Subgroups — Q₈×#99×C₁₀₁ #38804663

Order 25856.

1354 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₄×Q₈×C₁₀₁	C₂	1	1	yes	maximal, characteristic
2	Q₈×C₂²⋊C₄×C₁₀₁	C₂	1	2	yes	maximal, complemented
3	C₁₀₁×#1996	C₂	1	6	yes	maximal, complemented
4	C₁₀₁×#1799	C₂	1	3	yes	maximal
5	C₄×#99×C₁₀₁	C₂	1	3	yes	maximal
6	C₂³×Q₈×C₁₀₁	C₄	1	1	yes	characteristic, complemented
7	C₂³×Q₈×C₁₀₁	C₂²	1	1	yes	characteristic
8	D₄×Q₈×C₁₀₁	—	2	2	no	—
9	D₄×Q₈×C₁₀₁	—	2	6	no	—
10	C₂×C₄⋊Q₈×C₁₀₁	C₄	1	3	yes	complemented
11	C₂×C₂²⋊Q₈×C₁₀₁	C₄	1	3	yes	complemented
12	C₂×C₂²⋊Q₈×C₁₀₁	C₂²	1	3	yes	—
13	C₂×C₄×Q₈×C₁₀₁	—	2	2	no	—
14	C₂×C₄×Q₈×C₁₀₁	C₄	1	1	yes	characteristic, complemented
15	C₂×C₄×D₄×C₁₀₁	C₂²	1	3	yes	—
16	C₂×#99×C₁₀₁	C₂²	1	3	yes	—
17	C₂×#99×C₁₀₁	C₂²	1	1	yes	characteristic
18	#391×C₁₀₁	—	2	6	no	—
19	#380×C₁₀₁	C₂²	1	6	yes	—
20	C₄×C₂²⋊C₄×C₁₀₁	C₂²	1	6	yes	—
21	#342×C₁₀₁	C₂²	1	6	yes	—
22	#342×C₁₀₁	C₂²	1	6	yes	—
23	C₂²×Q₈×C₁₀₁	—	2	3	no	—
24	C₂²×Q₈×C₁₀₁	—	2	1	no	—
25	C₂²×Q₈×C₁₀₁	—	4	4	no	—
26	C₂²×Q₈×C₁₀₁	—	4	4	no	—
27	C₂²×Q₈×C₁₀₁	C₂×C₄	1	1	yes	characteristic
28	C₂²×Q₈×C₁₀₁	C₂×C₄	1	3	yes	—
29	C₂²×Q₈×C₁₀₁	C₂×C₄	1	3	yes	—
30	C₂²×Q₈×C₁₀₁	D₄	1	2	yes	—
31	C₂²×Q₈×C₁₀₁	D₄	1	6	yes	—
32	C₂²×D₄×C₁₀₁	C₂³	1	1	yes	characteristic
33	C₂³×C₄×C₁₀₁	C₂×C₄	1	3	yes	—
34	C₂³×C₄×C₁₀₁	C₂³	1	3	yes	—
35	C₄⋊Q₈×C₁₀₁	—	2	6	no	—
36	C₄⋊Q₈×C₁₀₁	—	2	6	no	—
37	C₂²⋊Q₈×C₁₀₁	—	2	6	no	—
38	C₂²⋊Q₈×C₁₀₁	—	2	6	no	—
39	C₂²⋊Q₈×C₁₀₁	—	2	6	no	—
40	C₂²⋊Q₈×C₁₀₁	—	2	6	no	—
41	C₄×Q₈×C₁₀₁	—	2	3	no	—
42	C₄×Q₈×C₁₀₁	—	2	1	no	—
43	C₄×Q₈×C₁₀₁	—	4	8	no	—
44	C₄×D₄×C₁₀₁	—	2	6	no	—
45	C₄×D₄×C₁₀₁	—	2	6	no	—
46	C₂×C₄⋊C₄×C₁₀₁	—	2	6	no	—
47	C₂×C₄⋊C₄×C₁₀₁	C₂×C₄	1	3	yes	—
48	C₂×C₄⋊C₄×C₁₀₁	C₂×C₄	1	3	yes	—
49	C₂×C₄⋊C₄×C₁₀₁	C₂×C₄	1	6	yes	—
