Finite Group Databasebeta

← #10830663

Subgroups — #10830663

Order 768.

1564 conjugacy classes of subgroups.

The subgroup lattice has 920 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#5554C211yesmaximal, characteristic
2C2×C4×#214C211yesmaximal, characteristic, complemented
3C2×#4845C211yesmaximal, characteristic, complemented
4C2×#4783C211yesmaximal, characteristic, complemented
5C2×#4776C211yesmaximal, characteristic, complemented
6#74240C211yesmaximal, characteristic, complemented
7C3×#1804C211yesmaximal, characteristic, complemented
8#70470C211yesmaximal, characteristic, complemented
9#70199C211yesmaximal, characteristic, complemented
10#70198C211yesmaximal, characteristic, complemented
11#69551C211yesmaximal, characteristic, complemented
12#68888C211yesmaximal, characteristic, complemented
13#68887C211yesmaximal, characteristic, complemented
14#68824C211yesmaximal, characteristic, complemented
15#68823C211yesmaximal, characteristic, complemented
16#24247—31nomaximal, Sylow
17C22×#237C2211yescharacteristic
18C22×D3×D4C2211yescharacteristic
19C2×C3×C4×D4C2211yescharacteristic
20C22×#214C2211yescharacteristic
21C2×#930—21no—
22C22×(C2×D3)⋊C4—21no—
23C22×Dic12C2211yescharacteristic, complemented
24C22×#204C2211yescharacteristic
25#5554—24no—
26#5554—24no—
27C2×#897C2211yescharacteristic
28C2×#897C2211yescharacteristic
29C2×#897C2211yescharacteristic, complemented
30C2×#895C2211yescharacteristic
31C2×#886—21no—
32C2×#882—21no—
33C2×#875C2211yescharacteristic
34C2×C4×D12C2211yescharacteristic
35C2×C4×Dic6C2211yescharacteristic, complemented
36C2×C3×C4⋊C8C2211yescharacteristic, complemented
37C2×C3×#102C2211yescharacteristic
38C2×C3×#102C2211yescharacteristic
39C3×#382C2211yescharacteristic, complemented
40C2×#832C2211yescharacteristic
41C2×#821C2211yescharacteristic
42C2×(C2×D3)⋊C8C2211yescharacteristic
43C2×(C2×D3)⋊C8C2211yescharacteristic
44C2×(C2×D3)⋊C8C2211yescharacteristic, complemented
45C2×(C2×D3)⋊C8C2211yescharacteristic, complemented
46C2×#816C2211yescharacteristic, complemented
47C4×#214—24no—
48#4987C2211yescharacteristic
49#4987C2211yescharacteristic, complemented
50C2×#810C2211yescharacteristic, complemented
51C2×#810C2211yescharacteristic, complemented
52C2×#810C2211yescharacteristic, complemented
53C2×#809C2211yescharacteristic
54C2×#809C2211yescharacteristic
55C2×#808C2211yescharacteristic, complemented
56C2×C4×C3⋊C8C2211yescharacteristic, complemented
