Subgroups — #16859275

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	#14521772	C₂	1	1	yes	maximal, characteristic, complemented
2	#14521764	C₂	1	1	yes	maximal, characteristic, complemented
3	#14521759	C₂	1	1	yes	maximal, characteristic, complemented
4	#14521749	C₂	1	2	yes	maximal, complemented
5	#14521740	C₂	1	2	yes	maximal, complemented
6	#14521739	C₂	1	2	yes	maximal, complemented
7	#14521728	C₂	1	4	yes	maximal, complemented
8	#14521704	C₂	1	1	yes	maximal, characteristic, complemented
9	#14521695	C₂	1	2	yes	maximal, complemented
10	#14521606	C₂	1	1	yes	maximal, characteristic, complemented
11	#14521583	C₂	1	2	yes	maximal, complemented
12	#14521577	C₂	1	4	yes	maximal, complemented
13	#14521556	C₂	1	2	yes	maximal, complemented
14	C₄×#92495	C₂	1	2	yes	maximal, complemented
15	C₂×C₄×D₁₂₄	C₂	1	1	yes	maximal, characteristic, complemented
16	#117×D₃₁	C₂	1	2	yes	maximal, complemented
17	C₄×#41×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×#41×C₃₁	C₂²	1	1	yes	characteristic
19	C₂×#92495	C₂²	1	2	yes	—
20	C₂²×D₁₂₄	C₂²	1	1	yes	characteristic
21	C₂²×C₄×D₃₁	C₂²	1	2	yes	—
22	C₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic, complemented
23	C₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic, complemented
24	C₄×D₄×C₃₁	C₂²	1	2	yes	—
25	C₄×D₄×C₃₁	C₂²	1	2	yes	—
26	C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic, complemented
27	C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic, complemented
28	C₃₁×#117	C₂²	1	1	yes	characteristic
29	C₃₁×#117	C₂²	1	2	yes	complemented
30	C₂×C₄²×C₃₁	C₂²	1	1	yes	characteristic
31	C₂×C₄²×C₃₁	C₂²	1	2	yes	complemented
32	#11758523	C₂²	1	2	yes	complemented
33	#11758523	C₂²	1	2	yes	complemented
34	#11758515	C₂²	1	2	yes	complemented
35	#11758515	C₂²	1	2	yes	complemented
36	#11758514	C₂²	1	4	yes	—
37	#11758512	C₂²	1	4	yes	—
38	#11758507	C₂²	1	2	yes	—
39	#11758506	C₂²	1	4	yes	complemented
40	C₄×C₂²⋊D₃₁	C₂²	1	4	yes	complemented
41	C₄×C₂²⋊D₃₁	C₂²	1	4	yes	complemented
42	C₄×C₂²⋊D₃₁	C₂²	1	4	yes	complemented
43	C₂×(C₂×D₃₁)⋊C₄	C₂²	1	2	yes	—
44	#11758503	C₂²	1	2	yes	—
45	#11758503	C₂²	1	2	yes	complemented
