Finite Group Databasebeta

← #10827553

Subgroups — #10827553

Order 768.

1286 conjugacy classes of subgroups.

The subgroup lattice has 826 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#5532C211yesmaximal, characteristic
2#82751C211yesmaximal, characteristic, complemented
3C2×#4806C211yesmaximal, characteristic, complemented
4C2×#4802C211yesmaximal, characteristic, complemented
5C3×#1873C211yesmaximal, characteristic, complemented
6#71699C211yesmaximal, characteristic, complemented
7#71585C211yesmaximal, characteristic, complemented
8#70276C211yesmaximal, characteristic, complemented
9#70231C211yesmaximal, characteristic, complemented
10#69962C211yesmaximal, characteristic, complemented
11#69958C211yesmaximal, characteristic, complemented
12#68910C211yesmaximal, characteristic, complemented
13#68896C211yesmaximal, characteristic, complemented
14#68885C211yesmaximal, characteristic, complemented
15#68813C211yesmaximal, characteristic, complemented
16#23977—31nomaximal, Sylow
17C22×D3×Q8C2211yescharacteristic
18C2×C3×C22⋊Q8C2211yescharacteristic
19C2×C3×#117C2211yescharacteristic
20C22×#215C2211yescharacteristic
21C2×#930C2211yescharacteristic
22C2×C4×#67C2211yescharacteristic
23C2×#924C2211yescharacteristic
24C22×#204C2211yescharacteristic
25C22×ΓL(1,𝔽25)C2211yescharacteristic
26#5532—24no—
27#5532—24no—
28C2×#895C2211yescharacteristic
29C2×#893C2211yescharacteristic
30C2×#892C2211yescharacteristic
31C2×#888C2211yescharacteristic
32C2×#885—21no—
33C2×#884—21no—
34C2×#875—21no—
35C2×#872—21no—
36C2×C3×#103C2211yescharacteristic
37C2×C3×#103C2211yescharacteristic
38C2×C3×C22⋊C8C2211yescharacteristic
39#5229C2211yescharacteristic
40C2×#835C2211yescharacteristic
41C2×#830C2211yescharacteristic
42C2×#821C2211yescharacteristic
43C2×(C2×D3)⋊C8C2211yescharacteristic
44C2×#816C2211yescharacteristic
45#4989—21no—
46#4987C2211yescharacteristic
47#4979—21no—
48#4973C2211yescharacteristic
49C2×#810C2211yescharacteristic
50C2×#810C2211yescharacteristic
51C2×#809C2211yescharacteristic
52#4956—21no—
53#4947—21no—
54#4806—24no—
55#4802—24no—
56C3×#340C2211yescharacteristic
57C3×#340C2211yescharacteristic
58#4551C2211yescharacteristic
59#4550C2211yescharacteristic
60#4550C2211yescharacteristic
61#4529C2211yescharacteristic
62#4529C2211yescharacteristic
63#4529C2211yescharacteristic
64C2×#555—31no—
65C2×#448—31no—
66C2×#419—31no—
67#2409—31no—
68#2024—31no—
69#2024—31no—
70#2000—31no—
71#2000—31no—
