Subgroups — #27173953

Order 12928.

1252 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×D₄×D₁₀₁	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×D₄₀₄	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#15692217	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₂²⋊C₄×D₁₀₁	C₂	1	2	yes	maximal, complemented
5	#20265080	C₂	1	1	yes	maximal, characteristic, complemented
6	#20265053	C₂	1	2	yes	maximal, complemented
7	#20265053	C₂	1	2	yes	maximal, complemented
8	#20265034	C₂	1	1	yes	maximal, characteristic, complemented
9	#20265032	C₂	1	2	yes	maximal, complemented
10	C₄×#13108051	C₂	1	1	yes	maximal, characteristic, complemented
11	#390×C₁₀₁	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂⁴×D₁₀₁	C₂²	1	2	yes	—
13	C₂²×D₄₀₄	C₂²	1	1	yes	characteristic
14	C₂²×C₂²⋊D₁₀₁	C₂²	1	2	yes	—
15	C₂×D₄×D₁₀₁	—	2	4	no	—
16	C₂×D₄×D₁₀₁	—	2	4	no	—
17	C₂×D₄×D₁₀₁	C₄	1	8	yes	complemented
18	C₂²×C₄×D₁₀₁	C₂²	1	1	yes	characteristic
19	C₂²×C₄×D₁₀₁	C₂²	1	2	yes	complemented
20	C₂²×C₄×D₁₀₁	C₂²	1	2	yes	complemented
21	C₄×D₄₀₄	—	2	4	no	—
22	#15692217	—	2	4	no	—
23	C₂×C₄⋊Dic₁₀₁	C₂²	1	1	yes	characteristic, complemented
24	C₂×C₂²⋊Dic₁₀₁	C₂²	1	2	yes	complemented
25	C₂×C₂²⋊Dic₁₀₁	C₂²	1	2	yes	complemented
26	C₂×#13108051	C₂²	1	1	yes	characteristic
27	C₂×#13108051	C₂²	1	2	yes	—
28	C₂×#13108051	C₂²	1	1	yes	characteristic
29	C₂×#13108051	C₂²	1	2	yes	complemented
30	C₂×#13108051	C₂²	1	2	yes	complemented
31	C₂²⋊C₄×D₁₀₁	—	2	8	no	—
32	C₂×C₄×Dic₁₀₁	C₂²	1	1	yes	characteristic, complemented
33	#15692162	C₂²	1	1	yes	characteristic, complemented
34	#15692162	C₂²	1	1	yes	characteristic, complemented
35	#15692162	C₂²	1	2	yes	complemented
36	C₂²×D₄×C₁₀₁	C₂²	1	1	yes	characteristic
37	C₂×C₄⋊C₄×C₁₀₁	C₂²	1	1	yes	characteristic, complemented
38	C₂×C₂²⋊C₄×C₁₀₁	C₂²	1	2	yes	complemented
39	C₂×C₂²⋊C₄×C₁₀₁	C₂²	1	2	yes	complemented
40	C₂×C₄²×C₁₀₁	C₂²	1	1	yes	characteristic, complemented
41	C₂³×D₁₀₁	—	2	4	no	—
