Subgroups — C₂²×#410×C₇₁ #31880939

Order 18176.

5278 conjugacy classes of subgroups.

The subgroup lattice has 378 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×#41×C₇₁	C₂	1	1	yes	maximal, characteristic
2	C₂²×#117×C₇₁	C₂	1	2	yes	maximal, complemented
3	C₂×#410×C₇₁	C₂	1	24	yes	maximal, direct product factor
4	C₂²×#99×C₇₁	C₂	1	4	yes	maximal, complemented
5	C₂²×#41×C₇₁	—	2	2	no	—
6	C₂²×#41×C₇₁	—	2	12	no	—
7	C₂²×#41×C₇₁	—	2	2	no	—
8	C₂²×#41×C₇₁	C₄	1	12	yes	complemented
9	C₂²×#41×C₇₁	C₂²	1	12	yes	—
10	C₂³×Q₈×C₇₁	C₄	1	1	yes	characteristic, complemented
11	C₂³×D₄×C₇₁	C₄	1	1	yes	characteristic, complemented
12	C₂³×D₄×C₇₁	C₂²	1	2	yes	—
13	C₂⁴×C₄×C₇₁	C₄	1	2	yes	complemented
14	C₂⁴×C₄×C₇₁	C₂²	1	1	yes	characteristic
15	C₂×#117×C₇₁	—	2	12	no	—
16	C₂×#117×C₇₁	C₂²	1	24	yes	complemented
17	C₂²×C₄⋊C₄×C₇₁	—	2	2	no	—
18	C₂²×C₂²⋊C₄×C₇₁	C₂²	1	4	yes	—
19	C₂²×C₄²×C₇₁	—	2	2	no	—
20	#410×C₇₁	C₂²	1	64	yes	direct product factor
21	C₂×#99×C₇₁	C₂²	1	48	yes	complemented
22	C₂⁵×C₇₁	C₂×C₄	1	2	yes	—
23	C₂⁵×C₇₁	C₂³	1	1	yes	characteristic
24	C₂×#41×C₇₁	—	2	24	no	—
25	C₂×#41×C₇₁	—	2	48	no	—
26	C₂×#41×C₇₁	—	2	24	no	—
27	C₂×#41×C₇₁	—	2	24	no	—
28	C₂×#41×C₇₁	—	2	24	no	—
29	C₂×#41×C₇₁	—	2	48	no	—
30	C₂×#41×C₇₁	C₂×C₄	1	48	yes	complemented
31	C₂×#41×C₇₁	C₂³	1	16	yes	—
32	C₂²×Q₈×C₇₁	—	2	6	no	—
33	C₂²×Q₈×C₇₁	—	2	2	no	—
34	C₂²×Q₈×C₇₁	C₂×C₄	1	12	yes	complemented
35	C₂²×D₄×C₇₁	—	2	4	no	—
36	C₂²×D₄×C₇₁	—	2	12	no	—
37	C₂²×D₄×C₇₁	—	2	6	no	—
38	C₂²×D₄×C₇₁	—	2	2	no	—
39	C₂²×D₄×C₇₁	C₂×C₄	1	12	yes	—
40	C₂²×D₄×C₇₁	C₂×C₄	1	12	yes	complemented
41	C₂²×D₄×C₇₁	C₂³	1	12	yes	—
42	C₂³×C₄×C₇₁	—	2	12	no	—
43	C₂³×C₄×C₇₁	—	2	2	no	—
44	C₂³×C₄×C₇₁	—	2	2	no	—
45	C₂³×C₄×C₇₁	—	2	4	no	—
46	C₂³×C₄×C₇₁	C₂×C₄	1	2	yes	—
47	C₂³×C₄×C₇₁	C₂×C₄	1	1	yes	characteristic
48	C₂³×C₄×C₇₁	C₂×C₄	1	6	yes	—
49	C₂³×C₄×C₇₁	C₂×C₄	1	1	yes	characteristic
50	C₂³×C₄×C₇₁	C₂×C₄	1	24	yes	complemented
51	C₂³×C₄×C₇₁	D₄	1	2	yes	—
