Finite Group Databasebeta

← #10831000

Subgroups — #10831000

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
2#82812C211yesmaximal, characteristic, complemented
3C2×#5049C211yesmaximal, characteristic, complemented
4#82640C211yesmaximal, characteristic, complemented
5C2×#5039C211yesmaximal, characteristic, complemented
6C2×#4729C211yesmaximal, characteristic, complemented
7C3×#2000C211yesmaximal, characteristic, complemented
8#72051C211yesmaximal, characteristic, complemented
9#70267C211yesmaximal, characteristic, complemented
10#70257C211yesmaximal, characteristic, complemented
11#70198C211yesmaximal, characteristic, complemented
12#70190C211yesmaximal, characteristic, complemented
13#69961C211yesmaximal, characteristic, complemented
14#68870C211yesmaximal, characteristic, complemented
15#68862C211yesmaximal, characteristic, complemented
16#24277—31nomaximal, Sylow
17C22×#239C2211yescharacteristic
18C22×D3×D4C2211yescharacteristic
19C22×C3×SD16C2211yescharacteristic
20C2×C3×C22⋊Q8C2211yescharacteristic, complemented
21C2×C3×#121C2211yescharacteristic
22C22×#215C2211yescharacteristic
23C2×#937—21no—
24C22×#213C2211yescharacteristic
25C2×#930C2211yescharacteristic
26C2×#930C2211yescharacteristic, complemented
27C2×C4×#67C2211yescharacteristic
28C22×#208C2211yescharacteristic, complemented
29C2×#914—24no—
30C2×#914—24no—
31C2×#914—24no—
32C22×D24C2211yescharacteristic
33C22×ΓL(1,𝔽25)C2211yescharacteristic
34C2×C3×#103C2211yescharacteristic, complemented
35C2×C3×#102C2211yescharacteristic
36C2×C3×C22⋊C8C2211yescharacteristic, complemented
37#5229C2211yescharacteristic, complemented
38C2×#835C2211yescharacteristic, complemented
39#5223—21no—
40#5221C2211yescharacteristic
41C2×#832C2211yescharacteristic
42C2×#821C2211yescharacteristic
43C2×#821C2211yescharacteristic, complemented
44C2×(C2×D3)⋊C8C2211yescharacteristic
45C2×Dic3⋊C8C2211yescharacteristic, complemented
46C2×C8×Dic3C2211yescharacteristic, complemented
47#5049—24no—
48#5039—24no—
49#4991—21no—
50#4989—21no—
51#4988C2211yescharacteristic
52#4988C2211yescharacteristic, complemented
53#4987C2211yescharacteristic
54#4987C2211yescharacteristic
55C2×#809C2211yescharacteristic
56C2×#809C2211yescharacteristic, complemented
57C2×#808C2211yescharacteristic, complemented
58C2×#807C2211yescharacteristic, complemented
59#4960—21no—
60#4959—21no—
61#4956—21no—
62#4955—21no—
63#4729—24no—
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#2055—31no—
73#2054—31no—
74#2000D311yescharacteristic, complemented
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×D4—21no—
84C22×C3×D4C2311yescharacteristic
85C23×C3×C4C2311yescharacteristic
86C22×#67—21no—
87C22×#67—21no—
88C22×#67—21no—
89C22×#67D411yescharacteristic
90C2×#239—22no—
91C2×#239—22no—
92C2×#239—22no—
93C2×#239—22no—
94C2×#239—41no—
95C2×#239—41no—
96C2×D3×D4—22no—
97C2×D3×D4—22no—
98C2×D3×D4—22no—
99C2×D3×D4—22no—
100C2×D3×D4—41no—
101C2×D3×D4—41no—
102C22×D12—21no—
103C22×D12C2311yescharacteristic
104C22×D12C2311yescharacteristic
105C22×C4×D3—21no—
106C22×C4×D3C2311yescharacteristic
107C2×C3×SD16—22no—