72#1895—31no—
73#1877—31no—
74#1877—31no—
75#1873—31no—
76#1873D311yescharacteristic, complemented
77#1870—31no—
78#1825—31no—
79C22×C3×Q8C2311yescharacteristic
80C23×C3×C4C2311yescharacteristic
81C22×#67—21no—
82C22×#67D411yescharacteristic
83C2×D3×Q8—22no—
84C2×D3×Q8—22no—
85C2×D3×Q8—22no—
86C2×D3×Q8—22no—
87C2×D3×Q8—41no—
88C2×D3×Q8—41no—
89C22×D12—21no—
90C22×D12C2311yescharacteristic
91C22×C4×D3—21no—
92C22×C4×D3—21no—
93C22×C4×D3C2311yescharacteristic
94C22×Dic6—21no—
95C22×Dic6—21no—
96C22×Dic6C2311yescharacteristic
97C22×C3×C8C2311yescharacteristic
98C22×C3×C8C2311yescharacteristic
99C3×C22⋊Q8—22no—
100C3×C22⋊Q8—41no—
101C3×#117—22no—
102C3×#117—22no—
103C2×C3×C4⋊C4—21no—
104C2×C3×C4⋊C4C2311yescharacteristic
105C2×C3×C4⋊C4C2311yescharacteristic
106C2×C3×C4⋊C4C2311yescharacteristic
107C2×C3×C22⋊C4—21no—
108C2×C3×C22⋊C4—21no—
109C2×C3×C42—21no—
110C2×#217—21no—
111C2×#217D411yescharacteristic
112C2×#215—22no—
113C2×#215—22no—
114C2×#215—41no—
115#930—22no—
116#930—22no—
117C4×#67—22no—
118C4×#67—22no—
119C2×(C2×D3)⋊C4—21no—
120C2×(C2×D3)⋊C4—21no—
121C2×(C2×D3)⋊C4—21no—
122C2×(C2×D3)⋊C4—21no—
123C2×(C2×D3)⋊C4—21no—
124C2×(C2×D3)⋊C4D411yescharacteristic
125C2×C4⋊Dic3C2311yescharacteristic
126C2×C4⋊Dic3C2311yescharacteristic
127#924—22no—
128#924—41no—
129C2×Dic3⋊C4—21no—
130C2×Dic3⋊C4—21no—
131C2×Dic3⋊C4D411yescharacteristic
132C2×C4×Dic3—21no—
133C2×C4×Dic3C2311yescharacteristic
134C22×C3⋊C8C2311yescharacteristic
135C22×C3⋊C8C2311yescharacteristic
136C2×#204—22no—
137C2×#204—22no—
138C2×#204—41no—
139C2×ΓL(1,𝔽25)—22no—
140C2×ΓL(1,𝔽25)—41no—
141C2×ΓL(1,𝔽25)—41no—
142#895—22no—
143#895D414yes—
144#893—22no—
145#893—22no—
146#892—22no—
147#892D414yes—
148#888—22no—
149#888—22no—
150#885—28no—
151#884—28no—
152#875—28no—
153#872—28no—
154C3×#103—22no—
155C3×#103—22no—
156C3×C22⋊C8—41no—
157#835—22no—
158C3⋊#95—21no—
159C3⋊#95—21no—
160C3⋊#95—21no—
161C3⋊#95—21no—
162C3⋊#95—21no—
163#830—41no—
164#821—41no—
165(C2×D3)⋊C8—22no—
166#816—22no—
167#810—22no—
168#810—22no—
169#809—41no—
170C23×Q8—31no—
171C22×SD16—31no—
172C22×SD16—31no—
173C22×M16—31no—
174#555—64no—
175#555—64no—
176C2×C4⋊Q8—31no—
177C2×#124—61no—
178C2×#124—61no—
179C2×C22⋊Q8—31no—
180C2×C22⋊Q8C2×D311yescharacteristic
181C2×#121—31no—
182C2×#121—31no—
183C2×#121—61no—
184C2×C4×D4—31no—
185C2×C4×D4—31no—
186C2×#117—31no—
187C2×#117—61no—
188C2×#117C2×D311yescharacteristic
189#448—64no—
190#419—64no—
191C2×#103—31no—
