Subgroups — C₂×#20242734 #26198596

Order 12032.

786 conjugacy classes of subgroups.

The subgroup lattice has 402 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#15689495	C₂	1	1	yes	maximal, characteristic
2	C₂×#15689408	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×Q₈×C₄₇⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
4	#20242734	C₂	1	8	yes	maximal, direct product factor
5	C₂×#15688873	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#15688868	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#15688867	C₂	1	1	yes	maximal, characteristic
8	C₂×C₄₇×#460	C₂	1	1	yes	maximal, characteristic
9	C₂²×#10625335	—	2	1	no	—
10	C₂²×#10625335	—	2	1	no	—
11	C₂×#13094024	C₂²	1	1	yes	characteristic
12	#15689495	—	2	2	no	—
13	#15689495	C₂²	1	4	yes	—
14	#15689408	—	2	2	no	—
15	#15689408	C₂²	1	4	yes	complemented
16	Q₈×C₄₇⋊C₈	—	2	2	no	—
17	Q₈×C₄₇⋊C₈	C₂²	1	4	yes	complemented
18	C₂×#13093955	—	2	1	no	—
19	C₂×C₄⋊(C₄₇⋊C₈)	—	2	1	no	—
20	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
21	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
22	C₂×#13093948	—	2	1	no	—
23	C₂×C₄×C₄₇⋊C₈	—	2	1	no	—
24	C₂×C₄×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
25	#15688873	C₂²	1	4	yes	complemented
26	#15688868	C₂²	1	4	yes	complemented
27	#15688867	C₂²	1	4	yes	—
28	C₂²×SD₁₆×C₄₇	—	2	1	no	—
29	C₂×#127×C₄₇	C₂²	1	1	yes	characteristic
30	C₂×C₄×Q₈×C₄₇	C₂²	1	1	yes	characteristic
31	C₄₇×#460	—	2	2	no	—
32	C₄₇×#460	C₂²	1	4	yes	—
33	C₂×C₄⋊C₈×C₄₇	C₂²	1	1	yes	characteristic
34	C₂×#102×C₄₇	—	2	1	no	—
35	C₂²×Dic₉₄	—	2	1	no	—
36	C₂×#10625335	—	2	4	no	—
37	C₂×#10625335	—	2	4	no	—
38	C₂×#10625335	—	4	4	no	—
39	C₂×#10625335	—	4	4	no	—
40	C₂²×C₄₇⋊C₈	—	2	1	no	—
41	C₂²×C₄₇⋊C₈	—	2	1	no	—
42	C₂²×C₄₇⋊C₈	D₄	1	1	yes	characteristic
43	C₂²×C₄₇⋊C₈	D₄	1	1	yes	characteristic
44	#13094024	—	2	1	no	—
45	#13094024	—	2	1	no	—
46	#13094024	—	2	1	no	—
47	#13094024	C₂³	1	2	yes	—
48	C₂×C₄⋊Dic₄₇	—	2	1	no	—
49	C₂×C₄⋊Dic₄₇	—	2	1	no	—
50	#13093955	—	2	4	no	—
51	C₄⋊(C₄₇⋊C₈)	—	2	1	no	—
52	C₄⋊(C₄₇⋊C₈)	—	2	1	no	—
53	C₄⋊(C₄₇⋊C₈)	—	2	4	no	—
54	C₄⋊(C₄₇⋊C₈)	C₂³	1	2	yes	—
55	C₄⋊(C₄₇⋊C₈)	C₂³	1	2	yes	—
56	#13093948	—	2	4	no	—
57	C₄×C₄₇⋊C₈	—	2	4	no	—
