Finite Group Databasebeta

← #26222008

Subgroups — #26222008

Order 12032.

1560 conjugacy classes of subgroups.

The subgroup lattice has 822 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689597C211yesmaximal, characteristic
2C2×#15689273C211yesmaximal, characteristic
3C2×#15689221C211yesmaximal, characteristic, complemented
4C2×C4×#10625336C211yesmaximal, characteristic, complemented
5#20243725C211yesmaximal, characteristic, complemented
6#20243725C211yesmaximal, characteristic, complemented
7#20243701C211yesmaximal, characteristic, complemented
8#20243648C211yesmaximal, characteristic, complemented
9#20243634C211yesmaximal, characteristic, complemented
10#20243585C211yesmaximal, characteristic, complemented
11#20243318C211yesmaximal, characteristic
12#20243216C211yesmaximal, characteristic, complemented
13C4×#13093944C211yesmaximal, characteristic, complemented
14#20243154C211yesmaximal, characteristic, complemented
15C47×#2323C211yesmaximal, characteristic, complemented
16C23×D188C2211yescharacteristic
17C22×#10625336C2211yescharacteristic
18C22×#10625336C2211yescharacteristic
19#15689597—24no—
20#15689597—24no—
21C2×C4×D188C2211yescharacteristic
22C2×C4×D188C2211yescharacteristic
23C2×C4×D188C2211yescharacteristic
24C2×C4×D188C2211yescharacteristic
25C2×#13093986—21no—
26C2×#13093986—21no—
27C2×#13093983C2211yescharacteristic
28C2×C22⋊C4×D47—21no—
29C2×C22⋊C4×D47—21no—
30#15689273C418yescomplemented
31#15689221—24no—
32C4×#10625336—24no—
33C2×#13093957C2211yescharacteristic, complemented
34C2×#13093955C2211yescharacteristic, complemented
35C2×#13093948C2211yescharacteristic, complemented
36C2×#13093948C2211yescharacteristic, complemented
37C2×#13093944C2211yescharacteristic
38C2×#13093944C2211yescharacteristic
39C2×#13093944C2211yescharacteristic
40C2×#13093944C2211yescharacteristic
41C2×#13093944C2211yescharacteristic
42C2×#13093944C2211yescharacteristic
43C2×C22⋊(C47⋊C8)C2211yescharacteristic
44C2×C22⋊(C47⋊C8)C2211yescharacteristic
45C2×#13093935C2211yescharacteristic, complemented
46C2×C4×C47⋊C8C2211yescharacteristic, complemented
47#15688885C2211yescharacteristic, complemented
48#15688885C2211yescharacteristic, complemented
49#15688885C2211yescharacteristic, complemented
50#15688885C2211yescharacteristic, complemented
51#15688878C2211yescharacteristic, complemented
52#15688878C2211yescharacteristic, complemented
53C2×C22⋊Q8×C47C2211yescharacteristic
54C2×C4×Q8×C47C2211yescharacteristic, complemented
55C2×#117×C47C2211yescharacteristic
56C47×#391C2211yescharacteristic, complemented
57C47×#389—21no—
58C47×#389C2211yescharacteristic, complemented
59C47×#388—21no—
60C47×#388—21no—
61C47×#387—21no—
62C47×#380C2211yescharacteristic
63C4×C4⋊C4×C47C2211yescharacteristic, complemented
64C24×D47—21no—
65C22×D188—21no—
66C22×D188—22no—
