Finite Group Databasebeta

← #10827381

Subgroups — #10827381

Order 768.

1304 conjugacy classes of subgroups.

The subgroup lattice has 826 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#5614C211yesmaximal, characteristic
2C2×#5170C211yesmaximal, characteristic, complemented
3#82751C211yesmaximal, characteristic, complemented
4C2×D3×#103C211yesmaximal, characteristic, complemented
5C3×#2000C211yesmaximal, characteristic, complemented
6#72047C211yesmaximal, characteristic, complemented
7#71693C211yesmaximal, characteristic, complemented
8#71685C211yesmaximal, characteristic, complemented
9#70232C211yesmaximal, characteristic, complemented
10#70202C211yesmaximal, characteristic, complemented
11#70171C211yesmaximal, characteristic, complemented
12#69957C211yesmaximal, characteristic, complemented
13#69931C211yesmaximal, characteristic, complemented
14#68911C211yesmaximal, characteristic, complemented
15#68872C211yesmaximal, characteristic, complemented
16#23964—31nomaximal, Sylow
17C22×D3×Q8C2211yescharacteristic
18C22×C3×SD16C2211yescharacteristic
19C2×C3×C22⋊Q8C2211yescharacteristic
20C2×C3×#121C2211yescharacteristic
21C2×#938—21no—
22C2×#938C2211yescharacteristic
23C2×#935—21no—
24C2×D4×Dic3C2211yescharacteristic
25C22×#214C2211yescharacteristic
26C2×C4×#67C2211yescharacteristic
27C2×#926C2211yescharacteristic
28C2×#924C2211yescharacteristic
29C22×D3×C8C2211yescharacteristic
30#5614—24no—
31#5614—24no—
32C2×D3×C4⋊C4C2211yescharacteristic
33C2×#890C2211yescharacteristic
34C2×#67⋊C4—21no—
35C2×#879—21no—
36C2×C3×#103C2211yescharacteristic
37C2×C3×#102C2211yescharacteristic
38C2×C3×C22⋊C8C2211yescharacteristic
39#5229C2211yescharacteristic
40C2×#835C2211yescharacteristic
41C2×#835C2211yescharacteristic
42C2×#832C2211yescharacteristic
43C2×#830C2211yescharacteristic
44#5170—24no—
45C2×(C2×D3)⋊C8C2211yescharacteristic
46C2×#816C2211yescharacteristic
47C2×#816C2211yescharacteristic
48#4989—21no—
49#4987C2211yescharacteristic
50#4979—21no—
51#4973C2211yescharacteristic
52C2×#810C2211yescharacteristic
53#4956—21no—
54#4947—21no—
55D3×#103—24no—
56C3×#340C2211yescharacteristic
57#4551C2211yescharacteristic
58#4551C2211yescharacteristic
59#4550C2211yescharacteristic
60#4550C2211yescharacteristic
61#4529C2211yescharacteristic
62#4529C2211yescharacteristic
63#4529C2211yescharacteristic
64C2×#553—31no—
65C2×#448—31no—
66C22×#103—31no—
67#2409—31no—
68#2026—31no—
69#2026—31no—
70#2000—31no—
71#2000D311yescharacteristic, complemented
72#1893—31no—
73#1877—31no—
74#1877—31no—
75#1873—31no—
76#1873—31no—
77#1869—31no—
78#1824—31no—
79C22×C3×Q8C2311yescharacteristic
80C22×C3×D4—21no—
81C22×C3×D4C2311yescharacteristic
82C23×C3×C4C2311yescharacteristic
83C22×#67—21no—
84C22×#67D411yescharacteristic
