	C₂×#536	C₂×D₄	1	1	yes	characteristic
211	C₂×#536	C₂×D₄	1	1	yes	characteristic
212	C₂×#536	C₂×D₄	1	1	yes	characteristic
213	C₂×#536	C₂×D₄	1	1	yes	characteristic
214	C₂×#536	C₂×D₄	1	1	yes	characteristic
215	C₂×#536	C₂×D₄	1	1	yes	characteristic
216	C₂×#536	C₂⁴	1	1	yes	characteristic
217	C₂×#536	C₂⁴	1	1	yes	characteristic
218	C₂×#535	C₂²⋊C₄	1	1	yes	characteristic
219	C₂×#535	C₂²⋊C₄	1	1	yes	characteristic
220	C₂×#535	C₂²⋊C₄	1	1	yes	characteristic
221	C₂×#535	C₂²⋊C₄	1	1	yes	characteristic
222	C₂×#535	C₂²⋊C₄	1	1	yes	characteristic
223	C₂×#535	C₂²⋊C₄	1	1	yes	characteristic
224	C₂×#535	C₂²⋊C₄	1	1	yes	characteristic
225	C₂×#535	C₂²⋊C₄	1	1	yes	characteristic
226	C₂×#535	C₂²×C₄	1	1	yes	characteristic
227	C₂×#535	C₂×D₄	1	1	yes	characteristic
228	C₂×#535	C₂×D₄	1	1	yes	characteristic
229	C₂×#535	C₂×D₄	1	1	yes	characteristic
230	C₂×#535	C₂×D₄	1	1	yes	characteristic
231	C₂×#535	C₂×D₄	1	1	yes	characteristic
232	C₂×#535	C₂×D₄	1	1	yes	characteristic
233	C₂×#535	C₂×D₄	1	1	yes	characteristic
234	C₂×#535	C₂×D₄	1	1	yes	characteristic
235	C₂×#535	C₂×D₄	1	1	yes	characteristic
236	C₂×#535	C₂×D₄	1	1	yes	characteristic
237	C₂×#535	C₂×D₄	1	1	yes	characteristic
238	C₂×#535	C₂×D₄	1	1	yes	characteristic
239	C₂×#535	C₂×D₄	1	1	yes	characteristic
240	C₂×#535	C₂⁴	1	1	yes	characteristic
241	C₂×#535	C₂⁴	1	1	yes	characteristic
242	C₂×#532	C₂²⋊C₄	1	1	yes	characteristic
243	C₂×#532	C₂²⋊C₄	1	1	yes	characteristic
244	C₂×#532	C₂²⋊C₄	1	1	yes	characteristic
245	C₂×#532	C₂²⋊C₄	1	1	yes	characteristic
246	C₂×#532	C₂²⋊C₄	1	1	yes	characteristic
247	C₂×#532	C₂²⋊C₄	1	1	yes	characteristic
248	C₂×#532	C₂²⋊C₄	1	1	yes	characteristic
249	C₂×#532	C₂²⋊C₄	1	1	yes	characteristic
250	C₂×#532	C₂²⋊C₄	1	1	yes	characteristic
251	C₂×#532	C₂²⋊C₄	1	1	yes	characteristic
252	C₂×#532	C₂²⋊C₄	1	1	yes	characteristic
253	C₂×#532	C₂²⋊C₄	1	1	yes	characteristic
254	C₂×#532	C₂²⋊C₄	1	1	yes	characteristic
255	C₂×#532	C₂²⋊C₄	1	1	yes	characteristic
256	C₂×#532	C₂²⋊C₄	1	1	yes	characteristic
257	C₂×#532	C₂²⋊C₄	1	1	yes	characteristic
258	C₂×#532	C₂²×C₄	1	1	yes	characteristic
259	C₂×#532	C₂²×C₄	1	1	yes	characteristic
260	C₂×#532	C₂²×C₄	1	1	yes	characteristic
261	C₂×#532	C₂²×C₄	1	1	yes	characteristic
262	C₂×#532	C₂²×C₄	1	1	yes	characteristic
263	C₂×#532	C₂²×C₄	1	1	yes	characteristic
264	C₂×#532	C₂²×C₄	1	1	yes	characteristic
265	C₂×#532	C₂²×C₄	1	1	yes	characteristic
266	C₂×#532	C₂×D₄	1	1	yes	characteristic
267	C₂×#532	C₂×D₄	1	1	yes	characteristic
268	C₂×#532	C₂×D₄	1	1	yes	characteristic
269	C₂×#532	C₂×D₄	1	1	yes	characteristic
270	C₂×#532	C₂×D₄	1	1	yes	characteristic
271	C₂×#532	C₂×D₄	1	1	yes	characteristic
272	C₂×#532	C₂×D₄	1	1	yes	characteristic
273	C₂×#532	C₂×D₄	1	1	yes	characteristic
