Subgroups — C₂×#13092927 #15686638

Order 2944.

1880 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	C₂²×#67290	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂³×C₄×D₂₃	C₂	1	1	yes	maximal, characteristic, complemented
3	#13092927	C₂	1	16	yes	maximal, direct product factor
4	C₂×#10625054	C₂	1	2	yes	maximal, complemented
5	C₂×#10625068	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#10625095	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#10625109	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#10625108	C₂	1	2	yes	maximal, complemented
9	C₂×D₄×Dic₂₃	C₂	1	2	yes	maximal, complemented
10	C₂×(C₂²⋊D₂₃)⋊C₄	C₂	1	2	yes	maximal, complemented
11	C₂×#10625063	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₂₃×#121	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂⁴×D₂₃	C₂²	1	1	yes	characteristic
14	C₂²×D₄×C₂₃	C₂²	1	2	yes	—
15	C₂²×D₄×C₂₃	C₂²	1	1	yes	characteristic, complemented
16	C₂³×C₄×C₂₃	C₂²	1	1	yes	characteristic
17	C₂²×C₂²⋊D₂₃	C₂²	1	2	yes	—
18	C₂²×C₂²⋊D₂₃	C₂²	1	2	yes	—
19	C₂³×Dic₂₃	C₂²	1	1	yes	characteristic
20	C₂³×Dic₂₃	C₂²	1	2	yes	complemented
21	C₂×#67290	—	2	8	no	—
22	C₂×#67290	C₂²	1	8	yes	complemented
23	C₂²×C₄×D₂₃	—	2	8	no	—
24	C₂²×C₄×D₂₃	C₂²	1	1	yes	characteristic
25	C₂²×C₄×D₂₃	C₂²	1	1	yes	characteristic
26	C₂²×C₄×D₂₃	C₂²	1	1	yes	characteristic
27	C₂²×C₄×D₂₃	C₂²	1	1	yes	characteristic
28	C₂²×C₄×D₂₃	C₂²	1	8	yes	complemented
29	C₂²×Dic₄₆	C₂²	1	1	yes	characteristic, complemented
30	C₂₃×#121	C₂²	1	8	yes	complemented
31	C₂×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic, complemented
32	C₂×C₂²⋊C₄×C₂₃	C₂²	1	2	yes	complemented
33	C₂×C₂²⋊Dic₂₃	C₂²	1	2	yes	—
34	C₂×C₂²⋊Dic₂₃	C₂²	1	2	yes	complemented
35	#10625109	C₂²	1	8	yes	complemented
36	#10625108	C₂²	1	16	yes	complemented
37	D₄×Dic₂₃	C₂²	1	16	yes	complemented
38	C₂×(C₂×D₂₃)⋊C₄	C₂²	1	2	yes	—
39	C₂×(C₂×D₂₃)⋊C₄	C₂²	1	2	yes	—
40	C₂×C₄⋊Dic₂₃	C₂²	1	1	yes	characteristic, complemented
41	C₂×C₄⋊Dic₂₃	C₂²	1	2	yes	complemented
42	#10625095	C₂²	1	8	yes	complemented
43	C₂×Dic₂₃⋊C₄	C₂²	1	2	yes	complemented
44	C₂×C₄×Dic₂₃	C₂²	1	2	yes	complemented
45	#10625068	C₂²	1	8	yes	complemented
46	#10625063	C₂²	1	8	yes	complemented
