Subgroups — C₁₀₁×#23446 #38805597

Order 25856.

1994 conjugacy classes of subgroups.

The subgroup lattice has 466 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₀₁×#3449	C₂	1	1	yes	maximal, characteristic
2	C₂×#536×C₁₀₁	C₂	1	2	yes	maximal, complemented
3	C₂×#410×C₁₀₁	C₂	1	2	yes	maximal, complemented
4	C₁₀₁×#2310	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₀₁×#2022	C₂	1	8	yes	maximal, complemented
6	C₁₀₁×#1740	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂²×#41×C₁₀₁	C₂²	1	2	yes	—
8	C₂³×Q₈×C₁₀₁	C₂²	1	1	yes	characteristic
9	#537×C₁₀₁	—	2	2	no	—
10	#536×C₁₀₁	—	2	2	no	—
11	#536×C₁₀₁	—	2	8	no	—
12	#536×C₁₀₁	—	2	8	no	—
13	#535×C₁₀₁	—	2	2	no	—
14	#534×C₁₀₁	C₂²	1	4	yes	—
15	#532×C₁₀₁	—	2	2	no	—
16	C₂×C₄⋊Q₈×C₁₀₁	—	2	2	no	—
17	C₂×#124×C₁₀₁	—	2	2	no	—
18	#525×C₁₀₁	—	2	4	no	—
19	C₂×#123×C₁₀₁	C₂²	1	8	yes	—
20	C₂×C₂²⋊Q₈×C₁₀₁	—	2	4	no	—
21	C₂×#117×C₁₀₁	C₂²	1	1	yes	characteristic
22	C₂×#117×C₁₀₁	C₂²	1	2	yes	—
23	C₂×#117×C₁₀₁	C₂²	1	1	yes	characteristic
24	#410×C₁₀₁	—	2	8	no	—
25	C₂×#99×C₁₀₁	C₂²	1	8	yes	—
26	#391×C₁₀₁	—	2	2	no	—
27	#391×C₁₀₁	—	2	2	no	—
28	#381×C₁₀₁	C₂²	1	4	yes	—
29	#342×C₁₀₁	C₂²	1	4	yes	—
30	C₂×#41×C₁₀₁	—	2	4	no	—
31	C₂×#41×C₁₀₁	—	2	2	no	—
32	C₂×#41×C₁₀₁	—	2	2	no	—
33	C₂×#41×C₁₀₁	—	2	2	no	—
34	C₂×#41×C₁₀₁	—	2	4	no	—
35	C₂×#41×C₁₀₁	—	2	4	no	—
36	C₂×#41×C₁₀₁	—	2	2	no	—
37	C₂×#41×C₁₀₁	—	2	4	no	—
38	C₂²×Q₈×C₁₀₁	—	2	2	no	—
39	C₂²×Q₈×C₁₀₁	—	2	2	no	—
40	C₂²×Q₈×C₁₀₁	—	2	4	no	—
41	C₂²×Q₈×C₁₀₁	—	2	1	no	—
42	C₂²×Q₈×C₁₀₁	—	2	1	no	—
43	C₂²×Q₈×C₁₀₁	—	2	2	no	—
44	C₂²×Q₈×C₁₀₁	D₄	1	2	yes	—
45	C₂²×Q₈×C₁₀₁	D₄	1	4	yes	complemented
46	C₂²×D₄×C₁₀₁	D₄	1	2	yes	—
47	C₂²×D₄×C₁₀₁	C₂³	1	4	yes	—
48	C₂³×C₄×C₁₀₁	D₄	1	4	yes	—
49	C₂³×C₄×C₁₀₁	C₂³	1	2	yes	—
