Finite Group Databasebeta

← C3×#11043 #10629650

Subgroups — C3×#11043 #10629650

Order 768.

1454 conjugacy classes of subgroups.

The subgroup lattice has 630 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×#99C212yesmaximal
2C2×C3×#386C211yesmaximal, characteristic
3C2×C3×#380C211yesmaximal, characteristic, complemented
4C2×C3×#342C212yesmaximal, complemented
5C3×C22⋊#95C211yesmaximal, characteristic, complemented
6#11043C311yesmaximal, characteristic, direct product factor, Sylow
7C23×C3×D4C2211yescharacteristic
8C24×C3×C4C2211yescharacteristic
9C22×C3×C4⋊C4—21no—
10C22×C3×C22⋊C4C412yescomplemented
11C22×C3×C22⋊C4C2211yescharacteristic
12C22×C3×C22⋊C4C2212yes—
13C22×C3×C22⋊C4C2212yes—
14C2×C3×#99—24no—
15C2×C3×#99—24no—
16C2×C3×#99—24no—
17C3×#386—21no—
18C3×#386—22no—
19C3×#386—21no—
20C3×#380—24no—
21C2×C3×#95—21no—
22C2×C3×#95—22no—
23C2×C3×#95C412yescomplemented
24C3×#342—24no—
25C22×#99C2×C312yes—
26C2×#386C2×C311yescharacteristic
27C2×#380C2×C311yescharacteristic, complemented
28C2×#342C2×C312yescomplemented
29C22⋊#95C2×C311yescharacteristic, complemented
30C25×C3C2×C411yescharacteristic
31C25×C3C2311yescharacteristic
32C22×C3×D4—21no—
33C22×C3×D4—21no—
34C22×C3×D4—22no—
35C22×C3×D4—22no—
36C22×C3×D4—21no—
37C22×C3×D4—21no—
38C22×C3×D4—22no—
39C22×C3×D4—22no—
40C22×C3×D4D412yes—
41C22×C3×D4Q812yes—
42C23×C3×C4—22no—
43C23×C3×C4—22no—
44C23×C3×C4—22no—
45C23×C3×C4—22no—
46C23×C3×C4—44no—
47C23×C3×C4C2×C411yescharacteristic
48C23×C3×C4C2×C412yes—
49C23×C3×C4C2×C412yes—
50C23×C3×C4D411yescharacteristic
51C23×C3×C4D412yes—
52C23×C3×C4D411yescharacteristic
53C2×C3×C4⋊C4—24no—
54C2×C3×C4⋊C4—44no—
55C2×C3×C22⋊C4—22no—
56C2×C3×C22⋊C4—22no—
57C2×C3×C22⋊C4—22no—
58C2×C3×C22⋊C4—22no—
59C2×C3×C22⋊C4—22no—
60C2×C3×C22⋊C4—22no—
61C2×C3×C22⋊C4—22no—
62C2×C3×C22⋊C4—22no—
63C2×C3×C22⋊C4—22no—
64C2×C3×C22⋊C4—21no—
65C2×C3×C22⋊C4—21no—
66C2×C3×C22⋊C4—22no—
67C2×C3×C22⋊C4—22no—
68C2×C3×C22⋊C4—22no—
69C2×C3×C22⋊C4—22no—
70C2×C3×C22⋊C4—22no—
71C2×C3×C22⋊C4—44no—
72C2×C3×C22⋊C4D414yes—
73C2×C3×C22⋊C4D414yes—
74C3×#99—216no—
75C3×#95—24no—
76C3×#95—22no—
77C3×#95—22no—
78C3×#95—44no—
79C23×D4C22×C311yescharacteristic
80C24×C4C22×C311yescharacteristic
81C22×C4⋊C4—21no—
82C22×C22⋊C4C3×C412yescomplemented
83C22×C22⋊C4C22×C311yescharacteristic
84C22×C22⋊C4C22×C312yes—
85C22×C22⋊C4C22×C312yes—
86C2×#99—24no—
87C2×#99—24no—
88C2×#99—24no—
89#386—21no—
90#386—22no—
91#386—21no—
92#380—24no—
93C2×#95—21no—
94C2×#95—22no—
95C2×#95C3×C412yescomplemented
96#342—24no—
97C24×C3—21no—
98C24×C3—21no—
99C24×C3—22no—
100C24×C3—22no—
101C24×C3—42no—
102C24×C3—42no—
103C24×C3—42no—
104C24×C3—42no—
105C24×C3C4⋊C412yescomplemented
