Finite Group Databasebeta

← #10830982

Subgroups — #10830982

Order 768.

1614 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×#932C211yesmaximal, characteristic, complemented
2C3×#2408C211yesmaximal, characteristic, complemented
3C2×#5038C211yesmaximal, characteristic, complemented
4C2×#5041C211yesmaximal, characteristic, complemented
5#82402C211yesmaximal, characteristic, complemented
6C2×#5011C211yesmaximal, characteristic, complemented
7#72128C211yesmaximal, characteristic, complemented
8#71685C211yesmaximal, characteristic, complemented
9#71684C211yesmaximal, characteristic, complemented
10#69651C211yesmaximal, characteristic, complemented
11#69650C211yesmaximal, characteristic, complemented
12#69649C211yesmaximal, characteristic, complemented
13#69648C211yesmaximal, characteristic, complemented
14#69522C211yesmaximal, characteristic, complemented
15#69513C211yesmaximal, characteristic, complemented
16#24275—31nomaximal, Sylow
17C23×C3×D4C2211yescharacteristic
18C22×#235C2211yescharacteristic
19C2×C3×#121C2211yescharacteristic
20C2×C3×#121C2211yescharacteristic
21C2×C3×#120—21no—
22C2×C3×C4×D4C2211yescharacteristic
23C22×#214C2211yescharacteristic
24C22×#214C2211yescharacteristic
25C2×#932—24no—
26C2×#932—24no—
27C2×#932—24no—
28C22×#213C2211yescharacteristic
29C22×#213C2211yescharacteristic
30C2×#930C2211yescharacteristic, complemented
31C2×#924C2211yescharacteristic, complemented
32C22×#208C2211yescharacteristic
33C23×C3⋊C8C2211yescharacteristic, complemented
34C3×#394—21no—
35C3×#392—21no—
36C3×#390C2211yescharacteristic
37C3×#390C2211yescharacteristic
38C3×#380C2211yescharacteristic
39C3×#379—21no—
40#5223—21no—
41C2×#832C2211yescharacteristic
42C2×#832C2211yescharacteristic
43C2×#832C2211yescharacteristic
44C2×#832C2211yescharacteristic
45#5212C2211yescharacteristic
46C2×#830C2211yescharacteristic
47C2×#830C2211yescharacteristic, complemented
48#5041—24no—
49#5038—24no—
50#5011—24no—
51#4989—21no—
52C2×#810C2211yescharacteristic, complemented
53C2×#810C2211yescharacteristic, complemented
54C2×#809C2211yescharacteristic, complemented
55C2×#809C2211yescharacteristic, complemented
56C2×#808C2211yescharacteristic, complemented
57C2×#807C2211yescharacteristic, complemented
58#4959—21no—
59#4956—21no—
60#4939C2211yescharacteristic, complemented
61#4929C2211yescharacteristic, complemented
62C2×C4⋊(C3⋊C8)C2211yescharacteristic, complemented
63C2×#803C2211yescharacteristic, complemented
64#4529C2211yescharacteristic, complemented
65#4529C2211yescharacteristic, complemented
66C22×AGL(1,ℤ/8)—31no—
67C2×#466—31no—
68C2×#465—31no—
69C2×#435—31no—
70#2408D311yescharacteristic, complemented
71#2407—31no—
72#2055—31no—
73#2054—31no—
74#2000—31no—
75#1999—31no—
76#1973—31no—
77#1972—31no—
78#1809—31no—
79#1788—31no—
80#1786—31no—
81C25×C3—21no—
82C22×C3×D4—22no—
83C22×C3×D4—22no—
84C22×C3×D4—21no—
85C22×C3×D4—21no—
86C22×C3×D4—22no—