42	C₂³×D₁₀₁	—	2	4	no	—
43	C₂³×D₁₀₁	—	2	4	no	—
44	C₂³×D₁₀₁	—	2	4	no	—
45	C₂³×D₁₀₁	—	4	2	no	—
46	C₂³×D₁₀₁	—	4	2	no	—
47	C₂³×D₁₀₁	C₂×C₄	1	8	yes	complemented
48	C₂³×D₁₀₁	C₂³	1	2	yes	—
49	C₂³×D₁₀₁	C₂³	1	1	yes	characteristic
50	C₂×D₄₀₄	C₂×C₄	1	4	yes	—
51	C₂×D₄₀₄	D₄	1	4	yes	—
52	C₂×D₄₀₄	D₄	1	4	yes	—
53	C₂×C₂²⋊D₁₀₁	—	2	4	no	—
54	C₂×C₂²⋊D₁₀₁	—	2	4	no	—
55	C₂×C₂²⋊D₁₀₁	C₂×C₄	1	8	yes	complemented
56	D₄×D₁₀₁	—	2	32	no	—
57	C₂²×Dic₁₀₁	C₂³	1	2	yes	—
58	C₂²×Dic₁₀₁	C₂³	1	1	yes	characteristic
59	C₂²×Dic₁₀₁	C₂³	1	1	yes	characteristic
60	C₂²×Dic₁₀₁	C₂³	1	1	yes	characteristic
61	C₂×C₄×D₁₀₁	—	2	2	no	—
62	C₂×C₄×D₁₀₁	—	2	2	no	—
63	C₂×C₄×D₁₀₁	—	2	4	no	—
64	C₂×C₄×D₁₀₁	—	2	4	no	—
65	C₂×C₄×D₁₀₁	—	2	4	no	—
66	C₂×C₄×D₁₀₁	—	2	4	no	—
67	C₂×C₄×D₁₀₁	—	4	2	no	—
68	C₂×C₄×D₁₀₁	—	4	2	no	—
69	C₂×C₄×D₁₀₁	C₂×C₄	1	4	yes	complemented
70	C₄⋊Dic₁₀₁	—	2	2	no	—
71	C₂²⋊Dic₁₀₁	—	2	4	no	—
72	C₂²⋊Dic₁₀₁	—	4	2	no	—
73	#13108051	—	2	4	no	—
74	#13108051	—	2	4	no	—
75	#13108051	—	2	4	no	—
76	#13108051	—	2	2	no	—
77	#13108051	D₄	1	4	yes	complemented
78	C₄×Dic₁₀₁	—	2	2	no	—
79	C₂⁴×C₁₀₁	C₂³	1	2	yes	—
80	C₂×D₄×C₁₀₁	—	2	2	no	—
81	C₂×D₄×C₁₀₁	—	2	2	no	—
82	C₂×D₄×C₁₀₁	C₂×C₄	1	4	yes	complemented
83	C₂²×C₄×C₁₀₁	C₂³	1	2	yes	—
84	C₂²×C₄×C₁₀₁	C₂³	1	1	yes	characteristic
85	C₂²×C₄×C₁₀₁	C₂³	1	1	yes	characteristic
86	C₂²×C₄×C₁₀₁	C₂³	1	1	yes	characteristic
87	C₄⋊C₄×C₁₀₁	—	2	2	no	—
88	C₂²⋊C₄×C₁₀₁	—	2	4	no	—
89	C₂²⋊C₄×C₁₀₁	—	4	2	no	—
90	C₄²×C₁₀₁	—	2	2	no	—
91	C₂³×C₁₀₁	—	2	2	no	—
92	C₂³×C₁₀₁	—	2	2	no	—
93	C₂³×C₁₀₁	—	2	2	no	—
94	C₂³×C₁₀₁	—	2	2	no	—
95	C₂³×C₁₀₁	—	2	2	no	—
96	C₂³×C₁₀₁	—	2	2	no	—
97	C₂³×C₁₀₁	C₂²×C₄	1	4	yes	—
98	C₂³×C₁₀₁	C₂⁴	1	1	yes	characteristic
99	C₂²×D₁₀₁	—	2	2	no	—
100	C₂²×D₁₀₁	—	2	1	no	—
101	C₂²×D₁₀₁	—	2	1	no	—
102	C₂²×D₁₀₁	—	2	2	no	—
103	C₂²×D₁₀₁	—	2	2	no	—
104	C₂²×D₁₀₁	—	2	2	no	—
105	C₂²×D₁₀₁	—	2	1	no	—
106	C₂²×D₁₀₁	—	2	1	no	—
107	C₂²×D₁₀₁	—	2	16	no	—
108	C₂²×D₁₀₁	—	2	16	no	—
109	C₂²×D₁₀₁	—	4	8	no	—
110	C₂²×D₁₀₁	—	4	8	no	—