50	C₂³×C₄×C₁₀₁	C₂³	1	1	yes	characteristic
51	C₄⋊Q₈×C₁₀₁	—	2	16	no	—
52	C₄⋊Q₈×C₁₀₁	—	2	2	no	—
53	#127×C₁₀₁	—	2	2	no	—
54	#124×C₁₀₁	—	2	16	no	—
55	#124×C₁₀₁	—	2	4	no	—
56	#123×C₁₀₁	—	2	16	no	—
57	#123×C₁₀₁	—	2	8	no	—
58	#123×C₁₀₁	—	2	16	no	—
59	C₂²⋊Q₈×C₁₀₁	—	2	32	no	—
60	C₂²⋊Q₈×C₁₀₁	—	2	8	no	—
61	#121×C₁₀₁	—	2	8	no	—
62	#121×C₁₀₁	—	2	8	no	—
63	#120×C₁₀₁	—	2	8	no	—
64	C₄×D₄×C₁₀₁	—	2	8	no	—
65	#117×C₁₀₁	—	2	2	no	—
66	#117×C₁₀₁	—	2	2	no	—
67	#117×C₁₀₁	—	2	4	no	—
68	#117×C₁₀₁	—	2	4	no	—
69	#117×C₁₀₁	D₄	1	8	yes	complemented
70	C₂×C₄⋊C₄×C₁₀₁	—	2	2	no	—
71	C₂×C₄⋊C₄×C₁₀₁	—	2	8	no	—
72	C₂×C₄⋊C₄×C₁₀₁	—	2	1	no	—
73	C₂×C₄⋊C₄×C₁₀₁	D₄	1	2	yes	—
74	C₂×C₂²⋊C₄×C₁₀₁	—	2	8	no	—
75	C₂×C₂²⋊C₄×C₁₀₁	C₂³	1	2	yes	—
76	C₂×C₂²⋊C₄×C₁₀₁	C₂³	1	2	yes	—
77	C₂×C₂²⋊C₄×C₁₀₁	C₂³	1	4	yes	—
78	C₂×C₄²×C₁₀₁	—	2	2	no	—
79	C₂×C₄²×C₁₀₁	—	2	1	no	—
80	C₂×C₄²×C₁₀₁	D₄	1	2	yes	—
81	#99×C₁₀₁	—	2	16	no	—
82	#95×C₁₀₁	—	2	8	no	—
83	C₂⁴×C₁₀₁	C₂×D₄	1	4	yes	—
84	C₂⁴×C₁₀₁	C₂⁴	1	1	yes	characteristic
85	#41×C₁₀₁	—	4	4	no	—
86	#41×C₁₀₁	—	4	4	no	—
87	#41×C₁₀₁	—	4	4	no	—
88	#41×C₁₀₁	—	4	4	no	—
89	#41×C₁₀₁	—	4	4	no	—
90	#41×C₁₀₁	—	4	4	no	—
91	#41×C₁₀₁	—	4	4	no	—
92	#41×C₁₀₁	—	4	4	no	—
93	C₂×Q₈×C₁₀₁	—	2	8	no	—
94	C₂×Q₈×C₁₀₁	—	2	2	no	—
95	C₂×Q₈×C₁₀₁	—	2	8	no	—
96	C₂×Q₈×C₁₀₁	—	2	2	no	—
97	C₂×Q₈×C₁₀₁	—	2	4	no	—
98	C₂×Q₈×C₁₀₁	—	2	4	no	—
99	C₂×Q₈×C₁₀₁	—	2	4	no	—
100	C₂×Q₈×C₁₀₁	—	2	4	no	—
101	C₂×Q₈×C₁₀₁	—	4	1	no	—
102	C₂×Q₈×C₁₀₁	—	4	1	no	—
103	C₂×Q₈×C₁₀₁	—	4	2	no	—
104	C₂×Q₈×C₁₀₁	—	4	4	no	—
105	C₂×Q₈×C₁₀₁	—	4	4	no	—
106	C₂×Q₈×C₁₀₁	—	4	2	no	—
107	C₂×Q₈×C₁₀₁	—	4	2	no	—
108	C₂×D₄×C₁₀₁	—	2	4	no	—
109	C₂×D₄×C₁₀₁	—	2	4	no	—
110	C₂×D₄×C₁₀₁	—	2	4	no	—
111	C₂×D₄×C₁₀₁	—	2	4	no	—
112	C₂×D₄×C₁₀₁	—	2	4	no	—
113	C₂×D₄×C₁₀₁	—	2	4	no	—