87C22×C3×D4—21no—
88C22×C3×D4—22no—
89C22×C3×D4—41no—
90C22×C3×D4—41no—
91C22×C3×D4D411yescharacteristic
92C22×C3×D4C2311yescharacteristic
93C22×C3×D4C2311yescharacteristic
94C23×C3×C4C2311yescharacteristic
95C23×C3×C4C2311yescharacteristic
96C22×#67—21no—
97C22×#67—21no—
98C2×#235—22no—
99C2×#235—22no—
100C2×#235—22no—
101C2×#235—22no—
102C2×#235—41no—
103C2×#235—41no—
104C22×D12C2311yescharacteristic
105C22×C4×D3—21no—
106C22×Dic6C2311yescharacteristic
107C3×#121—22no—
108C3×#121—22no—
109C3×#121—41no—
110C3×#121—41no—
111C3×#120—44no—
112C3×C4×D4—22no—
113C3×C4×D4—22no—
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⋊C4—21no—
123C2×C3×C22⋊C4—21no—
124C2×C3×C22⋊C4D411yescharacteristic
125C2×C3×C22⋊C4D411yescharacteristic
126C2×C3×C42C2311yescharacteristic
127C2×#217—21no—
128C2×#217—21no—
129C2×#214—22no—
130C2×#214—22no—
131C2×#214—22no—
132C2×#214—22no—
133C2×#214—22no—
134C2×#214D414yescomplemented
135#932—232no—
136C2×#213—22no—
137C2×#213—22no—
138C2×#213—22no—
139C2×#213—22no—
140C2×#213—22no—
141C2×#213D414yescomplemented
142#930—22no—
143#930—41no—
144C2×(C2×D3)⋊C4—21no—
145C2×(C2×D3)⋊C4—21no—
146C2×(C2×D3)⋊C4—21no—
147C2×C4⋊Dic3C2311yescharacteristic
148C2×C4⋊Dic3C2311yescharacteristic
149#924—22no—
150#924—41no—
151C2×Dic3⋊C4—21no—
152C2×#208—22no—
153C2×#208—22no—
154C2×#208D414yescomplemented
155C22×C3⋊C8—22no—
156C22×C3⋊C8—22no—
157C22×C3⋊C8—22no—
158C22×C3⋊C8C2311yescharacteristic
159C22×C3⋊C8C2311yescharacteristic
160C22×C3⋊C8C2311yescharacteristic
161C22×C3⋊C8C2311yescharacteristic
162C3×#95—21no—
163#832—22no—
164#832—22no—
165#832—41no—
166#832—41no—
167C3⋊#95—21no—
168C3⋊#95—21no—
169C3⋊#95—21no—
170#830—22no—
171#830—22no—
172#810—22no—
173#810—41no—
174#809—22no—
175#809—41no—
176#808—22no—
177#807—22no—
178C4⋊(C3⋊C8)—22no—
179#803—22no—
180C22×#41—31no—
181C23×D4C2×D311yescharacteristic
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—
190C23×C8—31no—
191C2×C22⋊Q8—31no—
192C2×#121—31no—
193C2×#121C2×D311yescharacteristic
194C2×#121C2×D311yescharacteristic
195C2×#120—21no—
196C2×C4×D4C2×D311yescharacteristic
197#466—64no—
198#465—64no—
199#435—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×#97—31no—
214#394—21no—
215#394—61no—
216#392—21no—
217#392—61no—
218#391—31no—
219#390—31no—
220#390C2×D311yescharacteristic
221#390C2×D311yescharacteristic
222#386—61no—
223#385—61no—
224#380—31no—
225#380C2×D311yescharacteristic
226#379—21no—
227#340—31no—
228#340—31no—
229C24×C3—21no—
230C24×C3—21no—
231C24×C3—42no—
232C24×C3—42no—
233C24×C3—42no—
234C24×C3—42no—
235C24×C3—42no—
236C24×C3—81no—
237C24×C3—81no—
238C24×C3C2×D411yescharacteristic
239C24×C3C2×D411yescharacteristic
240C23×D3—21no—
241C2×C3×D4—28no—
242C2×C3×D4—22no—
243C2×C3×D4—22no—
244C2×C3×D4—21no—
245C2×C3×D4—21no—
246C2×C3×D4—21no—
247C2×C3×D4—21no—
248C2×C3×D4—21no—
249C2×C3×D4—21no—
250C2×C3×D4—21no—
251C2×C3×D4—21no—
252C2×C3×D4—21no—
