Finite Group Databasebeta

← D47×#2880 #27079720

Subgroups — D47×#2880 #27079720

Order 12032.

5206 conjugacy classes of subgroups.

The subgroup lattice has 792 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#41×D47C211yesmaximal, characteristic
2C2×#131×D47C212yesmaximal, complemented
3#20251838C213yesmaximal, complemented
4#20251837C211yesmaximal, characteristic, complemented
5#20251836C216yesmaximal, complemented
6#20251835C212yesmaximal, complemented
7#20251834C213yesmaximal, complemented
8#408×D47C216yesmaximal, complemented
9#407×D47C213yesmaximal, complemented
10C2×C22⋊C8×D47C213yesmaximal, complemented
11C47×#2880C211yesmaximal, characteristic, complemented
12C22×#10625354C411yescharacteristic
13C22×#10625350C2213yes—
14C22×#10625352C413yes—
15C2×#41×D47—216no—
16C2×#41×D47C411yescharacteristic
17C2×#41×D47C413yes—
18C2×#41×D47C411yescharacteristic
19C2×#41×D47C413yes—
20C2×#41×D47C2213yes—
21C2×#41×D47C2211yescharacteristic
22C2×#41×D47C2213yes—
23C2×#41×D47C2211yescharacteristic
24C22×Q8×D47C411yescharacteristic
25C22×D4×D47C413yes—
26C23×C4×D47C2213yes—
27C2×#13094032C2216yescomplemented
28C2×#13094031C2212yescomplemented
29C2×#13094030C2216yescomplemented
30#131×D47—216no—
31C2×M16×D47C2216yescomplemented
32C22×C8×D47C2216yescomplemented
33#15689091C2216yescomplemented
34#15689090C2216yescomplemented
35#15689089C2216yescomplemented
36#15689088C22112yescomplemented
37#15689088C22112yescomplemented
38#15689087C2213yescomplemented
39#15689086C2216yescomplemented
40#15689085C2216yescomplemented
41#15689085C2216yescomplemented
42C2×C22⋊(C47⋊C8)C2213yescomplemented
43C2×(C2×D47)⋊C8C2216yescomplemented
44C22⋊C8×D47C2211yescharacteristic
45C22⋊C8×D47C2213yes—
46C22⋊C8×D47C2216yescomplemented
47C22⋊C8×D47C2213yescomplemented
48C22⋊C8×D47C2213yescomplemented
49C22⋊C8×D47C2216yescomplemented
50C22⋊C8×D47C2216yescomplemented
51C22×#41×C47C2211yescharacteristic
52C2×#131×C47C2212yescomplemented
53C47×#408C2216yescomplemented
54C47×#407C2213yescomplemented
55C2×C22⋊C8×C47C2213yescomplemented
56C24×D47C2×C413yes—
57C2×#10625354—28no—
58C2×#10625354C2×C411yescharacteristic
59C2×#10625354C2×C413yes—
60C2×#10625354C2×C413yes—
61C2×#10625354C2×C411yescharacteristic
62C2×#10625350—224no—
63C2×#10625350C2×C416yes—
64C2×#10625350C2×C413yes—
65C2×#10625350C2×C413yes—
66C2×#10625350C2316yes—
67C2×#10625350C2313yes—
68C2×#10625350C2313yes—
69C2×#10625352—224no—
70C2×#10625352C2×C413yes—
71C2×#10625352C2×C416yes—
72C2×#10625352C2×C416yes—
73C2×#10625352C2×C413yes—
74C2×#10625352C2×C413yes—
75C2×#10625352C2×C413yes—
76#41×D47—28no—
77#41×D47—28no—
78#41×D47—28no—
79#41×D47—224no—
80#41×D47—224no—
81#41×D47—224no—
82#41×D47—224no—
83#41×D47D4116yes—
84C22×Dic94C2×C413yes—
85C2×Q8×D47—28no—
