Finite Group Databasebeta

← #10823177

Subgroups — #10823177

Order 768.

1410 conjugacy classes of subgroups.

The subgroup lattice has 798 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#915C211yesmaximal, characteristic
2C2×#4839C211yesmaximal, characteristic, complemented
3C2×D3×#103C211yesmaximal, characteristic, complemented
4C2×#4772C211yesmaximal, characteristic
5#76610C211yesmaximal, characteristic, complemented
6#76294C211yesmaximal, characteristic
7C3×#2055C211yesmaximal, characteristic, complemented
8#72051C211yesmaximal, characteristic, complemented
9#70487C211yesmaximal, characteristic, complemented
10#70285C211yesmaximal, characteristic, complemented
11#70217C211yesmaximal, characteristic, complemented
12#69681C211yesmaximal, characteristic, complemented
13#69651C211yesmaximal, characteristic, complemented
14#68867C211yesmaximal, characteristic, complemented
15#68864C211yesmaximal, characteristic, complemented
16#23545—31nomaximal, Sylow
17C22×D3×Q8C2211yescharacteristic
18C22×#237C2211yescharacteristic
19C22×C3×SD16C2211yescharacteristic
20C22×#216C2211yescharacteristic
21C22×#214C2211yescharacteristic
22C2×#915—24no—
23C2×#915—24no—
24C2×#915—24no—
25C22×Dic12C2211yescharacteristic
26C22×ΓL(1,𝔽25)C2211yescharacteristic
27C22×D3×C8C2211yescharacteristic
28C2×#892C2211yescharacteristic
29C2×D3×C4⋊C4C2211yescharacteristic
30C2×#872C2211yescharacteristic
31C2×C3×C4⋊C8C2211yescharacteristic
32C2×C3×#103C2211yescharacteristic
33C2×C3×#102C2211yescharacteristic
34C3×#391C2211yescharacteristic
35C3×#390C2211yescharacteristic
36#5229C2211yescharacteristic
37C2×#835C2211yescharacteristic
38#5221C2211yescharacteristic
39C2×#832C2211yescharacteristic
40C2×#816C2211yescharacteristic
41C2×#816C2211yescharacteristic
42C2×Dic3⋊C8C2211yescharacteristic
43C2×Dic3⋊C8C2211yescharacteristic
44#4973C2211yescharacteristic
45#4973C2211yescharacteristic
46C2×#810C2211yescharacteristic
47C2×#810C2211yescharacteristic
48#4956—21no—
49#4956—21no—
50#4942—21no—
51#4942—21no—
52#4929C2211yescharacteristic
53#4929C2211yescharacteristic
54C2×C4⋊(C3⋊C8)C2211yescharacteristic
55#4839—24no—
56D3×#103—24no—
57#4772—24no—
58#4664—21no—
59#4664—21no—
60#4646—21no—
61#4646—21no—
62C3×#340C2211yescharacteristic
63#4551C2211yescharacteristic
64#4529C2211yescharacteristic
65#4529C2211yescharacteristic
66C22×#137—31no—
67C2×#424—31no—
68C2×#416—31no—
69C22×#103—31no—
70#2311—31no—
71#2310—31no—
72#2056—31no—
73#2056—31no—
74#2056—31no—
75#2056—31no—
76#2055—31no—
77#2055—31no—
78#2055—31no—
79#2055D311yescharacteristic, complemented
80#1736—31no—
81C22×C3×Q8C2311yescharacteristic
82C22×C3×D4C2311yescharacteristic
83C22×#67—21no—
84C23×Dic3—21no—
85C2×D3×Q8—22no—
86C2×D3×Q8—22no—
87C2×D3×Q8—22no—
88C2×D3×Q8—22no—
89C2×D3×Q8—22no—
