Finite Group Databasebeta

← #10830632

Subgroups — #10830632

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×#5630C211yesmaximal, characteristic, complemented
2C2×#5172C211yesmaximal, characteristic, complemented
3C2×#5165C211yesmaximal, characteristic, complemented
4#82666C211yesmaximal, characteristic, complemented
5C2×#5036C211yesmaximal, characteristic, complemented
6C2×#4756C211yesmaximal, characteristic, complemented
7C3×#2000C211yesmaximal, characteristic, complemented
8#71695C211yesmaximal, characteristic, complemented
9#70267C211yesmaximal, characteristic, complemented
10#70226C211yesmaximal, characteristic, complemented
11#70204C211yesmaximal, characteristic, complemented
12#69959C211yesmaximal, characteristic, complemented
13#69916C211yesmaximal, characteristic, complemented
14#68893C211yesmaximal, characteristic, complemented
15#68822C211yesmaximal, characteristic, complemented
16#24245—31nomaximal, Sylow
17C22×#239C2211yescharacteristic
18C23×D12C2211yescharacteristic
19C22×C3×SD16C2211yescharacteristic, complemented
20C2×C3×C22⋊Q8C2211yescharacteristic
21C2×C3×#121C2211yescharacteristic
22C2×#947C2211yescharacteristic
23C2×#938C2211yescharacteristic, complemented
24C2×D4×Dic3C2211yescharacteristic, complemented
25C22×#213C2211yescharacteristic
26C22×#213C2211yescharacteristic
27C2×C4×#67C2211yescharacteristic
28#5630—24no—
29#5630—24no—
30C2×#895—21no—
31C2×#895C2211yescharacteristic
32C2×#894—21no—
33C2×#893C2211yescharacteristic
34C2×#882—21no—
35C2×D3×C22⋊C4—21no—
36C2×C3×#103C2211yescharacteristic, complemented
37C2×C3×#102C2211yescharacteristic, complemented
38C2×C3×C22⋊C8C2211yescharacteristic
39C2×#835C2211yescharacteristic, complemented
40C2×#835C2211yescharacteristic, complemented
41#5223—21no—
42#5220—21no—
43#5212C2211yescharacteristic
44C2×#830C2211yescharacteristic
45#5172—24no—
46#5165—24no—
47C2×#821C2211yescharacteristic
48C2×#821C2211yescharacteristic
49C2×#821C2211yescharacteristic
50C2×#821C2211yescharacteristic
51C2×(C2×D3)⋊C8C2211yescharacteristic, complemented
52C2×(C2×D3)⋊C8C2211yescharacteristic, complemented
53C2×Dic3⋊C8C2211yescharacteristic, complemented
54C2×C8×Dic3C2211yescharacteristic, complemented
55#5036—24no—
56#4987C2211yescharacteristic, complemented
57#4977C2211yescharacteristic, complemented
58C2×#809C2211yescharacteristic
59C2×#809C2211yescharacteristic
60C2×#807C2211yescharacteristic, complemented
61#4958—21no—
62#4952—21no—
63#4756—24no—
64C3×#340C2211yescharacteristic, complemented
65#4529C2211yescharacteristic, complemented
66C2×#546—31no—
67C2×#463—31no—
68C2×#449—31no—
69C2×#447—31no—
70C2×C4×D8—31no—
71#2535—31no—
72#2036—31no—
73#2033—31no—
74#2000D311yescharacteristic, complemented
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×D4—21no—
84C22×C3×D4C2311yescharacteristic
85C23×C3×C4C2311yescharacteristic
86C22×#67—21no—
87C22×#67D411yescharacteristic
88C23×Dic3—21no—
89C2×#239—22no—
