Subgroups — #28404334

Order 14464.

1660 conjugacy classes of subgroups.

The subgroup lattice has 798 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#16813668	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#16813667	C₂	1	1	yes	maximal, characteristic, complemented
3	#20299250	C₂	1	1	yes	maximal, characteristic, complemented
4	#20299247	C₂	1	1	yes	maximal, characteristic, complemented
5	#20299246	C₂	1	2	yes	maximal, complemented
6	#20299244	C₂	1	1	yes	maximal, characteristic, complemented
7	#20299243	C₂	1	1	yes	maximal, characteristic, complemented
8	#20299241	C₂	1	1	yes	maximal, characteristic, complemented
9	#20299238	C₂	1	2	yes	maximal, complemented
10	#20299237	C₂	1	2	yes	maximal, complemented
11	#20299232	C₂	1	1	yes	maximal, characteristic, complemented
12	D₄×C₂²⋊D₁₁₃	C₂	1	1	yes	maximal, characteristic, complemented
13	#20299230	C₂	1	2	yes	maximal, complemented
14	#20299178	C₂	1	1	yes	maximal, characteristic, complemented
15	#20299177	C₂	1	1	yes	maximal, characteristic, complemented
16	#20299159	C₂	1	2	yes	maximal, complemented
17	#20299158	C₂	1	2	yes	maximal, complemented
18	#20299147	C₂	1	1	yes	maximal, characteristic, complemented
19	#20299145	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×#16813595	C₂	1	2	yes	maximal, complemented
21	#121×D₁₁₃	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	#16813668	—	2	8	no	—
25	#16813667	—	2	8	no	—
26	C₂×#14268648	C₂²	1	1	yes	characteristic, complemented
27	C₂×#14268648	C₂²	1	1	yes	characteristic, complemented
28	C₂×#14268647	C₂²	1	1	yes	characteristic, complemented
29	C₂×#14268647	C₂²	1	1	yes	characteristic, complemented
30	C₂×#14268647	C₂²	1	1	yes	characteristic, complemented
31	C₂×#14268647	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	C₂²×D₄₅₂	C₂²	1	2	yes	complemented
36	C₂²×D₄₅₂	C₂²	1	1	yes	characteristic, complemented
37	C₂²×C₂²⋊D₁₁₃	C₂²	1	2	yes	complemented
38	C₂²×C₂²⋊D₁₁₃	C₂²	1	2	yes	complemented
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	2	yes	complemented
43	C₂×D₄×D₁₁₃	C₂²	1	1	yes	characteristic, complemented
44	C₂×D₄×D₁₁₃	C₂²	1	2	yes	complemented
45	C₂×D₄×D₁₁₃	C₂²	1	1	yes	characteristic, complemented
46	C₂×D₄×D₁₁₃	C₂²	1	2	yes	complemented
47	C₂²×C₄×D₁₁₃	C₂²	1	2	yes	complemented
48	#16813621	C₂²	1	1	yes	characteristic, complemented
49	#16813620	C₂²	1	1	yes	characteristic, complemented
50	#16813618	C₂²	1	1	yes	characteristic, complemented
51	#16813618	C₂²	1	1	yes	characteristic, complemented
52	#16813610	C₂²	1	1	yes	characteristic, complemented
53	#16813608	C₂²	1	1	yes	characteristic, complemented
54	#16813608	C₂²	1	1	yes	characteristic, complemented
55	#16813607	C₂²	1	2	yes	complemented
56	#16813607	C₂²	1	2	yes	complemented
57	#16813606	C₂²	1	2	yes	complemented
58	#16813605	C₂²	1	2	yes	complemented
59	#16813604	C₂²	1	2	yes	complemented
60	#16813604	C₂²	1	2	yes	complemented
61	#16813603	C₂²	1	2	yes	complemented
62	#16813602	C₂²	1	1	yes	characteristic, complemented
63	#16813601	C₂²	1	1	yes	characteristic, complemented
64	#16813600	C₂²	1	2	yes	complemented
65	#16813599	C₂²	1	2	yes	complemented
66	#16813598	C₂²	1	1	yes	characteristic, complemented
67	#16813597	C₂²	1	2	yes	complemented
68	#16813597	C₂²	1	1	yes	characteristic, complemented
69	#16813597	C₂²	1	1	yes	characteristic, complemented
70	#16813596	C₂²	1	2	yes	complemented
71	#16813596	C₂²	1	1	yes	characteristic, complemented
