Subgroups — #28404336

Order 14464.

1660 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	C₂×#16813668	C₂	1	2	yes	maximal, complemented
2	#20299253	C₂	1	2	yes	maximal, complemented
3	#20299251	C₂	1	2	yes	maximal, complemented
4	#20299244	C₂	1	4	yes	maximal, complemented
5	#20299241	C₂	1	4	yes	maximal, complemented
6	D₄×D₄₅₂	C₂	1	2	yes	maximal, complemented
7	#20299233	C₂	1	2	yes	maximal, complemented
8	#20299176	C₂	1	2	yes	maximal, complemented
9	#20299156	C₂	1	4	yes	maximal, complemented
10	#20299148	C₂	1	1	yes	maximal, characteristic, complemented
11	#121×D₁₁₃	C₂	1	4	yes	maximal, complemented
12	C₂×C₄×D₄₅₂	C₂	1	1	yes	maximal, characteristic, complemented
13	#532×C₁₁₃	C₂	1	1	yes	maximal, characteristic, complemented
14	#16813668	—	2	16	no	—
15	C₂×#14268648	C₂²	1	4	yes	complemented
16	C₂×#14268647	C₂²	1	2	yes	complemented
17	C₂×#14268647	C₂²	1	4	yes	complemented
18	C₂²×D₄₅₂	C₂²	1	1	yes	characteristic
19	C₂²×D₄₅₂	C₂²	1	4	yes	complemented
20	C₂×D₄×D₁₁₃	C₂²	1	8	yes	complemented
21	C₂×D₄×D₁₁₃	C₂²	1	4	yes	complemented
22	C₂×D₄×D₁₁₃	C₂²	1	4	yes	complemented
23	C₂²×C₄×D₁₁₃	C₂²	1	2	yes	complemented
24	#16813622	C₂²	1	1	yes	characteristic, complemented
25	#16813619	C₂²	1	1	yes	characteristic, complemented
26	#16813610	C₂²	1	2	yes	complemented
27	#16813607	C₂²	1	8	yes	complemented
28	#16813604	C₂²	1	8	yes	complemented
29	#16813601	C₂²	1	4	yes	complemented
30	#16813598	C₂²	1	4	yes	complemented
31	#16813597	C₂²	1	4	yes	complemented
32	#16813596	C₂²	1	2	yes	complemented
33	#16813596	C₂²	1	2	yes	complemented
34	#16813596	C₂²	1	4	yes	complemented
35	#16813595	C₂²	1	8	yes	complemented
36	#16813594	C₂²	1	8	yes	complemented
37	#16813593	C₂²	1	4	yes	complemented
38	#16813593	C₂²	1	4	yes	complemented
39	#16813592	C₂²	1	8	yes	complemented
40	#16813590	C₂²	1	8	yes	complemented
41	C₄×D₄₅₂	C₂²	1	2	yes	complemented
42	C₄×D₄₅₂	C₂²	1	2	yes	complemented
43	C₄×D₄₅₂	C₂²	1	2	yes	complemented
44	C₄×D₄₅₂	C₂²	1	2	yes	complemented
45	C₄×D₄₅₂	C₂²	1	2	yes	complemented
