Finite Group Databasebeta

← C3×#19091 #10637698

Subgroups — C3×#19091 #10637698

Order 768.

854 conjugacy classes of subgroups.

The subgroup lattice has 610 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#3561C211yesmaximal, characteristic
2C3×#3240C211yesmaximal, characteristic, complemented
3C3×#3237C211yesmaximal, characteristic, complemented
4C3×#3215C211yesmaximal, characteristic, complemented
5C3×#1664C212yesmaximal, complemented
6C3×#1662C212yesmaximal, complemented
7C3×#1661C212yesmaximal, complemented
8C3×#1660C212yesmaximal, complemented
9C3×#1537C211yesmaximal, characteristic, complemented
10C3×#1535C211yesmaximal, characteristic, complemented
11C3×#1533C211yesmaximal, characteristic, complemented
12#19091C311yesmaximal, characteristic, direct product factor, Sylow
13C3×#563C2212yes—
14C3×#562C2212yes—
15C3×#556—21no—
16C3×#551—22no—
17C3×D4×Q8—21no—
18C3×#548—21no—
19C3×#546—21no—
20C3×#543—21no—
21C3×#542—21no—
22C3×#542—22no—
23C3×#538—21no—
24C3×#536—21no—
25C3×#533C2211yescharacteristic
26C3×#533C2211yescharacteristic
27C3×#529C2211yescharacteristic
28C2×C3×#124C2211yescharacteristic
29C3×#501C2212yescomplemented
30C3×#501C2211yescharacteristic, complemented
31C3×#501C2211yescharacteristic, complemented
32C3×#497C2212yes—
33C3×#491C2212yescomplemented
34C3×#489C2212yes—
35C3×#489C2211yescharacteristic, complemented
36C3×#489C2211yescharacteristic, complemented
37C3×#485—21no—
38C3×#485—22no—
39C3×#482—21no—
40C3×#479—21no—
41C3×#478—21no—
42C3×#477—21no—
43C3×#475—21no—
44C3×#464—22no—
45C3×#451—21no—
46C3×#450—21no—
47C3×#432C2211yescharacteristic
48C3×#432C2211yescharacteristic
49C3×#432C2211yescharacteristic
50C3×#330C2212yescomplemented
51C3×#330C2212yescomplemented
52C3×#330C2212yescomplemented
53C3×#329C2212yes—
54C3×#329C2212yes—
55C3×#329C2212yescomplemented
56#3561C2×C311yescharacteristic
57#3240C2×C311yescharacteristic, complemented
58#3237C2×C311yescharacteristic, complemented
59#3215C2×C311yescharacteristic, complemented
60#1664C2×C312yescomplemented
61#1662C2×C312yescomplemented
62#1661C2×C312yescomplemented
63#1660C2×C312yescomplemented
64#1537C2×C311yescharacteristic, complemented
65#1535C2×C311yescharacteristic, complemented
66#1533C2×C311yescharacteristic, complemented
67C2×C3×#41—21no—
68C22×C3×Q8—21no—
69C22×C3×Q8D411yescharacteristic
70C22×C3×D4D411yescharacteristic
71C2×C3×Q16—22no—
72C2×C3×SD16—22no—
73C3×C4⋊Q8—21no—
74C3×C4⋊Q8—22no—
75C3×C4⋊Q8D411yescharacteristic
76C3×C4⋊Q8D411yescharacteristic
77C3×C4⋊Q8C2311yescharacteristic
78C3×C4⋊Q8C2311yescharacteristic
79C3×#126—22no—
80C3×#126—22no—
81C3×#126—22no—
82C3×#126—21no—
83C3×#125—21no—
84C3×#125C2312yes—
85C3×#125C2311yescharacteristic
86C3×#124—21no—
87C3×#124—22no—
88C3×#124—22no—
89C3×#124—21no—
90C3×#124—21no—
91C3×#124D412yes—
92C3×#124C2311yescharacteristic
