Finite Group Databasebeta

← C3×#70385 #11792038

Subgroups — C3×#70385 #11792038

Order 1152.

1041 conjugacy classes of subgroups.

The subgroup lattice has 614 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5830C211yesmaximal, characteristic, complemented
2C2×C3×#949C211yesmaximal, characteristic, complemented
3C2×C3×#874C211yesmaximal, characteristic, complemented
4C2×C32×#104C211yesmaximal, characteristic, complemented
5C3×#5131C211yesmaximal, characteristic, complemented
6C2×C3×#823C211yesmaximal, characteristic, complemented
7C3×#4523C211yesmaximal, characteristic, complemented
8C3×#2002—31nomaximal
9#70385C311yesmaximal, characteristic, direct product factor
10C2×C32×#41C2211yescharacteristic
11C22×C3×D12—22no—
12C22×C3×D12C2211yescharacteristic
13C22×C3×D12C2211yescharacteristic
14C2×C32×M16C2211yescharacteristic
15C2×C32×C42C2211yescharacteristic
16C3×#949—22no—
17C3×#949—22no—
18C3×#947—21no—
19C2×C3×#215—21no—
20C3×#940—21no—
21C3×#937—22no—
22C2×C3×#213—21no—
23C3×#930—22no—
24C3×#926C2211yescharacteristic
25C2×C3×#208C2211yescharacteristic
26C3×#874—22no—
27C3×#874—22no—
28C32×#104—22no—
29C3×#823—22no—
30C3×#821—22no—
31C2×C3×AGL(1,ℤ/8)—31no—
32C3×#535—31no—
33C2×C3×#127—31no—
34#5830C2×C311yescharacteristic, complemented
35C2×#949C2×C311yescharacteristic, complemented
36C2×#874C2×C311yescharacteristic, complemented
37C2×C3×#104—21no—
38C2×C3×#104D311yescharacteristic, complemented
39C2×C3×#104C2×C311yescharacteristic, complemented
40C3×#418—31no—
41C2×C3×#100—31no—
42#5131C2×C311yescharacteristic, complemented
43C2×#823C2×C311yescharacteristic, complemented
44C3×#339—31no—
45#4523C2×C311yescharacteristic, complemented
46C23×C3×D3—21no—
47C23×C3×D3D412yes—
48C32×#41—21no—
49C32×#41—21no—
50C32×#41—21no—
51C32×#41—21no—
52C2×C32×Q8D411yescharacteristic, complemented
53C2×C32×D4—21no—
54C2×C32×D4D411yescharacteristic, complemented
55C22×C32×C4—21no—
56C22×C32×C4—21no—
57C22×C32×C4C2311yescharacteristic
58C2×C3×#67—24no—
59C2×C3×D12—21no—
60C2×C3×D12—21no—
61C2×C3×D12—21no—
62C2×C3×D12—21no—
63C2×C3×D12—28no—
64C2×C3×D12—21no—
65C2×C3×D12—21no—
66C2×C3×D12—21no—
67C2×C3×D12—21no—
68C2×C3×D12—21no—
69C2×C3×D12—21no—
70C2×C3×D12—21no—
71C2×C3×D12—48no—
72C2×C3×D12D412yescomplemented
73C32×M16—21no—
74C32×M16—21no—
75C2×C32×C8—21no—
76C32×C42—21no—
77C32×C42D412yescomplemented
78C3×#217—21no—
79C3×#215—24no—
80C3×#213—24no—
81C3×(C2×D3)⋊C4—24no—
82C3×C4⋊Dic3D412yescomplemented
83C3×C4×Dic3—21no—
84C3×#208—21no—
85C3×#208D412yescomplemented
86C2×C3×C3⋊C8—21no—
87#2002—31noSylow
88C2×C3×#41—21no—
89C2×C3×#41C2×D311yescharacteristic
90C2×C3×#41C22×C311yescharacteristic
91C22×C3×D4—31no—
92C22×C3×D4—31no—
93C22×C3×D4—62no—
94C22×D12—22no—
95C22×D12C22×C311yescharacteristic
96C22×D12C22×C311yescharacteristic
97C3×AGL(1,ℤ/8)—62no—
98C3×AGL(1,ℤ/8)—62no—
99C2×C3×SD16—61no—
100C2×C3×D8—61no—
101C2×C3×M16—21no—
102C2×C3×M16—31no—
103C2×C3×M16C2×D311yescharacteristic
104C2×C3×M16C22×C311yescharacteristic
105C3×#127—62no—
106C3×#127—61no—
107C3×#127—62no—
108C3×#124—61no—
109C3×#121—62no—
110C3×#120—62no—
111C3×#117—31no—
112C2×C3×C42—21no—
113C2×C3×C42C2×D311yescharacteristic
114C2×C3×C42C22×C311yescharacteristic
115#949—22no—
116#949—22no—
117#947—21no—
118C2×#215—21no—
119#940—21no—
