Finite Group Databasebeta

← #27079726

Subgroups — #27079726

Order 12032.

5134 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×#15689888C212yesmaximal, complemented
3#20251838C213yesmaximal, complemented
4#20251837C211yesmaximal, characteristic, complemented
5#20251836C216yesmaximal, complemented
6#20251835C212yesmaximal, complemented
7#20251834C213yesmaximal, complemented
8#20251830C216yesmaximal, complemented
9C2×#15689085C213yesmaximal, complemented
10#407×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—
27#15689888—216no—
28C2×#13094032C2216yescomplemented
29C2×#13094031C2212yescomplemented
30C2×#13094030C2216yescomplemented
31C22×#10625324C2216yescomplemented
32C2×M16×D47C2216yescomplemented
33#15689091C2216yescomplemented
34#15689090C2216yescomplemented
35#15689089C2216yescomplemented
36#15689088C22112yescomplemented
37#15689088C22112yescomplemented
38#15689087C2213yescomplemented
39#15689086C2216yescomplemented
40#15689085C2213yes—
41#15689085C2211yescharacteristic
42#15689085C2216yescomplemented
43#15689085C2213yescomplemented
44#15689085C2213yescomplemented
45#15689085C2216yescomplemented
46#15689085C2216yescomplemented
47C2×C22⋊(C47⋊C8)C2213yescomplemented
48C2×(C2×D47)⋊C8C2216yescomplemented
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×D47C2313yes—
108C22×C4×D47C2313yes—
109C22×C4×D47C2313yes—
110C22×C4×D47C2311yescharacteristic
111C22×C4×D47C2313yes—
112C22×C4×D47C2313yes—
113#13094032—224no—
114#13094031—28no—
115#13094030—224no—
116C2×#10625329C2316yescomplemented
117C2×#10625324—224no—
118C2×#10625324C2316yes—
119C2×#10625324C2312yes—
120C2×#10625324C2316yescomplemented
121C2×#10625324C2316yescomplemented
122M16×D47—224no—
123C22×C47⋊C8C2316yescomplemented
124C2×C8×D47C23112yescomplemented
125C22⋊(C47⋊C8)C2313yes—
126C22⋊(C47⋊C8)C2311yescharacteristic
127C22⋊(C47⋊C8)C2316yescomplemented
128C22⋊(C47⋊C8)C2316yescomplemented
129(C2×D47)⋊C8C2316yes—
130(C2×D47)⋊C8C2312yes—
131(C2×D47)⋊C8C23112yescomplemented
132(C2×D47)⋊C8C2316yescomplemented
133(C2×D47)⋊C8C2316yescomplemented
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×C47C2313yes—
146C22⋊C8×C47C2311yescharacteristic
147C22⋊C8×C47C2316yescomplemented
148C22⋊C8×C47C2316yescomplemented
149C24×C47C22×C413yes—
150C23×D47—212no—
151C23×D47—46no—
152C23×D47—46no—
153C23×D47C22×C411yescharacteristic
154C23×D47C22×C413yes—
155C23×D47C22×C413yes—
156C23×D47C22×C413yes—
157C23×D47C22×C413yes—
158C23×D47C22×C413yes—
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×D47C2413yes—
246C2×C4×D47C2411yescharacteristic
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⋊C8C2416yes—
258C2×C47⋊C8C2412yes—
259#10625324—212no—
260#10625324—24no—
261#10625324—212no—
262#10625324—212no—
263C8×D47—224no—
264C23×C47—26no—
265C23×C47—26no—
266C23×C47—43no—
267C23×C47C23×C413yes—
268C23×C47C23×C413yes—
269C23×C47C23×C411yescharacteristic
270C22×D47—22no—
271C22×D47—22no—
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—43no—
281C22×D47—43no—
282C22×D47—43no—
283C22×D47—43no—
284C22×D47—43no—
285C22×D47—43no—
286C22×D47—43no—
287C22×D47—448no—
288C22×D47C2×C22⋊C4112yes—
289C22×D47C23×C413yes—
290C22×D47C23×C411yescharacteristic
291C22×D47C23×C413yes—
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×D4112yes—
340C4×D47C22×D414yes—
341Dic94—26no—
342Dic94—212no—
343Dic94C2×C22⋊C4112yes—
344C8×C47—26no—
345C8×C47—22no—
346C47⋊C8—26no—
347C47⋊C8—22no—
348#60064—471nomaximal, Sylow
349C22×C47—21no—
350C22×C47—21no—
351C22×C47—23no—
352C22×C47—23no—
353C22×C47—23no—
354C22×C47—23no—
355C22×C47—23no—
356C22×C47—412no—
357C22×C47C22×C22⋊C416yes—
358C22×C47#56812yescomplemented
