Finite Group Databasebeta

← #28335774

Subgroups — #28335774

Order 13696.

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

normal subgroups only

This group has 196 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#20293037C211yesmaximal, characteristic, complemented
3#20293036C211yesmaximal, characteristic, complemented
4#20293021C211yesmaximal, characteristic
5#20292368C211yesmaximal, characteristic, complemented
6#20292366C211yesmaximal, characteristic
7#330×C107C211yesmaximal, characteristic, complemented
8C2×Dic428—21no—
9C2×#13133807—21no—
10#16812109C2211yescharacteristic
11#16812108—21no—
12#16812104—21no—
13#16812104—21no—
14#16812101C2211yescharacteristic
15#16812097C2211yescharacteristic
16#16812094—21no—
17#16812089—21no—
18#16812087—21no—
19#16812043—21no—
20#16812042—21no—
21#16812041—21no—
22#16812040—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—
32Dic428—42no—
33#13133807—42no—
34C2×C107⋊C8—21no—
35C4⋊Dic107—21no—
36C4⋊Dic107—21no—
37C4⋊Dic107—21no—
38C4⋊Dic107D411yescharacteristic
39C4⋊Dic107D411yescharacteristic
40Dic107⋊C4—21no—
41Dic107⋊C4—21no—
42Dic107⋊C4—21no—
43(C2×D107)⋊C4—21no—
44(C2×D107)⋊C4—21no—
45(C2×D107)⋊C4—21no—
46(C2×D107)⋊C4—21no—
47(C2×D107)⋊C4—21no—
48C4×Dic107—21no—
49C2×C8×C107—21no—
50C2×C8×C107—21no—
51C4⋊C4×C107—21no—
52C4⋊C4×C107—21no—
53C4⋊C4×C107D411yescharacteristic
54C4⋊C4×C107D411yescharacteristic
55C42×C107C2311yescharacteristic
56C22×D107—21no—
57C2×C4×C107—21no—
58C2×C4×C107—21no—
59C2×C4×C107C2×D411yescharacteristic
60C2×C4×C107C2×D411yescharacteristic
61C2×C4×C107C2×D411yescharacteristic
62C2×Dic107—21no—
63C2×Dic107—21no—
64C2×Dic107—21no—
65C2×Dic107—41no—
66D428—41no—
67C4×D107—81no—
68Dic214—41no—
69Dic214—41no—
70Dic214—41no—
71Dic214—81no—
72C8×C107—22no—
73C8×C107—22no—
74C107⋊C8—22no—
75C22×C107#12011yescharacteristic
76C2×D107—41no—
77C2×D107—41no—
78C2×D107—41no—
79C4×C107—21no—
80C4×C107—21no—
81C4×C107—21no—
82C4×C107—41no—
83C4×C107—41no—
84Dic107—41no—
85Dic107—41no—
86Dic107—41no—
87Dic107—81no—
88C2×C107#45311yescharacteristic
89C2×C107#45611yescharacteristic
90C2×C107#45611yescharacteristic
91D107—81no—
92#1660—1071nomaximal, Sylow
93C107#166011yescharacteristic, complemented, Sylow
94#563—1071no—
95#501—1071no—
96#501—1071no—
97#497—1071no—
98#330—1071no—
99#330D10711yescharacteristic, complemented
100#329—1071no—
101C2×Q16—2141no—
102C2×SD16—2141no—
103C4⋊Q8—1071no—
104C4⋊Q8—2141no—
105#126—2141no—
106#126—2141no—
107#125—1071no—
108#125C2×D10711yescharacteristic
109#124—1071no—
110#123—2141no—
111C22⋊Q8—2141no—
112C22⋊Q8—2141no—
113#107—2141no—
114#107—2141no—
115#106—2141no—
116#106—2141no—
117#97—1071no—
118#97C2×D10711yescharacteristic
119#97C2×D10711yescharacteristic
120C2×Q8—1071no—
121C2×Q8—2141no—
122C2×Q8—2141no—
123C2×D4—1071no—
124C22×C4—2141no—
125Q16—4282no—
126SD16—4282no—
127C2×C8—21no—
128C2×C8—21no—
129C2×C8—2141no—
130C4⋊C4—21no—
131C4⋊C4—21no—
132C4⋊C4—1071no—
133C4⋊C4—1071no—
134C4⋊C4—2141no—
135C4⋊C4—2141no—
136C4⋊C4—2141no—
137C4⋊C4—2141no—
138C4⋊C4—2141no—
139C4⋊C4—2141no—
140C4⋊C4D42811yescharacteristic
141C4⋊C4D42811yescharacteristic
142C22⋊C4—2141no—
143C22⋊C4—2141no—
144C22⋊C4—2141no—
145C22⋊C4—2141no—
146C22⋊C4—2141no—
147C42—2141no—
148C42C22×D10711yescharacteristic
149C23—2141no—
150Q8—8561no—
151Q8—4281no—
152Q8—4281no—
153Q8—4281no—
154D4—4281no—
155C2×C4—21no—
156C2×C4—21no—
157C2×C4—8561no—
158C2×C4—4281no—
159C2×C4—2141no—
160C2×C4—2141no—
161C2×C4—2141no—
162C2×C4D4×D10711yescharacteristic
163C2×C4D4×D10711yescharacteristic
164C2×C4C2×D42811yescharacteristic
165C8—22no—
166C8—22no—
167C8—2142no—
168C22—4281no—
169C22—4281no—
170C22—4281no—
171C22#1681207911yescharacteristic
172C4—21no—
173C4—21no—
174C4—21no—
175C4—41no—
176C4—41no—
177C4—8561no—
178C4—4281no—
179C4—4281no—
180C4—4281no—
181C2—8561no—
182C2#2029279611yescharacteristic
183C2#2029281111yescharacteristic
184C2#2029281211yescharacteristic
subgroupG/H
centerC22#16812079
commutator, cosocleC42×C107C23
FrattiniC42C22×D107
Fitting#330×C107C2
socleC22×C107#120
prime radicalC2×D428D4
hypercenter#330D107
hypocenterC107#1660
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. #20293037C2semidirect
3. #20293036C2semidirect
5. #20292368C2semidirect
7. #330×C107C2semidirect
93. C107#1660semidirect
99. #330D107semidirect

Maximal subgroups

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

subgroupindex
#202933812
#202930372
#202930362
#202930212
#202923682
#202923662
#330×C1072
#1660107