Finite Group Databasebeta

← #10828178

Subgroups — #10828178

Order 768.

1344 conjugacy classes of subgroups.

The subgroup lattice has 830 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#5576C211yesmaximal, characteristic
2C2×#4863C211yesmaximal, characteristic, complemented
3C2×D3×#103C211yesmaximal, characteristic, complemented
4#76232C211yesmaximal, characteristic, complemented
5C3×#1865C211yesmaximal, characteristic, complemented
6#71629C211yesmaximal, characteristic, complemented
7#70582C211yesmaximal, characteristic, complemented
8#70267C211yesmaximal, characteristic, complemented
9#70267C211yesmaximal, characteristic, complemented
10#70266C211yesmaximal, characteristic, complemented
11#69628C211yesmaximal, characteristic, complemented
12#68883C211yesmaximal, characteristic, complemented
13#68824C211yesmaximal, characteristic, complemented
14#68668C211yesmaximal, characteristic, complemented
15#68630C211yesmaximal, characteristic, complemented
16#24036—31nomaximal, Sylow
17C22×#239C2211yescharacteristic
18C22×D3×Q8C2211yescharacteristic
19C2×C3×C4×Q8C2211yescharacteristic
20C22×D3×C8C2211yescharacteristic
21#5576—24no—
22#5576—24no—
23C2×#897—21no—
24C2×#897C2211yescharacteristic
25C2×#895—21no—
26C2×#895C2211yescharacteristic
27C2×D3×C4⋊C4C2211yescharacteristic
28C2×#875—21no—
29C2×#875C2211yescharacteristic
30C2×C4×D12—21no—
31C2×C4×D12C2211yescharacteristic
32C2×C3×#106C2211yescharacteristic
33C2×C3×#103C2211yescharacteristic
34C2×C3×#103C2211yescharacteristic
35C3×#389C2211yescharacteristic
36C2×#835C2211yescharacteristic
37C2×#835C2211yescharacteristic
38C2×#821C2211yescharacteristic
39C2×#821C2211yescharacteristic
40C2×(C2×D3)⋊C8C2211yescharacteristic
41C2×(C2×D3)⋊C8C2211yescharacteristic
42C2×(C2×D3)⋊C8C2211yescharacteristic
43C2×#816C2211yescharacteristic
44C2×#816C2211yescharacteristic
45#4993—21no—
46#4989—21no—
47#4987C2211yescharacteristic
48#4987C2211yescharacteristic
49#4987C2211yescharacteristic
50C2×#810C2211yescharacteristic
51C2×#810C2211yescharacteristic
52C2×#809C2211yescharacteristic
53C2×#809C2211yescharacteristic
54C2×#808C2211yescharacteristic
55#4928C2211yescharacteristic
56#4863—24no—
57D3×#103—24no—
58#4665—21no—
59#4660—21no—
60C3×#340C2211yescharacteristic
61C3×#336C2211yescharacteristic
62#4529C2211yescharacteristic
63#4524C2211yescharacteristic
64C2×#548—31no—
65C2×#481—31no—
66C22×#103—31no—
67#2487—31no—
68#2042—31no—
69#2042—31no—
