Group #19212175 — subgroups

Subgroups — #19212175

Order 5888.

528 conjugacy classes of subgroups; only the 159 normal subgroups are shown.

normal subgroups only

This group has 528 conjugacy classes of subgroups — too many to draw. Only its 159 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	#15673143	C₂	1	2	yes	maximal, complemented
2	#15671223	C₂	1	2	yes	maximal, complemented
3	#15671218	C₂	1	2	yes	maximal
4	C₄×C₂₃×#124	C₂	1	1	yes	maximal, characteristic
5	C₂×C₄×C₂₃⋊C₈	—	2	2	no	—
6	#13092172	—	2	2	no	—
7	#13092172	C₂²	1	4	yes	—
8	C₂×C₂₃×#124	C₄	1	1	yes	characteristic
9	C₂×C₄×Q₈×C₂₃	C₄	1	1	yes	characteristic
10	C₂×C₄×D₄×C₂₃	C₄	1	1	yes	characteristic
11	C₂₃×#391	C₂²	1	1	yes	characteristic
12	C₂₃×#390	C₂²	1	1	yes	characteristic
13	C₂₃×#388	—	2	2	no	—
14	C₂₃×#382	C₄	1	1	yes	characteristic
15	C₄×C₂²⋊C₄×C₂₃	—	2	2	no	—
16	C₄³×C₂₃	C₂²	1	1	yes	characteristic
17	C₂²×Q₈×C₂₃	C₂×C₄	1	1	yes	characteristic
18	C₂²×D₄×C₂₃	C₂×C₄	1	1	yes	characteristic
19	C₂³×C₄×C₂₃	—	2	1	no	—
20	C₂₃×#124	—	2	2	no	—
21	C₂₃×#124	C₈	1	4	yes	complemented
22	C₄×Q₈×C₂₃	—	4	2	no	—
23	C₄×D₄×C₂₃	—	4	2	no	—
24	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
25	C₂×C₄⋊C₄×C₂₃	C₂×C₄	1	1	yes	characteristic
26	C₂×C₄⋊C₄×C₂₃	C₂×C₄	1	1	yes	characteristic
27	C₂×C₂²⋊C₄×C₂₃	—	2	2	no	—
28	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
29	C₂×C₂²⋊C₄×C₂₃	—	2	2	no	—
30	C₂×C₄²×C₂₃	—	2	1	no	—
31	C₂×C₄²×C₂₃	C₂×C₄	1	1	yes	characteristic
32	C₂×C₄²×C₂₃	C₂×C₄	1	1	yes	characteristic
33	C₂×C₄²×C₂₃	D₄	1	2	yes	—
34	C₂×C₄²×C₂₃	D₄	1	2	yes	—
35	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
36	C₂²×C₂₃⋊C₈	—	2	4	no	—
37	C₂₃×#95	—	2	2	no	—
38	C₂₃×#95	—	2	2	no	—
39	C₄×C₂₃⋊C₈	—	2	8	no	—
40	C₂⁴×C₂₃	—	2	1	no	—
41	C₂×Q₈×C₂₃	—	2	1	no	—
42	C₂×Q₈×C₂₃	—	4	1	no	—
43	C₂×Q₈×C₂₃	—	4	1	no	—
44	C₂×Q₈×C₂₃	C₂×C₈	1	2	yes	—
45	C₂×D₄×C₂₃	—	2	1	no	—
46	C₂×D₄×C₂₃	—	4	1	no	—
47	C₂×D₄×C₂₃	—	4	1	no	—
48	C₂×D₄×C₂₃	C₂×C₈	1	2	yes	—
49	C₂²×C₄×C₂₃	—	2	1	no	—
50	C₂²×C₄×C₂₃	—	2	1	no	—
