Subgroups — C₁₀₁×#10948 #38793099

Order 25856.

1074 conjugacy classes of subgroups.

The subgroup lattice has 378 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#418×C₁₀₁	C₂	1	2	yes	maximal
2	C₁₀₁×#2873	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₀₁×#2309	C₂	1	1	yes	maximal, characteristic
4	C₁₀₁×#1740	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×H(3,ℤ/4)×C₁₀₁	C₂	1	2	yes	maximal, complemented
6	C₂³×D₄×C₁₀₁	C₂²	1	1	yes	characteristic
7	C₂²×M₁₆×C₁₀₁	C₂²	1	2	yes	—
8	C₂×#117×C₁₀₁	C₂²	1	2	yes	—
9	C₂×#117×C₁₀₁	C₂²	1	1	yes	characteristic
10	C₂×#117×C₁₀₁	C₂²	1	1	yes	characteristic
11	#418×C₁₀₁	—	2	4	no	—
12	#418×C₁₀₁	C₄	1	8	yes	complemented
13	C₂×#102×C₁₀₁	—	2	4	no	—
14	#405×C₁₀₁	—	2	4	no	—
15	C₄×M₁₆×C₁₀₁	—	2	2	no	—
16	#390×C₁₀₁	—	2	2	no	—
17	#390×C₁₀₁	C₄	1	4	yes	complemented
18	#379×C₁₀₁	—	2	2	no	—
19	#342×C₁₀₁	—	2	2	no	—
20	H(3,ℤ/4)×C₁₀₁	—	2	4	no	—
21	C₂⁵×C₁₀₁	—	2	1	no	—
22	C₂²×D₄×C₁₀₁	—	2	2	no	—
23	C₂²×D₄×C₁₀₁	—	2	2	no	—
24	C₂²×D₄×C₁₀₁	—	2	1	no	—
25	C₂²×D₄×C₁₀₁	—	2	2	no	—
26	C₂²×D₄×C₁₀₁	—	2	2	no	—
27	C₂²×D₄×C₁₀₁	—	2	2	no	—
28	C₂²×D₄×C₁₀₁	C₂×C₄	1	4	yes	—
29	C₂²×D₄×C₁₀₁	C₂×C₄	1	2	yes	—
30	C₂³×C₄×C₁₀₁	C₂³	1	1	yes	characteristic
31	C₂×M₁₆×C₁₀₁	—	2	2	no	—
32	C₂×M₁₆×C₁₀₁	—	2	2	no	—
33	C₂×M₁₆×C₁₀₁	—	2	2	no	—
34	C₂×M₁₆×C₁₀₁	—	2	2	no	—
35	C₂×M₁₆×C₁₀₁	C₂×C₄	1	4	yes	—
36	C₂×M₁₆×C₁₀₁	D₄	1	4	yes	—
37	C₂²×C₈×C₁₀₁	D₄	1	4	yes	—
38	#117×C₁₀₁	—	2	2	no	—
39	#117×C₁₀₁	—	2	2	no	—
40	#117×C₁₀₁	—	2	2	no	—
41	#117×C₁₀₁	—	2	2	no	—
42	#117×C₁₀₁	—	2	2	no	—
43	#117×C₁₀₁	—	2	2	no	—
44	#117×C₁₀₁	—	2	2	no	—
45	#117×C₁₀₁	C₂×C₄	1	4	yes	—
46	C₂×C₄⋊C₄×C₁₀₁	—	2	2	no	—
47	C₂×C₄⋊C₄×C₁₀₁	—	2	1	no	—
48	C₂×C₄⋊C₄×C₁₀₁	C₂×C₄	1	2	yes	—
49	C₂×C₂²⋊C₄×C₁₀₁	—	2	2	no	—
50	C₂×C₂²⋊C₄×C₁₀₁	—	2	1	no	—
51	C₂×C₂²⋊C₄×C₁₀₁	—	2	8	no	—
52	C₂×C₂²⋊C₄×C₁₀₁	D₄	1	2	yes	—
53	C₂×C₄²×C₁₀₁	—	2	2	no	—
54	C₂×C₄²×C₁₀₁	C₂×C₄	1	2	yes	—
55	C₂×C₄²×C₁₀₁	D₄	1	2	yes	—
56	#102×C₁₀₁	—	2	16	no	—
57	#97×C₁₀₁	—	2	4	no	—
