Subgroups — C₂×#20265683 #27184369

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	C₂⁴×Dic₁₀₁	C₂	1	1	yes	maximal, characteristic, complemented
3	#20265683	C₂	1	16	yes	maximal, direct product factor
4	C₂×#15692239	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#15692236	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#15692232	C₂	1	2	yes	maximal, complemented
7	C₂×#15692227	C₂	1	2	yes	maximal, complemented
8	C₂×#15692224	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×D₄×Dic₁₀₁	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×#120×C₁₀₁	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×#13108073	—	2	8	no	—
14	C₂×#13108073	C₂²	1	8	yes	complemented
15	C₂²×Dic₂₀₂	C₂²	1	1	yes	characteristic, complemented
16	C₂²×C₂²⋊D₁₀₁	C₂²	1	1	yes	characteristic
17	C₂²×C₂²⋊D₁₀₁	C₂²	1	2	yes	—
18	C₂²×C₂²⋊D₁₀₁	C₂²	1	1	yes	characteristic, complemented
19	C₂³×Dic₁₀₁	—	2	8	no	—
20	C₂³×Dic₁₀₁	C₂²	1	2	yes	—
21	C₂³×Dic₁₀₁	C₂²	1	2	yes	—
22	C₂³×Dic₁₀₁	C₂²	1	1	yes	characteristic
23	C₂³×Dic₁₀₁	C₂²	1	1	yes	characteristic
24	C₂³×Dic₁₀₁	C₂²	1	8	yes	complemented
25	C₂³×Dic₁₀₁	C₂²	1	1	yes	characteristic, complemented
26	C₂²×C₄×D₁₀₁	C₂²	1	1	yes	characteristic, complemented
27	#15692239	C₂²	1	8	yes	complemented
28	#15692236	C₂²	1	8	yes	complemented
29	#15692232	C₂²	1	16	yes	complemented
30	#15692227	C₂²	1	16	yes	complemented
31	#15692224	C₂²	1	8	yes	complemented
32	D₄×Dic₁₀₁	C₂²	1	16	yes	complemented
33	#15692215	C₂²	1	16	yes	complemented
34	#15692211	C₂²	1	8	yes	complemented
35	C₂×C₄⋊Dic₁₀₁	C₂²	1	2	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×C₂²⋊Dic₁₀₁	C₂²	1	2	yes	—
40	C₂×C₂²⋊Dic₁₀₁	C₂²	1	2	yes	complemented
41	C₂×#13108051	C₂²	1	2	yes	complemented
42	C₂×C₄×Dic₁₀₁	C₂²	1	2	yes	complemented
43	C₂⁵×C₁₀₁	C₂²	1	1	yes	characteristic
44	C₂²×D₄×C₁₀₁	C₂²	1	1	yes	characteristic
45	C₂²×D₄×C₁₀₁	C₂²	1	2	yes	—
46	#120×C₁₀₁	C₂²	1	8	yes	complemented
47	C₂×C₂²⋊C₄×C₁₀₁	C₂²	1	1	yes	characteristic
