Finite Group Databasebeta

← #10831006

Subgroups — #10831006

Order 768.

1608 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×#949C211yesmaximal, characteristic, complemented
2#84097C211yesmaximal, characteristic, complemented
3C2×#4812C211yesmaximal, characteristic, complemented
4C2×#4782C211yesmaximal, characteristic, complemented
5C2×#4729C211yesmaximal, characteristic, complemented
6#74016C211yesmaximal, characteristic, complemented
7C3×#1788C211yesmaximal, characteristic, complemented
8#70280C211yesmaximal, characteristic, complemented
9#70272C211yesmaximal, characteristic, complemented
10#70257C211yesmaximal, characteristic, complemented
11#70212C211yesmaximal, characteristic, complemented
12#70204C211yesmaximal, characteristic, complemented
13#70190C211yesmaximal, characteristic, complemented
14#69959C211yesmaximal, characteristic, complemented
15#69513C211yesmaximal, characteristic, complemented
16#24277—31nomaximal, Sylow
17C22×C3×#41C2211yescharacteristic
18C23×D12C2211yescharacteristic
19C2×#949—24no—
20C2×#949—24no—
21C2×#949—24no—
22C2×#946C2211yescharacteristic, complemented
23C22×#215C2211yescharacteristic
24C22×#215C2211yescharacteristic
25C2×#938C2211yescharacteristic, complemented
26C22×#213C2211yescharacteristic
27C22×#213C2211yescharacteristic
28C2×C4×#67C2211yescharacteristic
29C22×#208C2211yescharacteristic
30C22×ΓL(1,𝔽25)C2211yescharacteristic, complemented
31C2×#895C2211yescharacteristic
32C2×#895C2211yescharacteristic
33C2×#882—21no—
34C2×C3×#103C2211yescharacteristic, complemented
35C2×C3×#103C2211yescharacteristic, complemented
36C2×C3×#102C2211yescharacteristic, complemented
37C2×C3×#102C2211yescharacteristic, complemented
38C2×C3×C22⋊C8C2211yescharacteristic
39C3×#380C2211yescharacteristic
40#5229C2211yescharacteristic, complemented
41#5223—21no—
42#5222—21no—
43#5221C2211yescharacteristic, complemented
44#5213—21no—
45#5212C2211yescharacteristic
46#5210—21no—
47C2×#821C2211yescharacteristic
48C2×#821C2211yescharacteristic
49C2×#821C2211yescharacteristic
50C2×#821C2211yescharacteristic
51C2×(C2×D3)⋊C8C2211yescharacteristic, complemented
52C2×Dic3⋊C8C2211yescharacteristic, complemented
53C2×C8×Dic3C2211yescharacteristic, complemented
54#4988C2211yescharacteristic
55#4988C2211yescharacteristic
56C2×#808C2211yescharacteristic, complemented
57C2×#807C2211yescharacteristic, complemented
58#4955—21no—
59#4812—24no—
60#4782—24no—
61#4729—24no—
62#4672—21no—
63#4671—21no—
64#4529C2211yescharacteristic, complemented
65#4529C2211yescharacteristic, complemented
66C22×AGL(1,ℤ/8)—31no—
67C2×#469—31no—
68C2×#468—31no—
69C2×#436—31no—