57#4845—24no—
58#4783—24no—
59#4776—24no—
60#4672—21no—
61#4670—21no—
62#4670—21no—
63#4661—21no—
64C3×#340C2211yescharacteristic, complemented
65C3×#340C2211yescharacteristic, complemented
66C2×#546—31no—
67C2×#464—31no—
68C2×#452—31no—
69C2×#450—31no—
70C2×C4×SD16—31no—
71#2536—31no—
72#2035—31no—
73#2034—31no—
74#2001—31no—
75#2000—31no—
76#1958—31no—
77#1954—31no—
78#1804D311yescharacteristic, complemented
79#1788—31no—
80#1786—31no—
81C24×D3—21no—
82C22×C3×D4C2311yescharacteristic
83C23×C3×C4—21no—
84C22×#67—21no—
85C22×#67—21no—
86C23×Dic3—21no—
87C2×#237—22no—
88C2×#237—22no—
89C2×#237—22no—
90C2×#237—22no—
91C2×#237—41no—
92C2×#237—41no—
93C2×D3×D4—22no—
94C2×D3×D4—22no—
95C2×D3×D4—22no—
96C2×D3×D4—22no—
97C2×D3×D4—41no—
98C2×D3×D4—41no—
99C22×D12—21no—
100C22×D12D411yescharacteristic
101C22×D12C2311yescharacteristic
102C22×C4×D3C2311yescharacteristic
103C22×C4×D3C2311yescharacteristic
104C22×Dic6C2311yescharacteristic
105C22×Dic6C2311yescharacteristic
106C22×C3×C8C2311yescharacteristic
107C22×C3×C8C2311yescharacteristic
108C3×C4×D4—22no—
109C3×C4×D4D414yes—
110C2×C3×C4⋊C4C2311yescharacteristic
111C2×C3×C4⋊C4C2311yescharacteristic
112C2×C3×C4⋊C4C2311yescharacteristic
113C2×C3×C22⋊C4—21no—
114C2×C3×C42C2311yescharacteristic
115C2×#214—22no—
116C2×#214—22no—
117C2×#214D414yescomplemented
118#930—28no—
119C2×(C2×D3)⋊C4—28no—
120C2×(C2×D3)⋊C4—21no—
121C2×(C2×D3)⋊C4—21no—
122C2×(C2×D3)⋊C4—21no—
123C2×(C2×D3)⋊C4—21no—
124C2×(C2×D3)⋊C4—21no—
125C2×(C2×D3)⋊C4—21no—
126C2×(C2×D3)⋊C4—21no—
127C2×(C2×D3)⋊C4—21no—
128C2×(C2×D3)⋊C4D411yescharacteristic
129C2×(C2×D3)⋊C4D411yescharacteristic
130C2×C4⋊Dic3—21no—
131C2×C4⋊Dic3—21no—
132C2×C4⋊Dic3—21no—
133C2×C4⋊Dic3D411yescharacteristic
134C2×C4⋊Dic3C2311yescharacteristic
135C2×Dic3⋊C4—21no—
136C2×C4×Dic3—21no—
137C22×C3⋊C8C2311yescharacteristic
138C22×C3⋊C8C2311yescharacteristic
139C2×Dic12—22no—
140C2×Dic12—22no—
141C2×Dic12—41no—
142C2×#204—22no—
143C2×#204—22no—
144C2×#204—41no—
145#897—22no—
146#897—22no—
147#897—22no—
148#897—22no—
149#897—41no—
150#897—41no—
151#895—22no—
152#895—22no—
153#886—28no—
154#882—28no—
155#875—22no—
156#875D414yes—
157C4×D12—22no—
158C4×D12—22no—
159C4×Dic6—22no—
160C4×Dic6—22no—
161C3×C4⋊C8—22no—
162C3×#102—22no—
163C3×#102—22no—
164C3×#95—21no—
165C3×#95—21no—
166#832—22no—
167C3⋊#95—21no—
168C3⋊#95—21no—
169#821—22no—
170(C2×D3)⋊C8—22no—
171(C2×D3)⋊C8—22no—
172(C2×D3)⋊C8—41no—
173(C2×D3)⋊C8—41no—
