Finite Group Databasebeta

← #10830666

Subgroups — #10830666

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×C3×#452C211yesmaximal, characteristic, complemented
3C2×#5185C211yesmaximal, characteristic, complemented
4C2×#5169C211yesmaximal, characteristic, complemented
5C2×Dic3×SD16C211yesmaximal, characteristic, complemented
6#82777C211yesmaximal, characteristic, complemented
7#72135C211yesmaximal, characteristic, complemented
8#72071C211yesmaximal, characteristic, complemented
9#71699C211yesmaximal, characteristic, complemented
10#70243C211yesmaximal, characteristic, complemented
11#70226C211yesmaximal, characteristic, complemented
12#70198C211yesmaximal, characteristic, complemented
13#70154C211yesmaximal, characteristic, complemented
14#69935C211yesmaximal, characteristic, complemented
15#69916C211yesmaximal, characteristic, complemented
16#24247—31nomaximal, Sylow
17C22×C3×#41C2211yescharacteristic
18C22×D3×D4C2211yescharacteristic
19C22×C3×Q16C2211yescharacteristic, complemented
20C22×C3×SD16C2211yescharacteristic
21C2×C3×C22⋊Q8C2211yescharacteristic, complemented
22#5829—24no—
23#5829—24no—
24C2×#947C2211yescharacteristic
25C2×#946C2211yescharacteristic
26C2×#946C2211yescharacteristic
27C2×Q8×Dic3C2211yescharacteristic, complemented
28C22×#215C2211yescharacteristic
29C2×#939—21no—
30C2×#937—21no—
31C2×D4×Dic3C2211yescharacteristic
32C2×#930C2211yescharacteristic
33C2×#929—21no—
34C2×C4×#67C2211yescharacteristic
35C22×(C2×D3)⋊C4—21no—
36C3×#452—24no—
37C2×C3×#103C2211yescharacteristic, complemented
38C2×C3×#102C2211yescharacteristic
39C2×C3×C22⋊C8C2211yescharacteristic, complemented
40C2×#835C2211yescharacteristic, complemented
41C2×#835C2211yescharacteristic, complemented
42C2×#835C2211yescharacteristic, complemented
43C2×#832C2211yescharacteristic
44C2×#832C2211yescharacteristic
45#5212C2211yescharacteristic, complemented
46C2×#830C2211yescharacteristic, complemented
47#5185—24no—
48#5169—24no—
49Dic3×SD16—24no—
50C2×#821C2211yescharacteristic
51C2×#821C2211yescharacteristic
52C2×(C2×D3)⋊C8C2211yescharacteristic
53C2×(C2×D3)⋊C8C2211yescharacteristic
54C2×#817C2211yescharacteristic, complemented
55C2×Dic3⋊C8C2211yescharacteristic, complemented
56C2×C8×Dic3C2211yescharacteristic, complemented
57#4990—21no—
58#4987C2211yescharacteristic
59#4982—21no—
60#4977C2211yescharacteristic, complemented
61C2×#809C2211yescharacteristic
62#4961—21no—
63#4945—21no—
64#4551C2211yescharacteristic, complemented
65#4529C2211yescharacteristic, complemented
66C2×#546—31no—
67C2×#464—31no—
68C2×#452D311yescharacteristic, complemented
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#1788—31no—
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×Q8C2311yescharacteristic
90C22×C3×D4—21no—
91C22×C3×D4C2311yescharacteristic
92C23×C3×C4—21no—
93C23×C3×C4C2311yescharacteristic
94C22×#67—21no—
95C22×#67—21no—
96C22×#67D411yescharacteristic
97C23×Dic3—21no—
98C2×D3×D4—22no—
99C2×D3×D4—22no—
100C2×D3×D4—22no—
101C2×D3×D4—22no—
102C2×D3×D4—41no—
103C2×D3×D4—41no—
104C22×D12C2311yescharacteristic
105C22×C4×D3C2311yescharacteristic
106C2×C3×Q16—22no—
107C2×C3×Q16—22no—
108C2×C3×Q16—41no—
109C2×C3×SD16—22no—
110C2×C3×SD16—22no—
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—
119C2×#217—21no—
120C2×#217—21no—
121C2×#217D411yescharacteristic
122#947—22no—
123#947D414yes—
124#946—22no—
125#946—22no—
126#946—22no—
127#946—41no—
128Q8×Dic3—22no—
129Q8×Dic3—22no—
130C2×#215—22no—
131C2×#215—22no—
132C2×#215—41no—
133#939—28no—
134#937—28no—
135D4×Dic3—22no—
136D4×Dic3D414yes—
137#930—22no—
138#930—22no—
139#929—28no—
140C4×#67—22no—
141C4×#67—22no—
142C2×(C2×D3)⋊C4—28no—
143C2×(C2×D3)⋊C4—21no—
144C2×(C2×D3)⋊C4—21no—
145C2×(C2×D3)⋊C4—21no—
146C2×(C2×D3)⋊C4—21no—
147C2×(C2×D3)⋊C4—21no—
148C2×(C2×D3)⋊C4—21no—
149C2×(C2×D3)⋊C4D411yescharacteristic
150C2×C4⋊Dic3—21no—
151C2×C4⋊Dic3C2311yescharacteristic
152C2×C4⋊Dic3C2311yescharacteristic
153C2×C4⋊Dic3C2311yescharacteristic
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×#103—22no—
162C3×#102—22no—
163C3×C22⋊C8—22no—
164#835—22no—
165#835—22no—
166#835—41no—
167#832—22no—
168#832—22no—
169C3⋊#95—21no—
170C3⋊#95—21no—
171C3⋊#95—21no—
172C3⋊#95—21no—
173#830—41no—
174#821—22no—
175#821—22no—
176(C2×D3)⋊C8—22no—
177(C2×D3)⋊C8—41no—
178#817—22no—
179Dic3⋊C8—22no—
180C8×Dic3—22no—
181#809—41no—
182C22×#41C2×D311yescharacteristic
183C23×D4—31no—
184C22×Q16C2×D311yescharacteristic, complemented
185C22×SD16—31no—
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, complemented
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—24no—
203#450—64no—
204C4×SD16—64no—
205C2×#106—31no—
206C2×C4⋊C8—31no—
207C2×#103—31no—
208C2×#103—31no—
209C2×#103—31no—
210C2×#103C2×D311yescharacteristic, complemented
211C2×#102—31no—
212C2×#102—31no—
213C2×#102—31no—
214C2×#102—31no—
215C2×#102—31no—
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#380—31no—
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×Q8—21no—
252C2×C3×Q8—21no—
253C2×C3×Q8—21no—
254C2×C3×Q8—21no—
255C2×C3×Q8—21no—
256C2×C3×Q8C2×D412yes—
257C2×C3×Q8C2×D412yes—
258C2×C3×D4—24no—
259C2×C3×D4—21no—
260C2×C3×D4—21no—
