Subgroups — #28403958

Order 14464.

1040 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20299215	C₂	1	2	yes	maximal, complemented
2	#20299213	C₂	1	2	yes	maximal, complemented
3	#20299211	C₂	1	1	yes	maximal, characteristic, complemented
4	#20299210	C₂	1	1	yes	maximal, characteristic, complemented
5	#20299202	C₂	1	1	yes	maximal, characteristic, complemented
6	#20299191	C₂	1	4	yes	maximal, complemented
7	#20299180	C₂	1	4	yes	maximal, complemented
8	#20299154	C₂	1	1	yes	maximal, characteristic, complemented
9	#20299146	C₂	1	1	yes	maximal, characteristic, complemented
10	#20299129	C₂	1	4	yes	maximal, complemented
11	#20299125	C₂	1	4	yes	maximal, complemented
12	#20299108	C₂	1	2	yes	maximal, complemented
13	C₄×#14268646	C₂	1	2	yes	maximal, complemented
14	#117×D₁₁₃	C₂	1	1	yes	maximal, characteristic, complemented
15	#540×C₁₁₃	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#14268646	C₂²	1	2	yes	—
17	C₂²×C₄×D₁₁₃	C₂²	1	1	yes	characteristic
18	#16813622	C₂²	1	1	yes	characteristic, complemented
19	#16813621	C₂²	1	2	yes	complemented
20	#16813617	C₂²	1	4	yes	—
21	#16813615	C₂²	1	4	yes	—
22	#16813615	C₂²	1	4	yes	complemented
23	#16813615	C₂²	1	4	yes	complemented
24	#16813614	C₂²	1	1	yes	characteristic, complemented
25	#16813613	C₂²	1	4	yes	complemented
26	#16813612	C₂²	1	4	yes	complemented
27	#16813609	C₂²	1	4	yes	—
28	#16813609	C₂²	1	2	yes	complemented
29	#16813608	C₂²	1	4	yes	—
30	#16813605	C₂²	1	4	yes	—
31	#16813604	C₂²	1	4	yes	—
32	#16813603	C₂²	1	4	yes	—
33	#16813603	C₂²	1	4	yes	complemented
34	#16813602	C₂²	1	2	yes	—
35	#16813601	C₂²	1	2	yes	—
36	#16813601	C₂²	1	4	yes	complemented
37	#16813600	C₂²	1	4	yes	—
38	#16813599	C₂²	1	4	yes	complemented
39	#16813594	C₂²	1	4	yes	—
40	#16813593	C₂²	1	2	yes	—
41	#16813593	C₂²	1	4	yes	—
42	#16813590	C₂²	1	4	yes	—
43	C₄×Dic₂₂₆	C₂²	1	2	yes	complemented
44	#16813587	C₂²	1	2	yes	complemented
45	#16813587	C₂²	1	4	yes	complemented
46	D₄×Dic₁₁₃	C₂²	1	4	yes	—
47	D₄×Dic₁₁₃	C₂²	1	2	yes	complemented
48	D₄×Dic₁₁₃	C₂²	1	4	yes	complemented
49	C₄×C₂²⋊D₁₁₃	C₂²	1	4	yes	—
50	#16813582	C₂²	1	4	yes	—
51	#16813582	C₂²	1	4	yes	—
52	#16813581	C₂²	1	1	yes	characteristic
