Subgroups — #27185200

Order 12928.

1042 conjugacy classes of subgroups.

The subgroup lattice has 646 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20265899	C₂	1	1	yes	maximal, characteristic, complemented
2	#20265895	C₂	1	1	yes	maximal, characteristic, complemented
3	#20265886	C₂	1	1	yes	maximal, characteristic, complemented
4	#20265876	C₂	1	2	yes	maximal, complemented
5	#20265871	C₂	1	1	yes	maximal, characteristic, complemented
6	#20265868	C₂	1	1	yes	maximal, characteristic, complemented
7	#20265860	C₂	1	2	yes	maximal, complemented
8	#20265856	C₂	1	2	yes	maximal, complemented
9	#20265851	C₂	1	2	yes	maximal, complemented
10	#20265826	C₂	1	1	yes	maximal, characteristic, complemented
11	#20265822	C₂	1	1	yes	maximal, characteristic, complemented
12	#20265815	C₂	1	1	yes	maximal, characteristic, complemented
13	#20265799	C₂	1	1	yes	maximal, characteristic, complemented
14	#20265785	C₂	1	1	yes	maximal, characteristic, complemented
15	#20265769	C₂	1	2	yes	maximal, complemented
16	#20265760	C₂	1	2	yes	maximal, complemented
17	#20265711	C₂	1	1	yes	maximal, characteristic, complemented
18	#20265711	C₂	1	2	yes	maximal, complemented
19	#20265711	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×#15692249	C₂	1	2	yes	maximal, complemented
21	#20265656	C₂	1	1	yes	maximal, characteristic, complemented
22	#20265649	C₂	1	1	yes	maximal, characteristic, complemented
23	C₄×#41×C₁₀₁	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#13108073	C₂²	1	1	yes	characteristic
25	C₂×D₄×D₁₀₁	C₂²	1	1	yes	characteristic
26	#15692254	C₂²	1	1	yes	characteristic, complemented
27	#15692253	C₂²	1	1	yes	characteristic, complemented
28	#15692250	C₂²	1	2	yes	—
29	#15692250	C₂²	1	2	yes	complemented
30	#15692249	C₂²	1	2	yes	—
31	#15692249	C₂²	1	2	yes	—
32	#15692249	C₂²	1	2	yes	—
33	#15692249	C₂²	1	1	yes	characteristic
34	#15692249	C₂²	1	2	yes	complemented
35	#15692249	C₂²	1	2	yes	complemented
36	#15692249	C₂²	1	2	yes	complemented
37	#15692249	C₂²	1	2	yes	complemented
38	#15692249	C₂²	1	1	yes	characteristic, complemented
39	#15692248	C₂²	1	2	yes	complemented
40	#15692247	C₂²	1	2	yes	complemented
41	#15692247	C₂²	1	1	yes	characteristic, complemented
42	#15692247	C₂²	1	1	yes	characteristic, complemented
43	#15692246	C₂²	1	1	yes	characteristic, complemented
44	#15692245	C₂²	1	2	yes	complemented
45	#15692245	C₂²	1	2	yes	complemented
46	#15692244	C₂²	1	1	yes	characteristic
47	#15692243	C₂²	1	1	yes	characteristic
48	#15692243	C₂²	1	1	yes	characteristic
49	#15692243	C₂²	1	2	yes	complemented
50	#15692241	C₂²	1	2	yes	—
51	#15692240	C₂²	1	2	yes	—
52	#15692240	C₂²	1	2	yes	complemented
53	#15692239	C₂²	1	2	yes	—
54	#15692238	C₂²	1	2	yes	—
55	#15692238	C₂²	1	1	yes	characteristic
56	#15692238	C₂²	1	2	yes	complemented
57	#15692238	C₂²	1	2	yes	complemented
58	#15692238	C₂²	1	1	yes	characteristic, complemented
59	#15692237	C₂²	1	2	yes	complemented