47	#10625054	C₂²	1	16	yes	complemented
48	(C₂²⋊D₂₃)⋊C₄	C₂²	1	16	yes	complemented
49	C₂⁴×C₂₃	C₂³	1	2	yes	—
50	C₂⁴×C₂₃	C₂³	1	1	yes	characteristic
51	C₂³×D₂₃	—	2	4	no	—
52	C₂³×D₂₃	—	2	4	no	—
53	C₂³×D₂₃	—	2	4	no	—
54	C₂³×D₂₃	C₂³	1	4	yes	—
55	C₂³×D₂₃	C₂³	1	1	yes	characteristic
56	C₂³×D₂₃	C₂³	1	1	yes	characteristic
57	C₂×D₄×C₂₃	—	2	8	no	—
58	C₂×D₄×C₂₃	—	2	4	no	—
59	C₂×D₄×C₂₃	C₂³	1	8	yes	—
60	C₂×D₄×C₂₃	C₂³	1	4	yes	complemented
61	C₂²×C₄×C₂₃	—	2	4	no	—
62	C₂²×C₄×C₂₃	C₂³	1	2	yes	—
63	C₂²×C₄×C₂₃	C₂³	1	1	yes	characteristic
64	C₂²×C₄×C₂₃	C₂³	1	4	yes	—
65	C₂²×C₄×C₂₃	C₂³	1	1	yes	characteristic
66	C₂×C₂²⋊D₂₃	—	2	8	no	—
67	C₂×C₂²⋊D₂₃	—	2	8	no	—
68	C₂×C₂²⋊D₂₃	C₂³	1	8	yes	—
69	C₂×C₂²⋊D₂₃	C₂³	1	8	yes	—
70	C₂²×Dic₂₃	—	2	4	no	—
71	C₂²×Dic₂₃	—	2	8	no	—
72	C₂²×Dic₂₃	C₂³	1	2	yes	—
73	C₂²×Dic₂₃	C₂³	1	2	yes	—
74	C₂²×Dic₂₃	C₂³	1	1	yes	characteristic
75	C₂²×Dic₂₃	C₂³	1	4	yes	—
76	C₂²×Dic₂₃	C₂³	1	1	yes	characteristic
77	C₂²×Dic₂₃	C₂³	1	8	yes	complemented
78	#67290	—	2	32	no	—
79	C₂×C₄×D₂₃	—	2	4	no	—
80	C₂×C₄×D₂₃	—	2	4	no	—
81	C₂×C₄×D₂₃	—	2	4	no	—
82	C₂×C₄×D₂₃	—	2	32	no	—
83	C₂×C₄×D₂₃	D₄	1	8	yes	complemented
84	C₂×C₄×D₂₃	C₂³	1	4	yes	—
85	C₂×C₄×D₂₃	C₂³	1	4	yes	—
86	C₂×C₄×D₂₃	C₂³	1	4	yes	—
87	C₂×C₄×D₂₃	C₂³	1	4	yes	—
88	C₂×Dic₄₆	—	2	4	no	—
89	C₂×Dic₄₆	C₂³	1	4	yes	complemented
90	C₄⋊C₄×C₂₃	C₂³	1	4	yes	complemented
91	C₂²⋊C₄×C₂₃	C₂³	1	8	yes	complemented
92	C₂²⋊Dic₂₃	C₂³	1	8	yes	—
93	C₂²⋊Dic₂₃	C₂³	1	8	yes	complemented
94	(C₂×D₂₃)⋊C₄	C₂³	1	8	yes	—
95	(C₂×D₂₃)⋊C₄	C₂³	1	8	yes	—
96	C₄⋊Dic₂₃	C₂³	1	8	yes	complemented
97	C₄⋊Dic₂₃	C₂³	1	4	yes	complemented
98	Dic₂₃⋊C₄	C₂³	1	8	yes	complemented
99	C₄×Dic₂₃	C₂³	1	8	yes	complemented
100	C₂³×C₂₃	—	2	2	no	—
101	C₂³×C₂₃	—	2	2	no	—
102	C₂³×C₂₃	—	2	4	no	—
103	C₂³×C₂₃	—	2	4	no	—
104	C₂³×C₂₃	—	2	4	no	—
105	C₂³×C₂₃	#41	1	4	yes	complemented
106	C₂³×C₂₃	C₂⁴	1	4	yes	—
107	C₂³×C₂₃	C₂⁴	1	2	yes	—
108	C₂³×C₂₃	C₂⁴	1	1	yes	characteristic
109	C₂²×D₂₃	—	2	32	no	—
110	C₂²×D₂₃	—	2	2	no	—
111	C₂²×D₂₃	—	2	2	no	—
112	C₂²×D₂₃	—	2	2	no	—
113	C₂²×D₂₃	—	2	2	no	—
114	C₂²×D₂₃	—	2	8	no	—
115	C₂²×D₂₃	—	2	8	no	—
116	C₂²×D₂₃	—	2	8	no	—
117	C₂²×D₂₃	C₂×D₄	1	4	yes	—
118	C₂²×D₂₃	#41	1	4	yes	complemented
