Finite Group Databasebeta

← C3×#11062 #10629669

Subgroups — C3×#11062 #10629669

Order 768.

878 conjugacy classes of subgroups.

The subgroup lattice has 572 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#424C211yesmaximal, characteristic
2C2×C3×#419C211yesmaximal, characteristic
3C22×C3×#103C211yesmaximal, characteristic
4C22×C3×#101C211yesmaximal, characteristic
5C2×C3×#343C211yesmaximal, characteristic
6C2×C3×#341C211yesmaximal, characteristic
7C3×#1736C211yesmaximal, characteristic
8#11062C311yesmaximal, characteristic, direct product factor, Sylow
9C23×C3×Q8C2211yescharacteristic
10C22×C3×M16C2211yescharacteristic
11C22×C3×M16C2211yescharacteristic
12C22×C3×M16C2211yescharacteristic
13C23×C3×C8C2211yescharacteristic
14C2×C3×#117C2211yescharacteristic
15C22×C3×C4⋊C4C2211yescharacteristic
16C3×#424—22no—
17C3×#424—22no—
18C2×C3×C4⋊C8—22no—
19C3×#419—22no—
20C3×#419C414yescomplemented
21C2×C3×#103—22no—
22C2×C3×#103—22no—
23C2×C3×#103—22no—
24C2×C3×#103—22no—
25C2×C3×#101—22no—
26C2×C3×#101—22no—
27C2×C3×#101—22no—
28C3×#343—22no—
29C3×#341—22no—
30C3×#340—22no—
31C2×#424C2×C311yescharacteristic
32C2×#419C2×C311yescharacteristic
33C22×#103C2×C311yescharacteristic
34C22×#101C2×C311yescharacteristic
35C2×#343C2×C311yescharacteristic
36C2×#341C2×C311yescharacteristic
37#1736C2×C311yescharacteristic
38C22×C3×Q8—21no—
39C22×C3×Q8—21no—
40C22×C3×Q8—21no—
41C22×C3×Q8—21no—
42C22×C3×Q8—21no—
43C22×C3×Q8—21no—
44C22×C3×Q8—21no—
45C22×C3×Q8—21no—
46C22×C3×Q8—21no—
47C22×C3×Q8—21no—
48C22×C3×Q8—21no—
49C22×C3×Q8C2×C412yes—
50C22×C3×Q8D412yes—
51C22×C3×Q8Q812yes—
52C23×C3×C4—21no—
53C23×C3×C4—21no—
54C23×C3×C4C2311yescharacteristic
55C2×C3×M16—21no—
56C2×C3×M16—21no—
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×M16—21no—
68C2×C3×M16—21no—
69C2×C3×M16—21no—
70C2×C3×M16C2×C412yes—
71C2×C3×M16D412yes—
72C2×C3×M16D412yes—
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×C8D412yes—
83C3×#117—21no—
84C3×#117—21no—
85C3×#117C2×C412yes—
86C3×#117D412yes—
87C2×C3×C4⋊C4—21no—
88C2×C3×C4⋊C4—21no—
89C2×C3×C4⋊C4—21no—
90C2×C3×C4⋊C4—21no—
91C2×C3×C4⋊C4—21no—
92C2×C3×C4⋊C4D412yes—
93C2×C3×C4⋊C4D412yes—
94C2×C3×C22⋊C4—21no—
95C2×C3×C42—21no—
96C3×C4⋊C8—28no—
97C3×#103—28no—
98C3×#103—28no—
99C3×#101—28no—
100C23×Q8C22×C311yescharacteristic
101C22×M16C22×C311yescharacteristic
102C22×M16C22×C311yescharacteristic
103C22×M16C22×C311yescharacteristic
104C23×C8C22×C311yescharacteristic
105C2×#117C22×C311yescharacteristic
106C22×C4⋊C4C22×C311yescharacteristic
107#424—22no—
108#424—22no—
109C2×C4⋊C8—22no—
110#419—22no—
111#419C3×C414yescomplemented
112C2×#103—22no—
113C2×#103—22no—
