Finite Group Databasebeta

← #44548990

Subgroups — #44548990

Order 32128.

196 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 196 conjugacy classes of subgroups — too many to draw. Only its 59 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#125×D251C211yesmaximal, characteristic
2#30631742C212yesmaximal
3#30631429C211yesmaximal, characteristic, complemented
4#30631428C212yesmaximal, complemented
5#330×C251C211yesmaximal, characteristic, complemented
6#22548707C2211yescharacteristic
7#22548706C412yes—
8#22548705—22no—
9C4⋊C4×D251—22no—
10C4⋊C4×D251C412yes—
11C42×D251C2211yescharacteristic
12Dic251⋊C8—22no—
13(C2×D251)⋊C8—22no—
14#22548626C2212yes—
15#125×C251C2211yescharacteristic
16#97×C251C2212yes—
17C2×C4×D251—22no—
18C2×C4×D251C2×C411yescharacteristic
19C2×C4×D251D412yes—
20C2×C251⋊C8—22no—
21C4⋊Dic251—22no—
22C4⋊Dic251C2×C412yes—
23Dic251⋊C4—22no—
24Dic251⋊C4—22no—
25Dic251⋊C4—22no—
26C4×Dic251C2×C411yescharacteristic
27C4×Dic251D412yes—
28C2×C8×C251—22no—
29C4⋊C4×C251—22no—
30C4⋊C4×C251C2×C412yes—
31C42×C251C2311yescharacteristic
32C22×D251C22⋊C411yescharacteristic
33C2×Dic251—22no—
34C2×Dic251C22⋊C412yes—
35C2×Dic251C22⋊C411yescharacteristic
36C4×D251—22no—
37C4×D251—42no—
38C4×D251—44no—
39C251⋊C8—42no—
40C2×C4×C251—22no—
41C2×C4×C251C22×C411yescharacteristic
42C2×C4×C251C2×D412yes—
43C8×C251—42no—
44C22×C251C2×C22⋊C411yescharacteristic
45C2×D251—22no—
46C2×D251#10112yes—
47C4×C251—21no—
48C4×C251—22no—
49C4×C251—42no—
50Dic251—21no—
51Dic251—22no—
52Dic251—42no—
53C2×C251C2×#10111yescharacteristic
54C2×C251#42112yes—
55D251—22no—
56C251#153411yescharacteristic, complemented, Sylow
57#1534—2511nomaximal, Sylow
58C2×#125—2511no—
59#432—2512no—
60#330—2511no—
61#330—2512no—
62#330D25111yescharacteristic, complemented
63#125—5022no—
64#125—2512no—
65#125—2511no—
66#125C2×D25111yescharacteristic
67C2×C4⋊C4—5022no—
68C2×C4⋊C4—2512no—
69C2×C42—2511no—
70C4⋊C8—5022no—
71C22⋊C8—5022no—
72#97—2512no—
73#97C2×D25112yes—
74C22×C4—5022no—
75C22×C4—2512no—
76C22×C4—2511no—
77C2×C8—22no—
78C2×C8—5022no—
79C4⋊C4—22no—
80C4⋊C4—5022no—
81C4⋊C4—5022no—
82C4⋊C4—5022no—
83C4⋊C4—5022no—
84C4⋊C4—2512no—
85C4⋊C4C4×D25112yes—
86C42—2511no—
87C42—2512no—
88C42C22×D25111yescharacteristic
89C23—2511no—
90C2×C4—22no—
91C2×C4—10042no—
92C2×C4—10044no—
93C2×C4—5022no—
94C2×C4—5022no—
95C2×C4—2512no—
96C2×C4—2511no—
97C2×C4C2×C4×D25111yescharacteristic
98C2×C4D4×D25112yes—
99C8—42no—
100C8—10042no—
101C22—5022no—
102C22—2512no—
103C22C22⋊C4×D25111yescharacteristic
104C4—22no—
105C4—21no—
106C4—42no—
107C4—10042no—
108C4—5022no—
109C4—5021no—
110C2—5022no—
111C2#101×D25111yescharacteristic
112C2#3063170212yes—
subgroupG/H
centerC22C22⋊C4×D251
commutatorC2×C4×C251C22×C4
FrattiniC42C22×D251
Fitting#330×C251C2
socleC22×C251C2×C22⋊C4
prime radicalC22×D251C22⋊C4
cosocleC42×C251C23
hypercenter#330D251
hypocenterC251#1534
LCSG ▷ C2×C4×C251 ▷ C22×C251 ▷ C251
UCSC1 ◁ C22 ◁ C42 ◁ #330

Complements

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

NH ≅ G/Ntype
3. #30631429C2semidirect
4. #30631428C2semidirect
5. #330×C251C2semidirect
56. C251#1534semidirect
62. #330D251semidirect

Maximal subgroups

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

subgroupindex
#125×D2512
#306317422
#306314292
#306314282
#330×C2512
#1534251