Subgroups — #72249359

Order 2048.

At least 11744 conjugacy classes of subgroups; only the 1772 normal subgroups are shown.

The subgroup lattice has 886 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#72240785	C₂	1	8	yes	maximal, complemented
2	#72240781	C₂	1	8	yes	maximal, complemented
3	#72239172	C₂	1	1	yes	maximal, characteristic, complemented
4	#72239169	C₂	1	1	yes	maximal, characteristic, complemented
5	#72239161	C₂	1	1	yes	maximal, characteristic, complemented
6	#72239048	C₂	1	1	yes	maximal, characteristic, complemented
7	#72239041	C₂	1	1	yes	maximal, characteristic, complemented
8	#72239035	C₂	1	1	yes	maximal, characteristic, complemented
9	#72239025	C₂	1	1	yes	maximal, characteristic, complemented
10	#72239008	C₂	1	1	yes	maximal, characteristic, complemented
11	#72238998	C₂	1	1	yes	maximal, characteristic, complemented
12	#72238966	C₂	1	1	yes	maximal, characteristic, complemented
13	#72238774	C₂	1	1	yes	maximal, characteristic, complemented
14	#72237572	C₂	1	1	yes	maximal, characteristic, complemented
15	#72237162	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×D₄×#525	C₂	1	1	yes	maximal, characteristic, complemented
17	#72214831	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂²×D₄×#41	C₂²	1	1	yes	characteristic
19	C₂⁴×C₄×D₄	C₂²	1	1	yes	characteristic
20	#10575872	C₂²	1	1	yes	characteristic, complemented
21	#10575094	C₂²	1	1	yes	characteristic, complemented
22	C₂×#60558	C₂²	1	1	yes	characteristic
23	C₂×#60558	C₂²	1	1	yes	characteristic, complemented
24	#7633331	C₂²	1	1	yes	characteristic, complemented
25	C₂×#36624	C₂²	1	1	yes	characteristic
26	D₄×#525	C₂²	1	8	yes	—
27	C₂×#34936	C₂²	1	1	yes	characteristic
28	C₂×#34935	C₂²	1	1	yes	characteristic
29	C₂×D₄×#117	C₂²	1	1	yes	characteristic
30	C₂×C₄×#525	C₂²	1	1	yes	characteristic
31	#6629272	C₂²	1	4	yes	complemented
32	#6629271	C₂²	1	4	yes	complemented
33	#6372471	C₂²	1	1	yes	characteristic, complemented
34	#6370997	C₂²	1	1	yes	characteristic, complemented
35	#6370977	C₂²	1	1	yes	characteristic
36	#6370977	C₂²	1	1	yes	characteristic, complemented
37	#6370924	C₂²	1	1	yes	characteristic, complemented
38	#6370924	C₂²	1	1	yes	characteristic, complemented
39	#6370924	C₂²	1	1	yes	characteristic, complemented
40	#6348730	C₂²	1	4	yes	complemented
41	#6348729	C₂²	1	4	yes	complemented
42	#6344036	C₂²	1	1	yes	characteristic, complemented
43	#6343381	C₂²	1	1	yes	characteristic, complemented
44	#6343377	C₂²	1	1	yes	characteristic, complemented
45	#6343016	C₂²	1	1	yes	characteristic, complemented
46	#6342924	C₂²	1	1	yes	characteristic, complemented
47	#6342924	C₂²	1	1	yes	characteristic, complemented
48	C₂×#17448	C₂²	1	1	yes	characteristic
49	C₂×#17448	C₂²	1	1	yes	characteristic
50	C₂×#17448	C₂²	1	1	yes	characteristic, complemented
51	C₂×#17448	C₂²	1	1	yes	characteristic, complemented
52	#414681	C₂²	1	4	yes	complemented
53	#411706	C₂²	1	4	yes	complemented
54	#353774	C₂²	1	1	yes	characteristic, complemented
55	#235217	C₂²	1	4	yes	complemented
56	#235216	C₂²	1	4	yes	complemented
57	#234286	C₂²	1	4	yes	complemented
58	#234285	C₂²	1	4	yes	complemented
59	#233589	C₂²	1	4	yes	complemented
60	#233588	C₂²	1	4	yes	complemented
61	#198023	C₂²	1	4	yes	complemented
62	#198022	C₂²	1	4	yes	complemented
63	#186510	C₂²	1	8	yes	complemented
64	#184859	C₂²	1	8	yes	complemented
65	#181801	C₂²	1	1	yes	characteristic, complemented
66	#181430	C₂²	1	1	yes	characteristic, complemented
67	#181240	C₂²	1	1	yes	characteristic, complemented
68	#181174	C₂²	1	1	yes	characteristic, complemented
69	#180863	C₂²	1	1	yes	characteristic, complemented
70	#115381	C₂²	1	8	yes	complemented
71	#112888	C₂²	1	8	yes	complemented
72	#111640	C₂²	1	8	yes	complemented
73	#111559	C₂²	1	8	yes	complemented
74	#105688	C₂²	1	8	yes	complemented
75	C₂⁵×D₄	D₄	1	1	yes	characteristic
76	C₂×D₄×#41	D₄	1	4	yes	complemented
77	C₂×D₄×#41	C₂³	1	4	yes	—
78	C₂²×#550	D₄	1	1	yes	characteristic, complemented
79	C₂²×#547	D₄	1	1	yes	characteristic, complemented
80	C₂²×D₄×Q₈	D₄	1	1	yes	characteristic, complemented
81	C₂²×D₄²	D₄	1	1	yes	characteristic, complemented
82	C₂×#3444	C₂³	1	1	yes	characteristic
83	C₂²×#532	C₂³	1	1	yes	characteristic
84	C₂²×#525	D₄	1	1	yes	characteristic
85	C₂²×C₄×#41	C₂³	1	1	yes	characteristic
86	C₂³×C₄×D₄	D₄	1	1	yes	characteristic
87	C₂³×C₄×D₄	D₄	1	1	yes	characteristic
88	C₂³×C₄×D₄	D₄	1	4	yes	—
89	C₂³×C₄×D₄	C₂³	1	4	yes	—
90	C₂³×C₄×D₄	C₂³	1	1	yes	characteristic
91	C₂³×C₄×D₄	C₂³	1	1	yes	characteristic
92	C₂⁴×C₄⋊C₄	D₄	1	1	yes	characteristic
93	C₂⁴×C₄²	C₂³	1	1	yes	characteristic
94	#60941	C₂³	1	2	yes	complemented
95	#60940	C₂³	1	2	yes	complemented
96	C₂×#3110	D₄	1	2	yes	complemented
97	C₂×#3109	D₄	1	2	yes	complemented
98	C₂×#3101	C₂³	1	2	yes	—
99	C₂×#3101	C₂³	1	2	yes	complemented
100	C₂×#3100	C₂³	1	2	yes	—