50	C₂×C₂²⋊C₄×C₁₀₁	C₂×C₄	1	3	yes	—
51	C₂×C₂²⋊C₄×C₁₀₁	C₂³	1	6	yes	—
52	C₂×C₂²⋊C₄×C₁₀₁	C₂³	1	3	yes	—
53	C₂×C₂²⋊C₄×C₁₀₁	C₂³	1	2	yes	—
54	C₂×C₄²×C₁₀₁	—	2	6	no	—
55	C₂×C₄²×C₁₀₁	C₂×C₄	1	3	yes	—
56	#99×C₁₀₁	—	2	6	no	—
57	#99×C₁₀₁	Q₈	1	4	yes	direct product factor
58	#95×C₁₀₁	—	2	6	no	—
59	#95×C₁₀₁	—	2	6	no	—
60	C₂⁴×C₁₀₁	C₂²×C₄	1	1	yes	characteristic
61	C₂⁴×C₁₀₁	C₂⁴	1	1	yes	characteristic
62	C₂×Q₈×C₁₀₁	—	2	8	no	—
63	C₂×Q₈×C₁₀₁	—	2	4	no	—
64	C₂×Q₈×C₁₀₁	—	2	3	no	—
65	C₂×Q₈×C₁₀₁	—	2	3	no	—
66	C₂×Q₈×C₁₀₁	—	4	6	no	—
67	C₂×Q₈×C₁₀₁	—	4	12	no	—
68	C₂×Q₈×C₁₀₁	—	4	6	no	—
69	C₂×Q₈×C₁₀₁	—	4	12	no	—
70	C₂×Q₈×C₁₀₁	—	4	4	no	—
71	C₂×Q₈×C₁₀₁	C₂²⋊C₄	1	3	yes	—
72	C₂×Q₈×C₁₀₁	C₂²⋊C₄	1	6	yes	—
73	C₂×Q₈×C₁₀₁	C₂²⋊C₄	1	6	yes	—
74	C₂×Q₈×C₁₀₁	C₂²⋊C₄	1	1	yes	characteristic
75	C₂×D₄×C₁₀₁	—	2	2	no	—
76	C₂×D₄×C₁₀₁	—	2	2	no	—
77	C₂×D₄×C₁₀₁	C₂×Q₈	1	2	yes	—
78	C₂×D₄×C₁₀₁	#41	1	2	yes	—
79	C₂²×C₄×C₁₀₁	—	2	2	no	—
80	C₂²×C₄×C₁₀₁	—	2	3	no	—
81	C₂²×C₄×C₁₀₁	—	2	3	no	—
82	C₂²×C₄×C₁₀₁	—	2	6	no	—
83	C₂²×C₄×C₁₀₁	—	4	6	no	—
84	C₂²×C₄×C₁₀₁	—	4	6	no	—
85	C₂²×C₄×C₁₀₁	C₂²×C₄	1	3	yes	—
86	C₂²×C₄×C₁₀₁	C₂²×C₄	1	1	yes	characteristic
87	C₂²×C₄×C₁₀₁	C₂²×C₄	1	3	yes	—
88	C₂²×C₄×C₁₀₁	C₂²×C₄	1	3	yes	—
89	C₂²×C₄×C₁₀₁	C₂²×C₄	1	3	yes	—
90	C₂²×C₄×C₁₀₁	C₂×D₄	1	6	yes	—
91	C₂²×C₄×C₁₀₁	C₂×D₄	1	6	yes	—
92	C₄⋊C₄×C₁₀₁	—	2	6	no	—
93	C₄⋊C₄×C₁₀₁	—	2	3	no	—
94	C₄⋊C₄×C₁₀₁	—	2	3	no	—
95	C₄⋊C₄×C₁₀₁	—	2	12	no	—
96	C₄⋊C₄×C₁₀₁	—	4	12	no	—
97	C₂²⋊C₄×C₁₀₁	—	2	6	no	—
98	C₂²⋊C₄×C₁₀₁	—	2	2	no	—
99	C₂²⋊C₄×C₁₀₁	—	2	6	no	—
100	C₂²⋊C₄×C₁₀₁	—	2	6	no	—
101	C₂²⋊C₄×C₁₀₁	—	2	6	no	—
102	C₂²⋊C₄×C₁₀₁	C₂×Q₈	1	4	yes	complemented
103	C₄²×C₁₀₁	—	2	3	no	—
104	C₄²×C₁₀₁	—	2	3	no	—
105	C₄²×C₁₀₁	—	4	12	no	—
106	C₂³×C₁₀₁	—	2	1	no	—
107	C₂³×C₁₀₁	—	2	1	no	—
