Finite Group Databasebeta

← #34069648

Subgroups — #34069648

Order 19328.

314 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 314 conjugacy classes of subgroups — too many to draw. Only its 93 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#23752690C211yesmaximal, characteristic, complemented
2#23752229C212yesmaximal
3C2×#18012658C211yesmaximal, characteristic, complemented
4#23751968C212yesmaximal, complemented
5#536×C151C211yesmaximal, characteristic
6C2×#14558988C2212yes—
7Q8×Dic151—24no—
8#18012698—22no—
9#18012698C2212yes—
10#18012666—24no—
11#18012658—22no—
12C2×#41×C151C2211yescharacteristic
13C22×Q8×C151C2211yescharacteristic
14C4⋊Q8×C151C412yescomplemented
15#124×C151C412yescomplemented
16#123×C151—22no—
17C22⋊Q8×C151—22no—
18#117×C151C2211yescharacteristic
19#14558988—22no—
20#14558988—22no—
21C2×C151⋊C8—22no—
22C4⋊Dic151—24no—
23C4⋊Dic151—22no—
24C22⋊Dic151—22no—
25C4×Dic151—24no—
26C4×Dic151D414yes—
27#41×C151—22no—
28#41×C151—22no—
29C2×Q8×C151—22no—
30C2×Q8×C151—22no—
31C2×Q8×C151C2×C411yescharacteristic
32C2×Q8×C151C2×C412yes—
33C2×Q8×C151D412yes—
34C2×D4×C151—21no—
35C2×D4×C151C2×C411yescharacteristic
36C22×C4×C151—21no—
37C22×C4×C151D412yes—
38C22×C4×C151C2311yescharacteristic
39C4⋊C4×C151—24no—
40C4⋊C4×C151—21no—
41C22⋊C4×C151—21no—
42C22⋊C4×C151—24no—
43C42×C151C2×C412yes—
44C2×Dic151—24no—
45C151⋊C8—42no—
46C23×C151—21no—
47C23×C151C2×D411yescharacteristic
48Q8×C151—24no—
49Q8×C151—24no—
50Q8×C151—22no—
51D4×C151—22no—
52D4×C151—41no—
53D4×C151—41no—
54C2×C4×C151—22no—
55C2×C4×C151—22no—
56C2×C4×C151—21no—
57C2×C4×C151—22no—
58C2×C4×C151—42no—
59C2×C4×C151C22⋊C414yes—
60C2×C4×C151C22×C411yescharacteristic
61C2×C4×C151C2×D412yes—
62C2×C4×C151C2×D411yescharacteristic
63C2×C4×C151#4112yes—
64C22×C151—41no—
65C22×C151—42no—
66C22×C151—41no—
67C22×C151C2×C22⋊C411yescharacteristic
68C22×C151#12011yescharacteristic
69C22×C151#12311yescharacteristic
70C4×C151—24no—
71C4×C151—42no—
72C4×C151—41no—
73C4×C151C4×D412yes—
74C4×C151#12112yes—
75Dic151—44no—
76C2×C151—21no—
77C2×C151—21no—
78C2×C151—21no—
79C2×C151—81no—
80C2×C151#38611yescharacteristic
81C151#191211yescharacteristic, complemented, Sylow
82#1912—1511nomaximal, Sylow
83#536D15111yescharacteristic
84#519—1511no—
85#421—1512no—
86C2×#101—1511no—
87H(3,ℤ/4)—1512no—
88C2×#41C2×D15111yescharacteristic
89C22×Q8C2×D15111yescharacteristic
90C2×M16—1512no—
91C4⋊Q8Dic15112yescomplemented
92#124Dic15112yescomplemented
93#123—22no—
94C22⋊Q8—22no—
95C4×Q8—3024no—
96#117—3022no—
97#117—1512no—
98#117C2×D15111yescharacteristic
99#104—3024no—
100#101—3022no—
101#41—22no—
102#41—22no—
103C2×Q8—22no—
104C2×Q8—22no—
105C2×Q8C2×Dic15111yescharacteristic
106C2×Q8C2×Dic15112yes—
107C2×Q8C22⋊D15112yes—
108C2×D4—21no—
109C2×D4C2×Dic15111yescharacteristic
110C22×C4—21no—
111C22×C4C22⋊D15112yes—
112C22×C4C22×D15111yescharacteristic
113M16—3022no—
114M16—3022no—
115C2×C8—3022no—
116C4⋊C4—24no—
117C4⋊C4—21no—
118C4⋊C4—3024no—
119C4⋊C4—3022no—
120C22⋊C4—21no—
121C22⋊C4—24no—
122C22⋊C4—3022no—
123C42—3024no—
124C42—1514no—
125C42C2×Dic15112yes—
126C23—21no—
127C23C2×C22⋊D15111yescharacteristic
128Q8—24no—
129Q8—24no—
130Q8—22no—
131D4—22no—
132D4—41no—
133D4—41no—
134C2×C4—22no—
135C2×C4—22no—
136C2×C4—22no—
137C2×C4—21no—
138C2×C4—42no—
139C2×C4—3024no—
140C2×C4C22⋊Dic15114yes—
141C2×C4C22×Dic15111yescharacteristic
142C2×C4D4×D15112yes—
143C2×C4C2×C22⋊D15111yescharacteristic
144C2×C4#1455900312yes—
145C8—6042no—
146C22—41no—
147C22—42no—
148C22—41no—
149C22C2×C22⋊Dic15111yescharacteristic
150C22#1801270711yescharacteristic
151C22#1801272011yescharacteristic
152C4—24no—
153C4—42no—
154C4—41no—
155C4—6044no—
156C4D4×Dic15112yes—
157C4#1801271112yes—
158C2—21no—
159C2—21no—
160C2—21no—
161C2—81no—
162C2#2375209211yescharacteristic
subgroupG/H
centerC2#23752092
commutatorC2×C4×C151C22×C4
FrattiniC22×C4C22×D151
Fitting#536×C151C2
socleC2×C151#386
prime radicalC2×#41×C151C22
cosocleC22×C4×C151C23
hypercenter#536D151
hypocenterC151#1912
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C2 ◁ C22×C4 ◁ #536

Complements

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

NH ≅ G/Ntype
1. #23752690C2semidirect
3. C2×#18012658C2semidirect
4. #23751968C2semidirect
14. C4⋊Q8×C151C4semidirect
15. #124×C151C4semidirect
81. C151#1912semidirect
91. C4⋊Q8Dic151semidirect
92. #124Dic151semidirect

Maximal subgroups

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

subgroupindex
#237526902
#237522292
C2×#180126582
#237519682
#536×C1512
#1912151