Finite Group Databasebeta

← #17953648

Subgroups — #17953648

Order 4352.

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

normal subgroups only

This group has 384 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#14544037C212yesmaximal
2#14543635C214yesmaximal, complemented
3#14531281C211yesmaximal, characteristic
4#11763829C2214yes—
5#11763655—22no—
6#11763653—22no—
7C2×#10587558C2211yescharacteristic
8#11762700—22no—
9#11762693—22no—
10C4×#63225C2212yes—
11C4×#63227C412yes—
12#11762655C411yescharacteristic
13C43×C17C411yescharacteristic
14C22×C4×D17C2×C411yescharacteristic
15C2×C42×C17—22no—
16C2×C42×C17C2×C411yescharacteristic
17C2×C42×C17C2×C412yes—
18C2×#63227—22no—
19C2×#63227D412yes—
20C2×#63225—22no—
21C2×#63225D412yes—
22C2×C4×Dic17C2×C412yes—
23C2×C4×Dic17C2311yescharacteristic
24#10587558—24no—
25C22⋊#3624—24no—
26#10587544—24no—
27#10587542—24no—
28#10587502—22no—
29#10587502—22no—
30#10587502—22no—
31C23×D17C22⋊C411yescharacteristic
32C22×C4×C17—22no—
33C22×C4×C17C22⋊C412yes—
34C22×C4×C17C22×C411yescharacteristic
35C22×Dic17—22no—
36C22×Dic17C22⋊C411yescharacteristic
37C22×Dic17C2×D412yes—
38C2×C4×D17—22no—
39C2×C4×D17—42no—
40C2×#3624—44no—
41C42×C17—22no—
42C42×C17—42no—
43C42×C17—44no—
44#63227—24no—
45#63227—44no—
46#63225—24no—
47#63225—44no—
48C4×Dic17—42no—
49C4×Dic17#4114yes—
50#8744—171nomaximal, Sylow
51C23×C17C2×C22⋊C411yescharacteristic
52C22×D17—21no—
53C22×D17—22no—
54C22×D17—42no—
55C2×C4×C17—22no—
56C2×C4×C17—24no—
57C2×C4×C17—22no—
58C2×C4×C17—42no—
59C2×C4×C17—42no—
60C2×C4×C17—42no—
61C2×C4×C17#11712yes—
62C2×Dic17—21no—
63C2×Dic17—22no—
64C2×Dic17—42no—
65C2×Dic17—42no—
66C2×Dic17—42no—
67C2×Dic17—42no—
68C2×Dic17#12314yes—
69C4×D17—44no—
70#3624—84no—
71#2298—171no—
72#1464—172no—
73#1285—174no—
74C22×C17—22no—
75C22×C17#38111yescharacteristic
76C22×C17#41312yes—
77C2×D17—41no—
78C2×D17—42no—
79C2×D17—82no—
80C4×C17—22no—
81C4×C17—44no—
82C4×C17—42no—
83Dic17—24no—
84Dic17—41no—
85Dic17—82no—
86C2×#117—171no—
87#432—174no—
88#388—342no—
89#387—342no—
90C4×C4⋊C4—172no—
91C4×C22⋊C4—172no—
92#376—171no—
93C43#59511yescharacteristic
94#324—342no—
95#323—342no—
96C2×C17—22no—
97C2×C17#182211yescharacteristic
98C2×C17#182712yes—
99D17—81no—
100C23×C4—171no—
101#117—344no—
102C2×C4⋊C4—172no—
103C2×C4⋊C4—342no—
104C2×C22⋊C4—172no—
105C2×C22⋊C4—342no—
106C2×C42—22no—
107C2×C42—171no—
108C2×C42—172no—
109C2×C42C2×#59511yescharacteristic
110C2×C42C2×#59512yes—
111C4⋊C8—344no—
112C22⋊C8—344no—
113#97—344no—
114#95—342no—
115#95—342no—
116#95—342no—
117C17#874411yescharacteristic, complemented, Sylow
118C24—171no—
119C22×C4—22no—
120C22×C4—172no—
121C22×C4—171no—
122C22×C4—342no—
123C22×C4—342no—
124C22×C4—682no—
125C22×C4C22⋊#59512yes—
126C22×C4C22×#59511yescharacteristic
127C2×C8—684no—
128C4⋊C4—344no—
129C4⋊C4—684no—
130C22⋊C4—344no—
131C22⋊C4—684no—
132C42—22no—
133C42—42no—
134C42—44no—
135C42—174no—
136C42—682no—
137C23—341no—
138C23—342no—
139C23—682no—
140C23C2×C22⋊#59511yescharacteristic
141C2×C4—22no—
142C2×C4—24no—
143C2×C4—22no—
144C2×C4—42no—
145C2×C4—42no—
146C2×C4—42no—
147C2×C4—174no—
148C2×C4—341no—
149C2×C4—342no—
150C2×C4—684no—
151C2×C4—682no—
152C2×C4—682no—
153C2×C4—682no—
154C2×C4—682no—
155C2×C4#1058767712yes—
156C8—1364no—
157C22—22no—
158C22—681no—
159C22—682no—
160C22—1362no—
161C22#1176375211yescharacteristic
162C22#1176379512yes—
163C4—22no—
164C4—44no—
165C4—42no—
166C4—344no—
167C4—681no—
168C4—1362no—
169C2—22no—
170C2—1361no—
171C2#1454468511yescharacteristic
172C2#1454469312yes—
subgroupG/H
centerC22#11763752
commutatorC22×C4×C17C22×C4
FrattiniC22×C4C22×#595
FittingC43×C17C4
socleC22×C17#381
prime radicalC23×D17C22⋊C4
cosocleC2×C4×Dic17C23
hypercenterC43#595
hypocenterC17#8744
LCSG ▷ C22×C4×C17 ▷ C22×C17 ▷ C17
UCSC1 ◁ C22 ◁ C22×C4 ◁ C43

Complements

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

NH ≅ G/Ntype
2. #14543635C2semidirect
117. C17#8744semidirect

Maximal subgroups

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

subgroupindex
#145440372
#145436352
#145312812
#874417