Finite Group Databasebeta

← #14544068

Subgroups — #14544068

Order 2176.

214 conjugacy classes of subgroups; only the 58 normal subgroups are shown.

normal subgroups only

This group has 214 conjugacy classes of subgroups — too many to draw. Only its 58 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#11763829C211yesmaximal, characteristic, complemented
2#11763825C211yesmaximal, characteristic, complemented
3#11763654C212yesmaximal, complemented
4#11763653C212yesmaximal
5C2×#10587584C211yesmaximal, characteristic
6C2×C4⋊C4×C17C411yescharacteristic
7C2×#63227C411yescharacteristic
8C2×#63227C411yescharacteristic
9C2×#63227C2211yescharacteristic
10C2×C4⋊Dic17C2211yescharacteristic
11C2×#63225C411yescharacteristic
12C2×C4×Dic17C2211yescharacteristic
13#10587584—21no—
14#10587584—21no—
15#10587584—21no—
16#10587584—21no—
17C22⋊#3624C2212yes—
18C22⋊#3624C2212yes—
19#10587544—21no—
20#10587542—21no—
21C4⋊#3624—21no—
22C4×#3624—21no—
23C23×D17C2×C411yescharacteristic
24C22×C4×C17C2×C411yescharacteristic
25C22×C4×C17C2×C411yescharacteristic
26C22×C4×C17C2×C411yescharacteristic
27C22×Dic17C2×C411yescharacteristic
28C22×Dic17C2×C411yescharacteristic
29C22×Dic17C2311yescharacteristic
30C2×#3624—22no—
31C2×#3624—22no—
32C4⋊C4×C17—21no—
33C4⋊C4×C17—21no—
34#63227—21no—
35#63227—21no—
36#63227—21no—
37#63227—21no—
38#63227—21no—
39#63227—21no—
40C4⋊Dic17—21no—
41C4⋊Dic17—21no—
42#63225—21no—
43#63225—21no—
44C4×Dic17D411yescharacteristic
45C4×Dic17D411yescharacteristic
46C4×Dic17D411yescharacteristic
47C4×Dic17D411yescharacteristic
48C23×C17C22×C411yescharacteristic
49C22×D17—21no—
50C22×D17—22no—
51C22×D17—41no—
52C22×D17—41no—
53C2×C4×C17—22no—
54C2×C4×C17—21no—
55C2×C4×C17—21no—
56C2×C4×C17—22no—
57C2×C4×C17—41no—
58C2×C4×C17C22⋊C411yescharacteristic
59C2×C4×C17C22⋊C411yescharacteristic
60C2×Dic17—21no—
61C2×Dic17—41no—
62C2×Dic17—41no—
63C2×Dic17—41no—
64C2×Dic17C22⋊C411yescharacteristic
65C2×Dic17C22⋊C411yescharacteristic
66C2×Dic17C2×D411yescharacteristic
67C2×Dic17C2×D411yescharacteristic
68#3624—42no—
69#3624—42no—
70#1473—171nomaximal, Sylow
71C22×C17—21no—
72C22×C17—21no—
73C22×C17C2×C22⋊C411yescharacteristic
74C22×C17#13112yes—
75C2×D17—41no—
76C2×D17—41no—
77C2×D17—41no—
78C2×D17—82no—
79C4×C17—21no—
80C4×C17—21no—
81C4×C17—41no—
82C4×C17—41no—
83Dic17—21no—
84Dic17—21no—
85Dic17—21no—
86Dic17—21no—
87Dic17—41no—
88C2×#126—171no—
89#432—171no—
90#431—171no—
91#324—172no—
92#323—172no—
93C2×C17—22no—
94C2×C17#40811yescharacteristic
95C2×C17#41011yescharacteristic
96C2×C17#41311yescharacteristic
97D17—81no—
98#126—341no—
99#126—341no—
100#126—341no—
101#126—341no—
102C2×C4⋊C4—171no—
103C2×C4⋊C4—171no—
104C2×C4⋊C4#59511yescharacteristic
105C2×C22⋊C4—171no—
106C2×C22⋊C4—171no—
107C2×C22⋊C4—171no—
108C2×C42—171no—
109C4⋊C8—341no—
110C4⋊C8—341no—
111C22⋊C8—172no—
112C22⋊C8—172no—
113#97—341no—
114C4×C8—341no—
115C17#147311yescharacteristic, complemented, Sylow
116C24—171no—
117C22×C4—171no—
118C22×C4—171no—
119C22×C4—171no—
120C22×C4C2×#59511yescharacteristic
121C22×C4C2×#59511yescharacteristic
122C22×C4C2×#59511yescharacteristic
123C2×C8—342no—
124C2×C8—342no—
125C4⋊C4—21no—
126C4⋊C4—21no—
127C4⋊C4—341no—
128C4⋊C4—341no—
129C4⋊C4—341no—
130C4⋊C4—341no—
131C22⋊C4—341no—
132C22⋊C4—341no—
133C22⋊C4—341no—
134C22⋊C4—341no—
135C22⋊C4—341no—
136C22⋊C4—341no—
137C42—171no—
138C42—171no—
139C42—171no—
140C42—171no—
141C23—341no—
142C23—342no—
143C23—681no—
144C23—681no—
145C23C22×#59511yescharacteristic
146C2×C4—22no—
147C2×C4—22no—
148C2×C4—21no—
149C2×C4—21no—
150C2×C4—41no—
151C2×C4—171no—
152C2×C4—171no—
153C2×C4—171no—
154C2×C4—171no—
155C2×C4—341no—
156C2×C4—681no—
157C2×C4—681no—
158C2×C4—681no—
159C2×C4C22⋊#59511yescharacteristic
160C2×C4C22⋊#59511yescharacteristic
161C8—682no—
162C8—682no—
163C22—21no—
164C22—21no—
165C22—681no—
166C22—681no—
167C22—681no—
168C22—1362no—
169C22#1058767812yes—
170C22C2×C22⋊#59511yescharacteristic
171C4—21no—
172C4—21no—
173C4—41no—
174C4—41no—
175C4—341no—
176C4—341no—
177C4—341no—
178C4—341no—
179C4—681no—
180C2—22no—
181C2—1361no—
182C2#1176378211yescharacteristic
183C2#1176379011yescharacteristic
184C2#1176379511yescharacteristic
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#1473
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. #11763829C2semidirect
2. #11763825C2semidirect
3. #11763654C2semidirect
115. C17#1473semidirect

Maximal subgroups

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

subgroupindex
#117638292
#117638252
#117636542
#117636532
C2×#105875842
#147317