Finite Group Databasebeta

← #17953637

Subgroups — #17953637

Order 4352.

418 conjugacy classes of subgroups; only the 72 normal subgroups are shown.

normal subgroups only

This group has 418 conjugacy classes of subgroups — too many to draw. Only its 72 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#14544685C211yesmaximal, characteristic
2#14544681C211yesmaximal, characteristic
3#14543632C214yesmaximal
4#14531279C211yesmaximal, characteristic
5#11763781C2212yes—
6#11763752C2212yes—
7#11763689—22no—
8#11763687—22no—
9C2×#10587558C2211yescharacteristic
10#11762698—22no—
11#11762691—22no—
12C4×#63225C412yescomplemented
13C4×#63227C2212yes—
14C42×Dic17C411yescharacteristic, complemented
15C17×#376C411yescharacteristic, complemented
16C22×C4×D17C2311yescharacteristic
17C2×C22⋊#595—22no—
18C2×#63247—22no—
19C2×C42×C17C2×C411yescharacteristic
20C2×C42×C17C2×C412yes—
21C2×#63227—22no—
22C2×#63227D412yes—
23C2×#63225—22no—
24C2×#63225D412yes—
25C2×C4×Dic17—22no—
26C2×C4×Dic17C2×C412yes—
27C2×C4×Dic17C2×C411yescharacteristic
28#10587558—24no—
29(C2×#595)⋊C4—24no—
30#10587543—24no—
31C17×#95—22no—
32#10587502—22no—
33#10587502—22no—
34C23×D17C2×D411yescharacteristic
35C22×#595—42no—
36C22×C4×C17—22no—
37C22×C4×C17C22⋊C412yes—
38C22×C4×C17C22×C411yescharacteristic
39C22×Dic17—22no—
40C22×Dic17C22⋊C412yes—
41C22×Dic17C2×D411yescharacteristic
42C2×C4×D17—42no—
43C2×C4×D17#4114yes—
44C22⋊#595—44no—
45#63247—44no—
46C2×#3624—42no—
47C42×C17—22no—
48C42×C17—42no—
49#63227—24no—
50#63227—44no—
51#63225—24no—
52#63225—44no—
53C4×Dic17—22no—
54C4×Dic17—44no—
55C4×Dic17—42no—
56#8740—171nomaximal, Sylow
57C23×C17C2×C22⋊C411yescharacteristic
58C22×D17—22no—
59C22×D17—42no—
60C22×D17#12312yes—
61C2×#595—82no—
62C2×#595—84no—
63C2×C4×C17—22no—
64C2×C4×C17—22no—
65C2×C4×C17—42no—
66C2×C4×C17—42no—
67C2×C4×C17—42no—
68C2×C4×C17—42no—
69C2×C4×C17#11712yes—
70C2×Dic17—22no—
71C2×Dic17—24no—
72C2×Dic17—22no—
73C2×Dic17—42no—
74C2×Dic17—42no—
75C2×Dic17—42no—
76C2×Dic17#12312yes—
77C4×D17—44no—
78#3624—82no—
79#2298—171no—
80#1822—171no—
81#1820—171no—
82#1284—174no—
83C22×C17—22no—
84C22×C17#38111yescharacteristic
85C22×C17#41012yes—
86C2×D17—22no—
87C2×D17—24no—
88C2×D17—82no—
89#595—162no—
90C4×C17—22no—
91C4×C17—42no—
92C4×C17—82no—
93Dic17—22no—
94Dic17—44no—
95Dic17—42no—
96C2×#117—171no—
97#407—172no—
98#388—342no—
99#387—342no—
100#381—172no—
101C4×C4⋊C4—172no—
102C4×C22⋊C4—172no—
103#376#59511yescharacteristic, complemented
104C43—171no—
105#343—342no—
106#342—342no—
107C2×C17—22no—
108C2×C17#182011yescharacteristic
109C2×C17#182712yes—
110D17—42no—
111C23×C4—171no—
112C2×M16—342no—
113#117—344no—
114C2×C4⋊C4—172no—
115C2×C4⋊C4—342no—
116C2×C22⋊C4—172no—
117C2×C22⋊C4—342no—
118C2×C22⋊C4—342no—
119C2×C42—171no—
120C2×C42—172no—
121C2×C42—342no—
122C2×C42C2×#59511yescharacteristic
123C2×C42C2×#59512yes—
124C22⋊C8—344no—
125#95—22no—
126#95—342no—
127#95—342no—
128#95—344no—
129C17#874011yescharacteristic, complemented, Sylow
130C24—171no—
131C22×C4—22no—
132C22×C4—171no—
133C22×C4—174no—
134C22×C4—172no—
135C22×C4—342no—
136C22×C4—682no—
137C22×C4—682no—
138C22×C4C22⋊#59512yes—
139C22×C4C22×#59511yescharacteristic
140M16—684no—
141C2×C8—682no—
142C4⋊C4—344no—
143C4⋊C4—684no—
144C22⋊C4—344no—
145C22⋊C4—684no—
146C22⋊C4—684no—
147C42—22no—
148C42—42no—
149C42—342no—
150C42—682no—
151C42—684no—
152C23—172no—
153C23—342no—
154C23—682no—
155C23C2×C22⋊#59511yescharacteristic
156C2×C4—22no—
157C2×C4—22no—
158C2×C4—42no—
159C2×C4—42no—
160C2×C4—42no—
161C2×C4—42no—
162C2×C4—172no—
163C2×C4—342no—
164C2×C4—344no—
165C2×C4—342no—
166C2×C4—684no—
167C2×C4—682no—
168C2×C4—682no—
169C2×C4—682no—
170C2×C4—1362no—
171C2×C4—1364no—
172C2×C4#1058767712yes—
173C8—1362no—
174C22—22no—
175C22—342no—
176C22—344no—
177C22—1362no—
178C22#1176375211yescharacteristic
179C22#1176378812yes—
180C4—22no—
181C4—42no—
182C4—82no—
183C4—2722no—
184C4—342no—
185C4—684no—
186C4—682no—
187C2—22no—
188C2—682no—
189C2#1454468111yescharacteristic
190C2#1454469412yes—
subgroupG/H
centerC22#11763752
commutatorC22×C4×C17C22×C4
FrattiniC22×C4C22×#595
FittingC17×#376C4
socleC22×C17#381
prime radicalC23×D17C2×D4
cosocleC22×C4×D17C23
hypercenter#376#595
hypocenterC17#8740
LCSG ▷ C22×C4×C17 ▷ C22×C17 ▷ C17
UCSC1 ◁ C22 ◁ C22×C4 ◁ #376

Complements

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

NH ≅ G/Ntype
12. C4×#63225C4semidirect
14. C42×Dic17C4semidirect
15. C17×#376C4semidirect
103. #376#595semidirect
129. C17#8740semidirect

Maximal subgroups

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

subgroupindex
#145446852
#145446812
#145436322
#145312792
#874017