Subgroups — C₁₀₁×#18219 #38800370

Order 25856.

1154 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×#3497	C₂	1	1	yes	maximal, characteristic
2	C₁₀₁×#3103	C₂	1	2	yes	maximal, complemented
3	C₁₀₁×#2581	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₀₁×#1616	C₂	1	4	yes	maximal, complemented
5	C₁₀₁×#1604	C₂	1	4	yes	maximal, complemented
6	C₁₀₁×#1517	C₂	1	2	yes	maximal, complemented
7	C₁₀₁×#1461	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×2₋¹⁺⁴×C₁₀₁	—	2	1	no	—
9	#550×C₁₀₁	—	2	2	no	—
10	D₄×Q₈×C₁₀₁	—	2	2	no	—
11	#548×C₁₀₁	—	2	4	no	—
12	#537×C₁₀₁	—	2	1	no	—
13	#537×C₁₀₁	C₂²	1	4	yes	—
14	#532×C₁₀₁	—	2	2	no	—
15	#532×C₁₀₁	C₂²	1	2	yes	—
16	C₂×C₄×Q₈×C₁₀₁	C₂²	1	1	yes	characteristic
17	C₂×C₄×Q₈×C₁₀₁	C₂²	1	1	yes	characteristic
18	#481×C₁₀₁	C₂²	1	4	yes	—
19	#475×C₁₀₁	—	2	2	no	—
20	#460×C₁₀₁	—	2	2	no	—
21	#448×C₁₀₁	C₂²	1	4	yes	—
22	C₄×SD₁₆×C₁₀₁	—	2	4	no	—
23	#431×C₁₀₁	C₂²	1	2	yes	—
24	#400×C₁₀₁	C₂²	1	2	yes	—
25	#395×C₁₀₁	C₂²	1	2	yes	—
26	#391×C₁₀₁	—	2	1	no	—
27	#389×C₁₀₁	—	2	1	no	—
28	#387×C₁₀₁	—	2	2	no	—
29	#382×C₁₀₁	C₂²	1	1	yes	characteristic
30	#327×C₁₀₁	C₂²	1	8	yes	—
31	#324×C₁₀₁	C₂²	1	4	yes	—
32	2₋¹⁺⁴×C₁₀₁	—	4	4	no	—
33	2₋¹⁺⁴×C₁₀₁	—	4	4	no	—
34	C₂×#41×C₁₀₁	—	2	4	no	—
35	C₂×#41×C₁₀₁	—	2	4	no	—
36	C₂×#41×C₁₀₁	—	2	2	no	—
37	C₂²×Q₈×C₁₀₁	—	2	4	no	—
38	C₂²×Q₈×C₁₀₁	D₄	1	1	yes	characteristic
39	C₂²×Q₈×C₁₀₁	C₂³	1	1	yes	characteristic
40	C₂×SD₁₆×C₁₀₁	—	2	4	no	—
41	C₄⋊Q₈×C₁₀₁	—	2	2	no	—
42	C₄⋊Q₈×C₁₀₁	D₄	1	2	yes	—
43	#127×C₁₀₁	—	2	2	no	—
44	#127×C₁₀₁	D₄	1	2	yes	—
45	#124×C₁₀₁	—	2	4	no	—
46	#124×C₁₀₁	—	2	2	no	—
47	C₂²⋊Q₈×C₁₀₁	—	2	4	no	—
48	C₂²⋊Q₈×C₁₀₁	—	2	8	no	—
49	#121×C₁₀₁	—	2	4	no	—
50	#121×C₁₀₁	—	2	8	no	—
51	#121×C₁₀₁	—	2	2	no	—
52	#121×C₁₀₁	—	2	4	no	—
53	#121×C₁₀₁	C₂³	1	4	yes	—
54	C₄×Q₈×C₁₀₁	—	2	2	no	—
55	C₄×Q₈×C₁₀₁	—	2	2	no	—
56	C₄×Q₈×C₁₀₁	—	2	2	no	—
57	C₄×Q₈×C₁₀₁	—	2	2	no	—
58	C₄×D₄×C₁₀₁	—	2	4	no	—
59	C₄×D₄×C₁₀₁	—	2	4	no	—
60	C₄×D₄×C₁₀₁	—	2	2	no	—
61	C₄×D₄×C₁₀₁	D₄	1	4	yes	—
