Finite Group Databasebeta

← #10830658

Subgroups — #10830658

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×#5806C211yesmaximal, characteristic
2C2×C3×#450C211yesmaximal, characteristic, complemented
3C2×#5173C211yesmaximal, characteristic, complemented
4C2×#5166C211yesmaximal, characteristic, complemented
5C2×Dic3×SD16C211yesmaximal, characteristic, complemented
6#82777C211yesmaximal, characteristic, complemented
7#72128C211yesmaximal, characteristic, complemented
8#72054C211yesmaximal, characteristic, complemented
9#71700C211yesmaximal, characteristic, complemented
10#70199C211yesmaximal, characteristic, complemented
11#70176C211yesmaximal, characteristic, complemented
12#70158C211yesmaximal, characteristic, complemented
13#70154C211yesmaximal, characteristic, complemented
14#69936C211yesmaximal, characteristic, complemented
15#69916C211yesmaximal, characteristic, complemented
16#24247—31nomaximal, Sylow
17C23×C3×D4C2211yescharacteristic
18C22×#237C2211yescharacteristic
19C22×C3×SD16C2211yescharacteristic
20C22×C3×SD16C2211yescharacteristic
21C2×C3×C22⋊Q8C2211yescharacteristic
22C2×#953—21no—
23C22×#217—21no—
24C2×#946C2211yescharacteristic, complemented
25C2×Q8×Dic3C2211yescharacteristic, complemented
26C22×#216C2211yescharacteristic, complemented
27#5806—24no—
28#5806—24no—
29C2×#939—21no—
30C2×#938C2211yescharacteristic
31C2×#936C2211yescharacteristic
32C2×#935—21no—
33C2×D4×Dic3C2211yescharacteristic
34C2×C4×#67C2211yescharacteristic
35C2×#924C2211yescharacteristic
36C3×#450—24no—
37C2×C3×#102C2211yescharacteristic
38C2×C3×#102C2211yescharacteristic
39C2×C3×C22⋊C8C2211yescharacteristic
40C2×#835C2211yescharacteristic, complemented
41C2×#832C2211yescharacteristic
42C2×#832C2211yescharacteristic
43C2×#832C2211yescharacteristic
44C2×#832C2211yescharacteristic
45#5212C2211yescharacteristic
46C2×#830C2211yescharacteristic
47#5173—24no—
48#5166—24no—
49Dic3×SD16—24no—
50C2×(C2×D3)⋊C8C2211yescharacteristic, complemented
51C2×(C2×D3)⋊C8C2211yescharacteristic, complemented
52C2×#817C2211yescharacteristic, complemented
53C2×#816C2211yescharacteristic, complemented
54C2×#816C2211yescharacteristic, complemented
55C2×Dic3⋊C8C2211yescharacteristic, complemented
56C2×C8×Dic3C2211yescharacteristic, complemented
57#4990—21no—
58#4987C2211yescharacteristic, complemented
59#4982—21no—
60#4977C2211yescharacteristic, complemented
61C2×#810C2211yescharacteristic, complemented
62#4961—21no—
63#4945—21no—
64#4551C2211yescharacteristic, complemented
65#4529C2211yescharacteristic, complemented
66C2×#546—31no—
67C2×#464—31no—
68C2×#452—31no—
69C2×#450D311yescharacteristic, complemented
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#1788—31no—
80#1786—31no—
81C25×C3—21no—
82C22×C3×Q8C2311yescharacteristic
83C22×C3×D4—22no—
84C22×C3×D4—22no—
85C22×C3×D4—22no—
86C22×C3×D4—22no—
87C22×C3×D4—21no—
88C22×C3×D4—41no—
89C22×C3×D4—41no—