67C22×D188—22no—
68C22×D188—22no—
69C22×D188—22no—
70C22×D188—22no—
71C22×D188C2×C414yes—
72C22×D188C2311yescharacteristic
73C22×D188C2311yescharacteristic
74C22×C4×D47—21no—
75C22×C4×D47—21no—
76C22×C4×D47—21no—
77C22×C4×D47—21no—
78C2×#10625336—22no—
79C2×#10625336—22no—
80C2×#10625336—22no—
81C2×#10625336—22no—
82C2×#10625336C2×C414yescomplemented
83C2×#10625336C2×C414yescomplemented
84C22×C47⋊C8C2311yescharacteristic
85C22×C47⋊C8C2311yescharacteristic
86C22×C47⋊C8C2311yescharacteristic
87C22×C47⋊C8C2311yescharacteristic
88C4×D188—22no—
89C4×D188—22no—
90C4×D188—22no—
91C4×D188—22no—
92C4×D188—22no—
93C4×D188—22no—
94C4×D188D414yes—
95C4×D188D414yes—
96#13093986—28no—
97#13093986—28no—
98#13093983—22no—
99#13093983—22no—
100C2×C4⋊Dic47C2311yescharacteristic
101C2×C4⋊Dic47C2311yescharacteristic
102C2×C22⋊Dic47—21no—
103C2×(C2×D47)⋊C4—21no—
104C2×(C2×D47)⋊C4—21no—
105C2×(C2×D47)⋊C4—21no—
106C2×(C2×D47)⋊C4—21no—
107C22⋊C4×D47—28no—
108C22⋊C4×D47—28no—
109C2×C4×Dic47—21no—
110#13093957—22no—
111#13093955—22no—
112#13093948—22no—
113#13093948—22no—
114#13093944—22no—
115#13093944—22no—
116#13093944—22no—
117#13093944—22no—
118#13093944C2×C414yescomplemented
119#13093944C2×C414yescomplemented
120C22⋊(C47⋊C8)—22no—
121C22⋊(C47⋊C8)C2×C414yescomplemented
122#13093935—22no—
123C4×C47⋊C8—22no—
124C22×Q8×C47C2311yescharacteristic
125C23×C4×C47C2311yescharacteristic
126C22⋊Q8×C47—22no—
127C22⋊Q8×C47C2×C414yescomplemented
128C4×Q8×C47—22no—
129C4×Q8×C47—22no—
130#117×C47—22no—
131#117×C47—22no—
132C2×C4⋊C4×C47—21no—
133C2×C4⋊C4×C47—21no—
134C2×C4⋊C4×C47—21no—
135C2×C4⋊C4×C47D411yescharacteristic
136C2×C4⋊C4×C47D411yescharacteristic
137C2×C4⋊C4×C47C2311yescharacteristic
138C2×C4⋊C4×C47C2311yescharacteristic
139C2×C4⋊C4×C47C2311yescharacteristic
140C2×C22⋊C4×C47—21no—
141C2×C22⋊C4×C47—21no—
142C2×C22⋊C4×C47D411yescharacteristic
143C2×C22⋊C4×C47D411yescharacteristic
144C2×C42×C47—21no—
145C2×C42×C47—21no—
146C2×C42×C47C2311yescharacteristic
147C2×C42×C47C2311yescharacteristic
148#95×C47—21no—
149#95×C47—21no—
150#95×C47—21no—
151#95×C47—21no—
152#95×C47—21no—
153C24×C47C2×D411yescharacteristic
154C23×D47—21no—
155C23×D47—21no—
156C23×D47—24no—
157C23×D47—24no—
158C23×D47—24no—
159C23×D47—81no—
160C23×D47—81no—
161C23×D47—81no—
162C23×D47—81no—
163C2×Q8×C47—21no—
164C2×Q8×C47—21no—
165C2×Q8×C47—21no—
166C2×Q8×C47—21no—
167C2×Q8×C47—21no—
168C2×Q8×C47C22×C412yes—
169C22×C4×C47—21no—
170C22×C4×C47—21no—
171C22×C4×C47—21no—
172C22×C4×C47—21no—
173C22×C4×C47—21no—
174C22×C4×C47—21no—
175C22×C4×C47—21no—
176C22×C4×C47—21no—
177C22×C4×C47C22×C412yes—
178C22×C4×C47C2×D411yescharacteristic
179C22×C4×C47C2×D411yescharacteristic
180C22×C4×C47C2×D411yescharacteristic
181C22×C4×C47C2×D411yescharacteristic
182C22×C4×C47C2×D411yescharacteristic
183C22×C4×C47#4112yes—