114C2×#103—22no—
115C2×#103—22no—
116C2×#101—22no—
117C2×#101—22no—
118C2×#101—22no—
119#343—22no—
120#341—22no—
121#340—22no—
122C24×C3#4111yescharacteristic
123C2×C3×Q8—22no—
124C2×C3×Q8—22no—
125C2×C3×Q8—22no—
126C2×C3×Q8—22no—
127C2×C3×Q8—22no—
128C2×C3×Q8—22no—
129C2×C3×Q8—22no—
130C2×C3×Q8—22no—
131C2×C3×Q8—22no—
132C2×C3×Q8—22no—
133C2×C3×Q8—22no—
134C2×C3×Q8—22no—
135C2×C3×Q8—22no—
136C2×C3×Q8—22no—
137C2×C3×Q8—22no—
138C2×C3×Q8—41no—
139C2×C3×Q8—41no—
140C2×C3×Q8—41no—
141C2×C3×Q8—41no—
142C2×C3×Q8—41no—
143C2×C3×Q8—41no—
144C2×C3×Q8—41no—
145C2×C3×Q8—41no—
146C2×C3×Q8—41no—
147C2×C3×Q8—41no—
148C2×C3×Q8—41no—
149C2×C3×Q8—41no—
150C2×C3×Q8C4⋊C414yes—
151C22×C3×C4—22no—
152C22×C3×C4—22no—
153C22×C3×C4—22no—
154C22×C3×C4—22no—
155C22×C3×C4—22no—
156C22×C3×C4—41no—
157C22×C3×C4—41no—
158C22×C3×C4—41no—
159C22×C3×C4—41no—
160C22×C3×C4—41no—
161C22×C3×C4—41no—
162C22×C3×C4—82no—
163C22×C3×C4C22×C411yescharacteristic
164C22×C3×C4C2×D411yescharacteristic
165C22×C3×C4C2×D411yescharacteristic
166C22×C3×C4C2×D411yescharacteristic
167C22×C3×C4C2×D411yescharacteristic
168C22×C3×C4C2×D411yescharacteristic
169C22×C3×C4C2×D411yescharacteristic
170C22×C3×C4C2×D411yescharacteristic
171C22×C3×C4C2×Q811yescharacteristic
172C22×C3×C4#4111yescharacteristic
173C22×C3×C4#4111yescharacteristic
174C22×C3×C4#4111yescharacteristic
175C22×C3×C4#4111yescharacteristic
176C22×C3×C4#4111yescharacteristic
177C3×M16—22no—
178C3×M16—22no—
179C3×M16—22no—
180C3×M16—22no—
181C3×M16—22no—
182C3×M16—22no—
183C3×M16—41no—
184C3×M16—41no—
185C3×M16—41no—
186C3×M16—41no—
187C3×M16—41no—
188C3×M16—41no—
189C2×C3×C8—22no—
190C2×C3×C8—22no—
191C2×C3×C8—22no—
192C2×C3×C8—22no—
193C2×C3×C8—22no—
194C2×C3×C8—22no—
195C2×C3×C8—41no—
196C2×C3×C8—41no—
197C2×C3×C8—41no—
198C2×C3×C8—41no—
199C2×C3×C8—41no—
200C2×C3×C8—41no—
201C2×C3×C8—41no—
202C2×C3×C8—41no—
203C2×C3×C8—41no—
204C2×C3×C8—41no—
205C3×C4⋊C4—22no—
206C3×C4⋊C4—22no—
207C3×C4⋊C4—22no—
208C3×C4⋊C4—41no—
209C3×C4⋊C4—41no—
210C3×C4⋊C4C22⋊C414yes—
211C3×C22⋊C4—22no—
212C3×C22⋊C4—22no—
213C3×C42—22no—
214C3×C42—22no—
215C22×Q8—21no—
216C22×Q8—21no—
217C22×Q8—21no—
218C22×Q8—21no—
219C22×Q8—21no—
220C22×Q8—21no—
221C22×Q8—21no—
222C22×Q8—21no—
223C22×Q8—21no—
224C22×Q8—21no—
225C22×Q8—21no—
226C22×Q8C2×C3×C412yes—
227C22×Q8C3×D412yes—
228C22×Q8C3×Q812yes—
229C23×C4—21no—
230C23×C4—21no—
231C23×C4C23×C311yescharacteristic
232C2×M16—21no—
233C2×M16—21no—
234C2×M16—21no—
235C2×M16—21no—
236C2×M16—21no—
237C2×M16—21no—
238C2×M16—21no—
239C2×M16—21no—
240C2×M16—21no—
241C2×M16—21no—
242C2×M16—21no—
243C2×M16—21no—
244C2×M16—21no—
245C2×M16—21no—
246C2×M16—21no—