261C2×C3×D4—21no—
262C2×C3×D4—42no—
263C2×C3×D4—42no—
264C2×C3×D4C2×D412yes—
265C2×C3×D4C2×D412yes—
266C2×C3×D4#4112yes—
267C22×C3×C4—24no—
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×C4—21no—
276C22×C3×C4—21no—
277C22×C3×C4—42no—
278C22×C3×C4—42no—
279C22×C3×C4C2×D411yescharacteristic
280C22×C3×C4C2411yescharacteristic
281C2×#67—24no—
282C2×#67—22no—
283C2×#67—24no—
284C2×#67—22no—
285C2×#67—41no—
286C2×#67—42no—
287C2×#67—42no—
288C2×#67—81no—
289C2×#67—81no—
290C22×Dic3—21no—
291C22×Dic3—24no—
292C22×Dic3—21no—
293C22×Dic3—21no—
294C22×Dic3—81no—
295C22×Dic3—81no—
296C22×Dic3C2×D411yescharacteristic
297C22×Dic3C2×D411yescharacteristic
298C22×Dic3C2×D411yescharacteristic
299D3×D4—44no—
300D3×D4—44no—
301D3×D4—44no—
302D3×D4—44no—
303C2×D12—21no—
304C2×D12—21no—
305C2×D12—21no—
306C2×D12—21no—
307C2×D12—21no—
308C2×D12C2×D412yes—
309C2×C4×D3—21no—
310C2×C4×D3—21no—
311C2×C4×D3—21no—
312C2×C4×D3—21no—
313C2×C4×D3—21no—
314C2×C4×D3—21no—
315C3×Q16—44no—
316C3×SD16—28no—
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—22no—
328#217—24no—
329#217—42no—
330#215—44no—
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—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—61no—
358C2×#41—22no—
359C2×#41—22no—
360C2×#41—22no—
361C2×#41—22no—
362C2×#41—41no—
363C2×#41—41no—
364C22×Q8C22×D311yescharacteristic
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—22no—
383C2×Q16—22no—
384C2×Q16—41no—
385C2×SD16—22no—
386C2×SD16—22no—
387C2×SD16—62no—
388C2×SD16—62no—
389C2×SD16—121no—
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—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—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—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—62no—
441#103—62no—
442#103—121no—
443#102—22no—
444#102—62no—
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—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—22no—
497C3×Q8—22no—
498C3×Q8—41no—
499C3×Q8—41no—
500C3×Q8—41no—
501C3×Q8—41no—
502C3×D4—22no—
503C3×D4—22no—
504C3×D4—22no—
505C3×D4—48no—
506C3×D4#12114yes—
507C2×C3×C4—21no—
508C2×C3×C4—22no—
509C2×C3×C4—22no—
510C2×C3×C4—21no—
511C2×C3×C4—21no—
512C2×C3×C4—48no—
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×C4C22×D411yescharacteristic
525C2×C3×C4C22×D411yescharacteristic
526C2×C3×C4C22×D411yescharacteristic
527C2×C3×C4C2×#4111yescharacteristic
528C2×C3×C4H(5,𝔽2)11yescharacteristic
529C2×C3×C4H(5,𝔽2)11yescharacteristic
530#67—44no—
531#67—48no—
532#67—84no—
533C2×Dic3—21no—
534C2×Dic3—21no—
535C2×Dic3—21no—
536C2×Dic3—21no—
537C2×Dic3—21no—
538C2×Dic3—22no—
539C2×Dic3—21no—
540C2×Dic3—21no—
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—
552D12—22no—
553D12—22no—
554D12—41no—
555D12—41no—
556C4×D3—41no—
557C4×D3—41no—
558C4×D3—41no—
559C4×D3—41no—
560C3×C8—22no—
561C3×C8—41no—
562C3⋊C8—41no—
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—21no—
585C2×Q8—21no—
586C2×Q8—21no—
587C2×Q8—21no—
588C2×Q8—21no—
589C2×Q8D3×D412yes—
590C2×Q8C2×#6712yes—
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×D4D3×D412yes—
617C2×D4#23712yes—
618C2×D4C2×#6712yes—
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—44no—
649SD16—28no—
650SD16—124no—
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—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—42no—
729C3×C4—81no—
730C3×C4C2×#12111yescharacteristic
731C3×C4#53511yescharacteristic
732C3×C4D4211yescharacteristic
733C3×C4#54611yescharacteristic
734Dic3—22no—
735Dic3—22no—
736Dic3—41no—
737Dic3—42no—
738Dic3—81no—
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—22no—
779Q8—22no—
780Q8—41no—
781Q8—41no—
782Q8—41no—
783Q8—41no—
784D4—22no—
785D4—22no—
786D4—22no—
787D4—48no—
788D4—62no—
789D4—62no—
790D4—124no—
791D4—128no—
792D4—121no—
793D4—121no—
794D4—244no—
795D4#93914yes—
796C2×C4—22no—
797C2×C4—21no—
798C2×C4—21no—
799C2×C4—22no—
800C2×C4—21no—
801C2×C4—32no—
802C2×C4—32no—
803C2×C4—48no—
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—61no—
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—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—
886C22D3×#12011yescharacteristic
887C22#559111yescharacteristic
888C22D3×#13511yescharacteristic
889C22#577011yescharacteristic
890C22#577711yescharacteristic
891C22#577811yescharacteristic
892C22D4×#6711yescharacteristic
893C4—41no—
894C4—42no—
895C4—42no—
896C4—62no—
897C4—62no—
898C4—81no—
899C4—122no—
900C4—121no—
901C4—241no—
902C4—241no—
903C4#559111yescharacteristic
904C4#559211yescharacteristic
905C4D4×#6711yescharacteristic
906C4C2×#93911yescharacteristic
907C3#2424711yescharacteristic, complemented, Sylow
908C2—44no—
909C2—81no—
910C2—122no—
911C2—242no—
912C2#8022611yescharacteristic
913C2#8022911yescharacteristic
914C2#8024611yescharacteristic
915C2#8025811yescharacteristic
916C2#8258211yescharacteristic
917C2#8391911yescharacteristic
918C2#8399111yescharacteristic
subgroupG/H
centerC23C2×D3×D4
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC2×C3×#452C2
socleC23×C3C22×D4
prime radicalC2×#5829C2
hypercenterC2×#452D3
hypocenterC3#24247
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#452

