Finite Group Databasebeta

← #10944115

Subgroups — #10944115

Order 768.

1406 conjugacy classes of subgroups.

The subgroup lattice has 804 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#5504C211yesmaximal, characteristic
2#82786C211yesmaximal, characteristic, complemented
3C2×#5047C211yesmaximal, characteristic
4C2×#4795C211yesmaximal, characteristic, complemented
5C2×#4818C211yesmaximal, characteristic, complemented
6C2×#4733C211yesmaximal, characteristic
7C3×#1872C211yesmaximal, characteristic, complemented
8#71559C211yesmaximal, characteristic, complemented
9#70281C211yesmaximal, characteristic, complemented
10#70276C211yesmaximal, characteristic, complemented
11#69909C211yesmaximal, characteristic, complemented
12#68908C211yesmaximal, characteristic, complemented
13#68905C211yesmaximal, characteristic, complemented
14#68896C211yesmaximal, characteristic, complemented
15#68893C211yesmaximal, characteristic, complemented
16#32916—31nomaximal, Sylow
17C22×#235C2211yescharacteristic
18C2×C3×C22⋊Q8C2211yescharacteristic
19C22×C3×C4⋊C4C2211yescharacteristic
20C2×#944C2211yescharacteristic
21C22×#216C2211yescharacteristic
22C22×#215C2211yescharacteristic
23C2×C4×#67—21no—
24C2×C4×#67—21no—
25C2×#926C2211yescharacteristic
26C2×#924C2211yescharacteristic
27C22×Dic12C2211yescharacteristic
28C22×#204C2211yescharacteristic
29#5504—24no—
30#5504—24no—
31C2×#893C2211yescharacteristic
32C2×#893C2211yescharacteristic
33C2×#892—21no—
34C2×D3×C4⋊C4—21no—
35C2×#887C2211yescharacteristic
36C2×#887C2211yescharacteristic
37C2×C3×#103C2211yescharacteristic
38C2×C3×#103C2211yescharacteristic
39C2×C3×C22⋊C8C2211yescharacteristic
40#5229C2211yescharacteristic
41C2×#830C2211yescharacteristic
42C2×#821C2211yescharacteristic
43C2×#816C2211yescharacteristic
44C2×Dic3⋊C8C2211yescharacteristic
45C2×Dic3⋊C8C2211yescharacteristic
46#5047—24no—
47#4982—21no—
48#4982—21no—
49#4977C2211yescharacteristic
50#4973C2211yescharacteristic
51C2×#810C2211yescharacteristic
52C2×#810C2211yescharacteristic
53C2×#810C2211yescharacteristic
54C2×#809C2211yescharacteristic
55#4952—21no—
56#4952—21no—
57#4818—24no—
58#4795—24no—
59#4733—24no—
60C3×#340C2211yescharacteristic
61C3×#340C2211yescharacteristic
62#4550C2211yescharacteristic
63#4550C2211yescharacteristic
64#4529C2211yescharacteristic
65#4529C2211yescharacteristic
66C2×#520—31no—
67C2×#462—31no—
68C2×#461—31no—
69C2×#452—31no—
70C2×#452—31no—
71#2621—31no—
72#1878—31no—
73#1878—31no—
74#1877—31no—
75#1877—31no—
76#1872—31no—
77#1872D311yescharacteristic, complemented
78#1805—31no—
79#1804—31no—
80#1798—31no—
81C22×C3×Q8C2311yescharacteristic
82C23×C3×C4—21no—
83C23×C3×C4C2311yescharacteristic
84C22×#67—21no—
85C2×#235—22no—
86C2×#235—22no—
87C2×#235—22no—
88C2×#235—22no—
