Finite Group Databasebeta

← #10830627

Subgroups — #10830627

Order 768.

1628 conjugacy classes of subgroups.

The subgroup lattice has 960 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#5676C211yesmaximal, characteristic, complemented
2C2×C3×#463C211yesmaximal, characteristic, complemented
3C2×#5172C211yesmaximal, characteristic, complemented
4C2×#5156C211yesmaximal, characteristic, complemented
5#82416C211yesmaximal, characteristic, complemented
6C2×C4×#213C211yesmaximal, characteristic, complemented
7#72054C211yesmaximal, characteristic, complemented
8#72043C211yesmaximal, characteristic, complemented
9#71725C211yesmaximal, characteristic, complemented
10#70480C211yesmaximal, characteristic, complemented
11#70470C211yesmaximal, characteristic, complemented
12#70275C211yesmaximal, characteristic, complemented
13#70267C211yesmaximal, characteristic, complemented
14#70206C211yesmaximal, characteristic, complemented
15#70198C211yesmaximal, characteristic, complemented
16#24245—31nomaximal, Sylow
17C22×#239C2211yescharacteristic
18C22×D3×D4C2211yescharacteristic
19C22×C3×SD16C2211yescharacteristic, complemented
20C22×C3×D8C2211yescharacteristic
21C2×C3×#124C2211yescharacteristic
22C2×C3×C4×D4C2211yescharacteristic, complemented
23C2×#946C2211yescharacteristic
24C2×#938C2211yescharacteristic
25C2×#938C2211yescharacteristic
26C2×#938C2211yescharacteristic, complemented
27C22×#213C2211yescharacteristic
28#5676—24no—
29#5676—24no—
30C2×#884—21no—
31C2×#883—21no—
32C2×#882—21no—
33C2×D3×C22⋊C4—21no—
34C2×C4×D12C2211yescharacteristic
35C2×C4×D12C2211yescharacteristic
36C3×#463—24no—
37C2×C3×C4⋊C8C2211yescharacteristic, complemented
38C2×C3×#103C2211yescharacteristic, complemented
39C2×C3×#102C2211yescharacteristic
40C2×#835C2211yescharacteristic, complemented
41C2×#835C2211yescharacteristic, complemented
42C2×#832C2211yescharacteristic
43C2×#832C2211yescharacteristic
44C2×#832C2211yescharacteristic, complemented
45#5213—21no—
46#5213—21no—
47#5172—24no—
48#5156—24no—
49C2×#821C2211yescharacteristic
50C2×#821C2211yescharacteristic
51C2×(C2×D3)⋊C8C2211yescharacteristic
52C2×(C2×D3)⋊C8C2211yescharacteristic
53C2×(C2×D3)⋊C8C2211yescharacteristic, complemented
54C2×(C2×D3)⋊C8C2211yescharacteristic, complemented
55C4×#213—24no—
56#4987C2211yescharacteristic
57#4987C2211yescharacteristic, complemented
58C2×#809C2211yescharacteristic
59C2×#807C2211yescharacteristic, complemented
60#4960—21no—
61#4953—21no—