53	#16813580	C₂²	1	2	yes	—
54	#16813580	C₂²	1	2	yes	—
55	#16813579	C₂²	1	1	yes	characteristic
56	#16813579	C₂²	1	1	yes	characteristic
57	#16813578	C₂²	1	2	yes	—
58	#16813578	C₂²	1	4	yes	complemented
59	C₄⋊C₄×D₁₁₃	C₂²	1	2	yes	—
60	C₂²⋊C₄×D₁₁₃	C₂²	1	2	yes	—
61	C₂×C₄×Dic₁₁₃	C₂²	1	4	yes	complemented
62	C₄²×D₁₁₃	C₂²	1	1	yes	characteristic
63	C₄²×D₁₁₃	C₂²	1	1	yes	characteristic
64	#127×C₁₁₃	C₂²	1	1	yes	characteristic, complemented
65	#125×C₁₁₃	C₂²	1	1	yes	characteristic, complemented
66	#123×C₁₁₃	C₂²	1	4	yes	complemented
67	#121×C₁₁₃	C₂²	1	2	yes	—
68	#121×C₁₁₃	C₂²	1	4	yes	—
69	C₄×D₄×C₁₁₃	C₂²	1	2	yes	complemented
70	#117×C₁₁₃	C₂²	1	1	yes	characteristic
71	C₂³×D₁₁₃	C₂³	1	1	yes	characteristic
72	#14268646	—	2	8	no	—
73	C₂×Dic₂₂₆	C₂³	1	2	yes	—
74	C₂×Dic₂₂₆	C₂³	1	4	yes	—
75	C₂×C₂²⋊D₁₁₃	C₂³	1	4	yes	—
76	C₂×C₂²⋊D₁₁₃	C₂³	1	4	yes	—
77	C₂²×Dic₁₁₃	C₂³	1	4	yes	—
78	C₂²×Dic₁₁₃	C₂³	1	1	yes	characteristic
79	C₂²×Dic₁₁₃	C₂³	1	4	yes	—
80	C₂×C₄×D₁₁₃	—	2	4	no	—
81	C₂×C₄×D₁₁₃	C₂³	1	1	yes	characteristic
82	C₂×C₄×D₁₁₃	C₂³	1	1	yes	characteristic
83	C₂×C₄×D₁₁₃	C₂³	1	1	yes	characteristic
84	C₂×C₄×D₁₁₃	C₂³	1	2	yes	—
85	C₂×C₄×D₁₁₃	C₂³	1	2	yes	—
86	C₂×C₄×D₁₁₃	C₂³	1	1	yes	characteristic
87	C₄⋊Dic₁₁₃	C₂³	1	2	yes	—
88	C₄⋊Dic₁₁₃	C₂³	1	2	yes	—
89	C₄⋊Dic₁₁₃	C₂³	1	4	yes	—
90	C₄⋊Dic₁₁₃	C₂³	1	4	yes	—
91	#14268626	C₂³	1	2	yes	—
92	#14268626	C₂³	1	2	yes	—
93	#14268626	C₂³	1	4	yes	—
94	#14268626	C₂³	1	4	yes	—
95	#14268626	C₂³	1	4	yes	—
96	#14268626	C₂³	1	4	yes	—
97	#14268626	C₂³	1	4	yes	—
98	C₂²⋊Dic₁₁₃	C₂³	1	2	yes	—
99	C₂²⋊Dic₁₁₃	C₂³	1	4	yes	—
100	C₂²⋊Dic₁₁₃	C₂³	1	4	yes	—
101	C₂²⋊Dic₁₁₃	C₂³	1	4	yes	—
102	C₂²⋊Dic₁₁₃	C₂³	1	4	yes	—
103	C₂²⋊Dic₁₁₃	C₂³	1	4	yes	—
104	#14268624	C₂³	1	2	yes	—
105	#14268624	C₂³	1	2	yes	—
106	#14268624	C₂³	1	4	yes	—
107	#14268624	C₂³	1	4	yes	—
108	C₄×Dic₁₁₃	C₂³	1	2	yes	—
109	C₄×Dic₁₁₃	C₂³	1	2	yes	—
110	C₄×Dic₁₁₃	C₂³	1	1	yes	characteristic
111	C₄×Dic₁₁₃	C₂³	1	1	yes	characteristic
112	C₄×Dic₁₁₃	C₂³	1	4	yes	—
113	C₄×Dic₁₁₃	C₂³	1	4	yes	—
114	C₄×Dic₁₁₃	C₂³	1	4	yes	—
115	C₂×D₄×C₁₁₃	C₂³	1	2	yes	—
116	C₂×D₄×C₁₁₃	C₂³	1	4	yes	—
117	C₂×D₄×C₁₁₃	C₂³	1	4	yes	—
118	C₂²×C₄×C₁₁₃	C₂³	1	1	yes	characteristic
