Subgroups — #16859271

Order 3968.

1132 conjugacy classes of subgroups.

The subgroup lattice has 674 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14521770	C₂	1	1	yes	maximal, characteristic, complemented
2	#14521763	C₂	1	1	yes	maximal, characteristic, complemented
3	#14521757	C₂	1	1	yes	maximal, characteristic, complemented
4	#14521751	C₂	1	1	yes	maximal, characteristic, complemented
5	#14521746	C₂	1	1	yes	maximal, characteristic, complemented
6	#14521741	C₂	1	1	yes	maximal, characteristic, complemented
7	#14521736	C₂	1	2	yes	maximal, complemented
8	#14521733	C₂	1	1	yes	maximal, characteristic, complemented
9	#14521730	C₂	1	2	yes	maximal, complemented
10	#14521722	C₂	1	2	yes	maximal, complemented
11	#14521699	C₂	1	1	yes	maximal, characteristic, complemented
12	#14521686	C₂	1	2	yes	maximal, complemented
13	#14521602	C₂	1	1	yes	maximal, characteristic, complemented
14	#14521581	C₂	1	2	yes	maximal, complemented
15	#14521579	C₂	1	2	yes	maximal, complemented
16	#14521579	C₂	1	2	yes	maximal, complemented
17	#14521556	C₂	1	1	yes	maximal, characteristic, complemented
18	#41×Dic₃₁	C₂	1	1	yes	maximal, characteristic, complemented
19	C₄×#92497	C₂	1	2	yes	maximal, complemented
20	C₂×C₄×C₂²⋊D₃₁	C₂	1	1	yes	maximal, characteristic, complemented
21	C₂×#11758503	C₂	1	1	yes	maximal, characteristic, complemented
22	#117×D₃₁	C₂	1	1	yes	maximal, characteristic, complemented
23	C₃₁×#525	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#41×C₃₁	C₂²	1	1	yes	characteristic
25	C₂³×C₄×C₃₁	C₂²	1	1	yes	characteristic
26	C₂²×C₂²⋊D₃₁	C₂²	1	1	yes	characteristic
27	C₂×#92497	C₂²	1	2	yes	—
28	C₂²×C₄×D₃₁	C₂²	1	1	yes	characteristic
29	C₃₁×#123	C₂²	1	2	yes	—
30	C₃₁×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
31	C₃₁×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
32	C₃₁×#121	C₂²	1	1	yes	characteristic, complemented
33	C₃₁×#121	C₂²	1	1	yes	characteristic, complemented
34	C₃₁×#120	C₂²	1	2	yes	—
35	C₄×D₄×C₃₁	C₂²	1	2	yes	complemented
36	C₄×D₄×C₃₁	C₂²	1	2	yes	complemented
37	C₃₁×#117	C₂²	1	1	yes	characteristic
38	C₂×C₂²⋊Dic₃₁	C₂²	1	2	yes	—
39	C₂×C₂²⋊Dic₃₁	C₂²	1	1	yes	characteristic
40	#11758523	C₂²	1	1	yes	characteristic, complemented
41	#11758523	C₂²	1	1	yes	characteristic, complemented
42	Q₈×Dic₃₁	C₂²	1	1	yes	characteristic, complemented
43	Q₈×Dic₃₁	C₂²	1	1	yes	characteristic, complemented
44	#11758516	C₂²	1	2	yes	—
45	#11758516	C₂²	1	2	yes	—
46	#11758515	C₂²	1	2	yes	—
47	#11758515	C₂²	1	1	yes	characteristic, complemented
48	#11758515	C₂²	1	1	yes	characteristic, complemented
49	#11758514	C₂²	1	2	yes	—
50	#11758513	C₂²	1	2	yes	complemented
51	#11758512	C₂²	1	2	yes	—
52	#11758512	C₂²	1	2	yes	complemented
53	#11758512	C₂²	1	2	yes	complemented
54	D₄×Dic₃₁	C₂²	1	2	yes	—
55	D₄×Dic₃₁	C₂²	1	2	yes	—
56	D₄×Dic₃₁	C₂²	1	1	yes	characteristic, complemented
57	D₄×Dic₃₁	C₂²	1	2	yes	complemented
58	D₄×Dic₃₁	C₂²	1	1	yes	characteristic, complemented
59	C₄×C₂²⋊D₃₁	C₂²	1	1	yes	characteristic
60	C₄×C₂²⋊D₃₁	C₂²	1	1	yes	characteristic
