Subgroups — #26186399

Order 12032.

678 conjugacy classes of subgroups.

The subgroup lattice has 410 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20252464	C₂	1	1	yes	maximal, characteristic, complemented
2	#20252412	C₂	1	1	yes	maximal, characteristic, complemented
3	#20242253	C₂	1	2	yes	maximal, complemented
4	#20242218	C₂	1	2	yes	maximal, complemented
5	#20242212	C₂	1	2	yes	maximal, complemented
6	D₈×C₄₇⋊C₈	C₂	1	2	yes	maximal, complemented
7	#20242168	C₂	1	1	yes	maximal, characteristic, complemented
8	#20241831	C₂	1	1	yes	maximal, characteristic, complemented
9	#20241805	C₂	1	1	yes	maximal, characteristic, complemented
10	#20241683	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄₇×#3100	C₂	1	1	yes	maximal, characteristic
12	#15689201	C₂²	1	2	yes	complemented
13	#15689195	—	2	2	no	—
14	D₄×C₄₇⋊C₈	—	2	2	no	—
15	D₄×C₄₇⋊C₈	C₂²	1	2	yes	—
16	D₄×C₄₇⋊C₈	C₂²	1	2	yes	—
17	D₄×C₄₇⋊C₈	C₂²	1	2	yes	complemented
18	#15689180	C₂²	1	1	yes	characteristic
19	#15689176	C₂²	1	1	yes	characteristic
20	#15689176	C₂²	1	1	yes	characteristic
21	#15689090	—	2	2	no	—
22	C₂×C₂²⋊(C₄₇⋊C₈)	—	2	2	no	—
23	C₄×#10625329	C₂²	1	1	yes	characteristic
24	#15688876	C₂²	1	2	yes	complemented
25	#15688874	C₂²	1	2	yes	complemented
26	D₄⋊(C₄₇⋊C₈)	C₂²	1	2	yes	—
27	D₄⋊(C₄₇⋊C₈)	C₂²	1	2	yes	—
28	D₄⋊(C₄₇⋊C₈)	C₂²	1	2	yes	complemented
29	D₄⋊(C₄₇⋊C₈)	C₂²	1	2	yes	complemented
30	#15688845	C₂²	1	1	yes	characteristic, complemented
31	#15688845	C₂²	1	1	yes	characteristic, complemented
32	#15688844	C₂²	1	1	yes	characteristic, complemented
33	C₈×C₄₇⋊C₈	C₂²	1	1	yes	characteristic, complemented
34	C₄₇×#532	C₂²	1	1	yes	characteristic
35	C₂×C₄×D₄×C₄₇	C₂²	1	1	yes	characteristic
36	C₄₇×#480	C₄	1	2	yes	—
37	C₄₇×#474	C₄	1	2	yes	—
38	C₄₇×#459	C₄	1	2	yes	—
39	C₄₇×#447	C₄	1	2	yes	—
40	C₄×D₈×C₄₇	C₂²	1	2	yes	—
41	C₄×D₈×C₄₇	C₂²	1	2	yes	—
42	C₄₇×#431	C₂²	1	1	yes	characteristic
43	C₂×#10625329	—	2	1	no	—
44	C₂×#10625329	—	2	2	no	—
45	C₂²×C₄₇⋊C₈	—	2	2	no	—
46	C₂²×C₄₇⋊C₈	—	2	2	no	—
47	C₂²×C₄₇⋊C₈	—	2	2	no	—
48	C₄⋊(C₄₇⋊C₈)	D₄	1	2	yes	—
49	C₄⋊(C₄₇⋊C₈)	C₂³	1	2	yes	—
50	C₄⋊(C₄₇⋊C₈)	C₂³	1	2	yes	—
51	C₂²⋊(C₄₇⋊C₈)	—	2	1	no	—
52	C₂²⋊(C₄₇⋊C₈)	—	2	1	no	—
53	C₂²⋊(C₄₇⋊C₈)	—	2	2	no	—
54	C₂²⋊(C₄₇⋊C₈)	—	2	2	no	—