86C2×Q8×D47C2×C411yescharacteristic
87C2×Q8×D47C2×C413yes—
88C2×Q8×D47C2×C413yes—
89C2×Q8×D47C2×C411yescharacteristic
90C22×D188C2×C413yes—
91C22×C22⋊D47C2×C416yes—
92C2×D4×D47—224no—
93C2×D4×D47C2×C416yes—
94C2×D4×D47C2×C413yes—
95C2×D4×D47C2×C416yes—
96C2×D4×D47C2×C413yes—
97C2×D4×D47C2×C413yes—
98C2×D4×D47C2×C413yes—
99C23×Dic47C2×C413yes—
100C22×C4×D47—224no—
101C22×C4×D47C2×C413yes—
102C22×C4×D47C2×C413yes—
103C22×C4×D47C2×C413yes—
104C22×C4×D47C2×C413yes—
105C22×C4×D47C2×C413yes—
106C22×C4×D47C2×C413yes—
107C22×C4×D47C2311yescharacteristic
108C22×C4×D47C2313yes—
109C22×C4×D47C2313yes—
110C22×C4×D47C2313yes—
111C22×C4×D47C2313yes—
112C22×C4×D47C2313yes—
113#13094032—224no—
114#13094031—28no—
115#13094030—224no—
116C2×#10625329C2316yescomplemented
117C2×#10625324C23112yescomplemented
118M16×D47—224no—
119C22×C47⋊C8C2316yescomplemented
120C2×C8×D47—224no—
121C2×C8×D47C2312yes—
122C2×C8×D47C2316yes—
123C2×C8×D47C2316yescomplemented
124C2×C8×D47C2316yescomplemented
125C22⋊(C47⋊C8)C2311yescharacteristic
126C22⋊(C47⋊C8)C2313yes—
127C22⋊(C47⋊C8)C2316yescomplemented
128C22⋊(C47⋊C8)C2316yescomplemented
129(C2×D47)⋊C8C2312yes—
130(C2×D47)⋊C8C2316yes—
131(C2×D47)⋊C8C2316yescomplemented
132(C2×D47)⋊C8C2316yescomplemented
133(C2×D47)⋊C8C23112yescomplemented
134C2×#41×C47—28no—
135C2×#41×C47C2×C411yescharacteristic
136C2×#41×C47C2×C413yes—
137C2×#41×C47C2313yes—
138C2×#41×C47C2311yescharacteristic
139C22×Q8×C47C2×C411yescharacteristic
140C22×D4×C47C2×C413yes—
141C23×C4×C47C2313yes—
142#131×C47—28no—
143C2×M16×C47C2316yescomplemented
144C22×C8×C47C2316yescomplemented
145C22⋊C8×C47C2311yescharacteristic
146C22⋊C8×C47C2313yes—
147C22⋊C8×C47C2316yescomplemented
148C22⋊C8×C47C2316yescomplemented
149C24×C47C22×C413yes—
150C23×D47—212no—
151C23×D47—212no—
152C23×D47—46no—
153C23×D47C22×C413yes—
154C23×D47C22×C413yes—
155C23×D47C22×C413yes—
156C23×D47C22×C413yes—
157C23×D47C22×C413yes—
158C23×D47C22×C411yescharacteristic
159#41×C47—24no—
160#41×C47—212no—
161#41×C47—212no—
162#41×C47C2×D418yes—
163C2×Q8×C47—24no—
164C2×Q8×C47C22×C413yes—
165C2×Q8×C47C22×C411yescharacteristic
166C2×D4×C47—212no—
167C2×D4×C47C22×C416yes—
168C2×D4×C47C22×C413yes—
169C2×D4×C47C22×C413yes—
170C22×C4×C47—212no—
171C22×C4×C47C22×C413yes—
172C22×C4×C47C22×C413yes—
173C22×C4×C47C22×C413yes—
174C22×C4×C47C2411yescharacteristic
175C22×C4×C47C2413yes—
176C22×C4×C47C2413yes—
177C2×C22⋊D47—224no—
178C2×C22⋊D47C22×C416yes—
179C2×C22⋊D47C22×C416yes—
180C2×C22⋊D47C22×C416yes—
181C2×C22⋊D47C22×C416yes—
182C22×Dic47—212no—
183C22×Dic47C22×C411yescharacteristic
184C22×Dic47C22×C413yes—
185C22×Dic47C22×C413yes—
186C22×Dic47C22×C413yes—
187C22×Dic47C22×C413yes—
188C22×Dic47C22×C413yes—
189#10625354—24no—
190#10625354—212no—
191#10625354—212no—