61	C₄×C₂²⋊D₃₁	C₂²	1	1	yes	characteristic
62	C₄×C₂²⋊D₃₁	C₂²	1	1	yes	characteristic
63	C₄×C₂²⋊D₃₁	C₂²	1	1	yes	characteristic
64	C₄×C₂²⋊D₃₁	C₂²	1	1	yes	characteristic
65	C₄×C₂²⋊D₃₁	C₂²	1	1	yes	characteristic
66	C₄×C₂²⋊D₃₁	C₂²	1	1	yes	characteristic
67	C₄×C₂²⋊D₃₁	C₂²	1	2	yes	complemented
68	C₄×C₂²⋊D₃₁	C₂²	1	2	yes	complemented
69	C₂×(C₂×D₃₁)⋊C₄	C₂²	1	1	yes	characteristic
70	#11758503	C₂²	1	1	yes	characteristic
71	#11758503	C₂²	1	2	yes	—
72	#11758503	C₂²	1	1	yes	characteristic
73	#11758503	C₂²	1	1	yes	characteristic, complemented
74	#11758503	C₂²	1	1	yes	characteristic, complemented
75	#11758503	C₂²	1	2	yes	complemented
76	#11758503	C₂²	1	2	yes	complemented
77	C₂×C₄⋊Dic₃₁	C₂²	1	1	yes	characteristic, complemented
78	C₂×C₄⋊Dic₃₁	C₂²	1	1	yes	characteristic, complemented
79	C₂×Dic₃₁⋊C₄	C₂²	1	1	yes	characteristic
80	C₂×C₄×Dic₃₁	C₂²	1	1	yes	characteristic
81	C₂×C₄×Dic₃₁	C₂²	1	2	yes	complemented
82	C₂×C₄×Dic₃₁	C₂²	1	2	yes	complemented
83	#11758475	C₂²	1	2	yes	complemented
84	#11758475	C₂²	1	2	yes	complemented
85	#11758474	C₂²	1	2	yes	complemented
86	#11758469	C₂²	1	2	yes	complemented
87	#11758469	C₂²	1	1	yes	characteristic, complemented
88	#11758469	C₂²	1	1	yes	characteristic, complemented
89	C₄⋊C₄×D₃₁	C₂²	1	1	yes	characteristic, complemented
90	C₄⋊C₄×D₃₁	C₂²	1	1	yes	characteristic, complemented
91	#11758467	C₂²	1	1	yes	characteristic, complemented
92	#11758467	C₂²	1	1	yes	characteristic, complemented
93	#11758467	C₂²	1	2	yes	complemented
94	#11758466	C₂²	1	2	yes	complemented
95	#11758466	C₂²	1	2	yes	complemented
96	#11758465	C₂²	1	1	yes	characteristic, complemented
97	#11758465	C₂²	1	1	yes	characteristic, complemented
98	#11758464	C₂²	1	2	yes	complemented
99	#11758463	C₂²	1	2	yes	—
100	#11758463	C₂²	1	2	yes	complemented
101	#11758462	C₂²	1	2	yes	—
102	#11758462	C₂²	1	2	yes	complemented
103	#11758460	C₂²	1	2	yes	—
104	#11758460	C₂²	1	2	yes	complemented
105	(C₂²⋊D₃₁)⋊C₄	C₂²	1	2	yes	—
106	(C₂²⋊D₃₁)⋊C₄	C₂²	1	2	yes	complemented
107	C₂²⋊C₄×D₃₁	C₂²	1	2	yes	—
108	#11758456	C₂²	1	2	yes	complemented
109	#11758456	C₂²	1	2	yes	complemented
110	#11758456	C₂²	1	2	yes	complemented
111	#11758456	C₂²	1	2	yes	complemented
112	#11758455	C₂²	1	2	yes	—
113	#11758455	C₂²	1	2	yes	—
114	#11758455	C₂²	1	2	yes	complemented
115	#11758455	C₂²	1	2	yes	complemented
116	#11758454	C₂²	1	2	yes	—
117	#11758454	C₂²	1	2	yes	complemented
118	#11758454	C₂²	1	2	yes	complemented
119	#11758449	C₂²	1	2	yes	complemented
120	C₄²×D₃₁	C₂²	1	2	yes	complemented
121	C₄×Dic₆₂	C₂²	1	2	yes	complemented
122	C₄×Dic₆₂	C₂²	1	2	yes	complemented
123	C₂⁴×C₃₁	C₂³	1	1	yes	characteristic
124	C₂³×D₃₁	C₂³	1	1	yes	characteristic
125	#41×C₃₁	—	2	4	no	—
126	C₂×Q₈×C₃₁	C₂³	1	1	yes	characteristic
127	C₂×D₄×C₃₁	C₂³	1	2	yes	—
128	C₂×D₄×C₃₁	C₂³	1	1	yes	characteristic
129	C₂×D₄×C₃₁	C₂³	1	2	yes	—
130	C₂×D₄×C₃₁	C₂³	1	2	yes	—
131	C₂²×C₄×C₃₁	—	2	4	no	—
132	C₂²×C₄×C₃₁	C₂³	1	1	yes	characteristic
133	C₂²×C₄×C₃₁	C₂³	1	2	yes	—
134	C₂²×C₄×C₃₁	C₂³	1	1	yes	characteristic