46	C₂×C₄⋊Dic₃₁	C₂²	1	1	yes	characteristic
47	#11758501	C₂²	1	2	yes	—
48	#11758501	C₂²	1	2	yes	—
49	#11758501	C₂²	1	2	yes	complemented
50	#11758475	C₂²	1	4	yes	complemented
51	#11758473	C₂²	1	4	yes	complemented
52	#11758471	C₂²	1	4	yes	—
53	#11758469	C₂²	1	2	yes	complemented
54	#11758469	C₂²	1	2	yes	complemented
55	C₄⋊C₄×D₃₁	C₂²	1	2	yes	complemented
56	C₄⋊C₄×D₃₁	C₂²	1	2	yes	complemented
57	#11758466	C₂²	1	4	yes	complemented
58	#11758462	C₂²	1	4	yes	complemented
59	#11758461	C₂²	1	4	yes	—
60	#11758460	C₂²	1	4	yes	complemented
61	C₂²⋊C₄×D₃₁	C₂²	1	4	yes	—
62	#11758456	C₂²	1	4	yes	complemented
63	#11758454	C₂²	1	4	yes	—
64	#11758453	C₂²	1	4	yes	complemented
65	#11758452	C₂²	1	2	yes	—
66	C₄×D₁₂₄	C₂²	1	2	yes	—
67	C₄×D₁₂₄	C₂²	1	1	yes	characteristic
68	C₄×D₁₂₄	C₂²	1	2	yes	—
69	C₄×D₁₂₄	C₂²	1	1	yes	characteristic
70	C₄×D₁₂₄	C₂²	1	1	yes	characteristic
71	C₄×D₁₂₄	C₂²	1	2	yes	—
72	C₄×D₁₂₄	C₂²	1	1	yes	characteristic
73	#11758449	C₂²	1	4	yes	complemented
74	#11758449	C₂²	1	4	yes	complemented
75	C₄²×D₃₁	C₂²	1	4	yes	complemented
76	#11758447	C₂²	1	2	yes	complemented
77	#11758447	C₂²	1	2	yes	complemented
78	#11758446	C₂²	1	1	yes	characteristic, complemented
79	#11758446	C₂²	1	1	yes	characteristic, complemented
80	C₄×Dic₆₂	C₂²	1	2	yes	complemented
81	C₄×Dic₆₂	C₂²	1	2	yes	complemented
82	C₄×Dic₆₂	C₂²	1	2	yes	complemented
83	C₂³×D₃₁	C₂³	1	2	yes	—
84	#41×C₃₁	—	2	4	no	—
85	C₂×Q₈×C₃₁	C₂³	1	1	yes	characteristic
86	C₂×D₄×C₃₁	C₂³	1	2	yes	—
87	C₂×D₄×C₃₁	C₂³	1	1	yes	characteristic
88	C₂²×C₄×C₃₁	C₂³	1	1	yes	characteristic
89	C₂²×C₄×C₃₁	C₂³	1	2	yes	—
90	C₂²×C₄×C₃₁	C₂³	1	2	yes	—
91	C₂²×C₄×C₃₁	C₂³	1	1	yes	characteristic
92	C₂²×C₄×C₃₁	C₂³	1	2	yes	—
93	C₂²×C₄×C₃₁	C₂³	1	1	yes	characteristic
94	C₂×C₂²⋊D₃₁	C₂³	1	4	yes	—
95	C₂×C₂²⋊D₃₁	C₂³	1	4	yes	—
96	C₂²×Dic₃₁	C₂³	1	2	yes	—
97	#92495	—	2	8	no	—
98	C₂×D₁₂₄	—	2	4	no	—
99	C₂×D₁₂₄	C₂³	1	1	yes	characteristic
100	C₂×D₁₂₄	C₂³	1	2	yes	—
101	C₂×D₁₂₄	C₂³	1	1	yes	characteristic
102	C₂×C₄×D₃₁	—	2	8	no	—
103	C₂×C₄×D₃₁	C₂³	1	2	yes	—
104	C₂×C₄×D₃₁	C₂³	1	4	yes	—
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×C₄×D₃₁	C₂³	1	4	yes	—
109	C₂×Dic₆₂	C₂³	1	2	yes	—
