Finite Group Databasebeta

← #10830634

Subgroups — #10830634

Order 768.

1628 conjugacy classes of subgroups.

The subgroup lattice has 960 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#5630C211yesmaximal, characteristic, complemented
2C2×#4872C211yesmaximal, characteristic, complemented
3C2×#4819C211yesmaximal, characteristic, complemented
4C2×#4810C211yesmaximal, characteristic, complemented
5C2×#4732C211yesmaximal, characteristic, complemented
6#73933C211yesmaximal, characteristic, complemented
7C3×#2036C211yesmaximal, characteristic, complemented
8#71699C211yesmaximal, characteristic, complemented
9#70634C211yesmaximal, characteristic, complemented
10#70267C211yesmaximal, characteristic, complemented
11#70226C211yesmaximal, characteristic, complemented
12#69916C211yesmaximal, characteristic, complemented
13#69521C211yesmaximal, characteristic, complemented
14#68893C211yesmaximal, characteristic, complemented
15#68886C211yesmaximal, characteristic, complemented
16#24245—31nomaximal, Sylow
17C22×#239C2211yescharacteristic
18C23×D12C2211yescharacteristic
19C2×C3×C22⋊Q8C2211yescharacteristic
20C2×#947C2211yescharacteristic
21C22×#215C2211yescharacteristic, complemented
22C2×#930C2211yescharacteristic
23C2×C4×#67C2211yescharacteristic
24C22×D24C2211yescharacteristic
25C22×D24C2211yescharacteristic
26#5630—24no—
27#5630—24no—
28C2×#895—21no—
29C2×#895C2211yescharacteristic
30C2×#895C2211yescharacteristic, complemented
31C2×#894—21no—
32C2×#893C2211yescharacteristic
33C2×#893C2211yescharacteristic, complemented
34C2×#882—21no—
35C2×D3×C22⋊C4—21no—
36C2×C3×#107C2211yescharacteristic, complemented
37C2×C3×#103C2211yescharacteristic, complemented
38C2×C3×#103C2211yescharacteristic, complemented
39C2×C3×C22⋊C8C2211yescharacteristic
40C3×#380C2211yescharacteristic
41C2×#835C2211yescharacteristic, complemented
42C2×#830C2211yescharacteristic
43C2×#821C2211yescharacteristic
44C2×#821C2211yescharacteristic
45C2×(C2×D3)⋊C8C2211yescharacteristic, complemented
46C2×(C2×D3)⋊C8C2211yescharacteristic, complemented
47C2×Dic3⋊C8C2211yescharacteristic, complemented
48C2×C8×Dic3C2211yescharacteristic, complemented
49#4987C2211yescharacteristic, complemented
50#4977C2211yescharacteristic, complemented
51C2×#809C2211yescharacteristic
52C2×#809C2211yescharacteristic
53C2×#809C2211yescharacteristic
54C2×#809C2211yescharacteristic
55C2×#809C2211yescharacteristic, complemented
56#4960—21no—
57#4956—21no—
58#4872—24no—
59#4819—24no—
60#4810—24no—