192#10625354C22⋊C418yes—
193Q8×D47—24no—
194Q8×D47—212no—
195Q8×D47—212no—
196Q8×D47C22⋊C418yes—
197#10625352—212no—
198#10625352—224no—
199#10625352—224no—
200#10625352—212no—
201#10625352—212no—
202#10625352C22⋊C4124yes—
203D4×D47—224no—
204D4×D47—212no—
205D4×D47—224no—
206D4×D47—212no—
207D4×D47—212no—
208D4×D47C22⋊C4124yes—
209#10625350—212no—
210#10625350—224no—
211#10625350—212no—
212#10625350—224no—
213#10625350—212no—
214#10625350C2×D4124yes—
215C2×D188—212no—
216C2×D188C22×C416yes—
217C2×D188C22×C413yes—
218C2×D188C22×C413yes—
219C2×C4×D47—212no—
220C2×C4×D47—212no—
221C2×C4×D47—212no—
222C2×C4×D47—212no—
223C2×C4×D47—212no—
224C2×C4×D47—212no—
225C2×C4×D47—212no—
226C2×C4×D47—24no—
227C2×C4×D47—212no—
228C2×C4×D47—212no—
229C2×C4×D47—212no—
230C2×C4×D47C22×C411yescharacteristic
231C2×C4×D47C22×C411yescharacteristic
232C2×C4×D47C22×C413yes—
233C2×C4×D47C22×C413yes—
234C2×C4×D47C22×C413yes—
235C2×C4×D47C22×C413yes—
236C2×C4×D47C22×C413yes—
237C2×C4×D47C22×C413yes—
238C2×C4×D47C22×C413yes—
239C2×C4×D47C22×C413yes—
240C2×C4×D47C22×C413yes—
241C2×C4×D47C22×C413yes—
242C2×C4×D47C2×D4124yes—
243C2×C4×D47C2411yescharacteristic
244C2×C4×D47C2413yes—
245C2×C4×D47C2411yescharacteristic
246C2×C4×D47C2413yes—
247C2×Dic94—212no—
248C2×Dic94C22×C413yes—
249C2×Dic94C22×C416yes—
250C2×Dic94C22×C413yes—
251M16×C47—212no—
252C2×C8×C47—212no—
253C2×C8×C47C2412yes—
254C2×C8×C47C2416yes—
255#10625329—212no—
256C2×C47⋊C8—212no—
257C2×C47⋊C8C2412yes—
258C2×C47⋊C8C2416yes—
259#10625324—224no—
260C8×D47—24no—
261C8×D47—212no—
262C8×D47—212no—
263C8×D47—212no—
264C23×C47—26no—
265C23×C47—26no—
266C23×C47—43no—
267C23×C47C23×C413yes—
268C23×C47C23×C413yes—
269C23×C47C23×C411yescharacteristic
270C22×D47—22no—
271C22×D47—26no—
272C22×D47—22no—
273C22×D47—26no—
274C22×D47—26no—
275C22×D47—26no—
276C22×D47—26no—
277C22×D47—26no—
278C22×D47—26no—
279C22×D47—26no—
280C22×D47—26no—
281C22×D47—26no—
282C22×D47—26no—
283C22×D47—43no—
284C22×D47—43no—
285C22×D47—43no—
286C22×D47—448no—
287C22×D47C2×C22⋊C4112yes—
288C22×D47#13114yescomplemented
289C22×D47C23×C413yes—
290C22×D47C23×C413yes—
291C22×D47C23×C411yescharacteristic
292C22×D47C23×C411yescharacteristic
293Q8×C47—26no—
294Q8×C47C2×C22⋊C414yes—
295D4×C47—212no—
296D4×C47—26no—
297D4×C47C2×C22⋊C4112yes—
298C2×C4×C47—26no—
299C2×C4×C47—26no—
300C2×C4×C47—26no—
301C2×C4×C47—22no—
302C2×C4×C47—26no—
303C2×C4×C47C23×C413yes—
304C2×C4×C47C23×C411yescharacteristic
305C2×C4×C47C23×C413yes—
306C2×C4×C47C22×D4112yes—
307C2×C4×C47C2511yescharacteristic
308C22⋊D47—212no—
309C22⋊D47—212no—
310C22⋊D47—212no—
311C22⋊D47C2×C22⋊C4124yes—
312C2×Dic47—26no—
313C2×Dic47—26no—
314C2×Dic47—22no—
315C2×Dic47—26no—
316C2×Dic47—26no—
317C2×Dic47C2×C22⋊C4112yes—
318C2×Dic47C23×C413yes—
