Subgroups — D₄×#14556068 #32150666

Order 18176.

734 conjugacy classes of subgroups.

The subgroup lattice has 356 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#14556068	C₂	1	2	yes	maximal, complemented
2	#22590172	C₂	1	2	yes	maximal, complemented
3	#22590166	C₂	1	4	yes	maximal, complemented
4	D₄×C₇₁⋊C₁₆	C₂	1	2	yes	maximal, complemented
5	#22590096	C₂	1	1	yes	maximal, characteristic, complemented
6	#22589951	C₂	1	2	yes	maximal, complemented
7	C₄×#14556068	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₈×D₄×C₇₁	C₂	1	1	yes	maximal, characteristic
9	C₂×#14556068	—	2	8	no	—
10	C₂×#14556068	C₂²	1	2	yes	—
11	C₂×#14556068	C₂²	1	1	yes	characteristic
12	C₂×#14556068	C₂²	1	1	yes	characteristic
13	C₂×#14556068	C₂²	1	4	yes	complemented
14	C₂²×C₇₁⋊C₁₆	C₂²	1	4	yes	complemented
15	C₄⋊(C₇₁⋊C₁₆)	C₂²	1	2	yes	complemented
16	C₄⋊(C₇₁⋊C₁₆)	C₂²	1	2	yes	complemented
17	C₂²⋊(C₇₁⋊C₁₆)	C₂²	1	4	yes	complemented
18	C₂²⋊(C₇₁⋊C₁₆)	C₂²	1	4	yes	complemented
19	#17985775	C₂²	1	2	yes	complemented
20	C₄×C₇₁⋊C₁₆	C₂²	1	2	yes	complemented
21	C₂³×C₈×C₇₁	C₂²	1	2	yes	—
22	C₂×C₄×D₄×C₇₁	C₄	1	1	yes	characteristic
23	C₈×D₄×C₇₁	C₄	1	2	yes	—
24	C₈×D₄×C₇₁	C₄	1	1	yes	characteristic
25	C₈×D₄×C₇₁	C₄	1	1	yes	characteristic
26	C₈×D₄×C₇₁	C₂²	1	1	yes	characteristic
27	C₈×D₄×C₇₁	C₂²	1	2	yes	—
28	C₈×D₄×C₇₁	C₂²	1	1	yes	characteristic
29	C₂×C₄⋊C₈×C₇₁	C₄	1	1	yes	characteristic
30	C₂×C₂²⋊C₈×C₇₁	C₄	1	2	yes	—
31	C₂×C₄×C₈×C₇₁	C₂²	1	1	yes	characteristic
32	#14556068	—	2	8	no	—
33	#14556068	—	2	4	no	—
34	#14556068	—	2	2	no	—
35	#14556068	D₄	1	4	yes	direct product factor
36	C₂×C₇₁⋊C₁₆	—	2	8	no	—
37	C₂×C₇₁⋊C₁₆	C₂³	1	4	yes	—
38	C₂×C₇₁⋊C₁₆	C₂³	1	2	yes	—
39	C₂×C₇₁⋊C₁₆	C₂³	1	2	yes	—
40	C₂²×D₄×C₇₁	C₈	1	1	yes	characteristic
41	C₂³×C₄×C₇₁	C₂×C₄	1	2	yes	—
42	C₂²×C₈×C₇₁	—	2	4	no	—
43	C₂²×C₈×C₇₁	—	2	4	no	—
44	C₂²×C₈×C₇₁	C₂×C₄	1	1	yes	characteristic