60	#15692236	C₂²	1	2	yes	complemented
61	#15692235	C₂²	1	1	yes	characteristic
62	#15692234	C₂²	1	1	yes	characteristic, complemented
63	#15692234	C₂²	1	1	yes	characteristic, complemented
64	#15692234	C₂²	1	2	yes	complemented
65	#15692233	C₂²	1	2	yes	complemented
66	#15692233	C₂²	1	2	yes	complemented
67	#15692232	C₂²	1	2	yes	complemented
68	#15692232	C₂²	1	2	yes	complemented
69	#15692231	C₂²	1	1	yes	characteristic
70	#15692231	C₂²	1	1	yes	characteristic, complemented
71	#15692230	C₂²	1	1	yes	characteristic
72	#15692229	C₂²	1	1	yes	characteristic
73	#15692229	C₂²	1	1	yes	characteristic
74	#15692229	C₂²	1	2	yes	—
75	#15692228	C₂²	1	2	yes	complemented
76	#15692227	C₂²	1	2	yes	—
77	#15692227	C₂²	1	2	yes	complemented
78	#15692225	C₂²	1	2	yes	—
79	#15692223	C₂²	1	2	yes	—
80	C₄×Dic₂₀₂	C₂²	1	1	yes	characteristic, complemented
81	C₄×Dic₂₀₂	C₂²	1	2	yes	complemented
82	C₄×Dic₂₀₂	C₂²	1	1	yes	characteristic, complemented
83	#15692220	C₂²	1	1	yes	characteristic, complemented
84	C₄×D₄₀₄	C₂²	1	1	yes	characteristic
85	C₄×D₄₀₄	C₂²	1	1	yes	characteristic
86	C₄×D₄₀₄	C₂²	1	2	yes	complemented
87	D₄×Dic₁₀₁	C₂²	1	1	yes	characteristic
88	D₄×Dic₁₀₁	C₂²	1	1	yes	characteristic
89	#15692217	C₂²	1	1	yes	characteristic
90	C₄×C₂²⋊D₁₀₁	C₂²	1	2	yes	—
91	C₄×C₂²⋊D₁₀₁	C₂²	1	1	yes	characteristic
92	C₄×C₂²⋊D₁₀₁	C₂²	1	2	yes	complemented
93	C₄×C₂²⋊D₁₀₁	C₂²	1	1	yes	characteristic, complemented
94	C₄×C₂²⋊D₁₀₁	C₂²	1	2	yes	complemented
95	#15692215	C₂²	1	2	yes	—
96	#15692215	C₂²	1	2	yes	complemented
97	#15692213	C₂²	1	1	yes	characteristic
98	#15692212	C₂²	1	1	yes	characteristic
99	#15692212	C₂²	1	1	yes	characteristic, complemented
100	#15692212	C₂²	1	2	yes	complemented
101	#15692212	C₂²	1	2	yes	complemented
102	#15692212	C₂²	1	2	yes	complemented
103	#15692211	C₂²	1	2	yes	complemented
104	C₂×#13108053	C₂²	1	2	yes	complemented
105	C₂×#13108053	C₂²	1	2	yes	complemented
106	C₂×#13108053	C₂²	1	2	yes	complemented
107	C₄⋊C₄×D₁₀₁	C₂²	1	1	yes	characteristic, complemented
108	C₂×#13108051	C₂²	1	2	yes	—
109	C₂×#13108051	C₂²	1	2	yes	—
110	C₂×#13108051	C₂²	1	2	yes	—
111	C₂²⋊C₄×D₁₀₁	C₂²	1	2	yes	—
112	C₂×#41×C₁₀₁	C₂²	1	1	yes	characteristic
113	C₄×Q₈×C₁₀₁	C₂²	1	1	yes	characteristic, complemented
114	C₄×Q₈×C₁₀₁	C₂²	1	1	yes	characteristic, complemented
115	C₄×D₄×C₁₀₁	C₂²	1	1	yes	characteristic
116	C₄×D₄×C₁₀₁	C₂²	1	1	yes	characteristic
117	C₄×D₄×C₁₀₁	C₂²	1	2	yes	complemented
118	C₄×D₄×C₁₀₁	C₂²	1	2	yes	complemented
119	#117×C₁₀₁	C₂²	1	2	yes	complemented
120	#117×C₁₀₁	C₂²	1	1	yes	characteristic, complemented
121	C₂×C₄²×C₁₀₁	C₂²	1	2	yes	complemented
122	C₂×C₄²×C₁₀₁	C₂²	1	1	yes	characteristic, complemented
123	C₂³×D₁₀₁	C₂³	1	2	yes	—
124	#13108073	—	2	4	no	—
125	C₂×Dic₂₀₂	C₂³	1	1	yes	characteristic
126	C₂×Dic₂₀₂	C₂³	1	1	yes	characteristic
127	C₂×Dic₂₀₂	C₂³	1	2	yes	—
128	C₂×D₄₀₄	C₂³	1	1	yes	characteristic
129	C₂×D₄₀₄	C₂³	1	1	yes	characteristic
130	C₂×D₄₀₄	C₂³	1	2	yes	—
