Finite Group Databasebeta

← #10830636

Subgroups — #10830636

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×#5829C211yesmaximal, characteristic, complemented
2C2×C3×#449C211yesmaximal, characteristic, complemented
3C2×#5165C211yesmaximal, characteristic, complemented
4C2×#5156C211yesmaximal, characteristic, complemented
5C2×Dic3×D8C211yesmaximal, characteristic, complemented
6#82666C211yesmaximal, characteristic, complemented
7#72135C211yesmaximal, characteristic, complemented
8#72054C211yesmaximal, characteristic, complemented
9#71684C211yesmaximal, characteristic, complemented
10#70244C211yesmaximal, characteristic, complemented
11#70226C211yesmaximal, characteristic, complemented
12#70198C211yesmaximal, characteristic, complemented
13#70154C211yesmaximal, characteristic, complemented
14#69934C211yesmaximal, characteristic, complemented
15#69916C211yesmaximal, characteristic, complemented
16#24245—31nomaximal, Sylow
17C22×C3×#41C2211yescharacteristic
18C22×D3×D4C2211yescharacteristic
19C22×C3×SD16C2211yescharacteristic, complemented
20C22×C3×D8C2211yescharacteristic
21C2×C3×#121C2211yescharacteristic, complemented
22#5829—24no—
23#5829—24no—
24C2×#947C2211yescharacteristic
25C2×#946C2211yescharacteristic
26C2×#939—21no—
27C2×#938C2211yescharacteristic
28C2×#937—21no—
29C2×D4×Dic3C2211yescharacteristic
30C2×D4×Dic3C2211yescharacteristic, complemented
31C22×#213C2211yescharacteristic
32C2×#930C2211yescharacteristic
33C2×#929—21no—
34C2×C4×#67C2211yescharacteristic
35C22×(C2×D3)⋊C4—21no—
36C3×#449—24no—
37C2×C3×#103C2211yescharacteristic, complemented
38C2×C3×#102C2211yescharacteristic
39C2×C3×C22⋊C8C2211yescharacteristic, complemented
40C2×#835C2211yescharacteristic, complemented
41C2×#835C2211yescharacteristic, complemented
42#5223—21no—
43#5220—21no—
44C2×#832C2211yescharacteristic
45C2×#832C2211yescharacteristic
46C2×#832C2211yescharacteristic, complemented
47#5212C2211yescharacteristic, complemented
48C2×#830C2211yescharacteristic, complemented
49#5165—24no—
50#5156—24no—
51Dic3×D8—24no—
52C2×#821C2211yescharacteristic
53C2×#821C2211yescharacteristic
54C2×(C2×D3)⋊C8C2211yescharacteristic
55C2×(C2×D3)⋊C8C2211yescharacteristic
56C2×#818C2211yescharacteristic, complemented
57C2×Dic3⋊C8C2211yescharacteristic, complemented
58C2×C8×Dic3C2211yescharacteristic, complemented
59#4987C2211yescharacteristic
60#4977C2211yescharacteristic, complemented
61C2×#809C2211yescharacteristic
62#4958—21no—
63#4952—21no—
64#4551C2211yescharacteristic, complemented
65#4529C2211yescharacteristic, complemented
66C2×#546—31no—
67C2×#463—31no—
68C2×#449D311yescharacteristic, complemented
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—
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×D4—21no—
90C22×C3×D4—21no—
91C22×C3×D4C2311yescharacteristic
92C22×C3×D4C2311yescharacteristic
93C23×C3×C4—21no—
94C23×C3×C4C2311yescharacteristic
95C22×#67—21no—
96C22×#67—21no—
