Finite Group Databasebeta

← C3×#70053 #11792350

Subgroups — C3×#70053 #11792350

Order 1152.

775 conjugacy classes of subgroups.

The subgroup lattice has 606 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#951C211yesmaximal, characteristic, complemented
2C3×#5822C211yesmaximal, characteristic
3C3×#5526C211yesmaximal, characteristic, complemented
4C32×#410C211yesmaximal, characteristic, complemented
5C3×#5005C211yesmaximal, characteristic, complemented
6C3×#5004C211yesmaximal, characteristic, complemented
7C3×#4533C211yesmaximal, characteristic, complemented
8C3×#2009—31nomaximal
9#70053C311yesmaximal, characteristic, direct product factor
10C2×C32×#41C2211yescharacteristic
11C2×C3×#235C2211yescharacteristic
12C22×C3×Dic6C2211yescharacteristic
13C32×#117C2211yescharacteristic
14C32×#117C2211yescharacteristic
15C3×#951—21no—
16C3×#951—22no—
17C3×#951—22no—
18C3×#950—22no—
19C3×#949—21no—
20C2×C3×#216—21no—
21C3×#942—21no—
22C2×C3×#214—21no—
23C3×#932—21no—
24C2×C3×#208C2211yescharacteristic
25C2×C3×#208C2211yescharacteristic
26C3×#897—22no—
27C3×#886—22no—
28C3×#875—21no—
29C3×#869—21no—
30C32×#99—22no—
31C3×#810—22no—
32C3×#805—22no—
33C3×#575—31no—
34C2×C3×#137—31no—
35C3×#536—31no—
36C2×#951C2×C311yescharacteristic, complemented
37#5822C2×C311yescharacteristic
38#5526C2×C311yescharacteristic, complemented
39C3×#421—31no—
40C3×#419—31no—
41C3×#410—21no—
42C3×#410D311yescharacteristic, complemented
43C3×#410C2×C311yescharacteristic, complemented
44#5005C2×C311yescharacteristic, complemented
45#5004C2×C311yescharacteristic, complemented
46C3×#344—31no—
47#4533C2×C311yescharacteristic, complemented
48C32×#41—21no—
49C32×#41—21no—
50C32×#41—21no—
51C32×#41—21no—
52C2×C32×Q8D411yescharacteristic
53C2×C32×D4—21no—
54C2×C32×D4D411yescharacteristic
55C22×C32×C4—21no—
56C22×C32×C4C2311yescharacteristic
57C2×C3×#67—21no—
58C22×C3×Dic3—21no—
59C3×#235—21no—
60C3×#235—21no—
61C3×#235—21no—
62C3×#235—21no—
63C2×C3×D12D411yescharacteristic
64C2×C3×C4×D3—21no—
65C2×C3×Dic6—21no—
66C2×C3×Dic6—21no—
67C2×C3×Dic6—21no—
68C2×C3×Dic6—21no—
69C2×C3×Dic6—21no—
70C2×C3×Dic6D412yes—
71C2×C3×Dic6D411yescharacteristic
72C32×C4⋊C4—21no—
73C32×C4⋊C4—21no—
74C32×C22⋊C4—21no—
75C32×C22⋊C4D412yes—
76C32×C42—21no—
77C32×C42—21no—
78C3×#216—22no—
79C3×#216—24no—
80C3×#215—22no—
81C3×#214—22no—
82C3×#214—24no—
83C3×#213—22no—
84C3×(C2×D3)⋊C4—24no—
85C3×C4⋊Dic3—24no—
86C3×#208—21no—
87C3×#208—21no—
88C3×#208—21no—
89C3×#208D412yes—
90C2×C3×C3⋊C8—21no—
91C2×C3×C3⋊C8D412yes—
92#2009—31noSylow
93C2×C3×#41—21no—
94C2×C3×#41—31no—
95C2×C3×#41C2×D311yescharacteristic
96C2×C3×#41C22×C311yescharacteristic
97C22×C3×Q8—31no—