70#2035—31no—
71#2035—31no—
72#1893—31no—
73#1869—31no—
74#1865—31no—
75#1865D311yescharacteristic, complemented
76#1788—31no—
77#1788—31no—
78#1787—31no—
79C22×C3×Q8C2311yescharacteristic
80C2×#239—22no—
81C2×#239—22no—
82C2×#239—22no—
83C2×#239—22no—
84C2×#239—41no—
85C2×#239—41no—
86C2×D3×Q8—22no—
87C2×D3×Q8—22no—
88C2×D3×Q8—22no—
89C2×D3×Q8—41no—
90C2×D3×Q8—41no—
91C2×D3×Q8D414yes—
92C22×D12—21no—
93C22×D12—21no—
94C22×D12D411yescharacteristic
95C22×D12C2311yescharacteristic
96C22×C4×D3—21no—
97C22×C4×D3—21no—
98C22×C4×D3—21no—
99C22×C4×D3C2311yescharacteristic
100C22×C4×D3C2311yescharacteristic
101C22×Dic6—21no—
102C22×Dic6C2311yescharacteristic
103C22×C3×C8C2311yescharacteristic
104C22×C3×C8C2311yescharacteristic
105C3×C4×Q8—22no—
106C3×C4×Q8—22no—
107C2×C3×C4⋊C4—21no—
108C2×C3×C4⋊C4—21no—
109C2×C3×C4⋊C4C2311yescharacteristic
110C2×C3×C4⋊C4C2311yescharacteristic
111C2×C3×C4⋊C4C2311yescharacteristic
112C2×C3×C42—21no—
113C2×C3×C42C2311yescharacteristic
114C2×(C2×D3)⋊C4—21no—
115C2×(C2×D3)⋊C4—21no—
116C2×(C2×D3)⋊C4—21no—
117C2×(C2×D3)⋊C4—21no—
118C2×(C2×D3)⋊C4—21no—
119C2×(C2×D3)⋊C4—21no—
120C2×(C2×D3)⋊C4—21no—
121C2×(C2×D3)⋊C4D411yescharacteristic
122C2×(C2×D3)⋊C4D411yescharacteristic
123C2×C4⋊Dic3—21no—
124C2×C4⋊Dic3D411yescharacteristic
125C2×C4⋊Dic3C2311yescharacteristic
126C2×C4⋊Dic3C2311yescharacteristic
127C2×Dic3⋊C4—21no—
128C2×Dic3⋊C4—21no—
129C22×C3⋊C8C2311yescharacteristic
130C22×C3⋊C8C2311yescharacteristic
131C2×D3×C8—22no—
132C2×D3×C8—41no—
133C2×D3×C8—41no—
134#897—28no—
135#897—22no—
136#897—22no—
137#895—28no—
138#895—22no—
139#895D414yes—
140D3×C4⋊C4—22no—
141D3×C4⋊C4—22no—
142#875—28no—
143#875—22no—
144#875—22no—
145C4×D12—28no—
146C4×D12—22no—
147C4×D12—22no—
148C3×#106—22no—
149C3×#103—22no—
150C3×#103—22no—
151C3×#95—21no—
152#835—22no—
153#835—22no—
154C3⋊#95—21no—
155C3⋊#95—21no—
156C3⋊#95—21no—
157C3⋊#95—21no—
158#821—22no—
159#821—41no—
160(C2×D3)⋊C8—22no—
161(C2×D3)⋊C8—41no—
162(C2×D3)⋊C8—41no—
163#816—22no—
164#816—41no—
165#810—22no—
166#810—41no—
167#809—22no—
168#809—41no—
169#808—22no—
170C22×#41—31no—
171C23×Q8—31no—
172C23×C8—31no—
173#548—64no—
174#548—64no—
175C2×#124—31no—
176C2×#124—61no—
177C2×C22⋊Q8—31no—
178C2×C22⋊Q8—61no—
179C2×#121—31no—
180C2×#121—61no—
181C2×C4×Q8C2×D311yescharacteristic
182C2×C4×D4—31no—
183C2×C4×D4—61no—
184C22×C4⋊C4—31no—
185#481—64no—
186C2×#106—31no—
187C2×#106C2×D311yescharacteristic
188C2×#103—31no—
189C2×#103—31no—