97C22×#67—21no—
98C22×#67D411yescharacteristic
99C23×Dic3—21no—
100C23×Dic3—21no—
101C2×D3×D4—22no—
102C2×D3×D4—22no—
103C2×D3×D4—22no—
104C2×D3×D4—22no—
105C2×D3×D4—41no—
106C2×D3×D4—41no—
107C22×D12C2311yescharacteristic
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×D8D414yescomplemented
115C22×C3×C8C2311yescharacteristic
116C22×C3×C8C2311yescharacteristic
117C3×#121—22no—
118C3×#121—41no—
119C2×C3×C4⋊C4C2311yescharacteristic
120C2×C3×C22⋊C4—21no—
121C2×#217—21no—
122C2×#217—21no—
123C2×#217—21no—
124C2×#217—21no—
125C2×#217D411yescharacteristic
126#947—22no—
127#947D414yescomplemented
128#946—22no—
129#946—22no—
130#939—28no—
131#938—22no—
132#938—41no—
133#937—28no—
134D4×Dic3—22no—
135D4×Dic3—22no—
136D4×Dic3—22no—
137D4×Dic3D414yescomplemented
138C2×#213—22no—
139C2×#213—22no—
140C2×#213—41no—
141#930—22no—
142#930—22no—
143#929—28no—
144C4×#67—22no—
145C4×#67—22no—
146C2×(C2×D3)⋊C4—28no—
147C2×(C2×D3)⋊C4—21no—
148C2×(C2×D3)⋊C4—21no—
149C2×(C2×D3)⋊C4—21no—
150C2×(C2×D3)⋊C4—21no—
151C2×(C2×D3)⋊C4—21no—
152C2×(C2×D3)⋊C4D411yescharacteristic
153C2×C4⋊Dic3C2311yescharacteristic
154C2×C4⋊Dic3C2311yescharacteristic
155C2×C4⋊Dic3C2311yescharacteristic
156C2×Dic3⋊C4—21no—
157C2×Dic3⋊C4D411yescharacteristic
158C2×C4×Dic3C2311yescharacteristic
159C22×C3⋊C8C2311yescharacteristic
160C22×C3⋊C8C2311yescharacteristic
161C3×#103—22no—
162C3×#102—22no—
163C3×C22⋊C8—22no—
164#835—22no—
165#835—41no—
166#832—22no—
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#818—22no—
179Dic3⋊C8—22no—
180C8×Dic3—22no—
181#809—41no—
182C22×#41C2×D311yescharacteristic
183C23×D4—31no—
184C22×SD16C2×D311yescharacteristic, complemented
185C22×D8—31no—
186C22×D8C2×D311yescharacteristic
187#546—64no—
188#546—64no—
189C2×#124—31no—
190C2×#123—61no—
191C2×C22⋊Q8—31no—
192C2×#121—31no—
193C2×#121—31no—
194C2×#121—61no—
195C2×#121C2×D311yescharacteristic, complemented
196C2×#120—61no—
197C2×C4×D4—31no—
198C2×C4×D4—31no—
199C2×C4×D4—31no—
200C22×C22⋊C4—61no—
201#463—64no—
202#449—24no—
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
217C2×C22⋊C8—31no—
218C2×C22⋊C8—31no—
219C2×C22⋊C8—31no—
220C2×C22⋊C8C2×D311yescharacteristic, complemented
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—
233C24×C3C2×D411yescharacteristic
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
243C3×#41—44no—
244C3×#41—44no—
245C3×#41—44no—
246C3×#41—44no—
247C2×C3×Q8—21no—
248C2×C3×Q8—21no—
249C2×C3×Q8—21no—
250C2×C3×Q8—21no—
251C2×C3×Q8—21no—
252C2×C3×Q8C2×D412yes—
253C2×C3×D4—24no—
254C2×C3×D4—21no—
255C2×C3×D4—21no—
256C2×C3×D4—21no—
257C2×C3×D4—21no—
258C2×C3×D4—21no—
259C2×C3×D4—21no—
260C2×C3×D4—21no—
261C2×C3×D4—21no—
262C2×C3×D4—42no—
263C2×C3×D4—42no—
264C2×C3×D4—42no—
265C2×C3×D4—42no—
266C2×C3×D4—81no—
267C2×C3×D4C2×D412yes—
268C2×C3×D4C2×D412yes—
269C2×C3×D4C2×D412yes—
270C2×C3×D4#4112yes—
271C22×C3×C4—24no—
272C22×C3×C4—21no—
273C22×C3×C4—21no—
274C22×C3×C4—21no—
275C22×C3×C4—21no—
