Finite Group Databasebeta

← #10822170

Subgroups — #10822170

Order 768.

2014 conjugacy classes of subgroups.

The subgroup lattice has 842 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#575C211yesmaximal, characteristic, complemented
2C2×#5833C211yesmaximal, characteristic, complemented
3C2×#5822C211yesmaximal, characteristic, complemented
4#84087C211yesmaximal, characteristic, complemented
5C2×#5236C211yesmaximal, characteristic, complemented
6C2×#5139C211yesmaximal, characteristic, complemented
7#72110C214yesmaximal, complemented
8#72098C214yesmaximal, complemented
9C2×#4554C211yesmaximal, characteristic, complemented
10#23409—31nomaximal, Sylow
11C22×C3×#41C2211yescharacteristic
12C22×C3×#41C2211yescharacteristic
13C22×#235C2211yescharacteristic
14C3×#575—24no—
15C3×#575—24no—
16C2×C3×#137—21no—
17C2×C3×#137C2212yescomplemented
18C2×C3×AGL(1,ℤ/8)—21no—
19C2×C3×AGL(1,ℤ/8)C2212yescomplemented
20C2×C3×#135—22no—
21C22×C3×M16C2211yescharacteristic
22#5833—22no—
23#5833—22no—
24#5833—22no—
25#5833C2214yes—
26C2×#951—21no—
27#5822—24no—
28#5822—24no—
29C2×#950—22no—
30C2×#949—21no—
31C2×#946—21no—
32C2×#942C2212yescomplemented
33C2×#939—22no—
34C2×#938—21no—
35C2×#932C2212yescomplemented
36C2×#930—21no—
37C2×#926C2211yescharacteristic
38C22×C4⋊Dic3C2211yescharacteristic
39C2×#924—21no—
40C22×#208C2211yescharacteristic
41#5236—24no—
42C2×#837C2214yescomplemented
43#5229C2212yescomplemented
44#5221C2212yescomplemented
45#5220—22no—
46#5212—22no—
47#5139—24no—
48C2×#825C2214yescomplemented
49#4554C2214yescomplemented
50C2×#575—31no—
51C2×#575D311yescharacteristic, complemented
52C2×#537—31no—
53C2×#421—31no—
54C2×#421—31no—
55#2311—31no—
56#2007—34no—
57#2006—34no—
58C2×#343—31no—
59C2×C3×#41—21no—
60C2×C3×#41—21no—
61C2×C3×#41—22no—
62C2×C3×#41—21no—
63C2×C3×#41—21no—
64C2×C3×#41—22no—
65C2×C3×#41—22no—
66C2×C3×#41—22no—
67C2×C3×#41—22no—
68C2×C3×#41—21no—
69C2×C3×#41—21no—
70C2×C3×#41—22no—
71C2×C3×#41—22no—
72C2×C3×#41D412yes—
73C2×C3×#41D414yescomplemented
74C2×C3×#41C2312yes—
75C22×C3×Q8D411yescharacteristic
76C22×C3×Q8C2311yescharacteristic
77C22×C3×D4—21no—
78C22×C3×D4—21no—
79C22×C3×D4D411yescharacteristic
80C22×C3×D4C2311yescharacteristic
81C23×C3×C4—21no—
82C23×C3×C4—21no—
83C23×C3×C4C2311yescharacteristic
84C22×#67—21no—
85C22×#67—22no—
86C23×Dic3D412yes—
87C2×#235—21no—
88C2×#235—21no—
89C2×#235—22no—
90C2×#235—22no—
91C2×#235—22no—
92C2×#235—22no—
93C2×#235D412yes—
94C2×#235C2312yes—
