Subgroups — #28403959

Order 14464.

1040 conjugacy classes of subgroups.

The subgroup lattice has 406 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20299220	C₂	1	2	yes	maximal, complemented
2	#20299213	C₂	1	2	yes	maximal, complemented
3	#20299206	C₂	1	2	yes	maximal, complemented
4	#20299199	C₂	1	2	yes	maximal, complemented
5	#20299190	C₂	1	4	yes	maximal, complemented
6	#20299181	C₂	1	4	yes	maximal, complemented
7	#20299151	C₂	1	1	yes	maximal, characteristic, complemented
8	#20299144	C₂	1	1	yes	maximal, characteristic, complemented
9	#20299132	C₂	1	4	yes	maximal, complemented
10	#20299126	C₂	1	4	yes	maximal, complemented
11	#20299110	C₂	1	1	yes	maximal, characteristic, complemented
12	#20299105	C₂	1	1	yes	maximal, characteristic, complemented
13	C₄×#14268647	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×#16813579	C₂	1	1	yes	maximal, characteristic, complemented
15	C₄×#41×C₁₁₃	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#14268647	C₂²	1	1	yes	characteristic
17	C₂²×C₄×D₁₁₃	C₂²	1	1	yes	characteristic
18	#16813621	C₂²	1	2	yes	complemented
19	#16813620	C₂²	1	1	yes	characteristic, complemented
20	#16813618	C₂²	1	1	yes	characteristic, complemented
21	#16813617	C₂²	1	4	yes	—
22	#16813616	C₂²	1	4	yes	—
23	#16813616	C₂²	1	4	yes	complemented
24	#16813615	C₂²	1	4	yes	complemented
25	#16813614	C₂²	1	4	yes	complemented
26	#16813613	C₂²	1	2	yes	complemented
27	#16813612	C₂²	1	4	yes	complemented
28	#16813611	C₂²	1	1	yes	characteristic, complemented
29	#16813610	C₂²	1	4	yes	—
30	#16813609	C₂²	1	1	yes	characteristic, complemented
31	#16813608	C₂²	1	4	yes	—
32	#16813607	C₂²	1	4	yes	—
33	#16813606	C₂²	1	2	yes	—
34	#16813605	C₂²	1	4	yes	—
35	#16813605	C₂²	1	4	yes	complemented
36	#16813604	C₂²	1	4	yes	complemented
37	#16813603	C₂²	1	2	yes	—
38	#16813602	C₂²	1	2	yes	—
39	#16813601	C₂²	1	4	yes	complemented
40	#16813600	C₂²	1	4	yes	complemented
41	#16813599	C₂²	1	4	yes	—