190C2×#103—31no—
191C2×#103—31no—
192C2×#103—31no—
193C2×#103—31no—
194C2×#103—64no—
195C2×#103C2×D311yescharacteristic
196C2×#103C2×D311yescharacteristic
197C2×#102—31no—
198C2×#102—31no—
199C2×#102—31no—
200C2×#102—31no—
201C2×C22⋊C8—31no—
202C2×C22⋊C8—31no—
203C2×C22⋊C8—31no—
204#400—61no—
205#399—61no—
206#389—31no—
207#389C2×D311yescharacteristic
208#386—61no—
209#385—61no—
210#380—31no—
211#380—31no—
212#380—31no—
213#340—31no—
214#340C2×D311yescharacteristic
215#336—31no—
216#336C2×D311yescharacteristic
217C23×D3—21no—
218C23×D3C2×D411yescharacteristic
219C23×D3C2×D411yescharacteristic
220C2×C3×Q8—21no—
221C2×C3×Q8—21no—
222C2×C3×Q8—21no—
223C2×C3×Q8C2×D412yes—
224C2×C3×Q8#4112yes—
225C2×C3×Q8#4112yes—
226C22×C3×C4—21no—
227C22×C3×C4—21no—
228C22×C3×C4—21no—
229C22×C3×C4—21no—
230C22×C3×C4C2×D411yescharacteristic
231C22×C3×C4C2×D411yescharacteristic
232C22×C3×C4C2411yescharacteristic
233C22×Dic3—21no—
234C22×Dic3—21no—
235C22×Dic3—21no—
236C22×Dic3C2×D411yescharacteristic
237C22×Dic3C2×D411yescharacteristic
238#239—44no—
239#239—44no—
240#239—44no—
241#239—44no—
242D3×Q8—28no—
243D3×Q8—44no—
244D3×Q8—44no—
245D3×Q8—44no—
246C2×D12—21no—
247C2×D12—21no—
248C2×D12—21no—
249C2×D12—21no—
250C2×D12—24no—
251C2×D12—22no—
252C2×D12—24no—
253C2×D12—22no—
254C2×D12—22no—
255C2×D12—21no—
256C2×D12—42no—
257C2×D12—42no—
258C2×D12—42no—
259C2×D12—42no—
260C2×D12C2×D412yes—
261C2×C4×D3—21no—
262C2×C4×D3—21no—
263C2×C4×D3—21no—
264C2×C4×D3—21no—
265C2×C4×D3—24no—
266C2×C4×D3—24no—
267C2×C4×D3—21no—
268C2×C4×D3—21no—
269C2×C4×D3—21no—
270C2×C4×D3—21no—
271C2×C4×D3—21no—
272C2×C4×D3—21no—
273C2×C4×D3—42no—
274C2×C4×D3—42no—
275C2×C4×D3—42no—
276C2×C4×D3—42no—
277C2×C4×D3—42no—
278C2×C4×D3—81no—
279C2×C4×D3—81no—
280C2×C4×D3C2×D412yes—
281C2×C4×D3C2×D412yes—
282C2×Dic6—21no—
283C2×Dic6—21no—
284C2×Dic6—21no—
285C2×Dic6—21no—
286C2×Dic6—21no—
287C2×Dic6—24no—
288C2×Dic6—42no—
289C2×Dic6—42no—
290C2×Dic6C2×D412yes—
291C2×C3×C8—21no—
292C2×C3×C8—21no—
293C2×C3×C8—21no—
294C2×C3×C8—21no—
295C2×C3×C8—21no—
296C2×C3×C8—21no—
297C3×C4⋊C4—24no—
298C3×C4⋊C4—21no—
299C3×C4⋊C4—21no—
300C3×C4⋊C4—21no—
301C3×C4⋊C4—21no—
302C3×C4⋊C4—21no—
303C3×C4⋊C4—81no—
304C3×C4⋊C4C2×D412yes—
305C3×C42—24no—
306C3×C42—21no—
307C3×C42—21no—
308(C2×D3)⋊C4—24no—
309(C2×D3)⋊C4—24no—
310(C2×D3)⋊C4—24no—
311(C2×D3)⋊C4—22no—
312(C2×D3)⋊C4—22no—
313(C2×D3)⋊C4—24no—
314(C2×D3)⋊C4—42no—
315(C2×D3)⋊C4—81no—
316(C2×D3)⋊C4—81no—
317C4⋊Dic3—24no—