90C2×#239—22no—
91C2×#239—22no—
92C2×#239—22no—
93C2×#239—41no—
94C2×#239—41no—
95C22×D12—21no—
96C22×D12—21no—
97C22×D12—21no—
98C22×D12—22no—
99C22×D12—22no—
100C22×D12—22no—
101C22×D12—22no—
102C22×D12—41no—
103C22×D12—41no—
104C22×D12C2311yescharacteristic
105C22×D12C2311yescharacteristic
106C22×C4×D3—21no—
107C22×C4×D3—21no—
108C22×C4×D3C2311yescharacteristic
109C2×C3×SD16—22no—
110C2×C3×SD16—22no—
111C2×C3×SD16—41no—
112C22×C3×C8C2311yescharacteristic
113C22×C3×C8C2311yescharacteristic
114C3×C22⋊Q8—22no—
115C3×C22⋊Q8—22no—
116C3×#121—22no—
117C3×#121—41no—
118C2×C3×C4⋊C4—21no—
119C2×C3×C4⋊C4C2311yescharacteristic
120C2×C3×C4⋊C4C2311yescharacteristic
121C2×C3×C22⋊C4—21no—
122C2×C3×C22⋊C4—21no—
123C2×#217—21no—
124C2×#217—21no—
125C2×#217—21no—
126C2×#217D411yescharacteristic
127#947—22no—
128#947D414yescomplemented
129#938—22no—
130#938—41no—
131D4×Dic3—22no—
132D4×Dic3—22no—
133C2×#213—22no—
134C2×#213—22no—
135C2×#213—22no—
136C2×#213—22no—
137C2×#213—41no—
138C2×#213D414yescomplemented
139C4×#67—22no—
140C4×#67—22no—
141C2×(C2×D3)⋊C4—21no—
142C2×(C2×D3)⋊C4—21no—
143C2×(C2×D3)⋊C4—21no—
144C2×(C2×D3)⋊C4—21no—
145C2×(C2×D3)⋊C4—21no—
146C2×(C2×D3)⋊C4D411yescharacteristic
147C2×C4⋊Dic3C2311yescharacteristic
148C2×C4⋊Dic3C2311yescharacteristic
149C2×Dic3⋊C4D411yescharacteristic
150C2×C4×Dic3C2311yescharacteristic
151C22×C3⋊C8C2311yescharacteristic
152C22×C3⋊C8C2311yescharacteristic
153#895—28no—
154#895—22no—
155#895—22no—
156#894—28no—
157#893—22no—
158#893D414yescomplemented
159#882—28no—
160D3×C22⋊C4—28no—
161C3×#103—41no—
162C3×#102—22no—
163C3×C22⋊C8—41no—
164#835—22no—
165#835—22no—
166C3⋊#95—21no—
167C3⋊#95—21no—
168C3⋊#95—21no—
169C3⋊#95—21no—
170#830—22no—
171#821—22no—
172#821—22no—
173#821—22no—
174#821—41no—
175(C2×D3)⋊C8—22no—
176(C2×D3)⋊C8—41no—
177Dic3⋊C8—22no—
178C8×Dic3—22no—
179#809—22no—
180#809—22no—
181#807—22no—
182C22×#41—31no—
183C23×D4—31no—
184C22×SD16C2×D311yescharacteristic, complemented
185C22×D8—31no—
186C22×D8—31no—
187#546—64no—
188#546—64no—
189C2×#124—31no—
190C2×#123—61no—
191C2×C22⋊Q8C2×D311yescharacteristic
192C2×#121—31no—
193C2×#121—31no—
194C2×#121—61no—
195C2×#121C2×D311yescharacteristic
196C2×#120—61no—
197C2×C4×D4—31no—
198C2×C4×D4—31no—
199C2×C4×D4—31no—
200C22×C22⋊C4—61no—
201#463—64no—
202#449—64no—
203#447—64no—
204C4×D8—64no—
205C2×#107—31no—
206C2×C4⋊C8—31no—
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, complemented
217C2×C22⋊C8—31no—
218C2×C22⋊C8—31no—
219C2×C22⋊C8—31no—
220C2×C22⋊C8C2×D311yescharacteristic
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#340C2×D311yescharacteristic, complemented
231C24×C3—21no—
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—
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—42no—
255C2×C3×D4—42no—
256C2×C3×D4—81no—
257C2×C3×D4C2×D412yes—
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×C4C2411yescharacteristic
269C2×#67—22no—
270C2×#67—22no—
271C2×#67—41no—
