Subgroups — C₂²×C₂₃×#485 #19208129

Order 5888.

2358 conjugacy classes of subgroups.

The subgroup lattice has 332 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	1	yes	maximal, characteristic
2	C₂²×C₂₃×#117	C₂	1	1	yes	maximal, characteristic
3	C₂×C₂₃×#485	C₂	1	24	yes	maximal, direct product factor
4	C₂²×C₂₃×#107	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂²×C₂₃×#106	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×C₂₃×#103	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂²×C₂₃×#103	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×C₂₃×C₂²⋊C₈	C₂	1	1	yes	maximal, characteristic
9	C₂³×Q₈×C₂₃	C₂²	1	1	yes	characteristic
10	C₂⁴×C₄×C₂₃	C₂²	1	1	yes	characteristic
11	C₂³×C₈×C₂₃	C₂²	1	1	yes	characteristic
12	C₂³×C₈×C₂₃	C₂²	1	1	yes	characteristic
13	C₂×C₂₃×C₂²⋊Q₈	—	2	6	no	—
14	C₂×C₂₃×C₂²⋊Q₈	C₂²	1	12	yes	—
15	C₂×C₂₃×#117	—	2	6	no	—
16	C₂×C₂₃×#117	C₂²	1	12	yes	—
17	C₂²×C₄⋊C₄×C₂₃	—	2	1	no	—
18	C₂²×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
19	C₂²×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
20	C₂²×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
21	C₂²×C₂²⋊C₄×C₂₃	—	2	1	no	—
22	C₂²×C₂²⋊C₄×C₂₃	—	2	1	no	—
23	C₂²×C₄²×C₂₃	—	2	1	no	—
24	C₂₃×#485	C₂²	1	64	yes	direct product factor
25	C₂×C₂₃×#107	C₂²	1	12	yes	complemented
26	C₂×C₂₃×#106	C₂²	1	12	yes	complemented
27	C₂×C₂₃×#103	C₂²	1	12	yes	complemented
28	C₂×C₂₃×#103	C₂²	1	12	yes	complemented
29	C₂×C₂₃×C₂²⋊C₈	C₂²	1	12	yes	—
30	C₂⁵×C₂₃	D₄	1	1	yes	characteristic
31	C₂²×Q₈×C₂₃	—	2	3	no	—
32	C₂²×Q₈×C₂₃	—	2	4	no	—
33	C₂²×Q₈×C₂₃	—	2	4	no	—
34	C₂²×Q₈×C₂₃	C₂³	1	6	yes	—
35	C₂³×C₄×C₂₃	—	2	4	no	—
36	C₂³×C₄×C₂₃	—	2	4	no	—
37	C₂³×C₄×C₂₃	—	2	1	no	—
38	C₂³×C₄×C₂₃	—	2	1	no	—
39	C₂³×C₄×C₂₃	—	2	1	no	—
40	C₂³×C₄×C₂₃	—	2	1	no	—
41	C₂³×C₄×C₂₃	D₄	1	6	yes	—
42	C₂³×C₄×C₂₃	D₄	1	1	yes	characteristic
43	C₂³×C₄×C₂₃	C₂³	1	6	yes	—
44	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
45	C₂²×C₈×C₂₃	—	2	4	no	—
46	C₂²×C₈×C₂₃	—	2	4	no	—