108C2×C3×SD16—22no—
109C2×C3×SD16—22no—
110C22×C3×C8C2311yescharacteristic
111C22×C3×C8C2311yescharacteristic
112C3×C22⋊Q8—22no—
113C3×C22⋊Q8—41no—
114C3×#121—22no—
115C3×#121—41no—
116C2×C3×C4⋊C4—21no—
117C2×C3×C4⋊C4C2311yescharacteristic
118C2×C3×C4⋊C4C2311yescharacteristic
119C2×C3×C22⋊C4—21no—
120C2×C3×C22⋊C4—21no—
121C2×#217—21no—
122C2×#217—21no—
123C2×#217D411yescharacteristic
124C2×#215—22no—
125C2×#215—22no—
126C2×#215D414yescomplemented
127#937—44no—
128C2×#213—22no—
129C2×#213—22no—
130C2×#213D414yescomplemented
131#930—22no—
132#930—22no—
133#930—41no—
134#930—41no—
135C4×#67—22no—
136C4×#67—22no—
137C2×(C2×D3)⋊C4—21no—
138C2×(C2×D3)⋊C4—21no—
139C2×(C2×D3)⋊C4—21no—
140C2×(C2×D3)⋊C4—21no—
141C2×(C2×D3)⋊C4—21no—
142C2×(C2×D3)⋊C4—21no—
143C2×(C2×D3)⋊C4—21no—
144C2×(C2×D3)⋊C4—21no—
145C2×(C2×D3)⋊C4D411yescharacteristic
146C2×C4⋊Dic3C2311yescharacteristic
147C2×C4⋊Dic3C2311yescharacteristic
148C2×Dic3⋊C4D411yescharacteristic
149C2×C4×Dic3C2311yescharacteristic
150C2×#208—22no—
151C2×#208—22no—
152C2×#208—22no—
153C22×C3⋊C8C2311yescharacteristic
154C22×C3⋊C8C2311yescharacteristic
155#914—232no—
156C2×D24—22no—
157C2×D24—22no—
158C2×D24—22no—
159C2×ΓL(1,𝔽25)—22no—
160C2×ΓL(1,𝔽25)—22no—
161C2×ΓL(1,𝔽25)D414yescomplemented
162C3×#103—41no—
163C3×#102—41no—
164C3×C22⋊C8—22no—
165#835—22no—
166#832—22no—
167C3⋊#95—21no—
168C3⋊#95—21no—
169C3⋊#95—21no—
170C3⋊#95—21no—
171#821—41no—
172#821—41no—
173(C2×D3)⋊C8—22no—
174Dic3⋊C8—22no—
175C8×Dic3—22no—
176#809—22no—
177#809—22no—
178#808—22no—
179#807—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⋊Q8C2×D311yescharacteristic, complemented
192C2×#121—31no—
193C2×#121—31no—
194C2×#121C2×D311yescharacteristic
195C2×#120—61no—
196C2×C4×D4—31no—
197#469—64no—
198#468—64no—
199#436—64no—
200C2×#107—31no—
201C2×#106—31no—
202C2×C4⋊C8—31no—
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⋊C8C2×D311yescharacteristic, complemented
213C2×C4×C8—31no—
214#394—61no—
215#394—61no—
216#392—61no—
217#392—61no—
218#391—31no—
219#390—31no—
220#390—31no—
221#390—31no—
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—
230C24×C3C2×D411yescharacteristic
231C23×D3—21no—
232C23×D3—21no—
233C23×D3—42no—
234C23×D3—42no—
235C23×D3—42no—
236C23×D3—42no—
237C23×D3—42no—
238C23×D3—81no—
239C23×D3—81no—
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×D4—42no—
253C2×C3×D4—42no—
254C2×C3×D4—81no—
255C2×C3×D4C2×D412yes—
256C22×C3×C4—21no—
257C22×C3×C4—21no—
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×C4C2×D411yescharacteristic
266C22×C3×C4C2411yescharacteristic
267C2×#67—22no—
268C2×#67—22no—
269C2×#67—41no—
270C2×#67—42no—
271C2×#67—42no—
272C2×#67—42no—
273C2×#67—42no—
274C2×#67—42no—
275C2×#67—42no—
276C2×#67—42no—
277C2×#67—81no—
278C2×#67—81no—
279C22×Dic3—21no—
280C22×Dic3—21no—
281C22×Dic3C2×D411yescharacteristic
282C22×Dic3C2×D411yescharacteristic
283C22×Dic3C2×D411yescharacteristic
284#239—28no—
285#239—44no—
286#239—44no—
287#239—44no—
288D3×D4—28no—
289D3×D4—44no—
290D3×D4—44no—
291D3×D4—44no—
292C2×D12—21no—
293C2×D12—21no—
294C2×D12—21no—
295C2×D12—21no—
296C2×D12—21no—
