Finite Group Databasebeta

← C3×#11068 #10629675

Subgroups — C3×#11068 #10629675

Order 768.

934 conjugacy classes of subgroups.

The subgroup lattice has 626 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#424C211yesmaximal, characteristic, complemented
2C22×C3×#104C211yesmaximal, characteristic
3C2×C3×#416C211yesmaximal, characteristic
4C2×C3×#408C211yesmaximal, characteristic
5C2×C3×#341C211yesmaximal, characteristic, complemented
6C2×C3×#339C211yesmaximal, characteristic, complemented
7C2×C3×#336C211yesmaximal, characteristic, complemented
8#11068C311yesmaximal, characteristic, direct product factor, Sylow
9C22×C3×#41C2211yescharacteristic
10C22×C3×M16C2211yescharacteristic
11C22×C3×M16C2211yescharacteristic
12C23×C3×C8C2211yescharacteristic
13C23×C3×C8C2211yescharacteristic
14C2×C3×#117C2211yescharacteristic
15C22×C3×C42C2211yescharacteristic
16C3×#424—22no—
17C3×#424—22no—
18C2×C3×C4⋊C8—22no—
19C2×C3×#104—22no—
20C2×C3×#104—22no—
21C2×C3×#104—22no—
22C3×#416—22no—
23C3×#416—22no—
24C2×C3×#103C412yescomplemented
25C2×C3×#102C412yescomplemented
26C3×#408—22no—
27C3×#408—22no—
28C2×C3×C22⋊C8—22no—
29C3×#341—22no—
30C3×#339—22no—
31C3×#336—22no—
32C2×#424C2×C311yescharacteristic, complemented
33C22×#104C2×C311yescharacteristic
34C2×#416C2×C311yescharacteristic
35C2×#408C2×C311yescharacteristic
36C2×#341C2×C311yescharacteristic, complemented
37C2×#339C2×C311yescharacteristic, complemented
38C2×#336C2×C311yescharacteristic, complemented
39C2×C3×#41—21no—
40C2×C3×#41—21no—
41C2×C3×#41—21no—
42C2×C3×#41—21no—
43C2×C3×#41—21no—
44C2×C3×#41—21no—
45C2×C3×#41—21no—
46C2×C3×#41—21no—
47C2×C3×#41—21no—
48C2×C3×#41—21no—
49C2×C3×#41D412yes—
50C2×C3×#41Q812yes—
51C22×C3×Q8C2×C411yescharacteristic
52C22×C3×D4—21no—
53C22×C3×D4C2×C411yescharacteristic
54C23×C3×C4—21no—
55C23×C3×C4—21no—
56C23×C3×C4C2311yescharacteristic
57C2×C3×M16—21no—
58C2×C3×M16—21no—
59C2×C3×M16—21no—
60C2×C3×M16—21no—
61C2×C3×M16—21no—
62C2×C3×M16—21no—
63C2×C3×M16—21no—
64C2×C3×M16—21no—
65C2×C3×M16—21no—
66C2×C3×M16—21no—
67C2×C3×M16D412yes—
68C2×C3×M16D412yes—
69C22×C3×C8—21no—
70C22×C3×C8—21no—
71C22×C3×C8—21no—
72C22×C3×C8—21no—
73C22×C3×C8—21no—
74C22×C3×C8—21no—
75C22×C3×C8—21no—
76C22×C3×C8—21no—
77C22×C3×C8—21no—
78C22×C3×C8—21no—
79C22×C3×C8—21no—
80C22×C3×C8—21no—
81C22×C3×C8—21no—
82C22×C3×C8—21no—
83C22×C3×C8C2×C412yes—
84C22×C3×C8D412yes—
85C3×#117—21no—
86C3×#117—21no—
87C3×#117D412yes—
88C3×#117D412yes—