62#4936C2211yescharacteristic, complemented
63C2×C4×C3⋊C8C2211yescharacteristic, complemented
64#4551C2211yescharacteristic, complemented
65#4551C2211yescharacteristic, complemented
66C2×#546—31no—
67C2×#463D311yescharacteristic, complemented
68C2×#449—31no—
69C2×#447—31no—
70C2×C4×D8—31no—
71#2535—31no—
72#2036—31no—
73#2033—31no—
74#2000—31no—
75#1999—31no—
76#1958—31no—
77#1954—31no—
78#1804—31no—
79#1788—31no—
80#1786—31no—
81C24×D3—21no—
82C22×C3×Q8C2311yescharacteristic
83C22×C3×D4C2311yescharacteristic
84C22×C3×D4C2311yescharacteristic
85C23×C3×C4—21no—
86C22×#67—21no—
87C22×#67—21no—
88C22×#67—21no—
89C22×#67—21no—
90C2×#239—22no—
91C2×#239—22no—
92C2×#239—22no—
93C2×#239—22no—
94C2×#239—41no—
95C2×#239—41no—
96C2×D3×D4—22no—
97C2×D3×D4—22no—
98C2×D3×D4—22no—
99C2×D3×D4—22no—
100C2×D3×D4—41no—
101C2×D3×D4—41no—
102C22×D12—21no—
103C22×D12D411yescharacteristic
104C22×D12C2311yescharacteristic
105C22×C4×D3—21no—
106C22×C4×D3—21no—
107C22×C4×D3C2311yescharacteristic
108C22×C4×D3C2311yescharacteristic
109C2×C3×SD16—22no—
110C2×C3×SD16—22no—
111C2×C3×SD16—41no—
112C2×C3×D8—22no—
113C2×C3×D8—22no—
114C2×C3×D8—41no—
115C22×C3×C8C2311yescharacteristic
116C22×C3×C8C2311yescharacteristic
117C3×#124—22no—
118C3×#124D414yescomplemented
119C3×C4×D4—22no—
120C3×C4×D4—22no—
121C2×C3×C4⋊C4C2311yescharacteristic
122C2×C3×C22⋊C4—21no—
123C2×C3×C22⋊C4—21no—
124C2×C3×C22⋊C4—21no—
125C2×C3×C42C2311yescharacteristic
126C2×#217—21no—
127C2×#217—21no—
128C2×#217—21no—
129#946—22no—
130#946—22no—
131#938—22no—
132#938—22no—
133#938—22no—
134#938—22no—
135#938—41no—
136#938—41no—
137C2×#213—22no—
138C2×#213—22no—
139C2×#213D414yescomplemented
140C2×(C2×D3)⋊C4—21no—
141C2×(C2×D3)⋊C4—21no—
142C2×(C2×D3)⋊C4—21no—
143C2×(C2×D3)⋊C4—21no—
144C2×(C2×D3)⋊C4D411yescharacteristic
145C2×(C2×D3)⋊C4D411yescharacteristic
146C2×C4⋊Dic3D411yescharacteristic
147C2×C4⋊Dic3C2311yescharacteristic
148C2×C4⋊Dic3C2311yescharacteristic
149C2×C4⋊Dic3C2311yescharacteristic
150C2×Dic3⋊C4—21no—
151C22×C3⋊C8C2311yescharacteristic
152C22×C3⋊C8C2311yescharacteristic
153#884—28no—
154#883—28no—
155#882—28no—
156D3×C22⋊C4—28no—
157C4×D12—22no—
158C4×D12—22no—
159C4×D12—22no—
160C4×D12D414yescomplemented
161C3×C4⋊C8—22no—
162C3×#103—22no—
163C3×#102—22no—
164#835—22no—
165#835—41no—
166#832—22no—
167#832—22no—
168#832—41no—
169C3⋊#95—21no—
170C3⋊#95—21no—
171C3⋊#95—21no—
172C3⋊#95—21no—
173#821—22no—
174#821—22no—
175(C2×D3)⋊C8—22no—
176(C2×D3)⋊C8—22no—
177(C2×D3)⋊C8—41no—
178(C2×D3)⋊C8—41no—