89C2×#235—22no—
90C2×#235D414yes—
91C22×D12C2311yescharacteristic
92C22×C4×D3—21no—
93C22×C4×D3—21no—
94C22×C4×D3—21no—
95C22×Dic6C2311yescharacteristic
96C22×Dic6C2311yescharacteristic
97C22×C3×C8C2311yescharacteristic
98C22×C3×C8C2311yescharacteristic
99C3×C22⋊Q8—22no—
100C3×C22⋊Q8—22no—
101C2×C3×C4⋊C4—21no—
102C2×C3×C4⋊C4—22no—
103C2×C3×C4⋊C4—22no—
104C2×C3×C4⋊C4—21no—
105C2×C3×C4⋊C4C2311yescharacteristic
106C2×C3×C4⋊C4C2311yescharacteristic
107C2×C3×C4⋊C4C2311yescharacteristic
108C2×C3×C22⋊C4—21no—
109C2×#217—21no—
110C2×#217D411yescharacteristic
111C2×#217D411yescharacteristic
112#944—22no—
113#944—22no—
114C2×#216—22no—
115C2×#216—22no—
116C2×#216—22no—
117C2×#215—22no—
118C2×#215—22no—
119C2×#215—22no—
120C4×#67—28no—
121C4×#67—28no—
122C2×(C2×D3)⋊C4—21no—
123C2×(C2×D3)⋊C4—21no—
124#926—22no—
125#926—22no—
126C2×C4⋊Dic3D411yescharacteristic
127C2×C4⋊Dic3D411yescharacteristic
128C2×C4⋊Dic3C2311yescharacteristic
129#924—22no—
130#924—22no—
131C2×Dic3⋊C4—21no—
132C2×Dic3⋊C4—21no—
133C2×Dic3⋊C4—21no—
134C2×Dic3⋊C4—21no—
135C2×Dic3⋊C4—21no—
136C2×C4×Dic3—21no—
137C2×C4×Dic3—21no—
138C2×C4×Dic3C2311yescharacteristic
139C2×C4×Dic3C2311yescharacteristic
140C22×C3⋊C8C2311yescharacteristic
141C22×C3⋊C8C2311yescharacteristic
142C2×Dic12—22no—
143C2×Dic12—22no—
144C2×Dic12—22no—
145C2×#204—22no—
146C2×#204—22no—
147C2×#204—22no—
148#893—22no—
149#893—22no—
150#893—22no—
151#893D414yes—
152#892—28no—
153D3×C4⋊C4—28no—
154#887—22no—
155#887—22no—
156#887—22no—
157#887D414yes—
158C3×#103—22no—
159C3×#103—22no—
160C3×C22⋊C8—22no—
161C3⋊#95—21no—
162C3⋊#95—21no—
163C3⋊#95—21no—
164C3⋊#95—21no—
165C3⋊#95—21no—
166C3⋊#95—21no—
167#830—22no—
168#821—22no—
169#816—22no—
170Dic3⋊C8—22no—
171Dic3⋊C8—22no—
172#810—22no—
173#810—22no—
174#810—22no—
175#809—22no—
176C22×#41—31no—
177C22×Q16—31no—
178C22×Q16—31no—
179C22×SD16—31no—
180C22×SD16—31no—
181C2×C4⋊Q8—31no—
182C2×C22⋊Q8—31no—
183C2×C22⋊Q8C2×D311yescharacteristic
184#520—64no—
185#520—64no—
186C2×C4×Q8—31no—
187C2×C4×Q8—31no—
188C2×C4×D4—31no—
189C2×C4×D4—31no—
190C2×C4×D4—61no—
191C2×C4×D4—61no—
192C2×#117—31no—
193C2×#117—61no—
194C22×C4⋊C4—61no—
195C22×C4⋊C4C2×D311yescharacteristic
196#462—64no—
197#461—64no—
198#452—64no—
199#452—64no—
200C2×C4⋊C8—31no—
201C2×C4⋊C8—31no—
202C2×#103—31no—
203C2×#103—31no—
204C2×#103—31no—
205C2×#103—31no—
206C2×#103C2×D311yescharacteristic
207C2×#103C2×D311yescharacteristic
208C2×#102—31no—
209C2×#102—31no—
210C2×C22⋊C8—31no—
211C2×C22⋊C8C2×D311yescharacteristic
212#398—61no—
213#398—61no—
214#397—61no—
215#397—61no—
216#391—31no—
217#391—31no—
218#382—31no—
219#340—31no—
220#340—31no—
221#340C2×D311yescharacteristic
222#340C2×D311yescharacteristic
223#336—31no—
224#336—31no—
225C24×C3C2×D411yescharacteristic
226C23×D3—21no—
