Finite Group Databasebeta

← #10832809

Subgroups — #10832809

Order 768.

1632 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×#4883C211yesmaximal, characteristic, complemented
3C2×#4810C211yesmaximal, characteristic, complemented
4C2×#4804C211yesmaximal, characteristic, complemented
5C2×#4732C211yesmaximal, characteristic, complemented
6#74019C211yesmaximal, characteristic, complemented
7C3×#2036C211yesmaximal, characteristic, complemented
8#71699C211yesmaximal, characteristic, complemented
9#70638C211yesmaximal, characteristic, complemented
10#70279C211yesmaximal, characteristic, complemented
11#70277C211yesmaximal, characteristic, complemented
12#69957C211yesmaximal, characteristic, complemented
13#69521C211yesmaximal, characteristic, complemented
14#68897C211yesmaximal, characteristic, complemented
15#68881C211yesmaximal, characteristic, complemented
16#24428—31nomaximal, Sylow
17C22×#239C2211yescharacteristic
18C23×D12C2211yescharacteristic
19C2×C3×C22⋊Q8C2211yescharacteristic
20C2×#947C2211yescharacteristic
21C22×#215C2211yescharacteristic, complemented
22C2×#930C2211yescharacteristic
23C2×C4×#67C2211yescharacteristic
24C22×D24C2211yescharacteristic
25C22×D24C2211yescharacteristic
26C22×D3×C8C2211yescharacteristic, complemented
27#5630—24no—
28#5630—24no—
29C2×#895—21no—
30C2×#895C2211yescharacteristic
31C2×#895C2211yescharacteristic, complemented
32C2×#894—21no—
33C2×#893C2211yescharacteristic
34C2×#892C2211yescharacteristic, complemented
35C2×#882—21no—
36C2×D3×C22⋊C4—21no—
37C2×C3×#107C2211yescharacteristic, complemented
38C2×C3×#103C2211yescharacteristic, complemented
39C2×C3×#103C2211yescharacteristic, complemented
40C2×C3×C22⋊C8C2211yescharacteristic
41C3×#380C2211yescharacteristic
42C2×#835C2211yescharacteristic, complemented
43C2×#830C2211yescharacteristic
44C2×#821C2211yescharacteristic
45C2×#821C2211yescharacteristic
46C2×(C2×D3)⋊C8C2211yescharacteristic, complemented
47#4988C2211yescharacteristic, complemented
48#4972C2211yescharacteristic, complemented
49C2×#809C2211yescharacteristic
50C2×#809C2211yescharacteristic
51C2×#809C2211yescharacteristic
52C2×#809C2211yescharacteristic
53C2×#809C2211yescharacteristic, complemented
54#4960—21no—
55#4957—21no—
56#4883—24no—
57#4810—24no—
58#4804—24no—
59#4732—24no—
60#4672—21no—
61#4669—21no—
62C3×#340C2211yescharacteristic, complemented
63#4550C2211yescharacteristic, complemented
64#4550C2211yescharacteristic, complemented
65#4529C2211yescharacteristic, complemented
66C2×#546—31no—
67C2×#466—31no—
68C2×#449—31no—
69C2×#447—31no—
70C2×#416—31no—
71#2414—31no—
72#2042—31no—
73#2036D311yescharacteristic, complemented
