Subgroups — #28404217

Order 14464.

1560 conjugacy classes of subgroups.

The subgroup lattice has 390 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#16813668	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×#14268648	C₂	1	1	yes	maximal, characteristic, complemented
3	#20299251	C₂	1	4	yes	maximal, complemented
4	#20299250	C₂	1	4	yes	maximal, complemented
5	#20299241	C₂	1	4	yes	maximal, complemented
6	#20299239	C₂	1	4	yes	maximal, complemented
7	#20299172	C₂	1	1	yes	maximal, characteristic, complemented
8	#20299159	C₂	1	4	yes	maximal, complemented
9	#20299110	C₂	1	1	yes	maximal, characteristic, complemented
10	#20299105	C₂	1	1	yes	maximal, characteristic, complemented
11	#123×D₁₁₃	C₂	1	4	yes	maximal, complemented
12	#20299072	C₂	1	1	yes	maximal, characteristic, complemented
13	#536×C₁₁₃	C₂	1	1	yes	maximal, characteristic, complemented
14	#16813668	—	2	8	no	—
15	C₂×#14268648	—	2	8	no	—
16	C₂×#14268648	C₂²	1	4	yes	complemented
17	C₂×#14268648	C₂²	1	4	yes	complemented
18	C₂×#14268648	C₂²	1	2	yes	complemented
19	C₂×#14268647	C₂²	1	1	yes	characteristic
20	C₂×#14268647	C₂²	1	2	yes	complemented
21	C₂²×D₄₅₂	C₂²	1	1	yes	characteristic
22	C₂²×D₄₅₂	C₂²	1	2	yes	complemented
23	C₂²×D₄₅₂	C₂²	1	2	yes	complemented
24	C₂×D₄×D₁₁₃	C₂²	1	4	yes	—
25	C₂×D₄×D₁₁₃	C₂²	1	2	yes	complemented
26	C₂²×C₄×D₁₁₃	C₂²	1	2	yes	complemented
27	C₂²×C₄×D₁₁₃	C₂²	1	1	yes	characteristic, complemented
28	#16813620	C₂²	1	2	yes	complemented
29	#16813611	C₂²	1	2	yes	complemented
30	#16813607	C₂²	1	8	yes	complemented
31	#16813607	C₂²	1	8	yes	complemented
32	#16813606	C₂²	1	2	yes	complemented
33	#16813605	C₂²	1	4	yes	complemented
34	#16813604	C₂²	1	8	yes	complemented
35	#16813603	C₂²	1	2	yes	complemented
36	#16813602	C₂²	1	2	yes	complemented
37	#16813598	C₂²	1	2	yes	complemented
38	#16813598	C₂²	1	4	yes	complemented
39	#16813597	C₂²	1	2	yes	complemented
40	#16813597	C₂²	1	8	yes	complemented
41	#16813595	C₂²	1	8	yes	complemented