119	C₂²×D₂₃	C₂⁴	1	2	yes	—
120	C₂²×D₂₃	C₂⁴	1	2	yes	—
121	D₄×C₂₃	—	2	16	no	—
122	D₄×C₂₃	—	2	8	no	—
123	C₂×C₄×C₂₃	—	2	2	no	—
124	C₂×C₄×C₂₃	—	2	4	no	—
125	C₂×C₄×C₂₃	—	2	8	no	—
126	C₂×C₄×C₂₃	C₂×D₄	1	4	yes	—
127	C₂×C₄×C₂₃	C₂⁴	1	4	yes	—
128	C₂×C₄×C₂₃	C₂⁴	1	2	yes	—
129	C₂×C₄×C₂₃	C₂⁴	1	2	yes	—
130	C₂²⋊D₂₃	—	2	16	no	—
131	C₂²⋊D₂₃	—	2	16	no	—
132	C₂×Dic₂₃	—	2	4	no	—
133	C₂×Dic₂₃	—	2	2	no	—
134	C₂×Dic₂₃	—	2	4	no	—
135	C₂×Dic₂₃	—	2	8	no	—
136	C₂×Dic₂₃	—	2	16	no	—
137	C₂×Dic₂₃	C₂×D₄	1	4	yes	—
138	C₂×Dic₂₃	C₂⁴	1	4	yes	—
139	C₂×Dic₂₃	C₂⁴	1	4	yes	—
140	C₂×Dic₂₃	C₂⁴	1	2	yes	—
141	C₂×Dic₂₃	C₂⁴	1	2	yes	—
142	C₄×D₂₃	—	2	8	no	—
143	C₄×D₂₃	—	2	8	no	—
144	C₄×D₂₃	—	2	8	no	—
145	C₄×D₂₃	C₂×D₄	1	16	yes	complemented
146	Dic₄₆	—	2	8	no	—
147	C₂×#525	—	23	1	no	maximal, Sylow
148	C₂²×C₂₃	—	2	8	no	—
149	C₂²×C₂₃	—	2	2	no	—
150	C₂²×C₂₃	—	2	2	no	—
151	C₂²×C₂₃	—	2	4	no	—
152	C₂²×C₂₃	—	2	4	no	—
153	C₂²×C₂₃	—	2	4	no	—
154	C₂²×C₂₃	—	4	8	no	—
155	C₂²×C₂₃	C₂²×D₄	1	2	yes	—
156	C₂²×C₂₃	C₂×#41	1	2	yes	—
157	C₂²×C₂₃	C₂×#41	1	2	yes	—
158	C₂²×C₂₃	C₂×#41	1	4	yes	complemented
159	C₂²×C₂₃	C₂⁵	1	1	yes	characteristic
160	C₂×D₂₃	—	2	32	no	—
161	C₂×D₂₃	—	2	8	no	—
162	C₂×D₂₃	—	2	8	no	—
163	C₂×D₂₃	—	2	2	no	—
164	C₂×D₂₃	—	2	2	no	—
165	C₂×D₂₃	—	2	2	no	—
166	C₂×D₂₃	—	2	2	no	—
167	C₂×D₂₃	C₂²×D₄	1	4	yes	—
168	C₂×D₂₃	C₂×#41	1	4	yes	complemented
169	C₄×C₂₃	—	2	2	no	—
170	C₄×C₂₃	—	2	4	no	—
171	C₄×C₂₃	C₂²×D₄	1	4	yes	—
172	Dic₂₃	—	2	4	no	—
173	Dic₂₃	—	2	2	no	—
174	Dic₂₃	—	2	4	no	—
175	Dic₂₃	C₂²×D₄	1	4	yes	—
176	C₂²×#41	—	23	1	no	—
177	C₂⁴×C₄	—	23	1	no	—
178	#525	—	23	16	no	—
179	C₂×#123	—	23	2	no	—
180	C₂×C₂²⋊Q₈	—	23	1	no	—
181	C₂×C₂²⋊Q₈	—	23	1	no	—
182	C₂×#121	—	23	1	no	—
183	C₂×#121	D₂₃	1	1	yes	characteristic, complemented
184	C₂×#120	—	23	2	no	—
185	C₂×C₄×D₄	—	23	2	no	—
186	C₂×C₄×D₄	—	23	2	no	—
187	C₂×#117	—	23	1	no	—
188	C₂×C₂₃	—	2	4	no	—
189	C₂×C₂₃	—	4	4	no	—
190	C₂×C₂₃	#525	1	4	yes	complemented
191	C₂×C₂₃	C₂³×D₄	1	1	yes	characteristic
192	C₂×C₂₃	C₂²×#41	1	1	yes	characteristic
193	C₂×C₂₃	C₂²×#41	1	1	yes	characteristic
194	D₂₃	—	2	4	no	—
195	D₂₃	—	2	4	no	—
196	C₂⁵	—	23	1	no	—
197	C₂×#41	—	23	8	no	—
198	C₂×#41	—	46	8	no	—
199	C₂²×Q₈	—	23	1	no	—
