Finite Group Databasebeta

← C3×#10588883 #13143496

Subgroups — C3×#10588883 #13143496

Order 1728.

516 conjugacy classes of subgroups.

The subgroup lattice has 440 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#63715C211yesmaximal, characteristic
2C3×C9×#137C211yesmaximal, characteristic, complemented
3C3×#63509C211yesmaximal, characteristic, complemented
4C3×#63505C211yesmaximal, characteristic, complemented
5C3×#63396C211yesmaximal, characteristic, complemented
6C3×#63384C211yesmaximal, characteristic, complemented
7C3×#63383C211yesmaximal, characteristic, complemented
8C3×#5202—31nomaximal
9#10588883C311yesmaximal, characteristic, direct product factor
10C3×C9×#41C2211yescharacteristic
11C2×C3×Q8×C9C2211yescharacteristic, complemented
12C3×#3701—21no—
13C3×D4×D9—22no—
14C3×D4×D9—21no—
15C3×#3697—21no—
16C3×#3697C2211yescharacteristic
17C2×C3×D36—21no—
18C2×C3×D36C2211yescharacteristic
19C3×C9×Q16—21no—
20C3×C9×SD16—21no—
21C3×C9×M16C2211yescharacteristic, complemented
22C3×#3675—21no—
23C3×#3674—21no—
24C3×(C2×D9)⋊C4—22no—
25C3×C4×Dic9C2211yescharacteristic, complemented
26C3×#3667C2211yescharacteristic, complemented
27C3×#1009—31no—
28C32×#137D311yescharacteristic
29C3×#947—31no—
30C3×#942—31no—
31#63715C2×C311yescharacteristic
32C3×#837—31no—
33C3×#825—31no—
34C3×#823—31no—
35C9×#137—21no—
36C9×#137C2×C311yescharacteristic, complemented
37#63509C2×C311yescharacteristic, complemented
38#63505C2×C311yescharacteristic, complemented
39#63396C2×C311yescharacteristic, complemented
40#63384C2×C311yescharacteristic, complemented
41#63383C2×C311yescharacteristic, complemented
42C22×C3×D9—22no—
43C22×C3×D9D412yes—
44C3×Q8×C9—21no—
45C3×Q8×C9—21no—
46C3×Q8×C9D411yescharacteristic
47C3×D4×C9—21no—
48C3×D4×C9D411yescharacteristic
49C2×C3×C4×C9—21no—
50C2×C3×C4×C9—21no—
51C2×C3×C4×C9C2311yescharacteristic
52C3×#611—22no—
53C3×#611—21no—
54C2×C3×Dic9—21no—
55C3×D36—22no—
56C3×D36—21no—
57C3×D36—21no—
58C3×D36D411yescharacteristic
59C3×C4×D9—22no—
60C3×C4×D9—21no—
61C3×Dic18D411yescharacteristic
62C3×C8×C9—21no—
63C3×C9⋊C8—21no—
64C3×#455—91no—
65#5202—31no—
66C32×#41C2×D311yescharacteristic
67C2×C32×Q8C2×D311yescharacteristic
68C3×#239—61no—
69C3×D3×D4—62no—
70C3×D3×D4—61no—
71C3×#235—31no—
72C3×#235—61no—
73C2×C3×D12—31no—
74C2×C3×D12—61no—
75C32×Q16—21no—
76C32×SD16—21no—
77C32×M16C2×D311yescharacteristic
78C3×#216—61no—
79C3×#215—61no—
80C3×(C2×D3)⋊C4—62no—
81C3×C4×Dic3—31no—
82C3×#208—31no—
83C9×#41—21no—
84C9×#41C22×C311yescharacteristic
85C2×Q8×C9—21no—
86C2×Q8×C9C22×C311yescharacteristic, complemented
87#3701—21no—
88D4×D9—22no—
89D4×D9—21no—
90#3697—21no—
91#3697C22×C311yescharacteristic
92C2×D36—21no—
93C2×D36C22×C311yescharacteristic
94C9×Q16—22no—
95C9×Q16—21no—
96C9×SD16—22no—
97C9×SD16—21no—
98C9×M16—21no—
99C9×M16C22×C311yescharacteristic, complemented
100#3675—21no—
101#3674—21no—
102(C2×D9)⋊C4—22no—
103C4×Dic9C22×C311yescharacteristic, complemented
104#3667C22×C311yescharacteristic, complemented
105C22×C3×C9—21no—
106C22×C3×C9C2×D411yescharacteristic
107C2×C3×D9—22no—
108C2×C3×D9—21no—
109C2×C3×D9—42no—
110C2×C3×D9—82no—
111C3×C4×C9—21no—
112C3×C4×C9—41no—
113C3×C4×C9C2×D411yescharacteristic
114C3×C4×C9C2×D411yescharacteristic
115C3×Dic9—21no—