131	C₂×C₂²⋊D₁₀₁	C₂³	1	2	yes	—
132	C₂×C₂²⋊D₁₀₁	C₂³	1	2	yes	—
133	C₂×C₂²⋊D₁₀₁	C₂³	1	1	yes	characteristic
134	C₂×C₂²⋊D₁₀₁	C₂³	1	2	yes	—
135	C₂×C₂²⋊D₁₀₁	C₂³	1	1	yes	characteristic
136	D₄×D₁₀₁	—	2	4	no	—
137	C₂²×Dic₁₀₁	C₂³	1	2	yes	—
138	C₂²×Dic₁₀₁	C₂³	1	2	yes	—
139	C₂²×Dic₁₀₁	C₂³	1	2	yes	—
140	C₂×C₄×D₁₀₁	C₂³	1	1	yes	characteristic
141	C₂×C₄×D₁₀₁	C₂³	1	1	yes	characteristic
142	C₂×C₄×D₁₀₁	C₂³	1	2	yes	—
143	C₂×C₄×D₁₀₁	C₂³	1	2	yes	—
144	C₂×C₄×D₁₀₁	C₂³	1	2	yes	—
145	C₄⋊Dic₁₀₁	C₂³	1	1	yes	characteristic
146	C₄⋊Dic₁₀₁	C₂³	1	1	yes	characteristic
147	C₄⋊Dic₁₀₁	C₂³	1	1	yes	characteristic
148	C₄⋊Dic₁₀₁	C₂³	1	2	yes	—
149	C₄⋊Dic₁₀₁	C₂³	1	1	yes	characteristic
150	C₄⋊Dic₁₀₁	C₂³	1	2	yes	—
151	#13108053	C₂³	1	2	yes	—
152	#13108053	C₂³	1	1	yes	characteristic
153	#13108053	C₂³	1	1	yes	characteristic
154	#13108053	C₂³	1	1	yes	characteristic
155	#13108053	C₂³	1	2	yes	—
156	#13108053	C₂³	1	2	yes	—
157	#13108053	C₂³	1	2	yes	—
158	#13108053	C₂³	1	2	yes	—
159	#13108053	C₂³	1	2	yes	—
160	#13108053	C₂³	1	2	yes	—
161	#13108053	C₂³	1	2	yes	—
162	#13108053	C₂³	1	2	yes	—
163	#13108053	C₂³	1	1	yes	characteristic
164	#13108053	C₂³	1	1	yes	characteristic
165	#13108053	C₂³	1	1	yes	characteristic
166	#13108053	C₂³	1	1	yes	characteristic
167	#13108053	C₂³	1	2	yes	—
168	#13108053	C₂³	1	2	yes	—
169	#13108053	C₂³	1	2	yes	—
170	#13108053	C₂³	1	1	yes	characteristic
171	C₂²⋊Dic₁₀₁	C₂³	1	2	yes	—
172	C₂²⋊Dic₁₀₁	C₂³	1	2	yes	—
173	C₂²⋊Dic₁₀₁	C₂³	1	1	yes	characteristic
174	C₂²⋊Dic₁₀₁	C₂³	1	2	yes	—
175	C₂²⋊Dic₁₀₁	C₂³	1	1	yes	characteristic
176	#13108051	C₂³	1	1	yes	characteristic
177	#13108051	C₂³	1	2	yes	—
178	#13108051	C₂³	1	1	yes	characteristic
179	#13108051	C₂³	1	1	yes	characteristic
180	#13108051	C₂³	1	1	yes	characteristic
181	#13108051	C₂³	1	2	yes	—
182	#13108051	C₂³	1	2	yes	—
183	#13108051	C₂³	1	2	yes	—
184	#13108051	C₂³	1	2	yes	—
185	#13108051	C₂³	1	2	yes	—
186	#13108051	C₂³	1	2	yes	—
187	#13108051	C₂³	1	2	yes	—
188	#13108051	C₂³	1	2	yes	—
189	#13108051	C₂³	1	1	yes	characteristic
190	#13108051	C₂³	1	1	yes	characteristic
191	#13108051	C₂³	1	1	yes	characteristic
192	#13108051	C₂³	1	2	yes	—
193	#13108051	C₂³	1	2	yes	—
194	#13108051	C₂³	1	2	yes	—
195	#13108051	C₂³	1	1	yes	characteristic
196	C₄×Dic₁₀₁	C₂³	1	2	yes	—
197	C₄×Dic₁₀₁	C₂³	1	2	yes	—
198	C₄×Dic₁₀₁	C₂³	1	1	yes	characteristic
199	C₄×Dic₁₀₁	C₂³	1	2	yes	—
200	C₄×Dic₁₀₁	C₂³	1	1	yes	characteristic
201	#41×C₁₀₁	—	2	4	no	—
202	C₂×Q₈×C₁₀₁	C₂³	1	1	yes	characteristic
203	C₂×D₄×C₁₀₁	C₂³	1	2	yes	—
204	C₂×D₄×C₁₀₁	C₂³	1	1	yes	characteristic
205	C₂²×C₄×C₁₀₁	C₂³	1	2	yes	—
206	C₂²×C₄×C₁₀₁	C₂³	1	1	yes	characteristic
207	C₂²×C₄×C₁₀₁	C₂³	1	2	yes	—
208	C₂²×C₄×C₁₀₁	C₂³	1	2	yes	—
209	C₂²×C₄×C₁₀₁	C₂³	1	1	yes	characteristic
210	C₂²×C₄×C₁₀₁	C₂³	1	1	yes	characteristic
211	C₄⋊C₄×C₁₀₁	C₂³	1	1	yes	characteristic
212	C₄⋊C₄×C₁₀₁	C₂³	1	1	yes	characteristic
213	C₄⋊C₄×C₁₀₁	C₂³	1	2	yes	—
214	C₄⋊C₄×C₁₀₁	C₂³	1	2	yes	—
215	C₂²⋊C₄×C₁₀₁	C₂³	1	2	yes	—
