Subgroups — #28404270

Order 14464.

1052 conjugacy classes of subgroups.

The subgroup lattice has 380 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20299285	C₂	1	4	yes	maximal, complemented
2	#20299283	C₂	1	4	yes	maximal, complemented
3	#20299274	C₂	1	4	yes	maximal, complemented
4	#20299271	C₂	1	4	yes	maximal, complemented
5	#20299224	C₂	1	1	yes	maximal, characteristic, complemented
6	#20299192	C₂	1	4	yes	maximal, complemented
7	#20299157	C₂	1	1	yes	maximal, characteristic
8	#20299125	C₂	1	4	yes	maximal, complemented
9	C₂×#16813605	C₂	1	1	yes	maximal, characteristic, complemented
10	#20299073	C₂	1	1	yes	maximal, characteristic, complemented
11	#20299071	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#16813581	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×#123×C₁₁₃	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂²×C₂²⋊D₁₁₃	C₂²	1	1	yes	characteristic
15	#16813617	C₂²	1	4	yes	complemented
16	#16813617	C₂²	1	4	yes	complemented
17	#16813615	C₂²	1	4	yes	complemented
18	#16813615	C₂²	1	4	yes	complemented
19	#16813613	C₂²	1	4	yes	complemented
20	#16813612	C₂²	1	4	yes	complemented
21	#16813612	C₂²	1	4	yes	complemented
22	#16813608	C₂²	1	4	yes	complemented
23	#16813606	C₂²	1	4	yes	complemented
24	#16813605	C₂²	1	4	yes	—
25	#16813605	C₂²	1	2	yes	—
26	#16813605	C₂²	1	2	yes	complemented
27	#16813605	C₂²	1	2	yes	complemented
28	#16813604	C₂²	1	4	yes	complemented
29	#16813603	C₂²	1	2	yes	—
30	#16813602	C₂²	1	4	yes	complemented
31	#16813601	C₂²	1	4	yes	complemented
32	#16813599	C₂²	1	4	yes	complemented
33	#16813599	C₂²	1	4	yes	complemented
34	#16813599	C₂²	1	4	yes	complemented
35	#16813594	C₂²	1	4	yes	—
36	#16813591	C₂²	1	2	yes	—
37	#16813590	C₂²	1	2	yes	—
38	#16813587	C₂²	1	4	yes	complemented
39	D₄×Dic₁₁₃	C₂²	1	4	yes	—
40	D₄×Dic₁₁₃	C₂²	1	4	yes	complemented
41	C₄×C₂²⋊D₁₁₃	C₂²	1	4	yes	—
42	#16813582	C₂²	1	4	yes	complemented
43	#16813582	C₂²	1	4	yes	complemented
44	#16813581	C₂²	1	4	yes	complemented
45	#16813581	C₂²	1	4	yes	complemented
46	#16813581	C₂²	1	2	yes	complemented
47	#16813580	C₂²	1	4	yes	complemented
48	#16813578	C₂²	1	4	yes	complemented
49	#16813578	C₂²	1	2	yes	complemented
50	C₂×C₄⋊Dic₁₁₃	C₂²	1	2	yes	complemented
