Finite Group Databasebeta

← #10830635

Subgroups — #10830635

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×#5550C211yesmaximal, characteristic, complemented
2C3×#2535C211yesmaximal, characteristic, complemented
3C2×#5037C211yesmaximal, characteristic, complemented
4C2×#5036C211yesmaximal, characteristic, complemented
5C2×#5016C211yesmaximal, characteristic, complemented
6C2×C4×#213C211yesmaximal, characteristic, complemented
7#71685C211yesmaximal, characteristic, complemented
8#71684C211yesmaximal, characteristic, complemented
9#71614C211yesmaximal, characteristic, complemented
10#69556C211yesmaximal, characteristic, complemented
11#69551C211yesmaximal, characteristic, complemented
12#69527C211yesmaximal, characteristic, complemented
13#69523C211yesmaximal, characteristic, complemented
14#69522C211yesmaximal, characteristic, complemented
15#69521C211yesmaximal, characteristic, complemented
16#24245—31nomaximal, Sylow
17C22×#235C2211yescharacteristic
18C23×D12C2211yescharacteristic
19C2×C3×#121C2211yescharacteristic
20C2×C3×#121C2211yescharacteristic, complemented
21C2×C3×C4×D4C2211yescharacteristic
22C2×C3×C4×D4C2211yescharacteristic, complemented
23C2×#937—21no—
24C22×#214C2211yescharacteristic, complemented
25C22×#213C2211yescharacteristic
26C22×#213C2211yescharacteristic
27C2×#930C2211yescharacteristic
28C2×#924C2211yescharacteristic
29#5550—24no—
30#5550—24no—
31C2×#894—21no—
32C2×#884—21no—
33C2×D3×C22⋊C4—21no—
34C2×#875C2211yescharacteristic
35C2×C4×D12C2211yescharacteristic
36C3×#397—21no—
37C3×#392—21no—
38C3×#386—21no—
39C3×#386—21no—
40C3×#382C2211yescharacteristic, complemented
41C3×#380C2211yescharacteristic
42C3×#380C2211yescharacteristic, complemented
43C2×#832C2211yescharacteristic, complemented
44C2×#830C2211yescharacteristic
45C2×#830C2211yescharacteristic
46C2×#830C2211yescharacteristic, complemented
47C2×#830C2211yescharacteristic, complemented
48#5037—24no—
49#5036—24no—
50#5016—24no—
51C4×#213—24no—
52C2×#810C2211yescharacteristic, complemented
53C2×#810C2211yescharacteristic, complemented
54C2×#810C2211yescharacteristic, complemented
55C2×#809C2211yescharacteristic
56C2×#809C2211yescharacteristic
57C2×#809C2211yescharacteristic
58C2×#809C2211yescharacteristic
59C2×#809C2211yescharacteristic
60C2×#809C2211yescharacteristic
61C2×#807C2211yescharacteristic, complemented
62C2×C4⋊(C3⋊C8)C2211yescharacteristic, complemented
63C2×C4×C3⋊C8C2211yescharacteristic, complemented
64#4529C2211yescharacteristic, complemented
65#4529C2211yescharacteristic, complemented
66C2×#546—31no—
67C2×#463—31no—
68C2×#449—31no—
69C2×#447—31no—
70C2×C4×D8—31no—
71#2535D311yescharacteristic, complemented
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×D4—21no—
83C22×C3×D4—21no—
84C22×C3×D4D411yescharacteristic
85C22×C3×D4C2311yescharacteristic
86C23×C3×C4—21no—
87C23×C3×C4C2311yescharacteristic
88C23×C3×C4C2311yescharacteristic
