Subgroups — #16854400

Order 3968.

520 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11758478	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₈×D₃₁	C₂	1	1	yes	maximal, characteristic, complemented
3	#14521558	C₂	1	1	yes	maximal, characteristic
4	#14521123	C₂	1	1	yes	maximal, characteristic, complemented
5	#14521121	C₂	1	1	yes	maximal, characteristic, complemented
6	#14521119	C₂	1	1	yes	maximal, characteristic, complemented
7	#14521117	C₂	1	1	yes	maximal, characteristic, complemented
8	C₈×D₁₂₄	C₂	1	1	yes	maximal, characteristic, complemented
9	C₈×C₂²⋊D₃₁	C₂	1	1	yes	maximal, characteristic, complemented
10	C₈×C₂²⋊D₃₁	C₂	1	1	yes	maximal, characteristic, complemented
11	#14521074	C₂	1	1	yes	maximal, characteristic, complemented
12	#14521014	C₂	1	1	yes	maximal, characteristic, complemented
13	#14521011	C₂	1	1	yes	maximal, characteristic, complemented
14	#14521003	C₂	1	1	yes	maximal, characteristic, complemented
15	C₈×D₄×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#92495	C₂²	1	1	yes	characteristic
17	C₂²×C₄×D₃₁	C₂²	1	1	yes	characteristic
18	C₂²×C₈×C₃₁	C₂²	1	1	yes	characteristic
19	C₂²×C₈×C₃₁	C₂²	1	1	yes	characteristic, complemented
20	C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic
21	#11758516	C₄	1	1	yes	characteristic
22	#11758514	C₄	1	1	yes	characteristic
23	C₄×C₂²⋊D₃₁	C₂²	1	1	yes	characteristic
24	C₄×C₂²⋊D₃₁	C₂²	1	1	yes	characteristic
25	C₂×#92474	C₂²	1	1	yes	characteristic, complemented
26	C₂²×C₃₁⋊C₈	C₂²	1	1	yes	characteristic
27	#11758478	—	2	4	no	—
28	C₂×#92469	C₂²	1	1	yes	characteristic
29	C₂×#92469	C₂²	1	1	yes	characteristic
30	C₂×#92469	C₂²	1	1	yes	characteristic, complemented
31	C₂×C₈×D₃₁	—	2	4	no	—
32	C₂×C₈×D₃₁	C₂²	1	1	yes	characteristic
33	C₂×C₈×D₃₁	C₂²	1	1	yes	characteristic
34	C₂×C₈×D₃₁	C₂²	1	1	yes	characteristic
35	C₂×C₈×D₃₁	C₂²	1	1	yes	characteristic
36	C₂×C₈×D₃₁	C₂²	1	1	yes	characteristic, complemented
37	#11758473	C₄	1	1	yes	characteristic
38	#11758471	C₄	1	1	yes	characteristic
39	#11758461	C₄	1	1	yes	characteristic
40	#11758460	C₄	1	1	yes	characteristic
41	#11758459	C₄	1	1	yes	characteristic
