Subgroups — C₂×#20265797 #27184509

Order 12928.

1132 conjugacy classes of subgroups.

The subgroup lattice has 416 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20265797	C₂	1	16	yes	maximal, direct product factor
2	C₂×#15692253	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#15692250	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#15692248	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#15692244	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#15692241	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#15692241	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#15692240	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×#15692238	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#15692233	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×#15692233	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#15692228	C₂	1	1	yes	maximal, characteristic
13	C₂×#15692220	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×C₄×C₂²⋊D₁₀₁	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×#15692213	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₂²⋊Q₈×C₁₀₁	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂²×Dic₂₀₂	C₂²	1	1	yes	characteristic
18	C₂²×Dic₂₀₂	C₂²	1	1	yes	characteristic
19	C₂²×D₄₀₄	C₂²	1	1	yes	characteristic
20	C₂²×C₂²⋊D₁₀₁	C₂²	1	1	yes	characteristic
21	C₂²×C₂²⋊D₁₀₁	C₂²	1	1	yes	characteristic
22	C₂²×C₄×D₁₀₁	C₂²	1	1	yes	characteristic
23	C₂²×C₄×D₁₀₁	C₂²	1	1	yes	characteristic
24	#15692253	C₂²	1	8	yes	complemented
25	#15692250	C₂²	1	8	yes	complemented
26	#15692248	C₂²	1	8	yes	complemented
27	#15692244	C₂²	1	8	yes	complemented
28	#15692241	C₂²	1	8	yes	complemented
29	#15692241	C₂²	1	8	yes	complemented
30	#15692240	C₂²	1	8	yes	complemented
31	#15692238	C₂²	1	8	yes	complemented
32	#15692233	C₂²	1	8	yes	complemented
33	#15692233	C₂²	1	8	yes	complemented
34	#15692228	C₂²	1	8	yes	—
35	#15692220	C₂²	1	8	yes	complemented
36	C₄×C₂²⋊D₁₀₁	C₂²	1	8	yes	complemented
37	#15692213	C₂²	1	8	yes	complemented
38	C₂×C₄⋊Dic₁₀₁	C₂²	1	1	yes	characteristic
39	C₂×#13108053	C₂²	1	1	yes	characteristic