72	#16813595	C₂²	1	1	yes	characteristic, complemented
73	#16813595	C₂²	1	2	yes	complemented
74	#16813595	C₂²	1	1	yes	characteristic, complemented
75	#16813595	C₂²	1	2	yes	complemented
76	#16813595	C₂²	1	2	yes	complemented
77	#16813595	C₂²	1	2	yes	complemented
78	#16813595	C₂²	1	2	yes	complemented
79	#16813595	C₂²	1	2	yes	complemented
80	#16813595	C₂²	1	2	yes	complemented
81	#16813595	C₂²	1	2	yes	complemented
82	#16813595	C₂²	1	2	yes	complemented
83	#16813594	C₂²	1	2	yes	complemented
84	#16813594	C₂²	1	2	yes	complemented
85	#16813594	C₂²	1	2	yes	complemented
86	#16813593	C₂²	1	2	yes	complemented
87	#16813593	C₂²	1	1	yes	characteristic, complemented
88	#16813593	C₂²	1	1	yes	characteristic, complemented
89	#16813592	C₂²	1	2	yes	complemented
90	#16813592	C₂²	1	2	yes	complemented
91	#16813592	C₂²	1	2	yes	complemented
92	#16813591	C₂²	1	2	yes	complemented
93	#16813590	C₂²	1	2	yes	complemented
94	#16813590	C₂²	1	2	yes	complemented
95	#16813590	C₂²	1	2	yes	complemented
96	C₄×D₄₅₂	C₂²	1	1	yes	characteristic, complemented
97	C₄×D₄₅₂	C₂²	1	1	yes	characteristic, complemented
98	D₄×Dic₁₁₃	C₂²	1	1	yes	characteristic, complemented
99	#16813584	C₂²	1	1	yes	characteristic, complemented
100	C₄×C₂²⋊D₁₁₃	C₂²	1	2	yes	complemented
101	C₄×C₂²⋊D₁₁₃	C₂²	1	1	yes	characteristic, complemented
102	C₄×C₂²⋊D₁₁₃	C₂²	1	1	yes	characteristic, complemented
103	#16813582	C₂²	1	2	yes	complemented
104	#16813582	C₂²	1	2	yes	complemented
105	#16813582	C₂²	1	2	yes	complemented
106	C₂×#14268626	C₂²	1	2	yes	complemented
107	C₄⋊C₄×D₁₁₃	C₂²	1	1	yes	characteristic, complemented
108	C₄⋊C₄×D₁₁₃	C₂²	1	2	yes	complemented
109	C₂×#14268624	C₂²	1	2	yes	complemented
110	C₂²⋊C₄×D₁₁₃	C₂²	1	2	yes	complemented
111	C₂²⋊C₄×D₁₁₃	C₂²	1	2	yes	complemented
112	C₂²⋊C₄×D₁₁₃	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	2	yes	complemented
120	#121×C₁₁₃	C₂²	1	1	yes	characteristic, 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	2	yes	—
126	C₂³×D₁₁₃	C₂³	1	2	yes	—
127	C₂³×D₁₁₃	C₂³	1	2	yes	—
128	C₂³×D₁₁₃	C₂³	1	2	yes	—
129	#14268648	—	2	4	no	—
130	#14268648	—	2	4	no	—
131	#14268647	—	2	8	no	—
132	#14268647	—	2	4	no	—
133	#14268647	—	2	4	no	—
134	#14268647	—	2	4	no	—
135	#14268646	—	2	4	no	—
136	#14268646	—	2	8	no	—
137	#14268646	—	2	4	no	—
138	C₂×Dic₂₂₆	C₂³	1	1	yes	characteristic
139	C₂×Dic₂₂₆	C₂³	1	1	yes	characteristic
140	C₂×Dic₂₂₆	C₂³	1	1	yes	characteristic
141	C₂×D₄₅₂	—	2	8	no	—
142	C₂×D₄₅₂	—	2	4	no	—
143	C₂×D₄₅₂	C₂³	1	2	yes	—
144	C₂×D₄₅₂	C₂³	1	2	yes	—
145	C₂×D₄₅₂	C₂³	1	2	yes	—
146	C₂×D₄₅₂	C₂³	1	1	yes	characteristic
147	C₂×D₄₅₂	C₂³	1	1	yes	characteristic
148	C₂×D₄₅₂	C₂³	1	1	yes	characteristic
149	C₂×D₄₅₂	C₂³	1	1	yes	characteristic
150	C₂×D₄₅₂	C₂³	1	2	yes	—
151	C₂×D₄₅₂	C₂³	1	1	yes	characteristic
152	C₂×C₂²⋊D₁₁₃	—	2	8	no	—
153	C₂×C₂²⋊D₁₁₃	—	2	8	no	—
154	C₂×C₂²⋊D₁₁₃	—	4	4	no	—
155	C₂×C₂²⋊D₁₁₃	C₂³	1	2	yes	—
156	C₂×C₂²⋊D₁₁₃	C₂³	1	1	yes	characteristic
157	C₂×C₂²⋊D₁₁₃	C₂³	1	1	yes	characteristic
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	2	yes	—
162	C₂×C₂²⋊D₁₁₃	C₂³	1	1	yes	characteristic
163	C₂×C₂²⋊D₁₁₃	C₂³	1	2	yes	—
164	C₂×C₂²⋊D₁₁₃	C₂³	1	1	yes	characteristic
165	C₂×C₂²⋊D₁₁₃	C₂³	1	1	yes	characteristic
166	C₂×C₂²⋊D₁₁₃	C₂³	1	1	yes	characteristic
167	C₂×C₂²⋊D₁₁₃	C₂³	1	2	yes	—
168	C₂×C₂²⋊D₁₁₃	C₂³	1	2	yes	—
169	C₂×C₂²⋊D₁₁₃	C₂³	1	2	yes	—
170	C₂×C₂²⋊D₁₁₃	C₂³	1	2	yes	—
171	D₄×D₁₁₃	—	2	8	no	—
172	D₄×D₁₁₃	—	2	8	no	—