58	C₄×C₄₇⋊C₈	D₄	1	2	yes	—
59	C₄×C₄₇⋊C₈	C₂³	1	2	yes	—
60	C₂²×Q₈×C₄₇	D₄	1	1	yes	characteristic
61	C₂²×D₄×C₄₇	—	2	1	no	—
62	C₂²×D₄×C₄₇	—	2	1	no	—
63	C₂²×D₄×C₄₇	—	2	1	no	—
64	C₂×SD₁₆×C₄₇	—	2	4	no	—
65	C₂×SD₁₆×C₄₇	—	4	4	no	—
66	C₂²×C₈×C₄₇	—	2	1	no	—
67	#127×C₄₇	—	2	1	no	—
68	#127×C₄₇	—	2	1	no	—
69	#127×C₄₇	—	2	1	no	—
70	#127×C₄₇	C₂³	1	2	yes	—
71	C₄×Q₈×C₄₇	—	2	1	no	—
72	C₄×Q₈×C₄₇	—	2	1	no	—
73	C₄×Q₈×C₄₇	D₄	1	2	yes	—
74	C₄×Q₈×C₄₇	C₂³	1	2	yes	—
75	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
76	C₂×C₄⋊C₄×C₄₇	D₄	1	1	yes	characteristic
77	C₂×C₄²×C₄₇	—	2	1	no	—
78	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
79	C₄⋊C₈×C₄₇	—	2	1	no	—
80	C₄⋊C₈×C₄₇	C₂³	1	2	yes	—
81	#102×C₄₇	—	2	4	no	—
82	C₂⁴×C₄₇	—	4	1	no	—
83	C₂×Q₈×C₄₇	—	2	1	no	—
84	C₂×Q₈×C₄₇	—	2	2	no	—
85	C₂×Q₈×C₄₇	SD₁₆	1	4	yes	complemented
86	C₂×Q₈×C₄₇	C₂×D₄	1	2	yes	—
87	C₂×D₄×C₄₇	—	2	2	no	—
88	C₂×D₄×C₄₇	—	2	2	no	—
89	C₂×D₄×C₄₇	—	2	2	no	—
90	C₂×D₄×C₄₇	—	4	1	no	—
91	C₂×D₄×C₄₇	—	4	1	no	—
92	C₂×D₄×C₄₇	—	4	1	no	—
93	C₂×D₄×C₄₇	—	4	2	no	—
94	C₂×D₄×C₄₇	—	4	2	no	—
95	C₂×D₄×C₄₇	—	4	2	no	—
96	C₂×D₄×C₄₇	—	4	2	no	—
97	C₂×D₄×C₄₇	—	8	2	no	—
98	C₂²×C₄×C₄₇	—	2	1	no	—
99	C₂²×C₄×C₄₇	—	2	1	no	—
100	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
101	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
102	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
103	C₂²×Dic₄₇	—	4	1	no	—
104	C₂×Dic₉₄	—	2	2	no	—
105	C₂×Dic₉₄	—	4	2	no	—
106	C₂×Dic₉₄	—	4	2	no	—
107	C₂×Dic₉₄	—	4	1	no	—
108	SD₁₆×C₄₇	—	4	8	no	—
109	C₂×C₈×C₄₇	—	2	2	no	—
110	C₂×C₈×C₄₇	—	4	2	no	—
111	C₄⋊C₄×C₄₇	—	2	2	no	—
112	C₄⋊C₄×C₄₇	—	2	1	no	—
113	C₄⋊C₄×C₄₇	—	2	2	no	—
114	C₄⋊C₄×C₄₇	C₂×D₄	1	2	yes	—
115	C₄²×C₄₇	—	2	2	no	—
116	C₄²×C₄₇	—	2	2	no	—
117	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
118	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
119	C₄²×C₄₇	#41	1	1	yes	characteristic
120	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
121	#10625335	—	4	8	no	—
122	#10625335	—	4	8	no	—
123	C₄⋊Dic₄₇	—	2	2	no	—
124	C₄⋊Dic₄₇	—	2	2	no	—
125	C₄⋊Dic₄₇	—	4	1	no	—
126	C₄⋊Dic₄₇	—	4	1	no	—
127	C₂×C₄₇⋊C₈	—	2	2	no	—
128	C₂×C₄₇⋊C₈	—	2	2	no	—
129	C₂×C₄₇⋊C₈	—	2	2	no	—
130	C₂×C₄₇⋊C₈	—	4	2	no	—