42	#16813593	C₂²	1	2	yes	complemented
43	#16813592	C₂²	1	2	yes	complemented
44	#16813592	C₂²	1	8	yes	complemented
45	#16813590	C₂²	1	2	yes	complemented
46	C₄×D₄₅₂	C₂²	1	4	yes	complemented
47	C₄×D₄₅₂	C₂²	1	4	yes	complemented
48	#16813584	C₂²	1	4	yes	complemented
49	C₄×C₂²⋊D₁₁₃	C₂²	1	4	yes	complemented
50	#16813581	C₂²	1	1	yes	characteristic, complemented
51	C₄⋊C₄×D₁₁₃	C₂²	1	8	yes	complemented
52	C₂²⋊C₄×D₁₁₃	C₂²	1	4	yes	complemented
53	C₂²⋊C₄×D₁₁₃	C₂²	1	8	yes	complemented
54	C₂×#41×C₁₁₃	C₂²	1	1	yes	characteristic
55	C₂²×Q₈×C₁₁₃	C₂²	1	1	yes	characteristic, complemented
56	C₄⋊Q₈×C₁₁₃	C₂²	1	2	yes	complemented
57	#124×C₁₁₃	C₂²	1	2	yes	complemented
58	#123×C₁₁₃	C₂²	1	4	yes	complemented
59	C₂²⋊Q₈×C₁₁₃	C₂²	1	4	yes	complemented
60	#117×C₁₁₃	C₂²	1	1	yes	characteristic, complemented
61	C₂³×D₁₁₃	C₂³	1	4	yes	—
62	C₂³×D₁₁₃	C₂³	1	1	yes	characteristic
63	C₂³×D₁₁₃	C₂³	1	2	yes	—
64	#14268648	—	2	16	no	—
65	#14268648	—	2	16	no	—
66	#14268648	—	2	8	no	—
67	#14268647	—	2	4	no	—
68	#14268647	—	2	8	no	—
69	C₂×Dic₂₂₆	C₂³	1	1	yes	characteristic
70	C₂×D₄₅₂	—	2	8	no	—
71	C₂×D₄₅₂	—	2	8	no	—
72	C₂×D₄₅₂	D₄	1	8	yes	complemented
73	C₂×D₄₅₂	C₂³	1	8	yes	—
74	C₂×D₄₅₂	C₂³	1	4	yes	—
75	C₂×D₄₅₂	C₂³	1	1	yes	characteristic
76	C₂×D₄₅₂	C₂³	1	4	yes	—
77	C₂×D₄₅₂	C₂³	1	2	yes	—
78	C₂×D₄₅₂	C₂³	1	2	yes	—
79	C₂×C₂²⋊D₁₁₃	C₂³	1	2	yes	—
80	C₂×C₂²⋊D₁₁₃	C₂³	1	4	yes	—
81	C₂×C₂²⋊D₁₁₃	C₂³	1	4	yes	—
82	D₄×D₁₁₃	—	2	16	no	—
83	D₄×D₁₁₃	—	2	8	no	—
84	C₂²×Dic₁₁₃	C₂³	1	1	yes	characteristic
85	C₂×C₄×D₁₁₃	—	2	8	no	—
86	C₂×C₄×D₁₁₃	—	2	4	no	—
87	C₂×C₄×D₁₁₃	C₂³	1	8	yes	—
88	C₂×C₄×D₁₁₃	C₂³	1	4	yes	—
89	C₂×C₄×D₁₁₃	C₂³	1	2	yes	—
90	C₂×C₄×D₁₁₃	C₂³	1	2	yes	—
91	C₂×C₄×D₁₁₃	C₂³	1	2	yes	—
92	C₂×C₄×D₁₁₃	C₂³	1	8	yes	—
93	C₄⋊Dic₁₁₃	C₂³	1	4	yes	—
94	C₄⋊Dic₁₁₃	C₂³	1	2	yes	—
95	#14268626	C₂³	1	4	yes	—
96	#14268626	C₂³	1	8	yes	—
97	C₂²⋊Dic₁₁₃	C₂³	1	2	yes	—
98	C₂²⋊Dic₁₁₃	C₂³	1	4	yes	—
99	#14268624	C₂³	1	4	yes	—
100	#14268624	C₂³	1	8	yes	—
101	#14268624	C₂³	1	8	yes	—
