Subgroups — #72311882

Order 2048.

At least 9832 conjugacy classes of subgroups; only the 2248 normal subgroups are shown.

The subgroup lattice has 883 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#72311853	C₂	1	4	yes	maximal, complemented
2	#72311846	C₂	1	4	yes	maximal, complemented
3	#72311717	C₂	1	4	yes	maximal, complemented
4	C₂×#154168	C₂	1	1	yes	maximal, characteristic, complemented
5	#72311585	C₂	1	4	yes	maximal, complemented
6	#72311535	C₂	1	2	yes	maximal, complemented
7	#72311440	C₂	1	2	yes	maximal, complemented
8	#72261973	C₂	1	4	yes	maximal, complemented
9	#72237674	C₂	1	1	yes	maximal, characteristic, complemented
10	#72236479	C₂	1	1	yes	maximal, characteristic
11	#72219244	C₂	1	4	yes	maximal, complemented
12	C₂×#62773	C₄	1	1	yes	characteristic, complemented
13	C₂⁴×C₄×D₄	C₂²	1	1	yes	characteristic
14	C₂×#36614	C₂²	1	2	yes	—
15	#7630948	C₂²	1	2	yes	—
16	#7630947	C₄	1	2	yes	complemented
17	#7630945	C₄	1	2	yes	complemented
18	#7630944	C₂²	1	2	yes	—
19	#7630943	C₄	1	2	yes	complemented
20	#7630943	C₂²	1	2	yes	—
21	#7630941	C₄	1	1	yes	characteristic, complemented
22	#7630941	C₂²	1	1	yes	characteristic
23	#7630940	C₄	1	1	yes	characteristic, complemented
24	#7630940	C₂²	1	1	yes	characteristic
25	#7628472	C₄	1	2	yes	complemented
26	#7628472	C₂²	1	2	yes	—
27	#7628282	C₄	1	2	yes	complemented
28	#7628174	C₄	1	2	yes	complemented
29	#7628174	C₂²	1	2	yes	—
30	#7625417	C₄	1	1	yes	characteristic, complemented
31	C₂³×#380	C₂²	1	2	yes	complemented
32	C₂×#20579	C₂²	1	2	yes	complemented
33	#196886	C₂²	1	16	yes	complemented
34	#196858	C₂²	1	16	yes	complemented
35	#196822	C₂²	1	8	yes	complemented
36	#196818	C₂²	1	8	yes	complemented
37	#184781	C₂²	1	2	yes	complemented
38	#184781	C₂²	1	2	yes	complemented
39	#184774	C₂²	1	2	yes	complemented
40	#184773	C₂²	1	2	yes	complemented
41	#184743	C₂²	1	2	yes	—
42	#184743	C₂²	1	2	yes	complemented
43	#154168	C₂²	1	2	yes	—
44	#154168	C₂²	1	2	yes	complemented
45	#154168	C₂²	1	2	yes	complemented
46	#154168	C₂²	1	2	yes	complemented
47	C₂×#7557	C₂²	1	2	yes	complemented
48	C₂×#7555	C₂²	1	2	yes	complemented
49	#97104	C₂²	1	16	yes	complemented
50	#97103	C₂²	1	8	yes	complemented
51	#97102	C₂²	1	8	yes	complemented
52	#97099	C₂²	1	16	yes	complemented
53	#97097	C₂²	1	8	yes	complemented
54	#97096	C₂²	1	8	yes	complemented
55	C₂⁵×D₄	D₄	1	1	yes	characteristic
56	C₂⁶×C₄	D₄	1	1	yes	characteristic
57	C₂⁶×C₄	C₂³	1	1	yes	characteristic
58	C₂×#3492	C₂×C₄	1	2	yes	—
59	C₂×#3505	C₂×C₄	1	2	yes	complemented
60	C₂×#3490	C₂×C₄	1	2	yes	—
61	C₂×#3501	C₂×C₄	1	1	yes	characteristic, complemented
62	C₂×#3496	C₂×C₄	1	1	yes	characteristic, complemented
63	C₂×#3460	C₂×C₄	1	2	yes	complemented
64	C₂×#3459	C₂×C₄	1	2	yes	complemented
65	C₂²×#525	C₂×C₄	1	2	yes	—
66	C₂²×#525	D₄	1	4	yes	—
67	C₂³×C₄×D₄	C₂×C₄	1	1	yes	characteristic
68	C₂³×C₄×D₄	C₂×C₄	1	1	yes	characteristic
69	C₂³×C₄×D₄	C₂×C₄	1	1	yes	characteristic
70	C₂³×C₄×D₄	C₂×C₄	1	1	yes	characteristic
71	C₂³×C₄×D₄	C₂×C₄	1	1	yes	characteristic
72	C₂³×C₄×D₄	C₂×C₄	1	1	yes	characteristic
73	C₂³×C₄×D₄	C₂×C₄	1	1	yes	characteristic
74	C₂³×C₄×D₄	C₂×C₄	1	1	yes	characteristic
75	C₂³×C₄×D₄	D₄	1	1	yes	characteristic
76	C₂³×C₄×D₄	D₄	1	1	yes	characteristic
77	C₂³×C₄×D₄	D₄	1	1	yes	characteristic
78	C₂³×C₄×D₄	D₄	1	1	yes	characteristic
79	C₂³×C₄×D₄	D₄	1	1	yes	characteristic
80	C₂³×C₄×D₄	D₄	1	1	yes	characteristic
81	C₂³×C₄×D₄	D₄	1	1	yes	characteristic
82	C₂³×C₄×D₄	D₄	1	1	yes	characteristic
83	C₂³×C₄×D₄	D₄	1	1	yes	characteristic
84	C₂³×C₄×D₄	D₄	1	1	yes	characteristic
85	C₂³×C₄×D₄	D₄	1	1	yes	characteristic
86	C₂³×C₄×D₄	D₄	1	1	yes	characteristic
87	C₂³×C₄×D₄	C₂³	1	1	yes	characteristic
88	C₂³×C₄×D₄	C₂³	1	1	yes	characteristic
89	C₂³×C₄×D₄	C₂³	1	1	yes	characteristic
90	C₂³×C₄×D₄	C₂³	1	1	yes	characteristic
91	C₂⁴×C₄⋊C₄	C₂³	1	1	yes	characteristic
92	C₂⁴×C₂²⋊C₄	D₄	1	1	yes	characteristic
93	C₂⁴×C₂²⋊C₄	C₂³	1	1	yes	characteristic
94	C₂⁴×C₄²	D₄	1	1	yes	characteristic
95	#36614	C₂×C₄	1	4	yes	—
96	#36614	C₂×C₄	1	4	yes	—
97	#36614	D₄	1	8	yes	—
98	#36614	D₄	1	8	yes	—
99	#36614	C₂³	1	4	yes	—
100	#36614	C₂³	1	4	yes	—
101	C₂×#2848	C₂×C₄	1	2	yes	—
102	C₂×#2848	D₄	1	4	yes	—
103	C₂×#2848	C₂³	1	2	yes	—
104	C₂×#2847	C₂×C₄	1	2	yes	—
105	C₂×#2847	D₄	1	4	yes	—
106	C₂×#2847	C₂³	1	2	yes	—
107	#35224	C₂×C₄	1	2	yes	—
108	#35224	C₂³	1	2	yes	—
109	#35223	C₂×C₄	1	2	yes	—
110	#35223	C₂³	1	2	yes	—
111	#35174	C₂×C₄	1	2	yes	complemented
112	#35174	C₂×C₄	1	2	yes	complemented
113	#35168	C₂×C₄	1	2	yes	complemented
114	#35168	C₂×C₄	1	2	yes	complemented
115	#35091	C₂×C₄	1	4	yes	complemented
116	#35091	C₂×C₄	1	4	yes	complemented
117	#35057	C₂×C₄	1	4	yes	—
118	#35050	C₂×C₄	1	4	yes	—
119	#35010	C₂×C₄	1	2	yes	complemented
120	#35010	C₂×C₄	1	2	yes	complemented
121	#35000	C₂×C₄	1	2	yes	complemented
122	#35000	C₂×C₄	1	2	yes	complemented
123	#34989	C₂×C₄	1	4	yes	—