93C3×#124C2312yes—
94C3×#123—22no—
95C3×#123—22no—
96C3×#123—21no—
97C3×#123—22no—
98C3×#123—22no—
99C3×C22⋊Q8—22no—
100C3×C22⋊Q8—22no—
101C3×C22⋊Q8—21no—
102C3×C22⋊Q8—22no—
103C3×C22⋊Q8—22no—
104C3×C22⋊Q8—22no—
105C3×C22⋊Q8—21no—
106C3×C22⋊Q8—21no—
107C3×C22⋊Q8—22no—
108C3×C22⋊Q8—22no—
109C3×C22⋊Q8—21no—
110C3×C22⋊Q8—21no—
111C3×C22⋊Q8D411yescharacteristic
112C3×#121—21no—
113C3×#121—22no—
114C3×#121—22no—
115C3×#121D411yescharacteristic
116C3×#120—22no—
117C3×C4×Q8—21no—
118C3×C4×Q8—21no—
119C3×C4×Q8—21no—
120C3×C4×Q8—21no—
121C3×C4×Q8—21no—
122C3×C4×Q8D411yescharacteristic
123C3×C4×D4—22no—
124C3×C4×D4—21no—
125C3×C4×D4—22no—
126C3×C4×D4—21no—
127C3×C4×D4D411yescharacteristic
128C3×#117—22no—
129C3×#117—21no—
130C3×#117—21no—
131C3×#117D412yes—
132C2×C3×C22⋊C4—22no—
133C2×C3×C22⋊C4—21no—
134C2×C3×C22⋊C4—21no—
135C2×C3×C42C2311yescharacteristic
136C3×#107—22no—
137C3×#107—21no—
138C3×#107—21no—
139C3×#106—22no—
140C3×#106—21no—
141C3×#106—21no—
142C3×C4⋊C8—21no—
143C3×C4⋊C8—21no—
144C3×C4⋊C8—21no—
145C3×#103—22no—
146C3×#103—21no—
147C3×#103—21no—
148C3×#103—22no—
149C3×#103—22no—
150C3×#102—22no—
151C3×#102—21no—
152C3×#102—21no—
153C3×C22⋊C8—21no—
154C3×C22⋊C8—21no—
155C3×C22⋊C8—21no—
156C3×#97C2312yes—
157C3×#97C2311yescharacteristic
158C3×#97C2311yescharacteristic
159C3×#97C2312yes—
160#563C22×C312yes—
161#562C22×C312yes—
162#556—21no—
163#551—22no—
164D4×Q8—21no—
165#548—21no—
166#546—21no—
167#543—21no—
168#542—21no—
169#542—22no—
170#538—21no—
171#536—21no—
172#533C22×C311yescharacteristic
173#533C22×C311yescharacteristic
174#529C22×C311yescharacteristic
175C2×#124C22×C311yescharacteristic
176#501C22×C311yescharacteristic, complemented
177#501C22×C312yescomplemented
178#501C22×C311yescharacteristic, complemented
179#497C22×C312yes—
180#491C22×C312yescomplemented
181#489C22×C312yes—
182#489C22×C311yescharacteristic, complemented
183#489C22×C311yescharacteristic, complemented
184#485—21no—
185#485—22no—
186#482—21no—
187#479—21no—
188#478—21no—
189#477—21no—
190#475—21no—
191#464—22no—
192#451—21no—
193#450—21no—
194#432C22×C311yescharacteristic
195#432C22×C311yescharacteristic
196#432C22×C311yescharacteristic
197#330C22×C312yescomplemented
198#330C22×C312yescomplemented
199#330C22×C312yescomplemented
200#329C22×C312yes—
201#329C22×C312yes—
202#329C22×C312yescomplemented
203C24×C3—21no—
204C3×#41—82no—
205C2×C3×Q8—22no—
206C2×C3×Q8—21no—
207C2×C3×Q8—21no—
208C2×C3×Q8—21no—
209C2×C3×Q8—21no—
210C2×C3×Q8—21no—
211C2×C3×Q8—82no—
212C2×C3×Q8—81no—
213C2×C3×Q8C2×D411yescharacteristic
214C2×C3×Q8C2×D412yes—
215C2×C3×D4—21no—
216C2×C3×D4—22no—
217C2×C3×D4—22no—
218C2×C3×D4—21no—
219C2×C3×D4—81no—
220C2×C3×D4C2×D411yescharacteristic
221C2×C3×D4C2×D412yes—
222C22×C3×C4—22no—
223C22×C3×C4—22no—
224C22×C3×C4—22no—
225C22×C3×C4—21no—
226C22×C3×C4—21no—
227C22×C3×C4C2×D411yescharacteristic