62	C₂×C₄⋊C₄×C₁₀₁	—	2	2	no	—
63	C₂×C₄⋊C₄×C₁₀₁	—	2	1	no	—
64	C₂×C₄⋊C₄×C₁₀₁	—	2	1	no	—
65	C₂×C₄⋊C₄×C₁₀₁	D₄	1	1	yes	characteristic
66	C₂×C₄⋊C₄×C₁₀₁	C₂³	1	1	yes	characteristic
67	C₂×C₄⋊C₄×C₁₀₁	C₂³	1	2	yes	—
68	C₂×C₄²×C₁₀₁	—	2	1	no	—
69	C₂×C₄²×C₁₀₁	D₄	1	2	yes	—
70	C₂×C₄²×C₁₀₁	C₂³	1	1	yes	characteristic
71	#106×C₁₀₁	—	2	4	no	—
72	C₄⋊C₈×C₁₀₁	—	2	2	no	—
73	#103×C₁₀₁	—	2	4	no	—
74	#102×C₁₀₁	—	2	4	no	—
75	C₂²⋊C₈×C₁₀₁	C₂³	1	4	yes	—
76	C₄×C₈×C₁₀₁	—	2	2	no	—
77	#95×C₁₀₁	—	2	2	no	—
78	#95×C₁₀₁	—	2	2	no	—
79	#95×C₁₀₁	—	2	2	no	—
80	#95×C₁₀₁	—	2	1	no	—
81	#95×C₁₀₁	C₂³	1	2	yes	—
82	#41×C₁₀₁	—	4	8	no	—
83	#41×C₁₀₁	—	4	16	no	—
84	#41×C₁₀₁	—	4	8	no	—
85	#41×C₁₀₁	—	4	4	no	—
86	#41×C₁₀₁	—	4	4	no	—
87	C₂×Q₈×C₁₀₁	—	2	4	no	—
88	C₂×Q₈×C₁₀₁	—	2	2	no	—
89	C₂×Q₈×C₁₀₁	—	2	2	no	—
90	C₂×Q₈×C₁₀₁	—	2	2	no	—
91	C₂×Q₈×C₁₀₁	—	2	2	no	—
92	C₂×Q₈×C₁₀₁	—	4	2	no	—
93	C₂×Q₈×C₁₀₁	—	4	16	no	—
94	C₂×Q₈×C₁₀₁	SD₁₆	1	4	yes	complemented
95	C₂×D₄×C₁₀₁	—	2	4	no	—
96	C₂×D₄×C₁₀₁	—	2	4	no	—
97	C₂×D₄×C₁₀₁	—	2	4	no	—
98	C₂×D₄×C₁₀₁	—	2	2	no	—
99	C₂×D₄×C₁₀₁	—	2	2	no	—
100	C₂×D₄×C₁₀₁	C₂×D₄	1	4	yes	—
101	C₂²×C₄×C₁₀₁	—	2	8	no	—
102	C₂²×C₄×C₁₀₁	—	2	1	no	—
103	C₂²×C₄×C₁₀₁	—	2	4	no	—
104	C₂²×C₄×C₁₀₁	—	2	2	no	—
105	C₂²×C₄×C₁₀₁	—	2	1	no	—
106	C₂²×C₄×C₁₀₁	C₂×D₄	1	2	yes	—
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	1	yes	characteristic
110	C₂²×C₄×C₁₀₁	C₂⁴	1	1	yes	characteristic
111	SD₁₆×C₁₀₁	—	4	8	no	—
112	C₂×C₈×C₁₀₁	—	2	4	no	—
113	C₄⋊C₄×C₁₀₁	—	2	4	no	—
114	C₄⋊C₄×C₁₀₁	—	2	2	no	—
115	C₄⋊C₄×C₁₀₁	—	2	2	no	—
116	C₄⋊C₄×C₁₀₁	—	2	4	no	—
117	C₄⋊C₄×C₁₀₁	—	2	2	no	—
118	C₄⋊C₄×C₁₀₁	—	4	4	no	—
119	C₄⋊C₄×C₁₀₁	—	4	1	no	—
120	C₄⋊C₄×C₁₀₁	—	4	1	no	—
121	C₄⋊C₄×C₁₀₁	—	4	2	no	—
122	C₄⋊C₄×C₁₀₁	C₂×D₄	1	4	yes	—
123	C₂²⋊C₄×C₁₀₁	—	2	8	no	—
124	C₂²⋊C₄×C₁₀₁	—	2	4	no	—
125	C₂²⋊C₄×C₁₀₁	—	2	4	no	—
126	C₄²×C₁₀₁	—	2	2	no	—
127	C₄²×C₁₀₁	—	2	2	no	—
128	C₄²×C₁₀₁	—	4	2	no	—
129	C₄²×C₁₀₁	C₂×D₄	1	2	yes	—
130	C₄²×C₁₀₁	C₂×D₄	1	2	yes	—
131	C₂³×C₁₀₁	—	2	4	no	—
132	C₂³×C₁₀₁	C₂²×D₄	1	1	yes	characteristic