47	C₂²×C₈×C₂₃	C₂³	1	6	yes	—
48	C₂²×C₈×C₂₃	C₂³	1	6	yes	—
49	C₂₃×C₂²⋊Q₈	—	2	24	no	—
50	C₂₃×C₂²⋊Q₈	C₂³	1	16	yes	—
51	C₂₃×#117	—	2	24	no	—
52	C₂₃×#117	C₂³	1	16	yes	—
53	C₂×C₄⋊C₄×C₂₃	—	2	12	no	—
54	C₂×C₄⋊C₄×C₂₃	—	2	3	no	—
55	C₂×C₄⋊C₄×C₂₃	—	2	3	no	—
56	C₂×C₄⋊C₄×C₂₃	—	2	3	no	—
57	C₂×C₄⋊C₄×C₂₃	C₂³	1	6	yes	—
58	C₂×C₄⋊C₄×C₂₃	C₂³	1	6	yes	—
59	C₂×C₄⋊C₄×C₂₃	C₂³	1	6	yes	—
60	C₂×C₂²⋊C₄×C₂₃	—	2	12	no	—
61	C₂×C₂²⋊C₄×C₂₃	—	2	12	no	—
62	C₂×C₄²×C₂₃	—	2	12	no	—
63	C₂₃×#107	C₂³	1	16	yes	complemented
64	C₂₃×#106	C₂³	1	16	yes	complemented
65	C₂₃×#103	C₂³	1	16	yes	complemented
66	C₂₃×#103	C₂³	1	16	yes	complemented
67	C₂₃×C₂²⋊C₈	C₂³	1	16	yes	—
68	C₂⁴×C₂₃	—	2	4	no	—
69	C₂⁴×C₂₃	—	2	4	no	—
70	C₂⁴×C₂₃	—	2	4	no	—
71	C₂⁴×C₂₃	C₂×D₄	1	6	yes	—
72	C₂⁴×C₂₃	C₂×D₄	1	1	yes	characteristic
73	C₂×Q₈×C₂₃	—	2	6	no	—
74	C₂×Q₈×C₂₃	—	2	12	no	—
75	C₂×Q₈×C₂₃	—	2	12	no	—
76	C₂×Q₈×C₂₃	—	4	12	no	—
77	C₂×Q₈×C₂₃	C₂⁴	1	4	yes	—
78	C₂²×C₄×C₂₃	—	2	4	no	—
79	C₂²×C₄×C₂₃	—	2	24	no	—
80	C₂²×C₄×C₂₃	—	2	12	no	—
81	C₂²×C₄×C₂₃	—	2	12	no	—
82	C₂²×C₄×C₂₃	—	2	6	no	—
83	C₂²×C₄×C₂₃	—	2	6	no	—
84	C₂²×C₄×C₂₃	—	2	6	no	—
85	C₂²×C₄×C₂₃	—	2	6	no	—
86	C₂²×C₄×C₂₃	—	4	4	no	—
87	C₂²×C₄×C₂₃	—	4	4	no	—
88	C₂²×C₄×C₂₃	—	4	4	no	—
89	C₂²×C₄×C₂₃	—	4	4	no	—
90	C₂²×C₄×C₂₃	C₂×D₄	1	6	yes	—
91	C₂²×C₄×C₂₃	C₂×D₄	1	12	yes	—
92	C₂²×C₄×C₂₃	C₂×D₄	1	3	yes	—
93	C₂²×C₄×C₂₃	#41	1	4	yes	—
94	C₂²×C₄×C₂₃	#41	1	4	yes	—
95	C₂²×C₄×C₂₃	C₂⁴	1	4	yes	—
96	C₂²×C₄×C₂₃	C₂⁴	1	3	yes	—
97	C₂×C₈×C₂₃	—	2	12	no	—
98	C₂×C₈×C₂₃	—	2	12	no	—
99	C₂×C₈×C₂₃	C₂⁴	1	4	yes	—
100	C₂×C₈×C₂₃	C₂⁴	1	4	yes	—
101	C₄⋊C₄×C₂₃	—	2	16	no	—
102	C₄⋊C₄×C₂₃	—	2	6	no	—
103	C₄⋊C₄×C₂₃	—	2	6	no	—
104	C₄⋊C₄×C₂₃	—	2	6	no	—
105	C₄⋊C₄×C₂₃	C₂⁴	1	4	yes	—
106	C₄⋊C₄×C₂₃	C₂⁴	1	4	yes	—
107	C₄⋊C₄×C₂₃	C₂⁴	1	4	yes	—
108	C₂²⋊C₄×C₂₃	—	2	16	no	—
109	C₂²⋊C₄×C₂₃	—	2	16	no	—
110	C₄²×C₂₃	—	2	16	no	—
111	C₂²×#485	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
112	C₂³×C₂₃	—	2	12	no	—
113	C₂³×C₂₃	—	2	12	no	—
114	C₂³×C₂₃	—	2	12	no	—
