Finite Group Databasebeta

← #72220077

Subgroups — #72220077

Order 2592.

527 conjugacy classes of subgroups; only the 81 normal subgroups are shown.

normal subgroups only

This group has 527 conjugacy classes of subgroups — too many to draw. Only its 81 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×#611⋊C3C211yesmaximal, characteristic
2#13047994C211yesmaximal, characteristic, complemented
33−1+2×#217C211yesmaximal, characteristic, complemented
4C3×#63580—31nomaximal
5#63365⋊C3—31nomaximal
6#11720329C311yesmaximal, characteristic, complemented
7C23×C3×3−1+2C2211yescharacteristic
8C22×C3×AGL(1,ℤ/9)C411yescharacteristic, complemented
9C2×C3⋊(3−1+2⋊C4)—21no—
10C3×#611⋊C3—21no—
11C3×#611⋊C3—21no—
12C2×Dic3×3−1+2—21no—
13C2×C3×3−1+2⋊C4C411yescharacteristic, complemented
14C2×C32×#67—31no—
15C3×#3757—31no—
16C32×#217D311yescharacteristic
17C2×#611⋊C3—21no—
18C2×#611⋊C3D311yescharacteristic
19C2×C3×#611C2×C311yescharacteristic
20C22⋊C4×3−1+2—31no—
21#88551C2×C311yescharacteristic, complemented
22#3676⋊C3—31no—
23#3676⋊C3—61no—
24C9×#217—21no—
25C9×#217C2×C311yescharacteristic, complemented
26C22×C3×3−1+2—41no—
27C22×C3×3−1+2C2×C411yescharacteristic
28C22×C3×3−1+2D411yescharacteristic
29C22×C3×3−1+2D411yescharacteristic
30C2×C3×AGL(1,ℤ/9)—21no—
31C2×C3×AGL(1,ℤ/9)—41no—
32C3⋊(3−1+2⋊C4)—41no—
33Dic3×3−1+2—41no—
34C3×3−1+2⋊C4—21no—
35C3×#834—91no—
36C3×#806—91no—
37#63580—31no—
38#63365—31no—
39C23×C33C2×D311yescharacteristic
40C22×C32×D3—31no—
41C2×C3×C3⋊Dic3—61no—
42C32×#67—61no—
43C32×#67—61no—
44C2×C32×Dic3—21no—
45C2×C32×Dic3—31no—
46C23×3−1+2—21no—
47C23×3−1+2—21no—
48C23×3−1+2—41no—
49C23×3−1+2C2×D311yescharacteristic
50C23×C3×C9—21no—
51C23×C3×C9C22×C311yescharacteristic
52C22×AGL(1,ℤ/9)—21no—
53C22×AGL(1,ℤ/9)Dic311yescharacteristic, complemented
54C22×C3×D9C3×C411yescharacteristic, complemented
55C2×C4×3−1+2—61no—
56C2×C3⋊Dic9—21no—
57#611⋊C3—22no—
58#611⋊C3—22no—
59#611⋊C3—21no—
60#611⋊C3—21no—
61C2×3−1+2⋊C4—21no—
62C2×3−1+2⋊C4—62no—
63C2×3−1+2⋊C4—61no—
64C2×3−1+2⋊C4Dic311yescharacteristic, complemented
65C3×#611—21no—
66C3×#611—21no—
67C2×C9×Dic3—22no—
68C2×C9×Dic3—21no—
69C2×C3×Dic9C3×C411yescharacteristic, complemented
70C2×C3×3−1+2—21no—
71C2×C3×3−1+2—21no—
72C2×C3×3−1+2—21no—
73C2×C3×3−1+2C22⋊C411yescharacteristic
74C3×AGL(1,ℤ/9)—41no—
75C2×C32×D4—91no—
76C2×C3×#67—31no—
77C2×C3×#67—31no—
78C2×C3×#67—61no—
79C32×C22⋊C4—31no—
80#3757—31no—
81C3×#217—31no—
82C3×#217—91no—
83C3×#217—91no—
84C3×#217—181no—
85C3×#217C3×D311yescharacteristic
86C2×#611C3×D311yescharacteristic
87C9×C22⋊C4—31no—
88C9×C22⋊C4—61no—
89#3676—31no—
90#3676—61no—
91C22×C33—41no—
92C22×C33C4×D311yescharacteristic
93C22×C33D1211yescharacteristic
94C22×C33#6711yescharacteristic
95C2×C32×D3—61no—
96C2×C32×D3—121no—
97C3×C3⋊Dic3—121no—