135	C₂²×C₄×C₃₁	C₂³	1	1	yes	characteristic
136	C₂²×C₄×C₃₁	C₂³	1	1	yes	characteristic
137	C₂²×C₄×C₃₁	C₂³	1	1	yes	characteristic
138	C₂²×C₄×C₃₁	C₂³	1	1	yes	characteristic
139	C₂×C₂²⋊D₃₁	—	2	4	no	—
140	C₂×C₂²⋊D₃₁	C₂³	1	2	yes	—
141	C₂×C₂²⋊D₃₁	C₂³	1	1	yes	characteristic
142	C₂×C₂²⋊D₃₁	C₂³	1	1	yes	characteristic
143	C₂×C₂²⋊D₃₁	C₂³	1	1	yes	characteristic
144	C₂×C₂²⋊D₃₁	C₂³	1	2	yes	—
145	C₂×C₂²⋊D₃₁	C₂³	1	1	yes	characteristic
146	C₂²×Dic₃₁	C₂³	1	1	yes	characteristic
147	C₂²×Dic₃₁	C₂³	1	2	yes	—
148	C₂²×Dic₃₁	C₂³	1	2	yes	—
149	C₂²×Dic₃₁	C₂³	1	1	yes	characteristic
150	C₂²×Dic₃₁	C₂³	1	1	yes	characteristic
151	C₂²×Dic₃₁	C₂³	1	2	yes	—
152	C₂²×Dic₃₁	C₂³	1	2	yes	—
153	#92497	—	2	8	no	—
154	C₂×C₄×D₃₁	—	2	4	no	—
155	C₂×C₄×D₃₁	C₂³	1	1	yes	characteristic
156	C₂×C₄×D₃₁	C₂³	1	2	yes	—
157	C₂×C₄×D₃₁	C₂³	1	1	yes	characteristic
158	C₂×C₄×D₃₁	C₂³	1	1	yes	characteristic
159	C₂×C₄×D₃₁	C₂³	1	1	yes	characteristic
160	C₂×C₄×D₃₁	C₂³	1	2	yes	—
161	C₂×Dic₆₂	C₂³	1	2	yes	—
162	C₂×Dic₆₂	C₂³	1	2	yes	—
163	C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
164	C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
165	C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
166	C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
167	C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
168	C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
169	C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
170	C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
171	C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
172	C₄²×C₃₁	C₂³	1	2	yes	—
173	C₂²⋊Dic₃₁	C₂³	1	2	yes	—
174	C₂²⋊Dic₃₁	C₂³	1	1	yes	characteristic
175	C₂²⋊Dic₃₁	C₂³	1	2	yes	—
176	C₂²⋊Dic₃₁	C₂³	1	2	yes	—
177	C₂²⋊Dic₃₁	C₂³	1	1	yes	characteristic
178	C₂²⋊Dic₃₁	C₂³	1	2	yes	—
179	C₂²⋊Dic₃₁	C₂³	1	2	yes	—
180	C₂²⋊Dic₃₁	C₂³	1	1	yes	characteristic
181	C₂²⋊Dic₃₁	C₂³	1	1	yes	characteristic
182	C₂²⋊Dic₃₁	C₂³	1	2	yes	—
183	C₂²⋊Dic₃₁	C₂³	1	2	yes	—
184	C₂²⋊Dic₃₁	C₂³	1	2	yes	—
185	(C₂×D₃₁)⋊C₄	C₂³	1	2	yes	—
186	(C₂×D₃₁)⋊C₄	C₂³	1	2	yes	—
187	(C₂×D₃₁)⋊C₄	C₂³	1	2	yes	—
188	(C₂×D₃₁)⋊C₄	C₂³	1	1	yes	characteristic
189	(C₂×D₃₁)⋊C₄	C₂³	1	1	yes	characteristic
190	(C₂×D₃₁)⋊C₄	C₂³	1	2	yes	—
191	(C₂×D₃₁)⋊C₄	C₂³	1	1	yes	characteristic
192	(C₂×D₃₁)⋊C₄	C₂³	1	1	yes	characteristic
193	C₄⋊Dic₃₁	C₂³	1	2	yes	—
194	C₄⋊Dic₃₁	C₂³	1	2	yes	—
195	C₄⋊Dic₃₁	C₂³	1	2	yes	—
196	C₄⋊Dic₃₁	C₂³	1	2	yes	—
197	C₄⋊Dic₃₁	C₂³	1	2	yes	—
198	C₄⋊Dic₃₁	C₂³	1	2	yes	—
199	C₄⋊Dic₃₁	C₂³	1	1	yes	characteristic
200	C₄⋊Dic₃₁	C₂³	1	1	yes	characteristic
201	C₄⋊Dic₃₁	C₂³	1	1	yes	characteristic
202	C₄⋊Dic₃₁	C₂³	1	1	yes	characteristic
203	Dic₃₁⋊C₄	C₂³	1	2	yes	—
204	Dic₃₁⋊C₄	C₂³	1	2	yes	—
205	Dic₃₁⋊C₄	C₂³	1	2	yes	—
206	Dic₃₁⋊C₄	C₂³	1	2	yes	—
207	Dic₃₁⋊C₄	C₂³	1	2	yes	—
208	Dic₃₁⋊C₄	C₂³	1	2	yes	—
209	Dic₃₁⋊C₄	C₂³	1	1	yes	characteristic
210	Dic₃₁⋊C₄	C₂³	1	2	yes	—
211	Dic₃₁⋊C₄	C₂³	1	1	yes	characteristic
212	Dic₃₁⋊C₄	C₂³	1	2	yes	—
213	Dic₃₁⋊C₄	C₂³	1	1	yes	characteristic
214	Dic₃₁⋊C₄	C₂³	1	1	yes	characteristic
215	C₄×Dic₃₁	C₂³	1	1	yes	characteristic
