Finite Group Databasebeta

← #14544061

Subgroups — #14544061

Order 2176.

322 conjugacy classes of subgroups; only the 64 normal subgroups are shown.

normal subgroups only

This group has 322 conjugacy classes of subgroups — too many to draw. Only its 64 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, complemented
2#11763777C211yesmaximal, characteristic, complemented
3#11763653C214yesmaximal, complemented
4C2×#10587581C211yesmaximal, characteristic
5C22×D68C412yes—
6C22×D68C411yescharacteristic
7C22×C4×D17C2211yescharacteristic
8C2×#63243—21no—
9C2×#63242—21no—
10C2×C4⋊C4×C17C411yescharacteristic
11C2×#63227C2212yes—
12#10587581—21no—
13#10587581—21no—
14#10587581—21no—
15#10587581—21no—
16C22⋊#3624C2212yes—
17C22⋊#3624C2212yes—
18#10587543—21no—
19#10587543—21no—
20C23×D17C2×C411yescharacteristic
21C23×D17C2×C412yes—
22C22×C4×C17C2×C412yes—
23C22×C4×C17C2×C411yescharacteristic
24C22×Dic17C2311yescharacteristic
25C2×D68—22no—
26C2×D68—22no—
27C2×D68—21no—
28C2×D68—21no—
29C2×D68—42no—
30C2×D68—44no—
31C2×C4×D17—42no—
32C2×C4×D17D411yescharacteristic
33C2×C4×D17D411yescharacteristic
34C2×C4×D17D411yescharacteristic
35C2×C4×D17D411yescharacteristic
36C2×#3624—22no—
37C2×#3624—22no—
38#63243—42no—
39#63242—42no—
40C4⋊C4×C17—21no—
41C4⋊C4×C17—21no—
42#63227—22no—
43#63227—22no—
44C23×C17C22×C411yescharacteristic
45C22×D17—22no—
46C22×D17—22no—
47C22×D17—22no—
48C22×D17—24no—
49C22×D17—41no—
50C22×D17—42no—
51C22×D17—42no—
52C22×D17C22⋊C411yescharacteristic
53C22×D17C22⋊C411yescharacteristic
54C2×C4×C17—22no—
55C2×C4×C17—22no—
56C2×C4×C17—42no—
57C2×C4×C17C22⋊C411yescharacteristic
58C2×C4×C17C22⋊C411yescharacteristic
59C2×Dic17—41no—
60C2×Dic17C2×D411yescharacteristic
61C2×Dic17C2×D411yescharacteristic
62D68—42no—
63D68—44no—
64D68—44no—
65D68—42no—
66C4×D17—22no—
67C4×D17—22no—
68C4×D17—41no—
69C4×D17—41no—
70#3624—42no—
71#3624—42no—
72#1471—171nomaximal, Sylow
73C22×C17—21no—
74C22×C17—21no—
75C22×C17C2×C22⋊C411yescharacteristic
76C22×C17#13112yes—
77C2×D17—21no—
78C2×D17—21no—
79C2×D17—21no—
80C2×D17—21no—
81C2×D17—21no—
82C2×D17—44no—
83C2×D17—42no—
84C2×D17—42no—
85C2×D17—42no—
86C2×D17—84no—
87C2×D17#10012yes—
88C4×C17—21no—
89C4×C17—42no—
90C4×C17#9912yes—
91Dic17—21no—
92Dic17—21no—
93C2×#121—171no—
94#407—171no—
95C2×C22⋊C8—171no—
96#323—174no—
97C2×C17—22no—
98C2×C17#40811yescharacteristic
99C2×C17C2×#9911yescharacteristic
100C2×C17C2×#10011yescharacteristic
101D17—22no—
102D17—41no—
103D17—82no—
104C22×D4—172no—
105C22×D4—171no—
106C23×C4—171no—
107C2×M16—341no—
108C22×C8—341no—
109#121—341no—
110#121—341no—
111#121—341no—
112#121—341no—
113C2×C4⋊C4#59511yescharacteristic
114C2×C22⋊C4—172no—
115C22⋊C8—172no—
116C22⋊C8—172no—
117C22⋊C8—341no—
118C22⋊C8—341no—
119C17#147111yescharacteristic, complemented, Sylow
120C24—171no—
121C24—172no—
122C2×D4—342no—
123C2×D4—342no—
124C2×D4—341no—
125C2×D4—341no—
126C2×D4—682no—
127C2×D4—684no—
128C22×C4—171no—
129C22×C4—171no—
130C22×C4—171no—
131C22×C4—171no—
132C22×C4—171no—
133C22×C4—682no—
134C22×C4C2×#59512yes—
135C22×C4C2×#59511yescharacteristic
136M16—682no—
137C2×C8—342no—
138C2×C8—342no—
139C2×C8—682no—
140C4⋊C4—21no—
141C4⋊C4—21no—
142C22⋊C4—342no—
143C22⋊C4—342no—
144C23—171no—
145C23—171no—
146C23—342no—
147C23—342no—
148C23—342no—
149C23—344no—
150C23—681no—
151C23—682no—
152C23—682no—
153C23C22×#59511yescharacteristic
154D4—682no—
155D4—684no—
156D4—684no—
157D4—682no—
158C2×C4—22no—
159C2×C4—22no—
160C2×C4—42no—
161C2×C4—171no—
162C2×C4—171no—
163C2×C4—342no—
164C2×C4—342no—
165C2×C4—681no—
166C2×C4—681no—
167C2×C4—681no—
168C2×C4C22⋊#59511yescharacteristic
169C2×C4C22⋊#59511yescharacteristic
170C8—682no—
171C8—682no—
172C22—21no—
173C22—21no—
174C22—172no—
175C22—341no—
176C22—341no—
177C22—341no—
178C22—341no—
179C22—341no—
180C22—684no—
181C22—682no—
182C22—682no—
183C22—682no—
184C22—1364no—
185C22#1058768012yes—
186C22C2×C22⋊#59511yescharacteristic
187C4—21no—
188C4—42no—
189C4—341no—
190C4—341no—
191C4#1058753912yes—
192C2—22no—
193C2—342no—
194C2—681no—
195C2—1362no—
196C2#1176378411yescharacteristic
197C2C2×#1058753911yescharacteristic
198C2D17⋊#10011yescharacteristic
subgroupG/H
centerC22C2×C22⋊#595
commutatorC23×C17C22×C4
FrattiniC23C22×#595
FittingC2×C4⋊C4×C17C4
socleC22×C17C2×C22⋊C4
prime radicalC2×#10587581C2
cosocleC22×Dic17C23
hypercenterC2×C4⋊C4#595
hypocenterC17#1471
LCSG ▷ C23×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
1. #11763780C2semidirect
2. #11763777C2semidirect
3. #11763653C2semidirect
119. C17#1471semidirect

Maximal subgroups

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

subgroupindex
#117637802
#117637772
#117636532
C2×#105875812
#147117