Subgroups — C₂×#20242775 #26198533

Order 12032.

790 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#15689526	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#15689328	C₂	1	1	yes	maximal, characteristic
3	C₂×D₄×C₄₇⋊C₈	C₂	1	1	yes	maximal, characteristic
4	#20242775	C₂	1	8	yes	maximal, direct product factor
5	C₂×#15688875	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#15688870	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#15688869	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₄₇×#461	C₂	1	1	yes	maximal, characteristic
9	C₂²×#10625335	—	2	1	no	—
10	C₂³×C₄₇⋊C₈	—	2	1	no	—
11	C₂×#13094024	C₂²	1	1	yes	characteristic
12	#15689526	—	2	2	no	—
13	#15689526	C₂²	1	4	yes	complemented
14	#15689328	—	2	2	no	—
15	#15689328	C₂²	1	4	yes	—
16	D₄×C₄₇⋊C₈	—	2	2	no	—
17	D₄×C₄₇⋊C₈	C₂²	1	4	yes	—
18	C₂×#13093957	—	2	1	no	—
19	C₂×#13093957	—	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×#13093947	—	2	1	no	—
23	C₂×C₂²⋊(C₄₇⋊C₈)	—	2	1	no	—
24	C₂×C₄×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
25	#15688875	C₂²	1	4	yes	complemented
26	#15688870	C₂²	1	4	yes	complemented
27	#15688869	C₂²	1	4	yes	complemented
28	C₂²×SD₁₆×C₄₇	—	2	1	no	—
29	C₂×C₄⋊Q₈×C₄₇	C₂²	1	1	yes	characteristic
30	C₂×C₄×D₄×C₄₇	C₂²	1	1	yes	characteristic
31	C₄₇×#461	—	2	2	no	—
32	C₄₇×#461	C₂²	1	4	yes	—
33	C₂×C₄⋊C₈×C₄₇	C₂²	1	1	yes	characteristic
34	C₂×#103×C₄₇	—	2	1	no	—
35	C₂²×Dic₉₄	—	2	1	no	—
36	C₂×#10625335	—	2	4	no	—
37	C₂×#10625335	—	4	4	no	—
38	C₂²×C₄₇⋊C₈	—	2	1	no	—
39	C₂²×C₄₇⋊C₈	—	2	1	no	—
40	C₂²×C₄₇⋊C₈	—	2	4	no	—
41	C₂²×C₄₇⋊C₈	—	4	4	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	#13093957	—	2	4	no	—
51	#13093957	—	2	4	no	—
52	C₄⋊(C₄₇⋊C₈)	—	2	1	no	—
53	C₄⋊(C₄₇⋊C₈)	—	2	1	no	—
54	C₄⋊(C₄₇⋊C₈)	C₂³	1	2	yes	—
55	C₄⋊(C₄₇⋊C₈)	C₂³	1	2	yes	—
56	#13093947	—	2	4	no	—
57	C₂²⋊(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	—	2	1	no	—
61	C₂²×D₄×C₄₇	D₄	1	1	yes	characteristic
62	C₂³×C₄×C₄₇	—	2	1	no	—
63	C₂×SD₁₆×C₄₇	—	2	4	no	—
64	C₂×SD₁₆×C₄₇	—	4	4	no	—
65	C₂²×C₈×C₄₇	—	2	1	no	—
66	C₄⋊Q₈×C₄₇	—	2	1	no	—
67	C₄⋊Q₈×C₄₇	—	2	1	no	—
68	C₄⋊Q₈×C₄₇	—	2	1	no	—
69	C₄⋊Q₈×C₄₇	C₂³	1	2	yes	—
70	C₄×D₄×C₄₇	—	2	1	no	—
71	C₄×D₄×C₄₇	—	2	1	no	—
72	C₄×D₄×C₄₇	D₄	1	2	yes	—
73	C₄×D₄×C₄₇	C₂³	1	2	yes	—
74	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
75	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
76	C₂×C₄⋊C₄×C₄₇	D₄	1	1	yes	characteristic
77	C₂×C₂²⋊C₄×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	#103×C₄₇	—	2	4	no	—
