Finite Group Databasebeta

← #17981194

Subgroups — #17981194

Order 4352.

202 conjugacy classes of subgroups; only the 45 normal subgroups are shown.

normal subgroups only

This group has 202 conjugacy classes of subgroups — too many to draw. Only its 45 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#14545858C212yesmaximal
2#14544966C211yesmaximal, characteristic
3#11763928—22no—
4C4×#63242C2211yescharacteristic
5#11763753C411yescharacteristic
6#11763682—22no—
7#125×D17C411yescharacteristic
8C2×C4⋊#595—21no—
9C2×#63242D412yes—
10#10587670—42no—
11#10587666—24no—
12#10587665—42no—
13C17×#125C811yescharacteristic
14C4⋊C4×D17—21no—
15C4⋊C4×D17—41no—
16#10587576—21no—
17#10587575—41no—
18C42×D17C2×C411yescharacteristic
19#10587556C811yescharacteristic
20(C2×#595)⋊C4—41no—
21C4×#3624—41no—
22C22×#595—41no—
23C2×C4×D17—21no—
24C2×C4×D17—41no—
25C2×C4×D17C22⋊C411yescharacteristic
26C2×#3624—22no—
27C4⋊#595—42no—
28#63242—22no—
29#63242SD1612yes—
30#63242Q1612yes—
31#63241—44no—
32C4⋊C4×C17—21no—
33C4⋊C4×C17—41no—
34C42×C17C2×C811yescharacteristic
35C4⋊Dic17—21no—
36C4⋊Dic17—41no—
37#63225—41no—
38#63225—41no—
39#63225—41no—
40C4×Dic17—21no—
41C4×Dic17M1611yescharacteristic
42#7135—171nomaximal, Sylow
43C22×D17#10011yescharacteristic
44C2×#595—82no—
45C2×#595—81no—
46C2×C4×C17—21no—
47C2×C4×C17—41no—
48C2×C4×C17C22⋊C811yescharacteristic
49C2×Dic17—21no—
50C2×Dic17—41no—
51C2×Dic17#9911yescharacteristic
52C4×D17—42no—
53C4×D17—82no—
54C4×D17#10312yes—
55C4×D17#10412yes—
56#3624—22no—
57#3624—22no—
58#1991—171no—
59#1376—172no—
60C22×C17#32311yescharacteristic
61C2×D17—22no—
62C2×D17#32911yescharacteristic
63C2×D17#33311yescharacteristic
64#595—161no—
65C4×C17—41no—
66C4×C17—81no—
67C4×C17Q8⋊C812yes—
68Dic17—41no—
69Dic17—81no—
70Dic17#32812yes—
71C2×#125—171no—
72C2×M32—342no—
73C2×C4×C8—171no—
74#382—171no—
75#340—342no—
76C2×C17—21no—
77C2×C17#127211yescharacteristic
78D17—21no—
79D17#136612yes—
80C22×C8—172no—
81#125—171no—
82#125—341no—
83#125—681no—
84#125#363311yescharacteristic
85C2×C4⋊C4—341no—
86C2×C4⋊C4—341no—
87C2×C4⋊C4—681no—
88C2×C42—171no—
89M32—344no—
90M32—682no—
91C2×C16—682no—
92C4×C8—681no—
93#95—681no—
94C17#713511yescharacteristic, complemented, Sylow
95C22×C4—171no—
96C22×C4—341no—
97C22×C4—681no—
98C22×C4—681no—
99C2×C8—172no—
100C2×C8—172no—
101C2×C8—342no—
102C2×C8—342no—
103C4⋊C4—21no—
104C4⋊C4—41no—
105C4⋊C4—341no—
106C4⋊C4—681no—
107C4⋊C4—681no—
108C4⋊C4—681no—
109C4⋊C4—681no—
110C4⋊C4—682no—
111C42—171no—
112C42—341no—
113C42C2×#363311yescharacteristic
114C16—684no—
115C23—171no—
116C2×C4—21no—
117C2×C4—41no—
118C2×C4—171no—
119C2×C4—172no—
120C2×C4—172no—
121C2×C4—341no—
122C2×C4—682no—
123C2×C4—681no—
124C2×C4—1362no—
125C2×C4—1361no—
126C2×C4—1362no—
127C2×C4C22⋊#363311yescharacteristic
128C8—342no—
129C8—342no—
130C22—171no—
131C22—171no—
132C22—342no—
133C22#1176389411yescharacteristic
134C4—41no—
135C4—81no—
136C4—2721no—
137C4—172no—
138C4—681no—
139C4—1361no—
140C4Q8⋊#363312yes—
141C2—21no—
142C2—172no—
143C2—341no—
144C2#1454578511yescharacteristic
subgroupG/H
centerC2#14545785
commutatorC42×C17C2×C8
FrattiniC42C2×#3633
FittingC17×#125C8
socleC2×C17#1272
prime radicalC22×D17#100
cosocleC4×#63242C22
hypercenter#125#3633
hypocenterC17#7135
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
94. C17#7135semidirect

Maximal subgroups

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

subgroupindex
#145458582
#145449662
#713517