Subgroups — C₈×#13133182 #27382697

Order 13568.

1070 conjugacy classes of subgroups.

The subgroup lattice has 358 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₈×Dic₁₀₆	C₂	1	1	yes	maximal, characteristic
2	C₂×#16810747	C₂	1	1	yes	maximal, characteristic
3	C₄×#13133182	C₂	1	1	yes	maximal, characteristic
4	C₄⋊C₄×#88322	C₂	1	1	yes	maximal, characteristic
5	C₈×#11719919	C₂	1	2	yes	maximal
6	#20274576	C₂	1	2	yes	maximal
7	C₄⋊C₈×Dic₅₃	C₂	1	1	yes	maximal, characteristic
8	#20274563	C₂	1	2	yes	maximal
9	C₄×C₈×Dic₅₃	C₂	1	1	yes	maximal, characteristic
10	C₄×C₈×Dic₅₃	C₂	1	2	yes	maximal
11	C₈×C₄⋊C₄×C₅₃	C₂	1	1	yes	maximal, characteristic
12	C₂×C₄×Dic₁₀₆	C₂²	1	1	yes	characteristic
13	C₂×#13133182	C₄	1	2	yes	—
14	C₈×Dic₁₀₆	C₄	1	8	yes	complemented
15	#16810747	C₄	1	8	yes	complemented
16	C₂×C₄⋊#88322	C₂²	1	1	yes	characteristic
17	C₂×#13133146	C₂²	1	2	yes	—
18	C₂×#13133146	C₂²	1	2	yes	—
19	C₂×C₄×#88322	C₂²	1	2	yes	—
20	C₂×C₄×#88322	C₂²	1	1	yes	characteristic
21	C₂×C₈×Dic₅₃	C₂²	1	1	yes	characteristic
22	C₂×C₈×Dic₅₃	C₂²	1	2	yes	—
23	C₂×C₈×Dic₅₃	C₂²	1	1	yes	characteristic
24	C₂×C₈×Dic₅₃	C₂²	1	1	yes	characteristic
25	C₂×C₈×Dic₅₃	C₂²	1	2	yes	—
26	C₂×C₈×Dic₅₃	C₂²	1	2	yes	—
27	C₂×C₈×Dic₅₃	C₂²	1	1	yes	characteristic
28	C₄⋊C₄×Dic₅₃	C₄	1	2	yes	—
29	C₄×#11719919	C₂²	1	2	yes	—
30	#16810474	C₄	1	4	yes	—
31	C₄²×Dic₅₃	C₂²	1	2	yes	—
32	C₄²×Dic₅₃	C₂²	1	1	yes	characteristic
33	#16810378	C₂²	1	2	yes	—
34	#16810377	C₂²	1	2	yes	—
35	C₂×C₄⋊C₈×C₅₃	C₂²	1	1	yes	characteristic
36	C₂×C₄×C₈×C₅₃	C₂²	1	2	yes	—
37	C₂×C₄×C₈×C₅₃	C₂²	1	1	yes	characteristic
38	C₄×C₄⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
39	C₅₃×#336	C₂²	1	2	yes	—
40	C₂²×Dic₁₀₆	C₂×C₄	1	1	yes	characteristic
41	C₂²×#88322	C₂³	1	2	yes	—
42	C₂²×#88322	C₂³	1	1	yes	characteristic
43	C₂²×#88322	C₂³	1	1	yes	characteristic
44	C₄×Dic₁₀₆	C₂×C₄	1	4	yes	—
45	C₄×Dic₁₀₆	C₂×C₄	1	4	yes	—
46	#13133182	C₈	1	16	yes	direct product factor
47	C₂×C₄⋊Dic₅₃	C₂×C₄	1	1	yes	characteristic
48	C₂×#11719919	C₂×C₄	1	2	yes	—
