Subgroups — #26370636

Order 12032.

694 conjugacy classes of subgroups.

The subgroup lattice has 424 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#15689564	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#15689553	C₂	1	1	yes	maximal, characteristic
3	#20252265	C₂	1	1	yes	maximal, characteristic, complemented
4	#20245447	C₂	1	2	yes	maximal, complemented
5	#20245440	C₂	1	2	yes	maximal, complemented
6	#20245435	C₂	1	2	yes	maximal, complemented
7	#20245430	C₂	1	2	yes	maximal, complemented
8	#20245147	C₂	1	1	yes	maximal, characteristic, complemented
9	#20245100	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#15688927	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄₇×#3156	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#13094046	C₂²	1	1	yes	characteristic
13	#15689603	—	2	1	no	—
14	#15689564	—	2	4	no	—
15	#15689553	—	2	4	no	—
16	C₂×#13093970	C₂²	1	2	yes	—
17	C₂×#13093970	C₂²	1	1	yes	characteristic
18	C₂×#13093968	C₂²	1	1	yes	characteristic
19	C₂×#13093967	C₂²	1	2	yes	—
20	C₂×#13093967	C₂²	1	1	yes	characteristic
21	C₂×#13093965	C₂²	1	1	yes	characteristic
22	C₂×#13093964	C₂²	1	1	yes	characteristic
23	C₂²×C₄₇⋊C₁₆	C₂²	1	1	yes	characteristic
24	#15689225	—	2	2	no	—
25	C₄×Dic₁₈₈	C₂²	1	2	yes	—
26	C₄×D₃₇₆	C₂²	1	2	yes	—
27	C₂×#13093958	C₂²	1	1	yes	characteristic
28	#15689125	—	2	1	no	—
29	C₄⋊(C₄₇⋊C₁₆)	C₂²	1	2	yes	—
30	C₄⋊(C₄₇⋊C₁₆)	C₂²	1	2	yes	—
31	#15688927	C₂²	1	2	yes	—
32	#15688927	C₂²	1	2	yes	—
33	#15688927	C₂²	1	2	yes	—
34	#15688924	C₂²	1	2	yes	—
35	C₂×#137×C₄₇	—	2	1	no	—
36	C₂×#135×C₄₇	C₂²	1	1	yes	characteristic
37	C₂²×Q₁₆×C₄₇	C₂²	1	1	yes	characteristic
38	C₄₇×#536	—	2	1	no	—
39	C₄₇×#497	—	2	2	no	—
40	C₄₇×#495	C₂²	1	2	yes	—
41	C₄₇×#494	C₂²	1	2	yes	—
42	C₄₇×#405	C₂²	1	1	yes	characteristic
43	C₂×#10625350	—	2	1	no	—
44	#13094046	—	2	2	no	—
45	#13094046	D₄	1	4	yes	—
46	C₂×Dic₁₈₈	C₂³	1	1	yes	characteristic
47	C₂×#10625325	—	2	1	no	—
48	C₂×D₃₇₆	C₂³	1	1	yes	characteristic
49	C₄×Dic₉₄	—	2	2	no	—
50	C₄×D₁₈₈	—	2	2	no	—
51	(C₂²⋊D₄₇)⋊C₄	—	4	2	no	—
52	#13093982	—	4	1	no	—
53	C₂×C₄⋊Dic₄₇	—	2	1	no	—
54	C₄⋊C₄×D₄₇	—	4	1	no	—
55	#13093970	—	2	2	no	—