95C22×D12D411yescharacteristic
96C22×C4×D3—21no—
97C22×Dic6D411yescharacteristic
98C3×#137—28no—
99C3×#137—24no—
100C3×#137—24no—
101C3×AGL(1,ℤ/8)—28no—
102C3×AGL(1,ℤ/8)—24no—
103C3×AGL(1,ℤ/8)—24no—
104C3×#135—216no—
105C2×C3×Q16—22no—
106C2×C3×SD16—22no—
107C2×C3×SD16—22no—
108C2×C3×D8—22no—
109C2×C3×M16—21no—
110C2×C3×M16—22no—
111C2×C3×M16D414yescomplemented
112C2×C3×M16C2312yes—
113C22×C3×C8—21no—
114C2×#217—22no—
115C2×#217—21no—
116C2×#217—24no—
117#951—28no—
118#950—216no—
119#949—28no—
120#946—24no—
121#946—24no—
122C2×#216—22no—
123#942—24no—
124#942—24no—
125C2×#215—22no—
126#939—28no—
127#939—28no—
128#938—24no—
129#938—24no—
130C2×#214—22no—
131#932—24no—
132#932—24no—
133C2×#213—22no—
134#930—24no—
135#930—24no—
136C2×(C2×D3)⋊C4—22no—
137#926—22no—
138#926—22no—
139C2×C4⋊Dic3—21no—
140C2×C4⋊Dic3—21no—
141C2×C4⋊Dic3—21no—
142C2×C4⋊Dic3—21no—
143C2×C4⋊Dic3—21no—
144C2×C4⋊Dic3D412yes—
145C2×C4⋊Dic3C2312yes—
146#924—24no—
147#924—24no—
148C2×Dic3⋊C4—22no—
149C2×C4×Dic3C2312yes—
150C2×#208—21no—
151C2×#208—22no—
152C2×#208D414yescomplemented
153C2×#208C2312yes—
154C22×C3⋊C8—21no—
155#837—28no—
156C3⋊#95—24no—
157#825—28no—
158C22×#41—31no—
159C22×#41C2×D311yescharacteristic
160C22×#41C2×D311yescharacteristic
161#575—24no—
162#575—24no—
163#575—64no—
164#575—64no—
165C2×#137—21no—
166C2×#137—32no—
167C2×#137—61no—
168C2×#137C2×D312yescomplemented
169C2×AGL(1,ℤ/8)—21no—
170C2×AGL(1,ℤ/8)—32no—
171C2×AGL(1,ℤ/8)—61no—
172C2×AGL(1,ℤ/8)C2×D312yescomplemented
173C2×#135—22no—
174C2×#135—62no—
175C22×M16—31no—
176C22×M16C2×D311yescharacteristic
177#537—34no—
178#537—62no—
179#537—62no—
180#537—62no—
181C2×C22⋊Q8—61no—
182C2×C22⋊Q8—61no—
183C2×#121—61no—
184C2×#121—62no—
185C2×#121—61no—
186C2×#117—31no—
187C22×C4⋊C4—31no—
188#421—64no—
189#421—64no—
190C2×#104—34no—
191C2×#104—34no—
192#391—32no—
193#390—32no—
194#386—62no—
195#380—62no—
196#343—34no—
197C24×C3—21no—
198C24×C3—21no—
199C24×C3C2×D411yescharacteristic
200C23×D3—21no—
201C3×#41—24no—
202C3×#41—24no—
203C3×#41—24no—
204C3×#41—24no—
205C3×#41—24no—
206C3×#41—24no—
207C3×#41—22no—
208C3×#41—22no—
209C3×#41—22no—
210C3×#41—22no—
211C3×#41—42no—
212C3×#41—42no—
213C3×#41—42no—
214C3×#41—42no—
215C3×#41—42no—
216C3×#41—42no—
217C3×#41—42no—
218C3×#41—42no—
219C2×C3×Q8—21no—
220C2×C3×Q8—21no—
221C2×C3×Q8—22no—
222C2×C3×Q8—22no—
223C2×C3×Q8—21no—
224C2×C3×Q8—21no—
225C2×C3×Q8—21no—
226C2×C3×Q8—21no—
227C2×C3×Q8C2×D412yes—
