Finite Group Databasebeta

← C2×#23752358 #34078312

Subgroups — C2×#23752358 #34078312

Order 19328.

812 conjugacy classes of subgroups; only the 165 normal subgroups are shown.

normal subgroups only

This group has 812 conjugacy classes of subgroups — too many to draw. Only its 165 normal subgroups are shown.

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

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14559003C211yesmaximal, characteristic, complemented
2C22×#14558993C211yesmaximal, characteristic, complemented
3C22×#14558989C211yesmaximal, characteristic, complemented
4C2×#18012714C211yesmaximal, characteristic, complemented
5#23752358C218yesmaximal, direct product factor
6C2×#18012662C211yesmaximal, characteristic, complemented
7C2×(C2×D151)⋊C8C211yesmaximal, characteristic, complemented
8C2×#102×C151C211yesmaximal, characteristic, complemented
9C2×#14559003—24no—
10C2×#14559003—24no—
11C2×#14559003—22no—
12C2×#14559003C2214yescomplemented
13C22×Dic302C2211yescharacteristic
14C22×D604—21no—
15C22×D604C2211yescharacteristic
16C22×C22⋊D151—21no—
17C23×Dic151—21no—
18C22×C4×D151C2211yescharacteristic
19C2×#14558993—24no—
20C2×#14558993C2214yescomplemented
21C2×#14558989—24no—
22C2×#14558989C2214yescomplemented
23C22×C151⋊C8C2211yescharacteristic
24#18012714—22no—
25#18012714C2214yescomplemented
26C2×(C2×D151)⋊C4—21no—
27#18012662C2214yescomplemented
28(C2×D151)⋊C8C2214yescomplemented
29C22×D4×C151C2211yescharacteristic
30C22×C8×C151C2211yescharacteristic
31C2×C4⋊C4×C151C2211yescharacteristic
32#102×C151C2214yescomplemented
33C23×D151—21no—
34C23×D151D411yescharacteristic
35#14559003—216no—
36#14559003—28no—
37#14559003—28no—
38C2×Dic302—21no—
39C2×Dic302—22no—
40C2×Dic302D414yescomplemented
41C2×Dic302C2312yes—
42C2×D604—24no—
43C2×D604—22no—
44C2×D604—22no—
45C2×D604—21no—
46C2×D604—44no—
47C2×D604C2312yes—
48C2×C22⋊D151—28no—
49C2×C22⋊D151—24no—
50C22×Dic151—28no—
51C22×Dic151—24no—
52C22×Dic151—21no—
53C22×Dic151D411yescharacteristic
54C2×C4×D151—22no—
55C2×C4×D151—22no—
56C2×C4×D151D412yes—
57C2×C4×D151C2312yes—
58#14558993—28no—
59#14558989—28no—
60C2×C151⋊C8—22no—
61C2×C151⋊C8C2312yes—
62(C2×D151)⋊C4—24no—
63C24×C151—21no—
64C2×D4×C151—21no—
65C2×D4×C151—22no—
66C2×D4×C151D414yescomplemented
67C2×D4×C151C2312yes—
68C22×C4×C151—21no—
69C22×C4×C151C2311yescharacteristic
70C2×C8×C151—22no—
71C2×C8×C151C2312yes—
72C4⋊C4×C151—21no—
73C4⋊C4×C151C2312yes—
74C22×D151—22no—
75C22×D151—22no—
76C22×D151—22no—
77C22×D151—22no—
78C22×D151—42no—
79C22×D151—42no—
80C22×D151—42no—
81C22×D151C2×D412yes—
82Dic302—24no—
83Dic302—22no—
84Dic302C2×D414yescomplemented
85D604—22no—
86D604—22no—
87D604—48no—
88D604—42no—
89C22⋊D151—216no—
90C2×Dic151—216no—
91C2×Dic151—22no—
92C2×Dic151—24no—
93C2×Dic151—22no—
94C2×Dic151C2×D412yes—
95C4×D151—24no—
96C4×D151—22no—
97C4×D151—22no—
98C151⋊C8—22no—
99C23×C151—24no—
100C23×C151—22no—
101C23×C151—42no—
102C23×C151—42no—
103C23×C151C2×D411yescharacteristic
104D4×C151—24no—
105D4×C151—22no—
106D4×C151C2×D414yescomplemented
107C2×C4×C151—22no—
108C2×C4×C151—42no—
109C2×C4×C151C2×D411yescharacteristic
110C2×C4×C151C2×D412yes—
111C2×C4×C151C2×D412yes—
112C2×C4×C151C2411yescharacteristic
113C8×C151—22no—
114C22×C151—24no—
115C22×C151—42no—
116C22×C151—42no—
117C22×C151—48no—
118C22×C151#12012yes—
119C22×C151#13512yes—
120C22×C151AGL(1,ℤ/8)12yes—
121C22×C151C22×D411yescharacteristic
122C2×D151—22no—
123C2×D151—22no—
124C2×D151—22no—
125C2×D151—44no—
126C2×D151—42no—
127C2×D151—42no—
128C2×D151—42no—
129C2×D151—84no—
130C4×C151—42no—
131C4×C151#12012yes—
132C4×C151C22×D411yescharacteristic
133C4×C151C22×D411yescharacteristic
134Dic151—22no—
135Dic151—24no—
136C2×C151—44no—
137C2×C151#44914yescomplemented
138C2×C151C2×#12011yescharacteristic
139C2×C151C2×#13511yescharacteristic
140C2×C151C2×AGL(1,ℤ/8)11yescharacteristic
141D151—42no—
142D151—82no—
143C151C2×#44911yescharacteristic, complemented, Sylow
