Finite Group Databasebeta

← #10829370

Subgroups — #10829370

Order 768.

1556 conjugacy classes of subgroups.

The subgroup lattice has 940 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#3505C211yesmaximal, characteristic, complemented
2#82834C211yesmaximal, characteristic, complemented
3#82723C211yesmaximal, characteristic, complemented
4C4×#937C211yesmaximal, characteristic, complemented
5#71851C212yesmaximal, complemented
6#71850C212yesmaximal, complemented
7#71701C211yesmaximal, characteristic, complemented
8#71686C211yesmaximal, characteristic, complemented
9#71657C212yesmaximal, complemented
10#71654C212yesmaximal, complemented
11#71619C211yesmaximal, characteristic, complemented
12#24140—31nomaximal, Sylow
13C23×C4×D3C2211yescharacteristic
14C3×#553—21no—
15C3×#553—22no—
16C3×#552—21no—
17C3×#551—22no—
18C3×#548—21no—
19C3×#546—21no—
20C3×#539—21no—
21C3×#538—21no—
22C3×#534C2212yes—
23C3×#529—21no—
24C3×#525—21no—
25C2×C3×C22⋊Q8C2211yescharacteristic
26C2×C3×#121C2211yescharacteristic
27C3×#518C2212yes—
28C2×C3×C4×D4C2211yescharacteristic
29C2×#946—21no—
30C2×#938—21no—
31C2×#937C2211yescharacteristic
32C2×#937C2212yes—
33C2×C4×#67—21no—
34#5220C2212yes—
35#5220C2211yescharacteristic
36C2×#834C2212yes—
37C2×#834C2212yes—
38C2×#834C2212yes—
39#5212C2211yescharacteristic
40#5212C2211yescharacteristic
41C4×#217C2211yescharacteristic
42#4989—22no—
43#4989—21no—
44#4987—21no—
45#4987—21no—
46#4956—22no—
47#4956—21no—
48#4955C2212yes—
49#4955C2211yescharacteristic
50#4946C2212yes—
51#4946C2211yescharacteristic
52C4×(C2×D3)⋊C4—21no—
53#4526C2212yes—
54#4526C2212yes—
55#4526C2212yes—
56#3505D311yescharacteristic, complemented
57#2848—31no—
58#2847—31no—
59C4×#120—31no—
60#2044—32no—
61#2021—32no—
62#1996—31no—
63#1964—31no—
64#1889—32no—
65#1867—32no—
66#1799—31no—
67C24×D3C2311yescharacteristic
68C2×C3×#41—21no—
69C22×C3×Q8D411yescharacteristic, complemented
70C22×C3×D4D411yescharacteristic, complemented
71C22×C3×D4C2311yescharacteristic
72C22×C3×D4C2312yes—
73C23×C3×C4D411yescharacteristic, complemented
74C23×C3×C4C2311yescharacteristic
75C22×#67—21no—
76C22×#67—22no—
77C23×Dic3C2311yescharacteristic
78C22×C4×D3—21no—
79C22×C4×D3—21no—
80C22×C4×D3—21no—
81C22×C4×D3—21no—
82C22×C4×D3—21no—
83C22×C4×D3—21no—
84C22×C4×D3—44no—
85C3×#126—22no—
86C3×#126—22no—
87C3×#126—22no—
88C3×#125—21no—
89C3×#125—22no—
90C3×#124—21no—
91C3×#124—22no—