228C2×C3×Q8C2×D412yescomplemented
229C2×C3×D4—22no—
230C2×C3×D4—24no—
231C2×C3×D4—22no—
232C2×C3×D4—22no—
233C2×C3×D4—21no—
234C2×C3×D4—22no—
235C2×C3×D4—21no—
236C2×C3×D4—21no—
237C2×C3×D4—21no—
238C2×C3×D4—21no—
239C2×C3×D4—21no—
240C2×C3×D4—41no—
241C2×C3×D4—41no—
242C2×C3×D4—42no—
243C2×C3×D4—42no—
244C2×C3×D4—42no—
245C2×C3×D4C2×D412yes—
246C2×C3×D4C2×D412yescomplemented
247C22×C3×C4—21no—
248C22×C3×C4—21no—
249C22×C3×C4—22no—
250C22×C3×C4—24no—
251C22×C3×C4—22no—
252C22×C3×C4—41no—
253C22×C3×C4—41no—
254C22×C3×C4—42no—
255C22×C3×C4—42no—
256C22×C3×C4—42no—
257C22×C3×C4C2×D411yescharacteristic
258C22×C3×C4C2×D411yescharacteristic
259C22×C3×C4C2×D411yescharacteristic
260C22×C3×C4C2×D412yes—
261C22×C3×C4C2×D412yes—
262C22×C3×C4C2×D411yescharacteristic
263C22×C3×C4C2×D411yescharacteristic
264C22×C3×C4C2×D412yes—
265C22×C3×C4#4112yes—
266C22×C3×C4C2411yescharacteristic
267C2×#67—22no—
268C2×#67—22no—
269C2×#67—28no—
270C2×#67—42no—
271C2×#67—42no—
272C2×#67—84no—
273C22×Dic3—21no—
274C22×Dic3—22no—
275C22×Dic3—22no—
276C22×Dic3—22no—
277C22×Dic3—82no—
278C22×Dic3C2×D414yes—
279#235—24no—
280#235—24no—
281#235—22no—
282#235—22no—
283#235—22no—
284#235—22no—
285#235—42no—
286#235—42no—
287#235—42no—
288#235—42no—
289C2×D12—22no—
290C2×D12—22no—
291C2×D12—21no—
292C2×D12C2×D412yes—
293C2×C4×D3—22no—
294C2×C4×D3—22no—
295C2×C4×D3—42no—
296C2×C4×D3—42no—
297C2×Dic6—22no—
298C2×Dic6—22no—
299C2×Dic6—21no—
300C2×Dic6C2×D412yes—
301C3×Q16—28no—
302C3×SD16—28no—
303C3×SD16—28no—
304C3×D8—28no—
305C3×M16—24no—
306C3×M16—22no—
307C3×M16C2×D414yescomplemented
308C2×C3×C8—24no—
309C2×C3×C8—22no—
310#217—28no—
311#217—42no—
312#217—84no—
313#216—28no—
314#215—28no—
315#214—28no—
316#213—28no—
317(C2×D3)⋊C4—28no—
318C4⋊Dic3—22no—
319C4⋊Dic3—22no—
320C4⋊Dic3—22no—
321C4⋊Dic3—22no—
322C4⋊Dic3—42no—
323Dic3⋊C4—28no—
324C4×Dic3—22no—
325C4×Dic3—22no—
326#208—24no—
327#208—22no—
328#208C2×D414yescomplemented
329C2×C3⋊C8—24no—
330C2×C3⋊C8—22no—
331C2×#41—21no—
332C2×#41—21no—
333C2×#41—22no—
334C2×#41—21no—
335C2×#41—21no—
336C2×#41—22no—
337C2×#41—22no—
338C2×#41—22no—
339C2×#41—21no—
340C2×#41—21no—
341C2×#41—22no—
342C2×#41—22no—
343C2×#41—22no—
344C2×#41—32no—
345C2×#41—32no—
346C2×#41—61no—
347C2×#41—61no—
348C2×#41—62no—
349C2×#41—62no—
350C2×#41—62no—
351C2×#41—62no—
352C2×#41#6712yes—
353C2×#41#6714yescomplemented
354C2×#41C22×D312yes—
355C22×Q8—31no—
356C22×Q8#6711yescharacteristic
357C22×Q8C22×D311yescharacteristic
