Subgroups — C₄×#10625067 #15675930

Order 2944.

656 conjugacy classes of subgroups.

The subgroup lattice has 386 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#10625067	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×Dic₄₆	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₄²×D₂₃	C₂	1	1	yes	maximal, characteristic
4	#13092321	C₂	1	1	yes	maximal, characteristic, complemented
5	#13092312	C₂	1	1	yes	maximal, characteristic, complemented
6	#13092303	C₂	1	1	yes	maximal, characteristic, complemented
7	#13092299	C₂	1	1	yes	maximal, characteristic, complemented
8	#13092291	C₂	1	1	yes	maximal, characteristic
9	#13092288	C₂	1	1	yes	maximal, characteristic
10	#13092276	C₂	1	1	yes	maximal, characteristic
11	C₄×Dic₂₃⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
12	C₄×Dic₂₃⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
13	C₄×(C₂×D₂₃)⋊C₄	C₂	1	1	yes	maximal, characteristic
14	C₄×(C₂×D₂₃)⋊C₄	C₂	1	1	yes	maximal, characteristic
15	C₄×C₄⋊C₄×C₂₃	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×C₄×D₂₃	C₂²	1	1	yes	characteristic
17	C₂²×C₄×D₂₃	C₂²	1	1	yes	characteristic
18	C₂²×C₄×D₂₃	C₂²	1	1	yes	characteristic
19	C₂²×Dic₄₆	C₂²	1	1	yes	characteristic
20	C₂×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
21	C₂×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
22	C₂×C₄²×C₂₃	C₂²	1	1	yes	characteristic
23	C₂×C₄²×C₂₃	C₂²	1	1	yes	characteristic
24	C₂×C₄²×C₂₃	C₂²	1	1	yes	characteristic
25	C₂×(C₂×D₂₃)⋊C₄	C₂²	1	1	yes	characteristic
26	C₂×(C₂×D₂₃)⋊C₄	C₂²	1	1	yes	characteristic
27	C₂×(C₂×D₂₃)⋊C₄	C₂²	1	1	yes	characteristic
28	C₂×(C₂×D₂₃)⋊C₄	C₂²	1	1	yes	characteristic
29	C₂×C₄⋊Dic₂₃	C₂²	1	1	yes	characteristic
30	C₂×Dic₂₃⋊C₄	C₂²	1	1	yes	characteristic
31	C₂×Dic₂₃⋊C₄	C₂²	1	1	yes	characteristic
32	C₂×Dic₂₃⋊C₄	C₂²	1	1	yes	characteristic
33	C₂×Dic₂₃⋊C₄	C₂²	1	1	yes	characteristic
34	C₂×Dic₂₃⋊C₄	C₂²	1	1	yes	characteristic
35	C₂×Dic₂₃⋊C₄	C₂²	1	1	yes	characteristic
36	C₂×C₄×Dic₂₃	C₂²	1	1	yes	characteristic
37	C₂×C₄×Dic₂₃	C₂²	1	1	yes	characteristic
38	C₂×C₄×Dic₂₃	C₂²	1	1	yes	characteristic
39	C₂×C₄×Dic₂₃	C₂²	1	1	yes	characteristic
40	C₂×C₄×Dic₂₃	C₂²	1	1	yes	characteristic
