Subgroups — #28404600

Order 14464.

1252 conjugacy classes of subgroups.

The subgroup lattice has 736 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20299312	C₂	1	1	yes	maximal, characteristic, complemented
2	#20299303	C₂	1	1	yes	maximal, characteristic, complemented
3	#20299296	C₂	1	1	yes	maximal, characteristic, complemented
4	#20299295	C₂	1	1	yes	maximal, characteristic, complemented
5	#20299291	C₂	1	2	yes	maximal, complemented
6	#20299266	C₂	1	1	yes	maximal, characteristic, complemented
7	#20299245	C₂	1	1	yes	maximal, characteristic, complemented
8	#20299242	C₂	1	2	yes	maximal, complemented
9	#20299242	C₂	1	1	yes	maximal, characteristic, complemented
10	#20299237	C₂	1	2	yes	maximal, complemented
11	D₄×C₂²⋊D₁₁₃	C₂	1	1	yes	maximal, characteristic, complemented
12	D₄×C₂²⋊D₁₁₃	C₂	1	2	yes	maximal, complemented
13	#20299198	C₂	1	2	yes	maximal, complemented
14	#20299186	C₂	1	2	yes	maximal, complemented
15	#20299180	C₂	1	2	yes	maximal, complemented
16	#20299143	C₂	1	1	yes	maximal, characteristic, complemented
17	#20299129	C₂	1	1	yes	maximal, characteristic, complemented
18	#20299109	C₂	1	1	yes	maximal, characteristic, complemented
19	#20299108	C₂	1	1	yes	maximal, characteristic, complemented
20	#121×D₁₁₃	C₂	1	1	yes	maximal, characteristic, complemented
21	#20299071	C₂	1	2	yes	maximal, complemented
22	C₂×C₄×C₂²⋊D₁₁₃	C₂	1	1	yes	maximal, characteristic, complemented
23	C₂×#121×C₁₁₃	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#14268647	C₂²	1	1	yes	characteristic, complemented
25	C₂×#14268646	C₂²	1	1	yes	characteristic, complemented
26	C₂×#14268646	C₂²	1	2	yes	complemented
27	C₂²×C₂²⋊D₁₁₃	C₂²	1	1	yes	characteristic
28	C₂²×C₂²⋊D₁₁₃	C₂²	1	2	yes	—
29	C₂×D₄×D₁₁₃	C₂²	1	2	yes	complemented
30	C₂×D₄×D₁₁₃	C₂²	1	1	yes	characteristic, complemented
31	C₂²×C₄×D₁₁₃	C₂²	1	1	yes	characteristic, complemented
32	#16813621	C₂²	1	1	yes	characteristic, complemented
33	#16813618	C₂²	1	1	yes	characteristic, complemented
34	#16813618	C₂²	1	2	yes	complemented
35	#16813617	C₂²	1	2	yes	complemented
36	#16813615	C₂²	1	2	yes	complemented
37	#16813615	C₂²	1	2	yes	complemented
38	#16813613	C₂²	1	1	yes	characteristic, complemented
39	#16813612	C₂²	1	2	yes	complemented
40	#16813609	C₂²	1	2	yes	complemented
41	#16813609	C₂²	1	1	yes	characteristic, complemented
42	#16813608	C₂²	1	2	yes	complemented
43	#16813608	C₂²	1	2	yes	complemented
44	#16813607	C₂²	1	2	yes	complemented
45	#16813605	C₂²	1	2	yes	complemented
46	#16813604	C₂²	1	2	yes	complemented
47	#16813604	C₂²	1	2	yes	complemented
48	#16813603	C₂²	1	2	yes	complemented
49	#16813603	C₂²	1	2	yes	complemented
50	#16813603	C₂²	1	2	yes	complemented
51	#16813602	C₂²	1	1	yes	characteristic, complemented
52	#16813601	C₂²	1	1	yes	characteristic, complemented
53	#16813601	C₂²	1	2	yes	complemented
54	#16813601	C₂²	1	1	yes	characteristic, complemented
55	#16813600	C₂²	1	2	yes	complemented
56	#16813597	C₂²	1	1	yes	characteristic, complemented
57	#16813596	C₂²	1	1	yes	characteristic, complemented
58	#16813596	C₂²	1	2	yes	complemented
59	#16813596	C₂²	1	1	yes	characteristic, complemented
60	#16813595	C₂²	1	2	yes	complemented
61	#16813595	C₂²	1	2	yes	complemented
62	#16813594	C₂²	1	2	yes	complemented
63	#16813594	C₂²	1	2	yes	complemented
64	#16813594	C₂²	1	2	yes	complemented
65	#16813594	C₂²	1	2	yes	complemented
66	#16813594	C₂²	1	2	yes	complemented
