Subgroups — #28404132

Order 14464.

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	#20299318	C₂	1	1	yes	maximal, characteristic, complemented
2	#20299313	C₂	1	1	yes	maximal, characteristic, complemented
3	#20299305	C₂	1	1	yes	maximal, characteristic, complemented
4	#20299294	C₂	1	2	yes	maximal, complemented
5	#20299288	C₂	1	2	yes	maximal, complemented
6	#20299283	C₂	1	2	yes	maximal, complemented
7	#20299274	C₂	1	4	yes	maximal, complemented
8	#20299252	C₂	1	1	yes	maximal, characteristic, complemented
9	#20299242	C₂	1	2	yes	maximal, complemented
10	#20299155	C₂	1	1	yes	maximal, characteristic, complemented
11	#20299130	C₂	1	2	yes	maximal, complemented
12	#20299128	C₂	1	4	yes	maximal, complemented
13	#20299109	C₂	1	2	yes	maximal, complemented
14	C₄×#14268647	C₂	1	1	yes	maximal, characteristic, complemented
15	C₄×#14268646	C₂	1	2	yes	maximal, complemented
16	C₂×#16813581	C₂	1	2	yes	maximal, complemented
17	C₂×C₄×D₄×C₁₁₃	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×#14268647	C₂²	1	1	yes	characteristic
19	C₂×#14268646	C₂²	1	2	yes	—
20	#16813622	C₂²	1	1	yes	characteristic, complemented
21	#16813622	C₂²	1	1	yes	characteristic, complemented
22	#16813617	C₂²	1	4	yes	complemented
23	#16813615	C₂²	1	4	yes	complemented
24	#16813615	C₂²	1	4	yes	complemented
25	#16813614	C₂²	1	2	yes	complemented
26	#16813613	C₂²	1	2	yes	complemented
27	#16813612	C₂²	1	4	yes	complemented
28	#16813609	C₂²	1	2	yes	—
29	#16813608	C₂²	1	4	yes	complemented
30	#16813606	C₂²	1	4	yes	complemented
31	#16813605	C₂²	1	4	yes	—
32	#16813604	C₂²	1	4	yes	complemented
33	#16813603	C₂²	1	4	yes	—
34	#16813602	C₂²	1	2	yes	complemented
35	#16813601	C₂²	1	2	yes	—
36	#16813601	C₂²	1	2	yes	—
37	#16813601	C₂²	1	2	yes	complemented
38	#16813601	C₂²	1	2	yes	complemented
39	#16813599	C₂²	1	4	yes	complemented
40	#16813596	C₂²	1	2	yes	complemented
41	#16813596	C₂²	1	2	yes	complemented
42	#16813594	C₂²	1	4	yes	—
43	#16813593	C₂²	1	2	yes	—
44	#16813591	C₂²	1	4	yes	—
