Subgroups — C₂×#20265923 #27185257

Order 12928.

1152 conjugacy classes of subgroups.

The subgroup lattice has 440 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20265923	C₂	1	16	yes	maximal, direct product factor
2	C₂×#15692245	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#15692244	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#15692241	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#15692240	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#15692240	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#15692238	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#15692237	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×#15692235	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#15692233	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×#15692231	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#15692230	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×#15692229	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×#15692228	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×#15692228	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×D₄₀₄	C₂²	1	1	yes	characteristic
19	C₂²×D₄₀₄	C₂²	1	1	yes	characteristic
20	C₂²×D₄₀₄	C₂²	1	1	yes	characteristic
21	C₂²×C₂²⋊D₁₀₁	C₂²	1	1	yes	characteristic
22	C₂²×C₂²⋊D₁₀₁	C₂²	1	1	yes	characteristic
23	C₂²×C₂²⋊D₁₀₁	C₂²	1	1	yes	characteristic
24	C₂²×C₄×D₁₀₁	C₂²	1	1	yes	characteristic
25	C₂²×C₄×D₁₀₁	C₂²	1	1	yes	characteristic
26	C₂²×C₄×D₁₀₁	C₂²	1	1	yes	characteristic
27	#15692245	C₂²	1	8	yes	complemented
28	#15692244	C₂²	1	8	yes	complemented
29	#15692241	C₂²	1	8	yes	complemented
30	#15692240	C₂²	1	8	yes	complemented
31	#15692240	C₂²	1	8	yes	complemented
32	#15692238	C₂²	1	8	yes	complemented
33	#15692237	C₂²	1	8	yes	complemented
34	#15692235	C₂²	1	8	yes	complemented
35	#15692233	C₂²	1	8	yes	complemented
36	#15692231	C₂²	1	8	yes	complemented
37	#15692230	C₂²	1	8	yes	complemented
38	#15692229	C₂²	1	8	yes	complemented
39	#15692228	C₂²	1	8	yes	complemented
