Group #19212331 — subgroups

Subgroups — #19212331

Order 5888.

440 conjugacy classes of subgroups; only the 127 normal subgroups are shown.

normal subgroups only

This group has 440 conjugacy classes of subgroups — too many to draw. Only its 127 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×#10625040	C₂	1	1	yes	maximal, characteristic
2	#15673540	C₂	1	1	yes	maximal, characteristic
3	#15671221	C₂	1	4	yes	maximal
4	C₂₃×#1839	C₂	1	1	yes	maximal, characteristic
5	C₂×#10625040	C₄	1	1	yes	characteristic
6	C₂×C₄×Dic₄₆	—	2	1	no	—
7	#13092323	—	2	1	no	—
8	#13092315	—	2	1	no	—
9	#13092315	C₂²	1	2	yes	—
10	#13092287	C₄	1	1	yes	characteristic
11	C₄×C₄⋊Dic₂₃	—	2	1	no	—
12	C₄×C₄⋊Dic₂₃	C₄	1	2	yes	—
13	#13092172	—	2	1	no	—
14	#13092172	—	2	1	no	—
15	#13092172	C₂²	1	2	yes	—
16	C₄³×C₂₃	C₂²	1	1	yes	characteristic
17	C₂₃×#336	—	2	1	no	—
18	C₂₃×#336	—	2	1	no	—
19	C₂₃×#336	C₂²	1	2	yes	—
20	C₂²×Dic₄₆	—	2	1	no	—
21	C₂²×C₈×C₂₃	—	2	2	no	—
22	C₂×C₄²×C₂₃	C₂×C₄	1	1	yes	characteristic
23	C₂×C₄²×C₂₃	C₂×C₄	1	1	yes	characteristic
24	C₂×C₄²×C₂₃	D₄	1	1	yes	characteristic
25	C₂×C₄²×C₂₃	D₄	1	1	yes	characteristic
26	C₂×C₄²×C₂₃	D₄	1	1	yes	characteristic
27	C₂×C₄²×C₂₃	D₄	1	1	yes	characteristic
28	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
29	C₂×C₄⋊Dic₂₃	—	2	1	no	—
30	C₂×C₄⋊Dic₂₃	—	2	1	no	—
31	C₂×C₄⋊Dic₂₃	—	2	1	no	—
32	C₂×C₄⋊Dic₂₃	C₂×C₄	1	2	yes	—
33	C₂×C₄⋊Dic₂₃	C₂×C₄	1	2	yes	—
34	C₂×Dic₂₃⋊C₄	—	2	2	no	—
35	C₂×C₄×Dic₂₃	—	2	2	no	—
36	C₂²×C₂₃⋊C₈	—	2	2	no	—
37	#10625040	—	2	2	no	—
38	#10625040	C₈	1	4	yes	complemented
39	C₄×Dic₄₆	—	4	4	no	—
40	C₂₃⋊#95	—	2	2	no	—
41	C₂₃⋊#95	—	2	2	no	—
42	C₂²×C₄×C₂₃	C₂²⋊C₄	1	1	yes	characteristic
43	C₂²×C₄×C₂₃	C₂²⋊C₄	1	1	yes	characteristic
44	C₂²×C₄×C₂₃	C₂²⋊C₄	1	1	yes	characteristic
45	C₂²×C₄×C₂₃	C₂²⋊C₄	1	1	yes	characteristic
46	C₂²×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
47	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
48	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
49	C₂²×Dic₂₃	—	2	2	no	—
