Finite Group Databasebeta

← #10830668

Subgroups — #10830668

Order 768.

1564 conjugacy classes of subgroups.

The subgroup lattice has 920 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#5829C211yesmaximal, characteristic
2C2×#5239C211yesmaximal, characteristic, complemented
3C2×#4798C211yesmaximal, characteristic, complemented
4C2×#4776C211yesmaximal, characteristic, complemented
5C2×#4758C211yesmaximal, characteristic, complemented
6#73934C211yesmaximal, characteristic, complemented
7C3×#1788C211yesmaximal, characteristic, complemented
8#70274C211yesmaximal, characteristic, complemented
9#70273C211yesmaximal, characteristic, complemented
10#70226C211yesmaximal, characteristic, complemented
11#70198C211yesmaximal, characteristic, complemented
12#70154C211yesmaximal, characteristic, complemented
13#69962C211yesmaximal, characteristic, complemented
14#69916C211yesmaximal, characteristic, complemented
15#69524C211yesmaximal, characteristic, complemented
16#24247—31nomaximal, Sylow
17C22×C3×#41C2211yescharacteristic
18C22×D3×D4C2211yescharacteristic
19#5829—24no—
20#5829—24no—
21C2×#947C2211yescharacteristic
22C2×#946C2211yescharacteristic
23C22×#216C2211yescharacteristic, complemented
24C2×#939—21no—
25C2×#937—21no—
26C2×D4×Dic3C2211yescharacteristic
27C22×#214C2211yescharacteristic
28C2×#930C2211yescharacteristic
29C2×#929—21no—
30C2×C4×#67C2211yescharacteristic
31C22×(C2×D3)⋊C4—21no—
32C2×#924C2211yescharacteristic, complemented
33C22×#204C2211yescharacteristic
34C2×#897C2211yescharacteristic
35C2×#887C2211yescharacteristic, complemented
36C2×C3×#103C2211yescharacteristic, complemented
37C2×C3×#103C2211yescharacteristic, complemented
38C2×C3×#102C2211yescharacteristic
39C2×C3×#102C2211yescharacteristic
40C2×C3×C22⋊C8C2211yescharacteristic, complemented
41C3×#380C2211yescharacteristic, complemented
42#5239—24no—
43C2×#835C2211yescharacteristic, complemented
44C2×#832C2211yescharacteristic
45C2×#830C2211yescharacteristic, complemented
46C2×#821C2211yescharacteristic
47C2×(C2×D3)⋊C8C2211yescharacteristic
48C2×(C2×D3)⋊C8C2211yescharacteristic
49C2×#816C2211yescharacteristic, complemented
50C2×Dic3⋊C8C2211yescharacteristic, complemented
51C2×C8×Dic3C2211yescharacteristic, complemented
52#4987C2211yescharacteristic
53#4977C2211yescharacteristic, complemented
54C2×#809C2211yescharacteristic
55C2×#809C2211yescharacteristic
56C2×#808C2211yescharacteristic, complemented
57#4959—21no—
58#4951—21no—
59#4798—24no—
60#4776—24no—
61#4758—24no—
62#4669—21no—
63#4657—21no—
64#4551C2211yescharacteristic, complemented
65#4529C2211yescharacteristic, complemented
66C2×#546—31no—
67C2×#464—31no—
68C2×#452—31no—
69C2×#450—31no—
70C2×C4×SD16—31no—
71#2536—31no—
72#2035—31no—
73#2034—31no—
