Finite Group Databasebeta

← C3×#70327 #11784954

Subgroups — C3×#70327 #11784954

Order 1152.

1271 conjugacy classes of subgroups.

The subgroup lattice has 671 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#1004C211yesmaximal, characteristic
2C32×#418C211yesmaximal, characteristic, complemented
3C3×#5215C211yesmaximal, characteristic, complemented
4C3×#5139C211yesmaximal, characteristic, complemented
5C3×#5132C211yesmaximal, characteristic, complemented
6C3×#5006C211yesmaximal, characteristic, complemented
7C3×#5005C211yesmaximal, characteristic, complemented
8C3×#1795—31nomaximal
9#70327C311yesmaximal, characteristic, direct product factor
10C22×C32×D4C2211yescharacteristic
11C22×C3×#67—22no—
12C3×#1004—22no—
13C3×#1004—22no—
14C3×#1004—22no—
15C3×#1004—22no—
16C2×C3×#237—21no—
17C2×C3×#237C412yescomplemented
18C2×C3×D3×D4—21no—
19C2×C3×D3×D4C412yescomplemented
20C2×C3×#235C2211yescharacteristic
21C2×C3×#235C2211yescharacteristic
22C2×C32×M16C2211yescharacteristic, complemented
23C32×#117C2211yescharacteristic, complemented
24C3×#926C2211yescharacteristic, complemented
25C2×C3×#208C2211yescharacteristic, complemented
26C32×#102—22no—
27C3×#832—22no—
28C3×#825—22no—
29C3×#824—21no—
30C3×#823—21no—
31C3×#806—22no—
32C3×#805—22no—
33C2×C3×H(5,𝔽2)—31no—
34C2×#1004C2×C311yescharacteristic
35C3×#421—31no—
36C3×#421—31no—
37C3×#418—21no—
38C3×#418—31no—
39C3×#418D311yescharacteristic, complemented
40C3×#418C2×C311yescharacteristic, complemented
41C3×#413—31no—
42C3×#410—31no—
43#5215C2×C311yescharacteristic, complemented
44#5139C2×C311yescharacteristic, complemented
45#5132C2×C311yescharacteristic, complemented
46#5006C2×C311yescharacteristic, complemented
47#5005C2×C311yescharacteristic, complemented
48C24×C32—21no—
49C23×C3×D3—22no—
50C2×C32×D4—21no—
51C2×C32×D4—21no—
52C2×C32×D4—21no—
53C2×C32×D4C2×C412yes—
54C2×C32×D4D412yes—
55C2×C32×D4D412yes—
56C22×C32×C4C2311yescharacteristic
57C2×C3×#67—28no—
58C2×C3×#67—28no—
59C2×C3×#67—21no—
60C2×C3×#67—22no—
61C2×C3×#67—22no—
62C2×C3×#67D412yes—
63C22×C3×Dic3—22no—
64C3×#237—24no—
65C3×#237—24no—
66C3×#237—24no—
67C3×#237—24no—
68C3×D3×D4—24no—
69C3×D3×D4—24no—
70C3×D3×D4—24no—
71C3×D3×D4—24no—
72C3×#235—21no—
73C3×#235—21no—
74C3×#235—21no—
75C3×#235—21no—
76C3×#235—21no—
77C3×#235—21no—
78C3×#235D412yes—
79C3×#235D412yes—
80C2×C3×D12C2×C411yescharacteristic
81C2×C3×D12D411yescharacteristic
82C2×C3×C4×D3—21no—
83C2×C3×C4×D3C2×C412yes—
84C2×C3×Dic6C2×C411yescharacteristic
85C2×C3×Dic6D411yescharacteristic
86C32×M16—21no—
87C32×M16—21no—