272C2×#67—42no—
273C2×#67—42no—
274C2×#67—81no—
275C22×Dic3—21no—
276C22×Dic3—21no—
277C22×Dic3—42no—
278C22×Dic3—81no—
279C22×Dic3—81no—
280C22×Dic3C2×D411yescharacteristic
281C22×Dic3C2×D411yescharacteristic
282C22×Dic3C2×D411yescharacteristic
283#239—44no—
284#239—44no—
285#239—44no—
286#239—44no—
287C2×D12—21no—
288C2×D12—21no—
289C2×D12—21no—
290C2×D12—21no—
291C2×D12—21no—
292C2×D12—21no—
293C2×D12—21no—
294C2×D12—24no—
295C2×D12—24no—
296C2×D12—21no—
297C2×D12—24no—
298C2×D12—44no—
299C2×D12—44no—
300C2×D12—44no—
301C2×D12—42no—
302C2×D12—42no—
303C2×D12—42no—
304C2×D12—42no—
305C2×D12—44no—
306C2×D12—81no—
307C2×D12—81no—
308C2×D12C2×D412yes—
309C2×D12C2×D412yes—
310C2×D12C2×D412yes—
311C2×D12#4112yes—
312C2×C4×D3—24no—
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—
325C2×C3×C8—21no—
326C2×C3×C8—21no—
327C2×C3×C8—21no—
328C2×C3×C8—21no—
329C2×C3×C8—21no—
330C2×C3×C8—21no—
331C3×C4⋊C4—24no—
332C3×C4⋊C4—21no—
333C3×C4⋊C4—21no—
334C3×C4⋊C4—21no—
335C3×C4⋊C4C2×D412yes—
336C3×C22⋊C4—24no—
337C3×C22⋊C4—42no—
338#217—22no—
339#217—42no—
340#217—42no—
341#217—81no—
342#213—28no—
343#213—44no—
344(C2×D3)⋊C4—24no—
345(C2×D3)⋊C4—24no—
346(C2×D3)⋊C4—24no—
347(C2×D3)⋊C4—24no—
348(C2×D3)⋊C4—22no—
349(C2×D3)⋊C4—81no—
350C4⋊Dic3—21no—
351C4⋊Dic3—21no—
352C4⋊Dic3—21no—
353C4⋊Dic3—21no—
354Dic3⋊C4—22no—
355C4×Dic3C2×D412yes—
356C4×Dic3C2×D412yes—
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—21no—
372C22×D4—31no—
373C22×D4—31no—
374C22×D4—31no—
375C22×D4—62no—
376C22×D4—62no—
377C22×D4—62no—
378C22×D4—62no—
379C22×D4—61no—
380C22×D4—61no—
381C22×D4—61no—
382C22×D4—61no—
383C22×D4—121no—
384C22×D4—121no—
385C22×D4C22×D311yescharacteristic
386C23×C4—31no—
387C23×C4—61no—
388C23×C4—61no—
389C23×C4—61no—
390C23×C4C22×D311yescharacteristic
391C2×SD16—22no—
392C2×SD16—22no—
393C2×SD16—41no—
394C2×D8—34no—
395C2×D8—62no—
396C2×D8—62no—
397C2×D8—62no—
398C2×D8—62no—
399C2×D8—121no—
400C22×C8—31no—
401C22×C8—31no—
402C22×C8C22×D311yescharacteristic
403C22×C8C22×D311yescharacteristic
404#124—34no—
405#124—62no—
406#123—68no—
407C22⋊Q8—22no—
408C22⋊Q8—22no—
409#121—22no—
410#121—41no—
411#121—62no—
412#121—68no—
413#121—62no—
414#121—62no—
415#121—121no—
416#120—68no—
417C4×D4—34no—
418C4×D4—62no—
419C4×D4—62no—
420C4×D4—62no—
421C4×D4—62no—
422C4×D4—62no—
423C2×C4⋊C4—21no—
424C2×C4⋊C4—31no—
425C2×C4⋊C4—31no—
426C2×C4⋊C4—31no—
427C2×C4⋊C4C22×D311yescharacteristic
428C2×C4⋊C4C22×D311yescharacteristic
429C2×C22⋊C4—21no—
430C2×C22⋊C4—21no—
431C2×C22⋊C4—31no—
432C2×C22⋊C4—31no—
433C2×C22⋊C4—68no—
434C2×C22⋊C4—61no—
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×C42—31no—
443#107—62no—
444C4⋊C8—62no—
445#103—41no—
446#103—62no—
447#103—62no—
448#102—22no—
449#102—62no—
450#102—62no—
451#102—62no—
452#102—62no—
453#102—62no—
454#102—121no—
455C22⋊C8—41no—
456C22⋊C8—62no—
457C22⋊C8—62no—
458C22⋊C8—121no—
459C4×C8—62no—
460#95—61no—
461#95—61no—
462#95—61no—
463#95—61no—
