Finite Group Databasebeta

← #10831004

Subgroups — #10831004

Order 768.

1608 conjugacy classes of subgroups.

The subgroup lattice has 950 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#949C211yesmaximal, characteristic, complemented
2C3×#2407C211yesmaximal, characteristic, complemented
3C2×#5049C211yesmaximal, characteristic, complemented
4C2×#5039C211yesmaximal, characteristic, complemented
5#82403C211yesmaximal, characteristic, complemented
6C2×#5012C211yesmaximal, characteristic, complemented
7#72135C211yesmaximal, characteristic, complemented
8#71699C211yesmaximal, characteristic, complemented
9#71684C211yesmaximal, characteristic, complemented
10#69680C211yesmaximal, characteristic, complemented
11#69676C211yesmaximal, characteristic, complemented
12#69650C211yesmaximal, characteristic, complemented
13#69647C211yesmaximal, characteristic, complemented
14#69521C211yesmaximal, characteristic, complemented
15#69513C211yesmaximal, characteristic, complemented
16#24277—31nomaximal, Sylow
17C22×C3×#41C2211yescharacteristic
18C23×D12C2211yescharacteristic
19C2×C3×C22⋊Q8C2211yescharacteristic, complemented
20C2×C3×#121C2211yescharacteristic, complemented
21C2×C3×C4×D4C2211yescharacteristic
22C2×#949—24no—
23C2×#949—24no—
24C2×#949—24no—
25C22×#215C2211yescharacteristic
26C22×#215C2211yescharacteristic
27C2×#937—21no—
28C22×#213C2211yescharacteristic
29C22×#213C2211yescharacteristic
30C2×#930C2211yescharacteristic
31C2×#930C2211yescharacteristic
32C22×#208C2211yescharacteristic
33C22×#208C2211yescharacteristic, complemented
34C3×#394—21no—
35C3×#392—21no—
36C3×#391C2211yescharacteristic, complemented
37C3×#390C2211yescharacteristic, complemented
38C3×#386—21no—
39C3×#385—21no—
40C3×#380C2211yescharacteristic
41C2×#835C2211yescharacteristic, complemented
42C2×#835C2211yescharacteristic, complemented
43C2×#832C2211yescharacteristic, complemented
44C2×#832C2211yescharacteristic, complemented
45#5212C2211yescharacteristic
46C2×#830C2211yescharacteristic
47C2×#830C2211yescharacteristic, complemented
48#5049—24no—
49#5039—24no—
50#5012—24no—
51#4991—21no—
52C2×#809C2211yescharacteristic
53C2×#809C2211yescharacteristic
54C2×#809C2211yescharacteristic
55C2×#809C2211yescharacteristic
56C2×#808C2211yescharacteristic, complemented
57C2×#807C2211yescharacteristic, complemented
58#4960—21no—
59#4955—21no—
60#4939C2211yescharacteristic
61#4939C2211yescharacteristic
62C2×C4⋊(C3⋊C8)C2211yescharacteristic, complemented
63C2×C4×C3⋊C8C2211yescharacteristic, complemented
64#4529C2211yescharacteristic, complemented
65#4529C2211yescharacteristic, complemented
66C22×AGL(1,ℤ/8)—31no—
67C2×#469—31no—
68C2×#468—31no—
69C2×#436—31no—
70#2408—31no—
71#2407D311yescharacteristic, complemented
72#2055—31no—
73#2054—31no—
74#2000—31no—
75#1999—31no—
76#1970—31no—
