Finite Group Databasebeta

← #28335505

Subgroups — #28335505

Order 13696.

202 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 202 conjugacy classes of subgroups — too many to draw. Only its 53 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#20293258C211yesmaximal, characteristic
2#20292963C212yesmaximal
3#20292566C211yesmaximal, characteristic
4#20292365C212yesmaximal
5#324×C107C211yesmaximal, characteristic
6#16812108—22no—
7#16812100—22no—
8#16812088—21no—
9#16812088C2212yes—
10#16812068—21no—
11C2×C4⋊Dic107C2211yescharacteristic
12#16812043—22no—
13#16812034—22no—
14C107⋊#95—21no—
15C107⋊#95—21no—
16C107⋊#95C2211yescharacteristic
17C2×C4⋊C4×C107C2211yescharacteristic
18C22⋊C8×C107C2212yes—
19C2×Dic214—21no—
20C2×Dic214D412yes—
21C22×Dic107—21no—
22C22×Dic107—21no—
23C4⋊Dic107—21no—
24C4⋊Dic107—21no—
25C4⋊Dic107—21no—
26C4⋊Dic107—22no—
27C4⋊Dic107D412yes—
28Dic107⋊C4—22no—
29Dic107⋊C4—22no—
30C22⋊Dic107—22no—
31C4×Dic107—22no—
32C22×C4×C107D411yescharacteristic
33C22×C4×C107D411yescharacteristic
34C22×C4×C107C2311yescharacteristic
35C2×C8×C107—22no—
36C4⋊C4×C107—22no—
37C23×C107C2×D411yescharacteristic
38C2×C4×C107—21no—
39C2×C4×C107—21no—
40C2×C4×C107—21no—
41C2×C4×C107—41no—
42C2×C4×C107—41no—
43C2×C4×C107Q1612yes—
44C2×C4×C107C2×D412yes—
45C2×Dic107—22no—
46C2×Dic107—22no—
47C2×Dic107—41no—
48C2×Dic107—41no—
49C2×Dic107—42no—
50C2×Dic107—41no—
51C2×Dic107—41no—
52Dic214—42no—
53Dic214—81no—
54C8×C107—42no—
55C22×C107—21no—
56C22×C107—21no—
57C22×C107#12011yescharacteristic
58C22×C107C2×Q1611yescharacteristic
59C22×C107#13711yescharacteristic
60C4×C107—22no—
61C4×C107—22no—
62C4×C107—41no—
63Dic107—42no—
64Dic107—42no—
65Dic107—81no—
66Dic107—81no—
67C2×C107—21no—
68C2×C107—21no—
69C2×C107#45111yescharacteristic
70C2×C107#45411yescharacteristic
71C2×C107#45811yescharacteristic
72#1617—1071nomaximal, Sylow
73C107#161711yescharacteristic, complemented, Sylow
74#544—1071no—
75#484—1072no—
76#400—1071no—
77#328—1072no—
78#324D10711yescharacteristic
79C4⋊Q8—2142no—
80#125—2142no—
81C22⋊Q8—1072no—
82C22⋊Q8—2141no—
83#117—2141no—
84C2×C4⋊C4—1071no—
85C2×C4⋊C4C2×D10711yescharacteristic
86#107—2142no—
87#103—2142no—
88C22⋊C8C2×D10712yes—
89#95—1071no—
90#95—2141no—
91#95—2141no—
92C2×Q8—1072no—
93C2×Q8—2141no—
94C22×C4—2141no—
95C22×C4—2141no—
96C22×C4D42811yescharacteristic
97C22×C4D42811yescharacteristic
98C22×C4C22×D10711yescharacteristic
99C2×C8—22no—
100C4⋊C4—22no—
101C4⋊C4—1072no—
102C4⋊C4—2141no—
103C4⋊C4—2141no—
104C4⋊C4—2141no—
105C4⋊C4—2142no—
106C4⋊C4—2142no—
107C4⋊C4—2142no—
108C22⋊C4—2142no—
109C42—2142no—
110C23C2×D42811yescharacteristic
111Q8—8561no—
112Q8—4282no—
113C2×C4—21no—
114C2×C4—21no—
115C2×C4—21no—
116C2×C4—41no—
117C2×C4—41no—
118C2×C4—4281no—
119C2×C4—4281no—
120C2×C4—4282no—
121C2×C4—4281no—
122C2×C4—4281no—
123C2×C4—2142no—
124C2×C4—2142no—
125C2×C4Dic42812yes—
126C2×C4D4×D10712yes—
127C8—42no—
128C22—21no—
129C22—21no—
130C22#1681207911yescharacteristic
131C22C2×Dic42811yescharacteristic
132C22#1681214211yescharacteristic
133C4—22no—
134C4—22no—
135C4—41no—
136C4—8561no—
137C4—8561no—
138C4—4282no—
139C4—4282no—
140C2—21no—
141C2—21no—
142C2#2029278511yescharacteristic
143C2#2029280211yescharacteristic
144C2#2029281811yescharacteristic
subgroupG/H
centerC22#16812079
commutator, cosocleC22×C4×C107C23
FrattiniC22×C4C22×D107
Fitting#324×C107C2
socleC22×C107#120
prime radicalC23×C107C2×D4
hypercenter#324D107
hypocenterC107#1617
LCSG ▷ C22×C4×C107 ▷ C22×C107 ▷ C107
UCSC1 ◁ C22 ◁ C22×C4 ◁ #324

Complements

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

NH ≅ G/Ntype
73. C107#1617semidirect

Maximal subgroups

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

subgroupindex
#202932582
#202929632
#202925662
#202923652
#324×C1072
#1617107