48	C₂×C₂²⋊C₄×C₁₀₁	C₂²	1	2	yes	—
49	C₂³×D₁₀₁	C₂³	1	1	yes	characteristic
50	#13108073	—	2	32	no	—
51	C₂×Dic₂₀₂	—	2	4	no	—
52	C₂×Dic₂₀₂	C₂³	1	4	yes	complemented
53	C₂×C₂²⋊D₁₀₁	—	2	4	no	—
54	C₂×C₂²⋊D₁₀₁	—	2	8	no	—
55	C₂×C₂²⋊D₁₀₁	—	2	4	no	—
56	C₂×C₂²⋊D₁₀₁	C₂³	1	4	yes	—
57	C₂×C₂²⋊D₁₀₁	C₂³	1	8	yes	—
58	C₂×C₂²⋊D₁₀₁	C₂³	1	4	yes	complemented
59	C₂²×Dic₁₀₁	—	2	4	no	—
60	C₂²×Dic₁₀₁	—	2	8	no	—
61	C₂²×Dic₁₀₁	—	2	8	no	—
62	C₂²×Dic₁₀₁	—	2	4	no	—
63	C₂²×Dic₁₀₁	—	2	32	no	—
64	C₂²×Dic₁₀₁	D₄	1	8	yes	complemented
65	C₂²×Dic₁₀₁	C₂³	1	2	yes	—
66	C₂²×Dic₁₀₁	C₂³	1	8	yes	—
67	C₂²×Dic₁₀₁	C₂³	1	8	yes	—
68	C₂²×Dic₁₀₁	C₂³	1	4	yes	—
69	C₂²×Dic₁₀₁	C₂³	1	1	yes	characteristic
70	C₂²×Dic₁₀₁	C₂³	1	2	yes	—
71	C₂²×Dic₁₀₁	C₂³	1	1	yes	characteristic
72	C₂²×Dic₁₀₁	C₂³	1	1	yes	characteristic
73	C₂²×Dic₁₀₁	C₂³	1	4	yes	—
74	C₂²×Dic₁₀₁	C₂³	1	4	yes	complemented
75	C₂×C₄×D₁₀₁	—	2	4	no	—
76	C₂×C₄×D₁₀₁	C₂³	1	4	yes	complemented
77	C₄⋊Dic₁₀₁	C₂³	1	8	yes	complemented
78	#13108053	C₂³	1	8	yes	complemented
79	#13108053	C₂³	1	8	yes	complemented
80	C₂²⋊Dic₁₀₁	C₂³	1	4	yes	—
81	C₂²⋊Dic₁₀₁	C₂³	1	8	yes	—
82	C₂²⋊Dic₁₀₁	C₂³	1	8	yes	complemented
83	#13108051	C₂³	1	8	yes	complemented
84	C₄×Dic₁₀₁	C₂³	1	8	yes	complemented
85	C₂⁴×C₁₀₁	—	2	4	no	—
86	C₂⁴×C₁₀₁	—	2	8	no	—
87	C₂⁴×C₁₀₁	C₂³	1	4	yes	—
88	C₂⁴×C₁₀₁	C₂³	1	1	yes	characteristic
89	C₂⁴×C₁₀₁	C₂³	1	1	yes	characteristic
90	C₂⁴×C₁₀₁	C₂³	1	2	yes	—
91	C₂×D₄×C₁₀₁	—	2	4	no	—
92	C₂×D₄×C₁₀₁	—	2	8	no	—
93	C₂×D₄×C₁₀₁	C₂³	1	4	yes	—
94	C₂×D₄×C₁₀₁	C₂³	1	8	yes	—
95	C₂²×C₄×C₁₀₁	C₂³	1	1	yes	characteristic
96	C₂²×C₄×C₁₀₁	C₂³	1	2	yes	—
97	C₂²⋊C₄×C₁₀₁	C₂³	1	4	yes	—
98	C₂²⋊C₄×C₁₀₁	C₂³	1	8	yes	—
99	C₂³×C₁₀₁	—	2	32	no	—
100	C₂³×C₁₀₁	—	2	8	no	—
101	C₂³×C₁₀₁	—	2	4	no	—
102	C₂³×C₁₀₁	—	2	4	no	—
103	C₂³×C₁₀₁	—	2	4	no	—
104	C₂³×C₁₀₁	—	2	16	no	—
105	C₂³×C₁₀₁	—	2	2	no	—
106	C₂³×C₁₀₁	—	2	4	no	—
107	C₂³×C₁₀₁	C₂×D₄	1	4	yes	—
108	C₂³×C₁₀₁	#41	1	8	yes	complemented
109	C₂³×C₁₀₁	C₂⁴	1	2	yes	—