85C23×Dic3—21no—
86C2×D3×Q8—22no—
87C2×D3×Q8—22no—
88C2×D3×Q8—22no—
89C2×D3×Q8—22no—
90C2×D3×Q8—41no—
91C2×D3×Q8—41no—
92C22×C4×D3—21no—
93C22×C4×D3—21no—
94C22×C4×D3C2311yescharacteristic
95C22×Dic6—21no—
96C22×Dic6C2311yescharacteristic
97C2×C3×SD16—22no—
98C2×C3×SD16—22no—
99C2×C3×SD16—41no—
100C22×C3×C8C2311yescharacteristic
101C22×C3×C8C2311yescharacteristic
102C3×C22⋊Q8—22no—
103C3×C22⋊Q8—41no—
104C3×#121—22no—
105C3×#121—22no—
106C2×C3×C4⋊C4—21no—
107C2×C3×C4⋊C4C2311yescharacteristic
108C2×C3×C4⋊C4C2311yescharacteristic
109C2×C3×C22⋊C4—21no—
110C2×C3×C22⋊C4—21no—
111C2×#217—21no—
112C2×#217—21no—
113C2×#217—21no—
114C2×#217—21no—
115C2×#217D411yescharacteristic
116#938—28no—
117#938—22no—
118#938D414yes—
119#935—28no—
120D4×Dic3—22no—
121D4×Dic3—22no—
122C2×#214—22no—
123C2×#214—22no—
124C2×#214—41no—
125C4×#67—22no—
126C4×#67—22no—
127C2×(C2×D3)⋊C4—21no—
128C2×(C2×D3)⋊C4D411yescharacteristic
129#926—22no—
130#926—22no—
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×D3×C8—22no—
146C2×D3×C8—41no—
147C2×D3×C8—41no—
148D3×C4⋊C4—22no—
149D3×C4⋊C4D414yes—
150#890—22no—
151#890—22no—
152#67⋊C4—28no—
153#879—28no—
154C3×#103—22no—
155C3×#102—41no—
156C3×C22⋊C8—41no—
157#835—22no—
158#835—22no—
159#832—41no—
160C3⋊#95—21no—
161C3⋊#95—21no—
162C3⋊#95—21no—
163C3⋊#95—21no—
164C3⋊#95—21no—
165#830—41no—
166(C2×D3)⋊C8—22no—
167#816—22no—
168#816—22no—
169#810—22no—
170C23×Q8—31no—
171C22×SD16—31no—
172C22×SD16C2×D311yescharacteristic
173C23×C8—31no—
174#553—64no—
175#553—64no—
176C2×#126—61no—
177C2×#125—31no—
178C2×#123—61no—
179C2×C22⋊Q8—31no—
180C2×C22⋊Q8C2×D311yescharacteristic
181C2×#121—31no—
182C2×#121—61no—
183C2×#121C2×D311yescharacteristic
184C2×C4×D4—31no—
185C2×C4×D4—31no—
186C2×C4×D4—61no—
187C2×#117—31no—
188C22×C4⋊C4—31no—
189#448—64no—
190C2×#103—31no—
191C2×#103—31no—
192C2×#103—31no—
193C2×#103—31no—
194C2×#103—31no—
195C2×#103—64no—
196C2×#103C2×D311yescharacteristic
197C2×#102—31no—
198C2×#102C2×D311yescharacteristic
199C2×C22⋊C8—31no—
200C2×C22⋊C8—31no—
201C2×C22⋊C8C2×D311yescharacteristic
202#395—61no—
203#393—61no—
204#391—31no—
205#391—31no—
206#386—61no—
207#385—61no—
208#380—31no—
209#340—31no—
210#340—31no—
211#340—31no—
212#340—31no—
213#340—31no—
214#340C2×D311yescharacteristic
215#336—31no—
216#336—31no—
217C24×C3—21no—
218C24×C3C2×D411yescharacteristic
219C23×D3C2×D411yescharacteristic
220C2×C3×Q8—21no—
221C2×C3×Q8—21no—
222C2×C3×Q8—21no—
223C2×C3×Q8—21no—
224C2×C3×Q8—21no—
225C2×C3×Q8#4112yes—
226C2×C3×D4—24no—
227C2×C3×D4—21no—
228C2×C3×D4—21no—
229C2×C3×D4—21no—
230C2×C3×D4—21no—
231C2×C3×D4—21no—
232C2×C3×D4—81no—
233C2×C3×D4—81no—
234C2×C3×D4C2×D412yes—
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×C4—21no—
242C22×C3×C4—21no—
243C22×C3×C4—21no—