70#2408—31no—
71#2407—31no—
72#2055—31no—
73#2054—31no—
74#2000—31no—
75#1999—31no—
76#1970—31no—
77#1968—31no—
78#1809—31no—
79#1788D311yescharacteristic, complemented
80#1786—31no—
81C24×D3—21no—
82C2×C3×#41—22no—
83C2×C3×#41—22no—
84C2×C3×#41—22no—
85C2×C3×#41—22no—
86C2×C3×#41—41no—
87C2×C3×#41—41no—
88C22×C3×Q8C2311yescharacteristic
89C22×C3×D4—21no—
90C22×C3×D4C2311yescharacteristic
91C23×C3×C4—21no—
92C23×C3×C4C2311yescharacteristic
93C22×#67—21no—
94C22×#67D411yescharacteristic
95C22×D12—22no—
96C22×D12—22no—
97C22×D12—22no—
98C22×D12—22no—
99C22×D12—21no—
100C22×D12—21no—
101C22×D12—21no—
102C22×D12—41no—
103C22×D12—41no—
104C22×D12C2311yescharacteristic
105C22×D12C2311yescharacteristic
106C22×C4×D3C2311yescharacteristic
107C22×C3×C8C2311yescharacteristic
108C22×C3×C8C2311yescharacteristic
109C2×C3×C4⋊C4C2311yescharacteristic
110C2×C3×C4⋊C4C2311yescharacteristic
111C2×C3×C22⋊C4—21no—
112C2×#217—21no—
113C2×#217—21no—
114C2×#217—21no—
115C2×#217—21no—
116C2×#217D411yescharacteristic
117#949—232no—
118#946—22no—
119#946—41no—
120C2×#215—22no—
121C2×#215—22no—
122C2×#215—22no—
123C2×#215—22no—
124C2×#215—22no—
125C2×#215D414yescomplemented
126#938—22no—
127#938—41no—
128C2×#213—22no—
129C2×#213—22no—
130C2×#213—22no—
131C2×#213—22no—
132C2×#213—22no—
133C2×#213D414yescomplemented
134C4×#67—22no—
135C4×#67—22no—
136C2×(C2×D3)⋊C4—21no—
137C2×(C2×D3)⋊C4—21no—
138C2×(C2×D3)⋊C4—21no—
139C2×(C2×D3)⋊C4—21no—
140C2×(C2×D3)⋊C4—21no—
141C2×(C2×D3)⋊C4—21no—
142C2×(C2×D3)⋊C4—21no—
143C2×(C2×D3)⋊C4D411yescharacteristic
144C2×C4⋊Dic3C2311yescharacteristic
145C2×C4⋊Dic3C2311yescharacteristic
146C2×Dic3⋊C4—21no—
147C2×Dic3⋊C4D411yescharacteristic
148C2×C4×Dic3C2311yescharacteristic
149C2×#208—22no—
150C2×#208—22no—
151C2×#208D414yescomplemented
152C22×C3⋊C8C2311yescharacteristic
153C22×C3⋊C8C2311yescharacteristic
154C2×ΓL(1,𝔽25)—22no—
155C2×ΓL(1,𝔽25)—22no—
156C2×ΓL(1,𝔽25)—22no—
157#895—22no—
158#895—22no—
159#895—41no—
160#895—41no—
161#882—44no—
162C3×#103—22no—
163C3×#103—41no—
164C3×#102—22no—
165C3×#102—41no—
166C3×C22⋊C8—22no—
167C3×#95—21no—
168C3⋊#95—21no—
169C3⋊#95—21no—
170C3⋊#95—21no—
171#821—22no—
172#821—22no—
173#821—41no—
174#821—41no—
175(C2×D3)⋊C8—22no—
176Dic3⋊C8—22no—
177C8×Dic3—22no—
178#808—22no—
179#807—22no—
180C22×#41C2×D311yescharacteristic
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×D8—31no—
189C22×M16—31no—
190C22×M16—31no—
191C2×C22⋊Q8—31no—
192C2×#121—31no—
193C2×#121—31no—
194C2×#121—31no—
195C2×#120—61no—
196C2×C4×D4—31no—
197#469—64no—
198#468—64no—
199#436—64no—
200C2×#107—31no—
201C2×#106—31no—
202C2×C4⋊C8—31no—
