Subgroups — C₂×#20265685 #27184371

Order 12928.

1880 conjugacy classes of subgroups.

The subgroup lattice has 348 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#13108073	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂³×C₄×D₁₀₁	C₂	1	1	yes	maximal, characteristic, complemented
3	#20265685	C₂	1	16	yes	maximal, direct product factor
4	C₂×#15692238	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#15692233	C₂	1	2	yes	maximal, complemented
6	C₂×#15692228	C₂	1	2	yes	maximal, complemented
7	C₂×#15692225	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#15692223	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×#15692217	C₂	1	2	yes	maximal, complemented
10	C₂×#15692215	C₂	1	2	yes	maximal, complemented
11	C₂×#15692211	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#123×C₁₀₁	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂⁴×D₁₀₁	C₂²	1	1	yes	characteristic
14	C₂×#13108073	—	2	8	no	—
15	C₂×#13108073	C₂²	1	8	yes	complemented
16	C₂²×Dic₂₀₂	C₂²	1	1	yes	characteristic, complemented
17	C₂²×D₄₀₄	C₂²	1	2	yes	—
18	C₂²×C₂²⋊D₁₀₁	C₂²	1	1	yes	characteristic
19	C₂²×C₂²⋊D₁₀₁	C₂²	1	2	yes	—
20	C₂²×C₂²⋊D₁₀₁	C₂²	1	1	yes	characteristic, complemented
21	C₂³×Dic₁₀₁	C₂²	1	1	yes	characteristic
22	C₂³×Dic₁₀₁	C₂²	1	1	yes	characteristic, complemented
23	C₂²×C₄×D₁₀₁	—	2	8	no	—
24	C₂²×C₄×D₁₀₁	C₂²	1	2	yes	—
25	C₂²×C₄×D₁₀₁	C₂²	1	2	yes	—
26	C₂²×C₄×D₁₀₁	C₂²	1	8	yes	complemented
27	C₂²×C₄×D₁₀₁	C₂²	1	1	yes	characteristic, complemented
28	#15692238	C₂²	1	8	yes	complemented
29	#15692233	C₂²	1	16	yes	complemented
30	#15692228	C₂²	1	16	yes	complemented
31	#15692225	C₂²	1	8	yes	complemented
32	#15692223	C₂²	1	8	yes	complemented
33	#15692217	C₂²	1	16	yes	complemented
34	#15692215	C₂²	1	16	yes	complemented
35	#15692211	C₂²	1	8	yes	complemented
36	C₂×#13108053	C₂²	1	2	yes	complemented
37	C₂×#13108053	C₂²	1	2	yes	complemented
38	C₂×C₂²⋊Dic₁₀₁	C₂²	1	1	yes	characteristic
39	C₂×#13108051	C₂²	1	2	yes	—
40	C₂×#13108051	C₂²	1	2	yes	—
41	C₂×#13108051	C₂²	1	2	yes	complemented
42	C₂×C₄×Dic₁₀₁	C₂²	1	2	yes	complemented
43	C₂²×D₄×C₁₀₁	C₂²	1	1	yes	characteristic