108	C₂³×C₁₀₁	—	4	1	no	—
109	C₂³×C₁₀₁	—	4	1	no	—
110	C₂³×C₁₀₁	—	4	1	no	—
111	C₂³×C₁₀₁	—	4	1	no	—
112	C₂³×C₁₀₁	C₄×Q₈	1	2	yes	complemented
113	C₂³×C₁₀₁	C₂³×C₄	1	1	yes	characteristic
114	C₂³×C₁₀₁	C₂²×D₄	1	2	yes	—
115	C₂³×C₁₀₁	C₂²×Q₈	1	1	yes	characteristic
116	C₂³×C₁₀₁	C₂×#41	1	1	yes	characteristic
117	C₂³×C₁₀₁	2₋¹⁺⁴	1	2	yes	—
118	Q₈×C₁₀₁	—	2	6	no	—
119	Q₈×C₁₀₁	—	2	12	no	—
120	Q₈×C₁₀₁	—	4	6	no	—
121	Q₈×C₁₀₁	—	4	6	no	—
122	Q₈×C₁₀₁	—	4	6	no	—
123	Q₈×C₁₀₁	#99	1	4	yes	direct product factor
124	D₄×C₁₀₁	—	2	4	no	—
125	D₄×C₁₀₁	—	2	4	no	—
126	C₂×C₄×C₁₀₁	—	2	1	no	—
127	C₂×C₄×C₁₀₁	—	2	1	no	—
128	C₂×C₄×C₁₀₁	—	2	12	no	—
129	C₂×C₄×C₁₀₁	—	2	6	no	—
130	C₂×C₄×C₁₀₁	—	2	3	no	—
131	C₂×C₄×C₁₀₁	—	2	3	no	—
132	C₂×C₄×C₁₀₁	—	2	4	no	—
133	C₂×C₄×C₁₀₁	—	4	3	no	—
134	C₂×C₄×C₁₀₁	—	4	6	no	—
135	C₂×C₄×C₁₀₁	—	4	6	no	—
136	C₂×C₄×C₁₀₁	—	4	2	no	—
137	C₂×C₄×C₁₀₁	—	4	2	no	—
138	C₂×C₄×C₁₀₁	—	4	6	no	—
139	C₂×C₄×C₁₀₁	—	4	3	no	—
140	C₂×C₄×C₁₀₁	—	4	3	no	—
141	C₂×C₄×C₁₀₁	—	4	6	no	—
142	C₂×C₄×C₁₀₁	—	4	6	no	—
143	C₂×C₄×C₁₀₁	—	4	6	no	—
144	C₂×C₄×C₁₀₁	C₂×C₂²⋊C₄	1	3	yes	—
145	C₂×C₄×C₁₀₁	C₂×C₂²⋊C₄	1	6	yes	—
146	C₂×C₄×C₁₀₁	C₂×C₂²⋊C₄	1	3	yes	—
147	C₂×C₄×C₁₀₁	C₄×Q₈	1	2	yes	complemented
148	C₂²×C₁₀₁	—	2	2	no	—
149	C₂²×C₁₀₁	—	2	1	no	—
150	C₂²×C₁₀₁	—	2	2	no	—
151	C₂²×C₁₀₁	—	2	1	no	—
152	C₂²×C₁₀₁	—	2	2	no	—
153	C₂²×C₁₀₁	—	4	1	no	—
154	C₂²×C₁₀₁	—	4	1	no	—
155	C₂²×C₁₀₁	—	4	2	no	—
156	C₂²×C₁₀₁	—	4	2	no	—
157	C₂²×C₁₀₁	—	4	2	no	—
158	C₂²×C₁₀₁	—	4	1	no	—
159	C₂²×C₁₀₁	—	4	1	no	—
160	C₂²×C₁₀₁	C₂²×C₂²⋊C₄	1	1	yes	characteristic
161	C₂²×C₁₀₁	C₂×C₄×Q₈	1	1	yes	characteristic
162	C₂²×C₁₀₁	#519	1	1	yes	characteristic
163	C₂²×C₁₀₁	#548	1	2	yes	—
164	C₂²×C₁₀₁	D₄×Q₈	1	2	yes	—
165	C₄×C₁₀₁	—	2	2	no	—
166	C₄×C₁₀₁	—	2	3	no	—
