Finite Group Databasebeta

← #10823427

Subgroups — #10823427

Order 768.

1260 conjugacy classes of subgroups.

The subgroup lattice has 788 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#5600C211yesmaximal, characteristic, complemented
2C2×#5152C211yesmaximal, characteristic, complemented
3Dic3×#121C211yesmaximal, characteristic, complemented
4C2×#4757C211yesmaximal, characteristic, complemented
5C3×#1999C211yesmaximal, characteristic
6#72045C211yesmaximal, characteristic, complemented
7#71685C211yesmaximal, characteristic, complemented
8#71679C211yesmaximal, characteristic, complemented
9#70178C211yesmaximal, characteristic, complemented
10#70164C211yesmaximal, characteristic, complemented
11#70152C211yesmaximal, characteristic, complemented
12#69936C211yesmaximal, characteristic, complemented
13#69906C211yesmaximal, characteristic, complemented
14#68828C211yesmaximal, characteristic, complemented
15#68783C211yesmaximal, characteristic, complemented
16#23575—31nomaximal, Sylow
17C22×C3×D8C2211yescharacteristic
18C2×C3×#121C2211yescharacteristic
19C2×C3×#121C2211yescharacteristic
20C2×#936C2211yescharacteristic
21C2×#935—21no—
22C2×D4×Dic3—21no—
23C2×D4×Dic3—21no—
24C2×D4×Dic3C2211yescharacteristic
25C2×D4×Dic3C2211yescharacteristic
26C22×#214C2211yescharacteristic
27C2×#924C2211yescharacteristic
28C22×C4×Dic3C2211yescharacteristic
29#5600—24no—
30#5600—24no—
31C2×#890C2211yescharacteristic
32C2×#887C2211yescharacteristic
33C2×#879—21no—
34C2×#877—21no—
35C2×C3×#102C2211yescharacteristic
36C2×C3×#102C2211yescharacteristic
37C2×C3×C22⋊C8C2211yescharacteristic
38#5221C2211yescharacteristic
39#5220—21no—
40C2×#832C2211yescharacteristic
41C2×#832C2211yescharacteristic
42C2×#832C2211yescharacteristic
43#5212C2211yescharacteristic
44C2×#830C2211yescharacteristic
45#5152—24no—
46C2×#817C2211yescharacteristic
47C2×#816C2211yescharacteristic
48C2×#816C2211yescharacteristic
49C2×#815C2211yescharacteristic
50C2×#815C2211yescharacteristic
51#4984C2211yescharacteristic
52Dic3×C4⋊C4C2211yescharacteristic
53C2×#810C2211yescharacteristic
54C2×#807C2211yescharacteristic
55#4951—21no—
56Dic3×C22⋊C4—21no—
57#4757—24no—
58C3×#340C2211yescharacteristic
59#4551C2211yescharacteristic
60#4550C2211yescharacteristic
61#4550C2211yescharacteristic
62#4529C2211yescharacteristic
63#4529C2211yescharacteristic
64C2×#529—31no—
65C2×#442—31no—
66C2×#440—31no—
67C4×#121—31no—
68#2059—31no—
69#2042—31no—
70#2035—31no—
71#2033—31no—
72#2025—31no—
73#2012—31no—
74#2000—31no—
75#1999D311yescharacteristic
76#1763—31no—
77#1762—31no—
78#1749—31no—
79C22×C3×D4—21no—
80C22×C3×D4—21no—
81C22×C3×D4C2311yescharacteristic
82C22×C3×D4C2311yescharacteristic
83C23×C3×C4C2311yescharacteristic
84C23×Dic3—21no—