74#2001—31no—
75#2000—31no—
76#1958—31no—
77#1954—31no—
78#1804—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×#67—21no—
95C22×#67D411yescharacteristic
96C23×Dic3—21no—
97C2×D3×D4—22no—
98C2×D3×D4—22no—
99C2×D3×D4—22no—
100C2×D3×D4—22no—
101C2×D3×D4—41no—
102C2×D3×D4—41no—
103C22×D12C2311yescharacteristic
104C22×C4×D3C2311yescharacteristic
105C22×Dic6C2311yescharacteristic
106C22×C3×C8C2311yescharacteristic
107C22×C3×C8C2311yescharacteristic
108C2×C3×C4⋊C4C2311yescharacteristic
109C2×C3×C4⋊C4C2311yescharacteristic
110C2×C3×C22⋊C4—21no—
111C2×#217—21no—
112C2×#217—21no—
113C2×#217D411yescharacteristic
114#947—22no—
115#947D414yes—
116#946—22no—
117#946—22no—
118C2×#216—22no—
119C2×#216—22no—
120C2×#216—41no—
121#939—28no—
122#937—28no—
123D4×Dic3—22no—
124D4×Dic3D414yes—
125C2×#214—22no—
126C2×#214—22no—
127C2×#214D414yescomplemented
128#930—22no—
129#930—22no—
130#929—28no—
131C4×#67—22no—
132C4×#67—22no—
133C2×(C2×D3)⋊C4—28no—
134C2×(C2×D3)⋊C4—21no—
135C2×(C2×D3)⋊C4—21no—
136C2×(C2×D3)⋊C4—21no—
137C2×(C2×D3)⋊C4—21no—
138C2×(C2×D3)⋊C4—21no—
139C2×(C2×D3)⋊C4—21no—
140C2×(C2×D3)⋊C4D411yescharacteristic
141C2×C4⋊Dic3—21no—
142C2×C4⋊Dic3C2311yescharacteristic
143C2×C4⋊Dic3C2311yescharacteristic
144#924—22no—
145#924—41no—
146C2×Dic3⋊C4—21no—
147C2×Dic3⋊C4—21no—
148C2×Dic3⋊C4—21no—
149C2×Dic3⋊C4D411yescharacteristic
150C2×C4×Dic3—21no—
151C2×C4×Dic3C2311yescharacteristic
152C22×C3⋊C8C2311yescharacteristic
153C22×C3⋊C8C2311yescharacteristic
154C2×#204—22no—
155C2×#204—22no—
156C2×#204—41no—
157#897—22no—
158#897—41no—
159#887—22no—
160#887—22no—
161C3×#103—22no—
162C3×#103—41no—
163C3×#102—22no—
164C3×#102—22no—
165C3×C22⋊C8—41no—
166C3×#95—21no—
167#835—22no—
168#832—22no—
169C3⋊#95—21no—
170C3⋊#95—21no—
171C3⋊#95—21no—
172#830—22no—
173#821—41no—
174(C2×D3)⋊C8—22no—
175(C2×D3)⋊C8—41no—
176#816—22no—
177Dic3⋊C8—22no—
178C8×Dic3—22no—
179#809—22no—
180#809—22no—
181#808—22no—
182C22×#41C2×D311yescharacteristic
183C23×D4—31no—
184C22×Q16—31no—
185C22×SD16—31no—
186C22×SD16—31no—
187#546—64no—
188#546—64no—
189C2×#124—31no—
190C2×#123—61no—
191C2×C22⋊Q8—31no—
192C2×C22⋊Q8—31no—
193C2×C22⋊Q8—31no—
194C2×#121—31no—
195C2×#121—61no—
196C2×#120—61no—
197C2×C4×Q8—31no—
198C2×C4×D4—31no—
199C2×C4×D4—31no—
200C22×C22⋊C4—61no—
201#464—64no—
202#452—64no—
203#450—64no—
204C4×SD16—64no—
205C2×#106—31no—
206C2×C4⋊C8—31no—
207C2×#103—31no—
208C2×#103—31no—
209C2×#103C2×D311yescharacteristic, complemented
210C2×#103C2×D311yescharacteristic, complemented
211C2×#102—31no—
212C2×#102—31no—
213C2×#102—31no—
214C2×#102—31no—
215C2×#102C2×D311yescharacteristic
216C2×#102C2×D311yescharacteristic
217C2×C22⋊C8—31no—
218C2×C22⋊C8—31no—
219C2×C22⋊C8—31no—
220C2×C22⋊C8C2×D311yescharacteristic, complemented
