Subgroups — C₁₀₁×#23812 #38805963

Order 25856.

1022 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	C₂×#440×C₁₀₁	C₂	1	2	yes	maximal, complemented
2	C₂×C₄×Q₁₆×C₁₀₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₄×D₈×C₁₀₁	C₂	1	1	yes	maximal, characteristic
4	C₁₀₁×#2326	C₂	1	2	yes	maximal, complemented
5	C₁₀₁×#2095	C₂	1	2	yes	maximal, complemented
6	C₁₀₁×#2093	C₂	1	2	yes	maximal, complemented
7	C₁₀₁×#2015	C₂	1	2	yes	maximal, complemented
8	C₁₀₁×#2012	C₂	1	2	yes	maximal
9	C₁₀₁×#1746	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂²×Q₁₆×C₁₀₁	C₂²	1	1	yes	characteristic
11	C₂²×SD₁₆×C₁₀₁	C₂²	1	2	yes	—
12	C₂²×D₈×C₁₀₁	C₂²	1	1	yes	characteristic
13	C₂×#124×C₁₀₁	C₂²	1	2	yes	—
14	C₂×C₄×Q₈×C₁₀₁	C₂²	1	2	yes	—
15	C₂×C₄×D₄×C₁₀₁	C₂²	1	2	yes	—
16	#440×C₁₀₁	—	2	8	no	—
17	C₄×Q₁₆×C₁₀₁	—	2	4	no	—
18	C₄×D₈×C₁₀₁	—	2	4	no	—
19	C₂×#107×C₁₀₁	C₂²	1	1	yes	characteristic
20	C₂×#107×C₁₀₁	C₂²	1	1	yes	characteristic
21	C₂×#107×C₁₀₁	C₂²	1	2	yes	—
22	C₂×#103×C₁₀₁	C₂²	1	2	yes	—
23	C₂×#103×C₁₀₁	C₂²	1	2	yes	—
24	C₂×#102×C₁₀₁	C₂²	1	2	yes	—
25	C₂×#102×C₁₀₁	C₂²	1	2	yes	—
26	C₂×#97×C₁₀₁	C₂²	1	1	yes	characteristic
27	C₂×C₄×C₈×C₁₀₁	C₂²	1	1	yes	characteristic
28	#391×C₁₀₁	C₂²	1	2	yes	—
29	#390×C₁₀₁	C₂²	1	2	yes	—
30	#388×C₁₀₁	—	2	4	no	—
31	#385×C₁₀₁	—	2	4	no	—
32	#384×C₁₀₁	C₂²	1	2	yes	—
33	#376×C₁₀₁	C₂²	1	1	yes	characteristic
34	#336×C₁₀₁	C₂²	1	2	yes	—
35	#336×C₁₀₁	C₂²	1	2	yes	—
36	C₂²×Q₈×C₁₀₁	C₂³	1	2	yes	—
37	C₂²×D₄×C₁₀₁	C₂³	1	2	yes	—
38	C₂³×C₄×C₁₀₁	—	2	2	no	—
39	C₂×Q₁₆×C₁₀₁	—	2	4	no	—
40	C₂×Q₁₆×C₁₀₁	—	2	2	no	—
41	C₂×SD₁₆×C₁₀₁	—	2	4	no	—
42	C₂×SD₁₆×C₁₀₁	—	2	4	no	—
43	C₂×SD₁₆×C₁₀₁	—	2	4	no	—
44	C₂×D₈×C₁₀₁	—	2	4	no	—
45	C₂×D₈×C₁₀₁	—	2	2	no	—
46	C₂²×C₈×C₁₀₁	C₂³	1	1	yes	characteristic
47	C₂²×C₈×C₁₀₁	C₂³	1	1	yes	characteristic
48	C₂²×C₈×C₁₀₁	C₂³	1	2	yes	—
49	#124×C₁₀₁	—	2	4	no	—
50	#124×C₁₀₁	—	2	4	no	—
51	C₄×Q₈×C₁₀₁	—	2	4	no	—
52	C₄×Q₈×C₁₀₁	—	2	4	no	—
53	C₄×D₄×C₁₀₁	—	2	4	no	—
