Subgroups — C₄×#15692225 #27173636

Order 12928.

1224 conjugacy classes of subgroups.

The subgroup lattice has 354 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₄×D₁₀₁	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#15692225	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄×D₄₀₄	C₂	1	2	yes	maximal, complemented
4	C₂×C₄×C₂²⋊D₁₀₁	C₂	1	1	yes	maximal, characteristic, complemented
5	#20265055	C₂	1	2	yes	maximal, complemented
6	#20265054	C₂	1	1	yes	maximal, characteristic, complemented
7	#20265052	C₂	1	1	yes	maximal, characteristic, complemented
8	#20265051	C₂	1	2	yes	maximal, complemented
9	#20265032	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄×#13108051	C₂	1	2	yes	maximal, complemented
11	C₄×C₂²⋊C₄×C₁₀₁	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂⁴×D₁₀₁	C₂²	1	1	yes	characteristic
13	C₂²×D₄₀₄	C₂²	1	2	yes	—
14	C₂²×C₂²⋊D₁₀₁	C₂²	1	1	yes	characteristic
15	C₂³×Dic₁₀₁	C₂²	1	1	yes	characteristic
16	C₂²×C₄×D₁₀₁	—	2	8	no	—
17	C₂²×C₄×D₁₀₁	—	2	4	no	—
18	C₂²×C₄×D₁₀₁	C₂²	1	2	yes	—
19	C₂²×C₄×D₁₀₁	C₂²	1	2	yes	—
20	C₂²×C₄×D₁₀₁	C₂²	1	1	yes	characteristic, complemented
21	#15692225	C₄	1	8	yes	direct product factor
22	C₄×D₄₀₄	—	2	8	no	—
23	C₄×C₂²⋊D₁₀₁	—	2	4	no	—
24	C₂×C₄⋊Dic₁₀₁	C₂²	1	2	yes	complemented
25	C₂×#13108053	C₂²	1	1	yes	characteristic, complemented
26	C₂×C₂²⋊Dic₁₀₁	C₂²	1	1	yes	characteristic
27	C₂×#13108051	C₂²	1	2	yes	—
28	C₂×#13108051	C₂²	1	2	yes	—
29	C₂×#13108051	C₂²	1	2	yes	—
30	C₂×#13108051	C₂²	1	2	yes	complemented
31	C₂×#13108051	C₂²	1	1	yes	characteristic, complemented
32	C₂×C₄×Dic₁₀₁	C₂²	1	1	yes	characteristic, complemented
33	#15692162	C₂²	1	2	yes	complemented
34	#15692162	C₂²	1	2	yes	complemented
35	C₂³×C₄×C₁₀₁	C₂²	1	1	yes	characteristic
36	C₂×C₂²⋊C₄×C₁₀₁	C₂²	1	1	yes	characteristic
37	C₂×C₂²⋊C₄×C₁₀₁	C₂²	1	1	yes	characteristic
38	C₂×C₄²×C₁₀₁	C₂²	1	2	yes	complemented
39	#95×C₁₀₁	C₂²	1	2	yes	complemented
40	C₂³×D₁₀₁	—	2	2	no	—
41	C₂³×D₁₀₁	—	2	2	no	—
42	C₂³×D₁₀₁	—	2	4	no	—
43	C₂³×D₁₀₁	—	2	4	no	—
44	C₂³×D₁₀₁	C₂×C₄	1	4	yes	complemented
45	C₂³×D₁₀₁	C₂³	1	1	yes	characteristic
