Finite Group Databasebeta

← #17981839

Subgroups — #17981839

Order 4352.

306 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 306 conjugacy classes of subgroups — too many to draw. Only its 141 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#14545983C211yesmaximal, characteristic
2C4×#10587665C211yesmaximal, characteristic
3#14545801C212yesmaximal, complemented
4C8×#63241C212yesmaximal, complemented
5#14543982C211yesmaximal, characteristic
6C2×#10587665C412yes—
7#11763912C412yes—
8#11763906C412yes—
9C4×#63241C412yes—
10C4×#63241C2211yescharacteristic
11C4×#63241C2211yescharacteristic
12C4×#63241C2212yes—
13#11763827C411yescharacteristic
14C4×#63242C2211yescharacteristic
15#11763650C412yes—
16C8×#3624C2212yes—
17#11762761C411yescharacteristic
18C2×#63242C2×C411yescharacteristic
19C2×#63242C2×C411yescharacteristic
20C2×#63241C2×C412yes—
21C2×#63241C2×C414yes—
22C2×#63241C2×C412yes—
23#10587665—24no—
24C2×#63218C812yes—
25C42×D17C2×C411yescharacteristic
26#10587544C812yes—
27#10587543C812yes—
28C4×#3624C2×C411yescharacteristic
29C4×#3624C2×C411yescharacteristic
30C4×#3624C2×C411yescharacteristic
31C4×#3624C2×C412yes—
32C4×#3624C2311yescharacteristic
33C17×#97C811yescharacteristic
34C8×Dic17C2×C412yes—
35#10587474C811yescharacteristic
36C2×C4×D17C4211yescharacteristic
37C2×C4×D17C2×C811yescharacteristic
38C2×C4×D17C2×C811yescharacteristic
39C2×#3624C4211yescharacteristic
40C2×#3624C4211yescharacteristic
41C2×#3624C2×C814yes—
42C2×#3624C22×C411yescharacteristic
43C2×#3624C22×C411yescharacteristic
44#63242—22no—
45#63242—22no—
46#63241—22no—
47#63241—24no—
48#63241M1614yescomplemented
49C2×C8×C17C2×C812yes—
50C42×C17C2×C811yescharacteristic
51C4×Dic17C4211yescharacteristic
52C4×Dic17C2×C811yescharacteristic
53C4×Dic17C22×C411yescharacteristic
54C2×#3622C2×C812yes—
55#63218C1618yescomplemented
56C16×M16—171nomaximal, Sylow
57C22×D17C4×C811yescharacteristic
58C2×C4×C17C4×C811yescharacteristic
59C2×C4×C17C4×C811yescharacteristic
60C2×C4×C17C22×C811yescharacteristic
61C2×Dic17C4×C811yescharacteristic
62C2×Dic17C2×C4211yescharacteristic
63C2×Dic17C22×C811yescharacteristic
64C4×D17—21no—
65C4×D17—21no—
66C4×D17—22no—
67C4×D17C2×C1614yes—
68#3624—21no—
69#3624—21no—
70#3624—24no—
71#3624C2×M1612yes—
72#3624#13112yes—
73C8×C17C2×C1614yescomplemented
74#3622C2×C1614yescomplemented
75#2162—171no—
76C2×C4×C16—171no—
77C8×M16—171no—
78#1312—172no—
79C8×C16—172no—
80C22×C17C2×C4×C811yescharacteristic
81C2×D17—21no—
82C2×D17—21no—
83C2×D17C4×C1612yes—
84C4×C17—21no—
85C4×C17—21no—
86C4×C17C22×C1612yes—
87Dic17C4×C1612yes—
88Dic17C4×M1611yescharacteristic
89Dic17#40511yescharacteristic
90Dic17#50412yes—
91C22×C16—172no—
92#431—171no—
93C4×M16—171no—
94C2×C4×C8—171no—
95C4⋊C16—172no—
96C22⋊C16—172no—
97C4×C16—171no—
98C4×C16—172no—
99C4×C16—171no—
100C4×C16—172no—
101#322—172no—
102C82—172no—
103C2×C17C8×M1611yescharacteristic
104C2×C17C2×C4×C1611yescharacteristic
105C2×C17#210811yescharacteristic
106D17—22no—
107C2×M16—172no—
108C22×C8—171no—
109C22×C8—171no—
110C2×C42—171no—
111C2×C16—172no—
112C2×C16—172no—
113C2×C16—174no—
114C2×C16—344no—
115C4⋊C8—172no—
116C22⋊C8—172no—
117#97—171no—
118#97#363311yescharacteristic
119C4×C8—171no—
120C4×C8—172no—
121C4×C8—171no—
122C4×C8—171no—
123C4×C8—171no—
124C4×C8—172no—
125C17C16×M1611yescharacteristic, complemented, Sylow
126C22×C4—171no—
127C22×C4—171no—
128C22×C4—171no—
129M16—178no—
130C2×C8—171no—
131C2×C8—171no—
132C2×C8—172no—
133C2×C8—171no—
134C2×C8—171no—
135C2×C8—174no—
136C2×C8—342no—
137C2×C8—342no—
138C2×C8C2×#363312yes—
139C42—171no—
140C42—171no—
141C42—171no—
142C42C2×#363311yescharacteristic
143C16—174no—
144C16—344no—
145C16—342no—
146C23—171no—
147C2×C4—171no—
148C2×C4—171no—
149C2×C4—171no—
150C2×C4—174no—
151C2×C4—341no—
152C2×C4—341no—
153C2×C4—342no—
154C2×C4C4×#363311yescharacteristic
155C2×C4C4×#363311yescharacteristic
156C2×C4C22×#363311yescharacteristic
157C8—172no—
158C8—172no—
159C8—174no—
160C8—341no—
161C8—341no—
162C8—344no—
163C8#1058766514yescomplemented
164C22—172no—
165C22—341no—
166C22—341no—
167C22C2×C4×#363311yescharacteristic
168C4—21no—
169C4—21no—
170C4—172no—
171C4—172no—
172C4—171no—
173C4—171no—
174C4C2×#1058766512yes—
175C2—342no—
176C2M16×#363311yescharacteristic
177C2C4×#1058766511yescharacteristic
178C2#1454594711yescharacteristic
subgroupG/H
center, FrattiniC2×C4C22×#3633
commutatorC2×C17C2×C4×C16
FittingC17×#97C8
socleC22×C17C2×C4×C8
prime radicalC22×D17C4×C8
cosocleC4×#3624C23
hypercenter#97#3633
hypocenterC17C16×M16
LCSG ▷ C2×C17 ▷ C17
UCSC1 ◁ C2×C4 ◁ #97

Complements

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

NH ≅ G/Ntype
3. #14545801C2semidirect
4. C8×#63241C2semidirect
48. #63241M16semidirect
55. #63218C16semidirect
73. C8×C17C2×C16semidirect
74. #3622C2×C16semidirect
125. C17C16×M16semidirect
163. C8#10587665semidirect

Maximal subgroups

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

subgroupindex
#145459832
C4×#105876652
#145458012
C8×#632412
#145439822
C16×M1617