102	#14268624	C₂³	1	4	yes	—
103	#14268624	C₂³	1	4	yes	—
104	C₄×Dic₁₁₃	C₂³	1	2	yes	—
105	#41×C₁₁₃	—	2	4	no	—
106	C₂×Q₈×C₁₁₃	—	2	4	no	—
107	C₂×Q₈×C₁₁₃	C₂³	1	2	yes	—
108	C₂×Q₈×C₁₁₃	C₂³	1	1	yes	characteristic
109	C₂×Q₈×C₁₁₃	C₂³	1	2	yes	—
110	C₂×D₄×C₁₁₃	C₂³	1	2	yes	—
111	C₂×D₄×C₁₁₃	C₂³	1	1	yes	characteristic
112	C₂²×C₄×C₁₁₃	C₂³	1	2	yes	—
113	C₂²×C₄×C₁₁₃	C₂³	1	2	yes	—
114	C₂²×C₄×C₁₁₃	C₂³	1	1	yes	characteristic
115	C₄⋊C₄×C₁₁₃	C₂³	1	8	yes	—
116	C₄⋊C₄×C₁₁₃	C₂³	1	2	yes	—
117	C₂²⋊C₄×C₁₁₃	C₂³	1	2	yes	—
118	C₂²⋊C₄×C₁₁₃	C₂³	1	8	yes	—
119	C₄²×C₁₁₃	C₂³	1	2	yes	—
120	C₂³×C₁₁₃	C₂⁴	1	2	yes	—
121	C₂³×C₁₁₃	C₂⁴	1	1	yes	characteristic
122	C₂²×D₁₁₃	—	2	2	no	—
123	C₂²×D₁₁₃	—	2	8	no	—
124	C₂²×D₁₁₃	—	4	4	no	—
125	C₂²×D₁₁₃	—	4	2	no	—
126	C₂²×D₁₁₃	—	4	8	no	—
127	C₂²×D₁₁₃	C₂×D₄	1	8	yes	—
128	C₂²×D₁₁₃	C₂⁴	1	2	yes	—
129	C₂²×D₁₁₃	C₂⁴	1	2	yes	—
130	C₂²×D₁₁₃	C₂⁴	1	4	yes	—
131	Q₈×C₁₁₃	—	2	4	no	—
132	Q₈×C₁₁₃	—	2	4	no	—
133	Q₈×C₁₁₃	—	2	2	no	—
134	D₄×C₁₁₃	—	2	4	no	—
135	D₄×C₁₁₃	—	2	2	no	—
136	C₂×C₄×C₁₁₃	—	2	4	no	—
137	C₂×C₄×C₁₁₃	—	2	4	no	—
138	C₂×C₄×C₁₁₃	C₂×D₄	1	4	yes	—
139	C₂×C₄×C₁₁₃	C₂⁴	1	4	yes	—
140	C₂×C₄×C₁₁₃	C₂⁴	1	4	yes	—
141	C₂×C₄×C₁₁₃	C₂⁴	1	2	yes	—
142	C₂×C₄×C₁₁₃	C₂⁴	1	1	yes	characteristic
143	C₂×C₄×C₁₁₃	C₂⁴	1	1	yes	characteristic
144	C₂²⋊D₁₁₃	—	2	4	no	—
145	C₂²⋊D₁₁₃	—	2	8	no	—
146	C₂²⋊D₁₁₃	—	4	4	no	—
147	C₂×Dic₁₁₃	—	2	2	no	—
148	C₂×Dic₁₁₃	C₂⁴	1	4	yes	—
149	C₂×Dic₁₁₃	C₂⁴	1	2	yes	—
150	C₂×Dic₁₁₃	C₂⁴	1	2	yes	—
151	D₄₅₂	—	2	8	no	—
152	D₄₅₂	—	2	16	no	—
153	D₄₅₂	—	2	2	no	—
154	D₄₅₂	—	4	4	no	—
155	D₄₅₂	C₂×D₄	1	8	yes	—
156	D₄₅₂	C₂×D₄	1	8	yes	—
157	C₄×D₁₁₃	—	2	16	no	—
158	C₄×D₁₁₃	—	2	8	no	—
159	C₄×D₁₁₃	—	2	4	no	—
160	C₄×D₁₁₃	—	2	4	no	—
161	C₄×D₁₁₃	—	2	4	no	—
162	C₄×D₁₁₃	—	4	8	no	—
163	Dic₂₂₆	—	2	2	no	—
164	C₂²×C₁₁₃	—	2	2	no	—
165	C₂²×C₁₁₃	—	2	2	no	—
166	C₂²×C₁₁₃	—	2	4	no	—
167	C₂²×C₁₁₃	C₂²×D₄	1	2	yes	—
168	C₂²×C₁₁₃	C₂⁵	1	1	yes	characteristic
169	C₂×D₁₁₃	—	2	8	no	—
170	C₂×D₁₁₃	—	2	2	no	—
171	C₂×D₁₁₃	—	2	2	no	—