46	C₄×D₄₅₂	C₂²	1	2	yes	complemented
47	C₂×C₄⋊Dic₁₁₃	C₂²	1	1	yes	characteristic, complemented
48	C₄⋊C₄×D₁₁₃	C₂²	1	4	yes	complemented
49	C₂×#14268624	C₂²	1	2	yes	complemented
50	C₂²⋊C₄×D₁₁₃	C₂²	1	8	yes	complemented
51	C₂×#41×C₁₁₃	C₂²	1	2	yes	complemented
52	C₄⋊Q₈×C₁₁₃	C₂²	1	1	yes	characteristic, complemented
53	#127×C₁₁₃	C₂²	1	1	yes	characteristic, complemented
54	#124×C₁₁₃	C₂²	1	2	yes	complemented
55	#121×C₁₁₃	C₂²	1	2	yes	complemented
56	#121×C₁₁₃	C₂²	1	2	yes	complemented
57	C₄×D₄×C₁₁₃	C₂²	1	2	yes	complemented
58	C₄×D₄×C₁₁₃	C₂²	1	2	yes	complemented
59	C₂×C₄²×C₁₁₃	C₂²	1	1	yes	characteristic, complemented
60	C₂³×D₁₁₃	C₂³	1	8	yes	—
61	C₂³×D₁₁₃	C₂³	1	2	yes	—
62	#14268648	—	2	16	no	—
63	#14268647	—	2	8	no	—
64	#14268647	—	2	16	no	—
65	C₂×Dic₂₂₆	C₂³	1	2	yes	—
66	C₂×D₄₅₂	—	2	16	no	—
67	C₂×D₄₅₂	D₄	1	8	yes	complemented
68	C₂×D₄₅₂	C₂³	1	2	yes	—
69	C₂×D₄₅₂	C₂³	1	8	yes	—
70	C₂×D₄₅₂	C₂³	1	2	yes	—
71	C₂×D₄₅₂	C₂³	1	2	yes	—
72	C₂×D₄₅₂	C₂³	1	2	yes	—
73	C₂×D₄₅₂	C₂³	1	2	yes	—
74	C₂×C₂²⋊D₁₁₃	C₂³	1	8	yes	—
75	C₂×C₂²⋊D₁₁₃	C₂³	1	4	yes	—
76	C₂×C₂²⋊D₁₁₃	C₂³	1	8	yes	—
77	D₄×D₁₁₃	—	2	32	no	—
78	D₄×D₁₁₃	—	2	16	no	—
79	D₄×D₁₁₃	—	4	8	no	—
80	C₂²×Dic₁₁₃	C₂³	1	2	yes	—
81	C₂×C₄×D₁₁₃	—	4	4	no	—
82	C₂×C₄×D₁₁₃	C₂³	1	8	yes	—
83	C₂×C₄×D₁₁₃	C₂³	1	4	yes	—
84	C₂×C₄×D₁₁₃	C₂³	1	4	yes	—
85	C₂×C₄×D₁₁₃	C₂³	1	4	yes	—
86	C₄⋊Dic₁₁₃	C₂³	1	2	yes	—
87	C₄⋊Dic₁₁₃	C₂³	1	2	yes	—
88	C₄⋊Dic₁₁₃	C₂³	1	2	yes	—
89	C₄⋊Dic₁₁₃	C₂³	1	2	yes	—
90	#14268626	C₂³	1	8	yes	—
91	C₂²⋊Dic₁₁₃	C₂³	1	8	yes	—
92	#14268624	C₂³	1	4	yes	—
93	#14268624	C₂³	1	8	yes	—
94	#14268624	C₂³	1	4	yes	—
95	#14268624	C₂³	1	4	yes	—
96	#14268624	C₂³	1	4	yes	—
97	#41×C₁₁₃	—	2	8	no	—
98	C₂×Q₈×C₁₁₃	C₂³	1	2	yes	—
99	C₂×D₄×C₁₁₃	C₂³	1	2	yes	—
100	C₂×D₄×C₁₁₃	C₂³	1	2	yes	—
101	C₂×D₄×C₁₁₃	C₂³	1	4	yes	—
102	C₂×D₄×C₁₁₃	C₂³	1	2	yes	—
103	C₂²×C₄×C₁₁₃	C₂³	1	1	yes	characteristic
104	C₂²×C₄×C₁₁₃	C₂³	1	4	yes	—
105	C₂²×C₄×C₁₁₃	C₂³	1	1	yes	characteristic
106	C₂²×C₄×C₁₁₃	C₂³	1	1	yes	characteristic
107	C₄⋊C₄×C₁₁₃	C₂³	1	2	yes	—
108	C₄⋊C₄×C₁₁₃	C₂³	1	2	yes	—
