Subgroups — C₄×#396×C₁₀₁ #38796016

Order 25856.

1966 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	C₂×#396×C₁₀₁	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×C₄⋊C₄×C₁₀₁	C₂	1	3	yes	maximal, complemented
3	C₂×C₄×C₂²⋊C₄×C₁₀₁	C₂	1	3	yes	maximal
4	C₁₀₁×#1443	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₀₁×#1441	C₂	1	3	yes	maximal, complemented
6	C₁₀₁×#1439	C₂	1	3	yes	maximal
7	C₄×#95×C₁₀₁	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂⁴×C₄×C₁₀₁	C₂²	1	1	yes	characteristic
9	C₂²×C₄⋊C₄×C₁₀₁	C₂²	1	3	yes	—
10	C₂²×C₄⋊C₄×C₁₀₁	C₂²	1	3	yes	—
11	C₂²×C₂²⋊C₄×C₁₀₁	C₂²	1	3	yes	—
12	C₂²×C₂²⋊C₄×C₁₀₁	C₂²	1	3	yes	—
13	C₂²×C₄²×C₁₀₁	C₂²	1	3	yes	—
14	C₂²×C₄²×C₁₀₁	C₂²	1	3	yes	—
15	#396×C₁₀₁	C₄	1	8	yes	direct product factor
16	C₄×C₄⋊C₄×C₁₀₁	—	2	12	no	—
17	C₄×C₂²⋊C₄×C₁₀₁	—	2	12	no	—
18	C₂×#95×C₁₀₁	C₂²	1	3	yes	—
19	C₂×#95×C₁₀₁	C₂²	1	3	yes	—
20	C₂×#95×C₁₀₁	C₂²	1	3	yes	—
21	C₂×#95×C₁₀₁	C₂²	1	3	yes	—
22	C₂×#95×C₁₀₁	C₂²	1	3	yes	—
23	C₂×#95×C₁₀₁	C₂²	1	1	yes	characteristic
24	C₂⁵×C₁₀₁	C₂³	1	1	yes	characteristic
25	C₂³×C₄×C₁₀₁	—	2	6	no	—
26	C₂³×C₄×C₁₀₁	—	2	6	no	—
27	C₂³×C₄×C₁₀₁	Q₈	1	4	yes	—
28	C₂³×C₄×C₁₀₁	C₂³	1	3	yes	—
29	C₂³×C₄×C₁₀₁	C₂³	1	3	yes	—
30	C₂³×C₄×C₁₀₁	C₂³	1	1	yes	characteristic
31	C₂³×C₄×C₁₀₁	C₂³	1	3	yes	—
32	C₂³×C₄×C₁₀₁	C₂³	1	3	yes	—
33	C₂³×C₄×C₁₀₁	C₂³	1	1	yes	characteristic
34	C₂×C₄⋊C₄×C₁₀₁	—	2	6	no	—
35	C₂×C₄⋊C₄×C₁₀₁	—	2	6	no	—
36	C₂×C₄⋊C₄×C₁₀₁	—	2	6	no	—
37	C₂×C₄⋊C₄×C₁₀₁	—	2	6	no	—
38	C₂×C₄⋊C₄×C₁₀₁	—	2	6	no	—
39	C₂×C₄⋊C₄×C₁₀₁	C₂×C₄	1	12	yes	complemented
40	C₂×C₂²⋊C₄×C₁₀₁	—	2	6	no	—
41	C₂×C₂²⋊C₄×C₁₀₁	—	2	6	no	—
42	C₂×C₂²⋊C₄×C₁₀₁	—	2	6	no	—
43	C₂×C₂²⋊C₄×C₁₀₁	—	2	6	no	—
44	C₂×C₂²⋊C₄×C₁₀₁	—	2	6	no	—
45	C₂×C₂²⋊C₄×C₁₀₁	C₂×C₄	1	12	yes	—
46	C₂×C₄²×C₁₀₁	—	2	6	no	—
47	C₂×C₄²×C₁₀₁	—	2	6	no	—
48	C₂×C₄²×C₁₀₁	—	2	6	no	—
49	C₂×C₄²×C₁₀₁	—	2	6	no	—
