Finite Group Databasebeta

← #10831002

Subgroups — #10831002

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×#914C211yesmaximal, characteristic, complemented
2C2×#4838C211yesmaximal, characteristic, complemented
3C2×#4812C211yesmaximal, characteristic, complemented
4C2×#4782C211yesmaximal, characteristic, complemented
5#76618C211yesmaximal, characteristic, complemented
6#76436C211yesmaximal, characteristic, complemented
7C3×#2055C211yesmaximal, characteristic, complemented
8#72054C211yesmaximal, characteristic, complemented
9#70481C211yesmaximal, characteristic, complemented
10#70267C211yesmaximal, characteristic, complemented
11#70198C211yesmaximal, characteristic, complemented
12#69676C211yesmaximal, characteristic, complemented
13#69647C211yesmaximal, characteristic, complemented
14#68886C211yesmaximal, characteristic, complemented
15#68870C211yesmaximal, characteristic, complemented
16#24277—31nomaximal, Sylow
17C22×#239C2211yescharacteristic
18C22×D3×D4C2211yescharacteristic
19C22×C3×SD16C2211yescharacteristic
20C2×#946C2211yescharacteristic, complemented
21C22×#215C2211yescharacteristic
22C2×#938C2211yescharacteristic
23C22×#213C2211yescharacteristic
24C2×#914—24no—
25C2×#914—24no—
26C2×#914—24no—
27C22×D24C2211yescharacteristic
28C22×ΓL(1,𝔽25)C2211yescharacteristic
29C22×ΓL(1,𝔽25)C2211yescharacteristic, complemented
30C2×#895C2211yescharacteristic
31C2×#895C2211yescharacteristic, complemented
32C2×#882—21no—
33C2×C4×D12C2211yescharacteristic
34C2×C3×C4⋊C8C2211yescharacteristic, complemented
35C2×C3×#103C2211yescharacteristic, complemented
36C2×C3×#102C2211yescharacteristic
37C3×#391C2211yescharacteristic, complemented
38C3×#390C2211yescharacteristic
39C2×#835C2211yescharacteristic, complemented
40C2×#832C2211yescharacteristic
41C2×#821C2211yescharacteristic
42C2×#821C2211yescharacteristic, complemented
43C2×(C2×D3)⋊C8C2211yescharacteristic
44C2×(C2×D3)⋊C8C2211yescharacteristic, complemented
45#4987C2211yescharacteristic
46#4987C2211yescharacteristic
47C2×#809C2211yescharacteristic
48C2×#809C2211yescharacteristic, complemented
49C2×#808C2211yescharacteristic, complemented
50C2×#807C2211yescharacteristic, complemented
51#4961—21no—
52#4960—21no—
53#4955—21no—
54#4939C2211yescharacteristic
55#4939C2211yescharacteristic, complemented
56C2×C4×C3⋊C8C2211yescharacteristic, complemented
57#4838—24no—
58#4812—24no—
59#4782—24no—
60#4672—21no—
61#4671—21no—
62#4668—21no—
63#4665—21no—
64C3×#340C2211yescharacteristic, complemented
65#4551C2211yescharacteristic, complemented
66C22×AGL(1,ℤ/8)—31no—
67C2×#469—31no—
68C2×#468—31no—
69C2×#436—31no—
70#2408—31no—
71#2407—31no—
72#2055D311yescharacteristic, complemented
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—
