Subgroups — #26201477

Order 12032.

662 conjugacy classes of subgroups.

The subgroup lattice has 434 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20254340	C₂	1	1	yes	maximal, characteristic, complemented
2	#20253388	C₂	1	1	yes	maximal, characteristic
3	#20252412	C₂	1	1	yes	maximal, characteristic, complemented
4	#20242827	C₂	1	2	yes	maximal, complemented
5	#20242813	C₂	1	2	yes	maximal, complemented
6	#20242751	C₂	1	2	yes	maximal, complemented
7	#20242731	C₂	1	2	yes	maximal, complemented
8	#20242169	C₂	1	1	yes	maximal, characteristic, complemented
9	#20242094	C₂	1	1	yes	maximal, characteristic, complemented
10	#20242053	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄₇×#3110	C₂	1	1	yes	maximal, characteristic, complemented
12	#15689673	C₂²	1	1	yes	characteristic
13	#15689502	C₂²	1	1	yes	characteristic, complemented
14	#15689497	C₂²	1	1	yes	characteristic, complemented
15	#15689475	C₂²	1	1	yes	characteristic, complemented
16	#15689471	C₂²	1	1	yes	characteristic, complemented
17	#15689436	—	2	1	no	—
18	#15689403	C₂²	1	2	yes	—
19	#15689345	—	2	2	no	—
20	#15689318	C₂²	1	2	yes	—
21	#15689283	—	2	2	no	—
22	#15689257	—	2	1	no	—
23	C₄×#10625334	—	2	2	no	—
24	D₄×C₄₇⋊C₈	—	2	2	no	—
25	D₄×C₄₇⋊C₈	C₂²	1	2	yes	—
26	D₄×C₄₇⋊C₈	C₂²	1	2	yes	—
27	#15689176	C₂²	1	1	yes	characteristic
28	#15689176	C₂²	1	1	yes	characteristic
29	#15689176	C₂²	1	1	yes	characteristic
30	C₂×C₂²⋊(C₄₇⋊C₈)	—	2	2	no	—
31	#15688875	C₂²	1	2	yes	complemented
32	#15688873	C₂²	1	2	yes	complemented
33	#15688869	C₂²	1	2	yes	complemented
34	#15688869	C₂²	1	2	yes	complemented
35	#15688868	C₂²	1	2	yes	complemented
36	#15688866	C₂²	1	2	yes	complemented
37	C₄₇×#533	C₂²	1	1	yes	characteristic
38	C₂×C₄×D₄×C₄₇	C₂²	1	1	yes	characteristic
39	C₄₇×#484	—	2	1	no	—
40	C₄₇×#474	C₂²	1	2	yes	—
41	C₄₇×#461	C₂²	1	2	yes	—
42	C₄₇×#450	—	2	1	no	—
43	C₄₇×#440	—	2	2	no	—
44	C₄₇×#432	C₂²	1	1	yes	characteristic
45	C₂×#10625350	—	2	1	no	—
46	C₂×#10625337	—	2	2	no	—
47	C₂×#10625336	—	2	2	no	—
48	C₂×#10625334	—	2	2	no	—
49	C₂²×C₄₇⋊C₈	—	2	2	no	—
50	C₂²×C₄₇⋊C₈	—	2	2	no	—
51	#13094024	C₂³	1	1	yes	characteristic
52	#13094021	C₂³	1	1	yes	characteristic
53	#13094012	—	2	1	no	—
54	#13093998	—	2	1	no	—
55	#13093998	—	2	1	no	—
56	C₄×D₁₈₈	—	2	1	no	—