247C2×M16C2×C3×C412yes—
248C2×M16C3×D412yes—
249C2×M16C3×D412yes—
250C22×C8—21no—
251C22×C8—21no—
252C22×C8—21no—
253C22×C8—21no—
254C22×C8—21no—
255C22×C8—21no—
256C22×C8—21no—
257C22×C8—21no—
258C22×C8—21no—
259C22×C8C3×D412yes—
260#117—21no—
261#117—21no—
262#117C2×C3×C412yes—
263#117C3×D412yes—
264C2×C4⋊C4—21no—
265C2×C4⋊C4—21no—
266C2×C4⋊C4—21no—
267C2×C4⋊C4—21no—
268C2×C4⋊C4—21no—
269C2×C4⋊C4C3×D412yes—
270C2×C4⋊C4C3×D412yes—
271C2×C22⋊C4—21no—
272C2×C42—21no—
273C4⋊C8—28no—
274#103—28no—
275#103—28no—
276#101—28no—
277C23×C3—22no—
278C23×C3—22no—
279C23×C3C4×D411yescharacteristic
280C23×C3#12111yescharacteristic
281C23×C3C22⋊Q811yescharacteristic
282C23×C3#12311yescharacteristic
283C23×C3#12311yescharacteristic
284C23×C3#12311yescharacteristic
285C23×C3#12611yescharacteristic
286C3×Q8—24no—
287C3×Q8—24no—
288C3×Q8—42no—
289C3×Q8—42no—
290C3×Q8—42no—
291C3×Q8—42no—
292C3×Q8—42no—
293C3×Q8—42no—
294C2×C3×C4—24no—
295C2×C3×C4—24no—
296C2×C3×C4—42no—
297C2×C3×C4—42no—
298C2×C3×C4—42no—
299C2×C3×C4—42no—
300C2×C3×C4—42no—
301C2×C3×C4—42no—
302C2×C3×C4—42no—
303C2×C3×C4—42no—
304C2×C3×C4—42no—
305C2×C3×C4—82no—
306C2×C3×C4—82no—
307C2×C3×C4—82no—
308C2×C3×C4C2×C22⋊C411yescharacteristic
309C2×C3×C4C2×C4⋊C411yescharacteristic
310C2×C3×C4#11711yescharacteristic
311C2×C3×C4C4×D411yescharacteristic
312C2×C3×C4C4×D411yescharacteristic
313C2×C3×C4C4×D411yescharacteristic
314C2×C3×C4#12011yescharacteristic
315C2×C3×C4#12011yescharacteristic
316C2×C3×C4#12011yescharacteristic
317C2×C3×C4#12111yescharacteristic
318C2×C3×C4#12111yescharacteristic
319C2×C3×C4#12111yescharacteristic
320C2×C3×C4#12111yescharacteristic
321C2×C3×C4#12111yescharacteristic
322C2×C3×C4#12111yescharacteristic
323C2×C3×C4#12111yescharacteristic
324C2×C3×C4C22⋊Q811yescharacteristic
325C2×C3×C4C22⋊Q811yescharacteristic
326C2×C3×C4C22⋊Q811yescharacteristic
327C2×C3×C4C22⋊Q811yescharacteristic
328C2×C3×C4C22⋊Q811yescharacteristic
329C2×C3×C4#12311yescharacteristic
330C2×C3×C4#12311yescharacteristic
331C2×C3×C4#12411yescharacteristic
332C2×C3×C4#12411yescharacteristic
333C2×C3×C4#12411yescharacteristic
334C2×C3×C4#12611yescharacteristic
335C2×C3×C4#12711yescharacteristic
336C3×C8—42no—
337C3×C8—42no—
338C3×C8—42no—
339C3×C8—42no—
340C24C3×#4111yescharacteristic
341C2×Q8—22no—
342C2×Q8—22no—
343C2×Q8—22no—
344C2×Q8—22no—
345C2×Q8—22no—
346C2×Q8—22no—
347C2×Q8—22no—
348C2×Q8—22no—
349C2×Q8—22no—
350C2×Q8—22no—
351C2×Q8—22no—
352C2×Q8—22no—
353C2×Q8—22no—
354C2×Q8—22no—
355C2×Q8—22no—
356C2×Q8—41no—
357C2×Q8—41no—
358C2×Q8—41no—
359C2×Q8—41no—
360C2×Q8—41no—
361C2×Q8—41no—
362C2×Q8—41no—
363C2×Q8—41no—
364C2×Q8—41no—