52	C₂³×C₄×C₇₁	D₄	1	12	yes	—
53	C₂³×C₄×C₇₁	D₄	1	2	yes	—
54	C₂³×C₄×C₇₁	C₂³	1	6	yes	—
55	#117×C₇₁	—	2	48	no	—
56	#117×C₇₁	C₂³	1	32	yes	complemented
57	C₂×C₄⋊C₄×C₇₁	—	2	24	no	—
58	C₂×C₂²⋊C₄×C₇₁	—	2	12	no	—
59	C₂×C₂²⋊C₄×C₇₁	C₂³	1	24	yes	—
60	C₂×C₄²×C₇₁	—	2	24	no	—
61	#99×C₇₁	C₂³	1	64	yes	complemented
62	C₂⁴×C₇₁	—	2	6	no	—
63	C₂⁴×C₇₁	—	2	2	no	—
64	C₂⁴×C₇₁	—	4	4	no	—
65	C₂⁴×C₇₁	—	4	8	no	—
66	C₂⁴×C₇₁	C₂²×C₄	1	1	yes	characteristic
67	C₂⁴×C₇₁	C₂²×C₄	1	12	yes	—
68	C₂⁴×C₇₁	C₂²×C₄	1	3	yes	—
69	C₂⁴×C₇₁	C₂×D₄	1	2	yes	—
70	C₂⁴×C₇₁	C₂×D₄	1	6	yes	—
71	C₂⁴×C₇₁	C₂⁴	1	3	yes	—
72	#41×C₇₁	—	2	96	no	—
73	#41×C₇₁	—	2	96	no	—
74	#41×C₇₁	—	2	32	no	—
75	#41×C₇₁	—	2	32	no	—
76	C₂×Q₈×C₇₁	—	2	24	no	—
77	C₂×Q₈×C₇₁	—	2	24	no	—
78	C₂×Q₈×C₇₁	C₂²×C₄	1	16	yes	complemented
79	C₂×D₄×C₇₁	—	2	24	no	—
80	C₂×D₄×C₇₁	—	2	24	no	—
81	C₂×D₄×C₇₁	—	2	24	no	—
82	C₂×D₄×C₇₁	—	2	24	no	—
83	C₂×D₄×C₇₁	—	2	24	no	—
84	C₂×D₄×C₇₁	—	2	24	no	—
85	C₂×D₄×C₇₁	C₂²×C₄	1	24	yes	—
86	C₂×D₄×C₇₁	C₂²×C₄	1	16	yes	complemented
87	C₂×D₄×C₇₁	C₂⁴	1	8	yes	—
88	C₂²×C₄×C₇₁	—	2	6	no	—
89	C₂²×C₄×C₇₁	—	2	2	no	—
90	C₂²×C₄×C₇₁	—	2	48	no	—
91	C₂²×C₄×C₇₁	—	2	24	no	—
92	C₂²×C₄×C₇₁	—	2	24	no	—
93	C₂²×C₄×C₇₁	—	2	24	no	—
94	C₂²×C₄×C₇₁	—	4	16	no	—
95	C₂²×C₄×C₇₁	C₂²⋊C₄	1	1	yes	characteristic
96	C₂²×C₄×C₇₁	C₂²⋊C₄	1	6	yes	—
97	C₂²×C₄×C₇₁	C₂²⋊C₄	1	6	yes	—
98	C₂²×C₄×C₇₁	C₂²⋊C₄	1	2	yes	—
99	C₂²×C₄×C₇₁	C₂²⋊C₄	1	12	yes	—
100	C₂²×C₄×C₇₁	C₂²⋊C₄	1	24	yes	—
101	C₂²×C₄×C₇₁	C₂²⋊C₄	1	12	yes	—
102	C₂²×C₄×C₇₁	C₂²⋊C₄	1	1	yes	characteristic
103	C₂²×C₄×C₇₁	C₂²×C₄	1	12	yes	—
104	C₂²×C₄×C₇₁	C₂²×C₄	1	6	yes	—
105	C₂²×C₄×C₇₁	C₂²×C₄	1	6	yes	—
106	C₂²×C₄×C₇₁	C₂²×C₄	1	12	yes	—
107	C₂²×C₄×C₇₁	C₂²×C₄	1	32	yes	complemented
108	C₂²×C₄×C₇₁	C₂×D₄	1	12	yes	—
109	C₂²×C₄×C₇₁	C₂×D₄	1	12	yes	—
110	C₂²×C₄×C₇₁	C₂×D₄	1	24	yes	—
111	C₂²×C₄×C₇₁	C₂⁴	1	4	yes	—
112	C₄⋊C₄×C₇₁	—	2	32	no	—
113	C₂²⋊C₄×C₇₁	—	2	24	no	—
114	C₂²⋊C₄×C₇₁	C₂⁴	1	16	yes	—
115	C₄²×C₇₁	—	2	32	no	—
116	C₂³×C₇₁	—	2	8	no	—
