Finite Group Databasebeta

← #10822695

Subgroups — #10822695

Order 768.

1650 conjugacy classes of subgroups.

The subgroup lattice has 910 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#5606C211yesmaximal, characteristic
2C2×#4861C211yesmaximal, characteristic, complemented
3C2×#4771C211yesmaximal, characteristic, complemented
4C2×#4771C211yesmaximal, characteristic, complemented
5C2×#4726C211yesmaximal, characteristic, complemented
6D3×#380C211yesmaximal, characteristic, complemented
7C3×#2034C211yesmaximal, characteristic, complemented
8#71680C211yesmaximal, characteristic, complemented
9#70582C211yesmaximal, characteristic, complemented
10#70206C211yesmaximal, characteristic, complemented
11#70175C211yesmaximal, characteristic, complemented
12#69937C211yesmaximal, characteristic, complemented
13#69527C211yesmaximal, characteristic, complemented
14#68867C211yesmaximal, characteristic, complemented
15#68824C211yesmaximal, characteristic, complemented
16#23482—31nomaximal, Sylow
17C22×#237C2211yescharacteristic
18C23×C4×D3C2211yescharacteristic
19C2×C3×#121C2211yescharacteristic
20C2×#938C2211yescharacteristic
21C2×#937—21no—
22C2×D4×Dic3—21no—
23C2×#924C2211yescharacteristic
24C22×ΓL(1,𝔽25)C2211yescharacteristic
25C22×ΓL(1,𝔽25)C2211yescharacteristic
26#5606—24no—
27#5606—24no—
28C2×#897C2211yescharacteristic
29C2×#892C2211yescharacteristic
30C2×D3×C4⋊C4C2211yescharacteristic
31C2×D3×C4⋊C4C2211yescharacteristic
32C2×#883—21no—
33C2×#67⋊C4—21no—
34C2×D3×C22⋊C4—21no—
35C2×C3×#106C2211yescharacteristic, complemented
36C2×C3×#102C2211yescharacteristic, complemented
37C2×C3×#102C2211yescharacteristic, complemented
38C2×C3×C22⋊C8C2211yescharacteristic
39C3×#380C2211yescharacteristic
40C2×#832C2211yescharacteristic, complemented
41C2×#832C2211yescharacteristic, complemented
42#5212C2211yescharacteristic
43C2×#830C2211yescharacteristic
44C2×(C2×D3)⋊C8C2211yescharacteristic
45C2×(C2×D3)⋊C8C2211yescharacteristic
46C2×#818C2211yescharacteristic, complemented
47C2×#816C2211yescharacteristic, complemented
48C2×#816C2211yescharacteristic, complemented
49#4987C2211yescharacteristic
50#4987C2211yescharacteristic
51C2×#810C2211yescharacteristic, complemented
52C2×#810C2211yescharacteristic, complemented
53C2×#808C2211yescharacteristic, complemented
54C2×#807C2211yescharacteristic, complemented
55#4942—21no—
56#4861—24no—
57#4771—24no—
58#4771—24no—
59#4726—24no—
60#4667—21no—
61D3×#95—21no—
62C3×#340C2211yescharacteristic, complemented
63#4551C2211yescharacteristic, complemented
64#4529C2211yescharacteristic, complemented
65#4529C2211yescharacteristic, complemented
66C2×#525—31no—
67C2×#428—31no—
68C2×#417—31no—
69C2×#417—31no—
70C2×#407—31no—
71C2×#380—31no—
72#2036—31no—
73#2036—31no—
74#2035—31no—