221C2×C4×C8—31no—
222#398—61no—
223#394—61no—
224#388—61no—
225#388—61no—
226#382—31no—
227#380—31no—
228#380C2×D311yescharacteristic, complemented
229#340—31no—
230#340—31no—
231C24×C3—21no—
232C24×C3C2×D411yescharacteristic
233C23×D3—21no—
234C23×D3—24no—
235C23×D3—42no—
236C23×D3—42no—
237C23×D3—42no—
238C23×D3—42no—
239C23×D3—81no—
240C23×D3—81no—
241C23×D3C2×D411yescharacteristic
242C3×#41—44no—
243C3×#41—44no—
244C3×#41—44no—
245C3×#41—44no—
246C2×C3×Q8—21no—
247C2×C3×Q8—21no—
248C2×C3×Q8—21no—
249C2×C3×Q8—21no—
250C2×C3×Q8—21no—
251C2×C3×Q8C2×D412yes—
252C2×C3×D4—24no—
253C2×C3×D4—21no—
254C2×C3×D4—21no—
255C2×C3×D4—21no—
256C2×C3×D4—42no—
257C2×C3×D4—42no—
258C2×C3×D4C2×D412yes—
259C2×C3×D4C2×D412yes—
260C2×C3×D4#4112yes—
261C22×C3×C4—24no—
262C22×C3×C4—21no—
263C22×C3×C4—21no—
264C22×C3×C4—21no—
265C22×C3×C4—21no—
266C22×C3×C4—21no—
267C22×C3×C4—21no—
268C22×C3×C4—21no—
269C22×C3×C4—21no—
270C22×C3×C4—21no—
271C22×C3×C4—42no—
272C22×C3×C4—42no—
273C22×C3×C4C2×D411yescharacteristic
274C22×C3×C4C2411yescharacteristic
275C2×#67—24no—
276C2×#67—22no—
277C2×#67—24no—
278C2×#67—22no—
279C2×#67—41no—
280C2×#67—42no—
281C2×#67—42no—
282C2×#67—81no—
283C2×#67—81no—
284C22×Dic3—21no—
285C22×Dic3—21no—
286C22×Dic3—24no—
287C22×Dic3—21no—
288C22×Dic3—81no—
289C22×Dic3—81no—
290C22×Dic3C2×D411yescharacteristic
291C22×Dic3C2×D411yescharacteristic
292C22×Dic3C2×D411yescharacteristic
293D3×D4—44no—
294D3×D4—44no—
295D3×D4—44no—
296D3×D4—44no—
297C2×D12—21no—
298C2×D12—21no—
299C2×D12—21no—
300C2×D12—21no—
301C2×D12—21no—
302C2×D12C2×D412yes—
303C2×C4×D3—21no—
304C2×C4×D3—21no—
305C2×C4×D3—21no—
306C2×C4×D3—21no—
307C2×C4×D3—21no—
308C2×C4×D3—21no—
309C2×Dic6—21no—
310C2×Dic6—21no—
311C2×Dic6—21no—
312C2×Dic6—21no—
313C2×Dic6—21no—
314C2×Dic6C2×D412yes—
315C2×C3×C8—21no—
316C2×C3×C8—21no—
317C2×C3×C8—21no—
318C2×C3×C8—21no—
319C2×C3×C8—21no—
320C2×C3×C8—21no—
321C3×C4⋊C4—21no—
322C3×C4⋊C4—21no—
323C3×C4⋊C4—21no—
324C3×C4⋊C4—21no—
325C3×C22⋊C4—42no—
326#217—22no—
327#217—24no—
328#217—42no—
329#216—44no—
330#214—28no—
331(C2×D3)⋊C4—24no—
332(C2×D3)⋊C4—24no—
333(C2×D3)⋊C4—22no—
334(C2×D3)⋊C4—24no—
335(C2×D3)⋊C4—24no—
336(C2×D3)⋊C4—42no—
337(C2×D3)⋊C4—42no—
338C4⋊Dic3—21no—
339C4⋊Dic3—21no—
340C4⋊Dic3—21no—
341C4⋊Dic3—42no—
342C4⋊Dic3C2×D412yes—
343Dic3⋊C4—24no—
344Dic3⋊C4—22no—
345Dic3⋊C4—42no—
346Dic3⋊C4—42no—
347C4×Dic3—42no—
348C4×Dic3C2×D412yes—
349C4×Dic3C2×D412yes—
350C2×C3⋊C8—21no—
351C2×C3⋊C8—21no—
352C2×C3⋊C8—21no—
353C2×C3⋊C8—21no—
354C2×C3⋊C8—21no—
355C2×C3⋊C8C2×D412yes—
356#204—44no—
357C25—61no—
358C2×#41—22no—
359C2×#41—22no—
360C2×#41—22no—
361C2×#41—22no—
362C2×#41—41no—
363C2×#41—41no—
364C22×Q8—31no—
365C22×Q8C22×D311yescharacteristic
