Subgroups — C₂²×C₂₃×#536 #19210306

Order 5888.

11406 conjugacy classes of subgroups.

The subgroup lattice has 318 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×#41×C₂₃	C₂	1	1	yes	maximal, characteristic
2	C₂⁴×Q₈×C₂₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₂₃×#536	C₂	1	48	yes	maximal, direct product factor
4	C₂²×C₂₃×C₄⋊Q₈	C₂	1	2	yes	maximal, complemented
5	C₂²×C₂₃×#124	C₂	1	2	yes	maximal, complemented
6	C₂²×C₂₃×#123	C₂	1	4	yes	maximal, complemented
7	C₂²×C₂₃×C₂²⋊Q₈	C₂	1	4	yes	maximal, complemented
8	C₂²×C₂₃×#117	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂²×#41×C₂₃	—	2	16	no	—
10	C₂²×#41×C₂₃	C₂²	1	24	yes	—
11	C₂³×Q₈×C₂₃	—	2	16	no	—
12	C₂³×Q₈×C₂₃	C₂²	1	2	yes	—
13	C₂³×Q₈×C₂₃	C₂²	1	2	yes	—
14	C₂³×Q₈×C₂₃	C₂²	1	1	yes	characteristic
15	C₂³×Q₈×C₂₃	C₂²	1	24	yes	complemented
16	C₂³×D₄×C₂₃	C₂²	1	2	yes	—
17	C₂³×D₄×C₂₃	C₂²	1	1	yes	characteristic
18	C₂⁴×C₄×C₂₃	C₂²	1	2	yes	—
19	C₂⁴×C₄×C₂₃	C₂²	1	2	yes	—
20	C₂⁴×C₄×C₂₃	C₂²	1	1	yes	characteristic
21	C₂₃×#536	C₂²	1	256	yes	direct product factor
22	C₂×C₂₃×C₄⋊Q₈	C₂²	1	48	yes	complemented
23	C₂×C₂₃×#124	C₂²	1	48	yes	complemented
24	C₂×C₂₃×#123	C₂²	1	96	yes	complemented
25	C₂×C₂₃×C₂²⋊Q₈	C₂²	1	96	yes	complemented
26	C₂×C₂₃×#117	C₂²	1	24	yes	complemented
27	C₂²×C₄⋊C₄×C₂₃	C₂²	1	2	yes	—
28	C₂²×C₄⋊C₄×C₂₃	C₂²	1	8	yes	—
29	C₂²×C₂²⋊C₄×C₂₃	C₂²	1	2	yes	—
30	C₂²×C₂²⋊C₄×C₂₃	C₂²	1	8	yes	—
31	C₂²×C₄²×C₂₃	C₂²	1	2	yes	—
32	C₂⁵×C₂₃	C₂³	1	2	yes	—
33	C₂⁵×C₂₃	C₂³	1	1	yes	characteristic
34	C₂×#41×C₂₃	—	2	192	no	—
35	C₂×#41×C₂₃	C₂³	1	64	yes	—
36	C₂²×Q₈×C₂₃	—	2	16	no	—
37	C₂²×Q₈×C₂₃	—	2	16	no	—
38	C₂²×Q₈×C₂₃	—	2	192	no	—
39	C₂²×Q₈×C₂₃	—	2	8	no	—
40	C₂²×Q₈×C₂₃	C₂³	1	24	yes	—
41	C₂²×Q₈×C₂₃	C₂³	1	24	yes	—
42	C₂²×Q₈×C₂₃	C₂³	1	12	yes	—
43	C₂²×Q₈×C₂₃	C₂³	1	64	yes	complemented
44	C₂²×D₄×C₂₃	—	2	16	no	—
45	C₂²×D₄×C₂₃	—	2	8	no	—
46	C₂²×D₄×C₂₃	C₂³	1	24	yes	—
47	C₂²×D₄×C₂₃	C₂³	1	12	yes	—
48	C₂³×C₄×C₂₃	—	2	16	no	—
49	C₂³×C₄×C₂₃	—	2	16	no	—
50	C₂³×C₄×C₂₃	D₄	1	16	yes	—
51	C₂³×C₄×C₂₃	C₂³	1	24	yes	—