101	C₂×#3100	C₂³	1	2	yes	complemented
102	#60484	C₂³	1	2	yes	complemented
103	C₂×#3077	D₄	1	2	yes	complemented
104	#60415	C₂³	1	2	yes	complemented
105	C₂×#3036	D₄	1	2	yes	complemented
106	C₂×#2920	C₂³	1	1	yes	characteristic
107	C₂×#2920	C₂³	1	1	yes	characteristic
108	C₂×#2920	C₂³	1	1	yes	characteristic
109	C₂×#2920	C₂³	1	1	yes	characteristic
110	C₂×#2920	C₂³	1	1	yes	characteristic
111	C₂×#2920	C₂³	1	1	yes	characteristic
112	#36625	C₂³	1	2	yes	complemented
113	#36624	D₄	1	4	yes	—
114	#36624	C₂³	1	4	yes	—
115	#36624	C₂³	1	2	yes	complemented
116	C₂×#2854	D₄	1	2	yes	—
117	C₂×#2847	D₄	1	2	yes	—
118	#34936	D₄	1	4	yes	complemented
119	#34936	C₂³	1	4	yes	—
120	#34935	D₄	1	4	yes	complemented
121	#34935	C₂³	1	4	yes	—
122	C₂×#2536	D₄	1	2	yes	complemented
123	C₂×#2535	D₄	1	2	yes	complemented
124	C₂×#2397	D₄	1	4	yes	complemented
125	D₄×#117	D₄	1	4	yes	complemented
126	D₄×#117	C₂³	1	4	yes	—
127	C₄×#525	D₄	1	4	yes	—
128	C₄×#525	C₂³	1	4	yes	—
129	C₂×#2297	D₄	1	1	yes	characteristic
130	C₂×#2296	D₄	1	1	yes	characteristic
131	C₂×#2293	D₄	1	2	yes	complemented
132	#34012	C₂³	1	1	yes	characteristic
133	C₂×#2285	C₂³	1	1	yes	characteristic
134	C₂×#2280	D₄	1	1	yes	characteristic
135	C₂×C₄²×D₄	D₄	1	2	yes	complemented
136	C₂×C₄×#117	C₂³	1	1	yes	characteristic
137	#21329	C₂³	1	2	yes	complemented
138	#21209	C₂³	1	2	yes	complemented
139	#20733	D₄	1	4	yes	complemented
140	#20732	C₂³	1	4	yes	—
141	#20732	C₂³	1	4	yes	complemented
142	#20714	C₂³	1	4	yes	complemented
143	#20714	C₂³	1	4	yes	complemented
144	#20654	C₂³	1	4	yes	complemented
145	#20626	C₂³	1	4	yes	complemented
146	C₄×#418	D₄	1	4	yes	complemented
147	#17704	C₂³	1	4	yes	complemented
148	#17575	C₂³	1	2	yes	complemented
149	#17574	C₂³	1	2	yes	complemented
150	#17574	C₂³	1	4	yes	complemented
151	#17485	C₂³	1	4	yes	complemented
152	C₂×#1490	D₄	1	4	yes	complemented
153	C₂×#1486	C₂³	1	4	yes	—
154	C₂×#1486	C₂³	1	4	yes	—
155	C₂×#1486	C₂³	1	4	yes	complemented
156	C₂×#1486	C₂³	1	4	yes	complemented
157	#17437	C₂³	1	4	yes	complemented
158	#17437	C₂³	1	4	yes	complemented
159	C₂×#1478	D₄	1	4	yes	complemented
160	#10836	C₂³	1	4	yes	complemented
161	#8095	C₂³	1	4	yes	complemented
162	#7981	C₂³	1	4	yes	complemented
163	#7957	C₂³	1	4	yes	complemented
164	#7866	C₂³	1	4	yes	complemented
165	#7854	C₂³	1	4	yes	complemented
166	C₂³×#41	C₂×D₄	1	1	yes	characteristic
167	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
168	C₂⁴×D₄	C₂×D₄	1	4	yes	—
169	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
170	C₂⁵×C₄	C₂×D₄	1	1	yes	characteristic
171	C₂⁵×C₄	C₂×D₄	1	1	yes	characteristic
172	C₂⁵×C₄	C₂×D₄	1	1	yes	characteristic
173	C₂×#550	C₂×D₄	1	4	yes	—
174	C₂×D₄×Q₈	C₂×D₄	1	4	yes	—
175	C₂×#547	C₂×D₄	1	4	yes	—
176	C₂×D₄²	C₂×D₄	1	4	yes	—
177	C₂×#533	C₂×D₄	1	1	yes	characteristic, complemented
178	C₂×#533	C₂×D₄	1	1	yes	characteristic, complemented
179	C₂×#533	C₂⁴	1	1	yes	characteristic
180	C₂×#532	C₂×D₄	1	2	yes	—
181	C₂×#532	C₂×D₄	1	2	yes	—
182	C₂×#532	C₂×D₄	1	2	yes	—
183	C₂×#532	C₂×D₄	1	1	yes	characteristic, complemented
184	C₂×#532	C₂×D₄	1	1	yes	characteristic, complemented
185	C₂×#532	C₂⁴	1	1	yes	characteristic
186	C₂×#532	C₂⁴	1	2	yes	—
187	C₂²×C₄⋊Q₈	C₂×D₄	1	1	yes	characteristic
188	C₂²×#127	C₂×D₄	1	1	yes	characteristic
189	C₂×#525	C₂×D₄	1	4	yes	—
190	C₂²×#121	C₂×D₄	1	2	yes	—
191	C₂×C₄×#41	C₂×D₄	1	2	yes	—
192	C₂×C₄×#41	C₂×D₄	1	2	yes	—
193	C₂×C₄×#41	C₂×D₄	1	2	yes	—
194	C₂×C₄×#41	C₂⁴	1	2	yes	—
195	C₂²×C₄×Q₈	C₂×D₄	1	1	yes	characteristic
196	C₂²×C₄×Q₈	C₂×D₄	1	1	yes	characteristic
197	C₂²×C₄×D₄	C₂×D₄	1	1	yes	characteristic
198	C₂²×C₄×D₄	C₂×D₄	1	2	yes	—
199	C₂²×C₄×D₄	C₂×D₄	1	1	yes	characteristic
200	C₂²×C₄×D₄	C₂×D₄	1	2	yes	—
201	C₂²×C₄×D₄	C₂×D₄	1	2	yes	—
202	C₂²×C₄×D₄	C₂×D₄	1	2	yes	—
203	C₂²×C₄×D₄	C₂×D₄	1	2	yes	—
204	C₂²×C₄×D₄	C₂×D₄	1	2	yes	—
205	C₂²×C₄×D₄	C₂×D₄	1	1	yes	characteristic
206	C₂²×C₄×D₄	C₂×D₄	1	2	yes	—
207	C₂²×C₄×D₄	C₂×D₄	1	1	yes	characteristic
208	C₂²×C₄×D₄	C₂×D₄	1	2	yes	—
209	C₂²×C₄×D₄	C₂×D₄	1	2	yes	—
210	C₂²×C₄×D₄	C₂×D₄	1	2	yes	—
211	C₂²×C₄×D₄	C₂×D₄	1	1	yes	characteristic
212	C₂²×C₄×D₄	C₂×D₄	1	1	yes	characteristic
213	C₂²×C₄×D₄	C₂×D₄	1	2	yes	—
214	C₂²×C₄×D₄	C₂×D₄	1	2	yes	—
215	C₂²×C₄×D₄	C₂×D₄	1	2	yes	—
216	C₂²×C₄×D₄	C₂×D₄	1	2	yes	—
217	C₂²×C₄×D₄	C₂×D₄	1	4	yes	—
218	C₂²×C₄×D₄	C₂×D₄	1	4	yes	—
219	C₂²×C₄×D₄	C₂×D₄	1	2	yes	—
220	C₂²×C₄×D₄	#41	1	2	yes	—
221	C₂²×C₄×D₄	#41	1	2	yes	—
222	C₂²×C₄×D₄	C₂⁴	1	2	yes	—
223	C₂²×C₄×D₄	C₂⁴	1	2	yes	—
224	C₂²×#117	C₂×D₄	1	1	yes	characteristic
225	C₂²×#117	C₂×D₄	1	1	yes	characteristic
226	C₂²×#117	C₂×D₄	1	1	yes	characteristic
227	C₂³×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
228	C₂³×C₄⋊C₄	C₂×D₄	1	4	yes	—
229	C₂³×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
230	C₂³×C₄²	C₂×D₄	1	1	yes	characteristic
231	C₂³×C₄²	C₂×D₄	1	1	yes	characteristic
232	C₂³×C₄²	C₂×D₄	1	2	yes	—
233	C₂³×C₄²	C₂×D₄	1	2	yes	—
