Finite Group Databasebeta

← #10830977

Subgroups — #10830977

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×#908C211yesmaximal, characteristic, complemented
2C2×C3×#435C211yesmaximal, characteristic, complemented
3C2×#5115C211yesmaximal, characteristic, complemented
4C2×#5114C211yesmaximal, characteristic, complemented
5#82403C211yesmaximal, characteristic, complemented
6#82402C211yesmaximal, characteristic, complemented
7#71988C211yesmaximal, characteristic, complemented
8#70482C211yesmaximal, characteristic, complemented
9#70481C211yesmaximal, characteristic, complemented
10#69962C211yesmaximal, characteristic, complemented
11#69961C211yesmaximal, characteristic, complemented
12#69960C211yesmaximal, characteristic, complemented
13#69959C211yesmaximal, characteristic, complemented
14#69826C211yesmaximal, characteristic, complemented
15#69825C211yesmaximal, characteristic, complemented
16#24275—31nomaximal, Sylow
17C22×#235C2211yescharacteristic
18C23×D12C2211yescharacteristic
19C22×C3×M16C2211yescharacteristic
20C23×C3×C8C2211yescharacteristic, complemented
21C2×C3×C4×D4C2211yescharacteristic
22C2×#937—21no—
23C2×#930C2211yescharacteristic
24C2×#930C2211yescharacteristic
25C2×#930C2211yescharacteristic, complemented
26C2×#924C2211yescharacteristic, complemented
27C2×#908—24no—
28C2×#908—24no—
29C2×#908—24no—
30C22×D24C2211yescharacteristic
31C22×D24C2211yescharacteristic
32C22×#204C2211yescharacteristic
33C22×#204C2211yescharacteristic
34C3×#435—24no—
35C2×C3×C4⋊C8C2211yescharacteristic, complemented
36C2×C3×C22⋊C8C2211yescharacteristic
37C2×C3×C22⋊C8C2211yescharacteristic, complemented
38C2×C3×#97C2211yescharacteristic, complemented
39#5223—21no—
40#5212C2211yescharacteristic
41#5212C2211yescharacteristic
42#5115—24no—
43#5114—24no—
44C2×#821C2211yescharacteristic
45C2×#821C2211yescharacteristic
46C2×#821C2211yescharacteristic
47C2×#821C2211yescharacteristic
48C2×#821C2211yescharacteristic, complemented
49C2×#821C2211yescharacteristic, complemented
50C2×#818C2211yescharacteristic, complemented
51C2×#817C2211yescharacteristic, complemented
52C2×#816C2211yescharacteristic, complemented
53C2×#816C2211yescharacteristic, complemented
54#4991—21no—
55#4989—21no—
56#4960—21no—
57#4959—21no—
58#4956—21no—
59#4955—21no—
60#4939C2211yescharacteristic
61#4939C2211yescharacteristic
62#4939C2211yescharacteristic, complemented
63#4929C2211yescharacteristic, complemented
64#4551C2211yescharacteristic, complemented
65#4551C2211yescharacteristic, complemented
66C22×AGL(1,ℤ/8)—31no—
67C2×#466—31no—
68C2×#465—31no—
69C2×#435D311yescharacteristic, complemented
70#2408—31no—
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—
81C24×D3—21no—
82C22×C3×D4D411yescharacteristic
83C23×C3×C4C2311yescharacteristic
84C23×C3×C4C2311yescharacteristic
85C22×#67—21no—
86C22×#67—21no—