184C22×C4×C47C2411yescharacteristic
185C22×Dic47—21no—
186C22×Dic47—21no—
187C2×D188—24no—
188C2×D188—24no—
189C2×D188—28no—
190C2×D188—28no—
191C2×D188—24no—
192C2×D188—21no—
193C2×D188—21no—
194C2×D188—21no—
195C2×D188—21no—
196C2×D188—21no—
197C2×D188—21no—
198C2×D188—28no—
199C2×D188—28no—
200C2×D188C22×C412yes—
201C2×D188C22×C412yes—
202C2×D188C2×D412yes—
203C2×D188C2×D412yes—
204C2×D188#4112yes—
205C2×D188#4112yes—
206C2×C4×D47—24no—
207C2×C4×D47—24no—
208C2×C4×D47—24no—
209C2×C4×D47—24no—
210C2×C4×D47—81no—
211C2×C4×D47—81no—
212C2×C4×D47—81no—
213C2×C4×D47—81no—
214C2×C4×D47—81no—
215C2×C4×D47—81no—
216C2×C4×D47—81no—
217C2×C4×D47—81no—
218C4⋊C4×C47—24no—
219C4⋊C4×C47—22no—
220C4⋊C4×C47—22no—
221C4⋊C4×C47—21no—
222C4⋊C4×C47—21no—
223C4⋊C4×C47—21no—
224C4⋊C4×C47—21no—
225C4⋊C4×C47—21no—
226C4⋊C4×C47—42no—
227C4⋊C4×C47—81no—
228C4⋊C4×C47C22×C412yes—
229C22⋊C4×C47—24no—
230C22⋊C4×C47—22no—
231C22⋊C4×C47—22no—
232C22⋊C4×C47—81no—
233C42×C47—21no—
234C42×C47—21no—
235C42×C47—42no—
236C42×C47—81no—
237C42×C47C2×D412yes—
238C42×C47C2×D412yes—
239C22⋊Dic47—24no—
240#10625336—28no—
241#10625336—28no—
242(C2×D47)⋊C4—24no—
243(C2×D47)⋊C4—24no—
244(C2×D47)⋊C4—24no—
245(C2×D47)⋊C4—24no—
246C4⋊Dic47—21no—
247C4⋊Dic47—21no—
248C4⋊Dic47C2×D412yes—
249C4⋊Dic47C2×D412yes—
250C4×Dic47—24no—
251C2×C47⋊C8—21no—
252C2×C47⋊C8—21no—
253C2×C47⋊C8—21no—
254C2×C47⋊C8—21no—
255C2×C47⋊C8—21no—
256C2×C47⋊C8—21no—
257C2×C47⋊C8—21no—
258C2×C47⋊C8—21no—
259C2×C47⋊C8—21no—
260C2×C47⋊C8—21no—
261C2×C47⋊C8C22×C412yes—
262C2×C47⋊C8C22×C412yes—
263C23×C47—21no—
264C23×C47—21no—
265C23×C47—21no—
266C23×C47—21no—
267C23×C47—21no—
268C23×C47—21no—
269C23×C47C4×D412yes—
270C23×C47C22×D411yescharacteristic
271C22×D47—22no—
272C22×D47—22no—
273C22×D47—22no—
274C22×D47—22no—
275C22×D47—22no—
276C22×D47—22no—
277C22×D47—216no—
278C22×D47—41no—
279C22×D47—41no—
280C22×D47—41no—
281C22×D47—41no—
282C22×D47—41no—
283C22×D47—41no—
284C22×D47—41no—
285C22×D47—41no—
286C22×D47—84no—
287C22×D47—84no—
288C22×D47—84no—
289C22×D47—84no—
290C22×D47—84no—
291C22×D47—84no—
292Q8×C47—22no—
293Q8×C47—22no—
294Q8×C47—41no—
295Q8×C47—41no—
296C2×C4×C47—21no—
297C2×C4×C47—21no—
298C2×C4×C47—21no—
299C2×C4×C47—21no—
300C2×C4×C47—21no—
301C2×C4×C47—21no—
302C2×C4×C47—22no—
303C2×C4×C47—22no—
304C2×C4×C47—22no—
305C2×C4×C47—22no—
306C2×C4×C47—22no—
307C2×C4×C47—22no—
308C2×C4×C47—21no—
309C2×C4×C47—21no—
310C2×C4×C47—21no—
311C2×C4×C47—21no—
312C2×C4×C47—21no—
313C2×C4×C47—21no—
314C2×C4×C47—41no—
315C2×C4×C47—41no—
316C2×C4×C47—41no—
317C2×C4×C47—41no—
318C2×C4×C47—41no—
319C2×C4×C47—41no—
320C2×C4×C47—41no—
321C2×C4×C47—41no—
322C2×C4×C47—41no—
323C2×C4×C47—41no—
324C2×C4×C47C4×D412yes—
325C2×C4×C47#12012yes—
326C2×C4×C47#12012yes—
327C2×C4×C47C23×C411yescharacteristic
328C2×C4×C47C22×D411yescharacteristic