49	C₂×#11719919	C₂×C₄	1	4	yes	—
50	C₂×C₄×Dic₅₃	C₂×C₄	1	2	yes	—
51	C₂×C₄×Dic₅₃	C₂×C₄	1	4	yes	—
52	C₂×C₄×Dic₅₃	C₂×C₄	1	4	yes	—
53	C₂×C₄×Dic₅₃	C₂×C₄	1	2	yes	—
54	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
55	C₂×C₄×Dic₅₃	C₂³	1	2	yes	—
56	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
57	C₄⋊#88322	C₂×C₄	1	4	yes	—
58	#13133146	C₂×C₄	1	8	yes	—
59	#13133146	C₂×C₄	1	8	yes	—
60	C₄×#88322	—	2	4	no	—
61	C₄×#88322	C₂×C₄	1	4	yes	—
62	C₈×Dic₅₃	—	2	2	no	—
63	C₈×Dic₅₃	—	2	2	no	—
64	C₈×Dic₅₃	—	2	4	no	—
65	C₈×Dic₅₃	—	2	2	no	—
66	C₈×Dic₅₃	C₂×C₄	1	8	yes	—
67	C₈×Dic₅₃	C₂×C₄	1	8	yes	—
68	C₈×Dic₅₃	Q₈	1	4	yes	complemented
69	#13133124	C₂×C₄	1	4	yes	—
70	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
71	C₂²×C₈×C₅₃	C₂³	1	2	yes	—
72	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
73	C₂×C₄⋊C₄×C₅₃	C₂×C₄	1	2	yes	—
74	C₂×C₄²×C₅₃	C₂³	1	2	yes	—
75	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
76	C₄⋊C₈×C₅₃	C₂×C₄	1	4	yes	—
77	C₄×C₈×C₅₃	—	2	4	no	—
78	C₄×C₈×C₅₃	C₂×C₄	1	4	yes	—
79	#95×C₅₃	C₂×C₄	1	2	yes	—
80	C₂²×C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
81	C₂²×C₄×C₅₃	C₂²×C₄	1	4	yes	—
82	C₂²×C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
83	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
84	C₂²×Dic₅₃	C₂²×C₄	1	2	yes	—
85	C₂²×Dic₅₃	C₂²×C₄	1	2	yes	—
86	C₂²×Dic₅₃	C₂²×C₄	1	2	yes	—
87	C₂²×Dic₅₃	C₂²×C₄	1	2	yes	—
88	C₂×Dic₁₀₆	C₄²	1	4	yes	—
89	C₂×Dic₁₀₆	C₂×C₈	1	8	yes	—
90	C₂×C₈×C₅₃	—	2	2	no	—
91	C₂×C₈×C₅₃	—	2	1	no	—
92	C₂×C₈×C₅₃	—	2	1	no	—
93	C₂×C₈×C₅₃	—	2	2	no	—
94	C₂×C₈×C₅₃	C₂²×C₄	1	2	yes	—
95	C₂×C₈×C₅₃	C₂²×C₄	1	4	yes	—
96	C₂×C₈×C₅₃	C₂²×C₄	1	2	yes	—
97	C₂×C₈×C₅₃	C₂×Q₈	1	2	yes	—
98	C₂×C₈×C₅₃	#41	1	2	yes	—
99	C₄⋊C₄×C₅₃	C₂×C₈	1	8	yes	—
100	C₄²×C₅₃	—	2	2	no	—
101	C₄²×C₅₃	—	2	2	no	—
102	C₄²×C₅₃	C₂²×C₄	1	2	yes	—
103	C₄²×C₅₃	C₂²×C₄	1	2	yes	—
104	C₄⋊Dic₅₃	C₄²	1	4	yes	—
105	#11719919	C₄²	1	8	yes	—
106	#11719919	C₂×C₈	1	16	yes	—
107	C₄×Dic₅₃	—	2	1	no	—
108	C₄×Dic₅₃	—	2	1	no	—
109	C₄×Dic₅₃	—	2	4	no	—
110	C₄×Dic₅₃	—	2	8	no	—
111	C₄×Dic₅₃	C₂×C₈	1	8	yes	—