110	C₂×Dic₆₂	C₂³	1	2	yes	—
111	C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
112	C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
113	C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
114	C₄⋊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	2	yes	—
121	C₄²×C₃₁	C₂³	1	1	yes	characteristic
122	C₄²×C₃₁	C₂³	1	1	yes	characteristic
123	C₄²×C₃₁	C₂³	1	2	yes	—
124	C₄²×C₃₁	C₂³	1	2	yes	—
125	C₂²⋊Dic₃₁	C₂³	1	4	yes	—
126	C₂²⋊Dic₃₁	C₂³	1	4	yes	—
127	C₂²⋊Dic₃₁	C₂³	1	4	yes	—
128	(C₂×D₃₁)⋊C₄	C₂³	1	2	yes	—
129	(C₂×D₃₁)⋊C₄	C₂³	1	4	yes	—
130	(C₂×D₃₁)⋊C₄	C₂³	1	4	yes	—
131	(C₂×D₃₁)⋊C₄	C₂³	1	4	yes	—
132	(C₂×D₃₁)⋊C₄	C₂³	1	2	yes	—
133	(C₂×D₃₁)⋊C₄	C₂³	1	2	yes	—
134	(C₂×D₃₁)⋊C₄	C₂³	1	2	yes	—
135	(C₂×D₃₁)⋊C₄	C₂³	1	4	yes	—
136	C₄⋊Dic₃₁	C₂³	1	1	yes	characteristic
137	C₄⋊Dic₃₁	C₂³	1	2	yes	—
138	C₄⋊Dic₃₁	C₂³	1	2	yes	—
139	C₄⋊Dic₃₁	C₂³	1	2	yes	—
140	C₄⋊Dic₃₁	C₂³	1	2	yes	—
141	C₄⋊Dic₃₁	C₂³	1	1	yes	characteristic
142	C₄⋊Dic₃₁	C₂³	1	2	yes	—
143	Dic₃₁⋊C₄	C₂³	1	4	yes	—
144	Dic₃₁⋊C₄	C₂³	1	4	yes	—
145	Dic₃₁⋊C₄	C₂³	1	4	yes	—
146	Dic₃₁⋊C₄	C₂³	1	4	yes	—
147	Dic₃₁⋊C₄	C₂³	1	4	yes	—
148	Dic₃₁⋊C₄	C₂³	1	4	yes	—
149	C₄×Dic₃₁	C₂³	1	4	yes	—
150	C₄×Dic₃₁	C₂³	1	4	yes	—
151	C₄×Dic₃₁	C₂³	1	4	yes	—
152	C₂³×C₃₁	C₂⁴	1	2	yes	—
153	C₂³×C₃₁	C₂⁴	1	1	yes	characteristic
154	C₂²×D₃₁	—	2	4	no	—
155	C₂²×D₃₁	—	2	4	no	—
156	C₂²×D₃₁	—	4	2	no	—
157	C₂²×D₃₁	C₂⁴	1	2	yes	—
158	C₂²×D₃₁	C₂⁴	1	2	yes	—
159	Q₈×C₃₁	—	2	2	no	—
160	D₄×C₃₁	—	2	4	no	—
161	D₄×C₃₁	—	2	2	no	—
162	C₂×C₄×C₃₁	—	2	2	no	—
163	C₂×C₄×C₃₁	—	2	4	no	—
164	C₂×C₄×C₃₁	—	2	4	no	—
165	C₂×C₄×C₃₁	—	4	1	no	—
166	C₂×C₄×C₃₁	—	4	2	no	—
167	C₂×C₄×C₃₁	#41	1	4	yes	complemented
168	C₂×C₄×C₃₁	C₂⁴	1	2	yes	—
169	C₂×C₄×C₃₁	C₂⁴	1	2	yes	—
170	C₂×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
171	C₂×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
172	C₂×C₄×C₃₁	C₂⁴	1	2	yes	—
173	C₂×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
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	C₂²⋊D₃₁	—	2	8	no	—
178	C₂²⋊D₃₁	—	4	4	no	—
179	C₂×Dic₃₁	—	2	4	no	—
180	C₂×Dic₃₁	C₂⁴	1	2	yes	—
181	C₂×Dic₃₁	C₂⁴	1	4	yes	—
182	C₂×Dic₃₁	C₂⁴	1	4	yes	—
183	C₂×Dic₃₁	C₂⁴	1	2	yes	—
