Subgroups — C₁₀₁×#18685 #38800836

Order 25856.

930 conjugacy classes of subgroups.

The subgroup lattice has 390 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₀₁×#3544	C₂	1	1	yes	maximal, characteristic
2	C₁₀₁×#3238	C₂	1	2	yes	maximal, complemented
3	C₂×#494×C₁₀₁	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₀₁×#1634	C₂	1	2	yes	maximal, complemented
5	C₁₀₁×#1633	C₂	1	2	yes	maximal, complemented
6	C₁₀₁×#1632	C₂	1	4	yes	maximal, complemented
7	C₁₀₁×#1558	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₀₁×#1494	C₂	1	2	yes	maximal, complemented
9	C₂²×Q₁₆×C₁₀₁	—	2	2	no	—
10	#563×C₁₀₁	—	2	2	no	—
11	Q₈²×C₁₀₁	C₂²	1	1	yes	characteristic
12	#555×C₁₀₁	C₂²	1	1	yes	characteristic
13	#554×C₁₀₁	C₂²	1	2	yes	—
14	#552×C₁₀₁	—	2	2	no	—
15	#547×C₁₀₁	—	2	2	no	—
16	#544×C₁₀₁	—	2	2	no	—
17	#542×C₁₀₁	—	2	2	no	—
18	#536×C₁₀₁	—	2	2	no	—
19	C₂×C₄⋊Q₈×C₁₀₁	C₂²	1	1	yes	characteristic
20	C₂×C₄⋊Q₈×C₁₀₁	C₂²	1	1	yes	characteristic
21	#529×C₁₀₁	C₂²	1	2	yes	—
22	#501×C₁₀₁	—	2	2	no	—
23	#494×C₁₀₁	—	2	2	no	—
24	#494×C₁₀₁	C₂²	1	2	yes	—
25	#494×C₁₀₁	C₂²	1	2	yes	—
26	#489×C₁₀₁	—	2	2	no	—
27	#483×C₁₀₁	—	2	2	no	—
28	#480×C₁₀₁	—	2	2	no	—
29	#477×C₁₀₁	C₂²	1	4	yes	—
30	#476×C₁₀₁	C₂²	1	4	yes	—
31	#432×C₁₀₁	C₂²	1	2	yes	—
32	C₂×C₄×C₈×C₁₀₁	C₂²	1	1	yes	characteristic
33	#333×C₁₀₁	C₂²	1	2	yes	—
34	#333×C₁₀₁	C₂²	1	2	yes	—
35	Q₈⋊C₈×C₁₀₁	C₂²	1	4	yes	—
36	D₄⋊C₈×C₁₀₁	C₂²	1	4	yes	—
37	C₂×#41×C₁₀₁	—	2	2	no	—
38	C₂²×Q₈×C₁₀₁	—	2	1	no	—
39	C₂²×Q₈×C₁₀₁	D₄	1	2	yes	—
40	C₂×Q₁₆×C₁₀₁	—	2	4	no	—
41	C₂×Q₁₆×C₁₀₁	—	2	4	no	—
42	C₂×Q₁₆×C₁₀₁	—	4	8	no	—
43	C₂²×C₈×C₁₀₁	—	2	1	no	—
44	C₄⋊Q₈×C₁₀₁	—	2	2	no	—
45	C₄⋊Q₈×C₁₀₁	—	2	2	no	—
46	C₄⋊Q₈×C₁₀₁	—	2	2	no	—
47	C₄⋊Q₈×C₁₀₁	—	2	2	no	—
48	C₄⋊Q₈×C₁₀₁	—	2	2	no	—
49	C₄⋊Q₈×C₁₀₁	—	2	1	no	—
50	C₄⋊Q₈×C₁₀₁	D₄	1	2	yes	—
51	C₄⋊Q₈×C₁₀₁	C₂³	1	2	yes	—
52	C₄⋊Q₈×C₁₀₁	C₂³	1	1	yes	characteristic
53	C₄⋊Q₈×C₁₀₁	C₂³	1	1	yes	characteristic
54	#126×C₁₀₁	—	2	4	no	—
55	#126×C₁₀₁	—	2	2	no	—
56	#125×C₁₀₁	—	2	4	no	—
