Subgroups — C₂×#13093024 #15686760

Order 2944.

1004 conjugacy classes of subgroups.

The subgroup lattice has 368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13093024	C₂	1	16	yes	maximal, direct product factor
2	C₂×#10625059	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#10625050	C₂	1	1	yes	maximal, characteristic
4	C₂×#10625050	C₂	1	1	yes	maximal, characteristic
5	C₂×#10625050	C₂	1	1	yes	maximal, characteristic
6	C₂×#10625041	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#10625061	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#10625060	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×#10625060	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#10625060	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×#10625049	C₂	1	1	yes	maximal, characteristic
12	C₂×#10625049	C₂	1	1	yes	maximal, characteristic
13	C₂×C₄×Dic₄₆	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×#10625058	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×#10625048	C₂	1	1	yes	maximal, characteristic
16	C₂×C₂₃×#126	C₂	1	1	yes	maximal, characteristic
17	C₂³×Dic₂₃	C₂²	1	1	yes	characteristic
18	C₂²×Dic₄₆	C₂²	1	1	yes	characteristic
19	C₂²×Dic₄₆	C₂²	1	1	yes	characteristic
20	C₂₃×#126	C₂²	1	8	yes	—
21	C₂×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
22	C₂×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
23	C₂×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
24	C₂×C₂²⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
25	C₂×C₂²⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
26	C₂×C₂²⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
27	C₂×C₄²×C₂₃	C₂²	1	1	yes	characteristic
28	C₂×C₂²⋊Dic₂₃	C₂²	1	1	yes	characteristic
29	C₂×C₂²⋊Dic₂₃	C₂²	1	1	yes	characteristic
30	C₂×C₂²⋊Dic₂₃	C₂²	1	1	yes	characteristic
31	C₂×C₄⋊Dic₂₃	C₂²	1	1	yes	characteristic
32	C₂×C₄⋊Dic₂₃	C₂²	1	1	yes	characteristic
33	C₂×C₄⋊Dic₂₃	C₂²	1	1	yes	characteristic
34	C₂×C₄⋊Dic₂₃	C₂²	1	1	yes	characteristic
35	C₂×C₄⋊Dic₂₃	C₂²	1	1	yes	characteristic
36	C₂×Dic₂₃⋊C₄	C₂²	1	1	yes	characteristic
37	C₂×Dic₂₃⋊C₄	C₂²	1	1	yes	characteristic
38	C₂×Dic₂₃⋊C₄	C₂²	1	1	yes	characteristic
39	C₂×Dic₂₃⋊C₄	C₂²	1	1	yes	characteristic
40	C₂×Dic₂₃⋊C₄	C₂²	1	1	yes	characteristic
41	C₂×Dic₂₃⋊C₄	C₂²	1	1	yes	characteristic
42	C₂×Dic₂₃⋊C₄	C₂²	1	1	yes	characteristic
