Subgroups — #26117346

Order 12032.

746 conjugacy classes of subgroups.

The subgroup lattice has 440 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#15689495	C₂	1	1	yes	maximal, characteristic, complemented
2	#20248561	C₂	1	1	yes	maximal, characteristic, complemented
3	#20244316	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#15688871	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×D₄⋊(C₄₇⋊C₈)	C₂	1	1	yes	maximal, characteristic, complemented
6	#20241227	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₄₇×#459	C₂	1	1	yes	maximal, characteristic
8	C₂²×#10625335	—	2	2	no	—
9	C₂×#13094024	C₂²	1	1	yes	characteristic
10	#15689495	—	2	2	no	—
11	#15689495	—	2	2	no	—
12	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
13	C₂×#13093945	—	2	2	no	—
14	C₂×C₄×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
15	#15689035	—	2	2	no	—
16	#15689026	—	2	1	no	—
17	#15688988	—	2	1	no	—
18	#15688983	—	2	2	no	—
19	C₄×C₄⋊Dic₄₇	C₂²	1	1	yes	characteristic
20	#15688871	—	2	2	no	—
21	D₄⋊(C₄₇⋊C₈)	—	2	2	no	—
22	C₂²×D₈×C₄₇	—	2	1	no	—
23	C₂×#127×C₄₇	C₂²	1	1	yes	characteristic
24	C₂×C₄×D₄×C₄₇	C₂²	1	1	yes	characteristic
25	C₄₇×#459	—	2	2	no	—
26	C₄₇×#459	—	2	2	no	—
27	C₂×C₄⋊C₈×C₄₇	C₂²	1	1	yes	characteristic
28	C₂×#102×C₄₇	—	2	1	no	—
29	C₂²×Dic₉₄	D₄	1	2	yes	—
30	C₂×#10625335	—	2	8	no	—
31	C₂×#10625335	—	4	8	no	—
32	C₂²×C₄₇⋊C₈	—	2	1	no	—
33	C₂²×C₄₇⋊C₈	—	2	1	no	—
34	#13094024	—	2	1	no	—
35	#13094024	—	2	1	no	—
36	#13094024	—	2	1	no	—
37	#13094024	—	2	1	no	—
38	C₂×C₄⋊Dic₄₇	—	2	1	no	—
39	C₂×C₄⋊Dic₄₇	—	2	1	no	—
40	C₂×C₄⋊Dic₄₇	D₄	1	2	yes	—
41	C₂×C₂²⋊Dic₄₇	—	2	4	no	—
42	C₂×C₄×Dic₄₇	—	2	1	no	—
43	C₄⋊(C₄₇⋊C₈)	—	2	1	no	—
44	C₄⋊(C₄₇⋊C₈)	—	2	1	no	—
45	#13093945	—	4	4	no	—
46	C₄×C₄₇⋊C₈	—	2	1	no	—
47	C₄×C₄₇⋊C₈	D₄	1	2	yes	—
48	C₄₇⋊#95	—	2	4	no	—
49	C₄₇⋊#95	—	2	1	no	—
50	C₂²×D₄×C₄₇	—	2	1	no	—
51	C₂²×D₄×C₄₇	—	2	1	no	—
52	C₂²×D₄×C₄₇	—	2	1	no	—
53	C₂²×D₄×C₄₇	D₄	1	1	yes	characteristic
54	C₂³×C₄×C₄₇	—	2	1	no	—
55	C₂×D₈×C₄₇	—	2	4	no	—
56	C₂×D₈×C₄₇	—	4	2	no	—
57	C₂×D₈×C₄₇	—	4	2	no	—
58	C₂²×C₈×C₄₇	—	2	1	no	—
59	#127×C₄₇	—	2	1	no	—
60	#127×C₄₇	—	2	1	no	—
61	#127×C₄₇	—	2	1	no	—
62	#127×C₄₇	D₄	1	2	yes	—
63	C₄×D₄×C₄₇	—	2	1	no	—
