Finite Group Databasebeta

← C3×#69031 #11792362

Subgroups — C3×#69031 #11792362

Order 1152.

741 conjugacy classes of subgroups.

The subgroup lattice has 586 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5748C211yesmaximal, characteristic
2C2×C3×#909C211yesmaximal, characteristic, complemented
3C3×#5526C211yesmaximal, characteristic, complemented
4C3×#5139C211yesmaximal, characteristic, complemented
5C3×#5120C211yesmaximal, characteristic, complemented
6C3×#5006C211yesmaximal, characteristic, complemented
7C32×#344C211yesmaximal, characteristic, complemented
8C3×#2009—31nomaximal
9#69031C311yesmaximal, characteristic, direct product factor
10C2×C3×#235C2211yescharacteristic
11C2×C3×#235C2211yescharacteristic
12C22×C3×Dic6C2211yescharacteristic
13C2×C32×M16C2211yescharacteristic
14C2×C32×M16C2211yescharacteristic
15C32×#117C2211yescharacteristic
16C3×#926C2211yescharacteristic
17C3×#909—22no—
18C3×#909—21no—
19C3×#909—21no—
20C3×#909—22no—
21C3×#908—21no—
22C3×#908—21no—
23C2×C3×Dic12—21no—
24C3×#904—22no—
25C2×C3×#204—21no—
26C3×#897—22no—
27C3×#886—22no—
28C3×#875—21no—
29C3×#869—21no—
30C3×#825—22no—
31C3×#816—22no—
32C3×#806—22no—
33C3×#575—31no—
34C2×C3×#137—31no—
35C3×#536—31no—
36#5748C2×C311yescharacteristic
37C2×#909C2×C311yescharacteristic, complemented
38#5526C2×C311yescharacteristic, complemented
39C3×#421—31no—
40C3×#419—31no—
41C3×#410—31no—
42#5139C2×C311yescharacteristic, complemented
43#5120C2×C311yescharacteristic, complemented
44#5006C2×C311yescharacteristic, complemented
45C3×#344—21no—
46C3×#344D311yescharacteristic, complemented
47C3×#344C2×C311yescharacteristic, complemented
48C22×C32×C4C2311yescharacteristic
49C2×C3×#67—21no—
50C2×C3×#67—21no—
51C22×C3×Dic3—21no—
52C3×#235—21no—
53C3×#235—21no—
54C3×#235—21no—
55C3×#235—21no—
56C3×#235—21no—
57C3×#235—21no—
58C3×#235—21no—
59C3×#235—21no—
60C2×C3×D12D411yescharacteristic
61C2×C3×D12D411yescharacteristic
62C2×C3×C4×D3—21no—
63C2×C3×C4×D3—21no—
64C2×C3×Dic6—21no—
65C2×C3×Dic6—21no—
66C2×C3×Dic6—21no—
67C2×C3×Dic6—21no—
68C2×C3×Dic6—21no—
69C2×C3×Dic6D412yes—
70C2×C3×Dic6D411yescharacteristic
71C2×C3×Dic6D411yescharacteristic
72C32×M16—21no—
73C32×M16—21no—
74C32×M16—21no—
75C32×M16D412yes—
76C2×C32×C8—21no—
77C2×C32×C8D412yes—
78C32×C4⋊C4—21no—
79C32×C22⋊C4D412yes—
80C32×C42—21no—
81C3×#217—21no—
82C3×(C2×D3)⋊C4—24no—
83C3×C4⋊Dic3—24no—
84C3×C4⋊Dic3—21no—
85C3×C4×Dic3—21no—
86C3×Dic12—22no—
87C3×Dic12—24no—
88C3×D24—22no—
89C3×#204—24no—
90C3×#204—22no—
91C3×#204—22no—
92#2009—31noSylow
93C2×C3×#41—31no—
94C2×C3×#41—31no—
95C22×C3×Q8—31no—
96C2×#235C22×C311yescharacteristic
