Finite Group Databasebeta

← #10827344

Subgroups — #10827344

Order 768.

1494 conjugacy classes of subgroups.

The subgroup lattice has 844 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#5611C211yesmaximal, characteristic
2C2×#5170C211yesmaximal, characteristic, complemented
3#82751C211yesmaximal, characteristic, complemented
4C2×D3×#103C211yesmaximal, characteristic, complemented
5C3×#2000C211yesmaximal, characteristic, complemented
6#72047C211yesmaximal, characteristic, complemented
7#71692C211yesmaximal, characteristic, complemented
8#71685C211yesmaximal, characteristic, complemented
9#70231C211yesmaximal, characteristic, complemented
10#70202C211yesmaximal, characteristic, complemented
11#70171C211yesmaximal, characteristic, complemented
12#69957C211yesmaximal, characteristic, complemented
13#69930C211yesmaximal, characteristic, complemented
14#68910C211yesmaximal, characteristic, complemented
15#68871C211yesmaximal, characteristic, complemented
16#23961—31nomaximal, Sylow
17C22×D3×Q8C2211yescharacteristic
18C22×#237—21no—
19C22×C3×SD16C2211yescharacteristic
20C2×C3×C22⋊Q8C2211yescharacteristic
21C2×C3×#121C2211yescharacteristic
22C2×#938C2211yescharacteristic
23C2×#935—21no—
24C2×D4×Dic3C2211yescharacteristic
25C22×#214C2211yescharacteristic
26C2×C4×#67C2211yescharacteristic
27C22×C4⋊Dic3C2211yescharacteristic
28C2×#924C2211yescharacteristic
29C22×D3×C8C2211yescharacteristic
30#5611—24no—
31#5611—24no—
32C2×D3×C4⋊C4C2211yescharacteristic
33C2×#888C2211yescharacteristic
34C2×#883—21no—
35C2×#878—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×#547—31no—
65C2×#448—31no—
66C22×#103—31no—
67#2409—31no—
68#2024—31no—
69#2024—31no—
70#2000—31no—
71#2000D311yescharacteristic, complemented
72#1893—31no—
73#1877—31no—
74#1877—31no—
75#1872—31no—
76#1872—31no—
77#1869—31no—
78#1823—31no—
79C22×C3×Q8C2311yescharacteristic
80C22×C3×D4—21no—
81C22×C3×D4C2311yescharacteristic
82C23×C3×C4C2311yescharacteristic
83C22×#67—21no—
84C22×#67D411yescharacteristic
85C23×Dic3—21no—
86C23×Dic3—21no—
87C2×D3×Q8—22no—
88C2×D3×Q8—22no—
89C2×D3×Q8—22no—
90C2×D3×Q8—22no—
91C2×D3×Q8—41no—
92C2×D3×Q8—41no—
93C2×#237—28no—
94C2×#237—44no—
95C2×#237—44no—
96C22×C4×D3—21no—
97C22×C4×D3—21no—
98C22×C4×D3C2311yescharacteristic
99C22×Dic6—21no—
100C22×Dic6—21no—
101C22×Dic6C2311yescharacteristic
102C2×C3×SD16—22no—
103C2×C3×SD16—22no—