244C22×C3×C4C2×D411yescharacteristic
245C22×C3×C4C2411yescharacteristic
246C2×#67—24no—
247C2×#67—22no—
248C2×#67—22no—
249C2×#67—22no—
250C2×#67—42no—
251C2×#67—42no—
252C22×Dic3—21no—
253C22×Dic3—21no—
254C22×Dic3—21no—
255C22×Dic3—24no—
256C22×Dic3—21no—
257C22×Dic3—81no—
258C22×Dic3—81no—
259C22×Dic3C2×D411yescharacteristic
260C22×Dic3C2×D411yescharacteristic
261C22×Dic3C2×D411yescharacteristic
262D3×Q8—28no—
263D3×Q8—44no—
264D3×Q8—44no—
265D3×Q8—44no—
266C2×C4×D3—21no—
267C2×C4×D3—21no—
268C2×C4×D3—21no—
269C2×C4×D3—21no—
270C2×C4×D3—24no—
271C2×C4×D3—42no—
272C2×C4×D3—42no—
273C2×C4×D3—42no—
274C2×C4×D3—81no—
275C2×C4×D3—81no—
276C2×C4×D3C2×D412yes—
277C2×C4×D3C2×D412yes—
278C2×Dic6—21no—
279C2×Dic6—21no—
280C2×Dic6—21no—
281C2×Dic6—21no—
282C2×Dic6—21no—
283C2×Dic6—42no—
284C2×Dic6—42no—
285C2×Dic6—42no—
286C2×Dic6#4112yes—
287C3×SD16—44no—
288C2×C3×C8—21no—
289C2×C3×C8—21no—
290C2×C3×C8—21no—
291C2×C3×C8—21no—
292C2×C3×C8—21no—
293C2×C3×C8—21no—
294C3×C4⋊C4—21no—
295C3×C4⋊C4—21no—
296C3×C4⋊C4—21no—
297C3×C4⋊C4—42no—
298C3×C4⋊C4C2×D412yes—
299C3×C22⋊C4—24no—
300C3×C22⋊C4—42no—
301#217—24no—
302#217—24no—
303#217—24no—
304#217—22no—
305#217—42no—
306#214—44no—
307(C2×D3)⋊C4—22no—
308(C2×D3)⋊C4—42no—
309C4⋊Dic3—24no—
310C4⋊Dic3—21no—
311C4⋊Dic3—21no—
312C4⋊Dic3—21no—
313C4⋊Dic3—21no—
314C4⋊Dic3C2×D412yes—
315C4⋊Dic3C2×D412yes—
316Dic3⋊C4—24no—
317Dic3⋊C4—22no—
318Dic3⋊C4—24no—
319Dic3⋊C4—42no—
320C4×Dic3—24no—
321C4×Dic3—21no—
322C4×Dic3—21no—
323C2×C3⋊C8—21no—
324C2×C3⋊C8—21no—
325C2×C3⋊C8—21no—
326C2×C3⋊C8—21no—
327C2×C3⋊C8—21no—
328C2×C3⋊C8—21no—
329D3×C8—44no—
330C22×Q8—31no—
331C22×Q8—61no—
332C22×Q8—62no—
333C22×Q8—62no—
334C22×Q8—62no—
335C22×Q8—62no—
336C22×Q8—121no—
337C22×Q8—121no—
338C22×Q8C22×D311yescharacteristic
339C22×D4—21no—
340C22×D4—31no—
341C22×D4—61no—
342C22×D4C22×D311yescharacteristic
343C23×C4—31no—
344C23×C4—61no—
345C23×C4—61no—
346C23×C4—61no—
347C23×C4C22×D311yescharacteristic
348C2×SD16—22no—
349C2×SD16—22no—
350C2×SD16—41no—
351C2×SD16—62no—
352C2×SD16—62no—
353C2×SD16—121no—
354C22×C8—31no—
355C22×C8—31no—
356C22×C8—62no—
357C22×C8—121no—
358C22×C8—121no—
359C22×C8C22×D311yescharacteristic
360C22×C8C22×D311yescharacteristic
361#126—68no—
362#125—62no—
363#125—62no—
364#123—68no—
365C22⋊Q8—22no—
366C22⋊Q8—41no—
367C22⋊Q8—62no—
368C22⋊Q8—121no—
369#121—22no—
370#121—22no—
371#121—34no—
372#121—62no—
373#121—68no—
374C4×D4—68no—
375C4×D4—62no—
376C4×D4—62no—
377C4×D4—62no—
378C4×D4—62no—
379#117—62no—
380#117—62no—
381C2×C4⋊C4—21no—
382C2×C4⋊C4—31no—
383C2×C4⋊C4—31no—
384C2×C4⋊C4—34no—
385C2×C4⋊C4—31no—
386C2×C4⋊C4—31no—
387C2×C4⋊C4—62no—
388C2×C4⋊C4—61no—
389C2×C4⋊C4—61no—
390C2×C4⋊C4—61no—
391C2×C4⋊C4—61no—
392C2×C4⋊C4C22×D311yescharacteristic
