Subgroups — C₂×#20242806 #26198656

Order 12032.

722 conjugacy classes of subgroups.

The subgroup lattice has 390 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#15689471	C₂	1	1	yes	maximal, characteristic
2	C₂×#15689323	C₂	1	1	yes	maximal, characteristic
3	C₂×Q₈×C₄₇⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
4	#20242806	C₂	1	8	yes	maximal, direct product factor
5	C₂×#15688873	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#15688872	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#15688866	C₂	1	1	yes	maximal, characteristic
8	C₂×C₄₇×#477	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂²×#10625336	—	2	1	no	—
10	C₂×#13094021	C₂²	1	1	yes	characteristic
11	#15689471	—	2	2	no	—
12	#15689471	C₂²	1	4	yes	—
13	#15689323	—	2	2	no	—
14	#15689323	C₂²	1	4	yes	—
15	Q₈×C₄₇⋊C₈	—	2	2	no	—
16	Q₈×C₄₇⋊C₈	C₂²	1	4	yes	complemented
17	C₂×C₄⋊(C₄₇⋊C₈)	—	2	1	no	—
18	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
19	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
20	C₂×#13093944	—	2	1	no	—
21	C₂×#13093944	—	2	1	no	—
22	C₂×#13093944	—	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	#15688872	C₂²	1	4	yes	complemented
27	#15688866	C₂²	1	4	yes	—
28	C₂×C₄⋊Q₈×C₄₇	C₂²	1	1	yes	characteristic
29	C₂×C₄×Q₈×C₄₇	C₂²	1	1	yes	characteristic
30	C₄₇×#477	—	2	2	no	—
31	C₄₇×#477	C₂²	1	4	yes	complemented
32	C₂×#107×C₄₇	—	2	1	no	—
33	C₂×C₄⋊C₈×C₄₇	C₂²	1	1	yes	characteristic
34	C₂×#103×C₄₇	—	2	1	no	—
35	C₂²×D₁₈₈	—	2	1	no	—
36	C₂²×D₁₈₈	—	2	1	no	—
37	C₂²×D₁₈₈	—	2	1	no	—
38	C₂×#10625336	—	2	4	no	—
39	C₂×#10625336	—	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	#13094021	—	2	1	no	—
45	#13094021	—	2	1	no	—
46	#13094021	—	2	1	no	—
47	#13094021	C₂³	1	2	yes	—
48	C₄⋊(C₄₇⋊C₈)	—	2	1	no	—
49	C₄⋊(C₄₇⋊C₈)	—	2	1	no	—
50	C₄⋊(C₄₇⋊C₈)	—	2	4	no	—
51	C₄⋊(C₄₇⋊C₈)	C₂³	1	2	yes	—
52	C₄⋊(C₄₇⋊C₈)	C₂³	1	2	yes	—
53	#13093944	—	2	4	no	—
54	#13093944	—	2	4	no	—
55	#13093944	—	2	4	no	—
56	C₄×C₄₇⋊C₈	—	2	4	no	—
57	C₄×C₄₇⋊C₈	D₄	1	2	yes	—
58	C₄×C₄₇⋊C₈	C₂³	1	2	yes	—
59	C₂²×Q₈×C₄₇	—	2	1	no	—
60	C₂²×Q₈×C₄₇	D₄	1	1	yes	characteristic
61	C₂²×C₈×C₄₇	—	2	1	no	—
62	C₄⋊Q₈×C₄₇	—	2	1	no	—
63	C₄⋊Q₈×C₄₇	—	2	1	no	—
64	C₄⋊Q₈×C₄₇	—	2	1	no	—
65	C₄⋊Q₈×C₄₇	C₂³	1	2	yes	—
66	C₄×Q₈×C₄₇	—	2	1	no	—
67	C₄×Q₈×C₄₇	—	2	1	no	—
68	C₄×Q₈×C₄₇	D₄	1	2	yes	—
69	C₄×Q₈×C₄₇	C₂³	1	2	yes	—
70	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
71	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
