Subgroups — #31966500

Order 18176.

666 conjugacy classes of subgroups.

The subgroup lattice has 418 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22597457	C₂	1	1	yes	maximal, characteristic
2	C₄×#14556135	C₂	1	1	yes	maximal, characteristic
3	#22587108	C₂	1	2	yes	maximal, complemented
4	#22587105	C₂	1	2	yes	maximal, complemented
5	#22587101	C₂	1	2	yes	maximal, complemented
6	#22587098	C₂	1	2	yes	maximal, complemented
7	#22587093	C₂	1	1	yes	maximal, characteristic, complemented
8	#22587090	C₂	1	1	yes	maximal, characteristic, complemented
9	#22587086	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#17985751	C₂	1	1	yes	maximal, characteristic, complemented
11	C₇₁×#2989	C₂	1	1	yes	maximal, characteristic
12	C₂×#14556135	C₄	1	1	yes	characteristic
13	C₂×#14556135	C₄	1	1	yes	characteristic
14	#17986130	—	2	1	no	—
15	#17986077	—	2	1	no	—
16	#17986071	—	2	2	no	—
17	#17986056	C₂²	1	2	yes	—
18	#17986052	C₂²	1	1	yes	characteristic
19	#17986023	C₂²	1	2	yes	—
20	C₂×C₄⋊(C₇₁⋊C₈)	C₂²	1	1	yes	characteristic
21	#17985955	C₄	1	2	yes	—
22	#17985955	C₄	1	2	yes	—
23	#17985955	C₄	1	1	yes	characteristic
24	#17985955	C₄	1	1	yes	characteristic
25	C₄×#11765849	C₂²	1	1	yes	characteristic
26	C₄×#11765849	C₂²	1	2	yes	—
27	C₂×C₄×C₇₁⋊C₈	C₂²	1	1	yes	characteristic
28	C₂×C₄×C₇₁⋊C₈	C₂²	1	2	yes	—
29	#17985751	C₂²	1	2	yes	—
30	#17985751	C₂²	1	2	yes	—
31	#17985751	C₂²	1	1	yes	characteristic
32	#17985751	C₂²	1	1	yes	characteristic
33	#17985751	C₂²	1	2	yes	—
34	#17985751	C₂²	1	2	yes	—
35	#17985749	C₂²	1	1	yes	characteristic
36	#17985749	C₂²	1	1	yes	characteristic
37	#17985749	C₂²	1	2	yes	—
38	#17985749	C₂²	1	2	yes	—
39	C₄×#41×C₇₁	C₂²	1	1	yes	characteristic
40	#446×C₇₁	—	2	1	no	—
41	#436×C₇₁	—	2	1	no	—
42	#435×C₇₁	—	2	2	no	—
43	#432×C₇₁	C₂²	1	2	yes	—
44	#431×C₇₁	C₂²	1	1	yes	characteristic
45	#423×C₇₁	C₂²	1	2	yes	—
46	C₂×C₄⋊C₈×C₇₁	C₂²	1	1	yes	characteristic
47	#14556135	—	2	4	no	—
48	#14556135	—	2	4	no	—