192C2×#103—31no—
193C2×#103—31no—
194C2×#103—31no—
195C2×#103C2×D311yescharacteristic
196C2×#103C2×D311yescharacteristic
197C2×#102—31no—
198C2×#102—31no—
199C2×C22⋊C8—31no—
200C2×C22⋊C8—31no—
201C2×C22⋊C8C2×D311yescharacteristic
202#395—61no—
203#393—61no—
204#391—31no—
205#391—31no—
206#386—61no—
207#385—61no—
208#380—31no—
209#340—31no—
210#340—31no—
211#340—31no—
212#340—31no—
213#340C2×D311yescharacteristic
214#340C2×D311yescharacteristic
215#336—31no—
216#336—31no—
217C24×C3C2×D411yescharacteristic
218C23×D3—21no—
219C23×D3C2×D411yescharacteristic
220C2×C3×Q8—21no—
221C2×C3×Q8—21no—
222C2×C3×Q8—21no—
223C2×C3×Q8—21no—
224C2×C3×Q8—21no—
225C2×C3×Q8#4112yes—
226C22×C3×C4—21no—
227C22×C3×C4—21no—
228C22×C3×C4—21no—
229C22×C3×C4—21no—
230C22×C3×C4—21no—
231C22×C3×C4—21no—
232C22×C3×C4—21no—
233C22×C3×C4—21no—
234C22×C3×C4—21no—
235C22×C3×C4—21no—
236C22×C3×C4C2×D411yescharacteristic
237C22×C3×C4C2411yescharacteristic
238C2×#67—22no—
239C2×#67—24no—
240C2×#67—22no—
241C2×#67—41no—
242C2×#67—81no—
243C2×#67—81no—
244C22×Dic3—21no—
245C22×Dic3—21no—
246C22×Dic3—21no—
247C22×Dic3C2×D411yescharacteristic
248C22×Dic3C2×D411yescharacteristic
249C22×Dic3C2×D411yescharacteristic
250D3×Q8—28no—
251D3×Q8—44no—
252D3×Q8—44no—
253D3×Q8—44no—
254C2×D12—21no—
255C2×D12—21no—
256C2×D12—21no—
257C2×D12—21no—
258C2×D12—21no—
259C2×D12—24no—
260C2×D12—81no—
261C2×D12—81no—
262C2×D12C2×D412yes—
263C2×C4×D3—21no—
264C2×C4×D3—21no—
265C2×C4×D3—21no—
266C2×C4×D3—21no—
267C2×C4×D3—24no—
268C2×C4×D3—42no—
269C2×C4×D3—42no—
270C2×C4×D3—42no—
271C2×C4×D3—42no—
272C2×C4×D3—42no—
273C2×C4×D3C2×D412yes—
274C2×C4×D3C2×D412yes—
275C2×Dic6—21no—
276C2×Dic6—21no—
277C2×Dic6—21no—
278C2×Dic6—21no—
279C2×Dic6—21no—
280C2×Dic6—24no—
281C2×Dic6—42no—
282C2×Dic6—42no—
283C2×Dic6—42no—
284C2×Dic6—81no—
285C2×Dic6—81no—
286C2×Dic6#4112yes—
287C2×C3×C8—21no—
288C2×C3×C8—21no—
289C2×C3×C8—21no—
290C2×C3×C8—21no—
291C2×C3×C8—21no—
292C2×C3×C8—21no—
293C3×C4⋊C4—21no—
294C3×C4⋊C4—21no—
295C3×C4⋊C4—21no—
296C3×C4⋊C4—21no—
297C3×C4⋊C4—42no—
298C3×C4⋊C4C2×D412yes—
299C3×C4⋊C4C2×D412yes—
300C3×C22⋊C4—24no—
301C3×C22⋊C4—42no—
302C3×C42—24no—
303#217—22no—
304#217—42no—
305#215—44no—
306(C2×D3)⋊C4—24no—
307(C2×D3)⋊C4—24no—
308(C2×D3)⋊C4—22no—
309(C2×D3)⋊C4—24no—
310(C2×D3)⋊C4—24no—
311(C2×D3)⋊C4—42no—
312C4⋊Dic3—21no—
313C4⋊Dic3—21no—
314C4⋊Dic3—21no—
315C4⋊Dic3C2×D412yes—
316Dic3⋊C4—24no—
317Dic3⋊C4—22no—
318Dic3⋊C4—42no—
319C4×Dic3—21no—