104C2×C3×SD16—41no—
105C22×C3×C8C2311yescharacteristic
106C22×C3×C8C2311yescharacteristic
107C3×C22⋊Q8—22no—
108C3×C22⋊Q8—41no—
109C3×#121—22no—
110C3×#121—22no—
111C2×C3×C4⋊C4—21no—
112C2×C3×C4⋊C4C2311yescharacteristic
113C2×C3×C4⋊C4C2311yescharacteristic
114C2×C3×C22⋊C4—21no—
115C2×C3×C22⋊C4—21no—
116C2×#217—21no—
117C2×#217—21no—
118C2×#217—21no—
119C2×#217D411yescharacteristic
120#938—22no—
121#938D414yes—
122#935—28no—
123D4×Dic3—22no—
124D4×Dic3—22no—
125C2×#214—22no—
126C2×#214—22no—
127C2×#214—41no—
128C4×#67—22no—
129C4×#67—22no—
130C2×(C2×D3)⋊C4—21no—
131C2×(C2×D3)⋊C4D411yescharacteristic
132C2×C4⋊Dic3—21no—
133C2×C4⋊Dic3—22no—
134C2×C4⋊Dic3—22no—
135C2×C4⋊Dic3C2311yescharacteristic
136C2×C4⋊Dic3C2311yescharacteristic
137C2×C4⋊Dic3C2311yescharacteristic
138#924—22no—
139#924—41no—
140C2×Dic3⋊C4—21no—
141C2×Dic3⋊C4—21no—
142C2×Dic3⋊C4—21no—
143C2×Dic3⋊C4D411yescharacteristic
144C2×C4×Dic3C2311yescharacteristic
145C22×C3⋊C8C2311yescharacteristic
146C22×C3⋊C8C2311yescharacteristic
147C2×D3×C8—22no—
148C2×D3×C8—41no—
149C2×D3×C8—41no—
150D3×C4⋊C4—22no—
151D3×C4⋊C4D414yes—
152#888—22no—
153#888—22no—
154#883—28no—
155#878—28no—
156C3×#103—22no—
157C3×#102—41no—
158C3×C22⋊C8—41no—
159#835—22no—
160#835—22no—
161#832—41no—
162C3⋊#95—21no—
163C3⋊#95—21no—
164C3⋊#95—21no—
165C3⋊#95—21no—
166C3⋊#95—21no—
167#830—41no—
168(C2×D3)⋊C8—22no—
169#816—22no—
170#816—22no—
171#810—22no—
172C22×#41—61no—
173C23×Q8—31no—
174C22×SD16—31no—
175C22×SD16C2×D311yescharacteristic
176C23×C8—31no—
177#547—64no—
178#547—64no—
179C2×C4⋊Q8—31no—
180C2×#123—61no—
181C2×#123—61no—
182C2×C22⋊Q8—31no—
183C2×C22⋊Q8—61no—
184C2×C22⋊Q8C2×D311yescharacteristic
185C2×#121—31no—
186C2×#121C2×D311yescharacteristic
187C2×C4×D4—31no—
188C2×C4×D4—31no—
189C22×C4⋊C4—31no—
190C22×C4⋊C4—31no—
191#448—64no—
192C2×#103—31no—
193C2×#103—31no—
194C2×#103—31no—
195C2×#103—31no—
196C2×#103—31no—
197C2×#103—64no—
198C2×#103C2×D311yescharacteristic
199C2×#102—31no—
200C2×#102C2×D311yescharacteristic
201C2×C22⋊C8—31no—
202C2×C22⋊C8—31no—
203C2×C22⋊C8C2×D311yescharacteristic
204#395—61no—
205#393—61no—
206#391—31no—
207#391—31no—
208#386—61no—
209#385—61no—
210#380—31no—
211#340—31no—
212#340—31no—
213#340—31no—
214#340—31no—
215#340—31no—
216#340C2×D311yescharacteristic
217#336—31no—
218#336—31no—
219C24×C3—21no—
220C24×C3C2×D411yescharacteristic