82C22×C3×Q8C2311yescharacteristic
83C22×C3×D4C2311yescharacteristic
84C22×#67—21no—
85C22×#67—21no—
86C2×#239—22no—
87C2×#239—22no—
88C2×#239—22no—
89C2×#239—22no—
90C2×#239—41no—
91C2×#239—41no—
92C2×D3×D4—22no—
93C2×D3×D4—22no—
94C2×D3×D4—22no—
95C2×D3×D4—22no—
96C2×D3×D4—41no—
97C2×D3×D4—41no—
98C22×D12—21no—
99C22×D12—21no—
100C22×D12—21no—
101C22×D12D411yescharacteristic
102C22×D12C2311yescharacteristic
103C22×D12C2311yescharacteristic
104C22×C4×D3—21no—
105C22×C4×D3C2311yescharacteristic
106C22×C4×D3C2311yescharacteristic
107C2×C3×SD16—22no—
108C2×C3×SD16—22no—
109C2×C3×SD16—22no—
110C22×C3×C8C2311yescharacteristic
111C22×C3×C8C2311yescharacteristic
112C2×C3×C4⋊C4C2311yescharacteristic
113C2×C3×C4⋊C4C2311yescharacteristic
114C2×C3×C22⋊C4—21no—
115C2×C3×C22⋊C4—21no—
116C2×C3×C42C2311yescharacteristic
117C2×#217—21no—
118#946—22no—
119#946—41no—
120C2×#215—22no—
121C2×#215—22no—
122C2×#215D414yescomplemented
123#938—22no—
124#938—41no—
125C2×#213—22no—
126C2×#213—22no—
127C2×#213D414yescomplemented
128C2×(C2×D3)⋊C4—21no—
129C2×(C2×D3)⋊C4—21no—
130C2×(C2×D3)⋊C4—21no—
131C2×(C2×D3)⋊C4—21no—
132C2×(C2×D3)⋊C4—21no—
133C2×(C2×D3)⋊C4—21no—
134C2×(C2×D3)⋊C4—21no—
135C2×(C2×D3)⋊C4—21no—
136C2×(C2×D3)⋊C4—21no—
137C2×(C2×D3)⋊C4D411yescharacteristic
138C2×(C2×D3)⋊C4D411yescharacteristic
139C2×C4⋊Dic3D411yescharacteristic
140C2×C4⋊Dic3C2311yescharacteristic
141C2×C4⋊Dic3C2311yescharacteristic
142C2×Dic3⋊C4—21no—
143C22×C3⋊C8C2311yescharacteristic
144C22×C3⋊C8C2311yescharacteristic
145#914—232no—
146C2×D24—22no—
147C2×D24—22no—
148C2×D24—22no—
149C2×ΓL(1,𝔽25)—22no—
150C2×ΓL(1,𝔽25)—22no—
151C2×ΓL(1,𝔽25)—22no—
152C2×ΓL(1,𝔽25)—22no—
153C2×ΓL(1,𝔽25)—22no—
154C2×ΓL(1,𝔽25)D414yescomplemented
155#895—22no—
156#895—22no—
157#895—41no—
158#895—41no—
159#882—44no—
160C4×D12—22no—
161C4×D12—22no—
162C3×C4⋊C8—22no—
163C3×#103—22no—
164C3×#102—22no—
165C3×#95—21no—
166C3×#95—21no—
167#835—41no—
168#832—41no—
169C3⋊#95—21no—
170C3⋊#95—21no—
171#821—22no—
172#821—22no—
173(C2×D3)⋊C8—22no—
174(C2×D3)⋊C8—22no—
175#809—41no—
176#809—41no—
177#808—22no—
178#807—22no—
179C4×C3⋊C8—22no—
180C22×#41—31no—
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×SD16C2×D311yescharacteristic
187C22×D8—31no—
188C22×D8—31no—
189C22×M16—31no—
190C22×M16—31no—
191C2×C22⋊Q8—31no—
192C2×#121—31no—
193C2×#121—31no—
194C2×#121—31no—
195C2×#120—61no—
196C2×C4×D4—31no—
197#469—64no—
198#468—64no—
199#436—64no—
200C2×#107—31no—
201C2×#106—31no—
202C2×C4⋊C8C2×D311yescharacteristic, complemented
203C2×#103—31no—
204C2×#103C2×D311yescharacteristic, complemented
205C2×#102—31no—
206C2×#102—31no—
207C2×#102—31no—
208C2×#102—31no—
209C2×#102—31no—
210C2×#102C2×D311yescharacteristic
211C2×C22⋊C8—31no—
212C2×C22⋊C8—31no—
213C2×C4×C8—31no—
214#394—61no—