42	#16813598	C₂²	1	2	yes	—
43	#16813597	C₂²	1	2	yes	—
44	#16813596	C₂²	1	4	yes	—
45	#16813595	C₂²	1	4	yes	—
46	#16813594	C₂²	1	4	yes	—
47	#16813593	C₂²	1	2	yes	—
48	#16813592	C₂²	1	2	yes	—
49	#16813590	C₂²	1	2	yes	—
50	C₄×Dic₂₂₆	C₂²	1	2	yes	complemented
51	C₄×Dic₂₂₆	C₂²	1	4	yes	complemented
52	C₄×D₄₅₂	C₂²	1	4	yes	—
53	C₄×D₄₅₂	C₂²	1	2	yes	complemented
54	C₄×C₂²⋊D₁₁₃	C₂²	1	4	yes	—
55	C₄×C₂²⋊D₁₁₃	C₂²	1	4	yes	—
56	C₄×C₂²⋊D₁₁₃	C₂²	1	4	yes	complemented
57	#16813581	C₂²	1	1	yes	characteristic
58	#16813579	C₂²	1	2	yes	—
59	#16813579	C₂²	1	2	yes	—
60	#16813579	C₂²	1	2	yes	—
61	#16813579	C₂²	1	2	yes	—
62	#16813579	C₂²	1	2	yes	complemented
63	C₂×#14268626	C₂²	1	2	yes	—
64	C₂×#14268624	C₂²	1	2	yes	—
65	C₂×C₄×Dic₁₁₃	C₂²	1	1	yes	characteristic
66	C₄²×D₁₁₃	C₂²	1	2	yes	complemented
67	C₂×#41×C₁₁₃	C₂²	1	1	yes	characteristic
68	C₄×Q₈×C₁₁₃	C₂²	1	2	yes	complemented
69	C₄×D₄×C₁₁₃	C₂²	1	4	yes	—
70	C₄×D₄×C₁₁₃	C₂²	1	2	yes	complemented
71	#117×C₁₁₃	C₂²	1	1	yes	characteristic
72	#117×C₁₁₃	C₂²	1	2	yes	complemented
73	C₂×C₄²×C₁₁₃	C₂²	1	1	yes	characteristic
74	C₂×C₄²×C₁₁₃	C₂²	1	2	yes	complemented
75	C₂³×D₁₁₃	C₂³	1	1	yes	characteristic
76	#14268647	—	2	4	no	—
77	C₂×Dic₂₂₆	C₂³	1	1	yes	characteristic
78	C₂×Dic₂₂₆	C₂³	1	4	yes	—
79	C₂×D₄₅₂	C₂³	1	1	yes	characteristic
80	C₂×D₄₅₂	C₂³	1	4	yes	—
81	C₂×C₂²⋊D₁₁₃	C₂³	1	2	yes	—
82	C₂×C₂²⋊D₁₁₃	C₂³	1	4	yes	—
83	C₂×C₂²⋊D₁₁₃	C₂³	1	4	yes	—
84	C₂²×Dic₁₁₃	C₂³	1	1	yes	characteristic
85	C₂²×Dic₁₁₃	C₂³	1	2	yes	—
86	C₂×C₄×D₁₁₃	—	2	4	no	—
87	C₂×C₄×D₁₁₃	C₂³	1	2	yes	—
88	C₂×C₄×D₁₁₃	C₂³	1	2	yes	—
89	C₂×C₄×D₁₁₃	C₂³	1	2	yes	—
90	C₂×C₄×D₁₁₃	C₂³	1	4	yes	—
91	C₄⋊Dic₁₁₃	C₂³	1	2	yes	—
92	C₄⋊Dic₁₁₃	C₂³	1	4	yes	—
93	C₄⋊Dic₁₁₃	C₂³	1	4	yes	—
94	#14268626	C₂³	1	2	yes	—
95	#14268626	C₂³	1	2	yes	—
96	#14268626	C₂³	1	2	yes	—
97	#14268626	C₂³	1	2	yes	—
98	#14268626	C₂³	1	4	yes	—
99	#14268626	C₂³	1	4	yes	—
100	#14268626	C₂³	1	4	yes	—
101	#14268626	C₂³	1	4	yes	—
102	#14268626	C₂³	1	4	yes	—
103	C₂²⋊Dic₁₁₃	C₂³	1	2	yes	—
