Subgroups — #32017149

Order 18176.

722 conjugacy classes of subgroups.

The subgroup lattice has 388 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22597006	C₂	1	2	yes	maximal, complemented
2	#22589229	C₂	1	2	yes	maximal
3	#22588990	C₂	1	4	yes	maximal, complemented
4	#22588512	C₂	1	1	yes	maximal, characteristic, complemented
5	#22588360	C₂	1	2	yes	maximal, complemented
6	#22588221	C₂	1	2	yes	maximal, complemented
7	C₈×C₄⋊Dic₇₁	C₂	1	1	yes	maximal, characteristic, complemented
8	C₄×#135×C₇₁	C₂	1	1	yes	maximal, characteristic
9	#17986060	—	2	4	no	—
10	#17986056	—	2	2	no	—
11	#17986052	—	2	2	no	—
12	C₂×#14556064	C₂²	1	2	yes	—
13	C₂×#14556064	C₂²	1	2	yes	—
14	#17986023	C₂²	1	2	yes	—
15	C₂×C₄⋊(C₇₁⋊C₈)	C₂²	1	1	yes	characteristic
16	C₂×#14556055	C₂²	1	4	yes	—
17	#17985966	C₂²	1	4	yes	—
18	#17985955	C₂²	1	4	yes	—
19	C₂×C₈×Dic₇₁	C₂²	1	2	yes	—
20	C₄×C₄⋊Dic₇₁	C₂²	1	1	yes	characteristic
21	#17985758	C₂²	1	4	yes	—
22	#17985753	C₂²	1	2	yes	—
23	C₂×#135×C₇₁	C₂²	1	1	yes	characteristic
24	C₄×#41×C₇₁	C₂²	1	2	yes	—
25	C₄×Q₁₆×C₇₁	C₄	1	1	yes	characteristic, complemented
26	C₄×Q₁₆×C₇₁	C₄	1	1	yes	characteristic, complemented
27	C₄×SD₁₆×C₇₁	C₄	1	2	yes	complemented
28	C₄×SD₁₆×C₇₁	C₄	1	2	yes	complemented
29	C₄×D₈×C₇₁	C₄	1	1	yes	characteristic, complemented
30	C₄×D₈×C₇₁	C₄	1	1	yes	characteristic, complemented
31	#427×C₇₁	C₂²	1	1	yes	characteristic
32	#416×C₇₁	C₂²	1	2	yes	—
33	C₂×C₄×C₈×C₇₁	C₂²	1	1	yes	characteristic
34	C₂×#11765849	C₂³	1	4	yes	—
35	C₂²×C₇₁⋊C₈	C₂³	1	2	yes	—
36	C₂×C₄⋊Dic₇₁	—	2	1	no	—
37	C₂×C₄×Dic₇₁	C₂³	1	2	yes	—
38	#14556064	—	2	4	no	—
39	#14556064	—	4	2	no	—
40	C₄⋊(C₇₁⋊C₈)	—	2	2	no	—
41	C₄⋊(C₇₁⋊C₈)	—	2	2	no	—
42	C₄⋊(C₇₁⋊C₈)	D₄	1	1	yes	characteristic
43	C₄⋊(C₇₁⋊C₈)	D₄	1	1	yes	characteristic
44	C₄⋊(C₇₁⋊C₈)	D₄	1	2	yes	—
45	#14556055	—	4	4	no	—
46	C₂²⋊(C₇₁⋊C₈)	—	2	4	no	—
47	C₂²⋊(C₇₁⋊C₈)	—	2	4	no	—
48	#14556039	—	2	4	no	—
49	C₄×C₇₁⋊C₈	—	2	4	no	—
50	C₈×Dic₇₁	—	2	4	no	—
51	C₇₁⋊#95	—	2	1	no	—
52	C₂×#41×C₇₁	C₂³	1	2	yes	—
53	#135×C₇₁	—	2	2	no	—
54	#135×C₇₁	—	2	2	no	—
55	C₂×Q₁₆×C₇₁	C₂×C₄	1	1	yes	characteristic
56	C₂×SD₁₆×C₇₁	C₂×C₄	1	2	yes	—
57	C₂×D₈×C₇₁	C₂×C₄	1	1	yes	characteristic
58	C₂²×C₈×C₇₁	C₂³	1	1	yes	characteristic