366C22×D4—21no—
367C22×D4—31no—
368C22×D4—31no—
369C22×D4—61no—
370C22×D4—62no—
371C22×D4—61no—
372C22×D4—62no—
373C22×D4—62no—
374C22×D4—62no—
375C22×D4—121no—
376C22×D4—121no—
377C22×D4C22×D311yescharacteristic
378C23×C4—21no—
379C23×C4—31no—
380C23×C4—61no—
381C23×C4C22×D311yescharacteristic
382C2×Q16—62no—
383C2×Q16—62no—
384C2×Q16—121no—
385C2×SD16—34no—
386C2×SD16—62no—
387C2×SD16—62no—
388C2×SD16—62no—
389C2×SD16—62no—
390C2×SD16—121no—
391C22×C8—31no—
392C22×C8—31no—
393C22×C8C22×D311yescharacteristic
394C22×C8C22×D311yescharacteristic
395#124—34no—
396#124—62no—
397#123—68no—
398C22⋊Q8—62no—
399C22⋊Q8—62no—
400C22⋊Q8—62no—
401C22⋊Q8—62no—
402C22⋊Q8—121no—
403C22⋊Q8—121no—
404#121—62no—
405#121—62no—
406#121—68no—
407#120—68no—
408C4×Q8—62no—
409C4×Q8—62no—
410C4×D4—34no—
411C4×D4—62no—
412C4×D4—62no—
413C4×D4—62no—
414C2×C4⋊C4—31no—
415C2×C4⋊C4—31no—
416C2×C4⋊C4—31no—
417C2×C4⋊C4—61no—
418C2×C4⋊C4—61no—
419C2×C4⋊C4—61no—
420C2×C4⋊C4—61no—
421C2×C4⋊C4C22×D311yescharacteristic
422C2×C4⋊C4C22×D311yescharacteristic
423C2×C22⋊C4—21no—
424C2×C22⋊C4—31no—
425C2×C22⋊C4—31no—
426C2×C22⋊C4—61no—
427C2×C22⋊C4—61no—
428C2×C22⋊C4—61no—
429C2×C22⋊C4—68no—
430C2×C22⋊C4—61no—
431C2×C22⋊C4—61no—
432C2×C22⋊C4—61no—
433C2×C22⋊C4—61no—
434C2×C22⋊C4—61no—
435C2×C42—31no—
436C2×C42—61no—
437#106—62no—
438C4⋊C8—62no—
439#103—22no—
440#103—41no—
441#103—62no—
442#103—62no—
443#102—22no—
444#102—22no—
445#102—62no—
446#102—62no—
447#102—62no—
448#102—121no—
449C22⋊C8—41no—
450C22⋊C8—62no—
451C22⋊C8—62no—
452C22⋊C8—121no—
453C4×C8—62no—
454#95—21no—
455#95—61no—
456#95—61no—
457#95—61no—
458C23×C3—22no—
459C23×C3—22no—
460C23×C3—22no—
461C23×C3—21no—
462C23×C3—21no—
463C23×C3—21no—
464C23×C3—21no—
465C23×C3—21no—
466C23×C3—21no—
467C23×C3—21no—
468C23×C3—41no—
469C23×C3—41no—
470C23×C3—41no—
471C23×C3—41no—
472C23×C3C22×D411yescharacteristic
473C22×D3—21no—
474C22×D3—21no—
475C22×D3—21no—
476C22×D3—21no—
477C22×D3—21no—
478C22×D3—21no—
479C22×D3—22no—
480C22×D3—48no—
481C22×D3—48no—
482C22×D3—41no—
483C22×D3—41no—
484C22×D3—41no—
485C22×D3—41no—
486C22×D3—41no—
487C22×D3—41no—
488C22×D3—84no—
489C22×D3—84no—
490C22×D3—84no—
491C22×D3—84no—
492C22×D3—84no—
493C22×D3#13512yes—
494C3×Q8—22no—
495C3×Q8—22no—
496C3×Q8—41no—
497C3×Q8—41no—
498C3×D4—22no—
499C3×D4—22no—
500C3×D4—22no—
501C3×D4—48no—
502C3×D4#12114yes—
503C2×C3×C4—21no—
504C2×C3×C4—22no—
505C2×C3×C4—21no—
506C2×C3×C4—21no—
507C2×C3×C4—48no—
508C2×C3×C4—41no—
509C2×C3×C4—41no—
510C2×C3×C4—41no—
511C2×C3×C4—41no—
512C2×C3×C4—41no—
513C2×C3×C4—41no—
514C2×C3×C4—41no—
515C2×C3×C4—41no—
516C2×C3×C4—41no—
517C2×C3×C4—41no—
518C2×C3×C4—41no—
519C2×C3×C4—41no—
520C2×C3×C4C22×D411yescharacteristic
521C2×C3×C4C22×D411yescharacteristic