77#1968—31no—
78#1809—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×D4D411yescharacteristic
92C22×C3×D4C2311yescharacteristic
93C23×C3×C4—21no—
94C23×C3×C4C2311yescharacteristic
95C23×C3×C4C2311yescharacteristic
96C22×#67—21no—
97C22×#67—21no—
98C22×D12—22no—
99C22×D12—22no—
100C22×D12—22no—
101C22×D12—22no—
102C22×D12—21no—
103C22×D12—41no—
104C22×D12—41no—
105C22×D12C2311yescharacteristic
106C22×D12C2311yescharacteristic
107C3×C22⋊Q8—22no—
108C3×C22⋊Q8—41no—
109C3×#121—22no—
110C3×#121—41no—
111C3×C4×D4—22no—
112C3×C4×D4—22no—
113C2×C3×C4⋊C4—21no—
114C2×C3×C4⋊C4D411yescharacteristic
115C2×C3×C4⋊C4C2311yescharacteristic
116C2×C3×C4⋊C4C2311yescharacteristic
117C2×C3×C22⋊C4—21no—
118C2×C3×C22⋊C4—21no—
119C2×C3×C22⋊C4—21no—
120C2×C3×C22⋊C4—21no—
121C2×C3×C22⋊C4—21no—
122C2×C3×C22⋊C4D411yescharacteristic
123C2×C3×C22⋊C4D411yescharacteristic
124C2×C3×C42C2311yescharacteristic
125C2×#217—21no—
126#949—232no—
127C2×#215—22no—
128C2×#215—22no—
129C2×#215—22no—
130C2×#215—22no—
131C2×#215—22no—
132C2×#215D414yescomplemented
133#937—44no—
134C2×#213—22no—
135C2×#213—22no—
136C2×#213—22no—
137C2×#213—22no—
138C2×#213—22no—
139C2×#213D414yescomplemented
140#930—22no—
141#930—22no—
142#930—41no—
143#930—41no—
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)⋊C4—21no—
150C2×C4⋊Dic3C2311yescharacteristic
151C2×C4⋊Dic3C2311yescharacteristic
152C2×#208—22no—
153C2×#208—22no—
154C2×#208—22no—
155C2×#208—22no—
156C2×#208—22no—
157C2×#208D414yescomplemented
158C22×C3⋊C8C2311yescharacteristic
159C22×C3⋊C8C2311yescharacteristic
160C22×C3⋊C8C2311yescharacteristic
161C22×C3⋊C8C2311yescharacteristic
162C3×#95—21no—
163C3×#95—21no—
164C3×#95—21no—
165#835—22no—
166#835—41no—
167#832—22no—
168#832—41no—
169C3⋊#95—21no—
170#830—22no—
171#830—22no—
172#809—22no—
173#809—22no—
174#809—41no—
175#809—41no—
176#808—22no—
177#807—22no—
178C4⋊(C3⋊C8)—22no—
179C4×C3⋊C8—22no—
180C22×#41C2×D311yescharacteristic
181C23×D4—31no—
182C2×AGL(1,ℤ/8)—64no—
183C2×AGL(1,ℤ/8)—64no—
184C2×AGL(1,ℤ/8)—64no—
185C22×SD16—31no—
186C22×SD16—31no—
187C22×D8—31no—
188C22×D8—31no—
189C22×M16—31no—
190C22×M16—31no—
191C2×C22⋊Q8C2×D311yescharacteristic, complemented
192C2×#121—31no—
193C2×#121—31no—
194C2×#121C2×D311yescharacteristic, complemented
195C2×#120—61no—
196C2×C4×D4C2×D311yescharacteristic
197#469—64no—
198#468—64no—
199#436—64no—
200C2×#107—31no—
201C2×#106—31no—
202C2×C4⋊C8—31no—
203C2×#103—31no—
204C2×#103—31no—
205C2×#102—31no—
206C2×#102—31no—
207C2×#102—31no—
208C2×#102—31no—
209C2×#102—31no—
210C2×#102—31no—
211C2×C22⋊C8—31no—
212C2×C22⋊C8—31no—
213C2×C4×C8—31no—
214#394—21no—
215#394—61no—
216#392—21no—
217#392—61no—
218#391C2×D311yescharacteristic, complemented
219#390—31no—
220#390—31no—
221#390C2×D311yescharacteristic, complemented
222#386—21no—
223#385—21no—