297C2×D12—21no—
298C2×D12—21no—
299C2×D12—21no—
300C2×D12—21no—
301C2×D12—21no—
302C2×D12—42no—
303C2×D12—42no—
304C2×D12—42no—
305C2×D12C2×D412yes—
306C2×D12C2×D412yes—
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×C4⋊C4—42no—
328C3×C22⋊C4—42no—
329C3×C22⋊C4—42no—
330#217—22no—
331#217—42no—
332#217—81no—
333#215—28no—
334#213—28no—
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—81no—
342(C2×D3)⋊C4—81no—
343(C2×D3)⋊C4—81no—
344C4⋊Dic3—21no—
345C4⋊Dic3—21no—
346C4⋊Dic3—21no—
347C4⋊Dic3—21no—
348Dic3⋊C4—22no—
349C4×Dic3—21no—
350C4×Dic3—21no—
351#208—44no—
352C2×C3⋊C8—21no—
353C2×C3⋊C8—21no—
354C2×C3⋊C8—21no—
355C2×C3⋊C8C2×D412yes—
356C2×C3⋊C8C2×D412yes—
357C2×C3⋊C8C2×D412yes—
358D24—28no—
359ΓL(1,𝔽25)—28no—
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—21no—
369C22×D4—31no—
370C22×D4—31no—
371C22×D4—31no—
372C22×D4—61no—
373C22×D4—62no—
374C22×D4—62no—
375C22×D4—61no—
376C22×D4—62no—
377C22×D4—62no—
378C22×D4—61no—
379C22×D4—61no—
380C22×D4—121no—
381C22×D4—121no—
382C22×D4C22×D311yescharacteristic
383C23×C4—31no—
384C23×C4—61no—
385C23×C4C22×D311yescharacteristic
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—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—62no—
419C4×D4—62no—
420C2×C4⋊C4—21no—
421C2×C4⋊C4—31no—
422C2×C4⋊C4—31no—
423C2×C4⋊C4—31no—
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×C42—31no—
441#107—62no—
442#106—62no—
443C4⋊C8—62no—
444#103—41no—
445#103—62no—
446#102—41no—
447#102—62no—
448#102—62no—
449#102—62no—
450#102—121no—
451#102—121no—
452C22⋊C8—22no—
453C22⋊C8—62no—
454C4×C8—62no—
455#95—61no—
456#95—61no—
457#95—61no—
458#95—61no—
459C23×C3—21no—
460C23×C3—21no—
461C23×C3—22no—
462C23×C3—21no—
463C23×C3—21no—
464C23×C3—21no—
465C23×C3—21no—
466C23×C3—21no—
467C23×C3—41no—
468C23×C3—41no—
469C23×C3—41no—
470C23×C3—41no—
471C23×C3—41no—
472C23×C3—41no—
473C23×C3C22×D411yescharacteristic
474C22×D3—21no—
475C22×D3—21no—
476C22×D3—21no—
477C22×D3—21no—
478C22×D3—21no—
479C22×D3—21no—
480C22×D3—22no—
481C22×D3—22no—
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—
510C3×D4—84no—
511C2×C3×C4—21no—
512C2×C3×C4—21no—
513C2×C3×C4—21no—
514C2×C3×C4—22no—
515C2×C3×C4—41no—
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×C4—41no—
525C2×C3×C4—41no—
526C2×C3×C4—41no—
527C2×C3×C4C22×D411yescharacteristic
528C2×C3×C4C22×D411yescharacteristic
529C2×C3×C4C22×D411yescharacteristic
530C2×C3×C4C2×#4111yescharacteristic
531C2×C3×C4H(5,𝔽2)11yescharacteristic
532C2×C3×C4H(5,𝔽2)11yescharacteristic
533#67—44no—
534#67—48no—
535#67—84no—
536#67—84no—
537C2×Dic3—21no—
538C2×Dic3—21no—
539C2×Dic3—21no—
540C2×Dic3—21no—
541C2×Dic3—21no—
542C2×Dic3—21no—
543C2×Dic3—21no—
544C2×Dic3—41no—
545C2×Dic3—41no—
546C2×Dic3—41no—
547C2×Dic3—41no—
548C2×Dic3—41no—
549C2×Dic3—41no—
550C2×Dic3#12112yes—
551C2×Dic3AGL(1,ℤ/8)12yescomplemented
552D12—22no—
553D12—22no—
554D12—22no—
555D12—22no—
556D12—48no—
557D12—41no—
558D12—41no—
559D12—41no—
560D12—41no—
561C4×D3—22no—
562C4×D3—22no—
563C4×D3—22no—
564C4×D3—22no—
565C4×D3—48no—
566C3×C8—22no—
567C3×C8—41no—
568C3⋊C8—41no—