45	C₄×Dic₂₂₆	C₂²	1	1	yes	characteristic, complemented
46	C₄×Dic₂₂₆	C₂²	1	1	yes	characteristic, complemented
47	C₄×Dic₂₂₆	C₂²	1	2	yes	complemented
48	C₄×Dic₂₂₆	C₂²	1	2	yes	complemented
49	#16813587	C₂²	1	2	yes	complemented
50	C₄×D₄₅₂	C₂²	1	1	yes	characteristic, complemented
51	C₄×D₄₅₂	C₂²	1	1	yes	characteristic, complemented
52	D₄×Dic₁₁₃	C₂²	1	2	yes	—
53	C₄×C₂²⋊D₁₁₃	C₂²	1	2	yes	—
54	C₄×C₂²⋊D₁₁₃	C₂²	1	2	yes	—
55	C₄×C₂²⋊D₁₁₃	C₂²	1	4	yes	complemented
56	C₄×C₂²⋊D₁₁₃	C₂²	1	4	yes	complemented
57	#16813582	C₂²	1	4	yes	complemented
58	#16813581	C₂²	1	4	yes	—
59	#16813581	C₂²	1	1	yes	characteristic
60	#16813581	C₂²	1	2	yes	—
61	#16813581	C₂²	1	2	yes	complemented
62	#16813581	C₂²	1	2	yes	complemented
63	#16813581	C₂²	1	4	yes	complemented
64	#16813580	C₂²	1	2	yes	complemented
65	#16813579	C₂²	1	2	yes	complemented
66	#16813578	C₂²	1	4	yes	complemented
67	C₂×C₄⋊Dic₁₁₃	C₂²	1	2	yes	complemented
68	C₂×C₄⋊Dic₁₁₃	C₂²	1	2	yes	complemented
69	C₂×C₂²⋊Dic₁₁₃	C₂²	1	4	yes	—
70	C₂×C₄×Dic₁₁₃	C₂²	1	4	yes	complemented
71	C₄²×D₁₁₃	C₂²	1	2	yes	complemented
72	C₂²×D₄×C₁₁₃	C₂²	1	1	yes	characteristic
73	C₂³×C₄×C₁₁₃	C₂²	1	2	yes	—
74	C₄×D₄×C₁₁₃	C₂²	1	2	yes	—
75	C₄×D₄×C₁₁₃	C₂²	1	1	yes	characteristic
76	C₄×D₄×C₁₁₃	C₂²	1	1	yes	characteristic
77	C₄×D₄×C₁₁₃	C₂²	1	1	yes	characteristic
78	C₄×D₄×C₁₁₃	C₂²	1	2	yes	—
79	C₄×D₄×C₁₁₃	C₂²	1	1	yes	characteristic
80	C₂×C₄⋊C₄×C₁₁₃	C₂²	1	1	yes	characteristic
81	C₂×C₂²⋊C₄×C₁₁₃	C₂²	1	2	yes	—
82	C₂×C₄²×C₁₁₃	C₂²	1	1	yes	characteristic
83	#14268647	—	2	4	no	—
84	#14268646	—	2	8	no	—
85	C₂×Dic₂₂₆	C₂³	1	2	yes	—
86	C₂×Dic₂₂₆	C₂³	1	1	yes	characteristic
87	C₂×Dic₂₂₆	C₂³	1	2	yes	—
88	C₂×D₄₅₂	C₂³	1	1	yes	characteristic
89	C₂×C₂²⋊D₁₁₃	C₂³	1	4	yes	—
90	C₂×C₂²⋊D₁₁₃	C₂³	1	2	yes	—
91	C₂×C₂²⋊D₁₁₃	C₂³	1	4	yes	—
92	C₂²×Dic₁₁₃	C₂³	1	4	yes	—
93	C₂²×Dic₁₁₃	C₂³	1	4	yes	—
94	C₂×C₄×D₁₁₃	C₂³	1	2	yes	—
95	C₂×C₄×D₁₁₃	C₂³	1	2	yes	—
96	C₂×C₄×D₁₁₃	C₂³	1	2	yes	—
97	C₄⋊Dic₁₁₃	C₂³	1	1	yes	characteristic
98	C₄⋊Dic₁₁₃	C₂³	1	1	yes	characteristic
99	C₄⋊Dic₁₁₃	C₂³	1	2	yes	—
100	C₄⋊Dic₁₁₃	C₂³	1	2	yes	—