216	C₄×Dic₃₁	C₂³	1	1	yes	characteristic
217	C₄×Dic₃₁	C₂³	1	2	yes	—
218	C₄×Dic₃₁	C₂³	1	2	yes	—
219	C₄×Dic₃₁	C₂³	1	2	yes	—
220	C₄×Dic₃₁	C₂³	1	2	yes	—
221	C₄×Dic₃₁	C₂³	1	2	yes	—
222	C₄×Dic₃₁	C₂³	1	2	yes	—
223	C₄×Dic₃₁	C₂³	1	2	yes	—
224	C₄×Dic₃₁	C₂³	1	2	yes	—
225	C₄×Dic₃₁	C₂³	1	1	yes	characteristic
226	C₄×Dic₃₁	C₂³	1	1	yes	characteristic
227	C₂³×C₃₁	—	2	2	no	—
228	C₂³×C₃₁	—	2	2	no	—
229	C₂³×C₃₁	—	4	1	no	—
230	C₂³×C₃₁	C₂⁴	1	1	yes	characteristic
231	C₂³×C₃₁	C₂⁴	1	2	yes	—
232	C₂³×C₃₁	C₂⁴	1	1	yes	characteristic
233	C₂³×C₃₁	C₂⁴	1	1	yes	characteristic
234	C₂²×D₃₁	—	2	2	no	—
235	C₂²×D₃₁	—	2	2	no	—
236	C₂²×D₃₁	—	4	1	no	—
237	C₂²×D₃₁	C₂⁴	1	1	yes	characteristic
238	C₂²×D₃₁	C₂⁴	1	1	yes	characteristic
239	Q₈×C₃₁	—	2	2	no	—
240	D₄×C₃₁	—	2	4	no	—
241	D₄×C₃₁	—	2	4	no	—
242	D₄×C₃₁	—	2	2	no	—
243	D₄×C₃₁	—	4	2	no	—
244	C₂×C₄×C₃₁	—	2	2	no	—
245	C₂×C₄×C₃₁	—	2	2	no	—
246	C₂×C₄×C₃₁	—	2	2	no	—
247	C₂×C₄×C₃₁	—	2	2	no	—
248	C₂×C₄×C₃₁	—	2	2	no	—
249	C₂×C₄×C₃₁	—	2	4	no	—
250	C₂×C₄×C₃₁	#41	1	4	yes	complemented
251	C₂×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
252	C₂×C₄×C₃₁	C₂⁴	1	2	yes	—
253	C₂×C₄×C₃₁	C₂⁴	1	2	yes	—
254	C₂×C₄×C₃₁	C₂⁴	1	2	yes	—
255	C₂×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
256	C₂×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
257	C₂×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
258	C₂²⋊D₃₁	—	2	2	no	—
259	C₂²⋊D₃₁	—	2	4	no	—
260	C₂²⋊D₃₁	—	2	2	no	—
261	C₂²⋊D₃₁	—	2	2	no	—
262	C₂²⋊D₃₁	—	4	2	no	—
263	C₂²⋊D₃₁	#41	1	4	yes	complemented
264	C₂×Dic₃₁	—	2	2	no	—
265	C₂×Dic₃₁	—	2	4	no	—
266	C₂×Dic₃₁	—	2	4	no	—
267	C₂×Dic₃₁	—	2	2	no	—
268	C₂×Dic₃₁	—	4	1	no	—
269	C₂×Dic₃₁	—	4	2	no	—
270	C₂×Dic₃₁	—	4	2	no	—
271	C₂×Dic₃₁	C₂⁴	1	1	yes	characteristic
272	C₂×Dic₃₁	C₂⁴	1	1	yes	characteristic
273	C₂×Dic₃₁	C₂⁴	1	2	yes	—
274	C₂×Dic₃₁	C₂⁴	1	2	yes	—
275	C₂×Dic₃₁	C₂⁴	1	1	yes	characteristic
276	C₂×Dic₃₁	C₂⁴	1	2	yes	—
277	C₂×Dic₃₁	C₂⁴	1	2	yes	—
278	C₂×Dic₃₁	C₂⁴	1	1	yes	characteristic
279	C₂×Dic₃₁	C₂⁴	1	1	yes	characteristic
280	C₂×Dic₃₁	C₂⁴	1	1	yes	characteristic
281	C₄×D₃₁	—	2	4	no	—
282	C₄×D₃₁	—	2	2	no	—
283	C₄×D₃₁	—	2	2	no	—
284	C₄×D₃₁	—	2	2	no	—
285	C₄×D₃₁	—	2	2	no	—
286	C₄×D₃₁	—	4	2	no	—
287	Dic₆₂	—	2	4	no	—
288	Dic₆₂	—	4	2	no	—
289	#3475	—	31	1	no	maximal, Sylow
290	C₂²×C₃₁	—	2	1	no	—
291	C₂²×C₃₁	—	2	1	no	—
292	C₂²×C₃₁	—	2	1	no	—
293	C₂²×C₃₁	—	2	1	no	—
294	C₂²×C₃₁	—	2	2	no	—
295	C₂²×C₃₁	—	2	1	no	—
296	C₂²×C₃₁	—	2	1	no	—
297	C₂²×C₃₁	—	2	2	no	—
298	C₂²×C₃₁	—	2	2	no	—
299	C₂²×C₃₁	—	2	1	no	—
300	C₂²×C₃₁	—	4	4	no	—
301	C₂²×C₃₁	C₂×#41	1	2	yes	—
302	C₂²×C₃₁	C₂×#41	1	2	yes	—
303	C₂²×C₃₁	C₂⁵	1	1	yes	characteristic
304	C₂×D₃₁	—	2	1	no	—
305	C₂×D₃₁	—	2	1	no	—
306	C₂×D₃₁	—	2	1	no	—
307	C₂×D₃₁	—	2	1	no	—
308	C₂×D₃₁	—	2	1	no	—
309	C₂×D₃₁	—	4	4	no	—
310	C₂×D₃₁	C₂×#41	1	2	yes	—
311	C₄×C₃₁	—	2	2	no	—
312	C₄×C₃₁	—	2	1	no	—
313	C₄×C₃₁	—	2	1	no	—
314	C₄×C₃₁	—	2	2	no	—
315	C₄×C₃₁	—	2	2	no	—
316	C₄×C₃₁	C₂×#41	1	2	yes	—
317	C₄×C₃₁	C₂×#41	1	2	yes	—
318	Dic₃₁	—	2	2	no	—
319	Dic₃₁	—	2	1	no	—
320	Dic₃₁	—	2	1	no	—
321	Dic₃₁	—	2	2	no	—