179#809—22no—
180#807—22no—
181C4×C3⋊C8—22no—
182C22×#41—31no—
183C23×D4—31no—
184C22×SD16C2×D311yescharacteristic, complemented
185C22×D8—31no—
186C22×D8C2×D311yescharacteristic
187#546—64no—
188#546—64no—
189C2×#124C2×D311yescharacteristic
190C2×#123—61no—
191C2×C22⋊Q8—31no—
192C2×#121—31no—
193C2×#121—31no—
194C2×#121—31no—
195C2×#121—61no—
196C2×#120—61no—
197C2×C4×D4—31no—
198C2×C4×D4—31no—
199C2×C4×D4C2×D311yescharacteristic, complemented
200C22×C22⋊C4—61no—
201#463—24no—
202#449—64no—
203#447—64no—
204C4×D8—64no—
205C2×#107—31no—
206C2×C4⋊C8C2×D311yescharacteristic, complemented
207C2×#103—31no—
208C2×#103—31no—
209C2×#103C2×D311yescharacteristic, complemented
210C2×#102—31no—
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⋊C8—31no—
221C2×C4×C8—31no—
222#397—61no—
223#392—61no—
224#386—61no—
225#386—61no—
226#382—31no—
227#380—31no—
228#380—31no—
229#340—31no—
230#340—31no—
231C24×C3—21no—
232C24×C3—21no—
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
242C23×D3C2×D411yescharacteristic
243C2×C3×Q8—21no—
244C2×C3×Q8—21no—
245C2×C3×Q8—21no—
246C2×C3×Q8—21no—
247C2×C3×Q8—21no—
248C2×C3×Q8C2×D412yes—
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—21no—
258C2×C3×D4—21no—
259C2×C3×D4C2×D412yes—
260C2×C3×D4C2×D412yes—
261C22×C3×C4—21no—
262C22×C3×C4—21no—
263C22×C3×C4—42no—
264C22×C3×C4—81no—
265C22×C3×C4—81no—
266C22×C3×C4C2×D411yescharacteristic
267C22×C3×C4C2×D411yescharacteristic
268C22×C3×C4C2411yescharacteristic
269C2×#67—24no—
270C2×#67—24no—
271C2×#67—42no—
272C2×#67—42no—
273C2×#67—42no—
274C2×#67—42no—
275C2×#67—42no—
276C2×#67—42no—
277C2×#67—81no—
278C2×#67—81no—
279C2×#67—81no—
280C2×#67—81no—
281C22×Dic3—21no—
282C22×Dic3—21no—
283C22×Dic3—21no—
284C22×Dic3C2×D411yescharacteristic
285C22×Dic3C2×D411yescharacteristic
286#239—44no—
287#239—44no—
288#239—44no—
289#239—44no—
290D3×D4—44no—
291D3×D4—44no—
292D3×D4—44no—
293D3×D4—44no—
294C2×D12—21no—
295C2×D12—21no—
296C2×D12—21no—
297C2×D12—24no—
298C2×D12—22no—
299C2×D12—22no—
300C2×D12—41no—
301C2×D12—42no—
302C2×D12—42no—
303C2×D12C2×D412yes—
304C2×D12C2×D412yes—
305C2×D12#4112yes—
306C2×C4×D3—24no—
307C2×C4×D3—21no—
308C2×C4×D3—21no—
309C2×C4×D3—21no—
310C2×C4×D3—21no—
311C2×C4×D3—21no—
312C2×C4×D3—21no—
313C2×C4×D3—21no—
314C2×C4×D3—21no—
315C2×C4×D3—21no—
316C2×C4×D3—21no—
317C2×C4×D3—21no—
318C2×C4×D3—21no—
319C2×C4×D3—24no—
320C2×C4×D3—42no—
321C2×C4×D3—42no—
322C2×C4×D3—81no—
323C2×C4×D3—81no—
324C3×SD16—44no—
325C3×D8—44no—
