Finite Group Databasebeta

← C3×#11064 #10629671

Subgroups — C3×#11064 #10629671

Order 768.

958 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
1C2×C3×#419C211yesmaximal, characteristic
2C2×C3×#419C211yesmaximal, characteristic
3C3×#2317C211yesmaximal, characteristic
4C2×C3×#391C211yesmaximal, characteristic
5C2×C3×#343C211yesmaximal, characteristic
6C2×C3×#339C211yesmaximal, characteristic
7C2×C3×#339C211yesmaximal, characteristic
8#11064C311yesmaximal, characteristic, direct product factor, Sylow
9C23×C3×Q8C2211yescharacteristic
10C22×C3×M16C2211yescharacteristic
11C22×C3×M16C2211yescharacteristic
12C2×C3×#117C2211yescharacteristic
13C2×C3×#117C2211yescharacteristic
14C22×C3×C4⋊C4C2211yescharacteristic
15C22×C3×C42C2211yescharacteristic
16C3×#419—22no—
17C3×#419—22no—
18C3×#419—22no—
19C3×#419C414yescomplemented
20C2×C3×#103—21no—
21C2×C3×#103—21no—
22C2×C3×#103—22no—
23C3×#391—22no—
24C3×#391—22no—
25C3×#389—22no—
26C3×#385—22no—
27C3×#384—21no—
28C3×#382—21no—
29C2×C3×#95—22no—
30C3×#343—22no—
31C3×#339—22no—
32C3×#339—22no—
33C2×#419C2×C311yescharacteristic
34C2×#419C2×C311yescharacteristic
35#2317C2×C311yescharacteristic
36C2×#391C2×C311yescharacteristic
37C2×#343C2×C311yescharacteristic
38C2×#339C2×C311yescharacteristic
39C2×#339C2×C311yescharacteristic
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×Q8—21no—
50C22×C3×Q8—21no—
51C22×C3×Q8C2×C412yes—
52C22×C3×Q8D412yes—
53C22×C3×Q8Q812yes—
54C23×C3×C4—21no—
55C23×C3×C4—21no—
56C23×C3×C4D412yes—
57C23×C3×C4C2311yescharacteristic
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×M16C2×C412yes—
69C2×C3×M16D412yes—
70C22×C3×C8—21no—
71C22×C3×C8—21no—
72C3×#117—21no—
73C3×#117—21no—
74C3×#117—21no—
75C3×#117—21no—
76C3×#117—21no—
77C3×#117—21no—
78C3×#117C2×C412yes—
79C3×#117D412yes—
80C2×C3×C4⋊C4—21no—
81C2×C3×C4⋊C4—21no—
82C2×C3×C4⋊C4—21no—
83C2×C3×C4⋊C4—21no—
84C2×C3×C4⋊C4—21no—
85C2×C3×C4⋊C4—21no—
86C2×C3×C4⋊C4—24no—
87C2×C3×C4⋊C4D411yescharacteristic
88C2×C3×C4⋊C4D411yescharacteristic
89C2×C3×C4⋊C4D412yes—
90C2×C3×C22⋊C4—21no—
91C2×C3×C22⋊C4—21no—
92C2×C3×C42—21no—
93C2×C3×C42—21no—
94C2×C3×C42—21no—
95C2×C3×C42—21no—
96C2×C3×C42—21no—
97C2×C3×C42—21no—
98C2×C3×C42—21no—
99C2×C3×C42D412yes—
100C3×#103—24no—
101C3×#103—24no—
102C3×#103—28no—
103C3×#95—28no—
104C3×#95—24no—
105C23×Q8C22×C311yescharacteristic
106C22×M16C22×C311yescharacteristic
107C22×M16C22×C311yescharacteristic
108C2×#117C22×C311yescharacteristic
109C2×#117C22×C311yescharacteristic
110C22×C4⋊C4C22×C311yescharacteristic
111C22×C42C22×C311yescharacteristic
112#419—22no—
113#419—22no—
114#419—22no—
115#419C3×C414yescomplemented
116C2×#103—21no—
117C2×#103—21no—
118C2×#103—22no—
119#391—22no—
120#391—22no—
121#389—22no—