72	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
73	C₂×C₄⋊C₄×C₄₇	D₄	1	1	yes	characteristic
74	C₂×C₄²×C₄₇	—	2	1	no	—
75	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
76	#107×C₄₇	—	2	4	no	—
77	C₄⋊C₈×C₄₇	—	2	1	no	—
78	C₄⋊C₈×C₄₇	C₂³	1	2	yes	—
79	#103×C₄₇	—	2	4	no	—
80	C₂³×D₄₇	—	4	1	no	—
81	C₂×Q₈×C₄₇	—	2	1	no	—
82	C₂×Q₈×C₄₇	—	2	2	no	—
83	C₂×Q₈×C₄₇	—	2	2	no	—
84	C₂×Q₈×C₄₇	—	4	1	no	—
85	C₂×Q₈×C₄₇	—	8	2	no	—
86	C₂×Q₈×C₄₇	SD₁₆	1	4	yes	—
87	C₂×Q₈×C₄₇	C₂×D₄	1	2	yes	—
88	C₂²×C₄×C₄₇	—	2	1	no	—
89	C₂²×C₄×C₄₇	—	2	1	no	—
90	C₂²×C₄×C₄₇	—	4	1	no	—
91	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
92	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
93	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
94	C₂×D₁₈₈	—	2	2	no	—
95	C₂×D₁₈₈	—	2	2	no	—
96	C₂×D₁₈₈	—	2	2	no	—
97	C₂×D₁₈₈	—	4	2	no	—
98	C₂×D₁₈₈	—	4	2	no	—
99	C₂×D₁₈₈	—	4	2	no	—
100	C₂×D₁₈₈	—	4	2	no	—
101	C₂×D₁₈₈	—	4	1	no	—
102	C₂×D₁₈₈	—	4	1	no	—
103	C₂×D₁₈₈	—	4	1	no	—
104	C₂×D₁₈₈	—	8	2	no	—
105	C₂×C₈×C₄₇	—	2	2	no	—
106	C₂×C₈×C₄₇	—	4	2	no	—
107	C₄⋊C₄×C₄₇	—	2	2	no	—
108	C₄⋊C₄×C₄₇	—	2	1	no	—
109	C₄⋊C₄×C₄₇	—	2	2	no	—
110	C₄⋊C₄×C₄₇	—	2	2	no	—
111	C₄⋊C₄×C₄₇	—	2	2	no	—
112	C₄⋊C₄×C₄₇	—	4	1	no	—
113	C₄⋊C₄×C₄₇	—	4	1	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	#10625336	—	4	8	no	—
122	C₂×C₄₇⋊C₈	—	2	2	no	—
123	C₂×C₄₇⋊C₈	—	2	2	no	—
124	C₂×C₄₇⋊C₈	—	2	2	no	—
125	C₂×C₄₇⋊C₈	—	2	2	no	—
126	C₂×C₄₇⋊C₈	—	4	2	no	—
127	C₂×C₄₇⋊C₈	—	4	2	no	—
128	C₂×C₄₇⋊C₈	C₂×D₄	1	2	yes	—
129	C₂×C₄₇⋊C₈	C₂×D₄	1	2	yes	—
130	C₂³×C₄₇	#121	1	1	yes	characteristic
131	C₂²×D₄₇	—	4	2	no	—
132	C₂²×D₄₇	—	8	2	no	—
133	C₂²×D₄₇	—	8	2	no	—
134	C₂²×D₄₇	—	8	2	no	—
135	Q₈×C₄₇	—	2	2	no	—
136	Q₈×C₄₇	—	2	4	no	—
137	Q₈×C₄₇	—	8	2	no	—
138	Q₈×C₄₇	—	8	2	no	—
139	Q₈×C₄₇	C₂×SD₁₆	1	4	yes	—
140	C₂×C₄×C₄₇	—	2	2	no	—
141	C₂×C₄×C₄₇	—	2	4	no	—
142	C₂×C₄×C₄₇	—	2	2	no	—
143	C₂×C₄×C₄₇	—	2	2	no	—
144	C₂×C₄×C₄₇	—	4	2	no	—
145	C₂×C₄×C₄₇	—	4	2	no	—
146	C₂×C₄×C₄₇	—	8	2	no	—
147	C₂×C₄×C₄₇	#121	1	1	yes	characteristic
148	C₂×C₄×C₄₇	#121	1	1	yes	characteristic
149	C₂×C₄×C₄₇	#121	1	1	yes	characteristic
150	C₂×C₄×C₄₇	C₂×SD₁₆	1	2	yes	—
151	C₂×C₄×C₄₇	#135	1	2	yes	—
152	C₂×C₄×C₄₇	#135	1	2	yes	—
153	C₂×C₄×C₄₇	#137	1	2	yes	—
154	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
155	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
156	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
157	D₁₈₈	—	4	2	no	—
158	D₁₈₈	—	4	2	no	—
159	D₁₈₈	—	4	2	no	—
160	D₁₈₈	—	4	2	no	—