89C22×#67—21no—
90C22×#67—21no—
91C2×#235—22no—
92C2×#235—22no—
93C2×#235—22no—
94C2×#235—22no—
95C2×#235—41no—
96C2×#235—41no—
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×Dic6C2311yescharacteristic
109C3×#121—22no—
110C3×#121—22no—
111C3×#121—41no—
112C3×#121—41no—
113C3×C4×D4—22no—
114C3×C4×D4—22no—
115C3×C4×D4—22no—
116C3×C4×D4—22no—
117C2×C3×C4⋊C4D411yescharacteristic
118C2×C3×C4⋊C4C2311yescharacteristic
119C2×C3×C4⋊C4C2311yescharacteristic
120C2×C3×C4⋊C4C2311yescharacteristic
121C2×C3×C22⋊C4—21no—
122C2×C3×C22⋊C4—21no—
123C2×C3×C22⋊C4—21no—
124C2×C3×C22⋊C4—21no—
125C2×C3×C22⋊C4—21no—
126C2×C3×C22⋊C4D411yescharacteristic
127C2×C3×C22⋊C4D411yescharacteristic
128C2×C3×C42C2311yescharacteristic
129C2×#217—21no—
130#937—28no—
131C2×#214—22no—
132C2×#214—22no—
133C2×#214—41no—
134C2×#213—22no—
135C2×#213—22no—
136C2×#213—22no—
137C2×#213—22no—
138C2×#213—41no—
139C2×#213D414yescomplemented
140#930—22no—
141#930—22no—
142C2×(C2×D3)⋊C4—21no—
143C2×(C2×D3)⋊C4—21no—
144C2×(C2×D3)⋊C4—21no—
145C2×(C2×D3)⋊C4—21no—
146C2×C4⋊Dic3C2311yescharacteristic
147#924—22no—
148#924—22no—
149C2×Dic3⋊C4—21no—
150C22×C3⋊C8C2311yescharacteristic
151C22×C3⋊C8C2311yescharacteristic
152C22×C3⋊C8C2311yescharacteristic
153C22×C3⋊C8C2311yescharacteristic
154#894—28no—
155#884—28no—
156D3×C22⋊C4—28no—
157#875—22no—
158#875D414yescomplemented
159C4×D12—22no—
160C4×D12D414yescomplemented
161C3×#95—21no—
162C3×#95—21no—
163C3×#95—21no—
164C3×#95—21no—
165#832—22no—
166#830—22no—
167#830—22no—
168#830—41no—
169#830—41no—
170#810—22no—
171#810—22no—
172#810—41no—
173#809—22no—
174#809—22no—
175#809—22no—
176#809—22no—
177#809—22no—
178#809—41no—
179#807—22no—
180C4⋊(C3⋊C8)—22no—
181C4×C3⋊C8—22no—
182C22×#41—31no—
183C23×D4—31no—
184C22×SD16—31no—
185C22×D8—31no—
186C22×D8—31no—
187#546—64no—
188#546—64no—
189C2×#124—31no—
190C2×#123—61no—
191C2×C22⋊Q8—31no—
192C2×#121—31no—
193C2×#121—61no—
194C2×#121C2×D311yescharacteristic
195C2×#121C2×D311yescharacteristic, complemented
196C2×#120—61no—
197C2×C4×D4—31no—
198C2×C4×D4C2×D311yescharacteristic
199C2×C4×D4C2×D311yescharacteristic, complemented
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×#103—31no—
210C2×#102—31no—
211C2×#102—31no—
212C2×#102—31no—
213C2×#102—31no—
214C2×#102—31no—
215C2×#102—31no—
216C2×#102—31no—
217C2×C22⋊C8—31no—
218C2×C22⋊C8—31no—
219C2×C22⋊C8—31no—
220C2×C22⋊C8—31no—
221C2×C4×C8—31no—
222#397—21no—
223#392—21no—
224#386—21no—
225#386—21no—
226#382C2×D311yescharacteristic, complemented
227#380C2×D311yescharacteristic
228#380C2×D311yescharacteristic, complemented
229#340—31no—
230#340—31no—
231C24×C3—21no—
232C24×C3C2×D411yescharacteristic
233C24×C3C2×D411yescharacteristic
234C23×D3—21no—
235C23×D3—21no—
236C23×D3—24no—
237C23×D3—42no—
238C23×D3—42no—
239C23×D3—42no—
240C23×D3—42no—
241C23×D3—81no—
242C23×D3—81no—
243C2×C3×D4—22no—
244C2×C3×D4—22no—
