Finite Group Databasebeta

← #14543658

Subgroups — #14543658

Order 2176.

276 conjugacy classes of subgroups; only the 60 normal subgroups are shown.

normal subgroups only

This group has 276 conjugacy classes of subgroups — too many to draw. Only its 60 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#95×D17C211yesmaximal, characteristic
4C22×C4×D17—21no—
5C22×C4×D17C2211yescharacteristic
6C2×C22⋊#595—21no—
7C2×C4⋊#595C412yescomplemented
8C2×#63242—21no—
9C22⋊#3624—21no—
10(C2×#595)⋊C4—21no—
11#10587543C412yescomplemented
12C17×#95C411yescharacteristic, complemented
13#10587502—21no—
14#10587502C411yescharacteristic, complemented
15C23×D17D411yescharacteristic
16C22×#595—22no—
17C22×C4×C17—21no—
18C22×C4×C17C2×C411yescharacteristic
19C22×Dic17—21no—
20C22×Dic17D411yescharacteristic
21C2×C4×D17—24no—
22C2×C4×D17—42no—
23C2×C4×D17—42no—
24C2×C4×D17—41no—
25C2×C4×D17—41no—
26C2×C4×D17C2×C411yescharacteristic
27C2×C4×D17C2×C411yescharacteristic
28C2×C4×D17D411yescharacteristic
29C2×C4×D17Q811yescharacteristic
30C22⋊#595—41no—
31C22⋊#595—41no—
32C2×#3624—22no—
33C4⋊#595—42no—
34#63242—42no—
35C23×C17C22⋊C411yescharacteristic
36C22×D17—22no—
37C22×D17—22no—
38C22×D17C22⋊C411yescharacteristic
39C22×D17C4⋊C411yescharacteristic
40C22×D17D811yescharacteristic
41C22×D17SD1611yescharacteristic
42C22×D17SD1611yescharacteristic
43C22×D17Q1611yescharacteristic
44C2×#595—42no—
45C2×#595—42no—
46C2×#595—42no—
47C2×C4×C17—22no—
48C2×C4×C17—41no—
49C2×C4×C17—41no—
50C2×C4×C17—41no—
51C2×C4×C17C4211yescharacteristic
52C2×C4×C17C4⋊C411yescharacteristic
53C2×Dic17—22no—
54C2×Dic17—41no—
55C2×Dic17—41no—
56C2×Dic17—41no—
57C2×Dic17C22⋊C411yescharacteristic
58C2×Dic17C4⋊C411yescharacteristic
59C4×D17—22no—
60C4×D17—22no—
61C4×D17—41no—
62C4×D17—41no—
63C4×D17—44no—
64C4×D17—44no—
65#3624—42no—
66#1294—171nomaximal, Sylow
67C22×C17—21no—
68C22×C17—21no—
69C22×C17#9511yescharacteristic
70C22×C17#10211yescharacteristic
71C22×C17#10311yescharacteristic
72C2×D17—21no—
73C2×D17—21no—
74C2×D17—22no—
75C2×D17—22no—
76C2×D17—22no—
77C2×D17—22no—
78C2×D17#9912yes—
79C2×D17#10211yescharacteristic
80C2×D17#10311yescharacteristic
81C2×D17#10412yes—
82C2×D17#10611yescharacteristic
83C2×D17#10711yescharacteristic
84#595—82no—
85C4×C17—21no—
86C4×C17—21no—
87C4×C17—42no—
88Dic17—21no—
89Dic17—21no—
90Dic17—42no—
91C2×C22⋊C8—171no—
92#380—171no—
93C2×#95—171no—
94C2×C17—21no—
95C2×C17—21no—
96C2×C17#33911yescharacteristic
97C2×C17#34011yescharacteristic
98C2×C17#34211yescharacteristic
99D17—21no—
100D17—21no—
101D17#32712yes—
102D17#32812yes—
103C23×C4—171no—
104C23×C4—341no—
105C22×C8—341no—
106C2×C4⋊C4—172no—
107C2×C22⋊C4—341no—
108C22⋊C8—172no—
109C22⋊C8—341no—
110#95—171no—
111#95—341no—
112#95—341no—
113#95#59511yescharacteristic, complemented
114C17#129411yescharacteristic, complemented, Sylow
115C24—171no—
116C22×C4—21no—
117C22×C4—171no—
118C22×C4—171no—
119C22×C4—171no—
120C22×C4—171no—
121C22×C4—171no—
122C22×C4—344no—
123C22×C4—341no—
124C22×C4—342no—
125C22×C4—682no—
126C22×C4—681no—
127C22×C4—681no—
128C22×C4—682no—
129C22×C4C2×#59511yescharacteristic
130C2×C8—342no—
131C2×C8—682no—
132C4⋊C4—682no—
133C22⋊C4—681no—
134C22⋊C4—681no—
135C23—171no—
136C23—171no—
137C23—171no—
138C23—171no—
139C23—171no—
140C23—171no—
141C23—342no—
142C23—342no—
143C23C22⋊#59511yescharacteristic
144C2×C4—22no—
145C2×C4—41no—
146C2×C4—41no—
147C2×C4—41no—
148C2×C4—171no—
149C2×C4—171no—
150C2×C4—342no—
151C2×C4—342no—
152C2×C4—342no—
153C2×C4—681no—
154C2×C4—681no—
155C2×C4—684no—
156C2×C4—684no—
157C2×C4—681no—
158C2×C4—681no—
159C2×C4—681no—
160C2×C4—682no—
161C2×C4—682no—
162C2×C4—682no—
163C2×C4C4×#59511yescharacteristic
164C2×C4C4⋊#59511yescharacteristic
165C8—682no—
166C22—21no—
167C22—21no—
168C22—172no—
169C22—171no—
170C22—171no—
171C22—172no—
172C22—171no—
173C22—171no—
174C22—342no—
175C22—342no—
176C22—342no—
177C22—342no—
178C22—341no—
179C22—341no—
180C22(C2×#595)⋊C411yescharacteristic
181C22#1058754711yescharacteristic
182C22#1058754911yescharacteristic
183C4—21no—
184C4—21no—
185C4—42no—
186C4—341no—
187C4—341no—
188C4—682no—
189C4—1362no—
190C2—21no—
191C2—21no—
192C2—172no—
193C2—172no—
194C2—341no—
195C2—341no—
196C2#1176368011yescharacteristic
197C2#1176368211yescharacteristic
198C2#1176368611yescharacteristic
subgroupG/H
centerC22(C2×#595)⋊C4
commutatorC2×C4×C17C42
FrattiniC22×C4C2×#595
FittingC17×#95C4
socleC22×C17#95
prime radicalC23×D17D4
cosocleC22×C4×D17C22
hypercenter#95#595
hypocenterC17#1294
LCSG ▷ C2×C4×C17 ▷ C22×C17 ▷ C17
UCSC1 ◁ C22 ◁ C22×C4 ◁ #95

Complements

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

NH ≅ G/Ntype
7. C2×C4⋊#595C4semidirect
11. #10587543C4semidirect
12. C17×#95C4semidirect
14. #10587502C4semidirect
113. #95#595semidirect
114. C17#1294semidirect

Maximal subgroups

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

subgroupindex
#117637772
#117637512
#95×D172
#129417