98C2×#235C22×C311yescharacteristic
99C22×Dic6C22×C311yescharacteristic
100C3×#137—62no—
101C3×#137—62no—
102C3×#137—61no—
103C3×#137—61no—
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—31no—
110C2×C3×M16—31no—
111C3×C4⋊Q8—61no—
112C3×#124—61no—
113C3×#123—62no—
114C3×C22⋊Q8—62no—
115C3×#117—21no—
116C3×#117—21no—
117C3×#117C2×D311yescharacteristic
118C3×#117C2×D311yescharacteristic
119C3×#117C22×C311yescharacteristic
120C3×#117C22×C311yescharacteristic
121#951—21no—
122#951—22no—
123#951—22no—
124#950—22no—
125#949—21no—
126C2×#216—21no—
127#942—21no—
128C2×#214—21no—
129#932—21no—
130C2×#208C22×C311yescharacteristic
131C2×#208C22×C311yescharacteristic
132#897—22no—
133#886—22no—
134#875—21no—
135#869—21no—
136C3×#104—62no—
137C3×#103—62no—
138C3×#99—24no—
139C3×#99—22no—
140C3×#99—22no—
141#810—22no—
142#805—22no—
143C23×C32—21no—
144C23×C32C2×D411yescharacteristic
145C22×C3×D3—21no—
146C32×Q8—21no—
147C32×Q8—21no—
148C32×D4—21no—
149C32×D4—21no—
150C32×D4—41no—
151C32×D4—41no—
152C2×C32×C4—21no—
153C2×C32×C4—22no—
154C2×C32×C4—41no—
155C2×C32×C4—41no—
156C2×C32×C4—41no—
157C2×C32×C4C2×D411yescharacteristic
158C2×C32×C4C2×D411yescharacteristic
159C2×C32×C4C2×D411yescharacteristic
160C2×C32×C4C2×D411yescharacteristic
161C2×C32×C4C2×D411yescharacteristic
162C2×C32×C4#4111yescharacteristic
163C3×#67—41no—
164C3×#67—41no—
165C2×C3×Dic3—21no—
166C2×C3×Dic3—22no—
167C2×C3×Dic3—41no—
168C2×C3×Dic3—41no—
169C3×D12—21no—
170C3×D12—21no—
171C3×C4×D3—41no—
172C3×C4×D3—41no—
173C3×Dic6—22no—
174C3×Dic6—21no—
175C3×Dic6—22no—
176C3×Dic6—21no—
177C3×Dic6—41no—
178C3×Dic6—41no—
179C3×C3⋊C8—22no—
180C3×C3⋊C8—22no—
181#575—31no—
182C2×#137—31no—
183#536—31no—
184#421—31no—
185#419—31no—
186#410C3×D311yescharacteristic, complemented
187#344—31no—
188C3×#41—21no—
189C3×#41—21no—
190C3×#41—21no—
191C3×#41—21no—
192C3×#41—21no—
193C3×#41—21no—
194C3×#41—21no—
195C3×#41—21no—
196C3×#41—41no—
197C3×#41—41no—
198C3×#41—41no—
199C3×#41—41no—
200C3×#41—61no—
201C3×#41—61no—
202C3×#41—61no—
203C3×#41—61no—
204C2×C3×Q8—21no—
205C2×C3×Q8—32no—
206C2×C3×Q8—31no—
207C2×C3×Q8—61no—
208C2×C3×Q8—61no—
209C2×C3×Q8—61no—
210C2×C3×Q8—61no—
211C2×C3×Q8—61no—
212C2×C3×Q8D1211yescharacteristic
213C2×C3×Q8C3×D411yescharacteristic
214C2×C3×D4—22no—
215C2×C3×D4—21no—
216C2×C3×D4—21no—
217C2×C3×D4—21no—
218C2×C3×D4—31no—
219C2×C3×D4—61no—
220C2×C3×D4D1211yescharacteristic
221C2×C3×D4C3×D411yescharacteristic
222C22×C3×C4—22no—
223C22×C3×C4—21no—
224C22×C3×C4—21no—
225C22×C3×C4—21no—
226C22×C3×C4—61no—
227C22×C3×C4—61no—
228C22×C3×C4C22×D311yescharacteristic
229C22×C3×C4C23×C311yescharacteristic
230C2×#67—21no—
231C22×Dic3—21no—
232#235—21no—