133	Q₈×C₁₀₁	—	2	8	no	—
134	Q₈×C₁₀₁	—	2	4	no	—
135	Q₈×C₁₀₁	—	4	2	no	—
136	Q₈×C₁₀₁	—	4	8	no	—
137	Q₈×C₁₀₁	—	4	4	no	—
138	D₄×C₁₀₁	—	4	4	no	—
139	D₄×C₁₀₁	—	4	4	no	—
140	D₄×C₁₀₁	—	4	8	no	—
141	D₄×C₁₀₁	—	4	4	no	—
142	D₄×C₁₀₁	—	4	4	no	—
143	D₄×C₁₀₁	—	4	4	no	—
144	D₄×C₁₀₁	—	8	4	no	—
145	C₂×C₄×C₁₀₁	—	2	2	no	—
146	C₂×C₄×C₁₀₁	—	2	2	no	—
147	C₂×C₄×C₁₀₁	—	2	2	no	—
148	C₂×C₄×C₁₀₁	—	2	2	no	—
149	C₂×C₄×C₁₀₁	—	2	4	no	—
150	C₂×C₄×C₁₀₁	—	4	1	no	—
151	C₂×C₄×C₁₀₁	—	4	1	no	—
152	C₂×C₄×C₁₀₁	—	4	16	no	—
153	C₂×C₄×C₁₀₁	—	4	1	no	—
154	C₂×C₄×C₁₀₁	—	4	1	no	—
155	C₂×C₄×C₁₀₁	—	4	8	no	—
156	C₂×C₄×C₁₀₁	—	4	2	no	—
157	C₂×C₄×C₁₀₁	—	4	2	no	—
158	C₂×C₄×C₁₀₁	—	4	2	no	—
159	C₂×C₄×C₁₀₁	—	4	2	no	—
160	C₂×C₄×C₁₀₁	—	4	1	no	—
161	C₂×C₄×C₁₀₁	—	4	2	no	—
162	C₂×C₄×C₁₀₁	#120	1	1	yes	characteristic
163	C₂×C₄×C₁₀₁	#120	1	1	yes	characteristic
164	C₂×C₄×C₁₀₁	#120	1	2	yes	—
165	C₂×C₄×C₁₀₁	C₂×SD₁₆	1	4	yes	—
166	C₂×C₄×C₁₀₁	C₂×SD₁₆	1	2	yes	—
167	C₂×C₄×C₁₀₁	AGL(1,ℤ/8)	1	2	yes	—
168	C₂×C₄×C₁₀₁	C₂²×D₄	1	2	yes	—
169	C₈×C₁₀₁	—	4	4	no	—
170	C₂²×C₁₀₁	—	2	1	no	—
171	C₂²×C₁₀₁	—	2	1	no	—
172	C₂²×C₁₀₁	—	4	4	no	—
173	C₂²×C₁₀₁	—	4	4	no	—
174	C₂²×C₁₀₁	—	4	4	no	—
175	C₂²×C₁₀₁	C₂×#120	1	1	yes	characteristic
176	C₂²×C₁₀₁	C₂²×SD₁₆	1	1	yes	characteristic
177	C₂²×C₁₀₁	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
178	C₄×C₁₀₁	—	2	4	no	—
179	C₄×C₁₀₁	—	2	1	no	—
180	C₄×C₁₀₁	—	2	1	no	—
181	C₄×C₁₀₁	—	2	2	no	—
182	C₄×C₁₀₁	—	4	4	no	—
183	C₄×C₁₀₁	—	4	2	no	—
184	C₄×C₁₀₁	—	4	2	no	—
185	C₄×C₁₀₁	—	8	2	no	—
186	C₄×C₁₀₁	—	8	1	no	—
187	C₄×C₁₀₁	#450	1	4	yes	—
188	#18219	C₁₀₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
189	C₂×C₁₀₁	—	2	1	no	—
190	C₂×C₁₀₁	—	2	1	no	—
191	C₂×C₁₀₁	—	8	4	no	—
192	C₂×C₁₀₁	C₂×#450	1	1	yes	characteristic
193	C₂×C₁₀₁	#3020	1	1	yes	characteristic
194	C₂×C₁₀₁	#3025	1	1	yes	characteristic
195	#3497	C₂×C₁₀₁	1	1	yes	characteristic
196	#3103	C₂×C₁₀₁	1	2	yes	complemented
197	#2581	C₂×C₁₀₁	1	1	yes	characteristic, complemented