109	C₂²⋊C₄×C₁₁₃	C₂³	1	4	yes	—
110	C₂²⋊C₄×C₁₁₃	C₂³	1	4	yes	—
111	C₄²×C₁₁₃	C₂³	1	1	yes	characteristic
112	C₄²×C₁₁₃	C₂³	1	1	yes	characteristic
113	C₄²×C₁₁₃	C₂³	1	1	yes	characteristic
114	C₄²×C₁₁₃	C₂³	1	1	yes	characteristic
115	C₂³×C₁₁₃	C₂⁴	1	4	yes	—
116	C₂³×C₁₁₃	C₂⁴	1	1	yes	characteristic
117	C₂²×D₁₁₃	—	2	16	no	—
118	C₂²×D₁₁₃	—	4	2	no	—
119	C₂²×D₁₁₃	—	4	2	no	—
120	C₂²×D₁₁₃	—	4	8	no	—
121	C₂²×D₁₁₃	—	4	8	no	—
122	C₂²×D₁₁₃	C₂×D₄	1	8	yes	complemented
123	C₂²×D₁₁₃	C₂⁴	1	4	yes	—
124	C₂²×D₁₁₃	C₂⁴	1	4	yes	—
125	Q₈×C₁₁₃	—	2	4	no	—
126	D₄×C₁₁₃	—	2	8	no	—
127	D₄×C₁₁₃	—	2	4	no	—
128	D₄×C₁₁₃	—	2	4	no	—
129	D₄×C₁₁₃	—	4	2	no	—
130	C₂×C₄×C₁₁₃	—	2	8	no	—
131	C₂×C₄×C₁₁₃	—	2	2	no	—
132	C₂×C₄×C₁₁₃	—	4	1	no	—
133	C₂×C₄×C₁₁₃	C₂×D₄	1	4	yes	complemented
134	C₂×C₄×C₁₁₃	C₂⁴	1	1	yes	characteristic
135	C₂×C₄×C₁₁₃	C₂⁴	1	1	yes	characteristic
136	C₂×C₄×C₁₁₃	C₂⁴	1	1	yes	characteristic
137	C₂×C₄×C₁₁₃	C₂⁴	1	4	yes	—
138	C₂×C₄×C₁₁₃	C₂⁴	1	1	yes	characteristic
139	C₂×C₄×C₁₁₃	C₂⁴	1	1	yes	characteristic
140	C₂×C₄×C₁₁₃	C₂⁴	1	1	yes	characteristic
141	C₂²⋊D₁₁₃	—	2	8	no	—
142	C₂²⋊D₁₁₃	—	2	16	no	—
143	C₂²⋊D₁₁₃	—	4	8	no	—
144	C₂×Dic₁₁₃	—	4	2	no	—
145	C₂×Dic₁₁₃	C₂⁴	1	4	yes	—
146	C₂×Dic₁₁₃	C₂⁴	1	4	yes	—
147	D₄₅₂	—	2	16	no	—
148	D₄₅₂	—	2	4	no	—
149	D₄₅₂	—	2	4	no	—
150	D₄₅₂	—	4	2	no	—
151	D₄₅₂	C₂×D₄	1	8	yes	complemented
152	D₄₅₂	C₂×D₄	1	8	yes	complemented
153	C₄×D₁₁₃	—	2	16	no	—
154	C₄×D₁₁₃	—	2	8	no	—
155	C₄×D₁₁₃	—	2	8	no	—
156	C₄×D₁₁₃	—	4	4	no	—
157	Dic₂₂₆	—	2	4	no	—
158	C₂²×C₁₁₃	—	2	1	no	—
159	C₂²×C₁₁₃	—	2	1	no	—
160	C₂²×C₁₁₃	—	2	4	no	—
161	C₂²×C₁₁₃	—	2	4	no	—
162	C₂²×C₁₁₃	—	2	4	no	—
163	C₂²×C₁₁₃	C₂²×D₄	1	2	yes	—
164	C₂²×C₁₁₃	C₂⁵	1	1	yes	characteristic
165	C₂×D₁₁₃	—	2	4	no	—
166	C₂×D₁₁₃	—	2	4	no	—
167	C₂×D₁₁₃	—	2	4	no	—
168	C₂×D₁₁₃	—	2	4	no	—
169	C₂×D₁₁₃	—	2	4	no	—
170	C₂×D₁₁₃	—	4	8	no	—
171	C₂×D₁₁₃	—	8	16	no	—
172	C₂×D₁₁₃	C₂²×D₄	1	8	yes	—
173	C₄×C₁₁₃	—	2	4	no	—
174	C₄×C₁₁₃	—	2	1	no	—
175	C₄×C₁₁₃	—	2	1	no	—
176	C₄×C₁₁₃	—	2	1	no	—
177	C₄×C₁₁₃	C₂²×D₄	1	2	yes	—
178	C₄×C₁₁₃	C₂²×D₄	1	2	yes	—
179	C₄×C₁₁₃	H(5,𝔽₂)	1	2	yes	complemented
