Subgroups — #28404624

Order 14464.

1124 conjugacy classes of subgroups.

The subgroup lattice has 462 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20299321	C₂	1	1	yes	maximal, characteristic, complemented
2	#20299309	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	#20299252	C₂	1	1	yes	maximal, characteristic, complemented
7	#20299251	C₂	1	1	yes	maximal, characteristic, complemented
8	#20299243	C₂	1	2	yes	maximal, complemented
9	#20299222	C₂	1	2	yes	maximal, complemented
10	#20299197	C₂	1	4	yes	maximal, complemented
11	#20299153	C₂	1	1	yes	maximal, characteristic, complemented
12	#20299135	C₂	1	1	yes	maximal, characteristic, complemented
13	#20299111	C₂	1	2	yes	maximal, complemented
14	C₂×#16813598	C₂	1	2	yes	maximal, complemented
15	#20299077	C₂	1	2	yes	maximal, complemented
16	C₄×D₄×D₁₁₃	C₂	1	1	yes	maximal, characteristic, complemented
17	D₄×Q₈×C₁₁₃	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×#14268648	C₂²	1	2	yes	complemented
19	C₂×#14268646	C₂²	1	2	yes	—
20	C₂×D₄×D₁₁₃	C₂²	1	1	yes	characteristic
21	C₂²×C₄×D₁₁₃	C₂²	1	2	yes	—
22	#16813622	C₂²	1	1	yes	characteristic, complemented
23	#16813617	C₂²	1	4	yes	complemented
24	#16813617	C₂²	1	4	yes	complemented
25	#16813617	C₂²	1	2	yes	complemented
26	#16813613	C₂²	1	1	yes	characteristic, complemented
27	#16813613	C₂²	1	4	yes	complemented
28	#16813613	C₂²	1	2	yes	complemented
29	#16813611	C₂²	1	4	yes	complemented
30	#16813611	C₂²	1	1	yes	characteristic, complemented
31	#16813610	C₂²	1	2	yes	—
32	#16813607	C₂²	1	2	yes	—
33	#16813607	C₂²	1	4	yes	complemented
34	#16813607	C₂²	1	4	yes	complemented
35	#16813606	C₂²	1	4	yes	—
36	#16813606	C₂²	1	4	yes	complemented
37	#16813602	C₂²	1	2	yes	—
38	#16813602	C₂²	1	2	yes	complemented
39	#16813598	C₂²	1	4	yes	—
40	#16813598	C₂²	1	1	yes	characteristic
41	#16813598	C₂²	1	2	yes	—
42	#16813598	C₂²	1	2	yes	complemented
43	#16813598	C₂²	1	4	yes	complemented
44	#16813598	C₂²	1	2	yes	complemented
45	#16813598	C₂²	1	4	yes	complemented