64	C₄×D₄×C₄₇	—	2	1	no	—
65	C₄×D₄×C₄₇	—	2	1	no	—
66	C₄×D₄×C₄₇	—	2	1	no	—
67	C₂×C₄⋊C₄×C₄₇	D₄	1	1	yes	characteristic
68	C₂×C₂²⋊C₄×C₄₇	—	2	1	no	—
69	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
70	C₄⋊C₈×C₄₇	—	2	1	no	—
71	C₄⋊C₈×C₄₇	D₄	1	2	yes	—
72	#102×C₄₇	—	2	4	no	—
73	C₂⁴×C₄₇	—	2	1	no	—
74	C₂⁴×C₄₇	—	4	1	no	—
75	C₂×D₄×C₄₇	—	2	1	no	—
76	C₂×D₄×C₄₇	—	2	2	no	—
77	C₂×D₄×C₄₇	—	2	2	no	—
78	C₂×D₄×C₄₇	—	2	1	no	—
79	C₂×D₄×C₄₇	—	2	2	no	—
80	C₂×D₄×C₄₇	—	2	1	no	—
81	C₂×D₄×C₄₇	—	2	1	no	—
82	C₂×D₄×C₄₇	—	2	1	no	—
83	C₂×D₄×C₄₇	—	4	4	no	—
84	C₂×D₄×C₄₇	—	4	1	no	—
85	C₂×D₄×C₄₇	—	4	1	no	—
86	C₂×D₄×C₄₇	—	4	1	no	—
87	C₂×D₄×C₄₇	—	4	1	no	—
88	C₂×D₄×C₄₇	—	4	2	no	—
89	C₂×D₄×C₄₇	—	4	1	no	—
90	C₂×D₄×C₄₇	—	4	1	no	—
91	C₂×D₄×C₄₇	—	4	2	no	—
92	C₂×D₄×C₄₇	—	4	1	no	—
93	C₂×D₄×C₄₇	SD₁₆	1	2	yes	complemented
94	C₂²×C₄×C₄₇	—	2	1	no	—
95	C₂²×C₄×C₄₇	—	4	1	no	—
96	C₂²×C₄×C₄₇	—	4	1	no	—
97	C₂²×C₄×C₄₇	—	4	2	no	—
98	C₂²×C₄×C₄₇	—	4	2	no	—
99	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
100	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
101	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
102	C₂²×Dic₄₇	—	2	2	no	—
103	C₂²×Dic₄₇	—	2	2	no	—
104	C₂×Dic₉₄	—	2	2	no	—
105	C₂×Dic₉₄	—	2	2	no	—
106	C₂×Dic₉₄	—	4	4	no	—
107	D₈×C₄₇	—	4	8	no	—
108	C₂×C₈×C₄₇	—	2	2	no	—
109	C₂×C₈×C₄₇	—	4	1	no	—
110	C₂×C₈×C₄₇	—	4	1	no	—
111	C₄⋊C₄×C₄₇	—	2	1	no	—
112	C₄⋊C₄×C₄₇	—	2	1	no	—
113	C₂²⋊C₄×C₄₇	—	4	1	no	—
114	C₂²⋊C₄×C₄₇	—	4	1	no	—
115	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
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	C₂²⋊Dic₄₇	—	8	4	no	—
120	#10625335	—	4	16	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	C₄⋊Dic₄₇	—	4	1	no	—
126	C₄⋊Dic₄₇	—	4	1	no	—
127	C₄×Dic₄₇	—	4	1	no	—
128	C₄×Dic₄₇	—	4	1	no	—
129	C₂×C₄₇⋊C₈	—	2	4	no	—
130	C₂×C₄₇⋊C₈	—	2	2	no	—
131	C₂×C₄₇⋊C₈	—	4	1	no	—
132	C₂×C₄₇⋊C₈	—	4	2	no	—
133	C₂³×C₄₇	—	2	2	no	—
134	C₂³×C₄₇	—	4	1	no	—
135	C₂³×C₄₇	—	4	2	no	—
136	C₂³×C₄₇	—	4	1	no	—
137	C₂³×C₄₇	—	4	2	no	—
138	C₂³×C₄₇	—	4	2	no	—
139	C₂³×C₄₇	—	8	1	no	—
140	C₂³×C₄₇	—	8	2	no	—
141	C₂³×C₄₇	—	8	1	no	—
142	C₂³×C₄₇	—	8	2	no	—
143	C₂³×C₄₇	#120	1	1	yes	characteristic
144	D₄×C₄₇	—	2	2	no	—
145	D₄×C₄₇	—	2	2	no	—