49	C₂×#11765849	—	2	2	no	—
50	C₂×#11765849	C₂×C₄	1	2	yes	—
51	C₂×#11765849	C₂×C₄	1	2	yes	—
52	C₂×#11765849	C₂×C₄	1	1	yes	characteristic
53	C₂×#11765849	C₂×C₄	1	1	yes	characteristic
54	C₂²×C₇₁⋊C₈	—	2	1	no	—
55	C₂²×C₇₁⋊C₈	C₂×C₄	1	2	yes	—
56	C₂²×C₇₁⋊C₈	C₂×C₄	1	2	yes	—
57	C₂²×C₇₁⋊C₈	C₂×C₄	1	1	yes	characteristic
58	C₂²×C₇₁⋊C₈	C₂×C₄	1	1	yes	characteristic
59	C₄⋊(C₇₁⋊C₈)	—	2	2	no	—
60	C₄⋊(C₇₁⋊C₈)	—	2	1	no	—
61	C₄⋊(C₇₁⋊C₈)	C₂³	1	1	yes	characteristic
62	C₄⋊(C₇₁⋊C₈)	C₂³	1	1	yes	characteristic
63	C₄⋊(C₇₁⋊C₈)	C₂³	1	2	yes	—
64	C₂²⋊(C₇₁⋊C₈)	—	2	1	no	—
65	C₂²⋊(C₇₁⋊C₈)	—	2	2	no	—
66	#14556039	—	2	2	no	—
67	#14556039	C₂×C₄	1	2	yes	—
68	#14556039	C₂×C₄	1	2	yes	—
69	#14556039	C₂×C₄	1	2	yes	—
70	C₄×C₇₁⋊C₈	—	2	1	no	—
71	C₄×C₇₁⋊C₈	C₂×C₄	1	2	yes	—
72	C₄×C₇₁⋊C₈	C₂×C₄	1	1	yes	characteristic
73	C₄×C₇₁⋊C₈	C₂×C₄	1	1	yes	characteristic
74	C₄×C₇₁⋊C₈	C₂×C₄	1	2	yes	—
75	C₄×C₇₁⋊C₈	C₂³	1	1	yes	characteristic
76	C₄×C₇₁⋊C₈	C₂³	1	1	yes	characteristic
77	C₄×C₇₁⋊C₈	C₂³	1	2	yes	—
78	C₂×#41×C₇₁	C₂×C₄	1	1	yes	characteristic
79	C₂×M₁₆×C₇₁	—	2	2	no	—
80	C₂²×C₈×C₇₁	—	2	1	no	—
81	C₄×Q₈×C₇₁	D₄	1	1	yes	characteristic
82	C₄×Q₈×C₇₁	Q₈	1	1	yes	characteristic
83	C₄×D₄×C₇₁	D₄	1	2	yes	—
84	C₄×D₄×C₇₁	D₄	1	1	yes	characteristic
85	C₄×D₄×C₇₁	Q₈	1	2	yes	—
86	C₄×D₄×C₇₁	Q₈	1	1	yes	characteristic
87	#117×C₇₁	C₂×C₄	1	2	yes	—
88	#117×C₇₁	C₂×C₄	1	1	yes	characteristic
89	C₂×C₄²×C₇₁	C₂³	1	1	yes	characteristic
90	C₂×C₄²×C₇₁	C₂³	1	2	yes	—
91	C₄⋊C₈×C₇₁	—	2	1	no	—
92	C₄⋊C₈×C₇₁	—	2	2	no	—
93	C₄⋊C₈×C₇₁	C₂³	1	2	yes	—
94	C₄⋊C₈×C₇₁	C₂³	1	1	yes	characteristic
95	C₄⋊C₈×C₇₁	C₂³	1	1	yes	characteristic
96	C₂²⋊C₈×C₇₁	—	2	1	no	—
97	C₂²⋊C₈×C₇₁	—	2	2	no	—
98	#97×C₇₁	—	2	2	no	—
99	C₄×C₈×C₇₁	—	2	1	no	—
100	#11765849	—	2	2	no	—
101	#11765849	—	2	4	no	—
102	#11765849	—	2	4	no	—
103	#11765849	—	8	2	no	—
104	#11765849	M₁₆	1	4	yes	complemented
105	C₂×C₇₁⋊C₈	—	2	2	no	—
106	C₂×C₇₁⋊C₈	—	2	4	no	—
107	C₂×C₇₁⋊C₈	—	2	4	no	—
108	C₂×C₇₁⋊C₈	—	2	1	no	—