172	C₂×D₁₁₃	—	2	2	no	—
173	C₂×D₁₁₃	—	2	4	no	—
174	C₂×D₁₁₃	—	2	2	no	—
175	C₂×D₁₁₃	—	4	8	no	—
176	C₂×D₁₁₃	—	4	4	no	—
177	C₂×D₁₁₃	—	8	8	no	—
178	C₂×D₁₁₃	C₂²×D₄	1	8	yes	—
179	C₄×C₁₁₃	—	2	2	no	—
180	C₄×C₁₁₃	—	2	4	no	—
181	C₄×C₁₁₃	—	2	4	no	—
182	C₄×C₁₁₃	C₂²×D₄	1	2	yes	—
183	C₄×C₁₁₃	C₂²×D₄	1	2	yes	—
184	Dic₁₁₃	—	2	2	no	—
185	Dic₁₁₃	—	2	2	no	—
186	Dic₁₁₃	—	2	4	no	—
187	C₂×C₁₁₃	—	2	2	no	—
188	C₂×C₁₁₃	—	4	2	no	—
189	C₂×C₁₁₃	C₂³×D₄	1	1	yes	characteristic
190	C₂×C₁₁₃	#585	1	2	yes	—
191	D₁₁₃	—	2	8	no	—
192	D₁₁₃	—	4	2	no	—
193	D₁₁₃	—	4	2	no	—
194	#3485	—	113	1	no	maximal, Sylow
195	C₁₁₃	#3485	1	1	yes	characteristic, complemented, Sylow
196	C₂×H(5,𝔽₂)	—	113	1	no	—
197	C₂²×#41	—	113	1	no	—
198	#547	—	113	4	no	—
199	#547	—	113	4	no	—
200	#546	—	113	4	no	—
201	#546	—	113	4	no	—
202	#536	—	113	1	no	—
203	#536	D₁₁₃	1	1	yes	characteristic, complemented
204	#534	—	113	4	no	—
205	#525	—	113	1	no	—
206	#525	—	113	1	no	—
207	C₂×#123	—	113	4	no	—
208	#518	—	113	1	no	—
209	H(5,𝔽₂)	—	226	8	no	—
210	C₂×#41	—	113	4	no	—
211	C₂×#41	—	113	4	no	—
212	C₂×#41	—	113	2	no	—
213	C₂×#41	—	113	1	no	—
214	C₂×#41	—	113	2	no	—
215	C₂×#41	—	226	8	no	—
216	C₂×#41	C₂×D₁₁₃	1	1	yes	characteristic
217	C₂²×Q₈	C₂×D₁₁₃	1	1	yes	characteristic, complemented
218	C₂²×D₄	—	113	4	no	—
219	C₂²×D₄	—	113	2	no	—
220	C₂²×D₄	—	113	1	no	—
221	C₂²×D₄	—	113	2	no	—
222	C₂²×D₄	—	113	2	no	—
223	C₂³×C₄	—	113	2	no	—
224	C₂³×C₄	—	113	1	no	—
225	C₄⋊Q₈	—	113	2	no	—
226	C₄⋊Q₈	C₂×D₁₁₃	1	2	yes	complemented
227	#124	—	113	2	no	—
228	#124	C₂×D₁₁₃	1	2	yes	complemented
229	#123	—	113	2	no	—
230	#123	—	113	4	no	—
231	#123	—	113	8	no	—
232	#123	—	113	8	no	—
233	#123	—	113	2	no	—
234	#123	—	113	8	no	—
235	#123	C₂×D₁₁₃	1	4	yes	complemented
236	C₂²⋊Q₈	—	113	2	no	—
237	C₂²⋊Q₈	—	113	4	no	—
238	C₂²⋊Q₈	—	113	2	no	—
239	C₂²⋊Q₈	C₂×D₁₁₃	1	4	yes	complemented
240	#121	—	113	2	no	—
241	#121	—	113	2	no	—
242	#121	—	113	8	no	—
243	#121	—	113	8	no	—
244	#120	—	113	2	no	—
245	#120	—	113	2	no	—
