Subgroups — #28404058

Order 14464.

1648 conjugacy classes of subgroups.

The subgroup lattice has 778 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#14268646	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#41×D₁₁₃	C₂	1	1	yes	maximal, characteristic, complemented
3	#20299266	C₂	1	1	yes	maximal, characteristic, complemented
4	#20299261	C₂	1	1	yes	maximal, characteristic, complemented
5	#20299257	C₂	1	1	yes	maximal, characteristic, complemented
6	#20299256	C₂	1	1	yes	maximal, characteristic, complemented
7	#20299247	C₂	1	1	yes	maximal, characteristic, complemented
8	#20299246	C₂	1	2	yes	maximal, complemented
9	#20299243	C₂	1	1	yes	maximal, characteristic, complemented
10	#20299238	C₂	1	2	yes	maximal, complemented
11	#20299237	C₂	1	2	yes	maximal, complemented
12	D₄×C₂²⋊D₁₁₃	C₂	1	1	yes	maximal, characteristic, complemented
13	#20299230	C₂	1	2	yes	maximal, complemented
14	#20299147	C₂	1	1	yes	maximal, characteristic, complemented
15	#20299143	C₂	1	2	yes	maximal, complemented
16	#20299111	C₂	1	1	yes	maximal, characteristic, complemented
17	#20299108	C₂	1	1	yes	maximal, characteristic, complemented
18	#20299106	C₂	1	2	yes	maximal, complemented
19	#20299104	C₂	1	2	yes	maximal, complemented
20	C₄×#14268646	C₂	1	1	yes	maximal, characteristic, complemented
21	C₂×#16813582	C₂	1	2	yes	maximal, complemented
22	C₄×D₄×D₁₁₃	C₂	1	1	yes	maximal, characteristic, complemented
23	#546×C₁₁₃	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#14268648	C₂²	1	1	yes	characteristic, complemented
25	C₂×#14268647	C₂²	1	1	yes	characteristic, complemented
26	C₂×#14268647	C₂²	1	2	yes	complemented
27	C₂×#14268646	—	2	8	no	—
28	C₂×#14268646	C₂²	1	1	yes	characteristic
29	C₂×#14268646	C₂²	1	1	yes	characteristic, complemented
30	C₂×#14268646	C₂²	1	2	yes	complemented
31	C₂×#14268646	C₂²	1	2	yes	complemented
32	C₂×#14268646	C₂²	1	1	yes	characteristic, complemented
33	C₂×#14268646	C₂²	1	2	yes	complemented
34	C₂×#14268646	C₂²	1	1	yes	characteristic, complemented
35	#41×D₁₁₃	—	2	8	no	—
36	C₂²×Dic₂₂₆	C₂²	1	1	yes	characteristic, complemented
37	C₂×Q₈×D₁₁₃	C₂²	1	1	yes	characteristic, complemented
38	C₂²×C₂²⋊D₁₁₃	C₂²	1	2	yes	—
39	C₂²×C₂²⋊D₁₁₃	C₂²	1	2	yes	complemented
40	C₂×D₄×D₁₁₃	C₂²	1	1	yes	characteristic
41	C₂×D₄×D₁₁₃	C₂²	1	2	yes	complemented
42	C₂×D₄×D₁₁₃	C₂²	1	1	yes	characteristic, complemented
43	C₂³×Dic₁₁₃	C₂²	1	2	yes	complemented
44	C₂²×C₄×D₁₁₃	C₂²	1	1	yes	characteristic, complemented
45	C₂²×C₄×D₁₁₃	C₂²	1	1	yes	characteristic, complemented
46	C₂²×C₄×D₁₁₃	C₂²	1	2	yes	complemented
47	#16813621	C₂²	1	2	yes	complemented
48	#16813620	C₂²	1	1	yes	characteristic, complemented
49	#16813618	C₂²	1	2	yes	complemented
50	#16813618	C₂²	1	1	yes	characteristic, complemented
51	#16813610	C₂²	1	1	yes	characteristic, complemented
52	#16813608	C₂²	1	2	yes	complemented
53	#16813608	C₂²	1	2	yes	complemented
54	#16813607	C₂²	1	2	yes	complemented
55	#16813606	C₂²	1	2	yes	complemented
56	#16813605	C₂²	1	2	yes	complemented
57	#16813604	C₂²	1	2	yes	complemented
58	#16813603	C₂²	1	2	yes	complemented
59	#16813602	C₂²	1	1	yes	characteristic, complemented
60	#16813601	C₂²	1	1	yes	characteristic, complemented
61	#16813600	C₂²	1	2	yes	complemented
62	#16813600	C₂²	1	2	yes	complemented
63	#16813599	C₂²	1	2	yes	complemented
64	#16813599	C₂²	1	2	yes	complemented
65	#16813598	C₂²	1	1	yes	characteristic, complemented
66	#16813597	C₂²	1	1	yes	characteristic, complemented
67	#16813596	C₂²	1	1	yes	characteristic, complemented
68	#16813596	C₂²	1	2	yes	complemented
69	#16813595	C₂²	1	2	yes	complemented
70	#16813595	C₂²	1	2	yes	complemented