228C22×C3×C4C2×D411yescharacteristic
229C22×C3×C4C2×D411yescharacteristic
230C3×Q16—82no—
231C3×SD16—82no—
232C2×C3×C8—21no—
233C2×C3×C8—21no—
234C2×C3×C8—22no—
235C2×C3×C8—22no—
236C3×C4⋊C4—22no—
237C3×C4⋊C4—22no—
238C3×C4⋊C4—22no—
239C3×C4⋊C4—22no—
240C3×C4⋊C4—21no—
241C3×C4⋊C4—21no—
242C3×C4⋊C4—21no—
243C3×C4⋊C4—21no—
244C3×C4⋊C4—21no—
245C3×C4⋊C4—21no—
246C3×C4⋊C4—22no—
247C3×C4⋊C4—22no—
248C3×C4⋊C4—21no—
249C3×C4⋊C4—21no—
250C3×C4⋊C4—21no—
251C3×C4⋊C4—21no—
252C3×C4⋊C4—41no—
253C3×C4⋊C4—41no—
254C3×C4⋊C4C2×D412yes—
255C3×C4⋊C4C2×D412yes—
256C3×C4⋊C4C2×D411yescharacteristic
257C3×C4⋊C4C2×D411yescharacteristic
258C3×C22⋊C4—22no—
259C3×C22⋊C4—22no—
260C3×C22⋊C4—22no—
261C3×C22⋊C4—22no—
262C3×C22⋊C4—22no—
263C3×C22⋊C4—21no—
264C3×C22⋊C4—22no—
265C3×C22⋊C4—22no—
266C3×C22⋊C4—22no—
267C3×C22⋊C4—21no—
268C3×C22⋊C4—21no—
269C3×C22⋊C4—22no—
270C3×C22⋊C4—22no—
271C3×C22⋊C4—21no—
272C3×C22⋊C4—21no—
273C3×C22⋊C4—41no—
274C3×C42—22no—
275C3×C42—22no—
276C3×C42—21no—
277C3×C42—41no—
278C3×C42C2×D411yescharacteristic
279C3×C42C2×D411yescharacteristic
280C3×C42C2×D411yescharacteristic
281C3×C42C2411yescharacteristic
282C2×#41—21no—
283C22×Q8—21no—
284C22×Q8C3×D411yescharacteristic
285C22×D4C3×D411yescharacteristic
286C2×Q16—22no—
287C2×SD16—22no—
288C4⋊Q8—21no—
289C4⋊Q8—22no—
290C4⋊Q8C3×D411yescharacteristic
291C4⋊Q8C3×D411yescharacteristic
292C4⋊Q8C23×C311yescharacteristic
293C4⋊Q8C23×C311yescharacteristic
294#126—22no—
295#126—22no—
296#126—22no—
297#126—21no—
298#125—21no—
299#125C23×C311yescharacteristic
300#125C23×C312yes—
301#124—21no—
302#124—22no—
303#124—22no—
304#124—21no—
305#124—21no—
306#124C3×D412yes—
307#124C23×C312yes—
308#124C23×C311yescharacteristic
309#123—22no—
310#123—22no—
311#123—21no—
312#123—22no—
313#123—22no—
314C22⋊Q8—22no—
315C22⋊Q8—22no—
316C22⋊Q8—21no—
317C22⋊Q8—22no—
318C22⋊Q8—22no—
319C22⋊Q8—22no—
320C22⋊Q8—21no—
321C22⋊Q8—21no—
322C22⋊Q8—22no—
323C22⋊Q8—22no—
324C22⋊Q8—21no—
325C22⋊Q8—21no—
326C22⋊Q8C3×D411yescharacteristic
327#121—21no—
328#121—22no—
329#121—22no—
330#121C3×D411yescharacteristic
331#120—22no—
332C4×Q8—21no—
333C4×Q8—21no—
334C4×Q8—21no—
335C4×Q8—21no—
336C4×Q8—21no—
337C4×Q8C3×D411yescharacteristic
338C4×D4—22no—
339C4×D4—21no—
340C4×D4—22no—
341C4×D4—21no—
342C4×D4C3×D411yescharacteristic
343#117—22no—
344#117—21no—
345#117—21no—
346#117C3×D412yes—
347C2×C22⋊C4—22no—
348C2×C22⋊C4—21no—
349C2×C22⋊C4—21no—
350C2×C42C23×C311yescharacteristic
351#107—22no—
352#107—21no—
353#107—21no—
354#106—22no—
355#106—21no—
356#106—21no—
357C4⋊C8—21no—
358C4⋊C8—21no—
359C4⋊C8—21no—
360#103—22no—
361#103—21no—
362#103—21no—
363#103—22no—
364#103—22no—
365#102—22no—
366#102—21no—
367#102—21no—
368C22⋊C8—21no—
369C22⋊C8—21no—
370C22⋊C8—21no—
371#97C23×C312yes—
372#97C23×C311yescharacteristic
373#97C23×C311yescharacteristic
374#97C23×C312yes—