75#2035—31no—
76#2034—31no—
77#2034D311yescharacteristic, complemented
78#2033—31no—
79#2033—31no—
80#1736—31no—
81C24×D3D411yescharacteristic
82C22×C3×D4—21no—
83C22×C3×D4C2311yescharacteristic
84C23×C3×C4C2311yescharacteristic
85C22×#67—21no—
86C22×#67—21no—
87C23×Dic3—21no—
88C23×Dic3D411yescharacteristic
89C2×#237—22no—
90C2×#237—22no—
91C2×#237—22no—
92C2×#237—22no—
93C2×#237—22no—
94C2×#237D414yes—
95C22×C4×D3—22no—
96C22×C4×D3—22no—
97C22×C4×D3—22no—
98C22×C4×D3—22no—
99C22×C4×D3—22no—
100C22×C4×D3—22no—
101C22×C4×D3—21no—
102C22×C4×D3—21no—
103C22×C4×D3D411yescharacteristic
104C22×C4×D3D411yescharacteristic
105C22×C4×D3C2311yescharacteristic
106C22×C4×D3C2311yescharacteristic
107C22×Dic6C2311yescharacteristic
108C22×C3×C8C2311yescharacteristic
109C22×C3×C8C2311yescharacteristic
110C3×#121—22no—
111C3×#121—22no—
112C2×C3×C4⋊C4C2311yescharacteristic
113C2×C3×C4⋊C4C2311yescharacteristic
114C2×C3×C4⋊C4C2311yescharacteristic
115C2×C3×C22⋊C4—21no—
116C2×C3×C22⋊C4—21no—
117C2×#217—21no—
118C2×#217—21no—
119C2×#217—21no—
120#938—22no—
121#938—22no—
122#937—28no—
123D4×Dic3—28no—
124C2×(C2×D3)⋊C4—21no—
125C2×(C2×D3)⋊C4—21no—
126C2×(C2×D3)⋊C4—21no—
127C2×(C2×D3)⋊C4—21no—
128C2×C4⋊Dic3—21no—
129C2×C4⋊Dic3C2311yescharacteristic
130C2×C4⋊Dic3C2311yescharacteristic
131C2×C4⋊Dic3C2311yescharacteristic
132#924—22no—
133#924—22no—
134C2×Dic3⋊C4—21no—
135C2×Dic3⋊C4—21no—
136C2×Dic3⋊C4—21no—
137C2×C4×Dic3—21no—
138C22×C3⋊C8C2311yescharacteristic
139C22×C3⋊C8C2311yescharacteristic
140C2×ΓL(1,𝔽25)—22no—
141C2×ΓL(1,𝔽25)—22no—
142C2×ΓL(1,𝔽25)—22no—
143C2×ΓL(1,𝔽25)—22no—
144C2×ΓL(1,𝔽25)—22no—
145C2×ΓL(1,𝔽25)D414yescomplemented
146#897—22no—
147#897—22no—
148#892—22no—
149#892D414yes—
150D3×C4⋊C4—22no—
151D3×C4⋊C4—22no—
152D3×C4⋊C4—22no—
153D3×C4⋊C4—22no—
154#883—28no—
155#67⋊C4—28no—
156D3×C22⋊C4—44no—
157C3×#106—22no—
158C3×#102—22no—
159C3×#102—22no—
160C3×C22⋊C8—22no—
161C3×#95—21no—
162#832—22no—
163#832—22no—
164C3⋊#95—21no—
165C3⋊#95—21no—
166C3⋊#95—21no—
167#830—22no—
168(C2×D3)⋊C8—22no—
169(C2×D3)⋊C8—22no—
170#818—22no—
171#816—22no—
172#816—22no—
173#810—22no—
174#810—22no—
175#808—22no—
176#807—22no—
177C22×#41—31no—
178C24×C4—31no—
179C22×M16—31no—
180C22×M16—31no—
181#525—64no—
182#525—64no—
183C2×#123—61no—
184C2×C22⋊Q8—31no—
185C2×C22⋊Q8—31no—
186C2×#121—31no—
187C2×#121C2×D311yescharacteristic
188C2×#120—61no—
189C2×C4×D4—61no—
190C2×C4×D4—61no—
191C2×#117—31no—
192C22×C4⋊C4—31no—
193C22×C4⋊C4—31no—
194C22×C22⋊C4—61no—
195#428—64no—
196C2×#107—31no—
197C2×#107—31no—
198C2×#106—31no—
199C2×#106C2×D311yescharacteristic, complemented
200#417—64no—
201#417—64no—
202C2×#103—31no—
203C2×#103—31no—
204C2×#103—31no—
205C2×#103—31no—
206C2×#102—31no—
207C2×#102—31no—
208C2×#102C2×D311yescharacteristic, complemented