43	C₂×Dic₂₃⋊C₄	C₂²	1	1	yes	characteristic
44	C₂×Dic₂₃⋊C₄	C₂²	1	1	yes	characteristic
45	C₂×Dic₂₃⋊C₄	C₂²	1	1	yes	characteristic
46	C₂×Dic₂₃⋊C₄	C₂²	1	1	yes	characteristic
47	C₂×Dic₂₃⋊C₄	C₂²	1	1	yes	characteristic
48	C₂×C₄×Dic₂₃	C₂²	1	1	yes	characteristic
49	C₂×C₄×Dic₂₃	C₂²	1	1	yes	characteristic
50	C₂×C₄×Dic₂₃	C₂²	1	1	yes	characteristic
51	C₂×C₄×Dic₂₃	C₂²	1	1	yes	characteristic
52	C₂×C₄×Dic₂₃	C₂²	1	1	yes	characteristic
53	#10625061	C₂²	1	8	yes	complemented
54	#10625060	C₂²	1	8	yes	complemented
55	#10625060	C₂²	1	8	yes	complemented
56	#10625060	C₂²	1	8	yes	complemented
57	#10625059	C₂²	1	8	yes	complemented
58	#10625058	C₂²	1	8	yes	complemented
59	#10625050	C₂²	1	8	yes	—
60	#10625050	C₂²	1	8	yes	—
61	#10625050	C₂²	1	8	yes	—
62	#10625049	C₂²	1	8	yes	—
63	#10625049	C₂²	1	8	yes	—
64	#10625048	C₂²	1	8	yes	—
65	#10625041	C₂²	1	8	yes	complemented
66	C₄×Dic₄₆	C₂²	1	8	yes	complemented
67	C₂⁴×C₂₃	C₂³	1	1	yes	characteristic
68	C₂²×C₄×C₂₃	C₂³	1	1	yes	characteristic
69	C₂²×C₄×C₂₃	C₂³	1	1	yes	characteristic
70	C₂²×C₄×C₂₃	C₂³	1	1	yes	characteristic
71	C₂²×C₄×C₂₃	C₂³	1	1	yes	characteristic
72	C₂²×C₄×C₂₃	C₂³	1	1	yes	characteristic
73	C₂²×C₄×C₂₃	C₂³	1	1	yes	characteristic
74	C₂²×Dic₂₃	—	2	4	no	—
75	C₂²×Dic₂₃	C₂³	1	4	yes	—
76	C₂²×Dic₂₃	C₂³	1	1	yes	characteristic
77	C₂²×Dic₂₃	C₂³	1	1	yes	characteristic
78	C₂²×Dic₂₃	C₂³	1	1	yes	characteristic
79	C₂²×Dic₂₃	C₂³	1	1	yes	characteristic
80	C₂²×Dic₂₃	C₂³	1	1	yes	characteristic
81	C₂²×Dic₂₃	C₂³	1	1	yes	characteristic
82	C₂²×Dic₂₃	C₂³	1	1	yes	characteristic
83	C₂²×Dic₂₃	C₂³	1	1	yes	characteristic
84	C₂×Dic₄₆	—	2	4	no	—
85	C₂×Dic₄₆	—	2	4	no	—
86	C₂×Dic₄₆	C₂³	1	4	yes	—
87	C₂×Dic₄₆	C₂³	1	4	yes	—
88	C₄⋊C₄×C₂₃	C₂³	1	4	yes	—
89	C₄⋊C₄×C₂₃	C₂³	1	4	yes	—
90	C₄⋊C₄×C₂₃	C₂³	1	4	yes	—
91	C₂²⋊C₄×C₂₃	C₂³	1	4	yes	—
92	C₂²⋊C₄×C₂₃	C₂³	1	4	yes	—
93	C₂²⋊C₄×C₂₃	C₂³	1	4	yes	—
94	C₄²×C₂₃	C₂³	1	4	yes	—
95	C₂²⋊Dic₂₃	C₂³	1	4	yes	—
96	C₂²⋊Dic₂₃	C₂³	1	4	yes	—
97	C₂²⋊Dic₂₃	C₂³	1	4	yes	—
98	C₄⋊Dic₂₃	C₂³	1	4	yes	—
99	C₄⋊Dic₂₃	C₂³	1	4	yes	—
100	C₄⋊Dic₂₃	C₂³	1	4	yes	—
101	C₄⋊Dic₂₃	C₂³	1	4	yes	—
102	C₄⋊Dic₂₃	C₂³	1	4	yes	—
103	Dic₂₃⋊C₄	C₂³	1	4	yes	—
104	Dic₂₃⋊C₄	C₂³	1	4	yes	—
105	Dic₂₃⋊C₄	C₂³	1	4	yes	—
106	Dic₂₃⋊C₄	C₂³	1	4	yes	—
107	Dic₂₃⋊C₄	C₂³	1	4	yes	—
108	Dic₂₃⋊C₄	C₂³	1	4	yes	—
109	Dic₂₃⋊C₄	C₂³	1	4	yes	—
110	Dic₂₃⋊C₄	C₂³	1	4	yes	—