46	C₂³×D₁₀₁	C₂³	1	2	yes	—
47	C₂×D₄₀₄	—	2	4	no	—
48	C₂×D₄₀₄	—	2	4	no	—
49	C₂×D₄₀₄	C₂×C₄	1	8	yes	complemented
50	C₂×C₂²⋊D₁₀₁	—	2	2	no	—
51	C₂×C₂²⋊D₁₀₁	—	2	2	no	—
52	C₂×C₂²⋊D₁₀₁	C₂×C₄	1	4	yes	complemented
53	C₂²×Dic₁₀₁	—	2	2	no	—
54	C₂²×Dic₁₀₁	—	2	4	no	—
55	C₂²×Dic₁₀₁	C₂³	1	1	yes	characteristic
56	C₂²×Dic₁₀₁	C₂³	1	1	yes	characteristic
57	C₂²×Dic₁₀₁	C₂³	1	1	yes	characteristic
58	C₂²×Dic₁₀₁	C₂³	1	2	yes	—
59	C₂×C₄×D₁₀₁	—	2	32	no	—
60	C₂×C₄×D₁₀₁	—	2	4	no	—
61	C₂×C₄×D₁₀₁	—	2	4	no	—
62	C₂×C₄×D₁₀₁	—	2	4	no	—
63	C₂×C₄×D₁₀₁	—	2	4	no	—
64	C₂×C₄×D₁₀₁	—	2	4	no	—
65	C₂×C₄×D₁₀₁	—	2	2	no	—
66	C₂×C₄×D₁₀₁	—	2	4	no	—
67	C₂×C₄×D₁₀₁	D₄	1	8	yes	complemented
68	C₄⋊Dic₁₀₁	—	2	4	no	—
69	#13108053	—	2	2	no	—
70	C₂²⋊Dic₁₀₁	—	2	2	no	—
71	#13108051	—	2	4	no	—
72	#13108051	—	2	4	no	—
73	#13108051	—	2	2	no	—
74	#13108051	—	2	4	no	—
75	#13108051	C₂×C₄	1	8	yes	complemented
76	C₄×Dic₁₀₁	—	2	2	no	—
77	C₂⁴×C₁₀₁	C₂³	1	1	yes	characteristic
78	C₂²×C₄×C₁₀₁	—	2	4	no	—
79	C₂²×C₄×C₁₀₁	D₄	1	4	yes	complemented
80	C₂²×C₄×C₁₀₁	C₂³	1	2	yes	—
81	C₂²×C₄×C₁₀₁	C₂³	1	2	yes	—
82	C₂²×C₄×C₁₀₁	C₂³	1	1	yes	characteristic
83	C₂²×C₄×C₁₀₁	C₂³	1	1	yes	characteristic
84	C₂²⋊C₄×C₁₀₁	—	2	2	no	—
85	C₂²⋊C₄×C₁₀₁	C₂×C₄	1	4	yes	complemented
86	C₄²×C₁₀₁	—	2	4	no	—
87	C₂³×C₁₀₁	—	2	2	no	—
88	C₂³×C₁₀₁	—	2	2	no	—
89	C₂³×C₁₀₁	C₂²×C₄	1	2	yes	—
90	C₂³×C₁₀₁	C₂×D₄	1	2	yes	—
91	C₂³×C₁₀₁	#41	1	2	yes	—
92	C₂³×C₁₀₁	C₂⁴	1	1	yes	characteristic
93	C₂²×D₁₀₁	—	2	8	no	—
94	C₂²×D₁₀₁	—	2	16	no	—
95	C₂²×D₁₀₁	—	2	8	no	—
96	C₂²×D₁₀₁	—	2	8	no	—
97	C₂²×D₁₀₁	—	2	2	no	—
98	C₂²×D₁₀₁	—	2	2	no	—
99	C₂²×D₁₀₁	—	2	2	no	—
100	C₂²×D₁₀₁	—	2	2	no	—
101	C₂²×D₁₀₁	—	2	16	no	—
102	C₂²×D₁₀₁	—	2	1	no	—
103	C₂²×D₁₀₁	—	2	2	no	—
104	C₂²×D₁₀₁	—	2	1	no	—
105	C₂²×D₁₀₁	—	2	2	no	—
106	C₂²×D₁₀₁	C₂²×C₄	1	4	yes	—
107	C₂²×D₁₀₁	C₂²×C₄	1	2	yes	complemented
108	C₂²×D₁₀₁	C₂×D₄	1	4	yes	—
109	C₂²×D₁₀₁	#41	1	4	yes	—
110	C₂×C₄×C₁₀₁	—	2	2	no	—
111	C₂×C₄×C₁₀₁	—	2	2	no	—
112	C₂×C₄×C₁₀₁	—	2	2	no	—
113	C₂×C₄×C₁₀₁	—	2	8	no	—
114	C₂×C₄×C₁₀₁	—	2	2	no	—
115	C₂×C₄×C₁₀₁	—	2	2	no	—
116	C₂×C₄×C₁₀₁	—	2	2	no	—
