Finite Group Databasebeta

← D3×#5113 #11857791

Subgroups — D3×#5113 #11857791

Order 1152.

1663 conjugacy classes of subgroups.

The subgroup lattice has 772 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D3×#235C211yesmaximal, characteristic
2C22×C3×D3×C8C211yesmaximal, characteristic, complemented
3D3×#926C211yesmaximal, characteristic, complemented
4#10592812C211yesmaximal, characteristic, complemented
5C3×#5113C211yesmaximal, characteristic, complemented
6#10591105C211yesmaximal, characteristic, complemented
7#10591084C211yesmaximal, characteristic, complemented
8#10590954C212yesmaximal, complemented
9D3×#821C212yesmaximal, complemented
10#10590690C212yesmaximal, complemented
11D3×#816C212yesmaximal, complemented
12C2×#5113—31nomaximal
13D3×#416—31nomaximal
14C2×#3828C2211yescharacteristic
15C2×C3×#235C2211yescharacteristic
16C22×C3×C4×D3C2211yescharacteristic
17C2×D3×#67—21no—
18C2×#3804—21no—
19D3×#235—24no—
20D3×#235C418yescomplemented
21C2×D3×D12C2211yescharacteristic
22C2×C4×D32—21no—
23C2×#3799C2211yescharacteristic
24C2×#3798—21no—
25C2×#3795C2211yescharacteristic
26C2×D3×Dic6C2211yescharacteristic
27C22×C32×C8C2211yescharacteristic, complemented
28#64135C2211yescharacteristic, complemented
29C3×#926C2211yescharacteristic, complemented
30C22×C3×C3⋊C8C2211yescharacteristic, complemented
31C2×C3×D3×C8—24no—
32C2×C3×D3×C8C2212yes—
33C2×C3×D3×C8C2212yescomplemented
34D3×#217—21no—
35#63955—21no—
36D3×C4⋊Dic3C2212yes—
37C4×D3×Dic3—21no—
38#63855—21no—
39#63841C2212yescomplemented
40#63648C2212yescomplemented
41#63643C2212yescomplemented
42C3×#821C2212yescomplemented
43C3×#816C2212yescomplemented
44#63567C2212yescomplemented
45#63566C2212yescomplemented
46#63564C2212yescomplemented
47#63563C2212yescomplemented
48C2×D3×#41—31no—
49C22×#235—31no—
50C23×C3×C8—31no—
51C2×#926—31no—
52C22×D3×C8D311yescharacteristic, complemented
53D3×#117—31no—
54C3×#416—31no—
55#5233—31no—
56#5113—31no—
57#5113—31no—
58#5113—31no—
59#5113—31no—
60#5113—32no—
61#5113—32no—
62#5113—61no—
63#5113D311yescharacteristic, direct product factor
64C2×#821—32no—
65C2×#816—32no—
66#5002—31no—
67#4804—32no—
68D3×#103—32no—
69#4772—32no—
70D3×#102—32no—
71C23×C3×D3D411yescharacteristic
72C22×D32—21no—
73C22×C32×C4C2311yescharacteristic
74C2×#638—21no—
75#3828—22no—
76#3828C2×C414yescomplemented
77C2×C4⋊(C3⋊D3)C2311yescharacteristic
78C2×C4×C3⋊D3—21no—
79C2×#634C2311yescharacteristic
80C2×C3×#67—21no—
81C22×C3×Dic3D411yescharacteristic