87C22×#67—21no—
88C22×#67—21no—
89C2×#235—22no—
90C2×#235—22no—
91C2×#235—22no—
92C2×#235—22no—
93C2×#235—41no—
94C2×#235—41no—
95C22×D12—22no—
96C22×D12—22no—
97C22×D12—22no—
98C22×D12—22no—
99C22×D12—21no—
100C22×D12—41no—
101C22×D12—41no—
102C22×D12C2311yescharacteristic
103C22×D12C2311yescharacteristic
104C22×D12C2311yescharacteristic
105C22×C4×D3—21no—
106C22×Dic6C2311yescharacteristic
107C2×C3×M16—22no—
108C2×C3×M16—22no—
109C2×C3×M16D414yescomplemented
110C22×C3×C8—22no—
111C22×C3×C8—22no—
112C22×C3×C8—22no—
113C22×C3×C8C2311yescharacteristic
114C22×C3×C8C2311yescharacteristic
115C22×C3×C8C2311yescharacteristic
116C22×C3×C8C2311yescharacteristic
117C3×C4×D4—22no—
118C3×C4×D4—22no—
119C2×C3×C4⋊C4D411yescharacteristic
120C2×C3×C22⋊C4D411yescharacteristic
121C2×C3×C22⋊C4D411yescharacteristic
122C2×C3×C42C2311yescharacteristic
123C2×#217—21no—
124C2×#217—21no—
125C2×#217—21no—
126#937—44no—
127#930—22no—
128#930—22no—
129#930—22no—
130#930—41no—
131#930—41no—
132#930—41no—
133C2×(C2×D3)⋊C4—21no—
134C2×(C2×D3)⋊C4—21no—
135C2×(C2×D3)⋊C4—21no—
136C2×(C2×D3)⋊C4—21no—
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×C4⋊Dic3C2311yescharacteristic
143C2×C4⋊Dic3C2311yescharacteristic
144C2×C4⋊Dic3C2311yescharacteristic
145C2×C4⋊Dic3C2311yescharacteristic
146#924—22no—
147#924—41no—
148C2×Dic3⋊C4—21no—
149#908—232no—
150C2×D24—22no—
151C2×D24—22no—
152C2×D24—22no—
153C2×D24—22no—
154C2×D24—22no—
155C2×D24D414yescomplemented
156C2×#204—22no—
157C2×#204—22no—
158C2×#204—22no—
159C2×#204—22no—
160C2×#204—22no—
161C2×#204D414yescomplemented
162C3×C4⋊C8—22no—
163C3×C22⋊C8—22no—
164C3×C22⋊C8—22no—
165C3×#97—22no—
166C3⋊#95—21no—
167C3⋊#95—21no—
168C3⋊#95—21no—
169C3⋊#95—21no—
170#821—22no—
171#821—22no—
172#821—22no—
173#821—41no—
174#821—41no—
175#821—41no—
176#818—22no—
177#817—22no—
178#816—22no—
179#816—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×SD16—31no—
187C22×D8—31no—
188C22×D8—31no—
189C22×M16C2×D311yescharacteristic
190C23×C8C2×D311yescharacteristic, complemented
191C2×C22⋊Q8—31no—
192C2×#121—31no—
193C2×#121—31no—
194C2×#121—31no—
195C2×#120—61no—
196C2×C4×D4C2×D311yescharacteristic
197#466—64no—
198#465—64no—
199#435—24no—
200C2×#107—31no—
201C2×#106—31no—
202C2×C4⋊C8C2×D311yescharacteristic, complemented
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⋊C8C2×D311yescharacteristic
212C2×C22⋊C8C2×D311yescharacteristic, complemented
213C2×#97C2×D311yescharacteristic, complemented
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×C3C2×D411yescharacteristic
230C24×C3C2×D411yescharacteristic
231C23×D3—21no—
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—
241C2×C3×D4—22no—
242C2×C3×D4—22no—
243C2×C3×D4—41no—
244C22×C3×C4—21no—
245C22×C3×C4—21no—
246C22×C3×C4—21no—
247C22×C3×C4—21no—
248C22×C3×C4—21no—
249C22×C3×C4—21no—
250C22×C3×C4—21no—
