Finite Group Databasebeta

← #27080268

Subgroups — #27080268

Order 12032.

2742 conjugacy classes of subgroups.

The subgroup lattice has 746 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689888C211yesmaximal, characteristic, complemented
2#41×C22⋊D47C211yesmaximal, characteristic
3#20252130C213yesmaximal, complemented
4M16×C22⋊D47C213yesmaximal, complemented
5#20252113C213yesmaximal, complemented
6#20252110C213yesmaximal, complemented
7#20252098C213yesmaximal, complemented
8#20252091C213yesmaximal, complemented
9#20252089C213yesmaximal, complemented
10C2×#15689199C213yesmaximal, complemented
11#20251954C211yesmaximal, characteristic, complemented
12#20251837C211yesmaximal, characteristic, complemented
13#20251835C211yesmaximal, characteristic, complemented
14#131×Dic47C211yesmaximal, characteristic, complemented
15C2×C47×#568C211yesmaximal, characteristic, complemented
16C2×#41×D47C2211yescharacteristic
17#15689888—28no—
18C2×#13094032C2213yescomplemented
19C2×#13094031C2211yescharacteristic
20C2×#13094031C2211yescharacteristic
21C2×#13094030C2213yescomplemented
22C22×#10625324C2213yescomplemented
23C2×M16×D47C2213yescomplemented
24#15689792C411yescharacteristic
25Q8×C22⋊D47C411yescharacteristic
26#15689784C411yescharacteristic
27#15689780C411yescharacteristic
28#15689772C413yes—
29#15689767C413yes—
30#15689761C413yes—
31D4×C22⋊D47C413yes—
32#15689669C2213yes—
33#15689634C2213yes—
34#15689630C2213yes—
35#41×Dic47C2211yescharacteristic
36C2×C4×C22⋊D47C2213yes—
37#15689199C2211yescharacteristic
38#15689199C2213yes—
39#15689199C2213yescomplemented
40#15689199C2213yescomplemented
41#15689199C2213yescomplemented
42#15689199C2213yescomplemented
43#15689199C2213yescomplemented
44#15689199C2213yescomplemented
45#15689199C2216yescomplemented
46#15689194C2216yescomplemented
47#15689194C2216yescomplemented
48#15689192C2216yescomplemented
49#15689192C2216yescomplemented
50C8×C22⋊D47C2216yescomplemented
51C8×C22⋊D47C2216yescomplemented
52#15689151C2213yescomplemented
53#15689149C2213yescomplemented
54#15689146C2213yescomplemented
55C2×Dic47⋊C8C2213yescomplemented
56#15689091C2213yescomplemented
57#15689090C2213yescomplemented
58#15689090C2213yescomplemented
59#15689089C2213yescomplemented
60#15689087C2213yescomplemented
61#15689086C2213yescomplemented
62C2×C22⋊(C47⋊C8)C2213yescomplemented
63C2×(C2×D47)⋊C8C2213yescomplemented
64#15689081C2213yescomplemented
65#15689078C2213yescomplemented
66M16×Dic47C2213yescomplemented
67C2×C8×Dic47C2213yescomplemented
68C22×#41×C47C2211yescharacteristic
69C47×#568—28no—
70C2×#131×C47C2211yescharacteristic
71C2×#131×C47C2211yescharacteristic
72C2×#131×C47C2213yescomplemented