104	C₂²⋊Dic₁₁₃	C₂³	1	4	yes	—
105	C₂²⋊Dic₁₁₃	C₂³	1	4	yes	—
106	#14268624	C₂³	1	2	yes	—
107	#14268624	C₂³	1	2	yes	—
108	#14268624	C₂³	1	2	yes	—
109	#14268624	C₂³	1	2	yes	—
110	#14268624	C₂³	1	4	yes	—
111	#14268624	C₂³	1	4	yes	—
112	#14268624	C₂³	1	4	yes	—
113	#14268624	C₂³	1	4	yes	—
114	#14268624	C₂³	1	4	yes	—
115	C₄×Dic₁₁₃	C₂³	1	2	yes	—
116	C₄×Dic₁₁₃	C₂³	1	4	yes	—
117	C₄×Dic₁₁₃	C₂³	1	2	yes	—
118	C₄×Dic₁₁₃	C₂³	1	1	yes	characteristic
119	C₄×Dic₁₁₃	C₂³	1	1	yes	characteristic
120	#41×C₁₁₃	—	2	4	no	—
121	C₂×Q₈×C₁₁₃	C₂³	1	1	yes	characteristic
122	C₂×D₄×C₁₁₃	C₂³	1	2	yes	—
123	C₂×D₄×C₁₁₃	C₂³	1	1	yes	characteristic
124	C₂²×C₄×C₁₁₃	C₂³	1	2	yes	—
125	C₂²×C₄×C₁₁₃	C₂³	1	2	yes	—
126	C₂²×C₄×C₁₁₃	C₂³	1	4	yes	—
127	C₂²×C₄×C₁₁₃	C₂³	1	1	yes	characteristic
128	C₄⋊C₄×C₁₁₃	C₂³	1	2	yes	—
129	C₄⋊C₄×C₁₁₃	C₂³	1	4	yes	—
130	C₂²⋊C₄×C₁₁₃	C₂³	1	2	yes	—
131	C₂²⋊C₄×C₁₁₃	C₂³	1	4	yes	—
132	C₄²×C₁₁₃	C₂³	1	1	yes	characteristic
133	C₄²×C₁₁₃	C₂³	1	1	yes	characteristic
134	C₄²×C₁₁₃	C₂³	1	2	yes	—
135	C₄²×C₁₁₃	C₂³	1	2	yes	—
136	C₄²×C₁₁₃	C₂³	1	4	yes	—
137	C₂³×C₁₁₃	C₂⁴	1	2	yes	—
138	C₂³×C₁₁₃	C₂⁴	1	1	yes	characteristic
139	C₂²×D₁₁₃	—	2	2	no	—
140	C₂²×D₁₁₃	—	4	2	no	—
141	C₂²×D₁₁₃	C₂⁴	1	2	yes	—
142	C₂²×D₁₁₃	C₂⁴	1	2	yes	—
143	Q₈×C₁₁₃	—	2	2	no	—
144	D₄×C₁₁₃	—	2	4	no	—
145	D₄×C₁₁₃	—	2	2	no	—
146	C₂×C₄×C₁₁₃	—	2	4	no	—
147	C₂×C₄×C₁₁₃	—	4	4	no	—
148	C₂×C₄×C₁₁₃	—	4	2	no	—
149	C₂×C₄×C₁₁₃	#41	1	4	yes	—
150	C₂×C₄×C₁₁₃	C₂⁴	1	2	yes	—
151	C₂×C₄×C₁₁₃	C₂⁴	1	2	yes	—
152	C₂×C₄×C₁₁₃	C₂⁴	1	4	yes	—
153	C₂×C₄×C₁₁₃	C₂⁴	1	2	yes	—
154	C₂×C₄×C₁₁₃	C₂⁴	1	1	yes	characteristic
155	C₂×C₄×C₁₁₃	C₂⁴	1	1	yes	characteristic
156	C₂²⋊D₁₁₃	—	2	4	no	—
157	C₂²⋊D₁₁₃	—	4	4	no	—
158	C₂²⋊D₁₁₃	—	4	4	no	—
159	C₂×Dic₁₁₃	—	2	2	no	—
160	C₂×Dic₁₁₃	—	4	2	no	—
161	C₂×Dic₁₁₃	C₂⁴	1	2	yes	—
162	C₂×Dic₁₁₃	C₂⁴	1	2	yes	—
163	C₂×Dic₁₁₃	C₂⁴	1	4	yes	—
164	C₂×Dic₁₁₃	C₂⁴	1	2	yes	—
165	C₂×Dic₁₁₃	C₂⁴	1	2	yes	—
166	D₄₅₂	—	2	2	no	—
167	D₄₅₂	—	4	4	no	—
168	C₄×D₁₁₃	—	2	4	no	—
169	C₄×D₁₁₃	—	2	4	no	—