90C22×C3×D4C2311yescharacteristic
91C22×C3×D4C2311yescharacteristic
92C23×C3×C4C2311yescharacteristic
93C22×#67—21no—
94C22×#67—21no—
95C22×#67D411yescharacteristic
96C23×Dic3—21no—
97C23×Dic3—21no—
98C2×#237—22no—
99C2×#237—22no—
100C2×#237—22no—
101C2×#237—22no—
102C2×#237—41no—
103C2×#237—41no—
104C22×C4×D3C2311yescharacteristic
105C22×Dic6C2311yescharacteristic
106C2×C3×SD16—22no—
107C2×C3×SD16—22no—
108C2×C3×SD16—22no—
109C2×C3×SD16—22no—
110C2×C3×SD16—41no—
111C2×C3×SD16D414yescomplemented
112C22×C3×C8C2311yescharacteristic
113C22×C3×C8C2311yescharacteristic
114C3×C22⋊Q8—22no—
115C3×C22⋊Q8—41no—
116C2×C3×C4⋊C4—21no—
117C2×C3×C4⋊C4C2311yescharacteristic
118C2×C3×C22⋊C4—21no—
119#953—28no—
120C2×#217—28no—
121C2×#217—21no—
122C2×#217—21no—
123C2×#217—21no—
124C2×#217—21no—
125C2×#217—21no—
126C2×#217—21no—
127C2×#217D411yescharacteristic
128#946—22no—
129#946—41no—
130Q8×Dic3—22no—
131Q8×Dic3—22no—
132C2×#216—22no—
133C2×#216—22no—
134C2×#216—41no—
135#939—28no—
136#938—22no—
137#938—22no—
138#936—22no—
139#936D414yes—
140#935—28no—
141D4×Dic3—22no—
142D4×Dic3D414yes—
143C4×#67—22no—
144C4×#67—22no—
145C2×(C2×D3)⋊C4—21no—
146C2×(C2×D3)⋊C4—21no—
147C2×(C2×D3)⋊C4D411yescharacteristic
148C2×C4⋊Dic3—21no—
149C2×C4⋊Dic3C2311yescharacteristic
150C2×C4⋊Dic3C2311yescharacteristic
151C2×C4⋊Dic3C2311yescharacteristic
152#924—22no—
153#924—22no—
154C2×Dic3⋊C4—21no—
155C2×Dic3⋊C4—21no—
156C2×Dic3⋊C4D411yescharacteristic
157C2×C4×Dic3—21no—
158C2×C4×Dic3C2311yescharacteristic
159C22×C3⋊C8C2311yescharacteristic
160C22×C3⋊C8C2311yescharacteristic
161C3×#102—22no—
162C3×#102—22no—
163C3×C22⋊C8—22no—
164#835—22no—
165#832—22no—
166#832—22no—
167#832—22no—
168#832—41no—
169C3⋊#95—21no—
170C3⋊#95—21no—
171C3⋊#95—21no—
172C3⋊#95—21no—
173#830—41no—
174(C2×D3)⋊C8—22no—
175(C2×D3)⋊C8—41no—
176#817—22no—
177#816—22no—
178#816—22no—
179Dic3⋊C8—22no—
180C8×Dic3—22no—
181#810—41no—
182C22×#41—31no—
183C23×D4C2×D311yescharacteristic
184C22×Q16—31no—
185C22×SD16C2×D311yescharacteristic
186C22×SD16C2×D311yescharacteristic
187#546—64no—
188#546—64no—
189C2×#124—31no—
190C2×#123—61no—
191C2×C22⋊Q8—31no—
192C2×C22⋊Q8—31no—
193C2×C22⋊Q8C2×D311yescharacteristic
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—24no—
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×#102C2×D311yescharacteristic
216C2×#102C2×D311yescharacteristic
217C2×C22⋊C8—31no—
218C2×C22⋊C8—31no—
219C2×C22⋊C8—31no—
220C2×C22⋊C8C2×D311yescharacteristic
221C2×C4×C8—31no—
222#398—61no—
223#394—61no—
224#388—61no—
225#388—61no—
226#382—31no—
227#380—31no—
228#380—31no—
229#340—31no—
230#340—31no—
231C24×C3—21no—
232C24×C3—24no—
233C24×C3—21no—
234C24×C3—42no—
235C24×C3—42no—
236C24×C3—42no—
237C24×C3—42no—
238C24×C3—81no—
239C24×C3—81no—
240C24×C3C2×D411yescharacteristic
241C23×D3C2×D411yescharacteristic
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—24no—
249C2×C3×D4—21no—
250C2×C3×D4—21no—