161	D₁₈₈	—	8	2	no	—
162	D₁₈₈	—	8	2	no	—
163	D₁₈₈	—	8	2	no	—
164	D₁₈₈	—	8	2	no	—
165	C₈×C₄₇	—	4	2	no	—
166	C₄₇⋊C₈	—	2	2	no	—
167	C₄₇⋊C₈	—	2	2	no	—
168	C₄₇⋊C₈	—	4	2	no	—
169	C₄₇⋊C₈	—	4	2	no	—
170	C₂×#1678	—	47	1	no	maximal, Sylow
171	C₂²×C₄₇	#464	1	2	yes	—
172	C₂²×C₄₇	#465	1	2	yes	—
173	C₂²×C₄₇	#472	1	2	yes	—
174	C₂²×C₄₇	C₂×#121	1	1	yes	characteristic
175	C₂×D₄₇	—	8	2	no	—
176	C₂×D₄₇	—	8	2	no	—
177	C₂×D₄₇	—	8	2	no	—
178	C₂×D₄₇	—	16	4	no	—
179	C₄×C₄₇	—	2	4	no	—
180	C₄×C₄₇	—	2	1	no	—
181	C₄×C₄₇	—	2	1	no	—
182	C₄×C₄₇	—	4	2	no	—
183	C₄×C₄₇	—	8	2	no	—
184	C₄×C₄₇	#464	1	2	yes	—
185	C₄×C₄₇	#465	1	2	yes	—
186	C₄×C₄₇	C₂²×SD₁₆	1	1	yes	characteristic
187	C₄×C₄₇	C₂×#135	1	1	yes	characteristic
188	C₄×C₄₇	C₂×#135	1	1	yes	characteristic
189	C₄×C₄₇	C₂×#137	1	1	yes	characteristic
190	C₂×#486	—	47	1	no	—
191	C₂×#477	D₄₇	1	1	yes	characteristic, complemented
192	C₂×#460	—	47	1	no	—
193	C₂×C₈×Q₈	—	47	1	no	—
194	#1678	—	47	8	no	—
195	C₂×#334	—	47	1	no	—
196	C₂×#333	—	47	1	no	—
197	C₂×#331	—	47	1	no	—
198	C₂×C₄₇	#1678	1	4	yes	complemented
199	C₂×C₄₇	C₂×#464	1	1	yes	characteristic
200	C₂×C₄₇	C₂×#465	1	1	yes	characteristic
201	C₂×C₄₇	C₂×#472	1	1	yes	characteristic
202	D₄₇	—	16	2	no	—
203	C₂²×SD₁₆	—	94	1	no	—
204	C₂×C₄⋊Q₈	C₂×D₄₇	1	1	yes	characteristic
205	C₂×#127	—	47	1	no	—
206	C₂×C₄×Q₈	C₂×D₄₇	1	1	yes	characteristic
207	#486	—	47	4	no	—
208	#486	—	94	2	no	—
209	#477	—	2	2	no	—
210	#477	C₂×D₄₇	1	4	yes	complemented
211	#460	—	47	4	no	—
212	#460	—	94	2	no	—
213	C₈×Q₈	—	47	4	no	—
214	C₈×Q₈	—	94	2	no	—
215	C₂×#107	—	2	1	no	—
216	C₂×C₄⋊C₈	—	47	1	no	—
217	C₂×C₄⋊C₈	—	47	1	no	—
218	C₂×C₄⋊C₈	—	94	1	no	—
219	C₂×C₄⋊C₈	C₂×D₄₇	1	1	yes	characteristic
220	C₂×#103	—	2	1	no	—
221	C₂×#102	—	94	1	no	—
222	C₂×#102	—	94	1	no	—
223	C₂×#102	—	94	1	no	—
224	C₂×C₄×C₈	—	47	1	no	—
225	C₂×C₄×C₈	—	94	1	no	—
226	#334	—	47	4	no	—
227	#333	—	47	4	no	—
228	#331	—	47	4	no	—
229	C₄₇	C₂×#1678	1	1	yes	characteristic, complemented, Sylow
230	C₂²×Q₈	—	2	1	no	—
231	C₂²×Q₈	C₂²⋊D₄₇	1	1	yes	characteristic
232	C₂²×D₄	—	94	1	no	—
233	C₂²×D₄	—	94	1	no	—
234	C₂²×D₄	—	94	1	no	—
235	C₂×SD₁₆	—	94	4	no	—
236	C₂×SD₁₆	—	188	4	no	—
237	C₂²×C₈	—	2	1	no	—
238	C₂²×C₈	—	47	1	no	—
239	C₂²×C₈	—	47	1	no	—
240	C₂²×C₈	—	94	1	no	—
241	C₂²×C₈	—	94	1	no	—
242	C₄⋊Q₈	—	2	1	no	—
243	C₄⋊Q₈	—	2	1	no	—
244	C₄⋊Q₈	—	2	1	no	—
245	C₄⋊Q₈	C₂²×D₄₇	1	2	yes	—
246	#127	—	47	2	no	—
247	#127	—	94	1	no	—
248	#127	—	94	1	no	—
249	#127	—	94	1	no	—
