Finite Group Databasebeta

← #14517428

Subgroups — #14517428

Order 1944.

480 conjugacy classes of subgroups; only the 72 normal subgroups are shown.

normal subgroups only

This group has 480 conjugacy classes of subgroups — too many to draw. Only its 72 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
1C22×#6891C211yesmaximal, characteristic, complemented
2C2×#92259C211yesmaximal, characteristic, complemented
3#11757563C211yesmaximal, characteristic, complemented
4C32×#638C311yesmaximal, characteristic
5#67×3−1+2—31nomaximal
6#638⋊C9C313yesmaximal, complemented
7C2×#6891—21no—
8C2×#6891C2211yescharacteristic
9#92259—21no—
10C22×C34C2×C311yescharacteristic
11C2×C32×C3⋊D3C2×C311yescharacteristic
12C32×C3⋊Dic3C2×C311yescharacteristic
13C22×C3×3−1+2—21no—
14C22×C3×3−1+2D311yescharacteristic, complemented
15C2×D3×3−1+2—31no—
16Dic3×3−1+2—31no—
17C22×C32⋊C9—23no—
18C22×C32⋊C9C2×C313yescomplemented
19C2×(C3⋊D3)⋊C9C2×C313yescomplemented
20(C3⋊Dic3)⋊C9C2×C313yescomplemented
21#6891D411yescharacteristic, complemented, Sylow
22C3×#638—31no—
23C3×#638C3211yescharacteristic
24C32×#67—31no—
25C32×#67—91no—
26D4×3−1+2—91no—
27C9×#67—33no—
28C2×C34—21no—
29C2×C34C22×C311yescharacteristic
30C32×C3⋊D3—21no—
31C2×C3×3−1+2—22no—
32C2×C3×3−1+2—21no—
33C2×C3×3−1+2—21no—
34C2×C3×3−1+2C2×D311yescharacteristic
35D3×3−1+2—61no—
36C2×C32⋊C9—26no—
37C2×C32⋊C9—23no—
38C2×C32⋊C9—23no—
39C2×C32⋊C9C22×C313yes—
40(C3⋊D3)⋊C9—23no—
41C22×C33—21no—
42C22×C33—31no—
43C22×C33—31no—
44C22×C33—63no—
45C22×C33—61no—
46C22×C33—61no—
47C22×C33C3×D311yescharacteristic
48C22×C33C2×C3211yescharacteristic
49C2×C3×C3⋊D3—31no—
50C2×C3×C3⋊D3C2×C3211yescharacteristic
51C2×C32×D3—31no—
52C2×C32×D3—91no—
53C3×C3⋊Dic3—31no—
54C3×C3⋊Dic3C2×C3211yescharacteristic
55C32×Dic3—31no—
56C32×Dic3—91no—
57C22×3−1+2—31no—
58C22×3−1+2—61no—
59C22×3−1+2—62no—
60C22×3−1+2—61no—
61C22×3−1+2—91no—
62C22×C3×C9—23no—
63C22×C3×C9C3×D313yescomplemented
64C2×D3×C9—33no—
65C4×3−1+2—91no—
66C9×Dic3—33no—
67C34C3×D411yescharacteristic
68C3×3−1+2—21no—
69C3×3−1+2#6711yescharacteristic, complemented
70C32⋊C9—23no—
71C32⋊C9C3×D413yescomplemented
72C32×D4—91no—
73#6383−1+211yescharacteristic, complemented
74C3×#67—31no—
75C3×#67—91no—
76C3×#67—91no—
77C3×#67—93no—
78D4×C9—93no—
79C2×C33—22no—
80C2×C33—21no—
81C2×C33—21no—
82C2×C33—21no—
83C2×C33—31no—
84C2×C33—31no—
85C2×C33—63no—
86C2×C33—61no—
87C2×C33—61no—
88C2×C33—61no—
89C2×C33—61no—
90C2×C33—62no—
91C2×C33—62no—
92C2×C33—66no—
93C2×C33C2×C3×D311yescharacteristic
94C2×C33C22×C3211yescharacteristic
95C3×C3⋊D3—21no—
96C3×C3⋊D3—61no—
97C32×D3—61no—
98C32×D3—181no—
99C2×3−1+2—31no—
100C2×3−1+2—61no—
101C2×3−1+2—61no—
102C2×3−1+2—62no—
103C2×3−1+2—64no—
104C2×3−1+2—62no—
105C2×3−1+2—62no—
106C2×3−1+2—61no—
107C2×3−1+2—181no—
108C2×C3×C9—26no—
109C2×C3×C9—23no—
110C2×C3×C9—23no—
111C2×C3×C9C2×C3×D313yes—
112D3×C9—63no—
113C22×C32—23no—
114C22×C32—21no—
115C22×C32—21no—
116C22×C32—33no—
117C22×C32—31no—
118C22×C32—31no—
119C22×C32—61no—
120C22×C32—61no—
121C22×C32—61no—
122C22×C32—63no—
123C22×C32—63no—
124C22×C32—63no—
125C22×C32—61no—
126C22×C32—61no—
127C22×C32—63no—
128C22×C32—91no—
129C22×C32(C3⋊D3)⋊C311yescharacteristic
130C22×C32C2×3−1+211yescharacteristic, complemented
131C22×C32C32×D311yescharacteristic
132C2×C3⋊D3C2×3−1+211yescharacteristic, complemented
133C2×C3×D3—31no—
134C2×C3×D3—91no—
135C2×C3×D3—91no—
136C2×C3×D3—93no—
137C32×C4—91no—
138C3⋊Dic3C2×3−1+211yescharacteristic, complemented
139C3×Dic3—31no—
140C3×Dic3—91no—