50	C₂²×Dic₂₃	—	2	2	no	—
51	C₂×Dic₄₆	—	2	4	no	—
52	C₂×Dic₄₆	—	4	2	no	—
53	C₂×Dic₄₆	—	4	2	no	—
54	C₂×C₈×C₂₃	—	4	2	no	—
55	C₂×C₈×C₂₃	—	4	2	no	—
56	C₂×C₈×C₂₃	—	4	2	no	—
57	C₄²×C₂₃	—	2	2	no	—
58	C₄²×C₂₃	—	2	2	no	—
59	C₄²×C₂₃	—	2	2	no	—
60	C₄²×C₂₃	—	4	1	no	—
61	C₄²×C₂₃	—	4	1	no	—
62	C₄²×C₂₃	—	4	1	no	—
63	C₄²×C₂₃	C₂×C₈	1	2	yes	—
64	C₄²×C₂₃	M₁₆	1	2	yes	—
65	C₄⋊Dic₂₃	—	2	4	no	—
66	C₄⋊Dic₂₃	—	2	2	no	—
67	C₄⋊Dic₂₃	—	4	2	no	—
68	C₄⋊Dic₂₃	—	4	2	no	—
69	C₄⋊Dic₂₃	—	4	2	no	—
70	C₄⋊Dic₂₃	C₂×C₈	1	4	yes	—
71	Dic₂₃⋊C₄	—	4	4	no	—
72	C₄×Dic₂₃	—	4	4	no	—
73	C₂×C₂₃⋊C₈	—	4	2	no	—
74	C₂×C₂₃⋊C₈	—	4	2	no	—
75	C₂×C₂₃⋊C₈	—	4	2	no	—
76	#7604	—	23	1	no	maximal, Sylow
77	C₂³×C₂₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
78	C₂×C₄×C₂₃	—	2	1	no	—
79	C₂×C₄×C₂₃	—	2	1	no	—
80	C₂×C₄×C₂₃	—	2	1	no	—
81	C₂×C₄×C₂₃	—	2	1	no	—
82	C₂×C₄×C₂₃	—	2	1	no	—
83	C₂×C₄×C₂₃	—	2	1	no	—
84	C₂×C₄×C₂₃	—	2	1	no	—
85	C₂×C₄×C₂₃	—	2	1	no	—
86	C₂×C₄×C₂₃	—	2	1	no	—
87	C₂×C₄×C₂₃	—	2	1	no	—
88	C₂×C₄×C₂₃	—	2	1	no	—
89	C₂×C₄×C₂₃	—	2	1	no	—
90	C₂×C₄×C₂₃	—	2	1	no	—
91	C₂×C₄×C₂₃	—	2	1	no	—
92	C₂×C₄×C₂₃	—	2	1	no	—
93	C₂×C₄×C₂₃	C₂²⋊C₈	1	2	yes	—
94	C₂×C₄×C₂₃	C₂²⋊C₈	1	2	yes	—
95	C₂×C₄×C₂₃	#101	1	2	yes	—
96	C₂×C₄×C₂₃	C₂²×C₈	1	1	yes	characteristic
97	C₂×C₄×C₂₃	C₂×M₁₆	1	1	yes	characteristic
98	C₂×C₄×C₂₃	AGL(1,ℤ/8)	1	2	yes	—
99	C₂×C₄×C₂₃	#137	1	2	yes	—
100	C₂×Dic₂₃	—	2	4	no	—
101	C₂×Dic₂₃	—	4	2	no	—
102	C₂×Dic₂₃	—	4	2	no	—
103	C₂×Dic₂₃	—	4	2	no	—
104	C₂×Dic₂₃	—	4	2	no	—
105	C₂×Dic₂₃	—	4	2	no	—
106	Dic₄₆	—	4	8	no	—
107	C₈×C₂₃	—	8	2	no	—
108	C₂₃⋊C₈	—	8	2	no	—
109	C₄×C₄⋊Q₈	—	23	1	no	—
110	#1839	—	23	1	no	—
111	#1839	D₂₃	1	1	yes	characteristic
112	#1271	—	23	4	no	—
113	C₂²×C₂₃	C₂×C₂²⋊C₈	1	1	yes	characteristic
114	C₂²×C₂₃	#410	1	1	yes	characteristic
115	C₂²×C₂₃	C₂×#101	1	1	yes	characteristic
116	C₂²×C₂₃	#418	1	1	yes	characteristic
117	C₂²×C₂₃	#419	1	1	yes	characteristic
118	C₂²×C₂₃	#421	1	1	yes	characteristic
119	C₂²×C₂₃	#421	1	1	yes	characteristic
120	C₄×C₂₃	—	2	2	no	—
121	C₄×C₂₃	—	2	1	no	—
122	C₄×C₂₃	—	2	1	no	—
