Finite Group Databasebeta

← #14543684

Subgroups — #14543684

Order 2176.

200 conjugacy classes of subgroups; only the 46 normal subgroups are shown.

normal subgroups only

This group has 200 conjugacy classes of subgroups — too many to draw. Only its 46 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#11763780C211yesmaximal, characteristic
2#11763751C211yesmaximal, characteristic
3#11762772C211yesmaximal, characteristic
4C22×C4×D17C2211yescharacteristic
5C2×C22⋊#595C412yes—
6C2×C4⋊#595—21no—
7C2×#63243—21no—
8C2×M16×C17C411yescharacteristic, complemented
9C2×#63223C411yescharacteristic, complemented
10C22⋊#3624C412yescomplemented
11(C2×#595)⋊C4—21no—
12#10587543—21no—
13#10587491—21no—
14#10587491—21no—
15C23×D17C2×C411yescharacteristic
16C22×#595—22no—
17C22×C4×C17C2×C411yescharacteristic
18C22×Dic17C2×C411yescharacteristic
19C2×C4×D17—41no—
20C2×C4×D17—41no—
21C2×C4×D17D411yescharacteristic
22C2×C4×D17D411yescharacteristic
23C2×C4×D17D411yescharacteristic
24C2×C4×D17Q811yescharacteristic
25C22⋊#595—42no—
26C2×#3624—22no—
27C4⋊#595—41no—
28C4⋊#595—41no—
29#63243—41no—
30#63243—41no—
31M16×C17—41no—
32C2×C8×C17—21no—
33#63223—41no—
34C2×#3622—21no—
35C23×C17C4211yescharacteristic
36C22×D17—21no—
37C22×D17—21no—
38C22×D17—41no—
39C22×D17—41no—
40C22×D17C22⋊C411yescharacteristic
41C22×D17C4⋊C411yescharacteristic
42C2×#595—42no—
43C2×#595—42no—
44C2×#595—42no—
45C2×C4×C17—21no—
46C2×C4×C17—21no—
47C2×C4×C17C22⋊C411yescharacteristic
48C2×C4×C17C4⋊C411yescharacteristic
49C2×Dic17—41no—
50C2×Dic17C22⋊C411yescharacteristic
51C2×Dic17C4⋊C411yescharacteristic
52C4×D17—21no—
53C4×D17—21no—
54C4×D17—21no—
55C4×D17—21no—
56C4×D17—41no—
57C4×D17—41no—
58#3624—42no—
59C8×C17—41no—
60#3622—41no—
61#1305—171nomaximal, Sylow
62C22×C17—21no—
63C22×C17—21no—
64C22×C17—21no—
65C22×C17#9511yescharacteristic
66C2×D17—21no—
67C2×D17—21no—
68C2×D17—21no—
69C2×D17—21no—
70C2×D17—21no—
71C2×D17—42no—
72C2×D17—42no—
73C2×D17#10011yescharacteristic
74C2×D17#10111yescharacteristic
75#595—82no—
76C4×C17—21no—
77C4×C17#9911yescharacteristic
78C4×C17#9911yescharacteristic
79Dic17—21no—
80Dic17—21no—
81#407—171no—
82#407—171no—
83#380—171no—
84C2×C17—41no—
85C2×C17#34211yescharacteristic
86C2×C17#34311yescharacteristic
87C2×C17#34411yescharacteristic
88D17—21no—
89D17—21no—
90D17—41no—
91C23×C4—171no—
92C2×M16—171no—
93C2×M16—341no—
94C2×M16#59511yescharacteristic, complemented
95C2×C4⋊C4—341no—
96C2×C22⋊C4—172no—
97C22⋊C8—172no—
98C22⋊C8—341no—
99C22⋊C8—341no—
100C22⋊C8—341no—
101#95—341no—
102C17#130511yescharacteristic, complemented, Sylow
103C24—171no—
104C22×C4—171no—
105C22×C4—171no—
106C22×C4—171no—
107C22×C4—171no—
108C22×C4—171no—
109C22×C4—342no—
110C22×C4—681no—
111C22×C4—681no—
112C22×C4C2×#59511yescharacteristic
113M16—41no—
114M16—681no—
115M16—681no—
116M16—681no—
117C2×C8—21no—
118C2×C8—342no—
119C2×C8—341no—
120C4⋊C4—681no—
121C4⋊C4—681no—
122C22⋊C4—682no—
123C23—171no—
124C23—171no—
125C23—341no—
126C23—341no—
127C23—681no—
128C23—681no—
129C23C4×#59511yescharacteristic
130C2×C4—21no—
131C2×C4—21no—
132C2×C4—171no—
133C2×C4—171no—
134C2×C4—341no—
135C2×C4—341no—
136C2×C4—341no—
137C2×C4—341no—
138C2×C4—681no—
139C2×C4—681no—
140C2×C4—681no—
141C2×C4—682no—
142C2×C4—682no—
143C2×C4—682no—
144C2×C4C4⋊#59511yescharacteristic
145C2×C4C22⋊#59511yescharacteristic
146C8—41no—
147C8—682no—
148C8—681no—
149C22—21no—
150C22—21no—
151C22—21no—
152C22—171no—
153C22—171no—
154C22—341no—
155C22—341no—
156C22—341no—
157C22—341no—
158C22—341no—
159C22—682no—
160C22—682no—
161C22(C2×#595)⋊C411yescharacteristic
162C4—21no—
163C4—341no—
164C4—341no—
165C4—1362no—
166C4#1058753911yescharacteristic
167C4#1058755111yescharacteristic
168C2—41no—
169C2—341no—
170C2—341no—
171C2—681no—
172C2#1176368711yescharacteristic
173C2#1176368811yescharacteristic
174C2#1176369211yescharacteristic
subgroupG/H
centerC22(C2×#595)⋊C4
commutatorC23×C17C42
FrattiniC22×C4C2×#595
FittingC2×M16×C17C4
socleC22×C17#95
prime radicalC23×D17C2×C4
cosocleC22×C4×D17C22
hypercenterC2×M16#595
hypocenterC17#1305
LCSG ▷ C23×C17 ▷ C22×C17 ▷ C17
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
8. C2×M16×C17C4semidirect
9. C2×#63223C4semidirect
10. C22⋊#3624C4semidirect
94. C2×M16#595semidirect
102. C17#1305semidirect

Maximal subgroups

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

subgroupindex
#117637802
#117637512
#117627722
#130517