224#380—31no—
225#380C2×D311yescharacteristic
226#379—61no—
227#340—31no—
228#340—31no—
229C24×C3—21no—
230C24×C3C2×D411yescharacteristic
231C24×C3C2×D411yescharacteristic
232C23×D3—21no—
233C23×D3—21no—
234C23×D3—42no—
235C23×D3—42no—
236C23×D3—42no—
237C23×D3—42no—
238C23×D3—42no—
239C23×D3—81no—
240C23×D3—81no—
241C3×#41—28no—
242C3×#41—44no—
243C3×#41—44no—
244C3×#41—44no—
245C2×C3×Q8—21no—
246C2×C3×Q8—21no—
247C2×C3×Q8—21no—
248C2×C3×Q8—21no—
249C2×C3×Q8—21no—
250C2×C3×Q8C2×D412yes—
251C2×C3×D4—22no—
252C2×C3×D4—22no—
253C2×C3×D4—21no—
254C2×C3×D4—21no—
255C2×C3×D4—21no—
256C2×C3×D4—21no—
257C2×C3×D4—21no—
258C2×C3×D4—41no—
259C2×C3×D4—42no—
260C2×C3×D4—42no—
261C2×C3×D4—42no—
262C2×C3×D4—42no—
263C2×C3×D4—42no—
264C2×C3×D4—81no—
265C2×C3×D4C2×D412yes—
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—21no—
274C22×C3×C4—21no—
275C22×C3×C4—21no—
276C22×C3×C4—21no—
277C22×C3×C4—21no—
278C22×C3×C4—21no—
279C22×C3×C4—42no—
280C22×C3×C4—42no—
281C22×C3×C4—42no—
282C22×C3×C4C2×D412yes—
283C22×C3×C4C2×D411yescharacteristic
284C22×C3×C4C2×D411yescharacteristic
285C22×C3×C4C2×D411yescharacteristic
286C22×C3×C4C2×D411yescharacteristic
287C22×C3×C4#4112yes—
288C22×C3×C4C2411yescharacteristic
289C2×#67—42no—
290C2×#67—42no—
291C2×#67—42no—
292C2×#67—42no—
293C2×#67—81no—
294C2×#67—81no—
295C22×Dic3—21no—
296C22×Dic3—21no—
297C2×D12—28no—
298C2×D12—21no—
299C2×D12—21no—
300C2×D12—21no—
301C2×D12—21no—
302C2×D12—21no—
303C2×D12—21no—
304C2×D12—21no—
305C2×D12—21no—
306C2×D12—21no—
307C2×D12—21no—
308C2×D12—44no—
309C2×D12—44no—
310C2×D12—42no—
311C2×D12—42no—
312C2×D12—44no—
313C2×D12—42no—
314C2×D12C2×D412yes—
315C2×D12C2×D412yes—
316C3×C4⋊C4—22no—
317C3×C4⋊C4—21no—
318C3×C4⋊C4—21no—
319C3×C4⋊C4—21no—
320C3×C4⋊C4—21no—
321C3×C4⋊C4—42no—
322C3×C22⋊C4—22no—
323C3×C22⋊C4—22no—
324C3×C22⋊C4—42no—
325C3×C22⋊C4—42no—
326C3×C22⋊C4—42no—
327C3×C22⋊C4—81no—
328C3×C22⋊C4—81no—
329C3×C42—21no—
330C3×C42—21no—
331#217—42no—
332#215—28no—
333#215—28no—
334#213—28no—
335#213—28no—
336(C2×D3)⋊C4—42no—
337(C2×D3)⋊C4—42no—
338(C2×D3)⋊C4—42no—
339(C2×D3)⋊C4—42no—
340(C2×D3)⋊C4—81no—
341(C2×D3)⋊C4—81no—
342C4⋊Dic3—21no—
343C4⋊Dic3—21no—
344C4⋊Dic3—21no—
345C4⋊Dic3—21no—
346#208—28no—
347#208—44no—
348C2×C3⋊C8—21no—
349C2×C3⋊C8—21no—
350C2×C3⋊C8—21no—
351C2×C3⋊C8—21no—
352C2×C3⋊C8—21no—
353C2×C3⋊C8—21no—
354C2×C3⋊C8—21no—
355C2×C3⋊C8—21no—
356C2×C3⋊C8C2×D412yes—
357C2×C3⋊C8C2×D412yes—
358C2×C3⋊C8C2×D412yes—
359C2×C3⋊C8C2×D412yes—
360C25—61no—
361C2×#41—22no—
362C2×#41—22no—
363C2×#41—22no—
364C2×#41—22no—
365C2×#41—41no—
366C2×#41—41no—
367C22×Q8C22×D311yescharacteristic
368C22×D4—21no—
369C22×D4—21no—
370C22×D4—31no—
371C22×D4—31no—
372C22×D4—62no—
373C22×D4—62no—
374C22×D4—61no—
375C22×D4—61no—
376C22×D4—62no—
377C22×D4—62no—
378C22×D4—61no—
379C22×D4—121no—
