Finite Group Databasebeta

← #10822706

Subgroups — #10822706

Order 768.

1610 conjugacy classes of subgroups.

The subgroup lattice has 936 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#5607C211yesmaximal, characteristic
2C2×#4861C211yesmaximal, characteristic, complemented
3C2×#4770C211yesmaximal, characteristic, complemented
4C2×D3×#102C211yesmaximal, characteristic, complemented
5C2×#4727C211yesmaximal, characteristic, complemented
6#74003C211yesmaximal, characteristic, complemented
7C3×#2034C211yesmaximal, characteristic, complemented
8#71680C211yesmaximal, characteristic, complemented
9#70581C211yesmaximal, characteristic, complemented
10#70206C211yesmaximal, characteristic, complemented
11#70175C211yesmaximal, characteristic, complemented
12#69934C211yesmaximal, characteristic, complemented
13#69523C211yesmaximal, characteristic, complemented
14#68866C211yesmaximal, characteristic, complemented
15#68823C211yesmaximal, characteristic, complemented
16#23483—31nomaximal, Sylow
17C22×D3×D4C2211yescharacteristic
18C22×#235C2211yescharacteristic
19C2×C3×#121C2211yescharacteristic
20C2×#940—21no—
21C2×#938C2211yescharacteristic
22C2×#937—21no—
23C2×#930C2211yescharacteristic
24C22×ΓL(1,𝔽25)C2211yescharacteristic
25C22×D3×C8C2211yescharacteristic
26#5607—24no—
27#5607—24no—
28C2×#895C2211yescharacteristic
29C2×#892C2211yescharacteristic
30C2×#892C2211yescharacteristic
31C2×D3×C4⋊C4C2211yescharacteristic
32C2×#885—21no—
33C2×#882—21no—
34C2×C3×#106C2211yescharacteristic, complemented
35C2×C3×#102C2211yescharacteristic
36C2×C3×#102C2211yescharacteristic
37C2×C3×C22⋊C8C2211yescharacteristic, complemented
38C3×#380C2211yescharacteristic, complemented
39C2×#832C2211yescharacteristic
40C2×#832C2211yescharacteristic
41#5212C2211yescharacteristic, complemented
42C2×#830C2211yescharacteristic, complemented
43C2×#821C2211yescharacteristic
44C2×#821C2211yescharacteristic
45C2×(C2×D3)⋊C8C2211yescharacteristic, complemented
46C2×(C2×D3)⋊C8C2211yescharacteristic, complemented
47C2×#818C2211yescharacteristic, complemented
48#4987C2211yescharacteristic, complemented
49#4987C2211yescharacteristic, complemented
50C2×#809C2211yescharacteristic
51C2×#809C2211yescharacteristic
52C2×#808C2211yescharacteristic, complemented
53C2×#807C2211yescharacteristic, complemented
54#4957—21no—
55#4956—21no—
56#4861—24no—
57#4770—24no—
58D3×#102—24no—
59#4727—24no—
60#4665—21no—
61#4646—21no—
62C3×#340C2211yescharacteristic, complemented
63#4551C2211yescharacteristic, complemented
64#4529C2211yescharacteristic, complemented
65#4529C2211yescharacteristic, complemented
