Subgroups — #28404415

Order 14464.

1152 conjugacy classes of subgroups.

The subgroup lattice has 458 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20299296	C₂	1	4	yes	maximal, complemented
2	#20299296	C₂	1	2	yes	maximal, complemented
3	#20299290	C₂	1	2	yes	maximal, complemented
4	#20299275	C₂	1	4	yes	maximal, complemented
5	#20299259	C₂	1	2	yes	maximal, complemented
6	#20299239	C₂	1	2	yes	maximal, complemented
7	#20299197	C₂	1	2	yes	maximal, complemented
8	#20299188	C₂	1	2	yes	maximal, complemented
9	#20299160	C₂	1	2	yes	maximal, complemented
10	#20299134	C₂	1	2	yes	maximal, complemented
11	#20299111	C₂	1	2	yes	maximal, complemented
12	C₂×#16813596	C₂	1	1	yes	maximal, characteristic, complemented
13	#20299071	C₂	1	2	yes	maximal, complemented
14	C₂×C₄×C₂²⋊D₁₁₃	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×C₂²⋊Q₈×C₁₁₃	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#14268648	C₂²	1	2	yes	complemented
17	C₂²×D₄₅₂	C₂²	1	1	yes	characteristic, complemented
18	C₂²×C₂²⋊D₁₁₃	C₂²	1	1	yes	characteristic
19	C₂²×C₂²⋊D₁₁₃	C₂²	1	2	yes	—
20	C₂²×C₄×D₁₁₃	C₂²	1	1	yes	characteristic, complemented
21	#16813617	C₂²	1	4	yes	complemented
22	#16813617	C₂²	1	4	yes	complemented
23	#16813617	C₂²	1	4	yes	complemented
24	#16813613	C₂²	1	2	yes	complemented
25	#16813613	C₂²	1	4	yes	complemented
26	#16813611	C₂²	1	4	yes	complemented
27	#16813611	C₂²	1	2	yes	complemented
28	#16813607	C₂²	1	4	yes	complemented
29	#16813607	C₂²	1	4	yes	complemented
30	#16813607	C₂²	1	4	yes	complemented
31	#16813606	C₂²	1	4	yes	—
32	#16813606	C₂²	1	4	yes	complemented
33	#16813598	C₂²	1	4	yes	complemented
34	#16813598	C₂²	1	2	yes	complemented
35	#16813597	C₂²	1	2	yes	complemented
36	#16813597	C₂²	1	4	yes	complemented
37	#16813596	C₂²	1	2	yes	—
38	#16813596	C₂²	1	2	yes	—
39	#16813596	C₂²	1	2	yes	complemented
40	#16813596	C₂²	1	4	yes	complemented
41	#16813596	C₂²	1	2	yes	complemented
42	#16813596	C₂²	1	4	yes	complemented
43	#16813592	C₂²	1	4	yes	—