57	#125×C₁₀₁	—	2	2	no	—
58	#125×C₁₀₁	D₄	1	2	yes	—
59	#124×C₁₀₁	—	2	2	no	—
60	#124×C₁₀₁	—	2	2	no	—
61	#124×C₁₀₁	D₄	1	2	yes	—
62	#123×C₁₀₁	—	2	4	no	—
63	#123×C₁₀₁	—	2	4	no	—
64	#123×C₁₀₁	—	2	2	no	—
65	C₂²⋊Q₈×C₁₀₁	—	2	4	no	—
66	C₂²⋊Q₈×C₁₀₁	—	2	4	no	—
67	C₂²⋊Q₈×C₁₀₁	—	2	4	no	—
68	C₂²⋊Q₈×C₁₀₁	—	2	2	no	—
69	C₂²⋊Q₈×C₁₀₁	D₄	1	2	yes	—
70	#121×C₁₀₁	—	2	2	no	—
71	#121×C₁₀₁	D₄	1	2	yes	—
72	C₄×Q₈×C₁₀₁	—	2	2	no	—
73	C₄×Q₈×C₁₀₁	C₂³	1	2	yes	—
74	C₄×D₄×C₁₀₁	—	2	2	no	—
75	C₄×D₄×C₁₀₁	—	2	2	no	—
76	C₄×D₄×C₁₀₁	C₂³	1	2	yes	—
77	#117×C₁₀₁	—	2	2	no	—
78	#117×C₁₀₁	—	2	2	no	—
79	#117×C₁₀₁	—	2	2	no	—
80	C₂×C₄⋊C₄×C₁₀₁	—	2	2	no	—
81	C₂×C₄⋊C₄×C₁₀₁	—	2	2	no	—
82	C₂×C₄⋊C₄×C₁₀₁	—	2	2	no	—
83	C₂×C₄²×C₁₀₁	C₂³	1	1	yes	characteristic
84	#107×C₁₀₁	—	2	4	no	—
85	#106×C₁₀₁	—	2	4	no	—
86	C₄⋊C₈×C₁₀₁	C₂³	1	4	yes	—
87	#103×C₁₀₁	—	2	4	no	—
88	#102×C₁₀₁	—	2	4	no	—
89	C₂²⋊C₈×C₁₀₁	—	2	2	no	—
90	#97×C₁₀₁	—	2	2	no	—
91	C₄×C₈×C₁₀₁	—	2	1	no	—
92	C₄×C₈×C₁₀₁	C₂³	1	2	yes	—
93	#41×C₁₀₁	—	8	4	no	—
94	C₂×Q₈×C₁₀₁	—	2	2	no	—
95	C₂×Q₈×C₁₀₁	—	2	2	no	—
96	C₂×Q₈×C₁₀₁	—	2	2	no	—
97	C₂×Q₈×C₁₀₁	—	4	4	no	—
98	C₂×Q₈×C₁₀₁	—	4	4	no	—
99	C₂×Q₈×C₁₀₁	—	4	1	no	—
100	C₂×Q₈×C₁₀₁	C₂×D₄	1	2	yes	—
101	C₂×Q₈×C₁₀₁	C₂×D₄	1	2	yes	—
102	C₂×Q₈×C₁₀₁	C₂×D₄	1	2	yes	—
103	C₂×D₄×C₁₀₁	—	2	2	no	—
104	C₂×D₄×C₁₀₁	—	2	2	no	—
105	C₂×D₄×C₁₀₁	C₂×D₄	1	2	yes	—
106	C₂²×C₄×C₁₀₁	—	2	2	no	—
107	C₂²×C₄×C₁₀₁	—	2	4	no	—
108	C₂²×C₄×C₁₀₁	—	2	2	no	—
109	C₂²×C₄×C₁₀₁	—	4	1	no	—
110	C₂²×C₄×C₁₀₁	C₂×D₄	1	2	yes	—
111	C₂²×C₄×C₁₀₁	C₂×D₄	1	1	yes	characteristic
112	Q₁₆×C₁₀₁	—	4	8	no	—
113	Q₁₆×C₁₀₁	—	4	8	no	—
114	C₂×C₈×C₁₀₁	—	2	4	no	—
115	C₂×C₈×C₁₀₁	—	2	2	no	—
116	C₂×C₈×C₁₀₁	—	2	4	no	—
117	C₄⋊C₄×C₁₀₁	—	2	4	no	—
118	C₄⋊C₄×C₁₀₁	—	2	4	no	—
119	C₄⋊C₄×C₁₀₁	—	2	4	no	—
120	C₄⋊C₄×C₁₀₁	—	2	4	no	—
121	C₄⋊C₄×C₁₀₁	—	2	2	no	—
122	C₄⋊C₄×C₁₀₁	—	2	2	no	—
123	C₄⋊C₄×C₁₀₁	—	2	2	no	—
124	C₄⋊C₄×C₁₀₁	—	2	2	no	—
125	C₄⋊C₄×C₁₀₁	—	2	2	no	—
126	C₄⋊C₄×C₁₀₁	—	2	2	no	—
127	C₄⋊C₄×C₁₀₁	—	2	4	no	—
128	C₄⋊C₄×C₁₀₁	—	4	2	no	—
129	C₄⋊C₄×C₁₀₁	C₂×D₄	1	2	yes	—
