Subgroups — #16859269

Order 3968.

1132 conjugacy classes of subgroups.

The subgroup lattice has 460 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14521769	C₂	1	1	yes	maximal, characteristic, complemented
2	#14521764	C₂	1	1	yes	maximal, characteristic, complemented
3	#14521756	C₂	1	1	yes	maximal, characteristic, complemented
4	#14521745	C₂	1	2	yes	maximal, complemented
5	#14521739	C₂	1	2	yes	maximal, complemented
6	#14521734	C₂	1	2	yes	maximal, complemented
7	#14521725	C₂	1	4	yes	maximal, complemented
8	#14521703	C₂	1	1	yes	maximal, characteristic, complemented
9	#14521693	C₂	1	2	yes	maximal, complemented
10	#14521606	C₂	1	1	yes	maximal, characteristic, complemented
11	#14521581	C₂	1	2	yes	maximal, complemented
12	#14521579	C₂	1	4	yes	maximal, complemented
13	#14521560	C₂	1	2	yes	maximal, complemented
14	C₄×#92495	C₂	1	1	yes	maximal, characteristic, complemented
15	C₄×#92497	C₂	1	2	yes	maximal, complemented
16	C₂×#11758503	C₂	1	2	yes	maximal, complemented
17	C₂×C₄×D₄×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂²×D₄×C₃₁	C₂²	1	1	yes	characteristic
19	C₂³×C₄×C₃₁	C₂²	1	2	yes	—
20	C₂×#92497	C₂²	1	2	yes	—
21	C₂×#92495	C₂²	1	1	yes	characteristic
22	C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic
23	C₄×D₄×C₃₁	C₂²	1	2	yes	—
24	C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic
25	C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic
26	C₄×D₄×C₃₁	C₂²	1	2	yes	—
27	C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic
28	C₂×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
29	C₂×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	—
30	C₂×C₄²×C₃₁	C₂²	1	1	yes	characteristic
31	#11758530	C₂²	1	4	yes	—
32	C₂×C₂²⋊Dic₃₁	C₂²	1	4	yes	—
33	#11758516	C₂²	1	4	yes	—
34	#11758515	C₂²	1	2	yes	—
35	#11758513	C₂²	1	2	yes	—
36	#11758512	C₂²	1	4	yes	—
37	D₄×Dic₃₁	C₂²	1	2	yes	—
38	#11758507	C₂²	1	2	yes	complemented
39	#11758507	C₂²	1	2	yes	complemented
40	#11758506	C₂²	1	4	yes	—
41	C₄×C₂²⋊D₃₁	C₂²	1	2	yes	—
42	C₄×C₂²⋊D₃₁	C₂²	1	2	yes	—
43	C₄×C₂²⋊D₃₁	C₂²	1	4	yes	complemented
44	C₄×C₂²⋊D₃₁	C₂²	1	4	yes	complemented
45	#11758503	C₂²	1	2	yes	—
46	#11758503	C₂²	1	4	yes	—
47	#11758503	C₂²	1	1	yes	characteristic
48	#11758503	C₂²	1	2	yes	complemented
49	#11758503	C₂²	1	2	yes	complemented
50	#11758503	C₂²	1	4	yes	complemented
