Subgroups — #537×D₁₀₁ #27184452

Order 12928.

1640 conjugacy classes of subgroups.

The subgroup lattice has 356 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#41×D₁₀₁	C₂	1	2	yes	maximal, complemented
2	#20265758	C₂	1	1	yes	maximal, characteristic, complemented
3	#20265757	C₂	1	4	yes	maximal, complemented
4	#20265756	C₂	1	4	yes	maximal, complemented
5	#20265755	C₂	1	2	yes	maximal, complemented
6	#20265754	C₂	1	4	yes	maximal, complemented
7	C₂²⋊Q₈×D₁₀₁	C₂	1	4	yes	maximal, complemented
8	#121×D₁₀₁	C₂	1	4	yes	maximal, complemented
9	#121×D₁₀₁	C₂	1	4	yes	maximal, complemented
10	C₂×C₄⋊C₄×D₁₀₁	C₂	1	1	yes	maximal, characteristic, complemented
11	#537×C₁₀₁	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#13108075	C₂²	1	2	yes	complemented
13	C₂×#13108074	C₂²	1	2	yes	complemented
14	C₂×#13108074	C₂²	1	4	yes	complemented
15	C₂×#13108073	C₂²	1	4	yes	complemented
16	C₂×#13108073	C₂²	1	2	yes	complemented
17	#41×D₁₀₁	—	2	16	no	—
18	C₂×Q₈×D₁₀₁	C₂²	1	2	yes	—
19	C₂×D₄×D₁₀₁	C₂²	1	2	yes	—
20	C₂×D₄×D₁₀₁	C₂²	1	4	yes	—
21	C₂×D₄×D₁₀₁	C₂²	1	4	yes	—
22	C₂²×C₄×D₁₀₁	C₂²	1	4	yes	—
23	C₂²×C₄×D₁₀₁	C₂²	1	2	yes	—
24	C₂²×C₄×D₁₀₁	C₂²	1	1	yes	characteristic
25	#15692235	C₂²	1	4	yes	complemented
26	#15692234	C₂²	1	4	yes	complemented
27	#15692233	C₂²	1	8	yes	complemented
28	#15692232	C₂²	1	8	yes	complemented
29	#15692231	C₂²	1	4	yes	complemented
30	#15692230	C₂²	1	4	yes	complemented
31	#15692230	C₂²	1	4	yes	complemented
32	#15692229	C₂²	1	4	yes	complemented
33	#15692229	C₂²	1	4	yes	complemented
34	#15692228	C₂²	1	8	yes	complemented
35	#15692228	C₂²	1	8	yes	complemented
36	#15692227	C₂²	1	8	yes	complemented
37	#15692227	C₂²	1	8	yes	complemented
38	#15692226	C₂²	1	4	yes	complemented
39	#15692226	C₂²	1	4	yes	complemented
40	C₂×C₄⋊Dic₁₀₁	C₂²	1	1	yes	characteristic, complemented
41	C₂×#13108053	C₂²	1	2	yes	complemented
42	C₄⋊C₄×D₁₀₁	C₂²	1	4	yes	—
43	C₄⋊C₄×D₁₀₁	C₂²	1	4	yes	—
44	C₄⋊C₄×D₁₀₁	C₂²	1	4	yes	complemented
45	C₂²⋊C₄×D₁₀₁	C₂²	1	8	yes	—
46	C₂×#41×C₁₀₁	C₂²	1	2	yes	complemented
47	C₂²⋊Q₈×C₁₀₁	C₂²	1	4	yes	complemented