119	C₂²×C₄×C₁₁₃	C₂³	1	4	yes	—
120	C₄⋊C₄×C₁₁₃	C₂³	1	2	yes	—
121	C₄⋊C₄×C₁₁₃	C₂³	1	2	yes	—
122	C₄⋊C₄×C₁₁₃	C₂³	1	4	yes	—
123	C₂²⋊C₄×C₁₁₃	C₂³	1	2	yes	—
124	C₂²⋊C₄×C₁₁₃	C₂³	1	4	yes	—
125	C₂²⋊C₄×C₁₁₃	C₂³	1	4	yes	—
126	C₄²×C₁₁₃	C₂³	1	1	yes	characteristic
127	C₄²×C₁₁₃	C₂³	1	1	yes	characteristic
128	C₂³×C₁₁₃	C₂⁴	1	1	yes	characteristic
129	C₂³×C₁₁₃	C₂⁴	1	4	yes	—
130	C₂²×D₁₁₃	—	2	2	no	—
131	C₂²×D₁₁₃	—	4	2	no	—
132	C₂²×D₁₁₃	C₂⁴	1	1	yes	characteristic
133	C₂²×D₁₁₃	C₂⁴	1	1	yes	characteristic
134	D₄×C₁₁₃	—	2	4	no	—
135	D₄×C₁₁₃	—	4	4	no	—
136	D₄×C₁₁₃	—	4	4	no	—
137	C₂×C₄×C₁₁₃	—	2	2	no	—
138	C₂×C₄×C₁₁₃	—	4	4	no	—
139	C₂×C₄×C₁₁₃	C₂⁴	1	2	yes	—
140	C₂×C₄×C₁₁₃	C₂⁴	1	2	yes	—
141	C₂×C₄×C₁₁₃	C₂⁴	1	1	yes	characteristic
142	C₂×C₄×C₁₁₃	C₂⁴	1	4	yes	—
143	C₂×C₄×C₁₁₃	C₂⁴	1	1	yes	characteristic
144	C₂²⋊D₁₁₃	—	2	8	no	—
145	C₂²⋊D₁₁₃	—	4	4	no	—
146	C₂×Dic₁₁₃	—	2	2	no	—
147	C₂×Dic₁₁₃	—	2	8	no	—
148	C₂×Dic₁₁₃	—	4	4	no	—
149	C₂×Dic₁₁₃	C₂⁴	1	2	yes	—
150	C₂×Dic₁₁₃	C₂⁴	1	2	yes	—
151	C₂×Dic₁₁₃	C₂⁴	1	4	yes	—
152	C₂×Dic₁₁₃	C₂⁴	1	4	yes	—
153	C₂×Dic₁₁₃	C₂⁴	1	1	yes	characteristic
154	C₂×Dic₁₁₃	C₂⁴	1	1	yes	characteristic
155	C₄×D₁₁₃	—	2	2	no	—
156	C₄×D₁₁₃	—	2	2	no	—
157	C₄×D₁₁₃	—	2	2	no	—
158	C₄×D₁₁₃	—	4	2	no	—
159	C₄×D₁₁₃	—	4	2	no	—
160	C₄×D₁₁₃	#41	1	4	yes	—
161	Dic₂₂₆	—	2	4	no	—
162	Dic₂₂₆	—	4	4	no	—
163	C₂²×C₁₁₃	—	2	4	no	—
164	C₂²×C₁₁₃	—	2	1	no	—
165	C₂²×C₁₁₃	—	2	4	no	—
166	C₂²×C₁₁₃	—	2	4	no	—
167	C₂²×C₁₁₃	—	2	2	no	—
168	C₂²×C₁₁₃	C₂⁵	1	1	yes	characteristic
169	C₂×D₁₁₃	—	2	2	no	—
170	C₂×D₁₁₃	—	2	1	no	—
171	C₂×D₁₁₃	—	2	2	no	—
172	C₂×D₁₁₃	—	4	4	no	—
173	C₂×D₁₁₃	C₂×#41	1	2	yes	—
174	C₄×C₁₁₃	—	2	1	no	—
175	C₄×C₁₁₃	—	2	4	no	—
176	C₄×C₁₁₃	—	2	2	no	—
177	C₄×C₁₁₃	—	2	2	no	—
178	C₄×C₁₁₃	C₂×#41	1	2	yes	—
179	Dic₁₁₃	—	2	4	no	—
180	Dic₁₁₃	—	2	1	no	—
181	Dic₁₁₃	—	2	2	no	—
182	Dic₁₁₃	—	2	4	no	—
183	Dic₁₁₃	—	2	2	no	—
184	Dic₁₁₃	C₂×#41	1	2	yes	—
185	C₂×C₁₁₃	—	4	1	no	—
186	C₂×C₁₁₃	—	4	4	no	—
187	C₂×C₁₁₃	C₂²×#41	1	1	yes	characteristic
188	C₂×C₁₁₃	#585	1	2	yes	—
189	D₁₁₃	—	2	2	no	—
190	D₁₁₃	—	4	1	no	—
191	#3455	—	113	1	no	maximal, Sylow
192	C₁₁₃	#3455	1	1	yes	characteristic, complemented, Sylow
193	#542	—	113	2	no	—
194	#542	—	113	2	no	—
