Finite Group Databasebeta

← #14544063

Subgroups — #14544063

Order 2176.

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

normal subgroups only

This group has 270 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#11763779C211yesmaximal, characteristic
2C2×C22⋊#3624C211yesmaximal, characteristic
3#11763655C212yesmaximal, complemented
4#11763654C212yesmaximal, complemented
5C2×#10587564C211yesmaximal, characteristic
6C23×Dic17C2211yescharacteristic
7C22×Dic34C411yescharacteristic
8C2×#63247—21no—
9C22×#3624—21no—
10C2×C22⋊C4×C17C411yescharacteristic
11C2×C22⋊Dic17C411yescharacteristic
12C2×C4⋊Dic17C2211yescharacteristic
13C2×#63225C411yescharacteristic
14C2×#63225C2211yescharacteristic
15#10587564—21no—
16#10587564—21no—
17#10587564—21no—
18#10587564—21no—
19C22⋊#3624—21no—
20C22⋊#3624—21no—
21C22⋊#3624C2212yes—
22C22⋊#3624C2212yes—
23C24×C17C2×C411yescharacteristic
24C22×C4×C17C2×C411yescharacteristic
25C22×C4×C17C2×C411yescharacteristic
26C22×Dic17—42no—
27C22×Dic17C2×C411yescharacteristic
28C22×Dic17C2×C411yescharacteristic
29C22×Dic17C2×C411yescharacteristic
30C22×Dic17D411yescharacteristic
31C22×Dic17D411yescharacteristic
32C22×Dic17D411yescharacteristic
33C22×Dic17D411yescharacteristic
34C22×Dic17C2311yescharacteristic
35C2×Dic34—21no—
36C2×Dic34—21no—
37C2×Dic34—42no—
38#63247—42no—
39C2×#3624—22no—
40C2×#3624—22no—
41C2×#3624—42no—
42C22⋊C4×C17—21no—
43C22⋊C4×C17—21no—
44C22⋊Dic17—21no—
45C22⋊Dic17—21no—
46C4⋊Dic17—21no—
47C4⋊Dic17—21no—
48#63225—21no—
49#63225—21no—
50#63225—21no—
51#63225—21no—
52C23×C17—22no—
53C23×C17—22no—
54C23×C17—41no—
55C23×C17C22⋊C411yescharacteristic
56C23×C17C22⋊C411yescharacteristic
57C23×C17C22×C411yescharacteristic
58C2×C4×C17—21no—
59C2×C4×C17—21no—
60C2×C4×C17—22no—
61C2×C4×C17—41no—
62C2×Dic17—22no—
63C2×Dic17—22no—
64C2×Dic17—22no—
65C2×Dic17—21no—
66C2×Dic17—21no—
67C2×Dic17—22no—
68C2×Dic17—41no—
69C2×Dic17—41no—
70C2×Dic17—41no—
71C2×Dic17—41no—
72C2×Dic17C22⋊C411yescharacteristic
73C2×Dic17C22⋊C411yescharacteristic
74C2×Dic17C2×D411yescharacteristic
75C2×Dic17C2×D411yescharacteristic
76Dic34—42no—
77Dic34—42no—
78#3624—42no—
79#3624—42no—
80#1472—171nomaximal, Sylow
81C22×C17—21no—
82C22×C17—21no—
83C22×C17—21no—
84C22×C17—21no—
85C22×C17—21no—
86C22×C17—21no—
87C22×C17—21no—
88C22×C17—44no—
89C22×C17#10112yes—
90C22×C17C2×C22⋊C411yescharacteristic
91C22×C17#13112yes—
92C4×C17—41no—
93C4×C17—41no—
94Dic17—21no—
95Dic17—21no—
96Dic17—21no—
97Dic17—41no—
98Dic17—41no—
99Dic17#9912yes—
100C2×C22⋊Q8—171no—
101#407—171no—
102C2×C22⋊C8—171no—
