Subgroups — C₂×C₁₀₁×#1491 #38799596

Order 25856.

1302 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	C₂²×C₄×Q₈×C₁₀₁	C₂	1	1	yes	maximal, characteristic
2	C₂×#432×C₁₀₁	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄×M₁₆×C₁₀₁	C₂	1	1	yes	maximal, characteristic
4	C₁₀₁×#1491	C₂	1	8	yes	maximal, direct product factor
5	C₂×Q₈⋊C₈×C₁₀₁	C₂	1	4	yes	maximal, complemented
6	C₂³×Q₈×C₁₀₁	C₄	1	1	yes	characteristic
7	C₂²×M₁₆×C₁₀₁	—	2	1	no	—
8	C₂×C₄×Q₈×C₁₀₁	—	2	1	no	—
9	C₂×C₄×Q₈×C₁₀₁	—	2	2	no	—
10	C₂×C₄×Q₈×C₁₀₁	—	2	2	no	—
11	C₂×C₄×Q₈×C₁₀₁	—	2	1	no	—
12	C₂×C₄×Q₈×C₁₀₁	C₄	1	4	yes	—
13	C₂×C₄×Q₈×C₁₀₁	C₄	1	2	yes	—
14	C₂×C₄×Q₈×C₁₀₁	C₂²	1	2	yes	—
15	C₂×C₄×Q₈×C₁₀₁	C₂²	1	4	yes	—
16	C₂²×C₄⋊C₄×C₁₀₁	—	2	1	no	—
17	C₂²×C₄⋊C₄×C₁₀₁	C₄	1	1	yes	characteristic
18	C₂²×C₄²×C₁₀₁	—	2	1	no	—
19	C₂²×C₄²×C₁₀₁	C₂²	1	1	yes	characteristic
20	#432×C₁₀₁	—	2	2	no	—
21	#432×C₁₀₁	C₂²	1	4	yes	—
22	C₂×C₄⋊C₈×C₁₀₁	C₂²	1	2	yes	—
23	C₂×C₂²⋊C₈×C₁₀₁	—	2	1	no	—
24	C₄×M₁₆×C₁₀₁	—	2	2	no	—
25	C₄×M₁₆×C₁₀₁	C₂²	1	4	yes	—
26	C₂×#97×C₁₀₁	—	2	1	no	—
27	C₂×#97×C₁₀₁	—	2	1	no	—
28	C₂×C₄×C₈×C₁₀₁	C₂²	1	2	yes	—
29	Q₈⋊C₈×C₁₀₁	C₂²	1	16	yes	complemented
30	C₂²×Q₈×C₁₀₁	—	2	8	no	—
31	C₂²×Q₈×C₁₀₁	—	2	2	no	—
32	C₂²×Q₈×C₁₀₁	—	2	1	no	—
33	C₂²×Q₈×C₁₀₁	C₂×C₄	1	4	yes	—
34	C₂²×Q₈×C₁₀₁	C₂×C₄	1	2	yes	—
35	C₂³×C₄×C₁₀₁	—	2	1	no	—
36	C₂³×C₄×C₁₀₁	—	2	1	no	—
37	C₂³×C₄×C₁₀₁	C₂×C₄	1	1	yes	characteristic
38	C₂³×C₄×C₁₀₁	D₄	1	1	yes	characteristic
39	C₂³×C₄×C₁₀₁	D₄	1	1	yes	characteristic
40	C₂×M₁₆×C₁₀₁	—	2	8	no	—
41	C₂×M₁₆×C₁₀₁	—	2	4	no	—
42	C₂²×C₈×C₁₀₁	—	2	2	no	—
43	C₂²×C₈×C₁₀₁	—	2	2	no	—
44	C₄×Q₈×C₁₀₁	—	2	4	no	—
45	C₄×Q₈×C₁₀₁	—	2	4	no	—
46	C₄×Q₈×C₁₀₁	—	2	4	no	—
47	C₄×Q₈×C₁₀₁	—	2	2	no	—
48	C₄×Q₈×C₁₀₁	—	2	4	no	—
49	C₄×Q₈×C₁₀₁	—	2	4	no	—
50	C₄×Q₈×C₁₀₁	—	2	2	no	—
51	C₄×Q₈×C₁₀₁	C₂×C₄	1	4	yes	—
52	C₄×Q₈×C₁₀₁	C₂×C₄	1	8	yes	—
53	C₄×Q₈×C₁₀₁	C₂³	1	4	yes	—
54	C₂×C₄⋊C₄×C₁₀₁	—	2	4	no	—
55	C₂×C₄⋊C₄×C₁₀₁	—	2	2	no	—