46	#16813597	C₂²	1	1	yes	characteristic
47	#16813597	C₂²	1	2	yes	—
48	#16813596	C₂²	1	4	yes	—
49	#16813596	C₂²	1	2	yes	complemented
50	#16813592	C₂²	1	4	yes	—
51	Q₈×Dic₁₁₃	C₂²	1	2	yes	complemented
52	C₄×Dic₂₂₆	C₂²	1	2	yes	complemented
53	#16813587	C₂²	1	2	yes	complemented
54	C₄×D₄₅₂	C₂²	1	2	yes	—
55	C₄×D₄₅₂	C₂²	1	1	yes	characteristic
56	C₄×D₄₅₂	C₂²	1	1	yes	characteristic, complemented
57	D₄×Dic₁₁₃	C₂²	1	1	yes	characteristic
58	#16813584	C₂²	1	4	yes	—
59	#16813584	C₂²	1	1	yes	characteristic
60	C₄×C₂²⋊D₁₁₃	C₂²	1	2	yes	—
61	C₄×C₂²⋊D₁₁₃	C₂²	1	4	yes	complemented
62	#16813582	C₂²	1	2	yes	—
63	#16813582	C₂²	1	4	yes	complemented
64	#16813580	C₂²	1	2	yes	—
65	#16813580	C₂²	1	2	yes	complemented
66	#16813579	C₂²	1	2	yes	complemented
67	#16813578	C₂²	1	4	yes	complemented
68	C₂×C₄⋊Dic₁₁₃	C₂²	1	2	yes	complemented
69	C₂×#14268626	C₂²	1	4	yes	complemented
70	C₄⋊C₄×D₁₁₃	C₂²	1	1	yes	characteristic
71	C₄⋊C₄×D₁₁₃	C₂²	1	2	yes	complemented
72	C₂×#14268624	C₂²	1	4	yes	—
73	C₂²⋊C₄×D₁₁₃	C₂²	1	2	yes	—
74	C₄²×D₁₁₃	C₂²	1	1	yes	characteristic
75	C₂²×Q₈×C₁₁₃	C₂²	1	2	yes	complemented
76	C₄⋊Q₈×C₁₁₃	C₂²	1	2	yes	complemented
77	C₄⋊Q₈×C₁₁₃	C₂²	1	1	yes	characteristic, complemented
78	C₂²⋊Q₈×C₁₁₃	C₂²	1	4	yes	complemented
79	C₂²⋊Q₈×C₁₁₃	C₂²	1	2	yes	complemented
80	C₄×Q₈×C₁₁₃	C₂²	1	1	yes	characteristic, complemented
81	C₄×D₄×C₁₁₃	C₂²	1	1	yes	characteristic
82	C₄×D₄×C₁₁₃	C₂²	1	2	yes	—
83	C₂³×D₁₁₃	C₂³	1	2	yes	—
84	#14268648	—	4	4	no	—
85	#14268646	—	2	8	no	—
86	C₂×Dic₂₂₆	C₂³	1	2	yes	—
87	C₂×D₄₅₂	C₂³	1	2	yes	—
88	C₂×D₄₅₂	C₂³	1	1	yes	characteristic
89	C₂×D₄₅₂	C₂³	1	1	yes	characteristic
90	C₂×D₄₅₂	C₂³	1	4	yes	—
91	C₂×C₂²⋊D₁₁₃	C₂³	1	2	yes	—
92	C₂×C₂²⋊D₁₁₃	C₂³	1	4	yes	—
93	D₄×D₁₁₃	—	2	4	no	—
94	C₂²×Dic₁₁₃	C₂³	1	4	yes	—
95	C₂²×Dic₁₁₃	C₂³	1	2	yes	—
96	C₂×C₄×D₁₁₃	—	4	4	no	—
97	C₂×C₄×D₁₁₃	C₂³	1	1	yes	characteristic
98	C₂×C₄×D₁₁₃	C₂³	1	1	yes	characteristic
99	C₂×C₄×D₁₁₃	C₂³	1	1	yes	characteristic
100	C₂×C₄×D₁₁₃	C₂³	1	2	yes	—
101	C₂×C₄×D₁₁₃	C₂³	1	2	yes	—
102	C₂×C₄×D₁₁₃	C₂³	1	2	yes	—
103	C₂×C₄×D₁₁₃	C₂³	1	4	yes	—