41	#10625067	C₄	1	8	yes	direct product factor
42	C₄²×D₂₃	—	2	4	no	—
43	C₄×Dic₄₆	—	2	4	no	—
44	C₂₃×#95	C₂²	1	1	yes	characteristic
45	C₂₃×#95	C₂²	1	1	yes	characteristic
46	C₂₃⋊#95	C₂²	1	1	yes	characteristic
47	C₂₃⋊#95	C₂²	1	1	yes	characteristic
48	C₂₃⋊#95	C₂²	1	1	yes	characteristic
49	C₂₃⋊#95	C₂²	1	1	yes	characteristic
50	C₂₃⋊#95	C₂²	1	1	yes	characteristic
51	C₂₃⋊#95	C₂²	1	1	yes	characteristic
52	C₂₃⋊#95	C₂²	1	1	yes	characteristic
53	C₂₃⋊#95	C₂²	1	1	yes	characteristic
54	C₂³×D₂₃	C₂³	1	1	yes	characteristic
55	C₂²×C₄×C₂₃	C₂³	1	1	yes	characteristic
56	C₂²×C₄×C₂₃	C₂³	1	1	yes	characteristic
57	C₂²×C₄×C₂₃	C₂³	1	1	yes	characteristic
58	C₂²×C₄×C₂₃	C₂³	1	1	yes	characteristic
59	C₂²×C₄×C₂₃	C₂³	1	1	yes	characteristic
60	C₂²×C₄×C₂₃	C₂³	1	1	yes	characteristic
61	C₂²×C₄×C₂₃	C₂³	1	1	yes	characteristic
62	C₂²×Dic₂₃	C₂³	1	1	yes	characteristic
63	C₂²×Dic₂₃	C₂³	1	1	yes	characteristic
64	C₂²×Dic₂₃	C₂³	1	1	yes	characteristic
65	C₂²×Dic₂₃	C₂³	1	1	yes	characteristic
66	C₂²×Dic₂₃	C₂³	1	1	yes	characteristic
67	C₂²×Dic₂₃	C₂³	1	1	yes	characteristic
68	C₂²×Dic₂₃	C₂³	1	1	yes	characteristic
69	C₂×C₄×D₂₃	—	2	2	no	—
70	C₂×C₄×D₂₃	—	2	2	no	—
71	C₂×C₄×D₂₃	—	2	2	no	—
72	C₂×C₄×D₂₃	—	2	2	no	—
73	C₂×C₄×D₂₃	—	2	2	no	—
74	C₂×C₄×D₂₃	—	2	2	no	—
75	C₂×C₄×D₂₃	—	2	2	no	—
76	C₂×C₄×D₂₃	C₂×C₄	1	4	yes	—
77	C₂×C₄×D₂₃	Q₈	1	4	yes	complemented
78	C₂×Dic₄₆	—	2	2	no	—
79	C₂×Dic₄₆	—	2	2	no	—
80	C₂×Dic₄₆	C₂×C₄	1	4	yes	complemented
81	C₄⋊C₄×C₂₃	—	2	2	no	—
82	C₄⋊C₄×C₂₃	C₂×C₄	1	4	yes	complemented
83	C₄²×C₂₃	—	2	2	no	—
84	C₄²×C₂₃	—	2	2	no	—
85	C₄²×C₂₃	—	2	2	no	—
86	(C₂×D₂₃)⋊C₄	—	2	2	no	—
87	(C₂×D₂₃)⋊C₄	—	2	2	no	—
88	(C₂×D₂₃)⋊C₄	C₂×C₄	1	4	yes	—
89	(C₂×D₂₃)⋊C₄	C₂×C₄	1	4	yes	—
90	C₄⋊Dic₂₃	—	2	2	no	—
91	Dic₂₃⋊C₄	—	2	2	no	—
92	Dic₂₃⋊C₄	—	2	2	no	—
93	Dic₂₃⋊C₄	—	2	2	no	—
94	Dic₂₃⋊C₄	—	2	2	no	—
95	Dic₂₃⋊C₄	C₂×C₄	1	4	yes	complemented
96	Dic₂₃⋊C₄	C₂×C₄	1	4	yes	complemented
97	C₄×Dic₂₃	—	2	2	no	—
98	C₄×Dic₂₃	—	2	2	no	—
99	C₄×Dic₂₃	—	2	2	no	—
100	C₄×Dic₂₃	—	2	2	no	—
101	C₄×Dic₂₃	D₄	1	4	yes	—
102	C₂³×C₂₃	C₂⁴	1	1	yes	characteristic
103	C₂²×D₂₃	—	2	1	no	—
104	C₂²×D₂₃	—	2	1	no	—
105	C₂²×D₂₃	—	2	1	no	—
106	C₂²×D₂₃	—	2	1	no	—
107	C₂²×D₂₃	C₂²×C₄	1	2	yes	—
108	C₂²×D₂₃	C₂×Q₈	1	2	yes	—