326C2×C3×C8—21no—
327C2×C3×C8—21no—
328C2×C3×C8—21no—
329C2×C3×C8—21no—
330C2×C3×C8—21no—
331C2×C3×C8—21no—
332C3×C4⋊C4—21no—
333C3×C4⋊C4—21no—
334C3×C22⋊C4—24no—
335C3×C22⋊C4—24no—
336C3×C22⋊C4—42no—
337C3×C42C2×D412yes—
338C3×C42C2×D412yes—
339#217—24no—
340#217—42no—
341#217—42no—
342#213—28no—
343(C2×D3)⋊C4—24no—
344(C2×D3)⋊C4—22no—
345(C2×D3)⋊C4—22no—
346(C2×D3)⋊C4—24no—
347(C2×D3)⋊C4—81no—
348(C2×D3)⋊C4—81no—
349C4⋊Dic3—22no—
350C4⋊Dic3—21no—
351C4⋊Dic3—21no—
352C4⋊Dic3—21no—
353C4⋊Dic3—21no—
354C4⋊Dic3—21no—
355C4⋊Dic3C2×D412yes—
356Dic3⋊C4—24no—
357C2×C3⋊C8—21no—
358C2×C3⋊C8—21no—
359C2×C3⋊C8—21no—
360C2×C3⋊C8—21no—
361C2×C3⋊C8—21no—
362C2×C3⋊C8C2×D412yes—
363C25—61no—
364C2×#41—62no—
365C2×#41—62no—
366C2×#41—62no—
367C2×#41—62no—
368C2×#41—121no—
369C2×#41—121no—
370C22×Q8C22×D311yescharacteristic
371C22×D4—31no—
372C22×D4—31no—
373C22×D4—61no—
374C22×D4—61no—
375C22×D4—62no—
376C22×D4—62no—
377C22×D4—62no—
378C22×D4—61no—
379C22×D4—62no—
380C22×D4—61no—
381C22×D4—61no—
382C22×D4—121no—
383C22×D4—121no—
384C22×D4C22×D311yescharacteristic
385C22×D4C22×D311yescharacteristic
386C23×C4—21no—
387C23×C4—31no—
388C23×C4—31no—
389C23×C4—61no—
390C23×C4—61no—
391C2×SD16—22no—
392C2×SD16—22no—
393C2×SD16—41no—
394C2×D8—22no—
395C2×D8—22no—
396C2×D8—34no—
397C2×D8—41no—
398C2×D8—62no—
399C2×D8—62no—
400C22×C8—31no—
401C22×C8—31no—
402C22×C8C22×D311yescharacteristic
403C22×C8C22×D311yescharacteristic
404#124—22no—
405#124#6714yescomplemented
406#123—68no—
407C22⋊Q8—62no—
408C22⋊Q8—62no—
409#121—68no—
410#121—62no—
411#121—62no—
412#121—62no—
413#121—62no—
414#121—121no—
415#121—121no—
416#120—68no—
417C4×D4—22no—
418C4×D4—22no—
419C4×D4—34no—
420C4×D4—62no—
421C4×D4—62no—
422C4×D4—62no—
423C2×C4⋊C4—31no—
424C2×C4⋊C4—31no—
425C2×C4⋊C4—31no—
426C2×C4⋊C4—31no—
427C2×C4⋊C4—61no—
428C2×C4⋊C4C22×D311yescharacteristic
429C2×C22⋊C4—21no—
430C2×C22⋊C4—21no—
431C2×C22⋊C4—21no—
432C2×C22⋊C4—31no—
433C2×C22⋊C4—31no—
434C2×C22⋊C4—68no—
435C2×C22⋊C4—61no—
436C2×C22⋊C4—61no—
437C2×C22⋊C4—61no—
438C2×C22⋊C4—61no—
439C2×C22⋊C4—61no—
440C2×C22⋊C4—61no—
441C2×C22⋊C4—61no—
442C2×C42C22×D311yescharacteristic
443#107—62no—
444C4⋊C8—22no—
445#103—22no—
446#103—62no—
447#103—121no—
448#102—22no—
449#102—62no—
450#102—62no—
451#102—62no—
452#102—62no—
453#102—62no—
454#102—121no—
455C22⋊C8—62no—
456C22⋊C8—62no—
457C22⋊C8—121no—
458C22⋊C8—121no—
459C4×C8—62no—
460#95—61no—
461#95—61no—
462#95—61no—
463#95—61no—
464C23×C3—22no—
465C23×C3—22no—