85C23×Dic3—21no—
86C23×Dic3D411yescharacteristic
87C23×Dic3D411yescharacteristic
88C22×Dic6C2311yescharacteristic
89C2×C3×D8—22no—
90C2×C3×D8—22no—
91C2×C3×D8—22no—
92C22×C3×C8C2311yescharacteristic
93C22×C3×C8C2311yescharacteristic
94C3×#121—22no—
95C3×#121—22no—
96C3×#121—22no—
97C3×#121—22no—
98C2×C3×C4⋊C4C2311yescharacteristic
99C2×C3×C4⋊C4C2311yescharacteristic
100C2×C3×C22⋊C4—21no—
101C2×C3×C22⋊C4—21no—
102C2×#217—21no—
103C2×#217—21no—
104C2×#217—21no—
105C2×#217—21no—
106C2×#217—21no—
107C2×#217—21no—
108C2×#217—21no—
109C2×#217—21no—
110#936—22no—
111#936—22no—
112#935—28no—
113D4×Dic3—28no—
114D4×Dic3—22no—
115D4×Dic3—22no—
116D4×Dic3—22no—
117D4×Dic3—44no—
118D4×Dic3D414yescomplemented
119C2×#214—22no—
120C2×#214—22no—
121C2×#214—22no—
122C2×C4⋊Dic3—21no—
123C2×C4⋊Dic3—21no—
124C2×C4⋊Dic3C2311yescharacteristic
125C2×C4⋊Dic3C2311yescharacteristic
126C2×C4⋊Dic3C2311yescharacteristic
127#924—22no—
128#924—22no—
129C2×Dic3⋊C4—21no—
130C2×Dic3⋊C4—21no—
131C2×Dic3⋊C4—21no—
132C2×C4×Dic3—21no—
133C2×C4×Dic3—22no—
134C2×C4×Dic3—22no—
135C2×C4×Dic3—21no—
136C2×C4×Dic3D411yescharacteristic
137C2×C4×Dic3D411yescharacteristic
138C2×C4×Dic3C2311yescharacteristic
139C2×C4×Dic3C2311yescharacteristic
140C22×C3⋊C8C2311yescharacteristic
141C22×C3⋊C8C2311yescharacteristic
142#890—22no—
143#890—22no—
144#887—22no—
145#887D414yescomplemented
146#879—28no—
147#877—28no—
148C3×#102—22no—
149C3×#102—22no—
150C3×C22⋊C8—22no—
151#832—22no—
152#832—22no—
153#832—22no—
154C3⋊#95—21no—
155C3⋊#95—21no—
156C3⋊#95—21no—
157#830—22no—
158#817—22no—
159#816—22no—
160#816—22no—
161#815—22no—
162#815—22no—
163#810—22no—
164#807—22no—
165C22×SD16—31no—
166C22×D8C2×D311yescharacteristic
167#529—64no—
168#529—64no—
169C2×#126—61no—
170C2×#125—31no—
171C2×#124—31no—
172C2×#123—61no—
173C2×C22⋊Q8—31no—
174C2×#121C2×D311yescharacteristic
175C2×#121C2×D311yescharacteristic
176C2×C4×Q8—31no—
177C2×C4×D4—31no—
178C2×C4×D4—31no—
179C2×C4×D4—61no—
180C2×C4×D4—61no—
181C2×#117—61no—
182C22×C42—31no—
183#442—64no—
184#440—64no—
185C2×#107—31no—
186C2×#106—31no—
187C2×#103—31no—
188C2×#103—31no—
189C2×#103—31no—
190C2×#102—31no—
191C2×#102—31no—
192C2×#102—31no—
193C2×#102C2×D311yescharacteristic
194C2×#102C2×D311yescharacteristic
195C2×C22⋊C8—31no—
196C2×C22⋊C8C2×D311yescharacteristic
197C2×#97—31no—
198C2×#97—31no—
199#390—31no—
200#389—31no—
201#388—61no—
202#386—61no—
203#380—31no—
204C4×C4⋊C4—31no—
205C4×C22⋊C4—61no—
206#340—31no—
207#340—31no—
208#340—31no—
209#340C2×D311yescharacteristic
210#336—31no—
211#336—31no—
212C24×C3—21no—
213C24×C3—21no—
214C24×C3C2×D411yescharacteristic
215C2×C3×D4—24no—
216C2×C3×D4—24no—
217C2×C3×D4—21no—
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—42no—