101	C₄⋊Dic₁₁₃	C₂³	1	4	yes	—
102	C₄⋊Dic₁₁₃	C₂³	1	4	yes	—
103	C₄⋊Dic₁₁₃	C₂³	1	2	yes	—
104	C₄⋊Dic₁₁₃	C₂³	1	2	yes	—
105	#14268626	C₂³	1	4	yes	—
106	#14268626	C₂³	1	4	yes	—
107	#14268626	C₂³	1	2	yes	—
108	#14268626	C₂³	1	2	yes	—
109	#14268626	C₂³	1	4	yes	—
110	#14268626	C₂³	1	4	yes	—
111	C₂²⋊Dic₁₁₃	C₂³	1	2	yes	—
112	C₂²⋊Dic₁₁₃	C₂³	1	4	yes	—
113	C₂²⋊Dic₁₁₃	C₂³	1	4	yes	—
114	C₂²⋊Dic₁₁₃	C₂³	1	4	yes	—
115	C₂²⋊Dic₁₁₃	C₂³	1	4	yes	—
116	C₂²⋊Dic₁₁₃	C₂³	1	4	yes	—
117	#14268624	C₂³	1	2	yes	—
118	#14268624	C₂³	1	2	yes	—
119	#14268624	C₂³	1	4	yes	—
120	#14268624	C₂³	1	4	yes	—
121	C₄×Dic₁₁₃	C₂³	1	2	yes	—
122	C₄×Dic₁₁₃	C₂³	1	2	yes	—
123	C₄×Dic₁₁₃	C₂³	1	2	yes	—
124	C₄×Dic₁₁₃	C₂³	1	4	yes	—
125	C₄×Dic₁₁₃	C₂³	1	4	yes	—
126	C₄×Dic₁₁₃	C₂³	1	4	yes	—
127	C₂⁴×C₁₁₃	C₂³	1	2	yes	—
128	C₂×D₄×C₁₁₃	—	2	4	no	—
129	C₂×D₄×C₁₁₃	C₂³	1	1	yes	characteristic
130	C₂×D₄×C₁₁₃	C₂³	1	2	yes	—
131	C₂×D₄×C₁₁₃	C₂³	1	1	yes	characteristic
132	C₂²×C₄×C₁₁₃	—	2	8	no	—
133	C₂²×C₄×C₁₁₃	C₂³	1	2	yes	—
134	C₂²×C₄×C₁₁₃	C₂³	1	2	yes	—
135	C₂²×C₄×C₁₁₃	C₂³	1	2	yes	—
136	C₂²×C₄×C₁₁₃	C₂³	1	2	yes	—
137	C₂²×C₄×C₁₁₃	C₂³	1	2	yes	—
138	C₂²×C₄×C₁₁₃	C₂³	1	1	yes	characteristic
139	C₂²×C₄×C₁₁₃	C₂³	1	1	yes	characteristic
140	C₂²×C₄×C₁₁₃	C₂³	1	1	yes	characteristic
141	C₄⋊C₄×C₁₁₃	C₂³	1	1	yes	characteristic
142	C₄⋊C₄×C₁₁₃	C₂³	1	1	yes	characteristic
143	C₄⋊C₄×C₁₁₃	C₂³	1	2	yes	—
144	C₂²⋊C₄×C₁₁₃	C₂³	1	2	yes	—
145	C₂²⋊C₄×C₁₁₃	C₂³	1	2	yes	—
146	C₂²⋊C₄×C₁₁₃	C₂³	1	2	yes	—
147	C₂²⋊C₄×C₁₁₃	C₂³	1	2	yes	—
148	C₄²×C₁₁₃	C₂³	1	1	yes	characteristic
149	C₄²×C₁₁₃	C₂³	1	1	yes	characteristic
150	C₄²×C₁₁₃	C₂³	1	1	yes	characteristic
151	C₄²×C₁₁₃	C₂³	1	1	yes	characteristic
152	C₂³×C₁₁₃	—	2	4	no	—
153	C₂³×C₁₁₃	—	2	4	no	—
154	C₂³×C₁₁₃	—	4	2	no	—
155	C₂³×C₁₁₃	C₂⁴	1	2	yes	—
156	C₂³×C₁₁₃	C₂⁴	1	2	yes	—
157	C₂³×C₁₁₃	C₂⁴	1	1	yes	characteristic
158	C₂²×D₁₁₃	C₂⁴	1	2	yes	—
159	D₄×C₁₁₃	—	2	4	no	—
160	D₄×C₁₁₃	—	2	2	no	—
161	D₄×C₁₁₃	#41	1	4	yes	complemented
162	C₂×C₄×C₁₁₃	—	2	4	no	—
163	C₂×C₄×C₁₁₃	—	2	4	no	—
164	C₂×C₄×C₁₁₃	—	2	4	no	—
165	C₂×C₄×C₁₁₃	—	2	4	no	—