320C4×Dic3—21no—
321C4×Dic3—24no—
322C2×C3⋊C8—21no—
323C2×C3⋊C8—21no—
324C2×C3⋊C8—21no—
325C2×C3⋊C8—21no—
326C2×C3⋊C8—21no—
327C2×C3⋊C8—21no—
328#204—44no—
329ΓL(1,𝔽25)—44no—
330C22×Q8—31no—
331C22×Q8—61no—
332C22×Q8—61no—
333C22×Q8—62no—
334C22×Q8—62no—
335C22×Q8—62no—
336C22×Q8—62no—
337C22×Q8—121no—
338C22×Q8—121no—
339C22×Q8C22×D311yescharacteristic
340C22×D4—31no—
341C22×D4—31no—
342C22×D4—61no—
343C22×D4—61no—
344C23×C4—31no—
345C23×C4—61no—
346C23×C4—61no—
347C23×C4C22×D311yescharacteristic
348C2×SD16—62no—
349C2×SD16—62no—
350C2×SD16—62no—
351C2×SD16—62no—
352C2×SD16—121no—
353C2×SD16—121no—
354C2×M16—62no—
355C2×M16—121no—
356C2×M16—121no—
357C22×C8—31no—
358C22×C8—31no—
359C22×C8C22×D311yescharacteristic
360C22×C8C22×D311yescharacteristic
361C4⋊Q8—62no—
362C4⋊Q8—62no—
363#124—68no—
364#124—68no—
365C22⋊Q8—22no—
366C22⋊Q8—41no—
367C22⋊Q8—62no—
368C22⋊Q8—121no—
369#121—34no—
370#121—68no—
371#121—62no—
372#121—62no—
373#121—62no—
374C4×D4—62no—
375C4×D4—62no—
376C4×D4—62no—
377C4×D4—62no—
378#117—22no—
379#117—22no—
380#117—34no—
381#117—68no—
382#117—62no—
383C2×C4⋊C4—21no—
384C2×C4⋊C4—31no—
385C2×C4⋊C4—31no—
386C2×C4⋊C4—31no—
387C2×C4⋊C4—61no—
388C2×C4⋊C4—61no—
389C2×C4⋊C4C22×D311yescharacteristic
390C2×C4⋊C4C22×D311yescharacteristic
391C2×C4⋊C4C22×D311yescharacteristic
392C2×C22⋊C4—21no—
393C2×C22⋊C4—21no—
394C2×C22⋊C4—31no—
395C2×C22⋊C4—31no—
396C2×C22⋊C4—61no—
397C2×C22⋊C4—61no—
398C2×C22⋊C4—61no—
399C2×C22⋊C4—61no—
400C2×C22⋊C4—61no—
401C2×C22⋊C4—61no—
402C2×C42—21no—
403C2×C42—31no—
404C2×C42—61no—
405#103—22no—
406#103—22no—
407#103—62no—
408#103—62no—
409#103—62no—
410#103—62no—
411#102—121no—
412#102—121no—
413C22⋊C8—41no—
414C22⋊C8—62no—
415C22⋊C8—121no—
416#95—61no—
417#95—61no—
418#95—61no—
419#95—61no—
420#95—61no—
421C23×C3—21no—
422C23×C3—21no—
423C23×C3—21no—
424C23×C3—21no—
425C23×C3—21no—
426C23×C3—21no—
427C23×C3—21no—
428C23×C3C22×D411yescharacteristic
429C22×D3—21no—
430C22×D3—21no—
431C22×D3—21no—
432C22×D3—21no—
433C22×D3—21no—
434C22×D3—21no—
435C22×D3—22no—
436C22×D3—41no—
437C22×D3—41no—
438C22×D3—41no—
439C22×D3—41no—
440C22×D3—41no—
441C22×D3—41no—
442C22×D3#12012yes—
443C3×Q8—22no—
444C3×Q8—22no—
445C3×Q8—41no—
446C3×Q8—41no—
447C2×C3×C4—22no—
448C2×C3×C4—21no—
449C2×C3×C4—22no—
450C2×C3×C4—21no—
451C2×C3×C4—22no—
452C2×C3×C4—21no—
453C2×C3×C4—41no—
454C2×C3×C4—41no—
455C2×C3×C4—41no—
456C2×C3×C4—41no—
457C2×C3×C4—41no—
458C2×C3×C4—41no—
459C2×C3×C4—41no—