82	C₂⁴×C₄₇	—	2	1	no	—
83	C₂×Q₈×C₄₇	—	2	2	no	—
84	C₂×Q₈×C₄₇	—	4	1	no	—
85	C₂×Q₈×C₄₇	—	4	2	no	—
86	C₂×Q₈×C₄₇	—	4	2	no	—
87	C₂×D₄×C₄₇	—	2	1	no	—
88	C₂×D₄×C₄₇	—	2	2	no	—
89	C₂×D₄×C₄₇	D₈	1	4	yes	—
90	C₂×D₄×C₄₇	C₂×D₄	1	2	yes	—
91	C₂²×C₄×C₄₇	—	2	1	no	—
92	C₂²×C₄×C₄₇	—	2	2	no	—
93	C₂²×C₄×C₄₇	—	2	2	no	—
94	C₂²×C₄×C₄₇	—	4	2	no	—
95	C₂²×C₄×C₄₇	—	4	2	no	—
96	C₂²×C₄×C₄₇	—	4	1	no	—
97	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
98	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
99	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
100	C₂²×Dic₄₇	—	4	1	no	—
101	C₂×Dic₉₄	—	2	2	no	—
102	C₂×Dic₉₄	—	4	2	no	—
103	C₂×Dic₉₄	—	4	2	no	—
104	C₂×Dic₉₄	—	4	1	no	—
105	SD₁₆×C₄₇	—	4	8	no	—
106	C₂×C₈×C₄₇	—	2	2	no	—
107	C₂×C₈×C₄₇	—	4	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	—	4	1	no	—
112	C₄⋊C₄×C₄₇	—	4	1	no	—
113	C₄⋊C₄×C₄₇	C₂×D₄	1	2	yes	—
114	C₂²⋊C₄×C₄₇	—	2	2	no	—
115	C₂²⋊C₄×C₄₇	—	2	2	no	—
116	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
117	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
118	C₄²×C₄₇	#41	1	1	yes	characteristic
119	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
120	#10625335	—	4	8	no	—
121	C₄⋊Dic₄₇	—	2	2	no	—
122	C₄⋊Dic₄₇	—	2	2	no	—
123	C₄⋊Dic₄₇	—	4	1	no	—
124	C₄⋊Dic₄₇	—	4	1	no	—
125	C₂×C₄₇⋊C₈	—	2	2	no	—
126	C₂×C₄₇⋊C₈	—	2	2	no	—
127	C₂×C₄₇⋊C₈	—	2	2	no	—
128	C₂×C₄₇⋊C₈	—	4	2	no	—
129	C₂×C₄₇⋊C₈	—	4	2	no	—
130	C₂×C₄₇⋊C₈	—	4	8	no	—
131	C₂×C₄₇⋊C₈	SD₁₆	1	4	yes	complemented
132	C₂×C₄₇⋊C₈	C₂×D₄	1	2	yes	—
133	C₂×C₄₇⋊C₈	C₂×D₄	1	2	yes	—
134	C₂³×C₄₇	—	2	2	no	—
135	C₂³×C₄₇	—	2	4	no	—
136	C₂³×C₄₇	—	4	2	no	—
137	C₂³×C₄₇	—	4	2	no	—
138	C₂³×C₄₇	#121	1	1	yes	characteristic
139	Q₈×C₄₇	—	4	2	no	—
140	Q₈×C₄₇	—	4	2	no	—
141	Q₈×C₄₇	—	8	2	no	—
142	D₄×C₄₇	—	2	2	no	—
143	D₄×C₄₇	—	2	4	no	—
144	D₄×C₄₇	C₂×D₈	1	4	yes	—
145	C₂×C₄×C₄₇	—	2	2	no	—
146	C₂×C₄×C₄₇	—	2	2	no	—
147	C₂×C₄×C₄₇	—	4	2	no	—
148	C₂×C₄×C₄₇	—	4	2	no	—
149	C₂×C₄×C₄₇	—	4	2	no	—
150	C₂×C₄×C₄₇	—	4	4	no	—
151	C₂×C₄×C₄₇	—	4	2	no	—
152	C₂×C₄×C₄₇	—	8	2	no	—
153	C₂×C₄×C₄₇	#121	1	1	yes	characteristic
154	C₂×C₄×C₄₇	#121	1	1	yes	characteristic
155	C₂×C₄×C₄₇	#121	1	1	yes	characteristic
156	C₂×C₄×C₄₇	C₂×D₈	1	2	yes	—
157	C₂×C₄×C₄₇	C₂×SD₁₆	1	2	yes	—
158	C₂×C₄×C₄₇	#135	1	2	yes	—
159	C₂×C₄×C₄₇	#137	1	2	yes	—
160	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
161	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
162	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
163	C₂×Dic₄₇	—	4	2	no	—