221C23×D3C2×D411yescharacteristic
222C2×C3×Q8—21no—
223C2×C3×Q8—21no—
224C2×C3×Q8—21no—
225C2×C3×Q8—21no—
226C2×C3×Q8—21no—
227C2×C3×Q8#4112yescomplemented
228C2×C3×D4—24no—
229C2×C3×D4—21no—
230C2×C3×D4—21no—
231C2×C3×D4—21no—
232C2×C3×D4—21no—
233C2×C3×D4—21no—
234C2×C3×D4—42no—
235C2×C3×D4—42no—
236C2×C3×D4C2×D412yes—
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×C4—21no—
245C22×C3×C4—21no—
246C22×C3×C4C2×D411yescharacteristic
247C22×C3×C4C2411yescharacteristic
248C2×#67—22no—
249C2×#67—22no—
250C2×#67—24no—
251C2×#67—42no—
252C2×#67—42no—
253C2×#67SD1614yescomplemented
254C22×Dic3—24no—
255C22×Dic3—24no—
256C22×Dic3—21no—
257C22×Dic3—21no—
258C22×Dic3—21no—
259C22×Dic3—21no—
260C22×Dic3—42no—
261C22×Dic3—42no—
262C22×Dic3—42no—
263C22×Dic3—42no—
264C22×Dic3C2×D411yescharacteristic
265C22×Dic3C2×D411yescharacteristic
266C22×Dic3C2×D411yescharacteristic
267D3×Q8—28no—
268D3×Q8—44no—
269D3×Q8—44no—
270D3×Q8—44no—
271#237—432no—
272C2×C4×D3—21no—
273C2×C4×D3—21no—
274C2×C4×D3—21no—
275C2×C4×D3—21no—
276C2×C4×D3—24no—
277C2×C4×D3—42no—
278C2×C4×D3—42no—
279C2×C4×D3—42no—
280C2×C4×D3—42no—
281C2×C4×D3—42no—
282C2×C4×D3C2×D412yes—
283C2×C4×D3C2×D412yes—
284C2×Dic6—21no—
285C2×Dic6—21no—
286C2×Dic6—21no—
287C2×Dic6—21no—
288C2×Dic6—24no—
289C2×Dic6—21no—
290C2×Dic6—42no—
291C2×Dic6—42no—
292C2×Dic6—42no—
293C2×Dic6—42no—
294C2×Dic6—42no—
295C2×Dic6#4112yescomplemented
296C3×SD16—44no—
297C2×C3×C8—21no—
298C2×C3×C8—21no—
299C2×C3×C8—21no—
300C2×C3×C8—21no—
301C2×C3×C8—21no—
302C2×C3×C8—21no—
303C3×C4⋊C4—21no—
304C3×C4⋊C4—21no—
305C3×C4⋊C4—21no—
306C3×C4⋊C4—42no—
307C3×C4⋊C4C2×D412yes—
308C3×C22⋊C4—24no—
309C3×C22⋊C4—42no—
310#217—24no—
311#217—24no—
312#217—22no—
313#217—42no—
314#214—44no—
315(C2×D3)⋊C4—22no—
316(C2×D3)⋊C4—42no—
317C4⋊Dic3—24no—
318C4⋊Dic3—21no—
319C4⋊Dic3—21no—
320C4⋊Dic3—21no—
321C4⋊Dic3—21no—
322C4⋊Dic3C2×D412yes—
323C4⋊Dic3C2×D412yes—
324Dic3⋊C4—24no—
325Dic3⋊C4—22no—
326Dic3⋊C4—24no—
327Dic3⋊C4—42no—
328C4×Dic3—21no—
329C4×Dic3—21no—
330C2×C3⋊C8—21no—
331C2×C3⋊C8—21no—
332C2×C3⋊C8—21no—
333C2×C3⋊C8—21no—
334C2×C3⋊C8—21no—
335C2×C3⋊C8—21no—
336D3×C8—44no—
337C2×#41—68no—
338C2×#41—124no—
339C2×#41—124no—
340C22×Q8—31no—
341C22×Q8—61no—
342C22×Q8—61no—
343C22×Q8—62no—
344C22×Q8—62no—
345C22×Q8—62no—
346C22×Q8—62no—
347C22×Q8—121no—
348C22×Q8—121no—
349C22×Q8C22×D311yescharacteristic
350C22×D4—21no—