44	#16813592	C₂²	1	4	yes	complemented
45	Q₈×Dic₁₁₃	C₂²	1	2	yes	complemented
46	#16813584	C₂²	1	4	yes	complemented
47	#16813584	C₂²	1	2	yes	complemented
48	C₄×C₂²⋊D₁₁₃	C₂²	1	2	yes	—
49	C₄×C₂²⋊D₁₁₃	C₂²	1	2	yes	—
50	C₄×C₂²⋊D₁₁₃	C₂²	1	2	yes	complemented
51	C₄×C₂²⋊D₁₁₃	C₂²	1	4	yes	complemented
52	C₄×C₂²⋊D₁₁₃	C₂²	1	2	yes	complemented
53	C₄×C₂²⋊D₁₁₃	C₂²	1	4	yes	complemented
54	#16813582	C₂²	1	4	yes	complemented
55	#16813582	C₂²	1	4	yes	complemented
56	#16813580	C₂²	1	4	yes	complemented
57	#16813580	C₂²	1	2	yes	complemented
58	#16813578	C₂²	1	4	yes	complemented
59	C₂×C₄⋊Dic₁₁₃	C₂²	1	1	yes	characteristic, complemented
60	C₂×#14268626	C₂²	1	1	yes	characteristic, complemented
61	C₂×C₂²⋊Dic₁₁₃	C₂²	1	1	yes	characteristic
62	C₂×#14268624	C₂²	1	2	yes	complemented
63	C₂×#14268624	C₂²	1	1	yes	characteristic, complemented
64	C₂²⋊C₄×D₁₁₃	C₂²	1	4	yes	complemented
65	C₂×C₄×Dic₁₁₃	C₂²	1	1	yes	characteristic, complemented
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	complemented
69	C₂²⋊Q₈×C₁₁₃	C₂²	1	2	yes	complemented
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	1	yes	characteristic, complemented
73	C₂×C₄⋊C₄×C₁₁₃	C₂²	1	2	yes	complemented
74	C₂×C₂²⋊C₄×C₁₁₃	C₂²	1	2	yes	—
75	C₂³×D₁₁₃	C₂³	1	2	yes	—
76	C₂³×D₁₁₃	C₂³	1	1	yes	characteristic
77	#14268648	—	4	4	no	—
78	C₂×D₄₅₂	—	4	2	no	—
79	C₂×D₄₅₂	C₂³	1	2	yes	—
80	C₂×D₄₅₂	C₂³	1	4	yes	—
81	C₂×D₄₅₂	C₂³	1	4	yes	—
82	C₂×D₄₅₂	C₂³	1	2	yes	—
83	C₂×C₂²⋊D₁₁₃	—	2	4	no	—
84	C₂×C₂²⋊D₁₁₃	—	2	8	no	—
85	C₂×C₂²⋊D₁₁₃	C₂³	1	4	yes	—
86	C₂×C₂²⋊D₁₁₃	C₂³	1	2	yes	—
87	C₂×C₂²⋊D₁₁₃	C₂³	1	2	yes	—
88	C₂×C₂²⋊D₁₁₃	C₂³	1	4	yes	—
89	C₂²×Dic₁₁₃	C₂³	1	1	yes	characteristic
90	C₂²×Dic₁₁₃	C₂³	1	2	yes	—
91	C₂²×Dic₁₁₃	C₂³	1	1	yes	characteristic
92	C₂²×Dic₁₁₃	C₂³	1	1	yes	characteristic
93	C₂×C₄×D₁₁₃	—	4	2	no	—
94	C₂×C₄×D₁₁₃	C₂³	1	2	yes	—
95	C₂×C₄×D₁₁₃	C₂³	1	4	yes	—
96	C₂×C₄×D₁₁₃	C₂³	1	4	yes	—
97	C₂×C₄×D₁₁₃	C₂³	1	2	yes	—
98	C₄⋊Dic₁₁₃	C₂³	1	2	yes	—
99	C₄⋊Dic₁₁₃	C₂³	1	2	yes	—
100	C₄⋊Dic₁₁₃	C₂³	1	4	yes	—