61#4732—24no—
62#4675—21no—
63#4665—21no—
64C3×#340C2211yescharacteristic, complemented
65#4529C2211yescharacteristic, complemented
66C2×#546—31no—
67C2×#463—31no—
68C2×#449—31no—
69C2×#447—31no—
70C2×C4×D8—31no—
71#2535—31no—
72#2036D311yescharacteristic, complemented
73#2033—31no—
74#2000—31no—
75#1999—31no—
76#1958—31no—
77#1954—31no—
78#1804—31no—
79#1788—31no—
80#1786—31no—
81C24×D3—21no—
82C22×C3×Q8C2311yescharacteristic
83C23×C3×C4C2311yescharacteristic
84C22×#67—21no—
85C22×#67D411yescharacteristic
86C2×#239—22no—
87C2×#239—22no—
88C2×#239—22no—
89C2×#239—22no—
90C2×#239—41no—
91C2×#239—41no—
92C22×D12—21no—
93C22×D12—21no—
94C22×D12—21no—
95C22×D12—22no—
96C22×D12—22no—
97C22×D12—22no—
98C22×D12—22no—
99C22×D12—21no—
100C22×D12—41no—
101C22×D12—41no—
102C22×D12C2311yescharacteristic
103C22×D12C2311yescharacteristic
104C22×D12C2311yescharacteristic
105C22×C4×D3—21no—
106C22×C4×D3—21no—
107C22×C4×D3—21no—
108C22×C4×D3C2311yescharacteristic
109C22×C3×C8C2311yescharacteristic
110C22×C3×C8C2311yescharacteristic
111C3×C22⋊Q8—22no—
112C3×C22⋊Q8—22no—
113C2×C3×C4⋊C4—21no—
114C2×C3×C4⋊C4C2311yescharacteristic
115C2×C3×C4⋊C4C2311yescharacteristic
116C2×C3×C4⋊C4C2311yescharacteristic
117C2×C3×C22⋊C4—21no—
118C2×C3×C22⋊C4—21no—
119C2×#217D411yescharacteristic
120#947—22no—
121#947D414yescomplemented
122C2×#215—22no—
123C2×#215—22no—
124C2×#215—41no—
125#930—22no—
126#930—41no—
127C4×#67—22no—
128C4×#67—22no—
129C2×(C2×D3)⋊C4—21no—
130C2×(C2×D3)⋊C4—21no—
131C2×(C2×D3)⋊C4—21no—
132C2×(C2×D3)⋊C4—21no—
133C2×(C2×D3)⋊C4—21no—
134C2×(C2×D3)⋊C4—21no—
135C2×(C2×D3)⋊C4—21no—
136C2×(C2×D3)⋊C4—21no—
137C2×(C2×D3)⋊C4D411yescharacteristic
138C2×C4⋊Dic3C2311yescharacteristic
139C2×Dic3⋊C4D411yescharacteristic
140C2×C4×Dic3C2311yescharacteristic
141C22×C3⋊C8C2311yescharacteristic
142C22×C3⋊C8C2311yescharacteristic
143C2×D24—22no—
144C2×D24—22no—
145C2×D24—22no—
146C2×D24—22no—
147C2×D24—41no—
148C2×D24D414yescomplemented
149#895—28no—
150#895—22no—
151#895—22no—
152#895—22no—
153#895—41no—
154#894—28no—
155#893—22no—
156#893—22no—
157#893—22no—
158#893D414yescomplemented
159#882—28no—
160D3×C22⋊C4—28no—
161C3×#107—22no—
162C3×#103—22no—
163C3×#103—22no—
164C3×C22⋊C8—22no—
165C3×#95—21no—
166#835—41no—
167C3⋊#95—21no—
168C3⋊#95—21no—
169C3⋊#95—21no—
170#830—41no—
171#821—22no—
172#821—22no—
173(C2×D3)⋊C8—22no—
174(C2×D3)⋊C8—41no—
175Dic3⋊C8—22no—
176C8×Dic3—22no—
177#809—22no—
178#809—22no—
179#809—22no—
180#809—22no—
181#809—41no—
182C22×#41—31no—