109	C₂²×D₂₃	#41	1	2	yes	—
110	C₂×C₄×C₂₃	—	2	1	no	—
111	C₂×C₄×C₂₃	—	2	1	no	—
112	C₂×C₄×C₂₃	—	2	1	no	—
113	C₂×C₄×C₂₃	—	2	1	no	—
114	C₂×C₄×C₂₃	—	2	1	no	—
115	C₂×C₄×C₂₃	—	2	1	no	—
116	C₂×C₄×C₂₃	—	2	1	no	—
117	C₂×C₄×C₂₃	—	2	1	no	—
118	C₂×C₄×C₂₃	—	2	1	no	—
119	C₂×C₄×C₂₃	—	2	1	no	—
120	C₂×C₄×C₂₃	—	2	1	no	—
121	C₂×C₄×C₂₃	—	2	1	no	—
122	C₂×C₄×C₂₃	—	2	1	no	—
123	C₂×C₄×C₂₃	—	2	1	no	—
124	C₂×C₄×C₂₃	C₂²×C₄	1	2	yes	—
125	C₂×C₄×C₂₃	C₂²×C₄	1	2	yes	—
126	C₂×C₄×C₂₃	C₂²×C₄	1	2	yes	—
127	C₂×C₄×C₂₃	C₂×D₄	1	2	yes	—
128	C₂×C₄×C₂₃	C₂×Q₈	1	2	yes	—
129	C₂×C₄×C₂₃	#41	1	2	yes	—
130	C₂×C₄×C₂₃	#41	1	2	yes	—
131	C₂×Dic₂₃	—	2	1	no	—
132	C₂×Dic₂₃	—	2	1	no	—
133	C₂×Dic₂₃	—	2	1	no	—
134	C₂×Dic₂₃	—	2	1	no	—
135	C₂×Dic₂₃	—	2	1	no	—
136	C₂×Dic₂₃	—	2	1	no	—
137	C₂×Dic₂₃	—	2	1	no	—
138	C₂×Dic₂₃	—	2	1	no	—
139	C₂×Dic₂₃	—	2	1	no	—
140	C₂×Dic₂₃	—	2	1	no	—
141	C₂×Dic₂₃	—	2	1	no	—
142	C₂×Dic₂₃	—	2	1	no	—
143	C₂×Dic₂₃	—	2	1	no	—
144	C₂×Dic₂₃	—	2	1	no	—
145	C₂×Dic₂₃	C₂²×C₄	1	2	yes	—
146	C₂×Dic₂₃	C₂²×C₄	1	2	yes	—
147	C₂×Dic₂₃	C₂²×C₄	1	2	yes	—
148	C₂×Dic₂₃	C₂×D₄	1	2	yes	—
149	C₂×Dic₂₃	C₂×D₄	1	2	yes	—
150	C₂×Dic₂₃	C₂×Q₈	1	2	yes	—
151	C₂×Dic₂₃	#41	1	2	yes	—
152	C₄×D₂₃	—	2	8	no	—
153	C₄×D₂₃	—	2	8	no	—
154	C₄×D₂₃	—	2	8	no	—
155	Dic₄₆	—	2	8	no	—
156	C₄×C₂²⋊Q₈	—	23	1	no	maximal, Sylow
157	C₂²×C₂₃	C₂³×C₄	1	1	yes	characteristic
158	C₂²×C₂₃	C₂²×D₄	1	1	yes	characteristic
159	C₂²×C₂₃	C₂²×Q₈	1	1	yes	characteristic
160	C₂²×C₂₃	C₂×#41	1	1	yes	characteristic
161	C₂²×C₂₃	C₂×#41	1	1	yes	characteristic
162	C₂²×C₂₃	C₂×#41	1	1	yes	characteristic
163	C₂²×C₂₃	C₂×#41	1	1	yes	characteristic
164	C₂×D₂₃	—	2	2	no	—
165	C₂×D₂₃	—	2	2	no	—
166	C₂×D₂₃	—	2	2	no	—
167	C₂×D₂₃	—	2	2	no	—
168	C₂×D₂₃	—	2	2	no	—
169	C₂×D₂₃	—	2	2	no	—
170	C₂×D₂₃	C₄×Q₈	1	4	yes	complemented
171	C₄×C₂₃	—	2	2	no	—
172	C₄×C₂₃	—	2	2	no	—
173	C₄×C₂₃	—	2	2	no	—
174	C₄×C₂₃	—	2	2	no	—
175	C₄×C₂₃	—	4	1	no	—
176	C₄×C₂₃	—	4	1	no	—
177	C₄×C₂₃	C₂²⋊Q₈	1	4	yes	complemented
178	Dic₂₃	—	2	2	no	—
179	Dic₂₃	—	2	2	no	—
180	Dic₂₃	—	2	2	no	—
181	Dic₂₃	—	2	2	no	—
182	Dic₂₃	—	4	1	no	—
183	Dic₂₃	—	4	1	no	—
184	Dic₂₃	C₄×D₄	1	4	yes	—
185	C₂×C₂²⋊Q₈	—	23	1	no	—
186	C₂×C₄×Q₈	—	23	1	no	—
187	C₂²×C₄²	—	23	1	no	—