56	#13093970	—	2	4	no	—
57	#13093968	—	2	2	no	—
58	#13093967	—	2	2	no	—
59	#13093967	—	2	4	no	—
60	#13093965	—	2	2	no	—
61	#13093964	—	2	2	no	—
62	C₂×C₄₇⋊C₁₆	—	2	2	no	—
63	C₂×C₄₇⋊C₁₆	C₂³	1	1	yes	characteristic
64	C₂×C₄₇⋊C₁₆	C₂³	1	1	yes	characteristic
65	C₂×C₄₇⋊C₁₆	C₂³	1	2	yes	—
66	#13093958	—	2	1	no	—
67	#13093958	C₂³	1	2	yes	—
68	#13093949	—	2	2	no	—
69	#13093946	—	2	2	no	—
70	C₂×#41×C₄₇	—	2	1	no	—
71	C₂²×Q₈×C₄₇	—	2	1	no	—
72	#137×C₄₇	—	4	4	no	—
73	#135×C₄₇	—	2	2	no	—
74	#135×C₄₇	—	2	2	no	—
75	C₂×Q₁₆×C₄₇	—	2	2	no	—
76	C₂×Q₁₆×C₄₇	—	2	2	no	—
77	C₂×Q₁₆×C₄₇	—	2	1	no	—
78	C₂×Q₁₆×C₄₇	—	2	2	no	—
79	C₂×Q₁₆×C₄₇	C₂³	1	1	yes	characteristic
80	C₂×Q₁₆×C₄₇	C₂³	1	2	yes	—
81	C₂×SD₁₆×C₄₇	—	2	2	no	—
82	C₂×SD₁₆×C₄₇	—	2	1	no	—
83	C₂×D₈×C₄₇	C₂³	1	1	yes	characteristic
84	C₂×M₁₆×C₄₇	D₄	1	1	yes	characteristic
85	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
86	C₄⋊Q₈×C₄₇	—	2	2	no	—
87	#124×C₄₇	—	2	2	no	—
88	#123×C₄₇	—	4	2	no	—
89	C₂²⋊Q₈×C₄₇	—	4	1	no	—
90	C₂²⋊Q₈×C₄₇	—	4	1	no	—
91	#117×C₄₇	D₄	1	1	yes	characteristic
92	#97×C₄₇	D₄	1	2	yes	—
93	C₄×C₈×C₄₇	C₂³	1	2	yes	—
94	#41×C₄₇	—	4	2	no	—
95	#41×C₄₇	—	4	2	no	—
96	C₂×Q₈×C₄₇	—	2	2	no	—
97	C₂×Q₈×C₄₇	—	2	1	no	—
98	C₂×Q₈×C₄₇	—	4	1	no	—
99	C₂×Q₈×C₄₇	—	4	2	no	—
100	C₂×Q₈×C₄₇	—	4	2	no	—
101	C₂×D₄×C₄₇	—	2	1	no	—
102	C₂×D₄×C₄₇	—	4	1	no	—
103	C₂²×C₄×C₄₇	—	4	1	no	—
104	C₂²×C₄×C₄₇	—	4	1	no	—
105	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
106	C₂×C₂²⋊D₄₇	—	4	1	no	—
107	C₂²×Dic₄₇	—	4	1	no	—
108	#10625350	—	2	4	no	—
109	#10625350	—	4	2	no	—
110	C₂×D₁₈₈	—	2	1	no	—
111	C₂×C₄×D₄₇	—	4	1	no	—
112	C₂×C₄×D₄₇	—	4	2	no	—
113	C₂×Dic₉₄	—	2	1	no	—
114	Q₁₆×C₄₇	—	2	2	no	—
115	Q₁₆×C₄₇	—	2	1	no	—
116	Q₁₆×C₄₇	—	2	2	no	—
117	Q₁₆×C₄₇	—	2	1	no	—
118	Q₁₆×C₄₇	—	4	4	no	—
119	Q₁₆×C₄₇	—	4	2	no	—
120	SD₁₆×C₄₇	—	4	4	no	—
121	SD₁₆×C₄₇	—	4	2	no	—
122	D₈×C₄₇	—	2	1	no	—
123	D₈×C₄₇	—	2	1	no	—
124	M₁₆×C₄₇	—	2	2	no	—
125	C₂×C₈×C₄₇	C₂×D₄	1	2	yes	—
126	C₂×C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
127	C₂×C₈×C₄₇	C₂×D₄	1	2	yes	—
128	C₂×C₈×C₄₇	#41	1	2	yes	—
129	C₂×C₈×C₄₇	C₂⁴	1	1	yes	characteristic
130	C₄⋊C₄×C₄₇	—	4	2	no	—
131	C₄⋊C₄×C₄₇	—	4	2	no	—