233#235—21no—
234#235—21no—
235#235—21no—
236C2×D12C3×D411yescharacteristic
237C2×C4×D3—21no—
238C2×Dic6—21no—
239C2×Dic6—21no—
240C2×Dic6—21no—
241C2×Dic6—21no—
242C2×Dic6—21no—
243C2×Dic6C3×D411yescharacteristic
244C2×Dic6C3×D412yes—
245C3×Q16—64no—
246C3×Q16—62no—
247C3×SD16—64no—
248C3×SD16—62no—
249C3×SD16—62no—
250C3×D8—62no—
251C3×M16—32no—
252C3×M16—61no—
253C3×M16—61no—
254C3×M16—61no—
255C2×C3×C8—32no—
256C2×C3×C8—61no—
257C3×C4⋊C4—21no—
258C3×C4⋊C4—21no—
259C3×C4⋊C4—21no—
260C3×C4⋊C4—21no—
261C3×C4⋊C4—41no—
262C3×C4⋊C4—41no—
263C3×C4⋊C4—64no—
264C3×C22⋊C4—22no—
265C3×C22⋊C4—21no—
266C3×C22⋊C4—21no—
267C3×C22⋊C4—22no—
268C3×C22⋊C4—64no—
269C3×C22⋊C4#6712yes—
270C3×C22⋊C4C3×D412yes—
271C3×C42—21no—
272C3×C42—21no—
273C3×C42—21no—
274C3×C42—21no—
275C3×C42—41no—
276C3×C42—41no—
277#216—22no—
278#216—24no—
279#215—22no—
280#214—22no—
281#214—24no—
282#213—22no—
283(C2×D3)⋊C4—24no—
284C4⋊Dic3—24no—
285#208—21no—
286#208—21no—
287#208—21no—
288#208C3×D412yes—
289C2×C3⋊C8—21no—
290C2×C3⋊C8C3×D412yes—
291C22×C32—41no—
292C22×C32—41no—
293C22×C32—81no—
294C22×C32#12011yescharacteristic
295C22×C32#12111yescharacteristic
296C22×C32#12711yescharacteristic
297C2×C3×D3—42no—
298C2×C3×D3—41no—
299C32×C4—41no—
300C32×C4—42no—
301C32×C4—81no—
302C32×C4#12011yescharacteristic
303C32×C4#12011yescharacteristic
304C32×C4#12111yescharacteristic
305C32×C4#12111yescharacteristic
306C3×Dic3—42no—
307C3×Dic3—41no—
308C2×#41—31no—
309C2×#41C2×C3×D311yescharacteristic
310C22×Q8—31no—
311#137—62no—
312#137—62no—
313#137—61no—
314#137—61no—
315AGL(1,ℤ/8)—61no—
316AGL(1,ℤ/8)—61no—
317#135—62no—
318C2×Q16—61no—
319C2×SD16—61no—
320C2×M16—31no—
321C2×M16—31no—
322C4⋊Q8—61no—
323#124—61no—
324#123—62no—
325C22⋊Q8—62no—
326#117C2×C3×D311yescharacteristic
327#117C2×C3×D311yescharacteristic
328#104—62no—
329#103—62no—
330#99—22no—
331C23×C3—22no—
332C23×C3—21no—
333C23×C3—21no—
334C23×C3—21no—
335C23×C3—61no—
336C23×C3C2×#6711yescharacteristic
337C23×C3C2×C3×D411yescharacteristic
338C22×D3—21no—
339C3×Q8—21no—
340C3×Q8—21no—
341C3×Q8—21no—
342C3×Q8—21no—
343C3×Q8—41no—
344C3×Q8—41no—
345C3×Q8—62no—
346C3×Q8—61no—
347C3×Q8—62no—
348C3×Q8—61no—
349C3×Q8—121no—
350C3×Q8—121no—
351C3×D4—21no—
352C3×D4—21no—
353C3×D4—21no—
354C3×D4—21no—
355C3×D4—41no—
356C3×D4—41no—
357C3×D4—42no—
358C3×D4—42no—
359C3×D4—41no—
360C3×D4—41no—
361C3×D4—41no—
362C3×D4—41no—
363C3×D4—61no—
364C3×D4—61no—
365C3×D4—121no—
366C3×D4—121no—
367C2×C3×C4—22no—
368C2×C3×C4—21no—
369C2×C3×C4—22no—
370C2×C3×C4—22no—
371C2×C3×C4—21no—
372C2×C3×C4—21no—
373C2×C3×C4—21no—
374C2×C3×C4—21no—
375C2×C3×C4—21no—
376C2×C3×C4—21no—
377C2×C3×C4—21no—
378C2×C3×C4—42no—
379C2×C3×C4—42no—