174#816—22no—
175#810—22no—
176#810—22no—
177#810—41no—
178#809—22no—
179#809—41no—
180#808—22no—
181C4×C3⋊C8—22no—
182C22×#41—31no—
183C23×D4—31no—
184C22×Q16—31no—
185C22×SD16—31no—
186C22×SD16—31no—
187#546—64no—
188#546—64no—
189C2×#124—31no—
190C2×#123—61no—
191C2×C22⋊Q8—31no—
192C2×C22⋊Q8—31no—
193C2×C22⋊Q8—31no—
194C2×#121—31no—
195C2×#121—61no—
196C2×#120—61no—
197C2×C4×Q8—31no—
198C2×C4×D4—31no—
199C2×C4×D4C2×D311yescharacteristic
200C22×C22⋊C4—61no—
201#464—64no—
202#452—64no—
203#450—64no—
204C4×SD16—64no—
205C2×#106—31no—
206C2×C4⋊C8C2×D311yescharacteristic, complemented
207C2×#103—31no—
208C2×#103—31no—
209C2×#103—31no—
210C2×#103—31no—
211C2×#102—31no—
212C2×#102—31no—
213C2×#102—31no—
214C2×#102—31no—
215C2×#102C2×D311yescharacteristic
216C2×#102C2×D311yescharacteristic
217C2×C22⋊C8—31no—
218C2×C22⋊C8—31no—
219C2×C22⋊C8—31no—
220C2×C22⋊C8—31no—
221C2×C4×C8—31no—
222#398—61no—
223#394—61no—
224#388—61no—
225#388—61no—
226#382C2×D311yescharacteristic, complemented
227#380—31no—
228#380—31no—
229#340C2×D311yescharacteristic, complemented
230#340C2×D311yescharacteristic, complemented
231C24×C3—21no—
232C23×D3—21no—
233C23×D3—24no—
234C23×D3—42no—
235C23×D3—42no—
236C23×D3—42no—
237C23×D3—42no—
238C23×D3—81no—
239C23×D3—81no—
240C23×D3C2×D411yescharacteristic
241C23×D3C2×D411yescharacteristic
242C2×C3×D4—21no—
243C2×C3×D4—21no—
244C2×C3×D4—21no—
245C2×C3×D4C2×D412yes—
246C2×C3×D4C2×D412yes—
247C2×C3×D4#4112yes—
248C22×C3×C4—21no—
249C22×C3×C4—24no—
250C22×C3×C4—21no—
251C22×C3×C4—21no—
252C22×C3×C4—81no—
253C22×C3×C4—81no—
254C22×C3×C4C2×D411yescharacteristic
255C22×C3×C4C2×D411yescharacteristic
256C22×C3×C4C2411yescharacteristic
257C2×#67—24no—
258C2×#67—24no—
259C2×#67—42no—
260C2×#67—42no—
261C2×#67—42no—
262C2×#67—42no—
263C22×Dic3—24no—
264C22×Dic3—21no—
265C22×Dic3—21no—
266C22×Dic3—21no—
267C22×Dic3—42no—
268C22×Dic3—42no—
269C22×Dic3C2×D411yescharacteristic
270C22×Dic3C2×D411yescharacteristic
271#237—44no—
272#237—44no—
273#237—44no—
274#237—44no—
275D3×D4—44no—
276D3×D4—44no—
277D3×D4—44no—
278D3×D4—44no—
279C2×D12—21no—
280C2×D12—21no—
281C2×D12—21no—
282C2×D12—21no—
283C2×D12—22no—
284C2×D12—22no—
285C2×D12—21no—
286C2×D12—24no—
287C2×D12—41no—
288C2×D12—81no—
289C2×D12—81no—
290C2×D12C2×D412yes—
291C2×C4×D3—21no—
292C2×C4×D3—21no—
293C2×C4×D3—21no—
294C2×C4×D3—21no—
295C2×C4×D3—21no—
296C2×C4×D3—21no—
297C2×C4×D3—21no—
298C2×C4×D3—21no—
299C2×C4×D3—21no—
300C2×C4×D3—21no—