203C2×#103C2×D311yescharacteristic, complemented
204C2×#103C2×D311yescharacteristic, complemented
205C2×#102—31no—
206C2×#102—31no—
207C2×#102—31no—
208C2×#102—31no—
209C2×#102C2×D311yescharacteristic, complemented
210C2×#102C2×D311yescharacteristic, complemented
211C2×C22⋊C8—31no—
212C2×C22⋊C8C2×D311yescharacteristic
213C2×C4×C8—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#380C2×D311yescharacteristic
226#379—61no—
227#340—31no—
228#340—31no—
229C24×C3—21no—
230C24×C3C2×D411yescharacteristic
231C23×D3—21no—
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
241C3×#41—28no—
242C3×#41—44no—
243C3×#41—44no—
244C3×#41—44no—
245C2×C3×Q8—21no—
246C2×C3×Q8—21no—
247C2×C3×Q8—21no—
248C2×C3×Q8—21no—
249C2×C3×Q8—21no—
250C2×C3×Q8C2×D412yes—
251C2×C3×D4—21no—
252C2×C3×D4—21no—
253C2×C3×D4—21no—
254C2×C3×D4—21no—
255C2×C3×D4—21no—
256C2×C3×D4—42no—
257C2×C3×D4—42no—
258C2×C3×D4—42no—
259C2×C3×D4C2×D412yes—
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×C4—42no—
268C22×C3×C4—42no—
269C22×C3×C4—42no—
270C22×C3×C4C2×D411yescharacteristic
271C22×C3×C4C2×D412yes—
272C22×C3×C4#4112yes—
273C22×C3×C4C2411yescharacteristic
274C2×#67—22no—
275C2×#67—22no—
276C2×#67—41no—
277C2×#67—42no—
278C2×#67—42no—
279C2×#67—81no—
280C22×Dic3—21no—
281C22×Dic3—21no—
282C22×Dic3C2×D411yescharacteristic
283C22×Dic3C2×D411yescharacteristic
284C22×Dic3C2×D411yescharacteristic
285C2×D12—28no—
286C2×D12—21no—
287C2×D12—21no—
288C2×D12—21no—
289C2×D12—21no—
290C2×D12—21no—
291C2×D12—21no—
292C2×D12—21no—
293C2×D12—21no—
294C2×D12—21no—
295C2×D12—21no—
296C2×D12—44no—
297C2×D12—44no—
298C2×D12—42no—
299C2×D12—42no—
300C2×D12—44no—
301C2×D12—42no—
302C2×D12—42no—
303C2×D12—42no—
304C2×D12—42no—
305C2×D12—42no—
306C2×D12—81no—
307C2×D12—81no—
308C2×D12C2×D412yes—
309C2×D12C2×D412yes—
310C2×C4×D3—21no—
311C2×C4×D3—21no—
312C2×C4×D3—21no—
313C2×C4×D3—21no—
314C2×C4×D3—21no—
315C2×C4×D3—21no—
316C2×C3×C8—21no—
317C2×C3×C8—21no—
318C2×C3×C8—21no—
319C2×C3×C8—21no—
320C2×C3×C8—21no—
321C2×C3×C8—21no—
322C3×C4⋊C4—21no—
323C3×C4⋊C4—21no—
324C3×C4⋊C4—21no—
325C3×C4⋊C4—21no—
326C3×C22⋊C4—42no—
327#217—22no—
328#217—42no—
329#217—42no—
330#217—81no—
331#217—81no—
332#215—28no—
333#215—28no—
334#213—28no—
335#213—28no—
336(C2×D3)⋊C4—22no—
337(C2×D3)⋊C4—42no—
338(C2×D3)⋊C4—42no—
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—
352#208—28no—
353C2×C3⋊C8—21no—
354C2×C3⋊C8—21no—
355C2×C3⋊C8C2×D412yes—
356C2×C3⋊C8C2×D412yes—
357C2×C3⋊C8C2×D412yes—
358C2×C3⋊C8C2×D412yes—
359ΓL(1,𝔽25)—44no—
360C25—61no—
361C2×#41—22no—
362C2×#41—22no—
363C2×#41—22no—
364C2×#41—22no—
365C2×#41—41no—