114	C₂×D₄×C₁₀₁	—	2	8	no	—
115	C₂×D₄×C₁₀₁	—	2	2	no	—
116	C₂×D₄×C₁₀₁	—	2	4	no	—
117	C₂×D₄×C₁₀₁	—	2	2	no	—
118	C₂×D₄×C₁₀₁	—	2	4	no	—
119	C₂²×C₄×C₁₀₁	—	2	2	no	—
120	C₂²×C₄×C₁₀₁	—	2	4	no	—
121	C₂²×C₄×C₁₀₁	—	2	4	no	—
122	C₂²×C₄×C₁₀₁	—	2	4	no	—
123	C₂²×C₄×C₁₀₁	—	2	2	no	—
124	C₂²×C₄×C₁₀₁	—	2	4	no	—
125	C₂²×C₄×C₁₀₁	—	2	4	no	—
126	C₂²×C₄×C₁₀₁	—	2	8	no	—
127	C₂²×C₄×C₁₀₁	—	2	8	no	—
128	C₂²×C₄×C₁₀₁	—	2	2	no	—
129	C₂²×C₄×C₁₀₁	C₂×D₄	1	4	yes	—
130	C₂²×C₄×C₁₀₁	C₂×D₄	1	4	yes	—
131	C₂²×C₄×C₁₀₁	C₂×D₄	1	4	yes	—
132	C₂²×C₄×C₁₀₁	C₂×D₄	1	2	yes	—
133	C₂²×C₄×C₁₀₁	C₂×D₄	1	2	yes	—
134	C₂²×C₄×C₁₀₁	C₂×D₄	1	2	yes	—
135	C₂²×C₄×C₁₀₁	C₂×D₄	1	1	yes	characteristic
136	C₂²×C₄×C₁₀₁	C₂×D₄	1	1	yes	characteristic
137	C₂²×C₄×C₁₀₁	C₂×D₄	1	4	yes	—
138	C₂²×C₄×C₁₀₁	#41	1	2	yes	—
139	C₄⋊C₄×C₁₀₁	—	2	32	no	—
140	C₄⋊C₄×C₁₀₁	—	2	8	no	—
141	C₄⋊C₄×C₁₀₁	—	2	8	no	—
142	C₄⋊C₄×C₁₀₁	—	2	4	no	—
143	C₄⋊C₄×C₁₀₁	—	4	2	no	—
144	C₂²⋊C₄×C₁₀₁	—	2	32	no	—
145	C₂²⋊C₄×C₁₀₁	—	2	16	no	—
146	C₂²⋊C₄×C₁₀₁	—	2	4	no	—
147	C₂²⋊C₄×C₁₀₁	—	2	4	no	—
148	C₂²⋊C₄×C₁₀₁	—	2	4	no	—
149	C₂²⋊C₄×C₁₀₁	C₂×D₄	1	8	yes	—
150	C₄²×C₁₀₁	—	2	8	no	—
151	C₄²×C₁₀₁	—	2	2	no	—
152	C₄²×C₁₀₁	—	2	2	no	—
153	C₄²×C₁₀₁	—	4	2	no	—
154	C₂³×C₁₀₁	—	2	4	no	—
155	C₂³×C₁₀₁	—	2	4	no	—
156	C₂³×C₁₀₁	—	2	4	no	—
157	C₂³×C₁₀₁	—	4	2	no	—
158	C₂³×C₁₀₁	—	4	8	no	—
159	C₂³×C₁₀₁	C₂²×D₄	1	2	yes	—
160	C₂³×C₁₀₁	C₂²×D₄	1	1	yes	characteristic
161	C₂³×C₁₀₁	C₂²×D₄	1	1	yes	characteristic
162	C₂³×C₁₀₁	C₂²×D₄	1	2	yes	—
163	C₂³×C₁₀₁	C₂×#41	1	1	yes	characteristic
164	Q₈×C₁₀₁	—	4	4	no	—
165	Q₈×C₁₀₁	—	4	8	no	—
166	Q₈×C₁₀₁	—	4	4	no	—
167	Q₈×C₁₀₁	—	4	4	no	—
168	Q₈×C₁₀₁	—	4	4	no	—
169	D₄×C₁₀₁	—	4	4	no	—
170	D₄×C₁₀₁	—	4	4	no	—
171	D₄×C₁₀₁	—	4	4	no	—
172	D₄×C₁₀₁	—	4	4	no	—
173	D₄×C₁₀₁	—	4	4	no	—
174	D₄×C₁₀₁	—	4	4	no	—