116C3×Dic9—41no—
117C3×H(5,𝔽2)—91no—
118#1009—31no—
119C3×#137—21no—
120C3×#137—91no—
121C3×#137D911yescharacteristic, complemented
122C3×#137C3×D311yescharacteristic
123C3×#124—91no—
124#947—31no—
125#942—31no—
126C3×#104—91no—
127C3×#104—91no—
128C3×#100—91no—
129#837—31no—
130#825—31no—
131#823—31no—
132C22×C3×D3—32no—
133C22×C3×D3—62no—
134C32×Q8—21no—
135C32×Q8—21no—
136C32×Q8#6711yescharacteristic
137C32×D4—21no—
138C32×D4#6711yescharacteristic
139C2×C32×C4—21no—
140C2×C32×C4—21no—
141C2×C32×C4C22×D311yescharacteristic
142C3×#67—62no—
143C3×#67—61no—
144C2×C3×Dic3—61no—
145C3×D12—31no—
146C3×D12—62no—
147C3×D12—61no—
148C3×D12—61no—
149C3×C4×D3—62no—
150C3×C4×D3—61no—
151C3×Dic6—31no—
152C22×D9—22no—
153C22×D9C3×D412yes—
154C32×C8—21no—
155C3×C3⋊C8—61no—
156Q8×C9—22no—
157Q8×C9—21no—
158Q8×C9—21no—
159Q8×C9—21no—
160Q8×C9—41no—
161Q8×C9C3×D411yescharacteristic
162D4×C9—21no—
163D4×C9—21no—
164D4×C9—41no—
165D4×C9C3×D411yescharacteristic
166C2×C4×C9—21no—
167C2×C4×C9—21no—
168C2×C4×C9—21no—
169C2×C4×C9—41no—
170C2×C4×C9—41no—
171C2×C4×C9C23×C311yescharacteristic
172#611—22no—
173#611—21no—
174C2×Dic9—21no—
175D36—22no—
176D36—21no—
177D36—21no—
178D36C3×D411yescharacteristic
179C4×D9—22no—
180C4×D9—21no—
181Dic18C3×D411yescharacteristic
182C8×C9—22no—
183C8×C9—21no—
184C9⋊C8—21no—
185#455—91noSylow
186C2×C3×C9—21no—
187C2×C3×C9—41no—
188C2×C3×C9#12011yescharacteristic
189C3×D9—42no—
190C3×D9—41no—
191C3×#41—21no—
192C3×#41—91no—
193C3×#41—181no—
194C3×#41—181no—
195C3×#41C2×D911yescharacteristic
196C3×#41C2×C3×D311yescharacteristic
197C2×C3×Q8—21no—
198C2×C3×Q8C2×D911yescharacteristic, complemented
199C2×C3×Q8C2×C3×D311yescharacteristic
200C2×C3×D4—91no—
201C2×C3×D4—181no—
202C2×C3×D4—182no—
203C2×C3×D4—181no—
204#239—61no—
205D3×D4—62no—
206D3×D4—61no—
207#235—31no—
208#235—61no—
209C2×D12—31no—
210C2×D12—61no—
211C3×Q16—22no—
212C3×Q16—21no—
213C3×Q16—21no—
214C3×Q16—181no—
215C3×SD16—22no—
216C3×SD16—21no—
217C3×SD16—21no—
218C3×SD16—181no—
219C3×M16—21no—
220C3×M16—91no—
221C3×M16C2×D911yescharacteristic, complemented
222C3×M16C2×C3×D311yescharacteristic
223C3×C22⋊C4—182no—
224C3×C42—91no—
225#216—61no—
226#215—61no—
227(C2×D3)⋊C4—62no—
228C4×Dic3—31no—
229#208—31no—
230C22×C32—21no—
231C22×C32D3×D411yescharacteristic
232C2×C3×D3—61no—
233C2×C3×D3—62no—
234C2×C3×D3—122no—
235C2×C3×D3—242no—
236C32×C4—21no—
237C32×C4—41no—
238C32×C4D3×D411yescharacteristic
239C32×C4C2×#6711yescharacteristic
240C3×Dic3—61no—
241C3×Dic3—121no—
242C22×C9—21no—
243C22×C9—21no—
244C22×C9—41no—
245C22×C9C2×C3×D411yescharacteristic
246C2×D9—22no—
247C2×D9—21no—
248C2×D9—42no—
249C2×D9—82no—
250C4×C9—21no—
251C4×C9—21no—
252C4×C9—21no—
253C4×C9—41no—
254C4×C9—42no—
255C4×C9—41no—
256C4×C9C2×C3×D411yescharacteristic
257C4×C9C2×C3×D411yescharacteristic
258Dic9—21no—
259Dic9—41no—
260H(5,𝔽2)—91no—
261#137—91no—
262#137C3×D911yescharacteristic, complemented
263#124—91no—
264#104—91no—
265#104—91no—
266#100—91no—
267C3×C9#45511yescharacteristic, complemented, Sylow
268C23×C3—92no—
269C23×C3—182no—
270C22×D3—32no—
271C22×D3—62no—
272C3×Q8—22no—
273C3×Q8—21no—
274C3×Q8—21no—
275C3×Q8—21no—
276C3×Q8—21no—
277C3×Q8—21no—
278C3×Q8—41no—
279C3×Q8—91no—
280C3×Q8#61111yescharacteristic