50	C₂×C₄²×C₁₀₁	—	2	6	no	—
51	C₂×C₄²×C₁₀₁	D₄	1	12	yes	—
52	#95×C₁₀₁	—	2	6	no	—
53	#95×C₁₀₁	—	2	6	no	—
54	#95×C₁₀₁	—	2	6	no	—
55	#95×C₁₀₁	—	2	6	no	—
56	#95×C₁₀₁	—	2	6	no	—
57	#95×C₁₀₁	C₂×C₄	1	4	yes	complemented
58	C₂⁴×C₁₀₁	—	2	3	no	—
59	C₂⁴×C₁₀₁	—	2	3	no	—
60	C₂⁴×C₁₀₁	—	2	3	no	—
61	C₂⁴×C₁₀₁	—	2	3	no	—
62	C₂⁴×C₁₀₁	C₂²×C₄	1	2	yes	—
63	C₂⁴×C₁₀₁	C₂×Q₈	1	2	yes	—
64	C₂⁴×C₁₀₁	#41	1	2	yes	—
65	C₂⁴×C₁₀₁	C₂⁴	1	1	yes	characteristic
66	C₂²×C₄×C₁₀₁	—	2	3	no	—
67	C₂²×C₄×C₁₀₁	—	2	3	no	—
68	C₂²×C₄×C₁₀₁	—	2	3	no	—
69	C₂²×C₄×C₁₀₁	—	2	3	no	—
70	C₂²×C₄×C₁₀₁	—	2	3	no	—
71	C₂²×C₄×C₁₀₁	—	2	3	no	—
72	C₂²×C₄×C₁₀₁	—	2	3	no	—
73	C₂²×C₄×C₁₀₁	—	2	3	no	—
74	C₂²×C₄×C₁₀₁	—	2	3	no	—
75	C₂²×C₄×C₁₀₁	—	2	3	no	—
76	C₂²×C₄×C₁₀₁	—	2	3	no	—
77	C₂²×C₄×C₁₀₁	—	2	3	no	—
78	C₂²×C₄×C₁₀₁	—	2	3	no	—
79	C₂²×C₄×C₁₀₁	—	2	3	no	—
80	C₂²×C₄×C₁₀₁	—	2	3	no	—
81	C₂²×C₄×C₁₀₁	—	2	3	no	—
82	C₂²×C₄×C₁₀₁	—	2	3	no	—
83	C₂²×C₄×C₁₀₁	—	2	3	no	—
84	C₂²×C₄×C₁₀₁	—	2	3	no	—
85	C₂²×C₄×C₁₀₁	—	2	3	no	—
86	C₂²×C₄×C₁₀₁	—	2	3	no	—
87	C₂²×C₄×C₁₀₁	—	2	3	no	—
88	C₂²×C₄×C₁₀₁	—	2	3	no	—
89	C₂²×C₄×C₁₀₁	—	2	3	no	—
90	C₂²×C₄×C₁₀₁	—	2	24	no	—
91	C₂²×C₄×C₁₀₁	—	4	12	no	—
92	C₂²×C₄×C₁₀₁	—	4	4	no	—
93	C₂²×C₄×C₁₀₁	C₂²×C₄	1	6	yes	—
94	C₂²×C₄×C₁₀₁	C₂²×C₄	1	6	yes	—
95	C₂²×C₄×C₁₀₁	C₂×D₄	1	6	yes	—
96	C₂²×C₄×C₁₀₁	C₂×D₄	1	6	yes	—
97	C₂²×C₄×C₁₀₁	C₂×D₄	1	6	yes	—
98	C₂²×C₄×C₁₀₁	C₂×Q₈	1	2	yes	—
99	C₂²×C₄×C₁₀₁	C₂×Q₈	1	2	yes	—
100	C₂²×C₄×C₁₀₁	#41	1	6	yes	—
101	C₂²×C₄×C₁₀₁	#41	1	6	yes	—
102	C₂²×C₄×C₁₀₁	#41	1	6	yes	—
103	C₄⋊C₄×C₁₀₁	—	2	24	no	—
104	C₄⋊C₄×C₁₀₁	—	2	24	no	—
105	C₂²⋊C₄×C₁₀₁	—	2	24	no	—
106	C₂²⋊C₄×C₁₀₁	—	2	24	no	—
107	C₄²×C₁₀₁	—	2	24	no	—
108	C₄²×C₁₀₁	—	4	12	no	—
109	C₂³×C₁₀₁	—	2	6	no	—
110	C₂³×C₁₀₁	—	2	6	no	—
111	C₂³×C₁₀₁	—	2	6	no	—
112	C₂³×C₁₀₁	—	2	6	no	—
113	C₂³×C₁₀₁	—	2	6	no	—
114	C₂³×C₁₀₁	—	2	6	no	—
