Finite Group Databasebeta

← #26236996

Subgroups — #26236996

Order 12032.

1114 conjugacy classes of subgroups.

The subgroup lattice has 740 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689262C211yesmaximal, characteristic
2C2×C4×#10625336C211yesmaximal, characteristic, complemented
3C2×#15689132C211yesmaximal, characteristic, complemented
4#20246424C211yesmaximal, characteristic
5#20244272C211yesmaximal, characteristic, complemented
6#20244067C211yesmaximal, characteristic, complemented
7#20244019C211yesmaximal, characteristic, complemented
8#20243824C211yesmaximal, characteristic
9#20243743C211yesmaximal, characteristic, complemented
10#20243725C211yesmaximal, characteristic, complemented
11#20243642C211yesmaximal, characteristic, complemented
12#20243585C211yesmaximal, characteristic, complemented
13#20243218C211yesmaximal, characteristic, complemented
14#20243172C211yesmaximal, characteristic, complemented
15Q8×C22⋊C4×C47C211yesmaximal, characteristic, complemented
16C22×#10625336C2211yescharacteristic
17C22×#10625336C2211yescharacteristic
18C22×#10625329C2211yescharacteristic
19C2×#13093998C2211yescharacteristic
20C2×C4×D188C2211yescharacteristic
21C2×#13093983C2211yescharacteristic
22#15689262C418yescomplemented
23C4×#10625336—24no—
24C2×#13093957C2211yescharacteristic
25C2×#13093955C2211yescharacteristic
26#15689132—24no—
27C2×#13093948C2211yescharacteristic
28C2×#13093948C2211yescharacteristic
29C2×#13093948C2211yescharacteristic
30C2×#13093948C2211yescharacteristic
31C2×#13093948C2211yescharacteristic
32C2×#13093948C2211yescharacteristic
33C2×#13093944C2211yescharacteristic
34C2×#13093944C2211yescharacteristic
35C2×C22⋊(C47⋊C8)C2211yescharacteristic
36C2×#13093935C2211yescharacteristic
37C2×C4×C47⋊C8C2211yescharacteristic
38#15689025C2211yescharacteristic
39#15689023—21no—
40#15689021C2211yescharacteristic
41#15689012—21no—
42#15688999—21no—
43C4×C4⋊Dic47C2211yescharacteristic
44#15688970—21no—
45#15688885C2211yescharacteristic
46#15688885C2211yescharacteristic
47#15688885C2211yescharacteristic
48#15688885C2211yescharacteristic
49#15688878C2211yescharacteristic
50#15688878C2211yescharacteristic
51C23×Q8×C47C2211yescharacteristic
52C2×C4×Q8×C47C2211yescharacteristic
53C2×C4×Q8×C47C2211yescharacteristic
54C47×#391—21no—
55C47×#391—21no—
56C47×#391C2211yescharacteristic
57C47×#391C2211yescharacteristic
58C47×#380—21no—
59C47×#380C2211yescharacteristic
60C4×C22⋊C4×C47—21no—
61C4×C22⋊C4×C47C2211yescharacteristic