109	C₂×C₇₁⋊C₈	—	2	1	no	—
110	C₂×C₇₁⋊C₈	—	2	2	no	—
111	C₂×C₇₁⋊C₈	—	8	1	no	—
112	C₂×C₇₁⋊C₈	M₁₆	1	4	yes	complemented
113	C₂×C₇₁⋊C₈	C₂²×C₄	1	1	yes	characteristic
114	C₂×C₇₁⋊C₈	C₂²×C₄	1	1	yes	characteristic
115	C₂×C₇₁⋊C₈	C₂²×C₄	1	2	yes	—
116	C₂×C₇₁⋊C₈	C₂²×C₄	1	1	yes	characteristic
117	C₂×C₇₁⋊C₈	C₂²×C₄	1	2	yes	—
118	C₂×C₇₁⋊C₈	C₂²×C₄	1	1	yes	characteristic
119	#41×C₇₁	—	2	2	no	—
120	#41×C₇₁	—	2	2	no	—
121	C₂×Q₈×C₇₁	C₄⋊C₄	1	1	yes	characteristic
122	C₂×D₄×C₇₁	C₄⋊C₄	1	2	yes	—
123	C₂×D₄×C₇₁	C₄⋊C₄	1	1	yes	characteristic
124	C₂²×C₄×C₇₁	C₂²×C₄	1	2	yes	—
125	C₂²×C₄×C₇₁	C₂²×C₄	1	1	yes	characteristic
126	C₂²×C₄×C₇₁	C₂×D₄	1	1	yes	characteristic
127	C₂²×C₄×C₇₁	C₂×D₄	1	2	yes	—
128	C₂²×C₄×C₇₁	C₂×Q₈	1	2	yes	—
129	C₂²×C₄×C₇₁	C₂×Q₈	1	1	yes	characteristic
130	M₁₆×C₇₁	—	8	2	no	—
131	C₂×C₈×C₇₁	—	2	1	no	—
132	C₂×C₈×C₇₁	—	2	1	no	—
133	C₂×C₈×C₇₁	—	2	2	no	—
134	C₂×C₈×C₇₁	—	8	1	no	—
135	C₄⋊C₄×C₇₁	C₄⋊C₄	1	2	yes	—
136	C₄⋊C₄×C₇₁	C₄⋊C₄	1	1	yes	characteristic
137	C₄⋊C₄×C₇₁	C₄⋊C₄	1	2	yes	—
138	C₄⋊C₄×C₇₁	C₄⋊C₄	1	1	yes	characteristic
139	C₂²⋊C₄×C₇₁	C₄⋊C₄	1	2	yes	—
140	C₂²⋊C₄×C₇₁	C₄⋊C₄	1	2	yes	—
141	C₂²⋊C₄×C₇₁	C₄⋊C₄	1	2	yes	—
142	C₄²×C₇₁	C₂²×C₄	1	1	yes	characteristic
143	C₄²×C₇₁	C₂²×C₄	1	2	yes	—
144	C₄²×C₇₁	C₂×D₄	1	1	yes	characteristic
145	C₄²×C₇₁	C₂×D₄	1	2	yes	—
146	C₄²×C₇₁	C₂×Q₈	1	2	yes	—
147	C₄²×C₇₁	C₂×Q₈	1	1	yes	characteristic
148	C₄²×C₇₁	C₂⁴	1	1	yes	characteristic
149	C₂³×C₇₁	C₂×C₄⋊C₄	1	2	yes	—
150	C₂³×C₇₁	C₂×C₄⋊C₄	1	1	yes	characteristic
151	Q₈×C₇₁	—	2	2	no	—
152	D₄×C₇₁	—	2	4	no	—
153	D₄×C₇₁	—	2	2	no	—
154	C₂×C₄×C₇₁	—	2	2	no	—
155	C₂×C₄×C₇₁	—	2	2	no	—
156	C₂×C₄×C₇₁	—	2	1	no	—
157	C₂×C₄×C₇₁	—	2	2	no	—
158	C₂×C₄×C₇₁	—	2	1	no	—
159	C₂×C₄×C₇₁	—	2	2	no	—
160	C₂×C₄×C₇₁	—	4	1	no	—
161	C₂×C₄×C₇₁	—	4	2	no	—
162	C₂×C₄×C₇₁	C₂×C₄⋊C₄	1	1	yes	characteristic
163	C₂×C₄×C₇₁	C₂×C₄⋊C₄	1	2	yes	—
164	C₂×C₄×C₇₁	C₂×C₄⋊C₄	1	1	yes	characteristic
165	C₂×C₄×C₇₁	C₂×C₄⋊C₄	1	2	yes	—
166	C₂×C₄×C₇₁	C₂×C₄⋊C₄	1	2	yes	—