74#2012—31no—
75#2000—31no—
76#1879—31no—
77#1875—31no—
78#1869—31no—
79#1862—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—41no—
90C2×#239—41no—
91C2×#239D414yescomplemented
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×D3C2311yescharacteristic
108C22×C3×C8C2311yescharacteristic
109C22×C3×C8C2311yescharacteristic
110C3×C22⋊Q8—22no—
111C3×C22⋊Q8—22no—
112C2×C3×C4⋊C4—21no—
113C2×C3×C4⋊C4C2311yescharacteristic
114C2×C3×C4⋊C4C2311yescharacteristic
115C2×C3×C4⋊C4C2311yescharacteristic
116C2×C3×C22⋊C4—21no—
117C2×C3×C22⋊C4—21no—
118C2×#217D411yescharacteristic
119#947—22no—
120#947—22no—
121C2×#215—22no—
122C2×#215—41no—
123C2×#215—41no—
124#930—22no—
125#930—41no—
126C4×#67—22no—
127C4×#67—22no—
128C2×(C2×D3)⋊C4—21no—
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⋊C4—21no—
140C2×Dic3⋊C4D411yescharacteristic
141C2×C4×Dic3—21no—
142C2×C4×Dic3C2311yescharacteristic
143C22×C3⋊C8C2311yescharacteristic
144C22×C3⋊C8C2311yescharacteristic
145C2×D24—22no—
146C2×D24—22no—
147C2×D24—22no—
148C2×D24—22no—
149C2×D24—22no—
150C2×D24—41no—
151C2×D3×C8—22no—
152C2×D3×C8—22no—
153C2×D3×C8—41no—
154#895—28no—
155#895—22no—
156#895—22no—
157#895—22no—
158#895D414yescomplemented
159#894—28no—
160#893—22no—
161#893—22no—
162#892—22no—
163#892—41no—
164#882—28no—
165D3×C22⋊C4—28no—
166C3×#107—22no—
167C3×#103—22no—
168C3×#103—22no—
169C3×C22⋊C8—22no—
170C3×#95—21no—
171#835—22no—
172C3⋊#95—21no—
173#830—41no—
174#821—22no—
175#821D414yescomplemented
176(C2×D3)⋊C8—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—
187C23×C8—31no—
188#546—64no—
189#546—64no—
190C2×#124—31no—
191C2×#123—61no—
192C2×C22⋊Q8C2×D311yescharacteristic
193C2×#121—31no—
194C2×#121—31no—
195C2×#121—31no—
196C2×#121—61no—
197C2×#120—61no—
198C2×C4×D4—31no—
199C2×C4×D4—31no—
200C2×#117—31no—
201C22×C22⋊C4—61no—
202#466—64no—
203#449—64no—
204#447—64no—
205C2×#107C2×D311yescharacteristic, complemented
206#416—64no—
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⋊C8C2×D311yescharacteristic
220#394—61no—
221#392—61no—
222#390—31no—
223#390—61no—
224#389—31no—
225#388—61no—
226#380C2×D311yescharacteristic
227#340—31no—
228#340C2×D311yescharacteristic, complemented
229#336—31no—
230#336—31no—
231C24×C3C2×D411yescharacteristic
232C23×D3—21no—
233C23×D3—21no—
234C23×D3—24no—
235C23×D3—21no—
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—28no—
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—24no—
283C2×D12—24no—
284C2×D12—21no—
285C2×D12—21no—
286C2×D12—21no—
287C2×D12—21no—
288C2×D12—21no—
289C2×D12—21no—
290C2×D12—21no—
291C2×D12—24no—
292C2×D12—44no—
293C2×D12—44no—