111	C₂²×D₁₀₁	—	4	8	no	—
112	C₂²×D₁₀₁	—	4	8	no	—
113	C₂²×D₁₀₁	—	4	8	no	—
114	C₂²×D₁₀₁	C₂²×C₄	1	4	yes	—
115	C₂²×D₁₀₁	C₂²×C₄	1	2	yes	—
116	C₂²×D₁₀₁	C₂×D₄	1	4	yes	—
117	C₂²×D₁₀₁	C₂×D₄	1	4	yes	—
118	C₂²×D₁₀₁	C₂×D₄	1	2	yes	—
119	C₂²×D₁₀₁	#41	1	2	yes	—
120	D₄×C₁₀₁	—	2	8	no	—
121	C₂×C₄×C₁₀₁	—	2	1	no	—
122	C₂×C₄×C₁₀₁	—	2	1	no	—
123	C₂×C₄×C₁₀₁	—	2	1	no	—
124	C₂×C₄×C₁₀₁	—	2	2	no	—
125	C₂×C₄×C₁₀₁	—	2	2	no	—
126	C₂×C₄×C₁₀₁	—	2	1	no	—
127	C₂×C₄×C₁₀₁	—	2	1	no	—
128	C₂×C₄×C₁₀₁	—	2	2	no	—
129	C₂×C₄×C₁₀₁	C₂²×C₄	1	2	yes	—
130	C₂×C₄×C₁₀₁	C₂×D₄	1	2	yes	—
131	C₂×C₄×C₁₀₁	C₂×D₄	1	2	yes	—
132	C₂×C₄×C₁₀₁	C₂×D₄	1	2	yes	complemented
133	C₂²⋊D₁₀₁	—	2	16	no	—
134	C₂×Dic₁₀₁	—	2	1	no	—
135	C₂×Dic₁₀₁	—	2	1	no	—
136	C₂×Dic₁₀₁	—	2	1	no	—
137	C₂×Dic₁₀₁	—	2	1	no	—
138	C₂×Dic₁₀₁	—	2	1	no	—
139	C₂×Dic₁₀₁	—	2	2	no	—
140	C₂×Dic₁₀₁	—	2	2	no	—
141	C₂×Dic₁₀₁	—	2	1	no	—
142	C₂×Dic₁₀₁	—	2	1	no	—
143	C₂×Dic₁₀₁	—	2	2	no	—
144	C₂×Dic₁₀₁	C₂²×C₄	1	2	yes	—
145	C₂×Dic₁₀₁	C₂×D₄	1	2	yes	complemented
146	D₄₀₄	C₂²⋊C₄	1	16	yes	complemented
147	C₄×D₁₀₁	—	2	8	no	—
148	C₄×D₁₀₁	—	4	8	no	—
149	C₄×D₁₀₁	—	4	8	no	—
150	C₂²×C₁₀₁	—	2	4	no	—
151	C₂²×C₁₀₁	—	2	4	no	—
152	C₂²×C₁₀₁	—	2	4	no	—
153	C₂²×C₁₀₁	—	4	2	no	—
154	C₂²×C₁₀₁	—	4	2	no	—
155	C₂²×C₁₀₁	—	4	2	no	—
156	C₂²×C₁₀₁	—	4	2	no	—
157	C₂²×C₁₀₁	C₂³×C₄	1	1	yes	characteristic
158	C₂²×C₁₀₁	C₂²×D₄	1	1	yes	characteristic
159	C₂²×C₁₀₁	C₂²×D₄	1	1	yes	characteristic
160	C₂²×C₁₀₁	C₂²×D₄	1	1	yes	characteristic
161	C₂²×C₁₀₁	C₂×#41	1	1	yes	characteristic
162	C₂²×C₁₀₁	H(5,𝔽₂)	1	1	yes	characteristic
163	C₂²×C₁₀₁	H(5,𝔽₂)	1	1	yes	characteristic
164	C₂×D₁₀₁	—	2	2	no	—
165	C₂×D₁₀₁	—	2	4	no	—
166	C₂×D₁₀₁	—	2	2	no	—
167	C₂×D₁₀₁	—	2	4	no	—
168	C₂×D₁₀₁	—	2	4	no	—
169	C₂×D₁₀₁	—	2	4	no	—
170	C₂×D₁₀₁	—	2	2	no	—
171	C₂×D₁₀₁	—	2	2	no	—
172	C₂×D₁₀₁	—	2	2	no	—
173	C₂×D₁₀₁	—	2	2	no	—
174	C₂×D₁₀₁	—	2	4	no	—
175	C₂×D₁₀₁	—	2	4	no	—
176	C₂×D₁₀₁	—	4	32	no	—
177	C₂×D₁₀₁	C₂×C₂²⋊C₄	1	8	yes	complemented