167	C₄×C₁₀₁	—	2	6	no	—
168	C₄×C₁₀₁	—	4	4	no	—
169	C₄×C₁₀₁	—	4	3	no	—
170	C₄×C₁₀₁	—	4	3	no	—
171	C₄×C₁₀₁	—	8	6	no	—
172	C₄×C₁₀₁	C₂×#99	1	6	yes	—
173	Q₈×#99	C₁₀₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
174	C₂×C₁₀₁	—	2	2	no	—
175	C₂×C₁₀₁	—	2	2	no	—
176	C₂×C₁₀₁	—	2	1	no	—
177	C₂×C₁₀₁	—	2	1	no	—
178	C₂×C₁₀₁	—	4	2	no	—
179	C₂×C₁₀₁	Q₈×C₂²⋊C₄	1	1	yes	characteristic
180	C₂×C₁₀₁	C₂²×#99	1	1	yes	characteristic
181	C₂×C₁₀₁	#2884	1	1	yes	characteristic
182	C₂×D₄×Q₈	C₂×C₁₀₁	1	1	yes	characteristic
183	Q₈×C₂²⋊C₄	C₂×C₁₀₁	1	2	yes	complemented
184	#1996	C₂×C₁₀₁	1	6	yes	complemented
185	#1799	C₂×C₁₀₁	1	3	yes	—
186	C₄×#99	C₂×C₁₀₁	1	3	yes	—
187	C₁₀₁	Q₈×#99	1	1	yes	characteristic, direct product factor, Sylow
188	C₂³×Q₈	C₄×C₁₀₁	1	1	yes	characteristic, complemented
189	C₂³×Q₈	C₂²×C₁₀₁	1	1	yes	characteristic
190	D₄×Q₈	—	2	2	no	—
191	D₄×Q₈	—	2	6	no	—
192	C₂×C₄⋊Q₈	C₄×C₁₀₁	1	3	yes	complemented
193	C₂×C₂²⋊Q₈	C₄×C₁₀₁	1	3	yes	complemented
194	C₂×C₂²⋊Q₈	C₂²×C₁₀₁	1	3	yes	—
195	C₂×C₄×Q₈	—	2	2	no	—
196	C₂×C₄×Q₈	C₄×C₁₀₁	1	1	yes	characteristic, complemented
197	C₂×C₄×D₄	C₂²×C₁₀₁	1	3	yes	—
198	C₂×#99	C₂²×C₁₀₁	1	3	yes	—
199	C₂×#99	C₂²×C₁₀₁	1	1	yes	characteristic
200	#391	—	2	6	no	—
201	#380	C₂²×C₁₀₁	1	6	yes	—
202	C₄×C₂²⋊C₄	C₂²×C₁₀₁	1	6	yes	—
203	#342	C₂²×C₁₀₁	1	6	yes	—
204	#342	C₂²×C₁₀₁	1	6	yes	—
205	C₂²×Q₈	—	2	3	no	—
206	C₂²×Q₈	—	2	1	no	—
207	C₂²×Q₈	—	4	4	no	—
208	C₂²×Q₈	—	4	4	no	—
209	C₂²×Q₈	C₂×C₄×C₁₀₁	1	1	yes	characteristic
210	C₂²×Q₈	C₂×C₄×C₁₀₁	1	3	yes	—
211	C₂²×Q₈	C₂×C₄×C₁₀₁	1	3	yes	—
212	C₂²×Q₈	D₄×C₁₀₁	1	2	yes	—
213	C₂²×Q₈	D₄×C₁₀₁	1	6	yes	—
214	C₂²×D₄	C₂³×C₁₀₁	1	1	yes	characteristic
215	C₂³×C₄	C₂×C₄×C₁₀₁	1	3	yes	—
216	C₂³×C₄	C₂³×C₁₀₁	1	3	yes	—