319C2×Dic47C23×C411yescharacteristic
320C2×Dic47C23×C413yes—
321C2×Dic47C23×C411yescharacteristic
322D188—212no—
323D188—26no—
324D188C2×C22⋊C4112yes—
325C4×D47—22no—
326C4×D47—26no—
327C4×D47—26no—
328C4×D47—26no—
329C4×D47—26no—
330C4×D47—26no—
331C4×D47—22no—
332C4×D47—26no—
333C4×D47—22no—
334C4×D47—26no—
335C4×D47—26no—
336C4×D47—26no—
337C4×D47C2×C22⋊C4112yes—
338C4×D47C2×C22⋊C4112yes—
339C4×D47C22×D414yes—
340C4×D47C22×D4112yes—
341Dic94—26no—
342Dic94—212no—
343Dic94C2×C22⋊C4112yes—
344C8×C47—22no—
345C8×C47—26no—
346C47⋊C8—22no—
347C47⋊C8—26no—
348C2×#2880—471nomaximal, Sylow
349C22×C47—21no—
350C22×C47—23no—
351C22×C47—21no—
352C22×C47—23no—
353C22×C47—23no—
354C22×C47—23no—
355C22×C47—23no—
356C22×C47—412no—
357C22×C47C22×C22⋊C416yes—
358C22×C47C2×#13112yescomplemented
359C22×C47C24×C411yescharacteristic
360C2×D47—21no—
361C2×D47—23no—
362C2×D47—21no—
363C2×D47—23no—
364C2×D47—28no—
365C2×D47—224no—
366C2×D47—23no—
367C2×D47—23no—
368C2×D47—23no—
369C2×D47—412no—
370C2×D47—412no—
371C2×D47—412no—
372C2×D47—412no—
373C2×D47C22×C22⋊C416yes—
374C2×D47C22×C22⋊C412yes—
375C2×D47C2×#13112yes—
376C2×D47C2×#13112yescomplemented
377C2×D47#56812yes—
378C4×C47—23no—
379C4×C47—21no—
380C4×C47C22×C22⋊C416yes—
381C4×C47C23×D412yes—
382Dic47—23no—
383Dic47—21no—
384Dic47C22×C22⋊C416yes—
385Dic47C22×C22⋊C412yes—
386C23×#41—471no—
387C22×#131—472no—
388#2880—476no—
389#2880—473no—
390#2880—473no—
391#2880—471no—
392#2880—472no—
393#2880D4711yescharacteristic, direct product factor
394C2×#408—476no—
395C2×#407—473no—
396C22×C22⋊C8—473no—
397C2×C47—22no—
398C2×C47—26no—
399C2×C47—43no—
400C2×C47C23×C22⋊C411yescharacteristic
401C2×C47C22×#13111yescharacteristic
402C2×C47C2×#56811yescharacteristic
403D47—22no—
404D47—26no—
405D47—43no—
406D47#288014yesdirect product factor
407C22×#41—471no—
408C22×#41—473no—
409C22×#41—471no—
410C22×#41—471no—
411C22×#41—473no—
412C22×#41—473no—
413C22×#41—473no—
414C22×#41—471no—
415C22×#41—471no—
416C22×#41—473no—
417C22×#41—473no—
418C22×#41—9416no—
419C22×#41C2×D4711yescharacteristic
420C23×Q8—471no—
421C23×D4—473no—
422C24×C4—473no—
423C2×#131—472no—
424C2×#131—476no—
425C2×#131—476no—
426C2×#131—9416no—
427C2×#131C2×D4712yescomplemented
428C22×M16—476no—
429C23×C8—476no—
430#408—476no—
431#408—476no—
432#408—476no—
433#408—4712no—
434#408—4712no—
435#408C2×D4716yescomplemented
436#407—473no—
437#407—476no—
438#407—476no—
439#407—476no—
440#407C2×D4713yescomplemented
441C2×C22⋊C8—473no—
442C2×C22⋊C8—476no—
443C2×C22⋊C8—471no—
444C2×C22⋊C8—473no—
445C2×C22⋊C8—473no—
446C2×C22⋊C8—473no—
447C2×C22⋊C8—476no—
448C2×C22⋊C8—476no—
449C2×C22⋊C8—476no—
450C2×C22⋊C8C2×D4713yescomplemented
451C47C2×#288011yescharacteristic, complemented, Sylow
452C25—473no—
453C2×#41—28no—
