Subgroups — #28404370

Order 14464.

1100 conjugacy classes of subgroups.

The subgroup lattice has 440 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20299306	C₂	1	2	yes	maximal, complemented
2	#20299303	C₂	1	4	yes	maximal, complemented
3	#20299303	C₂	1	2	yes	maximal, complemented
4	#20299302	C₂	1	4	yes	maximal, complemented
5	Q₈×C₂²⋊D₁₁₃	C₂	1	2	yes	maximal, complemented
6	#20299261	C₂	1	2	yes	maximal, complemented
7	#20299227	C₂	1	2	yes	maximal, complemented
8	#20299224	C₂	1	2	yes	maximal, complemented
9	#20299223	C₂	1	2	yes	maximal, complemented
10	#20299150	C₂	1	2	yes	maximal, complemented
11	C₂×#16813601	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²⋊Q₈×D₁₁₃	C₂	1	2	yes	maximal, complemented
13	#20299071	C₂	1	2	yes	maximal
14	C₂×C₄×C₂²⋊D₁₁₃	C₂	1	1	yes	maximal, characteristic
15	C₂×C₂²⋊Q₈×C₁₁₃	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×Dic₂₂₆	C₂²	1	1	yes	characteristic, complemented
17	C₂×Q₈×D₁₁₃	C₂²	1	2	yes	complemented
18	C₂²×C₂²⋊D₁₁₃	C₂²	1	1	yes	characteristic
19	C₂²×C₄×D₁₁₃	C₂²	1	1	yes	characteristic
20	#16813621	C₂²	1	2	yes	complemented
21	#16813621	C₂²	1	4	yes	complemented
22	#16813620	C₂²	1	4	yes	complemented
23	#16813620	C₂²	1	2	yes	complemented
24	#16813612	C₂²	1	4	yes	complemented
25	#16813612	C₂²	1	4	yes	complemented
26	#16813612	C₂²	1	4	yes	complemented
27	#16813602	C₂²	1	4	yes	complemented
28	#16813602	C₂²	1	2	yes	complemented
29	#16813601	C₂²	1	2	yes	—
30	#16813601	C₂²	1	2	yes	—
31	#16813601	C₂²	1	2	yes	complemented
32	#16813601	C₂²	1	4	yes	complemented
33	#16813601	C₂²	1	2	yes	complemented
34	#16813601	C₂²	1	4	yes	complemented
35	#16813600	C₂²	1	4	yes	complemented
36	#16813600	C₂²	1	4	yes	complemented
37	#16813600	C₂²	1	4	yes	complemented
38	#16813599	C₂²	1	4	yes	—
39	#16813599	C₂²	1	4	yes	—
40	#16813599	C₂²	1	4	yes	complemented
41	#16813599	C₂²	1	4	yes	complemented
42	#16813598	C₂²	1	4	yes	complemented
43	#16813598	C₂²	1	2	yes	complemented