274	C₂×#532	C₂×D₄	1	1	yes	characteristic
275	C₂×#532	C₂×D₄	1	1	yes	characteristic
276	C₂×#532	C₂×D₄	1	1	yes	characteristic
277	C₂×#532	C₂×D₄	1	1	yes	characteristic
278	C₂×#532	C₂×D₄	1	1	yes	characteristic
279	C₂×#532	C₂×D₄	1	1	yes	characteristic
280	C₂×#532	C₂⁴	1	1	yes	characteristic
281	C₂×#532	C₂⁴	1	1	yes	characteristic
282	C₂²×C₄⋊Q₈	C₂²⋊C₄	1	1	yes	characteristic
283	C₂²×C₄⋊Q₈	C₂²⋊C₄	1	1	yes	characteristic
284	C₂²×C₄⋊Q₈	C₂²×C₄	1	1	yes	characteristic
285	C₂²×C₄⋊Q₈	C₂²×C₄	1	1	yes	characteristic
286	C₂²×C₄⋊Q₈	C₂²×C₄	1	1	yes	characteristic
287	C₂²×C₄⋊Q₈	C₂×D₄	1	1	yes	characteristic
288	C₂²×#127	C₂²⋊C₄	1	1	yes	characteristic
289	C₂²×#127	C₂²⋊C₄	1	1	yes	characteristic
290	C₂²×#127	C₂×D₄	1	1	yes	characteristic
291	C₂²×#127	C₂×D₄	1	1	yes	characteristic
292	C₂²×#127	C₂×D₄	1	1	yes	characteristic
293	C₂²×#127	C₂×D₄	1	1	yes	characteristic
294	C₂²×#124	C₂²⋊C₄	1	1	yes	characteristic
295	C₂²×#124	C₂²⋊C₄	1	1	yes	characteristic
296	C₂²×#124	C₂²⋊C₄	1	1	yes	characteristic
297	C₂²×#124	C₂²⋊C₄	1	1	yes	characteristic
298	C₂²×#124	C₂²⋊C₄	1	1	yes	characteristic
299	C₂²×#124	C₂²⋊C₄	1	1	yes	characteristic
300	C₂²×#124	C₂²×C₄	1	1	yes	characteristic
301	C₂²×#124	C₂²×C₄	1	1	yes	characteristic
302	C₂²×#124	C₂×D₄	1	1	yes	characteristic
303	C₂²×#124	C₂×D₄	1	1	yes	characteristic
304	C₂²×#124	C₂×D₄	1	1	yes	characteristic
305	C₂²×#124	C₂⁴	1	1	yes	characteristic
306	#3428	C₂²×C₄	1	2	yes	—
307	C₂×#519	C₂²×C₄	1	2	yes	—
308	C₂×#519	C₂²×C₄	1	2	yes	—
309	C₂×C₄×#41	C₂²⋊C₄	1	1	yes	characteristic
310	C₂×C₄×#41	C₂²⋊C₄	1	1	yes	characteristic
311	C₂×C₄×#41	C₂²⋊C₄	1	1	yes	characteristic
312	C₂×C₄×#41	C₂²⋊C₄	1	1	yes	characteristic
313	C₂×C₄×#41	C₂×D₄	1	1	yes	characteristic
314	C₂×C₄×#41	C₂×D₄	1	1	yes	characteristic
315	C₂×C₄×#41	C₂×D₄	1	1	yes	characteristic
316	C₂×C₄×#41	C₂×D₄	1	1	yes	characteristic
317	C₂²×#117	C₂²⋊C₄	1	1	yes	characteristic
318	C₂²×#117	C₂×D₄	1	1	yes	characteristic
319	C₂²×#117	C₂×D₄	1	1	yes	characteristic
320	C₂³×C₄²	C₂²⋊C₄	1	1	yes	characteristic
321	C₂³×C₄²	C₂²⋊C₄	1	1	yes	characteristic
322	C₂³×C₄²	C₂×D₄	1	1	yes	characteristic
323	C₂×#456	C₂²×C₄	1	4	yes	—
324	C₂×#456	C₂²×C₄	1	4	yes	—
325	C₂×#456	C₂²×C₄	1	4	yes	—
326	C₂×#456	C₂²×C₄	1	4	yes	—
327	C₂×#454	C₂²×C₄	1	4	yes	—
328	C₂×#454	C₂²×C₄	1	4	yes	—
329	C₂×#454	C₂²×C₄	1	4	yes	—
330	C₂×#454	C₂⁴	1	4	yes	—
331	C₂×#413	C₂²×C₄	1	2	yes	—
332	C₂×#413	C₂²×C₄	1	2	yes	—
333	C₂²×#101	C₂²×C₄	1	2	yes	—
334	C₂²×#101	C₂²×C₄	1	2	yes	—
335	C₂²×#101	C₂²×C₄	1	2	yes	—
336	C₂²×#101	C₂²×C₄	1	2	yes	—
337	C₂×#354	C₂⁴	1	8	yes	—
338	#1888	C₂²×C₄	1	4	yes	—
339	#1888	C₂²×C₄	1	4	yes	—
340	#1888	C₂²×C₄	1	4	yes	—
341	#1888	C₂⁴	1	4	yes	—
342	#1886	C₂²×C₄	1	4	yes	—
343	#1886	C₂²×C₄	1	4	yes	—
344	#1886	C₂²×C₄	1	4	yes	—