164	C₂×Dic₄₇	—	8	2	no	—
165	Dic₉₄	—	4	2	no	—
166	Dic₉₄	—	4	2	no	—
167	Dic₉₄	—	8	2	no	—
168	C₈×C₄₇	—	4	2	no	—
169	C₄₇⋊C₈	—	2	2	no	—
170	C₄₇⋊C₈	—	4	2	no	—
171	C₄₇⋊C₈	—	4	2	no	—
172	C₄₇⋊C₈	C₂×SD₁₆	1	4	yes	complemented
173	C₂×#1673	—	47	1	no	maximal, Sylow
174	C₂²×C₄₇	—	2	4	no	—
175	C₂²×C₄₇	—	4	8	no	—
176	C₂²×C₄₇	—	4	2	no	—
177	C₂²×C₄₇	—	4	2	no	—
178	C₂²×C₄₇	#461	1	2	yes	—
179	C₂²×C₄₇	#466	1	2	yes	—
180	C₂²×C₄₇	#473	1	2	yes	—
181	C₂²×C₄₇	C₂×#121	1	1	yes	characteristic
182	C₄×C₄₇	—	2	1	no	—
183	C₄×C₄₇	—	2	1	no	—
184	C₄×C₄₇	—	4	2	no	—
185	C₄×C₄₇	—	8	2	no	—
186	C₄×C₄₇	#461	1	2	yes	—
187	C₄×C₄₇	#466	1	2	yes	—
188	C₄×C₄₇	C₂²×D₈	1	1	yes	characteristic
189	C₄×C₄₇	C₂²×SD₁₆	1	1	yes	characteristic
190	C₄×C₄₇	C₂×#135	1	1	yes	characteristic
191	C₄×C₄₇	C₂×#137	1	1	yes	characteristic
192	Dic₄₇	—	8	2	no	—
193	C₂×#500	—	47	1	no	—
194	C₂×#461	—	47	1	no	—
195	C₂×#461	D₄₇	1	1	yes	characteristic
196	C₂×C₈×D₄	—	47	1	no	—
197	#1673	—	47	8	no	—
198	C₂×#335	—	47	1	no	—
199	C₂×#332	—	47	1	no	—
200	C₂×#332	—	47	1	no	—
201	C₂×C₄₇	—	4	4	no	—
202	C₂×C₄₇	#1673	1	4	yes	complemented
203	C₂×C₄₇	C₂×#461	1	1	yes	characteristic
204	C₂×C₄₇	C₂×#466	1	1	yes	characteristic
205	C₂×C₄₇	C₂×#473	1	1	yes	characteristic
206	C₂²×SD₁₆	—	2	1	no	—
207	C₂²×SD₁₆	—	94	1	no	—
208	C₂³×C₈	—	94	1	no	—
209	C₂×C₄⋊Q₈	—	47	1	no	—
210	C₂×C₄⋊Q₈	C₂×D₄₇	1	1	yes	characteristic
211	C₂×C₄×D₄	C₂×D₄₇	1	1	yes	characteristic
212	#500	—	47	4	no	—
213	#500	—	94	2	no	—
214	#461	—	2	2	no	—
215	#461	—	47	4	no	—
216	#461	—	94	2	no	—
217	#461	C₂×D₄₇	1	4	yes	—
218	C₈×D₄	—	47	4	no	—
219	C₈×D₄	—	94	2	no	—
220	C₂×#107	—	94	1	no	—
221	C₂×#107	—	94	1	no	—
222	C₂×C₄⋊C₈	—	47	1	no	—
223	C₂×C₄⋊C₈	—	47	1	no	—
224	C₂×C₄⋊C₈	C₂×D₄₇	1	1	yes	characteristic
225	C₂×#103	—	2	1	no	—
226	C₂×#103	—	94	1	no	—
227	C₂×C₂²⋊C₈	—	94	1	no	—
228	C₂×C₄×C₈	—	47	1	no	—
229	#335	—	47	4	no	—
230	#332	—	47	4	no	—
231	#332	—	47	4	no	—
232	C₄₇	C₂×#1673	1	1	yes	characteristic, complemented, Sylow
233	C₂²×Q₈	—	2	1	no	—
234	C₂²×Q₈	—	94	1	no	—
235	C₂²×D₄	C₂²⋊D₄₇	1	1	yes	characteristic
236	C₂³×C₄	—	2	1	no	—
237	C₂×SD₁₆	—	2	4	no	—
238	C₂×SD₁₆	—	4	4	no	—
239	C₂×SD₁₆	—	94	4	no	—
240	C₂×SD₁₆	—	188	4	no	—
241	C₂²×C₈	—	2	1	no	—
242	C₂²×C₈	—	47	1	no	—
243	C₂²×C₈	—	47	1	no	—
244	C₂²×C₈	—	94	4	no	—
245	C₂²×C₈	—	94	1	no	—
246	C₂²×C₈	—	94	1	no	—
247	C₂²×C₈	—	188	4	no	—
248	C₄⋊Q₈	—	2	1	no	—
249	C₄⋊Q₈	—	2	1	no	—
250	C₄⋊Q₈	—	2	1	no	—
251	C₄⋊Q₈	—	47	2	no	—
252	C₄⋊Q₈	—	94	1	no	—
253	C₄⋊Q₈	—	94	1	no	—