44	Q₈×Dic₁₁₃	C₂²	1	2	yes	complemented
45	#16813587	C₂²	1	4	yes	complemented
46	#16813587	C₂²	1	2	yes	complemented
47	C₄×C₂²⋊D₁₁₃	C₂²	1	2	yes	—
48	C₄×C₂²⋊D₁₁₃	C₂²	1	2	yes	—
49	C₄×C₂²⋊D₁₁₃	C₂²	1	4	yes	—
50	C₄×C₂²⋊D₁₁₃	C₂²	1	2	yes	—
51	C₄×C₂²⋊D₁₁₃	C₂²	1	4	yes	—
52	C₄×C₂²⋊D₁₁₃	C₂²	1	2	yes	—
53	#16813582	C₂²	1	4	yes	—
54	#16813582	C₂²	1	4	yes	—
55	#16813578	C₂²	1	4	yes	—
56	C₂×C₄⋊Dic₁₁₃	C₂²	1	1	yes	characteristic, complemented
57	C₂×#14268626	C₂²	1	1	yes	characteristic
58	C₂×#14268626	C₂²	1	2	yes	complemented
59	C₄⋊C₄×D₁₁₃	C₂²	1	4	yes	complemented
60	C₄⋊C₄×D₁₁₃	C₂²	1	2	yes	complemented
61	C₂×C₂²⋊Dic₁₁₃	C₂²	1	1	yes	characteristic
62	C₂×C₂²⋊Dic₁₁₃	C₂²	1	2	yes	—
63	C₂×#14268624	C₂²	1	1	yes	characteristic
64	C₂²⋊C₄×D₁₁₃	C₂²	1	4	yes	—
65	C₂×C₄×Dic₁₁₃	C₂²	1	1	yes	characteristic
66	C₂²×Q₈×C₁₁₃	C₂²	1	1	yes	characteristic, complemented
67	C₂³×C₄×C₁₁₃	C₂²	1	1	yes	characteristic
68	C₂²⋊Q₈×C₁₁₃	C₂²	1	2	yes	—
69	C₂²⋊Q₈×C₁₁₃	C₂²	1	2	yes	—
70	C₂²⋊Q₈×C₁₁₃	C₂²	1	2	yes	complemented
71	C₂²⋊Q₈×C₁₁₃	C₂²	1	2	yes	complemented
72	C₂×C₄⋊C₄×C₁₁₃	C₂²	1	2	yes	complemented
73	C₂×C₄⋊C₄×C₁₁₃	C₂²	1	1	yes	characteristic, complemented
74	C₂×C₂²⋊C₄×C₁₁₃	C₂²	1	2	yes	—
75	C₂³×D₁₁₃	C₂³	1	1	yes	characteristic
76	C₂×Dic₂₂₆	—	4	2	no	—
77	C₂×Dic₂₂₆	C₂³	1	2	yes	—
78	C₂×Dic₂₂₆	C₂³	1	4	yes	—
79	C₂×Dic₂₂₆	C₂³	1	4	yes	—
80	C₂×Dic₂₂₆	C₂³	1	2	yes	—
81	Q₈×D₁₁₃	—	4	4	no	—
82	C₂×C₂²⋊D₁₁₃	Q₈	1	8	yes	complemented
83	C₂×C₂²⋊D₁₁₃	C₂³	1	2	yes	—
84	C₂×C₂²⋊D₁₁₃	C₂³	1	2	yes	—
85	C₂²×Dic₁₁₃	C₂³	1	1	yes	characteristic
86	C₂²×Dic₁₁₃	C₂³	1	1	yes	characteristic
87	C₂²×Dic₁₁₃	C₂³	1	2	yes	—
88	C₂²×Dic₁₁₃	C₂³	1	2	yes	—
89	C₂²×Dic₁₁₃	C₂³	1	1	yes	characteristic
90	C₂×C₄×D₁₁₃	—	4	2	no	—
91	C₂×C₄×D₁₁₃	C₂³	1	2	yes	—
92	C₂×C₄×D₁₁₃	C₂³	1	4	yes	—
93	C₂×C₄×D₁₁₃	C₂³	1	4	yes	—
94	C₂×C₄×D₁₁₃	C₂³	1	2	yes	—
95	C₄⋊Dic₁₁₃	C₂³	1	2	yes	—
96	C₄⋊Dic₁₁₃	C₂³	1	4	yes	—
97	C₄⋊Dic₁₁₃	C₂³	1	2	yes	—
98	C₄⋊Dic₁₁₃	C₂³	1	4	yes	—
99	#14268626	C₂³	1	4	yes	—
100	#14268626	C₂³	1	4	yes	—
