Finite Group Databasebeta

← C9×#4827 #13141979

Subgroups — C9×#4827 #13141979

Order 1728.

482 conjugacy classes of subgroups.

The subgroup lattice has 426 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C9×#1010C211yesmaximal, characteristic, complemented
2C9×#949C211yesmaximal, characteristic, complemented
3C9×#908C211yesmaximal, characteristic, complemented
4C9×#875C211yesmaximal, characteristic, complemented
5C3×C9×#104C211yesmaximal, characteristic, complemented
6C9×#824C211yesmaximal, characteristic, complemented
7C9×#805C211yesmaximal, characteristic, complemented
8C3×#4827C311yesmaximal, characteristic
9C9×#454—31nomaximal
10C3×C9×#41C2211yescharacteristic
11D3×Q8×C9—21no—
12C9×#237—21no—
13C9×#237—22no—
14C9×#235—21no—
15C9×#235C2211yescharacteristic
16C2×C9×D12C2211yescharacteristic
17C2×C9×Dic6—21no—
18C2×C9×Dic6C2211yescharacteristic
19C3×C9×M16C2211yescharacteristic
20C3×C42×C9C2211yescharacteristic
21C9×#215—21no—
22C9×#213—21no—
23C9×(C2×D3)⋊C4—22no—
24C9×#208C2211yescharacteristic
25C9×D24—21no—
26C9×#204—21no—
27C3×#1010C2×C311yescharacteristic
28C3×#949C2×C311yescharacteristic
29C3×#908C2×C311yescharacteristic
30C3×#875C2×C311yescharacteristic
31C9×2−1+4—31no—
32C32×#104C2×C311yescharacteristic
33C3×#824C2×C311yescharacteristic
34C3×#805C2×C311yescharacteristic
35C9×AGL(1,ℤ/8)—31no—
36C9×AGL(1,ℤ/8)—31no—
37C9×#124—31no—
38C9×#104—21no—
39C9×#104—31no—
40C9×#104D311yescharacteristic, complemented
41C9×#101—31no—
42C22×D3×C9—21no—
43C3×Q8×C9D411yescharacteristic
44C3×D4×C9—21no—
45C3×D4×C9D411yescharacteristic
46C2×C3×C4×C9—21no—
47C2×C3×C4×C9—21no—
48C2×C3×C4×C9C2311yescharacteristic
49C9×#67—22no—
50C9×#67—21no—
51C2×C9×Dic3—22no—
52C2×C9×Dic3D412yes—
53C9×D12—21no—
54C9×D12—21no—
55C9×D12D411yescharacteristic
56C4×D3×C9—22no—
57C4×D3×C9—21no—
58C9×Dic6—22no—
59C9×Dic6—21no—
60C9×Dic6—21no—
61C9×Dic6D411yescharacteristic
62C3×C8×C9—21no—
63C9×C3⋊C8—21no—
64C3×#454—31no—
65#4827C911yescharacteristic, direct product factor
66C32×#41C22×C311yescharacteristic
67C3×D3×Q8—21no—
68C3×#237—21no—
69C3×#237—22no—
70C3×#235—21no—
71C3×#235C22×C311yescharacteristic
72C2×C3×D12C22×C311yescharacteristic
73C2×C3×Dic6—21no—
74C2×C3×Dic6C22×C311yescharacteristic
75C32×M16C22×C311yescharacteristic
76C32×C42C22×C311yescharacteristic
77C3×#215—21no—
78C3×#213—21no—
79C3×(C2×D3)⋊C4—22no—
80C3×#208C22×C311yescharacteristic
81C3×D24—21no—
82C3×#204—21no—
83C9×#41—21no—
84C9×#41—31no—
85C9×#41—61no—
86C9×#41—62no—
87C9×#41—61no—
88C9×#41C2×D311yescharacteristic
89C2×Q8×C9—31no—
90C2×Q8×C9—61no—
91C2×Q8×C9—61no—
92C2×D4×C9—31no—
