Subgroups — C₁₀₁×#18548 #38800699

Order 25856.

1156 conjugacy classes of subgroups.

The subgroup lattice has 450 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₀₁×#3483	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₀₁×#3151	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₀₁×#3038	C₂	1	2	yes	maximal, complemented
4	C₁₀₁×#1624	C₂	1	2	yes	maximal, complemented
5	C₁₀₁×#1623	C₂	1	2	yes	maximal, complemented
6	C₁₀₁×#1621	C₂	1	4	yes	maximal, complemented
7	C₁₀₁×#1560	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₀₁×#1489	C₂	1	2	yes	maximal, complemented
9	C₂×AGL(1,ℤ/8)×C₁₀₁	—	2	2	no	—
10	C₂×AGL(1,ℤ/8)×C₁₀₁	—	2	2	no	—
11	Q₈²×C₁₀₁	C₂²	1	1	yes	characteristic, complemented
12	#555×C₁₀₁	—	2	2	no	—
13	#555×C₁₀₁	—	2	2	no	—
14	#555×C₁₀₁	C₂²	1	1	yes	characteristic, complemented
15	#550×C₁₀₁	—	2	2	no	—
16	#550×C₁₀₁	C₂²	1	2	yes	complemented
17	#532×C₁₀₁	—	2	2	no	—
18	#532×C₁₀₁	—	2	2	no	—
19	#532×C₁₀₁	C₂²	1	1	yes	characteristic
20	C₂×#127×C₁₀₁	C₂²	1	1	yes	characteristic
21	C₄×#41×C₁₀₁	—	2	2	no	—
22	C₄×#41×C₁₀₁	C₂²	1	2	yes	—
23	#496×C₁₀₁	—	2	2	no	—
24	#493×C₁₀₁	C₂²	1	2	yes	—
25	#492×C₁₀₁	C₂²	1	2	yes	—
26	#460×C₁₀₁	—	2	2	no	—
27	#460×C₁₀₁	C₂²	1	4	yes	—
28	#459×C₁₀₁	—	2	2	no	—
29	#459×C₁₀₁	C₂²	1	4	yes	—
30	#423×C₁₀₁	C₂²	1	2	yes	—
31	#418×C₁₀₁	—	2	2	no	—
32	C₄×M₁₆×C₁₀₁	C₂²	1	1	yes	characteristic
33	#333×C₁₀₁	C₂²	1	2	yes	complemented
34	#331×C₁₀₁	C₂²	1	2	yes	complemented
35	Q₈⋊C₈×C₁₀₁	C₂²	1	4	yes	complemented
36	D₄⋊C₈×C₁₀₁	C₂²	1	4	yes	complemented
37	C₂×#41×C₁₀₁	—	2	2	no	—
38	C₂×#41×C₁₀₁	—	2	2	no	—
39	C₂×#41×C₁₀₁	D₄	1	2	yes	—
40	C₂×#41×C₁₀₁	D₄	1	2	yes	—
41	C₂²×D₄×C₁₀₁	—	2	2	no	—
42	C₂²×D₄×C₁₀₁	—	2	1	no	—
43	AGL(1,ℤ/8)×C₁₀₁	—	4	8	no	—
44	AGL(1,ℤ/8)×C₁₀₁	—	4	8	no	—
45	C₂×SD₁₆×C₁₀₁	—	2	4	no	—
46	C₂×SD₁₆×C₁₀₁	—	2	4	no	—
47	C₂×D₈×C₁₀₁	—	2	4	no	—
48	C₂×D₈×C₁₀₁	—	2	4	no	—
49	C₂×M₁₆×C₁₀₁	—	2	1	no	—
50	C₂×M₁₆×C₁₀₁	—	2	2	no	—
51	C₄⋊Q₈×C₁₀₁	—	2	2	no	—
52	C₄⋊Q₈×C₁₀₁	—	2	2	no	—
53	C₄⋊Q₈×C₁₀₁	C₂³	1	1	yes	characteristic