170	C₄×D₁₁₃	—	2	4	no	—
171	C₄×D₁₁₃	—	4	4	no	—
172	Dic₂₂₆	—	2	2	no	—
173	Dic₂₂₆	—	4	4	no	—
174	C₂²×C₁₁₃	—	2	2	no	—
175	C₂²×C₁₁₃	—	2	2	no	—
176	C₂²×C₁₁₃	—	2	4	no	—
177	C₂²×C₁₁₃	C₂×#41	1	2	yes	—
178	C₂²×C₁₁₃	C₂⁵	1	1	yes	characteristic
179	C₂×D₁₁₃	—	2	2	no	—
180	C₂×D₁₁₃	—	2	2	no	—
181	C₂×D₁₁₃	—	2	4	no	—
182	C₂×D₁₁₃	—	2	2	no	—
183	C₂×D₁₁₃	—	2	2	no	—
184	C₂×D₁₁₃	—	4	4	no	—
185	C₄×C₁₁₃	—	2	2	no	—
186	C₄×C₁₁₃	—	2	4	no	—
187	C₄×C₁₁₃	—	2	2	no	—
188	C₄×C₁₁₃	—	2	2	no	—
189	C₄×C₁₁₃	C₂×#41	1	2	yes	—
190	C₄×C₁₁₃	C₂×#41	1	2	yes	—
191	Dic₁₁₃	—	2	2	no	—
192	Dic₁₁₃	—	2	2	no	—
193	Dic₁₁₃	—	2	2	no	—
194	Dic₁₁₃	—	2	4	no	—
195	Dic₁₁₃	—	2	2	no	—
196	C₂×C₁₁₃	—	2	2	no	—
197	C₂×C₁₁₃	—	4	2	no	—
198	C₂×C₁₁₃	C₂²×#41	1	1	yes	characteristic
199	C₂×C₁₁₃	#585	1	2	yes	—
200	D₁₁₃	—	4	2	no	—
201	D₁₁₃	—	4	2	no	—
202	#3455	—	113	1	no	maximal, Sylow
203	C₁₁₃	#3455	1	1	yes	characteristic, complemented, Sylow
204	#542	—	113	2	no	—
205	#542	—	113	2	no	—
206	#541	—	113	2	no	—
207	#540	—	113	2	no	—
208	#539	—	113	4	no	—
209	#538	—	113	4	no	—
210	#533	—	113	1	no	—
211	#532	—	113	1	no	—
212	#529	—	113	4	no	—
213	#529	—	113	4	no	—
214	#525	—	113	1	no	—
215	#525	—	113	1	no	—
216	C₄×#41	—	113	1	no	—
217	C₄×#41	D₁₁₃	1	1	yes	characteristic, complemented
218	C₂×#117	—	113	1	no	—
219	C₂×#41	—	113	1	no	—
220	C₂×#41	C₂×D₁₁₃	1	1	yes	characteristic
221	C₂³×C₄	—	113	1	no	—
222	C₄⋊Q₈	—	113	1	no	—
223	C₄⋊Q₈	—	113	2	no	—
224	#127	—	113	1	no	—
225	#126	—	113	4	no	—
226	#126	—	113	4	no	—
227	#126	—	113	4	no	—
228	#126	—	113	4	no	—
229	#125	—	113	4	no	—
230	#125	—	113	2	no	—
231	#125	—	113	4	no	—
232	#124	—	113	1	no	—
233	#124	—	113	1	no	—
234	#124	—	113	4	no	—
235	#124	—	113	4	no	—
236	#123	—	113	2	no	—
237	#123	—	113	4	no	—
238	#123	—	113	4	no	—
239	#123	—	113	4	no	—
240	#123	—	113	2	no	—
241	#123	—	113	4	no	—
242	C₂²⋊Q₈	—	113	2	no	—
243	C₂²⋊Q₈	—	113	4	no	—
244	C₂²⋊Q₈	—	113	2	no	—
245	C₂²⋊Q₈	—	113	4	no	—
246	C₂²⋊Q₈	—	113	4	no	—
247	#121	—	113	2	no	—