88C2×C32×C8—21no—
89C32×C4⋊C4—21no—
90C32×C22⋊C4—21no—
91C32×C42—21no—
92C3×#217—21no—
93C3×C4⋊Dic3—21no—
94C3×C4×Dic3—21no—
95C3×#208—21no—
96C3×#208—21no—
97C2×C3×C3⋊C8—21no—
98#1795—31noSylow
99C3×H(5,𝔽2)—62no—
100C3×H(5,𝔽2)—62no—
101C3×H(5,𝔽2)—62no—
102C3×H(5,𝔽2)—62no—
103C2×C3×#41—31no—
104C2×C3×#41—32no—
105C2×C3×#41—31no—
106C2×C3×#41—61no—
107C22×C3×D4—21no—
108C22×C3×D4—32no—
109C22×C3×D4—61no—
110C22×C3×D4—62no—
111C22×C3×D4C2×D311yescharacteristic
112C22×C3×D4C22×C311yescharacteristic
113C22×#67—22no—
114#1004—22no—
115#1004—22no—
116#1004—22no—
117#1004—22no—
118C2×#237—21no—
119C2×#237C3×C412yescomplemented
120C2×D3×D4—21no—
121C2×D3×D4C3×C412yescomplemented
122C2×#235C22×C311yescharacteristic
123C2×#235C22×C311yescharacteristic
124C2×C3×M16—21no—
125C2×C3×M16—31no—
126C2×C3×M16C2×D311yescharacteristic, complemented
127C2×C3×M16C22×C311yescharacteristic, complemented
128C3×#117—21no—
129C3×#117—31no—
130C3×#117C2×D311yescharacteristic, complemented
131C3×#117C22×C311yescharacteristic, complemented
132#926C22×C311yescharacteristic, complemented
133C2×#208C22×C311yescharacteristic, complemented
134C3×#104—62no—
135C3×#104—62no—
136C3×#102—24no—
137C3×#102—22no—
138C3×#102—22no—
139C3×#102—62no—
140C3×#101—61no—
141C3×#100—61no—
142C3×#99—62no—
143#832—22no—
144#825—22no—
145#824—21no—
146#823—21no—
147#806—22no—
148#805—22no—
149C23×C32—22no—
150C23×C32—22no—
151C23×C32—22no—
152C23×C32—82no—
153C23×C32C2×D411yescharacteristic
154C22×C3×D3—21no—
155C22×C3×D3—28no—
156C22×C3×D3—84no—
157C22×C3×D3C22⋊C412yes—
158C32×D4—22no—
159C32×D4—22no—
160C32×D4—22no—
161C32×D4C22⋊C414yes—
162C2×C32×C4—41no—
163C2×C32×C4C22×C411yescharacteristic
164C2×C32×C4C2×D411yescharacteristic
165C2×C32×C4C2×D411yescharacteristic
166C2×C32×C4C2×D411yescharacteristic
167C2×C32×C4C2×D411yescharacteristic
168C2×C32×C4C2×D411yescharacteristic
169C3×#67—28no—
170C3×#67—28no—
171C3×#67—22no—
172C3×#67—22no—
173C3×#67—22no—
174C3×#67—22no—
175C2×C3×Dic3—28no—
176C2×C3×Dic3—21no—
177C2×C3×Dic3—41no—
178C2×C3×Dic3C22⋊C412yes—
179C3×D12—21no—
180C3×D12—21no—
181C3×D12—21no—
182C3×D12C22⋊C412yes—
183C3×C4×D3—22no—
184C3×C4×D3—22no—
185C3×C4×D3—22no—
186C3×C4×D3—22no—
187C3×Dic6—21no—
188C3×Dic6—21no—
189C3×Dic6—21no—
190C3×Dic6C22⋊C412yes—
191C32×C8—41no—
192C3×C3⋊C8—41no—
193C2×H(5,𝔽2)—31no—
194#421—31no—
195#421—31no—
196#418—31no—
197#418C3×D311yescharacteristic, complemented
198#413—31no—
199#410—31no—
200C24×C3—21no—
201C24×C3—21no—
202C24×C3—41no—
203C24×C3—62no—
204C23×D3—22no—
205C3×#41—32no—
