Subgroups — #16859098

Order 3968.

1040 conjugacy classes of subgroups.

The subgroup lattice has 650 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14521673	C₂	1	1	yes	maximal, characteristic, complemented
2	#14521670	C₂	1	1	yes	maximal, characteristic, complemented
3	#14521668	C₂	1	1	yes	maximal, characteristic, complemented
4	#14521659	C₂	1	1	yes	maximal, characteristic, complemented
5	#14521657	C₂	1	1	yes	maximal, characteristic, complemented
6	#14521652	C₂	1	1	yes	maximal, characteristic, complemented
7	#14521650	C₂	1	1	yes	maximal, characteristic, complemented
8	#14521645	C₂	1	2	yes	maximal, complemented
9	#14521640	C₂	1	2	yes	maximal, complemented
10	#14521635	C₂	1	2	yes	maximal, complemented
11	#14521633	C₂	1	2	yes	maximal, complemented
12	#14521604	C₂	1	1	yes	maximal, characteristic, complemented
13	#14521598	C₂	1	1	yes	maximal, characteristic, complemented
14	#14521585	C₂	1	2	yes	maximal, complemented
15	#14521582	C₂	1	2	yes	maximal, complemented
16	#14521578	C₂	1	2	yes	maximal, complemented
17	#14521576	C₂	1	2	yes	maximal, complemented
18	#14521562	C₂	1	1	yes	maximal, characteristic, complemented
19	#14521559	C₂	1	1	yes	maximal, characteristic, complemented
20	C₄×#92499	C₂	1	1	yes	maximal, characteristic, complemented
21	C₄×#92497	C₂	1	1	yes	maximal, characteristic, complemented
22	#117×D₃₁	C₂	1	1	yes	maximal, characteristic, complemented
23	C₃₁×#542	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#92499	C₂²	1	1	yes	characteristic
25	C₂×#92497	C₂²	1	1	yes	characteristic
26	C₂²×C₄×D₃₁	C₂²	1	1	yes	characteristic
27	C₃₁×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
28	C₃₁×#126	C₂²	1	2	yes	complemented
29	C₃₁×#124	C₂²	1	2	yes	—
30	C₃₁×#124	C₂²	1	1	yes	characteristic, complemented
31	C₃₁×#123	C₂²	1	2	yes	—
32	C₃₁×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
33	C₃₁×C₂²⋊Q₈	C₂²	1	2	yes	complemented
34	C₃₁×#121	C₂²	1	1	yes	characteristic
35	C₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic, complemented
36	C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic, complemented
37	C₃₁×#117	C₂²	1	1	yes	characteristic
38	#11758524	C₂²	1	2	yes	—
39	#11758523	C₂²	1	2	yes	—
40	#11758523	C₂²	1	1	yes	characteristic
41	#11758523	C₂²	1	2	yes	complemented
42	Q₈×Dic₃₁	C₂²	1	2	yes	complemented
43	Q₈×Dic₃₁	C₂²	1	1	yes	characteristic, complemented
44	#11758521	C₂²	1	1	yes	characteristic, complemented
45	#11758517	C₂²	1	1	yes	characteristic, complemented
46	#11758516	C₂²	1	2	yes	—
47	#11758515	C₂²	1	2	yes	—
48	#11758515	C₂²	1	1	yes	characteristic
49	#11758514	C₂²	1	2	yes	—
50	D₄×Dic₃₁	C₂²	1	2	yes	—
51	D₄×Dic₃₁	C₂²	1	1	yes	characteristic, complemented
52	#11758507	C₂²	1	2	yes	—
53	#11758507	C₂²	1	1	yes	characteristic
54	#11758506	C₂²	1	2	yes	complemented
