Finite Group Databasebeta

← #10831003

Subgroups — #10831003

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×C3×#468C211yesmaximal, characteristic, complemented
3C2×#5135C211yesmaximal, characteristic, complemented
4C2×#5128C211yesmaximal, characteristic, complemented
5#82812C211yesmaximal, characteristic, complemented
6#82640C211yesmaximal, characteristic, complemented
7#72049C211yesmaximal, characteristic, complemented
8#71699C211yesmaximal, characteristic, complemented
9#71684C211yesmaximal, characteristic, complemented
10#70631C211yesmaximal, characteristic, complemented
11#70628C211yesmaximal, characteristic, complemented
12#70280C211yesmaximal, characteristic, complemented
13#70267C211yesmaximal, characteristic, complemented
14#70212C211yesmaximal, characteristic, complemented
15#70198C211yesmaximal, characteristic, complemented
16#24277—31nomaximal, Sylow
17C22×#239C2211yescharacteristic
18C22×D3×D4C2211yescharacteristic
19C22×C3×SD16C2211yescharacteristic
20C22×C3×M16C2211yescharacteristic, complemented
21C2×C3×C22⋊Q8C2211yescharacteristic, complemented
22C2×C3×#121C2211yescharacteristic
23C22×#215C2211yescharacteristic
24C2×#937—21no—
25C22×#213C2211yescharacteristic
26C2×#930C2211yescharacteristic
27C2×#930C2211yescharacteristic, complemented
28C2×C4×#67C2211yescharacteristic
29C2×#914—24no—
30C2×#914—24no—
31C2×#914—24no—
32C22×D24C2211yescharacteristic
33C22×ΓL(1,𝔽25)C2211yescharacteristic
34C3×#468—24no—
35C2×C3×#107C2211yescharacteristic, complemented
36C2×C3×#103C2211yescharacteristic, complemented
37C2×C3×#102C2211yescharacteristic
38#5229C2211yescharacteristic, complemented
39C2×#835C2211yescharacteristic, complemented
40#5223—21no—
41#5221C2211yescharacteristic
42C2×#832C2211yescharacteristic
43C2×#830C2211yescharacteristic, complemented
44#5135—24no—
45#5128—24no—
46C2×#821C2211yescharacteristic
47C2×#821C2211yescharacteristic, complemented
48C2×(C2×D3)⋊C8C2211yescharacteristic
49C2×#817C2211yescharacteristic, complemented
50C2×Dic3⋊C8C2211yescharacteristic, complemented
51C2×C8×Dic3C2211yescharacteristic, complemented
52#4991—21no—
53#4989—21no—
54#4988C2211yescharacteristic
55#4988C2211yescharacteristic, complemented
56#4987C2211yescharacteristic
57#4987C2211yescharacteristic
58C2×#809C2211yescharacteristic
59C2×#809C2211yescharacteristic, complemented
60#4960—21no—
61#4959—21no—
62#4956—21no—
63#4955—21no—
64#4529C2211yescharacteristic, complemented
65#4529C2211yescharacteristic, complemented
66C22×AGL(1,ℤ/8)—31no—
67C2×#469—31no—
68C2×#468D311yescharacteristic, complemented
69C2×#436—31no—
70#2408—31no—
71#2407—31no—
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—
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×SD16D414yescomplemented
110C2×C3×M16—22no—
111C2×C3×M16—22no—
112C2×C3×M16—22no—
113C22×C3×C8C2311yescharacteristic
114C22×C3×C8C2311yescharacteristic
115C3×C22⋊Q8—22no—
116C3×C22⋊Q8—41no—
117C3×#121—22no—
118C3×#121—41no—
119C2×C3×C4⋊C4—21no—
120C2×C3×C4⋊C4C2311yescharacteristic
121C2×C3×C4⋊C4C2311yescharacteristic
122C2×C3×C22⋊C4—21no—
123C2×C3×C22⋊C4—21no—
124C2×#217—21no—
125C2×#217—21no—
126C2×#217D411yescharacteristic
127C2×#215—22no—
128C2×#215—22no—
129C2×#215—22no—
130#937—44no—
131C2×#213—22no—
132C2×#213—22no—
133C2×#213—22no—
134#930—22no—
135#930—22no—
136#930—41no—
137#930—41no—
138C4×#67—22no—
139C4×#67—22no—
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)⋊C4—21no—
146C2×(C2×D3)⋊C4—21no—
147C2×(C2×D3)⋊C4—21no—
148C2×(C2×D3)⋊C4D411yescharacteristic
149C2×C4⋊Dic3C2311yescharacteristic
150C2×C4⋊Dic3C2311yescharacteristic
151C2×Dic3⋊C4D411yescharacteristic
152C2×C4×Dic3C2311yescharacteristic
153C22×C3⋊C8C2311yescharacteristic
154C22×C3⋊C8C2311yescharacteristic
155#914—232no—
156C2×D24—22no—
157C2×D24—22no—
158C2×D24D414yescomplemented
159C2×ΓL(1,𝔽25)—22no—
160C2×ΓL(1,𝔽25)—22no—
161C2×ΓL(1,𝔽25)D414yescomplemented