40	#15692228	C₂²	1	8	yes	complemented
41	C₂×C₄⋊Dic₁₀₁	C₂²	1	1	yes	characteristic
42	C₂×C₄⋊Dic₁₀₁	C₂²	1	1	yes	characteristic
43	C₂×#13108053	C₂²	1	1	yes	characteristic
44	C₂×#13108053	C₂²	1	1	yes	characteristic
45	C₂×#13108053	C₂²	1	1	yes	characteristic
46	C₂×#13108053	C₂²	1	1	yes	characteristic
47	C₂×#13108053	C₂²	1	1	yes	characteristic
48	C₂×C₂²⋊Dic₁₀₁	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×#13108051	C₂²	1	1	yes	characteristic
56	C₂×#13108051	C₂²	1	1	yes	characteristic
57	C₂×#13108051	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	C₂³×D₁₀₁	C₂³	1	1	yes	characteristic
70	C₂×Dic₂₀₂	—	4	2	no	—
71	C₂×Dic₂₀₂	C₂³	1	4	yes	—
72	C₂×D₄₀₄	—	4	2	no	—
73	C₂×D₄₀₄	—	4	2	no	—
74	C₂×D₄₀₄	—	4	2	no	—
75	C₂×D₄₀₄	C₂³	1	4	yes	—
76	C₂×D₄₀₄	C₂³	1	4	yes	—
77	C₂×D₄₀₄	C₂³	1	4	yes	—
78	C₂×C₂²⋊D₁₀₁	—	4	2	no	—
79	C₂×C₂²⋊D₁₀₁	—	4	2	no	—
80	C₂×C₂²⋊D₁₀₁	—	4	2	no	—
81	C₂×C₂²⋊D₁₀₁	C₂³	1	4	yes	—
82	C₂×C₂²⋊D₁₀₁	C₂³	1	4	yes	—
83	C₂×C₂²⋊D₁₀₁	C₂³	1	4	yes	—
84	C₂²×Dic₁₀₁	C₂³	1	1	yes	characteristic
85	C₂²×Dic₁₀₁	C₂³	1	1	yes	characteristic
86	C₂²×Dic₁₀₁	C₂³	1	1	yes	characteristic
87	C₂²×Dic₁₀₁	C₂³	1	1	yes	characteristic
88	C₂²×Dic₁₀₁	C₂³	1	1	yes	characteristic
89	C₂×C₄×D₁₀₁	—	4	2	no	—
90	C₂×C₄×D₁₀₁	—	4	2	no	—
91	C₂×C₄×D₁₀₁	—	4	2	no	—
92	C₂×C₄×D₁₀₁	C₂³	1	4	yes	—
93	C₂×C₄×D₁₀₁	C₂³	1	4	yes	—
94	C₂×C₄×D₁₀₁	C₂³	1	4	yes	—
95	C₄⋊Dic₁₀₁	C₂³	1	4	yes	—
96	C₄⋊Dic₁₀₁	C₂³	1	4	yes	—
97	#13108053	C₂³	1	4	yes	—
98	#13108053	C₂³	1	4	yes	—
99	#13108053	C₂³	1	4	yes	—
100	#13108053	C₂³	1	4	yes	—
101	#13108053	C₂³	1	4	yes	—
102	C₂²⋊Dic₁₀₁	C₂³	1	4	yes	—
103	#13108051	C₂³	1	4	yes	—
104	#13108051	C₂³	1	4	yes	—
105	#13108051	C₂³	1	4	yes	—
106	#13108051	C₂³	1	4	yes	—
107	#13108051	C₂³	1	4	yes	—
108	#13108051	C₂³	1	4	yes	—
109	#13108051	C₂³	1	4	yes	—
110	#13108051	C₂³	1	4	yes	—
111	#13108051	C₂³	1	4	yes	—
112	C₄×Dic₁₀₁	C₂³	1	4	yes	—
113	C₂⁴×C₁₀₁	C₂³	1	1	yes	characteristic
114	C₂×Q₈×C₁₀₁	—	4	2	no	—
115	C₂×Q₈×C₁₀₁	C₂³	1	4	yes	—
116	C₂²×C₄×C₁₀₁	—	4	2	no	—
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	1	yes	characteristic