245C2×C3×D4—21no—
246C2×C3×D4—21no—
247C2×C3×D4—21no—
248C2×C3×D4—21no—
249C2×C3×D4—21no—
250C2×C3×D4—41no—
251C2×C3×D4—42no—
252C2×C3×D4—42no—
253C2×C3×D4—42no—
254C2×C3×D4—42no—
255C2×C3×D4—81no—
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×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—42no—
274C22×C3×C4—81no—
275C22×C3×C4—81no—
276C22×C3×C4C2×D411yescharacteristic
277C22×C3×C4C2×D411yescharacteristic
278C22×C3×C4C2×D411yescharacteristic
279C22×C3×C4C2×D411yescharacteristic
280C22×C3×C4C2411yescharacteristic
281C2×#67—24no—
282C2×#67—24no—
283C2×#67—42no—
284C2×#67—42no—
285C2×#67—81no—
286C2×#67—81no—
287C22×Dic3—21no—
288C22×Dic3—21no—
289#235—44no—
290#235—44no—
291#235—44no—
292#235—44no—
293C2×D12—21no—
294C2×D12—21no—
295C2×D12—21no—
296C2×D12—21no—
297C2×D12—21no—
298C2×D12—21no—
299C2×D12—21no—
300C2×D12—24no—
301C2×D12—21no—
302C2×D12—44no—
303C2×D12—44no—
304C2×D12—44no—
305C2×D12—42no—
306C2×D12—42no—
307C2×D12—44no—
308C2×D12C2×D412yes—
309C2×D12C2×D412yes—
310C2×D12C2×D412yes—
311C2×D12#4112yes—
312C2×C4×D3—24no—
313C2×C4×D3—24no—
314C2×C4×D3—42no—
315C2×C4×D3—42no—
316C2×C4×D3—81no—
317C2×C4×D3—81no—
318C2×Dic6—21no—
319C2×Dic6—21no—
320C2×Dic6—21no—
321C2×Dic6—21no—
322C2×Dic6—21no—
323C2×Dic6C2×D412yes—
324C3×C4⋊C4—22no—
325C3×C4⋊C4—21no—
326C3×C4⋊C4—21no—
327C3×C4⋊C4—21no—
328C3×C4⋊C4—21no—
329C3×C4⋊C4—21no—
330C3×C4⋊C4—21no—
331C3×C22⋊C4—22no—
332C3×C22⋊C4—22no—
333C3×C22⋊C4—42no—
334C3×C22⋊C4—42no—
335C3×C22⋊C4—42no—
336C3×C22⋊C4—81no—
337C3×C22⋊C4—81no—
338C3×C42C2×D412yes—
339C3×C42C2×D412yes—
340#217—24no—
341#214—44no—
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—
348C4⋊Dic3—21no—
349C4⋊Dic3C2×D412yes—
350Dic3⋊C4—24no—
351C2×C3⋊C8—21no—
352C2×C3⋊C8—21no—
353C2×C3⋊C8—21no—
354C2×C3⋊C8—21no—
355C2×C3⋊C8—21no—
356C2×C3⋊C8—21no—
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×Q8—31no—
371C22×D4—21no—
372C22×D4—21no—
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—121no—
383C22×D4—121no—
384C22×D4#6711yescharacteristic
385C22×D4C22×D311yescharacteristic
386C23×C4—21no—
387C23×C4—61no—
388C23×C4—61no—
389C23×C4C22×D311yescharacteristic
390C23×C4C22×D311yescharacteristic
391C2×SD16—62no—
392C2×SD16—62no—
393C2×SD16—121no—
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×C8—31no—
403C22×C8—31no—
404#124—34no—
405#124—62no—
406#123—68no—
407C22⋊Q8—62no—
408C22⋊Q8—62no—
409#121—22no—
410#121—22no—
411#121—41no—
412#121—41no—
413#121—68no—
414#121—62no—
415#121—62no—
416#120—68no—
417C4×D4—22no—
418C4×D4—22no—
419C4×D4—22no—
420C4×D4—22no—
421C4×D4—34no—
422C4×D4—62no—
423C2×C4⋊C4—31no—
424C2×C4⋊C4—61no—
425C2×C4⋊C4#6711yescharacteristic
426C2×C4⋊C4C22×D311yescharacteristic
427C2×C4⋊C4C22×D311yescharacteristic
428C2×C4⋊C4C22×D311yescharacteristic
429C2×C22⋊C4—21no—
430C2×C22⋊C4—21no—
431C2×C22⋊C4—21no—
432C2×C22⋊C4—21no—
433C2×C22⋊C4—21no—
