Finite Group Databasebeta

← #10830981

Subgroups — #10830981

Order 768.

1614 conjugacy classes of subgroups.

The subgroup lattice has 950 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#911C211yesmaximal, characteristic, complemented
2C2×C3×#466C211yesmaximal, characteristic, complemented
3C2×#5114C211yesmaximal, characteristic, complemented
4C2×#5111C211yesmaximal, characteristic, complemented
5#82701C211yesmaximal, characteristic, complemented
6#82640C211yesmaximal, characteristic, complemented
7#72039C211yesmaximal, characteristic, complemented
8#71685C211yesmaximal, characteristic, complemented
9#71684C211yesmaximal, characteristic, complemented
10#70631C211yesmaximal, characteristic, complemented
11#70629C211yesmaximal, characteristic, complemented
12#70217C211yesmaximal, characteristic, complemented
13#70212C211yesmaximal, characteristic, complemented
14#70199C211yesmaximal, characteristic, complemented
15#70198C211yesmaximal, characteristic, complemented
16#24275—31nomaximal, Sylow
17C22×#237C2211yescharacteristic
18C22×D3×D4C2211yescharacteristic
19C22×C3×D8C2211yescharacteristic
20C23×C3×C8C2211yescharacteristic, complemented
21C2×C3×#121C2211yescharacteristic
22C2×C3×#121C2211yescharacteristic, complemented
23C2×#937—21no—
24C22×#214C2211yescharacteristic
25C22×#213C2211yescharacteristic
26C2×#930C2211yescharacteristic
27C2×C4×#67C2211yescharacteristic
28C2×#924C2211yescharacteristic, complemented
29C2×#911—24no—
30C2×#911—24no—
31C2×#911—24no—
32C22×#204C2211yescharacteristic
33C22×ΓL(1,𝔽25)C2211yescharacteristic
34C3×#466—24no—
35C2×C3×#107C2211yescharacteristic, complemented
36C2×C3×#102C2211yescharacteristic
37C2×C3×#102C2211yescharacteristic, complemented
38#5223—21no—
39#5223—21no—
40#5221C2211yescharacteristic
41#5221C2211yescharacteristic, complemented
42#5220—21no—
43C2×#832C2211yescharacteristic
44C2×#832C2211yescharacteristic, complemented
45C2×#830C2211yescharacteristic, complemented
46#5114—24no—
47C2×#821C2211yescharacteristic
48#5111—24no—
49C2×(C2×D3)⋊C8C2211yescharacteristic
50C2×#817C2211yescharacteristic, complemented
51C2×#816C2211yescharacteristic, complemented
52C2×#815C2211yescharacteristic, complemented
53C2×Dic3⋊C8C2211yescharacteristic, complemented
54#4988C2211yescharacteristic
55#4987C2211yescharacteristic
56#4987C2211yescharacteristic
57#4973C2211yescharacteristic, complemented
58C2×#810C2211yescharacteristic, complemented
59C2×#809C2211yescharacteristic
60#4959—21no—
61#4959—21no—
62#4955—21no—
63#4946—21no—