51	C₂×#14268626	C₂²	1	2	yes	complemented
52	C₂×C₂²⋊Dic₁₁₃	C₂²	1	1	yes	characteristic
53	C₂×C₂²⋊Dic₁₁₃	C₂²	1	1	yes	characteristic
54	C₂×C₂²⋊Dic₁₁₃	C₂²	1	1	yes	characteristic
55	C₂×C₂²⋊Dic₁₁₃	C₂²	1	2	yes	complemented
56	C₂×#14268624	C₂²	1	2	yes	complemented
57	C₂²⋊C₄×D₁₁₃	C₂²	1	2	yes	complemented
58	C₂×C₄×Dic₁₁₃	C₂²	1	2	yes	complemented
59	C₂²×D₄×C₁₁₃	C₂²	1	1	yes	characteristic
60	C₂³×C₄×C₁₁₃	C₂²	1	1	yes	characteristic
61	#123×C₁₁₃	C₂²	1	4	yes	—
62	#123×C₁₁₃	C₂²	1	2	yes	complemented
63	#123×C₁₁₃	C₂²	1	2	yes	complemented
64	C₂×C₄⋊C₄×C₁₁₃	C₂²	1	2	yes	complemented
65	C₂×C₂²⋊C₄×C₁₁₃	C₂²	1	1	yes	characteristic
66	C₂×C₂²⋊C₄×C₁₁₃	C₂²	1	2	yes	complemented
67	C₂³×D₁₁₃	C₂³	1	1	yes	characteristic
68	C₂×Dic₂₂₆	C₂³	1	4	yes	—
69	C₂×C₂²⋊D₁₁₃	—	2	4	no	—
70	C₂×C₂²⋊D₁₁₃	C₂³	1	2	yes	—
71	C₂×C₂²⋊D₁₁₃	C₂³	1	2	yes	—
72	C₂×C₂²⋊D₁₁₃	C₂³	1	4	yes	—
73	C₂²×Dic₁₁₃	C₂³	1	1	yes	characteristic
74	C₂²×Dic₁₁₃	C₂³	1	2	yes	—
75	C₂²×Dic₁₁₃	C₂³	1	2	yes	—
76	C₂²×Dic₁₁₃	C₂³	1	2	yes	—
77	C₂²×Dic₁₁₃	C₂³	1	4	yes	—
78	C₂×C₄×D₁₁₃	C₂³	1	4	yes	—
79	C₄⋊Dic₁₁₃	C₂³	1	4	yes	—
80	C₄⋊Dic₁₁₃	C₂³	1	4	yes	—
81	C₄⋊Dic₁₁₃	C₂³	1	4	yes	—
82	C₄⋊Dic₁₁₃	C₂³	1	4	yes	—
83	#14268626	C₂³	1	4	yes	—
84	#14268626	C₂³	1	4	yes	—
85	#14268626	C₂³	1	4	yes	—
86	#14268626	C₂³	1	4	yes	—
87	#14268626	C₂³	1	4	yes	—
88	#14268626	C₂³	1	4	yes	—
89	C₂²⋊Dic₁₁₃	C₂³	1	2	yes	—
90	C₂²⋊Dic₁₁₃	C₂³	1	2	yes	—
91	C₂²⋊Dic₁₁₃	C₂³	1	2	yes	—
92	C₂²⋊Dic₁₁₃	C₂³	1	2	yes	—
93	C₂²⋊Dic₁₁₃	C₂³	1	2	yes	—
94	C₂²⋊Dic₁₁₃	C₂³	1	2	yes	—
95	C₂²⋊Dic₁₁₃	C₂³	1	4	yes	—
96	C₂²⋊Dic₁₁₃	C₂³	1	4	yes	—
97	#14268624	C₂³	1	4	yes	—
98	#14268624	C₂³	1	4	yes	—
99	#14268624	C₂³	1	4	yes	—
100	#14268624	C₂³	1	4	yes	—
101	C₄×Dic₁₁₃	C₂³	1	4	yes	—
102	C₄×Dic₁₁₃	C₂³	1	4	yes	—
103	C₄×Dic₁₁₃	C₂³	1	4	yes	—
104	C₄×Dic₁₁₃	C₂³	1	4	yes	—
105	C₂⁴×C₁₁₃	C₂³	1	1	yes	characteristic
106	C₂⁴×C₁₁₃	C₂³	1	1	yes	characteristic
107	C₂×D₄×C₁₁₃	—	2	4	no	—
108	C₂×D₄×C₁₁₃	C₂³	1	2	yes	—
109	C₂×D₄×C₁₁₃	C₂³	1	2	yes	—
110	C₂²×C₄×C₁₁₃	—	2	4	no	—
111	C₂²×C₄×C₁₁₃	C₂³	1	1	yes	characteristic
112	C₂²×C₄×C₁₁₃	C₂³	1	2	yes	—
113	C₂²×C₄×C₁₁₃	C₂³	1	1	yes	characteristic
114	C₂²×C₄×C₁₁₃	C₂³	1	2	yes	—
115	C₂²×C₄×C₁₁₃	C₂³	1	1	yes	characteristic
116	C₂²×C₄×C₁₁₃	C₂³	1	2	yes	—
117	C₄⋊C₄×C₁₁₃	C₂³	1	4	yes	—