132	C₄⋊C₄×C₄₇	D₈	1	1	yes	characteristic
133	C₄⋊C₄×C₄₇	D₈	1	1	yes	characteristic
134	C₂²⋊C₄×C₄₇	—	4	2	no	—
135	C₂²⋊C₄×C₄₇	—	4	2	no	—
136	C₂²⋊C₄×C₄₇	D₈	1	2	yes	—
137	C₄²×C₄₇	C₂×D₄	1	2	yes	—
138	(C₂×D₄₇)⋊C₄	—	4	2	no	—
139	C₄⋊Dic₄₇	—	2	2	no	—
140	C₄⋊Dic₄₇	—	4	1	no	—
141	Dic₄₇⋊C₄	—	4	2	no	—
142	C₄×Dic₄₇	—	4	2	no	—
143	Dic₁₈₈	—	2	1	no	—
144	Dic₁₈₈	C₂×D₄	1	2	yes	—
145	D₃₇₆	—	2	1	no	—
146	D₃₇₆	C₂×D₄	1	2	yes	—
147	#10625325	—	2	4	no	—
148	C₄₇⋊C₁₆	—	2	1	no	—
149	C₄₇⋊C₁₆	—	2	1	no	—
150	C₄₇⋊C₁₆	—	2	2	no	—
151	C₂³×C₄₇	—	4	1	no	—
152	C₂³×C₄₇	C₂×D₈	1	1	yes	characteristic
153	C₂²×D₄₇	—	4	1	no	—
154	Q₈×C₄₇	—	4	1	no	—
155	Q₈×C₄₇	—	4	2	no	—
156	Q₈×C₄₇	—	4	2	no	—
157	Q₈×C₄₇	—	4	1	no	—
158	Q₈×C₄₇	—	8	2	no	—
159	D₄×C₄₇	—	4	1	no	—
160	D₄×C₄₇	—	4	1	no	—
161	D₄×C₄₇	—	8	2	no	—
162	C₂×C₄×C₄₇	—	4	2	no	—
163	C₂×C₄×C₄₇	—	4	1	no	—
164	C₂×C₄×C₄₇	—	8	2	no	—
165	C₂×C₄×C₄₇	—	8	2	no	—
166	C₂×C₄×C₄₇	#121	1	2	yes	—
167	C₂×C₄×C₄₇	C₂×D₈	1	2	yes	—
168	C₂×C₄×C₄₇	C₂×D₈	1	2	yes	—
169	C₂×C₄×C₄₇	C₂×D₈	1	1	yes	characteristic
170	C₂×C₄×C₄₇	AGL(1,ℤ/8)	1	2	yes	—
171	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
172	C₂²⋊D₄₇	—	4	4	no	—
173	C₂×Dic₄₇	—	4	1	no	—
174	C₂×Dic₄₇	—	4	2	no	—
175	C₂×Dic₄₇	—	16	1	no	—
176	D₁₈₈	—	2	2	no	—
177	D₁₈₈	—	4	1	no	—
178	C₄×D₄₇	—	4	4	no	—
179	C₄×D₄₇	—	16	2	no	—
180	Dic₉₄	—	2	2	no	—
181	Dic₉₄	—	4	1	no	—
182	C₈×C₄₇	—	2	2	no	—
183	C₈×C₄₇	#121	1	2	yes	—
184	C₈×C₄₇	C₂²×D₄	1	1	yes	characteristic
185	C₈×C₄₇	C₂×#41	1	1	yes	characteristic
186	#33590	—	47	1	no	maximal, Sylow
187	C₂²×C₄₇	—	2	1	no	—
188	C₂²×C₄₇	—	2	1	no	—
189	C₂²×C₄₇	—	8	1	no	—
190	C₂²×C₄₇	—	8	1	no	—
191	C₂²×C₄₇	—	8	1	no	—
192	C₂²×C₄₇	#459	1	2	yes	—
193	C₂²×C₄₇	C₂²×D₈	1	1	yes	characteristic
194	C₂×D₄₇	—	4	2	no	—
195	C₂×D₄₇	—	8	1	no	—
196	C₂×D₄₇	—	8	1	no	—
197	C₄×C₄₇	—	2	2	no	—
198	C₄×C₄₇	—	2	2	no	—
199	C₄×C₄₇	—	8	1	no	—
200	C₄×C₄₇	—	8	2	no	—
201	C₄×C₄₇	#459	1	2	yes	—
202	C₄×C₄₇	C₂×#121	1	1	yes	characteristic
203	C₄×C₄₇	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
204	Dic₄₇	—	4	2	no	—
205	Dic₄₇	—	8	2	no	—
206	C₂×#510	—	47	1	no	—
207	C₂×#508	—	47	1	no	—
208	#3156	D₄₇	1	1	yes	characteristic, complemented
