Finite Group Databasebeta

← D9×#936 #13150978

Subgroups — D9×#936 #13150978

Order 1728.

1066 conjugacy classes of subgroups.

The subgroup lattice has 456 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×D4×D9C211yesmaximal, characteristic
2C2×D9×Dic6C211yesmaximal, characteristic, complemented
3#11721836C211yesmaximal, characteristic, complemented
4C9×#936C211yesmaximal, characteristic, complemented
5D9×#217C214yesmaximal, complemented
6#11721257C214yesmaximal, complemented
7C4×Dic3×D9C211yesmaximal, characteristic, complemented
8#11720951C211yesmaximal, characteristic, complemented
9#11720948C211yesmaximal, characteristic, complemented
10D3×#936—31nomaximal
11D9×#124—31nomaximal
12C23×C3×D9C2212yes—
13C2×C3×D4×C9C2211yescharacteristic
14C2×#6226C2211yescharacteristic, complemented
15C2×C3×#611C2212yes—
16C3×D4×D9—24no—
17C2×C3×D36C2211yescharacteristic
18C2×C3×C4×D9C2211yescharacteristic
19C2×C9×Dic6C2211yescharacteristic, complemented
20C2×Dic3×D9C2212yes—
21C2×Dic3×D9C2212yes—
22C2×#6189C2212yescomplemented
23D9×Dic6—24no—
24#88551C2214yescomplemented
25C4×C3⋊Dic9C2211yescharacteristic, complemented
26C9×#217C2214yescomplemented
27C4×C9×Dic3C2211yescharacteristic, complemented
28(C2×D9)⋊Dic3C2214yescomplemented
29(C2×D9)⋊Dic3C2214yescomplemented
30Dic3×Dic9C2212yescomplemented
31C2×C3×D3×D4—31no—
32C2×D3×Dic6—31no—
33#64145—31no—
34C3×#936D311yescharacteristic
35D3×#217—34no—
36#63959—34no—
37C4×D3×Dic3—31no—
38#63863—31no—
39#63860—31no—
40C2×Q8×D9—31no—
41C2×D4×D9D311yescharacteristic
42C9×#124—31no—
43#63509—31no—
44#63498—31no—
45#63498—61no—
46#63447—34no—
47C22⋊C4×D9—34no—
48#63437—31no—
49C42×D9—31no—
50C23×C3×C9C2312yes—
51C22×C3×D9—24no—
52C22×C3×D9—28no—
53C22×C3×D9C2312yes—
54C22×C3×D9C2311yescharacteristic
55C3×D4×C9—22no—
56C2×C3×C4×C9C2311yescharacteristic
57C2×C3⋊Dic9C2312yes—
58C2×C3⋊Dic9C2312yes—
59#6226—22no—
60C3×#611—24no—
61C2×C9×Dic3C2312yes—
62C2×C9×Dic3C2312yes—
63C2×C3×Dic9C2311yescharacteristic
64C3×D36—22no—
65C3×C4×D9D414yes—
66C9×Dic6—22no—
67Dic3×D9—24no—
68Dic3×D9—24no—
69#6189—24no—
70C2×#936—91no—
71D3×#124—91no—
72C23×C3×D3—32no—
73C2×C32×D4C2×D311yescharacteristic
74C2×#634—31no—
75C2×C3×#67—32no—
76C3×D3×D4—64no—
77C2×C3×D12—31no—
78C2×C3×C4×D3—31no—
79C2×C3×Dic6C2×D311yescharacteristic
80C2×#627—32no—
81C2×D3×Dic3—32no—
82C2×D3×Dic3—32no—
83D3×Dic6—64no—
84C23×D9C2×D312yes—
85#3757—34no—
86C4×C3⋊Dic3—31no—
87C3×#217C2×D314yes—
88C3×C4×Dic3C2×D311yescharacteristic
89(C2×D3)⋊Dic3—34no—
90(C2×D3)⋊Dic3—34no—
91Dic32—32no—
92C2×Q8×C9—31no—
93C2×D4×C9—21no—
94C2×D4×C9C2×D311yescharacteristic
95C2×#611C2×D312yes—
96Q8×D9—64no—
97D4×D9—24no—
98C2×D36C2×D311yescharacteristic
99C2×C4×D9—32no—
100C2×C4×D9—32no—
101C2×C4×D9C2×D311yescharacteristic
102C2×Dic18—31no—
103C2×Dic18—32no—
104C2×Dic18—61no—
105C9×C22⋊C4—34no—
106C42×C9—31no—
107#3676—34no—
108#3676—64no—
109(C2×D9)⋊C4—34no—
110(C2×D9)⋊C4—34no—
111C4×Dic9—31no—
112C4×Dic9—32no—
113C4×Dic9—61no—
114C22×C3×C9—22no—
115C22×C3×C9—24no—
116C22×C3×C9C2411yescharacteristic
117C2×C3×D9—22no—
118C2×C3×D9—24no—
119C2×C3×D9—48no—
120C2×C3×D9C2×D412yes—
121C2×C3×D9#4114yes—
122C3×C4×C9C2×D412yes—
123C3⋊Dic9—22no—