251C22×C3×C4—21no—
252C22×C3×C4—21no—
253C22×C3×C4—21no—
254C22×C3×C4C2×D411yescharacteristic
255C22×C3×C4C2×D411yescharacteristic
256C22×C3×C4C2×D411yescharacteristic
257C22×C3×C4C2×D411yescharacteristic
258C22×C3×C4C2×D412yes—
259C22×C3×C4#4112yes—
260C22×C3×C4C2411yescharacteristic
261C2×#67—42no—
262C2×#67—42no—
263C2×#67—42no—
264C2×#67—42no—
265C2×#67—42no—
266C2×#67—42no—
267C2×#67—42no—
268C2×#67—42no—
269C2×#67—42no—
270C2×#67—81no—
271C2×#67—81no—
272C2×#67—81no—
273C22×Dic3—21no—
274C22×Dic3—21no—
275C22×Dic3—21no—
276C22×Dic3—21no—
277C22×Dic3—21no—
278#235—28no—
279#235—44no—
280#235—44no—
281#235—44no—
282C2×D12—28no—
283C2×D12—21no—
284C2×D12—21no—
285C2×D12—21no—
286C2×D12—21no—
287C2×D12—21no—
288C2×D12—21no—
289C2×D12—21no—
290C2×D12—21no—
291C2×D12—21no—
292C2×D12—21no—
293C2×D12—21no—
294C2×D12—21no—
295C2×D12—21no—
296C2×D12—21no—
297C2×D12—21no—
298C2×D12—44no—
299C2×D12—44no—
300C2×D12—42no—
301C2×D12—42no—
302C2×D12—44no—
303C2×D12—42no—
304C2×D12C2×D412yes—
305C2×D12C2×D412yes—
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×M16—28no—
317C2×C3×C8—21no—
318C2×C3×C8—21no—
319C2×C3×C8—21no—
320C2×C3×C8—21no—
321C2×C3×C8—21no—
322C2×C3×C8—21no—
323C2×C3×C8—21no—
324C2×C3×C8—21no—
325C2×C3×C8—44no—
326C2×C3×C8C2×D412yes—
327C2×C3×C8C2×D412yes—
328C2×C3×C8C2×D412yes—
329C2×C3×C8C2×D412yes—
330C3×C4⋊C4—22no—
331C3×C22⋊C4—22no—
332C3×C22⋊C4—22no—
333C3×C42—21no—
334C3×C42—21no—
335#217—42no—
336#217—42no—
337#217—81no—
338(C2×D3)⋊C4—42no—
339(C2×D3)⋊C4—42no—
340(C2×D3)⋊C4—42no—
341(C2×D3)⋊C4—42no—
342(C2×D3)⋊C4—42no—
343(C2×D3)⋊C4—42no—
344(C2×D3)⋊C4—81no—
345(C2×D3)⋊C4—81no—
346(C2×D3)⋊C4—81no—
347C4⋊Dic3—21no—
348C4⋊Dic3—21no—
349C4⋊Dic3—21no—
350C4⋊Dic3—21no—
351C4⋊Dic3—21no—
352C4⋊Dic3—21no—
353C4⋊Dic3—21no—
354C4⋊Dic3—21no—
355Dic3⋊C4—42no—
356D24—28no—
357D24—28no—
358#204—28no—
359#204—28no—
360C25—61no—
361C2×#41—62no—
362C2×#41—62no—
363C2×#41—62no—
364C2×#41—62no—
365C2×#41—121no—
366C2×#41—121no—
367C22×Q8—31no—
368C22×D4—31no—
369C22×D4—31no—
370C22×D4—31no—
371C22×D4—62no—
372C22×D4—62no—
373C22×D4—61no—
374C22×D4—61no—
375C22×D4—61no—
376C22×D4—61no—
377C22×D4—61no—
378C22×D4—62no—
379C22×D4—62no—
380C22×D4—121no—
381C22×D4—121no—
382C22×D4D1211yescharacteristic
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—22no—
400C2×M16—22no—
401C2×M16#6714yescomplemented
402C22×C8—22no—
403C22×C8—22no—
404C22×C8—22no—
405C22×C8C22×D311yescharacteristic
406C22×C8C22×D311yescharacteristic
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—22no—
419C4×D4—22no—
420C2×C4⋊C4—31no—
421C2×C4⋊C4—31no—
422C2×C4⋊C4—31no—
423C2×C4⋊C4—31no—
424C2×C4⋊C4—61no—
425C2×C4⋊C4D1211yescharacteristic
426C2×C22⋊C4—61no—
427C2×C22⋊C4—61no—
428C2×C22⋊C4—61no—
429C2×C22⋊C4—61no—
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⋊C4D1211yescharacteristic