351C22×D4—31no—
352C22×D4—61no—
353C22×D4C22×D311yescharacteristic
354C23×C4—31no—
355C23×C4—61no—
356C23×C4—61no—
357C23×C4—61no—
358C23×C4—61no—
359C23×C4C22×D311yescharacteristic
360C2×SD16—22no—
361C2×SD16—22no—
362C2×SD16—41no—
363C2×SD16—62no—
364C2×SD16—62no—
365C2×SD16—121no—
366C22×C8—31no—
367C22×C8—31no—
368C22×C8—62no—
369C22×C8—121no—
370C22×C8—121no—
371C22×C8C22×D311yescharacteristic
372C22×C8C22×D311yescharacteristic
373C4⋊Q8—62no—
374C4⋊Q8—62no—
375#123—68no—
376#123—68no—
377C22⋊Q8—22no—
378C22⋊Q8—41no—
379C22⋊Q8—68no—
380C22⋊Q8—62no—
381C22⋊Q8—121no—
382#121—22no—
383#121—22no—
384#121—34no—
385#121—62no—
386C4×D4—62no—
387C4×D4—62no—
388C4×D4—62no—
389C4×D4—62no—
390C2×C4⋊C4—21no—
391C2×C4⋊C4—31no—
392C2×C4⋊C4—31no—
393C2×C4⋊C4—34no—
394C2×C4⋊C4—31no—
395C2×C4⋊C4—31no—
396C2×C4⋊C4—62no—
397C2×C4⋊C4—62no—
398C2×C4⋊C4—62no—
399C2×C4⋊C4—61no—
400C2×C4⋊C4—61no—
401C2×C4⋊C4—61no—
402C2×C4⋊C4—61no—
403C2×C4⋊C4C22×D311yescharacteristic
404C2×C4⋊C4C22×D311yescharacteristic
405C2×C22⋊C4—21no—
406C2×C22⋊C4—21no—
407C2×C22⋊C4—31no—
408C2×C22⋊C4—31no—
409C2×C22⋊C4—61no—
410C2×C22⋊C4—61no—
411C2×C22⋊C4—61no—
412C2×C22⋊C4—61no—
413C2×C42—31no—
414#103—22no—
415#103—62no—
416#103—62no—
417#103—62no—
418#103—62no—
419#103—62no—
420#102—41no—
421#102—121no—
422C22⋊C8—41no—
423C22⋊C8—62no—
424C22⋊C8—121no—
425#95—61no—
426#95—61no—
427#95—61no—
428#95—61no—
429#95—61no—
430C23×C3—21no—
431C23×C3—21no—
432C23×C3—21no—
433C23×C3—21no—
434C23×C3—21no—
435C23×C3—21no—
436C23×C3—22no—
437C23×C3—41no—
438C23×C3—41no—
439C23×C3—41no—
440C23×C3—41no—
441C23×C3—41no—
442C23×C3—41no—
443C23×C3C2×SD1612yes—
444C23×C3C22×D411yescharacteristic
445C22×D3—21no—
446C22×D3—21no—
447C22×D3—21no—
448C22×D3—21no—
449C22×D3#12012yes—
450C22×D3C2×SD1612yes—
451C22×D3AGL(1,ℤ/8)12yes—
452C3×Q8—22no—
453C3×Q8—22no—
454C3×Q8—41no—
455C3×Q8—41no—
456C3×D4—22no—
457C3×D4—22no—
458C3×D4—48no—
459C3×D4—41no—
460C3×D4—41no—
461C2×C3×C4—22no—
462C2×C3×C4—21no—
463C2×C3×C4—21no—
464C2×C3×C4—22no—
465C2×C3×C4—21no—
466C2×C3×C4—41no—
467C2×C3×C4—41no—
468C2×C3×C4—41no—
469C2×C3×C4—41no—
470C2×C3×C4—41no—
471C2×C3×C4—41no—
472C2×C3×C4—41no—
473C2×C3×C4—41no—
474C2×C3×C4—41no—
475C2×C3×C4—41no—
476C2×C3×C4—41no—
477C2×C3×C4C22×D411yescharacteristic
478C2×C3×C4C22×D411yescharacteristic
479C2×C3×C4C2×#4111yescharacteristic
480C2×C3×C4C2×#4111yescharacteristic