101	C₄⋊Dic₁₁₃	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	C₂²⋊Dic₁₁₃	C₂³	1	2	yes	—
107	C₂²⋊Dic₁₁₃	C₂³	1	2	yes	—
108	#14268624	C₂³	1	4	yes	—
109	#14268624	C₂³	1	4	yes	—
110	#14268624	C₂³	1	4	yes	—
111	#14268624	C₂³	1	2	yes	—
112	#14268624	C₂³	1	2	yes	—
113	#14268624	C₂³	1	4	yes	—
114	#14268624	C₂³	1	4	yes	—
115	#14268624	C₂³	1	4	yes	—
116	#14268624	C₂³	1	4	yes	—
117	#14268624	C₂³	1	4	yes	—
118	C₄×Dic₁₁₃	C₂³	1	2	yes	—
119	C₄×Dic₁₁₃	C₂³	1	2	yes	—
120	C₄×Dic₁₁₃	C₂³	1	4	yes	—
121	C₄×Dic₁₁₃	C₂³	1	4	yes	—
122	C₂⁴×C₁₁₃	C₂³	1	1	yes	characteristic
123	C₂×Q₈×C₁₁₃	—	4	2	no	—
124	C₂×Q₈×C₁₁₃	C₂³	1	2	yes	—
125	C₂×Q₈×C₁₁₃	C₂³	1	2	yes	—
126	C₂²×C₄×C₁₁₃	—	4	2	no	—
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	1	yes	characteristic
132	C₂²×C₄×C₁₁₃	C₂³	1	2	yes	—
133	C₂²×C₄×C₁₁₃	C₂³	1	2	yes	—
134	C₂²×C₄×C₁₁₃	C₂³	1	1	yes	characteristic
135	C₄⋊C₄×C₁₁₃	C₂³	1	2	yes	—
136	C₄⋊C₄×C₁₁₃	C₂³	1	4	yes	—
137	C₄⋊C₄×C₁₁₃	C₂³	1	4	yes	—
138	C₄⋊C₄×C₁₁₃	C₂³	1	2	yes	—
139	C₂²⋊C₄×C₁₁₃	C₂³	1	4	yes	—
140	C₂²⋊C₄×C₁₁₃	C₂³	1	4	yes	—
141	C₂³×C₁₁₃	—	4	1	no	—
142	C₂³×C₁₁₃	—	4	1	no	—
143	C₂³×C₁₁₃	#41	1	4	yes	complemented
144	C₂³×C₁₁₃	C₂⁴	1	1	yes	characteristic
145	C₂³×C₁₁₃	C₂⁴	1	1	yes	characteristic
146	C₂³×C₁₁₃	C₂⁴	1	1	yes	characteristic
147	C₂²×D₁₁₃	—	2	2	no	—
148	C₂²×D₁₁₃	—	2	4	no	—
149	C₂²×D₁₁₃	—	4	1	no	—
150	C₂²×D₁₁₃	—	4	1	no	—
151	C₂²×D₁₁₃	—	4	2	no	—
152	C₂²×D₁₁₃	—	4	2	no	—
153	C₂²×D₁₁₃	C₂⁴	1	2	yes	—
154	C₂²×D₁₁₃	C₂⁴	1	4	yes	—
155	Q₈×C₁₁₃	—	2	4	no	—
156	Q₈×C₁₁₃	—	4	2	no	—
157	C₂×C₄×C₁₁₃	—	2	2	no	—
158	C₂×C₄×C₁₁₃	—	2	2	no	—
159	C₂×C₄×C₁₁₃	—	2	2	no	—
160	C₂×C₄×C₁₁₃	—	4	1	no	—
161	C₂×C₄×C₁₁₃	—	4	1	no	—
162	C₂×C₄×C₁₁₃	—	4	1	no	—
163	C₂×C₄×C₁₁₃	—	4	2	no	—
164	C₂×C₄×C₁₁₃	—	4	2	no	—
165	C₂×C₄×C₁₁₃	C₂⁴	1	4	yes	—
166	C₂×C₄×C₁₁₃	C₂⁴	1	4	yes	—
167	C₂×C₄×C₁₁₃	C₂⁴	1	1	yes	characteristic
168	C₂×C₄×C₁₁₃	C₂⁴	1	1	yes	characteristic
169	C₂×C₄×C₁₁₃	C₂⁴	1	1	yes	characteristic
170	C₂×C₄×C₁₁₃	C₂⁴	1	1	yes	characteristic
171	C₂²⋊D₁₁₃	—	2	4	no	—
172	C₂²⋊D₁₁₃	—	2	8	no	—