42	#11758455	C₄	1	1	yes	characteristic
43	C₄×D₁₂₄	C₂²	1	1	yes	characteristic
44	#11758449	C₂²	1	1	yes	characteristic
45	C₃₁×C₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
46	C₃₁×C₂²⋊C₈	C₂²	1	1	yes	characteristic
47	C₃₁×C₂²⋊C₈	C₂²	1	1	yes	characteristic, complemented
48	C₄×C₈×C₃₁	C₂²	1	1	yes	characteristic, complemented
49	C₂²⋊(C₃₁⋊C₈)	C₂²	1	1	yes	characteristic
50	C₂²⋊(C₃₁⋊C₈)	C₂²	1	1	yes	characteristic, complemented
51	(C₂×D₃₁)⋊C₈	C₂²	1	1	yes	characteristic
52	(C₂×D₃₁)⋊C₈	C₂²	1	1	yes	characteristic
53	(C₂×D₃₁)⋊C₈	C₂²	1	1	yes	characteristic, complemented
54	(C₂×D₃₁)⋊C₈	C₂²	1	1	yes	characteristic, complemented
55	#11758403	C₂²	1	1	yes	characteristic, complemented
56	Dic₃₁⋊C₈	C₂²	1	1	yes	characteristic, complemented
57	Dic₃₁⋊C₈	C₂²	1	1	yes	characteristic, complemented
58	C₈×Dic₃₁	C₂²	1	1	yes	characteristic, complemented
59	C₄⋊(C₃₁⋊C₈)	C₂²	1	1	yes	characteristic, complemented
60	#11758391	C₂²	1	1	yes	characteristic, complemented
61	C₂³×D₃₁	C₂×C₄	1	1	yes	characteristic
62	C₂×D₄×C₃₁	C₂×C₄	1	1	yes	characteristic
63	C₂²×C₄×C₃₁	C₂³	1	1	yes	characteristic
64	C₂²×C₄×C₃₁	C₂³	1	1	yes	characteristic
65	C₂×C₂²⋊D₃₁	C₂×C₄	1	1	yes	characteristic
66	C₂×C₂²⋊D₃₁	C₂×C₄	1	1	yes	characteristic
67	C₂×C₂²⋊D₃₁	C₂×C₄	1	1	yes	characteristic
68	C₂×C₂²⋊D₃₁	C₂×C₄	1	1	yes	characteristic
69	C₂²×Dic₃₁	C₂×C₄	1	1	yes	characteristic
70	#92495	—	2	2	no	—
71	#92495	—	2	2	no	—
72	C₂×D₁₂₄	C₂×C₄	1	1	yes	characteristic
73	C₂×D₁₂₄	C₂×C₄	1	1	yes	characteristic
74	C₂×C₄×D₃₁	—	2	2	no	—
75	C₂×C₄×D₃₁	—	2	2	no	—
76	C₂×C₄×D₃₁	C₂×C₄	1	1	yes	characteristic
77	C₂×C₄×D₃₁	C₂×C₄	1	1	yes	characteristic
78	C₂×C₄×D₃₁	C₂³	1	1	yes	characteristic
79	C₂×C₄×D₃₁	C₂³	1	1	yes	characteristic
80	C₂×C₄×D₃₁	C₂³	1	1	yes	characteristic
81	C₂×Dic₆₂	C₂×C₄	1	1	yes	characteristic
82	C₂×C₈×C₃₁	—	2	2	no	—
83	C₂×C₈×C₃₁	—	2	2	no	—
84	C₂×C₈×C₃₁	C₂³	1	1	yes	characteristic
85	C₂×C₈×C₃₁	C₂³	1	1	yes	characteristic
86	C₂×C₈×C₃₁	C₂³	1	1	yes	characteristic
87	C₂×C₈×C₃₁	C₂³	1	1	yes	characteristic
88	C₄⋊C₄×C₃₁	C₂×C₄	1	1	yes	characteristic
89	C₂²⋊C₄×C₃₁	C₂×C₄	1	1	yes	characteristic