92C3×#123—22no—
93C3×#123—22no—
94C3×#123—22no—
95C3×#123—22no—
96C3×#123—22no—
97C3×C22⋊Q8—21no—
98C3×C22⋊Q8—22no—
99C3×C22⋊Q8—21no—
100C3×C22⋊Q8—21no—
101C3×C22⋊Q8—21no—
102C3×C22⋊Q8—21no—
103C3×#121—21no—
104C3×#121—22no—
105C3×#121—21no—
106C3×#121—21no—
107C3×#121—21no—
108C3×#121—21no—
109C3×#121—22no—
110C3×#121—22no—
111C3×#120—22no—
112C3×#120—22no—
113C3×C4×Q8—21no—
114C3×C4×D4—22no—
115C3×C4×D4—21no—
116C3×C4×D4—21no—
117C3×C4×D4—21no—
118C3×C4×D4—21no—
119C3×C4×D4—21no—
120C3×C4×D4—22no—
121C3×C4×D4—22no—
122C3×C4×D4—22no—
123C3×C4×D4—22no—
124C3×#117—21no—
125C3×#117—22no—
126C3×#117—22no—
127C2×C3×C4⋊C4D411yescharacteristic, complemented
128C2×C3×C4⋊C4D411yescharacteristic, complemented
129C2×C3×C4⋊C4D411yescharacteristic, complemented
130C2×C3×C4⋊C4D412yescomplemented
131C2×C3×C22⋊C4—22no—
132C2×C3×C22⋊C4D411yescharacteristic, complemented
133C2×C3×C22⋊C4D412yescomplemented
134C2×C3×C22⋊C4C2311yescharacteristic
135C2×C3×C22⋊C4C2312yes—
136C2×C3×C42D411yescharacteristic, complemented
137C2×#217—21no—
138C2×#217—22no—
139C2×#217C2312yes—
140C2×#217C2311yescharacteristic
141C2×#217C2312yes—
142C2×#217C2311yescharacteristic
143#946—44no—
144#938—44no—
145#937—22no—
146#937—22no—
147#937—24no—
148#937—42no—
149C4×#67—44no—
150C2×(C2×D3)⋊C4—21no—
151C2×(C2×D3)⋊C4—21no—
152C2×(C2×D3)⋊C4—22no—
153C2×(C2×D3)⋊C4—21no—
154C2×(C2×D3)⋊C4—22no—
155C2×(C2×D3)⋊C4—22no—
156C2×C4⋊Dic3—21no—
157C2×C4⋊Dic3—21no—
158C2×Dic3⋊C4—21no—
159C2×Dic3⋊C4—22no—
160C2×C4×Dic3—21no—
161#834—24no—
162#834—42no—
163#834—42no—
164C3⋊#95—21no—
165C3⋊#95—21no—
166C3⋊#95—22no—
167C3⋊#95—21no—
168C3⋊#95—21no—
169C3⋊#95—22no—
170C3⋊#95—21no—
171C24×C4—31no—
172#553—21no—
173#553—22no—
174#552—21no—
175#551—22no—
176#548—21no—
177#546—21no—
178#539—21no—
179#538—21no—
180#534C2×D312yes—
181#529—21no—
182#525—21no—
183C2×C22⋊Q8—61no—
184C2×C22⋊Q8C2×D311yescharacteristic
185C2×#121—61no—
186C2×#121C2×D311yescharacteristic
187C2×#120—31no—
188C2×#120—32no—
189#518C2×D312yes—
190C2×C4×D4—61no—
191C2×C4×D4C2×D311yescharacteristic
192C2×#99—32no—
193C2×#99—32no—
194C2×#99—32no—
195#386—32no—
196#386—31no—
197#386—62no—
198#386—61no—
199#385—32no—
200#385—31no—
201#385—62no—
202#385—61no—
203#380—31no—
204#380—31no—
205#380—61no—
206#380—61no—
207#379—32no—
208#379—31no—
209C4×C22⋊C4—31no—
210C4×C22⋊C4—61no—
211#342—32no—
212#342—32no—
213#342—32no—
214C24×C3C2×D412yes—