178	C₂×D₁₀₁	C₄×D₄	1	4	yes	complemented
179	C₄×C₁₀₁	—	2	2	no	—
180	C₄×C₁₀₁	—	4	2	no	—
181	C₄×C₁₀₁	—	4	1	no	—
182	C₄×C₁₀₁	C₂×C₂²⋊C₄	1	4	yes	complemented
183	Dic₁₀₁	—	2	2	no	—
184	Dic₁₀₁	—	2	2	no	—
185	Dic₁₀₁	—	4	2	no	—
186	Dic₁₀₁	—	4	1	no	—
187	C₂×C₁₀₁	—	4	4	no	—
188	C₂×C₁₀₁	C₂²×C₂²⋊C₄	1	1	yes	characteristic
189	C₂×C₁₀₁	C₂×C₄×D₄	1	1	yes	characteristic
190	C₂×C₁₀₁	#518	1	1	yes	characteristic
191	C₂×C₁₀₁	D₄²	1	1	yes	characteristic
192	C₂×C₁₀₁	D₄²	1	1	yes	characteristic
193	C₂×C₁₀₁	#546	1	1	yes	characteristic
194	C₂×C₁₀₁	#546	1	1	yes	characteristic
195	D₁₀₁	—	2	4	no	—
196	D₁₀₁	—	2	8	no	—
197	D₄×C₂²⋊C₄	—	101	1	no	maximal, Sylow
198	C₁₀₁	D₄×C₂²⋊C₄	1	1	yes	characteristic, complemented, Sylow
199	C₂³×D₄	—	101	1	no	—
200	C₂×C₄×D₄	—	101	1	no	—
201	C₂×C₄×D₄	—	101	1	no	—
202	C₂²×C₂²⋊C₄	—	101	2	no	—
203	#390	—	101	1	no	—
204	#390	D₁₀₁	1	1	yes	characteristic, complemented
205	#386	—	101	2	no	—
206	#386	—	101	2	no	—
207	#380	—	101	1	no	—
208	#379	—	101	2	no	—
209	C₄×C₂²⋊C₄	—	101	1	no	—
210	C₂⁵	—	101	2	no	—
211	C₂²×D₄	—	101	2	no	—
212	C₂²×D₄	—	101	8	no	—
213	C₂²×D₄	—	101	1	no	—
214	C₂²×D₄	—	202	4	no	—
215	C₂²×D₄	—	202	4	no	—
216	C₂²×D₄	C₂×D₁₀₁	1	1	yes	characteristic
217	C₂³×C₄	—	101	1	no	—
218	C₂³×C₄	—	101	2	no	—
219	C₂³×C₄	—	101	2	no	—
220	C₄×D₄	—	202	4	no	—
221	C₄×D₄	—	202	4	no	—
222	C₂×C₄⋊C₄	—	101	1	no	—
223	C₂×C₄⋊C₄	C₂×D₁₀₁	1	1	yes	characteristic, complemented
224	C₂×C₂²⋊C₄	—	101	1	no	—
225	C₂×C₂²⋊C₄	—	101	2	no	—
226	C₂×C₂²⋊C₄	—	101	2	no	—
227	C₂×C₂²⋊C₄	—	101	2	no	—
228	C₂×C₂²⋊C₄	—	101	2	no	—
229	C₂×C₂²⋊C₄	—	101	2	no	—
230	C₂×C₂²⋊C₄	—	101	1	no	—
231	C₂×C₂²⋊C₄	—	202	8	no	—
232	C₂×C₂²⋊C₄	C₂×D₁₀₁	1	2	yes	complemented
233	C₂×C₂²⋊C₄	C₂×D₁₀₁	1	2	yes	complemented
234	C₂×C₄²	—	101	1	no	—
235	C₂×C₄²	C₂×D₁₀₁	1	1	yes	characteristic, complemented
236	#95	—	101	1	no	—
237	#95	—	101	1	no	—
238	#95	—	101	2	no	—
239	C₂⁴	—	101	1	no	—
240	C₂⁴	—	101	2	no	—
241	C₂⁴	—	101	8	no	—
242	C₂⁴	—	404	2	no	—
243	C₂⁴	—	404	2	no	—