184	D₁₂₄	—	2	4	no	—
185	D₁₂₄	—	2	2	no	—
186	D₁₂₄	#41	1	4	yes	complemented
187	C₄×D₃₁	—	2	8	no	—
188	C₄×D₃₁	—	2	4	no	—
189	C₄×D₃₁	—	2	4	no	—
190	C₄×D₃₁	—	2	4	no	—
191	C₄×D₃₁	—	2	4	no	—
192	C₄×D₃₁	—	4	4	no	—
193	Dic₆₂	—	2	4	no	—
194	Dic₆₂	—	4	2	no	—
195	#3475	—	31	1	no	maximal, Sylow
196	C₂²×C₃₁	—	2	1	no	—
197	C₂²×C₃₁	—	2	1	no	—
198	C₂²×C₃₁	—	2	2	no	—
199	C₂²×C₃₁	—	2	2	no	—
200	C₂²×C₃₁	—	2	2	no	—
201	C₂²×C₃₁	C₂×#41	1	2	yes	—
202	C₂²×C₃₁	C₂⁵	1	1	yes	characteristic
203	C₂×D₃₁	—	2	2	no	—
204	C₂×D₃₁	—	2	2	no	—
205	C₂×D₃₁	—	2	2	no	—
206	C₂×D₃₁	—	2	2	no	—
207	C₂×D₃₁	—	2	2	no	—
208	C₂×D₃₁	—	4	8	no	—
209	C₂×D₃₁	C₂×#41	1	4	yes	—
210	C₄×C₃₁	—	2	2	no	—
211	C₄×C₃₁	—	2	1	no	—
212	C₄×C₃₁	—	2	2	no	—
213	C₄×C₃₁	—	2	1	no	—
214	C₄×C₃₁	—	2	2	no	—
215	C₄×C₃₁	—	2	1	no	—
216	C₄×C₃₁	C₂×#41	1	2	yes	—
217	C₄×C₃₁	C₂×#41	1	2	yes	—
218	C₄×C₃₁	C₂×#41	1	2	yes	—
219	Dic₃₁	—	2	4	no	—
220	Dic₃₁	—	2	2	no	—
221	Dic₃₁	—	2	2	no	—
222	Dic₃₁	—	2	4	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	D₃₁	1	1	yes	characteristic, complemented
238	C₂×C₄×D₄	—	31	1	no	—
239	C₂×#117	—	31	2	no	—
240	C₂×C₃₁	—	2	2	no	—
241	C₂×C₃₁	—	4	2	no	—
242	C₂×C₃₁	C₂²×#41	1	1	yes	characteristic
243	C₂×C₃₁	C₂²×#41	1	1	yes	characteristic
244	C₂×C₃₁	#585	1	1	yes	characteristic
245	D₃₁	—	2	4	no	—
246	D₃₁	—	4	2	no	—
247	C₂×#41	—	31	2	no	—
248	C₂×#41	C₂×D₃₁	1	1	yes	characteristic
249	C₂²×D₄	—	31	1	no	—
250	C₂³×C₄	—	31	2	no	—
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	4	no	—
260	#124	—	31	2	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	2	no	—
272	#121	—	31	2	no	—
273	#121	—	31	2	no	—
274	#121	—	31	4	no	—
275	#120	—	31	4	no	—
276	C₄×Q₈	—	31	2	no	—
277	C₄×Q₈	—	31	2	no	—
278	C₄×Q₈	—	31	2	no	—
279	C₄×Q₈	C₂×D₃₁	1	1	yes	characteristic, complemented
280	C₄×Q₈	C₂×D₃₁	1	1	yes	characteristic, complemented
281	C₄×D₄	—	31	4	no	—
282	C₄×D₄	—	31	4	no	—
283	C₄×D₄	—	31	4	no	—
284	C₄×D₄	—	31	1	no	—
285	C₄×D₄	—	31	1	no	—
286	C₄×D₄	—	31	2	no	—
287	C₄×D₄	—	31	1	no	—
288	C₄×D₄	—	31	2	no	—
289	C₄×D₄	—	31	1	no	—
290	C₄×D₄	—	31	2	no	—
291	C₄×D₄	C₂×D₃₁	1	2	yes	—
292	C₄×D₄	C₂×D₃₁	1	2	yes	—
293	C₄×D₄	C₂×D₃₁	1	1	yes	characteristic, complemented
