Finite Group Databasebeta

← #10822698

Subgroups — #10822698

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×#5627C211yesmaximal, characteristic
2C2×#4861C211yesmaximal, characteristic, complemented
3C2×#4803C211yesmaximal, characteristic, complemented
4C2×#4803C211yesmaximal, characteristic, complemented
5C2×#4726C211yesmaximal, characteristic, complemented
6D3×#380C211yesmaximal, characteristic, complemented
7C3×#2035C211yesmaximal, characteristic, complemented
8#71694C211yesmaximal, characteristic, complemented
9#70581C211yesmaximal, characteristic, complemented
10#70275C211yesmaximal, characteristic, complemented
11#70244C211yesmaximal, characteristic, complemented
12#69934C211yesmaximal, characteristic, complemented
13#69523C211yesmaximal, characteristic, complemented
14#68867C211yesmaximal, characteristic, complemented
15#68823C211yesmaximal, characteristic, complemented
16#23482—31nomaximal, Sylow
17C22×#239C2211yescharacteristic
18C23×C4×D3C2211yescharacteristic
19C2×C3×C22⋊Q8C2211yescharacteristic
20C2×#946C2211yescharacteristic
21C2×#930C2211yescharacteristic
22C22×ΓL(1,𝔽25)C2211yescharacteristic
23C22×ΓL(1,𝔽25)C2211yescharacteristic
24#5627—24no—
25#5627—24no—
26C2×#895C2211yescharacteristic
27C2×#894—21no—
28C2×#893—21no—
29C2×#892C2211yescharacteristic
30C2×D3×C4⋊C4C2211yescharacteristic
31C2×D3×C4⋊C4C2211yescharacteristic
32C2×#882—21no—
33C2×#67⋊C4—21no—
34C2×D3×C22⋊C4—21no—
35C2×C3×#106C2211yescharacteristic, complemented
36C2×C3×#103C2211yescharacteristic, complemented
37C2×C3×#103C2211yescharacteristic, complemented
38C2×C3×C22⋊C8C2211yescharacteristic
39C3×#380C2211yescharacteristic
40C2×#835C2211yescharacteristic, complemented
41C2×#835C2211yescharacteristic, complemented
42#5212C2211yescharacteristic
43C2×#830C2211yescharacteristic
44C2×#821C2211yescharacteristic, complemented
45C2×#821C2211yescharacteristic, complemented
46C2×(C2×D3)⋊C8C2211yescharacteristic
47C2×(C2×D3)⋊C8C2211yescharacteristic
48C2×#818C2211yescharacteristic, complemented
49#4987C2211yescharacteristic
50#4987C2211yescharacteristic
51C2×#809C2211yescharacteristic, complemented
52C2×#809C2211yescharacteristic, complemented
53C2×#808C2211yescharacteristic, complemented
54C2×#807C2211yescharacteristic, complemented
55#4942—21no—
56#4861—24no—
57#4803—24no—
58#4803—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#2035D311yescharacteristic, complemented
76#2034—31no—
77#2034—31no—
78#2033—31no—
79#2033—31no—
80#1736—31no—
81C24×D3D411yescharacteristic
82C22×C3×Q8C2311yescharacteristic
83C23×C3×C4C2311yescharacteristic
84C22×#67—21no—
85C23×Dic3D411yescharacteristic
86C2×#239—22no—
87C2×#239—22no—
88C2×#239—22no—
89C2×#239—22no—
90C2×#239—22no—
91C2×#239D414yes—
92C22×D12—21no—
93C22×D12—21no—
94C22×D12C2311yescharacteristic
95C22×C4×D3—21no—
96C22×C4×D3—22no—
97C22×C4×D3—22no—
98C22×C4×D3—22no—
99C22×C4×D3—22no—
100C22×C4×D3—22no—
101C22×C4×D3—22no—
102C22×C4×D3—21no—
103C22×C4×D3—21no—
104C22×C4×D3D411yescharacteristic
105C22×C4×D3D411yescharacteristic