460C2×C3×C4—41no—
461C2×C3×C4—41no—
462C2×C3×C4—41no—
463C2×C3×C4—41no—
464C2×C3×C4—41no—
465C2×C3×C4—41no—
466C2×C3×C4C22×D411yescharacteristic
467C2×C3×C4C22×D411yescharacteristic
468C2×C3×C4C2×#4111yescharacteristic
469C2×C3×C4C2×#4111yescharacteristic
470C2×C3×C4H(5,𝔽2)11yescharacteristic
471C2×C3×C4H(5,𝔽2)11yescharacteristic
472#67—44no—
473#67—84no—
474C2×Dic3—21no—
475C2×Dic3—21no—
476C2×Dic3—21no—
477C2×Dic3—21no—
478C2×Dic3—22no—
479C2×Dic3—21no—
480C2×Dic3—22no—
481C2×Dic3—21no—
482C2×Dic3—21no—
483C2×Dic3—41no—
484C2×Dic3—41no—
485C2×Dic3—41no—
486C2×Dic3—41no—
487C2×Dic3—41no—
488C2×Dic3—41no—
489C2×Dic3—41no—
490C2×Dic3#12012yes—
491C2×Dic3#13712yes—
492D12—22no—
493D12—22no—
494D12—41no—
495D12—41no—
496D12—84no—
497C4×D3—22no—
498C4×D3—22no—
499C4×D3—22no—
500C4×D3—22no—
501C4×D3—48no—
502C4×D3—48no—
503Dic6—22no—
504Dic6—22no—
505Dic6—48no—
506Dic6—41no—
507Dic6—41no—
508Dic6—84no—
509C3×C8—41no—
510C3×C8—41no—
511C3⋊C8—41no—
512C3⋊C8—41no—
513C24—31no—
514C24—61no—
515C24D3×D411yescharacteristic
516C2×Q8—21no—
517C2×Q8—21no—
518C2×Q8—21no—
519C2×Q8—21no—
520C2×Q8—21no—
521C2×Q8—32no—
522C2×Q8—64no—
523C2×Q8—61no—
524C2×Q8—68no—
525C2×Q8—61no—
526C2×Q8—61no—
527C2×Q8—61no—
528C2×Q8—61no—
529C2×Q8—122no—
530C2×Q8—122no—
531C2×Q8—122no—
532C2×Q8—124no—
533C2×Q8—124no—
534C2×Q8—124no—
535C2×Q8—241no—
536C2×Q8—241no—
537C2×Q8#23512yes—
538C2×D4—32no—
539C2×D4—64no—
540C2×D4—62no—
541C2×D4—62no—
542C2×D4—64no—
543C2×D4—61no—
544C2×D4—61no—
545C2×D4—61no—
546C2×D4—61no—
547C2×D4—61no—
548C2×D4—121no—
549C2×D4—241no—
550C2×D4—241no—
551C2×D4—241no—
552C2×D4—241no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—21no—
559C22×C4—21no—
560C22×C4—21no—
561C22×C4—21no—
562C22×C4—21no—
563C22×C4—31no—
564C22×C4—31no—
565C22×C4—32no—
566C22×C4—32no—
567C22×C4—31no—
568C22×C4—64no—
569C22×C4—61no—
570C22×C4—61no—
571C22×C4—61no—
572C22×C4—61no—
573C22×C4—61no—
574C22×C4—61no—
575C22×C4—61no—
576C22×C4—122no—
577C22×C4—122no—
578C22×C4—122no—
579C22×C4—122no—
580C22×C4—122no—
581C22×C4D3×D411yescharacteristic
582C22×C4C23×D311yescharacteristic
583SD16—124no—
584SD16—124no—
585M16—124no—
586C2×C8—21no—
587C2×C8—21no—
588C2×C8—21no—
589C2×C8—21no—
590C2×C8—21no—
591C2×C8—21no—
592C2×C8—61no—
593C2×C8—61no—
594C2×C8—61no—
595C2×C8—61no—
596C2×C8—61no—
597C2×C8—61no—
598C4⋊C4—21no—
599C4⋊C4—21no—
600C4⋊C4—21no—
601C4⋊C4—21no—
602C4⋊C4—32no—
603C4⋊C4—42no—
604C4⋊C4—62no—
605C4⋊C4—64no—