45	C₂²×C₈×C₇₁	C₂×C₄	1	2	yes	—
46	C₂²×C₈×C₇₁	C₂×C₄	1	2	yes	—
47	C₂²×C₈×C₇₁	C₂×C₄	1	2	yes	—
48	C₂²×C₈×C₇₁	C₂³	1	2	yes	—
49	C₂²×C₈×C₇₁	C₂³	1	2	yes	—
50	C₂²×C₈×C₇₁	C₂³	1	1	yes	characteristic
51	C₄×D₄×C₇₁	C₈	1	2	yes	—
52	C₄×D₄×C₇₁	C₈	1	1	yes	characteristic
53	C₄×D₄×C₇₁	C₈	1	1	yes	characteristic
54	C₄×D₄×C₇₁	C₂×C₄	1	2	yes	—
55	C₄×D₄×C₇₁	C₂×C₄	1	1	yes	characteristic
56	C₄×D₄×C₇₁	C₂×C₄	1	1	yes	characteristic
57	C₂×C₄⋊C₄×C₇₁	C₈	1	1	yes	characteristic
58	C₂×C₂²⋊C₄×C₇₁	C₈	1	2	yes	—
59	C₂×C₄²×C₇₁	C₂×C₄	1	1	yes	characteristic
60	C₄⋊C₈×C₇₁	C₂×C₄	1	1	yes	characteristic
61	C₄⋊C₈×C₇₁	C₂×C₄	1	2	yes	—
62	C₄⋊C₈×C₇₁	C₂×C₄	1	1	yes	characteristic
63	C₂²⋊C₈×C₇₁	C₂×C₄	1	2	yes	—
64	C₂²⋊C₈×C₇₁	C₂×C₄	1	2	yes	—
65	C₂²⋊C₈×C₇₁	C₂×C₄	1	2	yes	—
66	C₂²⋊C₈×C₇₁	C₂×C₄	1	2	yes	—
67	C₄×C₈×C₇₁	C₂×C₄	1	1	yes	characteristic
68	C₄×C₈×C₇₁	C₂×C₄	1	1	yes	characteristic
69	C₄×C₈×C₇₁	C₂³	1	1	yes	characteristic
70	C₄×C₈×C₇₁	C₂³	1	1	yes	characteristic
71	C₇₁⋊C₁₆	—	2	4	no	—
72	C₇₁⋊C₁₆	—	2	2	no	—
73	C₇₁⋊C₁₆	C₂×D₄	1	4	yes	complemented
74	C₂⁴×C₇₁	C₂×C₈	1	2	yes	—
75	C₂×D₄×C₇₁	—	2	4	no	—
76	C₂×D₄×C₇₁	C₂×C₈	1	2	yes	—
77	C₂×D₄×C₇₁	C₂×C₈	1	1	yes	characteristic
78	C₂×D₄×C₇₁	C₂×C₈	1	1	yes	characteristic
79	C₂²×C₄×C₇₁	—	2	4	no	—
80	C₂²×C₄×C₇₁	—	2	4	no	—
81	C₂²×C₄×C₇₁	C₂×C₈	1	1	yes	characteristic
82	C₂²×C₄×C₇₁	C₂×C₈	1	2	yes	—
83	C₂²×C₄×C₇₁	C₂×C₈	1	2	yes	—
84	C₂²×C₄×C₇₁	C₂×C₈	1	2	yes	—
85	C₂²×C₄×C₇₁	C₂×C₈	1	1	yes	characteristic
86	C₂²×C₄×C₇₁	C₂²×C₄	1	2	yes	—
87	C₂²×C₄×C₇₁	C₂²×C₄	1	2	yes	—
88	C₂²×C₄×C₇₁	C₂²×C₄	1	1	yes	characteristic
89	C₂×C₈×C₇₁	—	2	4	no	—
90	C₂×C₈×C₇₁	—	2	2	no	—
91	C₂×C₈×C₇₁	—	2	4	no	—
92	C₂×C₈×C₇₁	—	2	4	no	—
93	C₂×C₈×C₇₁	—	2	2	no	—
94	C₂×C₈×C₇₁	—	2	2	no	—
95	C₂×C₈×C₇₁	—	2	2	no	—
96	C₂×C₈×C₇₁	—	2	2	no	—
97	C₂×C₈×C₇₁	C₂²×C₄	1	1	yes	characteristic
98	C₂×C₈×C₇₁	C₂²×C₄	1	1	yes	characteristic
99	C₂×C₈×C₇₁	C₂²×C₄	1	2	yes	—
