Finite Group Databasebeta

← #10846068

Subgroups — #10846068

Order 768.

1118 conjugacy classes of subgroups.

The subgroup lattice has 834 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#466C211yesmaximal, characteristic, complemented
2C2×#5153C211yesmaximal, characteristic, complemented
3C2×#5111C211yesmaximal, characteristic, complemented
4#82668C211yesmaximal, characteristic, complemented
5#82667C211yesmaximal, characteristic, complemented
6C2×#4780C211yesmaximal, characteristic, complemented
7#72043C211yesmaximal, characteristic, complemented
8#71972C211yesmaximal, characteristic, complemented
9#71685C211yesmaximal, characteristic, complemented
10#71679C211yesmaximal, characteristic, complemented
11#70635C211yesmaximal, characteristic, complemented
12#70615C211yesmaximal, characteristic, complemented
13#70203C211yesmaximal, characteristic, complemented
14#70159C211yesmaximal, characteristic, complemented
15#70152C211yesmaximal, characteristic, complemented
16#25397—31nomaximal, Sylow
17C22×C3×D8C2211yescharacteristic
18C23×C3×C8C2211yescharacteristic
19C2×C3×#121C2211yescharacteristic
20C2×C3×#121C2211yescharacteristic
21C2×#939—21no—
22C2×#938C2211yescharacteristic
23C2×#938C2211yescharacteristic
24C2×#936C2211yescharacteristic
25C2×D4×Dic3C2211yescharacteristic
26C22×#214C2211yescharacteristic
27C2×C4×#67C2211yescharacteristic
28C2×#924C2211yescharacteristic
29C22×ΓL(1,𝔽25)C2211yescharacteristic
30C2×#897C2211yescharacteristic
31C3×#466—24no—
32C2×C3×#107C2211yescharacteristic
33C2×C3×#102C2211yescharacteristic
34C2×C3×#102C2211yescharacteristic
35#5223—21no—
36#5222—21no—
37#5221—21no—
38C2×#832C2211yescharacteristic
39C2×#832C2211yescharacteristic
40C2×#832C2211yescharacteristic
41#5212C2211yescharacteristic
42C2×#830C2211yescharacteristic
43#5153—24no—
44#5111—24no—
45C2×(C2×D3)⋊C8C2211yescharacteristic
46C2×#816C2211yescharacteristic
47C2×#816C2211yescharacteristic
48C2×#815C2211yescharacteristic
49C2×Dic3⋊C8C2211yescharacteristic
50#4987C2211yescharacteristic
51#4975C2211yescharacteristic
52Dic3×C4⋊C4C2211yescharacteristic
53C2×#810C2211yescharacteristic
54C2×#807C2211yescharacteristic
55#4959—21no—
56#4957—21no—
57#4949—21no—
58#4942—21no—
59#4780—24no—
60#4551C2211yescharacteristic
61#4551C2211yescharacteristic
62#4529C2211yescharacteristic
63#4529C2211yescharacteristic
64C2×#468—31no—
65C2×#466D311yescharacteristic, complemented
66C2×#463—31no—
67C2×#435—31no—
68#2540—31no—