198	#1616	C₂×C₁₀₁	1	4	yes	complemented
199	#1604	C₂×C₁₀₁	1	4	yes	complemented
200	#1517	C₂×C₁₀₁	1	2	yes	complemented
201	#1461	C₂×C₁₀₁	1	1	yes	characteristic, complemented
202	C₁₀₁	#18219	1	1	yes	characteristic, direct product factor, Sylow
203	C₂×2₋¹⁺⁴	—	2	1	no	—
204	#550	—	2	2	no	—
205	D₄×Q₈	—	2	2	no	—
206	#548	—	2	4	no	—
207	#537	—	2	1	no	—
208	#537	C₂²×C₁₀₁	1	4	yes	—
209	#532	—	2	2	no	—
210	#532	C₂²×C₁₀₁	1	2	yes	—
211	C₂×C₄×Q₈	C₂²×C₁₀₁	1	1	yes	characteristic
212	C₂×C₄×Q₈	C₂²×C₁₀₁	1	1	yes	characteristic
213	#481	C₂²×C₁₀₁	1	4	yes	—
214	#475	—	2	2	no	—
215	#460	—	2	2	no	—
216	#448	C₂²×C₁₀₁	1	4	yes	—
217	C₄×SD₁₆	—	2	4	no	—
218	#431	C₂²×C₁₀₁	1	2	yes	—
219	#400	C₂²×C₁₀₁	1	2	yes	—
220	#395	C₂²×C₁₀₁	1	2	yes	—
221	#391	—	2	1	no	—
222	#389	—	2	1	no	—
223	#387	—	2	2	no	—
224	#382	C₂²×C₁₀₁	1	1	yes	characteristic
225	#327	C₂²×C₁₀₁	1	8	yes	—
226	#324	C₂²×C₁₀₁	1	4	yes	—
227	2₋¹⁺⁴	—	4	4	no	—
228	2₋¹⁺⁴	—	4	4	no	—
229	C₂×#41	—	2	4	no	—
230	C₂×#41	—	2	4	no	—
231	C₂×#41	—	2	2	no	—
232	C₂²×Q₈	—	2	4	no	—
233	C₂²×Q₈	D₄×C₁₀₁	1	1	yes	characteristic
234	C₂²×Q₈	C₂³×C₁₀₁	1	1	yes	characteristic
235	C₂×SD₁₆	—	2	4	no	—
236	C₄⋊Q₈	—	2	2	no	—
237	C₄⋊Q₈	D₄×C₁₀₁	1	2	yes	—
238	#127	—	2	2	no	—
239	#127	D₄×C₁₀₁	1	2	yes	—
240	#124	—	2	4	no	—
241	#124	—	2	2	no	—
242	C₂²⋊Q₈	—	2	4	no	—
243	C₂²⋊Q₈	—	2	8	no	—
244	#121	—	2	4	no	—
245	#121	—	2	8	no	—
246	#121	—	2	2	no	—
247	#121	—	2	4	no	—
248	#121	C₂³×C₁₀₁	1	4	yes	—
249	C₄×Q₈	—	2	2	no	—
250	C₄×Q₈	—	2	2	no	—
251	C₄×Q₈	—	2	2	no	—
252	C₄×Q₈	—	2	2	no	—
253	C₄×D₄	—	2	4	no	—
254	C₄×D₄	—	2	4	no	—
255	C₄×D₄	—	2	2	no	—
256	C₄×D₄	D₄×C₁₀₁	1	4	yes	—
257	C₂×C₄⋊C₄	—	2	1	no	—
258	C₂×C₄⋊C₄	—	2	1	no	—
259	C₂×C₄⋊C₄	—	2	2	no	—
260	C₂×C₄⋊C₄	D₄×C₁₀₁	1	1	yes	characteristic
261	C₂×C₄⋊C₄	C₂³×C₁₀₁	1	1	yes	characteristic
262	C₂×C₄⋊C₄	C₂³×C₁₀₁	1	2	yes	—
263	C₂×C₄²	—	2	1	no	—
264	C₂×C₄²	D₄×C₁₀₁	1	2	yes	—
265	C₂×C₄²	C₂³×C₁₀₁	1	1	yes	characteristic
266	#106	—	2	4	no	—
267	C₄⋊C₈	—	2	2	no	—