173	D₄×D₁₁₃	—	2	4	no	—
174	D₄×D₁₁₃	—	2	8	no	—
175	D₄×D₁₁₃	—	2	4	no	—
176	D₄×D₁₁₃	—	4	4	no	—
177	D₄×D₁₁₃	D₄	1	8	yes	complemented
178	C₂²×Dic₁₁₃	C₂³	1	2	yes	—
179	C₂²×Dic₁₁₃	C₂³	1	2	yes	—
180	C₂²×Dic₁₁₃	C₂³	1	2	yes	—
181	C₂×C₄×D₁₁₃	—	4	4	no	—
182	C₂×C₄×D₁₁₃	C₂³	1	1	yes	characteristic
183	C₂×C₄×D₁₁₃	C₂³	1	2	yes	—
184	C₂×C₄×D₁₁₃	C₂³	1	2	yes	—
185	C₂×C₄×D₁₁₃	C₂³	1	2	yes	—
186	C₂×C₄×D₁₁₃	C₂³	1	2	yes	—
187	C₂×C₄×D₁₁₃	C₂³	1	1	yes	characteristic
188	C₂×C₄×D₁₁₃	C₂³	1	1	yes	characteristic
189	C₂×C₄×D₁₁₃	C₂³	1	1	yes	characteristic
190	C₂×C₄×D₁₁₃	C₂³	1	2	yes	—
191	C₂×C₄×D₁₁₃	C₂³	1	2	yes	—
192	C₂×C₄×D₁₁₃	C₂³	1	1	yes	characteristic
193	C₄⋊Dic₁₁₃	C₂³	1	1	yes	characteristic
194	C₄⋊Dic₁₁₃	C₂³	1	2	yes	—
195	C₄⋊Dic₁₁₃	C₂³	1	1	yes	characteristic
196	#14268626	C₂³	1	1	yes	characteristic
197	#14268626	C₂³	1	2	yes	—
198	#14268626	C₂³	1	2	yes	—
199	#14268626	C₂³	1	1	yes	characteristic
200	#14268626	C₂³	1	2	yes	—
201	#14268626	C₂³	1	2	yes	—
202	#14268626	C₂³	1	2	yes	—
203	C₂²⋊Dic₁₁₃	C₂³	1	2	yes	—
204	C₂²⋊Dic₁₁₃	C₂³	1	2	yes	—
205	C₂²⋊Dic₁₁₃	C₂³	1	2	yes	—
206	C₂²⋊Dic₁₁₃	C₂³	1	1	yes	characteristic
207	C₂²⋊Dic₁₁₃	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	1	yes	characteristic
215	#14268624	C₂³	1	2	yes	—
216	#14268624	C₂³	1	2	yes	—
217	#14268624	C₂³	1	2	yes	—
218	#14268624	C₂³	1	1	yes	characteristic
219	#14268624	C₂³	1	1	yes	characteristic
220	C₄×Dic₁₁₃	C₂³	1	1	yes	characteristic
221	C₄×Dic₁₁₃	C₂³	1	1	yes	characteristic
222	C₄×Dic₁₁₃	C₂³	1	1	yes	characteristic
223	C₂⁴×C₁₁₃	C₂³	1	2	yes	—
224	#41×C₁₁₃	—	2	4	no	—
225	C₂×Q₈×C₁₁₃	C₂³	1	1	yes	characteristic
226	C₂×D₄×C₁₁₃	—	2	4	no	—
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	1	yes	characteristic
231	C₂×D₄×C₁₁₃	C₂³	1	2	yes	—
232	C₂×D₄×C₁₁₃	C₂³	1	1	yes	characteristic
233	C₂²×C₄×C₁₁₃	C₂³	1	2	yes	—
234	C₂²×C₄×C₁₁₃	C₂³	1	1	yes	characteristic
235	C₂²×C₄×C₁₁₃	C₂³	1	1	yes	characteristic
236	C₂²×C₄×C₁₁₃	C₂³	1	2	yes	—
237	C₄⋊C₄×C₁₁₃	C₂³	1	1	yes	characteristic
238	C₄⋊C₄×C₁₁₃	C₂³	1	2	yes	—
239	C₄⋊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	C₂²⋊C₄×C₁₁₃	C₂³	1	1	yes	characteristic
247	C₄²×C₁₁₃	C₂³	1	1	yes	characteristic
248	C₂³×C₁₁₃	—	2	4	no	—
249	C₂³×C₁₁₃	—	4	2	no	—
250	C₂³×C₁₁₃	—	4	2	no	—
251	C₂³×C₁₁₃	C₂⁴	1	1	yes	characteristic
252	C₂³×C₁₁₃	C₂⁴	1	2	yes	—
253	C₂³×C₁₁₃	C₂⁴	1	1	yes	characteristic
254	C₂³×C₁₁₃	C₂⁴	1	2	yes	—
255	C₂²×D₁₁₃	—	2	4	no	—
256	C₂²×D₁₁₃	—	2	4	no	—
257	C₂²×D₁₁₃	—	2	4	no	—
258	C₂²×D₁₁₃	—	4	2	no	—
259	C₂²×D₁₁₃	—	4	2	no	—
260	C₂²×D₁₁₃	—	4	2	no	—
261	C₂²×D₁₁₃	—	4	2	no	—
262	C₂²×D₁₁₃	—	4	2	no	—
263	C₂²×D₁₁₃	—	4	2	no	—
264	C₂²×D₁₁₃	—	4	2	no	—
265	C₂²×D₁₁₃	—	4	2	no	—
266	C₂²×D₁₁₃	C₂×D₄	1	8	yes	complemented
267	C₂²×D₁₁₃	C₂⁴	1	2	yes	—
268	C₂²×D₁₁₃	C₂⁴	1	1	yes	characteristic
269	C₂²×D₁₁₃	C₂⁴	1	1	yes	characteristic
270	C₂²×D₁₁₃	C₂⁴	1	2	yes	—
271	C₂²×D₁₁₃	C₂⁴	1	1	yes	characteristic
272	Q₈×C₁₁₃	—	2	2	no	—
273	D₄×C₁₁₃	—	2	4	no	—
274	D₄×C₁₁₃	—	2	4	no	—
275	D₄×C₁₁₃	—	2	2	no	—
276	D₄×C₁₁₃	—	4	1	no	—
277	D₄×C₁₁₃	—	4	2	no	—
278	D₄×C₁₁₃	C₂×D₄	1	4	yes	complemented
279	C₂×C₄×C₁₁₃	—	2	4	no	—
280	C₂×C₄×C₁₁₃	—	2	2	no	—
281	C₂×C₄×C₁₁₃	—	2	2	no	—
282	C₂×C₄×C₁₁₃	—	4	2	no	—
283	C₂×C₄×C₁₁₃	C₂⁴	1	1	yes	characteristic
284	C₂×C₄×C₁₁₃	C₂⁴	1	1	yes	characteristic
285	C₂×C₄×C₁₁₃	C₂⁴	1	2	yes	—
286	C₂×C₄×C₁₁₃	C₂⁴	1	1	yes	characteristic
287	C₂×C₄×C₁₁₃	C₂⁴	1	2	yes	—
288	C₂×C₄×C₁₁₃	C₂⁴	1	1	yes	characteristic
289	C₂×C₄×C₁₁₃	C₂⁴	1	1	yes	characteristic