244	C₂⁴	—	202	4	no	—
245	C₂⁴	—	202	4	no	—
246	C₂⁴	—	202	4	no	—
247	C₂⁴	—	202	4	no	—
248	C₂⁴	C₂²×D₁₀₁	1	2	yes	—
249	C₂×D₄	—	2	2	no	—
250	C₂×D₄	—	2	2	no	—
251	C₂×D₄	—	101	8	no	—
252	C₂×D₄	—	101	4	no	—
253	C₂×D₄	—	101	4	no	—
254	C₂×D₄	—	101	4	no	—
255	C₂×D₄	—	202	32	no	—
256	C₂×D₄	—	202	4	no	—
257	C₂×D₄	—	202	4	no	—
258	C₂×D₄	C₄×D₁₀₁	1	4	yes	complemented
259	C₂²×C₄	—	101	1	no	—
260	C₂²×C₄	—	101	1	no	—
261	C₂²×C₄	—	101	4	no	—
262	C₂²×C₄	—	101	1	no	—
263	C₂²×C₄	—	101	2	no	—
264	C₂²×C₄	—	404	2	no	—
265	C₂²×C₄	—	404	2	no	—
266	C₂²×C₄	—	202	4	no	—
267	C₂²×C₄	—	202	4	no	—
268	C₂²×C₄	—	202	4	no	—
269	C₂²×C₄	—	202	4	no	—
270	C₂²×C₄	—	202	2	no	—
271	C₂²×C₄	—	202	2	no	—
272	C₂²×C₄	C₂²×D₁₀₁	1	1	yes	characteristic
273	C₂²×C₄	C₂²×D₁₀₁	1	2	yes	—
274	C₂²×C₄	C₂²×D₁₀₁	1	1	yes	characteristic
275	C₂²×C₄	C₂²×D₁₀₁	1	1	yes	characteristic
276	C₄⋊C₄	—	2	2	no	—
277	C₄⋊C₄	—	202	2	no	—
278	C₂²⋊C₄	—	2	4	no	—
279	C₂²⋊C₄	—	4	2	no	—
280	C₂²⋊C₄	—	101	4	no	—
281	C₂²⋊C₄	—	404	2	no	—
282	C₂²⋊C₄	—	202	2	no	—
283	C₂²⋊C₄	—	202	4	no	—
284	C₂²⋊C₄	—	202	4	no	—
285	C₂²⋊C₄	—	202	4	no	—
286	C₂²⋊C₄	—	202	4	no	—
287	C₄²	—	2	2	no	—
288	C₄²	—	202	2	no	—
289	C₂³	—	2	2	no	—
290	C₂³	—	2	2	no	—
291	C₂³	—	2	2	no	—
292	C₂³	—	2	2	no	—
293	C₂³	—	2	2	no	—
294	C₂³	—	2	2	no	—
295	C₂³	—	101	2	no	—
296	C₂³	—	101	4	no	—
297	C₂³	—	101	2	no	—
298	C₂³	—	101	4	no	—
299	C₂³	—	101	4	no	—
300	C₂³	—	101	2	no	—
301	C₂³	—	404	8	no	—
302	C₂³	—	404	8	no	—
303	C₂³	—	404	8	no	—
304	C₂³	—	404	8	no	—
305	C₂³	—	404	8	no	—
306	C₂³	—	202	16	no	—
307	C₂³	—	202	16	no	—
308	C₂³	—	202	2	no	—
309	C₂³	—	202	1	no	—
310	C₂³	—	202	1	no	—
311	C₂³	—	202	2	no	—
312	C₂³	—	202	2	no	—
313	C₂³	—	202	1	no	—
314	C₂³	—	202	2	no	—
315	C₂³	—	202	1	no	—
316	C₂³	C₂×C₄×D₁₀₁	1	4	yes	—
317	C₂³	C₂³×D₁₀₁	1	1	yes	characteristic
318	D₄	—	2	8	no	—
319	D₄	—	101	16	no	—
320	D₄	—	202	16	no	—
321	C₂×C₄	—	2	1	no	—
322	C₂×C₄	—	2	1	no	—
323	C₂×C₄	—	2	1	no	—
324	C₂×C₄	—	2	2	no	—