93C9×SD16—61no—
94C9×SD16—61no—
95C9×D8—61no—
96C9×D8—61no—
97C9×M16—21no—
98C9×M16—31no—
99C9×M16C2×D311yescharacteristic
100C9×C22⋊C4—62no—
101C42×C9—21no—
102C42×C9C2×D311yescharacteristic
103C22×C3×C9—21no—
104C22×C3×C9C2×D411yescharacteristic
105C2×D3×C9—21no—
106C2×D3×C9—42no—
107C2×D3×C9—41no—
108C3×C4×C9—21no—
109C3×C4×C9—41no—
110C3×C4×C9C2×D411yescharacteristic
111C3×C4×C9C2×D411yescharacteristic
112C9×Dic3—22no—
113C9×Dic3—21no—
114C3×2−1+4—31no—
115#1010C2×C911yescharacteristic, complemented
116C3×AGL(1,ℤ/8)—31no—
117C3×AGL(1,ℤ/8)—31no—
118C3×#124—31no—
119#949C2×C911yescharacteristic, complemented
120#908C2×C911yescharacteristic, complemented
121#875C2×C911yescharacteristic, complemented
122C3×#104—21no—
123C3×#104—31no—
124C3×#104C2×C911yescharacteristic, complemented
125C3×#104C3×D311yescharacteristic
126C3×#101—31no—
127#824C2×C911yescharacteristic, complemented
128#805C2×C911yescharacteristic, complemented
129C22×C3×D3—21no—
130C32×Q8C3×D411yescharacteristic
131C32×D4—21no—
132C32×D4C3×D411yescharacteristic
133C2×C32×C4—21no—
134C2×C32×C4—21no—
135C2×C32×C4C23×C311yescharacteristic
136C3×#67—22no—
137C3×#67—21no—
138C2×C3×Dic3—22no—
139C2×C3×Dic3C3×D412yes—
140C3×D12—21no—
141C3×D12—21no—
142C3×D12C3×D411yescharacteristic
143C3×C4×D3—22no—
144C3×C4×D3—21no—
145C3×Dic6—22no—
146C3×Dic6—21no—
147C3×Dic6—21no—
148C3×Dic6C3×D411yescharacteristic
149C23×C9—61no—
150C32×C8—21no—
151C3×C3⋊C8—21no—
152Q8×C9—21no—
153Q8×C9—31no—
154Q8×C9—62no—
155Q8×C9—61no—
156Q8×C9—61no—
157Q8×C9D1211yescharacteristic
158D4×C9—21no—
159D4×C9—21no—
160D4×C9—31no—
161D4×C9—41no—
162D4×C9—62no—
163D4×C9—61no—
164D4×C9—61no—
165D4×C9—61no—
166D4×C9D1211yescharacteristic
167C2×C4×C9—21no—
168C2×C4×C9—21no—
169C2×C4×C9—21no—
170C2×C4×C9—32no—
171C2×C4×C9—41no—
172C2×C4×C9—41no—
173C2×C4×C9—62no—
174C2×C4×C9—62no—
175C2×C4×C9—61no—
176C2×C4×C9C22×D311yescharacteristic
177C8×C9—21no—
178C8×C9—41no—
179C8×C9—61no—
180#454—31noSylow
181C2×C3×C9—21no—
182C2×C3×C9—41no—
183C2×C3×C9#12011yescharacteristic
184D3×C9—41no—
185D3×C9—81no—
186C3×#41—21no—
187C3×#41—31no—
188C3×#41—61no—
189C3×#41—62no—
190C3×#41—61no—
191C3×#41C22×C911yescharacteristic
192C3×#41C2×C3×D311yescharacteristic
193C2×C3×Q8—31no—
194C2×C3×Q8—61no—
195C2×C3×Q8—61no—
196C2×C3×D4—31no—
197D3×Q8—21no—
198#237—21no—
199#237—22no—
200#235—21no—
201#235C22×C911yescharacteristic
202C2×D12C22×C911yescharacteristic
203C2×Dic6—21no—
204C2×Dic6C22×C911yescharacteristic
205C3×SD16—61no—
206C3×SD16—61no—
207C3×D8—61no—
208C3×D8—61no—
209C3×M16—21no—
210C3×M16—31no—
211C3×M16C22×C911yescharacteristic
