Finite Group Databasebeta

← #46835687

Subgroups — #46835687

Order 34688.

196 conjugacy classes of subgroups; only the 49 normal subgroups are shown.

normal subgroups only

This group has 196 conjugacy classes of subgroups — too many to draw. Only its 49 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#31774267C211yesmaximal, characteristic, complemented
2#31774256C212yesmaximal, complemented
3#31773639C211yesmaximal, characteristic, complemented
4#31773637C212yesmaximal, complemented
5#562×C271C211yesmaximal, characteristic
6#22576160C2211yescharacteristic
7#22576084—22no—
8#22576083—22no—
9#22576081—22no—
10#22576071C2212yes—
11#22576071C2211yescharacteristic
12#125×C271C2211yescharacteristic
13#124×C271C2212yes—
14#123×C271—22no—
15C22⋊Q8×C271—22no—
16#121×C271—22no—
17C2×Dic542—21no—
18C2×C271⋊C8—22no—
19C2×C271⋊C8—21no—
20C4⋊Dic271—22no—
21C2×Q8×C271D412yes—
22C2×D4×C271—22no—
23C2×D4×C271D412yes—
24C22×C4×C271—22no—
25C4⋊C4×C271—22no—
26C4⋊C4×C271—22no—
27C4⋊C4×C271D412yes—
28C22⋊C4×C271—22no—
29C22⋊C4×C271—22no—
30C22⋊C4×C271—22no—
31C42×C271C2311yescharacteristic
32Dic542—42no—
33C2×Dic271—41no—
34C271⋊C8—41no—
35C271⋊C8—42no—
36C23×C271—22no—
37Q8×C271—42no—
38D4×C271—42no—
39D4×C271—82no—
40C2×C4×C271—22no—
41C2×C4×C271—22no—
42C2×C4×C271—82no—
43C2×C4×C271C2×D411yescharacteristic
44C2×C4×C271C2×D412yes—
45C22×C271—42no—
46C22×C271—42no—
47C22×C271—42no—
48C22×C271#12011yescharacteristic
49C4×C271—21no—
50C4×C271—22no—
51C4×C271—42no—
52C4×C271—42no—
53Dic271—81no—
54C2×C271—82no—
55C2×C271#45411yescharacteristic
56C2×C271#45512yes—
57C271#166211yescharacteristic, complemented, Sylow
58#1662—2711nomaximal, Sylow
59#562D27111yescharacteristic
60#491—2711no—
61#489—2712no—
62#330—2711no—
63#329—2712no—
64C4⋊Q8—2711no—
65#125C2×D27111yescharacteristic
66#124C2×D27112yes—
67#123—22no—
68C22⋊Q8—22no—
69#121—22no—
70#103—5422no—
71#103—5422no—
72#102—5422no—
73#97—2711no—
74#97—2712no—
75C2×Q8—5421no—
76C2×Q8C22⋊D27112yes—
77C2×D4—22no—
78C2×D4C22⋊D27112yes—
79C22×C4—22no—
80C2×C8—5422no—
81C2×C8—5421no—
82C4⋊C4—22no—
83C4⋊C4—22no—
84C4⋊C4—5422no—
85C4⋊C4C22⋊D27112yes—
86C22⋊C4—22no—
87C22⋊C4—22no—
88C22⋊C4—22no—
89C42C22×D27111yescharacteristic
90C23—22no—
91Q8—42no—
92Q8—10842no—
93D4—42no—
94D4—82no—
95C2×C4—22no—
96C2×C4—22no—
97C2×C4—82no—
98C2×C4—10841no—
99C2×C4C2×C22⋊D27111yescharacteristic
100C2×C4C2×C22⋊D27112yes—
101C8—10841no—
102C8—10842no—
103C22—42no—
104C22—42no—
105C22—42no—
106C22#2257612911yescharacteristic
107C4—21no—
108C4—22no—
109C4—42no—
110C4—42no—
111C4—21681no—
112C2—82no—
113C2#3177407011yescharacteristic
114C2#3177407512yes—
subgroupG/H
centerC22#22576129
commutator, cosocleC42×C271C23
FrattiniC42C22×D271
Fitting, prime radical#562×C271C2
socleC22×C271#120
hypercenter#562D271
hypocenterC271#1662
LCSG ▷ C42×C271 ▷ C22×C271 ▷ C271
UCSC1 ◁ C22 ◁ C42 ◁ #562

Complements

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

NH ≅ G/Ntype
1. #31774267C2semidirect
2. #31774256C2semidirect
3. #31773639C2semidirect
4. #31773637C2semidirect
57. C271#1662semidirect

Maximal subgroups

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

subgroupindex
#317742672
#317742562
#317736392
#317736372
#562×C2712
#1662271