206C3×#41—32no—
207C3×#41—64no—
208C3×#41—64no—
209C3×#41—64no—
210C3×#41—64no—
211C3×#41—61no—
212C3×#41—61no—
213C3×#41—61no—
214C3×#41—61no—
215C3×#41—61no—
216C3×#41—61no—
217C2×C3×Q8—31no—
218C2×C3×Q8—31no—
219C2×C3×D4—21no—
220C2×C3×D4—21no—
221C2×C3×D4—21no—
222C2×C3×D4—21no—
223C2×C3×D4—21no—
224C2×C3×D4—21no—
225C2×C3×D4—22no—
226C2×C3×D4—22no—
227C2×C3×D4—22no—
228C2×C3×D4—32no—
229C2×C3×D4—31no—
230C2×C3×D4—31no—
231C2×C3×D4—41no—
232C2×C3×D4—41no—
233C2×C3×D4—41no—
234C2×C3×D4—62no—
235C2×C3×D4—64no—
236C2×C3×D4—64no—
237C2×C3×D4—64no—
238C2×C3×D4—62no—
239C2×C3×D4—68no—
240C2×C3×D4—68no—
241C2×C3×D4—61no—
242C2×C3×D4—64no—
243C2×C3×D4C4×D312yes—
244C2×C3×D4D1212yes—
245C2×C3×D4#6712yes—
246C2×C3×D4C2×C3×C412yes—
247C2×C3×D4C3×D412yes—
248C2×C3×D4C3×D412yes—
249C22×C3×C4—21no—
250C22×C3×C4—32no—
251C22×C3×C4—62no—
252C22×C3×C4—61no—
253C22×C3×C4C22×D311yescharacteristic
254C22×C3×C4C23×C311yescharacteristic
255C2×#67—28no—
256C2×#67—28no—
257C2×#67—21no—
258C2×#67—22no—
259C2×#67—22no—
260C2×#67C3×D412yes—
261C22×Dic3—22no—
262#237—24no—
263#237—24no—
264#237—24no—
265#237—24no—
266D3×D4—24no—
267D3×D4—24no—
268D3×D4—24no—
269D3×D4—24no—
270#235—21no—
271#235—21no—
272#235—21no—
273#235—21no—
274#235—21no—
275#235—21no—
276#235C3×D412yes—
277#235C3×D412yes—
278C2×D12C2×C3×C411yescharacteristic
279C2×D12C3×D411yescharacteristic
280C2×C4×D3—21no—
281C2×C4×D3C2×C3×C412yes—
282C2×Dic6C2×C3×C411yescharacteristic
283C2×Dic6C3×D411yescharacteristic
284C3×M16—21no—
285C3×M16—21no—
286C3×M16—21no—
287C3×M16—21no—
288C3×M16—41no—
289C3×M16—41no—
290C3×M16—61no—
291C3×M16—61no—
292C2×C3×C8—22no—
293C2×C3×C8—21no—
294C2×C3×C8—21no—
295C2×C3×C8—61no—
296C3×C4⋊C4—22no—
297C3×C4⋊C4—21no—
298C3×C4⋊C4—21no—
299C3×C4⋊C4—61no—
300C3×C22⋊C4—21no—
301C3×C22⋊C4—21no—
302C3×C22⋊C4—41no—
303C3×C22⋊C4—61no—
304C3×C42—21no—
305C3×C42—21no—
306C3×C42—41no—
307C3×C42—61no—
308#217—21no—
309C4⋊Dic3—21no—
310C4×Dic3—21no—
311#208—21no—
312#208—21no—
313C2×C3⋊C8—21no—
314C22×C32—24no—
315C22×C32—41no—
316C22×C32—44no—
317C22×C32—82no—
318C22×C32—82no—
319C22×C32C2×C22⋊C411yescharacteristic
320C22×C32#12011yescharacteristic
321C22×C32#12011yescharacteristic
322C2×C3×D3—22no—
323C2×C3×D3—22no—
324C2×C3×D3—42no—
325C2×C3×D3—42no—
326C2×C3×D3—88no—
327C32×C4—81no—
328C32×C4C2×C22⋊C411yescharacteristic
329C32×C4C2×C22⋊C411yescharacteristic
330C32×C4#12011yescharacteristic
331C32×C4#12011yescharacteristic
332C3×Dic3—22no—
333C3×Dic3—22no—
334C3×Dic3—81no—
335H(5,𝔽2)—62no—
336H(5,𝔽2)—62no—
337H(5,𝔽2)—62no—
338H(5,𝔽2)—62no—