115	C₂³×C₁₀₁	—	4	3	no	—
116	C₂³×C₁₀₁	—	4	3	no	—
117	C₂³×C₁₀₁	—	4	1	no	—
118	C₂³×C₁₀₁	—	4	3	no	—
119	C₂³×C₁₀₁	—	4	3	no	—
120	C₂³×C₁₀₁	—	4	3	no	—
121	C₂³×C₁₀₁	C₄×Q₈	1	4	yes	—
122	C₂³×C₁₀₁	C₂³×C₄	1	1	yes	characteristic
123	C₂³×C₁₀₁	C₂²×D₄	1	3	yes	—
124	C₂³×C₁₀₁	C₂²×Q₈	1	1	yes	characteristic
125	C₂³×C₁₀₁	C₂×#41	1	3	yes	—
126	C₂³×C₁₀₁	C₂×#41	1	1	yes	characteristic
127	C₂³×C₁₀₁	C₂×#41	1	3	yes	—
128	C₂³×C₁₀₁	C₂×#41	1	3	yes	—
129	C₂×C₄×C₁₀₁	—	2	6	no	—
130	C₂×C₄×C₁₀₁	—	2	6	no	—
131	C₂×C₄×C₁₀₁	—	2	6	no	—
132	C₂×C₄×C₁₀₁	—	2	6	no	—
133	C₂×C₄×C₁₀₁	—	2	6	no	—
134	C₂×C₄×C₁₀₁	—	2	6	no	—
135	C₂×C₄×C₁₀₁	—	2	6	no	—
136	C₂×C₄×C₁₀₁	—	2	6	no	—
137	C₂×C₄×C₁₀₁	—	2	6	no	—
138	C₂×C₄×C₁₀₁	—	2	6	no	—
139	C₂×C₄×C₁₀₁	—	2	6	no	—
140	C₂×C₄×C₁₀₁	—	2	6	no	—
141	C₂×C₄×C₁₀₁	—	2	6	no	—
142	C₂×C₄×C₁₀₁	—	2	6	no	—
143	C₂×C₄×C₁₀₁	—	2	6	no	—
144	C₂×C₄×C₁₀₁	—	2	6	no	—
145	C₂×C₄×C₁₀₁	—	4	3	no	—
146	C₂×C₄×C₁₀₁	—	4	3	no	—
147	C₂×C₄×C₁₀₁	—	4	3	no	—
148	C₂×C₄×C₁₀₁	—	4	3	no	—
149	C₂×C₄×C₁₀₁	—	4	3	no	—
150	C₂×C₄×C₁₀₁	—	4	3	no	—
151	C₂×C₄×C₁₀₁	—	4	1	no	—
152	C₂×C₄×C₁₀₁	—	4	3	no	—
153	C₂×C₄×C₁₀₁	—	4	3	no	—
154	C₂×C₄×C₁₀₁	—	4	3	no	—
155	C₂×C₄×C₁₀₁	—	4	3	no	—
156	C₂×C₄×C₁₀₁	—	4	3	no	—
157	C₂×C₄×C₁₀₁	—	4	3	no	—
158	C₂×C₄×C₁₀₁	—	4	3	no	—
159	C₂×C₄×C₁₀₁	—	4	16	no	—
160	C₂×C₄×C₁₀₁	C₄×D₄	1	12	yes	—
161	C₂×C₄×C₁₀₁	#121	1	12	yes	—
162	C₂×C₄×C₁₀₁	C₂²⋊Q₈	1	12	yes	—
163	C₂×C₄×C₁₀₁	#126	1	4	yes	—
164	C₂²×C₁₀₁	—	2	12	no	—
165	C₂²×C₁₀₁	—	4	2	no	—
166	C₂²×C₁₀₁	—	4	2	no	—
167	C₂²×C₁₀₁	—	4	6	no	—
168	C₂²×C₁₀₁	—	4	6	no	—
169	C₂²×C₁₀₁	—	4	2	no	—
170	C₂²×C₁₀₁	—	4	6	no	—
171	C₂²×C₁₀₁	C₂×C₄×D₄	1	3	yes	—
172	C₂²×C₁₀₁	C₂×C₄×Q₈	1	1	yes	characteristic
173	C₂²×C₁₀₁	C₄×#41	1	3	yes	—
174	C₂²×C₁₀₁	C₂×#121	1	3	yes	—
175	C₂²×C₁₀₁	C₂×C₂²⋊Q₈	1	3	yes	—
176	C₂²×C₁₀₁	#525	1	3	yes	—
177	C₂²×C₁₀₁	#525	1	3	yes	—