209	#2951	—	47	1	no	—
210	#2211	—	47	2	no	—
211	#2210	—	47	2	no	—
212	#2209	—	47	2	no	—
213	#2208	—	47	2	no	—
214	#2151	—	47	1	no	—
215	#2139	—	47	1	no	—
216	C₂×#358	—	47	1	no	—
217	C₂×C₄₇	—	2	2	no	—
218	C₂×C₄₇	—	16	1	no	—
219	C₂×C₄₇	C₂×#459	1	1	yes	characteristic
220	C₂×C₄₇	#3416	1	1	yes	characteristic
221	C₂×C₄₇	#3417	1	1	yes	characteristic
222	D₄₇	—	8	2	no	—
223	C₂×#137	—	2	1	no	—
224	C₂×#135	—	47	1	no	—
225	C₂×#135	C₂×D₄₇	1	1	yes	characteristic
226	C₂²×Q₁₆	C₂×D₄₇	1	1	yes	characteristic
227	#536	—	2	1	no	—
228	#520	—	94	1	no	—
229	#510	—	94	4	no	—
230	#508	—	94	4	no	—
231	C₂×Q₃₂	—	47	1	no	—
232	C₂×Q₃₂	—	47	2	no	—
233	C₂×SD₃₂	—	47	1	no	—
234	C₂×SD₃₂	—	47	2	no	—
235	C₂×SD₃₂	—	47	1	no	—
236	C₂×D₁₆	—	47	1	no	—
237	C₂×M₃₂	—	47	1	no	—
238	C₂²×C₁₆	—	47	1	no	—
239	#497	—	2	2	no	—
240	#495	C₂×D₄₇	1	2	yes	—
241	#494	C₂×D₄₇	1	2	yes	—
242	#440	—	94	2	no	—
243	C₄×Q₁₆	—	47	2	no	—
244	C₄×D₈	—	47	2	no	—
245	C₂×#107	—	47	1	no	—
246	#417	—	94	1	no	—
247	#405	C₂×D₄₇	1	1	yes	characteristic
248	C₄⋊C₁₆	—	47	2	no	—
249	C₄⋊C₁₆	—	47	2	no	—
250	#358	—	47	2	no	—
251	#358	—	47	2	no	—
252	#358	—	47	2	no	—
253	#357	—	47	2	no	—
254	C₄₇	#33590	1	1	yes	characteristic, complemented, Sylow
255	C₂×#41	—	2	1	no	—
256	C₂×#41	—	94	1	no	—
257	C₂²×Q₈	—	2	1	no	—
258	#137	—	4	4	no	—
259	#135	—	2	2	no	—
260	#135	—	2	2	no	—
261	#135	—	47	4	no	—
262	#135	—	94	2	no	—
263	C₂×Q₁₆	—	2	2	no	—
264	C₂×Q₁₆	—	2	2	no	—
265	C₂×Q₁₆	—	2	1	no	—
266	C₂×Q₁₆	—	2	2	no	—
267	C₂×Q₁₆	—	47	1	no	—
268	C₂×Q₁₆	C₂²×D₄₇	1	2	yes	—
269	C₂×Q₁₆	C₂²×D₄₇	1	1	yes	characteristic
270	C₂×SD₁₆	—	2	1	no	—
271	C₂×SD₁₆	—	2	2	no	—
272	C₂×SD₁₆	—	94	1	no	—
273	C₂×D₈	—	47	1	no	—
274	C₂×D₈	C₂²×D₄₇	1	1	yes	characteristic
275	C₂×M₁₆	C₂²⋊D₄₇	1	1	yes	characteristic
276	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
277	C₄⋊Q₈	—	2	2	no	—
278	#124	—	2	2	no	—
279	#123	—	4	2	no	—
280	C₂²⋊Q₈	—	4	1	no	—
281	C₂²⋊Q₈	—	4	1	no	—
282	C₄×Q₈	—	94	2	no	—
283	C₄×D₄	—	94	2	no	—
284	C₄×D₄	—	188	2	no	—
285	#117	—	188	1	no	—
286	#117	C₂²⋊D₄₇	1	1	yes	characteristic
287	C₂×C₄⋊C₄	—	94	1	no	—
288	C₂×C₄⋊C₄	—	188	1	no	—
289	Q₃₂	—	94	2	no	—
290	Q₃₂	—	94	4	no	—
291	SD₃₂	—	94	2	no	—
