Finite Group Databasebeta

← #10830665

Subgroups — #10830665

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×#5550C211yesmaximal, characteristic
2C3×#2536C211yesmaximal, characteristic, complemented
3C2×#5047C211yesmaximal, characteristic, complemented
4C2×#5046C211yesmaximal, characteristic, complemented
5C2×#5028C211yesmaximal, characteristic, complemented
6C2×C4×#215C211yesmaximal, characteristic, complemented
7#71700C211yesmaximal, characteristic, complemented
8#71699C211yesmaximal, characteristic, complemented
9#71614C211yesmaximal, characteristic, complemented
10#69556C211yesmaximal, characteristic, complemented
11#69551C211yesmaximal, characteristic, complemented
12#69526C211yesmaximal, characteristic, complemented
13#69524C211yesmaximal, characteristic, complemented
14#69522C211yesmaximal, characteristic, complemented
15#69521C211yesmaximal, characteristic, complemented
16#24247—31nomaximal, Sylow
17C22×#235C2211yescharacteristic
18C23×D12C2211yescharacteristic
19C2×C3×C22⋊Q8C2211yescharacteristic
20C2×C3×C22⋊Q8C2211yescharacteristic, complemented
21C2×C3×C4×Q8C2211yescharacteristic, complemented
22C2×C3×C4×D4C2211yescharacteristic
23C22×#216C2211yescharacteristic, complemented
24C22×#215C2211yescharacteristic
25C22×#215C2211yescharacteristic
26C2×#937—21no—
27C2×#930C2211yescharacteristic
28C2×#924C2211yescharacteristic
29#5550—24no—
30#5550—24no—
31C2×#894—21no—
32C2×#884—21no—
33C2×D3×C22⋊C4—21no—
34C2×#875C2211yescharacteristic
35C2×C4×D12C2211yescharacteristic
36C3×#398—21no—
37C3×#394—21no—
38C3×#388—21no—
39C3×#388—21no—
40C3×#382C2211yescharacteristic, complemented
41C3×#380C2211yescharacteristic
42C3×#380C2211yescharacteristic, complemented
43C2×#835C2211yescharacteristic, complemented
44C2×#830C2211yescharacteristic
45C2×#830C2211yescharacteristic
46C2×#830C2211yescharacteristic, complemented
47C2×#830C2211yescharacteristic, complemented
48#5047—24no—
49#5046—24no—
50#5028—24no—
51C4×#215—24no—
52C2×#810C2211yescharacteristic, complemented
53C2×#810C2211yescharacteristic, complemented
54C2×#810C2211yescharacteristic, complemented
55C2×#809C2211yescharacteristic
56C2×#809C2211yescharacteristic
57C2×#809C2211yescharacteristic
58C2×#809C2211yescharacteristic
59C2×#809C2211yescharacteristic
60C2×#809C2211yescharacteristic
61C2×#808C2211yescharacteristic, complemented
62C2×C4⋊(C3⋊C8)C2211yescharacteristic, complemented
63C2×C4×C3⋊C8C2211yescharacteristic, complemented
64#4529C2211yescharacteristic, complemented
65#4529C2211yescharacteristic, complemented
66C2×#546—31no—
67C2×#464—31no—
68C2×#452—31no—
69C2×#450—31no—
70C2×C4×SD16—31no—
71#2536D311yescharacteristic, complemented
72#2035—31no—
73#2034—31no—
74#2001—31no—
75#2000—31no—
76#1958—31no—
77#1954—31no—
78#1804—31no—
79#1788—31no—
80#1786—31no—
81C24×D3—21no—
82C22×C3×Q8C2311yescharacteristic
83C22×C3×D4D411yescharacteristic