301C2×C4×D3—21no—
302C2×C4×D3—21no—
303C2×Dic6—21no—
304C2×Dic6—21no—
305C2×Dic6—21no—
306C2×Dic6—21no—
307C2×Dic6—21no—
308C2×Dic6—21no—
309C2×Dic6—21no—
310C2×Dic6—21no—
311C2×Dic6—21no—
312C2×Dic6—21no—
313C2×Dic6C2×D412yes—
314C2×Dic6C2×D412yes—
315C2×C3×C8—21no—
316C2×C3×C8—21no—
317C2×C3×C8—21no—
318C2×C3×C8—21no—
319C2×C3×C8—21no—
320C2×C3×C8—21no—
321C3×C4⋊C4—21no—
322C3×C4⋊C4—21no—
323C3×C4⋊C4—21no—
324C3×C4⋊C4—21no—
325C3×C4⋊C4—21no—
326C3×C4⋊C4C2×D412yes—
327C3×C22⋊C4—24no—
328C3×C42C2×D412yes—
329C3×C42C2×D412yes—
330#214—28no—
331(C2×D3)⋊C4—24no—
332(C2×D3)⋊C4—24no—
333(C2×D3)⋊C4—22no—
334(C2×D3)⋊C4—22no—
335(C2×D3)⋊C4—24no—
336(C2×D3)⋊C4—24no—
337(C2×D3)⋊C4—42no—
338(C2×D3)⋊C4—42no—
339(C2×D3)⋊C4—42no—
340(C2×D3)⋊C4—42no—
341C4⋊Dic3—24no—
342C4⋊Dic3—22no—
343C4⋊Dic3—21no—
344C4⋊Dic3—21no—
345C4⋊Dic3—42no—
346C4⋊Dic3—42no—
347Dic3⋊C4—42no—
348C4×Dic3—42no—
349C2×C3⋊C8—21no—
350C2×C3⋊C8—21no—
351C2×C3⋊C8—21no—
352C2×C3⋊C8—21no—
353C2×C3⋊C8—21no—
354C2×C3⋊C8C2×D412yes—
355Dic12—44no—
356#204—44no—
357C25—61no—
358C2×#41—62no—
359C2×#41—62no—
360C2×#41—62no—
361C2×#41—62no—
362C2×#41—121no—
363C2×#41—121no—
364C22×Q8—31no—
365C22×Q8—31no—
366C22×D4—31no—
367C22×D4—31no—
368C22×D4—61no—
369C22×D4—61no—
370C22×D4—62no—
371C22×D4—61no—
372C22×D4—62no—
373C22×D4—62no—
374C22×D4—62no—
375C22×D4—121no—
376C22×D4—121no—
377C22×D4C22×D311yescharacteristic
378C23×C4—21no—
379C23×C4—31no—
380C23×C4—31no—
381C23×C4—61no—
382C2×Q16—62no—
383C2×Q16—62no—
384C2×Q16—121no—
385C2×SD16—34no—
386C2×SD16—62no—
387C2×SD16—62no—
388C2×SD16—62no—
389C2×SD16—62no—
390C2×SD16—121no—
391C22×C8—31no—
392C22×C8—31no—
393C22×C8C22×D311yescharacteristic
394C22×C8C22×D311yescharacteristic
395#124—34no—
396#124—62no—
397#123—68no—
398C22⋊Q8—62no—
399C22⋊Q8—62no—
400C22⋊Q8—62no—
401C22⋊Q8—62no—
402C22⋊Q8—121no—
403C22⋊Q8—121no—
404#121—62no—
405#121—68no—
406#121—62no—
407#120—68no—
408C4×Q8—62no—
409C4×Q8—62no—
410C4×D4—22no—
411C4×D4—62no—
412C4×D4—62no—
413C4×D4D1214yes—
414C2×C4⋊C4—31no—
415C2×C4⋊C4—31no—
416C2×C4⋊C4—61no—
417C2×C4⋊C4—61no—
418C2×C4⋊C4—61no—
419C2×C4⋊C4—61no—
420C2×C4⋊C4C22×D311yescharacteristic
421C2×C4⋊C4C22×D311yescharacteristic
422C2×C4⋊C4C22×D311yescharacteristic
423C2×C22⋊C4—21no—
424C2×C22⋊C4—31no—
425C2×C22⋊C4—31no—
426C2×C22⋊C4—61no—
427C2×C22⋊C4—61no—
428C2×C22⋊C4—68no—
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×C42—61no—
436C2×C42C22×D311yescharacteristic