124	#34989	C₂³	1	4	yes	—
125	#34988	C₂×C₄	1	4	yes	—
126	#34988	C₂³	1	4	yes	—
127	#34987	C₂×C₄	1	4	yes	complemented
128	#34987	C₂×C₄	1	4	yes	complemented
129	#34985	C₂×C₄	1	2	yes	complemented
130	#34985	C₂×C₄	1	2	yes	complemented
131	#34984	C₂×C₄	1	2	yes	complemented
132	#34984	C₂×C₄	1	2	yes	complemented
133	#34982	C₂×C₄	1	2	yes	—
134	#34982	C₂³	1	2	yes	—
135	#34981	C₂×C₄	1	2	yes	—
136	#34981	C₂³	1	2	yes	—
137	#34562	C₂×C₄	1	4	yes	complemented
138	#34562	C₂×C₄	1	4	yes	complemented
139	#34185	C₂×C₄	1	2	yes	complemented
140	#34181	C₂×C₄	1	1	yes	characteristic, complemented
141	#34181	C₂×C₄	1	1	yes	characteristic, complemented
142	#34178	C₂×C₄	1	2	yes	—
143	#34176	C₂×C₄	1	2	yes	—
144	#34058	C₂×C₄	1	2	yes	complemented
145	#34057	C₂×C₄	1	2	yes	complemented
146	C₂×#2280	C₂×C₄	1	2	yes	—
147	C₂×#2280	D₄	1	4	yes	—
148	C₂²×#380	C₂³	1	4	yes	—
149	C₂²×#380	C₂³	1	4	yes	—
150	C₂³×#95	C₂³	1	4	yes	—
151	#20579	C₂³	1	4	yes	—
152	#20579	C₂³	1	4	yes	—
153	C₂×#1779	C₂³	1	4	yes	—
154	#9147	C₂³	1	32	yes	—
155	#9143	C₂³	1	32	yes	—
156	#8299	C₂³	1	4	yes	—
157	#8299	C₂³	1	4	yes	—
158	#8298	C₂³	1	4	yes	—
159	#8298	C₂³	1	4	yes	—
160	#7557	C₂³	1	4	yes	—
161	#7557	C₂³	1	4	yes	—
162	#7555	C₂³	1	4	yes	—
163	#7555	C₂³	1	4	yes	—
164	C₂⁷	C₂×D₄	1	1	yes	characteristic
165	C₂⁷	C₂×D₄	1	1	yes	characteristic
166	C₂³×#41	C₂²⋊C₄	1	2	yes	complemented
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	1	yes	characteristic
171	C₂⁴×D₄	C₂²⋊C₄	1	1	yes	characteristic
172	C₂⁴×D₄	C₂²⋊C₄	1	1	yes	characteristic
173	C₂⁴×D₄	C₂²⋊C₄	1	1	yes	characteristic
174	C₂⁴×D₄	C₂²⋊C₄	1	1	yes	characteristic
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	1	yes	characteristic
179	C₂⁵×C₄	C₂²⋊C₄	1	1	yes	characteristic
180	C₂⁵×C₄	C₂²⋊C₄	1	1	yes	characteristic
181	C₂⁵×C₄	C₂²⋊C₄	1	1	yes	characteristic
182	C₂⁵×C₄	C₂²⋊C₄	1	1	yes	characteristic
183	C₂⁵×C₄	C₂²⋊C₄	1	1	yes	characteristic
184	C₂⁵×C₄	C₂²⋊C₄	1	1	yes	characteristic
185	C₂⁵×C₄	C₂²⋊C₄	1	1	yes	characteristic
186	C₂⁵×C₄	C₂²⋊C₄	1	1	yes	characteristic
187	C₂⁵×C₄	C₂²×C₄	1	1	yes	characteristic
188	C₂⁵×C₄	C₂²×C₄	1	1	yes	characteristic
189	C₂⁵×C₄	C₂²×C₄	1	1	yes	characteristic
190	C₂⁵×C₄	C₂²×C₄	1	1	yes	characteristic
191	C₂⁵×C₄	C₂×D₄	1	1	yes	characteristic
192	C₂⁵×C₄	C₂×D₄	1	1	yes	characteristic
193	C₂⁵×C₄	C₂×D₄	1	1	yes	characteristic
194	C₂⁵×C₄	C₂×D₄	1	1	yes	characteristic
195	C₂⁵×C₄	C₂×D₄	1	1	yes	characteristic
196	C₂⁵×C₄	C₂×D₄	1	1	yes	characteristic
197	C₂⁵×C₄	C₂×D₄	1	1	yes	characteristic
198	C₂⁵×C₄	C₂×D₄	1	1	yes	characteristic
199	C₂⁵×C₄	C₂×D₄	1	4	yes	—
200	C₂⁵×C₄	C₂×D₄	1	1	yes	characteristic
201	C₂⁵×C₄	C₂×D₄	1	1	yes	characteristic
202	C₂⁵×C₄	C₂×D₄	1	1	yes	characteristic
203	C₂⁵×C₄	C₂×D₄	1	4	yes	—
204	C₂⁵×C₄	C₂×D₄	1	4	yes	—
205	C₂⁵×C₄	C₂×D₄	1	4	yes	—
206	C₂⁵×C₄	C₂×D₄	1	1	yes	characteristic
207	C₂⁵×C₄	C₂×D₄	1	1	yes	characteristic
208	C₂⁵×C₄	C₂×D₄	1	1	yes	characteristic
209	C₂⁵×C₄	C₂⁴	1	1	yes	characteristic
210	C₂⁵×C₄	C₂⁴	1	1	yes	characteristic
211	C₂⁵×C₄	C₂⁴	1	1	yes	characteristic
212	C₂×#544	C₂²×C₄	1	2	yes	—
213	C₂×#543	C₂²×C₄	1	2	yes	—
214	C₂×#539	C₂²×C₄	1	4	yes	—
215	C₂×#538	C₂²×C₄	1	4	yes	—
216	C₂×#537	C₂²×C₄	1	2	yes	—
217	C₂×#534	C₂²×C₄	1	2	yes	—
218	C₂×#525	C₂²⋊C₄	1	8	yes	complemented
219	C₂×#525	C₂²⋊C₄	1	4	yes	complemented
220	C₂×#525	C₂²⋊C₄	1	8	yes	complemented
221	C₂×#525	C₂²⋊C₄	1	4	yes	complemented
222	C₂×#525	C₂²×C₄	1	4	yes	—
223	C₂×#525	C₂²×C₄	1	4	yes	—
224	C₂×#525	C₂×D₄	1	8	yes	—
225	C₂×#525	C₂×D₄	1	8	yes	—
226	C₂²×C₂²⋊Q₈	C₂²⋊C₄	1	4	yes	complemented
227	C₂²×C₂²⋊Q₈	C₂²⋊C₄	1	2	yes	complemented
228	C₂²×C₂²⋊Q₈	C₂²×C₄	1	2	yes	—
229	C₂²×C₂²⋊Q₈	C₂×D₄	1	4	yes	—
230	C₂²×#121	C₂²⋊C₄	1	4	yes	complemented
231	C₂²×#121	C₂²⋊C₄	1	2	yes	complemented
232	C₂²×#121	C₂²×C₄	1	2	yes	—
233	C₂²×#121	C₂×D₄	1	4	yes	—
234	C₂²×C₄×D₄	C₂²⋊C₄	1	1	yes	characteristic
235	C₂²×C₄×D₄	C₂²⋊C₄	1	1	yes	characteristic
236	C₂²×C₄×D₄	C₂²⋊C₄	1	1	yes	characteristic
237	C₂²×C₄×D₄	C₂²⋊C₄	1	1	yes	characteristic
238	C₂²×C₄×D₄	C₂²⋊C₄	1	1	yes	characteristic
239	C₂²×C₄×D₄	C₂²⋊C₄	1	1	yes	characteristic
240	C₂²×C₄×D₄	C₂²⋊C₄	1	1	yes	characteristic
241	C₂²×C₄×D₄	C₂²⋊C₄	1	1	yes	characteristic
242	C₂²×C₄×D₄	C₂²⋊C₄	1	1	yes	characteristic
243	C₂²×C₄×D₄	C₂²⋊C₄	1	1	yes	characteristic
244	C₂²×C₄×D₄	C₂²⋊C₄	1	1	yes	characteristic
245	C₂²×C₄×D₄	C₂²⋊C₄	1	1	yes	characteristic
246	C₂²×C₄×D₄	C₂²⋊C₄	1	1	yes	characteristic
247	C₂²×C₄×D₄	C₂²⋊C₄	1	1	yes	characteristic
248	C₂²×C₄×D₄	C₂²⋊C₄	1	1	yes	characteristic
249	C₂²×C₄×D₄	C₂²⋊C₄	1	1	yes	characteristic
250	C₂²×C₄×D₄	C₂²⋊C₄	1	1	yes	characteristic
251	C₂²×C₄×D₄	C₂²⋊C₄	1	1	yes	characteristic
252	C₂²×C₄×D₄	C₂²⋊C₄	1	1	yes	characteristic
253	C₂²×C₄×D₄	C₂²⋊C₄	1	1	yes	characteristic
254	C₂²×C₄×D₄	C₂²⋊C₄	1	1	yes	characteristic
255	C₂²×C₄×D₄	C₂²⋊C₄	1	1	yes	characteristic
256	C₂²×C₄×D₄	C₂²⋊C₄	1	1	yes	characteristic
257	C₂²×C₄×D₄	C₂²⋊C₄	1	1	yes	characteristic
258	C₂²×C₄×D₄	C₂²⋊C₄	1	1	yes	characteristic
