Finite Group Databasebeta

← #34069632

Subgroups — #34069632

Order 19328.

312 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 312 conjugacy classes of subgroups — too many to draw. Only its 89 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
1#23752783C211yesmaximal, characteristic
2#23752222C212yesmaximal, complemented
3#23752186C211yesmaximal, characteristic
4#23751969C212yesmaximal, complemented
5#568×C151C211yesmaximal, characteristic
6C22×Dic302C2211yescharacteristic
7#18012737C412yescomplemented
8#18012726C412yescomplemented
9#18012720—22no—
10#18012718—22no—
11#18012698C2212yes—
12#18012698C2211yescharacteristic
13#18012664—24no—
14#18012654—22no—
15C2×#41×C151C2211yescharacteristic
16#131×C151—24no—
17C2×M16×C151—22no—
18C2×M16×C151C2212yes—
19C2×Dic302—21no—
20C2×Dic302—22no—
21C2×Dic302—22no—
22C2×Dic302C2×C412yes—
23C22×Dic151—21no—
24C4⋊Dic151—21no—
25C4⋊Dic151—22no—
26Dic151⋊C4—24no—
27C22⋊Dic151—24no—
28C22⋊Dic151—21no—
29C22⋊Dic151—22no—
30C4×Dic151—22no—
31C4×Dic151C2×C412yes—
32#41×C151—22no—
33#41×C151—22no—
34C2×Q8×C151C2×C411yescharacteristic
35C2×D4×C151C2×C411yescharacteristic
36C2×D4×C151D412yes—
37C22×C4×C151D412yes—
38C22×C4×C151C2311yescharacteristic
39M16×C151—24no—
40M16×C151—22no—
41M16×C151—22no—
42C2×C8×C151—24no—
43C2×C8×C151D414yes—
44Dic302—24no—
45Dic302—41no—
46Dic302—41no—
47C2×Dic151—22no—
48C2×Dic151—22no—
49C2×Dic151—42no—
50C2×Dic151—42no—
51C23×C151C22⋊C412yes—
52C23×C151C2×D411yescharacteristic
53Q8×C151—22no—
54D4×C151—24no—
55D4×C151—22no—
56C2×C4×C151—22no—
57C2×C4×C151—22no—
58C2×C4×C151C22⋊C412yes—
59C2×C4×C151C22×C411yescharacteristic
60C2×C4×C151C2×D412yes—
61C2×C4×C151C2×D411yescharacteristic
62C2×C4×C151#4112yes—
63C8×C151—24no—
64C22×C151—22no—
65C22×C151—41no—
66C22×C151—42no—
67C22×C151C2×C22⋊C411yescharacteristic
68C22×C151#12112yes—
69C4×C151—22no—
70C4×C151C4×D412yes—
71C4×C151#12011yescharacteristic
72C4×C151#12311yescharacteristic
73Dic151—42no—
74Dic151—42no—
75Dic151—82no—
76C2×C151—21no—
77C2×C151—22no—
78C2×C151—42no—
79C2×C151#38611yescharacteristic
80C151#190911yescharacteristic, complemented, Sylow
81#1909—1511nomaximal, Sylow
82#568D15111yescharacteristic
83#536—1511no—
84#419—1512no—
85#410—1511no—
86H(3,ℤ/4)—1512no—
87C2×#41C2×D15111yescharacteristic
88C22×Q8—1511no—
89#131—24no—
90C2×M16—22no—
91C2×M16C2×D15112yes—
92C4⋊Q8—1512no—
93#124—1512no—
94#123—3022no—
95C22⋊Q8—3022no—
96#117—1512no—
97#117—1511no—
98#103—3024no—
99#99—3022no—
100#41—22no—
101#41—22no—
102C2×Q8—3021no—
103C2×Q8—3022no—
104C2×Q8—3022no—
105C2×Q8—1512no—
106C2×Q8C4×D15111yescharacteristic
107C2×D4C4×D15111yescharacteristic
108C2×D4D60412yes—
109C22×C4—3021no—
110C22×C4C22⋊D15112yes—
111C22×C4C22×D15111yescharacteristic
112M16—24no—
113M16—22no—
114M16—22no—
115C2×C8—24no—
116C2×C8C22⋊D15114yes—
117C4⋊C4—3024no—
118C4⋊C4—3021no—
119C4⋊C4—3022no—
120C22⋊C4—3024no—
121C22⋊C4—3021no—
122C22⋊C4—3022no—
123C42—3022no—
124C42—1512no—
125C23(C2×D151)⋊C412yes—
126C23C2×D60411yescharacteristic
127Q8—22no—
128Q8—3024no—
129Q8—6041no—
130Q8—6041no—
131D4—24no—
132D4—22no—
133C2×C4—22no—
134C2×C4—22no—
135C2×C4—3022no—
136C2×C4—3022no—
137C2×C4—6042no—
138C2×C4—6042no—
139C2×C4(C2×D151)⋊C412yes—
140C2×C4C2×C4×D15111yescharacteristic
141C2×C4C2×C22⋊D15112yes—
142C2×C4C2×C22⋊D15111yescharacteristic
143C2×C4#1455900412yes—
144C8—24no—
145C22—22no—
146C22—41no—
147C22—42no—
148C22C2×(C2×D151)⋊C411yescharacteristic
149C22#1801271312yes—
150C4—22no—
151C4—6042no—
152C4—6042no—
153C4—12082no—
154C4C4×C22⋊D15112yes—
155C4#1801270811yescharacteristic
156C4#1801272211yescharacteristic
157C2—21no—
158C2—22no—
159C2—42no—
160C2#2375209111yescharacteristic
subgroupG/H
centerC2#23752091
commutatorC2×C4×C151C22×C4
FrattiniC22×C4C22×D151
Fitting#568×C151C2
socleC2×C151#386
prime radicalC2×#41×C151C22
cosocleC22×C4×C151C23
hypercenter#568D151
hypocenterC151#1909
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C2 ◁ C22×C4 ◁ #568

Complements

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

NH ≅ G/Ntype
2. #23752222C2semidirect
4. #23751969C2semidirect
7. #18012737C4semidirect
8. #18012726C4semidirect
80. C151#1909semidirect

Maximal subgroups

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

subgroupindex
#237527832
#237522222
#237521862
#237519692
#568×C1512
#1909151