228C2×C3×D4—42no—
229C2×C3×D4—42no—
230C2×C3×D4—42no—
231C2×C3×D4C2×D412yes—
232C2×C3×D4#4112yes—
233C22×C3×C4—21no—
234C22×C3×C4—21no—
235C22×C3×C4—21no—
236C22×C3×C4—21no—
237C22×C3×C4—21no—
238C22×C3×C4—21no—
239C22×C3×C4—21no—
240C22×C3×C4—21no—
241C22×C3×C4C2×D411yescharacteristic
242C22×C3×C4C2411yescharacteristic
243C22×Dic3—22no—
244C22×Dic3—21no—
245C22×Dic3—21no—
246C22×Dic3—24no—
247C22×Dic3—22no—
248C22×Dic3—22no—
249C22×Dic3—21no—
250C22×Dic3—21no—
251C22×Dic3—41no—
252C22×Dic3—41no—
253C22×Dic3—41no—
254C22×Dic3—42no—
255C22×Dic3—42no—
256C22×Dic3—42no—
257C22×Dic3—42no—
258C22×Dic3—42no—
259C22×Dic3C2×D411yescharacteristic
260C22×Dic3C2×D411yescharacteristic
261C22×Dic3C2×D411yescharacteristic
262C22×Dic3C2×D411yescharacteristic
263C2×Dic6—21no—
264C2×Dic6—21no—
265C2×Dic6—21no—
266C2×Dic6—21no—
267C2×Dic6—21no—
268C2×Dic6C2×D412yes—
269C3×D8—28no—
270C2×C3×C8—21no—
271C2×C3×C8—21no—
272C2×C3×C8—21no—
273C2×C3×C8—21no—
274C2×C3×C8—21no—
275C2×C3×C8#4112yes—
276C3×C4⋊C4—21no—
277C3×C4⋊C4—21no—
278C3×C4⋊C4C2×D412yes—
279C3×C4⋊C4#4112yes—
280C3×C22⋊C4—24no—
281C3×C22⋊C4—24no—
282#217—24no—
283#217—24no—
284#217—24no—
285#217—24no—
286#217—42no—
287#217—42no—
288#217—42no—
289#217—42no—
290#214—28no—
291C4⋊Dic3—24no—
292C4⋊Dic3—21no—
293C4⋊Dic3—21no—
294C4⋊Dic3—21no—
295C4⋊Dic3—21no—
296C4⋊Dic3—21no—
297C4⋊Dic3—42no—
298C4⋊Dic3C2×D412yes—
299Dic3⋊C4—24no—
300Dic3⋊C4—24no—
301Dic3⋊C4—24no—
302C4×Dic3—21no—
303C4×Dic3—21no—
304C4×Dic3—22no—
305C4×Dic3—24no—
306C4×Dic3—22no—
307C4×Dic3—42no—
308C4×Dic3C2×D412yes—
309C4×Dic3C2×D412yes—
310C2×C3⋊C8—21no—
311C2×C3⋊C8—21no—
312C2×C3⋊C8—21no—
313C2×C3⋊C8—21no—
314C2×C3⋊C8—21no—
315C2×C3⋊C8#4112yes—
316C22×Q8—31no—
317C22×D4—21no—
318C22×D4—21no—
319C22×D4C22×D311yescharacteristic
320C22×D4C22×D311yescharacteristic
321C23×C4—31no—
322C23×C4—31no—
323C23×C4—61no—
324C23×C4—61no—
325C23×C4C22×D311yescharacteristic
326C2×SD16—62no—
327C2×SD16—62no—
328C2×SD16—62no—
329C2×D8—22no—
330C2×D8—22no—
331C2×D8—22no—
332C22×C8—31no—
333C22×C8—31no—
334C22×C8C22×D311yescharacteristic
335C22×C8C22×D311yescharacteristic
336#126—68no—
337#125—62no—
338#125—62no—
339#124—62no—
340#124—62no—
341#123—68no—
342C22⋊Q8—62no—
343C22⋊Q8—62no—
344#121—22no—
345#121—22no—
346#121—22no—
347#121—22no—
348C4×Q8—34no—
349C4×Q8—62no—
350C4×D4—34no—
351C4×D4—62no—
352C4×D4—62no—
353C4×D4—62no—
354C4×D4—68no—
355C4×D4—124no—
356#117—68no—
357C2×C4⋊C4—31no—
358C2×C4⋊C4—31no—
359C2×C4⋊C4—31no—
360C2×C4⋊C4—61no—
361C2×C4⋊C4—61no—
362C2×C4⋊C4—61no—
363C2×C4⋊C4—61no—
364C2×C4⋊C4—61no—
365C2×C4⋊C4C22×D311yescharacteristic
366C2×C4⋊C4C22×D311yescharacteristic
367C2×C22⋊C4—21no—
368C2×C22⋊C4—21no—
369C2×C22⋊C4—61no—
370C2×C22⋊C4—61no—
371C2×C22⋊C4—61no—