111	Dic₂₃⋊C₄	C₂³	1	4	yes	—
112	Dic₂₃⋊C₄	C₂³	1	4	yes	—
113	Dic₂₃⋊C₄	C₂³	1	4	yes	—
114	Dic₂₃⋊C₄	C₂³	1	4	yes	—
115	C₄×Dic₂₃	C₂³	1	4	yes	—
116	C₄×Dic₂₃	C₂³	1	4	yes	—
117	C₄×Dic₂₃	C₂³	1	4	yes	—
118	C₄×Dic₂₃	C₂³	1	4	yes	—
119	C₄×Dic₂₃	C₂³	1	4	yes	—
120	C₂³×C₂₃	—	2	2	no	—
121	C₂³×C₂₃	—	2	2	no	—
122	C₂³×C₂₃	—	2	2	no	—
123	C₂³×C₂₃	C₂⁴	1	2	yes	—
124	C₂³×C₂₃	C₂⁴	1	1	yes	characteristic
125	C₂×C₄×C₂₃	—	2	2	no	—
126	C₂×C₄×C₂₃	—	2	2	no	—
127	C₂×C₄×C₂₃	—	2	2	no	—
128	C₂×C₄×C₂₃	—	2	2	no	—
129	C₂×C₄×C₂₃	—	2	2	no	—
130	C₂×C₄×C₂₃	—	2	2	no	—
131	C₂×C₄×C₂₃	C₂⁴	1	2	yes	—
132	C₂×C₄×C₂₃	C₂⁴	1	2	yes	—
133	C₂×C₄×C₂₃	C₂⁴	1	2	yes	—
134	C₂×C₄×C₂₃	C₂⁴	1	2	yes	—
135	C₂×C₄×C₂₃	C₂⁴	1	2	yes	—
136	C₂×C₄×C₂₃	C₂⁴	1	2	yes	—
137	C₂×Dic₂₃	—	2	2	no	—
138	C₂×Dic₂₃	—	2	2	no	—
139	C₂×Dic₂₃	—	2	2	no	—
140	C₂×Dic₂₃	—	2	2	no	—
141	C₂×Dic₂₃	—	2	2	no	—
142	C₂×Dic₂₃	—	2	2	no	—
143	C₂×Dic₂₃	—	2	2	no	—
144	C₂×Dic₂₃	—	2	8	no	—
145	C₂×Dic₂₃	#41	1	4	yes	—
146	C₂×Dic₂₃	C₂⁴	1	2	yes	—
147	C₂×Dic₂₃	C₂⁴	1	2	yes	—
148	C₂×Dic₂₃	C₂⁴	1	2	yes	—
149	C₂×Dic₂₃	C₂⁴	1	2	yes	—
150	C₂×Dic₂₃	C₂⁴	1	2	yes	—
151	C₂×Dic₂₃	C₂⁴	1	2	yes	—
152	C₂×Dic₂₃	C₂⁴	1	2	yes	—
153	C₂×Dic₂₃	C₂⁴	1	2	yes	—
154	Dic₄₆	—	2	8	no	—
155	Dic₄₆	—	2	8	no	—
156	C₂×#541	—	23	1	no	maximal, Sylow
157	C₂²×C₂₃	—	2	2	no	—
158	C₂²×C₂₃	—	2	2	no	—
159	C₂²×C₂₃	—	2	2	no	—
160	C₂²×C₂₃	—	4	4	no	—
161	C₂²×C₂₃	C₂×#41	1	2	yes	—
162	C₂²×C₂₃	2₋¹⁺⁴	1	2	yes	—
163	C₂²×C₂₃	2₋¹⁺⁴	1	2	yes	—
164	C₂²×C₂₃	C₂⁵	1	1	yes	characteristic
165	C₄×C₂₃	—	2	2	no	—
166	C₄×C₂₃	—	2	2	no	—
167	C₄×C₂₃	—	2	2	no	—
168	C₄×C₂₃	—	2	2	no	—
169	C₄×C₂₃	—	2	2	no	—
170	C₄×C₂₃	—	2	2	no	—
171	Dic₂₃	—	2	2	no	—
172	Dic₂₃	—	2	2	no	—
173	Dic₂₃	—	2	2	no	—
174	Dic₂₃	—	2	2	no	—
175	Dic₂₃	—	2	2	no	—
176	Dic₂₃	—	2	2	no	—
177	Dic₂₃	—	2	2	no	—
178	Dic₂₃	C₂×#41	1	4	yes	—
179	#541	—	23	16	no	—
180	C₂×C₄⋊Q₈	—	23	1	no	—
181	C₂×#126	—	23	1	no	—
182	C₂×#126	—	23	1	no	—
183	C₂×#126	—	23	1	no	—
184	C₂×#126	D₂₃	1	1	yes	characteristic
185	C₂×#125	—	23	1	no	—
186	C₂×#125	—	23	1	no	—
187	C₂×#125	—	23	1	no	—
188	C₂×#125	—	23	1	no	—
189	C₂×#125	—	23	1	no	—
190	C₂×C₂²⋊Q₈	—	23	1	no	—
191	C₂×C₂²⋊Q₈	—	23	1	no	—
192	C₂×C₄×Q₈	—	23	1	no	—
193	C₂×C₄×Q₈	—	23	1	no	—
194	C₂×#117	—	23	1	no	—
195	C₂×C₂₃	—	4	2	no	—
196	C₂×C₂₃	#541	1	4	yes	complemented
197	C₂×C₂₃	C₂²×#41	1	1	yes	characteristic
198	C₂×C₂₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