234	C₂³×C₄²	C₂×D₄	1	2	yes	—
235	C₂³×C₄²	C₂×D₄	1	1	yes	characteristic
236	C₂³×C₄²	C₂⁴	1	2	yes	—
237	C₂³×C₄²	C₂⁴	1	1	yes	characteristic
238	C₂×#476	C₂×D₄	1	4	yes	complemented
239	C₂×#474	C₂×D₄	1	4	yes	complemented
240	C₂×#461	C₂×D₄	1	4	yes	complemented
241	C₂×#459	C₂×D₄	1	4	yes	complemented
242	C₂×#432	C₂×D₄	1	2	yes	complemented
243	C₂×#432	C₂×D₄	1	2	yes	complemented
244	C₂×#431	C₂×D₄	1	2	yes	complemented
245	C₂×#431	C₂×D₄	1	2	yes	complemented
246	C₂×#431	C₂×D₄	1	2	yes	complemented
247	C₂×#431	C₂⁴	1	2	yes	—
248	C₂×#431	C₂⁴	1	2	yes	—
249	C₂×#431	C₂⁴	1	2	yes	—
250	C₂×#431	C₂⁴	1	2	yes	—
251	C₂×#423	C₂×D₄	1	2	yes	complemented
252	C₂×#423	C₂⁴	1	2	yes	—
253	C₂×#423	C₂⁴	1	2	yes	—
254	C₂×C₄×M₁₆	C₂×D₄	1	2	yes	complemented
255	C₂×C₄×M₁₆	C₂×D₄	1	2	yes	complemented
256	#2854	C₂×D₄	1	8	yes	—
257	#2847	C₂×D₄	1	8	yes	—
258	#2536	C₂×D₄	1	8	yes	—
259	#2535	C₂×D₄	1	8	yes	—
260	#2397	C₂×D₄	1	16	yes	—
261	#2297	C₂×D₄	1	4	yes	—
262	#2296	C₂×D₄	1	4	yes	—
263	#2293	C₂×D₄	1	8	yes	—
264	#2285	C₂×D₄	1	2	yes	—
265	#2285	C₂×D₄	1	2	yes	—
266	#2285	C₂×D₄	1	2	yes	—
267	#2285	C₂⁴	1	2	yes	—
268	#2285	C₂⁴	1	2	yes	—
269	#2283	C₂×D₄	1	2	yes	complemented
270	C₂×#382	C₂×D₄	1	2	yes	—
271	#2280	C₂×D₄	1	4	yes	—
272	C₂×#380	C₂×D₄	1	2	yes	—
273	C₄²×D₄	C₂×D₄	1	8	yes	—
274	C₄×#117	C₂×D₄	1	2	yes	—
275	C₄×#117	C₂×D₄	1	2	yes	—
276	C₄×#117	C₂×D₄	1	2	yes	—
277	C₄×#117	C₂×D₄	1	2	yes	complemented
278	C₄×#117	C₂⁴	1	2	yes	—
279	C₂×C₄×C₄⋊C₄	C₂×D₄	1	2	yes	—
280	C₂×#376	C₂×D₄	1	2	yes	—
281	C₂×C₄³	C₂×D₄	1	2	yes	—
282	C₄×#102	C₂×D₄	1	16	yes	complemented
283	C₂×D₄⋊C₈	C₂×D₄	1	16	yes	complemented
284	C₂⁶	#120	1	1	yes	characteristic
285	C₂²×#41	#120	1	2	yes	—
286	C₂²×#41	C₂²×D₄	1	2	yes	—
287	C₂³×Q₈	#120	1	1	yes	characteristic
288	C₂³×D₄	#120	1	1	yes	characteristic
289	C₂³×D₄	#120	1	1	yes	characteristic
290	C₂³×D₄	#120	1	2	yes	—
291	C₂³×D₄	#120	1	2	yes	—
292	C₂³×D₄	#120	1	2	yes	—
293	C₂³×D₄	#120	1	2	yes	—
294	C₂³×D₄	#120	1	2	yes	—
295	C₂³×D₄	#120	1	1	yes	characteristic
296	C₂³×D₄	#120	1	2	yes	—
297	C₂³×D₄	#121	1	2	yes	—
298	C₂³×D₄	#121	1	2	yes	—
299	C₂³×D₄	C₂²×D₄	1	2	yes	—
300	C₂³×D₄	C₂²×D₄	1	2	yes	—
301	C₂⁴×C₄	#120	1	1	yes	characteristic
302	C₂⁴×C₄	#120	1	2	yes	—
303	C₂⁴×C₄	#120	1	2	yes	—
304	C₂⁴×C₄	#120	1	1	yes	characteristic
305	C₂⁴×C₄	#120	1	2	yes	—
306	C₂⁴×C₄	#120	1	1	yes	characteristic
307	C₂⁴×C₄	C₂²×D₄	1	2	yes	—
308	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
309	C₂⁴×C₄	C₂²×D₄	1	2	yes	—
310	C₂⁴×C₄	C₂²×D₄	1	2	yes	—
311	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
312	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
313	C₂×C₄⋊Q₈	#120	1	2	yes	—
314	C₂×C₄⋊Q₈	C₂²×D₄	1	2	yes	—
315	C₂×C₄⋊Q₈	C₂²×D₄	1	1	yes	characteristic, complemented
316	C₂×C₄⋊Q₈	C₂²×D₄	1	1	yes	characteristic, complemented
317	C₂×C₄⋊Q₈	C₂²×D₄	1	1	yes	characteristic, complemented
318	C₂×#127	#120	1	2	yes	—
319	C₂×#127	C₂²×D₄	1	2	yes	—
320	C₂×#127	C₂²×D₄	1	1	yes	characteristic, complemented
321	#525	AGL(1,ℤ/8)	1	16	yes	complemented
322	C₂×#121	#120	1	4	yes	—
323	C₂×#121	C₂²×D₄	1	4	yes	—
324	C₂×C₄×Q₈	#120	1	2	yes	—
325	C₂×C₄×Q₈	#120	1	2	yes	—
326	C₂×C₄×Q₈	C₂²×D₄	1	2	yes	—
327	C₂×C₄×Q₈	C₂²×D₄	1	2	yes	—
328	C₂×C₄×D₄	#120	1	4	yes	—
329	C₂×C₄×D₄	#120	1	4	yes	—
330	C₂×C₄×D₄	#120	1	4	yes	—
331	C₂×C₄×D₄	#120	1	2	yes	—
332	C₂×C₄×D₄	#120	1	2	yes	—
333	C₂×C₄×D₄	#120	1	4	yes	—
334	C₂×C₄×D₄	#120	1	2	yes	—
335	C₂×C₄×D₄	#120	1	2	yes	—
336	C₂×C₄×D₄	#120	1	2	yes	—
337	C₂×C₄×D₄	#120	1	2	yes	—
338	C₂×C₄×D₄	#120	1	4	yes	—
339	C₂×C₄×D₄	#120	1	2	yes	—
340	C₂×C₄×D₄	#120	1	2	yes	—
341	C₂×C₄×D₄	#120	1	4	yes	—
342	C₂×C₄×D₄	#120	1	2	yes	—
343	C₂×C₄×D₄	#120	1	2	yes	—
344	C₂×C₄×D₄	#120	1	4	yes	—
345	C₂×C₄×D₄	#121	1	4	yes	—
346	C₂×C₄×D₄	#121	1	4	yes	—
347	C₂×C₄×D₄	#121	1	2	yes	—
348	C₂×C₄×D₄	#121	1	2	yes	—
349	C₂×C₄×D₄	#121	1	4	yes	—
350	C₂×C₄×D₄	#121	1	2	yes	—
351	C₂×C₄×D₄	#121	1	2	yes	—
352	C₂×C₄×D₄	#121	1	4	yes	—
353	C₂×C₄×D₄	#121	1	2	yes	—
354	C₂×C₄×D₄	#121	1	2	yes	—
355	C₂×C₄×D₄	#121	1	4	yes	—
356	C₂×C₄×D₄	#121	1	2	yes	—
357	C₂×C₄×D₄	#121	1	2	yes	—
358	C₂×C₄×D₄	#121	1	4	yes	—
359	C₂×C₄×D₄	#127	1	2	yes	—
360	C₂×C₄×D₄	#127	1	2	yes	—
361	C₂×C₄×D₄	#127	1	4	yes	—
362	C₂×C₄×D₄	#127	1	2	yes	—
363	C₂×C₄×D₄	#127	1	2	yes	—
364	C₂×C₄×D₄	#127	1	4	yes	—
365	C₂×C₄×D₄	C₂²×D₄	1	2	yes	—
366	C₂×C₄×D₄	C₂²×D₄	1	2	yes	—
367	C₂×C₄×D₄	C₂²×D₄	1	4	yes	—
368	C₂×C₄×D₄	C₂²×D₄	1	4	yes	—
369	C₂×C₄×D₄	C₂²×D₄	1	4	yes	—
370	C₂×C₄×D₄	C₂²×D₄	1	4	yes	—
371	C₂×C₄×D₄	C₂²×D₄	1	2	yes	—
372	C₂×C₄×D₄	C₂²×D₄	1	2	yes	—
373	C₂×C₄×D₄	C₂²×D₄	1	2	yes	—
374	C₂×C₄×D₄	C₂²×D₄	1	2	yes	—
375	C₂×C₄×D₄	C₂²×D₄	1	4	yes	—
376	C₂×C₄×D₄	C₂²×D₄	1	4	yes	—
377	C₂×C₄×D₄	C₂×#41	1	4	yes	—
378	C₂×#117	#120	1	2	yes	—
379	C₂×#117	#120	1	2	yes	—
380	C₂×#117	#120	1	2	yes	—
381	C₂×#117	C₂²×D₄	1	2	yes	—
382	C₂×#117	C₂²×D₄	1	2	yes	—
383	C₂×#117	C₂²×D₄	1	2	yes	—
384	C₂²×C₄⋊C₄	#120	1	2	yes	—