54	#127×C₁₀₁	—	2	2	no	—
55	#127×C₁₀₁	—	2	2	no	—
56	#127×C₁₀₁	—	2	2	no	—
57	#127×C₁₀₁	—	2	1	no	—
58	#127×C₁₀₁	C₂³	1	2	yes	—
59	#127×C₁₀₁	C₂³	1	1	yes	characteristic
60	#124×C₁₀₁	—	2	2	no	—
61	#124×C₁₀₁	—	2	4	no	—
62	#124×C₁₀₁	—	2	2	no	—
63	#124×C₁₀₁	D₄	1	2	yes	—
64	#121×C₁₀₁	—	2	4	no	—
65	#121×C₁₀₁	—	2	4	no	—
66	#121×C₁₀₁	—	2	2	no	—
67	#121×C₁₀₁	—	2	4	no	—
68	#121×C₁₀₁	—	2	2	no	—
69	#121×C₁₀₁	—	2	2	no	—
70	C₄×Q₈×C₁₀₁	—	2	2	no	—
71	C₄×Q₈×C₁₀₁	D₄	1	2	yes	—
72	C₄×Q₈×C₁₀₁	C₂³	1	2	yes	—
73	C₄×D₄×C₁₀₁	—	2	4	no	—
74	C₄×D₄×C₁₀₁	—	2	4	no	—
75	C₄×D₄×C₁₀₁	—	2	2	no	—
76	C₄×D₄×C₁₀₁	—	2	2	no	—
77	C₄×D₄×C₁₀₁	—	2	2	no	—
78	C₄×D₄×C₁₀₁	—	2	2	no	—
79	C₄×D₄×C₁₀₁	D₄	1	2	yes	—
80	C₄×D₄×C₁₀₁	C₂³	1	2	yes	—
81	#117×C₁₀₁	—	2	4	no	—
82	#117×C₁₀₁	—	2	2	no	—
83	#117×C₁₀₁	—	2	2	no	—
84	#117×C₁₀₁	D₄	1	2	yes	—
85	C₂×C₄²×C₁₀₁	—	2	2	no	—
86	C₂×C₄²×C₁₀₁	—	2	2	no	—
87	C₂×C₄²×C₁₀₁	C₂³	1	1	yes	characteristic
88	C₄⋊C₈×C₁₀₁	—	2	2	no	—
89	C₄⋊C₈×C₁₀₁	C₂³	1	4	yes	—
90	#102×C₁₀₁	—	2	4	no	—
91	#102×C₁₀₁	—	2	4	no	—
92	#97×C₁₀₁	—	2	1	no	—
93	C₄×C₈×C₁₀₁	C₂³	1	2	yes	—
94	C₂⁴×C₁₀₁	—	4	1	no	—
95	#41×C₁₀₁	—	2	4	no	—
96	#41×C₁₀₁	—	4	2	no	—
97	#41×C₁₀₁	—	4	4	no	—
98	#41×C₁₀₁	—	4	4	no	—
99	#41×C₁₀₁	—	4	4	no	—
100	#41×C₁₀₁	—	8	4	no	—
101	C₂×Q₈×C₁₀₁	—	2	2	no	—
102	C₂×Q₈×C₁₀₁	C₂×D₄	1	2	yes	—
103	C₂×Q₈×C₁₀₁	C₂×D₄	1	2	yes	—
104	C₂×D₄×C₁₀₁	—	2	4	no	—
105	C₂×D₄×C₁₀₁	—	2	2	no	—
106	C₂×D₄×C₁₀₁	—	2	2	no	—
107	C₂×D₄×C₁₀₁	—	2	4	no	—
108	C₂×D₄×C₁₀₁	—	2	2	no	—
109	C₂×D₄×C₁₀₁	—	2	2	no	—
110	C₂×D₄×C₁₀₁	—	2	4	no	—
111	C₂×D₄×C₁₀₁	—	2	2	no	—
112	C₂×D₄×C₁₀₁	—	4	4	no	—
113	C₂×D₄×C₁₀₁	—	4	4	no	—
114	C₂×D₄×C₁₀₁	—	4	4	no	—
115	C₂×D₄×C₁₀₁	—	4	2	no	—
116	C₂×D₄×C₁₀₁	—	4	1	no	—
117	C₂×D₄×C₁₀₁	C₂×D₄	1	2	yes	—
118	C₂×D₄×C₁₀₁	C₂×D₄	1	2	yes	—
119	C₂²×C₄×C₁₀₁	—	2	4	no	—
120	C₂²×C₄×C₁₀₁	—	2	2	no	—
121	C₂²×C₄×C₁₀₁	—	2	2	no	—
122	C₂²×C₄×C₁₀₁	—	2	2	no	—
123	C₂²×C₄×C₁₀₁	—	2	2	no	—
124	C₂²×C₄×C₁₀₁	C₂×D₄	1	2	yes	—
125	C₂²×C₄×C₁₀₁	C₂×D₄	1	1	yes	characteristic
126	SD₁₆×C₁₀₁	—	4	8	no	—