51	C₂²×C₄×C₂₃	—	2	1	no	—
52	C₂²×C₄×C₂₃	—	4	2	no	—
53	C₂²×C₄×C₂₃	—	4	4	no	—
54	C₂²×C₄×C₂₃	C₂²⋊C₄	1	1	yes	characteristic
55	C₂²×C₄×C₂₃	C₂²⋊C₄	1	2	yes	—
56	C₂²×C₄×C₂₃	C₂²⋊C₄	1	1	yes	characteristic
57	C₂²×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
58	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
59	C₄⋊C₄×C₂₃	—	4	1	no	—
60	C₄⋊C₄×C₂₃	—	4	1	no	—
61	C₄⋊C₄×C₂₃	—	4	2	no	—
62	C₂²⋊C₄×C₂₃	—	2	8	no	—
63	C₂²⋊C₄×C₂₃	—	4	2	no	—
64	C₂²⋊C₄×C₂₃	—	4	4	no	—
65	C₄²×C₂₃	—	2	2	no	—
66	C₄²×C₂₃	—	2	4	no	—
67	C₄²×C₂₃	—	2	4	no	—
68	C₄²×C₂₃	—	4	1	no	—
69	C₄²×C₂₃	—	4	2	no	—
70	C₄²×C₂₃	C₂×C₈	1	2	yes	—
71	C₄²×C₂₃	M₁₆	1	2	yes	—
72	C₂×C₂₃⋊C₈	—	2	8	no	—
73	C₂×C₂₃⋊C₈	—	4	4	no	—
74	C₂×C₂₃⋊C₈	—	4	4	no	—
75	#7567	—	23	1	no	maximal, Sylow
76	C₂³×C₂₃	—	2	2	no	—
77	C₂³×C₂₃	—	4	1	no	—
78	C₂³×C₂₃	—	4	1	no	—
79	C₂³×C₂₃	—	4	2	no	—
80	C₂³×C₂₃	—	4	2	no	—
81	C₂³×C₂₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
82	Q₈×C₂₃	—	4	2	no	—
83	Q₈×C₂₃	—	4	2	no	—
84	D₄×C₂₃	—	4	2	no	—
85	D₄×C₂₃	—	4	2	no	—
86	C₂×C₄×C₂₃	—	2	2	no	—
87	C₂×C₄×C₂₃	—	2	1	no	—
88	C₂×C₄×C₂₃	—	2	1	no	—
89	C₂×C₄×C₂₃	—	2	2	no	—
90	C₂×C₄×C₂₃	—	2	2	no	—
91	C₂×C₄×C₂₃	—	2	2	no	—
92	C₂×C₄×C₂₃	—	2	2	no	—
93	C₂×C₄×C₂₃	—	2	1	no	—
94	C₂×C₄×C₂₃	—	2	2	no	—
95	C₂×C₄×C₂₃	—	4	1	no	—
96	C₂×C₄×C₂₃	—	4	1	no	—
97	C₂×C₄×C₂₃	—	4	1	no	—
98	C₂×C₄×C₂₃	—	4	1	no	—
99	C₂×C₄×C₂₃	—	4	2	no	—
100	C₂×C₄×C₂₃	—	4	2	no	—
101	C₂×C₄×C₂₃	—	8	4	no	—
102	C₂×C₄×C₂₃	C₂²⋊C₈	1	4	yes	—
103	C₂×C₄×C₂₃	#100	1	2	yes	—
104	C₂×C₄×C₂₃	#104	1	4	yes	—
105	C₂×C₄×C₂₃	C₂²×C₈	1	1	yes	characteristic
106	C₂×C₄×C₂₃	C₂×M₁₆	1	1	yes	characteristic
107	C₂×C₄×C₂₃	#135	1	4	yes	—
108	C₂₃⋊C₈	—	4	8	no	—
109	C₄×#124	D₂₃	1	1	yes	characteristic
110	#1744	—	23	2	no	—
111	#1272	—	23	2	no	—
112	#1270	—	23	2	no	—
113	C₂²×C₂₃	—	4	2	no	—
114	C₂²×C₂₃	—	4	4	no	—
115	C₂²×C₂₃	—	8	1	no	—
116	C₂²×C₂₃	—	8	2	no	—
117	C₂²×C₂₃	—	8	1	no	—
118	C₂²×C₂₃	C₂×C₂²⋊C₈	1	1	yes	characteristic
119	C₂²×C₂₃	#410	1	1	yes	characteristic
120	C₂²×C₂₃	C₂×#100	1	1	yes	characteristic