385	C₂²×C₄⋊C₄	#120	1	2	yes	—
386	C₂²×C₄⋊C₄	#120	1	2	yes	—
387	C₂²×C₄⋊C₄	#120	1	1	yes	characteristic
388	C₂²×C₄⋊C₄	#120	1	1	yes	characteristic
389	C₂²×C₄⋊C₄	#120	1	2	yes	—
390	C₂²×C₄⋊C₄	#120	1	2	yes	—
391	C₂²×C₄⋊C₄	#120	1	1	yes	characteristic
392	C₂²×C₄⋊C₄	#120	1	1	yes	characteristic
393	C₂²×C₄⋊C₄	#120	1	2	yes	—
394	C₂²×C₄⋊C₄	#121	1	2	yes	—
395	C₂²×C₄⋊C₄	#121	1	2	yes	—
396	C₂²×C₄⋊C₄	C₂²×D₄	1	2	yes	—
397	C₂²×C₄⋊C₄	C₂²×D₄	1	2	yes	—
398	C₂²×C₄²	#120	1	2	yes	—
399	C₂²×C₄²	#120	1	2	yes	—
400	C₂²×C₄²	#120	1	2	yes	—
401	C₂²×C₄²	#120	1	2	yes	—
402	C₂²×C₄²	#120	1	2	yes	—
403	C₂²×C₄²	C₂²×D₄	1	2	yes	—
404	C₂²×C₄²	C₂²×D₄	1	2	yes	—
405	C₂²×C₄²	C₂²×D₄	1	2	yes	—
406	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
407	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
408	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
409	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
410	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
411	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
412	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
413	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
414	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
415	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
416	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
417	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
418	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
419	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
420	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
421	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
422	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
423	C₂²×C₄²	C₂×#41	1	1	yes	characteristic
424	C₂²×C₄²	C₂×#41	1	1	yes	characteristic
425	C₂²×C₄²	H(5,𝔽₂)	1	1	yes	characteristic
426	C₂²×C₄²	H(5,𝔽₂)	1	1	yes	characteristic
427	C₂²×C₄²	H(5,𝔽₂)	1	1	yes	characteristic
428	C₂²×C₄²	H(5,𝔽₂)	1	1	yes	characteristic
429	C₂²×C₄²	H(5,𝔽₂)	1	1	yes	characteristic
430	C₂²×C₄²	H(5,𝔽₂)	1	1	yes	characteristic
431	C₂²×C₄²	H(5,𝔽₂)	1	1	yes	characteristic
432	C₂²×C₄²	H(5,𝔽₂)	1	1	yes	characteristic
433	C₂²×C₄²	C₂⁵	1	1	yes	characteristic
434	C₂×C₄⋊C₈	C₂²×D₄	1	4	yes	complemented
435	C₂×C₄⋊C₈	C₂²×D₄	1	4	yes	complemented
436	C₂×C₄×C₈	C₂²×D₄	1	4	yes	complemented
437	C₂×C₄×C₈	C₂²×D₄	1	4	yes	complemented
438	#382	#120	1	4	yes	—
439	#382	C₂²×D₄	1	4	yes	—
440	#380	#120	1	4	yes	—
441	#380	C₂²×D₄	1	4	yes	—
442	C₄×C₄⋊C₄	#120	1	4	yes	—
443	C₄×C₄⋊C₄	C₂²×D₄	1	4	yes	—
444	C₄×C₄⋊C₄	C₂²×D₄	1	4	yes	complemented
445	#376	#120	1	4	yes	—
446	#376	C₂²×D₄	1	4	yes	—
447	C₂×#95	#120	1	4	yes	—
448	C₄³	#120	1	4	yes	—
449	C₄³	C₂²×D₄	1	4	yes	—
450	C₂⁵	C₂×#120	1	2	yes	—
451	C₂⁵	C₂×#120	1	1	yes	characteristic
452	C₂×#41	C₂×AGL(1,ℤ/8)	1	8	yes	—
453	C₂²×Q₈	C₂×#120	1	2	yes	—
454	C₂²×D₄	#392	1	2	yes	—
455	C₂²×D₄	#392	1	2	yes	—
456	C₂²×D₄	#392	1	4	yes	—
457	C₂²×D₄	#392	1	4	yes	—
458	C₂²×D₄	#392	1	2	yes	—
459	C₂²×D₄	#392	1	2	yes	—
460	C₂²×D₄	C₂×#120	1	2	yes	—
461	C₂²×D₄	C₂×#120	1	2	yes	—
462	C₂²×D₄	C₂×#120	1	4	yes	—
463	C₂²×D₄	C₂×#120	1	4	yes	—
464	C₂²×D₄	C₂×#120	1	4	yes	—
465	C₂²×D₄	C₂×#120	1	2	yes	—
466	C₂²×D₄	C₂×#121	1	4	yes	—
467	C₂³×C₄	C₂×#120	1	2	yes	—
468	C₂³×C₄	C₂×#120	1	1	yes	characteristic
469	C₂³×C₄	C₂×#120	1	1	yes	characteristic
470	C₂³×C₄	C₂×#120	1	1	yes	characteristic
471	C₂³×C₄	C₂×#120	1	1	yes	characteristic
472	C₂³×C₄	C₂×#120	1	1	yes	characteristic
473	C₂³×C₄	C₂×#120	1	1	yes	characteristic
474	C₂³×C₄	C₂×#120	1	1	yes	characteristic
475	C₂³×C₄	C₂×#120	1	2	yes	—
476	C₂³×C₄	C₂×#120	1	2	yes	—
477	C₂³×C₄	C₂×#120	1	1	yes	characteristic
478	C₂³×C₄	C₂×#120	1	1	yes	characteristic
479	C₂³×C₄	C₂×#120	1	1	yes	characteristic
480	C₂³×C₄	C₂×#120	1	1	yes	characteristic
481	C₂³×C₄	C₂×#120	1	1	yes	characteristic
482	C₂³×C₄	C₂×#120	1	1	yes	characteristic
483	C₂³×C₄	C₂×#120	1	1	yes	characteristic
484	C₂³×C₄	C₂×#120	1	1	yes	characteristic
485	C₂³×C₄	C₂×#120	1	1	yes	characteristic
486	C₂³×C₄	C₂×#120	1	1	yes	characteristic
487	C₂³×C₄	C₂×#121	1	1	yes	characteristic
488	C₂³×C₄	C₂×#121	1	1	yes	characteristic
489	C₂³×C₄	#534	1	1	yes	characteristic
490	C₂³×C₄	#534	1	1	yes	characteristic
491	C₂³×C₄	#534	1	1	yes	characteristic
492	C₂³×C₄	#534	1	1	yes	characteristic
493	C₂³×C₄	D₄²	1	1	yes	characteristic
494	C₂³×C₄	D₄²	1	1	yes	characteristic
495	C₂³×C₄	D₄²	1	1	yes	characteristic
496	C₂³×C₄	D₄²	1	1	yes	characteristic
497	C₂³×C₄	D₄²	1	1	yes	characteristic
498	C₂³×C₄	D₄²	1	1	yes	characteristic
499	C₂³×C₄	D₄²	1	1	yes	characteristic
500	C₂³×C₄	D₄²	1	1	yes	characteristic
501	C₂³×C₄	D₄²	1	1	yes	characteristic
502	C₂³×C₄	D₄²	1	1	yes	characteristic
503	C₂³×C₄	D₄²	1	1	yes	characteristic
504	C₂³×C₄	D₄²	1	1	yes	characteristic
505	C₂³×C₄	#546	1	1	yes	characteristic
506	C₂³×C₄	#546	1	1	yes	characteristic
507	C₂³×C₄	#546	1	1	yes	characteristic
508	C₂³×C₄	#546	1	1	yes	characteristic
