Finite Group Databasebeta

← C3×#3524⋊C3 #11919768

Subgroups — C3×#3524⋊C3 #11919768

Order 1152.

610 conjugacy classes of subgroups.

The subgroup lattice has 478 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#557⋊C3C211yesmaximal, characteristic, complemented
2C3×C4⋊(#41⋊C3)C211yesmaximal, characteristic, complemented
3C3×#548⋊C3C211yesmaximal, characteristic, complemented
4C3×#548⋊C3C211yesmaximal, characteristic, complemented
5C3×#520⋊C3C211yesmaximal, characteristic, complemented
6C3×#519⋊C3C211yesmaximal, characteristic, complemented
7C3×C4×#41⋊C3C211yesmaximal, characteristic, complemented
8C3×#3524C311yesmaximal, characteristic, complemented
9#3524⋊C3C313yesmaximal, direct product factor
10C2×C3×#41⋊C3C2211yescharacteristic
11C2×C3×#41⋊C3C2211yescharacteristic
12C22×C3×SL(2,𝔽3)C2211yescharacteristic
13C32×#126—41nomaximal
14C3×C4×SL(2,𝔽3)C2211yescharacteristic
15C3×C4×SL(2,𝔽3)C2211yescharacteristic
16C3×C4×SL(2,𝔽3)C2211yescharacteristic
17C3×C4×SL(2,𝔽3)C2211yescharacteristic
18C3×#559—31no—
19C3×#557C2×C311yescharacteristic, complemented
20C3×#555—31no—
21C3×#553—31no—
22C3×#552—31no—
23C3×#550C2×C311yescharacteristic, complemented
24C3×#548C2×C311yescharacteristic
25C3×#548C2×C311yescharacteristic
26C3×#542—31no—
27C3×#540—31no—
28C3×#529—31no—
29C3×#529—31no—
30C3×#520C2×C311yescharacteristic, complemented
31C3×#519C2×C311yescharacteristic
32C3×C4×#41C2×C311yescharacteristic, complemented
33#557⋊C3C2×C313yescomplemented
34C4⋊(#41⋊C3)C2×C313yescomplemented
35#548⋊C3C2×C313yescomplemented
36#548⋊C3C2×C313yescomplemented
37#520⋊C3C2×C313yescomplemented
38#519⋊C3C2×C313yescomplemented
39C4×#41⋊C3C2×C313yescomplemented
40C3×#41⋊C3—21no—
41C3×#41⋊C3—21no—
42C2×C3×SL(2,𝔽3)—21no—
43C2×C3×SL(2,𝔽3)C2311yescharacteristic
44C32×C4⋊C4—41no—
45C32×C4⋊C4—41no—
46C32×C4⋊C4—41no—
47C32×C22⋊C4—41no—
48C32×C22⋊C4—41no—
49C32×C22⋊C4—41no—
50C32×C42—41no—
51#3524C3211yescharacteristic, complemented, Sylow
52C2×C3×#41C22×C311yescharacteristic
53C2×C3×#41C22×C311yescharacteristic
54C22×C3×Q8C22×C311yescharacteristic
55C2×#41⋊C3C22×C313yes—
56C2×#41⋊C3C22×C313yes—
57C22×SL(2,𝔽3)C22×C313yes—
58C3×C4⋊Q8—31no—
59C3×#127—31no—
60C3×#126—32no—
61C3×#126—31no—
62C3×#126—43no—
63C3×#126A411yescharacteristic
64C3×#125—31no—
65C3×#125—31no—
66C3×#125—31no—
67C3×#124—32no—
68C3×#124—31no—
69C3×#124—31no—
70C3×#124—31no—
71C3×#123—32no—
72C3×#123—32no—
73C3×#123—31no—
74C3×#123—31no—
75C3×C22⋊Q8—31no—
76C3×C22⋊Q8—31no—
77C3×C22⋊Q8—31no—
78C3×#121—31no—
79C3×#121—31no—
80C3×#121—32no—
81C3×#121—31no—
82C3×#121—31no—
83C3×#121—31no—
84C3×C4×Q8—31no—
85C3×C4×Q8—31no—
86C3×C4×Q8—31no—
87C3×C4×Q8C22×C311yescharacteristic
88C3×C4×Q8C22×C311yescharacteristic
89C3×C4×Q8C22×C311yescharacteristic
90C3×C4×Q8C22×C311yescharacteristic
91C3×C4×D4—32no—
92C3×C4×D4—31no—
93C3×C4×D4—31no—
94C3×C4×D4—31no—
95C3×C4×D4—31no—
96C3×C4×D4—31no—
97C3×C4×D4—31no—
98C3×C4×D4—31no—
99C3×#117—32no—
100C3×#117—31no—
101C3×#117—31no—
102C3×#117—31no—
103C3×#117—31no—
104C2×C3×C4⋊C4—31no—
105C2×C3×C42—31no—
106C4×SL(2,𝔽3)C22×C313yes—
107C4×SL(2,𝔽3)C22×C313yes—
108C4×SL(2,𝔽3)C22×C313yes—
109C4×SL(2,𝔽3)C22×C313yes—
110C23×C32—41no—
111C2×C32×C4—41no—
112C2×C32×C4—41no—
113C2×C32×C4—41no—
114C2×C32×C4—41no—
115C2×C32×C4—41no—
116C2×C32×C4—41no—
117C3×SL(2,𝔽3)#4111yescharacteristic
118#559—31no—
119#557C2×C3211yescharacteristic, complemented
120#555—31no—
121#553—31no—
122#552—31no—
123#550C2×C3211yescharacteristic, complemented