100	C₂×C₈×C₇₁	C₂²×C₄	1	2	yes	—
101	C₂×C₈×C₇₁	C₂²×C₄	1	1	yes	characteristic
102	C₂×C₈×C₇₁	C₂×D₄	1	2	yes	—
103	C₂×C₈×C₇₁	#41	1	2	yes	—
104	C₂×C₈×C₇₁	C₂⁴	1	1	yes	characteristic
105	C₄⋊C₄×C₇₁	C₂×C₈	1	2	yes	—
106	C₄⋊C₄×C₇₁	C₂×C₈	1	1	yes	characteristic
107	C₄⋊C₄×C₇₁	C₂×C₈	1	1	yes	characteristic
108	C₂²⋊C₄×C₇₁	C₂×C₈	1	2	yes	—
109	C₂²⋊C₄×C₇₁	C₂×C₈	1	2	yes	—
110	C₂²⋊C₄×C₇₁	C₂×C₈	1	2	yes	—
111	C₂²⋊C₄×C₇₁	C₂×C₈	1	2	yes	—
112	C₄²×C₇₁	C₂×C₈	1	1	yes	characteristic
113	C₄²×C₇₁	C₂×C₈	1	1	yes	characteristic
114	C₄²×C₇₁	C₂²×C₄	1	1	yes	characteristic
115	C₄²×C₇₁	C₂²×C₄	1	1	yes	characteristic
116	C₂³×C₇₁	—	2	4	no	—
117	C₂³×C₇₁	—	2	4	no	—
118	C₂³×C₇₁	—	4	2	no	—
119	C₂³×C₇₁	C₂²×C₈	1	2	yes	—
120	C₂³×C₇₁	C₂²×C₈	1	1	yes	characteristic
121	C₂³×C₇₁	C₂²×C₈	1	2	yes	—
122	D₄×C₇₁	—	2	4	no	—
123	D₄×C₇₁	—	2	2	no	—
124	D₄×C₇₁	M₃₂	1	4	yes	complemented
125	C₂×C₄×C₇₁	—	2	4	no	—
126	C₂×C₄×C₇₁	—	2	2	no	—
127	C₂×C₄×C₇₁	—	2	2	no	—
128	C₂×C₄×C₇₁	—	2	2	no	—
129	C₂×C₄×C₇₁	—	2	2	no	—
130	C₂×C₄×C₇₁	—	2	4	no	—
131	C₂×C₄×C₇₁	—	2	4	no	—
132	C₂×C₄×C₇₁	—	2	2	no	—
133	C₂×C₄×C₇₁	—	4	1	no	—
134	C₂×C₄×C₇₁	C₄×D₄	1	2	yes	—
135	C₂×C₄×C₇₁	C₂²×C₈	1	1	yes	characteristic
136	C₂×C₄×C₇₁	C₂²×C₈	1	1	yes	characteristic
137	C₂×C₄×C₇₁	C₂²×C₈	1	1	yes	characteristic
138	C₂×C₄×C₇₁	C₂²×C₈	1	2	yes	—
139	C₂×C₄×C₇₁	C₂²×C₈	1	2	yes	—
140	C₂×C₄×C₇₁	C₂²×C₈	1	1	yes	characteristic
141	C₂×C₄×C₇₁	C₂²×C₈	1	1	yes	characteristic
142	C₂×C₄×C₇₁	#131	1	2	yes	—
143	C₂×C₄×C₇₁	C₂³×C₄	1	1	yes	characteristic
144	C₈×C₇₁	—	2	2	no	—
145	C₈×C₇₁	—	2	2	no	—
146	C₈×C₇₁	—	2	1	no	—
147	C₈×C₇₁	—	2	1	no	—
148	C₈×C₇₁	C₄×D₄	1	2	yes	—
149	C₈×C₇₁	C₂²×D₄	1	1	yes	characteristic
150	C₈×C₇₁	C₂×#41	1	1	yes	characteristic
151	C₂²×C₇₁	—	2	1	no	—
152	C₂²×C₇₁	—	2	1	no	—
153	C₂²×C₇₁	—	2	2	no	—
154	C₂²×C₇₁	—	2	2	no	—
155	C₂²×C₇₁	—	2	2	no	—
156	C₂²×C₇₁	—	2	2	no	—
157	C₂²×C₇₁	—	2	2	no	—
158	C₂²×C₇₁	—	4	8	no	—