318C4⋊Dic3—22no—
319C4⋊Dic3—21no—
320C4⋊Dic3—21no—
321C4⋊Dic3—21no—
322C4⋊Dic3—21no—
323Dic3⋊C4—42no—
324Dic3⋊C4—81no—
325C2×C3⋊C8—21no—
326C2×C3⋊C8—21no—
327C2×C3⋊C8—21no—
328C2×C3⋊C8—21no—
329C2×C3⋊C8—21no—
330C2×C3⋊C8—21no—
331D3×C8—44no—
332C2×#41—62no—
333C2×#41—62no—
334C2×#41—62no—
335C2×#41—62no—
336C2×#41—121no—
337C2×#41—121no—
338C22×Q8—34no—
339C22×Q8—31no—
340C22×Q8—61no—
341C22×Q8—62no—
342C22×Q8—62no—
343C22×Q8—62no—
344C22×Q8—121no—
345C22×Q8—121no—
346C22×Q8C22×D311yescharacteristic
347C22×D4—31no—
348C22×D4—31no—
349C22×D4—61no—
350C22×D4—61no—
351C23×C4—31no—
352C23×C4—31no—
353C23×C4—61no—
354C23×C4—61no—
355C23×C4—61no—
356C22×C8—31no—
357C22×C8—31no—
358C22×C8—62no—
359C22×C8—121no—
360C22×C8—121no—
361C22×C8C22×D311yescharacteristic
362C22×C8C22×D311yescharacteristic
363#124—62no—
364#124—62no—
365#124—68no—
366C22⋊Q8—62no—
367C22⋊Q8—68no—
368C22⋊Q8—62no—
369#121—34no—
370#121—62no—
371#121—68no—
372C4×Q8—22no—
373C4×Q8—22no—
374C4×D4—62no—
375C4×D4—62no—
376C4×D4—68no—
377C2×C4⋊C4—21no—
378C2×C4⋊C4—21no—
379C2×C4⋊C4—31no—
380C2×C4⋊C4—31no—
381C2×C4⋊C4—31no—
382C2×C4⋊C4—62no—
383C2×C4⋊C4—62no—
384C2×C4⋊C4—61no—
385C2×C4⋊C4—61no—
386C2×C4⋊C4—61no—
387C2×C4⋊C4C22×D311yescharacteristic
388C2×C4⋊C4C22×D311yescharacteristic
389C2×C4⋊C4C22×D311yescharacteristic
390C2×C22⋊C4—31no—
391C2×C22⋊C4—31no—
392C2×C22⋊C4—61no—
393C2×C22⋊C4—61no—
394C2×C22⋊C4—61no—
395C2×C22⋊C4—61no—
396C2×C22⋊C4—61no—
397C2×C22⋊C4—61no—
398C2×C22⋊C4—61no—
399C2×C42—21no—
400C2×C42C22×D311yescharacteristic
401#106—22no—
402#106—62no—
403#103—22no—
404#103—22no—
405#103—62no—
406#103—62no—
407#103—62no—
408#103—62no—
409#103—121no—
410#103—121no—
411#102—62no—
412#102—62no—
413#102—121no—
414#102—121no—
415C22⋊C8—62no—
416C22⋊C8—121no—
417C22⋊C8—121no—
418#95—21no—
419#95—61no—
420#95—61no—
421#95—61no—
422#95—61no—
423C23×C3C22×D411yescharacteristic
424C22×D3—21no—
425C22×D3—21no—
426C22×D3—21no—
427C22×D3—21no—
428C22×D3—21no—
429C22×D3—22no—
430C22×D3—21no—
431C22×D3—21no—
432C22×D3—21no—
433C22×D3—21no—
434C22×D3—21no—
435C22×D3—21no—
436C22×D3—41no—
437C22×D3—41no—
438C22×D3—41no—
439C22×D3—41no—
440C22×D3—41no—
441C22×D3—41no—
442C22×D3#12012yes—
443C22×D3#13512yes—
444C22×D3#13712yes—
445C3×Q8—22no—
446C3×Q8—22no—
447C3×Q8—22no—
448C3×Q8#12314yes—
449C2×C3×C4—22no—
450C2×C3×C4—22no—
451C2×C3×C4—22no—
452C2×C3×C4—21no—
453C2×C3×C4—22no—
454C2×C3×C4—21no—
455C2×C3×C4—21no—
456C2×C3×C4—21no—