90C2×D3×Q8D414yes—
91C2×#237—22no—
92C2×#237—22no—
93C2×#237—22no—
94C2×#237—22no—
95C2×#237—22no—
96C2×#237D414yes—
97C22×C4×D3—21no—
98C22×C4×D3—21no—
99C22×C4×D3C2311yescharacteristic
100C22×Dic6—21no—
101C22×Dic6C2311yescharacteristic
102C22×Dic6C2311yescharacteristic
103C2×C3×SD16—22no—
104C2×C3×SD16—22no—
105C2×C3×SD16—22no—
106C22×C3×C8C2311yescharacteristic
107C22×C3×C8C2311yescharacteristic
108C2×C3×C4⋊C4C2311yescharacteristic
109C2×C3×C4⋊C4C2311yescharacteristic
110C2×C3×C22⋊C4—21no—
111C2×C3×C22⋊C4—21no—
112C2×C3×C42C2311yescharacteristic
113C2×#217—21no—
114C2×#217—21no—
115C2×#216—22no—
116C2×#216—22no—
117C2×#216—22no—
118C2×#214—22no—
119C2×#214—22no—
120C2×#214—22no—
121C2×(C2×D3)⋊C4—21no—
122C2×(C2×D3)⋊C4D411yescharacteristic
123C2×(C2×D3)⋊C4D411yescharacteristic
124C2×C4⋊Dic3C2311yescharacteristic
125C2×C4⋊Dic3C2311yescharacteristic
126C2×Dic3⋊C4—21no—
127C2×Dic3⋊C4D411yescharacteristic
128C2×Dic3⋊C4D411yescharacteristic
129C2×C4×Dic3—21no—
130C2×C4×Dic3C2311yescharacteristic
131C22×C3⋊C8C2311yescharacteristic
132C22×C3⋊C8C2311yescharacteristic
133#915—232no—
134C2×Dic12—22no—
135C2×Dic12—22no—
136C2×Dic12—22no—
137C2×ΓL(1,𝔽25)—22no—
138C2×ΓL(1,𝔽25)—22no—
139C2×ΓL(1,𝔽25)D414yes—
140C2×D3×C8—22no—
141C2×D3×C8—22no—
142C2×D3×C8—22no—
143#892—22no—
144#892—22no—
145D3×C4⋊C4—22no—
146D3×C4⋊C4—22no—
147#872—22no—
148#872—22no—
149C3×C4⋊C8—22no—
150C3×#103—22no—
151C3×#102—22no—
152C3×#95—21no—
153C3×#95—21no—
154#835—22no—
155#832—22no—
156C3⋊#95—21no—
157C3⋊#95—21no—
158C3⋊#95—21no—
159C3⋊#95—21no—
160C3⋊#95—21no—
161C3⋊#95—21no—
162C3⋊#95—21no—
163C3⋊#95—21no—
164C3⋊#95—21no—
165C3⋊#95—21no—
166#816—22no—
167#816—22no—
168Dic3⋊C8—22no—
169Dic3⋊C8—22no—
170#810—22no—
171#810—22no—
172C4⋊(C3⋊C8)—22no—
173C22×#41—31no—
174C23×Q8—31no—
175C2×#137—64no—
176C2×#137—64no—
177C2×#137—64no—
178C22×Q16—31no—
179C22×Q16—31no—
180C22×SD16—31no—
181C22×SD16C2×D311yescharacteristic
182C22×M16—31no—
183C23×C8—31no—
184C2×#117—31no—
185C2×#117—31no—
186C22×C4⋊C4—31no—
187#424—64no—
188C2×C4⋊C8—31no—
189C2×C4⋊C8—31no—
190C2×C4⋊C8—31no—
191C2×C4⋊C8C2×D311yescharacteristic
192#416—64no—
193C2×#103—31no—
194C2×#103—31no—
195C2×#103—31no—
196C2×#103—31no—
197C2×#103—31no—
198C2×#103—64no—
199C2×#103C2×D311yescharacteristic
200C2×#102—31no—
201C2×#102C2×D311yescharacteristic
202#391—31no—
203#391—31no—
204#391—31no—
205#391—31no—
206#391—31no—
207#391—61no—
208#391—61no—
209#391C2×D311yescharacteristic
210#390—31no—
211#390C2×D311yescharacteristic
212#386—61no—
213#386—61no—
214#381—61no—
215#381—61no—
216#380—61no—
217#380—61no—
218#340—31no—
219#340—31no—
220#340—31no—
221#340C2×D311yescharacteristic
222C24×C3—21no—
223C23×D3C2×D411yescharacteristic
224C2×C3×Q8—21no—
225C2×C3×Q8—21no—
226C2×C3×Q8—21no—