44	C₂³×C₄×C₁₀₁	C₂²	1	1	yes	characteristic
45	#123×C₁₀₁	C₂²	1	8	yes	complemented
46	C₂×C₄⋊C₄×C₁₀₁	C₂²	1	2	yes	complemented
47	C₂×C₂²⋊C₄×C₁₀₁	C₂²	1	1	yes	characteristic
48	C₂×C₂²⋊C₄×C₁₀₁	C₂²	1	2	yes	complemented
49	C₂³×D₁₀₁	—	2	4	no	—
50	C₂³×D₁₀₁	—	2	8	no	—
51	C₂³×D₁₀₁	C₂³	1	4	yes	—
52	C₂³×D₁₀₁	C₂³	1	1	yes	characteristic
53	C₂³×D₁₀₁	C₂³	1	2	yes	—
54	#13108073	—	2	32	no	—
55	C₂×Dic₂₀₂	—	2	4	no	—
56	C₂×Dic₂₀₂	C₂³	1	4	yes	complemented
57	C₂×D₄₀₄	—	2	8	no	—
58	C₂×D₄₀₄	C₂³	1	8	yes	—
59	C₂×C₂²⋊D₁₀₁	—	2	4	no	—
60	C₂×C₂²⋊D₁₀₁	—	2	8	no	—
61	C₂×C₂²⋊D₁₀₁	—	2	4	no	—
62	C₂×C₂²⋊D₁₀₁	C₂³	1	4	yes	—
63	C₂×C₂²⋊D₁₀₁	C₂³	1	8	yes	—
64	C₂×C₂²⋊D₁₀₁	C₂³	1	4	yes	complemented
65	C₂²×Dic₁₀₁	—	2	4	no	—
66	C₂²×Dic₁₀₁	D₄	1	8	yes	complemented
67	C₂²×Dic₁₀₁	C₂³	1	1	yes	characteristic
68	C₂²×Dic₁₀₁	C₂³	1	2	yes	—
69	C₂²×Dic₁₀₁	C₂³	1	1	yes	characteristic
70	C₂²×Dic₁₀₁	C₂³	1	1	yes	characteristic
71	C₂²×Dic₁₀₁	C₂³	1	4	yes	—
72	C₂²×Dic₁₀₁	C₂³	1	4	yes	complemented
73	C₂×C₄×D₁₀₁	—	2	8	no	—
74	C₂×C₄×D₁₀₁	—	2	8	no	—
75	C₂×C₄×D₁₀₁	—	2	4	no	—
76	C₂×C₄×D₁₀₁	—	2	32	no	—
77	C₂×C₄×D₁₀₁	C₂³	1	8	yes	—
78	C₂×C₄×D₁₀₁	C₂³	1	8	yes	—
79	C₂×C₄×D₁₀₁	C₂³	1	4	yes	complemented
80	#13108053	C₂³	1	8	yes	complemented
81	#13108053	C₂³	1	8	yes	complemented
82	C₂²⋊Dic₁₀₁	C₂³	1	4	yes	—
83	#13108051	C₂³	1	8	yes	—
84	#13108051	C₂³	1	8	yes	—
85	#13108051	C₂³	1	8	yes	complemented
86	C₄×Dic₁₀₁	C₂³	1	8	yes	complemented
87	C₂⁴×C₁₀₁	C₂³	1	1	yes	characteristic
88	C₂⁴×C₁₀₁	C₂³	1	1	yes	characteristic
89	C₂×D₄×C₁₀₁	—	2	4	no	—
90	C₂×D₄×C₁₀₁	C₂³	1	4	yes	—
91	C₂²×C₄×C₁₀₁	—	2	4	no	—
92	C₂²×C₄×C₁₀₁	C₂³	1	2	yes	—
93	C₂²×C₄×C₁₀₁	C₂³	1	4	yes	—
94	C₂²×C₄×C₁₀₁	C₂³	1	1	yes	characteristic
95	C₂²×C₄×C₁₀₁	C₂³	1	2	yes	—
96	C₄⋊C₄×C₁₀₁	C₂³	1	8	yes	complemented
97	C₂²⋊C₄×C₁₀₁	C₂³	1	4	yes	—
98	C₂²⋊C₄×C₁₀₁	C₂³	1	8	yes	complemented
99	C₂³×C₁₀₁	—	2	4	no	—
100	C₂³×C₁₀₁	—	2	2	no	—
101	C₂³×C₁₀₁	—	2	4	no	—
102	C₂³×C₁₀₁	C₂×D₄	1	4	yes	—
103	C₂³×C₁₀₁	C₂⁴	1	2	yes	—
104	C₂³×C₁₀₁	C₂⁴	1	2	yes	—
105	C₂³×C₁₀₁	C₂⁴	1	1	yes	characteristic
106	C₂²×D₁₀₁	—	2	32	no	—
107	C₂²×D₁₀₁	—	2	8	no	—
108	C₂²×D₁₀₁	—	2	4	no	—
109	C₂²×D₁₀₁	—	2	4	no	—
110	C₂²×D₁₀₁	—	2	16	no	—
111	C₂²×D₁₀₁	—	2	2	no	—