159	C₂²×C₇₁	C₈×D₄	1	2	yes	—
160	C₂²×C₇₁	C₂×M₃₂	1	4	yes	complemented
161	C₂²×C₇₁	C₂³×C₈	1	1	yes	characteristic
162	C₄×C₇₁	—	2	1	no	—
163	C₄×C₇₁	—	2	1	no	—
164	C₄×C₇₁	—	2	1	no	—
165	C₄×C₇₁	—	2	2	no	—
166	C₄×C₇₁	—	2	2	no	—
167	C₄×C₇₁	C₈×D₄	1	2	yes	—
168	C₄×C₇₁	C₂×M₃₂	1	2	yes	complemented
169	C₄×C₇₁	C₂×C₄×D₄	1	1	yes	characteristic
170	C₄×C₇₁	C₂×#131	1	1	yes	characteristic
171	D₄×M₃₂	—	71	1	no	maximal, Sylow
172	C₂×C₇₁	—	2	2	no	—
173	C₂×C₇₁	—	2	4	no	—
174	C₂×C₇₁	—	4	2	no	—
175	C₂×C₇₁	C₂×C₈×D₄	1	1	yes	characteristic
176	C₂×C₇₁	C₂²×M₃₂	1	1	yes	characteristic
177	C₂×C₇₁	#3407	1	1	yes	characteristic
178	C₂²×M₃₂	—	71	2	no	—
179	C₂×C₈×D₄	D₇₁	1	1	yes	characteristic
180	#2169	—	71	2	no	—
181	#2168	—	71	4	no	—
182	D₄×C₁₆	—	71	2	no	—
183	#2150	—	71	1	no	—
184	#2112	—	71	2	no	—
185	C₄×M₃₂	—	71	1	no	—
186	C₇₁	D₄×M₃₂	1	1	yes	characteristic, complemented, Sylow
187	C₂³×C₈	C₂×D₇₁	1	2	yes	—
188	C₂×C₄×D₄	Dic₇₁	1	1	yes	characteristic
189	C₂×M₃₂	—	71	1	no	—
190	C₂×M₃₂	—	71	1	no	—
191	C₂×M₃₂	—	71	2	no	—
192	C₂×M₃₂	—	71	4	no	—
193	C₂×M₃₂	—	142	8	no	—
194	C₂²×C₁₆	—	71	4	no	—
195	C₈×D₄	Dic₇₁	1	2	yes	—
196	C₈×D₄	Dic₇₁	1	1	yes	characteristic
197	C₈×D₄	Dic₇₁	1	1	yes	characteristic
198	C₈×D₄	C₂×D₇₁	1	1	yes	characteristic
199	C₈×D₄	C₂×D₇₁	1	2	yes	—
200	C₈×D₄	C₂×D₇₁	1	1	yes	characteristic
201	C₂×C₄⋊C₈	Dic₇₁	1	1	yes	characteristic
202	C₂×C₂²⋊C₈	Dic₇₁	1	2	yes	—
203	C₂×C₄×C₈	C₂×D₇₁	1	1	yes	characteristic
204	C₄⋊C₁₆	—	71	2	no	—
205	C₄⋊C₁₆	—	71	2	no	—
206	C₂²⋊C₁₆	—	71	4	no	—
207	C₂²⋊C₁₆	—	71	4	no	—
208	#346	—	71	2	no	—
209	C₄×C₁₆	—	71	2	no	—
210	C₂²×D₄	C₇₁⋊C₈	1	1	yes	characteristic
211	C₂³×C₄	C₂×Dic₇₁	1	2	yes	—
212	C₂²×C₈	—	2	4	no	—
213	C₂²×C₈	—	2	4	no	—
214	C₂²×C₈	C₂×Dic₇₁	1	2	yes	—
215	C₂²×C₈	C₂×Dic₇₁	1	2	yes	—
216	C₂²×C₈	C₂×Dic₇₁	1	2	yes	—
217	C₂²×C₈	C₂×Dic₇₁	1	1	yes	characteristic
218	C₂²×C₈	C₂²×D₇₁	1	2	yes	—
