Finite Group Databasebeta

← C3×#70351 #11792359

Subgroups — C3×#70351 #11792359

Order 1152.

771 conjugacy classes of subgroups.

The subgroup lattice has 598 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5816C211yesmaximal, characteristic, complemented
2C2×C3×#942C211yesmaximal, characteristic, complemented
3C3×#5748C211yesmaximal, characteristic
4C32×#419C211yesmaximal, characteristic, complemented
5C3×#5006C211yesmaximal, characteristic, complemented
6C3×#5005C211yesmaximal, characteristic, complemented
7C3×#4556C211yesmaximal, characteristic, complemented
8C3×#2009—31nomaximal
9#70351C311yesmaximal, characteristic, direct product factor
10C22×C32×Q8C2211yescharacteristic
11C2×C3×#235C2211yescharacteristic
12C2×C3×#235C2211yescharacteristic
13C2×C32×M16C2211yescharacteristic
14C32×#117C2211yescharacteristic
15C3×#947—21no—
16C3×#946—22no—
17C3×#944—21no—
18C2×C3×#216—21no—
19C3×#942—22no—
20C3×#942—22no—
21C2×C3×#215—21no—
22C3×#929—22no—
23C3×#926C2211yescharacteristic
24C2×C3×#208C2211yescharacteristic
25C3×#909—21no—
26C3×#909—21no—
27C3×#908—21no—
28C3×#908—21no—
29C3×#904—22no—
30C32×#103—22no—
31C3×#806—22no—
32C3×#805—22no—
33C3×#575—31no—
34C2×C3×#137—31no—
35C3×#536—31no—
36#5816C2×C311yescharacteristic, complemented
37C2×#942C2×C311yescharacteristic, complemented
38#5748C2×C311yescharacteristic
39C3×#421—31no—
40C3×#419—21no—
41C3×#419D311yescharacteristic, complemented
42C3×#419C2×C311yescharacteristic, complemented
43C3×#410—31no—
44#5006C2×C311yescharacteristic, complemented
45#5005C2×C311yescharacteristic, complemented
46C3×#344—31no—
47#4556C2×C311yescharacteristic, complemented
48C2×C32×Q8—21no—
49C2×C32×Q8—21no—
50C2×C32×Q8—21no—
51C2×C32×Q8—21no—
52C2×C32×Q8—21no—
53C2×C32×Q8D412yes—
54C22×C32×C4—21no—
55C22×C32×C4C2311yescharacteristic
56C2×C3×#67—21no—
57C2×C3×#67—21no—
58C3×#235—21no—
59C3×#235—21no—
60C3×#235—21no—
61C3×#235—21no—
62C3×#235—21no—
63C3×#235—21no—
64C3×#235—21no—
65C3×#235—21no—
66C2×C3×D12D411yescharacteristic
67C2×C3×D12D411yescharacteristic
68C2×C3×C4×D3—21no—
69C2×C3×C4×D3—21no—
70C2×C3×Dic6D411yescharacteristic
71C2×C3×Dic6D411yescharacteristic
72C32×M16—21no—
73C32×M16—21no—
74C2×C32×C8D412yes—
75C32×C4⋊C4—21no—
76C32×C22⋊C4—21no—
77C32×C42—21no—
78C3×#217D412yes—
79C3×#216—24no—
80C3×#215—24no—
81C3×(C2×D3)⋊C4—24no—
82C3×C4⋊Dic3—21no—
83C3×Dic3⋊C4—24no—
84C3×C4×Dic3—21no—
85C3×#208—21no—
86C3×#208D412yes—
87C2×C3×C3⋊C8—21no—
88C3×Dic12—22no—
89C3×D24—22no—
90C3×#204—22no—
91C3×#204—22no—
92#2009—31noSylow
93C2×C3×#41—31no—
94C2×C3×#41—31no—
95C22×C3×Q8—21no—
96C22×C3×Q8C2×D311yescharacteristic
97C22×C3×Q8C22×C311yescharacteristic