195	#541	—	113	1	no	—
196	#541	—	113	1	no	—
197	#540	—	113	1	no	—
198	#540	D₁₁₃	1	1	yes	characteristic, complemented
199	#539	—	113	4	no	—
200	#538	—	113	4	no	—
201	#533	—	113	1	no	—
202	#532	—	113	1	no	—
203	#529	—	113	4	no	—
204	#529	—	113	4	no	—
205	#525	—	113	2	no	—
206	C₄×#41	—	113	2	no	—
207	C₂×#117	—	113	1	no	—
208	C₂×#41	—	113	2	no	—
209	C₂³×C₄	—	113	1	no	—
210	C₄⋊Q₈	—	113	2	no	—
211	C₄⋊Q₈	—	113	1	no	—
212	#127	C₂×D₁₁₃	1	1	yes	characteristic, complemented
213	#126	—	113	4	no	—
214	#126	—	113	4	no	—
215	#126	—	113	4	no	—
216	#126	—	113	4	no	—
217	#125	—	113	4	no	—
218	#125	—	113	4	no	—
219	#125	—	113	1	no	—
220	#125	C₂×D₁₁₃	1	1	yes	characteristic, complemented
221	#124	—	113	4	no	—
222	#124	—	113	2	no	—
223	#124	—	113	4	no	—
224	#123	—	113	4	no	—
225	#123	—	113	4	no	—
226	#123	—	113	4	no	—
227	#123	—	113	4	no	—
228	#123	C₂×D₁₁₃	1	4	yes	complemented
229	C₂²⋊Q₈	—	113	2	no	—
230	C₂²⋊Q₈	—	113	4	no	—
231	C₂²⋊Q₈	—	113	2	no	—
232	C₂²⋊Q₈	—	113	4	no	—
233	C₂²⋊Q₈	—	113	4	no	—
234	#121	—	113	2	no	—
235	#121	—	113	4	no	—
236	#121	—	113	4	no	—
237	#121	C₂×D₁₁₃	1	2	yes	—
238	#121	C₂×D₁₁₃	1	4	yes	—
239	#120	—	113	4	no	—
240	C₄×Q₈	—	113	2	no	—
241	C₄×Q₈	—	113	4	no	—
242	C₄×Q₈	—	113	2	no	—
243	C₄×D₄	—	113	2	no	—
244	C₄×D₄	—	113	4	no	—
245	C₄×D₄	—	113	4	no	—
246	C₄×D₄	—	113	4	no	—
247	C₄×D₄	—	113	4	no	—
248	C₄×D₄	—	113	4	no	—
249	C₄×D₄	C₂×D₁₁₃	1	2	yes	complemented
250	#117	—	113	1	no	—
251	#117	—	113	2	no	—
252	#117	—	113	2	no	—
253	#117	—	113	2	no	—
254	#117	—	113	4	no	—
255	#117	—	113	1	no	—
256	#117	—	113	1	no	—
257	#117	C₂×D₁₁₃	1	1	yes	characteristic
258	C₂×C₄⋊C₄	—	113	2	no	—
259	C₂×C₂²⋊C₄	—	113	2	no	—
260	C₂×C₄²	—	113	4	no	—
261	C₂×C₄²	—	113	1	no	—
262	C₂×C₄²	—	113	1	no	—
263	C₂⁴	—	113	1	no	—
264	#41	—	226	8	no	—
265	C₂×Q₈	—	113	4	no	—
266	C₂×Q₈	—	113	2	no	—
267	C₂×D₄	—	113	4	no	—
268	C₂×D₄	—	113	4	no	—
269	C₂×D₄	C₂²×D₁₁₃	1	2	yes	—
270	C₂×D₄	C₂²×D₁₁₃	1	4	yes	—
271	C₂×D₄	C₂²×D₁₁₃	1	4	yes	—
272	C₂²×C₄	—	113	1	no	—
273	C₂²×C₄	—	113	4	no	—
274	C₂²×C₄	—	113	4	no	—
275	C₂²×C₄	—	113	1	no	—
276	C₂²×C₄	—	113	2	no	—
277	C₂²×C₄	—	113	2	no	—
278	C₂²×C₄	—	113	1	no	—
279	C₂²×C₄	—	113	1	no	—
280	C₂²×C₄	—	113	1	no	—
