Finite Group Databasebeta

← #17981186

Subgroups — #17981186

Order 4352.

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

normal subgroups only

This group has 206 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#14545856C212yesmaximal
2#14544967C211yesmaximal, characteristic
3#11763928—22no—
4#11763768C2211yescharacteristic
5#11763755C411yescharacteristic
6#11763682—22no—
7#125×D17C411yescharacteristic
8C2×C4⋊#595—21no—
9C2×C4⋊#595—41no—
10C2×#63242D412yes—
11#10587670—42no—
12#10587666—42no—
13#10587665—24no—
14C17×#125C811yescharacteristic
15C4⋊C4×D17—21no—
16C4⋊C4×D17—41no—
17#10587576—21no—
18#10587575—41no—
19C42×D17C2×C411yescharacteristic
20#10587556C811yescharacteristic
21#10587542—41no—
22C22×#595—41no—
23C2×C4×D17—21no—
24C2×C4×D17—41no—
25C2×C4×D17C22⋊C411yescharacteristic
26C2×#3624—22no—
27C4⋊#595—42no—
28C4⋊#595—82no—
29#63242—22no—
30#63242SD1612yes—
31#63242Q1612yes—
32#63241—44no—
33C4⋊C4×C17—21no—
34C4⋊C4×C17—41no—
35C42×C17C2×C811yescharacteristic
36C4⋊Dic17—21no—
37C4⋊Dic17—41no—
38#63225—41no—
39#63225—41no—
40#63225—41no—
41C4×Dic17—21no—
42C4×Dic17M1611yescharacteristic
43#7130—171nomaximal, Sylow
44C22×D17#10011yescharacteristic
45C2×#595—82no—
46C2×#595—81no—
47C2×C4×C17—21no—
48C2×C4×C17—41no—
49C2×C4×C17C22⋊C811yescharacteristic
50C2×Dic17—21no—
51C2×Dic17—41no—
52C2×Dic17#9911yescharacteristic
53C4×D17—41no—
54C4×D17—41no—
55C4×D17—81no—
56C4×D17—81no—
57C4×D17#10312yes—
58C4×D17#10412yes—
59#3624—22no—
60#3624—22no—
61#1992—171no—
62#1375—172no—
63C22×C17#32311yescharacteristic
64C2×D17—21no—
65C2×D17—21no—
66C2×D17#32911yescharacteristic
67C2×D17#33311yescharacteristic
68#595—161no—
69C4×C17—41no—
70C4×C17—81no—
71C4×C17Q8⋊C812yes—
72Dic17—41no—
73Dic17—81no—
74Dic17#32812yes—
75C2×#125—171no—
76C2×M32—342no—
77C2×#97—171no—
78#384—171no—
79#340—342no—
80C2×C17—21no—
81C2×C17#127211yescharacteristic
82D17—21no—
83D17#135511yescharacteristic
84D17#135611yescharacteristic
85C22×C8—172no—
86#125—171no—
87#125—341no—
88#125—681no—
89#125#363311yescharacteristic
90C2×C4⋊C4—341no—
91C2×C4⋊C4—341no—
92C2×C4⋊C4—681no—
93C2×C4⋊C4—681no—
94C2×C42—171no—
95M32—682no—
96M32—682no—
97C2×C16—344no—
98#97—681no—
99C17#713011yescharacteristic, complemented, Sylow
100C22×C4—171no—
101C22×C4—341no—
102C22×C4—681no—
103C22×C4—681no—
104C2×C8—172no—
105C2×C8—172no—
106C2×C8—342no—
107C2×C8—342no—
108C4⋊C4—21no—
109C4⋊C4—41no—
110C4⋊C4—341no—
111C4⋊C4—681no—
112C4⋊C4—681no—
113C4⋊C4—681no—
114C4⋊C4—681no—
115C4⋊C4—682no—
116C4⋊C4—1362no—
117C42—171no—
118C42—341no—
119C42C2×#363311yescharacteristic
120C16—684no—
121C23—171no—
122C2×C4—21no—
123C2×C4—41no—
124C2×C4—171no—
125C2×C4—172no—
126C2×C4—172no—
127C2×C4—341no—
128C2×C4—681no—
129C2×C4—681no—
130C2×C4—681no—
131C2×C4—1361no—
132C2×C4—1361no—
133C2×C4—1361no—
134C2×C4—1362no—
135C2×C4C22⋊#363311yescharacteristic
136C8—342no—
137C8—342no—
138C22—171no—
139C22—171no—
140C22—341no—
141C22—341no—
142C22#1176389411yescharacteristic
143C4—41no—
144C4—81no—
145C4—2721no—
146C4—172no—
147C4—681no—
148C4—1361no—
149C4Q8⋊#363312yes—
150C2—21no—
151C2—171no—
152C2—171no—
153C2—341no—
154C2#1454578511yescharacteristic
subgroupG/H
centerC2#14545785
commutatorC42×C17C2×C8
FrattiniC42C2×#3633
FittingC17×#125C8
socleC2×C17#1272
prime radicalC22×D17#100
cosocle#11763768C22
hypercenter#125#3633
hypocenterC17#7130
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
99. C17#7130semidirect

Maximal subgroups

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

subgroupindex
#145458562
#145449672
#713017