281C3×Q8C3×#6711yescharacteristic
282C3×D4—21no—
283C3×D4—21no—
284C3×D4—21no—
285C3×D4—41no—
286C3×D4—91no—
287C3×D4—182no—
288C3×D4—182no—
289C3×D4—181no—
290C3×D4—181no—
291C3×D4—181no—
292C3×D4#61111yescharacteristic
293C3×D4C3×#6711yescharacteristic
294C2×C3×C4—21no—
295C2×C3×C4—21no—
296C2×C3×C4—21no—
297C2×C3×C4—21no—
298C2×C3×C4—21no—
299C2×C3×C4—41no—
300C2×C3×C4—41no—
301C2×C3×C4—182no—
302C2×C3×C4—181no—
303C2×C3×C4—181no—
304C2×C3×C4C22×D911yescharacteristic
305C2×C3×C4C22×C3×D311yescharacteristic
306#67—62no—
307#67—61no—
308C2×Dic3—61no—
309D12—31no—
310D12—62no—
311D12—61no—
312D12—61no—
313C4×D3—62no—
314C4×D3—61no—
315Dic6—31no—
316C3×C8—22no—
317C3×C8—21no—
318C3×C8—21no—
319C3×C8—181no—
320C3⋊C8—61no—
321C2×C32—21no—
322C2×C32—41no—
323C2×C32#93711yescharacteristic
324C3×D3—122no—
325C3×D3—121no—
326C2×C9—21no—
327C2×C9—21no—
328C2×C9—41no—
329C2×C9—41no—
330C2×C9—81no—
331C2×C9C3×#12011yescharacteristic
332D9—42no—
333D9—41no—
334#41—91no—
335#41—181no—
336#41—181no—
337#41C2×C3×D911yescharacteristic
338C2×Q8C2×C3×D911yescharacteristic, complemented
339C2×D4—91no—
340C2×D4—181no—
341C2×D4—182no—
342C2×D4—181no—
343Q16—21no—
344Q16—181no—
345SD16—21no—
346SD16—181no—
347M16—91no—
348M16C2×C3×D911yescharacteristic, complemented
349C22⋊C4—182no—
350C42—91no—
351C22×C3—21no—
352C22×C3—21no—
353C22×C3—21no—
354C22×C3—41no—
355C22×C3—181no—
356C22×C3—182no—
357C22×C3—362no—
358C22×C3—722no—
359C22×C3D4×D911yescharacteristic
360C22×C3C3×D3×D411yescharacteristic
361C2×D3—61no—
362C2×D3—62no—
363C2×D3—122no—
364C2×D3—242no—
365C3×C4—21no—
366C3×C4—21no—
367C3×C4—21no—
368C3×C4—21no—
369C3×C4—41no—
370C3×C4—42no—
371C3×C4—41no—
372C3×C4—41no—
373C3×C4—181no—
374C3×C4—361no—
375C3×C4D4×D911yescharacteristic
376C3×C4C2×#61111yescharacteristic
377C3×C4C3×D3×D411yescharacteristic
378C3×C4C2×C3×#6711yescharacteristic
379Dic3—61no—
380Dic3—121no—
381C32#520211yescharacteristic
382C9—21no—
383C9C3×#45511yescharacteristic, complemented
384C23—92no—
385C23—182no—
386Q8—21no—
387Q8—21no—
388Q8—91no—
389Q8C3×#61111yescharacteristic
390D4—21no—
391D4—91no—
392D4—182no—
393D4—182no—
394D4—181no—
395D4—181no—
396D4—181no—
397D4C3×#61111yescharacteristic
398C2×C4—21no—
399C2×C4—21no—
400C2×C4—182no—
401C2×C4—181no—
402C2×C4—181no—
403C2×C4C22×C3×D911yescharacteristic
404C8—21no—
405C8—181no—
406C2×C3—21no—
407C2×C3—21no—
408C2×C3—21no—
409C2×C3—41no—
410C2×C3—41no—
411C2×C3—41no—
412C2×C3—81no—
413C2×C3—362no—
414C2×C3—361no—
415C2×C3#6349911yescharacteristic
416C2×C3C3×#93711yescharacteristic
417D3—122no—
418D3—121no—
419C22—21no—
420C22—181no—
421C22—182no—
422C22—362no—
423C22—722no—
424C22C3×D4×D911yescharacteristic
425C4—21no—
426C4—41no—
427C4—181no—
428C4—361no—
429C4C3×D4×D911yescharacteristic
430C4C2×C3×#61111yescharacteristic
431C3—21no—
432C3#1058888311yescharacteristic, direct product factor
433C3C3×#520211yescharacteristic
434C2—21no—
435C2—41no—
436C2—362no—
437C2—361no—
438C2C3×#6349911yescharacteristic
subgroupG/H
centerC2×C3#63499
commutator, cosocleC2×C4×C9C23×C3
FrattiniC2×C3×C4C22×C3×D3
FittingC3×C9×#137C2
socleC2×C32#937
prime radicalC3×#63715C2
hypercenterC3×#137D9
hypocenterC9C3×#455
LCSG ▷ C2×C4×C9 ▷ C2×C9 ▷ C9
UCSC1 ◁ C2×C3 ◁ C2×C3×C4 ◁ C3×#137