55	C₄×C₂²⋊D₃₁	C₂²	1	2	yes	—
56	#11758503	C₂²	1	1	yes	characteristic
57	#11758501	C₂²	1	1	yes	characteristic
58	C₂×C₄×Dic₃₁	C₂²	1	2	yes	complemented
59	#11758475	C₂²	1	2	yes	—
60	#11758475	C₂²	1	2	yes	complemented
61	#11758475	C₂²	1	2	yes	complemented
62	#11758474	C₂²	1	2	yes	—
63	#11758474	C₂²	1	1	yes	characteristic
64	#11758473	C₂²	1	2	yes	complemented
65	#11758472	C₂²	1	1	yes	characteristic
66	#11758471	C₂²	1	2	yes	—
67	#11758471	C₂²	1	2	yes	—
68	#11758470	C₂²	1	2	yes	—
69	#11758470	C₂²	1	2	yes	—
70	#11758470	C₂²	1	1	yes	characteristic, complemented
71	#11758469	C₂²	1	1	yes	characteristic
72	#11758469	C₂²	1	1	yes	characteristic
73	#11758469	C₂²	1	1	yes	characteristic
74	#11758469	C₂²	1	1	yes	characteristic
75	#11758469	C₂²	1	2	yes	complemented
76	C₄⋊C₄×D₃₁	C₂²	1	1	yes	characteristic
77	C₄⋊C₄×D₃₁	C₂²	1	1	yes	characteristic
78	#11758467	C₂²	1	1	yes	characteristic, complemented
79	#11758467	C₂²	1	1	yes	characteristic, complemented
80	#11758467	C₂²	1	2	yes	complemented
81	#11758466	C₂²	1	2	yes	complemented
82	#11758466	C₂²	1	2	yes	complemented
83	#11758464	C₂²	1	2	yes	complemented
84	#11758464	C₂²	1	1	yes	characteristic, complemented
85	#11758463	C₂²	1	2	yes	—
86	#11758463	C₂²	1	2	yes	complemented
87	#11758462	C₂²	1	2	yes	—
88	#11758462	C₂²	1	2	yes	—
89	#11758461	C₂²	1	2	yes	—
90	#11758461	C₂²	1	2	yes	—
91	#11758461	C₂²	1	2	yes	—
92	#11758460	C₂²	1	2	yes	—
93	#11758460	C₂²	1	2	yes	—
94	#11758460	C₂²	1	2	yes	complemented
95	#11758460	C₂²	1	2	yes	complemented
96	#11758459	C₂²	1	2	yes	—
97	(C₂²⋊D₃₁)⋊C₄	C₂²	1	2	yes	—
98	(C₂²⋊D₃₁)⋊C₄	C₂²	1	2	yes	—
99	(C₂²⋊D₃₁)⋊C₄	C₂²	1	2	yes	—
100	(C₂²⋊D₃₁)⋊C₄	C₂²	1	2	yes	complemented
101	(C₂²⋊D₃₁)⋊C₄	C₂²	1	2	yes	complemented
102	C₂²⋊C₄×D₃₁	C₂²	1	1	yes	characteristic
103	C₂²⋊C₄×D₃₁	C₂²	1	1	yes	characteristic
104	#11758456	C₂²	1	2	yes	—
105	#11758456	C₂²	1	2	yes	—
106	#11758456	C₂²	1	2	yes	complemented
107	#11758455	C₂²	1	2	yes	complemented
108	#11758454	C₂²	1	1	yes	characteristic
109	#11758454	C₂²	1	1	yes	characteristic
110	#11758454	C₂²	1	2	yes	complemented
111	#11758453	C₂²	1	2	yes	—
112	#11758452	C₂²	1	1	yes	characteristic, complemented
113	C₄×D₁₂₄	C₂²	1	2	yes	—
114	C₄×D₁₂₄	C₂²	1	1	yes	characteristic, complemented
115	#11758449	C₂²	1	1	yes	characteristic
116	#11758449	C₂²	1	1	yes	characteristic
117	C₄²×D₃₁	C₂²	1	1	yes	characteristic
118	C₄²×D₃₁	C₂²	1	1	yes	characteristic
119	C₄²×D₃₁	C₂²	1	2	yes	complemented
120	#11758447	C₂²	1	2	yes	complemented
121	#11758446	C₂²	1	1	yes	characteristic, complemented
122	C₄×Dic₆₂	C₂²	1	1	yes	characteristic, complemented
123	C₂³×D₃₁	C₂³	1	1	yes	characteristic
124	C₂×Q₈×C₃₁	C₂³	1	1	yes	characteristic
125	C₂×Q₈×C₃₁	C₂³	1	2	yes	—
126	C₂×D₄×C₃₁	C₂³	1	1	yes	characteristic
127	C₂×D₄×C₃₁	C₂³	1	2	yes	—