52	C₂³×C₄×C₂₃	C₂³	1	24	yes	—
53	C₂³×C₄×C₂₃	C₂³	1	2	yes	—
54	C₂³×C₄×C₂₃	C₂³	1	4	yes	—
55	C₂³×C₄×C₂₃	C₂³	1	4	yes	—
56	C₂³×C₄×C₂₃	C₂³	1	12	yes	—
57	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
58	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
59	C₂₃×C₄⋊Q₈	C₂³	1	128	yes	complemented
60	C₂₃×#124	C₂³	1	128	yes	complemented
61	C₂₃×#123	C₂³	1	256	yes	complemented
62	C₂₃×C₂²⋊Q₈	C₂³	1	256	yes	complemented
63	C₂₃×#117	C₂³	1	64	yes	complemented
64	C₂×C₄⋊C₄×C₂₃	C₂³	1	24	yes	—
65	C₂×C₄⋊C₄×C₂₃	C₂³	1	96	yes	—
66	C₂×C₂²⋊C₄×C₂₃	C₂³	1	24	yes	—
67	C₂×C₂²⋊C₄×C₂₃	C₂³	1	96	yes	—
68	C₂×C₄²×C₂₃	C₂³	1	24	yes	—
69	C₂⁴×C₂₃	—	2	8	no	—
70	C₂⁴×C₂₃	—	2	8	no	—
71	C₂⁴×C₂₃	—	2	16	no	—
72	C₂⁴×C₂₃	C₂×D₄	1	8	yes	—
73	C₂⁴×C₂₃	C₂⁴	1	12	yes	—
74	C₂⁴×C₂₃	C₂⁴	1	6	yes	—
75	C₂⁴×C₂₃	C₂⁴	1	1	yes	characteristic
76	#41×C₂₃	—	2	256	no	—
77	C₂×Q₈×C₂₃	—	2	96	no	—
78	C₂×Q₈×C₂₃	—	2	96	no	—
79	C₂×Q₈×C₂₃	—	2	256	no	—
80	C₂×Q₈×C₂₃	—	2	48	no	—
81	C₂×Q₈×C₂₃	C₂⁴	1	32	yes	—
82	C₂×Q₈×C₂₃	C₂⁴	1	32	yes	—
83	C₂×Q₈×C₂₃	C₂⁴	1	16	yes	—
84	C₂×D₄×C₂₃	—	2	96	no	—
85	C₂×D₄×C₂₃	—	2	48	no	—
86	C₂×D₄×C₂₃	C₂⁴	1	32	yes	—
87	C₂×D₄×C₂₃	C₂⁴	1	16	yes	—
88	C₂²×C₄×C₂₃	—	2	8	no	—
89	C₂²×C₄×C₂₃	—	2	96	no	—
90	C₂²×C₄×C₂₃	—	2	16	no	—
91	C₂²×C₄×C₂₃	—	2	16	no	—
92	C₂²×C₄×C₂₃	—	2	96	no	—
93	C₂²×C₄×C₂₃	C₂×D₄	1	8	yes	—
94	C₂²×C₄×C₂₃	C₂×D₄	1	8	yes	—
95	C₂²×C₄×C₂₃	C₂×D₄	1	96	yes	—
96	C₂²×C₄×C₂₃	C₂⁴	1	24	yes	—
97	C₂²×C₄×C₂₃	C₂⁴	1	24	yes	—
98	C₂²×C₄×C₂₃	C₂⁴	1	12	yes	—
99	C₂²×C₄×C₂₃	C₂⁴	1	32	yes	—
100	C₂²×C₄×C₂₃	C₂⁴	1	32	yes	—
101	C₂²×C₄×C₂₃	C₂⁴	1	6	yes	—
102	C₂²×C₄×C₂₃	C₂⁴	1	6	yes	—
103	C₂²×C₄×C₂₃	C₂⁴	1	16	yes	—
104	C₄⋊C₄×C₂₃	C₂⁴	1	32	yes	—
105	C₄⋊C₄×C₂₃	C₂⁴	1	128	yes	—
106	C₂²⋊C₄×C₂₃	C₂⁴	1	32	yes	—
107	C₂²⋊C₄×C₂₃	C₂⁴	1	128	yes	—
108	C₄²×C₂₃	C₂⁴	1	32	yes	—
109	C₂²×#536	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
110	C₂³×C₂₃	—	2	32	no	—
111	C₂³×C₂₃	—	2	24	no	—
112	C₂³×C₂₃	—	2	24	no	—
113	C₂³×C₂₃	—	2	48	no	—
114	C₂³×C₂₃	—	4	32	no	—
115	C₂³×C₂₃	C₂²×D₄	1	24	yes	—
116	C₂³×C₂₃	C₂²×D₄	1	4	yes	—
117	C₂³×C₂₃	2₋¹⁺⁴	1	8	yes	—