97C2×#235C22×C311yescharacteristic
98C22×Dic6C22×C311yescharacteristic
99C3×#137—62no—
100C3×#137—61no—
101C3×#137—61no—
102C3×#137—62no—
103C3×AGL(1,ℤ/8)—61no—
104C3×AGL(1,ℤ/8)—61no—
105C3×#135—62no—
106C2×C3×Q16—61no—
107C2×C3×SD16—61no—
108C2×C3×M16—21no—
109C2×C3×M16—21no—
110C2×C3×M16C2×D311yescharacteristic
111C2×C3×M16C2×D311yescharacteristic
112C2×C3×M16C22×C311yescharacteristic
113C2×C3×M16C22×C311yescharacteristic
114C3×C4⋊Q8—61no—
115C3×#124—61no—
116C3×#123—62no—
117C3×C22⋊Q8—62no—
118C3×#117—21no—
119C3×#117—31no—
120C3×#117C2×D311yescharacteristic
121C3×#117C22×C311yescharacteristic
122#926C22×C311yescharacteristic
123#909—22no—
124#909—21no—
125#909—21no—
126#909—22no—
127#908—21no—
128#908—21no—
129C2×Dic12—21no—
130#904—22no—
131C2×#204—21no—
132#897—22no—
133#886—22no—
134#875—21no—
135#869—21no—
136C3×#104—62no—
137C3×#103—62no—
138C3×#99—62no—
139#825—22no—
140#816—22no—
141#806—22no—
142C23×C32C2×D411yescharacteristic
143C22×C3×D3—21no—
144C22×C3×D3—21no—
145C2×C32×C4—22no—
146C2×C32×C4C2×D411yescharacteristic
147C2×C32×C4C2×D411yescharacteristic
148C2×C32×C4C2×D411yescharacteristic
149C2×C32×C4C2×D411yescharacteristic
150C2×C32×C4C2×D411yescharacteristic
151C2×C32×C4#4111yescharacteristic
152C3×#67—41no—
153C3×#67—41no—
154C3×#67—41no—
155C3×#67—41no—
156C2×C3×Dic3—21no—
157C2×C3×Dic3—22no—
158C2×C3×Dic3—21no—
159C2×C3×Dic3—41no—
160C2×C3×Dic3—41no—
161C2×C3×Dic3—41no—
162C3×D12—21no—
163C3×D12—21no—
164C3×D12—21no—
165C3×D12—21no—
166C3×C4×D3—41no—
167C3×C4×D3—41no—
168C3×C4×D3—41no—
169C3×C4×D3—41no—
170C3×Dic6—22no—
171C3×Dic6—21no—
172C3×Dic6—21no—
173C3×Dic6—21no—
174C3×Dic6—22no—
175C3×Dic6—21no—
176C3×Dic6—41no—
177C3×Dic6—41no—
178C32×C8—22no—
179C32×C8—22no—
180#575—31no—
181C2×#137—31no—
182#536—31no—
183#421—31no—
184#419—31no—
185#410—31no—
186#344C3×D311yescharacteristic, complemented
187C3×#41—61no—
188C3×#41—61no—
189C3×#41—61no—
190C3×#41—61no—
191C3×#41—61no—
192C3×#41—61no—
193C3×#41—61no—
194C3×#41—61no—
195C2×C3×Q8—32no—
196C2×C3×Q8—31no—
197C2×C3×Q8—31no—
198C2×C3×Q8—61no—
199C2×C3×Q8—61no—
200C2×C3×Q8—61no—
201C2×C3×Q8—61no—
202C2×C3×Q8—61no—
203C2×C3×D4—31no—
204C2×C3×D4—31no—
205C2×C3×D4—61no—
206C2×C3×D4—61no—
207C22×C3×C4—21no—
208C22×C3×C4—61no—
209C22×C3×C4—61no—
210C22×C3×C4—61no—
211C22×C3×C4C22×D311yescharacteristic
212C22×C3×C4C23×C311yescharacteristic
213C2×#67—21no—
214C2×#67—21no—
215C22×Dic3—21no—
216#235—21no—
217#235—21no—
218#235—21no—
219#235—21no—
220#235—21no—
221#235—21no—
222#235—21no—
223#235—21no—
224C2×D12C3×D411yescharacteristic
225C2×D12C3×D411yescharacteristic