59	C₂²×C₈×C₇₁	C₂³	1	1	yes	characteristic
60	C₄×Q₈×C₇₁	C₂×C₄	1	2	yes	—
61	C₄×Q₈×C₇₁	C₂×C₄	1	2	yes	—
62	C₄×D₄×C₇₁	—	2	2	no	—
63	C₄×D₄×C₇₁	—	2	2	no	—
64	C₄×D₄×C₇₁	C₂×C₄	1	2	yes	—
65	C₄×D₄×C₇₁	C₂×C₄	1	2	yes	—
66	#117×C₇₁	—	2	2	no	—
67	#117×C₇₁	C₂³	1	2	yes	—
68	C₂×C₄²×C₇₁	—	2	2	no	—
69	C₂×C₄²×C₇₁	C₂³	1	1	yes	characteristic
70	#107×C₇₁	C₂×C₄	1	1	yes	characteristic
71	#107×C₇₁	C₂×C₄	1	1	yes	characteristic
72	#106×C₇₁	C₂×C₄	1	2	yes	—
73	#103×C₇₁	C₂×C₄	1	2	yes	—
74	#103×C₇₁	C₂×C₄	1	2	yes	—
75	#102×C₇₁	C₂×C₄	1	2	yes	—
76	#102×C₇₁	C₂×C₄	1	2	yes	—
77	C₄×C₈×C₇₁	C₂×C₄	1	1	yes	characteristic
78	C₄×C₈×C₇₁	C₂×C₄	1	1	yes	characteristic
79	C₄×C₈×C₇₁	C₂×C₄	1	1	yes	characteristic
80	C₄×C₈×C₇₁	C₂×C₄	1	1	yes	characteristic
81	C₂²×Dic₇₁	—	2	2	no	—
82	#11765849	—	2	4	no	—
83	#11765849	—	2	4	no	—
84	C₂×C₇₁⋊C₈	—	2	2	no	—
85	C₂×C₇₁⋊C₈	—	2	2	no	—
86	C₂×C₇₁⋊C₈	—	2	4	no	—
87	C₂×C₇₁⋊C₈	C₂×D₄	1	2	yes	—
88	C₂×C₇₁⋊C₈	C₂×D₄	1	2	yes	—
89	C₄⋊Dic₇₁	—	2	4	no	—
90	C₄×Dic₇₁	—	2	2	no	—
91	C₄×Dic₇₁	—	2	2	no	—
92	#41×C₇₁	—	2	2	no	—
93	#41×C₇₁	—	2	2	no	—
94	#41×C₇₁	—	2	2	no	—
95	#41×C₇₁	—	2	2	no	—
96	C₂×Q₈×C₇₁	C₂²×C₄	1	2	yes	—
97	C₂×D₄×C₇₁	—	2	2	no	—
98	C₂×D₄×C₇₁	C₂²×C₄	1	2	yes	—
99	C₂²×C₄×C₇₁	—	2	2	no	—
100	C₂²×C₄×C₇₁	—	2	2	no	—
101	C₂²×C₄×C₇₁	—	2	2	no	—
102	C₂²×C₄×C₇₁	#41	1	1	yes	characteristic
103	C₂²×C₄×C₇₁	#41	1	1	yes	characteristic
104	C₂²×C₄×C₇₁	C₂⁴	1	1	yes	characteristic
105	Q₁₆×C₇₁	—	2	2	no	—
106	SD₁₆×C₇₁	—	2	4	no	—
107	D₈×C₇₁	—	2	2	no	—
108	C₂×C₈×C₇₁	—	2	1	no	—
109	C₂×C₈×C₇₁	—	2	1	no	—
110	C₂×C₈×C₇₁	C₂²×C₄	1	1	yes	characteristic
111	C₂×C₈×C₇₁	C₂²×C₄	1	1	yes	characteristic
112	C₂×C₈×C₇₁	C₂²×C₄	1	1	yes	characteristic
113	C₂×C₈×C₇₁	C₂²×C₄	1	1	yes	characteristic
114	C₂×C₈×C₇₁	#41	1	2	yes	—
115	C₂×C₈×C₇₁	#41	1	2	yes	—
116	C₄⋊C₄×C₇₁	—	2	2	no	—
117	C₄⋊C₄×C₇₁	—	2	2	no	—
118	C₄⋊C₄×C₇₁	C₂²×C₄	1	2	yes	—
119	C₄⋊C₄×C₇₁	C₂²×C₄	1	2	yes	—
120	C₂²⋊C₄×C₇₁	—	2	2	no	—
121	C₂²⋊C₄×C₇₁	—	2	2	no	—
122	C₂²⋊C₄×C₇₁	—	2	2	no	—
123	C₄²×C₇₁	—	2	2	no	—
124	C₄²×C₇₁	—	2	2	no	—
125	C₄²×C₇₁	—	2	2	no	—
126	C₄²×C₇₁	C₂²×C₄	1	1	yes	characteristic
127	C₄²×C₇₁	C₂²×C₄	1	1	yes	characteristic
128	C₄²×C₇₁	C₂×D₄	1	1	yes	characteristic