106C22×C4×D3C2311yescharacteristic
107C22×C4×D3C2311yescharacteristic
108C22×C3×C8C2311yescharacteristic
109C22×C3×C8C2311yescharacteristic
110C3×C22⋊Q8—22no—
111C3×C22⋊Q8—22no—
112C2×C3×C4⋊C4—21no—
113C2×C3×C4⋊C4C2311yescharacteristic
114C2×C3×C4⋊C4C2311yescharacteristic
115C2×C3×C4⋊C4C2311yescharacteristic
116C2×C3×C22⋊C4—21no—
117C2×C3×C22⋊C4—21no—
118C2×#217—21no—
119#946—22no—
120#946—22no—
121#930—22no—
122#930—22no—
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)⋊C4—21no—
129C2×C4⋊Dic3C2311yescharacteristic
130C2×C4⋊Dic3C2311yescharacteristic
131C2×C4⋊Dic3C2311yescharacteristic
132C2×Dic3⋊C4—21no—
133C2×Dic3⋊C4—21no—
134C2×Dic3⋊C4—21no—
135C2×C4×Dic3—21no—
136C22×C3⋊C8C2311yescharacteristic
137C22×C3⋊C8C2311yescharacteristic
138C2×ΓL(1,𝔽25)—22no—
139C2×ΓL(1,𝔽25)—22no—
140C2×ΓL(1,𝔽25)—22no—
141C2×ΓL(1,𝔽25)—22no—
142C2×ΓL(1,𝔽25)—22no—
143C2×ΓL(1,𝔽25)D414yescomplemented
144#895—22no—
145#895—22no—
146#894—28no—
147#893—28no—
148#892—22no—
149#892D414yes—
150D3×C4⋊C4—22no—
151D3×C4⋊C4—22no—
152D3×C4⋊C4—22no—
153D3×C4⋊C4—22no—
154#882—28no—
155#67⋊C4—28no—
156D3×C22⋊C4—44no—
157C3×#106—22no—
158C3×#103—22no—
159C3×#103—22no—
160C3×C22⋊C8—22no—
161C3×#95—21no—
162#835—22no—
163#835—22no—
164C3⋊#95—21no—
165C3⋊#95—21no—
166C3⋊#95—21no—
167#830—22no—
168#821—22no—
169#821—22no—
170(C2×D3)⋊C8—22no—
171(C2×D3)⋊C8—22no—
172#818—22no—
173#809—22no—
174#809—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⋊Q8C2×D311yescharacteristic
186C2×#121—31no—
187C2×#121—31no—
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×#103C2×D311yescharacteristic, complemented
205C2×#103C2×D311yescharacteristic, complemented
206C2×#102—31no—
207C2×#102—31no—
208C2×#102—31no—
209C2×#102—31no—
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×C3C2×D411yescharacteristic
227C23×D3—22no—
228C23×D3—22no—
229C23×D3—22no—
230C23×D3—21no—
231C23×D3—22no—
232C23×D3—22no—
233C23×D3—41no—
234C23×D3—41no—
235C23×D3C2×D411yescharacteristic
236C23×D3C2×D411yescharacteristic
237C2×C3×Q8—21no—
238C2×C3×Q8—21no—
239C2×C3×Q8—21no—
240C2×C3×Q8—21no—
241C2×C3×Q8—21no—
242C2×C3×Q8C2×D412yes—
243C22×C3×C4—21no—
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×C4C2×D411yescharacteristic
254C22×C3×C4C2411yescharacteristic
255C2×#67—24no—
256C2×#67—42no—
257C2×#67—42no—
258C22×Dic3—21no—
259C22×Dic3—22no—
260C22×Dic3—22no—
261C22×Dic3—22no—
262C22×Dic3—21no—
263C22×Dic3—21no—
264C22×Dic3C2×D411yescharacteristic
265C22×Dic3C2×D411yescharacteristic
266#239—28no—
267#239—28no—
268#239—44no—
269#239—44no—
270C2×D12—21no—
271C2×D12—21no—
272C2×D12—21no—
273C2×D12—21no—
274C2×D12—24no—
275C2×D12—24no—
276C2×D12—21no—
277C2×D12—42no—
278C2×D12—42no—
279C2×D12—42no—
280C2×D12—42no—
281C2×D12C2×D412yes—
282C2×C4×D3—22no—
283C2×C4×D3—22no—
284C2×C4×D3—22no—
285C2×C4×D3—21no—
286C2×C4×D3—21no—
287C2×C4×D3—21no—
288C2×C4×D3—21no—
289C2×C4×D3—21no—
290C2×C4×D3—21no—
291C2×C4×D3—24no—
292C2×C4×D3—22no—
293C2×C4×D3—22no—
294C2×C4×D3—22no—
295C2×C4×D3—42no—
296C2×C4×D3—42no—
