Finite Group Databasebeta

← #28335534

Subgroups — #28335534

Order 13696.

236 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 236 conjugacy classes of subgroups — too many to draw. Only its 55 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#20293338C211yesmaximal, characteristic, complemented
2#20293001C211yesmaximal, characteristic, complemented
3#20292828C211yesmaximal, characteristic, complemented
4#20292823C211yesmaximal, characteristic
5#20292357C211yesmaximal, characteristic, complemented
6#20292354C211yesmaximal, characteristic, complemented
7#333×C107C211yesmaximal, characteristic, complemented
8C2×#13133807—21no—
9C2×#13133805—22no—
10C2×D856—21no—
11#16812106C2211yescharacteristic
12#16812100—21no—
13#16812089—21no—
14#16812085—22no—
15C4×Dic214C2211yescharacteristic
16C4×D428C2211yescharacteristic
17#16812071—21no—
18C4⋊C4×D107—21no—
19#16812031—21no—
20#16812031—21no—
21C4×C107⋊C8C2211yescharacteristic
22C4⋊Q8×C107C2211yescharacteristic
23C4⋊C8×C107C2211yescharacteristic
24C4⋊C8×C107C2211yescharacteristic
25C2×Dic214D411yescharacteristic
26C2×D428—21no—
27C2×D428—21no—
28C2×D428—21no—
29C2×D428D411yescharacteristic
30C2×C4×D107—21no—
31C2×C4×D107—22no—
32#13133807—42no—
33#13133805—44no—
34D856—42no—
35C2×C107⋊C8—21no—
36C4⋊Dic107—22no—
37C4⋊Dic107D411yescharacteristic
38C4⋊Dic107D411yescharacteristic
39Dic107⋊C4—22no—
40Dic107⋊C4—21no—
41(C2×D107)⋊C4—22no—
42(C2×D107)⋊C4—21no—
43C4×Dic107—21no—
44C2×Q8×C107D412yes—
45C2×C8×C107—21no—
46C2×C8×C107—21no—
47C4⋊C4×C107—21no—
48C4⋊C4×C107—21no—
49C42×C107C2311yescharacteristic
50C22×D107—21no—
51C22×D107—41no—
52Q8×C107—42no—
53C2×C4×C107—22no—
54C2×C4×C107C2×D411yescharacteristic
55C2×C4×C107C2×D411yescharacteristic
56C2×C4×C107C2×D411yescharacteristic
57C2×Dic107—21no—
58C2×Dic107—21no—
59C2×Dic107—21no—
60D428—21no—
61D428—42no—
62D428—41no—
63D428—41no—
64D428—41no—
65D428—41no—
66D428SD1612yescomplemented
67C4×D107—41no—
68C4×D107—41no—
69C4×D107—82no—
70Dic214—21no—
71Dic214—21no—
72C8×C107—41no—
73C8×C107—41no—
74C107⋊C8—22no—
75C22×C107#12011yescharacteristic
76C2×D107—22no—
77C2×D107—41no—
78C2×D107—41no—
79C2×D107—81no—
80C2×D107—81no—
81C2×D107—81no—
82C4×C107—21no—
83C4×C107—42no—
84C4×C107C2×SD1611yescharacteristic
85C4×C107#13511yescharacteristic
86C4×C107AGL(1,ℤ/8)11yescharacteristic
87C4×C107#13711yescharacteristic
88Dic107—41no—
89Dic107—41no—
90Dic107—41no—
91C2×C107#44811yescharacteristic
92C2×C107#44911yescharacteristic
93C2×C107#45311yescharacteristic
94D107—42no—
95D107—161no—
96#1622—1071nomaximal, Sylow
97C107#162211yescharacteristic, complemented, Sylow
98#554—1071no—
99#492—1071no—
100#460—1071no—
101#459—1071no—
102#333D10711yescharacteristic, complemented
103Q8⋊C8—1071no—
104D4⋊C8—1071no—
105C2×SD16—2141no—
106C2×SD16—2142no—
107C2×D8—2141no—
108C4⋊Q8C2×D10711yescharacteristic
109#127—1071no—
110#125—2141no—
111C22⋊Q8—2141no—
112C22⋊Q8—2142no—
113C4×Q8—1071no—
114C4×D4—1071no—
115C4×D4—2141no—
116C2×C4⋊C4—2141no—
117C4⋊C8C2×D10711yescharacteristic
118C4⋊C8C2×D10711yescharacteristic
119#102—2141no—
120#102—2141no—
121C4×C8—1071no—
122C2×Q8—1071no—
123C2×Q8D42812yes—
124C2×D4—1071no—
125C2×D4—2141no—
126C2×D4—2141no—
127C2×D4—2141no—
128C22×C4—2142no—
129C22×C4—2141no—
130SD16—4282no—
131SD16—4284no—
132D8—4282no—
133C2×C8—21no—
134C2×C8—21no—
135C2×C8—2141no—
136C4⋊C4—21no—
137C4⋊C4—21no—
138C4⋊C4—1071no—
139C4⋊C4—1071no—
140C4⋊C4—2142no—
141C4⋊C4—2142no—
142C4⋊C4—2141no—
143C22⋊C4—2142no—
144C22⋊C4—2141no—
145C42—2141no—
146C42C22×D10711yescharacteristic
147C23—4281no—
148C23—2141no—
149Q8—42no—
150Q8—2141no—
151Q8—2141no—
152D4—1072no—
153D4—4282no—
154D4—4281no—
155D4—4281no—
156D4—4281no—
157D4—4281no—
158D4—2141no—
159C2×C4—22no—
160C2×C4—8562no—
161C2×C4—4281no—
162C2×C4—4281no—
163C2×C4—2141no—
164C2×C4—2141no—
165C2×C4—2141no—
166C2×C4D4×D10711yescharacteristic
167C2×C4D4×D10711yescharacteristic
168C2×C4C2×D42811yescharacteristic
169C8—41no—
170C8—41no—
171C8—2142no—
172C22—8561no—
173C22—8561no—
174C22—8561no—
175C22—4281no—
176C22—4281no—
177C22—2142no—
178C22#1681207911yescharacteristic
179C4—21no—
180C4—42no—
181C4—4281no—
182C4—4281no—
183C4—4281no—
184C4SD16×D10711yescharacteristic
185C4#1681213211yescharacteristic
186C4#1681213611yescharacteristic
187C4#1681214111yescharacteristic
188C2—4282no—
189C2—17121no—
190C2#2029276711yescharacteristic
191C2#2029277511yescharacteristic
192C2#2029279711yescharacteristic
subgroupG/H
centerC22#16812079
commutator, cosocleC42×C107C23
FrattiniC42C22×D107
Fitting#333×C107C2
socleC22×C107#120
prime radical#20292823C2
hypercenter#333D107
hypocenterC107#1622
LCSG ▷ C42×C107 ▷ C22×C107 ▷ C107
UCSC1 ◁ C22 ◁ C42 ◁ #333

Complements

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

NH ≅ G/Ntype
1. #20293338C2semidirect
2. #20293001C2semidirect
3. #20292828C2semidirect
5. #20292357C2semidirect
6. #20292354C2semidirect
7. #333×C107C2semidirect
66. D428SD16semidirect
97. C107#1622semidirect
102. #333D107semidirect

Maximal subgroups

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

subgroupindex
#202933382
#202930012
#202928282
#202928232
#202923572
#202923542
#333×C1072
#1622107