129	C₄²×C₇₁	C₂×D₄	1	1	yes	characteristic
130	C₂³×C₇₁	—	2	2	no	—
131	C₂³×C₇₁	C₂×#41	1	1	yes	characteristic
132	Q₈×C₇₁	—	2	2	no	—
133	Q₈×C₇₁	—	2	2	no	—
134	D₄×C₇₁	—	2	2	no	—
135	D₄×C₇₁	—	2	2	no	—
136	D₄×C₇₁	—	4	2	no	—
137	D₄×C₇₁	—	4	2	no	—
138	C₂×C₄×C₇₁	—	2	2	no	—
139	C₂×C₄×C₇₁	—	2	2	no	—
140	C₂×C₄×C₇₁	—	2	2	no	—
141	C₂×C₄×C₇₁	—	2	2	no	—
142	C₂×C₄×C₇₁	—	4	1	no	—
143	C₂×C₄×C₇₁	—	4	2	no	—
144	C₂×C₄×C₇₁	—	4	2	no	—
145	C₂×C₄×C₇₁	—	4	4	no	—
146	C₂×C₄×C₇₁	—	8	2	no	—
147	C₂×C₄×C₇₁	C₄×D₄	1	1	yes	characteristic
148	C₂×C₄×C₇₁	C₄×D₄	1	1	yes	characteristic
149	C₂×C₄×C₇₁	C₄×D₄	1	1	yes	characteristic
150	C₂×C₄×C₇₁	C₄×D₄	1	1	yes	characteristic
151	C₂×C₄×C₇₁	C₂³×C₄	1	1	yes	characteristic
152	C₂×C₄×C₇₁	C₂²×D₄	1	1	yes	characteristic
153	C₂×C₄×C₇₁	C₂×#41	1	1	yes	characteristic
154	C₂×C₄×C₇₁	C₂×#41	1	1	yes	characteristic
155	C₂×C₄×C₇₁	H(5,𝔽₂)	1	1	yes	characteristic
156	C₂×C₄×C₇₁	2₋¹⁺⁴	1	1	yes	characteristic
157	C₂×Dic₇₁	—	2	4	no	—
158	C₂×Dic₇₁	—	4	2	no	—
159	C₂×Dic₇₁	—	4	2	no	—
160	C₈×C₇₁	—	2	1	no	—
161	C₈×C₇₁	—	2	1	no	—
162	C₈×C₇₁	#117	1	2	yes	—
163	C₈×C₇₁	#117	1	2	yes	—
164	C₇₁⋊C₈	—	2	2	no	—
165	C₇₁⋊C₈	—	2	2	no	—
166	C₇₁⋊C₈	—	4	4	no	—
167	C₂²×C₇₁	—	2	1	no	—
168	C₂²×C₇₁	—	2	1	no	—
169	C₂²×C₇₁	—	4	2	no	—
170	C₂²×C₇₁	—	4	2	no	—
171	C₂²×C₇₁	—	4	2	no	—
172	C₂²×C₇₁	C₂×C₄×D₄	1	1	yes	characteristic
173	C₂²×C₇₁	#555	1	1	yes	characteristic
174	C₂²×C₇₁	#556	1	1	yes	characteristic
175	C₄×C₇₁	—	2	1	no	—
176	C₄×C₇₁	—	2	1	no	—
177	C₄×C₇₁	—	2	1	no	—
178	C₄×C₇₁	—	4	2	no	—
179	C₄×C₇₁	—	4	2	no	—
180	C₄×C₇₁	—	4	2	no	—
181	C₄×C₇₁	#443	1	2	yes	—
182	C₄×C₇₁	C₂×#117	1	1	yes	characteristic
183	C₄×C₇₁	#520	1	1	yes	characteristic
184	C₄×C₇₁	#547	1	1	yes	characteristic
185	C₄×C₇₁	#550	1	1	yes	characteristic
186	Dic₇₁	—	4	4	no	—
187	#22802	—	71	1	no	maximal, Sylow
188	C₂×C₇₁	—	2	1	no	—
189	C₂×C₇₁	—	2	1	no	—
190	C₂×C₇₁	—	8	2	no	—
191	C₂×C₇₁	#2354	1	1	yes	characteristic
192	C₂×C₇₁	C₂×#443	1	1	yes	characteristic
193	C₂×C₇₁	#2957	1	1	yes	characteristic
194	C₄×#135	D₇₁	1	1	yes	characteristic
195	#2925	—	71	2	no	—
196	#1974	—	71	2	no	—
197	#1929	—	71	4	no	—
198	#1848	—	71	1	no	—
199	#1806	—	71	2	no	—
200	#1772	—	71	2	no	—
201	C₈×C₄⋊C₄	—	71	1	no	—
