Subgroups — C₁₀₁×#18524 #38800675

Order 25856.

1716 conjugacy classes of subgroups.

The subgroup lattice has 368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₄²×C₁₀₁	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₀₁×#3151	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₀₁×#3109	C₂	1	2	yes	maximal, complemented
4	C₁₀₁×#1629	C₂	1	4	yes	maximal, complemented
5	C₁₀₁×#1619	C₂	1	4	yes	maximal, complemented
6	C₁₀₁×#1555	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₀₁×#1490	C₂	1	2	yes	maximal, complemented
8	C₂³×D₄×C₁₀₁	—	2	2	no	—
9	C₂×AGL(1,ℤ/8)×C₁₀₁	—	2	2	no	—
10	D₄²×C₁₀₁	—	2	2	no	—
11	D₄²×C₁₀₁	—	2	4	no	—
12	D₄²×C₁₀₁	C₂²	1	4	yes	—
13	#532×C₁₀₁	C₂²	1	1	yes	characteristic, complemented
14	C₂×#127×C₁₀₁	C₂²	1	1	yes	characteristic
15	C₂×#121×C₁₀₁	—	2	2	no	—
16	C₂×#120×C₁₀₁	—	2	2	no	—
17	C₂×C₄×D₄×C₁₀₁	C₂²	1	2	yes	—
18	#496×C₁₀₁	—	2	2	no	—
19	#493×C₁₀₁	C₂²	1	2	yes	complemented
20	#492×C₁₀₁	C₂²	1	2	yes	complemented
21	#481×C₁₀₁	—	2	2	no	—
22	#476×C₁₀₁	C₂²	1	4	yes	complemented
23	#459×C₁₀₁	C₂²	1	4	yes	complemented
24	#447×C₁₀₁	—	2	2	no	—
25	#442×C₁₀₁	—	2	4	no	—
26	#432×C₁₀₁	C₂²	1	2	yes	complemented
27	C₄×M₁₆×C₁₀₁	C₂²	1	1	yes	characteristic, complemented
28	#331×C₁₀₁	C₂²	1	4	yes	complemented
29	D₄⋊C₈×C₁₀₁	C₂²	1	8	yes	complemented
30	C₂⁵×C₁₀₁	—	2	2	no	—
31	C₂×#41×C₁₀₁	—	2	1	no	—
32	C₂²×D₄×C₁₀₁	—	2	4	no	—
33	C₂²×D₄×C₁₀₁	—	2	8	no	—
34	C₂²×D₄×C₁₀₁	—	2	8	no	—
35	C₂²×D₄×C₁₀₁	—	2	2	no	—
36	C₂²×D₄×C₁₀₁	—	4	16	no	—
37	C₂²×D₄×C₁₀₁	D₄	1	2	yes	—
38	C₂²×D₄×C₁₀₁	D₄	1	2	yes	—
39	C₂³×C₄×C₁₀₁	—	2	2	no	—
40	AGL(1,ℤ/8)×C₁₀₁	—	4	8	no	—
41	C₂×SD₁₆×C₁₀₁	—	2	4	no	—
42	C₂×D₈×C₁₀₁	—	2	4	no	—
43	C₂×D₈×C₁₀₁	—	2	4	no	—
44	C₂×M₁₆×C₁₀₁	—	2	1	no	—
45	C₄⋊Q₈×C₁₀₁	C₂³	1	1	yes	characteristic, complemented
46	#127×C₁₀₁	—	2	2	no	—
47	#127×C₁₀₁	D₄	1	2	yes	—
48	#127×C₁₀₁	C₂³	1	2	yes	—
49	#127×C₁₀₁	C₂³	1	1	yes	characteristic, complemented
50	#124×C₁₀₁	—	2	1	no	—
51	#121×C₁₀₁	—	2	8	no	—
52	#121×C₁₀₁	—	2	8	no	—
53	#121×C₁₀₁	—	2	2	no	—
54	#120×C₁₀₁	—	2	8	no	—