101	#14268626	C₂³	1	4	yes	—
102	#14268626	C₂³	1	2	yes	—
103	#14268626	C₂³	1	2	yes	—
104	#14268626	C₂³	1	4	yes	—
105	#14268626	C₂³	1	4	yes	—
106	#14268626	C₂³	1	4	yes	—
107	#14268626	C₂³	1	4	yes	—
108	#14268626	C₂³	1	4	yes	—
109	C₂²⋊Dic₁₁₃	C₂³	1	4	yes	—
110	C₂²⋊Dic₁₁₃	C₂³	1	2	yes	—
111	C₂²⋊Dic₁₁₃	C₂³	1	2	yes	—
112	C₂²⋊Dic₁₁₃	C₂³	1	4	yes	—
113	#14268624	C₂³	1	4	yes	—
114	#14268624	C₂³	1	4	yes	—
115	#14268624	C₂³	1	2	yes	—
116	#14268624	C₂³	1	2	yes	—
117	C₄×Dic₁₁₃	C₂³	1	2	yes	—
118	C₄×Dic₁₁₃	C₂³	1	2	yes	—
119	C₄×Dic₁₁₃	C₂³	1	4	yes	—
120	C₄×Dic₁₁₃	C₂³	1	4	yes	—
121	C₂⁴×C₁₁₃	C₂³	1	1	yes	characteristic
122	C₂×Q₈×C₁₁₃	—	4	2	no	—
123	C₂×Q₈×C₁₁₃	C₂³	1	2	yes	—
124	C₂×Q₈×C₁₁₃	C₂³	1	2	yes	—
125	C₂²×C₄×C₁₁₃	—	4	2	no	—
126	C₂²×C₄×C₁₁₃	C₂³	1	1	yes	characteristic
127	C₂²×C₄×C₁₁₃	C₂³	1	1	yes	characteristic
128	C₂²×C₄×C₁₁₃	C₂³	1	1	yes	characteristic
129	C₂²×C₄×C₁₁₃	C₂³	1	1	yes	characteristic
130	C₂²×C₄×C₁₁₃	C₂³	1	1	yes	characteristic
131	C₂²×C₄×C₁₁₃	C₂³	1	2	yes	—
132	C₂²×C₄×C₁₁₃	C₂³	1	2	yes	—
133	C₂²×C₄×C₁₁₃	C₂³	1	1	yes	characteristic
134	C₄⋊C₄×C₁₁₃	C₂³	1	4	yes	—
135	C₄⋊C₄×C₁₁₃	C₂³	1	2	yes	—
136	C₄⋊C₄×C₁₁₃	C₂³	1	2	yes	—
137	C₄⋊C₄×C₁₁₃	C₂³	1	4	yes	—
138	C₂²⋊C₄×C₁₁₃	C₂³	1	4	yes	—
139	C₂²⋊C₄×C₁₁₃	C₂³	1	4	yes	—
140	C₂³×C₁₁₃	—	4	1	no	—
141	C₂³×C₁₁₃	—	4	1	no	—
142	C₂³×C₁₁₃	C₂×Q₈	1	4	yes	complemented
143	C₂³×C₁₁₃	C₂⁴	1	1	yes	characteristic
144	C₂³×C₁₁₃	C₂⁴	1	1	yes	characteristic
145	C₂³×C₁₁₃	C₂⁴	1	1	yes	characteristic
146	C₂²×D₁₁₃	—	4	1	no	—
147	C₂²×D₁₁₃	—	4	1	no	—
148	C₂²×D₁₁₃	C₂×Q₈	1	4	yes	complemented
149	C₂²×D₁₁₃	C₂⁴	1	2	yes	—
150	Q₈×C₁₁₃	—	2	4	no	—
151	Q₈×C₁₁₃	—	4	2	no	—
152	C₂×C₄×C₁₁₃	—	2	2	no	—
153	C₂×C₄×C₁₁₃	—	2	2	no	—
154	C₂×C₄×C₁₁₃	—	2	2	no	—
155	C₂×C₄×C₁₁₃	—	4	1	no	—
156	C₂×C₄×C₁₁₃	—	4	1	no	—
157	C₂×C₄×C₁₁₃	—	4	1	no	—
158	C₂×C₄×C₁₁₃	—	4	2	no	—
159	C₂×C₄×C₁₁₃	—	4	2	no	—
160	C₂×C₄×C₁₁₃	C₂⁴	1	4	yes	—
161	C₂×C₄×C₁₁₃	C₂⁴	1	4	yes	—
162	C₂×C₄×C₁₁₃	C₂⁴	1	1	yes	characteristic
163	C₂×C₄×C₁₁₃	C₂⁴	1	1	yes	characteristic