281	C₂²×C₄	—	226	4	no	—
282	C₂²×C₄	C₂²×D₁₁₃	1	1	yes	characteristic
283	C₂²×C₄	C₂²×D₁₁₃	1	4	yes	—
284	C₄⋊C₄	—	113	2	no	—
285	C₄⋊C₄	—	113	2	no	—
286	C₄⋊C₄	—	113	2	no	—
287	C₄⋊C₄	—	113	2	no	—
288	C₄⋊C₄	—	113	4	no	—
289	C₄⋊C₄	—	113	4	no	—
290	C₄⋊C₄	—	113	4	no	—
291	C₄⋊C₄	—	113	4	no	—
292	C₄⋊C₄	—	113	4	no	—
293	C₄⋊C₄	—	113	4	no	—
294	C₄⋊C₄	—	113	4	no	—
295	C₄⋊C₄	C₂²×D₁₁₃	1	2	yes	—
296	C₄⋊C₄	C₂²×D₁₁₃	1	2	yes	—
297	C₄⋊C₄	C₂²×D₁₁₃	1	4	yes	—
298	C₂²⋊C₄	—	113	2	no	—
299	C₂²⋊C₄	—	113	4	no	—
300	C₂²⋊C₄	—	113	4	no	—
301	C₂²⋊C₄	—	113	4	no	—
302	C₂²⋊C₄	—	113	4	no	—
303	C₂²⋊C₄	—	113	4	no	—
304	C₂²⋊C₄	—	113	2	no	—
305	C₂²⋊C₄	—	113	2	no	—
306	C₂²⋊C₄	—	113	4	no	—
307	C₂²⋊C₄	—	113	4	no	—
308	C₂²⋊C₄	C₂²×D₁₁₃	1	2	yes	—
309	C₂²⋊C₄	C₂²×D₁₁₃	1	4	yes	—
310	C₂²⋊C₄	C₂²×D₁₁₃	1	4	yes	—
311	C₄²	—	113	2	no	—
312	C₄²	—	113	2	no	—
313	C₄²	—	113	4	no	—
314	C₄²	—	113	1	no	—
315	C₄²	—	113	1	no	—
316	C₄²	—	113	4	no	—
317	C₄²	—	113	4	no	—
318	C₄²	C₂²×D₁₁₃	1	1	yes	characteristic
319	C₄²	C₂²×D₁₁₃	1	1	yes	characteristic
320	C₂³	—	113	1	no	—
321	C₂³	—	113	1	no	—
322	C₂³	—	452	2	no	—
323	C₂³	—	226	2	no	—
324	C₂³	C₂³×D₁₁₃	1	1	yes	characteristic
325	C₂³	C₂³×D₁₁₃	1	4	yes	—
326	Q₈	—	452	4	no	—
327	Q₈	—	226	4	no	—
328	D₄	—	2	4	no	—
329	D₄	—	4	4	no	—
330	D₄	—	4	4	no	—
331	D₄	—	452	4	no	—
332	D₄	—	226	8	no	—
333	C₂×C₄	—	2	2	no	—
334	C₂×C₄	—	4	4	no	—
335	C₂×C₄	—	113	1	no	—
336	C₂×C₄	—	113	4	no	—
337	C₂×C₄	—	113	2	no	—
338	C₂×C₄	—	113	2	no	—
339	C₂×C₄	—	113	4	no	—
340	C₂×C₄	—	113	4	no	—
341	C₂×C₄	—	113	1	no	—
342	C₂×C₄	—	452	2	no	—
343	C₂×C₄	—	452	2	no	—
344	C₂×C₄	—	452	4	no	—
345	C₂×C₄	—	226	2	no	—
346	C₂×C₄	—	226	2	no	—
347	C₂×C₄	—	226	2	no	—
348	C₂×C₄	—	226	8	no	—
349	C₂×C₄	—	226	2	no	—
350	C₂×C₄	C₂³×D₁₁₃	1	2	yes	—
351	C₂×C₄	C₂³×D₁₁₃	1	4	yes	—
352	C₂×C₄	C₂³×D₁₁₃	1	2	yes	—
353	C₂×C₄	C₂³×D₁₁₃	1	1	yes	characteristic
354	C₂×C₄	C₂³×D₁₁₃	1	1	yes	characteristic
355	C₂²	—	2	1	no	—
356	C₂²	—	2	4	no	—
357	C₂²	—	2	4	no	—
358	C₂²	—	2	4	no	—
359	C₂²	—	2	2	no	—
360	C₂²	—	113	2	no	—
361	C₂²	—	452	4	no	—
362	C₂²	—	226	1	no	—
363	C₂²	—	226	2	no	—
364	C₂²	—	226	2	no	—
365	C₂²	C₂⁴×D₁₁₃	1	1	yes	characteristic
366	C₄	—	2	1	no	—
367	C₄	—	2	2	no	—