146	D₄×C₄₇	—	4	4	no	—
147	D₄×C₄₇	—	4	2	no	—
148	D₄×C₄₇	—	4	1	no	—
149	D₄×C₄₇	—	4	2	no	—
150	D₄×C₄₇	—	4	4	no	—
151	D₄×C₄₇	—	4	1	no	—
152	D₄×C₄₇	—	8	2	no	—
153	D₄×C₄₇	—	8	1	no	—
154	D₄×C₄₇	—	8	1	no	—
155	D₄×C₄₇	—	8	1	no	—
156	D₄×C₄₇	—	8	1	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	—	8	2	no	—
161	C₂×C₄×C₄₇	—	8	1	no	—
162	C₂×C₄×C₄₇	—	8	1	no	—
163	C₂×C₄×C₄₇	#120	1	1	yes	characteristic
164	C₂×C₄×C₄₇	#120	1	1	yes	characteristic
165	C₂×C₄×C₄₇	#121	1	1	yes	characteristic
166	C₂×C₄×C₄₇	#121	1	1	yes	characteristic
167	C₂×C₄×C₄₇	#121	1	1	yes	characteristic
168	C₂×C₄×C₄₇	#127	1	1	yes	characteristic
169	C₂×C₄×C₄₇	C₂×SD₁₆	1	1	yes	characteristic
170	C₂×C₄×C₄₇	#135	1	2	yes	—
171	C₂×C₄×C₄₇	#135	1	1	yes	characteristic
172	C₂×C₄×C₄₇	AGL(1,ℤ/8)	1	2	yes	—
173	C₂×C₄×C₄₇	AGL(1,ℤ/8)	1	1	yes	characteristic
174	C₂×C₄×C₄₇	#137	1	1	yes	characteristic
175	C₂×Dic₄₇	—	4	2	no	—
176	C₂×Dic₄₇	—	4	2	no	—
177	C₂×Dic₄₇	—	4	2	no	—
178	C₂×Dic₄₇	—	4	2	no	—
179	C₂×Dic₄₇	—	4	4	no	—
180	Dic₉₄	—	4	4	no	—
181	Dic₉₄	—	8	2	no	—
182	C₈×C₄₇	—	4	2	no	—
183	C₄₇⋊C₈	—	2	4	no	—
184	C₄₇⋊C₈	—	8	1	no	—
185	#10048	—	47	1	no	maximal, Sylow
186	C₂²×C₄₇	—	4	4	no	—
187	C₂²×C₄₇	—	4	2	no	—
188	C₂²×C₄₇	—	8	2	no	—
189	C₂²×C₄₇	—	8	1	no	—
190	C₂²×C₄₇	—	8	1	no	—
191	C₂²×C₄₇	—	8	2	no	—
192	C₂²×C₄₇	—	8	2	no	—
193	C₂²×C₄₇	—	8	2	no	—
194	C₂²×C₄₇	—	16	2	no	—
195	C₂²×C₄₇	—	16	2	no	—
196	C₂²×C₄₇	#392	1	1	yes	characteristic
197	C₂²×C₄₇	#448	1	1	yes	characteristic
198	C₂²×C₄₇	#449	1	2	yes	—
199	C₂²×C₄₇	#449	1	1	yes	characteristic
200	C₂²×C₄₇	#453	1	2	yes	—
201	C₄×C₄₇	—	2	1	no	—
202	C₄×C₄₇	—	2	1	no	—
203	C₄×C₄₇	—	8	1	no	—
204	C₄×C₄₇	#450	1	1	yes	characteristic
205	C₄×C₄₇	#452	1	1	yes	characteristic
206	C₄×C₄₇	#463	1	2	yes	—
207	C₄×C₄₇	#465	1	1	yes	characteristic
208	C₄×C₄₇	#468	1	1	yes	characteristic
209	C₄×C₄₇	#495	1	1	yes	characteristic
210	C₄×C₄₇	#496	1	1	yes	characteristic
211	Dic₄₇	—	8	2	no	—
212	Dic₄₇	—	8	2	no	—
213	C₂×#492	—	47	1	no	—
214	C₂×#459	D₄₇	1	1	yes	characteristic
215	#2563	—	47	1	no	—
216	#1982	—	47	1	no	—
217	C₂×#333	—	47	1	no	—
218	C₂×D₄⋊C₈	—	47	1	no	—
219	#1279	—	47	1	no	—
220	C₂×C₄₇	—	8	2	no	—
221	C₂×C₄₇	—	16	2	no	—
222	C₂×C₄₇	#1622	1	2	yes	—