250	C₄×Q₈	—	2	1	no	—
251	C₄×Q₈	—	2	1	no	—
252	C₄×Q₈	C₂²⋊D₄₇	1	2	yes	—
253	C₄×Q₈	C₂²×D₄₇	1	2	yes	—
254	C₂×C₄⋊C₄	—	2	1	no	—
255	C₂×C₄⋊C₄	—	2	1	no	—
256	C₂×C₄⋊C₄	—	2	1	no	—
257	C₂×C₄⋊C₄	C₂²⋊D₄₇	1	1	yes	characteristic
258	C₂×C₄²	—	2	1	no	—
259	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
260	#107	—	2	4	no	—
261	C₄⋊C₈	—	2	1	no	—
262	C₄⋊C₈	—	47	2	no	—
263	C₄⋊C₈	—	47	2	no	—
264	C₄⋊C₈	—	94	4	no	—
265	C₄⋊C₈	—	94	1	no	—
266	C₄⋊C₈	—	94	1	no	—
267	C₄⋊C₈	C₂²×D₄₇	1	2	yes	—
268	#103	—	2	4	no	—
269	#102	—	94	4	no	—
270	#102	—	94	4	no	—
271	#102	—	94	4	no	—
272	C₄×C₈	—	47	2	no	—
273	C₄×C₈	—	47	2	no	—
274	C₄×C₈	—	94	4	no	—
275	C₂⁴	—	188	1	no	—
276	C₂×Q₈	—	2	1	no	—
277	C₂×Q₈	—	2	2	no	—
278	C₂×Q₈	—	2	2	no	—
279	C₂×Q₈	—	4	1	no	—
280	C₂×Q₈	—	8	2	no	—
281	C₂×Q₈	#10625336	1	4	yes	—
282	C₂×Q₈	C₂×C₂²⋊D₄₇	1	2	yes	—
283	C₂×D₄	—	94	2	no	—
284	C₂×D₄	—	94	2	no	—
285	C₂×D₄	—	94	2	no	—
286	C₂×D₄	—	376	2	no	—
287	C₂×D₄	—	188	1	no	—
288	C₂×D₄	—	188	1	no	—
289	C₂×D₄	—	188	1	no	—
290	C₂×D₄	—	188	2	no	—
291	C₂×D₄	—	188	2	no	—
292	C₂×D₄	—	188	2	no	—
293	C₂×D₄	—	188	2	no	—
294	C₂²×C₄	—	2	1	no	—
295	C₂²×C₄	—	2	1	no	—
296	C₂²×C₄	—	4	1	no	—
297	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
298	C₂²×C₄	#10625352	1	1	yes	characteristic
299	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
300	SD₁₆	—	188	8	no	—
301	C₂×C₈	—	2	2	no	—
302	C₂×C₈	—	4	2	no	—
303	C₂×C₈	—	47	2	no	—
304	C₂×C₈	—	47	2	no	—
305	C₂×C₈	—	94	2	no	—
306	C₂×C₈	—	94	2	no	—
307	C₂×C₈	—	94	2	no	—
308	C₂×C₈	—	94	2	no	—
309	C₂×C₈	—	188	2	no	—
310	C₂×C₈	—	188	2	no	—
311	C₄⋊C₄	—	2	2	no	—
312	C₄⋊C₄	—	2	1	no	—
313	C₄⋊C₄	—	2	2	no	—
314	C₄⋊C₄	—	2	2	no	—
315	C₄⋊C₄	—	2	2	no	—
316	C₄⋊C₄	—	4	1	no	—
317	C₄⋊C₄	—	4	1	no	—
318	C₄⋊C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
319	C₄²	—	2	2	no	—
320	C₄²	—	2	2	no	—
321	C₄²	D₄×D₄₇	1	1	yes	characteristic
322	C₄²	#10625352	1	1	yes	characteristic
323	C₄²	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
324	C₄²	C₂³×D₄₇	1	1	yes	characteristic
325	C₂³	—	376	2	no	—
326	C₂³	—	376	2	no	—
327	C₂³	—	376	2	no	—
328	C₂³	—	188	2	no	—
329	C₂³	#13093996	1	1	yes	characteristic
330	Q₈	—	2	4	no	—
331	Q₈	—	2	2	no	—
332	Q₈	—	8	2	no	—
333	Q₈	—	8	2	no	—
334	Q₈	C₂×#10625336	1	4	yes	—
335	D₄	—	376	2	no	—
336	D₄	—	376	2	no	—
337	D₄	—	376	2	no	—
338	D₄	—	376	2	no	—
339	D₄	—	188	2	no	—
340	D₄	—	188	2	no	—
341	D₄	—	188	2	no	—
342	D₄	—	188	2	no	—
343	C₂×C₄	—	2	4	no	—
344	C₂×C₄	—	2	2	no	—
345	C₂×C₄	—	2	2	no	—