162C3×#107—22no—
163C3×#103—22no—
164C3×#102—22no—
165#835—41no—
166#832—41no—
167C3⋊#95—21no—
168C3⋊#95—21no—
169C3⋊#95—21no—
170C3⋊#95—21no—
171#830—22no—
172#821—22no—
173#821—22no—
174(C2×D3)⋊C8—22no—
175#817—22no—
176Dic3⋊C8—22no—
177C8×Dic3—22no—
178#809—41no—
179#809—41no—
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×M16C2×D311yescharacteristic, complemented
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—24no—
199#436—64no—
200C2×#107C2×D311yescharacteristic, complemented
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⋊C8—31no—
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#340—31no—
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—
317C3×M16—44no—
318C2×C3×C8—21no—
319C2×C3×C8—21no—
320C2×C3×C8—21no—
321C2×C3×C8C2×D412yes—
322C2×C3×C8C2×D412yes—
323C2×C3×C8C2×D412yes—
324C3×C4⋊C4—21no—
325C3×C4⋊C4—21no—
326C3×C4⋊C4—21no—
327C3×C4⋊C4—21no—
328C3×C4⋊C4—42no—
329C3×C22⋊C4—42no—
330C3×C22⋊C4—42no—
331#217—22no—
332#217—42no—
333#217—81no—
334#215—28no—
335#213—28no—
336(C2×D3)⋊C4—22no—
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—21no—
346C4⋊Dic3—21no—
347C4⋊Dic3—21no—
348C4⋊Dic3—21no—
349Dic3⋊C4—22no—
350C4×Dic3—21no—
351C4×Dic3—21no—
352C2×C3⋊C8—21no—
353C2×C3⋊C8—21no—
354C2×C3⋊C8—21no—
355C2×C3⋊C8—21no—
356C2×C3⋊C8—21no—
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—62no—
390C2×SD16—62no—
391C2×SD16—62no—
392C2×SD16#6714yescomplemented
393C2×D8—34no—
394C2×D8—62no—
395C2×D8—62no—
396C2×D8—62no—
397C2×D8—62no—
398C2×D8—62no—
399C2×M16—22no—
400C2×M16—22no—
401C2×M16—22no—
402C2×M16—34no—
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—22no—
442#106—62no—
443C4⋊C8—62no—
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—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—41no—
567C3×C8#12014yescomplemented
568C3⋊C8—22no—
569C3⋊C8—41no—
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×Q8C2×#6712yes—
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×D4C2×#6712yes—
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—44no—
662M16—68no—
663C2×C8—21no—
664C2×C8—21no—
665C2×C8—21no—
666C2×C8—32no—
667C2×C8—61no—
668C2×C8—61no—
669C2×C8—61no—
670C2×C8—61no—
671C2×C8—61no—
672C2×C8D3×D412yes—
673C2×C8D3×D412yes—
674C2×C8C2×#6712yes—
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—41no—
705C22×C3—41no—
706C22×C3—42no—
707C22×C3—42no—
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×C4#100411yescharacteristic
861C2×C4D3×#4111yescharacteristic
862C2×C4#100911yescharacteristic
863C2×C4C22×#6711yescharacteristic
864C8—41no—
865C8—62no—
866C8—121no—
867C8#93714yescomplemented
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—42no—
882C22—41no—
883C22—41no—
884C22—41no—
885C22—41no—
886C22—41no—
887C22—42no—
888C22—41no—
889C22—42no—
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—
916C22D3×#12111yescharacteristic
917C22#560911yescharacteristic
918C22D3×AGL(1,ℤ/8)11yescharacteristic
919C22#577411yescharacteristic
920C22#577711yescharacteristic
921C22#577811yescharacteristic
922C22D4×#6711yescharacteristic
923C4—41no—
924C4—42no—
925C4—62no—
926C4—62no—
927C4—81no—
928C4—81no—
929C4—121no—
930C4—241no—
931C4—241no—
932C4#560711yescharacteristic
933C4#561211yescharacteristic
934C4C2×#93711yescharacteristic
935C4#582911yescharacteristic
936C3#2427711yescharacteristic, complemented, Sylow
937C2—81no—
938C2—82no—
939C2—122no—
940C2—242no—
941C2—242no—
942C2#8080511yescharacteristic
943C2#8080911yescharacteristic
944C2#8083811yescharacteristic
945C2#8083911yescharacteristic
946C2#8264011yescharacteristic
947C2#8395911yescharacteristic
948C2#8399111yescharacteristic
subgroupG/H
centerC23C2×D3×D4
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC2×C3×#468C2
socleC23×C3C22×D4
hypercenterC2×#468D3
hypocenterC3#24277
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#468

