Subgroups — C₁₀₁×#17631 #38799782

Order 25856.

1138 conjugacy classes of subgroups.

The subgroup lattice has 366 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₀₁×#3497	C₂	1	1	yes	maximal, characteristic
2	C₁₀₁×#2983	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₀₁×#2356	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₀₁×#1517	C₂	1	2	yes	maximal, complemented
5	C₁₀₁×#1514	C₂	1	4	yes	maximal, complemented
6	C₁₀₁×#1505	C₂	1	4	yes	maximal, complemented
7	C₁₀₁×#1502	C₂	1	2	yes	maximal, complemented
8	C₂×2₋¹⁺⁴×C₁₀₁	—	2	1	no	—
9	#550×C₁₀₁	C₄	1	4	yes	complemented
10	D₄×Q₈×C₁₀₁	C₄	1	4	yes	complemented
11	#548×C₁₀₁	—	2	4	no	—
12	#537×C₁₀₁	—	2	1	no	—
13	#537×C₁₀₁	—	2	2	no	—
14	#532×C₁₀₁	C₂²	1	2	yes	—
15	#532×C₁₀₁	C₂²	1	4	yes	—
16	C₂×C₄×Q₈×C₁₀₁	C₂²	1	1	yes	characteristic
17	#446×C₁₀₁	—	2	4	no	—
18	#432×C₁₀₁	C₂²	1	4	yes	—
19	#431×C₁₀₁	C₂²	1	2	yes	—
20	#391×C₁₀₁	—	2	1	no	—
21	#387×C₁₀₁	—	2	2	no	—
22	#383×C₁₀₁	C₂²	1	2	yes	—
23	#382×C₁₀₁	C₂²	1	1	yes	characteristic
24	C₄×C₄⋊C₄×C₁₀₁	—	2	1	no	—
25	C₄×C₄⋊C₄×C₁₀₁	C₂²	1	1	yes	characteristic
26	#376×C₁₀₁	C₂²	1	2	yes	—
27	#327×C₁₀₁	C₂²	1	4	yes	—
28	#327×C₁₀₁	C₂²	1	4	yes	—
29	#327×C₁₀₁	C₂²	1	8	yes	—
30	2₋¹⁺⁴×C₁₀₁	—	4	4	no	—
31	2₋¹⁺⁴×C₁₀₁	—	4	4	no	—
32	C₂×#41×C₁₀₁	—	2	4	no	—
33	C₂×#41×C₁₀₁	—	2	4	no	—
34	C₂×#41×C₁₀₁	—	2	2	no	—
35	C₂²×Q₈×C₁₀₁	—	2	4	no	—
36	C₂²×Q₈×C₁₀₁	D₄	1	1	yes	characteristic
37	C₄⋊Q₈×C₁₀₁	C₂×C₄	1	2	yes	—
38	C₄⋊Q₈×C₁₀₁	C₂×C₄	1	4	yes	—
39	#127×C₁₀₁	C₂×C₄	1	2	yes	—
40	#127×C₁₀₁	C₂×C₄	1	4	yes	—
41	#124×C₁₀₁	—	2	2	no	—
42	#124×C₁₀₁	—	2	4	no	—
43	C₂²⋊Q₈×C₁₀₁	—	2	8	no	—
44	C₂²⋊Q₈×C₁₀₁	—	2	4	no	—
45	#121×C₁₀₁	—	2	4	no	—
46	#121×C₁₀₁	—	2	2	no	—
47	#121×C₁₀₁	—	2	8	no	—
48	#121×C₁₀₁	—	2	4	no	—
49	#121×C₁₀₁	C₂³	1	4	yes	—
50	C₄×Q₈×C₁₀₁	C₂×C₄	1	4	yes	—
51	C₄×Q₈×C₁₀₁	D₄	1	4	yes	—
52	C₄×D₄×C₁₀₁	—	2	2	no	—
53	C₄×D₄×C₁₀₁	—	2	4	no	—
54	C₄×D₄×C₁₀₁	C₂×C₄	1	4	yes	—
55	C₄×D₄×C₁₀₁	C₂×C₄	1	8	yes	—
56	C₂×C₄⋊C₄×C₁₀₁	—	2	1	no	—
57	C₂×C₄⋊C₄×C₁₀₁	—	2	1	no	—