62C22×D188C2311yescharacteristic
63C22×C22⋊D47—21no—
64C22×C4×D47—21no—
65C2×#10625336—22no—
66C2×#10625336—22no—
67C2×#10625336—41no—
68C2×#10625336—41no—
69C2×#10625336C2×C414yes—
70C2×#10625336C2×C414yes—
71C2×#10625329—22no—
72C2×#10625329—22no—
73C2×#10625329—41no—
74C22×C47⋊C8C2311yescharacteristic
75C22×C47⋊C8C2311yescharacteristic
76C22×C47⋊C8C2311yescharacteristic
77C22×C47⋊C8C2311yescharacteristic
78#13093998—22no—
79#13093998C2×C414yes—
80C4×D188—22no—
81C4×D188—41no—
82#13093983—22no—
83#13093983—41no—
84C2×C4⋊Dic47C2311yescharacteristic
85C2×C4⋊Dic47C2311yescharacteristic
86C2×C4⋊Dic47C2311yescharacteristic
87C2×Dic47⋊C4—21no—
88C2×C22⋊Dic47—21no—
89C2×(C2×D47)⋊C4—21no—
90C2×(C2×D47)⋊C4—21no—
91C2×(C2×D47)⋊C4—21no—
92C2×(C2×D47)⋊C4—21no—
93C2×C4×Dic47—21no—
94C2×C4×Dic47—21no—
95#13093957—41no—
96#13093955—22no—
97#13093948—22no—
98#13093948—22no—
99#13093948—22no—
100#13093948C2×C414yescomplemented
101#13093948C2×C414yescomplemented
102#13093948D414yescomplemented
103#13093944—22no—
104#13093944—41no—
105C22⋊(C47⋊C8)C2×C414yescomplemented
106#13093935—41no—
107C4×C47⋊C8—22no—
108C47⋊#95—21no—
109C47⋊#95—21no—
110C22×Q8×C47—21no—
111C22×Q8×C47—22no—
112C22×Q8×C47—22no—
113C22×Q8×C47—22no—
114C22×Q8×C47—41no—
115C22×Q8×C47—41no—
116C22×Q8×C47C2×C414yescomplemented
117C22×Q8×C47C2311yescharacteristic
118C22×Q8×C47C2311yescharacteristic
119C23×C4×C47—21no—
120C23×C4×C47C2311yescharacteristic
121C4×Q8×C47—22no—
122C4×Q8×C47—22no—
123C4×Q8×C47—41no—
124C4×Q8×C47—41no—
125C2×C4⋊C4×C47—21no—
126C2×C4⋊C4×C47—21no—
127C2×C4⋊C4×C47C2311yescharacteristic
128C2×C4⋊C4×C47C2311yescharacteristic
129C2×C22⋊C4×C47—21no—
130C2×C22⋊C4×C47D411yescharacteristic
131C2×C22⋊C4×C47D411yescharacteristic
132C2×C42×C47—21no—
133C2×C42×C47—21no—
134C2×C42×C47C2311yescharacteristic
135C2×C42×C47C2311yescharacteristic
136#95×C47—21no—
137#95×C47—21no—
138#95×C47—21no—
139#95×C47—21no—
140#95×C47—21no—
141#95×C47D411yescharacteristic
142#95×C47D411yescharacteristic
143C24×C47C2×D411yescharacteristic
144C23×D47—21no—
145C2×Q8×C47—24no—
146C2×Q8×C47—21no—
147C2×Q8×C47—21no—
148C2×Q8×C47—21no—
149C2×Q8×C47—21no—
150C2×Q8×C47—28no—
151C2×Q8×C47—21no—
152C2×Q8×C47—21no—
153C2×Q8×C47—21no—
154C2×Q8×C47—21no—
155C2×Q8×C47—42no—
156C2×Q8×C47—42no—
157C2×Q8×C47—44no—
158C2×Q8×C47—44no—
159C2×Q8×C47—44no—
160C2×Q8×C47C22×C412yes—
161C2×Q8×C47C22×C412yes—
162C2×Q8×C47C2×D412yes—
163C2×Q8×C47#4112yes—
164C22×C4×C47—21no—
165C22×C4×C47—21no—
166C22×C4×C47—21no—