56	C₂×C₄⋊C₄×C₁₀₁	—	2	1	no	—
57	C₂×C₄⋊C₄×C₁₀₁	—	2	2	no	—
58	C₂×C₄⋊C₄×C₁₀₁	—	2	2	no	—
59	C₂×C₄⋊C₄×C₁₀₁	—	2	4	no	—
60	C₂×C₄⋊C₄×C₁₀₁	C₂×C₄	1	4	yes	—
61	C₂×C₄⋊C₄×C₁₀₁	C₂×C₄	1	2	yes	—
62	C₂×C₄²×C₁₀₁	—	2	2	no	—
63	C₂×C₄²×C₁₀₁	—	2	4	no	—
64	C₂×C₄²×C₁₀₁	—	2	4	no	—
65	C₂×C₄²×C₁₀₁	—	2	2	no	—
66	C₂×C₄²×C₁₀₁	C₂×C₄	1	2	yes	—
67	C₂×C₄²×C₁₀₁	C₂×C₄	1	1	yes	characteristic
68	C₂×C₄²×C₁₀₁	D₄	1	1	yes	characteristic
69	C₂×C₄²×C₁₀₁	D₄	1	2	yes	—
70	C₂×C₄²×C₁₀₁	D₄	1	2	yes	—
71	C₂×C₄²×C₁₀₁	D₄	1	1	yes	characteristic
72	C₂×C₄²×C₁₀₁	C₂³	1	2	yes	—
73	C₂×C₄²×C₁₀₁	C₂³	1	1	yes	characteristic
74	C₄⋊C₈×C₁₀₁	—	2	2	no	—
75	C₄⋊C₈×C₁₀₁	C₂³	1	4	yes	—
76	C₂²⋊C₈×C₁₀₁	—	2	4	no	—
77	#97×C₁₀₁	—	2	4	no	—
78	#97×C₁₀₁	—	2	4	no	—
79	C₄×C₈×C₁₀₁	—	2	2	no	—
80	C₄×C₈×C₁₀₁	C₂³	1	4	yes	—
81	C₂⁴×C₁₀₁	C₂²⋊C₄	1	1	yes	characteristic
82	C₂×Q₈×C₁₀₁	—	2	16	no	—
83	C₂×Q₈×C₁₀₁	—	2	8	no	—
84	C₂×Q₈×C₁₀₁	—	2	16	no	—
85	C₂×Q₈×C₁₀₁	—	2	4	no	—
86	C₂×Q₈×C₁₀₁	—	2	2	no	—
87	C₂×Q₈×C₁₀₁	—	2	4	no	—
88	C₂×Q₈×C₁₀₁	M₁₆	1	8	yes	complemented
89	C₂×Q₈×C₁₀₁	C₂²×C₄	1	4	yes	—
90	C₂²×C₄×C₁₀₁	—	2	8	no	—
91	C₂²×C₄×C₁₀₁	—	2	4	no	—
92	C₂²×C₄×C₁₀₁	—	2	4	no	—
93	C₂²×C₄×C₁₀₁	—	2	2	no	—
94	C₂²×C₄×C₁₀₁	—	2	4	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	—	4	4	no	—
99	C₂²×C₄×C₁₀₁	C₂²⋊C₄	1	1	yes	characteristic
100	C₂²×C₄×C₁₀₁	C₂²⋊C₄	1	2	yes	—
101	C₂²×C₄×C₁₀₁	C₂²⋊C₄	1	2	yes	—
102	C₂²×C₄×C₁₀₁	C₂²⋊C₄	1	1	yes	characteristic
103	C₂²×C₄×C₁₀₁	C₂²⋊C₄	1	1	yes	characteristic
104	C₂²×C₄×C₁₀₁	C₂²⋊C₄	1	2	yes	—
105	C₂²×C₄×C₁₀₁	C₂²×C₄	1	2	yes	—
106	C₂²×C₄×C₁₀₁	C₂²×C₄	1	1	yes	characteristic
107	C₂²×C₄×C₁₀₁	C₂×D₄	1	2	yes	—
108	C₂²×C₄×C₁₀₁	C₂×D₄	1	1	yes	characteristic
109	C₂²×C₄×C₁₀₁	C₂×D₄	1	2	yes	—
110	C₂²×C₄×C₁₀₁	C₂×D₄	1	1	yes	characteristic
111	M₁₆×C₁₀₁	—	2	16	no	—
112	C₂×C₈×C₁₀₁	—	2	8	no	—
113	C₂×C₈×C₁₀₁	—	2	4	no	—
114	C₂×C₈×C₁₀₁	—	2	4	no	—
115	C₂×C₈×C₁₀₁	—	4	4	no	—
116	C₄⋊C₄×C₁₀₁	—	2	8	no	—