464C23×C3—21no—
465C23×C3—21no—
466C23×C3—21no—
467C23×C3—21no—
468C23×C3—21no—
469C23×C3—21no—
470C23×C3—22no—
471C23×C3—41no—
472C23×C3—41no—
473C23×C3—41no—
474C23×C3—41no—
475C23×C3—41no—
476C23×C3—41no—
477C23×C3#13512yes—
478C23×C3C22×D411yescharacteristic
479C22×D3—22no—
480C22×D3—22no—
481C22×D3—22no—
482C22×D3—22no—
483C22×D3—21no—
484C22×D3—21no—
485C22×D3—21no—
486C22×D3—21no—
487C22×D3—21no—
488C22×D3—21no—
489C22×D3—21no—
490C22×D3—48no—
491C22×D3—41no—
492C22×D3—41no—
493C22×D3—41no—
494C22×D3—41no—
495C22×D3—48no—
496C22×D3—41no—
497C22×D3—41no—
498C22×D3—41no—
499C22×D3—41no—
500C22×D3—41no—
501C22×D3—41no—
502C22×D3—84no—
503C22×D3—84no—
504C22×D3—84no—
505C22×D3—84no—
506C22×D3—84no—
507C3×Q8—22no—
508C3×Q8—22no—
509C3×Q8—41no—
510C3×Q8—41no—
511C3×D4—22no—
512C3×D4—22no—
513C3×D4—41no—
514C3×D4—41no—
515C3×D4—84no—
516C2×C3×C4—21no—
517C2×C3×C4—22no—
518C2×C3×C4—22no—
519C2×C3×C4—21no—
520C2×C3×C4—21no—
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—41no—
530C2×C3×C4—41no—
531C2×C3×C4—41no—
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—44no—
539#67—84no—
540C2×Dic3—21no—
541C2×Dic3—21no—
542C2×Dic3—21no—
543C2×Dic3—21no—
544C2×Dic3—21no—
545C2×Dic3—21no—
546C2×Dic3—21no—
547C2×Dic3—41no—
548C2×Dic3—41no—
549C2×Dic3—41no—
550C2×Dic3—41no—
551C2×Dic3—41no—
552C2×Dic3—41no—
553C2×Dic3—84no—
554C2×Dic3#12012yes—
555C2×Dic3#12012yes—
556D12—22no—
557D12—22no—
558D12—22no—
559D12—22no—
560D12—22no—
561D12—48no—
562D12—48no—
563D12—41no—
564D12—41no—
565D12—84no—
566D12#12114yes—
567C4×D3—48no—
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—31no—
579C24—64no—
580C24—61no—
581C24—61no—
582C24—122no—
583C24—122no—
584C24—122no—
585C24—122no—
586C24—241no—
587C24—241no—
588C24D3×D411yescharacteristic
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×Q8D3×D412yes—
599C2×D4—21no—
600C2×D4—21no—
601C2×D4—21no—
602C2×D4—21no—
603C2×D4—21no—
604C2×D4—32no—
605C2×D4—32no—
606C2×D4—32no—
607C2×D4—32no—
608C2×D4—42no—
609C2×D4—42no—
610C2×D4—64no—
611C2×D4—64no—
612C2×D4—64no—
613C2×D4—62no—
614C2×D4—62no—
615C2×D4—61no—
616C2×D4—61no—
617C2×D4—61no—
618C2×D4—61no—
619C2×D4—61no—
620C2×D4—61no—
621C2×D4—61no—
622C2×D4—61no—
623C2×D4—81no—
624C2×D4—122no—
625C2×D4—122no—
626C2×D4—124no—
627C2×D4—124no—
628C2×D4—124no—
629C2×D4—124no—
630C2×D4—122no—
631C2×D4—122no—
632C2×D4—121no—
633C2×D4—122no—
634C2×D4—122no—
635C2×D4—241no—
636C2×D4—241no—
637C2×D4—241no—
638C2×D4D3×D412yes—
639C22×C4—21no—
640C22×C4—21no—
641C22×C4—21no—
642C22×C4—21no—
643C22×C4—21no—
644C22×C4—21no—
645C22×C4—21no—
646C22×C4—21no—
647C22×C4—21no—
648C22×C4—31no—
649C22×C4—31no—
650C22×C4—31no—
651C22×C4—64no—
652C22×C4—64no—
653C22×C4—61no—
654C22×C4—61no—
655C22×C4—61no—
656C22×C4—61no—
657C22×C4—61no—
658C22×C4—61no—
659C22×C4—61no—
660C22×C4—61no—
661C22×C4—122no—
662C22×C4—122no—
663C22×C4—122no—
664C22×C4—241no—
665C22×C4—241no—
666C22×C4—241no—
667C22×C4—241no—