67	#16813594	C₂²	1	2	yes	complemented
68	#16813593	C₂²	1	1	yes	characteristic, complemented
69	#16813593	C₂²	1	2	yes	complemented
70	#16813593	C₂²	1	1	yes	characteristic, complemented
71	#16813593	C₂²	1	2	yes	complemented
72	#16813591	C₂²	1	2	yes	complemented
73	#16813591	C₂²	1	2	yes	complemented
74	#16813591	C₂²	1	2	yes	complemented
75	#16813590	C₂²	1	2	yes	complemented
76	#16813590	C₂²	1	2	yes	complemented
77	#16813590	C₂²	1	2	yes	complemented
78	#16813587	C₂²	1	1	yes	characteristic, complemented
79	D₄×Dic₁₁₃	C₂²	1	2	yes	complemented
80	D₄×Dic₁₁₃	C₂²	1	2	yes	complemented
81	D₄×Dic₁₁₃	C₂²	1	1	yes	characteristic, complemented
82	D₄×Dic₁₁₃	C₂²	1	1	yes	characteristic, complemented
83	#16813584	C₂²	1	1	yes	characteristic, complemented
84	C₄×C₂²⋊D₁₁₃	C₂²	1	1	yes	characteristic
85	C₄×C₂²⋊D₁₁₃	C₂²	1	2	yes	—
86	C₄×C₂²⋊D₁₁₃	C₂²	1	1	yes	characteristic
87	C₄×C₂²⋊D₁₁₃	C₂²	1	1	yes	characteristic, complemented
88	C₄×C₂²⋊D₁₁₃	C₂²	1	2	yes	complemented
89	C₄×C₂²⋊D₁₁₃	C₂²	1	1	yes	characteristic, complemented
90	C₄×C₂²⋊D₁₁₃	C₂²	1	1	yes	characteristic, complemented
91	C₄×C₂²⋊D₁₁₃	C₂²	1	2	yes	complemented
92	C₄×C₂²⋊D₁₁₃	C₂²	1	1	yes	characteristic, complemented
93	C₄×C₂²⋊D₁₁₃	C₂²	1	1	yes	characteristic, complemented
94	C₄×C₂²⋊D₁₁₃	C₂²	1	1	yes	characteristic, complemented
95	C₄×C₂²⋊D₁₁₃	C₂²	1	2	yes	complemented
96	#16813582	C₂²	1	2	yes	complemented
97	#16813582	C₂²	1	2	yes	complemented
98	#16813582	C₂²	1	2	yes	complemented
99	#16813582	C₂²	1	2	yes	complemented
100	#16813581	C₂²	1	1	yes	characteristic, complemented
101	#16813580	C₂²	1	1	yes	characteristic, complemented
102	#16813578	C₂²	1	2	yes	complemented
103	#16813578	C₂²	1	2	yes	complemented
104	C₂×#14268626	C₂²	1	1	yes	characteristic, complemented
105	C₄⋊C₄×D₁₁₃	C₂²	1	1	yes	characteristic, complemented
106	C₂×C₂²⋊Dic₁₁₃	C₂²	1	1	yes	characteristic, complemented
107	C₂×C₂²⋊Dic₁₁₃	C₂²	1	2	yes	complemented
108	C₂×#14268624	C₂²	1	1	yes	characteristic, complemented
109	C₂²⋊C₄×D₁₁₃	C₂²	1	2	yes	complemented
110	C₂²⋊C₄×D₁₁₃	C₂²	1	2	yes	complemented
111	C₂×C₄×Dic₁₁₃	C₂²	1	1	yes	characteristic, complemented
112	C₂²×D₄×C₁₁₃	C₂²	1	1	yes	characteristic, complemented
113	C₂²×D₄×C₁₁₃	C₂²	1	2	yes	complemented
114	C₂³×C₄×C₁₁₃	C₂²	1	1	yes	characteristic, complemented
115	#121×C₁₁₃	C₂²	1	1	yes	characteristic
116	#121×C₁₁₃	C₂²	1	1	yes	characteristic, complemented
117	#121×C₁₁₃	C₂²	1	2	yes	complemented
118	#121×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	C₂×C₄⋊C₄×C₁₁₃	C₂²	1	1	yes	characteristic, complemented
122	C₂×C₂²⋊C₄×C₁₁₃	C₂²	1	2	yes	complemented
123	C₂³×D₁₁₃	C₂³	1	1	yes	characteristic
124	C₂³×D₁₁₃	C₂³	1	2	yes	—
125	#14268647	—	4	2	no	—
126	#14268646	—	4	2	no	—
127	#14268646	—	4	4	no	—
128	C₂×Dic₂₂₆	C₂³	1	1	yes	characteristic
129	C₂×Dic₂₂₆	C₂³	1	2	yes	—
130	C₂×D₄₅₂	C₂³	1	1	yes	characteristic
131	C₂×D₄₅₂	C₂³	1	2	yes	—
132	C₂×C₂²⋊D₁₁₃	—	2	4	no	—
133	C₂×C₂²⋊D₁₁₃	—	2	8	no	—
134	C₂×C₂²⋊D₁₁₃	C₂³	1	2	yes	—
135	C₂×C₂²⋊D₁₁₃	C₂³	1	2	yes	—
136	C₂×C₂²⋊D₁₁₃	C₂³	1	1	yes	characteristic
137	C₂×C₂²⋊D₁₁₃	C₂³	1	1	yes	characteristic
138	C₂×C₂²⋊D₁₁₃	C₂³	1	2	yes	—
139	C₂×C₂²⋊D₁₁₃	C₂³	1	1	yes	characteristic
140	C₂×C₂²⋊D₁₁₃	C₂³	1	2	yes	—
141	C₂×C₂²⋊D₁₁₃	C₂³	1	2	yes	—
142	C₂×C₂²⋊D₁₁₃	C₂³	1	2	yes	—
143	C₂×C₂²⋊D₁₁₃	C₂³	1	2	yes	—
144	C₂×C₂²⋊D₁₁₃	C₂³	1	2	yes	—
145	C₂×C₂²⋊D₁₁₃	C₂³	1	2	yes	—
146	C₂×C₂²⋊D₁₁₃	C₂³	1	1	yes	characteristic
147	D₄×D₁₁₃	—	4	2	no	—
148	D₄×D₁₁₃	—	4	4	no	—