366C2×#41—41no—
367C22×Q8C22×D311yescharacteristic
368C22×D4—21no—
369C22×D4—31no—
370C22×D4—31no—
371C22×D4—31no—
372C22×D4—62no—
373C22×D4—62no—
374C22×D4—61no—
375C22×D4—61no—
376C22×D4—61no—
377C22×D4—62no—
378C22×D4—62no—
379C22×D4—61no—
380C22×D4—121no—
381C22×D4—121no—
382C22×D4C22×D311yescharacteristic
383C23×C4—21no—
384C23×C4—31no—
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—34no—
394C2×D8—62no—
395C2×D8—62no—
396C2×D8—62no—
397C2×D8—62no—
398C2×D8—62no—
399C2×M16—34no—
400C2×M16—62no—
401C2×M16—62no—
402C2×M16—62no—
403C2×M16—62no—
404C2×M16—62no—
405C22×C8—31no—
406C22×C8—31no—
407C22×C8C22×D311yescharacteristic
408C22×C8C22×D311yescharacteristic
409C22⋊Q8—62no—
410C22⋊Q8—121no—
411#121—62no—
412#121—62no—
413#121—62no—
414#121—121no—
415#121—121no—
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—31no—
428C2×C22⋊C4—31no—
429C2×C22⋊C4—61no—
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—62no—
442#106—62no—
443C4⋊C8—62no—
444#103—22no—
445#103—41no—
446#102—22no—
447#102—41no—
448#102—62no—
449#102—62no—
450#102—121no—
451#102—121no—
452C22⋊C8—22no—
453C22⋊C8—62no—
454C4×C8—62no—
455#95—21no—
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—41no—
467C23×C3—41no—
468C23×C3—41no—
469C23×C3—41no—
470C23×C3—41no—
471C23×C3—41no—
472C23×C3#12112yes—
473C23×C3C22×D411yescharacteristic
474C22×D3—21no—
475C22×D3—21no—
476C22×D3—22no—
477C22×D3—22no—
478C22×D3—21no—
479C22×D3—21no—
480C22×D3—21no—
481C22×D3—21no—
482C22×D3—21no—
483C22×D3—48no—
484C22×D3—41no—
485C22×D3—41no—
486C22×D3—41no—
487C22×D3—41no—
488C22×D3—41no—
489C22×D3—41no—
490C22×D3—41no—
491C22×D3—41no—
492C22×D3—41no—
493C22×D3—41no—
494C22×D3—41no—
495C22×D3—41no—
496C22×D3—84no—
497C22×D3—84no—
498C22×D3—84no—
499C22×D3—84no—
500C22×D3—84no—
501C22×D3—84no—
502C3×Q8—22no—
503C3×Q8—22no—
504C3×Q8—41no—
505C3×Q8—41no—
506C3×D4—22no—
507C3×D4—22no—
508C3×D4—48no—
509C3×D4—41no—
510C3×D4—41no—
511C2×C3×C4—21no—
512C2×C3×C4—21no—
513C2×C3×C4—22no—
514C2×C3×C4—22no—
515C2×C3×C4—22no—
516C2×C3×C4—22no—
517C2×C3×C4—22no—
518C2×C3×C4—48no—
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×C4—41no—
526C2×C3×C4—41no—
527C2×C3×C4#12112yes—
528C2×C3×C4C22×D411yescharacteristic
529C2×C3×C4C22×D411yescharacteristic
530C2×C3×C4C22×D411yescharacteristic
531C2×C3×C4C2×#4111yescharacteristic
532C2×C3×C4H(5,𝔽2)11yescharacteristic
533C2×C3×C4H(5,𝔽2)11yescharacteristic
534#67—44no—
535#67—84no—
536C2×Dic3—21no—
537C2×Dic3—21no—
538C2×Dic3—21no—
539C2×Dic3—21no—
540C2×Dic3—21no—
541C2×Dic3—21no—
542C2×Dic3—21no—
543C2×Dic3—21no—
544C2×Dic3—41no—
545C2×Dic3—41no—