58	C₄×C₈×C₁₀₁	—	2	4	no	—
59	C₂⁴×C₁₀₁	—	2	2	no	—
60	C₂⁴×C₁₀₁	—	2	4	no	—
61	C₂⁴×C₁₀₁	—	4	2	no	—
62	C₂⁴×C₁₀₁	—	4	1	no	—
63	C₂⁴×C₁₀₁	—	4	1	no	—
64	C₂⁴×C₁₀₁	—	8	4	no	—
65	C₂⁴×C₁₀₁	C₂×D₄	1	1	yes	characteristic
66	C₂×D₄×C₁₀₁	—	2	4	no	—
67	C₂×D₄×C₁₀₁	—	2	4	no	—
68	C₂×D₄×C₁₀₁	—	2	2	no	—
69	C₂×D₄×C₁₀₁	—	2	4	no	—
70	C₂×D₄×C₁₀₁	—	2	4	no	—
71	C₂×D₄×C₁₀₁	—	2	4	no	—
72	C₂×D₄×C₁₀₁	—	2	4	no	—
73	C₂×D₄×C₁₀₁	—	2	4	no	—
74	C₂×D₄×C₁₀₁	—	4	1	no	—
75	C₂×D₄×C₁₀₁	—	4	2	no	—
76	C₂×D₄×C₁₀₁	—	4	2	no	—
77	C₂×D₄×C₁₀₁	—	4	2	no	—
78	C₂×D₄×C₁₀₁	—	4	1	no	—
79	C₂×D₄×C₁₀₁	—	4	2	no	—
80	C₂×D₄×C₁₀₁	—	4	2	no	—
81	C₂×D₄×C₁₀₁	C₄²	1	4	yes	—
82	C₂²×C₄×C₁₀₁	—	2	2	no	—
83	C₂²×C₄×C₁₀₁	—	4	2	no	—
84	C₂²×C₄×C₁₀₁	C₂²⋊C₄	1	4	yes	—
85	C₂²×C₄×C₁₀₁	C₂²×C₄	1	2	yes	—
86	C₂²×C₄×C₁₀₁	C₂²×C₄	1	1	yes	characteristic
87	C₂²×C₄×C₁₀₁	C₂×D₄	1	2	yes	—
88	C₂²×C₄×C₁₀₁	C₂×D₄	1	2	yes	—
89	C₂²×C₄×C₁₀₁	C₂×D₄	1	1	yes	characteristic
90	C₂²×C₄×C₁₀₁	#41	1	2	yes	—
91	C₂²×C₄×C₁₀₁	#41	1	2	yes	—
92	C₂²×C₄×C₁₀₁	#41	1	2	yes	—
93	M₁₆×C₁₀₁	—	2	4	no	—
94	M₁₆×C₁₀₁	—	2	4	no	—
95	M₁₆×C₁₀₁	—	2	4	no	—
96	M₁₆×C₁₀₁	—	2	4	no	—
97	C₂×C₈×C₁₀₁	—	2	4	no	—
98	C₂×C₈×C₁₀₁	—	2	4	no	—
99	C₂×C₈×C₁₀₁	C₂²⋊C₄	1	8	yes	complemented
100	C₄⋊C₄×C₁₀₁	—	2	4	no	—
101	C₄⋊C₄×C₁₀₁	—	2	4	no	—
102	C₄⋊C₄×C₁₀₁	—	4	2	no	—
103	C₄⋊C₄×C₁₀₁	—	4	2	no	—
104	C₂²⋊C₄×C₁₀₁	—	2	4	no	—
105	C₂²⋊C₄×C₁₀₁	—	2	4	no	—
106	C₂²⋊C₄×C₁₀₁	—	4	1	no	—
107	C₂²⋊C₄×C₁₀₁	—	4	1	no	—
108	C₂²⋊C₄×C₁₀₁	—	4	2	no	—
109	C₂²⋊C₄×C₁₀₁	—	8	8	no	—
110	C₄²×C₁₀₁	—	2	2	no	—
111	C₄²×C₁₀₁	—	2	2	no	—
112	C₄²×C₁₀₁	—	2	4	no	—
113	C₄²×C₁₀₁	—	2	4	no	—
114	C₄²×C₁₀₁	—	4	2	no	—
115	C₂³×C₁₀₁	—	2	4	no	—
116	C₂³×C₁₀₁	—	4	2	no	—
117	C₂³×C₁₀₁	—	4	8	no	—
118	C₂³×C₁₀₁	—	4	2	no	—
119	C₂³×C₁₀₁	—	4	4	no	—
120	C₂³×C₁₀₁	—	4	2	no	—
121	C₂³×C₁₀₁	—	4	4	no	—
122	C₂³×C₁₀₁	—	8	8	no	—
123	C₂³×C₁₀₁	—	8	8	no	—
124	C₂³×C₁₀₁	—	8	4	no	—
125	C₂³×C₁₀₁	—	8	4	no	—
126	C₂³×C₁₀₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
127	C₂³×C₁₀₁	C₄×D₄	1	2	yes	—