219	C₂²×C₈	C₂²×D₇₁	1	2	yes	—
220	C₂²×C₈	C₂²×D₇₁	1	1	yes	characteristic
221	C₄×D₄	C₇₁⋊C₈	1	2	yes	—
222	C₄×D₄	C₇₁⋊C₈	1	1	yes	characteristic
223	C₄×D₄	C₇₁⋊C₈	1	1	yes	characteristic
224	C₄×D₄	C₂×Dic₇₁	1	2	yes	—
225	C₄×D₄	C₂×Dic₇₁	1	1	yes	characteristic
226	C₄×D₄	C₂×Dic₇₁	1	1	yes	characteristic
227	C₂×C₄⋊C₄	C₇₁⋊C₈	1	1	yes	characteristic
228	C₂×C₂²⋊C₄	C₇₁⋊C₈	1	2	yes	—
229	C₂×C₄²	C₂×Dic₇₁	1	1	yes	characteristic
230	M₃₂	—	71	4	no	—
231	M₃₂	—	142	8	no	—
232	M₃₂	—	142	4	no	—
233	M₃₂	—	142	2	no	—
234	C₂×C₁₆	—	71	2	no	—
235	C₂×C₁₆	—	71	2	no	—
236	C₂×C₁₆	—	71	4	no	—
237	C₂×C₁₆	—	142	8	no	—
238	C₄⋊C₈	C₂×Dic₇₁	1	1	yes	characteristic
239	C₄⋊C₈	C₂×Dic₇₁	1	2	yes	—
240	C₄⋊C₈	C₂×Dic₇₁	1	1	yes	characteristic
241	C₂²⋊C₈	C₂×Dic₇₁	1	2	yes	—
242	C₂²⋊C₈	C₂×Dic₇₁	1	2	yes	—
243	C₂²⋊C₈	C₂×Dic₇₁	1	2	yes	—
244	C₂²⋊C₈	C₂×Dic₇₁	1	2	yes	—
245	C₄×C₈	C₂×Dic₇₁	1	1	yes	characteristic
246	C₄×C₈	C₂×Dic₇₁	1	1	yes	characteristic
247	C₄×C₈	C₂²×D₇₁	1	1	yes	characteristic
248	C₄×C₈	C₂²×D₇₁	1	1	yes	characteristic
249	C₂⁴	C₂×C₇₁⋊C₈	1	2	yes	—
250	C₂×D₄	—	2	4	no	—
251	C₂×D₄	C₂×C₇₁⋊C₈	1	2	yes	—
252	C₂×D₄	C₂×C₇₁⋊C₈	1	1	yes	characteristic
253	C₂×D₄	C₂×C₇₁⋊C₈	1	1	yes	characteristic
254	C₂²×C₄	—	2	4	no	—
255	C₂²×C₄	—	2	4	no	—
256	C₂²×C₄	C₂×C₇₁⋊C₈	1	1	yes	characteristic
257	C₂²×C₄	C₂×C₇₁⋊C₈	1	2	yes	—
258	C₂²×C₄	C₂×C₇₁⋊C₈	1	2	yes	—
259	C₂²×C₄	C₂×C₇₁⋊C₈	1	2	yes	—
260	C₂²×C₄	C₂×C₇₁⋊C₈	1	1	yes	characteristic
261	C₂²×C₄	C₂²×Dic₇₁	1	2	yes	—
262	C₂²×C₄	C₂²×Dic₇₁	1	2	yes	—
263	C₂²×C₄	C₂²×Dic₇₁	1	1	yes	characteristic
264	C₂×C₈	—	2	4	no	—
265	C₂×C₈	—	2	2	no	—
266	C₂×C₈	—	2	2	no	—
267	C₂×C₈	—	2	2	no	—
268	C₂×C₈	—	2	2	no	—
269	C₂×C₈	—	2	2	no	—
270	C₂×C₈	—	2	4	no	—
271	C₂×C₈	—	2	4	no	—
272	C₂×C₈	C₂²×Dic₇₁	1	1	yes	characteristic
273	C₂×C₈	C₂²×Dic₇₁	1	1	yes	characteristic
274	C₂×C₈	C₂²×Dic₇₁	1	2	yes	—
275	C₂×C₈	C₂²×Dic₇₁	1	2	yes	—
276	C₂×C₈	C₂²×Dic₇₁	1	1	yes	characteristic