112	C₂²×D₁₀₁	—	2	4	no	—
113	C₂²×D₁₀₁	#41	1	8	yes	complemented
114	C₂²×D₁₀₁	C₂⁴	1	2	yes	—
115	C₂²×D₁₀₁	C₂⁴	1	4	yes	—
116	D₄×C₁₀₁	—	2	8	no	—
117	C₂×C₄×C₁₀₁	—	2	8	no	—
118	C₂×C₄×C₁₀₁	—	2	4	no	—
119	C₂×C₄×C₁₀₁	—	2	2	no	—
120	C₂×C₄×C₁₀₁	—	2	4	no	—
121	C₂×C₄×C₁₀₁	C₂⁴	1	4	yes	—
122	C₂×C₄×C₁₀₁	C₂⁴	1	4	yes	—
123	C₂×C₄×C₁₀₁	C₂⁴	1	2	yes	—
124	C₂²⋊D₁₀₁	—	2	8	no	—
125	C₂²⋊D₁₀₁	—	2	16	no	—
126	C₂²⋊D₁₀₁	—	2	8	no	—
127	C₂×Dic₁₀₁	—	2	2	no	—
128	C₂×Dic₁₀₁	—	2	4	no	—
129	C₂×Dic₁₀₁	—	2	8	no	—
130	C₂×Dic₁₀₁	C₂×D₄	1	4	yes	—
131	C₂×Dic₁₀₁	C₂×D₄	1	4	yes	—
132	C₂×Dic₁₀₁	C₂×D₄	1	16	yes	complemented
133	C₂×Dic₁₀₁	C₂⁴	1	4	yes	—
134	C₂×Dic₁₀₁	C₂⁴	1	2	yes	—
135	C₂×Dic₁₀₁	C₂⁴	1	2	yes	—
136	C₂×Dic₁₀₁	C₂⁴	1	2	yes	—
137	D₄₀₄	—	2	16	no	—
138	C₄×D₁₀₁	—	2	16	no	—
139	C₄×D₁₀₁	—	2	16	no	—
140	C₄×D₁₀₁	—	2	8	no	—
141	Dic₂₀₂	—	2	8	no	—
142	C₂²×C₁₀₁	—	2	8	no	—
143	C₂²×C₁₀₁	—	2	4	no	—
144	C₂²×C₁₀₁	—	2	2	no	—
145	C₂²×C₁₀₁	—	2	4	no	—
146	C₂²×C₁₀₁	—	4	4	no	—
147	C₂²×C₁₀₁	C₂²×D₄	1	4	yes	—
148	C₂²×C₁₀₁	C₂²×D₄	1	2	yes	—
149	C₂²×C₁₀₁	C₂×#41	1	4	yes	—
150	C₂²×C₁₀₁	C₂⁵	1	1	yes	characteristic
151	C₂×D₁₀₁	—	2	32	no	—
152	C₂×D₁₀₁	—	2	16	no	—
153	C₂×D₁₀₁	—	2	4	no	—
154	C₂×D₁₀₁	—	2	4	no	—
155	C₂×D₁₀₁	—	2	2	no	—
156	C₂×D₁₀₁	—	2	4	no	—
157	C₂×D₁₀₁	—	4	4	no	—
158	C₂×D₁₀₁	C₂×#41	1	8	yes	complemented
159	C₄×C₁₀₁	—	2	2	no	—
160	C₄×C₁₀₁	—	2	4	no	—
161	C₄×C₁₀₁	—	2	4	no	—
162	Dic₁₀₁	—	2	2	no	—
163	Dic₁₀₁	—	2	4	no	—
164	Dic₁₀₁	C₂²×D₄	1	4	yes	—
165	Dic₁₀₁	C₂²×D₄	1	4	yes	—
166	C₂×C₁₀₁	—	2	4	no	—
167	C₂×C₁₀₁	—	4	2	no	—
168	C₂×C₁₀₁	#525	1	4	yes	complemented
169	C₂×C₁₀₁	C₂³×D₄	1	1	yes	characteristic
170	C₂×C₁₀₁	C₂²×#41	1	2	yes	—
171	D₁₀₁	—	2	8	no	—
172	D₁₀₁	—	4	2	no	—
173	C₂×#525	—	101	1	no	maximal, Sylow
174	C₁₀₁	C₂×#525	1	1	yes	characteristic, complemented, Sylow
175	C₂²×#41	—	101	1	no	—
176	C₂⁴×C₄	—	101	1	no	—
177	#525	—	101	16	no	—
178	C₂×#123	—	101	1	no	—
179	C₂×#123	D₁₀₁	1	1	yes	characteristic, complemented
180	C₂×C₂²⋊Q₈	—	101	2	no	—
181	C₂×#121	—	101	2	no	—
182	C₂×#120	—	101	1	no	—
183	C₂×#120	—	101	1	no	—
184	C₂×C₄×D₄	—	101	2	no	—
185	C₂×C₄×D₄	—	101	2	no	—
186	C₂×#117	—	101	1	no	—
187	C₂⁵	—	101	1	no	—
188	C₂×#41	—	101	8	no	—
