Subgroups — #37581982

Order 24448.

548 conjugacy classes of subgroups.

The subgroup lattice has 416 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#20259349	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#20259346	C₂	1	1	yes	maximal, characteristic, complemented
3	#27133212	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄×D₄×D₁₉₁	C₂	1	1	yes	maximal, characteristic, complemented
5	#27132879	C₂	1	1	yes	maximal, characteristic, complemented
6	#27132878	C₂	1	1	yes	maximal, characteristic, complemented
7	#27132875	C₂	1	1	yes	maximal, characteristic, complemented
8	#27132867	C₂	1	1	yes	maximal, characteristic, complemented
9	#27132866	C₂	1	1	yes	maximal, characteristic, complemented
10	#27132857	C₂	1	1	yes	maximal, characteristic, complemented
11	#27132856	C₂	1	1	yes	maximal, characteristic, complemented
12	#27132685	C₂	1	1	yes	maximal, characteristic, complemented
13	#27132663	C₂	1	1	yes	maximal, characteristic, complemented
14	#27132661	C₂	1	1	yes	maximal, characteristic, complemented
15	#463×C₁₉₁	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#15690288	C₂²	1	1	yes	characteristic
17	C₂×#15690286	C₂²	1	1	yes	characteristic
18	C₂×D₄×D₁₉₁	C₂²	1	1	yes	characteristic
19	C₂²×C₄×D₁₉₁	—	2	1	no	—
20	#20259349	—	2	4	no	—
21	#20259346	—	2	4	no	—
22	C₂×#15690276	C₂²	1	1	yes	characteristic
23	C₂×#15690275	C₂²	1	1	yes	characteristic
24	C₂×#15690274	C₂²	1	1	yes	characteristic
25	C₂×D₁₅₂₈	C₂²	1	1	yes	characteristic
26	C₂×#15690272	C₂²	1	1	yes	characteristic
27	C₂×#15690272	C₂²	1	1	yes	characteristic
28	C₂×#15690270	C₂²	1	1	yes	characteristic
29	C₂×#15690270	C₂²	1	1	yes	characteristic
30	#20259320	C₂²	1	1	yes	characteristic, complemented
31	#20259318	C₂²	1	1	yes	characteristic, complemented
32	#20259310	C₂²	1	1	yes	characteristic, complemented
33	#20259295	—	2	1	no	—
34	#20259295	—	2	1	no	—
35	C₄×D₇₆₄	C₂²	1	1	yes	characteristic
36	D₄×Dic₁₉₁	C₂²	1	1	yes	characteristic
37	#20259284	C₂²	1	1	yes	characteristic
38	C₄×C₂²⋊D₁₉₁	—	2	1	no	—
39	(C₂²⋊D₁₉₁)⋊C₄	—	2	1	no	—