55	#120×C₁₀₁	—	2	8	no	—
56	C₄×D₄×C₁₀₁	—	2	2	no	—
57	C₄×D₄×C₁₀₁	—	2	2	no	—
58	C₄×D₄×C₁₀₁	—	2	2	no	—
59	C₄×D₄×C₁₀₁	D₄	1	4	yes	—
60	C₄×D₄×C₁₀₁	C₂³	1	4	yes	—
61	C₂×C₄⋊C₄×C₁₀₁	D₄	1	2	yes	—
62	C₂×C₂²⋊C₄×C₁₀₁	—	2	2	no	—
63	C₂×C₂²⋊C₄×C₁₀₁	—	2	2	no	—
64	C₂×C₄²×C₁₀₁	C₂³	1	1	yes	characteristic
65	#106×C₁₀₁	—	2	4	no	—
66	C₄⋊C₈×C₁₀₁	C₂³	1	4	yes	complemented
67	#102×C₁₀₁	—	2	4	no	—
68	#102×C₁₀₁	—	2	4	no	—
69	C₂²⋊C₈×C₁₀₁	—	2	2	no	—
70	#97×C₁₀₁	—	2	1	no	—
71	#97×C₁₀₁	—	2	2	no	—
72	C₄×C₈×C₁₀₁	C₂³	1	2	yes	complemented
73	C₂⁴×C₁₀₁	—	2	2	no	—
74	C₂⁴×C₁₀₁	—	2	8	no	—
75	C₂⁴×C₁₀₁	—	2	2	no	—
76	C₂⁴×C₁₀₁	—	4	16	no	—
77	C₂⁴×C₁₀₁	—	8	4	no	—
78	#41×C₁₀₁	—	4	4	no	—
79	C₂×Q₈×C₁₀₁	—	2	1	no	—
80	C₂×D₄×C₁₀₁	—	2	8	no	—
81	C₂×D₄×C₁₀₁	—	2	16	no	—
82	C₂×D₄×C₁₀₁	—	2	2	no	—
83	C₂×D₄×C₁₀₁	—	2	4	no	—
84	C₂×D₄×C₁₀₁	—	2	2	no	—
85	C₂×D₄×C₁₀₁	—	2	4	no	—
86	C₂×D₄×C₁₀₁	—	2	2	no	—
87	C₂×D₄×C₁₀₁	—	2	1	no	—
88	C₂×D₄×C₁₀₁	—	4	8	no	—
89	C₂×D₄×C₁₀₁	—	4	4	no	—
90	C₂×D₄×C₁₀₁	—	4	32	no	—
91	C₂×D₄×C₁₀₁	—	4	16	no	—
92	C₂×D₄×C₁₀₁	—	4	16	no	—
93	C₂×D₄×C₁₀₁	—	4	16	no	—
94	C₂×D₄×C₁₀₁	—	4	1	no	—
95	C₂×D₄×C₁₀₁	C₂×D₄	1	4	yes	—
96	C₂×D₄×C₁₀₁	C₂×D₄	1	4	yes	—
97	C₂²×C₄×C₁₀₁	—	2	2	no	—
98	C₂²×C₄×C₁₀₁	—	2	4	no	—
99	C₂²×C₄×C₁₀₁	—	2	4	no	—
100	C₂²×C₄×C₁₀₁	—	4	8	no	—
101	C₂²×C₄×C₁₀₁	—	4	1	no	—
102	C₂²×C₄×C₁₀₁	C₂×D₄	1	2	yes	—
103	C₂²×C₄×C₁₀₁	C₂×D₄	1	1	yes	characteristic
104	SD₁₆×C₁₀₁	—	4	8	no	—
105	D₈×C₁₀₁	—	4	8	no	—
106	D₈×C₁₀₁	—	4	8	no	—
107	M₁₆×C₁₀₁	—	2	4	no	—
108	C₂×C₈×C₁₀₁	—	2	2	no	—
109	C₂×C₈×C₁₀₁	—	2	4	no	—
110	C₄⋊C₄×C₁₀₁	—	2	2	no	—
111	C₄⋊C₄×C₁₀₁	—	2	2	no	—
112	C₄⋊C₄×C₁₀₁	C₂×D₄	1	4	yes	—
113	C₂²⋊C₄×C₁₀₁	—	2	8	no	—
114	C₂²⋊C₄×C₁₀₁	—	2	4	no	—
115	C₂²⋊C₄×C₁₀₁	—	2	4	no	—
116	C₂²⋊C₄×C₁₀₁	—	4	2	no	—
117	C₄²×C₁₀₁	C₂×D₄	1	2	yes	—
118	C₄²×C₁₀₁	C₂×D₄	1	1	yes	characteristic
119	C₄²×C₁₀₁	C₂⁴	1	1	yes	characteristic
120	C₂³×C₁₀₁	—	2	8	no	—
121	C₂³×C₁₀₁	—	2	4	no	—
122	C₂³×C₁₀₁	—	2	4	no	—
123	C₂³×C₁₀₁	—	4	4	no	—
124	C₂³×C₁₀₁	—	4	8	no	—
125	C₂³×C₁₀₁	—	4	32	no	—
126	C₂³×C₁₀₁	—	4	4	no	—