164	C₂×C₄×C₁₁₃	C₂⁴	1	1	yes	characteristic
165	C₂×C₄×C₁₁₃	C₂⁴	1	1	yes	characteristic
166	C₂²⋊D₁₁₃	C₂×Q₈	1	8	yes	complemented
167	C₂²⋊D₁₁₃	C₂×Q₈	1	8	yes	complemented
168	C₂×Dic₁₁₃	—	4	1	no	—
169	C₂×Dic₁₁₃	—	4	1	no	—
170	C₂×Dic₁₁₃	—	4	2	no	—
171	C₂×Dic₁₁₃	—	4	2	no	—
172	C₂×Dic₁₁₃	C₂×Q₈	1	4	yes	complemented
173	C₂×Dic₁₁₃	C₂⁴	1	2	yes	—
174	C₂×Dic₁₁₃	C₂⁴	1	4	yes	—
175	C₂×Dic₁₁₃	C₂⁴	1	4	yes	—
176	C₂×Dic₁₁₃	C₂⁴	1	2	yes	—
177	C₂×Dic₁₁₃	C₂⁴	1	2	yes	—
178	C₄×D₁₁₃	—	2	4	no	—
179	C₄×D₁₁₃	—	4	2	no	—
180	C₄×D₁₁₃	—	4	4	no	—
181	C₄×D₁₁₃	—	4	4	no	—
182	Dic₂₂₆	—	2	4	no	—
183	Dic₂₂₆	—	4	4	no	—
184	Dic₂₂₆	—	4	2	no	—
185	Dic₂₂₆	—	4	4	no	—
186	C₂²×C₁₁₃	—	2	1	no	—
187	C₂²×C₁₁₃	—	2	1	no	—
188	C₂²×C₁₁₃	—	2	1	no	—
189	C₂²×C₁₁₃	—	2	1	no	—
190	C₂²×C₁₁₃	—	2	1	no	—
191	C₂²×C₁₁₃	—	2	1	no	—
192	C₂²×C₁₁₃	—	4	4	no	—
193	C₂²×C₁₁₃	C₂²×Q₈	1	2	yes	—
194	C₂²×C₁₁₃	C₂²×Q₈	1	2	yes	—
195	C₂²×C₁₁₃	C₂²×Q₈	1	2	yes	—
196	C₂²×C₁₁₃	C₂⁵	1	1	yes	characteristic
197	C₂×D₁₁₃	—	2	2	no	—
198	C₂×D₁₁₃	—	2	2	no	—
199	C₂×D₁₁₃	—	4	4	no	—
200	C₂×D₁₁₃	C₂²×Q₈	1	4	yes	—
201	C₄×C₁₁₃	—	2	1	no	—
202	C₄×C₁₁₃	—	2	4	no	—
203	C₄×C₁₁₃	—	2	1	no	—
204	C₄×C₁₁₃	—	2	1	no	—
205	C₄×C₁₁₃	—	2	4	no	—
206	C₄×C₁₁₃	H(5,𝔽₂)	1	2	yes	—
207	Dic₁₁₃	—	2	4	no	—
208	Dic₁₁₃	—	2	2	no	—
209	Dic₁₁₃	—	2	2	no	—
210	Dic₁₁₃	—	2	4	no	—
211	Dic₁₁₃	C₂²×Q₈	1	4	yes	—
212	C₂×C₁₁₃	—	2	2	no	—
213	C₂×C₁₁₃	—	2	2	no	—
214	C₂×C₁₁₃	—	2	2	no	—
215	C₂×C₁₁₃	C₂³×Q₈	1	1	yes	characteristic
216	C₂×C₁₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
217	C₂×C₁₁₃	#585	1	1	yes	characteristic
218	D₁₁₃	—	2	4	no	—
219	#3501	—	113	1	no	maximal, Sylow
220	C₁₁₃	#3501	1	1	yes	characteristic, complemented, Sylow
221	#554	—	113	4	no	—
222	#554	—	113	2	no	—
223	#554	—	113	2	no	—
224	#554	—	113	4	no	—
225	D₄×Q₈	—	113	2	no	—
226	D₄×Q₈	—	113	2	no	—
227	#544	—	113	2	no	—
228	#543	—	113	2	no	—
229	#543	—	113	2	no	—
230	#533	—	113	2	no	—
231	C₂×C₂²⋊Q₈	—	113	1	no	—
232	C₂×C₂²⋊Q₈	—	113	2	no	—