128	C₂³×C₁₀₁	#121	1	2	yes	—
129	C₂³×C₁₀₁	#124	1	1	yes	characteristic
130	C₂³×C₁₀₁	#127	1	1	yes	characteristic
131	D₄×C₁₀₁	—	2	8	no	—
132	D₄×C₁₀₁	—	4	4	no	—
133	D₄×C₁₀₁	—	4	4	no	—
134	D₄×C₁₀₁	—	4	4	no	—
135	C₂×C₄×C₁₀₁	—	2	4	no	—
136	C₂×C₄×C₁₀₁	—	4	4	no	—
137	C₂×C₄×C₁₀₁	—	4	4	no	—
138	C₂×C₄×C₁₀₁	—	4	2	no	—
139	C₂×C₄×C₁₀₁	—	4	4	no	—
140	C₂×C₄×C₁₀₁	—	8	4	no	—
141	C₂×C₄×C₁₀₁	C₂×C₄²	1	1	yes	characteristic
142	C₂×C₄×C₁₀₁	C₂×C₂²⋊C₄	1	2	yes	—
143	C₂×C₄×C₁₀₁	#117	1	2	yes	—
144	C₂×C₄×C₁₀₁	#117	1	1	yes	characteristic
145	C₂×C₄×C₁₀₁	C₄×D₄	1	2	yes	—
146	C₂×C₄×C₁₀₁	C₄×D₄	1	2	yes	—
147	C₂×C₄×C₁₀₁	C₄×D₄	1	2	yes	—
148	C₂×C₄×C₁₀₁	C₄×D₄	1	2	yes	—
149	C₂×C₄×C₁₀₁	C₄×D₄	1	2	yes	—
150	C₂×C₄×C₁₀₁	#120	1	1	yes	characteristic
151	C₂×C₄×C₁₀₁	#121	1	2	yes	—
152	C₂×C₄×C₁₀₁	#121	1	2	yes	—
153	C₂×C₄×C₁₀₁	#123	1	2	yes	—
154	C₂×C₄×C₁₀₁	#123	1	1	yes	characteristic
155	C₂×C₄×C₁₀₁	#124	1	2	yes	—
156	C₂×C₄×C₁₀₁	#126	1	2	yes	—
157	C₈×C₁₀₁	—	2	8	no	—
158	C₂²×C₁₀₁	—	2	2	no	—
159	C₂²×C₁₀₁	—	2	4	no	—
160	C₂²×C₁₀₁	—	4	2	no	—
161	C₂²×C₁₀₁	—	4	1	no	—
162	C₂²×C₁₀₁	—	4	1	no	—
163	C₂²×C₁₀₁	—	4	8	no	—
164	C₂²×C₁₀₁	—	4	4	no	—
165	C₂²×C₁₀₁	—	8	4	no	—
166	C₂²×C₁₀₁	—	8	8	no	—
167	C₂²×C₁₀₁	—	8	8	no	—
168	C₂²×C₁₀₁	—	8	4	no	—
169	C₂²×C₁₀₁	C₄×C₂²⋊C₄	1	1	yes	characteristic
170	C₂²×C₁₀₁	#386	1	1	yes	characteristic
171	C₂²×C₁₀₁	#388	1	2	yes	—
172	C₂²×C₁₀₁	#390	1	2	yes	—
173	C₂²×C₁₀₁	#390	1	1	yes	characteristic
174	C₄×C₁₀₁	—	4	4	no	—
175	C₄×C₁₀₁	—	8	2	no	—
176	C₄×C₁₀₁	—	8	4	no	—
177	C₄×C₁₀₁	C₄×C₂²⋊C₄	1	2	yes	—
178	C₄×C₁₀₁	#386	1	2	yes	—
179	C₄×C₁₀₁	#388	1	2	yes	—
180	C₄×C₁₀₁	#388	1	2	yes	—
181	#10948	C₁₀₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
182	C₂×C₁₀₁	—	2	1	no	—
183	C₂×C₁₀₁	—	2	2	no	—
184	C₂×C₁₀₁	—	2	1	no	—
185	C₂×C₁₀₁	—	2	2	no	—
186	C₂×C₁₀₁	—	8	4	no	—
187	C₂×C₁₀₁	#1437	1	1	yes	characteristic
188	C₂×C₁₀₁	#1910	1	2	yes	—
189	C₂×#418	C₂×C₁₀₁	1	2	yes	—
190	#2873	C₂×C₁₀₁	1	1	yes	characteristic, complemented