149	C₂²×Dic₁₁₃	C₂³	1	1	yes	characteristic
150	C₂²×Dic₁₁₃	C₂³	1	1	yes	characteristic
151	C₂²×Dic₁₁₃	C₂³	1	2	yes	—
152	C₂²×Dic₁₁₃	C₂³	1	1	yes	characteristic
153	C₂²×Dic₁₁₃	C₂³	1	2	yes	—
154	C₂²×Dic₁₁₃	C₂³	1	2	yes	—
155	C₂×C₄×D₁₁₃	—	4	2	no	—
156	C₂×C₄×D₁₁₃	C₂³	1	1	yes	characteristic
157	C₂×C₄×D₁₁₃	C₂³	1	1	yes	characteristic
158	C₂×C₄×D₁₁₃	C₂³	1	1	yes	characteristic
159	C₂×C₄×D₁₁₃	C₂³	1	2	yes	—
160	C₂×C₄×D₁₁₃	C₂³	1	2	yes	—
161	C₂×C₄×D₁₁₃	C₂³	1	2	yes	—
162	C₂×C₄×D₁₁₃	C₂³	1	1	yes	characteristic
163	C₄⋊Dic₁₁₃	C₂³	1	1	yes	characteristic
164	C₄⋊Dic₁₁₃	C₂³	1	1	yes	characteristic
165	C₄⋊Dic₁₁₃	C₂³	1	2	yes	—
166	C₄⋊Dic₁₁₃	C₂³	1	2	yes	—
167	#14268626	C₂³	1	2	yes	—
168	#14268626	C₂³	1	1	yes	characteristic
169	#14268626	C₂³	1	1	yes	characteristic
170	#14268626	C₂³	1	1	yes	characteristic
171	#14268626	C₂³	1	1	yes	characteristic
172	#14268626	C₂³	1	2	yes	—
173	#14268626	C₂³	1	2	yes	—
174	#14268626	C₂³	1	2	yes	—
175	#14268626	C₂³	1	2	yes	—
176	#14268626	C₂³	1	2	yes	—
177	C₂²⋊Dic₁₁₃	C₂³	1	2	yes	—
178	C₂²⋊Dic₁₁₃	C₂³	1	2	yes	—
179	C₂²⋊Dic₁₁₃	C₂³	1	1	yes	characteristic
180	C₂²⋊Dic₁₁₃	C₂³	1	1	yes	characteristic
181	C₂²⋊Dic₁₁₃	C₂³	1	2	yes	—
182	C₂²⋊Dic₁₁₃	C₂³	1	1	yes	characteristic
183	C₂²⋊Dic₁₁₃	C₂³	1	1	yes	characteristic
184	C₂²⋊Dic₁₁₃	C₂³	1	2	yes	—
185	C₂²⋊Dic₁₁₃	C₂³	1	2	yes	—
186	C₂²⋊Dic₁₁₃	C₂³	1	2	yes	—
187	C₂²⋊Dic₁₁₃	C₂³	1	2	yes	—
188	C₂²⋊Dic₁₁₃	C₂³	1	2	yes	—
189	C₂²⋊Dic₁₁₃	C₂³	1	2	yes	—
190	#14268624	C₂³	1	1	yes	characteristic
191	#14268624	C₂³	1	2	yes	—
192	#14268624	C₂³	1	2	yes	—
193	#14268624	C₂³	1	2	yes	—
194	#14268624	C₂³	1	1	yes	characteristic
195	#14268624	C₂³	1	1	yes	characteristic
196	#14268624	C₂³	1	1	yes	characteristic
197	#14268624	C₂³	1	2	yes	—
198	#14268624	C₂³	1	2	yes	—
199	#14268624	C₂³	1	2	yes	—
200	C₄×Dic₁₁₃	C₂³	1	1	yes	characteristic
201	C₄×Dic₁₁₃	C₂³	1	1	yes	characteristic
202	C₄×Dic₁₁₃	C₂³	1	1	yes	characteristic
203	C₄×Dic₁₁₃	C₂³	1	1	yes	characteristic
204	C₄×Dic₁₁₃	C₂³	1	2	yes	—
205	C₄×Dic₁₁₃	C₂³	1	2	yes	—
206	C₄×Dic₁₁₃	C₂³	1	2	yes	—
207	C₂⁴×C₁₁₃	C₂³	1	1	yes	characteristic
208	C₂⁴×C₁₁₃	C₂³	1	2	yes	—
209	C₂×D₄×C₁₁₃	—	4	2	no	—
210	C₂×D₄×C₁₁₃	—	4	4	no	—
211	C₂×D₄×C₁₁₃	C₂³	1	2	yes	—
212	C₂×D₄×C₁₁₃	C₂³	1	1	yes	characteristic
213	C₂×D₄×C₁₁₃	C₂³	1	1	yes	characteristic
214	C₂×D₄×C₁₁₃	C₂³	1	2	yes	—
215	C₂×D₄×C₁₁₃	C₂³	1	2	yes	—
216	C₂×D₄×C₁₁₃	C₂³	1	2	yes	—
217	C₂×D₄×C₁₁₃	C₂³	1	2	yes	—
218	C₂²×C₄×C₁₁₃	—	4	2	no	—
219	C₂²×C₄×C₁₁₃	C₂³	1	1	yes	characteristic
220	C₂²×C₄×C₁₁₃	C₂³	1	1	yes	characteristic
221	C₂²×C₄×C₁₁₃	C₂³	1	1	yes	characteristic
222	C₂²×C₄×C₁₁₃	C₂³	1	1	yes	characteristic
223	C₂²×C₄×C₁₁₃	C₂³	1	1	yes	characteristic
224	C₂²×C₄×C₁₁₃	C₂³	1	2	yes	—
225	C₂²×C₄×C₁₁₃	C₂³	1	1	yes	characteristic
226	C₄⋊C₄×C₁₁₃	C₂³	1	1	yes	characteristic
227	C₄⋊C₄×C₁₁₃	C₂³	1	1	yes	characteristic
228	C₄⋊C₄×C₁₁₃	C₂³	1	2	yes	—
229	C₂²⋊C₄×C₁₁₃	C₂³	1	2	yes	—
230	C₂²⋊C₄×C₁₁₃	C₂³	1	2	yes	—
231	C₂²⋊C₄×C₁₁₃	C₂³	1	2	yes	—
232	C₂²⋊C₄×C₁₁₃	C₂³	1	2	yes	—
233	C₂³×C₁₁₃	—	2	2	no	—
234	C₂³×C₁₁₃	—	2	2	no	—
235	C₂³×C₁₁₃	—	2	4	no	—
236	C₂³×C₁₁₃	—	4	1	no	—
237	C₂³×C₁₁₃	—	4	2	no	—
238	C₂³×C₁₁₃	—	4	2	no	—
239	C₂³×C₁₁₃	C₂⁴	1	2	yes	—
240	C₂³×C₁₁₃	C₂⁴	1	2	yes	—
241	C₂³×C₁₁₃	C₂⁴	1	1	yes	characteristic
242	C₂³×C₁₁₃	C₂⁴	1	1	yes	characteristic
243	C₂³×C₁₁₃	C₂⁴	1	1	yes	characteristic
244	C₂²×D₁₁₃	—	2	2	no	—
245	C₂²×D₁₁₃	—	2	2	no	—
246	C₂²×D₁₁₃	—	2	4	no	—
247	C₂²×D₁₁₃	—	4	1	no	—
248	C₂²×D₁₁₃	—	4	2	no	—
249	C₂²×D₁₁₃	—	4	2	no	—
