Subgroups — #16859321

Order 3968.

1242 conjugacy classes of subgroups.

The subgroup lattice has 470 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14521784	C₂	1	1	yes	maximal, characteristic, complemented
2	#14521759	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	#14521743	C₂	1	2	yes	maximal, complemented
6	#14521723	C₂	1	4	yes	maximal, complemented
7	#14521695	C₂	1	2	yes	maximal, complemented
8	#14521687	C₂	1	2	yes	maximal, complemented
9	D₄×D₁₂₄	C₂	1	1	yes	maximal, characteristic, complemented
10	#14521599	C₂	1	1	yes	maximal, characteristic, complemented
11	#14521586	C₂	1	2	yes	maximal, complemented
12	#14521583	C₂	1	2	yes	maximal, complemented
13	#14521558	C₂	1	4	yes	maximal, complemented
14	C₄×#92495	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×C₄×D₁₂₄	C₂	1	2	yes	maximal, complemented
16	C₄×D₄×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×D₄×D₃₁	C₂²	1	2	yes	—
20	C₂×#92495	C₂²	1	1	yes	characteristic
21	C₂×#92495	C₂²	1	2	yes	complemented
22	C₂²×D₁₂₄	C₂²	1	2	yes	—
23	C₂²×C₄×D₃₁	C₂²	1	4	yes	complemented
24	C₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic, complemented
25	C₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic, complemented
26	C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic
27	C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic
28	C₄×D₄×C₃₁	C₂²	1	2	yes	complemented
29	C₄×D₄×C₃₁	C₂²	1	2	yes	complemented
30	C₃₁×#117	C₂²	1	2	yes	complemented
31	C₃₁×#117	C₂²	1	1	yes	characteristic, complemented
32	C₂×C₄²×C₃₁	C₂²	1	2	yes	complemented
33	C₂×C₄²×C₃₁	C₂²	1	1	yes	characteristic, complemented
34	#11758524	C₂²	1	2	yes	complemented
35	#11758523	C₂²	1	2	yes	complemented
36	#11758516	C₂²	1	4	yes	complemented
37	#11758514	C₂²	1	4	yes	complemented
38	D₄×Dic₃₁	C₂²	1	2	yes	—
39	#11758507	C₂²	1	2	yes	—
40	#11758507	C₂²	1	2	yes	complemented
41	#11758507	C₂²	1	2	yes	complemented
42	#11758506	C₂²	1	4	yes	complemented
43	C₄×C₂²⋊D₃₁	C₂²	1	2	yes	complemented
44	C₄×C₂²⋊D₃₁	C₂²	1	4	yes	complemented
45	C₄×C₂²⋊D₃₁	C₂²	1	2	yes	complemented
46	C₂×(C₂×D₃₁)⋊C₄	C₂²	1	4	yes	complemented
47	#11758503	C₂²	1	1	yes	characteristic, complemented
48	C₂×C₄⋊Dic₃₁	C₂²	1	2	yes	complemented
49	#11758501	C₂²	1	2	yes	complemented
50	#11758475	C₂²	1	4	yes	complemented
51	#11758473	C₂²	1	4	yes	complemented
52	#11758472	C₂²	1	2	yes	—