437#106—62no—
438C4⋊C8—22no—
439#103—62no—
440#103—62no—
441#103—62no—
442#103—121no—
443#102—22no—
444#102—22no—
445#102—62no—
446#102—62no—
447#102—62no—
448#102—121no—
449C22⋊C8—62no—
450C22⋊C8—62no—
451C22⋊C8—121no—
452C22⋊C8—121no—
453C4×C8—62no—
454#95—21no—
455#95—21no—
456#95—61no—
457#95—61no—
458C23×C3—22no—
459C23×C3—22no—
460C23×C3—22no—
461C23×C3—41no—
462C23×C3—41no—
463C23×C3—41no—
464C23×C3—41no—
465C23×C3C22×D411yescharacteristic
466C22×D3—21no—
467C22×D3—21no—
468C22×D3—21no—
469C22×D3—21no—
470C22×D3—21no—
471C22×D3—21no—
472C22×D3—22no—
473C22×D3—21no—
474C22×D3—21no—
475C22×D3—21no—
476C22×D3—21no—
477C22×D3—21no—
478C22×D3—21no—
479C22×D3—21no—
480C22×D3—48no—
481C22×D3—48no—
482C22×D3—41no—
483C22×D3—41no—
484C22×D3—41no—
485C22×D3—41no—
486C22×D3—41no—
487C22×D3—41no—
488C22×D3—84no—
489C22×D3—84no—
490C22×D3—84no—
491C22×D3—84no—
492C22×D3—84no—
493C22×D3#13512yes—
494C3×D4—22no—
495C3×D4—22no—
496C3×D4—22no—
497C3×D4#12114yes—
498C2×C3×C4—21no—
499C2×C3×C4—21no—
500C2×C3×C4—21no—
501C2×C3×C4—21no—
502C2×C3×C4—22no—
503C2×C3×C4—41no—
504C2×C3×C4—41no—
505C2×C3×C4—41no—
506C2×C3×C4—41no—
507C2×C3×C4—41no—
508C2×C3×C4—41no—
509C2×C3×C4—41no—
510C2×C3×C4—41no—
511C2×C3×C4—84no—
512C2×C3×C4#12012yes—
513C2×C3×C4#12012yes—
514C2×C3×C4C22×D411yescharacteristic
515C2×C3×C4C22×D411yescharacteristic
516C2×C3×C4C22×D411yescharacteristic
517C2×C3×C4C2×#4111yescharacteristic
518C2×C3×C4H(5,𝔽2)11yescharacteristic
519C2×C3×C4H(5,𝔽2)11yescharacteristic
520#67—48no—
521#67—48no—
522C2×Dic3—21no—
523C2×Dic3—22no—
524C2×Dic3—21no—
525C2×Dic3—22no—
526C2×Dic3—21no—
527C2×Dic3—21no—
528C2×Dic3—21no—
529C2×Dic3—21no—
530C2×Dic3—48no—
531C2×Dic3—41no—
532C2×Dic3—41no—
533C2×Dic3—41no—
534C2×Dic3—41no—
535C2×Dic3—41no—
536C2×Dic3—41no—
537C2×Dic3—41no—
538D12—22no—
539D12—22no—
540D12—44no—
541D12—41no—
542D12—41no—
543D12—84no—
544C4×D3—41no—
545C4×D3—41no—
546C4×D3—41no—
547C4×D3—41no—
548C4×D3—41no—
549C4×D3—41no—
550C4×D3—41no—
551C4×D3—41no—
552Dic6—22no—
553Dic6—22no—
554Dic6—22no—
555Dic6—22no—
556Dic6—41no—
557Dic6—41no—
558Dic6—41no—
559Dic6—41no—
560C3×C8—41no—
561C3×C8—41no—
562C3⋊C8—22no—
563C3⋊C8—41no—
564C24—21no—
565C24—31no—
566C24—31no—
567C24—64no—
568C24—61no—
569C24—122no—
570C24—122no—
571C24—122no—
572C24—122no—
573C24—241no—
574C24—241no—
575#41—124no—
576#41—124no—
577#41—124no—
578#41—124no—
579C2×Q8—32no—
580C2×Q8—32no—
581C2×Q8—61no—
582C2×Q8—61no—
