Subgroups — C₁₀₁×#25918 #38808069

Order 25856.

1194 conjugacy classes of subgroups.

The subgroup lattice has 398 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×#3138	C₂	1	2	yes	maximal, complemented
3	C₁₀₁×#2541	C₂	1	1	yes	maximal, characteristic
4	C₁₀₁×#2027	C₂	1	4	yes	maximal, complemented
5	C₁₀₁×#1986	C₂	1	2	yes	maximal, complemented
6	C₁₀₁×#1887	C₂	1	4	yes	maximal, complemented
7	C₄×#100×C₁₀₁	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	C₂²	1	2	yes	—
12	#543×C₁₀₁	—	2	2	no	—
13	#533×C₁₀₁	C₂²	1	2	yes	—
14	C₂×#127×C₁₀₁	C₂²	1	2	yes	—
15	C₂×#127×C₁₀₁	C₂²	1	1	yes	characteristic
16	C₂×C₂²⋊Q₈×C₁₀₁	—	2	2	no	—
17	C₂×#121×C₁₀₁	—	2	2	no	—
18	#518×C₁₀₁	C₂²	1	2	yes	—
19	C₂×C₄×D₄×C₁₀₁	C₂²	1	1	yes	characteristic
20	#490×C₁₀₁	—	2	4	no	—
21	#486×C₁₀₁	—	2	2	no	—
22	#486×C₁₀₁	—	2	2	no	—
23	#418×C₁₀₁	C₂²	1	8	yes	—
24	C₂×#100×C₁₀₁	C₂²	1	2	yes	—
25	C₄×M₁₆×C₁₀₁	C₂²	1	2	yes	—
26	#392×C₁₀₁	—	2	2	no	—
27	#390×C₁₀₁	C₂²	1	2	yes	—
28	C₄×C₄⋊C₄×C₁₀₁	C₂²	1	1	yes	characteristic
29	#343×C₁₀₁	C₂²	1	2	yes	—
30	#339×C₁₀₁	C₂²	1	8	yes	—
31	C₂²×Q₈×C₁₀₁	—	2	2	no	—
32	C₂²×D₄×C₁₀₁	—	2	4	no	—
33	C₂²×D₄×C₁₀₁	—	2	1	no	—
34	C₂²×D₄×C₁₀₁	—	2	1	no	—
35	C₂²×D₄×C₁₀₁	C₂³	1	2	yes	—
36	C₂²×D₄×C₁₀₁	C₂³	1	1	yes	characteristic
37	C₂³×C₄×C₁₀₁	D₄	1	2	yes	—
38	C₂×M₁₆×C₁₀₁	C₂³	1	4	yes	—
39	C₄⋊Q₈×C₁₀₁	—	2	4	no	—
40	C₄⋊Q₈×C₁₀₁	D₄	1	2	yes	complemented
41	C₄⋊Q₈×C₁₀₁	D₄	1	2	yes	complemented
42	#127×C₁₀₁	—	2	8	no	—
43	#127×C₁₀₁	—	2	2	no	—
44	#127×C₁₀₁	—	2	2	no	—
45	#125×C₁₀₁	—	2	4	no	—
46	#125×C₁₀₁	D₄	1	4	yes	complemented
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	8	no	—
51	C₂²⋊Q₈×C₁₀₁	—	2	2	no	—
52	C₂²⋊Q₈×C₁₀₁	—	2	4	no	—
53	C₂²⋊Q₈×C₁₀₁	—	2	2	no	—
54	#121×C₁₀₁	—	4	8	no	—
55	C₄×Q₈×C₁₀₁	—	2	2	no	—
56	C₄×Q₈×C₁₀₁	—	2	2	no	—
57	C₄×D₄×C₁₀₁	—	2	4	no	—
58	C₄×D₄×C₁₀₁	—	2	4	no	—
59	C₄×D₄×C₁₀₁	—	2	2	no	—
60	C₄×D₄×C₁₀₁	—	2	2	no	—
61	#117×C₁₀₁	C₂³	1	4	yes	—
62	C₂×C₄⋊C₄×C₁₀₁	—	2	2	no	—
