Finite Group Databasebeta

← #10822721

Subgroups — #10822721

Order 768.

1482 conjugacy classes of subgroups.

The subgroup lattice has 886 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#5608C211yesmaximal, characteristic
2C2×#4881C211yesmaximal, characteristic, complemented
3C2×#4771C211yesmaximal, characteristic, complemented
4C2×#4772C211yesmaximal, characteristic, complemented
5C2×#4727C211yesmaximal, characteristic, complemented
6#74003C211yesmaximal, characteristic, complemented
7C3×#2033C211yesmaximal, characteristic, complemented
8#71680C211yesmaximal, characteristic, complemented
9#70635C211yesmaximal, characteristic, complemented
10#70206C211yesmaximal, characteristic, complemented
11#70176C211yesmaximal, characteristic, complemented
12#69936C211yesmaximal, characteristic, complemented
13#69527C211yesmaximal, characteristic, complemented
14D3×#340C211yesmaximal, characteristic, complemented
15#68824C211yesmaximal, characteristic, complemented
16#23485—31nomaximal, Sylow
17C22×#237C2211yescharacteristic
18C22×#235C2211yescharacteristic
19C2×C3×#121C2211yescharacteristic
20C2×#939—21no—
21C2×#938—21no—
22C2×#938C2211yescharacteristic
23C2×#924C2211yescharacteristic
24C22×ΓL(1,𝔽25)C2211yescharacteristic
25C22×D3×C8C2211yescharacteristic
26#5608—24no—
27#5608—24no—
28C2×#897C2211yescharacteristic
29C2×#892C2211yescharacteristic
30C2×D3×C4⋊C4C2211yescharacteristic
31C2×D3×C4⋊C4C2211yescharacteristic
32C2×#884—21no—
33C2×#878—21no—
34C2×C3×#107C2211yescharacteristic
35C2×C3×#102C2211yescharacteristic
36C2×C3×#102C2211yescharacteristic
37C2×C3×C22⋊C8C2211yescharacteristic
38C3×#380C2211yescharacteristic
39C2×#832C2211yescharacteristic
40C2×#832C2211yescharacteristic
41#5212C2211yescharacteristic
42C2×#830C2211yescharacteristic
43C2×(C2×D3)⋊C8C2211yescharacteristic
44C2×(C2×D3)⋊C8C2211yescharacteristic
45C2×#817C2211yescharacteristic
46C2×#816C2211yescharacteristic
47C2×#816C2211yescharacteristic
48#4987C2211yescharacteristic
49#4987C2211yescharacteristic
50C2×#810C2211yescharacteristic
51C2×#810C2211yescharacteristic
52C2×#808C2211yescharacteristic
53C2×#807C2211yescharacteristic
54#4957—21no—
55#4956—21no—
56#4881—24no—
57#4772—24no—
58#4771—24no—
59#4727—24no—
60#4665—21no—
61#4646—21no—
62C3×#340C2211yescharacteristic
63#4551C2211yescharacteristic
64#4529C2211yescharacteristic
65#4529C2211yescharacteristic
66C2×#537—31no—
67C2×#428—31no—
68C2×#417—31no—
69C2×#416—31no—
70C2×#408—31no—
71#2311—31no—
72#2036—31no—
73#2036—31no—