183C23×D4—31no—
184C22×SD16—31no—
185C22×D8—31no—
186C22×D8—31no—
187#546—64no—
188#546—64no—
189C2×#124—31no—
190C2×#123—61no—
191C2×C22⋊Q8C2×D311yescharacteristic
192C2×#121—31no—
193C2×#121—31no—
194C2×#121—31no—
195C2×#121—61no—
196C2×#120—61no—
197C2×C4×D4—31no—
198C2×C4×D4—31no—
199C2×C4×D4—31no—
200C22×C22⋊C4—61no—
201#463—64no—
202#449—64no—
203#447—64no—
204C4×D8—64no—
205C2×#107C2×D311yescharacteristic, complemented
206C2×C4⋊C8—31no—
207C2×#103—31no—
208C2×#103C2×D311yescharacteristic, complemented
209C2×#103C2×D311yescharacteristic, complemented
210C2×#102—31no—
211C2×#102—31no—
212C2×#102—31no—
213C2×#102—31no—
214C2×#102—31no—
215C2×#102—31no—
216C2×#102—31no—
217C2×C22⋊C8—31no—
218C2×C22⋊C8—31no—
219C2×C22⋊C8—31no—
220C2×C22⋊C8C2×D311yescharacteristic
221C2×C4×C8—31no—
222#397—61no—
223#392—61no—
224#386—61no—
225#386—61no—
226#382—31no—
227#380—31no—
228#380C2×D311yescharacteristic
229#340—31no—
230#340C2×D311yescharacteristic, complemented
231C24×C3C2×D411yescharacteristic
232C23×D3—21no—
233C23×D3—21no—
234C23×D3—21no—
235C23×D3—24no—
236C23×D3—42no—
237C23×D3—42no—
238C23×D3—42no—
239C23×D3—42no—
240C23×D3—81no—
241C23×D3—81no—
242C23×D3C2×D411yescharacteristic
243C2×C3×Q8—21no—
244C2×C3×Q8—21no—
245C2×C3×Q8—21no—
246C2×C3×Q8—21no—
247C2×C3×Q8—21no—
248C2×C3×Q8C2×D412yes—
249C22×C3×C4—21no—
250C22×C3×C4—21no—
251C22×C3×C4—21no—
252C22×C3×C4—21no—
253C22×C3×C4—21no—
254C22×C3×C4—21no—
255C22×C3×C4—21no—
256C22×C3×C4—21no—
257C22×C3×C4—21no—
258C22×C3×C4—21no—
259C22×C3×C4C2×D411yescharacteristic
260C22×C3×C4C2411yescharacteristic
261C2×#67—22no—
262C2×#67—22no—
263C2×#67—41no—
264C2×#67—42no—
265C2×#67—42no—
266C2×#67—81no—
267C22×Dic3—21no—
268C22×Dic3C2×D411yescharacteristic
269C22×Dic3C2×D411yescharacteristic
270C22×Dic3C2×D411yescharacteristic
271#239—44no—
272#239—44no—
273#239—44no—
274#239—44no—
275C2×D12—21no—
276C2×D12—21no—
277C2×D12—21no—
278C2×D12—21no—
279C2×D12—21no—
280C2×D12—21no—
281C2×D12—21no—
282C2×D12—21no—
283C2×D12—21no—
284C2×D12—21no—
285C2×D12—21no—
286C2×D12—24no—
287C2×D12—24no—
288C2×D12—21no—
289C2×D12—21no—
290C2×D12—24no—
291C2×D12—44no—
292C2×D12—44no—
293C2×D12—44no—
294C2×D12—42no—
295C2×D12—42no—
296C2×D12—42no—
297C2×D12—42no—
298C2×D12—44no—
299C2×D12—42no—
300C2×D12—42no—
301C2×D12—81no—
302C2×D12—81no—
303C2×D12—81no—
304C2×D12C2×D412yes—
305C2×D12C2×D412yes—
306C2×D12C2×D412yes—
307C2×D12C2×D412yes—
308C2×D12#4112yes—
309C2×C4×D3—24no—
