Finite Group Databasebeta

← C2×#23752460 #34078700

Subgroups — C2×#23752460 #34078700

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×#14558991C211yesmaximal, characteristic, complemented
2C22×#14558988C211yesmaximal, characteristic, complemented
3C2×#18012713C211yesmaximal, characteristic
4#23752460C218yesmaximal, direct product factor
5C2×#18012672C211yesmaximal, characteristic, complemented
6C2×#18012663C211yesmaximal, characteristic, complemented
7C2×#18012659C211yesmaximal, characteristic, complemented
8C2×C22⋊Q8×C151C211yesmaximal, characteristic, complemented
9C22×D604C2211yescharacteristic
10C22×C22⋊D151—21no—
11C2×#14558991—24no—
12C2×#14558991C2214yescomplemented
13C2×#14558988—24no—
14C2×#14558988C2214yescomplemented
15C22×C151⋊C8C2211yescharacteristic
16C22×C151⋊C8C2211yescharacteristic
17#18012713—22no—
18#18012713C2214yes—
19C2×C4⋊Dic151C2211yescharacteristic
20C2×(C2×D151)⋊C4—21no—
21#18012672C2214yescomplemented
22#18012663C2214yescomplemented
23#18012659C2214yescomplemented
24C22×Q8×C151C2211yescharacteristic
25C23×C4×C151C2211yescharacteristic
26C22⋊Q8×C151—22no—
27C22⋊Q8×C151C2214yescomplemented
28C2×C4⋊C4×C151—21no—
29C2×C4⋊C4×C151C2211yescharacteristic
30C2×C22⋊C4×C151—21no—
31C23×D151—21no—
32C2×D604—22no—
33C2×D604—21no—
34C2×D604—22no—
35C2×D604C2312yes—
36C2×C22⋊D151—24no—
37C2×C22⋊D151—44no—
38C22×Dic151—21no—
39#14558991—28no—
40#14558988—28no—
41C2×C151⋊C8—22no—
42C2×C151⋊C8D414yescomplemented
43C2×C151⋊C8C2312yes—
44C2×C151⋊C8C2312yes—
45C4⋊Dic151—21no—
46C4⋊Dic151C2312yes—
47(C2×D151)⋊C4—24no—
48C24×C151D411yescharacteristic
49C2×Q8×C151—21no—
50C2×Q8×C151—22no—
51C2×Q8×C151—22no—
52C2×Q8×C151C2312yes—
53C22×C4×C151—22no—
54C22×C4×C151—22no—
55C22×C4×C151—21no—
56C22×C4×C151—21no—
57C22×C4×C151D411yescharacteristic
58C22×C4×C151D412yes—
59C22×C4×C151C2312yes—
60C22×C4×C151C2311yescharacteristic
61C4⋊C4×C151—24no—
62C4⋊C4×C151—21no—
63C4⋊C4×C151C2312yes—
64C22⋊C4×C151—24no—
65C22×D151—22no—
66C22×D151—42no—
67C22×D151—42no—
68C22×D151—42no—
69D604—22no—
70D604—22no—
71D604—42no—
72C22⋊D151—48no—
73C2×Dic151—22no—
74C2×Dic151—42no—
75C151⋊C8—22no—
76C151⋊C8C2×D414yescomplemented
77C23×C151—22no—
78C23×C151—22no—
79C23×C151—22no—
80C23×C151C2×D412yes—
81C23×C151C2×D411yescharacteristic
82Q8×C151—22no—
83Q8×C151—22no—
84Q8×C151—42no—
85C2×C4×C151—22no—
86C2×C4×C151—24no—
87C2×C4×C151—22no—
88C2×C4×C151—22no—
89C2×C4×C151—22no—
90C2×C4×C151—22no—
91C2×C4×C151—42no—
92C2×C4×C151—42no—
93C2×C4×C151C2×D412yes—
94C2×C4×C151C2×D412yes—
95C2×C4×C151C2×D411yescharacteristic
96C2×C4×C151#4112yes—
97C2×C4×C151C2411yescharacteristic
98C22×C151—22no—
99C22×C151—22no—
100C22×C151—22no—
101C22×C151—44no—
102C22×C151#12112yes—
103C22×C151AGL(1,ℤ/8)12yes—
104C22×C151#13712yes—
105C22×C151C22×D411yescharacteristic
106C2×D151—42no—
107C2×D151—42no—
108C2×D151—42no—
109C2×D151—84no—
110C4×C151—22no—
111C4×C151—42no—
112C4×C151—42no—
113C4×C151#12112yes—
114C4×C151C22×D411yescharacteristic
115C4×C151C2×#4111yescharacteristic
116Dic151—42no—
117C2×C151—42no—
118C2×C151#46814yescomplemented
119C2×C151C2×#12111yescharacteristic
120C2×C151C2×AGL(1,ℤ/8)11yescharacteristic
121C2×C151C2×#13711yescharacteristic
122D151—82no—
123C151C2×#46811yescharacteristic, complemented, Sylow
124C2×#468—1511nomaximal, Sylow
125C22×SD16—1511no—
126C22×M16—1511no—
127C2×C22⋊Q8D15111yescharacteristic, complemented
128C2×#121—1511no—