84C23×C3×C4C2311yescharacteristic
85C23×C3×C4C2311yescharacteristic
86C22×#67—21no—
87C22×#67—21no—
88C2×#235—22no—
89C2×#235—22no—
90C2×#235—22no—
91C2×#235—22no—
92C2×#235—41no—
93C2×#235—41no—
94C22×D12—21no—
95C22×D12—22no—
96C22×D12—22no—
97C22×D12—22no—
98C22×D12—22no—
99C22×D12—41no—
100C22×D12—41no—
101C22×D12C2311yescharacteristic
102C22×D12C2311yescharacteristic
103C22×C4×D3—21no—
104C22×C4×D3—21no—
105C22×Dic6C2311yescharacteristic
106C3×C22⋊Q8—22no—
107C3×C22⋊Q8—22no—
108C3×C22⋊Q8—41no—
109C3×C22⋊Q8—41no—
110C3×C4×Q8—22no—
111C3×C4×Q8—22no—
112C3×C4×D4—22no—
113C3×C4×D4—22no—
114C2×C3×C4⋊C4—21no—
115C2×C3×C4⋊C4—21no—
116C2×C3×C4⋊C4—21no—
117C2×C3×C4⋊C4D411yescharacteristic
118C2×C3×C4⋊C4C2311yescharacteristic
119C2×C3×C4⋊C4C2311yescharacteristic
120C2×C3×C4⋊C4C2311yescharacteristic
121C2×C3×C22⋊C4—21no—
122C2×C3×C22⋊C4—21no—
123C2×C3×C22⋊C4—21no—
124C2×C3×C22⋊C4—21no—
125C2×C3×C22⋊C4D411yescharacteristic
126C2×C3×C22⋊C4D411yescharacteristic
127C2×C3×C42—21no—
128C2×C3×C42C2311yescharacteristic
129C2×#217—21no—
130C2×#216—22no—
131C2×#216—22no—
132C2×#216—41no—
133C2×#215—22no—
134C2×#215—22no—
135C2×#215—22no—
136C2×#215—22no—
137C2×#215—41no—
138C2×#215D414yescomplemented
139#937—28no—
140#930—22no—
141#930—22no—
142C2×(C2×D3)⋊C4—21no—
143C2×(C2×D3)⋊C4—21no—
144C2×(C2×D3)⋊C4—21no—
145C2×(C2×D3)⋊C4—21no—
146C2×C4⋊Dic3C2311yescharacteristic
147#924—22no—
148#924—22no—
149C2×Dic3⋊C4—21no—
150C22×C3⋊C8C2311yescharacteristic
151C22×C3⋊C8C2311yescharacteristic
152C22×C3⋊C8C2311yescharacteristic
153C22×C3⋊C8C2311yescharacteristic
154#894—28no—
155#884—28no—
156D3×C22⋊C4—28no—
157#875—22no—
158#875D414yes—
159C4×D12—22no—
160C4×D12D414yes—
161C3×#95—21no—
162C3×#95—21no—
163C3×#95—21no—
164C3×#95—21no—
165#835—22no—
166#830—22no—
167#830—22no—
168#830—41no—
169#830—41no—
170#810—22no—
171#810—22no—
172#810—41no—
173#809—22no—
174#809—22no—
175#809—22no—
176#809—22no—
177#809—22no—
178#809—41no—
179#808—22no—
180C4⋊(C3⋊C8)—22no—
181C4×C3⋊C8—22no—
182C22×#41—31no—
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⋊Q8C2×D311yescharacteristic
193C2×C22⋊Q8C2×D311yescharacteristic, complemented
194C2×#121—31no—
195C2×#121—61no—
196C2×#120—61no—
197C2×C4×Q8C2×D311yescharacteristic, complemented
198C2×C4×D4—31no—
199C2×C4×D4C2×D311yescharacteristic
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×#103—31no—
210C2×#103—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⋊C8—31no—
221C2×C4×C8—31no—
222#398—21no—
223#394—21no—
224#388—21no—
225#388—21no—
226#382C2×D311yescharacteristic, complemented
227#380C2×D311yescharacteristic
228#380C2×D311yescharacteristic, complemented
229#340—31no—
230#340—31no—
231C24×C3C2×D411yescharacteristic
232C24×C3C2×D411yescharacteristic
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—
242C2×C3×Q8—21no—
243C2×C3×Q8—21no—
244C2×C3×Q8—21no—
245C2×C3×Q8—21no—
246C2×C3×Q8—21no—