124#548C2×C3211yescharacteristic
125#548C2×C3211yescharacteristic
126#542—31no—
127#540—31no—
128#529—31no—
129#529—31no—
130#520C2×C3211yescharacteristic, complemented
131#519C2×C3211yescharacteristic
132C4×#41C2×C3211yescharacteristic, complemented
133C3×#41—21no—
134C3×#41—21no—
135C3×#41—61no—
136C3×#41—61no—
137C2×C3×Q8—21no—
138C2×C3×Q8—31no—
139C2×C3×Q8—31no—
140C2×C3×Q8—61no—
141C2×C3×Q8C23×C311yescharacteristic
142C2×C3×D4—31no—
143C2×C3×D4—31no—
144C2×C3×D4—32no—
145C2×C3×D4—31no—
146C2×C3×D4—31no—
147C2×C3×D4—31no—
148C22×C3×C4—31no—
149C22×C3×C4—32no—
150C22×C3×C4—31no—
151C22×C3×C4—31no—
152C22×C3×C4—31no—
153C22×C3×C4—31no—
154#41⋊C3—23no—
155#41⋊C3—23no—
156C2×SL(2,𝔽3)—23no—
157C2×SL(2,𝔽3)C23×C313yes—
158C3×C4⋊C4—31no—
159C3×C4⋊C4—31no—
160C3×C4⋊C4—31no—
161C3×C4⋊C4—31no—
162C3×C4⋊C4—32no—
163C3×C4⋊C4—31no—
164C3×C4⋊C4—31no—
165C3×C4⋊C4—31no—
166C3×C4⋊C4—31no—
167C3×C4⋊C4—31no—
168C3×C4⋊C4—31no—
169C3×C4⋊C4—31no—
170C3×C4⋊C4—43no—
171C3×C4⋊C4—43no—
172C3×C4⋊C4—43no—
173C3×C4⋊C4C2×A411yescharacteristic
174C3×C4⋊C4C2×A411yescharacteristic
175C3×C4⋊C4C2×A411yescharacteristic
176C3×C22⋊C4—32no—
177C3×C22⋊C4—32no—
178C3×C22⋊C4—32no—
179C3×C22⋊C4—31no—
180C3×C22⋊C4—31no—
181C3×C22⋊C4—31no—
182C3×C22⋊C4—31no—
183C3×C22⋊C4—31no—
184C3×C22⋊C4—31no—
185C3×C22⋊C4—31no—
186C3×C22⋊C4—43no—
187C3×C22⋊C4—43no—
188C3×C22⋊C4—43no—
189C3×C22⋊C4C2×A411yescharacteristic
190C3×C22⋊C4C2×A411yescharacteristic
191C3×C22⋊C4C2×A411yescharacteristic
192C3×C42—32no—
193C3×C42—31no—
194C3×C42—31no—
195C3×C42—31no—
196C3×C42—31no—
197C3×C42—31no—
198C3×C42—43no—
199C3×C42C2×A411yescharacteristic
200C22×C32—41no—
201C22×C32—81no—
202C22×C32—81no—
203C22×C32—81no—
204C32×C4—81no—
205C32×C4—81no—
206C32×C4—81no—
207C32×C4—81no—
208C32×C4—81no—
209C32×C4—81no—
210C2×#41C22×C3211yescharacteristic
211C2×#41C22×C3211yescharacteristic
212C22×Q8C22×C3211yescharacteristic
213C4⋊Q8—31no—
214#127—31no—
215#126—32no—
216#126—31no—
217#126C3×A411yescharacteristic
218#125—31no—
219#125—31no—
220#125—31no—
221#124—32no—
222#124—31no—
223#124—31no—
224#124—31no—
225#123—32no—
226#123—32no—
227#123—31no—
228#123—31no—
229C22⋊Q8—31no—
230C22⋊Q8—31no—
231C22⋊Q8—31no—
232#121—31no—
233#121—31no—
234#121—32no—
235#121—31no—
236#121—31no—
237#121—31no—
238C4×Q8—31no—
239C4×Q8—31no—
240C4×Q8—31no—
241C4×Q8C22×C3211yescharacteristic
242C4×Q8C22×C3211yescharacteristic
243C4×Q8C22×C3211yescharacteristic
244C4×Q8C22×C3211yescharacteristic
245C4×D4—32no—
246C4×D4—31no—
247C4×D4—31no—
248C4×D4—31no—
249C4×D4—31no—
250C4×D4—31no—
251C4×D4—31no—
252C4×D4—31no—
253#117—32no—
254#117—31no—
255#117—31no—
256#117—31no—
257#117—31no—
258C2×C4⋊C4—31no—
259C2×C42—31no—
260C23×C3—31no—
261C23×C3—31no—
262C23×C3—43no—
263C23×C3C22×A411yescharacteristic
264C3×Q8—31no—
265C3×Q8—61no—
266C3×Q8—61no—
267C3×Q8—121no—
268C3×Q8C3×#4111yescharacteristic
269C3×D4—61no—
270C3×D4—61no—
271C3×D4—61no—
272C3×D4—61no—
273C3×D4—121no—
274C3×D4—121no—
275C3×D4—121no—
276C3×D4—122no—
277C2×C3×C4—31no—
278C2×C3×C4—31no—
279C2×C3×C4—31no—
280C2×C3×C4—31no—
281C2×C3×C4—31no—
282C2×C3×C4—31no—
283C2×C3×C4—43no—
284C2×C3×C4—43no—
285C2×C3×C4—43no—
286C2×C3×C4—43no—
287C2×C3×C4—43no—
288C2×C3×C4—43no—
289C2×C3×C4—61no—
290C2×C3×C4—61no—
291C2×C3×C4—61no—
292C2×C3×C4—61no—
293C2×C3×C4—61no—
294C2×C3×C4—61no—
295C2×C3×C4—121no—
296C2×C3×C4—121no—
297C2×C3×C4—122no—
298C2×C3×C4C22×A411yescharacteristic