345	#1886	C₂²×C₄	1	4	yes	—
346	#1785	C₂²×C₄	1	4	yes	—
347	#1785	C₂²×C₄	1	4	yes	—
348	#1785	C₂²×C₄	1	4	yes	—
349	#1784	C₂²×C₄	1	4	yes	—
350	#1533	C₂⁴	1	8	yes	—
351	C₂×2₋¹⁺⁴	C₂³×C₄	1	4	yes	—
352	C₂²×#41	#99	1	1	yes	characteristic
353	C₂²×#41	#99	1	1	yes	characteristic
354	C₂²×#41	#99	1	1	yes	characteristic
355	C₂²×#41	#99	1	1	yes	characteristic
356	C₂²×#41	C₂×C₂²⋊C₄	1	1	yes	characteristic
357	C₂²×#41	C₂×C₂²⋊C₄	1	1	yes	characteristic
358	C₂²×#41	C₂×C₂²⋊C₄	1	1	yes	characteristic
359	C₂²×#41	C₂×C₂²⋊C₄	1	1	yes	characteristic
360	C₂²×#41	C₂×C₂²⋊C₄	1	1	yes	characteristic
361	C₂²×#41	C₂×C₂²⋊C₄	1	1	yes	characteristic
362	C₂²×#41	C₂×C₂²⋊C₄	1	1	yes	characteristic
363	C₂²×#41	C₂×C₂²⋊C₄	1	1	yes	characteristic
364	C₂²×#41	C₂×C₂²⋊C₄	1	1	yes	characteristic
365	C₂²×#41	C₂×C₂²⋊C₄	1	1	yes	characteristic
366	C₂²×#41	C₂×C₂²⋊C₄	1	1	yes	characteristic
367	C₂²×#41	C₂×C₂²⋊C₄	1	1	yes	characteristic
368	C₂²×#41	C₂×C₂²⋊C₄	1	1	yes	characteristic
369	C₂²×#41	C₂×C₂²⋊C₄	1	1	yes	characteristic
370	C₂²×#41	C₂×C₂²⋊C₄	1	1	yes	characteristic
371	C₂²×#41	C₂×C₂²⋊C₄	1	1	yes	characteristic
372	C₂²×#41	C₂×C₂²⋊C₄	1	1	yes	characteristic
373	C₂²×#41	C₂×C₂²⋊C₄	1	1	yes	characteristic
374	C₂²×#41	C₂×C₂²⋊C₄	1	1	yes	characteristic
375	C₂²×#41	C₂×C₂²⋊C₄	1	1	yes	characteristic
376	C₂²×#41	C₂×C₂²⋊C₄	1	1	yes	characteristic
377	C₂²×#41	C₂×C₂²⋊C₄	1	1	yes	characteristic
378	C₂²×#41	C₂×C₂²⋊C₄	1	1	yes	characteristic
379	C₂²×#41	C₂×C₂²⋊C₄	1	1	yes	characteristic
380	C₂²×#41	C₂×C₂²⋊C₄	1	1	yes	characteristic
381	C₂²×#41	C₂×C₂²⋊C₄	1	1	yes	characteristic
382	C₂²×#41	C₂×C₂²⋊C₄	1	1	yes	characteristic
383	C₂²×#41	C₂×C₂²⋊C₄	1	1	yes	characteristic
384	C₂²×#41	C₂³×C₄	1	1	yes	characteristic
385	C₂²×#41	C₂³×C₄	1	1	yes	characteristic
386	C₂²×#41	C₂³×C₄	1	1	yes	characteristic
387	C₂²×#41	C₂³×C₄	1	1	yes	characteristic
388	C₂²×#41	C₂²×D₄	1	1	yes	characteristic
389	C₂²×#41	C₂²×D₄	1	1	yes	characteristic
390	C₂²×#41	C₂²×D₄	1	1	yes	characteristic
391	C₂²×#41	C₂²×D₄	1	1	yes	characteristic
392	C₂³×Q₈	#99	1	1	yes	characteristic
393	C₂³×Q₈	C₂×C₂²⋊C₄	1	1	yes	characteristic
394	C₂³×Q₈	C₂×C₂²⋊C₄	1	1	yes	characteristic
395	C₂³×Q₈	C₂×C₂²⋊C₄	1	1	yes	characteristic
396	C₂³×Q₈	C₂×C₂²⋊C₄	1	1	yes	characteristic
397	C₂³×Q₈	C₂×C₂²⋊C₄	1	1	yes	characteristic
398	C₂³×Q₈	C₂×C₂²⋊C₄	1	1	yes	characteristic
399	C₂³×Q₈	C₂×C₂²⋊C₄	1	1	yes	characteristic
400	C₂³×Q₈	C₂×C₂²⋊C₄	1	1	yes	characteristic
401	C₂³×Q₈	C₂×C₂²⋊C₄	1	1	yes	characteristic
402	C₂³×Q₈	C₂³×C₄	1	1	yes	characteristic
403	C₂³×Q₈	C₂³×C₄	1	1	yes	characteristic
404	C₂³×Q₈	C₂³×C₄	1	1	yes	characteristic
405	C₂³×D₄	#99	1	1	yes	characteristic
406	C₂³×D₄	#99	1	1	yes	characteristic
407	C₂³×D₄	#99	1	1	yes	characteristic
