Finite Group Databasebeta

← C3×#29630 #10648237

Subgroups — C3×#29630 #10648237

Order 768.

1494 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×#535C211yesmaximal, characteristic, complemented
2C2×C3×#449C211yesmaximal, characteristic, complemented
3C2×C3×#447C211yesmaximal, characteristic, complemented
4C3×#2624C211yesmaximal, characteristic, complemented
5C3×#2042C212yesmaximal, complemented
6C3×#2041C212yesmaximal, complemented
7C3×#2012C212yesmaximal, complemented
8C3×#2011C212yesmaximal, complemented
9C3×#1818C211yesmaximal, characteristic, complemented
10C3×#1788C211yesmaximal, characteristic, complemented
11C3×#1786C211yesmaximal, characteristic, complemented
12#29630C311yesmaximal, characteristic, direct product factor, Sylow
13C22×C3×#41C2211yescharacteristic
14C23×C3×D4C2211yescharacteristic
15C22×C3×SD16C2211yescharacteristic, complemented
16C22×C3×D8C2212yes—
17C22×C3×D8C2211yescharacteristic, complemented
18C3×#535—24no—
19C3×#535—24no—
20C2×C3×#127C2212yes—
21C2×C3×#124C2212yes—
22C2×C3×#121—21no—
23C2×C3×#121—21no—
24C2×C3×#121C2211yescharacteristic
25C2×C3×#120—22no—
26C2×C3×#117C2211yescharacteristic
27C3×#449—24no—
28C3×#447—24no—
29C2×C3×#103C2211yescharacteristic, complemented
30C2×C3×#103C2212yescomplemented
31C2×C3×#102C2212yes—
32C2×C3×#102C2212yes—
33C2×C3×#102C2212yes—
34C2×C3×#102C2211yescharacteristic, complemented
35C2×C3×#102C2212yescomplemented
36C2×C3×C22⋊C8C2211yescharacteristic
37C2×C3×C22⋊C8C2211yescharacteristic
38C3×#399—21no—
39C3×#397—21no—
40C3×#394—22no—
41C3×#390C2212yescomplemented
42C3×#389C2212yescomplemented
43C3×#380C2211yescharacteristic
44C3×#336C2212yescomplemented
45C3×#336C2212yescomplemented
46C2×#535C2×C311yescharacteristic, complemented
47C2×#449C2×C311yescharacteristic, complemented
48C2×#447C2×C311yescharacteristic, complemented
49#2624C2×C311yescharacteristic, complemented
50#2042C2×C312yescomplemented
51#2041C2×C312yescomplemented
52#2012C2×C312yescomplemented
53#2011C2×C312yescomplemented
54#1818C2×C311yescharacteristic, complemented
55#1788C2×C311yescharacteristic, complemented
56#1786C2×C311yescharacteristic, complemented
57C25×C3—21no—
58C2×C3×#41—22no—
59C2×C3×#41—42no—
60C2×C3×#41—42no—
61C2×C3×#41D414yes—
62C22×C3×Q8C2311yescharacteristic
63C22×C3×D4—21no—
64C22×C3×D4—21no—
65C22×C3×D4—21no—
66C22×C3×D4—22no—
67C22×C3×D4—22no—
68C22×C3×D4—22no—
69C22×C3×D4—42no—
70C22×C3×D4—42no—
71C22×C3×D4D414yes—
72C22×C3×D4C2311yescharacteristic
73C22×C3×D4C2312yes—
74C22×C3×D4C2311yescharacteristic
75C23×C3×C4—21no—
76C23×C3×C4C2311yescharacteristic
77C2×C3×SD16—22no—
78C2×C3×SD16—42no—
79C2×C3×D8—24no—
80C2×C3×D8—22no—
81C2×C3×D8—42no—
82C2×C3×D8—42no—
83C2×C3×D8—42no—
84C22×C3×C8C2312yes—
85C22×C3×C8C2311yescharacteristic
86C22×C3×C8C2311yescharacteristic
87C3×#127—24no—
88C3×#127—24no—
89C3×#124—24no—
90C3×#124—24no—