121	C₂²×C₄×C₁₀₁	C₂³	1	1	yes	characteristic
122	C₂²×C₄×C₁₀₁	C₂³	1	1	yes	characteristic
123	C₂²×C₄×C₁₀₁	C₂³	1	4	yes	—
124	C₄⋊C₄×C₁₀₁	C₂³	1	4	yes	—
125	C₄⋊C₄×C₁₀₁	C₂³	1	4	yes	—
126	C₄⋊C₄×C₁₀₁	C₂³	1	4	yes	—
127	C₂²⋊C₄×C₁₀₁	C₂³	1	4	yes	—
128	C₂²⋊C₄×C₁₀₁	C₂³	1	4	yes	—
129	C₂³×C₁₀₁	—	2	2	no	—
130	C₂³×C₁₀₁	—	2	2	no	—
131	C₂³×C₁₀₁	—	2	2	no	—
132	C₂³×C₁₀₁	C₂⁴	1	2	yes	—
133	C₂³×C₁₀₁	C₂⁴	1	1	yes	characteristic
134	C₂²×D₁₀₁	—	2	2	no	—
135	C₂²×D₁₀₁	—	2	2	no	—
136	C₂²×D₁₀₁	—	2	2	no	—
137	C₂²×D₁₀₁	—	2	2	no	—
138	C₂²×D₁₀₁	—	2	2	no	—
139	C₂²×D₁₀₁	—	2	2	no	—
140	C₂²×D₁₀₁	—	2	2	no	—
141	C₂²×D₁₀₁	—	2	2	no	—
142	C₂²×D₁₀₁	—	2	2	no	—
143	C₂²×D₁₀₁	C₂⁴	1	2	yes	—
144	C₂²×D₁₀₁	C₂⁴	1	2	yes	—
145	C₂²×D₁₀₁	C₂⁴	1	2	yes	—
146	Q₈×C₁₀₁	—	4	4	no	—
147	C₂×C₄×C₁₀₁	—	2	2	no	—
148	C₂×C₄×C₁₀₁	—	2	2	no	—
149	C₂×C₄×C₁₀₁	—	2	2	no	—
150	C₂×C₄×C₁₀₁	—	2	2	no	—
151	C₂×C₄×C₁₀₁	—	2	2	no	—
152	C₂×C₄×C₁₀₁	—	2	2	no	—
153	C₂×C₄×C₁₀₁	—	4	4	no	—
154	C₂×C₄×C₁₀₁	C₂⁴	1	2	yes	—
155	C₂×C₄×C₁₀₁	C₂⁴	1	2	yes	—
156	C₂×C₄×C₁₀₁	C₂⁴	1	2	yes	—
157	C₂×C₄×C₁₀₁	C₂⁴	1	2	yes	—
158	C₂×C₄×C₁₀₁	C₂⁴	1	2	yes	—
159	C₂×C₄×C₁₀₁	C₂⁴	1	2	yes	—
160	C₂²⋊D₁₀₁	—	4	4	no	—
161	C₂²⋊D₁₀₁	—	4	4	no	—
162	C₂²⋊D₁₀₁	—	4	4	no	—
163	C₂×Dic₁₀₁	—	2	2	no	—
164	C₂×Dic₁₀₁	—	2	2	no	—
165	C₂×Dic₁₀₁	—	2	2	no	—
166	C₂×Dic₁₀₁	—	2	2	no	—
167	C₂×Dic₁₀₁	—	2	2	no	—
168	C₂×Dic₁₀₁	C₂⁴	1	2	yes	—
169	C₂×Dic₁₀₁	C₂⁴	1	2	yes	—
170	C₂×Dic₁₀₁	C₂⁴	1	2	yes	—
171	C₂×Dic₁₀₁	C₂⁴	1	2	yes	—
172	C₂×Dic₁₀₁	C₂⁴	1	2	yes	—
173	D₄₀₄	—	4	4	no	—
174	D₄₀₄	—	4	4	no	—
175	D₄₀₄	—	4	4	no	—
176	C₄×D₁₀₁	—	4	4	no	—
177	C₄×D₁₀₁	—	4	4	no	—
178	C₄×D₁₀₁	—	4	4	no	—
179	Dic₂₀₂	—	4	4	no	—
180	C₂²×C₁₀₁	—	2	2	no	—
181	C₂²×C₁₀₁	—	2	2	no	—
182	C₂²×C₁₀₁	—	2	2	no	—
183	C₂²×C₁₀₁	—	4	4	no	—
184	C₂²×C₁₀₁	H(5,𝔽₂)	1	2	yes	—
185	C₂²×C₁₀₁	H(5,𝔽₂)	1	2	yes	—
186	C₂²×C₁₀₁	2₋¹⁺⁴	1	2	yes	—
187	C₂²×C₁₀₁	C₂⁵	1	1	yes	characteristic
188	C₂×D₁₀₁	—	2	2	no	—
189	C₂×D₁₀₁	—	2	2	no	—
190	C₂×D₁₀₁	—	2	2	no	—
191	C₂×D₁₀₁	—	2	2	no	—
192	C₂×D₁₀₁	—	2	2	no	—
193	C₂×D₁₀₁	—	2	2	no	—
