Subgroups — C₁₀₁×#18359 #38800510

Order 25856.

1004 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₀₁×#3501	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₀₁×#3215	C₂	1	2	yes	maximal, complemented
3	C₁₀₁×#2631	C₂	1	1	yes	maximal, characteristic
4	C₁₀₁×#1602	C₂	1	4	yes	maximal, complemented
5	C₁₀₁×#1596	C₂	1	4	yes	maximal, complemented
6	C₁₀₁×#1515	C₂	1	2	yes	maximal, complemented
7	C₁₀₁×#1466	C₂	1	1	yes	maximal, characteristic, complemented
8	#554×C₁₀₁	—	2	2	no	—
9	#554×C₁₀₁	—	2	4	no	—
10	D₄×Q₈×C₁₀₁	—	2	2	no	—
11	#544×C₁₀₁	—	2	1	no	—
12	#543×C₁₀₁	C₂²	1	4	yes	—
13	#533×C₁₀₁	C₂²	1	2	yes	—
14	C₂×#124×C₁₀₁	C₂²	1	1	yes	characteristic
15	C₂×C₂²⋊Q₈×C₁₀₁	—	2	2	no	—
16	#518×C₁₀₁	—	2	1	no	—
17	C₂×C₄×D₄×C₁₀₁	C₂²	1	1	yes	characteristic
18	#497×C₁₀₁	—	2	2	no	—
19	#489×C₁₀₁	—	2	2	no	—
20	#464×C₁₀₁	—	2	4	no	—
21	#451×C₁₀₁	C₂²	1	4	yes	—
22	#450×C₁₀₁	C₂²	1	4	yes	—
23	#432×C₁₀₁	C₂²	1	2	yes	—
24	#397×C₁₀₁	—	2	1	no	—
25	#393×C₁₀₁	C₂²	1	2	yes	—
26	#392×C₁₀₁	—	2	1	no	—
27	#392×C₁₀₁	C₂²	1	2	yes	—
28	#386×C₁₀₁	—	2	2	no	—
29	#383×C₁₀₁	C₂²	1	1	yes	characteristic
30	#328×C₁₀₁	C₂²	1	8	yes	—
31	#323×C₁₀₁	C₂²	1	4	yes	—
32	C₂²×Q₈×C₁₀₁	—	2	2	no	—
33	C₂²×Q₈×C₁₀₁	C₂³	1	1	yes	characteristic
34	C₂²×D₄×C₁₀₁	—	2	2	no	—
35	C₂²×D₄×C₁₀₁	D₄	1	1	yes	characteristic
36	C₂²×D₄×C₁₀₁	C₂³	1	1	yes	characteristic
37	C₂³×C₄×C₁₀₁	D₄	1	2	yes	—
38	C₂×Q₁₆×C₁₀₁	—	2	4	no	—
39	C₂×SD₁₆×C₁₀₁	—	2	4	no	—
40	C₄⋊Q₈×C₁₀₁	—	2	4	no	—
41	C₄⋊Q₈×C₁₀₁	D₄	1	2	yes	complemented
42	C₄⋊Q₈×C₁₀₁	D₄	1	2	yes	complemented
43	#125×C₁₀₁	—	2	4	no	—
44	#125×C₁₀₁	—	2	2	no	—
45	#124×C₁₀₁	—	2	2	no	—
46	#124×C₁₀₁	—	2	2	no	—
47	C₂²⋊Q₈×C₁₀₁	—	2	4	no	—
48	C₂²⋊Q₈×C₁₀₁	—	2	4	no	—
49	C₂²⋊Q₈×C₁₀₁	—	2	8	no	—
50	C₂²⋊Q₈×C₁₀₁	—	2	2	no	—