408	C₂³×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
409	C₂³×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
410	C₂³×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
411	C₂³×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
412	C₂³×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
413	C₂³×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
414	C₂³×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
415	C₂³×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
416	C₂³×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
417	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
418	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
419	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
420	C₂⁴×C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
421	C₂⁴×C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
422	C₂⁴×C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
423	#532	#99	1	4	yes	—
424	#532	#99	1	4	yes	—
425	C₂×C₄⋊Q₈	C₂×C₂²⋊C₄	1	1	yes	characteristic
426	C₂×C₄⋊Q₈	C₂×C₂²⋊C₄	1	1	yes	characteristic
427	C₂×C₄⋊Q₈	C₂×C₂²⋊C₄	1	1	yes	characteristic
428	C₂×C₄⋊Q₈	C₂×C₂²⋊C₄	1	1	yes	characteristic
429	C₂×C₄⋊Q₈	C₂×C₂²⋊C₄	1	1	yes	characteristic
430	C₂×C₄⋊Q₈	C₂×C₂²⋊C₄	1	1	yes	characteristic
431	C₂×C₄⋊Q₈	C₂×C₂²⋊C₄	1	1	yes	characteristic
432	C₂×C₄⋊Q₈	C₂×C₂²⋊C₄	1	1	yes	characteristic
433	C₂×C₄⋊Q₈	C₂×C₂²⋊C₄	1	1	yes	characteristic
434	C₂×C₄⋊Q₈	C₂×C₂²⋊C₄	1	1	yes	characteristic
435	C₂×C₄⋊Q₈	C₂³×C₄	1	1	yes	characteristic
436	C₂×C₄⋊Q₈	C₂³×C₄	1	1	yes	characteristic
437	C₂×C₄⋊Q₈	C₂³×C₄	1	1	yes	characteristic
438	C₂×C₄⋊Q₈	C₂³×C₄	1	1	yes	characteristic
439	C₂×C₄⋊Q₈	C₂²×D₄	1	1	yes	characteristic
440	C₂×C₄⋊Q₈	C₂²×D₄	1	1	yes	characteristic
441	C₂×#127	C₂×C₂²⋊C₄	1	1	yes	characteristic
442	C₂×#127	C₂×C₂²⋊C₄	1	1	yes	characteristic
443	C₂×#127	C₂×C₂²⋊C₄	1	1	yes	characteristic
444	C₂×#127	C₂×C₂²⋊C₄	1	1	yes	characteristic
445	C₂×#127	C₂×C₂²⋊C₄	1	1	yes	characteristic
446	C₂×#127	C₂×C₂²⋊C₄	1	1	yes	characteristic
447	C₂×#127	C₂×C₂²⋊C₄	1	1	yes	characteristic
448	C₂×#127	C₂×C₂²⋊C₄	1	1	yes	characteristic
449	C₂×#127	C₂×C₂²⋊C₄	1	1	yes	characteristic
450	C₂×#127	C₂×C₂²⋊C₄	1	1	yes	characteristic
451	C₂×#127	C₂²×D₄	1	1	yes	characteristic
452	C₂×#127	C₂²×D₄	1	1	yes	characteristic
453	C₂×#127	C₂²×D₄	1	1	yes	characteristic
454	C₂×#127	C₂²×D₄	1	1	yes	characteristic
455	C₂×#127	C₂²×D₄	1	1	yes	characteristic
456	C₂×#127	C₂²×D₄	1	1	yes	characteristic
457	C₂×#124	C₂×C₂²⋊C₄	1	1	yes	characteristic
458	C₂×#124	C₂×C₂²⋊C₄	1	1	yes	characteristic
459	C₂×#124	C₂×C₂²⋊C₄	1	1	yes	characteristic
460	C₂×#124	C₂×C₂²⋊C₄	1	1	yes	characteristic
461	C₂×#124	C₂×C₂²⋊C₄	1	1	yes	characteristic
462	C₂×#124	C₂×C₂²⋊C₄	1	1	yes	characteristic
