Finite Group Databasebeta

← #28338436

Subgroups — #28338436

Order 13696.

206 conjugacy classes of subgroups; only the 47 normal subgroups are shown.

normal subgroups only

This group has 206 conjugacy classes of subgroups — too many to draw. Only its 47 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#20293441C211yesmaximal, characteristic
2C2×#16812055C211yesmaximal, characteristic, complemented
3#20292899C211yesmaximal, characteristic, complemented
4#20292444C211yesmaximal, characteristic, complemented
5#20292434C211yesmaximal, characteristic, complemented
6#20292412C211yesmaximal, characteristic, complemented
7#510×C107C211yesmaximal, characteristic, complemented
8#16812156—21no—
9#16812140—21no—
10#16812139—21no—
11#16812138—22no—
12#16812128—21no—
13C2×Dic428C2211yescharacteristic
14Q16×D107—21no—
15#16812115C2211yescharacteristic
16#16812055—22no—
17C2×C107⋊C16C2211yescharacteristic
18#16812045C2211yescharacteristic
19#16812028—21no—
20#135×C107C2211yescharacteristic
21C2×Q16×C107C2211yescharacteristic
22Q32×C107—21no—
23SD32×C107—21no—
24M32×C107C2211yescharacteristic
25#13133818—41no—
26#13133818D411yescharacteristic
27#13133817—22no—
28#13133817—42no—
29C2×Dic214—21no—
30C2×Dic214—41no—
31Q8×D107—22no—
32Dic428—21no—
33Dic428D412yes—
34#13133808—22no—
35#13133808—41no—
36#13133806—22no—
37#13133805—41no—
38#13133802—21no—
39#13133802D411yescharacteristic
40#13133801—21no—
41C8×D107—21no—
42C107⋊C16—21no—
43#41×C107—21no—
44C2×Q8×C107—21no—
45Q16×C107—21no—
46Q16×C107—21no—
47Q16×C107D411yescharacteristic
48SD16×C107—21no—
49D8×C107D411yescharacteristic
50C2×C8×C107C2311yescharacteristic
51C16×C107—21no—
52Q8×C107—21no—
53Q8×C107—41no—
54Q8×C107—41no—
55D4×C107—21no—
56D4×C107—41no—
57C2×C4×C107—41no—
58C2×C4×C107—41no—
59C2×C4×C107C2×D411yescharacteristic
60C22⋊D107—21no—
61C22⋊D107—42no—
62C2×Dic107—42no—
63C2×Dic107—41no—
64D428D811yescharacteristic
65C4×D107—21no—
66C4×D107—42no—
67Dic214—22no—
68Dic214—42no—
69Dic214—41no—
70Dic214D811yescharacteristic
71C8×C107C2×D411yescharacteristic
72C8×C107C2×D411yescharacteristic
73C107⋊C8—21no—
74C107⋊C8—41no—
75C22×C107—41no—
76C22×C107AGL(1,ℤ/8)11yescharacteristic
77C2×D107—21no—
78C4×C107—41no—
79C4×C107—81no—
80C4×C107#12011yescharacteristic
81C4×C107C2×D811yescharacteristic
82Dic107—21no—
83Dic107—42no—
84C2×C107—21no—
85C2×C107—81no—
86C2×C107#44711yescharacteristic
87D107—41no—
88#2195—1071nomaximal, Sylow
89C107#219511yescharacteristic, complemented, Sylow
90#578—1071no—
91#510D10711yescharacteristic, complemented
92C2×Q32—1071no—
93#473—1071no—
94#362—1071no—
95#359—1071no—
96#350—1071no—
972−1+4—2141no—
98#137—2141no—
99#137—2142no—
100#137—2141no—
101#135—2141no—
102#135C2×D10711yescharacteristic
103C2×Q16—1071no—
104C2×Q16—2141no—
105C2×Q16C2×D10711yescharacteristic
106#131—1071no—
107Q32—21no—
108Q32—2142no—
109SD32—21no—
110M32C2×D10711yescharacteristic
111C2×C16—1071no—
112#108—1071no—
113#101—2141no—
114#41—21no—
115#41—1071no—
116#41—4281no—
117#41—4282no—
118#41—2142no—
119C2×Q8—21no—
120C2×Q8—4281no—
121C2×Q8—2142no—
122C2×Q8—2141no—
123Q16—21no—
124Q16—21no—
125Q16—1072no—
126Q16—4281no—
127Q16—2142no—
128Q16—2141no—
129Q16C22⋊D10711yescharacteristic
130SD16—21no—
131SD16—4281no—
132SD16—2142no—
133D8C22⋊D10711yescharacteristic
134M16—1071no—
135M16—2141no—
136M16—2141no—
137C2×C8—2141no—
138C2×C8C22×D10711yescharacteristic
139C16—21no—
140C16—2141no—
141Q8—21no—
142Q8—41no—
143Q8—41no—
144Q8—1071no—
145Q8—4282no—
146Q8—4281no—
147Q8—2142no—
148D4—21no—
149D4—41no—
150D4—1071no—
151D4—4282no—
152D4—2141no—
153C2×C4—41no—
154C2×C4—41no—
155C2×C4—4282no—
156C2×C4—4281no—
157C2×C4—4282no—
158C2×C4—2141no—
159C2×C4D4×D10711yescharacteristic
160C8—4281no—
161C8—2141no—
162C8D4×D10711yescharacteristic
163C8C2×C22⋊D10711yescharacteristic
164C22—41no—
165C22—2141no—
166C22#1681213311yescharacteristic
167C4—41no—
168C4—81no—
169C4—4282no—
170C4—2141no—
171C4#1681207711yescharacteristic
172C4D8×D10711yescharacteristic
173C2—21no—
174C2—81no—
175C2—4281no—
176C2#2029275911yescharacteristic
subgroupG/H
centerC2#20292759
commutator, cosocleC2×C8×C107C23
FrattiniC2×C8C22×D107
Fitting#510×C107C2
socleC2×C107#447
prime radical#20293441C2
hypercenter#510D107
hypocenterC107#2195
LCSG ▷ C2×C8×C107 ▷ C4×C107 ▷ C2×C107 ▷ C107
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ #510

Complements

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

NH ≅ G/Ntype
2. C2×#16812055C2semidirect
3. #20292899C2semidirect
4. #20292444C2semidirect
5. #20292434C2semidirect
6. #20292412C2semidirect
7. #510×C107C2semidirect
89. C107#2195semidirect
91. #510D107semidirect

Maximal subgroups

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

subgroupindex
#202934412
C2×#168120552
#202928992
#202924442
#202924342
#202924122
#510×C1072
#2195107