130	C₄⋊C₄×C₁₀₁	C₂×D₄	1	2	yes	—
131	C₂²⋊C₄×C₁₀₁	—	2	4	no	—
132	C₂²⋊C₄×C₁₀₁	—	2	4	no	—
133	C₂²⋊C₄×C₁₀₁	—	2	2	no	—
134	C₂²⋊C₄×C₁₀₁	—	2	2	no	—
135	C₂²⋊C₄×C₁₀₁	—	2	2	no	—
136	C₂²⋊C₄×C₁₀₁	—	2	2	no	—
137	C₂²⋊C₄×C₁₀₁	—	2	2	no	—
138	C₄²×C₁₀₁	—	2	2	no	—
139	C₄²×C₁₀₁	—	2	2	no	—
140	C₄²×C₁₀₁	—	2	2	no	—
141	C₄²×C₁₀₁	C₂×D₄	1	1	yes	characteristic
142	C₄²×C₁₀₁	C₂×D₄	1	2	yes	—
143	C₄²×C₁₀₁	C₂⁴	1	1	yes	characteristic
144	C₂³×C₁₀₁	—	2	2	no	—
145	C₂³×C₁₀₁	#120	1	1	yes	characteristic
146	Q₈×C₁₀₁	—	2	4	no	—
147	Q₈×C₁₀₁	—	4	2	no	—
148	Q₈×C₁₀₁	—	4	2	no	—
149	Q₈×C₁₀₁	—	4	4	no	—
150	Q₈×C₁₀₁	—	8	2	no	—
151	Q₈×C₁₀₁	—	8	2	no	—
152	Q₈×C₁₀₁	—	8	2	no	—
153	D₄×C₁₀₁	—	2	4	no	—
154	D₄×C₁₀₁	—	4	4	no	—
155	D₄×C₁₀₁	—	8	2	no	—
156	C₂×C₄×C₁₀₁	—	2	2	no	—
157	C₂×C₄×C₁₀₁	—	2	4	no	—
158	C₂×C₄×C₁₀₁	—	2	2	no	—
159	C₂×C₄×C₁₀₁	—	2	2	no	—
160	C₂×C₄×C₁₀₁	—	2	2	no	—
161	C₂×C₄×C₁₀₁	—	2	2	no	—
162	C₂×C₄×C₁₀₁	—	2	2	no	—
163	C₂×C₄×C₁₀₁	—	4	4	no	—
164	C₂×C₄×C₁₀₁	—	4	4	no	—
165	C₂×C₄×C₁₀₁	—	4	2	no	—
166	C₂×C₄×C₁₀₁	—	8	4	no	—
167	C₂×C₄×C₁₀₁	—	8	2	no	—
168	C₂×C₄×C₁₀₁	#120	1	2	yes	—
169	C₂×C₄×C₁₀₁	#120	1	1	yes	characteristic
170	C₂×C₄×C₁₀₁	C₂²×D₄	1	1	yes	characteristic
171	C₂×C₄×C₁₀₁	C₂²×D₄	1	2	yes	—
172	C₈×C₁₀₁	—	2	4	no	—
173	C₈×C₁₀₁	—	4	4	no	—
174	C₂²×C₁₀₁	—	2	2	no	—
175	C₂²×C₁₀₁	—	4	2	no	—
176	C₂²×C₁₀₁	—	4	2	no	—
177	C₂²×C₁₀₁	—	4	2	no	—
178	C₂²×C₁₀₁	#453	1	2	yes	—
179	C₂²×C₁₀₁	C₂×#120	1	1	yes	characteristic
180	C₄×C₁₀₁	—	2	2	no	—
181	C₄×C₁₀₁	—	2	1	no	—
182	C₄×C₁₀₁	—	2	1	no	—
183	C₄×C₁₀₁	—	4	2	no	—
184	C₄×C₁₀₁	—	4	2	no	—
185	C₄×C₁₀₁	—	4	2	no	—
186	C₄×C₁₀₁	—	4	2	no	—
187	C₄×C₁₀₁	—	4	2	no	—
188	C₄×C₁₀₁	—	8	2	no	—
189	C₄×C₁₀₁	#578	1	4	yes	—
190	#18685	C₁₀₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
191	C₂×C₁₀₁	—	2	2	no	—
192	C₂×C₁₀₁	—	8	2	no	—
193	C₂×C₁₀₁	#3011	1	2	yes	—
194	C₂×C₁₀₁	C₂×#453	1	1	yes	characteristic
195	#3544	C₂×C₁₀₁	1	1	yes	characteristic
196	#3238	C₂×C₁₀₁	1	2	yes	complemented
197	C₂×#494	C₂×C₁₀₁	1	1	yes	characteristic, complemented