121	C₂²×C₂₃	#416	1	2	yes	—
122	C₂²×C₂₃	C₂×#104	1	2	yes	—
123	C₄×C₂₃	—	2	1	no	—
124	C₄×C₂₃	—	2	1	no	—
125	C₄×C₂₃	—	2	4	no	—
126	C₄×C₂₃	—	2	4	no	—
127	C₄×C₂₃	—	4	1	no	—
128	C₄×C₂₃	—	4	2	no	—
129	C₄×C₂₃	—	8	1	no	—
130	C₄×C₂₃	—	8	1	no	—
131	C₄×C₂₃	#329	1	4	yes	—
132	C₂×#124	Dic₂₃	1	1	yes	characteristic
133	C₂×C₄×Q₈	Dic₂₃	1	1	yes	characteristic
134	C₂×C₄×D₄	Dic₂₃	1	1	yes	characteristic
135	C₂×C₄×C₈	—	46	2	no	—
136	#391	C₂×D₂₃	1	1	yes	characteristic
137	#390	C₂×D₂₃	1	1	yes	characteristic
138	#388	—	2	2	no	—
139	#382	Dic₂₃	1	1	yes	characteristic
140	C₄×C₂²⋊C₄	—	2	2	no	—
141	C₄³	C₂×D₂₃	1	1	yes	characteristic
142	#336	—	23	4	no	—
143	#336	—	46	2	no	—
144	C₂×C₂₃	—	8	2	no	—
145	C₂×C₂₃	#1460	1	1	yes	characteristic
146	C₂×C₂₃	#1476	1	2	yes	—
147	C₂×C₂₃	#1500	1	2	yes	—
148	C₂×C₂₃	C₂×#329	1	1	yes	characteristic
149	C₂×C₂₃	#1543	1	1	yes	characteristic
150	C₂²×Q₈	C₂×Dic₂₃	1	1	yes	characteristic
151	C₂²×D₄	C₂×Dic₂₃	1	1	yes	characteristic
152	C₂³×C₄	—	2	1	no	—
153	C₂²×C₈	—	46	4	no	—
154	#124	—	2	2	no	—
155	#124	C₂₃⋊C₈	1	4	yes	complemented
156	C₄×Q₈	—	4	2	no	—
157	C₄×D₄	—	4	2	no	—
158	C₂×C₄⋊C₄	—	2	1	no	—
159	C₂×C₄⋊C₄	C₂×Dic₂₃	1	1	yes	characteristic
160	C₂×C₄⋊C₄	C₂×Dic₂₃	1	1	yes	characteristic
161	C₂×C₂²⋊C₄	—	2	2	no	—
162	C₂×C₂²⋊C₄	—	2	1	no	—
163	C₂×C₂²⋊C₄	—	2	2	no	—
164	C₂×C₄²	—	2	1	no	—
165	C₂×C₄²	C₂×Dic₂₃	1	1	yes	characteristic
166	C₂×C₄²	C₂×Dic₂₃	1	1	yes	characteristic
167	C₂×C₄²	C₂²⋊D₂₃	1	2	yes	—
168	C₂×C₄²	C₂²⋊D₂₃	1	2	yes	—
169	C₂×C₄²	C₂²×D₂₃	1	1	yes	characteristic
170	C₄×C₈	—	46	8	no	—
171	#95	—	2	2	no	—
172	#95	—	2	2	no	—
173	C₂₃	#7567	1	1	yes	characteristic, complemented, Sylow
174	C₂⁴	—	2	1	no	—
175	C₂×Q₈	—	2	1	no	—
176	C₂×Q₈	—	4	1	no	—
177	C₂×Q₈	—	4	1	no	—
178	C₂×Q₈	C₂×C₂₃⋊C₈	1	2	yes	—
179	C₂×D₄	—	2	1	no	—
180	C₂×D₄	—	4	1	no	—
181	C₂×D₄	—	4	1	no	—
182	C₂×D₄	C₂×C₂₃⋊C₈	1	2	yes	—
183	C₂²×C₄	—	2	1	no	—
184	C₂²×C₄	—	2	1	no	—
185	C₂²×C₄	—	2	1	no	—
186	C₂²×C₄	—	4	2	no	—
187	C₂²×C₄	—	4	4	no	—
188	C₂²×C₄	C₂²⋊Dic₂₃	1	1	yes	characteristic