127	SD₁₆×C₁₀₁	—	4	8	no	—
128	D₈×C₁₀₁	—	4	8	no	—
129	D₈×C₁₀₁	—	4	8	no	—
130	M₁₆×C₁₀₁	—	2	4	no	—
131	M₁₆×C₁₀₁	—	4	4	no	—
132	C₂×C₈×C₁₀₁	—	2	2	no	—
133	C₂×C₈×C₁₀₁	—	2	4	no	—
134	C₄⋊C₄×C₁₀₁	—	2	4	no	—
135	C₄⋊C₄×C₁₀₁	—	2	2	no	—
136	C₄⋊C₄×C₁₀₁	—	2	2	no	—
137	C₄⋊C₄×C₁₀₁	—	2	2	no	—
138	C₄⋊C₄×C₁₀₁	C₂×D₄	1	2	yes	—
139	C₄⋊C₄×C₁₀₁	C₂×D₄	1	2	yes	—
140	C₂²⋊C₄×C₁₀₁	—	2	4	no	—
141	C₂²⋊C₄×C₁₀₁	—	2	4	no	—
142	C₂²⋊C₄×C₁₀₁	—	2	2	no	—
143	C₂²⋊C₄×C₁₀₁	—	2	4	no	—
144	C₂²⋊C₄×C₁₀₁	—	2	2	no	—
145	C₂²⋊C₄×C₁₀₁	—	2	2	no	—
146	C₄²×C₁₀₁	—	2	2	no	—
147	C₄²×C₁₀₁	—	2	2	no	—
148	C₄²×C₁₀₁	—	2	2	no	—
149	C₄²×C₁₀₁	—	2	2	no	—
150	C₄²×C₁₀₁	—	2	2	no	—
151	C₄²×C₁₀₁	C₂×D₄	1	1	yes	characteristic
152	C₄²×C₁₀₁	C₂×D₄	1	2	yes	—
153	C₄²×C₁₀₁	C₂⁴	1	1	yes	characteristic
154	C₂³×C₁₀₁	—	2	2	no	—
155	C₂³×C₁₀₁	—	2	2	no	—
156	C₂³×C₁₀₁	—	4	2	no	—
157	C₂³×C₁₀₁	—	8	4	no	—
158	C₂³×C₁₀₁	—	8	2	no	—
159	C₂³×C₁₀₁	#120	1	1	yes	characteristic
160	Q₈×C₁₀₁	—	2	2	no	—
161	Q₈×C₁₀₁	—	4	2	no	—
162	Q₈×C₁₀₁	—	8	2	no	—
163	Q₈×C₁₀₁	AGL(1,ℤ/8)	1	4	yes	complemented
164	D₄×C₁₀₁	—	2	2	no	—
165	D₄×C₁₀₁	—	2	2	no	—
166	D₄×C₁₀₁	—	4	4	no	—
167	D₄×C₁₀₁	—	4	2	no	—
168	D₄×C₁₀₁	—	4	8	no	—
169	D₄×C₁₀₁	—	4	4	no	—
170	D₄×C₁₀₁	—	4	2	no	—
171	D₄×C₁₀₁	—	4	4	no	—
172	D₄×C₁₀₁	—	4	2	no	—
173	D₄×C₁₀₁	—	4	4	no	—
174	D₄×C₁₀₁	—	8	4	no	—
175	D₄×C₁₀₁	—	8	2	no	—
176	D₄×C₁₀₁	—	8	2	no	—
177	D₄×C₁₀₁	—	8	4	no	—
178	D₄×C₁₀₁	—	8	2	no	—
179	C₂×C₄×C₁₀₁	—	2	2	no	—
180	C₂×C₄×C₁₀₁	—	2	2	no	—
181	C₂×C₄×C₁₀₁	—	2	2	no	—
182	C₂×C₄×C₁₀₁	—	2	2	no	—
183	C₂×C₄×C₁₀₁	—	2	2	no	—
184	C₂×C₄×C₁₀₁	—	2	2	no	—
185	C₂×C₄×C₁₀₁	—	2	2	no	—
186	C₂×C₄×C₁₀₁	—	4	4	no	—
187	C₂×C₄×C₁₀₁	—	4	8	no	—
188	C₂×C₄×C₁₀₁	—	4	2	no	—
189	C₂×C₄×C₁₀₁	—	4	2	no	—
190	C₂×C₄×C₁₀₁	—	4	4	no	—
191	C₂×C₄×C₁₀₁	—	4	4	no	—
192	C₂×C₄×C₁₀₁	#120	1	2	yes	—
193	C₂×C₄×C₁₀₁	#120	1	1	yes	characteristic
194	C₂×C₄×C₁₀₁	C₂²×D₄	1	1	yes	characteristic
195	C₂×C₄×C₁₀₁	C₂²×D₄	1	2	yes	—
196	C₈×C₁₀₁	—	2	4	no	—
197	C₈×C₁₀₁	—	4	4	no	—
198	C₂²×C₁₀₁	—	2	2	no	—
199	C₂²×C₁₀₁	—	2	1	no	—