454C2×#41—4716no—
455C2×#41—471no—
456C2×#41—473no—
457C2×#41—473no—
458C2×#41—471no—
459C2×#41—473no—
460C2×#41—476no—
461C2×#41—473no—
462C2×#41—476no—
463C2×#41—473no—
464C2×#41—473no—
465C2×#41—476no—
466C2×#41—473no—
467C2×#41—473no—
468C2×#41—473no—
469C2×#41—476no—
470C2×#41—473no—
471C2×#41—9424no—
472C2×#41—9424no—
473C2×#41—9424no—
474C2×#41—9424no—
475C2×#41—948no—
476C2×#41—948no—
477C2×#41—948no—
478C2×#41—9424no—
479C2×#41—9424no—
480C2×#41—948no—
481C2×#41C4×D4711yescharacteristic
482C2×#41C4×D4713yes—
483C2×#41C22×D4713yes—
484C2×#41C22×D4711yescharacteristic
485C22×Q8—471no—
486C22×Q8—473no—
487C22×Q8—473no—
488C22×Q8—471no—
489C22×Q8—473no—
490C22×Q8—948no—
491C22×Q8C4×D4711yescharacteristic
492C22×D4—473no—
493C22×D4—476no—
494C22×D4—473no—
495C22×D4—476no—
496C22×D4—473no—
497C22×D4—476no—
498C22×D4—473no—
499C22×D4—473no—
500C22×D4—9424no—
501C22×D4C4×D4713yes—
502C23×C4—473no—
503C23×C4—473no—
504C23×C4—473no—
505C23×C4—473no—
506C23×C4—473no—
507C23×C4—473no—
508C23×C4—473no—
509C23×C4—473no—
510C23×C4—471no—
511C23×C4—473no—
512C23×C4—473no—
513C23×C4—473no—
514C23×C4—473no—
515C23×C4—9424no—
516C23×C4C22×D4713yes—
517#131—28no—
518#131—9424no—
519#131—9424no—
520#131—948no—
521C2×M16—476no—
522C2×M16—4712no—
523C2×M16—9424no—
524C2×M16C22×D4716yescomplemented
525C22×C8—476no—
526C22×C8—472no—
527C22×C8—476no—
528C22×C8—476no—
529C22×C8—476no—
530C22×C8—9424no—
531C22×C8C22×D4716yescomplemented
532C22⋊C8—471no—
533C22⋊C8—473no—
534C22⋊C8—476no—
535C22⋊C8—476no—
536C22⋊C8—472no—
537C22⋊C8—476no—
538C22⋊C8—476no—
539C22⋊C8—476no—
540C22⋊C8—4712no—
541C22⋊C8C22×D4711yescharacteristic
542C22⋊C8C22×D4713yes—
543C22⋊C8C22×D4716yescomplemented
544C22⋊C8C22×D4716yescomplemented
545C24—471no—
546C24—473no—
547C24—473no—
548C24—473no—
549C24—473no—
550C24—473no—
551C24—9412no—
552C24—9412no—
553C24—1886no—
554C24C2×C4×D4713yes—
555#41—24no—
556#41—212no—
557#41—212no—
558#41—478no—
559#41—4724no—
560#41—4724no—
561#41—9424no—
562#41—9424no—
563#41—9412no—
564#41—9412no—
565#41—9424no—
566#41—9412no—
567#41—9412no—
568#41—9424no—
569#41—9412no—
570#41—9412no—
571#41—944no—
572#41—9412no—
573#41—9412no—
574#41D4×D4718yes—
575C2×Q8—24no—
576C2×Q8—478no—
577C2×Q8—473no—
578C2×Q8—476no—
579C2×Q8—473no—
580C2×Q8—9412no—
581C2×Q8—9412no—
582C2×Q8—9412no—
583C2×Q8—944no—
584C2×Q8C2×C4×D4713yes—
585C2×Q8C2×C4×D4711yescharacteristic
586C2×D4—212no—
587C2×D4—476no—
588C2×D4—4724no—
589C2×D4—476no—
590C2×D4—476no—
591C2×D4—476no—
592C2×D4—473no—
593C2×D4—476no—
594C2×D4—473no—
595C2×D4—9412no—
596C2×D4—9412no—
597C2×D4—9424no—
598C2×D4—9412no—
599C2×D4—9424no—
600C2×D4—9424no—
601C2×D4—9412no—
602C2×D4C2×C4×D4716yes—
603C2×D4C2×C4×D4713yes—
604C2×D4C2×C4×D4713yes—
605C22×C4—212no—