55	C₂²⋊(C₄₇⋊C₈)	—	2	2	no	—
56	C₂²⋊(C₄₇⋊C₈)	—	2	2	no	—
57	C₂²⋊(C₄₇⋊C₈)	D₄	1	2	yes	—
58	#13093935	—	2	1	no	—
59	#13093935	—	2	1	no	—
60	C₄×C₄₇⋊C₈	—	2	1	no	—
61	C₄×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
62	C₄×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
63	C₄×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
64	C₄×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
65	C₂×#41×C₄₇	—	2	1	no	—
66	C₂²×D₄×C₄₇	C₂×C₄	1	1	yes	characteristic
67	C₂³×C₄×C₄₇	—	2	1	no	—
68	C₂×D₈×C₄₇	C₂×C₄	1	2	yes	—
69	C₂×D₈×C₄₇	C₂×C₄	1	2	yes	—
70	C₄⋊Q₈×C₄₇	C₂×C₄	1	1	yes	characteristic
71	#127×C₄₇	C₂×C₄	1	1	yes	characteristic
72	#124×C₄₇	—	2	1	no	—
73	#121×C₄₇	—	2	1	no	—
74	#121×C₄₇	C₂×C₄	1	2	yes	—
75	C₄×D₄×C₄₇	—	2	1	no	—
76	C₄×D₄×C₄₇	—	2	1	no	—
77	C₄×D₄×C₄₇	—	2	1	no	—
78	C₄×D₄×C₄₇	C₂×C₄	1	2	yes	—
79	C₄×D₄×C₄₇	C₂³	1	2	yes	—
80	C₄×D₄×C₄₇	C₂³	1	2	yes	—
81	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
82	C₂×C₂²⋊C₄×C₄₇	—	2	1	no	—
83	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
84	#107×C₄₇	C₂×C₄	1	2	yes	—
85	#107×C₄₇	C₂×C₄	1	2	yes	—
86	C₄⋊C₈×C₄₇	C₂×C₄	1	2	yes	—
87	#102×C₄₇	C₂×C₄	1	2	yes	—
88	#102×C₄₇	C₂×C₄	1	2	yes	—
89	#102×C₄₇	C₂×C₄	1	2	yes	—
90	#102×C₄₇	C₂×C₄	1	2	yes	—
91	C₂²⋊C₈×C₄₇	C₂×C₄	1	2	yes	—
92	C₄×C₈×C₄₇	C₂³	1	1	yes	characteristic
93	C₄×C₈×C₄₇	C₂³	1	1	yes	characteristic
94	C₂⁴×C₄₇	—	2	1	no	—
95	#41×C₄₇	—	8	2	no	—
96	C₂×Q₈×C₄₇	—	2	1	no	—
97	C₂×D₄×C₄₇	—	2	4	no	—
98	C₂×D₄×C₄₇	—	2	2	no	—
99	C₂×D₄×C₄₇	—	2	1	no	—
100	C₂×D₄×C₄₇	—	2	1	no	—
101	C₂×D₄×C₄₇	—	2	1	no	—
102	C₂×D₄×C₄₇	C₂²×C₄	1	2	yes	—
103	C₂×D₄×C₄₇	C₂²×C₄	1	2	yes	—
104	C₂²×C₄×C₄₇	—	2	1	no	—
105	C₂²×C₄×C₄₇	—	2	2	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	C₂²×C₄	1	1	yes	characteristic
110	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
111	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
112	D₈×C₄₇	—	2	4	no	—
113	D₈×C₄₇	—	2	4	no	—
114	C₂×C₈×C₄₇	C₂²×C₄	1	2	yes	—
115	C₂×C₈×C₄₇	C₂²×C₄	1	2	yes	—
116	C₄⋊C₄×C₄₇	—	2	1	no	—
117	C₄⋊C₄×C₄₇	—	2	1	no	—
118	C₄⋊C₄×C₄₇	C₂²×C₄	1	2	yes	—
119	C₄⋊C₄×C₄₇	C₂²×C₄	1	2	yes	—
120	C₂²⋊C₄×C₄₇	—	2	2	no	—
121	C₂²⋊C₄×C₄₇	—	2	2	no	—
122	C₂²⋊C₄×C₄₇	—	2	2	no	—
123	C₂²⋊C₄×C₄₇	—	2	2	no	—
124	C₄²×C₄₇	C₂²×C₄	1	1	yes	characteristic