104	C₂×C₄×D₁₁₃	C₂³	1	2	yes	—
105	C₄⋊Dic₁₁₃	C₂³	1	1	yes	characteristic
106	C₄⋊Dic₁₁₃	C₂³	1	1	yes	characteristic
107	C₄⋊Dic₁₁₃	C₂³	1	2	yes	—
108	C₄⋊Dic₁₁₃	C₂³	1	4	yes	—
109	C₄⋊Dic₁₁₃	C₂³	1	2	yes	—
110	C₄⋊Dic₁₁₃	C₂³	1	2	yes	—
111	C₄⋊Dic₁₁₃	C₂³	1	4	yes	—
112	#14268626	C₂³	1	2	yes	—
113	#14268626	C₂³	1	4	yes	—
114	#14268626	C₂³	1	2	yes	—
115	#14268626	C₂³	1	4	yes	—
116	#14268626	C₂³	1	4	yes	—
117	#14268626	C₂³	1	2	yes	—
118	C₂²⋊Dic₁₁₃	C₂³	1	2	yes	—
119	#14268624	C₂³	1	2	yes	—
120	#14268624	C₂³	1	2	yes	—
121	#14268624	C₂³	1	2	yes	—
122	#14268624	C₂³	1	4	yes	—
123	#14268624	C₂³	1	4	yes	—
124	#14268624	C₂³	1	4	yes	—
125	#14268624	C₂³	1	2	yes	—
126	#14268624	C₂³	1	2	yes	—
127	#14268624	C₂³	1	4	yes	—
128	#14268624	C₂³	1	4	yes	—
129	#14268624	C₂³	1	2	yes	—
130	#14268624	C₂³	1	2	yes	—
131	C₄×Dic₁₁₃	C₂³	1	1	yes	characteristic
132	C₄×Dic₁₁₃	C₂³	1	1	yes	characteristic
133	C₄×Dic₁₁₃	C₂³	1	1	yes	characteristic
134	C₄×Dic₁₁₃	C₂³	1	4	yes	—
135	C₄×Dic₁₁₃	C₂³	1	4	yes	—
136	C₂×Q₈×C₁₁₃	—	4	4	no	—
137	C₂×Q₈×C₁₁₃	C₂³	1	2	yes	—
138	C₂×Q₈×C₁₁₃	C₂³	1	1	yes	characteristic
139	C₂×Q₈×C₁₁₃	C₂³	1	4	yes	—
140	C₂×D₄×C₁₁₃	C₂³	1	1	yes	characteristic
141	C₂²×C₄×C₁₁₃	C₂³	1	2	yes	—
142	C₂²×C₄×C₁₁₃	C₂³	1	4	yes	—
143	C₄⋊C₄×C₁₁₃	C₂³	1	1	yes	characteristic
144	C₄⋊C₄×C₁₁₃	C₂³	1	2	yes	—
145	C₄⋊C₄×C₁₁₃	C₂³	1	2	yes	—
146	C₄⋊C₄×C₁₁₃	C₂³	1	1	yes	characteristic
147	C₄⋊C₄×C₁₁₃	C₂³	1	4	yes	—
148	C₄⋊C₄×C₁₁₃	C₂³	1	2	yes	—
149	C₂²⋊C₄×C₁₁₃	C₂³	1	2	yes	—
150	C₂²⋊C₄×C₁₁₃	C₂³	1	4	yes	—
151	C₄²×C₁₁₃	C₂³	1	1	yes	characteristic
152	C₄²×C₁₁₃	C₂³	1	2	yes	—
153	C₂³×C₁₁₃	C₂⁴	1	2	yes	—
154	C₂²×D₁₁₃	—	2	4	no	—
155	C₂²×D₁₁₃	—	2	4	no	—
156	C₂²×D₁₁₃	—	4	2	no	—
157	C₂²×D₁₁₃	C₂⁴	1	2	yes	—
158	C₂²×D₁₁₃	C₂⁴	1	2	yes	—
159	C₂²×D₁₁₃	C₂⁴	1	1	yes	characteristic
160	Q₈×C₁₁₃	—	2	2	no	—
161	Q₈×C₁₁₃	—	2	4	no	—
162	Q₈×C₁₁₃	—	4	4	no	—
163	D₄×C₁₁₃	#41	1	4	yes	complemented
164	C₂×C₄×C₁₁₃	—	2	4	no	—
165	C₂×C₄×C₁₁₃	—	4	4	no	—
166	C₂×C₄×C₁₁₃	C₂⁴	1	2	yes	—
167	C₂×C₄×C₁₁₃	C₂⁴	1	1	yes	characteristic
168	C₂×C₄×C₁₁₃	C₂⁴	1	2	yes	—