122#385—22no—
123#384—21no—
124#382—21no—
125C2×#95—22no—
126#343—22no—
127#339—22no—
128#339—22no—
129C24×C3C2×D411yescharacteristic
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—22no—
139C2×C3×Q8—22no—
140C2×C3×Q8—22no—
141C2×C3×Q8—22no—
142C2×C3×Q8—22no—
143C2×C3×Q8—22no—
144C2×C3×Q8—22no—
145C2×C3×Q8—41no—
146C2×C3×Q8—41no—
147C2×C3×Q8—41no—
148C2×C3×Q8—41no—
149C2×C3×Q8—41no—
150C2×C3×Q8—41no—
151C2×C3×Q8—41no—
152C2×C3×Q8—41no—
153C2×C3×Q8—41no—
154C2×C3×Q8—41no—
155C2×C3×Q8—41no—
156C2×C3×Q8—41no—
157C2×C3×Q8C4⋊C414yescomplemented
158C22×C3×C4—24no—
159C22×C3×C4—22no—
160C22×C3×C4—22no—
161C22×C3×C4—22no—
162C22×C3×C4—22no—
163C22×C3×C4—22no—
164C22×C3×C4—22no—
165C22×C3×C4—21no—
166C22×C3×C4—22no—
167C22×C3×C4—21no—
168C22×C3×C4—22no—
169C22×C3×C4—42no—
170C22×C3×C4—41no—
171C22×C3×C4—41no—
172C22×C3×C4—41no—
173C22×C3×C4—41no—
174C22×C3×C4—41no—
175C22×C3×C4—41no—
176C22×C3×C4—44no—
177C22×C3×C4C22×C411yescharacteristic
178C22×C3×C4C2×D411yescharacteristic
179C22×C3×C4C2×D411yescharacteristic
180C22×C3×C4C2×D411yescharacteristic
181C22×C3×C4C2×D411yescharacteristic
182C22×C3×C4C2×D411yescharacteristic
183C22×C3×C4C2×D411yescharacteristic
184C22×C3×C4C2×Q811yescharacteristic
185C22×C3×C4#4111yescharacteristic
186C22×C3×C4#4111yescharacteristic
187C22×C3×C4#4111yescharacteristic
188C22×C3×C4#4111yescharacteristic
189C22×C3×C4#4111yescharacteristic
190C22×C3×C4#4111yescharacteristic
191C3×M16—22no—
192C3×M16—22no—
193C3×M16—22no—
194C3×M16—22no—
195C3×M16—41no—
196C3×M16—41no—
197C3×M16—41no—
198C3×M16—41no—
199C2×C3×C8—22no—
200C2×C3×C8—22no—
201C2×C3×C8—41no—
202C2×C3×C8—41no—
203C2×C3×C8—41no—
204C2×C3×C8—41no—
205C3×C4⋊C4—22no—
206C3×C4⋊C4—21no—
207C3×C4⋊C4—21no—
208C3×C4⋊C4—21no—
209C3×C4⋊C4—21no—
210C3×C4⋊C4—41no—
211C3×C4⋊C4—41no—
212C3×C4⋊C4—41no—
213C3×C4⋊C4—41no—
214C3×C4⋊C4—84no—
215C3×C4⋊C4C22⋊C414yes—
216C3×C22⋊C4—22no—
217C3×C22⋊C4—22no—
218C3×C22⋊C4—41no—
219C3×C22⋊C4—41no—
220C3×C42—22no—
221C3×C42—22no—
222C3×C42—22no—
223C3×C42—22no—
224C3×C42—41no—
225C3×C42—41no—
226C3×C42—41no—
227C3×C42—41no—
228C22×Q8—21no—
229C22×Q8—21no—
230C22×Q8—21no—
231C22×Q8—21no—
232C22×Q8—21no—
233C22×Q8—21no—
234C22×Q8—21no—
235C22×Q8—21no—
236C22×Q8—21no—
237C22×Q8—21no—
238C22×Q8—21no—
239C22×Q8C2×C3×C412yes—
240C22×Q8C3×D412yes—
241C22×Q8C3×Q812yes—
242C23×C4—21no—
243C23×C4—21no—
244C23×C4C3×D412yes—
245C23×C4C23×C311yescharacteristic
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×M16—21no—
256C2×M16C2×C3×C412yes—
257C2×M16C3×D412yes—
258C22×C8—21no—
259C22×C8—21no—
260#117—21no—
261#117—21no—
262#117—21no—
263#117—21no—
264#117—21no—
265#117—21no—
266#117C2×C3×C412yes—
267#117C3×D412yes—
268C2×C4⋊C4—21no—
269C2×C4⋊C4—21no—
270C2×C4⋊C4—21no—