48	#121×C₁₀₁	C₂²	1	4	yes	complemented
49	#121×C₁₀₁	C₂²	1	4	yes	complemented
50	C₂×C₄⋊C₄×C₁₀₁	C₂²	1	1	yes	characteristic, complemented
51	C₂³×D₁₀₁	C₂³	1	4	yes	—
52	C₂³×D₁₀₁	C₂³	1	1	yes	characteristic
53	#13108075	—	2	8	no	—
54	#13108074	—	2	8	no	—
55	#13108074	—	2	16	no	—
56	#13108073	—	2	16	no	—
57	#13108073	—	2	8	no	—
58	C₂×Dic₂₀₂	C₂³	1	4	yes	—
59	C₂×Dic₂₀₂	C₂³	1	2	yes	—
60	Q₈×D₁₀₁	—	2	8	no	—
61	C₂×D₄₀₄	C₂³	1	4	yes	—
62	C₂×D₄₀₄	C₂³	1	2	yes	—
63	C₂×D₄₀₄	C₂³	1	4	yes	—
64	C₂×C₂²⋊D₁₀₁	C₂³	1	4	yes	—
65	C₂×C₂²⋊D₁₀₁	C₂³	1	4	yes	—
66	C₂×C₂²⋊D₁₀₁	C₂³	1	4	yes	—
67	C₂×C₂²⋊D₁₀₁	C₂³	1	8	yes	—
68	D₄×D₁₀₁	—	2	16	no	—
69	D₄×D₁₀₁	—	2	8	no	—
70	D₄×D₁₀₁	—	4	8	no	—
71	C₂²×Dic₁₀₁	C₂³	1	4	yes	—
72	C₂²×Dic₁₀₁	C₂³	1	2	yes	—
73	C₂²×Dic₁₀₁	C₂³	1	1	yes	characteristic
74	C₂×C₄×D₁₀₁	—	2	16	no	—
75	C₂×C₄×D₁₀₁	—	4	4	no	—
76	C₂×C₄×D₁₀₁	D₄	1	8	yes	complemented
77	C₂×C₄×D₁₀₁	C₂³	1	4	yes	—
78	C₂×C₄×D₁₀₁	C₂³	1	4	yes	—
79	C₂×C₄×D₁₀₁	C₂³	1	4	yes	—
80	C₂×C₄×D₁₀₁	C₂³	1	4	yes	—
81	C₂×C₄×D₁₀₁	C₂³	1	4	yes	—
82	C₂×C₄×D₁₀₁	C₂³	1	2	yes	—
83	C₂×C₄×D₁₀₁	C₂³	1	2	yes	—
84	C₄⋊Dic₁₀₁	C₂³	1	4	yes	—
85	C₄⋊Dic₁₀₁	C₂³	1	4	yes	—
86	#13108053	C₂³	1	8	yes	—
87	#13108053	C₂³	1	8	yes	—
88	C₂²⋊Dic₁₀₁	C₂³	1	8	yes	—
89	#13108051	C₂³	1	8	yes	—
90	#13108051	C₂³	1	8	yes	—
91	#41×C₁₀₁	—	2	8	no	—
92	C₂×Q₈×C₁₀₁	C₂³	1	2	yes	—
93	C₂×D₄×C₁₀₁	C₂³	1	2	yes	—
94	C₂×D₄×C₁₀₁	C₂³	1	4	yes	—
95	C₂×D₄×C₁₀₁	C₂³	1	4	yes	—
96	C₂²×C₄×C₁₀₁	C₂³	1	4	yes	—
97	C₂²×C₄×C₁₀₁	C₂³	1	2	yes	—
98	C₂²×C₄×C₁₀₁	C₂³	1	1	yes	characteristic
99	C₄⋊C₄×C₁₀₁	C₂³	1	4	yes	—
100	C₄⋊C₄×C₁₀₁	C₂³	1	4	yes	—
101	C₂²⋊C₄×C₁₀₁	C₂³	1	8	yes	—
102	C₂³×C₁₀₁	C₂⁴	1	4	yes	—
103	C₂³×C₁₀₁	C₂⁴	1	1	yes	characteristic
104	C₂²×D₁₀₁	—	2	2	no	—
105	C₂²×D₁₀₁	—	2	2	no	—
106	C₂²×D₁₀₁	—	2	8	no	—
107	C₂²×D₁₀₁	—	2	8	no	—
108	C₂²×D₁₀₁	—	2	8	no	—
109	C₂²×D₁₀₁	C₂×D₄	1	4	yes	—
110	C₂²×D₁₀₁	C₂⁴	1	4	yes	—
111	C₂²×D₁₀₁	C₂⁴	1	1	yes	characteristic
112	C₂²×D₁₀₁	C₂⁴	1	1	yes	characteristic
113	Q₈×C₁₀₁	—	2	4	no	—
114	D₄×C₁₀₁	—	2	8	no	—
115	D₄×C₁₀₁	—	2	4	no	—
116	D₄×C₁₀₁	—	4	4	no	—
117	C₂×C₄×C₁₀₁	—	2	8	no	—
118	C₂×C₄×C₁₀₁	—	4	2	no	—
119	C₂×C₄×C₁₀₁	C₂×D₄	1	4	yes	complemented
