Subgroups — #28404446

Order 14464.

1232 conjugacy classes of subgroups.

The subgroup lattice has 414 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20299332	C₂	1	4	yes	maximal, complemented
2	#20299266	C₂	1	4	yes	maximal, complemented
3	#20299240	C₂	1	4	yes	maximal, complemented
4	#20299237	C₂	1	4	yes	maximal, complemented
5	#20299204	C₂	1	1	yes	maximal, characteristic, complemented
6	#20299203	C₂	1	1	yes	maximal, characteristic, complemented
7	#20299202	C₂	1	1	yes	maximal, characteristic, complemented
8	#20299164	C₂	1	2	yes	maximal, complemented
9	#20299154	C₂	1	1	yes	maximal, characteristic, complemented
10	#20299145	C₂	1	2	yes	maximal, complemented
11	#20299143	C₂	1	2	yes	maximal, complemented
12	#127×D₁₁₃	C₂	1	1	yes	maximal, characteristic, complemented
13	#20299070	C₂	1	2	yes	maximal, complemented
14	#20299066	C₂	1	1	yes	maximal, characteristic, complemented
15	#540×C₁₁₃	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#14268647	C₂²	1	1	yes	characteristic
17	C₂×#14268647	C₂²	1	4	yes	complemented
18	C₂×#14268646	C₂²	1	4	yes	complemented
19	C₂×D₄×D₁₁₃	C₂²	1	2	yes	—
20	C₂×D₄×D₁₁₃	C₂²	1	4	yes	—
21	#16813621	C₂²	1	2	yes	complemented
22	#16813619	C₂²	1	1	yes	characteristic
23	#16813618	C₂²	1	4	yes	—
24	#16813618	C₂²	1	2	yes	—
25	#16813618	C₂²	1	4	yes	complemented
26	#16813614	C₂²	1	1	yes	characteristic, complemented
27	#16813608	C₂²	1	4	yes	complemented
28	#16813608	C₂²	1	4	yes	complemented
29	#16813608	C₂²	1	4	yes	complemented
30	#16813607	C₂²	1	4	yes	complemented
31	#16813607	C₂²	1	4	yes	complemented
32	#16813603	C₂²	1	4	yes	complemented
33	#16813600	C₂²	1	4	yes	—
34	#16813597	C₂²	1	4	yes	complemented
35	#16813597	C₂²	1	2	yes	complemented
36	#16813596	C₂²	1	2	yes	complemented
37	#16813595	C₂²	1	4	yes	complemented
38	#16813595	C₂²	1	4	yes	complemented
39	#16813594	C₂²	1	4	yes	complemented
40	#16813594	C₂²	1	4	yes	complemented
41	#16813593	C₂²	1	2	yes	complemented
42	#16813592	C₂²	1	4	yes	—
43	#16813590	C₂²	1	4	yes	—
44	#16813587	C₂²	1	4	yes	complemented