125	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
126	C₄²×C₄₇	#41	1	1	yes	characteristic
127	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
128	#10625329	—	4	2	no	—
129	#10625329	—	8	2	no	—
130	C₂×C₄₇⋊C₈	—	2	1	no	—
131	C₂×C₄₇⋊C₈	—	2	2	no	—
132	C₂×C₄₇⋊C₈	—	2	2	no	—
133	C₂×C₄₇⋊C₈	—	2	1	no	—
134	C₂×C₄₇⋊C₈	—	8	2	no	—
135	C₂×C₄₇⋊C₈	—	8	2	no	—
136	C₂×C₄₇⋊C₈	—	8	2	no	—
137	C₂×C₄₇⋊C₈	C₂×D₄	1	2	yes	—
138	C₂×C₄₇⋊C₈	C₂×D₄	1	2	yes	—
139	C₂³×C₄₇	—	2	4	no	—
140	C₂³×C₄₇	—	2	2	no	—
141	C₂³×C₄₇	—	2	2	no	—
142	C₂³×C₄₇	—	8	1	no	—
143	C₂³×C₄₇	—	8	1	no	—
144	C₂³×C₄₇	C₄×D₄	1	1	yes	characteristic
145	Q₈×C₄₇	—	8	1	no	—
146	D₄×C₄₇	—	2	4	no	—
147	D₄×C₄₇	—	2	2	no	—
148	D₄×C₄₇	—	2	2	no	—
149	D₄×C₄₇	—	2	2	no	—
150	D₄×C₄₇	—	8	1	no	—
151	D₄×C₄₇	—	8	1	no	—
152	D₄×C₄₇	—	8	2	no	—
153	D₄×C₄₇	#131	1	4	yes	—
154	C₂×C₄×C₄₇	—	2	2	no	—
155	C₂×C₄×C₄₇	—	2	2	no	—
156	C₂×C₄×C₄₇	—	2	2	no	—
157	C₂×C₄×C₄₇	—	2	2	no	—
158	C₂×C₄×C₄₇	—	4	1	no	—
159	C₂×C₄×C₄₇	—	4	2	no	—
160	C₂×C₄×C₄₇	—	4	2	no	—
161	C₂×C₄×C₄₇	—	4	2	no	—
162	C₂×C₄×C₄₇	—	4	2	no	—
163	C₂×C₄×C₄₇	—	8	2	no	—
164	C₂×C₄×C₄₇	—	8	1	no	—
165	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
166	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
167	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
168	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
169	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
170	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
171	C₈×C₄₇	—	2	2	no	—
172	C₈×C₄₇	—	2	2	no	—
173	C₄₇⋊C₈	—	2	2	no	—
174	C₄₇⋊C₈	—	2	2	no	—
175	C₄₇⋊C₈	—	2	2	no	—
176	C₄₇⋊C₈	—	4	1	no	—
177	C₄₇⋊C₈	—	4	2	no	—
178	C₄₇⋊C₈	—	4	2	no	—
179	#17922	—	47	1	no	maximal, Sylow
180	C₂²×C₄₇	—	2	1	no	—
181	C₂²×C₄₇	—	2	4	no	—
182	C₂²×C₄₇	—	2	1	no	—
183	C₂²×C₄₇	—	2	1	no	—
184	C₂²×C₄₇	—	4	2	no	—
185	C₂²×C₄₇	—	4	2	no	—
186	C₂²×C₄₇	—	4	2	no	—
187	C₂²×C₄₇	—	4	2	no	—
188	C₂²×C₄₇	—	4	2	no	—
189	C₂²×C₄₇	—	8	4	no	—
190	C₂²×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
191	C₄×C₄₇	—	2	1	no	—
192	C₄×C₄₇	—	2	1	no	—
193	C₄×C₄₇	—	2	1	no	—
194	C₄×C₄₇	—	2	1	no	—
195	C₄×C₄₇	—	4	2	no	—
196	C₄×C₄₇	—	4	2	no	—
197	C₄×C₄₇	C₂×#131	1	2	yes	—
198	C₄×C₄₇	#576	1	2	yes	—
199	#3100	D₄₇	1	1	yes	characteristic