227C2×C3×Q8—21no—
228C2×C3×Q8—21no—
229C2×C3×Q8—21no—
230C2×C3×Q8—21no—
231C2×C3×Q8—21no—
232C2×C3×Q8—21no—
233C22×C3×C4—21no—
234C22×C3×C4—21no—
235C22×C3×C4—21no—
236C22×C3×C4—21no—
237C22×C3×C4—21no—
238C22×C3×C4—21no—
239C22×C3×C4—24no—
240C22×C3×C4—21no—
241C22×C3×C4—21no—
242C22×C3×C4—81no—
243C22×C3×C4—81no—
244C22×C3×C4C2×D411yescharacteristic
245C22×C3×C4C2×D412yes—
246C22×C3×C4#4112yes—
247C22×C3×C4C2411yescharacteristic
248C2×#67—24no—
249C2×#67—24no—
250C2×#67—24no—
251C22×Dic3—21no—
252C22×Dic3—21no—
253C22×Dic3—21no—
254C22×Dic3C2×D411yescharacteristic
255C22×Dic3C2×D411yescharacteristic
256C22×Dic3C2×D411yescharacteristic
257C22×Dic3C2×D411yescharacteristic
258#235—28no—
259#235—28no—
260#235—28no—
261#235—28no—
262C2×D12—21no—
263C2×D12—21no—
264C2×D12—21no—
265C2×D12C2×D412yes—
266C2×D12C2×D412yes—
267C2×D12#4112yes—
268C2×C4×D3—24no—
269C2×C4×D3—24no—
270C2×C4×D3—24no—
271C2×C4×D3—24no—
272C2×C4×D3—24no—
273C2×C4×D3—81no—
274C2×C4×D3—81no—
275C2×C4×D3—81no—
276C2×C4×D3—81no—
277C2×Dic6—21no—
278C2×Dic6—21no—
279C2×Dic6—21no—
280C2×Dic6—21no—
281C2×Dic6—21no—
282C2×Dic6—21no—
283C2×Dic6—21no—
284C2×Dic6—21no—
285C2×Dic6—21no—
286C2×Dic6C2×D412yes—
287C2×Dic6C2×D412yes—
288C2×Dic6#4112yes—
289C2×C3×C8—21no—
290C2×C3×C8—21no—
291C2×C3×C8—21no—
292C2×C3×C8—21no—
293C2×C3×C8—21no—
294C2×C3×C8—21no—
295C3×C4⋊C4—24no—
296C3×C4⋊C4—21no—
297C3×C4⋊C4—21no—
298C3×C4⋊C4—21no—
299C3×C4⋊C4—21no—
300C3×C4⋊C4—42no—
301C3×C4⋊C4C2×D412yes—
302C3×C4⋊C4C2×D412yes—
303C3×C22⋊C4—42no—
304#217—22no—
305#217—22no—
306#217—42no—
307#216—44no—
308#215—44no—
309(C2×D3)⋊C4—24no—
310(C2×D3)⋊C4—24no—
311C4⋊Dic3—22no—
312C4⋊Dic3—22no—
313C4⋊Dic3—21no—
314C4⋊Dic3—21no—
315Dic3⋊C4—24no—
316Dic3⋊C4—24no—
317Dic3⋊C4—42no—
318Dic3⋊C4—42no—
319Dic3⋊C4—42no—
320C4×Dic3—24no—
321C4×Dic3—21no—
322C4×Dic3—21no—
323C4×Dic3—24no—
324C4×Dic3C2×D412yes—
325C4×Dic3C2×D412yes—
326C2×C3⋊C8—21no—
327C2×C3⋊C8—21no—
328C2×C3⋊C8—21no—
329C2×C3⋊C8—21no—
330C2×C3⋊C8—21no—
331C2×C3⋊C8—21no—
332Dic12—44no—
333#204—44no—
334C2×#41—34no—
335C2×#41—62no—
336C2×#41—62no—
337C2×#41—62no—
338C2×#41—62no—
339C2×#41—62no—
340C22×Q8—31no—
341C22×Q8—31no—
342C22×Q8C22×D311yescharacteristic
343C22×D4—31no—
344C22×D4—61no—
345C23×C4—21no—
346C23×C4—61no—
347C23×C4—61no—
348C23×C4—61no—
349C23×C4C22×D311yescharacteristic
350C2×Q16—62no—
351C2×Q16—62no—
352C2×Q16—62no—
353C2×Q16—62no—
354C2×Q16—62no—
355C2×Q16—62no—
356C2×SD16—62no—
357C2×SD16—62no—
358C2×SD16—62no—
359C2×SD16—62no—
360C2×SD16—62no—
361C2×SD16—62no—
362C22×C8—31no—
363C22×C8—31no—
364C22×C8C22×D311yescharacteristic
365C22×C8C22×D311yescharacteristic
366C4⋊Q8—62no—
367C4⋊Q8—62no—
368C22⋊Q8—22no—
369C22⋊Q8—22no—
370C22⋊Q8—62no—
371C22⋊Q8—62no—
372C4×Q8—34no—
373C4×Q8—62no—