117	C₂×C₄×C₁₀₁	C₂²×C₄	1	4	yes	complemented
118	C₂×C₄×C₁₀₁	C₂×D₄	1	4	yes	—
119	C₂×C₄×C₁₀₁	C₂×D₄	1	2	yes	—
120	C₂×C₄×C₁₀₁	C₂×D₄	1	2	yes	—
121	C₂²⋊D₁₀₁	—	2	8	no	—
122	C₂×Dic₁₀₁	—	2	8	no	—
123	C₂×Dic₁₀₁	—	2	1	no	—
124	C₂×Dic₁₀₁	—	2	2	no	—
125	C₂×Dic₁₀₁	—	2	2	no	—
126	C₂×Dic₁₀₁	—	2	1	no	—
127	C₂×Dic₁₀₁	—	2	1	no	—
128	C₂×Dic₁₀₁	—	2	2	no	—
129	C₂×Dic₁₀₁	—	2	1	no	—
130	C₂×Dic₁₀₁	—	2	2	no	—
131	C₂×Dic₁₀₁	C₂²×C₄	1	2	yes	complemented
132	C₂×Dic₁₀₁	C₂×D₄	1	4	yes	—
133	D₄₀₄	—	2	16	no	—
134	C₄×D₁₀₁	—	2	16	no	—
135	C₄×D₁₀₁	—	2	16	no	—
136	C₄×D₁₀₁	—	4	4	no	—
137	C₂²×C₁₀₁	—	2	4	no	—
138	C₂²×C₁₀₁	—	2	2	no	—
139	C₂²×C₁₀₁	—	2	2	no	—
140	C₂²×C₁₀₁	—	2	4	no	—
141	C₂²×C₁₀₁	C₄×D₄	1	4	yes	complemented
142	C₂²×C₁₀₁	C₂³×C₄	1	1	yes	characteristic
143	C₂²×C₁₀₁	C₂²×D₄	1	2	yes	—
144	C₂²×C₁₀₁	C₂²×D₄	1	1	yes	characteristic
145	C₂²×C₁₀₁	C₂×#41	1	2	yes	—
146	C₂²×C₁₀₁	C₂×#41	1	1	yes	characteristic
147	C₂×D₁₀₁	—	2	32	no	—
148	C₂×D₁₀₁	—	2	4	no	—
149	C₂×D₁₀₁	—	2	4	no	—
150	C₂×D₁₀₁	—	2	4	no	—
151	C₂×D₁₀₁	—	2	4	no	—
152	C₂×D₁₀₁	—	2	4	no	—
153	C₂×D₁₀₁	—	2	4	no	—
154	C₂×D₁₀₁	—	2	4	no	—
155	C₂×D₁₀₁	—	2	2	no	—
156	C₂×D₁₀₁	—	4	1	no	—
157	C₂×D₁₀₁	—	4	2	no	—
158	C₂×D₁₀₁	—	4	1	no	—
159	C₂×D₁₀₁	C₄×D₄	1	8	yes	complemented
160	C₄×C₁₀₁	—	2	4	no	—
161	C₄×C₁₀₁	—	2	2	no	—
162	C₄×C₁₀₁	—	4	2	no	—
163	C₄×C₁₀₁	#120	1	4	yes	complemented
164	Dic₁₀₁	—	2	2	no	—
165	Dic₁₀₁	—	2	4	no	—
166	Dic₁₀₁	—	4	1	no	—
167	Dic₁₀₁	—	4	1	no	—
168	C₂×C₁₀₁	—	2	4	no	—
169	C₂×C₁₀₁	C₂×C₄×D₄	1	2	yes	—
170	C₂×C₁₀₁	C₂×C₄×D₄	1	1	yes	characteristic
171	C₂×C₁₀₁	C₂×#120	1	1	yes	characteristic
172	C₂×C₁₀₁	#525	1	2	yes	—
173	C₂×C₁₀₁	#525	1	1	yes	characteristic
174	D₁₀₁	—	2	8	no	—
175	D₁₀₁	—	4	2	no	—
176	C₄×#120	—	101	1	no	maximal, Sylow
177	C₁₀₁	C₄×#120	1	1	yes	characteristic, complemented, Sylow
178	C₂⁴×C₄	—	101	1	no	—
179	C₂×#120	—	101	1	no	—
180	C₂×C₄×D₄	—	101	1	no	—
181	C₂×C₄×D₄	—	101	2	no	—
182	#386	—	101	1	no	—
183	#386	—	101	2	no	—
184	#385	—	101	1	no	—
185	#385	—	101	2	no	—
186	#379	—	101	1	no	—
187	C₄×C₂²⋊C₄	—	101	2	no	—
188	C₄×C₂²⋊C₄	D₁₀₁	1	1	yes	characteristic, complemented