297C2×C4×D3—44no—
298C2×C4×D3—44no—
299C2×C4×D3—44no—
300C2×C4×D3—44no—
301C2×C4×D3—42no—
302C2×C4×D3—42no—
303C2×C4×D3—42no—
304C2×C4×D3—42no—
305C2×C4×D3—42no—
306C2×C4×D3—42no—
307C2×C4×D3C2×D412yes—
308C2×C4×D3C2×D412yes—
309C2×C4×D3C2×D412yes—
310C2×C4×D3#4112yes—
311C2×C4×D3#4112yes—
312C2×C4×D3#4112yes—
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—24no—
320C3×C4⋊C4—21no—
321C3×C4⋊C4—21no—
322C3×C4⋊C4—21no—
323C3×C4⋊C4—21no—
324C3×C4⋊C4—21no—
325C3×C4⋊C4C2×D412yes—
326C3×C22⋊C4—24no—
327C3×C22⋊C4—42no—
328#217—42no—
329(C2×D3)⋊C4—24no—
330(C2×D3)⋊C4—24no—
331(C2×D3)⋊C4—24no—
332(C2×D3)⋊C4—24no—
333(C2×D3)⋊C4—42no—
334(C2×D3)⋊C4—42no—
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×Q8C22×D311yescharacteristic
361C22×D4—31no—
362C22×D4—61no—
363C22×D4—61no—
364C22×D4—61no—
365C23×C4—31no—
366C23×C4—31no—
367C23×C4—31no—
368C23×C4—31no—
369C23×C4—31no—
370C23×C4—61no—
371C23×C4—62no—
372C23×C4—62no—
373C23×C4—62no—
374C23×C4—62no—
375C23×C4—62no—
376C23×C4—62no—
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—22no—
392C22⋊Q8—22no—
393C22⋊Q8—62no—
394C22⋊Q8—62no—
395#121—62no—
396#121—62no—
397#121—62no—
398#121—62no—
399#120—68no—
400C4×D4—68no—
401C4×D4—68no—
402#117—34no—
403#117—62no—
404C2×C4⋊C4—21no—
405C2×C4⋊C4—31no—
406C2×C4⋊C4—31no—
407C2×C4⋊C4—31no—
408C2×C4⋊C4—62no—
409C2×C4⋊C4—62no—
410C2×C4⋊C4—62no—
411C2×C4⋊C4—62no—
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—22no—
434#103—22no—
435#103—62no—
436#103—62no—
437#102—62no—
438#102—62no—
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×C3AGL(1,ℤ/8)12yes—
456C23×C3C22×D411yescharacteristic
457C22×D3—21no—
458C22×D3—21no—
459C22×D3—21no—
460C22×D3—21no—
461C22×D3—28no—
462C22×D3—21no—
463C22×D3—21no—
464C22×D3—21no—
465C22×D3—21no—
466C22×D3—21no—
467C22×D3—21no—
468C22×D3—22no—
469C22×D3—44no—
470C22×D3—44no—
471C22×D3—44no—
472C22×D3—44no—
473C22×D3—44no—
474C22×D3—44no—
475C22×D3—41no—
476C22×D3—41no—
477C22×D3—41no—
478C22×D3—41no—
479C22×D3—41no—
480C22×D3—41no—
481C22×D3#12012yes—
482C22×D3#12112yes—
483C22×D3#12312yes—
484C22×D3#13712yes—
485C3×Q8—22no—
486C3×Q8—22no—
487C3×Q8—41no—
488C3×Q8—41no—
489C2×C3×C4—22no—
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×C4—41no—
507C2×C3×C4—41no—
508C2×C3×C4C22×D411yescharacteristic
509C2×C3×C4C22×D411yescharacteristic
510C2×C3×C4C22×D411yescharacteristic
511C2×C3×C4C2×#4111yescharacteristic
512C2×C3×C4C2×#4111yescharacteristic
513C2×C3×C4C2×#4111yescharacteristic
514#67—48no—
515C2×Dic3—22no—
516C2×Dic3—21no—
517C2×Dic3—21no—
518C2×Dic3—21no—
519C2×Dic3—41no—
520C2×Dic3—41no—
521C2×Dic3—44no—
522C2×Dic3—41no—
523C2×Dic3—41no—
524C2×Dic3—41no—
525C2×Dic3—41no—
526C2×Dic3—41no—
527C2×Dic3—41no—
528C2×Dic3#12012yes—
529C2×Dic3#12112yes—
530C2×Dic3#12312yes—
531D12—22no—
532D12—22no—
533D12—48no—
534D12—48no—
535D12—41no—
536D12—41no—
537C4×D3—44no—
538C4×D3—41no—
539C4×D3—41no—
540C4×D3—41no—
541C4×D3—41no—
542C4×D3—44no—
543C4×D3—48no—
544C4×D3—84no—
545C4×D3—84no—
546C4×D3#12114yes—