74#2035—31no—
75#2035—31no—
76#2034—31no—
77#2034—31no—
78#2033—31no—
79#2033D311yescharacteristic, complemented
80C2×#340—31no—
81C22×C3×D4—21no—
82C22×C3×D4C2311yescharacteristic
83C23×C3×C4C2311yescharacteristic
84C22×#67—21no—
85C22×#67—21no—
86C22×#67D411yescharacteristic
87C22×#67D411yescharacteristic
88C23×Dic3—21no—
89C2×#237—22no—
90C2×#237—22no—
91C2×#237—22no—
92C2×#237—22no—
93C2×#237—22no—
94C2×#237D414yes—
95C2×#235—22no—
96C2×#235—22no—
97C2×#235—22no—
98C2×#235—22no—
99C2×#235—22no—
100C2×#235—22no—
101C22×D12D411yescharacteristic
102C22×C4×D3—21no—
103C22×C4×D3—21no—
104C22×C4×D3C2311yescharacteristic
105C22×C4×D3C2311yescharacteristic
106C22×Dic6D411yescharacteristic
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#939—28no—
121#938—28no—
122#938—22no—
123#938—22no—
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)D414yescomplemented
143C2×D3×C8—22no—
144C2×D3×C8—22no—
145C2×D3×C8—22no—
146#897—22no—
147#897—22no—
148#892—22no—
149#892—22no—
150D3×C4⋊C4—22no—
151D3×C4⋊C4—22no—
152D3×C4⋊C4—22no—
153D3×C4⋊C4D414yes—
154#884—28no—
155#878—28no—
156C3×#107—22no—
157C3×#102—22no—
158C3×#102—22no—
159C3×C22⋊C8—22no—
160C3×#95—21no—
161#832—22no—
162#832—22no—
163C3⋊#95—21no—
164C3⋊#95—21no—
165C3⋊#95—21no—
166#830—22no—
167(C2×D3)⋊C8—22no—
168(C2×D3)⋊C8—22no—
169#817—22no—
170#816—22no—
171#816—22no—
172#810—22no—
173#810—22no—
174#808—22no—
175#807—22no—
176C22×#41—31no—
177C22×#41—31no—
178C22×M16—31no—
179C23×C8—31no—
180#537—64no—
181#537—64no—
182C2×C22⋊Q8—31no—
183C2×C22⋊Q8—31no—
184C2×C22⋊Q8—61no—
185C2×#121—31no—
186C2×#121—61no—
187C2×#121—61no—
188C2×#121—61no—
189C2×#121C2×D311yescharacteristic
190C2×#117—31no—
191C22×C4⋊C4—31no—
192C22×C4⋊C4—31no—
193#428—64no—
194C2×#107—31no—
195C2×#107C2×D311yescharacteristic
196C2×#106—31no—
197C2×#106—31no—
198#417—64no—
199#416—64no—
200C2×#103—31no—
201C2×#103—31no—
202C2×#103—31no—
203C2×#103—31no—
204C2×#102—31no—
205C2×#102—31no—
206C2×#102C2×D311yescharacteristic
207C2×#102C2×D311yescharacteristic
208#408—64no—
209C2×C22⋊C8—31no—
210C2×C22⋊C8—31no—
211C2×C22⋊C8—31no—
212C2×C22⋊C8C2×D311yescharacteristic
213#391—61no—
214#390—61no—
215#386—61no—
216#386—61no—
217#380—31no—
218#380—31no—
219#380—31no—
220#380C2×D311yescharacteristic
221#340—31no—
222#340—31no—
223#340—31no—
224#340C2×D311yescharacteristic
225C24×C3—21no—
226C24×C3C2×D411yescharacteristic
227C23×D3C2×D411yescharacteristic
228C23×D3C2×D411yescharacteristic
229C2×C3×D4—24no—
230C2×C3×D4—21no—