199	C₂×C₂₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
200	C₂²×Q₈	—	23	1	no	—
201	C₂²×Q₈	—	23	1	no	—
202	C₂³×C₄	—	23	1	no	—
203	C₄⋊Q₈	—	23	8	no	—
204	#126	—	23	8	no	—
205	#126	—	23	8	no	—
206	#126	—	23	8	no	—
207	#126	C₂×D₂₃	1	8	yes	—
208	#125	—	23	8	no	—
209	#125	—	23	8	no	—
210	#125	—	23	8	no	—
211	#125	—	23	8	no	—
212	#125	—	23	8	no	—
213	C₂²⋊Q₈	—	23	8	no	—
214	C₂²⋊Q₈	—	23	8	no	—
215	C₄×Q₈	—	23	8	no	—
216	C₄×Q₈	—	23	8	no	—
217	#117	—	23	8	no	—
218	C₂×C₄⋊C₄	—	23	1	no	—
219	C₂×C₄⋊C₄	—	23	1	no	—
220	C₂×C₄⋊C₄	—	23	1	no	—
221	C₂×C₄⋊C₄	—	23	1	no	—
222	C₂×C₄⋊C₄	—	23	1	no	—
223	C₂×C₄⋊C₄	—	23	1	no	—
224	C₂×C₄⋊C₄	—	23	1	no	—
225	C₂×C₄⋊C₄	—	23	1	no	—
226	C₂×C₄⋊C₄	—	23	1	no	—
227	C₂×C₄⋊C₄	—	23	1	no	—
228	C₂×C₄⋊C₄	—	23	1	no	—
229	C₂×C₄⋊C₄	—	23	1	no	—
230	C₂×C₄⋊C₄	—	23	1	no	—
231	C₂×C₄⋊C₄	—	23	1	no	—
232	C₂×C₄⋊C₄	—	23	1	no	—
233	C₂×C₄⋊C₄	—	23	1	no	—
234	C₂×C₄⋊C₄	—	23	1	no	—
235	C₂×C₄⋊C₄	C₂×D₂₃	1	1	yes	characteristic
236	C₂×C₄⋊C₄	C₂×D₂₃	1	1	yes	characteristic
237	C₂×C₄⋊C₄	C₂×D₂₃	1	1	yes	characteristic
238	C₂×C₂²⋊C₄	—	23	1	no	—
239	C₂×C₂²⋊C₄	—	23	1	no	—
240	C₂×C₂²⋊C₄	—	23	1	no	—
241	C₂×C₂²⋊C₄	C₂×D₂₃	1	1	yes	characteristic
242	C₂×C₂²⋊C₄	C₂×D₂₃	1	1	yes	characteristic
243	C₂×C₂²⋊C₄	C₂×D₂₃	1	1	yes	characteristic
244	C₂×C₄²	—	23	1	no	—
245	C₂×C₄²	—	23	1	no	—
246	C₂×C₄²	—	23	1	no	—
247	C₂×C₄²	—	23	1	no	—
248	C₂×C₄²	—	23	1	no	—
249	C₂×C₄²	C₂×D₂₃	1	1	yes	characteristic
250	C₂₃	C₂×#541	1	1	yes	characteristic, complemented, Sylow
251	C₂⁴	C₂²×D₂₃	1	1	yes	characteristic
252	C₂×Q₈	—	23	4	no	—
253	C₂×Q₈	—	23	4	no	—
254	C₂×Q₈	—	46	4	no	—
255	C₂×Q₈	—	46	4	no	—
256	C₂²×C₄	—	23	1	no	—
257	C₂²×C₄	—	23	4	no	—
258	C₂²×C₄	—	23	1	no	—
259	C₂²×C₄	—	23	1	no	—
260	C₂²×C₄	—	23	1	no	—
261	C₂²×C₄	—	23	1	no	—
262	C₂²×C₄	—	23	1	no	—
263	C₂²×C₄	—	23	1	no	—
264	C₂²×C₄	—	23	1	no	—
265	C₂²×C₄	—	46	4	no	—
266	C₂²×C₄	C₂²×D₂₃	1	1	yes	characteristic
267	C₂²×C₄	C₂²×D₂₃	1	1	yes	characteristic
268	C₂²×C₄	C₂²×D₂₃	1	1	yes	characteristic
269	C₂²×C₄	C₂²×D₂₃	1	1	yes	characteristic
270	C₂²×C₄	C₂²×D₂₃	1	1	yes	characteristic
271	C₂²×C₄	C₂²×D₂₃	1	1	yes	characteristic
272	C₄⋊C₄	—	23	4	no	—
273	C₄⋊C₄	—	23	4	no	—
274	C₄⋊C₄	—	23	4	no	—
275	C₄⋊C₄	—	23	4	no	—
276	C₄⋊C₄	—	23	4	no	—
277	C₄⋊C₄	—	23	4	no	—
278	C₄⋊C₄	—	23	4	no	—
279	C₄⋊C₄	—	23	4	no	—
280	C₄⋊C₄	—	23	4	no	—