64#4529C2211yescharacteristic, complemented
65#4529C2211yescharacteristic, complemented
66C22×AGL(1,ℤ/8)—31no—
67C2×#466D311yescharacteristic, complemented
68C2×#465—31no—
69C2×#435—31no—
70#2408—31no—
71#2407—31no—
72#2055—31no—
73#2054—31no—
74#2000—31no—
75#1999—31no—
76#1973—31no—
77#1972—31no—
78#1809—31no—
79#1788—31no—
80#1786—31no—
81C24×D3—21no—
82C22×C3×D4—21no—
83C22×C3×D4—21no—
84C22×C3×D4C2311yescharacteristic
85C22×C3×D4C2311yescharacteristic
86C23×C3×C4C2311yescharacteristic
87C22×#67—21no—
88C22×#67—21no—
89C22×#67—21no—
90C22×#67D411yescharacteristic
91C23×Dic3—21no—
92C2×#237—22no—
93C2×#237—22no—
94C2×#237—22no—
95C2×#237—22no—
96C2×#237—41no—
97C2×#237—41no—
98C2×D3×D4—22no—
99C2×D3×D4—22no—
100C2×D3×D4—22no—
101C2×D3×D4—22no—
102C2×D3×D4—41no—
103C2×D3×D4—41no—
104C22×D12C2311yescharacteristic
105C22×C4×D3C2311yescharacteristic
106C22×Dic6C2311yescharacteristic
107C2×C3×D8—22no—
108C2×C3×D8—22no—
109C2×C3×D8D414yescomplemented
110C22×C3×C8—22no—
111C22×C3×C8—22no—
112C22×C3×C8—22no—
113C22×C3×C8C2311yescharacteristic
114C22×C3×C8C2311yescharacteristic
115C3×#121—22no—
116C3×#121—22no—
117C3×#121—41no—
118C3×#121—41no—
119C2×C3×C4⋊C4C2311yescharacteristic
120C2×C3×C4⋊C4C2311yescharacteristic
121C2×C3×C22⋊C4—21no—
122C2×C3×C22⋊C4—21no—
123C2×#217—21no—
124C2×#217—21no—
125C2×#217—21no—
126C2×#217—21no—
127C2×#217—21no—
128C2×#217D411yescharacteristic
129#937—44no—
130C2×#214—22no—
131C2×#214—22no—
132C2×#214—22no—
133C2×#213—22no—
134C2×#213—22no—
135C2×#213—22no—
136#930—22no—
137#930—41no—
138C4×#67—22no—
139C4×#67—22no—
140C2×(C2×D3)⋊C4—21no—
141C2×(C2×D3)⋊C4—21no—
142C2×(C2×D3)⋊C4—21no—
143C2×(C2×D3)⋊C4—21no—
144C2×(C2×D3)⋊C4—21no—
145C2×(C2×D3)⋊C4D411yescharacteristic
146C2×C4⋊Dic3C2311yescharacteristic
147C2×C4⋊Dic3C2311yescharacteristic
148#924—22no—
149#924—41no—
150C2×Dic3⋊C4—21no—
151C2×Dic3⋊C4D411yescharacteristic
152C2×C4×Dic3C2311yescharacteristic
153C22×C3⋊C8C2311yescharacteristic
154C22×C3⋊C8C2311yescharacteristic
155#911—232no—
156C2×#204—22no—
157C2×#204—22no—
158C2×#204D414yescomplemented
159C2×ΓL(1,𝔽25)—22no—
160C2×ΓL(1,𝔽25)—22no—
161C2×ΓL(1,𝔽25)D414yescomplemented
162C3×#107—22no—
163C3×#102—22no—
164C3×#102—22no—
165#832—41no—
166#832—41no—
167C3⋊#95—21no—
168C3⋊#95—21no—
169C3⋊#95—21no—
170C3⋊#95—21no—
171#830—22no—
172#821—22no—
173(C2×D3)⋊C8—22no—
174#817—22no—
175#816—22no—
176#815—22no—
177Dic3⋊C8—22no—
178#810—41no—
179#809—41no—
180C22×#41—31no—
181C23×D4—31no—
182C2×AGL(1,ℤ/8)—64no—
183C2×AGL(1,ℤ/8)—64no—
184C2×AGL(1,ℤ/8)—64no—