606C4⋊C4—61no—
607C4⋊C4—61no—
608C4⋊C4—61no—
609C4⋊C4—122no—
610C4⋊C4D3×D412yes—
611C4⋊C4D3×D412yes—
612C22⋊C4—24no—
613C22⋊C4—42no—
614C22⋊C4—64no—
615C22⋊C4—62no—
616C22⋊C4—64no—
617C22⋊C4—64no—
618C22⋊C4—64no—
619C22⋊C4—62no—
620C22⋊C4—122no—
621C22⋊C4—122no—
622C42—24no—
623C42—64no—
624C42—61no—
625C42—61no—
626C22×C3—41no—
627C22×C3—41no—
628C22×C3—41no—
629C22×C3—41no—
630C22×C3—41no—
631C22×C3—41no—
632C22×C3—41no—
633C22×C3C2×#12011yescharacteristic
634C22×C3#54611yescharacteristic
635C22×C3#54611yescharacteristic
636C22×C3C2×#13711yescharacteristic
637C22×C3#57511yescharacteristic
638C22×C3#57711yescharacteristic
639C22×C3#57711yescharacteristic
640C2×D3—22no—
641C2×D3—22no—
642C2×D3—22no—
643C2×D3—41no—
644C2×D3—41no—
645C2×D3—41no—
646C2×D3—41no—
647C2×D3—42no—
648C2×D3—42no—
649C2×D3—42no—
650C2×D3—81no—
651C2×D3—81no—
652C2×D3—81no—
653C2×D3—81no—
654C3×C4—42no—
655C3×C4—41no—
656C3×C4—42no—
657C3×C4—42no—
658C3×C4—81no—
659C3×C4#52511yescharacteristic
660C3×C4#53511yescharacteristic
661C3×C4#54611yescharacteristic
662C3×C4#54611yescharacteristic
663Dic3—22no—
664Dic3—22no—
665Dic3—42no—
666Dic3—41no—
667Dic3—42no—
668Dic3—81no—
669C23—21no—
670C23—21no—
671C23—21no—
672C23—21no—
673C23—21no—
674C23—21no—
675C23—21no—
676C23—32no—
677C23—61no—
678C23—61no—
679C23—61no—
680C23—61no—
681C23—61no—
682C23—61no—
683C23—62no—
684C23—121no—
685C23—121no—
686C23—121no—
687C23—121no—
688C23—121no—
689C23—121no—
690C23C2×D3×D411yescharacteristic
691Q8—22no—
692Q8—22no—
693Q8—41no—
694Q8—41no—
695Q8—62no—
696Q8—62no—
697Q8—128no—
698Q8—121no—
699Q8—121no—
700Q8—244no—
701D4—62no—
702D4—62no—
703D4—124no—
704D4—121no—
705D4—121no—
706D4—244no—
707D4—244no—
708C2×C4—21no—
709C2×C4—22no—
710C2×C4—21no—
711C2×C4—21no—
712C2×C4—22no—
713C2×C4—22no—
714C2×C4—32no—
715C2×C4—32no—
716C2×C4—41no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—41no—
720C2×C4—41no—
721C2×C4—41no—
722C2×C4—41no—
723C2×C4—41no—
724C2×C4—41no—
725C2×C4—41no—
726C2×C4—41no—
727C2×C4—41no—
728C2×C4—41no—
729C2×C4—61no—
730C2×C4—61no—
731C2×C4—61no—
732C2×C4—61no—
733C2×C4—62no—
734C2×C4—62no—
735C2×C4—62no—
736C2×C4—62no—
737C2×C4—62no—
738C2×C4—61no—
739C2×C4—61no—
740C2×C4—61no—
741C2×C4—62no—
742C2×C4—128no—
743C2×C4—128no—
744C2×C4—121no—
745C2×C4—121no—
746C2×C4—121no—
747C2×C4—121no—
748C2×C4—121no—
749C2×C4—121no—
750C2×C4—121no—
751C2×C4C2×#23511yescharacteristic
752C2×C4C2×D3×D411yescharacteristic