128	C₂²×C₄×C₃₁	C₂³	1	1	yes	characteristic
129	C₂²×C₄×C₃₁	C₂³	1	2	yes	—
130	C₂×C₂²⋊D₃₁	C₂³	1	2	yes	—
131	C₂×C₂²⋊D₃₁	C₂³	1	2	yes	—
132	C₂×C₂²⋊D₃₁	C₂³	1	2	yes	—
133	C₂×C₂²⋊D₃₁	C₂³	1	2	yes	—
134	C₂×C₂²⋊D₃₁	C₂³	1	2	yes	—
135	C₂²×Dic₃₁	C₂³	1	1	yes	characteristic
136	C₂²×Dic₃₁	C₂³	1	2	yes	—
137	C₂²×Dic₃₁	C₂³	1	2	yes	—
138	#92499	—	2	4	no	—
139	#92497	—	2	4	no	—
140	C₂×D₁₂₄	C₂³	1	2	yes	—
141	C₂×D₁₂₄	C₂³	1	1	yes	characteristic
142	C₂×D₁₂₄	C₂³	1	2	yes	—
143	C₂×C₄×D₃₁	—	2	4	no	—
144	C₂×C₄×D₃₁	C₂³	1	2	yes	—
145	C₂×C₄×D₃₁	C₂³	1	1	yes	characteristic
146	C₂×C₄×D₃₁	C₂³	1	1	yes	characteristic
147	C₂×C₄×D₃₁	C₂³	1	1	yes	characteristic
148	C₂×C₄×D₃₁	C₂³	1	1	yes	characteristic
149	C₂×C₄×D₃₁	C₂³	1	1	yes	characteristic
150	C₂×C₄×D₃₁	C₂³	1	1	yes	characteristic
151	C₂×C₄×D₃₁	C₂³	1	1	yes	characteristic
152	C₂×C₄×D₃₁	C₂³	1	2	yes	—
153	C₂×C₄×D₃₁	C₂³	1	2	yes	—
154	C₂×C₄×D₃₁	C₂³	1	1	yes	characteristic
155	C₂×Dic₆₂	C₂³	1	1	yes	characteristic
156	C₂×Dic₆₂	C₂³	1	2	yes	—
157	C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
158	C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
159	C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
160	C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
161	C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
162	C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
163	C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
164	C₂²⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
165	C₂²⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
166	C₂²⋊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	C₄²×C₃₁	C₂³	1	1	yes	characteristic
172	C₄²×C₃₁	C₂³	1	1	yes	characteristic
173	C₄²×C₃₁	C₂³	1	2	yes	—
174	C₂²⋊Dic₃₁	C₂³	1	1	yes	characteristic
175	C₂²⋊Dic₃₁	C₂³	1	1	yes	characteristic
176	C₂²⋊Dic₃₁	C₂³	1	2	yes	—
177	C₂²⋊Dic₃₁	C₂³	1	2	yes	—
178	C₂²⋊Dic₃₁	C₂³	1	2	yes	—
179	(C₂×D₃₁)⋊C₄	C₂³	1	1	yes	characteristic
180	(C₂×D₃₁)⋊C₄	C₂³	1	1	yes	characteristic
181	(C₂×D₃₁)⋊C₄	C₂³	1	1	yes	characteristic
182	(C₂×D₃₁)⋊C₄	C₂³	1	1	yes	characteristic
183	(C₂×D₃₁)⋊C₄	C₂³	1	2	yes	—
184	(C₂×D₃₁)⋊C₄	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	2	yes	—
189	(C₂×D₃₁)⋊C₄	C₂³	1	2	yes	—
190	(C₂×D₃₁)⋊C₄	C₂³	1	2	yes	—
191	(C₂×D₃₁)⋊C₄	C₂³	1	2	yes	—
192	(C₂×D₃₁)⋊C₄	C₂³	1	2	yes	—
193	C₄⋊Dic₃₁	C₂³	1	1	yes	characteristic
194	C₄⋊Dic₃₁	C₂³	1	1	yes	characteristic
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	2	yes	—
200	C₄⋊Dic₃₁	C₂³	1	1	yes	characteristic
201	C₄⋊Dic₃₁	C₂³	1	1	yes	characteristic
202	Dic₃₁⋊C₄	C₂³	1	2	yes	—
203	Dic₃₁⋊C₄	C₂³	1	1	yes	characteristic
204	Dic₃₁⋊C₄	C₂³	1	2	yes	—
205	Dic₃₁⋊C₄	C₂³	1	2	yes	—
206	Dic₃₁⋊C₄	C₂³	1	1	yes	characteristic
207	Dic₃₁⋊C₄	C₂³	1	1	yes	characteristic
208	Dic₃₁⋊C₄	C₂³	1	1	yes	characteristic
209	Dic₃₁⋊C₄	C₂³	1	2	yes	—