123	C₄×C₂₃	—	2	2	no	—
124	C₄×C₂₃	—	2	2	no	—
125	C₄×C₂₃	—	2	2	no	—
126	C₄×C₂₃	—	2	2	no	—
127	C₄×C₂₃	—	4	1	no	—
128	Dic₂₃	—	4	4	no	—
129	Dic₂₃	—	8	2	no	—
130	C₂×C₄⋊Q₈	—	23	1	no	—
131	C₂×C₄×Q₈	—	46	1	no	—
132	#391	—	46	1	no	—
133	#389	—	23	2	no	—
134	#389	—	46	1	no	—
135	#384	—	23	1	no	—
136	C₄×C₄⋊C₄	—	23	2	no	—
137	C₄×C₄⋊C₄	—	46	1	no	—
138	C₄³	C₂×D₂₃	1	1	yes	characteristic
139	#336	—	2	1	no	—
140	#336	—	2	1	no	—
141	#336	—	23	2	no	—
142	#336	—	46	1	no	—
143	#336	—	46	1	no	—
144	#336	C₂×D₂₃	1	2	yes	—
145	C₂×C₂₃	#1461	1	1	yes	characteristic
146	C₂×C₂₃	#1478	1	1	yes	characteristic
147	C₂×C₂₃	#1479	1	1	yes	characteristic
148	C₂×C₂₃	#1514	1	1	yes	characteristic
149	C₂×C₂₃	#1515	1	1	yes	characteristic
150	C₂×C₂₃	#1537	1	1	yes	characteristic
151	C₂×C₂₃	#1556	1	1	yes	characteristic
152	C₂²×Q₈	—	46	1	no	—
153	C₂²×C₈	—	2	2	no	—
154	C₂²×C₈	—	46	2	no	—
155	C₄⋊Q₈	—	23	4	no	—
156	C₄⋊Q₈	—	46	2	no	—
157	C₄×Q₈	—	92	4	no	—
158	C₂×C₄⋊C₄	—	23	2	no	—
159	C₂×C₄⋊C₄	—	23	2	no	—
160	C₂×C₄⋊C₄	—	46	1	no	—
161	C₂×C₄⋊C₄	—	46	1	no	—
162	C₂×C₄⋊C₄	—	46	1	no	—
163	C₂×C₄⋊C₄	—	46	2	no	—
164	C₂×C₄²	—	46	2	no	—
165	C₂×C₄²	C₄×D₂₃	1	1	yes	characteristic
166	C₂×C₄²	C₄×D₂₃	1	1	yes	characteristic
167	C₂×C₄²	D₉₂	1	1	yes	characteristic
168	C₂×C₄²	D₉₂	1	1	yes	characteristic
169	C₂×C₄²	C₂²⋊D₂₃	1	1	yes	characteristic
170	C₂×C₄²	C₂²⋊D₂₃	1	1	yes	characteristic
171	C₂×C₄²	C₂²×D₂₃	1	1	yes	characteristic
172	#95	—	46	2	no	—
173	#95	—	46	2	no	—
174	C₂₃	#7604	1	1	yes	characteristic, complemented, Sylow
175	C₂×Q₈	—	46	4	no	—
176	C₂×Q₈	—	92	2	no	—
177	C₂×Q₈	—	92	2	no	—
178	C₂²×C₄	—	46	2	no	—
179	C₂²×C₄	—	46	2	no	—
180	C₂²×C₄	(C₂×D₂₃)⋊C₄	1	1	yes	characteristic
181	C₂²×C₄	(C₂×D₂₃)⋊C₄	1	1	yes	characteristic
182	C₂²×C₄	(C₂×D₂₃)⋊C₄	1	1	yes	characteristic
183	C₂²×C₄	(C₂×D₂₃)⋊C₄	1	1	yes	characteristic
184	C₂²×C₄	C₂×C₄×D₂₃	1	1	yes	characteristic
185	C₂²×C₄	C₂×D₉₂	1	1	yes	characteristic
186	C₂²×C₄	C₂×C₂²⋊D₂₃	1	1	yes	characteristic
187	C₂×C₈	—	4	2	no	—
188	C₂×C₈	—	4	2	no	—
189	C₂×C₈	—	4	2	no	—
190	C₂×C₈	—	92	2	no	—