110	C₂³×C₁₀₁	C₂⁴	1	2	yes	—
111	C₂³×C₁₀₁	C₂⁴	1	4	yes	—
112	C₂³×C₁₀₁	C₂⁴	1	1	yes	characteristic
113	C₂²×D₁₀₁	—	2	2	no	—
114	C₂²×D₁₀₁	—	2	4	no	—
115	C₂²×D₁₀₁	C₂⁴	1	2	yes	—
116	D₄×C₁₀₁	—	2	8	no	—
117	D₄×C₁₀₁	—	2	16	no	—
118	C₂×C₄×C₁₀₁	—	2	2	no	—
119	C₂×C₄×C₁₀₁	—	2	4	no	—
120	C₂×C₄×C₁₀₁	C₂⁴	1	4	yes	—
121	C₂×C₄×C₁₀₁	C₂⁴	1	2	yes	—
122	C₂²⋊D₁₀₁	—	2	8	no	—
123	C₂²⋊D₁₀₁	—	2	16	no	—
124	C₂²⋊D₁₀₁	—	2	8	no	—
125	C₂×Dic₁₀₁	—	2	8	no	—
126	C₂×Dic₁₀₁	—	2	4	no	—
127	C₂×Dic₁₀₁	—	2	2	no	—
128	C₂×Dic₁₀₁	—	2	4	no	—
129	C₂×Dic₁₀₁	—	2	16	no	—
130	C₂×Dic₁₀₁	—	2	16	no	—
131	C₂×Dic₁₀₁	—	2	8	no	—
132	C₂×Dic₁₀₁	C₂×D₄	1	4	yes	—
133	C₂×Dic₁₀₁	C₂×D₄	1	4	yes	—
134	C₂×Dic₁₀₁	C₂×D₄	1	16	yes	complemented
135	C₂×Dic₁₀₁	C₂⁴	1	4	yes	—
136	C₂×Dic₁₀₁	C₂⁴	1	4	yes	—
137	C₂×Dic₁₀₁	C₂⁴	1	2	yes	—
138	C₂×Dic₁₀₁	C₂⁴	1	2	yes	—
139	C₂×Dic₁₀₁	C₂⁴	1	2	yes	—
140	C₄×D₁₀₁	—	2	8	no	—
141	Dic₂₀₂	—	2	8	no	—
142	C₂²×C₁₀₁	—	2	32	no	—
143	C₂²×C₁₀₁	—	2	8	no	—
144	C₂²×C₁₀₁	—	2	16	no	—
145	C₂²×C₁₀₁	—	2	4	no	—
146	C₂²×C₁₀₁	—	2	4	no	—
147	C₂²×C₁₀₁	—	2	4	no	—
148	C₂²×C₁₀₁	—	2	2	no	—
149	C₂²×C₁₀₁	—	2	4	no	—
150	C₂²×C₁₀₁	—	4	4	no	—
151	C₂²×C₁₀₁	C₂²×D₄	1	4	yes	—
152	C₂²×C₁₀₁	C₂²×D₄	1	2	yes	—
153	C₂²×C₁₀₁	C₂×#41	1	4	yes	—
154	C₂²×C₁₀₁	C₂×#41	1	8	yes	complemented
155	C₂²×C₁₀₁	C₂⁵	1	1	yes	characteristic
156	C₂×D₁₀₁	—	2	2	no	—
157	C₂×D₁₀₁	—	2	4	no	—
158	C₂×D₁₀₁	—	4	4	no	—
159	C₄×C₁₀₁	—	2	2	no	—
160	C₄×C₁₀₁	—	2	4	no	—
161	Dic₁₀₁	—	2	2	no	—
162	Dic₁₀₁	—	2	4	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	—	2	8	no	—
168	C₂×C₁₀₁	—	4	2	no	—
169	C₂×C₁₀₁	#525	1	4	yes	complemented
170	C₂×C₁₀₁	C₂³×D₄	1	1	yes	characteristic
171	C₂×C₁₀₁	C₂²×#41	1	2	yes	—
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	—	101	1	no	—
180	C₂×C₂²⋊Q₈	—	101	2	no	—
181	C₂×#121	—	101	2	no	—
182	C₂×#120	—	101	1	no	—
183	C₂×#120	D₁₀₁	1	1	yes	characteristic, complemented
184	C₂×C₄×D₄	—	101	2	no	—
185	C₂×C₄×D₄	—	101	2	no	—
186	C₂×#117	—	101	1	no	—