365C2×Q8—41no—
366C2×Q8—41no—
367C2×Q8—41no—
368C2×Q8C3×C4⋊C414yes—
369C22×C4—22no—
370C22×C4—22no—
371C22×C4—22no—
372C22×C4—22no—
373C22×C4—22no—
374C22×C4—41no—
375C22×C4—41no—
376C22×C4—41no—
377C22×C4—41no—
378C22×C4—41no—
379C22×C4—41no—
380C22×C4—82no—
381C22×C4C22×C3×C411yescharacteristic
382C22×C4C2×C3×D411yescharacteristic
383C22×C4C2×C3×D411yescharacteristic
384C22×C4C2×C3×D411yescharacteristic
385C22×C4C2×C3×D411yescharacteristic
386C22×C4C2×C3×D411yescharacteristic
387C22×C4C2×C3×D411yescharacteristic
388C22×C4C2×C3×D411yescharacteristic
389C22×C4C2×C3×Q811yescharacteristic
390C22×C4C3×#4111yescharacteristic
391C22×C4C3×#4111yescharacteristic
392C22×C4C3×#4111yescharacteristic
393C22×C4C3×#4111yescharacteristic
394C22×C4C3×#4111yescharacteristic
395M16—22no—
396M16—22no—
397M16—22no—
398M16—22no—
399M16—22no—
400M16—22no—
401M16—41no—
402M16—41no—
403M16—41no—
404M16—41no—
405M16—41no—
406M16—41no—
407C2×C8—22no—
408C2×C8—22no—
409C2×C8—22no—
410C2×C8—22no—
411C2×C8—22no—
412C2×C8—22no—
413C2×C8—41no—
414C2×C8—41no—
415C2×C8—41no—
416C2×C8—41no—
417C2×C8—41no—
418C2×C8—41no—
419C2×C8—41no—
420C2×C8—41no—
421C2×C8—41no—
422C2×C8—41no—
423C4⋊C4—22no—
424C4⋊C4—22no—
425C4⋊C4—22no—
426C4⋊C4—41no—
427C4⋊C4—41no—
428C4⋊C4C3×C22⋊C414yes—
429C22⋊C4—22no—
430C22⋊C4—22no—
431C42—22no—
432C42—22no—
433C22×C3—22no—
434C22×C3—22no—
435C22×C3—22no—
436C22×C3—22no—
437C22×C3—21no—
438C22×C3—21no—
439C22×C3—21no—
440C22×C3—21no—
441C22×C3#38511yescharacteristic
442C22×C3#38611yescharacteristic
443C22×C3#38811yescharacteristic
444C22×C3#39411yescharacteristic
445C22×C3#39611yescharacteristic
446C22×C3#39711yescharacteristic
447C22×C3#39911yescharacteristic
448C22×C3#47112yes—
449C22×C3#47312yes—
450C3×C4—44no—
451C3×C4—44no—
452C3×C4—82no—
453C3×C4#38011yescharacteristic
454C3×C4#38511yescharacteristic
455C3×C4#38811yescharacteristic
456C3×C4#39011yescharacteristic
457C3×C4#39211yescharacteristic
458C3×C4#39311yescharacteristic
459C3×C4#39411yescharacteristic
460C3×C4#39611yescharacteristic
461C23—22no—
462C23—22no—
463C23C3×C4×D411yescharacteristic
464C23C3×#12111yescharacteristic
465C23C3×C22⋊Q811yescharacteristic
466C23C3×#12311yescharacteristic
467C23C3×#12311yescharacteristic
468C23C3×#12311yescharacteristic
469C23C3×#12611yescharacteristic
470Q8—24no—
471Q8—24no—
472Q8—42no—
473Q8—42no—
474Q8—42no—
475Q8—42no—
476Q8—42no—
477Q8—42no—
478C2×C4—24no—
479C2×C4—24no—
480C2×C4—42no—
481C2×C4—42no—
482C2×C4—42no—
483C2×C4—42no—
484C2×C4—42no—
485C2×C4—42no—
486C2×C4—42no—
487C2×C4—42no—
488C2×C4—42no—
489C2×C4—82no—
490C2×C4—82no—
491C2×C4—82no—
492C2×C4C2×C3×C22⋊C411yescharacteristic