547C4×D3#12114yes—
548C4×D3#12314yes—
549C4×D3#12414yes—
550C3×C8—22no—
551C3×C8—41no—
552C3⋊C8—22no—
553C3⋊C8—41no—
554C24—31no—
555C24—31no—
556C24—62no—
557C24—62no—
558C24—62no—
559C24—62no—
560C24—62no—
561C24—61no—
562C24—121no—
563C24—121no—
564C24D3×D411yescharacteristic
565#41—68no—
566#41—68no—
567#41—124no—
568#41—124no—
569C2×Q8—21no—
570C2×Q8—21no—
571C2×Q8—21no—
572C2×Q8—21no—
573C2×Q8—21no—
574C2×Q8D3×D412yes—
575C2×D4—32no—
576C2×D4—64no—
577C2×D4—64no—
578C2×D4—64no—
579C2×D4—61no—
580C2×D4—61no—
581C2×D4—61no—
582C2×D4—61no—
583C2×D4—61no—
584C2×D4—122no—
585C2×D4—122no—
586C2×D4—122no—
587C2×D4—122no—
588C2×D4—122no—
589C2×D4—122no—
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—21no—
600C22×C4—31no—
601C22×C4—32no—
602C22×C4—32no—
603C22×C4—32no—
604C22×C4—32no—
605C22×C4—32no—
606C22×C4—32no—
607C22×C4—31no—
608C22×C4—62no—
609C22×C4—64no—
610C22×C4—62no—
611C22×C4—62no—
612C22×C4—62no—
613C22×C4—62no—
614C22×C4—62no—
615C22×C4—62no—
616C22×C4—62no—
617C22×C4—62no—
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—24no—
656C4⋊C4—21no—
657C4⋊C4—21no—
658C4⋊C4—21no—
659C4⋊C4—21no—
660C4⋊C4—21no—
661C4⋊C4—32no—
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×C3C2×#12011yescharacteristic
689C22×C3C2×#12111yescharacteristic
690C22×C3C2×#12311yescharacteristic
691C22×C3C2×AGL(1,ℤ/8)11yescharacteristic
692C22×C3C2×#13711yescharacteristic
693C22×C3#57511yescharacteristic
694C22×C3#57511yescharacteristic
695C2×D3—22no—
696C2×D3—22no—
697C2×D3—22no—
698C2×D3—22no—
699C2×D3—22no—
700C2×D3—22no—
701C2×D3—22no—
702C2×D3—22no—
703C2×D3—22no—
704C2×D3—416no—
705C2×D3—41no—
706C2×D3—41no—
707C2×D3—41no—
708C2×D3—41no—
709C2×D3—42no—
710C2×D3—42no—
711C2×D3—42no—
712C2×D3—81no—
713C2×D3—81no—
714C2×D3—81no—
715C2×D3—81no—
716C2×D3#39414yes—
717C3×C4—41no—
718C3×C4—42no—
719C3×C4—42no—
720C3×C4—81no—
721C3×C4—81no—
722C3×C4C2×#12111yescharacteristic
723C3×C4C2×#12111yescharacteristic
724C3×C4C2×#12311yescharacteristic
725C3×C4C2×#12411yescharacteristic
726Dic3—41no—
727Dic3—42no—
728Dic3—81no—
729Dic3—81no—
730Dic3#39414yes—
731C23—21no—
732C23—21no—
733C23—21no—
734C23—21no—
735C23—21no—
736C23—21no—
737C23—32no—
738C23—32no—
739C23—32no—
740C23—32no—
741C23—68no—
742C23—61no—
743C23—61no—
744C23—61no—
745C23—61no—
746C23—61no—
747C23—61no—
748C23—61no—
749C23—61no—
750C23—61no—
751C23—61no—
752C23—62no—
753C23—124no—
754C23—124no—
755C23—124no—
756C23—124no—
757C23—124no—
758C23—124no—
759C23—121no—
760C23—121no—
761C23—121no—
762C23—121no—
763C23—121no—
764C23—121no—
765C23#91412yes—
766C23C2×D3×D411yescharacteristic
767Q8—22no—
768Q8—22no—
769Q8—41no—
770Q8—41no—
771D4—62no—
772D4—62no—
773D4—128no—
774D4—128no—
775D4—128no—
776D4—121no—
777D4—121no—
778C2×C4—21no—
779C2×C4—22no—
780C2×C4—22no—
781C2×C4—21no—
782C2×C4—21no—
783C2×C4—32no—
784C2×C4—32no—
785C2×C4—32no—
786C2×C4—34no—
787C2×C4—34no—
788C2×C4—34no—
789C2×C4—34no—
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—41no—
802C2×C4—41no—
803C2×C4—41no—
