Finite Group Databasebeta

← #28335452

Subgroups — #28335452

Order 13696.

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

normal subgroups only

This group has 228 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#20292955C212yesmaximal, complemented
2#20292552C211yesmaximal, characteristic
3#20292364C212yesmaximal, complemented
4#20292351C211yesmaximal, characteristic
5#543×C107C211yesmaximal, characteristic
6C2×C4⋊Dic107C2211yescharacteristic
7C2×C22⋊Dic107—21no—
8#16812040—22no—
9#16812033—22no—
10C22⋊(C107⋊C8)C2212yes—
11C107⋊#95—21no—
12C107⋊#95C2211yescharacteristic
13C22⋊Q8×C107—22no—
14C22⋊Q8×C107—21no—
15C22⋊Q8×C107—22no—
16C22⋊Q8×C107C2212yes—
17C2×C22⋊C4×C107—21no—
18C2×C22⋊C4×C107C2211yescharacteristic
19C22×Dic107—21no—
20C22×Dic107—21no—
21C2×C107⋊C8—22no—
22C4⋊Dic107—22no—
23C22⋊Dic107—42no—
24C24×C107D411yescharacteristic
25C2×Q8×C107—21no—
26C2×Q8×C107D412yes—
27C22×C4×C107—21no—
28C22×C4×C107—21no—
29C22×C4×C107D411yescharacteristic
30C22×C4×C107C2311yescharacteristic
31C4⋊C4×C107—21no—
32C4⋊C4×C107—22no—
33C4⋊C4×C107—22no—
34C4⋊C4×C107D412yes—
35C22⋊C4×C107—22no—
36C22⋊C4×C107—22no—
37C22⋊C4×C107—22no—
38C23×C107—21no—
39C23×C107—21no—
40C23×C107—41no—
41C23×C107—41no—
42C23×C107SD1612yes—
43C23×C107C2×D411yescharacteristic
44Q8×C107—42no—
45Q8×C107—81no—
46C2×C4×C107—22no—
47C2×C4×C107—21no—
48C2×C4×C107—22no—
49C2×C4×C107—41no—
50C2×C4×C107—41no—
51C2×C4×C107—81no—
52C2×C4×C107—81no—
53C2×C4×C107C2×D412yes—
54C2×Dic107—41no—
55C2×Dic107—41no—
56C2×Dic107—41no—
57C2×Dic107—41no—
58C2×Dic107—41no—
59C2×Dic107—41no—
60C107⋊C8—42no—
61C22×C107—21no—
62C22×C107—21no—
63C22×C107—22no—
64C22×C107—42no—
65C22×C107—41no—
66C22×C107—41no—
67C22×C107—81no—
68C22×C107#12011yescharacteristic
69C22×C107C2×SD1611yescharacteristic
70C22×C107#13711yescharacteristic
71C4×C107—22no—
72C4×C107—41no—
73C4×C107—42no—
74C4×C107—42no—
75Dic107—81no—
76Dic107—81no—
77C2×C107—21no—
78C2×C107—21no—
79C2×C107—42no—
80C2×C107#44811yescharacteristic
81C2×C107#45511yescharacteristic
82C2×C107#45811yescharacteristic
83#1608—1071nomaximal, Sylow
84C107#160811yescharacteristic, complemented, Sylow
85#543D10711yescharacteristic
86#483—1072no—
87#397—1071no—
88#328—1072no—
89#323—1071no—
90C22⋊Q8—22no—
91C22⋊Q8—21no—
92C22⋊Q8—22no—
93C22⋊Q8C2×D10712yes—
94C2×C4⋊C4—1071no—
95C2×C22⋊C4—21no—
96C2×C22⋊C4—2141no—
97C2×C22⋊C4C2×D10711yescharacteristic
98#106—2142no—
99#103—2142no—
100C22⋊C8—1072no—
101#95—1071no—
102#95—2141no—
103C24C22⋊D10711yescharacteristic
104C2×Q8—21no—
105C2×Q8C22⋊D10712yes—
106C22×C4—21no—
107C22×C4—21no—
108C22×C4—2141no—
109C22×C4—2141no—
110C22×C4C22⋊D10711yescharacteristic
111C22×C4C22×D10711yescharacteristic
112C2×C8—2142no—
113C4⋊C4—21no—
114C4⋊C4—22no—
115C4⋊C4—22no—
116C4⋊C4—2142no—
117C4⋊C4C22⋊D10712yes—
118C22⋊C4—22no—
119C22⋊C4—22no—
120C22⋊C4—22no—
121C22⋊C4—4282no—
122C23—21no—
123C23—21no—
124C23—41no—
125C23—41no—
126C23#1313380512yes—
127C23C2×C22⋊D10711yescharacteristic
128Q8—42no—
129Q8—81no—
130C2×C4—22no—
131C2×C4—21no—
132C2×C4—22no—
133C2×C4—41no—
134C2×C4—41no—
135C2×C4—81no—
136C2×C4—81no—
137C2×C4—4281no—
138C2×C4—4281no—
139C2×C4—4281no—
140C2×C4—4281no—
141C2×C4—4281no—
142C2×C4—4281no—
143C2×C4C2×C22⋊D10712yes—
144C8—4282no—
145C22—21no—
146C22—21no—
147C22—22no—
148C22—42no—
149C22—41no—
150C22—41no—
151C22—81no—
152C22#1681207811yescharacteristic
153C22C2×#1313380511yescharacteristic
154C22#1681214011yescharacteristic
155C4—22no—
156C4—41no—
157C4—42no—
158C4—42no—
159C4—8561no—
160C4—8561no—
161C2—21no—
162C2—21no—
163C2—42no—
164C2#2029276611yescharacteristic
165C2#2029280511yescharacteristic
166C2#2029281711yescharacteristic
subgroupG/H
centerC22#16812078
commutator, cosocleC22×C4×C107C23
FrattiniC22×C4C22×D107
Fitting#543×C107C2
socleC22×C107#120
prime radicalC24×C107D4
hypercenter#543D107
hypocenterC107#1608
LCSG ▷ C22×C4×C107 ▷ C22×C107 ▷ C107
UCSC1 ◁ C22 ◁ C22×C4 ◁ #543

Complements

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

NH ≅ G/Ntype
1. #20292955C2semidirect
3. #20292364C2semidirect
84. C107#1608semidirect

Maximal subgroups

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

subgroupindex
#202929552
#202925522
#202923642
#202923512
#543×C1072
#1608107