217	C₄⋊Q₈	—	2	6	no	—
218	C₄⋊Q₈	—	2	6	no	—
219	C₂²⋊Q₈	—	2	6	no	—
220	C₂²⋊Q₈	—	2	6	no	—
221	C₂²⋊Q₈	—	2	6	no	—
222	C₂²⋊Q₈	—	2	6	no	—
223	C₄×Q₈	—	2	3	no	—
224	C₄×Q₈	—	2	1	no	—
225	C₄×Q₈	—	4	8	no	—
226	C₄×D₄	—	2	6	no	—
227	C₄×D₄	—	2	6	no	—
228	C₂×C₄⋊C₄	—	2	6	no	—
229	C₂×C₄⋊C₄	C₂×C₄×C₁₀₁	1	3	yes	—
230	C₂×C₄⋊C₄	C₂×C₄×C₁₀₁	1	3	yes	—
231	C₂×C₄⋊C₄	C₂×C₄×C₁₀₁	1	6	yes	—
232	C₂×C₂²⋊C₄	C₂×C₄×C₁₀₁	1	3	yes	—
233	C₂×C₂²⋊C₄	C₂³×C₁₀₁	1	6	yes	—
234	C₂×C₂²⋊C₄	C₂³×C₁₀₁	1	3	yes	—
235	C₂×C₂²⋊C₄	C₂³×C₁₀₁	1	2	yes	—
236	C₂×C₄²	—	2	6	no	—
237	C₂×C₄²	C₂×C₄×C₁₀₁	1	3	yes	—
238	#99	—	2	6	no	—
239	#99	Q₈×C₁₀₁	1	4	yes	direct product factor
240	#95	—	2	6	no	—
241	#95	—	2	6	no	—
242	C₂⁴	C₂²×C₄×C₁₀₁	1	1	yes	characteristic
243	C₂⁴	C₂⁴×C₁₀₁	1	1	yes	characteristic
244	C₂×Q₈	—	2	8	no	—
245	C₂×Q₈	—	2	4	no	—
246	C₂×Q₈	—	2	3	no	—
247	C₂×Q₈	—	2	3	no	—
248	C₂×Q₈	—	4	6	no	—
249	C₂×Q₈	—	4	12	no	—
250	C₂×Q₈	—	4	6	no	—
251	C₂×Q₈	—	4	12	no	—
252	C₂×Q₈	—	4	4	no	—
253	C₂×Q₈	C₂²⋊C₄×C₁₀₁	1	3	yes	—
254	C₂×Q₈	C₂²⋊C₄×C₁₀₁	1	6	yes	—
255	C₂×Q₈	C₂²⋊C₄×C₁₀₁	1	6	yes	—
256	C₂×Q₈	C₂²⋊C₄×C₁₀₁	1	1	yes	characteristic
257	C₂×D₄	—	2	2	no	—
258	C₂×D₄	—	2	2	no	—
259	C₂×D₄	C₂×Q₈×C₁₀₁	1	2	yes	—
260	C₂×D₄	#41×C₁₀₁	1	2	yes	—
261	C₂²×C₄	—	2	2	no	—
262	C₂²×C₄	—	2	3	no	—
263	C₂²×C₄	—	2	3	no	—
264	C₂²×C₄	—	2	6	no	—
265	C₂²×C₄	—	4	6	no	—
266	C₂²×C₄	—	4	6	no	—
267	C₂²×C₄	C₂²×C₄×C₁₀₁	1	3	yes	—
268	C₂²×C₄	C₂²×C₄×C₁₀₁	1	1	yes	characteristic
269	C₂²×C₄	C₂²×C₄×C₁₀₁	1	3	yes	—
270	C₂²×C₄	C₂²×C₄×C₁₀₁	1	3	yes	—
271	C₂²×C₄	C₂²×C₄×C₁₀₁	1	3	yes	—
272	C₂²×C₄	C₂×D₄×C₁₀₁	1	6	yes	—
273	C₂²×C₄	C₂×D₄×C₁₀₁	1	6	yes	—
274	C₄⋊C₄	—	2	6	no	—
275	C₄⋊C₄	—	2	3	no	—
276	C₄⋊C₄	—	2	3	no	—
277	C₄⋊C₄	—	2	12	no	—
278	C₄⋊C₄	—	4	12	no	—
279	C₂²⋊C₄	—	2	6	no	—