120	C₂×C₄×C₁₀₁	C₂⁴	1	4	yes	—
121	C₂×C₄×C₁₀₁	C₂⁴	1	4	yes	—
122	C₂×C₄×C₁₀₁	C₂⁴	1	2	yes	—
123	C₂²⋊D₁₀₁	—	2	8	no	—
124	C₂²⋊D₁₀₁	—	2	8	no	—
125	C₂²⋊D₁₀₁	—	2	8	no	—
126	C₂²⋊D₁₀₁	—	4	8	no	—
127	C₂×Dic₁₀₁	—	2	8	no	—
128	C₂×Dic₁₀₁	—	4	2	no	—
129	C₂×Dic₁₀₁	C₂×D₄	1	4	yes	complemented
130	C₂×Dic₁₀₁	C₂⁴	1	4	yes	—
131	C₂×Dic₁₀₁	C₂⁴	1	4	yes	—
132	C₂×Dic₁₀₁	C₂⁴	1	2	yes	—
133	D₄₀₄	—	2	8	no	—
134	D₄₀₄	—	2	4	no	—
135	D₄₀₄	—	4	4	no	—
136	C₄×D₁₀₁	—	2	8	no	—
137	C₄×D₁₀₁	—	2	8	no	—
138	C₄×D₁₀₁	—	2	8	no	—
139	C₄×D₁₀₁	—	2	8	no	—
140	C₄×D₁₀₁	—	4	4	no	—
141	C₄×D₁₀₁	C₂×D₄	1	8	yes	—
142	C₄×D₁₀₁	C₂×D₄	1	8	yes	complemented
143	Dic₂₀₂	—	2	4	no	—
144	Dic₂₀₂	—	2	8	no	—
145	C₂²×C₁₀₁	—	2	1	no	—
146	C₂²×C₁₀₁	—	2	1	no	—
147	C₂²×C₁₀₁	—	2	4	no	—
148	C₂²×C₁₀₁	—	2	4	no	—
149	C₂²×C₁₀₁	—	2	4	no	—
150	C₂²×C₁₀₁	C₂²×D₄	1	2	yes	—
151	C₂²×C₁₀₁	C₂⁵	1	1	yes	characteristic
152	C₂×D₁₀₁	—	2	1	no	—
153	C₂×D₁₀₁	—	2	1	no	—
154	C₂×D₁₀₁	—	2	8	no	—
155	C₂×D₁₀₁	—	2	4	no	—
156	C₂×D₁₀₁	—	2	4	no	—
157	C₂×D₁₀₁	—	2	4	no	—
158	C₂×D₁₀₁	—	4	16	no	—
159	C₂×D₁₀₁	C₂²×D₄	1	2	yes	—
160	C₂×D₁₀₁	C₂²×D₄	1	2	yes	—
161	C₂×D₁₀₁	H(5,𝔽₂)	1	2	yes	—
162	C₂×D₁₀₁	2₋¹⁺⁴	1	2	yes	—
163	C₄×C₁₀₁	—	2	4	no	—
164	C₄×C₁₀₁	—	2	4	no	—
165	C₄×C₁₀₁	C₂²×D₄	1	4	yes	—
166	Dic₁₀₁	—	2	4	no	—
167	Dic₁₀₁	—	2	4	no	—
168	Dic₁₀₁	C₂²×D₄	1	4	yes	—
169	C₂×C₁₀₁	—	2	2	no	—
170	C₂×C₁₀₁	—	4	4	no	—
171	C₂×C₁₀₁	C₂³×D₄	1	1	yes	characteristic
172	C₂×C₁₀₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
173	C₂×C₁₀₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
174	D₁₀₁	—	2	2	no	—
175	D₁₀₁	—	4	4	no	—
176	D₁₀₁	#537	1	4	yes	direct product factor
177	C₂×#537	—	101	1	no	maximal, Sylow
178	C₁₀₁	C₂×#537	1	1	yes	characteristic, complemented, Sylow
179	C₂²×#41	—	101	2	no	—
180	#537	—	101	2	no	—
181	#537	—	101	4	no	—
182	#537	—	101	4	no	—
183	#537	—	101	4	no	—
184	#537	—	101	1	no	—
185	#537	D₁₀₁	1	1	yes	characteristic, direct product factor
186	C₂×C₂²⋊Q₈	—	101	4	no	—
187	C₂×#121	—	101	4	no	—
188	C₂×#121	—	101	4	no	—
189	C₂²×C₄⋊C₄	—	101	1	no	—
190	C₂×#41	—	101	2	no	—
191	C₂×#41	—	101	4	no	—
192	C₂×#41	—	101	2	no	—
193	C₂×#41	—	101	4	no	—
