Subgroups — C₂×#13093064 #15686849

Order 2944.

1900 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#67288	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×D₄×D₂₃	C₂	1	1	yes	maximal, characteristic, complemented
3	#13093064	C₂	1	16	yes	maximal, direct product factor
4	C₂×#10625107	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#10625054	C₂	1	2	yes	maximal, complemented
6	C₂×#10625068	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#10625109	C₂	1	2	yes	maximal, complemented
8	C₂×#10625108	C₂	1	2	yes	maximal, complemented
9	C₂×#10625064	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₄×C₂²⋊D₂₃	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₂²⋊C₄×D₂₃	C₂	1	2	yes	maximal, complemented
12	C₂×C₂₃×#121	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂⁴×D₂₃	C₂²	1	2	yes	—
14	C₂²×D₄×C₂₃	C₂²	1	1	yes	characteristic
15	C₂²×D₄×C₂₃	C₂²	1	2	yes	complemented
16	C₂³×C₄×C₂₃	C₂²	1	1	yes	characteristic, complemented
17	C₂²×C₂²⋊D₂₃	C₂²	1	1	yes	characteristic
18	C₂²×C₂²⋊D₂₃	C₂²	1	2	yes	—
19	C₂²×C₂²⋊D₂₃	C₂²	1	2	yes	complemented
20	C₂×D₄×D₂₃	—	2	8	no	—
21	C₂×D₄×D₂₃	C₂²	1	8	yes	complemented
22	C₂×#67288	—	2	8	no	—
23	C₂×#67288	C₂²	1	8	yes	complemented
24	C₂²×D₉₂	C₂²	1	1	yes	characteristic
25	C₂²×C₄×D₂₃	C₂²	1	1	yes	characteristic
26	C₂²×C₄×D₂₃	C₂²	1	2	yes	complemented
27	C₂²×C₄×D₂₃	C₂²	1	2	yes	complemented
28	C₂²×Dic₄₆	C₂²	1	1	yes	characteristic, complemented
29	C₂₃×#121	C₂²	1	8	yes	complemented
30	C₂×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic, complemented
31	C₂×C₂²⋊C₄×C₂₃	C₂²	1	2	yes	complemented
32	C₂×C₂²⋊Dic₂₃	C₂²	1	1	yes	characteristic, complemented
33	C₂×C₂²⋊Dic₂₃	C₂²	1	2	yes	complemented
34	C₂×C₂²⋊Dic₂₃	C₂²	1	2	yes	complemented
35	#10625109	C₂²	1	16	yes	complemented
36	#10625108	C₂²	1	16	yes	complemented
37	#10625107	C₂²	1	8	yes	complemented
38	C₄×C₂²⋊D₂₃	C₂²	1	8	yes	complemented
39	C₂×(C₂×D₂₃)⋊C₄	C₂²	1	1	yes	characteristic