118	C₄⋊C₄×C₁₁₃	C₂³	1	4	yes	—
119	C₂²⋊C₄×C₁₁₃	C₂³	1	2	yes	—
120	C₂²⋊C₄×C₁₁₃	C₂³	1	4	yes	—
121	C₂²⋊C₄×C₁₁₃	C₂³	1	2	yes	—
122	C₂²⋊C₄×C₁₁₃	C₂³	1	4	yes	—
123	C₂³×C₁₁₃	—	2	2	no	—
124	C₂³×C₁₁₃	—	4	2	no	—
125	C₂³×C₁₁₃	—	4	2	no	—
126	C₂³×C₁₁₃	#41	1	4	yes	—
127	C₂³×C₁₁₃	C₂⁴	1	2	yes	—
128	C₂³×C₁₁₃	C₂⁴	1	1	yes	characteristic
129	C₂³×C₁₁₃	C₂⁴	1	1	yes	characteristic
130	C₂³×C₁₁₃	C₂⁴	1	1	yes	characteristic
131	C₂²×D₁₁₃	—	2	2	no	—
132	C₂²×D₁₁₃	—	4	2	no	—
133	C₂²×D₁₁₃	C₂⁴	1	2	yes	—
134	D₄×C₁₁₃	—	2	4	no	—
135	D₄×C₁₁₃	—	2	4	no	—
136	C₂×C₄×C₁₁₃	—	2	4	no	—
137	C₂×C₄×C₁₁₃	—	2	4	no	—
138	C₂×C₄×C₁₁₃	—	2	2	no	—
139	C₂×C₄×C₁₁₃	—	2	2	no	—
140	C₂×C₄×C₁₁₃	—	2	2	no	—
141	C₂×C₄×C₁₁₃	—	4	2	no	—
142	C₂×C₄×C₁₁₃	C₂⁴	1	4	yes	—
143	C₂×C₄×C₁₁₃	C₂⁴	1	2	yes	—
144	C₂×C₄×C₁₁₃	C₂⁴	1	2	yes	—
145	C₂×C₄×C₁₁₃	C₂⁴	1	2	yes	—
146	C₂²⋊D₁₁₃	—	2	4	no	—
147	C₂²⋊D₁₁₃	—	2	4	no	—
148	C₂²⋊D₁₁₃	—	4	4	no	—
149	C₂×Dic₁₁₃	—	2	2	no	—
150	C₂×Dic₁₁₃	—	4	2	no	—
151	C₂×Dic₁₁₃	—	4	4	no	—
152	C₂×Dic₁₁₃	—	4	2	no	—
153	C₂×Dic₁₁₃	—	4	2	no	—
154	C₂×Dic₁₁₃	C₂⁴	1	4	yes	—
155	C₂×Dic₁₁₃	C₂⁴	1	4	yes	—
156	C₂×Dic₁₁₃	C₂⁴	1	2	yes	—
157	C₂×Dic₁₁₃	C₂⁴	1	4	yes	—
158	C₄×D₁₁₃	—	4	4	no	—
159	Dic₂₂₆	—	4	4	no	—
160	C₂²×C₁₁₃	—	2	2	no	—
161	C₂²×C₁₁₃	—	2	2	no	—
162	C₂²×C₁₁₃	—	2	2	no	—
163	C₂²×C₁₁₃	—	2	2	no	—
164	C₂²×C₁₁₃	—	2	4	no	—
165	C₂²×C₁₁₃	—	4	4	no	—
166	C₂²×C₁₁₃	—	8	2	no	—
167	C₂²×C₁₁₃	C₂×#41	1	2	yes	—
168	C₂²×C₁₁₃	C₂×#41	1	2	yes	—
169	C₂²×C₁₁₃	C₂×#41	1	2	yes	—
170	C₂²×C₁₁₃	C₂⁵	1	1	yes	characteristic
171	C₂×D₁₁₃	—	2	2	no	—
172	C₂×D₁₁₃	—	2	4	no	—
173	C₂×D₁₁₃	—	8	2	no	—
174	C₄×C₁₁₃	—	2	2	no	—
175	C₄×C₁₁₃	—	2	2	no	—
176	C₄×C₁₁₃	—	2	2	no	—
177	C₄×C₁₁₃	—	2	4	no	—
178	Dic₁₁₃	—	2	2	no	—
179	Dic₁₁₃	—	2	4	no	—
180	Dic₁₁₃	—	2	4	no	—
181	Dic₁₁₃	—	2	4	no	—
182	C₂×C₁₁₃	—	2	2	no	—
183	C₂×C₁₁₃	—	2	2	no	—
184	C₂×C₁₁₃	—	2	2	no	—
185	C₂×C₁₁₃	—	4	2	no	—
186	C₂×C₁₁₃	C₂²×#41	1	1	yes	characteristic
187	C₂×C₁₁₃	#585	1	2	yes	—
188	D₁₁₃	—	4	2	no	—
189	#3491	—	113	1	no	maximal, Sylow
190	C₁₁₃	#3491	1	1	yes	characteristic, complemented, Sylow
191	#552	—	113	4	no	—
192	#552	—	113	4	no	—
193	#551	—	113	4	no	—
194	#551	—	113	4	no	—
195	#543	—	113	1	no	—
196	#539	—	113	4	no	—
197	#534	—	113	1	no	—
198	#529	—	113	4	no	—
199	C₂×#123	—	113	1	no	—