178	C₂²×C₁₀₁	C₂×#126	1	1	yes	characteristic
179	C₂²×C₁₀₁	#529	1	3	yes	—
180	C₂²×C₁₀₁	#529	1	3	yes	—
181	C₂²×C₁₀₁	#529	1	3	yes	—
182	C₂²×C₁₀₁	#532	1	3	yes	—
183	C₂²×C₁₀₁	#533	1	3	yes	—
184	C₄×C₁₀₁	—	2	12	no	—
185	C₄×C₁₀₁	—	4	2	no	—
186	C₄×C₁₀₁	—	4	6	no	—
187	C₄×C₁₀₁	—	4	6	no	—
188	C₄×C₁₀₁	—	4	6	no	—
189	C₄×C₁₀₁	#396	1	8	yes	direct product factor
190	C₄×#396	C₁₀₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
191	C₂×C₁₀₁	—	4	4	no	—
192	C₂×C₁₀₁	C₄×#121	1	3	yes	—
193	C₂×C₁₀₁	C₄×C₂²⋊Q₈	1	3	yes	—
194	C₂×C₁₀₁	C₄×#126	1	1	yes	characteristic
195	C₂×C₁₀₁	C₂×#396	1	1	yes	characteristic
196	C₂×C₁₀₁	#2392	1	3	yes	—
197	C₂×C₁₀₁	#2396	1	3	yes	—
198	C₂×C₁₀₁	#2401	1	1	yes	characteristic
199	C₂×#396	C₂×C₁₀₁	1	1	yes	characteristic
200	C₂×C₄×C₄⋊C₄	C₂×C₁₀₁	1	3	yes	complemented
201	C₂×C₄×C₂²⋊C₄	C₂×C₁₀₁	1	3	yes	—
202	#1443	C₂×C₁₀₁	1	1	yes	characteristic, complemented
203	#1441	C₂×C₁₀₁	1	3	yes	complemented
204	#1439	C₂×C₁₀₁	1	3	yes	—
205	C₄×#95	C₂×C₁₀₁	1	1	yes	characteristic, complemented
206	C₁₀₁	C₄×#396	1	1	yes	characteristic, direct product factor, Sylow
207	C₂⁴×C₄	C₂²×C₁₀₁	1	1	yes	characteristic
208	C₂²×C₄⋊C₄	C₂²×C₁₀₁	1	3	yes	—
209	C₂²×C₄⋊C₄	C₂²×C₁₀₁	1	3	yes	—
210	C₂²×C₂²⋊C₄	C₂²×C₁₀₁	1	3	yes	—
211	C₂²×C₂²⋊C₄	C₂²×C₁₀₁	1	3	yes	—
212	C₂²×C₄²	C₂²×C₁₀₁	1	3	yes	—
213	C₂²×C₄²	C₂²×C₁₀₁	1	3	yes	—
214	#396	C₄×C₁₀₁	1	8	yes	direct product factor
215	C₄×C₄⋊C₄	—	2	12	no	—
216	C₄×C₂²⋊C₄	—	2	12	no	—
217	C₂×#95	C₂²×C₁₀₁	1	3	yes	—
218	C₂×#95	C₂²×C₁₀₁	1	3	yes	—
219	C₂×#95	C₂²×C₁₀₁	1	3	yes	—
220	C₂×#95	C₂²×C₁₀₁	1	3	yes	—
221	C₂×#95	C₂²×C₁₀₁	1	3	yes	—
222	C₂×#95	C₂²×C₁₀₁	1	1	yes	characteristic
223	C₂⁵	C₂³×C₁₀₁	1	1	yes	characteristic
224	C₂³×C₄	—	2	6	no	—
225	C₂³×C₄	—	2	6	no	—
226	C₂³×C₄	Q₈×C₁₀₁	1	4	yes	—
227	C₂³×C₄	C₂³×C₁₀₁	1	3	yes	—
228	C₂³×C₄	C₂³×C₁₀₁	1	3	yes	—
229	C₂³×C₄	C₂³×C₁₀₁	1	1	yes	characteristic