90	C₂²⋊C₄×C₃₁	C₂×C₄	1	1	yes	characteristic
91	C₄²×C₃₁	C₂³	1	1	yes	characteristic
92	C₂²⋊Dic₃₁	C₂×C₄	1	1	yes	characteristic
93	C₂²⋊Dic₃₁	C₂×C₄	1	1	yes	characteristic
94	(C₂×D₃₁)⋊C₄	C₂×C₄	1	1	yes	characteristic
95	(C₂×D₃₁)⋊C₄	C₂×C₄	1	1	yes	characteristic
96	(C₂×D₃₁)⋊C₄	C₂×C₄	1	1	yes	characteristic
97	(C₂×D₃₁)⋊C₄	C₂×C₄	1	1	yes	characteristic
98	(C₂×D₃₁)⋊C₄	C₂×C₄	1	1	yes	characteristic
99	(C₂×D₃₁)⋊C₄	C₂×C₄	1	1	yes	characteristic
100	C₄⋊Dic₃₁	C₂×C₄	1	1	yes	characteristic
101	Dic₃₁⋊C₄	C₂×C₄	1	1	yes	characteristic
102	Dic₃₁⋊C₄	C₂×C₄	1	1	yes	characteristic
103	Dic₃₁⋊C₄	C₂×C₄	1	1	yes	characteristic
104	Dic₃₁⋊C₄	C₂×C₄	1	1	yes	characteristic
105	C₄×Dic₃₁	C₂³	1	1	yes	characteristic
106	#92474	—	2	2	no	—
107	C₂×C₃₁⋊C₈	—	2	2	no	—
108	C₂×C₃₁⋊C₈	C₂³	1	1	yes	characteristic
109	C₂×C₃₁⋊C₈	C₂³	1	1	yes	characteristic
110	C₂×C₃₁⋊C₈	C₂³	1	1	yes	characteristic
111	C₂×C₃₁⋊C₈	C₂³	1	1	yes	characteristic
112	#92469	—	2	2	no	—
113	#92469	—	2	2	no	—
114	#92469	—	2	2	no	—
115	C₈×D₃₁	—	2	2	no	—
116	C₈×D₃₁	—	2	2	no	—
117	C₈×D₃₁	—	2	2	no	—
118	C₈×D₃₁	—	2	2	no	—
119	C₈×D₃₁	D₄	1	4	yes	complemented
120	C₂³×C₃₁	C₂²×C₄	1	1	yes	characteristic
121	C₂³×C₃₁	C₂²×C₄	1	1	yes	characteristic
122	C₂²×D₃₁	—	2	2	no	—
123	C₂²×D₃₁	—	2	2	no	—
124	C₂²×D₃₁	—	2	2	no	—
125	C₂²×D₃₁	C₂²×C₄	1	1	yes	characteristic
126	C₂²×D₃₁	C₂²×C₄	1	1	yes	characteristic
127	C₂²×D₃₁	C₂²×C₄	1	1	yes	characteristic
128	D₄×C₃₁	—	2	2	no	—
129	C₂×C₄×C₃₁	—	2	1	no	—
130	C₂×C₄×C₃₁	—	2	1	no	—
131	C₂×C₄×C₃₁	—	2	1	no	—
132	C₂×C₄×C₃₁	—	2	1	no	—
133	C₂×C₄×C₃₁	C₂²×C₄	1	1	yes	characteristic
134	C₂×C₄×C₃₁	C₂²×C₄	1	1	yes	characteristic
135	C₂×C₄×C₃₁	C₂²×C₄	1	1	yes	characteristic
136	C₂×C₄×C₃₁	C₂²×C₄	1	1	yes	characteristic
137	C₂×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
138	C₂²⋊D₃₁	—	2	2	no	—
139	C₂²⋊D₃₁	—	2	2	no	—
140	C₂²⋊D₃₁	—	2	2	no	—
141	C₂²⋊D₃₁	—	2	2	no	—
142	C₂×Dic₃₁	—	2	2	no	—
143	C₂×Dic₃₁	C₂²×C₄	1	1	yes	characteristic
144	C₂×Dic₃₁	C₂²×C₄	1	1	yes	characteristic
145	C₂×Dic₃₁	C₂²×C₄	1	1	yes	characteristic
146	C₂×Dic₃₁	C₂²×C₄	1	1	yes	characteristic
147	C₂×Dic₃₁	C₂²×C₄	1	1	yes	characteristic