189	C₂×#41	—	202	8	no	—
190	C₂²×Q₈	—	101	1	no	—
191	C₂²×D₄	—	101	2	no	—
192	C₂²×D₄	—	101	1	no	—
193	C₂²×D₄	—	101	1	no	—
194	C₂²×D₄	—	101	2	no	—
195	C₂²×D₄	C₂×D₁₀₁	1	1	yes	characteristic
196	C₂³×C₄	—	101	1	no	—
197	C₂³×C₄	—	101	1	no	—
198	C₂³×C₄	—	101	2	no	—
199	C₂³×C₄	—	101	2	no	—
200	C₂³×C₄	—	101	1	no	—
201	C₂³×C₄	—	101	8	no	—
202	C₂³×C₄	—	202	8	no	—
203	C₂³×C₄	C₂×D₁₀₁	1	1	yes	characteristic
204	#123	—	101	8	no	—
205	#123	C₂×D₁₀₁	1	8	yes	complemented
206	C₂²⋊Q₈	—	101	16	no	—
207	#121	—	101	16	no	—
208	#120	—	101	8	no	—
209	#120	—	101	8	no	—
210	C₄×D₄	—	101	16	no	—
211	C₄×D₄	—	101	16	no	—
212	#117	—	101	8	no	—
213	C₂×C₄⋊C₄	—	101	2	no	—
214	C₂×C₄⋊C₄	—	101	2	no	—
215	C₂×C₄⋊C₄	C₂×D₁₀₁	1	2	yes	complemented
216	C₂×C₂²⋊C₄	—	101	1	no	—
217	C₂×C₂²⋊C₄	—	101	2	no	—
218	C₂×C₂²⋊C₄	—	101	2	no	—
219	C₂×C₂²⋊C₄	—	101	2	no	—
220	C₂×C₂²⋊C₄	C₂×D₁₀₁	1	1	yes	characteristic
221	C₂×C₂²⋊C₄	C₂×D₁₀₁	1	2	yes	complemented
222	C₂×C₄²	—	101	2	no	—
223	C₂⁴	—	101	2	no	—
224	C₂⁴	—	101	4	no	—
225	C₂⁴	—	101	1	no	—
226	C₂⁴	—	202	8	no	—
227	C₂⁴	—	202	4	no	—
228	C₂⁴	C₂²×D₁₀₁	1	1	yes	characteristic
229	C₂⁴	C₂²×D₁₀₁	1	1	yes	characteristic
230	#41	—	202	32	no	—
231	C₂×Q₈	—	101	4	no	—
232	C₂×Q₈	—	202	4	no	—
233	C₂×D₄	—	2	4	no	—
234	C₂×D₄	—	101	8	no	—
235	C₂×D₄	—	101	4	no	—
236	C₂×D₄	—	101	4	no	—
237	C₂×D₄	—	101	8	no	—
238	C₂×D₄	—	202	8	no	—
239	C₂×D₄	—	202	4	no	—
240	C₂×D₄	—	202	8	no	—
241	C₂×D₄	—	202	4	no	—
242	C₂×D₄	C₂²×D₁₀₁	1	4	yes	—
243	C₂²×C₄	—	2	4	no	—
244	C₂²×C₄	—	101	8	no	—
245	C₂²×C₄	—	101	4	no	—
246	C₂²×C₄	—	101	1	no	—
247	C₂²×C₄	—	101	1	no	—
248	C₂²×C₄	—	101	4	no	—
249	C₂²×C₄	—	101	2	no	—
250	C₂²×C₄	—	101	1	no	—
251	C₂²×C₄	—	101	8	no	—
252	C₂²×C₄	—	101	8	no	—
253	C₂²×C₄	—	101	4	no	—
254	C₂²×C₄	—	202	8	no	—
255	C₂²×C₄	—	202	8	no	—
256	C₂²×C₄	—	202	32	no	—
257	C₂²×C₄	—	202	4	no	—
258	C₂²×C₄	—	202	4	no	—
259	C₂²×C₄	C₂²×D₁₀₁	1	4	yes	—
260	C₂²×C₄	C₂²×D₁₀₁	1	2	yes	—
261	C₂²×C₄	C₂²×D₁₀₁	1	1	yes	characteristic
262	C₂²×C₄	C₂²×D₁₀₁	1	2	yes	—
263	C₄⋊C₄	—	101	8	no	—
264	C₄⋊C₄	—	101	8	no	—
265	C₄⋊C₄	C₂²×D₁₀₁	1	8	yes	complemented
266	C₂²⋊C₄	—	101	4	no	—
267	C₂²⋊C₄	—	101	8	no	—
268	C₂²⋊C₄	—	101	8	no	—