141C3×Dic3—91no—
142C3×Dic3—93no—
143C22×C9—33no—
144C22×C9—63no—
145C22×C9—93no—
146C4×C9—93no—
147C33—21no—
148C33—31no—
149C33—31no—
150C33—63no—
151C33—61no—
152C33—61no—
153C33C3×#6711yescharacteristic
154C33C32×D411yescharacteristic
1553−1+2—31no—
1563−1+2—61no—
1573−1+2—62no—
1583−1+2—61no—
159C3×C9—23no—
160C3×C9C3×#6713yescomplemented
161C3×D4—91no—
162C3×D4—271no—
163#67—31no—
164#67—91no—
165C2×C32—21no—
166C2×C32—22no—
167C2×C32—26no—
168C2×C32—22no—
169C2×C32—23no—
170C2×C32—21no—
171C2×C32—21no—
172C2×C32—21no—
173C2×C32—21no—
174C2×C32—33no—
175C2×C32—31no—
176C2×C32—31no—
177C2×C32—61no—
178C2×C32—61no—
179C2×C32—61no—
180C2×C32—61no—
181C2×C32—62no—
182C2×C32—62no—
183C2×C32—62no—
184C2×C32—62no—
185C2×C32—62no—
186C2×C32—61no—
187C2×C32—63no—
188C2×C32—63no—
189C2×C32—63no—
190C2×C32—66no—
191C2×C32—66no—
192C2×C32—66no—
193C2×C32—66no—
194C2×C32—63no—
195C2×C32—61no—
196C2×C32—61no—
197C2×C32—63no—
198C2×C32—181no—
199C2×C32C2×(C3⋊D3)⋊C311yescharacteristic
200C2×C32C22×3−1+211yescharacteristic
201C2×C32C2×C32×D311yescharacteristic
202C3⋊D3—21no—
203C3×D3—61no—
204C3×D3—181no—
205C3×D3—181no—
206C3×D3—183no—
207C2×C9—33no—
208C2×C9—63no—
209C2×C9—66no—
210C2×C9—63no—
211C2×C9—183no—
212C22×C3—21no—
213C22×C3—31no—
214C22×C3—31no—
215C22×C3—63no—
216C22×C3—61no—
217C22×C3—61no—
218C22×C3—91no—
219C22×C3—271no—
220C22×C3C3×(C3⋊D3)⋊C311yescharacteristic
221C22×C3D3×3−1+211yescharacteristic
222C2×D3—31no—
223C2×D3—91no—
224C3×C4—91no—
225C3×C4—271no—
226Dic3—31no—
227Dic3—91no—
228C32—23no—
229C32—21no—
230C32—21no—
231C32—33no—
232C32—31no—
233C32—31no—
234C32—61no—
235C32—61no—
236C32—61no—
237C32—63no—
238C32—63no—
239C32—63no—
240C32—63no—
241C32—61no—
242C32—61no—
243C32#638⋊C311yescharacteristic
244C32D4×3−1+211yescharacteristic, complemented
245C32C32×#6711yescharacteristic
246C9—33no—
247C9—63no—
248D4—91noSylow
249C2×C3—22no—
250C2×C3—21no—
251C2×C3—21no—
252C2×C3—21no—
253C2×C3—31no—
254C2×C3—31no—
255C2×C3—61no—
256C2×C3—61no—
257C2×C3—62no—
258C2×C3—62no—
259C2×C3—66no—
260C2×C3—63no—
261C2×C3—61no—
262C2×C3—61no—
263C2×C3—181no—
264C2×C3—541no—
265C2×C3C2×C3×(C3⋊D3)⋊C311yescharacteristic
266C2×C3C2×D3×3−1+211yescharacteristic
267D3—61no—
268D3—181no—
269C22—91no—
270C22#9225911yescharacteristic, complemented
271C4—91no—
272C3—21no—
273C3—31no—
274C3—31no—
275C3—63no—
276C3—61no—
277C3—61no—
278C3C3×#638⋊C311yescharacteristic
279C3#67×3−1+211yescharacteristic
280C2—21no—
281C2—181no—
282C2C2×#9225911yescharacteristic
subgroupG/H
centerC2×C3C2×C3×(C3⋊D3)⋊C3
commutator, cosocleC2×C33C22×C32
Frattini, socleC2×C32C2×C32×D3
FittingC22×#6891C2
prime radicalC32×#638C3
hypercenterC22×C32(C3⋊D3)⋊C3
hypocenterC32D4×3−1+2
LCSG ▷ C2×C33 ▷ C32
UCSC1 ◁ C2×C3 ◁ C22×C32

Complements

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

NH ≅ G/Ntype
1. C22×#6891C2semidirect
2. C2×#92259C2semidirect
3. #11757563C2semidirect
6. #638⋊C9C3semidirect
14. C22×C3×3−1+2D3semidirect
18. C22×C32⋊C9C2×C3semidirect
19. C2×(C3⋊D3)⋊C9C2×C3semidirect
20. (C3⋊Dic3)⋊C9C2×C3semidirect
21. #6891D4semidirect
63. C22×C3×C9C3×D3semidirect
69. C3×3−1+2#67semidirect
71. C32⋊C9C3×D4semidirect
73. #6383−1+2semidirect
130. C22×C32C2×3−1+2semidirect
132. C2×C3⋊D3C2×3−1+2semidirect
138. C3⋊Dic3C2×3−1+2semidirect
160. C3×C9C3×#67semidirect
244. C32D4×3−1+2semidirect
270. C22#92259semidirect

Maximal subgroups

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

subgroupindex
C22×#68912
C2×#922592
#117575632
C32×#6383
#67×3−1+23
#638⋊C93