299C2×C3×C4C22×A411yescharacteristic
300C2×C3×C4C22×A411yescharacteristic
301C2×C3×C4C22×A411yescharacteristic
302C2×C3×C4C22×A411yescharacteristic
303C2×C3×C4C22×A411yescharacteristic
304SL(2,𝔽3)C3×#4113yes—
305C2×C32—41no—
306C2×C32—41no—
307C2×C32—41no—
308C2×C32—161no—
309#41—21no—
310#41—21no—
311#41—61no—
312#41—61no—
313C2×Q8—21no—
314C2×Q8—31no—
315C2×Q8—31no—
316C2×Q8—61no—
317C2×Q8C23×C3211yescharacteristic
318C2×D4—31no—
319C2×D4—31no—
320C2×D4—32no—
321C2×D4—31no—
322C2×D4—31no—
323C2×D4—31no—
324C22×C4—31no—
325C22×C4—32no—
326C22×C4—31no—
327C22×C4—31no—
328C22×C4—31no—
329C22×C4—31no—
330C4⋊C4—31no—
331C4⋊C4—31no—
332C4⋊C4—31no—
333C4⋊C4—31no—
334C4⋊C4—32no—
335C4⋊C4—31no—
336C4⋊C4—31no—
337C4⋊C4—31no—
338C4⋊C4—31no—
339C4⋊C4—31no—
340C4⋊C4—31no—
341C4⋊C4—31no—
342C4⋊C4C2×C3×A411yescharacteristic
343C4⋊C4C2×C3×A411yescharacteristic
344C4⋊C4C2×C3×A411yescharacteristic
345C22⋊C4—32no—
346C22⋊C4—32no—
347C22⋊C4—32no—
348C22⋊C4—31no—
349C22⋊C4—31no—
350C22⋊C4—31no—
351C22⋊C4—31no—
352C22⋊C4—31no—
353C22⋊C4—31no—
354C22⋊C4—31no—
355C22⋊C4C2×C3×A411yescharacteristic
356C22⋊C4C2×C3×A411yescharacteristic
357C22⋊C4C2×C3×A411yescharacteristic
358C42—32no—
359C42—31no—
360C42—31no—
361C42—31no—
362C42—31no—
363C42—31no—
364C42C2×C3×A411yescharacteristic
365C22×C3—21no—
366C22×C3—21no—
367C22×C3—21no—
368C22×C3—43no—
369C22×C3—61no—
370C22×C3—61no—
371C22×C3—61no—
372C22×C3—61no—
373C22×C3—61no—
374C22×C3—61no—
375C22×C3—83no—
376C22×C3—83no—
377C22×C3—83no—
378C22×C3C23×A411yescharacteristic
379C3×C4—21no—
380C3×C4—21no—
381C3×C4—21no—
382C3×C4—21no—
383C3×C4—21no—
384C3×C4—21no—
385C3×C4—31no—
386C3×C4—31no—
387C3×C4—61no—
388C3×C4—61no—
389C3×C4—61no—
390C3×C4—61no—
391C3×C4—61no—
392C3×C4—83no—
393C3×C4—83no—
394C3×C4—83no—
395C3×C4—83no—
396C3×C4—83no—
397C3×C4—83no—
398C32—41noSylow
399C23—31no—
400C23—31no—
401C23C22×C3×A411yescharacteristic
402Q8—31no—
403Q8—61no—
404Q8—61no—
405Q8—121no—
406Q8C32×#4111yescharacteristic
407D4—61no—
408D4—61no—
409D4—61no—
410D4—61no—
411D4—121no—
412D4—121no—
413D4—121no—
414D4—122no—
415C2×C4—31no—
416C2×C4—31no—
417C2×C4—31no—
418C2×C4—31no—
419C2×C4—31no—
420C2×C4—31no—
421C2×C4—61no—
422C2×C4—61no—
423C2×C4—61no—
424C2×C4—61no—
425C2×C4—61no—
426C2×C4—61no—
427C2×C4—121no—
428C2×C4—121no—
429C2×C4—122no—
430C2×C4C22×C3×A411yescharacteristic
431C2×C4C22×C3×A411yescharacteristic
432C2×C4C22×C3×A411yescharacteristic
433C2×C4C22×C3×A411yescharacteristic
434C2×C4C22×C3×A411yescharacteristic
435C2×C4C22×C3×A411yescharacteristic
436C2×C3—41no—
437C2×C3—43no—
438C2×C3—43no—
439C2×C3—43no—
440C2×C3—121no—
441C2×C3—121no—
442C2×C3—163no—
443C2×C3A4×#4111yescharacteristic
444C2×C3#594511yescharacteristic
445C2×C3#594511yescharacteristic
446C22—21no—
447C22—21no—
448C22—21no—
449C22—61no—
450C22—61no—
451C22—61no—
452C22—61no—
453C22—61no—
454C22—61no—
455C22C23×C3×A411yescharacteristic
456C4—21no—
457C4—21no—
458C4—21no—
459C4—21no—
460C4—21no—
461C4—21no—
462C4—31no—
463C4—31no—
464C4—61no—
465C4—61no—
466C4—61no—
467C4—61no—
468C4—61no—
469C3—43no—
470C3#3524⋊C311yescharacteristic, direct product factor
471C2—41no—
472C2—121no—
473C2—121no—
474C2C3×A4×#4111yescharacteristic
475C2C3×#594511yescharacteristic
476C2C3×#594511yescharacteristic
subgroupG/H
center, socleC22×C3C23×A4
commutator, cosocleC2×Q8C23×C32
FrattiniC22C23×C3×A4
FittingC3×#3524C3
hypercenterC3×#126A4
hypocenterQ8C32×#41
LCSG ▷ C2×Q8 ▷ Q8
UCSC1 ◁ C22×C3 ◁ C3×#126