329C2×C4×C47C22×D411yescharacteristic
330C2×C4×C47C2×#4111yescharacteristic
331C2×C4×C47C2×#4111yescharacteristic
332C2×C4×C47C2×#4111yescharacteristic
333C2×Dic47—22no—
334C2×Dic47—22no—
335C2×Dic47—41no—
336C2×Dic47—41no—
337C2×Dic47—41no—
338C2×Dic47—41no—
339D188—216no—
340D188—22no—
341D188—22no—
342D188—22no—
343D188—22no—
344D188—22no—
345D188—22no—
346D188C4×D414yes—
347D188C4×D414yes—
348C4×D47—84no—
349C4×D47—84no—
350C4×D47—84no—
351C4×D47—84no—
352C47⋊C8—22no—
353C47⋊C8—22no—
354C47⋊C8—41no—
355C47⋊C8—41no—
356#21459—471nomaximal, Sylow
357C22×C47—22no—
358C22×C47—22no—
359C22×C47—22no—
360C22×C47—41no—
361C22×C47—41no—
362C22×C47—41no—
363C22×C47—41no—
364C22×C47C2×C4×D411yescharacteristic
365C22×C47C2×#12011yescharacteristic
366C22×C47#52511yescharacteristic
367C22×C47#57611yescharacteristic
368C22×C47#57711yescharacteristic
369C22×C47#57711yescharacteristic
370C22×C47#57711yescharacteristic
371C2×D47—24no—
372C2×D47—24no—
373C2×D47—42no—
374C2×D47—42no—
375C2×D47—42no—
376C2×D47—42no—
377C2×D47—42no—
378C2×D47—42no—
379C2×D47—42no—
380C2×D47—42no—
381C2×D47—42no—
382C2×D47—42no—
383C2×D47—42no—
384C2×D47—42no—
385C2×D47—816no—
386C4×C47—22no—
387C4×C47—22no—
388C4×C47—22no—
389C4×C47—42no—
390C4×C47—41no—
391C4×C47—41no—
392C4×C47—42no—
393C4×C47—81no—
394C4×C47—81no—
395C4×C47C2×C4×D411yescharacteristic
396C4×C47C2×C4×D411yescharacteristic
397C4×C47#52511yescharacteristic
398C4×C47#52511yescharacteristic
399Dic47—42no—
400Dic47—42no—
401C2×#518—471no—
402C2×#450—471no—
403C2×#440—471no—
404C2×C4×SD16—471no—
405#2323D4711yescharacteristic, complemented
406#1877—471no—
407#1877—471no—
408#1873—471no—
409#1864—471no—
410#1862—471no—
411#1854—471no—
412#1786—471no—
413#1762—471no—
414C4×#102—471no—
415#1750—471no—
416C2×C47—42no—
417C2×C47C4×#12011yescharacteristic
418C2×C47#294611yescharacteristic
419C2×C47#294911yescharacteristic
420C2×C47#300911yescharacteristic
421C2×C47#301211yescharacteristic
422C2×C47#311811yescharacteristic
423C2×C47#312311yescharacteristic
424D47—44no—
425D47—44no—
426C23×D4—471no—
427C22×SD16—471no—
428C22×SD16—471no—
429C2×C22⋊Q8C2×D4711yescharacteristic
430#518—944no—
431#518—944no—
432C2×C4×Q8C2×D4711yescharacteristic, complemented
433C2×C4×D4—471no—
434C2×C4×D4—471no—
435C2×C4×D4—471no—
436C2×C4×D4—471no—
437C2×C4×D4—941no—
438C2×C4×D4—941no—
439C2×#117—471no—
440C2×#117C2×D4711yescharacteristic
441C22×C22⋊C4—941no—
442C22×C22⋊C4—941no—
443#450—478no—
444#440—944no—
445C4×SD16—944no—
446C2×#107—471no—
447C2×#106—471no—
448C2×#103—471no—
449C2×#103—471no—
450C2×#102—471no—
451C2×#102—471no—
452C2×#102—471no—
453C2×#102—471no—
454C2×#102—471no—
455C2×#102—471no—
456C2×C22⋊C8—471no—
457C2×C22⋊C8—471no—
458C2×#97—471no—
459C2×C4×C8—471no—
460#391C2×D4711yescharacteristic, complemented