148	D₁₂₄	—	2	2	no	—
149	D₁₂₄	—	2	2	no	—
150	C₄×D₃₁	—	2	2	no	—
151	C₄×D₃₁	—	2	1	no	—
152	C₄×D₃₁	—	2	1	no	—
153	C₄×D₃₁	—	2	1	no	—
154	C₄×D₃₁	—	2	1	no	—
155	C₄×D₃₁	—	2	2	no	—
156	C₄×D₃₁	C₂×D₄	1	2	yes	—
157	C₄×D₃₁	#41	1	2	yes	—
158	Dic₆₂	—	2	2	no	—
159	C₈×C₃₁	—	2	1	no	—
160	C₈×C₃₁	—	2	1	no	—
161	C₈×C₃₁	—	2	1	no	—
162	C₈×C₃₁	C₂×D₄	1	2	yes	—
163	C₃₁⋊C₈	—	2	1	no	—
164	C₃₁⋊C₈	—	2	1	no	—
165	C₃₁⋊C₈	—	2	1	no	—
166	C₃₁⋊C₈	C₂×D₄	1	2	yes	—
167	#2929	—	31	1	no	maximal, Sylow
168	C₂²×C₃₁	—	2	1	no	—
169	C₂²×C₃₁	—	2	1	no	—
170	C₂²×C₃₁	—	2	1	no	—
171	C₂²×C₃₁	—	2	1	no	—
172	C₂²×C₃₁	—	2	1	no	—
173	C₂²×C₃₁	#131	1	2	yes	complemented
174	C₂²×C₃₁	C₂³×C₄	1	1	yes	characteristic
175	C₂×D₃₁	—	2	8	no	—
176	C₂×D₃₁	—	2	1	no	—
177	C₂×D₃₁	—	2	1	no	—
178	C₂×D₃₁	—	2	1	no	—
179	C₂×D₃₁	—	2	1	no	—
180	C₂×D₃₁	—	2	1	no	—
181	C₂×D₃₁	—	2	1	no	—
182	C₂×D₃₁	—	2	1	no	—
183	C₂×D₃₁	C₄×D₄	1	2	yes	—
184	C₂×D₃₁	#131	1	2	yes	complemented
185	C₄×C₃₁	—	2	1	no	—
186	C₄×C₃₁	—	2	1	no	—
187	C₄×C₃₁	—	2	1	no	—
188	C₄×C₃₁	—	2	1	no	—
189	C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
190	C₄×C₃₁	C₂×#41	1	1	yes	characteristic
191	Dic₃₁	—	2	1	no	—
192	Dic₃₁	—	2	1	no	—
193	Dic₃₁	—	2	1	no	—
194	Dic₃₁	—	2	1	no	—
195	Dic₃₁	C₄×D₄	1	2	yes	—
196	C₂×#131	—	31	1	no	—
197	C₂³×C₈	—	31	1	no	—
198	#525	—	31	1	no	—
199	#435	—	31	1	no	—
200	#435	—	31	1	no	—
201	#435	—	31	1	no	—
202	#435	—	31	1	no	—
203	C₈×D₄	—	31	1	no	—
204	C₈×D₄	—	31	1	no	—
205	C₈×D₄	—	31	1	no	—
206	C₈×D₄	D₃₁	1	1	yes	characteristic, complemented
207	#424	—	31	1	no	—
208	#408	—	31	1	no	—
209	#407	—	31	1	no	—
210	#405	—	31	1	no	—
211	C₂×C₃₁	—	2	2	no	—
212	C₂×C₃₁	—	4	1	no	—
213	C₂×C₃₁	C₂×C₄×D₄	1	1	yes	characteristic
214	C₂×C₃₁	C₂×#131	1	1	yes	characteristic
215	C₂×C₃₁	C₂×#131	1	1	yes	characteristic
216	D₃₁	—	2	2	no	—
217	D₃₁	—	2	2	no	—
218	D₃₁	—	4	1	no	—
219	C₂×#41	—	31	1	no	—
220	C₂³×C₄	—	31	1	no	—
221	#131	—	62	4	no	—
222	C₂×M₁₆	—	31	1	no	—
223	C₂×M₁₆	—	31	1	no	—
224	C₂×M₁₆	—	31	1	no	—
225	C₂×M₁₆	—	31	1	no	—
226	C₂²×C₈	—	31	1	no	—
227	C₂²×C₈	—	31	1	no	—
228	C₂²×C₈	—	31	1	no	—
229	C₂²×C₈	—	31	1	no	—
230	C₂²×C₈	—	31	1	no	—