71	#16813595	C₂²	1	2	yes	complemented
72	#16813595	C₂²	1	2	yes	complemented
73	#16813594	C₂²	1	2	yes	complemented
74	#16813594	C₂²	1	2	yes	complemented
75	#16813594	C₂²	1	2	yes	complemented
76	#16813594	C₂²	1	2	yes	complemented
77	#16813593	C₂²	1	1	yes	characteristic, complemented
78	#16813592	C₂²	1	2	yes	complemented
79	#16813592	C₂²	1	2	yes	complemented
80	#16813591	C₂²	1	2	yes	complemented
81	#16813590	C₂²	1	2	yes	complemented
82	#16813590	C₂²	1	2	yes	complemented
83	C₄×Dic₂₂₆	C₂²	1	1	yes	characteristic, complemented
84	#16813587	C₂²	1	1	yes	characteristic, complemented
85	C₄×D₄₅₂	C₂²	1	1	yes	characteristic, complemented
86	D₄×Dic₁₁₃	C₂²	1	1	yes	characteristic, complemented
87	D₄×Dic₁₁₃	C₂²	1	1	yes	characteristic, complemented
88	D₄×Dic₁₁₃	C₂²	1	2	yes	complemented
89	#16813584	C₂²	1	1	yes	characteristic, complemented
90	#16813584	C₂²	1	2	yes	complemented
91	C₄×C₂²⋊D₁₁₃	C₂²	1	1	yes	characteristic
92	C₄×C₂²⋊D₁₁₃	C₂²	1	1	yes	characteristic, complemented
93	C₄×C₂²⋊D₁₁₃	C₂²	1	2	yes	complemented
94	#16813582	C₂²	1	1	yes	characteristic
95	#16813582	C₂²	1	2	yes	—
96	#16813582	C₂²	1	2	yes	complemented
97	#16813582	C₂²	1	1	yes	characteristic, complemented
98	#16813582	C₂²	1	2	yes	complemented
99	#16813582	C₂²	1	2	yes	complemented
100	#16813582	C₂²	1	2	yes	complemented
101	#16813582	C₂²	1	2	yes	complemented
102	#16813582	C₂²	1	2	yes	complemented
103	#16813582	C₂²	1	2	yes	complemented
104	#16813582	C₂²	1	2	yes	complemented
105	#16813580	C₂²	1	1	yes	characteristic, complemented
106	#16813578	C₂²	1	2	yes	complemented
107	C₂×#14268626	C₂²	1	2	yes	complemented
108	C₄⋊C₄×D₁₁₃	C₂²	1	1	yes	characteristic, complemented
109	C₂×#14268624	C₂²	1	2	yes	complemented
110	C₂²⋊C₄×D₁₁₃	C₂²	1	1	yes	characteristic, complemented
111	C₂²⋊C₄×D₁₁₃	C₂²	1	1	yes	characteristic, complemented
112	C₂×C₄×Dic₁₁₃	C₂²	1	2	yes	complemented
113	C₄²×D₁₁₃	C₂²	1	1	yes	characteristic, complemented
114	C₂×#41×C₁₁₃	C₂²	1	1	yes	characteristic, complemented
115	C₂²×D₄×C₁₁₃	C₂²	1	1	yes	characteristic, complemented
116	#124×C₁₁₃	C₂²	1	1	yes	characteristic, complemented
117	#123×C₁₁₃	C₂²	1	2	yes	complemented
118	C₂²⋊Q₈×C₁₁₃	C₂²	1	1	yes	characteristic, complemented
119	#121×C₁₁₃	C₂²	1	1	yes	characteristic, complemented
120	#121×C₁₁₃	C₂²	1	2	yes	complemented
121	#120×C₁₁₃	C₂²	1	2	yes	complemented
122	C₄×D₄×C₁₁₃	C₂²	1	1	yes	characteristic, complemented
123	C₄×D₄×C₁₁₃	C₂²	1	1	yes	characteristic, complemented
124	C₂×C₂²⋊C₄×C₁₁₃	C₂²	1	2	yes	complemented
125	C₂³×D₁₁₃	C₂³	1	1	yes	characteristic
126	C₂³×D₁₁₃	C₂³	1	1	yes	characteristic
127	C₂³×D₁₁₃	C₂³	1	2	yes	—
128	#14268648	—	2	4	no	—
129	#14268647	—	2	8	no	—
130	#14268647	—	2	4	no	—
131	#14268646	—	2	4	no	—
132	#14268646	—	2	8	no	—
133	#14268646	—	2	8	no	—
134	#14268646	—	2	8	no	—
135	#14268646	—	2	4	no	—
136	#14268646	—	2	4	no	—
137	#14268646	D₄	1	8	yes	complemented
138	C₂×Dic₂₂₆	—	2	4	no	—
139	C₂×Dic₂₂₆	C₂³	1	2	yes	—
140	C₂×Dic₂₂₆	C₂³	1	2	yes	—
141	C₂×Dic₂₂₆	C₂³	1	1	yes	characteristic
142	C₂×Dic₂₂₆	C₂³	1	1	yes	characteristic
143	Q₈×D₁₁₃	—	2	4	no	—
144	C₂×D₄₅₂	C₂³	1	1	yes	characteristic
145	C₂×D₄₅₂	C₂³	1	2	yes	—
146	C₂×D₄₅₂	C₂³	1	1	yes	characteristic
147	C₂×D₄₅₂	C₂³	1	2	yes	—
148	C₂×C₂²⋊D₁₁₃	—	2	8	no	—
149	C₂×C₂²⋊D₁₁₃	—	2	8	no	—
150	C₂×C₂²⋊D₁₁₃	C₂³	1	2	yes	—
151	C₂×C₂²⋊D₁₁₃	C₂³	1	2	yes	—
152	C₂×C₂²⋊D₁₁₃	C₂³	1	2	yes	—
153	C₂×C₂²⋊D₁₁₃	C₂³	1	1	yes	characteristic
154	C₂×C₂²⋊D₁₁₃	C₂³	1	2	yes	—
155	C₂×C₂²⋊D₁₁₃	C₂³	1	2	yes	—
156	C₂×C₂²⋊D₁₁₃	C₂³	1	2	yes	—
157	C₂×C₂²⋊D₁₁₃	C₂³	1	2	yes	—
158	C₂×C₂²⋊D₁₁₃	C₂³	1	2	yes	—
159	C₂×C₂²⋊D₁₁₃	C₂³	1	2	yes	—
160	C₂×C₂²⋊D₁₁₃	C₂³	1	2	yes	—