380C2×C3×C4—42no—
381C2×C3×C4—41no—
382C2×C3×C4—41no—
383C2×C3×C4—41no—
384C2×C3×C4—41no—
385C2×C3×C4—42no—
386C2×C3×C4—41no—
387C2×C3×C4—41no—
388C2×C3×C4—62no—
389C2×C3×C4—61no—
390C2×C3×C4—121no—
391C2×C3×C4—121no—
392C2×C3×C4—121no—
393C2×C3×C4—121no—
394C2×C3×C4C2×D1211yescharacteristic
395C2×C3×C4#23511yescharacteristic
396C2×C3×C4D3×D411yescharacteristic
397C2×C3×C4D3×D411yescharacteristic
398C2×C3×C4D3×D411yescharacteristic
399C2×C3×C4D3×D411yescharacteristic
400C2×C3×C4C2×C3×D411yescharacteristic
401C2×C3×C4C2×C3×D411yescharacteristic
402C2×C3×C4C2×C3×D411yescharacteristic
403C2×C3×C4C2×C3×D411yescharacteristic
404C2×C3×C4C2×C3×D411yescharacteristic
405C2×C3×C4C3×#4111yescharacteristic
406#67—41no—
407#67—41no—
408C2×Dic3—21no—
409C2×Dic3—22no—
410C2×Dic3—41no—
411C2×Dic3—41no—
412D12—21no—
413D12—21no—
414C4×D3—41no—
415C4×D3—41no—
416Dic6—22no—
417Dic6—21no—
418Dic6—22no—
419Dic6—21no—
420Dic6—41no—
421Dic6—41no—
422C3×C8—62no—
423C3×C8—62no—
424C3⋊C8—22no—
425C3⋊C8—22no—
426C2×C32—21no—
427C2×C32—21no—
428C2×C32—21no—
429C2×C32—81no—
430C2×C32#39211yescharacteristic
431C3×D3—81no—
432#41—21no—
433#41—21no—
434#41—21no—
435#41—21no—
436#41—61no—
437#41—61no—
438#41—61no—
439#41—61no—
440C2×Q8—32no—
441C2×Q8—31no—
442C2×Q8—61no—
443C2×Q8—61no—
444C2×Q8—61no—
445C2×Q8—61no—
446C2×Q8—61no—
447C2×Q8C3×D1211yescharacteristic
448C2×D4—21no—
449C2×D4—31no—
450C2×D4—61no—
451C2×D4C3×D1211yescharacteristic
452C22×C4—21no—
453C22×C4—61no—
454C22×C4—61no—
455C22×C4C22×C3×D311yescharacteristic
456Q16—64no—
457Q16—62no—
458SD16—64no—
459SD16—62no—
460SD16—62no—
461D8—62no—
462M16—32no—
463M16—61no—
464M16—61no—
465M16—61no—
466C2×C8—32no—
467C2×C8—61no—
468C4⋊C4—21no—
469C4⋊C4—21no—
470C4⋊C4—64no—
471C22⋊C4—21no—
472C22⋊C4—64no—
473C22⋊C4C3×#6712yes—
474C42—21no—
475C42—21no—
476C22×C3—21no—
477C22×C3—21no—
478C22×C3—21no—
479C22×C3—41no—
480C22×C3—41no—
481C22×C3—42no—
482C22×C3—41no—
483C22×C3—41no—
484C22×C3—81no—
485C22×C3—81no—
486C22×C3—81no—
487C22×C3—82no—
488C22×C3—122no—
489C22×C3—121no—
490C22×C3#93011yescharacteristic
491C22×C3#93711yescharacteristic
492C22×C3#94011yescharacteristic
493C22×C3C3×#12011yescharacteristic
494C22×C3C3×#12111yescharacteristic
495C22×C3C3×#12711yescharacteristic
496C2×D3—42no—
497C2×D3—41no—
498C3×C4—21no—
499C3×C4—21no—
500C3×C4—21no—
501C3×C4—21no—
502C3×C4—42no—
503C3×C4—42no—
504C3×C4—42no—
505C3×C4—41no—
506C3×C4—41no—
507C3×C4—82no—
508C3×C4—81no—
509C3×C4—81no—
510C3×C4—82no—
511C3×C4—121no—
512C3×C4—122no—
513C3×C4#88211yescharacteristic
514C3×C4#88211yescharacteristic
515C3×C4#88411yescharacteristic
516C3×C4#88411yescharacteristic
517C3×C4C3×#12011yescharacteristic