45	#16813587	C₂²	1	2	yes	complemented
46	C₄×D₄₅₂	C₂²	1	2	yes	complemented
47	D₄×Dic₁₁₃	C₂²	1	2	yes	complemented
48	#16813584	C₂²	1	2	yes	—
49	#16813584	C₂²	1	2	yes	complemented
50	C₄×C₂²⋊D₁₁₃	C₂²	1	4	yes	complemented
51	C₄×C₂²⋊D₁₁₃	C₂²	1	4	yes	complemented
52	#16813582	C₂²	1	2	yes	—
53	#16813582	C₂²	1	2	yes	complemented
54	#16813582	C₂²	1	4	yes	complemented
55	#16813582	C₂²	1	4	yes	complemented
56	#16813580	C₂²	1	2	yes	—
57	#16813579	C₂²	1	1	yes	characteristic
58	#16813579	C₂²	1	1	yes	characteristic, complemented
59	C₂×#14268624	C₂²	1	4	yes	—
60	C₂²⋊C₄×D₁₁₃	C₂²	1	4	yes	—
61	C₂×C₄×Dic₁₁₃	C₂²	1	1	yes	characteristic, complemented
62	C₄²×D₁₁₃	C₂²	1	1	yes	characteristic
63	C₄²×D₁₁₃	C₂²	1	1	yes	characteristic, complemented
64	#127×C₁₁₃	C₂²	1	1	yes	characteristic
65	#125×C₁₁₃	C₂²	1	1	yes	characteristic, complemented
66	#123×C₁₁₃	C₂²	1	4	yes	complemented
67	#121×C₁₁₃	C₂²	1	4	yes	complemented
68	#121×C₁₁₃	C₂²	1	2	yes	complemented
69	C₄×D₄×C₁₁₃	C₂²	1	2	yes	complemented
70	#117×C₁₁₃	C₂²	1	1	yes	characteristic, complemented
71	C₂³×D₁₁₃	C₂³	1	4	yes	—
72	#14268647	—	2	4	no	—
73	#14268647	—	4	8	no	—
74	#14268646	—	4	8	no	—
75	C₂×Dic₂₂₆	C₂³	1	1	yes	characteristic
76	C₂×Dic₂₂₆	C₂³	1	4	yes	—
77	C₂×D₄₅₂	C₂³	1	1	yes	characteristic
78	C₂×D₄₅₂	C₂³	1	2	yes	—
79	C₂×D₄₅₂	C₂³	1	4	yes	—
80	C₂×D₄₅₂	C₂³	1	4	yes	—
81	C₂×C₂²⋊D₁₁₃	C₂³	1	1	yes	characteristic
82	C₂×C₂²⋊D₁₁₃	C₂³	1	1	yes	characteristic
83	C₂×C₂²⋊D₁₁₃	C₂³	1	4	yes	—
84	C₂×C₂²⋊D₁₁₃	C₂³	1	4	yes	—
85	C₂×C₂²⋊D₁₁₃	C₂³	1	4	yes	—
86	C₂×C₂²⋊D₁₁₃	C₂³	1	4	yes	—
87	C₂×C₂²⋊D₁₁₃	C₂³	1	4	yes	—
88	D₄×D₁₁₃	—	2	8	no	—
89	D₄×D₁₁₃	—	4	8	no	—
90	C₂²×Dic₁₁₃	C₂³	1	2	yes	—
91	C₂²×Dic₁₁₃	C₂³	1	4	yes	—
92	C₂×C₄×D₁₁₃	C₂³	1	2	yes	—
93	C₂×C₄×D₁₁₃	C₂³	1	1	yes	characteristic
94	C₂×C₄×D₁₁₃	C₂³	1	2	yes	—
95	C₂×C₄×D₁₁₃	C₂³	1	4	yes	—
96	C₂×C₄×D₁₁₃	C₂³	1	4	yes	—
97	C₂×C₄×D₁₁₃	C₂³	1	1	yes	characteristic
98	C₄⋊Dic₁₁₃	C₂³	1	2	yes	—
99	#14268626	C₂³	1	2	yes	—
100	#14268626	C₂³	1	2	yes	—
101	#14268626	C₂³	1	4	yes	—
102	#14268626	C₂³	1	4	yes	—
103	C₂²⋊Dic₁₁₃	C₂³	1	4	yes	—
