Finite Group Databasebeta

← #28337404

Subgroups — #28337404

Order 13696.

260 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 260 conjugacy classes of subgroups — too many to draw. Only its 93 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#20293184C211yesmaximal, characteristic
2C4×#13133802C211yesmaximal, characteristic
3#20292387C214yesmaximal
4C4×C4⋊C4×C107C211yesmaximal, characteristic
5C2×#13133802C2212yes—
6#16812109C411yescharacteristic, complemented
7#16812109C411yescharacteristic, complemented
8#16812101C412yescomplemented
9#16812088—21no—
10#16812088—21no—
11C4×Dic214—21no—
12C4×Dic214—21no—
13#16812068C2212yes—
14#16812020—21no—
15C4×C107⋊C8—21no—
16C2×C4⋊C4×C107—21no—
17C2×C42×C107C2212yes—
18C2×C42×C107C2211yescharacteristic
19#95×C107—21no—
20C2×Dic214—21no—
21C2×Dic214—21no—
22#13133802—22no—
23#13133802Q814yescomplemented
24C2×C107⋊C8—22no—
25C4⋊Dic107—21no—
26C4⋊Dic107—21no—
27C4⋊Dic107C2×C412yes—
28C4⋊Dic107C2×C412yes—
29Dic107⋊C4—22no—
30Dic107⋊C4—22no—
31C22⋊Dic107—22no—
32C4×Dic107—22no—
33C22×C4×C107—22no—
34C22×C4×C107D411yescharacteristic
35C22×C4×C107D411yescharacteristic
36C22×C4×C107C2311yescharacteristic
37C4⋊C4×C107—24no—
38C42×C107—24no—
39C42×C107C2×C411yescharacteristic
40C42×C107C2×C411yescharacteristic
41C42×C107D411yescharacteristic
42C42×C107D411yescharacteristic
43C23×C107C2×D411yescharacteristic
44C2×C4×C107—22no—
45C2×C4×C107—24no—
46C2×C4×C107—41no—
47C2×C4×C107—42no—
48C2×C4×C107—42no—
49C2×C4×C107C22⋊C411yescharacteristic
50C2×C4×C107C22⋊C411yescharacteristic
51C2×C4×C107C22⋊C411yescharacteristic
52C2×C4×C107C22⋊C411yescharacteristic
53C2×C4×C107C22×C411yescharacteristic
54C2×C4×C107C2×D411yescharacteristic
55C2×C4×C107C2×Q812yes—
56C2×C4×C107#4112yes—
57C2×Dic107—22no—
58C2×Dic107—22no—
59Dic214—42no—
60Dic214—42no—
61C107⋊C8—24no—
62C22×C107—21no—
63C22×C107—21no—
64C22×C107C2×C22⋊C411yescharacteristic
65C22×C107#12411yescharacteristic
66C22×C107C4⋊Q811yescharacteristic
67C4×C107—21no—
68C4×C107—21no—
69C4×C107—21no—
70C4×C107—44no—
71C4×C107#10412yes—
72C4×C107C4×Q812yes—
73C4×C107C22⋊Q812yes—
74Dic107—42no—
75Dic107—42no—
76C2×C107—21no—
77C2×C107—21no—
78C2×C107#39111yescharacteristic
79C2×C107C2×#10411yescharacteristic
80C2×C107#42111yescharacteristic
81#1986—1071nomaximal, Sylow
82C107#198611yescharacteristic, complemented, Sylow
83#533—1071no—
84C4×M16—1071no—
85C4×C4⋊C4D10711yescharacteristic
86#339—1074no—
87C2×M16—1072no—
88C4⋊Q8—1071no—
89C4⋊Q8—1071no—
90#125—1072no—
91C22⋊Q8—2141no—
92C22⋊Q8—2141no—
93C4×Q8—2141no—
94C4×Q8—2141no—
95#117—1072no—
96C2×C4⋊C4—21no—
97C2×C42C2×D10712yes—
98C2×C42C2×D10711yescharacteristic
99#97—2141no—
100C4×C8—2141no—
101#95—21no—
102C2×Q8—2141no—
103C2×Q8—2141no—
104C22×C4—22no—
105C22×C4C22⋊D10711yescharacteristic
106C22×C4C22⋊D10711yescharacteristic
107C22×C4C22×D10711yescharacteristic
108M16—1074no—
109M16—2142no—
110C2×C8—2142no—
111C4⋊C4—24no—
112C4⋊C4—1072no—
113C4⋊C4—1072no—
114C4⋊C4—2142no—
115C4⋊C4—2142no—
116C4⋊C4—2141no—
117C4⋊C4—2141no—
118C22⋊C4—2142no—
119C42—24no—
120C42—2142no—
121C42C4×D10711yescharacteristic
122C42C4×D10711yescharacteristic
123C42D42811yescharacteristic
124C42D42811yescharacteristic
125C23C2×C22⋊D10711yescharacteristic
126Q8—4282no—
127Q8—4282no—
128C2×C4—22no—
129C2×C4—24no—
130C2×C4—41no—
131C2×C4—42no—
132C2×C4—42no—
133C2×C4—2142no—
134C2×C4—2142no—
135C2×C4(C2×D107)⋊C411yescharacteristic
136C2×C4(C2×D107)⋊C411yescharacteristic
137C2×C4(C2×D107)⋊C411yescharacteristic
138C2×C4(C2×D107)⋊C411yescharacteristic
139C2×C4C2×C4×D10711yescharacteristic
140C2×C4C2×D42811yescharacteristic
141C2×C4Q8×D10712yes—
142C2×C4#1313381712yes—
143C8—2144no—
144C22—21no—
145C22—21no—
146C22C2×(C2×D107)⋊C411yescharacteristic
147C22#1681209611yescharacteristic
148C22#1681210711yescharacteristic
149C4—21no—
150C4—21no—
151C4—21no—
152C4—44no—
153C4—4282no—
154C4—4282no—
155C4#1681203712yes—
156C4#1681207412yes—
157C4#1681208912yes—
158C2—21no—
159C2—21no—
160C2#2029253211yescharacteristic
161C2C2×#1681203711yescharacteristic
162C2#2029264511yescharacteristic
subgroupG/H
centerC2×C4C2×D428
commutatorC2×C4×C107C22×C4
FrattiniC22×C4C22×D107
FittingC4×C4⋊C4×C107C2
socleC22×C107C2×C22⋊C4
prime radicalC23×C107C2×D4
cosocleC22×C4×C107C23
hypercenterC4×C4⋊C4D107
hypocenterC107#1986
LCSG ▷ C2×C4×C107 ▷ C2×C107 ▷ C107
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C4×C4⋊C4

Complements

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

NH ≅ G/Ntype
6. #16812109C4semidirect
7. #16812109C4semidirect
8. #16812101C4semidirect
23. #13133802Q8semidirect
82. C107#1986semidirect

Maximal subgroups

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

subgroupindex
#202931842
C4×#131338022
#202923872
C4×C4⋊C4×C1072
#1986107