127	C₂³×C₁₀₁	—	4	4	no	—
128	C₂³×C₁₀₁	—	4	1	no	—
129	C₂³×C₁₀₁	—	8	8	no	—
130	C₂³×C₁₀₁	—	8	32	no	—
131	C₂³×C₁₀₁	#120	1	1	yes	characteristic
132	Q₈×C₁₀₁	—	4	2	no	—
133	D₄×C₁₀₁	—	2	8	no	—
134	D₄×C₁₀₁	—	2	4	no	—
135	D₄×C₁₀₁	—	4	4	no	—
136	D₄×C₁₀₁	—	4	8	no	—
137	D₄×C₁₀₁	—	4	2	no	—
138	D₄×C₁₀₁	—	4	32	no	—
139	D₄×C₁₀₁	—	4	8	no	—
140	D₄×C₁₀₁	—	4	4	no	—
141	D₄×C₁₀₁	—	8	2	no	—
142	D₄×C₁₀₁	—	8	2	no	—
143	D₄×C₁₀₁	AGL(1,ℤ/8)	1	8	yes	complemented
144	C₂×C₄×C₁₀₁	—	2	2	no	—
145	C₂×C₄×C₁₀₁	—	2	4	no	—
146	C₂×C₄×C₁₀₁	—	2	4	no	—
147	C₂×C₄×C₁₀₁	—	4	8	no	—
148	C₂×C₄×C₁₀₁	—	4	4	no	—
149	C₂×C₄×C₁₀₁	—	4	8	no	—
150	C₂×C₄×C₁₀₁	—	4	1	no	—
151	C₂×C₄×C₁₀₁	—	8	2	no	—
152	C₂×C₄×C₁₀₁	#120	1	1	yes	characteristic
153	C₂×C₄×C₁₀₁	#120	1	2	yes	—
154	C₂×C₄×C₁₀₁	C₂²×D₄	1	1	yes	characteristic
155	C₂×C₄×C₁₀₁	C₂²×D₄	1	2	yes	—
156	C₈×C₁₀₁	—	2	4	no	—
157	C₈×C₁₀₁	—	4	4	no	—
158	C₂²×C₁₀₁	—	2	2	no	—
159	C₂²×C₁₀₁	—	2	8	no	—
160	C₂²×C₁₀₁	—	4	16	no	—
161	C₂²×C₁₀₁	—	4	4	no	—
162	C₂²×C₁₀₁	—	4	4	no	—
163	C₂²×C₁₀₁	—	4	8	no	—
164	C₂²×C₁₀₁	—	4	4	no	—
165	C₂²×C₁₀₁	—	8	8	no	—
166	C₂²×C₁₀₁	—	8	32	no	—
167	C₂²×C₁₀₁	—	8	2	no	—
168	C₂²×C₁₀₁	—	8	1	no	—
169	C₂²×C₁₀₁	#453	1	2	yes	—
170	C₂²×C₁₀₁	C₂×#120	1	1	yes	characteristic
171	C₄×C₁₀₁	—	2	2	no	—
172	C₄×C₁₀₁	—	2	1	no	—
173	C₄×C₁₀₁	—	2	1	no	—
174	C₄×C₁₀₁	—	4	4	no	—
175	C₄×C₁₀₁	—	8	1	no	—
176	C₄×C₁₀₁	C₂×AGL(1,ℤ/8)	1	4	yes	—
177	#18524	C₁₀₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
178	C₂×C₁₀₁	—	2	2	no	—
179	C₂×C₁₀₁	—	4	8	no	—
180	C₂×C₁₀₁	—	8	4	no	—
181	C₂×C₁₀₁	—	16	1	no	—
182	C₂×C₁₀₁	#3003	1	2	yes	—
183	C₂×C₁₀₁	C₂×#453	1	1	yes	characteristic
184	C₂×D₄²	C₂×C₁₀₁	1	1	yes	characteristic, complemented
185	#3151	C₂×C₁₀₁	1	1	yes	characteristic, complemented
186	#3109	C₂×C₁₀₁	1	2	yes	complemented
187	#1629	C₂×C₁₀₁	1	4	yes	complemented
188	#1619	C₂×C₁₀₁	1	4	yes	complemented
189	#1555	C₂×C₁₀₁	1	1	yes	characteristic, complemented
190	#1490	C₂×C₁₀₁	1	2	yes	complemented
191	C₁₀₁	#18524	1	1	yes	characteristic, direct product factor, Sylow