200	C₂×#123	D₁₁₃	1	1	yes	characteristic, complemented
201	#518	—	113	1	no	—
202	#518	—	113	1	no	—
203	C₂×#117	—	113	1	no	—
204	C₂²×D₄	—	113	1	no	—
205	C₂²×D₄	C₂×D₁₁₃	1	1	yes	characteristic
206	C₂³×C₄	C₂×D₁₁₃	1	1	yes	characteristic
207	#126	—	113	4	no	—
208	#126	—	113	4	no	—
209	#126	—	113	4	no	—
210	#126	—	113	4	no	—
211	#125	—	113	4	no	—
212	#125	—	113	4	no	—
213	#125	—	113	4	no	—
214	#124	—	113	4	no	—
215	#123	—	113	2	no	—
216	#123	—	113	2	no	—
217	#123	—	113	2	no	—
218	#123	—	113	4	no	—
219	#123	—	113	2	no	—
220	#123	—	113	4	no	—
221	#123	—	113	4	no	—
222	#123	C₂×D₁₁₃	1	4	yes	—
223	#123	C₂×D₁₁₃	1	2	yes	complemented
224	#123	C₂×D₁₁₃	1	2	yes	complemented
225	C₂²⋊Q₈	—	113	4	no	—
226	C₂²⋊Q₈	—	113	4	no	—
227	C₂²⋊Q₈	—	113	4	no	—
228	C₂²⋊Q₈	—	113	4	no	—
229	C₂²⋊Q₈	—	113	4	no	—
230	#121	—	113	4	no	—
231	#120	—	113	2	no	—
232	#120	—	113	2	no	—
233	C₄×Q₈	—	113	4	no	—
234	C₄×D₄	—	113	4	no	—
235	C₄×D₄	—	113	4	no	—
236	C₄×D₄	—	113	4	no	—
237	C₄×D₄	—	113	4	no	—
238	C₄×D₄	—	113	4	no	—
239	#117	—	113	4	no	—
240	#117	—	113	4	no	—
241	#117	—	113	2	no	—
242	#117	—	113	4	no	—
243	#117	—	113	2	no	—
244	#117	—	113	4	no	—
245	C₂×C₄⋊C₄	—	113	2	no	—
246	C₂×C₄⋊C₄	—	113	2	no	—
247	C₂×C₄⋊C₄	C₂×D₁₁₃	1	2	yes	complemented
248	C₂×C₂²⋊C₄	—	113	1	no	—
249	C₂×C₂²⋊C₄	—	113	1	no	—
250	C₂×C₂²⋊C₄	—	113	1	no	—
251	C₂×C₂²⋊C₄	—	113	2	no	—
252	C₂×C₂²⋊C₄	—	113	2	no	—
253	C₂×C₂²⋊C₄	—	113	2	no	—
254	C₂×C₂²⋊C₄	C₂×D₁₁₃	1	1	yes	characteristic
255	C₂×C₂²⋊C₄	C₂×D₁₁₃	1	2	yes	complemented
256	C₂×C₄²	—	113	2	no	—
257	C₂⁴	—	113	1	no	—
258	C₂⁴	C₂²×D₁₁₃	1	1	yes	characteristic
259	C₂⁴	C₂²×D₁₁₃	1	1	yes	characteristic
260	C₂×Q₈	—	113	4	no	—
261	C₂×D₄	—	2	4	no	—
262	C₂×D₄	—	113	4	no	—
263	C₂×D₄	—	113	2	no	—
264	C₂×D₄	—	113	2	no	—
265	C₂×D₄	—	226	4	no	—
266	C₂×D₄	C₂²×D₁₁₃	1	2	yes	—
267	C₂×D₄	C₂²×D₁₁₃	1	2	yes	—
268	C₂²×C₄	—	2	4	no	—
269	C₂²×C₄	—	113	2	no	—
270	C₂²×C₄	—	113	2	no	—
271	C₂²×C₄	—	113	2	no	—
272	C₂²×C₄	—	113	4	no	—
273	C₂²×C₄	—	113	1	no	—
274	C₂²×C₄	—	113	4	no	—
275	C₂²×C₄	C₂²×D₁₁₃	1	1	yes	characteristic
276	C₂²×C₄	C₂²×D₁₁₃	1	2	yes	—
277	C₂²×C₄	C₂²×D₁₁₃	1	2	yes	—
278	C₂²×C₄	C₂²×D₁₁₃	1	1	yes	characteristic
279	C₂²×C₄	C₂²×D₁₁₃	1	1	yes	characteristic
280	C₂²×C₄	C₂²×D₁₁₃	1	2	yes	—