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	—	2	4	no	—
295	C₂²⋊D₁₁₃	—	2	4	no	—
296	C₂²⋊D₁₁₃	—	2	2	no	—
297	C₂²⋊D₁₁₃	—	2	2	no	—
298	C₂²⋊D₁₁₃	—	2	2	no	—
299	C₂²⋊D₁₁₃	—	2	2	no	—
300	C₂²⋊D₁₁₃	—	2	4	no	—
301	C₂²⋊D₁₁₃	—	2	2	no	—
302	C₂²⋊D₁₁₃	—	4	2	no	—
303	C₂²⋊D₁₁₃	—	4	2	no	—
304	C₂²⋊D₁₁₃	—	4	2	no	—
305	C₂²⋊D₁₁₃	C₂×D₄	1	8	yes	complemented
306	C₂×Dic₁₁₃	—	2	4	no	—
307	C₂×Dic₁₁₃	—	2	4	no	—
308	C₂×Dic₁₁₃	—	2	4	no	—
309	C₂×Dic₁₁₃	C₂⁴	1	1	yes	characteristic
310	C₂×Dic₁₁₃	C₂⁴	1	2	yes	—
311	C₂×Dic₁₁₃	C₂⁴	1	2	yes	—
312	C₂×Dic₁₁₃	C₂⁴	1	1	yes	characteristic
313	C₂×Dic₁₁₃	C₂⁴	1	1	yes	characteristic
314	C₂×Dic₁₁₃	C₂⁴	1	1	yes	characteristic
315	C₂×Dic₁₁₃	C₂⁴	1	1	yes	characteristic
316	D₄₅₂	—	2	2	no	—
317	D₄₅₂	—	2	4	no	—
318	D₄₅₂	—	2	4	no	—
319	D₄₅₂	—	2	4	no	—
320	D₄₅₂	—	2	2	no	—
321	D₄₅₂	—	2	2	no	—
322	D₄₅₂	—	4	2	no	—
323	D₄₅₂	—	4	1	no	—
324	D₄₅₂	C₂×D₄	1	4	yes	complemented
325	C₄×D₁₁₃	—	2	4	no	—
326	C₄×D₁₁₃	—	2	4	no	—
327	C₄×D₁₁₃	—	2	2	no	—
328	C₄×D₁₁₃	—	2	2	no	—
329	C₄×D₁₁₃	—	2	4	no	—
330	C₄×D₁₁₃	—	2	2	no	—
331	C₄×D₁₁₃	—	2	4	no	—
332	C₄×D₁₁₃	—	4	2	no	—
333	C₄×D₁₁₃	—	4	2	no	—
334	C₄×D₁₁₃	—	4	1	no	—
335	C₄×D₁₁₃	C₂×D₄	1	4	yes	complemented
336	Dic₂₂₆	—	2	2	no	—
337	Dic₂₂₆	—	2	2	no	—
338	Dic₂₂₆	—	2	2	no	—
339	C₂²×C₁₁₃	—	2	2	no	—
340	C₂²×C₁₁₃	—	2	2	no	—
341	C₂²×C₁₁₃	—	2	2	no	—
342	C₂²×C₁₁₃	—	2	1	no	—
343	C₂²×C₁₁₃	—	2	1	no	—
344	C₂²×C₁₁₃	—	2	1	no	—
345	C₂²×C₁₁₃	—	2	2	no	—
346	C₂²×C₁₁₃	—	2	1	no	—
347	C₂²×C₁₁₃	—	2	2	no	—
348	C₂²×C₁₁₃	—	2	1	no	—
349	C₂²×C₁₁₃	—	2	1	no	—
350	C₂²×C₁₁₃	—	8	4	no	—
351	C₂²×C₁₁₃	C₂²×D₄	1	4	yes	—
352	C₂²×C₁₁₃	C₂⁵	1	1	yes	characteristic
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	—	2	1	no	—
358	C₂×D₁₁₃	—	2	2	no	—
359	C₂×D₁₁₃	—	2	1	no	—
360	C₂×D₁₁₃	—	2	1	no	—
361	C₂×D₁₁₃	—	2	2	no	—
362	C₂×D₁₁₃	—	2	1	no	—
363	C₂×D₁₁₃	—	2	1	no	—
364	C₂×D₁₁₃	—	2	1	no	—
365	C₂×D₁₁₃	—	2	2	no	—
366	C₂×D₁₁₃	—	4	8	no	—
367	C₂×D₁₁₃	—	8	4	no	—
368	C₂×D₁₁₃	—	8	4	no	—
369	C₂×D₁₁₃	—	8	4	no	—
370	C₂×D₁₁₃	C₂²×D₄	1	4	yes	—
371	C₂×D₁₁₃	C₂²×D₄	1	2	yes	—
372	C₄×C₁₁₃	—	2	1	no	—
373	C₄×C₁₁₃	—	2	1	no	—
374	C₄×C₁₁₃	—	2	2	no	—
375	C₄×C₁₁₃	—	2	1	no	—
376	C₄×C₁₁₃	—	2	2	no	—
377	C₄×C₁₁₃	—	2	1	no	—
378	C₄×C₁₁₃	C₂²×D₄	1	2	yes	—
379	Dic₁₁₃	—	2	1	no	—
380	Dic₁₁₃	—	2	2	no	—
381	Dic₁₁₃	—	2	1	no	—
382	Dic₁₁₃	—	2	2	no	—
383	Dic₁₁₃	—	2	1	no	—
384	Dic₁₁₃	C₂²×D₄	1	2	yes	—
385	Dic₁₁₃	H(5,𝔽₂)	1	2	yes	complemented
386	C₂×C₁₁₃	—	2	4	no	—
387	C₂×C₁₁₃	—	4	1	no	—
388	C₂×C₁₁₃	—	4	2	no	—
389	C₂×C₁₁₃	—	4	1	no	—
390	C₂×C₁₁₃	C₂³×D₄	1	1	yes	characteristic
391	C₂×C₁₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
392	C₂×C₁₁₃	#585	1	1	yes	characteristic
393	D₁₁₃	—	2	2	no	—
394	D₁₁₃	—	2	4	no	—
395	D₁₁₃	—	4	2	no	—
396	D₁₁₃	—	4	1	no	—
397	D₁₁₃	—	4	1	no	—
398	#3496	—	113	1	no	maximal, Sylow
399	C₁₁₃	#3496	1	1	yes	characteristic, complemented, Sylow
400	C₂×H(5,𝔽₂)	—	113	1	no	—
401	C₂×H(5,𝔽₂)	—	113	1	no	—
402	#547	—	113	1	no	—
403	#547	—	113	2	no	—
404	#547	—	113	1	no	—
405	#546	—	113	1	no	—
406	#546	—	113	2	no	—
407	#546	—	113	1	no	—
408	#546	—	113	1	no	—
409	#546	—	113	2	no	—
410	#546	D₁₁₃	1	1	yes	characteristic, complemented
411	D₄²	—	113	1	no	—
412	D₄²	—	113	1	no	—
413	D₄²	—	113	2	no	—
414	#537	—	113	1	no	—
415	#537	—	113	1	no	—
416	#534	—	113	2	no	—
417	#534	—	113	2	no	—
418	#532	—	113	1	no	—
419	#532	—	113	1	no	—
420	C₂×#121	—	113	2	no	—
421	C₂×#121	—	113	2	no	—
422	C₂×C₄×D₄	—	113	1	no	—
423	H(5,𝔽₂)	—	226	8	no	—
