Finite Group Databasebeta

← #14544687

Subgroups — #14544687

Order 2176.

344 conjugacy classes of subgroups; only the 84 normal subgroups are shown.

normal subgroups only

This group has 344 conjugacy classes of subgroups — too many to draw. Only its 84 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#11763777C211yesmaximal, characteristic
2#11763751C211yesmaximal, characteristic
3#11763682C214yesmaximal, complemented
4C2×C4⋊C4×D17C211yesmaximal, characteristic
5C22×C4×D17—21no—
6C22×C4×D17C2211yescharacteristic
7C2×C22⋊#595—21no—
8C2×C4⋊#595C2212yes—
9C2×#63242C2212yes—
10C2×C4⋊C4×C17C411yescharacteristic, complemented
11C2×C4⋊Dic17C411yescharacteristic, complemented
12C2×#63225—21no—
13C4⋊C4×D17—21no—
14C4⋊C4×D17—21no—
15C4⋊C4×D17C412yescomplemented
16C4⋊C4×D17C2212yes—
17C22⋊#3624—21no—
18(C2×#595)⋊C4—21no—
19#10587543—21no—
20C23×D17D411yescharacteristic
21C22×#595—22no—
22C22×C4×C17—21no—
23C22×C4×C17C2×C411yescharacteristic
24C22×Dic17—21no—
25C22×Dic17D411yescharacteristic
26C2×C4×D17—24no—
27C2×C4×D17—22no—
28C2×C4×D17—22no—
29C2×C4×D17—42no—
30C2×C4×D17—42no—
31C2×C4×D17C2×C411yescharacteristic
32C2×C4×D17D411yescharacteristic
33C2×C4×D17D411yescharacteristic
34C2×C4×D17C2311yescharacteristic
35C22⋊#595—42no—
36C2×#3624—22no—
37C4⋊#595—24no—
38#63242—24no—
39C4⋊C4×C17—21no—
40C4⋊C4×C17C2×C412yes—
41C4⋊Dic17—21no—
42C4⋊Dic17C2×C412yes—
43#63225—22no—
44#63225—22no—
45C23×C17C22⋊C411yescharacteristic
46C22×D17—22no—
47C22×D17—22no—
48C22×D17C22⋊C411yescharacteristic
49C22×D17D812yes—
50C22×D17SD1612yes—
51C22×D17C2×D411yescharacteristic
52C2×#595—42no—
53C2×#595—42no—
54C2×#595—42no—
55C2×C4×C17—22no—
56C2×C4×C17—22no—
57C2×C4×C17—42no—
58C2×C4×C17C22⋊C411yescharacteristic
59C2×C4×C17C22×C411yescharacteristic
60C2×Dic17—22no—
61C2×Dic17—22no—
62C2×Dic17—42no—
63C2×Dic17C22⋊C411yescharacteristic
64C2×Dic17C2×D411yescharacteristic
65C4×D17—22no—
66C4×D17—22no—
67C4×D17—22no—
68C4×D17—44no—
69C4×D17—42no—
70C4×D17—42no—
71C4×D17#4114yes—
72#3624—42no—
73#1823—171nomaximal, Sylow
74C22×C17—21no—
75C22×C17—21no—
76C22×C17#10212yes—
77C22×C17C2×C22⋊C411yescharacteristic
78C2×D17—21no—
79C2×D17—21no—
80C2×D17—24no—
81C2×D17—24no—
82C2×D17#10212yes—
83C2×D17#12312yes—
84C2×D17C2×D811yescharacteristic
85C2×D17C2×SD1611yescharacteristic
86C2×D17#13712yes—
87#595—82no—
88C4×C17—21no—
89C4×C17—42no—
90C4×C17#11712yes—
91Dic17—21no—
92Dic17—42no—
93Dic17#12312yes—
94C22×C4⋊C4—171no—
95C2×C22⋊C8—171no—
96#380—171no—
97#340—174no—