188	#391	—	23	1	no	—
189	#389	—	23	1	no	—
190	#387	—	23	1	no	—
191	#387	—	23	1	no	—
192	#385	—	23	1	no	—
193	#385	—	23	1	no	—
194	#380	—	23	1	no	—
195	C₄×C₄⋊C₄	—	23	1	no	—
196	C₄×C₄⋊C₄	—	23	1	no	—
197	C₄×C₄⋊C₄	D₂₃	1	1	yes	characteristic, complemented
198	C₄×C₂²⋊C₄	—	23	1	no	—
199	C₄×C₂²⋊C₄	—	23	1	no	—
200	C₂×C₂₃	C₂×C₄×D₄	1	1	yes	characteristic
201	C₂×C₂₃	C₂×C₄×Q₈	1	1	yes	characteristic
202	C₂×C₂₃	C₄×#41	1	1	yes	characteristic
203	C₂×C₂₃	C₂×C₂²⋊Q₈	1	1	yes	characteristic
204	C₂×C₂₃	#525	1	1	yes	characteristic
205	C₂×C₂₃	#529	1	1	yes	characteristic
206	C₂×C₂₃	#533	1	1	yes	characteristic
207	D₂₃	—	2	4	no	—
208	C₂²×Q₈	—	23	1	no	—
209	C₂³×C₄	—	23	1	no	—
210	C₂³×C₄	—	23	1	no	—
211	C₂³×C₄	—	23	1	no	—
212	C₂²⋊Q₈	—	23	8	no	—
213	C₄×Q₈	—	46	4	no	—
214	C₂×C₄⋊C₄	—	23	1	no	—
215	C₂×C₄⋊C₄	—	23	1	no	—
216	C₂×C₄⋊C₄	—	23	1	no	—
217	C₂×C₄⋊C₄	—	23	1	no	—
218	C₂×C₄⋊C₄	—	23	1	no	—
219	C₂×C₄⋊C₄	—	23	1	no	—
220	C₂×C₄⋊C₄	—	23	1	no	—
221	C₂×C₄⋊C₄	C₂×D₂₃	1	1	yes	characteristic
222	C₂×C₄⋊C₄	C₂×D₂₃	1	1	yes	characteristic
223	C₂×C₂²⋊C₄	—	23	1	no	—
224	C₂×C₂²⋊C₄	—	23	1	no	—
225	C₂×C₂²⋊C₄	—	23	1	no	—
226	C₂×C₂²⋊C₄	—	23	1	no	—
227	C₂×C₄²	—	23	1	no	—
228	C₂×C₄²	—	23	1	no	—
229	C₂×C₄²	—	23	1	no	—
230	C₂×C₄²	—	23	1	no	—
231	C₂×C₄²	—	23	1	no	—
232	C₂×C₄²	—	46	4	no	—
233	C₂×C₄²	C₂×D₂₃	1	1	yes	characteristic
234	C₂×C₄²	C₂×D₂₃	1	1	yes	characteristic
235	C₂×C₄²	C₂×D₂₃	1	1	yes	characteristic
236	#95	—	23	1	no	—
237	#95	—	23	1	no	—
238	#95	—	23	1	no	—
239	#95	—	23	1	no	—
240	#95	—	23	1	no	—
241	#95	—	23	1	no	—
242	#95	—	23	1	no	—
243	#95	—	23	1	no	—
244	#95	C₂×D₂₃	1	1	yes	characteristic
245	#95	C₂×D₂₃	1	1	yes	characteristic
246	C₂₃	C₄×C₂²⋊Q₈	1	1	yes	characteristic, complemented, Sylow
247	C₂⁴	—	23	1	no	—
248	C₂×Q₈	—	23	4	no	—
249	C₂×Q₈	—	46	2	no	—
250	C₂×Q₈	—	46	2	no	—
251	C₂²×C₄	—	23	1	no	—
252	C₂²×C₄	—	23	1	no	—
253	C₂²×C₄	—	23	1	no	—
254	C₂²×C₄	—	23	1	no	—
255	C₂²×C₄	—	23	1	no	—
256	C₂²×C₄	—	23	4	no	—
257	C₂²×C₄	—	23	4	no	—
258	C₂²×C₄	—	23	1	no	—
259	C₂²×C₄	—	23	1	no	—
260	C₂²×C₄	—	46	2	no	—
261	C₂²×C₄	—	46	2	no	—
262	C₂²×C₄	—	46	2	no	—
263	C₂²×C₄	—	46	2	no	—
264	C₂²×C₄	—	46	2	no	—
265	C₂²×C₄	—	46	2	no	—
266	C₂²×C₄	—	46	2	no	—