40	(C₂²⋊D₁₉₁)⋊C₄	—	2	1	no	—
41	(C₂²⋊D₁₉₁)⋊C₄	—	2	1	no	—
42	C₄⋊C₄×D₁₉₁	C₂²	1	1	yes	characteristic
43	C₂²⋊C₄×D₁₉₁	—	2	1	no	—
44	C₄²×D₁₉₁	C₂²	1	1	yes	characteristic
45	C₄⋊(C₁₉₁⋊C₈)	C₂²	1	1	yes	characteristic, complemented
46	Dic₁₉₁⋊C₈	C₂²	1	1	yes	characteristic, complemented
47	Dic₁₉₁⋊C₈	C₂²	1	1	yes	characteristic, complemented
48	#20259247	C₂²	1	1	yes	characteristic, complemented
49	#20259246	C₂²	1	1	yes	characteristic, complemented
50	#20259245	C₂²	1	1	yes	characteristic, complemented
51	#20259244	C₂²	1	1	yes	characteristic, complemented
52	#20259243	C₂²	1	1	yes	characteristic, complemented
53	#20259242	C₂²	1	1	yes	characteristic, complemented
54	C₂×SD₁₆×C₁₉₁	C₂²	1	1	yes	characteristic
55	C₂×D₈×C₁₉₁	C₂²	1	1	yes	characteristic
56	#124×C₁₉₁	C₂²	1	1	yes	characteristic, complemented
57	C₄×D₄×C₁₉₁	C₂²	1	1	yes	characteristic
58	C₄⋊C₈×C₁₉₁	C₂²	1	1	yes	characteristic, complemented
59	#103×C₁₉₁	C₂²	1	1	yes	characteristic, complemented
60	#102×C₁₉₁	C₂²	1	1	yes	characteristic, complemented
61	C₂³×D₁₉₁	—	2	1	no	—
62	#15690288	—	2	2	no	—
63	#15690288	—	2	2	no	—
64	#15690286	—	2	2	no	—
65	#15690286	—	2	2	no	—
66	C₂×Dic₃₈₂	C₂³	1	1	yes	characteristic
67	C₂×D₇₆₄	—	2	1	no	—
68	C₂×D₇₆₄	C₂³	1	1	yes	characteristic
69	C₂×D₇₆₄	C₂³	1	1	yes	characteristic
70	C₂×C₂²⋊D₁₉₁	—	2	1	no	—
71	C₂×C₂²⋊D₁₉₁	—	2	1	no	—
72	C₂×C₂²⋊D₁₉₁	—	2	1	no	—
73	C₂×C₂²⋊D₁₉₁	—	2	1	no	—
74	D₄×D₁₉₁	—	2	2	no	—
75	D₄×D₁₉₁	D₄	1	4	yes	complemented
76	C₂²×Dic₁₉₁	—	2	1	no	—
77	C₂²×Dic₁₉₁	—	2	1	no	—
78	C₂×C₄×D₁₉₁	—	2	1	no	—
79	C₂×C₄×D₁₉₁	—	2	1	no	—
80	C₂×C₄×D₁₉₁	—	2	1	no	—
81	C₂×C₄×D₁₉₁	—	2	1	no	—
82	C₂×C₄×D₁₉₁	—	4	4	no	—
83	C₂×C₄×D₁₉₁	D₄	1	1	yes	characteristic
84	C₂×C₄×D₁₉₁	D₄	1	1	yes	characteristic
85	C₂×C₄×D₁₉₁	C₂³	1	1	yes	characteristic
86	#15690276	—	2	2	no	—
87	#15690275	—	2	2	no	—
88	#15690274	—	2	2	no	—
89	D₁₅₂₈	—	2	2	no	—
90	#15690272	—	2	2	no	—
91	#15690272	—	2	2	no	—
92	#15690270	—	2	2	no	—
93	#15690270	—	2	2	no	—
94	C₂×C₁₉₁⋊C₈	C₂³	1	1	yes	characteristic
95	C₂×C₁₉₁⋊C₈	C₂³	1	1	yes	characteristic
96	C₄⋊Dic₁₉₁	C₂³	1	1	yes	characteristic