189	C₂²×C₄	C₂²⋊Dic₂₃	1	2	yes	—
190	C₂²×C₄	C₂²⋊Dic₂₃	1	1	yes	characteristic
191	C₂²×C₄	C₂²×Dic₂₃	1	1	yes	characteristic
192	C₂²×C₄	C₂×C₂²⋊D₂₃	1	2	yes	—
193	C₂×C₈	—	46	8	no	—
194	C₂×C₈	—	92	4	no	—
195	C₂×C₈	—	92	4	no	—
196	C₄⋊C₄	—	4	1	no	—
197	C₄⋊C₄	—	4	1	no	—
198	C₄⋊C₄	—	4	2	no	—
199	C₂²⋊C₄	—	2	8	no	—
200	C₂²⋊C₄	—	4	2	no	—
201	C₂²⋊C₄	—	4	4	no	—
202	C₄²	—	2	4	no	—
203	C₄²	—	2	2	no	—
204	C₄²	—	2	4	no	—
205	C₄²	—	4	1	no	—
206	C₄²	—	4	2	no	—
207	C₄²	C₂×C₂₃⋊C₈	1	2	yes	—
208	C₄²	#67267	1	2	yes	—
209	C₂³	—	2	2	no	—
210	C₂³	—	4	1	no	—
211	C₂³	—	4	1	no	—
212	C₂³	—	4	2	no	—
213	C₂³	—	4	2	no	—
214	C₂³	C₂×C₂²⋊Dic₂₃	1	1	yes	characteristic
215	Q₈	—	4	2	no	—
216	Q₈	—	4	2	no	—
217	D₄	—	4	2	no	—
218	D₄	—	4	2	no	—
219	C₂×C₄	—	2	2	no	—
220	C₂×C₄	—	2	1	no	—
221	C₂×C₄	—	2	1	no	—
222	C₂×C₄	—	2	2	no	—
223	C₂×C₄	—	2	2	no	—
224	C₂×C₄	—	2	2	no	—
225	C₂×C₄	—	2	2	no	—
226	C₂×C₄	—	2	1	no	—
227	C₂×C₄	—	2	2	no	—
228	C₂×C₄	—	4	1	no	—
229	C₂×C₄	—	4	1	no	—
230	C₂×C₄	—	4	1	no	—
231	C₂×C₄	—	4	1	no	—
232	C₂×C₄	—	4	2	no	—
233	C₂×C₄	—	4	2	no	—
234	C₂×C₄	—	8	4	no	—
235	C₂×C₄	C₂²⋊(C₂₃⋊C₈)	1	4	yes	—
236	C₂×C₄	#10625015	1	2	yes	—
237	C₂×C₄	#10625019	1	4	yes	—
238	C₂×C₄	C₂²×C₂₃⋊C₈	1	1	yes	characteristic
239	C₂×C₄	C₂×#67267	1	1	yes	characteristic
240	C₂×C₄	#10625121	1	4	yes	—
241	C₈	—	92	8	no	—
242	C₂²	—	4	2	no	—
243	C₂²	—	4	4	no	—
244	C₂²	—	8	2	no	—
245	C₂²	—	8	1	no	—
246	C₂²	—	8	1	no	—
247	C₂²	C₂×C₂²⋊(C₂₃⋊C₈)	1	1	yes	characteristic
248	C₂²	#13092391	1	1	yes	characteristic
249	C₂²	C₂×#10625015	1	1	yes	characteristic
250	C₂²	#13092413	1	2	yes	—
251	C₂²	C₂×#10625019	1	2	yes	—
252	C₄	—	2	4	no	—
253	C₄	—	2	1	no	—
254	C₄	—	2	1	no	—
255	C₄	—	2	4	no	—
256	C₄	—	4	2	no	—
257	C₄	—	4	1	no	—
258	C₄	—	8	1	no	—
259	C₄	—	8	1	no	—
260	C₄	#13092157	1	4	yes	—
261	C₂	—	8	2	no	—
262	C₂	#15671718	1	1	yes	characteristic
263	C₂	#15671779	1	2	yes	—
264	C₂	#15671883	1	2	yes	—
265	C₂	C₂×#13092157	1	1	yes	characteristic
266	C₂	#15672059	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#15673143