191	C₂×C₈	—	92	2	no	—
192	C₂×C₈	—	92	2	no	—
193	C₄⋊C₄	—	23	4	no	—
194	C₄⋊C₄	—	46	2	no	—
195	C₄⋊C₄	—	46	4	no	—
196	C₄⋊C₄	—	92	2	no	—
197	C₄⋊C₄	—	92	2	no	—
198	C₄⋊C₄	—	92	2	no	—
199	C₄⋊C₄	—	92	4	no	—
200	C₄²	—	2	2	no	—
201	C₄²	—	2	2	no	—
202	C₄²	—	2	2	no	—
203	C₄²	—	4	1	no	—
204	C₄²	—	4	1	no	—
205	C₄²	—	4	1	no	—
206	C₄²	—	92	4	no	—
207	C₄²	C₈×D₂₃	1	2	yes	—
208	C₄²	#67262	1	2	yes	—
209	C₂³	C₂×(C₂×D₂₃)⋊C₄	1	1	yes	characteristic
210	Q₈	—	92	8	no	—
211	C₂×C₄	—	2	1	no	—
212	C₂×C₄	—	2	1	no	—
213	C₂×C₄	—	2	1	no	—
214	C₂×C₄	—	2	1	no	—
215	C₂×C₄	—	2	1	no	—
216	C₂×C₄	—	2	1	no	—
217	C₂×C₄	—	2	1	no	—
218	C₂×C₄	—	2	1	no	—
219	C₂×C₄	—	2	1	no	—
220	C₂×C₄	—	2	1	no	—
221	C₂×C₄	—	2	1	no	—
222	C₂×C₄	—	2	1	no	—
223	C₂×C₄	—	2	1	no	—
224	C₂×C₄	—	2	1	no	—
225	C₂×C₄	—	2	1	no	—
226	C₂×C₄	—	46	4	no	—
227	C₂×C₄	—	92	2	no	—
228	C₂×C₄	—	92	2	no	—
229	C₂×C₄	—	92	2	no	—
230	C₂×C₄	—	92	2	no	—
231	C₂×C₄	—	92	2	no	—
232	C₂×C₄	(C₂×D₂₃)⋊C₈	1	2	yes	—
233	C₂×C₄	(C₂×D₂₃)⋊C₈	1	2	yes	—
234	C₂×C₄	#10625006	1	2	yes	—
235	C₂×C₄	C₂×C₈×D₂₃	1	1	yes	characteristic
236	C₂×C₄	C₂×#67262	1	1	yes	characteristic
237	C₂×C₄	#10625080	1	2	yes	—
238	C₂×C₄	#10625120	1	2	yes	—
239	C₈	—	8	2	no	—
240	C₈	—	184	2	no	—
241	C₂²	C₂×(C₂×D₂₃)⋊C₈	1	1	yes	characteristic
242	C₂²	#13092390	1	1	yes	characteristic
243	C₂²	C₂×#10625006	1	1	yes	characteristic
244	C₂²	#13092421	1	1	yes	characteristic
245	C₂²	#13092427	1	1	yes	characteristic
246	C₂²	#13092433	1	1	yes	characteristic
247	C₂²	#13092435	1	1	yes	characteristic
248	C₄	—	2	2	no	—
249	C₄	—	2	2	no	—
250	C₄	—	2	2	no	—
251	C₄	—	2	1	no	—
252	C₄	—	2	1	no	—
253	C₄	—	2	2	no	—
254	C₄	—	2	2	no	—
255	C₄	—	4	1	no	—
256	C₄	—	92	4	no	—
257	C₄	—	184	2	no	—
258	C₂	#15671720	1	1	yes	characteristic
259	C₂	#15671787	1	1	yes	characteristic
260	C₂	#15671793	1	1	yes	characteristic
261	C₂	#15671943	1	1	yes	characteristic
262	C₂	#15671949	1	1	yes	characteristic
263	C₂	#15672034	1	1	yes	characteristic
264	C₂	#15672115	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₄×#10625040