481C2×C3×C4H(5,𝔽2)11yescharacteristic
482C2×C3×C4H(5,𝔽2)11yescharacteristic
483#67—28no—
484#67—48no—
485C2×Dic3—21no—
486C2×Dic3—21no—
487C2×Dic3—21no—
488C2×Dic3—21no—
489C2×Dic3—21no—
490C2×Dic3—22no—
491C2×Dic3—22no—
492C2×Dic3—22no—
493C2×Dic3—21no—
494C2×Dic3—21no—
495C2×Dic3—48no—
496C2×Dic3—48no—
497C2×Dic3—41no—
498C2×Dic3—41no—
499C2×Dic3—41no—
500C2×Dic3—41no—
501C2×Dic3—41no—
502C2×Dic3—41no—
503C2×Dic3—41no—
504C2×Dic3—41no—
505C2×Dic3—41no—
506C2×Dic3#12012yes—
507C2×Dic3C2×SD1612yes—
508C4×D3—22no—
509C4×D3—22no—
510C4×D3—22no—
511C4×D3—22no—
512C4×D3—48no—
513C4×D3—48no—
514Dic6—22no—
515Dic6—22no—
516Dic6—48no—
517Dic6—48no—
518Dic6—41no—
519Dic6—41no—
520C3×C8—41no—
521C3×C8—41no—
522C3⋊C8—41no—
523C3⋊C8—41no—
524C24—21no—
525C24—31no—
526C24D3×D411yescharacteristic
527#41—1232no—
528C2×Q8—21no—
529C2×Q8—21no—
530C2×Q8—21no—
531C2×Q8—21no—
532C2×Q8—21no—
533C2×Q8—32no—
534C2×Q8—64no—
535C2×Q8—61no—
536C2×Q8—68no—
537C2×Q8—61no—
538C2×Q8—61no—
539C2×Q8—61no—
540C2×Q8—61no—
541C2×Q8—122no—
542C2×Q8—122no—
543C2×Q8—122no—
544C2×Q8—122no—
545C2×Q8—122no—
546C2×Q8—124no—
547C2×Q8—124no—
548C2×Q8—124no—
549C2×Q8#23712yescomplemented
550C2×D4—24no—
551C2×D4—21no—
552C2×D4—21no—
553C2×D4—21no—
554C2×D4—21no—
555C2×D4—21no—
556C2×D4—34no—
557C2×D4—42no—
558C2×D4—42no—
559C2×D4—62no—
560C2×D4—62no—
561C2×D4—64no—
562C2×D4—122no—
563C2×D4—122no—
564C2×D4D3×D412yes—
565C22×C4—21no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—31no—
575C22×C4—31no—
576C22×C4—32no—
577C22×C4—32no—
578C22×C4—31no—
579C22×C4—64no—
580C22×C4—61no—
581C22×C4—61no—
582C22×C4—61no—
583C22×C4—61no—
584C22×C4—64no—
585C22×C4—64no—
586C22×C4—61no—
587C22×C4—61no—
588C22×C4—61no—
589C22×C4—61no—
590C22×C4—122no—
591C22×C4—122no—
592C22×C4—122no—
593C22×C4—122no—
594C22×C4—122no—
595C22×C4—122no—
596C22×C4—122no—
597C22×C4—122no—
598C22×C4—122no—
599C22×C4D3×D411yescharacteristic
600C22×C4C23×D311yescharacteristic
601SD16—44no—
602SD16—124no—
603C2×C8—21no—
604C2×C8—21no—
605C2×C8—21no—
606C2×C8—21no—
607C2×C8—21no—
608C2×C8—21no—
609C2×C8—61no—
610C2×C8—61no—
611C2×C8—61no—
612C2×C8—61no—
613C2×C8—61no—
614C2×C8—61no—
615C2×C8—124no—
616C4⋊C4—21no—
617C4⋊C4—21no—
618C4⋊C4—21no—
619C4⋊C4—32no—
620C4⋊C4—32no—
621C4⋊C4—42no—
622C4⋊C4—64no—
623C4⋊C4—62no—
624C4⋊C4—64no—
625C4⋊C4—64no—
626C4⋊C4—61no—
627C4⋊C4—61no—