215C24×C3C2×D411yescharacteristic
216C24×C3C2411yescharacteristic
217C23×D3—21no—
218C23×D3—21no—
219C23×D3—21no—
220C23×D3—21no—
221C23×D3—21no—
222C23×D3—21no—
223C23×D3—42no—
224C23×D3—42no—
225C23×D3#4112yescomplemented
226C3×#41—82no—
227C2×C3×Q8—21no—
228C2×C3×Q8—21no—
229C2×C3×Q8—42no—
230C2×C3×D4—21no—
231C2×C3×D4—22no—
232C2×C3×D4—21no—
233C2×C3×D4—22no—
234C2×C3×D4—22no—
235C2×C3×D4—21no—
236C2×C3×D4—21no—
237C2×C3×D4—22no—
238C2×C3×D4—21no—
239C2×C3×D4—22no—
240C2×C3×D4—21no—
241C2×C3×D4—22no—
242C2×C3×D4—22no—
243C2×C3×D4—22no—
244C2×C3×D4—21no—
245C2×C3×D4—21no—
246C2×C3×D4—42no—
247C22×C3×C4—22no—
248C22×C3×C4—22no—
249C22×C3×C4—21no—
250C22×C3×C4—21no—
251C22×C3×C4—42no—
252C22×C3×C4—42no—
253C22×C3×C4C2×D411yescharacteristic
254C22×C3×C4C2×D412yes—
255C22×C3×C4C2×D411yescharacteristic
256C22×C3×C4C2×D411yescharacteristic
257C22×C3×C4C2×D411yescharacteristic
258C22×C3×C4C2×D411yescharacteristic
259C22×C3×C4C2×D412yes—
260C22×C3×C4C2×D411yescharacteristic
261C22×C3×C4C2×D412yes—
262C22×C3×C4C2×D411yescharacteristic
263C22×C3×C4C2×D411yescharacteristic
264C22×C3×C4C2×D411yescharacteristic
265C2×#67—24no—
266C2×#67—42no—
267C2×#67—42no—
268C2×#67—44no—
269C2×#67—44no—
270C2×#67—44no—
271C22×Dic3—21no—
272C22×Dic3—21no—
273C22×Dic3—21no—
274C22×Dic3—21no—
275C22×Dic3—21no—
276C22×Dic3—22no—
277C22×Dic3—22no—
278C22×Dic3—42no—
279C2×C4×D3—24no—
280C2×C4×D3—24no—
281C2×C4×D3—24no—
282C2×C4×D3—42no—
283C2×C4×D3—42no—
284C2×C4×D3—42no—
285C2×C4×D3—42no—
286C2×C4×D3—42no—
287C2×C4×D3—42no—
288C2×C4×D3—42no—
289C2×C4×D3—42no—
290C2×C4×D3—42no—
291C2×C4×D3—41no—
292C2×C4×D3—41no—
293C2×C4×D3—41no—
294C2×C4×D3—41no—
295C3×C4⋊C4—22no—
296C3×C4⋊C4—22no—
297C3×C4⋊C4—22no—
298C3×C4⋊C4—22no—
299C3×C4⋊C4—21no—
300C3×C4⋊C4—22no—
301C3×C4⋊C4—21no—
302C3×C4⋊C4—21no—
303C3×C4⋊C4—21no—
304C3×C4⋊C4—21no—
305C3×C4⋊C4—22no—
306C3×C4⋊C4—21no—
307C3×C22⋊C4—22no—
308C3×C22⋊C4—22no—
309C3×C22⋊C4—22no—
310C3×C22⋊C4—22no—
311C3×C22⋊C4—22no—
312C3×C22⋊C4—22no—
313C3×C22⋊C4—21no—
314C3×C22⋊C4—22no—
315C3×C22⋊C4—21no—
316C3×C22⋊C4—22no—
317C3×C22⋊C4—22no—
318C3×C22⋊C4—21no—
319C3×C22⋊C4—21no—
320C3×C22⋊C4—22no—
321C3×C42—22no—
322C3×C42—22no—
323C3×C42—21no—
324C3×C42—21no—
325#217—21no—
326#217—22no—
327#217—22no—
328#217—21no—
329#217—22no—
330#217—22no—
331#217—21no—
332#217—42no—
333#217—44no—
334#217#4112yescomplemented
335(C2×D3)⋊C4—24no—
336(C2×D3)⋊C4—44no—