191	#2309	C₂×C₁₀₁	1	1	yes	characteristic
192	#1740	C₂×C₁₀₁	1	1	yes	characteristic, complemented
193	C₂×H(3,ℤ/4)	C₂×C₁₀₁	1	2	yes	complemented
194	C₁₀₁	#10948	1	1	yes	characteristic, direct product factor, Sylow
195	C₂³×D₄	C₂²×C₁₀₁	1	1	yes	characteristic
196	C₂²×M₁₆	C₂²×C₁₀₁	1	2	yes	—
197	C₂×#117	C₂²×C₁₀₁	1	2	yes	—
198	C₂×#117	C₂²×C₁₀₁	1	1	yes	characteristic
199	C₂×#117	C₂²×C₁₀₁	1	1	yes	characteristic
200	#418	—	2	4	no	—
201	#418	C₄×C₁₀₁	1	8	yes	complemented
202	C₂×#102	—	2	4	no	—
203	#405	—	2	4	no	—
204	C₄×M₁₆	—	2	2	no	—
205	#390	—	2	2	no	—
206	#390	C₄×C₁₀₁	1	4	yes	complemented
207	#379	—	2	2	no	—
208	#342	—	2	2	no	—
209	H(3,ℤ/4)	—	2	4	no	—
210	C₂⁵	—	2	1	no	—
211	C₂²×D₄	—	2	2	no	—
212	C₂²×D₄	—	2	2	no	—
213	C₂²×D₄	—	2	1	no	—
214	C₂²×D₄	—	2	2	no	—
215	C₂²×D₄	—	2	2	no	—
216	C₂²×D₄	—	2	2	no	—
217	C₂²×D₄	C₂×C₄×C₁₀₁	1	2	yes	—
218	C₂²×D₄	C₂×C₄×C₁₀₁	1	4	yes	—
219	C₂³×C₄	C₂³×C₁₀₁	1	1	yes	characteristic
220	C₂×M₁₆	—	2	2	no	—
221	C₂×M₁₆	—	2	2	no	—
222	C₂×M₁₆	—	2	2	no	—
223	C₂×M₁₆	—	2	2	no	—
224	C₂×M₁₆	C₂×C₄×C₁₀₁	1	4	yes	—
225	C₂×M₁₆	D₄×C₁₀₁	1	4	yes	—
226	C₂²×C₈	D₄×C₁₀₁	1	4	yes	—
227	#117	—	2	2	no	—
228	#117	—	2	2	no	—
229	#117	—	2	2	no	—
230	#117	—	2	2	no	—
231	#117	—	2	2	no	—
232	#117	—	2	2	no	—
233	#117	—	2	2	no	—
234	#117	C₂×C₄×C₁₀₁	1	4	yes	—
235	C₂×C₄⋊C₄	—	2	2	no	—
236	C₂×C₄⋊C₄	—	2	1	no	—
237	C₂×C₄⋊C₄	C₂×C₄×C₁₀₁	1	2	yes	—
238	C₂×C₂²⋊C₄	—	2	2	no	—
239	C₂×C₂²⋊C₄	—	2	1	no	—
240	C₂×C₂²⋊C₄	—	2	8	no	—
241	C₂×C₂²⋊C₄	D₄×C₁₀₁	1	2	yes	—
242	C₂×C₄²	—	2	2	no	—
243	C₂×C₄²	C₂×C₄×C₁₀₁	1	2	yes	—
244	C₂×C₄²	D₄×C₁₀₁	1	2	yes	—
245	#102	—	2	16	no	—
246	#97	—	2	4	no	—
247	C₄×C₈	—	2	4	no	—
248	C₂⁴	—	2	2	no	—
249	C₂⁴	—	2	4	no	—
250	C₂⁴	—	4	2	no	—
251	C₂⁴	—	4	1	no	—
252	C₂⁴	—	4	1	no	—
253	C₂⁴	—	8	4	no	—
254	C₂⁴	C₂×D₄×C₁₀₁	1	1	yes	characteristic
255	C₂×D₄	—	2	4	no	—
256	C₂×D₄	—	2	4	no	—
257	C₂×D₄	—	2	2	no	—
258	C₂×D₄	—	2	4	no	—
259	C₂×D₄	—	2	4	no	—
260	C₂×D₄	—	2	4	no	—
261	C₂×D₄	—	2	4	no	—
262	C₂×D₄	—	2	4	no	—