194	C₂×#41	—	101	2	no	—
195	C₂×#41	—	202	16	no	—
196	C₂×#41	C₂×D₁₀₁	1	2	yes	complemented
197	C₂²×Q₈	—	101	2	no	—
198	C₂²×D₄	—	101	4	no	—
199	C₂²×D₄	—	101	2	no	—
200	C₂²×D₄	—	101	4	no	—
201	C₂³×C₄	—	101	1	no	—
202	C₂³×C₄	—	101	2	no	—
203	C₂³×C₄	—	101	4	no	—
204	C₂²⋊Q₈	—	101	4	no	—
205	C₂²⋊Q₈	—	101	4	no	—
206	C₂²⋊Q₈	—	101	8	no	—
207	C₂²⋊Q₈	—	101	4	no	—
208	C₂²⋊Q₈	—	101	8	no	—
209	C₂²⋊Q₈	C₂×D₁₀₁	1	4	yes	complemented
210	#121	—	101	4	no	—
211	#121	—	101	4	no	—
212	#121	—	101	8	no	—
213	#121	—	101	8	no	—
214	#121	—	101	4	no	—
215	#121	—	101	4	no	—
216	#121	—	101	4	no	—
217	#121	—	101	4	no	—
218	#121	—	101	8	no	—
219	#121	—	101	8	no	—
220	#121	C₂×D₁₀₁	1	4	yes	complemented
221	#121	C₂×D₁₀₁	1	4	yes	complemented
222	C₂×C₄⋊C₄	—	101	2	no	—
223	C₂×C₄⋊C₄	—	101	1	no	—
224	C₂×C₄⋊C₄	—	101	4	no	—
225	C₂×C₄⋊C₄	—	101	4	no	—
226	C₂×C₄⋊C₄	—	101	4	no	—
227	C₂×C₄⋊C₄	C₂×D₁₀₁	1	1	yes	characteristic, complemented
228	C₂×C₂²⋊C₄	—	101	8	no	—
229	C₂⁴	—	101	1	no	—
230	C₂⁴	—	101	4	no	—
231	#41	—	2	8	no	—
232	#41	—	202	16	no	—
233	#41	—	202	16	no	—
234	#41	—	202	8	no	—
235	#41	—	202	8	no	—
236	#41	—	202	8	no	—
237	C₂×Q₈	—	101	4	no	—
238	C₂×Q₈	—	101	2	no	—
239	C₂×Q₈	—	202	8	no	—
240	C₂×Q₈	C₂²×D₁₀₁	1	2	yes	—
241	C₂×D₄	—	101	8	no	—
242	C₂×D₄	—	101	4	no	—
243	C₂×D₄	—	101	4	no	—
244	C₂×D₄	—	101	4	no	—
245	C₂×D₄	—	101	4	no	—
246	C₂×D₄	—	101	4	no	—
247	C₂×D₄	—	101	2	no	—
248	C₂×D₄	—	404	8	no	—
249	C₂×D₄	—	202	8	no	—
250	C₂×D₄	—	202	16	no	—
251	C₂×D₄	C₂²×D₁₀₁	1	4	yes	—
252	C₂×D₄	C₂²×D₁₀₁	1	2	yes	—
253	C₂×D₄	C₂²×D₁₀₁	1	4	yes	—
254	C₂²×C₄	—	101	1	no	—
255	C₂²×C₄	—	101	8	no	—
256	C₂²×C₄	—	101	2	no	—
257	C₂²×C₄	—	101	2	no	—
258	C₂²×C₄	—	101	2	no	—
259	C₂²×C₄	—	101	4	no	—
260	C₂²×C₄	—	101	4	no	—
261	C₂²×C₄	—	101	4	no	—
262	C₂²×C₄	—	101	4	no	—
263	C₂²×C₄	—	101	4	no	—
264	C₂²×C₄	—	101	4	no	—
265	C₂²×C₄	—	404	4	no	—
266	C₂²×C₄	—	202	16	no	—
267	C₂²×C₄	C₂²×D₁₀₁	1	4	yes	—
268	C₂²×C₄	C₂²×D₁₀₁	1	2	yes	—
269	C₂²×C₄	C₂²×D₁₀₁	1	1	yes	characteristic
270	C₄⋊C₄	—	101	8	no	—
271	C₄⋊C₄	—	101	8	no	—
272	C₄⋊C₄	—	101	4	no	—
273	C₄⋊C₄	—	101	4	no	—
274	C₄⋊C₄	C₂²×D₁₀₁	1	4	yes	—