173	C₂²⋊D₁₁₃	—	2	4	no	—
174	C₂²⋊D₁₁₃	—	2	8	no	—
175	C₂×Dic₁₁₃	—	2	4	no	—
176	C₂×Dic₁₁₃	—	2	2	no	—
177	C₂×Dic₁₁₃	—	4	1	no	—
178	C₂×Dic₁₁₃	—	4	1	no	—
179	C₂×Dic₁₁₃	C₂⁴	1	2	yes	—
180	C₂×Dic₁₁₃	C₂⁴	1	2	yes	—
181	C₂×Dic₁₁₃	C₂⁴	1	4	yes	—
182	C₂×Dic₁₁₃	C₂⁴	1	2	yes	—
183	D₄₅₂	—	2	4	no	—
184	D₄₅₂	—	4	2	no	—
185	D₄₅₂	—	4	4	no	—
186	D₄₅₂	—	4	4	no	—
187	C₄×D₁₁₃	—	2	4	no	—
188	C₄×D₁₁₃	—	4	2	no	—
189	C₄×D₁₁₃	—	4	4	no	—
190	C₄×D₁₁₃	—	4	4	no	—
191	C₂²×C₁₁₃	—	2	1	no	—
192	C₂²×C₁₁₃	—	2	1	no	—
193	C₂²×C₁₁₃	—	2	1	no	—
194	C₂²×C₁₁₃	—	2	1	no	—
195	C₂²×C₁₁₃	—	2	1	no	—
196	C₂²×C₁₁₃	—	2	1	no	—
197	C₂²×C₁₁₃	—	4	4	no	—
198	C₂²×C₁₁₃	C₂×#41	1	2	yes	—
199	C₂²×C₁₁₃	C₂×#41	1	2	yes	—
200	C₂²×C₁₁₃	C₂×#41	1	2	yes	—
201	C₂²×C₁₁₃	C₂⁵	1	1	yes	characteristic
202	C₂×D₁₁₃	—	2	2	no	—
203	C₂×D₁₁₃	—	2	4	no	—
204	C₂×D₁₁₃	—	2	2	no	—
205	C₂×D₁₁₃	—	2	4	no	—
206	C₂×D₁₁₃	—	2	4	no	—
207	C₂×D₁₁₃	—	2	2	no	—
208	C₂×D₁₁₃	—	4	4	no	—
209	C₂×D₁₁₃	—	8	4	no	—
210	C₄×C₁₁₃	—	2	1	no	—
211	C₄×C₁₁₃	—	2	4	no	—
212	C₄×C₁₁₃	—	2	1	no	—
213	C₄×C₁₁₃	—	2	1	no	—
214	C₄×C₁₁₃	—	2	4	no	—
215	C₄×C₁₁₃	H(5,𝔽₂)	1	2	yes	—
216	Dic₁₁₃	—	2	4	no	—
217	Dic₁₁₃	—	2	2	no	—
218	Dic₁₁₃	—	2	2	no	—
219	Dic₁₁₃	—	2	2	no	—
220	C₂×C₁₁₃	—	2	2	no	—
221	C₂×C₁₁₃	—	2	2	no	—
222	C₂×C₁₁₃	—	2	2	no	—
223	C₂×C₁₁₃	C₂²×#41	1	1	yes	characteristic
224	C₂×C₁₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
225	C₂×C₁₁₃	#585	1	1	yes	characteristic
226	D₁₁₃	—	4	2	no	—
227	D₁₁₃	—	4	4	no	—
228	#3505	—	113	1	no	maximal, Sylow
229	C₁₁₃	#3505	1	1	yes	characteristic, complemented, Sylow
230	#553	—	113	2	no	—
231	#553	—	113	4	no	—
232	#552	—	113	2	no	—
233	#551	—	113	4	no	—
234	#548	—	113	2	no	—
235	#546	—	113	2	no	—
236	#539	—	113	2	no	—
237	#538	—	113	2	no	—
238	#534	—	113	2	no	—
239	#529	—	113	2	no	—
240	#525	—	113	2	no	—
241	C₂×C₂²⋊Q₈	D₁₁₃	1	1	yes	characteristic, complemented
242	C₂×#121	—	113	1	no	—
243	#518	—	113	2	no	—
244	C₂×C₄×D₄	—	113	1	no	—
245	C₂×#41	—	113	2	no	—
246	C₂²×Q₈	C₂×D₁₁₃	1	1	yes	characteristic, complemented