358C22×D4—21no—
359C22×D4—21no—
360C22×D4—31no—
361C22×D4—61no—
362C22×D4—62no—
363C22×D4#6711yescharacteristic
364C22×D4C22×D311yescharacteristic
365C23×C4—21no—
366C23×C4—21no—
367C23×C4—32no—
368C23×C4—61no—
369C23×C4C22×D311yescharacteristic
370#137—28no—
371#137—24no—
372#137—24no—
373#137—64no—
374#137—68no—
375#137—64no—
376AGL(1,ℤ/8)—28no—
377AGL(1,ℤ/8)—24no—
378AGL(1,ℤ/8)—24no—
379AGL(1,ℤ/8)—64no—
380AGL(1,ℤ/8)—68no—
381AGL(1,ℤ/8)—64no—
382#135—216no—
383#135—616no—
384C2×Q16—22no—
385C2×Q16—62no—
386C2×SD16—22no—
387C2×SD16—22no—
388C2×SD16—62no—
389C2×SD16—62no—
390C2×D8—22no—
391C2×D8—62no—
392C2×M16—21no—
393C2×M16—22no—
394C2×M16—34no—
395C2×M16—32no—
396C2×M16—61no—
397C2×M16—62no—
398C2×M16#6714yescomplemented
399C2×M16C22×D312yes—
400C22×C8—21no—
401C22×C8—61no—
402C22⋊Q8—64no—
403C22⋊Q8—64no—
404C22⋊Q8—64no—
405C22⋊Q8—64no—
406#121—64no—
407#121—64no—
408#121—68no—
409#121—64no—
410#121—68no—
411#121—64no—
412#117—62no—
413#117—62no—
414C2×C4⋊C4—32no—
415C2×C4⋊C4—32no—
416C2×C4⋊C4—62no—
417C2×C4⋊C4—61no—
418C2×C4⋊C4—61no—
419C2×C4⋊C4—61no—
420C2×C4⋊C4—61no—
421C2×C4⋊C4—61no—
422C2×C22⋊C4—62no—
423C2×C22⋊C4—62no—
424C2×C22⋊C4—61no—
425C2×C22⋊C4—64no—
426C2×C42—32no—
427#104—68no—
428#104—68no—
429#95—64no—
430C23×C3—22no—
431C23×C3—22no—
432C23×C3—41no—
433C23×C3—41no—
434C23×C3—42no—
435C23×C3—42no—
436C23×C3—42no—
437C23×C3—42no—
438C23×C3—41no—
439C23×C3—41no—
440C23×C3—42no—
441C23×C3#12011yescharacteristic
442C23×C3#12011yescharacteristic
443C23×C3#12112yes—
444C23×C3#12712yes—
445C23×C3C22×D411yescharacteristic
446C22×D3—22no—
447C22×D3—42no—
448C22×D3—42no—
449C22×D3—42no—
450C3×Q8—22no—
451C3×Q8—22no—
452C3×Q8—22no—
453C3×Q8—22no—
454C3×Q8—41no—
455C3×Q8—41no—
456C3×Q8—42no—
457C3×D4—22no—
458C3×D4—22no—
459C3×D4—22no—
460C3×D4—22no—
461C3×D4—42no—
462C3×D4—42no—
463C3×D4—44no—
464C3×D4—44no—
465C3×D4—44no—
466C3×D4—41no—
467C3×D4—41no—
468C3×D4—42no—
469C2×C3×C4—22no—
470C2×C3×C4—22no—
471C2×C3×C4—41no—
472C2×C3×C4—41no—
473C2×C3×C4—42no—
474C2×C3×C4—42no—
475C2×C3×C4—42no—
476C2×C3×C4—44no—
477C2×C3×C4—44no—
478C2×C3×C4—44no—
479C2×C3×C4#12012yes—
480C2×C3×C4#12012yes—
481C2×C3×C4#12011yescharacteristic
482C2×C3×C4#12011yescharacteristic
483C2×C3×C4#12012yes—
484C2×C3×C4#12012yes—
485C2×C3×C4#12112yes—
486C2×C3×C4#12112yes—
487C2×C3×C4#12112yes—
488C2×C3×C4#12112yes—
489C2×C3×C4#12112yes—
490C2×C3×C4#12712yes—
491C2×C3×C4C22×D411yescharacteristic
492C2×C3×C4C22×D411yescharacteristic