233	C₂×C₂²⋊Q₈	D₁₁₃	1	1	yes	characteristic, complemented
234	#518	—	113	2	no	—
235	C₂×C₄×D₄	—	113	1	no	—
236	C₂²×Q₈	—	113	2	no	—
237	C₂²×Q₈	—	113	1	no	—
238	C₂²×Q₈	C₂×D₁₁₃	1	1	yes	characteristic, complemented
239	C₂²×D₄	—	113	1	no	—
240	C₂³×C₄	—	113	1	no	—
241	C₂³×C₄	C₂×D₁₁₃	1	1	yes	characteristic
242	C₄⋊Q₈	—	113	2	no	—
243	C₄⋊Q₈	—	113	4	no	—
244	C₄⋊Q₈	—	113	2	no	—
245	C₄⋊Q₈	—	113	4	no	—
246	#125	—	113	4	no	—
247	#125	—	113	4	no	—
248	#125	—	113	4	no	—
249	C₂²⋊Q₈	—	113	2	no	—
250	C₂²⋊Q₈	—	113	4	no	—
251	C₂²⋊Q₈	—	113	2	no	—
252	C₂²⋊Q₈	—	113	2	no	—
253	C₂²⋊Q₈	—	113	2	no	—
254	C₂²⋊Q₈	—	113	2	no	—
255	C₂²⋊Q₈	—	113	4	no	—
256	C₂²⋊Q₈	—	113	4	no	—
257	C₂²⋊Q₈	—	113	4	no	—
258	C₂²⋊Q₈	—	113	2	no	—
259	C₂²⋊Q₈	—	113	4	no	—
260	C₂²⋊Q₈	—	113	4	no	—
261	C₂²⋊Q₈	—	113	4	no	—
262	C₂²⋊Q₈	—	113	4	no	—
263	C₂²⋊Q₈	—	113	4	no	—
264	C₂²⋊Q₈	—	113	4	no	—
265	C₂²⋊Q₈	—	113	4	no	—
266	C₂²⋊Q₈	C₂×D₁₁₃	1	2	yes	—
267	C₂²⋊Q₈	C₂×D₁₁₃	1	2	yes	—
268	C₂²⋊Q₈	C₂×D₁₁₃	1	2	yes	complemented
269	C₂²⋊Q₈	C₂×D₁₁₃	1	2	yes	complemented
270	C₄×Q₈	—	113	2	no	—
271	C₄×Q₈	—	113	2	no	—
272	C₄×Q₈	—	113	4	no	—
273	C₄×D₄	—	113	2	no	—
274	C₄×D₄	—	113	2	no	—
275	C₄×D₄	—	113	2	no	—
276	C₄×D₄	—	113	2	no	—
277	C₄×D₄	—	113	4	no	—
278	C₄×D₄	—	113	4	no	—
279	C₄×D₄	—	113	4	no	—
280	C₄×D₄	—	113	4	no	—
281	#117	—	113	4	no	—
282	C₂×C₄⋊C₄	—	113	1	no	—
283	C₂×C₄⋊C₄	—	113	2	no	—
284	C₂×C₄⋊C₄	—	113	1	no	—
285	C₂×C₄⋊C₄	—	113	4	no	—
286	C₂×C₄⋊C₄	—	113	2	no	—
287	C₂×C₄⋊C₄	C₂×D₁₁₃	1	2	yes	complemented
288	C₂×C₄⋊C₄	C₂×D₁₁₃	1	1	yes	characteristic, complemented
289	C₂×C₂²⋊C₄	—	113	1	no	—
290	C₂×C₂²⋊C₄	—	113	2	no	—
291	C₂×C₂²⋊C₄	—	113	1	no	—
292	C₂×C₂²⋊C₄	—	113	4	no	—
293	C₂×C₂²⋊C₄	C₂×D₁₁₃	1	2	yes	—
294	C₂×C₄²	—	113	1	no	—
295	C₂⁴	—	113	1	no	—
296	C₂⁴	C₂²×D₁₁₃	1	1	yes	characteristic
297	C₂×Q₈	—	4	2	no	—
298	C₂×Q₈	—	113	4	no	—
299	C₂×Q₈	—	113	2	no	—
300	C₂×Q₈	—	113	4	no	—
301	C₂×Q₈	—	113	2	no	—
302	C₂×Q₈	—	452	2	no	—
303	C₂×Q₈	—	452	4	no	—
304	C₂×Q₈	C₂²×D₁₁₃	1	2	yes	—
305	C₂×Q₈	C₂²×D₁₁₃	1	2	yes	—