58	C₂×C₄⋊C₄×C₁₀₁	D₄	1	1	yes	characteristic
59	C₂×C₄⋊C₄×C₁₀₁	D₄	1	2	yes	—
60	C₂×C₄²×C₁₀₁	—	2	2	no	—
61	C₂×C₄²×C₁₀₁	—	2	1	no	—
62	C₂×C₄²×C₁₀₁	C₂³	1	1	yes	characteristic
63	C₂×C₄²×C₁₀₁	C₂³	1	2	yes	—
64	C₄⋊C₈×C₁₀₁	—	2	2	no	—
65	C₄⋊C₈×C₁₀₁	—	2	4	no	—
66	C₂²⋊C₈×C₁₀₁	C₂³	1	4	yes	—
67	#97×C₁₀₁	—	2	4	no	—
68	C₄×C₈×C₁₀₁	—	2	2	no	—
69	#95×C₁₀₁	—	2	2	no	—
70	#95×C₁₀₁	—	2	2	no	—
71	#95×C₁₀₁	—	2	1	no	—
72	#95×C₁₀₁	—	2	2	no	—
73	#95×C₁₀₁	C₂³	1	1	yes	characteristic
74	#95×C₁₀₁	C₂³	1	2	yes	—
75	#95×C₁₀₁	C₂³	1	1	yes	characteristic
76	#41×C₁₀₁	—	4	8	no	—
77	#41×C₁₀₁	—	4	8	no	—
78	#41×C₁₀₁	—	4	16	no	—
79	#41×C₁₀₁	—	4	4	no	—
80	#41×C₁₀₁	—	4	4	no	—
81	C₂×Q₈×C₁₀₁	—	2	4	no	—
82	C₂×Q₈×C₁₀₁	—	2	2	no	—
83	C₂×Q₈×C₁₀₁	—	2	2	no	—
84	C₂×Q₈×C₁₀₁	—	2	2	no	—
85	C₂×Q₈×C₁₀₁	—	4	16	no	—
86	C₂×Q₈×C₁₀₁	C₂²⋊C₄	1	4	yes	—
87	C₂×D₄×C₁₀₁	—	2	4	no	—
88	C₂×D₄×C₁₀₁	—	2	4	no	—
89	C₂×D₄×C₁₀₁	—	2	2	no	—
90	C₂×D₄×C₁₀₁	—	2	2	no	—
91	C₂×D₄×C₁₀₁	—	2	4	no	—
92	C₂×D₄×C₁₀₁	C₂²×C₄	1	4	yes	—
93	C₂²×C₄×C₁₀₁	—	2	1	no	—
94	C₂²×C₄×C₁₀₁	—	2	8	no	—
95	C₂²×C₄×C₁₀₁	—	2	4	no	—
96	C₂²×C₄×C₁₀₁	—	2	2	no	—
97	C₂²×C₄×C₁₀₁	—	2	1	no	—
98	C₂²×C₄×C₁₀₁	C₂×D₄	1	2	yes	—
99	C₂²×C₄×C₁₀₁	C₂×D₄	1	2	yes	—
100	C₂²×C₄×C₁₀₁	C₂×D₄	1	1	yes	characteristic
101	C₂²×C₄×C₁₀₁	C₂×D₄	1	1	yes	characteristic
102	C₂²×C₄×C₁₀₁	C₂⁴	1	1	yes	characteristic
103	C₂×C₈×C₁₀₁	—	2	4	no	—
104	C₄⋊C₄×C₁₀₁	—	2	2	no	—
105	C₄⋊C₄×C₁₀₁	—	2	4	no	—
106	C₄⋊C₄×C₁₀₁	—	4	2	no	—
107	C₄⋊C₄×C₁₀₁	—	4	2	no	—
108	C₄⋊C₄×C₁₀₁	C₂²⋊C₄	1	8	yes	—
109	C₄⋊C₄×C₁₀₁	C₂²⋊C₄	1	4	yes	—
110	C₄⋊C₄×C₁₀₁	C₂²×C₄	1	4	yes	—
111	C₂²⋊C₄×C₁₀₁	—	2	4	no	—
112	C₂²⋊C₄×C₁₀₁	—	2	8	no	—
113	C₂²⋊C₄×C₁₀₁	—	2	4	no	—
114	C₄²×C₁₀₁	—	4	4	no	—
115	C₄²×C₁₀₁	—	4	2	no	—
116	C₄²×C₁₀₁	C₂²×C₄	1	4	yes	—
117	C₄²×C₁₀₁	C₂²×C₄	1	2	yes	—
118	C₄²×C₁₀₁	C₂×D₄	1	2	yes	—
119	C₄²×C₁₀₁	C₂×D₄	1	4	yes	—
120	C₂³×C₁₀₁	—	2	4	no	—
121	C₂³×C₁₀₁	C₂²×D₄	1	1	yes	characteristic
122	Q₈×C₁₀₁	—	2	8	no	—
123	Q₈×C₁₀₁	—	4	8	no	—
124	Q₈×C₁₀₁	—	4	4	no	—
125	D₄×C₁₀₁	—	4	4	no	—