97	Dic₁₉₁⋊C₄	—	2	1	no	—
98	Dic₁₉₁⋊C₄	—	2	1	no	—
99	Dic₁₉₁⋊C₄	—	2	1	no	—
100	C₂²⋊Dic₁₉₁	—	2	1	no	—
101	(C₂×D₁₉₁)⋊C₄	—	2	1	no	—
102	(C₂×D₁₉₁)⋊C₄	—	2	1	no	—
103	(C₂×D₁₉₁)⋊C₄	—	2	1	no	—
104	(C₂×D₁₉₁)⋊C₄	—	2	1	no	—
105	C₄×Dic₁₉₁	D₄	1	1	yes	characteristic
106	C₄×Dic₁₉₁	D₄	1	1	yes	characteristic
107	C₄×Dic₁₉₁	C₂³	1	1	yes	characteristic
108	C₂×Q₈×C₁₉₁	C₂³	1	1	yes	characteristic
109	C₂×D₄×C₁₉₁	C₂³	1	1	yes	characteristic
110	C₂×D₄×C₁₉₁	C₂³	1	1	yes	characteristic
111	C₂²×C₄×C₁₉₁	—	2	1	no	—
112	SD₁₆×C₁₉₁	—	2	2	no	—
113	D₈×C₁₉₁	—	2	2	no	—
114	C₂×C₈×C₁₉₁	C₂³	1	1	yes	characteristic
115	C₂×C₈×C₁₉₁	C₂³	1	1	yes	characteristic
116	C₄⋊C₄×C₁₉₁	C₂³	1	1	yes	characteristic
117	C₂²⋊C₄×C₁₉₁	—	2	1	no	—
118	C₂²⋊C₄×C₁₉₁	—	2	1	no	—
119	C₂²⋊C₄×C₁₉₁	—	2	1	no	—
120	C₄²×C₁₉₁	C₂³	1	1	yes	characteristic
121	C₂²×D₁₉₁	—	2	1	no	—
122	C₂²×D₁₉₁	—	2	4	no	—
123	C₂²×D₁₉₁	—	2	1	no	—
124	C₂²×D₁₉₁	—	4	2	no	—
125	C₂²×D₁₉₁	—	4	2	no	—
126	C₂²×D₁₉₁	C₂×D₄	1	1	yes	characteristic
127	Dic₃₈₂	—	2	1	no	—
128	Dic₃₈₂	—	2	1	no	—
129	D₇₆₄	—	2	1	no	—
130	D₇₆₄	—	2	1	no	—
131	D₇₆₄	—	2	1	no	—
132	D₇₆₄	—	4	2	no	—
133	D₇₆₄	C₂×D₄	1	2	yes	—
134	C₂²⋊D₁₉₁	—	2	4	no	—
135	C₂²⋊D₁₉₁	—	4	2	no	—
136	C₂²⋊D₁₉₁	—	4	2	no	—
137	C₂²⋊D₁₉₁	—	4	2	no	—
138	C₂×Dic₁₉₁	—	2	1	no	—
139	C₂×Dic₁₉₁	—	2	1	no	—
140	C₂×Dic₁₉₁	—	4	2	no	—
141	C₂×Dic₁₉₁	—	4	2	no	—
142	C₂×Dic₁₉₁	C₂×D₄	1	1	yes	characteristic
143	C₂×Dic₁₉₁	C₂×D₄	1	1	yes	characteristic
144	C₂×Dic₁₉₁	C₂×D₄	1	1	yes	characteristic
145	C₄×D₁₉₁	—	2	2	no	—
146	C₄×D₁₉₁	—	4	1	no	—
147	C₄×D₁₉₁	—	4	2	no	—
148	C₄×D₁₉₁	—	4	2	no	—
149	C₄×D₁₉₁	—	4	2	no	—
150	C₄×D₁₉₁	—	4	2	no	—
151	C₄×D₁₉₁	C₂×D₄	1	2	yes	—
152	C₄×D₁₉₁	#41	1	2	yes	—
153	C₁₉₁⋊C₈	—	2	1	no	—
154	C₁₉₁⋊C₈	—	2	1	no	—
155	C₂³×C₁₉₁	—	2	1	no	—
156	C₂³×C₁₉₁	—	2	1	no	—
157	Q₈×C₁₉₁	—	2	1	no	—
158	Q₈×C₁₉₁	—	2	1	no	—
159	D₄×C₁₉₁	—	2	1	no	—
160	D₄×C₁₉₁	—	2	1	no	—
161	D₄×C₁₉₁	—	2	1	no	—
162	D₄×C₁₉₁	C₂×D₄	1	2	yes	—
163	C₂×C₄×C₁₉₁	—	2	1	no	—
164	C₂×C₄×C₁₉₁	—	2	1	no	—
165	C₂×C₄×C₁₉₁	—	4	2	no	—
166	C₂×C₄×C₁₉₁	C₂×D₄	1	1	yes	characteristic