215#394—61no—
216#392—61no—
217#392—61no—
218#391C2×D311yescharacteristic, complemented
219#390—31no—
220#390—31no—
221#390C2×D311yescharacteristic
222#386—61no—
223#385—61no—
224#380—31no—
225#380—31no—
226#379—61no—
227#340—31no—
228#340C2×D311yescharacteristic, complemented
229C24×C3—21no—
230C23×D3—21no—
231C23×D3—21no—
232C23×D3—42no—
233C23×D3—42no—
234C23×D3—42no—
235C23×D3—42no—
236C23×D3—42no—
237C23×D3—81no—
238C23×D3—81no—
239C23×D3C2×D411yescharacteristic
240C23×D3C2×D411yescharacteristic
241C2×C3×Q8—21no—
242C2×C3×Q8—21no—
243C2×C3×Q8—21no—
244C2×C3×Q8—21no—
245C2×C3×Q8—21no—
246C2×C3×Q8C2×D412yes—
247C2×C3×D4—21no—
248C2×C3×D4—21no—
249C2×C3×D4—21no—
250C2×C3×D4—21no—
251C2×C3×D4—21no—
252C2×C3×D4C2×D412yes—
253C22×C3×C4—21no—
254C22×C3×C4—21no—
255C22×C3×C4—21no—
256C22×C3×C4C2×D411yescharacteristic
257C22×C3×C4C2×D411yescharacteristic
258C22×C3×C4C2411yescharacteristic
259C2×#67—42no—
260C2×#67—42no—
261C2×#67—42no—
262C2×#67—42no—
263C2×#67—42no—
264C2×#67—81no—
265C22×Dic3—21no—
266C22×Dic3—21no—
267C22×Dic3C2×D411yescharacteristic
268C22×Dic3C2×D411yescharacteristic
269#239—28no—
270#239—44no—
271#239—44no—
272#239—44no—
273D3×D4—28no—
274D3×D4—44no—
275D3×D4—44no—
276D3×D4—44no—
277C2×D12—21no—
278C2×D12—21no—
279C2×D12—21no—
280C2×D12—21no—
281C2×D12—21no—
282C2×D12—21no—
283C2×D12—21no—
284C2×D12—21no—
285C2×D12—22no—
286C2×D12—22no—
287C2×D12—21no—
288C2×D12—21no—
289C2×D12—41no—
290C2×D12—42no—
291C2×D12—42no—
292C2×D12—42no—
293C2×D12—42no—
294C2×D12—42no—
295C2×D12—42no—
296C2×D12—42no—
297C2×D12—81no—
298C2×D12—81no—
299C2×D12C2×D412yes—
300C2×D12C2×D412yes—
301C2×C4×D3—21no—
302C2×C4×D3—21no—
303C2×C4×D3—21no—
304C2×C4×D3—21no—
305C2×C4×D3—21no—
306C2×C4×D3—21no—
307C2×C4×D3—21no—
308C2×C4×D3—21no—
309C2×C4×D3—21no—
310C2×C4×D3—21no—
311C2×C4×D3—42no—
312C2×C4×D3—42no—
313C2×C4×D3—42no—
314C2×C4×D3C2×D412yes—
315C2×C4×D3#4112yes—
316C3×SD16—28no—
317C2×C3×C8—21no—
318C2×C3×C8—21no—
319C2×C3×C8—21no—
320C2×C3×C8—21no—
321C2×C3×C8—21no—
322C2×C3×C8C2×D412yes—
323C3×C4⋊C4—21no—
324C3×C4⋊C4—21no—
325C3×C4⋊C4—21no—
326C3×C4⋊C4—21no—
327C3×C22⋊C4—42no—
328C3×C22⋊C4—81no—
329C3×C42—21no—
330C3×C42—21no—
331#217—42no—
332#215—28no—
333#213—28no—
334(C2×D3)⋊C4—22no—
335(C2×D3)⋊C4—22no—
336(C2×D3)⋊C4—42no—
337(C2×D3)⋊C4—42no—
338(C2×D3)⋊C4—42no—
339(C2×D3)⋊C4—42no—
340(C2×D3)⋊C4—42no—
341(C2×D3)⋊C4—42no—
342(C2×D3)⋊C4—81no—
343(C2×D3)⋊C4—81no—
344(C2×D3)⋊C4—81no—
345C4⋊Dic3—22no—
346C4⋊Dic3—21no—
347C4⋊Dic3—21no—
348C4⋊Dic3—21no—
349C4⋊Dic3—21no—
350Dic3⋊C4—42no—
351C2×C3⋊C8—21no—
352C2×C3⋊C8—21no—
353C2×C3⋊C8—21no—
354C2×C3⋊C8C2×D412yes—
355C2×C3⋊C8C2×D412yes—
356C2×C3⋊C8C2×D412yes—
357D24—28no—
358ΓL(1,𝔽25)—28no—
359ΓL(1,𝔽25)—44no—
360C25—61no—
361C2×#41—62no—