380C22×D4—121no—
381C22×D4#6711yescharacteristic
382C22×D4C22×D311yescharacteristic
383C23×C4—21no—
384C23×C4C22×D311yescharacteristic
385C23×C4C22×D311yescharacteristic
386AGL(1,ℤ/8)—632no—
387C2×SD16—34no—
388C2×SD16—62no—
389C2×SD16—62no—
390C2×SD16—62no—
391C2×SD16—62no—
392C2×SD16—62no—
393C2×D8—34no—
394C2×D8—62no—
395C2×D8—62no—
396C2×D8—62no—
397C2×D8—62no—
398C2×D8—62no—
399C2×M16—34no—
400C2×M16—62no—
401C2×M16—62no—
402C2×M16—62no—
403C2×M16—62no—
404C2×M16—62no—
405C22×C8—31no—
406C22×C8—31no—
407C22×C8—31no—
408C22×C8—31no—
409C22⋊Q8—22no—
410C22⋊Q8—41no—
411#121—22no—
412#121—41no—
413#121—62no—
414#121—62no—
415#121—121no—
416#121—121no—
417#120—124no—
418C4×D4—22no—
419C4×D4—22no—
420C2×C4⋊C4—21no—
421C2×C4⋊C4—31no—
422C2×C4⋊C4—31no—
423C2×C4⋊C4#6711yescharacteristic
424C2×C4⋊C4C22×D311yescharacteristic
425C2×C4⋊C4C22×D311yescharacteristic
426C2×C22⋊C4—21no—
427C2×C22⋊C4—21no—
428C2×C22⋊C4—21no—
429C2×C22⋊C4—21no—
430C2×C22⋊C4—21no—
431C2×C22⋊C4—61no—
432C2×C22⋊C4—61no—
433C2×C22⋊C4—61no—
434C2×C22⋊C4—61no—
435C2×C22⋊C4—61no—
436C2×C22⋊C4—61no—
437C2×C22⋊C4—61no—
438C2×C22⋊C4#6711yescharacteristic
439C2×C22⋊C4#6711yescharacteristic
440C2×C42C22×D311yescharacteristic
441#107—62no—
442#106—62no—
443C4⋊C8—62no—
444#103—62no—
445#103—121no—
446#102—62no—
447#102—62no—
448#102—62no—
449#102—121no—
450#102—121no—
451#102—121no—
452C22⋊C8—62no—
453C22⋊C8—62no—
454C4×C8—62no—
455#95—21no—
456#95—21no—
457#95—21no—
458#95—61no—
459C23×C3—21no—
460C23×C3—21no—
461C23×C3—21no—
462C23×C3—21no—
463C23×C3—21no—
464C23×C3—21no—
465C23×C3—21no—
466C23×C3—21no—
467C23×C3—22no—
468C23×C3—21no—
469C23×C3—21no—
470C23×C3—21no—
471C23×C3—21no—
472C23×C3—21no—
473C23×C3—41no—
474C23×C3—41no—
475C23×C3—41no—
476C23×C3—41no—
477C23×C3—41no—
478C23×C3—41no—
479C23×C3#12112yes—
480C23×C3C22×D411yescharacteristic
481C22×D3—22no—
482C22×D3—22no—
483C22×D3—48no—
484C22×D3—41no—
485C22×D3—41no—
486C22×D3—41no—
487C22×D3—41no—
488C22×D3—41no—
489C22×D3—41no—
490C22×D3—41no—
491C22×D3—41no—
492C22×D3—41no—
493C22×D3—41no—
494C22×D3—41no—
495C22×D3—41no—
496C22×D3—84no—
497C22×D3—84no—
498C22×D3—84no—
499C22×D3—84no—
500C22×D3—84no—
501C22×D3—84no—
502C3×Q8—22no—
503C3×Q8—22no—
504C3×Q8—41no—
505C3×Q8—41no—
506C3×D4—22no—
507C3×D4—22no—
508C3×D4—44no—
509C3×D4—48no—
510C3×D4—41no—
511C3×D4—41no—
512C3×D4—84no—
513C2×C3×C4—21no—
514C2×C3×C4—21no—
515C2×C3×C4—21no—
516C2×C3×C4—21no—
517C2×C3×C4—22no—
518C2×C3×C4—22no—
519C2×C3×C4—22no—
520C2×C3×C4—22no—
521C2×C3×C4—21no—
522C2×C3×C4—21no—
523C2×C3×C4—21no—
524C2×C3×C4—21no—
525C2×C3×C4—22no—
526C2×C3×C4—21no—
527C2×C3×C4—21no—
528C2×C3×C4—48no—
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#12112yes—
542C2×C3×C4AGL(1,ℤ/8)12yescomplemented
543C2×C3×C4C22×D411yescharacteristic