569C3⋊C8#12014yescomplemented
570C24—21no—
571C24—31no—
572C24—61no—
573C24—61no—
574C24—122no—
575C24—122no—
576C24—122no—
577C24—122no—
578C24—122no—
579C24—241no—
580C24—241no—
581C24D3×D411yescharacteristic
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—42no—
600C2×D4—42no—
601C2×D4—62no—
602C2×D4—68no—
603C2×D4—62no—
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—61no—
613C2×D4—61no—
614C2×D4—81no—
615C2×D4—122no—
616C2×D4—122no—
617C2×D4—122no—
618C2×D4—122no—
619C2×D4—124no—
620C2×D4—124no—
621C2×D4—124no—
622C2×D4—121no—
623C2×D4—122no—
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—31no—
642C22×C4—31no—
643C22×C4—32no—
644C22×C4—32no—
645C22×C4—31no—
646C22×C4—61no—
647C22×C4—61no—
648C22×C4—61no—
649C22×C4—61no—
650C22×C4—61no—
651C22×C4—61no—
652C22×C4—122no—
653C22×C4—122no—
654C22×C4—122no—
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—42no—
680C4⋊C4—62no—
681C4⋊C4—61no—
682C4⋊C4—61no—
683C4⋊C4—61no—
684C4⋊C4—61no—
685C22⋊C4—42no—
686C22⋊C4—42no—
687C22⋊C4—62no—
688C22⋊C4—62no—
689C22⋊C4—122no—
690C22⋊C4—122no—
691C22⋊C4—122no—
692C22⋊C4—122no—
693C22⋊C4—122no—
694C22⋊C4—122no—
695C22⋊C4—241no—
696C22⋊C4—241no—
697C22⋊C4—241no—
698C22⋊C4—241no—
699C42—61no—
700C42—61no—
701C22×C3—42no—
702C22×C3—41no—
703C22×C3—41no—
704C22×C3—42no—
705C22×C3—41no—
706C22×C3—42no—
707C22×C3—41no—
708C22×C3—41no—
709C22×C3—41no—
710C22×C3—41no—
711C22×C3—81no—
712C22×C3—81no—
713C22×C3—81no—
714C22×C3—81no—
715C22×C3C2×#12111yescharacteristic
716C22×C3D4211yescharacteristic
717C22×C3D4211yescharacteristic
718C22×C3C2×AGL(1,ℤ/8)11yescharacteristic
719C22×C3#57511yescharacteristic
720C22×C3#57611yescharacteristic
721C22×C3#57711yescharacteristic
722C2×D3—22no—
723C2×D3—22no—
724C2×D3—22no—
725C2×D3—41no—
726C2×D3—41no—
727C2×D3—41no—
728C2×D3—41no—
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—42no—
745C3×C4—41no—
746C3×C4—81no—
747C3×C4—81no—
748C3×C4C2×#12011yescharacteristic
749C3×C4#53511yescharacteristic
750C3×C4#54611yescharacteristic
751C3×C4#54611yescharacteristic
752Dic3—22no—
753Dic3—22no—
754Dic3—41no—
755Dic3—81no—
756Dic3—81no—
757C23—21no—
758C23—21no—
759C23—21no—
760C23—21no—
761C23—21no—
762C23—22no—
763C23—21no—
764C23—21no—
765C23—32no—
766C23—41no—
767C23—41no—
768C23—41no—
769C23—41no—
770C23—41no—
771C23—41no—
772C23—61no—
773C23—61no—
774C23—61no—
775C23—61no—
776C23—61no—
777C23—61no—
778C23—62no—
779C23—62no—
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—84no—
813D4—128no—
814D4—124no—
815D4—128no—
816D4—121no—
817D4—121no—
818D4—121no—
819D4—121no—
820D4—244no—
821D4—244no—
822C2×C4—21no—
823C2×C4—22no—
824C2×C4—21no—
825C2×C4—21no—
826C2×C4—32no—
827C2×C4—32no—
828C2×C4—41no—
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—41no—
838C2×C4—41no—
839C2×C4—41no—
840C2×C4—61no—
841C2×C4—61no—
842C2×C4—61no—
843C2×C4—61no—
844C2×C4—62no—
845C2×C4—62no—
846C2×C4—62no—
847C2×C4—62no—
848C2×C4—61no—
849C2×C4—61no—
850C2×C4—61no—
851C2×C4—128no—
852C2×C4—121no—
853C2×C4—121no—
854C2×C4—121no—
855C2×C4—121no—
856C2×C4—121no—
857C2×C4—121no—
858C2×C4C2×D3×D411yescharacteristic