216	C₂²⋊C₄×C₁₀₁	C₂³	1	2	yes	—
217	C₂²⋊C₄×C₁₀₁	C₂³	1	2	yes	—
218	C₄²×C₁₀₁	C₂³	1	1	yes	characteristic
219	C₄²×C₁₀₁	C₂³	1	1	yes	characteristic
220	C₄²×C₁₀₁	C₂³	1	2	yes	—
221	C₄²×C₁₀₁	C₂³	1	1	yes	characteristic
222	C₄²×C₁₀₁	C₂³	1	1	yes	characteristic
223	C₄²×C₁₀₁	C₂³	1	2	yes	—
224	C₄²×C₁₀₁	C₂³	1	2	yes	—
225	C₂³×C₁₀₁	C₂⁴	1	1	yes	characteristic
226	C₂³×C₁₀₁	C₂⁴	1	2	yes	—
227	C₂²×D₁₀₁	—	2	4	no	—
228	C₂²×D₁₀₁	—	4	2	no	—
229	C₂²×D₁₀₁	—	4	2	no	—
230	C₂²×D₁₀₁	C₂⁴	1	1	yes	characteristic
231	C₂²×D₁₀₁	C₂⁴	1	2	yes	—
232	C₂²×D₁₀₁	C₂⁴	1	1	yes	characteristic
233	Q₈×C₁₀₁	—	2	2	no	—
234	D₄×C₁₀₁	—	2	4	no	—
235	D₄×C₁₀₁	#41	1	4	yes	—
236	C₂×C₄×C₁₀₁	—	2	4	no	—
237	C₂×C₄×C₁₀₁	—	2	2	no	—
238	C₂×C₄×C₁₀₁	—	4	2	no	—
239	C₂×C₄×C₁₀₁	—	4	1	no	—
240	C₂×C₄×C₁₀₁	—	4	2	no	—
241	C₂×C₄×C₁₀₁	—	4	1	no	—
242	C₂×C₄×C₁₀₁	C₂⁴	1	1	yes	characteristic
243	C₂×C₄×C₁₀₁	C₂⁴	1	1	yes	characteristic
244	C₂×C₄×C₁₀₁	C₂⁴	1	1	yes	characteristic
245	C₂×C₄×C₁₀₁	C₂⁴	1	1	yes	characteristic
246	C₂×C₄×C₁₀₁	C₂⁴	1	2	yes	—
247	C₂×C₄×C₁₀₁	C₂⁴	1	1	yes	characteristic
248	C₂×C₄×C₁₀₁	C₂⁴	1	2	yes	—
249	C₂×C₄×C₁₀₁	C₂⁴	1	2	yes	—
250	C₂×C₄×C₁₀₁	C₂⁴	1	1	yes	characteristic
251	C₂²⋊D₁₀₁	—	2	4	no	—
252	C₂²⋊D₁₀₁	—	2	4	no	—
253	C₂²⋊D₁₀₁	—	4	1	no	—
254	C₂²⋊D₁₀₁	—	4	2	no	—
255	C₂²⋊D₁₀₁	—	4	1	no	—
256	C₂×Dic₁₀₁	—	2	4	no	—
257	C₂×Dic₁₀₁	—	4	2	no	—
258	C₂×Dic₁₀₁	—	4	2	no	—
259	C₂×Dic₁₀₁	C₂⁴	1	1	yes	characteristic
260	C₂×Dic₁₀₁	C₂⁴	1	2	yes	—
261	C₂×Dic₁₀₁	C₂⁴	1	1	yes	characteristic
262	C₂×Dic₁₀₁	C₂⁴	1	1	yes	characteristic
263	C₂×Dic₁₀₁	C₂⁴	1	2	yes	—
264	C₂×Dic₁₀₁	C₂⁴	1	1	yes	characteristic
265	C₂×Dic₁₀₁	C₂⁴	1	1	yes	characteristic
266	C₂×Dic₁₀₁	C₂⁴	1	2	yes	—
267	C₂×Dic₁₀₁	C₂⁴	1	1	yes	characteristic
268	D₄₀₄	—	2	2	no	—
269	D₄₀₄	—	4	1	no	—
270	D₄₀₄	—	4	2	no	—
271	C₄×D₁₀₁	—	2	2	no	—
272	C₄×D₁₀₁	—	2	2	no	—
273	C₄×D₁₀₁	—	4	2	no	—
274	C₄×D₁₀₁	—	4	2	no	—
275	C₄×D₁₀₁	—	4	2	no	—
276	Dic₂₀₂	—	2	2	no	—
277	Dic₂₀₂	—	4	2	no	—
278	Dic₂₀₂	—	4	1	no	—
279	C₂²×C₁₀₁	—	2	2	no	—
280	C₂²×C₁₀₁	—	2	2	no	—
281	C₂²×C₁₀₁	—	2	1	no	—
282	C₂²×C₁₀₁	—	2	1	no	—
283	C₂²×C₁₀₁	—	2	1	no	—
284	C₂²×C₁₀₁	C₂×#41	1	4	yes	—
285	C₂²×C₁₀₁	C₂⁵	1	1	yes	characteristic
286	C₂×D₁₀₁	—	2	1	no	—
287	C₂×D₁₀₁	—	2	1	no	—
288	C₂×D₁₀₁	—	2	2	no	—
289	C₂×D₁₀₁	—	2	1	no	—
290	C₂×D₁₀₁	—	2	2	no	—
291	C₂×D₁₀₁	—	2	2	no	—
292	C₂×D₁₀₁	—	2	1	no	—
293	C₂×D₁₀₁	—	2	1	no	—
294	C₂×D₁₀₁	—	2	1	no	—
295	C₂×D₁₀₁	—	8	4	no	—
296	C₄×C₁₀₁	—	2	1	no	—
297	C₄×C₁₀₁	—	2	2	no	—
298	C₄×C₁₀₁	—	2	2	no	—
299	C₄×C₁₀₁	—	2	1	no	—
300	C₄×C₁₀₁	—	2	1	no	—
301	C₄×C₁₀₁	—	2	2	no	—
302	C₄×C₁₀₁	—	2	1	no	—
303	C₄×C₁₀₁	—	2	1	no	—
304	C₄×C₁₀₁	C₂×#41	1	2	yes	—
305	Dic₁₀₁	—	2	2	no	—
306	Dic₁₀₁	—	2	1	no	—
307	Dic₁₀₁	—	2	1	no	—
308	Dic₁₀₁	—	2	1	no	—
309	Dic₁₀₁	—	2	1	no	—
310	Dic₁₀₁	—	2	2	no	—
311	Dic₁₀₁	—	2	1	no	—
312	Dic₁₀₁	—	2	2	no	—
313	Dic₁₀₁	—	2	1	no	—
314	C₂×C₁₀₁	—	2	4	no	—
315	C₂×C₁₀₁	—	4	1	no	—
316	C₂×C₁₀₁	C₂²×#41	1	1	yes	characteristic
317	C₂×C₁₀₁	#585	1	1	yes	characteristic