281	C₄⋊C₄	—	113	4	no	—
282	C₄⋊C₄	—	113	4	no	—
283	C₄⋊C₄	—	113	4	no	—
284	C₄⋊C₄	—	113	4	no	—
285	C₄⋊C₄	—	113	4	no	—
286	C₄⋊C₄	—	113	4	no	—
287	C₄⋊C₄	—	113	4	no	—
288	C₄⋊C₄	—	113	4	no	—
289	C₄⋊C₄	—	113	4	no	—
290	C₄⋊C₄	—	113	4	no	—
291	C₄⋊C₄	C₂²×D₁₁₃	1	4	yes	—
292	C₄⋊C₄	C₂²×D₁₁₃	1	4	yes	—
293	C₂²⋊C₄	—	113	2	no	—
294	C₂²⋊C₄	—	113	2	no	—
295	C₂²⋊C₄	—	113	2	no	—
296	C₂²⋊C₄	—	113	2	no	—
297	C₂²⋊C₄	—	113	2	no	—
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	4	no	—
305	C₂²⋊C₄	C₂²×D₁₁₃	1	2	yes	—
306	C₂²⋊C₄	C₂²×D₁₁₃	1	2	yes	—
307	C₂²⋊C₄	C₂²×D₁₁₃	1	4	yes	—
308	C₂²⋊C₄	C₂²×D₁₁₃	1	4	yes	—
309	C₄²	—	113	4	no	—
310	C₄²	—	113	4	no	—
311	C₄²	—	113	4	no	—
312	C₄²	—	113	4	no	—
313	C₂³	—	2	2	no	—
314	C₂³	—	4	2	no	—
315	C₂³	—	4	2	no	—
316	C₂³	—	113	2	no	—
317	C₂³	—	452	2	no	—
318	C₂³	—	226	2	no	—
319	C₂³	#14268646	1	4	yes	—
320	C₂³	C₂³×D₁₁₃	1	2	yes	—
321	C₂³	C₂³×D₁₁₃	1	1	yes	characteristic
322	C₂³	C₂³×D₁₁₃	1	1	yes	characteristic
323	C₂³	C₂³×D₁₁₃	1	1	yes	characteristic
324	Q₈	—	452	4	no	—
325	D₄	—	2	4	no	—
326	D₄	—	2	4	no	—
327	D₄	—	452	4	no	—
328	D₄	—	226	4	no	—
329	D₄	—	226	4	no	—
330	C₂×C₄	—	2	4	no	—
331	C₂×C₄	—	2	4	no	—
332	C₂×C₄	—	2	2	no	—
333	C₂×C₄	—	2	2	no	—
334	C₂×C₄	—	2	2	no	—
335	C₂×C₄	—	4	2	no	—
336	C₂×C₄	—	113	4	no	—
337	C₂×C₄	—	113	4	no	—
338	C₂×C₄	—	113	2	no	—
339	C₂×C₄	—	113	4	no	—
340	C₂×C₄	—	452	4	no	—
341	C₂×C₄	—	452	2	no	—
342	C₂×C₄	—	452	4	no	—
343	C₂×C₄	—	452	2	no	—
344	C₂×C₄	—	452	2	no	—
345	C₂×C₄	—	226	2	no	—
346	C₂×C₄	C₂³×D₁₁₃	1	2	yes	—
347	C₂×C₄	C₂³×D₁₁₃	1	2	yes	—
348	C₂×C₄	C₂³×D₁₁₃	1	4	yes	—
349	C₂×C₄	C₂³×D₁₁₃	1	2	yes	—
350	C₂²	—	2	2	no	—
351	C₂²	—	2	2	no	—
352	C₂²	—	2	2	no	—
353	C₂²	—	2	2	no	—
354	C₂²	—	2	4	no	—
355	C₂²	—	4	4	no	—
356	C₂²	—	8	2	no	—
357	C₂²	—	904	2	no	—
358	C₂²	—	226	2	no	—
359	C₂²	—	226	4	no	—
360	C₂²	C₂×#14268646	1	2	yes	—
361	C₂²	C₂×#14268646	1	2	yes	—
362	C₂²	C₂×#14268646	1	2	yes	—
363	C₂²	C₂⁴×D₁₁₃	1	1	yes	characteristic
364	C₄	—	2	2	no	—
365	C₄	—	2	2	no	—
366	C₄	—	2	2	no	—
367	C₄	—	2	4	no	—
368	C₄	—	226	2	no	—
369	C₄	—	226	4	no	—
370	C₄	—	226	4	no	—
371	C₄	—	226	4	no	—
372	C₂	—	2	2	no	—
373	C₂	—	2	2	no	—
374	C₂	—	2	2	no	—
375	C₂	—	4	2	no	—
376	C₂	—	452	2	no	—
377	C₂	C₂²×#14268646	1	1	yes	characteristic