89C2×C3×C4⋊C4C2×C412yes—
90C2×C3×C22⋊C4—21no—
91C2×C3×C42—21no—
92C2×C3×C42—21no—
93C2×C3×C42—21no—
94C2×C3×C42—21no—
95C2×C3×C42—21no—
96C2×C3×C42—21no—
97C2×C3×C42D412yes—
98C3×C4⋊C8—28no—
99C3×#104—28no—
100C3×#103—24no—
101C3×#102—24no—
102C3×C22⋊C8—28no—
103C22×#41C22×C311yescharacteristic
104C22×M16C22×C311yescharacteristic
105C22×M16C22×C311yescharacteristic
106C23×C8C22×C311yescharacteristic
107C23×C8C22×C311yescharacteristic
108C2×#117C22×C311yescharacteristic
109C22×C42C22×C311yescharacteristic
110#424—22no—
111#424—22no—
112C2×C4⋊C8—22no—
113C2×#104—22no—
114C2×#104—22no—
115C2×#104—22no—
116#416—22no—
117#416—22no—
118C2×#103C3×C412yescomplemented
119C2×#102C3×C412yescomplemented
120#408—22no—
121#408—22no—
122C2×C22⋊C8—22no—
123#341—22no—
124#339—22no—
125#336—22no—
126C24×C3—21no—
127C24×C3#4111yescharacteristic
128C3×#41—22no—
129C3×#41—22no—
130C3×#41—22no—
131C3×#41—22no—
132C3×#41—22no—
133C3×#41—22no—
134C3×#41—22no—
135C3×#41—22no—
136C3×#41—41no—
137C3×#41—41no—
138C3×#41—41no—
139C3×#41—41no—
140C3×#41—41no—
141C3×#41—41no—
142C3×#41—41no—
143C3×#41—41no—
144C2×C3×Q8—21no—
145C2×C3×Q8—21no—
146C2×C3×Q8—21no—
147C2×C3×Q8—21no—
148C2×C3×Q8—21no—
149C2×C3×Q8C4⋊C412yes—
150C2×C3×D4—22no—
151C2×C3×D4—22no—
152C2×C3×D4—21no—
153C2×C3×D4—21no—
154C2×C3×D4—21no—
155C2×C3×D4—21no—
156C2×C3×D4—21no—
157C2×C3×D4—41no—
158C2×C3×D4—41no—
159C2×C3×D4—41no—
160C2×C3×D4—41no—
161C2×C3×D4C4⋊C412yes—
162C22×C3×C4—24no—
163C22×C3×C4—22no—
164C22×C3×C4—21no—
165C22×C3×C4—22no—
166C22×C3×C4—22no—
167C22×C3×C4—22no—
168C22×C3×C4—42no—
169C22×C3×C4—41no—
170C22×C3×C4—41no—
171C22×C3×C4—41no—
172C22×C3×C4—41no—
173C22×C3×C4—41no—
174C22×C3×C4—41no—
175C22×C3×C4C22×C411yescharacteristic
176C22×C3×C4C2×D411yescharacteristic
177C22×C3×C4C2×D411yescharacteristic
178C22×C3×C4C2×D411yescharacteristic
179C22×C3×C4C2×D411yescharacteristic
180C22×C3×C4C2×D411yescharacteristic
181C22×C3×C4C2×D411yescharacteristic
182C22×C3×C4C2×D411yescharacteristic
183C22×C3×C4C2×Q811yescharacteristic
184C22×C3×C4#4111yescharacteristic
185C22×C3×C4#4111yescharacteristic
186C22×C3×C4#4111yescharacteristic
187C22×C3×C4#4111yescharacteristic
188C22×C3×C4#4111yescharacteristic
189C3×M16—22no—
190C3×M16—22no—
191C3×M16—22no—
192C3×M16—22no—
193C3×M16—41no—
194C3×M16—41no—
195C3×M16—41no—
196C3×M16—41no—
197C2×C3×C8—22no—
198C2×C3×C8—22no—
199C2×C3×C8—22no—
200C2×C3×C8—22no—
201C2×C3×C8—22no—
202C2×C3×C8—22no—