73C2×#131×C47C2213yescomplemented
74C22×M16×C47C2213yescomplemented
75C22×M16×C47C2213yescomplemented
76C2×#10625354C2×C411yescharacteristic
77C2×#10625350C2313yes—
78C2×#10625352C2×C413yes—
79#41×D47—24no—
80#41×D47—24no—
81C2×Q8×D47C2×C411yescharacteristic
82C22×C22⋊D47C2×C413yes—
83C2×D4×D47C2×C413yes—
84C22×C4×D47C2313yes—
85#13094032—212no—
86#13094031—24no—
87#13094031—24no—
88#13094030—212no—
89C2×#10625329C2313yes—
90C2×#10625329C2313yes—
91C2×#10625324—212no—
92C2×#10625324C2313yes—
93C2×#10625324C2311yescharacteristic
94C2×#10625324C2313yes—
95C2×#10625324C2313yes—
96M16×D47—212no—
97C22×C47⋊C8C2313yes—
98C22×C47⋊C8C2313yes—
99C2×C8×D47C2316yes—
100#13094022C2×C413yes—
101#13094020C2×C413yes—
102#13094013C2×C413yes—
103#13094011C2×C413yes—
104#13094007C2×C416yes—
105#13094005C2×C416yes—
106#13094003C2×C413yes—
107#13094003C2×C413yes—
108#13094000C2×C413yes—
109#13094000C2×C413yes—
110#13093998C2×C413yes—
111#13093998C2×C413yes—
112#13093996C2×C416yes—
113#13093996C2×C416yes—
114#13093995C2×C413yes—
115#13093995C2×C413yes—
116#13093993C2×C416yes—
117#13093992C2×C416yes—
118Q8×Dic47C2×C411yescharacteristic
119Q8×Dic47C2×C411yescharacteristic
120D4×Dic47C2×C413yes—
121D4×Dic47C2×C413yes—
122C4×C22⋊D47C2×C413yes—
123C4×C22⋊D47C2×C413yes—
124C4×C22⋊D47C2×C413yes—
125C4×C22⋊D47C2×C413yes—
126C4×C22⋊D47C2311yescharacteristic
127C4×C22⋊D47C2313yes—
128C4×C22⋊D47C2313yes—
129C4×C22⋊D47C2313yes—
130C4×C22⋊D47C2316yes—
131#13093983C2313yes—
132C2×Dic47⋊C4C2×C413yes—
133C2×C22⋊Dic47C2×C413yes—
134C2×(C2×D47)⋊C4C2×C413yes—
135C2×C4×Dic47C2313yes—
136Dic47⋊C8C2311yescharacteristic
137Dic47⋊C8C2313yes—
138Dic47⋊C8C2313yes—
139Dic47⋊C8C2313yes—
140Dic47⋊C8C2316yes—
141C22⋊(C47⋊C8)C2311yescharacteristic
142C22⋊(C47⋊C8)C2313yes—
143C22⋊(C47⋊C8)C2313yes—
144C22⋊(C47⋊C8)C2313yes—
145C22⋊(C47⋊C8)C2316yes—
146(C2×D47)⋊C8C2311yescharacteristic
147(C2×D47)⋊C8C2313yes—
148(C2×D47)⋊C8C2313yes—
149(C2×D47)⋊C8C2313yes—
150(C2×D47)⋊C8C2316yes—
151#13093934C2316yes—
152C8×Dic47C2311yescharacteristic
153C8×Dic47C2313yes—
154C8×Dic47C2313yes—
155C8×Dic47C2313yes—
156C2×#41×C47—24no—
157C2×#41×C47—24no—
158C2×#41×C47C2×C413yes—
159C2×#41×C47C2×C411yescharacteristic
160C2×#41×C47C2313yes—
161C2×#41×C47C2311yescharacteristic
162C22×Q8×C47C2×C411yescharacteristic
163C22×D4×C47C2×C413yes—
164C23×C4×C47C2313yes—
165#131×C47—24no—
166#131×C47—212no—
167#131×C47—212no—
168#131×C47D418yescomplemented
169C2×M16×C47—212no—
170C2×M16×C47—212no—
171C2×M16×C47C2313yes—
172C2×M16×C47C2311yescharacteristic
173C2×M16×C47C2313yes—
174C2×M16×C47C2313yes—
175C2×M16×C47C2313yes—
176C2×M16×C47C2313yes—
177C22×C8×C47C2313yes—
178C22×C8×C47C2316yes—
179C22×C8×C47C2313yes—