230	C₂³×C₄	C₂³×C₁₀₁	1	3	yes	—
231	C₂³×C₄	C₂³×C₁₀₁	1	3	yes	—
232	C₂³×C₄	C₂³×C₁₀₁	1	1	yes	characteristic
233	C₂×C₄⋊C₄	—	2	6	no	—
234	C₂×C₄⋊C₄	—	2	6	no	—
235	C₂×C₄⋊C₄	—	2	6	no	—
236	C₂×C₄⋊C₄	—	2	6	no	—
237	C₂×C₄⋊C₄	—	2	6	no	—
238	C₂×C₄⋊C₄	C₂×C₄×C₁₀₁	1	12	yes	complemented
239	C₂×C₂²⋊C₄	—	2	6	no	—
240	C₂×C₂²⋊C₄	—	2	6	no	—
241	C₂×C₂²⋊C₄	—	2	6	no	—
242	C₂×C₂²⋊C₄	—	2	6	no	—
243	C₂×C₂²⋊C₄	—	2	6	no	—
244	C₂×C₂²⋊C₄	C₂×C₄×C₁₀₁	1	12	yes	—
245	C₂×C₄²	—	2	6	no	—
246	C₂×C₄²	—	2	6	no	—
247	C₂×C₄²	—	2	6	no	—
248	C₂×C₄²	—	2	6	no	—
249	C₂×C₄²	—	2	6	no	—
250	C₂×C₄²	D₄×C₁₀₁	1	12	yes	—
251	#95	—	2	6	no	—
252	#95	—	2	6	no	—
253	#95	—	2	6	no	—
254	#95	—	2	6	no	—
255	#95	—	2	6	no	—
256	#95	C₂×C₄×C₁₀₁	1	4	yes	complemented
257	C₂⁴	—	2	3	no	—
258	C₂⁴	—	2	3	no	—
259	C₂⁴	—	2	3	no	—
260	C₂⁴	—	2	3	no	—
261	C₂⁴	C₂²×C₄×C₁₀₁	1	2	yes	—
262	C₂⁴	C₂×Q₈×C₁₀₁	1	2	yes	—
263	C₂⁴	#41×C₁₀₁	1	2	yes	—
264	C₂⁴	C₂⁴×C₁₀₁	1	1	yes	characteristic
265	C₂²×C₄	—	2	3	no	—
266	C₂²×C₄	—	2	3	no	—
267	C₂²×C₄	—	2	3	no	—
268	C₂²×C₄	—	2	3	no	—
269	C₂²×C₄	—	2	3	no	—
270	C₂²×C₄	—	2	3	no	—
271	C₂²×C₄	—	2	3	no	—
272	C₂²×C₄	—	2	3	no	—
273	C₂²×C₄	—	2	3	no	—
274	C₂²×C₄	—	2	3	no	—
275	C₂²×C₄	—	2	3	no	—
276	C₂²×C₄	—	2	3	no	—
277	C₂²×C₄	—	2	3	no	—
278	C₂²×C₄	—	2	3	no	—
279	C₂²×C₄	—	2	3	no	—
280	C₂²×C₄	—	2	3	no	—
281	C₂²×C₄	—	2	3	no	—
282	C₂²×C₄	—	2	3	no	—
283	C₂²×C₄	—	2	3	no	—
284	C₂²×C₄	—	2	3	no	—
285	C₂²×C₄	—	2	3	no	—
286	C₂²×C₄	—	2	3	no	—
287	C₂²×C₄	—	2	3	no	—
288	C₂²×C₄	—	2	3	no	—
289	C₂²×C₄	—	2	24	no	—
290	C₂²×C₄	—	4	12	no	—
291	C₂²×C₄	—	4	4	no	—
292	C₂²×C₄	C₂²×C₄×C₁₀₁	1	6	yes	—
293	C₂²×C₄	C₂²×C₄×C₁₀₁	1	6	yes	—
294	C₂²×C₄	C₂×D₄×C₁₀₁	1	6	yes	—
295	C₂²×C₄	C₂×D₄×C₁₀₁	1	6	yes	—
296	C₂²×C₄	C₂×D₄×C₁₀₁	1	6	yes	—
297	C₂²×C₄	C₂×Q₈×C₁₀₁	1	2	yes	—
298	C₂²×C₄	C₂×Q₈×C₁₀₁	1	2	yes	—
