Finite Group Databasebeta

← #17982376

Subgroups — #17982376

Order 4352.

478 conjugacy classes of subgroups; only the 233 normal subgroups are shown.

normal subgroups only

This group has 478 conjugacy classes of subgroups — too many to draw. Only its 233 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
1C2×#11763904C212yesmaximal
2#14545940C211yesmaximal, characteristic
3C2×#11763902C212yesmaximal
4C4×#10587665C211yesmaximal, characteristic
5#14544442C211yesmaximal, characteristic
6C2×#10587665C2211yescharacteristic
7C2×#10587665C2211yescharacteristic
8C2×#10587665C2212yes—
9#11763904C418yescomplemented
10#11763903C414yescomplemented
11#11763902C418yescomplemented
12C4×#63241C414yescomplemented
13C2×#10587532C412yes—
14C4×#63242C2211yescharacteristic
15C2×C8×#595C2212yes—
16#11763745C411yescharacteristic
17#97×D17C411yescharacteristic
18C2×C4×#595C2×C412yes—
19C2×#63242C2×C411yescharacteristic
20C2×#63242C2311yescharacteristic
21C2×#63241C2×C412yes—
22C2×#63241C2×C412yes—
23C2×#63241C2×C414yes—
24#10587665C2×C414yes—
25#10587665C2×C414yes—
26#10587665C2×C414yes—
27#10587665C2×C414yes—
28C2×C8×D17C2×C412yes—
29C42×D17C2×C411yescharacteristic
30(C2×#595)⋊C4C814yes—
31C4×#3624C2×C412yes—
32C4×#3624C2×C412yes—
33#10587532C818yes—
34C8×#595C2×C414yes—
35C8×#595C2×C414yes—
36C17×#97C811yescharacteristic
37#10587486C812yes—
38#10587474C811yescharacteristic
39C22×#595C2×C814yes—
40C2×C4×D17C2×C812yes—
41C2×C4×D17C22×C411yescharacteristic
42C2×#3624C4212yes—
43C2×#3624C22×C411yescharacteristic
44C2×#3624C22×C411yescharacteristic
45C4×#595C4214yes—
46C4×#595C2×C814yes—
47#63242C2×C814yes—
48#63242C22×C412yes—
49#63242C22×C412yes—
50#63241C4214yes—
51#63241C4218yes—
52#63241C4214yes—
53C2×C8×C17C2×C812yes—
54C42×C17C2×C811yescharacteristic
55C4×Dic17C4212yes—
56C4×Dic17C2×C811yescharacteristic
57C2×#3622C2×C812yes—
58C8×D17C4214yes—
59C8×D17C2×C814yes—
60#12539—171nomaximal, Sylow
61C22×D17C22×C811yescharacteristic
62C2×#595—28no—
63C2×#595C4×C818yes—
64C2×C4×C17C4×C812yes—
65C2×C4×C17C22×C811yescharacteristic
66C2×Dic17C4×C812yes—
67C2×Dic17C2×C4211yescharacteristic
68C4×D17—24no—
69C4×D17C2×C4212yes—
70C4×D17C22×C812yes—
71#3624C4×C814yes—
72#3624C2×C4211yescharacteristic
73#3624C2×C4212yes—
74#3624C2×C4211yescharacteristic
75C8×C17C4×C814yes—
76#3622C4×C814yes—
77C2×#346—171no—
78C2×#346—172no—
79C2×C4×C16—171no—
80C2×C4×C16—172no—
81#1726—171no—
82C22×C17C2×C4×C811yescharacteristic
83C2×D17C2×C4×C812yes—
84C2×D17#50414yes—
85#595—28no—
86C4×C17—22no—
87C4×C17C2×C4×C812yes—
88Dic17—22no—
89Dic17C4311yescharacteristic
90Dic17C2×C4×C811yescharacteristic
91C22×C16—171no—
92C22×C16—172no—
93C22×C16—171no—
94C2×#97—172no—
95C2×#97—171no—
96C2×C4×C8—172no—
97C2×C4×C8—171no—
98#376—171no—
99#346—174no—
100#346—178no—
101C4×C16—174no—
102C4×C16—178no—
103C2×C17C42×C811yescharacteristic
104C2×C17#210812yes—
105D17#210814yes—
106C22×C8—171no—
107C22×C8—171no—
108C22×C8—172no—
109C2×C42—172no—
110C2×C42—171no—
111C2×C16—174no—
112C2×C16—174no—
113C2×C16—174no—
114C2×C16—174no—
115C2×C16—172no—
116C2×C16—172no—
117C2×C16—174no—
118#97—178no—
119#97—172no—
120#97—171no—
121#97#363311yescharacteristic
122C4×C8—174no—
123C4×C8—172no—
124C4×C8—174no—
125C4×C8—172no—
126#95—174no—
127C17#1253911yescharacteristic, complemented, Sylow
128C22×C4—171no—
129C22×C4—174no—
130C22×C4—172no—
131C2×C8—174no—
132C2×C8—172no—
133C2×C8—172no—
134C2×C8—172no—
135C2×C8—171no—
136C2×C8—171no—
137C2×C8—172no—
138C2×C8—174no—
139C2×C8—174no—
140C2×C8C2×#363312yes—
141C42—174no—
142C42—174no—
143C42—172no—
144C42—171no—
145C42C2×#363311yescharacteristic
146C16—174no—
147C16—178no—
148C16—174no—
149C23—171no—
150C2×C4—171no—
151C2×C4—172no—
152C2×C4—172no—
153C2×C4—178no—
154C2×C4—172no—
155C2×C4—344no—
156C2×C4—348no—
157C2×C4C4×#363312yes—
158C2×C4C22×#363311yescharacteristic
159C8—171no—
160C8—172no—
161C8—171no—
162C8—174no—
163C8—174no—
164C8C4×#363314yes—
165C22—174no—
166C22—172no—
167C22C2×C4×#363311yescharacteristic
168C4—22no—
169C4—171no—
170C4—171no—
171C4—348no—
172C4—342no—
173C4C2×C4×#363312yes—
174C2—174no—
175C2C42×#363311yescharacteristic
176C2#1454594712yes—
subgroupG/H
center, FrattiniC2×C4C22×#3633
commutatorC2×C17C42×C8
FittingC17×#97C8
socleC22×C17C2×C4×C8
prime radicalC22×D17C22×C8
cosocleC2×#63242C23
hypercenter#97#3633
hypocenterC17#12539
LCSG ▷ C2×C17 ▷ C17
UCSC1 ◁ C2×C4 ◁ #97

Complements

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

NH ≅ G/Ntype
9. #11763904C4semidirect
10. #11763903C4semidirect
11. #11763902C4semidirect
12. C4×#63241C4semidirect
127. C17#12539semidirect

Maximal subgroups

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

subgroupindex
C2×#117639042
#145459402
C2×#117639022
C4×#105876652
#145444422
#1253917