169	C₂×C₄×C₁₁₃	C₂⁴	1	4	yes	—
170	C₂×C₄×C₁₁₃	C₂⁴	1	2	yes	—
171	C₂×C₄×C₁₁₃	C₂⁴	1	1	yes	characteristic
172	C₂×C₄×C₁₁₃	C₂⁴	1	1	yes	characteristic
173	C₂²⋊D₁₁₃	—	2	4	no	—
174	C₂²⋊D₁₁₃	—	2	8	no	—
175	C₂×Dic₁₁₃	—	2	8	no	—
176	C₂×Dic₁₁₃	—	4	2	no	—
177	C₂×Dic₁₁₃	C₂⁴	1	1	yes	characteristic
178	C₂×Dic₁₁₃	C₂⁴	1	4	yes	—
179	C₂×Dic₁₁₃	C₂⁴	1	1	yes	characteristic
180	C₂×Dic₁₁₃	C₂⁴	1	1	yes	characteristic
181	C₂×Dic₁₁₃	C₂⁴	1	2	yes	—
182	C₂×Dic₁₁₃	C₂⁴	1	2	yes	—
183	D₄₅₂	—	2	4	no	—
184	D₄₅₂	—	2	2	no	—
185	D₄₅₂	—	2	2	no	—
186	D₄₅₂	—	4	4	no	—
187	C₄×D₁₁₃	—	2	2	no	—
188	C₄×D₁₁₃	—	2	2	no	—
189	C₄×D₁₁₃	—	2	4	no	—
190	C₄×D₁₁₃	—	2	2	no	—
191	C₄×D₁₁₃	—	2	4	no	—
192	C₄×D₁₁₃	—	4	2	no	—
193	C₄×D₁₁₃	—	4	2	no	—
194	C₄×D₁₁₃	—	4	4	no	—
195	Dic₂₂₆	—	2	4	no	—
196	C₂²×C₁₁₃	—	2	2	no	—
197	C₂²×C₁₁₃	—	2	2	no	—
198	C₂²×C₁₁₃	C₂×#41	1	4	yes	—
199	C₂²×C₁₁₃	C₂⁵	1	1	yes	characteristic
200	C₂×D₁₁₃	—	2	1	no	—
201	C₂×D₁₁₃	—	2	1	no	—
202	C₂×D₁₁₃	—	2	2	no	—
203	C₂×D₁₁₃	—	2	2	no	—
204	C₂×D₁₁₃	—	2	2	no	—
205	C₂×D₁₁₃	—	2	2	no	—
206	C₂×D₁₁₃	—	2	2	no	—
207	C₂×D₁₁₃	—	2	2	no	—
208	C₂×D₁₁₃	—	4	8	no	—
209	C₂×D₁₁₃	2₋¹⁺⁴	1	2	yes	—
210	C₄×C₁₁₃	—	2	2	no	—
211	C₄×C₁₁₃	—	2	4	no	—
212	C₄×C₁₁₃	—	2	2	no	—
213	C₄×C₁₁₃	—	2	1	no	—
214	C₄×C₁₁₃	—	2	2	no	—
215	C₄×C₁₁₃	C₂×#41	1	2	yes	—
216	C₄×C₁₁₃	H(5,𝔽₂)	1	2	yes	—
217	Dic₁₁₃	—	2	4	no	—
218	Dic₁₁₃	—	2	2	no	—
219	Dic₁₁₃	—	2	1	no	—
220	Dic₁₁₃	—	2	2	no	—
221	Dic₁₁₃	—	2	1	no	—
222	Dic₁₁₃	—	2	1	no	—
223	C₂×C₁₁₃	—	2	4	no	—
224	C₂×C₁₁₃	C₂²×#41	1	1	yes	characteristic
225	C₂×C₁₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
226	C₂×C₁₁₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
227	D₁₁₃	—	2	2	no	—
228	D₁₁₃	—	4	2	no	—
229	D₁₁₃	—	4	2	no	—
230	#3520	—	113	1	no	maximal, Sylow
231	C₁₁₃	#3520	1	1	yes	characteristic, complemented, Sylow
232	#556	—	113	1	no	—
233	#554	—	113	2	no	—
234	#552	—	113	2	no	—
235	#551	—	113	4	no	—
236	D₄×Q₈	D₁₁₃	1	1	yes	characteristic, complemented
237	#548	—	113	2	no	—
238	#547	—	113	1	no	—
239	#547	—	113	1	no	—
240	#546	—	113	2	no	—