210	Dic₃₁⋊C₄	C₂³	1	2	yes	—
211	Dic₃₁⋊C₄	C₂³	1	2	yes	—
212	Dic₃₁⋊C₄	C₂³	1	2	yes	—
213	Dic₃₁⋊C₄	C₂³	1	2	yes	—
214	C₄×Dic₃₁	C₂³	1	2	yes	—
215	C₄×Dic₃₁	C₂³	1	1	yes	characteristic
216	C₄×Dic₃₁	C₂³	1	1	yes	characteristic
217	C₄×Dic₃₁	C₂³	1	1	yes	characteristic
218	C₄×Dic₃₁	C₂³	1	1	yes	characteristic
219	C₄×Dic₃₁	C₂³	1	1	yes	characteristic
220	C₄×Dic₃₁	C₂³	1	1	yes	characteristic
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	C₂³×C₃₁	C₂⁴	1	1	yes	characteristic
226	C₂³×C₃₁	C₂⁴	1	2	yes	—
227	C₂²×D₃₁	—	2	2	no	—
228	C₂²×D₃₁	—	4	1	no	—
229	C₂²×D₃₁	—	4	1	no	—
230	C₂²×D₃₁	C₂⁴	1	1	yes	characteristic
231	C₂²×D₃₁	C₂⁴	1	2	yes	—
232	C₂²×D₃₁	C₂⁴	1	1	yes	characteristic
233	Q₈×C₃₁	—	2	2	no	—
234	Q₈×C₃₁	—	4	2	no	—
235	D₄×C₃₁	—	2	2	no	—
236	D₄×C₃₁	—	4	2	no	—
237	C₂×C₄×C₃₁	—	2	2	no	—
238	C₂×C₄×C₃₁	—	4	2	no	—
239	C₂×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
240	C₂×C₄×C₃₁	C₂⁴	1	2	yes	—
241	C₂×C₄×C₃₁	C₂⁴	1	2	yes	—
242	C₂×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
243	C₂×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
244	C₂×C₄×C₃₁	C₂⁴	1	2	yes	—
245	C₂×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
246	C₂×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
247	C₂×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
248	C₂²⋊D₃₁	—	2	4	no	—
249	C₂²⋊D₃₁	—	4	2	no	—
250	C₂²⋊D₃₁	—	4	2	no	—
251	C₂²⋊D₃₁	—	4	2	no	—
252	C₂²⋊D₃₁	—	4	2	no	—
253	C₂×Dic₃₁	—	2	2	no	—
254	C₂×Dic₃₁	—	2	4	no	—
255	C₂×Dic₃₁	—	4	2	no	—
256	C₂×Dic₃₁	C₂⁴	1	1	yes	characteristic
257	C₂×Dic₃₁	C₂⁴	1	1	yes	characteristic
258	C₂×Dic₃₁	C₂⁴	1	1	yes	characteristic
259	C₂×Dic₃₁	C₂⁴	1	2	yes	—
260	C₂×Dic₃₁	C₂⁴	1	1	yes	characteristic
261	C₂×Dic₃₁	C₂⁴	1	2	yes	—
262	C₂×Dic₃₁	C₂⁴	1	2	yes	—
263	C₂×Dic₃₁	C₂⁴	1	1	yes	characteristic
264	C₂×Dic₃₁	C₂⁴	1	1	yes	characteristic
265	D₁₂₄	—	2	4	no	—
266	D₁₂₄	—	2	2	no	—
267	D₁₂₄	—	4	2	no	—
268	C₄×D₃₁	—	2	2	no	—
269	C₄×D₃₁	—	2	2	no	—
270	C₄×D₃₁	—	2	2	no	—
271	C₄×D₃₁	—	2	4	no	—
272	C₄×D₃₁	—	4	2	no	—
273	C₄×D₃₁	—	4	1	no	—
274	C₄×D₃₁	—	4	2	no	—
275	C₄×D₃₁	—	4	1	no	—
276	C₄×D₃₁	—	4	1	no	—
277	C₄×D₃₁	—	4	1	no	—
278	C₄×D₃₁	#41	1	4	yes	—
279	Dic₆₂	—	2	2	no	—
280	Dic₆₂	—	4	2	no	—
281	#3455	—	31	1	no	maximal, Sylow
282	C₂²×C₃₁	—	2	2	no	—
283	C₂²×C₃₁	—	2	1	no	—
284	C₂²×C₃₁	—	2	2	no	—
285	C₂²×C₃₁	—	2	1	no	—
286	C₂²×C₃₁	—	2	2	no	—
287	C₂²×C₃₁	—	2	1	no	—
288	C₂²×C₃₁	C₂⁵	1	1	yes	characteristic
289	C₂×D₃₁	—	2	1	no	—
290	C₂×D₃₁	—	2	1	no	—
291	C₂×D₃₁	—	2	1	no	—
292	C₂×D₃₁	—	2	2	no	—
293	C₂×D₃₁	—	2	2	no	—
294	C₂×D₃₁	—	2	2	no	—
295	C₂×D₃₁	—	2	1	no	—
296	C₂×D₃₁	—	2	1	no	—
297	C₂×D₃₁	—	4	4	no	—
298	C₂×D₃₁	C₂×#41	1	2	yes	—
299	C₄×C₃₁	—	2	1	no	—
300	C₄×C₃₁	—	2	2	no	—
301	C₄×C₃₁	—	2	1	no	—
302	C₄×C₃₁	—	2	1	no	—
303	C₄×C₃₁	—	2	1	no	—
304	C₄×C₃₁	—	2	2	no	—
305	C₄×C₃₁	—	2	1	no	—
306	C₄×C₃₁	—	2	2	no	—