66C2×#535—31no—
67C2×#428—31no—
68C2×#418—31no—
69C22×#102—31no—
70C2×#408—31no—
71#2311—31no—
72#2034—31no—
73#2034—31no—
74#2034—31no—
75#2034D311yescharacteristic, complemented
76#2033—31no—
77#2033—31no—
78#2033—31no—
79#2033—31no—
80#1735—31no—
81C24×D3—21no—
82C22×C3×D4—21no—
83C22×C3×D4C2311yescharacteristic
84C23×C3×C4C2311yescharacteristic
85C22×#67—21no—
86C22×#67—21no—
87C22×#67—21no—
88C22×#67D411yescharacteristic
89C22×#67D411yescharacteristic
90C2×D3×D4—22no—
91C2×D3×D4—22no—
92C2×D3×D4—22no—
93C2×D3×D4—22no—
94C2×D3×D4—22no—
95C2×D3×D4D414yes—
96C2×#235—22no—
97C2×#235—22no—
98C2×#235—22no—
99C2×#235—22no—
100C2×#235—22no—
101C2×#235—22no—
102C22×D12—21no—
103C22×D12D411yescharacteristic
104C22×D12C2311yescharacteristic
105C22×C4×D3—21no—
106C22×C4×D3C2311yescharacteristic
107C22×C4×D3C2311yescharacteristic
108C22×Dic6D411yescharacteristic
109C22×C3×C8C2311yescharacteristic
110C22×C3×C8C2311yescharacteristic
111C3×#121—22no—
112C3×#121—22no—
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—
119C2×#217—21no—
120#940—28no—
121#938—22no—
122#938—22no—
123#937—28no—
124#930—22no—
125#930—22no—
126C2×(C2×D3)⋊C4—21no—
127C2×(C2×D3)⋊C4—21no—
128C2×(C2×D3)⋊C4—21no—
129C2×(C2×D3)⋊C4—21no—
130C2×(C2×D3)⋊C4—21no—
131C2×(C2×D3)⋊C4—21no—
132C2×C4⋊Dic3C2311yescharacteristic
133C2×C4⋊Dic3C2311yescharacteristic
134C2×C4⋊Dic3C2311yescharacteristic
135C2×Dic3⋊C4—21no—
136C2×C4×Dic3—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#895—22no—
147#895—22no—
148#892—22no—
149#892—22no—
150#892—22no—
151#892D414yes—
152D3×C4⋊C4—22no—
153D3×C4⋊C4—22no—
154#885—28no—
155#882—28no—
156C3×#106—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#821—22no—
168#821—22no—
169(C2×D3)⋊C8—22no—
170(C2×D3)⋊C8—22no—
171#818—22no—
172#809—22no—
173#809—22no—
174#808—22no—
175#807—22no—
176C22×#41—31no—
177C23×D4—31no—
178C22×M16—31no—
179C23×C8—31no—
180#535—64no—
181#535—64no—
182C2×#127—61no—
183C2×#124—61no—
184C2×#121—31no—
185C2×#121—31no—
186C2×#121—31no—
187C2×#121C2×D311yescharacteristic
188C2×#120—61no—
189C2×#120—61no—
190C2×#117—31no—
191C2×#117—31no—
192C22×C4⋊C4—31no—
193#428—64no—
194C2×#107—31no—
195C2×#107—31no—
196C2×#106—31no—
197C2×#106C2×D311yescharacteristic, complemented
198#418—64no—
199C2×#102—31no—
200C2×#102—31no—
201C2×#102—31no—
202C2×#102—31no—
203C2×#102—31no—
204C2×#102—31no—
205C2×#102—64no—
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, complemented
213#391—61no—
214#390—61no—
215#386—61no—
216#386—61no—
217#380—31no—
218#380—31no—
219#380—31no—
220#380C2×D311yescharacteristic, complemented
221#340—31no—
222#340—31no—