457C2×C3×C4—21no—
458C2×C3×C4—21no—
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×C4C22×D411yescharacteristic
468C2×C3×C4C22×D411yescharacteristic
469C2×C3×C4C2×#4111yescharacteristic
470C2×C3×C4C2×#4111yescharacteristic
471C2×C3×C4H(5,𝔽2)11yescharacteristic
472C2×C3×C4H(5,𝔽2)11yescharacteristic
473C2×Dic3—21no—
474C2×Dic3—21no—
475C2×Dic3—21no—
476C2×Dic3—22no—
477C2×Dic3—21no—
478C2×Dic3—21no—
479C2×Dic3—41no—
480C2×Dic3—41no—
481C2×Dic3—41no—
482C2×Dic3—41no—
483C2×Dic3—41no—
484C2×Dic3—41no—
485C2×Dic3—41no—
486C2×Dic3—41no—
487C2×Dic3#12012yes—
488D12—22no—
489D12—22no—
490D12—48no—
491D12—44no—
492D12—48no—
493D12—41no—
494D12—41no—
495C4×D3—22no—
496C4×D3—22no—
497C4×D3—22no—
498C4×D3—22no—
499C4×D3—48no—
500C4×D3—48no—
501C4×D3—41no—
502C4×D3—41no—
503C4×D3—41no—
504C4×D3—41no—
505C4×D3—84no—
506Dic6—22no—
507Dic6—22no—
508Dic6—48no—
509Dic6—41no—
510Dic6—41no—
511C3×C8—41no—
512C3×C8—41no—
513C3⋊C8—41no—
514C3⋊C8—41no—
515C24—31no—
516C24—31no—
517C24—61no—
518#41—124no—
519#41—124no—
520#41—124no—
521#41—124no—
522C2×Q8—21no—
523C2×Q8—21no—
524C2×Q8—21no—
525C2×Q8—32no—
526C2×Q8—64no—
527C2×Q8—61no—
528C2×Q8—68no—
529C2×Q8—61no—
530C2×Q8—61no—
531C2×Q8—61no—
532C2×Q8—61no—
533C2×Q8—122no—
534C2×Q8—122no—
535C2×Q8—124no—
536C2×Q8—124no—
537C2×Q8—124no—
538C2×Q8#23512yes—
539C2×Q8D3×D412yes—
540C2×Q8#23912yes—
541C2×D4—32no—
542C2×D4—64no—
543C2×D4—62no—
544C2×D4—62no—
545C2×D4—62no—
546C2×D4—64no—
547C2×D4—61no—
548C2×D4—61no—
549C2×D4—61no—
550C2×D4—61no—
551C2×D4—61no—
552C2×D4—122no—
553C2×D4—122no—
554C2×D4—122no—
555C2×D4—122no—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—21no—
559C22×C4—21no—
560C22×C4—31no—
561C22×C4—32no—
562C22×C4—32no—
563C22×C4—31no—
564C22×C4—64no—
565C22×C4—64no—
566C22×C4—61no—
567C22×C4—61no—
568C22×C4—61no—
569C22×C4—61no—
570C22×C4—61no—
571C22×C4—61no—
572C22×C4—61no—
573C22×C4—61no—
574C22×C4—61no—
575C22×C4—61no—
576C22×C4—61no—
577C22×C4—61no—
578C22×C4—61no—
579C22×C4—122no—
580C22×C4—122no—
581C22×C4—122no—
582C22×C4—122no—
583C22×C4—122no—
584C22×C4—241no—
585C22×C4—241no—
586C22×C4D3×D411yescharacteristic
587C22×C4D3×D411yescharacteristic
588C22×C4C23×D311yescharacteristic
589C2×C8—21no—
590C2×C8—21no—
591C2×C8—21no—
592C2×C8—21no—
593C2×C8—21no—
594C2×C8—21no—
595C2×C8—61no—
596C2×C8—61no—
597C2×C8—61no—
598C2×C8—61no—
599C2×C8—61no—
600C2×C8—61no—
601C2×C8—124no—
602C4⋊C4—24no—
603C4⋊C4—21no—
604C4⋊C4—21no—