167	C₂×C₄×C₁₉₁	C₂×D₄	1	1	yes	characteristic
168	C₂×C₄×C₁₉₁	C₂⁴	1	1	yes	characteristic
169	C₈×C₁₉₁	—	2	1	no	—
170	C₈×C₁₉₁	—	2	1	no	—
171	C₂²×C₁₉₁	—	2	2	no	—
172	C₂²×C₁₉₁	—	4	1	no	—
173	C₂²×C₁₉₁	—	4	1	no	—
174	C₂²×C₁₉₁	—	4	1	no	—
175	C₂²×C₁₉₁	—	4	1	no	—
176	C₂²×C₁₉₁	—	4	1	no	—
177	C₂²×C₁₉₁	C₂²×D₄	1	1	yes	characteristic
178	C₂×D₁₉₁	—	2	1	no	—
179	C₂×D₁₉₁	—	2	1	no	—
180	C₂×D₁₉₁	—	2	2	no	—
181	C₂×D₁₉₁	—	4	8	no	—
182	C₂×D₁₉₁	—	4	1	no	—
183	C₂×D₁₉₁	—	4	1	no	—
184	C₂×D₁₉₁	—	4	1	no	—
185	C₂×D₁₉₁	—	4	1	no	—
186	C₂×D₁₉₁	—	4	1	no	—
187	C₂×D₁₉₁	#121	1	2	yes	—
188	C₄×C₁₉₁	—	2	1	no	—
189	C₄×C₁₉₁	—	2	1	no	—
190	C₄×C₁₉₁	—	4	1	no	—
191	C₄×C₁₉₁	—	4	1	no	—
192	C₄×C₁₉₁	C₂²×D₄	1	1	yes	characteristic
193	C₄×C₁₉₁	C₂×#41	1	1	yes	characteristic
194	Dic₁₉₁	—	2	1	no	—
195	Dic₁₉₁	—	4	1	no	—
196	Dic₁₉₁	—	4	1	no	—
197	Dic₁₉₁	#121	1	2	yes	—
198	Dic₁₉₁	AGL(1,ℤ/8)	1	2	yes	complemented
199	C₂×C₁₉₁	—	4	2	no	—
200	C₂×C₁₉₁	—	8	1	no	—
201	C₂×C₁₉₁	C₂×#121	1	1	yes	characteristic
202	C₂×C₁₉₁	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
203	C₂×C₁₉₁	#575	1	1	yes	characteristic
204	D₁₉₁	—	2	2	no	—
205	D₁₉₁	—	4	2	no	—
206	D₁₉₁	—	8	1	no	—
207	C₁₉₁	#3036	1	1	yes	characteristic, complemented, Sylow
208	#3036	—	191	1	no	maximal, Sylow
209	C₂×AGL(1,ℤ/8)	—	191	1	no	—
210	C₂×AGL(1,ℤ/8)	—	191	1	no	—
211	#532	—	191	1	no	—
212	C₂×C₄×D₄	—	191	1	no	—
213	#463	—	191	1	no	—
214	#463	—	191	1	no	—
215	#463	—	191	1	no	—
216	#463	D₁₉₁	1	1	yes	characteristic, complemented
217	#461	—	191	1	no	—
218	#461	—	191	1	no	—
219	#459	—	191	1	no	—
220	#459	—	191	1	no	—
221	#423	—	191	1	no	—
222	#417	—	191	1	no	—
223	#417	—	191	1	no	—
224	C₂×#41	—	191	1	no	—
225	C₂×#41	—	191	1	no	—
226	C₂²×D₄	—	191	1	no	—
227	C₂³×C₄	—	382	1	no	—
228	AGL(1,ℤ/8)	—	382	4	no	—
229	AGL(1,ℤ/8)	—	382	4	no	—
230	C₂×SD₁₆	—	191	1	no	—
231	C₂×SD₁₆	—	191	1	no	—
232	C₂×SD₁₆	—	191	1	no	—
233	C₂×SD₁₆	C₂×D₁₉₁	1	1	yes	characteristic
234	C₂×D₈	—	191	1	no	—
235	C₂×D₈	—	191	1	no	—
236	C₂×D₈	—	191	1	no	—
237	C₂×D₈	C₂×D₁₉₁	1	1	yes	characteristic
238	C₂×M₁₆	—	191	1	no	—
239	C₂×M₁₆	—	191	1	no	—