118	C₂³×C₂₃	C₂⁵	1	8	yes	—
119	C₂³×C₂₃	C₂⁵	1	4	yes	—
120	C₂³×C₂₃	C₂⁵	1	3	yes	—
121	Q₈×C₂₃	—	2	64	no	—
122	Q₈×C₂₃	—	2	64	no	—
123	Q₈×C₂₃	—	2	32	no	—
124	D₄×C₂₃	—	2	64	no	—
125	D₄×C₂₃	—	2	32	no	—
126	C₂×C₄×C₂₃	—	2	24	no	—
127	C₂×C₄×C₂₃	—	2	64	no	—
128	C₂×C₄×C₂₃	—	2	48	no	—
129	C₂×C₄×C₂₃	—	2	48	no	—
130	C₂×C₄×C₂₃	—	2	64	no	—
131	C₂×C₄×C₂₃	C₂²×D₄	1	24	yes	—
132	C₂×C₄×C₂₃	C₂²×D₄	1	24	yes	—
133	C₂×C₄×C₂₃	C₂²×D₄	1	64	yes	—
134	C₂×C₄×C₂₃	C₂⁵	1	16	yes	—
135	C₂×C₄×C₂₃	C₂⁵	1	16	yes	—
136	C₂×C₄×C₂₃	C₂⁵	1	8	yes	—
137	C₂×C₄×C₂₃	C₂⁵	1	4	yes	—
138	C₂×C₄×C₂₃	C₂⁵	1	4	yes	—
139	C₂³×#41	C₂×C₂₃	1	1	yes	characteristic
140	C₂⁴×Q₈	C₂×C₂₃	1	1	yes	characteristic, complemented
141	C₂×#536	C₂×C₂₃	1	48	yes	direct product factor
142	C₂²×C₄⋊Q₈	C₂×C₂₃	1	2	yes	complemented
143	C₂²×#124	C₂×C₂₃	1	2	yes	complemented
144	C₂²×#123	C₂×C₂₃	1	4	yes	complemented
145	C₂²×C₂²⋊Q₈	C₂×C₂₃	1	4	yes	complemented
146	C₂²×#117	C₂×C₂₃	1	1	yes	characteristic, complemented
147	C₂²×C₂₃	—	2	8	no	—
148	C₂²×C₂₃	—	2	48	no	—
149	C₂²×C₂₃	—	2	8	no	—
150	C₂²×C₂₃	—	2	16	no	—
151	C₂²×C₂₃	—	4	48	no	—
152	C₂²×C₂₃	#536	1	16	yes	direct product factor
153	C₂²×C₂₃	C₂³×D₄	1	8	yes	—
154	C₂²×C₂₃	C₂³×D₄	1	6	yes	—
155	C₂²×C₂₃	C₂×2₋¹⁺⁴	1	12	yes	—
156	C₂²×C₂₃	C₂⁶	1	1	yes	characteristic
157	C₄×C₂₃	—	2	8	no	—
158	C₄×C₂₃	—	2	16	no	—
159	C₄×C₂₃	—	2	16	no	—
160	C₄×C₂₃	C₂³×D₄	1	8	yes	—
161	C₄×C₂₃	C₂³×D₄	1	8	yes	—
162	C₂²×#41	—	2	16	no	—
163	C₂²×#41	C₂²×C₂₃	1	24	yes	—
164	C₂³×Q₈	—	2	16	no	—
165	C₂³×Q₈	C₂²×C₂₃	1	2	yes	—
166	C₂³×Q₈	C₂²×C₂₃	1	2	yes	—
167	C₂³×Q₈	C₂²×C₂₃	1	1	yes	characteristic
168	C₂³×Q₈	C₂²×C₂₃	1	24	yes	complemented
169	C₂³×D₄	C₂²×C₂₃	1	2	yes	—
170	C₂³×D₄	C₂²×C₂₃	1	1	yes	characteristic
171	C₂⁴×C₄	C₂²×C₂₃	1	2	yes	—
172	C₂⁴×C₄	C₂²×C₂₃	1	2	yes	—
173	C₂⁴×C₄	C₂²×C₂₃	1	1	yes	characteristic
174	#536	C₂²×C₂₃	1	256	yes	direct product factor
175	C₂×C₄⋊Q₈	C₂²×C₂₃	1	48	yes	complemented
176	C₂×#124	C₂²×C₂₃	1	48	yes	complemented
177	C₂×#123	C₂²×C₂₃	1	96	yes	complemented
178	C₂×C₂²⋊Q₈	C₂²×C₂₃	1	96	yes	complemented