115	C₂³×C₂₃	—	4	16	no	—
116	C₂³×C₂₃	#123	1	4	yes	—
117	C₂³×C₂₃	#135	1	4	yes	—
118	C₂³×C₂₃	#137	1	4	yes	—
119	C₂³×C₂₃	C₂²×D₄	1	4	yes	—
120	C₂³×C₂₃	C₂²×D₄	1	3	yes	—
121	Q₈×C₂₃	—	2	4	no	—
122	Q₈×C₂₃	—	2	4	no	—
123	Q₈×C₂₃	—	4	12	no	—
124	C₂×C₄×C₂₃	—	2	12	no	—
125	C₂×C₄×C₂₃	—	2	24	no	—
126	C₂×C₄×C₂₃	—	2	4	no	—
127	C₂×C₄×C₂₃	—	2	4	no	—
128	C₂×C₄×C₂₃	—	2	4	no	—
129	C₂×C₄×C₂₃	—	2	4	no	—
130	C₂×C₄×C₂₃	—	2	4	no	—
131	C₂×C₄×C₂₃	—	2	4	no	—
132	C₂×C₄×C₂₃	—	4	12	no	—
133	C₂×C₄×C₂₃	—	4	12	no	—
134	C₂×C₄×C₂₃	—	4	12	no	—
135	C₂×C₄×C₂₃	—	4	12	no	—
136	C₂×C₄×C₂₃	#123	1	12	yes	—
137	C₂×C₄×C₂₃	C₂²×D₄	1	4	yes	—
138	C₂×C₄×C₂₃	C₂²×D₄	1	3	yes	—
139	C₂×C₄×C₂₃	C₂×#41	1	6	yes	—
140	C₂×C₄×C₂₃	C₂×#41	1	6	yes	—
141	C₂×C₄×C₂₃	C₂⁵	1	1	yes	characteristic
142	C₈×C₂₃	—	2	4	no	—
143	C₈×C₂₃	—	2	4	no	—
144	C₂²×C₂²⋊Q₈	C₂×C₂₃	1	1	yes	characteristic
145	C₂²×#117	C₂×C₂₃	1	1	yes	characteristic
146	C₂×#485	C₂×C₂₃	1	24	yes	direct product factor
147	C₂²×#107	C₂×C₂₃	1	1	yes	characteristic, complemented
148	C₂²×#106	C₂×C₂₃	1	1	yes	characteristic, complemented
149	C₂²×#103	C₂×C₂₃	1	1	yes	characteristic, complemented
150	C₂²×#103	C₂×C₂₃	1	1	yes	characteristic, complemented
151	C₂²×C₂²⋊C₈	C₂×C₂₃	1	1	yes	characteristic
152	C₂²×C₂₃	—	2	4	no	—
153	C₂²×C₂₃	—	2	4	no	—
154	C₂²×C₂₃	—	2	4	no	—
155	C₂²×C₂₃	—	4	24	no	—
156	C₂²×C₂₃	#485	1	16	yes	direct product factor
157	C₂²×C₂₃	C₂×#123	1	6	yes	—
158	C₂²×C₂₃	C₂×#135	1	6	yes	—
159	C₂²×C₂₃	C₂×#137	1	6	yes	—
160	C₂²×C₂₃	C₂³×D₄	1	1	yes	characteristic
161	C₄×C₂₃	—	2	4	no	—
162	C₄×C₂₃	—	4	4	no	—
163	C₄×C₂₃	—	4	4	no	—
164	C₄×C₂₃	—	4	4	no	—
165	C₄×C₂₃	—	4	4	no	—
166	C₄×C₂₃	C₂×#123	1	6	yes	—
167	C₄×C₂₃	C₂²×#41	1	1	yes	characteristic
168	C₄×C₂₃	C₂²×#41	1	1	yes	characteristic
169	C₂³×Q₈	C₂²×C₂₃	1	1	yes	characteristic
170	C₂⁴×C₄	C₂²×C₂₃	1	1	yes	characteristic
171	C₂³×C₈	C₂²×C₂₃	1	1	yes	characteristic
172	C₂³×C₈	C₂²×C₂₃	1	1	yes	characteristic
173	C₂×C₂²⋊Q₈	—	2	6	no	—
174	C₂×C₂²⋊Q₈	C₂²×C₂₃	1	12	yes	—
175	C₂×#117	—	2	6	no	—