276C22×C3×C4—21no—
277C22×C3×C4—21no—
278C22×C3×C4—21no—
279C22×C3×C4—21no—
280C22×C3×C4—42no—
281C22×C3×C4—42no—
282C22×C3×C4C2×D411yescharacteristic
283C22×C3×C4C2411yescharacteristic
284C2×#67—24no—
285C2×#67—22no—
286C2×#67—24no—
287C2×#67—22no—
288C2×#67—41no—
289C2×#67—42no—
290C2×#67—42no—
291C2×#67—42no—
292C2×#67—42no—
293C2×#67—81no—
294C2×#67—81no—
295C2×#67—81no—
296C22×Dic3—21no—
297C22×Dic3—24no—
298C22×Dic3—21no—
299C22×Dic3—21no—
300C22×Dic3—42no—
301C22×Dic3—81no—
302C22×Dic3—81no—
303C22×Dic3—81no—
304C22×Dic3—81no—
305C22×Dic3C2×D411yescharacteristic
306C22×Dic3C2×D411yescharacteristic
307C22×Dic3C2×D411yescharacteristic
308D3×D4—44no—
309D3×D4—44no—
310D3×D4—44no—
311D3×D4—44no—
312C2×D12—21no—
313C2×D12—21no—
314C2×D12—21no—
315C2×D12—21no—
316C2×D12—21no—
317C2×D12C2×D412yes—
318C2×C4×D3—21no—
319C2×C4×D3—21no—
320C2×C4×D3—21no—
321C2×C4×D3—21no—
322C2×C4×D3—21no—
323C2×C4×D3—21no—
324C3×SD16—44no—
325C3×D8—28no—
326C2×C3×C8—21no—
327C2×C3×C8—21no—
328C2×C3×C8—21no—
329C2×C3×C8—21no—
330C2×C3×C8—21no—
331C2×C3×C8C2×D412yes—
332C3×C4⋊C4—21no—
333C3×C4⋊C4—21no—
334C3×C22⋊C4—42no—
335#217—22no—
336#217—24no—
337#217—42no—
338#217—42no—
339#217—81no—
340#213—44no—
341(C2×D3)⋊C4—24no—
342(C2×D3)⋊C4—24no—
343(C2×D3)⋊C4—22no—
344(C2×D3)⋊C4—24no—
345(C2×D3)⋊C4—24no—
346(C2×D3)⋊C4—81no—
347C4⋊Dic3—21no—
348C4⋊Dic3—21no—
349C4⋊Dic3—21no—
350C4⋊Dic3—21no—
351C4⋊Dic3—21no—
352C4⋊Dic3C2×D412yes—
353Dic3⋊C4—24no—
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⋊C8—21no—
363C25—61no—
364C2×#41—22no—
365C2×#41—22no—
366C2×#41—22no—
367C2×#41—22no—
368C2×#41—41no—
369C2×#41—41no—
370C22×Q8C22×D311yescharacteristic
371C22×D4—21no—
372C22×D4—21no—
373C22×D4—31no—
374C22×D4—31no—
375C22×D4—61no—
376C22×D4—62no—
377C22×D4—61no—
378C22×D4—62no—
379C22×D4—62no—
380C22×D4—62no—
381C22×D4—61no—
382C22×D4—121no—
383C22×D4—121no—
384C22×D4C22×D311yescharacteristic
385C22×D4C22×D311yescharacteristic
386C23×C4—21no—
387C23×C4—31no—
388C23×C4—61no—
389C23×C4—61no—
390C23×C4C22×D311yescharacteristic
391C2×SD16—22no—
392C2×SD16—22no—
393C2×SD16—41no—
394C2×D8—22no—
395C2×D8—22no—
396C2×D8—62no—
397C2×D8—62no—
398C2×D8—121no—
399C2×D8#6714yescomplemented
400C22×C8—31no—
401C22×C8—31no—
402C22×C8C22×D311yescharacteristic
403C22×C8C22×D311yescharacteristic
404#124—34no—
405#124—62no—
406#123—68no—
407C22⋊Q8—62no—
408C22⋊Q8—62no—
409#121—22no—
410#121—41no—
411#121—62no—
412#121—62no—
413#121—68no—
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—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—31no—
431C2×C22⋊C4—31no—
432C2×C22⋊C4—61no—
433C2×C22⋊C4—61no—
434C2×C22⋊C4—61no—
435C2×C22⋊C4—68no—
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—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—22no—
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—22no—
467C23×C3—21no—
468C23×C3—22no—
469C23×C3—21no—
470C23×C3—21no—
471C23×C3—21no—