51	C₂²⋊Q₈×C₁₀₁	—	2	4	no	—
52	C₂²⋊Q₈×C₁₀₁	—	2	8	no	—
53	C₂²⋊Q₈×C₁₀₁	C₂³	1	4	yes	—
54	C₄×Q₈×C₁₀₁	—	2	2	no	—
55	C₄×Q₈×C₁₀₁	D₄	1	4	yes	complemented
56	C₄×D₄×C₁₀₁	—	2	4	no	—
57	C₄×D₄×C₁₀₁	—	2	4	no	—
58	C₄×D₄×C₁₀₁	—	2	2	no	—
59	C₄×D₄×C₁₀₁	—	2	2	no	—
60	#117×C₁₀₁	—	2	2	no	—
61	C₂×C₄⋊C₄×C₁₀₁	—	2	2	no	—
62	C₂×C₄⋊C₄×C₁₀₁	—	2	4	no	—
63	C₂×C₄⋊C₄×C₁₀₁	D₄	1	1	yes	characteristic
64	C₂×C₂²⋊C₄×C₁₀₁	—	2	4	no	—
65	C₂×C₂²⋊C₄×C₁₀₁	—	2	1	no	—
66	C₂×C₂²⋊C₄×C₁₀₁	—	2	1	no	—
67	C₂×C₂²⋊C₄×C₁₀₁	—	2	2	no	—
68	C₂×C₂²⋊C₄×C₁₀₁	—	2	2	no	—
69	C₂×C₂²⋊C₄×C₁₀₁	C₂³	1	2	yes	—
70	C₂×C₄²×C₁₀₁	C₂³	1	1	yes	characteristic
71	C₄⋊C₈×C₁₀₁	—	2	2	no	—
72	#103×C₁₀₁	—	2	4	no	—
73	#102×C₁₀₁	—	2	4	no	—
74	C₂²⋊C₈×C₁₀₁	C₂³	1	4	yes	—
75	#97×C₁₀₁	—	2	2	no	—
76	#95×C₁₀₁	—	2	1	no	—
77	#95×C₁₀₁	—	2	2	no	—
78	#95×C₁₀₁	—	2	1	no	—
79	#95×C₁₀₁	C₂³	1	2	yes	—
80	C₂⁴×C₁₀₁	—	2	1	no	—
81	C₂⁴×C₁₀₁	C₂×D₄	1	2	yes	—
82	C₂×Q₈×C₁₀₁	—	2	4	no	—
83	C₂×Q₈×C₁₀₁	—	2	2	no	—
84	C₂×Q₈×C₁₀₁	—	2	2	no	—
85	C₂×Q₈×C₁₀₁	—	8	1	no	—
86	C₂×Q₈×C₁₀₁	—	8	4	no	—
87	C₂×Q₈×C₁₀₁	C₂×D₄	1	4	yes	—
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	—	4	4	no	—
92	C₂×D₄×C₁₀₁	—	8	1	no	—
93	C₂×D₄×C₁₀₁	—	8	2	no	—
94	C₂×D₄×C₁₀₁	—	8	2	no	—
95	C₂²×C₄×C₁₀₁	—	2	4	no	—
96	C₂²×C₄×C₁₀₁	—	2	4	no	—
97	C₂²×C₄×C₁₀₁	—	2	2	no	—
98	C₂²×C₄×C₁₀₁	—	2	2	no	—
99	C₂²×C₄×C₁₀₁	—	2	2	no	—
100	C₂²×C₄×C₁₀₁	—	2	1	no	—
101	C₂²×C₄×C₁₀₁	—	8	2	no	—
102	C₂²×C₄×C₁₀₁	C₂×D₄	1	1	yes	characteristic
103	C₂²×C₄×C₁₀₁	C₂×D₄	1	2	yes	—
104	C₂²×C₄×C₁₀₁	C₂×D₄	1	1	yes	characteristic
105	C₂²×C₄×C₁₀₁	C₂⁴	1	1	yes	characteristic
106	Q₁₆×C₁₀₁	—	8	4	no	—
107	SD₁₆×C₁₀₁	—	8	4	no	—
108	C₂×C₈×C₁₀₁	—	2	4	no	—
109	C₄⋊C₄×C₁₀₁	—	2	4	no	—
110	C₄⋊C₄×C₁₀₁	—	2	8	no	—
111	C₄⋊C₄×C₁₀₁	—	2	2	no	—