322	Dic₃₁	—	2	1	no	—
323	Dic₃₁	—	2	1	no	—
324	Dic₃₁	—	2	2	no	—
325	Dic₃₁	—	2	2	no	—
326	Dic₃₁	—	2	1	no	—
327	Dic₃₁	C₂×#41	1	2	yes	—
328	#556	—	31	1	no	—
329	#555	—	31	1	no	—
330	#554	—	31	1	no	—
331	#553	—	31	1	no	—
332	#553	—	31	1	no	—
333	#552	—	31	2	no	—
334	#552	—	31	1	no	—
335	#552	—	31	1	no	—
336	#551	—	31	2	no	—
337	#551	—	31	2	no	—
338	#547	—	31	1	no	—
339	#546	—	31	2	no	—
340	#533	—	31	1	no	—
341	#529	—	31	2	no	—
342	#529	—	31	2	no	—
343	#529	—	31	2	no	—
344	#525	—	31	1	no	—
345	#525	D₃₁	1	1	yes	characteristic, complemented
346	C₄×#41	—	31	1	no	—
347	C₄×#41	—	31	2	no	—
348	C₂×C₄×D₄	—	31	1	no	—
349	C₂×#117	—	31	1	no	—
350	C₂×#117	—	31	1	no	—
351	C₂×C₃₁	—	2	2	no	—
352	C₂×C₃₁	—	2	2	no	—
353	C₂×C₃₁	—	4	2	no	—
354	C₂×C₃₁	—	4	1	no	—
355	C₂×C₃₁	C₂²×#41	1	1	yes	characteristic
356	C₂×C₃₁	C₂²×#41	1	1	yes	characteristic
357	C₂×C₃₁	#585	1	1	yes	characteristic
358	D₃₁	—	2	2	no	—
359	D₃₁	—	4	1	no	—
360	C₂×#41	—	31	2	no	—
361	C₂×#41	C₂×D₃₁	1	1	yes	characteristic
362	C₂²×D₄	—	31	1	no	—
363	C₂³×C₄	—	31	1	no	—
364	C₂³×C₄	C₂×D₃₁	1	1	yes	characteristic
365	C₄⋊Q₈	—	31	1	no	—
366	C₄⋊Q₈	—	31	1	no	—
367	#126	—	31	2	no	—
368	#126	—	31	2	no	—
369	#126	—	31	2	no	—
370	#126	—	31	2	no	—
371	#126	—	31	2	no	—
372	#126	—	31	2	no	—
373	#125	—	31	2	no	—
374	#125	—	31	2	no	—
375	#125	—	31	2	no	—
376	#125	—	31	1	no	—
377	#125	—	31	1	no	—
378	#124	—	31	2	no	—
379	#124	—	31	2	no	—
380	#124	—	31	2	no	—
381	#123	—	31	2	no	—
382	#123	—	31	2	no	—
383	#123	—	31	2	no	—
384	#123	—	31	2	no	—
385	#123	—	31	2	no	—
386	#123	—	31	2	no	—
387	#123	—	31	2	no	—
388	#123	C₂×D₃₁	1	2	yes	—
389	C₂²⋊Q₈	—	31	1	no	—
390	C₂²⋊Q₈	—	31	1	no	—
391	C₂²⋊Q₈	—	31	2	no	—
392	C₂²⋊Q₈	—	31	2	no	—
393	C₂²⋊Q₈	—	31	2	no	—
394	C₂²⋊Q₈	—	31	2	no	—
395	C₂²⋊Q₈	—	31	2	no	—
396	C₂²⋊Q₈	C₂×D₃₁	1	1	yes	characteristic, complemented
397	C₂²⋊Q₈	C₂×D₃₁	1	1	yes	characteristic, complemented
398	#121	—	31	1	no	—
399	#121	—	31	1	no	—
400	#121	—	31	2	no	—
401	#121	—	31	2	no	—
402	#121	—	31	2	no	—
403	#121	C₂×D₃₁	1	1	yes	characteristic, complemented
404	#121	C₂×D₃₁	1	1	yes	characteristic, complemented
405	#120	—	31	2	no	—
406	#120	C₂×D₃₁	1	2	yes	—
407	C₄×Q₈	—	31	1	no	—
408	C₄×Q₈	—	31	1	no	—
409	C₄×Q₈	—	31	2	no	—
410	C₄×Q₈	—	31	2	no	—
411	C₄×Q₈	—	31	2	no	—
412	C₄×D₄	—	31	2	no	—
413	C₄×D₄	—	31	1	no	—
414	C₄×D₄	—	31	2	no	—
415	C₄×D₄	—	31	2	no	—
416	C₄×D₄	—	31	1	no	—
417	C₄×D₄	—	31	1	no	—
418	C₄×D₄	—	31	1	no	—
419	C₄×D₄	—	31	1	no	—
420	C₄×D₄	—	31	1	no	—
421	C₄×D₄	—	31	1	no	—
422	C₄×D₄	—	31	1	no	—
423	C₄×D₄	—	31	1	no	—
424	C₄×D₄	—	31	1	no	—
425	C₄×D₄	—	31	2	no	—
426	C₄×D₄	—	31	2	no	—
427	C₄×D₄	—	31	2	no	—
428	C₄×D₄	—	31	2	no	—
429	C₄×D₄	C₂×D₃₁	1	2	yes	complemented
430	C₄×D₄	C₂×D₃₁	1	2	yes	complemented
431	#117	—	31	1	no	—
432	#117	—	31	1	no	—
433	#117	—	31	2	no	—
434	#117	—	31	2	no	—
435	#117	—	31	1	no	—
436	#117	—	31	1	no	—
437	#117	—	31	2	no	—
438	#117	—	31	1	no	—
439	#117	—	31	1	no	—
440	#117	—	31	2	no	—
441	#117	—	31	2	no	—
442	#117	—	31	2	no	—
443	#117	—	31	2	no	—
444	#117	—	31	2	no	—