472C23×C3—21no—
473C23×C3—21no—
474C23×C3—21no—
475C23×C3—41no—
476C23×C3—41no—
477C23×C3—41no—
478C23×C3—41no—
479C23×C3—41no—
480C23×C3—41no—
481C23×C3—41no—
482C23×C3—41no—
483C23×C3—41no—
484C23×C3—41no—
485C23×C3C22×D411yescharacteristic
486C22×D3—21no—
487C22×D3—21no—
488C22×D3—21no—
489C22×D3—21no—
490C22×D3—21no—
491C22×D3—21no—
492C22×D3—22no—
493C22×D3—48no—
494C22×D3—48no—
495C22×D3—41no—
496C22×D3—41no—
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—22no—
516C3×D4—48no—
517C3×D4—41no—
518C3×D4—41no—
519C3×D4—84no—
520C3×D4#12114yes—
521C2×C3×C4—21no—
522C2×C3×C4—22no—
523C2×C3×C4—21no—
524C2×C3×C4—21no—
525C2×C3×C4—48no—
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×C4—41no—
533C2×C3×C4—41no—
534C2×C3×C4—41no—
535C2×C3×C4C22×D411yescharacteristic
536C2×C3×C4C22×D411yescharacteristic
537C2×C3×C4C22×D411yescharacteristic
538C2×C3×C4C2×#4111yescharacteristic
539C2×C3×C4H(5,𝔽2)11yescharacteristic
540C2×C3×C4H(5,𝔽2)11yescharacteristic
541#67—44no—
542#67—48no—
543#67—84no—
544#67—84no—
545C2×Dic3—21no—
546C2×Dic3—21no—
547C2×Dic3—21no—
548C2×Dic3—21no—
549C2×Dic3—21no—
550C2×Dic3—22no—
551C2×Dic3—21no—
552C2×Dic3—21no—
553C2×Dic3—41no—
554C2×Dic3—41no—
555C2×Dic3—41no—
556C2×Dic3—41no—
557C2×Dic3—41no—
558C2×Dic3—41no—
559C2×Dic3—41no—
560C2×Dic3—41no—
561C2×Dic3—84no—
562C2×Dic3—84no—
563C2×Dic3#12012yes—
564C2×Dic3#12012yes—
565D12—22no—
566D12—22no—
567D12—41no—
568D12—41no—
569C4×D3—41no—
570C4×D3—41no—
571C4×D3—41no—
572C4×D3—41no—
573C3×C8—22no—
574C3×C8—41no—
575C3⋊C8—41no—
576C3⋊C8—41no—
577C24—21no—
578C24—21no—
579C24—31no—
580C24—64no—
581C24—61no—
582C24—122no—
583C24—122no—
584C24—122no—
585C24—122no—
586C24—241no—
587C24—241no—
588C24D3×D411yescharacteristic
589#41—44no—
590#41—44no—
591#41—44no—
592#41—44no—
593C2×Q8—21no—
594C2×Q8—21no—
595C2×Q8—21no—
596C2×Q8—21no—
597C2×Q8—21no—
598C2×Q8D3×D412yes—
599C2×D4—24no—
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—32no—
609C2×D4—42no—
610C2×D4—42no—
611C2×D4—42no—
612C2×D4—42no—
613C2×D4—62no—
614C2×D4—62no—
615C2×D4—64no—
616C2×D4—64no—
617C2×D4—61no—
618C2×D4—61no—
619C2×D4—61no—
620C2×D4—61no—
621C2×D4—61no—
622C2×D4—81no—
623C2×D4—121no—
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—241no—
633C2×D4—241no—
634C2×D4—241no—
635C2×D4D3×D412yes—
636C2×D4#23712yes—
637C2×D4C2×#6712yes—
638C2×D4C2×#6712yes—
639C22×C4—24no—
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—42no—
652C22×C4—42no—
653C22×C4—64no—
654C22×C4—61no—
655C22×C4—61no—
656C22×C4—61no—
657C22×C4—61no—
658C22×C4—61no—
659C22×C4—61no—
660C22×C4—61no—
661C22×C4—61no—
662C22×C4—61no—
663C22×C4—122no—
664C22×C4—241no—
665C22×C4—241no—
666C22×C4—241no—
667C22×C4—241no—
668C22×C4D3×D411yescharacteristic
669C22×C4C23×D311yescharacteristic
670SD16—44no—
671D8—28no—
672D8—124no—
673C2×C8—21no—
674C2×C8—21no—
675C2×C8—21no—
676C2×C8—21no—
677C2×C8—21no—
678C2×C8—61no—
679C2×C8—61no—
680C2×C8—61no—