424	H(5,𝔽₂)	—	226	8	no	—
425	C₂×#41	—	113	1	no	—
426	C₂×#41	—	113	1	no	—
427	C₂×#41	—	113	1	no	—
428	C₂×#41	—	113	1	no	—
429	C₂×#41	—	113	2	no	—
430	C₂×#41	—	113	1	no	—
431	C₂×#41	—	113	1	no	—
432	C₂×#41	—	113	1	no	—
433	C₂×#41	—	113	2	no	—
434	C₂×#41	C₂×D₁₁₃	1	1	yes	characteristic, complemented
435	C₂²×D₄	—	113	1	no	—
436	C₂²×D₄	—	113	2	no	—
437	C₂²×D₄	—	113	2	no	—
438	C₂²×D₄	—	113	2	no	—
439	C₂²×D₄	—	113	2	no	—
440	C₂²×D₄	—	113	2	no	—
441	C₂²×D₄	—	113	2	no	—
442	C₂²×D₄	—	113	2	no	—
443	C₂²×D₄	—	113	1	no	—
444	C₂²×D₄	—	113	1	no	—
445	C₂²×D₄	—	113	2	no	—
446	C₂²×D₄	—	113	1	no	—
447	C₂²×D₄	C₂×D₁₁₃	1	1	yes	characteristic, complemented
448	C₂³×C₄	—	113	2	no	—
449	C₄⋊Q₈	—	113	1	no	—
450	C₄⋊Q₈	—	113	1	no	—
451	#127	—	113	1	no	—
452	#127	—	113	1	no	—
453	#124	—	113	1	no	—
454	#124	—	113	1	no	—
455	#124	—	113	1	no	—
456	#124	C₂×D₁₁₃	1	1	yes	characteristic, complemented
457	#123	—	113	2	no	—
458	#123	—	113	2	no	—
459	#123	—	113	2	no	—
460	#123	—	113	2	no	—
461	#123	—	113	2	no	—
462	#123	—	113	2	no	—
463	#123	—	113	2	no	—
464	#123	C₂×D₁₁₃	1	2	yes	complemented
465	C₂²⋊Q₈	—	113	1	no	—
466	C₂²⋊Q₈	—	113	1	no	—
467	C₂²⋊Q₈	—	113	2	no	—
468	C₂²⋊Q₈	—	113	1	no	—
469	C₂²⋊Q₈	—	113	2	no	—
470	C₂²⋊Q₈	C₂×D₁₁₃	1	1	yes	characteristic, complemented
471	#121	—	113	2	no	—
472	#121	—	113	2	no	—
473	#121	—	113	2	no	—
474	#121	—	113	1	no	—
475	#121	—	113	1	no	—
476	#121	—	113	2	no	—
477	#121	—	113	2	no	—
478	#121	—	113	1	no	—
479	#121	—	113	2	no	—
480	#121	—	113	1	no	—
481	#121	—	113	1	no	—
482	#121	—	113	1	no	—
483	#121	—	113	2	no	—
484	#121	—	113	1	no	—
485	#121	—	113	2	no	—
486	#121	—	113	2	no	—
487	#121	—	113	2	no	—
488	#121	—	113	2	no	—
489	#121	—	113	2	no	—
490	#121	—	113	2	no	—
491	#121	—	113	2	no	—
492	#121	—	113	2	no	—
493	#121	C₂×D₁₁₃	1	2	yes	complemented
494	#121	C₂×D₁₁₃	1	1	yes	characteristic, complemented
495	#120	—	113	2	no	—
496	#120	—	113	2	no	—
497	#120	—	113	2	no	—
498	#120	—	113	2	no	—
499	#120	—	113	2	no	—
500	#120	—	113	2	no	—
501	#120	—	113	2	no	—
502	#120	C₂×D₁₁₃	1	2	yes	complemented
503	C₄×D₄	—	113	1	no	—
504	C₄×D₄	—	113	2	no	—
505	C₄×D₄	—	113	1	no	—
506	C₄×D₄	—	113	1	no	—
507	C₄×D₄	—	113	1	no	—
508	C₄×D₄	—	113	2	no	—
509	C₄×D₄	—	113	2	no	—
510	C₄×D₄	—	113	2	no	—
511	C₄×D₄	—	113	1	no	—
512	C₄×D₄	—	113	1	no	—
513	C₄×D₄	C₂×D₁₁₃	1	1	yes	characteristic, complemented
514	C₄×D₄	C₂×D₁₁₃	1	1	yes	characteristic, complemented
515	C₂×C₄⋊C₄	—	113	2	no	—
516	C₂×C₄⋊C₄	—	113	1	no	—
517	C₂×C₄⋊C₄	—	113	2	no	—
518	C₂×C₂²⋊C₄	—	113	2	no	—
519	C₂×C₂²⋊C₄	—	113	2	no	—
520	C₂×C₂²⋊C₄	—	113	2	no	—
521	C₂×C₂²⋊C₄	—	113	2	no	—
522	C₂×C₂²⋊C₄	C₂×D₁₁₃	1	2	yes	complemented
523	C₂×C₄²	—	113	1	no	—
524	C₂⁴	—	113	2	no	—
525	C₂⁴	—	113	2	no	—
526	C₂⁴	—	113	2	no	—
527	C₂⁴	—	113	2	no	—
528	C₂⁴	C₂²×D₁₁₃	1	2	yes	—
529	#41	—	2	4	no	—
530	#41	—	226	4	no	—
531	#41	—	226	4	no	—
532	#41	—	226	8	no	—
533	#41	—	226	4	no	—
534	#41	—	226	4	no	—
535	#41	—	226	4	no	—
536	#41	—	226	8	no	—
537	#41	—	226	4	no	—
538	#41	—	226	4	no	—
539	C₂×Q₈	—	113	1	no	—
540	C₂×Q₈	—	113	1	no	—
541	C₂×Q₈	—	113	1	no	—
542	C₂×Q₈	C₂²×D₁₁₃	1	1	yes	characteristic
543	C₂×D₄	—	2	4	no	—
544	C₂×D₄	—	113	2	no	—
545	C₂×D₄	—	113	8	no	—
546	C₂×D₄	—	113	2	no	—
547	C₂×D₄	—	113	2	no	—
548	C₂×D₄	—	113	2	no	—
549	C₂×D₄	—	113	1	no	—
550	C₂×D₄	—	113	2	no	—
551	C₂×D₄	—	113	1	no	—
552	C₂×D₄	—	113	2	no	—
553	C₂×D₄	—	113	2	no	—
554	C₂×D₄	—	113	2	no	—
555	C₂×D₄	—	113	2	no	—