463	C₂×#124	C₂×C₂²⋊C₄	1	1	yes	characteristic
464	C₂×#124	C₂×C₂²⋊C₄	1	1	yes	characteristic
465	C₂×#124	C₂×C₂²⋊C₄	1	1	yes	characteristic
466	C₂×#124	C₂×C₂²⋊C₄	1	1	yes	characteristic
467	C₂×#124	C₂×C₂²⋊C₄	1	1	yes	characteristic
468	C₂×#124	C₂×C₂²⋊C₄	1	1	yes	characteristic
469	C₂×#124	C₂×C₂²⋊C₄	1	1	yes	characteristic
470	C₂×#124	C₂×C₂²⋊C₄	1	1	yes	characteristic
471	C₂×#124	C₂×C₂²⋊C₄	1	1	yes	characteristic
472	C₂×#124	C₂×C₂²⋊C₄	1	1	yes	characteristic
473	C₂×#124	C₂×C₂²⋊C₄	1	1	yes	characteristic
474	C₂×#124	C₂×C₂²⋊C₄	1	1	yes	characteristic
475	C₂×#124	C₂×C₂²⋊C₄	1	1	yes	characteristic
476	C₂×#124	C₂×C₂²⋊C₄	1	1	yes	characteristic
477	C₂×#124	C₂×C₂²⋊C₄	1	1	yes	characteristic
478	C₂×#124	C₂×C₂²⋊C₄	1	1	yes	characteristic
479	C₂×#124	C₂³×C₄	1	1	yes	characteristic
480	C₂×#124	C₂³×C₄	1	1	yes	characteristic
481	C₂×#124	C₂³×C₄	1	1	yes	characteristic
482	C₂×#124	C₂²×D₄	1	1	yes	characteristic
483	C₂×#124	C₂²×D₄	1	1	yes	characteristic
484	C₂×#124	C₂²×D₄	1	1	yes	characteristic
485	C₂×#124	C₂²×D₄	1	1	yes	characteristic
486	C₂×#124	C₂²×D₄	1	1	yes	characteristic
487	C₂×#124	C₂²×D₄	1	1	yes	characteristic
488	C₂×#124	H(5,𝔽₂)	1	4	yes	—
489	C₂×#124	H(5,𝔽₂)	1	4	yes	—
490	C₂×#124	C₂⁵	1	1	yes	characteristic
491	#519	C₂³×C₄	1	4	yes	—
492	C₂×#117	C₂×C₂²⋊C₄	1	1	yes	characteristic
493	C₂×#117	C₂×C₂²⋊C₄	1	1	yes	characteristic
494	C₂×#117	C₂×C₂²⋊C₄	1	1	yes	characteristic
495	C₂×#117	C₂×C₂²⋊C₄	1	1	yes	characteristic
496	C₂×#117	C₂×C₂²⋊C₄	1	1	yes	characteristic
497	C₂×#117	C₂×C₂²⋊C₄	1	1	yes	characteristic
498	C₂×#117	C₂×C₂²⋊C₄	1	1	yes	characteristic
499	C₂×#117	C₂×C₂²⋊C₄	1	1	yes	characteristic
500	C₂×#117	C₂²×D₄	1	1	yes	characteristic
501	C₂×#117	C₂²×D₄	1	1	yes	characteristic
502	C₂×#117	C₂²×D₄	1	1	yes	characteristic
503	C₂×#117	C₂²×D₄	1	1	yes	characteristic
504	C₂²×C₄²	C₂×C₂²⋊C₄	1	1	yes	characteristic
505	C₂²×C₄²	C₂×C₂²⋊C₄	1	1	yes	characteristic
506	C₂²×C₄²	C₂×C₂²⋊C₄	1	1	yes	characteristic
507	C₂²×C₄²	C₂×C₂²⋊C₄	1	1	yes	characteristic
508	C₂²×C₄²	C₂×C₂²⋊C₄	1	1	yes	characteristic
509	C₂²×C₄²	C₂×C₂²⋊C₄	1	1	yes	characteristic
510	C₂²×C₄²	C₂×C₂²⋊C₄	1	1	yes	characteristic
511	C₂²×C₄²	C₂×C₂²⋊C₄	1	1	yes	characteristic
512	C₂²×C₄²	C₂×C₂²⋊C₄	1	1	yes	characteristic
513	C₂²×C₄²	C₂×C₂²⋊C₄	1	1	yes	characteristic
514	C₂²×C₄²	C₂×C₂²⋊C₄	1	1	yes	characteristic
515	C₂²×C₄²	C₂×C₂²⋊C₄	1	1	yes	characteristic
516	C₂²×C₄²	C₂×C₂²⋊C₄	1	1	yes	characteristic
517	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
518	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
519	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
520	C₂×#101	C₂³×C₄	1	4	yes	—
521	C₂×#101	C₂³×C₄	1	4	yes	—
522	C₂⁵	C₂×#99	1	1	yes	characteristic
523	C₂⁵	C₂×#99	1	1	yes	characteristic
524	C₂⁵	C₂×#99	1	1	yes	characteristic