104	C₂²⋊Dic₁₁₃	C₂³	1	4	yes	—
105	#14268624	C₂³	1	2	yes	—
106	#14268624	C₂³	1	4	yes	—
107	#14268624	C₂³	1	4	yes	—
108	#14268624	C₂³	1	4	yes	—
109	#14268624	C₂³	1	2	yes	—
110	#14268624	C₂³	1	4	yes	—
111	#14268624	C₂³	1	4	yes	—
112	C₄×Dic₁₁₃	C₂³	1	1	yes	characteristic
113	C₄×Dic₁₁₃	C₂³	1	2	yes	—
114	C₄×Dic₁₁₃	C₂³	1	2	yes	—
115	C₄×Dic₁₁₃	C₂³	1	1	yes	characteristic
116	C₄×Dic₁₁₃	C₂³	1	2	yes	—
117	C₄×Dic₁₁₃	C₂³	1	4	yes	—
118	C₂×D₄×C₁₁₃	C₂³	1	2	yes	—
119	C₂×D₄×C₁₁₃	C₂³	1	4	yes	—
120	C₂×D₄×C₁₁₃	C₂³	1	4	yes	—
121	C₂²×C₄×C₁₁₃	C₂³	1	1	yes	characteristic
122	C₂²×C₄×C₁₁₃	C₂³	1	4	yes	—
123	C₄⋊C₄×C₁₁₃	C₂³	1	2	yes	—
124	C₄⋊C₄×C₁₁₃	C₂³	1	2	yes	—
125	C₄⋊C₄×C₁₁₃	C₂³	1	4	yes	—
126	C₂²⋊C₄×C₁₁₃	C₂³	1	4	yes	—
127	C₂²⋊C₄×C₁₁₃	C₂³	1	2	yes	—
128	C₂²⋊C₄×C₁₁₃	C₂³	1	4	yes	—
129	C₄²×C₁₁₃	C₂³	1	1	yes	characteristic
130	C₄²×C₁₁₃	C₂³	1	1	yes	characteristic
131	C₂³×C₁₁₃	C₂⁴	1	4	yes	—
132	C₂³×C₁₁₃	C₂⁴	1	1	yes	characteristic
133	C₂²×D₁₁₃	—	2	8	no	—
134	C₂²×D₁₁₃	—	4	4	no	—
135	C₂²×D₁₁₃	—	4	4	no	—
136	C₂²×D₁₁₃	C₂⁴	1	4	yes	—
137	C₂²×D₁₁₃	C₂⁴	1	1	yes	characteristic
138	C₂²×D₁₁₃	C₂⁴	1	1	yes	characteristic
139	D₄×C₁₁₃	—	2	4	no	—
140	D₄×C₁₁₃	—	4	4	no	—
141	D₄×C₁₁₃	—	4	4	no	—
142	C₂×C₄×C₁₁₃	—	2	2	no	—
143	C₂×C₄×C₁₁₃	—	4	4	no	—
144	C₂×C₄×C₁₁₃	C₂⁴	1	2	yes	—
145	C₂×C₄×C₁₁₃	C₂⁴	1	2	yes	—
146	C₂×C₄×C₁₁₃	C₂⁴	1	1	yes	characteristic
147	C₂×C₄×C₁₁₃	C₂⁴	1	4	yes	—
148	C₂×C₄×C₁₁₃	C₂⁴	1	1	yes	characteristic
149	C₂²⋊D₁₁₃	—	2	2	no	—
150	C₂²⋊D₁₁₃	—	2	8	no	—
151	C₂²⋊D₁₁₃	—	2	2	no	—
152	C₂²⋊D₁₁₃	—	2	8	no	—
153	C₂²⋊D₁₁₃	—	2	8	no	—
154	C₂²⋊D₁₁₃	—	4	4	no	—
155	C₂²⋊D₁₁₃	—	4	4	no	—
156	C₂×Dic₁₁₃	—	2	4	no	—
157	C₂×Dic₁₁₃	—	4	4	no	—
158	C₂×Dic₁₁₃	C₂⁴	1	1	yes	characteristic
159	C₂×Dic₁₁₃	C₂⁴	1	2	yes	—
160	C₂×Dic₁₁₃	C₂⁴	1	4	yes	—
161	C₂×Dic₁₁₃	C₂⁴	1	1	yes	characteristic
162	C₂×Dic₁₁₃	C₂⁴	1	2	yes	—
163	D₄₅₂	—	2	2	no	—
164	D₄₅₂	—	2	4	no	—
165	D₄₅₂	—	4	4	no	—
166	D₄₅₂	—	4	4	no	—
167	C₄×D₁₁₃	—	2	2	no	—
168	C₄×D₁₁₃	—	2	4	no	—
169	C₄×D₁₁₃	—	2	4	no	—
170	C₄×D₁₁₃	—	4	4	no	—
171	C₄×D₁₁₃	—	4	4	no	—
172	C₄×D₁₁₃	#41	1	4	yes	complemented
173	Dic₂₂₆	—	2	2	no	—