271C2×C4⋊C4—21no—
272C2×C4⋊C4—21no—
273C2×C4⋊C4—21no—
274C2×C4⋊C4—24no—
275C2×C4⋊C4C3×D411yescharacteristic
276C2×C4⋊C4C3×D411yescharacteristic
277C2×C4⋊C4C3×D412yes—
278C2×C22⋊C4—21no—
279C2×C22⋊C4—21no—
280C2×C42—21no—
281C2×C42—21no—
282C2×C42—21no—
283C2×C42—21no—
284C2×C42—21no—
285C2×C42—21no—
286C2×C42—21no—
287C2×C42C3×D412yes—
288#103—24no—
289#103—24no—
290#103—28no—
291#95—28no—
292#95—24no—
293C23×C3—22no—
294C23×C3—22no—
295C23×C3C4×D411yescharacteristic
296C23×C3#12011yescharacteristic
297C23×C3#12011yescharacteristic
298C23×C3#12111yescharacteristic
299C23×C3#12111yescharacteristic
300C23×C3C22⋊Q811yescharacteristic
301C23×C3#12411yescharacteristic
302C3×Q8—24no—
303C3×Q8—24no—
304C3×Q8—42no—
305C3×Q8—42no—
306C3×Q8—42no—
307C3×Q8—42no—
308C3×Q8—42no—
309C3×Q8—42no—
310C2×C3×C4—24no—
311C2×C3×C4—24no—
312C2×C3×C4—24no—
313C2×C3×C4—44no—
314C2×C3×C4—42no—
315C2×C3×C4—44no—
316C2×C3×C4—42no—
317C2×C3×C4—42no—
318C2×C3×C4—42no—
319C2×C3×C4—42no—
320C2×C3×C4—42no—
321C2×C3×C4—42no—
322C2×C3×C4—42no—
323C2×C3×C4—42no—
324C2×C3×C4—42no—
325C2×C3×C4—44no—
326C2×C3×C4—41no—
327C2×C3×C4—41no—
328C2×C3×C4—42no—
329C2×C3×C4—42no—
330C2×C3×C4—44no—
331C2×C3×C4—42no—
332C2×C3×C4—82no—
333C2×C3×C4C2×C22⋊C411yescharacteristic
334C2×C3×C4C2×C4⋊C411yescharacteristic
335C2×C3×C4#11711yescharacteristic
336C2×C3×C4C4×D411yescharacteristic
337C2×C3×C4C4×D411yescharacteristic
338C2×C3×C4C4×D411yescharacteristic
339C2×C3×C4#12011yescharacteristic
340C2×C3×C4#12111yescharacteristic
341C2×C3×C4#12111yescharacteristic
342C2×C3×C4#12111yescharacteristic
343C2×C3×C4#12111yescharacteristic
344C2×C3×C4#12111yescharacteristic
345C2×C3×C4#12111yescharacteristic
346C2×C3×C4C22⋊Q811yescharacteristic
347C2×C3×C4C22⋊Q811yescharacteristic
348C2×C3×C4C22⋊Q811yescharacteristic
349C2×C3×C4C22⋊Q811yescharacteristic
350C2×C3×C4C22⋊Q811yescharacteristic
351C2×C3×C4#12311yescharacteristic
352C2×C3×C4#12311yescharacteristic
353C2×C3×C4#12311yescharacteristic
354C2×C3×C4#12311yescharacteristic
355C2×C3×C4#12311yescharacteristic
356C2×C3×C4#12411yescharacteristic
357C2×C3×C4#12411yescharacteristic
358C2×C3×C4#12611yescharacteristic
359C2×C3×C4#12611yescharacteristic
360C2×C3×C4#12711yescharacteristic
361C3×C8—42no—
362C3×C8—42no—
363C24C2×C3×D411yescharacteristic
364C2×Q8—22no—
365C2×Q8—22no—
366C2×Q8—22no—
367C2×Q8—22no—
368C2×Q8—22no—
369C2×Q8—22no—
370C2×Q8—22no—
371C2×Q8—22no—
372C2×Q8—22no—
373C2×Q8—22no—
374C2×Q8—22no—
375C2×Q8—22no—
376C2×Q8—22no—
377C2×Q8—22no—
378C2×Q8—22no—
379C2×Q8—41no—
380C2×Q8—41no—
381C2×Q8—41no—
382C2×Q8—41no—
383C2×Q8—41no—
384C2×Q8—41no—
385C2×Q8—41no—
386C2×Q8—41no—
387C2×Q8—41no—
388C2×Q8—41no—
389C2×Q8—41no—
390C2×Q8—41no—
391C2×Q8C3×C4⋊C414yescomplemented