368	C₄	—	2	4	no	—
369	C₄	—	2	2	no	—
370	C₄	—	113	2	no	—
371	C₄	—	226	1	no	—
372	C₄	—	226	4	no	—
373	C₄	—	226	2	no	—
374	C₄	—	226	4	no	—
375	C₄	—	226	2	no	—
376	C₄	#41×D₁₁₃	1	2	yes	—
377	C₂	—	4	1	no	—
378	C₂	—	4	4	no	—
379	C₂	—	452	1	no	—
380	C₂	—	226	2	no	—
381	C₂	C₂×#41×D₁₁₃	1	1	yes	characteristic
382	C₂	#20299433	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₁₁₃
commutator, socle, cosocle	C₂²×C₁₁₃	C₂⁵
Fitting	#540×C₁₁₃	C₂
hypercenter	#540	D₁₁₃
hypocenter	C₁₁₃	#3455
LCS	G ▷ C₂²×C₁₁₃ ▷ C₁₁₃
UCS	C₁ ◁ C₂² ◁ #540

Complements

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

N	H ≅ G/N	type
1. #20299215	C₂	semidirect
2. #20299213	C₂	semidirect
3. #20299211	C₂	semidirect
4. #20299210	C₂	semidirect
5. #20299202	C₂	semidirect
6. #20299191	C₂	semidirect
7. #20299180	C₂	semidirect
8. #20299154	C₂	semidirect
9. #20299146	C₂	semidirect
10. #20299129	C₂	semidirect
11. #20299125	C₂	semidirect
12. #20299108	C₂	semidirect
13. C₄×#14268646	C₂	semidirect
14. #117×D₁₁₃	C₂	semidirect
15. #540×C₁₁₃	C₂	semidirect
18. #16813622	C₂²	semidirect
19. #16813621	C₂²	semidirect
22. #16813615	C₂²	semidirect
23. #16813615	C₂²	semidirect
24. #16813614	C₂²	semidirect
25. #16813613	C₂²	semidirect
26. #16813612	C₂²	semidirect
28. #16813609	C₂²	semidirect
33. #16813603	C₂²	semidirect
36. #16813601	C₂²	semidirect
38. #16813599	C₂²	semidirect
43. C₄×Dic₂₂₆	C₂²	semidirect
44. #16813587	C₂²	semidirect
45. #16813587	C₂²	semidirect
47. D₄×Dic₁₁₃	C₂²	semidirect
48. D₄×Dic₁₁₃	C₂²	semidirect
58. #16813578	C₂²	semidirect
61. C₂×C₄×Dic₁₁₃	C₂²	semidirect
64. #127×C₁₁₃	C₂²	semidirect
65. #125×C₁₁₃	C₂²	semidirect
66. #123×C₁₁₃	C₂²	semidirect
69. C₄×D₄×C₁₁₃	C₂²	semidirect
192. C₁₁₃	#3455	semidirect
198. #540	D₁₁₃	semidirect
212. #127	C₂×D₁₁₃	semidirect
220. #125	C₂×D₁₁₃	semidirect
228. #123	C₂×D₁₁₃	semidirect
249. C₄×D₄	C₂×D₁₁₃	semidirect

Maximal subgroups

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

subgroup	index
#20299215	2
#20299213	2
#20299211	2
#20299210	2
#20299202	2
#20299191	2
#20299180	2
#20299154	2
#20299146	2
#20299129	2
#20299125	2
#20299108	2
C₄×#14268646	2
#117×D₁₁₃	2
#540×C₁₁₃	2
#3455	113