461#389—21no—
462#389C2×D4711yescharacteristic, complemented
463#388—21no—
464#388—21no—
465#387—21no—
466#380C2×D4711yescharacteristic
467C4×C4⋊C4C2×D4711yescharacteristic, complemented
468#340—471no—
469#340—471no—
470#340—471no—
471#340—471no—
472#336—471no—
473#336—471no—
474C47#2145911yescharacteristic, complemented, Sylow
475C25—941no—
476C22×Q8C22×D4711yescharacteristic
477C22×D4—474no—
478C22×D4—471no—
479C22×D4—471no—
480C22×D4—942no—
481C22×D4—942no—
482C22×D4—942no—
483C22×D4—942no—
484C22×D4—942no—
485C22×D4—941no—
486C23×C4—941no—
487C23×C4—941no—
488C23×C4—941no—
489C23×C4—941no—
490C23×C4C22×D4711yescharacteristic
491C2×SD16—474no—
492C2×SD16—474no—
493C2×SD16—942no—
494C2×SD16—942no—
495C2×SD16—942no—
496C2×SD16—942no—
497C22×C8—471no—
498C22×C8—471no—
499C22×C8—471no—
500C22×C8—471no—
501C22⋊Q8—22no—
502C22⋊Q8C4×D4714yescomplemented
503C4×Q8—22no—
504C4×Q8—22no—
505C4×D4—474no—
506C4×D4—474no—
507C4×D4—942no—
508C4×D4—942no—
509C4×D4—942no—
510C4×D4—942no—
511C4×D4—948no—
512C4×D4—948no—
513C4×D4—942no—
514C4×D4—942no—
515#117—22no—
516#117—22no—
517#117—942no—
518#117—942no—
519C2×C4⋊C4—21no—
520C2×C4⋊C4—21no—
521C2×C4⋊C4—21no—
522C2×C4⋊C4—471no—
523C2×C4⋊C4—471no—
524C2×C4⋊C4C22⋊D4711yescharacteristic
525C2×C4⋊C4C22⋊D4711yescharacteristic
526C2×C4⋊C4C22×D4711yescharacteristic
527C2×C4⋊C4C22×D4711yescharacteristic
528C2×C4⋊C4C22×D4711yescharacteristic
529C2×C22⋊C4—21no—
530C2×C22⋊C4—21no—
531C2×C22⋊C4—948no—
532C2×C22⋊C4—948no—
533C2×C22⋊C4—941no—
534C2×C22⋊C4—941no—
535C2×C22⋊C4—941no—
536C2×C22⋊C4—941no—
537C2×C22⋊C4—941no—
538C2×C22⋊C4C22⋊D4711yescharacteristic
539C2×C22⋊C4C22⋊D4711yescharacteristic
540C2×C42—21no—
541C2×C42—21no—
542C2×C42—941no—
543C2×C42C22×D4711yescharacteristic
544C2×C42C22×D4711yescharacteristic
545#107—942no—
546#106—942no—
547#103—942no—
548#103—942no—
549#102—474no—
550#102—474no—
551#102—942no—
552#102—942no—
553#102—942no—
554#102—942no—
555C22⋊C8—474no—
556C22⋊C8—942no—
557#97—942no—
558C4×C8—942no—
559#95—21no—
560#95—21no—
561#95—21no—
562#95—21no—
563#95—21no—
564C24—944no—
565C24—944no—
566C24—944no—
567C24—941no—
568C24—941no—
569C24—3761no—
570C24—3761no—
571C24—3761no—
572C24—3761no—
573C24C2×C22⋊D4711yescharacteristic
574C2×Q8—21no—
575C2×Q8—21no—
576C2×Q8—21no—
577C2×Q8—21no—
578C2×Q8—21no—
579C2×Q8C2×C4×D4712yes—
580C2×D4—472no—
581C2×D4—472no—
582C2×D4—472no—
583C2×D4—472no—
584C2×D4—472no—
585C2×D4—472no—
586C2×D4—948no—
587C2×D4—948no—
588C2×D4—944no—
589C2×D4—944no—
590C2×D4—948no—
591C2×D4—948no—
592C2×D4—944no—
593C2×D4—941no—
594C2×D4—941no—
595C2×D4—941no—
596C2×D4—941no—
597C2×D4—941no—
598C2×D4—941no—
599C22×C4—21no—
600C22×C4—21no—
601C22×C4—21no—
602C22×C4—21no—
603C22×C4—21no—
604C22×C4—21no—
605C22×C4—21no—
606C22×C4—21no—
607C22×C4—944no—
608C22×C4—944no—
609C22×C4—941no—