223#340—31no—
224#340C2×D311yescharacteristic, complemented
225C24×C3—21no—
226C24×C3C2×D411yescharacteristic
227C23×D3—21no—
228C23×D3—24no—
229C23×D3—42no—
230C23×D3—42no—
231C23×D3—81no—
232C23×D3—81no—
233C23×D3—81no—
234C23×D3—81no—
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—81no—
244C2×C3×D4—81no—
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—22no—
258C2×#67—22no—
259C2×#67—22no—
260C2×#67—24no—
261C2×#67—24no—
262C2×#67—24no—
263C2×#67—22no—
264C2×#67—22no—
265C2×#67—22no—
266C2×#67—42no—
267C2×#67—42no—
268C2×#67—81no—
269C2×#67—81no—
270C2×#67—81no—
271C2×#67—81no—
272C22×Dic3—21no—
273C22×Dic3—21no—
274C22×Dic3—21no—
275C22×Dic3C2×D411yescharacteristic
276C22×Dic3C2×D411yescharacteristic
277D3×D4—28no—
278D3×D4—28no—
279D3×D4—44no—
280D3×D4—44no—
281#235—44no—
282#235—44no—
283#235—44no—
284#235—44no—
285C2×D12—21no—
286C2×D12—21no—
287C2×D12—21no—
288C2×D12—21no—
289C2×D12—22no—
290C2×D12—22no—
291C2×D12—22no—
292C2×D12—21no—
293C2×D12—24no—
294C2×D12—81no—
295C2×D12—81no—
296C2×D12C2×D412yes—
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×C4×D3—42no—
304C2×C4×D3—81no—
305C2×C4×D3—81no—
306C2×C4×D3C2×D412yes—
307C2×C4×D3C2×D412yes—
308C2×C4×D3C2×D412yes—
309C2×C4×D3#4112yes—
310C2×C4×D3#4112yes—
311C2×C4×D3#4112yes—
312C2×Dic6—22no—
313C2×Dic6—22no—
314C2×Dic6—22no—
315C2×C3×C8—21no—
316C2×C3×C8—21no—
317C2×C3×C8—21no—
318C2×C3×C8—21no—
319C2×C3×C8—21no—
320C2×C3×C8C2×D412yes—
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×C22⋊C4—81no—
329#217—24no—
330#217—81no—
331(C2×D3)⋊C4—24no—
332(C2×D3)⋊C4—24no—
333(C2×D3)⋊C4—24no—
334(C2×D3)⋊C4—42no—
335(C2×D3)⋊C4—81no—
336(C2×D3)⋊C4—81no—
337C4⋊Dic3—21no—
338C4⋊Dic3—21no—
339C4⋊Dic3—21no—
340C4⋊Dic3—21no—
341C4⋊Dic3—21no—
342C4⋊Dic3C2×D412yes—
343Dic3⋊C4—42no—
344C4×Dic3—24no—
345C4×Dic3—42no—
346C2×C3⋊C8—21no—
347C2×C3⋊C8—21no—
348C2×C3⋊C8—21no—
349C2×C3⋊C8—21no—
350C2×C3⋊C8—21no—
351C2×C3⋊C8C2×D412yes—
352ΓL(1,𝔽25)—28no—
353D3×C8—44no—
354C25—61no—
355C2×#41—62no—
356C2×#41—62no—
357C2×#41—62no—
358C2×#41—62no—
359C2×#41—62no—
360C2×#41—62no—
361C22×Q8—31no—
362C22×D4—21no—
363C22×D4—34no—
364C22×D4—31no—
365C22×D4—31no—
366C22×D4—31no—
367C22×D4—31no—
368C22×D4—61no—
369C22×D4—62no—
370C22×D4—62no—
371C22×D4—62no—
372C22×D4—62no—
373C22×D4—62no—
374C22×D4—61no—
375C22×D4—61no—
376C22×D4—61no—
377C22×D4C22×D311yescharacteristic
378C23×C4—31no—
379C23×C4—31no—
380C23×C4—61no—
381C23×C4C22×D311yescharacteristic
382C2×M16—34no—
383C2×M16—62no—
384C2×M16—62no—
385C22×C8—31no—
386C22×C8—31no—
387C22×C8—62no—
388C22×C8—62no—
389C22×C8—62no—