69#2537—31no—
70#2036—31no—
71#2033—31no—
72#2000—31no—
73#1999—31no—
74#1959—31no—
75#1947—31no—
76#1895—31no—
77#1892—31no—
78#1762—31no—
79C22×C3×D4—21no—
80C22×C3×D4—21no—
81C22×C3×D4C2311yescharacteristic
82C22×C3×D4C2311yescharacteristic
83C23×C3×C4C2311yescharacteristic
84C22×#67—21no—
85C22×#67—21no—
86C22×#67D411yescharacteristic
87C23×Dic3—21no—
88C22×C4×D3C2311yescharacteristic
89C22×Dic6C2311yescharacteristic
90C2×C3×D8—22no—
91C2×C3×D8—22no—
92C2×C3×D8—41no—
93C22×C3×C8—22no—
94C22×C3×C8—22no—
95C22×C3×C8—41no—
96C22×C3×C8C2311yescharacteristic
97C22×C3×C8C2311yescharacteristic
98C3×#121—22no—
99C3×#121—22no—
100C3×#121—41no—
101C3×#121—41no—
102C2×C3×C4⋊C4C2311yescharacteristic
103C2×C3×C4⋊C4C2311yescharacteristic
104C2×C3×C22⋊C4—21no—
105C2×C3×C22⋊C4—21no—
106C2×#217—21no—
107C2×#217—21no—
108C2×#217—21no—
109C2×#217—21no—
110C2×#217—21no—
111C2×#217—21no—
112C2×#217—21no—
113C2×#217D411yescharacteristic
114#939—44no—
115#938—22no—
116#938—22no—
117#938—41no—
118#938—41no—
119#936—22no—
120#936—22no—
121D4×Dic3—22no—
122D4×Dic3—22no—
123C2×#214—22no—
124C2×#214—22no—
125C2×#214—41no—
126C4×#67—22no—
127C4×#67—22no—
128C2×(C2×D3)⋊C4—21no—
129C2×(C2×D3)⋊C4—21no—
130C2×(C2×D3)⋊C4D411yescharacteristic
131C2×C4⋊Dic3—21no—
132C2×C4⋊Dic3C2311yescharacteristic
133C2×C4⋊Dic3C2311yescharacteristic
134C2×C4⋊Dic3C2311yescharacteristic
135#924—22no—
136#924—41no—
137C2×Dic3⋊C4—21no—
138C2×Dic3⋊C4—21no—
139C2×Dic3⋊C4—21no—
140C2×Dic3⋊C4D411yescharacteristic
141C2×C4×Dic3—21no—
142C2×C4×Dic3C2311yescharacteristic
143C22×C3⋊C8C2311yescharacteristic
144C22×C3⋊C8C2311yescharacteristic
145C2×ΓL(1,𝔽25)—22no—
146C2×ΓL(1,𝔽25)—22no—
147C2×ΓL(1,𝔽25)—41no—
148#897—22no—
149#897—41no—
150C3×#107—22no—
151C3×#102—22no—
152C3×#102D414yescomplemented
153#832—22no—
154#832—22no—
155#832—41no—
156C3⋊#95—21no—
157C3⋊#95—21no—
158C3⋊#95—21no—
159#830—22no—
160(C2×D3)⋊C8—22no—
161#816—22no—
162#816—22no—
163#815—22no—
164Dic3⋊C8D414yescomplemented
165#810—41no—
166#807—22no—
167C22×SD16—31no—
168C22×D8C2×D311yescharacteristic
169C22×M16—31no—
170C23×C8C2×D311yescharacteristic
171C2×#124—31no—
172C2×C22⋊Q8—31no—
173C2×C22⋊Q8—31no—
174C2×#121—31no—
175C2×#121—31no—
176C2×#121—61no—
177C2×#121C2×D311yescharacteristic
178C2×#121C2×D311yescharacteristic
179C2×C4×D4—31no—
180C2×C4×D4—31no—
181#468—64no—
182#466—24no—
183#463—64no—
184#435—64no—
185C2×#107—31no—
186C2×#107C2×D311yescharacteristic
187C2×C4⋊C8—31no—