131	C₂×C₄₇⋊C₈	—	4	2	no	—
132	C₂×C₄₇⋊C₈	SD₁₆	1	4	yes	complemented
133	C₂×C₄₇⋊C₈	C₂×D₄	1	2	yes	—
134	C₂×C₄₇⋊C₈	C₂×D₄	1	2	yes	—
135	C₂³×C₄₇	—	4	2	no	—
136	C₂³×C₄₇	—	8	2	no	—
137	C₂³×C₄₇	—	8	2	no	—
138	C₂³×C₄₇	—	8	2	no	—
139	C₂³×C₄₇	#121	1	1	yes	characteristic
140	Q₈×C₄₇	—	2	2	no	—
141	Q₈×C₄₇	—	2	4	no	—
142	Q₈×C₄₇	C₂×SD₁₆	1	4	yes	complemented
143	D₄×C₄₇	—	4	2	no	—
144	D₄×C₄₇	—	4	2	no	—
145	D₄×C₄₇	—	4	2	no	—
146	D₄×C₄₇	—	4	2	no	—
147	D₄×C₄₇	—	8	2	no	—
148	D₄×C₄₇	—	8	2	no	—
149	D₄×C₄₇	—	8	2	no	—
150	D₄×C₄₇	—	8	2	no	—
151	C₂×C₄×C₄₇	—	2	2	no	—
152	C₂×C₄×C₄₇	—	2	4	no	—
153	C₂×C₄×C₄₇	—	2	2	no	—
154	C₂×C₄×C₄₇	—	2	2	no	—
155	C₂×C₄×C₄₇	—	4	2	no	—
156	C₂×C₄×C₄₇	#121	1	1	yes	characteristic
157	C₂×C₄×C₄₇	#121	1	1	yes	characteristic
158	C₂×C₄×C₄₇	#121	1	1	yes	characteristic
159	C₂×C₄×C₄₇	C₂×SD₁₆	1	2	yes	—
160	C₂×C₄×C₄₇	C₂×SD₁₆	1	2	yes	—
161	C₂×C₄×C₄₇	#135	1	2	yes	—
162	C₂×C₄×C₄₇	AGL(1,ℤ/8)	1	2	yes	—
163	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
164	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
165	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
166	C₂×Dic₄₇	—	4	2	no	—
167	C₂×Dic₄₇	—	8	2	no	—
168	Dic₉₄	—	4	2	no	—
169	Dic₉₄	—	4	2	no	—
170	Dic₉₄	—	8	2	no	—
171	C₈×C₄₇	—	4	2	no	—
172	C₄₇⋊C₈	—	2	2	no	—
173	C₄₇⋊C₈	—	4	2	no	—
174	C₄₇⋊C₈	—	4	2	no	—
175	C₄₇⋊C₈	C₂×SD₁₆	1	4	yes	complemented
176	C₂×#1666	—	47	1	no	maximal, Sylow
177	C₂²×C₄₇	—	8	2	no	—
178	C₂²×C₄₇	—	8	2	no	—
179	C₂²×C₄₇	—	8	2	no	—
180	C₂²×C₄₇	—	16	4	no	—
181	C₂²×C₄₇	#460	1	2	yes	—
182	C₂²×C₄₇	#465	1	2	yes	—
183	C₂²×C₄₇	#471	1	2	yes	—
184	C₂²×C₄₇	C₂×#121	1	1	yes	characteristic
185	C₄×C₄₇	—	2	4	no	—
186	C₄×C₄₇	—	2	1	no	—
187	C₄×C₄₇	—	2	1	no	—
188	C₄×C₄₇	—	4	2	no	—
189	C₄×C₄₇	#460	1	2	yes	—
190	C₄×C₄₇	#465	1	2	yes	—
191	C₄×C₄₇	C₂²×SD₁₆	1	1	yes	characteristic
192	C₄×C₄₇	C₂²×SD₁₆	1	1	yes	characteristic
193	C₄×C₄₇	C₂×#135	1	1	yes	characteristic
194	C₄×C₄₇	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
195	Dic₄₇	—	8	2	no	—
196	C₂×#492	—	47	1	no	—
197	C₂×#475	—	47	1	no	—
198	C₂×#460	D₄₇	1	1	yes	characteristic
199	C₂×C₈×Q₈	—	47	1	no	—
200	#1666	—	47	8	no	—
201	C₂×#334	—	47	1	no	—
202	C₂×#332	—	47	1	no	—
203	C₂×#331	—	47	1	no	—
204	C₂×C₄₇	—	16	2	no	—
