Finite Group Databasebeta

← #46811422

Subgroups — #46811422

Order 34432.

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

normal subgroups only

This group has 314 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#31771179C211yesmaximal, characteristic
2#31770623C212yesmaximal
3C2×#22575372C211yesmaximal, characteristic, complemented
4#31770361C212yesmaximal, complemented
5#519×C269C211yesmaximal, characteristic, complemented
6C2×#16864402C2211yescharacteristic
7C2×#16864386C2212yes—
8#22575451C412yescomplemented
9#22575442C412yescomplemented
10#22575436—22no—
11#22575429—22no—
12#22575412C2211yescharacteristic
13#22575381—24no—
14#22575372—22no—
15C22×Q8×C269C2211yescharacteristic
16C4×Q8×C269—24no—
17#117×C269—22no—
18#117×C269C2212yes—
19#16864402—22no—
20#16864402—22no—
21C2×Dic538C2×C411yescharacteristic
22C2×D1076C2×C411yescharacteristic
23C2×C22⋊D269—21no—
24C2×C4×D269—21no—
25#16864386—22no—
26#16864386—22no—
27C2×#14524130—22no—
28C4⋊Dic269—21no—
29#16864381—24no—
30C22⋊Dic269—21no—
31#16864379—24no—
32C4×Dic269C2×C412yes—
33C2×Q8×C269—22no—
34C2×Q8×C269—22no—
35C2×Q8×C269C2×C412yes—
36C2×Q8×C269D412yes—
37C22×C4×C269D412yes—
38C22×C4×C269C2311yescharacteristic
39C4⋊C4×C269—24no—
40C4⋊C4×C269—22no—
41C22⋊C4×C269—22no—
42C42×C269—24no—
43C42×C269D414yes—
44C22×D269—21no—
45Dic538—22no—
46D1076—22no—
47C22⋊D269—41no—
48C22⋊D269—41no—
49C2×Dic269—22no—
50C2×Dic269—21no—
51C4×D269—42no—
52#14524130—42no—
53C23×C269C2×D411yescharacteristic
54Q8×C269—24no—
55Q8×C269—24no—
56C2×C4×C269—22no—
57C2×C4×C269—22no—
58C2×C4×C269—24no—
59C2×C4×C269C22⋊C414yes—
60C2×C4×C269C22×C411yescharacteristic
61C2×C4×C269C2×D412yes—
62C2×C4×C269C2×D411yescharacteristic
63C2×C4×C269#4112yes—
64C22×C269—41no—
65C22×C269C2×C22⋊C411yescharacteristic
66C22×C269#12011yescharacteristic
67C22×C269#12311yescharacteristic
68C2×D269—42no—
69C2×D269—41no—
70C4×C269—24no—
71C4×C269—44no—
72C4×C269C4×D412yes—
73C4×C269#12112yes—
74Dic269—42no—
75Dic269—41no—
76C2×C269—21no—
77C2×C269—21no—
78C2×C269—21no—
79C2×C269#38611yescharacteristic
80D269—81no—
81C269#191211yescharacteristic, complemented, Sylow
82#1912—2691nomaximal, Sylow
83#536—2691no—
84#519D26911yescharacteristic, complemented
85#421—2692no—
86C2×#101—2691no—
87H(3,ℤ/4)—2692no—
88C2×#41—2691no—
89C22×Q8C2×D26911yescharacteristic
90C2×M16—2692no—
91C4⋊Q8—2692no—
92#124—2692no—
93#123—5382no—
94C22⋊Q8—5382no—
95C4×Q8—24no—
96#117—22no—
97#117—2691no—
98#117C2×D26912yes—
99#104—5384no—
100#101—5382no—
101#41—5382no—
102#41—5382no—
103C2×Q8—22no—
104C2×Q8—22no—
105C2×Q8—2691no—
106C2×Q8C4×D26912yes—
107C2×Q8D107612yes—
108C2×D4—2691no—
109C2×D4—5381no—
110C22×C4—5381no—
111C22×C4C22⋊D26912yes—
112C22×C4C22×D26911yescharacteristic
113M16—5382no—
114M16—5382no—
115C2×C8—5382no—
116C4⋊C4—24no—
117C4⋊C4—22no—
118C4⋊C4—5384no—
119C4⋊C4—5381no—
120C22⋊C4—22no—
121C22⋊C4—5381no—
122C22⋊C4—5384no—
123C42—24no—
124C42—2692no—
125C42C22⋊D26914yes—
126C23—5381no—
127C23C2×C22⋊D26911yescharacteristic
128Q8—24no—
129Q8—24no—
130Q8—5382no—
131D4—5382no—
132D4—10761no—
133D4—10761no—
134C2×C4—22no—
135C2×C4—22no—
136C2×C4—24no—
137C2×C4—5382no—
138C2×C4—5381no—
139C2×C4—10762no—
140C2×C4#1686437914yes—
141C2×C4C2×C4×D26911yescharacteristic
142C2×C4C2×C22⋊D26912yes—
143C2×C4C2×D107611yescharacteristic
144C2×C4#1686440212yes—
145C8—10762no—
146C22—41no—
147C22—10762no—
148C22—10761no—
149C22C2×#1686437911yescharacteristic
150C22#2257542211yescharacteristic
151C22#2257543611yescharacteristic
152C4—24no—
153C4—44no—
154C4—10762no—
155C4—10761no—
156C4C4×C22⋊D26912yes—
157C4#2257542712yes—
158C2—21no—
159C2—21no—
160C2—21no—
161C2—21521no—
162C2#3177048411yescharacteristic
subgroupG/H
centerC2#31770484
commutatorC2×C4×C269C22×C4
FrattiniC22×C4C22×D269
Fitting#519×C269C2
socleC2×C269#386
prime radicalC2×#16864402C22
cosocleC22×C4×C269C23
hypercenter#519D269
hypocenterC269#1912
LCSG ▷ C2×C4×C269 ▷ C2×C269 ▷ C269
UCSC1 ◁ C2 ◁ C22×C4 ◁ #519

Complements

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

NH ≅ G/Ntype
3. C2×#22575372C2semidirect
4. #31770361C2semidirect
5. #519×C269C2semidirect
8. #22575451C4semidirect
9. #22575442C4semidirect
81. C269#1912semidirect
84. #519D269semidirect

Maximal subgroups

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

subgroupindex
#317711792
#317706232
C2×#225753722
#317703612
#519×C2692
#1912269