112	C₄×Dic₅₃	C₂×C₈	1	16	yes	—
113	C₄×Dic₅₃	C₂²×C₄	1	4	yes	—
114	C₄×Dic₅₃	C₂²×C₄	1	4	yes	—
115	C₄×Dic₅₃	C₂×Q₈	1	2	yes	—
116	C₄×Dic₅₃	#41	1	2	yes	—
117	C₂×#88322	—	2	2	no	—
118	C₂×#88322	—	2	1	no	—
119	C₂×#88322	—	2	1	no	—
120	C₂×#88322	—	2	2	no	—
121	C₂×#88322	C₂²×C₄	1	4	yes	—
122	C₂×#88322	C₂²×C₄	1	2	yes	—
123	C₂×#88322	C₂²×C₄	1	2	yes	—
124	C₂×#88322	C₂×Q₈	1	2	yes	—
125	C₂×#88322	#41	1	2	yes	—
126	C₂³×C₅₃	C₂³×C₄	1	1	yes	characteristic
127	C₂×C₄×C₅₃	—	2	4	no	—
128	C₂×C₄×C₅₃	—	2	2	no	—
129	C₂×C₄×C₅₃	—	2	4	no	—
130	C₂×C₄×C₅₃	C₂×C₄²	1	2	yes	—
131	C₂×C₄×C₅₃	C₂×C₄²	1	2	yes	—
132	C₂×C₄×C₅₃	C₂²×C₈	1	8	yes	—
133	C₂×C₄×C₅₃	C₂²×C₈	1	4	yes	—
134	C₂×C₄×C₅₃	C₂³×C₄	1	1	yes	characteristic
135	C₂×C₄×C₅₃	C₂³×C₄	1	1	yes	characteristic
136	C₂×C₄×C₅₃	C₂²×Q₈	1	1	yes	characteristic
137	C₂×C₄×C₅₃	C₂×#41	1	1	yes	characteristic
138	C₂×C₄×C₅₃	C₂×#41	1	1	yes	characteristic
139	C₂×C₄×C₅₃	C₂×#41	1	1	yes	characteristic
140	C₂×Dic₅₃	—	2	2	no	—
141	C₂×Dic₅₃	—	2	4	no	—
142	C₂×Dic₅₃	—	2	2	no	—
143	C₂×Dic₅₃	C₂×C₄²	1	4	yes	—
144	C₂×Dic₅₃	C₂×C₄²	1	4	yes	—
145	C₂×Dic₅₃	C₄×Q₈	1	4	yes	—
146	C₂×Dic₅₃	C₂²×C₈	1	4	yes	—
147	C₂×Dic₅₃	C₂²×C₈	1	8	yes	—
148	C₂×Dic₅₃	C₂²×C₈	1	4	yes	—
149	C₂×Dic₅₃	#131	1	4	yes	—
150	Dic₁₀₆	C₄×C₈	1	16	yes	complemented
151	C₈×C₅₃	—	2	4	no	—
152	C₈×C₅₃	—	2	2	no	—
153	C₈×C₅₃	C₄×Q₈	1	4	yes	complemented
154	#88322	—	2	2	no	—
155	#88322	—	2	4	no	—
156	#88322	C₄×Q₈	1	4	yes	complemented
157	C₄×C₈×Q₈	—	53	1	no	maximal, Sylow
158	C₂²×C₅₃	C₂²×C₄²	1	1	yes	characteristic
159	C₂²×C₅₃	C₂×C₄×Q₈	1	1	yes	characteristic
160	C₂²×C₅₃	C₄×#41	1	1	yes	characteristic
161	C₂²×C₅₃	C₂³×C₈	1	2	yes	—
162	C₂²×C₅₃	C₂×#131	1	2	yes	—
163	C₄×C₅₃	—	2	2	no	—
164	C₄×C₅₃	—	2	8	no	—
165	C₄×C₅₃	C₂×C₄×C₈	1	4	yes	—
166	C₄×C₅₃	C₂×C₄×Q₈	1	1	yes	characteristic
167	C₄×C₅₃	C₂×C₄×Q₈	1	1	yes	characteristic
168	C₄×C₅₃	C₄×#41	1	1	yes	characteristic
169	C₄×C₅₃	C₄×#41	1	1	yes	characteristic
170	Dic₅₃	—	2	4	no	—
171	Dic₅₃	—	2	4	no	—
172	Dic₅₃	C₂×C₄×C₈	1	8	yes	—
173	Dic₅₃	C₈×Q₈	1	8	yes	complemented