374C4×Q8—62no—
375C4×Q8—62no—
376C4×D4—34no—
377C4×D4—62no—
378C4×D4—62no—
379C4×D4—68no—
380C4×D4—68no—
381C4×D4—62no—
382#117—62no—
383#117—62no—
384#117—68no—
385C2×C4⋊C4—21no—
386C2×C4⋊C4—22no—
387C2×C4⋊C4—22no—
388C2×C4⋊C4—21no—
389C2×C4⋊C4—31no—
390C2×C4⋊C4—31no—
391C2×C4⋊C4—31no—
392C2×C4⋊C4—68no—
393C2×C4⋊C4—61no—
394C2×C4⋊C4—61no—
395C2×C4⋊C4—61no—
396C2×C4⋊C4—61no—
397C2×C4⋊C4—61no—
398C2×C4⋊C4C22×D311yescharacteristic
399C2×C4⋊C4C22×D311yescharacteristic
400C2×C4⋊C4C22×D311yescharacteristic
401C2×C22⋊C4—21no—
402C2×C22⋊C4—31no—
403C2×C22⋊C4—31no—
404C2×C22⋊C4—61no—
405C2×C22⋊C4—61no—
406C2×C22⋊C4—61no—
407C2×C42—31no—
408C2×C42—31no—
409C2×C42—61no—
410C2×C42—61no—
411C4⋊C8—62no—
412C4⋊C8—62no—
413#103—22no—
414#103—22no—
415#103—62no—
416#103—62no—
417#103—62no—
418#103—62no—
419#102—62no—
420#102—62no—
421C22⋊C8—22no—
422C22⋊C8—62no—
423#95—61no—
424#95—61no—
425#95—61no—
426#95—61no—
427#95—61no—
428#95—61no—
429C23×C3—21no—
430C23×C3—21no—
431C23×C3—21no—
432C23×C3—21no—
433C23×C3—21no—
434C23×C3—21no—
435C23×C3#12112yes—
436C23×C3C22×D411yescharacteristic
437C22×D3—22no—
438C22×D3—22no—
439C22×D3—22no—
440C22×D3—41no—
441C22×D3—41no—
442C22×D3—41no—
443C22×D3—41no—
444C3×Q8—41no—
445C3×Q8—41no—
446C3×Q8—41no—
447C3×Q8—41no—
448C2×C3×C4—21no—
449C2×C3×C4—21no—
450C2×C3×C4—22no—
451C2×C3×C4—22no—
452C2×C3×C4—22no—
453C2×C3×C4—22no—
454C2×C3×C4—22no—
455C2×C3×C4—22no—
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×C4—84no—
467C2×C3×C4#12112yes—
468C2×C3×C4C22×D411yescharacteristic
469C2×C3×C4C22×D411yescharacteristic
470C2×C3×C4C22×D411yescharacteristic
471C2×C3×C4C2×#4111yescharacteristic
472C2×C3×C4C2×#4111yescharacteristic
473C2×C3×C4C2×#4111yescharacteristic
474#67—216no—
475C2×Dic3—22no—
476C2×Dic3—22no—
477C2×Dic3—22no—
478C2×Dic3—21no—
479C2×Dic3—21no—
480C2×Dic3—21no—
481C2×Dic3—21no—
482C2×Dic3—21no—
483C2×Dic3—21no—
484C2×Dic3—21no—
485C2×Dic3—21no—
486C2×Dic3—21no—
487C2×Dic3—21no—
488C2×Dic3—41no—
489C2×Dic3—41no—
490C2×Dic3—41no—
491C2×Dic3—41no—
492C2×Dic3—41no—
493C2×Dic3—41no—
494C2×Dic3#12012yes—
495C2×Dic3#12012yes—
496D12—22no—
497D12—22no—
498D12—22no—
499D12#12114yes—
500C4×D3—216no—
501C4×D3—84no—
502C4×D3—84no—
503Dic6—22no—
504Dic6—22no—
505Dic6—22no—
506Dic6—41no—
507Dic6—41no—
508Dic6—41no—
509Dic6—41no—
510Dic6#12114yes—
511C3×C8—41no—
512C3×C8—41no—
513C3⋊C8—41no—
514C3⋊C8—41no—
515C24—61no—
516C24D3×D411yescharacteristic
517#41—68no—
518#41—68no—
519#41—68no—
520#41—68no—
521C2×Q8—21no—
522C2×Q8—21no—
523C2×Q8—21no—
524C2×Q8—21no—
525C2×Q8—21no—
526C2×Q8—21no—
527C2×Q8—32no—
528C2×Q8—32no—
529C2×Q8—32no—
530C2×Q8—61no—
531C2×Q8—61no—
532C2×Q8—61no—
533C2×Q8—61no—
534C2×Q8—61no—
535C2×Q8—61no—
536C2×Q8—61no—
537C2×Q8—61no—
538C2×Q8—61no—
539C2×D4—32no—
