Finite Group Databasebeta

← #28335498

Subgroups — #28335498

Order 13696.

246 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 246 conjugacy classes of subgroups — too many to draw. Only its 57 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#20292943C212yesmaximal, complemented
2#20292566C211yesmaximal, characteristic, complemented
3#20292361C212yesmaximal, complemented
4#20292353C211yesmaximal, characteristic, complemented
5#537×C107C211yesmaximal, characteristic
6C2×C4⋊Dic107C2211yescharacteristic
7#16812040—22no—
8#16812030—22no—
9C22⋊(C107⋊C8)C2212yes—
10C107⋊#95—21no—
11C107⋊#95—21no—
12C107⋊#95C2211yescharacteristic
13C2×#41×C107—21no—
14C22⋊Q8×C107—22no—
15#121×C107—22no—
16#121×C107—21no—
17#121×C107C2212yes—
18C2×C4⋊C4×C107C2211yescharacteristic
19C22×Dic107—21no—
20C22×Dic107—21no—
21C2×C107⋊C8—22no—
22C4⋊Dic107—22no—
23#41×C107—42no—
24#41×C107—42no—
25C2×Q8×C107—21no—
26C2×D4×C107—21no—
27C2×D4×C107—22no—
28C2×D4×C107—21no—
29C2×D4×C107D412yes—
30C22×C4×C107—22no—
31C22×C4×C107D411yescharacteristic
32C22×C4×C107D411yescharacteristic
33C22×C4×C107C2311yescharacteristic
34C4⋊C4×C107—21no—
35C4⋊C4×C107—22no—
36C4⋊C4×C107D412yes—
37C22⋊C4×C107—22no—
38C22⋊C4×C107—22no—
39C23×C107—22no—
40C23×C107C2×D411yescharacteristic
41Q8×C107—42no—
42D4×C107—42no—
43D4×C107—42no—
44D4×C107—42no—
45D4×C107—42no—
46D4×C107—81no—
47C2×C4×C107—21no—
48C2×C4×C107—21no—
49C2×C4×C107—21no—
50C2×C4×C107—22no—
51C2×C4×C107—41no—
52C2×C4×C107—44no—
53C2×C4×C107—41no—
54C2×C4×C107SD1612yes—
55C2×C4×C107C2×D412yes—
56C2×Dic107—41no—
57C2×Dic107—41no—
58C2×Dic107—42no—
59C2×Dic107—41no—
60C2×Dic107—41no—
61C107⋊C8—42no—
62C22×C107—21no—
63C22×C107—21no—
64C22×C107—42no—
65C22×C107—42no—
66C22×C107—42no—
67C22×C107#12011yescharacteristic
68C22×C107C2×SD1611yescharacteristic
69C22×C107AGL(1,ℤ/8)11yescharacteristic
70C4×C107—22no—
71C4×C107—22no—
72C4×C107—42no—
73C4×C107—41no—
74Dic107—81no—
75Dic107—81no—
76C2×C107—21no—
77C2×C107—21no—
78C2×C107—82no—
79C2×C107#45011yescharacteristic
80C2×C107#45411yescharacteristic
81C2×C107#45811yescharacteristic
82#1616—1071nomaximal, Sylow
83C107#161611yescharacteristic, complemented, Sylow
84#537D10711yescharacteristic
85#481—1072no—
86#400—1071no—
87#327—1072no—
88#324—1071no—
89C2×#41—21no—
90C22⋊Q8—22no—
91#121—22no—
92#121—21no—
93#121C2×D10712yes—
94C2×C4⋊C4—1071no—
95C2×C4⋊C4C2×D10711yescharacteristic
96#106—2142no—
97#102—2142no—
98C22⋊C8—1072no—
99#95—1071no—
100#95—2141no—
101#95—2141no—
102#41—42no—
103#41—42no—
104C2×Q8—21no—
105C2×D4—21no—
106C2×D4—22no—
107C2×D4—21no—
108C2×D4C22⋊D10712yes—
109C22×C4—22no—
110C22×C4—2141no—
111C22×C4—2141no—
112C22×C4C22⋊D10711yescharacteristic
113C22×C4C22⋊D10711yescharacteristic
114C22×C4C22×D10711yescharacteristic
115C2×C8—2142no—
116C4⋊C4—21no—
117C4⋊C4—22no—
118C4⋊C4—2142no—
119C4⋊C4C22⋊D10712yes—
120C22⋊C4—22no—
121C22⋊C4—22no—
122C23—22no—
123C23C2×C22⋊D10711yescharacteristic
124Q8—42no—
125D4—42no—
126D4—42no—
127D4—42no—
128D4—42no—
129D4—81no—
130C2×C4—21no—
131C2×C4—21no—
132C2×C4—21no—
133C2×C4—22no—
134C2×C4—41no—
135C2×C4—44no—
136C2×C4—41no—
137C2×C4—4281no—
138C2×C4—4281no—
139C2×C4—4282no—
140C2×C4—4281no—
141C2×C4—4281no—
142C2×C4#1313380612yes—
143C2×C4C2×C22⋊D10712yes—
144C8—4282no—
145C22—21no—
146C22—21no—
147C22—42no—
148C22—42no—
149C22—42no—
150C22#1681207811yescharacteristic
151C22C2×#1313380611yescharacteristic
152C22#1681213511yescharacteristic
153C4—22no—
154C4—22no—
155C4—42no—
156C4—41no—
157C4—8561no—
158C4—8561no—
159C2—21no—
160C2—21no—
161C2—82no—
162C2#2029277811yescharacteristic
163C2#2029280011yescharacteristic
164C2#2029281711yescharacteristic
subgroupG/H
centerC22#16812078
commutator, cosocleC22×C4×C107C23
FrattiniC22×C4C22×D107
Fitting, prime radical#537×C107C2
socleC22×C107#120
hypercenter#537D107
hypocenterC107#1616
LCSG ▷ C22×C4×C107 ▷ C22×C107 ▷ C107
UCSC1 ◁ C22 ◁ C22×C4 ◁ #537

Complements

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

NH ≅ G/Ntype
1. #20292943C2semidirect
2. #20292566C2semidirect
3. #20292361C2semidirect
4. #20292353C2semidirect
83. C107#1616semidirect

Maximal subgroups

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

subgroupindex
#202929432
#202925662
#202923612
#202923532
#537×C1072
#1616107