200	C₂²×C₁₀₁	—	4	2	no	—
201	C₂²×C₁₀₁	—	4	4	no	—
202	C₂²×C₁₀₁	—	4	2	no	—
203	C₂²×C₁₀₁	—	4	2	no	—
204	C₂²×C₁₀₁	—	4	2	no	—
205	C₂²×C₁₀₁	—	8	4	no	—
206	C₂²×C₁₀₁	—	8	2	no	—
207	C₂²×C₁₀₁	—	16	4	no	—
208	C₂²×C₁₀₁	C₂×#120	1	1	yes	characteristic
209	C₄×C₁₀₁	—	2	2	no	—
210	C₄×C₁₀₁	—	2	4	no	—
211	C₄×C₁₀₁	—	2	1	no	—
212	C₄×C₁₀₁	—	4	2	no	—
213	C₄×C₁₀₁	—	4	2	no	—
214	C₄×C₁₀₁	—	4	2	no	—
215	C₄×C₁₀₁	#453	1	2	yes	—
216	C₄×C₁₀₁	C₂×AGL(1,ℤ/8)	1	2	yes	—
217	C₄×C₁₀₁	#575	1	2	yes	—
218	#18548	C₁₀₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
219	C₂×C₁₀₁	—	4	1	no	—
220	C₂×C₁₀₁	—	8	2	no	—
221	C₂×C₁₀₁	—	8	2	no	—
222	C₂×C₁₀₁	—	16	2	no	—
223	C₂×C₁₀₁	#3006	1	2	yes	—
224	C₂×C₁₀₁	C₂×#453	1	1	yes	characteristic
225	#3483	C₂×C₁₀₁	1	1	yes	characteristic, complemented
226	#3151	C₂×C₁₀₁	1	1	yes	characteristic, complemented
227	#3038	C₂×C₁₀₁	1	2	yes	complemented
228	#1624	C₂×C₁₀₁	1	2	yes	complemented
229	#1623	C₂×C₁₀₁	1	2	yes	complemented
230	#1621	C₂×C₁₀₁	1	4	yes	complemented
231	#1560	C₂×C₁₀₁	1	1	yes	characteristic, complemented
232	#1489	C₂×C₁₀₁	1	2	yes	complemented
233	C₁₀₁	#18548	1	1	yes	characteristic, direct product factor, Sylow
234	C₂×AGL(1,ℤ/8)	—	2	2	no	—
235	C₂×AGL(1,ℤ/8)	—	2	2	no	—
236	Q₈²	C₂²×C₁₀₁	1	1	yes	characteristic, complemented
237	#555	—	2	2	no	—
238	#555	—	2	2	no	—
239	#555	C₂²×C₁₀₁	1	1	yes	characteristic, complemented
240	#550	—	2	2	no	—
241	#550	C₂²×C₁₀₁	1	2	yes	complemented
242	#532	—	2	2	no	—
243	#532	—	2	2	no	—
244	#532	C₂²×C₁₀₁	1	1	yes	characteristic
245	C₂×#127	C₂²×C₁₀₁	1	1	yes	characteristic
246	C₄×#41	—	2	2	no	—
247	C₄×#41	C₂²×C₁₀₁	1	2	yes	—
248	#496	—	2	2	no	—
249	#493	C₂²×C₁₀₁	1	2	yes	—
250	#492	C₂²×C₁₀₁	1	2	yes	—
251	#460	—	2	2	no	—
252	#460	C₂²×C₁₀₁	1	4	yes	—
253	#459	—	2	2	no	—
254	#459	C₂²×C₁₀₁	1	4	yes	—
255	#423	C₂²×C₁₀₁	1	2	yes	—
256	#418	—	2	2	no	—
257	C₄×M₁₆	C₂²×C₁₀₁	1	1	yes	characteristic
258	#333	C₂²×C₁₀₁	1	2	yes	complemented
259	#331	C₂²×C₁₀₁	1	2	yes	complemented