53	#11758471	C₂²	1	4	yes	complemented
54	#11758471	C₂²	1	4	yes	complemented
55	#11758470	C₂²	1	2	yes	complemented
56	C₄⋊C₄×D₃₁	C₂²	1	2	yes	complemented
57	#11758467	C₂²	1	2	yes	complemented
58	#11758461	C₂²	1	4	yes	complemented
59	#11758460	C₂²	1	4	yes	complemented
60	#11758459	C₂²	1	4	yes	—
61	(C₂²⋊D₃₁)⋊C₄	C₂²	1	4	yes	complemented
62	C₂²⋊C₄×D₃₁	C₂²	1	4	yes	complemented
63	#11758455	C₂²	1	4	yes	complemented
64	#11758453	C₂²	1	4	yes	complemented
65	#11758452	C₂²	1	2	yes	complemented
66	#11758452	C₂²	1	2	yes	complemented
67	#11758451	C₂²	1	1	yes	characteristic
68	C₄×D₁₂₄	C₂²	1	1	yes	characteristic
69	C₄×D₁₂₄	C₂²	1	2	yes	—
70	C₄×D₁₂₄	C₂²	1	1	yes	characteristic
71	C₄×D₁₂₄	C₂²	1	4	yes	complemented
72	C₄×D₁₂₄	C₂²	1	2	yes	complemented
73	C₄×D₁₂₄	C₂²	1	2	yes	complemented
74	C₄×D₁₂₄	C₂²	1	4	yes	complemented
75	C₄×D₁₂₄	C₂²	1	2	yes	complemented
76	#11758449	C₂²	1	2	yes	complemented
77	#11758449	C₂²	1	4	yes	complemented
78	C₄²×D₃₁	C₂²	1	2	yes	complemented
79	#11758447	C₂²	1	2	yes	complemented
80	#11758446	C₂²	1	1	yes	characteristic, complemented
81	C₄×Dic₆₂	C₂²	1	1	yes	characteristic, complemented
82	C₄×Dic₆₂	C₂²	1	1	yes	characteristic, complemented
83	C₂³×D₃₁	C₂³	1	4	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	2	yes	—
89	C₂²×C₄×C₃₁	C₂³	1	1	yes	characteristic
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	2	yes	—
96	C₂×C₂²⋊D₃₁	C₂³	1	4	yes	—
97	C₂²×Dic₃₁	C₂³	1	4	yes	—
98	D₄×D₃₁	—	2	8	no	—
99	#92495	—	2	4	no	—
100	#92495	—	4	4	no	—
101	C₂×D₁₂₄	—	2	8	no	—
102	C₂×D₁₂₄	C₂³	1	2	yes	—
103	C₂×D₁₂₄	C₂³	1	4	yes	—
104	C₂×D₁₂₄	C₂³	1	2	yes	—
105	C₂×D₁₂₄	C₂³	1	2	yes	—
106	C₂×D₁₂₄	C₂³	1	1	yes	characteristic
107	C₂×C₄×D₃₁	—	4	8	no	—
108	C₂×C₄×D₃₁	C₂³	1	2	yes	—
109	C₂×C₄×D₃₁	C₂³	1	2	yes	—
110	C₂×C₄×D₃₁	C₂³	1	2	yes	—
111	C₂×C₄×D₃₁	C₂³	1	4	yes	—
112	C₂×C₄×D₃₁	C₂³	1	4	yes	—
113	C₂×C₄×D₃₁	C₂³	1	4	yes	—
114	C₂×Dic₆₂	C₂³	1	1	yes	characteristic
115	C₂×Dic₆₂	C₂³	1	2	yes	—
116	C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
117	C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
118	C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
119	C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
120	C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
121	C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
122	C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
123	C₄²×C₃₁	C₂³	1	1	yes	characteristic
