Finite Group Databasebeta

← #28335097

Subgroups — #28335097

Order 13696.

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#20293183C211yesmaximal, characteristic
2#20292682C212yesmaximal
3#20292369C211yesmaximal, characteristic, complemented
4#20292368C212yesmaximal, complemented
5#330×C107C211yesmaximal, characteristic, complemented
6#16812108C412yes—
7#16812101C2211yescharacteristic
8#16812087—22no—
9#16812074—22no—
10#16812067C412yes—
11C42×D107C2211yescharacteristic
12Dic107⋊C8—22no—
13(C2×D107)⋊C8—22no—
14#16812020C2212yes—
15#125×C107C2211yescharacteristic
16#97×C107C2212yes—
17C2×Dic214—22no—
18C2×C4×D107C2×C411yescharacteristic
19C2×C4×D107D412yes—
20C2×C107⋊C8—22no—
21C4⋊Dic107C2×C412yes—
22Dic107⋊C4—22no—
23Dic107⋊C4—22no—
24(C2×D107)⋊C4—22no—
25C4×Dic107—22no—
26C4×Dic107C2×C411yescharacteristic
27C4×Dic107D412yes—
28C2×C8×C107—22no—
29C4⋊C4×C107—22no—
30C4⋊C4×C107C2×C412yes—
31C42×C107C2311yescharacteristic
32C22×D107C22⋊C411yescharacteristic
33C2×C4×C107—22no—
34C2×C4×C107C22×C411yescharacteristic
35C2×C4×C107C2×D412yes—
36C2×Dic107—22no—
37C2×Dic107C22⋊C412yes—
38C2×Dic107C22⋊C411yescharacteristic
39C4×D107—22no—
40C4×D107—42no—
41Dic214—44no—
42C8×C107—42no—
43C107⋊C8—42no—
44C22×C107C2×C22⋊C411yescharacteristic
45C2×D107—21no—
46C2×D107—22no—
47C4×C107—21no—
48C4×C107—22no—
49C4×C107—42no—
50Dic107—22no—
51Dic107—42no—
52Dic107#10112yes—
53C2×C107C2×#10111yescharacteristic
54C2×C107#42112yes—
55D107—41no—
56#1537—1071nomaximal, Sylow
57C107#153711yescharacteristic, complemented, Sylow
58#533—1071no—
59#432—1072no—
60#330—1071no—
61#330—1072no—
62#330D10711yescharacteristic, complemented
63C4⋊Q8—1072no—
64#125—1071no—
65#125C2×D10711yescharacteristic
66C22⋊Q8—2142no—
67C4×Q8—2142no—
68#117—1072no—
69C2×C42—1071no—
70C4⋊C8—2142no—
71C22⋊C8—2142no—
72#97—1072no—
73#97C2×D10712yes—
74C2×Q8—2142no—
75C22×C4—1072no—
76C22×C4—1071no—
77C2×C8—22no—
78C2×C8—2142no—
79C4⋊C4—22no—
80C4⋊C4—1072no—
81C4⋊C4—2142no—
82C4⋊C4—2142no—
83C4⋊C4C4×D10712yes—
84C22⋊C4—2142no—
85C42—1071no—
86C42—1072no—
87C42—2142no—
88C42C22×D10711yescharacteristic
89C23—1071no—
90Q8—4284no—
91C2×C4—22no—
92C2×C4—1071no—
93C2×C4—1072no—
94C2×C4—4282no—
95C2×C4—2142no—
96C2×C4—2142no—
97C2×C4C2×C4×D10711yescharacteristic
98C2×C4D4×D10712yes—
99C8—42no—
100C8—4282no—
101C22—2142no—
102C22—2141no—
103C22C22⋊C4×D10711yescharacteristic
104C4—22no—
105C4—21no—
106C4—42no—
107C4—1072no—
108C4—4282no—
109C4—2142no—
110C2—4281no—
111C2#101×D10711yescharacteristic
112C2#2029264212yes—
subgroupG/H
centerC22C22⋊C4×D107
commutatorC2×C4×C107C22×C4
FrattiniC42C22×D107
Fitting#330×C107C2
socleC22×C107C2×C22⋊C4
prime radicalC22×D107C22⋊C4
cosocleC42×C107C23
hypercenter#330D107
hypocenterC107#1537
LCSG ▷ C2×C4×C107 ▷ C22×C107 ▷ C107
UCSC1 ◁ C22 ◁ C42 ◁ #330

Complements

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

NH ≅ G/Ntype
3. #20292369C2semidirect
4. #20292368C2semidirect
5. #330×C107C2semidirect
57. C107#1537semidirect
62. #330D107semidirect

Maximal subgroups

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

subgroupindex
#202931832
#202926822
#202923692
#202923682
#330×C1072
#1537107