240	C₄⋊Q₈	—	191	1	no	—
241	#127	—	191	1	no	—
242	#124	—	191	1	no	—
243	#124	C₂×D₁₉₁	1	1	yes	characteristic, complemented
244	#121	—	382	1	no	—
245	#121	—	382	1	no	—
246	C₄×D₄	—	382	1	no	—
247	C₄×D₄	—	382	1	no	—
248	C₄×D₄	—	382	1	no	—
249	C₄×D₄	—	382	1	no	—
250	C₄×D₄	—	191	1	no	—
251	C₄×D₄	—	191	1	no	—
252	C₄×D₄	—	191	1	no	—
253	C₄×D₄	C₂×D₁₉₁	1	1	yes	characteristic
254	C₂×C₄⋊C₄	—	191	1	no	—
255	C₂×C₂²⋊C₄	—	382	1	no	—
256	C₂×C₄²	—	191	1	no	—
257	C₄⋊C₈	—	191	1	no	—
258	C₄⋊C₈	—	191	1	no	—
259	C₄⋊C₈	—	191	1	no	—
260	C₄⋊C₈	C₂×D₁₉₁	1	1	yes	characteristic, complemented
261	#103	—	191	1	no	—
262	#103	—	191	1	no	—
263	#103	—	191	1	no	—
264	#103	C₂×D₁₉₁	1	1	yes	characteristic, complemented
265	#102	—	191	1	no	—
266	#102	—	191	1	no	—
267	#102	—	191	1	no	—
268	#102	C₂×D₁₉₁	1	1	yes	characteristic, complemented
269	C₂⁴	—	382	1	no	—
270	#41	—	382	2	no	—
271	#41	—	382	2	no	—
272	#41	—	382	2	no	—
273	#41	—	382	2	no	—
274	C₂×Q₈	—	191	1	no	—
275	C₂×Q₈	C₂²×D₁₉₁	1	1	yes	characteristic
276	C₂×D₄	—	382	1	no	—
277	C₂×D₄	—	382	1	no	—
278	C₂×D₄	—	382	2	no	—
279	C₂×D₄	—	382	1	no	—
280	C₂×D₄	—	382	1	no	—
281	C₂×D₄	—	382	1	no	—
282	C₂×D₄	—	191	4	no	—
283	C₂×D₄	—	191	1	no	—
284	C₂×D₄	—	191	1	no	—
285	C₂×D₄	C₂²×D₁₉₁	1	1	yes	characteristic
286	C₂×D₄	C₂²×D₁₉₁	1	1	yes	characteristic
287	C₂²×C₄	—	2	1	no	—
288	C₂²×C₄	—	382	1	no	—
289	C₂²×C₄	—	382	1	no	—
290	C₂²×C₄	—	382	1	no	—
291	C₂²×C₄	—	382	1	no	—
292	C₂²×C₄	—	382	1	no	—
293	C₂²×C₄	—	382	1	no	—
294	C₂²×C₄	—	191	1	no	—
295	C₂²×C₄	—	191	1	no	—
296	C₂²×C₄	—	191	1	no	—
297	C₂²×C₄	—	764	4	no	—
298	SD₁₆	—	2	2	no	—
299	SD₁₆	—	382	2	no	—
300	SD₁₆	—	382	2	no	—
301	SD₁₆	—	382	2	no	—
302	D₈	—	2	2	no	—
303	D₈	—	382	2	no	—
304	D₈	—	382	2	no	—
305	D₈	—	382	2	no	—
306	M₁₆	—	382	2	no	—
307	M₁₆	—	382	2	no	—
308	C₂×C₈	—	191	1	no	—
309	C₂×C₈	—	191	1	no	—
310	C₂×C₈	C₂²×D₁₉₁	1	1	yes	characteristic
311	C₂×C₈	C₂²×D₁₉₁	1	1	yes	characteristic
312	C₄⋊C₄	—	382	1	no	—
313	C₄⋊C₄	—	382	1	no	—
314	C₄⋊C₄	—	382	1	no	—
315	C₄⋊C₄	—	191	1	no	—
316	C₄⋊C₄	C₂²×D₁₉₁	1	1	yes	characteristic