63	C₂×C₄⋊C₄×C₁₀₁	—	2	4	no	—
64	C₂×C₄⋊C₄×C₁₀₁	—	2	1	no	—
65	C₂×C₄⋊C₄×C₁₀₁	C₂³	1	1	yes	characteristic
66	C₂×C₂²⋊C₄×C₁₀₁	—	2	4	no	—
67	C₂×C₂²⋊C₄×C₁₀₁	—	2	4	no	—
68	C₂×C₂²⋊C₄×C₁₀₁	D₄	1	2	yes	—
69	C₂×C₄²×C₁₀₁	C₂³	1	2	yes	—
70	C₂×C₄²×C₁₀₁	C₂³	1	1	yes	characteristic
71	#102×C₁₀₁	—	2	8	no	—
72	#102×C₁₀₁	—	2	8	no	—
73	#100×C₁₀₁	—	2	4	no	—
74	#97×C₁₀₁	—	2	2	no	—
75	C₄×C₈×C₁₀₁	—	2	2	no	—
76	#95×C₁₀₁	—	2	1	no	—
77	C₂⁴×C₁₀₁	—	2	2	no	—
78	C₂⁴×C₁₀₁	C₂×D₄	1	2	yes	—
79	C₂×Q₈×C₁₀₁	—	2	4	no	—
80	C₂×Q₈×C₁₀₁	—	2	2	no	—
81	C₂×Q₈×C₁₀₁	—	2	2	no	—
82	C₂×Q₈×C₁₀₁	—	8	4	no	—
83	C₂×D₄×C₁₀₁	—	2	2	no	—
84	C₂×D₄×C₁₀₁	—	2	4	no	—
85	C₂×D₄×C₁₀₁	—	2	4	no	—
86	C₂×D₄×C₁₀₁	—	2	2	no	—
87	C₂×D₄×C₁₀₁	—	2	4	no	—
88	C₂×D₄×C₁₀₁	—	4	4	no	—
89	C₂×D₄×C₁₀₁	—	4	8	no	—
90	C₂×D₄×C₁₀₁	—	4	8	no	—
91	C₂×D₄×C₁₀₁	—	4	2	no	—
92	C₂×D₄×C₁₀₁	—	4	1	no	—
93	C₂×D₄×C₁₀₁	—	4	1	no	—
94	C₂×D₄×C₁₀₁	—	8	2	no	—
95	C₂×D₄×C₁₀₁	—	8	4	no	—
96	C₂×D₄×C₁₀₁	#41	1	4	yes	—
97	C₂²×C₄×C₁₀₁	—	2	2	no	—
98	C₂²×C₄×C₁₀₁	—	2	4	no	—
99	C₂²×C₄×C₁₀₁	—	2	4	no	—
100	C₂²×C₄×C₁₀₁	—	2	2	no	—
101	C₂²×C₄×C₁₀₁	—	2	2	no	—
102	C₂²×C₄×C₁₀₁	—	4	4	no	—
103	C₂²×C₄×C₁₀₁	C₂×D₄	1	1	yes	characteristic
104	C₂²×C₄×C₁₀₁	C₂×D₄	1	2	yes	—
105	C₂²×C₄×C₁₀₁	C₂×D₄	1	1	yes	characteristic
106	C₂²×C₄×C₁₀₁	C₂⁴	1	1	yes	characteristic
107	M₁₆×C₁₀₁	—	2	4	no	—
108	M₁₆×C₁₀₁	—	2	4	no	—
109	C₂×C₈×C₁₀₁	—	2	4	no	—
110	C₄⋊C₄×C₁₀₁	—	2	4	no	—
111	C₄⋊C₄×C₁₀₁	—	2	4	no	—
112	C₄⋊C₄×C₁₀₁	—	2	8	no	—
113	C₄⋊C₄×C₁₀₁	—	2	4	no	—
114	C₄⋊C₄×C₁₀₁	—	2	2	no	—
115	C₄⋊C₄×C₁₀₁	—	2	4	no	—
116	C₄⋊C₄×C₁₀₁	—	2	2	no	—
117	C₄⋊C₄×C₁₀₁	—	2	2	no	—
118	C₄⋊C₄×C₁₀₁	C₂×D₄	1	4	yes	—
119	C₄⋊C₄×C₁₀₁	C₂×D₄	1	4	yes	—
120	C₂²⋊C₄×C₁₀₁	—	2	8	no	—
121	C₂²⋊C₄×C₁₀₁	—	2	4	no	—
122	C₂²⋊C₄×C₁₀₁	—	2	4	no	—
123	C₂²⋊C₄×C₁₀₁	—	4	8	no	—
124	C₄²×C₁₀₁	—	2	4	no	—
125	C₄²×C₁₀₁	—	2	4	no	—
126	C₄²×C₁₀₁	C₂×D₄	1	2	yes	—
127	C₄²×C₁₀₁	C₂×D₄	1	2	yes	—
128	C₂³×C₁₀₁	—	2	2	no	—
129	C₂³×C₁₀₁	—	2	2	no	—
130	C₂³×C₁₀₁	—	4	2	no	—
131	C₂³×C₁₀₁	—	4	2	no	—