51	C₂×C₄⋊Dic₃₁	C₂²	1	2	yes	complemented
52	C₂×C₄⋊Dic₃₁	C₂²	1	2	yes	complemented
53	#11758501	C₂²	1	2	yes	—
54	#11758501	C₂²	1	2	yes	—
55	#11758501	C₂²	1	2	yes	complemented
56	#11758501	C₂²	1	2	yes	complemented
57	C₂×C₄×Dic₃₁	C₂²	1	4	yes	complemented
58	#11758475	C₂²	1	4	yes	complemented
59	#11758474	C₂²	1	2	yes	complemented
60	#11758469	C₂²	1	2	yes	complemented
61	#11758467	C₂²	1	2	yes	complemented
62	#11758466	C₂²	1	4	yes	complemented
63	#11758464	C₂²	1	2	yes	complemented
64	#11758463	C₂²	1	4	yes	complemented
65	#11758462	C₂²	1	4	yes	complemented
66	#11758460	C₂²	1	4	yes	complemented
67	(C₂²⋊D₃₁)⋊C₄	C₂²	1	4	yes	complemented
68	#11758456	C₂²	1	4	yes	complemented
69	#11758456	C₂²	1	4	yes	complemented
70	#11758455	C₂²	1	4	yes	complemented
71	#11758454	C₂²	1	4	yes	complemented
72	C₄×D₁₂₄	C₂²	1	1	yes	characteristic, complemented
73	C₄×D₁₂₄	C₂²	1	1	yes	characteristic, complemented
74	#11758449	C₂²	1	2	yes	complemented
75	C₄²×D₃₁	C₂²	1	2	yes	complemented
76	#11758447	C₂²	1	2	yes	complemented
77	#11758446	C₂²	1	1	yes	characteristic, complemented
78	#11758446	C₂²	1	1	yes	characteristic, complemented
79	C₄×Dic₆₂	C₂²	1	2	yes	complemented
80	C₄×Dic₆₂	C₂²	1	2	yes	complemented
81	C₄×Dic₆₂	C₂²	1	1	yes	characteristic, complemented
82	C₄×Dic₆₂	C₂²	1	1	yes	characteristic, complemented
83	C₂⁴×C₃₁	C₂³	1	2	yes	—
84	C₂×D₄×C₃₁	—	2	4	no	—
85	C₂×D₄×C₃₁	C₂³	1	2	yes	—
86	C₂×D₄×C₃₁	C₂³	1	1	yes	characteristic
87	C₂×D₄×C₃₁	C₂³	1	1	yes	characteristic
88	C₂²×C₄×C₃₁	—	2	8	no	—
89	C₂²×C₄×C₃₁	C₂³	1	2	yes	—
90	C₂²×C₄×C₃₁	C₂³	1	1	yes	characteristic
91	C₂²×C₄×C₃₁	C₂³	1	2	yes	—
92	C₂²×C₄×C₃₁	C₂³	1	2	yes	—
93	C₂²×C₄×C₃₁	C₂³	1	2	yes	—
94	C₂²×C₄×C₃₁	C₂³	1	2	yes	—
95	C₂²×C₄×C₃₁	C₂³	1	1	yes	characteristic
96	C₂²×C₄×C₃₁	C₂³	1	1	yes	characteristic
97	C₂×C₂²⋊D₃₁	C₂³	1	4	yes	—
98	C₂×C₂²⋊D₃₁	C₂³	1	2	yes	—
99	C₂×C₂²⋊D₃₁	C₂³	1	4	yes	—
100	C₂²×Dic₃₁	C₂³	1	4	yes	—
101	C₂²×Dic₃₁	C₂³	1	4	yes	—
102	#92497	—	2	8	no	—
103	#92495	—	2	4	no	—
104	C₂×D₁₂₄	C₂³	1	1	yes	characteristic
105	C₂×C₄×D₃₁	C₂³	1	2	yes	—
106	C₂×C₄×D₃₁	C₂³	1	2	yes	—
107	C₂×C₄×D₃₁	C₂³	1	2	yes	—
108	C₂×Dic₆₂	C₂³	1	1	yes	characteristic
109	C₂×Dic₆₂	C₂³	1	2	yes	—
110	C₂×Dic₆₂	C₂³	1	2	yes	—
111	C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
112	C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