40	C₂×(C₂×D₂₃)⋊C₄	C₂²	1	2	yes	—
41	C₂×(C₂×D₂₃)⋊C₄	C₂²	1	2	yes	complemented
42	C₂×C₄⋊Dic₂₃	C₂²	1	2	yes	complemented
43	C₂×Dic₂₃⋊C₄	C₂²	1	1	yes	characteristic, complemented
44	C₂×C₄×Dic₂₃	C₂²	1	1	yes	characteristic, complemented
45	#10625068	C₂²	1	8	yes	complemented
46	#10625064	C₂²	1	8	yes	complemented
47	#10625054	C₂²	1	16	yes	complemented
48	C₂²⋊C₄×D₂₃	C₂²	1	16	yes	complemented
49	C₂⁴×C₂₃	C₂³	1	2	yes	—
50	C₂⁴×C₂₃	C₂³	1	1	yes	characteristic
51	C₂³×D₂₃	—	2	8	no	—
52	C₂³×D₂₃	—	2	8	no	—
53	C₂³×D₂₃	—	4	4	no	—
54	C₂³×D₂₃	C₂³	1	8	yes	—
55	C₂³×D₂₃	C₂³	1	2	yes	—
56	C₂³×D₂₃	C₂³	1	1	yes	characteristic
57	C₂×D₄×C₂₃	—	2	4	no	—
58	C₂×D₄×C₂₃	—	4	4	no	—
59	C₂×D₄×C₂₃	C₂³	1	4	yes	—
60	C₂×D₄×C₂₃	C₂³	1	8	yes	complemented
61	C₂²×C₄×C₂₃	—	2	4	no	—
62	C₂²×C₄×C₂₃	C₂³	1	1	yes	characteristic
63	C₂²×C₄×C₂₃	C₂³	1	2	yes	—
64	C₂²×C₄×C₂₃	C₂³	1	1	yes	characteristic
65	C₂²×C₄×C₂₃	C₂³	1	4	yes	complemented
66	C₂×C₂²⋊D₂₃	—	2	8	no	—
67	C₂×C₂²⋊D₂₃	—	2	8	no	—
68	C₂×C₂²⋊D₂₃	—	2	4	no	—
69	C₂×C₂²⋊D₂₃	C₂³	1	8	yes	—
70	C₂×C₂²⋊D₂₃	C₂³	1	4	yes	—
71	C₂×C₂²⋊D₂₃	C₂³	1	8	yes	complemented
72	C₂²×Dic₂₃	C₂³	1	1	yes	characteristic
73	C₂²×Dic₂₃	C₂³	1	1	yes	characteristic
74	C₂²×Dic₂₃	C₂³	1	1	yes	characteristic
75	C₂²×Dic₂₃	C₂³	1	2	yes	—
76	D₄×D₂₃	—	2	32	no	—
77	#67288	—	2	32	no	—
78	C₂×D₉₂	D₄	1	8	yes	complemented
79	C₂×D₉₂	C₂³	1	4	yes	—
80	C₂×C₄×D₂₃	—	2	8	no	—
81	C₂×C₄×D₂₃	—	2	4	no	—
82	C₂×C₄×D₂₃	—	4	4	no	—
83	C₂×C₄×D₂₃	C₂³	1	4	yes	—
84	C₂×C₄×D₂₃	C₂³	1	8	yes	complemented
85	C₂×C₄×D₂₃	C₂³	1	8	yes	complemented
86	C₂×Dic₄₆	—	2	4	no	—
87	C₂×Dic₄₆	C₂³	1	4	yes	complemented
88	C₄⋊C₄×C₂₃	C₂³	1	4	yes	complemented
89	C₂²⋊C₄×C₂₃	C₂³	1	8	yes	complemented
90	C₂²⋊Dic₂₃	C₂³	1	8	yes	complemented
91	C₂²⋊Dic₂₃	C₂³	1	8	yes	complemented
92	C₂²⋊Dic₂₃	C₂³	1	4	yes	complemented
93	(C₂×D₂₃)⋊C₄	C₂³	1	4	yes	—
94	(C₂×D₂₃)⋊C₄	C₂³	1	8	yes	—
95	(C₂×D₂₃)⋊C₄	C₂³	1	8	yes	complemented
96	C₄⋊Dic₂₃	C₂³	1	8	yes	complemented