359C22×C47C24×C411yescharacteristic
360C2×D47—28no—
361C2×D47—21no—
362C2×D47—21no—
363C2×D47—21no—
364C2×D47—21no—
365C2×D47—23no—
366C2×D47—23no—
367C2×D47—23no—
368C2×D47—23no—
369C2×D47—23no—
370C2×D47—412no—
371C2×D47—412no—
372C2×D47—412no—
373C2×D47—412no—
374C2×D47—412no—
375C2×D47C22×C22⋊C412yes—
376C2×D47C22×C22⋊C416yes—
377C2×D47#56812yescomplemented
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—
387C2×#568—472no—
388#2880—476no—
389#2880—473no—
390#2880—473no—
391#2880—471no—
392#2880—472no—
393#2880D4711yescharacteristic, complemented
394#2879—476no—
395C2×#407—473no—
396C2×#407—473no—
397C2×C47—22no—
398C2×C47—26no—
399C2×C47—43no—
400C2×C47C23×C22⋊C411yescharacteristic
401C2×C47C2×#56811yescharacteristic
402C2×C47C2×#56811yescharacteristic
403D47—22no—
404D47—22no—
405D47—26no—
406D47—43no—
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—
423#568—9416no—
424C2×#131—472no—
425C2×#131—476no—
426C2×#131—476no—
427C2×#131C2×D4712yescomplemented
428C22×M16—476no—
429C22×M16—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—473no—
439#407—471no—
440#407—473no—
441#407—473no—
442#407—476no—
443#407—476no—
444#407—476no—
445#407C2×D4713yescomplemented
446C2×C22⋊C8—473no—
447C2×C22⋊C8—476no—
448C2×C22⋊C8—476no—
449C2×C22⋊C8—476no—
450C2×C22⋊C8C2×D4713yescomplemented
451C47#6006411yescharacteristic, 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—476no—
523C2×M16—472no—
524C2×M16—476no—
525C2×M16—476no—
526C2×M16—9424no—
527C2×M16—9424no—
528C2×M16C22×D4716yescomplemented
529C22×C8—476no—
530C22×C8—4712no—
531C22×C8C22×D4716yescomplemented
532C22⋊C8—473no—
533C22⋊C8—471no—
534C22⋊C8—476no—
535C22⋊C8—476no—
536C22⋊C8—476no—
537C22⋊C8—472no—
538C22⋊C8—4712no—
539C22⋊C8—476no—
540C22⋊C8—476no—
541C22⋊C8C22×D4713yes—
542C22⋊C8C22×D4711yescharacteristic
543C22⋊C8C22×D4716yescomplemented
544C22⋊C8C22×D4716yescomplemented
545C24—473no—
546C24—471no—
547C24—473no—
548C24—473no—
549C24—473no—
550C24—473no—
551C24—9412no—
552C24—1886no—
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—473no—
611C22×C4—471no—
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—944no—
649M16—9412no—
650M16—9412no—
651M16—9412no—
652M16—9412no—
653C2×C8—212no—
654C2×C8—476no—
655C2×C8—472no—
656C2×C8—9424no—
657C2×C8—9412no—
658C2×C8C23×D4716yes—
659C2×C8C23×D4712yes—
660C23—26no—
661C23—26no—
662C23—43no—
663C23—471no—
664C23—471no—
665C23—473no—
666C23—4712no—
667C23—473no—
668C23—942no—
669C23—942no—
670C23—946no—
671C23—946no—
672C23—946no—
673C23—946no—
674C23—946no—
675C23—942no—
676C23—946no—
677C23—946no—
678C23—1883no—
679C23—1883no—
680C23—1883no—
681C23—1883no—
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—4712no—
715C2×C4—474no—
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—946no—
743C8—942no—
744C22—21no—
745C22—21no—
746C22—23no—
747C22—23no—
748C22—23no—
749C22—23no—
750C22—23no—
751C22—412no—
752C22—472no—
753C22—476no—
754C22—472no—
755C22—948no—
756C22—941no—
757C22—941no—
758C22—943no—
759C22—941no—
760C22—941no—
761C22—943no—
762C22—943no—
763C22—943no—
764C22—943no—
765C22—18812no—
766C22—18812no—
767C22—18812no—
768C22—18812no—
769C22—18812no—
770C22C2×C22⋊C4×D4716yes—
771C22#1568988812yescomplemented
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—942no—
785C2—942no—
786C2—946no—
787C2—1883no—
788C2C22×C22⋊C4×D4711yescharacteristic
789C2#568×D4711yescharacteristic
790C2C2×#1568988811yescharacteristic
subgroupG/H
center, FrattiniC2×C4C24×D47
commutator, socleC22×C47C24×C4
FittingC47×#2880C2
prime radicalC22×#41×D47C2
cosocleC2×C4×C47C25
hypercenter#2880D47
hypocenterC47#60064
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ #2880