306	C₂×D₄	—	113	8	no	—
307	C₂×D₄	—	113	2	no	—
308	C₂×D₄	—	113	2	no	—
309	C₂²×C₄	—	4	2	no	—
310	C₂²×C₄	—	113	1	no	—
311	C₂²×C₄	—	113	1	no	—
312	C₂²×C₄	—	113	2	no	—
313	C₂²×C₄	—	113	2	no	—
314	C₂²×C₄	—	113	1	no	—
315	C₂²×C₄	—	113	4	no	—
316	C₂²×C₄	—	113	4	no	—
317	C₂²×C₄	—	113	2	no	—
318	C₂²×C₄	—	113	2	no	—
319	C₂²×C₄	—	452	2	no	—
320	C₂²×C₄	C₂²×D₁₁₃	1	1	yes	characteristic
321	C₂²×C₄	C₂²×D₁₁₃	1	1	yes	characteristic
322	C₂²×C₄	C₂²×D₁₁₃	1	1	yes	characteristic
323	C₂²×C₄	C₂²×D₁₁₃	1	1	yes	characteristic
324	C₂²×C₄	C₂²×D₁₁₃	1	2	yes	—
325	C₂²×C₄	C₂²×D₁₁₃	1	2	yes	—
326	C₂²×C₄	C₂²×D₁₁₃	1	1	yes	characteristic
327	C₂²×C₄	C₂²×D₁₁₃	1	1	yes	characteristic
328	C₄⋊C₄	—	113	4	no	—
329	C₄⋊C₄	—	113	2	no	—
330	C₄⋊C₄	—	113	2	no	—
331	C₄⋊C₄	—	113	2	no	—
332	C₄⋊C₄	—	113	4	no	—
333	C₄⋊C₄	—	113	2	no	—
334	C₄⋊C₄	—	113	4	no	—
335	C₄⋊C₄	—	113	4	no	—
336	C₄⋊C₄	—	113	4	no	—
337	C₄⋊C₄	—	113	4	no	—
338	C₄⋊C₄	—	113	4	no	—
339	C₄⋊C₄	—	113	4	no	—
340	C₄⋊C₄	—	113	4	no	—
341	C₄⋊C₄	—	113	4	no	—
342	C₄⋊C₄	C₂²×D₁₁₃	1	4	yes	—
343	C₄⋊C₄	C₂²×D₁₁₃	1	2	yes	—
344	C₄⋊C₄	C₂²×D₁₁₃	1	2	yes	—
345	C₄⋊C₄	C₂²×D₁₁₃	1	4	yes	—
346	C₂²⋊C₄	—	113	4	no	—
347	C₂²⋊C₄	—	113	2	no	—
348	C₂²⋊C₄	—	113	2	no	—
349	C₂²⋊C₄	—	113	4	no	—
350	C₂²⋊C₄	—	113	2	no	—
351	C₂²⋊C₄	—	113	2	no	—
352	C₂²⋊C₄	—	113	4	no	—
353	C₂²⋊C₄	—	113	4	no	—
354	C₂²⋊C₄	C₂²×D₁₁₃	1	4	yes	—
355	C₂²⋊C₄	C₂²×D₁₁₃	1	4	yes	—
356	C₄²	—	113	2	no	—
357	C₄²	—	113	2	no	—
358	C₄²	—	113	4	no	—
359	C₄²	—	113	4	no	—
360	C₂³	—	4	1	no	—
361	C₂³	—	4	1	no	—
362	C₂³	—	113	4	no	—
363	C₂³	—	113	2	no	—
364	C₂³	—	452	1	no	—
365	C₂³	—	452	1	no	—
366	C₂³	Q₈×D₁₁₃	1	4	yes	complemented
367	C₂³	C₂³×D₁₁₃	1	1	yes	characteristic
368	C₂³	C₂³×D₁₁₃	1	1	yes	characteristic
369	C₂³	C₂³×D₁₁₃	1	1	yes	characteristic
370	Q₈	—	2	4	no	—
371	Q₈	—	4	2	no	—
372	Q₈	—	452	2	no	—
373	Q₈	—	452	4	no	—
374	Q₈	—	452	4	no	—
375	Q₈	—	226	4	no	—
376	D₄	—	113	8	no	—
377	D₄	—	113	8	no	—
378	C₂×C₄	—	2	2	no	—
379	C₂×C₄	—	2	2	no	—