189	C₂⁵	—	101	1	no	—
190	C₂²×D₄	—	101	1	no	—
191	C₂²×D₄	—	101	2	no	—
192	C₂³×C₄	—	101	2	no	—
193	C₂³×C₄	—	101	1	no	—
194	C₂³×C₄	—	101	2	no	—
195	C₂³×C₄	—	101	1	no	—
196	C₂³×C₄	—	202	8	no	—
197	C₂³×C₄	—	202	4	no	—
198	C₂³×C₄	C₂×D₁₀₁	1	1	yes	characteristic
199	#120	—	101	8	no	—
200	C₄×D₄	—	202	8	no	—
201	C₄×D₄	—	202	4	no	—
202	C₂×C₄⋊C₄	—	101	1	no	—
203	C₂×C₄⋊C₄	—	101	2	no	—
204	C₂×C₂²⋊C₄	—	101	2	no	—
205	C₂×C₂²⋊C₄	—	101	1	no	—
206	C₂×C₂²⋊C₄	—	101	2	no	—
207	C₂×C₂²⋊C₄	—	101	2	no	—
208	C₂×C₂²⋊C₄	—	101	1	no	—
209	C₂×C₂²⋊C₄	—	101	2	no	—
210	C₂×C₂²⋊C₄	C₂×D₁₀₁	1	1	yes	characteristic
211	C₂×C₂²⋊C₄	C₂×D₁₀₁	1	1	yes	characteristic
212	C₂×C₄²	—	101	1	no	—
213	C₂×C₄²	C₂×D₁₀₁	1	2	yes	complemented
214	#95	—	101	2	no	—
215	#95	—	101	2	no	—
216	#95	C₂×D₁₀₁	1	2	yes	complemented
217	C₂⁴	—	101	2	no	—
218	C₂⁴	—	101	4	no	—
219	C₂⁴	—	101	1	no	—
220	C₂⁴	—	202	4	no	—
221	C₂⁴	—	202	4	no	—
222	C₂⁴	—	202	2	no	—
223	C₂⁴	—	202	2	no	—
224	C₂⁴	C₂²×D₁₀₁	1	1	yes	characteristic
225	C₂×D₄	—	101	4	no	—
226	C₂×D₄	—	101	8	no	—
227	C₂×D₄	—	202	4	no	—
228	C₂×D₄	—	202	4	no	—
229	C₂×D₄	—	202	2	no	—
230	C₂×D₄	—	202	2	no	—
231	C₂²×C₄	—	2	4	no	—
232	C₂²×C₄	—	101	1	no	—
233	C₂²×C₄	—	101	2	no	—
234	C₂²×C₄	—	101	8	no	—
235	C₂²×C₄	—	101	1	no	—
236	C₂²×C₄	—	101	1	no	—
237	C₂²×C₄	—	202	4	no	—
238	C₂²×C₄	—	202	4	no	—
239	C₂²×C₄	—	202	32	no	—
240	C₂²×C₄	—	202	4	no	—
241	C₂²×C₄	—	202	4	no	—
242	C₂²×C₄	—	202	2	no	—
243	C₂²×C₄	—	202	2	no	—
244	C₂²×C₄	—	202	4	no	—
245	C₂²×C₄	—	202	4	no	—
246	C₂²×C₄	—	202	4	no	—
247	C₂²×C₄	D₄₀₄	1	4	yes	complemented
248	C₂²×C₄	C₂²×D₁₀₁	1	2	yes	—
249	C₂²×C₄	C₂²×D₁₀₁	1	2	yes	—
250	C₂²×C₄	C₂²×D₁₀₁	1	1	yes	characteristic
251	C₂²×C₄	C₂²×D₁₀₁	1	1	yes	characteristic
252	C₄⋊C₄	—	202	4	no	—
253	C₄⋊C₄	—	202	2	no	—
254	C₂²⋊C₄	—	2	2	no	—
255	C₂²⋊C₄	—	101	8	no	—
256	C₂²⋊C₄	—	202	4	no	—
257	C₂²⋊C₄	—	202	4	no	—
258	C₂²⋊C₄	—	202	4	no	—
259	C₂²⋊C₄	—	202	2	no	—
260	C₂²⋊C₄	—	202	2	no	—
261	C₂²⋊C₄	C₄×D₁₀₁	1	4	yes	complemented
262	C₄²	—	2	4	no	—
263	C₄²	—	202	2	no	—
264	C₂³	—	2	2	no	—
265	C₂³	—	2	2	no	—
266	C₂³	—	101	4	no	—
267	C₂³	—	101	4	no	—