250	C₂²×D₁₁₃	C₂⁴	1	1	yes	characteristic
251	C₂²×D₁₁₃	C₂⁴	1	2	yes	—
252	C₂²×D₁₁₃	C₂⁴	1	1	yes	characteristic
253	D₄×C₁₁₃	—	2	4	no	—
254	D₄×C₁₁₃	—	2	4	no	—
255	D₄×C₁₁₃	—	2	2	no	—
256	D₄×C₁₁₃	—	2	2	no	—
257	D₄×C₁₁₃	—	4	2	no	—
258	D₄×C₁₁₃	—	4	2	no	—
259	D₄×C₁₁₃	—	4	2	no	—
260	C₂×C₄×C₁₁₃	—	2	2	no	—
261	C₂×C₄×C₁₁₃	—	2	2	no	—
262	C₂×C₄×C₁₁₃	—	2	2	no	—
263	C₂×C₄×C₁₁₃	—	4	1	no	—
264	C₂×C₄×C₁₁₃	—	4	1	no	—
265	C₂×C₄×C₁₁₃	—	4	1	no	—
266	C₂×C₄×C₁₁₃	—	4	2	no	—
267	C₂×C₄×C₁₁₃	C₂⁴	1	1	yes	characteristic
268	C₂×C₄×C₁₁₃	C₂⁴	1	1	yes	characteristic
269	C₂×C₄×C₁₁₃	C₂⁴	1	2	yes	—
270	C₂×C₄×C₁₁₃	C₂⁴	1	2	yes	—
271	C₂×C₄×C₁₁₃	C₂⁴	1	1	yes	characteristic
272	C₂×C₄×C₁₁₃	C₂⁴	1	1	yes	characteristic
273	C₂²⋊D₁₁₃	—	2	2	no	—
274	C₂²⋊D₁₁₃	—	2	4	no	—
275	C₂²⋊D₁₁₃	—	2	4	no	—
276	C₂²⋊D₁₁₃	—	2	4	no	—
277	C₂²⋊D₁₁₃	—	2	2	no	—
278	C₂²⋊D₁₁₃	—	2	4	no	—
279	C₂²⋊D₁₁₃	—	2	2	no	—
280	C₂²⋊D₁₁₃	—	4	2	no	—
281	C₂²⋊D₁₁₃	—	4	2	no	—
282	C₂²⋊D₁₁₃	—	4	2	no	—
283	C₂²⋊D₁₁₃	—	4	2	no	—
284	C₂²⋊D₁₁₃	—	4	2	no	—
285	C₂²⋊D₁₁₃	#41	1	4	yes	complemented
286	C₂×Dic₁₁₃	—	2	2	no	—
287	C₂×Dic₁₁₃	—	2	2	no	—
288	C₂×Dic₁₁₃	—	2	4	no	—
289	C₂×Dic₁₁₃	—	4	1	no	—
290	C₂×Dic₁₁₃	—	4	2	no	—
291	C₂×Dic₁₁₃	—	4	2	no	—
292	C₂×Dic₁₁₃	C₂⁴	1	1	yes	characteristic
293	C₂×Dic₁₁₃	C₂⁴	1	2	yes	—
294	C₂×Dic₁₁₃	C₂⁴	1	1	yes	characteristic
295	C₂×Dic₁₁₃	C₂⁴	1	1	yes	characteristic
296	C₂×Dic₁₁₃	C₂⁴	1	1	yes	characteristic
297	C₂×Dic₁₁₃	C₂⁴	1	2	yes	—
298	C₂×Dic₁₁₃	C₂⁴	1	2	yes	—
299	C₂×Dic₁₁₃	C₂⁴	1	1	yes	characteristic
300	C₂×Dic₁₁₃	C₂⁴	1	1	yes	characteristic
301	D₄₅₂	—	2	2	no	—
302	D₄₅₂	—	4	2	no	—
303	C₄×D₁₁₃	—	2	2	no	—
304	C₄×D₁₁₃	—	2	2	no	—
305	C₄×D₁₁₃	—	4	1	no	—
306	C₄×D₁₁₃	—	4	1	no	—
307	C₄×D₁₁₃	—	4	2	no	—
308	C₄×D₁₁₃	—	4	2	no	—
309	C₄×D₁₁₃	—	4	2	no	—
310	Dic₂₂₆	—	2	2	no	—
311	Dic₂₂₆	—	4	2	no	—
312	C₂²×C₁₁₃	—	2	1	no	—
313	C₂²×C₁₁₃	—	2	1	no	—
314	C₂²×C₁₁₃	—	2	1	no	—
315	C₂²×C₁₁₃	—	2	1	no	—
316	C₂²×C₁₁₃	—	2	2	no	—
317	C₂²×C₁₁₃	—	2	1	no	—
318	C₂²×C₁₁₃	—	2	2	no	—
319	C₂²×C₁₁₃	—	2	2	no	—
320	C₂²×C₁₁₃	—	2	2	no	—
321	C₂²×C₁₁₃	—	2	1	no	—
322	C₂²×C₁₁₃	—	2	2	no	—
323	C₂²×C₁₁₃	—	2	2	no	—
324	C₂²×C₁₁₃	—	2	1	no	—
325	C₂²×C₁₁₃	—	4	4	no	—
326	C₂²×C₁₁₃	—	8	4	no	—
327	C₂²×C₁₁₃	C₂×#41	1	2	yes	—
328	C₂²×C₁₁₃	H(5,𝔽₂)	1	2	yes	—
329	C₂²×C₁₁₃	C₂⁵	1	1	yes	characteristic
330	C₂×D₁₁₃	—	2	1	no	—
331	C₂×D₁₁₃	—	2	1	no	—
332	C₂×D₁₁₃	—	2	1	no	—
333	C₂×D₁₁₃	—	2	2	no	—
334	C₂×D₁₁₃	—	2	1	no	—
335	C₂×D₁₁₃	—	2	2	no	—
336	C₂×D₁₁₃	—	2	2	no	—
337	C₂×D₁₁₃	—	2	1	no	—
338	C₂×D₁₁₃	—	4	4	no	—
339	C₂×D₁₁₃	—	8	4	no	—
340	C₂×D₁₁₃	C₂×#41	1	2	yes	—
341	C₄×C₁₁₃	—	2	2	no	—
342	C₄×C₁₁₃	—	2	1	no	—
343	C₄×C₁₁₃	—	2	1	no	—
344	C₄×C₁₁₃	—	2	2	no	—
345	C₄×C₁₁₃	—	2	1	no	—
346	C₄×C₁₁₃	H(5,𝔽₂)	1	2	yes	—
347	Dic₁₁₃	—	2	1	no	—
348	Dic₁₁₃	—	2	2	no	—
349	Dic₁₁₃	—	2	2	no	—
350	Dic₁₁₃	—	2	1	no	—
351	Dic₁₁₃	—	2	2	no	—
352	Dic₁₁₃	—	2	1	no	—
353	Dic₁₁₃	—	2	1	no	—
354	Dic₁₁₃	—	2	1	no	—
355	Dic₁₁₃	C₂×#41	1	2	yes	—
356	C₂×C₁₁₃	—	2	2	no	—
357	C₂×C₁₁₃	—	2	2	no	—
358	C₂×C₁₁₃	—	4	2	no	—
359	C₂×C₁₁₃	—	4	1	no	—
360	C₂×C₁₁₃	—	4	2	no	—
361	C₂×C₁₁₃	C₂²×#41	1	1	yes	characteristic
362	C₂×C₁₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
363	C₂×C₁₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
364	D₁₁₃	—	2	2	no	—
365	D₁₁₃	—	4	1	no	—
366	D₁₁₃	—	4	2	no	—
367	#3519	—	113	1	no	maximal, Sylow
368	C₁₁₃	#3519	1	1	yes	characteristic, complemented, Sylow
369	#555	—	113	1	no	—
370	#554	—	113	1	no	—
371	#553	—	113	2	no	—
372	#553	—	113	1	no	—