194	C₂×D₁₀₁	—	2	2	no	—
195	C₂×D₁₀₁	—	2	2	no	—
196	C₂×D₁₀₁	—	2	2	no	—
197	C₂×D₁₀₁	—	4	4	no	—
198	C₂×D₁₀₁	—	4	4	no	—
199	C₂×D₁₀₁	—	4	4	no	—
200	C₄×C₁₀₁	—	2	2	no	—
201	C₄×C₁₀₁	—	2	2	no	—
202	C₄×C₁₀₁	—	2	2	no	—
203	C₄×C₁₀₁	—	2	2	no	—
204	C₄×C₁₀₁	—	2	2	no	—
205	C₄×C₁₀₁	—	2	2	no	—
206	Dic₁₀₁	—	2	2	no	—
207	Dic₁₀₁	—	2	2	no	—
208	Dic₁₀₁	—	2	2	no	—
209	Dic₁₀₁	—	2	2	no	—
210	Dic₁₀₁	—	2	2	no	—
211	C₂×C₁₀₁	—	4	2	no	—
212	C₂×C₁₀₁	#562	1	4	yes	complemented
213	C₂×C₁₀₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
214	C₂×C₁₀₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
215	C₂×C₁₀₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
216	D₁₀₁	—	4	2	no	—
217	D₁₀₁	—	4	2	no	—
218	D₁₀₁	—	4	2	no	—
219	C₂×#562	—	101	1	no	maximal, Sylow
220	C₁₀₁	C₂×#562	1	1	yes	characteristic, complemented, Sylow
221	#562	—	101	16	no	—
222	C₂×#125	—	101	1	no	—
223	C₂×#124	—	101	1	no	—
224	C₂×#124	—	101	1	no	—
225	C₂×#123	—	101	1	no	—
226	C₂×#123	—	101	1	no	—
227	C₂×#123	—	101	1	no	—
228	C₂×#123	—	101	1	no	—
229	C₂×C₂²⋊Q₈	—	101	1	no	—
230	C₂×C₂²⋊Q₈	—	101	1	no	—
231	C₂×C₂²⋊Q₈	—	101	1	no	—
232	C₂×C₂²⋊Q₈	D₁₀₁	1	1	yes	characteristic, complemented
233	C₂×#121	—	101	1	no	—
234	C₂×#121	—	101	1	no	—
235	C₂×#121	—	101	1	no	—
236	C₂×#121	—	101	1	no	—
237	C₂²×Q₈	—	101	1	no	—
238	C₂²×Q₈	C₂×D₁₀₁	1	1	yes	characteristic
239	C₂²×D₄	—	101	1	no	—
240	C₂²×D₄	—	101	1	no	—
241	C₂²×D₄	—	101	1	no	—
242	C₂²×D₄	—	101	1	no	—
243	C₂²×D₄	—	101	1	no	—
244	C₂²×D₄	—	101	1	no	—
245	C₂³×C₄	—	101	1	no	—
246	C₂³×C₄	—	101	1	no	—
247	C₂³×C₄	—	101	1	no	—
248	C₂³×C₄	C₂×D₁₀₁	1	1	yes	characteristic
249	#125	—	101	8	no	—
250	#124	—	101	8	no	—
251	#124	—	101	8	no	—
252	#123	—	101	8	no	—
253	#123	—	101	8	no	—
254	#123	—	101	8	no	—
255	#123	—	101	8	no	—
256	C₂²⋊Q₈	—	101	8	no	—
257	C₂²⋊Q₈	—	101	8	no	—
258	C₂²⋊Q₈	—	101	8	no	—
259	C₂²⋊Q₈	C₂×D₁₀₁	1	8	yes	complemented
260	#121	—	101	8	no	—
261	#121	—	101	8	no	—
262	#121	—	101	8	no	—
263	#121	—	101	8	no	—
264	C₂×C₄⋊C₄	—	101	1	no	—
265	C₂×C₄⋊C₄	—	101	1	no	—
266	C₂×C₄⋊C₄	—	101	1	no	—