188C2×#103—31no—
189C2×#103—31no—
190C2×#103—31no—
191C2×#102—31no—
192C2×#102—31no—
193C2×#102—31no—
194C2×#102C2×D311yescharacteristic
195C2×#102C2×D311yescharacteristic
196C2×C22⋊C8—31no—
197C2×C22⋊C8—31no—
198C2×#97—31no—
199#399—61no—
200#394—61no—
201#394—61no—
202#392—61no—
203#390—61no—
204#390—61no—
205#384—31no—
206#380—31no—
207#380—31no—
208#380—61no—
209C4×C4⋊C4—31no—
210#340—31no—
211#340—31no—
212#340—31no—
213#340—31no—
214C24×C3—21no—
215C24×C3—21no—
216C24×C3C2×D411yescharacteristic
217C23×D3C2×D411yescharacteristic
218C2×C3×D4—21no—
219C2×C3×D4—21no—
220C2×C3×D4—21no—
221C2×C3×D4—21no—
222C2×C3×D4—21no—
223C2×C3×D4—21no—
224C2×C3×D4—21no—
225C2×C3×D4—21no—
226C2×C3×D4—21no—
227C2×C3×D4—21no—
228C2×C3×D4—21no—
229C2×C3×D4—42no—
230C2×C3×D4—42no—
231C2×C3×D4—42no—
232C2×C3×D4—42no—
233C2×C3×D4—81no—
234C2×C3×D4—81no—
235C2×C3×D4C2×D412yes—
236C22×C3×C4—21no—
237C22×C3×C4—21no—
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×C4C2×D411yescharacteristic
245C22×C3×C4C2411yescharacteristic
246C2×#67—22no—
247C2×#67—22no—
248C2×#67—41no—
249C2×#67—42no—
250C2×#67—42no—
251C2×#67—42no—
252C2×#67—42no—
253C2×#67—81no—
254C2×#67—81no—
255C22×Dic3—21no—
256C22×Dic3—21no—
257C22×Dic3—21no—
258C22×Dic3—21no—
259C22×Dic3—42no—
260C22×Dic3—42no—
261C22×Dic3—42no—
262C22×Dic3C2×D411yescharacteristic
263C22×Dic3C2×D411yescharacteristic
264C22×Dic3C2×D411yescharacteristic
265C2×C4×D3—21no—
266C2×C4×D3—21no—
267C2×C4×D3—21no—
268C2×C4×D3—21no—
269C2×C4×D3—21no—
270C2×C4×D3—21no—
271C2×Dic6—21no—
272C2×Dic6—21no—
273C2×Dic6—21no—
274C2×Dic6—21no—
275C2×Dic6—21no—
276C2×Dic6—21no—
277C3×D8—44no—
278C2×C3×C8—21no—
279C2×C3×C8—21no—
280C2×C3×C8—21no—
281C2×C3×C8—21no—
282C2×C3×C8—44no—
283C2×C3×C8C2×D412yes—
284C2×C3×C8C2×D412yes—
285C3×C4⋊C4—21no—
286C3×C4⋊C4—21no—
287C3×C4⋊C4—21no—
288C3×C4⋊C4C2×D412yes—
289C3×C22⋊C4—42no—
290C3×C22⋊C4—42no—
291#217—22no—
292#217—42no—
293#217—42no—
294#217—42no—
295#217—42no—
296#217—42no—
297#217—42no—
298#217—42no—
299#214—44no—
300(C2×D3)⋊C4—22no—
301(C2×D3)⋊C4—42no—
302(C2×D3)⋊C4—42no—
303C4⋊Dic3—21no—
304C4⋊Dic3—21no—
305C4⋊Dic3—21no—
306C4⋊Dic3—21no—
307C4⋊Dic3—21no—
308C4⋊Dic3—42no—
309C4⋊Dic3#4112yes—
310Dic3⋊C4—22no—
311Dic3⋊C4—42no—
312Dic3⋊C4—42no—
313Dic3⋊C4—81no—
314C4×Dic3—81no—
315C4×Dic3C2×D412yes—
316C4×Dic3#4112yes—
317C2×C3⋊C8—21no—
318C2×C3⋊C8—21no—
319C2×C3⋊C8—21no—
320C2×C3⋊C8—21no—
321C2×C3⋊C8—21no—
322C2×C3⋊C8C2×D412yes—
323ΓL(1,𝔽25)—44no—