241	#542	—	113	2	no	—
242	#539	—	113	4	no	—
243	#533	—	113	1	no	—
244	#529	—	113	1	no	—
245	#525	—	113	2	no	—
246	C₂×C₂²⋊Q₈	—	113	2	no	—
247	#520	—	113	2	no	—
248	C₂×C₄×D₄	—	113	1	no	—
249	C₂×#41	—	113	2	no	—
250	C₂×#41	—	113	2	no	—
251	C₂²×Q₈	C₂×D₁₁₃	1	2	yes	complemented
252	C₂²×D₄	—	113	1	no	—
253	C₂³×C₄	—	113	2	no	—
254	C₄⋊Q₈	—	113	1	no	—
255	C₄⋊Q₈	C₂×D₁₁₃	1	1	yes	characteristic, complemented
256	C₄⋊Q₈	C₂×D₁₁₃	1	2	yes	complemented
257	#126	—	113	2	no	—
258	#126	—	113	4	no	—
259	#126	—	113	4	no	—
260	#125	—	113	1	no	—
261	#125	—	113	2	no	—
262	#125	—	113	4	no	—
263	#124	—	113	1	no	—
264	#124	—	113	4	no	—
265	#124	—	113	2	no	—
266	#123	—	113	4	no	—
267	#123	—	113	2	no	—
268	#123	—	113	4	no	—
269	#123	—	113	4	no	—
270	#123	—	113	4	no	—
271	C₂²⋊Q₈	—	113	1	no	—
272	C₂²⋊Q₈	—	113	2	no	—
273	C₂²⋊Q₈	—	113	4	no	—
274	C₂²⋊Q₈	—	113	4	no	—
275	C₂²⋊Q₈	—	113	2	no	—
276	C₂²⋊Q₈	—	113	2	no	—
277	C₂²⋊Q₈	—	113	4	no	—
278	C₂²⋊Q₈	—	113	2	no	—
279	C₂²⋊Q₈	—	113	2	no	—
280	C₂²⋊Q₈	C₂×D₁₁₃	1	2	yes	complemented
281	C₂²⋊Q₈	C₂×D₁₁₃	1	4	yes	complemented
282	#121	—	113	2	no	—
283	#121	—	113	4	no	—
284	#121	—	113	1	no	—
285	#121	—	113	2	no	—
286	#120	—	113	4	no	—
287	C₄×Q₈	—	113	2	no	—
288	C₄×Q₈	—	113	2	no	—
289	C₄×Q₈	—	113	2	no	—
290	C₄×Q₈	C₂×D₁₁₃	1	1	yes	characteristic, complemented
291	C₄×D₄	—	113	1	no	—
292	C₄×D₄	—	113	2	no	—
293	C₄×D₄	—	113	4	no	—
294	C₄×D₄	—	113	1	no	—
295	C₄×D₄	—	113	4	no	—
296	C₄×D₄	—	113	2	no	—
297	C₄×D₄	—	113	4	no	—
298	C₄×D₄	—	113	1	no	—
299	C₄×D₄	—	113	2	no	—
300	C₄×D₄	—	113	1	no	—
301	C₄×D₄	C₂×D₁₁₃	1	1	yes	characteristic
302	C₄×D₄	C₂×D₁₁₃	1	2	yes	—
303	#117	—	113	2	no	—
304	#117	—	113	2	no	—
305	#117	—	113	4	no	—
306	#117	—	113	2	no	—
307	C₂×C₄⋊C₄	—	113	4	no	—
308	C₂×C₄⋊C₄	—	113	2	no	—
309	C₂×C₄⋊C₄	—	113	1	no	—
310	C₂×C₄⋊C₄	—	113	2	no	—
311	C₂×C₂²⋊C₄	—	113	4	no	—
312	C₂×C₂²⋊C₄	—	113	2	no	—
313	C₂×C₄²	—	113	1	no	—
314	C₂⁴	—	113	2	no	—
315	#41	—	452	4	no	—
316	#41	—	226	8	no	—
317	C₂×Q₈	—	4	4	no	—
318	C₂×Q₈	—	113	2	no	—
319	C₂×Q₈	C₂²×D₁₁₃	1	2	yes	—