268	C₂³	—	101	4	no	—
269	C₂³	—	101	2	no	—
270	C₂³	—	202	16	no	—
271	C₂³	—	202	8	no	—
272	C₂³	—	202	16	no	—
273	C₂³	—	202	8	no	—
274	C₂³	—	202	2	no	—
275	C₂³	—	202	1	no	—
276	C₂³	—	202	2	no	—
277	C₂³	—	202	1	no	—
278	C₂³	—	202	2	no	—
279	C₂³	—	202	2	no	—
280	C₂³	—	202	2	no	—
281	C₂³	—	202	2	no	—
282	C₂³	—	202	8	no	—
283	C₂³	C₂×C₄×D₁₀₁	1	2	yes	—
284	C₂³	C₂×D₄₀₄	1	2	yes	—
285	C₂³	#13108074	1	2	yes	—
286	C₂³	C₂³×D₁₀₁	1	1	yes	characteristic
287	D₄	—	202	16	no	—
288	D₄	—	202	8	no	—
289	C₂×C₄	—	2	2	no	—
290	C₂×C₄	—	2	2	no	—
291	C₂×C₄	—	2	2	no	—
292	C₂×C₄	—	2	8	no	—
293	C₂×C₄	—	2	2	no	—
294	C₂×C₄	—	2	2	no	—
295	C₂×C₄	—	2	2	no	—
296	C₂×C₄	—	101	2	no	—
297	C₂×C₄	—	101	4	no	—
298	C₂×C₄	—	404	4	no	—
299	C₂×C₄	—	202	16	no	—
300	C₂×C₄	—	202	2	no	—
301	C₂×C₄	—	202	1	no	—
302	C₂×C₄	—	202	1	no	—
303	C₂×C₄	—	202	2	no	—
304	C₂×C₄	—	202	8	no	—
305	C₂×C₄	—	202	2	no	—
306	C₂×C₄	—	202	1	no	—
307	C₂×C₄	—	202	2	no	—
308	C₂×C₄	—	202	1	no	—
309	C₂×C₄	—	202	16	no	—
310	C₂×C₄	C₂×C₄×D₁₀₁	1	4	yes	complemented
311	C₂×C₄	D₄×D₁₀₁	1	4	yes	—
312	C₂×C₄	C₂×D₄₀₄	1	2	yes	—
313	C₂×C₄	C₂×D₄₀₄	1	2	yes	—
314	C₂²	—	2	4	no	—
315	C₂²	—	2	2	no	—
316	C₂²	—	2	4	no	—
317	C₂²	—	2	2	no	—
318	C₂²	—	101	8	no	—
319	C₂²	—	404	1	no	—
320	C₂²	—	404	2	no	—
321	C₂²	—	404	1	no	—
322	C₂²	—	202	32	no	—
323	C₂²	—	202	4	no	—
324	C₂²	—	202	2	no	—
325	C₂²	—	202	4	no	—
326	C₂²	—	202	4	no	—
327	C₂²	—	202	4	no	—
328	C₂²	—	202	4	no	—
329	C₂²	—	202	4	no	—
330	C₂²	—	202	4	no	—
331	C₂²	C₄×D₄₀₄	1	4	yes	complemented
332	C₂²	C₂²×C₄×D₁₀₁	1	1	yes	characteristic
333	C₂²	C₂×D₄×D₁₀₁	1	2	yes	—
334	C₂²	C₂²×D₄₀₄	1	1	yes	characteristic
335	C₂²	#41×D₁₀₁	1	2	yes	—
336	C₂²	C₂×#13108074	1	1	yes	characteristic
337	C₄	—	2	4	no	—
338	C₄	—	2	2	no	—
339	C₄	—	4	2	no	—
340	C₄	—	404	1	no	—
341	C₄	—	404	1	no	—
342	C₄	—	202	2	no	—
343	C₄	—	202	4	no	—
344	C₄	#15692225	1	4	yes	direct product factor
345	C₂	—	2	4	no	—
346	C₂	—	404	2	no	—
347	C₂	—	202	8	no	—
348	C₂	C₄×D₄×D₁₀₁	1	2	yes	—
349	C₂	C₂×C₄×D₄₀₄	1	1	yes	characteristic
350	C₂	C₂×#15692225	1	1	yes	characteristic
351	C₂	#20265686	1	2	yes	—