493C2×C4C2×C3×C4⋊C411yescharacteristic
494C2×C4C3×#11711yescharacteristic
495C2×C4C3×C4×D411yescharacteristic
496C2×C4C3×C4×D411yescharacteristic
497C2×C4C3×C4×D411yescharacteristic
498C2×C4C3×#12011yescharacteristic
499C2×C4C3×#12011yescharacteristic
500C2×C4C3×#12011yescharacteristic
501C2×C4C3×#12111yescharacteristic
502C2×C4C3×#12111yescharacteristic
503C2×C4C3×#12111yescharacteristic
504C2×C4C3×#12111yescharacteristic
505C2×C4C3×#12111yescharacteristic
506C2×C4C3×#12111yescharacteristic
507C2×C4C3×#12111yescharacteristic
508C2×C4C3×C22⋊Q811yescharacteristic
509C2×C4C3×C22⋊Q811yescharacteristic
510C2×C4C3×C22⋊Q811yescharacteristic
511C2×C4C3×C22⋊Q811yescharacteristic
512C2×C4C3×C22⋊Q811yescharacteristic
513C2×C4C3×#12311yescharacteristic
514C2×C4C3×#12311yescharacteristic
515C2×C4C3×#12411yescharacteristic
516C2×C4C3×#12411yescharacteristic
517C2×C4C3×#12411yescharacteristic
518C2×C4C3×#12611yescharacteristic
519C2×C4C3×#12711yescharacteristic
520C8—42no—
521C8—42no—
522C8—42no—
523C8—42no—
524C2×C3—21no—
525C2×C3—21no—
526C2×C3—21no—
527C2×C3—21no—
528C2×C3#143911yescharacteristic
529C2×C3#190812yes—
530C2×C3#204611yescharacteristic
531C2×C3#204711yescharacteristic
532C2×C3#206412yes—
533C22—21no—
534C22—21no—
535C22—21no—
536C22—21no—
537C22—22no—
538C22—22no—
539C22—22no—
540C22—22no—
541C22C3×#38511yescharacteristic
542C22C3×#38611yescharacteristic
543C22C3×#38811yescharacteristic
544C22C3×#39411yescharacteristic
545C22C3×#39611yescharacteristic
546C22C3×#39711yescharacteristic
547C22C3×#39911yescharacteristic
548C22C3×#47112yes—
549C22C3×#47312yes—
550C4—44no—
551C4—44no—
552C4—82no—
553C4C3×#38011yescharacteristic
554C4C3×#38511yescharacteristic
555C4C3×#38811yescharacteristic
556C4C3×#39011yescharacteristic
557C4C3×#39211yescharacteristic
558C4C3×#39311yescharacteristic
559C4C3×#39411yescharacteristic
560C4C3×#39611yescharacteristic
561C3#1106211yescharacteristic, direct product factor, Sylow
562C2—21no—
563C2—21no—
564C2—21no—
565C2—21no—
566C2C3×#143911yescharacteristic
567C2C3×#190812yes—
568C2C3×#204611yescharacteristic
569C2C3×#204711yescharacteristic
570C2C3×#206412yes—
subgroupG/H
center, socleC23×C3#121
commutatorC22×C4C22×C3×C4
Frattini, cosocleC23×C4C23×C3
prime radicalC24×C3#41
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C3 ◁ C23×C3×C4 ◁ G

Complements

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

NH ≅ G/Ntype
8. #11062C3direct (N × H)
20. C3×#419C4semidirect
111. #419C3×C4semidirect
561. C3#11062direct (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
C2×C3×#4192
C22×C3×#1032
C22×C3×#1012
C2×C3×#3432
C2×C3×#3412
C3×#17362
#110623