Finite Group Databasebeta

← #17981184

Subgroups — #17981184

Order 4352.

210 conjugacy classes of subgroups; only the 43 normal subgroups are shown.

normal subgroups only

This group has 210 conjugacy classes of subgroups — too many to draw. Only its 43 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#14545787C212yesmaximal
2#14544971C211yesmaximal, characteristic
3#11763922—22no—
4#11763813C411yescharacteristic
5#11763745C2211yescharacteristic
6#11763679—22no—
7#11763365C411yescharacteristic
8C2×C4×#595D412yes—
9C2×#63243—21no—
10C22⋊#3633—42no—
11C4⋊#3633—42no—
12C4×#3633—24no—
13C17×#125C811yescharacteristic, complemented
14#10587582—41no—
15#10587578—21no—
16#10587574—21no—
17#10587573—41no—
18C42×D17C2×C411yescharacteristic
19#10587556C811yescharacteristic, complemented
20(C2×#595)⋊C4—41no—
21C4⋊#3624—41no—
22C22×#595—22no—
23C2×#3633—44no—
24C2×C4×D17—21no—
25C2×C4×D17C22⋊C411yescharacteristic
26C2×Dic34—41no—
27C2×#3624—41no—
28C4×#595—22no—
29C4×#595SD1612yes—
30C4×#595Q1612yes—
31#63243—42no—
32C4⋊C4×C17—21no—
33C4⋊C4×C17—41no—
34C42×C17C2×C811yescharacteristic
35#63227—41no—
36C4⋊Dic17—21no—
37#63225—41no—
38#63225—41no—
39C4×Dic17—21no—
40C4×Dic17—41no—
41C4×Dic17M1611yescharacteristic
42#7129—171nomaximal, Sylow
43C22×D17#9911yescharacteristic
44C2×#595—22no—
45C2×#595—22no—
46C2×#595—82no—
47#3633—84no—
48C2×C4×C17—21no—
49C2×C4×C17—41no—
50C2×C4×C17C22⋊C811yescharacteristic
51C2×Dic17—21no—
52C2×Dic17—41no—
53C2×Dic17#10011yescharacteristic
54C4×D17—81no—
55C4×D17#10312yes—
56C4×D17#10412yes—
57Dic34—82no—
58#3624—81no—
59#1995—171no—
60#1274—172no—
61C22×C17#32311yescharacteristic
62C2×D17—41no—
63C2×D17#32812yes—
64#595—42no—
65#595—42no—
66C4×C17—41no—
67C4×C17—81no—
68C4×C17Q8⋊C812yes—
69Dic17—41no—
70Dic17—81no—
71Dic17#32911yescharacteristic
72Dic17#33311yescharacteristic
73#533—171no—
74#431—342no—
75#423—171no—
76#376—171no—
77#339—342no—
78C2×C17—21no—
79C2×C17#127211yescharacteristic
80D17—22no—
81C2×M16—341no—
82C4⋊Q8—341no—
83#125—171no—
84#125#363311yescharacteristic, complemented
85C22⋊Q8—681no—
86C4×Q8—681no—
87#117—341no—
88C2×C42—172no—
89C2×C42—171no—
90C4⋊C8—682no—
91C4⋊C8—681no—
92C22⋊C8—682no—
93C4×C8—344no—
94#95—681no—
95C17#712911yescharacteristic, complemented, Sylow
96C2×Q8—681no—
97C22×C4—171no—
98C22×C4—341no—
99C22×C4—342no—
100M16—682no—
101C2×C8—681no—
102C2×C8—684no—
103C4⋊C4—21no—
104C4⋊C4—41no—
105C4⋊C4—341no—
106C4⋊C4—681no—
107C4⋊C4—681no—
108C22⋊C4—681no—
109C42—172no—
110C42—172no—
111C42—171no—
112C42—341no—
113C42—342no—
114C42—681no—
115C42C2×#363311yescharacteristic
116C23—171no—
117Q8—1362no—
118C2×C4—21no—
119C2×C4—41no—
120C2×C4—171no—
121C2×C4—172no—
122C2×C4—172no—
123C2×C4—342no—
124C2×C4—342no—
125C2×C4—341no—
126C2×C4—681no—
127C2×C4—1361no—
128C2×C4—1362no—
129C2×C4C22⋊#363311yescharacteristic
130C8—1361no—
131C8—1364no—
132C22—172no—
133C22—681no—
134C22#1176389411yescharacteristic
135C4—41no—
136C4—81no—
137C4—171no—
138C4—171no—
139C4—681no—
140C4—682no—
141C4—682no—
142C4—1361no—
143C4Q8⋊#363312yes—
144C2—21no—
145C2—342no—
146C2#1454578511yescharacteristic
subgroupG/H
centerC2#14545785
commutatorC42×C17C2×C8
FrattiniC42C2×#3633
FittingC17×#125C8
socleC2×C17#1272
prime radicalC22×D17#99
cosocle#11763745C22
hypercenter#125#3633
hypocenterC17#7129
LCSG ▷ C42×C17 ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C2 ◁ C2×C4 ◁ C42 ◁ #125

Complements

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

NH ≅ G/Ntype
13. C17×#125C8semidirect
19. #10587556C8semidirect
84. #125#3633semidirect
95. C17#7129semidirect

Maximal subgroups

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

subgroupindex
#145457872
#145449712
#712917