522C2×C3×C4C22×D411yescharacteristic
523C2×C3×C4C2×#4111yescharacteristic
524C2×C3×C4H(5,𝔽2)11yescharacteristic
525C2×C3×C4H(5,𝔽2)11yescharacteristic
526#67—44no—
527#67—48no—
528#67—84no—
529C2×Dic3—21no—
530C2×Dic3—21no—
531C2×Dic3—21no—
532C2×Dic3—21no—
533C2×Dic3—21no—
534C2×Dic3—22no—
535C2×Dic3—22no—
536C2×Dic3—21no—
537C2×Dic3—21no—
538C2×Dic3—41no—
539C2×Dic3—41no—
540C2×Dic3—41no—
541C2×Dic3—41no—
542C2×Dic3—41no—
543C2×Dic3—41no—
544C2×Dic3—41no—
545C2×Dic3—84no—
546C2×Dic3#12012yes—
547C2×Dic3#12012yes—
548D12—22no—
549D12—22no—
550D12—41no—
551D12—41no—
552C4×D3—41no—
553C4×D3—41no—
554C4×D3—41no—
555C4×D3—41no—
556Dic6—22no—
557Dic6—22no—
558Dic6—41no—
559Dic6—41no—
560C3×C8—41no—
561C3×C8—41no—
562C3⋊C8—22no—
563C3⋊C8—41no—
564C24—21no—
565C24—31no—
566C24—64no—
567C24—61no—
568C24—122no—
569C24—122no—
570C24—122no—
571C24—122no—
572C24—241no—
573C24—241no—
574C24D3×D411yescharacteristic
575#41—44no—
576#41—44no—
577#41—44no—
578#41—44no—
579C2×Q8—21no—
580C2×Q8—21no—
581C2×Q8—21no—
582C2×Q8—21no—
583C2×Q8—21no—
584C2×Q8—32no—
585C2×Q8—61no—
586C2×Q8—61no—
587C2×Q8—61no—
588C2×Q8—61no—
589C2×Q8—61no—
590C2×Q8D3×D412yes—
591C2×D4—24no—
592C2×D4—21no—
593C2×D4—21no—
594C2×D4—21no—
595C2×D4—32no—
596C2×D4—42no—
597C2×D4—42no—
598C2×D4—62no—
599C2×D4—62no—
600C2×D4—64no—
601C2×D4—64no—
602C2×D4—61no—
603C2×D4—61no—
604C2×D4—61no—
605C2×D4—61no—
606C2×D4—61no—
607C2×D4—121no—
608C2×D4—122no—
609C2×D4—122no—
610C2×D4—124no—
611C2×D4—124no—
612C2×D4—124no—
613C2×D4—124no—
614C2×D4—241no—
615C2×D4—241no—
616C2×D4#23512yes—
617C2×D4D3×D412yes—
618C2×D4D3×D412yes—
619C22×C4—24no—
620C22×C4—21no—
621C22×C4—21no—
622C22×C4—21no—
623C22×C4—21no—
624C22×C4—21no—
625C22×C4—21no—
626C22×C4—21no—
627C22×C4—21no—
628C22×C4—21no—
629C22×C4—31no—
630C22×C4—31no—
631C22×C4—31no—
632C22×C4—42no—
633C22×C4—42no—
634C22×C4—64no—
635C22×C4—61no—
636C22×C4—61no—
637C22×C4—61no—
638C22×C4—61no—
639C22×C4—61no—
640C22×C4—61no—
641C22×C4—61no—
642C22×C4—61no—
643C22×C4—61no—
644C22×C4—241no—
645C22×C4—241no—
646C22×C4D3×D411yescharacteristic
647C22×C4C23×D311yescharacteristic
648Q16—124no—
649SD16—68no—
650SD16—124no—
651C2×C8—21no—
652C2×C8—21no—
653C2×C8—21no—
654C2×C8—21no—
655C2×C8—21no—
656C2×C8—21no—
657C2×C8—32no—
658C2×C8—61no—
659C2×C8—61no—
660C2×C8—61no—
661C2×C8—61no—
662C2×C8—61no—
663C4⋊C4—21no—
664C4⋊C4—21no—
665C4⋊C4—21no—
666C4⋊C4—21no—
667C4⋊C4—32no—
668C4⋊C4—62no—
669C4⋊C4—64no—
670C4⋊C4—61no—
671C4⋊C4—61no—
672C4⋊C4—61no—
673C4⋊C4—122no—
674C4⋊C4—122no—
675C4⋊C4—122no—
676C22⋊C4—42no—
677C22⋊C4—62no—
678C22⋊C4—64no—
679C22⋊C4—64no—
680C22⋊C4—64no—
681C22⋊C4—64no—
682C22⋊C4—62no—
683C22⋊C4—64no—
684C22⋊C4—122no—
685C22⋊C4—122no—
686C22⋊C4—122no—
687C42—32no—
688C42—32no—