373	#553	—	113	1	no	—
374	#550	—	113	1	no	—
375	#546	—	113	2	no	—
376	#546	—	113	1	no	—
377	#546	—	113	2	no	—
378	#546	—	113	1	no	—
379	D₄²	—	113	2	no	—
380	D₄²	—	113	1	no	—
381	#540	—	113	2	no	—
382	#538	—	113	2	no	—
383	#538	—	113	2	no	—
384	#532	—	113	1	no	—
385	#529	—	113	1	no	—
386	#525	—	113	1	no	—
387	#525	—	113	1	no	—
388	C₂×#121	—	113	1	no	—
389	C₂×#121	D₁₁₃	1	1	yes	characteristic, complemented
390	#518	—	113	2	no	—
391	C₂×C₄×D₄	—	113	1	no	—
392	C₂×#41	—	113	1	no	—
393	C₂×#41	—	113	2	no	—
394	C₂×#41	—	113	1	no	—
395	C₂²×D₄	—	113	1	no	—
396	C₂²×D₄	—	113	2	no	—
397	C₂²×D₄	—	113	2	no	—
398	C₂²×D₄	—	113	1	no	—
399	C₂²×D₄	C₂×D₁₁₃	1	1	yes	characteristic, complemented
400	C₂²×D₄	C₂×D₁₁₃	1	2	yes	complemented
401	C₂³×C₄	—	113	1	no	—
402	C₂³×C₄	C₂×D₁₁₃	1	1	yes	characteristic, complemented
403	C₄⋊Q₈	—	113	1	no	—
404	#127	—	113	1	no	—
405	#127	—	113	2	no	—
406	#126	—	113	2	no	—
407	#126	—	113	2	no	—
408	#126	—	113	2	no	—
409	#125	—	113	1	no	—
410	#125	—	113	2	no	—
411	#124	—	113	1	no	—
412	#124	—	113	2	no	—
413	#124	—	113	2	no	—
414	#124	—	113	2	no	—
415	#123	—	113	2	no	—
416	#123	—	113	2	no	—
417	#123	—	113	2	no	—
418	#123	—	113	2	no	—
419	#123	—	113	2	no	—
420	#123	—	113	2	no	—
421	#123	—	113	2	no	—
422	C₂²⋊Q₈	—	113	1	no	—
423	C₂²⋊Q₈	—	113	1	no	—
424	C₂²⋊Q₈	—	113	2	no	—
425	C₂²⋊Q₈	—	113	1	no	—
426	C₂²⋊Q₈	—	113	2	no	—
427	#121	—	113	1	no	—
428	#121	—	113	2	no	—
429	#121	—	113	1	no	—
430	#121	—	113	2	no	—
431	#121	—	113	2	no	—
432	#121	—	113	2	no	—
433	#121	—	113	2	no	—
434	#121	—	113	2	no	—
435	#121	—	113	2	no	—
436	#121	—	113	2	no	—
437	#121	—	113	1	no	—
438	#121	—	113	1	no	—
439	#121	—	113	2	no	—
440	#121	—	113	1	no	—
441	#121	—	113	2	no	—
442	#121	—	113	2	no	—
443	#121	C₂×D₁₁₃	1	1	yes	characteristic
444	#121	C₂×D₁₁₃	1	1	yes	characteristic, complemented
445	#121	C₂×D₁₁₃	1	2	yes	complemented
446	#121	C₂×D₁₁₃	1	2	yes	complemented
447	#121	C₂×D₁₁₃	1	1	yes	characteristic, complemented
448	#121	C₂×D₁₁₃	1	1	yes	characteristic, complemented
449	#120	—	113	2	no	—
450	#120	—	113	2	no	—
451	#120	—	113	2	no	—
452	#120	—	113	2	no	—
453	#120	—	113	2	no	—
454	#120	—	113	2	no	—
455	C₄×Q₈	—	113	1	no	—
456	C₄×D₄	—	113	2	no	—
457	C₄×D₄	—	113	2	no	—
458	C₄×D₄	—	113	1	no	—
459	C₄×D₄	—	113	1	no	—
460	C₄×D₄	—	113	1	no	—
461	C₄×D₄	—	113	1	no	—
462	C₄×D₄	—	113	1	no	—
463	C₄×D₄	—	113	1	no	—
464	C₄×D₄	—	113	1	no	—
465	C₄×D₄	—	113	1	no	—
466	C₄×D₄	—	113	1	no	—
467	C₄×D₄	—	113	1	no	—
468	C₄×D₄	—	113	2	no	—
469	C₄×D₄	—	113	2	no	—
470	C₄×D₄	—	113	2	no	—
471	C₄×D₄	—	113	2	no	—
472	C₄×D₄	—	113	1	no	—
473	C₄×D₄	—	113	2	no	—
474	C₄×D₄	—	113	2	no	—
475	C₄×D₄	—	113	2	no	—
476	C₄×D₄	—	113	2	no	—
477	#117	—	113	1	no	—
478	#117	—	113	1	no	—
479	#117	—	113	2	no	—
480	#117	—	113	2	no	—
481	C₂×C₄⋊C₄	—	113	1	no	—
482	C₂×C₄⋊C₄	—	113	1	no	—
483	C₂×C₄⋊C₄	C₂×D₁₁₃	1	1	yes	characteristic, complemented
484	C₂×C₂²⋊C₄	—	113	1	no	—
485	C₂×C₂²⋊C₄	—	113	2	no	—
486	C₂×C₂²⋊C₄	—	113	1	no	—
487	C₂×C₂²⋊C₄	—	113	2	no	—
488	C₂×C₂²⋊C₄	—	113	2	no	—
489	C₂×C₂²⋊C₄	C₂×D₁₁₃	1	2	yes	complemented
490	C₂×C₄²	—	113	1	no	—
491	C₂⁴	—	113	2	no	—
492	C₂⁴	—	113	1	no	—
493	C₂⁴	C₂²×D₁₁₃	1	1	yes	characteristic
494	C₂⁴	C₂²×D₁₁₃	1	2	yes	—
495	#41	—	452	2	no	—
496	#41	—	452	2	no	—
497	#41	—	452	4	no	—
498	C₂×Q₈	—	113	2	no	—
499	C₂×Q₈	—	113	1	no	—
500	C₂×D₄	—	4	2	no	—
501	C₂×D₄	—	4	4	no	—
502	C₂×D₄	—	113	1	no	—
503	C₂×D₄	—	113	2	no	—