226C2×C4×D3—21no—
227C2×C4×D3—21no—
228C2×Dic6—21no—
229C2×Dic6—21no—
230C2×Dic6—21no—
231C2×Dic6—21no—
232C2×Dic6—21no—
233C2×Dic6C3×D411yescharacteristic
234C2×Dic6C3×D412yes—
235C2×Dic6C3×D411yescharacteristic
236C3×Q16—64no—
237C3×Q16—62no—
238C3×SD16—64no—
239C3×SD16—62no—
240C3×SD16—62no—
241C3×D8—62no—
242C3×M16—21no—
243C3×M16—21no—
244C3×M16—21no—
245C3×M16—21no—
246C3×M16—21no—
247C3×M16—21no—
248C3×M16—22no—
249C3×M16—41no—
250C3×M16—41no—
251C3×M16—41no—
252C3×M16D1212yes—
253C3×M16C3×D412yes—
254C2×C3×C8—21no—
255C2×C3×C8—21no—
256C2×C3×C8—22no—
257C2×C3×C8—41no—
258C2×C3×C8D1212yes—
259C2×C3×C8C3×D412yes—
260C3×C4⋊C4—21no—
261C3×C4⋊C4—21no—
262C3×C4⋊C4—41no—
263C3×C4⋊C4—64no—
264C3×C4⋊C4—61no—
265C3×C22⋊C4—22no—
266C3×C22⋊C4—64no—
267C3×C22⋊C4—61no—
268C3×C22⋊C4D1212yes—
269C3×C22⋊C4C3×D412yes—
270C3×C42—21no—
271C3×C42—21no—
272C3×C42—41no—
273C3×C42—61no—
274#217—21no—
275(C2×D3)⋊C4—24no—
276C4⋊Dic3—24no—
277C4⋊Dic3—21no—
278C4×Dic3—21no—
279Dic12—22no—
280Dic12—24no—
281D24—22no—
282#204—24no—
283#204—22no—
284#204—22no—
285C22×C32—41no—
286C22×C32#12011yescharacteristic
287C22×C32#12111yescharacteristic
288C22×C32#12711yescharacteristic
289C2×C3×D3—42no—
290C2×C3×D3—41no—
291C2×C3×D3—41no—
292C2×C3×D3—81no—
293C32×C4—42no—
294C32×C4#12011yescharacteristic
295C32×C4#12011yescharacteristic
296C32×C4#12111yescharacteristic
297C32×C4#12111yescharacteristic
298C3×Dic3—42no—
299C3×Dic3—41no—
300C3×Dic3—41no—
301C3×Dic3—81no—
302C2×#41—31no—
303C2×#41—31no—
304C22×Q8—31no—
305#137—62no—
306#137—61no—
307#137—61no—
308#137—62no—
309AGL(1,ℤ/8)—61no—
310AGL(1,ℤ/8)—61no—
311#135—62no—
312C2×Q16—61no—
313C2×SD16—61no—
314C2×M16C2×C3×D311yescharacteristic
315C2×M16C2×C3×D311yescharacteristic
316C4⋊Q8—61no—
317#124—61no—
318#123—62no—
319C22⋊Q8—62no—
320#117—31no—
321#117C2×C3×D311yescharacteristic
322#104—62no—
323#103—62no—
324#99—62no—
325C23×C3—21no—
326C23×C3—61no—
327C23×C3—61no—
328C23×C3C2×D1211yescharacteristic
329C23×C3C2×C3×D411yescharacteristic
330C22×D3—21no—
331C22×D3—21no—
332C3×Q8—62no—
333C3×Q8—61no—
334C3×Q8—61no—
335C3×Q8—61no—
336C3×Q8—62no—
337C3×Q8—61no—
338C3×Q8—121no—
339C3×Q8—121no—
340C3×D4—61no—
341C3×D4—61no—
342C3×D4—61no—
343C3×D4—61no—
344C3×D4—121no—
345C3×D4—121no—
346C3×D4—121no—
347C3×D4—121no—
348C2×C3×C4—22no—
349C2×C3×C4—22no—
350C2×C3×C4—21no—
351C2×C3×C4—21no—
352C2×C3×C4—21no—
353C2×C3×C4—21no—
354C2×C3×C4—21no—
355C2×C3×C4—21no—
356C2×C3×C4—42no—
357C2×C3×C4—62no—
358C2×C3×C4—61no—
359C2×C3×C4—61no—
360C2×C3×C4—121no—
361C2×C3×C4—121no—
362C2×C3×C4—121no—
363C2×C3×C4—121no—
364C2×C3×C4—121no—
365C2×C3×C4—121no—