546C2×Dic3—41no—
547C2×Dic3—41no—
548C2×Dic3—41no—
549C2×Dic3—41no—
550C2×Dic3AGL(1,ℤ/8)12yescomplemented
551D12—22no—
552D12—22no—
553D12—22no—
554D12—22no—
555D12—48no—
556D12—41no—
557D12—41no—
558D12—41no—
559D12—41no—
560D12—84no—
561D12—84no—
562C4×D3—41no—
563C4×D3—41no—
564C4×D3—41no—
565C4×D3—41no—
566C3×C8—41no—
567C3×C8—41no—
568C3⋊C8—22no—
569C3⋊C8#12014yescomplemented
570C24—21no—
571C24—31no—
572C24—61no—
573C24—61no—
574C24—122no—
575C24—122no—
576C24—122no—
577C24—122no—
578C24—122no—
579C24—241no—
580C24—241no—
581C24D3×D411yescharacteristic
582#41—28no—
583#41—44no—
584#41—44no—
585#41—44no—
586C2×Q8—21no—
587C2×Q8—21no—
588C2×Q8—21no—
589C2×Q8—21no—
590C2×Q8—21no—
591C2×Q8D3×D412yes—
592C2×D4—21no—
593C2×D4—21no—
594C2×D4—21no—
595C2×D4—21no—
596C2×D4—21no—
597C2×D4—32no—
598C2×D4—32no—
599C2×D4—42no—
600C2×D4—42no—
601C2×D4—42no—
602C2×D4—68no—
603C2×D4—62no—
604C2×D4—62no—
605C2×D4—61no—
606C2×D4—61no—
607C2×D4—61no—
608C2×D4—61no—
609C2×D4—61no—
610C2×D4—61no—
611C2×D4—61no—
612C2×D4—61no—
613C2×D4—61no—
614C2×D4—61no—
615C2×D4—124no—
616C2×D4—124no—
617C2×D4—122no—
618C2×D4—122no—
619C2×D4—124no—
620C2×D4—122no—
621C2×D4—122no—
622C2×D4—122no—
623C2×D4—122no—
624C2×D4—121no—
625C2×D4—122no—
626C2×D4—122no—
627C2×D4—122no—
628C2×D4—241no—
629C2×D4—241no—
630C2×D4—241no—
631C2×D4D3×D412yes—
632C22×C4—21no—
633C22×C4—21no—
634C22×C4—21no—
635C22×C4—21no—
636C22×C4—21no—
637C22×C4—21no—
638C22×C4—21no—
639C22×C4—31no—
640C22×C4—31no—
641C22×C4—31no—
642C22×C4—42no—
643C22×C4—42no—
644C22×C4—42no—
645C22×C4—61no—
646C22×C4—61no—
647C22×C4—61no—
648C22×C4—61no—
649C22×C4—61no—
650C22×C4—61no—
651C22×C4—61no—
652C22×C4—61no—
653C22×C4#23512yes—
654C22×C4D3×D411yescharacteristic
655C22×C4D3×D412yes—
656C22×C4C23×D311yescharacteristic
657SD16—68no—
658SD16—68no—
659D8—68no—
660D8—68no—
661M16—68no—
662M16—124no—
663C2×C8—21no—
664C2×C8—21no—
665C2×C8—21no—
666C2×C8—21no—
667C2×C8—21no—
668C2×C8—21no—
669C2×C8—32no—
670C2×C8—32no—
671C2×C8—32no—
672C2×C8—32no—
673C2×C8—61no—
674C2×C8—61no—
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—62no—
687C22⋊C4—62no—
688C22⋊C4—122no—
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—81no—
712C22×C3—81no—
713C22×C3—81no—
714C22×C3—81no—
715C22×C3C2×#12111yescharacteristic
716C22×C3D4211yescharacteristic
717C22×C3D4211yescharacteristic
718C22×C3C2×AGL(1,ℤ/8)11yescharacteristic
719C22×C3#57511yescharacteristic
720C22×C3#57611yescharacteristic
721C22×C3#57711yescharacteristic
722C2×D3—41no—
723C2×D3—42no—
724C2×D3—42no—
725C2×D3—41no—
726C2×D3—42no—
727C2×D3—41no—
728C2×D3—42no—
729C2×D3—41no—