518C3×C4C3×#12011yescharacteristic
519C3×C4C3×#12111yescharacteristic
520C3×C4C3×#12111yescharacteristic
521Dic3—42no—
522Dic3—41no—
523C32#200911yescharacteristic, complemented, Sylow
524C23—21no—
525C23—61no—
526C23C2×C3×#6711yescharacteristic
527Q8—21no—
528Q8—21no—
529Q8—62no—
530Q8—61no—
531Q8—62no—
532Q8—61no—
533Q8—121no—
534Q8—121no—
535D4—21no—
536D4—21no—
537D4—41no—
538D4—41no—
539D4—61no—
540D4—61no—
541D4—121no—
542D4—121no—
543C2×C4—21no—
544C2×C4—22no—
545C2×C4—41no—
546C2×C4—41no—
547C2×C4—41no—
548C2×C4—62no—
549C2×C4—61no—
550C2×C4—121no—
551C2×C4—121no—
552C2×C4—121no—
553C2×C4—121no—
554C2×C4C2×C3×D1211yescharacteristic
555C2×C4C3×#23511yescharacteristic
556C2×C4C3×D3×D411yescharacteristic
557C2×C4C3×D3×D411yescharacteristic
558C2×C4C3×D3×D411yescharacteristic
559C2×C4C3×D3×D411yescharacteristic
560C8—62no—
561C8—62no—
562C2×C3—21no—
563C2×C3—21no—
564C2×C3—21no—
565C2×C3—21no—
566C2×C3—21no—
567C2×C3—21no—
568C2×C3—21no—
569C2×C3—41no—
570C2×C3—41no—
571C2×C3—41no—
572C2×C3—82no—
573C2×C3—81no—
574C2×C3—81no—
575C2×C3—241no—
576C2×C3#496011yescharacteristic
577C2×C3C3×#39211yescharacteristic
578D3—81no—
579C22—41no—
580C22—41no—
581C22—81no—
582C22—122no—
583C22—121no—
584C22C3×#93011yescharacteristic
585C22C3×#93711yescharacteristic
586C22C3×#94011yescharacteristic
587C4—42no—
588C4—41no—
589C4—81no—
590C4—121no—
591C4—122no—
592C4C3×#88211yescharacteristic
593C4C3×#88211yescharacteristic
594C4C3×#88411yescharacteristic
595C4C3×#88411yescharacteristic
596C3—21no—
597C3#7005311yescharacteristic, direct product factor
598C3C3×#200911yescharacteristic, complemented
599C2—21no—
600C2—21no—
601C2—21no—
602C2—81no—
603C2—241no—
604C2C3×#496011yescharacteristic
subgroupG/H
centerC2×C3#4960
commutator, cosocleC22×C3×C4C23×C3
FrattiniC22×C4C22×C3×D3
FittingC32×#410C2
socleC2×C32#392
prime radicalC3×#5822C2
hypercenterC3×#410D3
hypocenterC3C3×#2009
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C3 ◁ C22×C3×C4 ◁ C3×#410

Complements

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

NH ≅ G/Ntype
1. C2×C3×#951C2semidirect
3. C3×#5526C2semidirect
4. C32×#410C2semidirect
5. C3×#5005C2semidirect
6. C3×#5004C2semidirect
7. C3×#4533C2semidirect
9. #70053C3direct (N × H)
36. C2×#951C2×C3semidirect
38. #5526C2×C3semidirect
42. C3×#410D3semidirect
43. C3×#410C2×C3semidirect
44. #5005C2×C3semidirect
45. #5004C2×C3semidirect
47. #4533C2×C3semidirect
186. #410C3×D3semidirect
523. C32#2009semidirect
597. C3#70053direct (N × H)
598. C3C3×#2009semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#9512
C3×#58222
C3×#55262
C32×#4102
C3×#50052
C3×#50042
C3×#45332
C3×#20093
#700533