167C22×C4×C47—21no—
168C22×C4×C47—21no—
169C22×C4×C47—24no—
170C22×C4×C47—21no—
171C22×C4×C47—21no—
172C22×C4×C47—21no—
173C22×C4×C47—42no—
174C22×C4×C47—42no—
175C22×C4×C47C22×C412yes—
176C22×C4×C47C2×D411yescharacteristic
177C22×C4×C47C2×D411yescharacteristic
178C22×C4×C47C2×D411yescharacteristic
179C22×C4×C47C2×D411yescharacteristic
180C22×C4×C47C2×D411yescharacteristic
181C22×C4×C47#4112yes—
182C22×C4×C47C2411yescharacteristic
183C2×C22⋊D47—24no—
184C2×C22⋊D47—81no—
185C2×C22⋊D47—81no—
186C22×Dic47—21no—
187C22×Dic47—21no—
188C22×Dic47—21no—
189C2×D188—21no—
190C2×D188—21no—
191C2×D188—21no—
192C2×D188—21no—
193C2×D188—21no—
194C2×D188C22×C412yes—
195C2×C4×D47—42no—
196C2×C4×D47—42no—
197C2×C4×D47—81no—
198C4⋊C4×C47—21no—
199C4⋊C4×C47—21no—
200C4⋊C4×C47—21no—
201C4⋊C4×C47—21no—
202C4⋊C4×C47—42no—
203C4⋊C4×C47—42no—
204C22⋊C4×C47—22no—
205C22⋊C4×C47—41no—
206C22⋊C4×C47—42no—
207C42×C47—21no—
208C42×C47—21no—
209C42×C47—21no—
210C42×C47—21no—
211C42×C47—42no—
212C42×C47—42no—
213C22⋊Dic47—42no—
214#10625336—28no—
215#10625336—44no—
216(C2×D47)⋊C4—24no—
217(C2×D47)⋊C4—42no—
218(C2×D47)⋊C4—42no—
219(C2×D47)⋊C4—81no—
220C4⋊Dic47—21no—
221C4⋊Dic47—21no—
222C4⋊Dic47—21no—
223C4⋊Dic47—21no—
224C4⋊Dic47C22×C412yes—
225C4⋊Dic47C2×D412yes—
226Dic47⋊C4—81no—
227C4×Dic47—42no—
228C4×Dic47—81no—
229#10625329—44no—
230C2×C47⋊C8—21no—
231C2×C47⋊C8—21no—
232C2×C47⋊C8—21no—
233C2×C47⋊C8—21no—
234C2×C47⋊C8—21no—
235C2×C47⋊C8—21no—
236C2×C47⋊C8—21no—
237C2×C47⋊C8—21no—
238C2×C47⋊C8—21no—
239C2×C47⋊C8C22×C412yes—
240C2×C47⋊C8C22×C412yes—
241C2×C47⋊C8C2×D412yes—
242C23×C47—21no—
243C23×C47—21no—
244C23×C47—21no—
245C23×C47—21no—
246C23×C47—21no—
247C23×C47—21no—
248C23×C47C4×D412yes—
249C23×C47C22×D411yescharacteristic
250C22×D47—22no—
251C22×D47—41no—
252C22×D47—41no—
253C22×D47—41no—
254C22×D47—41no—
255C22×D47—41no—
256C22×D47—41no—
257Q8×C47—22no—
258Q8×C47—22no—
259Q8×C47—22no—
260Q8×C47—22no—
261Q8×C47—22no—
262Q8×C47—48no—
263Q8×C47—41no—
264Q8×C47—41no—
265Q8×C47C4×D414yes—
266C2×C4×C47—22no—
267C2×C4×C47—21no—
268C2×C4×C47—21no—
269C2×C4×C47—22no—
270C2×C4×C47—22no—
271C2×C4×C47—21no—
272C2×C4×C47—21no—
273C2×C4×C47—22no—
274C2×C4×C47—22no—
275C2×C4×C47—22no—
276C2×C4×C47—22no—
277C2×C4×C47—22no—
278C2×C4×C47—21no—
279C2×C4×C47—21no—
280C2×C4×C47—21no—
281C2×C4×C47—21no—
282C2×C4×C47—21no—
283C2×C4×C47—21no—
284C2×C4×C47—21no—
285C2×C4×C47—21no—
286C2×C4×C47—21no—
287C2×C4×C47—48no—
288C2×C4×C47—41no—
289C2×C4×C47—41no—
290C2×C4×C47—41no—