98C32×Dic3—41no—
99C32×Dic3—61no—
100C22×3−1+2—21no—
101C22×3−1+2—21no—
102C22×3−1+2—21no—
103C22×3−1+2—21no—
104C22×3−1+2—21no—
105C22×3−1+2—21no—
106C22×3−1+2—41no—
107C22×3−1+2—42no—
108C22×3−1+2—42no—
109C22×3−1+2—41no—
110C22×3−1+2—41no—
111C22×3−1+2—41no—
112C22×3−1+2—44no—
113C22×3−1+2C2×Dic311yescharacteristic
114C22×3−1+2#6711yescharacteristic
115C22×3−1+2#6711yescharacteristic
116C22×C3×C9—21no—
117C22×C3×C9—21no—
118C22×C3×C9—21no—
119C22×C3×C9—41no—
120C22×C3×C9—42no—
121C22×C3×C9C2×C3×C411yescharacteristic
122C22×C3×C9C3×D411yescharacteristic
123C22×C3×C9C3×D411yescharacteristic
124C2×AGL(1,ℤ/9)—22no—
125C2×AGL(1,ℤ/9)—21no—
126C2×AGL(1,ℤ/9)—42no—
127C2×AGL(1,ℤ/9)—41no—
128C2×C3×D9—21no—
129C2×C3×D9—41no—
130C4×3−1+2—121no—
131C3⋊Dic9—41no—
1323−1+2⋊C4—22no—
1333−1+2⋊C4—21no—
1343−1+2⋊C4—122no—
1353−1+2⋊C4—121no—
136C9×Dic3—42no—
137C9×Dic3—41no—
138C3×Dic9—21no—
139C3×#99—271no—
140#834—91no—
141#806—91no—
142C3×3−1+2#9911yescharacteristic, complemented, Sylow
143C23×C32—21no—
144C23×C32—31no—
145C23×C32—61no—
146C23×C32—91no—
147C23×C32D3211yescharacteristic
148C23×C32C2×C3×D311yescharacteristic
149C22×C3×D3—31no—
150C22×C3×D3—31no—
151C22×C3×D3—61no—
152C32×D4—181no—
153C32×D4—181no—
154C2×C32×C4—61no—
155C2×C32×C4—91no—
156C2×C3⋊Dic3—61no—
157C3×#67—62no—
158C3×#67—62no—
159C3×#67—61no—
160C3×#67—61no—
161C3×#67—61no—
162C3×#67—61no—
163C2×C3×Dic3—21no—
164C2×C3×Dic3—31no—
165C2×C3×Dic3—31no—
166C2×C3×Dic3—61no—
167C2×C3×Dic3—61no—
168C2×C3×Dic3—181no—
169C2×C3×Dic3—182no—
170C2×C3×Dic3—181no—
171C23×C9—21no—
172C23×C9—21no—
173C23×C9—41no—
174C23×C9C2×C3×D311yescharacteristic
175C22×D9C3×Dic311yescharacteristic, complemented
176C2×C4×C9—62no—
177C2×C4×C9—61no—
178#611—21no—
179#611—21no—
180C2×Dic9—62no—
181C2×Dic9—61no—
182C2×Dic9C3×Dic311yescharacteristic, complemented
183C2×C33—21no—
184C2×C33—21no—
185C2×C33—21no—
186C2×C33(C2×D3)⋊C411yescharacteristic
187C32×D3—121no—
188C2×3−1+2—21no—
189C2×3−1+2—22no—
190C2×3−1+2—22no—
191C2×3−1+2—21no—
192C2×3−1+2—21no—
193C2×3−1+2—21no—
194C2×3−1+2—21no—
195C2×3−1+2—41no—
196C2×3−1+2—41no—
197C2×3−1+2—41no—
198C2×3−1+2—42no—
199C2×3−1+2—42no—
200C2×3−1+2—41no—
201C2×3−1+2—41no—
202C2×3−1+2—42no—
203C2×3−1+2#21711yescharacteristic
204C2×C3×C9—21no—
205C2×C3×C9—22no—
206C2×C3×C9—21no—
207C2×C3×C9—21no—
208C2×C3×C9—21no—
209C2×C3×C9—41no—
210C2×C3×C9—41no—
211C2×C3×C9C3×C22⋊C411yescharacteristic
212AGL(1,ℤ/9)—42no—
213AGL(1,ℤ/9)—41no—
214C3×D9—41no—
215C2×C3×D4—91no—
216C2×C3×D4—91no—
217C2×C3×D4—181no—
218C2×#67—31no—
219C3×C22⋊C4—31no—
220C3×C22⋊C4—91no—
221C3×C22⋊C4—271no—
222#217—91no—
223#217—91no—
224#217—181no—
225#217AGL(1,ℤ/9)11yescharacteristic, complemented
226C22×C32—21no—
227C22×C32—21no—
228C22×C32—21no—
229C22×C32—31no—
230C22×C32—31no—