267	C₂×C₄⋊C₄	—	101	1	no	—
268	C₂×C₄⋊C₄	—	101	1	no	—
269	C₂×C₄⋊C₄	—	101	1	no	—
270	C₂×C₄⋊C₄	—	101	1	no	—
271	C₂×C₄⋊C₄	C₂×D₁₀₁	1	1	yes	characteristic
272	C₂×C₄⋊C₄	C₂×D₁₀₁	1	1	yes	characteristic
273	C₂×C₄⋊C₄	C₂×D₁₀₁	1	1	yes	characteristic
274	C₂×C₂²⋊C₄	—	101	1	no	—
275	C₂×C₂²⋊C₄	—	101	1	no	—
276	C₂×C₂²⋊C₄	—	101	1	no	—
277	C₂×C₂²⋊C₄	—	101	1	no	—
278	C₂×C₂²⋊C₄	—	101	1	no	—
279	C₂×C₂²⋊C₄	—	101	1	no	—
280	C₂×C₂²⋊C₄	—	101	1	no	—
281	C₂×C₂²⋊C₄	—	101	1	no	—
282	C₂×C₂²⋊C₄	—	101	1	no	—
283	C₂×C₂²⋊C₄	—	101	1	no	—
284	C₂×C₂²⋊C₄	C₂×D₁₀₁	1	1	yes	characteristic
285	C₂×C₂²⋊C₄	C₂×D₁₀₁	1	1	yes	characteristic
286	C₂×C₄²	—	101	1	no	—
287	C₂⁴	—	101	1	no	—
288	C₂⁴	—	101	1	no	—
289	C₂⁴	—	101	1	no	—
290	C₂⁴	C₂²×D₁₀₁	1	1	yes	characteristic
291	C₂×Q₈	—	4	2	no	—
292	C₂×Q₈	—	101	4	no	—
293	C₂×Q₈	—	404	2	no	—
294	C₂×Q₈	C₂²×D₁₀₁	1	4	yes	—
295	C₂×D₄	—	101	4	no	—
296	C₂×D₄	—	101	4	no	—
297	C₂×D₄	—	101	4	no	—
298	C₂×D₄	—	101	4	no	—
299	C₂×D₄	—	101	4	no	—
300	C₂×D₄	—	101	4	no	—
301	C₂×D₄	—	404	2	no	—
302	C₂×D₄	—	404	2	no	—
303	C₂×D₄	—	404	2	no	—
304	C₂×D₄	—	404	2	no	—
305	C₂×D₄	—	404	2	no	—
306	C₂×D₄	—	404	2	no	—
307	C₂²×C₄	—	4	2	no	—
308	C₂²×C₄	—	101	1	no	—
309	C₂²×C₄	—	101	1	no	—
310	C₂²×C₄	—	101	1	no	—
311	C₂²×C₄	—	101	1	no	—
312	C₂²×C₄	—	101	1	no	—
313	C₂²×C₄	—	101	4	no	—
314	C₂²×C₄	—	101	4	no	—
315	C₂²×C₄	—	101	4	no	—
316	C₂²×C₄	—	404	2	no	—
317	C₂²×C₄	—	404	2	no	—
318	C₂²×C₄	—	404	2	no	—
319	C₂²×C₄	C₂²×D₁₀₁	1	1	yes	characteristic
320	C₂²×C₄	C₂²×D₁₀₁	1	1	yes	characteristic
321	C₂²×C₄	C₂²×D₁₀₁	1	1	yes	characteristic
322	C₂²×C₄	C₂²×D₁₀₁	1	1	yes	characteristic
323	C₂²×C₄	C₂²×D₁₀₁	1	1	yes	characteristic
324	C₂²×C₄	C₂²×D₁₀₁	1	1	yes	characteristic
325	C₂²×C₄	C₂²×D₁₀₁	1	4	yes	—
326	C₄⋊C₄	—	101	4	no	—
327	C₄⋊C₄	—	101	4	no	—
328	C₄⋊C₄	—	101	4	no	—
329	C₄⋊C₄	—	101	4	no	—
330	C₄⋊C₄	—	101	4	no	—
331	C₄⋊C₄	—	101	4	no	—
332	C₄⋊C₄	—	101	4	no	—
333	C₄⋊C₄	C₂²×D₁₀₁	1	4	yes	—
334	C₄⋊C₄	C₂²×D₁₀₁	1	4	yes	—
335	C₄⋊C₄	C₂²×D₁₀₁	1	4	yes	—
336	C₂²⋊C₄	—	101	4	no	—
337	C₂²⋊C₄	—	101	4	no	—