307	C₄×C₃₁	C₂×#41	1	2	yes	—
308	Dic₃₁	—	2	2	no	—
309	Dic₃₁	—	2	1	no	—
310	Dic₃₁	—	2	2	no	—
311	Dic₃₁	—	2	2	no	—
312	Dic₃₁	—	2	1	no	—
313	Dic₃₁	—	2	1	no	—
314	Dic₃₁	—	2	1	no	—
315	Dic₃₁	—	2	1	no	—
316	Dic₃₁	C₂×#41	1	2	yes	—
317	#542	—	31	1	no	—
318	#542	—	31	1	no	—
319	#542	—	31	1	no	—
320	#542	D₃₁	1	1	yes	characteristic, complemented
321	#541	—	31	1	no	—
322	#541	—	31	1	no	—
323	#540	—	31	1	no	—
324	#540	—	31	1	no	—
325	#539	—	31	2	no	—
326	#539	—	31	2	no	—
327	#538	—	31	2	no	—
328	#538	—	31	2	no	—
329	#533	—	31	1	no	—
330	#532	—	31	1	no	—
331	#529	—	31	2	no	—
332	#529	—	31	2	no	—
333	#529	—	31	2	no	—
334	#529	—	31	2	no	—
335	#525	—	31	1	no	—
336	#525	—	31	1	no	—
337	C₄×#41	—	31	1	no	—
338	C₄×#41	—	31	1	no	—
339	C₂×#117	—	31	1	no	—
340	C₂×C₃₁	—	4	1	no	—
341	C₂×C₃₁	—	4	2	no	—
342	C₂×C₃₁	C₂²×#41	1	1	yes	characteristic
343	C₂×C₃₁	#585	1	1	yes	characteristic
344	C₂×C₃₁	#585	1	1	yes	characteristic
345	D₃₁	—	2	2	no	—
346	D₃₁	—	4	2	no	—
347	D₃₁	—	4	1	no	—
348	C₂×#41	—	31	1	no	—
349	C₂×#41	—	31	1	no	—
350	C₂³×C₄	—	31	1	no	—
351	C₄⋊Q₈	—	31	1	no	—
352	C₄⋊Q₈	—	31	1	no	—
353	C₄⋊Q₈	C₂×D₃₁	1	1	yes	characteristic, complemented
354	#127	—	31	1	no	—
355	#126	—	31	2	no	—
356	#126	—	31	2	no	—
357	#126	—	31	2	no	—
358	#126	—	31	2	no	—
359	#126	—	31	2	no	—
360	#126	—	31	2	no	—
361	#126	—	31	2	no	—
362	#126	C₂×D₃₁	1	2	yes	complemented
363	#125	—	31	2	no	—
364	#125	—	31	2	no	—
365	#125	—	31	2	no	—
366	#125	—	31	1	no	—
367	#125	—	31	1	no	—
368	#125	—	31	2	no	—
369	#124	—	31	2	no	—
370	#124	—	31	2	no	—
371	#124	—	31	2	no	—
372	#124	—	31	1	no	—
373	#124	C₂×D₃₁	1	2	yes	—
374	#124	C₂×D₃₁	1	1	yes	characteristic, complemented
375	#123	—	31	2	no	—
376	#123	—	31	2	no	—
377	#123	—	31	2	no	—
378	#123	—	31	2	no	—
379	#123	—	31	2	no	—
380	#123	—	31	2	no	—
381	#123	—	31	2	no	—
382	#123	—	31	2	no	—
383	#123	—	31	2	no	—
384	#123	C₂×D₃₁	1	2	yes	—
385	C₂²⋊Q₈	—	31	1	no	—
386	C₂²⋊Q₈	—	31	2	no	—
387	C₂²⋊Q₈	—	31	2	no	—
388	C₂²⋊Q₈	—	31	1	no	—
389	C₂²⋊Q₈	—	31	1	no	—
390	C₂²⋊Q₈	—	31	2	no	—
391	C₂²⋊Q₈	—	31	2	no	—
392	C₂²⋊Q₈	—	31	2	no	—
393	C₂²⋊Q₈	C₂×D₃₁	1	1	yes	characteristic
394	C₂²⋊Q₈	C₂×D₃₁	1	2	yes	complemented
395	#121	—	31	1	no	—
396	#121	—	31	2	no	—
397	#121	—	31	2	no	—
398	#121	—	31	1	no	—
399	#121	—	31	2	no	—
400	#121	—	31	1	no	—
401	#121	—	31	2	no	—
402	#121	—	31	2	no	—
403	#121	—	31	2	no	—
404	#121	C₂×D₃₁	1	1	yes	characteristic
405	#120	—	31	2	no	—
406	#120	—	31	2	no	—
407	C₄×Q₈	—	31	1	no	—
408	C₄×Q₈	—	31	2	no	—
409	C₄×Q₈	—	31	1	no	—
410	C₄×Q₈	—	31	2	no	—
411	C₄×Q₈	—	31	1	no	—
412	C₄×Q₈	C₂×D₃₁	1	1	yes	characteristic, complemented
413	C₄×D₄	—	31	1	no	—
414	C₄×D₄	—	31	2	no	—
415	C₄×D₄	—	31	2	no	—
416	C₄×D₄	—	31	2	no	—
417	C₄×D₄	—	31	1	no	—
418	C₄×D₄	—	31	2	no	—
419	C₄×D₄	—	31	2	no	—
420	C₄×D₄	—	31	2	no	—