259	C₂²×C₄×D₄	C₂²⋊C₄	1	1	yes	characteristic
260	C₂²×C₄×D₄	C₂²⋊C₄	1	1	yes	characteristic
261	C₂²×C₄×D₄	C₂²⋊C₄	1	1	yes	characteristic
262	C₂²×C₄×D₄	C₂²⋊C₄	1	1	yes	characteristic
263	C₂²×C₄×D₄	C₂²⋊C₄	1	1	yes	characteristic
264	C₂²×C₄×D₄	C₂²⋊C₄	1	1	yes	characteristic
265	C₂²×C₄×D₄	C₂²⋊C₄	1	1	yes	characteristic
266	C₂²×C₄×D₄	C₂²×C₄	1	1	yes	characteristic
267	C₂²×C₄×D₄	C₂²×C₄	1	1	yes	characteristic
268	C₂²×C₄×D₄	C₂²×C₄	1	1	yes	characteristic
269	C₂²×C₄×D₄	C₂²×C₄	1	1	yes	characteristic
270	C₂²×C₄×D₄	C₂²×C₄	1	1	yes	characteristic
271	C₂²×C₄×D₄	C₂²×C₄	1	1	yes	characteristic
272	C₂²×C₄×D₄	C₂²×C₄	1	1	yes	characteristic
273	C₂²×C₄×D₄	C₂²×C₄	1	1	yes	characteristic
274	C₂²×C₄×D₄	C₂²×C₄	1	1	yes	characteristic
275	C₂²×C₄×D₄	C₂²×C₄	1	1	yes	characteristic
276	C₂²×C₄×D₄	C₂²×C₄	1	1	yes	characteristic
277	C₂²×C₄×D₄	C₂²×C₄	1	1	yes	characteristic
278	C₂²×C₄×D₄	C₂²×C₄	1	1	yes	characteristic
279	C₂²×C₄×D₄	C₂²×C₄	1	1	yes	characteristic
280	C₂²×C₄×D₄	C₂²×C₄	1	1	yes	characteristic
281	C₂²×C₄×D₄	C₂²×C₄	1	1	yes	characteristic
282	C₂²×C₄×D₄	C₂×D₄	1	1	yes	characteristic
283	C₂²×C₄×D₄	C₂×D₄	1	1	yes	characteristic
284	C₂²×C₄×D₄	C₂×D₄	1	1	yes	characteristic
285	C₂²×C₄×D₄	C₂×D₄	1	1	yes	characteristic
286	C₂²×C₄×D₄	C₂×D₄	1	1	yes	characteristic
287	C₂²×C₄×D₄	C₂×D₄	1	1	yes	characteristic
288	C₂²×C₄×D₄	C₂×D₄	1	1	yes	characteristic
289	C₂²×C₄×D₄	C₂×D₄	1	1	yes	characteristic
290	C₂²×C₄×D₄	C₂×D₄	1	1	yes	characteristic
291	C₂²×C₄×D₄	C₂×D₄	1	1	yes	characteristic
292	C₂²×C₄×D₄	C₂×D₄	1	1	yes	characteristic
293	C₂²×C₄×D₄	C₂×D₄	1	1	yes	characteristic
294	C₂²×C₄×D₄	C₂×D₄	1	1	yes	characteristic
295	C₂²×C₄×D₄	C₂×D₄	1	1	yes	characteristic
296	C₂²×C₄×D₄	C₂×D₄	1	1	yes	characteristic
297	C₂²×C₄×D₄	C₂×D₄	1	1	yes	characteristic
298	C₂²×#117	C₂²⋊C₄	1	4	yes	complemented
299	C₂²×#117	C₂²⋊C₄	1	2	yes	complemented
300	C₂³×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
301	C₂³×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
302	C₂³×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
303	C₂³×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
304	C₂³×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
305	C₂³×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
306	C₂³×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
307	C₂³×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
308	C₂³×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
309	C₂³×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
310	C₂³×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
311	C₂³×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
312	C₂³×C₂²⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
313	C₂³×C₂²⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
314	C₂³×C₂²⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
315	C₂³×C₂²⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
316	C₂³×C₂²⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
317	C₂³×C₂²⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
318	C₂³×C₂²⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
319	C₂³×C₂²⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
320	C₂³×C₂²⋊C₄	C₂²×C₄	1	1	yes	characteristic
321	C₂³×C₂²⋊C₄	C₂²×C₄	1	1	yes	characteristic
322	C₂³×C₂²⋊C₄	C₂²×C₄	1	1	yes	characteristic
323	C₂³×C₂²⋊C₄	C₂²×C₄	1	1	yes	characteristic
324	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
325	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
326	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
327	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
328	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
329	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
330	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
331	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
332	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
333	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
334	C₂³×C₂²⋊C₄	C₂⁴	1	1	yes	characteristic
335	C₂³×C₂²⋊C₄	C₂⁴	1	1	yes	characteristic
336	C₂³×C₄²	C₂²⋊C₄	1	1	yes	characteristic
337	C₂³×C₄²	C₂²⋊C₄	1	1	yes	characteristic
338	C₂³×C₄²	C₂²⋊C₄	1	1	yes	characteristic
339	C₂³×C₄²	C₂²⋊C₄	1	1	yes	characteristic
340	C₂³×C₄²	C₂²⋊C₄	1	1	yes	characteristic
341	C₂³×C₄²	C₂²⋊C₄	1	1	yes	characteristic
342	C₂³×C₄²	C₂²⋊C₄	1	1	yes	characteristic
343	C₂³×C₄²	C₂²⋊C₄	1	1	yes	characteristic
344	C₂³×C₄²	C₂×D₄	1	1	yes	characteristic
345	C₂³×C₄²	C₂×D₄	1	1	yes	characteristic
346	C₂³×C₄²	C₂×D₄	1	1	yes	characteristic
347	C₂³×C₄²	C₂×D₄	1	1	yes	characteristic
348	#2848	C₂²⋊C₄	1	8	yes	complemented
349	#2848	C₂²⋊C₄	1	8	yes	complemented
350	#2848	C₂²⋊C₄	1	8	yes	complemented
351	#2848	C₂²×C₄	1	4	yes	—
352	#2848	C₂²×C₄	1	4	yes	—
353	#2848	C₂²×C₄	1	4	yes	—
354	#2848	C₂×D₄	1	8	yes	—
355	#2848	C₂×D₄	1	8	yes	—
356	#2848	C₂×D₄	1	8	yes	—
357	#2848	C₂⁴	1	4	yes	—
358	#2847	C₂²⋊C₄	1	8	yes	complemented
