Finite Group Databasebeta

← #26218155

Subgroups — #26218155

Order 12032.

1664 conjugacy classes of subgroups.

The subgroup lattice has 826 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689921C211yesmaximal, characteristic
2C2×#15689889C211yesmaximal, characteristic, complemented
3C2×#15689139C211yesmaximal, characteristic, complemented
4#20251907C211yesmaximal, characteristic, complemented
5#20243871C214yesmaximal, complemented
6#20243864C214yesmaximal, complemented
7C2×#15688895C211yesmaximal, characteristic, complemented
8C2×C47⋊#338C211yesmaximal, characteristic, complemented
9C2×C47×#413C211yesmaximal, characteristic, complemented
10C22×#10625350C2211yescharacteristic
11#15689921—22no—
12#15689921—22no—
13#15689921—22no—
14#15689921—22no—
15C2×#13094055C2212yes—
16C2×#13094054C412yescomplemented
17C2×#13094050C2212yes—
18C2×#13094049C412yescomplemented
19C2×#13094044C414yescomplemented
20#15689889—22no—
21#15689889—22no—
22#15689889—22no—
23#15689889C2214yes—
24C2×#13094032—22no—
25C2×#13094030—22no—
26C22×#10625329C2211yescharacteristic
27C22×#10625329C2211yescharacteristic
28C2×M16×D47—22no—
29C2×#13093983C2211yescharacteristic
30#15689139—22no—
31#15689139C2214yes—
32C2×#13093950—22no—
33#15689132C2212yescomplemented
34#15689128C2212yescomplemented
35#15689124—22no—
36#15689119—22no—
37#15688895C2214yescomplemented
38C47⋊#338C2214yescomplemented
39C22×#41×C47C2211yescharacteristic
40C22×M16×C47C2211yescharacteristic
41C22×M16×C47C2211yescharacteristic
42C47×#413—22no—
43C47×#413—22no—
44C2×#101×C47C2212yescomplemented
45C2×#100×C47C2212yescomplemented
46C2×#10625350—21no—
47C2×#10625350—21no—
48C2×#10625350—21no—
49C2×#10625350—21no—
50C2×#10625350—21no—
51C2×#10625350—21no—
52C2×#10625350C2×C412yes—
53C2×#10625350D412yes—
54C2×#10625350D412yes—
55C2×#10625350D412yes—
56C2×#10625350D412yes—
57C2×#10625350C2312yes—
58C22×Dic94C2×C411yescharacteristic
59C22×D188C2×C411yescharacteristic
60C22×C22⋊D47—21no—
61C22×C4×D47—21no—
62#13094055—24no—
63#13094055—24no—
64#13094054—24no—
65#13094054—24no—
66#13094050—24no—
67#13094050—24no—
68#13094049—24no—
69#13094049—24no—
70#13094044—28no—
71#13094044—28no—
72C2×#10625337C2×C414yescomplemented
73C2×#10625335C2×C414yescomplemented
74C2×#10625336C2×C414yescomplemented
75C2×#10625334C2×C414yescomplemented
76#13094032—28no—
77#13094032—28no—
78#13094030—28no—
79#13094030—28no—
80C2×#10625329—21no—
81C2×#10625329—21no—
82C2×#10625329—21no—
83C2×#10625329—21no—
84C2×#10625329—21no—
85C2×#10625329—21no—
86C2×#10625329—21no—
87C2×#10625329—21no—
88C2×#10625329C2×C412yes—
89C2×#10625329D412yes—
90C2×#10625329C2312yes—
91C2×#10625329C2312yes—
92C2×#10625324—24no—
93M16×D47—28no—
94M16×D47—28no—
95C22×C47⋊C8C2×C412yes—
96C22×C47⋊C8D412yes—
97C2×C8×D47—24no—
98#13093983—21no—
99#13093983—21no—
100#13093983—21no—
101#13093983C2312yes—
102C2×C4⋊Dic47—21no—
103C2×C22⋊Dic47—21no—
104C2×C4×Dic47—21no—
105#13093950—28no—
106#13093948—24no—
107#13093945—24no—
108C2×#41×C47—21no—
109C2×#41×C47—21no—
110C2×#41×C47—21no—
111C2×#41×C47—21no—
112C2×#41×C47—21no—
113C2×#41×C47—21no—
114C2×#41×C47—21no—
115C2×#41×C47—21no—
116C2×#41×C47—21no—
117C2×#41×C47—21no—
118C2×#41×C47C2×C412yes—
119C2×#41×C47C2×C412yes—
120C22×Q8×C47C2311yescharacteristic
121C22×D4×C47—21no—