174	Dic₂₂₆	—	2	8	no	—
175	C₂²×C₁₁₃	—	2	1	no	—
176	C₂²×C₁₁₃	—	2	4	no	—
177	C₂²×C₁₁₃	—	2	2	no	—
178	C₂²×C₁₁₃	—	2	4	no	—
179	C₂²×C₁₁₃	—	2	4	no	—
180	C₂²×C₁₁₃	C₂⁵	1	1	yes	characteristic
181	C₂×D₁₁₃	—	2	2	no	—
182	C₂×D₁₁₃	—	2	1	no	—
183	C₂×D₁₁₃	—	2	4	no	—
184	C₂×D₁₁₃	—	2	2	no	—
185	C₂×D₁₁₃	—	2	4	no	—
186	C₂×D₁₁₃	—	2	4	no	—
187	C₂×D₁₁₃	—	8	8	no	—
188	C₂×D₁₁₃	C₂×#41	1	2	yes	—
189	C₄×C₁₁₃	—	2	1	no	—
190	C₄×C₁₁₃	—	2	4	no	—
191	C₄×C₁₁₃	—	2	2	no	—
192	C₄×C₁₁₃	—	2	2	no	—
193	C₄×C₁₁₃	C₂×#41	1	2	yes	—
194	Dic₁₁₃	—	2	1	no	—
195	Dic₁₁₃	—	2	4	no	—
196	Dic₁₁₃	—	2	2	no	—
197	Dic₁₁₃	C₂×#41	1	2	yes	—
198	Dic₁₁₃	H(5,𝔽₂)	1	4	yes	—
199	C₂×C₁₁₃	—	4	4	no	—
200	C₂×C₁₁₃	—	4	1	no	—
201	C₂×C₁₁₃	C₂²×#41	1	1	yes	characteristic
202	C₂×C₁₁₃	C₂×H(5,𝔽₂)	1	2	yes	—
203	D₁₁₃	—	2	2	no	—
204	D₁₁₃	—	4	1	no	—
205	D₁₁₃	—	4	4	no	—
206	#3508	—	113	1	no	maximal, Sylow
207	C₁₁₃	#3508	1	1	yes	characteristic, complemented, Sylow
208	#559	—	113	4	no	—
209	#550	—	113	4	no	—
210	#546	—	113	4	no	—
211	#546	—	113	4	no	—
212	#540	—	113	1	no	—
213	#540	—	113	1	no	—
214	#540	—	113	1	no	—
215	#540	D₁₁₃	1	1	yes	characteristic, complemented
216	#535	—	113	2	no	—
217	#533	—	113	1	no	—
218	#532	—	113	2	no	—
219	#532	—	113	2	no	—
220	C₂×#127	—	113	1	no	—
221	#518	—	113	2	no	—
222	C₄×#41	—	113	1	no	—
223	C₂×#41	—	113	4	no	—
224	C₂×#41	—	113	4	no	—
225	C₂×#41	—	113	1	no	—
226	C₂²×D₄	—	113	4	no	—
227	C₂²×D₄	—	113	2	no	—
228	C₄⋊Q₈	—	113	2	no	—
229	#127	—	113	2	no	—
230	#127	—	113	4	no	—
231	#127	—	113	4	no	—
232	#127	—	113	1	no	—
233	#127	C₂×D₁₁₃	1	1	yes	characteristic
234	#125	—	113	1	no	—
235	#125	C₂×D₁₁₃	1	1	yes	characteristic, complemented
236	#124	—	113	4	no	—
237	#124	—	113	4	no	—
238	#124	—	113	4	no	—
239	#123	—	113	4	no	—
240	#123	—	113	4	no	—
241	#123	—	113	4	no	—
242	#123	C₂×D₁₁₃	1	4	yes	complemented
243	C₂²⋊Q₈	—	113	4	no	—
244	#121	—	113	2	no	—
245	#121	—	113	4	no	—
246	#121	—	113	4	no	—
247	#121	—	113	2	no	—
248	#121	—	113	2	no	—
249	#121	—	113	4	no	—
250	#121	—	113	4	no	—
251	#121	—	113	4	no	—
252	#121	C₂×D₁₁₃	1	2	yes	complemented