223	C₂×C₄₇	#1624	1	2	yes	—
224	C₂×C₄₇	#2000	1	1	yes	characteristic
225	C₂×C₄₇	#2002	1	1	yes	characteristic
226	C₂×C₄₇	#2012	1	1	yes	characteristic
227	C₂²×SD₁₆	—	94	2	no	—
228	C₂²×D₈	—	2	1	no	—
229	C₂×C₄⋊Q₈	—	47	1	no	—
230	C₂×#127	C₂×D₄₇	1	1	yes	characteristic
231	C₂×C₄×D₄	C₂×D₄₇	1	1	yes	characteristic
232	#492	—	94	2	no	—
233	#492	—	94	2	no	—
234	#459	—	2	2	no	—
235	#459	—	2	2	no	—
236	C₂×C₄⋊C₈	—	47	1	no	—
237	C₂×C₄⋊C₈	C₂×D₄₇	1	1	yes	characteristic
238	C₂×#102	—	2	1	no	—
239	C₂×#102	—	94	2	no	—
240	C₂×C₄×C₈	—	47	1	no	—
241	#393	—	94	2	no	—
242	#390	—	94	1	no	—
243	#382	—	94	1	no	—
244	#380	—	94	2	no	—
245	C₄×C₄⋊C₄	—	47	1	no	—
246	#333	—	94	2	no	—
247	D₄⋊C₈	—	94	2	no	—
248	C₄₇	#10048	1	1	yes	characteristic, complemented, Sylow
249	C₂²×Q₈	—	47	2	no	—
250	C₂²×D₄	—	2	1	no	—
251	C₂²×D₄	—	2	1	no	—
252	C₂²×D₄	—	2	1	no	—
253	C₂²×D₄	C₂²⋊D₄₇	1	1	yes	characteristic
254	C₂³×C₄	—	2	1	no	—
255	C₂×SD₁₆	—	94	8	no	—
256	C₂×SD₁₆	—	188	8	no	—
257	C₂×D₈	—	2	4	no	—
258	C₂×D₈	—	4	2	no	—
259	C₂×D₈	—	4	2	no	—
260	C₂²×C₈	—	2	1	no	—
261	C₂²×C₈	—	94	1	no	—
262	C₂²×C₈	—	94	1	no	—
263	C₄⋊Q₈	—	94	1	no	—
264	C₄⋊Q₈	—	94	1	no	—
265	C₄⋊Q₈	—	94	1	no	—
266	C₄⋊Q₈	—	94	1	no	—
267	#127	—	2	1	no	—
268	#127	—	2	1	no	—
269	#127	—	2	1	no	—
270	#127	C₂²⋊D₄₇	1	2	yes	—
271	C₄×D₄	—	2	1	no	—
272	C₄×D₄	—	2	1	no	—
273	C₄×D₄	—	2	1	no	—
274	C₄×D₄	—	2	1	no	—
275	C₂×C₄⋊C₄	—	47	2	no	—
276	C₂×C₄⋊C₄	—	94	1	no	—
277	C₂×C₄⋊C₄	—	94	1	no	—
278	C₂×C₄⋊C₄	C₂²⋊D₄₇	1	1	yes	characteristic
279	C₂×C₂²⋊C₄	—	2	1	no	—
280	C₂×C₂²⋊C₄	—	94	4	no	—
281	C₂×C₄²	—	94	1	no	—
282	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
283	C₄⋊C₈	—	2	1	no	—
284	C₄⋊C₈	—	94	1	no	—
285	C₄⋊C₈	—	94	1	no	—
286	C₄⋊C₈	C₂²⋊D₄₇	1	2	yes	—
287	#102	—	2	4	no	—
288	#102	—	188	4	no	—
289	C₄×C₈	—	47	2	no	—
290	C₄×C₈	—	94	1	no	—
291	#95	—	94	4	no	—
292	#95	—	94	1	no	—
293	C₂⁴	—	2	1	no	—
294	C₂⁴	—	4	1	no	—
295	C₂×Q₈	—	94	2	no	—
296	C₂×Q₈	—	94	2	no	—
297	C₂×Q₈	—	188	4	no	—
298	C₂×D₄	—	2	2	no	—
299	C₂×D₄	—	2	1	no	—
300	C₂×D₄	—	2	2	no	—
301	C₂×D₄	—	2	1	no	—
302	C₂×D₄	—	2	2	no	—
303	C₂×D₄	—	2	1	no	—
304	C₂×D₄	—	2	1	no	—
305	C₂×D₄	—	2	1	no	—
306	C₂×D₄	—	4	4	no	—
307	C₂×D₄	—	4	1	no	—
308	C₂×D₄	—	4	1	no	—