509	C₂³×C₄	C₂×AGL(1,ℤ/8)	1	8	yes	—
510	C₂³×C₄	C₂³×D₄	1	1	yes	characteristic
511	C₂³×C₄	C₂³×D₄	1	1	yes	characteristic
512	C₂³×C₄	C₂³×D₄	1	1	yes	characteristic
513	C₄×D₄	#392	1	4	yes	—
514	C₄×D₄	#392	1	4	yes	—
515	C₄×D₄	#392	1	4	yes	—
516	C₄×D₄	#392	1	4	yes	—
517	C₄×D₄	#392	1	4	yes	—
518	C₄×D₄	#392	1	4	yes	—
519	C₄×D₄	#392	1	4	yes	—
520	C₄×D₄	#392	1	4	yes	—
521	C₄×D₄	C₂×#120	1	4	yes	—
522	C₄×D₄	C₂×#120	1	4	yes	—
523	C₄×D₄	C₂×#121	1	4	yes	—
524	C₄×D₄	C₂×#121	1	4	yes	—
525	C₄×D₄	C₂×#121	1	4	yes	—
526	C₄×D₄	C₂×#121	1	4	yes	—
527	C₄×D₄	C₂×#127	1	4	yes	—
528	C₄×D₄	C₂×#127	1	4	yes	—
529	#117	C₂×AGL(1,ℤ/8)	1	8	yes	—
530	C₂×C₄⋊C₄	#392	1	2	yes	—
531	C₂×C₄⋊C₄	#392	1	2	yes	—
532	C₂×C₄⋊C₄	#392	1	2	yes	—
533	C₂×C₄⋊C₄	#392	1	2	yes	—
534	C₂×C₄⋊C₄	#392	1	4	yes	—
535	C₂×C₄⋊C₄	#392	1	4	yes	—
536	C₂×C₄⋊C₄	C₂×#120	1	4	yes	—
537	C₂×C₄⋊C₄	C₂×#120	1	2	yes	—
538	C₂×C₄⋊C₄	C₂×#120	1	2	yes	—
539	C₂×C₄⋊C₄	C₂×#120	1	4	yes	—
540	C₂×C₄⋊C₄	C₂×#120	1	2	yes	—
541	C₂×C₄⋊C₄	C₂×#120	1	2	yes	—
542	C₂×C₄⋊C₄	C₂×#120	1	4	yes	—
543	C₂×C₄⋊C₄	C₂×#121	1	4	yes	—
544	C₂×C₄²	C₂×#120	1	4	yes	—
545	C₂×C₄²	C₂×#120	1	4	yes	—
546	C₂×C₄²	C₂×#120	1	1	yes	characteristic
547	C₂×C₄²	C₂×#120	1	1	yes	characteristic
548	C₂×C₄²	C₂×#120	1	1	yes	characteristic
549	C₂×C₄²	C₂×#120	1	1	yes	characteristic
550	C₂×C₄²	C₂×#120	1	1	yes	characteristic
551	C₂×C₄²	C₂×#120	1	1	yes	characteristic
552	C₂×C₄²	C₂×#120	1	1	yes	characteristic
553	C₂×C₄²	C₂×#120	1	1	yes	characteristic
554	C₂×C₄²	C₂×#120	1	1	yes	characteristic
555	C₂×C₄²	C₂×#120	1	1	yes	characteristic
556	C₂×C₄²	C₂×#120	1	1	yes	characteristic
557	C₂×C₄²	C₂×#120	1	1	yes	characteristic
558	C₂×C₄²	C₂×#120	1	1	yes	characteristic
559	C₂×C₄²	C₂×#120	1	1	yes	characteristic
560	C₂×C₄²	C₂×#120	1	1	yes	characteristic
561	C₂×C₄²	C₂×#120	1	1	yes	characteristic
562	C₂×C₄²	C₂×#120	1	1	yes	characteristic
563	C₂×C₄²	C₂×#120	1	1	yes	characteristic
564	C₂×C₄²	C₂×#121	1	1	yes	characteristic
565	C₂×C₄²	C₂×#121	1	1	yes	characteristic
566	C₂×C₄²	C₂×#121	1	1	yes	characteristic
567	C₂×C₄²	C₂×#121	1	1	yes	characteristic
568	C₂×C₄²	C₂×#121	1	1	yes	characteristic
569	C₂×C₄²	C₂×#121	1	1	yes	characteristic
570	C₂×C₄²	C₂×#121	1	1	yes	characteristic
571	C₂×C₄²	C₂×#121	1	1	yes	characteristic
572	C₂×C₄²	C₂×#121	1	1	yes	characteristic
573	C₂×C₄²	C₂×#121	1	1	yes	characteristic
574	C₂×C₄²	C₂×#127	1	1	yes	characteristic
575	C₂×C₄²	C₂×#127	1	1	yes	characteristic
576	C₂×C₄²	C₂×#127	1	1	yes	characteristic
577	C₂×C₄²	C₂×#127	1	1	yes	characteristic
578	C₂×C₄²	#534	1	1	yes	characteristic
579	C₂×C₄²	#534	1	1	yes	characteristic
580	C₂×C₄²	#534	1	1	yes	characteristic
581	C₂×C₄²	#534	1	1	yes	characteristic
582	C₂×C₄²	#534	1	1	yes	characteristic
583	C₂×C₄²	#534	1	1	yes	characteristic
584	C₂×C₄²	#534	1	1	yes	characteristic
585	C₂×C₄²	#534	1	1	yes	characteristic
586	C₂×C₄²	#534	1	1	yes	characteristic
587	C₂×C₄²	#534	1	1	yes	characteristic
588	C₂×C₄²	#534	1	1	yes	characteristic
589	C₂×C₄²	#534	1	1	yes	characteristic
590	C₂×C₄²	#535	1	1	yes	characteristic
591	C₂×C₄²	#535	1	1	yes	characteristic
592	C₂×C₄²	#535	1	1	yes	characteristic
593	C₂×C₄²	#535	1	1	yes	characteristic
594	C₂×C₄²	#535	1	1	yes	characteristic
595	C₂×C₄²	#535	1	1	yes	characteristic
596	C₂×C₄²	#535	1	1	yes	characteristic
597	C₂×C₄²	#535	1	1	yes	characteristic
598	C₂×C₄²	D₄²	1	1	yes	characteristic
599	C₂×C₄²	D₄²	1	1	yes	characteristic
600	C₂×C₄²	D₄²	1	1	yes	characteristic
601	C₂×C₄²	D₄²	1	1	yes	characteristic
602	C₂×C₄²	D₄²	1	1	yes	characteristic
603	C₂×C₄²	D₄²	1	1	yes	characteristic
604	C₂×C₄²	D₄²	1	1	yes	characteristic
605	C₂×C₄²	D₄²	1	1	yes	characteristic
606	C₂×C₄²	D₄²	1	1	yes	characteristic
607	C₂×C₄²	D₄²	1	1	yes	characteristic
608	C₂×C₄²	D₄²	1	1	yes	characteristic
609	C₂×C₄²	D₄²	1	1	yes	characteristic
610	C₂×C₄²	D₄²	1	1	yes	characteristic
611	C₂×C₄²	D₄²	1	1	yes	characteristic
612	C₂×C₄²	D₄²	1	1	yes	characteristic
613	C₂×C₄²	D₄²	1	1	yes	characteristic
614	C₂×C₄²	D₄²	1	1	yes	characteristic
615	C₂×C₄²	D₄²	1	1	yes	characteristic
616	C₂×C₄²	D₄²	1	1	yes	characteristic
617	C₂×C₄²	D₄²	1	1	yes	characteristic
618	C₂×C₄²	D₄²	1	1	yes	characteristic
619	C₂×C₄²	D₄²	1	1	yes	characteristic
620	C₂×C₄²	D₄²	1	1	yes	characteristic
621	C₂×C₄²	D₄²	1	1	yes	characteristic
622	C₂×C₄²	D₄²	1	1	yes	characteristic
623	C₂×C₄²	D₄²	1	1	yes	characteristic
624	C₂×C₄²	D₄²	1	1	yes	characteristic
625	C₂×C₄²	D₄²	1	1	yes	characteristic
626	C₂×C₄²	D₄²	1	1	yes	characteristic
627	C₂×C₄²	D₄²	1	1	yes	characteristic
628	C₂×C₄²	D₄²	1	1	yes	characteristic
629	C₂×C₄²	D₄²	1	1	yes	characteristic
630	C₂×C₄²	D₄²	1	1	yes	characteristic
631	C₂×C₄²	D₄²	1	1	yes	characteristic
632	C₂×C₄²	D₄²	1	1	yes	characteristic
633	C₂×C₄²	D₄²	1	1	yes	characteristic
634	C₂×C₄²	#546	1	1	yes	characteristic
635	C₂×C₄²	#546	1	1	yes	characteristic
636	C₂×C₄²	#546	1	1	yes	characteristic