185C22×SD16—31no—
186C22×SD16—31no—
187C22×D8—31no—
188C22×D8C2×D311yescharacteristic
189C22×M16—31no—
190C23×C8C2×D311yescharacteristic, complemented
191C2×C22⋊Q8—31no—
192C2×#121—31no—
193C2×#121C2×D311yescharacteristic
194C2×#121C2×D311yescharacteristic, complemented
195C2×#120—61no—
196C2×C4×D4—31no—
197#466—24no—
198#465—64no—
199#435—64no—
200C2×#107C2×D311yescharacteristic, complemented
201C2×#106—31no—
202C2×C4⋊C8—31no—
203C2×#103—31no—
204C2×#103—31no—
205C2×#102—31no—
206C2×#102—31no—
207C2×#102—31no—
208C2×#102—31no—
209C2×#102C2×D311yescharacteristic
210C2×#102C2×D311yescharacteristic, complemented
211C2×C22⋊C8—31no—
212C2×C22⋊C8—31no—
213C2×#97—31no—
214#394—61no—
215#394—61no—
216#392—61no—
217#392—61no—
218#391—31no—
219#390—31no—
220#390—31no—
221#390—31no—
222#386—61no—
223#385—61no—
224#380—31no—
225#380—31no—
226#379—61no—
227#340—31no—
228#340—31no—
229C24×C3—21no—
230C24×C3—21no—
231C24×C3C2×D411yescharacteristic
232C23×D3—21no—
233C23×D3—42no—
234C23×D3—42no—
235C23×D3—42no—
236C23×D3—42no—
237C23×D3—42no—
238C23×D3—81no—
239C23×D3—81no—
240C23×D3C2×D411yescharacteristic
241C2×C3×D4—21no—
242C2×C3×D4—21no—
243C2×C3×D4—21no—
244C2×C3×D4—21no—
245C2×C3×D4—21no—
246C2×C3×D4—21no—
247C2×C3×D4—21no—
248C2×C3×D4—21no—
249C2×C3×D4—21no—
250C2×C3×D4—21no—
251C2×C3×D4—42no—
252C2×C3×D4—42no—
253C2×C3×D4—42no—
254C2×C3×D4—42no—
255C2×C3×D4—81no—
256C2×C3×D4—81no—
257C2×C3×D4C2×D412yes—
258C2×C3×D4C2×D412yes—
259C22×C3×C4—21no—
260C22×C3×C4—21no—
261C22×C3×C4—21no—
262C22×C3×C4—21no—
263C22×C3×C4—21no—
264C22×C3×C4—21no—
265C22×C3×C4—21no—
266C22×C3×C4—21no—
267C22×C3×C4C2×D411yescharacteristic
268C22×C3×C4C2411yescharacteristic
269C2×#67—22no—
270C2×#67—22no—
271C2×#67—41no—
272C2×#67—42no—
273C2×#67—42no—
274C2×#67—42no—
275C2×#67—42no—
276C2×#67—42no—
277C2×#67—42no—
278C2×#67—42no—
279C2×#67—42no—
280C2×#67—81no—
281C22×Dic3—21no—
282C22×Dic3—21no—
283C22×Dic3—21no—
284C22×Dic3—42no—
285C22×Dic3—42no—
286C22×Dic3—42no—
287C22×Dic3C2×D411yescharacteristic
288C22×Dic3C2×D411yescharacteristic
289C22×Dic3C2×D411yescharacteristic
290#237—28no—
291#237—44no—
292#237—44no—
293#237—44no—
294D3×D4—28no—
295D3×D4—44no—
296D3×D4—44no—
297D3×D4—44no—
298C2×D12—21no—
299C2×D12—21no—
300C2×D12—21no—
301C2×D12—21no—
302C2×D12—21no—
303C2×D12C2×D412yes—
304C2×C4×D3—21no—
305C2×C4×D3—21no—
306C2×C4×D3—21no—
307C2×C4×D3—21no—
308C2×C4×D3C2×D412yes—
309C2×C4×D3#4112yes—
310C2×Dic6—21no—
311C2×Dic6—21no—
312C2×Dic6—21no—
313C2×Dic6—21no—
314C2×Dic6—21no—
315C2×Dic6C2×D412yes—