317	C₂²⋊C₄	—	2	1	no	—
318	C₂²⋊C₄	—	2	1	no	—
319	C₂²⋊C₄	—	2	1	no	—
320	C₂²⋊C₄	—	382	1	no	—
321	C₂²⋊C₄	—	382	1	no	—
322	C₂²⋊C₄	—	382	1	no	—
323	C₂²⋊C₄	—	382	1	no	—
324	C₂²⋊C₄	—	382	1	no	—
325	C₄²	—	191	1	no	—
326	C₄²	—	191	1	no	—
327	C₄²	—	191	1	no	—
328	C₄²	C₂²×D₁₉₁	1	1	yes	characteristic
329	C₂³	—	2	1	no	—
330	C₂³	—	2	1	no	—
331	C₂³	—	382	4	no	—
332	C₂³	—	382	1	no	—
333	C₂³	—	382	1	no	—
334	C₂³	—	191	1	no	—
335	C₂³	—	764	2	no	—
336	C₂³	—	764	2	no	—
337	Q₈	—	2	1	no	—
338	Q₈	—	2	1	no	—
339	Q₈	—	382	1	no	—
340	Q₈	—	382	1	no	—
341	D₄	—	2	1	no	—
342	D₄	—	2	1	no	—
343	D₄	—	2	1	no	—
344	D₄	—	382	4	no	—
345	D₄	—	382	1	no	—
346	D₄	—	382	1	no	—
347	D₄	—	382	1	no	—
348	D₄	—	191	2	no	—
349	D₄	—	764	2	no	—
350	D₄	—	764	2	no	—
351	D₄	—	764	2	no	—
352	D₄	—	764	2	no	—
353	D₄	D₄×D₁₉₁	1	2	yes	—
354	C₂×C₄	—	2	1	no	—
355	C₂×C₄	—	2	1	no	—
356	C₂×C₄	—	4	2	no	—
357	C₂×C₄	—	382	2	no	—
358	C₂×C₄	—	382	1	no	—
359	C₂×C₄	—	382	1	no	—
360	C₂×C₄	—	191	1	no	—
361	C₂×C₄	—	191	1	no	—
362	C₂×C₄	—	191	1	no	—
363	C₂×C₄	—	191	2	no	—
364	C₂×C₄	—	191	2	no	—
365	C₂×C₄	—	764	1	no	—
366	C₂×C₄	—	764	2	no	—
367	C₂×C₄	—	764	2	no	—
368	C₂×C₄	—	764	2	no	—
369	C₂×C₄	—	764	2	no	—
370	C₂×C₄	—	764	2	no	—
371	C₂×C₄	—	764	2	no	—
372	C₂×C₄	D₄×D₁₉₁	1	1	yes	characteristic
373	C₂×C₄	D₄×D₁₉₁	1	1	yes	characteristic
374	C₂×C₄	C₂³×D₁₉₁	1	1	yes	characteristic
375	C₈	—	2	1	no	—
376	C₈	—	2	1	no	—
377	C₈	—	382	1	no	—
378	C₈	—	382	1	no	—
379	C₂²	—	2	2	no	—
380	C₂²	—	4	1	no	—
381	C₂²	—	4	1	no	—
382	C₂²	—	4	1	no	—
383	C₂²	—	4	1	no	—
384	C₂²	—	4	1	no	—
385	C₂²	—	382	1	no	—
386	C₂²	—	382	1	no	—
387	C₂²	—	382	2	no	—
388	C₂²	—	191	2	no	—
389	C₂²	—	764	8	no	—
390	C₂²	—	764	1	no	—
391	C₂²	—	764	1	no	—
392	C₂²	—	764	1	no	—
393	C₂²	—	764	1	no	—
394	C₂²	—	764	1	no	—
395	C₂²	C₂×D₄×D₁₉₁	1	1	yes	characteristic
396	C₄	—	2	1	no	—
397	C₄	—	2	1	no	—
398	C₄	—	4	1	no	—
399	C₄	—	4	1	no	—
400	C₄	—	382	1	no	—
401	C₄	—	191	2	no	—
402	C₄	—	191	2	no	—
403	C₄	—	764	1	no	—
404	C₄	—	764	1	no	—
405	C₄	C₂×D₄×D₁₉₁	1	1	yes	characteristic
406	C₄	#41×D₁₉₁	1	1	yes	characteristic