180	Dic₁₁₃	—	2	4	no	—
181	Dic₁₁₃	—	2	4	no	—
182	C₂×C₁₁₃	—	2	2	no	—
183	C₂×C₁₁₃	—	4	4	no	—
184	C₂×C₁₁₃	C₂³×D₄	1	1	yes	characteristic
185	C₂×C₁₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
186	C₂×C₁₁₃	#585	1	1	yes	characteristic
187	D₁₁₃	—	2	8	no	—
188	D₁₁₃	—	4	4	no	—
189	#3496	—	113	1	no	maximal, Sylow
190	C₁₁₃	#3496	1	1	yes	characteristic, complemented, Sylow
191	C₂×H(5,𝔽₂)	—	113	2	no	—
192	#547	—	113	2	no	—
193	#547	—	113	2	no	—
194	#546	—	113	4	no	—
195	#546	—	113	4	no	—
196	D₄²	—	113	2	no	—
197	D₄²	—	113	2	no	—
198	#537	—	113	2	no	—
199	#534	—	113	4	no	—
200	#532	—	113	1	no	—
201	#532	D₁₁₃	1	1	yes	characteristic, complemented
202	C₂×#121	—	113	4	no	—
203	C₂×C₄×D₄	—	113	1	no	—
204	H(5,𝔽₂)	—	226	16	no	—
205	C₂×#41	—	113	4	no	—
206	C₂×#41	—	113	2	no	—
207	C₂×#41	—	113	4	no	—
208	C₂×#41	C₂×D₁₁₃	1	2	yes	complemented
209	C₂²×D₄	—	113	4	no	—
210	C₂²×D₄	—	113	8	no	—
211	C₂²×D₄	—	113	4	no	—
212	C₂²×D₄	—	113	1	no	—
213	C₂²×D₄	—	113	4	no	—
214	C₂³×C₄	—	113	2	no	—
215	C₄⋊Q₈	—	113	1	no	—
216	C₄⋊Q₈	C₂×D₁₁₃	1	1	yes	characteristic, complemented
217	#127	—	113	1	no	—
218	#127	C₂×D₁₁₃	1	1	yes	characteristic, complemented
219	#124	—	113	2	no	—
220	#124	C₂×D₁₁₃	1	2	yes	complemented
221	#123	—	113	8	no	—
222	#123	—	113	8	no	—
223	C₂²⋊Q₈	—	113	4	no	—
224	C₂²⋊Q₈	—	113	4	no	—
225	#121	—	113	8	no	—
226	#121	—	113	4	no	—
227	#121	—	113	4	no	—
228	#121	—	113	2	no	—
229	#121	—	113	2	no	—
230	#121	—	113	4	no	—
231	#121	—	113	4	no	—
232	#121	—	113	8	no	—
233	#121	C₂×D₁₁₃	1	2	yes	complemented
234	#121	C₂×D₁₁₃	1	2	yes	complemented
235	#120	—	113	8	no	—
236	#120	—	113	8	no	—
237	C₄×D₄	—	113	2	no	—
238	C₄×D₄	—	113	2	no	—
239	C₄×D₄	—	113	2	no	—
240	C₄×D₄	—	113	2	no	—
241	C₄×D₄	—	113	2	no	—
242	C₄×D₄	—	113	2	no	—
243	C₄×D₄	C₂×D₁₁₃	1	2	yes	complemented
244	C₄×D₄	C₂×D₁₁₃	1	2	yes	complemented
245	C₂×C₄⋊C₄	—	113	1	no	—
246	C₂×C₄⋊C₄	—	113	4	no	—
247	C₂×C₂²⋊C₄	—	113	2	no	—
248	C₂×C₂²⋊C₄	—	113	8	no	—
249	C₂×C₄²	C₂×D₁₁₃	1	1	yes	characteristic, complemented