275	C₄⋊C₄	C₂²×D₁₀₁	1	4	yes	—
276	C₂²⋊C₄	—	101	8	no	—
277	C₂²⋊C₄	—	101	8	no	—
278	C₂²⋊C₄	—	101	8	no	—
279	C₂²⋊C₄	C₂²×D₁₀₁	1	8	yes	—
280	C₂³	—	101	1	no	—
281	C₂³	—	101	4	no	—
282	C₂³	—	101	1	no	—
283	C₂³	—	101	4	no	—
284	C₂³	—	202	8	no	—
285	C₂³	—	202	8	no	—
286	C₂³	—	202	8	no	—
287	C₂³	—	202	2	no	—
288	C₂³	—	202	2	no	—
289	C₂³	C₂³×D₁₀₁	1	4	yes	—
290	C₂³	C₂³×D₁₀₁	1	1	yes	characteristic
291	Q₈	—	2	4	no	—
292	Q₈	—	202	8	no	—
293	Q₈	—	202	4	no	—
294	D₄	—	2	8	no	—
295	D₄	—	2	4	no	—
296	D₄	—	4	4	no	—
297	D₄	—	404	4	no	—
298	D₄	—	404	8	no	—
299	D₄	—	202	8	no	—
300	D₄	—	202	8	no	—
301	D₄	—	202	8	no	—
302	D₄	—	202	8	no	—
303	D₄	—	202	4	no	—
304	C₂×C₄	—	2	8	no	—
305	C₂×C₄	—	4	2	no	—
306	C₂×C₄	—	101	4	no	—
307	C₂×C₄	—	101	2	no	—
308	C₂×C₄	—	101	8	no	—
309	C₂×C₄	—	101	8	no	—
310	C₂×C₄	—	101	4	no	—
311	C₂×C₄	—	101	4	no	—
312	C₂×C₄	—	404	4	no	—
313	C₂×C₄	—	404	2	no	—
314	C₂×C₄	—	202	8	no	—
315	C₂×C₄	—	202	8	no	—
316	C₂×C₄	—	202	8	no	—
317	C₂×C₄	—	202	8	no	—
318	C₂×C₄	—	202	8	no	—
319	C₂×C₄	D₄×D₁₀₁	1	4	yes	complemented
320	C₂×C₄	C₂³×D₁₀₁	1	4	yes	—
321	C₂×C₄	C₂³×D₁₀₁	1	4	yes	—
322	C₂×C₄	C₂³×D₁₀₁	1	2	yes	—
323	C₂²	—	2	1	no	—
324	C₂²	—	2	1	no	—
325	C₂²	—	2	4	no	—
326	C₂²	—	2	4	no	—
327	C₂²	—	2	4	no	—
328	C₂²	—	101	2	no	—
329	C₂²	—	101	2	no	—
330	C₂²	—	101	2	no	—
331	C₂²	—	101	2	no	—
332	C₂²	—	404	16	no	—
333	C₂²	—	202	8	no	—
334	C₂²	—	202	4	no	—
335	C₂²	—	202	4	no	—
336	C₂²	—	202	4	no	—
337	C₂²	—	202	1	no	—
338	C₂²	—	202	1	no	—
339	C₂²	C₂×D₄×D₁₀₁	1	2	yes	—
340	C₂²	C₂⁴×D₁₀₁	1	1	yes	characteristic
341	C₄	—	2	4	no	—
342	C₄	—	2	4	no	—
343	C₄	—	101	4	no	—
344	C₄	—	202	4	no	—
345	C₄	—	202	4	no	—
346	C₄	C₂×D₄×D₁₀₁	1	4	yes	—
347	C₂	—	2	2	no	—
348	C₂	—	4	4	no	—
349	C₂	—	101	4	no	—
350	C₂	—	404	4	no	—
351	C₂	—	202	2	no	—
352	C₂	C₂²×D₄×D₁₀₁	1	1	yes	characteristic
353	C₂	H(5,𝔽₂)×D₁₀₁	1	1	yes	characteristic
354	C₂	2₋¹⁺⁴×D₁₀₁	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₁₀₁
commutator, socle, cosocle	C₂²×C₁₀₁	C₂⁵
Fitting	#537×C₁₀₁	C₂
hypercenter	#537	D₁₀₁
hypocenter	C₁₀₁	C₂×#537
LCS	G ▷ C₂²×C₁₀₁ ▷ C₁₀₁
UCS	C₁ ◁ C₂² ◁ #537