681C2×C8—61no—
682C2×C8—61no—
683C2×C8—61no—
684C2×C8C2×#6712yes—
685C4⋊C4—21no—
686C4⋊C4—21no—
687C4⋊C4—32no—
688C4⋊C4—62no—
689C4⋊C4—64no—
690C4⋊C4—61no—
691C4⋊C4—61no—
692C4⋊C4—61no—
693C4⋊C4—61no—
694C4⋊C4—61no—
695C22⋊C4—42no—
696C22⋊C4—62no—
697C22⋊C4—64no—
698C22⋊C4—64no—
699C22⋊C4—64no—
700C22⋊C4—64no—
701C22⋊C4—62no—
702C22⋊C4—64no—
703C22⋊C4—122no—
704C22⋊C4—122no—
705C22⋊C4—241no—
706C22⋊C4—241no—
707C42—32no—
708C42—32no—
709C22×C3—24no—
710C22×C3—42no—
711C22×C3—42no—
712C22×C3—42no—
713C22×C3—42no—
714C22×C3—42no—
715C22×C3—42no—
716C22×C3—41no—
717C22×C3—42no—
718C22×C3—41no—
719C22×C3—41no—
720C22×C3—41no—
721C22×C3—42no—
722C22×C3—42no—
723C22×C3—41no—
724C22×C3—41no—
725C22×C3—41no—
726C22×C3—81no—
727C22×C3—81no—
728C22×C3—81no—
729C22×C3—81no—
730C22×C3C2×#12011yescharacteristic
731C22×C3D4211yescharacteristic
732C22×C3#54611yescharacteristic
733C22×C3C2×#13511yescharacteristic
734C22×C3#57511yescharacteristic
735C22×C3#57611yescharacteristic
736C22×C3#57611yescharacteristic
737C2×D3—22no—
738C2×D3—22no—
739C2×D3—22no—
740C2×D3—41no—
741C2×D3—41no—
742C2×D3—41no—
743C2×D3—41no—
744C2×D3—42no—
745C2×D3—42no—
746C2×D3—42no—
747C2×D3—816no—
748C2×D3—81no—
749C2×D3—81no—
750C2×D3—81no—
751C2×D3—81no—
752C3×C4—41no—
753C3×C4—42no—
754C3×C4—81no—
755C3×C4C2×#12111yescharacteristic
756C3×C4#53511yescharacteristic
757C3×C4D4211yescharacteristic
758C3×C4#54611yescharacteristic
759Dic3—22no—
760Dic3—22no—
761Dic3—41no—
762Dic3—42no—
763Dic3—81no—
764Dic3—81no—
765C23—22no—
766C23—22no—
767C23—22no—
768C23—21no—
769C23—21no—
770C23—21no—
771C23—21no—
772C23—22no—
773C23—21no—
774C23—21no—
775C23—21no—
776C23—32no—
777C23—41no—
778C23—41no—
779C23—41no—
780C23—41no—
781C23—41no—
782C23—41no—
783C23—41no—
784C23—41no—
785C23—41no—
786C23—41no—
787C23—61no—
788C23—61no—
789C23—61no—
790C23—61no—
791C23—61no—
792C23—61no—
793C23—62no—
794C23—128no—
795C23—128no—
796C23—121no—
797C23—121no—
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—22no—
817D4—48no—
818D4—41no—
819D4—41no—
820D4—62no—
821D4—62no—
822D4—84no—
823D4—124no—
824D4—128no—
825D4—121no—
826D4—121no—
827D4—244no—
828D4—244no—
829D4#93914yes—
830C2×C4—21no—
831C2×C4—21no—
832C2×C4—22no—
833C2×C4—21no—
834C2×C4—32no—
835C2×C4—32no—
836C2×C4—48no—
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—61no—
847C2×C4—61no—
848C2×C4—61no—
849C2×C4—61no—
850C2×C4—61no—
851C2×C4—62no—
852C2×C4—61no—
853C2×C4—61no—
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—121no—
866C2×C4—244no—
867C2×C4—244no—
868C2×C4C2×D3×D411yescharacteristic
869C2×C4C2×D3×D411yescharacteristic
870C2×C4C2×#23711yescharacteristic
871C2×C4#100411yescharacteristic
872C2×C4#100411yescharacteristic
873C2×C4C22×#6711yescharacteristic
874C8—22no—
875C8—41no—
876C8—121no—
877C8—121no—
878C2×C3—44no—
879C2×C3—81no—
880C2×C3—82no—
881C2×C3#240811yescharacteristic
882C2×C3#300211yescharacteristic
883C2×C3#300811yescharacteristic