277	C₂×C₈	D₄×D₇₁	1	2	yes	—
278	C₂×C₈	#11765864	1	2	yes	—
279	C₂×C₈	C₂³×D₇₁	1	1	yes	characteristic
280	C₄⋊C₄	C₂×C₇₁⋊C₈	1	2	yes	—
281	C₄⋊C₄	C₂×C₇₁⋊C₈	1	1	yes	characteristic
282	C₄⋊C₄	C₂×C₇₁⋊C₈	1	1	yes	characteristic
283	C₂²⋊C₄	C₂×C₇₁⋊C₈	1	2	yes	—
284	C₂²⋊C₄	C₂×C₇₁⋊C₈	1	2	yes	—
285	C₂²⋊C₄	C₂×C₇₁⋊C₈	1	2	yes	—
286	C₂²⋊C₄	C₂×C₇₁⋊C₈	1	2	yes	—
287	C₄²	C₂×C₇₁⋊C₈	1	1	yes	characteristic
288	C₄²	C₂×C₇₁⋊C₈	1	1	yes	characteristic
289	C₄²	C₂²×Dic₇₁	1	1	yes	characteristic
290	C₄²	C₂²×Dic₇₁	1	1	yes	characteristic
291	C₁₆	—	71	4	no	—
292	C₁₆	—	142	4	no	—
293	C₁₆	—	142	2	no	—
294	C₂³	—	2	4	no	—
295	C₂³	—	2	4	no	—
296	C₂³	—	4	2	no	—
297	C₂³	C₂²×C₇₁⋊C₈	1	2	yes	—
298	C₂³	C₂²×C₇₁⋊C₈	1	1	yes	characteristic
299	C₂³	C₂²×C₇₁⋊C₈	1	2	yes	—
300	D₄	—	2	4	no	—
301	D₄	—	2	2	no	—
302	D₄	#14556068	1	4	yes	direct product factor
303	C₂×C₄	—	2	4	no	—
304	C₂×C₄	—	2	4	no	—
305	C₂×C₄	—	2	4	no	—
306	C₂×C₄	—	2	2	no	—
307	C₂×C₄	—	2	2	no	—
308	C₂×C₄	—	2	2	no	—
309	C₂×C₄	—	2	2	no	—
310	C₂×C₄	—	2	2	no	—
311	C₂×C₄	—	4	1	no	—
312	C₂×C₄	D₄×Dic₇₁	1	2	yes	—
313	C₂×C₄	C₂²×C₇₁⋊C₈	1	1	yes	characteristic
314	C₂×C₄	C₂²×C₇₁⋊C₈	1	1	yes	characteristic
315	C₂×C₄	C₂²×C₇₁⋊C₈	1	1	yes	characteristic
316	C₂×C₄	C₂²×C₇₁⋊C₈	1	2	yes	—
317	C₂×C₄	C₂²×C₇₁⋊C₈	1	2	yes	—
318	C₂×C₄	C₂²×C₇₁⋊C₈	1	1	yes	characteristic
319	C₂×C₄	C₂²×C₇₁⋊C₈	1	1	yes	characteristic
320	C₂×C₄	#14556135	1	2	yes	—
321	C₂×C₄	C₂³×Dic₇₁	1	1	yes	characteristic
322	C₈	—	2	2	no	—
323	C₈	—	2	2	no	—
324	C₈	—	2	1	no	—
325	C₈	—	2	1	no	—
326	C₈	D₄×Dic₇₁	1	2	yes	—
327	C₈	C₂×D₄×D₇₁	1	1	yes	characteristic
328	C₈	C₂×#11765864	1	1	yes	characteristic
329	C₂²	—	2	2	no	—
330	C₂²	—	2	1	no	—
331	C₂²	—	2	1	no	—
332	C₂²	—	2	2	no	—
333	C₂²	—	2	2	no	—
334	C₂²	—	2	2	no	—
335	C₂²	—	2	2	no	—
336	C₂²	—	4	8	no	—
337	C₂²	D₄×C₇₁⋊C₈	1	2	yes	—
338	C₂²	C₂×#14556068	1	4	yes	complemented