466C23×C3—41no—
467C23×C3—41no—
468C23×C3—41no—
469C23×C3—41no—
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×C3C22×D411yescharacteristic
479C22×D3—21no—
480C22×D3—22no—
481C22×D3—21no—
482C22×D3—22no—
483C22×D3—21no—
484C22×D3—22no—
485C22×D3—21no—
486C22×D3—21no—
487C22×D3—21no—
488C22×D3—21no—
489C22×D3—21no—
490C22×D3—21no—
491C22×D3—21no—
492C22×D3—21no—
493C22×D3—21no—
494C22×D3—21no—
495C22×D3—48no—
496C22×D3—48no—
497C22×D3—41no—
498C22×D3—41no—
499C22×D3—41no—
500C22×D3—41no—
501C22×D3—84no—
502C22×D3—84no—
503C22×D3—84no—
504C22×D3—84no—
505C22×D3—84no—
506C22×D3#13512yes—
507C3×Q8—22no—
508C3×Q8—22no—
509C3×Q8—41no—
510C3×Q8—41no—
511C3×D4—22no—
512C3×D4—22no—
513C3×D4—22no—
514C3×D4—22no—
515C3×D4—41no—
516C3×D4—41no—
517C3×D4—41no—
518C3×D4—41no—
519C2×C3×C4—21no—
520C2×C3×C4—21no—
521C2×C3×C4—21no—
522C2×C3×C4—21no—
523C2×C3×C4—22no—
524C2×C3×C4—41no—
525C2×C3×C4—41no—
526C2×C3×C4—41no—
527C2×C3×C4—41no—
528C2×C3×C4—41no—
529C2×C3×C4—84no—
530C2×C3×C4#12012yes—
531C2×C3×C4#12012yes—
532C2×C3×C4C22×D411yescharacteristic
533C2×C3×C4C22×D411yescharacteristic
534C2×C3×C4C22×D411yescharacteristic
535C2×C3×C4C2×#4111yescharacteristic
536C2×C3×C4H(5,𝔽2)11yescharacteristic
537C2×C3×C4H(5,𝔽2)11yescharacteristic
538#67—48no—
539#67—84no—
540#67—84no—
541#67—84no—
542C2×Dic3—21no—
543C2×Dic3—22no—
544C2×Dic3—21no—
545C2×Dic3—21no—
546C2×Dic3—21no—
547C2×Dic3—21no—
548C2×Dic3—21no—
549C2×Dic3—41no—
550C2×Dic3—41no—
551C2×Dic3—41no—
552C2×Dic3—41no—
553C2×Dic3—41no—
554C2×Dic3—41no—
555C2×Dic3—41no—
556C2×Dic3—41no—
557D12—22no—
558D12—22no—
559D12—22no—
560D12—44no—
561D12—48no—
562D12#12114yes—
563C4×D3—48no—
564C4×D3—41no—
565C4×D3—41no—
566C4×D3—41no—
567C4×D3—41no—
568C4×D3—41no—
569C4×D3—41no—
570C4×D3—41no—
571C4×D3—41no—
572C4×D3—84no—
573C3×C8—41no—
574C3×C8—41no—
575C3⋊C8—22no—
576C3⋊C8—41no—
577C24—21no—
578C24—21no—
579C24—31no—
580C24—31no—
581C24—64no—
582C24—61no—
583C24—122no—
584C24—122no—
585C24—122no—
586C24—122no—
587C24—241no—
588C24—241no—
589#41—124no—
590#41—124no—
591#41—124no—
592#41—124no—
593C2×Q8—21no—
594C2×Q8—21no—
595C2×Q8—21no—
596C2×Q8—21no—
597C2×Q8—21no—
598C2×Q8C2×#6712yes—
599C2×D4—21no—
600C2×D4—21no—
601C2×D4—21no—
602C2×D4—21no—
603C2×D4—21no—
604C2×D4—21no—
605C2×D4—21no—
606C2×D4—21no—
607C2×D4—21no—
608C2×D4—21no—
609C2×D4—32no—
610C2×D4—32no—
611C2×D4—32no—
612C2×D4—62no—
613C2×D4—64no—
614C2×D4—64no—
615C2×D4—64no—
616C2×D4—62no—
617C2×D4—61no—
618C2×D4—61no—