54	C₄×D₄×C₁₀₁	—	2	4	no	—
55	C₂×C₄⋊C₄×C₁₀₁	—	2	2	no	—
56	C₂×C₄⋊C₄×C₁₀₁	—	2	4	no	—
57	C₂×C₄⋊C₄×C₁₀₁	C₂³	1	2	yes	—
58	C₂×C₄⋊C₄×C₁₀₁	C₂³	1	2	yes	—
59	C₂×C₂²⋊C₄×C₁₀₁	—	2	4	no	—
60	C₂×C₂²⋊C₄×C₁₀₁	—	2	2	no	—
61	C₂×C₂²⋊C₄×C₁₀₁	—	2	4	no	—
62	C₂×C₄²×C₁₀₁	—	2	2	no	—
63	C₂×C₄²×C₁₀₁	C₂³	1	2	yes	—
64	C₂×C₄²×C₁₀₁	C₂³	1	1	yes	characteristic
65	#107×C₁₀₁	—	2	2	no	—
66	#107×C₁₀₁	—	2	2	no	—
67	#107×C₁₀₁	—	2	4	no	—
68	#103×C₁₀₁	—	2	4	no	—
69	#103×C₁₀₁	—	2	4	no	—
70	#102×C₁₀₁	—	2	4	no	—
71	#102×C₁₀₁	—	2	4	no	—
72	#97×C₁₀₁	D₄	1	4	yes	—
73	C₄×C₈×C₁₀₁	D₄	1	4	yes	—
74	#95×C₁₀₁	—	2	4	no	—
75	#95×C₁₀₁	D₄	1	2	yes	—
76	#95×C₁₀₁	D₄	1	2	yes	—
77	C₂⁴×C₁₀₁	—	2	2	no	—
78	C₂×Q₈×C₁₀₁	—	2	2	no	—
79	C₂×Q₈×C₁₀₁	—	2	2	no	—
80	C₂×Q₈×C₁₀₁	—	2	2	no	—
81	C₂×Q₈×C₁₀₁	—	2	2	no	—
82	C₂×Q₈×C₁₀₁	—	2	2	no	—
83	C₂×Q₈×C₁₀₁	#41	1	4	yes	—
84	C₂×D₄×C₁₀₁	—	2	2	no	—
85	C₂×D₄×C₁₀₁	—	2	2	no	—
86	C₂×D₄×C₁₀₁	—	2	2	no	—
87	C₂×D₄×C₁₀₁	—	2	2	no	—
88	C₂×D₄×C₁₀₁	—	2	2	no	—
89	C₂×D₄×C₁₀₁	#41	1	4	yes	—
90	C₂²×C₄×C₁₀₁	—	2	2	no	—
91	C₂²×C₄×C₁₀₁	—	2	2	no	—
92	C₂²×C₄×C₁₀₁	—	2	2	no	—
93	C₂²×C₄×C₁₀₁	—	4	4	no	—
94	C₂²×C₄×C₁₀₁	—	8	4	no	—
95	C₂²×C₄×C₁₀₁	C₂×D₄	1	4	yes	—
96	C₂²×C₄×C₁₀₁	C₂×D₄	1	1	yes	characteristic
97	C₂²×C₄×C₁₀₁	C₂×D₄	1	1	yes	characteristic
98	C₂²×C₄×C₁₀₁	C₂⁴	1	1	yes	characteristic
99	Q₁₆×C₁₀₁	—	2	8	no	—
100	SD₁₆×C₁₀₁	—	2	16	no	—
101	D₈×C₁₀₁	—	2	8	no	—
102	C₂×C₈×C₁₀₁	—	2	2	no	—
103	C₂×C₈×C₁₀₁	—	2	2	no	—
104	C₂×C₈×C₁₀₁	—	2	2	no	—
105	C₂×C₈×C₁₀₁	—	2	2	no	—
106	C₂×C₈×C₁₀₁	C₂×D₄	1	2	yes	—
107	C₂×C₈×C₁₀₁	C₂×D₄	1	2	yes	—
108	C₂×C₈×C₁₀₁	C₂×D₄	1	4	yes	—
109	C₄⋊C₄×C₁₀₁	—	2	2	no	—
110	C₄⋊C₄×C₁₀₁	—	2	2	no	—
111	C₄⋊C₄×C₁₀₁	—	2	2	no	—
112	C₄⋊C₄×C₁₀₁	—	2	2	no	—
113	C₄⋊C₄×C₁₀₁	—	4	4	no	—
114	C₄⋊C₄×C₁₀₁	—	8	4	no	—
115	C₂²⋊C₄×C₁₀₁	—	2	16	no	—
116	C₂²⋊C₄×C₁₀₁	—	4	4	no	—
117	C₂²⋊C₄×C₁₀₁	—	8	4	no	—
118	C₄²×C₁₀₁	—	2	2	no	—
119	C₄²×C₁₀₁	—	2	2	no	—
120	C₄²×C₁₀₁	—	4	4	no	—
121	C₄²×C₁₀₁	C₂×D₄	1	2	yes	—
122	C₄²×C₁₀₁	C₂×D₄	1	2	yes	—