504	C₂×D₄	—	113	2	no	—
505	C₂×D₄	—	113	2	no	—
506	C₂×D₄	—	113	2	no	—
507	C₂×D₄	—	113	2	no	—
508	C₂×D₄	—	113	1	no	—
509	C₂×D₄	—	113	2	no	—
510	C₂×D₄	—	113	1	no	—
511	C₂×D₄	—	113	2	no	—
512	C₂×D₄	—	113	1	no	—
513	C₂×D₄	—	113	2	no	—
514	C₂×D₄	—	113	2	no	—
515	C₂×D₄	—	113	2	no	—
516	C₂×D₄	—	113	1	no	—
517	C₂×D₄	—	452	4	no	—
518	C₂×D₄	—	452	2	no	—
519	C₂×D₄	—	226	4	no	—
520	C₂×D₄	—	226	8	no	—
521	C₂×D₄	C₂²×D₁₁₃	1	2	yes	—
522	C₂×D₄	C₂²×D₁₁₃	1	2	yes	—
523	C₂×D₄	C₂²×D₁₁₃	1	1	yes	characteristic
524	C₂×D₄	C₂²×D₁₁₃	1	1	yes	characteristic
525	C₂×D₄	C₂²×D₁₁₃	1	2	yes	—
526	C₂×D₄	C₂²×D₁₁₃	1	2	yes	—
527	C₂×D₄	C₂²×D₁₁₃	1	2	yes	—
528	C₂²×C₄	—	4	2	no	—
529	C₂²×C₄	—	113	1	no	—
530	C₂²×C₄	—	113	2	no	—
531	C₂²×C₄	—	113	2	no	—
532	C₂²×C₄	—	113	1	no	—
533	C₂²×C₄	—	113	1	no	—
534	C₂²×C₄	—	113	2	no	—
535	C₂²×C₄	—	113	1	no	—
536	C₂²×C₄	—	113	2	no	—
537	C₂²×C₄	—	113	2	no	—
538	C₂²×C₄	—	113	2	no	—
539	C₂²×C₄	—	113	1	no	—
540	C₂²×C₄	—	113	1	no	—
541	C₂²×C₄	—	113	1	no	—
542	C₂²×C₄	—	452	2	no	—
543	C₂²×C₄	C₂²×D₁₁₃	1	1	yes	characteristic
544	C₂²×C₄	C₂²×D₁₁₃	1	1	yes	characteristic
545	C₂²×C₄	C₂²×D₁₁₃	1	1	yes	characteristic
546	C₂²×C₄	C₂²×D₁₁₃	1	1	yes	characteristic
547	C₂²×C₄	C₂²×D₁₁₃	1	1	yes	characteristic
548	C₂²×C₄	C₂²×D₁₁₃	1	2	yes	—
549	C₂²×C₄	C₂²×D₁₁₃	1	1	yes	characteristic
550	C₄⋊C₄	—	113	1	no	—
551	C₄⋊C₄	—	113	1	no	—
552	C₄⋊C₄	—	113	1	no	—
553	C₄⋊C₄	—	113	1	no	—
554	C₄⋊C₄	—	113	1	no	—
555	C₄⋊C₄	—	113	2	no	—
556	C₄⋊C₄	—	113	1	no	—
557	C₄⋊C₄	—	113	2	no	—
558	C₄⋊C₄	—	113	2	no	—
559	C₄⋊C₄	—	113	2	no	—
560	C₄⋊C₄	—	113	2	no	—
561	C₄⋊C₄	—	113	2	no	—
562	C₄⋊C₄	—	113	2	no	—
563	C₄⋊C₄	—	113	2	no	—
564	C₄⋊C₄	C₂²×D₁₁₃	1	1	yes	characteristic
565	C₄⋊C₄	C₂²×D₁₁₃	1	1	yes	characteristic
566	C₄⋊C₄	C₂²×D₁₁₃	1	2	yes	—
567	C₂²⋊C₄	—	113	1	no	—
568	C₂²⋊C₄	—	113	2	no	—
569	C₂²⋊C₄	—	113	2	no	—
570	C₂²⋊C₄	—	113	1	no	—
571	C₂²⋊C₄	—	113	2	no	—
572	C₂²⋊C₄	—	113	1	no	—
573	C₂²⋊C₄	—	113	1	no	—
574	C₂²⋊C₄	—	113	2	no	—
575	C₂²⋊C₄	—	113	2	no	—
576	C₂²⋊C₄	—	113	2	no	—
577	C₂²⋊C₄	—	113	2	no	—
578	C₂²⋊C₄	—	113	2	no	—
579	C₂²⋊C₄	—	113	2	no	—
580	C₂²⋊C₄	—	113	1	no	—
581	C₂²⋊C₄	—	113	1	no	—
582	C₂²⋊C₄	—	113	2	no	—
583	C₂²⋊C₄	—	113	2	no	—
584	C₂²⋊C₄	—	113	1	no	—
585	C₂²⋊C₄	—	113	2	no	—
586	C₂²⋊C₄	—	113	1	no	—
587	C₂²⋊C₄	—	113	2	no	—
588	C₂²⋊C₄	—	113	2	no	—
589	C₂²⋊C₄	—	113	2	no	—
590	C₂²⋊C₄	C₂²×D₁₁₃	1	2	yes	—
591	C₂²⋊C₄	C₂²×D₁₁₃	1	2	yes	—
592	C₂²⋊C₄	C₂²×D₁₁₃	1	2	yes	—
593	C₂²⋊C₄	C₂²×D₁₁₃	1	2	yes	—
594	C₄²	—	113	1	no	—
595	C₄²	—	113	1	no	—
596	C₄²	—	113	1	no	—
597	C₄²	—	113	1	no	—
598	C₄²	—	113	2	no	—
599	C₄²	—	113	2	no	—
600	C₄²	—	113	2	no	—
601	C₂³	—	2	2	no	—
602	C₂³	—	2	2	no	—
603	C₂³	—	2	4	no	—
604	C₂³	—	4	1	no	—
605	C₂³	—	4	2	no	—
606	C₂³	—	4	2	no	—
607	C₂³	—	113	1	no	—
608	C₂³	—	113	1	no	—
609	C₂³	—	113	2	no	—
610	C₂³	—	452	2	no	—
611	C₂³	—	452	2	no	—
612	C₂³	—	452	1	no	—
613	C₂³	—	226	4	no	—
614	C₂³	—	226	2	no	—
615	C₂³	—	226	2	no	—
616	C₂³	C₂³×D₁₁₃	1	2	yes	—
617	C₂³	C₂³×D₁₁₃	1	1	yes	characteristic
618	C₂³	C₂³×D₁₁₃	1	2	yes	—
619	C₂³	C₂³×D₁₁₃	1	1	yes	characteristic
620	C₂³	C₂³×D₁₁₃	1	1	yes	characteristic
621	Q₈	—	452	2	no	—
622	Q₈	—	226	2	no	—
623	D₄	—	2	4	no	—
624	D₄	—	2	4	no	—
625	D₄	—	2	2	no	—
626	D₄	—	2	2	no	—
627	D₄	—	4	2	no	—
628	D₄	—	4	2	no	—
629	D₄	—	4	2	no	—
630	D₄	—	113	4	no	—
631	D₄	—	452	2	no	—
632	D₄	—	452	2	no	—
633	D₄	—	452	2	no	—
634	D₄	—	452	2	no	—
635	D₄	—	452	2	no	—
636	D₄	—	452	2	no	—
637	D₄	—	226	2	no	—
638	D₄	—	226	4	no	—