359	#2847	C₂²⋊C₄	1	8	yes	complemented
360	#2847	C₂²⋊C₄	1	8	yes	complemented
361	#2847	C₂²×C₄	1	4	yes	—
362	#2847	C₂²×C₄	1	4	yes	—
363	#2847	C₂²×C₄	1	4	yes	—
364	#2847	C₂×D₄	1	8	yes	—
365	#2847	C₂×D₄	1	8	yes	—
366	#2847	C₂×D₄	1	8	yes	—
367	#2847	C₂⁴	1	4	yes	—
368	#2627	C₂²×C₄	1	4	yes	—
369	#2627	C₂²×C₄	1	4	yes	—
370	#2626	C₂²×C₄	1	4	yes	—
371	#2626	C₂²×C₄	1	4	yes	—
372	#2618	C₂²×C₄	1	4	yes	—
373	#2618	C₂²×C₄	1	4	yes	—
374	#2617	C₂²×C₄	1	4	yes	—
375	#2617	C₂²×C₄	1	4	yes	—
376	#2316	C₂²×C₄	1	2	yes	—
377	#2316	C₂²×C₄	1	2	yes	—
378	#2315	C₂²×C₄	1	2	yes	—
379	#2315	C₂²×C₄	1	2	yes	—
380	#2313	C₂²×C₄	1	4	yes	—
381	#2312	C₂²×C₄	1	4	yes	—
382	#2280	C₂²⋊C₄	1	8	yes	complemented
383	#2280	C₂²⋊C₄	1	4	yes	complemented
384	#2280	C₂²⋊C₄	1	8	yes	complemented
385	#2280	C₂²⋊C₄	1	4	yes	complemented
386	#2280	C₂²×C₄	1	4	yes	—
387	#2280	C₂²×C₄	1	4	yes	—
388	#2280	C₂×D₄	1	8	yes	—
389	#2280	C₂×D₄	1	8	yes	—
390	C₂×#380	C₂²⋊C₄	1	4	yes	complemented
391	C₂×#380	C₂²⋊C₄	1	4	yes	complemented
392	C₂×#380	C₂²⋊C₄	1	4	yes	complemented
393	C₂×#380	C₂²×C₄	1	2	yes	—
394	C₂×#380	C₂²×C₄	1	2	yes	—
395	C₂×#380	C₂×D₄	1	4	yes	—
396	C₂×#380	C₂×D₄	1	4	yes	—
397	C₂²×#95	C₂⁴	1	8	yes	—
398	#1779	C₂⁴	1	8	yes	—
399	C₂⁶	C₂×C₂²⋊C₄	1	1	yes	characteristic
400	C₂⁶	C₂×C₂²⋊C₄	1	1	yes	characteristic
401	C₂⁶	C₂×C₂²⋊C₄	1	1	yes	characteristic
402	C₂⁶	C₂×C₂²⋊C₄	1	1	yes	characteristic
403	C₂⁶	C₂×C₂²⋊C₄	1	1	yes	characteristic
404	C₂⁶	C₂×C₂²⋊C₄	1	1	yes	characteristic
405	C₂⁶	C₂×C₂²⋊C₄	1	1	yes	characteristic
406	C₂⁶	C₂×C₂²⋊C₄	1	1	yes	characteristic
407	C₂⁶	#120	1	4	yes	—
408	C₂⁶	#120	1	4	yes	—
409	C₂⁶	C₂²×D₄	1	1	yes	characteristic
410	C₂⁶	C₂²×D₄	1	1	yes	characteristic
411	C₂⁶	C₂²×D₄	1	1	yes	characteristic
412	C₂⁶	C₂²×D₄	1	1	yes	characteristic
413	C₂⁶	C₂²×D₄	1	1	yes	characteristic
414	C₂²×#41	C₂×C₂²⋊C₄	1	4	yes	—
415	C₂²×#41	C₂×C₂²⋊C₄	1	4	yes	complemented
416	C₂³×Q₈	C₂×C₂²⋊C₄	1	2	yes	complemented
417	C₂³×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
418	C₂³×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
419	C₂³×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
420	C₂³×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
421	C₂³×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
422	C₂³×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
423	C₂³×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
424	C₂³×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
425	C₂³×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
426	C₂³×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
427	C₂³×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
428	C₂³×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
429	C₂³×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
430	C₂³×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
431	C₂³×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
432	C₂³×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
433	C₂³×D₄	C₂×C₂²⋊C₄	1	2	yes	complemented
434	C₂³×D₄	AGL(1,ℤ/8)	1	4	yes	—
435	C₂³×D₄	#137	1	4	yes	—
436	C₂⁴×C₄	#99	1	8	yes	—
437	C₂⁴×C₄	C₂×C₂²⋊C₄	1	2	yes	—
438	C₂⁴×C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
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	C₂×C₂²⋊C₄	1	1	yes	characteristic
443	C₂⁴×C₄	C₂×C₂²⋊C₄	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	1	yes	characteristic
447	C₂⁴×C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
448	C₂⁴×C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
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	1	yes	characteristic
454	C₂⁴×C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
455	C₂⁴×C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
456	C₂⁴×C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
457	C₂⁴×C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
458	C₂⁴×C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
459	C₂⁴×C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
460	C₂⁴×C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
461	C₂⁴×C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
462	C₂⁴×C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
463	C₂⁴×C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
464	C₂⁴×C₄	C₂×C₂²⋊C₄	1	4	yes	—
465	C₂⁴×C₄	C₂×C₂²⋊C₄	1	4	yes	—
466	C₂⁴×C₄	C₂×C₂²⋊C₄	1	2	yes	—
467	C₂⁴×C₄	C₂×C₂²⋊C₄	1	2	yes	—
468	C₂⁴×C₄	C₂×C₂²⋊C₄	1	2	yes	—
469	C₂⁴×C₄	C₂×C₂²⋊C₄	1	4	yes	—
470	C₂⁴×C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
471	C₂⁴×C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
472	C₂⁴×C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
473	C₂⁴×C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
474	C₂⁴×C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
475	C₂⁴×C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
476	C₂⁴×C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