253C2×C3×D4—21no—
254C2×C3×D4—44no—
255C2×C3×D4—44no—
256C2×C3×D4—41no—
257C2×C3×D4—42no—
258C2×C3×D4—42no—
259C2×C3×D4—44no—
260C2×C3×D4—42no—
261C2×C3×D4—42no—
262C2×C3×D4—42no—
263C2×C3×D4—42no—
264C2×C3×D4—42no—
265C2×C3×D4—81no—
266C2×C3×D4—81no—
267C2×C3×D4C2×D412yes—
268C2×C3×D4C2×D412yes—
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—21no—
280C22×C3×C4—21no—
281C22×C3×C4C2×D412yes—
282C22×C3×C4C2×D411yescharacteristic
283C22×C3×C4C2×D411yescharacteristic
284C22×C3×C4C2×D411yescharacteristic
285C22×C3×C4C2×D411yescharacteristic
286C22×C3×C4#4112yes—
287C22×C3×C4C2411yescharacteristic
288C2×#67—42no—
289C2×#67—42no—
290C2×#67—42no—
291C2×#67—42no—
292C2×#67—42no—
293C2×#67—81no—
294C22×Dic3—21no—
295C22×Dic3—21no—
296C22×Dic3—21no—
297#235—28no—
298#235—44no—
299#235—44no—
300#235—44no—
301C2×D12—21no—
302C2×D12—21no—
303C2×D12—21no—
304C2×D12—21no—
305C2×D12—21no—
306C2×D12C2×D412yes—
307C2×C4×D3—42no—
308C2×C4×D3—42no—
309C2×C4×D3—42no—
310C2×Dic6—21no—
311C2×Dic6—21no—
312C2×Dic6—21no—
313C2×Dic6—21no—
314C2×Dic6—21no—
315C2×Dic6C2×D412yes—
316C3×C4⋊C4—22no—
317C3×C4⋊C4—21no—
318C3×C4⋊C4—21no—
319C3×C4⋊C4—21no—
320C3×C4⋊C4—21no—
321C3×C22⋊C4—22no—
322C3×C22⋊C4—22no—
323C3×C22⋊C4—42no—
324C3×C22⋊C4—42no—
325C3×C22⋊C4—42no—
326C3×C22⋊C4—42no—
327C3×C22⋊C4—42no—
328C3×C22⋊C4—81no—
329C3×C22⋊C4—81no—
330C3×C42—21no—
331C3×C42—21no—
332#217—42no—
333#217—81no—
334#214—28no—
335#214—28no—
336#213—28no—
337#213—28no—
338(C2×D3)⋊C4—42no—
339(C2×D3)⋊C4—42no—
340(C2×D3)⋊C4—81no—
341C4⋊Dic3—21no—
342C4⋊Dic3—21no—
343C4⋊Dic3—21no—
344C4⋊Dic3—21no—
345Dic3⋊C4—42no—
346#208—28no—
347C2×C3⋊C8—21no—
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—44no—
356C2×C3⋊C8C2×D412yes—
357C2×C3⋊C8C2×D412yes—
358C2×C3⋊C8C2×D412yes—
359C2×C3⋊C8C2×D412yes—
360C25—21no—
361C2×#41—62no—
362C2×#41—62no—
363C2×#41—62no—
364C2×#41—62no—
365C2×#41—121no—
366C2×#41—121no—
367C22×Q8—31no—
368C22×D4—22no—
369C22×D4—22no—
370C22×D4—21no—
371C22×D4—21no—
372C22×D4—22no—
373C22×D4—22no—
374C22×D4—21no—
375C22×D4—31no—
376C22×D4—41no—
377C22×D4—41no—
378C22×D4—61no—
379C22×D4—61no—
380C22×D4#6711yescharacteristic
381C22×D4C22×D311yescharacteristic
382C22×D4C22×D311yescharacteristic
383C23×C4—61no—
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—
402C22×C8—31no—
403C22×C8—31no—
404C22×C8—31no—
405C22×C8—31no—
406C22×C8—62no—
407C22×C8—62no—
408C22×C8—62no—
409C22⋊Q8—62no—
410C22⋊Q8—121no—
411#121—22no—
412#121—22no—
413#121—41no—
414#121—41no—
415#121—62no—
416#121—121no—
417#120—44no—
418C4×D4—22no—
419C4×D4—22no—
420C2×C4⋊C4—31no—
421C2×C4⋊C4—31no—
422C2×C4⋊C4—61no—
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—21no—
432C2×C22⋊C4—21no—
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—
454#97—62no—
455#95—21no—
456#95—61no—
457#95—61no—
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—21no—
468C23×C3—21no—
469C23×C3—21no—
470C23×C3—21no—