294C2×D12—44no—
295C2×D12—42no—
296C2×D12—42no—
297C2×D12—42no—
298C2×D12—42no—
299C2×D12—44no—
300C2×D12—42no—
301C2×D12—81no—
302C2×D12—81no—
303C2×D12—81no—
304C2×D12—81no—
305C2×D12C2×D412yes—
306C2×D12C2×D412yes—
307C2×D12C2×D412yes—
308C2×D12#4112yes—
309C2×C4×D3—21no—
310C2×C4×D3—21no—
311C2×C4×D3—21no—
312C2×C4×D3—21no—
313C2×C4×D3—24no—
314C2×C4×D3—24no—
315C2×C4×D3—42no—
316C2×C4×D3—42no—
317C2×C4×D3—81no—
318C2×C4×D3—81no—
319C2×C4×D3C2×D412yes—
320C2×C4×D3C2×D412yes—
321C2×C3×C8—21no—
322C2×C3×C8—21no—
323C2×C3×C8—21no—
324C2×C3×C8—21no—
325C2×C3×C8—21no—
326C2×C3×C8C2×D412yes—
327C3×C4⋊C4—24no—
328C3×C4⋊C4—21no—
329C3×C4⋊C4—21no—
330C3×C4⋊C4—21no—
331C3×C4⋊C4—21no—
332C3×C4⋊C4—21no—
333C3×C4⋊C4C2×D412yes—
334C3×C22⋊C4—24no—
335C3×C22⋊C4—81no—
336#217—22no—
337#215—44no—
338(C2×D3)⋊C4—24no—
339(C2×D3)⋊C4—24no—
340(C2×D3)⋊C4—24no—
341(C2×D3)⋊C4—22no—
342(C2×D3)⋊C4—24no—
343(C2×D3)⋊C4—42no—
344(C2×D3)⋊C4—42no—
345(C2×D3)⋊C4—42no—
346(C2×D3)⋊C4—42no—
347(C2×D3)⋊C4—81no—
348C4⋊Dic3—21no—
349C4⋊Dic3C2×D412yes—
350Dic3⋊C4—22no—
351Dic3⋊C4—81no—
352C4×Dic3—21no—
353C4×Dic3—21no—
354C4×Dic3—42no—
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—44no—
362D24—44no—
363D3×C8—44no—
364C25—61no—
365C2×#41—34no—
366C2×#41—62no—
367C2×#41—62no—
368C2×#41—62no—
369C2×#41—121no—
370C2×#41—121no—
371C22×Q8C22×D311yescharacteristic
372C22×D4—31no—
373C22×D4—31no—
374C22×D4—31no—
375C22×D4—31no—
376C22×D4—62no—
377C22×D4—62no—
378C22×D4—62no—
379C22×D4—62no—
380C22×D4—61no—
381C22×D4—61no—
382C22×D4—61no—
383C22×D4—61no—
384C22×D4—61no—
385C22×D4—121no—
386C22×D4—121no—
387C23×C4—31no—
388C23×C4—61no—
389C23×C4—61no—
390C23×C4C22×D311yescharacteristic
391C2×SD16—62no—
392C2×SD16—121no—
393C2×SD16—121no—
394C2×D8—62no—
395C2×D8—62no—
396C2×D8—62no—
397C2×D8—62no—
398C2×D8—62no—
399C2×D8—121no—
400C22×C8—31no—
401C22×C8—31no—
402C22×C8—62no—
403C22×C8—62no—
404C22×C8—121no—
405C22×C8C22×D311yescharacteristic
406C22×C8C22×D311yescharacteristic
407#124—62no—
408#124—62no—
409#123—68no—
410C22⋊Q8—22no—
411C22⋊Q8—22no—
412#121—34no—
413#121—62no—
414#121—68no—
415#121—62no—
416#121—62no—
417#121—62no—
418#121—121no—
419#120—68no—
420C4×D4—62no—
421C4×D4—62no—
422C4×D4—62no—
423C4×D4—62no—
424#117—62no—
425#117—121no—
426C2×C4⋊C4—21no—
427C2×C4⋊C4—31no—
428C2×C4⋊C4—31no—
429C2×C4⋊C4—61no—
430C2×C4⋊C4C22×D311yescharacteristic
431C2×C4⋊C4C22×D311yescharacteristic
432C2×C4⋊C4C22×D311yescharacteristic
433C2×C22⋊C4—21no—
434C2×C22⋊C4—21no—
435C2×C22⋊C4—31no—
436C2×C22⋊C4—31no—
437C2×C22⋊C4—68no—
438C2×C22⋊C4—61no—
439C2×C22⋊C4—61no—
440C2×C22⋊C4—61no—
441C2×C22⋊C4—61no—
442C2×C22⋊C4—61no—