525	C₂×#41	C₂×#99	1	4	yes	—
526	C₂×#41	C₂×#99	1	4	yes	—
527	C₂²×Q₈	C₂×#99	1	1	yes	characteristic
528	C₂²×Q₈	C₂×#99	1	1	yes	characteristic
529	C₂²×Q₈	C₂×#99	1	1	yes	characteristic
530	C₂²×Q₈	C₂×#99	1	1	yes	characteristic
531	C₂²×Q₈	C₂²×C₂²⋊C₄	1	1	yes	characteristic
532	C₂²×Q₈	C₂²×C₂²⋊C₄	1	1	yes	characteristic
533	C₂²×Q₈	C₂²×C₂²⋊C₄	1	1	yes	characteristic
534	C₂²×Q₈	C₂²×C₂²⋊C₄	1	1	yes	characteristic
535	C₂²×Q₈	C₂²×C₂²⋊C₄	1	1	yes	characteristic
536	C₂²×Q₈	C₂²×C₂²⋊C₄	1	1	yes	characteristic
537	C₂²×Q₈	C₂²×C₂²⋊C₄	1	1	yes	characteristic
538	C₂²×Q₈	#518	1	4	yes	—
539	C₂²×Q₈	C₂⁴×C₄	1	1	yes	characteristic
540	C₂²×D₄	AΣL(1,𝔽₁₆)	1	8	yes	—
541	C₂²×D₄	C₂×#99	1	1	yes	characteristic
542	C₂²×D₄	C₂×#99	1	1	yes	characteristic
543	C₂²×D₄	C₂×#99	1	1	yes	characteristic
544	C₂²×D₄	C₂×#99	1	1	yes	characteristic
545	C₂²×D₄	C₂×#99	1	1	yes	characteristic
546	C₂²×D₄	C₂×#99	1	1	yes	characteristic
547	C₂²×D₄	C₂×#99	1	1	yes	characteristic
548	C₂²×D₄	C₂×#99	1	1	yes	characteristic
549	C₂²×D₄	C₂×#99	1	1	yes	characteristic
550	C₂²×D₄	C₂×#99	1	1	yes	characteristic
551	C₂²×D₄	C₂×#99	1	1	yes	characteristic
552	C₂²×D₄	C₂×#99	1	1	yes	characteristic
553	C₂²×D₄	C₂²×C₂²⋊C₄	1	1	yes	characteristic
554	C₂²×D₄	C₂²×C₂²⋊C₄	1	1	yes	characteristic
555	C₂²×D₄	C₂²×C₂²⋊C₄	1	1	yes	characteristic
556	C₂²×D₄	C₂²×C₂²⋊C₄	1	1	yes	characteristic
557	C₂²×D₄	C₂²×C₂²⋊C₄	1	1	yes	characteristic
558	C₂²×D₄	C₂²×C₂²⋊C₄	1	1	yes	characteristic
559	C₂²×D₄	C₂²×C₂²⋊C₄	1	1	yes	characteristic
560	C₂²×D₄	#534	1	4	yes	—
561	C₂²×D₄	C₂³×D₄	1	1	yes	characteristic
562	C₂³×C₄	C₂×#99	1	1	yes	characteristic
563	C₂³×C₄	C₂×#99	1	1	yes	characteristic
564	C₂³×C₄	C₂×#99	1	1	yes	characteristic
565	C₂³×C₄	C₂×#99	1	1	yes	characteristic
566	C₂³×C₄	C₂×#99	1	1	yes	characteristic
567	C₂³×C₄	C₂×#99	1	1	yes	characteristic
568	C₂³×C₄	C₂×#99	1	1	yes	characteristic
569	C₂³×C₄	C₂×#99	1	1	yes	characteristic
570	C₂³×C₄	C₂×#99	1	1	yes	characteristic
571	C₂³×C₄	C₂²×C₂²⋊C₄	1	1	yes	characteristic
572	C₂³×C₄	C₂²×C₂²⋊C₄	1	1	yes	characteristic
573	C₂³×C₄	C₂²×C₂²⋊C₄	1	1	yes	characteristic
574	C₂³×C₄	C₂²×C₂²⋊C₄	1	1	yes	characteristic
575	C₂³×C₄	C₂²×C₂²⋊C₄	1	1	yes	characteristic
576	C₂³×C₄	C₂²×C₂²⋊C₄	1	1	yes	characteristic
577	C₂³×C₄	C₂²×C₂²⋊C₄	1	1	yes	characteristic
578	C₄⋊Q₈	C₂×#99	1	2	yes	—
579	C₄⋊Q₈	C₂×#99	1	2	yes	—
580	#127	C₂×#99	1	2	yes	—
581	#127	C₂×#99	1	2	yes	—
582	#124	C₂×#99	1	4	yes	—
583	#124	C₂×#99	1	4	yes	—
584	#124	#518	1	2	yes	—
585	#124	#518	1	2	yes	—
586	#124	#534	1	2	yes	—
587	#124	#534	1	2	yes	—
588	#124	#534	1	4	yes	—
589	#124	C₂×H(5,𝔽₂)	1	4	yes	—
590	C₂×C₄²	C₂×#99	1	2	yes	—
591	C₂×C₄²	C₂×#99	1	2	yes	—
592	C₂×C₄²	C₂²×C₂²⋊C₄	1	1	yes	characteristic
593	C₂×C₄²	C₂²×C₂²⋊C₄	1	1	yes	characteristic