294	C₄×D₄	C₂×D₃₁	1	1	yes	characteristic, complemented
295	#117	—	31	2	no	—
296	#117	—	31	2	no	—
297	#117	—	31	2	no	—
298	#117	—	31	2	no	—
299	#117	—	31	4	no	—
300	#117	—	31	4	no	—
301	#117	—	31	4	no	—
302	#117	C₂×D₃₁	1	1	yes	characteristic
303	#117	C₂×D₃₁	1	2	yes	complemented
304	C₂×C₄⋊C₄	—	31	1	no	—
305	C₂×C₄⋊C₄	—	31	2	no	—
306	C₂×C₄⋊C₄	—	31	2	no	—
307	C₂×C₂²⋊C₄	—	31	2	no	—
308	C₂×C₂²⋊C₄	—	31	4	no	—
309	C₂×C₄²	—	31	4	no	—
310	C₂×C₄²	C₂×D₃₁	1	1	yes	characteristic
311	C₂×C₄²	C₂×D₃₁	1	2	yes	complemented
312	C₃₁	#3475	1	1	yes	characteristic, complemented, Sylow
313	C₂⁴	—	31	2	no	—
314	#41	—	2	4	no	—
315	#41	—	62	8	no	—
316	C₂×Q₈	—	31	2	no	—
317	C₂×Q₈	—	31	2	no	—
318	C₂×Q₈	C₂²×D₃₁	1	1	yes	characteristic
319	C₂×D₄	—	31	4	no	—
320	C₂×D₄	—	31	4	no	—
321	C₂×D₄	—	31	1	no	—
322	C₂×D₄	—	31	2	no	—
323	C₂×D₄	—	31	1	no	—
324	C₂×D₄	—	62	4	no	—
325	C₂×D₄	C₂²×D₃₁	1	2	yes	—
326	C₂×D₄	C₂²×D₃₁	1	1	yes	characteristic
327	C₂²×C₄	—	31	2	no	—
328	C₂²×C₄	—	31	4	no	—
329	C₂²×C₄	—	31	2	no	—
330	C₂²×C₄	—	31	2	no	—
331	C₂²×C₄	—	31	2	no	—
332	C₂²×C₄	—	31	2	no	—
333	C₂²×C₄	—	31	4	no	—
334	C₂²×C₄	—	62	8	no	—
335	C₂²×C₄	C₂²×D₃₁	1	1	yes	characteristic
336	C₂²×C₄	C₂²×D₃₁	1	2	yes	—
337	C₂²×C₄	C₂²×D₃₁	1	2	yes	—
338	C₂²×C₄	C₂²×D₃₁	1	1	yes	characteristic
339	C₂²×C₄	C₂²×D₃₁	1	2	yes	—
340	C₂²×C₄	C₂²×D₃₁	1	1	yes	characteristic
341	C₄⋊C₄	—	31	4	no	—
342	C₄⋊C₄	—	31	4	no	—
343	C₄⋊C₄	—	31	4	no	—
344	C₄⋊C₄	—	31	4	no	—
345	C₄⋊C₄	—	31	4	no	—
346	C₄⋊C₄	—	31	4	no	—
347	C₄⋊C₄	—	31	1	no	—
348	C₄⋊C₄	—	31	2	no	—
349	C₄⋊C₄	—	31	2	no	—
350	C₄⋊C₄	—	31	1	no	—
351	C₄⋊C₄	—	31	2	no	—
352	C₄⋊C₄	—	31	2	no	—
353	C₄⋊C₄	—	31	2	no	—
354	C₄⋊C₄	C₂²×D₃₁	1	1	yes	characteristic
355	C₄⋊C₄	C₂²×D₃₁	1	1	yes	characteristic
356	C₄⋊C₄	C₂²×D₃₁	1	2	yes	—
357	C₄⋊C₄	C₂²×D₃₁	1	2	yes	—
358	C₂²⋊C₄	—	31	4	no	—
359	C₂²⋊C₄	—	31	4	no	—
360	C₂²⋊C₄	—	31	4	no	—
361	C₂²⋊C₄	—	31	2	no	—
362	C₂²⋊C₄	—	31	4	no	—
363	C₂²⋊C₄	—	31	4	no	—
364	C₂²⋊C₄	—	31	2	no	—
365	C₂²⋊C₄	—	31	2	no	—
366	C₂²⋊C₄	—	31	2	no	—
367	C₂²⋊C₄	—	31	4	no	—
368	C₂²⋊C₄	—	31	4	no	—
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	4	no	—
375	C₄²	C₂²×D₃₁	1	1	yes	characteristic