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#6711yescharacteristic
441C2×C22⋊C4#6711yescharacteristic
442C2×C42C22×D311yescharacteristic
443#107—62no—
444C4⋊C8—62no—
445#103—62no—
446#103—62no—
447#103—121no—
448#102—62no—
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—21no—
461#95—21no—
462#95—21no—
463#95—21no—
464C23×C3—21no—
465C23×C3—21no—
466C23×C3—21no—
467C23×C3—21no—
468C23×C3—21no—
469C23×C3—21no—
470C23×C3—21no—
471C23×C3—22no—
472C23×C3—21no—
473C23×C3—21no—
474C23×C3—21no—
475C23×C3—21no—
476C23×C3—21no—
477C23×C3—21no—
478C23×C3—41no—
479C23×C3—41no—
480C23×C3—41no—
481C23×C3—41no—
482C23×C3—41no—
483C23×C3—41no—
484C23×C3#13512yes—
485C23×C3C22×D411yescharacteristic
486C22×D3—22no—
487C22×D3—22no—
488C22×D3—22no—
489C22×D3—22no—
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×D4—22no—
508C3×D4—22no—
509C3×D4—44no—
510C3×D4—41no—
511C3×D4—41no—
512C3×D4—84no—
513C3×D4—84no—
514C2×C3×C4—21no—
515C2×C3×C4—21no—
516C2×C3×C4—21no—
517C2×C3×C4—21no—
518C2×C3×C4—21no—
519C2×C3×C4—21no—
520C2×C3×C4—21no—
521C2×C3×C4—21no—
522C2×C3×C4—21no—
523C2×C3×C4—21no—
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×C4—41no—
533C2×C3×C4—41no—
534C2×C3×C4—41no—
535C2×C3×C4—41no—
536C2×C3×C4—41no—
537C2×C3×C4—41no—
538C2×C3×C4—41no—
539C2×C3×C4—41no—
540C2×C3×C4—41no—
541C2×C3×C4—84no—
542C2×C3×C4#12012yes—
543C2×C3×C4#12012yes—
544C2×C3×C4C22×D411yescharacteristic
545C2×C3×C4C22×D411yescharacteristic
546C2×C3×C4C22×D411yescharacteristic
547C2×C3×C4C2×#4111yescharacteristic
548C2×C3×C4H(5,𝔽2)11yescharacteristic
549C2×C3×C4H(5,𝔽2)11yescharacteristic
550#67—48no—
551#67—84no—
552C2×Dic3—22no—
553C2×Dic3—22no—
554C2×Dic3—41no—
555C2×Dic3—41no—
556C2×Dic3—41no—
557C2×Dic3—41no—
558D12—22no—
559D12—22no—
560D12—22no—
561D12—22no—
562D12—22no—
563D12—48no—
564D12—41no—
565D12—41no—
566D12#12114yes—
567C4×D3—48no—
568C4×D3—84no—
569Dic6—22no—
570Dic6—22no—
571Dic6—41no—
572Dic6—41no—
573C3⋊C8—22no—
574C3⋊C8—41no—
575C3⋊C8—41no—
576C3⋊C8—41no—
577C24—21no—
578C24—64no—
579C24—61no—
580C24—61no—
581C24—122no—
582C24—122no—
583C24—122no—
584C24—122no—
585C24—241no—
586C24—241no—
587C24C2×#6711yescharacteristic
588C24C2×#6711yescharacteristic
589#41—124no—
590#41—124no—
591#41—124no—
592#41—124no—
593C2×Q8—32no—
594C2×Q8—61no—
595C2×Q8—61no—
596C2×Q8—61no—
597C2×Q8—61no—
598C2×Q8—61no—
599C2×D4—22no—
600C2×D4—22no—
601C2×D4—21no—
602C2×D4—21no—
603C2×D4—21no—
604C2×D4—21no—
605C2×D4—21no—
606C2×D4—32no—
607C2×D4—32no—
608C2×D4—32no—
609C2×D4—32no—
610C2×D4—41no—
611C2×D4—42no—
612C2×D4—42no—
613C2×D4—42no—
614C2×D4—42no—
615C2×D4—64no—
616C2×D4—64no—
617C2×D4—64no—
618C2×D4—61no—
619C2×D4—61no—
620C2×D4—61no—
621C2×D4—61no—
622C2×D4—61no—
623C2×D4—61no—
624C2×D4—61no—
625C2×D4—61no—
626C2×D4—81no—
627C2×D4—81no—
628C2×D4—122no—
629C2×D4—122no—
630C2×D4—124no—
631C2×D4—124no—
632C2×D4—124no—
633C2×D4—124no—
634C2×D4—122no—
635C2×D4—122no—