338	C₂²⋊C₄	—	101	4	no	—
339	C₂²⋊C₄	—	101	4	no	—
340	C₂²⋊C₄	—	101	4	no	—
341	C₂²⋊C₄	—	101	4	no	—
342	C₂²⋊C₄	—	101	4	no	—
343	C₂²⋊C₄	—	101	4	no	—
344	C₂²⋊C₄	—	101	4	no	—
345	C₂²⋊C₄	—	101	4	no	—
346	C₂²⋊C₄	C₂²×D₁₀₁	1	4	yes	—
347	C₂²⋊C₄	C₂²×D₁₀₁	1	4	yes	—
348	C₄²	—	101	4	no	—
349	C₂³	—	2	2	no	—
350	C₂³	—	2	2	no	—
351	C₂³	—	2	2	no	—
352	C₂³	—	101	2	no	—
353	C₂³	—	101	2	no	—
354	C₂³	—	101	2	no	—
355	C₂³	—	202	2	no	—
356	C₂³	—	202	2	no	—
357	C₂³	—	202	2	no	—
358	C₂³	—	202	2	no	—
359	C₂³	—	202	2	no	—
360	C₂³	—	202	2	no	—
361	C₂³	—	202	2	no	—
362	C₂³	—	202	2	no	—
363	C₂³	—	202	2	no	—
364	C₂³	C₂³×D₁₀₁	1	2	yes	—
365	C₂³	C₂³×D₁₀₁	1	1	yes	characteristic
366	Q₈	—	4	4	no	—
367	Q₈	—	404	4	no	—
368	D₄	—	404	4	no	—
369	D₄	—	404	4	no	—
370	D₄	—	404	4	no	—
371	D₄	—	404	4	no	—
372	D₄	—	404	4	no	—
373	D₄	—	404	4	no	—
374	C₂×C₄	—	2	2	no	—
375	C₂×C₄	—	2	2	no	—
376	C₂×C₄	—	2	2	no	—
377	C₂×C₄	—	2	2	no	—
378	C₂×C₄	—	2	2	no	—
379	C₂×C₄	—	2	2	no	—
380	C₂×C₄	—	4	4	no	—
381	C₂×C₄	—	101	2	no	—
382	C₂×C₄	—	101	2	no	—
383	C₂×C₄	—	101	2	no	—
384	C₂×C₄	—	101	2	no	—
385	C₂×C₄	—	101	2	no	—
386	C₂×C₄	—	404	4	no	—
387	C₂×C₄	—	404	4	no	—
388	C₂×C₄	—	404	4	no	—
389	C₂×C₄	—	202	2	no	—
390	C₂×C₄	—	202	2	no	—
391	C₂×C₄	—	202	2	no	—
392	C₂×C₄	—	202	2	no	—
393	C₂×C₄	—	202	2	no	—
394	C₂×C₄	C₂³×D₁₀₁	1	2	yes	—
395	C₂×C₄	C₂³×D₁₀₁	1	2	yes	—
396	C₂×C₄	C₂³×D₁₀₁	1	2	yes	—
397	C₂×C₄	C₂³×D₁₀₁	1	2	yes	—
398	C₂×C₄	C₂³×D₁₀₁	1	2	yes	—
399	C₂×C₄	C₂³×D₁₀₁	1	2	yes	—
400	C₂²	—	2	2	no	—
401	C₂²	—	2	2	no	—
402	C₂²	—	2	2	no	—
403	C₂²	—	4	4	no	—
404	C₂²	—	404	4	no	—
405	C₂²	—	404	4	no	—
406	C₂²	—	404	4	no	—
407	C₂²	—	202	2	no	—
408	C₂²	—	202	2	no	—
409	C₂²	—	202	2	no	—
410	C₂²	—	202	2	no	—
411	C₂²	—	202	2	no	—
412	C₂²	—	202	2	no	—
413	C₂²	—	202	2	no	—
414	C₂²	—	202	2	no	—
415	C₂²	—	202	2	no	—
416	C₂²	#15692300	1	2	yes	—
417	C₂²	#15692301	1	2	yes	—
418	C₂²	#15692303	1	2	yes	—
419	C₂²	C₂⁴×D₁₀₁	1	1	yes	characteristic
420	C₄	—	2	2	no	—
421	C₄	—	2	2	no	—
422	C₄	—	2	2	no	—
423	C₄	—	2	2	no	—
424	C₄	—	2	2	no	—
425	C₄	—	2	2	no	—