316C3×D8—28no—
317C2×C3×C8—21no—
318C2×C3×C8—21no—
319C2×C3×C8—21no—
320C2×C3×C8—44no—
321C2×C3×C8C2×D412yes—
322C2×C3×C8C2×D412yes—
323C2×C3×C8C2×D412yes—
324C3×C4⋊C4—21no—
325C3×C4⋊C4—21no—
326C3×C4⋊C4—21no—
327C3×C4⋊C4—21no—
328C3×C22⋊C4—42no—
329C3×C22⋊C4—42no—
330#217—22no—
331#217—42no—
332#217—42no—
333#217—42no—
334#217—81no—
335#217—81no—
336#214—28no—
337#213—28no—
338(C2×D3)⋊C4—22no—
339(C2×D3)⋊C4—42no—
340(C2×D3)⋊C4—42no—
341(C2×D3)⋊C4—42no—
342(C2×D3)⋊C4—81no—
343(C2×D3)⋊C4—81no—
344C4⋊Dic3—21no—
345C4⋊Dic3—21no—
346C4⋊Dic3—21no—
347C4⋊Dic3—21no—
348Dic3⋊C4—22no—
349Dic3⋊C4—42no—
350C4×Dic3—21no—
351C4×Dic3—21no—
352C2×C3⋊C8—21no—
353C2×C3⋊C8—21no—
354C2×C3⋊C8—21no—
355C2×C3⋊C8—21no—
356C2×C3⋊C8—21no—
357C2×C3⋊C8C2×D412yes—
358#204—28no—
359ΓL(1,𝔽25)—28no—
360C25—61no—
361C2×#41—62no—
362C2×#41—62no—
363C2×#41—62no—
364C2×#41—62no—
365C2×#41—121no—
366C2×#41—121no—
367C22×Q8—31no—
368C22×D4—21no—
369C22×D4—21no—
370C22×D4—31no—
371C22×D4—31no—
372C22×D4—62no—
373C22×D4—62no—
374C22×D4—61no—
375C22×D4—62no—
376C22×D4—62no—
377C22×D4—61no—
378C22×D4—61no—
379C22×D4—121no—
380C22×D4—121no—
381C22×D4C22×D311yescharacteristic
382C22×D4C22×D311yescharacteristic
383C23×C4—31no—
384C23×C4—61no—
385C23×C4C22×D311yescharacteristic
386AGL(1,ℤ/8)—632no—
387C2×SD16—34no—
388C2×SD16—62no—
389C2×SD16—62no—
390C2×SD16—62no—
391C2×SD16—62no—
392C2×SD16—62no—
393C2×D8—22no—
394C2×D8—22no—
395C2×D8—62no—
396C2×D8—62no—
397C2×D8—62no—
398C2×D8#6714yescomplemented
399C2×M16—34no—
400C2×M16—62no—
401C2×M16—62no—
402C22×C8—22no—
403C22×C8—22no—
404C22×C8—22no—
405C22×C8—31no—
406C22×C8—31no—
407C22×C8C22×D311yescharacteristic
408C22×C8C22×D311yescharacteristic
409C22⋊Q8—62no—
410C22⋊Q8—121no—
411#121—22no—
412#121—22no—
413#121—41no—
414#121—41no—
415#121—62no—
416#121—121no—
417#120—124no—
418C4×D4—62no—
419C4×D4—62no—
420C2×C4⋊C4—31no—
421C2×C4⋊C4—31no—
422C2×C4⋊C4—31no—
423C2×C4⋊C4—61no—
424C2×C4⋊C4C22×D311yescharacteristic
425C2×C4⋊C4C22×D311yescharacteristic
426C2×C22⋊C4—21no—
427C2×C22⋊C4—21no—
428C2×C22⋊C4—31no—
429C2×C22⋊C4—31no—
430C2×C22⋊C4—61no—
431C2×C22⋊C4—61no—
432C2×C22⋊C4—61no—
433C2×C22⋊C4—61no—
434C2×C22⋊C4—61no—
435C2×C22⋊C4—61no—
436C2×C22⋊C4—61no—
437C2×C22⋊C4—61no—
438C2×C22⋊C4—61no—
439C2×C22⋊C4—61no—
440C2×C42—31no—
441#107—22no—
442#106—62no—
443C4⋊C8—62no—
444#103—62no—
445#103—121no—
446#102—22no—
447#102—22no—
448#102—62no—
449#102—121no—
450#102—121no—
451#102—121no—
452C22⋊C8—62no—
453C22⋊C8—62no—
454#97—62no—
455#95—61no—
456#95—61no—