339C2×#41—31no—
340C2×#41—32no—
341C2×#41—31no—
342C2×#41—61no—
343C22×D4—32no—
344C22×D4—61no—
345C22×D4—62no—
346C22×D4C2×C3×D311yescharacteristic
347C2×M16—31no—
348C2×M16C2×C3×D311yescharacteristic, complemented
349#117—31no—
350#117C2×C3×D311yescharacteristic, complemented
351#104—62no—
352#104—62no—
353#102—22no—
354#102—62no—
355#101—61no—
356#100—61no—
357#99—62no—
358C23×C3—22no—
359C23×C3—22no—
360C23×C3—22no—
361C23×C3—22no—
362C23×C3—22no—
363C23×C3—22no—
364C23×C3—21no—
365C23×C3—32no—
366C23×C3—42no—
367C23×C3—42no—
368C23×C3—42no—
369C23×C3—68no—
370C23×C3—61no—
371C23×C3—82no—
372C23×C3—82no—
373C23×C3—84no—
374C23×C3—244no—
375C23×C3D3×D411yescharacteristic
376C23×C3C2×C3×D411yescharacteristic
377C22×D3—21no—
378C22×D3—28no—
379C22×D3—84no—
380C22×D3C3×C22⋊C412yes—
381C3×Q8—32no—
382C3×Q8—61no—
383C3×Q8—61no—
384C3×Q8—61no—
385C3×D4—22no—
386C3×D4—22no—
387C3×D4—22no—
388C3×D4—22no—
389C3×D4—22no—
390C3×D4—22no—
391C3×D4—24no—
392C3×D4—32no—
393C3×D4—42no—
394C3×D4—42no—
395C3×D4—42no—
396C3×D4—68no—
397C3×D4—68no—
398C3×D4—62no—
399C3×D4—62no—
400C3×D4—62no—
401C3×D4—62no—
402C3×D4—61no—
403C3×D4—61no—
404C3×D4—61no—
405C3×D4(C2×D3)⋊C414yes—
406C3×D4C3×C22⋊C414yes—
407C2×C3×C4—21no—
408C2×C3×C4—21no—
409C2×C3×C4—21no—
410C2×C3×C4—21no—
411C2×C3×C4—21no—
412C2×C3×C4—21no—
413C2×C3×C4—32no—
414C2×C3×C4—42no—
415C2×C3×C4—41no—
416C2×C3×C4—41no—
417C2×C3×C4—68no—
418C2×C3×C4—61no—
419C2×C3×C4—62no—
420C2×C3×C4—62no—
421C2×C3×C4—62no—
422C2×C3×C4—62no—
423C2×C3×C4—121no—
424C2×C3×C4C2×C4×D311yescharacteristic
425C2×C3×C4C2×D1211yescharacteristic
426C2×C3×C4D3×D411yescharacteristic
427C2×C3×C4D3×D411yescharacteristic
428C2×C3×C4D3×D411yescharacteristic
429C2×C3×C4C2×#6711yescharacteristic
430C2×C3×C4C22×C3×C411yescharacteristic
431C2×C3×C4C2×C3×D411yescharacteristic
432C2×C3×C4C2×C3×D411yescharacteristic
433C2×C3×C4C2×C3×D411yescharacteristic
434C2×C3×C4C2×C3×D411yescharacteristic
435C2×C3×C4C2×C3×D411yescharacteristic
436#67—28no—
437#67—28no—
438#67—22no—
439#67—22no—
440#67—22no—
441#67—22no—
442C2×Dic3—28no—
443C2×Dic3—21no—
444C2×Dic3—41no—
445C2×Dic3C3×C22⋊C412yes—
446D12—21no—
447D12—21no—
448D12—21no—
449D12C3×C22⋊C412yes—
450C4×D3—22no—
451C4×D3—22no—
452C4×D3—22no—
453C4×D3—22no—
454Dic6—21no—
455Dic6—21no—
456Dic6—21no—
457Dic6C3×C22⋊C412yes—
458C3×C8—42no—
459C3×C8—41no—
460C3×C8—41no—
461C3×C8—121no—
462C3⋊C8—41no—
463C2×C32—21no—
464C2×C32—21no—
465C2×C32—21no—
466C2×C32—44no—
467C2×C32#37911yescharacteristic
468C3×D3—42no—
469C3×D3—42no—
470C24—21no—