97	Dic₂₃⋊C₄	C₂³	1	4	yes	complemented
98	C₄×Dic₂₃	C₂³	1	4	yes	complemented
99	C₂³×C₂₃	—	2	2	no	—
100	C₂³×C₂₃	—	2	4	no	—
101	C₂³×C₂₃	—	2	2	no	—
102	C₂³×C₂₃	—	2	4	no	—
103	C₂³×C₂₃	—	2	2	no	—
104	C₂³×C₂₃	—	2	4	no	—
105	C₂³×C₂₃	C₂⁴	1	4	yes	—
106	C₂³×C₂₃	C₂⁴	1	2	yes	—
107	C₂³×C₂₃	C₂⁴	1	1	yes	characteristic
108	C₂²×D₂₃	—	2	2	no	—
109	C₂²×D₂₃	—	2	4	no	—
110	C₂²×D₂₃	—	2	4	no	—
111	C₂²×D₂₃	—	2	2	no	—
112	C₂²×D₂₃	—	2	16	no	—
113	C₂²×D₂₃	—	2	16	no	—
114	C₂²×D₂₃	—	4	8	no	—
115	C₂²×D₂₃	—	4	32	no	—
116	C₂²×D₂₃	C₂×D₄	1	8	yes	—
117	C₂²×D₂₃	#41	1	4	yes	complemented
118	C₂²×D₂₃	C₂⁴	1	4	yes	—
119	C₂²×D₂₃	C₂⁴	1	2	yes	—
120	D₄×C₂₃	—	2	8	no	—
121	D₄×C₂₃	—	4	8	no	—
122	C₂×C₄×C₂₃	—	2	2	no	—
123	C₂×C₄×C₂₃	—	2	4	no	—
124	C₂×C₄×C₂₃	—	2	8	no	—
125	C₂×C₄×C₂₃	C₂×D₄	1	4	yes	—
126	C₂×C₄×C₂₃	C₂⁴	1	2	yes	—
127	C₂×C₄×C₂₃	C₂⁴	1	4	yes	—
128	C₂×C₄×C₂₃	C₂⁴	1	2	yes	—
129	C₂²⋊D₂₃	—	2	16	no	—
130	C₂²⋊D₂₃	—	2	16	no	—
131	C₂²⋊D₂₃	—	2	8	no	—
132	C₂×Dic₂₃	—	2	4	no	—
133	C₂×Dic₂₃	—	2	2	no	—
134	C₂×Dic₂₃	—	2	2	no	—
135	C₂×Dic₂₃	—	2	2	no	—
136	C₂×Dic₂₃	C₂⁴	1	2	yes	—
137	C₂×Dic₂₃	C₂⁴	1	2	yes	—
138	C₂×Dic₂₃	C₂⁴	1	2	yes	—
139	C₂×Dic₂₃	C₂⁴	1	4	yes	—
140	D₉₂	C₂×D₄	1	16	yes	complemented
141	C₄×D₂₃	—	2	16	no	—
142	C₄×D₂₃	—	2	8	no	—
143	C₄×D₂₃	—	4	8	no	—
144	Dic₄₆	—	2	8	no	—
145	C₂×#546	—	23	1	no	maximal, Sylow
146	C₂²×C₂₃	—	2	2	no	—
147	C₂²×C₂₃	—	2	4	no	—
148	C₂²×C₂₃	—	2	2	no	—
149	C₂²×C₂₃	—	2	4	no	—
150	C₂²×C₂₃	—	2	2	no	—
151	C₂²×C₂₃	—	2	4	no	—
152	C₂²×C₂₃	—	4	8	no	—
153	C₂²×C₂₃	—	4	4	no	—
154	C₂²×C₂₃	C₂²×D₄	1	2	yes	—
155	C₂²×C₂₃	C₂×#41	1	2	yes	—
156	C₂²×C₂₃	H(5,𝔽₂)	1	2	yes	—
157	C₂²×C₂₃	C₂⁵	1	1	yes	characteristic
158	C₂×D₂₃	—	2	8	no	—
159	C₂×D₂₃	—	2	16	no	—
160	C₂×D₂₃	—	2	2	no	—
161	C₂×D₂₃	—	2	4	no	—
162	C₂×D₂₃	—	2	4	no	—
163	C₂×D₂₃	—	2	2	no	—
164	C₂×D₂₃	—	4	32	no	—
165	C₂×D₂₃	C₂²×D₄	1	8	yes	—
166	C₂×D₂₃	C₂×#41	1	4	yes	complemented
167	C₄×C₂₃	—	2	2	no	—
168	C₄×C₂₃	—	2	4	no	—
169	C₄×C₂₃	C₂²×D₄	1	4	yes	—