98C2×#235C22×C311yescharacteristic
99C2×#235C22×C311yescharacteristic
100C3×#137—61no—
101C3×#137—61no—
102C3×#137—62no—
103C3×#137—62no—
104C3×AGL(1,ℤ/8)—61no—
105C3×AGL(1,ℤ/8)—61no—
106C3×#135—62no—
107C2×C3×Q16—61no—
108C2×C3×SD16—61no—
109C2×C3×M16—21no—
110C2×C3×M16—31no—
111C2×C3×M16C2×D311yescharacteristic
112C2×C3×M16C22×C311yescharacteristic
113C3×C4⋊Q8—61no—
114C3×#124—61no—
115C3×#123—62no—
116C3×C22⋊Q8—62no—
117C3×#117—21no—
118C3×#117—31no—
119C3×#117C2×D311yescharacteristic
120C3×#117C22×C311yescharacteristic
121#947—21no—
122#946—22no—
123#944—21no—
124C2×#216—21no—
125#942—22no—
126#942—22no—
127C2×#215—21no—
128#929—22no—
129#926C22×C311yescharacteristic
130C2×#208C22×C311yescharacteristic
131#909—21no—
132#909—21no—
133#908—21no—
134#908—21no—
135#904—22no—
136C3×#104—62no—
137C3×#103—24no—
138C3×#103—22no—
139C3×#103—22no—
140C3×#99—62no—
141#806—22no—
142#805—22no—
143C23×C32C2×D411yescharacteristic
144C22×C3×D3—21no—
145C22×C3×D3—21no—
146C32×Q8—22no—
147C32×Q8—22no—
148C32×Q8—41no—
149C32×Q8—41no—
150C2×C32×C4—22no—
151C2×C32×C4—41no—
152C2×C32×C4—41no—
153C2×C32×C4—41no—
154C2×C32×C4C2×D411yescharacteristic
155C2×C32×C4C2×D411yescharacteristic
156C2×C32×C4C2×D411yescharacteristic
157C2×C32×C4C2×D411yescharacteristic
158C2×C32×C4C2×D411yescharacteristic
159C2×C32×C4#4111yescharacteristic
160C3×#67—41no—
161C3×#67—41no—
162C3×#67—41no—
163C3×#67—41no—
164C2×C3×Dic3—22no—
165C2×C3×Dic3—21no—
166C2×C3×Dic3—21no—
167C3×D12—21no—
168C3×D12—21no—
169C3×D12—21no—
170C3×D12—21no—
171C3×C4×D3—41no—
172C3×C4×D3—41no—
173C3×C4×D3—41no—
174C3×C4×D3—41no—
175C3×Dic6—21no—
176C3×Dic6—21no—
177C3×Dic6—21no—
178C3×Dic6—21no—
179C32×C8—22no—
180C3×C3⋊C8—22no—
181#575—31no—
182C2×#137—31no—
183#536—31no—
184#421—31no—
185#419C3×D311yescharacteristic, complemented
186#410—31no—
187#344—31no—
188C3×#41—61no—
189C3×#41—61no—
190C3×#41—61no—
191C3×#41—61no—
192C3×#41—61no—
193C3×#41—61no—
194C3×#41—61no—
195C3×#41—61no—
196C2×C3×Q8—21no—
197C2×C3×Q8—21no—
198C2×C3×Q8—22no—
199C2×C3×Q8—22no—
200C2×C3×Q8—21no—
201C2×C3×Q8—21no—
202C2×C3×Q8—21no—
203C2×C3×Q8—21no—
204C2×C3×Q8—21no—
205C2×C3×Q8—21no—
206C2×C3×Q8—21no—
207C2×C3×Q8—21no—
208C2×C3×Q8—22no—
209C2×C3×Q8—31no—
210C2×C3×Q8—31no—
211C2×C3×Q8—41no—
212C2×C3×Q8—41no—
213C2×C3×Q8—41no—
214C2×C3×Q8D1212yes—
215C2×C3×Q8C3×D412yes—
216C2×C3×D4—31no—
217C2×C3×D4—31no—
218C2×C3×D4—61no—
219C2×C3×D4—61no—
220C22×C3×C4—21no—
221C22×C3×C4—21no—
222C22×C3×C4—21no—
223C22×C3×C4—41no—
224C22×C3×C4—61no—
225C22×C3×C4—61no—
226C22×C3×C4C22×D311yescharacteristic
227C22×C3×C4C23×C311yescharacteristic
228C2×#67—21no—
229C2×#67—21no—
230#235—21no—