192	C₂³×D₄	—	2	2	no	—
193	C₂×AGL(1,ℤ/8)	—	2	2	no	—
194	D₄²	—	2	2	no	—
195	D₄²	—	2	4	no	—
196	D₄²	C₂²×C₁₀₁	1	4	yes	—
197	#532	C₂²×C₁₀₁	1	1	yes	characteristic, complemented
198	C₂×#127	C₂²×C₁₀₁	1	1	yes	characteristic
199	C₂×#121	—	2	2	no	—
200	C₂×#120	—	2	2	no	—
201	C₂×C₄×D₄	C₂²×C₁₀₁	1	2	yes	—
202	#496	—	2	2	no	—
203	#493	C₂²×C₁₀₁	1	2	yes	complemented
204	#492	C₂²×C₁₀₁	1	2	yes	complemented
205	#481	—	2	2	no	—
206	#476	C₂²×C₁₀₁	1	4	yes	complemented
207	#459	C₂²×C₁₀₁	1	4	yes	complemented
208	#447	—	2	2	no	—
209	#442	—	2	4	no	—
210	#432	C₂²×C₁₀₁	1	2	yes	complemented
211	C₄×M₁₆	C₂²×C₁₀₁	1	1	yes	characteristic, complemented
212	#331	C₂²×C₁₀₁	1	4	yes	complemented
213	D₄⋊C₈	C₂²×C₁₀₁	1	8	yes	complemented
214	C₂⁵	—	2	2	no	—
215	C₂×#41	—	2	1	no	—
216	C₂²×D₄	—	2	4	no	—
217	C₂²×D₄	—	2	8	no	—
218	C₂²×D₄	—	2	8	no	—
219	C₂²×D₄	—	2	2	no	—
220	C₂²×D₄	—	4	16	no	—
221	C₂²×D₄	D₄×C₁₀₁	1	2	yes	—
222	C₂²×D₄	D₄×C₁₀₁	1	2	yes	—
223	C₂³×C₄	—	2	2	no	—
224	AGL(1,ℤ/8)	—	4	8	no	—
225	C₂×SD₁₆	—	2	4	no	—
226	C₂×D₈	—	2	4	no	—
227	C₂×D₈	—	2	4	no	—
228	C₂×M₁₆	—	2	1	no	—
229	C₄⋊Q₈	C₂³×C₁₀₁	1	1	yes	characteristic, complemented
230	#127	—	2	2	no	—
231	#127	D₄×C₁₀₁	1	2	yes	—
232	#127	C₂³×C₁₀₁	1	2	yes	—
233	#127	C₂³×C₁₀₁	1	1	yes	characteristic, complemented
234	#124	—	2	1	no	—
235	#121	—	2	8	no	—
236	#121	—	2	8	no	—
237	#121	—	2	2	no	—
238	#120	—	2	8	no	—
239	#120	—	2	8	no	—
240	C₄×D₄	—	2	2	no	—
241	C₄×D₄	—	2	2	no	—
242	C₄×D₄	—	2	2	no	—
243	C₄×D₄	D₄×C₁₀₁	1	4	yes	—
244	C₄×D₄	C₂³×C₁₀₁	1	4	yes	—
245	C₂×C₄⋊C₄	D₄×C₁₀₁	1	2	yes	—
246	C₂×C₂²⋊C₄	—	2	2	no	—
247	C₂×C₂²⋊C₄	—	2	2	no	—
248	C₂×C₄²	C₂³×C₁₀₁	1	1	yes	characteristic
249	#106	—	2	4	no	—
250	C₄⋊C₈	C₂³×C₁₀₁	1	4	yes	complemented
251	#102	—	2	4	no	—
252	#102	—	2	4	no	—
253	C₂²⋊C₈	—	2	2	no	—
254	#97	—	2	1	no	—
255	#97	—	2	2	no	—
256	C₄×C₈	C₂³×C₁₀₁	1	2	yes	complemented
257	C₂⁴	—	2	2	no	—
258	C₂⁴	—	2	8	no	—
259	C₂⁴	—	2	2	no	—
260	C₂⁴	—	4	16	no	—
261	C₂⁴	—	8	4	no	—
262	#41	—	4	4	no	—
263	C₂×Q₈	—	2	1	no	—
264	C₂×D₄	—	2	8	no	—