82C3×#235—22no—
83C3×#235C2×C414yescomplemented
84C2×C3×D12C2311yescharacteristic
85C2×C3×C4×D3—21no—
86C2×C3×C4×D3C2×C414yes—
87C2×C3×C4×D3D411yescharacteristic
88C2×C3×C4×D3D411yescharacteristic
89C2×C3×C4×D3D414yes—
90C2×C3×C4×D3C2311yescharacteristic
91C2×C3×C4×D3C2311yescharacteristic
92C2×C3×Dic6C2311yescharacteristic
93D3×#67—28no—
94C2×#627—21no—
95C2×#626—21no—
96C2×#626—21no—
97C2×#625—21no—
98C2×#624—21no—
99#3804—28no—
100C2×D3×Dic3—21no—
101C2×D3×Dic3—21no—
102C2×D3×Dic3—22no—
103D3×D12—22no—
104D3×D12C2×C414yes—
105C4×D32—28no—
106#3799—22no—
107#3799C2×C414yescomplemented
108#3798—28no—
109#3795—22no—
110#3795C2×C414yescomplemented
111D3×Dic6—22no—
112D3×Dic6C2×C414yes—
113C2×C32×C8—22no—
114C2×C32×C8C2312yes—
115#3757—21no—
116C4⋊(C3⋊Dic3)C2312yes—
117C4×C3⋊Dic3—21no—
118C3×#217—21no—
119C3×C4⋊Dic3C2312yes—
120C3×C4×Dic3—21no—
121C2×C3×C3⋊C8—22no—
122C2×C3×C3⋊C8C2312yes—
123C3×D3×C8—24no—
124C3×D3×C8—24no—
125Dic3⋊Dic3—22no—
126(C2×D3)⋊Dic3—22no—
127Dic32—22no—
128C2×#416—91noSylow
129C2×C3×#41—31no—
130C23×C3×C4—31no—
131C22×#67—61no—
132D3×#41—38no—
133D3×#41—64no—
134C2×#239—31no—
135C2×D3×Q8—31no—
136C2×#237—31no—
137C2×#237—61no—
138C2×D3×D4—31no—
139C2×D3×D4—61no—
140C2×#235—31no—
141C2×#235—31no—
142C2×#235—38no—
143C2×#235—31no—
144C2×#235—31no—
145C2×#235—61no—
146C2×#235—61no—
147C2×#235—64no—
148C2×#235—61no—
149C2×#235—61no—
150C2×#235C2×D311yescharacteristic
151C22×D12—31no—
152C22×C4×D3—61no—
153C22×C4×D3—61no—
154C22×C4×D3C2×D311yescharacteristic
155C22×Dic6—31no—
156C22×C3×C8—21no—
157C22×C3×C8—31no—
158C22×C3×C8—32no—
159C22×C3×C8—32no—
160C22×C3×C8—64no—
161C22×C3×C8C2×D311yescharacteristic, complemented
162C22×C3×C8C2×D311yescharacteristic, complemented
163C3×#117—31no—
164C2×#217—61no—
165#926—31no—
166#926—31no—
167#926—32no—
168#926—61no—
169#926—61no—
170#926—61no—
171#926C2×D311yescharacteristic, complemented
172C2×C4⋊Dic3—32no—
173C2×C4×Dic3—61no—
174C22×C3⋊C8C2×D311yescharacteristic, complemented
175C2×D3×C8—24no—
176C2×D3×C8C2×D312yes—
177C2×D3×C8C2×D312yescomplemented
178#892—32no—
179D3×C4⋊C4—32no—
180D3×C22⋊C4—61no—
181#877—61no—
182#872—61no—
183C42×D3—61no—
184C3×#103—32no—
185C3×#102—32no—
186#835—32no—
187#832—32no—
188#821—32no—
189#821—32no—
190#821—32no—
191#821—32no—
192#821—62no—
193#821C2×D312yescomplemented
194#816—32no—
195#816—32no—
196#816—32no—
197#816—32no—
198#816—62no—
199#816C2×D312yescomplemented
200#810—32no—
201#809—32no—