170	Dic₂₃	—	2	4	no	—
171	Dic₂₃	—	2	2	no	—
172	Dic₂₃	—	2	2	no	—
173	Dic₂₃	—	2	2	no	—
174	C₂²×#41	—	23	1	no	—
175	C₂³×D₄	—	23	1	no	—
176	#546	—	23	16	no	—
177	C₂×#124	—	23	1	no	—
178	C₂×#123	—	23	2	no	—
179	C₂×C₂²⋊Q₈	—	23	1	no	—
180	C₂×#121	—	23	2	no	—
181	C₂×#121	D₂₃	1	1	yes	characteristic, complemented
182	C₂×#120	—	23	2	no	—
183	C₂×C₄×D₄	—	23	1	no	—
184	C₂×C₄×D₄	—	23	1	no	—
185	C₂²×C₂²⋊C₄	—	23	2	no	—
186	C₂×C₂₃	—	4	4	no	—
187	C₂×C₂₃	—	4	2	no	—
188	C₂×C₂₃	#546	1	4	yes	complemented
189	C₂×C₂₃	C₂³×D₄	1	1	yes	characteristic
190	C₂×C₂₃	C₂²×#41	1	1	yes	characteristic
191	C₂×C₂₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
192	D₂₃	—	2	4	no	—
193	D₂₃	—	2	8	no	—
194	C₂⁵	—	23	2	no	—
195	C₂×#41	—	23	8	no	—
196	C₂×#41	—	46	8	no	—
197	C₂²×Q₈	—	23	1	no	—
198	C₂²×D₄	—	23	1	no	—
199	C₂²×D₄	—	23	2	no	—
200	C₂²×D₄	—	23	2	no	—
201	C₂²×D₄	—	23	8	no	—
202	C₂²×D₄	—	23	1	no	—
203	C₂²×D₄	—	46	8	no	—
204	C₂²×D₄	C₂×D₂₃	1	1	yes	characteristic
205	C₂²×D₄	C₂×D₂₃	1	2	yes	complemented
206	C₂³×C₄	—	23	2	no	—
207	C₂³×C₄	—	23	1	no	—
208	C₂³×C₄	—	23	2	no	—
209	C₂³×C₄	C₂×D₂₃	1	1	yes	characteristic, complemented
210	#124	—	23	8	no	—
211	#123	—	23	16	no	—
212	C₂²⋊Q₈	—	23	8	no	—
213	#121	—	23	16	no	—
214	#121	C₂×D₂₃	1	8	yes	complemented
215	#120	—	23	16	no	—
216	C₄×D₄	—	23	8	no	—
217	C₄×D₄	—	23	8	no	—
218	C₂×C₄⋊C₄	—	23	1	no	—
219	C₂×C₄⋊C₄	—	23	2	no	—
220	C₂×C₄⋊C₄	C₂×D₂₃	1	1	yes	characteristic, complemented
221	C₂×C₂²⋊C₄	—	23	2	no	—
222	C₂×C₂²⋊C₄	—	23	1	no	—
223	C₂×C₂²⋊C₄	—	23	2	no	—
224	C₂×C₂²⋊C₄	—	23	1	no	—
225	C₂×C₂²⋊C₄	—	23	2	no	—
226	C₂×C₂²⋊C₄	—	23	2	no	—
227	C₂×C₂²⋊C₄	—	23	16	no	—
228	C₂×C₂²⋊C₄	C₂×D₂₃	1	2	yes	complemented
229	C₂×C₄²	—	23	1	no	—
230	C₂₃	C₂×#546	1	1	yes	characteristic, complemented, Sylow
231	C₂⁴	—	23	1	no	—
232	C₂⁴	—	23	2	no	—
233	C₂⁴	—	23	8	no	—
234	C₂⁴	—	46	8	no	—
235	C₂⁴	—	46	8	no	—
236	C₂⁴	—	92	4	no	—
237	C₂⁴	C₂²×D₂₃	1	2	yes	—
238	C₂⁴	C₂²×D₂₃	1	1	yes	characteristic