180C24×C47C22×C413yes—
181C23×D47C22×C413yes—
182#41×C47—24no—
183#41×C47—212no—
184#41×C47—26no—
185#41×C47—26no—
186#41×C47C2×D414yes—
187#41×C47#4114yes—
188C2×Q8×C47—24no—
189C2×Q8×C47C22×C413yes—
190C2×Q8×C47C22×C411yescharacteristic
191C2×D4×C47—212no—
192C2×D4×C47C22×C416yes—
193C2×D4×C47C22×C413yes—
194C2×D4×C47C22×C413yes—
195C22×C4×C47—26no—
196C22×C4×C47—26no—
197C22×C4×C47C22×C413yes—
198C22×C4×C47C22×C413yes—
199C22×C4×C47C22×C413yes—
200C22×C4×C47C2413yes—
201C22×C4×C47C2411yescharacteristic
202C22×C4×C47C2413yes—
203C2×C22⋊D47—46no—
204C2×C22⋊D47C22×C411yescharacteristic
205C2×C22⋊D47C22×C413yes—
206C2×C22⋊D47C22×C416yes—
207C2×C22⋊D47C22×C413yes—
208C2×C22⋊D47C22×C413yes—
209C2×C22⋊D47C22×C416yes—
210C22×Dic47C22×C413yes—
211C22×Dic47C22×C413yes—
212C22×Dic47C22×C413yes—
213#10625354—24no—
214Q8×D47—24no—
215#10625352—212no—
216D4×D47—212no—
217#10625350—26no—
218#10625350—26no—
219C2×D188C22×C413yes—
220C2×C4×D47—26no—
221C2×C4×D47—26no—
222C2×C4×D47C22×C413yes—
223C2×C4×D47C22×C413yes—
224C2×C4×D47C2413yes—
225C2×C4×D47C2411yescharacteristic
226C2×Dic94C22×C413yes—
227M16×C47—26no—
228M16×C47—26no—
229M16×C47—22no—
230M16×C47—26no—
231M16×C47—26no—
232M16×C47C2×D4112yescomplemented
233C2×C8×C47—26no—
234C2×C8×C47—212no—
235C2×C8×C47C2×D4112yescomplemented
236C2×C8×C47C2411yescharacteristic
237C2×C8×C47C2413yes—
238C2×C8×C47C2411yescharacteristic
239C2×C8×C47C2413yes—
240C22⋊Dic47C22×C411yescharacteristic
241C22⋊Dic47C22×C413yes—
242C22⋊Dic47C22×C413yes—
243C22⋊Dic47C22×C413yes—
244C22⋊Dic47C22×C416yes—
245C22⋊Dic47C22×C416yes—
246(C2×D47)⋊C4C22×C411yescharacteristic
247(C2×D47)⋊C4C22×C413yes—
248(C2×D47)⋊C4C22×C413yes—
249(C2×D47)⋊C4C22×C413yes—
250(C2×D47)⋊C4C22×C416yes—
251C4⋊Dic47C22×C413yes—
252C4⋊Dic47C22×C413yes—
253Dic47⋊C4C22×C411yescharacteristic
254Dic47⋊C4C22×C413yes—
255Dic47⋊C4C22×C413yes—
256Dic47⋊C4C22×C413yes—
257Dic47⋊C4C22×C416yes—
258C4×Dic47C22×C413yes—
259C4×Dic47C22×C413yes—
260C4×Dic47C2411yescharacteristic
261C4×Dic47C2413yes—
262#10625329—26no—
263#10625329—26no—
264C2×C47⋊C8—26no—
265C2×C47⋊C8—26no—
266C2×C47⋊C8C2411yescharacteristic
267C2×C47⋊C8C2413yes—
268C2×C47⋊C8C2413yes—
269C2×C47⋊C8C2411yescharacteristic
270#10625324—26no—
271#10625324—22no—
272#10625324—26no—
273#10625324—26no—
274C8×D47—212no—
275C23×C47—26no—
276C23×C47—43no—
277C23×C47—43no—
278C23×C47C23×C411yescharacteristic
279C23×C47C23×C413yes—
280C23×C47C23×C413yes—
281C22×D47—26no—
282C22×D47—43no—
283C22×D47—43no—
284C22×D47C23×C411yescharacteristic
285C22×D47C23×C413yes—
286Q8×C47—26no—
287Q8×C47C4×D414yes—
288D4×C47—212no—
289D4×C47—26no—
290D4×C47C4×D4112yes—
291C2×C4×C47—26no—
292C2×C4×C47—26no—
293C2×C4×C47—26no—