117	C₂³×C₇₁	—	2	4	no	—
118	C₂³×C₇₁	—	2	12	no	—
119	C₂³×C₇₁	—	2	12	no	—
120	C₂³×C₇₁	—	4	6	no	—
121	C₂³×C₇₁	—	4	12	no	—
122	C₂³×C₇₁	—	4	6	no	—
123	C₂³×C₇₁	—	4	24	no	—
124	C₂³×C₇₁	—	4	24	no	—
125	C₂³×C₇₁	—	4	8	no	—
126	C₂³×C₇₁	C₂×C₂²⋊C₄	1	3	yes	—
127	C₂³×C₇₁	C₂×C₂²⋊C₄	1	6	yes	—
128	C₂³×C₇₁	C₂×C₂²⋊C₄	1	6	yes	—
129	C₂³×C₇₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
130	C₂³×C₇₁	C₂³×C₄	1	3	yes	—
131	C₂³×C₇₁	C₂³×C₄	1	8	yes	—
132	C₂³×C₇₁	C₂³×C₄	1	3	yes	—
133	C₂³×C₇₁	C₂²×D₄	1	6	yes	—
134	C₂³×C₇₁	C₂²×D₄	1	6	yes	—
135	C₂³×C₇₁	C₂⁵	1	1	yes	characteristic
136	Q₈×C₇₁	—	2	32	no	—
137	D₄×C₇₁	—	2	48	no	—
138	D₄×C₇₁	—	2	16	no	—
139	D₄×C₇₁	—	2	32	no	—
140	C₂×C₄×C₇₁	—	2	12	no	—
141	C₂×C₄×C₇₁	—	2	12	no	—
142	C₂×C₄×C₇₁	—	2	32	no	—
143	C₂×C₄×C₇₁	—	2	32	no	—
144	C₂×C₄×C₇₁	—	2	16	no	—
145	C₂×C₄×C₇₁	—	4	48	no	—
146	C₂×C₄×C₇₁	C₂×C₂²⋊C₄	1	12	yes	—
147	C₂×C₄×C₇₁	C₂×C₂²⋊C₄	1	6	yes	—
148	C₂×C₄×C₇₁	C₂×C₂²⋊C₄	1	6	yes	—
149	C₂×C₄×C₇₁	C₂×C₂²⋊C₄	1	12	yes	—
150	C₂×C₄×C₇₁	C₂×C₂²⋊C₄	1	12	yes	—
151	C₂×C₄×C₇₁	C₂×C₂²⋊C₄	1	24	yes	—
152	C₂×C₄×C₇₁	C₂×C₂²⋊C₄	1	24	yes	—
153	C₂×C₄×C₇₁	C₂³×C₄	1	8	yes	—
154	C₂×C₄×C₇₁	C₂³×C₄	1	4	yes	—
155	C₂×C₄×C₇₁	C₂³×C₄	1	4	yes	—
156	C₂×C₄×C₇₁	C₂²×D₄	1	8	yes	—
157	C₂×C₄×C₇₁	C₂²×D₄	1	8	yes	—
158	C₂²×C₇₁	—	2	12	no	—
159	C₂²×C₇₁	—	2	6	no	—
160	C₂²×C₇₁	—	2	6	no	—
161	C₂²×C₇₁	—	2	12	no	—
162	C₂²×C₇₁	—	2	8	no	—
163	C₂²×C₇₁	—	4	6	no	—
164	C₂²×C₇₁	—	4	3	no	—
165	C₂²×C₇₁	—	4	6	no	—
166	C₂²×C₇₁	—	4	1	no	—
167	C₂²×C₇₁	—	4	8	no	—
168	C₂²×C₇₁	—	4	24	no	—
169	C₂²×C₇₁	—	4	24	no	—
170	C₂²×C₇₁	#410	1	4	yes	direct product factor
171	C₂²×C₇₁	C₂²×C₂²⋊C₄	1	3	yes	—
172	C₂²×C₇₁	C₂²×C₂²⋊C₄	1	6	yes	—
173	C₂²×C₇₁	C₂²×C₂²⋊C₄	1	3	yes	—
174	C₂²×C₇₁	C₂⁴×C₄	1	1	yes	characteristic
175	C₂²×C₇₁	C₂³×D₄	1	2	yes	—
176	C₄×C₇₁	—	2	8	no	—
177	C₄×C₇₁	—	4	16	no	—
178	C₄×C₇₁	C₂²×C₂²⋊C₄	1	4	yes	—
179	C₄×C₇₁	C₂²×C₂²⋊C₄	1	4	yes	—
180	C₄×C₇₁	C₂²×C₂²⋊C₄	1	8	yes	—
181	C₂²×#410	C₇₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