320	C₂×Q₈	C₂²×D₁₁₃	1	1	yes	characteristic
321	C₂×Q₈	C₂²×D₁₁₃	1	4	yes	—
322	C₂×D₄	—	113	4	no	—
323	C₂×D₄	—	113	2	no	—
324	C₂×D₄	—	113	4	no	—
325	C₂×D₄	—	113	2	no	—
326	C₂×D₄	—	113	1	no	—
327	C₂×D₄	—	113	1	no	—
328	C₂×D₄	—	226	4	no	—
329	C₂×D₄	C₂²×D₁₁₃	1	1	yes	characteristic
330	C₂²×C₄	—	113	2	no	—
331	C₂²×C₄	—	113	4	no	—
332	C₂²×C₄	—	113	2	no	—
333	C₂²×C₄	—	113	4	no	—
334	C₂²×C₄	—	113	2	no	—
335	C₂²×C₄	—	113	1	no	—
336	C₂²×C₄	—	113	1	no	—
337	C₂²×C₄	—	113	1	no	—
338	C₂²×C₄	—	113	2	no	—
339	C₂²×C₄	—	113	2	no	—
340	C₂²×C₄	—	452	4	no	—
341	C₂²×C₄	C₂²×D₁₁₃	1	2	yes	—
342	C₂²×C₄	C₂²×D₁₁₃	1	4	yes	—
343	C₄⋊C₄	—	113	1	no	—
344	C₄⋊C₄	—	113	2	no	—
345	C₄⋊C₄	—	113	4	no	—
346	C₄⋊C₄	—	113	1	no	—
347	C₄⋊C₄	—	113	2	no	—
348	C₄⋊C₄	—	113	2	no	—
349	C₄⋊C₄	—	113	4	no	—
350	C₄⋊C₄	—	113	4	no	—
351	C₄⋊C₄	—	113	4	no	—
352	C₄⋊C₄	—	113	2	no	—
353	C₄⋊C₄	—	113	2	no	—
354	C₄⋊C₄	—	113	2	no	—
355	C₄⋊C₄	—	113	4	no	—
356	C₄⋊C₄	C₂²×D₁₁₃	1	1	yes	characteristic
357	C₄⋊C₄	C₂²×D₁₁₃	1	2	yes	—
358	C₄⋊C₄	C₂²×D₁₁₃	1	1	yes	characteristic
359	C₄⋊C₄	C₂²×D₁₁₃	1	2	yes	—
360	C₄⋊C₄	C₂²×D₁₁₃	1	4	yes	—
361	C₄⋊C₄	C₂²×D₁₁₃	1	2	yes	—
362	C₂²⋊C₄	—	113	2	no	—
363	C₂²⋊C₄	—	113	2	no	—
364	C₂²⋊C₄	—	113	4	no	—
365	C₂²⋊C₄	—	113	2	no	—
366	C₂²⋊C₄	—	113	2	no	—
367	C₂²⋊C₄	—	113	4	no	—
368	C₂²⋊C₄	—	113	4	no	—
369	C₂²⋊C₄	—	113	2	no	—
370	C₂²⋊C₄	—	113	2	no	—
371	C₂²⋊C₄	—	113	4	no	—
372	C₂²⋊C₄	—	113	2	no	—
373	C₂²⋊C₄	—	113	4	no	—
374	C₂²⋊C₄	—	113	2	no	—
375	C₂²⋊C₄	C₂²×D₁₁₃	1	2	yes	—
376	C₂²⋊C₄	C₂²×D₁₁₃	1	4	yes	—
377	C₄²	—	113	1	no	—
378	C₄²	—	113	1	no	—
379	C₄²	—	113	1	no	—
380	C₄²	—	113	4	no	—
381	C₄²	—	113	4	no	—
382	C₄²	C₂²×D₁₁₃	1	1	yes	characteristic
383	C₄²	C₂²×D₁₁₃	1	2	yes	—
384	C₂³	—	113	1	no	—
385	C₂³	—	113	2	no	—
386	C₂³	—	113	2	no	—
387	C₂³	—	452	2	no	—
388	C₂³	—	226	4	no	—
389	C₂³	—	226	4	no	—
390	C₂³	C₂³×D₁₁₃	1	2	yes	—
391	Q₈	—	2	2	no	—
392	Q₈	—	2	4	no	—
393	Q₈	—	4	4	no	—
394	Q₈	—	226	4	no	—
395	D₄	—	452	4	no	—
396	D₄	—	226	4	no	—
397	D₄	—	226	4	no	—
398	D₄	—	226	8	no	—
399	D₄	—	226	2	no	—