231C22×C32—31no—
232C22×C32—41no—
233C22×C32—41no—
234C22×C32—42no—
235C22×C32—61no—
236C22×C32—61no—
237C22×C32—61no—
238C22×C32—121no—
239C22×C32—122no—
240C22×C32—181no—
241C22×C32—361no—
242C22×C32D3×Dic311yescharacteristic
243C22×C32#62511yescharacteristic
244C22×C32#62611yescharacteristic
245C22×C32C3×C4×D311yescharacteristic
246C22×C32C3×D1211yescharacteristic
247C22×C32C3×#6711yescharacteristic
248C2×C3×D3—62no—
249C2×C3×D3—61no—
250C2×C3×D3—61no—
251C2×C3×D3—122no—
252C2×C3×D3—121no—
253C2×C3×D3—121no—
254C32×C4—121no—
255C32×C4—181no—
256C3⋊Dic3—121no—
257C3×Dic3—41no—
258C3×Dic3—62no—
259C3×Dic3—61no—
260C3×Dic3—61no—
261C3×Dic3—121no—
262C3×Dic3—361no—
263C3×Dic3—361no—
264C3×Dic3—362no—
265C22×C9—21no—
266C22×C9—21no—
267C22×C9—21no—
268C22×C9—21no—
269C22×C9—21no—
270C22×C9—21no—
271C22×C9—41no—
272C22×C9—42no—
273C22×C9—42no—
274C22×C9—44no—
275C22×C9—41no—
276C22×C9—41no—
277C22×C9—41no—
278C22×C9C2×C3×Dic311yescharacteristic
279C22×C9C3×#6711yescharacteristic
280C22×C9C3×#6711yescharacteristic
281C2×D9—21no—
282C2×D9—41no—
283C4×C9—122no—
284C4×C9—121no—
285Dic9—21no—
286Dic9—122no—
287Dic9—121no—
288#99—271noSylow
289C33#80611yescharacteristic
2903−1+2—21no—
2913−1+2—21no—
2923−1+2—41no—
2933−1+2#83411yescharacteristic, complemented
294C3×C9—21no—
295C3×C9C3×#9911yescharacteristic, complemented
296C23×C3—21no—
297C23×C3—31no—
298C23×C3—61no—
299C23×C3—91no—
300C23×C3—91no—
301C23×C3—181no—
302C23×C3C2×AGL(1,ℤ/9)11yescharacteristic
303C23×C3C3×D3211yescharacteristic
304C22×D3—31no—
305C3×D4—181no—
306C3×D4—181no—
307C3×D4—182no—
308C3×D4—182no—
309C3×D4—181no—
310C3×D4—181no—
311C2×C3×C4—61no—
312C2×C3×C4—91no—
313C2×C3×C4—91no—
314C2×C3×C4—181no—
315C2×C3×C4—181no—
316C2×C3×C4—541no—
317#67—61no—
318#67—61no—
319C2×Dic3—21no—
320C2×Dic3—31no—
321C2×Dic3—182no—
322C2×Dic3—181no—
323C2×Dic3—181no—
324C2×C32—21no—
325C2×C32—21no—
326C2×C32—21no—
327C2×C32—22no—
328C2×C32—21no—
329C2×C32—21no—
330C2×C32—21no—
331C2×C32—21no—
332C2×C32—31no—
333C2×C32—41no—
334C2×C32—41no—
335C2×C32—61no—
336C2×C32—61no—
337C2×C32—61no—
338C2×C32—61no—
339C2×C32—62no—
340C2×C32—121no—
341C2×C32—121no—
342C2×C32—361no—
343C2×C32(C2×D3)⋊Dic311yescharacteristic
344C2×C32C3×(C2×D3)⋊C411yescharacteristic
345C3×D3—122no—
346C3×D3—121no—
347C3×D3—121no—
348C2×C9—22no—
349C2×C9—22no—
350C2×C9—21no—
351C2×C9—21no—
352C2×C9—21no—
353C2×C9—21no—
354C2×C9—21no—
355C2×C9—41no—
356C2×C9—41no—
357C2×C9—41no—
358C2×C9—41no—
359C2×C9—42no—
360C2×C9—42no—
361C2×C9—42no—
362C2×C9—41no—
363C2×C9C3×#21711yescharacteristic
364D9—41no—
365C2×D4—91no—
366C22⋊C4—31no—
367C22⋊C4—271no—
368C22×C3—21no—
369C22×C3—21no—
370C22×C3—21no—
371C22×C3—31no—
372C22×C3—31no—
373C22×C3—31no—
374C22×C3—41no—
375C22×C3—41no—
376C22×C3—42no—
377C22×C3—61no—