40	C₂×#13108053	C₂²	1	1	yes	characteristic
41	C₂×#13108053	C₂²	1	1	yes	characteristic
42	C₂×#13108053	C₂²	1	1	yes	characteristic
43	C₂×#13108053	C₂²	1	1	yes	characteristic
44	C₂×#13108053	C₂²	1	1	yes	characteristic
45	C₂×C₂²⋊Dic₁₀₁	C₂²	1	1	yes	characteristic
46	C₂×C₂²⋊Dic₁₀₁	C₂²	1	1	yes	characteristic
47	C₂×#13108051	C₂²	1	1	yes	characteristic
48	C₂×#13108051	C₂²	1	1	yes	characteristic
49	C₂×#13108051	C₂²	1	1	yes	characteristic
50	C₂×#13108051	C₂²	1	1	yes	characteristic
51	C₂×#13108051	C₂²	1	1	yes	characteristic
52	C₂×#13108051	C₂²	1	1	yes	characteristic
53	C₂×#13108051	C₂²	1	1	yes	characteristic
54	C₂×#13108051	C₂²	1	1	yes	characteristic
55	C₂×C₄×Dic₁₀₁	C₂²	1	1	yes	characteristic
56	C₂×C₄×Dic₁₀₁	C₂²	1	1	yes	characteristic
57	C₂×C₄×Dic₁₀₁	C₂²	1	1	yes	characteristic
58	C₂×C₄×Dic₁₀₁	C₂²	1	1	yes	characteristic
59	C₂²×Q₈×C₁₀₁	C₂²	1	1	yes	characteristic
60	C₂³×C₄×C₁₀₁	C₂²	1	1	yes	characteristic
61	C₂²⋊Q₈×C₁₀₁	C₂²	1	8	yes	complemented
62	C₂×C₄⋊C₄×C₁₀₁	C₂²	1	1	yes	characteristic
63	C₂×C₄⋊C₄×C₁₀₁	C₂²	1	1	yes	characteristic
64	C₂×C₄⋊C₄×C₁₀₁	C₂²	1	1	yes	characteristic
65	C₂×C₂²⋊C₄×C₁₀₁	C₂²	1	1	yes	characteristic
66	C₂×C₂²⋊C₄×C₁₀₁	C₂²	1	1	yes	characteristic
67	C₂³×D₁₀₁	C₂³	1	1	yes	characteristic
68	C₂³×D₁₀₁	C₂³	1	1	yes	characteristic
69	C₂×Dic₂₀₂	—	2	4	no	—
70	C₂×Dic₂₀₂	—	4	2	no	—
71	C₂×Dic₂₀₂	C₂³	1	4	yes	—
72	C₂×Dic₂₀₂	C₂³	1	4	yes	—
73	C₂×D₄₀₄	—	4	2	no	—
74	C₂×D₄₀₄	C₂³	1	4	yes	—
75	C₂×C₂²⋊D₁₀₁	—	2	4	no	—
76	C₂×C₂²⋊D₁₀₁	—	4	2	no	—
77	C₂×C₂²⋊D₁₀₁	C₂³	1	4	yes	—
78	C₂×C₂²⋊D₁₀₁	C₂³	1	4	yes	—
79	C₂²×Dic₁₀₁	C₂³	1	1	yes	characteristic
80	C₂²×Dic₁₀₁	C₂³	1	1	yes	characteristic
81	C₂²×Dic₁₀₁	C₂³	1	1	yes	characteristic
82	C₂²×Dic₁₀₁	C₂³	1	1	yes	characteristic
83	C₂²×Dic₁₀₁	C₂³	1	1	yes	characteristic
84	C₂²×Dic₁₀₁	C₂³	1	1	yes	characteristic
85	C₂×C₄×D₁₀₁	—	2	4	no	—
86	C₂×C₄×D₁₀₁	—	4	2	no	—
87	C₂×C₄×D₁₀₁	C₂³	1	4	yes	—
88	C₂×C₄×D₁₀₁	C₂³	1	4	yes	—
89	C₄⋊Dic₁₀₁	C₂³	1	4	yes	—
90	#13108053	C₂³	1	4	yes	—
91	#13108053	C₂³	1	4	yes	—
92	#13108053	C₂³	1	4	yes	—
93	#13108053	C₂³	1	4	yes	—
94	#13108053	C₂³	1	4	yes	—
95	#13108053	C₂³	1	4	yes	—