337(C2×D3)⋊C4—44no—
338(C2×D3)⋊C4—42no—
339(C2×D3)⋊C4—42no—
340(C2×D3)⋊C4—44no—
341C4⋊Dic3—42no—
342C4⋊Dic3—42no—
343Dic3⋊C4—42no—
344Dic3⋊C4—44no—
345C4×Dic3—42no—
346C25—31no—
347C2×#41—21no—
348C22×Q8#6711yescharacteristic, complemented
349C22×D4—61no—
350C22×D4—62no—
351C22×D4#6711yescharacteristic, complemented
352C22×D4C22×D311yescharacteristic
353C22×D4C22×D312yes—
354C23×C4—31no—
355C23×C4—61no—
356C23×C4—61no—
357C23×C4—61no—
358C23×C4—61no—
359C23×C4—61no—
360C23×C4—61no—
361C23×C4—124no—
362C23×C4#6711yescharacteristic, complemented
363C23×C4C22×D311yescharacteristic
364#126—22no—
365#126—22no—
366#126—22no—
367#125—21no—
368#125—22no—
369#124—21no—
370#124—22no—
371#123—22no—
372#123—22no—
373#123—22no—
374#123—22no—
375#123—22no—
376C22⋊Q8—21no—
377C22⋊Q8—22no—
378C22⋊Q8—21no—
379C22⋊Q8—21no—
380C22⋊Q8—21no—
381C22⋊Q8—21no—
382C22⋊Q8—124no—
383#121—21no—
384#121—22no—
385#121—21no—
386#121—21no—
387#121—21no—
388#121—21no—
389#121—22no—
390#121—22no—
391#121—124no—
392#120—22no—
393#120—22no—
394#120—62no—
395#120—62no—
396#120—64no—
397#120—122no—
398C4×Q8—21no—
399C4×D4—22no—
400C4×D4—21no—
401C4×D4—21no—
402C4×D4—21no—
403C4×D4—21no—
404C4×D4—21no—
405C4×D4—22no—
406C4×D4—22no—
407C4×D4—22no—
408C4×D4—22no—
409C4×D4—124no—
410#117—21no—
411#117—22no—
412#117—22no—
413C2×C4⋊C4—61no—
414C2×C4⋊C4—61no—
415C2×C4⋊C4—61no—
416C2×C4⋊C4—62no—
417C2×C4⋊C4#6711yescharacteristic, complemented
418C2×C4⋊C4#6711yescharacteristic, complemented
419C2×C4⋊C4#6711yescharacteristic, complemented
420C2×C4⋊C4#6712yescomplemented
421C2×C22⋊C4—22no—
422C2×C22⋊C4—31no—
423C2×C22⋊C4—32no—
424C2×C22⋊C4—31no—
425C2×C22⋊C4—32no—
426C2×C22⋊C4—61no—
427C2×C22⋊C4—61no—
428C2×C22⋊C4—62no—
429C2×C22⋊C4—61no—
430C2×C22⋊C4—62no—
431C2×C22⋊C4—62no—
432C2×C22⋊C4—61no—
433C2×C22⋊C4—62no—
434C2×C22⋊C4#6711yescharacteristic, complemented
435C2×C22⋊C4#6712yescomplemented
436C2×C22⋊C4C22×D311yescharacteristic
437C2×C22⋊C4C22×D312yes—
438C2×C42—61no—
439C2×C42#6711yescharacteristic, complemented
440#99—64no—
441#99—122no—
442#99—122no—
443#95—61no—
444#95—61no—
445#95—61no—
446#95—61no—
447#95—61no—
448#95—62no—
449#95—62no—
450C23×C3—21no—
451C23×C3—22no—
452C23×C3—21no—
453C23×C3—21no—
454C23×C3—22no—
455C23×C3—22no—
456C23×C3—41no—
457C23×C3—41no—
458C23×C3—41no—
459C23×C3—41no—
460C23×C3—42no—
461C23×C3—42no—
462C23×C3C22×D411yescharacteristic
463C23×C3C22×D411yescharacteristic