231C2×C3×D4—21no—
232C2×C3×D4—21no—
233C2×C3×D4—21no—
234C2×C3×D4—21no—
235C2×C3×D4—81no—
236C2×C3×D4—81no—
237C2×C3×D4C2×D412yes—
238C22×C3×C4—21no—
239C22×C3×C4—21no—
240C22×C3×C4—21no—
241C22×C3×C4—21no—
242C22×C3×C4—21no—
243C22×C3×C4—21no—
244C22×C3×C4—21no—
245C22×C3×C4—21no—
246C22×C3×C4—21no—
247C22×C3×C4C2×D411yescharacteristic
248C22×C3×C4C2411yescharacteristic
249C2×#67—24no—
250C2×#67—22no—
251C2×#67—22no—
252C2×#67—22no—
253C2×#67—24no—
254C2×#67—22no—
255C2×#67—22no—
256C2×#67—22no—
257C2×#67—42no—
258C2×#67—42no—
259C2×#67—81no—
260C2×#67—81no—
261C22×Dic3—21no—
262C22×Dic3—21no—
263C22×Dic3—24no—
264C22×Dic3—21no—
265C22×Dic3—21no—
266C22×Dic3—42no—
267C22×Dic3—42no—
268C22×Dic3C2×D411yescharacteristic
269C22×Dic3C2×D411yescharacteristic
270#237—28no—
271#237—28no—
272#237—44no—
273#237—44no—
274#235—44no—
275#235—44no—
276#235—44no—
277#235—44no—
278C2×D12—22no—
279C2×D12—22no—
280C2×D12—22no—
281C2×C4×D3—21no—
282C2×C4×D3—21no—
283C2×C4×D3—21no—
284C2×C4×D3—21no—
285C2×C4×D3—21no—
286C2×C4×D3—21no—
287C2×C4×D3—24no—
288C2×C4×D3—42no—
289C2×C4×D3—81no—
290C2×C4×D3—81no—
291C2×C4×D3—81no—
292C2×C4×D3—81no—
293C2×C4×D3C2×D412yes—
294C2×C4×D3C2×D412yes—
295C2×C4×D3C2×D412yes—
296C2×C4×D3#4112yes—
297C2×C4×D3#4112yes—
298C2×C4×D3#4112yes—
299C2×Dic6—21no—
300C2×Dic6—21no—
301C2×Dic6—21no—
302C2×Dic6—21no—
303C2×Dic6—21no—
304C2×Dic6—22no—
305C2×Dic6—22no—
306C2×Dic6—22no—
307C2×Dic6C2×D412yes—
308C2×C3×C8—21no—
309C2×C3×C8—21no—
310C2×C3×C8—21no—
311C2×C3×C8—21no—
312C2×C3×C8—21no—
313C2×C3×C8C2×D412yes—
314C3×C4⋊C4—21no—
315C3×C4⋊C4—21no—
316C3×C4⋊C4—21no—
317C3×C4⋊C4—21no—
318C3×C4⋊C4—21no—
319C3×C4⋊C4C2×D412yes—
320C3×C22⋊C4—24no—
321C3×C22⋊C4—81no—
322#217—24no—
323#217—24no—
324#217—81no—
325(C2×D3)⋊C4—24no—
326(C2×D3)⋊C4—42no—
327(C2×D3)⋊C4—81no—
328(C2×D3)⋊C4—81no—
329C4⋊Dic3—24no—
330C4⋊Dic3—21no—
331C4⋊Dic3—21no—
332C4⋊Dic3—21no—
333C4⋊Dic3—21no—
334C4⋊Dic3—21no—
335C4⋊Dic3C2×D412yes—
336Dic3⋊C4—24no—
337Dic3⋊C4—24no—
338Dic3⋊C4—42no—
339C4×Dic3—42no—
340C2×C3⋊C8—21no—
341C2×C3⋊C8—21no—
342C2×C3⋊C8—21no—
343C2×C3⋊C8—21no—
344C2×C3⋊C8—21no—
345C2×C3⋊C8C2×D412yes—
346ΓL(1,𝔽25)—28no—
347D3×C8—44no—
348C2×#41—34no—
349C2×#41—62no—
350C2×#41—62no—
351C2×#41—62no—
352C2×#41—62no—
353C2×#41—62no—
354C2×#41—62no—
355C2×#41—62no—
356C2×#41—62no—
357C2×#41—62no—
358C2×#41—62no—
359C2×#41—62no—
360C22×Q8—31no—
361C22×Q8—31no—
362C22×D4—21no—
363C22×D4—31no—
364C22×D4—31no—
365C22×D4—31no—
366C22×D4—61no—
367C22×D4—61no—
368C22×D4C22×D311yescharacteristic