583C2×Q8—61no—
584C2×Q8—61no—
585C2×Q8—61no—
586C2×Q8—61no—
587C2×Q8—61no—
588C2×Q8—61no—
589C2×Q8—61no—
590C2×Q8—61no—
591C2×D4—21no—
592C2×D4—21no—
593C2×D4—21no—
594C2×D4—32no—
595C2×D4—62no—
596C2×D4—64no—
597C2×D4—64no—
598C2×D4—64no—
599C2×D4—62no—
600C2×D4—61no—
601C2×D4—61no—
602C2×D4—61no—
603C2×D4—61no—
604C2×D4—61no—
605C2×D4—121no—
606C2×D4—122no—
607C2×D4—122no—
608C2×D4—124no—
609C2×D4—124no—
610C2×D4—124no—
611C2×D4—122no—
612C2×D4—122no—
613C2×D4—124no—
614C2×D4—241no—
615C2×D4—241no—
616C2×D4C2×D1212yes—
617C2×D4D3×D412yes—
618C2×D4#23912yes—
619C22×C4—21no—
620C22×C4—24no—
621C22×C4—21no—
622C22×C4—21no—
623C22×C4—31no—
624C22×C4—31no—
625C22×C4—64no—
626C22×C4—61no—
627C22×C4—61no—
628C22×C4—61no—
629C22×C4—61no—
630C22×C4—61no—
631C22×C4—61no—
632C22×C4—61no—
633C22×C4—61no—
634C22×C4—61no—
635C22×C4—61no—
636C22×C4—61no—
637C22×C4—61no—
638C22×C4—61no—
639C22×C4—61no—
640C22×C4—61no—
641C22×C4—81no—
642C22×C4—81no—
643C22×C4—122no—
644C22×C4—122no—
645C22×C4D3×D411yescharacteristic
646C22×C4D3×D411yescharacteristic
647C22×C4C23×D311yescharacteristic
648Q16—124no—
649SD16—68no—
650SD16—124no—
651C2×C8—21no—
652C2×C8—21no—
653C2×C8—21no—
654C2×C8—21no—
655C2×C8—21no—
656C2×C8—21no—
657C2×C8—32no—
658C2×C8—61no—
659C2×C8—61no—
660C2×C8—61no—
661C2×C8—61no—
662C2×C8—61no—
663C4⋊C4—21no—
664C4⋊C4—21no—
665C4⋊C4—21no—
666C4⋊C4—21no—
667C4⋊C4—21no—
668C4⋊C4—64no—
669C4⋊C4—62no—
670C4⋊C4—61no—
671C4⋊C4—61no—
672C4⋊C4—122no—
673C4⋊C4—122no—
674C4⋊C4—122no—
675C4⋊C4C2×D1212yes—
676C22⋊C4—24no—
677C22⋊C4—64no—
678C22⋊C4—64no—
679C22⋊C4—62no—
680C22⋊C4—62no—
681C22⋊C4—64no—
682C22⋊C4—64no—
683C22⋊C4—122no—
684C22⋊C4—122no—
685C22⋊C4—122no—
686C22⋊C4—122no—
687C42—122no—
688C42C2×D1212yes—
689C42D3×D412yes—
690C22×C3—24no—
691C22×C3—42no—
692C22×C3—42no—
693C22×C3—42no—
694C22×C3—42no—
695C22×C3—42no—
696C22×C3—42no—
697C22×C3C2×#12011yescharacteristic
698C22×C3D4211yescharacteristic
699C22×C3#54611yescharacteristic
700C22×C3C2×#13511yescharacteristic
701C22×C3#57511yescharacteristic
702C22×C3#57711yescharacteristic
703C22×C3#57711yescharacteristic
704C2×D3—22no—
705C2×D3—22no—
706C2×D3—22no—
707C2×D3—41no—
708C2×D3—41no—
709C2×D3—41no—
710C2×D3—41no—
711C2×D3—41no—
712C2×D3—42no—
713C2×D3—41no—
714C2×D3—42no—
715C2×D3—41no—
716C2×D3—42no—
717C2×D3—41no—
718C2×D3—41no—
719C2×D3—41no—
720C2×D3—41no—
721C2×D3—816no—
722C2×D3—81no—
723C2×D3—81no—
724C2×D3—81no—
725C2×D3—81no—