247C2×C3×Q8C2×D412yes—
248C2×C3×D4—22no—
249C2×C3×D4—22no—
250C2×C3×D4—41no—
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×C4—21no—
260C22×C3×C4—21no—
261C22×C3×C4—21no—
262C22×C3×C4—21no—
263C22×C3×C4—21no—
264C22×C3×C4—21no—
265C22×C3×C4—21no—
266C22×C3×C4—21no—
267C22×C3×C4C2×D411yescharacteristic
268C22×C3×C4C2×D411yescharacteristic
269C22×C3×C4C2×D411yescharacteristic
270C22×C3×C4C2×D411yescharacteristic
271C22×C3×C4C2411yescharacteristic
272C2×#67—24no—
273C2×#67—24no—
274C2×#67—42no—
275C2×#67—42no—
276C2×#67—81no—
277C2×#67—81no—
278C22×Dic3—21no—
279C22×Dic3—21no—
280#235—44no—
281#235—44no—
282#235—44no—
283#235—44no—
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—21no—
293C2×D12—44no—
294C2×D12—44no—
295C2×D12—44no—
296C2×D12—42no—
297C2×D12—42no—
298C2×D12—44no—
299C2×D12C2×D412yes—
300C2×D12C2×D412yes—
301C2×D12C2×D412yes—
302C2×D12#4112yes—
303C2×C4×D3—24no—
304C2×C4×D3—24no—
305C2×C4×D3—42no—
306C2×C4×D3—42no—
307C2×C4×D3—81no—
308C2×C4×D3—81no—
309C2×Dic6—21no—
310C2×Dic6—21no—
311C2×Dic6—21no—
312C2×Dic6—21no—
313C2×Dic6—21no—
314C2×Dic6C2×D412yes—
315C3×C4⋊C4—22no—
316C3×C4⋊C4—21no—
317C3×C4⋊C4—21no—
318C3×C4⋊C4—21no—
319C3×C4⋊C4—21no—
320C3×C4⋊C4—21no—
321C3×C4⋊C4—21no—
322C3×C4⋊C4—42no—
323C3×C4⋊C4—42no—
324C3×C4⋊C4—42no—
325C3×C22⋊C4—22no—
326C3×C22⋊C4—22no—
327C3×C22⋊C4—42no—
328C3×C22⋊C4—42no—
329C3×C22⋊C4—42no—
330C3×C22⋊C4—42no—
331C3×C42—42no—
332C3×C42C2×D412yes—
333C3×C42C2×D412yes—
334#217—24no—
335#216—44no—
336#215—28no—
337#215—44no—
338(C2×D3)⋊C4—24no—
339(C2×D3)⋊C4—24no—
340(C2×D3)⋊C4—24no—
341(C2×D3)⋊C4—24no—
342C4⋊Dic3—21no—
343C4⋊Dic3C2×D412yes—
344Dic3⋊C4—24no—
345C2×C3⋊C8—21no—
346C2×C3⋊C8—21no—
347C2×C3⋊C8—21no—
348C2×C3⋊C8—21no—
349C2×C3⋊C8—21no—
350C2×C3⋊C8—21no—
351C2×C3⋊C8—21no—
352C2×C3⋊C8—21no—
353C2×C3⋊C8—21no—
354C2×C3⋊C8—21no—
355C2×C3⋊C8—21no—
356C2×C3⋊C8C2×D412yes—
357C25—61no—
358C2×#41—62no—
359C2×#41—62no—
360C2×#41—62no—
361C2×#41—62no—
362C2×#41—121no—
363C2×#41—121no—
364C22×Q8—31no—
365C22×Q8C22×D311yescharacteristic
366C22×D4—31no—
367C22×D4—31no—
368C22×D4—62no—
369C22×D4—62no—
370C22×D4—62no—
371C22×D4—62no—
372C22×D4—61no—
373C22×D4—61no—
374C22×D4—61no—
375C22×D4—121no—
376C22×D4—121no—
377C22×D4#6711yescharacteristic
378C23×C4—61no—
379C23×C4—61no—
380C23×C4C22×D311yescharacteristic
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×C8—31no—
394C22×C8—31no—
395#124—34no—
396#124—62no—
397#123—68no—
398C22⋊Q8—22no—
399C22⋊Q8—22no—
400C22⋊Q8—41no—
401C22⋊Q8—41no—
402C22⋊Q8—62no—
403C22⋊Q8—62no—
404#121—68no—
405#121—62no—
406#121—62no—
407#120—68no—
408C4×Q8—22no—
409C4×Q8—22no—
410C4×D4—22no—
411C4×D4—22no—
412C4×D4—34no—
413C4×D4—62no—
414C2×C4⋊C4—21no—
415C2×C4⋊C4—21no—
416C2×C4⋊C4—21no—
417C2×C4⋊C4—31no—
418C2×C4⋊C4—61no—
419C2×C4⋊C4#6711yescharacteristic
420C2×C4⋊C4C22×D311yescharacteristic
421C2×C4⋊C4C22×D311yescharacteristic