639	D₄	—	226	2	no	—
640	D₄	—	226	4	no	—
641	D₄	—	226	4	no	—
642	D₄	—	226	2	no	—
643	D₄	—	226	4	no	—
644	D₄	—	226	2	no	—
645	C₂×C₄	—	2	2	no	—
646	C₂×C₄	—	2	2	no	—
647	C₂×C₄	—	2	2	no	—
648	C₂×C₄	—	4	1	no	—
649	C₂×C₄	—	4	1	no	—
650	C₂×C₄	—	4	1	no	—
651	C₂×C₄	—	4	2	no	—
652	C₂×C₄	—	113	1	no	—
653	C₂×C₄	—	113	1	no	—
654	C₂×C₄	—	113	2	no	—
655	C₂×C₄	—	113	1	no	—
656	C₂×C₄	—	113	1	no	—
657	C₂×C₄	—	113	1	no	—
658	C₂×C₄	—	113	2	no	—
659	C₂×C₄	—	113	2	no	—
660	C₂×C₄	—	113	1	no	—
661	C₂×C₄	—	452	1	no	—
662	C₂×C₄	—	452	1	no	—
663	C₂×C₄	—	452	2	no	—
664	C₂×C₄	—	452	2	no	—
665	C₂×C₄	—	452	2	no	—
666	C₂×C₄	—	452	1	no	—
667	C₂×C₄	—	452	2	no	—
668	C₂×C₄	—	452	2	no	—
669	C₂×C₄	—	226	2	no	—
670	C₂×C₄	—	226	4	no	—
671	C₂×C₄	—	226	2	no	—
672	C₂×C₄	—	226	2	no	—
673	C₂×C₄	—	226	2	no	—
674	C₂×C₄	C₂³×D₁₁₃	1	1	yes	characteristic
675	C₂×C₄	C₂³×D₁₁₃	1	1	yes	characteristic
676	C₂×C₄	C₂³×D₁₁₃	1	2	yes	—
677	C₂×C₄	C₂³×D₁₁₃	1	2	yes	—
678	C₂×C₄	C₂³×D₁₁₃	1	1	yes	characteristic
679	C₂×C₄	C₂³×D₁₁₃	1	1	yes	characteristic
680	C₂²	—	2	1	no	—
681	C₂²	—	2	1	no	—
682	C₂²	—	2	1	no	—
683	C₂²	—	2	1	no	—
684	C₂²	—	2	2	no	—
685	C₂²	—	2	1	no	—
686	C₂²	—	2	2	no	—
687	C₂²	—	2	1	no	—
688	C₂²	—	2	2	no	—
689	C₂²	—	2	2	no	—
690	C₂²	—	2	2	no	—
691	C₂²	—	2	2	no	—
692	C₂²	—	2	1	no	—
693	C₂²	—	4	4	no	—
694	C₂²	—	8	4	no	—
695	C₂²	—	113	2	no	—
696	C₂²	—	904	4	no	—
697	C₂²	—	452	4	no	—
698	C₂²	—	226	2	no	—
699	C₂²	—	226	1	no	—
700	C₂²	—	226	1	no	—
701	C₂²	—	226	2	no	—
702	C₂²	—	226	2	no	—
703	C₂²	—	226	1	no	—
704	C₂²	—	226	1	no	—
705	C₂²	—	226	1	no	—
706	C₂²	#41×D₁₁₃	1	2	yes	—
707	C₂²	#16813667	1	2	yes	—
708	C₂²	C₂⁴×D₁₁₃	1	1	yes	characteristic
709	C₄	—	2	1	no	—
710	C₄	—	2	1	no	—
711	C₄	—	2	1	no	—
712	C₄	—	2	2	no	—
713	C₄	—	2	2	no	—
714	C₄	—	113	2	no	—
715	C₄	—	226	1	no	—
716	C₄	—	226	2	no	—
717	C₄	—	226	1	no	—
718	C₄	—	226	1	no	—
719	C₄	—	226	1	no	—
720	C₄	—	226	2	no	—
721	C₄	—	226	2	no	—
722	C₄	—	226	1	no	—
723	C₄	#16813667	1	2	yes	—
724	C₂	—	2	2	no	—
725	C₂	—	2	2	no	—
726	C₂	—	4	1	no	—
727	C₂	—	4	2	no	—
728	C₂	—	4	2	no	—
729	C₂	—	452	2	no	—
730	C₂	—	452	1	no	—
731	C₂	—	226	2	no	—
732	C₂	C₂×#41×D₁₁₃	1	1	yes	characteristic
733	C₂	C₂×#16813667	1	1	yes	characteristic
734	C₂	C₂×#16813667	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₁₁₃
commutator, socle, cosocle	C₂²×C₁₁₃	C₂⁵
Fitting	C₂×#121×C₁₁₃	C₂
hypercenter	C₂×#121	D₁₁₃
hypocenter	C₁₁₃	#3519
LCS	G ▷ C₂²×C₁₁₃ ▷ C₁₁₃
UCS	C₁ ◁ C₂² ◁ C₂×#121

Complements

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

N	H ≅ G/N	type
1. #20299312	C₂	semidirect
2. #20299303	C₂	semidirect
3. #20299296	C₂	semidirect
4. #20299295	C₂	semidirect
5. #20299291	C₂	semidirect
6. #20299266	C₂	semidirect
7. #20299245	C₂	semidirect
8. #20299242	C₂	semidirect
9. #20299242	C₂	semidirect
10. #20299237	C₂	semidirect
11. D₄×C₂²⋊D₁₁₃	C₂	semidirect
12. D₄×C₂²⋊D₁₁₃	C₂	semidirect
13. #20299198	C₂	semidirect
14. #20299186	C₂	semidirect
15. #20299180	C₂	semidirect
16. #20299143	C₂	semidirect
17. #20299129	C₂	semidirect
18. #20299109	C₂	semidirect
19. #20299108	C₂	semidirect
20. #121×D₁₁₃	C₂	semidirect
21. #20299071	C₂	semidirect
22. C₂×C₄×C₂²⋊D₁₁₃	C₂	semidirect
23. C₂×#121×C₁₁₃	C₂	semidirect
24. C₂×#14268647	C₂²	semidirect
25. C₂×#14268646	C₂²	semidirect
26. C₂×#14268646	C₂²	semidirect
29. C₂×D₄×D₁₁₃	C₂²	semidirect
30. C₂×D₄×D₁₁₃	C₂²	semidirect
31. C₂²×C₄×D₁₁₃	C₂²	semidirect
32. #16813621	C₂²	semidirect