239	#41	—	46	32	no	—
240	C₂×Q₈	—	23	4	no	—
241	C₂×Q₈	—	46	4	no	—
242	C₂×D₄	—	2	4	no	—
243	C₂×D₄	—	4	4	no	—
244	C₂×D₄	—	23	4	no	—
245	C₂×D₄	—	23	8	no	—
246	C₂×D₄	—	23	8	no	—
247	C₂×D₄	—	23	8	no	—
248	C₂×D₄	—	23	4	no	—
249	C₂×D₄	—	46	32	no	—
250	C₂×D₄	—	46	8	no	—
251	C₂×D₄	—	46	8	no	—
252	C₂×D₄	—	46	4	no	—
253	C₂×D₄	C₂²×D₂₃	1	4	yes	—
254	C₂×D₄	C₂²×D₂₃	1	8	yes	complemented
255	C₂²×C₄	—	2	4	no	—
256	C₂²×C₄	—	23	1	no	—
257	C₂²×C₄	—	23	1	no	—
258	C₂²×C₄	—	23	2	no	—
259	C₂²×C₄	—	23	1	no	—
260	C₂²×C₄	—	23	8	no	—
261	C₂²×C₄	—	23	4	no	—
262	C₂²×C₄	—	23	8	no	—
263	C₂²×C₄	—	46	8	no	—
264	C₂²×C₄	—	46	4	no	—
265	C₂²×C₄	—	92	4	no	—
266	C₂²×C₄	C₂²×D₂₃	1	2	yes	—
267	C₂²×C₄	C₂²×D₂₃	1	1	yes	characteristic
268	C₂²×C₄	C₂²×D₂₃	1	1	yes	characteristic
269	C₂²×C₄	C₂²×D₂₃	1	4	yes	complemented
270	C₄⋊C₄	—	23	4	no	—
271	C₄⋊C₄	—	23	8	no	—
272	C₄⋊C₄	C₂²×D₂₃	1	4	yes	complemented
273	C₂²⋊C₄	—	23	8	no	—
274	C₂²⋊C₄	—	23	4	no	—
275	C₂²⋊C₄	—	23	8	no	—
276	C₂²⋊C₄	—	23	4	no	—
277	C₂²⋊C₄	—	23	8	no	—
278	C₂²⋊C₄	—	23	8	no	—
279	C₂²⋊C₄	C₂²×D₂₃	1	8	yes	complemented
280	C₄²	—	23	4	no	—
281	C₂³	—	2	2	no	—
282	C₂³	—	2	4	no	—
283	C₂³	—	2	2	no	—
284	C₂³	—	2	4	no	—
285	C₂³	—	2	2	no	—
286	C₂³	—	2	4	no	—
287	C₂³	—	23	8	no	—
288	C₂³	—	23	4	no	—
289	C₂³	—	23	2	no	—
290	C₂³	—	23	4	no	—
291	C₂³	—	46	16	no	—
292	C₂³	—	46	16	no	—
293	C₂³	—	46	2	no	—
294	C₂³	—	46	4	no	—
295	C₂³	—	46	2	no	—
296	C₂³	—	46	4	no	—
297	C₂³	—	92	8	no	—
298	C₂³	—	92	32	no	—
299	C₂³	C₂³×D₂₃	1	4	yes	—
300	C₂³	C₂³×D₂₃	1	2	yes	—
301	C₂³	C₂³×D₂₃	1	1	yes	characteristic
302	Q₈	—	46	8	no	—
303	D₄	—	2	8	no	—
304	D₄	—	4	8	no	—
305	D₄	—	23	16	no	—
306	D₄	—	46	16	no	—
307	D₄	—	46	16	no	—
308	D₄	—	46	8	no	—
309	C₂×C₄	—	2	2	no	—
310	C₂×C₄	—	2	4	no	—
311	C₂×C₄	—	2	8	no	—
312	C₂×C₄	—	23	2	no	—
313	C₂×C₄	—	23	2	no	—
314	C₂×C₄	—	23	4	no	—
315	C₂×C₄	—	23	2	no	—
316	C₂×C₄	—	46	16	no	—
317	C₂×C₄	—	46	2	no	—
318	C₂×C₄	—	46	4	no	—