96	C₂²⋊Dic₁₀₁	C₂³	1	4	yes	—
97	C₂²⋊Dic₁₀₁	C₂³	1	4	yes	—
98	#13108051	C₂³	1	4	yes	—
99	#13108051	C₂³	1	4	yes	—
100	#13108051	C₂³	1	4	yes	—
101	#13108051	C₂³	1	4	yes	—
102	#13108051	C₂³	1	4	yes	—
103	#13108051	C₂³	1	4	yes	—
104	#13108051	C₂³	1	4	yes	—
105	#13108051	C₂³	1	4	yes	—
106	C₄×Dic₁₀₁	C₂³	1	4	yes	—
107	C₄×Dic₁₀₁	C₂³	1	4	yes	—
108	C₄×Dic₁₀₁	C₂³	1	4	yes	—
109	C₄×Dic₁₀₁	C₂³	1	4	yes	—
110	C₂⁴×C₁₀₁	C₂³	1	1	yes	characteristic
111	C₂×Q₈×C₁₀₁	—	4	2	no	—
112	C₂×Q₈×C₁₀₁	C₂³	1	4	yes	—
113	C₂²×C₄×C₁₀₁	—	4	2	no	—
114	C₂²×C₄×C₁₀₁	C₂³	1	1	yes	characteristic
115	C₂²×C₄×C₁₀₁	C₂³	1	1	yes	characteristic
116	C₂²×C₄×C₁₀₁	C₂³	1	1	yes	characteristic
117	C₂²×C₄×C₁₀₁	C₂³	1	1	yes	characteristic
118	C₂²×C₄×C₁₀₁	C₂³	1	1	yes	characteristic
119	C₂²×C₄×C₁₀₁	C₂³	1	1	yes	characteristic
120	C₂²×C₄×C₁₀₁	C₂³	1	4	yes	—
121	C₄⋊C₄×C₁₀₁	C₂³	1	4	yes	—
122	C₄⋊C₄×C₁₀₁	C₂³	1	4	yes	—
123	C₄⋊C₄×C₁₀₁	C₂³	1	4	yes	—
124	C₂²⋊C₄×C₁₀₁	C₂³	1	4	yes	—
125	C₂²⋊C₄×C₁₀₁	C₂³	1	4	yes	—
126	C₂³×C₁₀₁	—	2	2	no	—
127	C₂³×C₁₀₁	—	2	2	no	—
128	C₂³×C₁₀₁	—	2	2	no	—
129	C₂³×C₁₀₁	C₂⁴	1	2	yes	—
130	C₂³×C₁₀₁	C₂⁴	1	1	yes	characteristic
131	C₂²×D₁₀₁	—	2	2	no	—
132	C₂²×D₁₀₁	—	2	2	no	—
133	C₂²×D₁₀₁	—	2	2	no	—
134	C₂²×D₁₀₁	—	2	2	no	—
135	C₂²×D₁₀₁	—	2	2	no	—
136	C₂²×D₁₀₁	—	2	2	no	—
137	C₂²×D₁₀₁	C₂⁴	1	2	yes	—
138	C₂²×D₁₀₁	C₂⁴	1	2	yes	—
139	Q₈×C₁₀₁	—	4	4	no	—
140	C₂×C₄×C₁₀₁	—	2	2	no	—
141	C₂×C₄×C₁₀₁	—	2	2	no	—
142	C₂×C₄×C₁₀₁	—	2	2	no	—
143	C₂×C₄×C₁₀₁	—	2	2	no	—
144	C₂×C₄×C₁₀₁	—	2	2	no	—
145	C₂×C₄×C₁₀₁	—	2	2	no	—
146	C₂×C₄×C₁₀₁	—	4	4	no	—
147	C₂×C₄×C₁₀₁	C₂⁴	1	2	yes	—
148	C₂×C₄×C₁₀₁	C₂⁴	1	2	yes	—
149	C₂×C₄×C₁₀₁	C₂⁴	1	2	yes	—
150	C₂×C₄×C₁₀₁	C₂⁴	1	2	yes	—
151	C₂×C₄×C₁₀₁	C₂⁴	1	2	yes	—
152	C₂×C₄×C₁₀₁	C₂⁴	1	2	yes	—
153	C₂²⋊D₁₀₁	—	2	8	no	—
154	C₂²⋊D₁₀₁	—	4	4	no	—
155	C₂×Dic₁₀₁	—	2	2	no	—
156	C₂×Dic₁₀₁	—	2	2	no	—
157	C₂×Dic₁₀₁	—	2	2	no	—
158	C₂×Dic₁₀₁	—	2	2	no	—
159	C₂×Dic₁₀₁	—	2	2	no	—
160	C₂×Dic₁₀₁	#41	1	4	yes	—
161	C₂×Dic₁₀₁	C₂⁴	1	2	yes	—
162	C₂×Dic₁₀₁	C₂⁴	1	2	yes	—
163	C₂×Dic₁₀₁	C₂⁴	1	2	yes	—
164	C₂×Dic₁₀₁	C₂⁴	1	2	yes	—
165	C₂×Dic₁₀₁	C₂⁴	1	2	yes	—
166	C₂×Dic₁₀₁	C₂⁴	1	2	yes	—