439C2×C22⋊C4D1211yescharacteristic
440C2×C42C22×D311yescharacteristic
441#107—62no—
442#106—62no—
443C4⋊C8—22no—
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—22no—
453C22⋊C8—22no—
454#97—22no—
455#95—61no—
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#12112yes—
472C23×C3AGL(1,ℤ/8)12yescomplemented
473C23×C3C22×D411yescharacteristic
474C22×D3—22no—
475C22×D3—22no—
476C22×D3—22no—
477C22×D3—48no—
478C22×D3—41no—
479C22×D3—41no—
480C22×D3—41no—
481C22×D3—41no—
482C22×D3—41no—
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—41no—
496C22×D3—84no—
497C22×D3—84no—
498C22×D3—84no—
499C22×D3—84no—
500C22×D3—84no—
501C22×D3—84no—
502C3×D4—44no—
503C2×C3×C4—21no—
504C2×C3×C4—21no—
505C2×C3×C4—22no—
506C2×C3×C4—22no—
507C2×C3×C4—22no—
508C2×C3×C4—22no—
509C2×C3×C4—21no—
510C2×C3×C4—21no—
511C2×C3×C4—21no—
512C2×C3×C4—21no—
513C2×C3×C4—21no—
514C2×C3×C4—21no—
515C2×C3×C4—21no—
516C2×C3×C4—21no—
517C2×C3×C4—21no—
518C2×C3×C4—41no—
519C2×C3×C4—41no—
520C2×C3×C4—41no—
521C2×C3×C4—41no—
522C2×C3×C4#12112yes—
523C2×C3×C4C22×D411yescharacteristic
524C2×C3×C4C22×D411yescharacteristic
525C2×C3×C4C22×D411yescharacteristic
526C2×C3×C4C2×#4111yescharacteristic
527C2×C3×C4H(5,𝔽2)11yescharacteristic
528C2×C3×C4H(5,𝔽2)11yescharacteristic
529#67—48no—
530#67—84no—
531#67—84no—
532#67—84no—
533C2×Dic3—22no—
534C2×Dic3—41no—
535C2×Dic3—41no—
536C2×Dic3—41no—
537C2×Dic3—41no—
538C2×Dic3—41no—
539C2×Dic3—41no—
540C2×Dic3—41no—
541C2×Dic3—41no—
542C2×Dic3—41no—
543C2×Dic3—41no—
544C2×Dic3—41no—
545C2×Dic3—41no—
546C2×Dic3—41no—
547C2×Dic3—41no—
548D12—22no—
549D12—22no—
550D12—22no—
551D12—22no—
552D12—22no—
553D12—22no—
554D12—48no—
555D12—41no—
556D12—41no—
557D12—41no—
558D12—41no—
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—61no—
571C24—61no—
572C24—61no—
573C24—122no—
574C24—122no—
575C24—122no—
576C24—122no—
577C24—122no—
578C24—241no—
579C24—241no—
580C24C2×D1211yescharacteristic
581C24C2×D1211yescharacteristic
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—22no—
593C2×D4—22no—
594C2×D4—32no—
595C2×D4—32no—
596C2×D4—32no—
597C2×D4—41no—
598C2×D4—68no—
599C2×D4—61no—
600C2×D4—61no—
601C2×D4—61no—
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—61no—
613C2×D4—61no—
614C2×D4—124no—
615C2×D4—124no—
616C2×D4—122no—
617C2×D4—122no—
618C2×D4—124no—
619C2×D4—122no—
620C2×D4—122no—
621C2×D4—122no—
622C2×D4—122no—
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×D4—241no—
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—61no—
643C22×C4—61no—
644C22×C4—61no—
645C22×C4—61no—
646C22×C4—61no—
647C22×C4—122no—
648C22×C4—122no—
649C22×C4—122no—
650C22×C4C2×D1211yescharacteristic
651C22×C4C2×D1211yescharacteristic
652C22×C4C2×D1211yescharacteristic
653C22×C4C2×D1211yescharacteristic
654C22×C4#23512yes—
655C22×C4C2×#6712yes—
656C22×C4C23×D311yescharacteristic