362C2×#41—62no—
363C2×#41—62no—
364C2×#41—62no—
365C2×#41—121no—
366C2×#41—121no—
367C22×Q8C22×D311yescharacteristic
368C22×D4—31no—
369C22×D4—31no—
370C22×D4—31no—
371C22×D4—61no—
372C22×D4—61no—
373C22×D4—61no—
374C22×D4—62no—
375C22×D4—62no—
376C22×D4—61no—
377C22×D4—62no—
378C22×D4—62no—
379C22×D4—61no—
380C22×D4—121no—
381C22×D4—121no—
382C22×D4C22×D311yescharacteristic
383C23×C4—31no—
384C23×C4—31no—
385C23×C4—61no—
386AGL(1,ℤ/8)—632no—
387C2×SD16—22no—
388C2×SD16—22no—
389C2×SD16—22no—
390C2×SD16—34no—
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×C8C22×D311yescharacteristic
408C22×C8C22×D311yescharacteristic
409C22⋊Q8—62no—
410C22⋊Q8—121no—
411#121—62no—
412#121—62no—
413#121—62no—
414#121—121no—
415#121—121no—
416#121—121no—
417#120—124no—
418C4×D4—62no—
419C4×D4—62no—
420C2×C4⋊C4—31no—
421C2×C4⋊C4—31no—
422C2×C4⋊C4—31no—
423C2×C4⋊C4—61no—
424C2×C4⋊C4C22×D311yescharacteristic
425C2×C4⋊C4C22×D311yescharacteristic
426C2×C22⋊C4—21no—
427C2×C22⋊C4—21no—
428C2×C22⋊C4—31no—
429C2×C22⋊C4—31no—
430C2×C22⋊C4—61no—
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—61no—
439C2×C22⋊C4—61no—
440C2×C42C22×D311yescharacteristic
441#107—62no—
442#106—62no—
443C4⋊C8—22no—
444#103—22no—
445#103—121no—
446#102—22no—
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—61no—
458#95—61no—
459C23×C3—22no—
460C23×C3—41no—
461C23×C3—41no—
462C23×C3—41no—
463C23×C3—41no—
464C23×C3—41no—
465C23×C3—41no—
466C23×C3C22×D411yescharacteristic
467C22×D3—21no—
468C22×D3—21no—
469C22×D3—21no—
470C22×D3—21no—
471C22×D3—21no—
472C22×D3—21no—
473C22×D3—21no—
474C22×D3—21no—
475C22×D3—22no—
476C22×D3—22no—
477C22×D3—21no—
478C22×D3—21no—
479C22×D3—21no—
480C22×D3—21no—
481C22×D3—21no—
482C22×D3—48no—
483C22×D3—41no—
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—84no—
496C22×D3—84no—
497C22×D3—84no—
498C22×D3—84no—
499C22×D3—84no—
500C22×D3—84no—
501C22×D3#12112yes—
502C3×Q8—22no—
503C3×Q8—22no—
504C3×Q8—41no—
505C3×Q8—41no—
506C3×D4—22no—
507C3×D4—22no—
508C3×D4—41no—
509C3×D4—41no—
510C2×C3×C4—21no—
511C2×C3×C4—21no—
512C2×C3×C4—21no—
513C2×C3×C4—22no—
514C2×C3×C4—21no—
515C2×C3×C4—21no—
516C2×C3×C4—41no—
517C2×C3×C4—41no—
518C2×C3×C4—41no—
519C2×C3×C4—41no—
520C2×C3×C4—41no—
521C2×C3×C4—41no—
522C2×C3×C4—41no—
523C2×C3×C4—41no—
524C2×C3×C4AGL(1,ℤ/8)12yescomplemented
525C2×C3×C4C22×D411yescharacteristic
526C2×C3×C4C22×D411yescharacteristic
527C2×C3×C4C22×D411yescharacteristic
528C2×C3×C4C2×#4111yescharacteristic
529C2×C3×C4H(5,𝔽2)11yescharacteristic
530C2×C3×C4H(5,𝔽2)11yescharacteristic
531#67—48no—
532#67—84no—
533C2×Dic3—21no—
534C2×Dic3—21no—
535C2×Dic3—21no—
536C2×Dic3—21no—
537C2×Dic3—21no—
538C2×Dic3—41no—
539C2×Dic3—41no—
540C2×Dic3—41no—
541C2×Dic3—41no—
542C2×Dic3—41no—
543C2×Dic3—41no—