124C3⋊Dic9—22no—
125C9×Dic3—22no—
126C9×Dic3—22no—
127C3×Dic9C2×D412yes—
128C22×C3×D4—91no—
129C2×D3×Q8—91no—
130C2×D3×D4—31no—
131C22×Dic6—91no—
132C3×#124—31no—
133C2×#217—94no—
134#947—91no—
135#936—91no—
136#936—91no—
137#936—91no—
138#936—94no—
139#936—91no—
140#936—181no—
141#936D911yescharacteristic, direct product factor
142C2×C4×Dic3—91no—
143#885—94no—
144D3×C22⋊C4—94no—
145#875—91no—
146C42×D3—91no—
147C23×C32C22×D312yes—
148C22×C3×D3—31no—
149C22×C3×D3—32no—
150C22×C3×D3—68no—
151C22×C3×D3—64no—
152C32×D4—22no—
153C2×C32×C4C22×D311yescharacteristic
154C2×C3⋊Dic3—32no—
155C2×C3⋊Dic3—32no—
156#634—62no—
157C3×#67—64no—
158C2×C3×Dic3—31no—
159C2×C3×Dic3C22×D312yes—
160C2×C3×Dic3C22×D312yes—
161C3×D12—62no—
162C3×C4×D3—34no—
163C3×Dic6—22no—
164#627—64no—
165D3×Dic3—64no—
166D3×Dic3—64no—
167C23×C9—22no—
168C23×C9C22×D312yes—
169C22×D9—28no—
170C22×D9—24no—
171C22×D9C22×D312yes—
172C22×D9C22×D311yescharacteristic
173Q8×C9—62no—
174D4×C9—22no—
175D4×C9—42no—
176C2×C4×C9—21no—
177C2×C4×C9—32no—
178C2×C4×C9—32no—
179C2×C4×C9C22×D311yescharacteristic
180#611—24no—
181C2×Dic9—32no—
182C2×Dic9—32no—
183C2×Dic9—62no—
184C2×Dic9—62no—
185C2×Dic9C22×D311yescharacteristic
186D36—22no—
187C4×D9—64no—
188C4×D9—64no—
189C4×D9#6714yes—
190Dic18—62no—
191Dic18—64no—
192Dic18—122no—
193C2×#124—271noSylow
194C2×C3×C9—42no—
195C2×C3×C9C22×D411yescharacteristic
196C2×C3×C9C2×#4112yes—
197C3×D9—42no—
198C3×D9#12414yescomplemented
199C24×C3—92no—
200C23×D3—32no—
201C2×C3×Q8—31no—
202C2×C3×D4—21no—
203C2×C3×D4—92no—
204C2×C3×D4—91no—
205C2×C3×D4—184no—
206C2×C3×D4C2×D911yescharacteristic
207C2×C3×D4D3211yescharacteristic
208C22×C3×C4—91no—
209C2×#67—32no—
210C22×Dic3—92no—
211C22×Dic3—92no—
212D3×Q8—184no—
213D3×D4—64no—
214C2×D12—31no—
215C2×C4×D3—31no—
216C2×C4×D3—92no—
217C2×C4×D3—92no—
218C2×Dic6—92no—
219C2×Dic6—91no—
220C2×Dic6—91no—
221C2×Dic6—92no—
222C2×Dic6—181no—
223C2×Dic6—184no—
224C2×Dic6C2×D911yescharacteristic, complemented
225C3×C22⋊C4—34no—
226C3×C42—31no—
227#217—94no—
228#217—94no—
229#217—94no—
230#217—94no—
231#217—184no—
232#217C2×D914yescomplemented
233(C2×D3)⋊C4—94no—
234(C2×D3)⋊C4—94no—
235C4×Dic3—92no—
236C4×Dic3—91no—
237C4×Dic3—91no—
238C4×Dic3—92no—
239C4×Dic3—181no—
240C4×Dic3C2×D911yescharacteristic, complemented
241C22×C32—22no—
242C22×C32—24no—
243C22×C32C23×D311yescharacteristic
244C2×C3×D3—32no—
245C2×C3×D3—34no—
246C2×C3×D3—62no—
247C2×C3×D3—64no—
248C2×C3×D3—128no—
249C32×C4D3×D412yes—
250C3⋊Dic3—62no—
251C3⋊Dic3—62no—
252C3×Dic3—22no—
253C3×Dic3—22no—
254C3×Dic3—32no—
255C22×C9—24no—
256C22×C9—22no—
257C22×C9—21no—
258C22×C9—42no—
259C22×C9—44no—
260C22×C9C23×D311yescharacteristic
261C2×D9—24no—
262C2×D9—22no—
263C2×D9—48no—
264C2×D9#23714yes—
265C2×D9C2×#6712yes—
266C4×C9—22no—
267C4×C9—62no—
268C4×C9—62no—
269C4×C9C2×#6712yes—
270Dic9—62no—
271Dic9—62no—
272Dic9—122no—
273Dic9—122no—
274Dic9C2×#6712yes—
275C22×Q8—271no—
276C22×D4—91no—
277#124—31no—
278#124—271no—
279#124—274no—
280#124—271no—
281#124—271no—
282C2×C22⋊C4—274no—
283C2×C42—271no—
284C3×C9C2×#12411yescharacteristic, complemented, Sylow
285C23×C3—22no—
286C23×C3—91no—
287C23×C3—92no—
288C23×C3—184no—
289C23×C3—188no—