292	SD₃₂	—	94	2	no	—
293	SD₃₂	—	94	4	no	—
294	D₁₆	—	94	2	no	—
295	M₃₂	—	94	2	no	—
296	C₂×C₁₆	—	47	2	no	—
297	C₂×C₁₆	—	47	1	no	—
298	C₂×C₁₆	—	47	1	no	—
299	C₂×C₁₆	—	94	2	no	—
300	#107	—	47	2	no	—
301	#107	—	94	1	no	—
302	#103	—	94	2	no	—
303	#102	—	94	2	no	—
304	#97	C₂²⋊D₄₇	1	2	yes	—
305	C₄×C₈	C₂²×D₄₇	1	2	yes	—
306	#41	—	4	2	no	—
307	#41	—	4	2	no	—
308	#41	—	94	4	no	—
309	#41	—	188	2	no	—
310	C₂×Q₈	—	2	2	no	—
311	C₂×Q₈	—	2	1	no	—
312	C₂×Q₈	—	4	1	no	—
313	C₂×Q₈	—	4	2	no	—
314	C₂×Q₈	—	4	2	no	—
315	C₂×Q₈	—	94	1	no	—
316	C₂×D₄	—	2	1	no	—
317	C₂×D₄	—	4	1	no	—
318	C₂×D₄	—	94	1	no	—
319	C₂×D₄	—	188	1	no	—
320	C₂²×C₄	—	4	1	no	—
321	C₂²×C₄	—	4	1	no	—
322	C₂²×C₄	—	188	1	no	—
323	C₂²×C₄	—	188	1	no	—
324	C₂²×C₄	—	188	2	no	—
325	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
326	Q₁₆	—	2	2	no	—
327	Q₁₆	—	2	1	no	—
328	Q₁₆	—	2	2	no	—
329	Q₁₆	—	2	1	no	—
330	Q₁₆	—	4	4	no	—
331	Q₁₆	—	4	2	no	—
332	Q₁₆	—	47	2	no	—
333	Q₁₆	—	94	1	no	—
334	SD₁₆	—	4	4	no	—
335	SD₁₆	—	4	2	no	—
336	SD₁₆	—	94	4	no	—
337	D₈	—	2	1	no	—
338	D₈	—	2	1	no	—
339	D₈	—	47	2	no	—
340	D₈	—	94	1	no	—
341	M₁₆	—	2	2	no	—
342	C₂×C₈	D₄×D₄₇	1	2	yes	—
343	C₂×C₈	#10625352	1	2	yes	—
344	C₂×C₈	C₂×C₂²⋊D₄₇	1	2	yes	—
345	C₂×C₈	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
346	C₂×C₈	C₂³×D₄₇	1	1	yes	characteristic
347	C₄⋊C₄	—	4	2	no	—
348	C₄⋊C₄	—	4	2	no	—
349	C₄⋊C₄	—	94	2	no	—
350	C₄⋊C₄	—	188	2	no	—
351	C₄⋊C₄	—	188	1	no	—
352	C₄⋊C₄	#10625334	1	1	yes	characteristic
353	C₄⋊C₄	#10625334	1	1	yes	characteristic
354	C₂²⋊C₄	—	4	2	no	—
355	C₂²⋊C₄	—	4	2	no	—
356	C₂²⋊C₄	—	188	2	no	—
357	C₂²⋊C₄	#10625334	1	2	yes	—
358	C₄²	—	188	2	no	—
359	C₄²	C₂×C₂²⋊D₄₇	1	2	yes	—
360	C₁₆	—	94	1	no	—
361	C₁₆	—	94	1	no	—
362	C₁₆	—	94	2	no	—
363	C₂³	—	4	1	no	—
364	C₂³	—	188	1	no	—
365	C₂³	C₂×#10625334	1	1	yes	characteristic
366	Q₈	—	4	1	no	—
367	Q₈	—	4	2	no	—
368	Q₈	—	4	2	no	—
369	Q₈	—	4	1	no	—
370	Q₈	—	8	2	no	—
371	Q₈	—	94	2	no	—
372	Q₈	—	188	1	no	—
373	D₄	—	4	1	no	—
374	D₄	—	4	1	no	—
375	D₄	—	8	2	no	—
376	D₄	—	94	2	no	—
377	D₄	—	188	4	no	—
378	D₄	—	188	1	no	—
379	C₂×C₄	—	4	2	no	—
380	C₂×C₄	—	4	1	no	—
381	C₂×C₄	—	8	2	no	—