668C22×C4D3×D411yescharacteristic
669C22×C4C23×D311yescharacteristic
670SD16—44no—
671D8—68no—
672D8—124no—
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—24no—
686C4⋊C4—21no—
687C4⋊C4—21no—
688C4⋊C4—21no—
689C4⋊C4—62no—
690C4⋊C4—61no—
691C4⋊C4—61no—
692C4⋊C4—61no—
693C4⋊C4—61no—
694C4⋊C4D3×D412yes—
695C22⋊C4—24no—
696C22⋊C4—42no—
697C22⋊C4—62no—
698C22⋊C4—64no—
699C22⋊C4—64no—
700C22⋊C4—64no—
701C22⋊C4—64no—
702C22⋊C4—62no—
703C22⋊C4—122no—
704C22⋊C4—122no—
705C22⋊C4—241no—
706C22⋊C4—241no—
707C42—32no—
708C42—32no—
709C22×C3—22no—
710C22×C3—22no—
711C22×C3—22no—
712C22×C3—41no—
713C22×C3—41no—
714C22×C3—41no—
715C22×C3—41no—
716C22×C3—42no—
717C22×C3—42no—
718C22×C3—42no—
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—42no—
732C2×D3—42no—
733C2×D3—42no—
734C2×D3—42no—
735C2×D3—42no—
736C2×D3—42no—
737C2×D3—41no—
738C2×D3—42no—
739C2×D3—41no—
740C2×D3—42no—
741C2×D3—41no—
742C2×D3—42no—
743C2×D3—41no—
744C2×D3—41no—
745C2×D3—41no—
746C2×D3—41no—
747C2×D3—816no—
748C2×D3—81no—
749C2×D3—81no—
750C2×D3—81no—
751C2×D3—81no—
752C3×C4—42no—
753C3×C4—41no—
754C3×C4—42no—
755C3×C4—81no—
756C3×C4C2×#12111yescharacteristic
757C3×C4#53511yescharacteristic
758C3×C4D4211yescharacteristic
759C3×C4#54611yescharacteristic
760Dic3—22no—
761Dic3—22no—
762Dic3—41no—
763Dic3—81no—
764Dic3—81no—
765C23—21no—
766C23—21no—
767C23—21no—
768C23—21no—
769C23—21no—
770C23—21no—
771C23—22no—
772C23—41no—
773C23—41no—
774C23—41no—
775C23—41no—
776C23—41no—
777C23—41no—
778C23—62no—
779C23—62no—
780C23—62no—
781C23—61no—
782C23—61no—
783C23—61no—
784C23—61no—
785C23—62no—
786C23—61no—
787C23—61no—
788C23—61no—
789C23—128no—
790C23—128no—
791C23—121no—
792C23—121no—
793C23—121no—
794C23—121no—
795C23—121no—
796C23—121no—
797C23—121no—
798C23—121no—
799C23—121no—
800C23—121no—
801C23—244no—
802C23—244no—
803C23—244no—
804C23—244no—
805C23—244no—
806C23#91612yes—
807C23C2×D3×D411yescharacteristic
808Q8—22no—
809Q8—22no—
810Q8—41no—
811Q8—41no—
812D4—22no—
813D4—22no—
814D4—34no—
815D4—41no—
816D4—41no—
817D4—62no—
818D4—62no—
819D4—62no—
820D4—62no—
821D4—62no—
822D4—84no—
823D4—128no—
824D4—128no—
825D4—124no—
826D4—121no—
827D4—121no—
828D4—244no—
829D4—244no—
830C2×C4—22no—
831C2×C4—22no—
832C2×C4—21no—
833C2×C4—21no—
834C2×C4—21no—
835C2×C4—32no—
836C2×C4—32no—
837C2×C4—41no—
838C2×C4—41no—
839C2×C4—41no—
840C2×C4—41no—
841C2×C4—41no—
842C2×C4—41no—
843C2×C4—41no—
844C2×C4—41no—
845C2×C4—41no—
846C2×C4—41no—
847C2×C4—41no—
848C2×C4—61no—
849C2×C4—61no—
850C2×C4—61no—
851C2×C4—61no—
852C2×C4—61no—
853C2×C4—61no—
854C2×C4—61no—
855C2×C4—128no—
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—121no—
866C2×C4—244no—
867C2×C4—244no—
868C2×C4C2×D3×D411yescharacteristic
869C2×C4C2×D3×D411yescharacteristic
870C2×C4C2×D3×D411yescharacteristic
871C2×C4#100411yescharacteristic
872C2×C4#100411yescharacteristic
873C2×C4D3×#4111yescharacteristic
874C8—41no—
875C8—41no—
876C8—62no—