369C23×C4—31no—
370C23×C4—31no—
371C23×C4—61no—
372C23×C4—61no—
373C23×C4—61no—
374C23×C4C22×D311yescharacteristic
375C2×M16—34no—
376C2×M16—62no—
377C2×M16—62no—
378C22×C8—31no—
379C22×C8—31no—
380C22×C8—62no—
381C22×C8—62no—
382C22×C8—62no—
383C22×C8C22×D311yescharacteristic
384C22×C8C22×D311yescharacteristic
385C22⋊Q8—68no—
386C22⋊Q8—62no—
387C22⋊Q8—62no—
388C22⋊Q8—62no—
389C22⋊Q8—62no—
390#121—22no—
391#121—22no—
392#121—68no—
393#121—62no—
394#121—68no—
395#121—68no—
396#121—62no—
397#117—62no—
398#117—62no—
399C2×C4⋊C4—31no—
400C2×C4⋊C4—34no—
401C2×C4⋊C4—31no—
402C2×C4⋊C4—31no—
403C2×C4⋊C4—62no—
404C2×C4⋊C4—62no—
405C2×C4⋊C4—62no—
406C2×C4⋊C4—61no—
407C2×C4⋊C4—61no—
408C2×C4⋊C4—61no—
409C2×C4⋊C4—61no—
410C2×C4⋊C4C22×D311yescharacteristic
411C2×C4⋊C4C22×D311yescharacteristic
412C2×C4⋊C4C22×D311yescharacteristic
413C2×C22⋊C4—21no—
414C2×C22⋊C4—21no—
415C2×C22⋊C4—61no—
416C2×C22⋊C4—61no—
417C2×C22⋊C4—61no—
418C2×C22⋊C4—61no—
419C2×C22⋊C4—61no—
420C2×C22⋊C4—61no—
421C2×C22⋊C4—61no—
422C2×C42—61no—
423#107—22no—
424#107—62no—
425#106—62no—
426#106—62no—
427#103—62no—
428#103—62no—
429#103—62no—
430#103—62no—
431#102—22no—
432#102—22no—
433#102—62no—
434#102—62no—
435C22⋊C8—22no—
436C22⋊C8—62no—
437C22⋊C8—62no—
438C22⋊C8—62no—
439#95—21no—
440#95—61no—
441#95—61no—
442#95—61no—
443C23×C3—21no—
444C23×C3—22no—
445C23×C3—21no—
446C23×C3—21no—
447C23×C3—21no—
448C23×C3—21no—
449C23×C3—21no—
450C23×C3—21no—
451C23×C3—41no—
452C23×C3—41no—
453C23×C3—41no—
454C23×C3—41no—
455C23×C3—41no—
456C23×C3—41no—
457C23×C3C22×D411yescharacteristic
458C22×D3—21no—
459C22×D3—21no—
460C22×D3—21no—
461C22×D3—21no—
462C22×D3—21no—
463C22×D3—21no—
464C22×D3—21no—
465C22×D3—21no—
466C22×D3—21no—
467C22×D3—21no—
468C22×D3—21no—
469C22×D3#12012yes—
470C22×D3#12112yes—
471C22×D3#12312yes—
472C3×D4—22no—
473C3×D4—22no—
474C3×D4—41no—
475C3×D4—41no—
476C3×D4—84no—
477C2×C3×C4—21no—
478C2×C3×C4—22no—
479C2×C3×C4—21no—
480C2×C3×C4—21no—
481C2×C3×C4—41no—
482C2×C3×C4—41no—
483C2×C3×C4—41no—
484C2×C3×C4—41no—
485C2×C3×C4—41no—
486C2×C3×C4—41no—
487C2×C3×C4—41no—
488C2×C3×C4—41no—
489C2×C3×C4—41no—
490C2×C3×C4—41no—
491C2×C3×C4—41no—
492C2×C3×C4—41no—
493C2×C3×C4C22×D411yescharacteristic
494C2×C3×C4C22×D411yescharacteristic
495C2×C3×C4C22×D411yescharacteristic
496C2×C3×C4C2×#4111yescharacteristic
497C2×C3×C4C2×#4111yescharacteristic
498C2×C3×C4C2×#4111yescharacteristic
499#67—44no—
500#67—48no—
501#67—44no—
502#67—84no—
503C2×Dic3—22no—
504C2×Dic3—22no—