247	C₂²×D₄	—	113	1	no	—
248	C₂²×D₄	—	113	2	no	—
249	C₂²×D₄	—	113	1	no	—
250	C₂³×C₄	—	113	1	no	—
251	C₂³×C₄	C₂×D₁₁₃	1	1	yes	characteristic
252	#126	—	113	4	no	—
253	#126	—	113	4	no	—
254	#126	—	113	4	no	—
255	#125	—	113	2	no	—
256	#125	—	113	4	no	—
257	#124	—	113	2	no	—
258	#124	—	113	4	no	—
259	#123	—	113	4	no	—
260	#123	—	113	4	no	—
261	#123	—	113	4	no	—
262	#123	—	113	4	no	—
263	#123	—	113	4	no	—
264	C₂²⋊Q₈	—	113	2	no	—
265	C₂²⋊Q₈	—	113	4	no	—
266	C₂²⋊Q₈	C₂×D₁₁₃	1	2	yes	complemented
267	C₂²⋊Q₈	C₂×D₁₁₃	1	2	yes	complemented
268	C₂²⋊Q₈	C₂×D₁₁₃	1	2	yes	complemented
269	C₂²⋊Q₈	C₂×D₁₁₃	1	2	yes	complemented
270	#121	—	113	2	no	—
271	#121	—	113	2	no	—
272	#121	—	113	2	no	—
273	#121	—	113	2	no	—
274	#121	—	113	4	no	—
275	#121	—	113	4	no	—
276	#121	—	113	2	no	—
277	#121	—	113	4	no	—
278	#120	—	113	4	no	—
279	#120	—	113	4	no	—
280	C₄×Q₈	—	113	2	no	—
281	C₄×D₄	—	113	2	no	—
282	C₄×D₄	—	113	2	no	—
283	C₄×D₄	—	113	2	no	—
284	C₄×D₄	—	113	2	no	—
285	C₄×D₄	—	113	4	no	—
286	C₄×D₄	—	113	4	no	—
287	C₄×D₄	—	113	4	no	—
288	C₄×D₄	—	113	2	no	—
289	C₄×D₄	—	113	4	no	—
290	C₄×D₄	—	113	4	no	—
291	#117	—	113	2	no	—
292	#117	—	113	4	no	—
293	#117	—	113	4	no	—
294	C₂×C₄⋊C₄	—	113	1	no	—
295	C₂×C₄⋊C₄	—	113	1	no	—
296	C₂×C₄⋊C₄	C₂×D₁₁₃	1	1	yes	characteristic, complemented
297	C₂×C₄⋊C₄	C₂×D₁₁₃	1	2	yes	complemented
298	C₂×C₂²⋊C₄	—	113	1	no	—
299	C₂×C₂²⋊C₄	—	113	1	no	—
300	C₂×C₂²⋊C₄	—	113	2	no	—
301	C₂×C₂²⋊C₄	—	113	4	no	—
302	C₂×C₂²⋊C₄	C₂×D₁₁₃	1	2	yes	—
303	C₂×C₄²	—	113	1	no	—
304	C₂⁴	—	113	2	no	—
305	C₂⁴	—	113	1	no	—
306	C₂⁴	C₂²×D₁₁₃	1	1	yes	characteristic
307	#41	—	452	4	no	—
308	C₂×Q₈	—	4	2	no	—
309	C₂×Q₈	C₂²×D₁₁₃	1	2	yes	—
310	C₂×Q₈	C₂²×D₁₁₃	1	2	yes	—
311	C₂×D₄	—	113	2	no	—
312	C₂×D₄	—	113	4	no	—
313	C₂×D₄	—	113	2	no	—
314	C₂×D₄	—	113	4	no	—
315	C₂×D₄	—	113	4	no	—
316	C₂×D₄	—	113	4	no	—
317	C₂×D₄	—	113	2	no	—
318	C₂×D₄	—	113	2	no	—
319	C₂×D₄	—	452	2	no	—
320	C₂×D₄	—	226	8	no	—
321	C₂×D₄	—	226	4	no	—
322	C₂²×C₄	—	4	2	no	—
323	C₂²×C₄	—	113	1	no	—