294C2×C4×C47—23no—
295C2×C4×C47—21no—
296C2×C4×C47—21no—
297C2×C4×C47—23no—
298C2×C4×C47C23×C411yescharacteristic
299C2×C4×C47C23×C413yes—
300C2×C4×C47C23×C413yes—
301C2×C4×C47C22×D416yes—
302C2×C4×C47C2×#4116yes—
303C2×C4×C47C2511yescharacteristic
304C22⋊D47—212no—
305C22⋊D47—22no—
306C22⋊D47—26no—
307C22⋊D47—43no—
308C22⋊D47—43no—
309C22⋊D47—46no—
310C2×Dic47—26no—
311C2×Dic47—26no—
312C2×Dic47—43no—
313C2×Dic47C23×C411yescharacteristic
314C2×Dic47C23×C413yes—
315C2×Dic47C23×C413yes—
316C2×Dic47C23×C413yes—
317C2×Dic47C23×C411yescharacteristic
318C2×Dic47C23×C411yescharacteristic
319D188—26no—
320C4×D47—26no—
321C4×D47—26no—
322C4×D47—23no—
323C4×D47—21no—
324C4×D47—21no—
325C4×D47—23no—
326Dic94—26no—
327C8×C47—21no—
328C8×C47—23no—
329C8×C47C22×D416yes—
330C8×C47C22×D412yes—
331C47⋊C8—23no—
332C47⋊C8—21no—
333C47⋊C8—21no—
334C47⋊C8—23no—
335#60147—471nomaximal, Sylow
336C22×C47—23no—
337C22×C47—23no—
338C22×C47—21no—
339C22×C47—23no—
340C22×C47—21no—
341C22×C47—23no—
342C22×C47—23no—
343C22×C47—21no—
344C22×C47—86no—
345C22×C47C2×C4×D416yes—
346C22×C47C24×C411yescharacteristic
347C2×D47—21no—
348C2×D47—23no—
349C2×D47—21no—
350C2×D47—23no—
351C2×D47—23no—
352C2×D47—21no—
353C2×D47—86no—
354C4×C47—21no—
355C4×C47—23no—
356C4×C47C2×C4×D416yes—
357C4×C47C23×D411yescharacteristic
358C4×C47C22×#4111yescharacteristic
359Dic47—23no—
360Dic47—21no—
361Dic47—23no—
362Dic47—21no—
363Dic47—23no—
364Dic47#56812yescomplemented
365C2×#568—471no—
366C2×#568D4711yescharacteristic, complemented
367D4×#41—471no—
368#2935—473no—
369D4×M16—473no—
370#2933—473no—
371#2933—473no—
372#2931—473no—
373#2930—473no—
374#2930—473no—
375C2×#436—473no—
376#2906—471no—
377#2880—471no—
378#2880—471no—
379C4×#131—471no—
380C2×C47—26no—
381C2×C47—43no—
382C2×C47—41no—
383C2×C47C22×C4×D411yescharacteristic
384C2×C47C2×#56811yescharacteristic
385C2×C47#357311yescharacteristic
386D47—43no—
387D47—41no—
388C22×#41—471no—
389C22×#41C2×D4711yescharacteristic
390#568—28no—
391#568—948no—
392C2×#131—471no—
393C2×#131—471no—
394C2×#131—473no—
395C2×#131—473no—
396C2×#131C2×D4711yescharacteristic
397C2×#131C2×D4711yescharacteristic
398C2×#131C2×D4713yescomplemented
399C2×#131C2×D4713yescomplemented
400C22×M16—473no—
401C22×M16—473no—
402C22×M16C2×D4713yescomplemented
403C22×M16C2×D4713yescomplemented
404#550—471no—
405D4×Q8—471no—
406#548—471no—
407#548—471no—
408#547—473no—
409#546—473no—
410#546—473no—
411D42—473no—
412#532—473no—
413#525—473no—
414#525—473no—
415C4×#41—471no—
416C2×C4×D4—473no—
417#436—471no—
418#436—473no—
419#436—473no—
420#436—473no—
421#436—473no—
422#436—473no—
423#436—473no—
424#436—473no—
425#436—476no—
426#435—476no—
427#435—476no—
