Finite Group Databasebeta

← #28335796

Subgroups — #28335796

Order 13696.

184 conjugacy classes of subgroups; only the 45 normal subgroups are shown.

normal subgroups only

This group has 184 conjugacy classes of subgroups — too many to draw. Only its 45 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#20293381C211yesmaximal, characteristic
2#20293036C211yesmaximal, characteristic, complemented
3#20292997C211yesmaximal, characteristic, complemented
4#20292987C211yesmaximal, characteristic
5#20292368C211yesmaximal, characteristic, complemented
6#20292366C211yesmaximal, characteristic
7#330×C107C211yesmaximal, characteristic, complemented
8#16812109C2211yescharacteristic
9#16812108—21no—
10#16812104—21no—
11#16812104—21no—
12#16812101C2211yescharacteristic
13#16812097C2211yescharacteristic
14#16812094—21no—
15#16812089—21no—
16#16812087—21no—
17#16812043—21no—
18#16812041—21no—
19#16812034—21no—
20#16812032—21no—
21#16812032—21no—
22#16812031—21no—
23#16812020C2211yescharacteristic
24#125×C107C2211yescharacteristic
25#97×C107C2211yescharacteristic
26#97×C107C2211yescharacteristic
27C2×Dic214—21no—
28C2×Dic214—21no—
29C2×Dic214D411yescharacteristic
30C2×D428D411yescharacteristic
31C2×C4×D107—21no—
32C2×C107⋊C8—21no—
33C4⋊Dic107—21no—
34C4⋊Dic107—21no—
35C4⋊Dic107—21no—
36C4⋊Dic107D411yescharacteristic
37C4⋊Dic107D411yescharacteristic
38Dic107⋊C4—21no—
39Dic107⋊C4—21no—
40Dic107⋊C4—21no—
41(C2×D107)⋊C4—21no—
42(C2×D107)⋊C4—21no—
43(C2×D107)⋊C4—21no—
44(C2×D107)⋊C4—21no—
45(C2×D107)⋊C4—21no—
46C4×Dic107—21no—
47C2×C8×C107—21no—
48C2×C8×C107—21no—
49C4⋊C4×C107—21no—
50C4⋊C4×C107—21no—
51C4⋊C4×C107D411yescharacteristic
52C4⋊C4×C107D411yescharacteristic
53C42×C107C2311yescharacteristic
54C22×D107—21no—
55C2×C4×C107—21no—
56C2×C4×C107—21no—
57C2×C4×C107C2×D411yescharacteristic
58C2×C4×C107C2×D411yescharacteristic
59C2×C4×C107C2×D411yescharacteristic
60C2×Dic107—21no—
61C2×Dic107—21no—
62C2×Dic107—21no—
63C2×Dic107—41no—
64D428—41no—
65C4×D107—81no—
66Dic214—41no—
67Dic214—42no—
68Dic214—81no—
69C8×C107—22no—
70C8×C107—41no—
71C107⋊C8—41no—
72C22×C107#12011yescharacteristic
73C2×D107—41no—
74C2×D107—41no—
75C2×D107—41no—
76C4×C107—21no—
77C4×C107—21no—
78C4×C107—21no—
79C4×C107—41no—
80C4×C107—41no—
81Dic107—41no—
82Dic107—41no—
83Dic107—41no—
84Dic107—81no—
85C2×C107#45411yescharacteristic
86C2×C107#45511yescharacteristic
87C2×C107#45611yescharacteristic
88D107—81no—
89#1664—1071nomaximal, Sylow
90C107#166411yescharacteristic, complemented, Sylow
91#563—1071no—
92#501—1071no—
93#491—1071no—
94#489—1071no—
95#330—1071no—
96#330D10711yescharacteristic, complemented
97#329—1071no—
98C4⋊Q8—1071no—
99C4⋊Q8—2141no—
100#126—2141no—
101#126—2141no—
102#125—1071no—
103#125C2×D10711yescharacteristic
104#124—1071no—
105#123—2141no—
106C22⋊Q8—2141no—
107C22⋊Q8—2141no—
108#107—2141no—
109#106—2141no—
110#103—2141no—
111#103—2141no—
112#103—2141no—
113#102—2141no—
114#97—1071no—
115#97C2×D10711yescharacteristic
116#97C2×D10711yescharacteristic
117C2×Q8—1071no—
118C2×Q8—2141no—
119C2×Q8—2141no—
120C2×D4—1071no—
121C22×C4—2141no—
122C2×C8—21no—
123C2×C8—21no—
124C2×C8—2141no—
125C4⋊C4—21no—
126C4⋊C4—21no—
127C4⋊C4—1071no—
128C4⋊C4—1071no—
129C4⋊C4—2141no—
130C4⋊C4—2141no—
131C4⋊C4—2141no—
132C4⋊C4—2141no—
133C4⋊C4—2141no—
134C4⋊C4—2141no—
135C4⋊C4D42811yescharacteristic
136C4⋊C4D42811yescharacteristic
137C22⋊C4—2141no—
138C22⋊C4—2141no—
139C22⋊C4—2141no—
140C22⋊C4—2141no—
141C22⋊C4—2141no—
142C42—2141no—
143C42C22×D10711yescharacteristic
144C23—2141no—
145Q8—8561no—
146Q8—4282no—
147Q8—4281no—
148D4—4281no—
149C2×C4—21no—
150C2×C4—21no—
151C2×C4—8561no—
152C2×C4—4281no—
153C2×C4—2141no—
154C2×C4—2141no—
155C2×C4—2141no—
156C2×C4D4×D10711yescharacteristic
157C2×C4D4×D10711yescharacteristic
158C2×C4C2×D42811yescharacteristic
159C8—22no—
160C8—41no—
161C8—4281no—
162C22—4281no—
163C22—4281no—
164C22—4281no—
165C22#1681207911yescharacteristic
166C4—21no—
167C4—21no—
168C4—21no—
169C4—41no—
170C4—41no—
171C4—8561no—
172C4—4281no—
173C4—4281no—
174C4—4281no—
175C2—8561no—
176C2#2029280211yescharacteristic
177C2#2029280611yescharacteristic
178C2#2029281111yescharacteristic
subgroupG/H
centerC22#16812079
commutator, cosocleC42×C107C23
FrattiniC42C22×D107
Fitting#330×C107C2
socleC22×C107#120
prime radicalC2×D428D4
hypercenter#330D107
hypocenterC107#1664
LCSG ▷ C42×C107 ▷ C22×C107 ▷ C107
UCSC1 ◁ C22 ◁ C42 ◁ #330

Complements

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

NH ≅ G/Ntype
2. #20293036C2semidirect
3. #20292997C2semidirect
5. #20292368C2semidirect
7. #330×C107C2semidirect
90. C107#1664semidirect
96. #330D107semidirect

Maximal subgroups

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

subgroupindex
#202933812
#202930362
#202929972
#202929872
#202923682
#202923662
#330×C1072
#1664107