251C2×C3×D4—21no—
252C2×C3×D4—21no—
253C2×C3×D4—21no—
254C2×C3×D4—21no—
255C2×C3×D4—21no—
256C2×C3×D4—21no—
257C2×C3×D4—42no—
258C2×C3×D4—42no—
259C2×C3×D4—44no—
260C2×C3×D4—44no—
261C2×C3×D4—44no—
262C2×C3×D4—44no—
263C2×C3×D4C2×D412yes—
264C2×C3×D4C2×D412yes—
265C2×C3×D4C2×D412yes—
266C2×C3×D4#4112yes—
267C22×C3×C4—21no—
268C22×C3×C4—21no—
269C22×C3×C4—21no—
270C22×C3×C4—21no—
271C22×C3×C4—21no—
272C22×C3×C4—21no—
273C22×C3×C4—21no—
274C22×C3×C4—21no—
275C22×C3×C4C2×D411yescharacteristic
276C22×C3×C4C2411yescharacteristic
277C2×#67—24no—
278C2×#67—22no—
279C2×#67—24no—
280C2×#67—22no—
281C2×#67—41no—
282C2×#67—42no—
283C2×#67—42no—
284C2×#67—81no—
285C2×#67—81no—
286C22×Dic3—24no—
287C22×Dic3—21no—
288C22×Dic3—21no—
289C22×Dic3—24no—
290C22×Dic3—21no—
291C22×Dic3—21no—
292C22×Dic3—42no—
293C22×Dic3—42no—
294C22×Dic3—81no—
295C22×Dic3—81no—
296C22×Dic3C2×D411yescharacteristic
297C22×Dic3C2×D411yescharacteristic
298C22×Dic3C2×D411yescharacteristic
299#237—44no—
300#237—44no—
301#237—44no—
302#237—44no—
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—
315C3×SD16—28no—
316C3×SD16—44no—
317C2×C3×C8—21no—
318C2×C3×C8—21no—
319C2×C3×C8—21no—
320C2×C3×C8—21no—
321C2×C3×C8—21no—
322C2×C3×C8C2×D412yes—
323C3×C4⋊C4—21no—
324C3×C4⋊C4—21no—
325C3×C4⋊C4—42no—
326C3×C22⋊C4—42no—
327#217—24no—
328#217—24no—
329#217—22no—
330#217—24no—
331#217—24no—
332#217—24no—
333#217—42no—
334#216—44no—
335(C2×D3)⋊C4—22no—
336(C2×D3)⋊C4—42no—
337(C2×D3)⋊C4—42no—
338C4⋊Dic3—21no—
339C4⋊Dic3—21no—
340C4⋊Dic3—21no—
341C4⋊Dic3—21no—
342C4⋊Dic3—21no—
343C4⋊Dic3—42no—
344C4⋊Dic3C2×D412yes—
345Dic3⋊C4—24no—
346Dic3⋊C4—22no—
347Dic3⋊C4—42no—
348C4×Dic3—42no—
349C4×Dic3C2×D412yes—
350C4×Dic3C2×D412yes—
351C2×C3⋊C8—21no—
352C2×C3⋊C8—21no—
353C2×C3⋊C8—21no—
354C2×C3⋊C8—21no—
355C2×C3⋊C8—21no—
356C2×C3⋊C8—21no—
357C25—21no—
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—22no—
367C22×D4—22no—
368C22×D4—22no—
369C22×D4—22no—
370C22×D4—21no—
371C22×D4—31no—
372C22×D4—41no—
373C22×D4—41no—
374C22×D4—61no—
375C22×D4—61no—
376C22×D4C22×D311yescharacteristic
377C22×D4C22×D311yescharacteristic
378C23×C4—31no—
379C23×C4—61no—
380C23×C4—61no—
381C23×C4C22×D311yescharacteristic
382C2×Q16—62no—
383C2×Q16—62no—
384C2×Q16—121no—
385C2×SD16—22no—
386C2×SD16—22no—
387C2×SD16—22no—
388C2×SD16—22no—
389C2×SD16—41no—
390C2×SD16#6714yescomplemented
391C22×C8—31no—
392C22×C8—31no—
393C22×C8C22×D311yescharacteristic
394C22×C8C22×D311yescharacteristic
395#124—34no—
396#124—62no—
397#123—68no—
398C22⋊Q8—22no—
399C22⋊Q8—41no—
400C22⋊Q8—62no—
401C22⋊Q8—62no—
402C22⋊Q8—62no—
403C22⋊Q8—121no—
404#121—62no—
405#121—68no—
406#121—62no—
407#120—68no—
408C4×Q8—62no—
409C4×Q8—62no—
410C4×D4—34no—
411C4×D4—62no—
412C4×D4—62no—
413C4×D4—62no—
414C2×C4⋊C4—21no—
415C2×C4⋊C4—31no—
416C2×C4⋊C4—31no—
417C2×C4⋊C4—31no—
418C2×C4⋊C4—31no—
419C2×C4⋊C4—61no—
420C2×C4⋊C4—61no—
421C2×C4⋊C4—61no—
