Subgroups — C₂×C₂₃×#3195 #19208364

Order 5888.

2322 conjugacy classes of subgroups.

The subgroup lattice has 334 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₂₃×C₂²⋊Q₈	C₂	1	2	yes	maximal
2	C₂₃×#3195	C₂	1	16	yes	maximal, direct product factor
3	C₂×C₂₃×#483	C₂	1	4	yes	maximal, complemented
4	C₂×C₂₃×#470	C₂	1	4	yes	maximal, complemented
5	C₂×C₂₃×#451	C₂	1	4	yes	maximal, complemented
6	C₂×C₂₃×#407	C₂	1	1	yes	maximal, characteristic
7	C₂³×Q₈×C₂₃	C₂²	1	2	yes	—
8	C₂⁴×C₄×C₂₃	C₂²	1	1	yes	characteristic
9	C₂²×Q₁₆×C₂₃	C₂²	1	4	yes	complemented
10	C₂²×M₁₆×C₂₃	C₂²	1	2	yes	—
11	C₂×C₂₃×C₂²⋊Q₈	—	2	2	no	—
12	C₂×C₂₃×C₂²⋊Q₈	—	2	8	no	—
13	C₂×C₂₃×C₂²⋊Q₈	—	2	2	no	—
14	C₂×C₂₃×C₂²⋊Q₈	C₂²	1	16	yes	—
15	C₂×C₂₃×C₂²⋊Q₈	C₂²	1	4	yes	—
16	C₂×C₂₃×C₂²⋊Q₈	C₂²	1	4	yes	—
17	C₂²×C₄⋊C₄×C₂₃	—	2	2	no	—
18	C₂²×C₄⋊C₄×C₂₃	C₂²	1	2	yes	—
19	C₂²×C₂²⋊C₄×C₂₃	—	2	2	no	—
20	C₂₃×#483	C₂²	1	32	yes	complemented
21	C₂₃×#470	C₂²	1	32	yes	complemented
22	C₂₃×#451	C₂²	1	32	yes	complemented
23	C₂×C₂₃×#106	C₂²	1	4	yes	complemented
24	C₂×C₂₃×#103	C₂²	1	8	yes	complemented
25	C₂₃×#407	C₂²	1	8	yes	—
26	C₂×C₂₃×C₂²⋊C₈	C₂²	1	4	yes	—
27	C₂⁵×C₂₃	D₄	1	1	yes	characteristic
28	C₂²×Q₈×C₂₃	—	2	4	no	—
29	C₂²×Q₈×C₂₃	—	2	2	no	—
30	C₂²×Q₈×C₂₃	—	4	8	no	—
31	C₂²×Q₈×C₂₃	C₂³	1	4	yes	—
32	C₂²×Q₈×C₂₃	C₂³	1	8	yes	—
33	C₂³×C₄×C₂₃	—	2	2	no	—
34	C₂³×C₄×C₂₃	—	2	2	no	—
35	C₂³×C₄×C₂₃	—	4	4	no	—
36	C₂³×C₄×C₂₃	D₄	1	2	yes	—
37	C₂³×C₄×C₂₃	D₄	1	4	yes	—
38	C₂³×C₄×C₂₃	D₄	1	1	yes	characteristic
39	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
40	C₂³×C₄×C₂₃	C₂³	1	2	yes	—
41	C₂³×C₄×C₂₃	C₂³	1	4	yes	—
42	C₂×Q₁₆×C₂₃	—	4	8	no	—
43	C₂×Q₁₆×C₂₃	C₂³	1	16	yes	complemented
44	C₂×M₁₆×C₂₃	—	4	4	no	—
45	C₂×M₁₆×C₂₃	C₂³	1	8	yes	—
46	C₂²×C₈×C₂₃	C₂³	1	4	yes	—
47	C₂₃×C₂²⋊Q₈	—	2	8	no	—
48	C₂₃×C₂²⋊Q₈	—	2	8	no	—
49	C₂₃×C₂²⋊Q₈	—	2	16	no	—
50	C₂₃×C₂²⋊Q₈	—	2	16	no	—
51	C₂₃×C₂²⋊Q₈	C₂³	1	16	yes	—
52	C₂₃×C₂²⋊Q₈	C₂³	1	16	yes	—
53	C₂×C₄⋊C₄×C₂₃	—	2	16	no	—