205	C₂×C₄₇	#1666	1	4	yes	complemented
206	C₂×C₄₇	C₂×#460	1	1	yes	characteristic
207	C₂×C₄₇	C₂×#465	1	1	yes	characteristic
208	C₂×C₄₇	C₂×#471	1	1	yes	characteristic
209	C₂²×SD₁₆	—	2	1	no	—
210	C₂²×SD₁₆	—	94	1	no	—
211	C₂²×SD₁₆	—	94	1	no	—
212	C₂×C₄⋊Q₈	—	47	1	no	—
213	C₂×#127	C₂×D₄₇	1	1	yes	characteristic
214	C₂×C₄×Q₈	C₂×D₄₇	1	1	yes	characteristic
215	#492	—	47	4	no	—
216	#492	—	94	2	no	—
217	#475	—	47	4	no	—
218	#475	—	94	2	no	—
219	#460	—	2	2	no	—
220	#460	C₂×D₄₇	1	4	yes	—
221	C₈×Q₈	—	47	4	no	—
222	C₈×Q₈	—	94	2	no	—
223	C₂×#106	—	94	1	no	—
224	C₂×C₄⋊C₈	—	47	1	no	—
225	C₂×C₄⋊C₈	—	47	1	no	—
226	C₂×C₄⋊C₈	—	94	1	no	—
227	C₂×C₄⋊C₈	C₂×D₄₇	1	1	yes	characteristic
228	C₂×#103	—	94	1	no	—
229	C₂×#102	—	2	1	no	—
230	C₂×C₄×C₈	—	47	1	no	—
231	C₂×C₄×C₈	—	94	1	no	—
232	#334	—	47	4	no	—
233	#332	—	47	4	no	—
234	#331	—	47	4	no	—
235	C₄₇	C₂×#1666	1	1	yes	characteristic, complemented, Sylow
236	C₂²×Q₈	—	94	1	no	—
237	C₂²×Q₈	C₂²⋊D₄₇	1	1	yes	characteristic
238	C₂²×D₄	—	2	1	no	—
239	C₂²×D₄	—	2	1	no	—
240	C₂²×D₄	—	2	1	no	—
241	C₂×SD₁₆	—	2	4	no	—
242	C₂×SD₁₆	—	4	4	no	—
243	C₂×SD₁₆	—	94	4	no	—
244	C₂×SD₁₆	—	94	4	no	—
245	C₂×SD₁₆	—	188	4	no	—
246	C₂×SD₁₆	—	188	4	no	—
247	C₂²×C₈	—	2	1	no	—
248	C₂²×C₈	—	47	1	no	—
249	C₂²×C₈	—	47	1	no	—
250	C₂²×C₈	—	94	1	no	—
251	C₂²×C₈	—	94	1	no	—
252	C₄⋊Q₈	—	47	2	no	—
253	C₄⋊Q₈	—	94	1	no	—
254	C₄⋊Q₈	—	94	1	no	—
255	C₄⋊Q₈	—	94	1	no	—
256	#127	—	2	1	no	—
257	#127	—	2	1	no	—
258	#127	—	2	1	no	—
259	#127	C₂²×D₄₇	1	2	yes	—
260	C₄×Q₈	—	2	1	no	—
261	C₄×Q₈	—	2	1	no	—
262	C₄×Q₈	C₂²⋊D₄₇	1	2	yes	—
263	C₄×Q₈	C₂²×D₄₇	1	2	yes	—
264	C₂×C₄⋊C₄	—	2	1	no	—
265	C₂×C₄⋊C₄	—	94	1	no	—
266	C₂×C₄⋊C₄	—	94	1	no	—
267	C₂×C₄⋊C₄	C₂²⋊D₄₇	1	1	yes	characteristic
268	C₂×C₄²	—	2	1	no	—
269	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
270	#106	—	94	4	no	—
271	C₄⋊C₈	—	2	1	no	—
272	C₄⋊C₈	—	47	2	no	—
273	C₄⋊C₈	—	47	2	no	—
274	C₄⋊C₈	—	94	4	no	—
275	C₄⋊C₈	—	94	1	no	—
276	C₄⋊C₈	—	94	1	no	—
277	C₄⋊C₈	C₂²×D₄₇	1	2	yes	—
278	#103	—	94	4	no	—
279	#102	—	2	4	no	—
280	C₄×C₈	—	47	2	no	—
281	C₄×C₈	—	47	2	no	—
282	C₄×C₈	—	94	4	no	—
283	C₂⁴	—	4	1	no	—
284	C₂×Q₈	—	2	1	no	—
285	C₂×Q₈	—	2	2	no	—
286	C₂×Q₈	—	94	2	no	—
287	C₂×Q₈	—	188	2	no	—