174	C₂×C₈×Q₈	—	53	1	no	—
175	C₂×C₈×Q₈	—	53	1	no	—
176	C₄²×Q₈	—	53	1	no	—
177	C₈×C₄⋊C₄	—	53	2	no	—
178	C₈×C₄⋊C₄	—	53	1	no	—
179	C₈×C₄⋊C₄	—	53	2	no	—
180	C₈×C₄⋊C₄	D₅₃	1	1	yes	characteristic
181	C₄×C₄⋊C₈	—	53	1	no	—
182	C₄×C₄⋊C₈	—	53	2	no	—
183	C₄²×C₈	—	53	2	no	—
184	C₄²×C₈	—	53	1	no	—
185	C₂×C₅₃	C₄²×Q₈	1	1	yes	characteristic
186	C₂×C₅₃	C₂²×C₄×C₈	1	1	yes	characteristic
187	C₂×C₅₃	C₄×#131	1	1	yes	characteristic
188	C₂×C₅₃	C₂×C₈×Q₈	1	2	yes	—
189	C₂×C₅₃	C₈×#41	1	2	yes	—
190	C₂×C₄×Q₈	—	53	2	no	—
191	C₂×C₄×Q₈	—	53	1	no	—
192	C₈×Q₈	—	53	8	no	—
193	C₈×Q₈	—	53	8	no	—
194	C₂×C₄⋊C₈	—	53	2	no	—
195	C₂×C₄⋊C₈	—	53	2	no	—
196	C₂×C₄⋊C₈	—	53	1	no	—
197	C₂×C₄⋊C₈	C₂×D₅₃	1	1	yes	characteristic
198	C₂×C₄×C₈	—	53	2	no	—
199	C₂×C₄×C₈	—	53	2	no	—
200	C₂×C₄×C₈	—	53	1	no	—
201	C₂×C₄×C₈	—	53	1	no	—
202	C₂×C₄×C₈	—	53	2	no	—
203	C₂×C₄×C₈	—	53	1	no	—
204	C₂×C₄×C₈	—	53	1	no	—
205	C₂×C₄×C₈	—	53	1	no	—
206	C₂×C₄×C₈	—	53	2	no	—
207	C₂×C₄×C₈	C₂×D₅₃	1	2	yes	—
208	C₂×C₄×C₈	C₂×D₅₃	1	1	yes	characteristic
209	C₄×C₄⋊C₄	—	53	2	no	—
210	C₄×C₄⋊C₄	—	53	2	no	—
211	C₄×C₄⋊C₄	—	53	4	no	—
212	C₄×C₄⋊C₄	C₂×D₅₃	1	1	yes	characteristic
213	C₄³	—	53	2	no	—
214	C₄³	—	53	1	no	—
215	#336	—	53	2	no	—
216	#336	—	53	2	no	—
217	#336	C₂×D₅₃	1	2	yes	—
218	C₅₃	C₄×C₈×Q₈	1	1	yes	characteristic, complemented, Sylow
219	C₂²×Q₈	—	53	1	no	—
220	C₂²×C₈	—	53	1	no	—
221	C₂²×C₈	—	53	2	no	—
222	C₂²×C₈	—	53	1	no	—
223	C₂²×C₈	C₂²×D₅₃	1	2	yes	—
224	C₂²×C₈	C₂²×D₅₃	1	1	yes	characteristic
225	C₂²×C₈	C₂²×D₅₃	1	1	yes	characteristic
226	C₄×Q₈	—	53	16	no	—
227	C₄×Q₈	—	53	4	no	—
228	C₄×Q₈	—	53	4	no	—
229	C₂×C₄⋊C₄	—	53	2	no	—
230	C₂×C₄⋊C₄	—	53	4	no	—
231	C₂×C₄⋊C₄	—	53	1	no	—
232	C₂×C₄⋊C₄	C₄×D₅₃	1	2	yes	—
233	C₂×C₄²	—	53	4	no	—
234	C₂×C₄²	—	53	2	no	—
235	C₂×C₄²	—	53	2	no	—
236	C₂×C₄²	—	53	1	no	—
237	C₂×C₄²	—	53	2	no	—
238	C₂×C₄²	—	53	4	no	—
239	C₂×C₄²	—	53	1	no	—
240	C₂×C₄²	C₂²×D₅₃	1	2	yes	—
241	C₂×C₄²	C₂²×D₅₃	1	1	yes	characteristic
242	C₄⋊C₈	—	53	8	no	—
243	C₄⋊C₈	—	53	8	no	—
244	C₄⋊C₈	—	53	4	no	—
245	C₄⋊C₈	C₄×D₅₃	1	4	yes	—