422C2×C4⋊C4C22×D311yescharacteristic
423C2×C22⋊C4—21no—
424C2×C22⋊C4—21no—
425C2×C22⋊C4—21no—
426C2×C22⋊C4—21no—
427C2×C22⋊C4—68no—
428C2×C22⋊C4—61no—
429C2×C22⋊C4—61no—
430C2×C22⋊C4—61no—
431C2×C22⋊C4—61no—
432C2×C22⋊C4—61no—
433C2×C22⋊C4#6711yescharacteristic
434C2×C22⋊C4#6711yescharacteristic
435C2×C42—21no—
436C2×C42C22×D311yescharacteristic
437#106—62no—
438C4⋊C8—62no—
439#103—62no—
440#103—62no—
441#103—62no—
442#103—121no—
443#102—62no—
444#102—62no—
445#102—62no—
446#102—62no—
447#102—62no—
448#102—121no—
449C22⋊C8—62no—
450C22⋊C8—62no—
451C22⋊C8—121no—
452C22⋊C8—121no—
453C4×C8—62no—
454#95—21no—
455#95—21no—
456#95—21no—
457#95—21no—
458C23×C3—21no—
459C23×C3—21no—
460C23×C3—21no—
461C23×C3—21no—
462C23×C3—21no—
463C23×C3—21no—
464C23×C3—21no—
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—22no—
475C22×D3—22no—
476C22×D3—22no—
477C22×D3—48no—
478C22×D3—41no—
479C22×D3—41no—
480C22×D3—41no—
481C22×D3—41no—
482C22×D3—48no—
483C22×D3—41no—
484C22×D3—41no—
485C22×D3—41no—
486C22×D3—41no—
487C22×D3—41no—
488C22×D3—41no—
489C22×D3—84no—
490C22×D3—84no—
491C22×D3—84no—
492C22×D3—84no—
493C22×D3—84no—
494C3×Q8—22no—
495C3×Q8—22no—
496C3×Q8—41no—
497C3×Q8—41no—
498C3×D4—44no—
499C2×C3×C4—21no—
500C2×C3×C4—21no—
501C2×C3×C4—21no—
502C2×C3×C4—21no—
503C2×C3×C4—21no—
504C2×C3×C4—21no—
505C2×C3×C4—22no—
506C2×C3×C4—21no—
507C2×C3×C4—21no—
508C2×C3×C4—21no—
509C2×C3×C4—21no—
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×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#12012yes—
530C2×C3×C4#12012yes—
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—48no—
538#67—84no—
539C2×Dic3—22no—
540C2×Dic3—22no—
541C2×Dic3—41no—
542C2×Dic3—41no—
543C2×Dic3—41no—
544C2×Dic3—41no—
545D12—22no—
546D12—22no—
547D12—22no—
548D12—22no—
549D12—22no—
550D12—48no—
551D12—41no—
552D12—41no—
553D12#12114yes—
554C4×D3—48no—
555C4×D3—84no—
556Dic6—22no—
557Dic6—22no—
558Dic6—41no—
559Dic6—41no—
560C3⋊C8—22no—
561C3⋊C8—41no—
562C3⋊C8—41no—
563C3⋊C8—41no—
564C24—64no—
565C24—61no—
566C24—61no—
567C24—122no—
568C24—122no—
569C24—122no—
570C24—122no—
571C24—241no—
572C24—241no—
573C24C2×#6711yescharacteristic
574C24C2×#6711yescharacteristic
575#41—124no—
576#41—124no—
577#41—124no—
578#41—124no—
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—22no—
592C2×D4—22no—
593C2×D4—32no—
594C2×D4—32no—
595C2×D4—32no—
596C2×D4—32no—
597C2×D4—41no—
598C2×D4—64no—
599C2×D4—64no—
600C2×D4—64no—
601C2×D4—61no—
602C2×D4—61no—
603C2×D4—61no—
604C2×D4—61no—
605C2×D4—61no—
606C2×D4—61no—
607C2×D4—61no—
608C2×D4—61no—
609C2×D4—122no—
610C2×D4—122no—
611C2×D4—124no—
612C2×D4—124no—
613C2×D4—124no—
614C2×D4—124no—
615C2×D4—122no—
616C2×D4—122no—
617C2×D4—241no—
618C2×D4—241no—
619C22×C4—21no—
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—21no—
630C22×C4—21no—
631C22×C4—21no—
632C22×C4—21no—
633C22×C4—21no—
634C22×C4—21no—