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×C4×D3—24no—
317C2×C4×D3—42no—
318C2×C4×D3—42no—
319C2×C4×D3—42no—
320C2×C4×D3—81no—
321C2×C4×D3—81no—
322C2×C4×D3—81no—
323C2×C4×D3—81no—
324C2×C3×C8—21no—
325C2×C3×C8—21no—
326C2×C3×C8—21no—
327C2×C3×C8—21no—
328C2×C3×C8—21no—
329C2×C3×C8C2×D412yes—
330C3×C4⋊C4—24no—
331C3×C4⋊C4—21no—
332C3×C4⋊C4—21no—
333C3×C4⋊C4—21no—
334C3×C4⋊C4—21no—
335C3×C4⋊C4—21no—
336C3×C4⋊C4C2×D412yes—
337C3×C22⋊C4—24no—
338C3×C22⋊C4—81no—
339#217—22no—
340#215—44no—
341(C2×D3)⋊C4—24no—
342(C2×D3)⋊C4—24no—
343(C2×D3)⋊C4—24no—
344(C2×D3)⋊C4—24no—
345(C2×D3)⋊C4—22no—
346(C2×D3)⋊C4—42no—
347(C2×D3)⋊C4—42no—
348(C2×D3)⋊C4—42no—
349(C2×D3)⋊C4—81no—
350C4⋊Dic3—21no—
351C4⋊Dic3—21no—
352Dic3⋊C4—22no—
353C4×Dic3C2×D412yes—
354C4×Dic3C2×D412yes—
355C2×C3⋊C8—21no—
356C2×C3⋊C8—21no—
357C2×C3⋊C8—21no—
358C2×C3⋊C8—21no—
359C2×C3⋊C8—21no—
360C2×C3⋊C8—21no—
361D24—28no—
362D24—44no—
363C25—61no—
364C2×#41—62no—
365C2×#41—62no—
366C2×#41—62no—
367C2×#41—62no—
368C2×#41—121no—
369C2×#41—121no—
370C22×Q8C22×D311yescharacteristic
371C22×D4—31no—
372C22×D4—31no—
373C22×D4—31no—
374C22×D4—31no—
375C22×D4—62no—
376C22×D4—62no—
377C22×D4—62no—
378C22×D4—62no—
379C22×D4—61no—
380C22×D4—61no—
381C22×D4—61no—
382C22×D4—61no—
383C22×D4—61no—
384C22×D4—121no—
385C22×D4—121no—
386C23×C4—31no—
387C23×C4—61no—
388C23×C4—61no—
389C23×C4—61no—
390C23×C4C22×D311yescharacteristic
391C2×SD16—62no—
392C2×SD16—62no—
393C2×SD16—121no—
394C2×D8—34no—
395C2×D8—62no—
396C2×D8—62no—
397C2×D8—62no—
398C2×D8—62no—
399C2×D8—121no—
400C22×C8—31no—
401C22×C8—31no—
402C22×C8C22×D311yescharacteristic
403C22×C8C22×D311yescharacteristic
404#124—34no—
405#124—62no—
406#123—68no—
407C22⋊Q8—22no—
408C22⋊Q8—22no—
409#121—62no—
410#121—68no—
411#121—62no—
412#121—62no—
413#121—62no—
414#121—121no—
415#121—121no—
416#120—68no—
417C4×D4—34no—
418C4×D4—62no—
419C4×D4—62no—
420C4×D4—62no—
421C4×D4—62no—
422C4×D4—62no—
423C2×C4⋊C4—21no—
424C2×C4⋊C4—31no—
425C2×C4⋊C4—31no—
426C2×C4⋊C4C22×D311yescharacteristic
427C2×C4⋊C4C22×D311yescharacteristic
428C2×C4⋊C4C22×D311yescharacteristic
429C2×C22⋊C4—21no—
430C2×C22⋊C4—21no—
431C2×C22⋊C4—31no—
432C2×C22⋊C4—31no—
433C2×C22⋊C4—68no—
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×C22⋊C4—61no—
441C2×C22⋊C4—61no—
442C2×C42—31no—
443#107—22no—
444C4⋊C8—62no—
445#103—22no—
446#103—22no—
447#103—121no—
448#102—62no—
449#102—62no—
450#102—62no—
451#102—62no—
452#102—62no—
453#102—62no—
454#102—121no—
455C22⋊C8—22no—
456C22⋊C8—62no—
457C22⋊C8—121no—