471C23×C3—22no—
472C23×C3—22no—
473C23×C3—48no—
474C23×C3—41no—
475C23×C3—41no—
476C23×C3—41no—
477C23×C3—41no—
478C23×C3—41no—
479C23×C3—41no—
480C23×C3—41no—
481C23×C3—41no—
482C23×C3—41no—
483C23×C3—41no—
484C23×C3—41no—
485C23×C3—41no—
486C23×C3—84no—
487C23×C3—84no—
488C23×C3—84no—
489C23×C3—84no—
490C23×C3—84no—
491C23×C3—84no—
492C23×C3#12112yes—
493C23×C3AGL(1,ℤ/8)12yescomplemented
494C23×C3C22×D411yescharacteristic
495C22×D3—22no—
496C22×D3—41no—
497C22×D3—41no—
498C22×D3—41no—
499C22×D3—41no—
500C22×D3—41no—
501C22×D3—41no—
502C3×D4—22no—
503C3×D4—22no—
504C3×D4—22no—
505C3×D4—22no—
506C3×D4—48no—
507C3×D4—44no—
508C3×D4—41no—
509C3×D4—41no—
510C3×D4—41no—
511C3×D4—41no—
512C3×D4—84no—
513C3×D4—84no—
514C2×C3×C4—21no—
515C2×C3×C4—21no—
516C2×C3×C4—22no—
517C2×C3×C4—22no—
518C2×C3×C4—22no—
519C2×C3×C4—22no—
520C2×C3×C4—21no—
521C2×C3×C4—21no—
522C2×C3×C4—21no—
523C2×C3×C4—21no—
524C2×C3×C4—21no—
525C2×C3×C4—21no—
526C2×C3×C4—21no—
527C2×C3×C4—21no—
528C2×C3×C4—21no—
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#12112yes—
540C2×C3×C4C22×D411yescharacteristic
541C2×C3×C4C22×D411yescharacteristic
542C2×C3×C4C22×D411yescharacteristic
543C2×C3×C4C2×#4111yescharacteristic
544C2×C3×C4H(5,𝔽2)11yescharacteristic
545C2×C3×C4H(5,𝔽2)11yescharacteristic
546#67—48no—
547#67—84no—
548C2×Dic3—22no—
549C2×Dic3—41no—
550C2×Dic3—41no—
551C2×Dic3—41no—
552C2×Dic3—41no—
553C2×Dic3—41no—
554C2×Dic3—41no—
555C2×Dic3—41no—
556C2×Dic3—41no—
557D12—22no—
558D12—22no—
559D12—41no—
560D12—41no—
561C4×D3—48no—
562Dic6—22no—
563Dic6—22no—
564Dic6—41no—
565Dic6—41no—
566C3⋊C8—22no—
567C3⋊C8—41no—
568C3⋊C8—41no—
569C3⋊C8#12014yescomplemented
570C24—21no—
571C24—21no—
572C24—42no—
573C24—42no—
574C24—42no—
575C24—42no—
576C24—42no—
577C24—61no—
578C24—81no—
579C24—81no—
580C24C2×#6711yescharacteristic
581C24C2×#6711yescharacteristic
582#41—68no—
583#41—124no—
584#41—124no—
585#41—124no—
586C2×Q8—32no—
587C2×Q8—61no—
588C2×Q8—61no—
589C2×Q8—61no—
590C2×Q8—61no—
591C2×Q8—61no—
592C2×D4—28no—
593C2×D4—22no—
594C2×D4—22no—
595C2×D4—21no—
596C2×D4—21no—
597C2×D4—21no—
598C2×D4—21no—
599C2×D4—21no—
600C2×D4—21no—
601C2×D4—21no—
602C2×D4—21no—
603C2×D4—21no—
604C2×D4—21no—
605C2×D4—32no—
606C2×D4—44no—
607C2×D4—44no—
608C2×D4—41no—
609C2×D4—42no—
610C2×D4—42no—
611C2×D4—44no—
612C2×D4—42no—
613C2×D4—42no—
614C2×D4—42no—
615C2×D4—42no—
616C2×D4—42no—
617C2×D4—61no—
618C2×D4—61no—
619C2×D4—61no—
620C2×D4—61no—
621C2×D4—61no—
622C2×D4—81no—
623C2×D4—81no—
624C2×D4—122no—
625C2×D4—122no—
626C2×D4—122no—
627C2×D4—122no—
628C2×D4—122no—
629C2×D4—241no—
630C2×D4D3×D412yes—
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—61no—
645C22×C4—61no—
646C22×C4—61no—
647C22×C4—122no—
648C22×C4—122no—
649C22×C4—122no—
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—
662C2×C8—32no—
663C2×C8—32no—
664C2×C8—32no—
665C2×C8—32no—
666C2×C8—61no—
667C2×C8—61no—
668C2×C8—61no—