372C2×C22⋊C4—61no—
373C2×C22⋊C4—61no—
374C2×C22⋊C4—61no—
375C2×C22⋊C4—61no—
376C2×C22⋊C4—61no—
377C2×C42—31no—
378C2×C42—31no—
379C2×C42—31no—
380C2×C42—31no—
381C2×C42—62no—
382C2×C42—62no—
383C2×C42—61no—
384C2×C42—61no—
385#107—62no—
386#106—62no—
387#103—62no—
388#103—62no—
389#103—62no—
390#102—22no—
391#102—22no—
392#102—62no—
393#102—62no—
394#102—62no—
395C22⋊C8—22no—
396C22⋊C8—62no—
397#97—62no—
398#97—62no—
399#95—61no—
400#95—61no—
401#95—61no—
402C23×C3—21no—
403C23×C3—21no—
404C23×C3—21no—
405C23×C3—21no—
406C23×C3—21no—
407C23×C3—21no—
408C23×C3—22no—
409C23×C3—22no—
410C23×C3—41no—
411C23×C3—41no—
412C23×C3—41no—
413C23×C3—41no—
414C23×C3—41no—
415C23×C3—41no—
416C23×C3—41no—
417C23×C3—41no—
418C23×C3—41no—
419C23×C3—41no—
420C23×C3—41no—
421C23×C3—41no—
422C23×C3AGL(1,ℤ/8)12yes—
423C23×C3C22×D411yescharacteristic
424C3×D4—22no—
425C3×D4—22no—
426C3×D4—22no—
427C3×D4—22no—
428C3×D4—48no—
429C3×D4—48no—
430C3×D4—41no—
431C3×D4—41no—
432C3×D4—41no—
433C3×D4—41no—
434C2×C3×C4—21no—
435C2×C3×C4—22no—
436C2×C3×C4—21no—
437C2×C3×C4—22no—
438C2×C3×C4—21no—
439C2×C3×C4—41no—
440C2×C3×C4—41no—
441C2×C3×C4—41no—
442C2×C3×C4—41no—
443C2×C3×C4—41no—
444C2×C3×C4—41no—
445C2×C3×C4—41no—
446C2×C3×C4—41no—
447C2×C3×C4C22×D411yescharacteristic
448C2×C3×C4C22×D411yescharacteristic
449C2×C3×C4C2×#4111yescharacteristic
450C2×C3×C4C2×#4111yescharacteristic
451C2×C3×C4C2×#4111yescharacteristic
452C2×C3×C4C2×#4111yescharacteristic
453C2×Dic3—21no—
454C2×Dic3—21no—
455C2×Dic3—21no—
456C2×Dic3—21no—
457C2×Dic3—21no—
458C2×Dic3—21no—
459C2×Dic3—22no—
460C2×Dic3—22no—
461C2×Dic3—21no—
462C2×Dic3—21no—
463C2×Dic3—21no—
464C2×Dic3—21no—
465C2×Dic3—44no—
466C2×Dic3—44no—
467C2×Dic3—48no—
468C2×Dic3—41no—
469C2×Dic3—41no—
470C2×Dic3—41no—
471C2×Dic3—41no—
472C2×Dic3—41no—
473C2×Dic3—41no—
474C2×Dic3—41no—
475C2×Dic3—41no—
476C2×Dic3—41no—
477C2×Dic3—41no—
478C2×Dic3—84no—
479C2×Dic3#12012yes—
480C2×Dic3#12012yes—
481Dic6—22no—
482Dic6—22no—
483Dic6—41no—
484Dic6—41no—
485C3×C8—22no—
486C3×C8—41no—
487C3⋊C8—22no—
488C3⋊C8—41no—
489C24—21no—
490C24—21no—
491C24D3×D411yescharacteristic
492C2×Q8—32no—
493C2×Q8—61no—
494C2×Q8—61no—
495C2×Q8—61no—
496C2×Q8—61no—
497C2×Q8—61no—
498C2×D4—24no—
499C2×D4—24no—
500C2×D4—21no—
501C2×D4—21no—
502C2×D4—21no—
503C2×D4—21no—
504C2×D4—21no—
505C2×D4—21no—
506C2×D4—21no—
507C2×D4—21no—
508C2×D4—21no—
509C2×D4—21no—
510C2×D4—42no—
511C2×D4—42no—
512C2×D4—42no—
513C2×D4—42no—
514C2×D4D3×D412yes—
515C2×D4#23712yes—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—21no—
523C22×C4—21no—
524C22×C4—31no—
525C22×C4—31no—
526C22×C4—31no—
527C22×C4—31no—
528C22×C4—62no—
529C22×C4—62no—
530C22×C4—64no—
531C22×C4—62no—
532C22×C4—61no—
533C22×C4—61no—
534C22×C4—61no—