458C22⋊C8—121no—
459C4×C8—62no—
460#95—21no—
461#95—61no—
462#95—61no—
463#95—61no—
464C23×C3—21no—
465C23×C3—21no—
466C23×C3—21no—
467C23×C3—21no—
468C23×C3—21no—
469C23×C3—21no—
470C23×C3#13512yes—
471C23×C3C22×D411yescharacteristic
472C22×D3—22no—
473C22×D3—22no—
474C22×D3—22no—
475C22×D3—22no—
476C22×D3—21no—
477C22×D3—22no—
478C22×D3—21no—
479C22×D3—21no—
480C22×D3—21no—
481C22×D3—21no—
482C22×D3—21no—
483C22×D3—21no—
484C22×D3—48no—
485C22×D3—41no—
486C22×D3—41no—
487C22×D3—41no—
488C22×D3—41no—
489C22×D3—48no—
490C22×D3—41no—
491C22×D3—41no—
492C22×D3—41no—
493C22×D3—41no—
494C22×D3—41no—
495C22×D3—41no—
496C22×D3—41no—
497C22×D3—41no—
498C22×D3—41no—
499C22×D3—41no—
500C22×D3—41no—
501C22×D3—41no—
502C22×D3—84no—
503C22×D3—84no—
504C22×D3—84no—
505C22×D3—84no—
506C22×D3—84no—
507C3×Q8—22no—
508C3×Q8—22no—
509C3×Q8—41no—
510C3×Q8—41no—
511C2×C3×C4—21no—
512C2×C3×C4—22no—
513C2×C3×C4—22no—
514C2×C3×C4—21no—
515C2×C3×C4—21no—
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×C4—41no—
526C2×C3×C4—41no—
527C2×C3×C4—41no—
528C2×C3×C4—41no—
529C2×C3×C4—41no—
530C2×C3×C4C22×D411yescharacteristic
531C2×C3×C4C22×D411yescharacteristic
532C2×C3×C4C22×D411yescharacteristic
533C2×C3×C4C2×#4111yescharacteristic
534C2×C3×C4H(5,𝔽2)11yescharacteristic
535C2×C3×C4H(5,𝔽2)11yescharacteristic
536#67—44no—
537#67—84no—
538C2×Dic3—21no—
539C2×Dic3—21no—
540C2×Dic3—21no—
541C2×Dic3—21no—
542C2×Dic3—21no—
543C2×Dic3—21no—
544C2×Dic3—21no—
545C2×Dic3—41no—
546C2×Dic3—41no—
547C2×Dic3—41no—
548C2×Dic3#12012yes—
549C2×Dic3#12012yes—
550D12—22no—
551D12—22no—
552D12—22no—
553D12—22no—
554D12—22no—
555D12—22no—
556D12—22no—
557D12—48no—
558D12—48no—
559D12—41no—
560D12—41no—
561D12—41no—
562D12—41no—
563D12—84no—
564D12—84no—
565D12#12114yes—
566C4×D3—48no—
567C4×D3—41no—
568C4×D3—41no—
569C4×D3—41no—
570C4×D3—41no—
571C4×D3—84no—
572C4×D3—84no—
573C3×C8—22no—
574C3×C8—41no—
575C3⋊C8—41no—
576C3⋊C8—41no—
577C24—31no—
578C24—64no—
579C24—61no—
580C24—61no—
581C24—61no—
582C24—122no—
583C24—122no—
584C24—122no—
585C24—122no—
586C24—241no—
587C24—241no—
588C24D3×D411yescharacteristic
589#41—124no—
590#41—124no—
591#41—124no—
592#41—124no—
593C2×Q8—21no—
594C2×Q8—21no—
595C2×Q8—21no—
596C2×Q8—21no—
597C2×Q8—21no—
598C2×Q8D3×D412yes—
599C2×D4—32no—
600C2×D4—32no—
601C2×D4—32no—
602C2×D4—32no—
603C2×D4—32no—
604C2×D4—64no—
605C2×D4—64no—
606C2×D4—64no—
607C2×D4—62no—
608C2×D4—62no—
609C2×D4—61no—
610C2×D4—61no—
611C2×D4—61no—
612C2×D4—61no—