227C2×C3×Q8—21no—
228C2×C3×Q8—21no—
229C2×C3×Q8C2×D412yes—
230C2×C3×D4—21no—
231C2×C3×D4—21no—
232C2×C3×D4—21no—
233C2×C3×D4—21no—
234C2×C3×D4—21no—
235C2×C3×D4C2×D412yes—
236C22×C3×C4—21no—
237C22×C3×C4—21no—
238C22×C3×C4—21no—
239C22×C3×C4C2×D411yescharacteristic
240C22×C3×C4C2×D411yescharacteristic
241C22×C3×C4C2411yescharacteristic
242C2×#67—24no—
243C2×#67—42no—
244C2×#67—42no—
245C22×Dic3—21no—
246C22×Dic3—21no—
247C22×Dic3—24no—
248C22×Dic3—21no—
249C22×Dic3—21no—
250C22×Dic3—42no—
251C22×Dic3—42no—
252C22×Dic3C2×D411yescharacteristic
253C22×Dic3C2×D411yescharacteristic
254C22×Dic3C2×D411yescharacteristic
255D3×Q8—28no—
256D3×Q8—28no—
257D3×Q8—44no—
258D3×Q8—44no—
259#237—28no—
260#237—28no—
261#237—44no—
262#237—44no—
263C2×C4×D3—24no—
264C2×C4×D3—42no—
265C2×C4×D3—42no—
266C2×C4×D3—42no—
267C2×C4×D3—81no—
268C2×C4×D3—81no—
269C2×C4×D3C2×D412yes—
270C2×C4×D3C2×D412yes—
271C2×C4×D3C2×D412yes—
272C2×C4×D3#4112yes—
273C2×C4×D3#4112yes—
274C2×C4×D3#4112yes—
275C2×Dic6—21no—
276C2×Dic6—21no—
277C2×Dic6—21no—
278C2×Dic6—21no—
279C2×Dic6—21no—
280C2×Dic6—21no—
281C2×Dic6—21no—
282C2×Dic6—21no—
283C2×Dic6—21no—
284C2×Dic6—21no—
285C2×Dic6—24no—
286C2×Dic6—42no—
287C2×Dic6—42no—
288C2×Dic6C2×D412yes—
289C2×Dic6C2×D412yes—
290C3×SD16—28no—
291C2×C3×C8—21no—
292C2×C3×C8—21no—
293C2×C3×C8—21no—
294C2×C3×C8—21no—
295C2×C3×C8—21no—
296C2×C3×C8C2×D412yes—
297C3×C4⋊C4—21no—
298C3×C4⋊C4—21no—
299C3×C4⋊C4—21no—
300C3×C4⋊C4—21no—
301C3×C22⋊C4—81no—
302C3×C22⋊C4—81no—
303C3×C42—21no—
304C3×C42—21no—
305#217—81no—
306#217—81no—
307#216—28no—
308#214—28no—
309(C2×D3)⋊C4—22no—
310(C2×D3)⋊C4—22no—
311(C2×D3)⋊C4—42no—
312C4⋊Dic3—21no—
313C4⋊Dic3—21no—
314C4⋊Dic3—21no—
315C4⋊Dic3—21no—
316Dic3⋊C4—22no—
317Dic3⋊C4—22no—
318Dic3⋊C4—42no—
319C4×Dic3—21no—
320C4×Dic3—21no—
321C4×Dic3—42no—
322C2×C3⋊C8—21no—
323C2×C3⋊C8—21no—
324C2×C3⋊C8—21no—
325C2×C3⋊C8—21no—
326C2×C3⋊C8—21no—
327C2×C3⋊C8C2×D412yes—
328Dic12—28no—
329ΓL(1,𝔽25)—28no—
330D3×C8—44no—
331C2×#41—34no—
332C2×#41—62no—
333C2×#41—62no—
334C2×#41—62no—
335C2×#41—62no—
336C2×#41—62no—
337C22×Q8—34no—
338C22×Q8—31no—
339C22×Q8—31no—
340C22×Q8—61no—
341C22×Q8—62no—
342C22×Q8—62no—
343C22×Q8—62no—
344C22×Q8—62no—
345C22×Q8—62no—
346C22×Q8C22×D311yescharacteristic
347C22×D4—61no—
348C22×D4C22×D311yescharacteristic
349C23×C4—31no—
350C23×C4—61no—
351C23×C4—61no—
352C23×C4—61no—
353#137—632no—
354C2×Q16—62no—
355C2×Q16—62no—
356C2×Q16—62no—
357C2×Q16—62no—
358C2×Q16—62no—
359C2×Q16—62no—
360C2×SD16—22no—
361C2×SD16—22no—
362C2×SD16—22no—
363C2×SD16—62no—
364C2×SD16—62no—
365C2×SD16—62no—
366C2×M16—34no—
367C2×M16—62no—
368C2×M16—62no—
369C22×C8—31no—
370C22×C8—31no—
371C22×C8—62no—
372C22×C8—62no—
373C22×C8—62no—
374C22×C8C22×D311yescharacteristic
375C22×C8C22×D311yescharacteristic