106C24×C3C22×C411yescharacteristic
107C24×C3C2×D411yescharacteristic
108C24×C3C2×D411yescharacteristic
109C24×C3C2×D411yescharacteristic
110C24×C3C2×D412yes—
111C24×C3C2×D412yes—
112C24×C3C2×Q811yescharacteristic
113C24×C3#4111yescharacteristic
114C24×C3#4111yescharacteristic
115C24×C3#4112yes—
116C24×C3#4112yes—
117C2×C3×D4—24no—
118C2×C3×D4—22no—
119C2×C3×D4—22no—
120C2×C3×D4—22no—
121C2×C3×D4—22no—
122C2×C3×D4—24no—
123C2×C3×D4—24no—
124C2×C3×D4—24no—
125C2×C3×D4—41no—
126C2×C3×D4—42no—
127C2×C3×D4—42no—
128C2×C3×D4—42no—
129C2×C3×D4—41no—
130C2×C3×D4—42no—
131C2×C3×D4—42no—
132C2×C3×D4—41no—
133C2×C3×D4—42no—
134C2×C3×D4—41no—
135C22×C3×C4—21no—
136C22×C3×C4—21no—
137C22×C3×C4—24no—
138C22×C3×C4—21no—
139C22×C3×C4—21no—
140C22×C3×C4—24no—
141C22×C3×C4—22no—
142C22×C3×C4—22no—
143C22×C3×C4—21no—
144C22×C3×C4—24no—
145C22×C3×C4—21no—
146C22×C3×C4—24no—
147C22×C3×C4—24no—
148C22×C3×C4—22no—
149C22×C3×C4—24no—
150C22×C3×C4—24no—
151C22×C3×C4—24no—
152C22×C3×C4—42no—
153C22×C3×C4—42no—
154C22×C3×C4—42no—
155C22×C3×C4—48no—
156C22×C3×C4—48no—
157C22×C3×C4—44no—
158C22×C3×C4—44no—
159C22×C3×C4—44no—
160C22×C3×C4—44no—
161C22×C3×C4—42no—
162C22×C3×C4—42no—
163C22×C3×C4—42no—
164C22×C3×C4—42no—
165C22×C3×C4—42no—
166C22×C3×C4—42no—
167C22×C3×C4C22⋊C412yes—
168C22×C3×C4C22⋊C412yes—
169C22×C3×C4C4⋊C412yescomplemented
170C3×C4⋊C4—48no—
171C3×C22⋊C4—24no—
172C3×C22⋊C4—24no—
173C3×C22⋊C4—24no—
174C3×C22⋊C4—24no—
175C3×C22⋊C4—44no—
176C3×C22⋊C4—42no—
177C3×C22⋊C4—42no—
178C3×C22⋊C4—42no—
179C3×C22⋊C4—42no—
180C3×C22⋊C4—41no—
181C3×C22⋊C4—42no—
182C3×C22⋊C4—41no—
183C3×C22⋊C4—44no—
184C25C2×C3×C411yescharacteristic
185C25C23×C311yescharacteristic
186C22×D4—21no—
187C22×D4—21no—
188C22×D4—22no—
189C22×D4—22no—
190C22×D4—21no—
191C22×D4—21no—
192C22×D4—22no—
193C22×D4—22no—
194C22×D4C3×D412yes—
195C22×D4C3×Q812yes—
196C23×C4—22no—
197C23×C4—22no—
198C23×C4—22no—
199C23×C4—22no—
200C23×C4—44no—
201C23×C4C2×C3×C411yescharacteristic
202C23×C4C2×C3×C412yes—
203C23×C4C2×C3×C412yes—
204C23×C4C3×D411yescharacteristic
205C23×C4C3×D412yes—
206C23×C4C3×D411yescharacteristic
207C2×C4⋊C4—24no—
208C2×C4⋊C4—44no—
209C2×C22⋊C4—22no—
210C2×C22⋊C4—22no—
211C2×C22⋊C4—22no—
212C2×C22⋊C4—22no—
213C2×C22⋊C4—22no—
214C2×C22⋊C4—22no—
215C2×C22⋊C4—22no—
216C2×C22⋊C4—22no—
217C2×C22⋊C4—22no—
218C2×C22⋊C4—22no—
219C2×C22⋊C4—21no—
220C2×C22⋊C4—21no—
221C2×C22⋊C4—22no—
222C2×C22⋊C4—22no—
223C2×C22⋊C4—22no—
224C2×C22⋊C4—22no—
225C2×C22⋊C4—44no—
226C2×C22⋊C4C3×D414yes—
227C2×C22⋊C4C3×D414yes—
228#99—216no—
229#95—24no—
230#95—22no—
231#95—22no—
232#95—44no—
233C23×C3—22no—
234C23×C3—22no—
235C23×C3—22no—
236C23×C3—22no—
237C23×C3—22no—
238C23×C3—22no—