175	D₄×C₁₀₁	—	8	8	no	—
176	C₂×C₄×C₁₀₁	—	2	8	no	—
177	C₂×C₄×C₁₀₁	—	2	8	no	—
178	C₂×C₄×C₁₀₁	—	2	4	no	—
179	C₂×C₄×C₁₀₁	—	2	4	no	—
180	C₂×C₄×C₁₀₁	—	2	4	no	—
181	C₂×C₄×C₁₀₁	—	2	4	no	—
182	C₂×C₄×C₁₀₁	—	2	4	no	—
183	C₂×C₄×C₁₀₁	—	4	8	no	—
184	C₂×C₄×C₁₀₁	—	4	2	no	—
185	C₂×C₄×C₁₀₁	—	4	4	no	—
186	C₂×C₄×C₁₀₁	—	4	2	no	—
187	C₂×C₄×C₁₀₁	—	4	8	no	—
188	C₂×C₄×C₁₀₁	—	4	8	no	—
189	C₂×C₄×C₁₀₁	—	4	4	no	—
190	C₂×C₄×C₁₀₁	—	4	4	no	—
191	C₂×C₄×C₁₀₁	—	4	2	no	—
192	C₂×C₄×C₁₀₁	#120	1	4	yes	—
193	C₂×C₄×C₁₀₁	#120	1	4	yes	—
194	C₂×C₄×C₁₀₁	#120	1	1	yes	characteristic
195	C₂×C₄×C₁₀₁	#120	1	1	yes	characteristic
196	C₂×C₄×C₁₀₁	#120	1	2	yes	—
197	C₂×C₄×C₁₀₁	#121	1	4	yes	—
198	C₂×C₄×C₁₀₁	#121	1	4	yes	—
199	C₂×C₄×C₁₀₁	#121	1	2	yes	—
200	C₂×C₄×C₁₀₁	#121	1	2	yes	—
201	C₂×C₄×C₁₀₁	#127	1	2	yes	—
202	C₂×C₄×C₁₀₁	#127	1	2	yes	—
203	C₂²×C₁₀₁	—	2	2	no	—
204	C₂²×C₁₀₁	—	2	4	no	—
205	C₂²×C₁₀₁	—	4	1	no	—
206	C₂²×C₁₀₁	—	4	2	no	—
207	C₂²×C₁₀₁	—	4	1	no	—
208	C₂²×C₁₀₁	—	4	8	no	—
209	C₂²×C₁₀₁	—	4	4	no	—
210	C₂²×C₁₀₁	—	4	8	no	—
211	C₂²×C₁₀₁	—	8	4	no	—
212	C₂²×C₁₀₁	C₂×#120	1	2	yes	—
213	C₂²×C₁₀₁	C₂×#120	1	1	yes	characteristic
214	C₂²×C₁₀₁	C₂×#121	1	1	yes	characteristic
215	C₂²×C₁₀₁	C₂×#121	1	2	yes	—
216	C₂²×C₁₀₁	C₂×#127	1	1	yes	characteristic
217	C₄×C₁₀₁	—	4	8	no	—
218	C₄×C₁₀₁	—	4	4	no	—
219	C₄×C₁₀₁	—	4	4	no	—
220	C₄×C₁₀₁	—	4	4	no	—
221	C₄×C₁₀₁	—	8	2	no	—
222	C₄×C₁₀₁	#392	1	2	yes	—
223	C₄×C₁₀₁	#392	1	4	yes	—
224	C₄×C₁₀₁	#392	1	2	yes	—
225	#23446	C₁₀₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
226	C₂×C₁₀₁	—	2	2	no	—
227	C₂×C₁₀₁	—	2	1	no	—
228	C₂×C₁₀₁	—	2	2	no	—
229	C₂×C₁₀₁	—	2	1	no	—
230	C₂×C₁₀₁	—	8	4	no	—
231	C₂×C₁₀₁	C₂×#392	1	1	yes	characteristic
232	C₂×C₁₀₁	#3028	1	2	yes	—
