Finite Group Databasebeta

← #28336263

Subgroups — #28336263

Order 13696.

284 conjugacy classes of subgroups; only the 113 normal subgroups are shown.

normal subgroups only

This group has 284 conjugacy classes of subgroups — too many to draw. Only its 113 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×#16812116C211yesmaximal, characteristic
2#20292611C211yesmaximal, characteristic
3#20292583C212yesmaximal, complemented
4#20292397C212yesmaximal, complemented
5#410×C107C211yesmaximal, characteristic
6#16812116—22no—
7#16812116—22no—
8C2×#13133802C412yescomplemented
9C2×#13133802C2212yes—
10C2×#13133802C2211yescharacteristic
11C22×C107⋊C8C412yescomplemented
12C22×C107⋊C8C2211yescharacteristic
13#16812028C412yescomplemented
14#16812026C412yescomplemented
15#16812020—22no—
16C4×C107⋊C8—22no—
17C2×#41×C107C2211yescharacteristic
18#117×C107C2212yes—
19#99×C107C414yes—
20#13133802—22no—
21#13133802—22no—
22#13133802—24no—
23#13133802C2×C414yes—
24C2×C107⋊C8—22no—
25C2×C107⋊C8—22no—
26C2×C107⋊C8—22no—
27C2×C107⋊C8C2×C412yes—
28C2×C107⋊C8C2×C411yescharacteristic
29C2×C107⋊C8C2×C411yescharacteristic
30C2×C107⋊C8D412yes—
31C2×C107⋊C8D412yes—
32#41×C107—22no—
33#41×C107—22no—
34C2×Q8×C107C2×C411yescharacteristic
35C2×D4×C107C2×C411yescharacteristic
36C2×D4×C107C2×C412yes—
37C22×C4×C107C2×C412yes—
38C22×C4×C107C2311yescharacteristic
39C4⋊C4×C107—22no—
40C22⋊C4×C107C2×C414yes—
41C42×C107—22no—
42C23×C107C4212yes—
43C23×C107C22×C411yescharacteristic
44Q8×C107—22no—
45D4×C107—24no—
46D4×C107—22no—
47C2×C4×C107—22no—
48C2×C4×C107—22no—
49C2×C4×C107—24no—
50C2×C4×C107C4212yes—
51C2×C4×C107C22×C411yescharacteristic
52C2×C4×C107C22×C411yescharacteristic
53C2×C4×C107C2×D412yes—
54C2×C4×C107#4112yes—
55C107⋊C8—22no—
56C107⋊C8—24no—
57C107⋊C8C22⋊C411yescharacteristic
58C107⋊C8C22⋊C411yescharacteristic
59C107⋊C8C22⋊C412yes—
60C22×C107—22no—
61C22×C107—41no—
62C22×C107—42no—
63C22×C107C2×C4211yescharacteristic
64C22×C107C4×D412yes—
65C4×C107—22no—
66C4×C107—44no—
67C4×C107C2×C22⋊C411yescharacteristic
68C4×C107#11711yescharacteristic
69C4×C107C4×D412yes—
70C2×C107—22no—
71C2×C107—21no—
72C2×C107—42no—
73C2×C107C4×C22⋊C411yescharacteristic
74#1757—1071nomaximal, Sylow
75C107#175711yescharacteristic, complemented, Sylow
76C2×#131—1071no—
77#413—1071no—
78#410D10711yescharacteristic
79#405—1072no—
80#344—1072no—
81C2×#41C2×D10711yescharacteristic
82#131—2142no—
83#131—2142no—
84C2×M16—1072no—
85C2×M16—1071no—
86C2×M16—1072no—
87C22×C8—1071no—
88C22×C8—1072no—
89#117C2×D10712yes—
90#101—1072no—
91#100—1072no—
92#99Dic10714yes—
93#97—2142no—
94C4×C8—2142no—
95#41—22no—
96#41—22no—
97C2×Q8C4×D10711yescharacteristic
98C2×D4C4×D10711yescharacteristic
99C2×D4C2×Dic10712yes—
100C22×C4C4×D10712yes—
101C22×C4C22×D10711yescharacteristic
102M16—1074no—
103M16—2144no—
104M16—2142no—
105M16—2142no—
106C2×C8—1071no—
107C2×C8—1071no—
108C2×C8—1072no—
109C2×C8—1072no—
110C2×C8—1072no—
111C2×C8—2142no—
112C2×C8—2142no—
113C2×C8—2142no—
114C4⋊C4—22no—
115C22⋊C4C2×Dic10714yes—
116C42—22no—
117C23C4×Dic10712yes—
118C23C22×Dic10711yescharacteristic
119Q8—22no—
120D4—24no—
121D4—22no—
122C2×C4—22no—
123C2×C4—22no—
124C2×C4—24no—
125C2×C4C4×Dic10712yes—
126C2×C4C2×C4×D10711yescharacteristic
127C2×C4C2×C4×D10711yescharacteristic
128C2×C4D4×D10712yes—
129C2×C4#1313381712yes—
130C8—1071no—
131C8—1071no—
132C8—1072no—
133C8—2142no—
134C8—2144no—
135C22—22no—
136C22—41no—
137C22—42no—
138C22C2×C4×Dic10711yescharacteristic
139C22D4×Dic10712yes—
140C4—22no—
141C4—44no—
142C4C22⋊C4×D10711yescharacteristic
143C4#1681206511yescharacteristic
144C4(C22⋊D107)⋊C412yes—
145C2—22no—
146C2—21no—
147C2—42no—
148C2C22⋊C4×Dic10711yescharacteristic
subgroupG/H
centerC4C22⋊C4×D107
commutatorC22×C107C2×C42
FrattiniC22×C4C22×D107
Fitting#410×C107C2
socleC2×C107C4×C22⋊C4
prime radicalC2×#41×C107C22
cosocleC22×C4×C107C23
hypercenter#410D107
hypocenterC107#1757
LCSG ▷ C22×C107 ▷ C2×C107 ▷ C107
UCSC1 ◁ C4 ◁ C22×C4 ◁ #410

Complements

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

NH ≅ G/Ntype
3. #20292583C2semidirect
4. #20292397C2semidirect
8. C2×#13133802C4semidirect
11. C22×C107⋊C8C4semidirect
13. #16812028C4semidirect
14. #16812026C4semidirect
75. C107#1757semidirect

Maximal subgroups

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

subgroupindex
C2×#168121162
#202926112
#202925832
#202923972
#410×C1072
#1757107