318	C₂×C₁₀₁	#585	1	1	yes	characteristic
319	D₁₀₁	—	4	1	no	—
320	D₁₀₁	—	4	2	no	—
321	D₁₀₁	—	4	1	no	—
322	#3521	—	101	1	no	maximal, Sylow
323	C₁₀₁	#3521	1	1	yes	characteristic, complemented, Sylow
324	#556	—	101	1	no	—
325	#556	—	101	1	no	—
326	#554	—	101	1	no	—
327	#553	—	101	2	no	—
328	#553	—	101	1	no	—
329	#552	—	101	1	no	—
330	#552	—	101	2	no	—
331	#551	—	101	2	no	—
332	#551	—	101	2	no	—
333	#547	—	101	1	no	—
334	#546	—	101	1	no	—
335	#546	—	101	1	no	—
336	#542	—	101	1	no	—
337	#541	—	101	1	no	—
338	#539	—	101	2	no	—
339	#538	—	101	2	no	—
340	#529	—	101	2	no	—
341	#529	—	101	1	no	—
342	#529	—	101	1	no	—
343	C₂×#126	—	101	2	no	—
344	#520	—	101	1	no	—
345	#518	—	101	1	no	—
346	C₄×#41	D₁₀₁	1	1	yes	characteristic, complemented
347	C₂×#41	—	101	1	no	—
348	C₂×#41	C₂×D₁₀₁	1	1	yes	characteristic
349	C₂²×D₄	—	101	1	no	—
350	C₄⋊Q₈	—	101	1	no	—
351	C₄⋊Q₈	—	101	1	no	—
352	#126	—	101	2	no	—
353	#126	—	101	2	no	—
354	#126	—	101	2	no	—
355	#126	—	101	1	no	—
356	#126	—	101	2	no	—
357	#126	—	101	2	no	—
358	#126	—	101	2	no	—
359	#126	—	101	2	no	—
360	#126	—	101	2	no	—
361	#126	—	101	2	no	—
362	#126	—	101	2	no	—
363	#126	—	101	1	no	—
364	#125	—	101	2	no	—
365	#125	—	101	2	no	—
366	#125	—	101	1	no	—
367	#125	—	101	2	no	—
368	#125	—	101	1	no	—
369	#125	—	101	1	no	—
370	#124	—	101	1	no	—
371	#124	—	101	2	no	—
372	#124	—	101	2	no	—
373	#124	—	101	1	no	—
374	#124	—	101	1	no	—
375	#123	—	101	2	no	—
376	#123	—	101	2	no	—
377	#123	—	101	2	no	—
378	#123	—	101	2	no	—
379	#123	—	101	1	no	—
380	#123	—	101	1	no	—
381	#123	—	101	2	no	—
382	#123	—	101	2	no	—
383	#123	—	101	2	no	—
384	#123	—	101	2	no	—
385	C₂²⋊Q₈	—	101	1	no	—
386	C₂²⋊Q₈	—	101	1	no	—
387	C₂²⋊Q₈	—	101	1	no	—
388	C₂²⋊Q₈	—	101	1	no	—
389	C₂²⋊Q₈	—	101	2	no	—
390	C₂²⋊Q₈	—	101	2	no	—
391	C₂²⋊Q₈	—	101	1	no	—
392	C₂²⋊Q₈	—	101	2	no	—
393	C₂²⋊Q₈	—	101	2	no	—
394	C₂²⋊Q₈	—	101	2	no	—
395	#121	—	101	2	no	—
396	#121	—	101	2	no	—
397	#121	—	101	1	no	—
398	#121	—	101	1	no	—
399	#121	—	101	2	no	—
400	#121	—	101	1	no	—
401	#121	—	101	2	no	—
402	#120	—	101	2	no	—
403	#120	—	101	2	no	—
404	C₄×Q₈	—	101	1	no	—
405	C₄×Q₈	—	101	1	no	—
406	C₄×Q₈	—	101	2	no	—
407	C₄×Q₈	—	101	1	no	—
408	C₄×Q₈	C₂×D₁₀₁	1	1	yes	characteristic, complemented
409	C₄×Q₈	C₂×D₁₀₁	1	1	yes	characteristic, complemented
410	C₄×D₄	—	101	1	no	—
411	C₄×D₄	—	101	1	no	—
412	C₄×D₄	—	101	2	no	—
413	C₄×D₄	—	101	2	no	—
414	C₄×D₄	—	101	1	no	—
415	C₄×D₄	—	101	1	no	—
416	C₄×D₄	—	101	2	no	—
417	C₄×D₄	—	101	1	no	—
418	C₄×D₄	—	101	2	no	—
419	C₄×D₄	—	101	2	no	—
420	C₄×D₄	—	101	1	no	—
421	C₄×D₄	—	101	1	no	—
422	C₄×D₄	—	101	2	no	—
423	C₄×D₄	C₂×D₁₀₁	1	1	yes	characteristic
424	C₄×D₄	C₂×D₁₀₁	1	1	yes	characteristic
425	C₄×D₄	C₂×D₁₀₁	1	2	yes	complemented
426	C₄×D₄	C₂×D₁₀₁	1	2	yes	complemented
427	#117	—	101	1	no	—
428	#117	—	101	2	no	—
429	#117	—	101	1	no	—
430	#117	—	101	1	no	—
431	#117	—	101	2	no	—
432	#117	—	101	2	no	—
433	#117	—	101	2	no	—
434	#117	C₂×D₁₀₁	1	2	yes	complemented