540C2×D4—32no—
541C2×D4—32no—
542C2×D4—64no—
543C2×D4—64no—
544C2×D4—64no—
545C2×D4—61no—
546C2×D4—61no—
547C2×D4—61no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—24no—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—31no—
558C22×C4—31no—
559C22×C4—31no—
560C22×C4—31no—
561C22×C4—64no—
562C22×C4—64no—
563C22×C4—64no—
564C22×C4—64no—
565C22×C4—61no—
566C22×C4—64no—
567C22×C4—61no—
568C22×C4—61no—
569C22×C4—81no—
570C22×C4—81no—
571C22×C4—241no—
572C22×C4—241no—
573C22×C4—241no—
574C22×C4—241no—
575C22×C4#23512yes—
576C22×C4D3×D411yescharacteristic
577C22×C4D3×D412yes—
578C22×C4C23×D311yescharacteristic
579Q16—124no—
580Q16—124no—
581SD16—124no—
582SD16—124no—
583C2×C8—21no—
584C2×C8—21no—
585C2×C8—21no—
586C2×C8—21no—
587C2×C8—21no—
588C2×C8—21no—
589C2×C8—61no—
590C2×C8—61no—
591C2×C8—61no—
592C2×C8—61no—
593C2×C8—61no—
594C2×C8—61no—
595C4⋊C4—24no—
596C4⋊C4—21no—
597C4⋊C4—21no—
598C4⋊C4—21no—
599C4⋊C4—21no—
600C4⋊C4—42no—
601C4⋊C4—62no—
602C4⋊C4—62no—
603C4⋊C4—64no—
604C4⋊C4—64no—
605C4⋊C4—61no—
606C4⋊C4—61no—
607C4⋊C4—122no—
608C4⋊C4—122no—
609C4⋊C4—122no—
610C4⋊C4D3×D412yes—
611C4⋊C4D3×D412yes—
612C22⋊C4—42no—
613C22⋊C4—64no—
614C22⋊C4—64no—
615C22⋊C4—62no—
616C22⋊C4—62no—
617C22⋊C4—122no—
618C42—32no—
619C42—32no—
620C42—64no—
621C42—64no—
622C42—61no—
623C42—61no—
624C22×C3—22no—
625C22×C3—22no—
626C22×C3—22no—
627C22×C3—41no—
628C22×C3—41no—
629C22×C3—41no—
630C22×C3—41no—
631C22×C3C2×#12011yescharacteristic
632C22×C3C2×#12111yescharacteristic
633C22×C3#52511yescharacteristic
634C22×C3#57711yescharacteristic
635C22×C3#57711yescharacteristic
636C22×C3#57811yescharacteristic
637C22×C3#57811yescharacteristic
638C2×D3—24no—
639C2×D3—42no—
640C2×D3—42no—
641C2×D3—42no—
642C2×D3—42no—
643C2×D3—42no—
644C2×D3—42no—
645C3×C4—22no—
646C3×C4—42no—
647C3×C4—42no—
648C3×C4—81no—
649C3×C4—81no—
650C3×C4C2×#12111yescharacteristic
651C3×C4C2×#12111yescharacteristic
652C3×C4#52511yescharacteristic
653C3×C4#52511yescharacteristic
654Dic3—24no—
655Dic3—22no—
656Dic3—22no—
657Dic3—41no—
658Dic3—41no—
659Dic3—81no—
660Dic3—81no—
661C23—21no—
662C23—21no—
663C23—21no—
664C23—21no—
665C23—21no—
666C23—21no—
667C23—62no—
668C23—62no—
669C23—62no—
670C23—121no—
671C23—121no—
672C23—121no—
673C23—121no—
674C23#88412yes—
675C23C2×D3×D411yescharacteristic
676Q8—34no—
677Q8—41no—
678Q8—41no—
679Q8—41no—
680Q8—41no—
681Q8—62no—
682Q8—62no—
683Q8—62no—
684Q8—121no—
685Q8—121no—
686Q8—121no—
687Q8—121no—
688D4—34no—
689D4—616no—
690D4—62no—
691D4—62no—
692D4—62no—
693C2×C4—21no—
694C2×C4—21no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—32no—
702C2×C4—32no—
703C2×C4—41no—
704C2×C4—41no—
705C2×C4—41no—
706C2×C4—41no—
707C2×C4—41no—
708C2×C4—41no—
709C2×C4—41no—
710C2×C4—41no—
711C2×C4—41no—