730C2×D3—42no—
731C2×D3—41no—
732C2×D3—42no—
733C2×D3—41no—
734C2×D3—41no—
735C2×D3—816no—
736C2×D3—81no—
737C2×D3—81no—
738C2×D3—81no—
739C2×D3—81no—
740C2×D3—81no—
741C2×D3—81no—
742C2×D3—81no—
743C2×D3—81no—
744C3×C4—22no—
745C3×C4—42no—
746C3×C4—81no—
747C3×C4—81no—
748C3×C4C2×#12011yescharacteristic
749C3×C4#53511yescharacteristic
750C3×C4#54611yescharacteristic
751C3×C4#54611yescharacteristic
752Dic3—22no—
753Dic3—41no—
754Dic3—41no—
755Dic3—81no—
756Dic3—81no—
757C23—21no—
758C23—21no—
759C23—21no—
760C23—21no—
761C23—21no—
762C23—21no—
763C23—22no—
764C23—41no—
765C23—41no—
766C23—41no—
767C23—41no—
768C23—41no—
769C23—41no—
770C23—61no—
771C23—61no—
772C23—61no—
773C23—61no—
774C23—61no—
775C23—61no—
776C23—62no—
777C23—62no—
778C23—61no—
779C23—128no—
780C23—121no—
781C23—121no—
782C23—121no—
783C23—121no—
784C23—121no—
785C23—121no—
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#88412yes—
799C23C2×D3×D411yescharacteristic
800Q8—22no—
801Q8—22no—
802Q8—41no—
803Q8—41no—
804D4—22no—
805D4—22no—
806D4—48no—
807D4—41no—
808D4—41no—
809D4—62no—
810D4—62no—
811D4—62no—
812D4—62no—
813D4—128no—
814D4—124no—
815D4—121no—
816D4—121no—
817D4—121no—
818D4—121no—
819D4—244no—
820D4—244no—
821D4—244no—
822C2×C4—21no—
823C2×C4—21no—
824C2×C4—22no—
825C2×C4—22no—
826C2×C4—22no—
827C2×C4—22no—
828C2×C4—22no—
829C2×C4—32no—
830C2×C4—48no—
831C2×C4—41no—
832C2×C4—41no—
833C2×C4—41no—
834C2×C4—41no—
835C2×C4—41no—
836C2×C4—41no—
837C2×C4—41no—
838C2×C4—41no—
839C2×C4—61no—
840C2×C4—61no—
841C2×C4—61no—
842C2×C4—61no—
843C2×C4—61no—
844C2×C4—61no—
845C2×C4—61no—
846C2×C4—61no—
847C2×C4—121no—
848C2×C4—121no—
849C2×C4—121no—
850C2×C4—121no—
851C2×C4—121no—
852C2×C4—121no—
853C2×C4—121no—
854C2×C4—121no—
855C2×C4—121no—
856C2×C4—121no—
857C2×C4#88412yes—
858C2×C4C2×#23511yescharacteristic
859C2×C4C2×D3×D411yescharacteristic
860C2×C4C2×D3×D411yescharacteristic
861C2×C4C2×D3×D411yescharacteristic
862C2×C4#100411yescharacteristic
863C2×C4#100411yescharacteristic
864C8—34no—
865C8—41no—
866C8—41no—
867C8—62no—
868C2×C3—42no—
869C2×C3—82no—
870C2×C3#240811yescharacteristic
871C2×C3#305511yescharacteristic
872C2×C3#306211yescharacteristic
873C2×C3#327211yescharacteristic
874C2×C3#327311yescharacteristic
875C2×C3#327411yescharacteristic
876C2×C3#327511yescharacteristic
877D3—81no—
878D3—82no—
879D3—82no—
880C22—22no—
881C22—22no—
882C22—22no—
883C22—41no—
884C22—41no—
885C22—41no—
886C22—41no—
887C22—42no—
888C22—42no—
889C22—42no—
890C22—81no—
891C22—81no—
892C22—81no—
893C22—81no—
894C22—121no—
895C22—121no—
896C22—122no—
897C22—122no—
898C22—121no—
899C22—122no—