212C3×M16C2×C3×D311yescharacteristic
213C3×C22⋊C4—62no—
214C3×C42—21no—
215C3×C42C22×C911yescharacteristic
216C3×C42C2×C3×D311yescharacteristic
217#215—21no—
218#213—21no—
219(C2×D3)⋊C4—22no—
220#208C22×C911yescharacteristic
221D24—21no—
222#204—21no—
223C22×C32—21no—
224C22×C32C2×C3×D411yescharacteristic
225C2×C3×D3—21no—
226C2×C3×D3—42no—
227C2×C3×D3—41no—
228C32×C4—21no—
229C32×C4—41no—
230C32×C4C2×C3×D411yescharacteristic
231C32×C4C2×C3×D411yescharacteristic
232C3×Dic3—22no—
233C3×Dic3—21no—
234C22×C9—21no—
235C22×C9—21no—
236C22×C9—41no—
237C22×C9—61no—
238C22×C9—122no—
239C22×C9—121no—
240C22×C9D3×D411yescharacteristic
241C4×C9—21no—
242C4×C9—21no—
243C4×C9—21no—
244C4×C9—41no—
245C4×C9—41no—
246C4×C9—42no—
247C4×C9—62no—
248C4×C9—61no—
249C4×C9C2×D1211yescharacteristic
250C4×C9D3×D411yescharacteristic
2512−1+4—31no—
252AGL(1,ℤ/8)—31no—
253AGL(1,ℤ/8)—31no—
254#124—31no—
255#104—31no—
256#104D3×C911yescharacteristic, complemented
257#101—31no—
258C3×C9#45411yescharacteristic, complemented, Sylow
259C23×C3—61no—
260C22×D3—21no—
261C3×Q8—21no—
262C3×Q8—31no—
263C3×Q8—62no—
264C3×Q8—61no—
265C3×Q8—61no—
266C3×Q8D4×C911yescharacteristic
267C3×Q8C3×D1211yescharacteristic
268C3×D4—21no—
269C3×D4—21no—
270C3×D4—21no—
271C3×D4—31no—
272C3×D4—41no—
273C3×D4—62no—
274C3×D4—61no—
275C3×D4—61no—
276C3×D4—61no—
277C3×D4D4×C911yescharacteristic
278C3×D4C3×D1211yescharacteristic
279C2×C3×C4—21no—
280C2×C3×C4—21no—
281C2×C3×C4—21no—
282C2×C3×C4—21no—
283C2×C3×C4—21no—
284C2×C3×C4—32no—
285C2×C3×C4—41no—
286C2×C3×C4—41no—
287C2×C3×C4—62no—
288C2×C3×C4—62no—
289C2×C3×C4—61no—
290C2×C3×C4C23×C911yescharacteristic
291C2×C3×C4C22×C3×D311yescharacteristic
292#67—22no—
293#67—21no—
294C2×Dic3—22no—
295C2×Dic3D4×C912yes—
296D12—21no—
297D12—21no—
298D12D4×C911yescharacteristic
299C4×D3—22no—
300C4×D3—21no—
301Dic6—22no—
302Dic6—21no—
303Dic6—21no—
304Dic6D4×C911yescharacteristic
305C3×C8—21no—
306C3×C8—21no—
307C3×C8—41no—
308C3×C8—61no—
309C3⋊C8—21no—
310C2×C32—21no—
311C2×C32—41no—
312C2×C32C3×#12011yescharacteristic
313C3×D3—41no—
314C3×D3—81no—
315C2×C9—21no—
316C2×C9—21no—
317C2×C9—41no—
318C2×C9—41no—
319C2×C9—81no—
320C2×C9—121no—
321C2×C9—241no—
322C2×C9#88211yescharacteristic
323#41—31no—
324#41—61no—
325#41—62no—
326#41—61no—
327#41C2×D3×C911yescharacteristic
328C2×Q8—31no—
329C2×Q8—61no—
330C2×Q8—61no—
331C2×D4—31no—
332SD16—61no—
333SD16—61no—
334D8—61no—
335D8—61no—
336M16—31no—
337M16C2×D3×C911yescharacteristic
338C22⋊C4—62no—
339C42C2×D3×C911yescharacteristic
340C22×C3—21no—
341C22×C3—21no—
342C22×C3—21no—
343C22×C3—41no—