669C2×C8—61no—
670C2×C8—61no—
671C2×C8—61no—
672C2×C8—61no—
673C2×C8—61no—
674C2×C8—124no—
675C4⋊C4—22no—
676C4⋊C4—21no—
677C4⋊C4—21no—
678C4⋊C4—21no—
679C4⋊C4—21no—
680C4⋊C4—61no—
681C4⋊C4—61no—
682C4⋊C4—61no—
683C4⋊C4—61no—
684C4⋊C4—122no—
685C22⋊C4—22no—
686C22⋊C4—22no—
687C22⋊C4—42no—
688C22⋊C4—42no—
689C22⋊C4—42no—
690C22⋊C4—42no—
691C22⋊C4—42no—
692C22⋊C4—81no—
693C22⋊C4—81no—
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—22no—
705C22×C3—22no—
706C22×C3—22no—
707C22×C3—41no—
708C22×C3—41no—
709C22×C3—41no—
710C22×C3—41no—
711C22×C3—41no—
712C22×C3—41no—
713C22×C3—41no—
714C22×C3—41no—
715C22×C3—42no—
716C22×C3—42no—
717C22×C3—42no—
718C22×C3—42no—
719C22×C3—42no—
720C22×C3—42no—
721C22×C3—816no—
722C22×C3—81no—
723C22×C3—81no—
724C22×C3—81no—
725C22×C3—81no—
726C22×C3—81no—
727C22×C3—81no—
728C22×C3—81no—
729C22×C3—81no—
730C22×C3C2×#12111yescharacteristic
731C22×C3D4211yescharacteristic
732C22×C3D4211yescharacteristic
733C22×C3C2×AGL(1,ℤ/8)11yescharacteristic
734C22×C3#57511yescharacteristic
735C22×C3#57611yescharacteristic
736C22×C3#57711yescharacteristic
737C2×D3—42no—
738C2×D3—42no—
739C2×D3—42no—
740C2×D3—81no—
741C2×D3—81no—
742C2×D3—81no—
743C2×D3—81no—
744C3×C4—22no—
745C3×C4—41no—
746C3×C4—41no—
747C3×C4—41no—
748C3×C4—81no—
749C3×C4—81no—
750C3×C4C2×#12011yescharacteristic
751C3×C4#53511yescharacteristic
752C3×C4#54611yescharacteristic
753C3×C4#54611yescharacteristic
754Dic3—42no—
755Dic3—81no—
756Dic3—81no—
757C23—21no—
758C23—21no—
759C23—21no—
760C23—21no—
761C23—21no—
762C23—21no—
763C23—21no—
764C23—21no—
765C23—21no—
766C23—21no—
767C23—21no—
768C23—21no—
769C23—22no—
770C23—22no—
771C23—48no—
772C23—41no—
773C23—41no—
774C23—41no—
775C23—41no—
776C23—41no—
777C23—41no—
778C23—41no—
779C23—41no—
780C23—41no—
781C23—41no—
782C23—41no—
783C23—41no—
784C23—62no—
785C23—84no—
786C23—84no—
787C23—84no—
788C23—84no—
789C23—84no—
790C23—84no—
791C23—121no—
792C23—121no—
793C23—121no—
794C23—121no—
795C23—121no—
796C23—121no—
797C23#93212yescomplemented
798C23#93912yes—
799C23C22×#6711yescharacteristic
800Q8—62no—
801Q8—62no—
802Q8—121no—
803Q8—121no—
804D4—22no—
805D4—22no—
806D4—22no—
807D4—22no—
808D4—48no—
809D4—44no—
810D4—41no—
811D4—41no—
812D4—41no—
813D4—41no—
814D4—62no—
815D4—62no—
816D4—84no—
817D4—84no—
818D4—128no—
819D4—121no—
820D4—121no—
821D4—244no—
822C2×C4—21no—
823C2×C4—21no—
824C2×C4—22no—
825C2×C4—22no—
826C2×C4—22no—
827C2×C4—22no—
828C2×C4—21no—
829C2×C4—21no—
830C2×C4—21no—
831C2×C4—21no—
832C2×C4—21no—
833C2×C4—21no—
834C2×C4—21no—
835C2×C4—21no—
836C2×C4—21no—
837C2×C4—41no—
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—62no—
848C2×C4—128no—
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#93912yes—
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—42no—
870C2×C3—82no—
871C2×C3—82no—
872C2×C3#240811yescharacteristic
873C2×C3#305511yescharacteristic