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—61no—
430C2×C22⋊C4—68no—
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—62no—
440#103—62no—
441#103—62no—
442#103—121no—
443#102—22no—
444#102—22no—
445#102—62no—
446#102—62no—
447#102—62no—
448#102—121no—
449C22⋊C8—22no—
450C22⋊C8—62no—
451C22⋊C8—121no—
452C22⋊C8—121no—
453C4×C8—62no—
454#95—61no—
455#95—61no—
456#95—61no—
457#95—61no—
458C23×C3—21no—
459C23×C3—22no—
460C23×C3—21no—
461C23×C3—22no—
462C23×C3—22no—
463C23×C3—21no—
464C23×C3—21no—
465C23×C3—21no—
466C23×C3—21no—
467C23×C3—22no—
468C23×C3—48no—
469C23×C3—48no—
470C23×C3—41no—
471C23×C3—41no—
472C23×C3—41no—
473C23×C3—41no—
474C23×C3—41no—
475C23×C3—41no—
476C23×C3—41no—
477C23×C3—41no—
478C23×C3—41no—
479C23×C3—41no—
480C23×C3—84no—
481C23×C3—84no—
482C23×C3—84no—
483C23×C3—84no—
484C23×C3—84no—
485C23×C3#13512yes—
486C23×C3C22×D411yescharacteristic
487C22×D3—21no—
488C22×D3—21no—
489C22×D3—21no—
490C22×D3—21no—
491C22×D3—21no—
492C22×D3—21no—
493C22×D3—21no—
494C3×Q8—22no—
495C3×Q8—22no—
496C3×Q8—41no—
497C3×Q8—41no—
498C3×D4—22no—
499C3×D4—22no—
500C3×D4—22no—
501C3×D4—22no—
502C3×D4—22no—
503C3×D4—48no—
504C3×D4—41no—
505C3×D4—41no—
506C3×D4#12114yes—
507C2×C3×C4—21no—
508C2×C3×C4—22no—
509C2×C3×C4—21no—
510C2×C3×C4—21no—
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—22no—
534C2×Dic3—22no—
535C2×Dic3—21no—
536C2×Dic3—21no—
537C2×Dic3—21no—
538C2×Dic3—48no—
539C2×Dic3—41no—
540C2×Dic3—41no—
541C2×Dic3—41no—
542C2×Dic3—41no—
543C2×Dic3—41no—
544C2×Dic3—41no—
545C2×Dic3—41no—
546C2×Dic3—41no—
547C2×Dic3—41no—
548C2×Dic3—41no—
549C2×Dic3—84no—
550C2×Dic3#12012yes—
551C2×Dic3#12012yes—
552C4×D3—41no—
553C4×D3—41no—
554C4×D3—41no—
555C4×D3—41no—
556Dic6—22no—
557Dic6—22no—
558Dic6—41no—
559Dic6—41no—
560C3×C8—22no—
561C3×C8—41no—
562C3⋊C8—41no—
563C3⋊C8—41no—
564C24—21no—
565C24—24no—
566C24—21no—
567C24—31no—
568C24—42no—
569C24—42no—
570C24—42no—
571C24—42no—
572C24—81no—
573C24—81no—
574C24D3×D411yescharacteristic
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×Q8C2×#6712yes—
591C2×D4—24no—
592C2×D4—21no—
593C2×D4—21no—
594C2×D4—21no—
595C2×D4—21no—
596C2×D4—21no—
597C2×D4—21no—
598C2×D4—21no—
599C2×D4—21no—
600C2×D4—42no—
601C2×D4—42no—
602C2×D4—44no—
603C2×D4—44no—
604C2×D4—44no—
605C2×D4—44no—
606C2×D4—62no—
607C2×D4—64no—
608C2×D4—62no—
609C2×D4—64no—
610C2×D4—121no—
611C2×D4—122no—
612C2×D4—122no—
613C2×D4—241no—
614C2×D4—241no—
615C2×D4D3×D412yes—
616C2×D4D3×D412yes—
617C2×D4#23712yes—
618C2×D4C2×#6712yes—
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—31no—
628C22×C4—31no—
629C22×C4—31no—
630C22×C4—64no—
631C22×C4—64no—
632C22×C4—61no—
633C22×C4—61no—
634C22×C4—61no—
635C22×C4—61no—
636C22×C4—61no—
637C22×C4—61no—
638C22×C4—61no—
639C22×C4—61no—
640C22×C4—61no—
641C22×C4—61no—
642C22×C4—122no—
643C22×C4—122no—
644C22×C4—241no—
645C22×C4—241no—
646C22×C4D3×D411yescharacteristic