120#937—22no—
121C2×#213—21no—
122#930—22no—
123#926C22×C311yescharacteristic
124C2×#208C22×C311yescharacteristic
125#874—22no—
126#874—22no—
127C3×#104—24no—
128C3×#104—22no—
129C3×#104—22no—
130C3×#102—62no—
131C3×#100—62no—
132#823—22no—
133#821—22no—
134C23×C32—21no—
135C23×C32C2×D411yescharacteristic
136C22×C3×D3—22no—
137C22×C3×D3—22no—
138C22×C3×D3—22no—
139C22×C3×D3—22no—
140C22×C3×D3—44no—
141C22×C3×D3—44no—
142C22×C3×D3—41no—
143C22×C3×D3—41no—
144C32×Q8—21no—
145C32×Q8—21no—
146C32×D4—21no—
147C32×D4—21no—
148C32×D4—41no—
149C32×D4—41no—
150C2×C32×C4—24no—
151C2×C32×C4—22no—
152C2×C32×C4—21no—
153C2×C32×C4—41no—
154C2×C32×C4—41no—
155C2×C32×C4C2×D411yescharacteristic
156C2×C32×C4C2×D411yescharacteristic
157C2×C32×C4C2×D411yescharacteristic
158C2×C32×C4C2×D411yescharacteristic
159C2×C32×C4C2×D411yescharacteristic
160C2×C32×C4#4111yescharacteristic
161C3×#67—84no—
162C2×C3×Dic3—22no—
163C3×D12—22no—
164C3×D12—22no—
165C3×D12—416no—
166C3×D12—41no—
167C3×D12—41no—
168C3×D12—41no—
169C3×D12—41no—
170C3×D12—41no—
171C3×D12—41no—
172C32×C8—41no—
173C3×C3⋊C8—22no—
174C2×AGL(1,ℤ/8)—31no—
175#535—31no—
176C2×#127—31no—
177C2×#104C3×D311yescharacteristic, complemented
178#418—31no—
179C2×#100—31no—
180#339—31no—
181C24×C3—32no—
182C24×C3—61no—
183C23×D3—21no—
184C23×D3C3×D412yes—
185C3×#41—22no—
186C3×#41—22no—
187C3×#41—21no—
188C3×#41—21no—
189C3×#41—21no—
190C3×#41—21no—
191C3×#41—21no—
192C3×#41—21no—
193C3×#41—21no—
194C3×#41—21no—
195C3×#41—41no—
196C3×#41—41no—
197C2×C3×Q8—21no—
198C2×C3×Q8D1211yescharacteristic, complemented
199C2×C3×Q8C3×D411yescharacteristic, complemented
200C2×C3×D4—21no—
201C2×C3×D4—21no—
202C2×C3×D4—21no—
203C2×C3×D4—32no—
204C2×C3×D4—41no—
205C2×C3×D4—68no—
206C2×C3×D4—64no—
207C2×C3×D4—61no—
208C2×C3×D4—61no—
209C2×C3×D4—61no—
210C2×C3×D4—61no—
211C2×C3×D4—61no—
212C2×C3×D4—61no—
213C2×C3×D4—61no—
214C2×C3×D4—61no—
215C2×C3×D4—61no—
216C2×C3×D4—61no—
217C2×C3×D4—61no—
218C2×C3×D4—128no—
219C2×C3×D4D1211yescharacteristic, complemented
220C2×C3×D4C3×D411yescharacteristic, complemented
221C22×C3×C4—21no—
222C22×C3×C4—21no—
223C22×C3×C4—21no—
224C22×C3×C4—21no—
225C22×C3×C4—21no—
226C22×C3×C4—41no—
227C22×C3×C4—41no—
228C22×C3×C4C22×D311yescharacteristic
229C22×C3×C4C23×C311yescharacteristic
230C2×#67—24no—
231C2×D12—21no—
232C2×D12—21no—
233C2×D12—21no—
234C2×D12—21no—
235C2×D12—28no—
236C2×D12—21no—
237C2×D12—21no—
238C2×D12—21no—
239C2×D12—21no—
240C2×D12—21no—
241C2×D12—21no—
242C2×D12—21no—
243C2×D12—48no—
244C2×D12C3×D412yescomplemented
245C3×SD16—64no—
246C3×D8—64no—
247C3×M16—22no—
248C3×M16—21no—
249C3×M16—21no—
250C3×M16—21no—
251C3×M16—21no—
252C3×M16—32no—
253C3×M16—41no—
254C3×M16—61no—
255C2×C3×C8—21no—
256C2×C3×C8—21no—
257C2×C3×C8—41no—
258C2×C3×C8—61no—
259C3×C4⋊C4—32no—
260C3×C22⋊C4—64no—
261C3×C22⋊C4—61no—
262C3×C42—21no—
263C3×C42—21no—
264C3×C42—22no—
265C3×C42—41no—
266C3×C42—61no—
267C3×C42#6712yescomplemented
268C3×C42C3×D412yescomplemented
269#217—21no—
270#215—24no—
271#213—24no—
272(C2×D3)⋊C4—24no—
273C4⋊Dic3C3×D412yescomplemented
274C4×Dic3—21no—
275#208—21no—
276#208C3×D412yescomplemented
277C2×C3⋊C8—21no—
278C22×C32—22no—
279C22×C32—41no—
280C22×C32—42no—
281C22×C32#12011yescharacteristic
282C22×C32#12011yescharacteristic
283C22×C32#12111yescharacteristic