324C22×Q8—31no—
325C22×D4—21no—
326C22×D4—21no—
327C22×D4—31no—
328C22×D4—61no—
329C22×D4—61no—
330C22×D4C22×D311yescharacteristic
331C22×D4C22×D311yescharacteristic
332C23×C4—31no—
333C23×C4—61no—
334C23×C4C22×D311yescharacteristic
335C2×SD16—62no—
336C2×SD16—62no—
337C2×SD16—121no—
338C2×D8—22no—
339C2×D8—22no—
340C2×D8—41no—
341C2×M16—62no—
342C2×M16—62no—
343C2×M16—121no—
344C22×C8—22no—
345C22×C8—22no—
346C22×C8—31no—
347C22×C8—31no—
348C22×C8—41no—
349C22×C8C22×D311yescharacteristic
350C22×C8C22×D311yescharacteristic
351#124—62no—
352#124—62no—
353C22⋊Q8—62no—
354C22⋊Q8—62no—
355C22⋊Q8—121no—
356C22⋊Q8—121no—
357#121—22no—
358#121—22no—
359#121—41no—
360#121—41no—
361#121—62no—
362#121—62no—
363#121—121no—
364#121—121no—
365#121—124no—
366C4×D4—62no—
367C4×D4—62no—
368C4×D4—62no—
369C4×D4—62no—
370C2×C4⋊C4—31no—
371C2×C4⋊C4—31no—
372C2×C4⋊C4—31no—
373C2×C4⋊C4—31no—
374C2×C4⋊C4—61no—
375C2×C4⋊C4—61no—
376C2×C4⋊C4—61no—
377C2×C4⋊C4—61no—
378C2×C4⋊C4C22×D311yescharacteristic
379C2×C4⋊C4C22×D311yescharacteristic
380C2×C22⋊C4—21no—
381C2×C22⋊C4—21no—
382C2×C22⋊C4—31no—
383C2×C22⋊C4—31no—
384C2×C22⋊C4—61no—
385C2×C22⋊C4—61no—
386C2×C22⋊C4—61no—
387C2×C22⋊C4—61no—
388C2×C22⋊C4—61no—
389C2×C22⋊C4—61no—
390C2×C22⋊C4—61no—
391C2×C22⋊C4—61no—
392C2×C22⋊C4—61no—
393C2×C42—31no—
394C2×C42—61no—
395#107—22no—
396#107—62no—
397C4⋊C8—34no—
398#103—62no—
399#103—62no—
400#103—121no—
401#102—22no—
402#102—62no—
403#102—62no—
404#102—121no—
405#102#6714yescomplemented
406C22⋊C8—62no—
407C22⋊C8—62no—
408#97—62no—
409#95—61no—
410#95—61no—
411#95—61no—
412C23×C3—21no—
413C23×C3—21no—
414C23×C3—21no—
415C23×C3—21no—
416C23×C3—21no—
417C23×C3—21no—
418C23×C3—22no—
419C23×C3—41no—
420C23×C3—41no—
421C23×C3—41no—
422C23×C3—41no—
423C23×C3—41no—
424C23×C3—41no—
425C23×C3—41no—
426C23×C3—41no—
427C23×C3—41no—
428C23×C3—41no—
429C23×C3—41no—
430C23×C3—41no—
431C23×C3—41no—
432C23×C3AGL(1,ℤ/8)12yes—
433C23×C3C22×D411yescharacteristic
434C22×D3—21no—
435C22×D3—21no—
436C22×D3—21no—
437C22×D3—21no—
438C22×D3—21no—
439C22×D3—21no—
440C22×D3—21no—
441C3×D4—22no—
442C3×D4—22no—
443C3×D4—41no—
444C3×D4—41no—
445C3×D4—41no—
446C3×D4—41no—
447C3×D4—41no—
448C3×D4—41no—
449C3×D4—84no—
450C3×D4—84no—
451C2×C3×C4—21no—
452C2×C3×C4—22no—
453C2×C3×C4—21no—
454C2×C3×C4—21no—
455C2×C3×C4—41no—
456C2×C3×C4—41no—
457C2×C3×C4—41no—
458C2×C3×C4—41no—
459C2×C3×C4—41no—
460C2×C3×C4—41no—
461C2×C3×C4—41no—
462C2×C3×C4—41no—
463C2×C3×C4—41no—