123	C₂³×C₁₀₁	—	2	4	no	—
124	C₂³×C₁₀₁	—	4	2	no	—
125	C₂³×C₁₀₁	—	4	2	no	—
126	C₂³×C₁₀₁	—	4	4	no	—
127	C₂³×C₁₀₁	—	4	4	no	—
128	C₂³×C₁₀₁	C₂²×D₄	1	1	yes	characteristic
129	Q₈×C₁₀₁	—	2	4	no	—
130	Q₈×C₁₀₁	—	2	4	no	—
131	Q₈×C₁₀₁	—	4	2	no	—
132	Q₈×C₁₀₁	—	4	2	no	—
133	D₄×C₁₀₁	—	2	4	no	—
134	D₄×C₁₀₁	—	2	4	no	—
135	D₄×C₁₀₁	—	4	2	no	—
136	D₄×C₁₀₁	—	4	2	no	—
137	C₂×C₄×C₁₀₁	—	2	2	no	—
138	C₂×C₄×C₁₀₁	—	2	2	no	—
139	C₂×C₄×C₁₀₁	—	2	4	no	—
140	C₂×C₄×C₁₀₁	—	2	4	no	—
141	C₂×C₄×C₁₀₁	—	2	4	no	—
142	C₂×C₄×C₁₀₁	—	2	4	no	—
143	C₂×C₄×C₁₀₁	—	4	2	no	—
144	C₂×C₄×C₁₀₁	—	4	2	no	—
145	C₂×C₄×C₁₀₁	—	4	2	no	—
146	C₂×C₄×C₁₀₁	—	4	2	no	—
147	C₂×C₄×C₁₀₁	—	4	4	no	—
148	C₂×C₄×C₁₀₁	—	4	4	no	—
149	C₂×C₄×C₁₀₁	—	8	8	no	—
150	C₂×C₄×C₁₀₁	#127	1	2	yes	—
151	C₂×C₄×C₁₀₁	#127	1	2	yes	—
152	C₂×C₄×C₁₀₁	C₂²×D₄	1	1	yes	characteristic
153	C₂×C₄×C₁₀₁	C₂²×D₄	1	1	yes	characteristic
154	C₂×C₄×C₁₀₁	C₂×#41	1	2	yes	—
155	C₂×C₄×C₁₀₁	C₂×#41	1	2	yes	—
156	C₈×C₁₀₁	—	2	2	no	—
157	C₈×C₁₀₁	—	2	4	no	—
158	C₈×C₁₀₁	—	2	2	no	—
159	C₂²×C₁₀₁	—	4	8	no	—
160	C₂²×C₁₀₁	—	4	4	no	—
161	C₂²×C₁₀₁	—	8	4	no	—
162	C₂²×C₁₀₁	—	8	2	no	—
163	C₂²×C₁₀₁	—	8	2	no	—
164	C₂²×C₁₀₁	#525	1	2	yes	—
165	C₂²×C₁₀₁	C₂×#127	1	1	yes	characteristic
166	C₂²×C₁₀₁	#576	1	2	yes	—
167	C₂²×C₁₀₁	#578	1	2	yes	—
168	C₄×C₁₀₁	—	2	2	no	—
169	C₄×C₁₀₁	—	2	2	no	—
170	C₄×C₁₀₁	—	4	4	no	—
171	C₄×C₁₀₁	—	4	4	no	—
172	C₄×C₁₀₁	—	8	2	no	—
173	C₄×C₁₀₁	—	8	2	no	—
174	C₄×C₁₀₁	#525	1	1	yes	characteristic
175	C₄×C₁₀₁	#525	1	2	yes	—
176	C₄×C₁₀₁	#525	1	1	yes	characteristic
177	#23812	C₁₀₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
178	C₂×C₁₀₁	—	8	4	no	—
179	C₂×C₁₀₁	#2397	1	1	yes	characteristic
180	C₂×C₁₀₁	#3124	1	4	yes	—
181	C₂×C₁₀₁	#3155	1	1	yes	characteristic
182	C₂×C₁₀₁	#3156	1	1	yes	characteristic
183	C₂×#440	C₂×C₁₀₁	1	2	yes	complemented
184	C₂×C₄×Q₁₆	C₂×C₁₀₁	1	1	yes	characteristic, complemented
185	C₂×C₄×D₈	C₂×C₁₀₁	1	1	yes	characteristic
186	#2326	C₂×C₁₀₁	1	2	yes	complemented