239C23×C3—22no—
240C23×C3—24no—
241C23×C3—42no—
242C23×C3—42no—
243C23×C3—42no—
244C23×C3—42no—
245C23×C3—44no—
246C23×C3—42no—
247C23×C3—42no—
248C23×C3—42no—
249C23×C3—42no—
250C23×C3—44no—
251C23×C3—44no—
252C23×C3—44no—
253C23×C3—41no—
254C23×C3—42no—
255C23×C3—41no—
256C23×C3—42no—
257C23×C3—42no—
258C23×C3—82no—
259C23×C3—82no—
260C23×C3—84no—
261C23×C3C2×C22⋊C411yescharacteristic
262C23×C3C2×C4⋊C411yescharacteristic
263C23×C3#11711yescharacteristic
264C23×C3C4×D412yes—
265C23×C3C4×D412yes—
266C23×C3#12011yescharacteristic
267C23×C3#12012yes—
268C23×C3#12111yescharacteristic
269C23×C3#12111yescharacteristic
270C23×C3#12112yes—
271C23×C3#12112yes—
272C23×C3#12112yes—
273C23×C3C22⋊Q811yescharacteristic
274C23×C3C22⋊Q811yescharacteristic
275C23×C3C22⋊Q812yes—
276C23×C3C22⋊Q812yes—
277C23×C3#12311yescharacteristic
278C23×C3#12312yes—
279C23×C3#12312yes—
280C23×C3#12411yescharacteristic
281C23×C3#12412yes—
282C23×C3#12612yes—
283C23×C3#12711yescharacteristic
284C3×D4—42no—
285C3×D4—42no—
286C3×D4—44no—
287C3×D4—44no—
288C3×D4—42no—
289C3×D4—42no—
290C2×C3×C4—24no—
291C2×C3×C4—24no—
292C2×C3×C4—22no—
293C2×C3×C4—22no—
294C2×C3×C4—22no—
295C2×C3×C4—24no—
296C2×C3×C4—22no—
297C2×C3×C4—22no—
298C2×C3×C4—22no—
299C2×C3×C4—48no—
300C2×C3×C4—48no—
301C2×C3×C4—42no—
302C2×C3×C4—42no—
303C2×C3×C4—41no—
304C2×C3×C4—42no—
305C2×C3×C4—41no—
306C2×C3×C4—44no—
307C2×C3×C4—44no—
308C2×C3×C4—48no—
309C2×C3×C4—42no—
310C2×C3×C4—44no—
311C2×C3×C4—44no—
312C2×C3×C4—42no—
313C2×C3×C4—42no—
314C2×C3×C4—84no—
315C2×C3×C4—84no—
316C2×C3×C4—82no—
317C2×C3×C4—82no—
318C2×C3×C4—84no—
319C2×C3×C4—84no—
320C2×C3×C4#9914yescomplemented
321C24—21no—
322C24—21no—
323C24—22no—
324C24—22no—
325C24—42no—
326C24—42no—
327C24—42no—
328C24—42no—
329C24C3×C4⋊C412yescomplemented
330C24C22×C3×C411yescharacteristic
331C24C2×C3×D411yescharacteristic
332C24C2×C3×D411yescharacteristic
333C24C2×C3×D411yescharacteristic
334C24C2×C3×D412yes—
335C24C2×C3×D412yes—
336C24C2×C3×Q811yescharacteristic
337C24C3×#4111yescharacteristic
338C24C3×#4111yescharacteristic
339C24C3×#4112yes—
340C24C3×#4112yes—
341C2×D4—24no—
342C2×D4—22no—
343C2×D4—22no—
344C2×D4—22no—
345C2×D4—22no—
346C2×D4—24no—
347C2×D4—24no—
348C2×D4—24no—
349C2×D4—41no—
350C2×D4—42no—
351C2×D4—42no—
352C2×D4—42no—
353C2×D4—41no—
354C2×D4—42no—
355C2×D4—42no—
356C2×D4—41no—
357C2×D4—42no—
358C2×D4—41no—
359C22×C4—21no—
360C22×C4—21no—
361C22×C4—24no—
362C22×C4—21no—
363C22×C4—21no—
364C22×C4—24no—
365C22×C4—22no—
366C22×C4—22no—
367C22×C4—21no—
368C22×C4—24no—
369C22×C4—21no—
370C22×C4—24no—
371C22×C4—24no—
372C22×C4—22no—
373C22×C4—24no—
374C22×C4—24no—
375C22×C4—24no—
376C22×C4—42no—
377C22×C4—42no—