291C2×C4×C47—41no—
292C2×C4×C47—41no—
293C2×C4×C47—41no—
294C2×C4×C47—41no—
295C2×C4×C47—41no—
296C2×C4×C47C4×D412yes—
297C2×C4×C47#13712yes—
298C2×C4×C47C23×C411yescharacteristic
299C2×C4×C47C22×D411yescharacteristic
300C2×C4×C47C2×#4111yescharacteristic
301C2×C4×C47C2×#4111yescharacteristic
302C2×C4×C47H(5,𝔽2)11yescharacteristic
303C2×C4×C47H(5,𝔽2)11yescharacteristic
304C22⋊D47—84no—
305C2×Dic47—22no—
306C2×Dic47—22no—
307C2×Dic47—41no—
308C2×Dic47—41no—
309C2×Dic47—41no—
310C2×Dic47—41no—
311C2×Dic47—41no—
312C2×Dic47—41no—
313C2×Dic47—41no—
314D188—22no—
315D188—22no—
316D188—41no—
317D188—41no—
318C4×D47—84no—
319C47⋊C8—22no—
320C47⋊C8—22no—
321C47⋊C8—22no—
322C47⋊C8—41no—
323#22885—471nomaximal, Sylow
324C22×C47—22no—
325C22×C47—22no—
326C22×C47—22no—
327C22×C47—41no—
328C22×C47—41no—
329C22×C47—41no—
330C22×C47—41no—
331C22×C47C2×C4×D411yescharacteristic
332C22×C47D4211yescharacteristic
333C22×C47#54611yescharacteristic
334C22×C47C2×#13711yescharacteristic
335C22×C47#57511yescharacteristic
336C22×C47#57711yescharacteristic
337C22×C47#57711yescharacteristic
338C2×D47—42no—
339C2×D47—42no—
340C2×D47—42no—
341C2×D47—81no—
342C2×D47—81no—
343C2×D47—81no—
344C2×D47—81no—
345C4×C47—22no—
346C4×C47—24no—
347C4×C47—22no—
348C4×C47—41no—
349C4×C47—42no—
350C4×C47—41no—
351C4×C47—41no—
352C4×C47—81no—
353C4×C47—81no—
354C4×C47C2×C4×D411yescharacteristic
355C4×C47#51811yescharacteristic
356C4×C47#54611yescharacteristic
357C4×C47#55111yescharacteristic
358Dic47—42no—
359Dic47—42no—
360Dic47—81no—
361C2×#448—471no—
362C2×C4×SD16—471no—
363C2×#419—471no—
364#2363—471no—
365Q8×C22⋊C4D4711yescharacteristic, complemented
366#1973—471no—
367#1933—471no—
368#1927—471no—
369#1895—471no—
370#1880—471no—
371#1877—471no—
372#1863—471no—
373#1854—471no—
374#1763—471no—
375#1753—471no—
376C2×C47—42no—
377C2×C47#235811yescharacteristic
378C2×C47C4×#13711yescharacteristic
379C2×C47#294911yescharacteristic
380C2×C47#326611yescharacteristic
381C2×C47#327111yescharacteristic
382C2×C47#332611yescharacteristic
383C2×C47#332911yescharacteristic
384D47—82no—
385C23×Q8C2×D4711yescharacteristic
386C22×SD16—471no—
387C22×SD16—471no—
388C22×M16—471no—
389C2×#121—471no—
390C2×C4×Q8C2×D4711yescharacteristic
391C2×C4×Q8C2×D4711yescharacteristic
392C2×C4×D4—471no—
393C2×#117—471no—
394#448—478no—
395C4×SD16—944no—
396C2×#107—471no—
397C2×#106—471no—
398#419—944no—
399C2×#103—471no—
400C2×#103—471no—
401C2×#103—471no—
402C2×#103—471no—
403C2×#103—471no—