187	C₂⁵	C₂×D₁₀₁	1	1	yes	characteristic
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	C₂×D₁₀₁	1	2	yes	—
195	C₂²×D₄	C₂×D₁₀₁	1	1	yes	characteristic
196	C₂³×C₄	—	101	1	no	—
197	C₂³×C₄	—	101	2	no	—
198	C₂³×C₄	—	101	2	no	—
199	C₂³×C₄	—	101	1	no	—
200	C₂³×C₄	—	101	1	no	—
201	C₂³×C₄	—	101	8	no	—
202	C₂³×C₄	—	101	1	no	—
203	C₂³×C₄	—	202	8	no	—
204	#123	—	101	8	no	—
205	#123	—	101	8	no	—
206	C₂²⋊Q₈	—	101	16	no	—
207	#121	—	101	16	no	—
208	#120	—	101	8	no	—
209	#120	C₂×D₁₀₁	1	8	yes	complemented
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	—	101	2	no	—
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	—
222	C₂×C₄²	—	101	2	no	—
223	C₂⁴	—	2	4	no	—
224	C₂⁴	—	2	8	no	—
225	C₂⁴	—	101	1	no	—
226	C₂⁴	C₂²×D₁₀₁	1	4	yes	—
227	C₂⁴	C₂²×D₁₀₁	1	1	yes	characteristic
228	C₂⁴	C₂²×D₁₀₁	1	1	yes	characteristic
229	C₂⁴	C₂²×D₁₀₁	1	2	yes	—
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	—	2	8	no	—
235	C₂×D₄	—	101	8	no	—
236	C₂×D₄	—	101	4	no	—
237	C₂×D₄	—	101	4	no	—
238	C₂×D₄	—	202	4	no	—
239	C₂×D₄	—	202	4	no	—
240	C₂×D₄	—	202	8	no	—
241	C₂×D₄	C₂²×D₁₀₁	1	8	yes	—
242	C₂×D₄	C₂²×D₁₀₁	1	4	yes	—
243	C₂²×C₄	—	101	8	no	—
244	C₂²×C₄	—	101	4	no	—
245	C₂²×C₄	—	101	1	no	—
246	C₂²×C₄	—	101	1	no	—
247	C₂²×C₄	—	101	8	no	—
248	C₂²×C₄	—	101	8	no	—
249	C₂²×C₄	—	101	4	no	—
250	C₂²×C₄	—	101	4	no	—
251	C₂²×C₄	—	101	2	no	—
252	C₂²×C₄	—	101	2	no	—
253	C₂²×C₄	—	101	1	no	—
254	C₂²×C₄	—	101	4	no	—
255	C₂²×C₄	—	202	4	no	—
256	C₂²×C₄	—	202	8	no	—
257	C₂²×C₄	—	202	8	no	—
258	C₂²×C₄	—	202	32	no	—
259	C₂²×C₄	—	202	4	no	—
260	C₂²×C₄	—	202	4	no	—
261	C₂²×C₄	C₂²×D₁₀₁	1	2	yes	—
262	C₂²×C₄	C₂²×D₁₀₁	1	1	yes	characteristic
263	C₄⋊C₄	—	101	8	no	—
264	C₄⋊C₄	—	101	8	no	—
265	C₄⋊C₄	—	101	8	no	—
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	—
272	C₄²	—	101	8	no	—
273	C₂³	—	2	32	no	—
274	C₂³	—	2	8	no	—
275	C₂³	—	2	4	no	—
276	C₂³	—	2	4	no	—
277	C₂³	—	2	4	no	—
278	C₂³	—	2	16	no	—
279	C₂³	—	2	2	no	—
280	C₂³	—	2	4	no	—