198	#1634	C₂×C₁₀₁	1	2	yes	complemented
199	#1633	C₂×C₁₀₁	1	2	yes	complemented
200	#1632	C₂×C₁₀₁	1	4	yes	complemented
201	#1558	C₂×C₁₀₁	1	1	yes	characteristic, complemented
202	#1494	C₂×C₁₀₁	1	2	yes	complemented
203	C₁₀₁	#18685	1	1	yes	characteristic, direct product factor, Sylow
204	C₂²×Q₁₆	—	2	2	no	—
205	#563	—	2	2	no	—
206	Q₈²	C₂²×C₁₀₁	1	1	yes	characteristic
207	#555	C₂²×C₁₀₁	1	1	yes	characteristic
208	#554	C₂²×C₁₀₁	1	2	yes	—
209	#552	—	2	2	no	—
210	#547	—	2	2	no	—
211	#544	—	2	2	no	—
212	#542	—	2	2	no	—
213	#536	—	2	2	no	—
214	C₂×C₄⋊Q₈	C₂²×C₁₀₁	1	1	yes	characteristic
215	C₂×C₄⋊Q₈	C₂²×C₁₀₁	1	1	yes	characteristic
216	#529	C₂²×C₁₀₁	1	2	yes	—
217	#501	—	2	2	no	—
218	#494	—	2	2	no	—
219	#494	C₂²×C₁₀₁	1	2	yes	—
220	#494	C₂²×C₁₀₁	1	2	yes	—
221	#489	—	2	2	no	—
222	#483	—	2	2	no	—
223	#480	—	2	2	no	—
224	#477	C₂²×C₁₀₁	1	4	yes	—
225	#476	C₂²×C₁₀₁	1	4	yes	—
226	#432	C₂²×C₁₀₁	1	2	yes	—
227	C₂×C₄×C₈	C₂²×C₁₀₁	1	1	yes	characteristic
228	#333	C₂²×C₁₀₁	1	2	yes	—
229	#333	C₂²×C₁₀₁	1	2	yes	—
230	Q₈⋊C₈	C₂²×C₁₀₁	1	4	yes	—
231	D₄⋊C₈	C₂²×C₁₀₁	1	4	yes	—
232	C₂×#41	—	2	2	no	—
233	C₂²×Q₈	—	2	1	no	—
234	C₂²×Q₈	D₄×C₁₀₁	1	2	yes	—
235	C₂×Q₁₆	—	2	4	no	—
236	C₂×Q₁₆	—	2	4	no	—
237	C₂×Q₁₆	—	4	8	no	—
238	C₂²×C₈	—	2	1	no	—
239	C₄⋊Q₈	—	2	2	no	—
240	C₄⋊Q₈	—	2	2	no	—
241	C₄⋊Q₈	—	2	2	no	—
242	C₄⋊Q₈	—	2	2	no	—
243	C₄⋊Q₈	—	2	2	no	—
244	C₄⋊Q₈	—	2	1	no	—
245	C₄⋊Q₈	D₄×C₁₀₁	1	2	yes	—
246	C₄⋊Q₈	C₂³×C₁₀₁	1	2	yes	—
247	C₄⋊Q₈	C₂³×C₁₀₁	1	1	yes	characteristic
248	C₄⋊Q₈	C₂³×C₁₀₁	1	1	yes	characteristic
249	#126	—	2	4	no	—
250	#126	—	2	2	no	—
251	#125	—	2	4	no	—
252	#125	—	2	2	no	—
253	#125	D₄×C₁₀₁	1	2	yes	—
254	#124	—	2	2	no	—
255	#124	—	2	2	no	—
256	#124	D₄×C₁₀₁	1	2	yes	—
257	#123	—	2	4	no	—
258	#123	—	2	4	no	—
259	#123	—	2	2	no	—
260	C₂²⋊Q₈	—	2	4	no	—
261	C₂²⋊Q₈	—	2	4	no	—
262	C₂²⋊Q₈	—	2	4	no	—
263	C₂²⋊Q₈	—	2	2	no	—
264	C₂²⋊Q₈	D₄×C₁₀₁	1	2	yes	—
265	#121	—	2	2	no	—
266	#121	D₄×C₁₀₁	1	2	yes	—
267	C₄×Q₈	—	2	2	no	—