91C3×#121—28no—
92C3×#121—28no—
93C3×#121—22no—
94C3×#121—22no—
95C3×#120—216no—
96C3×#117—22no—
97C3×#117—22no—
98C2×C3×C4⋊C4—22no—
99C2×C3×C4⋊C4D411yescharacteristic
100C2×C3×C4⋊C4D411yescharacteristic
101C2×C3×C4⋊C4C2312yes—
102C2×C3×C4⋊C4C2311yescharacteristic
103C2×C3×C22⋊C4—22no—
104C2×C3×C22⋊C4—22no—
105C2×C3×C22⋊C4—21no—
106C2×C3×C22⋊C4—21no—
107C2×C3×C22⋊C4—22no—
108C2×C3×C22⋊C4—22no—
109C2×C3×C22⋊C4D412yes—
110C2×C3×C42C2312yes—
111C3×#103—22no—
112C3×#103—42no—
113C3×#102—24no—
114C3×#102—22no—
115C3×#102—42no—
116C3×#102—42no—
117C3×#102—42no—
118C3×C22⋊C8—22no—
119C3×C22⋊C8—22no—
120C3×#95—21no—
121C3×#95—22no—
122C22×#41C22×C311yescharacteristic
123C23×D4C22×C311yescharacteristic
124C22×SD16C22×C311yescharacteristic, complemented
125C22×D8C22×C312yes—
126C22×D8C22×C311yescharacteristic, complemented
127#535—24no—
128#535—24no—
129C2×#127C22×C312yes—
130C2×#124C22×C312yes—
131C2×#121—21no—
132C2×#121—21no—
133C2×#121C22×C311yescharacteristic
134C2×#120—22no—
135C2×#117C22×C311yescharacteristic
136#449—24no—
137#447—24no—
138C2×#103C22×C311yescharacteristic, complemented
139C2×#103C22×C312yescomplemented
140C2×#102C22×C312yes—
141C2×#102C22×C312yes—
142C2×#102C22×C312yes—
143C2×#102C22×C311yescharacteristic, complemented
144C2×#102C22×C312yescomplemented
145C2×C22⋊C8C22×C311yescharacteristic
146C2×C22⋊C8C22×C311yescharacteristic
147#399—21no—
148#397—21no—
149#394—22no—
150#390C22×C312yescomplemented
151#389C22×C312yescomplemented
152#380C22×C311yescharacteristic
153#336C22×C312yescomplemented
154#336C22×C312yescomplemented
155C24×C3—22no—
156C24×C3—21no—
157C24×C3—24no—
158C24×C3—21no—
159C24×C3—44no—
160C24×C3—81no—
161C24×C3—82no—
162C24×C3—81no—
163C24×C3C2×D411yescharacteristic
164C3×#41—44no—
165C3×#41—44no—
166C3×#41—48no—
167C2×C3×Q8—21no—
168C2×C3×Q8—22no—
169C2×C3×Q8—22no—
170C2×C3×Q8C2×D412yes—
171C2×C3×D4—24no—
172C2×C3×D4—28no—
173C2×C3×D4—28no—
174C2×C3×D4—24no—
175C2×C3×D4—22no—
176C2×C3×D4—21no—
177C2×C3×D4—21no—
178C2×C3×D4—21no—
179C2×C3×D4—22no—
180C2×C3×D4—22no—
181C2×C3×D4—22no—
182C2×C3×D4—22no—
183C2×C3×D4—22no—
184C2×C3×D4—22no—
185C2×C3×D4—22no—
186C2×C3×D4—22no—
187C2×C3×D4—48no—
188C2×C3×D4—44no—
189C2×C3×D4—44no—
190C2×C3×D4—44no—
191C2×C3×D4—44no—
192C2×C3×D4—42no—
193C2×C3×D4—82no—
194C2×C3×D4—82no—
195C2×C3×D4—82no—
196C2×C3×D4—82no—
197C2×C3×D4—82no—
198C2×C3×D4C2×D414yes—
199C2×C3×D4C2×D412yes—
200C22×C3×C4—22no—
201C22×C3×C4—22no—
202C22×C3×C4—21no—
203C22×C3×C4—24no—
204C22×C3×C4—22no—
205C22×C3×C4—21no—
206C22×C3×C4—44no—
207C22×C3×C4C2×D412yes—
208C22×C3×C4C2×D412yes—
209C22×C3×C4C2×D411yescharacteristic
210C22×C3×C4C2×D412yes—
211C22×C3×C4C2×D412yes—
212C22×C3×C4C2411yescharacteristic
213C3×SD16—44no—
214C3×D8—48no—
215C3×D8—44no—
216C2×C3×C8—22no—
217C2×C3×C8—21no—
218C2×C3×C8—21no—
219C2×C3×C8—22no—
220C2×C3×C8—22no—