477	C₂⁴×C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
478	C₂⁴×C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
479	C₂⁴×C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
480	C₂⁴×C₄	C₂×C₂²⋊C₄	1	4	yes	—
481	C₂⁴×C₄	C₂×C₂²⋊C₄	1	4	yes	—
482	C₂⁴×C₄	C₂×C₂²⋊C₄	1	4	yes	—
483	C₂⁴×C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
484	C₂⁴×C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
485	C₂⁴×C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
486	C₂⁴×C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
487	C₂⁴×C₄	#120	1	2	yes	—
488	C₂⁴×C₄	#120	1	2	yes	—
489	C₂⁴×C₄	#120	1	2	yes	—
490	C₂⁴×C₄	#120	1	2	yes	—
491	C₂⁴×C₄	#120	1	2	yes	—
492	C₂⁴×C₄	#120	1	2	yes	—
493	C₂⁴×C₄	#120	1	4	yes	—
494	C₂⁴×C₄	#120	1	2	yes	—
495	C₂⁴×C₄	#120	1	4	yes	—
496	C₂⁴×C₄	#120	1	4	yes	—
497	C₂⁴×C₄	#120	1	2	yes	—
498	C₂⁴×C₄	#120	1	4	yes	—
499	C₂⁴×C₄	#120	1	4	yes	—
500	C₂⁴×C₄	#120	1	4	yes	—
501	C₂⁴×C₄	#120	1	4	yes	—
502	C₂⁴×C₄	#120	1	4	yes	—
503	C₂⁴×C₄	#120	1	4	yes	—
504	C₂⁴×C₄	#120	1	4	yes	—
505	C₂⁴×C₄	C₂³×C₄	1	1	yes	characteristic
506	C₂⁴×C₄	C₂³×C₄	1	1	yes	characteristic
507	C₂⁴×C₄	C₂³×C₄	1	1	yes	characteristic
508	C₂⁴×C₄	C₂³×C₄	1	1	yes	characteristic
509	C₂⁴×C₄	C₂³×C₄	1	1	yes	characteristic
510	C₂⁴×C₄	C₂³×C₄	1	1	yes	characteristic
511	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
512	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
513	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
514	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
515	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
516	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
517	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
518	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
519	C₂⁴×C₄	C₂²×D₄	1	4	yes	—
520	C₂⁴×C₄	C₂²×D₄	1	4	yes	—
521	C₂⁴×C₄	C₂²×D₄	1	4	yes	—
522	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
523	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
524	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
525	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
526	C₂⁴×C₄	C₂²×D₄	1	4	yes	—
527	C₂⁴×C₄	C₂²×D₄	1	4	yes	—
528	C₂⁴×C₄	C₂²×D₄	1	4	yes	—
529	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
530	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
531	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
532	C₂⁴×C₄	C₂⁵	1	1	yes	characteristic
533	C₂×C₂²⋊Q₈	C₂×C₂²⋊C₄	1	4	yes	—
534	C₂×C₂²⋊Q₈	C₂×C₂²⋊C₄	1	8	yes	—
535	C₂×C₂²⋊Q₈	C₂×C₂²⋊C₄	1	4	yes	complemented
536	C₂×C₂²⋊Q₈	C₂×C₂²⋊C₄	1	8	yes	complemented
537	C₂×C₂²⋊Q₈	C₂×C₂²⋊C₄	1	8	yes	complemented
538	C₂×C₂²⋊Q₈	C₂×C₂²⋊C₄	1	4	yes	complemented
539	C₂×C₂²⋊Q₈	C₂³×C₄	1	4	yes	—
540	C₂×C₂²⋊Q₈	C₂²×D₄	1	8	yes	—
541	C₂×#121	C₂×C₂²⋊C₄	1	4	yes	—
542	C₂×#121	C₂×C₂²⋊C₄	1	8	yes	—
543	C₂×#121	C₂×C₂²⋊C₄	1	8	yes	complemented
544	C₂×#121	C₂×C₂²⋊C₄	1	8	yes	complemented
545	C₂×#121	C₂×C₂²⋊C₄	1	4	yes	complemented
546	C₂×#121	C₂×C₂²⋊C₄	1	4	yes	complemented
547	C₂×#121	C₂³×C₄	1	4	yes	—
548	C₂×#121	C₂²×D₄	1	8	yes	—
549	C₂×#117	C₂×C₂²⋊C₄	1	8	yes	—
550	C₂×#117	C₂×C₂²⋊C₄	1	4	yes	—
551	C₂×#117	C₂×C₂²⋊C₄	1	8	yes	complemented
552	C₂×#117	C₂×C₂²⋊C₄	1	4	yes	complemented
553	C₂²×C₄⋊C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
554	C₂²×C₄⋊C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
555	C₂²×C₄⋊C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
556	C₂²×C₄⋊C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
557	C₂²×C₄⋊C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
558	C₂²×C₄⋊C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
559	C₂²×C₄⋊C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
560	C₂²×C₄⋊C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
561	C₂²×C₄⋊C₄	C₂×C₂²⋊C₄	1	4	yes	complemented
562	C₂²×C₄⋊C₄	C₂×C₂²⋊C₄	1	4	yes	complemented
563	C₂²×C₄⋊C₄	C₂×C₂²⋊C₄	1	2	yes	complemented
564	C₂²×C₄⋊C₄	C₂×C₂²⋊C₄	1	2	yes	complemented
565	C₂²×C₄⋊C₄	C₂³×C₄	1	1	yes	characteristic
566	C₂²×C₄⋊C₄	C₂³×C₄	1	1	yes	characteristic
567	C₂²×C₄⋊C₄	C₂³×C₄	1	1	yes	characteristic
568	C₂²×C₄⋊C₄	C₂³×C₄	1	1	yes	characteristic
569	C₂²×C₄⋊C₄	C₂²×D₄	1	1	yes	characteristic
570	C₂²×C₄⋊C₄	C₂²×D₄	1	1	yes	characteristic
571	C₂²×C₄⋊C₄	C₂²×D₄	1	1	yes	characteristic
572	C₂²×C₄⋊C₄	C₂²×D₄	1	1	yes	characteristic
573	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
574	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
575	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
576	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
577	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
578	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
579	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
580	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
581	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
582	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