464C2×C3×C4C22×D411yescharacteristic
465C2×C3×C4C22×D411yescharacteristic
466C2×C3×C4C2×#4111yescharacteristic
467C2×C3×C4C2×#4111yescharacteristic
468C2×C3×C4H(5,𝔽2)11yescharacteristic
469C2×C3×C4H(5,𝔽2)11yescharacteristic
470#67—44no—
471#67—84no—
472#67—84no—
473C2×Dic3—21no—
474C2×Dic3—21no—
475C2×Dic3—21no—
476C2×Dic3—21no—
477C2×Dic3—21no—
478C2×Dic3—21no—
479C2×Dic3—22no—
480C2×Dic3—21no—
481C2×Dic3—41no—
482C2×Dic3—41no—
483C2×Dic3—41no—
484C2×Dic3—41no—
485C2×Dic3—41no—
486C2×Dic3—41no—
487C2×Dic3—41no—
488C2×Dic3—41no—
489C2×Dic3—41no—
490C2×Dic3—41no—
491C2×Dic3—41no—
492C2×Dic3—84no—
493C2×Dic3#12112yes—
494C2×Dic3#12112yes—
495C4×D3—41no—
496C4×D3—41no—
497C4×D3—41no—
498C4×D3—41no—
499Dic6—41no—
500Dic6—41no—
501Dic6—41no—
502Dic6—41no—
503C3×C8—22no—
504C3×C8—22no—
505C3⋊C8—22no—
506C3⋊C8—41no—
507C24—21no—
508C24—21no—
509C24—31no—
510C24D3×D411yescharacteristic
511C2×Q8—61no—
512C2×Q8—61no—
513C2×Q8—61no—
514C2×Q8—61no—
515C2×Q8—61no—
516C2×Q8—61no—
517C2×D4—21no—
518C2×D4—21no—
519C2×D4—21no—
520C2×D4—21no—
521C2×D4—21no—
522C2×D4—21no—
523C2×D4—21no—
524C2×D4—21no—
525C2×D4—21no—
526C2×D4—21no—
527C2×D4—21no—
528C2×D4—42no—
529C2×D4—42no—
530C2×D4—42no—
531C2×D4—42no—
532C2×D4—62no—
533C2×D4—62no—
534C2×D4—81no—
535C2×D4—81no—
536C2×D4—121no—
537C2×D4—122no—
538C2×D4—122no—
539C2×D4—122no—
540C2×D4—122no—
541C2×D4—241no—
542C2×D4—241no—
543C2×D4C2×#6712yes—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—31no—
553C22×C4—31no—
554C22×C4—31no—
555C22×C4—61no—
556C22×C4—61no—
557C22×C4—61no—
558C22×C4—61no—
559C22×C4—61no—
560C22×C4—61no—
561C22×C4—61no—
562C22×C4—61no—
563C22×C4—61no—
564C22×C4—61no—
565C22×C4—122no—
566C22×C4—122no—
567C22×C4—122no—
568C22×C4D3×D411yescharacteristic
569C22×C4C23×D311yescharacteristic
570SD16—124no—
571D8—44no—
572M16—124no—
573C2×C8—21no—
574C2×C8—21no—
575C2×C8—21no—
576C2×C8—21no—
577C2×C8—32no—
578C2×C8—44no—
579C2×C8—61no—
580C2×C8—61no—
581C2×C8—61no—
582C2×C8—61no—
583C2×C8—61no—
584C2×C8D3×D412yes—
585C2×C8C2×#6712yes—
586C4⋊C4—21no—
587C4⋊C4—21no—
588C4⋊C4—21no—
589C4⋊C4—32no—
590C4⋊C4—62no—
591C4⋊C4—61no—
592C4⋊C4—61no—
593C4⋊C4—61no—
594C4⋊C4—61no—
595C4⋊C4—61no—
596C4⋊C4—122no—
597C4⋊C4—122no—
598C4⋊C4—122no—
599C4⋊C4—241no—
600C4⋊C4C2×#6712yes—
601C22⋊C4—42no—
602C22⋊C4—42no—
603C22⋊C4—62no—
604C22⋊C4—62no—
605C22⋊C4—122no—
606C22⋊C4—122no—
607C22⋊C4—122no—
608C22⋊C4—122no—
609C22⋊C4—122no—
610C22⋊C4—122no—
611C22⋊C4—122no—
