Finite Group Databasebeta

← #14544038

Subgroups — #14544038

Order 2176.

252 conjugacy classes of subgroups; only the 64 normal subgroups are shown.

normal subgroups only

This group has 252 conjugacy classes of subgroups — too many to draw. Only its 64 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#11763830C212yesmaximal, complemented
2#11763654C212yesmaximal, complemented
3#11763653C212yesmaximal
4C2×#10587578C211yesmaximal, characteristic
5C22×C4×D17C411yescharacteristic
6C2×C4⋊C4×C17C411yescharacteristic
7C2×#63227C411yescharacteristic
8C2×#63227C2211yescharacteristic
9C2×C4⋊Dic17C2211yescharacteristic
10C2×C4×Dic17C411yescharacteristic
11C2×C4×Dic17C2211yescharacteristic
12#10587578—22no—
13#10587578—22no—
14C22⋊#3624C2214yes—
15#10587542—22no—
16C4⋊#3624—22no—
17C23×D17C2×C411yescharacteristic
18C22×C4×C17C2×C411yescharacteristic
19C22×C4×C17C2×C411yescharacteristic
20C22×C4×C17C2×C411yescharacteristic
21C22×Dic17C2×C411yescharacteristic
22C22×Dic17C2×C411yescharacteristic
23C22×Dic17C2311yescharacteristic
24C2×C4×D17—22no—
25C2×C4×D17—22no—
26C2×C4×D17—21no—
27C2×C4×D17—21no—
28C2×#3624—24no—
29C4⋊C4×C17—22no—
30#63227—22no—
31#63227—22no—
32C4⋊Dic17—22no—
33C4×Dic17—21no—
34C4×Dic17—21no—
35C4×Dic17D412yes—
36C4×Dic17D412yes—
37C23×C17C22×C411yescharacteristic
38C22×D17—21no—
39C22×D17—21no—
40C22×D17—41no—
41C22×D17—41no—
42C22×D17M1612yes—
43C2×C4×C17—21no—
44C2×C4×C17—21no—
45C2×C4×C17—21no—
46C2×C4×C17—41no—
47C2×C4×C17—41no—
48C2×C4×C17C22⋊C412yes—
49C2×C4×C17M1612yes—
50C2×Dic17—21no—
51C2×Dic17—21no—
52C2×Dic17—21no—
53C2×Dic17—41no—
54C2×Dic17—41no—
55C2×Dic17C22⋊C411yescharacteristic
56C2×Dic17C22⋊C411yescharacteristic
57C2×Dic17C2×D412yes—
58C4×D17—24no—
59C4×D17—24no—
60#3624—44no—
61#1464—171nomaximal, Sylow
62C22×C17—21no—
63C22×C17—21no—
64C22×C17C2×C22⋊C411yescharacteristic
65C22×C17C2×M1611yescharacteristic
66C22×C17C2×M1611yescharacteristic
67C2×D17—22no—
68C2×D17—42no—
69C2×D17—41no—
70C2×D17—41no—
71C2×D17—42no—
72C4×C17—22no—
73C4×C17—22no—
74C4×C17—41no—
75Dic17—21no—
76Dic17—21no—
77Dic17—22no—
78Dic17—41no—
79C2×#117—171no—
80#432—172no—
81#324—172no—
82#323—172no—
83C2×C17—21no—
84C2×C17—21no—
85C2×C17#40711yescharacteristic
86C2×C17#41011yescharacteristic
87C2×C17#41311yescharacteristic
88D17—42no—
89C23×C4—171no—
90#117—342no—
91#117—342no—
92C2×C4⋊C4—171no—
93C2×C4⋊C4#59511yescharacteristic
94C2×C22⋊C4—171no—
95C2×C22⋊C4—171no—
96C2×C42—171no—
97C2×C42—171no—
98C4⋊C8—342no—
99C22⋊C8—174no—
100#97—342no—
101C17#146411yescharacteristic, complemented, Sylow
102C24—171no—
103C22×C4—171no—
104C22×C4—171no—
105C22×C4—171no—
106C22×C4—341no—
107C22×C4—341no—
108C22×C4—342no—
109C22×C4—342no—
110C22×C4C2×#59511yescharacteristic
111C22×C4C2×#59511yescharacteristic
112C22×C4C2×#59511yescharacteristic
113C2×C8—344no—
114C4⋊C4—22no—
115C4⋊C4—342no—
116C22⋊C4—342no—
117C22⋊C4—342no—
118C42—172no—
119C42—172no—
120C42—341no—
121C42—341no—
122C23—172no—
123C23—341no—
124C23—341no—
125C23—681no—
126C23—681no—
127C23C22×#59511yescharacteristic
128C2×C4—21no—
129C2×C4—21no—
130C2×C4—21no—
131C2×C4—41no—
132C2×C4—41no—
133C2×C4—171no—
134C2×C4—171no—
135C2×C4—172no—
136C2×C4—344no—
137C2×C4—344no—
138C2×C4—341no—
139C2×C4—341no—
140C2×C4—341no—
141C2×C4—681no—
142C2×C4—681no—
143C2×C4#6324312yes—
144C2×C4C22⋊#59512yes—
145C8—684no—
146C22—21no—
147C22—21no—
148C22—342no—
149C22—682no—
150C22—682no—
151C22—681no—
152C22—681no—
153C22C2×#6324311yescharacteristic
154C22D17⋊M1611yescharacteristic
155C22C2×C22⋊#59511yescharacteristic
156C4—22no—
157C4—22no—
158C4—41no—
159C4—341no—
160C4—341no—
161C4—342no—
162C4—681no—
163C2—21no—
164C2—21no—
165C2—682no—
166C2#1176378011yescharacteristic
167C2#1176379011yescharacteristic
168C2#1176379611yescharacteristic
subgroupG/H
centerC22C2×C22⋊#595
commutatorC23×C17C22×C4
FrattiniC23C22×#595
FittingC2×C4⋊C4×C17C4
socleC22×C17C2×C22⋊C4
prime radicalC23×D17C2×C4
cosocleC22×Dic17C23
hypercenterC2×C4⋊C4#595
hypocenterC17#1464
LCSG ▷ C23×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. #11763830C2semidirect
2. #11763654C2semidirect
101. C17#1464semidirect

Maximal subgroups

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

subgroupindex
#117638302
#117636542
#117636532
C2×#105875782
#146417