166	C₂×C₄×C₁₁₃	—	2	4	no	—
167	C₂×C₄×C₁₁₃	—	2	2	no	—
168	C₂×C₄×C₁₁₃	—	4	1	no	—
169	C₂×C₄×C₁₁₃	#41	1	4	yes	complemented
170	C₂×C₄×C₁₁₃	C₂⁴	1	1	yes	characteristic
171	C₂×C₄×C₁₁₃	C₂⁴	1	1	yes	characteristic
172	C₂×C₄×C₁₁₃	C₂⁴	1	1	yes	characteristic
173	C₂×C₄×C₁₁₃	C₂⁴	1	2	yes	—
174	C₂×C₄×C₁₁₃	C₂⁴	1	2	yes	—
175	C₂×C₄×C₁₁₃	C₂⁴	1	1	yes	characteristic
176	C₂×C₄×C₁₁₃	C₂⁴	1	1	yes	characteristic
177	C₂×C₄×C₁₁₃	C₂⁴	1	1	yes	characteristic
178	C₂²⋊D₁₁₃	—	2	8	no	—
179	C₂²⋊D₁₁₃	—	2	4	no	—
180	C₂²⋊D₁₁₃	—	4	4	no	—
181	C₂×Dic₁₁₃	—	2	8	no	—
182	C₂×Dic₁₁₃	—	4	4	no	—
183	C₂×Dic₁₁₃	C₂⁴	1	2	yes	—
184	C₂×Dic₁₁₃	C₂⁴	1	2	yes	—
185	C₂×Dic₁₁₃	C₂⁴	1	4	yes	—
186	C₂×Dic₁₁₃	C₂⁴	1	4	yes	—
187	C₂×Dic₁₁₃	C₂⁴	1	2	yes	—
188	D₄₅₂	—	2	2	no	—
189	C₄×D₁₁₃	—	2	4	no	—
190	C₄×D₁₁₃	—	2	4	no	—
191	C₄×D₁₁₃	—	4	2	no	—
192	Dic₂₂₆	—	2	4	no	—
193	Dic₂₂₆	—	2	2	no	—
194	Dic₂₂₆	—	4	2	no	—
195	C₂²×C₁₁₃	—	2	2	no	—
196	C₂²×C₁₁₃	—	2	1	no	—
197	C₂²×C₁₁₃	—	2	2	no	—
198	C₂²×C₁₁₃	—	2	1	no	—
199	C₂²×C₁₁₃	—	2	2	no	—
200	C₂²×C₁₁₃	—	2	2	no	—
201	C₂²×C₁₁₃	—	2	2	no	—
202	C₂²×C₁₁₃	—	4	8	no	—
203	C₂²×C₁₁₃	C₂×#41	1	2	yes	—
204	C₂²×C₁₁₃	C₂×#41	1	4	yes	—
205	C₂²×C₁₁₃	C₂⁵	1	1	yes	characteristic
206	C₂×D₁₁₃	—	2	2	no	—
207	C₂×D₁₁₃	—	2	2	no	—
208	C₂×D₁₁₃	—	2	2	no	—
209	C₄×C₁₁₃	—	2	2	no	—
210	C₄×C₁₁₃	—	2	2	no	—
211	C₄×C₁₁₃	—	2	1	no	—
212	C₄×C₁₁₃	—	2	1	no	—
213	C₄×C₁₁₃	—	2	1	no	—
214	C₄×C₁₁₃	C₂×#41	1	2	yes	—
215	C₄×C₁₁₃	C₂×#41	1	2	yes	—
216	C₄×C₁₁₃	C₂×#41	1	2	yes	—
217	Dic₁₁₃	—	2	2	no	—
218	Dic₁₁₃	—	2	4	no	—
219	Dic₁₁₃	—	2	2	no	—
220	Dic₁₁₃	—	2	4	no	—
221	Dic₁₁₃	—	2	2	no	—
222	C₂×C₁₁₃	—	2	2	no	—
223	C₂×C₁₁₃	—	2	4	no	—
224	C₂×C₁₁₃	—	4	2	no	—
225	C₂×C₁₁₃	C₂²×#41	1	1	yes	characteristic
226	C₂×C₁₁₃	C₂²×#41	1	1	yes	characteristic
227	C₂×C₁₁₃	#585	1	1	yes	characteristic
228	D₁₁₃	—	4	2	no	—
229	#3475	—	113	1	no	maximal, Sylow
230	C₁₁₃	#3475	1	1	yes	characteristic, complemented, Sylow
231	#556	—	113	1	no	—
232	#555	—	113	1	no	—
233	#554	—	113	1	no	—
234	#553	—	113	2	no	—
235	#552	—	113	2	no	—
236	#552	—	113	2	no	—