605C4⋊C4—21no—
606C4⋊C4—21no—
607C4⋊C4—21no—
608C4⋊C4—62no—
609C4⋊C4—64no—
610C4⋊C4—61no—
611C4⋊C4—61no—
612C4⋊C4—61no—
613C4⋊C4—61no—
614C4⋊C4—81no—
615C4⋊C4—122no—
616C4⋊C4—241no—
617C4⋊C4D3×D412yes—
618C22⋊C4—62no—
619C22⋊C4—64no—
620C22⋊C4—62no—
621C22⋊C4—64no—
622C22⋊C4—64no—
623C22⋊C4—64no—
624C22⋊C4—122no—
625C22⋊C4—241no—
626C22⋊C4—241no—
627C42—24no—
628C42—21no—
629C42—21no—
630C22×C3C2×#12011yescharacteristic
631C22×C3#54611yescharacteristic
632C22×C3#54611yescharacteristic
633C22×C3C2×#13511yescharacteristic
634C22×C3C2×#13711yescharacteristic
635C22×C3#57711yescharacteristic
636C22×C3#57711yescharacteristic
637C2×D3—22no—
638C2×D3—22no—
639C2×D3—22no—
640C2×D3—22no—
641C2×D3—22no—
642C2×D3—22no—
643C2×D3—42no—
644C2×D3—41no—
645C2×D3—41no—
646C2×D3—42no—
647C2×D3—41no—
648C2×D3—42no—
649C2×D3—41no—
650C2×D3—41no—
651C2×D3—41no—
652C2×D3—41no—
653C2×D3—81no—
654C2×D3—81no—
655C2×D3—81no—
656C2×D3—81no—
657C2×D3#45214yes—
658C3×C4—24no—
659C3×C4—41no—
660C3×C4—42no—
661C3×C4—41no—
662C3×C4—81no—
663C3×C4—81no—
664C3×C4C2×#12311yescharacteristic
665C3×C4#53411yescharacteristic
666C3×C4#54611yescharacteristic
667C3×C4#54611yescharacteristic
668Dic3—22no—
669Dic3—42no—
670Dic3—41no—
671Dic3—81no—
672Dic3—81no—
673C23—32no—
674C23—32no—
675C23—32no—
676C23—61no—
677C23—61no—
678C23—61no—
679C23—61no—
680C23—61no—
681C23—61no—
682C23—61no—
683C23—61no—
684C23—61no—
685C23—62no—
686C23—61no—
687C23—61no—
688C23—121no—
689C23—121no—
690C23—121no—
691C23—121no—
692C23—121no—
693C23—121no—
694C23C2×D3×D411yescharacteristic
695Q8—22no—
696Q8—22no—
697Q8—22no—
698Q8—62no—
699Q8—62no—
700Q8—128no—
701Q8—121no—
702Q8—121no—
703Q8#89414yes—
704D4—62no—
705D4—62no—
706D4—128no—
707D4—124no—
708D4—128no—
709D4—121no—
710D4—121no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—22no—
714C2×C4—21no—
715C2×C4—21no—
716C2×C4—21no—
717C2×C4—21no—
718C2×C4—21no—
719C2×C4—21no—
720C2×C4—22no—
721C2×C4—32no—
722C2×C4—41no—
723C2×C4—41no—
724C2×C4—41no—
725C2×C4—41no—
726C2×C4—41no—
727C2×C4—41no—
728C2×C4—41no—
729C2×C4—41no—
730C2×C4—61no—
731C2×C4—61no—
732C2×C4—62no—
733C2×C4—62no—
734C2×C4—62no—
735C2×C4—62no—
736C2×C4—61no—
737C2×C4—62no—
738C2×C4—61no—
739C2×C4—61no—
740C2×C4—128no—
741C2×C4—128no—
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—121no—
751C2×C4—121no—
752C2×C4—121no—
753C2×C4—121no—
754C2×C4—244no—
755C2×C4C2×#23511yescharacteristic
756C2×C4C2×D3×D411yescharacteristic