263	C₂×D₄	—	4	1	no	—
264	C₂×D₄	—	4	2	no	—
265	C₂×D₄	—	4	2	no	—
266	C₂×D₄	—	4	2	no	—
267	C₂×D₄	—	4	1	no	—
268	C₂×D₄	—	4	2	no	—
269	C₂×D₄	—	4	2	no	—
270	C₂×D₄	C₄²×C₁₀₁	1	4	yes	—
271	C₂²×C₄	—	2	2	no	—
272	C₂²×C₄	—	4	2	no	—
273	C₂²×C₄	C₂²⋊C₄×C₁₀₁	1	4	yes	—
274	C₂²×C₄	C₂²×C₄×C₁₀₁	1	2	yes	—
275	C₂²×C₄	C₂²×C₄×C₁₀₁	1	1	yes	characteristic
276	C₂²×C₄	C₂×D₄×C₁₀₁	1	2	yes	—
277	C₂²×C₄	C₂×D₄×C₁₀₁	1	2	yes	—
278	C₂²×C₄	C₂×D₄×C₁₀₁	1	1	yes	characteristic
279	C₂²×C₄	#41×C₁₀₁	1	2	yes	—
280	C₂²×C₄	#41×C₁₀₁	1	2	yes	—
281	C₂²×C₄	#41×C₁₀₁	1	2	yes	—
282	M₁₆	—	2	4	no	—
283	M₁₆	—	2	4	no	—
284	M₁₆	—	2	4	no	—
285	M₁₆	—	2	4	no	—
286	C₂×C₈	—	2	4	no	—
287	C₂×C₈	—	2	4	no	—
288	C₂×C₈	C₂²⋊C₄×C₁₀₁	1	8	yes	complemented
289	C₄⋊C₄	—	2	4	no	—
290	C₄⋊C₄	—	2	4	no	—
291	C₄⋊C₄	—	4	2	no	—
292	C₄⋊C₄	—	4	2	no	—
293	C₂²⋊C₄	—	2	4	no	—
294	C₂²⋊C₄	—	2	4	no	—
295	C₂²⋊C₄	—	4	1	no	—
296	C₂²⋊C₄	—	4	1	no	—
297	C₂²⋊C₄	—	4	2	no	—
298	C₂²⋊C₄	—	8	8	no	—
299	C₄²	—	2	2	no	—
300	C₄²	—	2	2	no	—
301	C₄²	—	2	4	no	—
302	C₄²	—	2	4	no	—
303	C₄²	—	4	2	no	—
304	C₂³	—	2	4	no	—
305	C₂³	—	4	2	no	—
306	C₂³	—	4	8	no	—
307	C₂³	—	4	2	no	—
308	C₂³	—	4	4	no	—
309	C₂³	—	4	2	no	—
310	C₂³	—	4	4	no	—
311	C₂³	—	8	8	no	—
312	C₂³	—	8	8	no	—
313	C₂³	—	8	4	no	—
314	C₂³	—	8	4	no	—
315	C₂³	C₂×C₂²⋊C₄×C₁₀₁	1	1	yes	characteristic
316	C₂³	C₄×D₄×C₁₀₁	1	2	yes	—
317	C₂³	#121×C₁₀₁	1	2	yes	—
318	C₂³	#124×C₁₀₁	1	1	yes	characteristic
319	C₂³	#127×C₁₀₁	1	1	yes	characteristic
320	D₄	—	2	8	no	—
321	D₄	—	4	4	no	—
322	D₄	—	4	4	no	—
323	D₄	—	4	4	no	—
324	C₂×C₄	—	2	4	no	—
325	C₂×C₄	—	4	4	no	—
326	C₂×C₄	—	4	4	no	—
327	C₂×C₄	—	4	2	no	—
328	C₂×C₄	—	4	4	no	—
329	C₂×C₄	—	8	4	no	—
330	C₂×C₄	C₂×C₄²×C₁₀₁	1	1	yes	characteristic
331	C₂×C₄	C₂×C₂²⋊C₄×C₁₀₁	1	2	yes	—
332	C₂×C₄	#117×C₁₀₁	1	2	yes	—
333	C₂×C₄	#117×C₁₀₁	1	1	yes	characteristic
334	C₂×C₄	C₄×D₄×C₁₀₁	1	2	yes	—
335	C₂×C₄	C₄×D₄×C₁₀₁	1	2	yes	—
336	C₂×C₄	C₄×D₄×C₁₀₁	1	2	yes	—
337	C₂×C₄	C₄×D₄×C₁₀₁	1	2	yes	—
338	C₂×C₄	C₄×D₄×C₁₀₁	1	2	yes	—