54	C₂×C₄⋊C₄×C₂₃	—	2	4	no	—
55	C₂×C₄⋊C₄×C₂₃	—	2	4	no	—
56	C₂×C₄⋊C₄×C₂₃	—	2	4	no	—
57	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
58	C₂×C₄⋊C₄×C₂₃	C₂³	1	4	yes	—
59	C₂×C₄⋊C₄×C₂₃	C₂³	1	8	yes	—
60	C₂×C₂²⋊C₄×C₂₃	—	2	16	no	—
61	C₂×C₂²⋊C₄×C₂₃	—	2	4	no	—
62	C₂×C₂²⋊C₄×C₂₃	—	2	4	no	—
63	C₂₃×#106	C₂³	1	16	yes	complemented
64	C₂₃×#103	C₂³	1	32	yes	complemented
65	C₂₃×C₂²⋊C₈	C₂³	1	16	yes	—
66	C₂⁴×C₂₃	—	2	8	no	—
67	C₂⁴×C₂₃	—	4	2	no	—
68	C₂⁴×C₂₃	C₂×D₄	1	1	yes	characteristic
69	C₂⁴×C₂₃	C₂×D₄	1	4	yes	—
70	C₂⁴×C₂₃	C₂×D₄	1	2	yes	—
71	C₂×Q₈×C₂₃	—	2	8	no	—
72	C₂×Q₈×C₂₃	—	2	4	no	—
73	C₂×Q₈×C₂₃	—	2	16	no	—
74	C₂×Q₈×C₂₃	—	4	16	no	—
75	C₂×Q₈×C₂₃	—	4	8	no	—
76	C₂×Q₈×C₂₃	—	4	16	no	—
77	C₂×Q₈×C₂₃	C₂⁴	1	8	yes	—
78	C₂²×C₄×C₂₃	—	2	4	no	—
79	C₂²×C₄×C₂₃	—	2	8	no	—
80	C₂²×C₄×C₂₃	—	2	8	no	—
81	C₂²×C₄×C₂₃	—	2	8	no	—
82	C₂²×C₄×C₂₃	—	2	4	no	—
83	C₂²×C₄×C₂₃	—	2	4	no	—
84	C₂²×C₄×C₂₃	—	4	8	no	—
85	C₂²×C₄×C₂₃	—	4	8	no	—
86	C₂²×C₄×C₂₃	—	4	4	no	—
87	C₂²×C₄×C₂₃	—	4	2	no	—
88	C₂²×C₄×C₂₃	—	4	8	no	—
89	C₂²×C₄×C₂₃	—	4	8	no	—
90	C₂²×C₄×C₂₃	C₂×D₄	1	4	yes	—
91	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
92	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
93	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
94	C₂²×C₄×C₂₃	C₂×D₄	1	8	yes	—
95	C₂²×C₄×C₂₃	C₂×D₄	1	4	yes	—
96	C₂²×C₄×C₂₃	C₂⁴	1	4	yes	—
97	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
98	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
99	Q₁₆×C₂₃	—	4	16	no	—
100	M₁₆×C₂₃	—	4	8	no	—
101	C₂×C₈×C₂₃	—	2	8	no	—
102	C₂×C₈×C₂₃	C₂⁴	1	8	yes	—
103	C₄⋊C₄×C₂₃	—	2	16	no	—
104	C₄⋊C₄×C₂₃	—	2	16	no	—
105	C₄⋊C₄×C₂₃	—	2	8	no	—
106	C₄⋊C₄×C₂₃	—	2	4	no	—
107	C₄⋊C₄×C₂₃	C₂⁴	1	8	yes	—
108	C₂²⋊C₄×C₂₃	—	2	16	no	—
109	C₂²⋊C₄×C₂₃	—	2	16	no	—
110	C₂×#3195	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
111	C₂³×C₂₃	—	2	4	no	—
112	C₂³×C₂₃	—	2	4	no	—
113	C₂³×C₂₃	—	2	2	no	—
114	C₂³×C₂₃	—	2	16	no	—
115	C₂³×C₂₃	—	2	4	no	—
116	C₂³×C₂₃	—	4	4	no	—