C₂

yes

maximal, complemented

#15671223

C₂

yes

maximal, complemented

#15671218

C₂

yes

maximal

C₄×C₂₃×#124

C₂

yes

maximal, characteristic

C₂×C₄×C₂₃⋊C₈

—

#13092172

—

#13092172

C₂²

yes

—

C₂×C₂₃×#124

C₄

yes

characteristic

C₂×C₄×Q₈×C₂₃

C₄

yes

characteristic

C₂×C₄×D₄×C₂₃

C₄

yes

characteristic

C₂₃×#391

C₂²

yes

characteristic

C₂₃×#390

C₂²

yes

characteristic

C₂₃×#388

—

C₂₃×#382

C₄

yes

characteristic

C₄×C₂²⋊C₄×C₂₃

—

C₄³×C₂₃

C₂²

yes

characteristic

C₂²×Q₈×C₂₃

C₂×C₄

yes

characteristic

C₂²×D₄×C₂₃

C₂×C₄

yes

characteristic

C₂³×C₄×C₂₃

—

C₂₃×#124

—

C₂₃×#124

C₈

yes

complemented

C₄×Q₈×C₂₃

—

C₄×D₄×C₂₃

—

C₂×C₄⋊C₄×C₂₃

—

C₂×C₄⋊C₄×C₂₃

C₂×C₄

yes

characteristic

C₂×C₄⋊C₄×C₂₃

C₂×C₄

yes

characteristic

C₂×C₂²⋊C₄×C₂₃

—

C₂×C₂²⋊C₄×C₂₃

—

C₂×C₂²⋊C₄×C₂₃

—

C₂×C₄²×C₂₃

—

C₂×C₄²×C₂₃

C₂×C₄

yes

characteristic

C₂×C₄²×C₂₃

C₂×C₄

yes

characteristic

C₂×C₄²×C₂₃

D₄

yes

—

C₂×C₄²×C₂₃

D₄

yes

—

C₂×C₄²×C₂₃

C₂³

yes

characteristic

C₂²×C₂₃⋊C₈

—

C₂₃×#95

—

C₂₃×#95

—

C₄×C₂₃⋊C₈

—

C₂⁴×C₂₃

—

C₂×Q₈×C₂₃

—

C₂×Q₈×C₂₃

—

C₂×Q₈×C₂₃

—

C₂×Q₈×C₂₃

C₂×C₈

yes

—

C₂×D₄×C₂₃

—

C₂×D₄×C₂₃

—

C₂×D₄×C₂₃

—

C₂×D₄×C₂₃

C₂×C₈

yes

—

C₂²×C₄×C₂₃

—

C₂²×C₄×C₂₃

—

C₂²×C₄×C₂₃

—

C₂²×C₄×C₂₃

—

C₂²×C₄×C₂₃

—

C₂²×C₄×C₂₃

C₂²⋊C₄

yes

characteristic

C₂²×C₄×C₂₃

C₂²⋊C₄

yes

—

C₂²×C₄×C₂₃

C₂²⋊C₄

yes

characteristic

C₂²×C₄×C₂₃

C₂²×C₄

yes

characteristic

C₂²×C₄×C₂₃

C₂×D₄

yes

—

C₄⋊C₄×C₂₃

—

C₄⋊C₄×C₂₃

—

C₄⋊C₄×C₂₃

—

C₂²⋊C₄×C₂₃

—

C₂²⋊C₄×C₂₃

—

C₂²⋊C₄×C₂₃

—

C₄²×C₂₃

—

C₄²×C₂₃

—

C₄²×C₂₃

—

C₄²×C₂₃

—

C₄²×C₂₃

—

C₄²×C₂₃

C₂×C₈

yes

—

C₄²×C₂₃

M₁₆

yes

—

C₂×C₂₃⋊C₈

—

C₂×C₂₃⋊C₈

—

C₂×C₂₃⋊C₈

—

#7567

—

maximal, Sylow

C₂³×C₂₃

—

C₂³×C₂₃

—

C₂³×C₂₃

—

C₂³×C₂₃

—

C₂³×C₂₃

—

C₂³×C₂₃

C₂×C₂²⋊C₄

yes

characteristic

Q₈×C₂₃

—

Q₈×C₂₃

—

D₄×C₂₃

—

D₄×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

—

100

C₂×C₄×C₂₃

—

101

C₂×C₄×C₂₃

—

102

C₂×C₄×C₂₃

C₂²⋊C₈

yes

—

103

C₂×C₄×C₂₃

#100

yes

—

104

C₂×C₄×C₂₃

#104

yes

—

105

C₂×C₄×C₂₃

C₂²×C₈

yes

characteristic

106

C₂×C₄×C₂₃

C₂×M₁₆

yes

characteristic

107

C₂×C₄×C₂₃

#135

yes

—

108

C₂₃⋊C₈

—

109