Complements

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

NH ≅ G/Ntype
1. C22×#914C2semidirect
2. C2×C3×#468C2semidirect
3. C2×#5135C2semidirect
4. C2×#5128C2semidirect
5. #82812C2semidirect
6. #82640C2semidirect
7. #72049C2semidirect
8. #71699C2semidirect
9. #71684C2semidirect
10. #70631C2semidirect
11. #70628C2semidirect
12. #70280C2semidirect
13. #70267C2semidirect
14. #70212C2semidirect
15. #70198C2semidirect
20. C22×C3×M16C22semidirect
21. C2×C3×C22⋊Q8C22semidirect
27. C2×#930C22semidirect
35. C2×C3×#107C22semidirect
36. C2×C3×#103C22semidirect
38. #5229C22semidirect
39. C2×#835C22semidirect
43. C2×#830C22semidirect
47. C2×#821C22semidirect
49. C2×#817C22semidirect
50. C2×Dic3⋊C8C22semidirect
51. C2×C8×Dic3C22semidirect
55. #4988C22semidirect
59. C2×#809C22semidirect
64. #4529C22semidirect
65. #4529C22semidirect
68. C2×#468D3semidirect
109. C2×C3×SD16D4semidirect
158. C2×D24D4semidirect
161. C2×ΓL(1,𝔽25)D4semidirect
190. C22×M16C2×D3semidirect
191. C2×C22⋊Q8C2×D3semidirect
200. C2×#107C2×D3semidirect
204. C2×#103C2×D3semidirect
392. C2×SD16#67semidirect
551. C2×Dic3AGL(1,ℤ/8)semidirect
567. C3×C8#120semidirect
867. C8#937semidirect
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×C3×#4682
C2×#51352
C2×#51282
#828122
#826402
#720492
#716992
#716842
#706312
#706282
#702802
#702672
#702122
#701982
#242773