753C2×C4C2×D3×D411yescharacteristic
754C2×C4#100411yescharacteristic
755C2×C4D3×#4111yescharacteristic
756C2×C4#100911yescharacteristic
757C8—41no—
758C8—41no—
759C8—121no—
760C8—121no—
761C2×C3—81no—
762C2×C3#240411yescharacteristic
763C2×C3#300711yescharacteristic
764C2×C3#300911yescharacteristic
765C2×C3#332111yescharacteristic
766C2×C3#332111yescharacteristic
767C2×C3#332911yescharacteristic
768C2×C3#332911yescharacteristic
769D3—42no—
770D3—82no—
771C22—41no—
772C22—41no—
773C22—41no—
774C22—41no—
775C22—41no—
776C22—41no—
777C22—41no—
778C22—62no—
779C22—62no—
780C22—62no—
781C22—121no—
782C22—121no—
783C22—121no—
784C22—121no—
785C22—122no—
786C22—122no—
787C22—122no—
788C22—241no—
789C22—241no—
790C22—241no—
791C22—241no—
792C22#549011yescharacteristic
793C22D3×#12011yescharacteristic
794C22#565411yescharacteristic
795C22#576811yescharacteristic
796C22#577011yescharacteristic
797C22D3×#13711yescharacteristic
798C22#577811yescharacteristic
799C4—42no—
800C4—42no—
801C4—41no—
802C4—42no—
803C4—62no—
804C4—62no—
805C4—81no—
806C4—121no—
807C4—122no—
808C4—122no—
809C4—241no—
810C4#554711yescharacteristic
811C4#555011yescharacteristic
812C4#560711yescharacteristic
813C4#561211yescharacteristic
814C3#2397711yescharacteristic, complemented, Sylow
815C2—81no—
816C2—122no—
817C2—242no—
818C2#7488611yescharacteristic
819C2#7886011yescharacteristic
820C2#7897311yescharacteristic
821C2#8022811yescharacteristic
822C2#8022911yescharacteristic
823C2#8155311yescharacteristic
824C2#8155511yescharacteristic
subgroupG/H
centerC23C2×D3×D4
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC3×#1873C2
socleC23×C3C22×D4
prime radicalC2×#5532C2
hypercenter#1873D3
hypocenterC3#23977
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1873

Complements

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

NH ≅ G/Ntype
2. #82751C2semidirect
3. C2×#4806C2semidirect
4. C2×#4802C2semidirect
5. C3×#1873C2semidirect
6. #71699C2semidirect
7. #71585C2semidirect
8. #70276C2semidirect
9. #70231C2semidirect
10. #69962C2semidirect
11. #69958C2semidirect
12. #68910C2semidirect
13. #68896C2semidirect
14. #68885C2semidirect
15. #68813C2semidirect
76. #1873D3semidirect
814. C3#23977semidirect

Maximal subgroups

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

subgroupindex
C2×#55322
#827512
C2×#48062
C2×#48022
C3×#18732
#716992
#715852
#702762
#702312
#699622
#699582
#689102
#688962
#688852
#688132
#239773