435	#117	C₂×D₁₀₁	1	1	yes	characteristic, complemented
436	C₂×C₄⋊C₄	—	101	2	no	—
437	C₂×C₄⋊C₄	—	101	2	no	—
438	C₂×C₄⋊C₄	—	101	2	no	—
439	C₂×C₄⋊C₄	—	101	1	no	—
440	C₂×C₂²⋊C₄	—	101	2	no	—
441	C₂×C₂²⋊C₄	—	101	2	no	—
442	C₂×C₂²⋊C₄	—	101	2	no	—
443	C₂×C₂²⋊C₄	—	101	2	no	—
444	C₂×C₄²	C₂×D₁₀₁	1	2	yes	complemented
445	C₂×C₄²	C₂×D₁₀₁	1	1	yes	characteristic, complemented
446	C₂⁴	—	101	2	no	—
447	#41	—	2	4	no	—
448	#41	—	202	4	no	—
449	C₂×Q₈	—	101	1	no	—
450	C₂×Q₈	—	101	2	no	—
451	C₂×Q₈	—	101	1	no	—
452	C₂×Q₈	C₂²×D₁₀₁	1	1	yes	characteristic
453	C₂×D₄	—	101	1	no	—
454	C₂×D₄	—	101	2	no	—
455	C₂×D₄	—	101	1	no	—
456	C₂×D₄	—	101	2	no	—
457	C₂×D₄	—	101	2	no	—
458	C₂×D₄	—	101	1	no	—
459	C₂×D₄	—	101	2	no	—
460	C₂×D₄	—	101	1	no	—
461	C₂×D₄	—	202	4	no	—
462	C₂×D₄	C₂²×D₁₀₁	1	2	yes	—
463	C₂×D₄	C₂²×D₁₀₁	1	1	yes	characteristic
464	C₂²×C₄	—	101	2	no	—
465	C₂²×C₄	—	101	2	no	—
466	C₂²×C₄	—	101	2	no	—
467	C₂²×C₄	—	101	2	no	—
468	C₂²×C₄	—	101	2	no	—
469	C₂²×C₄	—	101	2	no	—
470	C₂²×C₄	—	101	1	no	—
471	C₂²×C₄	—	101	1	no	—
472	C₂²×C₄	C₂²×D₁₀₁	1	2	yes	—
473	C₂²×C₄	C₂²×D₁₀₁	1	1	yes	characteristic
474	C₂²×C₄	C₂²×D₁₀₁	1	2	yes	—
475	C₂²×C₄	C₂²×D₁₀₁	1	2	yes	—
476	C₂²×C₄	C₂²×D₁₀₁	1	1	yes	characteristic
477	C₂²×C₄	C₂²×D₁₀₁	1	1	yes	characteristic
478	C₄⋊C₄	—	101	1	no	—
479	C₄⋊C₄	—	101	2	no	—
480	C₄⋊C₄	—	101	1	no	—
481	C₄⋊C₄	—	101	1	no	—
482	C₄⋊C₄	—	101	2	no	—
483	C₄⋊C₄	—	101	2	no	—
484	C₄⋊C₄	—	101	2	no	—
485	C₄⋊C₄	—	101	2	no	—
486	C₄⋊C₄	—	101	2	no	—
487	C₄⋊C₄	—	101	2	no	—
488	C₄⋊C₄	—	101	2	no	—
489	C₄⋊C₄	—	101	2	no	—
490	C₄⋊C₄	—	101	1	no	—
491	C₄⋊C₄	—	101	1	no	—
492	C₄⋊C₄	—	101	1	no	—
493	C₄⋊C₄	—	101	1	no	—
494	C₄⋊C₄	—	101	2	no	—
495	C₄⋊C₄	—	101	2	no	—
496	C₄⋊C₄	—	101	2	no	—
497	C₄⋊C₄	—	101	1	no	—
498	C₄⋊C₄	—	101	1	no	—
499	C₄⋊C₄	—	101	1	no	—
500	C₄⋊C₄	—	101	2	no	—
501	C₄⋊C₄	—	101	1	no	—
502	C₄⋊C₄	—	101	1	no	—
503	C₄⋊C₄	—	101	2	no	—
504	C₄⋊C₄	C₂²×D₁₀₁	1	1	yes	characteristic
505	C₄⋊C₄	C₂²×D₁₀₁	1	1	yes	characteristic
506	C₄⋊C₄	C₂²×D₁₀₁	1	2	yes	—
507	C₄⋊C₄	C₂²×D₁₀₁	1	2	yes	—
508	C₂²⋊C₄	—	101	2	no	—
509	C₂²⋊C₄	—	101	2	no	—
510	C₂²⋊C₄	—	101	1	no	—
511	C₂²⋊C₄	—	101	2	no	—
512	C₂²⋊C₄	—	101	1	no	—
513	C₂²⋊C₄	—	101	1	no	—
514	C₂²⋊C₄	—	101	1	no	—
515	C₂²⋊C₄	—	101	2	no	—
516	C₂²⋊C₄	—	101	1	no	—
517	C₂²⋊C₄	—	101	1	no	—
518	C₂²⋊C₄	—	101	2	no	—
519	C₂²⋊C₄	—	101	2	no	—
520	C₂²⋊C₄	—	101	2	no	—
521	C₂²⋊C₄	—	101	2	no	—
522	C₂²⋊C₄	—	101	2	no	—
523	C₂²⋊C₄	—	101	2	no	—
524	C₂²⋊C₄	—	101	2	no	—
525	C₂²⋊C₄	—	101	2	no	—
526	C₂²⋊C₄	—	101	1	no	—
527	C₂²⋊C₄	—	101	1	no	—
528	C₂²⋊C₄	—	101	1	no	—
529	C₂²⋊C₄	—	101	2	no	—
530	C₂²⋊C₄	—	101	2	no	—
531	C₂²⋊C₄	—	101	2	no	—
532	C₂²⋊C₄	—	101	1	no	—
533	C₂²⋊C₄	C₂²×D₁₀₁	1	2	yes	—
534	C₂²⋊C₄	C₂²×D₁₀₁	1	2	yes	—
535	C₂²⋊C₄	C₂²×D₁₀₁	1	2	yes	—
536	C₄²	—	101	2	no	—
537	C₄²	—	101	2	no	—
538	C₄²	—	101	2	no	—
539	C₄²	—	101	1	no	—
540	C₄²	—	101	1	no	—
541	C₄²	C₂²×D₁₀₁	1	1	yes	characteristic
542	C₄²	C₂²×D₁₀₁	1	1	yes	characteristic