268	C₄×Q₈	C₂³×C₁₀₁	1	2	yes	—
269	C₄×D₄	—	2	2	no	—
270	C₄×D₄	—	2	2	no	—
271	C₄×D₄	C₂³×C₁₀₁	1	2	yes	—
272	#117	—	2	2	no	—
273	#117	—	2	2	no	—
274	#117	—	2	2	no	—
275	C₂×C₄⋊C₄	—	2	2	no	—
276	C₂×C₄⋊C₄	—	2	2	no	—
277	C₂×C₄⋊C₄	—	2	2	no	—
278	C₂×C₄²	C₂³×C₁₀₁	1	1	yes	characteristic
279	#107	—	2	4	no	—
280	#106	—	2	4	no	—
281	C₄⋊C₈	C₂³×C₁₀₁	1	4	yes	—
282	#103	—	2	4	no	—
283	#102	—	2	4	no	—
284	C₂²⋊C₈	—	2	2	no	—
285	#97	—	2	2	no	—
286	C₄×C₈	—	2	1	no	—
287	C₄×C₈	C₂³×C₁₀₁	1	2	yes	—
288	#41	—	8	4	no	—
289	C₂×Q₈	—	2	2	no	—
290	C₂×Q₈	—	2	2	no	—
291	C₂×Q₈	—	2	2	no	—
292	C₂×Q₈	—	4	4	no	—
293	C₂×Q₈	—	4	4	no	—
294	C₂×Q₈	—	4	1	no	—
295	C₂×Q₈	C₂×D₄×C₁₀₁	1	2	yes	—
296	C₂×Q₈	C₂×D₄×C₁₀₁	1	2	yes	—
297	C₂×Q₈	C₂×D₄×C₁₀₁	1	2	yes	—
298	C₂×D₄	—	2	2	no	—
299	C₂×D₄	—	2	2	no	—
300	C₂×D₄	C₂×D₄×C₁₀₁	1	2	yes	—
301	C₂²×C₄	—	2	2	no	—
302	C₂²×C₄	—	2	4	no	—
303	C₂²×C₄	—	2	2	no	—
304	C₂²×C₄	—	4	1	no	—
305	C₂²×C₄	C₂×D₄×C₁₀₁	1	2	yes	—
306	C₂²×C₄	C₂×D₄×C₁₀₁	1	1	yes	characteristic
307	Q₁₆	—	4	8	no	—
308	Q₁₆	—	4	8	no	—
309	C₂×C₈	—	2	4	no	—
310	C₂×C₈	—	2	2	no	—
311	C₂×C₈	—	2	4	no	—
312	C₄⋊C₄	—	2	4	no	—
313	C₄⋊C₄	—	2	4	no	—
314	C₄⋊C₄	—	2	4	no	—
315	C₄⋊C₄	—	2	4	no	—
316	C₄⋊C₄	—	2	2	no	—
317	C₄⋊C₄	—	2	2	no	—
318	C₄⋊C₄	—	2	2	no	—
319	C₄⋊C₄	—	2	2	no	—
320	C₄⋊C₄	—	2	2	no	—
321	C₄⋊C₄	—	2	2	no	—
322	C₄⋊C₄	—	2	4	no	—
323	C₄⋊C₄	—	4	2	no	—
324	C₄⋊C₄	C₂×D₄×C₁₀₁	1	2	yes	—
325	C₄⋊C₄	C₂×D₄×C₁₀₁	1	2	yes	—
326	C₂²⋊C₄	—	2	4	no	—
327	C₂²⋊C₄	—	2	4	no	—
328	C₂²⋊C₄	—	2	2	no	—
329	C₂²⋊C₄	—	2	2	no	—
330	C₂²⋊C₄	—	2	2	no	—
331	C₂²⋊C₄	—	2	2	no	—
332	C₂²⋊C₄	—	2	2	no	—
333	C₄²	—	2	2	no	—
334	C₄²	—	2	2	no	—
335	C₄²	—	2	2	no	—
336	C₄²	C₂×D₄×C₁₀₁	1	1	yes	characteristic
337	C₄²	C₂×D₄×C₁₀₁	1	2	yes	—
338	C₄²	C₂⁴×C₁₀₁	1	1	yes	characteristic
339	C₂³	—	2	2	no	—
340	C₂³	#120×C₁₀₁	1	1	yes	characteristic
341	Q₈	—	2	4	no	—
342	Q₈	—	4	2	no	—
343	Q₈	—	4	2	no	—
344	Q₈	—	4	4	no	—
345	Q₈	—	8	2	no	—
346	Q₈	—	8	2	no	—
347	Q₈	—	8	2	no	—
348	D₄	—	2	4	no	—
349	D₄	—	4	4	no	—
