Finite Group Databasebeta

← C2×#23752459 #34078699

Subgroups — C2×#23752459 #34078699

Order 19328.

544 conjugacy classes of subgroups; only the 157 normal subgroups are shown.

normal subgroups only

This group has 544 conjugacy classes of subgroups — too many to draw. Only its 157 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×#14558993C211yesmaximal, characteristic, complemented
2C22×#14558987C211yesmaximal, characteristic, complemented
3C2×#18012719C211yesmaximal, characteristic, complemented
4C2×#18012714C211yesmaximal, characteristic
5#23752459C218yesmaximal, direct product factor
6C2×#18012662C211yesmaximal, characteristic, complemented
7C2×#18012659C211yesmaximal, characteristic, complemented
8C2×#107×C151C211yesmaximal, characteristic, complemented
9C22×Dic302C2211yescharacteristic
10C22×D604—21no—
11C22×D604C2211yescharacteristic
12C22×C4×D151C2211yescharacteristic
13C2×#14558993—24no—
14C2×#14558993C2214yescomplemented
15C2×#14558987—24no—
16C2×#14558987C2214yescomplemented
17C22×C151⋊C8C2211yescharacteristic
18#18012719—22no—
19#18012719C2214yescomplemented
20#18012714—22no—
21#18012714C2214yes—
22C2×C4⋊Dic151—21no—
23C2×(C2×D151)⋊C4—21no—
24C2×(C2×D151)⋊C4—21no—
25#18012662C2214yescomplemented
26#18012659C2214yescomplemented
27C22×C8×C151C2211yescharacteristic
28C2×C4⋊C4×C151C2211yescharacteristic
29C2×C4⋊C4×C151C2211yescharacteristic
30#107×C151C2214yescomplemented
31C23×D151—21no—
32C23×D151D411yescharacteristic
33C2×Dic302—21no—
34C2×Dic302—22no—
35C2×Dic302—22no—
36C2×Dic302C2312yes—
37C2×D604—24no—
38C2×D604—22no—
39C2×D604—21no—
40C2×D604—22no—
41C2×D604—44no—
42C2×D604C2312yes—
43C22×Dic151—21no—
44C22×Dic151D411yescharacteristic
45C2×C4×D151—22no—
46C2×C4×D151—22no—
47C2×C4×D151D412yes—
48C2×C4×D151C2312yes—
49#14558993—28no—
50#14558987—28no—
51C2×C151⋊C8—22no—
52C2×C151⋊C8C2312yes—
53C4⋊Dic151—24no—
54(C2×D151)⋊C4—24no—
55(C2×D151)⋊C4—24no—
56C22×C4×C151—21no—
57C22×C4×C151—21no—
58C22×C4×C151C2311yescharacteristic
59C2×C8×C151D414yescomplemented
60C2×C8×C151C2312yes—
61C4⋊C4×C151—21no—
62C4⋊C4×C151—21no—
63C4⋊C4×C151C2312yes—
64C4⋊C4×C151C2312yes—
65C22×D151—22no—
66C22×D151—22no—
67C22×D151—22no—
68C22×D151—22no—
69C22×D151—42no—
70C22×D151—42no—
71C22×D151—42no—
72C22×D151C2×D412yes—
73Dic302—22no—
74Dic302—22no—
75Dic302—42no—
76D604—22no—
77D604—22no—
78D604—48no—
79D604—42no—
80C2×Dic151—22no—
81C2×Dic151—22no—
82C2×Dic151—42no—
83C2×Dic151C2×D412yes—
84C4×D151—24no—
85C4×D151—22no—
86C4×D151—22no—
87C151⋊C8—22no—
88C23×C151C2×D411yescharacteristic
89C2×C4×C151—22no—
90C2×C4×C151—22no—
91C2×C4×C151—42no—
92C2×C4×C151—42no—
93C2×C4×C151C2×D411yescharacteristic
94C2×C4×C151C2×D412yes—
95C2×C4×C151#4112yes—
96C2×C4×C151C2411yescharacteristic
97C8×C151C2×D414yescomplemented
98C22×C151#12112yes—
99C22×C151AGL(1,ℤ/8)12yes—
100C22×C151#13712yes—
101C22×C151C22×D411yescharacteristic
102C2×D151—22no—
103C2×D151—22no—
104C2×D151—22no—
105C2×D151—44no—
106C2×D151—42no—
107C2×D151—42no—
108C2×D151—42no—
109C2×D151—84no—
110C4×C151—42no—
111C4×C151—42no—
112C4×C151#12112yes—
113C4×C151C22×D411yescharacteristic
114C4×C151C2×#4111yescharacteristic
115Dic151—22no—
116Dic151—42no—
117C2×C151#46814yescomplemented
118C2×C151C2×#12111yescharacteristic
119C2×C151C2×AGL(1,ℤ/8)11yescharacteristic
120C2×C151C2×#13711yescharacteristic
121D151—42no—
122D151—82no—
123C151C2×#46811yescharacteristic, complemented, Sylow
124C2×#468—1511nomaximal, Sylow
125C22×SD16—1511no—
126C22×M16—1511no—