179	C₂×#117	C₂²×C₂₃	1	24	yes	complemented
180	C₂²×C₄⋊C₄	C₂²×C₂₃	1	2	yes	—
181	C₂²×C₄⋊C₄	C₂²×C₂₃	1	8	yes	—
182	C₂²×C₂²⋊C₄	C₂²×C₂₃	1	2	yes	—
183	C₂²×C₂²⋊C₄	C₂²×C₂₃	1	8	yes	—
184	C₂²×C₄²	C₂²×C₂₃	1	2	yes	—
185	C₂×C₂₃	—	2	8	no	—
186	C₂×C₂₃	—	4	8	no	—
187	C₂×C₂₃	C₂×#536	1	12	yes	direct product factor
188	C₂×C₂₃	C₂⁴×D₄	1	1	yes	characteristic
189	C₂×C₂₃	C₂²×2₋¹⁺⁴	1	2	yes	—
190	C₂⁵	C₂³×C₂₃	1	2	yes	—
191	C₂⁵	C₂³×C₂₃	1	1	yes	characteristic
192	C₂×#41	—	2	192	no	—
193	C₂×#41	C₂³×C₂₃	1	64	yes	—
194	C₂²×Q₈	—	2	16	no	—
195	C₂²×Q₈	—	2	16	no	—
196	C₂²×Q₈	—	2	192	no	—
197	C₂²×Q₈	—	2	8	no	—
198	C₂²×Q₈	C₂³×C₂₃	1	24	yes	—
199	C₂²×Q₈	C₂³×C₂₃	1	24	yes	—
200	C₂²×Q₈	C₂³×C₂₃	1	12	yes	—
201	C₂²×Q₈	C₂³×C₂₃	1	64	yes	complemented
202	C₂²×D₄	—	2	16	no	—
203	C₂²×D₄	—	2	8	no	—
204	C₂²×D₄	C₂³×C₂₃	1	24	yes	—
205	C₂²×D₄	C₂³×C₂₃	1	12	yes	—
206	C₂³×C₄	—	2	16	no	—
207	C₂³×C₄	—	2	16	no	—
208	C₂³×C₄	D₄×C₂₃	1	16	yes	—
209	C₂³×C₄	C₂³×C₂₃	1	4	yes	—
210	C₂³×C₄	C₂³×C₂₃	1	4	yes	—
211	C₂³×C₄	C₂³×C₂₃	1	2	yes	—
212	C₂³×C₄	C₂³×C₂₃	1	24	yes	—
213	C₂³×C₄	C₂³×C₂₃	1	24	yes	—
214	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
215	C₂³×C₄	C₂³×C₂₃	1	12	yes	—
216	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
217	C₄⋊Q₈	C₂³×C₂₃	1	128	yes	complemented
218	#124	C₂³×C₂₃	1	128	yes	complemented
219	#123	C₂³×C₂₃	1	256	yes	complemented
220	C₂²⋊Q₈	C₂³×C₂₃	1	256	yes	complemented
221	#117	C₂³×C₂₃	1	64	yes	complemented
222	C₂×C₄⋊C₄	C₂³×C₂₃	1	24	yes	—
223	C₂×C₄⋊C₄	C₂³×C₂₃	1	96	yes	—
224	C₂×C₂²⋊C₄	C₂³×C₂₃	1	24	yes	—
225	C₂×C₂²⋊C₄	C₂³×C₂₃	1	96	yes	—
226	C₂×C₄²	C₂³×C₂₃	1	24	yes	—
227	C₂₃	C₂²×#536	1	1	yes	characteristic, direct product factor, Sylow
228	C₂⁴	—	2	8	no	—
229	C₂⁴	—	2	8	no	—
230	C₂⁴	—	2	16	no	—
231	C₂⁴	C₂×D₄×C₂₃	1	8	yes	—
232	C₂⁴	C₂⁴×C₂₃	1	12	yes	—
233	C₂⁴	C₂⁴×C₂₃	1	6	yes	—
234	C₂⁴	C₂⁴×C₂₃	1	1	yes	characteristic
235	#41	—	2	256	no	—
236	C₂×Q₈	—	2	96	no	—
237	C₂×Q₈	—	2	96	no	—
238	C₂×Q₈	—	2	256	no	—
239	C₂×Q₈	—	2	48	no	—
240	C₂×Q₈	C₂⁴×C₂₃	1	32	yes	—
241	C₂×Q₈	C₂⁴×C₂₃	1	32	yes	—