221C2×C3×C8—22no—
222C2×C3×C8—22no—
223C3×C4⋊C4—22no—
224C3×C4⋊C4—22no—
225C3×C4⋊C4—21no—
226C3×C4⋊C4—21no—
227C3×C4⋊C4—22no—
228C3×C4⋊C4—22no—
229C3×C4⋊C4—82no—
230C3×C22⋊C4—28no—
231C3×C22⋊C4—28no—
232C3×C22⋊C4—24no—
233C3×C22⋊C4—42no—
234C3×C22⋊C4—82no—
235C3×C22⋊C4—82no—
236C3×C22⋊C4—81no—
237C3×C42—22no—
238C3×C42—22no—
239C25—21no—
240C2×#41—22no—
241C2×#41—42no—
242C2×#41—42no—
243C2×#41C3×D414yes—
244C22×Q8C23×C311yescharacteristic
245C22×D4—21no—
246C22×D4—21no—
247C22×D4—21no—
248C22×D4—22no—
249C22×D4—22no—
250C22×D4—22no—
251C22×D4—42no—
252C22×D4—42no—
253C22×D4C3×D414yes—
254C22×D4C23×C311yescharacteristic
255C22×D4C23×C312yes—
256C22×D4C23×C311yescharacteristic
257C23×C4—21no—
258C23×C4C23×C311yescharacteristic
259C2×SD16—22no—
260C2×SD16—42no—
261C2×D8—24no—
262C2×D8—22no—
263C2×D8—42no—
264C2×D8—42no—
265C2×D8—42no—
266C22×C8C23×C312yes—
267C22×C8C23×C311yescharacteristic
268C22×C8C23×C311yescharacteristic
269#127—24no—
270#127—24no—
271#124—24no—
272#124—24no—
273#121—28no—
274#121—28no—
275#121—22no—
276#121—22no—
277#120—216no—
278#117—22no—
279#117—22no—
280C2×C4⋊C4—22no—
281C2×C4⋊C4C3×D411yescharacteristic
282C2×C4⋊C4C3×D411yescharacteristic
283C2×C4⋊C4C23×C311yescharacteristic
284C2×C4⋊C4C23×C312yes—
285C2×C22⋊C4—22no—
286C2×C22⋊C4—22no—
287C2×C22⋊C4—21no—
288C2×C22⋊C4—21no—
289C2×C22⋊C4—22no—
290C2×C22⋊C4—22no—
291C2×C22⋊C4C3×D412yes—
292C2×C42C23×C312yes—
293#103—22no—
294#103—42no—
295#102—24no—
296#102—22no—
297#102—42no—
298#102—42no—
299#102—42no—
300C22⋊C8—22no—
301C22⋊C8—22no—
302#95—21no—
303#95—22no—
304C23×C3—22no—
305C23×C3—21no—
306C23×C3—22no—
307C23×C3—21no—
308C23×C3—24no—
309C23×C3—22no—
310C23×C3—48no—
311C23×C3—42no—
312C23×C3—42no—
313C23×C3—42no—
314C23×C3—42no—
315C23×C3—41no—
316C23×C3—42no—
317C23×C3—42no—
318C23×C3—42no—
319C23×C3—41no—
320C23×C3—42no—
321C23×C3—41no—
322C23×C3—42no—
323C23×C3—41no—
324C23×C3—42no—
325C23×C3—41no—
326C23×C3—84no—
327C23×C3—84no—
328C23×C3—88no—
329C23×C3—88no—
330C23×C3#12012yes—
331C23×C3C22×D411yescharacteristic
332C3×Q8—22no—
333C3×Q8—22no—
334C3×Q8—42no—
335C3×D4—24no—
336C3×D4—22no—
337C3×D4—24no—
338C3×D4—22no—
339C3×D4—48no—
340C3×D4—48no—
341C3×D4—42no—
342C3×D4—42no—
343C3×D4—42no—
344C3×D4—42no—
345C3×D4—41no—
346C3×D4—41no—
347C3×D4—88no—
348C3×D4—88no—
349C3×D4—84no—
350C2×C3×C4—22no—
351C2×C3×C4—24no—
352C2×C3×C4—22no—
353C2×C3×C4—22no—
354C2×C3×C4—22no—
355C2×C3×C4—22no—
356C2×C3×C4—22no—
357C2×C3×C4—22no—
358C2×C3×C4—22no—
359C2×C3×C4—22no—
360C2×C3×C4—22no—
361C2×C3×C4—48no—
362C2×C3×C4—42no—
363C2×C3×C4—41no—
364C2×C3×C4—42no—
365C2×C3×C4—42no—
366C2×C3×C4—42no—
367C2×C3×C4—42no—
368C2×C3×C4#12012yes—
369C2×C3×C4C22×D411yescharacteristic
370C2×C3×C4C22×D411yescharacteristic
371C2×C3×C4H(5,𝔽2)12yes—
372C2×C3×C4H(5,𝔽2)12yes—
373C3×C8—42no—
374C3×C8—41no—
375C3×C8—41no—
376C24—22no—