57	C₄×D₁₈₈	—	2	1	no	—
58	#13093957	—	2	2	no	—
59	C₄⋊(C₄₇⋊C₈)	D₄	1	2	yes	—
60	C₄⋊(C₄₇⋊C₈)	C₂³	1	2	yes	—
61	C₄⋊(C₄₇⋊C₈)	C₂³	1	2	yes	—
62	#13093947	—	2	2	no	—
63	#13093945	—	2	2	no	—
64	#13093944	—	2	2	no	—
65	#13093944	—	2	2	no	—
66	C₂²⋊(C₄₇⋊C₈)	—	2	1	no	—
67	C₂²⋊(C₄₇⋊C₈)	—	2	1	no	—
68	C₂²⋊(C₄₇⋊C₈)	—	2	2	no	—
69	C₂²⋊(C₄₇⋊C₈)	—	2	2	no	—
70	C₂²⋊(C₄₇⋊C₈)	D₄	1	2	yes	—
71	C₄×C₄₇⋊C₈	—	2	1	no	—
72	C₄×C₄₇⋊C₈	—	2	1	no	—
73	C₄×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
74	C₄×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
75	C₂²×D₄×C₄₇	D₄	1	1	yes	characteristic
76	C₂³×C₄×C₄₇	—	2	1	no	—
77	C₂×SD₁₆×C₄₇	—	2	2	no	—
78	C₄⋊Q₈×C₄₇	C₂³	1	1	yes	characteristic
79	C₄⋊Q₈×C₄₇	C₂³	1	1	yes	characteristic
80	#125×C₄₇	—	2	1	no	—
81	C₂²⋊Q₈×C₄₇	—	2	1	no	—
82	C₂²⋊Q₈×C₄₇	—	2	1	no	—
83	C₄×Q₈×C₄₇	—	2	1	no	—
84	C₄×Q₈×C₄₇	—	2	1	no	—
85	C₄×D₄×C₄₇	—	2	1	no	—
86	C₄×D₄×C₄₇	—	2	1	no	—
87	C₄×D₄×C₄₇	D₄	1	2	yes	—
88	C₄×D₄×C₄₇	C₂³	1	2	yes	—
89	#117×C₄₇	—	2	1	no	—
90	C₂×C₄⋊C₄×C₄₇	D₄	1	1	yes	characteristic
91	C₂×C₂²⋊C₄×C₄₇	—	2	1	no	—
92	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
93	#107×C₄₇	—	2	2	no	—
94	C₄⋊C₈×C₄₇	C₂³	1	2	yes	—
95	#103×C₄₇	—	2	2	no	—
96	#102×C₄₇	—	2	2	no	—
97	C₂²⋊C₈×C₄₇	—	2	1	no	—
98	#97×C₄₇	—	2	1	no	—
99	C₂⁴×C₄₇	—	2	1	no	—
100	C₂×Q₈×C₄₇	—	2	1	no	—
101	C₂×Q₈×C₄₇	—	2	1	no	—
102	C₂×D₄×C₄₇	—	2	4	no	—
103	C₂×D₄×C₄₇	—	2	1	no	—
104	C₂×D₄×C₄₇	C₂×D₄	1	2	yes	—
105	C₂²×C₄×C₄₇	—	2	1	no	—
106	C₂²×C₄×C₄₇	—	2	2	no	—
107	C₂²×C₄×C₄₇	—	2	2	no	—
108	C₂²×C₄×C₄₇	—	8	2	no	—
109	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
110	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
111	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
112	C₂×C₂²⋊D₄₇	—	4	1	no	—
113	#10625350	—	8	2	no	—
114	C₂×D₁₈₈	—	2	1	no	—
115	C₂×D₁₈₈	—	2	1	no	—
116	C₂×D₁₈₈	—	2	1	no	—
117	C₂×C₄×D₄₇	—	4	1	no	—
118	C₂×Dic₉₄	—	2	1	no	—
119	SD₁₆×C₄₇	—	4	4	no	—
120	C₂×C₈×C₄₇	—	2	2	no	—
121	C₄⋊C₄×C₄₇	—	2	1	no	—
122	C₄⋊C₄×C₄₇	—	2	1	no	—
123	C₄⋊C₄×C₄₇	—	2	1	no	—
124	C₄⋊C₄×C₄₇	—	2	1	no	—
125	C₄⋊C₄×C₄₇	—	2	1	no	—
126	C₄⋊C₄×C₄₇	—	4	1	no	—
127	C₄⋊C₄×C₄₇	—	4	1	no	—
128	C₄⋊C₄×C₄₇	C₂×D₄	1	2	yes	—
129	C₂²⋊C₄×C₄₇	—	2	2	no	—
130	C₂²⋊C₄×C₄₇	—	2	2	no	—
131	C₂²⋊C₄×C₄₇	—	4	1	no	—
132	C₄²×C₄₇	—	4	1	no	—
133	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