113	C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
114	C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
115	C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
116	C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
117	C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
118	C₄²×C₃₁	C₂³	1	1	yes	characteristic
119	C₄²×C₃₁	C₂³	1	1	yes	characteristic
120	C₄²×C₃₁	C₂³	1	1	yes	characteristic
121	C₄²×C₃₁	C₂³	1	1	yes	characteristic
122	C₂²⋊Dic₃₁	C₂³	1	4	yes	—
123	C₂²⋊Dic₃₁	C₂³	1	4	yes	—
124	C₂²⋊Dic₃₁	C₂³	1	4	yes	—
125	C₂²⋊Dic₃₁	C₂³	1	4	yes	—
126	C₂²⋊Dic₃₁	C₂³	1	4	yes	—
127	C₂²⋊Dic₃₁	C₂³	1	2	yes	—
128	(C₂×D₃₁)⋊C₄	C₂³	1	2	yes	—
129	(C₂×D₃₁)⋊C₄	C₂³	1	2	yes	—
130	(C₂×D₃₁)⋊C₄	C₂³	1	4	yes	—
131	(C₂×D₃₁)⋊C₄	C₂³	1	4	yes	—
132	C₄⋊Dic₃₁	C₂³	1	2	yes	—
133	C₄⋊Dic₃₁	C₂³	1	2	yes	—
134	C₄⋊Dic₃₁	C₂³	1	1	yes	characteristic
135	C₄⋊Dic₃₁	C₂³	1	1	yes	characteristic
136	C₄⋊Dic₃₁	C₂³	1	2	yes	—
137	C₄⋊Dic₃₁	C₂³	1	2	yes	—
138	C₄⋊Dic₃₁	C₂³	1	4	yes	—
139	C₄⋊Dic₃₁	C₂³	1	4	yes	—
140	Dic₃₁⋊C₄	C₂³	1	4	yes	—
141	Dic₃₁⋊C₄	C₂³	1	4	yes	—
142	Dic₃₁⋊C₄	C₂³	1	2	yes	—
143	Dic₃₁⋊C₄	C₂³	1	2	yes	—
144	Dic₃₁⋊C₄	C₂³	1	4	yes	—
145	Dic₃₁⋊C₄	C₂³	1	4	yes	—
146	C₄×Dic₃₁	C₂³	1	4	yes	—
147	C₄×Dic₃₁	C₂³	1	2	yes	—
148	C₄×Dic₃₁	C₂³	1	2	yes	—
149	C₄×Dic₃₁	C₂³	1	2	yes	—
150	C₄×Dic₃₁	C₂³	1	4	yes	—
151	C₄×Dic₃₁	C₂³	1	4	yes	—
152	C₂³×C₃₁	—	2	4	no	—
153	C₂³×C₃₁	—	2	4	no	—
154	C₂³×C₃₁	—	4	2	no	—
155	C₂³×C₃₁	C₂⁴	1	2	yes	—
156	C₂³×C₃₁	C₂⁴	1	1	yes	characteristic
157	C₂³×C₃₁	C₂⁴	1	2	yes	—
158	C₂²×D₃₁	C₂⁴	1	2	yes	—
159	D₄×C₃₁	—	2	4	no	—
160	D₄×C₃₁	—	2	2	no	—
161	D₄×C₃₁	#41	1	4	yes	complemented
162	C₂×C₄×C₃₁	—	2	4	no	—
163	C₂×C₄×C₃₁	—	2	4	no	—
164	C₂×C₄×C₃₁	—	2	4	no	—
165	C₂×C₄×C₃₁	—	2	4	no	—
166	C₂×C₄×C₃₁	—	2	4	no	—
167	C₂×C₄×C₃₁	—	2	2	no	—
168	C₂×C₄×C₃₁	—	4	1	no	—
169	C₂×C₄×C₃₁	#41	1	4	yes	complemented
170	C₂×C₄×C₃₁	C₂⁴	1	2	yes	—
171	C₂×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
172	C₂×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
173	C₂×C₄×C₃₁	C₂⁴	1	2	yes	—
174	C₂×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
175	C₂×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
176	C₂×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
177	C₂×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
178	C₂²⋊D₃₁	—	2	4	no	—
179	C₂²⋊D₃₁	—	2	8	no	—
180	C₂²⋊D₃₁	—	4	4	no	—
181	C₂×Dic₃₁	—	2	8	no	—