377C24—21no—
378C24—24no—
379C24—21no—
380C24—44no—
381C24—81no—
382C24—82no—
383C24—81no—
384C24C2×C3×D411yescharacteristic
385#41—44no—
386#41—44no—
387#41—48no—
388C2×Q8—21no—
389C2×Q8—22no—
390C2×Q8—22no—
391C2×Q8C2×C3×D412yes—
392C2×D4—24no—
393C2×D4—28no—
394C2×D4—28no—
395C2×D4—24no—
396C2×D4—22no—
397C2×D4—21no—
398C2×D4—21no—
399C2×D4—21no—
400C2×D4—22no—
401C2×D4—22no—
402C2×D4—22no—
403C2×D4—22no—
404C2×D4—22no—
405C2×D4—22no—
406C2×D4—22no—
407C2×D4—22no—
408C2×D4—48no—
409C2×D4—44no—
410C2×D4—44no—
411C2×D4—44no—
412C2×D4—44no—
413C2×D4—42no—
414C2×D4—82no—
415C2×D4—82no—
416C2×D4—82no—
417C2×D4—82no—
418C2×D4—82no—
419C2×D4C2×C3×D414yes—
420C2×D4C2×C3×D412yes—
421C22×C4—22no—
422C22×C4—22no—
423C22×C4—21no—
424C22×C4—24no—
425C22×C4—22no—
426C22×C4—21no—
427C22×C4—44no—
428C22×C4C2×C3×D412yes—
429C22×C4C2×C3×D412yes—
430C22×C4C2×C3×D411yescharacteristic
431C22×C4C2×C3×D412yes—
432C22×C4C2×C3×D412yes—
433C22×C4C24×C311yescharacteristic
434SD16—44no—
435D8—48no—
436D8—44no—
437C2×C8—22no—
438C2×C8—21no—
439C2×C8—21no—
440C2×C8—22no—
441C2×C8—22no—
442C2×C8—22no—
443C2×C8—22no—
444C4⋊C4—22no—
445C4⋊C4—22no—
446C4⋊C4—21no—
447C4⋊C4—21no—
448C4⋊C4—22no—
449C4⋊C4—22no—
450C4⋊C4—82no—
451C22⋊C4—28no—
452C22⋊C4—28no—
453C22⋊C4—24no—
454C22⋊C4—42no—
455C22⋊C4—82no—
456C22⋊C4—82no—
457C22⋊C4—81no—
458C42—22no—
459C42—22no—
460C22×C3—22no—
461C22×C3—22no—
462C22×C3—22no—
463C22×C3—42no—
464C22×C3—42no—
465C22×C3—42no—
466C22×C3—44no—
467C22×C3—42no—
468C22×C3—44no—
469C22×C3—42no—
470C22×C3—44no—
471C22×C3—816no—
472C22×C3—82no—
473C22×C3—82no—
474C22×C3—82no—
475C22×C3—82no—
476C22×C3—82no—
477C22×C3—82no—
478C22×C3—81no—
479C22×C3—82no—
480C22×C3—82no—
481C22×C3—81no—
482C22×C3—81no—
483C22×C3C2×#12011yescharacteristic
484C22×C3#53512yes—
485C22×C3#57611yescharacteristic
486C22×C3#57612yes—
487C22×C3#57711yescharacteristic
488C3×C4—22no—
489C3×C4—42no—
490C3×C4—42no—
491C3×C4—42no—
492C3×C4—82no—
493C3×C4—81no—
494C3×C4#53412yes—
495C3×C4#53411yescharacteristic
496C3×C4#53411yescharacteristic
497C23—21no—
498C23—22no—
499C23—21no—
500C23—22no—
501C23—24no—
502C23—22no—
503C23—48no—
504C23—42no—
505C23—41no—
506C23—42no—
507C23—42no—
508C23—42no—
509C23—41no—
510C23—42no—
511C23—42no—
512C23—42no—
513C23—42no—
514C23—41no—
515C23—42no—
516C23—41no—
517C23—41no—
518C23—42no—
519C23—84no—
520C23—84no—
521C23—88no—
522C23—88no—
523C23C3×#12012yes—
524C23C22×C3×D411yescharacteristic
525Q8—22no—
526Q8—22no—
527Q8—42no—
528D4—24no—
529D4—22no—
530D4—24no—
531D4—22no—
532D4—48no—
533D4—48no—
534D4—42no—
535D4—42no—
536D4—42no—
537D4—42no—
538D4—41no—
539D4—41no—
540D4—88no—
541D4—88no—
542D4—84no—
543C2×C4—22no—
544C2×C4—24no—
545C2×C4—22no—
546C2×C4—22no—
547C2×C4—22no—
548C2×C4—22no—
549C2×C4—22no—
550C2×C4—22no—
551C2×C4—22no—
552C2×C4—22no—
553C2×C4—22no—
554C2×C4—48no—