267	C₂²×C₄	C₂²×D₂₃	1	1	yes	characteristic
268	C₂²×C₄	C₂²×D₂₃	1	1	yes	characteristic
269	C₂²×C₄	C₂²×D₂₃	1	1	yes	characteristic
270	C₂²×C₄	C₂²×D₂₃	1	1	yes	characteristic
271	C₂²×C₄	C₂²×D₂₃	1	1	yes	characteristic
272	C₂²×C₄	C₂²×D₂₃	1	1	yes	characteristic
273	C₂²×C₄	C₂²×D₂₃	1	1	yes	characteristic
274	C₄⋊C₄	—	2	2	no	—
275	C₄⋊C₄	—	23	4	no	—
276	C₄⋊C₄	—	23	4	no	—
277	C₄⋊C₄	—	46	2	no	—
278	C₄⋊C₄	—	46	2	no	—
279	C₄⋊C₄	—	46	2	no	—
280	C₄⋊C₄	—	46	2	no	—
281	C₄⋊C₄	—	46	2	no	—
282	C₄⋊C₄	C₄×D₂₃	1	4	yes	complemented
283	C₂²⋊C₄	—	23	4	no	—
284	C₂²⋊C₄	—	23	4	no	—
285	C₂²⋊C₄	—	46	2	no	—
286	C₂²⋊C₄	—	46	2	no	—
287	C₄²	—	2	2	no	—
288	C₄²	—	2	2	no	—
289	C₄²	—	2	2	no	—
290	C₄²	—	23	4	no	—
291	C₄²	—	46	2	no	—
292	C₄²	—	46	2	no	—
293	C₄²	—	46	2	no	—
294	C₄²	—	46	2	no	—
295	C₂³	—	23	2	no	—
296	C₂³	—	23	2	no	—
297	C₂³	—	23	2	no	—
298	C₂³	—	46	1	no	—
299	C₂³	—	46	1	no	—
300	C₂³	—	46	1	no	—
301	C₂³	—	46	1	no	—
302	C₂³	C₂³×D₂₃	1	1	yes	characteristic
303	Q₈	—	46	8	no	—
304	C₂×C₄	—	2	1	no	—
305	C₂×C₄	—	2	1	no	—
306	C₂×C₄	—	2	1	no	—
307	C₂×C₄	—	2	1	no	—
308	C₂×C₄	—	2	1	no	—
309	C₂×C₄	—	2	1	no	—
310	C₂×C₄	—	2	1	no	—
311	C₂×C₄	—	2	1	no	—
312	C₂×C₄	—	2	1	no	—
313	C₂×C₄	—	2	1	no	—
314	C₂×C₄	—	2	1	no	—
315	C₂×C₄	—	2	1	no	—
316	C₂×C₄	—	2	1	no	—
317	C₂×C₄	—	2	1	no	—
318	C₂×C₄	—	23	2	no	—
319	C₂×C₄	—	23	2	no	—
320	C₂×C₄	—	23	2	no	—
321	C₂×C₄	—	23	2	no	—
322	C₂×C₄	—	23	2	no	—
323	C₂×C₄	—	23	2	no	—
324	C₂×C₄	—	23	2	no	—
325	C₂×C₄	—	46	8	no	—
326	C₂×C₄	—	46	8	no	—
327	C₂×C₄	—	46	1	no	—
328	C₂×C₄	—	46	1	no	—
329	C₂×C₄	—	46	1	no	—
330	C₂×C₄	—	46	1	no	—
331	C₂×C₄	—	46	1	no	—
332	C₂×C₄	—	46	1	no	—
333	C₂×C₄	—	46	1	no	—
334	C₂×C₄	—	46	1	no	—
335	C₂×C₄	—	46	8	no	—
336	C₂×C₄	—	46	1	no	—
337	C₂×C₄	—	46	1	no	—
338	C₂×C₄	—	46	1	no	—
339	C₂×C₄	—	46	1	no	—
340	C₂×C₄	—	46	1	no	—
341	C₂×C₄	—	46	1	no	—
342	C₂×C₄	C₂×C₄×D₂₃	1	2	yes	—
343	C₂×C₄	C₂×C₄×D₂₃	1	2	yes	—
344	C₂×C₄	C₂×C₄×D₂₃	1	2	yes	—
345	C₂×C₄	#67288	1	2	yes	—
346	C₂×C₄	#67288	1	2	yes	—
347	C₂×C₄	D₄×D₂₃	1	2	yes	—
348	C₂×C₄	Q₈×D₂₃	1	2	yes	—
349	C₂²	—	23	4	no	—
350	C₂²	—	46	2	no	—
351	C₂²	—	46	2	no	—
352	C₂²	—	46	2	no	—
353	C₂²	—	46	2	no	—
354	C₂²	—	46	2	no	—
355	C₂²	—	46	2	no	—