182	C₂×Dic₃₁	—	4	4	no	—
183	C₂×Dic₃₁	C₂⁴	1	2	yes	—
184	C₂×Dic₃₁	C₂⁴	1	2	yes	—
185	C₂×Dic₃₁	C₂⁴	1	2	yes	—
186	C₂×Dic₃₁	C₂⁴	1	4	yes	—
187	C₂×Dic₃₁	C₂⁴	1	4	yes	—
188	D₁₂₄	—	2	2	no	—
189	C₄×D₃₁	—	2	4	no	—
190	C₄×D₃₁	—	2	4	no	—
191	C₄×D₃₁	—	4	2	no	—
192	Dic₆₂	—	2	2	no	—
193	Dic₆₂	—	2	4	no	—
194	Dic₆₂	—	4	2	no	—
195	#3475	—	31	1	no	maximal, Sylow
196	C₂²×C₃₁	—	2	2	no	—
197	C₂²×C₃₁	—	2	1	no	—
198	C₂²×C₃₁	—	2	2	no	—
199	C₂²×C₃₁	—	2	1	no	—
200	C₂²×C₃₁	—	2	2	no	—
201	C₂²×C₃₁	—	2	2	no	—
202	C₂²×C₃₁	—	2	2	no	—
203	C₂²×C₃₁	—	4	8	no	—
204	C₂²×C₃₁	C₂×#41	1	4	yes	—
205	C₂²×C₃₁	C₂×#41	1	2	yes	—
206	C₂²×C₃₁	C₂⁵	1	1	yes	characteristic
207	C₂×D₃₁	—	2	2	no	—
208	C₂×D₃₁	—	2	2	no	—
209	C₂×D₃₁	—	2	2	no	—
210	C₄×C₃₁	—	2	2	no	—
211	C₄×C₃₁	—	2	2	no	—
212	C₄×C₃₁	—	2	1	no	—
213	C₄×C₃₁	—	2	1	no	—
214	C₄×C₃₁	—	2	1	no	—
215	C₄×C₃₁	C₂×#41	1	2	yes	—
216	C₄×C₃₁	C₂×#41	1	2	yes	—
217	C₄×C₃₁	C₂×#41	1	2	yes	—
218	Dic₃₁	—	2	2	no	—
219	Dic₃₁	—	2	4	no	—
220	Dic₃₁	—	2	2	no	—
221	Dic₃₁	—	2	4	no	—
222	Dic₃₁	—	2	2	no	—
223	#556	—	31	1	no	—
224	#555	—	31	1	no	—
225	#554	—	31	1	no	—
226	#553	—	31	2	no	—
227	#552	—	31	2	no	—
228	#552	—	31	2	no	—
229	#551	—	31	4	no	—
230	#547	—	31	1	no	—
231	#546	—	31	2	no	—
232	#533	—	31	1	no	—
233	#529	—	31	4	no	—
234	#529	—	31	2	no	—
235	#525	—	31	2	no	—
236	C₄×#41	—	31	2	no	—
237	C₄×#41	—	31	1	no	—
238	C₂×C₄×D₄	D₃₁	1	1	yes	characteristic, complemented
239	C₂×#117	—	31	2	no	—
240	C₂×C₃₁	—	2	2	no	—
241	C₂×C₃₁	—	2	4	no	—
242	C₂×C₃₁	—	4	2	no	—
243	C₂×C₃₁	C₂²×#41	1	1	yes	characteristic
244	C₂×C₃₁	C₂²×#41	1	1	yes	characteristic
245	C₂×C₃₁	#585	1	1	yes	characteristic
246	D₃₁	—	4	2	no	—
247	C₂×#41	—	31	2	no	—
248	C₂×#41	—	31	1	no	—
249	C₂²×D₄	C₂×D₃₁	1	1	yes	characteristic
250	C₂³×C₄	C₂×D₃₁	1	2	yes	—
251	C₄⋊Q₈	—	31	1	no	—
252	C₄⋊Q₈	—	31	1	no	—
253	#126	—	31	4	no	—
254	#126	—	31	4	no	—
255	#126	—	31	4	no	—
256	#125	—	31	4	no	—
257	#125	—	31	2	no	—
258	#125	—	31	2	no	—
259	#124	—	31	2	no	—
260	#124	—	31	4	no	—
261	#123	—	31	4	no	—
262	#123	—	31	4	no	—
263	#123	—	31	4	no	—
264	#123	—	31	4	no	—
265	C₂²⋊Q₈	—	31	2	no	—
266	C₂²⋊Q₈	—	31	2	no	—
267	C₂²⋊Q₈	—	31	2	no	—
268	C₂²⋊Q₈	—	31	2	no	—
269	C₂²⋊Q₈	—	31	2	no	—
270	C₂²⋊Q₈	—	31	4	no	—
271	#121	—	31	4	no	—
272	#121	—	31	2	no	—
273	#121	—	31	2	no	—
274	#121	—	31	2	no	—
275	#120	—	31	4	no	—
276	C₄×Q₈	—	31	2	no	—