505C2×Dic3—21no—
506C2×Dic3—21no—
507C2×Dic3—21no—
508C2×Dic3—41no—
509C2×Dic3—41no—
510C2×Dic3—41no—
511C2×Dic3—41no—
512C2×Dic3—48no—
513C2×Dic3—41no—
514C2×Dic3—41no—
515C2×Dic3—41no—
516C2×Dic3—41no—
517C2×Dic3—41no—
518C2×Dic3—41no—
519C2×Dic3#12012yes—
520C2×Dic3#12112yes—
521C2×Dic3#12312yes—
522D12—44no—
523C4×D3—41no—
524C4×D3—41no—
525C4×D3—41no—
526C4×D3—41no—
527C4×D3—84no—
528C4×D3—84no—
529C4×D3#12114yes—
530C4×D3#12114yes—
531C4×D3#12314yes—
532C4×D3#12414yes—
533Dic6—22no—
534Dic6—22no—
535Dic6—41no—
536Dic6—41no—
537Dic6—44no—
538C3×C8—22no—
539C3×C8—41no—
540C3⋊C8—22no—
541C3⋊C8—41no—
542C24—21no—
543C24—31no—
544C24—31no—
545C24D3×D411yescharacteristic
546#41—68no—
547#41—68no—
548#41—124no—
549#41—124no—
550#41—124no—
551#41—124no—
552#41—124no—
553#41—124no—
554C2×Q8—32no—
555C2×Q8—62no—
556C2×Q8—62no—
557C2×Q8—62no—
558C2×Q8—61no—
559C2×Q8—61no—
560C2×Q8—61no—
561C2×Q8—61no—
562C2×Q8—61no—
563C2×D4—24no—
564C2×D4—21no—
565C2×D4—21no—
566C2×D4—21no—
567C2×D4—21no—
568C2×D4—21no—
569C2×D4—62no—
570C2×D4—62no—
571C2×D4—62no—
572C2×D4—62no—
573C2×D4—62no—
574C2×D4—62no—
575C2×D4—62no—
576C2×D4—64no—
577C2×D4—62no—
578C2×D4—62no—
579C2×D4—64no—
580C2×D4—81no—
581C2×D4—81no—
582C2×D4—122no—
583C2×D4—122no—
584C2×D4—241no—
585C2×D4—241no—
586C2×D4D3×D412yes—
587C22×C4—21no—
588C22×C4—21no—
589C22×C4—21no—
590C22×C4—21no—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—21no—
596C22×C4—31no—
597C22×C4—32no—
598C22×C4—32no—
599C22×C4—32no—
600C22×C4—32no—
601C22×C4—32no—
602C22×C4—32no—
603C22×C4—31no—
604C22×C4—64no—
605C22×C4—64no—
606C22×C4—61no—
607C22×C4—61no—
608C22×C4—61no—
609C22×C4—61no—
610C22×C4—61no—
611C22×C4—61no—
612C22×C4—61no—
613C22×C4—61no—
614C22×C4—61no—
615C22×C4—61no—
616C22×C4—122no—
617C22×C4—122no—
618C22×C4—122no—
619C22×C4—241no—
620C22×C4—241no—
621C22×C4—241no—
622C22×C4—241no—
623C22×C4D3×D411yescharacteristic
624C22×C4C23×D311yescharacteristic
625M16—68no—
626C2×C8—21no—
627C2×C8—21no—
628C2×C8—21no—
629C2×C8—21no—
630C2×C8—21no—
631C2×C8—32no—
632C2×C8—61no—
633C2×C8—61no—
634C2×C8—61no—
635C2×C8—61no—
636C2×C8—61no—
637C2×C8—124no—
638C2×C8D3×D412yes—
639C4⋊C4—21no—
640C4⋊C4—21no—
641C4⋊C4—21no—
642C4⋊C4—21no—
643C4⋊C4—21no—
644C4⋊C4—32no—
645C4⋊C4—64no—
646C4⋊C4—64no—
647C4⋊C4—64no—
648C4⋊C4—61no—
649C4⋊C4—61no—
650C4⋊C4—61no—
651C4⋊C4—61no—
652C4⋊C4—61no—
653C4⋊C4—122no—
654C4⋊C4D3×D412yes—
655C22⋊C4—24no—
656C22⋊C4—64no—
657C22⋊C4—64no—
658C22⋊C4—64no—
659C22⋊C4—81no—
660C22⋊C4—122no—