161	C₂×C₂²⋊D₁₁₃	C₂³	1	1	yes	characteristic
162	D₄×D₁₁₃	—	2	4	no	—
163	D₄×D₁₁₃	—	2	8	no	—
164	D₄×D₁₁₃	—	2	4	no	—
165	C₂²×Dic₁₁₃	—	2	8	no	—
166	C₂²×Dic₁₁₃	C₂³	1	2	yes	—
167	C₂²×Dic₁₁₃	C₂³	1	2	yes	—
168	C₂²×Dic₁₁₃	C₂³	1	1	yes	characteristic
169	C₂²×Dic₁₁₃	C₂³	1	2	yes	—
170	C₂²×Dic₁₁₃	C₂³	1	2	yes	—
171	C₂²×Dic₁₁₃	C₂³	1	2	yes	—
172	C₂²×Dic₁₁₃	C₂³	1	1	yes	characteristic
173	C₂²×Dic₁₁₃	C₂³	1	2	yes	—
174	C₂×C₄×D₁₁₃	—	2	8	no	—
175	C₂×C₄×D₁₁₃	—	2	4	no	—
176	C₂×C₄×D₁₁₃	—	2	4	no	—
177	C₂×C₄×D₁₁₃	C₂³	1	1	yes	characteristic
178	C₂×C₄×D₁₁₃	C₂³	1	1	yes	characteristic
179	C₂×C₄×D₁₁₃	C₂³	1	1	yes	characteristic
180	C₂×C₄×D₁₁₃	C₂³	1	1	yes	characteristic
181	C₂×C₄×D₁₁₃	C₂³	1	2	yes	—
182	C₂×C₄×D₁₁₃	C₂³	1	2	yes	—
183	C₂×C₄×D₁₁₃	C₂³	1	2	yes	—
184	C₂×C₄×D₁₁₃	C₂³	1	1	yes	characteristic
185	C₂×C₄×D₁₁₃	C₂³	1	1	yes	characteristic
186	C₂×C₄×D₁₁₃	C₂³	1	1	yes	characteristic
187	C₂×C₄×D₁₁₃	C₂³	1	1	yes	characteristic
188	C₂×C₄×D₁₁₃	C₂³	1	1	yes	characteristic
189	C₄⋊Dic₁₁₃	C₂³	1	1	yes	characteristic
190	C₄⋊Dic₁₁₃	C₂³	1	1	yes	characteristic
191	C₄⋊Dic₁₁₃	C₂³	1	2	yes	—
192	#14268626	C₂³	1	1	yes	characteristic
193	#14268626	C₂³	1	1	yes	characteristic
194	#14268626	C₂³	1	2	yes	—
195	#14268626	C₂³	1	2	yes	—
196	#14268626	C₂³	1	2	yes	—
197	#14268626	C₂³	1	2	yes	—
198	#14268626	C₂³	1	2	yes	—
199	#14268626	C₂³	1	2	yes	—
200	C₂²⋊Dic₁₁₃	C₂³	1	1	yes	characteristic
201	C₂²⋊Dic₁₁₃	C₂³	1	1	yes	characteristic
202	C₂²⋊Dic₁₁₃	C₂³	1	2	yes	—
203	C₂²⋊Dic₁₁₃	C₂³	1	2	yes	—
204	C₂²⋊Dic₁₁₃	C₂³	1	2	yes	—
205	#14268624	C₂³	1	1	yes	characteristic
206	#14268624	C₂³	1	1	yes	characteristic
207	#14268624	C₂³	1	1	yes	characteristic
208	#14268624	C₂³	1	1	yes	characteristic
209	#14268624	C₂³	1	2	yes	—
210	#14268624	C₂³	1	2	yes	—
211	#14268624	C₂³	1	2	yes	—
212	#14268624	C₂³	1	2	yes	—
213	#14268624	C₂³	1	2	yes	—
214	#14268624	C₂³	1	2	yes	—
215	#14268624	C₂³	1	2	yes	—
216	C₄×Dic₁₁₃	C₂³	1	1	yes	characteristic
217	C₄×Dic₁₁₃	C₂³	1	1	yes	characteristic
218	C₄×Dic₁₁₃	C₂³	1	1	yes	characteristic
219	C₄×Dic₁₁₃	C₂³	1	2	yes	—
220	C₄×Dic₁₁₃	C₂³	1	2	yes	—
221	C₄×Dic₁₁₃	C₂³	1	2	yes	—
222	C₂⁴×C₁₁₃	C₂³	1	2	yes	—
223	#41×C₁₁₃	—	2	4	no	—
224	C₂×Q₈×C₁₁₃	C₂³	1	1	yes	characteristic
225	C₂×D₄×C₁₁₃	—	2	4	no	—
226	C₂×D₄×C₁₁₃	C₂³	1	1	yes	characteristic
227	C₂×D₄×C₁₁₃	C₂³	1	2	yes	—
228	C₂×D₄×C₁₁₃	C₂³	1	1	yes	characteristic
229	C₂×D₄×C₁₁₃	C₂³	1	2	yes	—
230	C₂×D₄×C₁₁₃	C₂³	1	2	yes	—
231	C₂×D₄×C₁₁₃	C₂³	1	1	yes	characteristic
232	C₂²×C₄×C₁₁₃	C₂³	1	2	yes	—
233	C₂²×C₄×C₁₁₃	C₂³	1	1	yes	characteristic
234	C₂²×C₄×C₁₁₃	C₂³	1	1	yes	characteristic
235	C₂²×C₄×C₁₁₃	C₂³	1	2	yes	—
236	C₄⋊C₄×C₁₁₃	C₂³	1	1	yes	characteristic
237	C₄⋊C₄×C₁₁₃	C₂³	1	1	yes	characteristic
238	C₄⋊C₄×C₁₁₃	C₂³	1	2	yes	—
239	C₂²⋊C₄×C₁₁₃	C₂³	1	1	yes	characteristic
240	C₂²⋊C₄×C₁₁₃	C₂³	1	1	yes	characteristic
241	C₂²⋊C₄×C₁₁₃	C₂³	1	2	yes	—
242	C₂²⋊C₄×C₁₁₃	C₂³	1	2	yes	—
243	C₂²⋊C₄×C₁₁₃	C₂³	1	2	yes	—
244	C₂²⋊C₄×C₁₁₃	C₂³	1	2	yes	—
245	C₂²⋊C₄×C₁₁₃	C₂³	1	2	yes	—
246	C₄²×C₁₁₃	C₂³	1	1	yes	characteristic
247	C₂³×C₁₁₃	—	2	4	no	—
248	C₂³×C₁₁₃	—	2	4	no	—
249	C₂³×C₁₁₃	—	4	2	no	—
250	C₂³×C₁₁₃	C₂⁴	1	2	yes	—
251	C₂³×C₁₁₃	C₂⁴	1	1	yes	characteristic
252	C₂³×C₁₁₃	C₂⁴	1	2	yes	—
253	C₂³×C₁₁₃	C₂⁴	1	1	yes	characteristic
254	C₂²×D₁₁₃	—	2	4	no	—
255	C₂²×D₁₁₃	—	2	2	no	—
256	C₂²×D₁₁₃	—	2	2	no	—
257	C₂²×D₁₁₃	—	2	2	no	—
258	C₂²×D₁₁₃	—	2	2	no	—
259	C₂²×D₁₁₃	—	2	4	no	—
260	C₂²×D₁₁₃	—	4	1	no	—
261	C₂²×D₁₁₃	—	4	1	no	—
262	C₂²×D₁₁₃	—	4	2	no	—
263	C₂²×D₁₁₃	C₂⁴	1	2	yes	—
264	C₂²×D₁₁₃	C₂⁴	1	1	yes	characteristic
265	C₂²×D₁₁₃	C₂⁴	1	1	yes	characteristic
266	C₂²×D₁₁₃	C₂⁴	1	1	yes	characteristic
267	Q₈×C₁₁₃	—	2	2	no	—
268	D₄×C₁₁₃	—	2	4	no	—