277	C₄×Q₈	—	31	2	no	—
278	C₄×Q₈	—	31	1	no	—
279	C₄×Q₈	—	31	1	no	—
280	C₄×Q₈	—	31	2	no	—
281	C₄×D₄	—	31	2	no	—
282	C₄×D₄	—	31	4	no	—
283	C₄×D₄	—	31	2	no	—
284	C₄×D₄	—	31	2	no	—
285	C₄×D₄	—	31	4	no	—
286	C₄×D₄	—	31	4	no	—
287	C₄×D₄	—	31	1	no	—
288	C₄×D₄	—	31	1	no	—
289	C₄×D₄	C₂×D₃₁	1	1	yes	characteristic
290	C₄×D₄	C₂×D₃₁	1	1	yes	characteristic
291	C₄×D₄	C₂×D₃₁	1	2	yes	—
292	C₄×D₄	C₂×D₃₁	1	1	yes	characteristic
293	C₄×D₄	C₂×D₃₁	1	2	yes	—
294	C₄×D₄	C₂×D₃₁	1	1	yes	characteristic
295	#117	—	31	1	no	—
296	#117	—	31	2	no	—
297	#117	—	31	4	no	—
298	#117	—	31	4	no	—
299	#117	—	31	2	no	—
300	#117	—	31	2	no	—
301	#117	—	31	2	no	—
302	#117	—	31	4	no	—
303	#117	—	31	2	no	—
304	C₂×C₄⋊C₄	—	31	2	no	—
305	C₂×C₄⋊C₄	—	31	2	no	—
306	C₂×C₄⋊C₄	C₂×D₃₁	1	1	yes	characteristic
307	C₂×C₂²⋊C₄	—	31	4	no	—
308	C₂×C₂²⋊C₄	C₂×D₃₁	1	2	yes	—
309	C₂×C₄²	—	31	4	no	—
310	C₂×C₄²	—	31	2	no	—
311	C₂×C₄²	C₂×D₃₁	1	1	yes	characteristic
312	C₃₁	#3475	1	1	yes	characteristic, complemented, Sylow
313	C₂⁴	C₂²×D₃₁	1	2	yes	—
314	#41	—	62	8	no	—
315	#41	—	62	4	no	—
316	C₂×Q₈	—	31	1	no	—
317	C₂×Q₈	—	31	2	no	—
318	C₂×Q₈	—	31	2	no	—
319	C₂×D₄	—	2	4	no	—
320	C₂×D₄	—	31	2	no	—
321	C₂×D₄	—	31	4	no	—
322	C₂×D₄	—	31	4	no	—
323	C₂×D₄	—	31	1	no	—
324	C₂×D₄	C₂²×D₃₁	1	2	yes	—
325	C₂×D₄	C₂²×D₃₁	1	1	yes	characteristic
326	C₂×D₄	C₂²×D₃₁	1	1	yes	characteristic
327	C₂²×C₄	—	2	8	no	—
328	C₂²×C₄	—	31	4	no	—
329	C₂²×C₄	—	31	4	no	—
330	C₂²×C₄	—	31	2	no	—
331	C₂²×C₄	—	31	2	no	—
332	C₂²×C₄	—	31	2	no	—
333	C₂²×C₄	C₂²×D₃₁	1	1	yes	characteristic
334	C₂²×C₄	C₂²×D₃₁	1	2	yes	—
335	C₂²×C₄	C₂²×D₃₁	1	2	yes	—
336	C₂²×C₄	C₂²×D₃₁	1	2	yes	—
337	C₂²×C₄	C₂²×D₃₁	1	2	yes	—
338	C₂²×C₄	C₂²×D₃₁	1	2	yes	—
339	C₂²×C₄	C₂²×D₃₁	1	1	yes	characteristic
340	C₂²×C₄	C₂²×D₃₁	1	1	yes	characteristic
341	C₄⋊C₄	—	31	2	no	—
342	C₄⋊C₄	—	31	4	no	—
343	C₄⋊C₄	—	31	4	no	—
344	C₄⋊C₄	—	31	2	no	—
345	C₄⋊C₄	—	31	4	no	—
346	C₄⋊C₄	—	31	4	no	—
347	C₄⋊C₄	—	31	1	no	—
348	C₄⋊C₄	—	31	1	no	—
349	C₄⋊C₄	—	31	2	no	—
350	C₄⋊C₄	—	31	2	no	—
351	C₄⋊C₄	—	31	4	no	—
352	C₄⋊C₄	—	31	4	no	—
353	C₄⋊C₄	—	31	2	no	—
354	C₄⋊C₄	—	31	2	no	—
355	C₄⋊C₄	C₂²×D₃₁	1	1	yes	characteristic
356	C₄⋊C₄	C₂²×D₃₁	1	1	yes	characteristic
357	C₄⋊C₄	C₂²×D₃₁	1	2	yes	—
358	C₂²⋊C₄	—	31	2	no	—
359	C₂²⋊C₄	—	31	4	no	—
360	C₂²⋊C₄	—	31	4	no	—
361	C₂²⋊C₄	—	31	4	no	—
362	C₂²⋊C₄	—	31	4	no	—
363	C₂²⋊C₄	—	31	4	no	—