132	C₂³×C₁₀₁	—	4	4	no	—
133	C₂³×C₁₀₁	—	4	4	no	—
134	C₂³×C₁₀₁	—	4	2	no	—
135	C₂³×C₁₀₁	—	4	2	no	—
136	C₂³×C₁₀₁	—	4	2	no	—
137	C₂³×C₁₀₁	#124	1	4	yes	—
138	C₂³×C₁₀₁	C₂²×D₄	1	1	yes	characteristic
139	Q₈×C₁₀₁	—	4	4	no	—
140	Q₈×C₁₀₁	—	8	2	no	—
141	Q₈×C₁₀₁	—	8	4	no	—
142	D₄×C₁₀₁	—	2	8	no	—
143	D₄×C₁₀₁	—	4	8	no	—
144	D₄×C₁₀₁	—	8	2	no	—
145	D₄×C₁₀₁	—	8	4	no	—
146	D₄×C₁₀₁	—	8	16	no	—
147	D₄×C₁₀₁	—	8	2	no	—
148	C₂×C₄×C₁₀₁	—	2	2	no	—
149	C₂×C₄×C₁₀₁	—	2	4	no	—
150	C₂×C₄×C₁₀₁	—	2	4	no	—
151	C₂×C₄×C₁₀₁	—	2	4	no	—
152	C₂×C₄×C₁₀₁	—	2	2	no	—
153	C₂×C₄×C₁₀₁	—	4	1	no	—
154	C₂×C₄×C₁₀₁	—	4	2	no	—
155	C₂×C₄×C₁₀₁	—	4	2	no	—
156	C₂×C₄×C₁₀₁	—	4	4	no	—
157	C₂×C₄×C₁₀₁	—	4	2	no	—
158	C₂×C₄×C₁₀₁	—	8	2	no	—
159	C₂×C₄×C₁₀₁	—	8	4	no	—
160	C₂×C₄×C₁₀₁	—	8	4	no	—
161	C₂×C₄×C₁₀₁	#120	1	2	yes	—
162	C₂×C₄×C₁₀₁	#120	1	1	yes	characteristic
163	C₂×C₄×C₁₀₁	#120	1	1	yes	characteristic
164	C₂×C₄×C₁₀₁	C₂²×D₄	1	2	yes	—
165	C₂×C₄×C₁₀₁	C₂×#41	1	2	yes	—
166	C₂×C₄×C₁₀₁	2₋¹⁺⁴	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	4	no	—
176	C₂²×C₁₀₁	—	8	4	no	—
177	C₂²×C₁₀₁	—	8	2	no	—
178	C₂²×C₁₀₁	—	8	2	no	—
179	C₂²×C₁₀₁	—	8	2	no	—
180	C₂²×C₁₀₁	C₂×#120	1	1	yes	characteristic
181	C₂²×C₁₀₁	C₂×#124	1	1	yes	characteristic
182	C₂²×C₁₀₁	#536	1	1	yes	characteristic
183	C₄×C₁₀₁	—	2	1	no	—
184	C₄×C₁₀₁	—	2	2	no	—
185	C₄×C₁₀₁	—	4	4	no	—
186	C₄×C₁₀₁	—	4	2	no	—
187	C₄×C₁₀₁	—	4	4	no	—
188	C₄×C₁₀₁	—	4	4	no	—
189	C₄×C₁₀₁	#453	1	2	yes	—
190	C₄×C₁₀₁	#548	1	4	yes	—
191	#25918	C₁₀₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
192	C₂×C₁₀₁	—	2	1	no	—
193	C₂×C₁₀₁	—	2	1	no	—
194	C₂×C₁₀₁	—	4	4	no	—
195	C₂×C₁₀₁	—	16	2	no	—
196	C₂×C₁₀₁	#2436	1	1	yes	characteristic
197	C₂×C₁₀₁	C₂×#453	1	1	yes	characteristic
198	C₂×C₁₀₁	#3021	1	1	yes	characteristic
199	#3501	C₂×C₁₀₁	1	1	yes	characteristic, complemented
200	#3138	C₂×C₁₀₁	1	2	yes	complemented
201	#2541	C₂×C₁₀₁	1	1	yes	characteristic
202	#2027	C₂×C₁₀₁	1	4	yes	complemented