231	C₂²×C₈	—	31	1	no	—
232	C₂²×C₈	—	62	4	no	—
233	C₂²×C₈	C₂×D₃₁	1	1	yes	characteristic
234	C₂²×C₈	C₂×D₃₁	1	1	yes	characteristic, complemented
235	#123	—	31	1	no	—
236	#123	—	31	1	no	—
237	C₂²⋊Q₈	—	31	1	no	—
238	C₂²⋊Q₈	—	31	1	no	—
239	#121	—	31	1	no	—
240	#121	—	31	1	no	—
241	#120	—	31	1	no	—
242	#120	—	31	1	no	—
243	C₄×D₄	—	31	1	no	—
244	C₄×D₄	—	31	1	no	—
245	C₄×D₄	—	31	1	no	—
246	C₄×D₄	C₂×D₃₁	1	1	yes	characteristic
247	#117	—	31	1	no	—
248	C₄⋊C₈	—	31	1	no	—
249	C₄⋊C₈	—	31	1	no	—
250	C₄⋊C₈	—	31	1	no	—
251	C₄⋊C₈	C₂×D₃₁	1	1	yes	characteristic, complemented
252	C₂²⋊C₈	—	31	1	no	—
253	C₂²⋊C₈	—	31	1	no	—
254	C₂²⋊C₈	—	31	1	no	—
255	C₂²⋊C₈	—	31	1	no	—
256	C₂²⋊C₈	—	31	1	no	—
257	C₂²⋊C₈	—	31	1	no	—
258	C₂²⋊C₈	C₂×D₃₁	1	1	yes	characteristic
259	C₂²⋊C₈	C₂×D₃₁	1	1	yes	characteristic, complemented
260	#97	—	31	1	no	—
261	#97	—	31	1	no	—
262	C₄×C₈	—	31	1	no	—
263	C₄×C₈	C₂×D₃₁	1	1	yes	characteristic, complemented
264	C₃₁	#2929	1	1	yes	characteristic, complemented, Sylow
265	C₂⁴	—	31	1	no	—
266	#41	—	62	2	no	—
267	#41	—	62	2	no	—
268	C₂×Q₈	—	31	1	no	—
269	C₂×D₄	—	31	1	no	—
270	C₂×D₄	—	31	1	no	—
271	C₂×D₄	—	31	1	no	—
272	C₂×D₄	—	31	1	no	—
273	C₂×D₄	—	31	1	no	—
274	C₂×D₄	—	31	1	no	—
275	C₂×D₄	C₄×D₃₁	1	1	yes	characteristic
276	C₂²×C₄	—	31	1	no	—
277	C₂²×C₄	—	31	1	no	—
278	C₂²×C₄	—	31	1	no	—
279	C₂²×C₄	—	31	1	no	—
280	C₂²×C₄	—	31	1	no	—
281	C₂²×C₄	—	31	1	no	—
282	C₂²×C₄	—	62	2	no	—
283	C₂²×C₄	—	62	2	no	—
284	C₂²×C₄	C₂²×D₃₁	1	1	yes	characteristic
285	C₂²×C₄	C₂²×D₃₁	1	1	yes	characteristic
286	M₁₆	—	62	2	no	—
287	M₁₆	—	62	2	no	—
288	M₁₆	—	62	2	no	—
289	M₁₆	—	62	2	no	—
290	C₂×C₈	—	2	2	no	—
291	C₂×C₈	—	2	2	no	—
292	C₂×C₈	—	31	1	no	—
293	C₂×C₈	—	31	4	no	—
294	C₂×C₈	—	31	1	no	—
295	C₂×C₈	—	31	1	no	—
296	C₂×C₈	—	31	1	no	—
297	C₂×C₈	—	62	2	no	—
298	C₂×C₈	—	62	2	no	—
299	C₂×C₈	—	62	2	no	—
300	C₂×C₈	—	62	2	no	—
301	C₂×C₈	—	62	2	no	—
302	C₂×C₈	C₂²×D₃₁	1	1	yes	characteristic
303	C₂×C₈	C₂²×D₃₁	1	1	yes	characteristic
304	C₂×C₈	C₂²×D₃₁	1	1	yes	characteristic
305	C₂×C₈	C₂²×D₃₁	1	1	yes	characteristic
306	C₄⋊C₄	—	31	1	no	—
307	C₄⋊C₄	—	31	1	no	—
308	C₄⋊C₄	—	31	1	no	—