457#95—61no—
458#95—61no—
459C23×C3—21no—
460C23×C3—21no—
461C23×C3—21no—
462C23×C3—21no—
463C23×C3—21no—
464C23×C3—21no—
465C23×C3—22no—
466C23×C3—22no—
467C23×C3—41no—
468C23×C3—41no—
469C23×C3—41no—
470C23×C3—41no—
471C23×C3—41no—
472C23×C3—41no—
473C23×C3—41no—
474C23×C3—41no—
475C23×C3—41no—
476C23×C3—41no—
477C23×C3—41no—
478C23×C3—41no—
479C23×C3AGL(1,ℤ/8)12yescomplemented
480C23×C3C22×D411yescharacteristic
481C22×D3—21no—
482C22×D3—21no—
483C22×D3—21no—
484C22×D3—21no—
485C22×D3—21no—
486C22×D3—21no—
487C22×D3—22no—
488C22×D3—48no—
489C22×D3—41no—
490C22×D3—41no—
491C22×D3—41no—
492C22×D3—41no—
493C22×D3—41no—
494C22×D3—41no—
495C22×D3—84no—
496C22×D3—84no—
497C22×D3—84no—
498C22×D3—84no—
499C22×D3—84no—
500C22×D3—84no—
501C22×D3#12112yes—
502C3×D4—22no—
503C3×D4—22no—
504C3×D4—22no—
505C3×D4—22no—
506C3×D4—41no—
507C3×D4—41no—
508C3×D4—41no—
509C3×D4—41no—
510C3×D4—84no—
511C3×D4—84no—
512C2×C3×C4—21no—
513C2×C3×C4—21no—
514C2×C3×C4—21no—
515C2×C3×C4—41no—
516C2×C3×C4—41no—
517C2×C3×C4—41no—
518C2×C3×C4—41no—
519C2×C3×C4—41no—
520C2×C3×C4—41no—
521C2×C3×C4—41no—
522C2×C3×C4—41no—
523C2×C3×C4—41no—
524C2×C3×C4—41no—
525C2×C3×C4C22×D411yescharacteristic
526C2×C3×C4C22×D411yescharacteristic
527C2×C3×C4C22×D411yescharacteristic
528C2×C3×C4C2×#4111yescharacteristic
529C2×C3×C4H(5,𝔽2)11yescharacteristic
530C2×C3×C4H(5,𝔽2)11yescharacteristic
531#67—48no—
532#67—44no—
533#67—48no—
534#67—84no—
535C2×Dic3—21no—
536C2×Dic3—21no—
537C2×Dic3—21no—
538C2×Dic3—21no—
539C2×Dic3—22no—
540C2×Dic3—21no—
541C2×Dic3—21no—
542C2×Dic3—21no—
543C2×Dic3—21no—
544C2×Dic3—48no—
545C2×Dic3—41no—
546C2×Dic3—41no—
547C2×Dic3—41no—
548C2×Dic3—41no—
549C2×Dic3—41no—
550C2×Dic3—41no—
551C2×Dic3—41no—
552C2×Dic3—41no—
553C2×Dic3#12112yes—
554D12—22no—
555D12—22no—
556D12—41no—
557D12—41no—
558C4×D3—22no—
559C4×D3—22no—
560C4×D3—22no—
561C4×D3—22no—
562Dic6—22no—
563Dic6—22no—
564Dic6—41no—
565Dic6—41no—
566C3×C8—41no—
567C3×C8#12014yescomplemented
568C3⋊C8—22no—
569C3⋊C8—41no—
570C24—21no—
571C24—21no—
572C24—31no—
573C24—61no—
574C24—122no—
575C24—122no—
576C24—122no—
577C24—122no—
578C24—122no—
579C24—241no—
580C24—241no—
581C24D3×D411yescharacteristic
582#41—68no—
583#41—124no—
584#41—124no—
585#41—124no—
586C2×Q8—32no—
587C2×Q8—61no—
588C2×Q8—61no—
589C2×Q8—61no—
590C2×Q8—61no—
591C2×Q8—61no—
592C2×D4—21no—
593C2×D4—21no—
594C2×D4—21no—
595C2×D4—21no—
596C2×D4—21no—
597C2×D4—21no—
598C2×D4—21no—
599C2×D4—21no—
600C2×D4—21no—
601C2×D4—21no—
602C2×D4—32no—
603C2×D4—42no—
604C2×D4—42no—