610C22×C4—941no—
611C22×C4—944no—
612C22×C4—944no—
613C22×C4—3761no—
614C22×C4—3761no—
615C22×C4—3761no—
616C22×C4—3761no—
617C22×C4—3761no—
618C22×C4—3761no—
619C22×C4—3761no—
620C22×C4—3761no—
621C22×C4C2×C4×D4712yes—
622C22×C4#1062535012yes—
623C22×C4C2×C22⋊D4711yescharacteristic
624C22×C4C2×C22⋊D4711yescharacteristic
625C22×C4C2×C22⋊D4711yescharacteristic
626C22×C4C2×C22⋊D4711yescharacteristic
627C22×C4C2×C22⋊D4711yescharacteristic
628C22×C4C23×D4711yescharacteristic
629SD16—948no—
630SD16—948no—
631C2×C8—472no—
632C2×C8—472no—
633C2×C8—941no—
634C2×C8—941no—
635C2×C8—941no—
636C2×C8—941no—
637C2×C8—941no—
638C2×C8—941no—
639C2×C8—941no—
640C2×C8—941no—
641C2×C8—941no—
642C2×C8—941no—
643C4⋊C4—24no—
644C4⋊C4—22no—
645C4⋊C4—22no—
646C4⋊C4—21no—
647C4⋊C4—21no—
648C4⋊C4—21no—
649C4⋊C4—21no—
650C4⋊C4—21no—
651C4⋊C4—42no—
652C4⋊C4—81no—
653C4⋊C4—472no—
654C4⋊C4—472no—
655C4⋊C4—941no—
656C4⋊C4—941no—
657C4⋊C4C2×C4×D4712yes—
658C22⋊C4—24no—
659C22⋊C4—22no—
660C22⋊C4—22no—
661C22⋊C4—81no—
662C22⋊C4—944no—
663C22⋊C4—944no—
664C22⋊C4—944no—
665C22⋊C4—944no—
666C22⋊C4—944no—
667C42—21no—
668C42—21no—
669C42—42no—
670C42—81no—
671C42—944no—
672C42D4×D4712yes—
673C42D4×D4712yes—
674C23—21no—
675C23—21no—
676C23—21no—
677C23—21no—
678C23—21no—
679C23—21no—
680C23—9416no—
681C23—942no—
682C23—942no—
683C23—942no—
684C23—942no—
685C23—942no—
686C23—942no—
687C23—3764no—
688C23—3764no—
689C23—3764no—
690C23—3764no—
691C23—3764no—
692C23—3764no—
693C23—1881no—
694C23—1881no—
695C23—1881no—
696C23—1881no—
697C23—1881no—
698C23—1881no—
699C23—1881no—
700C23—1881no—
701C23C4×C22⋊D4712yes—
702C23C22×C22⋊D4711yescharacteristic
703Q8—22no—
704Q8—22no—
705Q8—41no—
706Q8—41no—
707D4—474no—
708D4—474no—
709D4—9416no—
710D4—942no—
711D4—942no—
712D4—942no—
713D4—942no—
714D4—942no—
715D4—942no—
716C2×C4—21no—
717C2×C4—21no—
718C2×C4—21no—
719C2×C4—21no—
720C2×C4—21no—
721C2×C4—21no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—22no—
726C2×C4—22no—
727C2×C4—22no—
728C2×C4—21no—
729C2×C4—21no—
730C2×C4—21no—
731C2×C4—21no—
732C2×C4—21no—
733C2×C4—21no—
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—41no—
743C2×C4—41no—
744C2×C4—942no—
745C2×C4—942no—
746C2×C4—3764no—
747C2×C4—3764no—
748C2×C4—3764no—
749C2×C4—3764no—
750C2×C4—1881no—
751C2×C4—1881no—
752C2×C4—1881no—
753C2×C4—1881no—
754C2×C4C4×C22⋊D4712yes—
755C2×C4#1309399212yes—
756C2×C4#1309399212yes—
757C2×C4C22×C4×D4711yescharacteristic
758C2×C4C2×D4×D4711yescharacteristic
759C2×C4C2×D4×D4711yescharacteristic
760C2×C4#41×D4711yescharacteristic
761C2×C4#41×D4711yescharacteristic
762C2×C4C2×#1062535011yescharacteristic
763C8—942no—
764C8—942no—
765C8—1881no—
766C8—1881no—
767C22—22no—
768C22—22no—
769C22—22no—
770C22—41no—
771C22—41no—
772C22—41no—
773C22—41no—
774C22—944no—
775C22—944no—