209C2×#102C2×D311yescharacteristic, complemented
210#407—64no—
211C2×C22⋊C8—31no—
212C2×C22⋊C8—31no—
213C2×C22⋊C8—31no—
214C2×C22⋊C8C2×D311yescharacteristic
215#380—31no—
216#380—31no—
217#380—31no—
218#380—61no—
219#380—61no—
220#380C2×D311yescharacteristic
221C2×#95—61no—
222#340—31no—
223#340—31no—
224#340—31no—
225#340C2×D311yescharacteristic, complemented
226C24×C3—21no—
227C24×C3C2×D411yescharacteristic
228C23×D3—22no—
229C23×D3—22no—
230C23×D3—22no—
231C23×D3—22no—
232C23×D3—22no—
233C23×D3—41no—
234C23×D3—41no—
235C23×D3C2×D411yescharacteristic
236C23×D3C2×D411yescharacteristic
237C2×C3×D4—24no—
238C2×C3×D4—21no—
239C2×C3×D4—21no—
240C2×C3×D4—21no—
241C2×C3×D4—21no—
242C2×C3×D4—21no—
243C2×C3×D4—42no—
244C2×C3×D4—42no—
245C2×C3×D4C2×D412yes—
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×C4—21no—
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—21no—
264C22×Dic3—21no—
265C22×Dic3—24no—
266C22×Dic3—22no—
267C22×Dic3—22no—
268C22×Dic3—22no—
269C22×Dic3—21no—
270C22×Dic3—21no—
271C22×Dic3—42no—
272C22×Dic3—42no—
273C22×Dic3C2×D411yescharacteristic
274C22×Dic3C2×D411yescharacteristic
275#237—28no—
276#237—28no—
277#237—44no—
278#237—44no—
279C2×C4×D3—22no—
280C2×C4×D3—22no—
281C2×C4×D3—22no—
282C2×C4×D3—21no—
283C2×C4×D3—21no—
284C2×C4×D3—21no—
285C2×C4×D3—21no—
286C2×C4×D3—21no—
287C2×C4×D3—21no—
288C2×C4×D3—22no—
289C2×C4×D3—22no—
290C2×C4×D3—22no—
291C2×C4×D3—44no—
292C2×C4×D3—44no—
293C2×C4×D3—44no—
294C2×C4×D3—44no—
295C2×C4×D3—42no—
296C2×C4×D3—42no—
297C2×C4×D3—42no—
298C2×C4×D3—42no—
299C2×C4×D3—42no—
300C2×C4×D3—42no—
301C2×C4×D3C2×D412yes—
302C2×C4×D3C2×D412yes—
303C2×C4×D3C2×D412yes—
304C2×C4×D3#4112yes—
305C2×C4×D3#4112yes—
306C2×C4×D3#4112yes—
307C2×Dic6—21no—
308C2×Dic6—21no—
309C2×Dic6—21no—
310C2×Dic6—21no—
311C2×Dic6—21no—
312C2×Dic6C2×D412yes—
313C2×C3×C8—21no—
314C2×C3×C8—21no—
315C2×C3×C8—21no—
316C2×C3×C8—21no—
317C2×C3×C8—21no—
318C2×C3×C8C2×D412yes—
319C3×C4⋊C4—21no—
320C3×C4⋊C4—21no—
321C3×C4⋊C4—21no—
322C3×C4⋊C4—21no—
323C3×C4⋊C4—21no—
324C3×C4⋊C4C2×D412yes—
325C3×C22⋊C4—24no—
326C3×C22⋊C4—42no—
327#217—24no—
328#217—24no—
329#217—42no—
330(C2×D3)⋊C4—24no—
331(C2×D3)⋊C4—24no—
332(C2×D3)⋊C4—42no—
333(C2×D3)⋊C4—42no—
334C4⋊Dic3—24no—
335C4⋊Dic3—21no—
336C4⋊Dic3—21no—
337C4⋊Dic3—21no—
338C4⋊Dic3—21no—
339C4⋊Dic3—21no—
340C4⋊Dic3C2×D412yes—
341Dic3⋊C4—24no—
342Dic3⋊C4—42no—
343Dic3⋊C4—42no—
344C4×Dic3—24no—
345C2×C3⋊C8—21no—
346C2×C3⋊C8—21no—
347C2×C3⋊C8—21no—
348C2×C3⋊C8—21no—
349C2×C3⋊C8—21no—
350C2×C3⋊C8C2×D412yes—
351ΓL(1,𝔽25)—28no—
352ΓL(1,𝔽25)—44no—
353C25—31no—
354C2×#41—34no—
355C2×#41—62no—
356C2×#41—62no—
357C2×#41—62no—
358C2×#41—62no—
359C2×#41—62no—
360C22×Q8—31no—
361C22×D4—21no—
362C22×D4—61no—
363C22×D4—61no—