253	#121	C₂×D₁₁₃	1	4	yes	complemented
254	#120	—	113	4	no	—
255	#120	—	113	4	no	—
256	C₄×Q₈	—	113	2	no	—
257	C₄×Q₈	—	113	4	no	—
258	C₄×D₄	—	113	2	no	—
259	C₄×D₄	—	113	4	no	—
260	C₄×D₄	—	113	4	no	—
261	C₄×D₄	—	113	2	no	—
262	C₄×D₄	—	113	2	no	—
263	C₄×D₄	—	113	2	no	—
264	C₄×D₄	—	113	2	no	—
265	C₄×D₄	—	113	4	no	—
266	C₄×D₄	—	113	4	no	—
267	C₄×D₄	—	113	2	no	—
268	C₄×D₄	C₂×D₁₁₃	1	2	yes	complemented
269	#117	—	113	2	no	—
270	#117	—	113	1	no	—
271	#117	—	113	1	no	—
272	#117	C₂×D₁₁₃	1	1	yes	characteristic, complemented
273	C₂×C₂²⋊C₄	—	113	4	no	—
274	C₂×C₂²⋊C₄	—	113	4	no	—
275	C₂×C₄²	—	113	1	no	—
276	C₂×C₄²	—	113	1	no	—
277	C₂×C₄²	—	113	1	no	—
278	C₂⁴	—	113	4	no	—
279	#41	—	452	8	no	—
280	#41	—	452	8	no	—
281	#41	—	226	4	no	—
282	C₂×Q₈	—	113	1	no	—
283	C₂×Q₈	—	113	4	no	—
284	C₂×D₄	—	113	4	no	—
285	C₂×D₄	—	113	4	no	—
286	C₂×D₄	—	113	1	no	—
287	C₂×D₄	—	113	4	no	—
288	C₂×D₄	—	113	1	no	—
289	C₂×D₄	—	113	4	no	—
290	C₂×D₄	—	113	4	no	—
291	C₂×D₄	—	113	4	no	—
292	C₂×D₄	—	113	4	no	—
293	C₂×D₄	—	113	1	no	—
294	C₂×D₄	—	113	2	no	—
295	C₂×D₄	—	452	8	no	—
296	C₂×D₄	—	226	8	no	—
297	C₂×D₄	C₂²×D₁₁₃	1	2	yes	—
298	C₂×D₄	C₂²×D₁₁₃	1	4	yes	—
299	C₂×D₄	C₂²×D₁₁₃	1	4	yes	—
300	C₂²×C₄	—	113	1	no	—
301	C₂²×C₄	—	113	4	no	—
302	C₂²×C₄	—	113	2	no	—
303	C₂²×C₄	—	113	4	no	—
304	C₂²×C₄	—	113	4	no	—
305	C₂²×C₄	—	113	1	no	—
306	C₂²×C₄	—	113	2	no	—
307	C₂²×C₄	—	113	2	no	—
308	C₂²×C₄	C₂²×D₁₁₃	1	1	yes	characteristic
309	C₂²×C₄	C₂²×D₁₁₃	1	4	yes	—
310	C₄⋊C₄	—	113	2	no	—
311	C₄⋊C₄	—	113	2	no	—
312	C₄⋊C₄	—	113	2	no	—
313	C₄⋊C₄	—	113	4	no	—
314	C₄⋊C₄	—	113	4	no	—
315	C₄⋊C₄	C₂²×D₁₁₃	1	2	yes	—
316	C₄⋊C₄	C₂²×D₁₁₃	1	2	yes	—
317	C₄⋊C₄	C₂²×D₁₁₃	1	4	yes	—
318	C₂²⋊C₄	—	113	4	no	—
319	C₂²⋊C₄	—	113	4	no	—
320	C₂²⋊C₄	—	113	2	no	—
321	C₂²⋊C₄	—	113	4	no	—
322	C₂²⋊C₄	—	113	4	no	—
323	C₂²⋊C₄	—	113	4	no	—
324	C₂²⋊C₄	—	113	2	no	—
325	C₂²⋊C₄	—	113	4	no	—
326	C₂²⋊C₄	—	113	4	no	—
327	C₂²⋊C₄	C₂²×D₁₁₃	1	4	yes	—
328	C₂²⋊C₄	C₂²×D₁₁₃	1	2	yes	—
329	C₂²⋊C₄	C₂²×D₁₁₃	1	4	yes	—
330	C₄²	—	113	1	no	—
331	C₄²	—	113	1	no	—
332	C₄²	—	113	2	no	—