378C22×C3—61no—
379C22×C3—61no—
380C22×C3—121no—
381C22×C3—122no—
382C22×C3—181no—
383C22×C3—182no—
384C22×C3—181no—
385C22×C3—361no—
386C22×C3—361no—
387C22×C3—362no—
388C22×C3C4×AGL(1,ℤ/9)11yescharacteristic
389C22×C3C4⋊AGL(1,ℤ/9)11yescharacteristic
390C22×C3#611⋊C311yescharacteristic
391C22×C3C3×D3×Dic311yescharacteristic
392C22×C3C3×#62511yescharacteristic
393C22×C3C3×#62611yescharacteristic
394C2×D3—61no—
395C2×D3—121no—
396C3×C4—121no—
397C3×C4—181no—
398C3×C4—182no—
399C3×C4—181no—
400C3×C4—361no—
401C3×C4—1081no—
402Dic3—41no—
403Dic3—61no—
404Dic3—361no—
405Dic3—362no—
406Dic3—361no—
407C32—21no—
408C32—31no—
409C32—61no—
410C32#6358011yescharacteristic
411C32C3×#80611yescharacteristic
412C9—21no—
413C9—21no—
414C9—41no—
415C9C3×#83411yescharacteristic, complemented
416C23—91no—
417C23D3×AGL(1,ℤ/9)11yescharacteristic
418D4—181no—
419D4—181no—
420C2×C4—61no—
421C2×C4—91no—
422C2×C4—541no—
423C2×C3—22no—
424C2×C3—21no—
425C2×C3—21no—
426C2×C3—21no—
427C2×C3—21no—
428C2×C3—21no—
429C2×C3—21no—
430C2×C3—21no—
431C2×C3—31no—
432C2×C3—41no—
433C2×C3—41no—
434C2×C3—61no—
435C2×C3—61no—
436C2×C3—61no—
437C2×C3—62no—
438C2×C3—61no—
439C2×C3—121no—
440C2×C3—121no—
441C2×C3—361no—
442C2×C3—362no—
443C2×C3—361no—
444C2×C3(C2×AGL(1,ℤ/9))⋊C411yescharacteristic
445C2×C3C3×(C2×D3)⋊Dic311yescharacteristic
446D3—121no—
447C22—41no—
448C22—181no—
449C22—361no—
450C22Dic3×AGL(1,ℤ/9)11yescharacteristic
451C22#6192⋊C311yescharacteristic
452C22#6194⋊C311yescharacteristic
453C4—121no—
454C4—181no—
455C4—1081no—
456C3—21no—
457C3—31no—
458C3—61no—
459C3#63365⋊C311yescharacteristic, complemented
460C3C3×#6358011yescharacteristic
461C2—21no—
462C2—21no—
463C2—21no—
464C2—361no—
465C2(C2×AGL(1,ℤ/9))⋊Dic311yescharacteristic
subgroupG/H
centerC2(C2×AGL(1,ℤ/9))⋊Dic3
commutatorC22×C3×C9C2×C3×C4
FrattiniC23×C3C3×D32
FittingC23×C3×3−1+2C22
socleC2×C32C3×(C2×D3)⋊C4
prime radicalC2×C3×#611⋊C3C2
cosocleC23×C3×C9C22×C3
hypercenterC23D3×AGL(1,ℤ/9)
hypocenterC3×C9C3×#99
LCSG ▷ C22×C3×C9 ▷ C2×C3×C9 ▷ C3×C9
UCSC1 ◁ C2 ◁ C23

Complements

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

NH ≅ G/Ntype
2. #13047994C2semidirect
3. 3−1+2×#217C2semidirect
6. #11720329C3semidirect
8. C22×C3×AGL(1,ℤ/9)C4semidirect
13. C2×C3×3−1+2⋊C4C4semidirect
21. #88551C2×C3semidirect
25. C9×#217C2×C3semidirect
53. C22×AGL(1,ℤ/9)Dic3semidirect
54. C22×C3×D9C3×C4semidirect
64. C2×3−1+2⋊C4Dic3semidirect
69. C2×C3×Dic9C3×C4semidirect
142. C3×3−1+2#99semidirect
175. C22×D9C3×Dic3semidirect
182. C2×Dic9C3×Dic3semidirect
225. #217AGL(1,ℤ/9)semidirect
293. 3−1+2#834semidirect
295. C3×C9C3×#99semidirect
415. C9C3×#834semidirect
459. C3#63365⋊C3semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#611⋊C32
#130479942
3−1+2×#2172
C3×#635803
#63365⋊C33
#117203293