237	#551	—	113	4	no	—
238	#547	—	113	1	no	—
239	#546	—	113	2	no	—
240	#533	—	113	1	no	—
241	#529	—	113	4	no	—
242	#529	—	113	2	no	—
243	#525	—	113	2	no	—
244	C₄×#41	—	113	2	no	—
245	C₄×#41	—	113	1	no	—
246	C₂×C₄×D₄	D₁₁₃	1	1	yes	characteristic, complemented
247	C₂×#117	—	113	2	no	—
248	C₂×#41	—	113	2	no	—
249	C₂×#41	—	113	1	no	—
250	C₂²×D₄	C₂×D₁₁₃	1	1	yes	characteristic
251	C₂³×C₄	C₂×D₁₁₃	1	2	yes	—
252	C₄⋊Q₈	—	113	1	no	—
253	C₄⋊Q₈	—	113	1	no	—
254	#126	—	113	4	no	—
255	#126	—	113	4	no	—
256	#126	—	113	4	no	—
257	#125	—	113	4	no	—
258	#125	—	113	2	no	—
259	#125	—	113	2	no	—
260	#124	—	113	2	no	—
261	#124	—	113	4	no	—
262	#123	—	113	4	no	—
263	#123	—	113	4	no	—
264	#123	—	113	4	no	—
265	#123	—	113	4	no	—
266	C₂²⋊Q₈	—	113	2	no	—
267	C₂²⋊Q₈	—	113	2	no	—
268	C₂²⋊Q₈	—	113	2	no	—
269	C₂²⋊Q₈	—	113	2	no	—
270	C₂²⋊Q₈	—	113	2	no	—
271	C₂²⋊Q₈	—	113	4	no	—
272	#121	—	113	2	no	—
273	#121	—	113	4	no	—
274	#121	—	113	2	no	—
275	#121	—	113	2	no	—
276	#120	—	113	4	no	—
277	C₄×Q₈	—	113	2	no	—
278	C₄×Q₈	—	113	2	no	—
279	C₄×Q₈	—	113	1	no	—
280	C₄×Q₈	—	113	1	no	—
281	C₄×Q₈	—	113	2	no	—
282	C₄×D₄	—	113	2	no	—
283	C₄×D₄	—	113	4	no	—
284	C₄×D₄	—	113	2	no	—
285	C₄×D₄	—	113	2	no	—
286	C₄×D₄	—	113	4	no	—
287	C₄×D₄	—	113	4	no	—
288	C₄×D₄	—	113	1	no	—
289	C₄×D₄	—	113	1	no	—
290	C₄×D₄	C₂×D₁₁₃	1	1	yes	characteristic
291	C₄×D₄	C₂×D₁₁₃	1	1	yes	characteristic
292	C₄×D₄	C₂×D₁₁₃	1	2	yes	—
293	C₄×D₄	C₂×D₁₁₃	1	1	yes	characteristic
294	C₄×D₄	C₂×D₁₁₃	1	2	yes	—
295	C₄×D₄	C₂×D₁₁₃	1	1	yes	characteristic
296	#117	—	113	1	no	—
297	#117	—	113	2	no	—
298	#117	—	113	4	no	—
299	#117	—	113	4	no	—
300	#117	—	113	2	no	—
301	#117	—	113	2	no	—
302	#117	—	113	2	no	—
303	#117	—	113	4	no	—
304	#117	—	113	2	no	—
305	C₂×C₄⋊C₄	—	113	2	no	—
306	C₂×C₄⋊C₄	—	113	2	no	—
307	C₂×C₄⋊C₄	C₂×D₁₁₃	1	1	yes	characteristic
308	C₂×C₂²⋊C₄	—	113	4	no	—
309	C₂×C₂²⋊C₄	C₂×D₁₁₃	1	2	yes	—
310	C₂×C₄²	—	113	4	no	—
311	C₂×C₄²	—	113	2	no	—
312	C₂×C₄²	C₂×D₁₁₃	1	1	yes	characteristic
313	C₂⁴	C₂²×D₁₁₃	1	2	yes	—
314	#41	—	226	8	no	—