390C22×C8C22×D311yescharacteristic
391C22×C8C22×D311yescharacteristic
392#127—68no—
393#124—68no—
394#121—22no—
395#121—22no—
396#121—62no—
397#121—62no—
398#121—62no—
399#121—62no—
400#121—62no—
401#121—62no—
402#120—68no—
403#120—68no—
404#117—34no—
405#117—62no—
406#117—62no—
407#117—62no—
408C2×C4⋊C4—31no—
409C2×C4⋊C4—31no—
410C2×C4⋊C4—31no—
411C2×C4⋊C4—62no—
412C2×C4⋊C4—62no—
413C2×C4⋊C4—61no—
414C2×C4⋊C4C22×D311yescharacteristic
415C2×C4⋊C4C22×D311yescharacteristic
416C2×C4⋊C4C22×D311yescharacteristic
417C2×C22⋊C4—21no—
418C2×C22⋊C4—21no—
419C2×C22⋊C4—61no—
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×C42—61no—
428C2×C42—61no—
429#107—62no—
430#107—62no—
431#106—22no—
432#106—62no—
433#102—22no—
434#102—22no—
435#102—62no—
436#102—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—22no—
450C23×C3—21no—
451C23×C3—21no—
452C23×C3—21no—
453C23×C3—21no—
454C23×C3—21no—
455C23×C3—21no—
456C23×C3—21no—
457C23×C3—41no—
458C23×C3—41no—
459C23×C3—41no—
460C23×C3—41no—
461C23×C3—41no—
462C23×C3—41no—
463C23×C3C22×D411yescharacteristic
464C22×D3—21no—
465C22×D3—21no—
466C22×D3—21no—
467C22×D3—21no—
468C22×D3—22no—
469C22×D3—21no—
470C22×D3—21no—
471C22×D3—21no—
472C22×D3—21no—
473C22×D3—21no—
474C22×D3—21no—
475C22×D3—21no—
476C22×D3—41no—
477C22×D3—41no—
478C22×D3—41no—
479C22×D3—41no—
480C22×D3—41no—
481C22×D3—41no—
482C22×D3—48no—
483C22×D3—84no—
484C22×D3—84no—
485C22×D3—84no—
486C22×D3—84no—
487C22×D3—84no—
488C22×D3—84no—
489C22×D3#12012yes—
490C22×D3#12112yes—
491C22×D3#12312yes—
492C3×D4—22no—
493C3×D4—22no—
494C3×D4—41no—
495C3×D4—41no—
496C3×D4—84no—
497C2×C3×C4—22no—
498C2×C3×C4—21no—
499C2×C3×C4—21no—
500C2×C3×C4—21no—
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×C4—41no—
509C2×C3×C4—41no—
510C2×C3×C4—41no—
511C2×C3×C4—41no—
512C2×C3×C4—41no—
513C2×C3×C4C22×D411yescharacteristic
514C2×C3×C4C22×D411yescharacteristic
515C2×C3×C4C22×D411yescharacteristic
516C2×C3×C4C2×#4111yescharacteristic
517C2×C3×C4C2×#4111yescharacteristic
518C2×C3×C4C2×#4111yescharacteristic
519#67—44no—
520#67—44no—
521#67—48no—
522#67—84no—
523#67—84no—
524C2×Dic3—22no—
525C2×Dic3—21no—
526C2×Dic3—21no—
527C2×Dic3—21no—
528C2×Dic3—41no—
529C2×Dic3—41no—
530C2×Dic3—41no—
531C2×Dic3—41no—
532C2×Dic3—41no—
533C2×Dic3—41no—
534C2×Dic3—41no—
535C2×Dic3—41no—
536C2×Dic3#12012yes—
537C2×Dic3#12112yes—
538C2×Dic3#12312yes—
539D12—22no—
540D12—22no—
541D12—44no—
542D12—41no—
543D12—41no—
544D12—84no—
545C4×D3—41no—
546C4×D3—41no—
547C4×D3—41no—
548C4×D3—41no—
549C4×D3—84no—
550C4×D3#12114yes—
551C4×D3#12114yes—
552C4×D3#12314yes—
553C4×D3#12414yes—
554Dic6—44no—
555C3×C8—22no—