594	C₂×C₄²	C₂²×C₂²⋊C₄	1	1	yes	characteristic
595	C₂×C₄²	C₂²×C₂²⋊C₄	1	1	yes	characteristic
596	C₂×C₄²	C₂²×C₂²⋊C₄	1	1	yes	characteristic
597	C₂×C₄²	C₂²×C₂²⋊C₄	1	1	yes	characteristic
598	C₂×C₄²	C₂²×C₂²⋊C₄	1	1	yes	characteristic
599	C₂×C₄²	#534	1	2	yes	—
600	C₂×C₄²	#534	1	2	yes	—
601	C₂×C₄²	C₂³×D₄	1	1	yes	characteristic
602	C₂⁴	C₂×AΣL(1,𝔽₁₆)	1	4	yes	—
603	C₂⁴	C₂×AΣL(1,𝔽₁₆)	1	4	yes	—
604	C₂⁴	C₂²×#99	1	1	yes	characteristic
605	C₂⁴	C₂²×#99	1	1	yes	characteristic
606	C₂⁴	C₂²×#99	1	1	yes	characteristic
607	C₂⁴	C₂²×#99	1	1	yes	characteristic
608	C₂⁴	C₂²×#99	1	1	yes	characteristic
609	C₂⁴	C₂²×#99	1	1	yes	characteristic
610	C₂⁴	C₂²×#99	1	1	yes	characteristic
611	C₂×Q₈	#2308	1	2	yes	—
612	C₂×Q₈	C₂²×#99	1	2	yes	—
613	C₂×Q₈	C₂²×#99	1	2	yes	—
614	C₂×Q₈	C₂×#518	1	2	yes	—
615	C₂×D₄	C₂×AΣL(1,𝔽₁₆)	1	4	yes	—
616	C₂×D₄	C₂×AΣL(1,𝔽₁₆)	1	4	yes	—
617	C₂×D₄	C₂×AΣL(1,𝔽₁₆)	1	4	yes	—
618	C₂×D₄	C₂×AΣL(1,𝔽₁₆)	1	4	yes	—
619	C₂×D₄	#2121	1	4	yes	—
620	C₂×D₄	#2308	1	2	yes	—
621	C₂×D₄	C₂²×#99	1	2	yes	—
622	C₂×D₄	C₂²×#99	1	2	yes	—
623	C₂×D₄	C₂×#534	1	2	yes	—
624	C₂²×C₄	C₂×AΣL(1,𝔽₁₆)	1	4	yes	—
625	C₂²×C₄	#2308	1	2	yes	—
626	C₂²×C₄	C₂²×#99	1	1	yes	characteristic
627	C₂²×C₄	C₂²×#99	1	1	yes	characteristic
628	C₂²×C₄	C₂²×#99	1	1	yes	characteristic
629	C₂²×C₄	C₂²×#99	1	1	yes	characteristic
630	C₂²×C₄	C₂²×#99	1	1	yes	characteristic
631	C₂²×C₄	C₂²×#99	1	1	yes	characteristic
632	C₂²×C₄	C₂²×#99	1	2	yes	—
633	C₂²×C₄	C₂²×#99	1	1	yes	characteristic
634	C₂²×C₄	C₂³×C₂²⋊C₄	1	1	yes	characteristic
635	C₄²	#2308	1	1	yes	characteristic
636	C₄²	#2308	1	1	yes	characteristic
637	C₄²	C₂²×#99	1	1	yes	characteristic
638	C₄²	C₂²×#99	1	1	yes	characteristic
639	C₄²	C₂²×#99	1	2	yes	—
640	C₄²	C₂×#534	1	2	yes	—
641	C₂³	#21746	1	2	yes	—
642	C₂³	C₂²×AΣL(1,𝔽₁₆)	1	2	yes	—
643	C₂³	C₂²×AΣL(1,𝔽₁₆)	1	2	yes	—
644	C₂³	C₂²×AΣL(1,𝔽₁₆)	1	2	yes	—
645	C₂³	C₂²×AΣL(1,𝔽₁₆)	1	2	yes	—
646	C₂³	C₂²×AΣL(1,𝔽₁₆)	1	2	yes	—
647	C₂³	C₂×#2121	1	2	yes	—
648	C₂³	C₂×#2121	1	2	yes	—
649	C₂³	C₂³×#99	1	1	yes	characteristic
650	C₂×C₄	#21746	1	2	yes	—
651	C₂×C₄	C₂²×AΣL(1,𝔽₁₆)	1	2	yes	—
652	C₂×C₄	C₂²×AΣL(1,𝔽₁₆)	1	2	yes	—
653	C₂×C₄	C₂×#2121	1	2	yes	—
654	C₂×C₄	C₂×#2308	1	1	yes	characteristic
655	C₂×C₄	C₂³×#99	1	1	yes	characteristic
656	C₂²	#496225	1	4	yes	—
657	C₂²	C₂×#21746	1	1	yes	characteristic
658	C₂²	C₂³×AΣL(1,𝔽₁₆)	1	1	yes	characteristic
659	C₂²	C₂²×#2121	1	1	yes	characteristic
660	C₂	C₂×#496225	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂	C₂×#496225
commutator	C₂²×Q₈	C₂⁴×C₄
Frattini, cosocle	C₂×#124	C₂⁵
prime radical	#72306293	C₂
LCS	G ▷ C₂²×Q₈ ▷ C₂×C₄ ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂ ◁ C₂⁴ ◁ C₂³×#41 ◁ C₂×#62812 ◁ G
LECS	G ▷ C₂×#124 ▷ C₂×C₄ ▷ C₂² ▷ C₂ ▷ C₁

