Finite Group Databasebeta

← #28336981

Subgroups — #28336981

Order 13696.

312 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 312 conjugacy classes of subgroups — too many to draw. Only its 85 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#20293394C211yesmaximal, characteristic
2#20293198C211yesmaximal, characteristic
3#20292635C212yesmaximal, complemented
4#20292383C212yesmaximal, complemented
5#410×C107C211yesmaximal, characteristic
6C22×Dic214C2211yescharacteristic
7#16812116—24no—
8C2×#13133802—22no—
9C2×#13133802C2212yes—
10#16812107C412yescomplemented
11#16812096C412yescomplemented
12#16812090—22no—
13#16812088—22no—
14#16812068C2211yescharacteristic
15#16812032—24no—
16C2×#41×C107C2211yescharacteristic
17#117×C107C2212yes—
18#99×C107—22no—
19C2×Dic214—22no—
20C2×Dic214—22no—
21C2×Dic214—21no—
22C2×Dic214C2×C412yes—
23C22×Dic107—21no—
24#13133802—24no—
25#13133802—22no—
26#13133802—22no—
27C2×C107⋊C8—24no—
28C2×C107⋊C8D414yes—
29C4⋊Dic107—21no—
30Dic107⋊C4—24no—
31C22⋊Dic107—24no—
32C22⋊Dic107—21no—
33C4×Dic107C2×C412yes—
34#41×C107—22no—
35#41×C107—22no—
36C2×Q8×C107C2×C411yescharacteristic
37C2×D4×C107C2×C411yescharacteristic
38C2×D4×C107D412yes—
39C22×C4×C107D412yes—
40C22×C4×C107C2311yescharacteristic
41C4⋊C4×C107—22no—
42C22⋊C4×C107—22no—
43C42×C107—22no—
44C23×C107C22⋊C412yes—
45C23×C107C2×D411yescharacteristic
46Q8×C107—22no—
47D4×C107—24no—
48D4×C107—22no—
49C2×C4×C107—22no—
50C2×C4×C107—22no—
51C2×C4×C107—42no—
52C2×C4×C107C22⋊C412yes—
53C2×C4×C107C22×C411yescharacteristic
54C2×C4×C107C2×D412yes—
55C2×C4×C107C2×D411yescharacteristic
56C2×C4×C107#4112yes—
57C2×Dic107—22no—
58C2×Dic107—22no—
59C2×Dic107—42no—
60Dic214—24no—
61Dic214—41no—
62Dic214—41no—
63C107⋊C8—24no—
64C22×C107—22no—
65C22×C107—41no—
66C22×C107—42no—
67C22×C107C2×C22⋊C411yescharacteristic
68C22×C107#12112yes—
69C4×C107—22no—
70C4×C107—82no—
71C4×C107C4×D412yes—
72C4×C107#12011yescharacteristic
73C4×C107#12311yescharacteristic
74Dic107—42no—
75Dic107—42no—
76C2×C107—21no—
77C2×C107—22no—
78C2×C107—42no—
79C2×C107#38611yescharacteristic
80#1909—1071nomaximal, Sylow
81C107#190911yescharacteristic, complemented, Sylow
82#568—1071no—
83#536—1071no—
84#419—1072no—
85#410D10711yescharacteristic
86H(3,ℤ/4)—1072no—
87C2×#41C2×D10711yescharacteristic
88C22×Q8—1071no—
89#131—2144no—
90C2×M16—1072no—
91C2×M16—2142no—
92C4⋊Q8—1072no—
93#124—1072no—
94#123—2142no—
95C22⋊Q8—2142no—
96#117—1071no—
97#117C2×D10712yes—
98#103—2144no—
99#99—22no—
100#41—22no—
101#41—22no—
102C2×Q8—1072no—
103C2×Q8—2142no—
104C2×Q8—2142no—
105C2×Q8—2141no—
106C2×Q8C4×D10711yescharacteristic
107C2×D4C4×D10711yescharacteristic
108C2×D4C22⋊D10712yes—
109C22×C4—2141no—
110C22×C4D42812yes—
111C22×C4C22×D10711yescharacteristic
112M16—2144no—
113M16—2142no—
114M16—2142no—
115C2×C8—1074no—
116C2×C8—2144no—
117C4⋊C4—22no—
118C4⋊C4—2144no—
119C4⋊C4—2141no—
120C22⋊C4—22no—
121C22⋊C4—2144no—
122C22⋊C4—2141no—
123C42—22no—
124C42—1072no—
125C23(C2×D107)⋊C412yes—
126C23C2×C22⋊D10711yescharacteristic
127Q8—22no—
128Q8—4281no—
129Q8—4281no—
130Q8—2144no—
131D4—24no—
132D4—22no—
133C2×C4—22no—
134C2×C4—22no—
135C2×C4—42no—
136C2×C4—4282no—
137C2×C4—2142no—
138C2×C4—2142no—
139C2×C4(C2×D107)⋊C412yes—
140C2×C4C2×C4×D10711yescharacteristic
141C2×C4D4×D10712yes—
142C2×C4C2×D42811yescharacteristic
143C2×C4#1313381712yes—
144C8—2144no—
145C22—22no—
146C22—41no—
147C22—42no—
148C22C2×(C2×D107)⋊C411yescharacteristic
149C22#1681208112yes—
150C4—22no—
151C4—82no—
152C4—4282no—
153C4—4282no—
154C4(C22⋊D107)⋊C412yes—
155C4#1681207911yescharacteristic
156C4#1681209311yescharacteristic
157C2—22no—
158C2—21no—
159C2—42no—
160C2#2029250411yescharacteristic
subgroupG/H
centerC2#20292504
commutatorC2×C4×C107C22×C4
FrattiniC22×C4C22×D107
Fitting#410×C107C2
socleC2×C107#386
prime radicalC2×#41×C107C22
cosocleC22×C4×C107C23
hypercenter#410D107
hypocenterC107#1909
LCSG ▷ C2×C4×C107 ▷ C2×C107 ▷ C107
UCSC1 ◁ C2 ◁ C22×C4 ◁ #410

Complements

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

NH ≅ G/Ntype
3. #20292635C2semidirect
4. #20292383C2semidirect
10. #16812107C4semidirect
11. #16812096C4semidirect
81. C107#1909semidirect

Maximal subgroups

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

subgroupindex
#202933942
#202931982
#202926352
#202923832
#410×C1072
#1909107