203C2×C3×C8—22no—
204C2×C3×C8—22no—
205C2×C3×C8—41no—
206C2×C3×C8—41no—
207C2×C3×C8—41no—
208C2×C3×C8—41no—
209C2×C3×C8—41no—
210C2×C3×C8—41no—
211C2×C3×C8—41no—
212C2×C3×C8—41no—
213C2×C3×C8—41no—
214C2×C3×C8—41no—
215C2×C3×C8—41no—
216C2×C3×C8—41no—
217C3×C4⋊C4—22no—
218C3×C4⋊C4C22⋊C414yes—
219C3×C22⋊C4—22no—
220C3×C22⋊C4—22no—
221C3×C42—22no—
222C3×C42—22no—
223C3×C42—22no—
224C3×C42—22no—
225C3×C42—41no—
226C3×C42—41no—
227C2×#41—21no—
228C2×#41—21no—
229C2×#41—21no—
230C2×#41—21no—
231C2×#41—21no—
232C2×#41—21no—
233C2×#41—21no—
234C2×#41—21no—
235C2×#41—21no—
236C2×#41—21no—
237C2×#41C3×D412yes—
238C2×#41C3×Q812yes—
239C22×Q8C2×C3×C411yescharacteristic
240C22×D4—21no—
241C22×D4C2×C3×C411yescharacteristic
242C23×C4—21no—
243C23×C4—21no—
244C23×C4C23×C311yescharacteristic
245C2×M16—21no—
246C2×M16—21no—
247C2×M16—21no—
248C2×M16—21no—
249C2×M16—21no—
250C2×M16—21no—
251C2×M16—21no—
252C2×M16—21no—
253C2×M16—21no—
254C2×M16—21no—
255C2×M16C3×D412yes—
256C2×M16C3×D412yes—
257C22×C8—21no—
258C22×C8—21no—
259C22×C8—21no—
260C22×C8—21no—
261C22×C8—21no—
262C22×C8—21no—
263C22×C8—21no—
264C22×C8—21no—
265C22×C8—21no—
266C22×C8—21no—
267C22×C8—21no—
268C22×C8—21no—
269C22×C8—21no—
270C22×C8—21no—
271C22×C8C2×C3×C412yes—
272C22×C8C3×D412yes—
273#117—21no—
274#117—21no—
275#117C3×D412yes—
276#117C3×D412yes—
277C2×C4⋊C4C2×C3×C412yes—
278C2×C22⋊C4—21no—
279C2×C42—21no—
280C2×C42—21no—
281C2×C42—21no—
282C2×C42—21no—
283C2×C42—21no—
284C2×C42—21no—
285C2×C42C3×D412yes—
286C4⋊C8—28no—
287#104—28no—
288#103—24no—
289#102—24no—
290C22⋊C8—28no—
291C23×C3—22no—
292C23×C3—22no—
293C23×C3—22no—
294C23×C3—41no—
295C23×C3—41no—
296C23×C3—42no—
297C23×C3—42no—
298C23×C3C4×D411yescharacteristic
299C23×C3#12111yescharacteristic
300C23×C3C22⋊Q811yescharacteristic
301C23×C3#12311yescharacteristic
302C23×C3#12311yescharacteristic
303C23×C3#12311yescharacteristic
304C23×C3#12611yescharacteristic
305C3×Q8—22no—
306C3×Q8—22no—
307C3×Q8—41no—
308C3×Q8—41no—
309C3×D4—22no—
310C3×D4—22no—
311C3×D4—42no—
312C3×D4—42no—
313C3×D4—42no—
314C3×D4—42no—
315C3×D4—41no—
316C3×D4—41no—
317C2×C3×C4—24no—
318C2×C3×C4—22no—
319C2×C3×C4—24no—
320C2×C3×C4—44no—
321C2×C3×C4—44no—
322C2×C3×C4—42no—
323C2×C3×C4—41no—
324C2×C3×C4—41no—
325C2×C3×C4—42no—
326C2×C3×C4—42no—
327C2×C3×C4—42no—
328C2×C3×C4—42no—
329C2×C3×C4—42no—
330C2×C3×C4—42no—
331C2×C3×C4—42no—
332C2×C3×C4C2×C22⋊C411yescharacteristic
333C2×C3×C4C2×C4⋊C411yescharacteristic