428#435—476no—
429#435—476no—
430C8×D4—476no—
431C8×D4—476no—
432#424—473no—
433#424—473no—
434#423—473no—
435C2×C4⋊C8—473no—
436#408—473no—
437#408—473no—
438#408—473no—
439#408—473no—
440#407—473no—
441#407—473no—
442C2×C22⋊C8—473no—
443C2×C22⋊C8—473no—
444#405—473no—
445#405—473no—
446C4×M16—473no—
447C2×C4×C8—473no—
448C47#6014711yescharacteristic, complemented, Sylow
449C2×#41—24no—
450C2×#41—24no—
451C2×#41—471no—
452C2×#41—473no—
453C2×#41—473no—
454C2×#41—944no—
455C2×#41—944no—
456C2×#41C4×D4713yes—
457C2×#41C4×D4711yescharacteristic
458C2×#41C22×D4713yes—
459C2×#41C22×D4711yescharacteristic
460C22×Q8—471no—
461C22×Q8C4×D4711yescharacteristic
462C22×D4—473no—
463C22×D4—473no—
464C22×D4C4×D4713yes—
465C23×C4—473no—
466C23×C4C22×D4713yes—
467#131—24no—
468#131—212no—
469#131—212no—
470#131—944no—
471#131—944no—
472#131—9412no—
473#131—9412no—
474#131C22⋊D4718yescomplemented
475C2×M16—212no—
476C2×M16—212no—
477C2×M16—473no—
478C2×M16—473no—
479C2×M16—473no—
480C2×M16—471no—
481C2×M16—473no—
482C2×M16—473no—
483C2×M16—9412no—
484C2×M16—9412no—
485C2×M16C22×D4713yes—
486C2×M16C22×D4711yescharacteristic
487C2×M16C22×D4713yes—
488C2×M16C22×D4713yes—
489C2×M16C22×D4713yes—
490C2×M16C22×D4713yes—
491C22×C8—473no—
492C22×C8—473no—
493C22×C8—476no—
494C22×C8C22×D4713yes—
495C22×C8C22×D4716yes—
496C22×C8C22×D4713yes—
497C4⋊Q8—473no—
498#127—473no—
499#124—473no—
500#124—473no—
501#123—476no—
502#123—476no—
503C22⋊Q8—473no—
504C22⋊Q8—473no—
505C22⋊Q8—473no—
506C22⋊Q8—473no—
507#121—473no—
508#121—473no—
509#121—476no—
510#121—476no—
511#121—473no—
512#121—473no—
513#120—476no—
514#120—476no—
515C4×Q8—471no—
516C4×Q8—471no—
517C4×D4—473no—
518C4×D4—473no—
519C4×D4—473no—
520C4×D4—473no—
521C4×D4—473no—
522C4×D4—473no—
523C4×D4—471no—
524C4×D4—473no—
525C4×D4—473no—
526C4×D4—473no—
527C4×D4—476no—
528#117—473no—
529C2×C4⋊C4—473no—
530C2×C22⋊C4—473no—
531C2×C22⋊C4—473no—
532C2×C42—473no—
533C4⋊C8—471no—
534C4⋊C8—473no—
535C4⋊C8—473no—
536C4⋊C8—473no—
537C4⋊C8—476no—
538C22⋊C8—471no—
539C22⋊C8—473no—
540C22⋊C8—473no—
541C22⋊C8—473no—
542C22⋊C8—476no—
543C22⋊C8—471no—
544C22⋊C8—473no—
545C22⋊C8—473no—
546C22⋊C8—473no—
547C22⋊C8—476no—
548#97—476no—
549C4×C8—471no—
550C4×C8—473no—
551C4×C8—473no—
552C4×C8—473no—
553C24—473no—
554C24C2×C4×D4713yes—
555#41—24no—
556#41—212no—
557#41—26no—
558#41—26no—
559#41—944no—
560#41—9412no—
561#41—946no—
562#41—946no—
563#41#1062535014yes—
564#41C2×C22⋊D4714yes—
565C2×Q8—24no—
566C2×Q8—473no—
567C2×Q8—944no—
568C2×Q8C2×C4×D4713yes—
569C2×Q8C2×C4×D4711yescharacteristic
570C2×D4—212no—
571C2×D4—471no—
572C2×D4—473no—
573C2×D4—476no—
574C2×D4—473no—
575C2×D4—473no—
576C2×D4—476no—