167	C₂×C₄×C₇₁	C₂×C₄⋊C₄	1	1	yes	characteristic
168	C₂×C₄×C₇₁	C₂×M₁₆	1	2	yes	—
169	C₂×C₄×C₇₁	C₂×M₁₆	1	2	yes	—
170	C₂×C₄×C₇₁	C₂³×C₄	1	1	yes	characteristic
171	C₂×C₄×C₇₁	C₂²×D₄	1	1	yes	characteristic
172	C₂×C₄×C₇₁	C₂²×Q₈	1	1	yes	characteristic
173	C₈×C₇₁	—	4	2	no	—
174	C₈×C₇₁	—	4	1	no	—
175	C₈×C₇₁	—	4	1	no	—
176	C₇₁⋊C₈	—	2	1	no	—
177	C₇₁⋊C₈	—	2	1	no	—
178	C₇₁⋊C₈	—	2	2	no	—
179	C₇₁⋊C₈	—	4	2	no	—
180	C₇₁⋊C₈	—	4	1	no	—
181	C₇₁⋊C₈	—	4	1	no	—
182	C₇₁⋊C₈	C₂×M₁₆	1	2	yes	—
183	C₇₁⋊C₈	C₂×M₁₆	1	4	yes	—
184	C₇₁⋊C₈	C₂×M₁₆	1	2	yes	—
185	C₂²×C₇₁	—	2	1	no	—
186	C₂²×C₇₁	—	2	1	no	—
187	C₂²×C₇₁	—	2	2	no	—
188	C₂²×C₇₁	—	2	2	no	—
189	C₂²×C₇₁	—	2	2	no	—
190	C₂²×C₇₁	#423	1	2	yes	—
191	C₂²×C₇₁	C₂²×C₄⋊C₄	1	1	yes	characteristic
192	C₄×C₇₁	—	2	2	no	—
193	C₄×C₇₁	—	2	1	no	—
194	C₄×C₇₁	—	2	2	no	—
195	C₄×C₇₁	—	2	1	no	—
196	C₄×C₇₁	—	2	1	no	—
197	C₄×C₇₁	—	2	2	no	—
198	C₄×C₇₁	#423	1	2	yes	—
199	C₄×C₇₁	C₂²×M₁₆	1	1	yes	characteristic
200	C₄×C₇₁	C₂²×M₁₆	1	1	yes	characteristic
201	C₄×C₇₁	#576	1	1	yes	characteristic
202	C₄×C₇₁	#578	1	1	yes	characteristic
203	#17799	—	71	1	no	maximal, Sylow
204	C₂×C₇₁	—	2	2	no	—
205	C₂×C₇₁	—	4	2	no	—
206	C₂×C₇₁	C₂×#423	1	1	yes	characteristic
207	C₂×C₇₁	#2913	1	1	yes	characteristic
208	C₂×C₇₁	#2916	1	1	yes	characteristic
209	#2989	—	71	1	no	—
210	#2989	D₇₁	1	1	yes	characteristic
211	C₄×#131	—	71	1	no	—
212	#1569	—	71	2	no	—
213	#1569	—	71	2	no	—
214	#1568	—	71	2	no	—
215	#1567	—	71	2	no	—
216	#1565	—	71	1	no	—
217	#1565	—	71	1	no	—
218	#1564	—	71	1	no	—
219	C₂×#335	—	71	1	no	—
220	C₇₁	#17799	1	1	yes	characteristic, complemented, Sylow
221	C₂×#131	—	71	1	no	—
222	C₂×#131	—	71	1	no	—
223	C₄×#41	C₂×D₇₁	1	1	yes	characteristic
224	#446	—	2	1	no	—
225	#446	—	142	1	no	—
226	#436	—	2	1	no	—
227	#436	—	142	1	no	—
228	#435	—	2	2	no	—
229	#435	—	142	2	no	—
230	#432	—	71	2	no	—
231	#432	C₂×D₇₁	1	2	yes	—
232	#431	—	71	1	no	—
233	#431	C₂×D₇₁	1	1	yes	characteristic
234	#423	—	71	2	no	—
235	#423	C₂×D₇₁	1	2	yes	—