260	Q₈⋊C₈	C₂²×C₁₀₁	1	4	yes	complemented
261	D₄⋊C₈	C₂²×C₁₀₁	1	4	yes	complemented
262	C₂×#41	—	2	2	no	—
263	C₂×#41	—	2	2	no	—
264	C₂×#41	D₄×C₁₀₁	1	2	yes	—
265	C₂×#41	D₄×C₁₀₁	1	2	yes	—
266	C₂²×D₄	—	2	1	no	—
267	C₂²×D₄	—	2	2	no	—
268	AGL(1,ℤ/8)	—	4	8	no	—
269	AGL(1,ℤ/8)	—	4	8	no	—
270	C₂×SD₁₆	—	2	4	no	—
271	C₂×SD₁₆	—	2	4	no	—
272	C₂×D₈	—	2	4	no	—
273	C₂×D₈	—	2	4	no	—
274	C₂×M₁₆	—	2	1	no	—
275	C₂×M₁₆	—	2	2	no	—
276	C₄⋊Q₈	—	2	2	no	—
277	C₄⋊Q₈	—	2	2	no	—
278	C₄⋊Q₈	C₂³×C₁₀₁	1	1	yes	characteristic
279	#127	—	2	2	no	—
280	#127	—	2	2	no	—
281	#127	—	2	2	no	—
282	#127	—	2	1	no	—
283	#127	C₂³×C₁₀₁	1	2	yes	—
284	#127	C₂³×C₁₀₁	1	1	yes	characteristic
285	#124	—	2	2	no	—
286	#124	—	2	4	no	—
287	#124	—	2	2	no	—
288	#124	D₄×C₁₀₁	1	2	yes	—
289	#121	—	2	4	no	—
290	#121	—	2	4	no	—
291	#121	—	2	2	no	—
292	#121	—	2	4	no	—
293	#121	—	2	2	no	—
294	#121	—	2	2	no	—
295	C₄×Q₈	—	2	2	no	—
296	C₄×Q₈	D₄×C₁₀₁	1	2	yes	—
297	C₄×Q₈	C₂³×C₁₀₁	1	2	yes	—
298	C₄×D₄	—	2	4	no	—
299	C₄×D₄	—	2	4	no	—
300	C₄×D₄	—	2	2	no	—
301	C₄×D₄	—	2	2	no	—
302	C₄×D₄	—	2	2	no	—
303	C₄×D₄	—	2	2	no	—
304	C₄×D₄	D₄×C₁₀₁	1	2	yes	—
305	C₄×D₄	C₂³×C₁₀₁	1	2	yes	—
306	#117	—	2	4	no	—
307	#117	—	2	2	no	—
308	#117	—	2	2	no	—
309	#117	D₄×C₁₀₁	1	2	yes	—
310	C₂×C₄²	—	2	2	no	—
311	C₂×C₄²	—	2	2	no	—
312	C₂×C₄²	C₂³×C₁₀₁	1	1	yes	characteristic
313	C₄⋊C₈	—	2	2	no	—
314	C₄⋊C₈	C₂³×C₁₀₁	1	4	yes	—
315	#102	—	2	4	no	—
316	#102	—	2	4	no	—
317	#97	—	2	1	no	—
318	C₄×C₈	C₂³×C₁₀₁	1	2	yes	—
319	C₂⁴	—	4	1	no	—
320	#41	—	2	4	no	—
321	#41	—	4	2	no	—
322	#41	—	4	4	no	—
323	#41	—	4	4	no	—
324	#41	—	4	4	no	—
325	#41	—	8	4	no	—
326	C₂×Q₈	—	2	2	no	—
327	C₂×Q₈	C₂×D₄×C₁₀₁	1	2	yes	—
328	C₂×Q₈	C₂×D₄×C₁₀₁	1	2	yes	—
329	C₂×D₄	—	2	4	no	—
330	C₂×D₄	—	2	2	no	—
331	C₂×D₄	—	2	2	no	—
332	C₂×D₄	—	2	4	no	—
333	C₂×D₄	—	2	2	no	—
334	C₂×D₄	—	2	2	no	—
335	C₂×D₄	—	2	4	no	—
336	C₂×D₄	—	2	2	no	—
337	C₂×D₄	—	4	4	no	—
338	C₂×D₄	—	4	4	no	—
339	C₂×D₄	—	4	4	no	—
340	C₂×D₄	—	4	2	no	—
341	C₂×D₄	—	4	1	no	—
342	C₂×D₄	C₂×D₄×C₁₀₁	1	2	yes	—