605C2×D4—42no—
606C2×D4—42no—
607C2×D4—68no—
608C2×D4—62no—
609C2×D4—62no—
610C2×D4—61no—
611C2×D4—61no—
612C2×D4—61no—
613C2×D4—61no—
614C2×D4—61no—
615C2×D4—81no—
616C2×D4—81no—
617C2×D4—122no—
618C2×D4—124no—
619C2×D4—124no—
620C2×D4—124no—
621C2×D4—121no—
622C2×D4—122no—
623C2×D4—122no—
624C2×D4—122no—
625C2×D4—122no—
626C2×D4—122no—
627C2×D4—122no—
628C2×D4—122no—
629C2×D4—241no—
630C2×D4C2×#6712yes—
631C2×D4C2×#6712yes—
632C22×C4—21no—
633C22×C4—21no—
634C22×C4—21no—
635C22×C4—21no—
636C22×C4—21no—
637C22×C4—21no—
638C22×C4—21no—
639C22×C4—21no—
640C22×C4—31no—
641C22×C4—32no—
642C22×C4—32no—
643C22×C4—31no—
644C22×C4—31no—
645C22×C4—61no—
646C22×C4—61no—
647C22×C4—61no—
648C22×C4—61no—
649C22×C4—61no—
650C22×C4—61no—
651C22×C4—61no—
652C22×C4—122no—
653C22×C4—122no—
654C22×C4—122no—
655C22×C4D3×D411yescharacteristic
656C22×C4C23×D311yescharacteristic
657SD16—68no—
658SD16—68no—
659D8—28no—
660D8—68no—
661M16—68no—
662C2×C8—21no—
663C2×C8—21no—
664C2×C8—21no—
665C2×C8—32no—
666C2×C8—44no—
667C2×C8—61no—
668C2×C8—61no—
669C2×C8—61no—
670C2×C8—61no—
671C2×C8—61no—
672C2×C8D3×D412yes—
673C2×C8D3×D412yes—
674C2×C8C2×#6712yes—
675C4⋊C4—21no—
676C4⋊C4—21no—
677C4⋊C4—21no—
678C4⋊C4—21no—
679C4⋊C4—62no—
680C4⋊C4—61no—
681C4⋊C4—61no—
682C4⋊C4—61no—
683C4⋊C4—61no—
684C4⋊C4—122no—
685C22⋊C4—42no—
686C22⋊C4—42no—
687C22⋊C4—62no—
688C22⋊C4—62no—
689C22⋊C4—122no—
690C22⋊C4—122no—
691C22⋊C4—122no—
692C22⋊C4—122no—
693C22⋊C4—122no—
694C22⋊C4—122no—
695C22⋊C4—241no—
696C22⋊C4—241no—
697C22⋊C4—241no—
698C22⋊C4—241no—
699C42—61no—
700C42—61no—
701C22×C3—22no—
702C22×C3—22no—
703C22×C3—22no—
704C22×C3—41no—
705C22×C3—41no—
706C22×C3—41no—
707C22×C3—41no—
708C22×C3—42no—
709C22×C3—42no—
710C22×C3—42no—
711C22×C3—42no—
712C22×C3—42no—
713C22×C3—42no—
714C22×C3—81no—
715C22×C3—81no—
716C22×C3—81no—
717C22×C3—81no—
718C22×C3—81no—
719C22×C3—81no—
720C22×C3—81no—
721C22×C3—81no—
722C22×C3C2×#12111yescharacteristic
723C22×C3D4211yescharacteristic
724C22×C3D4211yescharacteristic
725C22×C3C2×AGL(1,ℤ/8)11yescharacteristic
726C22×C3#57511yescharacteristic
727C22×C3#57611yescharacteristic
728C22×C3#57711yescharacteristic
729C2×D3—22no—
730C2×D3—22no—
731C2×D3—22no—
732C2×D3—41no—
733C2×D3—41no—
734C2×D3—41no—
735C2×D3—41no—
736C2×D3—42no—
737C2×D3—42no—
738C2×D3—42no—
739C2×D3—816no—
740C2×D3—81no—
741C2×D3—81no—
742C2×D3—81no—
743C2×D3—81no—
744C3×C4—41no—
745C3×C4—81no—
746C3×C4—81no—
747C3×C4C2×#12011yescharacteristic
748C3×C4#53511yescharacteristic
749C3×C4#54611yescharacteristic