324	C₂²×C₄	—	113	1	no	—
325	C₂²×C₄	—	113	1	no	—
326	C₂²×C₄	—	113	2	no	—
327	C₂²×C₄	—	113	4	no	—
328	C₂²×C₄	—	113	4	no	—
329	C₂²×C₄	—	113	2	no	—
330	C₂²×C₄	—	113	2	no	—
331	C₂²×C₄	—	452	2	no	—
332	C₂²×C₄	C₂²×D₁₁₃	1	1	yes	characteristic
333	C₂²×C₄	C₂²×D₁₁₃	1	1	yes	characteristic
334	C₂²×C₄	C₂²×D₁₁₃	1	1	yes	characteristic
335	C₂²×C₄	C₂²×D₁₁₃	1	1	yes	characteristic
336	C₂²×C₄	C₂²×D₁₁₃	1	1	yes	characteristic
337	C₂²×C₄	C₂²×D₁₁₃	1	2	yes	—
338	C₂²×C₄	C₂²×D₁₁₃	1	2	yes	—
339	C₂²×C₄	C₂²×D₁₁₃	1	1	yes	characteristic
340	C₄⋊C₄	—	113	2	no	—
341	C₄⋊C₄	—	113	2	no	—
342	C₄⋊C₄	—	113	2	no	—
343	C₄⋊C₄	—	113	2	no	—
344	C₄⋊C₄	—	113	4	no	—
345	C₄⋊C₄	—	113	4	no	—
346	C₄⋊C₄	—	113	4	no	—
347	C₄⋊C₄	—	113	4	no	—
348	C₄⋊C₄	C₂²×D₁₁₃	1	2	yes	—
349	C₄⋊C₄	C₂²×D₁₁₃	1	4	yes	—
350	C₄⋊C₄	C₂²×D₁₁₃	1	4	yes	—
351	C₄⋊C₄	C₂²×D₁₁₃	1	2	yes	—
352	C₂²⋊C₄	—	113	2	no	—
353	C₂²⋊C₄	—	113	2	no	—
354	C₂²⋊C₄	—	113	4	no	—
355	C₂²⋊C₄	—	113	2	no	—
356	C₂²⋊C₄	—	113	4	no	—
357	C₂²⋊C₄	—	113	4	no	—
358	C₂²⋊C₄	—	113	2	no	—
359	C₂²⋊C₄	—	113	4	no	—
360	C₂²⋊C₄	—	113	4	no	—
361	C₂²⋊C₄	—	113	4	no	—
362	C₂²⋊C₄	—	113	4	no	—
363	C₂²⋊C₄	—	113	4	no	—
364	C₂²⋊C₄	C₂²×D₁₁₃	1	4	yes	—
365	C₂²⋊C₄	C₂²×D₁₁₃	1	4	yes	—
366	C₄²	—	113	2	no	—
367	C₄²	—	113	2	no	—
368	C₄²	—	113	4	no	—
369	C₄²	—	113	4	no	—
370	C₂³	—	4	1	no	—
371	C₂³	—	4	1	no	—
372	C₂³	—	113	2	no	—
373	C₂³	—	113	4	no	—
374	C₂³	—	452	2	no	—
375	C₂³	—	452	2	no	—
376	C₂³	—	452	1	no	—
377	C₂³	—	452	1	no	—
378	C₂³	—	226	4	no	—
379	C₂³	—	226	2	no	—
380	C₂³	#14268648	1	4	yes	complemented
381	C₂³	C₂³×D₁₁₃	1	1	yes	characteristic
382	C₂³	C₂³×D₁₁₃	1	1	yes	characteristic
383	C₂³	C₂³×D₁₁₃	1	1	yes	characteristic
384	Q₈	—	2	4	no	—
385	Q₈	—	4	2	no	—
386	D₄	—	452	2	no	—
387	D₄	—	452	4	no	—
388	D₄	—	452	4	no	—
389	D₄	—	226	4	no	—
390	D₄	—	226	8	no	—
391	D₄	—	226	8	no	—
392	D₄	—	226	4	no	—
393	D₄	—	226	4	no	—
394	C₂×C₄	—	2	2	no	—
395	C₂×C₄	—	2	2	no	—
396	C₂×C₄	—	2	2	no	—
397	C₂×C₄	—	4	1	no	—
398	C₂×C₄	—	4	1	no	—
399	C₂×C₄	—	4	1	no	—