203	#1986	C₂×C₁₀₁	1	2	yes	complemented
204	#1887	C₂×C₁₀₁	1	4	yes	complemented
205	C₄×#100	C₂×C₁₀₁	1	1	yes	characteristic, complemented
206	C₁₀₁	#25918	1	1	yes	characteristic, direct product factor, Sylow
207	#554	—	2	2	no	—
208	#554	—	2	4	no	—
209	D₄×Q₈	—	2	2	no	—
210	#544	C₂²×C₁₀₁	1	2	yes	—
211	#543	—	2	2	no	—
212	#533	C₂²×C₁₀₁	1	2	yes	—
213	C₂×#127	C₂²×C₁₀₁	1	1	yes	characteristic
214	C₂×#127	C₂²×C₁₀₁	1	2	yes	—
215	C₂×C₂²⋊Q₈	—	2	2	no	—
216	C₂×#121	—	2	2	no	—
217	#518	C₂²×C₁₀₁	1	2	yes	—
218	C₂×C₄×D₄	C₂²×C₁₀₁	1	1	yes	characteristic
219	#490	—	2	4	no	—
220	#486	—	2	2	no	—
221	#486	—	2	2	no	—
222	#418	C₂²×C₁₀₁	1	8	yes	—
223	C₂×#100	C₂²×C₁₀₁	1	2	yes	—
224	C₄×M₁₆	C₂²×C₁₀₁	1	2	yes	—
225	#392	—	2	2	no	—
226	#390	C₂²×C₁₀₁	1	2	yes	—
227	C₄×C₄⋊C₄	C₂²×C₁₀₁	1	1	yes	characteristic
228	#343	C₂²×C₁₀₁	1	2	yes	—
229	#339	C₂²×C₁₀₁	1	8	yes	—
230	C₂²×Q₈	—	2	2	no	—
231	C₂²×D₄	—	2	4	no	—
232	C₂²×D₄	—	2	1	no	—
233	C₂²×D₄	—	2	1	no	—
234	C₂²×D₄	C₂³×C₁₀₁	1	2	yes	—
235	C₂²×D₄	C₂³×C₁₀₁	1	1	yes	characteristic
236	C₂³×C₄	D₄×C₁₀₁	1	2	yes	—
237	C₂×M₁₆	C₂³×C₁₀₁	1	4	yes	—
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	#127	—	2	8	no	—
242	#127	—	2	2	no	—
243	#127	—	2	2	no	—
244	#125	—	2	4	no	—
245	#125	D₄×C₁₀₁	1	4	yes	complemented
246	C₂²⋊Q₈	—	2	4	no	—
247	C₂²⋊Q₈	—	2	4	no	—
248	C₂²⋊Q₈	—	2	8	no	—
249	C₂²⋊Q₈	—	2	8	no	—
250	C₂²⋊Q₈	—	2	2	no	—
251	C₂²⋊Q₈	—	2	4	no	—
252	C₂²⋊Q₈	—	2	2	no	—
253	#121	—	4	8	no	—
254	C₄×Q₈	—	2	2	no	—
255	C₄×Q₈	—	2	2	no	—
256	C₄×D₄	—	2	4	no	—
257	C₄×D₄	—	2	4	no	—
258	C₄×D₄	—	2	2	no	—
259	C₄×D₄	—	2	2	no	—
260	#117	C₂³×C₁₀₁	1	4	yes	—
261	C₂×C₄⋊C₄	—	2	2	no	—
262	C₂×C₄⋊C₄	—	2	4	no	—
263	C₂×C₄⋊C₄	—	2	1	no	—
264	C₂×C₄⋊C₄	C₂³×C₁₀₁	1	1	yes	characteristic
265	C₂×C₂²⋊C₄	—	2	4	no	—
266	C₂×C₂²⋊C₄	—	2	4	no	—
267	C₂×C₂²⋊C₄	D₄×C₁₀₁	1	2	yes	—
268	C₂×C₄²	C₂³×C₁₀₁	1	2	yes	—
269	C₂×C₄²	C₂³×C₁₀₁	1	1	yes	characteristic
270	#102	—	2	8	no	—
271	#102	—	2	8	no	—
272	#100	—	2	4	no	—
273	#97	—	2	2	no	—