750C3×C4#54611yescharacteristic
751Dic3—22no—
752Dic3—42no—
753Dic3—41no—
754Dic3—41no—
755Dic3—81no—
756Dic3—81no—
757C23—21no—
758C23—21no—
759C23—21no—
760C23—21no—
761C23—21no—
762C23—21no—
763C23—22no—
764C23—22no—
765C23—32no—
766C23—41no—
767C23—41no—
768C23—41no—
769C23—41no—
770C23—41no—
771C23—41no—
772C23—41no—
773C23—41no—
774C23—41no—
775C23—41no—
776C23—41no—
777C23—41no—
778C23—61no—
779C23—61no—
780C23—61no—
781C23—61no—
782C23—61no—
783C23—61no—
784C23—62no—
785C23—128no—
786C23—121no—
787C23—121no—
788C23—121no—
789C23—121no—
790C23—121no—
791C23—121no—
792C23—244no—
793C23—244no—
794C23—244no—
795C23—244no—
796C23—244no—
797C23—244no—
798C23#91112yescomplemented
799C23C2×D3×D411yescharacteristic
800Q8—62no—
801Q8—62no—
802Q8—121no—
803Q8—121no—
804D4—22no—
805D4—22no—
806D4—22no—
807D4—22no—
808D4—41no—
809D4—41no—
810D4—41no—
811D4—41no—
812D4—62no—
813D4—62no—
814D4—84no—
815D4—84no—
816D4—128no—
817D4—124no—
818D4—128no—
819D4—121no—
820D4—121no—
821D4—244no—
822C2×C4—21no—
823C2×C4—21no—
824C2×C4—21no—
825C2×C4—32no—
826C2×C4—41no—
827C2×C4—41no—
828C2×C4—41no—
829C2×C4—41no—
830C2×C4—41no—
831C2×C4—41no—
832C2×C4—41no—
833C2×C4—41no—
834C2×C4—41no—
835C2×C4—41no—
836C2×C4—61no—
837C2×C4—61no—
838C2×C4—62no—
839C2×C4—62no—
840C2×C4—62no—
841C2×C4—62no—
842C2×C4—61no—
843C2×C4—61no—
844C2×C4—61no—
845C2×C4—61no—
846C2×C4—61no—
847C2×C4—61no—
848C2×C4—62no—
849C2×C4—128no—
850C2×C4—121no—
851C2×C4—121no—
852C2×C4—121no—
853C2×C4—121no—
854C2×C4—121no—
855C2×C4—121no—
856C2×C4—121no—
857C2×C4—121no—
858C2×C4C2×D3×D411yescharacteristic
859C2×C4C2×D3×D411yescharacteristic
860C2×C4#100411yescharacteristic
861C2×C4D3×#4111yescharacteristic
862C2×C4#100911yescharacteristic
863C2×C4C22×#6711yescharacteristic
864C8—41no—
865C8—62no—
866C8—121no—
867C8#93714yescomplemented
868C2×C3—42no—
869C2×C3—82no—
870C2×C3—82no—
871C2×C3#240811yescharacteristic
872C2×C3#305511yescharacteristic
873C2×C3#306211yescharacteristic
874C2×C3#326411yescharacteristic
875C2×C3#326511yescharacteristic
876C2×C3#326711yescharacteristic
877C2×C3#326811yescharacteristic
878D3—42no—
879D3—82no—
880C22—22no—
881C22—22no—
882C22—22no—
883C22—41no—
884C22—41no—
885C22—41no—
886C22—41no—
887C22—42no—
888C22—42no—
889C22—42no—
890C22—42no—
891C22—42no—
892C22—42no—
893C22—62no—
894C22—62no—
895C22—62no—
896C22—81no—
897C22—81no—
898C22—81no—
899C22—81no—
900C22—81no—
901C22—81no—
902C22—81no—
903C22—81no—
904C22—121no—
905C22—121no—
906C22—121no—
907C22—121no—
908C22—122no—
909C22—122no—