284C2×C3×D3—44no—
285C2×C3×D3—44no—
286C2×C3×D3—42no—
287C2×C3×D3—42no—
288C2×C3×D3—44no—
289C2×C3×D3—82no—
290C2×C3×D3—82no—
291C2×C3×D3—82no—
292C32×C4—24no—
293C32×C4—41no—
294C32×C4#12011yescharacteristic
295C32×C4#12111yescharacteristic
296C32×C4#12111yescharacteristic
297C32×C4#12711yescharacteristic
298C3×Dic3—42no—
299C2×#41C2×C3×D311yescharacteristic
300C22×D4—31no—
301C22×D4—31no—
302C22×D4—62no—
303AGL(1,ℤ/8)—62no—
304AGL(1,ℤ/8)—62no—
305C2×SD16—61no—
306C2×D8—61no—
307C2×M16—31no—
308C2×M16C2×C3×D311yescharacteristic
309#127—62no—
310#127—61no—
311#127—62no—
312#124—61no—
313#121—62no—
314#120—62no—
315#117—31no—
316C2×C42C2×C3×D311yescharacteristic
317#104—22no—
318#102—62no—
319#100—62no—
320C23×C3—21no—
321C23×C3—21no—
322C23×C3—21no—
323C23×C3—41no—
324C23×C3—62no—
325C23×C3—62no—
326C23×C3—62no—
327C23×C3—62no—
328C23×C3—124no—
329C23×C3—124no—
330C23×C3—121no—
331C23×C3—121no—
332C23×C3D3×D411yescharacteristic
333C23×C3C2×C3×D411yescharacteristic
334C22×D3—22no—
335C22×D3—22no—
336C22×D3—22no—
337C22×D3—22no—
338C22×D3—44no—
339C22×D3—44no—
340C22×D3—41no—
341C22×D3—41no—
342C3×Q8—22no—
343C3×Q8—21no—
344C3×Q8—21no—
345C3×Q8—21no—
346C3×Q8—21no—
347C3×Q8—41no—
348C3×D4—22no—
349C3×D4—21no—
350C3×D4—21no—
351C3×D4—21no—
352C3×D4—21no—
353C3×D4—41no—
354C3×D4—42no—
355C3×D4—42no—
356C3×D4—41no—
357C3×D4—41no—
358C3×D4—41no—
359C3×D4—41no—
360C3×D4—62no—
361C3×D4—62no—
362C3×D4—1216no—
363C3×D4—121no—
364C3×D4—121no—
365C3×D4—121no—
366C3×D4—121no—
367C3×D4—121no—
368C3×D4—121no—
369C3×D4—244no—
370C2×C3×C4—24no—
371C2×C3×C4—24no—
372C2×C3×C4—22no—
373C2×C3×C4—22no—
374C2×C3×C4—21no—
375C2×C3×C4—21no—
376C2×C3×C4—21no—
377C2×C3×C4—21no—
378C2×C3×C4—21no—
379C2×C3×C4—21no—
380C2×C3×C4—21no—
381C2×C3×C4—21no—
382C2×C3×C4—42no—
383C2×C3×C4—41no—
384C2×C3×C4—44no—
385C2×C3×C4—42no—
386C2×C3×C4—42no—
387C2×C3×C4—41no—
388C2×C3×C4—41no—
389C2×C3×C4—41no—
390C2×C3×C4—41no—
391C2×C3×C4—62no—
392C2×C3×C4C2×D1211yescharacteristic
393C2×C3×C4#23511yescharacteristic
394C2×C3×C4D3×D411yescharacteristic
395C2×C3×C4D3×D411yescharacteristic
396C2×C3×C4D3×D411yescharacteristic
397C2×C3×C4C2×#6711yescharacteristic
398C2×C3×C4C2×C3×D411yescharacteristic
399C2×C3×C4C2×C3×D411yescharacteristic
400C2×C3×C4C2×C3×D411yescharacteristic
401C2×C3×C4C2×C3×D411yescharacteristic
402C2×C3×C4C2×C3×D411yescharacteristic
403C2×C3×C4C3×#4111yescharacteristic
404#67—84no—
405C2×Dic3—22no—
406D12—22no—
407D12—22no—
408D12—416no—
409D12—41no—
410D12—41no—
411D12—41no—
412D12—41no—
413D12—41no—
414D12—41no—
415C3×C8—42no—
416C3×C8—41no—
417C3×C8—41no—
418C3×C8—62no—
419C3⋊C8—22no—
420C2×C32—21no—
421C2×C32—21no—
422C2×C32—81no—
423C2×C32#39211yescharacteristic
424C2×C32#45312yes—
425C3×D3—82no—
426C3×D3—82no—
427C24—32no—
428C24—61no—
429#41—21no—
430#41—21no—
431#41—21no—
432#41—21no—
433C2×Q8C3×D1211yescharacteristic, complemented
434C2×D4—21no—
435C2×D4—32no—
436C2×D4—68no—
437C2×D4—64no—
438C2×D4—61no—
439C2×D4—61no—
440C2×D4—61no—
441C2×D4—61no—
442C2×D4—61no—
443C2×D4—61no—
444C2×D4—61no—
445C2×D4—61no—
446C2×D4—61no—
447C2×D4—61no—
448C2×D4—61no—
449C2×D4—128no—
450C2×D4C3×D1211yescharacteristic, complemented
451C22×C4—21no—
452C22×C4—21no—
453C22×C4C22×C3×D311yescharacteristic
454SD16—64no—
455D8—64no—