366C2×C3×C4—121no—
367C2×C3×C4C2×D1211yescharacteristic
368C2×C3×C4C2×D1211yescharacteristic
369C2×C3×C4D3×D411yescharacteristic
370C2×C3×C4D3×D411yescharacteristic
371C2×C3×C4D3×D411yescharacteristic
372C2×C3×C4#23911yescharacteristic
373C2×C3×C4C2×C3×D411yescharacteristic
374C2×C3×C4C2×C3×D411yescharacteristic
375C2×C3×C4C2×C3×D411yescharacteristic
376C2×C3×C4C2×C3×D411yescharacteristic
377C2×C3×C4C2×C3×D411yescharacteristic
378C2×C3×C4C3×#4111yescharacteristic
379#67—41no—
380#67—41no—
381#67—41no—
382#67—41no—
383C2×Dic3—21no—
384C2×Dic3—22no—
385C2×Dic3—21no—
386C2×Dic3—41no—
387C2×Dic3—41no—
388C2×Dic3—41no—
389D12—21no—
390D12—21no—
391D12—21no—
392D12—21no—
393C4×D3—41no—
394C4×D3—41no—
395C4×D3—41no—
396C4×D3—41no—
397Dic6—22no—
398Dic6—21no—
399Dic6—21no—
400Dic6—21no—
401Dic6—22no—
402Dic6—21no—
403Dic6—41no—
404Dic6—41no—
405C3×C8—22no—
406C3×C8—22no—
407C3×C8—22no—
408C3×C8—22no—
409C3×C8—42no—
410C3×C8—42no—
411C2×C32—21no—
412C2×C32—21no—
413C2×C32—21no—
414C2×C32#39211yescharacteristic
415C3×D3—81no—
416C3×D3—81no—
417#41—61no—
418#41—61no—
419#41—61no—
420#41—61no—
421#41—61no—
422#41—61no—
423#41—61no—
424#41—61no—
425C2×Q8—32no—
426C2×Q8—31no—
427C2×Q8—31no—
428C2×Q8—61no—
429C2×Q8—61no—
430C2×Q8—61no—
431C2×Q8—61no—
432C2×Q8—61no—
433C2×D4—31no—
434C2×D4—31no—
435C2×D4—61no—
436C2×D4—61no—
437C22×C4—61no—
438C22×C4—61no—
439C22×C4—61no—
440C22×C4C22×C3×D311yescharacteristic
441Q16—64no—
442Q16—62no—
443SD16—64no—
444SD16—62no—
445SD16—62no—
446D8—62no—
447M16—21no—
448M16—21no—
449M16—21no—
450M16C3×D1212yes—
451C2×C8—21no—
452C2×C8C3×D1212yes—
453C4⋊C4—21no—
454C4⋊C4—64no—
455C4⋊C4—61no—
456C22⋊C4—64no—
457C22⋊C4—61no—
458C22⋊C4C3×D1212yes—
459C42—21no—
460C42—61no—
461C22×C3—21no—
462C22×C3—21no—
463C22×C3—21no—
464C22×C3—41no—
465C22×C3—41no—
466C22×C3—81no—
467C22×C3—122no—
468C22×C3—121no—
469C22×C3—121no—
470C22×C3—241no—
471C22×C3#87411yescharacteristic
472C22×C3#88211yescharacteristic
473C22×C3#89511yescharacteristic
474C22×C3C3×#12011yescharacteristic
475C22×C3C3×#12111yescharacteristic
476C22×C3C3×#12711yescharacteristic
477C2×D3—42no—
478C2×D3—41no—
479C2×D3—41no—
480C2×D3—81no—
481C3×C4—21no—
482C3×C4—21no—
483C3×C4—21no—
484C3×C4—21no—
485C3×C4—42no—
486C3×C4—42no—
487C3×C4—82no—
488C3×C4—121no—
489C3×C4—121no—
490C3×C4—122no—
491C3×C4—241no—
492C3×C4#88211yescharacteristic
493C3×C4#88211yescharacteristic
494C3×C4#89511yescharacteristic
495C3×C4#89511yescharacteristic
496C3×C4C3×#12011yescharacteristic
497C3×C4C3×#12011yescharacteristic
498C3×C4C3×#12111yescharacteristic
499C3×C4C3×#12111yescharacteristic
500Dic3—42no—