246	C₄×C₈	—	2	4	no	—
247	C₄×C₈	—	53	8	no	—
248	C₄×C₈	—	53	8	no	—
249	C₄×C₈	—	53	4	no	—
250	C₄×C₈	—	53	4	no	—
251	C₄×C₈	—	106	4	no	—
252	C₄×C₈	—	106	4	no	—
253	C₄×C₈	—	106	2	no	—
254	C₄×C₈	—	106	2	no	—
255	C₄×C₈	—	106	2	no	—
256	C₄×C₈	C₄×D₅₃	1	4	yes	—
257	#95	—	53	4	no	—
258	#95	C₄×D₅₃	1	2	yes	—
259	C₂×Q₈	—	53	4	no	—
260	C₂×Q₈	—	53	8	no	—
261	C₂²×C₄	—	53	2	no	—
262	C₂²×C₄	—	53	2	no	—
263	C₂²×C₄	—	53	2	no	—
264	C₂²×C₄	—	53	2	no	—
265	C₂²×C₄	C₂×C₄×D₅₃	1	1	yes	characteristic
266	C₂²×C₄	C₂×C₄×D₅₃	1	4	yes	—
267	C₂²×C₄	C₂×C₄×D₅₃	1	1	yes	characteristic
268	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
269	C₂×C₈	—	2	2	no	—
270	C₂×C₈	—	2	1	no	—
271	C₂×C₈	—	2	1	no	—
272	C₂×C₈	—	2	2	no	—
273	C₂×C₈	—	53	2	no	—
274	C₂×C₈	—	53	2	no	—
275	C₂×C₈	—	53	2	no	—
276	C₂×C₈	—	53	2	no	—
277	C₂×C₈	—	53	4	no	—
278	C₂×C₈	—	106	1	no	—
279	C₂×C₈	—	106	2	no	—
280	C₂×C₈	—	106	2	no	—
281	C₂×C₈	—	106	1	no	—
282	C₂×C₈	C₂×C₄×D₅₃	1	4	yes	—
283	C₂×C₈	C₂×C₄×D₅₃	1	2	yes	—
284	C₂×C₈	C₂×C₄×D₅₃	1	2	yes	—
285	C₂×C₈	#11719947	1	2	yes	—
286	C₂×C₈	Q₈×D₅₃	1	2	yes	—
287	C₄⋊C₄	—	53	8	no	—
288	C₄⋊C₄	—	53	4	no	—
289	C₄⋊C₄	—	53	16	no	—
290	C₄⋊C₄	C₈×D₅₃	1	8	yes	—
291	C₄²	—	2	2	no	—
292	C₄²	—	2	2	no	—
293	C₄²	—	53	16	no	—
294	C₄²	—	53	8	no	—
295	C₄²	—	53	4	no	—
296	C₄²	—	53	4	no	—
297	C₄²	—	53	2	no	—
298	C₄²	—	53	2	no	—
299	C₄²	—	106	4	no	—
300	C₄²	—	106	8	no	—
301	C₄²	—	106	1	no	—
302	C₄²	—	106	1	no	—
303	C₄²	C₂×C₄×D₅₃	1	2	yes	—
304	C₄²	C₂×C₄×D₅₃	1	2	yes	—
305	C₂³	C₂²×C₄×D₅₃	1	1	yes	characteristic
306	Q₈	—	53	16	no	—
307	C₂×C₄	—	2	4	no	—
308	C₂×C₄	—	2	2	no	—
309	C₂×C₄	—	2	4	no	—
310	C₂×C₄	—	53	4	no	—
311	C₂×C₄	—	53	4	no	—
312	C₂×C₄	—	53	4	no	—
313	C₂×C₄	—	53	8	no	—
314	C₂×C₄	—	53	4	no	—
315	C₂×C₄	—	53	4	no	—
316	C₂×C₄	—	53	4	no	—
317	C₂×C₄	—	106	2	no	—
318	C₂×C₄	—	106	4	no	—
319	C₂×C₄	—	106	2	no	—
320	C₂×C₄	C₄²×D₅₃	1	2	yes	—
321	C₂×C₄	C₄²×D₅₃	1	2	yes	—
322	C₂×C₄	C₂×C₈×D₅₃	1	8	yes	—
323	C₂×C₄	C₂×C₈×D₅₃	1	4	yes	—
324	C₂×C₄	C₂²×C₄×D₅₃	1	1	yes	characteristic
325	C₂×C₄	C₂²×C₄×D₅₃	1	1	yes	characteristic