544C2×C3×C4C22×D411yescharacteristic
545C2×C3×C4C22×D411yescharacteristic
546C2×C3×C4C2×#4111yescharacteristic
547C2×C3×C4H(5,𝔽2)11yescharacteristic
548C2×C3×C4H(5,𝔽2)11yescharacteristic
549#67—84no—
550#67—84no—
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—22no—
561D12—48no—
562D12—41no—
563D12—41no—
564D12—41no—
565D12—41no—
566C3⋊C8—22no—
567C3⋊C8—41no—
568C3⋊C8—41no—
569C3⋊C8#12014yescomplemented
570C24—21no—
571C24—61no—
572C24—61no—
573C24—122no—
574C24—122no—
575C24—122no—
576C24—122no—
577C24—122no—
578C24—241no—
579C24—241no—
580C24C2×#6711yescharacteristic
581C24C2×#6711yescharacteristic
582#41—28no—
583#41—44no—
584#41—44no—
585#41—44no—
586C2×Q8—21no—
587C2×Q8—21no—
588C2×Q8—21no—
589C2×Q8—21no—
590C2×Q8—21no—
591C2×Q8D3×D412yes—
592C2×D4—22no—
593C2×D4—22no—
594C2×D4—21no—
595C2×D4—21no—
596C2×D4—21no—
597C2×D4—21no—
598C2×D4—21no—
599C2×D4—32no—
600C2×D4—32no—
601C2×D4—41no—
602C2×D4—42no—
603C2×D4—42no—
604C2×D4—42no—
605C2×D4—42no—
606C2×D4—42no—
607C2×D4—68no—
608C2×D4—61no—
609C2×D4—61no—
610C2×D4—61no—
611C2×D4—61no—
612C2×D4—61no—
613C2×D4—61no—
614C2×D4—61no—
615C2×D4—61no—
616C2×D4—61no—
617C2×D4—61no—
618C2×D4—81no—
619C2×D4—124no—
620C2×D4—124no—
621C2×D4—122no—
622C2×D4—122no—
623C2×D4—124no—
624C2×D4—122no—
625C2×D4—122no—
626C2×D4—122no—
627C2×D4—122no—
628C2×D4—122no—
629C2×D4—241no—
630C2×D4—241no—
631C2×D4D3×D412yes—
632C22×C4—21no—
633C22×C4—21no—
634C22×C4—21no—
635C22×C4—21no—
636C22×C4—21no—
637C22×C4—21no—
638C22×C4—21no—
639C22×C4—21no—
640C22×C4—21no—
641C22×C4—21no—
642C22×C4—21no—
643C22×C4—21no—
644C22×C4—21no—
645C22×C4—42no—
646C22×C4—42no—
647C22×C4—42no—
648C22×C4—61no—
649C22×C4—61no—
650C22×C4D3×D412yes—
651C22×C4#23712yes—
652C22×C4C2×#6711yescharacteristic
653C22×C4C2×#6711yescharacteristic
654C22×C4C2×#6711yescharacteristic
655C22×C4C2×#6711yescharacteristic
656C22×C4C23×D311yescharacteristic
657SD16—68no—
658SD16—68no—
659D8—68no—
660D8—68no—
661M16—68no—
662M16—124no—
663C2×C8—32no—
664C2×C8—32no—
665C2×C8—32no—
666C2×C8—32no—
667C2×C8—61no—
668C2×C8—61no—
669C2×C8—61no—
670C2×C8—61no—
671C2×C8—61no—
672C2×C8—61no—
673C2×C8—61no—
674C2×C8—61no—
675C4⋊C4—22no—
676C4⋊C4—21no—
677C4⋊C4—21no—
678C4⋊C4—21no—
679C4⋊C4—21no—
680C4⋊C4—42no—
681C4⋊C4—61no—
682C4⋊C4—61no—
683C4⋊C4—61no—
684C4⋊C4—61no—
685C22⋊C4—22no—
686C22⋊C4—22no—
687C22⋊C4—42no—
688C22⋊C4—42no—
689C22⋊C4—42no—
690C22⋊C4—81no—
691C22⋊C4—81no—
692C22⋊C4—122no—
693C22⋊C4—122no—
694C22⋊C4—122no—
695C22⋊C4—122no—
696C22⋊C4—122no—
697C22⋊C4—241no—
698C22⋊C4—241no—
699C42—21no—
700C42—21no—
701C22×C3—22no—
702C22×C3—22no—
703C22×C3—22no—
704C22×C3—41no—
705C22×C3—41no—
706C22×C3—41no—
707C22×C3—41no—
708C22×C3—42no—
709C22×C3—41no—
710C22×C3—41no—
711C22×C3—42no—
712C22×C3—41no—
713C22×C3—42no—
714C22×C3—41no—
715C22×C3—41no—
716C22×C3—41no—