661C22⋊C4—241no—
662C22⋊C4—241no—
663C22⋊C4—241no—
664C42—122no—
665C22×C3—41no—
666C22×C3—41no—
667C22×C3—42no—
668C22×C3—41no—
669C22×C3—42no—
670C22×C3—41no—
671C22×C3—41no—
672C22×C3—42no—
673C22×C3—41no—
674C22×C3—41no—
675C22×C3—81no—
676C22×C3—81no—
677C22×C3—81no—
678C22×C3—81no—
679C22×C3C2×#12011yescharacteristic
680C22×C3C2×#12111yescharacteristic
681C22×C3C2×#12311yescharacteristic
682C22×C3#57611yescharacteristic
683C22×C3#57711yescharacteristic
684C22×C3#57711yescharacteristic
685C22×C3#57811yescharacteristic
686C2×D3—22no—
687C2×D3—22no—
688C2×D3—22no—
689C2×D3—22no—
690C2×D3—22no—
691C2×D3—22no—
692C2×D3—41no—
693C2×D3—41no—
694C2×D3—41no—
695C2×D3—41no—
696C2×D3—41no—
697C2×D3—41no—
698C2×D3—41no—
699C2×D3#39414yes—
700C3×C4—41no—
701C3×C4—42no—
702C3×C4—81no—
703C3×C4—81no—
704C3×C4C2×#12111yescharacteristic
705C3×C4C2×#12111yescharacteristic
706C3×C4C2×#12311yescharacteristic
707C3×C4C2×#12411yescharacteristic
708Dic3—42no—
709Dic3—41no—
710Dic3—42no—
711Dic3—81no—
712Dic3—81no—
713Dic3#39414yes—
714C23—21no—
715C23—21no—
716C23—21no—
717C23—21no—
718C23—21no—
719C23—22no—
720C23—21no—
721C23—21no—
722C23—32no—
723C23—32no—
724C23—32no—
725C23—41no—
726C23—41no—
727C23—41no—
728C23—41no—
729C23—41no—
730C23—41no—
731C23—61no—
732C23—61no—
733C23—61no—
734C23—61no—
735C23—61no—
736C23—61no—
737C23—61no—
738C23—61no—
739C23—61no—
740C23—61no—
741C23—61no—
742C23C2×D3×D411yescharacteristic
743Q8—62no—
744Q8—62no—
745Q8—124no—
746Q8—121no—
747Q8—121no—
748D4—22no—
749D4—22no—
750D4—41no—
751D4—41no—
752D4—84no—
753D4—124no—
754D4—124no—
755D4—124no—
756D4—128no—
757D4—244no—
758C2×C4—21no—
759C2×C4—21no—
760C2×C4—22no—
761C2×C4—21no—
762C2×C4—32no—
763C2×C4—32no—
764C2×C4—32no—
765C2×C4—34no—
766C2×C4—34no—
767C2×C4—34no—
768C2×C4—34no—
769C2×C4—41no—
770C2×C4—41no—
771C2×C4—41no—
772C2×C4—41no—
773C2×C4—41no—
774C2×C4—41no—
775C2×C4—41no—
776C2×C4—41no—
777C2×C4—41no—
778C2×C4—41no—
779C2×C4—41no—
780C2×C4—41no—
781C2×C4—61no—
782C2×C4—62no—
783C2×C4—61no—
784C2×C4—62no—
785C2×C4—61no—
786C2×C4—128no—
787C2×C4—121no—
788C2×C4—121no—
789C2×C4—121no—
790C2×C4—121no—
791C2×C4—121no—
792C2×C4—121no—
793C2×C4—121no—
794C2×C4—121no—
795C2×C4—121no—
796C2×C4—121no—
797C2×C4—121no—
798C2×C4—121no—
799C2×C4—121no—
800C2×C4—121no—
801C2×C4—244no—
802C2×C4—244no—
803C2×C4C2×D3×D411yescharacteristic
804C2×C4C2×D3×D411yescharacteristic
805C2×C4C2×D3×D411yescharacteristic
806C2×C4D3×#4111yescharacteristic
807C2×C4D3×#4111yescharacteristic