117	C₄⋊C₄×C₁₀₁	—	2	4	no	—
118	C₄⋊C₄×C₁₀₁	—	2	4	no	—
119	C₄⋊C₄×C₁₀₁	—	2	2	no	—
120	C₄⋊C₄×C₁₀₁	—	2	4	no	—
121	C₄⋊C₄×C₁₀₁	C₂²×C₄	1	4	yes	—
122	C₄²×C₁₀₁	—	2	8	no	—
123	C₄²×C₁₀₁	—	2	4	no	—
124	C₄²×C₁₀₁	—	2	4	no	—
125	C₄²×C₁₀₁	C₂²⋊C₄	1	2	yes	—
126	C₄²×C₁₀₁	C₂²⋊C₄	1	2	yes	—
127	C₄²×C₁₀₁	C₂²⋊C₄	1	2	yes	—
128	C₄²×C₁₀₁	C₂²×C₄	1	2	yes	—
129	C₄²×C₁₀₁	C₂²×C₄	1	1	yes	characteristic
130	C₄²×C₁₀₁	C₂×D₄	1	1	yes	characteristic
131	C₄²×C₁₀₁	C₂×D₄	1	2	yes	—
132	C₄²×C₁₀₁	C₂×D₄	1	2	yes	—
133	C₄²×C₁₀₁	C₂×D₄	1	1	yes	characteristic
134	C₄²×C₁₀₁	C₂⁴	1	1	yes	characteristic
135	C₂³×C₁₀₁	—	2	2	no	—
136	C₂³×C₁₀₁	—	2	2	no	—
137	C₂³×C₁₀₁	#104	1	4	yes	—
138	C₂³×C₁₀₁	C₂×C₂²⋊C₄	1	2	yes	—
139	C₂³×C₁₀₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
140	Q₈×C₁₀₁	—	2	16	no	—
141	Q₈×C₁₀₁	—	2	4	no	—
142	Q₈×C₁₀₁	—	2	8	no	—
143	Q₈×C₁₀₁	C₂×M₁₆	1	8	yes	complemented
144	C₂×C₄×C₁₀₁	—	2	16	no	—
145	C₂×C₄×C₁₀₁	—	2	4	no	—
146	C₂×C₄×C₁₀₁	—	2	8	no	—
147	C₂×C₄×C₁₀₁	—	2	2	no	—
148	C₂×C₄×C₁₀₁	—	2	2	no	—
149	C₂×C₄×C₁₀₁	—	2	2	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	—	2	4	no	—
154	C₂×C₄×C₁₀₁	—	2	4	no	—
155	C₂×C₄×C₁₀₁	—	2	4	no	—
156	C₂×C₄×C₁₀₁	—	2	4	no	—
157	C₂×C₄×C₁₀₁	—	2	4	no	—
158	C₂×C₄×C₁₀₁	—	4	8	no	—
159	C₂×C₄×C₁₀₁	—	4	4	no	—
160	C₂×C₄×C₁₀₁	C₂×C₂²⋊C₄	1	2	yes	—
161	C₂×C₄×C₁₀₁	C₂×C₂²⋊C₄	1	2	yes	—
162	C₂×C₄×C₁₀₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
163	C₂×C₄×C₁₀₁	C₂×C₂²⋊C₄	1	2	yes	—
164	C₂×C₄×C₁₀₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
165	C₂×C₄×C₁₀₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
166	C₂×C₄×C₁₀₁	C₂×M₁₆	1	4	yes	—
167	C₂×C₄×C₁₀₁	#137	1	4	yes	—
168	C₂×C₄×C₁₀₁	C₂³×C₄	1	1	yes	characteristic
169	C₂×C₄×C₁₀₁	C₂²×D₄	1	1	yes	characteristic
170	C₂×C₄×C₁₀₁	C₂²×D₄	1	1	yes	characteristic
171	C₈×C₁₀₁	—	2	8	no	—
172	C₈×C₁₀₁	—	4	4	no	—
173	C₂²×C₁₀₁	—	2	2	no	—
174	C₂²×C₁₀₁	—	2	2	no	—
175	C₂²×C₁₀₁	—	2	8	no	—