Complements

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

NH ≅ G/Ntype
2. C3×C9×#137C2semidirect
3. C3×#63509C2semidirect
4. C3×#63505C2semidirect
5. C3×#63396C2semidirect
6. C3×#63384C2semidirect
7. C3×#63383C2semidirect
9. #10588883C3direct (N × H)
11. C2×C3×Q8×C9C22semidirect
21. C3×C9×M16C22semidirect
25. C3×C4×Dic9C22semidirect
26. C3×#3667C22semidirect
36. C9×#137C2×C3semidirect
37. #63509C2×C3semidirect
38. #63505C2×C3semidirect
39. #63396C2×C3semidirect
40. #63384C2×C3semidirect
41. #63383C2×C3semidirect
86. C2×Q8×C9C22×C3semidirect
99. C9×M16C22×C3semidirect
103. C4×Dic9C22×C3semidirect
104. #3667C22×C3semidirect
121. C3×#137D9semidirect
198. C2×C3×Q8C2×D9semidirect
221. C3×M16C2×D9semidirect
262. #137C3×D9semidirect
267. C3×C9#455semidirect
338. C2×Q8C2×C3×D9semidirect
348. M16C2×C3×D9semidirect
383. C9C3×#455semidirect
432. C3#10588883direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#637152
C3×C9×#1372
C3×#635092
C3×#635052
C3×#633962
C3×#633842
C3×#633832
C3×#52023
#105888833