202C23×C32C2×D411yescharacteristic
203C22×C3⋊D3—21no—
204C22×C3×D3—24no—
205C22×C3×D3—21no—
206C22×C3×D3C22⋊C414yes—
207C22×C3×D3C2×D411yescharacteristic
208C22×C3×D3C2×D411yescharacteristic
209C2×D32—24no—
210C2×D32—44no—
211C2×C32×C4C22×C412yes—
212C2×C32×C4C2×D411yescharacteristic
213C2×C32×C4C2×D412yes—
214C2×C32×C4C2411yescharacteristic
215#638—24no—
216C2×C3⋊Dic3—21no—
217C2×C3⋊Dic3—22no—
218C4⋊(C3⋊D3)—21no—
219C4⋊(C3⋊D3)C22×C412yes—
220C4×C3⋊D3—24no—
221#634—21no—
222#634C22×C412yes—
223C3×#67—24no—
224C2×C3×Dic3—21no—
225C2×C3×Dic3—22no—
226C2×C3×Dic3C22⋊C414yes—
227C2×C3×Dic3C2×D411yescharacteristic
228C2×C3×Dic3C2×D411yescharacteristic
229C3×D12—21no—
230C3×D12C22×C412yes—
231C3×C4×D3—24no—
232C3×C4×D3C22⋊C414yes—
233C3×C4×D3C22⋊C414yes—
234C3×C4×D3C22×C412yes—
235C3×C4×D3C22×C412yes—
236C3×C4×D3C2×D412yes—
237C3×C4×D3C2×D412yes—
238C3×Dic6—21no—
239C3×Dic6C22×C412yes—
240#627—24no—
241#626—24no—
242#626—24no—
243#625—24no—
244#624—24no—
245D3×Dic3—24no—
246D3×Dic3—24no—
247D3×Dic3—44no—
248C32×C8—22no—
249C3×C3⋊C8—22no—
250C22×#41—91no—
251C23×C8—31no—
252C2×#117—91no—
253#416—31no—
254#416—92no—
255#416—92no—
256#416—91no—
257#416—91no—
258#416—91no—
259C2×#103—92no—
260C2×#102—92no—
261C24×C3—31no—
262C23×D3—61no—
263C23×D3—61no—
264C23×D3D1211yescharacteristic
265C3×#41—34no—
266C3×#41—62no—
267C2×C3×Q8—31no—
268C2×C3×D4—31no—
269C2×C3×D4—61no—
270C22×C3×C4—21no—
271C22×C3×C4—31no—
272C22×C3×C4—34no—
273C22×C3×C4—31no—
274C22×C3×C4—31no—
275C22×C3×C4—34no—
276C22×C3×C4—31no—
277C22×C3×C4—31no—
278C22×C3×C4—61no—
279C22×C3×C4C22×D311yescharacteristic
280C22×C3×C4C22×D311yescharacteristic
281C2×#67—21no—
282C2×#67—61no—
283C2×#67—68no—
284C2×#67—61no—
285C2×#67—61no—
286C2×#67—61no—
287C2×#67—61no—
288C2×#67—61no—
289C2×#67—121no—
290C22×Dic3—61no—
291C22×Dic3—62no—
292C22×Dic3—61no—
293C22×Dic3D1211yescharacteristic
294#239—34no—
295#239—62no—
296D3×Q8—34no—
297D3×Q8—62no—
298#237—34no—
299#237—68no—
300#237—62no—
301D3×D4—34no—
302D3×D4—68no—
303D3×D4—62no—
304#235—22no—
305#235—34no—
306#235—34no—
307#235—34no—
308#235—34no—
309#235—64no—
310#235—62no—
311#235—68no—
312#235—62no—
313#235—68no—
314#235—62no—
315#235—62no—
316#235—68no—
317#235—122no—
318#235C4×D314yescomplemented
319C2×D12—31no—
320C2×D12—31no—
321C2×D12—34no—
322C2×D12—61no—
323C2×D12—62no—
324C2×D12—61no—
325C2×D12—61no—
326C2×D12C22×D311yescharacteristic
327C2×C4×D3—21no—
328C2×C4×D3—68no—
329C2×C4×D3—61no—