583	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
584	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
585	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
586	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
587	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
588	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
589	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
590	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
591	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
592	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
593	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
594	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
595	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
596	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
597	C₂²×C₂²⋊C₄	C₂³×C₄	1	1	yes	characteristic
598	C₂²×C₂²⋊C₄	C₂³×C₄	1	1	yes	characteristic
599	C₂²×C₂²⋊C₄	C₂³×C₄	1	1	yes	characteristic
600	C₂²×C₂²⋊C₄	C₂³×C₄	1	1	yes	characteristic
601	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
602	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
603	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
604	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
605	C₂²×C₄²	#99	1	8	yes	—
606	C₂²×C₄²	C₂×C₂²⋊C₄	1	1	yes	characteristic
607	C₂²×C₄²	C₂×C₂²⋊C₄	1	1	yes	characteristic
608	C₂²×C₄²	C₂×C₂²⋊C₄	1	1	yes	characteristic
609	C₂²×C₄²	C₂×C₂²⋊C₄	1	1	yes	characteristic
610	C₂²×C₄²	C₂×C₂²⋊C₄	1	1	yes	characteristic
611	C₂²×C₄²	C₂×C₂²⋊C₄	1	1	yes	characteristic
612	C₂²×C₄²	C₂×C₂²⋊C₄	1	1	yes	characteristic
613	C₂²×C₄²	C₂×C₂²⋊C₄	1	1	yes	characteristic
614	C₂²×C₄²	C₂×C₂²⋊C₄	1	1	yes	characteristic
615	C₂²×C₄²	C₂×C₂²⋊C₄	1	1	yes	characteristic
616	C₂²×C₄²	C₂×C₂²⋊C₄	1	1	yes	characteristic
617	C₂²×C₄²	C₂×C₂²⋊C₄	1	1	yes	characteristic
618	C₂²×C₄²	C₂×C₂²⋊C₄	1	1	yes	characteristic
619	C₂²×C₄²	C₂×C₂²⋊C₄	1	1	yes	characteristic
620	C₂²×C₄²	C₂×C₂²⋊C₄	1	1	yes	characteristic
621	C₂²×C₄²	C₂×C₂²⋊C₄	1	1	yes	characteristic
622	#380	C₂×C₂²⋊C₄	1	8	yes	—
623	#380	C₂×C₂²⋊C₄	1	8	yes	—
624	#380	C₂×C₂²⋊C₄	1	8	yes	—
625	#380	C₂×C₂²⋊C₄	1	8	yes	complemented
626	#380	C₂×C₂²⋊C₄	1	4	yes	complemented
627	#380	C₂×C₂²⋊C₄	1	4	yes	complemented
628	#380	C₂×C₂²⋊C₄	1	8	yes	complemented
629	#380	C₂×C₂²⋊C₄	1	8	yes	complemented
630	#380	C₂×C₂²⋊C₄	1	8	yes	complemented
631	#380	C₂×C₂²⋊C₄	1	8	yes	complemented
632	#380	C₂³×C₄	1	4	yes	—
633	#380	C₂³×C₄	1	4	yes	—
634	#380	C₂²×D₄	1	8	yes	—
635	#380	C₂²×D₄	1	8	yes	—
636	C₂⁵	#379	1	2	yes	—
637	C₂⁵	#379	1	2	yes	—
638	C₂⁵	#379	1	4	yes	—
639	C₂⁵	#379	1	2	yes	—
640	C₂⁵	#379	1	2	yes	—
641	C₂⁵	#379	1	4	yes	—
642	C₂⁵	C₂×#99	1	4	yes	—
643	C₂⁵	#421	1	4	yes	—
644	C₂⁵	C₂²×C₂²⋊C₄	1	1	yes	characteristic
645	C₂⁵	C₂²×C₂²⋊C₄	1	1	yes	characteristic
646	C₂⁵	C₂²×C₂²⋊C₄	1	1	yes	characteristic
647	C₂⁵	C₂²×C₂²⋊C₄	1	1	yes	characteristic
648	C₂⁵	C₂²×C₂²⋊C₄	1	1	yes	characteristic
649	C₂⁵	C₂²×C₂²⋊C₄	1	1	yes	characteristic
650	C₂⁵	C₂²×C₂²⋊C₄	1	1	yes	characteristic
651	C₂⁵	C₂²×C₂²⋊C₄	1	1	yes	characteristic
652	C₂⁵	C₂²×C₂²⋊C₄	1	1	yes	characteristic
653	C₂⁵	C₂²×C₂²⋊C₄	1	1	yes	characteristic
654	C₂⁵	C₂×#120	1	2	yes	—
655	C₂⁵	C₂×#120	1	2	yes	—
656	C₂⁵	C₂×#120	1	4	yes	—
657	C₂⁵	C₂×#120	1	4	yes	—
658	C₂⁵	C₂×AGL(1,ℤ/8)	1	2	yes	—
659	C₂⁵	C₂×AGL(1,ℤ/8)	1	2	yes	—
660	C₂⁵	C₂×#137	1	2	yes	—
661	C₂⁵	C₂×#137	1	2	yes	—
662	C₂⁵	#575	1	4	yes	—
663	C₂⁵	C₂³×D₄	1	1	yes	characteristic
664	C₂²×Q₈	C₂²×C₂²⋊C₄	1	4	yes	—
665	C₂²×D₄	#417	1	4	yes	—
666	C₂²×D₄	#417	1	4	yes	—
667	C₂²×D₄	#417	1	4	yes	—
668	C₂²×D₄	#417	1	4	yes	—
669	C₂²×D₄	C₂²×C₂²⋊C₄	1	4	yes	—
670	C₂³×C₄	#379	1	2	yes	—
671	C₂³×C₄	#379	1	2	yes	—
672	C₂³×C₄	#379	1	2	yes	—
673	C₂³×C₄	#379	1	2	yes	—
674	C₂³×C₄	#379	1	2	yes	—
675	C₂³×C₄	#379	1	2	yes	—
676	C₂³×C₄	#379	1	2	yes	—
677	C₂³×C₄	#379	1	1	yes	characteristic
678	C₂³×C₄	#379	1	1	yes	characteristic
679	C₂³×C₄	#379	1	1	yes	characteristic
680	C₂³×C₄	#379	1	2	yes	—
681	C₂³×C₄	#379	1	2	yes	—
682	C₂³×C₄	#379	1	2	yes	—
683	C₂³×C₄	#379	1	2	yes	—
684	C₂³×C₄	#379	1	4	yes	—
685	C₂³×C₄	#379	1	2	yes	—
686	C₂³×C₄	#379	1	4	yes	—
687	C₂³×C₄	#379	1	4	yes	—
688	C₂³×C₄	#379	1	4	yes	—
689	C₂³×C₄	#379	1	2	yes	—
690	C₂³×C₄	#379	1	2	yes	—
691	C₂³×C₄	#379	1	1	yes	characteristic
692	C₂³×C₄	C₂×#99	1	4	yes	—
693	C₂³×C₄	C₂×#99	1	4	yes	—
694	C₂³×C₄	C₂×#99	1	4	yes	—
695	C₂³×C₄	C₂×#99	1	4	yes	—
696	C₂³×C₄	C₂×#99	1	4	yes	—
697	C₂³×C₄	C₂×#99	1	4	yes	—
698	C₂³×C₄	C₂×#99	1	4	yes	—
699	C₂³×C₄	C₂×#99	1	4	yes	—
700	C₂³×C₄	C₂×#99	1	4	yes	—
701	C₂³×C₄	#421	1	4	yes	—
702	C₂³×C₄	B(4,𝔽₂)	1	8	yes	—
703	C₂³×C₄	#458	1	8	yes	—
704	C₂³×C₄	C₂²×C₂²⋊C₄	1	1	yes	characteristic
705	C₂³×C₄	C₂²×C₂²⋊C₄	1	1	yes	characteristic
706	C₂³×C₄	C₂²×C₂²⋊C₄	1	1	yes	characteristic
707	C₂³×C₄	C₂²×C₂²⋊C₄	1	2	yes	—
708	C₂³×C₄	C₂²×C₂²⋊C₄	1	2	yes	—
709	C₂³×C₄	C₂²×C₂²⋊C₄	1	2	yes	—
710	C₂³×C₄	C₂²×C₂²⋊C₄	1	1	yes	characteristic
711	C₂³×C₄	C₂²×C₂²⋊C₄	1	1	yes	characteristic