445	#117	C₂×D₃₁	1	1	yes	characteristic
446	C₂×C₄⋊C₄	—	31	1	no	—
447	C₂×C₄⋊C₄	—	31	1	no	—
448	C₂×C₄⋊C₄	—	31	1	no	—
449	C₂×C₄⋊C₄	—	31	1	no	—
450	C₂×C₄⋊C₄	—	31	1	no	—
451	C₂×C₂²⋊C₄	—	31	2	no	—
452	C₂×C₂²⋊C₄	—	31	1	no	—
453	C₂×C₂²⋊C₄	—	31	1	no	—
454	C₂×C₂²⋊C₄	—	31	2	no	—
455	C₂×C₄²	—	31	2	no	—
456	C₂×C₄²	—	31	1	no	—
457	C₂×C₄²	—	31	2	no	—
458	C₂×C₄²	—	31	2	no	—
459	C₃₁	#3475	1	1	yes	characteristic, complemented, Sylow
460	C₂⁴	—	31	1	no	—
461	C₂⁴	C₂²×D₃₁	1	1	yes	characteristic
462	#41	—	2	4	no	—
463	#41	—	62	8	no	—
464	C₂×Q₈	—	31	2	no	—
465	C₂×Q₈	—	31	2	no	—
466	C₂×Q₈	C₂²×D₃₁	1	1	yes	characteristic
467	C₂×D₄	—	31	1	no	—
468	C₂×D₄	—	31	2	no	—
469	C₂×D₄	—	31	1	no	—
470	C₂×D₄	—	31	1	no	—
471	C₂×D₄	—	31	1	no	—
472	C₂×D₄	—	31	2	no	—
473	C₂×D₄	—	62	4	no	—
474	C₂×D₄	C₂²×D₃₁	1	2	yes	—
475	C₂×D₄	C₂²×D₃₁	1	1	yes	characteristic
476	C₂×D₄	C₂²×D₃₁	1	2	yes	—
477	C₂×D₄	C₂²×D₃₁	1	2	yes	—
478	C₂²×C₄	—	2	4	no	—
479	C₂²×C₄	—	31	2	no	—
480	C₂²×C₄	—	31	1	no	—
481	C₂²×C₄	—	31	2	no	—
482	C₂²×C₄	—	31	1	no	—
483	C₂²×C₄	—	31	1	no	—
484	C₂²×C₄	—	31	2	no	—
485	C₂²×C₄	—	31	2	no	—
486	C₂²×C₄	—	31	2	no	—
487	C₂²×C₄	—	31	1	no	—
488	C₂²×C₄	—	31	1	no	—
489	C₂²×C₄	—	31	1	no	—
490	C₂²×C₄	—	31	1	no	—
491	C₂²×C₄	—	31	2	no	—
492	C₂²×C₄	—	62	4	no	—
493	C₂²×C₄	C₂²×D₃₁	1	1	yes	characteristic
494	C₂²×C₄	C₂²×D₃₁	1	1	yes	characteristic
495	C₂²×C₄	C₂²×D₃₁	1	1	yes	characteristic
496	C₂²×C₄	C₂²×D₃₁	1	1	yes	characteristic
497	C₂²×C₄	C₂²×D₃₁	1	2	yes	—
498	C₂²×C₄	C₂²×D₃₁	1	1	yes	characteristic
499	C₂²×C₄	C₂²×D₃₁	1	1	yes	characteristic
500	C₄⋊C₄	—	31	1	no	—
501	C₄⋊C₄	—	31	2	no	—
502	C₄⋊C₄	—	31	2	no	—
503	C₄⋊C₄	—	31	1	no	—
504	C₄⋊C₄	—	31	1	no	—
505	C₄⋊C₄	—	31	1	no	—
506	C₄⋊C₄	—	31	2	no	—
507	C₄⋊C₄	—	31	2	no	—
508	C₄⋊C₄	—	31	2	no	—
509	C₄⋊C₄	—	31	2	no	—
510	C₄⋊C₄	—	31	2	no	—
511	C₄⋊C₄	—	31	2	no	—
512	C₄⋊C₄	—	31	1	no	—
513	C₄⋊C₄	—	31	1	no	—
514	C₄⋊C₄	—	31	1	no	—
515	C₄⋊C₄	—	31	1	no	—
516	C₄⋊C₄	—	31	2	no	—
517	C₄⋊C₄	—	31	2	no	—
518	C₄⋊C₄	—	31	2	no	—
519	C₄⋊C₄	—	31	2	no	—
520	C₄⋊C₄	—	31	2	no	—
521	C₄⋊C₄	—	31	2	no	—
522	C₄⋊C₄	C₂²×D₃₁	1	1	yes	characteristic
523	C₄⋊C₄	C₂²×D₃₁	1	1	yes	characteristic
524	C₄⋊C₄	C₂²×D₃₁	1	2	yes	—
525	C₄⋊C₄	C₂²×D₃₁	1	2	yes	—
526	C₂²⋊C₄	—	31	2	no	—
527	C₂²⋊C₄	—	31	1	no	—
528	C₂²⋊C₄	—	31	2	no	—
529	C₂²⋊C₄	—	31	2	no	—
530	C₂²⋊C₄	—	31	2	no	—
531	C₂²⋊C₄	—	31	1	no	—
532	C₂²⋊C₄	—	31	1	no	—
533	C₂²⋊C₄	—	31	1	no	—
534	C₂²⋊C₄	—	31	2	no	—
535	C₂²⋊C₄	—	31	2	no	—
536	C₂²⋊C₄	—	31	2	no	—
537	C₂²⋊C₄	—	31	2	no	—
538	C₂²⋊C₄	—	31	1	no	—
539	C₂²⋊C₄	—	31	2	no	—
540	C₂²⋊C₄	—	31	2	no	—
541	C₂²⋊C₄	—	31	1	no	—
542	C₂²⋊C₄	—	31	1	no	—
543	C₂²⋊C₄	—	31	1	no	—
544	C₂²⋊C₄	—	31	2	no	—
545	C₂²⋊C₄	—	31	2	no	—
546	C₂²⋊C₄	C₂²×D₃₁	1	2	yes	—
547	C₂²⋊C₄	C₂²×D₃₁	1	2	yes	—
548	C₂²⋊C₄	C₂²×D₃₁	1	2	yes	—
549	C₂²⋊C₄	C₂²×D₃₁	1	2	yes	—
550	C₂²⋊C₄	C₂²×D₃₁	1	2	yes	—
551	C₄²	—	31	2	no	—
552	C₄²	—	31	2	no	—
553	C₄²	—	31	2	no	—
554	C₄²	—	31	2	no	—
555	C₄²	—	31	2	no	—
556	C₄²	—	31	1	no	—
557	C₄²	—	31	1	no	—
558	C₄²	—	31	2	no	—
559	C₄²	—	31	2	no	—
560	C₄²	—	31	1	no	—
561	C₄²	—	31	1	no	—