364C22×D4C22×D311yescharacteristic
365C23×C4—31no—
366C23×C4—31no—
367C23×C4—31no—
368C23×C4—31no—
369C23×C4—31no—
370C23×C4—62no—
371C23×C4—62no—
372C23×C4—62no—
373C23×C4—62no—
374C23×C4—62no—
375C23×C4—62no—
376C23×C4—61no—
377C23×C4—61no—
378C23×C4—61no—
379C23×C4C22×D311yescharacteristic
380C2×M16—34no—
381C2×M16—62no—
382C2×M16—62no—
383C2×M16—62no—
384C2×M16—62no—
385C2×M16—62no—
386C22×C8—31no—
387C22×C8—31no—
388C22×C8C22×D311yescharacteristic
389C22×C8C22×D311yescharacteristic
390#123—68no—
391C22⋊Q8—62no—
392C22⋊Q8—62no—
393C22⋊Q8—62no—
394C22⋊Q8—62no—
395#121—22no—
396#121—22no—
397#121—62no—
398#121—62no—
399#120—68no—
400C4×D4—68no—
401C4×D4—68no—
402#117—34no—
403#117—62no—
404C2×C4⋊C4—31no—
405C2×C4⋊C4—31no—
406C2×C4⋊C4—31no—
407C2×C4⋊C4—62no—
408C2×C4⋊C4—62no—
409C2×C4⋊C4—62no—
410C2×C4⋊C4—62no—
411C2×C4⋊C4—61no—
412C2×C4⋊C4—61no—
413C2×C4⋊C4—61no—
414C2×C4⋊C4—61no—
415C2×C4⋊C4C22×D311yescharacteristic
416C2×C4⋊C4C22×D311yescharacteristic
417C2×C4⋊C4C22×D311yescharacteristic
418C2×C22⋊C4—21no—
419C2×C22⋊C4—21no—
420C2×C22⋊C4—61no—
421C2×C22⋊C4—61no—
422C2×C22⋊C4—61no—
423C2×C22⋊C4—61no—
424C2×C22⋊C4—61no—
425C2×C22⋊C4—61no—
426C2×C22⋊C4—61no—
427C2×C22⋊C4—124no—
428C2×C42—61no—
429#107—62no—
430#107—62no—
431#106—22no—
432#106—62no—
433#103—62no—
434#103—62no—
435#103—62no—
436#103—62no—
437#102—22no—
438#102—22no—
439#102—62no—
440#102—62no—
441C22⋊C8—22no—
442C22⋊C8—62no—
443C22⋊C8—62no—
444C22⋊C8—62no—
445#95—21no—
446#95—61no—
447#95—61no—
448#95—61no—
449C23×C3—21no—
450C23×C3—21no—
451C23×C3—21no—
452C23×C3—21no—
453C23×C3—21no—
454C23×C3—21no—
455C23×C3—22no—
456C23×C3—41no—
457C23×C3—41no—
458C23×C3—41no—
459C23×C3—41no—
460C23×C3—41no—
461C23×C3—41no—
462C23×C3#13712yes—
463C23×C3C22×D411yescharacteristic
464C22×D3—21no—
465C22×D3—21no—
466C22×D3—21no—
467C22×D3—21no—
468C22×D3—28no—
469C22×D3—21no—
470C22×D3—21no—
471C22×D3—21no—
472C22×D3—21no—
473C22×D3—21no—
474C22×D3—21no—
475C22×D3—44no—
476C22×D3—44no—
477C22×D3—44no—
478C22×D3—44no—
479C22×D3—44no—
480C22×D3—44no—
481C22×D3#12012yes—
482C22×D3#12112yes—
483C22×D3#12312yes—
484C22×D3AGL(1,ℤ/8)12yes—
485C3×D4—22no—
486C3×D4—22no—
487C3×D4—48no—
488C3×D4—41no—
489C3×D4—41no—
490C2×C3×C4—22no—
491C2×C3×C4—21no—
492C2×C3×C4—21no—
493C2×C3×C4—21no—
494C2×C3×C4—41no—
495C2×C3×C4—41no—
496C2×C3×C4—41no—
497C2×C3×C4—41no—
498C2×C3×C4—41no—
499C2×C3×C4—41no—
500C2×C3×C4—41no—
501C2×C3×C4—41no—
502C2×C3×C4—41no—
503C2×C3×C4—41no—
504C2×C3×C4—41no—
505C2×C3×C4—41no—
506C2×C3×C4C22×D411yescharacteristic
507C2×C3×C4C22×D411yescharacteristic
508C2×C3×C4C22×D411yescharacteristic
509C2×C3×C4C2×#4111yescharacteristic
510C2×C3×C4C2×#4111yescharacteristic
511C2×C3×C4C2×#4111yescharacteristic
512#67—48no—
513#67—48no—
514C2×Dic3—22no—