712C2×C4—41no—
713C2×C4—616no—
714C2×C4—62no—
715C2×C4—62no—
716C2×C4—61no—
717C2×C4—61no—
718C2×C4—61no—
719C2×C4—61no—
720C2×C4—62no—
721C2×C4—61no—
722C2×C4—61no—
723C2×C4—61no—
724C2×C4—61no—
725C2×C4—61no—
726C2×C4—61no—
727C2×C4—84no—
728C2×C4—121no—
729C2×C4—121no—
730C2×C4—121no—
731C2×C4—121no—
732C2×C4—121no—
733C2×C4—121no—
734C2×C4—244no—
735C2×C4—244no—
736C2×C4#88412yes—
737C2×C4C2×#23511yescharacteristic
738C2×C4C2×D3×D411yescharacteristic
739C2×C4C2×D3×D411yescharacteristic
740C2×C4C2×D3×D411yescharacteristic
741C2×C4D3×#4111yescharacteristic
742C2×C4D3×#4111yescharacteristic
743C8—41no—
744C8—41no—
745C8—121no—
746C8—121no—
747C2×C3—42no—
748C2×C3#284711yescharacteristic
749C2×C3#300911yescharacteristic
750C2×C3#301111yescharacteristic
751C2×C3#304611yescharacteristic
752C2×C3#304611yescharacteristic
753C2×C3#312011yescharacteristic
754C2×C3#312011yescharacteristic
755D3—44no—
756C22—22no—
757C22—22no—
758C22—22no—
759C22—41no—
760C22—41no—
761C22—41no—
762C22—41no—
763C22—64no—
764C22—122no—
765C22—122no—
766C22—122no—
767C22—122no—
768C22—122no—
769C22—122no—
770C22C2×#88411yescharacteristic
771C22D3×#12011yescharacteristic
772C22#565611yescharacteristic
773C22#576211yescharacteristic
774C22#576611yescharacteristic
775C22#577511yescharacteristic
776C22#577911yescharacteristic
777C4—22no—
778C4—42no—
779C4—42no—
780C4—62no—
781C4—62no—
782C4—64no—
783C4—81no—
784C4—81no—
785C4—121no—
786C4—121no—
787C4—241no—
788C4—241no—
789C4#554711yescharacteristic
790C4#554711yescharacteristic
791C4D3×#12111yescharacteristic
792C4D3×#12111yescharacteristic
793C3#3291611yescharacteristic, complemented, Sylow
794C2—42no—
795C2—124no—
796C2#7493511yescharacteristic
797C2#7881511yescharacteristic
798C2#7891211yescharacteristic
799C2#8014811yescharacteristic
800C2#8018511yescharacteristic
801C2#8141611yescharacteristic
802C2#8145611yescharacteristic
subgroupG/H
centerC23C2×D3×D4
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC3×#1872C2
socleC23×C3C22×D4
prime radicalC22×#235C22
hypercenter#1872D3
hypocenterC3#32916
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1872

Complements

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

NH ≅ G/Ntype
2. #82786C2semidirect
4. C2×#4795C2semidirect
5. C2×#4818C2semidirect
7. C3×#1872C2semidirect
8. #71559C2semidirect
9. #70281C2semidirect
10. #70276C2semidirect
11. #69909C2semidirect
12. #68908C2semidirect
13. #68905C2semidirect
14. #68896C2semidirect
15. #68893C2semidirect
77. #1872D3semidirect
793. C3#32916semidirect

Maximal subgroups

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

subgroupindex
C2×#55042
#827862
C2×#50472
C2×#47952
C2×#48182
C2×#47332
C3×#18722
#715592
#702812
#702762
#699092
#689082
#689052
#688962
#688932
#329163