248	#121	—	113	4	no	—
249	#121	—	113	4	no	—
250	#121	—	113	2	no	—
251	#121	—	113	4	no	—
252	#120	—	113	2	no	—
253	#120	—	113	2	no	—
254	C₄×Q₈	—	113	2	no	—
255	C₄×Q₈	—	113	4	no	—
256	C₄×Q₈	C₂×D₁₁₃	1	2	yes	complemented
257	C₄×D₄	—	113	4	no	—
258	C₄×D₄	—	113	4	no	—
259	C₄×D₄	—	113	4	no	—
260	C₄×D₄	—	113	2	no	—
261	C₄×D₄	—	113	4	no	—
262	C₄×D₄	C₂×D₁₁₃	1	4	yes	—
263	C₄×D₄	C₂×D₁₁₃	1	2	yes	complemented
264	#117	—	113	1	no	—
265	#117	—	113	2	no	—
266	#117	—	113	2	no	—
267	#117	—	113	2	no	—
268	#117	—	113	2	no	—
269	#117	—	113	2	no	—
270	#117	C₂×D₁₁₃	1	1	yes	characteristic
271	#117	C₂×D₁₁₃	1	2	yes	complemented
272	C₂×C₄⋊C₄	—	113	2	no	—
273	C₂×C₂²⋊C₄	—	113	2	no	—
274	C₂×C₄²	—	113	1	no	—
275	C₂×C₄²	—	113	2	no	—
276	C₂×C₄²	C₂×D₁₁₃	1	1	yes	characteristic
277	C₂×C₄²	C₂×D₁₁₃	1	2	yes	complemented
278	C₂⁴	—	113	1	no	—
279	#41	—	2	4	no	—
280	#41	—	226	4	no	—
281	C₂×Q₈	—	113	4	no	—
282	C₂×Q₈	—	113	1	no	—
283	C₂×Q₈	C₂²×D₁₁₃	1	1	yes	characteristic
284	C₂×D₄	—	113	4	no	—
285	C₂×D₄	—	113	4	no	—
286	C₂×D₄	—	113	2	no	—
287	C₂×D₄	—	113	4	no	—
288	C₂×D₄	—	113	1	no	—
289	C₂×D₄	C₂²×D₁₁₃	1	2	yes	—
290	C₂×D₄	C₂²×D₁₁₃	1	1	yes	characteristic
291	C₂²×C₄	—	113	2	no	—
292	C₂²×C₄	—	113	1	no	—
293	C₂²×C₄	—	113	4	no	—
294	C₂²×C₄	—	113	2	no	—
295	C₂²×C₄	—	113	2	no	—
296	C₂²×C₄	—	113	2	no	—
297	C₂²×C₄	—	226	4	no	—
298	C₂²×C₄	C₂²×D₁₁₃	1	2	yes	—
299	C₂²×C₄	C₂²×D₁₁₃	1	2	yes	—
300	C₂²×C₄	C₂²×D₁₁₃	1	4	yes	—
301	C₂²×C₄	C₂²×D₁₁₃	1	1	yes	characteristic
302	C₄⋊C₄	—	113	2	no	—
303	C₄⋊C₄	—	113	2	no	—
304	C₄⋊C₄	—	113	2	no	—
305	C₄⋊C₄	—	113	2	no	—
306	C₄⋊C₄	—	113	2	no	—
307	C₄⋊C₄	—	113	4	no	—
308	C₄⋊C₄	—	113	4	no	—
309	C₄⋊C₄	—	113	4	no	—
310	C₄⋊C₄	—	113	4	no	—
311	C₄⋊C₄	—	113	4	no	—
312	C₄⋊C₄	—	113	4	no	—
313	C₄⋊C₄	—	113	4	no	—
314	C₄⋊C₄	C₂²×D₁₁₃	1	2	yes	—
315	C₄⋊C₄	C₂²×D₁₁₃	1	4	yes	—
316	C₂²⋊C₄	—	113	2	no	—
317	C₂²⋊C₄	—	113	4	no	—
318	C₂²⋊C₄	—	113	4	no	—
319	C₂²⋊C₄	—	113	2	no	—
320	C₂²⋊C₄	—	113	2	no	—
321	C₂²⋊C₄	—	113	2	no	—