254	C₄⋊Q₈	—	94	1	no	—
255	C₄⋊Q₈	C₂²×D₄₇	1	2	yes	—
256	C₄×D₄	—	2	1	no	—
257	C₄×D₄	—	2	1	no	—
258	C₄×D₄	C₂²⋊D₄₇	1	2	yes	—
259	C₄×D₄	C₂²×D₄₇	1	2	yes	—
260	C₂×C₄⋊C₄	—	2	1	no	—
261	C₂×C₄⋊C₄	—	2	1	no	—
262	C₂×C₄⋊C₄	—	94	1	no	—
263	C₂×C₄⋊C₄	—	94	1	no	—
264	C₂×C₄⋊C₄	C₂²⋊D₄₇	1	1	yes	characteristic
265	C₂×C₂²⋊C₄	—	2	1	no	—
266	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
267	#107	—	94	4	no	—
268	#107	—	94	4	no	—
269	C₄⋊C₈	—	2	1	no	—
270	C₄⋊C₈	—	47	2	no	—
271	C₄⋊C₈	—	47	2	no	—
272	C₄⋊C₈	—	94	1	no	—
273	C₄⋊C₈	—	94	1	no	—
274	C₄⋊C₈	C₂²×D₄₇	1	2	yes	—
275	#103	—	2	4	no	—
276	#103	—	94	4	no	—
277	C₂²⋊C₈	—	94	4	no	—
278	C₄×C₈	—	47	2	no	—
279	C₄×C₈	—	47	2	no	—
280	C₂⁴	—	2	1	no	—
281	C₂×Q₈	—	2	2	no	—
282	C₂×Q₈	—	4	1	no	—
283	C₂×Q₈	—	4	2	no	—
284	C₂×Q₈	—	4	2	no	—
285	C₂×Q₈	—	94	2	no	—
286	C₂×Q₈	—	188	2	no	—
287	C₂×Q₈	—	188	2	no	—
288	C₂×Q₈	—	188	1	no	—
289	C₂×D₄	—	2	1	no	—
290	C₂×D₄	—	2	2	no	—
291	C₂×D₄	#10625334	1	4	yes	—
292	C₂×D₄	C₂×C₂²⋊D₄₇	1	2	yes	—
293	C₂²×C₄	—	2	1	no	—
294	C₂²×C₄	—	2	2	no	—
295	C₂²×C₄	—	2	2	no	—
296	C₂²×C₄	—	4	2	no	—
297	C₂²×C₄	—	4	2	no	—
298	C₂²×C₄	—	4	1	no	—
299	C₂²×C₄	—	188	1	no	—
300	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
301	C₂²×C₄	#10625352	1	1	yes	characteristic
302	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
303	SD₁₆	—	4	8	no	—
304	SD₁₆	—	188	8	no	—
305	C₂×C₈	—	2	2	no	—
306	C₂×C₈	—	4	2	no	—
307	C₂×C₈	—	47	4	no	—
308	C₂×C₈	—	47	2	no	—
309	C₂×C₈	—	47	2	no	—
310	C₂×C₈	—	94	2	no	—
311	C₂×C₈	—	94	2	no	—
312	C₂×C₈	—	94	2	no	—
313	C₂×C₈	—	188	8	no	—
314	C₂×C₈	—	188	2	no	—
315	C₂×C₈	—	188	2	no	—
316	C₄⋊C₄	—	2	1	no	—
317	C₄⋊C₄	—	2	2	no	—
318	C₄⋊C₄	—	2	2	no	—
319	C₄⋊C₄	—	4	1	no	—
320	C₄⋊C₄	—	4	1	no	—
321	C₄⋊C₄	—	94	2	no	—
322	C₄⋊C₄	—	94	2	no	—
323	C₄⋊C₄	—	188	1	no	—
324	C₄⋊C₄	—	188	1	no	—
325	C₄⋊C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
326	C₂²⋊C₄	—	2	2	no	—
327	C₂²⋊C₄	—	2	2	no	—
328	C₄²	D₄×D₄₇	1	1	yes	characteristic
329	C₄²	#10625352	1	1	yes	characteristic
330	C₄²	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
331	C₄²	C₂³×D₄₇	1	1	yes	characteristic
332	C₂³	—	2	4	no	—
333	C₂³	—	2	2	no	—
334	C₂³	—	4	2	no	—
335	C₂³	—	4	2	no	—
336	C₂³	#13093996	1	1	yes	characteristic
337	Q₈	—	4	2	no	—
338	Q₈	—	4	2	no	—
339	Q₈	—	8	2	no	—
340	Q₈	—	376	2	no	—
341	Q₈	—	188	2	no	—
342	Q₈	—	188	2	no	—
343	D₄	—	2	4	no	—
344	D₄	—	2	2	no	—
345	D₄	C₂×#10625334	1	4	yes	—
346	C₂×C₄	—	2	2	no	—
347	C₂×C₄	—	2	2	no	—
348	C₂×C₄	—	4	2	no	—
349	C₂×C₄	—	4	4	no	—
