Finite Group Databasebeta

← #49119897

Subgroups — #49119897

Order 36224.

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

normal subgroups only

This group has 194 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#31827021C211yesmaximal, characteristic
2#31826520C212yesmaximal
3#31826207C211yesmaximal, characteristic, complemented
4#31826206C212yesmaximal, complemented
5#330×C283C211yesmaximal, characteristic, complemented
6#22583609C412yes—
7#22583602C2211yescharacteristic
8#22583588—22no—
9#22583575—22no—
10#22583568C412yes—
11C42×D283C2211yescharacteristic
12Dic283⋊C8—22no—
13(C2×D283)⋊C8—22no—
14#22583521C2212yes—
15#125×C283C2211yescharacteristic
16#97×C283C2212yes—
17C2×Dic566—22no—
18C2×C4×D283C2×C411yescharacteristic
19C2×C4×D283D412yes—
20C2×C283⋊C8—22no—
21C4⋊Dic283C2×C412yes—
22Dic283⋊C4—22no—
23Dic283⋊C4—22no—
24(C2×D283)⋊C4—22no—
25C4×Dic283—22no—
26C4×Dic283C2×C411yescharacteristic
27C4×Dic283D412yes—
28C2×C8×C283—22no—
29C4⋊C4×C283—22no—
30C4⋊C4×C283C2×C412yes—
31C42×C283C2311yescharacteristic
32C22×D283C22⋊C411yescharacteristic
33Dic566—44no—
34C2×Dic283—22no—
35C2×Dic283C22⋊C412yes—
36C2×Dic283C22⋊C411yescharacteristic
37C4×D283—22no—
38C4×D283—42no—
39C283⋊C8—42no—
40C2×C4×C283—22no—
41C2×C4×C283C22×C411yescharacteristic
42C2×C4×C283C2×D412yes—
43C8×C283—42no—
44C22×C283C2×C22⋊C411yescharacteristic
45C2×D283—21no—
46C2×D283—22no—
47C4×C283—21no—
48C4×C283—22no—
49C4×C283—42no—
50Dic283—22no—
51Dic283—42no—
52Dic283#10112yes—
53C2×C283C2×#10111yescharacteristic
54C2×C283#42112yes—
55D283—41no—
56C283#153711yescharacteristic, complemented, Sylow
57#1537—2831nomaximal, Sylow
58#533—2831no—
59#432—2832no—
60#330—2831no—
61#330—2832no—
62#330D28311yescharacteristic, complemented
63C4⋊Q8—2832no—
64#125—2831no—
65#125C2×D28311yescharacteristic
66C22⋊Q8—5662no—
67C4×Q8—5662no—
68#117—2832no—
69C2×C42—2831no—
70C4⋊C8—5662no—
71C22⋊C8—5662no—
72#97—2832no—
73#97C2×D28312yes—
74C2×Q8—5662no—
75C22×C4—2831no—
76C22×C4—2832no—
77C2×C8—22no—
78C2×C8—5662no—
79C4⋊C4—22no—
80C4⋊C4—2832no—
81C4⋊C4—5662no—
82C4⋊C4—5662no—
83C4⋊C4C4×D28312yes—
84C22⋊C4—5662no—
85C42—2831no—
86C42—2832no—
87C42—5662no—
88C42C22×D28311yescharacteristic
89C23—2831no—
90Q8—11324no—
91C2×C4—22no—
92C2×C4—2831no—
93C2×C4—2832no—
94C2×C4—5662no—
95C2×C4—5662no—
96C2×C4—11322no—
97C2×C4C2×C4×D28311yescharacteristic
98C2×C4D4×D28312yes—
99C8—42no—
100C8—11322no—
101C22—5661no—
102C22—5662no—
103C22C22⋊C4×D28311yescharacteristic
104C4—21no—
105C4—22no—
106C4—42no—
107C4—2832no—
108C4—5662no—
109C4—11322no—
110C2—11321no—
111C2#101×D28311yescharacteristic
112C2#3182648012yes—
subgroupG/H
centerC22C22⋊C4×D283
commutatorC2×C4×C283C22×C4
FrattiniC42C22×D283
Fitting#330×C283C2
socleC22×C283C2×C22⋊C4
prime radicalC22×D283C22⋊C4
cosocleC42×C283C23
hypercenter#330D283
hypocenterC283#1537
LCSG ▷ C2×C4×C283 ▷ C22×C283 ▷ C283
UCSC1 ◁ C22 ◁ C42 ◁ #330

Complements

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

NH ≅ G/Ntype
3. #31826207C2semidirect
4. #31826206C2semidirect
5. #330×C283C2semidirect
56. C283#1537semidirect
62. #330D283semidirect

Maximal subgroups

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

subgroupindex
#318270212
#318265202
#318262072
#318262062
#330×C2832
#1537283