202	C₇₁	#22802	1	1	yes	characteristic, complemented, Sylow
203	C₂×#135	C₂×D₇₁	1	1	yes	characteristic
204	C₄×#41	C₂×D₇₁	1	2	yes	—
205	C₄×Q₁₆	Dic₇₁	1	1	yes	characteristic, complemented
206	C₄×Q₁₆	Dic₇₁	1	1	yes	characteristic, complemented
207	C₄×SD₁₆	Dic₇₁	1	2	yes	complemented
208	C₄×SD₁₆	Dic₇₁	1	2	yes	complemented
209	C₄×D₈	Dic₇₁	1	1	yes	characteristic, complemented
210	C₄×D₈	Dic₇₁	1	1	yes	characteristic, complemented
211	#433	—	142	4	no	—
212	#432	—	142	2	no	—
213	#431	—	142	2	no	—
214	C₂×#108	—	71	2	no	—
215	C₂×#108	—	71	2	no	—
216	#427	C₂×D₇₁	1	1	yes	characteristic
217	#423	—	71	2	no	—
218	C₂×C₄⋊C₈	—	71	1	no	—
219	C₂×#104	—	71	4	no	—
220	#416	C₂×D₇₁	1	2	yes	—
221	#408	—	71	4	no	—
222	#405	—	71	4	no	—
223	C₂×C₄×C₈	—	71	2	no	—
224	C₂×C₄×C₈	C₂×D₇₁	1	1	yes	characteristic
225	C₄×C₄⋊C₄	—	71	1	no	—
226	#339	—	71	4	no	—
227	#336	—	71	2	no	—
228	C₂×#41	C₂²×D₇₁	1	2	yes	—
229	#135	—	2	2	no	—
230	#135	—	2	2	no	—
231	C₂×Q₁₆	C₂×Dic₇₁	1	1	yes	characteristic
232	C₂×SD₁₆	C₂×Dic₇₁	1	2	yes	—
233	C₂×D₈	C₂×Dic₇₁	1	1	yes	characteristic
234	C₂×M₁₆	—	71	4	no	—
235	C₂²×C₈	—	71	2	no	—
236	C₂²×C₈	C₂²×D₇₁	1	1	yes	characteristic
237	C₂²×C₈	C₂²×D₇₁	1	1	yes	characteristic
238	C₄×Q₈	C₂×Dic₇₁	1	2	yes	—
239	C₄×Q₈	C₂×Dic₇₁	1	2	yes	—
240	C₄×D₄	—	2	2	no	—
241	C₄×D₄	—	2	2	no	—
242	C₄×D₄	C₂×Dic₇₁	1	2	yes	—
243	C₄×D₄	C₂×Dic₇₁	1	2	yes	—
244	#117	—	2	2	no	—
245	#117	C₂²×D₇₁	1	2	yes	—
246	C₂×C₄⋊C₄	—	142	1	no	—
247	C₂×C₄²	—	2	2	no	—
248	C₂×C₄²	—	71	2	no	—
249	C₂×C₄²	C₂²×D₇₁	1	1	yes	characteristic
250	#108	—	284	2	no	—
251	#108	—	142	4	no	—
252	#107	C₂×Dic₇₁	1	1	yes	characteristic
253	#107	C₂×Dic₇₁	1	1	yes	characteristic
254	#106	C₂×Dic₇₁	1	2	yes	—
255	C₄⋊C₈	—	71	1	no	—
256	C₄⋊C₈	—	71	1	no	—
257	C₄⋊C₈	—	71	2	no	—
258	C₄⋊C₈	—	142	2	no	—
259	C₄⋊C₈	—	142	2	no	—
260	#104	—	284	4	no	—
261	#103	C₂×Dic₇₁	1	2	yes	—
262	#103	C₂×Dic₇₁	1	2	yes	—
263	#102	C₂×Dic₇₁	1	2	yes	—
264	#102	C₂×Dic₇₁	1	2	yes	—
265	C₂²⋊C₈	—	142	4	no	—
266	C₂²⋊C₈	—	142	4	no	—
267	#97	—	142	4	no	—
268	C₄×C₈	—	142	4	no	—
269	C₄×C₈	—	142	4	no	—
270	C₄×C₈	C₂×Dic₇₁	1	1	yes	characteristic
271	C₄×C₈	C₂×Dic₇₁	1	1	yes	characteristic
272	C₄×C₈	C₂×Dic₇₁	1	1	yes	characteristic