350	C₂×C₄	—	4	2	no	—
351	C₂×C₄	—	4	2	no	—
352	C₂×C₄	—	4	2	no	—
353	C₂×C₄	—	8	2	no	—
354	C₂×C₄	—	376	2	no	—
355	C₂×C₄	—	188	2	no	—
356	C₂×C₄	#13093996	1	1	yes	characteristic
357	C₂×C₄	#13093996	1	1	yes	characteristic
358	C₂×C₄	#13093996	1	1	yes	characteristic
359	C₂×C₄	C₂×#10625334	1	2	yes	—
360	C₂×C₄	SD₁₆×D₄₇	1	2	yes	—
361	C₂×C₄	#13094044	1	2	yes	—
362	C₂×C₄	#13094053	1	2	yes	—
363	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
364	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
365	C₂×C₄	C₂×#10625352	1	1	yes	characteristic
366	C₈	—	4	2	no	—
367	C₈	—	47	4	no	—
368	C₈	—	94	2	no	—
369	C₈	—	188	2	no	—
370	C₈	—	188	2	no	—
371	C₂²	—	2	4	no	—
372	C₂²	—	4	8	no	—
373	C₂²	—	4	2	no	—
374	C₂²	—	4	2	no	—
375	C₂²	#15689326	1	2	yes	—
376	C₂²	#15689357	1	2	yes	—
377	C₂²	#15689396	1	2	yes	—
378	C₂²	C₂×#13093996	1	1	yes	characteristic
379	C₄	—	2	1	no	—
380	C₄	—	2	1	no	—
381	C₄	—	4	2	no	—
382	C₄	—	8	2	no	—
383	C₄	—	376	2	no	—
384	C₄	#15689326	1	2	yes	—
385	C₄	#15689357	1	2	yes	—
386	C₄	C₂²×#10625334	1	1	yes	characteristic
387	C₄	C₂×SD₁₆×D₄₇	1	1	yes	characteristic
388	C₄	C₂×#13094044	1	1	yes	characteristic
389	C₄	C₂×#13094053	1	1	yes	characteristic
390	C₂	—	4	4	no	—
391	C₂	#20242775	1	4	yes	direct product factor
392	C₂	C₂×#15689326	1	1	yes	characteristic
393	C₂	C₂×#15689357	1	1	yes	characteristic
394	C₂	C₂×#15689396	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	#13093996
commutator, cosocle	C₄²×C₄₇	C₂⁴
Frattini	C₄²	C₂³×D₄₇
Fitting	C₂×C₄₇×#461	C₂
socle	C₂³×C₄₇	#121
prime radical	C₂²×D₄×C₄₇	D₄
hypercenter	C₂×#461	D₄₇
hypocenter	C₄₇	C₂×#1673
LCS	G ▷ C₄²×C₄₇ ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×#461

Complements

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

N	H ≅ G/N	type
1. C₂×#15689526	C₂	semidirect
4. #20242775	C₂	direct (N × H)
5. C₂×#15688875	C₂	semidirect
6. C₂×#15688870	C₂	semidirect
7. C₂×#15688869	C₂	semidirect
13. #15689526	C₂²	semidirect
25. #15688875	C₂²	semidirect
26. #15688870	C₂²	semidirect
27. #15688869	C₂²	semidirect
131. C₂×C₄₇⋊C₈	SD₁₆	semidirect
172. C₄₇⋊C₈	C₂×SD₁₆	semidirect
202. C₂×C₄₇	#1673	semidirect
232. C₄₇	C₂×#1673	semidirect
391. C₂	#20242775	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×#15689526	2
C₂×#15689328	2
C₂×D₄×C₄₇⋊C₈	2
#20242775	2
C₂×#15688875	2
C₂×#15688870	2
C₂×#15688869	2
C₂×C₄₇×#461	2
C₂×#1673	47

Subgroups — C2×#20242775 #26198533

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#20242775 #26198533