Finite Group Databasebeta

← #37526415

Subgroups — #37526415

Order 22976.

158 conjugacy classes of subgroups; only the 51 normal subgroups are shown.

normal subgroups only

This group has 158 conjugacy classes of subgroups — too many to draw. Only its 51 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
1C2×#19153340C211yesmaximal, characteristic
2#26039971C212yesmaximal, complemented
3#26039930C211yesmaximal, characteristic, complemented
4#26039929C212yesmaximal, complemented
5#99×C359C211yesmaximal, characteristic, complemented
6#19153340—22no—
7#19153340—22no—
8C2×Dic718C411yescharacteristic, complemented
9C2×C22⋊D359C411yescharacteristic, complemented
10C2×C22⋊D359C2211yescharacteristic
11C22×Dic359C411yescharacteristic, complemented
12C22×Dic359C2211yescharacteristic
13C2×C4×D359C411yescharacteristic, complemented
14Dic359⋊C4—22no—
15C22⋊Dic359C2212yes—
16C4×Dic359—22no—
17C2×D4×C359C2211yescharacteristic
18C22⋊C4×C359C2212yes—
19C22×D359C2×C411yescharacteristic
20Dic718—22no—
21C22⋊D359—22no—
22C22⋊D359—22no—
23C2×Dic359—21no—
24C2×Dic359—21no—
25C2×Dic359—22no—
26C2×Dic359C2×C411yescharacteristic
27C2×Dic359C2×C411yescharacteristic
28C2×Dic359C2×C411yescharacteristic
29C2×Dic359D412yes—
30C2×Dic359D412yes—
31C4×D359—21no—
32C4×D359—21no—
33C23×C359C2×C411yescharacteristic
34C23×C359C2311yescharacteristic
35D4×C359—22no—
36C2×C4×C359—22no—
37C2×C4×C359C2×C411yescharacteristic
38C22×C359—21no—
39C22×C359—41no—
40C22×C359—41no—
41C22×C359C22×C411yescharacteristic
42C22×C359C2×D412yes—
43C2×D359—21no—
44C2×D359—41no—
45C4×C359—21no—
46C4×C359—42no—
47Dic359—21no—
48Dic359—42no—
49Dic359C22⋊C411yescharacteristic
50Dic359C22⋊C411yescharacteristic
51Dic359C22⋊C412yes—
52C2×C359—22no—
53C2×C359—21no—
54C2×C359—41no—
55C2×C359C2×C22⋊C411yescharacteristic
56D359—41no—
57C359#41011yescharacteristic, complemented, Sylow
58#410—3591nomaximal, Sylow
59C2×#41—3591no—
60#117—3592no—
61#99—3591no—
62#99—3592no—
63#99D35911yescharacteristic, complemented
64#41—7182no—
65#41—7182no—
66C2×Q8—3591no—
67C2×D4—3591no—
68C2×D4—3591no—
69C2×D4C2×D35911yescharacteristic
70C22×C4—3591no—
71C22×C4—3591no—
72C22×C4—3591no—
73C4⋊C4—7182no—
74C22⋊C4—3592no—
75C22⋊C4C2×D35912yes—
76C42—7182no—
77C23—3591no—
78C23C4×D35911yescharacteristic
79C23C22×D35911yescharacteristic
80Q8—7182no—
81D4—22no—
82D4—7182no—
83D4—7182no—
84C2×C4—22no—
85C2×C4—3591no—
86C2×C4—3591no—
87C2×C4—3592no—
88C2×C4—3592no—
89C2×C4—3591no—
90C2×C4—7181no—
91C2×C4—7181no—
92C2×C4—7181no—
93C2×C4—7181no—
94C2×C4—7182no—
95C2×C4C4×D35911yescharacteristic
96C22—21no—
97C22—41no—
98C22—41no—
99C22—14361no—
100C22—7181no—
101C22C2×C4×D35911yescharacteristic
102C22D4×D35912yes—
103C4—21no—
104C4—42no—
105C4—3591no—
106C4—3591no—
107C4—3592no—
108C4—14362no—
109C4—7181no—
110C2—22no—
111C2—21no—
112C2—41no—
113C2—14361no—
114C2C22⋊C4×D35911yescharacteristic
subgroupG/H
centerC2C22⋊C4×D359
commutatorC22×C359C22×C4
FrattiniC23C22×D359
Fitting#99×C359C2
socleC2×C359C2×C22⋊C4
prime radicalC2×#19153340C2
cosocleC23×C359C23
hypercenter#99D359
hypocenterC359#410
LCSG ▷ C22×C359 ▷ C2×C359 ▷ C359
UCSC1 ◁ C2 ◁ C23 ◁ #99

Complements

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

NH ≅ G/Ntype
2. #26039971C2semidirect
3. #26039930C2semidirect
4. #26039929C2semidirect
5. #99×C359C2semidirect
8. C2×Dic718C4semidirect
9. C2×C22⋊D359C4semidirect
11. C22×Dic359C4semidirect
13. C2×C4×D359C4semidirect
57. C359#410semidirect
63. #99D359semidirect

Maximal subgroups

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

subgroupindex
C2×#191533402
#260399712
#260399302
#260399292
#99×C3592
#410359