493C2×C3×C4C22×D411yescharacteristic
494C2×C3×C4C22×D411yescharacteristic
495C2×C3×C4C22×D411yescharacteristic
496C2×C3×C4C2×#4111yescharacteristic
497#67—42no—
498#67—42no—
499#67—44no—
500#67—88no—
501C2×Dic3—22no—
502C2×Dic3—24no—
503C2×Dic3—44no—
504C2×Dic3—42no—
505C2×Dic3—44no—
506C2×Dic3—42no—
507C2×Dic3—42no—
508C2×Dic3—42no—
509C2×Dic3—82no—
510D12—22no—
511D12—22no—
512D12—42no—
513C4×D3—42no—
514C4×D3—42no—
515C4×D3—44no—
516Dic6—22no—
517Dic6—22no—
518Dic6—42no—
519C3×C8—24no—
520C3⋊C8—24no—
521C24—21no—
522C24—21no—
523C24—61no—
524C24D3×D411yescharacteristic
525#41—24no—
526#41—24no—
527#41—24no—
528#41—24no—
529#41—24no—
530#41—24no—
531#41—22no—
532#41—22no—
533#41—22no—
534#41—22no—
535#41—42no—
536#41—42no—
537#41—42no—
538#41—42no—
539#41—42no—
540#41—42no—
541#41—42no—
542#41—42no—
543#41—64no—
544#41—64no—
545#41—62no—
546#41—62no—
547#41—62no—
548#41—62no—
549#41—122no—
550#41—122no—
551#41—122no—
552#41—122no—
553C2×Q8—21no—
554C2×Q8—21no—
555C2×Q8—22no—
556C2×Q8—22no—
557C2×Q8—21no—
558C2×Q8—21no—
559C2×Q8—21no—
560C2×Q8—21no—
561C2×Q8—32no—
562C2×Q8—61no—
563C2×Q8—62no—
564C2×Q8—62no—
565C2×Q8C2×#6712yes—
566C2×Q8C2×#6712yescomplemented
567C2×D4—22no—
568C2×D4—24no—
569C2×D4—22no—
570C2×D4—21no—
571C2×D4—22no—
572C2×D4—22no—
573C2×D4—21no—
574C2×D4—21no—
575C2×D4—21no—
576C2×D4—21no—
577C2×D4—21no—
578C2×D4—32no—
579C2×D4—41no—
580C2×D4—41no—
581C2×D4—42no—
582C2×D4—42no—
583C2×D4—42no—
584C2×D4—62no—
585C2×D4—62no—
586C2×D4—68no—
587C2×D4—62no—
588C2×D4—61no—
589C2×D4—62no—
590C2×D4—122no—
591C2×D4—122no—
592C2×D4—244no—
593C2×D4C2×#6712yes—
594C2×D4C2×#6712yescomplemented
595C22×C4—21no—
596C22×C4—21no—
597C22×C4—22no—
598C22×C4—24no—
599C22×C4—22no—
600C22×C4—34no—
601C22×C4—42no—
602C22×C4—41no—
603C22×C4—41no—
604C22×C4—42no—
605C22×C4—42no—
606C22×C4—62no—
607C22×C4—61no—
608C22×C4—62no—
609C22×C4—62no—
610C22×C4—62no—
611C22×C4—62no—
612C22×C4—122no—
613C22×C4—122no—
614C22×C4—242no—
615C22×C4D3×D411yescharacteristic
616C22×C4D3×D411yescharacteristic
617C22×C4D3×D411yescharacteristic
618C22×C4D3×D412yes—
619C22×C4#23712yes—
620C22×C4C2×#6712yes—
621C22×C4C2×#6711yescharacteristic
622C22×C4C2×#6711yescharacteristic
623C22×C4C2×#6712yes—
624C22×C4C23×D311yescharacteristic
625Q16—28no—
626Q16—68no—
627SD16—28no—
628SD16—28no—
629SD16—68no—
630SD16—68no—
631D8—28no—
632D8—68no—
633M16—24no—
634M16—22no—
635M16—34no—
636M16—64no—
637M16—62no—