647C22×C4C23×D311yescharacteristic
648Q16—124no—
649SD16—28no—
650SD16—44no—
651C2×C8—21no—
652C2×C8—21no—
653C2×C8—21no—
654C2×C8—21no—
655C2×C8—21no—
656C2×C8—61no—
657C2×C8—61no—
658C2×C8—61no—
659C2×C8—61no—
660C2×C8—61no—
661C2×C8—61no—
662C2×C8C2×#6712yes—
663C4⋊C4—21no—
664C4⋊C4—21no—
665C4⋊C4—32no—
666C4⋊C4—42no—
667C4⋊C4—62no—
668C4⋊C4—64no—
669C4⋊C4—61no—
670C4⋊C4—61no—
671C4⋊C4—61no—
672C4⋊C4—61no—
673C4⋊C4—61no—
674C4⋊C4—122no—
675C4⋊C4—122no—
676C22⋊C4—42no—
677C22⋊C4—62no—
678C22⋊C4—62no—
679C22⋊C4—64no—
680C22⋊C4—64no—
681C22⋊C4—64no—
682C22⋊C4—64no—
683C22⋊C4—64no—
684C22⋊C4—122no—
685C22⋊C4—122no—
686C22⋊C4—122no—
687C42—32no—
688C42—32no—
689C42—122no—
690C22×C3—24no—
691C22×C3—22no—
692C22×C3—22no—
693C22×C3—22no—
694C22×C3—41no—
695C22×C3—42no—
696C22×C3—42no—
697C22×C3—41no—
698C22×C3—41no—
699C22×C3—42no—
700C22×C3—42no—
701C22×C3—42no—
702C22×C3—41no—
703C22×C3—42no—
704C22×C3—42no—
705C22×C3—42no—
706C22×C3—42no—
707C22×C3—816no—
708C22×C3—81no—
709C22×C3—81no—
710C22×C3—81no—
711C22×C3—81no—
712C22×C3C2×#12011yescharacteristic
713C22×C3D4211yescharacteristic
714C22×C3#54611yescharacteristic
715C22×C3C2×#13511yescharacteristic
716C22×C3#57511yescharacteristic
717C22×C3#57711yescharacteristic
718C22×C3#57711yescharacteristic
719C2×D3—41no—
720C2×D3—41no—
721C2×D3—41no—
722C2×D3—41no—
723C2×D3—41no—
724C2×D3—41no—
725C2×D3—41no—
726C3×C4—41no—
727C3×C4—42no—
728C3×C4—81no—
729C3×C4C2×#12111yescharacteristic
730C3×C4#53511yescharacteristic
731C3×C4D4211yescharacteristic
732C3×C4#54611yescharacteristic
733Dic3—22no—
734Dic3—22no—
735Dic3—42no—
736Dic3—41no—
737Dic3—42no—
738Dic3—81no—
739Dic3—81no—
740C23—21no—
741C23—21no—
742C23—21no—
743C23—21no—
744C23—22no—
745C23—21no—
746C23—22no—
747C23—21no—
748C23—22no—
749C23—22no—
750C23—48no—
751C23—48no—
752C23—41no—
753C23—41no—
754C23—41no—
755C23—41no—
756C23—41no—
757C23—41no—
758C23—41no—
759C23—41no—
760C23—41no—
761C23—41no—
762C23—61no—
763C23—61no—
764C23—61no—
765C23—61no—
766C23—61no—
767C23—61no—
768C23—61no—
769C23—84no—
770C23—84no—
771C23—84no—
772C23—84no—
773C23—84no—
774C23#91612yes—
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—22no—
788D4—22no—
789D4—48no—
790D4—41no—
791D4—41no—
792D4—124no—
793D4—128no—
794D4—244no—
795D4#93914yes—
796C2×C4—22no—
797C2×C4—21no—
798C2×C4—21no—
799C2×C4—21no—
800C2×C4—32no—
801C2×C4—32no—
802C2×C4—41no—
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—61no—
812C2×C4—61no—
813C2×C4—61no—
814C2×C4—61no—
815C2×C4—61no—
816C2×C4—62no—
817C2×C4—61no—
818C2×C4—62no—
819C2×C4—61no—
820C2×C4—128no—
821C2×C4—121no—
822C2×C4—121no—
823C2×C4—121no—
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×D3×D411yescharacteristic
837C2×C4C2×D3×D411yescharacteristic
838C2×C4C2×#23711yescharacteristic
839C2×C4#100411yescharacteristic
840C2×C4#100411yescharacteristic
841C2×C4C22×#6711yescharacteristic
842C8—22no—
843C8—41no—