380	C₂×C₄	—	2	2	no	—
381	C₂×C₄	—	4	1	no	—
382	C₂×C₄	—	4	1	no	—
383	C₂×C₄	—	4	1	no	—
384	C₂×C₄	—	4	2	no	—
385	C₂×C₄	—	4	2	no	—
386	C₂×C₄	—	113	4	no	—
387	C₂×C₄	—	113	2	no	—
388	C₂×C₄	—	113	2	no	—
389	C₂×C₄	—	113	4	no	—
390	C₂×C₄	—	113	4	no	—
391	C₂×C₄	—	113	2	no	—
392	C₂×C₄	—	452	2	no	—
393	C₂×C₄	—	452	4	no	—
394	C₂×C₄	—	452	4	no	—
395	C₂×C₄	—	452	1	no	—
396	C₂×C₄	—	452	2	no	—
397	C₂×C₄	—	452	2	no	—
398	C₂×C₄	—	452	1	no	—
399	C₂×C₄	—	226	4	no	—
400	C₂×C₄	C₂³×D₁₁₃	1	1	yes	characteristic
401	C₂×C₄	C₂³×D₁₁₃	1	4	yes	—
402	C₂×C₄	C₂³×D₁₁₃	1	4	yes	—
403	C₂×C₄	C₂³×D₁₁₃	1	1	yes	characteristic
404	C₂×C₄	C₂³×D₁₁₃	1	1	yes	characteristic
405	C₂×C₄	C₂³×D₁₁₃	1	1	yes	characteristic
406	C₂²	—	2	1	no	—
407	C₂²	—	2	1	no	—
408	C₂²	—	2	1	no	—
409	C₂²	—	2	1	no	—
410	C₂²	—	2	1	no	—
411	C₂²	—	2	1	no	—
412	C₂²	—	4	4	no	—
413	C₂²	—	113	4	no	—
414	C₂²	—	452	4	no	—
415	C₂²	—	226	2	no	—
416	C₂²	—	226	2	no	—
417	C₂²	C₂×Q₈×D₁₁₃	1	2	yes	—
418	C₂²	C₂×Q₈×D₁₁₃	1	2	yes	—
419	C₂²	C₂×Q₈×D₁₁₃	1	2	yes	—
420	C₂²	C₂⁴×D₁₁₃	1	1	yes	characteristic
421	C₄	—	2	1	no	—
422	C₄	—	2	1	no	—
423	C₄	—	2	1	no	—
424	C₄	—	2	4	no	—
425	C₄	—	2	4	no	—
426	C₄	—	113	4	no	—
427	C₄	—	226	2	no	—
428	C₄	—	226	4	no	—
429	C₄	—	226	4	no	—
430	C₄	—	226	2	no	—
431	C₄	#16813667	1	2	yes	—
432	C₂	—	2	2	no	—
433	C₂	—	2	2	no	—
434	C₂	—	2	2	no	—
435	C₂	—	226	4	no	—
436	C₂	C₂²×Q₈×D₁₁₃	1	1	yes	characteristic
437	C₂	C₂×#16813667	1	1	yes	characteristic
438	C₂	#20299434	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₁₁₃
commutator, socle, cosocle	C₂²×C₁₁₃	C₂⁵
Fitting	C₂×C₂²⋊Q₈×C₁₁₃	C₂
prime radical	C₂²×C₂²⋊D₁₁₃	C₂²
hypercenter	C₂×C₂²⋊Q₈	D₁₁₃
hypocenter	C₁₁₃	#3501
LCS	G ▷ C₂²×C₁₁₃ ▷ C₁₁₃
UCS	C₁ ◁ C₂² ◁ C₂×C₂²⋊Q₈

Complements

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

N	H ≅ G/N	type
1. #20299306	C₂	semidirect
2. #20299303	C₂	semidirect
3. #20299303	C₂	semidirect
4. #20299302	C₂	semidirect
5. Q₈×C₂²⋊D₁₁₃	C₂	semidirect
6. #20299261	C₂	semidirect