124	C₄²×C₃₁	C₂³	1	1	yes	characteristic
125	C₄²×C₃₁	C₂³	1	2	yes	—
126	C₄²×C₃₁	C₂³	1	1	yes	characteristic
127	C₄²×C₃₁	C₂³	1	2	yes	—
128	C₄²×C₃₁	C₂³	1	1	yes	characteristic
129	C₄²×C₃₁	C₂³	1	2	yes	—
130	C₂²⋊Dic₃₁	C₂³	1	4	yes	—
131	C₂²⋊Dic₃₁	C₂³	1	2	yes	—
132	(C₂×D₃₁)⋊C₄	C₂³	1	2	yes	—
133	(C₂×D₃₁)⋊C₄	C₂³	1	2	yes	—
134	(C₂×D₃₁)⋊C₄	C₂³	1	4	yes	—
135	(C₂×D₃₁)⋊C₄	C₂³	1	4	yes	—
136	(C₂×D₃₁)⋊C₄	C₂³	1	4	yes	—
137	(C₂×D₃₁)⋊C₄	C₂³	1	4	yes	—
138	(C₂×D₃₁)⋊C₄	C₂³	1	4	yes	—
139	(C₂×D₃₁)⋊C₄	C₂³	1	4	yes	—
140	(C₂×D₃₁)⋊C₄	C₂³	1	4	yes	—
141	C₄⋊Dic₃₁	C₂³	1	1	yes	characteristic
142	C₄⋊Dic₃₁	C₂³	1	1	yes	characteristic
143	C₄⋊Dic₃₁	C₂³	1	2	yes	—
144	C₄⋊Dic₃₁	C₂³	1	2	yes	—
145	C₄⋊Dic₃₁	C₂³	1	4	yes	—
146	Dic₃₁⋊C₄	C₂³	1	2	yes	—
147	Dic₃₁⋊C₄	C₂³	1	2	yes	—
148	Dic₃₁⋊C₄	C₂³	1	4	yes	—
149	Dic₃₁⋊C₄	C₂³	1	4	yes	—
150	Dic₃₁⋊C₄	C₂³	1	4	yes	—
151	C₄×Dic₃₁	C₂³	1	2	yes	—
152	C₄×Dic₃₁	C₂³	1	2	yes	—
153	C₄×Dic₃₁	C₂³	1	2	yes	—
154	C₂³×C₃₁	C₂⁴	1	1	yes	characteristic
155	C₂³×C₃₁	C₂⁴	1	2	yes	—
156	C₂²×D₃₁	—	2	8	no	—
157	C₂²×D₃₁	—	2	8	no	—
158	C₂²×D₃₁	—	4	4	no	—
159	C₂²×D₃₁	C₂⁴	1	4	yes	—
160	C₂²×D₃₁	C₂⁴	1	2	yes	—
161	Q₈×C₃₁	—	2	2	no	—
162	D₄×C₃₁	—	2	4	no	—
163	D₄×C₃₁	#41	1	4	yes	complemented
164	C₂×C₄×C₃₁	—	2	4	no	—
165	C₂×C₄×C₃₁	—	2	4	no	—
166	C₂×C₄×C₃₁	—	2	2	no	—
167	C₂×C₄×C₃₁	—	2	2	no	—
168	C₂×C₄×C₃₁	—	2	4	no	—
169	C₂×C₄×C₃₁	—	2	2	no	—
170	C₂×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
171	C₂×C₄×C₃₁	C₂⁴	1	2	yes	—
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	2	yes	—
176	C₂×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
177	C₂×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
178	C₂×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
179	C₂²⋊D₃₁	—	2	8	no	—
180	C₂²⋊D₃₁	—	2	4	no	—
181	C₂²⋊D₃₁	—	4	4	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	D₁₂₄	—	2	8	no	—
188	D₁₂₄	—	2	4	no	—
189	D₁₂₄	—	2	4	no	—
190	D₁₂₄	—	4	2	no	—
191	D₁₂₄	#41	1	4	yes	complemented
192	C₄×D₃₁	—	2	4	no	—
193	C₄×D₃₁	—	2	4	no	—
194	C₄×D₃₁	—	2	4	no	—
195	C₄×D₃₁	—	2	8	no	—
196	C₄×D₃₁	—	4	4	no	—
197	C₄×D₃₁	—	4	4	no	—
198	Dic₆₂	—	2	2	no	—
199	Dic₆₂	—	4	2	no	—
200	#3481	—	31	1	no	maximal, Sylow
201	C₂²×C₃₁	—	2	2	no	—
202	C₂²×C₃₁	—	2	2	no	—
203	C₂²×C₃₁	—	2	1	no	—
204	C₂²×C₃₁	—	2	1	no	—
205	C₂²×C₃₁	—	2	1	no	—
206	C₂²×C₃₁	C₂×#41	1	4	yes	—
207	C₂²×C₃₁	C₂⁵	1	1	yes	characteristic
208	C₂×D₃₁	—	2	2	no	—