404C2×#103—471no—
405C2×#102—471no—
406C2×#102—471no—
407C2×C22⋊C8—471no—
408C2×#97—471no—
409C2×C4×C8—471no—
410#391—21no—
411#391—21no—
412#391C2×D4711yescharacteristic
413#391C2×D4711yescharacteristic
414#390—471no—
415#390—941no—
416#389—471no—
417#388—941no—
418#386—941no—
419#380—21no—
420#380C2×D4711yescharacteristic
421C4×C4⋊C4—471no—
422C4×C22⋊C4—21no—
423C4×C22⋊C4—941no—
424C4×C22⋊C4C2×D4711yescharacteristic
425#340—471no—
426#340—471no—
427#340—471no—
428#340—471no—
429#336—471no—
430#336—471no—
431C47#2288511yescharacteristic, complemented, Sylow
432C22×Q8—22no—
433C22×Q8—21no—
434C22×Q8—22no—
435C22×Q8—22no—
436C22×Q8—41no—
437C22×Q8—41no—
438C22×Q8C4×D4714yescomplemented
439C22×Q8C22×D4711yescharacteristic
440C22×Q8C22×D4711yescharacteristic
441C22×D4—471no—
442C22×D4—941no—
443C23×C4—21no—
444C23×C4—941no—
445C23×C4C22×D4711yescharacteristic
446C2×SD16—474no—
447C2×SD16—474no—
448C2×SD16—942no—
449C2×SD16—942no—
450C2×SD16—1881no—
451C2×SD16—1881no—
452C2×M16—942no—
453C2×M16—942no—
454C2×M16—1881no—
455C22×C8—471no—
456C22×C8—471no—
457C22×C8—471no—
458C22×C8—471no—
459#121—474no—
460#121—942no—
461C4×Q8—22no—
462C4×Q8—22no—
463C4×Q8—41no—
464C4×Q8—41no—
465C4×D4—942no—
466C4×D4—1881no—
467#117—942no—
468#117—1881no—
469C2×C4⋊C4—21no—
470C2×C4⋊C4—21no—
471C2×C4⋊C4—471no—
472C2×C4⋊C4—471no—
473C2×C4⋊C4—471no—
474C2×C4⋊C4—941no—
475C2×C4⋊C4C22×D4711yescharacteristic
476C2×C4⋊C4C22×D4711yescharacteristic
477C2×C22⋊C4—21no—
478C2×C22⋊C4—941no—
479C2×C22⋊C4—941no—
480C2×C22⋊C4—941no—
481C2×C22⋊C4—941no—
482C2×C22⋊C4—941no—
483C2×C22⋊C4C22⋊D4711yescharacteristic
484C2×C22⋊C4C22⋊D4711yescharacteristic
485C2×C42—21no—
486C2×C42—21no—
487C2×C42—941no—
488C2×C42—941no—
489C2×C42C22×D4711yescharacteristic
490C2×C42C22×D4711yescharacteristic
491#107—1881no—
492#106—942no—
493#103—474no—
494#103—474no—
495#103—474no—
496#103—942no—
497#103—942no—
498#103—942no—
499#102—942no—
500#102—1881no—
501C22⋊C8—474no—
502#97—1881no—
503C4×C8—942no—
504#95—21no—
505#95—21no—
506#95—21no—
507#95—21no—
508#95—21no—
509#95—941no—
510#95—941no—
511#95C22⋊D4711yescharacteristic
512#95C22⋊D4711yescharacteristic
513C24—941no—
514C24C2×C22⋊D4711yescharacteristic
515C2×Q8—24no—
516C2×Q8—21no—
517C2×Q8—21no—
518C2×Q8—21no—
519C2×Q8—21no—
520C2×Q8—28no—
521C2×Q8—21no—
522C2×Q8—21no—
523C2×Q8—21no—
524C2×Q8—21no—
525C2×Q8—42no—
526C2×Q8—42no—
527C2×Q8—44no—
528C2×Q8—44no—
529C2×Q8—44no—
530C2×Q8C2×C4×D4712yes—
531C2×Q8C2×C4×D4712yes—
532C2×Q8D4×D4712yes—