126	D₄×C₁₀₁	—	4	8	no	—
127	D₄×C₁₀₁	—	4	4	no	—
128	D₄×C₁₀₁	—	4	4	no	—
129	D₄×C₁₀₁	—	4	4	no	—
130	D₄×C₁₀₁	—	8	4	no	—
131	D₄×C₁₀₁	—	8	2	no	—
132	C₂×C₄×C₁₀₁	—	2	2	no	—
133	C₂×C₄×C₁₀₁	—	2	2	no	—
134	C₂×C₄×C₁₀₁	—	2	2	no	—
135	C₂×C₄×C₁₀₁	—	2	4	no	—
136	C₂×C₄×C₁₀₁	—	4	2	no	—
137	C₂×C₄×C₁₀₁	—	4	1	no	—
138	C₂×C₄×C₁₀₁	—	4	1	no	—
139	C₂×C₄×C₁₀₁	—	4	16	no	—
140	C₂×C₄×C₁₀₁	—	4	1	no	—
141	C₂×C₄×C₁₀₁	—	4	1	no	—
142	C₂×C₄×C₁₀₁	—	4	8	no	—
143	C₂×C₄×C₁₀₁	—	4	2	no	—
144	C₂×C₄×C₁₀₁	—	4	1	no	—
145	C₂×C₄×C₁₀₁	—	4	1	no	—
146	C₂×C₄×C₁₀₁	—	4	2	no	—
147	C₂×C₄×C₁₀₁	—	4	1	no	—
148	C₂×C₄×C₁₀₁	—	4	2	no	—
149	C₂×C₄×C₁₀₁	C₂×C₂²⋊C₄	1	2	yes	—
150	C₂×C₄×C₁₀₁	C₂×C₂²⋊C₄	1	4	yes	—
151	C₂×C₄×C₁₀₁	C₂×C₂²⋊C₄	1	4	yes	—
152	C₂×C₄×C₁₀₁	C₂×C₂²⋊C₄	1	2	yes	—
153	C₂×C₄×C₁₀₁	AGL(1,ℤ/8)	1	2	yes	—
154	C₂×C₄×C₁₀₁	AGL(1,ℤ/8)	1	2	yes	—
155	C₂×C₄×C₁₀₁	C₂³×C₄	1	1	yes	characteristic
156	C₂×C₄×C₁₀₁	C₂²×D₄	1	1	yes	characteristic
157	C₈×C₁₀₁	—	4	4	no	—
158	C₂²×C₁₀₁	—	2	1	no	—
159	C₂²×C₁₀₁	—	2	1	no	—
160	C₂²×C₁₀₁	—	4	4	no	—
161	C₂²×C₁₀₁	—	4	4	no	—
162	C₂²×C₁₀₁	—	4	4	no	—
163	C₂²×C₁₀₁	C₂²×C₂²⋊C₄	1	1	yes	characteristic
164	C₂²×C₁₀₁	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
165	C₂²×C₁₀₁	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
166	C₄×C₁₀₁	—	2	1	no	—
167	C₄×C₁₀₁	—	2	1	no	—
168	C₄×C₁₀₁	—	2	4	no	—
169	C₄×C₁₀₁	—	2	4	no	—
170	C₄×C₁₀₁	—	2	2	no	—
171	C₄×C₁₀₁	—	4	2	no	—
172	C₄×C₁₀₁	—	4	4	no	—
173	C₄×C₁₀₁	—	8	1	no	—
174	C₄×C₁₀₁	—	8	2	no	—
175	C₄×C₁₀₁	#418	1	4	yes	—
176	#17631	C₁₀₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
177	C₂×C₁₀₁	—	2	1	no	—
178	C₂×C₁₀₁	—	2	1	no	—
179	C₂×C₁₀₁	—	8	4	no	—
180	C₂×C₁₀₁	#2884	1	1	yes	characteristic
181	C₂×C₁₀₁	C₂×#418	1	1	yes	characteristic
182	C₂×C₁₀₁	#2901	1	1	yes	characteristic
183	#3497	C₂×C₁₀₁	1	1	yes	characteristic
184	#2983	C₂×C₁₀₁	1	1	yes	characteristic, complemented
185	#2356	C₂×C₁₀₁	1	1	yes	characteristic, complemented
186	#1517	C₂×C₁₀₁	1	2	yes	complemented