281	C₄⋊C₄	—	23	4	no	—
282	C₄⋊C₄	—	23	4	no	—
283	C₄⋊C₄	—	23	4	no	—
284	C₄⋊C₄	—	23	4	no	—
285	C₄⋊C₄	—	23	4	no	—
286	C₄⋊C₄	—	23	4	no	—
287	C₄⋊C₄	—	23	4	no	—
288	C₄⋊C₄	—	23	4	no	—
289	C₄⋊C₄	C₂²×D₂₃	1	4	yes	—
290	C₄⋊C₄	C₂²×D₂₃	1	4	yes	—
291	C₄⋊C₄	C₂²×D₂₃	1	4	yes	—
292	C₂²⋊C₄	—	23	4	no	—
293	C₂²⋊C₄	—	23	4	no	—
294	C₂²⋊C₄	—	23	4	no	—
295	C₂²⋊C₄	C₂²×D₂₃	1	4	yes	—
296	C₂²⋊C₄	C₂²×D₂₃	1	4	yes	—
297	C₂²⋊C₄	C₂²×D₂₃	1	4	yes	—
298	C₄²	—	23	4	no	—
299	C₄²	—	23	4	no	—
300	C₄²	—	23	4	no	—
301	C₄²	—	23	4	no	—
302	C₄²	—	23	4	no	—
303	C₄²	C₂²×D₂₃	1	4	yes	—
304	C₂³	—	2	2	no	—
305	C₂³	—	2	2	no	—
306	C₂³	—	2	2	no	—
307	C₂³	C₂³×D₂₃	1	2	yes	—
308	C₂³	C₂³×D₂₃	1	1	yes	characteristic
309	Q₈	—	46	8	no	—
310	Q₈	—	46	8	no	—
311	C₂×C₄	—	2	2	no	—
312	C₂×C₄	—	2	2	no	—
313	C₂×C₄	—	2	2	no	—
314	C₂×C₄	—	2	2	no	—
315	C₂×C₄	—	2	2	no	—
316	C₂×C₄	—	2	2	no	—
317	C₂×C₄	—	23	4	no	—
318	C₂×C₄	—	23	2	no	—
319	C₂×C₄	—	23	2	no	—
320	C₂×C₄	—	23	2	no	—
321	C₂×C₄	—	23	2	no	—
322	C₂×C₄	—	23	2	no	—
323	C₂×C₄	—	23	2	no	—
324	C₂×C₄	—	23	2	no	—
325	C₂×C₄	—	23	2	no	—
326	C₂×C₄	—	46	8	no	—
327	C₂×C₄	—	46	2	no	—
328	C₂×C₄	—	46	2	no	—
329	C₂×C₄	—	46	2	no	—
330	C₂×C₄	—	46	2	no	—
331	C₂×C₄	—	46	2	no	—
332	C₂×C₄	—	46	2	no	—
333	C₂×C₄	—	46	2	no	—
334	C₂×C₄	C₂³×D₂₃	1	2	yes	—
335	C₂×C₄	C₂³×D₂₃	1	2	yes	—
336	C₂×C₄	C₂³×D₂₃	1	2	yes	—
337	C₂×C₄	C₂³×D₂₃	1	2	yes	—
338	C₂×C₄	C₂³×D₂₃	1	2	yes	—
339	C₂×C₄	C₂³×D₂₃	1	2	yes	—
340	C₂²	—	2	2	no	—
341	C₂²	—	2	2	no	—
342	C₂²	—	2	2	no	—
343	C₂²	—	4	4	no	—
344	C₂²	#41×D₂₃	1	2	yes	—
345	C₂²	#10625161	1	2	yes	—
346	C₂²	#10625161	1	2	yes	—
347	C₂²	C₂⁴×D₂₃	1	1	yes	characteristic
348	C₄	—	2	2	no	—
349	C₄	—	2	2	no	—
350	C₄	—	2	2	no	—
351	C₄	—	2	2	no	—
352	C₄	—	2	2	no	—
353	C₄	—	2	2	no	—
354	C₄	—	23	4	no	—
355	C₄	—	46	2	no	—
356	C₄	—	46	2	no	—
357	C₄	—	46	2	no	—
358	C₄	—	46	2	no	—
359	C₄	—	46	2	no	—
360	C₄	—	46	2	no	—
361	C₄	—	46	2	no	—
362	C₂	—	4	2	no	—
363	C₂	#13093024	1	4	yes	direct product factor
364	C₂	C₂×#41×D₂₃	1	1	yes	characteristic
365	C₂	C₂×#10625161	1	1	yes	characteristic
366	C₂	C₂×#10625161	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂³×D₂₃
commutator, cosocle	C₂²×C₂₃	C₂⁵
Frattini	C₂²	C₂⁴×D₂₃
Fitting	C₂×C₂₃×#126	C₂
socle	C₂³×C₂₃	C₂⁴
prime radical	C₂⁴×C₂₃	C₂³
hypercenter	C₂×#126	D₂₃
hypocenter	C₂₃	C₂×#541
LCS	G ▷ C₂²×C₂₃ ▷ C₂₃
UCS	C₁ ◁ C₂³ ◁ C₂×#126

