Finite Group Databasebeta

← #34069645

Subgroups — #34069645

Order 19328.

314 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 314 conjugacy classes of subgroups — too many to draw. Only its 85 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#23752786C211yesmaximal, characteristic
2#23752690C211yesmaximal, characteristic, complemented
3#23752228C212yesmaximal
4#23751969C212yesmaximal, complemented
5C2×#101×C151C211yesmaximal, characteristic, complemented
6C2×#14559004C2211yescharacteristic
7#18012737C412yescomplemented
8#18012728C412yescomplemented
9#18012722—22no—
10#18012715—22no—
11Q8×Dic151—24no—
12#18012698—22no—
13#18012698C2211yescharacteristic
14#18012698C2212yes—
15#18012665—24no—
16C22×Q8×C151C2211yescharacteristic
17C2×M16×C151C2212yes—
18#101×C151—22no—
19#14559004—22no—
20#14559004—22no—
21C2×Dic302C2×C411yescharacteristic
22C2×D604C2×C411yescharacteristic
23C2×C22⋊D151—21no—
24C2×C4×D151—21no—
25C4⋊Dic151—24no—
26C4⋊Dic151—22no—
27C4⋊Dic151—21no—
28Dic151⋊C4—24no—
29C22⋊Dic151—22no—
30C22⋊Dic151—21no—
31(C2×D151)⋊C4—24no—
32C4×Dic151—24no—
33C4×Dic151C2×C412yes—
34C4×Dic151D414yes—
35C2×Q8×C151—22no—
36C2×Q8×C151—22no—
37C2×Q8×C151C2×C412yes—
38C2×Q8×C151D412yes—
39C22×C4×C151D412yes—
40C22×C4×C151C2311yescharacteristic
41M16×C151—22no—
42M16×C151—22no—
43C2×C8×C151—22no—
44C22×D151—21no—
45Dic302—22no—
46D604—22no—
47C22⋊D151—41no—
48C22⋊D151—41no—
49C2×Dic151—22no—
50C2×Dic151—21no—
51C2×Dic151—24no—
52C4×D151—42no—
53C23×C151C2×D411yescharacteristic
54Q8×C151—24no—
55Q8×C151—24no—
56C2×C4×C151—22no—
57C2×C4×C151—22no—
58C2×C4×C151C22⋊C414yes—
59C2×C4×C151C22×C411yescharacteristic
60C2×C4×C151C2×D412yes—
61C2×C4×C151C2×D411yescharacteristic
62C2×C4×C151#4112yes—
63C8×C151—42no—
64C22×C151—41no—
65C22×C151C2×C22⋊C411yescharacteristic
66C22×C151#12011yescharacteristic
67C22×C151#12311yescharacteristic
68C2×D151—42no—
69C2×D151—41no—
70C4×C151—24no—
71C4×C151C4×D412yes—
72C4×C151#12112yes—
73Dic151—44no—
74Dic151—42no—
75Dic151—41no—
76C2×C151—21no—
77C2×C151—21no—
78C2×C151—21no—
79C2×C151#38611yescharacteristic
80D151—81no—
81C151#191211yescharacteristic, complemented, Sylow
82#1912—1511nomaximal, Sylow
83#536—1511no—
84#519—1511no—
85#421—1512no—
86C2×#101D15111yescharacteristic, complemented
87H(3,ℤ/4)—1512no—
88C2×#41—1511no—
89C22×Q8C2×D15111yescharacteristic
90C2×M16C2×D15112yes—
91C4⋊Q8—1512no—
92#124—1512no—
93#123—3022no—
94C22⋊Q8—3022no—
95C4×Q8—3024no—
96#117—3022no—
97#117—1512no—
98#117—1511no—
99#104—3024no—
100#101—22no—
101#41—3022no—
102#41—3022no—
103C2×Q8—22no—
104C2×Q8—22no—
105C2×Q8—1511no—
106C2×Q8C4×D15112yes—
107C2×Q8C22⋊D15112yes—
108C2×D4—3021no—
109C2×D4—1511no—
110C22×C4—3021no—
111C22×C4D60412yes—
112C22×C4C22×D15111yescharacteristic
113M16—22no—
114M16—22no—
115C2×C8—22no—
116C4⋊C4—3024no—
117C4⋊C4—3024no—
118C4⋊C4—3022no—
119C4⋊C4—3021no—
120C22⋊C4—3022no—
121C22⋊C4—3021no—
122C22⋊C4—3024no—
123C42—3024no—
124C42—1512no—
125C42—1514no—
126C23—3021no—
127C23C2×D60411yescharacteristic
128Q8—24no—
129Q8—24no—
130Q8—3022no—
131D4—3022no—
132D4—6041no—
133D4—6041no—
134C2×C4—22no—
135C2×C4—22no—
136C2×C4—3022no—
137C2×C4—3021no—
138C2×C4—3024no—
139C2×C4—6042no—
140C2×C4(C2×D151)⋊C414yes—
141C2×C4C2×C4×D15111yescharacteristic
142C2×C4D4×D15112yes—
143C2×C4C2×C22⋊D15111yescharacteristic
144C2×C4#1455900312yes—
145C8—42no—
146C22—41no—
147C22—6042no—
148C22—6041no—
149C22C2×(C2×D151)⋊C411yescharacteristic
150C22#1801270911yescharacteristic
151C22#1801272311yescharacteristic
152C4—24no—
153C4—6044no—
154C4—6042no—
155C4—6041no—
156C4(C22⋊D151)⋊C412yes—
157C4#1801271112yes—
158C2—21no—
159C2—21no—
160C2—21no—
161C2—12081no—
162C2#2375208911yescharacteristic
subgroupG/H
centerC2#23752089
commutatorC2×C4×C151C22×C4
FrattiniC22×C4C22×D151
FittingC2×#101×C151C2
socleC2×C151#386
prime radicalC2×#14559004C22
cosocleC22×C4×C151C23
hypercenterC2×#101D151
hypocenterC151#1912
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C2 ◁ C22×C4 ◁ C2×#101

Complements

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

NH ≅ G/Ntype
2. #23752690C2semidirect
4. #23751969C2semidirect
5. C2×#101×C151C2semidirect
7. #18012737C4semidirect
8. #18012728C4semidirect
81. C151#1912semidirect
86. C2×#101D151semidirect

Maximal subgroups

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

subgroupindex
#237527862
#237526902
#237522282
#237519692
C2×#101×C1512
#1912151