269	D₄×C₁₁₃	—	2	4	no	—
270	D₄×C₁₁₃	—	2	2	no	—
271	D₄×C₁₁₃	—	2	2	no	—
272	D₄×C₁₁₃	—	4	2	no	—
273	D₄×C₁₁₃	C₂×D₄	1	4	yes	complemented
274	C₂×C₄×C₁₁₃	—	2	4	no	—
275	C₂×C₄×C₁₁₃	—	2	2	no	—
276	C₂×C₄×C₁₁₃	—	2	2	no	—
277	C₂×C₄×C₁₁₃	—	4	2	no	—
278	C₂×C₄×C₁₁₃	C₂⁴	1	1	yes	characteristic
279	C₂×C₄×C₁₁₃	C₂⁴	1	1	yes	characteristic
280	C₂×C₄×C₁₁₃	C₂⁴	1	2	yes	—
281	C₂×C₄×C₁₁₃	C₂⁴	1	1	yes	characteristic
282	C₂×C₄×C₁₁₃	C₂⁴	1	2	yes	—
283	C₂×C₄×C₁₁₃	C₂⁴	1	1	yes	characteristic
284	C₂×C₄×C₁₁₃	C₂⁴	1	1	yes	characteristic
285	C₂²⋊D₁₁₃	—	2	4	no	—
286	C₂²⋊D₁₁₃	—	2	4	no	—
287	C₂²⋊D₁₁₃	—	2	4	no	—
288	C₂²⋊D₁₁₃	—	2	4	no	—
289	C₂²⋊D₁₁₃	—	2	4	no	—
290	C₂²⋊D₁₁₃	—	2	4	no	—
291	C₂²⋊D₁₁₃	—	2	4	no	—
292	C₂²⋊D₁₁₃	—	2	2	no	—
293	C₂²⋊D₁₁₃	—	2	4	no	—
294	C₂²⋊D₁₁₃	—	4	2	no	—
295	C₂²⋊D₁₁₃	C₂×D₄	1	8	yes	complemented
296	C₂²⋊D₁₁₃	#41	1	4	yes	complemented
297	C₂×Dic₁₁₃	—	2	4	no	—
298	C₂×Dic₁₁₃	—	2	2	no	—
299	C₂×Dic₁₁₃	—	2	2	no	—
300	C₂×Dic₁₁₃	—	2	4	no	—
301	C₂×Dic₁₁₃	—	2	4	no	—
302	C₂×Dic₁₁₃	—	2	4	no	—
303	C₂×Dic₁₁₃	—	2	4	no	—
304	C₂×Dic₁₁₃	C₂×D₄	1	8	yes	complemented
305	C₂×Dic₁₁₃	C₂⁴	1	2	yes	—
306	C₂×Dic₁₁₃	C₂⁴	1	1	yes	characteristic
307	C₂×Dic₁₁₃	C₂⁴	1	1	yes	characteristic
308	C₂×Dic₁₁₃	C₂⁴	1	2	yes	—
309	C₂×Dic₁₁₃	C₂⁴	1	1	yes	characteristic
310	C₂×Dic₁₁₃	C₂⁴	1	1	yes	characteristic
311	C₂×Dic₁₁₃	C₂⁴	1	2	yes	—
312	C₂×Dic₁₁₃	C₂⁴	1	1	yes	characteristic
313	D₄₅₂	—	2	4	no	—
314	D₄₅₂	—	2	2	no	—
315	D₄₅₂	—	2	2	no	—
316	D₄₅₂	—	4	2	no	—
317	C₄×D₁₁₃	—	2	2	no	—
318	C₄×D₁₁₃	—	2	2	no	—
319	C₄×D₁₁₃	—	2	2	no	—
320	C₄×D₁₁₃	—	2	2	no	—
321	C₄×D₁₁₃	—	2	2	no	—
322	C₄×D₁₁₃	—	2	4	no	—
323	C₄×D₁₁₃	—	2	2	no	—
324	C₄×D₁₁₃	—	2	4	no	—
325	C₄×D₁₁₃	—	2	4	no	—
326	C₄×D₁₁₃	—	2	2	no	—
327	C₄×D₁₁₃	—	4	1	no	—
328	C₄×D₁₁₃	C₂×D₄	1	4	yes	complemented
329	Dic₂₂₆	—	2	2	no	—
330	Dic₂₂₆	—	2	4	no	—
331	Dic₂₂₆	—	2	4	no	—
332	Dic₂₂₆	C₂×D₄	1	4	yes	complemented
333	C₂²×C₁₁₃	—	2	1	no	—
334	C₂²×C₁₁₃	—	2	2	no	—
335	C₂²×C₁₁₃	—	2	2	no	—
336	C₂²×C₁₁₃	—	2	1	no	—
337	C₂²×C₁₁₃	—	2	2	no	—
338	C₂²×C₁₁₃	—	2	1	no	—
339	C₂²×C₁₁₃	—	2	2	no	—
340	C₂²×C₁₁₃	—	2	1	no	—
341	C₂²×C₁₁₃	—	2	2	no	—
342	C₂²×C₁₁₃	—	2	1	no	—
343	C₂²×C₁₁₃	—	4	8	no	—
344	C₂²×C₁₁₃	C₂²×D₄	1	4	yes	—
345	C₂²×C₁₁₃	C₂×#41	1	2	yes	complemented
346	C₂²×C₁₁₃	C₂⁵	1	1	yes	characteristic
347	C₂×D₁₁₃	—	2	1	no	—
348	C₂×D₁₁₃	—	2	1	no	—
349	C₂×D₁₁₃	—	2	1	no	—
350	C₂×D₁₁₃	—	2	1	no	—
351	C₂×D₁₁₃	—	2	2	no	—
352	C₂×D₁₁₃	—	2	1	no	—
353	C₂×D₁₁₃	—	2	1	no	—
354	C₂×D₁₁₃	—	2	2	no	—
355	C₂×D₁₁₃	—	2	1	no	—
356	C₂×D₁₁₃	—	2	2	no	—
357	C₂×D₁₁₃	—	4	4	no	—
358	C₂×D₁₁₃	—	4	8	no	—
359	C₂×D₁₁₃	—	4	4	no	—
360	C₂×D₁₁₃	C₂²×D₄	1	2	yes	—
361	C₂×D₁₁₃	C₂×#41	1	2	yes	complemented
362	C₄×C₁₁₃	—	2	1	no	—
363	C₄×C₁₁₃	—	2	2	no	—
364	C₄×C₁₁₃	—	2	1	no	—
365	C₄×C₁₁₃	—	2	1	no	—
366	C₄×C₁₁₃	—	2	1	no	—
367	C₄×C₁₁₃	—	2	2	no	—
368	C₄×C₁₁₃	C₂²×D₄	1	2	yes	—
369	Dic₁₁₃	—	2	1	no	—
370	Dic₁₁₃	—	2	2	no	—
371	Dic₁₁₃	—	2	1	no	—
372	Dic₁₁₃	—	2	2	no	—
373	Dic₁₁₃	—	2	1	no	—
374	Dic₁₁₃	C₂²×D₄	1	4	yes	—
375	Dic₁₁₃	C₂²×D₄	1	2	yes	—
376	Dic₁₁₃	C₂×#41	1	2	yes	complemented
377	C₂×C₁₁₃	—	2	2	no	—
378	C₂×C₁₁₃	—	2	4	no	—
379	C₂×C₁₁₃	—	4	1	no	—
380	C₂×C₁₁₃	—	4	2	no	—
381	C₂×C₁₁₃	C₂³×D₄	1	1	yes	characteristic
382	C₂×C₁₁₃	C₂²×#41	1	1	yes	characteristic
383	C₂×C₁₁₃	#585	1	1	yes	characteristic
384	D₁₁₃	—	2	2	no	—
385	D₁₁₃	—	2	2	no	—
386	D₁₁₃	—	4	2	no	—
387	D₁₁₃	—	4	1	no	—
388	D₄×#41	—	113	1	no	maximal, Sylow
389	C₁₁₃	D₄×#41	1	1	yes	characteristic, complemented, Sylow
390	C₂²×#41	—	113	1	no	—
391	C₂²×#41	—	113	1	no	—
392	#550	—	113	1	no	—
393	D₄×Q₈	—	113	1	no	—
394	#548	—	113	1	no	—
395	#548	—	113	1	no	—
396	#547	—	113	1	no	—
397	#547	—	113	2	no	—
398	#546	—	113	2	no	—
399	#546	—	113	1	no	—