187	#2095	C₂×C₁₀₁	1	2	yes	complemented
188	#2093	C₂×C₁₀₁	1	2	yes	complemented
189	#2015	C₂×C₁₀₁	1	2	yes	complemented
190	#2012	C₂×C₁₀₁	1	2	yes	—
191	#1746	C₂×C₁₀₁	1	1	yes	characteristic, complemented
192	C₁₀₁	#23812	1	1	yes	characteristic, direct product factor, Sylow
193	C₂²×Q₁₆	C₂²×C₁₀₁	1	1	yes	characteristic
194	C₂²×SD₁₆	C₂²×C₁₀₁	1	2	yes	—
195	C₂²×D₈	C₂²×C₁₀₁	1	1	yes	characteristic
196	C₂×#124	C₂²×C₁₀₁	1	2	yes	—
197	C₂×C₄×Q₈	C₂²×C₁₀₁	1	2	yes	—
198	C₂×C₄×D₄	C₂²×C₁₀₁	1	2	yes	—
199	#440	—	2	8	no	—
200	C₄×Q₁₆	—	2	4	no	—
201	C₄×D₈	—	2	4	no	—
202	C₂×#107	C₂²×C₁₀₁	1	1	yes	characteristic
203	C₂×#107	C₂²×C₁₀₁	1	2	yes	—
204	C₂×#107	C₂²×C₁₀₁	1	1	yes	characteristic
205	C₂×#103	C₂²×C₁₀₁	1	2	yes	—
206	C₂×#103	C₂²×C₁₀₁	1	2	yes	—
207	C₂×#102	C₂²×C₁₀₁	1	2	yes	—
208	C₂×#102	C₂²×C₁₀₁	1	2	yes	—
209	C₂×#97	C₂²×C₁₀₁	1	1	yes	characteristic
210	C₂×C₄×C₈	C₂²×C₁₀₁	1	1	yes	characteristic
211	#391	C₂²×C₁₀₁	1	2	yes	—
212	#390	C₂²×C₁₀₁	1	2	yes	—
213	#388	—	2	4	no	—
214	#385	—	2	4	no	—
215	#384	C₂²×C₁₀₁	1	2	yes	—
216	#376	C₂²×C₁₀₁	1	1	yes	characteristic
217	#336	C₂²×C₁₀₁	1	2	yes	—
218	#336	C₂²×C₁₀₁	1	2	yes	—
219	C₂²×Q₈	C₂³×C₁₀₁	1	2	yes	—
220	C₂²×D₄	C₂³×C₁₀₁	1	2	yes	—
221	C₂³×C₄	—	2	2	no	—
222	C₂×Q₁₆	—	2	4	no	—
223	C₂×Q₁₆	—	2	2	no	—
224	C₂×SD₁₆	—	2	4	no	—
225	C₂×SD₁₆	—	2	4	no	—
226	C₂×SD₁₆	—	2	4	no	—
227	C₂×D₈	—	2	4	no	—
228	C₂×D₈	—	2	2	no	—
229	C₂²×C₈	C₂³×C₁₀₁	1	1	yes	characteristic
230	C₂²×C₈	C₂³×C₁₀₁	1	2	yes	—
231	C₂²×C₈	C₂³×C₁₀₁	1	1	yes	characteristic
232	#124	—	2	4	no	—
233	#124	—	2	4	no	—
234	C₄×Q₈	—	2	4	no	—
235	C₄×Q₈	—	2	4	no	—
236	C₄×D₄	—	2	4	no	—
237	C₄×D₄	—	2	4	no	—
238	C₂×C₄⋊C₄	—	2	2	no	—
239	C₂×C₄⋊C₄	—	2	4	no	—
240	C₂×C₄⋊C₄	C₂³×C₁₀₁	1	2	yes	—
241	C₂×C₄⋊C₄	C₂³×C₁₀₁	1	2	yes	—
242	C₂×C₂²⋊C₄	—	2	4	no	—
243	C₂×C₂²⋊C₄	—	2	2	no	—
244	C₂×C₂²⋊C₄	—	2	4	no	—
245	C₂×C₄²	—	2	2	no	—
246	C₂×C₄²	C₂³×C₁₀₁	1	2	yes	—
247	C₂×C₄²	C₂³×C₁₀₁	1	1	yes	characteristic
248	#107	—	2	2	no	—