322	C₂²⋊C₄	—	113	2	no	—
323	C₂²⋊C₄	—	113	4	no	—
324	C₂²⋊C₄	—	113	4	no	—
325	C₂²⋊C₄	—	113	4	no	—
326	C₂²⋊C₄	—	113	4	no	—
327	C₂²⋊C₄	—	113	4	no	—
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	4	no	—
333	C₄²	—	113	2	no	—
334	C₄²	—	113	2	no	—
335	C₄²	C₂²×D₁₁₃	1	2	yes	—
336	C₄²	C₂²×D₁₁₃	1	4	yes	—
337	C₄²	C₂²×D₁₁₃	1	1	yes	characteristic
338	C₄²	C₂²×D₁₁₃	1	1	yes	characteristic
339	C₄²	C₂²×D₁₁₃	1	2	yes	—
340	C₂³	—	113	2	no	—
341	C₂³	—	113	2	no	—
342	C₂³	—	452	2	no	—
343	C₂³	—	226	2	no	—
344	C₂³	C₂³×D₁₁₃	1	2	yes	—
345	C₂³	C₂³×D₁₁₃	1	1	yes	characteristic
346	Q₈	—	2	2	no	—
347	Q₈	—	452	4	no	—
348	Q₈	—	226	2	no	—
349	D₄	—	2	4	no	—
350	D₄	—	2	2	no	—
351	D₄	—	452	4	no	—
352	D₄	—	452	4	no	—
353	D₄	—	452	4	no	—
354	D₄	—	226	4	no	—
355	D₄	—	226	2	no	—
356	C₂×C₄	—	2	4	no	—
357	C₂×C₄	—	4	2	no	—
358	C₂×C₄	—	4	4	no	—
359	C₂×C₄	—	113	2	no	—
360	C₂×C₄	—	113	2	no	—
361	C₂×C₄	—	113	4	no	—
362	C₂×C₄	—	113	2	no	—
363	C₂×C₄	—	113	2	no	—
364	C₂×C₄	—	452	4	no	—
365	C₂×C₄	—	452	2	no	—
366	C₂×C₄	—	226	2	no	—
367	C₂×C₄	—	226	4	no	—
368	C₂×C₄	—	226	4	no	—
369	C₂×C₄	—	226	4	no	—
370	C₂×C₄	#14268647	1	4	yes	—
371	C₂×C₄	C₂³×D₁₁₃	1	2	yes	—
372	C₂×C₄	C₂³×D₁₁₃	1	2	yes	—
373	C₂×C₄	C₂³×D₁₁₃	1	2	yes	—
374	C₂×C₄	C₂³×D₁₁₃	1	4	yes	—
375	C₂×C₄	C₂³×D₁₁₃	1	1	yes	characteristic
376	C₂×C₄	C₂³×D₁₁₃	1	1	yes	characteristic
377	C₂²	—	2	2	no	—
378	C₂²	—	2	2	no	—
379	C₂²	—	2	4	no	—
380	C₂²	—	452	4	no	—
381	C₂²	—	226	2	no	—
382	C₂²	—	226	2	no	—
383	C₂²	—	226	4	no	—
384	C₂²	—	226	2	no	—
385	C₂²	—	226	2	no	—
386	C₂²	C₂×#14268647	1	2	yes	—
387	C₂²	C₂⁴×D₁₁₃	1	1	yes	characteristic
388	C₄	—	2	2	no	—
389	C₄	—	2	2	no	—
390	C₄	—	2	2	no	—
391	C₄	—	2	4	no	—
392	C₄	—	226	2	no	—
393	C₄	—	226	2	no	—
394	C₄	—	226	2	no	—
395	C₄	—	226	4	no	—
396	C₄	—	226	2	no	—
397	C₄	C₂×#14268647	1	2	yes	—
398	C₄	C₂×#14268647	1	2	yes	—
399	C₂	—	2	2	no	—
400	C₂	—	4	2	no	—
401	C₂	—	452	2	no	—
402	C₂	—	452	2	no	—
403	C₂	C₂²×#14268647	1	1	yes	characteristic