400	#546	—	113	2	no	—
401	#546	D₁₁₃	1	1	yes	characteristic, complemented
402	D₄²	—	113	1	no	—
403	D₄²	—	113	2	no	—
404	#532	—	113	1	no	—
405	#532	—	113	2	no	—
406	#525	—	113	2	no	—
407	#525	—	113	1	no	—
408	#525	—	113	1	no	—
409	#525	—	113	2	no	—
410	C₄×#41	—	113	1	no	—
411	C₂×C₄×D₄	—	113	1	no	—
412	C₂×C₄×D₄	—	113	2	no	—
413	C₂×#41	—	113	1	no	—
414	C₂×#41	—	113	1	no	—
415	C₂×#41	—	113	2	no	—
416	C₂×#41	—	113	2	no	—
417	C₂×#41	—	113	1	no	—
418	C₂×#41	—	113	1	no	—
419	C₂×#41	—	113	2	no	—
420	C₂×#41	—	113	1	no	—
421	C₂×#41	—	113	2	no	—
422	C₂×#41	—	113	1	no	—
423	C₂×#41	—	226	8	no	—
424	C₂×#41	—	226	8	no	—
425	C₂×#41	C₂×D₁₁₃	1	1	yes	characteristic, complemented
426	C₂²×Q₈	—	113	1	no	—
427	C₂²×Q₈	—	113	1	no	—
428	C₂²×D₄	—	113	2	no	—
429	C₂²×D₄	—	113	2	no	—
430	C₂²×D₄	—	113	1	no	—
431	C₂²×D₄	—	113	2	no	—
432	C₂²×D₄	—	113	1	no	—
433	C₂²×D₄	C₂×D₁₁₃	1	1	yes	characteristic, complemented
434	C₂³×C₄	—	113	2	no	—
435	C₂³×C₄	—	113	2	no	—
436	C₂³×C₄	—	113	1	no	—
437	C₂³×C₄	—	113	1	no	—
438	C₄⋊Q₈	—	113	1	no	—
439	C₄⋊Q₈	—	113	2	no	—
440	#127	—	113	1	no	—
441	#127	—	113	2	no	—
442	#124	—	113	2	no	—
443	#124	—	113	2	no	—
444	#124	—	113	1	no	—
445	#124	C₂×D₁₁₃	1	1	yes	characteristic, complemented
446	#123	—	113	2	no	—
447	#123	—	113	2	no	—
448	#123	—	113	2	no	—
449	#123	—	113	2	no	—
450	#123	—	113	2	no	—
451	#123	C₂×D₁₁₃	1	2	yes	complemented
452	C₂²⋊Q₈	—	113	1	no	—
453	C₂²⋊Q₈	—	113	1	no	—
454	C₂²⋊Q₈	—	113	2	no	—
455	C₂²⋊Q₈	—	113	2	no	—
456	C₂²⋊Q₈	—	113	1	no	—
457	C₂²⋊Q₈	—	113	2	no	—
458	C₂²⋊Q₈	—	113	2	no	—
459	C₂²⋊Q₈	C₂×D₁₁₃	1	1	yes	characteristic, complemented
460	#121	—	113	1	no	—
461	#121	—	113	2	no	—
462	#121	—	113	2	no	—
463	#121	—	113	2	no	—
464	#121	—	113	2	no	—
465	#121	—	113	1	no	—
466	#121	—	113	2	no	—
467	#121	—	113	1	no	—
468	#121	—	113	2	no	—
469	#121	—	113	2	no	—
470	#121	—	113	2	no	—
471	#121	—	113	2	no	—
472	#121	C₂×D₁₁₃	1	1	yes	characteristic, complemented
473	#121	C₂×D₁₁₃	1	2	yes	complemented
474	#120	—	113	2	no	—
475	#120	—	113	2	no	—
476	#120	—	113	2	no	—
477	#120	—	113	2	no	—
478	#120	—	113	2	no	—
479	#120	C₂×D₁₁₃	1	2	yes	complemented
480	C₄×Q₈	—	113	1	no	—
481	C₄×Q₈	—	113	1	no	—
482	C₄×D₄	—	113	1	no	—
483	C₄×D₄	—	113	1	no	—
484	C₄×D₄	—	113	2	no	—
485	C₄×D₄	—	113	1	no	—
486	C₄×D₄	—	113	1	no	—
487	C₄×D₄	—	113	2	no	—
488	C₄×D₄	—	113	1	no	—
489	C₄×D₄	—	113	2	no	—
490	C₄×D₄	—	113	1	no	—
491	C₄×D₄	—	113	2	no	—
492	C₄×D₄	—	113	2	no	—
493	C₄×D₄	—	113	2	no	—
494	C₄×D₄	—	113	1	no	—
495	C₄×D₄	—	113	2	no	—
496	C₄×D₄	—	113	2	no	—
497	C₄×D₄	—	113	2	no	—
498	C₄×D₄	—	113	2	no	—
499	C₄×D₄	—	113	2	no	—
500	C₄×D₄	—	113	2	no	—
501	C₄×D₄	—	113	1	no	—
502	C₄×D₄	C₂×D₁₁₃	1	1	yes	characteristic, complemented
503	C₄×D₄	C₂×D₁₁₃	1	1	yes	characteristic, complemented
504	#117	—	113	1	no	—
505	#117	—	113	2	no	—
506	C₂×C₄⋊C₄	—	113	2	no	—
507	C₂×C₄⋊C₄	—	113	1	no	—
508	C₂×C₂²⋊C₄	—	113	2	no	—
509	C₂×C₂²⋊C₄	—	113	1	no	—
510	C₂×C₂²⋊C₄	—	113	1	no	—
511	C₂×C₂²⋊C₄	C₂×D₁₁₃	1	2	yes	complemented
512	C₂×C₄²	—	113	2	no	—
513	C₂×C₄²	—	113	1	no	—
514	C₂⁴	—	113	1	no	—
515	C₂⁴	—	113	2	no	—
516	C₂⁴	—	113	1	no	—
517	C₂⁴	C₂²×D₁₁₃	1	2	yes	—
518	#41	—	2	4	no	—
519	#41	—	113	8	no	—
520	#41	—	226	8	no	—
521	#41	—	226	4	no	—
522	#41	—	226	8	no	—
523	#41	—	226	8	no	—
524	#41	—	226	4	no	—
525	#41	—	226	4	no	—
526	#41	—	226	8	no	—
527	#41	—	226	4	no	—
528	#41	—	226	4	no	—
529	C₂×Q₈	—	113	1	no	—
530	C₂×Q₈	—	113	2	no	—
531	C₂×Q₈	—	113	2	no	—
532	C₂×Q₈	—	113	1	no	—
533	C₂×Q₈	—	226	4	no	—
534	C₂×Q₈	—	226	4	no	—
535	C₂×Q₈	C₂²×D₁₁₃	1	1	yes	characteristic
536	C₂×D₄	—	2	4	no	—
537	C₂×D₄	—	113	1	no	—
538	C₂×D₄	—	113	2	no	—