376	C₄²	C₂²×D₃₁	1	1	yes	characteristic
377	C₄²	C₂²×D₃₁	1	2	yes	—
378	C₄²	C₂²×D₃₁	1	2	yes	—
379	C₄²	C₂²×D₃₁	1	2	yes	—
380	C₄²	C₂²×D₃₁	1	1	yes	characteristic
381	C₄²	C₂²×D₃₁	1	1	yes	characteristic
382	C₂³	—	31	2	no	—
383	C₂³	—	31	2	no	—
384	C₂³	—	62	4	no	—
385	C₂³	—	62	4	no	—
386	C₂³	—	124	2	no	—
387	C₂³	C₂³×D₃₁	1	2	yes	—
388	C₂³	C₂³×D₃₁	1	1	yes	characteristic
389	Q₈	—	2	2	no	—
390	Q₈	—	62	4	no	—
391	Q₈	—	124	2	no	—
392	D₄	—	2	4	no	—
393	D₄	—	2	2	no	—
394	D₄	—	31	4	no	—
395	D₄	—	62	4	no	—
396	D₄	—	62	8	no	—
397	D₄	—	62	2	no	—
398	D₄	—	124	4	no	—
399	C₂×C₄	—	2	4	no	—
400	C₂×C₄	—	2	2	no	—
401	C₂×C₄	—	2	4	no	—
402	C₂×C₄	—	4	2	no	—
403	C₂×C₄	—	4	1	no	—
404	C₂×C₄	—	31	2	no	—
405	C₂×C₄	—	31	4	no	—
406	C₂×C₄	—	31	4	no	—
407	C₂×C₄	—	31	2	no	—
408	C₂×C₄	—	62	8	no	—
409	C₂×C₄	—	62	4	no	—
410	C₂×C₄	—	62	4	no	—
411	C₂×C₄	—	62	4	no	—
412	C₂×C₄	—	62	4	no	—
413	C₂×C₄	—	62	4	no	—
414	C₂×C₄	—	124	4	no	—
415	C₂×C₄	#92495	1	4	yes	complemented
416	C₂×C₄	C₂³×D₃₁	1	2	yes	—
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	2	yes	—
421	C₂×C₄	C₂³×D₃₁	1	1	yes	characteristic
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	1	no	—
426	C₂²	—	2	1	no	—
427	C₂²	—	2	2	no	—
428	C₂²	—	2	2	no	—
429	C₂²	—	2	2	no	—
430	C₂²	—	31	4	no	—
431	C₂²	—	62	2	no	—
432	C₂²	—	62	2	no	—
433	C₂²	—	62	2	no	—
434	C₂²	—	62	2	no	—
435	C₂²	—	62	2	no	—
436	C₂²	—	124	8	no	—
437	C₂²	C₂×#92495	1	2	yes	—
438	C₂²	C₂⁴×D₃₁	1	1	yes	characteristic
439	C₄	—	2	2	no	—
440	C₄	—	2	1	no	—
441	C₄	—	2	2	no	—
442	C₄	—	2	1	no	—
443	C₄	—	2	2	no	—
444	C₄	—	2	1	no	—
445	C₄	—	62	4	no	—
446	C₄	—	62	2	no	—
447	C₄	—	62	2	no	—
448	C₄	—	62	4	no	—
449	C₄	C₂×#92495	1	2	yes	—
450	C₄	C₂×#92495	1	2	yes	—
451	C₄	#41×D₃₁	1	2	yes	—
452	C₂	—	2	2	no	—
453	C₂	—	4	2	no	—
454	C₂	—	62	4	no	—
455	C₂	—	124	2	no	—
456	C₂	C₂×#41×D₃₁	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	C₄×#41×C₃₁	C₂
hypercenter	C₄×#41	D₃₁
hypocenter	C₃₁	#3475
LCS	G ▷ C₂²×C₃₁ ▷ C₃₁
UCS	C₁ ◁ C₂×C₄ ◁ C₄×#41

Complements

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

N	H ≅ G/N	type
1. #14521772	C₂	semidirect
2. #14521764	C₂	semidirect