176	C₂²×C₁₀₁	#407	1	2	yes	—
177	C₂²×C₁₀₁	#419	1	2	yes	—
178	C₂²×C₁₀₁	C₂×#104	1	4	yes	—
179	C₂²×C₁₀₁	C₂×#104	1	2	yes	—
180	C₂²×C₁₀₁	C₂²×C₂²⋊C₄	1	1	yes	characteristic
181	C₄×C₁₀₁	—	2	8	no	—
182	C₄×C₁₀₁	—	2	2	no	—
183	C₄×C₁₀₁	—	2	2	no	—
184	C₄×C₁₀₁	—	2	1	no	—
185	C₄×C₁₀₁	—	2	1	no	—
186	C₄×C₁₀₁	—	2	2	no	—
187	C₄×C₁₀₁	—	4	4	no	—
188	C₄×C₁₀₁	#407	1	2	yes	—
189	C₄×C₁₀₁	#419	1	2	yes	—
190	C₄×C₁₀₁	C₂²×M₁₆	1	2	yes	—
191	C₄×C₁₀₁	C₂×#137	1	2	yes	—
192	C₂×#1491	C₁₀₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
193	C₂×C₁₀₁	—	2	4	no	—
194	C₂×C₁₀₁	#1491	1	4	yes	direct product factor
195	C₂×C₁₀₁	C₂×#407	1	1	yes	characteristic
196	C₂×C₁₀₁	C₂×#419	1	1	yes	characteristic
197	C₂×C₁₀₁	C₂²×#104	1	1	yes	characteristic
198	C₂²×C₄×Q₈	C₂×C₁₀₁	1	1	yes	characteristic
199	C₂×#432	C₂×C₁₀₁	1	1	yes	characteristic
200	C₂×C₄×M₁₆	C₂×C₁₀₁	1	1	yes	characteristic
201	#1491	C₂×C₁₀₁	1	8	yes	direct product factor
202	C₂×Q₈⋊C₈	C₂×C₁₀₁	1	4	yes	complemented
203	C₁₀₁	C₂×#1491	1	1	yes	characteristic, direct product factor, Sylow
204	C₂³×Q₈	C₄×C₁₀₁	1	1	yes	characteristic
205	C₂²×M₁₆	—	2	1	no	—
206	C₂×C₄×Q₈	—	2	1	no	—
207	C₂×C₄×Q₈	—	2	2	no	—
208	C₂×C₄×Q₈	—	2	1	no	—
209	C₂×C₄×Q₈	—	2	2	no	—
210	C₂×C₄×Q₈	C₄×C₁₀₁	1	4	yes	—
211	C₂×C₄×Q₈	C₄×C₁₀₁	1	2	yes	—
212	C₂×C₄×Q₈	C₂²×C₁₀₁	1	2	yes	—
213	C₂×C₄×Q₈	C₂²×C₁₀₁	1	4	yes	—
214	C₂²×C₄⋊C₄	—	2	1	no	—
215	C₂²×C₄⋊C₄	C₄×C₁₀₁	1	1	yes	characteristic
216	C₂²×C₄²	—	2	1	no	—
217	C₂²×C₄²	C₂²×C₁₀₁	1	1	yes	characteristic
218	#432	—	2	2	no	—
219	#432	C₂²×C₁₀₁	1	4	yes	—
220	C₂×C₄⋊C₈	C₂²×C₁₀₁	1	2	yes	—
221	C₂×C₂²⋊C₈	—	2	1	no	—
222	C₄×M₁₆	—	2	2	no	—
223	C₄×M₁₆	C₂²×C₁₀₁	1	4	yes	—
224	C₂×#97	—	2	1	no	—
225	C₂×#97	—	2	1	no	—
226	C₂×C₄×C₈	C₂²×C₁₀₁	1	2	yes	—
227	Q₈⋊C₈	C₂²×C₁₀₁	1	16	yes	complemented
228	C₂²×Q₈	—	2	8	no	—
229	C₂²×Q₈	—	2	2	no	—
230	C₂²×Q₈	—	2	1	no	—
231	C₂²×Q₈	C₂×C₄×C₁₀₁	1	4	yes	—
232	C₂²×Q₈	C₂×C₄×C₁₀₁	1	2	yes	—