539	C₂×D₄	—	113	2	no	—
540	C₂×D₄	—	113	2	no	—
541	C₂×D₄	—	113	2	no	—
542	C₂×D₄	—	113	1	no	—
543	C₂×D₄	—	113	2	no	—
544	C₂×D₄	—	113	2	no	—
545	C₂×D₄	—	113	2	no	—
546	C₂×D₄	—	113	2	no	—
547	C₂×D₄	—	113	2	no	—
548	C₂×D₄	—	113	2	no	—
549	C₂×D₄	—	113	2	no	—
550	C₂×D₄	—	113	1	no	—
551	C₂×D₄	—	113	2	no	—
552	C₂×D₄	—	113	1	no	—
553	C₂×D₄	—	226	8	no	—
554	C₂×D₄	—	226	4	no	—
555	C₂×D₄	—	226	8	no	—
556	C₂×D₄	—	226	8	no	—
557	C₂×D₄	—	226	4	no	—
558	C₂×D₄	C₂²×D₁₁₃	1	1	yes	characteristic
559	C₂×D₄	C₂²×D₁₁₃	1	2	yes	—
560	C₂×D₄	C₂²×D₁₁₃	1	2	yes	—
561	C₂×D₄	C₂²×D₁₁₃	1	1	yes	characteristic
562	C₂×D₄	C₂²×D₁₁₃	1	2	yes	—
563	C₂×D₄	C₂²×D₁₁₃	1	1	yes	characteristic
564	C₂²×C₄	—	113	2	no	—
565	C₂²×C₄	—	113	1	no	—
566	C₂²×C₄	—	113	2	no	—
567	C₂²×C₄	—	113	2	no	—
568	C₂²×C₄	—	113	1	no	—
569	C₂²×C₄	—	113	1	no	—
570	C₂²×C₄	—	113	2	no	—
571	C₂²×C₄	—	113	2	no	—
572	C₂²×C₄	—	113	2	no	—
573	C₂²×C₄	—	113	1	no	—
574	C₂²×C₄	—	113	1	no	—
575	C₂²×C₄	—	113	1	no	—
576	C₂²×C₄	—	113	1	no	—
577	C₂²×C₄	—	113	1	no	—
578	C₂²×C₄	—	113	1	no	—
579	C₂²×C₄	—	113	2	no	—
580	C₂²×C₄	—	113	2	no	—
581	C₂²×C₄	—	113	1	no	—
582	C₂²×C₄	—	113	2	no	—
583	C₂²×C₄	—	113	1	no	—
584	C₂²×C₄	—	226	8	no	—
585	C₂²×C₄	—	226	4	no	—
586	C₂²×C₄	—	226	4	no	—
587	C₂²×C₄	—	226	8	no	—
588	C₂²×C₄	C₂²×D₁₁₃	1	2	yes	—
589	C₂²×C₄	C₂²×D₁₁₃	1	1	yes	characteristic
590	C₂²×C₄	C₂²×D₁₁₃	1	1	yes	characteristic
591	C₂²×C₄	C₂²×D₁₁₃	1	2	yes	—
592	C₄⋊C₄	—	113	1	no	—
593	C₄⋊C₄	—	113	1	no	—
594	C₄⋊C₄	—	113	2	no	—
595	C₄⋊C₄	—	113	2	no	—
596	C₄⋊C₄	—	113	2	no	—
597	C₄⋊C₄	—	113	1	no	—
598	C₄⋊C₄	—	113	2	no	—
599	C₄⋊C₄	—	113	2	no	—
600	C₄⋊C₄	—	113	1	no	—
601	C₄⋊C₄	—	113	2	no	—
602	C₄⋊C₄	—	113	2	no	—
603	C₄⋊C₄	C₂²×D₁₁₃	1	1	yes	characteristic
604	C₄⋊C₄	C₂²×D₁₁₃	1	1	yes	characteristic
605	C₄⋊C₄	C₂²×D₁₁₃	1	2	yes	—
606	C₂²⋊C₄	—	113	1	no	—
607	C₂²⋊C₄	—	113	1	no	—
608	C₂²⋊C₄	—	113	2	no	—
609	C₂²⋊C₄	—	113	2	no	—
610	C₂²⋊C₄	—	113	2	no	—
611	C₂²⋊C₄	—	113	1	no	—
612	C₂²⋊C₄	—	113	1	no	—
613	C₂²⋊C₄	—	113	2	no	—
614	C₂²⋊C₄	—	113	1	no	—
615	C₂²⋊C₄	—	113	2	no	—
616	C₂²⋊C₄	—	113	2	no	—
617	C₂²⋊C₄	—	113	1	no	—
618	C₂²⋊C₄	—	113	2	no	—
619	C₂²⋊C₄	—	113	2	no	—
620	C₂²⋊C₄	—	113	2	no	—
621	C₂²⋊C₄	—	113	2	no	—
622	C₂²⋊C₄	C₂²×D₁₁₃	1	1	yes	characteristic
623	C₂²⋊C₄	C₂²×D₁₁₃	1	1	yes	characteristic
624	C₂²⋊C₄	C₂²×D₁₁₃	1	2	yes	—
625	C₂²⋊C₄	C₂²×D₁₁₃	1	2	yes	—
626	C₂²⋊C₄	C₂²×D₁₁₃	1	2	yes	—
627	C₂²⋊C₄	C₂²×D₁₁₃	1	2	yes	—
628	C₂²⋊C₄	C₂²×D₁₁₃	1	2	yes	—
629	C₄²	—	113	1	no	—
630	C₄²	—	113	2	no	—
631	C₄²	—	113	1	no	—
632	C₄²	—	113	2	no	—
633	C₄²	—	113	2	no	—
634	C₄²	—	113	1	no	—
635	C₄²	C₂²×D₁₁₃	1	1	yes	characteristic
636	C₂³	—	2	4	no	—
637	C₂³	—	2	4	no	—
638	C₂³	—	4	2	no	—
639	C₂³	—	113	1	no	—
640	C₂³	—	113	1	no	—
641	C₂³	—	113	2	no	—
642	C₂³	—	113	1	no	—
643	C₂³	—	452	2	no	—
644	C₂³	—	452	1	no	—
645	C₂³	—	452	1	no	—
646	C₂³	—	226	2	no	—
647	C₂³	—	226	2	no	—
648	C₂³	—	226	4	no	—
649	C₂³	—	226	2	no	—
650	C₂³	—	226	4	no	—
651	C₂³	—	226	2	no	—
652	C₂³	C₂³×D₁₁₃	1	1	yes	characteristic
653	C₂³	C₂³×D₁₁₃	1	2	yes	—
654	C₂³	C₂³×D₁₁₃	1	2	yes	—
655	C₂³	C₂³×D₁₁₃	1	1	yes	characteristic
656	Q₈	—	2	2	no	—
657	Q₈	—	113	4	no	—
658	Q₈	—	226	4	no	—
659	Q₈	—	226	4	no	—
660	Q₈	—	226	2	no	—
661	D₄	—	2	4	no	—
662	D₄	—	2	4	no	—
663	D₄	—	2	2	no	—
664	D₄	—	2	2	no	—
665	D₄	—	4	2	no	—
666	D₄	—	113	8	no	—
667	D₄	—	113	4	no	—
668	D₄	—	452	2	no	—
669	D₄	—	452	2	no	—
670	D₄	—	226	4	no	—
671	D₄	—	226	2	no	—
672	D₄	—	226	4	no	—
673	D₄	—	226	4	no	—
674	D₄	—	226	2	no	—
675	D₄	—	226	4	no	—
676	D₄	—	226	4	no	—
677	D₄	—	226	4	no	—
678	D₄	—	226	4	no	—
679	D₄	—	226	4	no	—
680	D₄	—	226	4	no	—
681	D₄	—	226	2	no	—
682	D₄	D₄×D₁₁₃	1	4	yes	complemented