187	#1514	C₂×C₁₀₁	1	4	yes	complemented
188	#1505	C₂×C₁₀₁	1	4	yes	complemented
189	#1502	C₂×C₁₀₁	1	2	yes	complemented
190	C₁₀₁	#17631	1	1	yes	characteristic, direct product factor, Sylow
191	C₂×2₋¹⁺⁴	—	2	1	no	—
192	#550	C₄×C₁₀₁	1	4	yes	complemented
193	D₄×Q₈	C₄×C₁₀₁	1	4	yes	complemented
194	#548	—	2	4	no	—
195	#537	—	2	1	no	—
196	#537	—	2	2	no	—
197	#532	C₂²×C₁₀₁	1	2	yes	—
198	#532	C₂²×C₁₀₁	1	4	yes	—
199	C₂×C₄×Q₈	C₂²×C₁₀₁	1	1	yes	characteristic
200	#446	—	2	4	no	—
201	#432	C₂²×C₁₀₁	1	4	yes	—
202	#431	C₂²×C₁₀₁	1	2	yes	—
203	#391	—	2	1	no	—
204	#387	—	2	2	no	—
205	#383	C₂²×C₁₀₁	1	2	yes	—
206	#382	C₂²×C₁₀₁	1	1	yes	characteristic
207	C₄×C₄⋊C₄	—	2	1	no	—
208	C₄×C₄⋊C₄	C₂²×C₁₀₁	1	1	yes	characteristic
209	#376	C₂²×C₁₀₁	1	2	yes	—
210	#327	C₂²×C₁₀₁	1	4	yes	—
211	#327	C₂²×C₁₀₁	1	4	yes	—
212	#327	C₂²×C₁₀₁	1	8	yes	—
213	2₋¹⁺⁴	—	4	4	no	—
214	2₋¹⁺⁴	—	4	4	no	—
215	C₂×#41	—	2	4	no	—
216	C₂×#41	—	2	4	no	—
217	C₂×#41	—	2	2	no	—
218	C₂²×Q₈	—	2	4	no	—
219	C₂²×Q₈	D₄×C₁₀₁	1	1	yes	characteristic
220	C₄⋊Q₈	C₂×C₄×C₁₀₁	1	2	yes	—
221	C₄⋊Q₈	C₂×C₄×C₁₀₁	1	4	yes	—
222	#127	C₂×C₄×C₁₀₁	1	2	yes	—
223	#127	C₂×C₄×C₁₀₁	1	4	yes	—
224	#124	—	2	2	no	—
225	#124	—	2	4	no	—
226	C₂²⋊Q₈	—	2	8	no	—
227	C₂²⋊Q₈	—	2	4	no	—
228	#121	—	2	4	no	—
229	#121	—	2	2	no	—
230	#121	—	2	8	no	—
231	#121	—	2	4	no	—
232	#121	C₂³×C₁₀₁	1	4	yes	—
233	C₄×Q₈	C₂×C₄×C₁₀₁	1	4	yes	—
234	C₄×Q₈	D₄×C₁₀₁	1	4	yes	—
235	C₄×D₄	—	2	2	no	—
236	C₄×D₄	—	2	4	no	—
237	C₄×D₄	C₂×C₄×C₁₀₁	1	4	yes	—
238	C₄×D₄	C₂×C₄×C₁₀₁	1	8	yes	—
239	C₂×C₄⋊C₄	—	2	1	no	—
240	C₂×C₄⋊C₄	—	2	1	no	—
241	C₂×C₄⋊C₄	D₄×C₁₀₁	1	1	yes	characteristic
242	C₂×C₄⋊C₄	D₄×C₁₀₁	1	2	yes	—
243	C₂×C₄²	—	2	2	no	—
244	C₂×C₄²	—	2	1	no	—
245	C₂×C₄²	C₂³×C₁₀₁	1	2	yes	—
246	C₂×C₄²	C₂³×C₁₀₁	1	1	yes	characteristic
247	C₄⋊C₈	—	2	2	no	—
248	C₄⋊C₈	—	2	4	no	—
249	C₂²⋊C₈	C₂³×C₁₀₁	1	4	yes	—
250	#97	—	2	4	no	—
251	C₄×C₈	—	2	2	no	—
252	#95	—	2	2	no	—
253	#95	—	2	2	no	—
254	#95	—	2	1	no	—
255	#95	—	2	2	no	—
256	#95	C₂³×C₁₀₁	1	1	yes	characteristic
