Finite Group Databasebeta

← #28338423

Subgroups — #28338423

Order 13696.

210 conjugacy classes of subgroups; only the 49 normal subgroups are shown.

normal subgroups only

This group has 210 conjugacy classes of subgroups — too many to draw. Only its 49 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#20293444C211yesmaximal, characteristic, complemented
2#20293063C211yesmaximal, characteristic, complemented
3C2×#16812053C211yesmaximal, characteristic, complemented
4#20292442C211yesmaximal, characteristic, complemented
5#20292433C211yesmaximal, characteristic, complemented
6#20292411C211yesmaximal, characteristic, complemented
7#472×C107C211yesmaximal, characteristic, complemented
8#16812156—21no—
9#16812142—22no—
10#16812142—21no—
11#16812131—21no—
12#16812131C2211yescharacteristic
13C2×Dic428—21no—
14C2×Dic428C2211yescharacteristic
15#16812053—22no—
16#16812053—21no—
17#16812050—21no—
18#16812049C2211yescharacteristic
19C2×C107⋊C16C2211yescharacteristic
20AGL(1,ℤ/8)×C107—21no—
21C2×D8×C107C2211yescharacteristic
22#131×C107C2211yescharacteristic
23#108×C107C2211yescharacteristic
24#100×C107—21no—
25#13133818—22no—
26#13133818—21no—
27#13133817—42no—
28#13133817—41no—
29C2×Dic214—22no—
30C2×Dic214—21no—
31Q8×D107—41no—
32Dic428—22no—
33Dic428—21no—
34Dic428D411yescharacteristic
35Dic428D412yes—
36#13133807—22no—
37#13133807—21no—
38D856D411yescharacteristic
39C107⋊C16—21no—
40C107⋊C16—21no—
41#41×C107D411yescharacteristic
42C2×D4×C107—21no—
43SD16×C107—41no—
44D8×C107—21no—
45D8×C107—21no—
46D8×C107—41no—
47M16×C107—21no—
48M16×C107—21no—
49M16×C107D411yescharacteristic
50C2×C8×C107—21no—
51C2×C8×C107C2311yescharacteristic
52C23×C107—41no—
53Q8×C107D811yescharacteristic
54D4×C107—21no—
55D4×C107—41no—
56D4×C107—41no—
57D4×C107D811yescharacteristic
58C2×C4×C107—21no—
59C2×C4×C107C2×D411yescharacteristic
60C22⋊D107—42no—
61C22⋊D107—41no—
62C2×Dic107—42no—
63C2×Dic107—41no—
64D428—21no—
65C4×D107—42no—
66C4×D107—41no—
67Dic214—22no—
68Dic214—21no—
69Dic214—42no—
70Dic214—41no—
71C8×C107—21no—
72C8×C107—41no—
73C8×C107C2×D411yescharacteristic
74C8×C107C2×D411yescharacteristic
75C22×C107—21no—
76C22×C107—81no—
77C22×C107—161no—
78C22×C107AGL(1,ℤ/8)11yescharacteristic
79C2×D107—41no—
80C4×C107—21no—
81C4×C107#12011yescharacteristic
82C4×C107C2×D811yescharacteristic
83Dic107—41no—
84Dic107—42no—
85C2×C107—21no—
86C2×C107—41no—
87C2×C107—161no—
88C2×C107#44711yescharacteristic
89D107—81no—
90#2193—1071nomaximal, Sylow
91C107#219311yescharacteristic, complemented, Sylow
92#578—1071no—
93#509—1071no—
94C2×SD32—1071no—
95#472D10711yescharacteristic, complemented
96#362—1071no—
97#359—1071no—
98#350—1071no—
992−1+4—2141no—
100#137—2142no—
101#137—2141no—
102AGL(1,ℤ/8)—21no—
103#135—1071no—
104#135—2141no—
105C2×Q16—1071no—
106C2×Q16—2141no—
107C2×D8C2×D10711yescharacteristic
108#131C2×D10711yescharacteristic
109SD32—2142no—
110SD32—2141no—
111D16—2141no—
112M32—1071no—
113C2×C16—1071no—
114#108C2×D10711yescharacteristic
115#100—21no—
116#41—4282no—
117#41—4281no—
118#41—2142no—
119#41—2141no—
120#41C22⋊D10711yescharacteristic
121C2×Q8—4281no—
122C2×Q8—2142no—
123C2×Q8—2141no—
124C2×D4—21no—
125Q16—1072no—
126Q16—1071no—
127Q16—2142no—
128Q16—2141no—
129SD16—41no—
130SD16—2142no—
131SD16—2141no—
132D8—21no—
133D8—21no—
134D8—41no—
135D8—1071no—
136M16—21no—
137M16—21no—
138M16C22⋊D10711yescharacteristic
139C2×C8—21no—
140C2×C8C22×D10711yescharacteristic
141C16—2141no—
142C16—2141no—
143C23—41no—
144Q8—4282no—
145Q8—4281no—
146Q8—2142no—
147Q8—2141no—
148Q8#1313380311yescharacteristic
149D4—21no—
150D4—41no—
151D4—41no—
152D4—4282no—
153D4—4281no—
154D4—2141no—
155D4#1313380311yescharacteristic
156C2×C4—21no—
157C2×C4—4282no—
158C2×C4—4282no—
159C2×C4—4281no—
160C2×C4—4281no—
161C2×C4C2×C22⋊D10711yescharacteristic
162C8—21no—
163C8—41no—
164C8D4×D10711yescharacteristic
165C8D4×D10711yescharacteristic
166C22—21no—
167C22—81no—
168C22—161no—
169C22—4281no—
170C22#1681213411yescharacteristic
171C4—21no—
172C4—4282no—
173C4—4281no—
174C4#1681207711yescharacteristic
175C4C2×#1313380311yescharacteristic
176C2—21no—
177C2—41no—
178C2—161no—
179C2—8561no—
180C2#2029276011yescharacteristic
subgroupG/H
centerC2#20292760
commutator, cosocleC2×C8×C107C23
FrattiniC2×C8C22×D107
Fitting#472×C107C2
socleC2×C107#447
hypercenter#472D107
hypocenterC107#2193
LCSG ▷ C2×C8×C107 ▷ C4×C107 ▷ C2×C107 ▷ C107
UCSC1 ◁ C2 ◁ C2×C4 ◁ #131 ◁ #472

Complements

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

NH ≅ G/Ntype
1. #20293444C2semidirect
2. #20293063C2semidirect
3. C2×#16812053C2semidirect
4. #20292442C2semidirect
5. #20292433C2semidirect
6. #20292411C2semidirect
7. #472×C107C2semidirect
91. C107#2193semidirect
95. #472D107semidirect

Maximal subgroups

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

subgroupindex
#202934442
#202930632
C2×#168120532
#202924422
#202924332
#202924112
#472×C1072
#2193107