117	C₂³×C₂₃	—	4	16	no	—
118	C₂³×C₂₃	#137	1	8	yes	—
119	C₂³×C₂₃	C₂²×D₄	1	2	yes	—
120	C₂³×C₂₃	C₂²×D₄	1	4	yes	—
121	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
122	Q₈×C₂₃	—	2	16	no	—
123	Q₈×C₂₃	—	4	16	no	—
124	Q₈×C₂₃	—	4	8	no	—
125	C₂×C₄×C₂₃	—	2	2	no	—
126	C₂×C₄×C₂₃	—	2	4	no	—
127	C₂×C₄×C₂₃	—	2	4	no	—
128	C₂×C₄×C₂₃	—	2	8	no	—
129	C₂×C₄×C₂₃	—	2	4	no	—
130	C₂×C₄×C₂₃	—	2	8	no	—
131	C₂×C₄×C₂₃	—	2	8	no	—
132	C₂×C₄×C₂₃	—	2	8	no	—
133	C₂×C₄×C₂₃	—	4	8	no	—
134	C₂×C₄×C₂₃	—	4	4	no	—
135	C₂×C₄×C₂₃	—	4	16	no	—
136	C₂×C₄×C₂₃	—	4	8	no	—
137	C₂×C₄×C₂₃	—	4	16	no	—
138	C₂×C₄×C₂₃	—	4	8	no	—
139	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
140	C₂×C₄×C₂₃	C₂²×D₄	1	4	yes	—
141	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
142	C₂×C₄×C₂₃	H(5,𝔽₂)	1	4	yes	—
143	C₂×C₄×C₂₃	C₂⁵	1	1	yes	characteristic
144	C₈×C₂₃	—	2	8	no	—
145	C₂²×C₂²⋊Q₈	C₂×C₂₃	1	2	yes	—
146	#3195	C₂×C₂₃	1	16	yes	direct product factor
147	C₂×#483	C₂×C₂₃	1	4	yes	complemented
148	C₂×#470	C₂×C₂₃	1	4	yes	complemented
149	C₂×#451	C₂×C₂₃	1	4	yes	complemented
150	C₂×#407	C₂×C₂₃	1	1	yes	characteristic
151	C₂²×C₂₃	—	2	4	no	—
152	C₂²×C₂₃	—	2	16	no	—
153	C₂²×C₂₃	—	2	4	no	—
154	C₂²×C₂₃	—	2	2	no	—
155	C₂²×C₂₃	—	2	4	no	—
156	C₂²×C₂₃	—	4	16	no	—
157	C₂²×C₂₃	—	4	4	no	—
158	C₂²×C₂₃	#534	1	2	yes	—
159	C₂²×C₂₃	C₂×#137	1	8	yes	—
160	C₂²×C₂₃	C₂×#137	1	4	yes	—
161	C₂²×C₂₃	C₂³×D₄	1	1	yes	characteristic
162	C₄×C₂₃	—	2	2	no	—
163	C₄×C₂₃	—	2	4	no	—
164	C₄×C₂₃	—	4	8	no	—
165	C₄×C₂₃	—	4	8	no	—
166	C₄×C₂₃	#534	1	2	yes	—
167	C₄×C₂₃	C₂×H(5,𝔽₂)	1	2	yes	—
168	C₂³×Q₈	C₂²×C₂₃	1	2	yes	—
169	C₂⁴×C₄	C₂²×C₂₃	1	1	yes	characteristic
170	C₂²×Q₁₆	C₂²×C₂₃	1	4	yes	complemented
171	C₂²×M₁₆	C₂²×C₂₃	1	2	yes	—
172	C₂×C₂²⋊Q₈	—	2	2	no	—
173	C₂×C₂²⋊Q₈	—	2	2	no	—
174	C₂×C₂²⋊Q₈	—	2	8	no	—
175	C₂×C₂²⋊Q₈	C₂²×C₂₃	1	4	yes	—
176	C₂×C₂²⋊Q₈	C₂²×C₂₃	1	16	yes	—
177	C₂×C₂²⋊Q₈	C₂²×C₂₃	1	4	yes	—
178	C₂²×C₄⋊C₄	—	2	2	no	—
179	C₂²×C₄⋊C₄	C₂²×C₂₃	1	2	yes	—