393C2×C4⋊C4C22×D311yescharacteristic
394C2×C22⋊C4—21no—
395C2×C22⋊C4—21no—
396C2×C22⋊C4—31no—
397C2×C22⋊C4—31no—
398C2×C22⋊C4—61no—
399C2×C22⋊C4—61no—
400C2×C22⋊C4—61no—
401C2×C22⋊C4—61no—
402C2×C22⋊C4—61no—
403C2×C42—31no—
404C2×C42—61no—
405#103—22no—
406#103—62no—
407#103—62no—
408#103—62no—
409#103—62no—
410#103—62no—
411#102—41no—
412#102—121no—
413C22⋊C8—41no—
414C22⋊C8—62no—
415C22⋊C8—121no—
416#95—61no—
417#95—61no—
418#95—61no—
419#95—61no—
420#95—61no—
421C23×C3—21no—
422C23×C3—22no—
423C23×C3—21no—
424C23×C3—21no—
425C23×C3—21no—
426C23×C3—21no—
427C23×C3—21no—
428C23×C3—21no—
429C23×C3—41no—
430C23×C3—41no—
431C23×C3—41no—
432C23×C3—41no—
433C23×C3—41no—
434C23×C3—41no—
435C23×C3C22×D411yescharacteristic
436C22×D3—21no—
437C22×D3—21no—
438C22×D3—21no—
439C22×D3—21no—
440C22×D3#12012yes—
441C22×D3#13512yes—
442C22×D3#13712yes—
443C3×Q8—22no—
444C3×Q8—22no—
445C3×Q8—41no—
446C3×Q8—41no—
447C3×D4—22no—
448C3×D4—22no—
449C3×D4—41no—
450C3×D4—41no—
451C3×D4—84no—
452C2×C3×C4—21no—
453C2×C3×C4—22no—
454C2×C3×C4—21no—
455C2×C3×C4—22no—
456C2×C3×C4—21no—
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×C4—41no—
465C2×C3×C4—41no—
466C2×C3×C4—41no—
467C2×C3×C4—41no—
468C2×C3×C4C22×D411yescharacteristic
469C2×C3×C4C22×D411yescharacteristic
470C2×C3×C4C2×#4111yescharacteristic
471C2×C3×C4C2×#4111yescharacteristic
472C2×C3×C4H(5,𝔽2)11yescharacteristic
473C2×C3×C4H(5,𝔽2)11yescharacteristic
474#67—44no—
475#67—48no—
476C2×Dic3—21no—
477C2×Dic3—21no—
478C2×Dic3—21no—
479C2×Dic3—21no—
480C2×Dic3—22no—
481C2×Dic3—22no—
482C2×Dic3—22no—
483C2×Dic3—21no—
484C2×Dic3—21no—
485C2×Dic3—21no—
486C2×Dic3—21no—
487C2×Dic3—41no—
488C2×Dic3—41no—
489C2×Dic3—41no—
490C2×Dic3—41no—
491C2×Dic3—41no—
492C2×Dic3—41no—
493C2×Dic3—41no—
494C2×Dic3—41no—
495C2×Dic3—41no—
496C2×Dic3—84no—
497C2×Dic3#12012yes—
498C4×D3—22no—
499C4×D3—22no—
500C4×D3—22no—
501C4×D3—22no—
502C4×D3—48no—
503C4×D3—84no—
504Dic6—22no—
505Dic6—22no—
506Dic6—48no—
507Dic6—41no—
508Dic6—41no—
509C3×C8—41no—
510C3×C8—41no—
511C3⋊C8—41no—
512C3⋊C8—41no—
513C24—21no—
514C24—31no—
515C24D3×D411yescharacteristic
516C2×Q8—21no—
517C2×Q8—21no—
518C2×Q8—21no—
519C2×Q8—21no—
520C2×Q8—21no—
521C2×Q8—32no—
522C2×Q8—61no—
523C2×Q8—68no—
524C2×Q8—61no—
525C2×Q8—61no—
526C2×Q8—61no—
527C2×Q8—61no—
528C2×Q8—122no—
529C2×Q8—122no—
530C2×Q8—122no—
531C2×Q8—124no—
532C2×Q8—124no—
533C2×Q8—124no—
534C2×Q8#23712yes—
535C2×D4—24no—
536C2×D4—21no—
537C2×D4—21no—
538C2×D4—21no—
539C2×D4—21no—
540C2×D4—21no—
541C2×D4—64no—
542C2×D4—62no—
543C2×D4—62no—
544C2×D4—62no—
545C2×D4—81no—
546C2×D4—81no—
547C2×D4—122no—
548C2×D4—122no—
549C2×D4D3×D412yes—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—21no—
559C22×C4—31no—
560C22×C4—32no—
561C22×C4—32no—
562C22×C4—31no—
563C22×C4—31no—