717C22×C3—41no—
718C22×C3—81no—
719C22×C3—81no—
720C22×C3—81no—
721C22×C3—81no—
722C22×C3C2×#12111yescharacteristic
723C22×C3D4211yescharacteristic
724C22×C3D4211yescharacteristic
725C22×C3C2×AGL(1,ℤ/8)11yescharacteristic
726C22×C3#57511yescharacteristic
727C22×C3#57611yescharacteristic
728C22×C3#57711yescharacteristic
729C2×D3—42no—
730C2×D3—42no—
731C2×D3—42no—
732C2×D3—42no—
733C2×D3—42no—
734C2×D3—42no—
735C2×D3—816no—
736C2×D3—81no—
737C2×D3—81no—
738C2×D3—81no—
739C2×D3—81no—
740C2×D3—81no—
741C2×D3—81no—
742C2×D3—81no—
743C2×D3—81no—
744C3×C4—22no—
745C3×C4—22no—
746C3×C4—41no—
747C3×C4—42no—
748C3×C4—41no—
749C3×C4—81no—
750C3×C4—81no—
751C3×C4C2×#12011yescharacteristic
752C3×C4#53511yescharacteristic
753C3×C4#54611yescharacteristic
754C3×C4#54611yescharacteristic
755Dic3—81no—
756Dic3—81no—
757C23—21no—
758C23—21no—
759C23—21no—
760C23—21no—
761C23—21no—
762C23—21no—
763C23—21no—
764C23—22no—
765C23—21no—
766C23—21no—
767C23—21no—
768C23—21no—
769C23—21no—
770C23—21no—
771C23—41no—
772C23—41no—
773C23—41no—
774C23—41no—
775C23—41no—
776C23—41no—
777C23—62no—
778C23—62no—
779C23—128no—
780C23—121no—
781C23—121no—
782C23—121no—
783C23—121no—
784C23—121no—
785C23—121no—
786C23—121no—
787C23—121no—
788C23—121no—
789C23—121no—
790C23—121no—
791C23—121no—
792C23—244no—
793C23—244no—
794C23—244no—
795C23—244no—
796C23—244no—
797C23—244no—
798C23#93912yes—
799C23C22×#6711yescharacteristic
800Q8—22no—
801Q8—22no—
802Q8—41no—
803Q8—41no—
804D4—22no—
805D4—22no—
806D4—44no—
807D4—48no—
808D4—41no—
809D4—41no—
810D4—62no—
811D4—62no—
812D4—62no—
813D4—62no—
814D4—84no—
815D4—128no—
816D4—121no—
817D4—121no—
818D4—121no—
819D4—121no—
820D4—244no—
821D4—244no—
822C2×C4—21no—
823C2×C4—21no—
824C2×C4—21no—
825C2×C4—21no—
826C2×C4—22no—
827C2×C4—22no—
828C2×C4—22no—
829C2×C4—22no—
830C2×C4—21no—
831C2×C4—22no—
832C2×C4—21no—
833C2×C4—21no—
834C2×C4—21no—
835C2×C4—21no—
836C2×C4—21no—
837C2×C4—48no—
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—41no—
849C2×C4—41no—
850C2×C4—121no—
851C2×C4—121no—
852C2×C4—121no—
853C2×C4—121no—
854C2×C4—121no—
855C2×C4—121no—
856C2×C4#93912yes—
857C2×C4#94912yescomplemented
858C2×C4C2×D3×D411yescharacteristic
859C2×C4C2×D3×D411yescharacteristic
860C2×C4C2×D3×D411yescharacteristic
861C2×C4C2×#23711yescharacteristic
862C2×C4#100411yescharacteristic
863C2×C4#100411yescharacteristic
864C8—34no—
865C8—62no—
866C8—121no—
867C8—121no—
868C2×C3—42no—
869C2×C3—81no—
870C2×C3—82no—
871C2×C3#240811yescharacteristic
872C2×C3#305511yescharacteristic
873C2×C3#306211yescharacteristic
874C2×C3#327211yescharacteristic
875C2×C3#327311yescharacteristic
876C2×C3#327411yescharacteristic
877C2×C3#327511yescharacteristic
878D3—82no—
879D3—82no—
880C22—22no—
881C22—22no—
882C22—22no—
883C22—41no—
884C22—41no—
885C22—41no—