Complements

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

N	H ≅ G/N	type
1. #72306326	C₂	semidirect
2. #72306322	C₂	semidirect
3. #72306317	C₂	semidirect
4. #72306314	C₂	semidirect
5. #72306312	C₂	semidirect
6. #72306308	C₂	semidirect
7. #72306305	C₂	semidirect
8. #72306297	C₂	semidirect
10. #72306291	C₂	semidirect
11. C₂×#152674	C₂	semidirect
12. #10586091	C₄	semidirect
14. C₂×#60391	C₄	semidirect
16. C₂×#33361	C₂²	semidirect
17. #6437459	C₄	semidirect
19. #6437458	C₄	semidirect
21. #6437453	C₄	semidirect
24. #6437447	C₄	semidirect
26. #6437437	C₄	semidirect
27. C₂×#23909	C₄	semidirect
30. #6371457	C₄	semidirect
31. #6370706	C₄	semidirect
32. C₂×#17675	C₂²	semidirect
33. C₂×#13569	C₂²	semidirect
35. #493432	C₂²	semidirect
36. #493430	C₂²	semidirect
37. #493374	C₂²	semidirect
38. #493371	C₂²	semidirect
39. C₂×#12695	C₂²	semidirect
41. #187843	C₂²	semidirect
42. #187829	C₂²	semidirect
43. #187824	C₂²	semidirect
44. #187819	C₂²	semidirect
45. #187819	C₂²	semidirect
46. #152711	C₂²	semidirect
47. #152710	C₂²	semidirect
48. #152674	C₂²	semidirect
49. #152674	C₂²	semidirect
50. #152319	C₂²	semidirect
51. #152318	C₂²	semidirect
52. #152022	C₂²	semidirect
53. #152021	C₂²	semidirect
54. C₂×#7481	C₂²	semidirect
55. C₂×2₋¹⁺⁶	C₂×C₄	semidirect
58. #62852	C₂×C₄	semidirect
60. #62848	C₂×C₄	semidirect
61. #62811	C₂×C₄	semidirect
78. C₂×#3487	C₂×C₄	semidirect
79. C₂×#3487	C₂×C₄	semidirect
92. #62653	C₂×C₄	semidirect
94. C₂×#3022	C₂×C₄	semidirect
97. C₂×#3020	C₂×C₄	semidirect
98. C₂×#3020	C₂×C₄	semidirect
100. C₂×#3018	C₂×C₄	semidirect
101. C₂×#3018	C₂×C₄	semidirect
102. C₂²×#456	C₂×C₄	semidirect
103. C₂²×#456	C₂×C₄	semidirect
104. C₂²×#454	C₂×C₄	semidirect
106. C₂×#2889	C₂×C₄	semidirect
107. C₂×#2889	C₂×C₄	semidirect
111. #23917	C₂×C₄	semidirect
113. #23916	C₂×C₄	semidirect
114. #23916	C₂×C₄	semidirect
115. #23915	C₂×C₄	semidirect
117. #23911	C₂×C₄	semidirect
120. #23909	C₂×C₄	semidirect
121. #23909	C₂×C₄	semidirect
122. #23909	C₂×C₄	semidirect
123. #23909	C₂×C₄	semidirect
124. #23909	C₂×C₄	semidirect
128. #20955	C₂×C₄	semidirect
130. #20954	C₂×C₄	semidirect
131. #20954	C₂×C₄	semidirect
133. #20952	C₂×C₄	semidirect
134. #20952	C₂×C₄	semidirect
135. C₂×#1888	C₂×C₄	semidirect
137. C₂×#1886	C₂×C₄	semidirect
138. C₂×#1886	C₂×C₄	semidirect
140. #20593	C₂×C₄	semidirect
141. #20592	C₂×C₄	semidirect
142. #20591	C₂×C₄	semidirect
143. C₂×#1785	C₂×C₄	semidirect
144. C₂×#1785	C₂×C₄	semidirect

Maximal subgroups

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

subgroup	index
#72306326	2
#72306322	2
#72306317	2
#72306314	2
#72306312	2
#72306308	2
#72306305	2
#72306297	2
#72306293	2
#72306291	2
C₂×#152674	2