246	#120	—	113	8	no	—
247	C₄×D₄	—	113	4	no	—
248	C₄×D₄	—	113	4	no	—
249	C₄×D₄	—	113	4	no	—
250	C₄×D₄	—	113	4	no	—
251	#117	—	113	1	no	—
252	#117	C₂×D₁₁₃	1	1	yes	characteristic, complemented
253	C₂×C₄⋊C₄	—	113	8	no	—
254	C₂×C₂²⋊C₄	—	113	4	no	—
255	C₂×C₂²⋊C₄	—	113	8	no	—
256	C₂⁴	—	113	2	no	—
257	C₂⁴	—	113	4	no	—
258	C₂⁴	—	113	1	no	—
259	#41	—	2	4	no	—
260	#41	—	226	8	no	—
261	#41	—	226	16	no	—
262	#41	—	226	16	no	—
263	#41	—	226	8	no	—
264	#41	—	226	4	no	—
265	C₂×Q₈	—	2	4	no	—
266	C₂×Q₈	—	113	1	no	—
267	C₂×Q₈	C₂²×D₁₁₃	1	2	yes	—
268	C₂×Q₈	C₂²×D₁₁₃	1	1	yes	characteristic
269	C₂×Q₈	C₂²×D₁₁₃	1	2	yes	—
270	C₂×D₄	—	113	4	no	—
271	C₂×D₄	—	113	2	no	—
272	C₂×D₄	—	113	4	no	—
273	C₂×D₄	—	113	8	no	—
274	C₂×D₄	—	113	2	no	—
275	C₂×D₄	—	113	2	no	—
276	C₂×D₄	—	113	4	no	—
277	C₂×D₄	—	113	8	no	—
278	C₂×D₄	—	113	4	no	—
279	C₂×D₄	—	113	1	no	—
280	C₂×D₄	—	226	8	no	—
281	C₂×D₄	—	226	8	no	—
282	C₂×D₄	—	226	8	no	—
283	C₂×D₄	—	226	16	no	—
284	C₂×D₄	C₂²×D₁₁₃	1	2	yes	—
285	C₂×D₄	C₂²×D₁₁₃	1	1	yes	characteristic
286	C₂²×C₄	—	113	1	no	—
287	C₂²×C₄	—	113	8	no	—
288	C₂²×C₄	—	113	8	no	—
289	C₂²×C₄	—	113	4	no	—
290	C₂²×C₄	—	113	2	no	—
291	C₂²×C₄	—	113	2	no	—
292	C₂²×C₄	—	113	2	no	—
293	C₂²×C₄	—	226	8	no	—
294	C₂²×C₄	—	226	4	no	—
295	C₂²×C₄	C₂²×D₁₁₃	1	2	yes	—
296	C₂²×C₄	C₂²×D₁₁₃	1	2	yes	—
297	C₂²×C₄	C₂²×D₁₁₃	1	1	yes	characteristic
298	C₄⋊C₄	—	113	4	no	—
299	C₄⋊C₄	—	113	4	no	—
300	C₄⋊C₄	—	113	8	no	—
301	C₄⋊C₄	—	113	2	no	—
302	C₄⋊C₄	C₂²×D₁₁₃	1	8	yes	—
303	C₄⋊C₄	C₂²×D₁₁₃	1	2	yes	—
304	C₂²⋊C₄	—	113	2	no	—
305	C₂²⋊C₄	—	113	4	no	—
306	C₂²⋊C₄	—	113	4	no	—
307	C₂²⋊C₄	—	113	8	no	—
308	C₂²⋊C₄	—	113	8	no	—
309	C₂²⋊C₄	—	113	4	no	—
310	C₂²⋊C₄	—	113	4	no	—
311	C₂²⋊C₄	C₂²×D₁₁₃	1	2	yes	—
312	C₂²⋊C₄	C₂²×D₁₁₃	1	8	yes	—
313	C₄²	—	113	2	no	—
314	C₄²	C₂²×D₁₁₃	1	2	yes	—
315	C₂³	—	113	8	no	—
316	C₂³	—	113	4	no	—
317	C₂³	—	113	2	no	—
318	C₂³	—	113	2	no	—
319	C₂³	—	452	8	no	—
320	C₂³	—	452	2	no	—
321	C₂³	—	452	4	no	—
322	C₂³	—	226	8	no	—