392C22×C4—24no—
393C22×C4—22no—
394C22×C4—22no—
395C22×C4—22no—
396C22×C4—22no—
397C22×C4—22no—
398C22×C4—21no—
399C22×C4—22no—
400C22×C4—22no—
401C22×C4—21no—
402C22×C4—22no—
403C22×C4—42no—
404C22×C4—41no—
405C22×C4—41no—
406C22×C4—41no—
407C22×C4—41no—
408C22×C4—41no—
409C22×C4—41no—
410C22×C4—44no—
411C22×C4C22×C3×C411yescharacteristic
412C22×C4C2×C3×D411yescharacteristic
413C22×C4C2×C3×D411yescharacteristic
414C22×C4C2×C3×D411yescharacteristic
415C22×C4C2×C3×D411yescharacteristic
416C22×C4C2×C3×D411yescharacteristic
417C22×C4C2×C3×D411yescharacteristic
418C22×C4C2×C3×Q811yescharacteristic
419C22×C4C3×#4111yescharacteristic
420C22×C4C3×#4111yescharacteristic
421C22×C4C3×#4111yescharacteristic
422C22×C4C3×#4111yescharacteristic
423C22×C4C3×#4111yescharacteristic
424C22×C4C3×#4111yescharacteristic
425M16—22no—
426M16—22no—
427M16—22no—
428M16—22no—
429M16—41no—
430M16—41no—
431M16—41no—
432M16—41no—
433C2×C8—22no—
434C2×C8—22no—
435C2×C8—41no—
436C2×C8—41no—
437C2×C8—41no—
438C2×C8—41no—
439C4⋊C4—22no—
440C4⋊C4—21no—
441C4⋊C4—21no—
442C4⋊C4—21no—
443C4⋊C4—21no—
444C4⋊C4—41no—
445C4⋊C4—41no—
446C4⋊C4—41no—
447C4⋊C4—41no—
448C4⋊C4—84no—
449C4⋊C4C3×C22⋊C414yes—
450C22⋊C4—22no—
451C22⋊C4—22no—
452C22⋊C4—41no—
453C22⋊C4—41no—
454C42—22no—
455C42—22no—
456C42—22no—
457C42—22no—
458C42—41no—
459C42—41no—
460C42—41no—
461C42—41no—
462C22×C3—22no—
463C22×C3—22no—
464C22×C3—21no—
465C22×C3—21no—
466C22×C3—21no—
467C22×C3—21no—
468C22×C3—22no—
469C22×C3—22no—
470C22×C3#38511yescharacteristic
471C22×C3#38611yescharacteristic
472C22×C3#38811yescharacteristic
473C22×C3#39211yescharacteristic
474C22×C3#39311yescharacteristic
475C22×C3#39411yescharacteristic
476C22×C3#39611yescharacteristic
477C22×C3#45512yes—
478C22×C3#45612yes—
479C3×C4—44no—
480C3×C4—44no—
481C3×C4—44no—
482C3×C4—81no—
483C3×C4—82no—
484C3×C4—81no—
485C3×C4#38011yescharacteristic
486C3×C4#38511yescharacteristic
487C3×C4#38811yescharacteristic
488C3×C4#39011yescharacteristic
489C3×C4#39411yescharacteristic
490C3×C4#39611yescharacteristic
491C3×C4#39711yescharacteristic
492C3×C4#39911yescharacteristic
493C23—22no—
494C23—22no—
495C23C3×C4×D411yescharacteristic
496C23C3×#12011yescharacteristic
497C23C3×#12011yescharacteristic
498C23C3×#12111yescharacteristic
499C23C3×#12111yescharacteristic
500C23C3×C22⋊Q811yescharacteristic
501C23C3×#12411yescharacteristic
502Q8—24no—
503Q8—24no—
504Q8—42no—
505Q8—42no—
506Q8—42no—
507Q8—42no—
508Q8—42no—
509Q8—42no—
510C2×C4—24no—
511C2×C4—24no—
512C2×C4—24no—
513C2×C4—42no—
514C2×C4—44no—
515C2×C4—44no—
516C2×C4—42no—
517C2×C4—42no—
518C2×C4—42no—
519C2×C4—42no—
520C2×C4—42no—
521C2×C4—42no—
522C2×C4—42no—
523C2×C4—42no—
524C2×C4—42no—
525C2×C4—44no—