400	D₄	—	226	2	no	—
401	D₄	#14268648	1	4	yes	complemented
402	C₂×C₄	—	2	4	no	—
403	C₂×C₄	—	4	4	no	—
404	C₂×C₄	—	113	1	no	—
405	C₂×C₄	—	113	4	no	—
406	C₂×C₄	—	113	1	no	—
407	C₂×C₄	—	113	1	no	—
408	C₂×C₄	—	113	2	no	—
409	C₂×C₄	—	113	2	no	—
410	C₂×C₄	—	452	2	no	—
411	C₂×C₄	—	452	2	no	—
412	C₂×C₄	—	452	4	no	—
413	C₂×C₄	—	452	2	no	—
414	C₂×C₄	—	226	2	no	—
415	C₂×C₄	—	226	8	no	—
416	C₂×C₄	—	226	2	no	—
417	C₂×C₄	—	226	4	no	—
418	C₂×C₄	—	226	2	no	—
419	C₂×C₄	—	226	4	no	—
420	C₂×C₄	C₂³×D₁₁₃	1	2	yes	—
421	C₂×C₄	C₂³×D₁₁₃	1	1	yes	characteristic
422	C₂×C₄	C₂³×D₁₁₃	1	4	yes	—
423	C₂×C₄	C₂³×D₁₁₃	1	2	yes	—
424	C₂×C₄	C₂³×D₁₁₃	1	2	yes	—
425	C₂×C₄	C₂³×D₁₁₃	1	1	yes	characteristic
426	C₂×C₄	C₂³×D₁₁₃	1	1	yes	characteristic
427	C₂²	—	2	2	no	—
428	C₂²	—	2	2	no	—
429	C₂²	—	113	2	no	—
430	C₂²	—	452	8	no	—
431	C₂²	—	226	2	no	—
432	C₂²	—	226	2	no	—
433	C₂²	—	226	2	no	—
434	C₂²	—	226	2	no	—
435	C₂²	—	226	2	no	—
436	C₂²	—	226	2	no	—
437	C₂²	—	226	1	no	—
438	C₂²	—	226	1	no	—
439	C₂²	C₂×#14268648	1	4	yes	—
440	C₂²	C₂⁴×D₁₁₃	1	1	yes	characteristic
441	C₄	—	2	2	no	—
442	C₄	—	2	2	no	—
443	C₄	—	2	4	no	—
444	C₄	—	2	1	no	—
445	C₄	—	2	2	no	—
446	C₄	—	226	2	no	—
447	C₄	—	226	1	no	—
448	C₄	—	226	4	no	—
449	C₄	—	226	1	no	—
450	C₄	—	226	2	no	—
451	C₄	—	226	1	no	—
452	C₄	C₂×#14268648	1	2	yes	—
453	C₄	#16813667	1	2	yes	—
454	C₂	—	2	4	no	—
455	C₂	—	452	2	no	—
456	C₂	—	452	2	no	—
457	C₂	—	226	2	no	—
458	C₂	C₂²×#14268648	1	1	yes	characteristic
459	C₂	C₂×#16813667	1	1	yes	characteristic
460	C₂	2₋¹⁺⁴×D₁₁₃	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₁₁₃
commutator, socle, cosocle	C₂²×C₁₁₃	C₂⁵
Fitting	D₄×Q₈×C₁₁₃	C₂
hypercenter	D₄×Q₈	D₁₁₃
hypocenter	C₁₁₃	#3520
LCS	G ▷ C₂²×C₁₁₃ ▷ C₁₁₃
UCS	C₁ ◁ C₂² ◁ D₄×Q₈

Complements

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

N	H ≅ G/N	type
1. #20299321	C₂	semidirect
2. #20299309	C₂	semidirect
3. #20299290	C₂	semidirect
4. #20299275	C₂	semidirect
5. #20299259	C₂	semidirect
6. #20299252	C₂	semidirect
7. #20299251	C₂	semidirect