209	C₂×D₃₁	—	2	2	no	—
210	C₂×D₃₁	—	2	4	no	—
211	C₂×D₃₁	—	2	4	no	—
212	C₂×D₃₁	—	2	4	no	—
213	C₂×D₃₁	—	4	16	no	—
214	C₂×D₃₁	C₂×#41	1	4	yes	—
215	C₄×C₃₁	—	2	1	no	—
216	C₄×C₃₁	—	2	2	no	—
217	C₄×C₃₁	—	2	1	no	—
218	C₄×C₃₁	—	2	2	no	—
219	C₄×C₃₁	—	2	1	no	—
220	C₄×C₃₁	—	2	2	no	—
221	C₄×C₃₁	C₂×#41	1	2	yes	—
222	C₄×C₃₁	C₂×#41	1	2	yes	—
223	C₄×C₃₁	H(5,𝔽₂)	1	2	yes	—
224	Dic₃₁	—	2	2	no	—
225	Dic₃₁	—	2	2	no	—
226	Dic₃₁	—	2	4	no	—
227	Dic₃₁	—	2	2	no	—
228	#559	—	31	1	no	—
229	#554	—	31	1	no	—
230	#554	—	31	1	no	—
231	#553	—	31	2	no	—
232	#553	—	31	2	no	—
233	#551	—	31	4	no	—
234	#546	—	31	2	no	—
235	#546	—	31	2	no	—
236	D₄²	—	31	1	no	—
237	#532	—	31	1	no	—
238	#529	—	31	2	no	—
239	#529	—	31	2	no	—
240	#525	—	31	4	no	—
241	C₄×#41	—	31	1	no	—
242	C₄×#41	D₃₁	1	1	yes	characteristic, complemented
243	C₂×C₄×D₄	—	31	2	no	—
244	C₂×C₄×D₄	—	31	2	no	—
245	C₂×C₃₁	—	2	4	no	—
246	C₂×C₃₁	—	4	1	no	—
247	C₂×C₃₁	C₂²×#41	1	1	yes	characteristic
248	C₂×C₃₁	C₂²×#41	1	1	yes	characteristic
249	C₂×C₃₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
250	D₃₁	—	2	4	no	—
251	D₃₁	—	4	4	no	—
252	C₂×#41	—	31	1	no	—
253	C₂×#41	—	31	2	no	—
254	C₂×#41	C₂×D₃₁	1	1	yes	characteristic
255	C₂²×D₄	—	31	2	no	—
256	C₂²×D₄	—	31	2	no	—
257	C₂³×C₄	—	31	4	no	—
258	C₄⋊Q₈	—	31	1	no	—
259	#127	—	31	1	no	—
260	#126	—	31	4	no	—
261	#126	—	31	4	no	—
262	#125	—	31	2	no	—
263	#125	—	31	2	no	—
264	#124	—	31	2	no	—
265	#124	—	31	2	no	—
266	#124	—	31	2	no	—
267	#123	—	31	4	no	—
268	#123	—	31	4	no	—
269	#123	—	31	4	no	—
270	#123	—	31	4	no	—
271	C₂²⋊Q₈	—	31	2	no	—
272	C₂²⋊Q₈	—	31	2	no	—
273	C₂²⋊Q₈	—	31	4	no	—
274	C₂²⋊Q₈	—	31	4	no	—
275	#121	—	31	4	no	—
276	#121	—	31	2	no	—
277	#121	—	31	2	no	—
278	#121	—	31	2	no	—
279	#121	—	31	2	no	—
280	#121	—	31	4	no	—
281	#120	—	31	4	no	—
282	#120	—	31	4	no	—
283	C₄×Q₈	—	31	1	no	—
284	C₄×Q₈	—	31	1	no	—
285	C₄×Q₈	C₂×D₃₁	1	1	yes	characteristic, complemented
286	C₄×Q₈	C₂×D₃₁	1	1	yes	characteristic, complemented
287	C₄×D₄	—	31	2	no	—
288	C₄×D₄	—	31	4	no	—
289	C₄×D₄	—	31	2	no	—
290	C₄×D₄	—	31	2	no	—
291	C₄×D₄	—	31	2	no	—
292	C₄×D₄	—	31	4	no	—
293	C₄×D₄	—	31	1	no	—
294	C₄×D₄	—	31	4	no	—
295	C₄×D₄	—	31	2	no	—
296	C₄×D₄	—	31	2	no	—
297	C₄×D₄	—	31	2	no	—
298	C₄×D₄	—	31	4	no	—
299	C₄×D₄	—	31	2	no	—
300	C₄×D₄	—	31	1	no	—
301	C₄×D₄	C₂×D₃₁	1	1	yes	characteristic
302	C₄×D₄	C₂×D₃₁	1	1	yes	characteristic
303	C₄×D₄	C₂×D₃₁	1	2	yes	complemented