421	C₄×D₄	—	31	2	no	—
422	C₄×D₄	—	31	2	no	—
423	C₄×D₄	—	31	2	no	—
424	C₄×D₄	—	31	2	no	—
425	C₄×D₄	—	31	1	no	—
426	C₄×D₄	C₂×D₃₁	1	1	yes	characteristic, complemented
427	#117	—	31	1	no	—
428	#117	—	31	1	no	—
429	#117	—	31	1	no	—
430	#117	—	31	1	no	—
431	#117	—	31	1	no	—
432	#117	—	31	2	no	—
433	#117	—	31	1	no	—
434	#117	—	31	1	no	—
435	#117	—	31	2	no	—
436	#117	—	31	1	no	—
437	#117	—	31	1	no	—
438	#117	C₂×D₃₁	1	1	yes	characteristic
439	C₂×C₄⋊C₄	—	31	1	no	—
440	C₂×C₄⋊C₄	—	31	1	no	—
441	C₂×C₂²⋊C₄	—	31	1	no	—
442	C₂×C₂²⋊C₄	—	31	1	no	—
443	C₂×C₄²	—	31	2	no	—
444	C₂×C₄²	—	31	1	no	—
445	C₂×C₄²	—	31	1	no	—
446	C₂×C₄²	—	31	2	no	—
447	C₃₁	#3455	1	1	yes	characteristic, complemented, Sylow
448	C₂⁴	—	31	1	no	—
449	#41	—	62	4	no	—
450	#41	—	62	4	no	—
451	C₂×Q₈	—	31	1	no	—
452	C₂×Q₈	—	31	2	no	—
453	C₂×Q₈	C₂²×D₃₁	1	1	yes	characteristic
454	C₂×Q₈	C₂²×D₃₁	1	2	yes	—
455	C₂×D₄	—	31	2	no	—
456	C₂×D₄	—	31	2	no	—
457	C₂×D₄	—	31	2	no	—
458	C₂×D₄	—	31	2	no	—
459	C₂×D₄	—	31	2	no	—
460	C₂×D₄	—	31	2	no	—
461	C₂×D₄	—	31	1	no	—
462	C₂×D₄	—	31	2	no	—
463	C₂×D₄	C₂²×D₃₁	1	1	yes	characteristic
464	C₂×D₄	C₂²×D₃₁	1	2	yes	—
465	C₂²×C₄	—	31	1	no	—
466	C₂²×C₄	—	31	2	no	—
467	C₂²×C₄	—	31	1	no	—
468	C₂²×C₄	—	31	2	no	—
469	C₂²×C₄	—	31	2	no	—
470	C₂²×C₄	—	31	1	no	—
471	C₂²×C₄	—	31	1	no	—
472	C₂²×C₄	—	31	1	no	—
473	C₂²×C₄	—	31	1	no	—
474	C₂²×C₄	—	31	1	no	—
475	C₂²×C₄	—	31	1	no	—
476	C₂²×C₄	—	31	1	no	—
477	C₂²×C₄	—	31	2	no	—
478	C₂²×C₄	—	31	2	no	—
479	C₂²×C₄	—	62	4	no	—
480	C₂²×C₄	C₂²×D₃₁	1	1	yes	characteristic
481	C₂²×C₄	C₂²×D₃₁	1	2	yes	—
482	C₄⋊C₄	—	31	1	no	—
483	C₄⋊C₄	—	31	1	no	—
484	C₄⋊C₄	—	31	1	no	—
485	C₄⋊C₄	—	31	1	no	—
486	C₄⋊C₄	—	31	2	no	—
487	C₄⋊C₄	—	31	2	no	—
488	C₄⋊C₄	—	31	2	no	—
489	C₄⋊C₄	—	31	2	no	—
490	C₄⋊C₄	—	31	2	no	—
491	C₄⋊C₄	—	31	2	no	—
492	C₄⋊C₄	—	31	2	no	—
493	C₄⋊C₄	—	31	2	no	—
494	C₄⋊C₄	—	31	1	no	—
495	C₄⋊C₄	—	31	1	no	—
496	C₄⋊C₄	—	31	1	no	—
497	C₄⋊C₄	—	31	1	no	—
498	C₄⋊C₄	—	31	2	no	—
499	C₄⋊C₄	—	31	2	no	—
500	C₄⋊C₄	—	31	2	no	—
501	C₄⋊C₄	—	31	2	no	—
502	C₄⋊C₄	—	31	2	no	—
503	C₄⋊C₄	C₂²×D₃₁	1	1	yes	characteristic
504	C₄⋊C₄	C₂²×D₃₁	1	1	yes	characteristic
505	C₄⋊C₄	C₂²×D₃₁	1	1	yes	characteristic
506	C₄⋊C₄	C₂²×D₃₁	1	2	yes	—
507	C₄⋊C₄	C₂²×D₃₁	1	1	yes	characteristic
508	C₄⋊C₄	C₂²×D₃₁	1	2	yes	—
509	C₄⋊C₄	C₂²×D₃₁	1	2	yes	—
510	C₂²⋊C₄	—	31	1	no	—
511	C₂²⋊C₄	—	31	1	no	—
512	C₂²⋊C₄	—	31	2	no	—
513	C₂²⋊C₄	—	31	2	no	—
514	C₂²⋊C₄	—	31	2	no	—
515	C₂²⋊C₄	—	31	1	no	—
516	C₂²⋊C₄	—	31	1	no	—
517	C₂²⋊C₄	—	31	1	no	—
518	C₂²⋊C₄	—	31	1	no	—
519	C₂²⋊C₄	—	31	2	no	—
520	C₂²⋊C₄	—	31	2	no	—
521	C₂²⋊C₄	—	31	2	no	—
522	C₂²⋊C₄	—	31	2	no	—
523	C₂²⋊C₄	—	31	2	no	—
524	C₂²⋊C₄	—	31	2	no	—
525	C₂²⋊C₄	—	31	2	no	—
526	C₂²⋊C₄	—	31	2	no	—
527	C₂²⋊C₄	—	31	2	no	—
528	C₂²⋊C₄	—	31	2	no	—
529	C₂²⋊C₄	C₂²×D₃₁	1	1	yes	characteristic