233	C₂³×C₄	—	2	1	no	—
234	C₂³×C₄	—	2	1	no	—
235	C₂³×C₄	C₂×C₄×C₁₀₁	1	1	yes	characteristic
236	C₂³×C₄	D₄×C₁₀₁	1	1	yes	characteristic
237	C₂³×C₄	D₄×C₁₀₁	1	1	yes	characteristic
238	C₂×M₁₆	—	2	8	no	—
239	C₂×M₁₆	—	2	4	no	—
240	C₂²×C₈	—	2	2	no	—
241	C₂²×C₈	—	2	2	no	—
242	C₄×Q₈	—	2	4	no	—
243	C₄×Q₈	—	2	4	no	—
244	C₄×Q₈	—	2	4	no	—
245	C₄×Q₈	—	2	2	no	—
246	C₄×Q₈	—	2	4	no	—
247	C₄×Q₈	—	2	4	no	—
248	C₄×Q₈	—	2	2	no	—
249	C₄×Q₈	C₂×C₄×C₁₀₁	1	4	yes	—
250	C₄×Q₈	C₂×C₄×C₁₀₁	1	8	yes	—
251	C₄×Q₈	C₂³×C₁₀₁	1	4	yes	—
252	C₂×C₄⋊C₄	—	2	4	no	—
253	C₂×C₄⋊C₄	—	2	2	no	—
254	C₂×C₄⋊C₄	—	2	1	no	—
255	C₂×C₄⋊C₄	—	2	2	no	—
256	C₂×C₄⋊C₄	—	2	2	no	—
257	C₂×C₄⋊C₄	—	2	4	no	—
258	C₂×C₄⋊C₄	C₂×C₄×C₁₀₁	1	4	yes	—
259	C₂×C₄⋊C₄	C₂×C₄×C₁₀₁	1	2	yes	—
260	C₂×C₄²	—	2	2	no	—
261	C₂×C₄²	—	2	4	no	—
262	C₂×C₄²	—	2	4	no	—
263	C₂×C₄²	—	2	2	no	—
264	C₂×C₄²	C₂×C₄×C₁₀₁	1	2	yes	—
265	C₂×C₄²	C₂×C₄×C₁₀₁	1	1	yes	characteristic
266	C₂×C₄²	D₄×C₁₀₁	1	1	yes	characteristic
267	C₂×C₄²	D₄×C₁₀₁	1	1	yes	characteristic
268	C₂×C₄²	D₄×C₁₀₁	1	2	yes	—
269	C₂×C₄²	D₄×C₁₀₁	1	2	yes	—
270	C₂×C₄²	C₂³×C₁₀₁	1	1	yes	characteristic
271	C₂×C₄²	C₂³×C₁₀₁	1	2	yes	—
272	C₄⋊C₈	—	2	2	no	—
273	C₄⋊C₈	C₂³×C₁₀₁	1	4	yes	—
274	C₂²⋊C₈	—	2	4	no	—
275	#97	—	2	4	no	—
276	#97	—	2	4	no	—
277	C₄×C₈	—	2	2	no	—
278	C₄×C₈	C₂³×C₁₀₁	1	4	yes	—
279	C₂⁴	C₂²⋊C₄×C₁₀₁	1	1	yes	characteristic
280	C₂×Q₈	—	2	16	no	—
281	C₂×Q₈	—	2	8	no	—
282	C₂×Q₈	—	2	16	no	—
283	C₂×Q₈	—	2	4	no	—
284	C₂×Q₈	—	2	2	no	—
285	C₂×Q₈	—	2	4	no	—
286	C₂×Q₈	M₁₆×C₁₀₁	1	8	yes	complemented
287	C₂×Q₈	C₂²×C₄×C₁₀₁	1	4	yes	—
288	C₂²×C₄	—	2	8	no	—
289	C₂²×C₄	—	2	4	no	—
290	C₂²×C₄	—	2	4	no	—
291	C₂²×C₄	—	2	2	no	—
292	C₂²×C₄	—	2	4	no	—
293	C₂²×C₄	—	2	4	no	—
294	C₂²×C₄	—	2	4	no	—
295	C₂²×C₄	—	2	2	no	—
296	C₂²×C₄	—	4	4	no	—
297	C₂²×C₄	C₂²⋊C₄×C₁₀₁	1	1	yes	characteristic
298	C₂²×C₄	C₂²⋊C₄×C₁₀₁	1	2	yes	—
299	C₂²×C₄	C₂²⋊C₄×C₁₀₁	1	2	yes	—
300	C₂²×C₄	C₂²⋊C₄×C₁₀₁	1	1	yes	characteristic