443C2×C22⋊C4—61no—
444C2×C22⋊C4—61no—
445C2×C22⋊C4—61no—
446C2×C22⋊C4—61no—
447C2×C42—31no—
448C2×C42—61no—
449#107—22no—
450#103—22no—
451#103—22no—
452#103—62no—
453#102—34no—
454#102—62no—
455#102—62no—
456#102—62no—
457#102—62no—
458#102—62no—
459#102—121no—
460C22⋊C8—22no—
461C22⋊C8—62no—
462C22⋊C8—121no—
463#95—21no—
464#95—61no—
465C23×C3—21no—
466C23×C3—21no—
467C23×C3—21no—
468C23×C3—21no—
469C23×C3—21no—
470C23×C3—21no—
471C23×C3#13512yes—
472C23×C3C22×D411yescharacteristic
473C22×D3—22no—
474C22×D3—21no—
475C22×D3—22no—
476C22×D3—21no—
477C22×D3—22no—
478C22×D3—21no—
479C22×D3—21no—
480C22×D3—21no—
481C22×D3—21no—
482C22×D3—22no—
483C22×D3—48no—
484C22×D3—41no—
485C22×D3—41no—
486C22×D3—41no—
487C22×D3—41no—
488C22×D3—48no—
489C22×D3—41no—
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—
507C22×D3#12012yes—
508C3×Q8—22no—
509C3×Q8—22no—
510C3×Q8—41no—
511C3×Q8—41no—
512C2×C3×C4—21no—
513C2×C3×C4—22no—
514C2×C3×C4—22no—
515C2×C3×C4—21no—
516C2×C3×C4—21no—
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×C4—41no—
531C2×C3×C4C22×D411yescharacteristic
532C2×C3×C4C22×D411yescharacteristic
533C2×C3×C4C22×D411yescharacteristic
534C2×C3×C4C2×#4111yescharacteristic
535C2×C3×C4H(5,𝔽2)11yescharacteristic
536C2×C3×C4H(5,𝔽2)11yescharacteristic
537#67—44no—
538#67—84no—
539C2×Dic3—21no—
540C2×Dic3—21no—
541C2×Dic3—21no—
542C2×Dic3—21no—
543C2×Dic3—22no—
544C2×Dic3—21no—
545C2×Dic3—21no—
546C2×Dic3—21no—
547C2×Dic3—21no—
548C2×Dic3—41no—
549C2×Dic3—41no—
550C2×Dic3#12012yes—
551D12—22no—
552D12—22no—
553D12—22no—
554D12—22no—
555D12—22no—
556D12—48no—
557D12—48no—
558D12—41no—
559D12—41no—
560D12—41no—
561D12—41no—
562D12—41no—
563D12—41no—
564D12—84no—
565D12—84no—
566D12#12114yes—
567C4×D3—22no—
568C4×D3—22no—
569C4×D3—22no—
570C4×D3—22no—
571C4×D3—48no—
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—68no—
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—64no—
604C2×D4—64no—
605C2×D4—64no—
606C2×D4—62no—
607C2×D4—62no—
608C2×D4—61no—
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—121no—
632C2×D4—122no—
633C2×D4—122no—
634C2×D4—241no—
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—32no—
651C22×C4—32no—
652C22×C4—31no—
653C22×C4—31no—
654C22×C4—64no—
655C22×C4—64no—
656C22×C4—61no—
657C22×C4—61no—
658C22×C4—61no—
659C22×C4—61no—
660C22×C4—61no—
661C22×C4—122no—
662C22×C4—122no—
663C22×C4—241no—
664C22×C4—241no—
665C22×C4D3×D411yescharacteristic
666C22×C4C23×D311yescharacteristic
667SD16—124no—
668D8—124no—
669D8—124no—
670C2×C8—21no—
671C2×C8—21no—
672C2×C8—21no—
673C2×C8—21no—
674C2×C8—21no—
675C2×C8—61no—
676C2×C8—61no—