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—21no—
649C22×C4—21no—
650C22×C4—21no—
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—42no—
655C22×C4—64no—
656C22×C4—61no—
657C22×C4—61no—
658C22×C4—64no—
659C22×C4—81no—
660C22×C4—81no—
661C22×C4—122no—
662C22×C4—122no—
663C22×C4—241no—
664C22×C4—241no—
665C22×C4C2×#6711yescharacteristic
666C22×C4C2×#6711yescharacteristic
667C22×C4C2×#6711yescharacteristic
668C22×C4C2×#6711yescharacteristic
669C22×C4C23×D311yescharacteristic
670SD16—124no—
671D8—68no—
672D8—124no—
673C2×C8—32no—
674C2×C8—61no—
675C2×C8—61no—
676C2×C8—61no—
677C2×C8—61no—
678C2×C8—61no—
679C2×C8—61no—
680C2×C8—61no—
681C2×C8—61no—
682C2×C8—61no—
683C2×C8—61no—
684C2×C8—61no—
685C4⋊C4—22no—
686C4⋊C4—21no—
687C4⋊C4—21no—
688C4⋊C4—21no—
689C4⋊C4—21no—
690C4⋊C4—21no—
691C4⋊C4—21no—
692C4⋊C4—32no—
693C4⋊C4—64no—
694C4⋊C4—61no—
695C22⋊C4—22no—
696C22⋊C4—22no—
697C22⋊C4—42no—
698C22⋊C4—42no—
699C22⋊C4—42no—
700C22⋊C4—64no—
701C22⋊C4—64no—
702C22⋊C4—64no—
703C22⋊C4—64no—
704C22⋊C4—64no—
705C22⋊C4—81no—
706C22⋊C4—81no—
707C42D3×D412yes—
708C42D3×D412yes—
709C22×C3—22no—
710C22×C3—22no—
711C22×C3—22no—
712C22×C3—41no—
713C22×C3—41no—
714C22×C3—41no—
715C22×C3—41no—
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—24no—
738C2×D3—42no—
739C2×D3—42no—
740C2×D3—42no—
741C2×D3—42no—
742C2×D3—42no—
743C2×D3—42no—
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—22no—
753C3×C4—22no—
754C3×C4—41no—
755C3×C4—41no—
756C3×C4—81no—
757C3×C4—81no—
758C3×C4—81no—
759C3×C4C2×#12111yescharacteristic
760C3×C4#53511yescharacteristic
761C3×C4D4211yescharacteristic
762C3×C4#54611yescharacteristic
763Dic3—42no—
764Dic3—42no—
765C23—21no—
766C23—21no—
767C23—21no—
768C23—21no—
769C23—21no—
770C23—21no—
771C23—21no—
772C23—22no—
773C23—21no—
774C23—21no—
775C23—21no—
776C23—21no—
777C23—21no—
778C23—21no—
779C23—41no—
780C23—41no—
781C23—41no—
782C23—41no—
783C23—41no—
784C23—41no—
785C23—62no—
786C23—62no—
787C23—62no—
788C23—62no—
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#95012yes—
807C23C22×#6711yescharacteristic
808Q8—62no—
809Q8—62no—
810Q8—121no—
811Q8—121no—
812D4—22no—
813D4—22no—
814D4—34no—
815D4—44no—
816D4—41no—
817D4—41no—
818D4—62no—
819D4—62no—
820D4—62no—
821D4—62no—
822D4—62no—
823D4—84no—
824D4—84no—
825D4—128no—
826D4—128no—
827D4—121no—
828D4—121no—
829D4—244no—
830C2×C4—21no—
831C2×C4—21no—
832C2×C4—21no—
833C2×C4—21no—
834C2×C4—21no—
835C2×C4—21no—
836C2×C4—21no—
837C2×C4—21no—
838C2×C4—21no—
839C2×C4—21no—
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—41no—
849C2×C4—41no—
850C2×C4—41no—
851C2×C4—41no—
852C2×C4—41no—
853C2×C4—41no—
854C2×C4—41no—
855C2×C4—41no—
856C2×C4—41no—
857C2×C4—62no—
858C2×C4—62no—
859C2×C4—84no—
860C2×C4—128no—
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×C4C2×D3×D411yescharacteristic
871C2×C4#100411yescharacteristic
872C2×C4D3×#4111yescharacteristic