182	C₂×C₇₁	—	2	2	no	—
183	C₂×C₇₁	—	2	3	no	—
184	C₂×C₇₁	—	2	1	no	—
185	C₂×C₇₁	—	2	6	no	—
186	C₂×C₇₁	—	4	8	no	—
187	C₂×C₇₁	C₂×#410	1	6	yes	direct product factor
188	C₂×C₇₁	C₂³×C₂²⋊C₄	1	1	yes	characteristic
189	C₂³×#41	C₂×C₇₁	1	1	yes	characteristic
190	C₂²×#117	C₂×C₇₁	1	2	yes	complemented
191	C₂×#410	C₂×C₇₁	1	24	yes	direct product factor
192	C₂²×#99	C₂×C₇₁	1	4	yes	complemented
193	C₇₁	C₂²×#410	1	1	yes	characteristic, direct product factor, Sylow
194	C₂²×#41	—	2	2	no	—
195	C₂²×#41	—	2	12	no	—
196	C₂²×#41	—	2	2	no	—
197	C₂²×#41	C₄×C₇₁	1	12	yes	complemented
198	C₂²×#41	C₂²×C₇₁	1	12	yes	—
199	C₂³×Q₈	C₄×C₇₁	1	1	yes	characteristic, complemented
200	C₂³×D₄	C₄×C₇₁	1	1	yes	characteristic, complemented
201	C₂³×D₄	C₂²×C₇₁	1	2	yes	—
202	C₂⁴×C₄	C₄×C₇₁	1	2	yes	complemented
203	C₂⁴×C₄	C₂²×C₇₁	1	1	yes	characteristic
204	C₂×#117	—	2	12	no	—
205	C₂×#117	C₂²×C₇₁	1	24	yes	complemented
206	C₂²×C₄⋊C₄	—	2	2	no	—
207	C₂²×C₂²⋊C₄	C₂²×C₇₁	1	4	yes	—
208	C₂²×C₄²	—	2	2	no	—
209	#410	C₂²×C₇₁	1	64	yes	direct product factor
210	C₂×#99	C₂²×C₇₁	1	48	yes	complemented
211	C₂⁵	C₂×C₄×C₇₁	1	2	yes	—
212	C₂⁵	C₂³×C₇₁	1	1	yes	characteristic
213	C₂×#41	—	2	24	no	—
214	C₂×#41	—	2	24	no	—
215	C₂×#41	—	2	48	no	—
216	C₂×#41	—	2	24	no	—
217	C₂×#41	—	2	24	no	—
218	C₂×#41	—	2	48	no	—
219	C₂×#41	C₂×C₄×C₇₁	1	48	yes	complemented
220	C₂×#41	C₂³×C₇₁	1	16	yes	—
221	C₂²×Q₈	—	2	6	no	—
222	C₂²×Q₈	—	2	2	no	—
223	C₂²×Q₈	C₂×C₄×C₇₁	1	12	yes	complemented
224	C₂²×D₄	—	2	4	no	—
225	C₂²×D₄	—	2	12	no	—
226	C₂²×D₄	—	2	6	no	—
227	C₂²×D₄	—	2	2	no	—
228	C₂²×D₄	C₂×C₄×C₇₁	1	12	yes	—
229	C₂²×D₄	C₂×C₄×C₇₁	1	12	yes	complemented
230	C₂²×D₄	C₂³×C₇₁	1	12	yes	—
231	C₂³×C₄	—	2	12	no	—
232	C₂³×C₄	—	2	2	no	—
233	C₂³×C₄	—	2	2	no	—
234	C₂³×C₄	—	2	4	no	—
235	C₂³×C₄	C₂×C₄×C₇₁	1	2	yes	—
236	C₂³×C₄	C₂×C₄×C₇₁	1	1	yes	characteristic
237	C₂³×C₄	C₂×C₄×C₇₁	1	1	yes	characteristic
238	C₂³×C₄	C₂×C₄×C₇₁	1	6	yes	—