613C2×D4—61no—
614C2×D4—61no—
615C2×D4—61no—
616C2×D4—61no—
617C2×D4—61no—
618C2×D4—61no—
619C2×D4—61no—
620C2×D4—61no—
621C2×D4—61no—
622C2×D4—122no—
623C2×D4—122no—
624C2×D4—124no—
625C2×D4—124no—
626C2×D4—124no—
627C2×D4—124no—
628C2×D4—122no—
629C2×D4—122no—
630C2×D4—122no—
631C2×D4—122no—
632C2×D4—121no—
633C2×D4—122no—
634C2×D4—122no—
635C2×D4—241no—
636C2×D4—241no—
637C2×D4—241no—
638C2×D4—241no—
639C22×C4—21no—
640C22×C4—21no—
641C22×C4—21no—
642C22×C4—21no—
643C22×C4—21no—
644C22×C4—21no—
645C22×C4—21no—
646C22×C4—21no—
647C22×C4—21no—
648C22×C4—21no—
649C22×C4—31no—
650C22×C4—31no—
651C22×C4—31no—
652C22×C4—64no—
653C22×C4—64no—
654C22×C4—61no—
655C22×C4—61no—
656C22×C4—61no—
657C22×C4—61no—
658C22×C4—61no—
659C22×C4—61no—
660C22×C4—61no—
661C22×C4—122no—
662C22×C4—122no—
663C22×C4—122no—
664C22×C4—241no—
665C22×C4—241no—
666C22×C4—241no—
667C22×C4—241no—
668C22×C4D3×D411yescharacteristic
669C22×C4C23×D311yescharacteristic
670SD16—124no—
671D8—68no—
672D8—124no—
673C2×C8—21no—
674C2×C8—21no—
675C2×C8—21no—
676C2×C8—21no—
677C2×C8—21no—
678C2×C8—61no—
679C2×C8—61no—
680C2×C8—61no—
681C2×C8—61no—
682C2×C8—61no—
683C2×C8—61no—
684C2×C8D3×D412yes—
685C4⋊C4—24no—
686C4⋊C4—21no—
687C4⋊C4—21no—
688C4⋊C4—21no—
689C4⋊C4—21no—
690C4⋊C4—21no—
691C4⋊C4—62no—
692C4⋊C4—61no—
693C4⋊C4—61no—
694C4⋊C4D3×D412yes—
695C22⋊C4—24no—
696C22⋊C4—62no—
697C22⋊C4—64no—
698C22⋊C4—64no—
699C22⋊C4—64no—
700C22⋊C4—64no—
701C22⋊C4—62no—
702C22⋊C4—81no—
703C22⋊C4—122no—
704C22⋊C4—122no—
705C22⋊C4—122no—
706C22⋊C4—241no—
707C42—32no—
708C42—32no—
709C22×C3—22no—
710C22×C3—22no—
711C22×C3—22no—
712C22×C3—41no—
713C22×C3—41no—
714C22×C3—41no—
715C22×C3—41no—
716C22×C3C2×#12011yescharacteristic
717C22×C3D4211yescharacteristic
718C22×C3#54611yescharacteristic
719C22×C3C2×#13511yescharacteristic
720C22×C3#57511yescharacteristic
721C22×C3#57611yescharacteristic
722C22×C3#57611yescharacteristic
723C2×D3—24no—
724C2×D3—42no—
725C2×D3—42no—
726C2×D3—42no—
727C2×D3—42no—
728C2×D3—42no—
729C2×D3—42no—
730C2×D3—41no—
731C2×D3—42no—
732C2×D3—42no—
733C2×D3—41no—
734C2×D3—42no—
735C2×D3—41no—
736C2×D3—42no—
737C2×D3—41no—
738C2×D3—42no—
739C2×D3—42no—
740C2×D3—41no—
741C2×D3—41no—
742C2×D3—41no—
743C2×D3—816no—
744C2×D3—81no—
745C2×D3—81no—
746C2×D3—81no—
747C2×D3—81no—
748C2×D3—81no—
749C2×D3—81no—
750C2×D3—81no—
751C2×D3—81no—
752C3×C4—42no—
753C3×C4—41no—
754C3×C4—42no—
755C3×C4—81no—
756C3×C4—81no—
757C3×C4C2×#12111yescharacteristic
758C3×C4#53511yescharacteristic