334C2×C3×C4#11711yescharacteristic
335C2×C3×C4C4×D411yescharacteristic
336C2×C3×C4C4×D411yescharacteristic
337C2×C3×C4C4×D411yescharacteristic
338C2×C3×C4#12011yescharacteristic
339C2×C3×C4#12011yescharacteristic
340C2×C3×C4#12011yescharacteristic
341C2×C3×C4#12111yescharacteristic
342C2×C3×C4#12111yescharacteristic
343C2×C3×C4#12111yescharacteristic
344C2×C3×C4#12111yescharacteristic
345C2×C3×C4#12111yescharacteristic
346C2×C3×C4#12111yescharacteristic
347C2×C3×C4#12111yescharacteristic
348C2×C3×C4C22⋊Q811yescharacteristic
349C2×C3×C4C22⋊Q811yescharacteristic
350C2×C3×C4C22⋊Q811yescharacteristic
351C2×C3×C4C22⋊Q811yescharacteristic
352C2×C3×C4C22⋊Q811yescharacteristic
353C2×C3×C4#12311yescharacteristic
354C2×C3×C4#12311yescharacteristic
355C2×C3×C4#12411yescharacteristic
356C2×C3×C4#12411yescharacteristic
357C2×C3×C4#12411yescharacteristic
358C2×C3×C4#12611yescharacteristic
359C2×C3×C4#12711yescharacteristic
360C3×C8—42no—
361C3×C8—42no—
362C3×C8—42no—
363C3×C8—42no—
364C24—21no—
365C24C3×#4111yescharacteristic
366#41—22no—
367#41—22no—
368#41—22no—
369#41—22no—
370#41—22no—
371#41—22no—
372#41—22no—
373#41—22no—
374#41—41no—
375#41—41no—
376#41—41no—
377#41—41no—
378#41—41no—
379#41—41no—
380#41—41no—
381#41—41no—
382C2×Q8—21no—
383C2×Q8—21no—
384C2×Q8—21no—
385C2×Q8—21no—
386C2×Q8—21no—
387C2×Q8C3×C4⋊C412yes—
388C2×D4—22no—
389C2×D4—22no—
390C2×D4—21no—
391C2×D4—21no—
392C2×D4—21no—
393C2×D4—21no—
394C2×D4—21no—
395C2×D4—41no—
396C2×D4—41no—
397C2×D4—41no—
398C2×D4—41no—
399C2×D4C3×C4⋊C412yes—
400C22×C4—24no—
401C22×C4—22no—
402C22×C4—21no—
403C22×C4—22no—
404C22×C4—22no—
405C22×C4—22no—
406C22×C4—42no—
407C22×C4—41no—
408C22×C4—41no—
409C22×C4—41no—
410C22×C4—41no—
411C22×C4—41no—
412C22×C4—41no—
413C22×C4C22×C3×C411yescharacteristic
414C22×C4C2×C3×D411yescharacteristic
415C22×C4C2×C3×D411yescharacteristic
416C22×C4C2×C3×D411yescharacteristic
417C22×C4C2×C3×D411yescharacteristic
418C22×C4C2×C3×D411yescharacteristic
419C22×C4C2×C3×D411yescharacteristic
420C22×C4C2×C3×D411yescharacteristic
421C22×C4C2×C3×Q811yescharacteristic
422C22×C4C3×#4111yescharacteristic
423C22×C4C3×#4111yescharacteristic
424C22×C4C3×#4111yescharacteristic
425C22×C4C3×#4111yescharacteristic
426C22×C4C3×#4111yescharacteristic
427M16—22no—
428M16—22no—
429M16—22no—
430M16—22no—
431M16—41no—
432M16—41no—
433M16—41no—
434M16—41no—
435C2×C8—22no—
436C2×C8—22no—
437C2×C8—22no—
438C2×C8—22no—
439C2×C8—22no—