657SD16—68no—
658SD16—68no—
659D8—68no—
660D8—68no—
661M16—28no—
662C2×C8—21no—
663C2×C8—21no—
664C2×C8—21no—
665C2×C8—21no—
666C2×C8—21no—
667C2×C8—21no—
668C2×C8—21no—
669C2×C8—21no—
670C2×C8—44no—
671C2×C8D3×D412yes—
672C2×C8D3×D412yes—
673C2×C8C2×#6712yes—
674C2×C8C2×#6712yes—
675C4⋊C4—22no—
676C4⋊C4—61no—
677C4⋊C4—61no—
678C4⋊C4—61no—
679C4⋊C4—61no—
680C4⋊C4—61no—
681C4⋊C4—61no—
682C4⋊C4—61no—
683C4⋊C4—61no—
684C4⋊C4—122no—
685C22⋊C4—22no—
686C22⋊C4—22no—
687C22⋊C4—122no—
688C22⋊C4—122no—
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—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×C3C2×#12111yescharacteristic
716C22×C3D4211yescharacteristic
717C22×C3D4211yescharacteristic
718C22×C3C2×AGL(1,ℤ/8)11yescharacteristic
719C22×C3#57511yescharacteristic
720C22×C3#57611yescharacteristic
721C22×C3#57711yescharacteristic
722C2×D3—42no—
723C2×D3—42no—
724C2×D3—42no—
725C2×D3—42no—
726C2×D3—42no—
727C2×D3—42no—
728C2×D3—42no—
729C2×D3—42no—
730C2×D3—42no—
731C2×D3—816no—
732C2×D3—81no—
733C2×D3—81no—
734C2×D3—81no—
735C2×D3—81no—
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—41no—
746C3×C4—41no—
747C3×C4—41no—
748C3×C4C2×#12011yescharacteristic
749C3×C4#53511yescharacteristic
750C3×C4#54611yescharacteristic
751C3×C4#54611yescharacteristic
752Dic3—42no—
753Dic3—81no—
754Dic3—81no—
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—62no—
770C23—62no—
771C23—62no—
772C23—128no—
773C23—121no—
774C23—121no—
775C23—121no—
776C23—121no—
777C23—121no—
778C23—121no—
779C23—121no—
780C23—121no—
781C23—121no—
782C23—121no—
783C23—121no—
784C23—121no—
785C23—121no—
786C23—121no—
787C23—121no—
788C23—121no—
789C23—121no—
790C23—121no—
791C23—244no—
792C23—244no—
793C23—244no—
794C23—244no—
795C23—244no—
796C23—244no—
797C23#90812yescomplemented
798C23#93012yes—
799C23C22×D1211yescharacteristic
800Q8—62no—
801Q8—62no—
802Q8—121no—
803Q8—121no—
804D4—44no—
805D4—62no—
806D4—62no—
807D4—62no—
808D4—62no—
809D4—62no—
810D4—62no—
811D4—128no—
812D4—128no—
813D4—121no—
814D4—121no—
815D4—121no—
816D4—121no—
817D4—121no—
818D4—121no—
819D4—244no—
820D4—244no—
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—62no—
842C2×C4—128no—
843C2×C4—121no—
844C2×C4—121no—
845C2×C4—121no—
846C2×C4—121no—
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#93012yes—
858C2×C4C2×#23511yescharacteristic
859C2×C4C2×D3×D411yescharacteristic
860C2×C4C2×D3×D411yescharacteristic
861C2×C4#100911yescharacteristic
862C2×C4#100911yescharacteristic
863C2×C4C22×#6711yescharacteristic
864C8—22no—
865C8—41no—
866C8—41no—
867C8#93714yescomplemented
868C2×C3—42no—
869C2×C3—42no—
870C2×C3#240811yescharacteristic
871C2×C3#305511yescharacteristic
872C2×C3#306211yescharacteristic
873C2×C3#326411yescharacteristic
874C2×C3#326511yescharacteristic
875C2×C3#326711yescharacteristic
876C2×C3#326811yescharacteristic