112	C₄⋊C₄×C₁₀₁	—	2	4	no	—
113	C₄⋊C₄×C₁₀₁	—	2	2	no	—
114	C₄⋊C₄×C₁₀₁	—	2	2	no	—
115	C₄⋊C₄×C₁₀₁	—	2	2	no	—
116	C₄⋊C₄×C₁₀₁	—	2	4	no	—
117	C₄⋊C₄×C₁₀₁	C₂×D₄	1	4	yes	—
118	C₂²⋊C₄×C₁₀₁	—	2	8	no	—
119	C₂²⋊C₄×C₁₀₁	—	2	4	no	—
120	C₂²⋊C₄×C₁₀₁	—	2	4	no	—
121	C₂²⋊C₄×C₁₀₁	—	4	2	no	—
122	C₂²⋊C₄×C₁₀₁	—	4	1	no	—
123	C₂²⋊C₄×C₁₀₁	—	4	1	no	—
124	C₂²⋊C₄×C₁₀₁	—	8	2	no	—
125	C₂²⋊C₄×C₁₀₁	—	8	2	no	—
126	C₄²×C₁₀₁	—	2	4	no	—
127	C₄²×C₁₀₁	C₂×D₄	1	2	yes	—
128	C₄²×C₁₀₁	C₂×D₄	1	2	yes	—
129	C₂³×C₁₀₁	—	2	2	no	—
130	C₂³×C₁₀₁	—	2	2	no	—
131	C₂³×C₁₀₁	—	4	2	no	—
132	C₂³×C₁₀₁	—	4	2	no	—
133	C₂³×C₁₀₁	—	4	1	no	—
134	C₂³×C₁₀₁	—	4	1	no	—
135	C₂³×C₁₀₁	—	4	2	no	—
136	C₂³×C₁₀₁	—	4	1	no	—
137	C₂³×C₁₀₁	—	4	2	no	—
138	C₂³×C₁₀₁	#137	1	4	yes	—
139	C₂³×C₁₀₁	C₂²×D₄	1	1	yes	characteristic
140	Q₈×C₁₀₁	—	4	4	no	—
141	Q₈×C₁₀₁	—	4	4	no	—
142	Q₈×C₁₀₁	—	4	4	no	—
143	Q₈×C₁₀₁	—	8	4	no	—
144	D₄×C₁₀₁	—	2	8	no	—
145	D₄×C₁₀₁	—	4	4	no	—
146	D₄×C₁₀₁	—	8	8	no	—
147	C₂×C₄×C₁₀₁	—	2	2	no	—
148	C₂×C₄×C₁₀₁	—	2	4	no	—
149	C₂×C₄×C₁₀₁	—	2	4	no	—
150	C₂×C₄×C₁₀₁	—	2	2	no	—
151	C₂×C₄×C₁₀₁	—	4	1	no	—
152	C₂×C₄×C₁₀₁	—	4	1	no	—
153	C₂×C₄×C₁₀₁	—	4	4	no	—
154	C₂×C₄×C₁₀₁	—	4	2	no	—
155	C₂×C₄×C₁₀₁	—	4	2	no	—
156	C₂×C₄×C₁₀₁	—	4	2	no	—
157	C₂×C₄×C₁₀₁	—	4	2	no	—
158	C₂×C₄×C₁₀₁	—	4	1	no	—
159	C₂×C₄×C₁₀₁	—	4	2	no	—
160	C₂×C₄×C₁₀₁	—	8	2	no	—
161	C₂×C₄×C₁₀₁	—	8	4	no	—
162	C₂×C₄×C₁₀₁	—	8	4	no	—
163	C₂×C₄×C₁₀₁	#120	1	2	yes	—
164	C₂×C₄×C₁₀₁	#120	1	1	yes	characteristic
165	C₂×C₄×C₁₀₁	#120	1	1	yes	characteristic
166	C₂×C₄×C₁₀₁	C₂²×D₄	1	2	yes	—
167	C₈×C₁₀₁	—	4	4	no	—
168	C₂²×C₁₀₁	—	2	1	no	—
169	C₂²×C₁₀₁	—	2	1	no	—
170	C₂²×C₁₀₁	—	2	4	no	—
171	C₂²×C₁₀₁	—	4	4	no	—
172	C₂²×C₁₀₁	—	4	2	no	—
173	C₂²×C₁₀₁	—	4	2	no	—
174	C₂²×C₁₀₁	—	8	2	no	—
175	C₂²×C₁₀₁	—	8	2	no	—