343	C₂×D₄	C₂×D₄×C₁₀₁	1	2	yes	—
344	C₂²×C₄	—	2	4	no	—
345	C₂²×C₄	—	2	2	no	—
346	C₂²×C₄	—	2	2	no	—
347	C₂²×C₄	—	2	2	no	—
348	C₂²×C₄	—	2	2	no	—
349	C₂²×C₄	C₂×D₄×C₁₀₁	1	2	yes	—
350	C₂²×C₄	C₂×D₄×C₁₀₁	1	1	yes	characteristic
351	SD₁₆	—	4	8	no	—
352	SD₁₆	—	4	8	no	—
353	D₈	—	4	8	no	—
354	D₈	—	4	8	no	—
355	M₁₆	—	2	4	no	—
356	M₁₆	—	4	4	no	—
357	C₂×C₈	—	2	2	no	—
358	C₂×C₈	—	2	4	no	—
359	C₄⋊C₄	—	2	4	no	—
360	C₄⋊C₄	—	2	2	no	—
361	C₄⋊C₄	—	2	2	no	—
362	C₄⋊C₄	—	2	2	no	—
363	C₄⋊C₄	C₂×D₄×C₁₀₁	1	2	yes	—
364	C₄⋊C₄	C₂×D₄×C₁₀₁	1	2	yes	—
365	C₂²⋊C₄	—	2	4	no	—
366	C₂²⋊C₄	—	2	4	no	—
367	C₂²⋊C₄	—	2	2	no	—
368	C₂²⋊C₄	—	2	4	no	—
369	C₂²⋊C₄	—	2	2	no	—
370	C₂²⋊C₄	—	2	2	no	—
371	C₄²	—	2	2	no	—
372	C₄²	—	2	2	no	—
373	C₄²	—	2	2	no	—
374	C₄²	—	2	2	no	—
375	C₄²	—	2	2	no	—
376	C₄²	C₂×D₄×C₁₀₁	1	1	yes	characteristic
377	C₄²	C₂×D₄×C₁₀₁	1	2	yes	—
378	C₄²	C₂⁴×C₁₀₁	1	1	yes	characteristic
379	C₂³	—	2	2	no	—
380	C₂³	—	2	2	no	—
381	C₂³	—	4	2	no	—
382	C₂³	—	8	4	no	—
383	C₂³	—	8	2	no	—
384	C₂³	#120×C₁₀₁	1	1	yes	characteristic
385	Q₈	—	2	2	no	—
386	Q₈	—	4	2	no	—
387	Q₈	—	8	2	no	—
388	Q₈	AGL(1,ℤ/8)×C₁₀₁	1	4	yes	complemented
389	D₄	—	2	2	no	—
390	D₄	—	2	2	no	—
391	D₄	—	4	4	no	—
392	D₄	—	4	2	no	—
393	D₄	—	4	8	no	—
394	D₄	—	4	4	no	—
395	D₄	—	4	2	no	—
396	D₄	—	4	4	no	—
397	D₄	—	4	2	no	—
398	D₄	—	4	4	no	—
399	D₄	—	8	4	no	—
400	D₄	—	8	2	no	—
401	D₄	—	8	2	no	—
402	D₄	—	8	4	no	—
403	D₄	—	8	2	no	—
404	C₂×C₄	—	2	2	no	—
405	C₂×C₄	—	2	2	no	—
406	C₂×C₄	—	2	2	no	—
407	C₂×C₄	—	2	2	no	—
408	C₂×C₄	—	2	2	no	—
409	C₂×C₄	—	2	2	no	—
410	C₂×C₄	—	2	2	no	—
411	C₂×C₄	—	4	4	no	—
412	C₂×C₄	—	4	8	no	—
413	C₂×C₄	—	4	4	no	—
414	C₂×C₄	—	4	4	no	—
415	C₂×C₄	—	4	2	no	—
416	C₂×C₄	—	4	2	no	—
417	C₂×C₄	#120×C₁₀₁	1	2	yes	—
418	C₂×C₄	#120×C₁₀₁	1	1	yes	characteristic
419	C₂×C₄	C₂²×D₄×C₁₀₁	1	1	yes	characteristic
420	C₂×C₄	C₂²×D₄×C₁₀₁	1	2	yes	—
421	C₈	—	2	4	no	—
422	C₈	—	4	4	no	—
423	C₂²	—	2	2	no	—
424	C₂²	—	2	1	no	—
425	C₂²	—	4	2	no	—
426	C₂²	—	4	4	no	—
427	C₂²	—	4	2	no	—
428	C₂²	—	4	2	no	—