556	C₂×D₄	—	113	1	no	—
557	C₂×D₄	—	113	2	no	—
558	C₂×D₄	—	113	1	no	—
559	C₂×D₄	—	113	1	no	—
560	C₂×D₄	—	113	1	no	—
561	C₂×D₄	—	113	1	no	—
562	C₂×D₄	—	113	1	no	—
563	C₂×D₄	—	113	2	no	—
564	C₂×D₄	—	113	2	no	—
565	C₂×D₄	—	113	2	no	—
566	C₂×D₄	—	113	1	no	—
567	C₂×D₄	—	113	2	no	—
568	C₂×D₄	—	113	1	no	—
569	C₂×D₄	—	113	1	no	—
570	C₂×D₄	—	452	4	no	—
571	C₂×D₄	—	452	4	no	—
572	C₂×D₄	—	226	4	no	—
573	C₂×D₄	—	226	8	no	—
574	C₂×D₄	—	226	8	no	—
575	C₂×D₄	—	226	4	no	—
576	C₂×D₄	—	226	8	no	—
577	C₂×D₄	—	226	8	no	—
578	C₂×D₄	—	226	8	no	—
579	C₂×D₄	—	226	8	no	—
580	C₂×D₄	—	226	4	no	—
581	C₂×D₄	C₂²×D₁₁₃	1	2	yes	—
582	C₂×D₄	C₂²×D₁₁₃	1	2	yes	—
583	C₂×D₄	C₂²×D₁₁₃	1	1	yes	characteristic
584	C₂×D₄	C₂²×D₁₁₃	1	1	yes	characteristic
585	C₂×D₄	C₂²×D₁₁₃	1	2	yes	—
586	C₂×D₄	C₂²×D₁₁₃	1	1	yes	characteristic
587	C₂²×C₄	—	113	1	no	—
588	C₂²×C₄	—	113	2	no	—
589	C₂²×C₄	—	113	2	no	—
590	C₂²×C₄	—	113	2	no	—
591	C₂²×C₄	—	113	1	no	—
592	C₂²×C₄	—	113	2	no	—
593	C₂²×C₄	—	113	2	no	—
594	C₂²×C₄	—	113	1	no	—
595	C₂²×C₄	—	113	2	no	—
596	C₂²×C₄	—	113	2	no	—
597	C₂²×C₄	—	113	2	no	—
598	C₂²×C₄	—	113	2	no	—
599	C₂²×C₄	—	113	1	no	—
600	C₂²×C₄	—	113	1	no	—
601	C₂²×C₄	—	452	4	no	—
602	C₂²×C₄	C₂²×D₁₁₃	1	2	yes	—
603	C₂²×C₄	C₂²×D₁₁₃	1	1	yes	characteristic
604	C₂²×C₄	C₂²×D₁₁₃	1	1	yes	characteristic
605	C₂²×C₄	C₂²×D₁₁₃	1	2	yes	—
606	C₄⋊C₄	—	113	1	no	—
607	C₄⋊C₄	—	113	2	no	—
608	C₄⋊C₄	—	113	1	no	—
609	C₄⋊C₄	—	113	2	no	—
610	C₄⋊C₄	—	113	1	no	—
611	C₄⋊C₄	—	113	2	no	—
612	C₄⋊C₄	—	113	2	no	—
613	C₄⋊C₄	—	113	2	no	—
614	C₄⋊C₄	—	113	2	no	—
615	C₄⋊C₄	—	113	1	no	—
616	C₄⋊C₄	C₂²×D₁₁₃	1	1	yes	characteristic
617	C₄⋊C₄	C₂²×D₁₁₃	1	2	yes	—
618	C₄⋊C₄	C₂²×D₁₁₃	1	1	yes	characteristic
619	C₂²⋊C₄	—	113	2	no	—
620	C₂²⋊C₄	—	113	2	no	—
621	C₂²⋊C₄	—	113	2	no	—
622	C₂²⋊C₄	—	113	1	no	—
623	C₂²⋊C₄	—	113	1	no	—
624	C₂²⋊C₄	—	113	1	no	—
625	C₂²⋊C₄	—	113	2	no	—
626	C₂²⋊C₄	—	113	1	no	—
627	C₂²⋊C₄	—	113	2	no	—
628	C₂²⋊C₄	—	113	2	no	—
629	C₂²⋊C₄	—	113	2	no	—
630	C₂²⋊C₄	—	113	2	no	—
631	C₂²⋊C₄	—	113	2	no	—
632	C₂²⋊C₄	—	113	2	no	—
633	C₂²⋊C₄	—	113	1	no	—
634	C₂²⋊C₄	—	113	1	no	—
635	C₂²⋊C₄	—	113	2	no	—
636	C₂²⋊C₄	C₂²×D₁₁₃	1	1	yes	characteristic
637	C₂²⋊C₄	C₂²×D₁₁₃	1	2	yes	—
638	C₂²⋊C₄	C₂²×D₁₁₃	1	2	yes	—
639	C₂²⋊C₄	C₂²×D₁₁₃	1	1	yes	characteristic
640	C₂²⋊C₄	C₂²×D₁₁₃	1	2	yes	—
641	C₂²⋊C₄	C₂²×D₁₁₃	1	2	yes	—
642	C₂²⋊C₄	C₂²×D₁₁₃	1	2	yes	—
643	C₄²	—	113	1	no	—
644	C₄²	—	113	1	no	—
645	C₄²	—	113	1	no	—
646	C₄²	C₂²×D₁₁₃	1	1	yes	characteristic
647	C₂³	—	2	4	no	—
648	C₂³	—	4	2	no	—
649	C₂³	—	4	2	no	—
650	C₂³	—	113	8	no	—
651	C₂³	—	113	2	no	—
652	C₂³	—	113	1	no	—
653	C₂³	—	113	2	no	—
654	C₂³	—	113	1	no	—
655	C₂³	—	113	1	no	—
656	C₂³	—	452	2	no	—
657	C₂³	—	452	2	no	—
658	C₂³	—	452	2	no	—
659	C₂³	—	452	2	no	—
660	C₂³	—	452	2	no	—
661	C₂³	—	452	2	no	—
662	C₂³	—	452	2	no	—
663	C₂³	—	452	2	no	—
664	C₂³	—	226	4	no	—
665	C₂³	—	226	4	no	—
666	C₂³	—	226	4	no	—
667	C₂³	C₂³×D₁₁₃	1	1	yes	characteristic
668	C₂³	C₂³×D₁₁₃	1	2	yes	—
669	C₂³	C₂³×D₁₁₃	1	1	yes	characteristic
670	C₂³	C₂³×D₁₁₃	1	2	yes	—
671	Q₈	—	2	2	no	—
672	Q₈	—	226	2	no	—
673	Q₈	—	226	2	no	—
674	Q₈	—	226	2	no	—
675	D₄	—	2	4	no	—
676	D₄	—	2	4	no	—
677	D₄	—	2	2	no	—
678	D₄	—	4	2	no	—
679	D₄	—	4	1	no	—
680	D₄	—	113	8	no	—
681	D₄	—	113	4	no	—
682	D₄	—	452	2	no	—
683	D₄	—	452	1	no	—
684	D₄	—	452	2	no	—
685	D₄	—	452	2	no	—
686	D₄	—	452	2	no	—
687	D₄	—	226	2	no	—
688	D₄	—	226	4	no	—
689	D₄	—	226	2	no	—
690	D₄	—	226	4	no	—
691	D₄	—	226	4	no	—