606C22×C4—473no—
607C22×C4—473no—
608C22×C4—473no—
609C22×C4—4724no—
610C22×C4—471no—
611C22×C4—473no—
612C22×C4—471no—
613C22×C4—473no—
614C22×C4—473no—
615C22×C4—473no—
616C22×C4—473no—
617C22×C4—471no—
618C22×C4—471no—
619C22×C4—473no—
620C22×C4—473no—
621C22×C4—473no—
622C22×C4—473no—
623C22×C4—473no—
624C22×C4—473no—
625C22×C4—473no—
626C22×C4—473no—
627C22×C4—471no—
628C22×C4—473no—
629C22×C4—944no—
630C22×C4—9412no—
631C22×C4—9412no—
632C22×C4—9412no—
633C22×C4—9412no—
634C22×C4—9412no—
635C22×C4—9412no—
636C22×C4—9412no—
637C22×C4—9412no—
638C22×C4—9412no—
639C22×C4—9412no—
640C22×C4—9412no—
641C22×C4C2×C4×D4713yes—
642C22×C4C2×C4×D4713yes—
643C22×C4C2×C4×D4713yes—
644C22×C4C23×D4711yescharacteristic
645C22×C4C23×D4713yes—
646C22×C4C23×D4713yes—
647M16—212no—
648M16—9424no—
649M16—9412no—
650C2×C8—212no—
651C2×C8—472no—
652C2×C8—476no—
653C2×C8—944no—
654C2×C8—9412no—
655C2×C8—9412no—
656C2×C8—9412no—
657C2×C8—9412no—
658C2×C8C23×D4712yes—
659C2×C8C23×D4716yes—
660C23—26no—
661C23—26no—
662C23—43no—
663C23—471no—
664C23—4712no—
665C23—474no—
666C23—471no—
667C23—473no—
668C23—473no—
669C23—942no—
670C23—946no—
671C23—946no—
672C23—942no—
673C23—946no—
674C23—946no—
675C23—946no—
676C23—946no—
677C23—946no—
678C23—946no—
679C23—946no—
680C23—946no—
681C23—946no—
682C23—1883no—
683C23—1883no—
684C23—1883no—
685C23—18848no—
686C23C22×C4×D4713yes—
687C23C22×C4×D4713yes—
688C23C22×C4×D4711yescharacteristic
689Q8—26no—
690Q8—4712no—
691Q8—9412no—
692Q8—946no—
693Q8C22⋊C4×D4714yes—
694D4—212no—
695D4—26no—
696D4—4724no—
697D4—4712no—
698D4—9412no—
699D4—9412no—
700D4—9412no—
701D4—9412no—
702D4—946no—
703D4C22⋊C4×D47112yes—
704C2×C4—26no—
705C2×C4—26no—
706C2×C4—26no—
707C2×C4—22no—
708C2×C4—26no—
709C2×C4—4712no—
710C2×C4—471no—
711C2×C4—473no—
712C2×C4—4712no—
713C2×C4—4712no—
714C2×C4—474no—
715C2×C4—4712no—
716C2×C4—471no—
717C2×C4—473no—
718C2×C4—942no—
719C2×C4—946no—
720C2×C4—946no—
721C2×C4—946no—
722C2×C4—942no—
723C2×C4—946no—
724C2×C4—946no—
725C2×C4—946no—
726C2×C4—942no—
727C2×C4—946no—
728C2×C4—946no—
729C2×C4—946no—
730C2×C4—946no—
731C2×C4—946no—
732C2×C4—946no—
733C2×C4—942no—
734C2×C4—946no—
735C2×C4C22×C4×D4711yescharacteristic
736C2×C4C22×C4×D4713yes—
737C2×C4C22×C4×D4713yes—
738C2×C4C2×D4×D47112yes—
739C2×C4C24×D4711yescharacteristic
740C8—22no—
741C8—26no—
742C8—942no—
743C8—946no—
744C22—21no—
745C22—23no—
746C22—21no—
747C22—23no—
748C22—23no—
749C22—23no—
750C22—23no—
751C22—412no—
752C22—472no—
753C22—472no—
754C22—472no—
755C22—476no—
756C22—472no—
757C22—948no—
758C22—9424no—
759C22—941no—
760C22—943no—
761C22—941no—
762C22—943no—
763C22—943no—
764C22—943no—
765C22—943no—
766C22—18812no—
767C22—18812no—
768C22—18812no—
769C22—18812no—
770C22C2×C22⋊C4×D4716yes—