309	C₂×D₄	—	4	1	no	—
310	C₂×D₄	—	4	1	no	—
311	C₂×D₄	—	4	2	no	—
312	C₂×D₄	—	4	1	no	—
313	C₂×D₄	—	4	2	no	—
314	C₂×D₄	—	4	1	no	—
315	C₂×D₄	—	4	1	no	—
316	C₂×D₄	#10625335	1	2	yes	complemented
317	C₂²×C₄	—	2	1	no	—
318	C₂²×C₄	—	4	1	no	—
319	C₂²×C₄	—	4	1	no	—
320	C₂²×C₄	—	4	2	no	—
321	C₂²×C₄	—	4	2	no	—
322	C₂²×C₄	—	94	2	no	—
323	C₂²×C₄	—	94	2	no	—
324	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
325	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
326	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
327	SD₁₆	—	188	16	no	—
328	D₈	—	4	8	no	—
329	C₂×C₈	—	2	2	no	—
330	C₂×C₈	—	4	1	no	—
331	C₂×C₈	—	4	1	no	—
332	C₂×C₈	—	94	4	no	—
333	C₂×C₈	—	94	2	no	—
334	C₂×C₈	—	188	1	no	—
335	C₂×C₈	—	188	2	no	—
336	C₄⋊C₄	—	2	1	no	—
337	C₄⋊C₄	—	2	1	no	—
338	C₄⋊C₄	—	94	2	no	—
339	C₄⋊C₄	—	94	2	no	—
340	C₄⋊C₄	—	188	1	no	—
341	C₄⋊C₄	—	188	1	no	—
342	C₄⋊C₄	—	188	1	no	—
343	C₄⋊C₄	—	188	1	no	—
344	C₂²⋊C₄	—	4	1	no	—
345	C₂²⋊C₄	—	4	1	no	—
346	C₂²⋊C₄	—	376	4	no	—
347	C₄²	—	188	1	no	—
348	C₄²	—	188	1	no	—
349	C₄²	D₄×D₄₇	1	1	yes	characteristic
350	C₄²	#10625352	1	1	yes	characteristic
351	C₄²	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
352	C₄²	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
353	C₂³	—	2	2	no	—
354	C₂³	—	4	2	no	—
355	C₂³	—	4	1	no	—
356	C₂³	—	4	1	no	—
357	C₂³	—	4	2	no	—
358	C₂³	—	4	2	no	—
359	C₂³	—	8	1	no	—
360	C₂³	—	8	2	no	—
361	C₂³	—	8	1	no	—
362	C₂³	—	8	2	no	—
363	C₂³	#13093992	1	1	yes	characteristic
364	Q₈	—	376	2	no	—
365	Q₈	—	188	4	no	—
366	D₄	—	2	2	no	—
367	D₄	—	2	2	no	—
368	D₄	—	4	4	no	—
369	D₄	—	4	2	no	—
370	D₄	—	4	1	no	—
371	D₄	—	4	2	no	—
372	D₄	—	4	4	no	—
373	D₄	—	4	1	no	—
374	D₄	—	8	2	no	—
375	D₄	—	8	1	no	—
376	D₄	—	8	1	no	—
377	D₄	—	8	1	no	—
378	D₄	—	8	1	no	—
379	C₂×C₄	—	2	2	no	—
380	C₂×C₄	—	4	2	no	—
381	C₂×C₄	—	4	1	no	—
382	C₂×C₄	—	8	1	no	—
383	C₂×C₄	—	8	1	no	—
384	C₂×C₄	—	8	2	no	—
385	C₂×C₄	—	188	2	no	—
386	C₂×C₄	—	188	2	no	—
387	C₂×C₄	—	188	2	no	—
388	C₂×C₄	—	188	2	no	—
389	C₂×C₄	—	188	4	no	—
390	C₂×C₄	#13093992	1	1	yes	characteristic
391	C₂×C₄	#13093993	1	1	yes	characteristic
392	C₂×C₄	#13093995	1	1	yes	characteristic
393	C₂×C₄	#13093996	1	1	yes	characteristic