884C2×C3#327311yescharacteristic
885C2×C3#328011yescharacteristic
886C2×C3#329711yescharacteristic
887C2×C3#332211yescharacteristic
888D3—42no—
889D3—82no—
890C22—24no—
891C22—42no—
892C22—42no—
893C22—42no—
894C22—42no—
895C22—42no—
896C22—42no—
897C22—41no—
898C22—42no—
899C22—42no—
900C22—41no—
901C22—41no—
902C22—41no—
903C22—41no—
904C22—41no—
905C22—41no—
906C22—42no—
907C22—62no—
908C22—62no—
909C22—62no—
910C22—81no—
911C22—81no—
912C22—81no—
913C22—81no—
914C22—121no—
915C22—121no—
916C22—121no—
917C22—121no—
918C22—122no—
919C22—122no—
920C22—122no—
921C22—2416no—
922C22—241no—
923C22—241no—
924C22—241no—
925C22—241no—
926C22D3×#12011yescharacteristic
927C22#559111yescharacteristic
928C22D3×#13511yescharacteristic
929C22#576911yescharacteristic
930C22#577311yescharacteristic
931C22#577411yescharacteristic
932C22D4×#6711yescharacteristic
933C4—41no—
934C4—42no—
935C4—62no—
936C4—62no—
937C4—81no—
938C4—121no—
939C4—122no—
940C4—241no—
941C4—241no—
942C4#559111yescharacteristic
943C4#559211yescharacteristic
944C4D4×#6711yescharacteristic
945C4C2×#93911yescharacteristic
946C3#2424511yescharacteristic, complemented, Sylow
947C2—44no—
948C2—81no—
949C2—82no—
950C2—122no—
951C2—242no—
952C2#8008211yescharacteristic
953C2#8008511yescharacteristic
954C2#8010211yescharacteristic
955C2#8011411yescharacteristic
956C2#8258211yescharacteristic
957C2#8391811yescharacteristic
958C2#8396111yescharacteristic
subgroupG/H
centerC23C2×D3×D4
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC2×C3×#449C2
socleC23×C3C22×D4
hypercenterC2×#449D3
hypocenterC3#24245
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#449

Complements

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

NH ≅ G/Ntype
1. C2×#5829C2semidirect
2. C2×C3×#449C2semidirect
3. C2×#5165C2semidirect
4. C2×#5156C2semidirect
5. C2×Dic3×D8C2semidirect
6. #82666C2semidirect
7. #72135C2semidirect
8. #72054C2semidirect
9. #71684C2semidirect
10. #70244C2semidirect
11. #70226C2semidirect
12. #70198C2semidirect
13. #70154C2semidirect
14. #69934C2semidirect
15. #69916C2semidirect
19. C22×C3×SD16C22semidirect
21. C2×C3×#121C22semidirect
30. C2×D4×Dic3C22semidirect
37. C2×C3×#103C22semidirect
39. C2×C3×C22⋊C8C22semidirect
40. C2×#835C22semidirect
41. C2×#835C22semidirect
46. C2×#832C22semidirect
47. #5212C22semidirect
48. C2×#830C22semidirect
56. C2×#818C22semidirect
57. C2×Dic3⋊C8C22semidirect
58. C2×C8×Dic3C22semidirect
60. #4977C22semidirect
64. #4551C22semidirect
65. #4529C22semidirect
68. C2×#449D3semidirect
114. C2×C3×D8D4semidirect
127. #947D4semidirect
137. D4×Dic3D4semidirect
184. C22×SD16C2×D3semidirect
195. C2×#121C2×D3semidirect
209. C2×#103C2×D3semidirect
220. C2×C22⋊C8C2×D3semidirect
399. C2×D8#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×#58292
C2×C3×#4492
C2×#51652
C2×#51562
C2×Dic3×D82
#826662
#721352
#720542
#716842
#702442
#702262
#701982
#701542
#699342
#699162
#242453