200	#2981	—	47	1	no	—
201	#2972	—	47	1	no	—
202	#1586	—	47	2	no	—
203	#1581	—	47	2	no	—
204	#1580	—	47	2	no	—
205	C₈×D₈	—	47	2	no	—
206	#1572	—	47	1	no	—
207	#1490	—	47	1	no	—
208	#1484	—	47	1	no	—
209	#1453	—	47	1	no	—
210	C₂×C₄₇	—	4	1	no	—
211	C₂×C₄₇	—	4	4	no	—
212	C₂×C₄₇	—	8	2	no	—
213	C₂×C₄₇	#2929	1	1	yes	characteristic
214	C₂×C₄₇	#2948	1	1	yes	characteristic
215	C₂×C₄₇	#2956	1	1	yes	characteristic
216	#532	C₂×D₄₇	1	1	yes	characteristic
217	C₂×C₄×D₄	C₂×D₄₇	1	1	yes	characteristic
218	#480	Dic₄₇	1	2	yes	—
219	#474	Dic₄₇	1	2	yes	—
220	#459	Dic₄₇	1	2	yes	—
221	#447	Dic₄₇	1	2	yes	—
222	C₄×D₈	C₂×D₄₇	1	2	yes	—
223	C₄×D₈	C₂×D₄₇	1	2	yes	—
224	#436	—	47	2	no	—
225	#435	—	94	2	no	—
226	C₈×D₄	—	47	2	no	—
227	C₈×D₄	—	47	2	no	—
228	C₈×D₄	—	47	2	no	—
229	C₈×D₄	—	94	2	no	—
230	#432	—	47	1	no	—
231	#431	—	47	1	no	—
232	#431	—	47	1	no	—
233	#431	C₂×D₄₇	1	1	yes	characteristic
234	#408	—	94	2	no	—
235	C₂×C₂²⋊C₈	—	94	2	no	—
236	C₄×M₁₆	—	47	1	no	—
237	#335	—	47	2	no	—
238	#334	—	47	2	no	—
239	D₄⋊C₈	—	47	2	no	—
240	D₄⋊C₈	—	47	2	no	—
241	D₄⋊C₈	—	47	2	no	—
242	D₄⋊C₈	—	47	2	no	—
243	#322	—	47	1	no	—
244	#322	—	47	1	no	—
245	#322	—	47	1	no	—
246	C₈²	—	47	1	no	—
247	C₄₇	#17922	1	1	yes	characteristic, complemented, Sylow
248	C₂×#41	—	2	1	no	—
249	C₂²×D₄	C₂×Dic₄₇	1	1	yes	characteristic
250	C₂³×C₄	—	2	1	no	—
251	C₂×D₈	C₂×Dic₄₇	1	2	yes	—
252	C₂×D₈	C₂×Dic₄₇	1	2	yes	—
253	C₂×M₁₆	—	94	2	no	—
254	C₂×M₁₆	—	94	1	no	—
255	C₂²×C₈	—	94	2	no	—
256	C₂²×C₈	—	94	2	no	—
257	C₂²×C₈	—	94	2	no	—
258	C₄⋊Q₈	C₂×Dic₄₇	1	1	yes	characteristic
259	#127	C₂×Dic₄₇	1	1	yes	characteristic
260	#124	—	2	1	no	—
261	#121	—	2	1	no	—
262	#121	C₂×Dic₄₇	1	2	yes	—
263	C₄×D₄	—	2	1	no	—
264	C₄×D₄	—	2	1	no	—
265	C₄×D₄	—	2	1	no	—
266	C₄×D₄	C₂×Dic₄₇	1	2	yes	—
267	C₄×D₄	C₂²×D₄₇	1	2	yes	—
268	C₄×D₄	C₂²×D₄₇	1	2	yes	—
269	C₂×C₄⋊C₄	C₂×Dic₄₇	1	1	yes	characteristic
270	C₂×C₂²⋊C₄	—	2	1	no	—
271	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
272	#107	C₂×Dic₄₇	1	2	yes	—
273	#107	C₂×Dic₄₇	1	2	yes	—
274	C₄⋊C₈	—	47	2	no	—
275	C₄⋊C₈	—	47	2	no	—
276	C₄⋊C₈	—	47	2	no	—
277	C₄⋊C₈	C₂×Dic₄₇	1	2	yes	—
278	#102	C₂×Dic₄₇	1	2	yes	—
279	#102	C₂×Dic₄₇	1	2	yes	—
280	#102	C₂×Dic₄₇	1	2	yes	—
281	#102	C₂×Dic₄₇	1	2	yes	—