250	C₂⁴	—	113	2	no	—
251	C₂⁴	—	113	8	no	—
252	#41	—	2	8	no	—
253	#41	—	226	16	no	—
254	#41	—	226	16	no	—
255	#41	—	226	8	no	—
256	C₂×Q₈	—	113	2	no	—
257	C₂×Q₈	C₂²×D₁₁₃	1	2	yes	—
258	C₂×D₄	—	113	8	no	—
259	C₂×D₄	—	113	8	no	—
260	C₂×D₄	—	113	4	no	—
261	C₂×D₄	—	113	8	no	—
262	C₂×D₄	—	113	2	no	—
263	C₂×D₄	—	113	2	no	—
264	C₂×D₄	—	113	2	no	—
265	C₂×D₄	—	113	2	no	—
266	C₂×D₄	—	113	8	no	—
267	C₂×D₄	—	113	2	no	—
268	C₂×D₄	—	452	8	no	—
269	C₂×D₄	—	226	16	no	—
270	C₂×D₄	—	226	16	no	—
271	C₂×D₄	—	226	32	no	—
272	C₂×D₄	C₂²×D₁₁₃	1	2	yes	—
273	C₂×D₄	C₂²×D₁₁₃	1	4	yes	—
274	C₂×D₄	C₂²×D₁₁₃	1	2	yes	—
275	C₂×D₄	C₂²×D₁₁₃	1	2	yes	—
276	C₂²×C₄	—	113	2	no	—
277	C₂²×C₄	—	113	4	no	—
278	C₂²×C₄	—	113	8	no	—
279	C₂²×C₄	—	113	4	no	—
280	C₂²×C₄	—	113	4	no	—
281	C₂²×C₄	—	452	4	no	—
282	C₂²×C₄	C₂²×D₁₁₃	1	1	yes	characteristic
283	C₂²×C₄	C₂²×D₁₁₃	1	4	yes	—
284	C₂²×C₄	C₂²×D₁₁₃	1	1	yes	characteristic
285	C₂²×C₄	C₂²×D₁₁₃	1	1	yes	characteristic
286	C₄⋊C₄	—	113	2	no	—
287	C₄⋊C₄	—	113	2	no	—
288	C₄⋊C₄	—	113	2	no	—
289	C₄⋊C₄	—	113	8	no	—
290	C₄⋊C₄	—	113	2	no	—
291	C₄⋊C₄	C₂²×D₁₁₃	1	2	yes	—
292	C₄⋊C₄	C₂²×D₁₁₃	1	2	yes	—
293	C₂²⋊C₄	—	113	8	no	—
294	C₂²⋊C₄	—	113	4	no	—
295	C₂²⋊C₄	—	113	4	no	—
296	C₂²⋊C₄	—	113	4	no	—
297	C₂²⋊C₄	—	113	8	no	—
298	C₂²⋊C₄	—	113	4	no	—
299	C₂²⋊C₄	C₂²×D₁₁₃	1	4	yes	—
300	C₂²⋊C₄	C₂²×D₁₁₃	1	4	yes	—
301	C₄²	C₂²×D₁₁₃	1	1	yes	characteristic
302	C₄²	C₂²×D₁₁₃	1	1	yes	characteristic
303	C₄²	C₂²×D₁₁₃	1	1	yes	characteristic
304	C₄²	C₂²×D₁₁₃	1	1	yes	characteristic
305	C₂³	—	113	8	no	—
306	C₂³	—	113	4	no	—
307	C₂³	—	113	4	no	—
308	C₂³	—	452	8	no	—
309	C₂³	—	452	8	no	—
310	C₂³	—	452	2	no	—
311	C₂³	—	452	2	no	—
312	C₂³	—	226	16	no	—
313	C₂³	C₂³×D₁₁₃	1	4	yes	—
314	C₂³	C₂³×D₁₁₃	1	1	yes	characteristic
315	Q₈	—	2	4	no	—
316	Q₈	—	226	4	no	—
317	D₄	—	2	8	no	—
318	D₄	—	2	4	no	—
319	D₄	—	2	4	no	—
320	D₄	—	4	2	no	—
321	D₄	—	113	8	no	—
322	D₄	—	113	8	no	—
323	D₄	—	452	2	no	—
324	D₄	—	452	8	no	—
325	D₄	—	226	16	no	—
326	D₄	—	226	16	no	—
327	D₄	—	226	8	no	—
328	D₄	—	226	4	no	—
329	D₄	—	226	4	no	—