577C2×D4—473no—
578C2×D4—9412no—
579C2×D4—1886no—
580C2×D4C2×C4×D4716yes—
581C2×D4C2×C4×D4713yes—
582C2×D4C2×C4×D4713yes—
583C22×C4—26no—
584C22×C4—26no—
585C22×C4—473no—
586C22×C4—473no—
587C22×C4—473no—
588C22×C4—473no—
589C22×C4—473no—
590C22×C4—473no—
591C22×C4—471no—
592C22×C4—946no—
593C22×C4—946no—
594C22×C4C2×C4×D4713yes—
595C22×C4C2×C4×D4713yes—
596C22×C4C2×C4×D4713yes—
597C22×C4C23×D4713yes—
598C22×C4C23×D4711yescharacteristic
599C22×C4C23×D4713yes—
600M16—26no—
601M16—26no—
602M16—22no—
603M16—26no—
604M16—26no—
605M16—946no—
606M16—946no—
607M16—946no—
608M16—942no—
609M16—946no—
610M16—946no—
611M16C2×C22⋊D47112yescomplemented
612C2×C8—26no—
613C2×C8—212no—
614C2×C8—471no—
615C2×C8—473no—
616C2×C8—473no—
617C2×C8—471no—
618C2×C8—946no—
619C2×C8—946no—
620C2×C8—9412no—
621C2×C8C2×C22⋊D47112yescomplemented
622C2×C8C23×D4711yescharacteristic
623C2×C8C23×D4713yes—
624C2×C8C23×D4711yescharacteristic
625C2×C8C23×D4713yes—
626C4⋊C4—471no—
627C4⋊C4—473no—
628C4⋊C4—473no—
629C4⋊C4—473no—
630C4⋊C4—476no—
631C4⋊C4—473no—
632C4⋊C4—473no—
633C22⋊C4—471no—
634C22⋊C4—473no—
635C22⋊C4—473no—
636C22⋊C4—473no—
637C22⋊C4—476no—
638C22⋊C4—476no—
639C22⋊C4—471no—
640C22⋊C4—473no—
641C22⋊C4—473no—
642C22⋊C4—473no—
643C22⋊C4—476no—
644C42—473no—
645C42—473no—
646C42—471no—
647C42—473no—
648C23—26no—
649C23—43no—
650C23—43no—
651C23—471no—
652C23—473no—
653C23—946no—
654C23—1883no—
655C23—1883no—
656C23C22×C4×D4711yescharacteristic
657C23C22×C4×D4713yes—
658C23C22×C4×D4713yes—
659Q8—26no—
660Q8—946no—
661Q8C4×C22⋊D4714yes—
662D4—212no—
663D4—26no—
664D4—946no—
665D4—942no—
666D4—9412no—
667D4—946no—
668D4—1886no—
669D4—1883no—
670D4—1883no—
671D4C4×C22⋊D47112yes—
672C2×C4—26no—
673C2×C4—26no—
674C2×C4—26no—
675C2×C4—23no—
676C2×C4—21no—
677C2×C4—21no—
678C2×C4—23no—
679C2×C4—471no—
680C2×C4—471no—
681C2×C4—473no—
682C2×C4—473no—
683C2×C4—471no—
684C2×C4—473no—
685C2×C4—946no—
686C2×C4—946no—
687C2×C4—946no—
688C2×C4—946no—
689C2×C4—943no—
690C2×C4—941no—
691C2×C4—941no—
692C2×C4—943no—
693C2×C4—1883no—
694C2×C4C22×C4×D4711yescharacteristic
695C2×C4C22×C4×D4713yes—
696C2×C4C22×C4×D4713yes—
697C2×C4C22×C22⋊D4716yes—
698C2×C4C2×#1062535016yes—
699C2×C4C24×D4711yescharacteristic
700C8—21no—
701C8—23no—
702C8—943no—
703C8—941no—
704C8—941no—
705C8—943no—
706C8C22×C22⋊D4716yes—
707C8C22×C22⋊D4712yes—
708C22—23no—
709C22—23no—
710C22—21no—
711C22—23no—
712C22—21no—
713C22—23no—
714C22—23no—
715C22—21no—
716C22—86no—
717C22—941no—
718C22—943no—
719C22—941no—
720C22—943no—
721C22—943no—
722C22—941no—
723C22—3766no—
724C22C2×C4×C22⋊D4716yes—
725C22C23×C4×D4711yescharacteristic
726C4—21no—
727C4—23no—
728C4—472no—
729C4—941no—
730C4—943no—