282	C₂²⋊C₈	—	47	2	no	—
283	C₂²⋊C₈	—	94	2	no	—
284	C₂²⋊C₈	—	94	2	no	—
285	C₂²⋊C₈	—	94	2	no	—
286	C₂²⋊C₈	—	94	2	no	—
287	C₂²⋊C₈	—	94	1	no	—
288	C₂²⋊C₈	—	94	1	no	—
289	C₂²⋊C₈	C₂×Dic₄₇	1	2	yes	—
290	#97	—	94	1	no	—
291	#97	—	94	1	no	—
292	C₄×C₈	—	47	1	no	—
293	C₄×C₈	—	47	1	no	—
294	C₄×C₈	—	47	1	no	—
295	C₄×C₈	—	47	1	no	—
296	C₄×C₈	—	94	1	no	—
297	C₄×C₈	C₂²×D₄₇	1	1	yes	characteristic
298	C₄×C₈	C₂²×D₄₇	1	1	yes	characteristic
299	C₂⁴	—	2	1	no	—
300	#41	—	8	2	no	—
301	C₂×Q₈	—	2	1	no	—
302	C₂×D₄	—	2	4	no	—
303	C₂×D₄	—	2	2	no	—
304	C₂×D₄	—	2	1	no	—
305	C₂×D₄	—	2	1	no	—
306	C₂×D₄	—	2	1	no	—
307	C₂×D₄	C₂²×Dic₄₇	1	2	yes	—
308	C₂×D₄	C₂²×Dic₄₇	1	2	yes	—
309	C₂²×C₄	—	2	1	no	—
310	C₂²×C₄	—	2	2	no	—
311	C₂²×C₄	—	2	2	no	—
312	C₂²×C₄	—	2	2	no	—
313	C₂²×C₄	—	8	2	no	—
314	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
315	C₂²×C₄	#10625352	1	1	yes	characteristic
316	C₂²×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
317	D₈	—	2	4	no	—
318	D₈	—	2	4	no	—
319	M₁₆	—	376	2	no	—
320	M₁₆	—	188	2	no	—
321	C₂×C₈	—	47	2	no	—
322	C₂×C₈	—	47	2	no	—
323	C₂×C₈	—	94	1	no	—
324	C₂×C₈	—	94	2	no	—
325	C₂×C₈	—	94	2	no	—
326	C₂×C₈	—	94	1	no	—
327	C₂×C₈	—	376	2	no	—
328	C₂×C₈	—	376	2	no	—
329	C₂×C₈	—	376	2	no	—
330	C₂×C₈	C₂²×Dic₄₇	1	2	yes	—
331	C₂×C₈	C₂²×Dic₄₇	1	2	yes	—
332	C₄⋊C₄	—	2	1	no	—
333	C₄⋊C₄	—	2	1	no	—
334	C₄⋊C₄	C₂²×Dic₄₇	1	2	yes	—
335	C₄⋊C₄	C₂²×Dic₄₇	1	2	yes	—
336	C₂²⋊C₄	—	2	2	no	—
337	C₂²⋊C₄	—	2	2	no	—
338	C₂²⋊C₄	—	2	2	no	—
339	C₂²⋊C₄	—	2	2	no	—
340	C₄²	D₄×D₄₇	1	1	yes	characteristic
341	C₄²	#10625352	1	1	yes	characteristic
342	C₄²	C₂²×Dic₄₇	1	1	yes	characteristic
343	C₄²	C₂³×D₄₇	1	1	yes	characteristic
344	C₂³	—	2	4	no	—
345	C₂³	—	2	2	no	—
346	C₂³	—	2	2	no	—
347	C₂³	—	8	1	no	—
348	C₂³	—	8	1	no	—
349	C₂³	D₄×Dic₄₇	1	1	yes	characteristic
350	Q₈	—	8	1	no	—
351	D₄	—	2	4	no	—
352	D₄	—	2	2	no	—
353	D₄	—	2	2	no	—
354	D₄	—	2	2	no	—
355	D₄	—	8	1	no	—
356	D₄	—	8	1	no	—
357	D₄	—	8	2	no	—
358	D₄	#13094031	1	4	yes	—
359	C₂×C₄	—	2	2	no	—
360	C₂×C₄	—	2	2	no	—
361	C₂×C₄	—	2	2	no	—
362	C₂×C₄	—	2	2	no	—
363	C₂×C₄	—	4	1	no	—
364	C₂×C₄	—	4	2	no	—
365	C₂×C₄	—	4	2	no	—
366	C₂×C₄	—	4	2	no	—
367	C₂×C₄	—	4	2	no	—
368	C₂×C₄	—	8	2	no	—
369	C₂×C₄	—	8	1	no	—