129#468—1518no—
130C2×#107—1511no—
131C2×#103—1511no—
132C2×#102—1511no—
133C22×Q8C2×D15111yescharacteristic
134C22×D4—3021no—
135C22×D4—1511no—
136C23×C4C2×D15111yescharacteristic
137C2×SD16—3024no—
138C2×SD16—1514no—
139C2×M16—3024no—
140C2×M16—1514no—
141C22×C8—1511no—
142C22×C8—1511no—
143C22⋊Q8—22no—
144C22⋊Q8C2×D15114yescomplemented
145#121—3022no—
146#121—1514no—
147C2×C4⋊C4—21no—
148C2×C4⋊C4—1511no—
149C2×C4⋊C4C2×D15111yescharacteristic
150C2×C22⋊C4—21no—
151C2×C22⋊C4—3021no—
152#107—1514no—
153#103—1514no—
154#102—1514no—
155C24—3021no—
156C24C22⋊D15111yescharacteristic
157C2×Q8—21no—
158C2×Q8—22no—
159C2×Q8—22no—
160C2×Q8C22×D15112yes—
161C2×D4—3024no—
162C2×D4—3022no—
163C2×D4—3021no—
164C2×D4—3022no—
165C2×D4—6044no—
166C2×D4—1512no—
167C22×C4—22no—
168C22×C4—22no—
169C22×C4—21no—
170C22×C4—21no—
171C22×C4—3021no—
172C22×C4C22⋊D15112yes—
173C22×C4C22⋊D15111yescharacteristic
174C22×C4C22×D15112yes—
175C22×C4C22×D15111yescharacteristic
176SD16—3028no—
177M16—3028no—
178C2×C8—3022no—
179C2×C8—1512no—
180C2×C8—1514no—
181C2×C8—1512no—
182C4⋊C4—24no—
183C4⋊C4—21no—
184C4⋊C4—3021no—
185C4⋊C4—1512no—
186C4⋊C4C22×D15112yes—
187C22⋊C4—24no—
188C22⋊C4—3024no—
189C23—22no—
190C23—22no—
191C23—22no—
192C23—3022no—
193C23—6042no—
194C23—6042no—
195C23—6042no—
196C23C2×C22⋊D15112yes—
197C23C2×C22⋊D15111yescharacteristic
198Q8—22no—
199Q8—22no—
200Q8—42no—
201D4—3022no—
202D4—3022no—
203D4—6048no—
204D4—6042no—
205C2×C4—22no—
206C2×C4—24no—
207C2×C4—22no—
208C2×C4—22no—
209C2×C4—22no—
210C2×C4—22no—
211C2×C4—42no—
212C2×C4—42no—
213C2×C4—3022no—
214C2×C4—6042no—
215C2×C4D4×D15112yes—
216C2×C4C2×C22⋊D15112yes—
217C2×C4C2×C22⋊D15111yescharacteristic
218C2×C4#1455900312yes—
219C2×C4C23×D15111yescharacteristic
220C8—3022no—
221C8—1514no—
222C22—22no—
223C22—22no—
224C22—22no—
225C22—44no—
226C22—6042no—
227C22—6042no—
228C22—6042no—
229C22—12084no—
230C22#1801271112yes—
231C22#1801276412yes—
232C22#1801277012yes—
233C22C22×C22⋊D15111yescharacteristic
234C4—22no—
235C4—42no—
236C4—42no—
237C4—6042no—
238C4#1801271112yes—
239C4C2×D4×D15111yescharacteristic
240C4C2×#1455900311yescharacteristic
241C2—42no—
242C2—12082no—
243C2#2375246014yesdirect product factor
244C2C2×#1801271111yescharacteristic
245C2C2×#1801276411yescharacteristic
246C2C2×#1801277011yescharacteristic
subgroupG/H
centerC23C2×C22⋊D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
FittingC2×C22⋊Q8×C151C2
socleC23×C151C2×D4
prime radicalC2×#18012713C2
hypercenterC2×C22⋊Q8D151
hypocenterC151C2×#468
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×C22⋊Q8

Complements

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

NH ≅ G/Ntype
1. C22×#14558991C2semidirect
2. C22×#14558988C2semidirect
4. #23752460C2direct (N × H)
5. C2×#18012672C2semidirect
6. C2×#18012663C2semidirect
7. C2×#18012659C2semidirect
8. C2×C22⋊Q8×C151C2semidirect
12. C2×#14558991C22semidirect
14. C2×#14558988C22semidirect
21. #18012672C22semidirect
22. #18012663C22semidirect
23. #18012659C22semidirect
27. C22⋊Q8×C151C22semidirect
42. C2×C151⋊C8D4semidirect
76. C151⋊C8C2×D4semidirect
118. C2×C151#468semidirect
123. C151C2×#468semidirect
127. C2×C22⋊Q8D151semidirect
144. C22⋊Q8C2×D151semidirect
243. C2#23752460direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145589912
C22×#145589882
C2×#180127132
#237524602
C2×#180126722
C2×#180126632
C2×#180126592
C2×C22⋊Q8×C1512
C2×#468151