315	#41	—	226	4	no	—
316	C₂×Q₈	—	113	2	no	—
317	C₂×Q₈	—	113	1	no	—
318	C₂×Q₈	—	113	2	no	—
319	C₂×D₄	—	2	4	no	—
320	C₂×D₄	—	113	4	no	—
321	C₂×D₄	—	113	2	no	—
322	C₂×D₄	—	113	4	no	—
323	C₂×D₄	—	113	1	no	—
324	C₂×D₄	C₂²×D₁₁₃	1	2	yes	—
325	C₂×D₄	C₂²×D₁₁₃	1	1	yes	characteristic
326	C₂×D₄	C₂²×D₁₁₃	1	1	yes	characteristic
327	C₂²×C₄	—	2	8	no	—
328	C₂²×C₄	—	113	4	no	—
329	C₂²×C₄	—	113	4	no	—
330	C₂²×C₄	—	113	2	no	—
331	C₂²×C₄	—	113	2	no	—
332	C₂²×C₄	—	113	2	no	—
333	C₂²×C₄	C₂²×D₁₁₃	1	1	yes	characteristic
334	C₂²×C₄	C₂²×D₁₁₃	1	2	yes	—
335	C₂²×C₄	C₂²×D₁₁₃	1	2	yes	—
336	C₂²×C₄	C₂²×D₁₁₃	1	2	yes	—
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	C₂²×C₄	C₂²×D₁₁₃	1	1	yes	characteristic
341	C₄⋊C₄	—	113	1	no	—
342	C₄⋊C₄	—	113	1	no	—
343	C₄⋊C₄	—	113	2	no	—
344	C₄⋊C₄	—	113	2	no	—
345	C₄⋊C₄	—	113	4	no	—
346	C₄⋊C₄	—	113	4	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	2	no	—
352	C₄⋊C₄	—	113	4	no	—
353	C₄⋊C₄	—	113	4	no	—
354	C₄⋊C₄	—	113	2	no	—
355	C₄⋊C₄	C₂²×D₁₁₃	1	1	yes	characteristic
356	C₄⋊C₄	C₂²×D₁₁₃	1	1	yes	characteristic
357	C₄⋊C₄	C₂²×D₁₁₃	1	2	yes	—
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	—	113	2	no	—
365	C₂²⋊C₄	—	113	4	no	—
366	C₂²⋊C₄	—	113	2	no	—
367	C₂²⋊C₄	—	113	4	no	—
368	C₂²⋊C₄	C₂²×D₁₁₃	1	2	yes	—
369	C₂²⋊C₄	C₂²×D₁₁₃	1	2	yes	—
370	C₂²⋊C₄	C₂²×D₁₁₃	1	2	yes	—
371	C₂²⋊C₄	C₂²×D₁₁₃	1	2	yes	—
372	C₄²	—	113	4	no	—
373	C₄²	—	113	4	no	—
374	C₄²	—	113	2	no	—
375	C₄²	—	113	2	no	—
376	C₄²	—	113	2	no	—
377	C₄²	—	113	4	no	—
378	C₄²	C₂²×D₁₁₃	1	1	yes	characteristic
379	C₄²	C₂²×D₁₁₃	1	1	yes	characteristic
380	C₄²	C₂²×D₁₁₃	1	1	yes	characteristic
381	C₄²	C₂²×D₁₁₃	1	1	yes	characteristic
382	C₂³	—	2	4	no	—
383	C₂³	—	2	4	no	—
384	C₂³	—	4	2	no	—
385	C₂³	—	113	2	no	—
386	C₂³	C₂³×D₁₁₃	1	2	yes	—
387	C₂³	C₂³×D₁₁₃	1	1	yes	characteristic
388	C₂³	C₂³×D₁₁₃	1	2	yes	—
389	Q₈	—	452	2	no	—
390	Q₈	—	226	2	no	—
391	Q₈	—	226	4	no	—
392	D₄	—	2	4	no	—
393	D₄	—	2	2	no	—
394	D₄	—	452	4	no	—
395	D₄	—	226	4	no	—
396	D₄	—	226	8	no	—
397	D₄	—	226	2	no	—