323	C₂³	—	226	2	no	—
324	C₂³	C₂³×D₁₁₃	1	2	yes	—
325	C₂³	C₂³×D₁₁₃	1	1	yes	characteristic
326	Q₈	—	2	4	no	—
327	Q₈	—	2	4	no	—
328	Q₈	—	2	2	no	—
329	Q₈	—	226	2	no	—
330	D₄	—	2	4	no	—
331	D₄	—	2	2	no	—
332	D₄	—	113	8	no	—
333	D₄	—	113	8	no	—
334	D₄	—	452	4	no	—
335	D₄	—	452	4	no	—
336	D₄	—	226	8	no	—
337	D₄	—	226	16	no	—
338	D₄	—	226	8	no	—
339	D₄	—	226	4	no	—
340	D₄	—	226	2	no	—
341	C₂×C₄	—	2	4	no	—
342	C₂×C₄	—	2	4	no	—
343	C₂×C₄	—	113	4	no	—
344	C₂×C₄	—	113	2	no	—
345	C₂×C₄	—	113	2	no	—
346	C₂×C₄	—	452	8	no	—
347	C₂×C₄	—	226	16	no	—
348	C₂×C₄	—	226	8	no	—
349	C₂×C₄	—	226	2	no	—
350	C₂×C₄	—	226	4	no	—
351	C₂×C₄	—	226	4	no	—
352	C₂×C₄	—	226	4	no	—
353	C₂×C₄	D₄×D₁₁₃	1	4	yes	—
354	C₂×C₄	C₂³×D₁₁₃	1	4	yes	—
355	C₂×C₄	C₂³×D₁₁₃	1	4	yes	—
356	C₂×C₄	C₂³×D₁₁₃	1	2	yes	—
357	C₂×C₄	C₂³×D₁₁₃	1	1	yes	characteristic
358	C₂×C₄	C₂³×D₁₁₃	1	1	yes	characteristic
359	C₂²	—	2	2	no	—
360	C₂²	—	2	2	no	—
361	C₂²	—	2	4	no	—
362	C₂²	—	113	8	no	—
363	C₂²	—	904	8	no	—
364	C₂²	—	452	4	no	—
365	C₂²	—	452	8	no	—
366	C₂²	—	226	2	no	—
367	C₂²	—	226	2	no	—
368	C₂²	—	226	2	no	—
369	C₂²	—	226	2	no	—
370	C₂²	—	226	4	no	—
371	C₂²	—	226	8	no	—
372	C₂²	C₂×D₄×D₁₁₃	1	2	yes	—
373	C₂²	C₂⁴×D₁₁₃	1	1	yes	characteristic
374	C₄	—	2	2	no	—
375	C₄	—	2	4	no	—
376	C₄	—	2	4	no	—
377	C₄	—	226	2	no	—
378	C₄	—	226	2	no	—
379	C₄	—	226	4	no	—
380	C₄	C₂×D₄×D₁₁₃	1	2	yes	—
381	C₄	C₂×D₄×D₁₁₃	1	2	yes	—
382	C₂	—	2	2	no	—
383	C₂	—	4	2	no	—
384	C₂	—	452	2	no	—
385	C₂	—	452	2	no	—
386	C₂	—	226	8	no	—
387	C₂	C₂²×D₄×D₁₁₃	1	1	yes	characteristic
388	C₂	#20299435	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₁₁₃
commutator, socle, cosocle	C₂²×C₁₁₃	C₂⁵
Fitting	#536×C₁₁₃	C₂
hypercenter	#536	D₁₁₃
hypocenter	C₁₁₃	#3485
LCS	G ▷ C₂²×C₁₁₃ ▷ C₁₁₃
UCS	C₁ ◁ C₂² ◁ #536

Complements

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

N	H ≅ G/N	type
1. C₂×#16813668	C₂	semidirect
2. C₂²×#14268648	C₂	semidirect
3. #20299251	C₂	semidirect
4. #20299250	C₂	semidirect