C₂

yes

maximal, characteristic

#15673540

C₂

yes

maximal, characteristic

#15671221

C₂

yes

maximal

C₂₃×#1839

C₂

yes

maximal, characteristic

C₂×#10625040

C₄

yes

characteristic

C₂×C₄×Dic₄₆

—

#13092323

—

#13092315

—

#13092315

C₂²

yes

—

#13092287

C₄

yes

characteristic

C₄×C₄⋊Dic₂₃

—

C₄×C₄⋊Dic₂₃

C₄

yes

—

#13092172

—

#13092172

—

#13092172

C₂²

yes

—

C₄³×C₂₃

C₂²

yes

characteristic

C₂₃×#336

—

C₂₃×#336

—

C₂₃×#336

C₂²

yes

—

C₂²×Dic₄₆

—

C₂²×C₈×C₂₃

—

C₂×C₄²×C₂₃

C₂×C₄

yes

characteristic

C₂×C₄²×C₂₃

C₂×C₄

yes

characteristic

C₂×C₄²×C₂₃

D₄

yes

characteristic

C₂×C₄²×C₂₃

D₄

yes

characteristic

C₂×C₄²×C₂₃

D₄

yes

characteristic

C₂×C₄²×C₂₃

D₄

yes

characteristic

C₂×C₄²×C₂₃

C₂³

yes

characteristic

C₂×C₄⋊Dic₂₃

—

C₂×C₄⋊Dic₂₃

—

C₂×C₄⋊Dic₂₃

—

C₂×C₄⋊Dic₂₃

C₂×C₄

yes

—

C₂×C₄⋊Dic₂₃

C₂×C₄

yes

—

C₂×Dic₂₃⋊C₄

—

C₂×C₄×Dic₂₃

—

C₂²×C₂₃⋊C₈

—

#10625040

—

#10625040

C₈

yes

complemented

C₄×Dic₄₆

—

C₂₃⋊#95

—

C₂₃⋊#95

—

C₂²×C₄×C₂₃

C₂²⋊C₄

yes

characteristic

C₂²×C₄×C₂₃

C₂²⋊C₄

yes

characteristic

C₂²×C₄×C₂₃

C₂²⋊C₄

yes

characteristic

C₂²×C₄×C₂₃

C₂²⋊C₄

yes

characteristic

C₂²×C₄×C₂₃

C₂²×C₄

yes

characteristic

C₂²×C₄×C₂₃

C₂×D₄

yes

characteristic

C₂²×C₄×C₂₃

C₂×D₄

yes

characteristic

C₂²×Dic₂₃

—

C₂²×Dic₂₃

—

C₂×Dic₄₆

—

C₂×Dic₄₆

—

C₂×Dic₄₆

—

C₂×C₈×C₂₃

—

C₂×C₈×C₂₃

—

C₂×C₈×C₂₃

—

C₄²×C₂₃

—

C₄²×C₂₃

—

C₄²×C₂₃

—

C₄²×C₂₃

—

C₄²×C₂₃

—

C₄²×C₂₃

—

C₄²×C₂₃

C₂×C₈

yes

—

C₄²×C₂₃

M₁₆

yes

—

C₄⋊Dic₂₃

—

C₄⋊Dic₂₃

—

C₄⋊Dic₂₃

—

C₄⋊Dic₂₃

—

C₄⋊Dic₂₃

—

C₄⋊Dic₂₃

C₂×C₈

yes

—

Dic₂₃⋊C₄

—

C₄×Dic₂₃

—

C₂×C₂₃⋊C₈

—

C₂×C₂₃⋊C₈

—

C₂×C₂₃⋊C₈

—

#7604

—

maximal, Sylow

C₂³×C₂₃

C₂×C₂²⋊C₄

yes

characteristic

C₂×C₄×C₂₃

—

C₂×C₄×C₂₃

—

C₂×C₄×C₂₃

—

C₂×C₄×C₂₃

—

C₂×C₄×C₂₃

—

C₂×C₄×C₂₃

—

C₂×C₄×C₂₃

—

C₂×C₄×C₂₃

—

C₂×C₄×C₂₃

—

C₂×C₄×C₂₃

—

C₂×C₄×C₂₃

—

C₂×C₄×C₂₃

—

C₂×C₄×C₂₃

—

C₂×C₄×C₂₃

—

C₂×C₄×C₂₃

—

C₂×C₄×C₂₃

C₂²⋊C₈

yes

—

C₂×C₄×C₂₃

C₂²⋊C₈

yes

—

C₂×C₄×C₂₃

#101

yes

—

C₂×C₄×C₂₃

C₂²×C₈

yes

characteristic

C₂×C₄×C₂₃

C₂×M₁₆

yes

characteristic

C₂×C₄×C₂₃

AGL(1,ℤ/8)