281	C₂³	—	101	2	no	—
282	C₂³	—	202	2	no	—
283	C₂³	—	202	4	no	—
284	C₂³	D₄×D₁₀₁	1	4	yes	—
285	C₂³	#13108073	1	8	yes	complemented
286	C₂³	C₂³×D₁₀₁	1	2	yes	—
287	C₂³	C₂³×D₁₀₁	1	2	yes	—
288	C₂³	C₂³×D₁₀₁	1	4	yes	—
289	C₂³	C₂³×D₁₀₁	1	1	yes	characteristic
290	Q₈	—	202	8	no	—
291	D₄	—	2	8	no	—
292	D₄	—	2	16	no	—
293	D₄	—	202	8	no	—
294	D₄	—	202	8	no	—
295	D₄	—	202	16	no	—
296	C₂×C₄	—	2	2	no	—
297	C₂×C₄	—	2	4	no	—
298	C₂×C₄	—	101	4	no	—
299	C₂×C₄	—	101	4	no	—
300	C₂×C₄	—	101	16	no	—
301	C₂×C₄	—	101	2	no	—
302	C₂×C₄	—	101	2	no	—
303	C₂×C₄	—	101	4	no	—
304	C₂×C₄	—	101	4	no	—
305	C₂×C₄	—	101	2	no	—
306	C₂×C₄	—	202	8	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	4	no	—
312	C₂×C₄	—	202	2	no	—
313	C₂×C₄	—	202	4	no	—
314	C₂×C₄	C₂³×D₁₀₁	1	4	yes	—
315	C₂×C₄	C₂³×D₁₀₁	1	2	yes	—
316	C₂²	—	2	32	no	—
317	C₂²	—	2	4	no	—
318	C₂²	—	2	4	no	—
319	C₂²	—	2	4	no	—
320	C₂²	—	2	8	no	—
321	C₂²	—	2	16	no	—
322	C₂²	—	2	2	no	—
323	C₂²	—	2	4	no	—
324	C₂²	—	4	4	no	—
325	C₂²	—	404	4	no	—
326	C₂²	—	202	2	no	—
327	C₂²	—	202	4	no	—
328	C₂²	C₂×D₄×D₁₀₁	1	4	yes	—
329	C₂²	C₂×D₄×D₁₀₁	1	2	yes	—
330	C₂²	C₂×#13108073	1	4	yes	—
331	C₂²	C₂×#13108073	1	8	yes	complemented
332	C₂²	C₂⁴×D₁₀₁	1	1	yes	characteristic
333	C₄	—	2	2	no	—
334	C₄	—	2	4	no	—
335	C₄	—	101	4	no	—
336	C₄	—	101	4	no	—
337	C₄	—	202	4	no	—
338	C₄	—	202	2	no	—
339	C₄	—	202	4	no	—
340	C₂	—	2	4	no	—
341	C₂	—	2	8	no	—
342	C₂	—	4	2	no	—
343	C₂	—	404	2	no	—
344	C₂	#20265683	1	4	yes	direct product factor
345	C₂	C₂²×D₄×D₁₀₁	1	1	yes	characteristic
346	C₂	C₂²×#13108073	1	2	yes	—

	subgroup	G/H
center	C₂³	C₂³×D₁₀₁
commutator, cosocle	C₂²×C₁₀₁	C₂⁵
Frattini	C₂²	C₂⁴×D₁₀₁
Fitting	C₂×#120×C₁₀₁	C₂
socle	C₂³×C₁₀₁	C₂⁴
hypercenter	C₂×#120	D₁₀₁
hypocenter	C₁₀₁	C₂×#525
LCS	G ▷ C₂²×C₁₀₁ ▷ C₁₀₁
UCS	C₁ ◁ C₂³ ◁ C₂×#120

Complements

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

N	H ≅ G/N	type
1. C₂²×#13108073	C₂	semidirect
2. C₂⁴×Dic₁₀₁	C₂	semidirect