689C42—122no—
690C22×C3—24no—
691C22×C3—42no—
692C22×C3—42no—
693C22×C3—42no—
694C22×C3—42no—
695C22×C3—42no—
696C22×C3—42no—
697C22×C3—41no—
698C22×C3—41no—
699C22×C3—41no—
700C22×C3—41no—
701C22×C3—41no—
702C22×C3—41no—
703C22×C3—41no—
704C22×C3C2×#12011yescharacteristic
705C22×C3D4211yescharacteristic
706C22×C3#54611yescharacteristic
707C22×C3C2×#13511yescharacteristic
708C22×C3#57511yescharacteristic
709C22×C3#57711yescharacteristic
710C22×C3#57711yescharacteristic
711C2×D3—22no—
712C2×D3—22no—
713C2×D3—22no—
714C2×D3—41no—
715C2×D3—41no—
716C2×D3—41no—
717C2×D3—41no—
718C2×D3—42no—
719C2×D3—42no—
720C2×D3—42no—
721C2×D3—816no—
722C2×D3—81no—
723C2×D3—81no—
724C2×D3—81no—
725C2×D3—81no—
726C3×C4—41no—
727C3×C4—42no—
728C3×C4—81no—
729C3×C4—81no—
730C3×C4C2×#12111yescharacteristic
731C3×C4#53511yescharacteristic
732C3×C4D4211yescharacteristic
733C3×C4#54611yescharacteristic
734Dic3—22no—
735Dic3—22no—
736Dic3—42no—
737Dic3—41no—
738Dic3—42no—
739Dic3—81no—
740C23—22no—
741C23—22no—
742C23—22no—
743C23—21no—
744C23—21no—
745C23—21no—
746C23—21no—
747C23—21no—
748C23—21no—
749C23—21no—
750C23—32no—
751C23—41no—
752C23—41no—
753C23—41no—
754C23—41no—
755C23—61no—
756C23—61no—
757C23—61no—
758C23—61no—
759C23—61no—
760C23—61no—
761C23—62no—
762C23—128no—
763C23—128no—
764C23—121no—
765C23—121no—
766C23—121no—
767C23—121no—
768C23—121no—
769C23—121no—
770C23—244no—
771C23—244no—
772C23—244no—
773C23—244no—
774C23—244no—
775C23C2×D3×D411yescharacteristic
776Q8—22no—
777Q8—22no—
778Q8—41no—
779Q8—41no—
780Q8—62no—
781Q8—62no—
782Q8—121no—
783Q8—121no—
784D4—22no—
785D4—22no—
786D4—22no—
787D4—48no—
788D4—62no—
789D4—62no—
790D4—124no—
791D4—128no—
792D4—121no—
793D4—121no—
794D4—244no—
795D4#88414yes—
796C2×C4—21no—
797C2×C4—21no—
798C2×C4—22no—
799C2×C4—21no—
800C2×C4—32no—
801C2×C4—32no—
802C2×C4—48no—
803C2×C4—41no—
804C2×C4—41no—
805C2×C4—41no—
806C2×C4—41no—
807C2×C4—41no—
808C2×C4—41no—
809C2×C4—41no—
810C2×C4—41no—
811C2×C4—41no—
812C2×C4—41no—
813C2×C4—41no—
814C2×C4—41no—
815C2×C4—61no—
816C2×C4—61no—
817C2×C4—61no—
818C2×C4—61no—
819C2×C4—61no—
820C2×C4—62no—
821C2×C4—61no—
822C2×C4—62no—
823C2×C4—61no—
824C2×C4—121no—
825C2×C4—121no—
826C2×C4—121no—
827C2×C4—121no—
828C2×C4—121no—
829C2×C4—121no—
830C2×C4—121no—
831C2×C4—121no—
832C2×C4—121no—
833C2×C4—121no—
834C2×C4—121no—
835C2×C4—244no—
836C2×C4C2×#23511yescharacteristic
837C2×C4C2×D3×D411yescharacteristic
838C2×C4C2×D3×D411yescharacteristic
839C2×C4C2×D3×D411yescharacteristic
840C2×C4#100411yescharacteristic
841C2×C4#100411yescharacteristic
842C8—41no—
843C8—41no—
844C8—62no—
845C8—121no—
846C2×C3—44no—
847C2×C3—81no—
848C2×C3#240811yescharacteristic
849C2×C3#300211yescharacteristic
850C2×C3#300911yescharacteristic
