Finite Group Databasebeta

← #17981154

Subgroups — #17981154

Order 4352.

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

normal subgroups only

This group has 242 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#14544911C211yesmaximal, characteristic
3#11763928—22no—
4C2×#10587549—22no—
5C4×#63242C2211yescharacteristic
6#11763755C411yescharacteristic
7C4⋊Q8×D17C411yescharacteristic
8C2×Q8×D17—21no—
9C2×C4⋊#595—21no—
10C2×C4⋊#595—41no—
11C2×#63242D412yes—
12#10587670—42no—
13#10587666—24no—
14#10587665—42no—
15C17×C4⋊Q8C811yescharacteristic
16#10587630—21no—
17C4⋊C4×D17—41no—
18#10587574—41no—
19C42×D17C2×C411yescharacteristic
20#10587555C811yescharacteristic
21#10587549—42no—
22#10587549—42no—
23C4×#3624—41no—
24C22×#595—41no—
25C2×Q8×C17—21no—
26Q8×D17—42no—
27Q8×D17—42no—
28C2×C4×D17—21no—
29C2×C4×D17—41no—
30C2×C4×D17C22⋊C411yescharacteristic
31C2×Dic34—21no—
32C2×Dic34—41no—
33C2×#3624—22no—
34C4⋊#595—42no—
35C4⋊#595—82no—
36#63242—22no—
37#63242D812yes—
38#63242SD1612yes—
39#63241—44no—
40C4⋊C4×C17—41no—
41C42×C17C2×C811yescharacteristic
42C4⋊Dic17—41no—
43#63225—42no—
44C4×Dic17—21no—
45C4×Dic17M1611yescharacteristic
46#7108—171nomaximal, Sylow
47C22×D17#10011yescharacteristic
48C2×#595—82no—
49C2×#595—81no—
50Q8×C17—42no—
51C2×C4×C17—21no—
52C2×C4×C17—41no—
53C2×C4×C17C22⋊C811yescharacteristic
54C2×Dic17—21no—
55C2×Dic17—41no—
56C2×Dic17#9911yescharacteristic
57C4×D17—22no—
58C4×D17—22no—
59C4×D17—81no—
60C4×D17—81no—
61C4×D17#10212yes—
62C4×D17#10412yes—
63Dic34—42no—
64Dic34—82no—
65#3624—22no—
66#3624—22no—
67#1956—171no—
68#1376—172no—
69C22×C17#32311yescharacteristic
70C2×D17—21no—
71C2×D17—21no—
72C2×D17#32911yescharacteristic
73C2×D17#33111yescharacteristic
74#595—161no—
75C4×C17—22no—
76C4×C17—81no—
77C4×C17D4⋊C812yes—
78Dic17—22no—
79Dic17—81no—
80Dic17#32712yes—
81C2×C4⋊Q8—171no—
82C2×M32—342no—
83C2×#103—342no—
84C2×C4×C8—171no—
85#384—171no—
86C2×C17—21no—
87C2×C17#127011yescharacteristic
88D17—21no—
89D17#135811yescharacteristic
90D17#135911yescharacteristic
91C22×Q8—341no—
92C22×C8—172no—
93C4⋊Q8—171no—
94C4⋊Q8—341no—
95C4⋊Q8—681no—
96C4⋊Q8#363311yescharacteristic
97C2×C4⋊C4—341no—
98C2×C4⋊C4—681no—
99C2×C4⋊C4—681no—
100C2×C42—171no—
101M32—344no—
102M32—682no—
103C2×C16—682no—
104#103—682no—
105#103—682no—
106C4×C8—681no—
107C17#710811yescharacteristic, complemented, Sylow
108C2×Q8—21no—
109C2×Q8—341no—
110C2×Q8—681no—
111C2×Q8—682no—
112C2×Q8—682no—
113C22×C4—171no—
114C22×C4—341no—
115C22×C4—681no—
116C22×C4—681no—
117C2×C8—172no—
118C2×C8—172no—
119C2×C8—342no—
120C2×C8—342no—
121C4⋊C4—41no—
122C4⋊C4—681no—
123C4⋊C4—682no—
124C4⋊C4—682no—
125C4⋊C4—1362no—
126C42—171no—
127C42—341no—
128C42C2×#363311yescharacteristic
129C16—684no—
130C23—171no—
131Q8—42no—
132Q8—682no—
133Q8—1362no—
134C2×C4—21no—
135C2×C4—41no—
136C2×C4—171no—
137C2×C4—172no—
138C2×C4—172no—
139C2×C4—342no—
140C2×C4—342no—
141C2×C4—341no—
142C2×C4—681no—
143C2×C4—1361no—
144C2×C4—1361no—
145C2×C4—1361no—
146C2×C4—1362no—
147C2×C4C22⋊#363311yescharacteristic
148C8—342no—
149C8—342no—
150C22—171no—
151C22—171no—
152C22—341no—
153C22—341no—
154C22#1176389411yescharacteristic
155C4—22no—
156C4—81no—
157C4—2721no—
158C4—172no—
159C4—342no—
160C4—1361no—
161C4D4⋊#363312yes—
162C2—21no—
163C2—171no—
164C2—171no—
165C2—341no—
166C2#1454578311yescharacteristic
subgroupG/H
centerC2#14545783
commutatorC42×C17C2×C8
FrattiniC42C2×#3633
FittingC17×C4⋊Q8C8
socleC2×C17#1270
prime radicalC22×D17#100
cosocleC4×#63242C22
hypercenterC4⋊Q8#3633
hypocenterC17#7108
LCSG ▷ C42×C17 ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C2 ◁ C2×C4 ◁ C42 ◁ C4⋊Q8

Complements

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

NH ≅ G/Ntype
107. C17#7108semidirect

Maximal subgroups

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

subgroupindex
#145458582
#145449112
#710817