326	C₂×C₄	C₂×Q₈×D₅₃	1	1	yes	characteristic
327	C₂×C₄	#41×D₅₃	1	1	yes	characteristic
328	C₂×C₄	#41×D₅₃	1	1	yes	characteristic
329	C₂×C₄	C₂×#11719947	1	1	yes	characteristic
330	C₈	—	2	4	no	—
331	C₈	—	2	2	no	—
332	C₈	—	53	4	no	—
333	C₈	—	106	2	no	—
334	C₈	—	106	4	no	—
335	C₈	#13133182	1	4	yes	direct product factor
336	C₂²	C₂×C₄²×D₅₃	1	1	yes	characteristic
337	C₂²	C₄×Q₈×D₅₃	1	1	yes	characteristic
338	C₂²	C₄×#11719947	1	1	yes	characteristic
339	C₂²	C₂²×C₈×D₅₃	1	2	yes	—
340	C₂²	#131×D₅₃	1	2	yes	—
341	C₄	—	2	2	no	—
342	C₄	—	2	8	no	—
343	C₄	—	53	8	no	—
344	C₄	—	53	8	no	—
345	C₄	—	106	4	no	—
346	C₄	—	106	4	no	—
347	C₄	C₄×C₈×D₅₃	1	4	yes	—
348	C₄	C₄×Q₈×D₅₃	1	1	yes	characteristic
349	C₄	C₂×#13133182	1	1	yes	characteristic
350	C₄	C₄×#11719947	1	1	yes	characteristic
351	C₄	#16811091	1	1	yes	characteristic
352	C₂	C₄×#13133182	1	1	yes	characteristic
353	C₂	C₂×C₄×C₈×D₅₃	1	1	yes	characteristic
354	C₂	#20283137	1	1	yes	characteristic
355	C₂	C₈×Q₈×D₅₃	1	2	yes	—
356	C₂	C₈×#11719947	1	2	yes	—

	subgroup	G/H
center	C₂²×C₈	C₂²×D₅₃
commutator	C₂×C₅₃	C₂²×C₄×C₈
Frattini	C₂²×C₄	C₂³×D₅₃
Fitting	C₈×C₄⋊C₄×C₅₃	C₂
socle, prime radical	C₂³×C₅₃	C₂³×C₄
cosocle	C₂²×C₄×C₅₃	C₂⁴
hypercenter	C₈×C₄⋊C₄	D₅₃
hypocenter	C₅₃	C₄×C₈×Q₈
LCS	G ▷ C₂×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂²×C₈ ◁ C₈×C₄⋊C₄

Complements

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

N	H ≅ G/N	type
14. C₈×Dic₁₀₆	C₄	semidirect
15. #16810747	C₄	semidirect
46. #13133182	C₈	direct (N × H)
68. C₈×Dic₅₃	Q₈	semidirect
150. Dic₁₀₆	C₄×C₈	semidirect
153. C₈×C₅₃	C₄×Q₈	semidirect
156. #88322	C₄×Q₈	semidirect
173. Dic₅₃	C₈×Q₈	semidirect
218. C₅₃	C₄×C₈×Q₈	semidirect
335. C₈	#13133182	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₈×Dic₁₀₆	2
C₂×#16810747	2
C₄×#13133182	2
C₄⋊C₄×#88322	2
C₈×#11719919	2
#20274576	2
C₄⋊C₈×Dic₅₃	2
#20274563	2
C₄×C₈×Dic₅₃	2
C₈×C₄⋊C₄×C₅₃	2
C₄×C₈×Q₈	53

Subgroups — C8×#13133182 #27382697

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈×#13133182 #27382697