844C8—121no—
845C8—121no—
846C2×C3—42no—
847C2×C3—44no—
848C2×C3—82no—
849C2×C3#240811yescharacteristic
850C2×C3#300211yescharacteristic
851C2×C3#300911yescharacteristic
852C2×C3#327511yescharacteristic
853C2×C3#328211yescharacteristic
854C2×C3#329611yescharacteristic
855C2×C3#332311yescharacteristic
856D3—81no—
857C22—22no—
858C22—22no—
859C22—24no—
860C22—22no—
861C22—42no—
862C22—42no—
863C22—41no—
864C22—42no—
865C22—41no—
866C22—42no—
867C22—41no—
868C22—42no—
869C22—41no—
870C22—42no—
871C22—42no—
872C22—42no—
873C22—42no—
874C22—816no—
875C22—81no—
876C22—81no—
877C22—81no—
878C22—81no—
879C22—121no—
880C22—121no—
881C22—121no—
882C22—121no—
883C22—121no—
884C22—121no—
885C22—121no—
886C22D3×#12011yescharacteristic
887C22#559111yescharacteristic
888C22C2×#91611yescharacteristic
889C22#576211yescharacteristic
890C22#577311yescharacteristic
891C22#577511yescharacteristic
892C22D4×#6711yescharacteristic
893C4—41no—
894C4—42no—
895C4—62no—
896C4—62no—
897C4—81no—
898C4—122no—
899C4—121no—
900C4—122no—
901C4—241no—
902C4—241no—
903C4#559111yescharacteristic
904C4#559211yescharacteristic
905C4D4×#6711yescharacteristic
906C4C2×#93911yescharacteristic
907C3#2424711yescharacteristic, complemented, Sylow
908C2—42no—
909C2—44no—
910C2—82no—
911C2—241no—
912C2#8014511yescharacteristic
913C2#8014811yescharacteristic
914C2#8015911yescharacteristic
915C2#8016411yescharacteristic
916C2#8258211yescharacteristic
917C2#8386711yescharacteristic
918C2#8396211yescharacteristic
subgroupG/H
centerC23C2×D3×D4
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC2×C3×#450C2
socleC23×C3C22×D4
prime radicalC2×#5806C2
hypercenterC2×#450D3
hypocenterC3#24247
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#450

Complements

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

NH ≅ G/Ntype
2. C2×C3×#450C2semidirect
3. C2×#5173C2semidirect
4. C2×#5166C2semidirect
5. C2×Dic3×SD16C2semidirect
6. #82777C2semidirect
7. #72128C2semidirect
8. #72054C2semidirect
9. #71700C2semidirect
10. #70199C2semidirect
11. #70176C2semidirect
12. #70158C2semidirect
13. #70154C2semidirect
14. #69936C2semidirect
15. #69916C2semidirect
24. C2×#946C22semidirect
25. C2×Q8×Dic3C22semidirect
26. C22×#216C22semidirect
40. C2×#835C22semidirect
50. C2×(C2×D3)⋊C8C22semidirect
51. C2×(C2×D3)⋊C8C22semidirect
52. C2×#817C22semidirect
53. C2×#816C22semidirect
54. C2×#816C22semidirect
55. C2×Dic3⋊C8C22semidirect
56. C2×C8×Dic3C22semidirect
58. #4987C22semidirect
60. #4977C22semidirect
61. C2×#810C22semidirect
64. #4551C22semidirect
65. #4529C22semidirect
69. C2×#450D3semidirect
111. C2×C3×SD16D4semidirect
390. C2×SD16#67semidirect
907. C3#24247semidirect

Maximal subgroups

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

subgroupindex
C2×#58062
C2×C3×#4502
C2×#51732
C2×#51662
C2×Dic3×SD162
#827772
#721282
#720542
#717002
#701992
#701762
#701582
#701542
#699362
#699162
#242473