134	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
135	C₄²×C₄₇	#41	1	1	yes	characteristic
136	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
137	#10625337	—	8	2	no	—
138	#10625336	—	8	2	no	—
139	#10625334	—	4	4	no	—
140	(C₂×D₄₇)⋊C₄	—	4	1	no	—
141	(C₂×D₄₇)⋊C₄	—	4	1	no	—
142	C₄⋊Dic₄₇	—	2	1	no	—
143	C₄⋊Dic₄₇	—	2	1	no	—
144	C₂×C₄₇⋊C₈	—	2	2	no	—
145	C₂×C₄₇⋊C₈	—	2	2	no	—
146	C₂×C₄₇⋊C₈	—	8	2	no	—
147	C₂×C₄₇⋊C₈	—	8	2	no	—
148	C₂×C₄₇⋊C₈	C₂×D₄	1	2	yes	—
149	C₂×C₄₇⋊C₈	C₂×D₄	1	2	yes	—
150	C₂³×C₄₇	—	2	4	no	—
151	C₂³×C₄₇	—	2	2	no	—
152	C₂³×C₄₇	—	8	1	no	—
153	C₂³×C₄₇	—	8	1	no	—
154	C₂³×C₄₇	#121	1	1	yes	characteristic
155	C₂²×D₄₇	—	4	1	no	—
156	Q₈×C₄₇	—	4	2	no	—
157	Q₈×C₄₇	—	4	2	no	—
158	D₄×C₄₇	—	2	4	no	—
159	D₄×C₄₇	—	2	2	no	—
160	D₄×C₄₇	#135	1	4	yes	—
161	C₂×C₄×C₄₇	—	2	2	no	—
162	C₂×C₄×C₄₇	—	2	2	no	—
163	C₂×C₄×C₄₇	—	2	2	no	—
164	C₂×C₄×C₄₇	—	4	1	no	—
165	C₂×C₄×C₄₇	—	4	2	no	—
166	C₂×C₄×C₄₇	—	4	2	no	—
167	C₂×C₄×C₄₇	—	4	1	no	—
168	C₂×C₄×C₄₇	—	4	1	no	—
169	C₂×C₄×C₄₇	—	8	2	no	—
170	C₂×C₄×C₄₇	—	8	1	no	—
171	C₂×C₄×C₄₇	#121	1	1	yes	characteristic
172	C₂×C₄×C₄₇	#121	1	1	yes	characteristic
173	C₂×C₄×C₄₇	#121	1	1	yes	characteristic
174	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
175	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
176	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
177	C₂²⋊D₄₇	—	8	2	no	—
178	C₂×Dic₄₇	—	4	1	no	—
179	D₁₈₈	—	4	2	no	—
180	D₁₈₈	—	4	2	no	—
181	D₁₈₈	—	8	1	no	—
182	C₄×D₄₇	—	8	2	no	—
183	Dic₉₄	—	4	2	no	—
184	C₈×C₄₇	—	4	2	no	—
185	C₄₇⋊C₈	—	2	2	no	—
186	C₄₇⋊C₈	—	2	2	no	—
187	C₄₇⋊C₈	—	4	2	no	—
188	C₄₇⋊C₈	—	4	2	no	—
189	#19388	—	47	1	no	maximal, Sylow
190	C₂²×C₄₇	—	2	1	no	—
191	C₂²×C₄₇	—	2	1	no	—
192	C₂²×C₄₇	—	2	4	no	—
193	C₂²×C₄₇	—	2	1	no	—
194	C₂²×C₄₇	—	4	2	no	—
195	C₂²×C₄₇	—	4	2	no	—
196	C₂²×C₄₇	—	8	4	no	—
197	C₂²×C₄₇	C₂×#121	1	1	yes	characteristic
198	C₂×D₄₇	—	8	1	no	—
199	C₂×D₄₇	—	8	1	no	—
200	C₂×D₄₇	—	8	1	no	—
201	C₄×C₄₇	—	2	1	no	—
202	C₄×C₄₇	—	2	1	no	—
203	C₄×C₄₇	—	2	1	no	—
204	C₄×C₄₇	—	2	1	no	—
205	C₄×C₄₇	—	4	2	no	—
206	C₄×C₄₇	—	8	1	no	—
207	C₄×C₄₇	—	8	1	no	—
208	C₄×C₄₇	C₂×#135	1	2	yes	—
209	C₄×C₄₇	#576	1	2	yes	—
210	Dic₄₇	—	8	1	no	—
211	#3210	—	47	1	no	—
212	#3110	D₄₇	1	1	yes	characteristic, complemented
213	#3100	—	47	1	no	—