167	D₄₀₄	—	4	4	no	—
168	C₄×D₁₀₁	—	2	8	no	—
169	C₄×D₁₀₁	—	4	4	no	—
170	Dic₂₀₂	—	2	8	no	—
171	Dic₂₀₂	—	4	4	no	—
172	C₂²×C₁₀₁	—	2	2	no	—
173	C₂²×C₁₀₁	—	2	2	no	—
174	C₂²×C₁₀₁	—	2	2	no	—
175	C₂²×C₁₀₁	—	4	4	no	—
176	C₂²×C₁₀₁	C₂×#41	1	2	yes	—
177	C₂²×C₁₀₁	H(5,𝔽₂)	1	2	yes	—
178	C₂²×C₁₀₁	2₋¹⁺⁴	1	2	yes	—
179	C₂²×C₁₀₁	C₂⁵	1	1	yes	characteristic
180	C₂×D₁₀₁	—	2	2	no	—
181	C₂×D₁₀₁	—	2	2	no	—
182	C₂×D₁₀₁	—	2	2	no	—
183	C₂×D₁₀₁	—	2	2	no	—
184	C₂×D₁₀₁	—	2	2	no	—
185	C₂×D₁₀₁	—	2	2	no	—
186	C₂×D₁₀₁	—	4	4	no	—
187	C₂×D₁₀₁	—	4	4	no	—
188	C₄×C₁₀₁	—	2	2	no	—
189	C₄×C₁₀₁	—	2	2	no	—
190	C₄×C₁₀₁	—	2	2	no	—
191	C₄×C₁₀₁	—	2	2	no	—
192	C₄×C₁₀₁	—	2	2	no	—
193	C₄×C₁₀₁	—	2	2	no	—
194	Dic₁₀₁	—	2	2	no	—
195	Dic₁₀₁	—	2	2	no	—
196	Dic₁₀₁	—	2	2	no	—
197	Dic₁₀₁	—	2	2	no	—
198	Dic₁₀₁	—	2	2	no	—
199	Dic₁₀₁	C₂×#41	1	4	yes	—
200	C₂×C₁₀₁	—	4	2	no	—
201	C₂×C₁₀₁	#542	1	4	yes	complemented
202	C₂×C₁₀₁	C₂²×#41	1	1	yes	characteristic
203	C₂×C₁₀₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
204	C₂×C₁₀₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
205	D₁₀₁	—	4	2	no	—
206	D₁₀₁	—	4	2	no	—
207	C₂×#542	—	101	1	no	maximal, Sylow
208	C₁₀₁	C₂×#542	1	1	yes	characteristic, complemented, Sylow
209	#542	—	101	16	no	—
210	C₂×C₄⋊Q₈	—	101	1	no	—
211	C₂×#126	—	101	1	no	—
212	C₂×#126	—	101	1	no	—
213	C₂×#124	—	101	1	no	—
214	C₂×#124	—	101	1	no	—
215	C₂×#124	—	101	1	no	—
216	C₂×#123	—	101	1	no	—
217	C₂×#123	—	101	1	no	—
218	C₂×C₂²⋊Q₈	—	101	1	no	—
219	C₂×C₂²⋊Q₈	—	101	1	no	—
220	C₂×C₂²⋊Q₈	D₁₀₁	1	1	yes	characteristic, complemented
221	C₂×#121	—	101	1	no	—
222	C₂×C₄×Q₈	—	101	1	no	—
223	C₂×C₄×D₄	—	101	1	no	—
224	C₂×#117	—	101	1	no	—
225	C₂²×Q₈	—	101	1	no	—
226	C₂²×Q₈	—	101	1	no	—
227	C₂²×Q₈	C₂×D₁₀₁	1	1	yes	characteristic
228	C₂²×D₄	—	101	1	no	—
229	C₂²×D₄	—	101	1	no	—
230	C₂²×D₄	—	101	1	no	—
231	C₂³×C₄	—	101	1	no	—
232	C₂³×C₄	—	101	1	no	—
233	C₂³×C₄	C₂×D₁₀₁	1	1	yes	characteristic
234	C₄⋊Q₈	—	101	8	no	—
235	#126	—	101	8	no	—
236	#126	—	101	8	no	—
237	#124	—	101	8	no	—
238	#124	—	101	8	no	—
239	#124	—	101	8	no	—
240	#123	—	101	8	no	—
241	#123	—	101	8	no	—
242	C₂²⋊Q₈	—	101	8	no	—