257	#95	C₂³×C₁₀₁	1	2	yes	—
258	#95	C₂³×C₁₀₁	1	1	yes	characteristic
259	#41	—	4	8	no	—
260	#41	—	4	8	no	—
261	#41	—	4	16	no	—
262	#41	—	4	4	no	—
263	#41	—	4	4	no	—
264	C₂×Q₈	—	2	4	no	—
265	C₂×Q₈	—	2	2	no	—
266	C₂×Q₈	—	2	2	no	—
267	C₂×Q₈	—	2	2	no	—
268	C₂×Q₈	—	4	16	no	—
269	C₂×Q₈	C₂²⋊C₄×C₁₀₁	1	4	yes	—
270	C₂×D₄	—	2	4	no	—
271	C₂×D₄	—	2	4	no	—
272	C₂×D₄	—	2	2	no	—
273	C₂×D₄	—	2	2	no	—
274	C₂×D₄	—	2	4	no	—
275	C₂×D₄	C₂²×C₄×C₁₀₁	1	4	yes	—
276	C₂²×C₄	—	2	1	no	—
277	C₂²×C₄	—	2	8	no	—
278	C₂²×C₄	—	2	4	no	—
279	C₂²×C₄	—	2	2	no	—
280	C₂²×C₄	—	2	1	no	—
281	C₂²×C₄	C₂×D₄×C₁₀₁	1	2	yes	—
282	C₂²×C₄	C₂×D₄×C₁₀₁	1	2	yes	—
283	C₂²×C₄	C₂×D₄×C₁₀₁	1	1	yes	characteristic
284	C₂²×C₄	C₂×D₄×C₁₀₁	1	1	yes	characteristic
285	C₂²×C₄	C₂⁴×C₁₀₁	1	1	yes	characteristic
286	C₂×C₈	—	2	4	no	—
287	C₄⋊C₄	—	2	2	no	—
288	C₄⋊C₄	—	2	4	no	—
289	C₄⋊C₄	—	4	2	no	—
290	C₄⋊C₄	—	4	2	no	—
291	C₄⋊C₄	C₂²⋊C₄×C₁₀₁	1	8	yes	—
292	C₄⋊C₄	C₂²⋊C₄×C₁₀₁	1	4	yes	—
293	C₄⋊C₄	C₂²×C₄×C₁₀₁	1	4	yes	—
294	C₂²⋊C₄	—	2	4	no	—
295	C₂²⋊C₄	—	2	8	no	—
296	C₂²⋊C₄	—	2	4	no	—
297	C₄²	—	4	4	no	—
298	C₄²	—	4	2	no	—
299	C₄²	C₂²×C₄×C₁₀₁	1	4	yes	—
300	C₄²	C₂²×C₄×C₁₀₁	1	2	yes	—
301	C₄²	C₂×D₄×C₁₀₁	1	2	yes	—
302	C₄²	C₂×D₄×C₁₀₁	1	4	yes	—
303	C₂³	—	2	4	no	—
304	C₂³	C₂²×D₄×C₁₀₁	1	1	yes	characteristic
305	Q₈	—	2	8	no	—
306	Q₈	—	4	8	no	—
307	Q₈	—	4	4	no	—
308	D₄	—	4	4	no	—
309	D₄	—	4	8	no	—
310	D₄	—	4	4	no	—
311	D₄	—	4	4	no	—
312	D₄	—	4	4	no	—
313	D₄	—	8	4	no	—
314	D₄	—	8	2	no	—
315	C₂×C₄	—	2	2	no	—
316	C₂×C₄	—	2	2	no	—
317	C₂×C₄	—	2	2	no	—
318	C₂×C₄	—	2	4	no	—
319	C₂×C₄	—	4	2	no	—
320	C₂×C₄	—	4	1	no	—
321	C₂×C₄	—	4	1	no	—
322	C₂×C₄	—	4	16	no	—
323	C₂×C₄	—	4	1	no	—
324	C₂×C₄	—	4	1	no	—
325	C₂×C₄	—	4	8	no	—
326	C₂×C₄	—	4	2	no	—
327	C₂×C₄	—	4	1	no	—
328	C₂×C₄	—	4	1	no	—
329	C₂×C₄	—	4	2	no	—
330	C₂×C₄	—	4	1	no	—
331	C₂×C₄	—	4	2	no	—
332	C₂×C₄	C₂×C₂²⋊C₄×C₁₀₁	1	2	yes	—
333	C₂×C₄	C₂×C₂²⋊C₄×C₁₀₁	1	4	yes	—
334	C₂×C₄	C₂×C₂²⋊C₄×C₁₀₁	1	4	yes	—
335	C₂×C₄	C₂×C₂²⋊C₄×C₁₀₁	1	2	yes	—