677C2×C8—61no—
678C2×C8—61no—
679C2×C8—61no—
680C2×C8—61no—
681C2×C8—124no—
682C2×C8D3×D412yes—
683C4⋊C4—24no—
684C4⋊C4—21no—
685C4⋊C4—21no—
686C4⋊C4—21no—
687C4⋊C4—21no—
688C4⋊C4—21no—
689C4⋊C4—32no—
690C4⋊C4—62no—
691C4⋊C4—61no—
692C4⋊C4—241no—
693C4⋊C4D3×D412yes—
694C22⋊C4—24no—
695C22⋊C4—64no—
696C22⋊C4—62no—
697C22⋊C4—64no—
698C22⋊C4—64no—
699C22⋊C4—64no—
700C22⋊C4—62no—
701C22⋊C4—81no—
702C22⋊C4—122no—
703C22⋊C4—122no—
704C22⋊C4—122no—
705C22⋊C4—122no—
706C22⋊C4—241no—
707C42—61no—
708C42—61no—
709C42—122no—
710C22×C3—22no—
711C22×C3—22no—
712C22×C3—22no—
713C22×C3—41no—
714C22×C3—41no—
715C22×C3—41no—
716C22×C3—41no—
717C22×C3C2×#12011yescharacteristic
718C22×C3D4211yescharacteristic
719C22×C3#54611yescharacteristic
720C22×C3C2×#13511yescharacteristic
721C22×C3#57511yescharacteristic
722C22×C3#57611yescharacteristic
723C22×C3#57611yescharacteristic
724C2×D3—22no—
725C2×D3—24no—
726C2×D3—22no—
727C2×D3—22no—
728C2×D3—42no—
729C2×D3—42no—
730C2×D3—41no—
731C2×D3—42no—
732C2×D3—41no—
733C2×D3—42no—
734C2×D3—41no—
735C2×D3—42no—
736C2×D3—41no—
737C2×D3—42no—
738C2×D3—42no—
739C2×D3—42no—
740C2×D3—42no—
741C2×D3—816no—
742C2×D3—81no—
743C2×D3—81no—
744C2×D3—81no—
745C2×D3—81no—
746C2×D3—81no—
747C2×D3—81no—
748C2×D3—81no—
749C2×D3—81no—
750C2×D3—81no—
751C2×D3—81no—
752C2×D3—81no—
753C3×C4—42no—
754C3×C4—41no—
755C3×C4—42no—
756C3×C4—81no—
757C3×C4—81no—
758C3×C4C2×#12111yescharacteristic
759C3×C4#53411yescharacteristic
760C3×C4D4211yescharacteristic
761C3×C4#54611yescharacteristic
762Dic3—22no—
763Dic3—41no—
764Dic3—41no—
765Dic3—42no—
766C23—21no—
767C23—21no—
768C23—21no—
769C23—21no—
770C23—21no—
771C23—21no—
772C23—32no—
773C23—61no—
774C23—62no—
775C23—61no—
776C23—61no—
777C23—61no—
778C23—61no—
779C23—62no—
780C23—61no—
781C23—62no—
782C23—62no—
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—121no—
802C23—244no—
803C23—244no—
804C23—244no—
805C23—244no—
806C23—244no—
807C23#91912yes—
808C23C2×D3×D411yescharacteristic
809Q8—22no—
810Q8—22no—
811Q8—41no—
812Q8—41no—
813D4—34no—
814D4—62no—
815D4—62no—
816D4—62no—
817D4—62no—
818D4—62no—
819D4—128no—
820D4—128no—
821D4—124no—
822D4—121no—
823D4—121no—
824D4—121no—
825D4—121no—
826D4—121no—
827D4—121no—
828D4—244no—
829D4—244no—
830D4—244no—
831C2×C4—21no—
832C2×C4—22no—
833C2×C4—22no—
834C2×C4—21no—
835C2×C4—21no—
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—62no—
854C2×C4—62no—
855C2×C4—62no—
856C2×C4—62no—
857C2×C4—61no—
858C2×C4—61no—
859C2×C4—61no—
860C2×C4—61no—
861C2×C4—61no—
862C2×C4—61no—
863C2×C4—62no—
864C2×C4—128no—
865C2×C4—121no—
866C2×C4—121no—
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#241011yescharacteristic