301	C₂²×C₄	C₂²⋊C₄×C₁₀₁	1	1	yes	characteristic
302	C₂²×C₄	C₂²⋊C₄×C₁₀₁	1	2	yes	—
303	C₂²×C₄	C₂²×C₄×C₁₀₁	1	2	yes	—
304	C₂²×C₄	C₂²×C₄×C₁₀₁	1	1	yes	characteristic
305	C₂²×C₄	C₂×D₄×C₁₀₁	1	2	yes	—
306	C₂²×C₄	C₂×D₄×C₁₀₁	1	1	yes	characteristic
307	C₂²×C₄	C₂×D₄×C₁₀₁	1	2	yes	—
308	C₂²×C₄	C₂×D₄×C₁₀₁	1	1	yes	characteristic
309	M₁₆	—	2	16	no	—
310	C₂×C₈	—	2	8	no	—
311	C₂×C₈	—	2	4	no	—
312	C₂×C₈	—	2	4	no	—
313	C₂×C₈	—	4	4	no	—
314	C₄⋊C₄	—	2	8	no	—
315	C₄⋊C₄	—	2	4	no	—
316	C₄⋊C₄	—	2	4	no	—
317	C₄⋊C₄	—	2	2	no	—
318	C₄⋊C₄	—	2	4	no	—
319	C₄⋊C₄	C₂²×C₄×C₁₀₁	1	4	yes	—
320	C₄²	—	2	8	no	—
321	C₄²	—	2	4	no	—
322	C₄²	—	2	4	no	—
323	C₄²	C₂²⋊C₄×C₁₀₁	1	2	yes	—
324	C₄²	C₂²⋊C₄×C₁₀₁	1	2	yes	—
325	C₄²	C₂²⋊C₄×C₁₀₁	1	2	yes	—
326	C₄²	C₂²×C₄×C₁₀₁	1	2	yes	—
327	C₄²	C₂²×C₄×C₁₀₁	1	1	yes	characteristic
328	C₄²	C₂×D₄×C₁₀₁	1	1	yes	characteristic
329	C₄²	C₂×D₄×C₁₀₁	1	2	yes	—
330	C₄²	C₂×D₄×C₁₀₁	1	2	yes	—
331	C₄²	C₂×D₄×C₁₀₁	1	1	yes	characteristic
332	C₄²	C₂⁴×C₁₀₁	1	1	yes	characteristic
333	C₂³	—	2	2	no	—
334	C₂³	—	2	2	no	—
335	C₂³	#104×C₁₀₁	1	4	yes	—
336	C₂³	C₂×C₂²⋊C₄×C₁₀₁	1	2	yes	—
337	C₂³	C₂×C₂²⋊C₄×C₁₀₁	1	1	yes	characteristic
338	Q₈	—	2	16	no	—
339	Q₈	—	2	8	no	—
340	Q₈	—	2	4	no	—
341	Q₈	C₂×M₁₆×C₁₀₁	1	8	yes	complemented
342	C₂×C₄	—	2	16	no	—
343	C₂×C₄	—	2	8	no	—
344	C₂×C₄	—	2	2	no	—
345	C₂×C₄	—	2	2	no	—
346	C₂×C₄	—	2	2	no	—
347	C₂×C₄	—	2	4	no	—
348	C₂×C₄	—	2	4	no	—
349	C₂×C₄	—	2	2	no	—
350	C₂×C₄	—	2	4	no	—
351	C₂×C₄	—	2	4	no	—
352	C₂×C₄	—	2	4	no	—
353	C₂×C₄	—	2	4	no	—
354	C₂×C₄	—	2	4	no	—
355	C₂×C₄	—	2	4	no	—
356	C₂×C₄	—	4	8	no	—
357	C₂×C₄	—	4	4	no	—
358	C₂×C₄	C₂×C₂²⋊C₄×C₁₀₁	1	2	yes	—
359	C₂×C₄	C₂×C₂²⋊C₄×C₁₀₁	1	2	yes	—
360	C₂×C₄	C₂×C₂²⋊C₄×C₁₀₁	1	1	yes	characteristic
361	C₂×C₄	C₂×C₂²⋊C₄×C₁₀₁	1	2	yes	—
362	C₂×C₄	C₂×C₂²⋊C₄×C₁₀₁	1	1	yes	characteristic
363	C₂×C₄	C₂×C₂²⋊C₄×C₁₀₁	1	1	yes	characteristic
364	C₂×C₄	C₂×M₁₆×C₁₀₁	1	4	yes	—
365	C₂×C₄	#137×C₁₀₁	1	4	yes	—