726C3×C4—22no—
727C3×C4—22no—
728C3×C4—42no—
729C3×C4—81no—
730C3×C4—81no—
731C3×C4C2×#12111yescharacteristic
732C3×C4#53511yescharacteristic
733C3×C4D4211yescharacteristic
734C3×C4#54611yescharacteristic
735Dic3—42no—
736Dic3—42no—
737Dic3—41no—
738Dic3—41no—
739Dic3—81no—
740C23—22no—
741C23—22no—
742C23—22no—
743C23—32no—
744C23—41no—
745C23—41no—
746C23—41no—
747C23—41no—
748C23—61no—
749C23—61no—
750C23—61no—
751C23—61no—
752C23—61no—
753C23—61no—
754C23—62no—
755C23—61no—
756C23—61no—
757C23—61no—
758C23—61no—
759C23—61no—
760C23—61no—
761C23—61no—
762C23—128no—
763C23—128no—
764C23—121no—
765C23—121no—
766C23—121no—
767C23—121no—
768C23—121no—
769C23—121no—
770C23—244no—
771C23—244no—
772C23—244no—
773C23—244no—
774C23—244no—
775C23C2×D3×D411yescharacteristic
776Q8—62no—
777Q8—62no—
778Q8—62no—
779Q8—62no—
780Q8—121no—
781Q8—121no—
782Q8—121no—
783Q8—121no—
784D4—22no—
785D4—22no—
786D4—22no—
787D4—62no—
788D4—62no—
789D4—124no—
790D4—128no—
791D4—128no—
792D4—121no—
793D4—121no—
794D4—244no—
795D4#89514yes—
796C2×C4—21no—
797C2×C4—21no—
798C2×C4—21no—
799C2×C4—21no—
800C2×C4—22no—
801C2×C4—41no—
802C2×C4—41no—
803C2×C4—41no—
804C2×C4—41no—
805C2×C4—41no—
806C2×C4—41no—
807C2×C4—41no—
808C2×C4—41no—
809C2×C4—61no—
810C2×C4—62no—
811C2×C4—61no—
812C2×C4—62no—
813C2×C4—61no—
814C2×C4—61no—
815C2×C4—61no—
816C2×C4—61no—
817C2×C4—84no—
818C2×C4—128no—
819C2×C4—121no—
820C2×C4—121no—
821C2×C4—121no—
822C2×C4—121no—
823C2×C4—121no—
824C2×C4—121no—
825C2×C4—121no—
826C2×C4—121no—
827C2×C4—121no—
828C2×C4—121no—
829C2×C4—121no—
830C2×C4—121no—
831C2×C4—121no—
832C2×C4—121no—
833C2×C4—121no—
834C2×C4#88212yes—
835C2×C4#88212yes—
836C2×C4C22×D1211yescharacteristic
837C2×C4C2×D3×D411yescharacteristic
838C2×C4C2×D3×D411yescharacteristic
839C2×C4C2×#23911yescharacteristic
840C2×C4#100911yescharacteristic
841C2×C4#100911yescharacteristic
842C8—41no—
843C8—41no—
844C8—62no—
845C8—121no—
846C2×C3—44no—
847C2×C3#240811yescharacteristic
848C2×C3#300211yescharacteristic
849C2×C3#300911yescharacteristic
850C2×C3#327511yescharacteristic
851C2×C3#328211yescharacteristic
852C2×C3#329611yescharacteristic
853C2×C3#332311yescharacteristic
854D3—42no—
855D3—81no—
856D3—82no—
857C22—24no—
858C22—42no—
859C22—42no—
860C22—42no—
861C22—42no—
862C22—42no—
863C22—42no—
864C22—62no—
865C22—62no—
866C22—62no—
867C22—121no—
868C22—121no—
869C22—121no—
870C22—121no—
871C22—121no—
872C22—122no—
873C22—121no—