299	C₂²×C₄	#41×C₁₀₁	1	6	yes	—
300	C₂²×C₄	#41×C₁₀₁	1	6	yes	—
301	C₂²×C₄	#41×C₁₀₁	1	6	yes	—
302	C₄⋊C₄	—	2	24	no	—
303	C₄⋊C₄	—	2	24	no	—
304	C₂²⋊C₄	—	2	24	no	—
305	C₂²⋊C₄	—	2	24	no	—
306	C₄²	—	2	24	no	—
307	C₄²	—	4	12	no	—
308	C₂³	—	2	6	no	—
309	C₂³	—	2	6	no	—
310	C₂³	—	2	6	no	—
311	C₂³	—	2	6	no	—
312	C₂³	—	2	6	no	—
313	C₂³	—	2	6	no	—
314	C₂³	—	4	3	no	—
315	C₂³	—	4	3	no	—
316	C₂³	—	4	1	no	—
317	C₂³	—	4	3	no	—
318	C₂³	—	4	3	no	—
319	C₂³	—	4	3	no	—
320	C₂³	C₄×Q₈×C₁₀₁	1	4	yes	—
321	C₂³	C₂³×C₄×C₁₀₁	1	1	yes	characteristic
322	C₂³	C₂²×D₄×C₁₀₁	1	3	yes	—
323	C₂³	C₂²×Q₈×C₁₀₁	1	1	yes	characteristic
324	C₂³	C₂×#41×C₁₀₁	1	3	yes	—
325	C₂³	C₂×#41×C₁₀₁	1	1	yes	characteristic
326	C₂³	C₂×#41×C₁₀₁	1	3	yes	—
327	C₂³	C₂×#41×C₁₀₁	1	3	yes	—
328	C₂×C₄	—	2	6	no	—
329	C₂×C₄	—	2	6	no	—
330	C₂×C₄	—	2	6	no	—
331	C₂×C₄	—	2	6	no	—
332	C₂×C₄	—	2	6	no	—
333	C₂×C₄	—	2	6	no	—
334	C₂×C₄	—	2	6	no	—
335	C₂×C₄	—	2	6	no	—
336	C₂×C₄	—	2	6	no	—
337	C₂×C₄	—	2	6	no	—
338	C₂×C₄	—	2	6	no	—
339	C₂×C₄	—	2	6	no	—
340	C₂×C₄	—	2	6	no	—
341	C₂×C₄	—	2	6	no	—
342	C₂×C₄	—	2	6	no	—
343	C₂×C₄	—	2	6	no	—
344	C₂×C₄	—	4	3	no	—
345	C₂×C₄	—	4	3	no	—
346	C₂×C₄	—	4	3	no	—
347	C₂×C₄	—	4	3	no	—
348	C₂×C₄	—	4	3	no	—
349	C₂×C₄	—	4	3	no	—
350	C₂×C₄	—	4	1	no	—
351	C₂×C₄	—	4	3	no	—
352	C₂×C₄	—	4	3	no	—
353	C₂×C₄	—	4	3	no	—
354	C₂×C₄	—	4	3	no	—
355	C₂×C₄	—	4	3	no	—
356	C₂×C₄	—	4	3	no	—
357	C₂×C₄	—	4	3	no	—
358	C₂×C₄	—	4	16	no	—
359	C₂×C₄	C₄×D₄×C₁₀₁	1	12	yes	—
360	C₂×C₄	#121×C₁₀₁	1	12	yes	—
361	C₂×C₄	C₂²⋊Q₈×C₁₀₁	1	12	yes	—
362	C₂×C₄	#126×C₁₀₁	1	4	yes	—
363	C₂²	—	2	12	no	—
364	C₂²	—	4	6	no	—
365	C₂²	—	4	6	no	—
366	C₂²	—	4	2	no	—
367	C₂²	—	4	6	no	—
368	C₂²	—	4	2	no	—
369	C₂²	—	4	2	no	—
370	C₂²	C₂×C₄×D₄×C₁₀₁	1	3	yes	—
371	C₂²	C₂×C₄×Q₈×C₁₀₁	1	1	yes	characteristic
372	C₂²	C₄×#41×C₁₀₁	1	3	yes	—
373	C₂²	C₂×#121×C₁₀₁	1	3	yes	—