269	C₂²⋊C₄	—	101	8	no	—
270	C₂²⋊C₄	C₂²×D₁₀₁	1	4	yes	—
271	C₂²⋊C₄	C₂²×D₁₀₁	1	8	yes	complemented
272	C₄²	—	101	8	no	—
273	C₂³	—	2	4	no	—
274	C₂³	—	2	2	no	—
275	C₂³	—	2	4	no	—
276	C₂³	—	101	8	no	—
277	C₂³	—	101	4	no	—
278	C₂³	—	101	2	no	—
279	C₂³	—	202	16	no	—
280	C₂³	—	202	32	no	—
281	C₂³	—	202	2	no	—
282	C₂³	—	202	4	no	—
283	C₂³	—	202	8	no	—
284	C₂³	—	202	4	no	—
285	C₂³	—	202	4	no	—
286	C₂³	D₄×D₁₀₁	1	4	yes	—
287	C₂³	C₂³×D₁₀₁	1	2	yes	—
288	C₂³	C₂³×D₁₀₁	1	2	yes	—
289	C₂³	C₂³×D₁₀₁	1	1	yes	characteristic
290	Q₈	—	202	8	no	—
291	D₄	—	2	8	no	—
292	D₄	—	202	16	no	—
293	D₄	—	202	8	no	—
294	D₄	—	202	16	no	—
295	D₄	—	202	8	no	—
296	C₂×C₄	—	2	8	no	—
297	C₂×C₄	—	2	4	no	—
298	C₂×C₄	—	2	2	no	—
299	C₂×C₄	—	2	4	no	—
300	C₂×C₄	—	101	4	no	—
301	C₂×C₄	—	101	4	no	—
302	C₂×C₄	—	101	16	no	—
303	C₂×C₄	—	101	2	no	—
304	C₂×C₄	—	101	2	no	—
305	C₂×C₄	—	101	4	no	—
306	C₂×C₄	—	101	2	no	—
307	C₂×C₄	—	202	16	no	—
308	C₂×C₄	—	202	16	no	—
309	C₂×C₄	—	202	8	no	—
310	C₂×C₄	—	202	8	no	—
311	C₂×C₄	—	202	2	no	—
312	C₂×C₄	—	202	4	no	—
313	C₂×C₄	C₂³×D₁₀₁	1	4	yes	—
314	C₂×C₄	C₂³×D₁₀₁	1	2	yes	—
315	C₂×C₄	C₂³×D₁₀₁	1	4	yes	—
316	C₂²	—	2	4	no	—
317	C₂²	—	2	8	no	—
318	C₂²	—	2	2	no	—
319	C₂²	—	2	4	no	—
320	C₂²	—	4	4	no	—
321	C₂²	—	101	8	no	—
322	C₂²	—	404	4	no	—
323	C₂²	—	202	32	no	—
324	C₂²	—	202	2	no	—
325	C₂²	—	202	4	no	—
326	C₂²	—	202	4	no	—
327	C₂²	—	202	4	no	—
328	C₂²	—	202	16	no	—
329	C₂²	C₂×D₄×D₁₀₁	1	4	yes	—
330	C₂²	C₂×D₄×D₁₀₁	1	2	yes	—
331	C₂²	#41×D₁₀₁	1	4	yes	—
332	C₂²	C₂⁴×D₁₀₁	1	1	yes	characteristic
333	C₄	—	2	4	no	—
334	C₄	—	2	2	no	—
335	C₄	—	2	4	no	—
336	C₄	—	101	4	no	—
337	C₄	—	101	4	no	—
338	C₄	—	202	2	no	—
339	C₄	—	202	4	no	—
340	C₂	—	2	4	no	—
341	C₂	—	4	2	no	—
342	C₂	—	404	2	no	—
343	C₂	—	202	8	no	—
344	C₂	#20265685	1	4	yes	direct product factor
345	C₂	C₂²×D₄×D₁₀₁	1	1	yes	characteristic
346	C₂	C₂×#41×D₁₀₁	1	2	yes	—

	subgroup	G/H
center	C₂³	C₂³×D₁₀₁
commutator, cosocle	C₂²×C₁₀₁	C₂⁵
Frattini	C₂²	C₂⁴×D₁₀₁
Fitting	C₂×#123×C₁₀₁	C₂
socle	C₂³×C₁₀₁	C₂⁴
hypercenter	C₂×#123	D₁₀₁
hypocenter	C₁₀₁	C₂×#525
LCS	G ▷ C₂²×C₁₀₁ ▷ C₁₀₁
UCS	C₁ ◁ C₂³ ◁ C₂×#123

Complements