515C2×Dic3—22no—
516C2×Dic3—21no—
517C2×Dic3—21no—
518C2×Dic3—21no—
519C2×Dic3—41no—
520C2×Dic3—41no—
521C2×Dic3—41no—
522C2×Dic3—41no—
523C2×Dic3—44no—
524C2×Dic3—48no—
525C2×Dic3—41no—
526C2×Dic3—41no—
527C2×Dic3—41no—
528C2×Dic3—41no—
529C2×Dic3—41no—
530C2×Dic3—41no—
531C2×Dic3#12012yes—
532C2×Dic3#12112yes—
533C2×Dic3#12312yes—
534C4×D3—44no—
535C4×D3—41no—
536C4×D3—41no—
537C4×D3—41no—
538C4×D3—41no—
539C4×D3—44no—
540C4×D3—84no—
541C4×D3—84no—
542C4×D3#12114yes—
543C4×D3#12114yes—
544C4×D3#12314yes—
545C4×D3#12414yes—
546Dic6—22no—
547Dic6—22no—
548Dic6—41no—
549Dic6—41no—
550C3×C8—22no—
551C3×C8—41no—
552C3⋊C8—22no—
553C3⋊C8—41no—
554C24—21no—
555C24—31no—
556C24—31no—
557C24—62no—
558C24—62no—
559C24—62no—
560C24—62no—
561C24—62no—
562C24—121no—
563C24—121no—
564C24D3×D411yescharacteristic
565#41—68no—
566#41—68no—
567#41—124no—
568#41—124no—
569C2×Q8—32no—
570C2×Q8—61no—
571C2×Q8—61no—
572C2×Q8—61no—
573C2×Q8—61no—
574C2×Q8—61no—
575C2×D4—24no—
576C2×D4—21no—
577C2×D4—21no—
578C2×D4—21no—
579C2×D4—21no—
580C2×D4—21no—
581C2×D4—42no—
582C2×D4—42no—
583C2×D4—64no—
584C2×D4—64no—
585C2×D4—122no—
586C2×D4—122no—
587C2×D4—122no—
588C2×D4—122no—
589C2×D4D3×D412yes—
590C22×C4—21no—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—21no—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—31no—
600C22×C4—32no—
601C22×C4—32no—
602C22×C4—32no—
603C22×C4—32no—
604C22×C4—32no—
605C22×C4—32no—
606C22×C4—31no—
607C22×C4—62no—
608C22×C4—62no—
609C22×C4—62no—
610C22×C4—62no—
611C22×C4—62no—
612C22×C4—62no—
613C22×C4—62no—
614C22×C4—64no—
615C22×C4—62no—
616C22×C4—62no—
617C22×C4—61no—
618C22×C4—61no—
619C22×C4—61no—
620C22×C4—61no—
621C22×C4—61no—
622C22×C4—61no—
623C22×C4—61no—
624C22×C4—61no—
625C22×C4—61no—
626C22×C4—61no—
627C22×C4—124no—
628C22×C4—124no—
629C22×C4—124no—
630C22×C4—124no—
631C22×C4—122no—
632C22×C4—122no—
633C22×C4—122no—
634C22×C4—122no—
635C22×C4—122no—
636C22×C4—122no—
637C22×C4—122no—
638C22×C4—122no—
639C22×C4D3×D411yescharacteristic
640C22×C4C23×D311yescharacteristic
641M16—68no—
642M16—124no—
643C2×C8—21no—
644C2×C8—21no—
645C2×C8—21no—
646C2×C8—21no—
647C2×C8—21no—
648C2×C8—32no—
649C2×C8—61no—
650C2×C8—61no—
651C2×C8—61no—
652C2×C8—61no—
653C2×C8—61no—
654C2×C8D3×D412yes—
655C4⋊C4—21no—
656C4⋊C4—21no—
657C4⋊C4—21no—
658C4⋊C4—21no—
659C4⋊C4—21no—
660C4⋊C4—32no—
661C4⋊C4—64no—
662C4⋊C4—64no—
663C4⋊C4—61no—
664C4⋊C4—61no—
665C4⋊C4—61no—
666C4⋊C4—61no—
667C4⋊C4—61no—
668C4⋊C4—122no—
669C4⋊C4—122no—
670C4⋊C4D3×D412yes—
671C22⋊C4—24no—
672C22⋊C4—42no—
673C22⋊C4—64no—
674C22⋊C4—64no—
675C22⋊C4—64no—
676C22⋊C4—64no—
677C22⋊C4—122no—
678C22⋊C4—122no—
679C22⋊C4—122no—
680C42—64no—
681C22×C3—22no—
682C22×C3—22no—
683C22×C3—22no—
684C22×C3—41no—
685C22×C3—41no—