880C2×C3#300211yescharacteristic
881C2×C3#300811yescharacteristic
882C2×C3#326811yescharacteristic
883C2×C3#328011yescharacteristic
884C2×C3#329711yescharacteristic
885C2×C3#331911yescharacteristic
886D3—42no—
887D3—44no—
888D3—82no—
889D3—161no—
890C22—22no—
891C22—22no—
892C22—22no—
893C22—41no—
894C22—41no—
895C22—41no—
896C22—41no—
897C22—62no—
898C22—64no—
899C22—62no—
900C22—62no—
901C22—122no—
902C22—121no—
903C22—122no—
904C22—121no—
905C22—122no—
906C22—121no—
907C22—122no—
908C22—121no—
909C22—122no—
910C22—122no—
911C22—122no—
912C22—122no—
913C22—122no—
914C22—2416no—
915C22—241no—
916C22—241no—
917C22—241no—
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—81no—
938C4—81no—
939C4—121no—
940C4—122no—
941C4—121no—
942C4D3×#12111yescharacteristic
943C4#560911yescharacteristic
944C4#565311yescharacteristic
945C4#567611yescharacteristic
946C3#2442811yescharacteristic, complemented, Sylow
947C2—42no—
948C2—122no—
949C2—124no—
950C2—242no—
951C2—481no—
952C2#7710811yescharacteristic
953C2#8008511yescharacteristic
954C2#8018211yescharacteristic
955C2#8077311yescharacteristic
956C2#8083611yescharacteristic
957C2#8148511yescharacteristic
958C2#8152811yescharacteristic
subgroupG/H
centerC23C2×D3×D4
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC3×#2036C2
socleC23×C3C22×D4
hypercenter#2036D3
hypocenterC3#24428
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×#4883C2semidirect
3. C2×#4810C2semidirect
4. C2×#4804C2semidirect
5. C2×#4732C2semidirect
6. #74019C2semidirect
7. C3×#2036C2semidirect
8. #71699C2semidirect
9. #70638C2semidirect
10. #70279C2semidirect
11. #70277C2semidirect
12. #69957C2semidirect
13. #69521C2semidirect
14. #68897C2semidirect
15. #68881C2semidirect
21. C22×#215C22semidirect
26. C22×D3×C8C22semidirect
31. C2×#895C22semidirect
34. C2×#892C22semidirect
37. C2×C3×#107C22semidirect
38. C2×C3×#103C22semidirect
39. C2×C3×#103C22semidirect
42. C2×#835C22semidirect
46. C2×(C2×D3)⋊C8C22semidirect
47. #4988C22semidirect
48. #4972C22semidirect
53. C2×#809C22semidirect
62. C3×#340C22semidirect
63. #4550C22semidirect
64. #4550C22semidirect
65. #4529C22semidirect
73. #2036D3semidirect
91. C2×#239D4semidirect
158. #895D4semidirect
175. #821D4semidirect
205. C2×#107C2×D3semidirect
208. C2×#103C2×D3semidirect
209. C2×#103C2×D3semidirect
228. #340C2×D3semidirect
946. C3#24428semidirect

Maximal subgroups

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

subgroupindex
C2×#56302
C2×#48832
C2×#48102
C2×#48042
C2×#47322
#740192
C3×#20362
#716992
#706382
#702792
#702772
#699572
#695212
#688972
#688812
#244283