874C22—121no—
875C22—121no—
876C22—122no—
877C22—121no—
878C22—121no—
879C22—121no—
880C22—122no—
881C22—2416no—
882C22—241no—
883C22—241no—
884C22—241no—
885C22—241no—
886C22C2×#88211yescharacteristic
887C22#560911yescharacteristic
888C22#563011yescharacteristic
889C22D3×#13511yescharacteristic
890C22#576811yescharacteristic
891C22#577511yescharacteristic
892C22#577511yescharacteristic
893C4—22no—
894C4—22no—
895C4—42no—
896C4—81no—
897C4—81no—
898C4—121no—
899C4—121no—
900C4—122no—
901C4—122no—
902C4—241no—
903C4C2×#89511yescharacteristic
904C4#552511yescharacteristic
905C4#560911yescharacteristic
906C4#563011yescharacteristic
907C3#2424711yescharacteristic, complemented, Sylow
908C2—44no—
909C2—122no—
910C2—241no—
911C2—242no—
912C2#7401611yescharacteristic
913C2#7883311yescharacteristic
914C2#7892911yescharacteristic
915C2#8055611yescharacteristic
916C2#8055811yescharacteristic
917C2#8118611yescharacteristic
918C2#8119311yescharacteristic
subgroupG/H
centerC23C2×D3×D4
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC3×#1804C2
socleC23×C3C22×D4
prime radicalC2×#5554C2
hypercenter#1804D3
hypocenterC3#24247
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1804

Complements

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

NH ≅ G/Ntype
2. C2×C4×#214C2semidirect
3. C2×#4845C2semidirect
4. C2×#4783C2semidirect
5. C2×#4776C2semidirect
6. #74240C2semidirect
7. C3×#1804C2semidirect
8. #70470C2semidirect
9. #70199C2semidirect
10. #70198C2semidirect
11. #69551C2semidirect
12. #68888C2semidirect
13. #68887C2semidirect
14. #68824C2semidirect
15. #68823C2semidirect
23. C22×Dic12C22semidirect
29. C2×#897C22semidirect
35. C2×C4×Dic6C22semidirect
36. C2×C3×C4⋊C8C22semidirect
39. C3×#382C22semidirect
44. C2×(C2×D3)⋊C8C22semidirect
45. C2×(C2×D3)⋊C8C22semidirect
46. C2×#816C22semidirect
49. #4987C22semidirect
50. C2×#810C22semidirect
51. C2×#810C22semidirect
52. C2×#810C22semidirect
55. C2×#808C22semidirect
56. C2×C4×C3⋊C8C22semidirect
64. C3×#340C22semidirect
65. C3×#340C22semidirect
78. #1804D3semidirect
117. C2×#214D4semidirect
206. C2×C4⋊C8C2×D3semidirect
226. #382C2×D3semidirect
229. #340C2×D3semidirect
230. #340C2×D3semidirect
907. C3#24247semidirect

Maximal subgroups

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

subgroupindex
C2×#55542
C2×C4×#2142
C2×#48452
C2×#47832
C2×#47762
#742402
C3×#18042
#704702
#701992
#701982
#695512
#688882
#688872
#688242
#688232
#242473