98C2×C17—22no—
99C2×C17#38111yescharacteristic
100C2×C17C2×#10211yescharacteristic
101C2×C17#41911yescharacteristic
102D17—22no—
103D17#48012yes—
104D17#48312yes—
105C23×C4—171no—
106C23×C4—341no—
107C22×C8—172no—
108C2×C4⋊C4—171no—
109C2×C4⋊C4—172no—
110C2×C4⋊C4—172no—
111C2×C4⋊C4—172no—
112C2×C4⋊C4—341no—
113C2×C4⋊C4—341no—
114C2×C4⋊C4—341no—
115C2×C4⋊C4#59511yescharacteristic, complemented
116C2×C22⋊C4—341no—
117C22⋊C8—341no—
118C22⋊C8—341no—
119#95—341no—
120C17#182311yescharacteristic, complemented, Sylow
121C24—171no—
122C22×C4—21no—
123C22×C4—171no—
124C22×C4—171no—
125C22×C4—171no—
126C22×C4—171no—
127C22×C4—171no—
128C22×C4—344no—
129C22×C4—342no—
130C22×C4—342no—
131C22×C4—341no—
132C22×C4—342no—
133C22×C4—682no—
134C22×C4—682no—
135C22×C4C2×#59511yescharacteristic
136C2×C8—344no—
137C2×C8—342no—
138C4⋊C4—21no—
139C4⋊C4—172no—
140C4⋊C4—342no—
141C4⋊C4—342no—
142C4⋊C4—344no—
143C4⋊C4—341no—
144C4⋊C4C2×#59512yes—
145C22⋊C4—682no—
146C23—171no—
147C23—171no—
148C23—172no—
149C23—172no—
150C23—342no—
151C23—342no—
152C23C22⋊#59511yescharacteristic
153C2×C4—22no—
154C2×C4—22no—
155C2×C4—42no—
156C2×C4—171no—
157C2×C4—174no—
158C2×C4—171no—
159C2×C4—342no—
160C2×C4—342no—
161C2×C4—342no—
162C2×C4—342no—
163C2×C4—342no—
164C2×C4—682no—
165C2×C4—682no—
166C2×C4—684no—
167C2×C4—682no—
168C2×C4—682no—
169C2×C4—682no—
170C2×C4—682no—
171C2×C4C22⋊#59511yescharacteristic
172C2×C4C22×#59511yescharacteristic
173C8—682no—
174C22—21no—
175C22—21no—
176C22—172no—
177C22—171no—
178C22—171no—
179C22—172no—
180C22—172no—
181C22—344no—
182C22—344no—
183C22—341no—
184C22—341no—
185C22#1058754712yes—
186C22C2×C22⋊#59511yescharacteristic
187C4—21no—
188C4—42no—
189C4—172no—
190C4—341no—
191C4—682no—
192C4—1362no—
193C4#1058767712yes—
194C2—22no—
195C2—172no—
196C2—172no—
197C2—342no—
198C2#1176375211yescharacteristic
199C2C2×#1058754711yescharacteristic
200C2#1176380211yescharacteristic
subgroupG/H
centerC22C2×C22⋊#595
commutatorC2×C4×C17C22×C4
FrattiniC2×C4C22×#595
FittingC2×C4⋊C4×C17C4
socleC22×C17C2×C22⋊C4
prime radicalC23×D17D4
cosocleC2×C4×D17C23
hypercenterC2×C4⋊C4#595
hypocenterC17#1823
LCSG ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
3. #11763682C2semidirect
10. C2×C4⋊C4×C17C4semidirect
11. C2×C4⋊Dic17C4semidirect
15. C4⋊C4×D17C4semidirect
115. C2×C4⋊C4#595semidirect
120. C17#1823semidirect

Maximal subgroups

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

subgroupindex
#117637772
#117637512
#117636822
C2×C4⋊C4×D172
#182317