874C2×C3#306211yescharacteristic
875C2×C3#326411yescharacteristic
876C2×C3#326511yescharacteristic
877C2×C3#326711yescharacteristic
878C2×C3#326811yescharacteristic
879D3—82no—
880C22—22no—
881C22—22no—
882C22—22no—
883C22—22no—
884C22—22no—
885C22—22no—
886C22—41no—
887C22—41no—
888C22—41no—
889C22—41no—
890C22—41no—
891C22—41no—
892C22—41no—
893C22—41no—
894C22—42no—
895C22—42no—
896C22—42no—
897C22—42no—
898C22—42no—
899C22—42no—
900C22—816no—
901C22—81no—
902C22—81no—
903C22—81no—
904C22—81no—
905C22—81no—
906C22—81no—
907C22—81no—
908C22—81no—
909C22—122no—
910C22—122no—
911C22—122no—
912C22—241no—
913C22—241no—
914C22—241no—
915C22—241no—
916C22C2×#93211yescharacteristic
917C22D4×#6711yescharacteristic
918C22D4×#6711yescharacteristic
919C22C2×#93911yescharacteristic
920C22#582211yescharacteristic
921C22#583511yescharacteristic
922C22#583611yescharacteristic
923C4—22no—
924C4—41no—
925C4—41no—
926C4—41no—
927C4—81no—
928C4—81no—
929C4—122no—
930C4—241no—
931C4—241no—
932C4D3×#12011yescharacteristic
933C4#559111yescharacteristic
934C4#559111yescharacteristic
935C4#559211yescharacteristic
936C3#2427511yescharacteristic, complemented, Sylow
937C2—42no—
938C2—42no—
939C2—82no—
940C2—82no—
941C2—242no—
942C2#8258211yescharacteristic
943C2#8262111yescharacteristic
944C2#8337911yescharacteristic
945C2#8348811yescharacteristic
946C2#8349111yescharacteristic
947C2#8350311yescharacteristic
948C2#8350711yescharacteristic
subgroupG/H
centerC23C22×#67
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC3×#2408C2
socleC23×C3C22×D4
hypercenter#2408D3
hypocenterC3#24275
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ #2408

Complements

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

NH ≅ G/Ntype
1. C22×#932C2semidirect
2. C3×#2408C2semidirect
3. C2×#5038C2semidirect
4. C2×#5041C2semidirect
5. #82402C2semidirect
6. C2×#5011C2semidirect
7. #72128C2semidirect
8. #71685C2semidirect
9. #71684C2semidirect
10. #69651C2semidirect
11. #69650C2semidirect
12. #69649C2semidirect
13. #69648C2semidirect
14. #69522C2semidirect
15. #69513C2semidirect
30. C2×#930C22semidirect
31. C2×#924C22semidirect
33. C23×C3⋊C8C22semidirect
47. C2×#830C22semidirect
52. C2×#810C22semidirect
53. C2×#810C22semidirect
54. C2×#809C22semidirect
55. C2×#809C22semidirect
56. C2×#808C22semidirect
57. C2×#807C22semidirect
60. #4939C22semidirect
61. #4929C22semidirect
62. C2×C4⋊(C3⋊C8)C22semidirect
63. C2×#803C22semidirect
64. #4529C22semidirect
65. #4529C22semidirect
70. #2408D3semidirect
134. C2×#214D4semidirect
141. C2×#213D4semidirect
154. C2×#208D4semidirect
493. C23×C3AGL(1,ℤ/8)semidirect
569. C3⋊C8#120semidirect
797. C23#932semidirect
936. C3#24275semidirect

Maximal subgroups

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

subgroupindex
C22×#9322
C3×#24082
C2×#50382
C2×#50412
#824022
C2×#50112
#721282
#716852
#716842
#696512
#696502
#696492
#696482
#695222
#695132
#242753