268	#103	—	2	4	no	—
269	#102	—	2	4	no	—
270	C₂²⋊C₈	C₂³×C₁₀₁	1	4	yes	—
271	C₄×C₈	—	2	2	no	—
272	#95	—	2	1	no	—
273	#95	—	2	2	no	—
274	#95	—	2	2	no	—
275	#95	—	2	2	no	—
276	#95	C₂³×C₁₀₁	1	2	yes	—
277	#41	—	4	8	no	—
278	#41	—	4	16	no	—
279	#41	—	4	8	no	—
280	#41	—	4	4	no	—
281	#41	—	4	4	no	—
282	C₂×Q₈	—	2	4	no	—
283	C₂×Q₈	—	2	2	no	—
284	C₂×Q₈	—	2	2	no	—
285	C₂×Q₈	—	2	2	no	—
286	C₂×Q₈	—	2	2	no	—
287	C₂×Q₈	—	4	2	no	—
288	C₂×Q₈	—	4	16	no	—
289	C₂×Q₈	SD₁₆×C₁₀₁	1	4	yes	complemented
290	C₂×D₄	—	2	4	no	—
291	C₂×D₄	—	2	4	no	—
292	C₂×D₄	—	2	4	no	—
293	C₂×D₄	—	2	2	no	—
294	C₂×D₄	—	2	2	no	—
295	C₂×D₄	C₂×D₄×C₁₀₁	1	4	yes	—
296	C₂²×C₄	—	2	8	no	—
297	C₂²×C₄	—	2	1	no	—
298	C₂²×C₄	—	2	4	no	—
299	C₂²×C₄	—	2	2	no	—
300	C₂²×C₄	—	2	1	no	—
301	C₂²×C₄	C₂×D₄×C₁₀₁	1	2	yes	—
302	C₂²×C₄	C₂×D₄×C₁₀₁	1	2	yes	—
303	C₂²×C₄	C₂×D₄×C₁₀₁	1	1	yes	characteristic
304	C₂²×C₄	C₂×D₄×C₁₀₁	1	1	yes	characteristic
305	C₂²×C₄	C₂⁴×C₁₀₁	1	1	yes	characteristic
306	SD₁₆	—	4	8	no	—
307	C₂×C₈	—	2	4	no	—
308	C₄⋊C₄	—	2	4	no	—
309	C₄⋊C₄	—	2	2	no	—
310	C₄⋊C₄	—	2	2	no	—
311	C₄⋊C₄	—	2	4	no	—
312	C₄⋊C₄	—	2	2	no	—
313	C₄⋊C₄	—	4	4	no	—
314	C₄⋊C₄	—	4	1	no	—
315	C₄⋊C₄	—	4	1	no	—
316	C₄⋊C₄	—	4	2	no	—
317	C₄⋊C₄	C₂×D₄×C₁₀₁	1	4	yes	—
318	C₂²⋊C₄	—	2	8	no	—
319	C₂²⋊C₄	—	2	4	no	—
320	C₂²⋊C₄	—	2	4	no	—
321	C₄²	—	2	2	no	—
322	C₄²	—	2	2	no	—
323	C₄²	—	4	2	no	—
324	C₄²	C₂×D₄×C₁₀₁	1	2	yes	—
325	C₄²	C₂×D₄×C₁₀₁	1	2	yes	—
326	C₂³	—	2	4	no	—
327	C₂³	C₂²×D₄×C₁₀₁	1	1	yes	characteristic
328	Q₈	—	2	8	no	—
329	Q₈	—	2	4	no	—
330	Q₈	—	4	8	no	—
331	Q₈	—	4	2	no	—
332	Q₈	—	4	4	no	—
333	D₄	—	4	4	no	—
334	D₄	—	4	8	no	—
335	D₄	—	4	4	no	—
336	D₄	—	4	4	no	—
337	D₄	—	4	4	no	—
338	D₄	—	4	4	no	—
339	D₄	—	8	4	no	—
340	C₂×C₄	—	2	2	no	—
341	C₂×C₄	—	2	2	no	—
342	C₂×C₄	—	2	2	no	—
343	C₂×C₄	—	2	2	no	—
344	C₂×C₄	—	2	4	no	—
345	C₂×C₄	—	4	1	no	—
346	C₂×C₄	—	4	1	no	—
347	C₂×C₄	—	4	16	no	—
348	C₂×C₄	—	4	1	no	—
349	C₂×C₄	—	4	1	no	—
350	C₂×C₄	—	4	8	no	—
351	C₂×C₄	—	4	2	no	—
352	C₂×C₄	—	4	2	no	—