910C22—122no—
911C22—2416no—
912C22—241no—
913C22—241no—
914C22—241no—
915C22—241no—
916C22D3×#12111yescharacteristic
917C22#560911yescharacteristic
918C22C2×#91111yescharacteristic
919C22#575711yescharacteristic
920C22#576811yescharacteristic
921C22#577011yescharacteristic
922C22D4×#6711yescharacteristic
923C4—41no—
924C4—62no—
925C4—81no—
926C4—81no—
927C4—121no—
928C4—121no—
929C4—122no—
930C4—241no—
931C4—241no—
932C4#560711yescharacteristic
933C4#561211yescharacteristic
934C4C2×#93711yescharacteristic
935C4#582911yescharacteristic
936C3#2427511yescharacteristic, complemented, Sylow
937C2—42no—
938C2—82no—
939C2—82no—
940C2—122no—
941C2—242no—
942C2#8071511yescharacteristic
943C2#8071811yescharacteristic
944C2#8072711yescharacteristic
945C2#8072811yescharacteristic
946C2#8264011yescharacteristic
947C2#8383711yescharacteristic
948C2#8392111yescharacteristic
subgroupG/H
centerC23C2×D3×D4
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC2×C3×#466C2
socleC23×C3C22×D4
hypercenterC2×#466D3
hypocenterC3#24275
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#466

Complements

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

NH ≅ G/Ntype
1. C22×#911C2semidirect
2. C2×C3×#466C2semidirect
3. C2×#5114C2semidirect
4. C2×#5111C2semidirect
5. #82701C2semidirect
6. #82640C2semidirect
7. #72039C2semidirect
8. #71685C2semidirect
9. #71684C2semidirect
10. #70631C2semidirect
11. #70629C2semidirect
12. #70217C2semidirect
13. #70212C2semidirect
14. #70199C2semidirect
15. #70198C2semidirect
20. C23×C3×C8C22semidirect
22. C2×C3×#121C22semidirect
28. C2×#924C22semidirect
35. C2×C3×#107C22semidirect
37. C2×C3×#102C22semidirect
41. #5221C22semidirect
44. C2×#832C22semidirect
45. C2×#830C22semidirect
50. C2×#817C22semidirect
51. C2×#816C22semidirect
52. C2×#815C22semidirect
53. C2×Dic3⋊C8C22semidirect
57. #4973C22semidirect
58. C2×#810C22semidirect
64. #4529C22semidirect
65. #4529C22semidirect
67. C2×#466D3semidirect
109. C2×C3×D8D4semidirect
158. C2×#204D4semidirect
161. C2×ΓL(1,𝔽25)D4semidirect
190. C23×C8C2×D3semidirect
194. C2×#121C2×D3semidirect
200. C2×#107C2×D3semidirect
210. C2×#102C2×D3semidirect
398. C2×D8#67semidirect
479. C23×C3AGL(1,ℤ/8)semidirect
567. C3×C8#120semidirect
798. C23#911semidirect
867. C8#937semidirect
936. C3#24275semidirect

Maximal subgroups

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

subgroupindex
C22×#9112
C2×C3×#4662
C2×#51142
C2×#51112
#827012
#826402
#720392
#716852
#716842
#706312
#706292
#702172
#702122
#701992
#701982
#242753