400	C₂×C₄	—	4	2	no	—
401	C₂×C₄	—	4	2	no	—
402	C₂×C₄	—	113	2	no	—
403	C₂×C₄	—	113	2	no	—
404	C₂×C₄	—	113	4	no	—
405	C₂×C₄	—	113	2	no	—
406	C₂×C₄	—	452	2	no	—
407	C₂×C₄	—	452	4	no	—
408	C₂×C₄	—	452	4	no	—
409	C₂×C₄	—	452	1	no	—
410	C₂×C₄	—	452	1	no	—
411	C₂×C₄	—	226	4	no	—
412	C₂×C₄	—	226	2	no	—
413	C₂×C₄	—	226	4	no	—
414	C₂×C₄	C₂³×D₁₁₃	1	1	yes	characteristic
415	C₂×C₄	C₂³×D₁₁₃	1	4	yes	—
416	C₂×C₄	C₂³×D₁₁₃	1	4	yes	—
417	C₂×C₄	C₂³×D₁₁₃	1	1	yes	characteristic
418	C₂×C₄	C₂³×D₁₁₃	1	1	yes	characteristic
419	C₂×C₄	C₂³×D₁₁₃	1	1	yes	characteristic
420	C₂²	—	2	1	no	—
421	C₂²	—	2	1	no	—
422	C₂²	—	2	1	no	—
423	C₂²	—	2	1	no	—
424	C₂²	—	2	1	no	—
425	C₂²	—	2	1	no	—
426	C₂²	—	4	4	no	—
427	C₂²	—	904	4	no	—
428	C₂²	—	452	4	no	—
429	C₂²	—	226	4	no	—
430	C₂²	—	226	2	no	—
431	C₂²	—	226	2	no	—
432	C₂²	—	226	4	no	—
433	C₂²	—	226	4	no	—
434	C₂²	—	226	2	no	—
435	C₂²	C₂×#14268648	1	2	yes	—
436	C₂²	C₂×#14268648	1	2	yes	—
437	C₂²	C₂×#14268648	1	2	yes	—
438	C₂²	C₂⁴×D₁₁₃	1	1	yes	characteristic
439	C₄	—	2	1	no	—
440	C₄	—	2	1	no	—
441	C₄	—	2	1	no	—
442	C₄	—	2	4	no	—
443	C₄	—	2	4	no	—
444	C₄	—	226	2	no	—
445	C₄	—	226	4	no	—
446	C₄	—	226	2	no	—
447	C₄	—	226	2	no	—
448	C₄	#16813667	1	2	yes	—
449	C₂	—	2	2	no	—
450	C₂	—	2	2	no	—
451	C₂	—	2	2	no	—
452	C₂	—	452	4	no	—
453	C₂	—	452	2	no	—
454	C₂	C₂²×#14268648	1	1	yes	characteristic
455	C₂	C₂×#16813667	1	1	yes	characteristic
456	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
hypercenter	C₂×C₂²⋊Q₈	D₁₁₃
hypocenter	C₁₁₃	#3505
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. #20299296	C₂	semidirect
2. #20299296	C₂	semidirect
3. #20299290	C₂	semidirect
4. #20299275	C₂	semidirect
5. #20299259	C₂	semidirect
6. #20299239	C₂	semidirect
7. #20299197	C₂	semidirect
8. #20299188	C₂	semidirect
9. #20299160	C₂	semidirect
10. #20299134	C₂	semidirect
11. #20299111	C₂	semidirect
12. C₂×#16813596	C₂	semidirect
13. #20299071	C₂	semidirect
14. C₂×C₄×C₂²⋊D₁₁₃	C₂	semidirect
15. C₂×C₂²⋊Q₈×C₁₁₃	C₂	semidirect