333	C₄²	—	113	2	no	—
334	C₄²	—	113	2	no	—
335	C₄²	—	113	4	no	—
336	C₄²	C₂²×D₁₁₃	1	1	yes	characteristic
337	C₄²	C₂²×D₁₁₃	1	1	yes	characteristic
338	C₂³	—	113	1	no	—
339	C₂³	—	113	4	no	—
340	C₂³	—	113	1	no	—
341	C₂³	—	452	4	no	—
342	C₂³	—	452	4	no	—
343	C₂³	—	226	8	no	—
344	C₂³	C₂³×D₁₁₃	1	4	yes	—
345	C₂³	C₂³×D₁₁₃	1	1	yes	characteristic
346	Q₈	—	226	8	no	—
347	Q₈	—	226	2	no	—
348	D₄	—	2	4	no	—
349	D₄	—	4	4	no	—
350	D₄	—	4	4	no	—
351	D₄	—	452	4	no	—
352	D₄	—	452	4	no	—
353	D₄	—	452	4	no	—
354	D₄	—	452	4	no	—
355	D₄	—	226	2	no	—
356	D₄	—	226	8	no	—
357	D₄	—	226	8	no	—
358	D₄	—	226	8	no	—
359	D₄	—	226	2	no	—
360	D₄	—	226	2	no	—
361	D₄	—	226	4	no	—
362	C₂×C₄	—	2	2	no	—
363	C₂×C₄	—	4	4	no	—
364	C₂×C₄	—	113	1	no	—
365	C₂×C₄	—	113	2	no	—
366	C₂×C₄	—	113	4	no	—
367	C₂×C₄	—	113	1	no	—
368	C₂×C₄	—	113	2	no	—
369	C₂×C₄	—	113	4	no	—
370	C₂×C₄	—	452	4	no	—
371	C₂×C₄	—	452	4	no	—
372	C₂×C₄	—	452	4	no	—
373	C₂×C₄	—	226	4	no	—
374	C₂×C₄	—	226	4	no	—
375	C₂×C₄	—	226	4	no	—
376	C₂×C₄	—	226	2	no	—
377	C₂×C₄	C₂³×D₁₁₃	1	1	yes	characteristic
378	C₂×C₄	C₂³×D₁₁₃	1	2	yes	—
379	C₂×C₄	C₂³×D₁₁₃	1	2	yes	—
380	C₂×C₄	C₂³×D₁₁₃	1	4	yes	—
381	C₂×C₄	C₂³×D₁₁₃	1	1	yes	characteristic
382	C₂²	—	2	1	no	—
383	C₂²	—	2	4	no	—
384	C₂²	—	2	4	no	—
385	C₂²	—	2	4	no	—
386	C₂²	—	2	2	no	—
387	C₂²	—	113	2	no	—
388	C₂²	—	904	8	no	—
389	C₂²	—	226	1	no	—
390	C₂²	—	226	4	no	—
391	C₂²	—	226	4	no	—
392	C₂²	—	226	4	no	—
393	C₂²	—	226	2	no	—
394	C₂²	—	226	2	no	—
395	C₂²	C₂⁴×D₁₁₃	1	1	yes	characteristic
396	C₄	—	2	1	no	—
397	C₄	—	2	2	no	—
398	C₄	—	2	4	no	—
399	C₄	—	2	2	no	—
400	C₄	—	113	2	no	—
401	C₄	—	113	4	no	—
402	C₄	—	226	1	no	—
403	C₄	—	226	2	no	—
404	C₄	—	226	4	no	—
405	C₄	#41×D₁₁₃	1	2	yes	—
406	C₂	—	4	4	no	—
407	C₂	—	4	1	no	—
408	C₂	—	452	4	no	—
409	C₂	—	452	1	no	—
410	C₂	—	226	2	no	—
411	C₂	C₂×#41×D₁₁₃	1	1	yes	characteristic
412	C₂	H(5,𝔽₂)×D₁₁₃	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	#3508
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. #20299332	C₂	semidirect
2. #20299266	C₂	semidirect