33. #16813618	C₂²	semidirect
34. #16813618	C₂²	semidirect
35. #16813617	C₂²	semidirect
36. #16813615	C₂²	semidirect
37. #16813615	C₂²	semidirect
38. #16813613	C₂²	semidirect
39. #16813612	C₂²	semidirect
40. #16813609	C₂²	semidirect
41. #16813609	C₂²	semidirect
42. #16813608	C₂²	semidirect
43. #16813608	C₂²	semidirect
44. #16813607	C₂²	semidirect
45. #16813605	C₂²	semidirect
46. #16813604	C₂²	semidirect
47. #16813604	C₂²	semidirect
48. #16813603	C₂²	semidirect
49. #16813603	C₂²	semidirect
50. #16813603	C₂²	semidirect
51. #16813602	C₂²	semidirect
52. #16813601	C₂²	semidirect
53. #16813601	C₂²	semidirect
54. #16813601	C₂²	semidirect
55. #16813600	C₂²	semidirect
56. #16813597	C₂²	semidirect
57. #16813596	C₂²	semidirect
58. #16813596	C₂²	semidirect
59. #16813596	C₂²	semidirect
60. #16813595	C₂²	semidirect
61. #16813595	C₂²	semidirect
62. #16813594	C₂²	semidirect
63. #16813594	C₂²	semidirect
64. #16813594	C₂²	semidirect
65. #16813594	C₂²	semidirect
66. #16813594	C₂²	semidirect
67. #16813594	C₂²	semidirect
68. #16813593	C₂²	semidirect
69. #16813593	C₂²	semidirect
70. #16813593	C₂²	semidirect
71. #16813593	C₂²	semidirect
72. #16813591	C₂²	semidirect
73. #16813591	C₂²	semidirect
74. #16813591	C₂²	semidirect
75. #16813590	C₂²	semidirect
76. #16813590	C₂²	semidirect
77. #16813590	C₂²	semidirect
78. #16813587	C₂²	semidirect
79. D₄×Dic₁₁₃	C₂²	semidirect
80. D₄×Dic₁₁₃	C₂²	semidirect
81. D₄×Dic₁₁₃	C₂²	semidirect
82. D₄×Dic₁₁₃	C₂²	semidirect
83. #16813584	C₂²	semidirect
87. C₄×C₂²⋊D₁₁₃	C₂²	semidirect
88. C₄×C₂²⋊D₁₁₃	C₂²	semidirect
89. C₄×C₂²⋊D₁₁₃	C₂²	semidirect
90. C₄×C₂²⋊D₁₁₃	C₂²	semidirect
91. C₄×C₂²⋊D₁₁₃	C₂²	semidirect
92. C₄×C₂²⋊D₁₁₃	C₂²	semidirect
93. C₄×C₂²⋊D₁₁₃	C₂²	semidirect
94. C₄×C₂²⋊D₁₁₃	C₂²	semidirect
95. C₄×C₂²⋊D₁₁₃	C₂²	semidirect
96. #16813582	C₂²	semidirect
97. #16813582	C₂²	semidirect
98. #16813582	C₂²	semidirect
99. #16813582	C₂²	semidirect
100. #16813581	C₂²	semidirect
101. #16813580	C₂²	semidirect
102. #16813578	C₂²	semidirect
103. #16813578	C₂²	semidirect
104. C₂×#14268626	C₂²	semidirect
105. C₄⋊C₄×D₁₁₃	C₂²	semidirect
106. C₂×C₂²⋊Dic₁₁₃	C₂²	semidirect
107. C₂×C₂²⋊Dic₁₁₃	C₂²	semidirect
108. C₂×#14268624	C₂²	semidirect
109. C₂²⋊C₄×D₁₁₃	C₂²	semidirect
110. C₂²⋊C₄×D₁₁₃	C₂²	semidirect
111. C₂×C₄×Dic₁₁₃	C₂²	semidirect
112. C₂²×D₄×C₁₁₃	C₂²	semidirect
113. C₂²×D₄×C₁₁₃	C₂²	semidirect
114. C₂³×C₄×C₁₁₃	C₂²	semidirect
116. #121×C₁₁₃	C₂²	semidirect
117. #121×C₁₁₃	C₂²	semidirect
118. #121×C₁₁₃	C₂²	semidirect
119. #121×C₁₁₃	C₂²	semidirect
120. #121×C₁₁₃	C₂²	semidirect
121. C₂×C₄⋊C₄×C₁₁₃	C₂²	semidirect
122. C₂×C₂²⋊C₄×C₁₁₃	C₂²	semidirect
285. C₂²⋊D₁₁₃	#41	semidirect
368. C₁₁₃	#3519	semidirect
389. C₂×#121	D₁₁₃	semidirect
399. C₂²×D₄	C₂×D₁₁₃	semidirect
400. C₂²×D₄	C₂×D₁₁₃	semidirect
402. C₂³×C₄	C₂×D₁₁₃	semidirect
444. #121	C₂×D₁₁₃	semidirect
445. #121	C₂×D₁₁₃	semidirect
446. #121	C₂×D₁₁₃	semidirect
447. #121	C₂×D₁₁₃	semidirect
448. #121	C₂×D₁₁₃	semidirect
483. C₂×C₄⋊C₄	C₂×D₁₁₃	semidirect
489. C₂×C₂²⋊C₄	C₂×D₁₁₃	semidirect

Maximal subgroups

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

subgroup	index
#20299312	2
#20299303	2
#20299296	2
#20299295	2
#20299291	2
#20299266	2
#20299245	2
#20299242	2
#20299237	2
D₄×C₂²⋊D₁₁₃	2
#20299198	2
#20299186	2
#20299180	2
#20299143	2
#20299129	2
#20299109	2
#20299108	2
#121×D₁₁₃	2
#20299071	2
C₂×C₄×C₂²⋊D₁₁₃	2
C₂×#121×C₁₁₃	2
#3519	113