530	C₂²⋊C₄	C₂²×D₃₁	1	1	yes	characteristic
531	C₂²⋊C₄	C₂²×D₃₁	1	2	yes	—
532	C₂²⋊C₄	C₂²×D₃₁	1	2	yes	—
533	C₂²⋊C₄	C₂²×D₃₁	1	2	yes	—
534	C₂²⋊C₄	C₂²×D₃₁	1	2	yes	—
535	C₂²⋊C₄	C₂²×D₃₁	1	2	yes	—
536	C₄²	—	31	1	no	—
537	C₄²	—	31	1	no	—
538	C₄²	—	31	2	no	—
539	C₄²	—	31	2	no	—
540	C₄²	—	31	1	no	—
541	C₄²	—	31	1	no	—
542	C₄²	—	31	1	no	—
543	C₄²	—	31	1	no	—
544	C₄²	—	31	2	no	—
545	C₄²	—	31	2	no	—
546	C₄²	—	31	2	no	—
547	C₄²	C₂²×D₃₁	1	1	yes	characteristic
548	C₄²	C₂²×D₃₁	1	1	yes	characteristic
549	C₄²	C₂²×D₃₁	1	2	yes	—
550	C₂³	—	31	1	no	—
551	C₂³	—	31	1	no	—
552	C₂³	—	31	2	no	—
553	C₂³	—	62	2	no	—
554	C₂³	—	124	1	no	—
555	C₂³	—	124	1	no	—
556	C₂³	C₂³×D₃₁	1	1	yes	characteristic
557	C₂³	C₂³×D₃₁	1	2	yes	—
558	Q₈	—	2	2	no	—
559	Q₈	—	4	2	no	—
560	Q₈	—	62	2	no	—
561	Q₈	—	124	2	no	—
562	D₄	—	2	2	no	—
563	D₄	—	4	2	no	—
564	D₄	—	62	4	no	—
565	D₄	—	62	4	no	—
566	D₄	—	62	2	no	—
567	D₄	—	124	2	no	—
568	D₄	—	124	2	no	—
569	D₄	—	124	2	no	—
570	D₄	—	124	2	no	—
571	D₄	—	124	2	no	—
572	C₂×C₄	—	2	2	no	—
573	C₂×C₄	—	4	2	no	—
574	C₂×C₄	—	31	1	no	—
575	C₂×C₄	—	31	4	no	—
576	C₂×C₄	—	31	1	no	—
577	C₂×C₄	—	31	1	no	—
578	C₂×C₄	—	31	2	no	—
579	C₂×C₄	—	31	2	no	—
580	C₂×C₄	—	31	2	no	—
581	C₂×C₄	—	31	1	no	—
582	C₂×C₄	—	31	1	no	—
583	C₂×C₄	—	31	1	no	—
584	C₂×C₄	—	62	2	no	—
585	C₂×C₄	—	62	4	no	—
586	C₂×C₄	—	62	2	no	—
587	C₂×C₄	—	62	2	no	—
588	C₂×C₄	—	62	4	no	—
589	C₂×C₄	—	62	2	no	—
590	C₂×C₄	—	124	1	no	—
591	C₂×C₄	—	124	2	no	—
592	C₂×C₄	—	124	1	no	—
593	C₂×C₄	—	124	1	no	—
594	C₂×C₄	—	124	2	no	—
595	C₂×C₄	—	124	1	no	—
596	C₂×C₄	—	124	2	no	—
597	C₂×C₄	C₂³×D₃₁	1	1	yes	characteristic
598	C₂×C₄	C₂³×D₃₁	1	2	yes	—
599	C₂×C₄	C₂³×D₃₁	1	1	yes	characteristic
600	C₂×C₄	C₂³×D₃₁	1	1	yes	characteristic
601	C₂×C₄	C₂³×D₃₁	1	1	yes	characteristic
602	C₂×C₄	C₂³×D₃₁	1	2	yes	—
603	C₂×C₄	C₂³×D₃₁	1	2	yes	—
604	C₂×C₄	C₂³×D₃₁	1	1	yes	characteristic
605	C₂×C₄	C₂³×D₃₁	1	1	yes	characteristic
606	C₂²	—	2	1	no	—
607	C₂²	—	2	2	no	—
608	C₂²	—	2	2	no	—
609	C₂²	—	2	1	no	—
610	C₂²	—	2	2	no	—
611	C₂²	—	2	1	no	—
612	C₂²	—	31	2	no	—
613	C₂²	—	62	1	no	—
614	C₂²	—	62	1	no	—
615	C₂²	—	62	1	no	—
616	C₂²	—	62	2	no	—
617	C₂²	—	62	2	no	—
618	C₂²	—	62	1	no	—
619	C₂²	—	62	2	no	—
620	C₂²	—	62	1	no	—
621	C₂²	—	124	4	no	—
622	C₂²	C₂⁴×D₃₁	1	1	yes	characteristic
623	C₄	—	2	1	no	—
624	C₄	—	2	2	no	—
625	C₄	—	2	1	no	—
626	C₄	—	2	2	no	—
627	C₄	—	2	2	no	—
628	C₄	—	2	1	no	—
629	C₄	—	2	1	no	—
630	C₄	—	2	1	no	—
631	C₄	—	31	2	no	—
632	C₄	—	62	1	no	—
633	C₄	—	62	2	no	—
634	C₄	—	62	1	no	—
635	C₄	—	62	1	no	—
636	C₄	—	62	1	no	—
637	C₄	—	62	1	no	—
638	C₄	—	62	2	no	—
639	C₄	—	62	2	no	—
640	C₄	#41×D₃₁	1	2	yes	—
641	C₂	—	4	1	no	—
642	C₂	—	4	2	no	—
643	C₂	—	62	2	no	—
644	C₂	—	124	1	no	—
645	C₂	—	124	2	no	—
646	C₂	C₂×#41×D₃₁	1	1	yes	characteristic
647	C₂	#14521884	1	1	yes	characteristic