Complements

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

NH ≅ G/Ntype
2. C2×C3×#452C2semidirect
3. C2×#5185C2semidirect
4. C2×#5169C2semidirect
5. C2×Dic3×SD16C2semidirect
6. #82777C2semidirect
7. #72135C2semidirect
8. #72071C2semidirect
9. #71699C2semidirect
10. #70243C2semidirect
11. #70226C2semidirect
12. #70198C2semidirect
13. #70154C2semidirect
14. #69935C2semidirect
15. #69916C2semidirect
19. C22×C3×Q16C22semidirect
21. C2×C3×C22⋊Q8C22semidirect
27. C2×Q8×Dic3C22semidirect
37. C2×C3×#103C22semidirect
39. C2×C3×C22⋊C8C22semidirect
40. C2×#835C22semidirect
41. C2×#835C22semidirect
42. C2×#835C22semidirect
45. #5212C22semidirect
46. C2×#830C22semidirect
54. C2×#817C22semidirect
55. C2×Dic3⋊C8C22semidirect
56. C2×C8×Dic3C22semidirect
60. #4977C22semidirect
64. #4551C22semidirect
65. #4529C22semidirect
68. C2×#452D3semidirect
111. C2×C3×SD16D4semidirect
184. C22×Q16C2×D3semidirect
193. C2×C22⋊Q8C2×D3semidirect
210. C2×#103C2×D3semidirect
220. C2×C22⋊C8C2×D3semidirect
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×#58292
C2×C3×#4522
C2×#51852
C2×#51692
C2×Dic3×SD162
#827772
#721352
#720712
#716992
#702432
#702262
#701982
#701542
#699352
#699162
#242473