330C2×C4×D3—61no—
331C2×C4×D3—61no—
332C2×C4×D3—61no—
333C2×C4×D3—61no—
334C2×C4×D3—61no—
335C2×C4×D3—68no—
336C2×C4×D3—62no—
337C2×C4×D3—121no—
338C2×C4×D3C4×D314yes—
339C2×C4×D3D1211yescharacteristic
340C2×C4×D3D1211yescharacteristic
341C2×C4×D3#6714yes—
342C2×C4×D3C22×D311yescharacteristic
343C2×C4×D3C22×D311yescharacteristic
344C2×Dic6—31no—
345C2×Dic6—31no—
346C2×Dic6—34no—
347C2×Dic6—61no—
348C2×Dic6—62no—
349C2×Dic6—61no—
350C2×Dic6—61no—
351C2×Dic6C22×D311yescharacteristic
352C2×C3×C8—22no—
353C2×C3×C8—22no—
354C2×C3×C8—22no—
355C2×C3×C8—32no—
356C2×C3×C8—42no—
357C2×C3×C8—64no—
358C2×C3×C8—64no—
359C2×C3×C8—62no—
360C2×C3×C8C22×D312yes—
361C2×C3×C8C22×D312yes—
362C3×C4⋊C4—32no—
363C3×C22⋊C4—61no—
364C3×C42—61no—
365#217—21no—
366#217—62no—
367#217—61no—
368#217—61no—
369#217—121no—
370(C2×D3)⋊C4—62no—
371C4⋊Dic3—32no—
372C4⋊Dic3—32no—
373C4⋊Dic3—62no—
374C4⋊Dic3—62no—
375C4⋊Dic3C22×D312yes—
376Dic3⋊C4—62no—
377C4×Dic3—21no—
378C4×Dic3—62no—
379C4×Dic3—61no—
380C4×Dic3—61no—
381C4×Dic3—62no—
382C4×Dic3—121no—
383C2×C3⋊C8—22no—
384C2×C3⋊C8C22×D312yes—
385D3×C8—24no—
386D3×C8—24no—
387C22×C32—22no—
388C22×C32C2×C22⋊C412yes—
389C22×C32C22×D411yescharacteristic
390C2×C3⋊D3—22no—
391C2×C3⋊D3—42no—
392C2×C3×D3—22no—
393C2×C3×D3—28no—
394C2×C3×D3—22no—
395C2×C3×D3—42no—
396C2×C3×D3C2×C22⋊C412yes—
397C2×C3×D3C2×C22⋊C412yes—
398C2×C3×D3#13514yes—
399D32—48no—
400C32×C4C2×C22⋊C412yes—
401C32×C4C23×C411yescharacteristic
402C32×C4C22×D411yescharacteristic
403C3⋊Dic3—22no—
404C3⋊Dic3—42no—
405C3×Dic3—22no—
406C3×Dic3—42no—
407C3×Dic3C2×C22⋊C412yes—
408C3×Dic3C2×C22⋊C412yes—
409C2×#41—31no—
410C2×#41—91no—
411C2×#41—91no—
412C2×#41—98no—
413C2×#41—91no—
414C2×#41—181no—
415C2×#41—181no—
416C2×#41—184no—
417C22×Q8—91no—
418C22×D4—91no—
419C22×D4—181no—
420C23×C4—31no—
421C23×C4—181no—
422C22×C8—31no—
423C22×C8—32no—
424C22×C8—32no—
425C22×C8—64no—
426C22×C8D3211yescharacteristic, complemented
427#117—31no—
428#117—92no—
429#117—91no—
430#117—181no—
431#117—181no—
432C2×C4⋊C4—92no—
433C2×C22⋊C4—181no—
434C2×C42—181no—
435#103—32no—
436#103—92no—
437#103—92no—
438#103—92no—
439#102—32no—
440#102—92no—
441#102—92no—
442#102—92no—
443C23×C3—21no—
444C23×C3—31no—
445C23×C3—34no—
446C23×C3—31no—
447C23×C3—64no—
448C23×C3—61no—
449C23×C3C2×D1211yescharacteristic
450C23×C3D3×D411yescharacteristic
451C22×D3—24no—
452C22×D3—21no—
453C22×D3—64no—
454C22×D3—61no—
455C22×D3—61no—
456C22×D3—64no—
457C22×D3—121no—
458C22×D3—124no—