535C22×C4—61no—
536C22×C4—122no—
537C22×C4—121no—
538C22×C4—121no—
539C22×C4—121no—
540C22×C4—122no—
541C22×C4—122no—
542C22×C4—122no—
543C22×C4—122no—
544C22×C4D3×D411yescharacteristic
545C22×C4C23×D311yescharacteristic
546SD16—68no—
547D8—28no—
548C2×C8—21no—
549C2×C8—21no—
550C2×C8—21no—
551C2×C8—21no—
552C2×C8—21no—
553C2×C8—32no—
554C2×C8—61no—
555C2×C8—61no—
556C2×C8—61no—
557C2×C8—61no—
558C2×C8—61no—
559C2×C8#23712yes—
560C4⋊C4—21no—
561C4⋊C4—21no—
562C4⋊C4—32no—
563C4⋊C4—64no—
564C4⋊C4—64no—
565C4⋊C4—64no—
566C4⋊C4—64no—
567C4⋊C4—61no—
568C4⋊C4—61no—
569C4⋊C4—61no—
570C4⋊C4—61no—
571C4⋊C4—61no—
572C4⋊C4—122no—
573C4⋊C4D3×D412yes—
574C4⋊C4#23712yes—
575C22⋊C4—24no—
576C22⋊C4—24no—
577C22⋊C4—64no—
578C22⋊C4—64no—
579C22⋊C4—64no—
580C22⋊C4—64no—
581C22⋊C4—122no—
582C22⋊C4—122no—
583C22⋊C4—122no—
584C22⋊C4—122no—
585C42—32no—
586C42—32no—
587C42—62no—
588C42—62no—
589C42—64no—
590C42—61no—
591C42—61no—
592C42—122no—
593C22×C3—22no—
594C22×C3—22no—
595C22×C3—22no—
596C22×C3—41no—
597C22×C3—41no—
598C22×C3—41no—
599C22×C3—41no—
600C22×C3—42no—
601C22×C3—42no—
602C22×C3—42no—
603C22×C3—42no—
604C22×C3—42no—
605C22×C3—42no—
606C22×C3—81no—
607C22×C3—81no—
608C22×C3—81no—
609C22×C3—81no—
610C22×C3—81no—
611C22×C3—81no—
612C22×C3—81no—
613C22×C3—81no—
614C22×C3C2×#12011yescharacteristic
615C22×C3#52511yescharacteristic
616C22×C3#53211yescharacteristic
617C22×C3C2×AGL(1,ℤ/8)11yescharacteristic
618C22×C3#57511yescharacteristic
619C22×C3#57511yescharacteristic
620C22×C3#57511yescharacteristic
621C3×C4—42no—
622C3×C4—41no—
623C3×C4—42no—
624C3×C4#52511yescharacteristic
625C3×C4#52511yescharacteristic
626C3×C4#53211yescharacteristic
627C3×C4#53211yescharacteristic
628Dic3—22no—
629Dic3—22no—
630Dic3—42no—
631Dic3—41no—
632Dic3—42no—
633Dic3—41no—
634Dic3—81no—
635Dic3—81no—
636C23—21no—
637C23—21no—
638C23—21no—
639C23—21no—
640C23—21no—
641C23—21no—
642C23—22no—
643C23—22no—
644C23—41no—
645C23—41no—
646C23—41no—
647C23—41no—
648C23—41no—
649C23—41no—
650C23—41no—
651C23—41no—
652C23—41no—
653C23—41no—
654C23—41no—
655C23—41no—
656C23#91112yes—
657C23C2×D3×D411yescharacteristic
658Q8—62no—
659Q8—62no—
660Q8—121no—
661Q8—121no—
662D4—22no—
663D4—22no—
664D4—22no—
665D4—22no—
666D4—48no—
667D4—48no—
668D4—41no—
669D4—41no—
670D4—41no—
671D4—41no—
672C2×C4—21no—
673C2×C4—22no—
674C2×C4—21no—
675C2×C4—22no—
676C2×C4—21no—
677C2×C4—32no—
678C2×C4—32no—
679C2×C4—41no—
680C2×C4—41no—
681C2×C4—41no—
682C2×C4—41no—
683C2×C4—41no—
684C2×C4—41no—
685C2×C4—41no—
686C2×C4—41no—
687C2×C4—61no—
688C2×C4—61no—
689C2×C4—61no—
690C2×C4—61no—
691C2×C4—61no—
692C2×C4—61no—
693C2×C4—61no—
694C2×C4—61no—
695C2×C4—61no—
696C2×C4—61no—
697C2×C4—62no—
698C2×C4—62no—
699C2×C4—124no—
700C2×C4—124no—