471C24—62no—
472#41—32no—
473#41—32no—
474#41—64no—
475#41—64no—
476#41—64no—
477#41—64no—
478#41—61no—
479#41—61no—
480#41—61no—
481#41—61no—
482#41—61no—
483#41—61no—
484C2×Q8—31no—
485C2×Q8—31no—
486C2×D4—21no—
487C2×D4—21no—
488C2×D4—21no—
489C2×D4—32no—
490C2×D4—31no—
491C2×D4—31no—
492C2×D4—62no—
493C2×D4—64no—
494C2×D4—64no—
495C2×D4—64no—
496C2×D4—62no—
497C2×D4—68no—
498C2×D4—68no—
499C2×D4—61no—
500C2×D4—64no—
501C2×D4C3×C4×D312yes—
502C2×D4C3×D1212yes—
503C2×D4C3×#6712yes—
504C22×C4—32no—
505C22×C4—62no—
506C22×C4—61no—
507C22×C4C22×C3×D311yescharacteristic
508M16—21no—
509M16—21no—
510M16—61no—
511M16—61no—
512C2×C8—21no—
513C2×C8—61no—
514C4⋊C4—21no—
515C4⋊C4—61no—
516C22⋊C4—21no—
517C22⋊C4—61no—
518C42—21no—
519C42—61no—
520C22×C3—24no—
521C22×C3—24no—
522C22×C3—21no—
523C22×C3—21no—
524C22×C3—21no—
525C22×C3—44no—
526C22×C3—41no—
527C22×C3—41no—
528C22×C3—44no—
529C22×C3—42no—
530C22×C3—44no—
531C22×C3—62no—
532C22×C3—62no—
533C22×C3—84no—
534C22×C3—82no—
535C22×C3—82no—
536C22×C3—82no—
537C22×C3—82no—
538C22×C3—84no—
539C22×C3—84no—
540C22×C3—122no—
541C22×C3—122no—
542C22×C3—248no—
543C22×C3D3×C22⋊C411yescharacteristic
544C22×C3#88211yescharacteristic
545C22×C3#93711yescharacteristic
546C22×C3C2×C3×C22⋊C411yescharacteristic
547C22×C3C3×#12011yescharacteristic
548C22×C3C3×#12011yescharacteristic
549C2×D3—22no—
550C2×D3—22no—
551C2×D3—42no—
552C2×D3—42no—
553C2×D3—88no—
554C3×C4—21no—
555C3×C4—21no—
556C3×C4—21no—
557C3×C4—21no—
558C3×C4—62no—
559C3×C4—62no—
560C3×C4—82no—
561C3×C4—81no—
562C3×C4—81no—
563C3×C4—241no—
564C3×C4D3×C22⋊C411yescharacteristic
565C3×C4#88211yescharacteristic
566C3×C4C2×(C2×D3)⋊C411yescharacteristic
567C3×C4#93711yescharacteristic
568C3×C4C2×C3×C22⋊C411yescharacteristic
569C3×C4C2×C3×C22⋊C411yescharacteristic
570C3×C4C3×#12011yescharacteristic
571C3×C4C3×#12011yescharacteristic
572Dic3—22no—
573Dic3—22no—
574Dic3—81no—
575C32#179511yescharacteristic, complemented, Sylow
576C23—22no—
577C23—22no—
578C23—22no—
579C23—32no—
580C23—68no—
581C23—61no—
582C23—82no—
583C23—244no—
584C23C3×D3×D411yescharacteristic
585Q8—32no—
586Q8—61no—
587Q8—61no—
588Q8—61no—
589D4—22no—
590D4—22no—
591D4—22no—
592D4—32no—
593D4—68no—
594D4—68no—
595D4—62no—
596D4—62no—
597D4—62no—
598D4—62no—
599D4—61no—
600D4—61no—
601D4—61no—
602D4C3×(C2×D3)⋊C414yes—
603C2×C4—32no—
604C2×C4—41no—
605C2×C4—68no—
606C2×C4—61no—
607C2×C4—62no—
608C2×C4—62no—
609C2×C4—62no—
610C2×C4—62no—
611C2×C4—121no—
612C2×C4C2×C3×C4×D311yescharacteristic
613C2×C4C2×C3×D1211yescharacteristic