yes

—

C₂×C₄×C₂₃

#137

yes

—

100

C₂×Dic₂₃

—

101

C₂×Dic₂₃

—

102

C₂×Dic₂₃

—

103

C₂×Dic₂₃

—

104

C₂×Dic₂₃

—

105

C₂×Dic₂₃

—

106

Dic₄₆

—

107

C₈×C₂₃

—

108

C₂₃⋊C₈

—

109

C₄×C₄⋊Q₈

—

110

#1839

—

111

#1839

D₂₃

yes

characteristic

112

#1271

—

113

C₂²×C₂₃

C₂×C₂²⋊C₈

yes

characteristic

114

C₂²×C₂₃

#410

yes

characteristic

115

C₂²×C₂₃

C₂×#101

yes

characteristic

116

C₂²×C₂₃

#418

yes

characteristic

117

C₂²×C₂₃

#419

yes

characteristic

118

C₂²×C₂₃

#421

yes

characteristic

119

C₂²×C₂₃

#421

yes

characteristic

120

C₄×C₂₃

—

121

C₄×C₂₃

—

122

C₄×C₂₃

—

123

C₄×C₂₃

—

124

C₄×C₂₃

—

125

C₄×C₂₃

—

126

C₄×C₂₃

—

127

C₄×C₂₃

—

128

Dic₂₃

—

129

Dic₂₃

—

130

C₂×C₄⋊Q₈

—

131

C₂×C₄×Q₈

—

132

#391

—

133

#389

—

134

#389

—

135

#384

—

136

C₄×C₄⋊C₄

—

137

C₄×C₄⋊C₄

—

138

C₄³

C₂×D₂₃

yes

characteristic

139

#336

—

140

#336

—

141

#336

—

142

#336

—

143

#336

—

144

#336

C₂×D₂₃

yes

—

145

C₂×C₂₃

#1461

yes

characteristic

146

C₂×C₂₃

#1478

yes

characteristic

147

C₂×C₂₃

#1479

yes

characteristic

148

C₂×C₂₃

#1514

yes

characteristic

149

C₂×C₂₃

#1515

yes

characteristic

150

C₂×C₂₃

#1537

yes

characteristic

151

C₂×C₂₃

#1556

yes

characteristic

152

C₂²×Q₈

—

153

C₂²×C₈

—

154

C₂²×C₈

—

155

C₄⋊Q₈

—

156

C₄⋊Q₈

—

157

C₄×Q₈

—

158

C₂×C₄⋊C₄

—

159

C₂×C₄⋊C₄

—

160

C₂×C₄⋊C₄

—

161

C₂×C₄⋊C₄

—

162

C₂×C₄⋊C₄

—

163

C₂×C₄⋊C₄

—

164

C₂×C₄²

—

165

C₂×C₄²

C₄×D₂₃

yes

characteristic

166

C₂×C₄²

C₄×D₂₃

yes

characteristic

167

C₂×C₄²

D₉₂

yes

characteristic

168

C₂×C₄²

D₉₂

yes

characteristic

169

C₂×C₄²

C₂²⋊D₂₃

yes

characteristic

170

C₂×C₄²

C₂²⋊D₂₃

yes

characteristic

171

C₂×C₄²

C₂²×D₂₃

yes

characteristic

172

#95

—

173

#95

—

174

C₂₃

#7604

yes

characteristic, complemented, Sylow

175

C₂×Q₈

—

176

C₂×Q₈

—

177

C₂×Q₈

—

178

C₂²×C₄

—

179

C₂²×C₄

—

180

C₂²×C₄

(C₂×D₂₃)⋊C₄

yes

characteristic

181

C₂²×C₄

(C₂×D₂₃)⋊C₄

yes

characteristic

182

C₂²×C₄

(C₂×D₂₃)⋊C₄

yes

characteristic

183

C₂²×C₄

(C₂×D₂₃)⋊C₄

yes

characteristic

184

C₂²×C₄

C₂×C₄×D₂₃

yes

characteristic

185

C₂²×C₄

C₂×D₉₂

yes

characteristic

186

C₂²×C₄

C₂×C₂²⋊D₂₃

yes

characteristic

187

C₂×C₈

—

188

C₂×C₈

—

189

C₂×C₈

—

190

C₂×C₈