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

N	H ≅ G/N	type
1. C₂²×#13108073	C₂	semidirect
2. C₂³×C₄×D₁₀₁	C₂	semidirect
3. #20265685	C₂	direct (N × H)
4. C₂×#15692238	C₂	semidirect
5. C₂×#15692233	C₂	semidirect
6. C₂×#15692228	C₂	semidirect
7. C₂×#15692225	C₂	semidirect
8. C₂×#15692223	C₂	semidirect
9. C₂×#15692217	C₂	semidirect
10. C₂×#15692215	C₂	semidirect
11. C₂×#15692211	C₂	semidirect
12. C₂×#123×C₁₀₁	C₂	semidirect
15. C₂×#13108073	C₂²	semidirect
16. C₂²×Dic₂₀₂	C₂²	semidirect
20. C₂²×C₂²⋊D₁₀₁	C₂²	semidirect
22. C₂³×Dic₁₀₁	C₂²	semidirect
26. C₂²×C₄×D₁₀₁	C₂²	semidirect
27. C₂²×C₄×D₁₀₁	C₂²	semidirect
28. #15692238	C₂²	semidirect
29. #15692233	C₂²	semidirect
30. #15692228	C₂²	semidirect
31. #15692225	C₂²	semidirect
32. #15692223	C₂²	semidirect
33. #15692217	C₂²	semidirect
34. #15692215	C₂²	semidirect
35. #15692211	C₂²	semidirect
36. C₂×#13108053	C₂²	semidirect
37. C₂×#13108053	C₂²	semidirect
41. C₂×#13108051	C₂²	semidirect
42. C₂×C₄×Dic₁₀₁	C₂²	semidirect
45. #123×C₁₀₁	C₂²	semidirect
46. C₂×C₄⋊C₄×C₁₀₁	C₂²	semidirect
48. C₂×C₂²⋊C₄×C₁₀₁	C₂²	semidirect
56. C₂×Dic₂₀₂	C₂³	semidirect
64. C₂×C₂²⋊D₁₀₁	C₂³	semidirect
66. C₂²×Dic₁₀₁	D₄	semidirect
72. C₂²×Dic₁₀₁	C₂³	semidirect
79. C₂×C₄×D₁₀₁	C₂³	semidirect
80. #13108053	C₂³	semidirect
81. #13108053	C₂³	semidirect
85. #13108051	C₂³	semidirect
86. C₄×Dic₁₀₁	C₂³	semidirect
96. C₄⋊C₄×C₁₀₁	C₂³	semidirect
98. C₂²⋊C₄×C₁₀₁	C₂³	semidirect
113. C₂²×D₁₀₁	#41	semidirect
132. C₂×Dic₁₀₁	C₂×D₄	semidirect
158. C₂×D₁₀₁	C₂×#41	semidirect
168. C₂×C₁₀₁	#525	semidirect
174. C₁₀₁	C₂×#525	semidirect
179. C₂×#123	D₁₀₁	semidirect
205. #123	C₂×D₁₀₁	semidirect
215. C₂×C₄⋊C₄	C₂×D₁₀₁	semidirect
221. C₂×C₂²⋊C₄	C₂×D₁₀₁	semidirect
265. C₄⋊C₄	C₂²×D₁₀₁	semidirect
271. C₂²⋊C₄	C₂²×D₁₀₁	semidirect
344. C₂	#20265685	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×#13108073	2
C₂³×C₄×D₁₀₁	2
#20265685	2
C₂×#15692238	2
C₂×#15692233	2
C₂×#15692228	2
C₂×#15692225	2
C₂×#15692223	2
C₂×#15692217	2
C₂×#15692215	2
C₂×#15692211	2
C₂×#123×C₁₀₁	2
C₂×#525	101

Subgroups — C2×#20265685 #27184371

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#20265685 #27184371