265	C₂×D₄	—	2	16	no	—
266	C₂×D₄	—	2	2	no	—
267	C₂×D₄	—	2	4	no	—
268	C₂×D₄	—	2	2	no	—
269	C₂×D₄	—	2	4	no	—
270	C₂×D₄	—	2	2	no	—
271	C₂×D₄	—	2	1	no	—
272	C₂×D₄	—	4	8	no	—
273	C₂×D₄	—	4	4	no	—
274	C₂×D₄	—	4	32	no	—
275	C₂×D₄	—	4	16	no	—
276	C₂×D₄	—	4	16	no	—
277	C₂×D₄	—	4	16	no	—
278	C₂×D₄	—	4	1	no	—
279	C₂×D₄	C₂×D₄×C₁₀₁	1	4	yes	—
280	C₂×D₄	C₂×D₄×C₁₀₁	1	4	yes	—
281	C₂²×C₄	—	2	2	no	—
282	C₂²×C₄	—	2	4	no	—
283	C₂²×C₄	—	2	4	no	—
284	C₂²×C₄	—	4	8	no	—
285	C₂²×C₄	—	4	1	no	—
286	C₂²×C₄	C₂×D₄×C₁₀₁	1	2	yes	—
287	C₂²×C₄	C₂×D₄×C₁₀₁	1	1	yes	characteristic
288	SD₁₆	—	4	8	no	—
289	D₈	—	4	8	no	—
290	D₈	—	4	8	no	—
291	M₁₆	—	2	4	no	—
292	C₂×C₈	—	2	2	no	—
293	C₂×C₈	—	2	4	no	—
294	C₄⋊C₄	—	2	2	no	—
295	C₄⋊C₄	—	2	2	no	—
296	C₄⋊C₄	C₂×D₄×C₁₀₁	1	4	yes	—
297	C₂²⋊C₄	—	2	8	no	—
298	C₂²⋊C₄	—	2	4	no	—
299	C₂²⋊C₄	—	2	4	no	—
300	C₂²⋊C₄	—	4	2	no	—
301	C₄²	C₂×D₄×C₁₀₁	1	2	yes	—
302	C₄²	C₂×D₄×C₁₀₁	1	1	yes	characteristic
303	C₄²	C₂⁴×C₁₀₁	1	1	yes	characteristic
304	C₂³	—	2	8	no	—
305	C₂³	—	2	4	no	—
306	C₂³	—	2	4	no	—
307	C₂³	—	4	4	no	—
308	C₂³	—	4	8	no	—
309	C₂³	—	4	32	no	—
310	C₂³	—	4	4	no	—
311	C₂³	—	4	4	no	—
312	C₂³	—	4	1	no	—
313	C₂³	—	8	8	no	—
314	C₂³	—	8	32	no	—
315	C₂³	#120×C₁₀₁	1	1	yes	characteristic
316	Q₈	—	4	2	no	—
317	D₄	—	2	8	no	—
318	D₄	—	2	4	no	—
319	D₄	—	4	4	no	—
320	D₄	—	4	8	no	—
321	D₄	—	4	2	no	—
322	D₄	—	4	32	no	—
323	D₄	—	4	8	no	—
324	D₄	—	4	4	no	—
325	D₄	—	8	2	no	—
326	D₄	—	8	2	no	—
327	D₄	AGL(1,ℤ/8)×C₁₀₁	1	8	yes	complemented
328	C₂×C₄	—	2	2	no	—
329	C₂×C₄	—	2	4	no	—
330	C₂×C₄	—	2	4	no	—
331	C₂×C₄	—	4	8	no	—
332	C₂×C₄	—	4	4	no	—
333	C₂×C₄	—	4	8	no	—
334	C₂×C₄	—	4	1	no	—
335	C₂×C₄	—	8	2	no	—
336	C₂×C₄	#120×C₁₀₁	1	1	yes	characteristic
337	C₂×C₄	#120×C₁₀₁	1	2	yes	—
338	C₂×C₄	C₂²×D₄×C₁₀₁	1	1	yes	characteristic
339	C₂×C₄	C₂²×D₄×C₁₀₁	1	2	yes	—
340	C₈	—	2	4	no	—
341	C₈	—	4	4	no	—
342	C₂²	—	2	2	no	—
343	C₂²	—	2	8	no	—
344	C₂²	—	4	16	no	—
345	C₂²	—	4	4	no	—
346	C₂²	—	4	4	no	—
347	C₂²	—	4	8	no	—
348	C₂²	—	4	4	no	—
349	C₂²	—	8	8	no	—
350	C₂²	—	8	32	no	—