556C3×C8—41no—
557C3⋊C8—22no—
558C3⋊C8—41no—
559C24—21no—
560C24—31no—
561C24—31no—
562C24—64no—
563C24—61no—
564C24—122no—
565C24—122no—
566C24—241no—
567C24—241no—
568C24—241no—
569C24—241no—
570C24D3×D411yescharacteristic
571#41—124no—
572#41—124no—
573#41—124no—
574#41—124no—
575C2×Q8—62no—
576C2×Q8—62no—
577C2×Q8—62no—
578C2×D4—24no—
579C2×D4—21no—
580C2×D4—21no—
581C2×D4—21no—
582C2×D4—21no—
583C2×D4—21no—
584C2×D4—32no—
585C2×D4—62no—
586C2×D4—62no—
587C2×D4—62no—
588C2×D4—64no—
589C2×D4—68no—
590C2×D4—68no—
591C2×D4—64no—
592C2×D4—62no—
593C2×D4—62no—
594C2×D4—62no—
595C2×D4—62no—
596C2×D4—62no—
597C2×D4—62no—
598C2×D4—64no—
599C2×D4—64no—
600C2×D4—61no—
601C2×D4—61no—
602C2×D4—61no—
603C2×D4—61no—
604C2×D4—61no—
605C2×D4—81no—
606C2×D4—81no—
607C2×D4—124no—
608C2×D4—124no—
609C2×D4—122no—
610C2×D4—122no—
611C2×D4—241no—
612C2×D4—241no—
613C2×D4—241no—
614C2×D4—241no—
615C2×D4—241no—
616C2×D4—241no—
617C2×D4D3×D412yes—
618C22×C4—21no—
619C22×C4—21no—
620C22×C4—21no—
621C22×C4—21no—
622C22×C4—21no—
623C22×C4—21no—
624C22×C4—21no—
625C22×C4—21no—
626C22×C4—21no—
627C22×C4—31no—
628C22×C4—32no—
629C22×C4—32no—
630C22×C4—32no—
631C22×C4—32no—
632C22×C4—32no—
633C22×C4—32no—
634C22×C4—31no—
635C22×C4—61no—
636C22×C4—61no—
637C22×C4—61no—
638C22×C4—61no—
639C22×C4—61no—
640C22×C4—61no—
641C22×C4—61no—
642C22×C4—61no—
643C22×C4—61no—
644C22×C4—122no—
645C22×C4—241no—
646C22×C4—241no—
647C22×C4D3×D411yescharacteristic
648C22×C4C23×D311yescharacteristic
649M16—68no—
650C2×C8—21no—
651C2×C8—21no—
652C2×C8—21no—
653C2×C8—21no—
654C2×C8—21no—
655C2×C8—32no—
656C2×C8—61no—
657C2×C8—61no—
658C2×C8—61no—
659C2×C8—61no—
660C2×C8—61no—
661C2×C8—124no—
662C2×C8D3×D412yes—
663C4⋊C4—21no—
664C4⋊C4—21no—
665C4⋊C4—21no—
666C4⋊C4—21no—
667C4⋊C4—21no—
668C4⋊C4—32no—
669C4⋊C4—61no—
670C4⋊C4—61no—
671C4⋊C4—61no—
672C4⋊C4—61no—
673C4⋊C4—61no—
674C4⋊C4—122no—
675C4⋊C4D3×D412yes—
676C22⋊C4—24no—
677C22⋊C4—64no—
678C22⋊C4—64no—
679C22⋊C4—64no—
680C22⋊C4—64no—
681C22⋊C4—81no—
682C22⋊C4—122no—
683C22⋊C4—241no—
684C22⋊C4—241no—
685C22⋊C4—241no—
686C42—64no—
687C42—122no—
688C22×C3—41no—
689C22×C3—41no—
690C22×C3—41no—
691C22×C3—42no—
692C22×C3—41no—
693C22×C3—42no—
694C22×C3—41no—
695C22×C3—42no—
696C22×C3—41no—
697C22×C3—41no—
698C22×C3—81no—
699C22×C3—81no—
700C22×C3—81no—
701C22×C3—81no—
702C22×C3C2×#12011yescharacteristic
703C22×C3C2×#12111yescharacteristic
704C22×C3C2×#12311yescharacteristic
705C22×C3#57611yescharacteristic
706C22×C3#57611yescharacteristic
707C22×C3#57711yescharacteristic
708C22×C3#57711yescharacteristic
709C2×D3—22no—
710C2×D3—22no—