Complements

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

N	H ≅ G/N	type
1. C₂×#41×D₁₀₁	C₂	semidirect
2. #20265758	C₂	semidirect
3. #20265757	C₂	semidirect
4. #20265756	C₂	semidirect
5. #20265755	C₂	semidirect
6. #20265754	C₂	semidirect
7. C₂²⋊Q₈×D₁₀₁	C₂	semidirect
8. #121×D₁₀₁	C₂	semidirect
9. #121×D₁₀₁	C₂	semidirect
10. C₂×C₄⋊C₄×D₁₀₁	C₂	semidirect
11. #537×C₁₀₁	C₂	semidirect
12. C₂×#13108075	C₂²	semidirect
13. C₂×#13108074	C₂²	semidirect
14. C₂×#13108074	C₂²	semidirect
15. C₂×#13108073	C₂²	semidirect
16. C₂×#13108073	C₂²	semidirect
25. #15692235	C₂²	semidirect
26. #15692234	C₂²	semidirect
27. #15692233	C₂²	semidirect
28. #15692232	C₂²	semidirect
29. #15692231	C₂²	semidirect
30. #15692230	C₂²	semidirect
31. #15692230	C₂²	semidirect
32. #15692229	C₂²	semidirect
33. #15692229	C₂²	semidirect
34. #15692228	C₂²	semidirect
35. #15692228	C₂²	semidirect
36. #15692227	C₂²	semidirect
37. #15692227	C₂²	semidirect
38. #15692226	C₂²	semidirect
39. #15692226	C₂²	semidirect
40. C₂×C₄⋊Dic₁₀₁	C₂²	semidirect
41. C₂×#13108053	C₂²	semidirect
44. C₄⋊C₄×D₁₀₁	C₂²	semidirect
46. C₂×#41×C₁₀₁	C₂²	semidirect
47. C₂²⋊Q₈×C₁₀₁	C₂²	semidirect
48. #121×C₁₀₁	C₂²	semidirect
49. #121×C₁₀₁	C₂²	semidirect
50. C₂×C₄⋊C₄×C₁₀₁	C₂²	semidirect
76. C₂×C₄×D₁₀₁	D₄	semidirect
119. C₂×C₄×C₁₀₁	C₂×D₄	semidirect
129. C₂×Dic₁₀₁	C₂×D₄	semidirect
142. C₄×D₁₀₁	C₂×D₄	semidirect
176. D₁₀₁	#537	direct (N × H)
178. C₁₀₁	C₂×#537	semidirect
185. #537	D₁₀₁	direct (N × H)
196. C₂×#41	C₂×D₁₀₁	semidirect
209. C₂²⋊Q₈	C₂×D₁₀₁	semidirect
220. #121	C₂×D₁₀₁	semidirect
221. #121	C₂×D₁₀₁	semidirect
227. C₂×C₄⋊C₄	C₂×D₁₀₁	semidirect
319. C₂×C₄	D₄×D₁₀₁	semidirect

Maximal subgroups

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

subgroup	index
C₂×#41×D₁₀₁	2
#20265758	2
#20265757	2
#20265756	2
#20265755	2
#20265754	2
C₂²⋊Q₈×D₁₀₁	2
#121×D₁₀₁	2
C₂×C₄⋊C₄×D₁₀₁	2
#537×C₁₀₁	2
C₂×#537	101

Subgroups — #537×D101 #27184452

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #537×D₁₀₁ #27184452