214	#2972	—	47	1	no	—
215	#1681	—	47	2	no	—
216	#1679	—	47	2	no	—
217	#1669	—	47	2	no	—
218	#1665	—	47	2	no	—
219	#1572	—	47	1	no	—
220	#1553	—	47	1	no	—
221	#1544	—	47	1	no	—
222	C₂×C₄₇	—	4	1	no	—
223	C₂×C₄₇	—	4	4	no	—
224	C₂×C₄₇	#3041	1	1	yes	characteristic
225	C₂×C₄₇	#3050	1	1	yes	characteristic
226	C₂×C₄₇	#3069	1	1	yes	characteristic
227	D₄₇	—	16	1	no	—
228	#533	C₂×D₄₇	1	1	yes	characteristic
229	#532	—	47	1	no	—
230	C₂×C₄×D₄	C₂×D₄₇	1	1	yes	characteristic
231	#494	—	47	1	no	—
232	#492	—	47	1	no	—
233	#487	—	47	1	no	—
234	#486	—	47	1	no	—
235	#484	—	2	1	no	—
236	#480	—	94	1	no	—
237	#474	—	47	2	no	—
238	#474	C₂×D₄₇	1	2	yes	—
239	#464	—	94	2	no	—
240	#461	C₂×D₄₇	1	2	yes	—
241	#459	—	47	2	no	—
242	#452	—	94	2	no	—
243	#450	—	2	1	no	—
244	#447	—	94	1	no	—
245	#440	—	2	2	no	—
246	C₄×D₈	—	94	2	no	—
247	C₈×D₄	—	47	2	no	—
248	C₈×D₄	—	47	2	no	—
249	C₈×D₄	—	94	2	no	—
250	#432	C₂×D₄₇	1	1	yes	characteristic
251	#431	—	47	1	no	—
252	#431	—	47	1	no	—
253	#431	—	47	1	no	—
254	C₂×C₂²⋊C₈	—	94	2	no	—
255	#335	—	47	2	no	—
256	#334	—	47	2	no	—
257	#332	—	47	2	no	—
258	#332	—	47	2	no	—
259	#332	—	47	2	no	—
260	#331	—	47	2	no	—
261	C₄₇	#19388	1	1	yes	characteristic, complemented, Sylow
262	C₂×#41	—	94	1	no	—
263	C₂²×D₄	C₂²⋊D₄₇	1	1	yes	characteristic
264	C₂³×C₄	—	2	1	no	—
265	C₂×Q₁₆	—	94	2	no	—
266	C₂×SD₁₆	—	2	2	no	—
267	C₂×SD₁₆	—	94	2	no	—
268	C₂×D₈	—	94	2	no	—
269	C₂²×C₈	—	94	2	no	—
270	C₂²×C₈	—	94	2	no	—
271	C₄⋊Q₈	—	47	1	no	—
272	C₄⋊Q₈	C₂²×D₄₇	1	1	yes	characteristic
273	C₄⋊Q₈	C₂²×D₄₇	1	1	yes	characteristic
274	#127	—	47	1	no	—
275	#125	—	2	1	no	—
276	#124	—	94	1	no	—
277	C₂²⋊Q₈	—	2	1	no	—
278	C₂²⋊Q₈	—	2	1	no	—
279	#121	—	94	1	no	—
280	#121	—	94	1	no	—
281	C₄×Q₈	—	2	1	no	—
282	C₄×Q₈	—	2	1	no	—
283	C₄×D₄	—	2	1	no	—
284	C₄×D₄	—	2	1	no	—
285	C₄×D₄	—	94	1	no	—
286	C₄×D₄	—	94	1	no	—
287	C₄×D₄	C₂²⋊D₄₇	1	2	yes	—
288	C₄×D₄	C₂²×D₄₇	1	2	yes	—
289	#117	—	2	1	no	—
290	C₂×C₄⋊C₄	C₂²⋊D₄₇	1	1	yes	characteristic
291	C₂×C₂²⋊C₄	—	2	1	no	—
292	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
293	#107	—	2	2	no	—
294	#107	—	94	2	no	—
295	C₄⋊C₈	—	47	2	no	—
296	C₄⋊C₈	—	47	2	no	—
297	C₄⋊C₈	—	47	2	no	—
298	C₄⋊C₈	C₂²×D₄₇	1	2	yes	—
299	#103	—	2	2	no	—
300	#103	—	94	2	no	—
301	#102	—	2	2	no	—
302	#102	—	94	2	no	—