364	C₂²⋊C₄	—	31	2	no	—
365	C₂²⋊C₄	—	31	4	no	—
366	C₂²⋊C₄	—	31	2	no	—
367	C₂²⋊C₄	—	31	4	no	—
368	C₂²⋊C₄	C₂²×D₃₁	1	2	yes	—
369	C₂²⋊C₄	C₂²×D₃₁	1	2	yes	—
370	C₂²⋊C₄	C₂²×D₃₁	1	2	yes	—
371	C₂²⋊C₄	C₂²×D₃₁	1	2	yes	—
372	C₄²	—	31	4	no	—
373	C₄²	—	31	4	no	—
374	C₄²	—	31	2	no	—
375	C₄²	—	31	2	no	—
376	C₄²	—	31	2	no	—
377	C₄²	—	31	4	no	—
378	C₄²	C₂²×D₃₁	1	1	yes	characteristic
379	C₄²	C₂²×D₃₁	1	1	yes	characteristic
380	C₄²	C₂²×D₃₁	1	1	yes	characteristic
381	C₄²	C₂²×D₃₁	1	1	yes	characteristic
382	C₂³	—	2	4	no	—
383	C₂³	—	2	4	no	—
384	C₂³	—	4	2	no	—
385	C₂³	—	31	2	no	—
386	C₂³	C₂³×D₃₁	1	2	yes	—
387	C₂³	C₂³×D₃₁	1	2	yes	—
388	C₂³	C₂³×D₃₁	1	1	yes	characteristic
389	Q₈	—	62	4	no	—
390	Q₈	—	62	2	no	—
391	Q₈	—	124	2	no	—
392	D₄	—	2	4	no	—
393	D₄	—	2	2	no	—
394	D₄	—	62	8	no	—
395	D₄	—	62	4	no	—
396	D₄	—	62	2	no	—
397	D₄	—	124	4	no	—
398	D₄	#92495	1	4	yes	complemented
399	C₂×C₄	—	2	4	no	—
400	C₂×C₄	—	2	2	no	—
401	C₂×C₄	—	2	4	no	—
402	C₂×C₄	—	2	4	no	—
403	C₂×C₄	—	2	4	no	—
404	C₂×C₄	—	2	4	no	—
405	C₂×C₄	—	4	1	no	—
406	C₂×C₄	—	31	2	no	—
407	C₂×C₄	—	31	2	no	—
408	C₂×C₄	—	31	2	no	—
409	C₂×C₄	—	31	4	no	—
410	C₂×C₄	—	31	4	no	—
411	C₂×C₄	—	62	8	no	—
412	C₂×C₄	—	62	4	no	—
413	C₂×C₄	—	62	4	no	—
414	C₂×C₄	—	124	2	no	—
415	C₂×C₄	—	124	4	no	—
416	C₂×C₄	#92497	1	4	yes	complemented
417	C₂×C₄	C₂³×D₃₁	1	2	yes	—
418	C₂×C₄	C₂³×D₃₁	1	1	yes	characteristic
419	C₂×C₄	C₂³×D₃₁	1	1	yes	characteristic
420	C₂×C₄	C₂³×D₃₁	1	1	yes	characteristic
421	C₂×C₄	C₂³×D₃₁	1	2	yes	—
422	C₂×C₄	C₂³×D₃₁	1	1	yes	characteristic
423	C₂×C₄	C₂³×D₃₁	1	1	yes	characteristic
424	C₂×C₄	C₂³×D₃₁	1	1	yes	characteristic
425	C₂²	—	2	2	no	—
426	C₂²	—	2	1	no	—
427	C₂²	—	2	1	no	—
428	C₂²	—	2	2	no	—
429	C₂²	—	2	2	no	—
430	C₂²	—	2	2	no	—
431	C₂²	—	2	2	no	—
432	C₂²	—	4	8	no	—
433	C₂²	—	62	2	no	—
434	C₂²	—	62	2	no	—
435	C₂²	—	62	2	no	—
436	C₂²	C₂×#92495	1	4	yes	—
437	C₂²	C₂×#92497	1	2	yes	—
438	C₂²	C₂⁴×D₃₁	1	1	yes	characteristic
439	C₄	—	2	2	no	—
440	C₄	—	2	2	no	—
441	C₄	—	2	1	no	—
442	C₄	—	2	1	no	—
443	C₄	—	2	1	no	—
444	C₄	—	62	2	no	—
445	C₄	—	62	2	no	—
446	C₄	—	62	4	no	—
447	C₄	—	62	2	no	—
448	C₄	—	62	4	no	—
449	C₄	C₂×#92495	1	2	yes	—
450	C₄	C₂×#92497	1	2	yes	—
451	C₄	C₂×#92497	1	2	yes	—
452	C₂	—	2	2	no	—
453	C₂	—	2	4	no	—
454	C₂	—	4	2	no	—
455	C₂	—	124	2	no	—
456	C₂	C₂²×#92497	1	1	yes	characteristic