280	C₂²⋊C₄	—	2	2	no	—
281	C₂²⋊C₄	—	2	6	no	—
282	C₂²⋊C₄	—	2	6	no	—
283	C₂²⋊C₄	—	2	6	no	—
284	C₂²⋊C₄	C₂×Q₈×C₁₀₁	1	4	yes	complemented
285	C₄²	—	2	3	no	—
286	C₄²	—	2	3	no	—
287	C₄²	—	4	12	no	—
288	C₂³	—	2	1	no	—
289	C₂³	—	2	1	no	—
290	C₂³	—	4	1	no	—
291	C₂³	—	4	1	no	—
292	C₂³	—	4	1	no	—
293	C₂³	—	4	1	no	—
294	C₂³	C₄×Q₈×C₁₀₁	1	2	yes	complemented
295	C₂³	C₂³×C₄×C₁₀₁	1	1	yes	characteristic
296	C₂³	C₂²×D₄×C₁₀₁	1	2	yes	—
297	C₂³	C₂²×Q₈×C₁₀₁	1	1	yes	characteristic
298	C₂³	C₂×#41×C₁₀₁	1	1	yes	characteristic
299	C₂³	2₋¹⁺⁴×C₁₀₁	1	2	yes	—
300	Q₈	—	2	6	no	—
301	Q₈	—	2	12	no	—
302	Q₈	—	4	6	no	—
303	Q₈	—	4	6	no	—
304	Q₈	—	4	6	no	—
305	Q₈	#99×C₁₀₁	1	4	yes	direct product factor
306	D₄	—	2	4	no	—
307	D₄	—	2	4	no	—
308	C₂×C₄	—	2	1	no	—
309	C₂×C₄	—	2	1	no	—
310	C₂×C₄	—	2	12	no	—
311	C₂×C₄	—	2	6	no	—
312	C₂×C₄	—	2	3	no	—
313	C₂×C₄	—	2	3	no	—
314	C₂×C₄	—	2	4	no	—
315	C₂×C₄	—	4	3	no	—
316	C₂×C₄	—	4	6	no	—
317	C₂×C₄	—	4	6	no	—
318	C₂×C₄	—	4	2	no	—
319	C₂×C₄	—	4	2	no	—
320	C₂×C₄	—	4	6	no	—
321	C₂×C₄	—	4	3	no	—
322	C₂×C₄	—	4	3	no	—
323	C₂×C₄	—	4	6	no	—
324	C₂×C₄	—	4	6	no	—
325	C₂×C₄	—	4	6	no	—
326	C₂×C₄	C₂×C₂²⋊C₄×C₁₀₁	1	3	yes	—
327	C₂×C₄	C₂×C₂²⋊C₄×C₁₀₁	1	6	yes	—
328	C₂×C₄	C₂×C₂²⋊C₄×C₁₀₁	1	3	yes	—
329	C₂×C₄	C₄×Q₈×C₁₀₁	1	2	yes	complemented
330	C₂²	—	2	2	no	—
331	C₂²	—	2	1	no	—
332	C₂²	—	2	2	no	—
333	C₂²	—	2	1	no	—
334	C₂²	—	2	2	no	—
335	C₂²	—	4	1	no	—
336	C₂²	—	4	1	no	—
337	C₂²	—	4	2	no	—
338	C₂²	—	4	2	no	—
339	C₂²	—	4	2	no	—
340	C₂²	—	4	1	no	—
341	C₂²	—	4	1	no	—
342	C₂²	C₂²×C₂²⋊C₄×C₁₀₁	1	1	yes	characteristic
343	C₂²	C₂×C₄×Q₈×C₁₀₁	1	1	yes	characteristic
344	C₂²	#519×C₁₀₁	1	1	yes	characteristic
345	C₂²	#548×C₁₀₁	1	2	yes	—
346	C₂²	D₄×Q₈×C₁₀₁	1	2	yes	—
347	C₄	—	2	2	no	—