692	D₄	—	226	2	no	—
693	D₄	—	226	4	no	—
694	D₄	—	226	2	no	—
695	D₄	—	226	2	no	—
696	D₄	—	226	2	no	—
697	D₄	—	226	2	no	—
698	D₄	—	226	2	no	—
699	D₄	—	226	4	no	—
700	D₄	—	226	4	no	—
701	D₄	—	226	4	no	—
702	D₄	—	226	4	no	—
703	D₄	—	226	4	no	—
704	D₄	—	226	2	no	—
705	D₄	D₄×D₁₁₃	1	4	yes	complemented
706	C₂×C₄	—	2	4	no	—
707	C₂×C₄	—	2	2	no	—
708	C₂×C₄	—	2	2	no	—
709	C₂×C₄	—	4	2	no	—
710	C₂×C₄	—	113	1	no	—
711	C₂×C₄	—	113	1	no	—
712	C₂×C₄	—	113	4	no	—
713	C₂×C₄	—	113	1	no	—
714	C₂×C₄	—	113	2	no	—
715	C₂×C₄	—	113	1	no	—
716	C₂×C₄	—	113	2	no	—
717	C₂×C₄	—	113	1	no	—
718	C₂×C₄	—	452	2	no	—
719	C₂×C₄	—	452	2	no	—
720	C₂×C₄	—	452	1	no	—
721	C₂×C₄	—	226	2	no	—
722	C₂×C₄	—	226	4	no	—
723	C₂×C₄	—	226	4	no	—
724	C₂×C₄	—	226	4	no	—
725	C₂×C₄	—	226	4	no	—
726	C₂×C₄	—	226	4	no	—
727	C₂×C₄	—	226	4	no	—
728	C₂×C₄	—	226	4	no	—
729	C₂×C₄	—	226	2	no	—
730	C₂×C₄	—	226	2	no	—
731	C₂×C₄	C₂³×D₁₁₃	1	1	yes	characteristic
732	C₂×C₄	C₂³×D₁₁₃	1	1	yes	characteristic
733	C₂×C₄	C₂³×D₁₁₃	1	2	yes	—
734	C₂×C₄	C₂³×D₁₁₃	1	1	yes	characteristic
735	C₂×C₄	C₂³×D₁₁₃	1	2	yes	—
736	C₂×C₄	C₂³×D₁₁₃	1	1	yes	characteristic
737	C₂×C₄	C₂³×D₁₁₃	1	1	yes	characteristic
738	C₂²	—	2	2	no	—
739	C₂²	—	2	2	no	—
740	C₂²	—	2	1	no	—
741	C₂²	—	2	1	no	—
742	C₂²	—	2	2	no	—
743	C₂²	—	2	1	no	—
744	C₂²	—	2	2	no	—
745	C₂²	—	2	1	no	—
746	C₂²	—	2	1	no	—
747	C₂²	—	2	1	no	—
748	C₂²	—	2	2	no	—
749	C₂²	—	8	4	no	—
750	C₂²	—	113	2	no	—
751	C₂²	—	113	4	no	—
752	C₂²	—	904	4	no	—
753	C₂²	—	904	4	no	—
754	C₂²	—	904	4	no	—
755	C₂²	—	452	8	no	—
756	C₂²	—	226	2	no	—
757	C₂²	—	226	1	no	—
758	C₂²	—	226	1	no	—
759	C₂²	—	226	1	no	—
760	C₂²	—	226	2	no	—
761	C₂²	—	226	1	no	—
762	C₂²	—	226	1	no	—
763	C₂²	—	226	1	no	—
764	C₂²	—	226	2	no	—
765	C₂²	—	226	1	no	—
766	C₂²	—	226	2	no	—
767	C₂²	—	226	1	no	—
768	C₂²	—	226	2	no	—
769	C₂²	C₂×D₄×D₁₁₃	1	4	yes	—
770	C₂²	C₂⁴×D₁₁₃	1	1	yes	characteristic
771	C₄	—	2	1	no	—
772	C₄	—	2	1	no	—
773	C₄	—	2	2	no	—
774	C₄	—	2	1	no	—
775	C₄	—	2	2	no	—
776	C₄	—	2	1	no	—
777	C₄	—	113	2	no	—
778	C₄	—	113	2	no	—
779	C₄	—	226	1	no	—
780	C₄	—	226	2	no	—
781	C₄	—	226	1	no	—
782	C₄	—	226	2	no	—
783	C₄	—	226	1	no	—
784	C₄	C₂×D₄×D₁₁₃	1	2	yes	—
785	C₂	—	2	4	no	—
786	C₂	—	4	1	no	—
787	C₂	—	4	2	no	—
788	C₂	—	4	1	no	—
789	C₂	—	452	1	no	—
790	C₂	—	452	2	no	—
791	C₂	—	452	1	no	—
792	C₂	—	226	4	no	—
793	C₂	—	226	2	no	—
794	C₂	C₂²×D₄×D₁₁₃	1	1	yes	characteristic
795	C₂	H(5,𝔽₂)×D₁₁₃	1	1	yes	characteristic
796	C₂	#20299434	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	#3496
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. C₂×#16813668	C₂	semidirect
2. C₂×#16813667	C₂	semidirect
3. #20299250	C₂	semidirect
4. #20299247	C₂	semidirect
5. #20299246	C₂	semidirect
6. #20299244	C₂	semidirect
7. #20299243	C₂	semidirect
8. #20299241	C₂	semidirect
9. #20299238	C₂	semidirect
10. #20299237	C₂	semidirect
11. #20299232	C₂	semidirect
12. D₄×C₂²⋊D₁₁₃	C₂	semidirect
13. #20299230	C₂	semidirect
14. #20299178	C₂	semidirect
15. #20299177	C₂	semidirect
16. #20299159	C₂	semidirect
17. #20299158	C₂	semidirect
18. #20299147	C₂	semidirect
19. #20299145	C₂	semidirect
20. C₂×#16813595	C₂	semidirect
21. #121×D₁₁₃	C₂	semidirect
22. C₄×D₄×D₁₁₃	C₂	semidirect
23. #546×C₁₁₃	C₂	semidirect
26. C₂×#14268648	C₂²	semidirect
27. C₂×#14268648	C₂²	semidirect
28. C₂×#14268647	C₂²	semidirect
29. C₂×#14268647	C₂²	semidirect
30. C₂×#14268647	C₂²	semidirect
31. C₂×#14268647	C₂²	semidirect