330	C₂×C₄	—	2	8	no	—
331	C₂×C₄	—	2	2	no	—
332	C₂×C₄	—	4	1	no	—
333	C₂×C₄	—	113	4	no	—
334	C₂×C₄	—	113	4	no	—
335	C₂×C₄	—	452	4	no	—
336	C₂×C₄	—	452	2	no	—
337	C₂×C₄	—	226	16	no	—
338	C₂×C₄	—	226	8	no	—
339	C₂×C₄	—	226	8	no	—
340	C₂×C₄	D₄×D₁₁₃	1	4	yes	complemented
341	C₂×C₄	C₂³×D₁₁₃	1	1	yes	characteristic
342	C₂×C₄	C₂³×D₁₁₃	1	1	yes	characteristic
343	C₂×C₄	C₂³×D₁₁₃	1	1	yes	characteristic
344	C₂×C₄	C₂³×D₁₁₃	1	4	yes	—
345	C₂×C₄	C₂³×D₁₁₃	1	1	yes	characteristic
346	C₂×C₄	C₂³×D₁₁₃	1	1	yes	characteristic
347	C₂×C₄	C₂³×D₁₁₃	1	1	yes	characteristic
348	C₂²	—	2	1	no	—
349	C₂²	—	2	1	no	—
350	C₂²	—	2	4	no	—
351	C₂²	—	2	4	no	—
352	C₂²	—	2	4	no	—
353	C₂²	—	113	8	no	—
354	C₂²	—	904	16	no	—
355	C₂²	—	452	8	no	—
356	C₂²	—	226	4	no	—
357	C₂²	—	226	4	no	—
358	C₂²	—	226	4	no	—
359	C₂²	—	226	4	no	—
360	C₂²	—	226	4	no	—
361	C₂²	C₂×D₄×D₁₁₃	1	2	yes	—
362	C₂²	C₂⁴×D₁₁₃	1	1	yes	characteristic
363	C₄	—	2	4	no	—
364	C₄	—	2	1	no	—
365	C₄	—	2	1	no	—
366	C₄	—	2	1	no	—
367	C₄	—	226	4	no	—
368	C₄	—	226	4	no	—
369	C₄	C₂×D₄×D₁₁₃	1	2	yes	—
370	C₄	C₂×D₄×D₁₁₃	1	2	yes	—
371	C₄	#16813668	1	2	yes	complemented
372	C₂	—	2	2	no	—
373	C₂	—	4	4	no	—
374	C₂	—	452	4	no	—
375	C₂	—	226	8	no	—
376	C₂	C₂²×D₄×D₁₁₃	1	1	yes	characteristic
377	C₂	C₂×#16813668	1	1	yes	characteristic
378	C₂	#20299434	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₁₁₃
commutator, socle, cosocle	C₂²×C₁₁₃	C₂⁵
Fitting	#532×C₁₁₃	C₂
hypercenter	#532	D₁₁₃
hypocenter	C₁₁₃	#3496
LCS	G ▷ C₂²×C₁₁₃ ▷ C₁₁₃
UCS	C₁ ◁ C₂² ◁ #532

Complements

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

N	H ≅ G/N	type
1. C₂×#16813668	C₂	semidirect
2. #20299253	C₂	semidirect
3. #20299251	C₂	semidirect
4. #20299244	C₂	semidirect
5. #20299241	C₂	semidirect
6. D₄×D₄₅₂	C₂	semidirect
7. #20299233	C₂	semidirect
8. #20299176	C₂	semidirect
9. #20299156	C₂	semidirect
10. #20299148	C₂	semidirect
11. #121×D₁₁₃	C₂	semidirect
12. C₂×C₄×D₄₅₂	C₂	semidirect
13. #532×C₁₁₃	C₂	semidirect
15. C₂×#14268648	C₂²	semidirect
16. C₂×#14268647	C₂²	semidirect