309	C₄⋊C₄	—	31	1	no	—
310	C₄⋊C₄	—	31	1	no	—
311	C₄⋊C₄	C₄×D₃₁	1	1	yes	characteristic
312	C₂²⋊C₄	—	31	1	no	—
313	C₂²⋊C₄	—	31	1	no	—
314	C₂²⋊C₄	—	31	1	no	—
315	C₂²⋊C₄	—	31	1	no	—
316	C₂²⋊C₄	—	31	1	no	—
317	C₂²⋊C₄	—	31	1	no	—
318	C₂²⋊C₄	—	31	1	no	—
319	C₂²⋊C₄	—	31	1	no	—
320	C₂²⋊C₄	C₄×D₃₁	1	1	yes	characteristic
321	C₂²⋊C₄	C₄×D₃₁	1	1	yes	characteristic
322	C₄²	—	31	1	no	—
323	C₄²	C₂²×D₃₁	1	1	yes	characteristic
324	C₂³	—	31	1	no	—
325	C₂³	—	31	1	no	—
326	C₂³	—	31	1	no	—
327	C₂³	—	62	2	no	—
328	C₂³	—	62	2	no	—
329	C₂³	—	62	2	no	—
330	C₂³	C₂×C₄×D₃₁	1	1	yes	characteristic
331	C₂³	C₂×C₄×D₃₁	1	1	yes	characteristic
332	Q₈	—	62	2	no	—
333	D₄	—	2	2	no	—
334	D₄	—	62	2	no	—
335	D₄	—	62	2	no	—
336	D₄	—	62	2	no	—
337	D₄	—	62	2	no	—
338	D₄	—	62	2	no	—
339	D₄	—	62	2	no	—
340	C₂×C₄	—	2	1	no	—
341	C₂×C₄	—	2	1	no	—
342	C₂×C₄	—	2	1	no	—
343	C₂×C₄	—	2	1	no	—
344	C₂×C₄	—	31	1	no	—
345	C₂×C₄	—	31	2	no	—
346	C₂×C₄	—	31	2	no	—
347	C₂×C₄	—	31	1	no	—
348	C₂×C₄	—	31	1	no	—
349	C₂×C₄	—	31	1	no	—
350	C₂×C₄	—	31	1	no	—
351	C₂×C₄	—	62	2	no	—
352	C₂×C₄	—	62	2	no	—
353	C₂×C₄	—	62	2	no	—
354	C₂×C₄	—	62	1	no	—
355	C₂×C₄	—	62	1	no	—
356	C₂×C₄	—	62	1	no	—
357	C₂×C₄	—	62	1	no	—
358	C₂×C₄	C₂×C₄×D₃₁	1	1	yes	characteristic
359	C₂×C₄	C₂×C₄×D₃₁	1	1	yes	characteristic
360	C₂×C₄	C₂×C₄×D₃₁	1	1	yes	characteristic
361	C₂×C₄	C₂×C₄×D₃₁	1	1	yes	characteristic
362	C₂×C₄	C₂³×D₃₁	1	1	yes	characteristic
363	C₈	—	2	1	no	—
364	C₈	—	2	1	no	—
365	C₈	—	2	1	no	—
366	C₈	—	31	2	no	—
367	C₈	—	62	1	no	—
368	C₈	—	62	1	no	—
369	C₈	—	62	1	no	—
370	C₈	D₄×D₃₁	1	2	yes	—
371	C₂²	—	2	1	no	—
372	C₂²	—	2	1	no	—
373	C₂²	—	2	1	no	—
374	C₂²	—	2	1	no	—
375	C₂²	—	2	1	no	—
376	C₂²	—	31	2	no	—
377	C₂²	—	31	2	no	—
378	C₂²	—	62	8	no	—
379	C₂²	—	62	1	no	—
380	C₂²	—	62	1	no	—
381	C₂²	—	62	1	no	—
382	C₂²	—	62	1	no	—
383	C₂²	—	62	1	no	—
384	C₂²	—	62	1	no	—
385	C₂²	—	62	1	no	—
386	C₂²	#11758478	1	2	yes	complemented
387	C₂²	C₂²×C₄×D₃₁	1	1	yes	characteristic
388	C₄	—	2	1	no	—
389	C₄	—	2	1	no	—
390	C₄	—	2	1	no	—
391	C₄	—	2	1	no	—
392	C₄	—	31	2	no	—
393	C₄	—	62	1	no	—
394	C₄	—	62	1	no	—
395	C₄	—	62	1	no	—