32. C₂×#14268646	C₂²	semidirect
33. C₂×#14268646	C₂²	semidirect
34. C₂×#14268646	C₂²	semidirect
35. C₂²×D₄₅₂	C₂²	semidirect
36. C₂²×D₄₅₂	C₂²	semidirect
37. C₂²×C₂²⋊D₁₁₃	C₂²	semidirect
38. C₂²×C₂²⋊D₁₁₃	C₂²	semidirect
39. C₂²×C₂²⋊D₁₁₃	C₂²	semidirect
41. C₂×D₄×D₁₁₃	C₂²	semidirect
42. C₂×D₄×D₁₁₃	C₂²	semidirect
43. C₂×D₄×D₁₁₃	C₂²	semidirect
44. C₂×D₄×D₁₁₃	C₂²	semidirect
45. C₂×D₄×D₁₁₃	C₂²	semidirect
46. C₂×D₄×D₁₁₃	C₂²	semidirect
47. C₂²×C₄×D₁₁₃	C₂²	semidirect
48. #16813621	C₂²	semidirect
49. #16813620	C₂²	semidirect
50. #16813618	C₂²	semidirect
51. #16813618	C₂²	semidirect
52. #16813610	C₂²	semidirect
53. #16813608	C₂²	semidirect
54. #16813608	C₂²	semidirect
55. #16813607	C₂²	semidirect
56. #16813607	C₂²	semidirect
57. #16813606	C₂²	semidirect
58. #16813605	C₂²	semidirect
59. #16813604	C₂²	semidirect
60. #16813604	C₂²	semidirect
61. #16813603	C₂²	semidirect
62. #16813602	C₂²	semidirect
63. #16813601	C₂²	semidirect
64. #16813600	C₂²	semidirect
65. #16813599	C₂²	semidirect
66. #16813598	C₂²	semidirect
67. #16813597	C₂²	semidirect
68. #16813597	C₂²	semidirect
69. #16813597	C₂²	semidirect
70. #16813596	C₂²	semidirect
71. #16813596	C₂²	semidirect
72. #16813595	C₂²	semidirect
73. #16813595	C₂²	semidirect
74. #16813595	C₂²	semidirect
75. #16813595	C₂²	semidirect
76. #16813595	C₂²	semidirect
77. #16813595	C₂²	semidirect
78. #16813595	C₂²	semidirect
79. #16813595	C₂²	semidirect
80. #16813595	C₂²	semidirect
81. #16813595	C₂²	semidirect
82. #16813595	C₂²	semidirect
83. #16813594	C₂²	semidirect
84. #16813594	C₂²	semidirect
85. #16813594	C₂²	semidirect
86. #16813593	C₂²	semidirect
87. #16813593	C₂²	semidirect
88. #16813593	C₂²	semidirect
89. #16813592	C₂²	semidirect
90. #16813592	C₂²	semidirect
91. #16813592	C₂²	semidirect
92. #16813591	C₂²	semidirect
93. #16813590	C₂²	semidirect
94. #16813590	C₂²	semidirect
95. #16813590	C₂²	semidirect
96. C₄×D₄₅₂	C₂²	semidirect
97. C₄×D₄₅₂	C₂²	semidirect
98. D₄×Dic₁₁₃	C₂²	semidirect
99. #16813584	C₂²	semidirect
100. C₄×C₂²⋊D₁₁₃	C₂²	semidirect
101. C₄×C₂²⋊D₁₁₃	C₂²	semidirect
102. C₄×C₂²⋊D₁₁₃	C₂²	semidirect
103. #16813582	C₂²	semidirect
104. #16813582	C₂²	semidirect
105. #16813582	C₂²	semidirect
106. C₂×#14268626	C₂²	semidirect
107. C₄⋊C₄×D₁₁₃	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. C₂²⋊C₄×D₁₁₃	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
177. D₄×D₁₁₃	D₄	semidirect
266. C₂²×D₁₁₃	C₂×D₄	semidirect
278. D₄×C₁₁₃	C₂×D₄	semidirect
305. C₂²⋊D₁₁₃	C₂×D₄	semidirect
324. D₄₅₂	C₂×D₄	semidirect
335. C₄×D₁₁₃	C₂×D₄	semidirect
385. Dic₁₁₃	H(5,𝔽₂)	semidirect
399. C₁₁₃	#3496	semidirect
410. #546	D₁₁₃	semidirect
434. C₂×#41	C₂×D₁₁₃	semidirect
447. C₂²×D₄	C₂×D₁₁₃	semidirect
456. #124	C₂×D₁₁₃	semidirect
464. #123	C₂×D₁₁₃	semidirect
470. C₂²⋊Q₈	C₂×D₁₁₃	semidirect
493. #121	C₂×D₁₁₃	semidirect
494. #121	C₂×D₁₁₃	semidirect
502. #120	C₂×D₁₁₃	semidirect
513. C₄×D₄	C₂×D₁₁₃	semidirect
514. C₄×D₄	C₂×D₁₁₃	semidirect
522. C₂×C₂²⋊C₄	C₂×D₁₁₃	semidirect
705. D₄	D₄×D₁₁₃	semidirect

Maximal subgroups

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

subgroup	index
C₂×#16813668	2
C₂×#16813667	2
#20299250	2
#20299247	2
#20299246	2
#20299244	2
#20299243	2
#20299241	2
#20299238	2
#20299237	2
#20299232	2
D₄×C₂²⋊D₁₁₃	2
#20299230	2
#20299178	2
#20299177	2
#20299159	2
#20299158	2
#20299147	2
#20299145	2
C₂×#16813595	2
#121×D₁₁₃	2
C₄×D₄×D₁₁₃	2
#546×C₁₁₃	2
#3496	113