242	C₂×Q₈	C₂⁴×C₂₃	1	16	yes	—
243	C₂×D₄	—	2	96	no	—
244	C₂×D₄	—	2	48	no	—
245	C₂×D₄	C₂⁴×C₂₃	1	32	yes	—
246	C₂×D₄	C₂⁴×C₂₃	1	16	yes	—
247	C₂²×C₄	—	2	8	no	—
248	C₂²×C₄	—	2	96	no	—
249	C₂²×C₄	—	2	16	no	—
250	C₂²×C₄	—	2	16	no	—
251	C₂²×C₄	—	2	96	no	—
252	C₂²×C₄	C₂×D₄×C₂₃	1	8	yes	—
253	C₂²×C₄	C₂×D₄×C₂₃	1	8	yes	—
254	C₂²×C₄	C₂×D₄×C₂₃	1	96	yes	—
255	C₂²×C₄	C₂⁴×C₂₃	1	24	yes	—
256	C₂²×C₄	C₂⁴×C₂₃	1	24	yes	—
257	C₂²×C₄	C₂⁴×C₂₃	1	12	yes	—
258	C₂²×C₄	C₂⁴×C₂₃	1	32	yes	—
259	C₂²×C₄	C₂⁴×C₂₃	1	32	yes	—
260	C₂²×C₄	C₂⁴×C₂₃	1	6	yes	—
261	C₂²×C₄	C₂⁴×C₂₃	1	6	yes	—
262	C₂²×C₄	C₂⁴×C₂₃	1	16	yes	—
263	C₄⋊C₄	C₂⁴×C₂₃	1	32	yes	—
264	C₄⋊C₄	C₂⁴×C₂₃	1	128	yes	—
265	C₂²⋊C₄	C₂⁴×C₂₃	1	32	yes	—
266	C₂²⋊C₄	C₂⁴×C₂₃	1	128	yes	—
267	C₄²	C₂⁴×C₂₃	1	32	yes	—
268	C₂³	—	2	24	no	—
269	C₂³	—	2	32	no	—
270	C₂³	—	2	24	no	—
271	C₂³	—	2	48	no	—
272	C₂³	—	4	32	no	—
273	C₂³	C₂²×D₄×C₂₃	1	24	yes	—
274	C₂³	C₂²×D₄×C₂₃	1	4	yes	—
275	C₂³	C₂₃×2₋¹⁺⁴	1	8	yes	—
276	C₂³	C₂⁵×C₂₃	1	8	yes	—
277	C₂³	C₂⁵×C₂₃	1	4	yes	—
278	C₂³	C₂⁵×C₂₃	1	3	yes	—
279	Q₈	—	2	64	no	—
280	Q₈	—	2	64	no	—
281	Q₈	—	2	32	no	—
282	D₄	—	2	64	no	—
283	D₄	—	2	32	no	—
284	C₂×C₄	—	2	24	no	—
285	C₂×C₄	—	2	64	no	—
286	C₂×C₄	—	2	48	no	—
287	C₂×C₄	—	2	48	no	—
288	C₂×C₄	—	2	64	no	—
289	C₂×C₄	C₂²×D₄×C₂₃	1	24	yes	—
290	C₂×C₄	C₂²×D₄×C₂₃	1	24	yes	—
291	C₂×C₄	C₂²×D₄×C₂₃	1	64	yes	—
292	C₂×C₄	C₂⁵×C₂₃	1	16	yes	—
293	C₂×C₄	C₂⁵×C₂₃	1	16	yes	—
294	C₂×C₄	C₂⁵×C₂₃	1	8	yes	—
295	C₂×C₄	C₂⁵×C₂₃	1	4	yes	—
296	C₂×C₄	C₂⁵×C₂₃	1	4	yes	—
297	C₂²	—	2	48	no	—
298	C₂²	—	2	8	no	—
299	C₂²	—	2	8	no	—
300	C₂²	—	2	16	no	—
301	C₂²	—	4	48	no	—
302	C₂²	C₂₃×#536	1	16	yes	direct product factor
303	C₂²	C₂³×D₄×C₂₃	1	8	yes	—
304	C₂²	C₂³×D₄×C₂₃	1	6	yes	—
305	C₂²	C₂×C₂₃×2₋¹⁺⁴	1	12	yes	—
306	C₂²	C₂⁶×C₂₃	1	1	yes	characteristic
307	C₄	—	2	8	no	—
308	C₄	—	2	16	no	—
309	C₄	—	2	16	no	—
310	C₄	C₂³×D₄×C₂₃	1	8	yes	—
311	C₄	C₂³×D₄×C₂₃	1	8	yes	—
312	C₂	—	2	8	no	—
313	C₂	—	4	8	no	—
314	C₂	C₂×C₂₃×#536	1	12	yes	direct product factor
315	C₂	C₂⁴×D₄×C₂₃	1	1	yes	characteristic