464C23×C3C22×D411yescharacteristic
465C23×C3C2×#4111yescharacteristic
466C23×C3C2×#4111yescharacteristic
467C23×C3H(5,𝔽2)11yescharacteristic
468C23×C32−1+411yescharacteristic
469C22×D3—22no—
470C22×D3—22no—
471C22×D3—22no—
472C22×D3—22no—
473C22×D3—22no—
474C22×D3—22no—
475C22×D3—22no—
476C22×D3—22no—
477C22×D3—22no—
478C22×D3—44no—
479C22×D3—44no—
480C22×D3—44no—
481C22×D3—44no—
482C22×D3—41no—
483C22×D3—41no—
484C22×D3—41no—
485C22×D3—41no—
486C22×D3—41no—
487C22×D3—41no—
488C22×D3—41no—
489C22×D3—41no—
490C22×D3—41no—
491C22×D3—41no—
492C3×Q8—42no—
493C3×Q8—81no—
494C3×D4—42no—
495C3×D4—42no—
496C3×D4—41no—
497C3×D4—41no—
498C3×D4—41no—
499C3×D4—42no—
500C3×D4—42no—
501C3×D4—41no—
502C3×D4—42no—
503C3×D4—81no—
504C3×D4—82no—
505C3×D4—82no—
506C2×C3×C4—22no—
507C2×C3×C4—22no—
508C2×C3×C4—22no—
509C2×C3×C4—21no—
510C2×C3×C4—22no—
511C2×C3×C4—21no—
512C2×C3×C4—21no—
513C2×C3×C4—22no—
514C2×C3×C4—22no—
515C2×C3×C4—21no—
516C2×C3×C4—21no—
517C2×C3×C4—22no—
518C2×C3×C4—22no—
519C2×C3×C4—41no—
520C2×C3×C4—41no—
521C2×C3×C4—41no—
522C2×C3×C4—42no—
523C2×C3×C4—41no—
524C2×C3×C4—42no—
525C2×C3×C4—41no—
526C2×C3×C4—42no—
527C2×C3×C4—81no—
528C2×C3×C4—82no—
529C2×C3×C4—82no—
530C2×C3×C4#12011yescharacteristic
531C2×C3×C4#12011yescharacteristic
532C2×C3×C4#12011yescharacteristic
533C2×C3×C4#12011yescharacteristic
534#67—48no—
535#67—88no—
536C2×Dic3—22no—
537C2×Dic3—22no—
538C2×Dic3—22no—
539C2×Dic3—22no—
540C2×Dic3—41no—
541C2×Dic3—41no—
542C2×Dic3—41no—
543C2×Dic3—41no—
544C2×Dic3—41no—
545C2×Dic3—41no—
546C2×Dic3—41no—
547C2×Dic3—42no—
548C2×Dic3—42no—
549C2×Dic3—42no—
550C2×Dic3—41no—
551C2×Dic3—42no—
552C2×Dic3—41no—
553C2×Dic3—42no—
554C2×Dic3—42no—
555C4×D3—44no—
556C4×D3—44no—
557C4×D3—44no—
558C4×D3—44no—
559C24—32no—
560C24—61no—
561C24—61no—
562C24—61no—
563C24—61no—
564C24—61no—
565C24—61no—
566C24—122no—
567C24—122no—
568C24C2×#6712yes—
569C24C2×#6711yescharacteristic
570C24C23×D311yescharacteristic
571#41—82no—
572C2×Q8—21no—
573C2×Q8—21no—
574C2×Q8—42no—
575C2×D4—22no—
576C2×D4—21no—
577C2×D4—21no—
578C2×D4—22no—
579C2×D4—21no—
580C2×D4—22no—
581C2×D4—22no—
582C2×D4—21no—
583C2×D4—21no—
584C2×D4—22no—
585C2×D4—21no—
586C2×D4—22no—
587C2×D4—22no—
588C2×D4—22no—
589C2×D4—21no—
590C2×D4—21no—
591C2×D4—42no—
592C2×D4—64no—
593C2×D4—122no—
594C2×D4—122no—
595C2×D4—124no—
596C2×D4—124no—
597C2×D4—124no—
598C22×C4—22no—