459C22×D3—124no—
460C22×D3(C2×D3)⋊C414yes—
461C22×D3C2×D1211yescharacteristic
462C22×D3C2×D1211yescharacteristic
463C3×Q8—32no—
464C3×Q8—61no—
465C3×D4—32no—
466C3×D4—64no—
467C3×D4—61no—
468C2×C3×C4—21no—
469C2×C3×C4—22no—
470C2×C3×C4—21no—
471C2×C3×C4—22no—
472C2×C3×C4—34no—
473C2×C3×C4—31no—
474C2×C3×C4—31no—
475C2×C3×C4—34no—
476C2×C3×C4—34no—
477C2×C3×C4—32no—
478C2×C3×C4—32no—
479C2×C3×C4—32no—
480C2×C3×C4—32no—
481C2×C3×C4—61no—
482C2×C3×C4—64no—
483C2×C3×C4—62no—
484C2×C3×C4C2×C4×D312yes—
485C2×C3×C4C2×C4×D312yes—
486C2×C3×C4C2×D1211yescharacteristic
487C2×C3×C4D3×D411yescharacteristic
488C2×C3×C4D3×D412yes—
489C2×C3×C4C2×#6712yes—
490C2×C3×C4C23×D311yescharacteristic
491C2×C3×C4C23×D311yescharacteristic
492#67—24no—
493#67—64no—
494#67—64no—
495#67—64no—
496#67—64no—
497#67—64no—
498#67—64no—
499#67—124no—
500C2×Dic3—21no—
501C2×Dic3—22no—
502C2×Dic3—64no—
503C2×Dic3—61no—
504C2×Dic3—61no—
505C2×Dic3—64no—
506C2×Dic3—62no—
507C2×Dic3—62no—
508C2×Dic3—121no—
509C2×Dic3—122no—
510C2×Dic3—124no—
511C2×Dic3(C2×D3)⋊C414yes—
512C2×Dic3C2×D1211yescharacteristic
513C2×Dic3C2×D1211yescharacteristic
514D12—21no—
515D12—32no—
516D12—32no—
517D12—62no—
518D12—64no—
519D12—64no—
520D12—61no—
521D12—61no—
522D12—121no—
523D12C2×C4×D312yes—
524C4×D3—24no—
525C4×D3—64no—
526C4×D3—64no—
527C4×D3—64no—
528C4×D3—64no—
529C4×D3—64no—
530C4×D3—64no—
531C4×D3—124no—
532C4×D3—124no—
533C4×D3(C2×D3)⋊C414yes—
534C4×D3(C2×D3)⋊C414yes—
535C4×D3C2×C4×D312yes—
536C4×D3C2×C4×D312yes—
537C4×D3C2×#6712yes—
538C4×D3C2×#6712yes—
539Dic6—21no—
540Dic6—32no—
541Dic6—32no—
542Dic6—62no—
543Dic6—64no—
544Dic6—61no—
545Dic6—61no—
546Dic6—64no—
547Dic6—121no—
548Dic6C2×C4×D312yes—
549C3×C8—22no—
550C3×C8—22no—
551C3×C8—42no—
552C3×C8—62no—
553C3⋊C8—22no—
554C2×C32—22no—
555C2×C32C22×C22⋊C411yescharacteristic
556C2×C32C2×#13512yes—
557C3⋊D3—42no—
558C3×D3—22no—
559C3×D3—42no—
560C3×D3#41614yescomplemented
561C24—31no—
562C24—181no—
563#41—34no—
564#41—62no—
565#41—94no—
566#41—94no—
567#41—94no—
568#41—188no—
569#41—188no—
570#41—182no—
571#41—182no—
572#41—182no—
573C2×Q8—31no—
574C2×Q8—94no—
575C2×Q8—91no—
576C2×Q8—181no—
577C2×Q8—182no—
578C2×D4—31no—
579C2×D4—61no—
580C2×D4—94no—
581C2×D4—91no—
582C2×D4—182no—
583C2×D4—181no—
584C2×D4—181no—
585C2×D4—188no—
586C2×D4—181no—
587C2×D4—181no—
588C22×C4—31no—
589C22×C4—31no—
590C22×C4—31no—
591C22×C4—34no—
592C22×C4—31no—
593C22×C4—31no—
594C22×C4—34no—
595C22×C4—61no—
