Finite Group Databasebeta

← C3×#63393⋊C3 #72220081

Subgroups — C3×#63393⋊C3 #72220081

Order 2592.

738 conjugacy classes of subgroups; only the 144 normal subgroups are shown.

normal subgroups only

This group has 738 conjugacy classes of subgroups — too many to draw. Only its 144 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×C3×D4×3−1+2C211yesmaximal, characteristic
2C3×#3676⋊C3C212yesmaximal, complemented
3C32×#834—31nomaximal
4#63393⋊C3C313yesmaximal, direct product factor
5C3×#63393C311yesmaximal, characteristic, complemented
6C23×C3×3−1+2C411yescharacteristic, complemented
7C23×C3×3−1+2C2211yescharacteristic
8C3×D4×3−1+2—22no—
9C2×C3×C4×3−1+2C411yescharacteristic, complemented
10C2×C3×3−1+2⋊C4—22no—
11C2×C33×D4D311yescharacteristic
12C32×#217—32no—
13C2×D4×3−1+2—23no—
14C2×D4×3−1+2C2×C313yes—
15C2×C3×D4×C9—21no—
16C2×C3×D4×C9C2×C311yescharacteristic
17#3676⋊C3C2×C316yescomplemented
18C3×#3676C2×C312yescomplemented
19C22×C3×3−1+2—21no—
20C22×C3×3−1+2—41no—
21C22×C3×3−1+2—41no—
22C22×C3×3−1+2C2×C411yescharacteristic
23C22×C3×3−1+2D412yes—
24C3×C4×3−1+2—21no—
25C3×3−1+2⋊C4—42no—
26C32×#99—91no—
27C3×#834—31no—
28C3×#834—33no—
29#63393C3211yescharacteristic, complemented
30C23×C33Dic311yescharacteristic
31C23×C33C2×D311yescharacteristic
32C33×D4—22no—
33C2×C33×C4Dic311yescharacteristic
34C2×C32×Dic3—62no—
35C23×3−1+2—23no—
36C23×3−1+2—23no—
37C23×3−1+2C3×C413yescomplemented
38C23×3−1+2C22×C313yes—
39C23×C3×C9—21no—
40C23×C3×C9—21no—
41C23×C3×C9C3×C411yescharacteristic, complemented
42C23×C3×C9C22×C311yescharacteristic
43D4×3−1+2—212no—
44D4×3−1+2—26no—
45C3×D4×C9—24no—
46C3×D4×C9—22no—
47C2×C4×3−1+2—23no—
48C2×C4×3−1+2C3×C413yescomplemented
49C2×C3×C4×C9—21no—
50C2×C3×C4×C9C3×C411yescharacteristic, complemented
51C2×3−1+2⋊C4—26no—
52C2×C3×Dic9—22no—
53C2×C3×3−1+2—21no—
54C2×C3×3−1+2—22no—
55C2×C3×3−1+2—41no—
56C2×C3×3−1+2C22⋊C411yescharacteristic
57C2×C32×D4—31no—
58C2×C32×D4—61no—
59C2×C32×D4C3×D311yescharacteristic
60C2×C32×D4C3×D313yes—
61C32×C22⋊C4—92no—
62C3×#217—32no—
63C3×#217—36no—
64C2×D4×C9—23no—
65C2×D4×C9—21no—
66C2×D4×C9C2×C3211yescharacteristic
67#3676C2×C3212yescomplemented
68C22×C33—21no—
69C22×C33—41no—
70C22×C33—41no—
71C22×C33C2×Dic311yescharacteristic
72C22×C33#6712yes—
73C33×C4—21no—
74C32×Dic3—122no—
75C22×3−1+2—23no—
76C22×3−1+2—26no—
77C22×3−1+2—26no—
78C22×3−1+2—23no—
79C22×3−1+2—43no—
80C22×3−1+2—46no—
81C22×3−1+2—46no—
82C22×3−1+2—43no—
83C22×3−1+2C2×C3×C413yes—
84C22×3−1+2C3×D416yes—
85C22×C3×C9—21no—
86C22×C3×C9—22no—
87C22×C3×C9—22no—
88C22×C3×C9—21no—
89C22×C3×C9—41no—
90C22×C3×C9—42no—
91C22×C3×C9—42no—
92C22×C3×C9—41no—
93C22×C3×C9C2×C3×C411yescharacteristic
94C22×C3×C9C3×D412yes—
95C4×3−1+2—26no—
96C4×3−1+2—23no—
97C3×C4×C9—22no—
98C3×C4×C9—21no—
993−1+2⋊C4—46no—
100C3×Dic9—42no—
101C3×#99—93no—
102C3×#99—91no—
103#834—31no—
104C3×3−1+2#9911yescharacteristic, complemented, Sylow
105C23×C32—31no—
106C23×C32—31no—
107C23×C32—61no—
108C23×C32—61no—
109C23×C32C3×Dic311yescharacteristic
110C23×C32C3×Dic313yes—
111C23×C32C2×C3×D311yescharacteristic
112C23×C32C2×C3×D313yes—
113C32×D4—22no—
114C32×D4—26no—
115C32×D4—62no—
116C32×D4—64no—
117C2×C32×C4—31no—
118C2×C32×C4—61no—
119C2×C32×C4—182no—
120C2×C32×C4C3×Dic311yescharacteristic
121C2×C32×C4C3×Dic313yes—
122C2×C3×Dic3—62no—
123C2×C3×Dic3—66no—
124C23×C9—23no—
125C23×C9—21no—
126C23×C9—23no—
127C23×C9—21no—
128C23×C9C32×C411yescharacteristic, complemented
129C23×C9C22×C3211yescharacteristic
130D4×C9—212no—
131D4×C9—24no—
132D4×C9—22no—
133C2×C4×C9—23no—
134C2×C4×C9—21no—
135C2×C4×C9C32×C411yescharacteristic, complemented
136C2×Dic9—22no—
137C2×C33—21no—
138C2×C33—22no—
139C2×C33—41no—
140C2×C33#21711yescharacteristic
141C2×3−1+2—26no—
142C2×3−1+2—23no—
143C2×3−1+2—23no—
144C2×3−1+2—26no—
145C2×3−1+2—46no—
146C2×3−1+2—46no—
147C2×3−1+2—43no—
148C2×3−1+2C3×C22⋊C413yes—
149C2×C3×C9—22no—
150C2×C3×C9—21no—
151C2×C3×C9—21no—
152C2×C3×C9—22no—
153C2×C3×C9—42no—
154C2×C3×C9—42no—