808C2×C4D3×#4111yescharacteristic
809C8—22no—
810C8—41no—
811C8—62no—
812C8—121no—
813C2×C3—81no—
814C2×C3—82no—
815C2×C3C2×#39411yescharacteristic
816C2×C3#301211yescharacteristic
817C2×C3#301311yescharacteristic
818C2×C3#306211yescharacteristic
819C2×C3#306311yescharacteristic
820C2×C3#309811yescharacteristic
821C2×C3#309911yescharacteristic
822D3—24no—
823D3—81no—
824C22—34no—
825C22—41no—
826C22—42no—
827C22—41no—
828C22—41no—
829C22—42no—
830C22—41no—
831C22—42no—
832C22—41no—
833C22—41no—
834C22—41no—
835C22—62no—
836C22—62no—
837C22—62no—
838C22—62no—
839C22—62no—
840C22—62no—
841C22—81no—
842C22—81no—
843C22—81no—
844C22—81no—
845C22—121no—
846C22—121no—
847C22—121no—
848C22—121no—
849C22—121no—
850C22—121no—
851C22—121no—
852C22D3×#12011yescharacteristic
853C22D3×#12111yescharacteristic
854C22D3×#12311yescharacteristic
855C22#575711yescharacteristic
856C22#577011yescharacteristic
857C22#577511yescharacteristic
858C22#577911yescharacteristic
859C4—34no—
860C4—41no—
861C4—42no—
862C4—81no—
863C4—81no—
864C4—121no—
865C4—122no—
866C4—122no—
867C4—241no—
868C4—241no—
869C4D3×#12111yescharacteristic
870C4D3×#12111yescharacteristic
871C4D3×#12311yescharacteristic
872C4D3×#12411yescharacteristic
873C3#2348511yescharacteristic, complemented, Sylow
874C2—64no—
875C2—81no—
876C2—82no—
877C2—241no—
878C2D3×#39411yescharacteristic
879C2#8000511yescharacteristic
880C2#8023211yescharacteristic
881C2#8071811yescharacteristic
882C2#8081011yescharacteristic
883C2#8128511yescharacteristic
884C2#8137711yescharacteristic
subgroupG/H
centerC23C2×D3×D4
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC3×#2033C2
socleC23×C3C22×D4
prime radicalC2×#5608C2
hypercenter#2033D3
hypocenterC3#23485
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C23×C4 ◁ #2033

Complements

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

NH ≅ G/Ntype
2. C2×#4881C2semidirect
3. C2×#4771C2semidirect
4. C2×#4772C2semidirect
5. C2×#4727C2semidirect
6. #74003C2semidirect
7. C3×#2033C2semidirect
8. #71680C2semidirect
9. #70635C2semidirect
10. #70206C2semidirect
11. #70176C2semidirect
12. #69936C2semidirect
13. #69527C2semidirect
14. D3×#340C2semidirect
15. #68824C2semidirect
79. #2033D3semidirect
142. C2×ΓL(1,𝔽25)D4semidirect
873. C3#23485semidirect

Maximal subgroups

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

subgroupindex
C2×#56082
C2×#48812
C2×#47712
C2×#47722
C2×#47272
#740032
C3×#20332
#716802
#706352
#702062
#701762
#699362
#695272
D3×#3402
#688242
#234853