457	C₂	C₂²×#92495	1	1	yes	characteristic
458	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	C₂×C₄×D₄×C₃₁	C₂
hypercenter	C₂×C₄×D₄	D₃₁
hypocenter	C₃₁	#3475
LCS	G ▷ C₂²×C₃₁ ▷ C₃₁
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄×D₄

Complements

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

N	H ≅ G/N	type
1. #14521769	C₂	semidirect
2. #14521764	C₂	semidirect
3. #14521756	C₂	semidirect
4. #14521745	C₂	semidirect
5. #14521739	C₂	semidirect
6. #14521734	C₂	semidirect
7. #14521725	C₂	semidirect
8. #14521703	C₂	semidirect
9. #14521693	C₂	semidirect
10. #14521606	C₂	semidirect
11. #14521581	C₂	semidirect
12. #14521579	C₂	semidirect
13. #14521560	C₂	semidirect
14. C₄×#92495	C₂	semidirect
15. C₄×#92497	C₂	semidirect
16. C₂×#11758503	C₂	semidirect
17. C₂×C₄×D₄×C₃₁	C₂	semidirect
38. #11758507	C₂²	semidirect
39. #11758507	C₂²	semidirect
43. C₄×C₂²⋊D₃₁	C₂²	semidirect
44. C₄×C₂²⋊D₃₁	C₂²	semidirect
48. #11758503	C₂²	semidirect
49. #11758503	C₂²	semidirect
50. #11758503	C₂²	semidirect
51. C₂×C₄⋊Dic₃₁	C₂²	semidirect
52. C₂×C₄⋊Dic₃₁	C₂²	semidirect
55. #11758501	C₂²	semidirect
56. #11758501	C₂²	semidirect
57. C₂×C₄×Dic₃₁	C₂²	semidirect
58. #11758475	C₂²	semidirect
59. #11758474	C₂²	semidirect
60. #11758469	C₂²	semidirect
61. #11758467	C₂²	semidirect
62. #11758466	C₂²	semidirect
63. #11758464	C₂²	semidirect
64. #11758463	C₂²	semidirect
65. #11758462	C₂²	semidirect
66. #11758460	C₂²	semidirect
67. (C₂²⋊D₃₁)⋊C₄	C₂²	semidirect
68. #11758456	C₂²	semidirect
69. #11758456	C₂²	semidirect
70. #11758455	C₂²	semidirect
71. #11758454	C₂²	semidirect
72. C₄×D₁₂₄	C₂²	semidirect
73. C₄×D₁₂₄	C₂²	semidirect
74. #11758449	C₂²	semidirect
75. C₄²×D₃₁	C₂²	semidirect
76. #11758447	C₂²	semidirect
77. #11758446	C₂²	semidirect
78. #11758446	C₂²	semidirect
79. C₄×Dic₆₂	C₂²	semidirect
80. C₄×Dic₆₂	C₂²	semidirect
81. C₄×Dic₆₂	C₂²	semidirect
82. C₄×Dic₆₂	C₂²	semidirect
161. D₄×C₃₁	#41	semidirect
169. C₂×C₄×C₃₁	#41	semidirect
238. C₂×C₄×D₄	D₃₁	semidirect
312. C₃₁	#3475	semidirect
398. D₄	#92495	semidirect
416. 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
#14521769	2
#14521764	2
#14521756	2
#14521745	2
#14521739	2
#14521734	2
#14521725	2
#14521703	2
#14521693	2
#14521606	2
#14521581	2
#14521579	2
#14521560	2
C₄×#92495	2
C₄×#92497	2
C₂×#11758503	2
C₂×C₄×D₄×C₃₁	2
#3475	31