274	C₄×C₈	—	2	2	no	—
275	#95	—	2	1	no	—
276	C₂⁴	—	2	2	no	—
277	C₂⁴	C₂×D₄×C₁₀₁	1	2	yes	—
278	C₂×Q₈	—	2	4	no	—
279	C₂×Q₈	—	2	2	no	—
280	C₂×Q₈	—	2	2	no	—
281	C₂×Q₈	—	8	4	no	—
282	C₂×D₄	—	2	2	no	—
283	C₂×D₄	—	2	4	no	—
284	C₂×D₄	—	2	4	no	—
285	C₂×D₄	—	2	2	no	—
286	C₂×D₄	—	2	4	no	—
287	C₂×D₄	—	4	4	no	—
288	C₂×D₄	—	4	8	no	—
289	C₂×D₄	—	4	8	no	—
290	C₂×D₄	—	4	2	no	—
291	C₂×D₄	—	4	1	no	—
292	C₂×D₄	—	4	1	no	—
293	C₂×D₄	—	8	2	no	—
294	C₂×D₄	—	8	4	no	—
295	C₂×D₄	#41×C₁₀₁	1	4	yes	—
296	C₂²×C₄	—	2	2	no	—
297	C₂²×C₄	—	2	4	no	—
298	C₂²×C₄	—	2	4	no	—
299	C₂²×C₄	—	2	2	no	—
300	C₂²×C₄	—	2	2	no	—
301	C₂²×C₄	—	4	4	no	—
302	C₂²×C₄	C₂×D₄×C₁₀₁	1	1	yes	characteristic
303	C₂²×C₄	C₂×D₄×C₁₀₁	1	2	yes	—
304	C₂²×C₄	C₂×D₄×C₁₀₁	1	1	yes	characteristic
305	C₂²×C₄	C₂⁴×C₁₀₁	1	1	yes	characteristic
306	M₁₆	—	2	4	no	—
307	M₁₆	—	2	4	no	—
308	C₂×C₈	—	2	4	no	—
309	C₄⋊C₄	—	2	4	no	—
310	C₄⋊C₄	—	2	4	no	—
311	C₄⋊C₄	—	2	8	no	—
312	C₄⋊C₄	—	2	4	no	—
313	C₄⋊C₄	—	2	2	no	—
314	C₄⋊C₄	—	2	4	no	—
315	C₄⋊C₄	—	2	2	no	—
316	C₄⋊C₄	—	2	2	no	—
317	C₄⋊C₄	C₂×D₄×C₁₀₁	1	4	yes	—
318	C₄⋊C₄	C₂×D₄×C₁₀₁	1	4	yes	—
319	C₂²⋊C₄	—	2	8	no	—
320	C₂²⋊C₄	—	2	4	no	—
321	C₂²⋊C₄	—	2	4	no	—
322	C₂²⋊C₄	—	4	8	no	—
323	C₄²	—	2	4	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	4	no	—
332	C₂³	—	4	4	no	—
333	C₂³	—	4	2	no	—
334	C₂³	—	4	2	no	—
335	C₂³	—	4	2	no	—
336	C₂³	#124×C₁₀₁	1	4	yes	—
337	C₂³	C₂²×D₄×C₁₀₁	1	1	yes	characteristic
338	Q₈	—	4	4	no	—
339	Q₈	—	8	2	no	—
340	Q₈	—	8	4	no	—
341	D₄	—	2	8	no	—
342	D₄	—	4	8	no	—
343	D₄	—	8	2	no	—
344	D₄	—	8	4	no	—
345	D₄	—	8	16	no	—
346	D₄	—	8	2	no	—
347	C₂×C₄	—	2	2	no	—
348	C₂×C₄	—	2	4	no	—
349	C₂×C₄	—	2	4	no	—
350	C₂×C₄	—	2	4	no	—
351	C₂×C₄	—	2	2	no	—
352	C₂×C₄	—	4	1	no	—
353	C₂×C₄	—	4	2	no	—
354	C₂×C₄	—	4	2	no	—
355	C₂×C₄	—	4	4	no	—
356	C₂×C₄	—	4	2	no	—
357	C₂×C₄	—	8	2	no	—
358	C₂×C₄	—	8	4	no	—
359	C₂×C₄	—	8	4	no	—
360	C₂×C₄	#120×C₁₀₁	1	2	yes	—
361	C₂×C₄	#120×C₁₀₁	1	1	yes	characteristic