440C2×C8—22no—
441C2×C8—22no—
442C2×C8—22no—
443C2×C8—41no—
444C2×C8—41no—
445C2×C8—41no—
446C2×C8—41no—
447C2×C8—41no—
448C2×C8—41no—
449C2×C8—41no—
450C2×C8—41no—
451C2×C8—41no—
452C2×C8—41no—
453C2×C8—41no—
454C2×C8—41no—
455C4⋊C4—22no—
456C4⋊C4C3×C22⋊C414yes—
457C22⋊C4—22no—
458C22⋊C4—22no—
459C42—22no—
460C42—22no—
461C42—22no—
462C42—22no—
463C42—41no—
464C42—41no—
465C22×C3—22no—
466C22×C3—22no—
467C22×C3—22no—
468C22×C3—22no—
469C22×C3—21no—
470C22×C3—21no—
471C22×C3—21no—
472C22×C3—21no—
473C22×C3—44no—
474C22×C3—42no—
475C22×C3—82no—
476C22×C3—81no—
477C22×C3—81no—
478C22×C3#38511yescharacteristic
479C22×C3#38611yescharacteristic
480C22×C3#38811yescharacteristic
481C22×C3#39411yescharacteristic
482C22×C3#39611yescharacteristic
483C22×C3#39711yescharacteristic
484C22×C3#39911yescharacteristic
485C22×C3#44312yes—
486C22×C3#44412yes—
487C3×C4—44no—
488C3×C4—44no—
489C3×C4—42no—
490C3×C4#38011yescharacteristic
491C3×C4#38511yescharacteristic
492C3×C4#38811yescharacteristic
493C3×C4#39011yescharacteristic
494C3×C4#39211yescharacteristic
495C3×C4#39311yescharacteristic
496C3×C4#39411yescharacteristic
497C3×C4#39611yescharacteristic
498C23—22no—
499C23—22no—
500C23—22no—
501C23—41no—
502C23—41no—
503C23—42no—
504C23—42no—
505C23C3×C4×D411yescharacteristic
506C23C3×#12111yescharacteristic
507C23C3×C22⋊Q811yescharacteristic
508C23C3×#12311yescharacteristic
509C23C3×#12311yescharacteristic
510C23C3×#12311yescharacteristic
511C23C3×#12611yescharacteristic
512Q8—22no—
513Q8—22no—
514Q8—41no—
515Q8—41no—
516D4—22no—
517D4—22no—
518D4—42no—
519D4—42no—
520D4—42no—
521D4—42no—
522D4—41no—
523D4—41no—
524C2×C4—24no—
525C2×C4—22no—
526C2×C4—24no—
527C2×C4—44no—
528C2×C4—44no—
529C2×C4—42no—
530C2×C4—41no—
531C2×C4—41no—
532C2×C4—42no—
533C2×C4—42no—
534C2×C4—42no—
535C2×C4—42no—
536C2×C4—42no—
537C2×C4—42no—
538C2×C4—42no—
539C2×C4C2×C3×C22⋊C411yescharacteristic
540C2×C4C2×C3×C4⋊C411yescharacteristic
541C2×C4C3×#11711yescharacteristic
542C2×C4C3×C4×D411yescharacteristic
543C2×C4C3×C4×D411yescharacteristic
544C2×C4C3×C4×D411yescharacteristic
545C2×C4C3×#12011yescharacteristic
546C2×C4C3×#12011yescharacteristic
547C2×C4C3×#12011yescharacteristic
548C2×C4C3×#12111yescharacteristic
549C2×C4C3×#12111yescharacteristic
550C2×C4C3×#12111yescharacteristic
551C2×C4C3×#12111yescharacteristic
552C2×C4C3×#12111yescharacteristic
553C2×C4C3×#12111yescharacteristic
554C2×C4C3×#12111yescharacteristic