273	C₄×C₈	C₂×Dic₇₁	1	1	yes	characteristic
274	#95	—	142	1	no	—
275	#41	—	2	2	no	—
276	#41	—	2	2	no	—
277	#41	—	2	2	no	—
278	#41	—	2	2	no	—
279	C₂×Q₈	C₂²×Dic₇₁	1	2	yes	—
280	C₂×D₄	—	2	2	no	—
281	C₂×D₄	C₂²×Dic₇₁	1	2	yes	—
282	C₂²×C₄	—	2	2	no	—
283	C₂²×C₄	—	2	2	no	—
284	C₂²×C₄	—	2	2	no	—
285	C₂²×C₄	—	142	2	no	—
286	C₂²×C₄	#11765864	1	1	yes	characteristic
287	C₂²×C₄	#11765864	1	1	yes	characteristic
288	C₂²×C₄	C₂³×D₇₁	1	1	yes	characteristic
289	Q₁₆	—	2	2	no	—
290	SD₁₆	—	2	4	no	—
291	D₈	—	2	2	no	—
292	M₁₆	—	142	4	no	—
293	M₁₆	—	142	4	no	—
294	C₂×C₈	—	2	1	no	—
295	C₂×C₈	—	2	1	no	—
296	C₂×C₈	—	71	2	no	—
297	C₂×C₈	—	71	2	no	—
298	C₂×C₈	—	142	4	no	—
299	C₂×C₈	—	142	2	no	—
300	C₂×C₈	—	142	2	no	—
301	C₂×C₈	C₂²×Dic₇₁	1	1	yes	characteristic
302	C₂×C₈	C₂²×Dic₇₁	1	1	yes	characteristic
303	C₂×C₈	C₂²×Dic₇₁	1	1	yes	characteristic
304	C₂×C₈	C₂²×Dic₇₁	1	1	yes	characteristic
305	C₂×C₈	#11765865	1	2	yes	—
306	C₂×C₈	#11765865	1	2	yes	—
307	C₄⋊C₄	—	2	2	no	—
308	C₄⋊C₄	—	2	2	no	—
309	C₄⋊C₄	—	142	4	no	—
310	C₄⋊C₄	C₂²×Dic₇₁	1	2	yes	—
311	C₄⋊C₄	C₂²×Dic₇₁	1	2	yes	—
312	C₂²⋊C₄	—	2	2	no	—
313	C₂²⋊C₄	—	2	2	no	—
314	C₂²⋊C₄	—	2	2	no	—
315	C₄²	—	2	2	no	—
316	C₄²	—	2	2	no	—
317	C₄²	—	2	2	no	—
318	C₄²	—	142	2	no	—
319	C₄²	—	142	2	no	—
320	C₄²	C₂²×Dic₇₁	1	1	yes	characteristic
321	C₄²	C₂²×Dic₇₁	1	1	yes	characteristic
322	C₄²	D₄×D₇₁	1	1	yes	characteristic
323	C₄²	D₄×D₇₁	1	1	yes	characteristic
324	C₂³	—	2	2	no	—
325	C₂³	C₂×#11765864	1	1	yes	characteristic
326	Q₈	—	2	2	no	—
327	Q₈	—	2	2	no	—
328	D₄	—	2	2	no	—
329	D₄	—	2	2	no	—
330	D₄	—	4	2	no	—
331	D₄	—	4	2	no	—
332	C₂×C₄	—	2	2	no	—
333	C₂×C₄	—	2	2	no	—
334	C₂×C₄	—	2	2	no	—
335	C₂×C₄	—	2	2	no	—
336	C₂×C₄	—	4	1	no	—
337	C₂×C₄	—	4	4	no	—
338	C₂×C₄	—	4	2	no	—
339	C₂×C₄	—	4	2	no	—
340	C₂×C₄	—	8	2	no	—
341	C₂×C₄	—	284	2	no	—
342	C₂×C₄	—	284	2	no	—
343	C₂×C₄	—	142	4	no	—
344	C₂×C₄	D₄×Dic₇₁	1	1	yes	characteristic
345	C₂×C₄	D₄×Dic₇₁	1	1	yes	characteristic
346	C₂×C₄	D₄×Dic₇₁	1	1	yes	characteristic
347	C₂×C₄	D₄×Dic₇₁	1	1	yes	characteristic
348	C₂×C₄	C₂³×Dic₇₁	1	1	yes	characteristic
349	C₂×C₄	C₂×D₄×D₇₁	1	1	yes	characteristic
350	C₂×C₄	C₂×#11765865	1	1	yes	characteristic
351	C₂×C₄	C₂×#11765865	1	1	yes	characteristic