544C2×Dic3#12112yes—
545D12—22no—
546D12—22no—
547D12—22no—
548D12—22no—
549D12—44no—
550D12—48no—
551D12—41no—
552D12—41no—
553D12—41no—
554D12—41no—
555D12—84no—
556D12—84no—
557C4×D3—22no—
558C4×D3—22no—
559C4×D3—22no—
560C4×D3—22no—
561C4×D3—48no—
562C4×D3—41no—
563C4×D3—41no—
564C4×D3—41no—
565C4×D3—41no—
566C3×C8—22no—
567C3×C8—41no—
568C3⋊C8—41no—
569C3⋊C8#12014yescomplemented
570C24—21no—
571C24—31no—
572C24—31no—
573C24—61no—
574C24—61no—
575C24—122no—
576C24—122no—
577C24—122no—
578C24—122no—
579C24—122no—
580C24—241no—
581C24—241no—
582#41—68no—
583#41—124no—
584#41—124no—
585#41—124no—
586C2×Q8—21no—
587C2×Q8—21no—
588C2×Q8—21no—
589C2×Q8—21no—
590C2×Q8—21no—
591C2×Q8D3×D412yes—
592C2×D4—21no—
593C2×D4—21no—
594C2×D4—21no—
595C2×D4—21no—
596C2×D4—21no—
597C2×D4—32no—
598C2×D4—32no—
599C2×D4—62no—
600C2×D4—68no—
601C2×D4—62no—
602C2×D4—61no—
603C2×D4—61no—
604C2×D4—61no—
605C2×D4—61no—
606C2×D4—61no—
607C2×D4—61no—
608C2×D4—61no—
609C2×D4—61no—
610C2×D4—61no—
611C2×D4—61no—
612C2×D4—121no—
613C2×D4—122no—
614C2×D4—122no—
615C2×D4—122no—
616C2×D4—122no—
617C2×D4—122no—
618C2×D4—122no—
619C2×D4—122no—
620C2×D4—122no—
621C2×D4—124no—
622C2×D4—124no—
623C2×D4—124no—
624C2×D4—122no—
625C2×D4—122no—
626C2×D4—122no—
627C2×D4—122no—
628C2×D4—241no—
629C2×D4—241no—
630C2×D4—241no—
631C2×D4D3×D412yes—
632C22×C4—21no—
633C22×C4—21no—
634C22×C4—21no—
635C22×C4—31no—
636C22×C4—32no—
637C22×C4—32no—
638C22×C4—31no—
639C22×C4—61no—
640C22×C4—61no—
641C22×C4—61no—
642C22×C4—61no—
643C22×C4—61no—
644C22×C4—61no—
645C22×C4—61no—
646C22×C4—61no—
647C22×C4—61no—
648C22×C4—61no—
649C22×C4—61no—
650C22×C4—61no—
651C22×C4—122no—
652C22×C4—122no—
653C22×C4—122no—
654C22×C4D3×D411yescharacteristic
655C22×C4D3×D411yescharacteristic
656C22×C4C23×D311yescharacteristic
657SD16—28no—
658SD16—68no—
659D8—68no—
660D8—68no—
661M16—68no—
662M16—124no—
663C2×C8—21no—
664C2×C8—21no—
665C2×C8—21no—
666C2×C8—21no—
667C2×C8—21no—
668C2×C8—32no—
669C2×C8—32no—
670C2×C8—32no—
671C2×C8—61no—
672C2×C8—61no—
673C2×C8—61no—
674C2×C8D3×D412yes—
675C4⋊C4—21no—
676C4⋊C4—21no—
677C4⋊C4—21no—
678C4⋊C4—21no—
679C4⋊C4—62no—
680C4⋊C4—61no—
681C4⋊C4—61no—
682C4⋊C4—61no—
683C4⋊C4—61no—
684C4⋊C4—122no—
685C22⋊C4—42no—
686C22⋊C4—62no—
687C22⋊C4—62no—
688C22⋊C4—81no—
689C22⋊C4—122no—
690C22⋊C4—122no—
691C22⋊C4—122no—
692C22⋊C4—122no—
693C22⋊C4—122no—
694C22⋊C4—122no—
695C22⋊C4—122no—
696C22⋊C4—241no—
697C22⋊C4—241no—
698C22⋊C4—241no—
699C42—21no—
700C42—21no—
701C22×C3—42no—
702C22×C3—42no—
703C22×C3—42no—
704C22×C3—81no—
705C22×C3—81no—
706C22×C3—81no—
707C22×C3—81no—
708C22×C3C2×#12111yescharacteristic
709C22×C3D4211yescharacteristic
710C22×C3D4211yescharacteristic
711C22×C3C2×AGL(1,ℤ/8)11yescharacteristic