8. #20299243	C₂	semidirect
9. #20299222	C₂	semidirect
10. #20299197	C₂	semidirect
11. #20299153	C₂	semidirect
12. #20299135	C₂	semidirect
13. #20299111	C₂	semidirect
14. C₂×#16813598	C₂	semidirect
15. #20299077	C₂	semidirect
16. C₄×D₄×D₁₁₃	C₂	semidirect
17. D₄×Q₈×C₁₁₃	C₂	semidirect
18. C₂×#14268648	C₂²	semidirect
22. #16813622	C₂²	semidirect
23. #16813617	C₂²	semidirect
24. #16813617	C₂²	semidirect
25. #16813617	C₂²	semidirect
26. #16813613	C₂²	semidirect
27. #16813613	C₂²	semidirect
28. #16813613	C₂²	semidirect
29. #16813611	C₂²	semidirect
30. #16813611	C₂²	semidirect
33. #16813607	C₂²	semidirect
34. #16813607	C₂²	semidirect
36. #16813606	C₂²	semidirect
38. #16813602	C₂²	semidirect
42. #16813598	C₂²	semidirect
43. #16813598	C₂²	semidirect
44. #16813598	C₂²	semidirect
45. #16813598	C₂²	semidirect
49. #16813596	C₂²	semidirect
51. Q₈×Dic₁₁₃	C₂²	semidirect
52. C₄×Dic₂₂₆	C₂²	semidirect
53. #16813587	C₂²	semidirect
56. C₄×D₄₅₂	C₂²	semidirect
61. C₄×C₂²⋊D₁₁₃	C₂²	semidirect
63. #16813582	C₂²	semidirect
65. #16813580	C₂²	semidirect
66. #16813579	C₂²	semidirect
67. #16813578	C₂²	semidirect
68. C₂×C₄⋊Dic₁₁₃	C₂²	semidirect
69. C₂×#14268626	C₂²	semidirect
71. C₄⋊C₄×D₁₁₃	C₂²	semidirect
75. C₂²×Q₈×C₁₁₃	C₂²	semidirect
76. C₄⋊Q₈×C₁₁₃	C₂²	semidirect
77. C₄⋊Q₈×C₁₁₃	C₂²	semidirect
78. C₂²⋊Q₈×C₁₁₃	C₂²	semidirect
79. C₂²⋊Q₈×C₁₁₃	C₂²	semidirect
80. C₄×Q₈×C₁₁₃	C₂²	semidirect
163. D₄×C₁₁₃	#41	semidirect
231. C₁₁₃	#3520	semidirect
236. D₄×Q₈	D₁₁₃	semidirect
251. C₂²×Q₈	C₂×D₁₁₃	semidirect
255. C₄⋊Q₈	C₂×D₁₁₃	semidirect
256. C₄⋊Q₈	C₂×D₁₁₃	semidirect
280. C₂²⋊Q₈	C₂×D₁₁₃	semidirect
281. C₂²⋊Q₈	C₂×D₁₁₃	semidirect
290. C₄×Q₈	C₂×D₁₁₃	semidirect
401. D₄	#14268648	semidirect

Maximal subgroups

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

subgroup	index
#20299321	2
#20299309	2
#20299290	2
#20299275	2
#20299259	2
#20299252	2
#20299251	2
#20299243	2
#20299222	2
#20299197	2
#20299153	2
#20299135	2
#20299111	2
C₂×#16813598	2
#20299077	2
C₄×D₄×D₁₁₃	2
D₄×Q₈×C₁₁₃	2
#3520	113