243	C₂²⋊Q₈	—	101	8	no	—
244	C₂²⋊Q₈	C₂×D₁₀₁	1	8	yes	complemented
245	#121	—	101	8	no	—
246	C₄×Q₈	—	101	8	no	—
247	C₄×D₄	—	101	8	no	—
248	#117	—	101	8	no	—
249	C₂×C₄⋊C₄	—	101	1	no	—
250	C₂×C₄⋊C₄	—	101	1	no	—
251	C₂×C₄⋊C₄	—	101	1	no	—
252	C₂×C₄⋊C₄	—	101	1	no	—
253	C₂×C₄⋊C₄	—	101	1	no	—
254	C₂×C₄⋊C₄	—	101	1	no	—
255	C₂×C₄⋊C₄	—	101	1	no	—
256	C₂×C₄⋊C₄	C₂×D₁₀₁	1	1	yes	characteristic
257	C₂×C₄⋊C₄	C₂×D₁₀₁	1	1	yes	characteristic
258	C₂×C₄⋊C₄	C₂×D₁₀₁	1	1	yes	characteristic
259	C₂×C₂²⋊C₄	—	101	1	no	—
260	C₂×C₂²⋊C₄	—	101	1	no	—
261	C₂×C₂²⋊C₄	—	101	1	no	—
262	C₂×C₂²⋊C₄	—	101	1	no	—
263	C₂×C₂²⋊C₄	—	101	1	no	—
264	C₂×C₂²⋊C₄	—	101	1	no	—
265	C₂×C₂²⋊C₄	—	101	1	no	—
266	C₂×C₂²⋊C₄	—	101	1	no	—
267	C₂×C₂²⋊C₄	—	101	1	no	—
268	C₂×C₂²⋊C₄	—	101	1	no	—
269	C₂×C₂²⋊C₄	C₂×D₁₀₁	1	1	yes	characteristic
270	C₂×C₂²⋊C₄	C₂×D₁₀₁	1	1	yes	characteristic
271	C₂×C₄²	—	101	1	no	—
272	C₂×C₄²	—	101	1	no	—
273	C₂×C₄²	—	101	1	no	—
274	C₂×C₄²	—	101	1	no	—
275	C₂⁴	—	101	1	no	—
276	C₂⁴	—	101	1	no	—
277	C₂⁴	C₂²×D₁₀₁	1	1	yes	characteristic
278	C₂×Q₈	—	4	2	no	—
279	C₂×Q₈	—	101	4	no	—
280	C₂×Q₈	—	101	4	no	—
281	C₂×Q₈	—	404	2	no	—
282	C₂×Q₈	—	202	4	no	—
283	C₂×Q₈	C₂²×D₁₀₁	1	4	yes	—
284	C₂×D₄	—	101	4	no	—
285	C₂×D₄	—	101	4	no	—
286	C₂×D₄	—	101	4	no	—
287	C₂×D₄	—	404	2	no	—
288	C₂×D₄	—	404	2	no	—
289	C₂×D₄	—	202	4	no	—
290	C₂²×C₄	—	4	2	no	—
291	C₂²×C₄	—	101	1	no	—
292	C₂²×C₄	—	101	1	no	—
293	C₂²×C₄	—	101	1	no	—
294	C₂²×C₄	—	101	1	no	—
295	C₂²×C₄	—	101	1	no	—
296	C₂²×C₄	—	101	1	no	—
297	C₂²×C₄	—	101	4	no	—
298	C₂²×C₄	—	101	4	no	—
299	C₂²×C₄	—	404	2	no	—
300	C₂²×C₄	—	202	4	no	—
301	C₂²×C₄	C₂²×D₁₀₁	1	1	yes	characteristic
302	C₂²×C₄	C₂²×D₁₀₁	1	1	yes	characteristic
303	C₂²×C₄	C₂²×D₁₀₁	1	1	yes	characteristic
304	C₂²×C₄	C₂²×D₁₀₁	1	1	yes	characteristic
305	C₂²×C₄	C₂²×D₁₀₁	1	1	yes	characteristic
306	C₂²×C₄	C₂²×D₁₀₁	1	1	yes	characteristic
307	C₂²×C₄	C₂²×D₁₀₁	1	4	yes	—
308	C₄⋊C₄	—	101	4	no	—
309	C₄⋊C₄	—	101	4	no	—
310	C₄⋊C₄	—	101	4	no	—
311	C₄⋊C₄	—	101	4	no	—
312	C₄⋊C₄	—	101	4	no	—
313	C₄⋊C₄	—	101	4	no	—
314	C₄⋊C₄	—	101	4	no	—
315	C₄⋊C₄	C₂²×D₁₀₁	1	4	yes	—
316	C₄⋊C₄	C₂²×D₁₀₁	1	4	yes	—