336	C₂×C₄	AGL(1,ℤ/8)×C₁₀₁	1	2	yes	—
337	C₂×C₄	AGL(1,ℤ/8)×C₁₀₁	1	2	yes	—
338	C₂×C₄	C₂³×C₄×C₁₀₁	1	1	yes	characteristic
339	C₂×C₄	C₂²×D₄×C₁₀₁	1	1	yes	characteristic
340	C₈	—	4	4	no	—
341	C₂²	—	2	1	no	—
342	C₂²	—	2	1	no	—
343	C₂²	—	4	4	no	—
344	C₂²	—	4	4	no	—
345	C₂²	—	4	4	no	—
346	C₂²	C₂²×C₂²⋊C₄×C₁₀₁	1	1	yes	characteristic
347	C₂²	C₂×AGL(1,ℤ/8)×C₁₀₁	1	1	yes	characteristic
348	C₂²	C₂×AGL(1,ℤ/8)×C₁₀₁	1	1	yes	characteristic
349	C₄	—	2	1	no	—
350	C₄	—	2	1	no	—
351	C₄	—	2	4	no	—
352	C₄	—	2	4	no	—
353	C₄	—	2	2	no	—
354	C₄	—	4	2	no	—
355	C₄	—	4	4	no	—
356	C₄	—	8	1	no	—
357	C₄	—	8	2	no	—
358	C₄	#418×C₁₀₁	1	4	yes	—
359	C₂	—	2	1	no	—
360	C₂	—	2	1	no	—
361	C₂	—	8	4	no	—
362	C₂	C₁₀₁×#2884	1	1	yes	characteristic
363	C₂	C₂×#418×C₁₀₁	1	1	yes	characteristic
364	C₂	C₁₀₁×#2901	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₀₁	C₂²×C₂²⋊C₄
commutator	C₂×C₄	C₂³×C₄×C₁₀₁
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₀₁
prime radical	C₁₀₁×#3497	C₂
LCS	G ▷ C₂×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₀₁ ◁ C₂×C₄×Q₈×C₁₀₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₀₁×#2983	C₂	semidirect
3. C₁₀₁×#2356	C₂	semidirect
4. C₁₀₁×#1517	C₂	semidirect
5. C₁₀₁×#1514	C₂	semidirect
6. C₁₀₁×#1505	C₂	semidirect
7. C₁₀₁×#1502	C₂	semidirect
9. #550×C₁₀₁	C₄	semidirect
10. D₄×Q₈×C₁₀₁	C₄	semidirect
176. #17631	C₁₀₁	direct (N × H)
184. #2983	C₂×C₁₀₁	semidirect
185. #2356	C₂×C₁₀₁	semidirect
186. #1517	C₂×C₁₀₁	semidirect
187. #1514	C₂×C₁₀₁	semidirect
188. #1505	C₂×C₁₀₁	semidirect
189. #1502	C₂×C₁₀₁	semidirect
190. C₁₀₁	#17631	direct (N × H)
192. #550	C₄×C₁₀₁	semidirect
193. D₄×Q₈	C₄×C₁₀₁	semidirect

Maximal subgroups

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

subgroup	index
C₁₀₁×#3497	2
C₁₀₁×#2983	2
C₁₀₁×#2356	2
C₁₀₁×#1517	2
C₁₀₁×#1514	2
C₁₀₁×#1505	2
C₁₀₁×#1502	2
#17631	101

Subgroups — C101×#17631 #38799782

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₀₁×#17631 #38799782