180	C₂²×C₂²⋊C₄	—	2	2	no	—
181	#483	C₂²×C₂₃	1	32	yes	complemented
182	#470	C₂²×C₂₃	1	32	yes	complemented
183	#451	C₂²×C₂₃	1	32	yes	complemented
184	C₂×#106	C₂²×C₂₃	1	4	yes	complemented
185	C₂×#103	C₂²×C₂₃	1	8	yes	complemented
186	#407	C₂²×C₂₃	1	8	yes	—
187	C₂×C₂²⋊C₈	C₂²×C₂₃	1	4	yes	—
188	C₂×C₂₃	—	2	8	no	—
189	C₂×C₂₃	—	4	2	no	—
190	C₂×C₂₃	#3195	1	4	yes	direct product factor
191	C₂×C₂₃	C₂×#534	1	1	yes	characteristic
192	C₂×C₂₃	C₂²×#137	1	2	yes	—
193	C₂⁵	D₄×C₂₃	1	1	yes	characteristic
194	C₂²×Q₈	—	2	2	no	—
195	C₂²×Q₈	—	2	4	no	—
196	C₂²×Q₈	—	4	8	no	—
197	C₂²×Q₈	C₂³×C₂₃	1	4	yes	—
198	C₂²×Q₈	C₂³×C₂₃	1	8	yes	—
199	C₂³×C₄	—	2	2	no	—
200	C₂³×C₄	—	2	2	no	—
201	C₂³×C₄	—	4	4	no	—
202	C₂³×C₄	D₄×C₂₃	1	2	yes	—
203	C₂³×C₄	D₄×C₂₃	1	4	yes	—
204	C₂³×C₄	D₄×C₂₃	1	1	yes	characteristic
205	C₂³×C₄	C₂³×C₂₃	1	2	yes	—
206	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
207	C₂³×C₄	C₂³×C₂₃	1	4	yes	—
208	C₂×Q₁₆	—	4	8	no	—
209	C₂×Q₁₆	C₂³×C₂₃	1	16	yes	complemented
210	C₂×M₁₆	—	4	4	no	—
211	C₂×M₁₆	C₂³×C₂₃	1	8	yes	—
212	C₂²×C₈	C₂³×C₂₃	1	4	yes	—
213	C₂²⋊Q₈	—	2	8	no	—
214	C₂²⋊Q₈	—	2	8	no	—
215	C₂²⋊Q₈	—	2	16	no	—
216	C₂²⋊Q₈	—	2	16	no	—
217	C₂²⋊Q₈	C₂³×C₂₃	1	16	yes	—
218	C₂²⋊Q₈	C₂³×C₂₃	1	16	yes	—
219	C₂×C₄⋊C₄	—	2	4	no	—
220	C₂×C₄⋊C₄	—	2	4	no	—
221	C₂×C₄⋊C₄	—	2	16	no	—
222	C₂×C₄⋊C₄	—	2	2	no	—
223	C₂×C₄⋊C₄	—	2	4	no	—
224	C₂×C₄⋊C₄	C₂³×C₂₃	1	4	yes	—
225	C₂×C₄⋊C₄	C₂³×C₂₃	1	8	yes	—
226	C₂×C₂²⋊C₄	—	2	4	no	—
227	C₂×C₂²⋊C₄	—	2	16	no	—
228	C₂×C₂²⋊C₄	—	2	4	no	—
229	#106	C₂³×C₂₃	1	16	yes	complemented
230	#103	C₂³×C₂₃	1	32	yes	complemented
231	C₂²⋊C₈	C₂³×C₂₃	1	16	yes	—
232	C₂₃	C₂×#3195	1	1	yes	characteristic, direct product factor, Sylow
233	C₂⁴	—	2	8	no	—
234	C₂⁴	—	4	2	no	—
235	C₂⁴	C₂×D₄×C₂₃	1	1	yes	characteristic
236	C₂⁴	C₂×D₄×C₂₃	1	4	yes	—
237	C₂⁴	C₂×D₄×C₂₃	1	2	yes	—
238	C₂×Q₈	—	2	8	no	—
239	C₂×Q₈	—	2	4	no	—
240	C₂×Q₈	—	2	16	no	—
241	C₂×Q₈	—	4	16	no	—
242	C₂×Q₈	—	4	8	no	—
243	C₂×Q₈	—	4	16	no	—