Complements

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

N	H ≅ G/N	type
1. #13093024	C₂	direct (N × H)
2. C₂×#10625059	C₂	semidirect
6. C₂×#10625041	C₂	semidirect
7. C₂×#10625061	C₂	semidirect
8. C₂×#10625060	C₂	semidirect
9. C₂×#10625060	C₂	semidirect
10. C₂×#10625060	C₂	semidirect
13. C₂×C₄×Dic₄₆	C₂	semidirect
14. C₂×#10625058	C₂	semidirect
53. #10625061	C₂²	semidirect
54. #10625060	C₂²	semidirect
55. #10625060	C₂²	semidirect
56. #10625060	C₂²	semidirect
57. #10625059	C₂²	semidirect
58. #10625058	C₂²	semidirect
65. #10625041	C₂²	semidirect
66. C₄×Dic₄₆	C₂²	semidirect
196. C₂×C₂₃	#541	semidirect
250. C₂₃	C₂×#541	semidirect
363. C₂	#13093024	direct (N × H)

Maximal subgroups

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

subgroup	index
#13093024	2
C₂×#10625059	2
C₂×#10625050	2
C₂×#10625041	2
C₂×#10625061	2
C₂×#10625060	2
C₂×#10625049	2
C₂×C₄×Dic₄₆	2
C₂×#10625058	2
C₂×#10625048	2
C₂×C₂₃×#126	2
C₂×#541	23

Subgroups — C2×#13093024 #15686760

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#13093024 #15686760