555C2×C4—42no—
556C2×C4—42no—
557C2×C4—42no—
558C2×C4—42no—
559C2×C4—41no—
560C2×C4—42no—
561C2×C4C3×#12012yes—
562C2×C4C22×C3×D411yescharacteristic
563C2×C4C22×C3×D411yescharacteristic
564C2×C4C3×H(5,𝔽2)12yes—
565C2×C4C3×H(5,𝔽2)12yes—
566C8—42no—
567C8—41no—
568C8—41no—
569C2×C3—42no—
570C2×C3—82no—
571C2×C3—84no—
572C2×C3—161no—
573C2×C3#261311yescharacteristic
574C2×C3#300811yescharacteristic
575C2×C3#301211yescharacteristic
576C2×C3#322012yes—
577C2×C3#322412yes—
578C22—22no—
579C22—22no—
580C22—22no—
581C22—42no—
582C22—42no—
583C22—42no—
584C22—44no—
585C22—42no—
586C22—44no—
587C22—42no—
588C22—44no—
589C22—816no—
590C22—82no—
591C22—82no—
592C22—82no—
593C22—82no—
594C22—82no—
595C22—82no—
596C22—82no—
597C22—82no—
598C22—81no—
599C22—81no—
600C22—81no—
601C22C2×C3×#12011yescharacteristic
602C22C3×#53512yes—
603C22C3×#57611yescharacteristic
604C22C3×#57612yes—
605C22C3×#57711yescharacteristic
606C4—22no—
607C4—42no—
608C4—42no—
609C4—42no—
610C4—82no—
611C4—81no—
612C4C3×#53412yes—
613C4C3×#53411yescharacteristic
614C4C3×#53411yescharacteristic
615C3#2963011yescharacteristic, direct product factor, Sylow
616C2—42no—
617C2—84no—
618C2—82no—
619C2—161no—
620C2C3×#261311yescharacteristic
621C2C3×#300811yescharacteristic
622C2C3×#301211yescharacteristic
623C2C3×#322012yes—
624C2C3×#322412yes—
subgroupG/H
center, socleC23×C3C22×D4
commutator, Frattini, cosocleC22×C4C24×C3
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C3 ◁ C2×C3×#117 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C3×#535C2semidirect
2. C2×C3×#449C2semidirect
3. C2×C3×#447C2semidirect
4. C3×#2624C2semidirect
5. C3×#2042C2semidirect
6. C3×#2041C2semidirect
7. C3×#2012C2semidirect
8. C3×#2011C2semidirect
9. C3×#1818C2semidirect
10. C3×#1788C2semidirect
11. C3×#1786C2semidirect
12. #29630C3direct (N × H)
15. C22×C3×SD16C22semidirect
17. C22×C3×D8C22semidirect
29. C2×C3×#103C22semidirect
30. C2×C3×#103C22semidirect
34. C2×C3×#102C22semidirect
35. C2×C3×#102C22semidirect
41. C3×#390C22semidirect
42. C3×#389C22semidirect
44. C3×#336C22semidirect
45. C3×#336C22semidirect
46. C2×#535C2×C3semidirect
47. C2×#449C2×C3semidirect
48. C2×#447C2×C3semidirect
49. #2624C2×C3semidirect
50. #2042C2×C3semidirect
51. #2041C2×C3semidirect
52. #2012C2×C3semidirect
53. #2011C2×C3semidirect
54. #1818C2×C3semidirect
55. #1788C2×C3semidirect
56. #1786C2×C3semidirect
124. C22×SD16C22×C3semidirect
126. C22×D8C22×C3semidirect
138. C2×#103C22×C3semidirect
139. C2×#103C22×C3semidirect
143. C2×#102C22×C3semidirect
144. C2×#102C22×C3semidirect
150. #390C22×C3semidirect
151. #389C22×C3semidirect
153. #336C22×C3semidirect
154. #336C22×C3semidirect
615. C3#29630direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#5352
C2×C3×#4492
C2×C3×#4472
C3×#26242
C3×#20422
C3×#20412
C3×#20122
C3×#20112
C3×#18182
C3×#17882
C3×#17862
#296303