7. #20299227	C₂	semidirect
8. #20299224	C₂	semidirect
9. #20299223	C₂	semidirect
10. #20299150	C₂	semidirect
11. C₂×#16813601	C₂	semidirect
12. C₂²⋊Q₈×D₁₁₃	C₂	semidirect
15. C₂×C₂²⋊Q₈×C₁₁₃	C₂	semidirect
16. C₂²×Dic₂₂₆	C₂²	semidirect
17. C₂×Q₈×D₁₁₃	C₂²	semidirect
20. #16813621	C₂²	semidirect
21. #16813621	C₂²	semidirect
22. #16813620	C₂²	semidirect
23. #16813620	C₂²	semidirect
24. #16813612	C₂²	semidirect
25. #16813612	C₂²	semidirect
26. #16813612	C₂²	semidirect
27. #16813602	C₂²	semidirect
28. #16813602	C₂²	semidirect
31. #16813601	C₂²	semidirect
32. #16813601	C₂²	semidirect
33. #16813601	C₂²	semidirect
34. #16813601	C₂²	semidirect
35. #16813600	C₂²	semidirect
36. #16813600	C₂²	semidirect
37. #16813600	C₂²	semidirect
40. #16813599	C₂²	semidirect
41. #16813599	C₂²	semidirect
42. #16813598	C₂²	semidirect
43. #16813598	C₂²	semidirect
44. Q₈×Dic₁₁₃	C₂²	semidirect
45. #16813587	C₂²	semidirect
46. #16813587	C₂²	semidirect
56. C₂×C₄⋊Dic₁₁₃	C₂²	semidirect
58. C₂×#14268626	C₂²	semidirect
59. C₄⋊C₄×D₁₁₃	C₂²	semidirect
60. C₄⋊C₄×D₁₁₃	C₂²	semidirect
66. C₂²×Q₈×C₁₁₃	C₂²	semidirect
70. C₂²⋊Q₈×C₁₁₃	C₂²	semidirect
71. C₂²⋊Q₈×C₁₁₃	C₂²	semidirect
72. C₂×C₄⋊C₄×C₁₁₃	C₂²	semidirect
73. C₂×C₄⋊C₄×C₁₁₃	C₂²	semidirect
82. C₂×C₂²⋊D₁₁₃	Q₈	semidirect
142. C₂³×C₁₁₃	C₂×Q₈	semidirect
148. C₂²×D₁₁₃	C₂×Q₈	semidirect
166. C₂²⋊D₁₁₃	C₂×Q₈	semidirect
167. C₂²⋊D₁₁₃	C₂×Q₈	semidirect
172. C₂×Dic₁₁₃	C₂×Q₈	semidirect
220. C₁₁₃	#3501	semidirect
233. C₂×C₂²⋊Q₈	D₁₁₃	semidirect
238. C₂²×Q₈	C₂×D₁₁₃	semidirect
268. C₂²⋊Q₈	C₂×D₁₁₃	semidirect
269. C₂²⋊Q₈	C₂×D₁₁₃	semidirect
287. C₂×C₄⋊C₄	C₂×D₁₁₃	semidirect
288. C₂×C₄⋊C₄	C₂×D₁₁₃	semidirect
366. C₂³	Q₈×D₁₁₃	semidirect

Maximal subgroups

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

subgroup	index
#20299306	2
#20299303	2
#20299302	2
Q₈×C₂²⋊D₁₁₃	2
#20299261	2
#20299227	2
#20299224	2
#20299223	2
#20299150	2
C₂×#16813601	2
C₂²⋊Q₈×D₁₁₃	2
#20299071	2
C₂×C₄×C₂²⋊D₁₁₃	2
C₂×C₂²⋊Q₈×C₁₁₃	2
#3501	113