596C22×C4—181no—
597C22×C4—188no—
598C22×C4—181no—
599C22×C4—181no—
600C22×C4—182no—
601C22×C4—181no—
602C22×C4C2×D3211yescharacteristic
603C2×C8—22no—
604C2×C8—32no—
605C2×C8—64no—
606C2×C8—64no—
607C2×C8—62no—
608C2×C8C2×D3212yes—
609C4⋊C4—32no—
610C4⋊C4—92no—
611C4⋊C4—182no—
612C22⋊C4—61no—
613C22⋊C4—182no—
614C22⋊C4—181no—
615C42—61no—
616C42—182no—
617C42—181no—
618C22×C3—22no—
619C22×C3—22no—
620C22×C3—21no—
621C22×C3—22no—
622C22×C3—32no—
623C22×C3—34no—
624C22×C3—32no—
625C22×C3—42no—
626C22×C3—68no—
627C22×C3—62no—
628C22×C3—62no—
629C22×C3—122no—
630C22×C3D3×C22⋊C412yes—
631C22×C3C2×(C2×D3)⋊C412yes—
632C22×C3C22×D1211yescharacteristic
633C22×C3C2×D3×D411yescharacteristic
634C2×D3—22no—
635C2×D3—28no—
636C2×D3—22no—
637C2×D3—42no—
638C2×D3—62no—
639C2×D3—62no—
640C2×D3—122no—
641C2×D3—128no—
642C2×D3—122no—
643C2×D3—122no—
644C2×D3—128no—
645C2×D3—242no—
646C2×D3#90414yes—
647C2×D3C2×(C2×D3)⋊C412yes—
648C2×D3C2×(C2×D3)⋊C412yes—
649C3×C4—21no—
650C3×C4—21no—
651C3×C4—22no—
652C3×C4—32no—
653C3×C4—32no—
654C3×C4—62no—
655C3×C4—122no—
656C3×C4D3×C22⋊C412yes—
657C3×C4C2×(C2×D3)⋊C412yes—
658C3×C4C22×C4×D311yescharacteristic
659C3×C4C22×C4×D311yescharacteristic
660C3×C4C2×D3×D411yescharacteristic
661C3×C4C22×#6711yescharacteristic
662Dic3—22no—
663Dic3—42no—
664Dic3—62no—
665Dic3—62no—
666Dic3—122no—
667Dic3—122no—
668Dic3—122no—
669Dic3—242no—
670Dic3C2×(C2×D3)⋊C412yes—
671Dic3C2×(C2×D3)⋊C412yes—
672C32C2×#41611yescharacteristic, complemented, Sylow
673C23—31no—
674C23—31no—
675C23—34no—
676C23—64no—
677C23—61no—
678C23—184no—
679C23—181no—
680C23—364no—
681C23D3×D1211yescharacteristic
682Q8—32no—
683Q8—61no—
684Q8—92no—
685Q8—184no—
686Q8—181no—
687D4—32no—
688D4—64no—
689D4—61no—
690D4—92no—
691D4—184no—
692D4—184no—
693D4—184no—
694D4—184no—
695D4—181no—
696C2×C4—31no—
697C2×C4—31no—
698C2×C4—34no—
699C2×C4—32no—
700C2×C4—32no—
701C2×C4—32no—
702C2×C4—32no—
703C2×C4—34no—
704C2×C4—34no—
705C2×C4—61no—
706C2×C4—64no—
707C2×C4—62no—
708C2×C4—184no—
709C2×C4—184no—
710C2×C4—184no—
711C2×C4—181no—
712C2×C4—184no—
713C2×C4—182no—
714C2×C4—364no—
715C2×C4C4×D3212yes—
716C2×C4D3×D1211yescharacteristic
717C2×C4D3×#6712yes—
718C2×C4C22×D3211yescharacteristic
719C8—22no—
720C8—62no—
721C2×C3—22no—
722C2×C3—22no—
723C2×C3—22no—
724C2×C3—21no—
725C2×C3—34no—
726C2×C3—42no—
727C2×C3—62no—
728C2×C3—122no—
729C2×C3C2×D3×C22⋊C411yescharacteristic
730C2×C3C2×#90412yes—
731C2×C3D3×#13512yes—
732C2×C3C22×(C2×D3)⋊C411yescharacteristic