103#324—172no—
104#324—172no—
105C2×C17—22no—
106C2×C17—22no—
107C2×C17—41no—
108C2×C17#40811yescharacteristic
109C2×C17C2×#9911yescharacteristic
110C2×C17C2×#10111yescharacteristic
111C22×Q8—171no—
112C23×C4—171no—
113C2×M16—341no—
114C22×C8—341no—
115C22⋊Q8—341no—
116C22⋊Q8—341no—
117C22⋊Q8—341no—
118C22⋊Q8—341no—
119C2×C4⋊C4—171no—
120C2×C4⋊C4—171no—
121C2×C4⋊C4—171no—
122C2×C22⋊C4—171no—
123C2×C22⋊C4#59511yescharacteristic
124C22⋊C8—172no—
125C22⋊C8—172no—
126C22⋊C8—341no—
127C22⋊C8—341no—
128C17#147211yescharacteristic, complemented, Sylow
129C24C2×#59511yescharacteristic
130C2×Q8—341no—
131C2×Q8—341no—
132C2×Q8—682no—
133C22×C4—171no—
134C22×C4—171no—
135C22×C4—171no—
136C22×C4—171no—
137C22×C4—171no—
138C22×C4—171no—
139C22×C4—171no—
140C22×C4—171no—
141C22×C4—682no—
142C22×C4C2×#59511yescharacteristic
143C22×C4C2×#59511yescharacteristic
144M16—682no—
145C2×C8—342no—
146C2×C8—342no—
147C2×C8—682no—
148C4⋊C4—341no—
149C4⋊C4—341no—
150C4⋊C4—341no—
151C4⋊C4—341no—
152C4⋊C4—341no—
153C4⋊C4—341no—
154C22⋊C4—21no—
155C22⋊C4—21no—
156C22⋊C4—341no—
157C22⋊C4—341no—
158C23—22no—
159C23—22no—
160C23—41no—
161C23C22⋊#59511yescharacteristic
162C23C22⋊#59511yescharacteristic
163C23C22×#59511yescharacteristic
164Q8—682no—
165Q8—682no—
166C2×C4—22no—
167C2×C4—21no—
168C2×C4—21no—
169C2×C4—41no—
170C2×C4—171no—
171C2×C4—171no—
172C2×C4—171no—
173C2×C4—171no—
174C2×C4—342no—
175C2×C4—342no—
176C2×C4—342no—
177C2×C4—342no—
178C2×C4—341no—
179C2×C4—341no—
180C2×C4—681no—
181C2×C4—681no—
182C2×C4—681no—
183C2×C4—681no—
184C8—682no—
185C8—682no—
186C22—21no—
187C22—21no—
188C22—21no—
189C22—21no—
190C22—21no—
191C22—21no—
192C22—21no—
193C22—44no—
194C22#1058754512yes—
195C22#1058767812yes—
196C22C2×C22⋊#59511yescharacteristic
197C4—41no—
198C4—41no—
199C4—172no—
200C4—341no—
201C4—341no—
202C4—341no—
203C4—681no—
204C4—681no—
205C2—22no—
206C2—22no—
207C2—41no—
208C2#1176378211yescharacteristic
209C2D17⋊#9911yescharacteristic
210C2C2×#1058754511yescharacteristic
subgroupG/H
centerC22C2×C22⋊#595
commutatorC23×C17C22×C4
FrattiniC23C22×#595
FittingC2×C22⋊C4×C17C4
socleC22×C17C2×C22⋊C4
prime radicalC24×C17C2×C4
cosocleC22×Dic17C23
hypercenterC2×C22⋊C4#595
hypocenterC17#1472
LCSG ▷ C23×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C24 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
3. #11763655C2semidirect
4. #11763654C2semidirect
128. C17#1472semidirect

Maximal subgroups

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

subgroupindex
#117637792
C2×C22⋊#36242
#117636552
#117636542
C2×#105875642
#147217