886C22—41no—
887C22—41no—
888C22—42no—
889C22—41no—
890C22—42no—
891C22—41no—
892C22—41no—
893C22—42no—
894C22—41no—
895C22—41no—
896C22—41no—
897C22—81no—
898C22—81no—
899C22—81no—
900C22—81no—
901C22—122no—
902C22—122no—
903C22—122no—
904C22—122no—
905C22—122no—
906C22—122no—
907C22—2416no—
908C22—241no—
909C22—241no—
910C22—241no—
911C22—241no—
912C22—241no—
913C22—241no—
914C22—241no—
915C22—241no—
916C22D4×#6711yescharacteristic
917C22D4×#6711yescharacteristic
918C22C2×#93911yescharacteristic
919C22C2×#94911yescharacteristic
920C22#582211yescharacteristic
921C22#583511yescharacteristic
922C22#583711yescharacteristic
923C4—22no—
924C4—22no—
925C4—41no—
926C4—42no—
927C4—41no—
928C4—81no—
929C4—81no—
930C4—241no—
931C4—241no—
932C4D3×#12011yescharacteristic
933C4#559111yescharacteristic
934C4#559111yescharacteristic
935C4#559211yescharacteristic
936C3#2427711yescharacteristic, complemented, Sylow
937C2—42no—
938C2—81no—
939C2—82no—
940C2—242no—
941C2—242no—
942C2#8258211yescharacteristic
943C2#8292411yescharacteristic
944C2#8342211yescharacteristic
945C2#8350411yescharacteristic
946C2#8352311yescharacteristic
947C2#8354411yescharacteristic
948C2#8357811yescharacteristic
subgroupG/H
centerC23C22×#67
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC3×#2407C2
socleC23×C3C22×D4
hypercenter#2407D3
hypocenterC3#24277
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ #2407

Complements

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

NH ≅ G/Ntype
1. C22×#949C2semidirect
2. C3×#2407C2semidirect
3. C2×#5049C2semidirect
4. C2×#5039C2semidirect
5. #82403C2semidirect
6. C2×#5012C2semidirect
7. #72135C2semidirect
8. #71699C2semidirect
9. #71684C2semidirect
10. #69680C2semidirect
11. #69676C2semidirect
12. #69650C2semidirect
13. #69647C2semidirect
14. #69521C2semidirect
15. #69513C2semidirect
19. C2×C3×C22⋊Q8C22semidirect
20. C2×C3×#121C22semidirect
33. C22×#208C22semidirect
36. C3×#391C22semidirect
37. C3×#390C22semidirect
41. C2×#835C22semidirect
42. C2×#835C22semidirect
43. C2×#832C22semidirect
44. C2×#832C22semidirect
47. C2×#830C22semidirect
56. C2×#808C22semidirect
57. C2×#807C22semidirect
62. C2×C4⋊(C3⋊C8)C22semidirect
63. C2×C4×C3⋊C8C22semidirect
64. #4529C22semidirect
65. #4529C22semidirect
71. #2407D3semidirect
132. C2×#215D4semidirect
139. C2×#213D4semidirect
157. C2×#208D4semidirect
191. C2×C22⋊Q8C2×D3semidirect
194. C2×#121C2×D3semidirect
218. #391C2×D3semidirect
221. #390C2×D3semidirect
542. C2×C3×C4AGL(1,ℤ/8)semidirect
569. C3⋊C8#120semidirect
857. C2×C4#949semidirect
936. C3#24277semidirect

Maximal subgroups

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

subgroupindex
C22×#9492
C3×#24072
C2×#50492
C2×#50392
#824032
C2×#50122
#721352
#716992
#716842
#696802
#696762
#696502
#696472
#695212
#695132
#242773