374	C₂²	C₂×C₂²⋊Q₈×C₁₀₁	1	3	yes	—
375	C₂²	#525×C₁₀₁	1	3	yes	—
376	C₂²	#525×C₁₀₁	1	3	yes	—
377	C₂²	C₂×#126×C₁₀₁	1	1	yes	characteristic
378	C₂²	#529×C₁₀₁	1	3	yes	—
379	C₂²	#529×C₁₀₁	1	3	yes	—
380	C₂²	#529×C₁₀₁	1	3	yes	—
381	C₂²	#532×C₁₀₁	1	3	yes	—
382	C₂²	#533×C₁₀₁	1	3	yes	—
383	C₄	—	2	12	no	—
384	C₄	—	4	6	no	—
385	C₄	—	4	6	no	—
386	C₄	—	4	6	no	—
387	C₄	—	4	2	no	—
388	C₄	#396×C₁₀₁	1	8	yes	direct product factor
389	C₂	—	4	4	no	—
390	C₂	C₄×#121×C₁₀₁	1	3	yes	—
391	C₂	C₄×C₂²⋊Q₈×C₁₀₁	1	3	yes	—
392	C₂	C₄×#126×C₁₀₁	1	1	yes	characteristic
393	C₂	C₂×#396×C₁₀₁	1	1	yes	characteristic
394	C₂	C₁₀₁×#2392	1	3	yes	—
395	C₂	C₁₀₁×#2396	1	3	yes	—
396	C₂	C₁₀₁×#2401	1	1	yes	characteristic

	subgroup	G/H
center	C₂³×C₄×C₁₀₁	C₂³
commutator	C₂³	C₂³×C₄×C₁₀₁
Frattini, cosocle	C₂⁴	C₂⁴×C₁₀₁
socle	C₂⁴×C₁₀₁	C₂⁴
prime radical	C₂⁵×C₁₀₁	C₂³
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₄×C₁₀₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₄×C₄⋊C₄×C₁₀₁	C₂	semidirect
4. C₁₀₁×#1443	C₂	semidirect
5. C₁₀₁×#1441	C₂	semidirect
7. C₄×#95×C₁₀₁	C₂	semidirect
15. #396×C₁₀₁	C₄	direct (N × H)
39. C₂×C₄⋊C₄×C₁₀₁	C₂×C₄	semidirect
57. #95×C₁₀₁	C₂×C₄	semidirect
189. C₄×C₁₀₁	#396	direct (N × H)
190. C₄×#396	C₁₀₁	direct (N × H)
200. C₂×C₄×C₄⋊C₄	C₂×C₁₀₁	semidirect
202. #1443	C₂×C₁₀₁	semidirect
203. #1441	C₂×C₁₀₁	semidirect
205. C₄×#95	C₂×C₁₀₁	semidirect
206. C₁₀₁	C₄×#396	direct (N × H)
214. #396	C₄×C₁₀₁	direct (N × H)
238. C₂×C₄⋊C₄	C₂×C₄×C₁₀₁	semidirect
256. #95	C₂×C₄×C₁₀₁	semidirect
388. C₄	#396×C₁₀₁	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×#396×C₁₀₁	2
C₂×C₄×C₄⋊C₄×C₁₀₁	2
C₂×C₄×C₂²⋊C₄×C₁₀₁	2
C₁₀₁×#1443	2
C₁₀₁×#1441	2
C₁₀₁×#1439	2
C₄×#95×C₁₀₁	2
C₄×#396	101

Subgroups — C4×#396×C101 #38796016

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×#396×C₁₀₁ #38796016