731C4—943no—
732C4—941no—
733C4—943no—
734C4C2×C4×C22⋊D4716yes—
735C4C23×C22⋊D4711yescharacteristic
736C4C22×#1062535011yescharacteristic
737C2—26no—
738C2—41no—
739C2—43no—
740C2—1881no—
741C2—1883no—
742C2C22×C4×C22⋊D4711yescharacteristic
743C2#568×D4711yescharacteristic
744C2#2025810111yescharacteristic
subgroupG/H
center, FrattiniC2×C4C24×D47
commutator, socleC22×C47C24×C4
FittingC2×C47×#568C2
prime radical#41×C22⋊D47C2
cosocleC2×C4×C47C25
hypercenterC2×#568D47
hypocenterC47#60147
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C2×#568

Complements

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

NH ≅ G/Ntype
1. C2×#15689888C2semidirect
3. #20252130C2semidirect
4. M16×C22⋊D47C2semidirect
5. #20252113C2semidirect
6. #20252110C2semidirect
7. #20252098C2semidirect
8. #20252091C2semidirect
9. #20252089C2semidirect
10. C2×#15689199C2semidirect
11. #20251954C2semidirect
12. #20251837C2semidirect
13. #20251835C2semidirect
14. #131×Dic47C2semidirect
15. C2×C47×#568C2semidirect
18. C2×#13094032C22semidirect
21. C2×#13094030C22semidirect
22. C22×#10625324C22semidirect
23. C2×M16×D47C22semidirect
39. #15689199C22semidirect
40. #15689199C22semidirect
41. #15689199C22semidirect
42. #15689199C22semidirect
43. #15689199C22semidirect
44. #15689199C22semidirect
45. #15689199C22semidirect
46. #15689194C22semidirect
47. #15689194C22semidirect
48. #15689192C22semidirect
49. #15689192C22semidirect
50. C8×C22⋊D47C22semidirect
51. C8×C22⋊D47C22semidirect
52. #15689151C22semidirect
53. #15689149C22semidirect
54. #15689146C22semidirect
55. C2×Dic47⋊C8C22semidirect
56. #15689091C22semidirect
57. #15689090C22semidirect
58. #15689090C22semidirect
59. #15689089C22semidirect
60. #15689087C22semidirect
61. #15689086C22semidirect
62. C2×C22⋊(C47⋊C8)C22semidirect
63. C2×(C2×D47)⋊C8C22semidirect
64. #15689081C22semidirect
65. #15689078C22semidirect
66. M16×Dic47C22semidirect
67. C2×C8×Dic47C22semidirect
72. C2×#131×C47C22semidirect
73. C2×#131×C47C22semidirect
74. C22×M16×C47C22semidirect
75. C22×M16×C47C22semidirect
168. #131×C47D4semidirect
232. M16×C47C2×D4semidirect
235. C2×C8×C47C2×D4semidirect
364. Dic47#568semidirect
366. C2×#568D47semidirect
398. C2×#131C2×D47semidirect
399. C2×#131C2×D47semidirect
402. C22×M16C2×D47semidirect
403. C22×M16C2×D47semidirect
448. C47#60147semidirect
474. #131C22⋊D47semidirect
611. M16C2×C22⋊D47semidirect
621. C2×C8C2×C22⋊D47semidirect

Maximal subgroups

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

subgroupindex
C2×#156898882
#41×C22⋊D472
#202521302
M16×C22⋊D472
#202521132
#202521102
#202520982
#202520912
#202520892
C2×#156891992
#202519542
#202518372
#202518352
#131×Dic472
C2×C47×#5682
#6014747