288	C₂×Q₈	—	188	2	no	—
289	C₂×Q₈	—	188	1	no	—
290	C₂×Q₈	#10625335	1	4	yes	complemented
291	C₂×Q₈	C₂×C₂²⋊D₄₇	1	2	yes	—
292	C₂×D₄	—	2	2	no	—
293	C₂×D₄	—	2	2	no	—
294	C₂×D₄	—	2	2	no	—
295	C₂×D₄	—	4	1	no	—
296	C₂×D₄	—	4	1	no	—
297	C₂×D₄	—	4	1	no	—
298	C₂×D₄	—	4	2	no	—
299	C₂×D₄	—	4	2	no	—
300	C₂×D₄	—	4	2	no	—
301	C₂×D₄	—	4	2	no	—
302	C₂×D₄	—	8	2	no	—
303	C₂²×C₄	—	2	1	no	—
304	C₂²×C₄	—	2	1	no	—
305	C₂²×C₄	—	188	1	no	—
306	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
307	C₂²×C₄	#10625352	1	1	yes	characteristic
308	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
309	SD₁₆	—	4	8	no	—
310	SD₁₆	—	188	8	no	—
311	SD₁₆	—	188	8	no	—
312	C₂×C₈	—	2	2	no	—
313	C₂×C₈	—	4	2	no	—
314	C₂×C₈	—	47	4	no	—
315	C₂×C₈	—	47	2	no	—
316	C₂×C₈	—	47	2	no	—
317	C₂×C₈	—	94	2	no	—
318	C₂×C₈	—	94	2	no	—
319	C₂×C₈	—	94	2	no	—
320	C₂×C₈	—	188	2	no	—
321	C₂×C₈	—	188	2	no	—
322	C₄⋊C₄	—	2	2	no	—
323	C₄⋊C₄	—	2	1	no	—
324	C₄⋊C₄	—	2	2	no	—
325	C₄⋊C₄	—	94	2	no	—
326	C₄⋊C₄	—	94	2	no	—
327	C₄⋊C₄	—	188	1	no	—
328	C₄⋊C₄	—	188	1	no	—
329	C₄⋊C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
330	C₄²	—	2	2	no	—
331	C₄²	—	2	2	no	—
332	C₄²	D₄×D₄₇	1	1	yes	characteristic
333	C₄²	#10625352	1	1	yes	characteristic
334	C₄²	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
335	C₄²	C₂³×D₄₇	1	1	yes	characteristic
336	C₂³	—	4	2	no	—
337	C₂³	—	8	2	no	—
338	C₂³	—	8	2	no	—
339	C₂³	—	8	2	no	—
340	C₂³	#13093996	1	1	yes	characteristic
341	Q₈	—	2	4	no	—
342	Q₈	—	2	2	no	—
343	Q₈	—	376	2	no	—
344	Q₈	—	188	2	no	—
345	Q₈	—	188	2	no	—
346	Q₈	C₂×#10625335	1	4	yes	complemented
347	D₄	—	4	2	no	—
348	D₄	—	4	2	no	—
349	D₄	—	4	2	no	—
350	D₄	—	4	2	no	—
351	D₄	—	8	2	no	—
352	D₄	—	8	2	no	—
353	D₄	—	8	2	no	—
354	D₄	—	8	2	no	—
355	C₂×C₄	—	2	4	no	—
356	C₂×C₄	—	2	2	no	—
357	C₂×C₄	—	2	2	no	—
358	C₂×C₄	—	2	2	no	—
359	C₂×C₄	—	4	2	no	—
360	C₂×C₄	—	376	2	no	—
361	C₂×C₄	—	188	2	no	—
362	C₂×C₄	#13093996	1	1	yes	characteristic
363	C₂×C₄	#13093996	1	1	yes	characteristic
364	C₂×C₄	#13093996	1	1	yes	characteristic
365	C₂×C₄	SD₁₆×D₄₇	1	2	yes	—
366	C₂×C₄	C₂×#10625335	1	2	yes	—
367	C₂×C₄	#13094044	1	2	yes	—
368	C₂×C₄	#13094051	1	2	yes	—
369	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