637	C₂×C₄²	#546	1	1	yes	characteristic
638	C₂×C₄²	#546	1	1	yes	characteristic
639	C₂×C₄²	#546	1	1	yes	characteristic
640	C₂×C₄²	#546	1	1	yes	characteristic
641	C₂×C₄²	#546	1	1	yes	characteristic
642	C₂×C₄²	#546	1	1	yes	characteristic
643	C₂×C₄²	#546	1	1	yes	characteristic
644	C₂×C₄²	#546	1	1	yes	characteristic
645	C₂×C₄²	#546	1	1	yes	characteristic
646	C₂×C₄²	C₂³×D₄	1	1	yes	characteristic
647	C₂×C₄²	C₂³×D₄	1	1	yes	characteristic
648	C₂×C₄²	C₂³×D₄	1	1	yes	characteristic
649	C₂×C₄²	C₂³×D₄	1	1	yes	characteristic
650	C₂×C₄²	C₂³×D₄	1	1	yes	characteristic
651	C₂×C₄²	C₂³×D₄	1	1	yes	characteristic
652	C₂×C₄²	C₂³×D₄	1	1	yes	characteristic
653	C₂×C₄²	C₂²×#41	1	1	yes	characteristic
654	C₂×C₄²	C₂×H(5,𝔽₂)	1	1	yes	characteristic
655	C₂×C₄²	C₂×H(5,𝔽₂)	1	1	yes	characteristic
656	C₂×C₄²	C₂×H(5,𝔽₂)	1	1	yes	characteristic
657	C₂×C₄²	C₂×H(5,𝔽₂)	1	1	yes	characteristic
658	#95	C₂×#120	1	8	yes	—
659	C₂⁴	#2403	1	1	yes	characteristic
660	C₂⁴	#2403	1	1	yes	characteristic
661	C₂⁴	#2410	1	1	yes	characteristic
662	C₂⁴	#2410	1	1	yes	characteristic
663	C₂⁴	#2846	1	1	yes	characteristic
664	C₂⁴	#2846	1	1	yes	characteristic
665	C₂⁴	#3003	1	4	yes	—
666	C₂⁴	C₂²×#120	1	1	yes	characteristic
667	C₂×Q₈	#3003	1	4	yes	complemented
668	C₂×D₄	#2010	1	8	yes	complemented
669	C₂×D₄	C₂×#392	1	4	yes	—
670	C₂×D₄	C₂×#392	1	4	yes	—
671	C₂×D₄	#3003	1	4	yes	complemented
672	C₂²×C₄	C₂×#392	1	1	yes	characteristic
673	C₂²×C₄	C₂×#392	1	1	yes	characteristic
674	C₂²×C₄	C₂×#392	1	1	yes	characteristic
675	C₂²×C₄	C₂×#392	1	1	yes	characteristic
676	C₂²×C₄	#2403	1	1	yes	characteristic
677	C₂²×C₄	#2403	1	1	yes	characteristic
678	C₂²×C₄	#2403	1	1	yes	characteristic
679	C₂²×C₄	#2403	1	1	yes	characteristic
680	C₂²×C₄	#2403	1	1	yes	characteristic
681	C₂²×C₄	#2403	1	1	yes	characteristic
682	C₂²×C₄	#2403	1	1	yes	characteristic
683	C₂²×C₄	#2403	1	1	yes	characteristic
684	C₂²×C₄	#2403	1	1	yes	characteristic
685	C₂²×C₄	#2403	1	1	yes	characteristic
686	C₂²×C₄	#2403	1	1	yes	characteristic
687	C₂²×C₄	#2403	1	1	yes	characteristic
688	C₂²×C₄	#2403	1	1	yes	characteristic
689	C₂²×C₄	#2403	1	1	yes	characteristic
690	C₂²×C₄	#2403	1	1	yes	characteristic
691	C₂²×C₄	#2403	1	1	yes	characteristic
692	C₂²×C₄	#2403	1	1	yes	characteristic
693	C₂²×C₄	#2403	1	1	yes	characteristic
694	C₂²×C₄	#2408	1	1	yes	characteristic
695	C₂²×C₄	#2408	1	1	yes	characteristic
696	C₂²×C₄	#2408	1	1	yes	characteristic
697	C₂²×C₄	#2408	1	1	yes	characteristic
698	C₂²×C₄	#2408	1	1	yes	characteristic
699	C₂²×C₄	#2408	1	1	yes	characteristic
700	C₂²×C₄	#2408	1	1	yes	characteristic
701	C₂²×C₄	#2408	1	1	yes	characteristic
702	C₂²×C₄	#2410	1	1	yes	characteristic
703	C₂²×C₄	#2410	1	1	yes	characteristic
704	C₂²×C₄	#2410	1	1	yes	characteristic
705	C₂²×C₄	#2410	1	1	yes	characteristic
706	C₂²×C₄	#2410	1	1	yes	characteristic
707	C₂²×C₄	#2410	1	1	yes	characteristic
708	C₂²×C₄	#2410	1	1	yes	characteristic
709	C₂²×C₄	#2410	1	1	yes	characteristic
710	C₂²×C₄	#2410	1	1	yes	characteristic
711	C₂²×C₄	#2410	1	1	yes	characteristic
712	C₂²×C₄	#2410	1	1	yes	characteristic
713	C₂²×C₄	#2410	1	1	yes	characteristic
714	C₂²×C₄	#2410	1	1	yes	characteristic
715	C₂²×C₄	#2410	1	1	yes	characteristic
716	C₂²×C₄	#2410	1	1	yes	characteristic
717	C₂²×C₄	#2410	1	1	yes	characteristic
718	C₂²×C₄	#2410	1	1	yes	characteristic
719	C₂²×C₄	#2410	1	1	yes	characteristic
720	C₂²×C₄	#2433	1	1	yes	characteristic
721	C₂²×C₄	#2433	1	1	yes	characteristic
722	C₂²×C₄	#2433	1	1	yes	characteristic
723	C₂²×C₄	#2433	1	1	yes	characteristic
724	C₂²×C₄	#2433	1	1	yes	characteristic
725	C₂²×C₄	#2433	1	1	yes	characteristic
726	C₂²×C₄	#2433	1	1	yes	characteristic
727	C₂²×C₄	#2433	1	1	yes	characteristic
728	C₂²×C₄	#2613	1	1	yes	characteristic
729	C₂²×C₄	#2613	1	1	yes	characteristic
730	C₂²×C₄	#2613	1	1	yes	characteristic
731	C₂²×C₄	#2613	1	1	yes	characteristic
732	C₂²×C₄	#2846	1	1	yes	characteristic
733	C₂²×C₄	#2846	1	1	yes	characteristic
734	C₂²×C₄	#2846	1	1	yes	characteristic
735	C₂²×C₄	#2846	1	1	yes	characteristic
736	C₂²×C₄	#2846	1	1	yes	characteristic
737	C₂²×C₄	#2846	1	1	yes	characteristic
738	C₂²×C₄	#3003	1	4	yes	—
739	C₂²×C₄	C₂²×#120	1	1	yes	characteristic
740	C₂²×C₄	C₂²×#120	1	1	yes	characteristic
741	C₂²×C₄	C₂²×#120	1	1	yes	characteristic
742	C₂²×C₄	C₂²×#120	1	1	yes	characteristic
743	C₂²×C₄	C₂²×#120	1	1	yes	characteristic
744	C₂²×C₄	C₂²×#120	1	1	yes	characteristic
745	C₂²×C₄	C₂²×#120	1	1	yes	characteristic
746	C₂²×C₄	C₂²×#121	1	1	yes	characteristic
747	C₂²×C₄	C₂×#534	1	1	yes	characteristic
748	C₂²×C₄	C₂×#534	1	1	yes	characteristic
749	C₂²×C₄	C₂×D₄²	1	1	yes	characteristic
750	C₂²×C₄	C₂×D₄²	1	1	yes	characteristic
751	C₂²×C₄	C₂×D₄²	1	1	yes	characteristic
752	C₂²×C₄	C₂×D₄²	1	1	yes	characteristic
753	C₂²×C₄	C₂×D₄²	1	1	yes	characteristic
754	C₂²×C₄	C₂×D₄²	1	1	yes	characteristic
755	C₂²×C₄	C₂×#546	1	1	yes	characteristic
