Finite Group Databasebeta

← #14544160

Subgroups — #14544160

Order 2176.

304 conjugacy classes of subgroups; only the 62 normal subgroups are shown.

normal subgroups only

This group has 304 conjugacy classes of subgroups — too many to draw. Only its 62 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
1C2×#10587543C211yesmaximal, characteristic, complemented
2C4×C22⋊#595C211yesmaximal, characteristic, complemented
3#11763662C212yesmaximal, complemented
4#11763660C212yesmaximal, complemented
5#11763319C211yesmaximal, characteristic
6C2×#63254C411yescharacteristic, complemented
7C22×C4×D17C2211yescharacteristic
8C2×C22⋊#595—21no—
9C22×#3624—21no—
10C2×C4×#595—21no—
11C17×#121C411yescharacteristic, complemented
12#10587624C2211yescharacteristic
13#10587623—21no—
14D4×Dic17—21no—
15#10587610C411yescharacteristic, complemented
16#10587583C2211yescharacteristic
17#10587578C411yescharacteristic, complemented
18#10587569—21no—
19#10587567—21no—
20(C2×#595)⋊C4C2212yes—
21#10587543—21no—
22#10587543C2212yes—
23C23×D17D411yescharacteristic
24C22×#595—22no—
25C2×D4×C17—21no—
26C2×D4×C17C2×C411yescharacteristic
27C22×C4×C17C2×C411yescharacteristic
28C2×C22⋊D17—21no—
29C2×C22⋊D17—21no—
30C22×Dic17—21no—
31C22×Dic17D411yescharacteristic
32#63254—42no—
33C2×C4×D17—42no—
34C2×C4×D17C2×C411yescharacteristic
35C2×C4×D17D411yescharacteristic
36C2×C4×D17D411yescharacteristic
37C2×C4×D17C2311yescharacteristic
38C2×Dic34C2×C411yescharacteristic
39C22⋊#595—24no—
40C2×#3624—22no—
41C2×#3624—42no—
42C4×#595—42no—
43C4⋊C4×C17C2×C411yescharacteristic
44C22⋊C4×C17—21no—
45C22⋊Dic17—21no—
46C22⋊Dic17—21no—
47#63227—21no—
48#63227—21no—
49C4⋊Dic17—21no—
50C4⋊Dic17C2×C411yescharacteristic
51#63225—21no—
52C4×Dic17—21no—
53C23×C17—21no—
54C23×C17C22⋊C411yescharacteristic
55C22×D17—22no—
56C22×D17—22no—
57C22×D17—41no—
58C22×D17C22⋊C411yescharacteristic
59C22×D17C2×D411yescharacteristic
60C2×#595—24no—
61C2×#595—42no—
62C2×#595—42no—
63D4×C17—41no—
64D4×C17—42no—
65C2×C4×C17—21no—
66C2×C4×C17—41no—
67C2×C4×C17C22⋊C411yescharacteristic
68C2×C4×C17C22×C411yescharacteristic
69C22⋊D17—42no—
70C22⋊D17—42no—
71C2×Dic17—22no—
72C2×Dic17—21no—
73C2×Dic17—21no—
74C2×Dic17—42no—
75C2×Dic17C22⋊C411yescharacteristic
76C2×Dic17C2×D411yescharacteristic
77C4×D17—22no—
78C4×D17—22no—
79C4×D17—41no—
80C4×D17—41no—
81Dic34—41no—
82#3624—42no—
83#1501—171nomaximal, Sylow
84C22×C17—21no—
85C22×C17—21no—
86C22×C17—41no—
87C22×C17—41no—
88C22×C17—41no—
89C22×C17#10412yes—
90C22×C17C2×C22⋊C411yescharacteristic
91C2×D17—21no—
92C2×D17—21no—
93C2×D17—21no—
94C2×D17—21no—
95C2×D17—21no—
96C2×D17—44no—
97C2×D17#13512yes—
98#595—44no—
99C4×C17—21no—
100C4×C17—21no—
101C4×C17—41no—
102Dic17—21no—
103Dic17—41no—
104Dic17—41no—
105Dic17#9912yes—
106#525—171no—
107C2×C22⋊C8—171no—
108C4×C22⋊C4—171no—
109#328—172no—