244	C₂×Q₈	C₂⁴×C₂₃	1	8	yes	—
245	C₂²×C₄	—	2	4	no	—
246	C₂²×C₄	—	2	8	no	—
247	C₂²×C₄	—	2	8	no	—
248	C₂²×C₄	—	2	4	no	—
249	C₂²×C₄	—	2	8	no	—
250	C₂²×C₄	—	2	4	no	—
251	C₂²×C₄	—	4	8	no	—
252	C₂²×C₄	—	4	8	no	—
253	C₂²×C₄	—	4	2	no	—
254	C₂²×C₄	—	4	4	no	—
255	C₂²×C₄	—	4	8	no	—
256	C₂²×C₄	—	4	8	no	—
257	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
258	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
259	C₂²×C₄	C₂×D₄×C₂₃	1	4	yes	—
260	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
261	C₂²×C₄	C₂×D₄×C₂₃	1	8	yes	—
262	C₂²×C₄	C₂×D₄×C₂₃	1	4	yes	—
263	C₂²×C₄	C₂⁴×C₂₃	1	4	yes	—
264	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
265	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
266	Q₁₆	—	4	16	no	—
267	M₁₆	—	4	8	no	—
268	C₂×C₈	—	2	8	no	—
269	C₂×C₈	C₂⁴×C₂₃	1	8	yes	—
270	C₄⋊C₄	—	2	16	no	—
271	C₄⋊C₄	—	2	16	no	—
272	C₄⋊C₄	—	2	8	no	—
273	C₄⋊C₄	—	2	4	no	—
274	C₄⋊C₄	C₂⁴×C₂₃	1	8	yes	—
275	C₂²⋊C₄	—	2	16	no	—
276	C₂²⋊C₄	—	2	16	no	—
277	C₂³	—	2	4	no	—
278	C₂³	—	2	4	no	—
279	C₂³	—	2	16	no	—
280	C₂³	—	2	4	no	—
281	C₂³	—	2	2	no	—
282	C₂³	—	4	4	no	—
283	C₂³	—	4	16	no	—
284	C₂³	C₂₃×#137	1	8	yes	—
285	C₂³	C₂²×D₄×C₂₃	1	2	yes	—
286	C₂³	C₂²×D₄×C₂₃	1	4	yes	—
287	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
288	Q₈	—	2	16	no	—
289	Q₈	—	4	16	no	—
290	Q₈	—	4	8	no	—
291	C₂×C₄	—	2	4	no	—
292	C₂×C₄	—	2	2	no	—
293	C₂×C₄	—	2	4	no	—
294	C₂×C₄	—	2	8	no	—
295	C₂×C₄	—	2	8	no	—
296	C₂×C₄	—	2	4	no	—
297	C₂×C₄	—	2	8	no	—
298	C₂×C₄	—	2	8	no	—
299	C₂×C₄	—	4	4	no	—
300	C₂×C₄	—	4	8	no	—
301	C₂×C₄	—	4	16	no	—
302	C₂×C₄	—	4	16	no	—
303	C₂×C₄	—	4	8	no	—
304	C₂×C₄	—	4	8	no	—
305	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
306	C₂×C₄	C₂²×D₄×C₂₃	1	4	yes	—
307	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
308	C₂×C₄	C₂₃×H(5,𝔽₂)	1	4	yes	—
309	C₂×C₄	C₂⁵×C₂₃	1	1	yes	characteristic
310	C₈	—	2	8	no	—
311	C₂²	—	2	4	no	—
312	C₂²	—	2	16	no	—
313	C₂²	—	2	4	no	—