346	C₂×C₄	—	2	2	no	—
347	C₂×C₄	—	4	2	no	—
348	C₂×C₄	—	4	2	no	—
349	C₂×C₄	—	8	2	no	—
350	C₂×C₄	#13093996	1	1	yes	characteristic
351	C₂×C₄	#13093996	1	1	yes	characteristic
352	C₂×C₄	#13093996	1	1	yes	characteristic
353	C₂×C₄	C₂×#10625336	1	2	yes	—
354	C₂×C₄	#13094044	1	2	yes	—
355	C₂×C₄	#13094047	1	2	yes	—
356	C₂×C₄	#13094056	1	2	yes	—
357	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
358	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
359	C₂×C₄	C₂×#10625352	1	1	yes	characteristic
360	C₈	—	4	2	no	—
361	C₈	—	94	2	no	—
362	C₈	—	94	2	no	—
363	C₈	—	188	2	no	—
364	C₈	—	188	2	no	—
365	C₂²	—	376	2	no	—
366	C₂²	—	376	2	no	—
367	C₂²	—	376	2	no	—
368	C₂²	—	752	4	no	—
369	C₂²	#15689347	1	2	yes	—
370	C₂²	#15689354	1	2	yes	—
371	C₂²	#15689391	1	2	yes	—
372	C₂²	C₂×#13093996	1	1	yes	characteristic
373	C₄	—	2	4	no	—
374	C₄	—	2	1	no	—
375	C₄	—	2	1	no	—
376	C₄	—	4	2	no	—
377	C₄	—	8	2	no	—
378	C₄	#15689347	1	2	yes	—
379	C₄	#15689354	1	2	yes	—
380	C₄	C₂²×#10625336	1	1	yes	characteristic
381	C₄	C₂×#13094044	1	1	yes	characteristic
382	C₄	C₂×#13094047	1	1	yes	characteristic
383	C₄	C₂×#13094056	1	1	yes	characteristic
384	C₂	—	752	2	no	—
385	C₂	#20242806	1	4	yes	direct product factor
386	C₂	C₂×#15689347	1	1	yes	characteristic
387	C₂	C₂×#15689354	1	1	yes	characteristic
388	C₂	C₂×#15689391	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	#13093996
commutator, cosocle	C₄²×C₄₇	C₂⁴
Frattini	C₄²	C₂³×D₄₇
Fitting	C₂×C₄₇×#477	C₂
socle	C₂³×C₄₇	#121
prime radical	C₂×#13094021	C₂²
hypercenter	C₂×#477	D₄₇
hypocenter	C₄₇	C₂×#1678
LCS	G ▷ C₄²×C₄₇ ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×#477

Complements

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

N	H ≅ G/N	type
3. C₂×Q₈×C₄₇⋊C₈	C₂	semidirect
4. #20242806	C₂	direct (N × H)
5. C₂×#15688873	C₂	semidirect
6. C₂×#15688872	C₂	semidirect
8. C₂×C₄₇×#477	C₂	semidirect
16. Q₈×C₄₇⋊C₈	C₂²	semidirect
25. #15688873	C₂²	semidirect
26. #15688872	C₂²	semidirect
31. C₄₇×#477	C₂²	semidirect
191. C₂×#477	D₄₇	semidirect
198. C₂×C₄₇	#1678	semidirect
210. #477	C₂×D₄₇	semidirect
229. C₄₇	C₂×#1678	semidirect
385. C₂	#20242806	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×#15689471	2
C₂×#15689323	2
C₂×Q₈×C₄₇⋊C₈	2
#20242806	2
C₂×#15688873	2
C₂×#15688872	2
C₂×#15688866	2
C₂×C₄₇×#477	2
C₂×#1678	47

Subgroups — C2×#20242806 #26198656

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#20242806 #26198656