290C23×C3C22×D912yes—
291C23×C3C2×D3212yes—
292C22×D3—31no—
293C22×D3—32no—
294C22×D3—64no—
295C22×D3—68no—
296C3×Q8—62no—
297C3×D4—22no—
298C3×D4—22no—
299C3×D4—42no—
300C3×D4—184no—
301C3×D4—182no—
302C2×C3×C4—21no—
303C2×C3×C4—32no—
304C2×C3×C4—32no—
305C2×C3×C4—91no—
306C2×C3×C4—94no—
307C2×C3×C4C22×D911yescharacteristic
308C2×C3×C4C2×D3211yescharacteristic
309#67—64no—
310C2×Dic3—31no—
311C2×Dic3—92no—
312C2×Dic3—92no—
313C2×Dic3—92no—
314C2×Dic3—92no—
315C2×Dic3—182no—
316C2×Dic3—182no—
317C2×Dic3—184no—
318C2×Dic3—184no—
319C2×Dic3C22×D912yes—
320C2×Dic3C22×D912yes—
321D12—62no—
322C4×D3—34no—
323C4×D3—184no—
324C4×D3—184no—
325Dic6—22no—
326Dic6—184no—
327Dic6—184no—
328Dic6—182no—
329Dic6—182no—
330Dic6—362no—
331C2×C32—42no—
332C2×C32C2×D3×D411yescharacteristic
333C2×C32D3×#4112yes—
334C3×D3—34no—
335C3×D3—122no—
336C2×C9—22no—
337C2×C9—21no—
338C2×C9—42no—
339C2×C9—82no—
340C2×C9C2×#23712yes—
341C2×C9C22×#6711yescharacteristic
342D9—42no—
343D9#93614yesdirect product factor
344C24—92no—
345C2×Q8—31no—
346C2×Q8—272no—
347C2×Q8—271no—
348C2×Q8—544no—
349C2×D4—92no—
350C2×D4—91no—
351C2×D4—184no—
352C2×D4D3×D911yescharacteristic
353C22×C4—91no—
354C22×C4—272no—
355C22×C4—272no—
356C22⋊C4—34no—
357C22⋊C4—274no—
358C22⋊C4—274no—
359C22⋊C4—274no—
360C42—31no—
361C42—272no—
362C42—271no—
363C22×C3—24no—
364C22×C3—22no—
365C22×C3—22no—
366C22×C3—24no—
367C22×C3—21no—
368C22×C3—42no—
369C22×C3—44no—
370C22×C3—92no—
371C22×C3—94no—
372C22×C3—182no—
373C22×C3—184no—
374C22×C3—368no—
375C22×C3C23×D911yescharacteristic
376C22×C3C22×D3211yescharacteristic
377C2×D3—34no—
378C2×D3—32no—
379C2×D3—64no—
380C2×D3—62no—
381C2×D3—128no—
382C3×C4—22no—
383C3×C4—62no—
384C3×C4—62no—
385C3×C4—92no—
386C3×C4D4×D912yes—
387C3×C4D3×#6712yes—
388Dic3—22no—
389Dic3—22no—
390Dic3—32no—
391Dic3—182no—
392Dic3—182no—
393Dic3—182no—
394Dic3—182no—
395Dic3—362no—
396Dic3—362no—
397C32D3×#12411yescharacteristic
398C9—21no—
399C9C2×#93611yescharacteristic, complemented
400C23—91no—
401C23—92no—
402C23—184no—
403C23—188no—
404C23C2×D3×D912yes—
405Q8—62no—
406Q8—544no—
407Q8—542no—
408D4—22no—
409D4—184no—
410D4—182no—
411C2×C4—32no—
412C2×C4—32no—
413C2×C4—91no—
414C2×C4—94no—
415C2×C4—272no—
416C2×C4—272no—
417C2×C4—544no—
418C2×C4—544no—
419C2×C4C2×D3×D911yescharacteristic
420C2×C3—22no—
421C2×C3—21no—
422C2×C3—42no—
423C2×C3—42no—
424C2×C3—82no—
425C2×C3—94no—
426C2×C3—362no—
427C2×C3C2×D4×D911yescharacteristic
428C2×C3#41×D912yes—
429C2×C3D3×#23712yes—
430C2×C3C2×D3×#6711yescharacteristic
431D3—34no—
432D3—122no—
433C22—24no—
434C22—22no—
435C22—94no—
436C22—92no—
437C22—184no—
438C22—182no—
439C22—368no—
440C22C22×D3×D911yescharacteristic
441C4—62no—
442C4—62no—
443C4—92no—
444C4—542no—
445C4—542no—
446C4D9×#6712yes—
447C3—21no—
448C3D9×#12411yescharacteristic, complemented
449C3D3×#93611yescharacteristic
450C2—42no—
451C2—94no—
452C2—362no—
453C2D9×#23712yes—
454C2C2×D9×#6711yescharacteristic
subgroupG/H
centerC22C22×D3×D9
commutator, cosocleC22×C3×C9C24
FrattiniC22×C3C22×D32
FittingC2×C3×D4×C9C22
socleC22×C32C23×D3
prime radicalC2×C3×D4×D9C2
hypercenterC2×D4D3×D9
hypocenterC3×C9C2×#124
LCSG ▷ C22×C3×C9 ▷ C3×C9
UCSC1 ◁ C22 ◁ C2×D4