366	C₂×C₄	C₂³×C₄×C₁₀₁	1	1	yes	characteristic
367	C₂×C₄	C₂²×D₄×C₁₀₁	1	1	yes	characteristic
368	C₂×C₄	C₂²×D₄×C₁₀₁	1	1	yes	characteristic
369	C₈	—	2	8	no	—
370	C₈	—	4	4	no	—
371	C₂²	—	2	8	no	—
372	C₂²	—	2	2	no	—
373	C₂²	—	2	2	no	—
374	C₂²	#407×C₁₀₁	1	2	yes	—
375	C₂²	#419×C₁₀₁	1	2	yes	—
376	C₂²	C₂×#104×C₁₀₁	1	4	yes	—
377	C₂²	C₂×#104×C₁₀₁	1	2	yes	—
378	C₂²	C₂²×C₂²⋊C₄×C₁₀₁	1	1	yes	characteristic
379	C₄	—	2	8	no	—
380	C₄	—	2	2	no	—
381	C₄	—	2	2	no	—
382	C₄	—	2	1	no	—
383	C₄	—	2	1	no	—
384	C₄	—	2	2	no	—
385	C₄	—	4	4	no	—
386	C₄	#407×C₁₀₁	1	2	yes	—
387	C₄	#419×C₁₀₁	1	2	yes	—
388	C₄	C₂²×M₁₆×C₁₀₁	1	2	yes	—
389	C₄	C₂×#137×C₁₀₁	1	2	yes	—
390	C₂	—	2	4	no	—
391	C₂	C₁₀₁×#1491	1	4	yes	direct product factor
392	C₂	C₂×#407×C₁₀₁	1	1	yes	characteristic
393	C₂	C₂×#419×C₁₀₁	1	1	yes	characteristic
394	C₂	C₂²×#104×C₁₀₁	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄×C₁₀₁	C₂×D₄
commutator	C₂×C₄	C₂³×C₄×C₁₀₁
Frattini, cosocle	C₄²	C₂⁴×C₁₀₁
socle	C₂³×C₁₀₁	C₂×C₂²⋊C₄
prime radical	C₂⁴×C₁₀₁	C₂²⋊C₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₁₀₁ ◁ C₂²×C₄²×C₁₀₁ ◁ G

Complements

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

N	H ≅ G/N	type
4. C₁₀₁×#1491	C₂	direct (N × H)
5. C₂×Q₈⋊C₈×C₁₀₁	C₂	semidirect
29. Q₈⋊C₈×C₁₀₁	C₂²	semidirect
88. C₂×Q₈×C₁₀₁	M₁₆	semidirect
143. Q₈×C₁₀₁	C₂×M₁₆	semidirect
192. C₂×#1491	C₁₀₁	direct (N × H)
194. C₂×C₁₀₁	#1491	direct (N × H)
201. #1491	C₂×C₁₀₁	direct (N × H)
202. C₂×Q₈⋊C₈	C₂×C₁₀₁	semidirect
203. C₁₀₁	C₂×#1491	direct (N × H)
227. Q₈⋊C₈	C₂²×C₁₀₁	semidirect
286. C₂×Q₈	M₁₆×C₁₀₁	semidirect
341. Q₈	C₂×M₁₆×C₁₀₁	semidirect
391. C₂	C₁₀₁×#1491	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₄×Q₈×C₁₀₁	2
C₂×#432×C₁₀₁	2
C₂×C₄×M₁₆×C₁₀₁	2
C₁₀₁×#1491	2
C₂×Q₈⋊C₈×C₁₀₁	2
C₂×#1491	101

Subgroups — C2×C101×#1491 #38799596

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₀₁×#1491 #38799596