348	C₄	—	2	3	no	—
349	C₄	—	2	6	no	—
350	C₄	—	4	4	no	—
351	C₄	—	4	3	no	—
352	C₄	—	4	3	no	—
353	C₄	—	8	6	no	—
354	C₄	C₂×#99×C₁₀₁	1	6	yes	—
355	C₂	—	2	2	no	—
356	C₂	—	2	2	no	—
357	C₂	—	2	1	no	—
358	C₂	—	2	1	no	—
359	C₂	—	4	2	no	—
360	C₂	Q₈×C₂²⋊C₄×C₁₀₁	1	1	yes	characteristic
361	C₂	C₂²×#99×C₁₀₁	1	1	yes	characteristic
362	C₂	C₁₀₁×#2884	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₀₁	C₂²×C₂²⋊C₄
commutator	C₂³	C₂³×C₄×C₁₀₁
Frattini, cosocle	C₂⁴	C₂⁴×C₁₀₁
prime radical	C₂²×D₄×C₁₀₁	C₂³
LCS	G ▷ C₂³ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₀₁ ◁ C₂³×Q₈×C₁₀₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. Q₈×C₂²⋊C₄×C₁₀₁	C₂	semidirect
3. C₁₀₁×#1996	C₂	semidirect
6. C₂³×Q₈×C₁₀₁	C₄	semidirect
10. C₂×C₄⋊Q₈×C₁₀₁	C₄	semidirect
11. C₂×C₂²⋊Q₈×C₁₀₁	C₄	semidirect
14. C₂×C₄×Q₈×C₁₀₁	C₄	semidirect
57. #99×C₁₀₁	Q₈	direct (N × H)
102. C₂²⋊C₄×C₁₀₁	C₂×Q₈	semidirect
112. C₂³×C₁₀₁	C₄×Q₈	semidirect
123. Q₈×C₁₀₁	#99	direct (N × H)
147. C₂×C₄×C₁₀₁	C₄×Q₈	semidirect
173. Q₈×#99	C₁₀₁	direct (N × H)
183. Q₈×C₂²⋊C₄	C₂×C₁₀₁	semidirect
184. #1996	C₂×C₁₀₁	semidirect
187. C₁₀₁	Q₈×#99	direct (N × H)
188. C₂³×Q₈	C₄×C₁₀₁	semidirect
192. C₂×C₄⋊Q₈	C₄×C₁₀₁	semidirect
193. C₂×C₂²⋊Q₈	C₄×C₁₀₁	semidirect
196. C₂×C₄×Q₈	C₄×C₁₀₁	semidirect
239. #99	Q₈×C₁₀₁	direct (N × H)
284. C₂²⋊C₄	C₂×Q₈×C₁₀₁	semidirect
294. C₂³	C₄×Q₈×C₁₀₁	semidirect
305. Q₈	#99×C₁₀₁	direct (N × H)
329. C₂×C₄	C₄×Q₈×C₁₀₁	semidirect

Maximal subgroups

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

subgroup	index
C₂×D₄×Q₈×C₁₀₁	2
Q₈×C₂²⋊C₄×C₁₀₁	2
C₁₀₁×#1996	2
C₁₀₁×#1799	2
C₄×#99×C₁₀₁	2
Q₈×#99	101

Subgroups — Q8×#99×C101 #38804663

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — Q₈×#99×C₁₀₁ #38804663