Finite Group Databasebeta

← #100×C3⋊D9 #13143872

Subgroups — #100×C3⋊D9 #13143872

Order 1728.

930 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 930 conjugacy classes of subgroups — too many to draw. Only its 149 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×D4×C3⋊D9C211yesmaximal, characteristic
2M16×C3⋊D9C212yesmaximal, complemented
3C3×C9×#100C211yesmaximal, characteristic, complemented
4#11720575C211yesmaximal, characteristic, complemented
5#11720557C212yesmaximal, complemented
6C3⋊D3×#100—31nomaximal
7D9×#100—33nomaximal
8C23×C3⋊D9C412yes—
9C2×C3×D4×C9C2211yescharacteristic
10C2×#6233C412yes—
11D4×C3⋊D9—22no—
12D4×C3⋊D9—22no—
13C2×C4⋊(C3⋊D9)C2211yescharacteristic
14C2×C4×C3⋊D9C2211yescharacteristic
15C3×C9×M16C2212yescomplemented
16#88532C2212yescomplemented
17#88523—22no—
18C8×C3⋊D9—22no—
19C2×D4×C3⋊D3—31no—
20M16×C3⋊D3—32no—
21C2×D4×D9—33no—
22C32×#100D311yescharacteristic
23#63660—31no—
24#63650—32no—
25M16×D9—36no—
26C9×#100D313yescomplemented
27#63391—33no—
28#63383—36no—
29C23×C3×C9C2×C412yes—
30C22×C3⋊D9—22no—
31C22×C3⋊D9—22no—
32C22×C3⋊D9—44no—
33C22×C3⋊D9C2×C411yescharacteristic
34C22×C3⋊D9C2×C412yes—
35C3×D4×C9—22no—
36C2×C3×C4×C9C2311yescharacteristic
37#6233—24no—
38C2×C3⋊Dic9C2×C411yescharacteristic
39C4⋊(C3⋊D9)—22no—
40C4×C3⋊D9D412yes—
41C4×C3⋊D9D412yes—
42C3×C8×C9—22no—
43C3⋊(C9⋊C8)—22no—
44D3×#100—93no—
45D3×#100—91no—
46C23×C3⋊D3—32no—
47C2×C32×D4C2×D311yescharacteristic
48C2×#638—32no—
49D4×C3⋊D3—62no—
50D4×C3⋊D3—62no—
51C2×C4⋊(C3⋊D3)—31no—
52C2×C4×C3⋊D3—31no—
53C23×D9—36no—
54C32×M16C2×D312yes—
55#3748—32no—
56#3743—62no—
57C8×C3⋊D3—62no—
58C2×D4×C9C2×D313yes—
59C2×#611—36no—
60D4×D9—66no—
61D4×D9—66no—
62C2×D36—33no—
63C2×C4×D9—33no—
64C9×M16C2×D316yescomplemented
65#3667—36no—
66#3663—66no—
67C8×D9—66no—
68C22×C3×C9—22no—
69C22×C3×C9—42no—
70C22×C3×C9C22×C411yescharacteristic
71C2×C3⋊D9—22no—
72C2×C3⋊D9—22no—
73C2×C3⋊D9—44no—
74C2×C3⋊D9—44no—
75C2×C3⋊D9—42no—
76C2×C3⋊D9C22⋊C411yescharacteristic
77C2×C3⋊D9C22⋊C411yescharacteristic
78C3×C4×C9C2×D412yes—
79C3⋊Dic9C22⋊C412yes—
80C2×D3×D4—93no—
81C2×D3×D4—91no—
82D3×M16—96no—
83D3×M16—92no—
84C3×#100D913yescomplemented
85C3×#100C3⋊D311yescharacteristic
86#833—93no—
87#833—91no—
88#823—96no—
89#823—92no—
90C23×C32C4×D312yes—
91C22×C3⋊D3—31no—
92C22×C3⋊D3—32no—
93C22×C3⋊D3—62no—
94C22×C3⋊D3—62no—
95C22×C3⋊D3—124no—
96C32×D4—22no—