304	C₄×D₄	C₂×D₃₁	1	2	yes	complemented
305	#117	—	31	1	no	—
306	#117	—	31	2	no	—
307	#117	—	31	4	no	—
308	#117	C₂×D₃₁	1	2	yes	complemented
309	#117	C₂×D₃₁	1	1	yes	characteristic, complemented
310	C₂×C₄⋊C₄	—	31	2	no	—
311	C₂×C₄⋊C₄	—	31	2	no	—
312	C₂×C₂²⋊C₄	—	31	4	no	—
313	C₂×C₂²⋊C₄	—	31	4	no	—
314	C₂×C₄²	—	31	2	no	—
315	C₂×C₄²	C₂×D₃₁	1	2	yes	complemented
316	C₂×C₄²	C₂×D₃₁	1	1	yes	characteristic, complemented
317	C₃₁	#3481	1	1	yes	characteristic, complemented, Sylow
318	C₂⁴	—	31	4	no	—
319	#41	—	2	4	no	—
320	#41	—	62	4	no	—
321	#41	—	124	4	no	—
322	C₂×Q₈	—	31	1	no	—
323	C₂×Q₈	—	31	2	no	—
324	C₂×Q₈	C₂²×D₃₁	1	1	yes	characteristic
325	C₂×D₄	—	31	2	no	—
326	C₂×D₄	—	31	4	no	—
327	C₂×D₄	—	31	4	no	—
328	C₂×D₄	—	31	1	no	—
329	C₂×D₄	—	31	4	no	—
330	C₂×D₄	—	31	2	no	—
331	C₂×D₄	—	31	2	no	—
332	C₂×D₄	—	31	2	no	—
333	C₂×D₄	—	62	8	no	—
334	C₂×D₄	—	62	8	no	—
335	C₂×D₄	C₂²×D₃₁	1	2	yes	—
336	C₂×D₄	C₂²×D₃₁	1	1	yes	characteristic
337	C₂²×C₄	—	31	4	no	—
338	C₂²×C₄	—	31	2	no	—
339	C₂²×C₄	—	31	2	no	—
340	C₂²×C₄	—	31	2	no	—
341	C₂²×C₄	—	31	4	no	—
342	C₂²×C₄	—	31	4	no	—
343	C₂²×C₄	—	31	4	no	—
344	C₂²×C₄	—	124	8	no	—
345	C₂²×C₄	C₂²×D₃₁	1	2	yes	—
346	C₂²×C₄	C₂²×D₃₁	1	2	yes	—
347	C₂²×C₄	C₂²×D₃₁	1	1	yes	characteristic
348	C₂²×C₄	C₂²×D₃₁	1	1	yes	characteristic
349	C₂²×C₄	C₂²×D₃₁	1	2	yes	—
350	C₂²×C₄	C₂²×D₃₁	1	1	yes	characteristic
351	C₄⋊C₄	—	31	4	no	—
352	C₄⋊C₄	—	31	2	no	—
353	C₄⋊C₄	—	31	2	no	—
354	C₄⋊C₄	—	31	4	no	—
355	C₄⋊C₄	—	31	4	no	—
356	C₄⋊C₄	—	31	1	no	—
357	C₄⋊C₄	—	31	2	no	—
358	C₄⋊C₄	—	31	2	no	—
359	C₄⋊C₄	—	31	4	no	—
360	C₄⋊C₄	—	31	1	no	—
361	C₄⋊C₄	C₂²×D₃₁	1	1	yes	characteristic
362	C₄⋊C₄	C₂²×D₃₁	1	1	yes	characteristic
363	C₄⋊C₄	C₂²×D₃₁	1	2	yes	—
364	C₄⋊C₄	C₂²×D₃₁	1	2	yes	—
365	C₂²⋊C₄	—	31	4	no	—
366	C₂²⋊C₄	—	31	2	no	—
367	C₂²⋊C₄	—	31	2	no	—
368	C₂²⋊C₄	—	31	4	no	—
369	C₂²⋊C₄	—	31	4	no	—
370	C₂²⋊C₄	—	31	4	no	—
371	C₂²⋊C₄	—	31	4	no	—
372	C₂²⋊C₄	—	31	4	no	—
373	C₂²⋊C₄	—	31	2	no	—
374	C₂²⋊C₄	—	31	4	no	—
375	C₂²⋊C₄	—	31	4	no	—
376	C₂²⋊C₄	C₂²×D₃₁	1	2	yes	—
377	C₂²⋊C₄	C₂²×D₃₁	1	2	yes	—
378	C₂²⋊C₄	C₂²×D₃₁	1	2	yes	—
379	C₄²	—	31	2	no	—
380	C₄²	—	31	2	no	—
381	C₄²	—	31	2	no	—
382	C₄²	C₂²×D₃₁	1	1	yes	characteristic
383	C₄²	C₂²×D₃₁	1	2	yes	—
384	C₄²	C₂²×D₃₁	1	2	yes	—
385	C₄²	C₂²×D₃₁	1	1	yes	characteristic
386	C₄²	C₂²×D₃₁	1	1	yes	characteristic
387	C₄²	C₂²×D₃₁	1	1	yes	characteristic