398	D₄	#14268647	1	4	yes	complemented
399	C₂×C₄	—	2	4	no	—
400	C₂×C₄	—	2	4	no	—
401	C₂×C₄	—	2	4	no	—
402	C₂×C₄	—	2	4	no	—
403	C₂×C₄	—	2	4	no	—
404	C₂×C₄	—	2	2	no	—
405	C₂×C₄	—	4	1	no	—
406	C₂×C₄	—	113	2	no	—
407	C₂×C₄	—	113	2	no	—
408	C₂×C₄	—	113	2	no	—
409	C₂×C₄	—	113	4	no	—
410	C₂×C₄	—	113	4	no	—
411	C₂×C₄	—	452	2	no	—
412	C₂×C₄	—	452	4	no	—
413	C₂×C₄	—	226	8	no	—
414	C₂×C₄	—	226	4	no	—
415	C₂×C₄	—	226	4	no	—
416	C₂×C₄	#14268646	1	4	yes	complemented
417	C₂×C₄	C₂³×D₁₁₃	1	2	yes	—
418	C₂×C₄	C₂³×D₁₁₃	1	1	yes	characteristic
419	C₂×C₄	C₂³×D₁₁₃	1	1	yes	characteristic
420	C₂×C₄	C₂³×D₁₁₃	1	1	yes	characteristic
421	C₂×C₄	C₂³×D₁₁₃	1	2	yes	—
422	C₂×C₄	C₂³×D₁₁₃	1	1	yes	characteristic
423	C₂×C₄	C₂³×D₁₁₃	1	1	yes	characteristic
424	C₂×C₄	C₂³×D₁₁₃	1	1	yes	characteristic
425	C₂²	—	2	2	no	—
426	C₂²	—	2	1	no	—
427	C₂²	—	2	1	no	—
428	C₂²	—	2	2	no	—
429	C₂²	—	2	2	no	—
430	C₂²	—	2	2	no	—
431	C₂²	—	2	2	no	—
432	C₂²	—	4	8	no	—
433	C₂²	—	226	2	no	—
434	C₂²	—	226	2	no	—
435	C₂²	—	226	2	no	—
436	C₂²	C₂×#14268646	1	2	yes	—
437	C₂²	C₂×#14268647	1	4	yes	—
438	C₂²	C₂⁴×D₁₁₃	1	1	yes	characteristic
439	C₄	—	2	2	no	—
440	C₄	—	2	2	no	—
441	C₄	—	2	1	no	—
442	C₄	—	2	1	no	—
443	C₄	—	2	1	no	—
444	C₄	—	226	2	no	—
445	C₄	—	226	2	no	—
446	C₄	—	226	4	no	—
447	C₄	—	226	2	no	—
448	C₄	—	226	4	no	—
449	C₄	C₂×#14268646	1	2	yes	—
450	C₄	C₂×#14268646	1	2	yes	—
451	C₄	C₂×#14268647	1	2	yes	—
452	C₂	—	2	2	no	—
453	C₂	—	2	4	no	—
454	C₂	—	4	2	no	—
455	C₂	—	452	2	no	—
456	C₂	C₂²×#14268646	1	1	yes	characteristic
457	C₂	C₂²×#14268647	1	1	yes	characteristic
458	C₂	#20299434	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂³×D₁₁₃
commutator, socle, cosocle	C₂²×C₁₁₃	C₂⁵
Frattini	C₂²	C₂⁴×D₁₁₃
Fitting	C₂×C₄×D₄×C₁₁₃	C₂
hypercenter	C₂×C₄×D₄	D₁₁₃
hypocenter	C₁₁₃	#3475
LCS	G ▷ C₂²×C₁₁₃ ▷ C₁₁₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄×D₄

Complements

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

N	H ≅ G/N	type
1. #20299318	C₂	semidirect
2. #20299313	C₂	semidirect
3. #20299305	C₂	semidirect