394	C₂×C₄	#13093996	1	1	yes	characteristic
395	C₂×C₄	#13094020	1	1	yes	characteristic
396	C₂×C₄	C₂×#10625335	1	1	yes	characteristic
397	C₂×C₄	#13094043	1	2	yes	—
398	C₂×C₄	#13094044	1	1	yes	characteristic
399	C₂×C₄	#13094048	1	2	yes	—
400	C₂×C₄	#13094050	1	1	yes	characteristic
401	C₂×C₄	#13094054	1	1	yes	characteristic
402	C₈	—	4	2	no	—
403	C₈	—	94	4	no	—
404	C₈	—	376	1	no	—
405	C₂²	—	4	4	no	—
406	C₂²	—	4	2	no	—
407	C₂²	—	8	2	no	—
408	C₂²	—	8	1	no	—
409	C₂²	—	8	1	no	—
410	C₂²	—	8	2	no	—
411	C₂²	—	8	2	no	—
412	C₂²	—	8	2	no	—
413	C₂²	—	16	2	no	—
414	C₂²	—	16	2	no	—
415	C₂²	#15689031	1	1	yes	characteristic
416	C₂²	#15689261	1	1	yes	characteristic
417	C₂²	#15689265	1	2	yes	—
418	C₂²	#15689266	1	1	yes	characteristic
419	C₂²	#15689289	1	2	yes	—
420	C₄	—	2	1	no	—
421	C₄	—	2	1	no	—
422	C₄	—	8	1	no	—
423	C₄	—	376	2	no	—
424	C₄	—	376	2	no	—
425	C₄	#15689274	1	1	yes	characteristic
426	C₄	#15689285	1	1	yes	characteristic
427	C₄	#15689336	1	2	yes	—
428	C₄	#15689350	1	1	yes	characteristic
429	C₄	#15689367	1	1	yes	characteristic
430	C₄	#15689506	1	1	yes	characteristic
431	C₄	#15689511	1	1	yes	characteristic
432	C₂	—	8	2	no	—
433	C₂	—	16	2	no	—
434	C₂	#20242458	1	2	yes	—
435	C₂	#20242470	1	2	yes	—
436	C₂	#20244391	1	1	yes	characteristic
437	C₂	#20244400	1	1	yes	characteristic
438	C₂	#20244463	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	#13093992
commutator, cosocle	C₂×C₄²×C₄₇	C₂³
Frattini	C₂×C₄²	C₂²×D₄₇
Fitting, prime radical	C₂×C₄₇×#459	C₂
socle	C₂³×C₄₇	#120
hypercenter	C₂×#459	D₄₇
hypocenter	C₄₇	#10048
LCS	G ▷ C₂×C₄²×C₄₇ ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×#459

Complements

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

N	H ≅ G/N	type
1. C₂×#15689495	C₂	semidirect
2. #20248561	C₂	semidirect
3. #20244316	C₂	semidirect
4. C₂×#15688871	C₂	semidirect
5. C₂×D₄⋊(C₄₇⋊C₈)	C₂	semidirect
6. #20241227	C₂	semidirect
93. C₂×D₄×C₄₇	SD₁₆	semidirect
248. C₄₇	#10048	semidirect
316. C₂×D₄	#10625335	semidirect

Maximal subgroups

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

subgroup	index
C₂×#15689495	2
#20248561	2
#20244316	2
C₂×#15688871	2
C₂×D₄⋊(C₄₇⋊C₈)	2
#20241227	2
C₂×C₄₇×#459	2
#10048	47