376#117—62no—
377#117—62no—
378#117—62no—
379#117—62no—
380C2×C4⋊C4—31no—
381C2×C4⋊C4—31no—
382C2×C4⋊C4—31no—
383C2×C4⋊C4—31no—
384C2×C4⋊C4—62no—
385C2×C4⋊C4—62no—
386C2×C4⋊C4—61no—
387C2×C4⋊C4C22×D311yescharacteristic
388C2×C4⋊C4C22×D311yescharacteristic
389C2×C22⋊C4—21no—
390C2×C22⋊C4—21no—
391C2×C22⋊C4—31no—
392C2×C22⋊C4—31no—
393C2×C22⋊C4—61no—
394C2×C22⋊C4—61no—
395C2×C22⋊C4—61no—
396C2×C42—31no—
397C2×C42—61no—
398C2×C42C22×D311yescharacteristic
399C4⋊C8—22no—
400C4⋊C8—62no—
401C4⋊C8—62no—
402C4⋊C8—62no—
403#103—22no—
404#103—62no—
405#103—62no—
406#103—62no—
407#103—62no—
408#103—62no—
409#102—22no—
410#102—62no—
411#95—21no—
412#95—21no—
413#95—61no—
414#95—61no—
415#95—61no—
416#95—61no—
417#95—61no—
418#95—61no—
419#95—61no—
420#95—61no—
421#95—61no—
422#95—61no—
423C23×C3—22no—
424C23×C3—41no—
425C23×C3—41no—
426C23×C3—41no—
427C23×C3—41no—
428C23×C3—41no—
429C23×C3—41no—
430C23×C3C22×D411yescharacteristic
431C22×D3—21no—
432C22×D3—21no—
433C22×D3—21no—
434C22×D3—21no—
435C22×D3#12112yes—
436C22×D3#12112yes—
437C22×D3#12112yes—
438C3×Q8—22no—
439C3×Q8—22no—
440C3×Q8—41no—
441C3×Q8—41no—
442C3×D4—22no—
443C3×D4—22no—
444C3×D4—41no—
445C3×D4—41no—
446C2×C3×C4—21no—
447C2×C3×C4—21no—
448C2×C3×C4—22no—
449C2×C3×C4—21no—
450C2×C3×C4—21no—
451C2×C3×C4—21no—
452C2×C3×C4—21no—
453C2×C3×C4—41no—
454C2×C3×C4—41no—
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×C4C22×D411yescharacteristic
462C2×C3×C4C22×D411yescharacteristic
463C2×C3×C4C22×D411yescharacteristic
464C2×C3×C4C2×#4111yescharacteristic
465C2×C3×C4C2×#4111yescharacteristic
466C2×C3×C4C2×#4111yescharacteristic
467#67—48no—
468C2×Dic3—21no—
469C2×Dic3—21no—
470C2×Dic3—22no—
471C2×Dic3—22no—
472C2×Dic3—21no—
473C2×Dic3—21no—
474C2×Dic3—21no—
475C2×Dic3—21no—
476C2×Dic3—41no—
477C2×Dic3—41no—
478C2×Dic3—41no—
479C2×Dic3—41no—
480C2×Dic3—48no—
481C2×Dic3—41no—
482C2×Dic3—41no—
483C2×Dic3—41no—
484C2×Dic3—41no—
485C2×Dic3—41no—
486C2×Dic3—41no—
487C2×Dic3#12112yes—
488C2×Dic3#12112yes—
489C2×Dic3#12112yes—
490C4×D3—48no—
491C4×D3—84no—
492C4×D3#12014yes—
493C4×D3#12314yes—
494C4×D3#12314yes—
495C4×D3#12414yes—
496Dic6—22no—
497Dic6—22no—
498Dic6—22no—
499Dic6—22no—
500Dic6—41no—
501Dic6—41no—
502Dic6—41no—
503Dic6—41no—
504Dic6—48no—
505C3×C8—22no—
506C3×C8—41no—
507C3⋊C8—22no—
508C3⋊C8—41no—
509C24—21no—
510C24—31no—
511#41—68no—
512#41—68no—
513#41—124no—
514#41—124no—
515C2×Q8—21no—
516C2×Q8—21no—
517C2×Q8—21no—
518C2×Q8—21no—
519C2×Q8—21no—
520C2×Q8—32no—
521C2×Q8—32no—
522C2×Q8—64no—
523C2×Q8—68no—
524C2×Q8—68no—
525C2×Q8—61no—
526C2×Q8—61no—
527C2×Q8—61no—
528C2×Q8—61no—
529C2×Q8—61no—
530C2×Q8—61no—
531C2×Q8—61no—
532C2×Q8—61no—
533C2×Q8—61no—
534C2×Q8—61no—
535C2×Q8—122no—
536C2×Q8—122no—
537C2×Q8—124no—
538C2×Q8—124no—