375C23×C3—22no—
376C23×C3—21no—
377C23×C3—42no—
378C23×C3—81no—
379C23×C3—81no—
380C23×C3#12011yescharacteristic
381C3×Q8—42no—
382C3×Q8—41no—
383C3×Q8—42no—
384C3×Q8—42no—
385C3×Q8—42no—
386C3×Q8—42no—
387C3×Q8—81no—
388C3×Q8—82no—
389C3×D4—42no—
390C3×D4—41no—
391C3×D4—42no—
392C3×D4—42no—
393C3×D4—82no—
394C3×D4—82no—
395C2×C3×C4—21no—
396C2×C3×C4—22no—
397C2×C3×C4—21no—
398C2×C3×C4—22no—
399C2×C3×C4—22no—
400C2×C3×C4—21no—
401C2×C3×C4—41no—
402C2×C3×C4—41no—
403C2×C3×C4—41no—
404C2×C3×C4—42no—
405C2×C3×C4—41no—
406C2×C3×C4—41no—
407C2×C3×C4—81no—
408C2×C3×C4—82no—
409C2×C3×C4—82no—
410C2×C3×C4—82no—
411C2×C3×C4#12011yescharacteristic
412C2×C3×C4#12011yescharacteristic
413C2×C3×C4#12011yescharacteristic
414C2×C3×C4C22×D411yescharacteristic
415C2×C3×C4C22×D411yescharacteristic
416C2×C3×C4C22×D411yescharacteristic
417C3×C8—42no—
418C3×C8—41no—
419C3×C8—41no—
420C3×C8—42no—
421C24—21no—
422#41—82no—
423C2×Q8—22no—
424C2×Q8—21no—
425C2×Q8—21no—
426C2×Q8—21no—
427C2×Q8—21no—
428C2×Q8—21no—
429C2×Q8—82no—
430C2×Q8—81no—
431C2×Q8C2×C3×D411yescharacteristic
432C2×Q8C2×C3×D412yes—
433C2×D4—21no—
434C2×D4—22no—
435C2×D4—22no—
436C2×D4—21no—
437C2×D4—81no—
438C2×D4C2×C3×D411yescharacteristic
439C2×D4C2×C3×D412yes—
440C22×C4—22no—
441C22×C4—22no—
442C22×C4—22no—
443C22×C4—21no—
444C22×C4—21no—
445C22×C4C2×C3×D411yescharacteristic
446C22×C4C2×C3×D411yescharacteristic
447C22×C4C2×C3×D411yescharacteristic
448Q16—82no—
449SD16—82no—
450C2×C8—21no—
451C2×C8—21no—
452C2×C8—22no—
453C2×C8—22no—
454C4⋊C4—22no—
455C4⋊C4—22no—
456C4⋊C4—22no—
457C4⋊C4—22no—
458C4⋊C4—21no—
459C4⋊C4—21no—
460C4⋊C4—21no—
461C4⋊C4—21no—
462C4⋊C4—21no—
463C4⋊C4—21no—
464C4⋊C4—22no—
465C4⋊C4—22no—
466C4⋊C4—21no—
467C4⋊C4—21no—
468C4⋊C4—21no—
469C4⋊C4—21no—
470C4⋊C4—41no—
471C4⋊C4—41no—
472C4⋊C4C2×C3×D412yes—
473C4⋊C4C2×C3×D412yes—
474C4⋊C4C2×C3×D411yescharacteristic
475C4⋊C4C2×C3×D411yescharacteristic
476C22⋊C4—22no—
477C22⋊C4—22no—
478C22⋊C4—22no—
479C22⋊C4—22no—
480C22⋊C4—22no—
481C22⋊C4—21no—
482C22⋊C4—22no—
483C22⋊C4—22no—
484C22⋊C4—22no—
485C22⋊C4—21no—
486C22⋊C4—21no—
487C22⋊C4—22no—
488C22⋊C4—22no—
489C22⋊C4—21no—
490C22⋊C4—21no—
491C22⋊C4—41no—
492C42—22no—
493C42—22no—
494C42—21no—
495C42—41no—
496C42C2×C3×D411yescharacteristic
497C42C2×C3×D411yescharacteristic
498C42C2×C3×D411yescharacteristic
499C42C24×C311yescharacteristic
500C22×C3—21no—
501C22×C3—21no—
502C22×C3—21no—
503C22×C3—41no—
504C22×C3—42no—
505C22×C3—41no—
506C22×C3—42no—
507C22×C3—42no—
508C22×C3—41no—
509C22×C3—162no—
510C22×C3C2×#12011yescharacteristic
511C3×C4—21no—
512C3×C4—21no—
513C3×C4—21no—
514C3×C4—21no—
515C3×C4—21no—
516C3×C4—21no—
517C3×C4—41no—
518C3×C4—42no—
519C3×C4—42no—
520C3×C4—41no—
521C3×C4—41no—
522C3×C4—42no—
523C3×C4—81no—
524C3×C4—81no—
525C23—22no—
526C23—21no—
527C23—42no—
528C23—81no—
529C23—81no—
530C23C3×#12011yescharacteristic