231#235—21no—
232#235—21no—
233#235—21no—
234#235—21no—
235#235—21no—
236#235—21no—
237#235—21no—
238C2×D12C3×D411yescharacteristic
239C2×D12C3×D411yescharacteristic
240C2×C4×D3—21no—
241C2×C4×D3—21no—
242C2×Dic6C3×D411yescharacteristic
243C2×Dic6C3×D411yescharacteristic
244C3×Q16—62no—
245C3×Q16—64no—
246C3×SD16—62no—
247C3×SD16—62no—
248C3×SD16—64no—
249C3×D8—62no—
250C3×M16—21no—
251C3×M16—21no—
252C3×M16—21no—
253C3×M16—21no—
254C3×M16—32no—
255C3×M16—41no—
256C3×M16—41no—
257C3×M16—61no—
258C2×C3×C8—22no—
259C2×C3×C8—61no—
260C2×C3×C8#6712yes—
261C2×C3×C8C3×D412yes—
262C3×C4⋊C4—22no—
263C3×C4⋊C4—21no—
264C3×C4⋊C4—21no—
265C3×C4⋊C4—64no—
266C3×C4⋊C4—61no—
267C3×C22⋊C4—21no—
268C3×C22⋊C4—21no—
269C3×C22⋊C4—32no—
270C3×C22⋊C4—41no—
271C3×C22⋊C4—64no—
272C3×C42—21no—
273C3×C42—21no—
274C3×C42—41no—
275C3×C42—61no—
276#217C3×D412yes—
277#216—24no—
278#215—24no—
279(C2×D3)⋊C4—24no—
280C4⋊Dic3—21no—
281Dic3⋊C4—24no—
282C4×Dic3—21no—
283#208—21no—
284#208C3×D412yes—
285C2×C3⋊C8—21no—
286Dic12—22no—
287D24—22no—
288#204—22no—
289#204—22no—
290C22×C32—41no—
291C22×C32#12011yescharacteristic
292C22×C32#12111yescharacteristic
293C22×C32#12711yescharacteristic
294C2×C3×D3—42no—
295C2×C3×D3—41no—
296C2×C3×D3—41no—
297C2×C3×D3—81no—
298C32×C4—42no—
299C32×C4—81no—
300C32×C4#12011yescharacteristic
301C32×C4#12011yescharacteristic
302C32×C4#12111yescharacteristic
303C32×C4#12111yescharacteristic
304C3×Dic3—42no—
305C3×Dic3—41no—
306C3×Dic3—41no—
307C2×#41—31no—
308C2×#41—31no—
309C22×Q8C2×C3×D311yescharacteristic
310#137—61no—
311#137—61no—
312#137—62no—
313#137—62no—
314AGL(1,ℤ/8)—61no—
315AGL(1,ℤ/8)—61no—
316#135—62no—
317C2×Q16—61no—
318C2×SD16—61no—
319C2×M16—31no—
320C2×M16C2×C3×D311yescharacteristic
321C4⋊Q8—61no—
322#124—61no—
323#123—62no—
324C22⋊Q8—62no—
325#117—31no—
326#117C2×C3×D311yescharacteristic
327#104—62no—
328#103—22no—
329#99—62no—
330C23×C3—21no—
331C23×C3—61no—
332C23×C3—61no—
333C23×C3D3×D411yescharacteristic
334C23×C3C2×C3×D411yescharacteristic
335C22×D3—21no—
336C22×D3—21no—
337C3×Q8—24no—
338C3×Q8—22no—
339C3×Q8—22no—
340C3×Q8—22no—
341C3×Q8—22no—
342C3×Q8—42no—
343C3×Q8—42no—
344C3×Q8—42no—
345C3×Q8—41no—
346C3×Q8—41no—
347C3×Q8—41no—
348C3×Q8—41no—
349C3×Q8—61no—
350C3×Q8—61no—
351C3×Q8—61no—
352C3×Q8—61no—
353C3×D4—61no—
354C3×D4—61no—
355C3×D4—61no—
356C3×D4—61no—
357C3×D4—121no—
358C3×D4—121no—
359C3×D4—121no—
360C3×D4—121no—
361C2×C3×C4—22no—
362C2×C3×C4—22no—
363C2×C3×C4—21no—
364C2×C3×C4—21no—
365C2×C3×C4—21no—
366C2×C3×C4—21no—
367C2×C3×C4—21no—
368C2×C3×C4—21no—
369C2×C3×C4—42no—
370C2×C3×C4—42no—
371C2×C3×C4—42no—
372C2×C3×C4—41no—
373C2×C3×C4—41no—
374C2×C3×C4—41no—