539C2×Q8D3×D412yes—
540C2×D4—21no—
541C2×D4—21no—
542C2×D4—21no—
543C2×D4—21no—
544C2×D4—21no—
545C2×D4—64no—
546C2×D4—122no—
547C2×D4—122no—
548C2×D4D3×D412yes—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—31no—
553C22×C4—32no—
554C22×C4—32no—
555C22×C4—32no—
556C22×C4—32no—
557C22×C4—32no—
558C22×C4—32no—
559C22×C4—31no—
560C22×C4—31no—
561C22×C4—64no—
562C22×C4—64no—
563C22×C4—61no—
564C22×C4—61no—
565C22×C4—61no—
566C22×C4—61no—
567C22×C4—122no—
568C22×C4—122no—
569C22×C4—122no—
570C22×C4—122no—
571C22×C4—122no—
572C22×C4—241no—
573C22×C4—241no—
574C22×C4D3×D411yescharacteristic
575C22×C4D3×D411yescharacteristic
576C22×C4C23×D311yescharacteristic
577Q16—68no—
578Q16—68no—
579SD16—28no—
580SD16—68no—
581M16—68no—
582C2×C8—21no—
583C2×C8—21no—
584C2×C8—21no—
585C2×C8—21no—
586C2×C8—21no—
587C2×C8—32no—
588C2×C8—61no—
589C2×C8—61no—
590C2×C8—61no—
591C2×C8—61no—
592C2×C8—61no—
593C2×C8—124no—
594C2×C8D3×D412yes—
595C4⋊C4—21no—
596C4⋊C4—21no—
597C4⋊C4—21no—
598C4⋊C4—21no—
599C4⋊C4—62no—
600C4⋊C4—62no—
601C4⋊C4—61no—
602C4⋊C4—61no—
603C4⋊C4—61no—
604C4⋊C4—61no—
605C4⋊C4—122no—
606C22⋊C4—62no—
607C22⋊C4—62no—
608C22⋊C4—81no—
609C22⋊C4—81no—
610C22⋊C4—122no—
611C22⋊C4—241no—
612C22⋊C4—241no—
613C42—21no—
614C42—21no—
615C42—61no—
616C42—61no—
617C42—122no—
618C22×C3—42no—
619C22×C3—42no—
620C22×C3—42no—
621C22×C3—81no—
622C22×C3—81no—
623C22×C3—81no—
624C22×C3—81no—
625C22×C3C2×#12111yescharacteristic
626C22×C3C2×#12111yescharacteristic
627C22×C3C2×#12111yescharacteristic
628C22×C3#57711yescharacteristic
629C22×C3#57711yescharacteristic
630C22×C3#57811yescharacteristic
631C22×C3#57811yescharacteristic
632C2×D3—22no—
633C2×D3—22no—
634C2×D3—22no—
635C2×D3—22no—
636C2×D3—22no—
637C2×D3—22no—
638C2×D3#39414yes—
639C3×C4—42no—
640C3×C4—41no—
641C3×C4—41no—
642C3×C4—81no—
643C3×C4—81no—
644C3×C4C2×#12011yescharacteristic
645C3×C4C2×#12311yescharacteristic
646C3×C4C2×#12311yescharacteristic
647C3×C4C2×#12411yescharacteristic
648Dic3—42no—
649Dic3—42no—
650Dic3—41no—
651Dic3—41no—
652Dic3—81no—
653Dic3—81no—
654Dic3#39414yes—
655C23—22no—
656C23—32no—
657C23—32no—
658C23—32no—
659C23—41no—
660C23—41no—
661C23—41no—
662C23—41no—
663C23—41no—
664C23—41no—
665C23—61no—
666C23—61no—
667C23—61no—
668C23—61no—
669C23C2×D3×D411yescharacteristic
670Q8—22no—
671Q8—22no—
672Q8—41no—
673Q8—41no—
674Q8—62no—
675Q8—62no—
676Q8—62no—
677Q8—62no—
678Q8—128no—
679Q8—121no—
680Q8—121no—
681Q8—121no—
682Q8—121no—
683D4—22no—
684D4—22no—
685D4—41no—
686D4—41no—
687D4—128no—
688C2×C4—21no—
689C2×C4—21no—
690C2×C4—21no—
691C2×C4—21no—
692C2×C4—21no—
693C2×C4—21no—
694C2×C4—22no—
695C2×C4—32no—
696C2×C4—32no—
697C2×C4—32no—
698C2×C4—34no—
699C2×C4—34no—
700C2×C4—34no—
701C2×C4—34no—
702C2×C4—41no—
703C2×C4—41no—
704C2×C4—41no—
705C2×C4—41no—