686C22×C3—41no—
687C22×C3—41no—
688C22×C3—42no—
689C22×C3—42no—
690C22×C3—42no—
691C22×C3—81no—
692C22×C3—81no—
693C22×C3—81no—
694C22×C3—81no—
695C22×C3C2×#12011yescharacteristic
696C22×C3C2×#12111yescharacteristic
697C22×C3C2×#12311yescharacteristic
698C22×C3C2×AGL(1,ℤ/8)11yescharacteristic
699C22×C3C2×#13711yescharacteristic
700C22×C3#57511yescharacteristic
701C22×C3#57511yescharacteristic
702C2×D3—22no—
703C2×D3—22no—
704C2×D3—22no—
705C2×D3—22no—
706C2×D3—22no—
707C2×D3—22no—
708C2×D3—22no—
709C2×D3—22no—
710C2×D3—22no—
711C2×D3—416no—
712C2×D3—41no—
713C2×D3—41no—
714C2×D3—41no—
715C2×D3—41no—
716C2×D3#39414yes—
717C3×C4—41no—
718C3×C4—42no—
719C3×C4—81no—
720C3×C4—81no—
721C3×C4C2×#12111yescharacteristic
722C3×C4C2×#12111yescharacteristic
723C3×C4C2×#12311yescharacteristic
724C3×C4C2×#12411yescharacteristic
725Dic3—42no—
726Dic3—41no—
727Dic3—42no—
728Dic3—81no—
729Dic3—81no—
730Dic3#39414yes—
731C23—21no—
732C23—21no—
733C23—21no—
734C23—21no—
735C23—21no—
736C23—21no—
737C23—22no—
738C23—32no—
739C23—32no—
740C23—32no—
741C23—32no—
742C23—41no—
743C23—41no—
744C23—41no—
745C23—41no—
746C23—41no—
747C23—41no—
748C23—68no—
749C23—61no—
750C23—61no—
751C23—61no—
752C23—61no—
753C23—61no—
754C23—61no—
755C23—61no—
756C23—61no—
757C23—61no—
758C23—61no—
759C23—124no—
760C23—124no—
761C23—124no—
762C23—124no—
763C23—124no—
764C23—124no—
765C23#91512yes—
766C23C2×D3×D411yescharacteristic
767Q8—62no—
768Q8—62no—
769Q8—121no—
770Q8—121no—
771D4—22no—
772D4—22no—
773D4—48no—
774D4—41no—
775D4—41no—
776D4—128no—
777D4—128no—
778C2×C4—21no—
779C2×C4—22no—
780C2×C4—21no—
781C2×C4—21no—
782C2×C4—32no—
783C2×C4—32no—
784C2×C4—32no—
785C2×C4—34no—
786C2×C4—34no—
787C2×C4—34no—
788C2×C4—34no—
789C2×C4—41no—
790C2×C4—41no—
791C2×C4—41no—
792C2×C4—41no—
793C2×C4—41no—
794C2×C4—41no—
795C2×C4—41no—
796C2×C4—41no—
797C2×C4—41no—
798C2×C4—41no—
799C2×C4—41no—
800C2×C4—41no—
801C2×C4—61no—
802C2×C4—62no—
803C2×C4—61no—
804C2×C4—62no—
805C2×C4—61no—
806C2×C4—124no—
807C2×C4—124no—
808C2×C4—128no—
809C2×C4—124no—
810C2×C4—121no—
811C2×C4—121no—
812C2×C4—121no—
813C2×C4—121no—
814C2×C4—121no—
815C2×C4—121no—
816C2×C4—121no—
817C2×C4—121no—
818C2×C4—121no—
819C2×C4—121no—
820C2×C4—121no—
821C2×C4—121no—
822C2×C4—121no—
823C2×C4—121no—
824C2×C4—244no—
825C2×C4—244no—
826C2×C4C2×D3×D411yescharacteristic
827C2×C4C2×D3×D411yescharacteristic
828C2×C4C2×D3×D411yescharacteristic
829C2×C4D3×#4111yescharacteristic
830C2×C4D3×#4111yescharacteristic
831C2×C4D3×#4111yescharacteristic
832C8—22no—
833C8—41no—
834C8—62no—
835C8—121no—
836C2×C3—42no—
837C2×C3—82no—
838C2×C3C2×#39411yescharacteristic
839C2×C3#300611yescharacteristic
840C2×C3#300711yescharacteristic
841C2×C3#305511yescharacteristic
842C2×C3#305611yescharacteristic