176	C₂×#117	C₂²×C₂₃	1	12	yes	—
177	C₂²×C₄⋊C₄	—	2	1	no	—
178	C₂²×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
179	C₂²×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
180	C₂²×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
181	C₂²×C₂²⋊C₄	—	2	1	no	—
182	C₂²×C₂²⋊C₄	—	2	1	no	—
183	C₂²×C₄²	—	2	1	no	—
184	#485	C₂²×C₂₃	1	64	yes	direct product factor
185	C₂×#107	C₂²×C₂₃	1	12	yes	complemented
186	C₂×#106	C₂²×C₂₃	1	12	yes	complemented
187	C₂×#103	C₂²×C₂₃	1	12	yes	complemented
188	C₂×#103	C₂²×C₂₃	1	12	yes	complemented
189	C₂×C₂²⋊C₈	C₂²×C₂₃	1	12	yes	—
190	C₂×C₂₃	—	4	4	no	—
191	C₂×C₂₃	C₂×#485	1	12	yes	direct product factor
192	C₂×C₂₃	C₂²×#123	1	1	yes	characteristic
193	C₂×C₂₃	C₂²×#135	1	1	yes	characteristic
194	C₂×C₂₃	C₂²×#137	1	1	yes	characteristic
195	C₂⁵	D₄×C₂₃	1	1	yes	characteristic
196	C₂²×Q₈	—	2	3	no	—
197	C₂²×Q₈	—	2	4	no	—
198	C₂²×Q₈	—	2	4	no	—
199	C₂²×Q₈	C₂³×C₂₃	1	6	yes	—
200	C₂³×C₄	—	2	4	no	—
201	C₂³×C₄	—	2	4	no	—
202	C₂³×C₄	—	2	1	no	—
203	C₂³×C₄	—	2	1	no	—
204	C₂³×C₄	—	2	1	no	—
205	C₂³×C₄	—	2	1	no	—
206	C₂³×C₄	D₄×C₂₃	1	1	yes	characteristic
207	C₂³×C₄	D₄×C₂₃	1	6	yes	—
208	C₂³×C₄	C₂³×C₂₃	1	6	yes	—
209	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
210	C₂²×C₈	—	2	4	no	—
211	C₂²×C₈	—	2	4	no	—
212	C₂²×C₈	C₂³×C₂₃	1	6	yes	—
213	C₂²×C₈	C₂³×C₂₃	1	6	yes	—
214	C₂²⋊Q₈	—	2	24	no	—
215	C₂²⋊Q₈	C₂³×C₂₃	1	16	yes	—
216	#117	—	2	24	no	—
217	#117	C₂³×C₂₃	1	16	yes	—
218	C₂×C₄⋊C₄	—	2	12	no	—
219	C₂×C₄⋊C₄	—	2	3	no	—
220	C₂×C₄⋊C₄	—	2	3	no	—
221	C₂×C₄⋊C₄	—	2	3	no	—
222	C₂×C₄⋊C₄	C₂³×C₂₃	1	6	yes	—
223	C₂×C₄⋊C₄	C₂³×C₂₃	1	6	yes	—
224	C₂×C₄⋊C₄	C₂³×C₂₃	1	6	yes	—
225	C₂×C₂²⋊C₄	—	2	12	no	—
226	C₂×C₂²⋊C₄	—	2	12	no	—
227	C₂×C₄²	—	2	12	no	—
228	#107	C₂³×C₂₃	1	16	yes	complemented
229	#106	C₂³×C₂₃	1	16	yes	complemented
230	#103	C₂³×C₂₃	1	16	yes	complemented
231	#103	C₂³×C₂₃	1	16	yes	complemented
232	C₂²⋊C₈	C₂³×C₂₃	1	16	yes	—
233	C₂₃	C₂²×#485	1	1	yes	characteristic, direct product factor, Sylow