303	#102	—	94	2	no	—
304	#102	—	94	2	no	—
305	C₂²⋊C₈	—	2	1	no	—
306	C₂²⋊C₈	—	47	2	no	—
307	C₂²⋊C₈	—	94	2	no	—
308	C₂²⋊C₈	—	94	2	no	—
309	C₂²⋊C₈	—	94	1	no	—
310	C₂²⋊C₈	—	94	1	no	—
311	#97	—	2	1	no	—
312	C₄×C₈	—	47	1	no	—
313	C₄×C₈	—	47	1	no	—
314	C₄×C₈	—	94	1	no	—
315	C₄×C₈	—	94	1	no	—
316	C₂⁴	—	2	1	no	—
317	#41	—	376	2	no	—
318	C₂×Q₈	—	2	1	no	—
319	C₂×Q₈	—	2	1	no	—
320	C₂×Q₈	—	94	1	no	—
321	C₂×D₄	—	2	4	no	—
322	C₂×D₄	—	2	1	no	—
323	C₂×D₄	—	94	1	no	—
324	C₂×D₄	—	94	1	no	—
325	C₂×D₄	—	94	1	no	—
326	C₂×D₄	—	188	1	no	—
327	C₂×D₄	C₂×C₂²⋊D₄₇	1	2	yes	—
328	C₂²×C₄	—	2	1	no	—
329	C₂²×C₄	—	2	2	no	—
330	C₂²×C₄	—	2	2	no	—
331	C₂²×C₄	—	8	2	no	—
332	C₂²×C₄	—	188	1	no	—
333	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
334	C₂²×C₄	#10625352	1	1	yes	characteristic
335	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
336	Q₁₆	—	376	2	no	—
337	SD₁₆	—	4	4	no	—
338	SD₁₆	—	376	2	no	—
339	D₈	—	188	4	no	—
340	C₂×C₈	—	2	2	no	—
341	C₂×C₈	—	47	2	no	—
342	C₂×C₈	—	47	2	no	—
343	C₂×C₈	—	94	2	no	—
344	C₂×C₈	—	94	2	no	—
345	C₂×C₈	—	376	2	no	—
346	C₂×C₈	—	376	2	no	—
347	C₄⋊C₄	—	2	1	no	—
348	C₄⋊C₄	—	2	1	no	—
349	C₄⋊C₄	—	2	1	no	—
350	C₄⋊C₄	—	2	1	no	—
351	C₄⋊C₄	—	2	1	no	—
352	C₄⋊C₄	—	4	1	no	—
353	C₄⋊C₄	—	4	1	no	—
354	C₄⋊C₄	—	94	1	no	—
355	C₄⋊C₄	—	94	1	no	—
356	C₄⋊C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
357	C₂²⋊C₄	—	2	2	no	—
358	C₂²⋊C₄	—	2	2	no	—
359	C₂²⋊C₄	—	4	1	no	—
360	C₂²⋊C₄	—	188	1	no	—
361	C₂²⋊C₄	—	188	1	no	—
362	C₄²	—	4	1	no	—
363	C₄²	D₄×D₄₇	1	1	yes	characteristic
364	C₄²	#10625352	1	1	yes	characteristic
365	C₄²	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
366	C₄²	C₂³×D₄₇	1	1	yes	characteristic
367	C₂³	—	2	4	no	—
368	C₂³	—	2	2	no	—
369	C₂³	—	8	1	no	—
370	C₂³	—	8	1	no	—
371	C₂³	—	188	1	no	—
372	C₂³	#13093996	1	1	yes	characteristic
373	Q₈	—	4	2	no	—
374	Q₈	—	4	2	no	—
375	Q₈	—	188	2	no	—
376	D₄	—	2	4	no	—
377	D₄	—	2	2	no	—
378	D₄	—	376	1	no	—
379	D₄	—	376	2	no	—
380	D₄	—	188	2	no	—
381	D₄	—	188	2	no	—
382	D₄	#13094044	1	4	yes	—
383	C₂×C₄	—	2	2	no	—
384	C₂×C₄	—	2	2	no	—
385	C₂×C₄	—	2	2	no	—
386	C₂×C₄	—	4	1	no	—
387	C₂×C₄	—	4	2	no	—
388	C₂×C₄	—	4	2	no	—
389	C₂×C₄	—	4	1	no	—
390	C₂×C₄	—	4	1	no	—
391	C₂×C₄	—	8	2	no	—
392	C₂×C₄	—	8	1	no	—
393	C₂×C₄	—	376	2	no	—
394	C₂×C₄	—	188	1	no	—