843C2×C3#309211yescharacteristic
844C2×C3#309311yescharacteristic
845D3—24no—
846D3—42no—
847C22—22no—
848C22—22no—
849C22—22no—
850C22—34no—
851C22—41no—
852C22—41no—
853C22—41no—
854C22—41no—
855C22—42no—
856C22—42no—
857C22—42no—
858C22—62no—
859C22—62no—
860C22—62no—
861C22—62no—
862C22—62no—
863C22—62no—
864C22—62no—
865C22—62no—
866C22—62no—
867C22—81no—
868C22—81no—
869C22—81no—
870C22—81no—
871C22—1216no—
872C22—121no—
873C22—121no—
874C22—121no—
875C22—121no—
876C22D3×#12011yescharacteristic
877C22D3×#12111yescharacteristic
878C22D3×#12311yescharacteristic
879C22C2×#91511yescharacteristic
880C22#576811yescharacteristic
881C22D3×AGL(1,ℤ/8)11yescharacteristic
882C22#577311yescharacteristic
883C4—34no—
884C4—42no—
885C4—41no—
886C4—81no—
887C4—81no—
888C4—121no—
889C4—122no—
890C4—122no—
891C4—241no—
892C4—241no—
893C4D3×#12111yescharacteristic
894C4D3×#12111yescharacteristic
895C4D3×#12311yescharacteristic
896C4D3×#12411yescharacteristic
897C3#2348211yescharacteristic, complemented, Sylow
898C2—42no—
899C2—64no—
900C2—82no—
901C2—122no—
902C2D3×#39411yescharacteristic
903C2#8008411yescharacteristic
904C2#8014711yescharacteristic
905C2#8065811yescharacteristic
906C2#8086411yescharacteristic
907C2#8132511yescharacteristic
908C2#8137211yescharacteristic
subgroupG/H
centerC23C2×D3×D4
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC3×#2034C2
socleC23×C3C22×D4
prime radicalC2×#5606C2
hypercenter#2034D3
hypocenterC3#23482
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C23×C4 ◁ #2034

Complements

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

NH ≅ G/Ntype
2. C2×#4861C2semidirect
3. C2×#4771C2semidirect
4. C2×#4771C2semidirect
5. C2×#4726C2semidirect
6. D3×#380C2semidirect
7. C3×#2034C2semidirect
8. #71680C2semidirect
9. #70582C2semidirect
10. #70206C2semidirect
11. #70175C2semidirect
12. #69937C2semidirect
13. #69527C2semidirect
14. #68867C2semidirect
15. #68824C2semidirect
35. C2×C3×#106C22semidirect
36. C2×C3×#102C22semidirect
37. C2×C3×#102C22semidirect
40. C2×#832C22semidirect
41. C2×#832C22semidirect
46. C2×#818C22semidirect
47. C2×#816C22semidirect
48. C2×#816C22semidirect
51. C2×#810C22semidirect
52. C2×#810C22semidirect
53. C2×#808C22semidirect
54. C2×#807C22semidirect
62. C3×#340C22semidirect
63. #4551C22semidirect
64. #4529C22semidirect
65. #4529C22semidirect
77. #2034D3semidirect
145. C2×ΓL(1,𝔽25)D4semidirect
199. C2×#106C2×D3semidirect
208. C2×#102C2×D3semidirect
209. C2×#102C2×D3semidirect
225. #340C2×D3semidirect
897. C3#23482semidirect

Maximal subgroups

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

subgroupindex
C2×#56062
C2×#48612
C2×#47712
C2×#47262
D3×#3802
C3×#20342
#716802
#705822
#702062
#701752
#699372
#695272
#688672
#688242
#234823