614C2×C4C3×D3×D411yescharacteristic
615C2×C4C3×D3×D411yescharacteristic
616C2×C4C3×D3×D411yescharacteristic
617C2×C4C2×C3×#6711yescharacteristic
618C8—41no—
619C8—121no—
620C2×C3—22no—
621C2×C3—21no—
622C2×C3—21no—
623C2×C3—21no—
624C2×C3—21no—
625C2×C3—21no—
626C2×C3—21no—
627C2×C3—21no—
628C2×C3—41no—
629C2×C3—41no—
630C2×C3—44no—
631C2×C3—44no—
632C2×C3—84no—
633C2×C3—122no—
634C2×C3—122no—
635C2×C3#495511yescharacteristic
636C2×C3C3×#37911yescharacteristic
637D3—42no—
638D3—42no—
639C22—24no—
640C22—41no—
641C22—44no—
642C22—62no—
643C22—62no—
644C22—82no—
645C22—82no—
646C22—122no—
647C22—122no—
648C22—248no—
649C22C3×D3×C22⋊C411yescharacteristic
650C22C3×#88211yescharacteristic
651C22C3×#93711yescharacteristic
652C4—62no—
653C4—62no—
654C4—81no—
655C4—241no—
656C4C3×D3×C22⋊C411yescharacteristic
657C4C3×#88211yescharacteristic
658C4C2×C3×(C2×D3)⋊C411yescharacteristic
659C4C3×#93711yescharacteristic
660C3—21no—
661C3#7032711yescharacteristic, direct product factor
662C3C3×#179511yescharacteristic, complemented
663C2—21no—
664C2—21no—
665C2—21no—
666C2—44no—
667C2—122no—
668C2—122no—
669C2C3×#495511yescharacteristic
subgroupG/H
centerC2×C3#4955
commutatorC2×C3×C4C22×C3×C4
FrattiniC22×C4C22×C3×D3
FittingC32×#418C2
socleC2×C32#379
prime radicalC2×C3×#1004C2
cosocleC22×C3×C4C23×C3
hypercenterC3×#418D3
hypocenterC3C3×#1795
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C3 ◁ C22×C3×C4 ◁ C3×#418

Complements

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

NH ≅ G/Ntype
2. C32×#418C2semidirect
3. C3×#5215C2semidirect
4. C3×#5139C2semidirect
5. C3×#5132C2semidirect
6. C3×#5006C2semidirect
7. C3×#5005C2semidirect
9. #70327C3direct (N × H)
17. C2×C3×#237C4semidirect
19. C2×C3×D3×D4C4semidirect
22. C2×C32×M16C22semidirect
23. C32×#117C22semidirect
24. C3×#926C22semidirect
25. C2×C3×#208C22semidirect
39. C3×#418D3semidirect
40. C3×#418C2×C3semidirect
43. #5215C2×C3semidirect
44. #5139C2×C3semidirect
45. #5132C2×C3semidirect
46. #5006C2×C3semidirect
47. #5005C2×C3semidirect
119. C2×#237C3×C4semidirect
121. C2×D3×D4C3×C4semidirect
126. C2×C3×M16C2×D3semidirect
127. C2×C3×M16C22×C3semidirect
130. C3×#117C2×D3semidirect
131. C3×#117C22×C3semidirect
132. #926C22×C3semidirect
133. C2×#208C22×C3semidirect
197. #418C3×D3semidirect
348. C2×M16C2×C3×D3semidirect
350. #117C2×C3×D3semidirect
575. C32#1795semidirect
661. C3#70327direct (N × H)
662. C3C3×#1795semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#10042
C32×#4182
C3×#52152
C3×#51392
C3×#51322
C3×#50062
C3×#50052
C3×#17953
#703273