356	C₂²	C₂²×C₄×D₂₃	1	1	yes	characteristic
357	C₂²	C₂×#67288	1	1	yes	characteristic
358	C₂²	C₂×#67288	1	1	yes	characteristic
359	C₂²	C₂×D₄×D₂₃	1	1	yes	characteristic
360	C₂²	C₂×Q₈×D₂₃	1	1	yes	characteristic
361	C₂²	#41×D₂₃	1	1	yes	characteristic
362	C₂²	#41×D₂₃	1	1	yes	characteristic
363	C₄	—	2	2	no	—
364	C₄	—	2	2	no	—
365	C₄	—	2	2	no	—
366	C₄	—	2	2	no	—
367	C₄	—	4	1	no	—
368	C₄	—	4	1	no	—
369	C₄	—	23	4	no	—
370	C₄	—	46	2	no	—
371	C₄	—	46	2	no	—
372	C₄	—	46	2	no	—
373	C₄	—	46	2	no	—
374	C₄	—	92	1	no	—
375	C₄	—	92	1	no	—
376	C₄	#10625067	1	4	yes	direct product factor
377	C₂	—	46	4	no	—
378	C₂	C₄×D₄×D₂₃	1	1	yes	characteristic
379	C₂	C₄×Q₈×D₂₃	1	1	yes	characteristic
380	C₂	C₄×#67288	1	1	yes	characteristic
381	C₂	C₂×#10625067	1	1	yes	characteristic
382	C₂	#13092926	1	1	yes	characteristic
383	C₂	#13092945	1	1	yes	characteristic
384	C₂	#13092971	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	C₂²×D₂₃
commutator	C₂²×C₂₃	C₂³×C₄
Frattini	C₂³	C₂³×D₂₃
Fitting	C₄×C₄⋊C₄×C₂₃	C₂
socle, cosocle	C₂³×C₂₃	C₂⁴
prime radical	C₂³×D₂₃	C₂³
hypercenter	C₄×C₄⋊C₄	D₂₃
hypocenter	C₂₃	C₄×C₂²⋊Q₈
LCS	G ▷ C₂²×C₂₃ ▷ C₂₃
UCS	C₁ ◁ C₂²×C₄ ◁ C₄×C₄⋊C₄

Complements

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

N	H ≅ G/N	type
2. C₂×C₄×Dic₄₆	C₂	semidirect
4. #13092321	C₂	semidirect
5. #13092312	C₂	semidirect
6. #13092303	C₂	semidirect
7. #13092299	C₂	semidirect
11. C₄×Dic₂₃⋊C₄	C₂	semidirect
12. C₄×Dic₂₃⋊C₄	C₂	semidirect
15. C₄×C₄⋊C₄×C₂₃	C₂	semidirect
41. #10625067	C₄	direct (N × H)
77. C₂×C₄×D₂₃	Q₈	semidirect
80. C₂×Dic₄₆	C₂×C₄	semidirect
82. C₄⋊C₄×C₂₃	C₂×C₄	semidirect
95. Dic₂₃⋊C₄	C₂×C₄	semidirect
96. Dic₂₃⋊C₄	C₂×C₄	semidirect
170. C₂×D₂₃	C₄×Q₈	semidirect
177. C₄×C₂₃	C₂²⋊Q₈	semidirect
197. C₄×C₄⋊C₄	D₂₃	semidirect
246. C₂₃	C₄×C₂²⋊Q₈	semidirect
282. C₄⋊C₄	C₄×D₂₃	semidirect
376. C₄	#10625067	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×#10625067	2
C₂×C₄×Dic₄₆	2
C₂×C₄²×D₂₃	2
#13092321	2
#13092312	2
#13092303	2
#13092299	2
#13092291	2
#13092288	2
#13092276	2
C₄×Dic₂₃⋊C₄	2
C₄×(C₂×D₂₃)⋊C₄	2
C₄×C₄⋊C₄×C₂₃	2
C₄×C₂²⋊Q₈	23

Subgroups — C4×#10625067 #15675930

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×#10625067 #15675930