319	C₂×C₄	—	46	2	no	—
320	C₂×C₄	—	46	2	no	—
321	C₂×C₄	—	46	8	no	—
322	C₂×C₄	—	92	8	no	—
323	C₂×C₄	D₄×D₂₃	1	4	yes	—
324	C₂×C₄	C₂³×D₂₃	1	4	yes	—
325	C₂×C₄	C₂³×D₂₃	1	2	yes	—
326	C₂×C₄	C₂³×D₂₃	1	2	yes	—
327	C₂²	—	2	2	no	—
328	C₂²	—	2	4	no	—
329	C₂²	—	2	2	no	—
330	C₂²	—	2	4	no	—
331	C₂²	—	2	2	no	—
332	C₂²	—	2	4	no	—
333	C₂²	—	4	8	no	—
334	C₂²	—	4	4	no	—
335	C₂²	—	23	8	no	—
336	C₂²	—	23	4	no	—
337	C₂²	—	46	2	no	—
338	C₂²	—	46	4	no	—
339	C₂²	—	46	4	no	—
340	C₂²	—	46	2	no	—
341	C₂²	—	46	8	no	—
342	C₂²	—	46	16	no	—
343	C₂²	—	92	32	no	—
344	C₂²	C₂×D₄×D₂₃	1	2	yes	—
345	C₂²	#10625155	1	2	yes	—
346	C₂²	#41×D₂₃	1	2	yes	—
347	C₂²	C₂⁴×D₂₃	1	1	yes	characteristic
348	C₄	—	2	2	no	—
349	C₄	—	2	4	no	—
350	C₄	—	46	2	no	—
351	C₄	—	46	4	no	—
352	C₄	—	46	2	no	—
353	C₄	—	46	2	no	—
354	C₄	C₂×D₄×D₂₃	1	4	yes	—
355	C₂	—	4	4	no	—
356	C₂	—	4	2	no	—
357	C₂	—	46	4	no	—
358	C₂	—	46	8	no	—
359	C₂	#13093064	1	4	yes	direct product factor
360	C₂	C₂²×D₄×D₂₃	1	1	yes	characteristic
361	C₂	C₂×#41×D₂₃	1	1	yes	characteristic
362	C₂	C₂×#10625155	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂³×D₂₃
commutator, cosocle	C₂²×C₂₃	C₂⁵
Frattini	C₂²	C₂⁴×D₂₃
Fitting	C₂×C₂₃×#121	C₂
socle	C₂³×C₂₃	C₂⁴
hypercenter	C₂×#121	D₂₃
hypocenter	C₂₃	C₂×#546
LCS	G ▷ C₂²×C₂₃ ▷ C₂₃
UCS	C₁ ◁ C₂³ ◁ C₂×#121

Complements

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

N	H ≅ G/N	type
1. C₂²×#67288	C₂	semidirect
2. C₂²×D₄×D₂₃	C₂	semidirect
3. #13093064	C₂	direct (N × H)
4. C₂×#10625107	C₂	semidirect
5. C₂×#10625054	C₂	semidirect
6. C₂×#10625068	C₂	semidirect
7. C₂×#10625109	C₂	semidirect
8. C₂×#10625108	C₂	semidirect
9. C₂×#10625064	C₂	semidirect
10. C₂×C₄×C₂²⋊D₂₃	C₂	semidirect
11. C₂×C₂²⋊C₄×D₂₃	C₂	semidirect
12. C₂×C₂₃×#121	C₂	semidirect
15. C₂²×D₄×C₂₃	C₂²	semidirect
16. C₂³×C₄×C₂₃	C₂²	semidirect
19. C₂²×C₂²⋊D₂₃	C₂²	semidirect
21. C₂×D₄×D₂₃	C₂²	semidirect
23. C₂×#67288	C₂²	semidirect
26. C₂²×C₄×D₂₃	C₂²	semidirect