317	C₄⋊C₄	C₂²×D₁₀₁	1	4	yes	—
318	C₂²⋊C₄	—	101	4	no	—
319	C₂²⋊C₄	—	101	4	no	—
320	C₂²⋊C₄	—	101	4	no	—
321	C₂²⋊C₄	—	101	4	no	—
322	C₂²⋊C₄	—	101	4	no	—
323	C₂²⋊C₄	—	101	4	no	—
324	C₂²⋊C₄	—	101	4	no	—
325	C₂²⋊C₄	—	101	4	no	—
326	C₂²⋊C₄	—	101	4	no	—
327	C₂²⋊C₄	—	101	4	no	—
328	C₂²⋊C₄	C₂²×D₁₀₁	1	4	yes	—
329	C₂²⋊C₄	C₂²×D₁₀₁	1	4	yes	—
330	C₄²	—	101	4	no	—
331	C₄²	—	101	4	no	—
332	C₄²	—	101	4	no	—
333	C₄²	—	101	4	no	—
334	C₂³	—	2	2	no	—
335	C₂³	—	2	2	no	—
336	C₂³	—	2	2	no	—
337	C₂³	—	101	2	no	—
338	C₂³	—	101	2	no	—
339	C₂³	—	202	2	no	—
340	C₂³	—	202	2	no	—
341	C₂³	—	202	2	no	—
342	C₂³	—	202	2	no	—
343	C₂³	—	202	2	no	—
344	C₂³	—	202	2	no	—
345	C₂³	C₂³×D₁₀₁	1	2	yes	—
346	C₂³	C₂³×D₁₀₁	1	1	yes	characteristic
347	Q₈	—	4	4	no	—
348	Q₈	—	404	4	no	—
349	Q₈	—	202	8	no	—
350	D₄	—	404	4	no	—
351	D₄	—	404	4	no	—
352	D₄	—	202	8	no	—
353	C₂×C₄	—	2	2	no	—
354	C₂×C₄	—	2	2	no	—
355	C₂×C₄	—	2	2	no	—
356	C₂×C₄	—	2	2	no	—
357	C₂×C₄	—	2	2	no	—
358	C₂×C₄	—	2	2	no	—
359	C₂×C₄	—	4	4	no	—
360	C₂×C₄	—	101	4	no	—
361	C₂×C₄	—	101	2	no	—
362	C₂×C₄	—	101	2	no	—
363	C₂×C₄	—	101	2	no	—
364	C₂×C₄	—	101	2	no	—
365	C₂×C₄	—	101	2	no	—
366	C₂×C₄	—	101	2	no	—
367	C₂×C₄	—	404	4	no	—
368	C₂×C₄	—	202	8	no	—
369	C₂×C₄	—	202	2	no	—
370	C₂×C₄	—	202	2	no	—
371	C₂×C₄	—	202	2	no	—
372	C₂×C₄	—	202	2	no	—
373	C₂×C₄	—	202	2	no	—
374	C₂×C₄	C₂³×D₁₀₁	1	2	yes	—
375	C₂×C₄	C₂³×D₁₀₁	1	2	yes	—
376	C₂×C₄	C₂³×D₁₀₁	1	2	yes	—
377	C₂×C₄	C₂³×D₁₀₁	1	2	yes	—
378	C₂×C₄	C₂³×D₁₀₁	1	2	yes	—
379	C₂×C₄	C₂³×D₁₀₁	1	2	yes	—
380	C₂²	—	2	2	no	—
381	C₂²	—	2	2	no	—
382	C₂²	—	2	2	no	—
383	C₂²	—	4	4	no	—
384	C₂²	—	404	4	no	—
385	C₂²	—	404	4	no	—
386	C₂²	—	202	2	no	—
387	C₂²	—	202	2	no	—
388	C₂²	—	202	2	no	—
389	C₂²	—	202	2	no	—
390	C₂²	—	202	2	no	—
391	C₂²	—	202	2	no	—
392	C₂²	#41×D₁₀₁	1	2	yes	—
393	C₂²	#15692300	1	2	yes	—
394	C₂²	#15692303	1	2	yes	—
395	C₂²	C₂⁴×D₁₀₁	1	1	yes	characteristic
396	C₄	—	2	2	no	—
397	C₄	—	2	2	no	—
398	C₄	—	2	2	no	—
399	C₄	—	2	2	no	—
400	C₄	—	2	2	no	—
401	C₄	—	2	2	no	—
402	C₄	—	101	4	no	—
403	C₄	—	202	2	no	—
404	C₄	—	202	2	no	—
405	C₄	—	202	2	no	—
406	C₄	—	202	2	no	—