233	#3449	C₂×C₁₀₁	1	1	yes	characteristic
234	C₂×#536	C₂×C₁₀₁	1	2	yes	complemented
235	C₂×#410	C₂×C₁₀₁	1	2	yes	complemented
236	#2310	C₂×C₁₀₁	1	1	yes	characteristic, complemented
237	#2022	C₂×C₁₀₁	1	8	yes	complemented
238	#1740	C₂×C₁₀₁	1	1	yes	characteristic, complemented
239	C₁₀₁	#23446	1	1	yes	characteristic, direct product factor, Sylow
240	C₂²×#41	C₂²×C₁₀₁	1	2	yes	—
241	C₂³×Q₈	C₂²×C₁₀₁	1	1	yes	characteristic
242	#537	—	2	2	no	—
243	#536	—	2	2	no	—
244	#536	—	2	8	no	—
245	#536	—	2	8	no	—
246	#535	—	2	2	no	—
247	#534	C₂²×C₁₀₁	1	4	yes	—
248	#532	—	2	2	no	—
249	C₂×C₄⋊Q₈	—	2	2	no	—
250	C₂×#124	—	2	2	no	—
251	#525	—	2	4	no	—
252	C₂×#123	C₂²×C₁₀₁	1	8	yes	—
253	C₂×C₂²⋊Q₈	—	2	4	no	—
254	C₂×#117	C₂²×C₁₀₁	1	1	yes	characteristic
255	C₂×#117	C₂²×C₁₀₁	1	2	yes	—
256	C₂×#117	C₂²×C₁₀₁	1	1	yes	characteristic
257	#410	—	2	8	no	—
258	C₂×#99	C₂²×C₁₀₁	1	8	yes	—
259	#391	—	2	2	no	—
260	#391	—	2	2	no	—
261	#381	C₂²×C₁₀₁	1	4	yes	—
262	#342	C₂²×C₁₀₁	1	4	yes	—
263	C₂×#41	—	2	2	no	—
264	C₂×#41	—	2	2	no	—
265	C₂×#41	—	2	2	no	—
266	C₂×#41	—	2	4	no	—
267	C₂×#41	—	2	4	no	—
268	C₂×#41	—	2	2	no	—
269	C₂×#41	—	2	4	no	—
270	C₂×#41	—	2	4	no	—
271	C₂²×Q₈	—	2	2	no	—
272	C₂²×Q₈	—	2	2	no	—
273	C₂²×Q₈	—	2	4	no	—
274	C₂²×Q₈	—	2	1	no	—
275	C₂²×Q₈	—	2	1	no	—
276	C₂²×Q₈	—	2	2	no	—
277	C₂²×Q₈	D₄×C₁₀₁	1	2	yes	—
278	C₂²×Q₈	D₄×C₁₀₁	1	4	yes	complemented
279	C₂²×D₄	D₄×C₁₀₁	1	2	yes	—
280	C₂²×D₄	C₂³×C₁₀₁	1	4	yes	—
281	C₂³×C₄	D₄×C₁₀₁	1	4	yes	—
282	C₂³×C₄	C₂³×C₁₀₁	1	2	yes	—
283	C₂³×C₄	C₂³×C₁₀₁	1	1	yes	characteristic
284	C₄⋊Q₈	—	2	16	no	—
285	C₄⋊Q₈	—	2	2	no	—
286	#127	—	2	2	no	—
287	#124	—	2	16	no	—
288	#124	—	2	4	no	—
289	#123	—	2	16	no	—
290	#123	—	2	8	no	—
291	#123	—	2	16	no	—
292	C₂²⋊Q₈	—	2	32	no	—
293	C₂²⋊Q₈	—	2	8	no	—