325	C₂×C₄	—	2	2	no	—
326	C₂×C₄	—	2	1	no	—
327	C₂×C₄	—	2	1	no	—
328	C₂×C₄	—	2	2	no	—
329	C₂×C₄	—	101	2	no	—
330	C₂×C₄	—	101	2	no	—
331	C₂×C₄	—	404	8	no	—
332	C₂×C₄	—	404	8	no	—
333	C₂×C₄	—	202	1	no	—
334	C₂×C₄	—	202	2	no	—
335	C₂×C₄	—	202	2	no	—
336	C₂×C₄	—	202	1	no	—
337	C₂×C₄	—	202	1	no	—
338	C₂×C₄	—	202	2	no	—
339	C₂×C₄	—	202	1	no	—
340	C₂×C₄	—	202	1	no	—
341	C₂×C₄	—	202	1	no	—
342	C₂×C₄	—	202	1	no	—
343	C₂×C₄	—	202	8	no	—
344	C₂×C₄	C₂×C₄×D₁₀₁	1	2	yes	—
345	C₂×C₄	D₄×D₁₀₁	1	2	yes	—
346	C₂×C₄	D₄×D₁₀₁	1	2	yes	—
347	C₂×C₄	D₄×D₁₀₁	1	2	yes	complemented
348	C₂²	—	2	4	no	—
349	C₂²	—	2	4	no	—
350	C₂²	—	2	4	no	—
351	C₂²	—	4	2	no	—
352	C₂²	—	4	2	no	—
353	C₂²	—	4	2	no	—
354	C₂²	—	4	2	no	—
355	C₂²	—	101	8	no	—
356	C₂²	—	101	4	no	—
357	C₂²	—	404	32	no	—
358	C₂²	—	202	4	no	—
359	C₂²	—	202	2	no	—
360	C₂²	—	202	4	no	—
361	C₂²	—	202	2	no	—
362	C₂²	—	202	2	no	—
363	C₂²	—	202	4	no	—
364	C₂²	—	202	2	no	—
365	C₂²	—	202	4	no	—
366	C₂²	—	202	2	no	—
367	C₂²	—	202	4	no	—
368	C₂²	—	202	2	no	—
369	C₂²	—	202	4	no	—
370	C₂²	C₂²×C₄×D₁₀₁	1	1	yes	characteristic
371	C₂²	C₂×D₄×D₁₀₁	1	1	yes	characteristic
372	C₂²	C₂×D₄×D₁₀₁	1	1	yes	characteristic
373	C₂²	C₂×D₄×D₁₀₁	1	1	yes	characteristic
374	C₂²	#41×D₁₀₁	1	1	yes	characteristic
375	C₂²	#15692300	1	1	yes	characteristic
376	C₂²	#15692301	1	1	yes	characteristic
377	C₄	—	2	2	no	—
378	C₄	—	4	2	no	—
379	C₄	—	4	1	no	—
380	C₄	—	404	2	no	—
381	C₄	—	404	1	no	—
382	C₄	—	202	2	no	—
383	C₄	—	202	2	no	—
384	C₄	C₂²⋊C₄×D₁₀₁	1	4	yes	complemented
385	C₂	—	4	4	no	—
386	C₂	—	202	4	no	—
387	C₂	—	202	8	no	—
388	C₂	C₂×C₂²⋊C₄×D₁₀₁	1	1	yes	characteristic
389	C₂	C₄×D₄×D₁₀₁	1	1	yes	characteristic
390	C₂	#20265649	1	1	yes	characteristic
391	C₂	#20265811	1	1	yes	characteristic
392	C₂	#20265812	1	1	yes	characteristic
393	C₂	#20265820	1	1	yes	characteristic
394	C₂	#20265824	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂³	C₂³×D₁₀₁
commutator	C₂²×C₁₀₁	C₂³×C₄