Complements

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

NH ≅ G/Ntype
1. C3×#557⋊C3C2semidirect
2. C3×C4⋊(#41⋊C3)C2semidirect
3. C3×#548⋊C3C2semidirect
4. C3×#548⋊C3C2semidirect
5. C3×#520⋊C3C2semidirect
6. C3×#519⋊C3C2semidirect
7. C3×C4×#41⋊C3C2semidirect
8. C3×#3524C3semidirect
9. #3524⋊C3C3direct (N × H)
19. C3×#557C2×C3semidirect
23. C3×#550C2×C3semidirect
30. C3×#520C2×C3semidirect
32. C3×C4×#41C2×C3semidirect
33. #557⋊C3C2×C3semidirect
34. C4⋊(#41⋊C3)C2×C3semidirect
35. #548⋊C3C2×C3semidirect
36. #548⋊C3C2×C3semidirect
37. #520⋊C3C2×C3semidirect
38. #519⋊C3C2×C3semidirect
39. C4×#41⋊C3C2×C3semidirect
51. #3524C32semidirect
119. #557C2×C32semidirect
123. #550C2×C32semidirect
130. #520C2×C32semidirect
132. C4×#41C2×C32semidirect
470. C3#3524⋊C3direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#557⋊C32
C3×C4⋊(#41⋊C3)2
C3×#548⋊C32
C3×#520⋊C32
C3×#519⋊C32
C3×C4×#41⋊C32
C3×#35243
#3524⋊C33
C32×#1264