543	C₄²	C₂²×D₁₀₁	1	1	yes	characteristic
544	C₄²	C₂²×D₁₀₁	1	2	yes	—
545	C₄²	C₂²×D₁₀₁	1	2	yes	—
546	C₄²	C₂²×D₁₀₁	1	1	yes	characteristic
547	C₄²	C₂²×D₁₀₁	1	2	yes	—
548	C₂³	—	101	1	no	—
549	C₂³	—	101	2	no	—
550	C₂³	—	101	1	no	—
551	C₂³	—	404	2	no	—
552	C₂³	—	404	2	no	—
553	C₂³	—	202	4	no	—
554	C₂³	C₂³×D₁₀₁	1	1	yes	characteristic
555	C₂³	C₂³×D₁₀₁	1	2	yes	—
556	Q₈	—	2	2	no	—
557	Q₈	—	404	1	no	—
558	Q₈	—	404	2	no	—
559	Q₈	—	202	2	no	—
560	D₄	—	2	4	no	—
561	D₄	—	404	1	no	—
562	D₄	—	404	2	no	—
563	D₄	—	404	2	no	—
564	D₄	—	404	1	no	—
565	D₄	—	404	1	no	—
566	D₄	—	202	4	no	—
567	D₄	—	202	4	no	—
568	D₄	—	202	2	no	—
569	D₄	#13108074	1	4	yes	—
570	C₂×C₄	—	2	4	no	—
571	C₂×C₄	—	2	2	no	—
572	C₂×C₄	—	4	2	no	—
573	C₂×C₄	—	4	1	no	—
574	C₂×C₄	—	4	2	no	—
575	C₂×C₄	—	4	1	no	—
576	C₂×C₄	—	101	1	no	—
577	C₂×C₄	—	101	2	no	—
578	C₂×C₄	—	101	1	no	—
579	C₂×C₄	—	101	2	no	—
580	C₂×C₄	—	101	1	no	—
581	C₂×C₄	—	101	1	no	—
582	C₂×C₄	—	101	2	no	—
583	C₂×C₄	—	101	1	no	—
584	C₂×C₄	—	101	1	no	—
585	C₂×C₄	—	404	2	no	—
586	C₂×C₄	—	404	2	no	—
587	C₂×C₄	—	404	2	no	—
588	C₂×C₄	—	404	2	no	—
589	C₂×C₄	—	404	2	no	—
590	C₂×C₄	—	202	4	no	—
591	C₂×C₄	—	202	2	no	—
592	C₂×C₄	—	202	2	no	—
593	C₂×C₄	C₂³×D₁₀₁	1	1	yes	characteristic
594	C₂×C₄	C₂³×D₁₀₁	1	2	yes	—
595	C₂×C₄	C₂³×D₁₀₁	1	1	yes	characteristic
596	C₂×C₄	C₂³×D₁₀₁	1	1	yes	characteristic
597	C₂×C₄	C₂³×D₁₀₁	1	1	yes	characteristic
598	C₂×C₄	C₂³×D₁₀₁	1	2	yes	—
599	C₂×C₄	C₂³×D₁₀₁	1	1	yes	characteristic
600	C₂×C₄	C₂³×D₁₀₁	1	2	yes	—
601	C₂×C₄	C₂³×D₁₀₁	1	1	yes	characteristic
602	C₂²	—	2	2	no	—
603	C₂²	—	2	2	no	—
604	C₂²	—	2	1	no	—
605	C₂²	—	2	1	no	—
606	C₂²	—	2	1	no	—
607	C₂²	—	808	4	no	—
608	C₂²	—	202	1	no	—
609	C₂²	—	202	1	no	—
610	C₂²	—	202	2	no	—
611	C₂²	—	202	1	no	—
612	C₂²	—	202	2	no	—
613	C₂²	—	202	2	no	—
614	C₂²	—	202	1	no	—
615	C₂²	—	202	1	no	—
616	C₂²	—	202	1	no	—
617	C₂²	C₂×#13108074	1	4	yes	—
618	C₂²	C₂⁴×D₁₀₁	1	1	yes	characteristic
619	C₄	—	2	1	no	—
620	C₄	—	2	2	no	—
621	C₄	—	2	1	no	—
622	C₄	—	2	1	no	—
623	C₄	—	2	2	no	—
624	C₄	—	2	1	no	—
625	C₄	—	2	1	no	—
626	C₄	—	2	2	no	—
627	C₄	—	202	1	no	—
628	C₄	—	202	1	no	—
629	C₄	—	202	2	no	—
630	C₄	—	202	2	no	—
631	C₄	—	202	1	no	—
632	C₄	—	202	1	no	—
633	C₄	—	202	2	no	—
634	C₄	—	202	1	no	—
635	C₄	—	202	1	no	—
636	C₄	C₂×#13108074	1	2	yes	—
637	C₂	—	2	4	no	—
638	C₂	—	4	1	no	—
639	C₂	—	404	1	no	—
640	C₂	—	404	2	no	—
641	C₂	—	404	1	no	—
642	C₂	C₂²×#13108074	1	1	yes	characteristic
643	C₂	#20266013	1	1	yes	characteristic
644	C₂	#20266013	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₁₀₁
commutator, socle, cosocle	C₂²×C₁₀₁	C₂⁵
Fitting	C₄×#41×C₁₀₁	C₂
hypercenter	C₄×#41	D₁₀₁
hypocenter	C₁₀₁	#3521
LCS	G ▷ C₂²×C₁₀₁ ▷ C₁₀₁
UCS	C₁ ◁ C₂² ◁ C₄×#41

Complements

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

N	H ≅ G/N	type
1. #20265899	C₂	semidirect
2. #20265895	C₂	semidirect
3. #20265886	C₂	semidirect
4. #20265876	C₂	semidirect
5. #20265871	C₂	semidirect
6. #20265868	C₂	semidirect