350	D₄	—	8	2	no	—
351	C₂×C₄	—	2	2	no	—
352	C₂×C₄	—	2	4	no	—
353	C₂×C₄	—	2	2	no	—
354	C₂×C₄	—	2	2	no	—
355	C₂×C₄	—	2	2	no	—
356	C₂×C₄	—	2	2	no	—
357	C₂×C₄	—	2	2	no	—
358	C₂×C₄	—	4	4	no	—
359	C₂×C₄	—	4	4	no	—
360	C₂×C₄	—	4	2	no	—
361	C₂×C₄	—	8	4	no	—
362	C₂×C₄	—	8	2	no	—
363	C₂×C₄	#120×C₁₀₁	1	2	yes	—
364	C₂×C₄	#120×C₁₀₁	1	1	yes	characteristic
365	C₂×C₄	C₂²×D₄×C₁₀₁	1	1	yes	characteristic
366	C₂×C₄	C₂²×D₄×C₁₀₁	1	2	yes	—
367	C₈	—	2	4	no	—
368	C₈	—	4	4	no	—
369	C₂²	—	2	2	no	—
370	C₂²	—	4	2	no	—
371	C₂²	—	4	2	no	—
372	C₂²	—	4	2	no	—
373	C₂²	#453×C₁₀₁	1	2	yes	—
374	C₂²	C₂×#120×C₁₀₁	1	1	yes	characteristic
375	C₄	—	2	2	no	—
376	C₄	—	2	1	no	—
377	C₄	—	2	1	no	—
378	C₄	—	4	2	no	—
379	C₄	—	4	2	no	—
380	C₄	—	4	2	no	—
381	C₄	—	4	2	no	—
382	C₄	—	4	2	no	—
383	C₄	—	8	2	no	—
384	C₄	#578×C₁₀₁	1	4	yes	—
385	C₂	—	2	2	no	—
386	C₂	—	8	2	no	—
387	C₂	C₁₀₁×#3011	1	2	yes	—
388	C₂	C₂×#453×C₁₀₁	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₀₁	C₂×#120
commutator, Frattini, cosocle	C₄²	C₂⁴×C₁₀₁
prime radical	C₁₀₁×#3544	C₂
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₀₁ ◁ C₂×C₄²×C₁₀₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₀₁×#3238	C₂	semidirect
3. C₂×#494×C₁₀₁	C₂	semidirect
4. C₁₀₁×#1634	C₂	semidirect
5. C₁₀₁×#1633	C₂	semidirect
6. C₁₀₁×#1632	C₂	semidirect
7. C₁₀₁×#1558	C₂	semidirect
8. C₁₀₁×#1494	C₂	semidirect
190. #18685	C₁₀₁	direct (N × H)
196. #3238	C₂×C₁₀₁	semidirect
197. C₂×#494	C₂×C₁₀₁	semidirect
198. #1634	C₂×C₁₀₁	semidirect
199. #1633	C₂×C₁₀₁	semidirect
200. #1632	C₂×C₁₀₁	semidirect
201. #1558	C₂×C₁₀₁	semidirect
202. #1494	C₂×C₁₀₁	semidirect
203. C₁₀₁	#18685	direct (N × H)

Maximal subgroups

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

subgroup	index
C₁₀₁×#3544	2
C₁₀₁×#3238	2
C₂×#494×C₁₀₁	2
C₁₀₁×#1634	2
C₁₀₁×#1633	2
C₁₀₁×#1632	2
C₁₀₁×#1558	2
C₁₀₁×#1494	2
#18685	101

Subgroups — C101×#18685 #38800836

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₀₁×#18685 #38800836