351	C₂²	—	8	2	no	—
352	C₂²	—	8	1	no	—
353	C₂²	#453×C₁₀₁	1	2	yes	—
354	C₂²	C₂×#120×C₁₀₁	1	1	yes	characteristic
355	C₄	—	2	2	no	—
356	C₄	—	2	1	no	—
357	C₄	—	2	1	no	—
358	C₄	—	4	4	no	—
359	C₄	—	8	1	no	—
360	C₄	C₂×AGL(1,ℤ/8)×C₁₀₁	1	4	yes	—
361	C₂	—	2	2	no	—
362	C₂	—	4	8	no	—
363	C₂	—	8	4	no	—
364	C₂	—	16	1	no	—
365	C₂	C₁₀₁×#3003	1	2	yes	—
366	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. C₂×D₄²×C₁₀₁	C₂	semidirect
2. C₁₀₁×#3151	C₂	semidirect
3. C₁₀₁×#3109	C₂	semidirect
4. C₁₀₁×#1629	C₂	semidirect
5. C₁₀₁×#1619	C₂	semidirect
6. C₁₀₁×#1555	C₂	semidirect
7. C₁₀₁×#1490	C₂	semidirect
13. #532×C₁₀₁	C₂²	semidirect
19. #493×C₁₀₁	C₂²	semidirect
20. #492×C₁₀₁	C₂²	semidirect
22. #476×C₁₀₁	C₂²	semidirect
23. #459×C₁₀₁	C₂²	semidirect
26. #432×C₁₀₁	C₂²	semidirect
27. C₄×M₁₆×C₁₀₁	C₂²	semidirect
28. #331×C₁₀₁	C₂²	semidirect
29. D₄⋊C₈×C₁₀₁	C₂²	semidirect
45. C₄⋊Q₈×C₁₀₁	C₂³	semidirect
49. #127×C₁₀₁	C₂³	semidirect
66. C₄⋊C₈×C₁₀₁	C₂³	semidirect
72. C₄×C₈×C₁₀₁	C₂³	semidirect
143. D₄×C₁₀₁	AGL(1,ℤ/8)	semidirect
177. #18524	C₁₀₁	direct (N × H)
184. C₂×D₄²	C₂×C₁₀₁	semidirect
185. #3151	C₂×C₁₀₁	semidirect
186. #3109	C₂×C₁₀₁	semidirect
187. #1629	C₂×C₁₀₁	semidirect
188. #1619	C₂×C₁₀₁	semidirect
189. #1555	C₂×C₁₀₁	semidirect
190. #1490	C₂×C₁₀₁	semidirect
191. C₁₀₁	#18524	direct (N × H)
197. #532	C₂²×C₁₀₁	semidirect
203. #493	C₂²×C₁₀₁	semidirect
204. #492	C₂²×C₁₀₁	semidirect
206. #476	C₂²×C₁₀₁	semidirect
207. #459	C₂²×C₁₀₁	semidirect
210. #432	C₂²×C₁₀₁	semidirect
211. C₄×M₁₆	C₂²×C₁₀₁	semidirect
212. #331	C₂²×C₁₀₁	semidirect
213. D₄⋊C₈	C₂²×C₁₀₁	semidirect
229. C₄⋊Q₈	C₂³×C₁₀₁	semidirect
233. #127	C₂³×C₁₀₁	semidirect
250. C₄⋊C₈	C₂³×C₁₀₁	semidirect
256. C₄×C₈	C₂³×C₁₀₁	semidirect
327. D₄	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
C₂×D₄²×C₁₀₁	2
C₁₀₁×#3151	2
C₁₀₁×#3109	2
C₁₀₁×#1629	2
C₁₀₁×#1619	2
C₁₀₁×#1555	2
C₁₀₁×#1490	2
#18524	101

Subgroups — C101×#18524 #38800675

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₀₁×#18524 #38800675