612C22⋊C4—122no—
613C22⋊C4—122no—
614C42—32no—
615C42—32no—
616C42—241no—
617C22×C3—22no—
618C22×C3—22no—
619C22×C3—22no—
620C22×C3—41no—
621C22×C3—41no—
622C22×C3—41no—
623C22×C3—41no—
624C22×C3—42no—
625C22×C3—42no—
626C22×C3—42no—
627C22×C3—81no—
628C22×C3—81no—
629C22×C3—81no—
630C22×C3—81no—
631C22×C3—81no—
632C22×C3—81no—
633C22×C3—81no—
634C22×C3—81no—
635C22×C3—81no—
636C22×C3—81no—
637C22×C3—81no—
638C22×C3C2×#12111yescharacteristic
639C22×C3D4211yescharacteristic
640C22×C3#54611yescharacteristic
641C22×C3C2×AGL(1,ℤ/8)11yescharacteristic
642C22×C3#57511yescharacteristic
643C22×C3#57611yescharacteristic
644C22×C3#57811yescharacteristic
645C2×D3—41no—
646C2×D3—41no—
647C2×D3—41no—
648C2×D3—41no—
649C2×D3—41no—
650C2×D3—41no—
651C2×D3—41no—
652C3×C4—41no—
653C3×C4—42no—
654C3×C4—81no—
655C3×C4#53211yescharacteristic
656C3×C4#54011yescharacteristic
657C3×C4D4211yescharacteristic
658C3×C4#55011yescharacteristic
659Dic3—22no—
660Dic3—22no—
661Dic3—41no—
662Dic3—42no—
663Dic3—81no—
664Dic3—81no—
665Dic3—81no—
666C23—21no—
667C23—21no—
668C23—21no—
669C23—21no—
670C23—21no—
671C23—21no—
672C23—22no—
673C23—41no—
674C23—41no—
675C23—41no—
676C23—41no—
677C23—41no—
678C23—41no—
679C23—41no—
680C23—41no—
681C23—41no—
682C23—41no—
683C23—41no—
684C23—41no—
685C23—41no—
686C23—61no—
687C23—61no—
688C23—61no—
689C23—61no—
690C23—61no—
691C23—61no—
692C23—61no—
693C23#91112yes—
694C23C2×D3×D411yescharacteristic
695Q8—121no—
696Q8—121no—
697Q8—121no—
698Q8—121no—
699D4—22no—
700D4—22no—
701D4—41no—
702D4—41no—
703D4—41no—
704D4—41no—
705D4—41no—
706D4—41no—
707D4—84no—
708D4—84no—
709D4—124no—
710D4—244no—
711D4—244no—
712C2×C4—21no—
713C2×C4—22no—
714C2×C4—21no—
715C2×C4—21no—
716C2×C4—32no—
717C2×C4—32no—
718C2×C4—41no—
719C2×C4—41no—
720C2×C4—41no—
721C2×C4—41no—
722C2×C4—41no—
723C2×C4—41no—
724C2×C4—41no—
725C2×C4—41no—
726C2×C4—41no—
727C2×C4—61no—
728C2×C4—61no—
729C2×C4—61no—
730C2×C4—61no—
731C2×C4—61no—
732C2×C4—61no—
733C2×C4—62no—
734C2×C4—61no—
735C2×C4—121no—
736C2×C4—121no—
737C2×C4—121no—
738C2×C4—121no—
739C2×C4—121no—
740C2×C4—121no—
741C2×C4—121no—
742C2×C4—121no—
743C2×C4—121no—
744C2×C4—121no—
745C2×C4—121no—
746C2×C4—121no—
747C2×C4—121no—
748C2×C4—121no—
749C2×C4—121no—
750C2×C4—244no—
751C2×C4C2×D3×D411yescharacteristic
752C2×C4#100411yescharacteristic
753C2×C4#100411yescharacteristic
754C2×C4D3×#4111yescharacteristic
755C2×C4D3×#4111yescharacteristic
756C2×C4C22×#6711yescharacteristic