628C4⋊C4—61no—
629C4⋊C4—61no—
630C4⋊C4—122no—
631C4⋊C4D3×D412yes—
632C22⋊C4—24no—
633C22⋊C4—42no—
634C22⋊C4—62no—
635C22⋊C4—62no—
636C22⋊C4—64no—
637C22⋊C4—64no—
638C22⋊C4—122no—
639C22⋊C4—122no—
640C42—61no—
641C42—61no—
642C22×C3—22no—
643C22×C3—22no—
644C22×C3—22no—
645C22×C3—41no—
646C22×C3—41no—
647C22×C3—41no—
648C22×C3—41no—
649C22×C3—42no—
650C22×C3—42no—
651C22×C3—42no—
652C22×C3—81no—
653C22×C3—81no—
654C22×C3—81no—
655C22×C3—81no—
656C22×C3C2×#12011yescharacteristic
657C22×C3#54611yescharacteristic
658C22×C3#54611yescharacteristic
659C22×C3C22×SD1611yescharacteristic
660C22×C3C2×AGL(1,ℤ/8)11yescharacteristic
661C22×C3#57811yescharacteristic
662C22×C3#57811yescharacteristic
663C2×D3—22no—
664C2×D3—22no—
665C2×D3—22no—
666C2×D3—22no—
667C2×D3—22no—
668C2×D3—22no—
669C2×D3#45014yes—
670C3×C4—42no—
671C3×C4—41no—
672C3×C4—42no—
673C3×C4—81no—
674C3×C4#52511yescharacteristic
675C3×C4#53511yescharacteristic
676C3×C4#54611yescharacteristic
677C3×C4#54611yescharacteristic
678Dic3—22no—
679Dic3—22no—
680Dic3—42no—
681Dic3—42no—
682Dic3—42no—
683Dic3—41no—
684Dic3—81no—
685C23—21no—
686C23—21no—
687C23—21no—
688C23—21no—
689C23—21no—
690C23—21no—
691C23—22no—
692C23—32no—
693C23—32no—
694C23—32no—
695C23—41no—
696C23—41no—
697C23—41no—
698C23—41no—
699C23—41no—
700C23—41no—
701C23—61no—
702C23—61no—
703C23—61no—
704C23—61no—
705C23D3×SD1612yes—
706C23C2×D3×D411yescharacteristic
707Q8—22no—
708Q8—22no—
709Q8—41no—
710Q8—41no—
711Q8—62no—
712Q8—62no—
713Q8—128no—
714Q8—128no—
715Q8—121no—
716Q8—121no—
717D4—22no—
718D4—22no—
719D4—48no—
720D4—41no—
721D4—41no—
722D4—68no—
723D4—128no—
724C2×C4—21no—
725C2×C4—22no—
726C2×C4—22no—
727C2×C4—21no—
728C2×C4—21no—
729C2×C4—32no—
730C2×C4—32no—
731C2×C4—41no—
732C2×C4—41no—
733C2×C4—41no—
734C2×C4—41no—
735C2×C4—41no—
736C2×C4—41no—
737C2×C4—41no—
738C2×C4—41no—
739C2×C4—41no—
740C2×C4—41no—
741C2×C4—41no—
742C2×C4—61no—
743C2×C4—61no—
744C2×C4—61no—
745C2×C4—61no—
746C2×C4—62no—
747C2×C4—62no—
748C2×C4—62no—
749C2×C4—62no—
750C2×C4—61no—
751C2×C4—61no—
752C2×C4—61no—
753C2×C4—62no—
754C2×C4—62no—
755C2×C4—62no—
756C2×C4—128no—
757C2×C4—128no—
758C2×C4—128no—
759C2×C4—128no—
760C2×C4—121no—
761C2×C4—121no—
762C2×C4—121no—
763C2×C4—121no—
764C2×C4—121no—
765C2×C4—121no—
766C2×C4—121no—
767C2×C4—121no—
768C2×C4—121no—
769C2×C4C2×D3×D411yescharacteristic