388	C₄²	C₂²×D₃₁	1	2	yes	—
389	C₂³	—	31	2	no	—
390	C₂³	—	31	4	no	—
391	C₂³	—	62	8	no	—
392	C₂³	—	62	8	no	—
393	C₂³	—	124	4	no	—
394	C₂³	C₂³×D₃₁	1	1	yes	characteristic
395	C₂³	C₂³×D₃₁	1	2	yes	—
396	Q₈	—	2	2	no	—
397	Q₈	—	62	2	no	—
398	Q₈	—	124	2	no	—
399	D₄	—	2	4	no	—
400	D₄	—	31	4	no	—
401	D₄	—	62	8	no	—
402	D₄	—	62	4	no	—
403	D₄	—	62	8	no	—
404	D₄	—	62	4	no	—
405	D₄	—	62	4	no	—
406	D₄	—	124	2	no	—
407	D₄	—	124	4	no	—
408	D₄	#92495	1	4	yes	complemented
409	C₂×C₄	—	2	4	no	—
410	C₂×C₄	—	2	2	no	—
411	C₂×C₄	—	2	4	no	—
412	C₂×C₄	—	2	2	no	—
413	C₂×C₄	—	2	4	no	—
414	C₂×C₄	—	2	2	no	—
415	C₂×C₄	—	31	2	no	—
416	C₂×C₄	—	31	2	no	—
417	C₂×C₄	—	31	2	no	—
418	C₂×C₄	—	31	4	no	—
419	C₂×C₄	—	62	4	no	—
420	C₂×C₄	—	62	4	no	—
421	C₂×C₄	—	62	4	no	—
422	C₂×C₄	—	62	8	no	—
423	C₂×C₄	—	124	4	no	—
424	C₂×C₄	—	124	4	no	—
425	C₂×C₄	—	124	4	no	—
426	C₂×C₄	C₂³×D₃₁	1	1	yes	characteristic
427	C₂×C₄	C₂³×D₃₁	1	1	yes	characteristic
428	C₂×C₄	C₂³×D₃₁	1	2	yes	—
429	C₂×C₄	C₂³×D₃₁	1	2	yes	—
430	C₂×C₄	C₂³×D₃₁	1	2	yes	—
431	C₂×C₄	C₂³×D₃₁	1	1	yes	characteristic
432	C₂×C₄	C₂³×D₃₁	1	1	yes	characteristic
433	C₂×C₄	C₂³×D₃₁	1	1	yes	characteristic
434	C₂×C₄	C₂³×D₃₁	1	1	yes	characteristic
435	C₂²	—	2	2	no	—
436	C₂²	—	2	2	no	—
437	C₂²	—	2	1	no	—
438	C₂²	—	2	1	no	—
439	C₂²	—	2	1	no	—
440	C₂²	—	31	4	no	—
441	C₂²	—	62	2	no	—
442	C₂²	—	62	2	no	—
443	C₂²	—	62	4	no	—
444	C₂²	—	62	4	no	—
445	C₂²	—	62	4	no	—
446	C₂²	—	124	16	no	—
447	C₂²	C₂×#92495	1	4	yes	—
448	C₂²	C₂⁴×D₃₁	1	1	yes	characteristic
449	C₄	—	2	1	no	—
450	C₄	—	2	2	no	—
451	C₄	—	2	1	no	—
452	C₄	—	2	2	no	—
453	C₄	—	2	2	no	—
454	C₄	—	2	1	no	—
455	C₄	—	62	2	no	—
456	C₄	—	62	2	no	—
457	C₄	—	62	2	no	—
458	C₄	—	62	4	no	—
459	C₄	C₂×#92495	1	2	yes	—
460	C₄	#41×D₃₁	1	2	yes	—
461	C₄	#11758566	1	2	yes	—
462	C₂	—	2	4	no	—
463	C₂	—	4	1	no	—
464	C₂	—	62	4	no	—
465	C₂	—	124	4	no	—
466	C₂	C₂×#41×D₃₁	1	1	yes	characteristic
467	C₂	C₂²×#92495	1	1	yes	characteristic
468	C₂	C₂×#11758566	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	#3481
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. #14521784	C₂	semidirect
2. #14521759	C₂	semidirect
3. #14521756	C₂	semidirect
4. #14521745	C₂	semidirect
5. #14521743	C₂	semidirect
6. #14521723	C₂	semidirect
7. #14521695	C₂	semidirect
8. #14521687	C₂	semidirect
9. D₄×D₁₂₄	C₂	semidirect
10. #14521599	C₂	semidirect
11. #14521586	C₂	semidirect
