Finite Group Databasebeta

← #28338424

Subgroups — #28338424

Order 13696.

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

normal subgroups only

This group has 210 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#20293440C211yesmaximal, characteristic, complemented
2#20293063C211yesmaximal, characteristic, complemented
3#20292894C211yesmaximal, characteristic, complemented
4#20292443C211yesmaximal, characteristic, complemented
5#20292435C211yesmaximal, characteristic, complemented
6#20292410C211yesmaximal, characteristic, complemented
7C2×SD32×C107C211yesmaximal, characteristic, complemented
8#16812157—21no—
9#16812141—22no—
10#16812140—21no—
11#16812135—21no—
12#16812132—21no—
13#16812131C2211yescharacteristic
14Q16×D107—21no—
15#16812115C2211yescharacteristic
16#16812053—21no—
17#16812050—21no—
18#16812049C2211yescharacteristic
19#16812045C2211yescharacteristic
20#16812026—21no—
21C2×Q16×C107C2211yescharacteristic
22C2×D8×C107C2211yescharacteristic
23SD32×C107—22no—
24C2×C16×C107C2211yescharacteristic
25#13133819—22no—
26#13133819—41no—
27#13133818—21no—
28#13133818—42no—
29#13133818D411yescharacteristic
30Q8×D107—22no—
31Q8×D107—41no—
32Dic428D411yescharacteristic
33#13133808—22no—
34#13133807—21no—
35#13133806—41no—
36#13133805—22no—
37D856D411yescharacteristic
38#13133803—41no—
39#13133802—21no—
40#13133802D411yescharacteristic
41#13133801—21no—
42C8×D107—21no—
43C107⋊C16—21no—
44C2×Q8×C107—21no—
45C2×D4×C107—21no—
46Q16×C107—21no—
47Q16×C107D412yes—
48D8×C107—21no—
49D8×C107—21no—
50C2×C8×C107C2311yescharacteristic
51C16×C107—21no—
52C23×C107—41no—
53Q8×C107—22no—
54Q8×C107—41no—
55D4×C107—41no—
56D4×C107—41no—
57C2×C4×C107—41no—
58C2×C4×C107C2×D411yescharacteristic
59C22⋊D107—21no—
60C22⋊D107—41no—
61D428—21no—
62D428—42no—
63D428D811yescharacteristic
64C4×D107—21no—
65C4×D107—42no—
66C4×D107—42no—
67C4×D107—41no—
68Dic214—21no—
69Dic214—42no—
70Dic214D811yescharacteristic
71C8×C107C2×D411yescharacteristic
72C8×C107C2×D411yescharacteristic
73C107⋊C8—21no—
74C107⋊C8—41no—
75C22×C107—81no—
76C22×C107—161no—
77C22×C107AGL(1,ℤ/8)11yescharacteristic
78C2×D107—21no—
79C2×D107—41no—
80C4×C107—42no—
81C4×C107#12011yescharacteristic
82C4×C107C2×D811yescharacteristic
83Dic107—21no—
84Dic107—41no—
85C2×C107—21no—
86C2×C107—161no—
87C2×C107#44711yescharacteristic
88D107—41no—
89D107—81no—
90#2193—1071nomaximal, Sylow
91C107#219311yescharacteristic, complemented, Sylow
92#578—1071no—
93#509—1071no—
94C2×SD32D10711yescharacteristic, complemented
95#472—1071no—
96#362—1071no—
97#359—1071no—
98#350—1071no—
992−1+4—2141no—
100#137—2141no—
101#137—2142no—
102AGL(1,ℤ/8)—2141no—
103#135—1071no—
104#135—2141no—
105C2×Q16—2141no—
106C2×Q16C2×D10711yescharacteristic
107C2×D8C2×D10711yescharacteristic
108#131—1071no—
109SD32—22no—
110SD32—2141no—
111D16—2141no—
112M32—1071no—
113C2×C16C2×D10711yescharacteristic
114#108—1071no—
115#100—2141no—
116#41—1071no—
117#41—4282no—
118#41—4281no—
119#41—2142no—
120#41—2141no—
121C2×Q8—21no—
122C2×Q8—4281no—
123C2×Q8—2142no—
124C2×D4—21no—
125Q16—21no—
126Q16—1071no—
127Q16—2142no—
128Q16C22⋊D10712yes—
129SD16—4281no—
130SD16—2142no—
131SD16—2141no—
132D8—21no—
133D8—21no—
134D8—1071no—
135D8—4281no—
136M16—1071no—
137M16—2141no—
138M16—2141no—
139C2×C8—2141no—
140C2×C8C22×D10711yescharacteristic
141C16—21no—
142C16—2141no—
143C23—41no—
144Q8—22no—
145Q8—41no—
146Q8—1071no—
147Q8—4282no—
148Q8—2141no—
149D4—41no—
150D4—41no—
151D4—1071no—
152D4—4282no—
153D4—4281no—
154D4—2141no—
155D4—2141no—
156C2×C4—41no—
157C2×C4—4282no—
158C2×C4—4282no—
159C2×C4—4281no—
160C2×C4—2141no—
161C2×C4D4×D10711yescharacteristic
162C8—4281no—
163C8—2141no—
164C8D4×D10711yescharacteristic
165C8C2×C22⋊D10711yescharacteristic
166C22—81no—
167C22—161no—
168C22—4281no—
169C22—2141no—
170C22#1681213311yescharacteristic
171C4—42no—
172C4—4281no—
173C4—2141no—
174C4#1681207711yescharacteristic
175C4D8×D10711yescharacteristic
176C2—21no—
177C2—161no—
178C2—8561no—
179C2—4281no—
180C2#2029275911yescharacteristic
subgroupG/H
centerC2#20292759
commutator, cosocleC2×C8×C107C23
FrattiniC2×C8C22×D107
FittingC2×SD32×C107C2
socleC2×C107#447
hypercenterC2×SD32D107
hypocenterC107#2193
LCSG ▷ C2×C8×C107 ▷ C4×C107 ▷ C2×C107 ▷ C107
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ C2×SD32

Complements

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

NH ≅ G/Ntype
1. #20293440C2semidirect
2. #20293063C2semidirect
3. #20292894C2semidirect
4. #20292443C2semidirect
5. #20292435C2semidirect
6. #20292410C2semidirect
7. C2×SD32×C107C2semidirect
91. C107#2193semidirect
94. C2×SD32D107semidirect

Maximal subgroups

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

subgroupindex
#202934402
#202930632
#202928942
#202924432
#202924352
#202924102
C2×SD32×C1072
#2193107