352	C₂	#20265689	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	C₂²×D₁₀₁
commutator	C₂²×C₁₀₁	C₂³×C₄
Frattini	C₂³	C₂³×D₁₀₁
Fitting	C₄×C₂²⋊C₄×C₁₀₁	C₂
socle, cosocle	C₂³×C₁₀₁	C₂⁴
prime radical	C₂×#15692225	C₂
hypercenter	C₄×C₂²⋊C₄	D₁₀₁
hypocenter	C₁₀₁	C₄×#120
LCS	G ▷ C₂²×C₁₀₁ ▷ C₁₀₁
UCS	C₁ ◁ C₂²×C₄ ◁ C₄×C₂²⋊C₄

Complements

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

N	H ≅ G/N	type
1. C₂³×C₄×D₁₀₁	C₂	semidirect
3. C₂×C₄×D₄₀₄	C₂	semidirect
4. C₂×C₄×C₂²⋊D₁₀₁	C₂	semidirect
5. #20265055	C₂	semidirect
6. #20265054	C₂	semidirect
7. #20265052	C₂	semidirect
8. #20265051	C₂	semidirect
9. #20265032	C₂	semidirect
10. C₄×#13108051	C₂	semidirect
11. C₄×C₂²⋊C₄×C₁₀₁	C₂	semidirect
20. C₂²×C₄×D₁₀₁	C₂²	semidirect
21. #15692225	C₄	direct (N × H)
24. C₂×C₄⋊Dic₁₀₁	C₂²	semidirect
25. C₂×#13108053	C₂²	semidirect
30. C₂×#13108051	C₂²	semidirect
31. C₂×#13108051	C₂²	semidirect
32. C₂×C₄×Dic₁₀₁	C₂²	semidirect
33. #15692162	C₂²	semidirect
34. #15692162	C₂²	semidirect
38. C₂×C₄²×C₁₀₁	C₂²	semidirect
39. #95×C₁₀₁	C₂²	semidirect
44. C₂³×D₁₀₁	C₂×C₄	semidirect
49. C₂×D₄₀₄	C₂×C₄	semidirect
52. C₂×C₂²⋊D₁₀₁	C₂×C₄	semidirect
67. C₂×C₄×D₁₀₁	D₄	semidirect
75. #13108051	C₂×C₄	semidirect
79. C₂²×C₄×C₁₀₁	D₄	semidirect
85. C₂²⋊C₄×C₁₀₁	C₂×C₄	semidirect
107. C₂²×D₁₀₁	C₂²×C₄	semidirect
117. C₂×C₄×C₁₀₁	C₂²×C₄	semidirect
131. C₂×Dic₁₀₁	C₂²×C₄	semidirect
141. C₂²×C₁₀₁	C₄×D₄	semidirect
159. C₂×D₁₀₁	C₄×D₄	semidirect
163. C₄×C₁₀₁	#120	semidirect
177. C₁₀₁	C₄×#120	semidirect
188. C₄×C₂²⋊C₄	D₁₀₁	semidirect
213. C₂×C₄²	C₂×D₁₀₁	semidirect
216. #95	C₂×D₁₀₁	semidirect
247. C₂²×C₄	D₄₀₄	semidirect
261. C₂²⋊C₄	C₄×D₁₀₁	semidirect
310. C₂×C₄	C₂×C₄×D₁₀₁	semidirect
331. C₂²	C₄×D₄₀₄	semidirect
344. C₄	#15692225	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂³×C₄×D₁₀₁	2
C₂×#15692225	2
C₂×C₄×D₄₀₄	2
C₂×C₄×C₂²⋊D₁₀₁	2
#20265055	2
#20265054	2
#20265052	2
#20265051	2
#20265032	2
C₄×#13108051	2
C₄×C₂²⋊C₄×C₁₀₁	2
C₄×#120	101

Subgroups — C4×#15692225 #27173636

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×#15692225 #27173636