155C2×C3×C9—41no—
156C2×C3×C9C3×C22⋊C411yescharacteristic
157C2×C3×D4—21no—
158C2×C3×D4—33no—
159C2×C3×D4AGL(1,ℤ/9)11yescharacteristic
160C2×C3×D4C32×D311yescharacteristic
161C3×C22⋊C4—96no—
162C3×C22⋊C4—92no—
163#217—32no—
164C22×C32—21no—
165C22×C32—23no—
166C22×C32—31no—
167C22×C32—32no—
168C22×C32—41no—
169C22×C32—41no—
170C22×C32—43no—
171C22×C32—43no—
172C22×C32—61no—
173C22×C32—62no—
174C22×C32—61no—
175C22×C32—62no—
176C22×C32—121no—
177C22×C32—121no—
178C22×C32—122no—
179C22×C32—122no—
180C22×C32C2×C3×Dic311yescharacteristic
181C22×C32C2×C3×Dic313yes—
182C22×C32C3×#6712yes—
183C22×C32C3×#6716yes—
184C32×C4—21no—
185C32×C4—23no—
186C32×C4—61no—
187C32×C4—62no—
188C32×C4—362no—
189C3×Dic3—122no—
190C3×Dic3—126no—
191C22×C9—26no—
192C22×C9—22no—
193C22×C9—21no—
194C22×C9—23no—
195C22×C9—21no—
196C22×C9—26no—
197C22×C9—22no—
198C22×C9—41no—
199C22×C9—41no—
200C22×C9—42no—
201C22×C9—46no—
202C22×C9—46no—
203C22×C9—42no—
204C22×C9C2×C32×C411yescharacteristic
205C22×C9C32×D412yes—
206C4×C9—26no—
207C4×C9—22no—
208C4×C9—21no—
209Dic9—42no—
210#99—91noSylow
211C33#83411yescharacteristic
2123−1+2—23no—
2133−1+2C3×#9913yescomplemented
214C3×C9—21no—
215C3×C9C3×#9911yescharacteristic, complemented
216C23×C3—21no—
217C23×C3—21no—
218C23×C3—33no—
219C23×C3—33no—
220C23×C33−1+2⋊C411yescharacteristic, complemented
221C23×C3C2×AGL(1,ℤ/9)11yescharacteristic
222C23×C3C32×Dic311yescharacteristic
223C23×C3C2×C32×D311yescharacteristic
224C3×D4—24no—
225C3×D4—22no—
226C3×D4—22no—
227C3×D4—66no—
228C2×C3×C4—21no—
229C2×C3×C4—33no—
230C2×C3×C4—186no—
231C2×C3×C4—182no—
232C2×C3×C43−1+2⋊C411yescharacteristic, complemented
233C2×C3×C4C32×Dic311yescharacteristic
234C2×Dic3—62no—
235C2×C32—21no—
236C2×C32—22no—
237C2×C32—23no—
238C2×C32—26no—
239C2×C32—31no—
240C2×C32—41no—
241C2×C32—43no—
242C2×C32—61no—
243C2×C32—62no—
244C2×C32—61no—
245C2×C32—62no—
246C2×C32—122no—
247C2×C32—121no—
248C2×C32—122no—
249C2×C32C3×#21711yescharacteristic
250C2×C32C3×#21713yes—
251C2×C9—26no—
252C2×C9—22no—
253C2×C9—22no—
254C2×C9—21no—
255C2×C9—23no—
256C2×C9—21no—
257C2×C9—42no—
258C2×C9—46no—
259C2×C9—46no—
260C2×C9—42no—
261C2×C9—41no—
262C2×C9C32×C22⋊C411yescharacteristic
263C2×D4C3×AGL(1,ℤ/9)11yescharacteristic
264C22⋊C4—92no—
265C22×C3—22no—
266C22×C3—21no—
267C22×C3—21no—
268C22×C3—21no—
269C22×C3—22no—
270C22×C3—33no—
271C22×C3—36no—
272C22×C3—41no—
273C22×C3—41no—
274C22×C3—41no—
275C22×C3—41no—
276C22×C3—42no—
277C22×C3—42no—
278C22×C3—63no—
279C22×C3—123no—
280C22×C3—123no—
281C22×C3C2×3−1+2⋊C411yescharacteristic
282C22×C3#611⋊C312yes—
283C22×C3C2×C32×Dic311yescharacteristic
284C22×C3C32×#6712yes—
285C3×C4—22no—
286C3×C4—21no—
287C3×C4—21no—
288C3×C4—63no—
289C3×C4—362no—
290C3×C4—366no—
291Dic3—122no—
292C32—31no—
293C32—61no—
294C32C3×#83411yescharacteristic
295C32C3×#83413yes—
296C9—23no—
297C9—21no—
298C9C32×#9911yescharacteristic, complemented
299C23C3×3−1+2⋊C411yescharacteristic, complemented
300C23C2×C3×AGL(1,ℤ/9)11yescharacteristic
301D4—22no—
302C2×C4—182no—
303C2×C4C3×3−1+2⋊C411yescharacteristic, complemented
304C2×C3—22no—
305C2×C3—22no—
306C2×C3—21no—
307C2×C3—22no—
308C2×C3—21no—
309C2×C3—21no—
310C2×C3—33no—
311C2×C3—42no—
312C2×C3—42no—
313C2×C3—41no—
314C2×C3—41no—
315C2×C3—66no—
316C2×C3—63no—
317C2×C3—123no—
318C2×C3#3676⋊C311yescharacteristic
319C2×C3C32×#21711yescharacteristic
320C22—21no—
321C22—41no—
322C22—41no—
323C22C2×C3×3−1+2⋊C411yescharacteristic
324C22C3×#611⋊C312yes—
325C4—21no—
326C4—362no—
327C3—21no—
328C3—33no—
329C3#63393⋊C311yescharacteristic, direct product factor
330C3C32×#83411yescharacteristic
331C2—22no—
332C2—21no—
333C2—41no—
334C2C3×#3676⋊C311yescharacteristic
subgroupG/H
centerC2×C3#3676⋊C3
commutatorC22×C9C2×C32×C4
FrattiniC23×C3C2×C32×D3
FittingC2×C3×D4×3−1+2C2
socleC2×C32C3×#217
prime radicalC2×C33×D4D3
cosocleC23×C9C22×C32
hypercenterC2×C3×D4AGL(1,ℤ/9)
hypocenterC9C32×#99
LCSG ▷ C22×C9 ▷ C2×C9 ▷ C9
UCSC1 ◁ C2×C3 ◁ C23×C3 ◁ C2×C3×D4