294	#121	—	2	8	no	—
295	#121	—	2	8	no	—
296	#120	—	2	8	no	—
297	C₄×D₄	—	2	8	no	—
298	#117	—	2	2	no	—
299	#117	—	2	2	no	—
300	#117	—	2	4	no	—
301	#117	—	2	4	no	—
302	#117	D₄×C₁₀₁	1	8	yes	complemented
303	C₂×C₄⋊C₄	—	2	2	no	—
304	C₂×C₄⋊C₄	—	2	8	no	—
305	C₂×C₄⋊C₄	—	2	1	no	—
306	C₂×C₄⋊C₄	D₄×C₁₀₁	1	2	yes	—
307	C₂×C₂²⋊C₄	—	2	8	no	—
308	C₂×C₂²⋊C₄	C₂³×C₁₀₁	1	2	yes	—
309	C₂×C₂²⋊C₄	C₂³×C₁₀₁	1	2	yes	—
310	C₂×C₂²⋊C₄	C₂³×C₁₀₁	1	4	yes	—
311	C₂×C₄²	—	2	2	no	—
312	C₂×C₄²	—	2	1	no	—
313	C₂×C₄²	D₄×C₁₀₁	1	2	yes	—
314	#99	—	2	16	no	—
315	#95	—	2	8	no	—
316	C₂⁴	C₂×D₄×C₁₀₁	1	4	yes	—
317	C₂⁴	C₂⁴×C₁₀₁	1	1	yes	characteristic
318	#41	—	4	4	no	—
319	#41	—	4	4	no	—
320	#41	—	4	4	no	—
321	#41	—	4	4	no	—
322	#41	—	4	4	no	—
323	#41	—	4	4	no	—
324	#41	—	4	4	no	—
325	#41	—	4	4	no	—
326	C₂×Q₈	—	2	8	no	—
327	C₂×Q₈	—	2	2	no	—
328	C₂×Q₈	—	2	8	no	—
329	C₂×Q₈	—	2	2	no	—
330	C₂×Q₈	—	2	4	no	—
331	C₂×Q₈	—	2	4	no	—
332	C₂×Q₈	—	2	4	no	—
333	C₂×Q₈	—	2	4	no	—
334	C₂×Q₈	—	4	1	no	—
335	C₂×Q₈	—	4	1	no	—
336	C₂×Q₈	—	4	2	no	—
337	C₂×Q₈	—	4	4	no	—
338	C₂×Q₈	—	4	4	no	—
339	C₂×Q₈	—	4	2	no	—
340	C₂×Q₈	—	4	2	no	—
341	C₂×D₄	—	2	4	no	—
342	C₂×D₄	—	2	4	no	—
343	C₂×D₄	—	2	4	no	—
344	C₂×D₄	—	2	4	no	—
345	C₂×D₄	—	2	4	no	—
346	C₂×D₄	—	2	4	no	—
347	C₂×D₄	—	2	8	no	—
348	C₂×D₄	—	2	2	no	—
349	C₂×D₄	—	2	4	no	—
350	C₂×D₄	—	2	2	no	—
351	C₂×D₄	—	2	4	no	—
352	C₂²×C₄	—	2	2	no	—
353	C₂²×C₄	—	2	4	no	—
354	C₂²×C₄	—	2	4	no	—
355	C₂²×C₄	—	2	4	no	—
356	C₂²×C₄	—	2	2	no	—
357	C₂²×C₄	—	2	4	no	—
358	C₂²×C₄	—	2	4	no	—
359	C₂²×C₄	—	2	8	no	—
360	C₂²×C₄	—	2	8	no	—
361	C₂²×C₄	—	2	2	no	—
362	C₂²×C₄	C₂×D₄×C₁₀₁	1	4	yes	—
363	C₂²×C₄	C₂×D₄×C₁₀₁	1	4	yes	—
364	C₂²×C₄	C₂×D₄×C₁₀₁	1	4	yes	—
365	C₂²×C₄	C₂×D₄×C₁₀₁	1	2	yes	—
366	C₂²×C₄	C₂×D₄×C₁₀₁	1	2	yes	—