352	C₂×C₄	#14556174	1	1	yes	characteristic
353	C₂×C₄	#14556175	1	1	yes	characteristic
354	C₈	—	2	1	no	—
355	C₈	—	2	1	no	—
356	C₈	—	284	4	no	—
357	C₈	—	142	2	no	—
358	C₈	—	142	2	no	—
359	C₈	#14556087	1	2	yes	—
360	C₈	#14556087	1	2	yes	—
361	C₂²	—	2	1	no	—
362	C₂²	—	2	1	no	—
363	C₂²	—	4	2	no	—
364	C₂²	—	4	2	no	—
365	C₂²	—	4	2	no	—
366	C₂²	C₂×D₄×Dic₇₁	1	1	yes	characteristic
367	C₂²	#17986714	1	1	yes	characteristic
368	C₂²	#17986719	1	1	yes	characteristic
369	C₄	—	2	1	no	—
370	C₄	—	2	1	no	—
371	C₄	—	2	1	no	—
372	C₄	—	4	2	no	—
373	C₄	—	4	2	no	—
374	C₄	—	4	2	no	—
375	C₄	—	284	4	no	—
376	C₄	#17986116	1	2	yes	—
377	C₄	C₂×#14556087	1	1	yes	characteristic
378	C₄	#17986482	1	1	yes	characteristic
379	C₄	#17986654	1	1	yes	characteristic
380	C₄	#17986670	1	1	yes	characteristic
381	C₂	—	2	1	no	—
382	C₂	—	2	1	no	—
383	C₂	—	8	2	no	—
384	C₂	#22591289	1	1	yes	characteristic
385	C₂	C₂×#17986116	1	1	yes	characteristic
386	C₂	#22597257	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₇₁
commutator	C₂×C₄×C₇₁	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₇₁
Fitting	C₄×#135×C₇₁	C₂
socle	C₂²×C₇₁	C₂×C₄×D₄
prime radical	C₂×#135×C₇₁	C₂²
cosocle	C₂²×C₄×C₇₁	C₂⁴
hypercenter	C₄×#135	D₇₁
hypocenter	C₇₁	#22802
LCS	G ▷ C₂×C₄×C₇₁ ▷ C₂×C₇₁ ▷ C₇₁
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ C₄×#135

Complements

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

N	H ≅ G/N	type
1. #22597006	C₂	semidirect
3. #22588990	C₂	semidirect
4. #22588512	C₂	semidirect
5. #22588360	C₂	semidirect
6. #22588221	C₂	semidirect
7. C₈×C₄⋊Dic₇₁	C₂	semidirect
25. C₄×Q₁₆×C₇₁	C₄	semidirect
26. C₄×Q₁₆×C₇₁	C₄	semidirect
27. C₄×SD₁₆×C₇₁	C₄	semidirect
28. C₄×SD₁₆×C₇₁	C₄	semidirect
29. C₄×D₈×C₇₁	C₄	semidirect
30. C₄×D₈×C₇₁	C₄	semidirect
202. C₇₁	#22802	semidirect
205. C₄×Q₁₆	Dic₇₁	semidirect
206. C₄×Q₁₆	Dic₇₁	semidirect
207. C₄×SD₁₆	Dic₇₁	semidirect
208. C₄×SD₁₆	Dic₇₁	semidirect
209. C₄×D₈	Dic₇₁	semidirect
210. C₄×D₈	Dic₇₁	semidirect

Maximal subgroups

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

subgroup	index
#22597006	2
#22589229	2
#22588990	2
#22588512	2
#22588360	2
#22588221	2
C₈×C₄⋊Dic₇₁	2
C₄×#135×C₇₁	2
#22802	71