239	C₂³×C₄	C₂×C₄×C₇₁	1	24	yes	complemented
240	C₂³×C₄	D₄×C₇₁	1	2	yes	—
241	C₂³×C₄	D₄×C₇₁	1	12	yes	—
242	C₂³×C₄	D₄×C₇₁	1	2	yes	—
243	C₂³×C₄	C₂³×C₇₁	1	6	yes	—
244	#117	—	2	48	no	—
245	#117	C₂³×C₇₁	1	32	yes	complemented
246	C₂×C₄⋊C₄	—	2	24	no	—
247	C₂×C₂²⋊C₄	—	2	12	no	—
248	C₂×C₂²⋊C₄	C₂³×C₇₁	1	24	yes	—
249	C₂×C₄²	—	2	24	no	—
250	#99	C₂³×C₇₁	1	64	yes	complemented
251	C₂⁴	—	2	6	no	—
252	C₂⁴	—	2	2	no	—
253	C₂⁴	—	4	4	no	—
254	C₂⁴	—	4	8	no	—
255	C₂⁴	C₂²×C₄×C₇₁	1	1	yes	characteristic
256	C₂⁴	C₂²×C₄×C₇₁	1	12	yes	—
257	C₂⁴	C₂²×C₄×C₇₁	1	3	yes	—
258	C₂⁴	C₂×D₄×C₇₁	1	2	yes	—
259	C₂⁴	C₂×D₄×C₇₁	1	6	yes	—
260	C₂⁴	C₂⁴×C₇₁	1	3	yes	—
261	#41	—	2	96	no	—
262	#41	—	2	96	no	—
263	#41	—	2	32	no	—
264	#41	—	2	32	no	—
265	C₂×Q₈	—	2	24	no	—
266	C₂×Q₈	—	2	24	no	—
267	C₂×Q₈	C₂²×C₄×C₇₁	1	16	yes	complemented
268	C₂×D₄	—	2	24	no	—
269	C₂×D₄	—	2	24	no	—
270	C₂×D₄	—	2	24	no	—
271	C₂×D₄	—	2	24	no	—
272	C₂×D₄	—	2	24	no	—
273	C₂×D₄	—	2	24	no	—
274	C₂×D₄	C₂²×C₄×C₇₁	1	24	yes	—
275	C₂×D₄	C₂²×C₄×C₇₁	1	16	yes	complemented
276	C₂×D₄	C₂⁴×C₇₁	1	8	yes	—
277	C₂²×C₄	—	2	6	no	—
278	C₂²×C₄	—	2	2	no	—
279	C₂²×C₄	—	2	48	no	—
280	C₂²×C₄	—	2	24	no	—
281	C₂²×C₄	—	2	24	no	—
282	C₂²×C₄	—	2	24	no	—
283	C₂²×C₄	—	4	16	no	—
284	C₂²×C₄	C₂²⋊C₄×C₇₁	1	6	yes	—
285	C₂²×C₄	C₂²⋊C₄×C₇₁	1	1	yes	characteristic
286	C₂²×C₄	C₂²⋊C₄×C₇₁	1	6	yes	—
287	C₂²×C₄	C₂²⋊C₄×C₇₁	1	2	yes	—
288	C₂²×C₄	C₂²⋊C₄×C₇₁	1	12	yes	—
289	C₂²×C₄	C₂²⋊C₄×C₇₁	1	12	yes	—
290	C₂²×C₄	C₂²⋊C₄×C₇₁	1	24	yes	—
291	C₂²×C₄	C₂²⋊C₄×C₇₁	1	1	yes	characteristic
292	C₂²×C₄	C₂²×C₄×C₇₁	1	12	yes	—
293	C₂²×C₄	C₂²×C₄×C₇₁	1	6	yes	—
294	C₂²×C₄	C₂²×C₄×C₇₁	1	6	yes	—
295	C₂²×C₄	C₂²×C₄×C₇₁	1	12	yes	—
296	C₂²×C₄	C₂²×C₄×C₇₁	1	32	yes	complemented
297	C₂²×C₄	C₂×D₄×C₇₁	1	12	yes	—
298	C₂²×C₄	C₂×D₄×C₇₁	1	12	yes	—
299	C₂²×C₄	C₂×D₄×C₇₁	1	24	yes	—
300	C₂²×C₄	C₂⁴×C₇₁	1	4	yes	—
301	C₄⋊C₄	—	2	32	no	—
302	C₂²⋊C₄	—	2	24	no	—
303	C₂²⋊C₄	C₂⁴×C₇₁	1	16	yes	—
304	C₄²	—	2	32	no	—
305	C₂³	—	2	8	no	—