900C22—121no—
901C22—122no—
902C22—121no—
903C22—121no—
904C22—122no—
905C22—121no—
906C22—122no—
907C22—2416no—
908C22—241no—
909C22—241no—
910C22—241no—
911C22—241no—
912C22—241no—
913C22—241no—
914C22—241no—
915C22—241no—
916C22C2×#88411yescharacteristic
917C22#559011yescharacteristic
918C22#559011yescharacteristic
919C22#576911yescharacteristic
920C22#577011yescharacteristic
921C22D3×AGL(1,ℤ/8)11yescharacteristic
922C22#577711yescharacteristic
923C4—22no—
924C4—42no—
925C4—62no—
926C4—81no—
927C4—81no—
928C4—121no—
929C4—121no—
930C4—241no—
931C4—241no—
932C4#549011yescharacteristic
933C4#549011yescharacteristic
934C4D3×#12011yescharacteristic
935C4#559211yescharacteristic
936C3#2427711yescharacteristic, complemented, Sylow
937C2—42no—
938C2—82no—
939C2—241no—
940C2—242no—
941C2—242no—
942C2#7382411yescharacteristic
943C2#7884011yescharacteristic
944C2#7888811yescharacteristic
945C2#8012411yescharacteristic
946C2#8012511yescharacteristic
947C2#8024311yescharacteristic
948C2#8026811yescharacteristic
subgroupG/H
centerC23C2×D3×D4
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC3×#1788C2
socleC23×C3C22×D4
hypercenter#1788D3
hypocenterC3#24277
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1788

Complements

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

NH ≅ G/Ntype
1. C22×#949C2semidirect
2. #84097C2semidirect
3. C2×#4812C2semidirect
4. C2×#4782C2semidirect
5. C2×#4729C2semidirect
6. #74016C2semidirect
7. C3×#1788C2semidirect
8. #70280C2semidirect
9. #70272C2semidirect
10. #70257C2semidirect
11. #70212C2semidirect
12. #70204C2semidirect
13. #70190C2semidirect
14. #69959C2semidirect
15. #69513C2semidirect
22. C2×#946C22semidirect
25. C2×#938C22semidirect
30. C22×ΓL(1,𝔽25)C22semidirect
34. C2×C3×#103C22semidirect
35. C2×C3×#103C22semidirect
36. C2×C3×#102C22semidirect
37. C2×C3×#102C22semidirect
40. #5229C22semidirect
43. #5221C22semidirect
51. C2×(C2×D3)⋊C8C22semidirect
52. C2×Dic3⋊C8C22semidirect
53. C2×C8×Dic3C22semidirect
56. C2×#808C22semidirect
57. C2×#807C22semidirect
64. #4529C22semidirect
65. #4529C22semidirect
79. #1788D3semidirect
125. C2×#215D4semidirect
133. C2×#213D4semidirect
151. C2×#208D4semidirect
203. C2×#103C2×D3semidirect
204. C2×#103C2×D3semidirect
209. C2×#102C2×D3semidirect
210. C2×#102C2×D3semidirect
550. C2×Dic3AGL(1,ℤ/8)semidirect
569. C3⋊C8#120semidirect
936. C3#24277semidirect

Maximal subgroups

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

subgroupindex
C22×#9492
#840972
C2×#48122
C2×#47822
C2×#47292
#740162
C3×#17882
#702802
#702722
#702572
#702122
#702042
#701902
#699592
#695132
#242773