771C22#131×D4712yescomplemented
772C22C23×C4×D4711yescharacteristic
773C4—21no—
774C4—23no—
775C4—472no—
776C4—476no—
777C4—941no—
778C4—943no—
779C4C2×C22⋊C4×D4716yes—
780C4C22×D4×D4712yes—
781C2—22no—
782C2—26no—
783C2—43no—
784C2—474no—
785C2—942no—
786C2—946no—
787C2—1883no—
788C2C22×C22⋊C4×D4711yescharacteristic
789C2C2×#131×D4711yescharacteristic
790C2#568×D4711yescharacteristic
subgroupG/H
center, FrattiniC2×C4C24×D47
commutator, socleC22×C47C24×C4
FittingC47×#2880C2
prime radicalC22×#41×D47C2
cosocleC2×C4×C47C25
hypercenter#2880D47
hypocenterC47C2×#2880
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ #2880

Complements

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

NH ≅ G/Ntype
2. C2×#131×D47C2semidirect
3. #20251838C2semidirect
4. #20251837C2semidirect
5. #20251836C2semidirect
6. #20251835C2semidirect
7. #20251834C2semidirect
8. #408×D47C2semidirect
9. #407×D47C2semidirect
10. C2×C22⋊C8×D47C2semidirect
11. C47×#2880C2semidirect
27. C2×#13094032C22semidirect
28. C2×#13094031C22semidirect
29. C2×#13094030C22semidirect
31. C2×M16×D47C22semidirect
32. C22×C8×D47C22semidirect
33. #15689091C22semidirect
34. #15689090C22semidirect
35. #15689089C22semidirect
36. #15689088C22semidirect
37. #15689088C22semidirect
38. #15689087C22semidirect
39. #15689086C22semidirect
40. #15689085C22semidirect
41. #15689085C22semidirect
42. C2×C22⋊(C47⋊C8)C22semidirect
43. C2×(C2×D47)⋊C8C22semidirect
46. C22⋊C8×D47C22semidirect
47. C22⋊C8×D47C22semidirect
48. C22⋊C8×D47C22semidirect
49. C22⋊C8×D47C22semidirect
50. C22⋊C8×D47C22semidirect
52. C2×#131×C47C22semidirect
53. C47×#408C22semidirect
54. C47×#407C22semidirect
55. C2×C22⋊C8×C47C22semidirect
116. C2×#10625329C23semidirect
117. C2×#10625324C23semidirect
119. C22×C47⋊C8C23semidirect
123. C2×C8×D47C23semidirect
124. C2×C8×D47C23semidirect
127. C22⋊(C47⋊C8)C23semidirect
128. C22⋊(C47⋊C8)C23semidirect
131. (C2×D47)⋊C8C23semidirect
132. (C2×D47)⋊C8C23semidirect
133. (C2×D47)⋊C8C23semidirect
143. C2×M16×C47C23semidirect
144. C22×C8×C47C23semidirect
147. C22⋊C8×C47C23semidirect
148. C22⋊C8×C47C23semidirect
288. C22×D47#131semidirect
358. C22×C47C2×#131semidirect
376. C2×D47C2×#131semidirect
393. #2880D47direct (N × H)
406. D47#2880direct (N × H)
427. C2×#131C2×D47semidirect
435. #408C2×D47semidirect
440. #407C2×D47semidirect
450. C2×C22⋊C8C2×D47semidirect
451. C47C2×#2880semidirect
524. C2×M16C22×D47semidirect
531. C22×C8C22×D47semidirect
543. C22⋊C8C22×D47semidirect
544. C22⋊C8C22×D47semidirect
771. C22#131×D47semidirect

Maximal subgroups

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

subgroupindex
C22×#41×D472
C2×#131×D472
#202518382
#202518372
#202518362
#202518352
#202518342
#408×D472
#407×D472
C2×C22⋊C8×D472
C47×#28802
C2×#288047