599C22×C4—22no—
600C22×C4—21no—
601C22×C4—21no—
602C22×C4—42no—
603C22×C4—42no—
604C22×C4—64no—
605C22×C4—64no—
606C22×C4—64no—
607C22×C4—61no—
608C22×C4—61no—
609C22×C4—61no—
610C22×C4—61no—
611C22×C4—61no—
612C22×C4—62no—
613C22×C4—62no—
614C22×C4—122no—
615C22×C4—122no—
616C22×C4—122no—
617C22×C4—122no—
618C22×C4—122no—
619C22×C4—122no—
620C22×C4—122no—
621C22×C4—122no—
622C22×C4—122no—
623C22×C4—122no—
624C22×C4—121no—
625C22×C4—121no—
626C22×C4—121no—
627C22×C4—121no—
628C22×C4C2×#6711yescharacteristic
629C22×C4C2×#6712yes—
630C22×C4C2×#6711yescharacteristic
631C22×C4C2×#6711yescharacteristic
632C22×C4C2×#6711yescharacteristic
633C22×C4C2×#6711yescharacteristic
634C22×C4C2×#6712yes—
635C22×C4C2×#6711yescharacteristic
636C22×C4C2×#6712yes—
637C22×C4C2×#6711yescharacteristic
638C22×C4C2×#6711yescharacteristic
639C22×C4C2×#6711yescharacteristic
640C4⋊C4—22no—
641C4⋊C4—22no—
642C4⋊C4—22no—
643C4⋊C4—22no—
644C4⋊C4—21no—
645C4⋊C4—22no—
646C4⋊C4—21no—
647C4⋊C4—21no—
648C4⋊C4—21no—
649C4⋊C4—21no—
650C4⋊C4—22no—
651C4⋊C4—21no—
652C4⋊C4—122no—
653C4⋊C4—122no—
654C4⋊C4—122no—
655C4⋊C4—124no—
656C22⋊C4—22no—
657C22⋊C4—22no—
658C22⋊C4—22no—
659C22⋊C4—22no—
660C22⋊C4—22no—
661C22⋊C4—22no—
662C22⋊C4—21no—
663C22⋊C4—22no—
664C22⋊C4—21no—
665C22⋊C4—22no—
666C22⋊C4—22no—
667C22⋊C4—21no—
668C22⋊C4—21no—
669C22⋊C4—22no—
670C22⋊C4—32no—
671C22⋊C4—64no—
672C22⋊C4—61no—
673C22⋊C4—62no—
674C22⋊C4—62no—
675C22⋊C4—61no—
676C22⋊C4—62no—
677C22⋊C4—62no—
678C22⋊C4—61no—
679C22⋊C4—124no—
680C22⋊C4—122no—
681C22⋊C4—124no—
682C22⋊C4—124no—
683C22⋊C4—122no—
684C22⋊C4—122no—
685C22⋊C4—124no—
686C42—22no—
687C42—22no—
688C42—21no—
689C42—21no—
690C42—122no—
691C22×C3—21no—
692C22×C3—21no—
693C22×C3—21no—
694C22×C3—21no—
695C22×C3—21no—
696C22×C3—21no—
697C22×C3—41no—
698C22×C3—41no—
699C22×C3—41no—
700C22×C3—41no—
701C22×C3—42no—
702C22×C3—41no—
703C22×C3—42no—
704C22×C3—41no—
705C22×C3—42no—
706C22×C3—42no—
707C22×C3—41no—
708C22×C3—82no—
709C22×C3—81no—
710C22×C3—82no—
711C22×C3C2×#12011yescharacteristic
712C22×C3#52511yescharacteristic
713C22×C3#53711yescharacteristic
714C22×C3#54611yescharacteristic
715C22×C3#54711yescharacteristic
716C22×C3#54811yescharacteristic
717C22×C3#55011yescharacteristic
718C2×D3—24no—
719C2×D3—24no—
720C2×D3—24no—
721C2×D3—42no—
722C2×D3—42no—
723C2×D3—42no—
724C2×D3—42no—
725C2×D3—42no—
726C2×D3—42no—
727C2×D3—42no—
728C2×D3—42no—
729C2×D3—42no—