706C2×C4—41no—
707C2×C4—41no—
708C2×C4—41no—
709C2×C4—41no—
710C2×C4—61no—
711C2×C4—61no—
712C2×C4—61no—
713C2×C4—61no—
714C2×C4—61no—
715C2×C4—61no—
716C2×C4—62no—
717C2×C4—62no—
718C2×C4—128no—
719C2×C4—128no—
720C2×C4—121no—
721C2×C4—121no—
722C2×C4—121no—
723C2×C4—121no—
724C2×C4—121no—
725C2×C4—121no—
726C2×C4—121no—
727C2×C4—121no—
728C2×C4—121no—
729C2×C4—121no—
730C2×C4—244no—
731C2×C4C2×D3×D411yescharacteristic
732C2×C4C2×D3×D411yescharacteristic
733C2×C4C2×D3×D411yescharacteristic
734C2×C4D3×#4111yescharacteristic
735C2×C4D3×#4111yescharacteristic
736C2×C4D3×#4111yescharacteristic
737C8—22no—
738C8—41no—
739C8—62no—
740C8—121no—
741C2×C3—82no—
742C2×C3C2×#39411yescharacteristic
743C2×C3#304311yescharacteristic
744C2×C3#304411yescharacteristic
745C2×C3#304611yescharacteristic
746C2×C3#304611yescharacteristic
747C2×C3#306311yescharacteristic
748C2×C3#306311yescharacteristic
749D3—24no—
750C22—34no—
751C22—42no—
752C22—42no—
753C22—42no—
754C22—62no—
755C22—62no—
756C22—62no—
757C22—62no—
758C22—62no—
759C22—62no—
760C22—81no—
761C22—81no—
762C22—81no—
763C22—81no—
764C22D3×#12111yescharacteristic
765C22D3×#12111yescharacteristic
766C22D3×#12111yescharacteristic
767C22#576211yescharacteristic
768C22#577111yescharacteristic
769C22#577511yescharacteristic
770C22#577911yescharacteristic
771C4—34no—
772C4—41no—
773C4—42no—
774C4—41no—
775C4—81no—
776C4—81no—
777C4—121no—
778C4—122no—
779C4—122no—
780C4—121no—
781C4—241no—
782C4—241no—
783C4D3×#12011yescharacteristic
784C4D3×#12311yescharacteristic
785C4D3×#12311yescharacteristic
786C4D3×#12411yescharacteristic
787C3#2354511yescharacteristic, complemented, Sylow
788C2—64no—
789C2—82no—
790C2D3×#39411yescharacteristic
791C2#8038511yescharacteristic
792C2#8043111yescharacteristic
793C2#8053911yescharacteristic
794C2#8060111yescharacteristic
795C2#8066211yescharacteristic
796C2#8081011yescharacteristic
subgroupG/H
centerC23C2×D3×D4
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC3×#2055C2
socleC23×C3C22×D4
prime radicalC22×#237C22
hypercenter#2055D3
hypocenterC3#23545
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2055

Complements

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

NH ≅ G/Ntype
2. C2×#4839C2semidirect
3. C2×D3×#103C2semidirect
5. #76610C2semidirect
7. C3×#2055C2semidirect
8. #72051C2semidirect
9. #70487C2semidirect
10. #70285C2semidirect
11. #70217C2semidirect
12. #69681C2semidirect
13. #69651C2semidirect
14. #68867C2semidirect
15. #68864C2semidirect
79. #2055D3semidirect
787. C3#23545semidirect

Maximal subgroups

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

subgroupindex
C22×#9152
C2×#48392
C2×D3×#1032
C2×#47722
#766102
#762942
C3×#20552
#720512
#704872
#702852
#702172
#696812
#696512
#688672
#688642
#235453