Finite Group Databasebeta

← #28335794

Subgroups — #28335794

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#20293377C211yesmaximal, characteristic
2#20293033C211yesmaximal, characteristic, complemented
3#20292995C211yesmaximal, characteristic, complemented
4#20292368C211yesmaximal, characteristic, complemented
5#20292368C211yesmaximal, characteristic, complemented
6#20292367C211yesmaximal, characteristic
7#489×C107C211yesmaximal, characteristic
8#16812107—21no—
9#16812102—21no—
10#16812102—21no—
11#16812101C2211yescharacteristic
12#16812101C2211yescharacteristic
13#16812090—21no—
14#16812086—21no—
15#16812086—21no—
16#16812042—21no—
17#16812040—21no—
18#16812033—21no—
19#16812033—21no—
20#16812020C2211yescharacteristic
21#16812020C2211yescharacteristic
22C4⋊Q8×C107C2211yescharacteristic
23#124×C107C2211yescharacteristic
24#103×C107—21no—
25#102×C107—21no—
26#97×C107C2211yescharacteristic
27C2×Dic214—21no—
28C22×Dic107—21no—
29C2×C107⋊C8—21no—
30C2×C107⋊C8—21no—
31C4⋊Dic107D411yescharacteristic
32C4⋊Dic107D411yescharacteristic
33C4⋊Dic107D411yescharacteristic
34C4⋊Dic107D411yescharacteristic
35Dic107⋊C4—21no—
36Dic107⋊C4—21no—
37Dic107⋊C4—21no—
38Dic107⋊C4—21no—
39Dic107⋊C4—21no—
40Dic107⋊C4—21no—
41C22⋊Dic107—21no—
42C22⋊Dic107—21no—
43C22⋊Dic107—21no—
44C4×Dic107—21no—
45C2×Q8×C107—21no—
46C2×Q8×C107D411yescharacteristic
47C2×D4×C107D411yescharacteristic
48C2×C8×C107—21no—
49C4⋊C4×C107—21no—
50C4⋊C4×C107—21no—
51C22⋊C4×C107—21no—
52C22⋊C4×C107—21no—
53C42×C107C2311yescharacteristic
54C23×C107—21no—
55Q8×C107—41no—
56Q8×C107—42no—
57D4×C107—41no—
58C2×C4×C107—21no—
59C2×C4×C107—41no—
60C2×C4×C107C2×D411yescharacteristic
61C2×C4×C107C2×D411yescharacteristic
62C2×C4×C107C2×D411yescharacteristic
63C2×Dic107—21no—
64C2×Dic107—21no—
65C2×Dic107—21no—
66C2×Dic107—21no—
67C2×Dic107—81no—
68Dic214—81no—
69C8×C107—41no—
70C107⋊C8—22no—
71C107⋊C8—41no—
72C22×C107—41no—
73C22×C107—41no—
74C22×C107—41no—
75C22×C107#12011yescharacteristic
76C4×C107—21no—
77C4×C107—21no—
78C4×C107—21no—
79C4×C107—41no—
80C4×C107—81no—
81Dic107—41no—
82Dic107—41no—
83Dic107—41no—
84Dic107—41no—
85C2×C107—81no—
86C2×C107#45411yescharacteristic
87C2×C107#45511yescharacteristic
88C2×C107#45611yescharacteristic
89#1664—1071nomaximal, Sylow
90C107#166411yescharacteristic, complemented, Sylow
91#563—1071no—
92#501—1071no—
93#491—1071no—
94#489D10711yescharacteristic
95#330—1071no—
96#330—1071no—
97#329—1071no—
98C4⋊Q8—2141no—
99C4⋊Q8C2×D10711yescharacteristic
100#126—2141no—
101#126—2141no—
102#125—1071no—
103#125—1071no—
104#124C2×D10711yescharacteristic
105#123—2141no—
106C22⋊Q8—2141no—
107C22⋊Q8—2141no—
108#107—2141no—
109#106—2141no—
110#103—21no—
111#103—2141no—
112#103—2141no—
113#102—21no—
114#97—1071no—
115#97—1071no—
116#97C2×D10711yescharacteristic
117C2×Q8—21no—
118C2×Q8—2141no—
119C2×Q8C22⋊D10711yescharacteristic
120C2×D4C22⋊D10711yescharacteristic
121C22×C4—2141no—
122C2×C8—21no—
123C2×C8—2141no—
124C2×C8—2141no—
125C4⋊C4—21no—
126C4⋊C4—21no—
127C4⋊C4—1071no—
128C4⋊C4—1071no—
129C4⋊C4—1071no—
130C4⋊C4—1071no—
131C4⋊C4—2141no—
132C4⋊C4—2141no—
133C4⋊C4—2141no—
134C4⋊C4—2141no—
135C4⋊C4—2141no—
136C4⋊C4—2141no—
137C22⋊C4—21no—
138C22⋊C4—21no—
139C22⋊C4—2141no—
140C22⋊C4—2141no—
141C22⋊C4—2141no—
142C42—2141no—
143C42C22×D10711yescharacteristic
144C23—21no—
145Q8—41no—
146Q8—42no—
147Q8—8561no—
148D4—41no—
149C2×C4—21no—
150C2×C4—41no—
151C2×C4—8561no—
152C2×C4—2141no—
153C2×C4—2141no—
154C2×C4—2141no—
155C2×C4—2141no—
156C2×C4D4×D10711yescharacteristic
157C2×C4D4×D10711yescharacteristic
158C2×C4C2×C22⋊D10711yescharacteristic
159C8—41no—
160C8—4281no—
161C8—2142no—
162C22—41no—
163C22—41no—
164C22—41no—
165C22#1681207711yescharacteristic
166C4—21no—
167C4—21no—
168C4—21no—
169C4—41no—
170C4—81no—
171C4—4281no—
172C4—4281no—
173C4—4281no—
174C4—4281no—
175C2—81no—
176C2#2029279811yescharacteristic
177C2#2029280411yescharacteristic
178C2#2029280811yescharacteristic
subgroupG/H
centerC22#16812077
commutator, cosocleC42×C107C23
FrattiniC42C22×D107
Fitting#489×C107C2
socleC22×C107#120
prime radicalC2×D4×C107D4
hypercenter#489D107
hypocenterC107#1664
LCSG ▷ C42×C107 ▷ C22×C107 ▷ C107
UCSC1 ◁ C22 ◁ C42 ◁ #489

Complements

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

NH ≅ G/Ntype
2. #20293033C2semidirect
3. #20292995C2semidirect
4. #20292368C2semidirect
5. #20292368C2semidirect
90. C107#1664semidirect

Maximal subgroups

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

subgroupindex
#202933772
#202930332
#202929952
#202923682
#202923672
#489×C1072
#1664107