711C2×D3—22no—
712C2×D3—22no—
713C2×D3—22no—
714C2×D3—22no—
715C2×D3—41no—
716C2×D3—41no—
717C2×D3—41no—
718C2×D3—42no—
719C2×D3—41no—
720C2×D3—42no—
721C2×D3—41no—
722C2×D3—42no—
723C2×D3—41no—
724C2×D3—41no—
725C2×D3—816no—
726C2×D3—81no—
727C2×D3—81no—
728C2×D3—81no—
729C2×D3—81no—
730C2×D3#39414yes—
731C3×C4—41no—
732C3×C4—42no—
733C3×C4—81no—
734C3×C4—81no—
735C3×C4C2×#12111yescharacteristic
736C3×C4C2×#12111yescharacteristic
737C3×C4C2×#12311yescharacteristic
738C3×C4C2×#12411yescharacteristic
739Dic3—41no—
740Dic3—42no—
741Dic3—81no—
742Dic3—81no—
743Dic3#39414yes—
744C23—21no—
745C23—21no—
746C23—21no—
747C23—21no—
748C23—21no—
749C23—22no—
750C23—21no—
751C23—21no—
752C23—32no—
753C23—32no—
754C23—32no—
755C23—41no—
756C23—41no—
757C23—41no—
758C23—41no—
759C23—41no—
760C23—41no—
761C23—61no—
762C23—61no—
763C23—61no—
764C23—61no—
765C23—61no—
766C23—61no—
767C23—61no—
768C23—61no—
769C23—61no—
770C23—62no—
771C23—61no—
772C23—61no—
773C23—128no—
774C23—121no—
775C23—121no—
776C23—121no—
777C23—121no—
778C23—121no—
779C23—121no—
780C23—244no—
781C23—244no—
782C23—244no—
783C23—244no—
784C23—244no—
785C23—244no—
786C23C2×D3×D411yescharacteristic
787Q8—124no—
788D4—22no—
789D4—22no—
790D4—41no—
791D4—41no—
792D4—62no—
793D4—62no—
794D4—84no—
795D4—128no—
796D4—124no—
797D4—124no—
798D4—124no—
799D4—121no—
800D4—121no—
801D4—244no—
802D4—244no—
803D4—244no—
804C2×C4—21no—
805C2×C4—22no—
806C2×C4—21no—
807C2×C4—21no—
808C2×C4—32no—
809C2×C4—32no—
810C2×C4—32no—
811C2×C4—34no—
812C2×C4—34no—
813C2×C4—34no—
814C2×C4—34no—
815C2×C4—41no—
816C2×C4—41no—
817C2×C4—41no—
818C2×C4—41no—
819C2×C4—41no—
820C2×C4—41no—
821C2×C4—41no—
822C2×C4—41no—
823C2×C4—41no—
824C2×C4—41no—
825C2×C4—41no—
826C2×C4—41no—
827C2×C4—61no—
828C2×C4—62no—
829C2×C4—61no—
830C2×C4—61no—
831C2×C4—121no—
832C2×C4—121no—
833C2×C4—121no—
834C2×C4—121no—
835C2×C4—121no—
836C2×C4—121no—
837C2×C4—121no—
838C2×C4—121no—
839C2×C4—121no—
840C2×C4—121no—
841C2×C4—121no—
842C2×C4—121no—
843C2×C4—244no—
844C2×C4C2×D3×D411yescharacteristic
845C2×C4C2×D3×D411yescharacteristic
846C2×C4C2×D3×D411yescharacteristic
847C2×C4D3×#4111yescharacteristic
848C2×C4D3×#4111yescharacteristic
849C2×C4D3×#4111yescharacteristic
850C8—22no—
851C8—41no—
852C8—62no—
853C8—121no—
854C2×C3—82no—
855C2×C3—81no—
856C2×C3C2×#39411yescharacteristic
857C2×C3#300811yescharacteristic
858C2×C3#300911yescharacteristic
859C2×C3#306211yescharacteristic
860C2×C3#306211yescharacteristic
861C2×C3#309611yescharacteristic
862C2×C3#309611yescharacteristic
863D3—24no—
864D3—81no—
865D3—82no—
866C22—34no—
867C22—41no—
868C22—42no—