97C2×C32×C4C22×D311yescharacteristic
98#638—64no—
99C2×C3⋊Dic3—31no—
100C4⋊(C3⋊D3)—62no—
101C4×C3⋊D3—32no—
102C4×C3⋊D3—32no—
103C23×C9C4×D316yes—
104C22×D9—33no—
105C22×D9—36no—
106C22×D9—66no—
107C22×D9—66no—
108C22×D9—1212no—
109C32×C8—22no—
110C3⋊(C3⋊C8)—62no—
111D4×C9—26no—
112C2×C4×C9C22×D313yes—
113#611—612no—
114C2×Dic9—33no—
115D36—66no—
116C4×D9—36no—
117C4×D9—36no—
118C8×C9—26no—
119C9⋊C8—66no—
120C2×#100—271noSylow
121C2×C3×C9—21no—
122C2×C3×C9—42no—
123C2×C3×C9C2×C22⋊C411yescharacteristic
124C3⋊D9—21no—
125C3⋊D9—42no—
126C3⋊D9#10012yesdirect product factor
127C23×D3—96no—
128C23×D3—92no—
129C2×C3×D4C2×D913yes—
130C2×C3×D4C2×C3⋊D311yescharacteristic
131C2×#67—96no—
132C2×#67—92no—
133D3×D4—182no—
134D3×D4—182no—
135D3×D4—186no—
136D3×D4—186no—
137C2×D12—93no—
138C2×D12—91no—
139C2×C4×D3—93no—
140C2×C4×D3—91no—
141C3×M16C2×D916yescomplemented
142C3×M16C2×C3⋊D312yes—
143#208—96no—
144#208—92no—
145ΓL(1,𝔽25)—182no—
146ΓL(1,𝔽25)—186no—
147D3×C8—182no—
148D3×C8—186no—
149C22×C32—22no—
150C22×C32—42no—
151C22×C32C2×C4×D311yescharacteristic
152C2×C3⋊D3—31no—
153C2×C3⋊D3—31no—
154C2×C3⋊D3—62no—
155C2×C3⋊D3—62no—
156C2×C3⋊D3—124no—
157C2×C3⋊D3—124no—
158C2×C3⋊D3—122no—
159C32×C4D3×D412yes—
160C3⋊Dic3—32no—
161C22×C9—26no—
162C22×C9—46no—
163C22×C9C2×C4×D313yes—
164C2×D9—33no—
165C2×D9—33no—
166C2×D9—66no—
167C2×D9—66no—
168C2×D9—1212no—
169C2×D9—1212no—
170C2×D9—126no—
171C4×C9D3×D416yes—
172Dic9—36no—
173C22×D4—271no—
174C2×M16—272no—
175#100—271no—
176#100—272no—
177#100C3⋊D911yescharacteristic, direct product factor
178C3×C9C2×#10011yescharacteristic, complemented, Sylow
179C23×C3C4×D916yes—
180C23×C3C4×C3⋊D312yes—
181C22×D3—93no—
182C22×D3—91no—
183C22×D3—96no—
184C22×D3—92no—
185C22×D3—182no—
186C22×D3—182no—
187C22×D3—186no—
188C22×D3—186no—
189C22×D3—364no—
190C22×D3—3612no—
191C3×D4—26no—
192C3×D4—22no—
193C2×C3×C4C22×D913yes—
194C2×C3×C4C22×C3⋊D311yescharacteristic
195#67—184no—
196#67—1812no—
197C2×Dic3—93no—
198C2×Dic3—91no—
199D12—186no—
200D12—182no—
201C4×D3—96no—
202C4×D3—96no—
203C4×D3—92no—
204C4×D3—92no—
205C3×C8—26no—
206C3×C8—22no—
207C3⋊C8—186no—
208C3⋊C8—182no—
209C2×C32—21no—
210C2×C32—42no—
211C2×C32D3×C22⋊C411yescharacteristic
212C3⋊D3—32no—
213C3⋊D3—61no—
214C3⋊D3—122no—
215C2×C9—23no—
216C2×C9—46no—
217C2×C9D3×C22⋊C413yes—
218D9—36no—
219D9—63no—
220D9—126no—
221C24—272no—
222C2×D4—272no—
223C2×D4—271no—
224C2×D4—542no—