564C22×C4—64no—
565C22×C4—61no—
566C22×C4—61no—
567C22×C4—61no—
568C22×C4—61no—
569C22×C4—61no—
570C22×C4—61no—
571C22×C4—61no—
572C22×C4—64no—
573C22×C4—61no—
574C22×C4—122no—
575C22×C4—122no—
576C22×C4—122no—
577C22×C4—241no—
578C22×C4—241no—
579C22×C4—241no—
580C22×C4—241no—
581C22×C4D3×D411yescharacteristic
582C22×C4C23×D311yescharacteristic
583SD16—44no—
584SD16—124no—
585C2×C8—21no—
586C2×C8—21no—
587C2×C8—21no—
588C2×C8—21no—
589C2×C8—21no—
590C2×C8—21no—
591C2×C8—61no—
592C2×C8—61no—
593C2×C8—61no—
594C2×C8—61no—
595C2×C8—61no—
596C2×C8—61no—
597C2×C8—124no—
598C4⋊C4—21no—
599C4⋊C4—21no—
600C4⋊C4—21no—
601C4⋊C4—32no—
602C4⋊C4—32no—
603C4⋊C4—42no—
604C4⋊C4—64no—
605C4⋊C4—62no—
606C4⋊C4—64no—
607C4⋊C4—64no—
608C4⋊C4—61no—
609C4⋊C4—61no—
610C4⋊C4—61no—
611C4⋊C4—61no—
612C4⋊C4—122no—
613C4⋊C4D3×D412yes—
614C22⋊C4—24no—
615C22⋊C4—42no—
616C22⋊C4—62no—
617C22⋊C4—62no—
618C22⋊C4—64no—
619C22⋊C4—64no—
620C22⋊C4—64no—
621C22⋊C4—122no—
622C22⋊C4—122no—
623C42—64no—
624C42—61no—
625C42—61no—
626C22×C3—41no—
627C22×C3—42no—
628C22×C3—41no—
629C22×C3—42no—
630C22×C3—42no—
631C22×C3—41no—
632C22×C3—41no—
633C22×C3—41no—
634C22×C3—41no—
635C22×C3—41no—
636C22×C3—81no—
637C22×C3—81no—
638C22×C3—81no—
639C22×C3—81no—
640C22×C3C2×#12011yescharacteristic
641C22×C3#54611yescharacteristic
642C22×C3#54611yescharacteristic
643C22×C3C2×#13511yescharacteristic
644C22×C3C2×#13711yescharacteristic
645C22×C3#57711yescharacteristic
646C22×C3#57711yescharacteristic
647C2×D3—22no—
648C2×D3—22no—
649C2×D3—22no—
650C2×D3—22no—
651C2×D3—22no—
652C2×D3—22no—
653C2×D3#45214yes—
654C3×C4—42no—
655C3×C4—41no—
656C3×C4—42no—
657C3×C4—81no—
658C3×C4#52511yescharacteristic
659C3×C4#53511yescharacteristic
660C3×C4#54611yescharacteristic
661C3×C4#54611yescharacteristic
662Dic3—22no—
663Dic3—42no—
664Dic3—41no—
665Dic3—42no—
666Dic3—42no—
667Dic3—41no—
668Dic3—81no—
669C23—21no—
670C23—21no—
671C23—21no—
672C23—21no—
673C23—22no—
674C23—21no—
675C23—21no—
676C23—21no—
677C23—32no—
678C23—32no—
679C23—32no—
680C23—41no—
681C23—41no—
682C23—41no—
683C23—41no—
684C23—41no—
685C23—41no—
686C23—61no—
687C23—61no—
688C23—61no—
689C23—61no—
690C23C2×D3×D411yescharacteristic
691Q8—22no—
692Q8—22no—
693Q8—41no—
694Q8—41no—
695Q8—62no—
696Q8—62no—
697Q8—128no—
698Q8—121no—
699Q8—121no—
700D4—22no—
701D4—22no—
702D4—41no—
703D4—41no—
704D4—84no—
705D4—124no—
706D4—128no—
707C2×C4—21no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—21no—
711C2×C4—21no—
712C2×C4—32no—
713C2×C4—41no—
714C2×C4—41no—
715C2×C4—41no—
716C2×C4—41no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—41no—
720C2×C4—41no—
721C2×C4—41no—
722C2×C4—41no—
723C2×C4—41no—
724C2×C4—61no—
725C2×C4—61no—
726C2×C4—62no—
727C2×C4—62no—
728C2×C4—62no—
729C2×C4—62no—