531Q8—42no—
532Q8—41no—
533Q8—42no—
534Q8—42no—
535Q8—42no—
536Q8—42no—
537Q8—81no—
538Q8—82no—
539D4—42no—
540D4—41no—
541D4—42no—
542D4—42no—
543D4—82no—
544D4—82no—
545C2×C4—21no—
546C2×C4—22no—
547C2×C4—21no—
548C2×C4—22no—
549C2×C4—22no—
550C2×C4—21no—
551C2×C4—41no—
552C2×C4—41no—
553C2×C4—41no—
554C2×C4—42no—
555C2×C4—41no—
556C2×C4—41no—
557C2×C4—81no—
558C2×C4—82no—
559C2×C4—82no—
560C2×C4—82no—
561C2×C4C3×#12011yescharacteristic
562C2×C4C3×#12011yescharacteristic
563C2×C4C3×#12011yescharacteristic
564C2×C4C22×C3×D411yescharacteristic
565C2×C4C22×C3×D411yescharacteristic
566C2×C4C22×C3×D411yescharacteristic
567C8—42no—
568C8—42no—
569C8—41no—
570C8—41no—
571C2×C3—41no—
572C2×C3—81no—
573C2×C3—82no—
574C2×C3#301911yescharacteristic
575C2×C3#302011yescharacteristic
576C2×C3#302211yescharacteristic
577C22—21no—
578C22—21no—
579C22—21no—
580C22—41no—
581C22—42no—
582C22—41no—
583C22—42no—
584C22—42no—
585C22—41no—
586C22—162no—
587C22C2×C3×#12011yescharacteristic
588C4—21no—
589C4—21no—
590C4—21no—
591C4—21no—
592C4—21no—
593C4—21no—
594C4—41no—
595C4—42no—
596C4—42no—
597C4—41no—
598C4—41no—
599C4—42no—
600C4—81no—
601C4—81no—
602C3#1909111yescharacteristic, direct product factor, Sylow
603C2—41no—
604C2—82no—
605C2—81no—
606C2C3×#301911yescharacteristic
607C2C3×#302011yescharacteristic
608C2C3×#302211yescharacteristic
subgroupG/H
center, socleC22×C3C2×#120
commutator, Frattini, cosocleC42C24×C3
prime radicalC3×#3561C2
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C3 ◁ C2×C3×C42 ◁ G

Complements

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

NH ≅ G/Ntype
2. C3×#3240C2semidirect
3. C3×#3237C2semidirect
4. C3×#3215C2semidirect
5. C3×#1664C2semidirect
6. C3×#1662C2semidirect
7. C3×#1661C2semidirect
8. C3×#1660C2semidirect
9. C3×#1537C2semidirect
10. C3×#1535C2semidirect
11. C3×#1533C2semidirect
12. #19091C3direct (N × H)
29. C3×#501C22semidirect
30. C3×#501C22semidirect
31. C3×#501C22semidirect
33. C3×#491C22semidirect
35. C3×#489C22semidirect
36. C3×#489C22semidirect
50. C3×#330C22semidirect
51. C3×#330C22semidirect
52. C3×#330C22semidirect
55. C3×#329C22semidirect
57. #3240C2×C3semidirect
58. #3237C2×C3semidirect
59. #3215C2×C3semidirect
60. #1664C2×C3semidirect
61. #1662C2×C3semidirect
62. #1661C2×C3semidirect
63. #1660C2×C3semidirect
64. #1537C2×C3semidirect
65. #1535C2×C3semidirect
66. #1533C2×C3semidirect
176. #501C22×C3semidirect
177. #501C22×C3semidirect
178. #501C22×C3semidirect
180. #491C22×C3semidirect
182. #489C22×C3semidirect
183. #489C22×C3semidirect
197. #330C22×C3semidirect
198. #330C22×C3semidirect
199. #330C22×C3semidirect
202. #329C22×C3semidirect
602. C3#19091direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#35612
C3×#32402
C3×#32372
C3×#32152
C3×#16642
C3×#16622
C3×#16612
C3×#16602
C3×#15372
C3×#15352
C3×#15332
#190913