804C2×C4—61no—
805C2×C4—62no—
806C2×C4—61no—
807C2×C4—61no—
808C2×C4—124no—
809C2×C4—128no—
810C2×C4—124no—
811C2×C4—124no—
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×C3C2×#39411yescharacteristic
838C2×C3#300611yescharacteristic
839C2×C3#300711yescharacteristic
840C2×C3#305511yescharacteristic
841C2×C3#305611yescharacteristic
842C2×C3#309211yescharacteristic
843C2×C3#309311yescharacteristic
844D3—24no—
845D3—42no—
846D3—82no—
847C22—22no—
848C22—22no—
849C22—22no—
850C22—34no—
851C22—41no—
852C22—41no—
853C22—41no—
854C22—41no—
855C22—62no—
856C22—62no—
857C22—62no—
858C22—62no—
859C22—62no—
860C22—62no—
861C22—62no—
862C22—62no—
863C22—62no—
864C22—1216no—
865C22—121no—
866C22—121no—
867C22—121no—
868C22—121no—
869C22—122no—
870C22—122no—
871C22—122no—
872C22—241no—
873C22—241no—
874C22—241no—
875C22—241no—
876C22D3×#12011yescharacteristic
877C22D3×#12111yescharacteristic
878C22D3×#12311yescharacteristic
879C22C2×#91411yescharacteristic
880C22#576811yescharacteristic
881C22D3×#13711yescharacteristic
882C22#577711yescharacteristic
883C4—34no—
884C4—41no—
885C4—42no—
886C4—42no—
887C4—81no—
888C4—81no—
889C4—121no—
890C4—122no—
891C4—241no—
892C4—241no—
893C4D3×#12111yescharacteristic
894C4D3×#12111yescharacteristic
895C4D3×#12311yescharacteristic
896C4D3×#12411yescharacteristic
897C3#2348211yescharacteristic, complemented, Sylow
898C2—42no—
899C2—64no—
900C2—122no—
901C2—242no—
902C2D3×#39411yescharacteristic
903C2#8004011yescharacteristic
904C2#8022811yescharacteristic
905C2#8065711yescharacteristic
906C2#8090411yescharacteristic
907C2#8142711yescharacteristic
908C2#8151611yescharacteristic
subgroupG/H
centerC23C2×D3×D4
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC3×#2035C2
socleC23×C3C22×D4
prime radicalC2×#5627C2
hypercenter#2035D3
hypocenterC3#23482
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C23×C4 ◁ #2035

Complements

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

NH ≅ G/Ntype
2. C2×#4861C2semidirect
3. C2×#4803C2semidirect
4. C2×#4803C2semidirect
5. C2×#4726C2semidirect
6. D3×#380C2semidirect
7. C3×#2035C2semidirect
8. #71694C2semidirect
9. #70581C2semidirect
10. #70275C2semidirect
11. #70244C2semidirect
12. #69934C2semidirect
13. #69523C2semidirect
14. #68867C2semidirect
15. #68823C2semidirect
35. C2×C3×#106C22semidirect
36. C2×C3×#103C22semidirect
37. C2×C3×#103C22semidirect
40. C2×#835C22semidirect
41. C2×#835C22semidirect
44. C2×#821C22semidirect
45. C2×#821C22semidirect
48. C2×#818C22semidirect
51. C2×#809C22semidirect
52. C2×#809C22semidirect
53. C2×#808C22semidirect
54. C2×#807C22semidirect
62. C3×#340C22semidirect
63. #4551C22semidirect
64. #4529C22semidirect
65. #4529C22semidirect
75. #2035D3semidirect
143. C2×ΓL(1,𝔽25)D4semidirect
199. C2×#106C2×D3semidirect
204. C2×#103C2×D3semidirect
205. C2×#103C2×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×#56272
C2×#48612
C2×#48032
C2×#47262
D3×#3802
C3×#20352
#716942
#705812
#702752
#702442
#699342
#695232
#688672
#688232
#234823