225C2×D4—542no—
226C2×D4C2×C3⋊D911yescharacteristic
227C22×C4—271no—
228M16—272no—
229M16—542no—
230M16C2×C3⋊D912yescomplemented
231C2×C8—542no—
232C22×C3—22no—
233C22×C3—26no—
234C22×C3—46no—
235C22×C3—42no—
236C22×C3C2×C4×D913yes—
237C22×C3C2×C4×C3⋊D311yescharacteristic
238C2×D3—91no—
239C2×D3—93no—
240C2×D3—91no—
241C2×D3—93no—
242C2×D3—182no—
243C2×D3—186no—
244C2×D3—182no—
245C2×D3—186no—
246C2×D3—364no—
247C2×D3—3612no—
248C2×D3—364no—
249C2×D3—3612no—
250C2×D3—362no—
251C2×D3—366no—
252C3×C4D4×D916yes—
253C3×C4D4×C3⋊D312yes—
254Dic3—92no—
255Dic3—96no—
256C32D3×#10011yescharacteristic
257C9D3×#10013yescomplemented
258C23—271no—
259C23—272no—
260C23—542no—
261C23—542no—
262C23—1084no—
263C23C4×C3⋊D912yes—
264D4—22no—
265D4—544no—
266D4—542no—
267C2×C4—271no—
268C2×C4—272no—
269C2×C4—272no—
270C2×C4C22×C3⋊D911yescharacteristic
271C8—22no—
272C8—542no—
273C2×C3—23no—
274C2×C3—21no—
275C2×C3—46no—
276C2×C3—42no—
277C2×C3C22⋊C4×D913yes—
278C2×C3C22⋊C4×C3⋊D311yescharacteristic
279D3—96no—
280D3—92no—
281D3—183no—
282D3—181no—
283D3—366no—
284D3—362no—
285C22—22no—
286C22—42no—
287C22—271no—
288C22—271no—
289C22—542no—
290C22—542no—
291C22—1082no—
292C22—1084no—
293C22—1084no—
294C22C2×C4×C3⋊D911yescharacteristic
295C4—272no—
296C4D4×C3⋊D912yes—
297C3D9×#10013yescomplemented
298C3C3⋊D3×#10011yescharacteristic
299C2—21no—
300C2—42no—
301C2—272no—
302C2—541no—
303C2—1082no—
304C2C22⋊C4×C3⋊D911yescharacteristic
subgroupG/H
centerC2C22⋊C4×C3⋊D9
commutatorC22×C3×C9C22×C4
FrattiniC2×C3×C4C22×C3⋊D3
FittingC3×C9×#100C2
socleC2×C32D3×C22⋊C4
prime radicalC2×D4×C3⋊D9C2
cosocleC2×C3×C4×C9C23
hypercenter#100C3⋊D9
hypocenterC3×C9C2×#100
LCSG ▷ C22×C3×C9 ▷ C2×C3×C9 ▷ C3×C9
UCSC1 ◁ C2 ◁ C2×C4 ◁ #100

Complements

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

NH ≅ G/Ntype
2. M16×C3⋊D9C2semidirect
3. C3×C9×#100C2semidirect
4. #11720575C2semidirect
5. #11720557C2semidirect
15. C3×C9×M16C22semidirect
16. #88532C22semidirect
26. C9×#100D3semidirect
64. C9×M16C2×D3semidirect
84. C3×#100D9semidirect
126. C3⋊D9#100direct (N × H)
141. C3×M16C2×D9semidirect
177. #100C3⋊D9direct (N × H)
178. C3×C9C2×#100semidirect
230. M16C2×C3⋊D9semidirect
257. C9D3×#100semidirect
297. C3D9×#100semidirect

Maximal subgroups

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

subgroupindex
C2×D4×C3⋊D92
M16×C3⋊D92
C3×C9×#1002
#117205752
#117205572
C3⋊D3×#1003
D9×#1003