144C2×#449—1511nomaximal, Sylow
145C22×#41—1511no—
146C22×SD16—1511no—
147C22×D8—1511no—
148C2×#121—1511no—
149#449—1518no—
150C2×#103—1511no—
151C2×#102D15111yescharacteristic, complemented
152C2×C22⋊C8—1511no—
153C2×#41—3024no—
154C2×#41—3024no—
155C2×#41—3022no—
156C2×#41—1514no—
157C22×Q8—1511no—
158C22×D4—3021no—
159C22×D4—3021no—
160C22×D4—1511no—
161C22×D4C2×D15111yescharacteristic
162C23×C4—3021no—
163C23×C4—1511no—
164C2×SD16—3024no—
165C2×SD16—1514no—
166C2×D8—3024no—
167C2×D8—1514no—
168C22×C8—1511no—
169C22×C8C2×D15111yescharacteristic
170#121—3022no—
171#121—1514no—
172C2×C4⋊C4C2×D15111yescharacteristic
173C2×C22⋊C4—3021no—
174#103—1514no—
175#102C2×D15114yescomplemented
176C22⋊C8—1514no—
177C24—21no—
178C24—3021no—
179C24—1511no—
180#41—30216no—
181#41—3028no—
182#41—3028no—
183C2×Q8—3021no—
184C2×Q8—3022no—
185C2×Q8—1514no—
186C2×Q8—1512no—
187C2×D4—21no—
188C2×D4—22no—
189C2×D4—3024no—
190C2×D4—3028no—
191C2×D4—3024no—
192C2×D4—3022no—
193C2×D4—3021no—
194C2×D4—3022no—
195C2×D4—6044no—
196C2×D4—1512no—
197C2×D4D60414yescomplemented
198C2×D4C22×D15112yes—
199C22×C4—21no—
200C22×C4—3028no—
201C22×C4—3021no—
202C22×C4—3024no—
203C22×C4—3022no—
204C22×C4—3022no—
205C22×C4—1511no—
206C22×C4—1512no—
207C22×C4—1512no—
208C22×C4C22×D15111yescharacteristic
209SD16—3028no—
210D8—3028no—
211C2×C8—22no—
212C2×C8—3022no—
213C2×C8—1512no—
214C2×C8C22×D15112yes—
215C4⋊C4—21no—
216C4⋊C4C22×D15112yes—
217C22⋊C4—3024no—
218C23—24no—
219C23—22no—
220C23—42no—
221C23—42no—
222C23—3022no—
223C23—3022no—
224C23—3022no—
225C23—3022no—
226C23—6042no—
227C23—6042no—
228C23—6042no—
229C23—1512no—
230C23D4×D15111yescharacteristic
231Q8—3024no—
232Q8—3022no—
233Q8—1514no—
234D4—24no—
235D4—22no—
236D4—30216no—
237D4—3022no—
238D4—3022no—
239D4—6048no—
240D4—6042no—
241D4C2×D60414yescomplemented
242C2×C4—22no—
243C2×C4—42no—
244C2×C4—30216no—
245C2×C4—3022no—
246C2×C4—3024no—
247C2×C4—3022no—
248C2×C4—3024no—
249C2×C4—3022no—
250C2×C4—3022no—
251C2×C4—1512no—
252C2×C4D4×D15111yescharacteristic
253C2×C4D4×D15112yes—
254C2×C4C2×D60412yes—
255C2×C4C23×D15111yescharacteristic
256C8—22no—
257C8—3022no—
258C22—24no—
259C22—42no—
260C22—42no—
261C22—48no—
262C22—3022no—
263C22—3022no—
264C22—3022no—
265C22—6044no—
266C22—6042no—
267C22—6042no—
268C22—6042no—
269C22—12084no—
270C22#1801270912yes—
271C22#1801276012yes—
272C22#1801276312yes—
273C22C2×D4×D15111yescharacteristic
274C4—42no—
275C4—3022no—
276C4—3024no—
277C4#1801270912yes—
278C4C2×D4×D15111yescharacteristic
279C4C22×D60411yescharacteristic
280C2—44no—
281C2—6042no—
282C2—12082no—
283C2#2375235814yesdirect product factor
284C2C2×#1801270911yescharacteristic
285C2C2×#1801276011yescharacteristic
286C2C2×#1801276311yescharacteristic
subgroupG/H
centerC23D4×D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
FittingC2×#102×C151C2
socleC23×C151C2×D4
hypercenterC2×#102D151
hypocenterC151C2×#449
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#102

Complements

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

NH ≅ G/Ntype
1. C22×#14559003C2semidirect
2. C22×#14558993C2semidirect
3. C22×#14558989C2semidirect
4. C2×#18012714C2semidirect
5. #23752358C2direct (N × H)
6. C2×#18012662C2semidirect
7. C2×(C2×D151)⋊C8C2semidirect
8. C2×#102×C151C2semidirect
12. C2×#14559003C22semidirect
20. C2×#14558993C22semidirect
22. C2×#14558989C22semidirect
25. #18012714C22semidirect
27. #18012662C22semidirect
28. (C2×D151)⋊C8C22semidirect
32. #102×C151C22semidirect
40. C2×Dic302D4semidirect
66. C2×D4×C151D4semidirect
84. Dic302C2×D4semidirect
106. D4×C151C2×D4semidirect
137. C2×C151#449semidirect
143. C151C2×#449semidirect
151. C2×#102D151semidirect
175. #102C2×D151semidirect
197. C2×D4D604semidirect
241. D4C2×D604semidirect
283. C2#23752358direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145590032
C22×#145589932
C22×#145589892
C2×#180127142
#237523582
C2×#180126622
C2×(C2×D151)⋊C82
C2×#102×C1512
C2×#449151