730C2×D3—42no—
731C2×D3—42no—
732C2×D3—42no—
733C3×C4—21no—
734C3×C4—21no—
735C3×C4—21no—
736C3×C4—41no—
737C3×C4—42no—
738C3×C4—41no—
739C3×C4—42no—
740C3×C4—41no—
741C3×C4—42no—
742C3×C4B(4,𝔽2)12yes—
743Dic3—42no—
744Dic3—42no—
745Dic3—82no—
746Dic3—81no—
747Dic3—82no—
748C23—21no—
749C23—21no—
750C23—22no—
751C23—22no—
752C23—22no—
753C23—21no—
754C23—41no—
755C23—41no—
756C23—41no—
757C23—41no—
758C23—42no—
759C23—42no—
760C23—62no—
761C23—62no—
762C23—62no—
763C23—62no—
764C23—62no—
765C23—62no—
766C23—62no—
767C23—62no—
768C23—62no—
769C23—121no—
770C23—121no—
771C23—121no—
772C23—121no—
773C23—121no—
774C23—121no—
775C23—124no—
776C23—124no—
777C23—124no—
778C23—124no—
779C23—121no—
780C23—121no—
781C23—121no—
782C23—121no—
783C23D3×#4111yescharacteristic
784C23D3×#4111yescharacteristic
785C23#100911yescharacteristic
786C23#101011yescharacteristic
787C23C22×#6711yescharacteristic
788C23C22×#6711yescharacteristic
789C23C22×#6711yescharacteristic
790Q8—42no—
791Q8—81no—
792D4—41no—
793D4—42no—
794D4—41no—
795D4—42no—
796D4—41no—
797D4—42no—
798D4—42no—
799D4—41no—
800D4—42no—
801D4—81no—
802D4—82no—
803D4—82no—
804D4—128no—
805D4—248no—
806C2×C4—22no—
807C2×C4—22no—
808C2×C4—22no—
809C2×C4—22no—
810C2×C4—21no—
811C2×C4—22no—
812C2×C4—21no—
813C2×C4—21no—
814C2×C4—22no—
815C2×C4—21no—
816C2×C4—21no—
817C2×C4—22no—
818C2×C4—22no—
819C2×C4—41no—
820C2×C4—41no—
821C2×C4—41no—
822C2×C4—42no—
823C2×C4—41no—
824C2×C4—42no—
825C2×C4—41no—
826C2×C4—42no—
827C2×C4—62no—
828C2×C4—62no—
829C2×C4—62no—
830C2×C4—62no—
831C2×C4—81no—
832C2×C4—82no—
833C2×C4—82no—
834C2×C4—124no—
835C2×C4—124no—
836C2×C4—124no—
837C2×C4—121no—
838C2×C4—121no—
839C2×C4—121no—
840C2×C4—121no—
841C2×C4—121no—
842C2×C4—121no—
843C2×C4—124no—
844C2×C4—121no—
845C2×C4—122no—
846C2×C4—122no—
847C2×C4—122no—
848C2×C4—121no—
849C2×C4—122no—
850C2×C4—122no—
851C2×C4—121no—
852C2×C4—122no—
853C2×C4#95311yescharacteristic
854C2×C4#95311yescharacteristic
855C2×C4#95311yescharacteristic
856C2×C4#95311yescharacteristic
857C2×C3—21no—
858C2×C3—21no—
859C2×C3—21no—
860C2×C3—21no—
861C2×C3—21no—
862C2×C3—21no—
863C2×C3—81no—
864C2×C3—82no—
865C2×C3#240711yescharacteristic
866C2×C3C2×B(4,𝔽2)11yescharacteristic
867C2×C3#302511yescharacteristic
868D3—44no—
869C22—21no—
870C22—21no—
871C22—21no—
872C22—21no—
873C22—21no—
874C22—21no—
875C22—41no—
876C22—41no—
877C22—41no—
878C22—41no—
879C22—42no—