869C22—41no—
870C22—41no—
871C22—42no—
872C22—41no—
873C22—41no—
874C22—42no—
875C22—41no—
876C22—41no—
877C22—62no—
878C22—62no—
879C22—62no—
880C22—62no—
881C22—62no—
882C22—62no—
883C22—81no—
884C22—81no—
885C22—81no—
886C22—81no—
887C22—121no—
888C22—122no—
889C22—121no—
890C22—121no—
891C22—122no—
892C22—121no—
893C22—121no—
894C22—122no—
895C22—121no—
896C22—121no—
897C22—2416no—
898C22—241no—
899C22—241no—
900C22—241no—
901C22—241no—
902C22D3×#12011yescharacteristic
903C22D3×#12111yescharacteristic
904C22D3×#12311yescharacteristic
905C22#576211yescharacteristic
906C22#576911yescharacteristic
907C22#577411yescharacteristic
908C22#577511yescharacteristic
909C4—34no—
910C4—42no—
911C4—41no—
912C4—81no—
913C4—81no—
914C4—121no—
915C4—122no—
916C4—241no—
917C4—241no—
918C4D3×#12111yescharacteristic
919C4D3×#12111yescharacteristic
920C4D3×#12311yescharacteristic
921C4D3×#12411yescharacteristic
922C3#2348311yescharacteristic, complemented, Sylow
923C2—64no—
924C2—81no—
925C2—82no—
926C2—241no—
927C2—242no—
928C2D3×#39411yescharacteristic
929C2#8008511yescharacteristic
930C2#8014811yescharacteristic
931C2#8066111yescharacteristic
932C2#8086711yescharacteristic
933C2#8132711yescharacteristic
934C2#8137411yescharacteristic
subgroupG/H
centerC23C2×D3×D4
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC3×#2034C2
socleC23×C3C22×D4
prime radicalC2×#5607C2
hypercenter#2034D3
hypocenterC3#23483
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×#4770C2semidirect
4. C2×D3×#102C2semidirect
5. C2×#4727C2semidirect
6. #74003C2semidirect
7. C3×#2034C2semidirect
8. #71680C2semidirect
9. #70581C2semidirect
10. #70206C2semidirect
11. #70175C2semidirect
12. #69934C2semidirect
13. #69523C2semidirect
14. #68866C2semidirect
15. #68823C2semidirect
34. C2×C3×#106C22semidirect
37. C2×C3×C22⋊C8C22semidirect
38. C3×#380C22semidirect
41. #5212C22semidirect
42. C2×#830C22semidirect
45. C2×(C2×D3)⋊C8C22semidirect
46. C2×(C2×D3)⋊C8C22semidirect
47. C2×#818C22semidirect
48. #4987C22semidirect
49. #4987C22semidirect
52. C2×#808C22semidirect
53. C2×#807C22semidirect
62. C3×#340C22semidirect
63. #4551C22semidirect
64. #4529C22semidirect
65. #4529C22semidirect
75. #2034D3semidirect
142. C2×ΓL(1,𝔽25)D4semidirect
197. C2×#106C2×D3semidirect
212. C2×C22⋊C8C2×D3semidirect
220. #380C2×D3semidirect
224. #340C2×D3semidirect
922. C3#23483semidirect

Maximal subgroups

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

subgroupindex
C2×#56072
C2×#48612
C2×#47702
C2×D3×#1022
C2×#47272
#740032
C3×#20342
#716802
#705812
#702062
#701752
#699342
#695232
#688662
#688232
#234833