683	C₂×C₄	—	2	4	no	—
684	C₂×C₄	—	2	2	no	—
685	C₂×C₄	—	2	2	no	—
686	C₂×C₄	—	4	2	no	—
687	C₂×C₄	—	113	8	no	—
688	C₂×C₄	—	113	1	no	—
689	C₂×C₄	—	113	1	no	—
690	C₂×C₄	—	113	2	no	—
691	C₂×C₄	—	113	4	no	—
692	C₂×C₄	—	113	2	no	—
693	C₂×C₄	—	113	1	no	—
694	C₂×C₄	—	113	1	no	—
695	C₂×C₄	—	113	1	no	—
696	C₂×C₄	—	113	2	no	—
697	C₂×C₄	—	452	1	no	—
698	C₂×C₄	—	226	2	no	—
699	C₂×C₄	—	226	4	no	—
700	C₂×C₄	—	226	4	no	—
701	C₂×C₄	—	226	2	no	—
702	C₂×C₄	—	226	4	no	—
703	C₂×C₄	—	226	2	no	—
704	C₂×C₄	—	226	2	no	—
705	C₂×C₄	—	226	2	no	—
706	C₂×C₄	—	226	2	no	—
707	C₂×C₄	—	226	4	no	—
708	C₂×C₄	—	226	2	no	—
709	C₂×C₄	—	226	4	no	—
710	C₂×C₄	—	226	4	no	—
711	C₂×C₄	—	226	4	no	—
712	C₂×C₄	—	226	4	no	—
713	C₂×C₄	—	226	2	no	—
714	C₂×C₄	—	226	2	no	—
715	C₂×C₄	C₂³×D₁₁₃	1	1	yes	characteristic
716	C₂×C₄	C₂³×D₁₁₃	1	2	yes	—
717	C₂×C₄	C₂³×D₁₁₃	1	1	yes	characteristic
718	C₂×C₄	C₂³×D₁₁₃	1	1	yes	characteristic
719	C₂×C₄	C₂³×D₁₁₃	1	1	yes	characteristic
720	C₂×C₄	C₂³×D₁₁₃	1	2	yes	—
721	C₂×C₄	C₂³×D₁₁₃	1	1	yes	characteristic
722	C₂²	—	2	1	no	—
723	C₂²	—	2	2	no	—
724	C₂²	—	2	2	no	—
725	C₂²	—	2	1	no	—
726	C₂²	—	2	1	no	—
727	C₂²	—	2	2	no	—
728	C₂²	—	2	1	no	—
729	C₂²	—	2	2	no	—
730	C₂²	—	2	1	no	—
731	C₂²	—	2	2	no	—
732	C₂²	—	4	8	no	—
733	C₂²	—	113	2	no	—
734	C₂²	—	113	2	no	—
735	C₂²	—	452	4	no	—
736	C₂²	—	452	8	no	—
737	C₂²	—	452	4	no	—
738	C₂²	—	226	2	no	—
739	C₂²	—	226	1	no	—
740	C₂²	—	226	1	no	—
741	C₂²	—	226	2	no	—
742	C₂²	—	226	1	no	—
743	C₂²	—	226	2	no	—
744	C₂²	—	226	1	no	—
745	C₂²	—	226	1	no	—
746	C₂²	—	226	1	no	—
747	C₂²	—	226	1	no	—
748	C₂²	C₂×D₄×D₁₁₃	1	4	yes	—
749	C₂²	#41×D₁₁₃	1	2	yes	complemented
750	C₂²	C₂⁴×D₁₁₃	1	1	yes	characteristic
751	C₄	—	2	1	no	—
752	C₄	—	2	1	no	—
753	C₄	—	2	2	no	—
754	C₄	—	2	1	no	—
755	C₄	—	2	1	no	—
756	C₄	—	2	2	no	—
757	C₄	—	113	2	no	—
758	C₄	—	113	4	no	—
759	C₄	—	113	2	no	—
760	C₄	—	226	1	no	—
761	C₄	—	226	1	no	—
762	C₄	—	226	2	no	—
763	C₄	—	226	2	no	—
764	C₄	—	226	1	no	—
765	C₄	C₂×D₄×D₁₁₃	1	2	yes	—
766	C₂	—	2	2	no	—
767	C₂	—	2	4	no	—
768	C₂	—	4	2	no	—
769	C₂	—	4	1	no	—
770	C₂	—	452	1	no	—
771	C₂	—	452	2	no	—
772	C₂	—	226	2	no	—
773	C₂	—	226	2	no	—
774	C₂	C₂²×D₄×D₁₁₃	1	1	yes	characteristic
775	C₂	C₂×#41×D₁₁₃	1	1	yes	characteristic
776	C₂	#20299433	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₁₁₃
commutator, socle, cosocle	C₂²×C₁₁₃	C₂⁵
Fitting	#546×C₁₁₃	C₂
hypercenter	#546	D₁₁₃
hypocenter	C₁₁₃	D₄×#41
LCS	G ▷ C₂²×C₁₁₃ ▷ C₁₁₃
UCS	C₁ ◁ C₂² ◁ #546

Complements

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

N	H ≅ G/N	type
1. C₂²×#14268646	C₂	semidirect
2. C₂×#41×D₁₁₃	C₂	semidirect
3. #20299266	C₂	semidirect
4. #20299261	C₂	semidirect
5. #20299257	C₂	semidirect
6. #20299256	C₂	semidirect
7. #20299247	C₂	semidirect
8. #20299246	C₂	semidirect
9. #20299243	C₂	semidirect
10. #20299238	C₂	semidirect
11. #20299237	C₂	semidirect
12. D₄×C₂²⋊D₁₁₃	C₂	semidirect
13. #20299230	C₂	semidirect
14. #20299147	C₂	semidirect
15. #20299143	C₂	semidirect
16. #20299111	C₂	semidirect
17. #20299108	C₂	semidirect
18. #20299106	C₂	semidirect
19. #20299104	C₂	semidirect
20. C₄×#14268646	C₂	semidirect
21. C₂×#16813582	C₂	semidirect
22. C₄×D₄×D₁₁₃	C₂	semidirect
23. #546×C₁₁₃	C₂	semidirect
24. C₂×#14268648	C₂²	semidirect
25. C₂×#14268647	C₂²	semidirect
26. C₂×#14268647	C₂²	semidirect
29. C₂×#14268646	C₂²	semidirect
30. C₂×#14268646	C₂²	semidirect
31. C₂×#14268646	C₂²	semidirect
32. C₂×#14268646	C₂²	semidirect
33. C₂×#14268646	C₂²	semidirect
34. C₂×#14268646	C₂²	semidirect
36. C₂²×Dic₂₂₆	C₂²	semidirect
37. C₂×Q₈×D₁₁₃	C₂²	semidirect
39. C₂²×C₂²⋊D₁₁₃	C₂²	semidirect
41. C₂×D₄×D₁₁₃	C₂²	semidirect