873C2×C4#100911yescharacteristic
874C8—62no—
875C8—121no—
876C8—121no—
877C8—121no—
878C2×C3—42no—
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—44no—
889D3—82no—
890C22—22no—
891C22—22no—
892C22—22no—
893C22—41no—
894C22—41no—
895C22—41no—
896C22—41no—
897C22—41no—
898C22—42no—
899C22—42no—
900C22—41no—
901C22—41no—
902C22—41no—
903C22—41no—
904C22—41no—
905C22—42no—
906C22—41no—
907C22—64no—
908C22—81no—
909C22—81no—
910C22—81no—
911C22—81no—
912C22—122no—
913C22—122no—
914C22—122no—
915C22—122no—
916C22—122no—
917C22—122no—
918C22—122no—
919C22—122no—
920C22—122no—
921C22—2416no—
922C22—241no—
923C22—241no—
924C22—241no—
925C22—241no—
926C22C2×#93711yescharacteristic
927C22D4×#6711yescharacteristic
928C22C2×#95011yescharacteristic
929C22#582211yescharacteristic
930C22#582911yescharacteristic
931C22#583511yescharacteristic
932C22#583511yescharacteristic
933C4—22no—
934C4—22no—
935C4—41no—
936C4—41no—
937C4—81no—
938C4—81no—
939C4—81no—
940C4—122no—
941C4—122no—
942C4D3×#12111yescharacteristic
943C4#560711yescharacteristic
944C4#560911yescharacteristic
945C4#561211yescharacteristic
946C3#2424511yescharacteristic, complemented, Sylow
947C2—42no—
948C2—81no—
949C2—82no—
950C2—124no—
951C2—242no—
952C2#8264011yescharacteristic
953C2#8292611yescharacteristic
954C2#8338311yescharacteristic
955C2#8350411yescharacteristic
956C2#8350511yescharacteristic
957C2#8361411yescharacteristic
958C2#8361711yescharacteristic
subgroupG/H
centerC23C22×#67
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC3×#2535C2
socleC23×C3C22×D4
hypercenter#2535D3
hypocenterC3#24245
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ #2535

Complements

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

NH ≅ G/Ntype
1. C2×#5550C2semidirect
2. C3×#2535C2semidirect
3. C2×#5037C2semidirect
4. C2×#5036C2semidirect
5. C2×#5016C2semidirect
6. C2×C4×#213C2semidirect
7. #71685C2semidirect
8. #71684C2semidirect
9. #71614C2semidirect
10. #69556C2semidirect
11. #69551C2semidirect
12. #69527C2semidirect
13. #69523C2semidirect
14. #69522C2semidirect
15. #69521C2semidirect
20. C2×C3×#121C22semidirect
22. C2×C3×C4×D4C22semidirect
24. C22×#214C22semidirect
40. C3×#382C22semidirect
42. C3×#380C22semidirect
43. C2×#832C22semidirect
46. C2×#830C22semidirect
47. C2×#830C22semidirect
52. C2×#810C22semidirect
53. C2×#810C22semidirect
54. C2×#810C22semidirect
61. C2×#807C22semidirect
62. C2×C4⋊(C3⋊C8)C22semidirect
63. C2×C4×C3⋊C8C22semidirect
64. #4529C22semidirect
65. #4529C22semidirect
71. #2535D3semidirect
139. C2×#213D4semidirect
158. #875D4semidirect
160. C4×D12D4semidirect
195. C2×#121C2×D3semidirect
199. C2×C4×D4C2×D3semidirect
226. #382C2×D3semidirect
228. #380C2×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×#55502
C3×#25352
C2×#50372
C2×#50362
C2×#50162
C2×C4×#2132
#716852
#716842
#716142
#695562
#695512
#695272
#695232
#695222
#695212
#242453