619C2×D4—61no—
620C2×D4—121no—
621C2×D4—122no—
622C2×D4—122no—
623C2×D4—122no—
624C2×D4—122no—
625C2×D4—124no—
626C2×D4—124no—
627C2×D4—124no—
628C2×D4—124no—
629C2×D4—122no—
630C2×D4—122no—
631C2×D4—122no—
632C2×D4—122no—
633C2×D4—241no—
634C2×D4—241no—
635C2×D4—241no—
636C2×D4—241no—
637C2×D4D3×D412yes—
638C2×D4C2×#6712yes—
639C22×C4—21no—
640C22×C4—21no—
641C22×C4—31no—
642C22×C4—31no—
643C22×C4—42no—
644C22×C4—64no—
645C22×C4—61no—
646C22×C4—61no—
647C22×C4—61no—
648C22×C4—61no—
649C22×C4—61no—
650C22×C4—61no—
651C22×C4—61no—
652C22×C4—61no—
653C22×C4—61no—
654C22×C4—61no—
655C22×C4—61no—
656C22×C4—61no—
657C22×C4—61no—
658C22×C4—64no—
659C22×C4—61no—
660C22×C4—61no—
661C22×C4—81no—
662C22×C4—81no—
663C22×C4—122no—
664C22×C4—122no—
665C22×C4—241no—
666C22×C4—241no—
667C22×C4D3×D411yescharacteristic
668C22×C4D3×D411yescharacteristic
669C22×C4C23×D311yescharacteristic
670SD16—44no—
671D8—44no—
672D8—68no—
673C2×C8—21no—
674C2×C8—21no—
675C2×C8—21no—
676C2×C8—21no—
677C2×C8—21no—
678C2×C8—21no—
679C2×C8—32no—
680C2×C8—61no—
681C2×C8—61no—
682C2×C8—61no—
683C2×C8—61no—
684C2×C8—61no—
685C4⋊C4—21no—
686C4⋊C4—21no—
687C4⋊C4—32no—
688C4⋊C4—64no—
689C4⋊C4—62no—
690C4⋊C4—61no—
691C4⋊C4—61no—
692C4⋊C4—61no—
693C4⋊C4—61no—
694C4⋊C4—61no—
695C22⋊C4—24no—
696C22⋊C4—24no—
697C22⋊C4—42no—
698C22⋊C4—64no—
699C22⋊C4—64no—
700C22⋊C4—62no—
701C22⋊C4—62no—
702C22⋊C4—64no—
703C22⋊C4—122no—
704C22⋊C4—122no—
705C22⋊C4—241no—
706C22⋊C4—241no—
707C42D3×D412yes—
708C42C2×#6712yes—
709C22×C3—42no—
710C22×C3—42no—
711C22×C3—42no—
712C22×C3—42no—
713C22×C3—42no—
714C22×C3—42no—
715C22×C3—81no—
716C22×C3—81no—
717C22×C3—81no—
718C22×C3—81no—
719C22×C3—81no—
720C22×C3—81no—
721C22×C3—81no—
722C22×C3—81no—
723C22×C3C2×#12011yescharacteristic
724C22×C3D4211yescharacteristic
725C22×C3#54611yescharacteristic
726C22×C3C2×#13511yescharacteristic
727C22×C3#57511yescharacteristic
728C22×C3#57611yescharacteristic
729C22×C3#57611yescharacteristic
730C2×D3—24no—
731C2×D3—22no—
732C2×D3—22no—
733C2×D3—22no—
734C2×D3—41no—
735C2×D3—42no—
736C2×D3—42no—
737C2×D3—41no—
738C2×D3—41no—
739C2×D3—42no—
740C2×D3—42no—
741C2×D3—42no—
742C2×D3—41no—
743C2×D3—42no—
744C2×D3—41no—
745C2×D3—41no—
746C2×D3—41no—
747C2×D3—41no—
748C2×D3—41no—
749C2×D3—41no—
750C2×D3—41no—
751C2×D3—816no—
752C3×C4—22no—
753C3×C4—22no—
754C3×C4—42no—
755C3×C4—81no—
756C3×C4C2×#12111yescharacteristic
757C3×C4#53511yescharacteristic
758C3×C4D4211yescharacteristic
759C3×C4#54611yescharacteristic