16. C₂×#14268648	C₂²	semidirect
17. C₂²×D₄₅₂	C₂²	semidirect
20. C₂²×C₄×D₁₁₃	C₂²	semidirect
21. #16813617	C₂²	semidirect
22. #16813617	C₂²	semidirect
23. #16813617	C₂²	semidirect
24. #16813613	C₂²	semidirect
25. #16813613	C₂²	semidirect
26. #16813611	C₂²	semidirect
27. #16813611	C₂²	semidirect
28. #16813607	C₂²	semidirect
29. #16813607	C₂²	semidirect
30. #16813607	C₂²	semidirect
32. #16813606	C₂²	semidirect
33. #16813598	C₂²	semidirect
34. #16813598	C₂²	semidirect
35. #16813597	C₂²	semidirect
36. #16813597	C₂²	semidirect
39. #16813596	C₂²	semidirect
40. #16813596	C₂²	semidirect
41. #16813596	C₂²	semidirect
42. #16813596	C₂²	semidirect
44. #16813592	C₂²	semidirect
45. Q₈×Dic₁₁₃	C₂²	semidirect
46. #16813584	C₂²	semidirect
47. #16813584	C₂²	semidirect
50. C₄×C₂²⋊D₁₁₃	C₂²	semidirect
51. C₄×C₂²⋊D₁₁₃	C₂²	semidirect
52. C₄×C₂²⋊D₁₁₃	C₂²	semidirect
53. C₄×C₂²⋊D₁₁₃	C₂²	semidirect
54. #16813582	C₂²	semidirect
55. #16813582	C₂²	semidirect
56. #16813580	C₂²	semidirect
57. #16813580	C₂²	semidirect
58. #16813578	C₂²	semidirect
59. C₂×C₄⋊Dic₁₁₃	C₂²	semidirect
60. C₂×#14268626	C₂²	semidirect
62. C₂×#14268624	C₂²	semidirect
63. C₂×#14268624	C₂²	semidirect
64. C₂²⋊C₄×D₁₁₃	C₂²	semidirect
65. C₂×C₄×Dic₁₁₃	C₂²	semidirect
66. C₂²×Q₈×C₁₁₃	C₂²	semidirect
68. C₂²⋊Q₈×C₁₁₃	C₂²	semidirect
69. 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
143. C₂³×C₁₁₃	#41	semidirect
229. C₁₁₃	#3505	semidirect
241. C₂×C₂²⋊Q₈	D₁₁₃	semidirect
246. C₂²×Q₈	C₂×D₁₁₃	semidirect
266. C₂²⋊Q₈	C₂×D₁₁₃	semidirect
267. C₂²⋊Q₈	C₂×D₁₁₃	semidirect
268. C₂²⋊Q₈	C₂×D₁₁₃	semidirect
269. C₂²⋊Q₈	C₂×D₁₁₃	semidirect
296. C₂×C₄⋊C₄	C₂×D₁₁₃	semidirect
297. C₂×C₄⋊C₄	C₂×D₁₁₃	semidirect
380. C₂³	#14268648	semidirect

Maximal subgroups

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

subgroup	index
#20299296	2
#20299290	2
#20299275	2
#20299259	2
#20299239	2
#20299197	2
#20299188	2
#20299160	2
#20299134	2
#20299111	2
C₂×#16813596	2
#20299071	2
C₂×C₄×C₂²⋊D₁₁₃	2
C₂×C₂²⋊Q₈×C₁₁₃	2
#3505	113