Finite Group Databasebeta

← #28334783

Subgroups — #28334783

Order 13696.

248 conjugacy classes of subgroups; only the 81 normal subgroups are shown.

normal subgroups only

This group has 248 conjugacy classes of subgroups — too many to draw. Only its 81 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×#16812074C211yesmaximal, characteristic
2#20292677C212yesmaximal
3#20292353C211yesmaximal, characteristic
4#20292352C212yesmaximal
5#324×C107C211yesmaximal, characteristic
6C22×Dic214C411yescharacteristic
7#16812074—22no—
8#16812074—22no—
9C2×Dic107⋊C4C411yescharacteristic
10C2×Dic107⋊C4C2211yescharacteristic
11C2×C4×Dic107C411yescharacteristic
12C2×C4×Dic107C411yescharacteristic
13C2×C4×Dic107C2211yescharacteristic
14Dic107⋊C8—22no—
15C22⋊(C107⋊C8)C2212yes—
16C8×Dic107—22no—
17C2×C4⋊C4×C107C2211yescharacteristic
18C22⋊C8×C107C2212yes—
19C2×Dic214—22no—
20C2×Dic214—22no—
21C2×Dic214C814yescomplemented
22C22×Dic107C2×C411yescharacteristic
23C22×Dic107C2×C411yescharacteristic
24C22×Dic107C2×C411yescharacteristic
25C22×Dic107C2×C411yescharacteristic
26C2×C107⋊C8—22no—
27Dic107⋊C4—22no—
28Dic107⋊C4—22no—
29C4×Dic107—21no—
30C4×Dic107—21no—
31C4×Dic107—21no—
32C4×Dic107—21no—
33C4×Dic107D412yes—
34C4×Dic107D412yes—
35C22×C4×C107C2×C411yescharacteristic
36C22×C4×C107C2×C411yescharacteristic
37C22×C4×C107C2311yescharacteristic
38C2×C8×C107—22no—
39C4⋊C4×C107—22no—
40C23×C107C22×C411yescharacteristic
41C2×C4×C107—21no—
42C2×C4×C107—21no—
43C2×C4×C107—21no—
44C2×C4×C107—41no—
45C2×C4×C107—41no—
46C2×C4×C107C2×C812yes—
47C2×C4×C107C2×D412yes—
48C2×Dic107—21no—
49C2×Dic107—21no—
50C2×Dic107—22no—
51C2×Dic107—21no—
52C2×Dic107—41no—
53C2×Dic107C22⋊C411yescharacteristic
54C2×Dic107C22⋊C412yes—
55C2×Dic107C22⋊C411yescharacteristic
56C2×Dic107C2×C812yes—
57C2×Dic107C2×C812yes—
58C2×Dic107M1612yes—
59Dic214—28no—
60C8×C107—42no—
61C107⋊C8—42no—
62C22×C107—21no—
63C22×C107—21no—
64C22×C107C2×C22⋊C411yescharacteristic
65C22×C107C22×C811yescharacteristic
66C22×C107C2×M1611yescharacteristic
67C4×C107—22no—
68C4×C107—22no—
69C4×C107—41no—
70Dic107—22no—
71Dic107—21no—
72Dic107—41no—
73Dic107C22⋊C814yes—
74Dic107#10112yes—
75C2×C107—21no—
76C2×C107—21no—
77C2×C107C2×C22⋊C811yescharacteristic
78C2×C107#41011yescharacteristic
79C2×C107C2×#10111yescharacteristic
80#1461—1071nomaximal, Sylow
81C107#146111yescharacteristic, complemented, Sylow
82C2×C4×Q8—1071no—
83#431—1072no—
84#324—1071no—
85#324—1072no—
86#324D10711yescharacteristic
87C22×Q8—1071no—
88C4×Q8—2142no—
89C4×Q8—2142no—
90C2×C4⋊C4—1071no—
91C2×C4⋊C4—1071no—
92C2×C4⋊C4C2×D10711yescharacteristic
93C2×C42—1071no—
94C2×C42—1071no—
95C2×C42—1071no—
96C4⋊C8—2142no—
97C22⋊C8—1072no—
98C22⋊C8C2×D10712yes—
99C4×C8—2142no—
100C2×Q8—1074no—
101C2×Q8—2142no—
102C2×Q8—2142no—
103C22×C4—1071no—
104C22×C4—1071no—
105C22×C4—1071no—
106C22×C4—1071no—
107C22×C4C4×D10711yescharacteristic
108C22×C4C4×D10711yescharacteristic
109C22×C4C22×D10711yescharacteristic
110C2×C8—22no—
111C2×C8—2142no—
112C4⋊C4—22no—
113C4⋊C4—2142no—
114C4⋊C4—2142no—
115C42—1072no—
116C42—1072no—
117C42—2141no—
118C42—2141no—
119C42—2141no—
120C42—2141no—
121C23C2×C4×D10711yescharacteristic
122Q8—2148no—
123C2×C4—21no—
124C2×C4—21no—
125C2×C4—21no—
126C2×C4—41no—
127C2×C4—41no—
128C2×C4—1071no—
129C2×C4—1072no—
130C2×C4—1072no—
131C2×C4—1072no—
132C2×C4—1071no—
133C2×C4—1072no—
134C2×C4—4281no—
135C2×C4—2142no—
136C2×C4—2141no—
137C2×C4—2141no—
138C2×C4—2141no—
139C2×C4C8×D10712yes—
140C2×C4D4×D10712yes—
141C8—42no—
142C8—4282no—
143C22—21no—
144C22—21no—
145C22C22⋊C4×D10711yescharacteristic
146C22C2×C8×D10711yescharacteristic
147C22M16×D10711yescharacteristic
148C4—22no—
149C4—22no—
150C4—41no—
151C4—1074no—
152C4—1072no—
153C4—4281no—
154C4—2142no—
155C4—2141no—
156C2—21no—
157C2—21no—
158C2C22⋊C8×D10711yescharacteristic
159C2#2029259911yescharacteristic
160C2#101×D10711yescharacteristic
subgroupG/H
centerC22C22⋊C4×D107
commutatorC22×C107C22×C8
FrattiniC22×C4C22×D107
Fitting#324×C107C2
socleC22×C107C2×C22⋊C4
prime radicalC23×C107C22×C4
cosocleC22×C4×C107C23
hypercenter#324D107
hypocenterC107#1461
LCSG ▷ C22×C107 ▷ C2×C107 ▷ C107
UCSC1 ◁ C22 ◁ C22×C4 ◁ #324

Complements

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

NH ≅ G/Ntype
21. C2×Dic214C8semidirect
81. C107#1461semidirect

Maximal subgroups

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

subgroupindex
C2×#168120742
#202926772
#202923532
#202923522
#324×C1072
#1461107