249	#107	—	2	2	no	—
250	#107	—	2	4	no	—
251	#103	—	2	4	no	—
252	#103	—	2	4	no	—
253	#102	—	2	4	no	—
254	#102	—	2	4	no	—
255	#97	D₄×C₁₀₁	1	4	yes	—
256	C₄×C₈	D₄×C₁₀₁	1	4	yes	—
257	#95	—	2	4	no	—
258	#95	D₄×C₁₀₁	1	2	yes	—
259	#95	D₄×C₁₀₁	1	2	yes	—
260	C₂⁴	—	2	2	no	—
261	C₂×Q₈	—	2	2	no	—
262	C₂×Q₈	—	2	2	no	—
263	C₂×Q₈	—	2	2	no	—
264	C₂×Q₈	—	2	2	no	—
265	C₂×Q₈	—	2	2	no	—
266	C₂×Q₈	#41×C₁₀₁	1	4	yes	—
267	C₂×D₄	—	2	2	no	—
268	C₂×D₄	—	2	2	no	—
269	C₂×D₄	—	2	2	no	—
270	C₂×D₄	—	2	2	no	—
271	C₂×D₄	—	2	2	no	—
272	C₂×D₄	#41×C₁₀₁	1	4	yes	—
273	C₂²×C₄	—	2	2	no	—
274	C₂²×C₄	—	2	2	no	—
275	C₂²×C₄	—	2	2	no	—
276	C₂²×C₄	—	4	4	no	—
277	C₂²×C₄	—	8	4	no	—
278	C₂²×C₄	C₂×D₄×C₁₀₁	1	4	yes	—
279	C₂²×C₄	C₂×D₄×C₁₀₁	1	1	yes	characteristic
280	C₂²×C₄	C₂×D₄×C₁₀₁	1	1	yes	characteristic
281	C₂²×C₄	C₂⁴×C₁₀₁	1	1	yes	characteristic
282	Q₁₆	—	2	8	no	—
283	SD₁₆	—	2	16	no	—
284	D₈	—	2	8	no	—
285	C₂×C₈	—	2	2	no	—
286	C₂×C₈	—	2	2	no	—
287	C₂×C₈	—	2	2	no	—
288	C₂×C₈	—	2	2	no	—
289	C₂×C₈	C₂×D₄×C₁₀₁	1	2	yes	—
290	C₂×C₈	C₂×D₄×C₁₀₁	1	2	yes	—
291	C₂×C₈	C₂×D₄×C₁₀₁	1	4	yes	—
292	C₄⋊C₄	—	2	2	no	—
293	C₄⋊C₄	—	2	2	no	—
294	C₄⋊C₄	—	2	2	no	—
295	C₄⋊C₄	—	2	2	no	—
296	C₄⋊C₄	—	4	4	no	—
297	C₄⋊C₄	—	8	4	no	—
298	C₂²⋊C₄	—	2	16	no	—
299	C₂²⋊C₄	—	4	4	no	—
300	C₂²⋊C₄	—	8	4	no	—
301	C₄²	—	2	2	no	—
302	C₄²	—	2	2	no	—
303	C₄²	—	4	4	no	—
304	C₄²	C₂×D₄×C₁₀₁	1	2	yes	—
305	C₄²	C₂×D₄×C₁₀₁	1	2	yes	—
306	C₂³	—	2	4	no	—
307	C₂³	—	4	2	no	—
308	C₂³	—	4	2	no	—
309	C₂³	—	4	4	no	—
310	C₂³	—	4	4	no	—
311	C₂³	C₂²×D₄×C₁₀₁	1	1	yes	characteristic
312	Q₈	—	2	4	no	—
313	Q₈	—	2	4	no	—
314	Q₈	—	4	2	no	—
315	Q₈	—	4	2	no	—
316	D₄	—	2	4	no	—
317	D₄	—	2	4	no	—
318	D₄	—	4	2	no	—
319	D₄	—	4	2	no	—
320	C₂×C₄	—	2	2	no	—
321	C₂×C₄	—	2	2	no	—
322	C₂×C₄	—	2	4	no	—
323	C₂×C₄	—	2	4	no	—
324	C₂×C₄	—	2	4	no	—
325	C₂×C₄	—	2	4	no	—
326	C₂×C₄	—	4	2	no	—
327	C₂×C₄	—	4	2	no	—
328	C₂×C₄	—	4	2	no	—
329	C₂×C₄	—	4	2	no	—
330	C₂×C₄	—	4	4	no	—
331	C₂×C₄	—	4	4	no	—
