Finite Group Databasebeta

← #17949793

Subgroups — #17949793

Order 4352.

408 conjugacy classes of subgroups; only the 118 normal subgroups are shown.

normal subgroups only

This group has 408 conjugacy classes of subgroups — too many to draw. Only its 118 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#14544699C212yesmaximal
2#14543602C214yesmaximal
3#125×Dic17C211yesmaximal, characteristic
4C2×C4⋊#3624—22no—
5#11763675—22no—
6#11763675C2214yes—
7#11762708C2212yes—
8#11762695—22no—
9#11762675C411yescharacteristic
10C4⋊C4×Dic17—22no—
11C4⋊C4×Dic17C412yes—
12C42×Dic17C2211yescharacteristic
13C2×C17×#125C411yescharacteristic
14C22×#3624—24no—
15C17×#125—22no—
16C17×#125C814yescomplemented
17C2×C4⋊C4×C17—22no—
18C2×C4⋊C4×C17C2×C412yes—
19C2×C42×C17C2×C411yescharacteristic
20C2×C4⋊Dic17—22no—
21C2×C4⋊Dic17C2×C412yes—
22C2×C4×Dic17—22no—
23C2×C4×Dic17C2×C411yescharacteristic
24C2×C4×Dic17D412yes—
25C2×C4×Dic17D412yes—
26C2×C4×Dic17C2311yescharacteristic
27C4⋊#3624—44no—
28#10587502—22no—
29#10587502—22no—
30#10587502—22no—
31C22×C4×C17—22no—
32C22×C4×C17C22⋊C412yes—
33C22×C4×C17C22×C411yescharacteristic
34C22×Dic17—22no—
35C22×Dic17C22⋊C411yescharacteristic
36C22×Dic17C22⋊C411yescharacteristic
37C22×Dic17C2×D412yes—
38C2×#3624—44no—
39C2×#3624—44no—
40C2×#3624—44no—
41C4⋊C4×C17—28no—
42C4⋊C4×C17—22no—
43C4⋊C4×C17C2×C814yes—
44C42×C17C2×C812yes—
45C42×C17M1612yes—
46C4⋊Dic17—42no—
47C4⋊Dic17—42no—
48C4⋊Dic17—42no—
49C4×Dic17—22no—
50C4×Dic17—22no—
51C4×Dic17—22no—
52C4×Dic17—42no—
53C4×Dic17—41no—
54C4×Dic17—44no—
55#7602—171nomaximal, Sylow
56C23×C17C2×C22⋊C411yescharacteristic
57C2×C4×C17—21no—
58C2×C4×C17—21no—
59C2×C4×C17—22no—
60C2×C4×C17—22no—
61C2×C4×C17—24no—
62C2×C4×C17—42no—
63C2×C4×C17—42no—
64C2×C4×C17C22⋊C814yes—
65C2×C4×C17C22×C811yescharacteristic
66C2×C4×C17C2×M1611yescharacteristic
67C2×Dic17—22no—
68C2×Dic17—22no—
69C2×Dic17—22no—
70C2×Dic17—21no—
71C2×Dic17—22no—
72C2×Dic17—42no—
73C2×Dic17—42no—
74C2×Dic17—42no—
75C2×Dic17#10112yes—
76C2×Dic17AGL(1,ℤ/8)12yes—
77C2×Dic17#13712yes—
78#3624—84no—
79C4×#125—171no—
80#1831—172no—
81#1271—174no—
82C22×C17C2×C22⋊C811yescharacteristic
83C22×C17#41011yescharacteristic
84C22×C17C2×#10111yescharacteristic
85C22×C17#41712yes—
86C22×C17#42112yes—
87C4×C17—21no—
88C4×C17—21no—
89C4×C17—24no—
90C4×C17—44no—
91Dic17—22no—
92Dic17—22no—
93Dic17—22no—
94Dic17—41no—
95Dic17—82no—
96C2×#125#59511yescharacteristic
97C2×C4⋊C8—342no—
98#389—172no—
99#387—342no—
100#382—171no—
101C4×C4⋊C4—172no—
102C4×C4⋊C4—342no—
103C43—171no—
104#336—174no—
105#336—342no—
106C2×C17#146111yescharacteristic
107C2×C17#147712yes—
108C2×C17#151212yes—
109C2×C17#153411yescharacteristic
110C2×C17#156111yescharacteristic
111C22×C8—344no—
112#125—22no—
113#125#362414yescomplemented
114C2×C4⋊C4—22no—
115C2×C4⋊C4—172no—
116C2×C4⋊C4—342no—
117C2×C4⋊C4C2×#59512yes—
118C2×C42—172no—
119C2×C42—171no—
120C2×C42—172no—
121C2×C42—171no—
122C2×C42—342no—
123C2×C42C2×#59511yescharacteristic
124C4⋊C8—684no—
125#95—342no—
126#95—342no—
127#95—342no—
128C17#760211yescharacteristic, complemented, Sylow
129C22×C4—22no—
130C22×C4—171no—
131C22×C4—172no—
132C22×C4—171no—
133C22×C4—342no—
134C22×C4C22⋊#59512yes—
135C22×C4C22×#59511yescharacteristic
136C2×C8—684no—
137C2×C8—684no—
138C2×C8—684no—
139C4⋊C4—22no—
140C4⋊C4—28no—
141C4⋊C4—682no—
142C4⋊C4—682no—
143C4⋊C4—682no—
144C4⋊C4C2×#362414yes—
145C42—342no—
146C42—342no—
147C42—342no—
148C42—681no—
149C42—682no—
150C42—684no—
151C42C2×#362412yes—
152C42#6324712yes—
153C23C2×C22⋊#59511yescharacteristic
154C2×C4—21no—
155C2×C4—21no—
156C2×C4—22no—
157C2×C4—22no—
158C2×C4—24no—
159C2×C4—42no—
160C2×C4—42no—
161C2×C4—172no—
162C2×C4—172no—
163C2×C4—172no—
164C2×C4—342no—
165C2×C4—342no—
166C2×C4—342no—
167C2×C4—341no—
168C2×C4—342no—
169C2×C4—682no—
170C2×C4—682no—
171C2×C4—682no—
172C2×C4C22⋊#362414yes—
173C2×C4C22×#362411yescharacteristic
174C2×C4C2×#6324711yescharacteristic
175C8—1364no—
176C22C2×C22⋊#362411yescharacteristic
177C22#1176379011yescharacteristic
178C22D17⋊#10111yescharacteristic
179C22#1176380012yes—
180C22#1176380612yes—
181C4—21no—
182C4—21no—
183C4—24no—
184C4—44no—
185C4—342no—
186C4—342no—
187C4—342no—
188C4—681no—
189C4—1362no—
190C2#1454402711yescharacteristic
191C2#1454407912yes—
192C2#1454419812yes—
193C2#1454426711yescharacteristic
194C2#1454432411yescharacteristic
subgroupG/H
centerC23C2×C22⋊#595
commutatorC2×C4×C17C22×C8
FrattiniC22×C4C22×#595
FittingC2×C17×#125C4
socle, prime radicalC23×C17C2×C22⋊C4
cosocleC2×C4×Dic17C23
hypercenterC2×#125#595
hypocenterC17#7602
LCSG ▷ C2×C4×C17 ▷ C22×C17 ▷ C17
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#125

Complements

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

NH ≅ G/Ntype
16. C17×#125C8semidirect
113. #125#3624semidirect
128. C17#7602semidirect

Maximal subgroups

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

subgroupindex
#145446992
#145436022
#125×Dic172
#760217