Finite Group Databasebeta

← #28344528

Subgroups — #28344528

Order 13696.

380 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 380 conjugacy classes of subgroups — too many to draw. Only its 133 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
1C2×#16812101C211yesmaximal, characteristic
2#20292566C212yesmaximal
3#20292565C212yesmaximal
4#20292560C214yesmaximal
5#20292558C212yesmaximal
6#20292557C212yesmaximal
7#20292493C211yesmaximal, characteristic
8C2×#125×C107C211yesmaximal, characteristic
9#16812101—24no—
10C2×C4⋊Dic107C2211yescharacteristic
11C2×C4⋊Dic107C2211yescharacteristic
12C2×C4⋊Dic107C2212yes—
13C2×Dic107⋊C4C2212yes—
14C2×Dic107⋊C4C2212yes—
15C2×Dic107⋊C4C2214yes—
16C107⋊#95C2212yes—
17C107⋊#95C2212yes—
18C107⋊#95C2214yes—
19C107⋊#95C2214yes—
20C107⋊#95C2214yes—
21#125×C107—24no—
22C2×C4⋊C4×C107C2212yes—
23C2×C4⋊C4×C107C2211yescharacteristic
24C2×C4⋊C4×C107C2212yes—
25C2×C4⋊C4×C107C2211yescharacteristic
26C2×C42×C107C2211yescharacteristic
27C22×Dic107C2312yes—
28C22×Dic107C2312yes—
29C22×Dic107C2314yes—
30C4⋊Dic107—22no—
31C4⋊Dic107—22no—
32C4⋊Dic107—42no—
33Dic107⋊C4—24no—
34Dic107⋊C4—24no—
35Dic107⋊C4—44no—
36C22×C4×C107C2312yes—
37C22×C4×C107C2312yes—
38C22×C4×C107C2311yescharacteristic
39C22×C4×C107C2311yescharacteristic
40C22×C4×C107C2311yescharacteristic
41C4⋊C4×C107—22no—
42C4⋊C4×C107—24no—
43C4⋊C4×C107—22no—
44C4⋊C4×C107—24no—
45C42×C107D414yes—
46C23×C107C2411yescharacteristic
47C2×C4×C107—21no—
48C2×C4×C107—22no—
49C2×C4×C107—21no—
50C2×C4×C107—22no—
51C2×C4×C107—22no—
52C2×C4×C107—22no—
53C2×C4×C107—22no—
54C2×C4×C107—24no—
55C2×C4×C107—22no—
56C2×C4×C107C2×D412yes—
57C2×C4×C107C2×D412yes—
58C2×C4×C107C2×D412yes—
59C2×Dic107—22no—
60C2×Dic107—22no—
61C2×Dic107—22no—
62C2×Dic107—24no—
63C2×Dic107—22no—
64C2×Dic107—24no—
65C2×Dic107—24no—
66C2×Dic107—24no—
67C22×C107C22×D411yescharacteristic
68C22×C107H(5,𝔽2)11yescharacteristic
69C22×C1072−1+412yes—
70C22×C1072−1+411yescharacteristic
71C22×C1072−1+412yes—
72C4×C107—22no—
73C4×C107—22no—
74C4×C107—22no—
75C4×C107—42no—
76C4×C107—42no—
77Dic107—42no—
78Dic107—42no—
79Dic107—44no—
80C2×C107#53611yescharacteristic
81C2×C107#53611yescharacteristic
82C2×C107#53711yescharacteristic
83C2×C107#56312yes—
84C2×C107#56412yes—
85#2822—1071nomaximal, Sylow
86C107#282211yescharacteristic, complemented, Sylow
87C2×#125—1071no—
88C2×#125D10711yescharacteristic
89#400—1072no—
90#400—1072no—
91#398—1072no—
92#398—1072no—
93#398—1074no—
94#382—1071no—
95#125—24no—
96#125—2144no—
97C2×C4⋊C4—1074no—
98C2×C4⋊C4—1072no—
99C2×C4⋊C4—1072no—
100C2×C4⋊C4—1072no—
101C2×C4⋊C4—1071no—
102C2×C4⋊C4—1071no—
103C2×C4⋊C4C2×D10712yes—
104C2×C4⋊C4C2×D10711yescharacteristic
105C2×C4⋊C4C2×D10712yes—
106C2×C4⋊C4C2×D10711yescharacteristic
107C2×C42C2×D10711yescharacteristic
108#95—1072no—
109#95—1072no—
110#95—1074no—
111#95—1074no—
112#95—1074no—
113C22×C4—1074no—
114C22×C4—1072no—
115C22×C4—1072no—
116C22×C4C22×D10712yes—
117C22×C4C22×D10712yes—
118C22×C4C22×D10711yescharacteristic
119C22×C4C22×D10711yescharacteristic
120C22×C4C22×D10711yescharacteristic
121C4⋊C4—24no—
122C4⋊C4—22no—
123C4⋊C4—24no—
124C4⋊C4—22no—
125C4⋊C4—4284no—
126C4⋊C4—4282no—
127C4⋊C4—2144no—
128C4⋊C4—2144no—
129C4⋊C4—2142no—
130C4⋊C4—2142no—
131C42C22⋊D10714yes—
132C23C23×D10711yescharacteristic
133C2×C4—21no—
134C2×C4—22no—
135C2×C4—21no—
136C2×C4—22no—
137C2×C4—22no—
138C2×C4—22no—
139C2×C4—22no—
140C2×C4—24no—
141C2×C4—22no—
142C2×C4—2142no—
143C2×C4—2142no—
144C2×C4—2144no—
145C2×C4—2142no—
146C2×C4—2144no—
147C2×C4—2142no—
148C2×C4—2144no—
149C2×C4—2144no—
150C2×C4C2×C22⋊D10712yes—
151C2×C4C2×C22⋊D10712yes—
152C2×C4C2×C22⋊D10712yes—
153C22C22×C22⋊D10711yescharacteristic
154C22#1681215511yescharacteristic
155C22#1681215612yes—
156C22#1681215611yescharacteristic
157C22#1681215712yes—
158C4—22no—
159C4—22no—
160C4—22no—
161C4—42no—
162C4—42no—
163C4—4284no—
164C4—4282no—
165C4—4282no—
166C2#2029319811yescharacteristic
167C2#2029320111yescharacteristic
168C2#2029320511yescharacteristic
169C2#2029338112yes—
170C2C107⋊#56412yes—
subgroupG/H
center, FrattiniC23C23×D107
commutator, socle, prime radical, cosocleC23×C107C24
FittingC2×#125×C107C2
hypercenterC2×#125D107
hypocenterC107#2822
LCSG ▷ C23×C107 ▷ C107
UCSC1 ◁ C23 ◁ C2×#125

Complements

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

NH ≅ G/Ntype
86. C107#2822semidirect

Maximal subgroups

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

subgroupindex
C2×#168121012
#202925662
#202925652
#202925602
#202925582
#202925572
#202924932
C2×#125×C1072
#2822107