638M16C2×#6714yescomplemented
639C2×C8—24no—
640C2×C8—22no—
641C2×C8—64no—
642C2×C8—62no—
643C4⋊C4—68no—
644C4⋊C4—62no—
645C4⋊C4—62no—
646C4⋊C4—62no—
647C4⋊C4—62no—
648C4⋊C4—122no—
649C22⋊C4—68no—
650C22⋊C4—68no—
651C22⋊C4—122no—
652C22⋊C4—244no—
653C42—62no—
654C42—62no—
655C22×C3—21no—
656C22×C3—21no—
657C22×C3—21no—
658C22×C3—21no—
659C22×C3—21no—
660C22×C3—21no—
661C22×C3—42no—
662C22×C3—42no—
663C22×C3—44no—
664C22×C3—42no—
665C22×C3—42no—
666C22×C3—42no—
667C22×C3—42no—
668C22×C3—82no—
669C22×C3—84no—
670C22×C3—81no—
671C22×C3—81no—
672C22×C3#39212yes—
673C22×C3#39212yes—
674C22×C3C2×#12011yescharacteristic
675C22×C3C2×#12111yescharacteristic
676C22×C3C2×#12711yescharacteristic
677C2×D3—42no—
678C2×D3—42no—
679C2×D3—42no—
680C2×D3—84no—
681C3×C4—42no—
682C3×C4—42no—
683C3×C4#39212yes—
684C3×C4#39212yes—
685C3×C4C2×#12011yescharacteristic
686C3×C4C2×#12011yescharacteristic
687C3×C4C2×#12111yescharacteristic
688C3×C4C2×#12111yescharacteristic
689Dic3—42no—
690Dic3—44no—
691Dic3—82no—
692C23—22no—
693C23—22no—
694C23—41no—
695C23—41no—
696C23—42no—
697C23—42no—
698C23—42no—
699C23—42no—
700C23—42no—
701C23—41no—
702C23—41no—
703C23—62no—
704C23—122no—
705C23—122no—
706C23—122no—
707C23#93711yescharacteristic
708C23#93711yescharacteristic
709C23#93912yes—
710C23#94012yes—
711C23C2×D3×D411yescharacteristic
712Q8—22no—
713Q8—22no—
714Q8—22no—
715Q8—22no—
716Q8—42no—
717Q8—41no—
718Q8—41no—
719Q8—62no—
720Q8—62no—
721Q8—122no—
722D4—22no—
723D4—22no—
724D4—22no—
725D4—22no—
726D4—44no—
727D4—44no—
728D4—44no—
729D4—42no—
730D4—42no—
731D4—42no—
732D4—41no—
733D4—41no—
734D4—62no—
735D4—62no—
736D4—124no—
737D4—122no—
738D4—122no—
739D4—122no—
740D4—248no—
741C2×C4—22no—
742C2×C4—22no—
743C2×C4—42no—
744C2×C4—41no—
745C2×C4—41no—
746C2×C4—44no—
747C2×C4—44no—
748C2×C4—44no—
749C2×C4—42no—
750C2×C4—42no—
751C2×C4—64no—
752C2×C4—62no—
753C2×C4—124no—
754C2×C4—122no—
755C2×C4—124no—
756C2×C4—122no—
757C2×C4—122no—
758C2×C4—124no—
759C2×C4—122no—
760C2×C4—122no—
761C2×C4—122no—
762C2×C4—242no—
763C2×C4#93711yescharacteristic
764C2×C4#93711yescharacteristic
765C2×C4#93712yes—
766C2×C4#93712yes—
767C2×C4#93812yes—
768C2×C4#93812yes—
769C2×C4#93912yes—
770C2×C4#93912yes—
771C2×C4#93912yes—
772C2×C4#94012yes—
773C2×C4#95312yes—
774C2×C4#95312yes—
775C2×C4C2×D3×D411yescharacteristic
776C2×C4C2×D3×D411yescharacteristic
777C2×C4C2×#23711yescharacteristic
778C2×C4C22×#6711yescharacteristic
779C2×C4C22×#6711yescharacteristic