236	C₂×C₄⋊C₈	—	71	1	no	—
237	C₂×C₄⋊C₈	C₂×D₇₁	1	1	yes	characteristic
238	#405	—	71	1	no	—
239	#405	—	71	2	no	—
240	#405	—	71	2	no	—
241	#405	—	71	1	no	—
242	C₄×M₁₆	—	71	1	no	—
243	C₄×M₁₆	—	71	2	no	—
244	C₂×C₄×C₈	—	71	1	no	—
245	C₂×C₄×C₈	—	71	2	no	—
246	#335	—	71	2	no	—
247	#335	—	71	2	no	—
248	#335	—	71	1	no	—
249	#335	—	71	1	no	—
250	#335	—	71	2	no	—
251	#335	—	71	2	no	—
252	#334	—	71	1	no	—
253	#334	—	71	1	no	—
254	#334	—	71	2	no	—
255	#334	—	71	2	no	—
256	C₂×#41	C₄×D₇₁	1	1	yes	characteristic
257	#131	—	142	4	no	—
258	#131	—	142	4	no	—
259	C₂×M₁₆	—	2	2	no	—
260	C₂×M₁₆	—	71	1	no	—
261	C₂×M₁₆	—	71	2	no	—
262	C₂×M₁₆	—	71	2	no	—
263	C₂×M₁₆	—	71	1	no	—
264	C₂×M₁₆	—	142	2	no	—
265	C₂²×C₈	—	2	1	no	—
266	C₂²×C₈	—	71	1	no	—
267	C₂²×C₈	—	71	2	no	—
268	C₂²×C₈	—	71	2	no	—
269	C₂²×C₈	—	71	1	no	—
270	C₂²×C₈	—	142	1	no	—
271	C₄×Q₈	Dic₁₄₂	1	1	yes	characteristic
272	C₄×Q₈	C₂²⋊D₇₁	1	1	yes	characteristic
273	C₄×D₄	Dic₁₄₂	1	2	yes	—
274	C₄×D₄	Dic₁₄₂	1	1	yes	characteristic
275	C₄×D₄	C₂²⋊D₇₁	1	2	yes	—
276	C₄×D₄	C₂²⋊D₇₁	1	1	yes	characteristic
277	#117	C₄×D₇₁	1	2	yes	—
278	#117	C₄×D₇₁	1	1	yes	characteristic
279	C₂×C₄²	C₂²×D₇₁	1	1	yes	characteristic
280	C₂×C₄²	C₂²×D₇₁	1	2	yes	—
281	C₄⋊C₈	—	2	1	no	—
282	C₄⋊C₈	—	2	2	no	—
283	C₄⋊C₈	—	71	1	no	—
284	C₄⋊C₈	—	71	2	no	—
285	C₄⋊C₈	—	71	1	no	—
286	C₄⋊C₈	—	142	1	no	—
287	C₄⋊C₈	—	142	2	no	—
288	C₄⋊C₈	C₂²×D₇₁	1	1	yes	characteristic
289	C₄⋊C₈	C₂²×D₇₁	1	2	yes	—
290	C₄⋊C₈	C₂²×D₇₁	1	1	yes	characteristic
291	C₂²⋊C₈	—	2	1	no	—
292	C₂²⋊C₈	—	2	2	no	—
293	C₂²⋊C₈	—	142	1	no	—
294	C₂²⋊C₈	—	142	2	no	—
295	#97	—	2	2	no	—
296	#97	—	71	2	no	—
297	#97	—	71	2	no	—
298	#97	—	71	2	no	—
299	#97	—	142	2	no	—
300	C₄×C₈	—	2	1	no	—
301	C₄×C₈	—	71	2	no	—
302	C₄×C₈	—	71	1	no	—
303	C₄×C₈	—	71	1	no	—
304	C₄×C₈	—	71	2	no	—
305	C₄×C₈	—	71	1	no	—
306	C₄×C₈	—	71	2	no	—
307	C₄×C₈	—	71	1	no	—
308	C₄×C₈	—	142	1	no	—
309	#41	—	2	2	no	—
310	#41	—	2	2	no	—
311	C₂×Q₈	Dic₇₁⋊C₄	1	1	yes	characteristic