712	C₂³×C₄	C₂²×C₂²⋊C₄	1	1	yes	characteristic
713	C₂³×C₄	C₂²×C₂²⋊C₄	1	1	yes	characteristic
714	C₂³×C₄	C₂²×C₂²⋊C₄	1	1	yes	characteristic
715	C₂³×C₄	C₂²×C₂²⋊C₄	1	1	yes	characteristic
716	C₂³×C₄	C₂²×C₂²⋊C₄	1	1	yes	characteristic
717	C₂³×C₄	C₂²×C₂²⋊C₄	1	1	yes	characteristic
718	C₂³×C₄	C₂²×C₂²⋊C₄	1	1	yes	characteristic
719	C₂³×C₄	C₂²×C₂²⋊C₄	1	1	yes	characteristic
720	C₂³×C₄	C₂²×C₂²⋊C₄	1	1	yes	characteristic
721	C₂³×C₄	C₂²×C₂²⋊C₄	1	1	yes	characteristic
722	C₂³×C₄	C₂²×C₂²⋊C₄	1	1	yes	characteristic
723	C₂³×C₄	C₂²×C₂²⋊C₄	1	2	yes	—
724	C₂³×C₄	C₂²×C₂²⋊C₄	1	4	yes	—
725	C₂³×C₄	C₂²×C₂²⋊C₄	1	2	yes	—
726	C₂³×C₄	C₂²×C₂²⋊C₄	1	2	yes	—
727	C₂³×C₄	C₂²×C₂²⋊C₄	1	4	yes	—
728	C₂³×C₄	C₂²×C₂²⋊C₄	1	4	yes	—
729	C₂³×C₄	C₂²×C₂²⋊C₄	1	1	yes	characteristic
730	C₂³×C₄	C₂²×C₂²⋊C₄	1	1	yes	characteristic
731	C₂³×C₄	C₂×#120	1	2	yes	—
732	C₂³×C₄	C₂×#120	1	2	yes	—
733	C₂³×C₄	C₂×#120	1	2	yes	—
734	C₂³×C₄	C₂×#120	1	2	yes	—
735	C₂³×C₄	C₂×#120	1	2	yes	—
736	C₂³×C₄	C₂×#120	1	2	yes	—
737	C₂³×C₄	C₂×#120	1	2	yes	—
738	C₂³×C₄	C₂×#120	1	4	yes	—
739	C₂³×C₄	C₂×#120	1	2	yes	—
740	C₂³×C₄	C₂×#120	1	4	yes	—
741	C₂³×C₄	C₂×#120	1	4	yes	—
742	C₂³×C₄	C₂×#120	1	2	yes	—
743	C₂³×C₄	C₂×#120	1	2	yes	—
744	C₂³×C₄	C₂×#120	1	4	yes	—
745	C₂³×C₄	C₂×AGL(1,ℤ/8)	1	2	yes	—
746	C₂³×C₄	C₂×#137	1	2	yes	—
747	C₂³×C₄	C₂⁴×C₄	1	1	yes	characteristic
748	C₂³×C₄	C₂³×D₄	1	4	yes	—
749	C₂³×C₄	C₂³×D₄	1	1	yes	characteristic
750	C₂×C₄⋊C₄	C₂²×C₂²⋊C₄	1	4	yes	—
751	C₂×C₄⋊C₄	C₂²×C₂²⋊C₄	1	8	yes	—
752	C₂×C₄⋊C₄	C₂²×C₂²⋊C₄	1	4	yes	—
753	C₂×C₄⋊C₄	C₂²×C₂²⋊C₄	1	8	yes	—
754	C₂×C₄²	C₂×#99	1	4	yes	—
755	C₂×C₄²	C₂×#99	1	4	yes	—
756	C₂×C₄²	C₂×#99	1	4	yes	—
757	C₂×C₄²	C₂×#99	1	4	yes	—
758	C₂⁴	C₂×#379	1	2	yes	—
759	C₂⁴	C₂×#379	1	2	yes	—
760	C₂⁴	C₂×#379	1	2	yes	—
761	C₂⁴	C₂×#379	1	2	yes	—
762	C₂⁴	C₂×#379	1	1	yes	characteristic
763	C₂⁴	C₂×#379	1	1	yes	characteristic
764	C₂⁴	C₂×#379	1	2	yes	—
765	C₂⁴	C₂²×#99	1	2	yes	—
766	C₂⁴	C₂²×#99	1	2	yes	—
767	C₂⁴	C₂²×#99	1	2	yes	—
768	C₂⁴	C₂²×#99	1	2	yes	—
769	C₂⁴	C₂×#417	1	2	yes	—
770	C₂⁴	C₂×#417	1	2	yes	—
771	C₂⁴	C₂×#417	1	2	yes	—
772	C₂⁴	C₂×#417	1	2	yes	—
773	C₂⁴	#2896	1	2	yes	—
774	C₂⁴	#2896	1	2	yes	—
775	C₂⁴	C₂×#421	1	2	yes	—
776	C₂⁴	C₂×#421	1	2	yes	—
777	C₂⁴	C₂×#421	1	2	yes	—
778	C₂⁴	C₂×#421	1	2	yes	—
779	C₂⁴	#3006	1	8	yes	—
780	C₂⁴	#3007	1	8	yes	—
781	C₂⁴	#3021	1	4	yes	—
782	C₂⁴	#3022	1	4	yes	—
783	C₂⁴	C₂×B(4,𝔽₂)	1	4	yes	—
784	C₂⁴	C₂×#458	1	4	yes	—
785	C₂⁴	C₂³×C₂²⋊C₄	1	1	yes	characteristic
786	C₂⁴	C₂²×#120	1	2	yes	—
787	C₂⁴	C₂²×AGL(1,ℤ/8)	1	1	yes	characteristic
788	C₂⁴	C₂²×#137	1	1	yes	characteristic
789	C₂⁴	C₂×#575	1	2	yes	—
790	C₂²×C₄	#1781	1	4	yes	—
791	C₂²×C₄	#1781	1	4	yes	—
792	C₂²×C₄	#1781	1	4	yes	—
793	C₂²×C₄	#1781	1	4	yes	—
794	C₂²×C₄	#1790	1	8	yes	—
795	C₂²×C₄	#1790	1	8	yes	—
796	C₂²×C₄	#1790	1	8	yes	—
797	C₂²×C₄	#1790	1	8	yes	—
798	C₂²×C₄	C₂×#379	1	2	yes	—
799	C₂²×C₄	C₂×#379	1	2	yes	—
800	C₂²×C₄	C₂×#379	1	1	yes	characteristic
801	C₂²×C₄	C₂×#379	1	1	yes	characteristic
802	C₂²×C₄	C₂×#379	1	2	yes	—
803	C₂²×C₄	C₂×#379	1	2	yes	—
804	C₂²×C₄	C₂×#379	1	1	yes	characteristic
805	C₂²×C₄	C₂×#379	1	1	yes	characteristic
806	C₂²×C₄	C₂²×#99	1	2	yes	—
807	C₂²×C₄	C₂²×#99	1	2	yes	—
808	C₂²×C₄	C₂²×#99	1	2	yes	—
809	C₂²×C₄	C₂²×#99	1	2	yes	—
810	C₂²×C₄	C₂²×#99	1	2	yes	—
811	C₂²×C₄	C₂²×#99	1	2	yes	—
812	C₂²×C₄	C₂²×#99	1	2	yes	—
813	C₂²×C₄	C₂²×#99	1	2	yes	—
814	C₂²×C₄	C₂²×#99	1	2	yes	—
815	C₂²×C₄	C₂²×#99	1	2	yes	—
816	C₂²×C₄	C₂×#417	1	2	yes	—
817	C₂²×C₄	C₂×#417	1	2	yes	—
818	C₂²×C₄	C₂×#421	1	2	yes	—
819	C₂²×C₄	C₂×#421	1	2	yes	—
820	C₂²×C₄	C₂×B(4,𝔽₂)	1	4	yes	—
821	C₂²×C₄	C₂×B(4,𝔽₂)	1	4	yes	—
822	C₂²×C₄	C₂×#458	1	4	yes	—
823	C₂²×C₄	C₂×#458	1	4	yes	—
824	C₂²×C₄	C₂³×C₂²⋊C₄	1	2	yes	—
825	C₂²×C₄	C₂²×#120	1	2	yes	—
826	C₂³	#17592	1	4	yes	complemented
827	C₂³	C₂×#1781	1	2	yes	—
828	C₂³	C₂×#1781	1	2	yes	—
829	C₂³	#20601	1	4	yes	—
830	C₂³	#20601	1	4	yes	—
831	C₂³	#20605	1	4	yes	—
832	C₂³	C₂×#1790	1	4	yes	—
833	C₂³	C₂×#1790	1	4	yes	—
834	C₂³	#20618	1	4	yes	—
835	C₂³	#20618	1	4	yes	—
836	C₂³	C₂²×#379	1	1	yes	characteristic
837	C₂³	C₂³×#99	1	1	yes	characteristic
838	C₂³	C₂³×#99	1	1	yes	characteristic
839	C₂³	C₂²×#417	1	1	yes	characteristic
840	C₂³	C₂×#2896	1	1	yes	characteristic
841	C₂³	C₂²×#421	1	1	yes	characteristic
842	C₂³	C₂²×#421	1	1	yes	characteristic
843	C₂³	C₂×#3006	1	2	yes	—
844	C₂³	C₂×#3007	1	2	yes	—
845	C₂³	C₂×#3021	1	2	yes	—
846	C₂³	C₂×#3022	1	2	yes	—
847	C₂³	C₂²×B(4,𝔽₂)	1	2	yes	—
848	C₂³	C₂²×#458	1	2	yes	—
849	C₂×C₄	#8534	1	16	yes	—
850	C₂×C₄	#17592	1	4	yes	complemented
851	C₂×C₄	C₂×#1781	1	2	yes	—
852	C₂×C₄	C₂×#1781	1	2	yes	—
853	C₂×C₄	C₂×#1781	1	2	yes	—
854	C₂×C₄	C₂×#1781	1	2	yes	—
855	C₂×C₄	C₂×#1790	1	4	yes	—
856	C₂×C₄	C₂×#1790	1	4	yes	—
857	C₂×C₄	C₂×#1790	1	4	yes	—
858	C₂×C₄	C₂×#1790	1	4	yes	—
859	C₂²	#185258	1	8	yes	—
860	C₂²	#186840	1	4	yes	—
861	C₂²	C₂×#8534	1	4	yes	—
862	C₂²	C₂×#17592	1	1	yes	characteristic