404	C₂	#20299434	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	C₂³×D₁₁₃
commutator, socle, cosocle	C₂²×C₁₁₃	C₂⁵
Frattini	C₂²	C₂⁴×D₁₁₃
Fitting	C₄×#41×C₁₁₃	C₂
hypercenter	C₄×#41	D₁₁₃
hypocenter	C₁₁₃	#3455
LCS	G ▷ C₂²×C₁₁₃ ▷ C₁₁₃
UCS	C₁ ◁ C₂×C₄ ◁ C₄×#41

Complements

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

N	H ≅ G/N	type
1. #20299220	C₂	semidirect
2. #20299213	C₂	semidirect
3. #20299206	C₂	semidirect
4. #20299199	C₂	semidirect
5. #20299190	C₂	semidirect
6. #20299181	C₂	semidirect
7. #20299151	C₂	semidirect
8. #20299144	C₂	semidirect
9. #20299132	C₂	semidirect
10. #20299126	C₂	semidirect
11. #20299110	C₂	semidirect
12. #20299105	C₂	semidirect
13. C₄×#14268647	C₂	semidirect
14. C₂×#16813579	C₂	semidirect
15. C₄×#41×C₁₁₃	C₂	semidirect
18. #16813621	C₂²	semidirect
19. #16813620	C₂²	semidirect
20. #16813618	C₂²	semidirect
23. #16813616	C₂²	semidirect
24. #16813615	C₂²	semidirect
25. #16813614	C₂²	semidirect
26. #16813613	C₂²	semidirect
27. #16813612	C₂²	semidirect
28. #16813611	C₂²	semidirect
30. #16813609	C₂²	semidirect
35. #16813605	C₂²	semidirect
36. #16813604	C₂²	semidirect
39. #16813601	C₂²	semidirect
40. #16813600	C₂²	semidirect
50. C₄×Dic₂₂₆	C₂²	semidirect
51. C₄×Dic₂₂₆	C₂²	semidirect
53. C₄×D₄₅₂	C₂²	semidirect
56. C₄×C₂²⋊D₁₁₃	C₂²	semidirect
62. #16813579	C₂²	semidirect
66. C₄²×D₁₁₃	C₂²	semidirect
68. C₄×Q₈×C₁₁₃	C₂²	semidirect
70. C₄×D₄×C₁₁₃	C₂²	semidirect
72. #117×C₁₁₃	C₂²	semidirect
74. C₂×C₄²×C₁₁₃	C₂²	semidirect
203. C₁₁₃	#3455	semidirect
217. C₄×#41	D₁₁₃	semidirect
256. C₄×Q₈	C₂×D₁₁₃	semidirect
263. C₄×D₄	C₂×D₁₁₃	semidirect
271. #117	C₂×D₁₁₃	semidirect
277. C₂×C₄²	C₂×D₁₁₃	semidirect

Maximal subgroups

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

subgroup	index
#20299220	2
#20299213	2
#20299206	2
#20299199	2
#20299190	2
#20299181	2
#20299151	2
#20299144	2
#20299132	2
#20299126	2
#20299110	2
#20299105	2
C₄×#14268647	2
C₂×#16813579	2
C₄×#41×C₁₁₃	2
#3455	113