—

191

C₂×C₈

—

192

C₂×C₈

—

193

C₄⋊C₄

—

194

C₄⋊C₄

—

195

C₄⋊C₄

—

196

C₄⋊C₄

—

197

C₄⋊C₄

—

198

C₄⋊C₄

—

199

C₄⋊C₄

—

200

C₄²

—

201

C₄²

—

202

C₄²

—

203

C₄²

—

204

C₄²

—

205

C₄²

—

206

C₄²

—

207

C₄²

C₈×D₂₃

yes

—

208

C₄²

#67262

yes

—

209

C₂³

C₂×(C₂×D₂₃)⋊C₄

yes

characteristic

210

Q₈

—

211

C₂×C₄

—

212

C₂×C₄

—

213

C₂×C₄

—

214

C₂×C₄

—

215

C₂×C₄

—

216

C₂×C₄

—

217

C₂×C₄

—

218

C₂×C₄

—

219

C₂×C₄

—

220

C₂×C₄

—

221

C₂×C₄

—

222

C₂×C₄

—

223

C₂×C₄

—

224

C₂×C₄

—

225

C₂×C₄

—

226

C₂×C₄

—

227

C₂×C₄

—

228

C₂×C₄

—

229

C₂×C₄

—

230

C₂×C₄

—

231

C₂×C₄

—

232

C₂×C₄

(C₂×D₂₃)⋊C₈

yes

—

233

C₂×C₄

(C₂×D₂₃)⋊C₈

yes

—

234

C₂×C₄

#10625006

yes

—

235

C₂×C₄

C₂×C₈×D₂₃

yes

characteristic

236

C₂×C₄

C₂×#67262

yes

characteristic

237

C₂×C₄

#10625080

yes

—

238

C₂×C₄

#10625120

yes

—

239

C₈

—

240

C₈

—

184

—

241

C₂²

C₂×(C₂×D₂₃)⋊C₈

yes

characteristic

242

C₂²

#13092390

yes

characteristic

243

C₂²

C₂×#10625006

yes

characteristic

244

C₂²

#13092421

yes

characteristic

245

C₂²

#13092427

yes

characteristic

246

C₂²

#13092433

yes

characteristic

247

C₂²

#13092435

yes

characteristic

248

C₄

—

249

C₄

—

250

C₄

—

251

C₄

—

252

C₄

—

253

C₄

—

254

C₄

—

255

C₄

—

256

C₄

—

257

C₄

—

184

—

258

C₂

#15671720

yes

characteristic

259

C₂

#15671787

yes

characteristic

260

C₂

#15671793

yes

characteristic

261

C₂

#15671943

yes

characteristic

262

C₂

#15671949

yes

characteristic

263

C₂

#15672034

yes

characteristic

264

C₂

#15672115

yes

characteristic

	subgroup	G/H
center	C₂³	C₂×(C₂×D₂₃)⋊C₄
commutator	C₂×C₄×C₂₃	C₂²×C₈
Frattini	C₂×C₄²	C₂²×D₂₃
Fitting	C₂₃×#1839	C₂
socle	C₂³×C₂₃	C₂×C₂²⋊C₄
hypercenter	#1839	D₂₃
hypocenter	C₂₃	#7604
LCS	G ▷ C₂×C₄×C₂₃ ▷ C₂²×C₂₃ ▷ C₂₃
UCS	C₁ ◁ C₂³ ◁ C₄³ ◁ #1839

subgroup

G/H

center

C₂³

C₂×(C₂×D₂₃)⋊C₄

commutator

C₂×C₄×C₂₃

C₂²×C₈

Frattini

C₂×C₄²

C₂²×D₂₃

Fitting

C₂₃×#1839

C₂

socle

C₂³×C₂₃

C₂×C₂²⋊C₄

D₂₃

C₂₃

G ▷ C₂×C₄×C₂₃ ▷ C₂²×C₂₃ ▷ C₂₃

UCS

C₁ ◁ C₂³ ◁ C₄³ ◁ #1839

N	H ≅ G/N	type
38. #10625040	C₈	semidirect
174. C₂₃	#7604	semidirect

H ≅ G/N

type

38. #10625040

C₈

semidirect

174. C₂₃

#7604

semidirect

Subgroups — #19212331

Conjugacy classes of subgroups

Complements