648	C₂	#14521886	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₃₁
commutator, socle, cosocle	C₂²×C₃₁	C₂⁵
Fitting	C₃₁×#542	C₂
hypercenter	#542	D₃₁
hypocenter	C₃₁	#3455
LCS	G ▷ C₂²×C₃₁ ▷ C₃₁
UCS	C₁ ◁ C₂² ◁ #542

Complements

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

N	H ≅ G/N	type
1. #14521673	C₂	semidirect
2. #14521670	C₂	semidirect
3. #14521668	C₂	semidirect
4. #14521659	C₂	semidirect
5. #14521657	C₂	semidirect
6. #14521652	C₂	semidirect
7. #14521650	C₂	semidirect
8. #14521645	C₂	semidirect
9. #14521640	C₂	semidirect
10. #14521635	C₂	semidirect
11. #14521633	C₂	semidirect
12. #14521604	C₂	semidirect
13. #14521598	C₂	semidirect
14. #14521585	C₂	semidirect
15. #14521582	C₂	semidirect
16. #14521578	C₂	semidirect
17. #14521576	C₂	semidirect
18. #14521562	C₂	semidirect
19. #14521559	C₂	semidirect
20. C₄×#92499	C₂	semidirect
21. C₄×#92497	C₂	semidirect
22. #117×D₃₁	C₂	semidirect
23. C₃₁×#542	C₂	semidirect
27. C₃₁×C₄⋊Q₈	C₂²	semidirect
28. C₃₁×#126	C₂²	semidirect
30. C₃₁×#124	C₂²	semidirect
33. C₃₁×C₂²⋊Q₈	C₂²	semidirect
35. C₄×Q₈×C₃₁	C₂²	semidirect
36. C₄×D₄×C₃₁	C₂²	semidirect
41. #11758523	C₂²	semidirect
42. Q₈×Dic₃₁	C₂²	semidirect
43. Q₈×Dic₃₁	C₂²	semidirect
44. #11758521	C₂²	semidirect
45. #11758517	C₂²	semidirect
51. D₄×Dic₃₁	C₂²	semidirect
54. #11758506	C₂²	semidirect
58. C₂×C₄×Dic₃₁	C₂²	semidirect
60. #11758475	C₂²	semidirect
61. #11758475	C₂²	semidirect
64. #11758473	C₂²	semidirect
70. #11758470	C₂²	semidirect
75. #11758469	C₂²	semidirect
78. #11758467	C₂²	semidirect
79. #11758467	C₂²	semidirect
80. #11758467	C₂²	semidirect
81. #11758466	C₂²	semidirect
82. #11758466	C₂²	semidirect
83. #11758464	C₂²	semidirect
84. #11758464	C₂²	semidirect
86. #11758463	C₂²	semidirect
94. #11758460	C₂²	semidirect
95. #11758460	C₂²	semidirect
100. (C₂²⋊D₃₁)⋊C₄	C₂²	semidirect
101. (C₂²⋊D₃₁)⋊C₄	C₂²	semidirect
106. #11758456	C₂²	semidirect
107. #11758455	C₂²	semidirect
110. #11758454	C₂²	semidirect
112. #11758452	C₂²	semidirect
114. C₄×D₁₂₄	C₂²	semidirect
119. C₄²×D₃₁	C₂²	semidirect
120. #11758447	C₂²	semidirect
121. #11758446	C₂²	semidirect
122. C₄×Dic₆₂	C₂²	semidirect
320. #542	D₃₁	semidirect
353. C₄⋊Q₈	C₂×D₃₁	semidirect
362. #126	C₂×D₃₁	semidirect
374. #124	C₂×D₃₁	semidirect
394. C₂²⋊Q₈	C₂×D₃₁	semidirect
412. C₄×Q₈	C₂×D₃₁	semidirect
426. C₄×D₄	C₂×D₃₁	semidirect
447. C₃₁	#3455	semidirect

Maximal subgroups

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

subgroup	index
#14521673	2
#14521670	2
#14521668	2
#14521659	2
#14521657	2
#14521652	2
#14521650	2
#14521645	2
#14521640	2
#14521635	2
#14521633	2
#14521604	2
#14521598	2
#14521585	2
#14521582	2
#14521578	2
#14521576	2
#14521562	2
#14521559	2
C₄×#92499	2
C₄×#92497	2
#117×D₃₁	2
C₃₁×#542	2
#3455	31