851C2×C3#327511yescharacteristic
852C2×C3#328211yescharacteristic
853C2×C3#329611yescharacteristic
854C2×C3#332311yescharacteristic
855D3—42no—
856D3—82no—
857C22—24no—
858C22—42no—
859C22—42no—
860C22—42no—
861C22—42no—
862C22—42no—
863C22—42no—
864C22—41no—
865C22—41no—
866C22—41no—
867C22—41no—
868C22—41no—
869C22—41no—
870C22—41no—
871C22—62no—
872C22—62no—
873C22—62no—
874C22—121no—
875C22—121no—
876C22—121no—
877C22—121no—
878C22—122no—
879C22—122no—
880C22—122no—
881C22—2416no—
882C22—241no—
883C22—241no—
884C22—241no—
885C22—241no—
886C22#549011yescharacteristic
887C22D3×#12011yescharacteristic
888C22#559011yescharacteristic
889C22D3×#13511yescharacteristic
890C22#577011yescharacteristic
891C22#577311yescharacteristic
892C22#577811yescharacteristic
893C4—41no—
894C4—42no—
895C4—62no—
896C4—62no—
897C4—81no—
898C4—81no—
899C4—121no—
900C4—122no—
901C4—122no—
902C4—241no—
903C4C2×#88411yescharacteristic
904C4#549011yescharacteristic
905C4#559011yescharacteristic
906C4#559211yescharacteristic
907C3#2424711yescharacteristic, complemented, Sylow
908C2—44no—
909C2—81no—
910C2—122no—
911C2—242no—
912C2#7382411yescharacteristic
913C2#7884511yescharacteristic
914C2#7890311yescharacteristic
915C2#8008211yescharacteristic
916C2#8009911yescharacteristic
917C2#8022911yescharacteristic
918C2#8024411yescharacteristic
subgroupG/H
centerC23C2×D3×D4
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC3×#1788C2
socleC23×C3C22×D4
prime radicalC2×#5829C2
hypercenter#1788D3
hypocenterC3#24247
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
2. C2×#5239C2semidirect
3. C2×#4798C2semidirect
4. C2×#4776C2semidirect
5. C2×#4758C2semidirect
6. #73934C2semidirect
7. C3×#1788C2semidirect
8. #70274C2semidirect
9. #70273C2semidirect
10. #70226C2semidirect
11. #70198C2semidirect
12. #70154C2semidirect
13. #69962C2semidirect
14. #69916C2semidirect
15. #69524C2semidirect
23. C22×#216C22semidirect
32. C2×#924C22semidirect
35. C2×#887C22semidirect
36. C2×C3×#103C22semidirect
37. C2×C3×#103C22semidirect
40. C2×C3×C22⋊C8C22semidirect
41. C3×#380C22semidirect
43. C2×#835C22semidirect
45. C2×#830C22semidirect
49. C2×#816C22semidirect
50. C2×Dic3⋊C8C22semidirect
51. C2×C8×Dic3C22semidirect
53. #4977C22semidirect
56. C2×#808C22semidirect
64. #4551C22semidirect
65. #4529C22semidirect
79. #1788D3semidirect
127. C2×#214D4semidirect
209. C2×#103C2×D3semidirect
210. C2×#103C2×D3semidirect
220. C2×C22⋊C8C2×D3semidirect
228. #380C2×D3semidirect
907. C3#24247semidirect

Maximal subgroups

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

subgroupindex
C2×#58292
C2×#52392
C2×#47982
C2×#47762
C2×#47582
#739342
C3×#17882
#702742
#702732
#702262
#701982
#701542
#699622
#699162
#695242
#242473