370	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
371	C₂×C₄	C₂×#10625352	1	1	yes	characteristic
372	C₈	—	4	2	no	—
373	C₈	—	47	4	no	—
374	C₈	—	94	2	no	—
375	C₈	—	188	2	no	—
376	C₈	—	188	2	no	—
377	C₂²	—	8	2	no	—
378	C₂²	—	8	2	no	—
379	C₂²	—	8	2	no	—
380	C₂²	—	16	4	no	—
381	C₂²	#15689321	1	2	yes	—
382	C₂²	#15689350	1	2	yes	—
383	C₂²	#15689384	1	2	yes	—
384	C₂²	C₂×#13093996	1	1	yes	characteristic
385	C₄	—	2	4	no	—
386	C₄	—	2	1	no	—
387	C₄	—	2	1	no	—
388	C₄	—	4	2	no	—
389	C₄	—	376	2	no	—
390	C₄	#15689321	1	2	yes	—
391	C₄	#15689350	1	2	yes	—
392	C₄	C₂×SD₁₆×D₄₇	1	1	yes	characteristic
393	C₄	C₂²×#10625335	1	1	yes	characteristic
394	C₄	C₂×#13094044	1	1	yes	characteristic
395	C₄	C₂×#13094051	1	1	yes	characteristic
396	C₂	—	16	2	no	—
397	C₂	#20242734	1	4	yes	direct product factor
398	C₂	C₂×#15689321	1	1	yes	characteristic
399	C₂	C₂×#15689350	1	1	yes	characteristic
400	C₂	C₂×#15689384	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	#13093996
commutator, cosocle	C₄²×C₄₇	C₂⁴
Frattini	C₄²	C₂³×D₄₇
Fitting	C₂×C₄₇×#460	C₂
socle	C₂³×C₄₇	#121
prime radical	C₂×#127×C₄₇	C₂²
hypercenter	C₂×#460	D₄₇
hypocenter	C₄₇	C₂×#1666
LCS	G ▷ C₄²×C₄₇ ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×#460

Complements

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

N	H ≅ G/N	type
2. C₂×#15689408	C₂	semidirect
3. C₂×Q₈×C₄₇⋊C₈	C₂	semidirect
4. #20242734	C₂	direct (N × H)
5. C₂×#15688873	C₂	semidirect
6. C₂×#15688868	C₂	semidirect
15. #15689408	C₂²	semidirect
17. Q₈×C₄₇⋊C₈	C₂²	semidirect
25. #15688873	C₂²	semidirect
26. #15688868	C₂²	semidirect
85. C₂×Q₈×C₄₇	SD₁₆	semidirect
132. C₂×C₄₇⋊C₈	SD₁₆	semidirect
142. Q₈×C₄₇	C₂×SD₁₆	semidirect
175. C₄₇⋊C₈	C₂×SD₁₆	semidirect
205. C₂×C₄₇	#1666	semidirect
235. C₄₇	C₂×#1666	semidirect
290. C₂×Q₈	#10625335	semidirect
346. Q₈	C₂×#10625335	semidirect
397. C₂	#20242734	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×#15689495	2
C₂×#15689408	2
C₂×Q₈×C₄₇⋊C₈	2
#20242734	2
C₂×#15688873	2
C₂×#15688868	2
C₂×#15688867	2
C₂×C₄₇×#460	2
C₂×#1666	47

Subgroups — C2×#20242734 #26198596

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#20242734 #26198596