635C22×C4—64no—
636C22×C4—61no—
637C22×C4—61no—
638C22×C4—64no—
639C22×C4—122no—
640C22×C4—122no—
641C22×C4—241no—
642C22×C4—241no—
643C22×C4C2×#6711yescharacteristic
644C22×C4C2×#6711yescharacteristic
645C22×C4C2×#6711yescharacteristic
646C22×C4C2×#6711yescharacteristic
647C22×C4C23×D311yescharacteristic
648Q16—124no—
649SD16—68no—
650SD16—124no—
651C2×C8—32no—
652C2×C8—61no—
653C2×C8—61no—
654C2×C8—61no—
655C2×C8—61no—
656C2×C8—61no—
657C2×C8—61no—
658C2×C8—61no—
659C2×C8—61no—
660C2×C8—61no—
661C2×C8—61no—
662C2×C8—61no—
663C4⋊C4—22no—
664C4⋊C4—21no—
665C4⋊C4—21no—
666C4⋊C4—21no—
667C4⋊C4—21no—
668C4⋊C4—21no—
669C4⋊C4—21no—
670C4⋊C4—32no—
671C4⋊C4—42no—
672C4⋊C4—42no—
673C4⋊C4—42no—
674C4⋊C4—64no—
675C4⋊C4—61no—
676C22⋊C4—22no—
677C22⋊C4—22no—
678C22⋊C4—42no—
679C22⋊C4—42no—
680C22⋊C4—42no—
681C22⋊C4—42no—
682C22⋊C4—64no—
683C22⋊C4—64no—
684C22⋊C4—64no—
685C22⋊C4—64no—
686C22⋊C4—64no—
687C42—42no—
688C42D3×D412yes—
689C42D3×D412yes—
690C22×C3—22no—
691C22×C3—22no—
692C22×C3—22no—
693C22×C3—41no—
694C22×C3—41no—
695C22×C3—41no—
696C22×C3—41no—
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—24no—
712C2×D3—42no—
713C2×D3—42no—
714C2×D3—42no—
715C2×D3—42no—
716C2×D3—42no—
717C2×D3—42no—
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—22no—
727C3×C4—22no—
728C3×C4—41no—
729C3×C4—41no—
730C3×C4—42no—
731C3×C4—81no—
732C3×C4—81no—
733C3×C4—81no—
734C3×C4C2×#12111yescharacteristic
735C3×C4#53511yescharacteristic
736C3×C4D4211yescharacteristic
737C3×C4#54611yescharacteristic
738Dic3—42no—
739Dic3—42no—
740C23—21no—
741C23—21no—
742C23—21no—
743C23—21no—
744C23—21no—
745C23—21no—
746C23—21no—
747C23—21no—
748C23—21no—
749C23—21no—
750C23—21no—
751C23—21no—
752C23—21no—
753C23—62no—
754C23—62no—
755C23—62no—
756C23—62no—
757C23—128no—
758C23—128no—
759C23—121no—
760C23—121no—
761C23—121no—
762C23—121no—
763C23—121no—
764C23—121no—
765C23—121no—
766C23—121no—
767C23—121no—
768C23—121no—
769C23—244no—
770C23—244no—
771C23—244no—
772C23—244no—
773C23—244no—
774C23#95012yes—
775C23C22×#6711yescharacteristic
776Q8—22no—
777Q8—22no—
778Q8—41no—
779Q8—41no—
780Q8—62no—
781Q8—62no—
782Q8—121no—
783Q8—121no—
784D4—34no—
785D4—44no—
786D4—62no—
787D4—62no—
788D4—62no—
789D4—62no—
790D4—62no—
791D4—128no—
792D4—128no—
793D4—121no—
794D4—121no—
795D4—244no—
796C2×C4—21no—
797C2×C4—21no—
798C2×C4—21no—
799C2×C4—21no—
800C2×C4—21no—
801C2×C4—21no—
802C2×C4—22no—
803C2×C4—21no—
804C2×C4—21no—
805C2×C4—21no—
806C2×C4—21no—
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—41no—
816C2×C4—41no—
817C2×C4—41no—
818C2×C4—41no—
819C2×C4—41no—
820C2×C4—41no—
821C2×C4—41no—
822C2×C4—41no—
823C2×C4—41no—
824C2×C4—41no—
825C2×C4—41no—
826C2×C4—62no—
827C2×C4—62no—
828C2×C4—128no—
829C2×C4—121no—
830C2×C4—121no—
831C2×C4—121no—
832C2×C4—121no—
833C2×C4—244no—
834C2×C4#93712yes—
835C2×C4#93712yes—
836C2×C4C2×D3×D411yescharacteristic