501Dic3—41no—
502Dic3—41no—
503Dic3—81no—
504C32#200911yescharacteristic, complemented, Sylow
505C23—61no—
506C23—61no—
507C23C2×C3×D1211yescharacteristic
508Q8—62no—
509Q8—61no—
510Q8—61no—
511Q8—61no—
512Q8—62no—
513Q8—61no—
514Q8—121no—
515Q8—121no—
516D4—61no—
517D4—61no—
518D4—61no—
519D4—61no—
520D4—121no—
521D4—121no—
522D4—121no—
523D4—121no—
524C2×C4—22no—
525C2×C4—62no—
526C2×C4—61no—
527C2×C4—61no—
528C2×C4—121no—
529C2×C4—121no—
530C2×C4—121no—
531C2×C4—121no—
532C2×C4—121no—
533C2×C4—121no—
534C2×C4—121no—
535C2×C4C2×C3×D1211yescharacteristic
536C2×C4C2×C3×D1211yescharacteristic
537C2×C4C3×D3×D411yescharacteristic
538C2×C4C3×D3×D411yescharacteristic
539C2×C4C3×D3×D411yescharacteristic
540C2×C4C3×#23911yescharacteristic
541C8—22no—
542C8—22no—
543C2×C3—21no—
544C2×C3—21no—
545C2×C3—21no—
546C2×C3—21no—
547C2×C3—21no—
548C2×C3—21no—
549C2×C3—21no—
550C2×C3—41no—
551C2×C3—41no—
552C2×C3—41no—
553C2×C3—241no—
554C2×C3—241no—
555C2×C3#467111yescharacteristic
556C2×C3C3×#39211yescharacteristic
557D3—81no—
558D3—81no—
559C22—41no—
560C22—122no—
561C22—121no—
562C22—121no—
563C22—241no—
564C22C3×#87411yescharacteristic
565C22C3×#88211yescharacteristic
566C22C3×#89511yescharacteristic
567C4—42no—
568C4—121no—
569C4—121no—
570C4—122no—
571C4—241no—
572C4C3×#88211yescharacteristic
573C4C3×#88211yescharacteristic
574C4C3×#89511yescharacteristic
575C4C3×#89511yescharacteristic
576C3—21no—
577C3#6903111yescharacteristic, direct product factor
578C3C3×#200911yescharacteristic, complemented
579C2—21no—
580C2—21no—
581C2—21no—
582C2—241no—
583C2—241no—
584C2C3×#467111yescharacteristic
subgroupG/H
centerC2×C3#4671
commutator, cosocleC22×C3×C4C23×C3
FrattiniC22×C4C22×C3×D3
FittingC32×#344C2
socleC2×C32#392
prime radicalC3×#5748C2
hypercenterC3×#344D3
hypocenterC3C3×#2009
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C3 ◁ C22×C3×C4 ◁ C3×#344

Complements

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

NH ≅ G/Ntype
2. C2×C3×#909C2semidirect
3. C3×#5526C2semidirect
4. C3×#5139C2semidirect
5. C3×#5120C2semidirect
6. C3×#5006C2semidirect
7. C32×#344C2semidirect
9. #69031C3direct (N × H)
37. C2×#909C2×C3semidirect
38. #5526C2×C3semidirect
42. #5139C2×C3semidirect
43. #5120C2×C3semidirect
44. #5006C2×C3semidirect
46. C3×#344D3semidirect
47. C3×#344C2×C3semidirect
186. #344C3×D3semidirect
504. C32#2009semidirect
577. C3#69031direct (N × H)
578. C3C3×#2009semidirect

Maximal subgroups

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

subgroupindex
C3×#57482
C2×C3×#9092
C3×#55262
C3×#51392
C3×#51202
C3×#50062
C32×#3442
C3×#20093
#690313