17. C₂×#14268647	C₂²	semidirect
19. C₂²×D₄₅₂	C₂²	semidirect
20. C₂×D₄×D₁₁₃	C₂²	semidirect
21. C₂×D₄×D₁₁₃	C₂²	semidirect
22. C₂×D₄×D₁₁₃	C₂²	semidirect
23. C₂²×C₄×D₁₁₃	C₂²	semidirect
24. #16813622	C₂²	semidirect
25. #16813619	C₂²	semidirect
26. #16813610	C₂²	semidirect
27. #16813607	C₂²	semidirect
28. #16813604	C₂²	semidirect
29. #16813601	C₂²	semidirect
30. #16813598	C₂²	semidirect
31. #16813597	C₂²	semidirect
32. #16813596	C₂²	semidirect
33. #16813596	C₂²	semidirect
34. #16813596	C₂²	semidirect
35. #16813595	C₂²	semidirect
36. #16813594	C₂²	semidirect
37. #16813593	C₂²	semidirect
38. #16813593	C₂²	semidirect
39. #16813592	C₂²	semidirect
40. #16813590	C₂²	semidirect
41. C₄×D₄₅₂	C₂²	semidirect
42. C₄×D₄₅₂	C₂²	semidirect
43. C₄×D₄₅₂	C₂²	semidirect
44. C₄×D₄₅₂	C₂²	semidirect
45. C₄×D₄₅₂	C₂²	semidirect
46. C₄×D₄₅₂	C₂²	semidirect
47. C₂×C₄⋊Dic₁₁₃	C₂²	semidirect
48. C₄⋊C₄×D₁₁₃	C₂²	semidirect
49. C₂×#14268624	C₂²	semidirect
50. C₂²⋊C₄×D₁₁₃	C₂²	semidirect
51. C₂×#41×C₁₁₃	C₂²	semidirect
52. C₄⋊Q₈×C₁₁₃	C₂²	semidirect
53. #127×C₁₁₃	C₂²	semidirect
54. #124×C₁₁₃	C₂²	semidirect
55. #121×C₁₁₃	C₂²	semidirect
56. #121×C₁₁₃	C₂²	semidirect
57. C₄×D₄×C₁₁₃	C₂²	semidirect
58. C₄×D₄×C₁₁₃	C₂²	semidirect
59. C₂×C₄²×C₁₁₃	C₂²	semidirect
67. C₂×D₄₅₂	D₄	semidirect
122. C₂²×D₁₁₃	C₂×D₄	semidirect
133. C₂×C₄×C₁₁₃	C₂×D₄	semidirect
151. D₄₅₂	C₂×D₄	semidirect
152. D₄₅₂	C₂×D₄	semidirect
179. C₄×C₁₁₃	H(5,𝔽₂)	semidirect
190. C₁₁₃	#3496	semidirect
201. #532	D₁₁₃	semidirect
208. C₂×#41	C₂×D₁₁₃	semidirect
216. C₄⋊Q₈	C₂×D₁₁₃	semidirect
218. #127	C₂×D₁₁₃	semidirect
220. #124	C₂×D₁₁₃	semidirect
233. #121	C₂×D₁₁₃	semidirect
234. #121	C₂×D₁₁₃	semidirect
243. C₄×D₄	C₂×D₁₁₃	semidirect
244. C₄×D₄	C₂×D₁₁₃	semidirect
249. C₂×C₄²	C₂×D₁₁₃	semidirect
340. C₂×C₄	D₄×D₁₁₃	semidirect
371. C₄	#16813668	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
#20299253	2
#20299251	2
#20299244	2
#20299241	2
D₄×D₄₅₂	2
#20299233	2
#20299176	2
#20299156	2
#20299148	2
#121×D₁₁₃	2
C₂×C₄×D₄₅₂	2
#532×C₁₁₃	2
#3496	113