176	C₂²×C₁₀₁	—	8	2	no	—
177	C₂²×C₁₀₁	—	8	1	no	—
178	C₂²×C₁₀₁	—	8	1	no	—
179	C₂²×C₁₀₁	—	8	1	no	—
180	C₂²×C₁₀₁	C₂×#120	1	1	yes	characteristic
181	C₂²×C₁₀₁	C₂×#137	1	2	yes	—
182	C₄×C₁₀₁	—	2	2	no	—
183	C₄×C₁₀₁	—	2	1	no	—
184	C₄×C₁₀₁	—	2	1	no	—
185	C₄×C₁₀₁	—	2	2	no	—
186	C₄×C₁₀₁	—	4	2	no	—
187	C₄×C₁₀₁	—	4	4	no	—
188	C₄×C₁₀₁	—	4	4	no	—
189	C₄×C₁₀₁	—	8	2	no	—
190	C₄×C₁₀₁	—	8	1	no	—
191	#18359	C₁₀₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
192	C₂×C₁₀₁	—	2	2	no	—
193	C₂×C₁₀₁	—	4	4	no	—
194	C₂×C₁₀₁	—	16	1	no	—
195	C₂×C₁₀₁	#3004	1	1	yes	characteristic
196	C₂×C₁₀₁	#3019	1	1	yes	characteristic
197	C₂×C₁₀₁	#3027	1	1	yes	characteristic
198	#3501	C₂×C₁₀₁	1	1	yes	characteristic, complemented
199	#3215	C₂×C₁₀₁	1	2	yes	complemented
200	#2631	C₂×C₁₀₁	1	1	yes	characteristic
201	#1602	C₂×C₁₀₁	1	4	yes	complemented
202	#1596	C₂×C₁₀₁	1	4	yes	complemented
203	#1515	C₂×C₁₀₁	1	2	yes	complemented
204	#1466	C₂×C₁₀₁	1	1	yes	characteristic, complemented
205	C₁₀₁	#18359	1	1	yes	characteristic, direct product factor, Sylow
206	#554	—	2	2	no	—
207	#554	—	2	4	no	—
208	D₄×Q₈	—	2	2	no	—
209	#544	—	2	1	no	—
210	#543	C₂²×C₁₀₁	1	4	yes	—
211	#533	C₂²×C₁₀₁	1	2	yes	—
212	C₂×#124	C₂²×C₁₀₁	1	1	yes	characteristic
213	C₂×C₂²⋊Q₈	—	2	2	no	—
214	#518	—	2	1	no	—
215	C₂×C₄×D₄	C₂²×C₁₀₁	1	1	yes	characteristic
216	#497	—	2	2	no	—
217	#489	—	2	2	no	—
218	#464	—	2	4	no	—
219	#451	C₂²×C₁₀₁	1	4	yes	—
220	#450	C₂²×C₁₀₁	1	4	yes	—
221	#432	C₂²×C₁₀₁	1	2	yes	—
222	#397	—	2	1	no	—
223	#393	C₂²×C₁₀₁	1	2	yes	—
224	#392	—	2	1	no	—
225	#392	C₂²×C₁₀₁	1	2	yes	—
226	#386	—	2	2	no	—
227	#383	C₂²×C₁₀₁	1	1	yes	characteristic
228	#328	C₂²×C₁₀₁	1	8	yes	—
229	#323	C₂²×C₁₀₁	1	4	yes	—
230	C₂²×Q₈	—	2	2	no	—