200	C₂²×D₄	—	23	2	no	—
201	C₂²×D₄	—	23	2	no	—
202	C₂²×D₄	C₂×D₂₃	1	2	yes	—
203	C₂²×D₄	C₂×D₂₃	1	1	yes	characteristic, complemented
204	C₂³×C₄	—	23	1	no	—
205	C₂³×C₄	—	23	1	no	—
206	C₂³×C₄	—	23	2	no	—
207	C₂³×C₄	—	23	1	no	—
208	C₂³×C₄	—	23	1	no	—
209	C₂³×C₄	—	23	1	no	—
210	C₂³×C₄	—	23	8	no	—
211	C₂³×C₄	—	46	8	no	—
212	C₂³×C₄	C₂×D₂₃	1	1	yes	characteristic
213	#123	—	23	16	no	—
214	C₂²⋊Q₈	—	23	8	no	—
215	C₂²⋊Q₈	—	23	8	no	—
216	#121	—	23	8	no	—
217	#121	C₂×D₂₃	1	8	yes	complemented
218	#120	—	23	16	no	—
219	C₄×D₄	—	23	16	no	—
220	C₄×D₄	—	23	16	no	—
221	#117	—	23	8	no	—
222	C₂×C₄⋊C₄	—	23	1	no	—
223	C₂×C₄⋊C₄	—	23	2	no	—
224	C₂×C₄⋊C₄	—	23	2	no	—
225	C₂×C₄⋊C₄	C₂×D₂₃	1	1	yes	characteristic, complemented
226	C₂×C₂²⋊C₄	—	23	2	no	—
227	C₂×C₂²⋊C₄	—	23	2	no	—
228	C₂×C₂²⋊C₄	—	23	2	no	—
229	C₂×C₂²⋊C₄	—	23	2	no	—
230	C₂×C₂²⋊C₄	C₂×D₂₃	1	2	yes	complemented
231	C₂×C₄²	—	23	2	no	—
232	C₂₃	C₂×#525	1	1	yes	characteristic, complemented, Sylow
233	C₂⁴	—	23	1	no	—
234	C₂⁴	—	23	1	no	—
235	C₂⁴	—	23	4	no	—
236	C₂⁴	—	46	4	no	—
237	C₂⁴	—	46	4	no	—
238	C₂⁴	—	46	4	no	—
239	C₂⁴	C₂²×D₂₃	1	2	yes	—
240	C₂⁴	C₂²×D₂₃	1	1	yes	characteristic
241	#41	—	46	32	no	—
242	C₂×Q₈	—	23	4	no	—
243	C₂×Q₈	—	46	4	no	—
244	C₂×D₄	—	2	8	no	—
245	C₂×D₄	—	2	4	no	—
246	C₂×D₄	—	23	8	no	—
247	C₂×D₄	—	23	8	no	—
248	C₂×D₄	—	46	8	no	—
249	C₂×D₄	—	46	8	no	—
250	C₂×D₄	C₂²×D₂₃	1	8	yes	—
251	C₂×D₄	C₂²×D₂₃	1	4	yes	complemented
252	C₂²×C₄	—	2	4	no	—
253	C₂²×C₄	—	23	1	no	—
254	C₂²×C₄	—	23	8	no	—
255	C₂²×C₄	—	23	4	no	—
256	C₂²×C₄	—	23	4	no	—
257	C₂²×C₄	—	23	8	no	—
258	C₂²×C₄	—	23	2	no	—
259	C₂²×C₄	—	23	1	no	—
260	C₂²×C₄	—	23	2	no	—
261	C₂²×C₄	—	23	4	no	—
262	C₂²×C₄	—	23	4	no	—
263	C₂²×C₄	—	23	4	no	—
264	C₂²×C₄	—	46	4	no	—
265	C₂²×C₄	—	46	32	no	—
266	C₂²×C₄	—	46	4	no	—
267	C₂²×C₄	—	46	4	no	—
268	C₂²×C₄	—	46	8	no	—
269	C₂²×C₄	—	46	4	no	—
270	C₂²×C₄	C₂²×D₂₃	1	4	yes	—
271	C₂²×C₄	C₂²×D₂₃	1	2	yes	—
272	C₂²×C₄	C₂²×D₂₃	1	1	yes	characteristic
273	C₂²×C₄	C₂²×D₂₃	1	1	yes	characteristic
274	C₄⋊C₄	—	23	4	no	—
275	C₄⋊C₄	—	23	8	no	—
276	C₄⋊C₄	—	23	8	no	—
277	C₄⋊C₄	C₂²×D₂₃	1	4	yes	complemented
278	C₂²⋊C₄	—	23	8	no	—
279	C₂²⋊C₄	—	23	8	no	—
280	C₂²⋊C₄	—	23	8	no	—