880C22—41no—
881C22—42no—
882C22—41no—
883C22—42no—
884C22—42no—
885C22—41no—
886C22—64no—
887C22—64no—
888C22—64no—
889C22—82no—
890C22—81no—
891C22—82no—
892C22—122no—
893C22—122no—
894C22—122no—
895C22—122no—
896C22—122no—
897C22—122no—
898C22—122no—
899C22—122no—
900C22—122no—
901C22—122no—
902C22—122no—
903C22—122no—
904C22#582411yescharacteristic
905C22#582811yescharacteristic
906C22#582911yescharacteristic
907C22#583111yescharacteristic
908C22#583311yescharacteristic
909C22#583411yescharacteristic
910C22C2×#95311yescharacteristic
911C4—21no—
912C4—21no—
913C4—21no—
914C4—42no—
915C4—41no—
916C4—41no—
917C4—42no—
918C4—41no—
919C4—42no—
920C4—122no—
921C4—122no—
922C4—242no—
923C4—242no—
924C4—241no—
925C4#524412yes—
926C3#2414011yescharacteristic, complemented, Sylow
927C2—21no—
928C2—21no—
929C2—21no—
930C2—21no—
931C2—21no—
932C2—21no—
933C2—81no—
934C2—82no—
935C2—124no—
936C2#8409711yescharacteristic
937C2C2×#524411yescharacteristic
938C2#8412511yescharacteristic
subgroupG/H
centerC22C2×#953
commutator, cosocleC24×C3C24
FrattiniC24C23×D3
FittingC3×#3505C2
socleC22×C3C2×#120
hypercenter#3505D3
hypocenterC3#24140
LCSG ▷ C24×C3 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ C23×C4 ◁ #3505

Complements

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

NH ≅ G/Ntype
1. C3×#3505C2semidirect
2. #82834C2semidirect
3. #82723C2semidirect
4. C4×#937C2semidirect
5. #71851C2semidirect
6. #71850C2semidirect
7. #71701C2semidirect
8. #71686C2semidirect
9. #71657C2semidirect
10. #71654C2semidirect
11. #71619C2semidirect
56. #3505D3semidirect
69. C22×C3×Q8D4semidirect
70. C22×C3×D4D4semidirect
73. C23×C3×C4D4semidirect
127. C2×C3×C4⋊C4D4semidirect
128. C2×C3×C4⋊C4D4semidirect
129. C2×C3×C4⋊C4D4semidirect
130. C2×C3×C4⋊C4D4semidirect
132. C2×C3×C22⋊C4D4semidirect
133. C2×C3×C22⋊C4D4semidirect
136. C2×C3×C42D4semidirect
225. C23×D3#41semidirect
334. #217#41semidirect
348. C22×Q8#67semidirect
351. C22×D4#67semidirect
362. C23×C4#67semidirect
417. C2×C4⋊C4#67semidirect
418. C2×C4⋊C4#67semidirect
419. C2×C4⋊C4#67semidirect
420. C2×C4⋊C4#67semidirect
434. C2×C22⋊C4#67semidirect
435. C2×C22⋊C4#67semidirect
439. C2×C42#67semidirect
926. C3#24140semidirect

Maximal subgroups

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

subgroupindex
C3×#35052
#828342
#827232
C4×#9372
#718512
#718502
#717012
#716862
#716572
#716542
#716192
#241403