837C2×C4C2×D3×D411yescharacteristic
838C2×C4C2×D3×D411yescharacteristic
839C2×C4#100411yescharacteristic
840C2×C4D3×#4111yescharacteristic
841C2×C4#100911yescharacteristic
842C8—62no—
843C8—121no—
844C8—121no—
845C8—121no—
846C2×C3—42no—
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—44no—
856D3—82no—
857C22—22no—
858C22—22no—
859C22—22no—
860C22—41no—
861C22—41no—
862C22—41no—
863C22—41no—
864C22—41no—
865C22—41no—
866C22—41no—
867C22—41no—
868C22—41no—
869C22—41no—
870C22—41no—
871C22—64no—
872C22—122no—
873C22—122no—
874C22—122no—
875C22—122no—
876C22—122no—
877C22—122no—
878C22—122no—
879C22—122no—
880C22—122no—
881C22—2416no—
882C22—241no—
883C22—241no—
884C22—241no—
885C22—241no—
886C22C2×#93711yescharacteristic
887C22D4×#6711yescharacteristic
888C22C2×#95011yescharacteristic
889C22#582211yescharacteristic
890C22#582911yescharacteristic
891C22#583711yescharacteristic
892C22#583711yescharacteristic
893C4—22no—
894C4—22no—
895C4—41no—
896C4—41no—
897C4—42no—
898C4—81no—
899C4—81no—
900C4—81no—
901C4—122no—
902C4—122no—
903C4D3×#12111yescharacteristic
904C4#560711yescharacteristic
905C4#560911yescharacteristic
906C4#561211yescharacteristic
907C3#2424711yescharacteristic, complemented, Sylow
908C2—42no—
909C2—81no—
910C2—124no—
911C2—242no—
912C2#8264011yescharacteristic
913C2#8292611yescharacteristic
914C2#8340411yescharacteristic
915C2#8354411yescharacteristic
916C2#8354511yescharacteristic
917C2#8359811yescharacteristic
918C2#8360111yescharacteristic
subgroupG/H
centerC23C22×#67
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC3×#2536C2
socleC23×C3C22×D4
prime radicalC2×#5550C2
hypercenter#2536D3
hypocenterC3#24247
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ #2536

Complements

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

NH ≅ G/Ntype
2. C3×#2536C2semidirect
3. C2×#5047C2semidirect
4. C2×#5046C2semidirect
5. C2×#5028C2semidirect
6. C2×C4×#215C2semidirect
7. #71700C2semidirect
8. #71699C2semidirect
9. #71614C2semidirect
10. #69556C2semidirect
11. #69551C2semidirect
12. #69526C2semidirect
13. #69524C2semidirect
14. #69522C2semidirect
15. #69521C2semidirect
20. C2×C3×C22⋊Q8C22semidirect
21. C2×C3×C4×Q8C22semidirect
23. C22×#216C22semidirect
40. C3×#382C22semidirect
42. C3×#380C22semidirect
43. C2×#835C22semidirect
46. C2×#830C22semidirect
47. C2×#830C22semidirect
52. C2×#810C22semidirect
53. C2×#810C22semidirect
54. C2×#810C22semidirect
61. C2×#808C22semidirect
62. C2×C4⋊(C3⋊C8)C22semidirect
63. C2×C4×C3⋊C8C22semidirect
64. #4529C22semidirect
65. #4529C22semidirect
71. #2536D3semidirect
138. C2×#215D4semidirect
193. C2×C22⋊Q8C2×D3semidirect
197. C2×C4×Q8C2×D3semidirect
226. #382C2×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×#55502
C3×#25362
C2×#50472
C2×#50462
C2×#50282
C2×C4×#2152
#717002
#716992
#716142
#695562
#695512
#695262
#695242
#695222
#695212
#242473