Complements

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

NH ≅ G/Ntype
2. C2×D9×Dic6C2semidirect
3. #11721836C2semidirect
4. C9×#936C2semidirect
5. D9×#217C2semidirect
6. #11721257C2semidirect
7. C4×Dic3×D9C2semidirect
8. #11720951C2semidirect
9. #11720948C2semidirect
14. C2×#6226C22semidirect
19. C2×C9×Dic6C22semidirect
22. C2×#6189C22semidirect
24. #88551C22semidirect
25. C4×C3⋊Dic9C22semidirect
26. C9×#217C22semidirect
27. C4×C9×Dic3C22semidirect
28. (C2×D9)⋊Dic3C22semidirect
29. (C2×D9)⋊Dic3C22semidirect
30. Dic3×Dic9C22semidirect
141. #936D9direct (N × H)
198. C3×D9#124semidirect
224. C2×Dic6C2×D9semidirect
232. #217C2×D9semidirect
240. C4×Dic3C2×D9semidirect
284. C3×C9C2×#124semidirect
343. D9#936direct (N × H)
399. C9C2×#936semidirect
448. C3D9×#124semidirect

Maximal subgroups

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

subgroupindex
C2×C3×D4×D92
C2×D9×Dic62
#117218362
C9×#9362
D9×#2172
#117212572
C4×Dic3×D92
#117209512
#117209482
D3×#9363
D9×#1243