Finite Group Databasebeta

← #28335471

Subgroups — #28335471

Order 13696.

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

normal subgroups only

This group has 210 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#20292958C212yesmaximal
3#20292557C211yesmaximal, characteristic
4#20292365C212yesmaximal
5#324×C107C211yesmaximal, characteristic
6#16812108—22no—
7#16812100—22no—
8#16812088—21no—
9#16812088C2212yes—
10#16812068—21no—
11C2×C4⋊Dic107C2211yescharacteristic
12C2×Dic107⋊C4—21no—
13#16812041—22no—
14#16812034—22no—
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—
30Dic107⋊C4—42no—
31C22⋊Dic107—22no—
32C4×Dic107—22no—
33C22×C4×C107D411yescharacteristic
34C22×C4×C107D411yescharacteristic
35C22×C4×C107C2311yescharacteristic
36C2×C8×C107—22no—
37C4⋊C4×C107—22no—
38C23×C107C2×D411yescharacteristic
39C2×C4×C107—21no—
40C2×C4×C107—21no—
41C2×C4×C107—21no—
42C2×C4×C107—41no—
43C2×C4×C107—41no—
44C2×C4×C107SD1612yes—
45C2×C4×C107C2×D412yes—
46C2×Dic107—22no—
47C2×Dic107—22no—
48C2×Dic107—22no—
49C2×Dic107—41no—
50C2×Dic107—41no—
51C2×Dic107—41no—
52C2×Dic107—41no—
53C2×Dic107—41no—
54Dic214—42no—
55Dic214—81no—
56C8×C107—42no—
57C22×C107—21no—
58C22×C107—21no—
59C22×C107#12011yescharacteristic
60C22×C107C2×SD1611yescharacteristic
61C22×C107#13711yescharacteristic
62C4×C107—22no—
63C4×C107—22no—
64C4×C107—41no—
65Dic107—42no—
66Dic107—42no—
67Dic107—42no—
68Dic107—81no—
69C2×C107—21no—
70C2×C107—21no—
71C2×C107#44811yescharacteristic
72C2×C107#45611yescharacteristic
73C2×C107#45811yescharacteristic
74#1611—1071nomaximal, Sylow
75C107#161111yescharacteristic, complemented, Sylow
76#544—1071no—
77#483—1072no—
78#398—1071no—
79#328—1072no—
80#324D10711yescharacteristic
81C4⋊Q8—2142no—
82#125—2142no—
83C22⋊Q8—1072no—
84C22⋊Q8—2141no—
85#117—2141no—
86C2×C4⋊C4—1071no—
87C2×C4⋊C4—2141no—
88C2×C4⋊C4C2×D10711yescharacteristic
89#106—2142no—
90#103—2142no—
91C22⋊C8C2×D10712yes—
92#95—1071no—
93#95—2141no—
94C2×Q8—1072no—
95C2×Q8—2141no—
96C22×C4—2141no—
97C22×C4—2141no—
98C22×C4D42811yescharacteristic
99C22×C4D42811yescharacteristic
100C22×C4C22×D10711yescharacteristic
101C2×C8—22no—
102C4⋊C4—22no—
103C4⋊C4—1072no—
104C4⋊C4—4282no—
105C4⋊C4—2141no—
106C4⋊C4—2141no—
107C4⋊C4—2141no—
108C4⋊C4—2142no—
109C4⋊C4—2142no—
110C4⋊C4—2142no—
111C22⋊C4—2142no—
112C42—2142no—
113C23C2×D42811yescharacteristic
114Q8—8561no—
115Q8—4282no—
116C2×C4—21no—
117C2×C4—21no—
118C2×C4—21no—
119C2×C4—41no—
120C2×C4—41no—
121C2×C4—4281no—
122C2×C4—4281no—
123C2×C4—4281no—
124C2×C4—4281no—
125C2×C4—4281no—
126C2×C4—2142no—
127C2×C4—2142no—
128C2×C4—2142no—
129C2×C4#1313380712yes—
130C2×C4D4×D10712yes—
131C8—42no—
132C22—21no—
133C22—21no—
134C22#1681207911yescharacteristic
135C22C2×#1313380711yescharacteristic
136C22#1681214211yescharacteristic
137C4—22no—
138C4—22no—
139C4—41no—
140C4—8561no—
141C4—4282no—
142C4—4282no—
143C4—4282no—
144C2—21no—
145C2—21no—
146C2#2029276811yescharacteristic
147C2#2029281211yescharacteristic
148C2#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#1611
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
75. C107#1611semidirect

Maximal subgroups

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

subgroupindex
#202932582
#202929582
#202925572
#202923652
#324×C1072
#1611107