562	C₄²	—	31	2	no	—
563	C₄²	C₂²×D₃₁	1	2	yes	—
564	C₂³	—	2	2	no	—
565	C₂³	—	2	2	no	—
566	C₂³	—	4	1	no	—
567	C₂³	—	31	1	no	—
568	C₂³	—	31	1	no	—
569	C₂³	—	62	2	no	—
570	C₂³	—	62	2	no	—
571	C₂³	—	124	1	no	—
572	C₂³	C₂³×D₃₁	1	1	yes	characteristic
573	C₂³	C₂³×D₃₁	1	2	yes	—
574	C₂³	C₂³×D₃₁	1	1	yes	characteristic
575	C₂³	C₂³×D₃₁	1	1	yes	characteristic
576	Q₈	—	2	2	no	—
577	Q₈	—	62	4	no	—
578	Q₈	—	124	2	no	—
579	D₄	—	2	4	no	—
580	D₄	—	2	4	no	—
581	D₄	—	2	2	no	—
582	D₄	—	4	2	no	—
583	D₄	—	31	4	no	—
584	D₄	—	62	2	no	—
585	D₄	—	62	2	no	—
586	D₄	—	62	4	no	—
587	D₄	—	62	2	no	—
588	D₄	—	124	2	no	—
589	C₂×C₄	—	2	2	no	—
590	C₂×C₄	—	2	2	no	—
591	C₂×C₄	—	2	2	no	—
592	C₂×C₄	—	2	2	no	—
593	C₂×C₄	—	2	2	no	—
594	C₂×C₄	—	2	4	no	—
595	C₂×C₄	—	31	1	no	—
596	C₂×C₄	—	31	2	no	—
597	C₂×C₄	—	31	1	no	—
598	C₂×C₄	—	31	1	no	—
599	C₂×C₄	—	31	2	no	—
600	C₂×C₄	—	31	1	no	—
601	C₂×C₄	—	31	2	no	—
602	C₂×C₄	—	31	2	no	—
603	C₂×C₄	—	31	1	no	—
604	C₂×C₄	—	31	1	no	—
605	C₂×C₄	—	62	4	no	—
606	C₂×C₄	—	62	2	no	—
607	C₂×C₄	—	62	4	no	—
608	C₂×C₄	—	62	2	no	—
609	C₂×C₄	—	62	4	no	—
610	C₂×C₄	—	62	2	no	—
611	C₂×C₄	—	62	2	no	—
612	C₂×C₄	—	62	2	no	—
613	C₂×C₄	—	62	2	no	—
614	C₂×C₄	—	124	2	no	—
615	C₂×C₄	—	124	2	no	—
616	C₂×C₄	—	124	2	no	—
617	C₂×C₄	—	124	1	no	—
618	C₂×C₄	#92497	1	4	yes	complemented
619	C₂×C₄	C₂³×D₃₁	1	1	yes	characteristic
620	C₂×C₄	C₂³×D₃₁	1	2	yes	—
621	C₂×C₄	C₂³×D₃₁	1	2	yes	—
622	C₂×C₄	C₂³×D₃₁	1	2	yes	—
623	C₂×C₄	C₂³×D₃₁	1	1	yes	characteristic
624	C₂×C₄	C₂³×D₃₁	1	1	yes	characteristic
625	C₂×C₄	C₂³×D₃₁	1	1	yes	characteristic
626	C₂²	—	2	1	no	—
627	C₂²	—	2	1	no	—
628	C₂²	—	2	1	no	—
629	C₂²	—	2	1	no	—
630	C₂²	—	2	2	no	—
631	C₂²	—	2	1	no	—
632	C₂²	—	2	1	no	—
633	C₂²	—	2	2	no	—
634	C₂²	—	2	2	no	—
635	C₂²	—	2	1	no	—
636	C₂²	—	4	4	no	—
637	C₂²	—	31	2	no	—
638	C₂²	—	62	1	no	—
639	C₂²	—	62	1	no	—
640	C₂²	—	62	1	no	—
641	C₂²	—	62	1	no	—
642	C₂²	—	62	1	no	—
643	C₂²	—	124	4	no	—
644	C₂²	C₂×#92497	1	2	yes	—
645	C₂²	#41×D₃₁	1	2	yes	—
646	C₂²	C₂⁴×D₃₁	1	1	yes	characteristic
647	C₄	—	2	2	no	—
648	C₄	—	2	1	no	—
649	C₄	—	2	1	no	—
650	C₄	—	2	2	no	—
651	C₄	—	2	2	no	—
652	C₄	—	31	2	no	—
653	C₄	—	62	2	no	—
654	C₄	—	62	1	no	—
655	C₄	—	62	2	no	—
656	C₄	—	62	1	no	—
657	C₄	—	62	1	no	—
658	C₄	—	62	2	no	—
659	C₄	—	62	1	no	—
660	C₄	—	62	2	no	—
661	C₄	—	62	1	no	—
662	C₄	C₂×#92497	1	2	yes	—
663	C₄	C₂×#92497	1	2	yes	—
664	C₂	—	2	2	no	—
665	C₂	—	2	2	no	—
666	C₂	—	4	1	no	—
667	C₂	—	4	2	no	—
668	C₂	—	62	2	no	—
669	C₂	—	124	1	no	—
670	C₂	C₂×#41×D₃₁	1	1	yes	characteristic
671	C₂	C₂²×#92497	1	1	yes	characteristic
672	C₂	#14521885	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂³×D₃₁
commutator, socle, cosocle	C₂²×C₃₁	C₂⁵
Frattini	C₂²	C₂⁴×D₃₁
Fitting	C₃₁×#525	C₂
hypercenter	#525	D₃₁
hypocenter	C₃₁	#3475
LCS	G ▷ C₂²×C₃₁ ▷ C₃₁
UCS	C₁ ◁ C₂×C₄ ◁ #525

Complements

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

N	H ≅ G/N	type
1. #14521770	C₂	semidirect
2. #14521763	C₂	semidirect
3. #14521757	C₂	semidirect
4. #14521751	C₂	semidirect
5. #14521746	C₂	semidirect