Fitting	#390×C₁₀₁	C₂
socle, cosocle	C₂³×C₁₀₁	C₂⁴
prime radical	C₂²×D₄×D₁₀₁	C₂
hypercenter	#390	D₁₀₁
hypocenter	C₁₀₁	D₄×C₂²⋊C₄
LCS	G ▷ C₂²×C₁₀₁ ▷ C₁₀₁
UCS	C₁ ◁ C₂³ ◁ #390

Complements

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

N	H ≅ G/N	type
2. C₂×C₄×D₄₀₄	C₂	semidirect
3. C₂×#15692217	C₂	semidirect
4. C₂×C₂²⋊C₄×D₁₀₁	C₂	semidirect
5. #20265080	C₂	semidirect
6. #20265053	C₂	semidirect
7. #20265053	C₂	semidirect
8. #20265034	C₂	semidirect
9. #20265032	C₂	semidirect
10. C₄×#13108051	C₂	semidirect
11. #390×C₁₀₁	C₂	semidirect
17. C₂×D₄×D₁₀₁	C₄	semidirect
19. C₂²×C₄×D₁₀₁	C₂²	semidirect
20. C₂²×C₄×D₁₀₁	C₂²	semidirect
23. C₂×C₄⋊Dic₁₀₁	C₂²	semidirect
24. C₂×C₂²⋊Dic₁₀₁	C₂²	semidirect
25. C₂×C₂²⋊Dic₁₀₁	C₂²	semidirect
29. C₂×#13108051	C₂²	semidirect
30. C₂×#13108051	C₂²	semidirect
32. C₂×C₄×Dic₁₀₁	C₂²	semidirect
33. #15692162	C₂²	semidirect
34. #15692162	C₂²	semidirect
35. #15692162	C₂²	semidirect
37. C₂×C₄⋊C₄×C₁₀₁	C₂²	semidirect
38. C₂×C₂²⋊C₄×C₁₀₁	C₂²	semidirect
39. C₂×C₂²⋊C₄×C₁₀₁	C₂²	semidirect
40. C₂×C₄²×C₁₀₁	C₂²	semidirect
47. C₂³×D₁₀₁	C₂×C₄	semidirect
55. C₂×C₂²⋊D₁₀₁	C₂×C₄	semidirect
69. C₂×C₄×D₁₀₁	C₂×C₄	semidirect
77. #13108051	D₄	semidirect
82. C₂×D₄×C₁₀₁	C₂×C₄	semidirect
132. C₂×C₄×C₁₀₁	C₂×D₄	semidirect
145. C₂×Dic₁₀₁	C₂×D₄	semidirect
146. D₄₀₄	C₂²⋊C₄	semidirect
177. C₂×D₁₀₁	C₂×C₂²⋊C₄	semidirect
178. C₂×D₁₀₁	C₄×D₄	semidirect
182. C₄×C₁₀₁	C₂×C₂²⋊C₄	semidirect
198. C₁₀₁	D₄×C₂²⋊C₄	semidirect
204. #390	D₁₀₁	semidirect
223. C₂×C₄⋊C₄	C₂×D₁₀₁	semidirect
232. C₂×C₂²⋊C₄	C₂×D₁₀₁	semidirect
233. C₂×C₂²⋊C₄	C₂×D₁₀₁	semidirect
235. C₂×C₄²	C₂×D₁₀₁	semidirect
258. C₂×D₄	C₄×D₁₀₁	semidirect
347. C₂×C₄	D₄×D₁₀₁	semidirect
384. C₄	C₂²⋊C₄×D₁₀₁	semidirect

Maximal subgroups

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

subgroup	index
C₂²×D₄×D₁₀₁	2
C₂×C₄×D₄₀₄	2
C₂×#15692217	2
C₂×C₂²⋊C₄×D₁₀₁	2
#20265080	2
#20265053	2
#20265034	2
#20265032	2
C₄×#13108051	2
#390×C₁₀₁	2
D₄×C₂²⋊C₄	101