712C22×C3#57511yescharacteristic
713C22×C3#57611yescharacteristic
714C22×C3#57711yescharacteristic
715C2×D3—22no—
716C2×D3—22no—
717C2×D3—22no—
718C2×D3—41no—
719C2×D3—41no—
720C2×D3—41no—
721C2×D3—41no—
722C2×D3—42no—
723C2×D3—41no—
724C2×D3—42no—
725C2×D3—41no—
726C2×D3—42no—
727C2×D3—41no—
728C2×D3—42no—
729C2×D3—41no—
730C2×D3—42no—
731C2×D3—41no—
732C2×D3—42no—
733C2×D3—41no—
734C2×D3—41no—
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—42no—
746C3×C4—41no—
747C3×C4—81no—
748C3×C4—81no—
749C3×C4C2×#12011yescharacteristic
750C3×C4#53511yescharacteristic
751C3×C4#54611yescharacteristic
752C3×C4#54611yescharacteristic
753Dic3—22no—
754Dic3—41no—
755Dic3—81no—
756Dic3—81no—
757C23—22no—
758C23—32no—
759C23—41no—
760C23—41no—
761C23—41no—
762C23—41no—
763C23—41no—
764C23—41no—
765C23—61no—
766C23—61no—
767C23—61no—
768C23—61no—
769C23—61no—
770C23—61no—
771C23—61no—
772C23—61no—
773C23—61no—
774C23—61no—
775C23—61no—
776C23—61no—
777C23—62no—
778C23—62no—
779C23—61no—
780C23—128no—
781C23—121no—
782C23—121no—
783C23—121no—
784C23—121no—
785C23—121no—
786C23—121no—
787C23—121no—
788C23—121no—
789C23—121no—
790C23—121no—
791C23—121no—
792C23—121no—
793C23—244no—
794C23—244no—
795C23—244no—
796C23—244no—
797C23—244no—
798C23—244no—
799C23C2×D3×D411yescharacteristic
800Q8—22no—
801Q8—22no—
802Q8—41no—
803Q8—41no—
804D4—22no—
805D4—22no—
806D4—41no—
807D4—41no—
808D4—62no—
809D4—62no—
810D4—62no—
811D4—62no—
812D4—124no—
813D4—128no—
814D4—128no—
815D4—121no—
816D4—121no—
817D4—121no—
818D4—121no—
819D4—244no—
820D4—244no—
821D4—244no—
822C2×C4—21no—
823C2×C4—21no—
824C2×C4—21no—
825C2×C4—21no—
826C2×C4—21no—
827C2×C4—22no—
828C2×C4—32no—
829C2×C4—41no—
830C2×C4—41no—
831C2×C4—41no—
832C2×C4—41no—
833C2×C4—41no—
834C2×C4—41no—
835C2×C4—41no—
836C2×C4—41no—
837C2×C4—61no—
838C2×C4—61no—
839C2×C4—62no—
840C2×C4—62no—
841C2×C4—62no—
842C2×C4—62no—
843C2×C4—61no—
844C2×C4—61no—
845C2×C4—61no—
846C2×C4—128no—
847C2×C4—121no—
848C2×C4—121no—
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#91412yescomplemented
858C2×C4C2×D3×D411yescharacteristic
859C2×C4C2×D3×D411yescharacteristic
860C2×C4C2×D3×D411yescharacteristic
861C2×C4D3×#4111yescharacteristic
862C2×C4#100911yescharacteristic
863C2×C4#100911yescharacteristic
864C8—22no—
865C8—34no—
866C8—41no—
867C8—121no—
868C2×C3—82no—
869C2×C3#240811yescharacteristic
870C2×C3#305511yescharacteristic
871C2×C3#306211yescharacteristic
872C2×C3#327211yescharacteristic
873C2×C3#327311yescharacteristic
874C2×C3#327411yescharacteristic
875C2×C3#327511yescharacteristic
876D3—42no—
877D3—81no—
878D3—82no—
879D3—82no—
880C22—42no—
881C22—42no—
882C22—42no—
883C22—62no—
884C22—62no—
885C22—62no—
886C22—81no—
887C22—81no—
888C22—81no—
889C22—81no—
890C22—121no—