759C3×C4D4211yescharacteristic
760C3×C4#54611yescharacteristic
761Dic3—22no—
762Dic3—22no—
763Dic3—41no—
764Dic3—81no—
765C23—21no—
766C23—21no—
767C23—21no—
768C23—21no—
769C23—21no—
770C23—21no—
771C23—62no—
772C23—62no—
773C23—62no—
774C23—61no—
775C23—61no—
776C23—61no—
777C23—61no—
778C23—61no—
779C23—62no—
780C23—61no—
781C23—62no—
782C23—61no—
783C23—128no—
784C23—128no—
785C23—121no—
786C23—121no—
787C23—121no—
788C23—121no—
789C23—121no—
790C23—121no—
791C23—121no—
792C23—121no—
793C23—121no—
794C23—121no—
795C23—121no—
796C23—121no—
797C23—121no—
798C23—121no—
799C23—121no—
800C23—121no—
801C23—244no—
802C23—244no—
803C23—244no—
804C23—244no—
805C23—244no—
806C23#91912yes—
807C23C2×D3×D411yescharacteristic
808Q8—22no—
809Q8—22no—
810Q8—41no—
811Q8—41no—
812D4—34no—
813D4—62no—
814D4—62no—
815D4—62no—
816D4—62no—
817D4—62no—
818D4—62no—
819D4—62no—
820D4—128no—
821D4—128no—
822D4—124no—
823D4—121no—
824D4—121no—
825D4—121no—
826D4—121no—
827D4—244no—
828D4—244no—
829D4—244no—
830C2×C4—21no—
831C2×C4—22no—
832C2×C4—22no—
833C2×C4—21no—
834C2×C4—21no—
835C2×C4—32no—
836C2×C4—32no—
837C2×C4—41no—
838C2×C4—41no—
839C2×C4—41no—
840C2×C4—41no—
841C2×C4—41no—
842C2×C4—41no—
843C2×C4—41no—
844C2×C4—41no—
845C2×C4—41no—
846C2×C4—41no—
847C2×C4—41no—
848C2×C4—41no—
849C2×C4—41no—
850C2×C4—41no—
851C2×C4—61no—
852C2×C4—61no—
853C2×C4—61no—
854C2×C4—61no—
855C2×C4—61no—
856C2×C4—61no—
857C2×C4—61no—
858C2×C4—128no—
859C2×C4—121no—
860C2×C4—121no—
861C2×C4—121no—
862C2×C4—121no—
863C2×C4—121no—
864C2×C4—121no—
865C2×C4—121no—
866C2×C4—244no—
867C2×C4—244no—
868C2×C4C2×D3×D411yescharacteristic
869C2×C4C2×D3×D411yescharacteristic
870C2×C4C2×D3×D411yescharacteristic
871C2×C4D3×#4111yescharacteristic
872C2×C4#100911yescharacteristic
873C2×C4#100911yescharacteristic
874C8—22no—
875C8—41no—
876C8—121no—
877C8—121no—
878C2×C3—42no—
879C2×C3#240811yescharacteristic
880C2×C3#300211yescharacteristic
881C2×C3#300811yescharacteristic
882C2×C3#327311yescharacteristic
883C2×C3#328011yescharacteristic
884C2×C3#329711yescharacteristic
885C2×C3#332211yescharacteristic
886D3—44no—
887D3—81no—
888D3—82no—
889D3—82no—
890C22—22no—
891C22—22no—
892C22—22no—
893C22—41no—
894C22—41no—
895C22—41no—
896C22—41no—
897C22—64no—
898C22—122no—
899C22—122no—
900C22—122no—
901C22—122no—
902C22—122no—
903C22—122no—
904C22—121no—
905C22—122no—
906C22—121no—
907C22—121no—
908C22—122no—
909C22—122no—
910C22—122no—
911C22—121no—
912C22—121no—
913C22—121no—