776C22—37616no—
777C22—1882no—
778C22—1882no—
779C22—1882no—
780C22—1882no—
781C22—1882no—
782C22—1882no—
783C22—1882no—
784C22—1882no—
785C22—1882no—
786C22—1882no—
787C22—1882no—
788C22—1882no—
789C22C2×C4×C22⋊D4711yescharacteristic
790C22C2×#1309399211yescharacteristic
791C22#1568963011yescharacteristic
792C22#1568992611yescharacteristic
793C22#1568993111yescharacteristic
794C22#1568993111yescharacteristic
795C22#1568993111yescharacteristic
796C4—22no—
797C4—22no—
798C4—22no—
799C4—41no—
800C4—42no—
801C4—42no—
802C4—41no—
803C4—81no—
804C4—81no—
805C4—1882no—
806C4—1882no—
807C4C4×D4×D4711yescharacteristic
808C4C4×D4×D4711yescharacteristic
809C4#1568963211yescharacteristic
810C4#1568963211yescharacteristic
811C2—42no—
812C2—1884no—
813C2—1884no—
814C2C4×#1309399211yescharacteristic
815C2#2025221611yescharacteristic
816C2#2025224711yescharacteristic
817C2#2025266311yescharacteristic
818C2#2025268911yescharacteristic
819C2#2025356611yescharacteristic
820C2#2025363511yescharacteristic
subgroupG/H
centerC23C22×C22⋊D47
commutatorC2×C4×C47C23×C4
FrattiniC22×C4C23×D47
FittingC47×#2323C2
socleC23×C47C22×D4
prime radicalC23×D188C22
cosocleC22×C4×C47C24
hypercenter#2323D47
hypocenterC47#21459
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×#117 ◁ #2323

Complements

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

NH ≅ G/Ntype
3. C2×#15689221C2semidirect
4. C2×C4×#10625336C2semidirect
5. #20243725C2semidirect
6. #20243725C2semidirect
7. #20243701C2semidirect
8. #20243648C2semidirect
9. #20243634C2semidirect
10. #20243585C2semidirect
12. #20243216C2semidirect
13. C4×#13093944C2semidirect
14. #20243154C2semidirect
15. C47×#2323C2semidirect
30. #15689273C4semidirect
33. C2×#13093957C22semidirect
34. C2×#13093955C22semidirect
35. C2×#13093948C22semidirect
36. C2×#13093948C22semidirect
45. C2×#13093935C22semidirect
46. C2×C4×C47⋊C8C22semidirect
47. #15688885C22semidirect
48. #15688885C22semidirect
49. #15688885C22semidirect
50. #15688885C22semidirect
51. #15688878C22semidirect
52. #15688878C22semidirect
54. C2×C4×Q8×C47C22semidirect
56. C47×#391C22semidirect
58. C47×#389C22semidirect
63. C4×C4⋊C4×C47C22semidirect
82. C2×#10625336C2×C4semidirect
83. C2×#10625336C2×C4semidirect
118. #13093944C2×C4semidirect
119. #13093944C2×C4semidirect
121. C22⋊(C47⋊C8)C2×C4semidirect
127. C22⋊Q8×C47C2×C4semidirect
405. #2323D47semidirect
432. C2×C4×Q8C2×D47semidirect
460. #391C2×D47semidirect
462. #389C2×D47semidirect
467. C4×C4⋊C4C2×D47semidirect
474. C47#21459semidirect
502. C22⋊Q8C4×D47semidirect

Maximal subgroups

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

subgroupindex
C2×#156895972
C2×#156892732
C2×#156892212
C2×C4×#106253362
#202437252
#202437012
#202436482
#202436342
#202435852
#202433182
#202432162
C4×#130939442
#202431542
C47×#23232
#2145947