382	C₂×C₄	—	8	2	no	—
383	C₂×C₄	—	188	2	no	—
384	C₂×C₄	—	188	1	no	—
385	C₂×C₄	—	188	4	no	—
386	C₂×C₄	—	752	2	no	—
387	C₂×C₄	—	752	1	no	—
388	C₂×C₄	#13093995	1	2	yes	—
389	C₂×C₄	C₂×#10625334	1	2	yes	—
390	C₂×C₄	C₂×#10625334	1	2	yes	—
391	C₂×C₄	C₂×#10625334	1	1	yes	characteristic
392	C₂×C₄	#13094050	1	2	yes	—
393	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
394	C₈	—	2	2	no	—
395	C₈	#13093995	1	2	yes	—
396	C₈	C₂×D₄×D₄₇	1	1	yes	characteristic
397	C₈	C₂×#10625352	1	1	yes	characteristic
398	C₂²	—	2	1	no	—
399	C₂²	—	2	1	no	—
400	C₂²	—	8	1	no	—
401	C₂²	—	8	1	no	—
402	C₂²	—	8	1	no	—
403	C₂²	—	376	1	no	—
404	C₂²	—	376	1	no	—
405	C₂²	—	188	2	no	—
406	C₂²	#15689315	1	2	yes	—
407	C₂²	C₂²×#10625334	1	1	yes	characteristic
408	C₄	—	2	2	no	—
409	C₄	—	2	2	no	—
410	C₄	—	8	1	no	—
411	C₄	—	8	2	no	—
412	C₄	—	376	2	no	—
413	C₄	—	188	2	no	—
414	C₄	#15689315	1	2	yes	—
415	C₄	C₂×#13093995	1	1	yes	characteristic
416	C₄	C₂×#13094050	1	1	yes	characteristic
417	C₂	—	2	2	no	—
418	C₂	—	16	1	no	—
419	C₂	—	376	2	no	—
420	C₂	C₂×#15689315	1	1	yes	characteristic
421	C₂	#20256532	1	1	yes	characteristic
422	C₂	#20256539	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂²×#10625334
commutator, cosocle	C₂×C₈×C₄₇	C₂⁴
Frattini	C₂×C₈	C₂³×D₄₇
Fitting	C₄₇×#3156	C₂
socle	C₂²×C₄₇	C₂²×D₈
prime radical	C₂×#15689553	C₂
hypercenter	#3156	D₄₇
hypocenter	C₄₇	#33590
LCS	G ▷ C₂×C₈×C₄₇ ▷ C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ #117 ◁ #405 ◁ #3156

Complements

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

N	H ≅ G/N	type
1. C₂×#15689564	C₂	semidirect
3. #20252265	C₂	semidirect
4. #20245447	C₂	semidirect
5. #20245440	C₂	semidirect
6. #20245435	C₂	semidirect
7. #20245430	C₂	semidirect
8. #20245147	C₂	semidirect
9. #20245100	C₂	semidirect
10. C₂×#15688927	C₂	semidirect
11. C₄₇×#3156	C₂	semidirect
208. #3156	D₄₇	semidirect
254. C₄₇	#33590	semidirect

Maximal subgroups

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

subgroup	index
C₂×#15689564	2
C₂×#15689553	2
#20252265	2
#20245447	2
#20245440	2
#20245435	2
#20245430	2
#20245147	2
#20245100	2
C₂×#15688927	2
C₄₇×#3156	2
#33590	47