877C8—121no—
878C2×C3—42no—
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—44no—
888D3—81no—
889D3—82no—
890C22—22no—
891C22—22no—
892C22—22no—
893C22—41no—
894C22—41no—
895C22—41no—
896C22—41no—
897C22—42no—
898C22—42no—
899C22—42no—
900C22—64no—
901C22—81no—
902C22—81no—
903C22—81no—
904C22—81no—
905C22—122no—
906C22—122no—
907C22—122no—
908C22—122no—
909C22—122no—
910C22—122no—
911C22—121no—
912C22—121no—
913C22—121no—
914C22—121no—
915C22—122no—
916C22—121no—
917C22—122no—
918C22—121no—
919C22—121no—
920C22—122no—
921C22—2416no—
922C22—241no—
923C22—241no—
924C22—241no—
925C22—241no—
926C22D3×#12011yescharacteristic
927C22#559011yescharacteristic
928C22#561011yescharacteristic
929C22C2×#91611yescharacteristic
930C22#576911yescharacteristic
931C22#577411yescharacteristic
932C22#577711yescharacteristic
933C4—41no—
934C4—42no—
935C4—42no—
936C4—62no—
937C4—62no—
938C4—81no—
939C4—121no—
940C4—241no—
941C4—241no—
942C4#559011yescharacteristic
943C4D3×#12111yescharacteristic
944C4#561011yescharacteristic
945C4#571511yescharacteristic
946C3#2424511yescharacteristic, complemented, Sylow
947C2—42no—
948C2—82no—
949C2—124no—
950C2—241no—
951C2—242no—
952C2#7666911yescharacteristic
953C2#8003811yescharacteristic
954C2#8008511yescharacteristic
955C2#8016811yescharacteristic
956C2#8024311yescharacteristic
957C2#8068111yescharacteristic
958C2#8084011yescharacteristic
subgroupG/H
centerC23C2×D3×D4
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC3×#2000C2
socleC23×C3C22×D4
hypercenter#2000D3
hypocenterC3#24245
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C23×C4 ◁ #2000

Complements

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

NH ≅ G/Ntype
1. C2×#5630C2semidirect
2. C2×#5172C2semidirect
3. C2×#5165C2semidirect
4. #82666C2semidirect
5. C2×#5036C2semidirect
6. C2×#4756C2semidirect
7. C3×#2000C2semidirect
8. #71695C2semidirect
9. #70267C2semidirect
10. #70226C2semidirect
11. #70204C2semidirect
12. #69959C2semidirect
13. #69916C2semidirect
14. #68893C2semidirect
15. #68822C2semidirect
19. C22×C3×SD16C22semidirect
23. C2×#938C22semidirect
24. C2×D4×Dic3C22semidirect
36. C2×C3×#103C22semidirect
37. C2×C3×#102C22semidirect
39. C2×#835C22semidirect
40. C2×#835C22semidirect
51. C2×(C2×D3)⋊C8C22semidirect
52. C2×(C2×D3)⋊C8C22semidirect
53. C2×Dic3⋊C8C22semidirect
54. C2×C8×Dic3C22semidirect
56. #4987C22semidirect
57. #4977C22semidirect
60. C2×#807C22semidirect
64. C3×#340C22semidirect
65. #4529C22semidirect
74. #2000D3semidirect
128. #947D4semidirect
138. C2×#213D4semidirect
158. #893D4semidirect
184. C22×SD16C2×D3semidirect
209. C2×#103C2×D3semidirect
216. C2×#102C2×D3semidirect
230. #340C2×D3semidirect
946. C3#24245semidirect

Maximal subgroups

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

subgroupindex
C2×#56302
C2×#51722
C2×#51652
#826662
C2×#50362
C2×#47562
C3×#20002
#716952
#702672
#702262
#702042
#699592
#699162
#688932
#688222
#242453