395	C₂×C₄	#13093996	1	1	yes	characteristic
396	C₂×C₄	#13093996	1	1	yes	characteristic
397	C₂×C₄	#13093996	1	1	yes	characteristic
398	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
399	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
400	C₂×C₄	C₂×#10625352	1	1	yes	characteristic
401	C₈	—	4	2	no	—
402	C₈	—	94	2	no	—
403	C₈	—	94	2	no	—
404	C₈	—	188	2	no	—
405	C₈	—	188	2	no	—
406	C₂²	—	2	1	no	—
407	C₂²	—	2	4	no	—
408	C₂²	—	2	1	no	—
409	C₂²	—	2	1	no	—
410	C₂²	—	4	2	no	—
411	C₂²	—	4	2	no	—
412	C₂²	—	8	4	no	—
413	C₂²	—	376	1	no	—
414	C₂²	—	376	1	no	—
415	C₂²	—	376	1	no	—
416	C₂²	C₂×#13093996	1	1	yes	characteristic
417	C₄	—	2	1	no	—
418	C₄	—	2	1	no	—
419	C₄	—	2	1	no	—
420	C₄	—	2	1	no	—
421	C₄	—	4	2	no	—
422	C₄	—	8	1	no	—
423	C₄	—	8	1	no	—
424	C₄	—	376	1	no	—
425	C₄	C₂×#13094044	1	2	yes	—
426	C₄	#15689927	1	2	yes	—
427	C₂	—	4	1	no	—
428	C₂	—	4	4	no	—
429	C₂	—	752	1	no	—
430	C₂	#20252893	1	1	yes	characteristic
431	C₂	#20252966	1	1	yes	characteristic
432	C₂	#20253122	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×#13093996
commutator, cosocle	C₄²×C₄₇	C₂⁴
Frattini	C₄²	C₂³×D₄₇
Fitting	C₄₇×#3110	C₂
socle	C₂²×C₄₇	C₂×#121
prime radical	#20253388	C₂
hypercenter	#3110	D₄₇
hypocenter	C₄₇	#19388
LCS	G ▷ C₄²×C₄₇ ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #3110

Complements

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

N	H ≅ G/N	type
1. #20254340	C₂	semidirect
3. #20252412	C₂	semidirect
4. #20242827	C₂	semidirect
5. #20242813	C₂	semidirect
6. #20242751	C₂	semidirect
7. #20242731	C₂	semidirect
8. #20242169	C₂	semidirect
9. #20242094	C₂	semidirect
10. #20242053	C₂	semidirect
11. C₄₇×#3110	C₂	semidirect
13. #15689502	C₂²	semidirect
14. #15689497	C₂²	semidirect
15. #15689475	C₂²	semidirect
16. #15689471	C₂²	semidirect
31. #15688875	C₂²	semidirect
32. #15688873	C₂²	semidirect
33. #15688869	C₂²	semidirect
34. #15688869	C₂²	semidirect
35. #15688868	C₂²	semidirect
36. #15688866	C₂²	semidirect
212. #3110	D₄₇	semidirect
261. C₄₇	#19388	semidirect

Maximal subgroups

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

subgroup	index
#20254340	2
#20253388	2
#20252412	2
#20242827	2
#20242813	2
#20242751	2
#20242731	2
#20242169	2
#20242094	2
#20242053	2
C₄₇×#3110	2
#19388	47