760Dic3—41no—
761Dic3—41no—
762Dic3—42no—
763Dic3—81no—
764Dic3—81no—
765C23—22no—
766C23—22no—
767C23—32no—
768C23—41no—
769C23—41no—
770C23—41no—
771C23—41no—
772C23—41no—
773C23—41no—
774C23—41no—
775C23—41no—
776C23—41no—
777C23—41no—
778C23—41no—
779C23—41no—
780C23—61no—
781C23—61no—
782C23—61no—
783C23—61no—
784C23—62no—
785C23—61no—
786C23—62no—
787C23—61no—
788C23—62no—
789C23—61no—
790C23—61no—
791C23—61no—
792C23—61no—
793C23—61no—
794C23—61no—
795C23—61no—
796C23—128no—
797C23—128no—
798C23—121no—
799C23—121no—
800C23—121no—
801C23—121no—
802C23—244no—
803C23—244no—
804C23—244no—
805C23—244no—
806C23—244no—
807C23C2×D3×D411yescharacteristic
808Q8—22no—
809Q8—22no—
810Q8—41no—
811Q8—41no—
812D4—22no—
813D4—22no—
814D4—22no—
815D4—22no—
816D4—34no—
817D4—41no—
818D4—41no—
819D4—41no—
820D4—41no—
821D4—62no—
822D4—62no—
823D4—62no—
824D4—124no—
825D4—128no—
826D4—128no—
827D4—244no—
828D4—244no—
829D4—244no—
830C2×C4—21no—
831C2×C4—21no—
832C2×C4—21no—
833C2×C4—21no—
834C2×C4—22no—
835C2×C4—41no—
836C2×C4—41no—
837C2×C4—41no—
838C2×C4—41no—
839C2×C4—41no—
840C2×C4—62no—
841C2×C4—61no—
842C2×C4—61no—
843C2×C4—61no—
844C2×C4—61no—
845C2×C4—61no—
846C2×C4—61no—
847C2×C4—84no—
848C2×C4—128no—
849C2×C4—121no—
850C2×C4—121no—
851C2×C4—121no—
852C2×C4—121no—
853C2×C4—121no—
854C2×C4—121no—
855C2×C4—121no—
856C2×C4—121no—
857C2×C4—121no—
858C2×C4—121no—
859C2×C4—121no—
860C2×C4—121no—
861C2×C4—121no—
862C2×C4—121no—
863C2×C4—121no—
864C2×C4—121no—
865C2×C4—244no—
866C2×C4#93712yes—
867C2×C4#93712yes—
868C2×C4C2×D3×D411yescharacteristic
869C2×C4C2×D3×D411yescharacteristic
870C2×C4#100411yescharacteristic
871C2×C4D3×#4111yescharacteristic
872C2×C4#100911yescharacteristic
873C2×C4C22×#6711yescharacteristic
874C8—41no—
875C8—41no—
876C8—62no—
877C8—121no—
878C2×C3—82no—
879C2×C3—82no—
880C2×C3#240811yescharacteristic
881C2×C3#300211yescharacteristic
882C2×C3#300811yescharacteristic
883C2×C3#327311yescharacteristic
884C2×C3#328011yescharacteristic
885C2×C3#329711yescharacteristic
886C2×C3#332211yescharacteristic
887D3—42no—
888D3—44no—
889D3—81no—
890C22—42no—
891C22—42no—
892C22—42no—
893C22—42no—
894C22—42no—
895C22—42no—
896C22—62no—
897C22—62no—
898C22—62no—
899C22—64no—
900C22—81no—
901C22—81no—
902C22—81no—
903C22—81no—
904C22—81no—
905C22—81no—
906C22—81no—
907C22—81no—
908C22—121no—
909C22—122no—
910C22—122no—
911C22—122no—
912C22—121no—
913C22—122no—
914C22—122no—
915C22—121no—
916C22—122no—
917C22—121no—