3. #20299240	C₂	semidirect
4. #20299237	C₂	semidirect
5. #20299204	C₂	semidirect
6. #20299203	C₂	semidirect
7. #20299202	C₂	semidirect
8. #20299164	C₂	semidirect
9. #20299154	C₂	semidirect
10. #20299145	C₂	semidirect
11. #20299143	C₂	semidirect
12. #127×D₁₁₃	C₂	semidirect
13. #20299070	C₂	semidirect
14. #20299066	C₂	semidirect
15. #540×C₁₁₃	C₂	semidirect
17. C₂×#14268647	C₂²	semidirect
18. C₂×#14268646	C₂²	semidirect
21. #16813621	C₂²	semidirect
25. #16813618	C₂²	semidirect
26. #16813614	C₂²	semidirect
27. #16813608	C₂²	semidirect
28. #16813608	C₂²	semidirect
29. #16813608	C₂²	semidirect
30. #16813607	C₂²	semidirect
31. #16813607	C₂²	semidirect
32. #16813603	C₂²	semidirect
34. #16813597	C₂²	semidirect
35. #16813597	C₂²	semidirect
36. #16813596	C₂²	semidirect
37. #16813595	C₂²	semidirect
38. #16813595	C₂²	semidirect
39. #16813594	C₂²	semidirect
40. #16813594	C₂²	semidirect
41. #16813593	C₂²	semidirect
44. #16813587	C₂²	semidirect
45. #16813587	C₂²	semidirect
46. C₄×D₄₅₂	C₂²	semidirect
47. D₄×Dic₁₁₃	C₂²	semidirect
49. #16813584	C₂²	semidirect
50. C₄×C₂²⋊D₁₁₃	C₂²	semidirect
51. C₄×C₂²⋊D₁₁₃	C₂²	semidirect
53. #16813582	C₂²	semidirect
54. #16813582	C₂²	semidirect
55. #16813582	C₂²	semidirect
58. #16813579	C₂²	semidirect
61. C₂×C₄×Dic₁₁₃	C₂²	semidirect
63. C₄²×D₁₁₃	C₂²	semidirect
65. #125×C₁₁₃	C₂²	semidirect
66. #123×C₁₁₃	C₂²	semidirect
67. #121×C₁₁₃	C₂²	semidirect
68. #121×C₁₁₃	C₂²	semidirect
69. C₄×D₄×C₁₁₃	C₂²	semidirect
70. #117×C₁₁₃	C₂²	semidirect
172. C₄×D₁₁₃	#41	semidirect
207. C₁₁₃	#3508	semidirect
215. #540	D₁₁₃	semidirect
235. #125	C₂×D₁₁₃	semidirect
242. #123	C₂×D₁₁₃	semidirect
252. #121	C₂×D₁₁₃	semidirect
253. #121	C₂×D₁₁₃	semidirect
268. C₄×D₄	C₂×D₁₁₃	semidirect
272. #117	C₂×D₁₁₃	semidirect

Maximal subgroups

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

subgroup	index
#20299332	2
#20299266	2
#20299240	2
#20299237	2
#20299204	2
#20299203	2
#20299202	2
#20299164	2
#20299154	2
#20299145	2
#20299143	2
#127×D₁₁₃	2
#20299070	2
#20299066	2
#540×C₁₁₃	2
#3508	113