877D3—82no—
878D3—82no—
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—122no—
895C22—122no—
896C22—122no—
897C22—122no—
898C22—122no—
899C22—122no—
900C22—122no—
901C22—122no—
902C22—122no—
903C22—2416no—
904C22—241no—
905C22—241no—
906C22—241no—
907C22—241no—
908C22—241no—
909C22—241no—
910C22—241no—
911C22—241no—
912C22—241no—
913C22—241no—
914C22—241no—
915C22—241no—
916C22D4×D1211yescharacteristic
917C22D4×D1211yescharacteristic
918C22C2×#90811yescharacteristic
919C22#574811yescharacteristic
920C22#575111yescharacteristic
921C22#575211yescharacteristic
922C22C2×#93011yescharacteristic
923C4—22no—
924C4—41no—
925C4—41no—
926C4—41no—
927C4—122no—
928C4—241no—
929C4—241no—
930C4—241no—
931C4—241no—
932C4#555011yescharacteristic
933C4#555011yescharacteristic
934C4C2×#93711yescharacteristic
935C4#583011yescharacteristic
936C3#2427511yescharacteristic, complemented, Sylow
937C2—42no—
938C2—42no—
939C2—242no—
940C2—242no—
941C2—242no—
942C2#7949311yescharacteristic
943C2#7949411yescharacteristic
944C2#7949611yescharacteristic
945C2#7949711yescharacteristic
946C2#8240311yescharacteristic
947C2#8377211yescharacteristic
948C2#8380211yescharacteristic
subgroupG/H
centerC23C22×D12
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC2×C3×#435C2
socleC23×C3C22×D4
hypercenterC2×#435D3
hypocenterC3#24275
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#435

Complements

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

NH ≅ G/Ntype
1. C22×#908C2semidirect
2. C2×C3×#435C2semidirect
3. C2×#5115C2semidirect
4. C2×#5114C2semidirect
5. #82403C2semidirect
6. #82402C2semidirect
7. #71988C2semidirect
8. #70482C2semidirect
9. #70481C2semidirect
10. #69962C2semidirect
11. #69961C2semidirect
12. #69960C2semidirect
13. #69959C2semidirect
14. #69826C2semidirect
15. #69825C2semidirect
20. C23×C3×C8C22semidirect
25. C2×#930C22semidirect
26. C2×#924C22semidirect
35. C2×C3×C4⋊C8C22semidirect
37. C2×C3×C22⋊C8C22semidirect
38. C2×C3×#97C22semidirect
48. C2×#821C22semidirect
49. C2×#821C22semidirect
50. C2×#818C22semidirect
51. C2×#817C22semidirect
52. C2×#816C22semidirect
53. C2×#816C22semidirect
62. #4939C22semidirect
63. #4929C22semidirect
64. #4551C22semidirect
65. #4551C22semidirect
69. C2×#435D3semidirect
109. C2×C3×M16D4semidirect
155. C2×D24D4semidirect
161. C2×#204D4semidirect
190. C23×C8C2×D3semidirect
202. C2×C4⋊C8C2×D3semidirect
212. C2×C22⋊C8C2×D3semidirect
213. C2×#97C2×D3semidirect
401. C2×M16#67semidirect
472. C23×C3AGL(1,ℤ/8)semidirect
569. C3×C8#120semidirect
797. C23#908semidirect
867. C8#937semidirect
936. C3#24275semidirect

Maximal subgroups

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

subgroupindex
C22×#9082
C2×C3×#4352
C2×#51152
C2×#51142
#824032
#824022
#719882
#704822
#704812
#699622
#699612
#699602
#699592
#698262
#698252
#242753