701C2×C4—128no—
702C2×C4—121no—
703C2×C4—121no—
704C2×C4—121no—
705C2×C4—121no—
706C2×C4—121no—
707C2×C4—121no—
708C2×C4—121no—
709C2×C4—121no—
710C2×C4—121no—
711C2×C4—121no—
712C2×C4—244no—
713C2×C4C2×D3×D411yescharacteristic
714C2×C4C2×D3×D411yescharacteristic
715C2×C4C2×#23711yescharacteristic
716C2×C4C2×#23711yescharacteristic
717C2×C4C2×#23711yescharacteristic
718C2×C4D3×#4111yescharacteristic
719C8—22no—
720C8—41no—
721C8—62no—
722C8—121no—
723C2×C3—42no—
724C2×C3—82no—
725C2×C3—82no—
726C2×C3#238811yescharacteristic
727C2×C3#300511yescharacteristic
728C2×C3#300611yescharacteristic
729C2×C3#311111yescharacteristic
730C2×C3#311411yescharacteristic
731C2×C3#318011yescharacteristic
732C2×C3#318311yescharacteristic
733C22—22no—
734C22—22no—
735C22—22no—
736C22—41no—
737C22—41no—
738C22—41no—
739C22—41no—
740C22—42no—
741C22—42no—
742C22—42no—
743C22—42no—
744C22—42no—
745C22—42no—
746C22—81no—
747C22—81no—
748C22—81no—
749C22—81no—
750C22—81no—
751C22—81no—
752C22—81no—
753C22—81no—
754C22#558611yescharacteristic
755C22D3×#12011yescharacteristic
756C22#559611yescharacteristic
757C22C2×#91111yescharacteristic
758C22#576811yescharacteristic
759C22#577311yescharacteristic
760C22#577311yescharacteristic
761C4—42no—
762C4—41no—
763C4—42no—
764C4—62no—
765C4—62no—
766C4—122no—
767C4—121no—
768C4—121no—
769C4—122no—
770C4—241no—
771C4—241no—
772C4#558611yescharacteristic
773C4#559611yescharacteristic
774C4#560611yescharacteristic
775C4#571611yescharacteristic
776C3#2357511yescharacteristic, complemented, Sylow
777C2—42no—
778C2—82no—
779C2—82no—
780C2#7666511yescharacteristic
781C2#7999111yescharacteristic
782C2#8000311yescharacteristic
783C2#8007011yescharacteristic
784C2#8008311yescharacteristic
785C2#8070111yescharacteristic
786C2#8085211yescharacteristic
subgroupG/H
centerC23C2×D3×D4
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
Fitting, prime radicalC3×#1999C2
socleC23×C3C22×D4
hypercenter#1999D3
hypocenterC3#23575
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1999

Complements

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

NH ≅ G/Ntype
1. C2×#5600C2semidirect
2. C2×#5152C2semidirect
3. Dic3×#121C2semidirect
4. C2×#4757C2semidirect
6. #72045C2semidirect
7. #71685C2semidirect
8. #71679C2semidirect
9. #70178C2semidirect
10. #70164C2semidirect
11. #70152C2semidirect
12. #69936C2semidirect
13. #69906C2semidirect
14. #68828C2semidirect
15. #68783C2semidirect
118. D4×Dic3D4semidirect
145. #887D4semidirect
776. C3#23575semidirect

Maximal subgroups

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

subgroupindex
C2×#56002
C2×#51522
Dic3×#1212
C2×#47572
C3×#19992
#720452
#716852
#716792
#701782
#701642
#701522
#699362
#699062
#688282
#687832
#235753