456M16—21no—
457M16—21no—
458M16—32no—
459M16—61no—
460C2×C8—21no—
461C2×C8—61no—
462C4⋊C4—32no—
463C22⋊C4—64no—
464C22⋊C4—61no—
465C42—21no—
466C42—61no—
467C42C3×#6712yescomplemented
468C22×C3—22no—
469C22×C3—22no—
470C22×C3—21no—
471C22×C3—21no—
472C22×C3—21no—
473C22×C3—42no—
474C22×C3—42no—
475C22×C3—41no—
476C22×C3—41no—
477C22×C3—42no—
478C22×C3—42no—
479C22×C3—82no—
480C22×C3—124no—
481C22×C3—124no—
482C22×C3—122no—
483C22×C3—122no—
484C22×C3—124no—
485C22×C3—242no—
486C22×C3—242no—
487C22×C3—242no—
488C22×C3#88211yescharacteristic
489C22×C3#88411yescharacteristic
490C22×C3#93711yescharacteristic
491C22×C3C3×#12011yescharacteristic
492C22×C3C3×#12011yescharacteristic
493C22×C3C3×#12111yescharacteristic
494C2×D3—44no—
495C2×D3—44no—
496C2×D3—42no—
497C2×D3—42no—
498C2×D3—44no—
499C2×D3—82no—
500C2×D3—82no—
501C2×D3—82no—
502C3×C4—24no—
503C3×C4—24no—
504C3×C4—21no—
505C3×C4—21no—
506C3×C4—21no—
507C3×C4—21no—
508C3×C4—44no—
509C3×C4—42no—
510C3×C4—41no—
511C3×C4—41no—
512C3×C4—122no—
513C3×C4#88211yescharacteristic
514C3×C4#88411yescharacteristic
515C3×C4#93011yescharacteristic
516C3×C4#94011yescharacteristic
517C3×C4C3×#12011yescharacteristic
518C3×C4C3×#12111yescharacteristic
519C3×C4C3×#12111yescharacteristic
520C3×C4C3×#12711yescharacteristic
521Dic3—42no—
522C32#200211yescharacteristic, complemented, Sylow
523C23—21no—
524C23—62no—
525C23—62no—
526C23—62no—
527C23—62no—
528C23—124no—
529C23—124no—
530C23—121no—
531C23—121no—
532C23C3×D3×D411yescharacteristic
533Q8—21no—
534Q8—21no—
535D4—21no—
536D4—21no—
537D4—41no—
538D4—41no—
539D4—62no—
540D4—62no—
541D4—1216no—
542D4—121no—
543D4—121no—
544D4—121no—
545D4—121no—
546D4—121no—
547D4—121no—
548D4—244no—
549C2×C4—24no—
550C2×C4—22no—
551C2×C4—21no—
552C2×C4—41no—
553C2×C4—41no—
554C2×C4—62no—
555C2×C4C2×C3×D1211yescharacteristic
556C2×C4C3×#23511yescharacteristic
557C2×C4C3×D3×D411yescharacteristic
558C2×C4C3×D3×D411yescharacteristic
559C2×C4C3×D3×D411yescharacteristic
560C2×C4C2×C3×#6711yescharacteristic
561C8—41no—
562C8—62no—
563C2×C3—21no—
564C2×C3—21no—
565C2×C3—21no—
566C2×C3—21no—
567C2×C3—21no—
568C2×C3—22no—
569C2×C3—41no—
570C2×C3—41no—
571C2×C3—82no—
572C2×C3—81no—
573C2×C3—81no—
574C2×C3—242no—
575C2×C3—242no—
576C2×C3#482212yes—
577C2×C3#496011yescharacteristic
578C2×C3C3×#39211yescharacteristic
579C2×C3C3×#45312yes—
580D3—82no—
581D3—82no—
582C22—22no—
583C22—41no—
584C22—42no—
585C22—124no—
586C22—124no—
587C22—122no—
588C22—122no—
589C22—124no—
590C22—242no—
591C22—242no—
592C22—242no—
593C22C3×#88211yescharacteristic
594C22C3×#88411yescharacteristic
595C22C3×#93711yescharacteristic
596C4—24no—
597C4—41no—
598C4—122no—
599C4C3×#88211yescharacteristic
600C4C3×#88411yescharacteristic
601C4C3×#93011yescharacteristic
602C4C3×#94011yescharacteristic
603C3—21no—
604C3#7038511yescharacteristic, direct product factor
605C3C3×#200211yescharacteristic, complemented
606C2—21no—
607C2—21no—
608C2—81no—
609C2—242no—
610C2—242no—
611C2C3×#482212yes—
612C2C3×#496011yescharacteristic
subgroupG/H
centerC22×C3#882
commutator, cosocleC22×C3×C4C23×C3
FrattiniC22×C4C22×C3×D3
FittingC2×C32×#104C2
socleC22×C32#120
hypercenterC2×C3×#104D3
hypocenterC3C3×#2002
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C22×C3×C4 ◁ C2×C3×#104