312	C₂×D₄	Dic₇₁⋊C₄	1	2	yes	—
313	C₂×D₄	Dic₇₁⋊C₄	1	1	yes	characteristic
314	C₂²×C₄	C₂×C₄×D₇₁	1	2	yes	—
315	C₂²×C₄	C₂×C₄×D₇₁	1	1	yes	characteristic
316	C₂²×C₄	C₂×C₂²⋊D₇₁	1	1	yes	characteristic
317	C₂²×C₄	C₂×C₂²⋊D₇₁	1	2	yes	—
318	C₂²×C₄	C₂×Dic₁₄₂	1	2	yes	—
319	C₂²×C₄	C₂×Dic₁₄₂	1	1	yes	characteristic
320	M₁₆	—	8	2	no	—
321	M₁₆	—	568	2	no	—
322	M₁₆	—	71	4	no	—
323	M₁₆	—	142	4	no	—
324	M₁₆	—	142	4	no	—
325	M₁₆	—	142	2	no	—
326	C₂×C₈	—	2	1	no	—
327	C₂×C₈	—	2	1	no	—
328	C₂×C₈	—	2	2	no	—
329	C₂×C₈	—	8	1	no	—
330	C₂×C₈	—	568	1	no	—
331	C₂×C₈	—	71	1	no	—
332	C₂×C₈	—	71	1	no	—
333	C₂×C₈	—	71	2	no	—
334	C₂×C₈	—	71	4	no	—
335	C₂×C₈	—	71	1	no	—
336	C₂×C₈	—	71	2	no	—
337	C₂×C₈	—	71	1	no	—
338	C₂×C₈	—	142	1	no	—
339	C₂×C₈	—	142	1	no	—
340	C₂×C₈	—	142	2	no	—
341	C₂×C₈	—	142	4	no	—
342	C₂×C₈	—	142	4	no	—
343	C₂×C₈	—	142	2	no	—
344	C₄⋊C₄	Dic₇₁⋊C₄	1	2	yes	—
345	C₄⋊C₄	Dic₇₁⋊C₄	1	1	yes	characteristic
346	C₄⋊C₄	Dic₇₁⋊C₄	1	2	yes	—
347	C₄⋊C₄	Dic₇₁⋊C₄	1	1	yes	characteristic
348	C₂²⋊C₄	Dic₇₁⋊C₄	1	2	yes	—
349	C₂²⋊C₄	Dic₇₁⋊C₄	1	2	yes	—
350	C₂²⋊C₄	Dic₇₁⋊C₄	1	2	yes	—
351	C₄²	C₂×C₄×D₇₁	1	1	yes	characteristic
352	C₄²	C₂×C₄×D₇₁	1	2	yes	—
353	C₄²	C₂×C₂²⋊D₇₁	1	1	yes	characteristic
354	C₄²	C₂×C₂²⋊D₇₁	1	2	yes	—
355	C₄²	C₂×Dic₁₄₂	1	2	yes	—
356	C₄²	C₂×Dic₁₄₂	1	1	yes	characteristic
357	C₄²	C₂³×D₇₁	1	1	yes	characteristic
358	C₂³	C₂×Dic₇₁⋊C₄	1	2	yes	—
359	C₂³	C₂×Dic₇₁⋊C₄	1	1	yes	characteristic
360	Q₈	—	2	2	no	—
361	D₄	—	2	4	no	—
362	D₄	—	2	2	no	—
363	C₂×C₄	—	2	2	no	—
364	C₂×C₄	—	2	2	no	—
365	C₂×C₄	—	2	1	no	—
366	C₂×C₄	—	2	2	no	—
367	C₂×C₄	—	2	1	no	—
368	C₂×C₄	—	2	2	no	—
369	C₂×C₄	—	4	1	no	—
370	C₂×C₄	—	4	2	no	—
371	C₂×C₄	C₂×Dic₇₁⋊C₄	1	1	yes	characteristic
372	C₂×C₄	C₂×Dic₇₁⋊C₄	1	2	yes	—
373	C₂×C₄	C₂×Dic₇₁⋊C₄	1	1	yes	characteristic
374	C₂×C₄	C₂×Dic₇₁⋊C₄	1	2	yes	—
375	C₂×C₄	C₂×Dic₇₁⋊C₄	1	2	yes	—
376	C₂×C₄	C₂×Dic₇₁⋊C₄	1	1	yes	characteristic
377	C₂×C₄	M₁₆×D₇₁	1	2	yes	—
378	C₂×C₄	M₁₆×D₇₁	1	2	yes	—