12. #14521583	C₂	semidirect
13. #14521558	C₂	semidirect
14. C₄×#92495	C₂	semidirect
15. C₂×C₄×D₁₂₄	C₂	semidirect
16. C₄×D₄×D₃₁	C₂	semidirect
17. C₄×#41×C₃₁	C₂	semidirect
21. C₂×#92495	C₂²	semidirect
23. C₂²×C₄×D₃₁	C₂²	semidirect
24. C₄×Q₈×C₃₁	C₂²	semidirect
25. C₄×Q₈×C₃₁	C₂²	semidirect
28. C₄×D₄×C₃₁	C₂²	semidirect
29. C₄×D₄×C₃₁	C₂²	semidirect
30. C₃₁×#117	C₂²	semidirect
31. C₃₁×#117	C₂²	semidirect
32. C₂×C₄²×C₃₁	C₂²	semidirect
33. C₂×C₄²×C₃₁	C₂²	semidirect
34. #11758524	C₂²	semidirect
35. #11758523	C₂²	semidirect
36. #11758516	C₂²	semidirect
37. #11758514	C₂²	semidirect
40. #11758507	C₂²	semidirect
41. #11758507	C₂²	semidirect
42. #11758506	C₂²	semidirect
43. C₄×C₂²⋊D₃₁	C₂²	semidirect
44. C₄×C₂²⋊D₃₁	C₂²	semidirect
45. C₄×C₂²⋊D₃₁	C₂²	semidirect
46. C₂×(C₂×D₃₁)⋊C₄	C₂²	semidirect
47. #11758503	C₂²	semidirect
48. C₂×C₄⋊Dic₃₁	C₂²	semidirect
49. #11758501	C₂²	semidirect
50. #11758475	C₂²	semidirect
51. #11758473	C₂²	semidirect
53. #11758471	C₂²	semidirect
54. #11758471	C₂²	semidirect
55. #11758470	C₂²	semidirect
56. C₄⋊C₄×D₃₁	C₂²	semidirect
57. #11758467	C₂²	semidirect
58. #11758461	C₂²	semidirect
59. #11758460	C₂²	semidirect
61. (C₂²⋊D₃₁)⋊C₄	C₂²	semidirect
62. C₂²⋊C₄×D₃₁	C₂²	semidirect
63. #11758455	C₂²	semidirect
64. #11758453	C₂²	semidirect
65. #11758452	C₂²	semidirect
66. #11758452	C₂²	semidirect
71. C₄×D₁₂₄	C₂²	semidirect
72. C₄×D₁₂₄	C₂²	semidirect
73. C₄×D₁₂₄	C₂²	semidirect
74. C₄×D₁₂₄	C₂²	semidirect
75. C₄×D₁₂₄	C₂²	semidirect
76. #11758449	C₂²	semidirect
77. #11758449	C₂²	semidirect
78. C₄²×D₃₁	C₂²	semidirect
79. #11758447	C₂²	semidirect
80. #11758446	C₂²	semidirect
81. C₄×Dic₆₂	C₂²	semidirect
82. C₄×Dic₆₂	C₂²	semidirect
163. D₄×C₃₁	#41	semidirect
191. D₁₂₄	#41	semidirect
242. C₄×#41	D₃₁	semidirect
285. C₄×Q₈	C₂×D₃₁	semidirect
286. C₄×Q₈	C₂×D₃₁	semidirect
303. C₄×D₄	C₂×D₃₁	semidirect
304. C₄×D₄	C₂×D₃₁	semidirect
308. #117	C₂×D₃₁	semidirect
309. #117	C₂×D₃₁	semidirect
315. C₂×C₄²	C₂×D₃₁	semidirect
316. C₂×C₄²	C₂×D₃₁	semidirect
317. C₃₁	#3481	semidirect
408. D₄	#92495	semidirect

Maximal subgroups

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

subgroup	index
#14521784	2
#14521759	2
#14521756	2
#14521745	2
#14521743	2
#14521723	2
#14521695	2
#14521687	2
D₄×D₁₂₄	2
#14521599	2
#14521586	2
#14521583	2
#14521558	2
C₄×#92495	2
C₂×C₄×D₁₂₄	2
C₄×D₄×D₃₁	2
C₄×#41×C₃₁	2
#3481	31