281	C₂²⋊C₄	—	23	8	no	—
282	C₂²⋊C₄	C₂²×D₂₃	1	8	yes	complemented
283	C₄²	—	23	8	no	—
284	C₂³	—	2	2	no	—
285	C₂³	—	2	2	no	—
286	C₂³	—	2	4	no	—
287	C₂³	—	2	4	no	—
288	C₂³	—	2	4	no	—
289	C₂³	—	23	4	no	—
290	C₂³	—	23	4	no	—
291	C₂³	—	23	2	no	—
292	C₂³	—	23	2	no	—
293	C₂³	—	46	8	no	—
294	C₂³	—	46	8	no	—
295	C₂³	—	46	32	no	—
296	C₂³	—	46	2	no	—
297	C₂³	—	46	2	no	—
298	C₂³	—	46	2	no	—
299	C₂³	—	46	8	no	—
300	C₂³	—	46	2	no	—
301	C₂³	#67290	1	4	yes	complemented
302	C₂³	C₂³×D₂₃	1	4	yes	—
303	C₂³	C₂³×D₂₃	1	2	yes	—
304	C₂³	C₂³×D₂₃	1	1	yes	characteristic
305	Q₈	—	46	8	no	—
306	D₄	—	2	16	no	—
307	D₄	—	2	8	no	—
308	D₄	—	46	16	no	—
309	D₄	—	46	16	no	—
310	C₂×C₄	—	2	2	no	—
311	C₂×C₄	—	2	4	no	—
312	C₂×C₄	—	2	8	no	—
313	C₂×C₄	—	23	4	no	—
314	C₂×C₄	—	23	2	no	—
315	C₂×C₄	—	23	16	no	—
316	C₂×C₄	—	23	4	no	—
317	C₂×C₄	—	23	2	no	—
318	C₂×C₄	—	23	4	no	—
319	C₂×C₄	—	46	8	no	—
320	C₂×C₄	—	46	8	no	—
321	C₂×C₄	—	46	8	no	—
322	C₂×C₄	—	46	16	no	—
323	C₂×C₄	—	46	2	no	—
324	C₂×C₄	—	46	4	no	—
325	C₂×C₄	—	46	4	no	—
326	C₂×C₄	—	46	8	no	—
327	C₂×C₄	D₄×D₂₃	1	4	yes	—
328	C₂×C₄	C₂³×D₂₃	1	4	yes	—
329	C₂×C₄	C₂³×D₂₃	1	2	yes	—
330	C₂×C₄	C₂³×D₂₃	1	2	yes	—
331	C₂²	—	2	8	no	—
332	C₂²	—	2	2	no	—
333	C₂²	—	2	2	no	—
334	C₂²	—	2	4	no	—
335	C₂²	—	2	4	no	—
336	C₂²	—	2	4	no	—
337	C₂²	—	4	8	no	—
338	C₂²	—	23	4	no	—
339	C₂²	—	23	4	no	—
340	C₂²	—	46	32	no	—
341	C₂²	—	46	8	no	—
342	C₂²	—	46	8	no	—
343	C₂²	—	46	2	no	—
344	C₂²	—	46	2	no	—
345	C₂²	—	46	2	no	—
346	C₂²	—	46	2	no	—
347	C₂²	C₂×D₄×D₂₃	1	2	yes	—
348	C₂²	C₂×#67290	1	2	yes	—
349	C₂²	C₂×#67290	1	4	yes	complemented
350	C₂²	#41×D₂₃	1	2	yes	—
351	C₂²	C₂⁴×D₂₃	1	1	yes	characteristic
352	C₄	—	2	2	no	—
353	C₄	—	2	4	no	—
354	C₄	—	23	4	no	—
355	C₄	—	46	2	no	—
356	C₄	—	46	4	no	—
357	C₄	—	46	4	no	—
358	C₄	C₂×D₄×D₂₃	1	4	yes	—
359	C₂	—	2	4	no	—
360	C₂	—	4	4	no	—
361	C₂	—	46	4	no	—
362	C₂	—	46	4	no	—
363	C₂	#13092927	1	4	yes	direct product factor
364	C₂	C₂²×D₄×D₂₃	1	1	yes	characteristic
365	C₂	C₂×#41×D₂₃	1	1	yes	characteristic
366	C₂	C₂²×#67290	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×#525
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×#67290	C₂	semidirect
2. C₂³×C₄×D₂₃	C₂	semidirect