396	C₄	—	62	1	no	—
397	C₄	C₂×D₄×D₃₁	1	1	yes	characteristic
398	C₄	#41×D₃₁	1	1	yes	characteristic
399	C₂	—	2	2	no	—
400	C₂	—	4	1	no	—
401	C₂	—	62	2	no	—
402	C₂	—	62	2	no	—
403	C₂	—	124	1	no	—
404	C₂	C₄×D₄×D₃₁	1	1	yes	characteristic
405	C₂	#131×D₃₁	1	1	yes	characteristic
406	C₂	C₂×#11758478	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₈	C₂²×D₃₁
commutator, socle	C₂²×C₃₁	C₂³×C₄
Frattini	C₂×C₄	C₂³×D₃₁
Fitting	C₈×D₄×C₃₁	C₂
prime radical	#14521558	C₂
cosocle	C₂×C₄×C₃₁	C₂⁴
hypercenter	C₈×D₄	D₃₁
hypocenter	C₃₁	#2929
LCS	G ▷ C₂²×C₃₁ ▷ C₃₁
UCS	C₁ ◁ C₂×C₈ ◁ C₈×D₄

Complements

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

N	H ≅ G/N	type
1. C₂×#11758478	C₂	semidirect
2. C₂²×C₈×D₃₁	C₂	semidirect
4. #14521123	C₂	semidirect
5. #14521121	C₂	semidirect
6. #14521119	C₂	semidirect
7. #14521117	C₂	semidirect
8. C₈×D₁₂₄	C₂	semidirect
9. C₈×C₂²⋊D₃₁	C₂	semidirect
10. C₈×C₂²⋊D₃₁	C₂	semidirect
11. #14521074	C₂	semidirect
12. #14521014	C₂	semidirect
13. #14521011	C₂	semidirect
14. #14521003	C₂	semidirect
15. C₈×D₄×C₃₁	C₂	semidirect
19. C₂²×C₈×C₃₁	C₂²	semidirect
25. C₂×#92474	C₂²	semidirect
30. C₂×#92469	C₂²	semidirect
36. C₂×C₈×D₃₁	C₂²	semidirect
45. C₃₁×C₄⋊C₈	C₂²	semidirect
47. C₃₁×C₂²⋊C₈	C₂²	semidirect
48. C₄×C₈×C₃₁	C₂²	semidirect
50. C₂²⋊(C₃₁⋊C₈)	C₂²	semidirect
53. (C₂×D₃₁)⋊C₈	C₂²	semidirect
54. (C₂×D₃₁)⋊C₈	C₂²	semidirect
55. #11758403	C₂²	semidirect
56. Dic₃₁⋊C₈	C₂²	semidirect
57. Dic₃₁⋊C₈	C₂²	semidirect
58. C₈×Dic₃₁	C₂²	semidirect
59. C₄⋊(C₃₁⋊C₈)	C₂²	semidirect
60. #11758391	C₂²	semidirect
119. C₈×D₃₁	D₄	semidirect
173. C₂²×C₃₁	#131	semidirect
184. C₂×D₃₁	#131	semidirect
206. C₈×D₄	D₃₁	semidirect
234. C₂²×C₈	C₂×D₃₁	semidirect
251. C₄⋊C₈	C₂×D₃₁	semidirect
259. C₂²⋊C₈	C₂×D₃₁	semidirect
263. C₄×C₈	C₂×D₃₁	semidirect
264. C₃₁	#2929	semidirect
386. C₂²	#11758478	semidirect

Maximal subgroups

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

subgroup	index
C₂×#11758478	2
C₂²×C₈×D₃₁	2
#14521558	2
#14521123	2
#14521121	2
#14521119	2
#14521117	2
C₈×D₁₂₄	2
C₈×C₂²⋊D₃₁	2
#14521074	2
#14521014	2
#14521011	2
#14521003	2
C₈×D₄×C₃₁	2
#2929	31