730C2×C4—61no—
731C2×C4—61no—
732C2×C4—61no—
733C2×C4—61no—
734C2×C4—62no—
735C2×C4—62no—
736C2×C4—61no—
737C2×C4—61no—
738C2×C4—62no—
739C2×C4—128no—
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—244no—
750C2×C4—244no—
751C2×C4C2×D3×D411yescharacteristic
752C2×C4C2×D3×D411yescharacteristic
753C2×C4C2×#23711yescharacteristic
754C2×C4#100411yescharacteristic
755C2×C4#100411yescharacteristic
756C2×C4D3×#4111yescharacteristic
757C8—41no—
758C8—41no—
759C8—121no—
760C8—121no—
761C2×C3—81no—
762C2×C3—82no—
763C2×C3#240411yescharacteristic
764C2×C3C2×#45211yescharacteristic
765C2×C3#300911yescharacteristic
766C2×C3#330111yescharacteristic
767C2×C3#330111yescharacteristic
768C2×C3#332011yescharacteristic
769C2×C3#332011yescharacteristic
770D3—24no—
771C22—34no—
772C22—42no—
773C22—41no—
774C22—41no—
775C22—41no—
776C22—42no—
777C22—41no—
778C22—41no—
779C22—41no—
780C22—42no—
781C22—41no—
782C22—62no—
783C22—62no—
784C22—62no—
785C22—62no—
786C22—62no—
787C22—62no—
788C22—81no—
789C22—81no—
790C22—81no—
791C22—81no—
792C22D3×#12011yescharacteristic
793C22#559111yescharacteristic
794C22#561011yescharacteristic
795C22#576211yescharacteristic
796C22D3×#13511yescharacteristic
797C22#577511yescharacteristic
798C22D3×#13711yescharacteristic
799C4—42no—
800C4—41no—
801C4—42no—
802C4—62no—
803C4—81no—
804C4—121no—
805C4—122no—
806C4—121no—
807C4—122no—
808C4—122no—
809C4—241no—
810C4#559111yescharacteristic
811C4#560611yescharacteristic
812C4#561011yescharacteristic
813C4#571511yescharacteristic
814C3#2396411yescharacteristic, complemented, Sylow
815C2—64no—
816C2—81no—
817C2—82no—
818C2#7675411yescharacteristic
819C2#8005311yescharacteristic
820C2#8010311yescharacteristic
821C2#8014811yescharacteristic
822C2D3×#45211yescharacteristic
823C2#8067211yescharacteristic
824C2#8082611yescharacteristic
subgroupG/H
centerC23C2×D3×D4
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC3×#2000C2
socleC23×C3C22×D4
prime radicalC2×#5614C2
hypercenter#2000D3
hypocenterC3#23964
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C23×C4 ◁ #2000

Complements

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

NH ≅ G/Ntype
2. C2×#5170C2semidirect
3. #82751C2semidirect
4. C2×D3×#103C2semidirect
5. C3×#2000C2semidirect
6. #72047C2semidirect
7. #71693C2semidirect
8. #71685C2semidirect
9. #70232C2semidirect
10. #70202C2semidirect
11. #70171C2semidirect
12. #69957C2semidirect
13. #69931C2semidirect
14. #68911C2semidirect
15. #68872C2semidirect
71. #2000D3semidirect
814. C3#23964semidirect

Maximal subgroups

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

subgroupindex
C2×#56142
C2×#51702
#827512
C2×D3×#1032
C3×#20002
#720472
#716932
#716852
#702322
#702022
#701712
#699572
#699312
#689112
#688722
#239643