344C22×C3—61no—
345C22×C3—122no—
346C22×C3—121no—
347C22×C3C2×D4×C911yescharacteristic
348C22×C3C3×D3×D411yescharacteristic
349C2×D3—21no—
350C2×D3—42no—
351C2×D3—41no—
352C3×C4—21no—
353C3×C4—21no—
354C3×C4—21no—
355C3×C4—21no—
356C3×C4—41no—
357C3×C4—41no—
358C3×C4—41no—
359C3×C4—42no—
360C3×C4—62no—
361C3×C4—61no—
362C3×C4C2×D4×C911yescharacteristic
363C3×C4C2×D4×C911yescharacteristic
364C3×C4C2×C3×D1211yescharacteristic
365C3×C4C3×D3×D411yescharacteristic
366Dic3—22no—
367Dic3—21no—
368C32C3×#45411yescharacteristic
369C9—21no—
370C9#482711yescharacteristic, direct product factor
371C23—61no—
372Q8—31no—
373Q8—62no—
374Q8—61no—
375Q8—61no—
376Q8C9×D1211yescharacteristic
377D4—21no—
378D4—31no—
379D4—62no—
380D4—61no—
381D4—61no—
382D4—61no—
383D4C9×D1211yescharacteristic
384C2×C4—21no—
385C2×C4—21no—
386C2×C4—32no—
387C2×C4—62no—
388C2×C4—62no—
389C2×C4—61no—
390C2×C4C22×D3×C911yescharacteristic
391C8—21no—
392C8—61no—
393C2×C3—21no—
394C2×C3—21no—
395C2×C3—21no—
396C2×C3—41no—
397C2×C3—41no—
398C2×C3—41no—
399C2×C3—81no—
400C2×C3—121no—
401C2×C3—241no—
402C2×C3C9×#12011yescharacteristic
403C2×C3C3×#88211yescharacteristic
404D3—41no—
405D3—81no—
406C22—21no—
407C22—61no—
408C22—122no—
409C22—121no—
410C22D3×D4×C911yescharacteristic
411C4—21no—
412C4—41no—
413C4—62no—
414C4—61no—
415C4C2×C9×D1211yescharacteristic
416C4D3×D4×C911yescharacteristic
417C3—21no—
418C3C9×#45411yescharacteristic, complemented
419C3C3×#482711yescharacteristic
420C2—21no—
421C2—41no—
422C2—121no—
423C2—241no—
424C2C9×#88211yescharacteristic
subgroupG/H
centerC2×C9#882
commutatorC2×C3×C4C23×C9
FrattiniC2×C3×C4C22×C3×D3
FittingC3×C9×#104C2
socleC2×C32C3×#120
prime radicalC3×#4827C3
cosocleC2×C32×C4C23×C3
hypercenterC9×#104D3
hypocenterC3C9×#454
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C9 ◁ C2×C4×C9 ◁ C9×#104

Complements

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

NH ≅ G/Ntype
1. C9×#1010C2semidirect
2. C9×#949C2semidirect
3. C9×#908C2semidirect
4. C9×#875C2semidirect
5. C3×C9×#104C2semidirect
6. C9×#824C2semidirect
7. C9×#805C2semidirect
40. C9×#104D3semidirect
65. #4827C9direct (N × H)
115. #1010C2×C9semidirect
119. #949C2×C9semidirect
120. #908C2×C9semidirect
121. #875C2×C9semidirect
124. C3×#104C2×C9semidirect
127. #824C2×C9semidirect
128. #805C2×C9semidirect
256. #104D3×C9semidirect
258. C3×C9#454semidirect
370. C9#4827direct (N × H)
418. C3C9×#454semidirect

Maximal subgroups

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

subgroupindex
C9×#10102
C9×#9492
C9×#9082
C9×#8752
C3×C9×#1042
C9×#8242
C9×#8052
C3×#48273
C9×#4543