6. #14521741	C₂	semidirect
7. #14521736	C₂	semidirect
8. #14521733	C₂	semidirect
9. #14521730	C₂	semidirect
10. #14521722	C₂	semidirect
11. #14521699	C₂	semidirect
12. #14521686	C₂	semidirect
13. #14521602	C₂	semidirect
14. #14521581	C₂	semidirect
15. #14521579	C₂	semidirect
16. #14521579	C₂	semidirect
17. #14521556	C₂	semidirect
18. #41×Dic₃₁	C₂	semidirect
19. C₄×#92497	C₂	semidirect
20. C₂×C₄×C₂²⋊D₃₁	C₂	semidirect
21. C₂×#11758503	C₂	semidirect
22. #117×D₃₁	C₂	semidirect
23. C₃₁×#525	C₂	semidirect
30. C₃₁×C₂²⋊Q₈	C₂²	semidirect
31. C₃₁×C₂²⋊Q₈	C₂²	semidirect
32. C₃₁×#121	C₂²	semidirect
33. C₃₁×#121	C₂²	semidirect
35. C₄×D₄×C₃₁	C₂²	semidirect
36. C₄×D₄×C₃₁	C₂²	semidirect
40. #11758523	C₂²	semidirect
41. #11758523	C₂²	semidirect
42. Q₈×Dic₃₁	C₂²	semidirect
43. Q₈×Dic₃₁	C₂²	semidirect
47. #11758515	C₂²	semidirect
48. #11758515	C₂²	semidirect
50. #11758513	C₂²	semidirect
52. #11758512	C₂²	semidirect
53. #11758512	C₂²	semidirect
56. D₄×Dic₃₁	C₂²	semidirect
57. D₄×Dic₃₁	C₂²	semidirect
58. D₄×Dic₃₁	C₂²	semidirect
67. C₄×C₂²⋊D₃₁	C₂²	semidirect
68. C₄×C₂²⋊D₃₁	C₂²	semidirect
73. #11758503	C₂²	semidirect
74. #11758503	C₂²	semidirect
75. #11758503	C₂²	semidirect
76. #11758503	C₂²	semidirect
77. C₂×C₄⋊Dic₃₁	C₂²	semidirect
78. C₂×C₄⋊Dic₃₁	C₂²	semidirect
81. C₂×C₄×Dic₃₁	C₂²	semidirect
82. C₂×C₄×Dic₃₁	C₂²	semidirect
83. #11758475	C₂²	semidirect
84. #11758475	C₂²	semidirect
85. #11758474	C₂²	semidirect
86. #11758469	C₂²	semidirect
87. #11758469	C₂²	semidirect
88. #11758469	C₂²	semidirect
89. C₄⋊C₄×D₃₁	C₂²	semidirect
90. C₄⋊C₄×D₃₁	C₂²	semidirect
91. #11758467	C₂²	semidirect
92. #11758467	C₂²	semidirect
93. #11758467	C₂²	semidirect
94. #11758466	C₂²	semidirect
95. #11758466	C₂²	semidirect
96. #11758465	C₂²	semidirect
97. #11758465	C₂²	semidirect
98. #11758464	C₂²	semidirect
100. #11758463	C₂²	semidirect
102. #11758462	C₂²	semidirect
104. #11758460	C₂²	semidirect
106. (C₂²⋊D₃₁)⋊C₄	C₂²	semidirect
108. #11758456	C₂²	semidirect
109. #11758456	C₂²	semidirect
110. #11758456	C₂²	semidirect
111. #11758456	C₂²	semidirect
114. #11758455	C₂²	semidirect
115. #11758455	C₂²	semidirect
117. #11758454	C₂²	semidirect
118. #11758454	C₂²	semidirect
119. #11758449	C₂²	semidirect
120. C₄²×D₃₁	C₂²	semidirect
121. C₄×Dic₆₂	C₂²	semidirect
122. C₄×Dic₆₂	C₂²	semidirect
250. C₂×C₄×C₃₁	#41	semidirect
263. C₂²⋊D₃₁	#41	semidirect
345. #525	D₃₁	semidirect
396. C₂²⋊Q₈	C₂×D₃₁	semidirect
397. C₂²⋊Q₈	C₂×D₃₁	semidirect
403. #121	C₂×D₃₁	semidirect
404. #121	C₂×D₃₁	semidirect
429. C₄×D₄	C₂×D₃₁	semidirect
430. C₄×D₄	C₂×D₃₁	semidirect
459. C₃₁	#3475	semidirect
618. C₂×C₄	#92497	semidirect

Maximal subgroups

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

subgroup	index
#14521770	2
#14521763	2
#14521757	2
#14521751	2
#14521746	2
#14521741	2
#14521736	2
#14521733	2
#14521730	2
#14521722	2
#14521699	2
#14521686	2
#14521602	2
#14521581	2
#14521579	2
#14521556	2
#41×Dic₃₁	2
C₄×#92497	2
C₂×C₄×C₂²⋊D₃₁	2
C₂×#11758503	2
#117×D₃₁	2
C₃₁×#525	2
#3475	31