378C22×C4—42no—
379C22×C4—48no—
380C22×C4—48no—
381C22×C4—44no—
382C22×C4—44no—
383C22×C4—44no—
384C22×C4—44no—
385C22×C4—42no—
386C22×C4—42no—
387C22×C4—42no—
388C22×C4—42no—
389C22×C4—42no—
390C22×C4—42no—
391C22×C4C3×C22⋊C412yes—
392C22×C4C3×C22⋊C412yes—
393C22×C4C3×C4⋊C412yescomplemented
394C4⋊C4—48no—
395C22⋊C4—24no—
396C22⋊C4—24no—
397C22⋊C4—24no—
398C22⋊C4—24no—
399C22⋊C4—44no—
400C22⋊C4—42no—
401C22⋊C4—42no—
402C22⋊C4—42no—
403C22⋊C4—42no—
404C22⋊C4—41no—
405C22⋊C4—42no—
406C22⋊C4—41no—
407C22⋊C4—44no—
408C22×C3—22no—
409C22×C3—22no—
410C22×C3—22no—
411C22×C3—22no—
412C22×C3—22no—
413C22×C3—22no—
414C22×C3—21no—
415C22×C3—21no—
416C22×C3—22no—
417C22×C3—22no—
418C22×C3—21no—
419C22×C3—22no—
420C22×C3—22no—
421C22×C3—21no—
422C22×C3—24no—
423C22×C3—22no—
424C22×C3—24no—
425C22×C3—22no—
426C22×C3—42no—
427C22×C3—42no—
428C22×C3—42no—
429C22×C3—42no—
430C22×C3—42no—
431C22×C3—42no—
432C22×C3—42no—
433C22×C3—42no—
434C22×C3—44no—
435C22×C3—42no—
436C22×C3—84no—
437C22×C3—84no—
438C22×C3—81no—
439C22×C3—81no—
440C22×C3—82no—
441C22×C3#38011yescharacteristic
442C22×C3#38512yes—
443C22×C3#38611yescharacteristic
444C22×C3#38812yes—
445C22×C3#39011yescharacteristic
446C22×C3#39211yescharacteristic
447C22×C3#39311yescharacteristic
448C22×C3#39412yes—
449C22×C3#39612yes—
450C22×C3#39711yescharacteristic
451C22×C3#39911yescharacteristic
452C22×C3C2×#9912yes—
453C22×C3#41012yes—
454C3×C4—24no—
455C3×C4—42no—
456C3×C4—42no—
457C3×C4—84no—
458C3×C4—84no—
459C3×C4—82no—
460C23—22no—
461C23—22no—
462C23—22no—
463C23—22no—
464C23—22no—
465C23—22no—
466C23—22no—
467C23—24no—
468C23—42no—
469C23—42no—
470C23—42no—
471C23—42no—
472C23—44no—
473C23—42no—
474C23—42no—
475C23—42no—
476C23—42no—
477C23—44no—
478C23—44no—
479C23—44no—
480C23—41no—
481C23—42no—
482C23—41no—
483C23—42no—
484C23—42no—
485C23—82no—
486C23—82no—
487C23—84no—
488C23C2×C3×C22⋊C411yescharacteristic
489C23C2×C3×C4⋊C411yescharacteristic
490C23C3×#11711yescharacteristic
491C23C3×C4×D412yes—
492C23C3×C4×D412yes—
493C23C3×#12011yescharacteristic
494C23C3×#12012yes—
495C23C3×#12111yescharacteristic
496C23C3×#12111yescharacteristic
497C23C3×#12112yes—
498C23C3×#12112yes—
499C23C3×#12112yes—
500C23C3×C22⋊Q811yescharacteristic
501C23C3×C22⋊Q811yescharacteristic
502C23C3×C22⋊Q812yes—
503C23C3×C22⋊Q812yes—
504C23C3×#12311yescharacteristic
505C23C3×#12312yes—
506C23C3×#12312yes—
507C23C3×#12411yescharacteristic
508C23C3×#12412yes—
509C23C3×#12612yes—
510C23C3×#12711yescharacteristic
511D4—42no—
512D4—42no—
513D4—44no—
514D4—44no—
515D4—42no—
516D4—42no—
517C2×C4—24no—
518C2×C4—24no—
519C2×C4—22no—
520C2×C4—22no—
521C2×C4—22no—
522C2×C4—24no—
523C2×C4—22no—