3. #20265683	C₂	direct (N × H)
4. C₂×#15692239	C₂	semidirect
5. C₂×#15692236	C₂	semidirect
6. C₂×#15692232	C₂	semidirect
7. C₂×#15692227	C₂	semidirect
8. C₂×#15692224	C₂	semidirect
9. C₂×D₄×Dic₁₀₁	C₂	semidirect
10. C₂×#15692215	C₂	semidirect
11. C₂×#15692211	C₂	semidirect
12. C₂×#120×C₁₀₁	C₂	semidirect
14. C₂×#13108073	C₂²	semidirect
15. C₂²×Dic₂₀₂	C₂²	semidirect
18. C₂²×C₂²⋊D₁₀₁	C₂²	semidirect
24. C₂³×Dic₁₀₁	C₂²	semidirect
25. C₂³×Dic₁₀₁	C₂²	semidirect
26. C₂²×C₄×D₁₀₁	C₂²	semidirect
27. #15692239	C₂²	semidirect
28. #15692236	C₂²	semidirect
29. #15692232	C₂²	semidirect
30. #15692227	C₂²	semidirect
31. #15692224	C₂²	semidirect
32. D₄×Dic₁₀₁	C₂²	semidirect
33. #15692215	C₂²	semidirect
34. #15692211	C₂²	semidirect
35. C₂×C₄⋊Dic₁₀₁	C₂²	semidirect
36. C₂×#13108053	C₂²	semidirect
37. C₂×#13108053	C₂²	semidirect
40. C₂×C₂²⋊Dic₁₀₁	C₂²	semidirect
41. C₂×#13108051	C₂²	semidirect
42. C₂×C₄×Dic₁₀₁	C₂²	semidirect
46. #120×C₁₀₁	C₂²	semidirect
52. C₂×Dic₂₀₂	C₂³	semidirect
58. C₂×C₂²⋊D₁₀₁	C₂³	semidirect
64. C₂²×Dic₁₀₁	D₄	semidirect
74. C₂²×Dic₁₀₁	C₂³	semidirect
76. C₂×C₄×D₁₀₁	C₂³	semidirect
77. C₄⋊Dic₁₀₁	C₂³	semidirect
78. #13108053	C₂³	semidirect
79. #13108053	C₂³	semidirect
82. C₂²⋊Dic₁₀₁	C₂³	semidirect
83. #13108051	C₂³	semidirect
84. C₄×Dic₁₀₁	C₂³	semidirect
108. C₂³×C₁₀₁	#41	semidirect
134. C₂×Dic₁₀₁	C₂×D₄	semidirect
154. C₂²×C₁₀₁	C₂×#41	semidirect
169. C₂×C₁₀₁	#525	semidirect
174. C₁₀₁	C₂×#525	semidirect
183. C₂×#120	D₁₀₁	semidirect
209. #120	C₂×D₁₀₁	semidirect
285. C₂³	#13108073	semidirect
331. C₂²	C₂×#13108073	semidirect
344. C₂	#20265683	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
C₂⁴×Dic₁₀₁	2
#20265683	2
C₂×#15692239	2
C₂×#15692236	2
C₂×#15692232	2
C₂×#15692227	2
C₂×#15692224	2
C₂×D₄×Dic₁₀₁	2
C₂×#15692215	2
C₂×#15692211	2
C₂×#120×C₁₀₁	2
C₂×#525	101

Subgroups — C2×#20265683 #27184369

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#20265683 #27184369