378	C₂	#20299434	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₁₁₃
commutator, socle, cosocle	C₂²×C₁₁₃	C₂⁵
Fitting	C₂×#123×C₁₁₃	C₂
prime radical	#20299157	C₂
hypercenter	C₂×#123	D₁₁₃
hypocenter	C₁₁₃	#3491
LCS	G ▷ C₂²×C₁₁₃ ▷ C₁₁₃
UCS	C₁ ◁ C₂² ◁ C₂×#123

Complements

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

N	H ≅ G/N	type
1. #20299285	C₂	semidirect
2. #20299283	C₂	semidirect
3. #20299274	C₂	semidirect
4. #20299271	C₂	semidirect
5. #20299224	C₂	semidirect
6. #20299192	C₂	semidirect
8. #20299125	C₂	semidirect
9. C₂×#16813605	C₂	semidirect
10. #20299073	C₂	semidirect
11. #20299071	C₂	semidirect
12. C₂×#16813581	C₂	semidirect
13. C₂×#123×C₁₁₃	C₂	semidirect
15. #16813617	C₂²	semidirect
16. #16813617	C₂²	semidirect
17. #16813615	C₂²	semidirect
18. #16813615	C₂²	semidirect
19. #16813613	C₂²	semidirect
20. #16813612	C₂²	semidirect
21. #16813612	C₂²	semidirect
22. #16813608	C₂²	semidirect
23. #16813606	C₂²	semidirect
26. #16813605	C₂²	semidirect
27. #16813605	C₂²	semidirect
28. #16813604	C₂²	semidirect
30. #16813602	C₂²	semidirect
31. #16813601	C₂²	semidirect
32. #16813599	C₂²	semidirect
33. #16813599	C₂²	semidirect
34. #16813599	C₂²	semidirect
38. #16813587	C₂²	semidirect
40. D₄×Dic₁₁₃	C₂²	semidirect
42. #16813582	C₂²	semidirect
43. #16813582	C₂²	semidirect
44. #16813581	C₂²	semidirect
45. #16813581	C₂²	semidirect
46. #16813581	C₂²	semidirect
47. #16813580	C₂²	semidirect
48. #16813578	C₂²	semidirect
49. #16813578	C₂²	semidirect
50. C₂×C₄⋊Dic₁₁₃	C₂²	semidirect
51. C₂×#14268626	C₂²	semidirect
55. C₂×C₂²⋊Dic₁₁₃	C₂²	semidirect
56. C₂×#14268624	C₂²	semidirect
57. C₂²⋊C₄×D₁₁₃	C₂²	semidirect
58. C₂×C₄×Dic₁₁₃	C₂²	semidirect
62. #123×C₁₁₃	C₂²	semidirect
63. #123×C₁₁₃	C₂²	semidirect
64. C₂×C₄⋊C₄×C₁₁₃	C₂²	semidirect
66. C₂×C₂²⋊C₄×C₁₁₃	C₂²	semidirect
190. C₁₁₃	#3491	semidirect
200. C₂×#123	D₁₁₃	semidirect
223. #123	C₂×D₁₁₃	semidirect
224. #123	C₂×D₁₁₃	semidirect
247. C₂×C₄⋊C₄	C₂×D₁₁₃	semidirect
255. 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
#20299285	2
#20299283	2
#20299274	2
#20299271	2
#20299224	2
#20299192	2
#20299157	2
#20299125	2
C₂×#16813605	2
#20299073	2
#20299071	2
C₂×#16813581	2
C₂×#123×C₁₁₃	2
#3491	113