316	C₂	C₂²×C₂₃×2₋¹⁺⁴	1	2	yes	—

	subgroup	G/H
center, socle	C₂⁴×C₂₃	C₂⁴
commutator, Frattini, cosocle	C₂²	C₂⁶×C₂₃
prime radical	C₂³×#41×C₂₃	C₂
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂⁴×C₂₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂⁴×Q₈×C₂₃	C₂	semidirect
3. C₂×C₂₃×#536	C₂	direct (N × H)
4. C₂²×C₂₃×C₄⋊Q₈	C₂	semidirect
5. C₂²×C₂₃×#124	C₂	semidirect
6. C₂²×C₂₃×#123	C₂	semidirect
7. C₂²×C₂₃×C₂²⋊Q₈	C₂	semidirect
8. C₂²×C₂₃×#117	C₂	semidirect
15. C₂³×Q₈×C₂₃	C₂²	semidirect
21. C₂₃×#536	C₂²	direct (N × H)
22. C₂×C₂₃×C₄⋊Q₈	C₂²	semidirect
23. C₂×C₂₃×#124	C₂²	semidirect
24. C₂×C₂₃×#123	C₂²	semidirect
25. C₂×C₂₃×C₂²⋊Q₈	C₂²	semidirect
26. C₂×C₂₃×#117	C₂²	semidirect
43. C₂²×Q₈×C₂₃	C₂³	semidirect
59. C₂₃×C₄⋊Q₈	C₂³	semidirect
60. C₂₃×#124	C₂³	semidirect
61. C₂₃×#123	C₂³	semidirect
62. C₂₃×C₂²⋊Q₈	C₂³	semidirect
63. C₂₃×#117	C₂³	semidirect
109. C₂²×#536	C₂₃	direct (N × H)
140. C₂⁴×Q₈	C₂×C₂₃	semidirect
141. C₂×#536	C₂×C₂₃	direct (N × H)
142. C₂²×C₄⋊Q₈	C₂×C₂₃	semidirect
143. C₂²×#124	C₂×C₂₃	semidirect
144. C₂²×#123	C₂×C₂₃	semidirect
145. C₂²×C₂²⋊Q₈	C₂×C₂₃	semidirect
146. C₂²×#117	C₂×C₂₃	semidirect
152. C₂²×C₂₃	#536	direct (N × H)
168. C₂³×Q₈	C₂²×C₂₃	semidirect
174. #536	C₂²×C₂₃	direct (N × H)
175. C₂×C₄⋊Q₈	C₂²×C₂₃	semidirect
176. C₂×#124	C₂²×C₂₃	semidirect
177. C₂×#123	C₂²×C₂₃	semidirect
178. C₂×C₂²⋊Q₈	C₂²×C₂₃	semidirect
179. C₂×#117	C₂²×C₂₃	semidirect
187. C₂×C₂₃	C₂×#536	direct (N × H)
201. C₂²×Q₈	C₂³×C₂₃	semidirect
217. C₄⋊Q₈	C₂³×C₂₃	semidirect
218. #124	C₂³×C₂₃	semidirect
219. #123	C₂³×C₂₃	semidirect
220. C₂²⋊Q₈	C₂³×C₂₃	semidirect
221. #117	C₂³×C₂₃	semidirect
227. C₂₃	C₂²×#536	direct (N × H)
302. C₂²	C₂₃×#536	direct (N × H)
314. C₂	C₂×C₂₃×#536	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂³×#41×C₂₃	2
C₂⁴×Q₈×C₂₃	2
C₂×C₂₃×#536	2
C₂²×C₂₃×C₄⋊Q₈	2
C₂²×C₂₃×#124	2
C₂²×C₂₃×#123	2
C₂²×C₂₃×C₂²⋊Q₈	2
C₂²×C₂₃×#117	2
C₂²×#536	23

Subgroups — C22×C23×#536 #19210306

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×C₂₃×#536 #19210306