314	C₂²	—	2	2	no	—
315	C₂²	—	2	4	no	—
316	C₂²	—	4	16	no	—
317	C₂²	—	4	4	no	—
318	C₂²	C₂₃×#534	1	2	yes	—
319	C₂²	C₂×C₂₃×#137	1	8	yes	—
320	C₂²	C₂×C₂₃×#137	1	4	yes	—
321	C₂²	C₂³×D₄×C₂₃	1	1	yes	characteristic
322	C₄	—	2	4	no	—
323	C₄	—	2	2	no	—
324	C₄	—	4	8	no	—
325	C₄	—	4	8	no	—
326	C₄	C₂₃×#534	1	2	yes	—
327	C₄	C₂×C₂₃×H(5,𝔽₂)	1	2	yes	—
328	C₂	—	2	8	no	—
329	C₂	—	4	2	no	—
330	C₂	C₂₃×#3195	1	4	yes	direct product factor
331	C₂	C₂×C₂₃×#534	1	1	yes	characteristic
332	C₂	C₂²×C₂₃×#137	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₂₃	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₂₃
prime radical	C₂⁵×C₂₃	D₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₂₃ ◁ C₂⁴×C₄×C₂₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂₃×#3195	C₂	direct (N × H)
3. C₂×C₂₃×#483	C₂	semidirect
4. C₂×C₂₃×#470	C₂	semidirect
5. C₂×C₂₃×#451	C₂	semidirect
9. C₂²×Q₁₆×C₂₃	C₂²	semidirect
20. C₂₃×#483	C₂²	semidirect
21. C₂₃×#470	C₂²	semidirect
22. C₂₃×#451	C₂²	semidirect
23. C₂×C₂₃×#106	C₂²	semidirect
24. C₂×C₂₃×#103	C₂²	semidirect
43. C₂×Q₁₆×C₂₃	C₂³	semidirect
63. C₂₃×#106	C₂³	semidirect
64. C₂₃×#103	C₂³	semidirect
110. C₂×#3195	C₂₃	direct (N × H)
146. #3195	C₂×C₂₃	direct (N × H)
147. C₂×#483	C₂×C₂₃	semidirect
148. C₂×#470	C₂×C₂₃	semidirect
149. C₂×#451	C₂×C₂₃	semidirect
170. C₂²×Q₁₆	C₂²×C₂₃	semidirect
181. #483	C₂²×C₂₃	semidirect
182. #470	C₂²×C₂₃	semidirect
183. #451	C₂²×C₂₃	semidirect
184. C₂×#106	C₂²×C₂₃	semidirect
185. C₂×#103	C₂²×C₂₃	semidirect
190. C₂×C₂₃	#3195	direct (N × H)
209. C₂×Q₁₆	C₂³×C₂₃	semidirect
229. #106	C₂³×C₂₃	semidirect
230. #103	C₂³×C₂₃	semidirect
232. C₂₃	C₂×#3195	direct (N × H)
330. C₂	C₂₃×#3195	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×C₂₃×C₂²⋊Q₈	2
C₂₃×#3195	2
C₂×C₂₃×#483	2
C₂×C₂₃×#470	2
C₂×C₂₃×#451	2
C₂×C₂₃×#407	2
C₂×#3195	23

Subgroups — C2×C23×#3195 #19208364

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₂₃×#3195 #19208364