110#327—172no—
111C2×C17—22no—
112C2×C17—81no—
113C2×C17C2×#9911yescharacteristic
114C2×C17#41611yescharacteristic
115C2×C17C2×#10411yescharacteristic
116D17—22no—
117D17—41no—
118C2×#41—171no—
119C23×C4—171no—
120C22×C8—341no—
121#123—341no—
122C22⋊Q8—171no—
123C22⋊Q8—171no—
124#121—171no—
125#121#59511yescharacteristic, complemented
126#120—341no—
127C4×D4—341no—
128C4×D4—341no—
129#117—171no—
130C2×C22⋊C4—341no—
131C2×C42—341no—
132C22⋊C8—172no—
133C22⋊C8—341no—
134#95—172no—
135C17#150111yescharacteristic, complemented, Sylow
136C24—171no—
137#41—682no—
138C2×Q8—171no—
139C2×D4—21no—
140C2×D4—341no—
141C2×D4—341no—
142C2×D4C2×#59511yescharacteristic
143C22×C4—171no—
144C22×C4—171no—
145C22×C4—171no—
146C22×C4—171no—
147C22×C4—171no—
148C22×C4—341no—
149C22×C4—342no—
150C22×C4—682no—
151C22×C4C2×#59511yescharacteristic
152C2×C8—342no—
153C2×C8—682no—
154C4⋊C4—171no—
155C4⋊C4—341no—
156C4⋊C4—341no—
157C4⋊C4C2×#59511yescharacteristic
158C22⋊C4—21no—
159C22⋊C4—341no—
160C22⋊C4—341no—
161C22⋊C4—341no—
162C22⋊C4—344no—
163C22⋊C4—341no—
164C42—341no—
165C42—682no—
166C23—21no—
167C23—171no—
168C23—171no—
169C23—342no—
170C23—342no—
171C23—681no—
172C23C22⋊#59511yescharacteristic
173Q8—681no—
174D4—41no—
175D4—42no—
176D4—682no—
177D4—682no—
178C2×C4—21no—
179C2×C4—41no—
180C2×C4—171no—
181C2×C4—171no—
182C2×C4—342no—
183C2×C4—342no—
184C2×C4—342no—
185C2×C4—344no—
186C2×C4—341no—
187C2×C4—341no—
188C2×C4—681no—
189C2×C4—681no—
190C2×C4—682no—
191C2×C4—682no—
192C2×C4—682no—
193C2×C4C22⋊#59511yescharacteristic
194C2×C4C22×#59511yescharacteristic
195C8—682no—
196C22—21no—
197C22—21no—
198C22—41no—
199C22—41no—
200C22—41no—
201C22—172no—
202C22—341no—
203C22—341no—
204C22—341no—
205C22—341no—
206C22—341no—
207C22—684no—
208C22#1058754812yes—
209C22C2×C22⋊#59511yescharacteristic
210C4—21no—
211C4—21no—
212C4—41no—
213C4—172no—
214C4—341no—
215C4—684no—
216C4—681no—
217C4—681no—
218C2—22no—
219C2—81no—
220C2—342no—
221C2—681no—
222C2D17⋊#9911yescharacteristic
223C2#1176379911yescharacteristic
224C2C2×#1058754811yescharacteristic
subgroupG/H
centerC22C2×C22⋊#595
commutatorC2×C4×C17C22×C4
FrattiniC2×C4C22×#595
FittingC17×#121C4
socleC22×C17C2×C22⋊C4
prime radical#11763319C2
cosocleC2×C4×D17C23
hypercenter#121#595
hypocenterC17#1501
LCSG ▷ C2×C4×C17 ▷ C22×C17 ▷ C17
UCSC1 ◁ C22 ◁ C22×C4 ◁ #121

Complements

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

NH ≅ G/Ntype
1. C2×#10587543C2semidirect
2. C4×C22⋊#595C2semidirect
3. #11763662C2semidirect
4. #11763660C2semidirect
6. C2×#63254C4semidirect
11. C17×#121C4semidirect
15. #10587610C4semidirect
17. #10587578C4semidirect
125. #121#595semidirect
135. C17#1501semidirect

Maximal subgroups

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

subgroupindex
C2×#105875432
C4×C22⋊#5952
#117636622
#117636602
#117633192
#150117