3. #13092927	C₂	direct (N × H)
4. C₂×#10625054	C₂	semidirect
5. C₂×#10625068	C₂	semidirect
6. C₂×#10625095	C₂	semidirect
7. C₂×#10625109	C₂	semidirect
8. C₂×#10625108	C₂	semidirect
9. C₂×D₄×Dic₂₃	C₂	semidirect
10. C₂×(C₂²⋊D₂₃)⋊C₄	C₂	semidirect
11. C₂×#10625063	C₂	semidirect
12. C₂×C₂₃×#121	C₂	semidirect
15. C₂²×D₄×C₂₃	C₂²	semidirect
20. C₂³×Dic₂₃	C₂²	semidirect
22. C₂×#67290	C₂²	semidirect
28. C₂²×C₄×D₂₃	C₂²	semidirect
29. C₂²×Dic₄₆	C₂²	semidirect
30. C₂₃×#121	C₂²	semidirect
31. C₂×C₄⋊C₄×C₂₃	C₂²	semidirect
32. C₂×C₂²⋊C₄×C₂₃	C₂²	semidirect
34. C₂×C₂²⋊Dic₂₃	C₂²	semidirect
35. #10625109	C₂²	semidirect
36. #10625108	C₂²	semidirect
37. D₄×Dic₂₃	C₂²	semidirect
40. C₂×C₄⋊Dic₂₃	C₂²	semidirect
41. C₂×C₄⋊Dic₂₃	C₂²	semidirect
42. #10625095	C₂²	semidirect
43. C₂×Dic₂₃⋊C₄	C₂²	semidirect
44. C₂×C₄×Dic₂₃	C₂²	semidirect
45. #10625068	C₂²	semidirect
46. #10625063	C₂²	semidirect
47. #10625054	C₂²	semidirect
48. (C₂²⋊D₂₃)⋊C₄	C₂²	semidirect
60. C₂×D₄×C₂₃	C₂³	semidirect
77. C₂²×Dic₂₃	C₂³	semidirect
83. C₂×C₄×D₂₃	D₄	semidirect
89. C₂×Dic₄₆	C₂³	semidirect
90. C₄⋊C₄×C₂₃	C₂³	semidirect
91. C₂²⋊C₄×C₂₃	C₂³	semidirect
93. C₂²⋊Dic₂₃	C₂³	semidirect
96. C₄⋊Dic₂₃	C₂³	semidirect
97. C₄⋊Dic₂₃	C₂³	semidirect
98. Dic₂₃⋊C₄	C₂³	semidirect
99. C₄×Dic₂₃	C₂³	semidirect
105. C₂³×C₂₃	#41	semidirect
118. C₂²×D₂₃	#41	semidirect
145. C₄×D₂₃	C₂×D₄	semidirect
158. C₂²×C₂₃	C₂×#41	semidirect
168. C₂×D₂₃	C₂×#41	semidirect
183. C₂×#121	D₂₃	semidirect
190. C₂×C₂₃	#525	semidirect
203. C₂²×D₄	C₂×D₂₃	semidirect
217. #121	C₂×D₂₃	semidirect
225. C₂×C₄⋊C₄	C₂×D₂₃	semidirect
230. C₂×C₂²⋊C₄	C₂×D₂₃	semidirect
232. C₂₃	C₂×#525	semidirect
251. C₂×D₄	C₂²×D₂₃	semidirect
277. C₄⋊C₄	C₂²×D₂₃	semidirect
282. C₂²⋊C₄	C₂²×D₂₃	semidirect
301. C₂³	#67290	semidirect
349. C₂²	C₂×#67290	semidirect
363. C₂	#13092927	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×#67290	2
C₂³×C₄×D₂₃	2
#13092927	2
C₂×#10625054	2
C₂×#10625068	2
C₂×#10625095	2
C₂×#10625109	2
C₂×#10625108	2
C₂×D₄×Dic₂₃	2
C₂×(C₂²⋊D₂₃)⋊C₄	2
C₂×#10625063	2
C₂×C₂₃×#121	2
C₂×#525	23

Subgroups — C2×#13092927 #15686638

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#13092927 #15686638