Complements

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

NH ≅ G/Ntype
1. C3×#5830C2semidirect
2. C2×C3×#949C2semidirect
3. C2×C3×#874C2semidirect
4. C2×C32×#104C2semidirect
5. C3×#5131C2semidirect
6. C2×C3×#823C2semidirect
7. C3×#4523C2semidirect
9. #70385C3direct (N × H)
34. #5830C2×C3semidirect
35. C2×#949C2×C3semidirect
36. C2×#874C2×C3semidirect
38. C2×C3×#104D3semidirect
39. C2×C3×#104C2×C3semidirect
42. #5131C2×C3semidirect
43. C2×#823C2×C3semidirect
45. #4523C2×C3semidirect
52. C2×C32×Q8D4semidirect
54. C2×C32×D4D4semidirect
72. C2×C3×D12D4semidirect
77. C32×C42D4semidirect
82. C3×C4⋊Dic3D4semidirect
85. C3×#208D4semidirect
177. C2×#104C3×D3semidirect
198. C2×C3×Q8D12semidirect
199. C2×C3×Q8C3×D4semidirect
219. C2×C3×D4D12semidirect
220. C2×C3×D4C3×D4semidirect
244. C2×D12C3×D4semidirect
267. C3×C42#67semidirect
268. C3×C42C3×D4semidirect
273. C4⋊Dic3C3×D4semidirect
276. #208C3×D4semidirect
433. C2×Q8C3×D12semidirect
450. C2×D4C3×D12semidirect
467. C42C3×#67semidirect
522. C32#2002semidirect
604. C3#70385direct (N × H)
605. C3C3×#2002semidirect

Maximal subgroups

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

subgroupindex
C3×#58302
C2×C3×#9492
C2×C3×#8742
C2×C32×#1042
C3×#51312
C2×C3×#8232
C3×#45232
C3×#20023
#703853