3. #14521759	C₂	semidirect
4. #14521749	C₂	semidirect
5. #14521740	C₂	semidirect
6. #14521739	C₂	semidirect
7. #14521728	C₂	semidirect
8. #14521704	C₂	semidirect
9. #14521695	C₂	semidirect
10. #14521606	C₂	semidirect
11. #14521583	C₂	semidirect
12. #14521577	C₂	semidirect
13. #14521556	C₂	semidirect
14. C₄×#92495	C₂	semidirect
15. C₂×C₄×D₁₂₄	C₂	semidirect
16. #117×D₃₁	C₂	semidirect
17. C₄×#41×C₃₁	C₂	semidirect
22. C₄×Q₈×C₃₁	C₂²	semidirect
23. C₄×Q₈×C₃₁	C₂²	semidirect
26. C₄×D₄×C₃₁	C₂²	semidirect
27. C₄×D₄×C₃₁	C₂²	semidirect
29. C₃₁×#117	C₂²	semidirect
31. C₂×C₄²×C₃₁	C₂²	semidirect
32. #11758523	C₂²	semidirect
33. #11758523	C₂²	semidirect
34. #11758515	C₂²	semidirect
35. #11758515	C₂²	semidirect
39. #11758506	C₂²	semidirect
40. C₄×C₂²⋊D₃₁	C₂²	semidirect
41. C₄×C₂²⋊D₃₁	C₂²	semidirect
42. C₄×C₂²⋊D₃₁	C₂²	semidirect
45. #11758503	C₂²	semidirect
49. #11758501	C₂²	semidirect
50. #11758475	C₂²	semidirect
51. #11758473	C₂²	semidirect
53. #11758469	C₂²	semidirect
54. #11758469	C₂²	semidirect
55. C₄⋊C₄×D₃₁	C₂²	semidirect
56. C₄⋊C₄×D₃₁	C₂²	semidirect
57. #11758466	C₂²	semidirect
58. #11758462	C₂²	semidirect
60. #11758460	C₂²	semidirect
62. #11758456	C₂²	semidirect
64. #11758453	C₂²	semidirect
73. #11758449	C₂²	semidirect
74. #11758449	C₂²	semidirect
75. C₄²×D₃₁	C₂²	semidirect
76. #11758447	C₂²	semidirect
77. #11758447	C₂²	semidirect
78. #11758446	C₂²	semidirect
79. #11758446	C₂²	semidirect
80. C₄×Dic₆₂	C₂²	semidirect
81. C₄×Dic₆₂	C₂²	semidirect
82. C₄×Dic₆₂	C₂²	semidirect
167. C₂×C₄×C₃₁	#41	semidirect
186. D₁₂₄	#41	semidirect
237. C₄×#41	D₃₁	semidirect
279. C₄×Q₈	C₂×D₃₁	semidirect
280. C₄×Q₈	C₂×D₃₁	semidirect
293. C₄×D₄	C₂×D₃₁	semidirect
294. C₄×D₄	C₂×D₃₁	semidirect
303. #117	C₂×D₃₁	semidirect
311. C₂×C₄²	C₂×D₃₁	semidirect
312. C₃₁	#3475	semidirect
415. C₂×C₄	#92495	semidirect

Maximal subgroups

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

subgroup	index
#14521772	2
#14521764	2
#14521759	2
#14521749	2
#14521740	2
#14521739	2
#14521728	2
#14521704	2
#14521695	2
#14521606	2
#14521583	2
#14521577	2
#14521556	2
C₄×#92495	2
C₂×C₄×D₁₂₄	2
#117×D₃₁	2
C₄×#41×C₃₁	2
#3475	31