756	C₂²×C₄	C₂×#546	1	1	yes	characteristic
757	C₂²×C₄	C₂²×AGL(1,ℤ/8)	1	4	yes	—
758	C₂²×C₄	#3585	1	4	yes	—
759	C₄⋊C₄	C₂×#392	1	4	yes	—
760	C₄⋊C₄	C₂×#392	1	4	yes	—
761	C₄²	C₂×#392	1	1	yes	characteristic
762	C₄²	C₂×#392	1	1	yes	characteristic
763	C₄²	C₂×#392	1	1	yes	characteristic
764	C₄²	C₂×#392	1	1	yes	characteristic
765	C₄²	#2403	1	1	yes	characteristic
766	C₄²	#2403	1	1	yes	characteristic
767	C₄²	#2403	1	1	yes	characteristic
768	C₄²	#2403	1	1	yes	characteristic
769	C₄²	#2403	1	1	yes	characteristic
770	C₄²	#2403	1	1	yes	characteristic
771	C₄²	#2403	1	1	yes	characteristic
772	C₄²	#2403	1	1	yes	characteristic
773	C₄²	#2403	1	1	yes	characteristic
774	C₄²	#2403	1	1	yes	characteristic
775	C₄²	#2403	1	1	yes	characteristic
776	C₄²	#2403	1	1	yes	characteristic
777	C₄²	#2408	1	1	yes	characteristic
778	C₄²	#2408	1	1	yes	characteristic
779	C₄²	#2408	1	1	yes	characteristic
780	C₄²	#2408	1	1	yes	characteristic
781	C₄²	#2408	1	1	yes	characteristic
782	C₄²	#2408	1	1	yes	characteristic
783	C₄²	#2408	1	1	yes	characteristic
784	C₄²	#2408	1	1	yes	characteristic
785	C₄²	#2410	1	1	yes	characteristic
786	C₄²	#2410	1	1	yes	characteristic
787	C₄²	#2410	1	1	yes	characteristic
788	C₄²	#2410	1	1	yes	characteristic
789	C₄²	#2410	1	1	yes	characteristic
790	C₄²	#2410	1	1	yes	characteristic
791	C₄²	#2410	1	1	yes	characteristic
792	C₄²	#2410	1	1	yes	characteristic
793	C₄²	#2410	1	1	yes	characteristic
794	C₄²	#2410	1	1	yes	characteristic
795	C₄²	#2410	1	1	yes	characteristic
796	C₄²	#2410	1	1	yes	characteristic
797	C₄²	#2433	1	1	yes	characteristic
798	C₄²	#2433	1	1	yes	characteristic
799	C₄²	#2433	1	1	yes	characteristic
800	C₄²	#2433	1	1	yes	characteristic
801	C₄²	#2433	1	1	yes	characteristic
802	C₄²	#2433	1	1	yes	characteristic
803	C₄²	#2433	1	1	yes	characteristic
804	C₄²	#2433	1	1	yes	characteristic
805	C₄²	#2613	1	1	yes	characteristic
806	C₄²	#2613	1	1	yes	characteristic
807	C₄²	#2613	1	1	yes	characteristic
808	C₄²	#2613	1	1	yes	characteristic
809	C₄²	#3003	1	8	yes	complemented
810	C₄²	C₂²×#120	1	1	yes	characteristic
811	C₄²	C₂²×#121	1	1	yes	characteristic
812	C₄²	C₂²×#121	1	1	yes	characteristic
813	C₄²	C₂²×#127	1	1	yes	characteristic
814	C₄²	C₂×#534	1	1	yes	characteristic
815	C₄²	C₂×#534	1	1	yes	characteristic
816	C₄²	C₂×#535	1	1	yes	characteristic
817	C₄²	C₂×#535	1	1	yes	characteristic
818	C₄²	C₂×D₄²	1	1	yes	characteristic
819	C₄²	C₂×D₄²	1	1	yes	characteristic
820	C₄²	C₂×D₄²	1	1	yes	characteristic
821	C₄²	C₂×D₄²	1	1	yes	characteristic
822	C₄²	C₂×D₄²	1	1	yes	characteristic
823	C₄²	C₂×D₄²	1	1	yes	characteristic
824	C₄²	C₂×#546	1	1	yes	characteristic
825	C₄²	C₂×#546	1	1	yes	characteristic
826	C₂³	#14715	1	1	yes	characteristic
827	C₂³	#14715	1	1	yes	characteristic
828	C₂³	#14715	1	1	yes	characteristic
829	C₂³	#14715	1	1	yes	characteristic
830	C₂³	C₂×#2403	1	1	yes	characteristic
831	C₂³	C₂×#2410	1	1	yes	characteristic
832	C₂³	C₂×#2846	1	1	yes	characteristic
833	C₂³	C₂×#3003	1	2	yes	—
834	C₂³	#60367	1	2	yes	—
835	D₄	C₂×#2010	1	8	yes	—
836	C₂×C₄	#14715	1	1	yes	characteristic
837	C₂×C₄	#14715	1	1	yes	characteristic
838	C₂×C₄	#14715	1	1	yes	characteristic
839	C₂×C₄	#14715	1	1	yes	characteristic
840	C₂×C₄	#14715	1	1	yes	characteristic
841	C₂×C₄	#14715	1	1	yes	characteristic
842	C₂×C₄	#14715	1	1	yes	characteristic
843	C₂×C₄	#14715	1	1	yes	characteristic
844	C₂×C₄	#14715	1	1	yes	characteristic
845	C₂×C₄	#14715	1	1	yes	characteristic
846	C₂×C₄	#14715	1	1	yes	characteristic
847	C₂×C₄	#14715	1	1	yes	characteristic
848	C₂×C₄	C₂×#2010	1	4	yes	—
849	C₂×C₄	C₂²×#392	1	1	yes	characteristic
850	C₂×C₄	C₂×#2613	1	1	yes	characteristic
851	C₂×C₄	C₂×#2403	1	1	yes	characteristic
852	C₂×C₄	C₂×#2403	1	1	yes	characteristic
853	C₂×C₄	C₂×#2403	1	1	yes	characteristic
854	C₂×C₄	C₂×#2410	1	1	yes	characteristic
855	C₂×C₄	C₂×#2410	1	1	yes	characteristic
856	C₂×C₄	C₂×#2410	1	1	yes	characteristic
857	C₂×C₄	C₂×#2408	1	1	yes	characteristic
858	C₂×C₄	C₂×#2408	1	1	yes	characteristic
859	C₂×C₄	C₂×#2433	1	1	yes	characteristic
860	C₂×C₄	C₂×#2433	1	1	yes	characteristic
861	C₂×C₄	C₂×#3003	1	2	yes	—
862	C₂×C₄	C₂×#3003	1	2	yes	—
863	C₂×C₄	#60367	1	2	yes	—
864	C₂×C₄	#60367	1	2	yes	—
865	C₂×C₄	D₄×AGL(1,ℤ/8)	1	4	yes	—
866	C₂×C₄	D₄×AGL(1,ℤ/8)	1	4	yes	—
867	C₂×C₄	D₄×AGL(1,ℤ/8)	1	4	yes	—
868	C₂×C₄	#61155	1	4	yes	—
869	C₂²	#393988	1	2	yes	—
870	C₂²	#394108	1	2	yes	—
871	C₂²	C₂×#14715	1	1	yes	characteristic
872	C₂²	#6437510	1	2	yes	—
873	C₂²	#6437838	1	2	yes	—
874	C₂²	#6628842	1	1	yes	characteristic
875	C₂²	#6628847	1	1	yes	characteristic
876	C₄	#393988	1	2	yes	—
877	C₄	C₂²×#2010	1	2	yes	—
878	C₄	#6437510	1	2	yes	—
879	C₄	#6437838	1	2	yes	—
880	C₄	#6442656	1	2	yes	—
881	C₄	#6443168	1	2	yes	—
882	C₂	C₂×#393988	1	1	yes	characteristic
883	C₂	C₂×#394108	1	1	yes	characteristic