375C2×C3×C4—41no—
376C2×C3×C4—42no—
377C2×C3×C4—41no—
378C2×C3×C4—41no—
379C2×C3×C4—62no—
380C2×C3×C4—61no—
381C2×C3×C4—61no—
382C2×C3×C4—121no—
383C2×C3×C4—121no—
384C2×C3×C4—121no—
385C2×C3×C4—121no—
386C2×C3×C4C2×D1211yescharacteristic
387C2×C3×C4#23511yescharacteristic
388C2×C3×C4D3×D411yescharacteristic
389C2×C3×C4D3×D411yescharacteristic
390C2×C3×C4D3×D411yescharacteristic
391C2×C3×C4C2×#6711yescharacteristic
392C2×C3×C4C2×C3×D411yescharacteristic
393C2×C3×C4C2×C3×D411yescharacteristic
394C2×C3×C4C2×C3×D411yescharacteristic
395C2×C3×C4C2×C3×D411yescharacteristic
396C2×C3×C4C2×C3×D411yescharacteristic
397C2×C3×C4C3×#4111yescharacteristic
398#67—41no—
399#67—41no—
400#67—41no—
401#67—41no—
402C2×Dic3—22no—
403C2×Dic3—21no—
404C2×Dic3—21no—
405D12—21no—
406D12—21no—
407D12—21no—
408D12—21no—
409C4×D3—41no—
410C4×D3—41no—
411C4×D3—41no—
412C4×D3—41no—
413Dic6—21no—
414Dic6—21no—
415Dic6—21no—
416Dic6—21no—
417C3×C8—22no—
418C3×C8—22no—
419C3×C8—42no—
420C3×C8—62no—
421C3⋊C8—22no—
422C2×C32—21no—
423C2×C32—21no—
424C2×C32—21no—
425C2×C32#39211yescharacteristic
426C3×D3—81no—
427C3×D3—81no—
428#41—61no—
429#41—61no—
430#41—61no—
431#41—61no—
432#41—61no—
433#41—61no—
434#41—61no—
435#41—61no—
436C2×Q8—21no—
437C2×Q8—21no—
438C2×Q8—21no—
439C2×Q8—21no—
440C2×Q8—21no—
441C2×Q8—31no—
442C2×Q8—31no—
443C2×Q8C3×D1212yes—
444C2×D4—31no—
445C2×D4—31no—
446C2×D4—61no—
447C2×D4—61no—
448C22×C4—21no—
449C22×C4—61no—
450C22×C4—61no—
451C22×C4C22×C3×D311yescharacteristic
452Q16—62no—
453Q16—64no—
454SD16—62no—
455SD16—62no—
456SD16—64no—
457D8—62no—
458M16—21no—
459M16—21no—
460M16—32no—
461M16—61no—
462C2×C8—61no—
463C2×C8C3×#6712yes—
464C4⋊C4—21no—
465C4⋊C4—64no—
466C4⋊C4—61no—
467C22⋊C4—21no—
468C22⋊C4—32no—
469C22⋊C4—64no—
470C42—21no—
471C42—61no—
472C22×C3—21no—
473C22×C3—21no—
474C22×C3—21no—
475C22×C3—41no—
476C22×C3—41no—
477C22×C3—42no—
478C22×C3—122no—
479C22×C3—121no—
480C22×C3—121no—
481C22×C3—241no—
482C22×C3#88211yescharacteristic
483C22×C3#88411yescharacteristic
484C22×C3#94011yescharacteristic
485C22×C3C3×#12011yescharacteristic
486C22×C3C3×#12111yescharacteristic
487C22×C3C3×#12711yescharacteristic
488C2×D3—42no—
489C2×D3—41no—
490C2×D3—41no—
491C2×D3—81no—
492C3×C4—21no—
493C3×C4—21no—
494C3×C4—21no—
495C3×C4—21no—
496C3×C4—44no—
497C3×C4—42no—
498C3×C4—42no—
499C3×C4—82no—
500C3×C4—81no—
501C3×C4—81no—
502C3×C4—122no—
503C3×C4—121no—
504C3×C4—121no—
505C3×C4#88211yescharacteristic
506C3×C4#88411yescharacteristic
507C3×C4#93011yescharacteristic
508C3×C4#93711yescharacteristic
509C3×C4C3×#12011yescharacteristic
510C3×C4C3×#12011yescharacteristic
511C3×C4C3×#12111yescharacteristic