891C22—121no—
892C22—121no—
893C22—121no—
894C22—121no—
895C22—121no—
896C22—122no—
897C22—121no—
898C22—122no—
899C22—122no—
900C22—121no—
901C22—122no—
902C22—121no—
903C22—121no—
904C22—122no—
905C22—121no—
906C22—122no—
907C22—2416no—
908C22—241no—
909C22—241no—
910C22—241no—
911C22—241no—
912C22—241no—
913C22—241no—
914C22—241no—
915C22—241no—
916C22D3×#12111yescharacteristic
917C22#560911yescharacteristic
918C22#560911yescharacteristic
919C22C2×#91411yescharacteristic
920C22#576811yescharacteristic
921C22#577411yescharacteristic
922C22#577811yescharacteristic
923C4—22no—
924C4—42no—
925C4—41no—
926C4—62no—
927C4—81no—
928C4—81no—
929C4—121no—
930C4—241no—
931C4—241no—
932C4D3×#12011yescharacteristic
933C4#565411yescharacteristic
934C4#565411yescharacteristic
935C4#567411yescharacteristic
936C3#2427711yescharacteristic, complemented, Sylow
937C2—82no—
938C2—122no—
939C2—241no—
940C2—242no—
941C2—242no—
942C2#7689511yescharacteristic
943C2#8040511yescharacteristic
944C2#8044611yescharacteristic
945C2#8055511yescharacteristic
946C2#8062911yescharacteristic
947C2#8065711yescharacteristic
948C2#8080911yescharacteristic
subgroupG/H
centerC23C2×D3×D4
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC3×#2055C2
socleC23×C3C22×D4
hypercenter#2055D3
hypocenterC3#24277
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2055

Complements

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

NH ≅ G/Ntype
1. C22×#914C2semidirect
2. C2×#4838C2semidirect
3. C2×#4812C2semidirect
4. C2×#4782C2semidirect
5. #76618C2semidirect
6. #76436C2semidirect
7. C3×#2055C2semidirect
8. #72054C2semidirect
9. #70481C2semidirect
10. #70267C2semidirect
11. #70198C2semidirect
12. #69676C2semidirect
13. #69647C2semidirect
14. #68886C2semidirect
15. #68870C2semidirect
20. C2×#946C22semidirect
29. C22×ΓL(1,𝔽25)C22semidirect
31. C2×#895C22semidirect
34. C2×C3×C4⋊C8C22semidirect
35. C2×C3×#103C22semidirect
37. C3×#391C22semidirect
39. C2×#835C22semidirect
42. C2×#821C22semidirect
44. C2×(C2×D3)⋊C8C22semidirect
48. C2×#809C22semidirect
49. C2×#808C22semidirect
50. C2×#807C22semidirect
55. #4939C22semidirect
56. C2×C4×C3⋊C8C22semidirect
64. C3×#340C22semidirect
65. #4551C22semidirect
72. #2055D3semidirect
122. C2×#215D4semidirect
127. C2×#213D4semidirect
154. C2×ΓL(1,𝔽25)D4semidirect
202. C2×C4⋊C8C2×D3semidirect
204. C2×#103C2×D3semidirect
218. #391C2×D3semidirect
228. #340C2×D3semidirect
524. C2×C3×C4AGL(1,ℤ/8)semidirect
569. C3⋊C8#120semidirect
857. C2×C4#914semidirect
936. C3#24277semidirect

Maximal subgroups

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

subgroupindex
C22×#9142
C2×#48382
C2×#48122
C2×#47822
#766182
#764362
C3×#20552
#720542
#704812
#702672
#701982
#696762
#696472
#688862
#688702
#242773