Finite Group Databasebeta

← #42122810

Subgroups — #42122810

Order 27712.

154 conjugacy classes of subgroups; only the 48 normal subgroups are shown.

normal subgroups only

This group has 154 conjugacy classes of subgroups — too many to draw. Only its 48 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
1D433⋊M16C211yesmaximal, characteristic, complemented
2#28357299C211yesmaximal, characteristic, complemented
3#28357285C214yesmaximal, complemented
4C2×#20294098C211yesmaximal, characteristic
5#20294107C2212yescomplemented
6#20294106—21no—
7#20294105—21no—
8C4⋊#13181884—21no—
9C22⋊#13181884—21no—
10C4×#13181884C2212yescomplemented
11#20294098—21no—
12#20294098—21no—
13#20294098C412yescomplemented
14#20294098C2212yes—
15C2×D1732—21no—
16C2×D1732C411yescharacteristic, complemented
17C2×C4×D433—21no—
18C2×C4×D433C2211yescharacteristic
19C2×Q8×C433C411yescharacteristic, complemented
20C2×#13181884—22no—
21#16812365—22no—
22C22×D433—21no—
23C22×D433D411yescharacteristic
24D1732—22no—
25D1732—22no—
26D1732—21no—
27D1732C2×C412yes—
28C2×Dic433D411yescharacteristic
29C4×D433—22no—
30C4×D433—22no—
31C4×D433C2×C411yescharacteristic
32C4×D433D411yescharacteristic
33C4×D433D411yescharacteristic
34C4×D433C2311yescharacteristic
35Q8×C433—21no—
36Q8×C433C2×C412yes—
37C2×C4×C433—21no—
38C2×C4×C433C2×C411yescharacteristic
39C22×C433C22⋊C411yescharacteristic
40C2×D433—22no—
41C2×D433—41no—
42C2×D433—42no—
43C2×D433C22⋊C411yescharacteristic
44C2×D433C2×D411yescharacteristic
45#13181884—42no—
46C4×C433—22no—
47C4×C433C22⋊C411yescharacteristic
48C4×C433C22×C411yescharacteristic
49Dic433C22⋊C411yescharacteristic
50Dic433C2×D411yescharacteristic
51C2×C433—21no—
52C2×C433C2×C22⋊C411yescharacteristic
53D433—21no—
54D433—21no—
55D433—42no—
56C433#42111yescharacteristic, complemented, Sylow
57#421—4331nomaximal, Sylow
58C2×#41—4331no—
59C2×M16—4331no—
60#117—4331no—
61#104—4334no—
62#41—8661no—
63#41—8661no—
64#41—4332no—
65#41—4332no—
66C2×Q8#1318188411yescharacteristic, complemented
67C2×D4—8661no—
68C2×D4—4331no—
69C22×C4—8661no—
70C22×C4—4331no—
71M16—8661no—
72M16—4332no—
73C2×C8—8661no—
74C4⋊C4—8661no—
75C22⋊C4—8661no—
76C42—4332no—
77C23—8661no—
78C23—4331no—
79Q8—21no—
80Q8C2×#1318188412yes—
81D4—8662no—
82D4—8662no—
83D4—8661no—
84D4—4332no—
85C2×C4—21no—
86C2×C4—8662no—
87C2×C4—8662no—
88C2×C4—8662no—
89C2×C4—4331no—
90C2×C4—4331no—
91C2×C4—4331no—
92C2×C4—4331no—
93C2×C4—4331no—
94C2×C4C2×#1318188411yescharacteristic
95C8—8662no—
96C22—8662no—
97C22—4331no—
98C22—4331no—
99C22—17321no—
100C22—17322no—
101C22C22⋊#1318188411yescharacteristic
102C4—22no—
103C4—4331no—
104C4—4331no—
105C4—17322no—
106C4C22⋊#1318188411yescharacteristic
107C4C22×#1318188411yescharacteristic
108C2—21no—
109C2—8661no—
110C2—8661no—
111C2—17322no—
112C2C2×C22⋊#1318188411yescharacteristic
subgroupG/H
centerC2C2×C22⋊#13181884
commutatorC4×C433C22×C4
FrattiniC4C22×#13181884
FittingC2×Q8×C433C4
socleC2×C433C2×C22⋊C4
prime radicalC2×#20294098C2
cosocleC4×D433C23
hypercenterC2×Q8#13181884
hypocenterC433#421
LCSG ▷ C4×C433 ▷ C2×C433 ▷ C433
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×Q8

Complements

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

NH ≅ G/Ntype
1. D433⋊M16C2semidirect
2. #28357299C2semidirect
3. #28357285C2semidirect
5. #20294107C22semidirect
10. C4×#13181884C22semidirect
13. #20294098C4semidirect
16. C2×D1732C4semidirect
19. C2×Q8×C433C4semidirect
56. C433#421semidirect
66. C2×Q8#13181884semidirect

Maximal subgroups

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

subgroupindex
D433⋊M162
#283572992
#283572852
C2×#202940982
#421433