362	C₂×C₄	#120×C₁₀₁	1	1	yes	characteristic
363	C₂×C₄	C₂²×D₄×C₁₀₁	1	2	yes	—
364	C₂×C₄	C₂×#41×C₁₀₁	1	2	yes	—
365	C₂×C₄	2₋¹⁺⁴×C₁₀₁	1	2	yes	—
366	C₈	—	4	4	no	—
367	C₂²	—	2	1	no	—
368	C₂²	—	2	1	no	—
369	C₂²	—	2	4	no	—
370	C₂²	—	4	4	no	—
371	C₂²	—	4	2	no	—
372	C₂²	—	4	2	no	—
373	C₂²	—	8	2	no	—
374	C₂²	—	8	4	no	—
375	C₂²	—	8	4	no	—
376	C₂²	—	8	2	no	—
377	C₂²	—	8	2	no	—
378	C₂²	—	8	2	no	—
379	C₂²	C₂×#120×C₁₀₁	1	1	yes	characteristic
380	C₂²	C₂×#124×C₁₀₁	1	1	yes	characteristic
381	C₂²	#536×C₁₀₁	1	1	yes	characteristic
382	C₄	—	2	1	no	—
383	C₄	—	2	2	no	—
384	C₄	—	4	4	no	—
385	C₄	—	4	2	no	—
386	C₄	—	4	4	no	—
387	C₄	—	4	4	no	—
388	C₄	#453×C₁₀₁	1	2	yes	—
389	C₄	#548×C₁₀₁	1	4	yes	—
390	C₂	—	2	1	no	—
391	C₂	—	2	1	no	—
392	C₂	—	4	4	no	—
393	C₂	—	16	2	no	—
394	C₂	C₁₀₁×#2436	1	1	yes	characteristic
395	C₂	C₂×#453×C₁₀₁	1	1	yes	characteristic
396	C₂	C₁₀₁×#3021	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₀₁	C₂×#120
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₀₁
prime radical	C₁₀₁×#2541	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ 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×#3138	C₂	semidirect
4. C₁₀₁×#2027	C₂	semidirect
5. C₁₀₁×#1986	C₂	semidirect
6. C₁₀₁×#1887	C₂	semidirect
7. C₄×#100×C₁₀₁	C₂	semidirect
40. C₄⋊Q₈×C₁₀₁	D₄	semidirect
41. C₄⋊Q₈×C₁₀₁	D₄	semidirect
46. #125×C₁₀₁	D₄	semidirect
191. #25918	C₁₀₁	direct (N × H)
199. #3501	C₂×C₁₀₁	semidirect
200. #3138	C₂×C₁₀₁	semidirect
202. #2027	C₂×C₁₀₁	semidirect
203. #1986	C₂×C₁₀₁	semidirect
204. #1887	C₂×C₁₀₁	semidirect
205. C₄×#100	C₂×C₁₀₁	semidirect
206. C₁₀₁	#25918	direct (N × H)
239. C₄⋊Q₈	D₄×C₁₀₁	semidirect
240. C₄⋊Q₈	D₄×C₁₀₁	semidirect
245. #125	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×#3138	2
C₁₀₁×#2541	2
C₁₀₁×#2027	2
C₁₀₁×#1986	2
C₁₀₁×#1887	2
C₄×#100×C₁₀₁	2
#25918	101

Subgroups — C101×#25918 #38808069

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₀₁×#25918 #38808069