231	C₂²×Q₈	C₂³×C₁₀₁	1	1	yes	characteristic
232	C₂²×D₄	—	2	2	no	—
233	C₂²×D₄	D₄×C₁₀₁	1	1	yes	characteristic
234	C₂²×D₄	C₂³×C₁₀₁	1	1	yes	characteristic
235	C₂³×C₄	D₄×C₁₀₁	1	2	yes	—
236	C₂×Q₁₆	—	2	4	no	—
237	C₂×SD₁₆	—	2	4	no	—
238	C₄⋊Q₈	—	2	4	no	—
239	C₄⋊Q₈	D₄×C₁₀₁	1	2	yes	complemented
240	C₄⋊Q₈	D₄×C₁₀₁	1	2	yes	complemented
241	#125	—	2	4	no	—
242	#125	—	2	2	no	—
243	#124	—	2	2	no	—
244	#124	—	2	2	no	—
245	C₂²⋊Q₈	—	2	4	no	—
246	C₂²⋊Q₈	—	2	4	no	—
247	C₂²⋊Q₈	—	2	8	no	—
248	C₂²⋊Q₈	—	2	2	no	—
249	C₂²⋊Q₈	—	2	4	no	—
250	C₂²⋊Q₈	—	2	8	no	—
251	C₂²⋊Q₈	C₂³×C₁₀₁	1	4	yes	—
252	C₄×Q₈	—	2	2	no	—
253	C₄×Q₈	D₄×C₁₀₁	1	4	yes	complemented
254	C₄×D₄	—	2	4	no	—
255	C₄×D₄	—	2	4	no	—
256	C₄×D₄	—	2	2	no	—
257	C₄×D₄	—	2	2	no	—
258	#117	—	2	2	no	—
259	C₂×C₄⋊C₄	—	2	2	no	—
260	C₂×C₄⋊C₄	—	2	4	no	—
261	C₂×C₄⋊C₄	D₄×C₁₀₁	1	1	yes	characteristic
262	C₂×C₂²⋊C₄	—	2	4	no	—
263	C₂×C₂²⋊C₄	—	2	1	no	—
264	C₂×C₂²⋊C₄	—	2	1	no	—
265	C₂×C₂²⋊C₄	—	2	2	no	—
266	C₂×C₂²⋊C₄	—	2	2	no	—
267	C₂×C₂²⋊C₄	C₂³×C₁₀₁	1	2	yes	—
268	C₂×C₄²	C₂³×C₁₀₁	1	1	yes	characteristic
269	C₄⋊C₈	—	2	2	no	—
270	#103	—	2	4	no	—
271	#102	—	2	4	no	—
272	C₂²⋊C₈	C₂³×C₁₀₁	1	4	yes	—
273	#97	—	2	2	no	—
274	#95	—	2	1	no	—
275	#95	—	2	1	no	—
276	#95	—	2	2	no	—
277	#95	C₂³×C₁₀₁	1	2	yes	—
278	C₂⁴	—	2	1	no	—
279	C₂⁴	C₂×D₄×C₁₀₁	1	2	yes	—
280	C₂×Q₈	—	2	4	no	—
281	C₂×Q₈	—	2	2	no	—
282	C₂×Q₈	—	2	2	no	—
283	C₂×Q₈	—	8	1	no	—
284	C₂×Q₈	—	8	4	no	—
285	C₂×Q₈	C₂×D₄×C₁₀₁	1	4	yes	—
286	C₂×D₄	—	2	4	no	—
287	C₂×D₄	—	2	2	no	—
288	C₂×D₄	—	2	2	no	—
289	C₂×D₄	—	4	4	no	—
290	C₂×D₄	—	8	1	no	—
291	C₂×D₄	—	8	2	no	—
292	C₂×D₄	—	8	2	no	—
293	C₂²×C₄	—	2	4	no	—
294	C₂²×C₄	—	2	4	no	—
295	C₂²×C₄	—	2	2	no	—
296	C₂²×C₄	—	2	2	no	—
297	C₂²×C₄	—	2	2	no	—
298	C₂²×C₄	—	2	1	no	—