306	C₂³	—	2	4	no	—
307	C₂³	—	2	12	no	—
308	C₂³	—	2	12	no	—
309	C₂³	—	4	6	no	—
310	C₂³	—	4	12	no	—
311	C₂³	—	4	6	no	—
312	C₂³	—	4	24	no	—
313	C₂³	—	4	24	no	—
314	C₂³	—	4	8	no	—
315	C₂³	C₂×C₂²⋊C₄×C₇₁	1	3	yes	—
316	C₂³	C₂×C₂²⋊C₄×C₇₁	1	6	yes	—
317	C₂³	C₂×C₂²⋊C₄×C₇₁	1	6	yes	—
318	C₂³	C₂×C₂²⋊C₄×C₇₁	1	1	yes	characteristic
319	C₂³	C₂³×C₄×C₇₁	1	3	yes	—
320	C₂³	C₂³×C₄×C₇₁	1	8	yes	—
321	C₂³	C₂³×C₄×C₇₁	1	3	yes	—
322	C₂³	C₂²×D₄×C₇₁	1	6	yes	—
323	C₂³	C₂²×D₄×C₇₁	1	6	yes	—
324	C₂³	C₂⁵×C₇₁	1	1	yes	characteristic
325	Q₈	—	2	32	no	—
326	D₄	—	2	48	no	—
327	D₄	—	2	16	no	—
328	D₄	—	2	32	no	—
329	C₂×C₄	—	2	12	no	—
330	C₂×C₄	—	2	12	no	—
331	C₂×C₄	—	2	32	no	—
332	C₂×C₄	—	2	32	no	—
333	C₂×C₄	—	2	16	no	—
334	C₂×C₄	—	4	48	no	—
335	C₂×C₄	C₂×C₂²⋊C₄×C₇₁	1	12	yes	—
336	C₂×C₄	C₂×C₂²⋊C₄×C₇₁	1	6	yes	—
337	C₂×C₄	C₂×C₂²⋊C₄×C₇₁	1	6	yes	—
338	C₂×C₄	C₂×C₂²⋊C₄×C₇₁	1	12	yes	—
339	C₂×C₄	C₂×C₂²⋊C₄×C₇₁	1	12	yes	—
340	C₂×C₄	C₂×C₂²⋊C₄×C₇₁	1	24	yes	—
341	C₂×C₄	C₂×C₂²⋊C₄×C₇₁	1	24	yes	—
342	C₂×C₄	C₂³×C₄×C₇₁	1	8	yes	—
343	C₂×C₄	C₂³×C₄×C₇₁	1	4	yes	—
344	C₂×C₄	C₂³×C₄×C₇₁	1	4	yes	—
345	C₂×C₄	C₂²×D₄×C₇₁	1	8	yes	—
346	C₂×C₄	C₂²×D₄×C₇₁	1	8	yes	—
347	C₂²	—	2	12	no	—
348	C₂²	—	2	6	no	—
349	C₂²	—	2	6	no	—
350	C₂²	—	2	12	no	—
351	C₂²	—	2	8	no	—
352	C₂²	—	4	6	no	—
353	C₂²	—	4	3	no	—
354	C₂²	—	4	6	no	—
355	C₂²	—	4	1	no	—
356	C₂²	—	4	8	no	—
357	C₂²	—	4	24	no	—
358	C₂²	—	4	24	no	—
359	C₂²	#410×C₇₁	1	4	yes	direct product factor
360	C₂²	C₂²×C₂²⋊C₄×C₇₁	1	3	yes	—
361	C₂²	C₂²×C₂²⋊C₄×C₇₁	1	6	yes	—
362	C₂²	C₂²×C₂²⋊C₄×C₇₁	1	3	yes	—
363	C₂²	C₂⁴×C₄×C₇₁	1	1	yes	characteristic
364	C₂²	C₂³×D₄×C₇₁	1	2	yes	—
365	C₄	—	2	8	no	—
366	C₄	—	4	16	no	—
367	C₄	C₂²×C₂²⋊C₄×C₇₁	1	4	yes	—
368	C₄	C₂²×C₂²⋊C₄×C₇₁	1	4	yes	—
369	C₄	C₂²×C₂²⋊C₄×C₇₁	1	8	yes	—
370	C₂	—	2	2	no	—
371	C₂	—	2	3	no	—
372	C₂	—	2	1	no	—
373	C₂	—	2	6	no	—
374	C₂	—	4	8	no	—
375	C₂	C₂×#410×C₇₁	1	6	yes	direct product factor
376	C₂	C₂³×C₂²⋊C₄×C₇₁	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄×C₇₁	C₂²⋊C₄