863	C₂²	C₂×#17592	1	1	yes	characteristic
864	C₂²	#6343373	1	1	yes	characteristic
865	C₂²	#6343373	1	1	yes	characteristic
866	C₂²	#6346599	1	2	yes	—
867	C₂²	#6346600	1	2	yes	—
868	C₂²	#6346607	1	2	yes	—
869	C₂²	#6346608	1	2	yes	—
870	C₂²	C₂²×#1781	1	1	yes	characteristic
871	C₂²	C₂×#20601	1	1	yes	characteristic
872	C₂²	C₂×#20605	1	1	yes	characteristic
873	C₂²	C₂²×#1790	1	2	yes	—
874	C₂²	C₂×#20618	1	2	yes	—
875	C₄	C₂×#8534	1	4	yes	—
876	C₄	C₂×#8534	1	4	yes	—
877	C₂	C₂²×#8534	1	1	yes	characteristic
878	C₂	C₂×#186840	1	1	yes	characteristic
879	C₂	C₂×#185258	1	2	yes	—
880	C₂	#72240377	1	2	yes	—
881	C₂	#72311040	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³	C₂²×#379
commutator	C₂³×C₄	C₂⁴×C₄
Frattini, cosocle	C₂⁴×C₄	C₂⁵
prime radical	#72236479	C₂
LCS	G ▷ C₂³×C₄ ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³ ◁ C₂⁶×C₄ ◁ G
LECS	G ▷ C₂⁴×C₄ ▷ C₂³ ▷ C₁

Complements

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

N	H ≅ G/N	type
1. #72311853	C₂	semidirect
2. #72311846	C₂	semidirect
3. #72311717	C₂	semidirect
4. C₂×#154168	C₂	semidirect
5. #72311585	C₂	semidirect
6. #72311535	C₂	semidirect
7. #72311440	C₂	semidirect
8. #72261973	C₂	semidirect
9. #72237674	C₂	semidirect
11. #72219244	C₂	semidirect
12. C₂×#62773	C₄	semidirect
16. #7630947	C₄	semidirect
17. #7630945	C₄	semidirect
19. #7630943	C₄	semidirect
21. #7630941	C₄	semidirect
23. #7630940	C₄	semidirect
25. #7628472	C₄	semidirect
27. #7628282	C₄	semidirect
28. #7628174	C₄	semidirect
30. #7625417	C₄	semidirect
31. C₂³×#380	C₂²	semidirect
32. C₂×#20579	C₂²	semidirect
33. #196886	C₂²	semidirect
34. #196858	C₂²	semidirect
35. #196822	C₂²	semidirect
36. #196818	C₂²	semidirect
37. #184781	C₂²	semidirect
38. #184781	C₂²	semidirect
39. #184774	C₂²	semidirect
40. #184773	C₂²	semidirect
42. #184743	C₂²	semidirect
44. #154168	C₂²	semidirect
45. #154168	C₂²	semidirect
46. #154168	C₂²	semidirect
47. C₂×#7557	C₂²	semidirect
48. C₂×#7555	C₂²	semidirect
49. #97104	C₂²	semidirect
50. #97103	C₂²	semidirect
51. #97102	C₂²	semidirect
52. #97099	C₂²	semidirect
53. #97097	C₂²	semidirect
54. #97096	C₂²	semidirect
59. C₂×#3505	C₂×C₄	semidirect
61. C₂×#3501	C₂×C₄	semidirect
62. C₂×#3496	C₂×C₄	semidirect
63. C₂×#3460	C₂×C₄	semidirect
64. C₂×#3459	C₂×C₄	semidirect
111. #35174	C₂×C₄	semidirect
112. #35174	C₂×C₄	semidirect
113. #35168	C₂×C₄	semidirect
114. #35168	C₂×C₄	semidirect
115. #35091	C₂×C₄	semidirect
116. #35091	C₂×C₄	semidirect
119. #35010	C₂×C₄	semidirect
120. #35010	C₂×C₄	semidirect
121. #35000	C₂×C₄	semidirect
122. #35000	C₂×C₄	semidirect
127. #34987	C₂×C₄	semidirect
128. #34987	C₂×C₄	semidirect
129. #34985	C₂×C₄	semidirect
130. #34985	C₂×C₄	semidirect
131. #34984	C₂×C₄	semidirect
132. #34984	C₂×C₄	semidirect
137. #34562	C₂×C₄	semidirect
138. #34562	C₂×C₄	semidirect
139. #34185	C₂×C₄	semidirect
140. #34181	C₂×C₄	semidirect
141. #34181	C₂×C₄	semidirect
144. #34058	C₂×C₄	semidirect
145. #34057	C₂×C₄	semidirect
166. C₂³×#41	C₂²⋊C₄	semidirect
218. C₂×#525	C₂²⋊C₄	semidirect
219. C₂×#525	C₂²⋊C₄	semidirect
220. C₂×#525	C₂²⋊C₄	semidirect
221. C₂×#525	C₂²⋊C₄	semidirect
226. C₂²×C₂²⋊Q₈	C₂²⋊C₄	semidirect
227. C₂²×C₂²⋊Q₈	C₂²⋊C₄	semidirect
230. C₂²×#121	C₂²⋊C₄	semidirect
231. C₂²×#121	C₂²⋊C₄	semidirect
298. C₂²×#117	C₂²⋊C₄	semidirect
299. C₂²×#117	C₂²⋊C₄	semidirect
348. #2848	C₂²⋊C₄	semidirect
349. #2848	C₂²⋊C₄	semidirect
350. #2848	C₂²⋊C₄	semidirect
358. #2847	C₂²⋊C₄	semidirect
359. #2847	C₂²⋊C₄	semidirect
360. #2847	C₂²⋊C₄	semidirect
382. #2280	C₂²⋊C₄	semidirect
383. #2280	C₂²⋊C₄	semidirect
384. #2280	C₂²⋊C₄	semidirect
385. #2280	C₂²⋊C₄	semidirect
390. C₂×#380	C₂²⋊C₄	semidirect
391. C₂×#380	C₂²⋊C₄	semidirect
392. C₂×#380	C₂²⋊C₄	semidirect
415. C₂²×#41	C₂×C₂²⋊C₄	semidirect
416. C₂³×Q₈	C₂×C₂²⋊C₄	semidirect
433. C₂³×D₄	C₂×C₂²⋊C₄	semidirect
535. C₂×C₂²⋊Q₈	C₂×C₂²⋊C₄	semidirect
536. C₂×C₂²⋊Q₈	C₂×C₂²⋊C₄	semidirect
537. C₂×C₂²⋊Q₈	C₂×C₂²⋊C₄	semidirect
538. C₂×C₂²⋊Q₈	C₂×C₂²⋊C₄	semidirect
543. C₂×#121	C₂×C₂²⋊C₄	semidirect
544. C₂×#121	C₂×C₂²⋊C₄	semidirect
545. C₂×#121	C₂×C₂²⋊C₄	semidirect
546. C₂×#121	C₂×C₂²⋊C₄	semidirect
551. C₂×#117	C₂×C₂²⋊C₄	semidirect
552. C₂×#117	C₂×C₂²⋊C₄	semidirect
561. C₂²×C₄⋊C₄	C₂×C₂²⋊C₄	semidirect
562. C₂²×C₄⋊C₄	C₂×C₂²⋊C₄	semidirect
563. C₂²×C₄⋊C₄	C₂×C₂²⋊C₄	semidirect
564. C₂²×C₄⋊C₄	C₂×C₂²⋊C₄	semidirect
625. #380	C₂×C₂²⋊C₄	semidirect
626. #380	C₂×C₂²⋊C₄	semidirect
627. #380	C₂×C₂²⋊C₄	semidirect
628. #380	C₂×C₂²⋊C₄	semidirect
629. #380	C₂×C₂²⋊C₄	semidirect
630. #380	C₂×C₂²⋊C₄	semidirect
631. #380	C₂×C₂²⋊C₄	semidirect
826. C₂³	#17592	semidirect
850. C₂×C₄	#17592	semidirect

Maximal subgroups

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

subgroup	index
#72311853	2
#72311846	2
#72311717	2
C₂×#154168	2
#72311585	2
#72311535	2
#72311440	2
#72261973	2
#72237674	2
#72236479	2
#72219244	2