332	C₂×C₄	—	8	8	no	—
333	C₂×C₄	#127×C₁₀₁	1	2	yes	—
334	C₂×C₄	#127×C₁₀₁	1	2	yes	—
335	C₂×C₄	C₂²×D₄×C₁₀₁	1	1	yes	characteristic
336	C₂×C₄	C₂²×D₄×C₁₀₁	1	1	yes	characteristic
337	C₂×C₄	C₂×#41×C₁₀₁	1	2	yes	—
338	C₂×C₄	C₂×#41×C₁₀₁	1	2	yes	—
339	C₈	—	2	2	no	—
340	C₈	—	2	4	no	—
341	C₈	—	2	2	no	—
342	C₂²	—	4	4	no	—
343	C₂²	—	4	8	no	—
344	C₂²	—	8	4	no	—
345	C₂²	—	8	2	no	—
346	C₂²	—	8	2	no	—
347	C₂²	#525×C₁₀₁	1	2	yes	—
348	C₂²	C₂×#127×C₁₀₁	1	1	yes	characteristic
349	C₂²	#576×C₁₀₁	1	2	yes	—
350	C₂²	#578×C₁₀₁	1	2	yes	—
351	C₄	—	2	2	no	—
352	C₄	—	2	2	no	—
353	C₄	—	4	4	no	—
354	C₄	—	4	4	no	—
355	C₄	—	8	2	no	—
356	C₄	—	8	2	no	—
357	C₄	#525×C₁₀₁	1	1	yes	characteristic
358	C₄	#525×C₁₀₁	1	2	yes	—
359	C₄	#525×C₁₀₁	1	1	yes	characteristic
360	C₂	—	8	4	no	—
361	C₂	C₁₀₁×#2397	1	1	yes	characteristic
362	C₂	C₁₀₁×#3124	1	4	yes	—
363	C₂	C₁₀₁×#3155	1	1	yes	characteristic
364	C₂	C₁₀₁×#3156	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₀₁	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₀₁
prime radical	C₂²×D₈×C₁₀₁	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₀₁ ◁ #376×C₁₀₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×#440×C₁₀₁	C₂	semidirect
2. C₂×C₄×Q₁₆×C₁₀₁	C₂	semidirect
4. C₁₀₁×#2326	C₂	semidirect
5. C₁₀₁×#2095	C₂	semidirect
6. C₁₀₁×#2093	C₂	semidirect
7. C₁₀₁×#2015	C₂	semidirect
9. C₁₀₁×#1746	C₂	semidirect
177. #23812	C₁₀₁	direct (N × H)
183. C₂×#440	C₂×C₁₀₁	semidirect
184. C₂×C₄×Q₁₆	C₂×C₁₀₁	semidirect
186. #2326	C₂×C₁₀₁	semidirect
187. #2095	C₂×C₁₀₁	semidirect
188. #2093	C₂×C₁₀₁	semidirect
189. #2015	C₂×C₁₀₁	semidirect
191. #1746	C₂×C₁₀₁	semidirect
192. C₁₀₁	#23812	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×#440×C₁₀₁	2
C₂×C₄×Q₁₆×C₁₀₁	2
C₂×C₄×D₈×C₁₀₁	2
C₁₀₁×#2326	2
C₁₀₁×#2095	2
C₁₀₁×#2093	2
C₁₀₁×#2015	2
C₁₀₁×#2012	2
C₁₀₁×#1746	2
#23812	101

Subgroups — C101×#23812 #38805963

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₀₁×#23812 #38805963