370	C₂×C₄	D₄×Dic₄₇	1	1	yes	characteristic
371	C₂×C₄	D₄×Dic₄₇	1	1	yes	characteristic
372	C₂×C₄	D₄×Dic₄₇	1	1	yes	characteristic
373	C₂×C₄	C₂³×Dic₄₇	1	1	yes	characteristic
374	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
375	C₂×C₄	C₂×#10625352	1	1	yes	characteristic
376	C₈	—	2	2	no	—
377	C₈	—	2	2	no	—
378	C₈	—	94	2	no	—
379	C₈	—	94	2	no	—
380	C₈	—	94	2	no	—
381	C₈	—	188	1	no	—
382	C₈	—	188	2	no	—
383	C₈	—	188	2	no	—
384	C₂²	—	2	1	no	—
385	C₂²	—	2	1	no	—
386	C₂²	—	2	1	no	—
387	C₂²	—	2	4	no	—
388	C₂²	—	4	2	no	—
389	C₂²	—	4	2	no	—
390	C₂²	—	4	2	no	—
391	C₂²	—	4	2	no	—
392	C₂²	—	4	2	no	—
393	C₂²	—	8	4	no	—
394	C₂²	C₂×D₄×Dic₄₇	1	1	yes	characteristic
395	C₄	—	2	1	no	—
396	C₄	—	2	1	no	—
397	C₄	—	2	1	no	—
398	C₄	—	2	1	no	—
399	C₄	—	4	2	no	—
400	C₄	—	4	2	no	—
401	C₄	C₂×#13094031	1	2	yes	—
402	C₄	#15689924	1	2	yes	—
403	C₂	—	4	1	no	—
404	C₂	—	4	4	no	—
405	C₂	—	8	2	no	—
406	C₂	#20252083	1	1	yes	characteristic
407	C₂	#20252240	1	1	yes	characteristic
408	C₂	#20252298	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₄₇
commutator	C₂×C₄×C₄₇	C₂³×C₄
Frattini	C₄²	C₂³×D₄₇
Fitting, prime radical	C₄₇×#3100	C₂
socle	C₂²×C₄₇	C₂×C₄×D₄
cosocle	C₄²×C₄₇	C₂⁴
hypercenter	#3100	D₄₇
hypocenter	C₄₇	#17922
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #3100

Complements

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

N	H ≅ G/N	type
1. #20252464	C₂	semidirect
2. #20252412	C₂	semidirect
3. #20242253	C₂	semidirect
4. #20242218	C₂	semidirect
5. #20242212	C₂	semidirect
6. D₈×C₄₇⋊C₈	C₂	semidirect
7. #20242168	C₂	semidirect
8. #20241831	C₂	semidirect
9. #20241805	C₂	semidirect
10. #20241683	C₂	semidirect
12. #15689201	C₂²	semidirect
17. D₄×C₄₇⋊C₈	C₂²	semidirect
24. #15688876	C₂²	semidirect
25. #15688874	C₂²	semidirect
28. D₄⋊(C₄₇⋊C₈)	C₂²	semidirect
29. D₄⋊(C₄₇⋊C₈)	C₂²	semidirect
30. #15688845	C₂²	semidirect
31. #15688845	C₂²	semidirect
32. #15688844	C₂²	semidirect
33. C₈×C₄₇⋊C₈	C₂²	semidirect
247. C₄₇	#17922	semidirect

Maximal subgroups

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

subgroup	index
#20252464	2
#20252412	2
#20242253	2
#20242218	2
#20242212	2
D₈×C₄₇⋊C₈	2
#20242168	2
#20241831	2
#20241805	2
#20241683	2
C₄₇×#3100	2
#17922	47