533C2×Q8#1062535212yes—
534C2×D4—472no—
535C2×D4—944no—
536C2×D4—941no—
537C2×D4—941no—
538C2×D4—941no—
539C2×D4—941no—
540C2×D4—941no—
541C2×D4—3761no—
542C2×D4—3761no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—24no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—42no—
553C22×C4—42no—
554C22×C4—941no—
555C22×C4—941no—
556C22×C4—941no—
557C22×C4—3761no—
558C22×C4—1882no—
559C22×C4—1882no—
560C22×C4C2×C4×D4712yes—
561C22×C4#1062535012yes—
562C22×C4C2×C22⋊D4711yescharacteristic
563C22×C4C2×C22⋊D4711yescharacteristic
564C22×C4C2×C22⋊D4711yescharacteristic
565C22×C4C2×C22⋊D4711yescharacteristic
566C22×C4C2×C22⋊D4711yescharacteristic
567C22×C4C23×D4711yescharacteristic
568SD16—948no—
569SD16—1884no—
570M16—1884no—
571C2×C8—472no—
572C2×C8—472no—
573C2×C8—472no—
574C2×C8—941no—
575C2×C8—941no—
576C2×C8—941no—
577C2×C8—941no—
578C2×C8—941no—
579C2×C8—941no—
580C2×C8—941no—
581C2×C8—941no—
582C2×C8—941no—
583C4⋊C4—21no—
584C4⋊C4—21no—
585C4⋊C4—21no—
586C4⋊C4—21no—
587C4⋊C4—42no—
588C4⋊C4—42no—
589C4⋊C4—472no—
590C4⋊C4—472no—
591C4⋊C4—941no—
592C4⋊C4—941no—
593C4⋊C4—941no—
594C4⋊C4—941no—
595C4⋊C4—3761no—
596C22⋊C4—22no—
597C22⋊C4—41no—
598C22⋊C4—42no—
599C22⋊C4—944no—
600C22⋊C4—3761no—
601C22⋊C4—1882no—
602C22⋊C4—1882no—
603C22⋊C4—1882no—
604C42—21no—
605C42—21no—
606C42—21no—
607C42—21no—
608C42—42no—
609C42—42no—
610C42—3761no—
611C42—1882no—
612C23—21no—
613C23—21no—
614C23—21no—
615C23—21no—
616C23—21no—
617C23—21no—
618C23—942no—
619C23—1881no—
620C23—1881no—
621C23—1881no—
622C23—1881no—
623C23—1881no—
624C23—1881no—
625C23C4×C22⋊D4712yes—
626C23C22×C22⋊D4711yescharacteristic
627Q8—22no—
628Q8—22no—
629Q8—22no—
630Q8—22no—
631Q8—22no—
632Q8—48no—
633Q8—41no—
634Q8—41no—
635Q8(C22⋊D47)⋊C414yes—
636D4—942no—
637D4—942no—
638D4—3764no—
639D4—1881no—
640D4—1881no—
641C2×C4—21no—
642C2×C4—22no—
643C2×C4—21no—
644C2×C4—22no—
645C2×C4—21no—
646C2×C4—22no—
647C2×C4—21no—
648C2×C4—22no—
649C2×C4—22no—
650C2×C4—22no—
651C2×C4—22no—
652C2×C4—21no—
653C2×C4—21no—
654C2×C4—21no—
655C2×C4—22no—
656C2×C4—21no—
657C2×C4—21no—
658C2×C4—21no—
659C2×C4—21no—
660C2×C4—21no—
661C2×C4—21no—
662C2×C4—48no—
663C2×C4—41no—
664C2×C4—41no—
665C2×C4—41no—
666C2×C4—41no—
667C2×C4—41no—
668C2×C4—41no—
669C2×C4—41no—
670C2×C4—41no—
671C2×C4—942no—
672C2×C4—942no—
673C2×C4—3764no—
674C2×C4—1881no—
675C2×C4—1881no—
676C2×C4—1881no—
677C2×C4—1881no—
678C2×C4—1881no—
679C2×C4—1881no—
680C2×C4—1881no—
681C2×C4C4×C22⋊D4712yes—
682C2×C4#1309405512yes—