299	C₂²×C₄	—	8	2	no	—
300	C₂²×C₄	C₂×D₄×C₁₀₁	1	1	yes	characteristic
301	C₂²×C₄	C₂×D₄×C₁₀₁	1	2	yes	—
302	C₂²×C₄	C₂×D₄×C₁₀₁	1	1	yes	characteristic
303	C₂²×C₄	C₂⁴×C₁₀₁	1	1	yes	characteristic
304	Q₁₆	—	8	4	no	—
305	SD₁₆	—	8	4	no	—
306	C₂×C₈	—	2	4	no	—
307	C₄⋊C₄	—	2	4	no	—
308	C₄⋊C₄	—	2	8	no	—
309	C₄⋊C₄	—	2	2	no	—
310	C₄⋊C₄	—	2	4	no	—
311	C₄⋊C₄	—	2	2	no	—
312	C₄⋊C₄	—	2	2	no	—
313	C₄⋊C₄	—	2	2	no	—
314	C₄⋊C₄	—	2	4	no	—
315	C₄⋊C₄	C₂×D₄×C₁₀₁	1	4	yes	—
316	C₂²⋊C₄	—	2	8	no	—
317	C₂²⋊C₄	—	2	4	no	—
318	C₂²⋊C₄	—	2	4	no	—
319	C₂²⋊C₄	—	4	2	no	—
320	C₂²⋊C₄	—	4	1	no	—
321	C₂²⋊C₄	—	4	1	no	—
322	C₂²⋊C₄	—	8	2	no	—
323	C₂²⋊C₄	—	8	2	no	—
324	C₄²	—	2	4	no	—
325	C₄²	C₂×D₄×C₁₀₁	1	2	yes	—
326	C₄²	C₂×D₄×C₁₀₁	1	2	yes	—
327	C₂³	—	2	2	no	—
328	C₂³	—	2	2	no	—
329	C₂³	—	4	2	no	—
330	C₂³	—	4	2	no	—
331	C₂³	—	4	1	no	—
332	C₂³	—	4	1	no	—
333	C₂³	—	4	2	no	—
334	C₂³	—	4	1	no	—
335	C₂³	—	4	2	no	—
336	C₂³	#137×C₁₀₁	1	4	yes	—
337	C₂³	C₂²×D₄×C₁₀₁	1	1	yes	characteristic
338	Q₈	—	4	4	no	—
339	Q₈	—	4	4	no	—
340	Q₈	—	4	4	no	—
341	Q₈	—	8	4	no	—
342	D₄	—	2	8	no	—
343	D₄	—	4	4	no	—
344	D₄	—	8	8	no	—
345	C₂×C₄	—	2	2	no	—
346	C₂×C₄	—	2	4	no	—
347	C₂×C₄	—	2	4	no	—
348	C₂×C₄	—	2	2	no	—
349	C₂×C₄	—	4	1	no	—
350	C₂×C₄	—	4	1	no	—
351	C₂×C₄	—	4	4	no	—
352	C₂×C₄	—	4	2	no	—
353	C₂×C₄	—	4	2	no	—
354	C₂×C₄	—	4	2	no	—
355	C₂×C₄	—	4	2	no	—
356	C₂×C₄	—	4	1	no	—
357	C₂×C₄	—	4	2	no	—
358	C₂×C₄	—	8	2	no	—
359	C₂×C₄	—	8	4	no	—
360	C₂×C₄	—	8	4	no	—
361	C₂×C₄	#120×C₁₀₁	1	2	yes	—
362	C₂×C₄	#120×C₁₀₁	1	1	yes	characteristic
363	C₂×C₄	#120×C₁₀₁	1	1	yes	characteristic
364	C₂×C₄	C₂²×D₄×C₁₀₁	1	2	yes	—
365	C₈	—	4	4	no	—
366	C₂²	—	2	1	no	—
367	C₂²	—	2	1	no	—
368	C₂²	—	2	4	no	—
369	C₂²	—	4	4	no	—
370	C₂²	—	4	2	no	—