367	C₂²×C₄	C₂×D₄×C₁₀₁	1	2	yes	—
368	C₂²×C₄	C₂×D₄×C₁₀₁	1	1	yes	characteristic
369	C₂²×C₄	C₂×D₄×C₁₀₁	1	1	yes	characteristic
370	C₂²×C₄	C₂×D₄×C₁₀₁	1	4	yes	—
371	C₂²×C₄	#41×C₁₀₁	1	2	yes	—
372	C₄⋊C₄	—	2	32	no	—
373	C₄⋊C₄	—	2	8	no	—
374	C₄⋊C₄	—	2	8	no	—
375	C₄⋊C₄	—	2	4	no	—
376	C₄⋊C₄	—	4	2	no	—
377	C₂²⋊C₄	—	2	32	no	—
378	C₂²⋊C₄	—	2	16	no	—
379	C₂²⋊C₄	—	2	4	no	—
380	C₂²⋊C₄	—	2	4	no	—
381	C₂²⋊C₄	—	2	4	no	—
382	C₂²⋊C₄	C₂×D₄×C₁₀₁	1	8	yes	—
383	C₄²	—	2	8	no	—
384	C₄²	—	2	2	no	—
385	C₄²	—	2	2	no	—
386	C₄²	—	4	2	no	—
387	C₂³	—	2	4	no	—
388	C₂³	—	2	4	no	—
389	C₂³	—	2	4	no	—
390	C₂³	—	4	2	no	—
391	C₂³	—	4	8	no	—
392	C₂³	C₂²×D₄×C₁₀₁	1	2	yes	—
393	C₂³	C₂²×D₄×C₁₀₁	1	1	yes	characteristic
394	C₂³	C₂²×D₄×C₁₀₁	1	1	yes	characteristic
395	C₂³	C₂²×D₄×C₁₀₁	1	2	yes	—
396	C₂³	C₂×#41×C₁₀₁	1	1	yes	characteristic
397	Q₈	—	4	4	no	—
398	Q₈	—	4	8	no	—
399	Q₈	—	4	4	no	—
400	Q₈	—	4	4	no	—
401	Q₈	—	4	4	no	—
402	D₄	—	4	4	no	—
403	D₄	—	4	4	no	—
404	D₄	—	4	4	no	—
405	D₄	—	4	4	no	—
406	D₄	—	4	4	no	—
407	D₄	—	4	4	no	—
408	D₄	—	8	8	no	—
409	C₂×C₄	—	2	4	no	—
410	C₂×C₄	—	2	8	no	—
411	C₂×C₄	—	2	4	no	—
412	C₂×C₄	—	2	8	no	—
413	C₂×C₄	—	2	4	no	—
414	C₂×C₄	—	2	4	no	—
415	C₂×C₄	—	2	4	no	—
416	C₂×C₄	—	4	8	no	—
417	C₂×C₄	—	4	2	no	—
418	C₂×C₄	—	4	4	no	—
419	C₂×C₄	—	4	2	no	—
420	C₂×C₄	—	4	8	no	—
421	C₂×C₄	—	4	8	no	—
422	C₂×C₄	—	4	4	no	—
423	C₂×C₄	—	4	4	no	—
424	C₂×C₄	—	4	2	no	—
425	C₂×C₄	#120×C₁₀₁	1	1	yes	characteristic
426	C₂×C₄	#120×C₁₀₁	1	1	yes	characteristic
427	C₂×C₄	#120×C₁₀₁	1	4	yes	—
428	C₂×C₄	#120×C₁₀₁	1	2	yes	—
429	C₂×C₄	#120×C₁₀₁	1	4	yes	—
430	C₂×C₄	#121×C₁₀₁	1	4	yes	—
431	C₂×C₄	#121×C₁₀₁	1	4	yes	—
432	C₂×C₄	#121×C₁₀₁	1	2	yes	—
433	C₂×C₄	#121×C₁₀₁	1	2	yes	—
434	C₂×C₄	#127×C₁₀₁	1	2	yes	—