733D3—22no—
734D3—42no—
735D3—122no—
736D3—122no—
737D3—242no—
738D3#511314yesdirect product factor
739C22—22no—
740C22—34no—
741C22—32no—
742C22—32no—
743C22—68no—
744C22—62no—
745C22—62no—
746C22—122no—
747C22—182no—
748C22—368no—
749C22—362no—
750C22D3×(C2×D3)⋊C412yes—
751C22C2×D3×D1211yescharacteristic
752C4—32no—
753C4—32no—
754C4—62no—
755C4—122no—
756C4—182no—
757C4—362no—
758C4D3×(C2×D3)⋊C412yes—
759C4C2×C4×D3211yescharacteristic
760C4C2×D3×#6711yescharacteristic
761C3—21no—
762C3D3×#41611yescharacteristic, complemented
763C3C2×#511311yescharacteristic, complemented
764C2—22no—
765C2—34no—
766C2—62no—
767C2—122no—
768C2—362no—
769C2D3×#90412yes—
770C2C2×D3×(C2×D3)⋊C411yescharacteristic
subgroupG/H
centerC2×C4D3×D12
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC22×C32×C8C22
socleC22×C32C22×D4
prime radicalC2×D3×#235C2
cosocleC2×C32×C4C24
hypercenterC22×C8D32
hypocenterC32C2×#416
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C22×C8

Complements

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

NH ≅ G/Ntype
2. C22×C3×D3×C8C2semidirect
3. D3×#926C2semidirect
4. #10592812C2semidirect
5. C3×#5113C2semidirect
6. #10591105C2semidirect
7. #10591084C2semidirect
8. #10590954C2semidirect
9. D3×#821C2semidirect
10. #10590690C2semidirect
11. D3×#816C2semidirect
20. D3×#235C4semidirect
27. C22×C32×C8C22semidirect
28. #64135C22semidirect
29. C3×#926C22semidirect
30. C22×C3×C3⋊C8C22semidirect
33. C2×C3×D3×C8C22semidirect
39. #63841C22semidirect
40. #63648C22semidirect
41. #63643C22semidirect
42. C3×#821C22semidirect
43. C3×#816C22semidirect
44. #63567C22semidirect
45. #63566C22semidirect
46. #63564C22semidirect
47. #63563C22semidirect
52. C22×D3×C8D3semidirect
63. #5113D3direct (N × H)
76. #3828C2×C4semidirect
83. C3×#235C2×C4semidirect
107. #3799C2×C4semidirect
110. #3795C2×C4semidirect
161. C22×C3×C8C2×D3semidirect
162. C22×C3×C8C2×D3semidirect
171. #926C2×D3semidirect
174. C22×C3⋊C8C2×D3semidirect
177. C2×D3×C8C2×D3semidirect
193. #821C2×D3semidirect
199. #816C2×D3semidirect
318. #235C4×D3semidirect
426. C22×C8D32semidirect
560. C3×D3#416semidirect
672. C32C2×#416semidirect
738. D3#5113direct (N × H)
762. C3D3×#416semidirect
763. C3C2×#5113semidirect

Maximal subgroups

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

subgroupindex
C2×D3×#2352
C22×C3×D3×C82
D3×#9262
#105928122
C3×#51132
#105911052
#105910842
#105909542
D3×#8212
#105906902
D3×#8162
C2×#51133
D3×#4163