429	C₂²	—	4	2	no	—
430	C₂²	—	8	4	no	—
431	C₂²	—	8	2	no	—
432	C₂²	—	16	4	no	—
433	C₂²	C₂×#120×C₁₀₁	1	1	yes	characteristic
434	C₄	—	2	2	no	—
435	C₄	—	2	4	no	—
436	C₄	—	2	1	no	—
437	C₄	—	4	2	no	—
438	C₄	—	4	2	no	—
439	C₄	—	4	2	no	—
440	C₄	#453×C₁₀₁	1	2	yes	—
441	C₄	C₂×AGL(1,ℤ/8)×C₁₀₁	1	2	yes	—
442	C₄	#575×C₁₀₁	1	2	yes	—
443	C₂	—	4	1	no	—
444	C₂	—	8	2	no	—
445	C₂	—	8	2	no	—
446	C₂	—	16	2	no	—
447	C₂	C₁₀₁×#3006	1	2	yes	—
448	C₂	C₂×#453×C₁₀₁	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₀₁	C₂×#120
commutator, Frattini, cosocle	C₄²	C₂⁴×C₁₀₁
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
1. C₁₀₁×#3483	C₂	semidirect
2. C₁₀₁×#3151	C₂	semidirect
3. C₁₀₁×#3038	C₂	semidirect
4. C₁₀₁×#1624	C₂	semidirect
5. C₁₀₁×#1623	C₂	semidirect
6. C₁₀₁×#1621	C₂	semidirect
7. C₁₀₁×#1560	C₂	semidirect
8. C₁₀₁×#1489	C₂	semidirect
11. Q₈²×C₁₀₁	C₂²	semidirect
14. #555×C₁₀₁	C₂²	semidirect
16. #550×C₁₀₁	C₂²	semidirect
33. #333×C₁₀₁	C₂²	semidirect
34. #331×C₁₀₁	C₂²	semidirect
35. Q₈⋊C₈×C₁₀₁	C₂²	semidirect
36. D₄⋊C₈×C₁₀₁	C₂²	semidirect
163. Q₈×C₁₀₁	AGL(1,ℤ/8)	semidirect
218. #18548	C₁₀₁	direct (N × H)
225. #3483	C₂×C₁₀₁	semidirect
226. #3151	C₂×C₁₀₁	semidirect
227. #3038	C₂×C₁₀₁	semidirect
228. #1624	C₂×C₁₀₁	semidirect
229. #1623	C₂×C₁₀₁	semidirect
230. #1621	C₂×C₁₀₁	semidirect
231. #1560	C₂×C₁₀₁	semidirect
232. #1489	C₂×C₁₀₁	semidirect
233. C₁₀₁	#18548	direct (N × H)
236. Q₈²	C₂²×C₁₀₁	semidirect
239. #555	C₂²×C₁₀₁	semidirect
241. #550	C₂²×C₁₀₁	semidirect
258. #333	C₂²×C₁₀₁	semidirect
259. #331	C₂²×C₁₀₁	semidirect
260. Q₈⋊C₈	C₂²×C₁₀₁	semidirect
261. D₄⋊C₈	C₂²×C₁₀₁	semidirect
388. Q₈	AGL(1,ℤ/8)×C₁₀₁	semidirect

Maximal subgroups

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

subgroup	index
C₁₀₁×#3483	2
C₁₀₁×#3151	2
C₁₀₁×#3038	2
C₁₀₁×#1624	2
C₁₀₁×#1623	2
C₁₀₁×#1621	2
C₁₀₁×#1560	2
C₁₀₁×#1489	2
#18548	101

Subgroups — C101×#18548 #38800699

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₀₁×#18548 #38800699