757C2×C4C2×D3×D411yescharacteristic
758C2×C4C2×#23911yescharacteristic
759C2×C4#100911yescharacteristic
760C2×C4#100911yescharacteristic
761C8—41no—
762C8—41no—
763C8—121no—
764C8—121no—
765C2×C3#240511yescharacteristic
766C2×C3C2×#45211yescharacteristic
767C2×C3#301011yescharacteristic
768C2×C3#330111yescharacteristic
769C2×C3#330111yescharacteristic
770C2×C3#331611yescharacteristic
771C2×C3#331611yescharacteristic
772D3—24no—
773D3—81no—
774D3—82no—
775C22—34no—
776C22—62no—
777C22—62no—
778C22—62no—
779C22—62no—
780C22—62no—
781C22—62no—
782C22—121no—
783C22—121no—
784C22—121no—
785C22—122no—
786C22—122no—
787C22—121no—
788C22—121no—
789C22—121no—
790C22—122no—
791C22—121no—
792C22—241no—
793C22—241no—
794C22—241no—
795C22—241no—
796C22#555011yescharacteristic
797C22D3×#12011yescharacteristic
798C22#563011yescharacteristic
799C22#576211yescharacteristic
800C22D3×#13511yescharacteristic
801C22D3×#13711yescharacteristic
802C22#577811yescharacteristic
803C4—24no—
804C4—41no—
805C4—42no—
806C4—41no—
807C4—62no—
808C4—81no—
809C4—81no—
810C4—121no—
811C4—122no—
812C4—241no—
813C4—241no—
814C4C2×#89411yescharacteristic
815C4#555011yescharacteristic
816C4#563011yescharacteristic
817C4#565311yescharacteristic
818C3#2403611yescharacteristic, complemented, Sylow
819C2—64no—
820C2—241no—
821C2—242no—
822C2#7459911yescharacteristic
823C2#7967911yescharacteristic
824C2#7984311yescharacteristic
825C2#8004111yescharacteristic
826C2D3×#45211yescharacteristic
827C2#8102411yescharacteristic
828C2#8124611yescharacteristic
subgroupG/H
centerC23C2×D3×D4
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC3×#1865C2
socleC23×C3C22×D4
prime radicalC2×#5576C2
hypercenter#1865D3
hypocenterC3#24036
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1865

Complements

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

NH ≅ G/Ntype
2. C2×#4863C2semidirect
3. C2×D3×#103C2semidirect
4. #76232C2semidirect
5. C3×#1865C2semidirect
6. #71629C2semidirect
7. #70582C2semidirect
8. #70267C2semidirect
9. #70267C2semidirect
10. #70266C2semidirect
11. #69628C2semidirect
12. #68883C2semidirect
13. #68824C2semidirect
14. #68668C2semidirect
15. #68630C2semidirect
75. #1865D3semidirect
818. C3#24036semidirect

Maximal subgroups

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

subgroupindex
C2×#55762
C2×#48632
C2×D3×#1032
#762322
C3×#18652
#716292
#705822
#702672
#702662
#696282
#688832
#688242
#686682
#686302
#240363