407	C₂	—	4	2	no	—
408	C₂	—	8	1	no	—
409	C₂	—	382	2	no	—
410	C₂	—	1528	1	no	—
411	C₂	—	764	2	no	—
412	C₂	#121×D₁₉₁	1	1	yes	characteristic
413	C₂	AGL(1,ℤ/8)×D₁₉₁	1	1	yes	characteristic
414	C₂	#27133460	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×D₄×D₁₉₁
commutator, cosocle	C₂×C₄×C₁₉₁	C₂⁴
Frattini	C₂×C₄	C₂³×D₁₉₁
Fitting	#463×C₁₉₁	C₂
socle	C₂²×C₁₉₁	C₂²×D₄
hypercenter	#463	D₁₉₁
hypocenter	C₁₉₁	#3036
LCS	G ▷ C₂×C₄×C₁₉₁ ▷ C₂×C₁₉₁ ▷ C₁₉₁
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #463

Complements

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

N	H ≅ G/N	type
1. C₂×#20259349	C₂	semidirect
2. C₂×#20259346	C₂	semidirect
3. #27133212	C₂	semidirect
4. C₄×D₄×D₁₉₁	C₂	semidirect
5. #27132879	C₂	semidirect
6. #27132878	C₂	semidirect
7. #27132875	C₂	semidirect
8. #27132867	C₂	semidirect
9. #27132866	C₂	semidirect
10. #27132857	C₂	semidirect
11. #27132856	C₂	semidirect
12. #27132685	C₂	semidirect
13. #27132663	C₂	semidirect
14. #27132661	C₂	semidirect
15. #463×C₁₉₁	C₂	semidirect
30. #20259320	C₂²	semidirect
31. #20259318	C₂²	semidirect
32. #20259310	C₂²	semidirect
45. C₄⋊(C₁₉₁⋊C₈)	C₂²	semidirect
46. Dic₁₉₁⋊C₈	C₂²	semidirect
47. Dic₁₉₁⋊C₈	C₂²	semidirect
48. #20259247	C₂²	semidirect
49. #20259246	C₂²	semidirect
50. #20259245	C₂²	semidirect
51. #20259244	C₂²	semidirect
52. #20259243	C₂²	semidirect
53. #20259242	C₂²	semidirect
56. #124×C₁₉₁	C₂²	semidirect
58. C₄⋊C₈×C₁₉₁	C₂²	semidirect
59. #103×C₁₉₁	C₂²	semidirect
60. #102×C₁₉₁	C₂²	semidirect
75. D₄×D₁₉₁	D₄	semidirect
198. Dic₁₉₁	AGL(1,ℤ/8)	semidirect
207. C₁₉₁	#3036	semidirect
216. #463	D₁₉₁	semidirect
243. #124	C₂×D₁₉₁	semidirect
260. C₄⋊C₈	C₂×D₁₉₁	semidirect
264. #103	C₂×D₁₉₁	semidirect
268. #102	C₂×D₁₉₁	semidirect

Maximal subgroups

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

subgroup	index
C₂×#20259349	2
C₂×#20259346	2
#27133212	2
C₄×D₄×D₁₉₁	2
#27132879	2
#27132878	2
#27132875	2
#27132867	2
#27132866	2
#27132857	2
#27132856	2
#27132685	2
#27132663	2
#27132661	2
#463×C₁₉₁	2
#3036	191