859C2×C4C2×D3×D411yescharacteristic
860C2×C4C2×D3×D411yescharacteristic
861C2×C4#100411yescharacteristic
862C2×C4#100411yescharacteristic
863C2×C4D3×#4111yescharacteristic
864C8—22no—
865C8—34no—
866C8—41no—
867C8—121no—
868C2×C3—82no—
869C2×C3—81no—
870C2×C3#240811yescharacteristic
871C2×C3#305511yescharacteristic
872C2×C3#306211yescharacteristic
873C2×C3#327211yescharacteristic
874C2×C3#327311yescharacteristic
875C2×C3#327411yescharacteristic
876C2×C3#327511yescharacteristic
877D3—42no—
878D3—82no—
879D3—82no—
880C22—41no—
881C22—41no—
882C22—42no—
883C22—41no—
884C22—42no—
885C22—41no—
886C22—42no—
887C22—41no—
888C22—41no—
889C22—41no—
890C22—62no—
891C22—62no—
892C22—62no—
893C22—81no—
894C22—81no—
895C22—81no—
896C22—81no—
897C22—121no—
898C22—121no—
899C22—121no—
900C22—121no—
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—
916C22#559011yescharacteristic
917C22#559011yescharacteristic
918C22D3×#12111yescharacteristic
919C22#576211yescharacteristic
920C22#576911yescharacteristic
921C22D3×AGL(1,ℤ/8)11yescharacteristic
922C22#577711yescharacteristic
923C4—41no—
924C4—42no—
925C4—62no—
926C4—62no—
927C4—81no—
928C4—81no—
929C4—121no—
930C4—241no—
931C4—241no—
932C4D3×#12011yescharacteristic
933C4#561011yescharacteristic
934C4#561011yescharacteristic
935C4#571511yescharacteristic
936C3#2427711yescharacteristic, complemented, Sylow
937C2—81no—
938C2—82no—
939C2—122no—
940C2—242no—
941C2—242no—
942C2#7666911yescharacteristic
943C2#8006211yescharacteristic
944C2#8012511yescharacteristic
945C2#8016711yescharacteristic
946C2#8024311yescharacteristic
947C2#8066111yescharacteristic
948C2#8080511yescharacteristic
subgroupG/H
centerC23C2×D3×D4
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC3×#2000C2
socleC23×C3C22×D4
hypercenter#2000D3
hypocenterC3#24277
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. C22×#914C2semidirect
2. #82812C2semidirect
3. C2×#5049C2semidirect
4. #82640C2semidirect
5. C2×#5039C2semidirect
6. C2×#4729C2semidirect
7. C3×#2000C2semidirect
8. #72051C2semidirect
9. #70267C2semidirect
10. #70257C2semidirect
11. #70198C2semidirect
12. #70190C2semidirect
13. #69961C2semidirect
14. #68870C2semidirect
15. #68862C2semidirect
20. C2×C3×C22⋊Q8C22semidirect
26. C2×#930C22semidirect
28. C22×#208C22semidirect
34. C2×C3×#103C22semidirect
36. C2×C3×C22⋊C8C22semidirect
37. #5229C22semidirect
38. C2×#835C22semidirect
43. C2×#821C22semidirect
45. C2×Dic3⋊C8C22semidirect
46. C2×C8×Dic3C22semidirect
52. #4988C22semidirect
56. C2×#809C22semidirect
57. C2×#808C22semidirect
58. C2×#807C22semidirect
64. C3×#340C22semidirect
65. #4551C22semidirect
74. #2000D3semidirect
126. C2×#215D4semidirect
130. C2×#213D4semidirect
161. C2×ΓL(1,𝔽25)D4semidirect
191. C2×C22⋊Q8C2×D3semidirect
204. C2×#103C2×D3semidirect
212. C2×C22⋊C8C2×D3semidirect
228. #340C2×D3semidirect
551. C2×Dic3AGL(1,ℤ/8)semidirect
569. C3⋊C8#120semidirect
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
#828122
C2×#50492
#826402
C2×#50392
C2×#47292
C3×#20002
#720512
#702672
#702572
#701982
#701902
#699612
#688702
#688622
#242773