512C3×C4C3×#12111yescharacteristic
513Dic3—42no—
514Dic3—41no—
515Dic3—41no—
516C32#200911yescharacteristic, complemented, Sylow
517C23—61no—
518C23—61no—
519C23C3×D3×D411yescharacteristic
520Q8—22no—
521Q8—22no—
522Q8—41no—
523Q8—41no—
524Q8—61no—
525Q8—61no—
526Q8—61no—
527Q8—61no—
528D4—61no—
529D4—61no—
530D4—61no—
531D4—61no—
532D4—121no—
533D4—121no—
534D4—121no—
535D4—121no—
536C2×C4—22no—
537C2×C4—41no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—62no—
541C2×C4—61no—
542C2×C4—61no—
543C2×C4—121no—
544C2×C4—121no—
545C2×C4—121no—
546C2×C4—121no—
547C2×C4C2×C3×D1211yescharacteristic
548C2×C4C3×#23511yescharacteristic
549C2×C4C3×D3×D411yescharacteristic
550C2×C4C3×D3×D411yescharacteristic
551C2×C4C3×D3×D411yescharacteristic
552C2×C4C2×C3×#6711yescharacteristic
553C8—22no—
554C8—62no—
555C2×C3—22no—
556C2×C3—21no—
557C2×C3—21no—
558C2×C3—21no—
559C2×C3—21no—
560C2×C3—21no—
561C2×C3—21no—
562C2×C3—21no—
563C2×C3—41no—
564C2×C3—41no—
565C2×C3—241no—
566C2×C3—241no—
567C2×C3#496011yescharacteristic
568C2×C3C3×#39211yescharacteristic
569D3—81no—
570D3—81no—
571C22—41no—
572C22—122no—
573C22—121no—
574C22—121no—
575C22—241no—
576C22C3×#88211yescharacteristic
577C22C3×#88411yescharacteristic
578C22C3×#94011yescharacteristic
579C4—42no—
580C4—81no—
581C4—122no—
582C4—121no—
583C4—121no—
584C4C3×#88211yescharacteristic
585C4C3×#88411yescharacteristic
586C4C3×#93011yescharacteristic
587C4C3×#93711yescharacteristic
588C3—21no—
589C3#7035111yescharacteristic, direct product factor
590C3C3×#200911yescharacteristic, complemented
591C2—21no—
592C2—21no—
593C2—21no—
594C2—241no—
595C2—241no—
596C2C3×#496011yescharacteristic
subgroupG/H
centerC2×C3#4960
commutator, cosocleC22×C3×C4C23×C3
FrattiniC22×C4C22×C3×D3
FittingC32×#419C2
socleC2×C32#392
prime radicalC3×#5748C2
hypercenterC3×#419D3
hypocenterC3C3×#2009
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C3 ◁ C22×C3×C4 ◁ C3×#419

Complements

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

NH ≅ G/Ntype
1. C3×#5816C2semidirect
2. C2×C3×#942C2semidirect
4. C32×#419C2semidirect
5. C3×#5006C2semidirect
6. C3×#5005C2semidirect
7. C3×#4556C2semidirect
9. #70351C3direct (N × H)
36. #5816C2×C3semidirect
37. C2×#942C2×C3semidirect
41. C3×#419D3semidirect
42. C3×#419C2×C3semidirect
44. #5006C2×C3semidirect
45. #5005C2×C3semidirect
47. #4556C2×C3semidirect
185. #419C3×D3semidirect
516. C32#2009semidirect
589. C3#70351direct (N × H)
590. C3C3×#2009semidirect

Maximal subgroups

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

subgroupindex
C3×#58162
C2×C3×#9422
C3×#57482
C32×#4192
C3×#50062
C3×#50052
C3×#45562
C3×#20093
#703513