353	C₂×C₄	—	4	2	no	—
354	C₂×C₄	—	4	2	no	—
355	C₂×C₄	—	4	1	no	—
356	C₂×C₄	—	4	2	no	—
357	C₂×C₄	#120×C₁₀₁	1	1	yes	characteristic
358	C₂×C₄	#120×C₁₀₁	1	1	yes	characteristic
359	C₂×C₄	#120×C₁₀₁	1	2	yes	—
360	C₂×C₄	C₂×SD₁₆×C₁₀₁	1	4	yes	—
361	C₂×C₄	C₂×SD₁₆×C₁₀₁	1	2	yes	—
362	C₂×C₄	AGL(1,ℤ/8)×C₁₀₁	1	2	yes	—
363	C₂×C₄	C₂²×D₄×C₁₀₁	1	2	yes	—
364	C₈	—	4	4	no	—
365	C₂²	—	2	1	no	—
366	C₂²	—	2	1	no	—
367	C₂²	—	4	4	no	—
368	C₂²	—	4	4	no	—
369	C₂²	—	4	4	no	—
370	C₂²	C₂×#120×C₁₀₁	1	1	yes	characteristic
371	C₂²	C₂²×SD₁₆×C₁₀₁	1	1	yes	characteristic
372	C₂²	C₂×AGL(1,ℤ/8)×C₁₀₁	1	1	yes	characteristic
373	C₄	—	2	4	no	—
374	C₄	—	2	1	no	—
375	C₄	—	2	1	no	—
376	C₄	—	2	2	no	—
377	C₄	—	4	4	no	—
378	C₄	—	4	2	no	—
379	C₄	—	4	2	no	—
380	C₄	—	8	2	no	—
381	C₄	—	8	1	no	—
382	C₄	#450×C₁₀₁	1	4	yes	—
383	C₂	—	2	1	no	—
384	C₂	—	2	1	no	—
385	C₂	—	8	4	no	—
386	C₂	C₂×#450×C₁₀₁	1	1	yes	characteristic
387	C₂	C₁₀₁×#3020	1	1	yes	characteristic
388	C₂	C₁₀₁×#3025	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₀₁	C₂×#120
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₀₁
prime radical	C₁₀₁×#3497	C₂
LCS	G ▷ C₂²×C₄ ▷ 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×#3103	C₂	semidirect
3. C₁₀₁×#2581	C₂	semidirect
4. C₁₀₁×#1616	C₂	semidirect
5. C₁₀₁×#1604	C₂	semidirect
6. C₁₀₁×#1517	C₂	semidirect
7. C₁₀₁×#1461	C₂	semidirect
94. C₂×Q₈×C₁₀₁	SD₁₆	semidirect
188. #18219	C₁₀₁	direct (N × H)
196. #3103	C₂×C₁₀₁	semidirect
197. #2581	C₂×C₁₀₁	semidirect
198. #1616	C₂×C₁₀₁	semidirect
199. #1604	C₂×C₁₀₁	semidirect
200. #1517	C₂×C₁₀₁	semidirect
201. #1461	C₂×C₁₀₁	semidirect
202. C₁₀₁	#18219	direct (N × H)
289. C₂×Q₈	SD₁₆×C₁₀₁	semidirect

Maximal subgroups

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

subgroup	index
C₁₀₁×#3497	2
C₁₀₁×#3103	2
C₁₀₁×#2581	2
C₁₀₁×#1616	2
C₁₀₁×#1604	2
C₁₀₁×#1517	2
C₁₀₁×#1461	2
#18219	101

Subgroups — C101×#18219 #38800370

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₀₁×#18219 #38800370