884	C₂	#72231796	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×#2433
commutator, Frattini, cosocle	C₂²×C₄²	C₂⁵
socle	C₂²	C₂×#14715
LCS	G ▷ C₂²×C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₄ ◁ C₂³×C₄² ◁ G
LECS	G ▷ C₂²×C₄² ▷ C₂² ▷ C₁

Complements

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

N	H ≅ G/N	type
1. #72240785	C₂	semidirect
2. #72240781	C₂	semidirect
3. #72239172	C₂	semidirect
4. #72239169	C₂	semidirect
5. #72239161	C₂	semidirect
6. #72239048	C₂	semidirect
7. #72239041	C₂	semidirect
8. #72239035	C₂	semidirect
9. #72239025	C₂	semidirect
10. #72239008	C₂	semidirect
11. #72238998	C₂	semidirect
12. #72238966	C₂	semidirect
13. #72238774	C₂	semidirect
14. #72237572	C₂	semidirect
15. #72237162	C₂	semidirect
16. C₂×D₄×#525	C₂	semidirect
17. #72214831	C₂	semidirect
20. #10575872	C₂²	semidirect
21. #10575094	C₂²	semidirect
23. C₂×#60558	C₂²	semidirect
24. #7633331	C₂²	semidirect
31. #6629272	C₂²	semidirect
32. #6629271	C₂²	semidirect
33. #6372471	C₂²	semidirect
34. #6370997	C₂²	semidirect
36. #6370977	C₂²	semidirect
37. #6370924	C₂²	semidirect
38. #6370924	C₂²	semidirect
39. #6370924	C₂²	semidirect
40. #6348730	C₂²	semidirect
41. #6348729	C₂²	semidirect
42. #6344036	C₂²	semidirect
43. #6343381	C₂²	semidirect
44. #6343377	C₂²	semidirect
45. #6343016	C₂²	semidirect
46. #6342924	C₂²	semidirect
47. #6342924	C₂²	semidirect
50. C₂×#17448	C₂²	semidirect
51. C₂×#17448	C₂²	semidirect
52. #414681	C₂²	semidirect
53. #411706	C₂²	semidirect
54. #353774	C₂²	semidirect
55. #235217	C₂²	semidirect
56. #235216	C₂²	semidirect
57. #234286	C₂²	semidirect
58. #234285	C₂²	semidirect
59. #233589	C₂²	semidirect
60. #233588	C₂²	semidirect
61. #198023	C₂²	semidirect
62. #198022	C₂²	semidirect
63. #186510	C₂²	semidirect
64. #184859	C₂²	semidirect
65. #181801	C₂²	semidirect
66. #181430	C₂²	semidirect
67. #181240	C₂²	semidirect
68. #181174	C₂²	semidirect
69. #180863	C₂²	semidirect
70. #115381	C₂²	semidirect
71. #112888	C₂²	semidirect
72. #111640	C₂²	semidirect
73. #111559	C₂²	semidirect
74. #105688	C₂²	semidirect
76. C₂×D₄×#41	D₄	semidirect
78. C₂²×#550	D₄	semidirect
79. C₂²×#547	D₄	semidirect
80. C₂²×D₄×Q₈	D₄	semidirect
81. C₂²×D₄²	D₄	semidirect
94. #60941	C₂³	semidirect
95. #60940	C₂³	semidirect
96. C₂×#3110	D₄	semidirect
97. C₂×#3109	D₄	semidirect
99. C₂×#3101	C₂³	semidirect
101. C₂×#3100	C₂³	semidirect
102. #60484	C₂³	semidirect
103. C₂×#3077	D₄	semidirect
104. #60415	C₂³	semidirect
105. C₂×#3036	D₄	semidirect
112. #36625	C₂³	semidirect
115. #36624	C₂³	semidirect
118. #34936	D₄	semidirect
120. #34935	D₄	semidirect
122. C₂×#2536	D₄	semidirect
123. C₂×#2535	D₄	semidirect
124. C₂×#2397	D₄	semidirect
125. D₄×#117	D₄	semidirect
131. C₂×#2293	D₄	semidirect
135. C₂×C₄²×D₄	D₄	semidirect
137. #21329	C₂³	semidirect
138. #21209	C₂³	semidirect
139. #20733	D₄	semidirect
141. #20732	C₂³	semidirect
142. #20714	C₂³	semidirect
143. #20714	C₂³	semidirect
144. #20654	C₂³	semidirect
145. #20626	C₂³	semidirect
146. C₄×#418	D₄	semidirect
147. #17704	C₂³	semidirect
148. #17575	C₂³	semidirect
149. #17574	C₂³	semidirect
150. #17574	C₂³	semidirect
151. #17485	C₂³	semidirect
152. C₂×#1490	D₄	semidirect
155. C₂×#1486	C₂³	semidirect
156. C₂×#1486	C₂³	semidirect
157. #17437	C₂³	semidirect
158. #17437	C₂³	semidirect
159. C₂×#1478	D₄	semidirect
160. #10836	C₂³	semidirect
161. #8095	C₂³	semidirect
162. #7981	C₂³	semidirect
163. #7957	C₂³	semidirect
164. #7866	C₂³	semidirect
165. #7854	C₂³	semidirect
177. C₂×#533	C₂×D₄	semidirect
178. C₂×#533	C₂×D₄	semidirect
183. C₂×#532	C₂×D₄	semidirect
184. C₂×#532	C₂×D₄	semidirect
238. C₂×#476	C₂×D₄	semidirect
239. C₂×#474	C₂×D₄	semidirect
240. C₂×#461	C₂×D₄	semidirect
241. C₂×#459	C₂×D₄	semidirect
242. C₂×#432	C₂×D₄	semidirect
243. C₂×#432	C₂×D₄	semidirect
244. C₂×#431	C₂×D₄	semidirect
245. C₂×#431	C₂×D₄	semidirect
246. C₂×#431	C₂×D₄	semidirect
251. C₂×#423	C₂×D₄	semidirect
254. C₂×C₄×M₁₆	C₂×D₄	semidirect
255. C₂×C₄×M₁₆	C₂×D₄	semidirect
269. #2283	C₂×D₄	semidirect
277. C₄×#117	C₂×D₄	semidirect
282. C₄×#102	C₂×D₄	semidirect
283. C₂×D₄⋊C₈	C₂×D₄	semidirect
315. C₂×C₄⋊Q₈	C₂²×D₄	semidirect
316. C₂×C₄⋊Q₈	C₂²×D₄	semidirect
317. C₂×C₄⋊Q₈	C₂²×D₄	semidirect
320. C₂×#127	C₂²×D₄	semidirect
321. #525	AGL(1,ℤ/8)	semidirect
434. C₂×C₄⋊C₈	C₂²×D₄	semidirect
435. C₂×C₄⋊C₈	C₂²×D₄	semidirect
436. C₂×C₄×C₈	C₂²×D₄	semidirect
437. C₂×C₄×C₈	C₂²×D₄	semidirect
444. C₄×C₄⋊C₄	C₂²×D₄	semidirect
667. C₂×Q₈	#3003	semidirect
668. C₂×D₄	#2010	semidirect
671. C₂×D₄	#3003	semidirect
809. C₄²	#3003	semidirect

Maximal subgroups

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

subgroup	index
#72240785	2
#72240781	2
#72239172	2
#72239169	2
#72239161	2
#72239048	2
#72239041	2
#72239035	2
#72239025	2
#72239008	2
#72238998	2
#72238966	2
#72238774	2
#72237572	2
#72237162	2
C₂×D₄×#525	2
#72214831	2