407	C₄	—	202	2	no	—
408	C₂	—	4	2	no	—
409	C₂	—	404	2	no	—
410	C₂	—	404	2	no	—
411	C₂	#20265797	1	4	yes	direct product factor
412	C₂	C₂×#41×D₁₀₁	1	1	yes	characteristic
413	C₂	C₂×#15692300	1	1	yes	characteristic
414	C₂	C₂×#15692303	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂³×D₁₀₁
commutator, cosocle	C₂²×C₁₀₁	C₂⁵
Frattini	C₂²	C₂⁴×D₁₀₁
Fitting	C₂×C₂²⋊Q₈×C₁₀₁	C₂
socle	C₂³×C₁₀₁	C₂⁴
prime radical	C₂×#15692228	C₂
hypercenter	C₂×C₂²⋊Q₈	D₁₀₁
hypocenter	C₁₀₁	C₂×#542
LCS	G ▷ C₂²×C₁₀₁ ▷ C₁₀₁
UCS	C₁ ◁ C₂³ ◁ C₂×C₂²⋊Q₈

Complements

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

N	H ≅ G/N	type
1. #20265797	C₂	direct (N × H)
2. C₂×#15692253	C₂	semidirect
3. C₂×#15692250	C₂	semidirect
4. C₂×#15692248	C₂	semidirect
5. C₂×#15692244	C₂	semidirect
6. C₂×#15692241	C₂	semidirect
7. C₂×#15692241	C₂	semidirect
8. C₂×#15692240	C₂	semidirect
9. C₂×#15692238	C₂	semidirect
10. C₂×#15692233	C₂	semidirect
11. C₂×#15692233	C₂	semidirect
13. C₂×#15692220	C₂	semidirect
14. C₂×C₄×C₂²⋊D₁₀₁	C₂	semidirect
15. C₂×#15692213	C₂	semidirect
16. C₂×C₂²⋊Q₈×C₁₀₁	C₂	semidirect
24. #15692253	C₂²	semidirect
25. #15692250	C₂²	semidirect
26. #15692248	C₂²	semidirect
27. #15692244	C₂²	semidirect
28. #15692241	C₂²	semidirect
29. #15692241	C₂²	semidirect
30. #15692240	C₂²	semidirect
31. #15692238	C₂²	semidirect
32. #15692233	C₂²	semidirect
33. #15692233	C₂²	semidirect
35. #15692220	C₂²	semidirect
36. C₄×C₂²⋊D₁₀₁	C₂²	semidirect
37. #15692213	C₂²	semidirect
61. C₂²⋊Q₈×C₁₀₁	C₂²	semidirect
201. C₂×C₁₀₁	#542	semidirect
208. C₁₀₁	C₂×#542	semidirect
220. C₂×C₂²⋊Q₈	D₁₀₁	semidirect
244. C₂²⋊Q₈	C₂×D₁₀₁	semidirect
411. C₂	#20265797	direct (N × H)

Maximal subgroups

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

subgroup	index
#20265797	2
C₂×#15692253	2
C₂×#15692250	2
C₂×#15692248	2
C₂×#15692244	2
C₂×#15692241	2
C₂×#15692240	2
C₂×#15692238	2
C₂×#15692233	2
C₂×#15692228	2
C₂×#15692220	2
C₂×C₄×C₂²⋊D₁₀₁	2
C₂×#15692213	2
C₂×C₂²⋊Q₈×C₁₀₁	2
C₂×#542	101

Subgroups — C2×#20265797 #27184509

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#20265797 #27184509