4. #20299294	C₂	semidirect
5. #20299288	C₂	semidirect
6. #20299283	C₂	semidirect
7. #20299274	C₂	semidirect
8. #20299252	C₂	semidirect
9. #20299242	C₂	semidirect
10. #20299155	C₂	semidirect
11. #20299130	C₂	semidirect
12. #20299128	C₂	semidirect
13. #20299109	C₂	semidirect
14. C₄×#14268647	C₂	semidirect
15. C₄×#14268646	C₂	semidirect
16. C₂×#16813581	C₂	semidirect
17. C₂×C₄×D₄×C₁₁₃	C₂	semidirect
20. #16813622	C₂²	semidirect
21. #16813622	C₂²	semidirect
22. #16813617	C₂²	semidirect
23. #16813615	C₂²	semidirect
24. #16813615	C₂²	semidirect
25. #16813614	C₂²	semidirect
26. #16813613	C₂²	semidirect
27. #16813612	C₂²	semidirect
29. #16813608	C₂²	semidirect
30. #16813606	C₂²	semidirect
32. #16813604	C₂²	semidirect
34. #16813602	C₂²	semidirect
37. #16813601	C₂²	semidirect
38. #16813601	C₂²	semidirect
39. #16813599	C₂²	semidirect
40. #16813596	C₂²	semidirect
41. #16813596	C₂²	semidirect
45. C₄×Dic₂₂₆	C₂²	semidirect
46. C₄×Dic₂₂₆	C₂²	semidirect
47. C₄×Dic₂₂₆	C₂²	semidirect
48. C₄×Dic₂₂₆	C₂²	semidirect
49. #16813587	C₂²	semidirect
50. C₄×D₄₅₂	C₂²	semidirect
51. C₄×D₄₅₂	C₂²	semidirect
55. C₄×C₂²⋊D₁₁₃	C₂²	semidirect
56. C₄×C₂²⋊D₁₁₃	C₂²	semidirect
57. #16813582	C₂²	semidirect
61. #16813581	C₂²	semidirect
62. #16813581	C₂²	semidirect
63. #16813581	C₂²	semidirect
64. #16813580	C₂²	semidirect
65. #16813579	C₂²	semidirect
66. #16813578	C₂²	semidirect
67. C₂×C₄⋊Dic₁₁₃	C₂²	semidirect
68. C₂×C₄⋊Dic₁₁₃	C₂²	semidirect
70. C₂×C₄×Dic₁₁₃	C₂²	semidirect
71. C₄²×D₁₁₃	C₂²	semidirect
161. D₄×C₁₁₃	#41	semidirect
169. C₂×C₄×C₁₁₃	#41	semidirect
230. C₁₁₃	#3475	semidirect
246. C₂×C₄×D₄	D₁₁₃	semidirect
398. D₄	#14268647	semidirect
416. C₂×C₄	#14268646	semidirect

Maximal subgroups

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

subgroup	index
#20299318	2
#20299313	2
#20299305	2
#20299294	2
#20299288	2
#20299283	2
#20299274	2
#20299252	2
#20299242	2
#20299155	2
#20299130	2
#20299128	2
#20299109	2
C₄×#14268647	2
C₄×#14268646	2
C₂×#16813581	2
C₂×C₄×D₄×C₁₁₃	2
#3475	113