127C2×C22⋊Q8—1511no—
128C2×#121—1511no—
129#468—1518no—
130C2×#107D15111yescharacteristic, complemented
131C2×#103—1511no—
132C2×#102—1511no—
133C22×Q8—1511no—
134C22×D4—3021no—
135C22×D4—1511no—
136C23×C4—1511no—
137C2×SD16—3024no—
138C2×SD16—1514no—
139C2×M16—3024no—
140C2×M16—1514no—
141C22×C8—1511no—
142C22×C8C2×D15111yescharacteristic
143C22⋊Q8—3022no—
144C22⋊Q8—1514no—
145#121—3022no—
146#121—1514no—
147C2×C4⋊C4—3021no—
148C2×C4⋊C4C2×D15111yescharacteristic
149C2×C4⋊C4C2×D15111yescharacteristic
150C2×C22⋊C4—3021no—
151C2×C22⋊C4—3021no—
152#107C2×D15114yescomplemented
153#103—1514no—
154#102—1514no—
155C24—3021no—
156C24—1511no—
157C2×Q8—3021no—
158C2×Q8—3022no—
159C2×Q8—3022no—
160C2×Q8—1512no—
161C2×D4—3024no—
162C2×D4—3021no—
163C2×D4—3022no—
164C2×D4—3022no—
165C2×D4—6044no—
166C2×D4—1512no—
167C22×C4—21no—
168C22×C4—21no—
169C22×C4—3022no—
170C22×C4—3022no—
171C22×C4—3021no—
172C22×C4—1511no—
173C22×C4—1512no—
174C22×C4—1512no—
175C22×C4C22×D15111yescharacteristic
176SD16—3028no—
177M16—3028no—
178C2×C8—3022no—
179C2×C8—1512no—
180C2×C8D60414yescomplemented
181C2×C8C22×D15112yes—
182C4⋊C4—21no—
183C4⋊C4—21no—
184C4⋊C4—3024no—
185C4⋊C4C22×D15112yes—
186C4⋊C4C22×D15112yes—
187C22⋊C4—3024no—
188C22⋊C4—3024no—
189C23—3022no—
190C23—3022no—
191C23—3022no—
192C23—3022no—
193C23—6042no—
194C23—6042no—
195C23—6042no—
196C23—1512no—
197C23D4×D15111yescharacteristic
198Q8—3022no—
199Q8—3022no—
200Q8—6042no—
201D4—3022no—
202D4—3022no—
203D4—6048no—
204D4—6042no—
205C2×C4—22no—
206C2×C4—22no—
207C2×C4—42no—
208C2×C4—42no—
209C2×C4—3022no—
210C2×C4—3024no—
211C2×C4—3022no—
212C2×C4—3022no—
213C2×C4—3022no—
214C2×C4—6042no—
215C2×C4—1512no—
216C2×C4D4×D15111yescharacteristic
217C2×C4C2×D60412yes—
218C2×C4#1455900512yes—
219C2×C4C23×D15111yescharacteristic
220C8—3022no—
221C8C2×D60414yescomplemented
222C22—3022no—
223C22—3022no—
224C22—3022no—
225C22—6044no—
226C22—6042no—
227C22—6042no—
228C22—6042no—
229C22—12084no—
230C22#1801271412yes—
231C22#1801276312yes—
232C22#1801277112yes—
233C22C2×D4×D15111yescharacteristic
234C4—42no—
235C4—42no—
236C4—3022no—
237C4—6042no—
238C4#1801271412yes—
239C4C22×D60411yescharacteristic
240C4C2×#1455900511yescharacteristic
241C2—6042no—
242C2—12082no—
243C2#2375245914yesdirect product factor
244C2C2×#1801271411yescharacteristic
245C2C2×#1801276311yescharacteristic
246C2C2×#1801277111yescharacteristic
subgroupG/H
centerC23D4×D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
FittingC2×#107×C151C2
socleC23×C151C2×D4
prime radicalC2×#18012714C2
hypercenterC2×#107D151
hypocenterC151C2×#468
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#107

Complements

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

NH ≅ G/Ntype
1. C22×#14558993C2semidirect
2. C22×#14558987C2semidirect
3. C2×#18012719C2semidirect
5. #23752459C2direct (N × H)
6. C2×#18012662C2semidirect
7. C2×#18012659C2semidirect
8. C2×#107×C151C2semidirect
14. C2×#14558993C22semidirect
16. C2×#14558987C22semidirect
19. #18012719C22semidirect
25. #18012662C22semidirect
26. #18012659C22semidirect
30. #107×C151C22semidirect
59. C2×C8×C151D4semidirect
97. C8×C151C2×D4semidirect
117. C2×C151#468semidirect
123. C151C2×#468semidirect
130. C2×#107D151semidirect
152. #107C2×D151semidirect
180. C2×C8D604semidirect
221. C8C2×D604semidirect
243. C2#23752459direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145589932
C22×#145589872
C2×#180127192
C2×#180127142
#237524592
C2×#180126622
C2×#180126592
C2×#107×C1512
C2×#468151