Finite Group Databasebeta

← #17949962

Subgroups — #17949962

Order 4352.

384 conjugacy classes of subgroups; only the 90 normal subgroups are shown.

normal subgroups only

This group has 384 conjugacy classes of subgroups — too many to draw. Only its 90 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#14544712C212yesmaximal
2#14543603C214yesmaximal
3#14531339C211yesmaximal, characteristic
4#11763675—22no—
5#11763675—22no—
6#11763675C2214yes—
7C2×#10587556C411yescharacteristic
8#11762705C2212yes—
9#11762691—22no—
10C4⋊C4×Dic17C412yes—
11#11762660—22no—
12C42×Dic17C2211yescharacteristic
13C17×#382C411yescharacteristic
14C22×#3624—24no—
15C2×C4⋊C4×C17C2×C412yes—
16C2×C42×C17C2×C411yescharacteristic
17C2×C4⋊Dic17C2×C412yes—
18C2×#63225—22no—
19C2×#63225—22no—
20C2×C4×Dic17—22no—
21C2×C4×Dic17C2×C411yescharacteristic
22C2×C4×Dic17D412yes—
23C2×C4×Dic17D412yes—
24C2×C4×Dic17C2311yescharacteristic
25#10587556—24no—
26C17×#95—22no—
27#10587502—22no—
28#10587502—22no—
29C22×C4×C17—22no—
30C22×C4×C17C22⋊C412yes—
31C22×C4×C17C22×C411yescharacteristic
32C22×Dic17—22no—
33C22×Dic17C22⋊C411yescharacteristic
34C22×Dic17C22⋊C411yescharacteristic
35C22×Dic17C2×D412yes—
36C2×#3624—44no—
37C2×#3624—44no—
38C2×#3624—44no—
39C4⋊C4×C17—42no—
40C42×C17—22no—
41C4⋊Dic17—22no—
42C4⋊Dic17M1614yes—
43#63225—28no—
44#63225—44no—
45C4×Dic17—22no—
46C4×Dic17—24no—
47C4×Dic17—42no—
48C4×Dic17—41no—
49C4×Dic17—44no—
50#7650—171nomaximal, Sylow
51C23×C17C2×C22⋊C411yescharacteristic
52C2×C4×C17—21no—
53C2×C4×C17—21no—
54C2×C4×C17—22no—
55C2×C4×C17—22no—
56C2×C4×C17—22no—
57C2×C4×C17—42no—
58C2×C4×C17—42no—
59C2×C4×C17—42no—
60C2×C4×C17C2×M1612yes—
61C2×Dic17—22no—
62C2×Dic17—22no—
63C2×Dic17—22no—
64C2×Dic17—24no—
65C2×Dic17—21no—
66C2×Dic17—22no—
67C2×Dic17—42no—
68C2×Dic17—42no—
69C2×Dic17#10112yes—
70C2×Dic17#13514yes—
71#3624—84no—
72C4×#125—171no—
73#1839—172no—
74#1271—174no—
75C22×C17#40711yescharacteristic
76C22×C17#41011yescharacteristic
77C22×C17C2×#10111yescharacteristic
78C22×C17#41612yes—
79C22×C17#42112yes—
80C4×C17—22no—
81C4×C17—42no—
82C4×C17—82no—
83Dic17—24no—
84Dic17—22no—
85Dic17—41no—
86Dic17—44no—
87C2×#125—171no—
88#389—172no—
89#387—342no—
90#382#59511yescharacteristic
91C4×C4⋊C4—172no—
92C4×C4⋊C4—342no—
93C43—171no—
94#336—174no—
95#336—342no—
96#336—342no—
97C2×C17#146711yescharacteristic
98C2×C17#148812yes—
99C2×C17#152112yes—
100C2×C17#153411yescharacteristic
101C2×C17#154411yescharacteristic
102C22×C8—344no—
103#125—344no—
104C2×C4⋊C4—172no—
105C2×C4⋊C4—342no—
106C2×C4⋊C4—342no—
107C2×C4⋊C4C2×#59512yes—
108C2×C42—172no—
109C2×C42—171no—
110C2×C42—172no—
111C2×C42—171no—
112C2×C42—342no—
113C2×C42C2×#59511yescharacteristic
114#95—22no—
115#95—342no—
116#95—342no—
117C17#765011yescharacteristic, complemented, Sylow
118C22×C4—22no—
119C22×C4—171no—
120C22×C4—172no—
121C22×C4—171no—
122C22×C4—342no—
123C22×C4C22⋊#59512yes—
124C22×C4C22×#59511yescharacteristic
125C2×C8—684no—
126C2×C8—684no—
127C2×C8—684no—
128C4⋊C4—42no—
129C4⋊C4—174no—
130C4⋊C4—348no—
131C4⋊C4—342no—
132C4⋊C4—684no—
133C42—22no—
134C42—342no—
135C42—344no—
136C42—681no—
137C42—682no—
138C42—684no—
139C23C2×C22⋊#59511yescharacteristic
140C2×C4—21no—
141C2×C4—21no—
142C2×C4—22no—
143C2×C4—22no—
144C2×C4—22no—
145C2×C4—42no—
146C2×C4—42no—
147C2×C4—42no—
148C2×C4—172no—
149C2×C4—174no—
150C2×C4—342no—
151C2×C4—342no—
152C2×C4—342no—
153C2×C4—344no—
154C2×C4—341no—
155C2×C4—342no—
156C2×C4—682no—
157C2×C4—682no—
158C2×C4D17⋊M1612yes—
159C8—1364no—
160C22#1176378111yescharacteristic
161C22#1176378911yescharacteristic
162C22D17⋊#10111yescharacteristic
163C22#1176379912yes—
164C22#1176380612yes—
165C4—22no—
166C4—42no—
167C4—82no—
168C4—344no—
169C4—342no—
170C4—681no—
171C4—684no—
172C2#1454404811yescharacteristic
173C2#1454411712yes—
174C2#1454422512yes—
175C2#1454426711yescharacteristic
176C2#1454429011yescharacteristic
subgroupG/H
centerC23C2×C22⋊#595
commutatorC22×C4×C17C22×C4
FrattiniC22×C4C22×#595
FittingC17×#382C4
socle, prime radicalC23×C17C2×C22⋊C4
cosocleC2×C4×Dic17C23
hypercenter#382#595
hypocenterC17#7650
LCSG ▷ C22×C4×C17 ▷ C22×C17 ▷ C17
UCSC1 ◁ C23 ◁ C2×C42 ◁ #382

Complements

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

NH ≅ G/Ntype
117. C17#7650semidirect

Maximal subgroups

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

subgroupindex
#145447122
#145436032
#145313392
#765017