526C2×C4—41no—
527C2×C4—41no—
528C2×C4—42no—
529C2×C4—42no—
530C2×C4—44no—
531C2×C4—42no—
532C2×C4—82no—
533C2×C4C2×C3×C22⋊C411yescharacteristic
534C2×C4C2×C3×C4⋊C411yescharacteristic
535C2×C4C3×#11711yescharacteristic
536C2×C4C3×C4×D411yescharacteristic
537C2×C4C3×C4×D411yescharacteristic
538C2×C4C3×C4×D411yescharacteristic
539C2×C4C3×#12011yescharacteristic
540C2×C4C3×#12111yescharacteristic
541C2×C4C3×#12111yescharacteristic
542C2×C4C3×#12111yescharacteristic
543C2×C4C3×#12111yescharacteristic
544C2×C4C3×#12111yescharacteristic
545C2×C4C3×#12111yescharacteristic
546C2×C4C3×C22⋊Q811yescharacteristic
547C2×C4C3×C22⋊Q811yescharacteristic
548C2×C4C3×C22⋊Q811yescharacteristic
549C2×C4C3×C22⋊Q811yescharacteristic
550C2×C4C3×C22⋊Q811yescharacteristic
551C2×C4C3×#12311yescharacteristic
552C2×C4C3×#12311yescharacteristic
553C2×C4C3×#12311yescharacteristic
554C2×C4C3×#12311yescharacteristic
555C2×C4C3×#12311yescharacteristic
556C2×C4C3×#12411yescharacteristic
557C2×C4C3×#12411yescharacteristic
558C2×C4C3×#12611yescharacteristic
559C2×C4C3×#12611yescharacteristic
560C2×C4C3×#12711yescharacteristic
561C8—42no—
562C8—42no—
563C2×C3—21no—
564C2×C3—21no—
565C2×C3—21no—
566C2×C3—21no—
567C2×C3#143911yescharacteristic
568C2×C3#188212yes—
569C2×C3#200411yescharacteristic
570C2×C3#200511yescharacteristic
571C2×C3#202812yes—
572C22—21no—
573C22—21no—
574C22—21no—
575C22—21no—
576C22—22no—
577C22—22no—
578C22—22no—
579C22—22no—
580C22C3×#38511yescharacteristic
581C22C3×#38611yescharacteristic
582C22C3×#38811yescharacteristic
583C22C3×#39211yescharacteristic
584C22C3×#39311yescharacteristic
585C22C3×#39411yescharacteristic
586C22C3×#39611yescharacteristic
587C22C3×#45512yes—
588C22C3×#45612yes—
589C4—44no—
590C4—44no—
591C4—44no—
592C4—82no—
593C4—81no—
594C4—81no—
595C4C3×#38011yescharacteristic
596C4C3×#38511yescharacteristic
597C4C3×#38811yescharacteristic
598C4C3×#39011yescharacteristic
599C4C3×#39411yescharacteristic
600C4C3×#39611yescharacteristic
601C4C3×#39711yescharacteristic
602C4C3×#39911yescharacteristic
603C3#1106411yescharacteristic, direct product factor, Sylow
604C2—21no—
605C2—21no—
606C2—21no—
607C2—21no—
608C2C3×#143911yescharacteristic
609C2C3×#188212yes—
610C2C3×#200411yescharacteristic
611C2C3×#200511yescharacteristic
612C2C3×#202812yes—
subgroupG/H
center, socleC23×C3#120
commutatorC22×C4C22×C3×C4
Frattini, cosocleC23×C4C23×C3
prime radicalC24×C3C2×D4
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. #11064C3direct (N × H)
19. C3×#419C4semidirect
115. #419C3×C4semidirect
157. C2×C3×Q8C4⋊C4semidirect
391. C2×Q8C3×C4⋊C4semidirect
603. C3#11064direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#4192
C3×#23172
C2×C3×#3912
C2×C3×#3432
C2×C3×#3392
#110643