234	C₂⁴	—	2	4	no	—
235	C₂⁴	—	2	4	no	—
236	C₂⁴	—	2	4	no	—
237	C₂⁴	C₂×D₄×C₂₃	1	6	yes	—
238	C₂⁴	C₂×D₄×C₂₃	1	1	yes	characteristic
239	C₂×Q₈	—	2	6	no	—
240	C₂×Q₈	—	2	12	no	—
241	C₂×Q₈	—	2	12	no	—
242	C₂×Q₈	—	4	12	no	—
243	C₂×Q₈	C₂⁴×C₂₃	1	4	yes	—
244	C₂²×C₄	—	2	4	no	—
245	C₂²×C₄	—	2	24	no	—
246	C₂²×C₄	—	2	12	no	—
247	C₂²×C₄	—	2	12	no	—
248	C₂²×C₄	—	2	6	no	—
249	C₂²×C₄	—	2	6	no	—
250	C₂²×C₄	—	2	6	no	—
251	C₂²×C₄	—	2	6	no	—
252	C₂²×C₄	—	4	4	no	—
253	C₂²×C₄	—	4	4	no	—
254	C₂²×C₄	—	4	4	no	—
255	C₂²×C₄	—	4	4	no	—
256	C₂²×C₄	C₂×D₄×C₂₃	1	6	yes	—
257	C₂²×C₄	C₂×D₄×C₂₃	1	12	yes	—
258	C₂²×C₄	C₂×D₄×C₂₃	1	3	yes	—
259	C₂²×C₄	#41×C₂₃	1	4	yes	—
260	C₂²×C₄	#41×C₂₃	1	4	yes	—
261	C₂²×C₄	C₂⁴×C₂₃	1	4	yes	—
262	C₂²×C₄	C₂⁴×C₂₃	1	3	yes	—
263	C₂×C₈	—	2	12	no	—
264	C₂×C₈	—	2	12	no	—
265	C₂×C₈	C₂⁴×C₂₃	1	4	yes	—
266	C₂×C₈	C₂⁴×C₂₃	1	4	yes	—
267	C₄⋊C₄	—	2	16	no	—
268	C₄⋊C₄	—	2	6	no	—
269	C₄⋊C₄	—	2	6	no	—
270	C₄⋊C₄	—	2	6	no	—
271	C₄⋊C₄	C₂⁴×C₂₃	1	4	yes	—
272	C₄⋊C₄	C₂⁴×C₂₃	1	4	yes	—
273	C₄⋊C₄	C₂⁴×C₂₃	1	4	yes	—
274	C₂²⋊C₄	—	2	16	no	—
275	C₂²⋊C₄	—	2	16	no	—
276	C₄²	—	2	16	no	—
277	C₂³	—	2	12	no	—
278	C₂³	—	2	12	no	—
279	C₂³	—	2	12	no	—
280	C₂³	—	4	16	no	—
281	C₂³	C₂₃×#123	1	4	yes	—
282	C₂³	C₂₃×#135	1	4	yes	—
283	C₂³	C₂₃×#137	1	4	yes	—
284	C₂³	C₂²×D₄×C₂₃	1	4	yes	—
285	C₂³	C₂²×D₄×C₂₃	1	3	yes	—
286	Q₈	—	2	4	no	—
287	Q₈	—	2	4	no	—
288	Q₈	—	4	12	no	—
289	C₂×C₄	—	2	12	no	—
290	C₂×C₄	—	2	4	no	—
291	C₂×C₄	—	2	4	no	—
292	C₂×C₄	—	2	24	no	—
293	C₂×C₄	—	2	4	no	—
294	C₂×C₄	—	2	4	no	—
295	C₂×C₄	—	2	4	no	—
296	C₂×C₄	—	2	4	no	—
297	C₂×C₄	—	4	12	no	—
298	C₂×C₄	—	4	12	no	—
299	C₂×C₄	—	4	12	no	—
300	C₂×C₄	—	4	12	no	—
301	C₂×C₄	C₂₃×#123	1	12	yes	—
302	C₂×C₄	C₂²×D₄×C₂₃	1	4	yes	—
303	C₂×C₄	C₂²×D₄×C₂₃	1	3	yes	—
304	C₂×C₄	C₂×#41×C₂₃	1	6	yes	—
305	C₂×C₄	C₂×#41×C₂₃	1	6	yes	—
306	C₂×C₄	C₂⁵×C₂₃	1	1	yes	characteristic
307	C₈	—	2	4	no	—
308	C₈	—	2	4	no	—
309	C₂²	—	2	4	no	—
310	C₂²	—	2	4	no	—
311	C₂²	—	2	4	no	—
312	C₂²	—	4	24	no	—