914C22—122no—
915C22—121no—
916C22—122no—
917C22—2416no—
918C22—241no—
919C22—241no—
920C22—241no—
921C22—241no—
922C22—241no—
923C22—241no—
924C22—241no—
925C22—241no—
926C22D3×#12011yescharacteristic
927C22#560911yescharacteristic
928C22#565411yescharacteristic
929C22C2×#91911yescharacteristic
930C22#576911yescharacteristic
931C22#577411yescharacteristic
932C22#577711yescharacteristic
933C4—41no—
934C4—42no—
935C4—42no—
936C4—62no—
937C4—62no—
938C4—81no—
939C4—81no—
940C4—121no—
941C4—241no—
942C4D3×#12111yescharacteristic
943C4#560911yescharacteristic
944C4#565411yescharacteristic
945C4#567411yescharacteristic
946C3#2424511yescharacteristic, complemented, Sylow
947C2—42no—
948C2—124no—
949C2—241no—
950C2—242no—
951C2—242no—
952C2#7689511yescharacteristic
953C2#8008511yescharacteristic
954C2#8018211yescharacteristic
955C2#8077311yescharacteristic
956C2#8083911yescharacteristic
957C2#8148511yescharacteristic
958C2#8154811yescharacteristic
subgroupG/H
centerC23C2×D3×D4
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC3×#2036C2
socleC23×C3C22×D4
hypercenter#2036D3
hypocenterC3#24245
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C23×C4 ◁ #2036

Complements

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

NH ≅ G/Ntype
1. C2×#5630C2semidirect
2. C2×#4872C2semidirect
3. C2×#4819C2semidirect
4. C2×#4810C2semidirect
5. C2×#4732C2semidirect
6. #73933C2semidirect
7. C3×#2036C2semidirect
8. #71699C2semidirect
9. #70634C2semidirect
10. #70267C2semidirect
11. #70226C2semidirect
12. #69916C2semidirect
13. #69521C2semidirect
14. #68893C2semidirect
15. #68886C2semidirect
21. C22×#215C22semidirect
30. C2×#895C22semidirect
33. C2×#893C22semidirect
36. C2×C3×#107C22semidirect
37. C2×C3×#103C22semidirect
38. C2×C3×#103C22semidirect
41. C2×#835C22semidirect
45. C2×(C2×D3)⋊C8C22semidirect
46. C2×(C2×D3)⋊C8C22semidirect
47. C2×Dic3⋊C8C22semidirect
48. C2×C8×Dic3C22semidirect
49. #4987C22semidirect
50. #4977C22semidirect
55. C2×#809C22semidirect
64. C3×#340C22semidirect
65. #4529C22semidirect
72. #2036D3semidirect
121. #947D4semidirect
148. C2×D24D4semidirect
158. #893D4semidirect
205. C2×#107C2×D3semidirect
208. C2×#103C2×D3semidirect
209. C2×#103C2×D3semidirect
230. #340C2×D3semidirect
946. C3#24245semidirect

Maximal subgroups

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

subgroupindex
C2×#56302
C2×#48722
C2×#48192
C2×#48102
C2×#47322
#739332
C3×#20362
#716992
#706342
#702672
#702262
#699162
#695212
#688932
#688862
#242453