Subgroups — C₂×#20299159 #28403876

Order 14464.

1984 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

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

	subgroup	G/H
center	C₂³	C₂³×D₁₁₃
commutator, cosocle	C₂²×C₁₁₃	C₂⁵
Frattini	C₂²	C₂⁴×D₁₁₃
Fitting	C₂×#123×C₁₁₃	C₂
socle	C₂³×C₁₁₃	C₂⁴
hypercenter	C₂×#123	D₁₁₃
hypocenter	C₁₁₃	C₂×#534
LCS	G ▷ C₂²×C₁₁₃ ▷ C₁₁₃
UCS	C₁ ◁ C₂³ ◁ C₂×#123

Complements

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

N	H ≅ G/N	type
1. C₂³×D₄₅₂	C₂	semidirect
2. C₂²×D₄×D₁₁₃	C₂	semidirect
3. #20299159	C₂	direct (N × H)
4. C₂×#16813607	C₂	semidirect
5. C₂×#16813605	C₂	semidirect
6. C₂×#16813597	C₂	semidirect
7. C₂×#16813595	C₂	semidirect
8. C₂×#16813592	C₂	semidirect
9. C₂×#16813592	C₂	semidirect
10. C₂×#16813590	C₂	semidirect
11. C₂×C₂²⋊C₄×D₁₁₃	C₂	semidirect
12. C₂×#123×C₁₁₃	C₂	semidirect
14. C₂⁴×D₁₁₃	C₂²	semidirect
15. C₂⁴×D₁₁₃	C₂²	semidirect
18. C₂²×D₄₅₂	C₂²	semidirect
19. C₂²×D₄₅₂	C₂²	semidirect
20. C₂²×D₄₅₂	C₂²	semidirect
21. C₂²×D₄₅₂	C₂²	semidirect
23. C₂²×C₂²⋊D₁₁₃	C₂²	semidirect
24. C₂²×C₂²⋊D₁₁₃	C₂²	semidirect
26. C₂×D₄×D₁₁₃	C₂²	semidirect
27. C₂²×C₄×D₁₁₃	C₂²	semidirect
28. C₂²×C₄×D₁₁₃	C₂²	semidirect
29. #16813607	C₂²	semidirect
30. #16813605	C₂²	semidirect
31. #16813597	C₂²	semidirect
32. #16813595	C₂²	semidirect
33. #16813592	C₂²	semidirect
34. #16813592	C₂²	semidirect
35. #16813590	C₂²	semidirect
36. C₂×#14268626	C₂²	semidirect
37. C₂×C₂²⋊Dic₁₁₃	C₂²	semidirect
38. C₂×#14268624	C₂²	semidirect
39. C₂×#14268624	C₂²	semidirect
40. C₂×#14268624	C₂²	semidirect
41. C₂×#14268624	C₂²	semidirect
42. C₂²⋊C₄×D₁₁₃	C₂²	semidirect
44. C₂³×C₄×C₁₁₃	C₂²	semidirect
45. #123×C₁₁₃	C₂²	semidirect
46. C₂×C₄⋊C₄×C₁₁₃	C₂²	semidirect
47. C₂×C₂²⋊C₄×C₁₁₃	C₂²	semidirect
48. C₂×C₂²⋊C₄×C₁₁₃	C₂²	semidirect
54. C₂³×D₁₁₃	D₄	semidirect
60. C₂³×D₁₁₃	C₂³	semidirect
61. C₂³×D₁₁₃	C₂³	semidirect
68. C₂×D₄₅₂	C₂³	semidirect
69. C₂×D₄₅₂	C₂³	semidirect
70. C₂×D₄₅₂	C₂³	semidirect
75. C₂×C₂²⋊D₁₁₃	C₂³	semidirect
76. C₂×C₂²⋊D₁₁₃	C₂³	semidirect
82. C₂×C₄×D₁₁₃	C₂³	semidirect
83. C₂×C₄×D₁₁₃	C₂³	semidirect
84. #14268626	C₂³	semidirect
85. C₂²⋊Dic₁₁₃	C₂³	semidirect
86. #14268624	C₂³	semidirect
87. #14268624	C₂³	semidirect
88. #14268624	C₂³	semidirect
89. #14268624	C₂³	semidirect
98. C₂²×C₄×C₁₁₃	C₂³	semidirect
99. C₄⋊C₄×C₁₁₃	C₂³	semidirect
100. C₂²⋊C₄×C₁₁₃	C₂³	semidirect
101. C₂²⋊C₄×C₁₁₃	C₂³	semidirect
126. C₂²×D₁₁₃	C₂×D₄	semidirect
184. C₂×C₁₁₃	#534	semidirect
192. C₁₁₃	C₂×#534	semidirect
198. C₂×#123	D₁₁₃	semidirect
222. C₂³×C₄	C₂×D₁₁₃	semidirect
225. #123	C₂×D₁₁₃	semidirect
232. C₂×C₄⋊C₄	C₂×D₁₁₃	semidirect
239. C₂×C₂²⋊C₄	C₂×D₁₁₃	semidirect
240. C₂×C₂²⋊C₄	C₂×D₁₁₃	semidirect
284. C₂²×C₄	C₂²×D₁₁₃	semidirect
286. C₄⋊C₄	C₂²×D₁₁₃	semidirect
292. C₂²⋊C₄	C₂²×D₁₁₃	semidirect
293. C₂²⋊C₄	C₂²×D₁₁₃	semidirect
380. C₂	#20299159	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂³×D₄₅₂	2
C₂²×D₄×D₁₁₃	2
#20299159	2
C₂×#16813607	2
C₂×#16813605	2
C₂×#16813597	2
C₂×#16813595	2
C₂×#16813592	2
C₂×#16813590	2
C₂×C₂²⋊C₄×D₁₁₃	2
C₂×#123×C₁₁₃	2
C₂×#534	113

Subgroups — C2×#20299159 #28403876

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#20299159 #28403876