C₄×#124

D₂₃

yes

characteristic

110

#1744

—

111

#1272

—

112

#1270

—

113

C₂²×C₂₃

—

114

C₂²×C₂₃

—

115

C₂²×C₂₃

—

116

C₂²×C₂₃

—

117

C₂²×C₂₃

—

118

C₂²×C₂₃

C₂×C₂²⋊C₈

yes

characteristic

119

C₂²×C₂₃

#410

yes

characteristic

120

C₂²×C₂₃

C₂×#100

yes

characteristic

121

C₂²×C₂₃

#416

yes

—

122

C₂²×C₂₃

C₂×#104

yes

—

123

C₄×C₂₃

—

124

C₄×C₂₃

—

125

C₄×C₂₃

—

126

C₄×C₂₃

—

127

C₄×C₂₃

—

128

C₄×C₂₃

—

129

C₄×C₂₃

—

130

C₄×C₂₃

—

131

C₄×C₂₃

#329

yes

—

132

C₂×#124

Dic₂₃

yes

characteristic

133

C₂×C₄×Q₈

Dic₂₃

yes

characteristic

134

C₂×C₄×D₄

Dic₂₃

yes

characteristic

135

C₂×C₄×C₈

—

136

#391

C₂×D₂₃

yes

characteristic

137

#390

C₂×D₂₃

yes

characteristic

138

#388

—

139

#382

Dic₂₃

yes

characteristic

140

C₄×C₂²⋊C₄

—

141

C₄³

C₂×D₂₃

yes

characteristic

142

#336

—

143

#336

—

144

C₂×C₂₃

—

145

C₂×C₂₃

#1460

yes

characteristic

146

C₂×C₂₃

#1476

yes

—

147

C₂×C₂₃

#1500

yes

—

148

C₂×C₂₃

C₂×#329

yes

characteristic

149

C₂×C₂₃

#1543

yes

characteristic

150

C₂²×Q₈

C₂×Dic₂₃

yes

characteristic

151

C₂²×D₄

C₂×Dic₂₃

yes

characteristic

152

C₂³×C₄

—

153

C₂²×C₈

—

154

#124

—

155

#124

C₂₃⋊C₈

yes

complemented

156

C₄×Q₈

—

157

C₄×D₄

—

158

C₂×C₄⋊C₄

—

159

C₂×C₄⋊C₄

C₂×Dic₂₃

yes

characteristic

160

C₂×C₄⋊C₄

C₂×Dic₂₃

yes

characteristic

161

C₂×C₂²⋊C₄

—

162

C₂×C₂²⋊C₄

—

163

C₂×C₂²⋊C₄

—

164

C₂×C₄²

—

165

C₂×C₄²

C₂×Dic₂₃

yes

characteristic

166

C₂×C₄²

C₂×Dic₂₃

yes

characteristic

167

C₂×C₄²

C₂²⋊D₂₃

yes

—

168

C₂×C₄²

C₂²⋊D₂₃

yes

—

169

C₂×C₄²

C₂²×D₂₃

yes

characteristic

170

C₄×C₈

—

171

#95

—

172

#95

—

173

C₂₃

#7567

yes

characteristic, complemented, Sylow

174

C₂⁴

—

175

C₂×Q₈

—

176

C₂×Q₈

—

177

C₂×Q₈

—

178

C₂×Q₈

C₂×C₂₃⋊C₈

yes

—

179

C₂×D₄

—

180

C₂×D₄

—

181

C₂×D₄

—

182

C₂×D₄

C₂×C₂₃⋊C₈

yes

—

183

C₂²×C₄

—

184

C₂²×C₄

—

185

C₂²×C₄

—

186

C₂²×C₄

—

187

C₂²×C₄

—

188

C₂²×C₄

C₂²⋊Dic₂₃

yes

characteristic

189

C₂²×C₄

C₂²⋊Dic₂₃

yes

—

190

C₂²×C₄

C₂²⋊Dic₂₃

yes

characteristic

191

C₂²×C₄

C₂²×Dic₂₃

yes

characteristic

192

C₂²×C₄

C₂×C₂²⋊D₂₃