commutator	C₂²	C₂⁴×C₄×C₇₁
Frattini, cosocle	C₂³	C₂⁵×C₇₁
socle	C₂³×C₇₁	C₂×C₂²⋊C₄
prime radical	C₂³×#41×C₇₁	C₂
LCS	G ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₇₁ ◁ C₂⁴×C₄×C₇₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂²×#117×C₇₁	C₂	semidirect
3. C₂×#410×C₇₁	C₂	direct (N × H)
4. C₂²×#99×C₇₁	C₂	semidirect
8. C₂²×#41×C₇₁	C₄	semidirect
10. C₂³×Q₈×C₇₁	C₄	semidirect
11. C₂³×D₄×C₇₁	C₄	semidirect
13. C₂⁴×C₄×C₇₁	C₄	semidirect
16. C₂×#117×C₇₁	C₂²	semidirect
20. #410×C₇₁	C₂²	direct (N × H)
21. C₂×#99×C₇₁	C₂²	semidirect
30. C₂×#41×C₇₁	C₂×C₄	semidirect
34. C₂²×Q₈×C₇₁	C₂×C₄	semidirect
40. C₂²×D₄×C₇₁	C₂×C₄	semidirect
50. C₂³×C₄×C₇₁	C₂×C₄	semidirect
56. #117×C₇₁	C₂³	semidirect
61. #99×C₇₁	C₂³	semidirect
78. C₂×Q₈×C₇₁	C₂²×C₄	semidirect
86. C₂×D₄×C₇₁	C₂²×C₄	semidirect
107. C₂²×C₄×C₇₁	C₂²×C₄	semidirect
170. C₂²×C₇₁	#410	direct (N × H)
181. C₂²×#410	C₇₁	direct (N × H)
187. C₂×C₇₁	C₂×#410	direct (N × H)
190. C₂²×#117	C₂×C₇₁	semidirect
191. C₂×#410	C₂×C₇₁	direct (N × H)
192. C₂²×#99	C₂×C₇₁	semidirect
193. C₇₁	C₂²×#410	direct (N × H)
197. C₂²×#41	C₄×C₇₁	semidirect
199. C₂³×Q₈	C₄×C₇₁	semidirect
200. C₂³×D₄	C₄×C₇₁	semidirect
202. C₂⁴×C₄	C₄×C₇₁	semidirect
205. C₂×#117	C₂²×C₇₁	semidirect
209. #410	C₂²×C₇₁	direct (N × H)
210. C₂×#99	C₂²×C₇₁	semidirect
219. C₂×#41	C₂×C₄×C₇₁	semidirect
223. C₂²×Q₈	C₂×C₄×C₇₁	semidirect
229. C₂²×D₄	C₂×C₄×C₇₁	semidirect
239. C₂³×C₄	C₂×C₄×C₇₁	semidirect
245. #117	C₂³×C₇₁	semidirect
250. #99	C₂³×C₇₁	semidirect
267. C₂×Q₈	C₂²×C₄×C₇₁	semidirect
275. C₂×D₄	C₂²×C₄×C₇₁	semidirect
296. C₂²×C₄	C₂²×C₄×C₇₁	semidirect
359. C₂²	#410×C₇₁	direct (N × H)
375. C₂	C₂×#410×C₇₁	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂³×#41×C₇₁	2
C₂²×#117×C₇₁	2
C₂×#410×C₇₁	2
C₂²×#99×C₇₁	2
C₂²×#410	71

Subgroups — C22×#410×C71 #31880939

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×#410×C₇₁ #31880939