339	C₂²	C₂³×C₇₁⋊C₈	1	1	yes	characteristic
340	C₄	—	2	2	no	—
341	C₄	—	2	2	no	—
342	C₄	—	2	1	no	—
343	C₄	—	2	1	no	—
344	C₄	—	2	1	no	—
345	C₄	D₄×C₇₁⋊C₈	1	2	yes	—
346	C₄	C₂×#14556068	1	2	yes	complemented
347	C₄	C₂×D₄×Dic₇₁	1	1	yes	characteristic
348	C₄	C₂×#14556135	1	1	yes	characteristic
349	C₂	—	2	2	no	—
350	C₂	—	2	4	no	—
351	C₂	—	4	2	no	—
352	C₂	C₂×D₄×C₇₁⋊C₈	1	1	yes	characteristic
353	C₂	C₂²×#14556068	1	1	yes	characteristic
354	C₂	#22601443	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₈	C₂³×D₇₁
commutator, socle	C₂²×C₇₁	C₂³×C₈
Fitting	C₂×C₈×D₄×C₇₁	C₂
prime radical	C₂²×D₄×C₇₁	C₈
cosocle	C₂×C₈×C₇₁	C₂⁴
hypercenter	C₂×C₈×D₄	D₇₁
hypocenter	C₇₁	D₄×M₃₂
LCS	G ▷ C₂²×C₇₁ ▷ C₇₁
UCS	C₁ ◁ C₂×C₈ ◁ C₂×C₈×D₄

Complements

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

N	H ≅ G/N	type
1. C₂²×#14556068	C₂	semidirect
2. #22590172	C₂	semidirect
3. #22590166	C₂	semidirect
4. D₄×C₇₁⋊C₁₆	C₂	semidirect
5. #22590096	C₂	semidirect
6. #22589951	C₂	semidirect
7. C₄×#14556068	C₂	semidirect
13. C₂×#14556068	C₂²	semidirect
14. C₂²×C₇₁⋊C₁₆	C₂²	semidirect
15. C₄⋊(C₇₁⋊C₁₆)	C₂²	semidirect
16. C₄⋊(C₇₁⋊C₁₆)	C₂²	semidirect
17. C₂²⋊(C₇₁⋊C₁₆)	C₂²	semidirect
18. C₂²⋊(C₇₁⋊C₁₆)	C₂²	semidirect
19. #17985775	C₂²	semidirect
20. C₄×C₇₁⋊C₁₆	C₂²	semidirect
35. #14556068	D₄	direct (N × H)
73. C₇₁⋊C₁₆	C₂×D₄	semidirect
124. D₄×C₇₁	M₃₂	semidirect
160. C₂²×C₇₁	C₂×M₃₂	semidirect
168. C₄×C₇₁	C₂×M₃₂	semidirect
186. C₇₁	D₄×M₃₂	semidirect
302. D₄	#14556068	direct (N × H)
338. C₂²	C₂×#14556068	semidirect
346. C₄	C₂×#14556068	semidirect

Maximal subgroups

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

subgroup	index
C₂²×#14556068	2
#22590172	2
#22590166	2
D₄×C₇₁⋊C₁₆	2
#22590096	2
#22589951	2
C₄×#14556068	2
C₂×C₈×D₄×C₇₁	2
D₄×M₃₂	71

Subgroups — D4×#14556068 #32150666

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₄×#14556068 #32150666