313	C₂²	C₂₃×#485	1	16	yes	direct product factor
314	C₂²	C₂×C₂₃×#123	1	6	yes	—
315	C₂²	C₂×C₂₃×#135	1	6	yes	—
316	C₂²	C₂×C₂₃×#137	1	6	yes	—
317	C₂²	C₂³×D₄×C₂₃	1	1	yes	characteristic
318	C₄	—	2	4	no	—
319	C₄	—	4	4	no	—
320	C₄	—	4	4	no	—
321	C₄	—	4	4	no	—
322	C₄	—	4	4	no	—
323	C₄	C₂×C₂₃×#123	1	6	yes	—
324	C₄	C₂²×#41×C₂₃	1	1	yes	characteristic
325	C₄	C₂²×#41×C₂₃	1	1	yes	characteristic
326	C₂	—	4	4	no	—
327	C₂	C₂×C₂₃×#485	1	12	yes	direct product factor
328	C₂	C₂²×C₂₃×#123	1	1	yes	characteristic
329	C₂	C₂²×C₂₃×#135	1	1	yes	characteristic
330	C₂	C₂²×C₂₃×#137	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
3. C₂×C₂₃×#485	C₂	direct (N × H)
4. C₂²×C₂₃×#107	C₂	semidirect
5. C₂²×C₂₃×#106	C₂	semidirect
6. C₂²×C₂₃×#103	C₂	semidirect
7. C₂²×C₂₃×#103	C₂	semidirect
24. C₂₃×#485	C₂²	direct (N × H)
25. C₂×C₂₃×#107	C₂²	semidirect
26. C₂×C₂₃×#106	C₂²	semidirect
27. C₂×C₂₃×#103	C₂²	semidirect
28. C₂×C₂₃×#103	C₂²	semidirect
63. C₂₃×#107	C₂³	semidirect
64. C₂₃×#106	C₂³	semidirect
65. C₂₃×#103	C₂³	semidirect
66. C₂₃×#103	C₂³	semidirect
111. C₂²×#485	C₂₃	direct (N × H)
146. C₂×#485	C₂×C₂₃	direct (N × H)
147. C₂²×#107	C₂×C₂₃	semidirect
148. C₂²×#106	C₂×C₂₃	semidirect
149. C₂²×#103	C₂×C₂₃	semidirect
150. C₂²×#103	C₂×C₂₃	semidirect
156. C₂²×C₂₃	#485	direct (N × H)
184. #485	C₂²×C₂₃	direct (N × H)
185. C₂×#107	C₂²×C₂₃	semidirect
186. C₂×#106	C₂²×C₂₃	semidirect
187. C₂×#103	C₂²×C₂₃	semidirect
188. C₂×#103	C₂²×C₂₃	semidirect
191. C₂×C₂₃	C₂×#485	direct (N × H)
228. #107	C₂³×C₂₃	semidirect
229. #106	C₂³×C₂₃	semidirect
230. #103	C₂³×C₂₃	semidirect
231. #103	C₂³×C₂₃	semidirect
233. C₂₃	C₂²×#485	direct (N × H)
313. C₂²	C₂₃×#485	direct (N × H)
327. C₂	C₂×C₂₃×#485	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
C₂²×C₂₃×#117	2
C₂×C₂₃×#485	2
C₂²×C₂₃×#107	2
C₂²×C₂₃×#106	2
C₂²×C₂₃×#103	2
C₂²×C₂₃×C₂²⋊C₈	2
C₂²×#485	23

Subgroups — C22×C23×#485 #19208129

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×C₂₃×#485 #19208129