yes

—

193

C₂×C₈

—

194

C₂×C₈

—

195

C₂×C₈

—

196

C₄⋊C₄

—

197

C₄⋊C₄

—

198

C₄⋊C₄

—

199

C₂²⋊C₄

—

200

C₂²⋊C₄

—

201

C₂²⋊C₄

—

202

C₄²

—

203

C₄²

—

204

C₄²

—

205

C₄²

—

206

C₄²

—

207

C₄²

C₂×C₂₃⋊C₈

yes

—

208

C₄²

#67267

yes

—

209

C₂³

—

210

C₂³

—

211

C₂³

—

212

C₂³

—

213

C₂³

—

214

C₂³

C₂×C₂²⋊Dic₂₃

yes

characteristic

215

Q₈

—

216

Q₈

—

217

D₄

—

218

D₄

—

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

—

233

C₂×C₄

—

234

C₂×C₄

—

235

C₂×C₄

C₂²⋊(C₂₃⋊C₈)

yes

—

236

C₂×C₄

#10625015

yes

—

237

C₂×C₄

#10625019

yes

—

238

C₂×C₄

C₂²×C₂₃⋊C₈

yes

characteristic

239

C₂×C₄

C₂×#67267

yes

characteristic

240

C₂×C₄

#10625121

yes

—

241

C₈

—

242

C₂²

—

243

C₂²

—

244

C₂²

—

245

C₂²

—

246

C₂²

—

247

C₂²

C₂×C₂²⋊(C₂₃⋊C₈)

yes

characteristic

248

C₂²

#13092391

yes

characteristic

249

C₂²

C₂×#10625015

yes

characteristic

250

C₂²

#13092413

yes

—

251

C₂²

C₂×#10625019

yes

—

252

C₄

—

253

C₄

—

254

C₄

—

255

C₄

—

256

C₄

—

257

C₄

—

258

C₄

—

259

C₄

—

260

C₄

#13092157

yes

—

261

C₂

—

262

C₂

#15671718

yes

characteristic

263

C₂

#15671779

yes

—

264

C₂

#15671883

yes

—

265

C₂

C₂×#13092157

yes

characteristic

266

C₂

#15672059

yes

characteristic

	subgroup	G/H
center	C₂²×C₄	C₂²⋊Dic₂₃
commutator	C₂×C₄×C₂₃	C₂²×C₈
Frattini	C₂×C₄²	C₂²×D₂₃
Fitting	C₄×C₂₃×#124	C₂
socle	C₂³×C₂₃	C₂×C₂²⋊C₄
hypercenter	C₄×#124	D₂₃
hypocenter	C₂₃	#7567
LCS	G ▷ C₂×C₄×C₂₃ ▷ C₂²×C₂₃ ▷ C₂₃
UCS	C₁ ◁ C₂²×C₄ ◁ C₄³ ◁ C₄×#124

subgroup

G/H

center

C₂²×C₄

C₂²⋊Dic₂₃

commutator

C₂×C₄×C₂₃

C₂²×C₈

Frattini

C₂×C₄²

C₂²×D₂₃

Fitting

C₄×C₂₃×#124

C₂

socle

C₂³×C₂₃

C₂×C₂²⋊C₄

D₂₃

C₂₃

G ▷ C₂×C₄×C₂₃ ▷ C₂²×C₂₃ ▷ C₂₃

UCS

C₁ ◁ C₂²×C₄ ◁ C₄³ ◁ C₄×#124

N	H ≅ G/N	type
1. #15673143	C₂	semidirect
2. #15671223	C₂	semidirect
21. C₂₃×#124	C₈	semidirect
155. #124	C₂₃⋊C₈	semidirect
173. C₂₃	#7567	semidirect

H ≅ G/N

type

1. #15673143

C₂

semidirect

2. #15671223

C₂

semidirect

21. C₂₃×#124

C₈

semidirect

155. #124

C₂₃⋊C₈

semidirect

173. C₂₃

#7567

semidirect

Subgroups — #19212175

Conjugacy classes of subgroups

Complements