524C2×C4—22no—
525C2×C4—22no—
526C2×C4—48no—
527C2×C4—48no—
528C2×C4—42no—
529C2×C4—42no—
530C2×C4—41no—
531C2×C4—42no—
532C2×C4—41no—
533C2×C4—44no—
534C2×C4—44no—
535C2×C4—48no—
536C2×C4—42no—
537C2×C4—44no—
538C2×C4—44no—
539C2×C4—42no—
540C2×C4—42no—
541C2×C4—84no—
542C2×C4—84no—
543C2×C4—82no—
544C2×C4—82no—
545C2×C4—84no—
546C2×C4—84no—
547C2×C4C3×#9914yescomplemented
548C2×C3—21no—
549C2×C3—22no—
550C2×C3—22no—
551C2×C3—22no—
552C2×C3—21no—
553C2×C3—22no—
554C2×C3—21no—
555C2×C3—21no—
556C2×C3—82no—
557C2×C3#143911yescharacteristic
558C2×C3#179912yes—
559C2×C3#189811yescharacteristic
560C2×C3#189911yescharacteristic
561C2×C3#196412yes—
562C22—22no—
563C22—22no—
564C22—22no—
565C22—22no—
566C22—22no—
567C22—22no—
568C22—21no—
569C22—21no—
570C22—22no—
571C22—22no—
572C22—21no—
573C22—22no—
574C22—22no—
575C22—21no—
576C22—24no—
577C22—22no—
578C22—24no—
579C22—22no—
580C22—42no—
581C22—42no—
582C22—42no—
583C22—42no—
584C22—42no—
585C22—42no—
586C22—42no—
587C22—42no—
588C22—44no—
589C22—42no—
590C22—84no—
591C22—84no—
592C22—81no—
593C22—81no—
594C22—82no—
595C22C3×#38011yescharacteristic
596C22C3×#38512yes—
597C22C3×#38611yescharacteristic
598C22C3×#38812yes—
599C22C3×#39011yescharacteristic
600C22C3×#39211yescharacteristic
601C22C3×#39311yescharacteristic
602C22C3×#39412yes—
603C22C3×#39612yes—
604C22C3×#39711yescharacteristic
605C22C3×#39911yescharacteristic
606C22C2×C3×#9912yes—
607C22C3×#41012yes—
608C4—24no—
609C4—42no—
610C4—42no—
611C4—84no—
612C4—84no—
613C4—82no—
614C3#1104311yescharacteristic, direct product factor, Sylow
615C2—21no—
616C2—22no—
617C2—22no—
618C2—22no—
619C2—21no—
620C2—22no—
621C2—21no—
622C2—21no—
623C2—82no—
624C2C3×#143911yescharacteristic
625C2C3×#179912yes—
626C2C3×#189811yescharacteristic
627C2C3×#189911yescharacteristic
628C2C3×#196412yes—
subgroupG/H
center, socleC23×C3C2×C22⋊C4
commutatorC24C22×C3×C4
Frattini, cosocleC25C23×C3
prime radicalC23×C3×D4C22
LCSG ▷ C24 ▷ C2 ▷ C1
UCSC1 ◁ C23×C3 ◁ C24×C3×C4 ◁ G

Complements

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

NH ≅ G/Ntype
3. C2×C3×#380C2semidirect
4. C2×C3×#342C2semidirect
5. C3×C22⋊#95C2semidirect
6. #11043C3direct (N × H)
10. C22×C3×C22⋊C4C4semidirect
23. C2×C3×#95C4semidirect
27. C2×#380C2×C3semidirect
28. C2×#342C2×C3semidirect
29. C22⋊#95C2×C3semidirect
82. C22×C22⋊C4C3×C4semidirect
95. C2×#95C3×C4semidirect
105. C24×C3C4⋊C4semidirect
169. C22×C3×C4C4⋊C4semidirect
320. C2×C3×C4#99semidirect
329. C24C3×C4⋊C4semidirect
393. C22×C4C3×C4⋊C4semidirect
547. C2×C4C3×#99semidirect
614. C3#11043direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C3×#992
C2×C3×#3862
C2×C3×#3802
C2×C3×#3422
C3×C22⋊#952
#110433