435	C₂×C₄	#127×C₁₀₁	1	2	yes	—
436	C₂²	—	2	2	no	—
437	C₂²	—	2	4	no	—
438	C₂²	—	4	1	no	—
439	C₂²	—	4	2	no	—
440	C₂²	—	4	1	no	—
441	C₂²	—	4	8	no	—
442	C₂²	—	4	8	no	—
443	C₂²	—	4	4	no	—
444	C₂²	—	8	4	no	—
445	C₂²	C₂×#120×C₁₀₁	1	2	yes	—
446	C₂²	C₂×#120×C₁₀₁	1	1	yes	characteristic
447	C₂²	C₂×#121×C₁₀₁	1	1	yes	characteristic
448	C₂²	C₂×#121×C₁₀₁	1	2	yes	—
449	C₂²	C₂×#127×C₁₀₁	1	1	yes	characteristic
450	C₄	—	4	8	no	—
451	C₄	—	4	4	no	—
452	C₄	—	4	4	no	—
453	C₄	—	4	4	no	—
454	C₄	—	8	2	no	—
455	C₄	#392×C₁₀₁	1	2	yes	—
456	C₄	#392×C₁₀₁	1	4	yes	—
457	C₄	#392×C₁₀₁	1	2	yes	—
458	C₂	—	2	2	no	—
459	C₂	—	2	1	no	—
460	C₂	—	2	2	no	—
461	C₂	—	2	1	no	—
462	C₂	—	8	4	no	—
463	C₂	C₂×#392×C₁₀₁	1	1	yes	characteristic
464	C₂	C₁₀₁×#3028	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₁₀₁	C₂×#120
commutator, Frattini, cosocle	C₂⁴	C₂⁴×C₁₀₁
prime radical	C₁₀₁×#3449	C₂
LCS	G ▷ C₂⁴ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₀₁ ◁ C₂³×C₄×C₁₀₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×#536×C₁₀₁	C₂	semidirect
3. C₂×#410×C₁₀₁	C₂	semidirect
4. C₁₀₁×#2310	C₂	semidirect
5. C₁₀₁×#2022	C₂	semidirect
6. C₁₀₁×#1740	C₂	semidirect
45. C₂²×Q₈×C₁₀₁	D₄	semidirect
69. #117×C₁₀₁	D₄	semidirect
225. #23446	C₁₀₁	direct (N × H)
234. C₂×#536	C₂×C₁₀₁	semidirect
235. C₂×#410	C₂×C₁₀₁	semidirect
236. #2310	C₂×C₁₀₁	semidirect
237. #2022	C₂×C₁₀₁	semidirect
238. #1740	C₂×C₁₀₁	semidirect
239. C₁₀₁	#23446	direct (N × H)
278. C₂²×Q₈	D₄×C₁₀₁	semidirect
302. #117	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×#3449	2
C₂×#536×C₁₀₁	2
C₂×#410×C₁₀₁	2
C₁₀₁×#2310	2
C₁₀₁×#2022	2
C₁₀₁×#1740	2
#23446	101

Subgroups — C101×#23446 #38805597

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₀₁×#23446 #38805597