757C8—22no—
758C8—22no—
759C8—62no—
760C8—121no—
761C2×C3—42no—
762C2×C3—82no—
763C2×C3—161no—
764C2×C3#242811yescharacteristic
765C2×C3#305511yescharacteristic
766C2×C3#306111yescharacteristic
767C2×C3#326411yescharacteristic
768C2×C3#326911yescharacteristic
769C2×C3#330811yescharacteristic
770C2×C3#331911yescharacteristic
771D3—81no—
772C22—22no—
773C22—22no—
774C22—22no—
775C22—41no—
776C22—41no—
777C22—41no—
778C22—41no—
779C22—42no—
780C22—42no—
781C22—42no—
782C22—81no—
783C22—81no—
784C22—81no—
785C22—81no—
786C22—81no—
787C22—81no—
788C22—81no—
789C22—81no—
790C22—81no—
791C22—81no—
792C22—81no—
793C22—121no—
794C22—121no—
795C22—121no—
796C22—121no—
797C22—121no—
798C22—121no—
799C22—121no—
800C22D3×#12111yescharacteristic
801C22#561011yescharacteristic
802C22C2×#91111yescharacteristic
803C22#575711yescharacteristic
804C22#576811yescharacteristic
805C22#577111yescharacteristic
806C22D4×#6711yescharacteristic
807C4—42no—
808C4—41no—
809C4—62no—
810C4—62no—
811C4—81no—
812C4—122no—
813C4—121no—
814C4—241no—
815C4—241no—
816C4—241no—
817C4#559911yescharacteristic
818C4#561511yescharacteristic
819C4D4×#6711yescharacteristic
820C4#583211yescharacteristic
821C3#2539711yescharacteristic, complemented, Sylow
822C2—42no—
823C2—82no—
824C2—161no—
825C2—241no—
826C2#8071511yescharacteristic
827C2#8071711yescharacteristic
828C2#8073311yescharacteristic
829C2#8073811yescharacteristic
830C2#8265011yescharacteristic
831C2#8383711yescharacteristic
832C2#8392511yescharacteristic
subgroupG/H
centerC23C2×D3×D4
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC2×C3×#466C2
socleC23×C3C22×D4
hypercenterC2×#466D3
hypocenterC3#25397
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#466

Complements

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

NH ≅ G/Ntype
1. C2×C3×#466C2semidirect
2. C2×#5153C2semidirect
3. C2×#5111C2semidirect
4. #82668C2semidirect
5. #82667C2semidirect
6. C2×#4780C2semidirect
7. #72043C2semidirect
8. #71972C2semidirect
9. #71685C2semidirect
10. #71679C2semidirect
11. #70635C2semidirect
12. #70615C2semidirect
13. #70203C2semidirect
14. #70159C2semidirect
15. #70152C2semidirect
65. C2×#466D3semidirect
152. C3×#102D4semidirect
164. Dic3⋊C8D4semidirect
405. #102#67semidirect
821. C3#25397semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#4662
C2×#51532
C2×#51112
#826682
#826672
C2×#47802
#720432
#719722
#716852
#716792
#706352
#706152
#702032
#701592
#701522
#253973