5. #20299241	C₂	semidirect
6. #20299239	C₂	semidirect
7. #20299172	C₂	semidirect
8. #20299159	C₂	semidirect
9. #20299110	C₂	semidirect
10. #20299105	C₂	semidirect
11. #123×D₁₁₃	C₂	semidirect
12. #20299072	C₂	semidirect
13. #536×C₁₁₃	C₂	semidirect
16. C₂×#14268648	C₂²	semidirect
17. C₂×#14268648	C₂²	semidirect
18. C₂×#14268648	C₂²	semidirect
20. C₂×#14268647	C₂²	semidirect
22. C₂²×D₄₅₂	C₂²	semidirect
23. C₂²×D₄₅₂	C₂²	semidirect
25. C₂×D₄×D₁₁₃	C₂²	semidirect
26. C₂²×C₄×D₁₁₃	C₂²	semidirect
27. C₂²×C₄×D₁₁₃	C₂²	semidirect
28. #16813620	C₂²	semidirect
29. #16813611	C₂²	semidirect
30. #16813607	C₂²	semidirect
31. #16813607	C₂²	semidirect
32. #16813606	C₂²	semidirect
33. #16813605	C₂²	semidirect
34. #16813604	C₂²	semidirect
35. #16813603	C₂²	semidirect
36. #16813602	C₂²	semidirect
37. #16813598	C₂²	semidirect
38. #16813598	C₂²	semidirect
39. #16813597	C₂²	semidirect
40. #16813597	C₂²	semidirect
41. #16813595	C₂²	semidirect
42. #16813593	C₂²	semidirect
43. #16813592	C₂²	semidirect
44. #16813592	C₂²	semidirect
45. #16813590	C₂²	semidirect
46. C₄×D₄₅₂	C₂²	semidirect
47. C₄×D₄₅₂	C₂²	semidirect
48. #16813584	C₂²	semidirect
49. C₄×C₂²⋊D₁₁₃	C₂²	semidirect
50. #16813581	C₂²	semidirect
51. C₄⋊C₄×D₁₁₃	C₂²	semidirect
52. C₂²⋊C₄×D₁₁₃	C₂²	semidirect
53. C₂²⋊C₄×D₁₁₃	C₂²	semidirect
55. C₂²×Q₈×C₁₁₃	C₂²	semidirect
56. C₄⋊Q₈×C₁₁₃	C₂²	semidirect
57. #124×C₁₁₃	C₂²	semidirect
58. #123×C₁₁₃	C₂²	semidirect
59. C₂²⋊Q₈×C₁₁₃	C₂²	semidirect
60. #117×C₁₁₃	C₂²	semidirect
72. C₂×D₄₅₂	D₄	semidirect
195. C₁₁₃	#3485	semidirect
203. #536	D₁₁₃	semidirect
217. C₂²×Q₈	C₂×D₁₁₃	semidirect
226. C₄⋊Q₈	C₂×D₁₁₃	semidirect
228. #124	C₂×D₁₁₃	semidirect
235. #123	C₂×D₁₁₃	semidirect
239. C₂²⋊Q₈	C₂×D₁₁₃	semidirect
252. #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
C₂×#16813668	2
C₂²×#14268648	2
#20299251	2
#20299250	2
#20299241	2
#20299239	2
#20299172	2
#20299159	2
#20299110	2
#20299105	2
#123×D₁₁₃	2
#20299072	2
#536×C₁₁₃	2
#3485	113