371	C₂²	—	4	2	no	—
372	C₂²	—	8	2	no	—
373	C₂²	—	8	2	no	—
374	C₂²	—	8	2	no	—
375	C₂²	—	8	1	no	—
376	C₂²	—	8	1	no	—
377	C₂²	—	8	1	no	—
378	C₂²	C₂×#120×C₁₀₁	1	1	yes	characteristic
379	C₂²	C₂×#137×C₁₀₁	1	2	yes	—
380	C₄	—	2	2	no	—
381	C₄	—	2	1	no	—
382	C₄	—	2	1	no	—
383	C₄	—	2	2	no	—
384	C₄	—	4	2	no	—
385	C₄	—	4	4	no	—
386	C₄	—	4	4	no	—
387	C₄	—	8	2	no	—
388	C₄	—	8	1	no	—
389	C₂	—	2	2	no	—
390	C₂	—	4	4	no	—
391	C₂	—	16	1	no	—
392	C₂	C₁₀₁×#3004	1	1	yes	characteristic
393	C₂	C₁₀₁×#3019	1	1	yes	characteristic
394	C₂	C₁₀₁×#3027	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₀₁	C₂×#120
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₀₁
prime radical	C₁₀₁×#2631	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₀₁ ◁ C₂×C₄²×C₁₀₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₀₁×#3501	C₂	semidirect
2. C₁₀₁×#3215	C₂	semidirect
4. C₁₀₁×#1602	C₂	semidirect
5. C₁₀₁×#1596	C₂	semidirect
6. C₁₀₁×#1515	C₂	semidirect
7. C₁₀₁×#1466	C₂	semidirect
41. C₄⋊Q₈×C₁₀₁	D₄	semidirect
42. C₄⋊Q₈×C₁₀₁	D₄	semidirect
55. C₄×Q₈×C₁₀₁	D₄	semidirect
191. #18359	C₁₀₁	direct (N × H)
198. #3501	C₂×C₁₀₁	semidirect
199. #3215	C₂×C₁₀₁	semidirect
201. #1602	C₂×C₁₀₁	semidirect
202. #1596	C₂×C₁₀₁	semidirect
203. #1515	C₂×C₁₀₁	semidirect
204. #1466	C₂×C₁₀₁	semidirect
205. C₁₀₁	#18359	direct (N × H)
239. C₄⋊Q₈	D₄×C₁₀₁	semidirect
240. C₄⋊Q₈	D₄×C₁₀₁	semidirect
253. C₄×Q₈	D₄×C₁₀₁	semidirect

Maximal subgroups

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

subgroup	index
C₁₀₁×#3501	2
C₁₀₁×#3215	2
C₁₀₁×#2631	2
C₁₀₁×#1602	2
C₁₀₁×#1596	2
C₁₀₁×#1515	2
C₁₀₁×#1466	2
#18359	101

Subgroups — C101×#18359 #38800510

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₀₁×#18359 #38800510