Complements

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

NH ≅ G/Ntype
2. C3×#3676⋊C3C2semidirect
4. #63393⋊C3C3direct (N × H)
5. C3×#63393C3semidirect
6. C23×C3×3−1+2C4semidirect
9. C2×C3×C4×3−1+2C4semidirect
17. #3676⋊C3C2×C3semidirect
18. C3×#3676C2×C3semidirect
29. #63393C32semidirect
37. C23×3−1+2C3×C4semidirect
41. C23×C3×C9C3×C4semidirect
48. C2×C4×3−1+2C3×C4semidirect
50. C2×C3×C4×C9C3×C4semidirect
67. #3676C2×C32semidirect
104. C3×3−1+2#99semidirect
128. C23×C9C32×C4semidirect
135. C2×C4×C9C32×C4semidirect
213. 3−1+2C3×#99semidirect
215. C3×C9C3×#99semidirect
220. C23×C33−1+2⋊C4semidirect
232. C2×C3×C43−1+2⋊C4semidirect
298. C9C32×#99semidirect
299. C23C3×3−1+2⋊C4semidirect
303. C2×C4C3×3−1+2⋊C4semidirect
329. C3#63393⋊C3direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×D4×3−1+22
C3×#3676⋊C32
C32×#8343
#63393⋊C33
C3×#633933