555C2×C4C3×C22⋊Q811yescharacteristic
556C2×C4C3×C22⋊Q811yescharacteristic
557C2×C4C3×C22⋊Q811yescharacteristic
558C2×C4C3×C22⋊Q811yescharacteristic
559C2×C4C3×C22⋊Q811yescharacteristic
560C2×C4C3×#12311yescharacteristic
561C2×C4C3×#12311yescharacteristic
562C2×C4C3×#12411yescharacteristic
563C2×C4C3×#12411yescharacteristic
564C2×C4C3×#12411yescharacteristic
565C2×C4C3×#12611yescharacteristic
566C2×C4C3×#12711yescharacteristic
567C8—42no—
568C8—42no—
569C8—42no—
570C8—42no—
571C2×C3—21no—
572C2×C3—21no—
573C2×C3—21no—
574C2×C3—21no—
575C2×C3—82no—
576C2×C3#143911yescharacteristic
577C2×C3#186612yes—
578C2×C3#187612yes—
579C2×C3#193711yescharacteristic
580C2×C3#193811yescharacteristic
581C22—22no—
582C22—22no—
583C22—22no—
584C22—22no—
585C22—21no—
586C22—21no—
587C22—21no—
588C22—21no—
589C22—44no—
590C22—42no—
591C22—82no—
592C22—81no—
593C22—81no—
594C22C3×#38511yescharacteristic
595C22C3×#38611yescharacteristic
596C22C3×#38811yescharacteristic
597C22C3×#39411yescharacteristic
598C22C3×#39611yescharacteristic
599C22C3×#39711yescharacteristic
600C22C3×#39911yescharacteristic
601C22C3×#44312yes—
602C22C3×#44412yes—
603C4—44no—
604C4—44no—
605C4—42no—
606C4C3×#38011yescharacteristic
607C4C3×#38511yescharacteristic
608C4C3×#38811yescharacteristic
609C4C3×#39011yescharacteristic
610C4C3×#39211yescharacteristic
611C4C3×#39311yescharacteristic
612C4C3×#39411yescharacteristic
613C4C3×#39611yescharacteristic
614C3#1106811yescharacteristic, direct product factor, Sylow
615C2—21no—
616C2—21no—
617C2—21no—
618C2—21no—
619C2—82no—
620C2C3×#143911yescharacteristic
621C2C3×#186612yes—
622C2C3×#187612yes—
623C2C3×#193711yescharacteristic
624C2C3×#193811yescharacteristic
subgroupG/H
centerC22×C3×C4C2×D4
commutatorC22×C4C22×C3×C4
Frattini, cosocleC23×C4C23×C3
socleC23×C3C4×D4
prime radicalC22×C3×#41C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C3×C4 ◁ C23×C3×C8 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C3×#424C2semidirect
5. C2×C3×#341C2semidirect
6. C2×C3×#339C2semidirect
7. C2×C3×#336C2semidirect
8. #11068C3direct (N × H)
24. C2×C3×#103C4semidirect
25. C2×C3×#102C4semidirect
32. C2×#424C2×C3semidirect
36. C2×#341C2×C3semidirect
37. C2×#339C2×C3semidirect
38. C2×#336C2×C3semidirect
118. C2×#103C3×C4semidirect
119. C2×#102C3×C4semidirect
614. C3#11068direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#4242
C22×C3×#1042
C2×C3×#4162
C2×C3×#4082
C2×C3×#3412
C2×C3×#3392
C2×C3×#3362
#110683