770C2×C4C2×D3×D411yescharacteristic
771C2×C4C2×#23711yescharacteristic
772C2×C4#100411yescharacteristic
773C2×C4#100411yescharacteristic
774C2×C4D3×#4111yescharacteristic
775C8—41no—
776C8—41no—
777C8—121no—
778C8—121no—
779C2×C3—42no—
780C2×C3—82no—
781C2×C3#240411yescharacteristic
782C2×C3C2×#45011yescharacteristic
783C2×C3#301111yescharacteristic
784C2×C3#329811yescharacteristic
785C2×C3#329811yescharacteristic
786C2×C3#330811yescharacteristic
787C2×C3#330811yescharacteristic
788D3—24no—
789C22—22no—
790C22—22no—
791C22—22no—
792C22—34no—
793C22—41no—
794C22—41no—
795C22—41no—
796C22—41no—
797C22—42no—
798C22—42no—
799C22—42no—
800C22—62no—
801C22—62no—
802C22—62no—
803C22—62no—
804C22—62no—
805C22—62no—
806C22—81no—
807C22—81no—
808C22—81no—
809C22—81no—
810C22D3×#12011yescharacteristic
811C22#559111yescharacteristic
812C22#561011yescharacteristic
813C22C2×D3×SD1611yescharacteristic
814C22#577111yescharacteristic
815C22D3×AGL(1,ℤ/8)11yescharacteristic
816C22#577911yescharacteristic
817C4—42no—
818C4—41no—
819C4—42no—
820C4—62no—
821C4—62no—
822C4—81no—
823C4—122no—
824C4—122no—
825C4—121no—
826C4—122no—
827C4—241no—
828C4#559111yescharacteristic
829C4#560611yescharacteristic
830C4#561011yescharacteristic
831C4#571511yescharacteristic
832C3#2396111yescharacteristic, complemented, Sylow
833C2—42no—
834C2—64no—
835C2—82no—
836C2#7675411yescharacteristic
837C2#8004911yescharacteristic
838C2#8010911yescharacteristic
839C2D3×#45011yescharacteristic
840C2#8023011yescharacteristic
841C2#8068911yescharacteristic
842C2#8082011yescharacteristic
subgroupG/H
centerC23C2×D3×D4
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC3×#2000C2
socleC23×C3C22×D4
prime radicalC2×#5611C2
hypercenter#2000D3
hypocenterC3#23961
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. #71692C2semidirect
8. #71685C2semidirect
9. #70231C2semidirect
10. #70202C2semidirect
11. #70171C2semidirect
12. #69957C2semidirect
13. #69930C2semidirect
14. #68910C2semidirect
15. #68871C2semidirect
71. #2000D3semidirect
227. C2×C3×Q8#41semidirect
253. C2×#67SD16semidirect
295. C2×Dic6#41semidirect
549. C2×Q8#237semidirect
832. C3#23961semidirect

Maximal subgroups

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

subgroupindex
C2×#56112
C2×#51702
#827512
C2×D3×#1032
C3×#20002
#720472
#716922
#716852
#702312
#702022
#701712
#699572
#699302
#689102
#688712
#239613