339	C₂×C₄	#120×C₁₀₁	1	1	yes	characteristic
340	C₂×C₄	#121×C₁₀₁	1	2	yes	—
341	C₂×C₄	#121×C₁₀₁	1	2	yes	—
342	C₂×C₄	#123×C₁₀₁	1	2	yes	—
343	C₂×C₄	#123×C₁₀₁	1	1	yes	characteristic
344	C₂×C₄	#124×C₁₀₁	1	2	yes	—
345	C₂×C₄	#126×C₁₀₁	1	2	yes	—
346	C₈	—	2	8	no	—
347	C₂²	—	2	2	no	—
348	C₂²	—	2	4	no	—
349	C₂²	—	4	2	no	—
350	C₂²	—	4	1	no	—
351	C₂²	—	4	1	no	—
352	C₂²	—	4	8	no	—
353	C₂²	—	4	4	no	—
354	C₂²	—	8	4	no	—
355	C₂²	—	8	8	no	—
356	C₂²	—	8	8	no	—
357	C₂²	—	8	4	no	—
358	C₂²	C₄×C₂²⋊C₄×C₁₀₁	1	1	yes	characteristic
359	C₂²	#386×C₁₀₁	1	1	yes	characteristic
360	C₂²	#388×C₁₀₁	1	2	yes	—
361	C₂²	#390×C₁₀₁	1	2	yes	—
362	C₂²	#390×C₁₀₁	1	1	yes	characteristic
363	C₄	—	4	4	no	—
364	C₄	—	8	2	no	—
365	C₄	—	8	4	no	—
366	C₄	C₄×C₂²⋊C₄×C₁₀₁	1	2	yes	—
367	C₄	#386×C₁₀₁	1	2	yes	—
368	C₄	#388×C₁₀₁	1	2	yes	—
369	C₄	#388×C₁₀₁	1	2	yes	—
370	C₂	—	2	1	no	—
371	C₂	—	2	2	no	—
372	C₂	—	2	1	no	—
373	C₂	—	2	2	no	—
374	C₂	—	8	4	no	—
375	C₂	C₁₀₁×#1437	1	1	yes	characteristic
376	C₂	C₁₀₁×#1910	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₁₀₁	#386
commutator	C₂×C₄	C₂×C₄²×C₁₀₁
Frattini, cosocle	C₂³×C₄	C₂³×C₁₀₁
prime radical	C₂³×D₄×C₁₀₁	C₂²
LCS	G ▷ C₂×C₄ ▷ 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. C₁₀₁×#2873	C₂	semidirect
4. C₁₀₁×#1740	C₂	semidirect
5. C₂×H(3,ℤ/4)×C₁₀₁	C₂	semidirect
12. #418×C₁₀₁	C₄	semidirect
17. #390×C₁₀₁	C₄	semidirect
99. C₂×C₈×C₁₀₁	C₂²⋊C₄	semidirect
181. #10948	C₁₀₁	direct (N × H)
190. #2873	C₂×C₁₀₁	semidirect
192. #1740	C₂×C₁₀₁	semidirect
193. C₂×H(3,ℤ/4)	C₂×C₁₀₁	semidirect
194. C₁₀₁	#10948	direct (N × H)
201. #418	C₄×C₁₀₁	semidirect
206. #390	C₄×C₁₀₁	semidirect
288. C₂×C₈	C₂²⋊C₄×C₁₀₁	semidirect

Maximal subgroups

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

subgroup	index
C₂×#418×C₁₀₁	2
C₁₀₁×#2873	2
C₁₀₁×#2309	2
C₁₀₁×#1740	2
C₂×H(3,ℤ/4)×C₁₀₁	2
#10948	101

Subgroups — C101×#10948 #38793099

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₀₁×#10948 #38793099