27. C₂²×C₄×D₂₃	C₂²	semidirect
28. C₂²×Dic₄₆	C₂²	semidirect
29. C₂₃×#121	C₂²	semidirect
30. C₂×C₄⋊C₄×C₂₃	C₂²	semidirect
31. C₂×C₂²⋊C₄×C₂₃	C₂²	semidirect
32. C₂×C₂²⋊Dic₂₃	C₂²	semidirect
33. C₂×C₂²⋊Dic₂₃	C₂²	semidirect
34. C₂×C₂²⋊Dic₂₃	C₂²	semidirect
35. #10625109	C₂²	semidirect
36. #10625108	C₂²	semidirect
37. #10625107	C₂²	semidirect
38. C₄×C₂²⋊D₂₃	C₂²	semidirect
41. C₂×(C₂×D₂₃)⋊C₄	C₂²	semidirect
42. C₂×C₄⋊Dic₂₃	C₂²	semidirect
43. C₂×Dic₂₃⋊C₄	C₂²	semidirect
44. C₂×C₄×Dic₂₃	C₂²	semidirect
45. #10625068	C₂²	semidirect
46. #10625064	C₂²	semidirect
47. #10625054	C₂²	semidirect
48. C₂²⋊C₄×D₂₃	C₂²	semidirect
60. C₂×D₄×C₂₃	C₂³	semidirect
65. C₂²×C₄×C₂₃	C₂³	semidirect
71. C₂×C₂²⋊D₂₃	C₂³	semidirect
78. C₂×D₉₂	D₄	semidirect
84. C₂×C₄×D₂₃	C₂³	semidirect
85. C₂×C₄×D₂₃	C₂³	semidirect
87. C₂×Dic₄₆	C₂³	semidirect
88. C₄⋊C₄×C₂₃	C₂³	semidirect
89. C₂²⋊C₄×C₂₃	C₂³	semidirect
90. C₂²⋊Dic₂₃	C₂³	semidirect
91. C₂²⋊Dic₂₃	C₂³	semidirect
92. C₂²⋊Dic₂₃	C₂³	semidirect
95. (C₂×D₂₃)⋊C₄	C₂³	semidirect
96. C₄⋊Dic₂₃	C₂³	semidirect
97. Dic₂₃⋊C₄	C₂³	semidirect
98. C₄×Dic₂₃	C₂³	semidirect
117. C₂²×D₂₃	#41	semidirect
140. D₉₂	C₂×D₄	semidirect
166. C₂×D₂₃	C₂×#41	semidirect
181. C₂×#121	D₂₃	semidirect
188. C₂×C₂₃	#546	semidirect
205. C₂²×D₄	C₂×D₂₃	semidirect
209. C₂³×C₄	C₂×D₂₃	semidirect
214. #121	C₂×D₂₃	semidirect
220. C₂×C₄⋊C₄	C₂×D₂₃	semidirect
228. C₂×C₂²⋊C₄	C₂×D₂₃	semidirect
230. C₂₃	C₂×#546	semidirect
254. C₂×D₄	C₂²×D₂₃	semidirect
269. C₂²×C₄	C₂²×D₂₃	semidirect
272. C₄⋊C₄	C₂²×D₂₃	semidirect
279. C₂²⋊C₄	C₂²×D₂₃	semidirect
359. C₂	#13093064	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×#67288	2
C₂²×D₄×D₂₃	2
#13093064	2
C₂×#10625107	2
C₂×#10625054	2
C₂×#10625068	2
C₂×#10625109	2
C₂×#10625108	2
C₂×#10625064	2
C₂×C₄×C₂²⋊D₂₃	2
C₂×C₂²⋊C₄×D₂₃	2
C₂×C₂₃×#121	2
C₂×#546	23

Subgroups — C2×#13093064 #15686849

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#13093064 #15686849