Finite Group Databasebeta

← #28336537

Subgroups — #28336537

Order 13696.

300 conjugacy classes of subgroups; only the 77 normal subgroups are shown.

normal subgroups only

This group has 300 conjugacy classes of subgroups — too many to draw. Only its 77 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×#16812065C211yesmaximal, characteristic
2#20292488C212yesmaximal
3#20292394C211yesmaximal, characteristic
4#20292393C212yesmaximal
5#342×C107C211yesmaximal, characteristic
6C23×Dic107C2211yescharacteristic
7#16812065—24no—
8C2×Dic107⋊C4C412yescomplemented
9C2×C22⋊Dic107C2212yes—
10C2×C22⋊Dic107C2211yescharacteristic
11C2×C4×Dic107C412yescomplemented
12C107⋊#95—24no—
13C2×C22⋊C4×C107C2212yes—
14C2×C22⋊C4×C107C2211yescharacteristic
15C22×Dic107—21no—
16C22×Dic107—22no—
17C22×Dic107—21no—
18C22×Dic107—22no—
19C22×Dic107C2×C411yescharacteristic
20C22×Dic107C2×C411yescharacteristic
21C22×Dic107C2×C412yes—
22C22×Dic107D414yes—
23Dic107⋊C4—24no—
24C22⋊Dic107—22no—
25C22⋊Dic107—22no—
26C22⋊Dic107—22no—
27C4×Dic107—24no—
28C24×C107C2311yescharacteristic
29C22×C4×C107—22no—
30C22×C4×C107C2×C412yes—
31C22⋊C4×C107—22no—
32C22⋊C4×C107—22no—
33C22⋊C4×C107—22no—
34C23×C107—42no—
35C23×C107C22×C411yescharacteristic
36C23×C107C2×D412yes—
37C23×C107#4111yescharacteristic
38C23×C107#4112yes—
39C23×C107#4111yescharacteristic
40C2×C4×C107—22no—
41C2×C4×C107—42no—
42C2×C4×C107—44no—
43C2×C4×C107—42no—
44C2×Dic107—21no—
45C2×Dic107—21no—
46C2×Dic107—21no—
47C2×Dic107—21no—
48C2×Dic107—24no—
49C2×Dic107—24no—
50C2×Dic107—22no—
51C2×Dic107—42no—
52C2×Dic107—44no—
53C2×Dic107—42no—
54C2×Dic107C22⋊C412yes—
55C2×Dic107C22⋊C412yes—
56C22×C107—22no—
57C22×C107—24no—
58C22×C107—41no—
59C22×C107—42no—
60C22×C107—41no—
61C22×C107C2×C22⋊C411yescharacteristic
62C22×C107#11711yescharacteristic
63C22×C107#11711yescharacteristic
64C22×C107#12312yes—
65C22×C107#12312yes—
66C4×C107—42no—
67C4×C107—82no—
68Dic107—22no—
69Dic107—22no—
70Dic107—42no—
71Dic107—82no—
72C2×C107—22no—
73C2×C107—22no—
74C2×C107—21no—
75C2×C107—21no—
76C2×C107#38111yescharacteristic
77C2×C107#41012yes—
78#1820—1071nomaximal, Sylow
79C107#182011yescharacteristic, complemented, Sylow
80C2×#117—1071no—
81#381—1072no—
82#342—1072no—
83#342—1071no—
84#342D10711yescharacteristic
85C23×C4—1071no—
86#117—2144no—
87C2×C4⋊C4—1072no—
88C2×C22⋊C4—1071no—
89C2×C22⋊C4—1072no—
90C2×C22⋊C4C2×D10712yes—
91C2×C22⋊C4C2×D10711yescharacteristic
92C2×C42—1072no—
93#95—2144no—
94C24C22×D10711yescharacteristic
95C22×C4—22no—
96C22×C4—1071no—
97C22×C4—1071no—
98C22×C4—1074no—
99C22×C4—1072no—
100C22×C4—2142no—
101C22×C4—2141no—
102C22×C4—2142no—
103C22×C4—2141no—
104C22×C4C4×D10712yes—
105C4⋊C4—2144no—
106C22⋊C4—22no—
107C22⋊C4—22no—
108C22⋊C4—22no—
109C22⋊C4—2142no—
110C22⋊C4—2142no—
111C22⋊C4—2142no—
112C42—2144no—
113C23—42no—
114C23C2×C4×D10711yescharacteristic
115C23D4×D10712yes—
116C23#1313381711yescharacteristic
117C23#1313381812yes—
118C23#1313381911yescharacteristic
119C2×C4—22no—
120C2×C4—42no—
121C2×C4—44no—
122C2×C4—42no—
123C2×C4—1072no—
124C2×C4—1072no—
125C2×C4—4284no—
126C2×C4—4282no—
127C2×C4—4282no—
128C2×C4—2142no—
129C2×C4—2141no—
130C2×C4—2141no—
131C2×C4—2141no—
132C2×C4—2141no—
133C2×C4—2144no—
134C2×C4—2144no—
135C22—22no—
136C22—24no—
137C22—41no—
138C22—42no—
139C22—41no—
140C22C22⋊C4×D10711yescharacteristic
141C22#1681206611yescharacteristic
142C22#1681206711yescharacteristic
143C22#1681209112yes—
144C22#1681209412yes—
145C4—42no—
146C4—82no—
147C4—8562no—
148C4—4282no—
149C4—2142no—
150C4—2142no—
151C2—22no—
152C2—22no—
153C2—21no—
154C2—21no—
155C2#2029248911yescharacteristic
156C2#2029259912yes—
subgroupG/H
centerC22C22⋊C4×D107
commutatorC23×C107C22×C4
FrattiniC24C22×D107
Fitting#342×C107C2
socleC22×C107C2×C22⋊C4
prime radical, cosocleC24×C107C23
hypercenter#342D107
hypocenterC107#1820
LCSG ▷ C23×C107 ▷ C2×C107 ▷ C107
UCSC1 ◁ C22 ◁ C24 ◁ #342

Complements

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

NH ≅ G/Ntype
8. C2×Dic107⋊C4C4semidirect
11. C2×C4×Dic107C4semidirect
79. C107#1820semidirect

Maximal subgroups

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

subgroupindex
C2×#168120652
#202924882
#202923942
#202923932
#342×C1072
#1820107