379	C₂×C₄	C₂²×C₄×D₇₁	1	1	yes	characteristic
380	C₂×C₄	C₂²×C₂²⋊D₇₁	1	1	yes	characteristic
381	C₂×C₄	C₂²×Dic₁₄₂	1	1	yes	characteristic
382	C₈	—	4	2	no	—
383	C₈	—	4	1	no	—
384	C₈	—	4	1	no	—
385	C₈	—	284	2	no	—
386	C₈	—	284	1	no	—
387	C₈	—	284	1	no	—
388	C₈	—	71	2	no	—
389	C₈	—	71	2	no	—
390	C₈	—	71	4	no	—
391	C₈	—	142	1	no	—
392	C₈	—	142	2	no	—
393	C₈	—	142	1	no	—
394	C₂²	—	2	1	no	—
395	C₂²	—	2	1	no	—
396	C₂²	—	2	2	no	—
397	C₂²	—	2	2	no	—
398	C₂²	—	2	2	no	—
399	C₂²	#17986022	1	2	yes	—
400	C₂²	C₂²×Dic₇₁⋊C₄	1	1	yes	characteristic
401	C₄	—	2	2	no	—
402	C₄	—	2	1	no	—
403	C₄	—	2	2	no	—
404	C₄	—	2	1	no	—
405	C₄	—	2	1	no	—
406	C₄	—	2	2	no	—
407	C₄	#17986022	1	2	yes	—
408	C₄	C₂×M₁₆×D₇₁	1	1	yes	characteristic
409	C₄	C₂×M₁₆×D₇₁	1	1	yes	characteristic
410	C₄	#17986802	1	1	yes	characteristic
411	C₄	#17986814	1	1	yes	characteristic
412	C₂	—	2	2	no	—
413	C₂	—	4	2	no	—
414	C₂	C₂×#17986022	1	1	yes	characteristic
415	C₂	#22596938	1	1	yes	characteristic
416	C₂	#22596949	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²×C₂²⋊D₇₁
commutator	C₂×C₄×C₇₁	C₂³×C₄
Frattini	C₄²	C₂³×D₇₁
Fitting	C₇₁×#2989	C₂
socle	C₂²×C₇₁	C₂²×C₄⋊C₄
prime radical	C₂×#41×C₇₁	C₂×C₄
cosocle	C₄²×C₇₁	C₂⁴
hypercenter	#2989	D₇₁
hypocenter	C₇₁	#17799
LCS	G ▷ C₂×C₄×C₇₁ ▷ C₂×C₇₁ ▷ C₇₁
UCS	C₁ ◁ C₂×C₄ ◁ C₄×#41 ◁ #2989

Complements

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

N	H ≅ G/N	type
3. #22587108	C₂	semidirect
4. #22587105	C₂	semidirect
5. #22587101	C₂	semidirect
6. #22587098	C₂	semidirect
7. #22587093	C₂	semidirect
8. #22587090	C₂	semidirect
9. #22587086	C₂	semidirect
10. C₂×#17985751	C₂	semidirect
104. #11765849	M₁₆	semidirect
112. C₂×C₇₁⋊C₈	M₁₆	semidirect
220. C₇₁	#17799	semidirect

Maximal subgroups

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

subgroup	index
#22597457	2
C₄×#14556135	2
#22587108	2
#22587105	2
#22587101	2
#22587098	2
#22587093	2
#22587090	2
#22587086	2
C₂×#17985751	2
C₇₁×#2989	2
#17799	71