42. C₂×D₄×D₁₁₃	C₂²	semidirect
43. C₂³×Dic₁₁₃	C₂²	semidirect
44. C₂²×C₄×D₁₁₃	C₂²	semidirect
45. C₂²×C₄×D₁₁₃	C₂²	semidirect
46. C₂²×C₄×D₁₁₃	C₂²	semidirect
47. #16813621	C₂²	semidirect
48. #16813620	C₂²	semidirect
49. #16813618	C₂²	semidirect
50. #16813618	C₂²	semidirect
51. #16813610	C₂²	semidirect
52. #16813608	C₂²	semidirect
53. #16813608	C₂²	semidirect
54. #16813607	C₂²	semidirect
55. #16813606	C₂²	semidirect
56. #16813605	C₂²	semidirect
57. #16813604	C₂²	semidirect
58. #16813603	C₂²	semidirect
59. #16813602	C₂²	semidirect
60. #16813601	C₂²	semidirect
61. #16813600	C₂²	semidirect
62. #16813600	C₂²	semidirect
63. #16813599	C₂²	semidirect
64. #16813599	C₂²	semidirect
65. #16813598	C₂²	semidirect
66. #16813597	C₂²	semidirect
67. #16813596	C₂²	semidirect
68. #16813596	C₂²	semidirect
69. #16813595	C₂²	semidirect
70. #16813595	C₂²	semidirect
71. #16813595	C₂²	semidirect
72. #16813595	C₂²	semidirect
73. #16813594	C₂²	semidirect
74. #16813594	C₂²	semidirect
75. #16813594	C₂²	semidirect
76. #16813594	C₂²	semidirect
77. #16813593	C₂²	semidirect
78. #16813592	C₂²	semidirect
79. #16813592	C₂²	semidirect
80. #16813591	C₂²	semidirect
81. #16813590	C₂²	semidirect
82. #16813590	C₂²	semidirect
83. C₄×Dic₂₂₆	C₂²	semidirect
84. #16813587	C₂²	semidirect
85. C₄×D₄₅₂	C₂²	semidirect
86. D₄×Dic₁₁₃	C₂²	semidirect
87. D₄×Dic₁₁₃	C₂²	semidirect
88. D₄×Dic₁₁₃	C₂²	semidirect
89. #16813584	C₂²	semidirect
90. #16813584	C₂²	semidirect
92. C₄×C₂²⋊D₁₁₃	C₂²	semidirect
93. C₄×C₂²⋊D₁₁₃	C₂²	semidirect
96. #16813582	C₂²	semidirect
97. #16813582	C₂²	semidirect
98. #16813582	C₂²	semidirect
99. #16813582	C₂²	semidirect
100. #16813582	C₂²	semidirect
101. #16813582	C₂²	semidirect
102. #16813582	C₂²	semidirect
103. #16813582	C₂²	semidirect
104. #16813582	C₂²	semidirect
105. #16813580	C₂²	semidirect
106. #16813578	C₂²	semidirect
107. C₂×#14268626	C₂²	semidirect
108. C₄⋊C₄×D₁₁₃	C₂²	semidirect
109. C₂×#14268624	C₂²	semidirect
110. C₂²⋊C₄×D₁₁₃	C₂²	semidirect
111. C₂²⋊C₄×D₁₁₃	C₂²	semidirect
112. C₂×C₄×Dic₁₁₃	C₂²	semidirect
113. C₄²×D₁₁₃	C₂²	semidirect
114. C₂×#41×C₁₁₃	C₂²	semidirect
115. C₂²×D₄×C₁₁₃	C₂²	semidirect
116. #124×C₁₁₃	C₂²	semidirect
117. #123×C₁₁₃	C₂²	semidirect
118. C₂²⋊Q₈×C₁₁₃	C₂²	semidirect
119. #121×C₁₁₃	C₂²	semidirect
120. #121×C₁₁₃	C₂²	semidirect
121. #120×C₁₁₃	C₂²	semidirect
122. C₄×D₄×C₁₁₃	C₂²	semidirect
123. C₄×D₄×C₁₁₃	C₂²	semidirect
124. C₂×C₂²⋊C₄×C₁₁₃	C₂²	semidirect
137. #14268646	D₄	semidirect
273. D₄×C₁₁₃	C₂×D₄	semidirect
295. C₂²⋊D₁₁₃	C₂×D₄	semidirect
296. C₂²⋊D₁₁₃	#41	semidirect
304. C₂×Dic₁₁₃	C₂×D₄	semidirect
328. C₄×D₁₁₃	C₂×D₄	semidirect
332. Dic₂₂₆	C₂×D₄	semidirect
345. C₂²×C₁₁₃	C₂×#41	semidirect
361. C₂×D₁₁₃	C₂×#41	semidirect
376. Dic₁₁₃	C₂×#41	semidirect
389. C₁₁₃	D₄×#41	semidirect
401. #546	D₁₁₃	semidirect
425. C₂×#41	C₂×D₁₁₃	semidirect
433. C₂²×D₄	C₂×D₁₁₃	semidirect
445. #124	C₂×D₁₁₃	semidirect
451. #123	C₂×D₁₁₃	semidirect
459. C₂²⋊Q₈	C₂×D₁₁₃	semidirect
472. #121	C₂×D₁₁₃	semidirect
473. #121	C₂×D₁₁₃	semidirect
479. #120	C₂×D₁₁₃	semidirect
502. C₄×D₄	C₂×D₁₁₃	semidirect
503. C₄×D₄	C₂×D₁₁₃	semidirect
511. C₂×C₂²⋊C₄	C₂×D₁₁₃	semidirect
682. D₄	D₄×D₁₁₃	semidirect
749. C₂²	#41×D₁₁₃	semidirect

Maximal subgroups

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

subgroup	index
C₂²×#14268646	2
C₂×#41×D₁₁₃	2
#20299266	2
#20299261	2
#20299257	2
#20299256	2
#20299247	2
#20299246	2
#20299243	2
#20299238	2
#20299237	2
D₄×C₂²⋊D₁₁₃	2
#20299230	2
#20299147	2
#20299143	2
#20299111	2
#20299108	2
#20299106	2
#20299104	2
C₄×#14268646	2
C₂×#16813582	2
C₄×D₄×D₁₁₃	2
#546×C₁₁₃	2
D₄×#41	113