Complements

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

NH ≅ G/Ntype
2. C2×#15689888C2semidirect
3. #20251838C2semidirect
4. #20251837C2semidirect
5. #20251836C2semidirect
6. #20251835C2semidirect
7. #20251834C2semidirect
8. #20251830C2semidirect
9. C2×#15689085C2semidirect
10. #407×D47C2semidirect
11. C47×#2880C2semidirect
28. C2×#13094032C22semidirect
29. C2×#13094031C22semidirect
30. C2×#13094030C22semidirect
31. C22×#10625324C22semidirect
32. C2×M16×D47C22semidirect
33. #15689091C22semidirect
34. #15689090C22semidirect
35. #15689089C22semidirect
36. #15689088C22semidirect
37. #15689088C22semidirect
38. #15689087C22semidirect
39. #15689086C22semidirect
42. #15689085C22semidirect
43. #15689085C22semidirect
44. #15689085C22semidirect
45. #15689085C22semidirect
46. #15689085C22semidirect
47. C2×C22⋊(C47⋊C8)C22semidirect
48. C2×(C2×D47)⋊C8C22semidirect
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
120. C2×#10625324C23semidirect
121. C2×#10625324C23semidirect
123. C22×C47⋊C8C23semidirect
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
358. C22×C47#568semidirect
377. C2×D47#568semidirect
393. #2880D47semidirect
427. C2×#131C2×D47semidirect
435. #408C2×D47semidirect
445. #407C2×D47semidirect
450. C2×C22⋊C8C2×D47semidirect
451. C47#60064semidirect
528. C2×M16C22×D47semidirect
531. C22×C8C22×D47semidirect
543. C22⋊C8C22×D47semidirect
544. C22⋊C8C22×D47semidirect
771. C22#15689888semidirect

Maximal subgroups

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

subgroupindex
C22×#41×D472
C2×#156898882
#202518382
#202518372
#202518362
#202518352
#202518342
#202518302
C2×#156890852
#407×D472
C47×#28802
#6006447