7. #20265860	C₂	semidirect
8. #20265856	C₂	semidirect
9. #20265851	C₂	semidirect
10. #20265826	C₂	semidirect
11. #20265822	C₂	semidirect
12. #20265815	C₂	semidirect
13. #20265799	C₂	semidirect
14. #20265785	C₂	semidirect
15. #20265769	C₂	semidirect
16. #20265760	C₂	semidirect
17. #20265711	C₂	semidirect
18. #20265711	C₂	semidirect
19. #20265711	C₂	semidirect
20. C₂×#15692249	C₂	semidirect
21. #20265656	C₂	semidirect
22. #20265649	C₂	semidirect
23. C₄×#41×C₁₀₁	C₂	semidirect
26. #15692254	C₂²	semidirect
27. #15692253	C₂²	semidirect
29. #15692250	C₂²	semidirect
34. #15692249	C₂²	semidirect
35. #15692249	C₂²	semidirect
36. #15692249	C₂²	semidirect
37. #15692249	C₂²	semidirect
38. #15692249	C₂²	semidirect
39. #15692248	C₂²	semidirect
40. #15692247	C₂²	semidirect
41. #15692247	C₂²	semidirect
42. #15692247	C₂²	semidirect
43. #15692246	C₂²	semidirect
44. #15692245	C₂²	semidirect
45. #15692245	C₂²	semidirect
49. #15692243	C₂²	semidirect
52. #15692240	C₂²	semidirect
56. #15692238	C₂²	semidirect
57. #15692238	C₂²	semidirect
58. #15692238	C₂²	semidirect
59. #15692237	C₂²	semidirect
60. #15692236	C₂²	semidirect
62. #15692234	C₂²	semidirect
63. #15692234	C₂²	semidirect
64. #15692234	C₂²	semidirect
65. #15692233	C₂²	semidirect
66. #15692233	C₂²	semidirect
67. #15692232	C₂²	semidirect
68. #15692232	C₂²	semidirect
70. #15692231	C₂²	semidirect
75. #15692228	C₂²	semidirect
77. #15692227	C₂²	semidirect
80. C₄×Dic₂₀₂	C₂²	semidirect
81. C₄×Dic₂₀₂	C₂²	semidirect
82. C₄×Dic₂₀₂	C₂²	semidirect
83. #15692220	C₂²	semidirect
86. C₄×D₄₀₄	C₂²	semidirect
92. C₄×C₂²⋊D₁₀₁	C₂²	semidirect
93. C₄×C₂²⋊D₁₀₁	C₂²	semidirect
94. C₄×C₂²⋊D₁₀₁	C₂²	semidirect
96. #15692215	C₂²	semidirect
99. #15692212	C₂²	semidirect
100. #15692212	C₂²	semidirect
101. #15692212	C₂²	semidirect
102. #15692212	C₂²	semidirect
103. #15692211	C₂²	semidirect
104. C₂×#13108053	C₂²	semidirect
105. C₂×#13108053	C₂²	semidirect
106. C₂×#13108053	C₂²	semidirect
107. C₄⋊C₄×D₁₀₁	C₂²	semidirect
113. C₄×Q₈×C₁₀₁	C₂²	semidirect
114. C₄×Q₈×C₁₀₁	C₂²	semidirect
117. C₄×D₄×C₁₀₁	C₂²	semidirect
118. C₄×D₄×C₁₀₁	C₂²	semidirect
119. #117×C₁₀₁	C₂²	semidirect
120. #117×C₁₀₁	C₂²	semidirect
121. C₂×C₄²×C₁₀₁	C₂²	semidirect
122. C₂×C₄²×C₁₀₁	C₂²	semidirect
323. C₁₀₁	#3521	semidirect
346. C₄×#41	D₁₀₁	semidirect
408. C₄×Q₈	C₂×D₁₀₁	semidirect
409. C₄×Q₈	C₂×D₁₀₁	semidirect
425. C₄×D₄	C₂×D₁₀₁	semidirect
426. C₄×D₄	C₂×D₁₀₁	semidirect
434. #117	C₂×D₁₀₁	semidirect
435. #117	C₂×D₁₀₁	semidirect
444. C₂×C₄²	C₂×D₁₀₁	semidirect
445. C₂×C₄²	C₂×D₁₀₁	semidirect

Maximal subgroups

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

subgroup	index
#20265899	2
#20265895	2
#20265886	2
#20265876	2
#20265871	2
#20265868	2
#20265860	2
#20265856	2
#20265851	2
#20265826	2
#20265822	2
#20265815	2
#20265799	2
#20265785	2
#20265769	2
#20265760	2
#20265711	2
C₂×#15692249	2
#20265656	2
#20265649	2
C₄×#41×C₁₀₁	2
#3521	101