918C22—121no—
919C22—121no—
920C22—121no—
921C22—121no—
922C22—121no—
923C22—121no—
924C22—121no—
925C22—2416no—
926C22#560911yescharacteristic
927C22#561211yescharacteristic
928C22D3×#13511yescharacteristic
929C22#576811yescharacteristic
930C22#577411yescharacteristic
931C22#577411yescharacteristic
932C22C2×#93711yescharacteristic
933C4—22no—
934C4—22no—
935C4—42no—
936C4—81no—
937C4—121no—
938C4—121no—
939C4—122no—
940C4—241no—
941C4—241no—
942C4D3×#12111yescharacteristic
943C4#560711yescharacteristic
944C4D4×#6711yescharacteristic
945C4#582911yescharacteristic
946C3#2424511yescharacteristic, complemented, Sylow
947C2—82no—
948C2—82no—
949C2—122no—
950C2—124no—
951C2—241no—
952C2#8055511yescharacteristic
953C2#8055711yescharacteristic
954C2#8055911yescharacteristic
955C2#8056511yescharacteristic
956C2#8264011yescharacteristic
957C2#8391111yescharacteristic
958C2#8394711yescharacteristic
subgroupG/H
centerC23C2×D3×D4
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC2×C3×#463C2
socleC23×C3C22×D4
hypercenterC2×#463D3
hypocenterC3#24245
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#463

Complements

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

NH ≅ G/Ntype
1. C2×#5676C2semidirect
2. C2×C3×#463C2semidirect
3. C2×#5172C2semidirect
4. C2×#5156C2semidirect
5. #82416C2semidirect
6. C2×C4×#213C2semidirect
7. #72054C2semidirect
8. #72043C2semidirect
9. #71725C2semidirect
10. #70480C2semidirect
11. #70470C2semidirect
12. #70275C2semidirect
13. #70267C2semidirect
14. #70206C2semidirect
15. #70198C2semidirect
19. C22×C3×SD16C22semidirect
22. C2×C3×C4×D4C22semidirect
26. C2×#938C22semidirect
37. C2×C3×C4⋊C8C22semidirect
38. C2×C3×#103C22semidirect
40. C2×#835C22semidirect
41. C2×#835C22semidirect
44. C2×#832C22semidirect
53. C2×(C2×D3)⋊C8C22semidirect
54. C2×(C2×D3)⋊C8C22semidirect
57. #4987C22semidirect
59. C2×#807C22semidirect
62. #4936C22semidirect
63. C2×C4×C3⋊C8C22semidirect
64. #4551C22semidirect
65. #4551C22semidirect
67. C2×#463D3semidirect
118. C3×#124D4semidirect
139. C2×#213D4semidirect
160. C4×D12D4semidirect
184. C22×SD16C2×D3semidirect
199. C2×C4×D4C2×D3semidirect
206. C2×C4⋊C8C2×D3semidirect
209. C2×#103C2×D3semidirect
405. #124#67semidirect
946. C3#24245semidirect

Maximal subgroups

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

subgroupindex
C2×#56762
C2×C3×#4632
C2×#51722
C2×#51562
#824162
C2×C4×#2132
#720542
#720432
#717252
#704802
#704702
#702752
#702672
#702062
#701982
#242453