780C2×C4C22×#6711yescharacteristic
781C8—24no—
782C8—64no—
783C2×C3—21no—
784C2×C3—22no—
785C2×C3—21no—
786C2×C3—22no—
787C2×C3—82no—
788C2×C3—82no—
789C2×C3C2×#39211yescharacteristic
790C2×C3#301911yescharacteristic
791C2×C3#302011yescharacteristic
792D3—82no—
793C22—21no—
794C22—21no—
795C22—21no—
796C22—21no—
797C22—21no—
798C22—21no—
799C22—42no—
800C22—42no—
801C22—44no—
802C22—42no—
803C22—42no—
804C22—42no—
805C22—42no—
806C22—82no—
807C22—84no—
808C22—81no—
809C22—81no—
810C22—122no—
811C22—122no—
812C22—122no—
813C22—244no—
814C22#522312yes—
815C22#522312yes—
816C22C2×#93711yescharacteristic
817C22C2×#93911yescharacteristic
818C22C2×#94011yescharacteristic
819C4—42no—
820C4—42no—
821C4—124no—
822C4—122no—
823C4—242no—
824C4#522312yes—
825C4#522312yes—
826C4C2×#93711yescharacteristic
827C4C2×#93811yescharacteristic
828C4C2×#93911yescharacteristic
829C4C2×#95311yescharacteristic
830C3#2340911yescharacteristic, complemented, Sylow
831C2—21no—
832C2—21no—
833C2—22no—
834C2—22no—
835C2—82no—
836C2—82no—
837C2—242no—
838C2#8400511yescharacteristic
839C2#8400611yescharacteristic
840C2C2×#522311yescharacteristic
subgroupG/H
centerC22C2×#937
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC2×C3×#575C2
socleC22×C3C2×#120
hypercenterC2×#575D3
hypocenterC3#23409
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#575

Complements

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

NH ≅ G/Ntype
1. C2×C3×#575C2semidirect
2. C2×#5833C2semidirect
3. C2×#5822C2semidirect
4. #84087C2semidirect
5. C2×#5236C2semidirect
6. C2×#5139C2semidirect
7. #72110C2semidirect
8. #72098C2semidirect
9. C2×#4554C2semidirect
17. C2×C3×#137C22semidirect
19. C2×C3×AGL(1,ℤ/8)C22semidirect
32. C2×#942C22semidirect
35. C2×#932C22semidirect
42. C2×#837C22semidirect
43. #5229C22semidirect
44. #5221C22semidirect
48. C2×#825C22semidirect
49. #4554C22semidirect
51. C2×#575D3semidirect
73. C2×C3×#41D4semidirect
111. C2×C3×M16D4semidirect
152. C2×#208D4semidirect
168. C2×#137C2×D3semidirect
172. C2×AGL(1,ℤ/8)C2×D3semidirect
228. C2×C3×Q8C2×D4semidirect
246. C2×C3×D4C2×D4semidirect
307. C3×M16C2×D4semidirect
328. #208C2×D4semidirect
353. C2×#41#67semidirect
398. C2×M16#67semidirect
566. C2×Q8C2×#67semidirect
594. C2×D4C2×#67semidirect
638. M16C2×#67semidirect
830. C3#23409semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#5752
C2×#58332
C2×#58222
#840872
C2×#52362
C2×#51392
#721102
#720982
C2×#45542
#234093