426	C₄	—	202	2	no	—
427	C₄	—	202	2	no	—
428	C₄	—	202	2	no	—
429	C₄	—	202	2	no	—
430	C₄	—	202	2	no	—
431	C₂	—	4	2	no	—
432	C₂	—	404	2	no	—
433	C₂	—	404	2	no	—
434	C₂	—	404	2	no	—
435	C₂	#20265923	1	4	yes	direct product factor
436	C₂	C₂×#15692300	1	1	yes	characteristic
437	C₂	C₂×#15692301	1	1	yes	characteristic
438	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
hypercenter	C₂×C₂²⋊Q₈	D₁₀₁
hypocenter	C₁₀₁	C₂×#562
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. #20265923	C₂	direct (N × H)
2. C₂×#15692245	C₂	semidirect
3. C₂×#15692244	C₂	semidirect
4. C₂×#15692241	C₂	semidirect
5. C₂×#15692240	C₂	semidirect
6. C₂×#15692240	C₂	semidirect
7. C₂×#15692238	C₂	semidirect
8. C₂×#15692237	C₂	semidirect
9. C₂×#15692235	C₂	semidirect
10. C₂×#15692233	C₂	semidirect
11. C₂×#15692231	C₂	semidirect
12. C₂×#15692230	C₂	semidirect
13. C₂×#15692229	C₂	semidirect
14. C₂×#15692228	C₂	semidirect
15. C₂×#15692228	C₂	semidirect
16. C₂×C₂²⋊Q₈×C₁₀₁	C₂	semidirect
27. #15692245	C₂²	semidirect
28. #15692244	C₂²	semidirect
29. #15692241	C₂²	semidirect
30. #15692240	C₂²	semidirect
31. #15692240	C₂²	semidirect
32. #15692238	C₂²	semidirect
33. #15692237	C₂²	semidirect
34. #15692235	C₂²	semidirect
35. #15692233	C₂²	semidirect
36. #15692231	C₂²	semidirect
37. #15692230	C₂²	semidirect
38. #15692229	C₂²	semidirect
39. #15692228	C₂²	semidirect
40. #15692228	C₂²	semidirect
61. C₂²⋊Q₈×C₁₀₁	C₂²	semidirect
212. C₂×C₁₀₁	#562	semidirect
220. C₁₀₁	C₂×#562	semidirect
232. C₂×C₂²⋊Q₈	D₁₀₁	semidirect
259. C₂²⋊Q₈	C₂×D₁₀₁	semidirect
435. C₂	#20265923	direct (N × H)

Maximal subgroups

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

subgroup	index
#20265923	2
C₂×#15692245	2
C₂×#15692244	2
C₂×#15692241	2
C₂×#15692240	2
C₂×#15692238	2
C₂×#15692237	2
C₂×#15692235	2
C₂×#15692233	2
C₂×#15692231	2
C₂×#15692230	2
C₂×#15692229	2
C₂×#15692228	2
C₂×C₂²⋊Q₈×C₁₀₁	2
C₂×#562	101

Subgroups — C2×#20265923 #27185257

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#20265923 #27185257