683C2×C4C22×C4×D4711yescharacteristic
684C2×C4C2×D4×D4711yescharacteristic
685C2×C4C2×#1062535211yescharacteristic
686C2×C4C2×#1062535011yescharacteristic
687C2×C4#1309406911yescharacteristic
688C2×C4#1309406911yescharacteristic
689C8—942no—
690C8—942no—
691C8—942no—
692C8—1881no—
693C22—22no—
694C22—22no—
695C22—22no—
696C22—41no—
697C22—41no—
698C22—41no—
699C22—41no—
700C22—3761no—
701C22—3761no—
702C22—3761no—
703C22—3761no—
704C22—1882no—
705C22—1882no—
706C22—1882no—
707C22C2×C4×C22⋊D4711yescharacteristic
708C22D4×C22⋊D4711yescharacteristic
709C22#1568976711yescharacteristic
710C22C2×#1309405511yescharacteristic
711C22#1568992111yescharacteristic
712C22#1568993111yescharacteristic
713C22#1568993111yescharacteristic
714C4—22no—
715C4—24no—
716C4—22no—
717C4—42no—
718C4—41no—
719C4—41no—
720C4—41no—
721C4—81no—
722C4—81no—
723C4—3761no—
724C4—1882no—
725C4—1882no—
726C4C2×(C22⋊D47)⋊C411yescharacteristic
727C4#1568959611yescharacteristic
728C4#1568976311yescharacteristic
729C4#1568979911yescharacteristic
730C2—42no—
731C2—3762no—
732C2#2024636711yescharacteristic
733C2C4×#1309405511yescharacteristic
734C2#2025224711yescharacteristic
735C2#2025489911yescharacteristic
736C2#2025497411yescharacteristic
737C2#2025564111yescharacteristic
738C2#2025568211yescharacteristic
subgroupG/H
centerC23C22×C22⋊D47
commutatorC2×C4×C47C23×C4
FrattiniC22×C4C23×D47
FittingQ8×C22⋊C4×C47C2
socleC23×C47C22×D4
prime radicalC2×#13093998C22
cosocleC22×C4×C47C24
hypercenterQ8×C22⋊C4D47
hypocenterC47#22885
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ Q8×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×C4×#10625336C2semidirect
3. C2×#15689132C2semidirect
5. #20244272C2semidirect
6. #20244067C2semidirect
7. #20244019C2semidirect
9. #20243743C2semidirect
10. #20243725C2semidirect
11. #20243642C2semidirect
12. #20243585C2semidirect
13. #20243218C2semidirect
14. #20243172C2semidirect
15. Q8×C22⋊C4×C47C2semidirect
22. #15689262C4semidirect
100. #13093948C2×C4semidirect
101. #13093948C2×C4semidirect
102. #13093948D4semidirect
105. C22⋊(C47⋊C8)C2×C4semidirect
116. C22×Q8×C47C2×C4semidirect
365. Q8×C22⋊C4D47semidirect
431. C47#22885semidirect
438. C22×Q8C4×D47semidirect

Maximal subgroups

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

subgroupindex
C2×#156892622
C2×C4×#106253362
C2×#156891322
#202464242
#202442722
#202440672
#202440192
#202438242
#202437432
#202437252
#202436422
#202435852
#202432182
#202431722
Q8×C22⋊C4×C472
#2288547