122C22×D4×C47C2311yescharacteristic
123C23×C4×C47—21no—
124C23×C4×C47C2311yescharacteristic
125C2×M16×C47—21no—
126C2×M16×C47—21no—
127C2×M16×C47—21no—
128C2×M16×C47—21no—
129C2×M16×C47—21no—
130C2×M16×C47—21no—
131C2×M16×C47—21no—
132C2×M16×C47—21no—
133C2×M16×C47D412yes—
134C2×M16×C47D412yes—
135C2×M16×C47C2312yes—
136C2×M16×C47C2312yes—
137C22×C8×C47—21no—
138C22×C8×C47—21no—
139#101×C47—24no—
140#100×C47—24no—
141C24×C47—21no—
142C24×C47#4111yescharacteristic
143C23×D47—21no—
144#41×C47—22no—
145#41×C47—22no—
146#41×C47—22no—
147#41×C47—22no—
148#41×C47—22no—
149#41×C47—22no—
150#41×C47—22no—
151#41×C47—22no—
152#41×C47—41no—
153#41×C47—41no—
154#41×C47—41no—
155#41×C47—41no—
156#41×C47—41no—
157#41×C47—41no—
158#41×C47—41no—
159#41×C47—41no—
160C2×Q8×C47—21no—
161C2×Q8×C47—21no—
162C2×Q8×C47—21no—
163C2×Q8×C47—21no—
164C2×Q8×C47—21no—
165C2×Q8×C47C22×C412yes—
166C2×D4×C47—22no—
167C2×D4×C47—22no—
168C2×D4×C47—21no—
169C2×D4×C47—21no—
170C2×D4×C47—21no—
171C2×D4×C47—21no—
172C2×D4×C47—21no—
173C2×D4×C47—41no—
174C2×D4×C47—41no—
175C2×D4×C47—41no—
176C2×D4×C47—41no—
177C2×D4×C47C22×C412yes—
178C22×C4×C47—21no—
179C22×C4×C47—22no—
180C22×C4×C47—22no—
181C22×C4×C47—41no—
182C22×C4×C47—41no—
183C22×C4×C47—41no—
184C22×C4×C47—41no—
185C22×C4×C47C22×C411yescharacteristic
186C22×C4×C47C22×C411yescharacteristic
187C22×C4×C47C2×D411yescharacteristic
188C22×C4×C47C2×D411yescharacteristic
189C22×C4×C47C2×D411yescharacteristic
190C22×C4×C47C2×D411yescharacteristic
191C22×C4×C47C2×D411yescharacteristic
192C22×C4×C47C2×D411yescharacteristic
193C22×C4×C47C2×D411yescharacteristic
194C22×C4×C47C2×D411yescharacteristic
195C22×C4×C47#4111yescharacteristic
196C22×C4×C47#4111yescharacteristic
197C22×C4×C47#4111yescharacteristic
198C22×C4×C47C2411yescharacteristic
199C2×C22⋊D47—22no—
200C2×C22⋊D47—22no—
201C2×C22⋊D47—22no—
202C2×C22⋊D47—22no—
203C2×C22⋊D47—22no—
204C2×C22⋊D47—22no—
205C22×Dic47—21no—
206C22×Dic47—41no—
207#10625350—22no—
208#10625350—22no—
209#10625350—22no—
210#10625350—22no—
211#10625350—22no—
212#10625350—22no—
213#10625350—22no—
214#10625350—22no—
215#10625350—22no—
216#10625350—22no—
217#10625350—22no—
218#10625350—22no—
219#10625350C22⋊C414yes—
220#10625350C22⋊C414yes—
221#10625350C2×D414yes—
222#10625350C2×D414yes—
223C2×D188—21no—
224C2×D188—21no—
225C2×D188—21no—
226C2×D188C22⋊C412yes—
227C2×D188C22⋊C412yes—
228C2×D188C22×C412yes—
229C2×C4×D47—22no—
230C2×C4×D47—22no—
231C2×C4×D47—22no—
232C2×C4×D47—22no—
233C2×C4×D47—22no—
234C2×C4×D47—22no—
235C2×Dic94—21no—
236C2×Dic94—21no—
237C2×Dic94—21no—
238C2×Dic94C22⋊C412yes—
239C2×Dic94C22⋊C412yes—
240C2×Dic94C22×C412yes—
241M16×C47—22no—
242M16×C47—22no—
243M16×C47—22no—
244M16×C47—22no—
245M16×C47—22no—
246M16×C47—41no—
247M16×C47—41no—
248M16×C47C2×D414yes—
249C2×C8×C47—22no—
250C2×C8×C47—22no—
251C2×C8×C47—22no—
252C2×C8×C47—22no—
253C2×C8×C47—41no—
254C2×C8×C47—41no—
255C22⋊Dic47—22no—
256C22⋊Dic47—41no—
257#10625337—28no—
258#10625336—28no—
259#10625335—28no—
260#10625334—28no—
261C4⋊Dic47—22no—
262C4⋊Dic47—41no—
263C4×Dic47—22no—
264C4×Dic47—41no—
265#10625329—22no—
266#10625329—22no—
267#10625329—22no—
268#10625329—22no—
269#10625329—22no—
270#10625329—22no—
271#10625329—22no—
272#10625329—22no—
273C2×C47⋊C8—22no—
274C2×C47⋊C8—22no—
275C2×C47⋊C8—22no—
276C2×C47⋊C8—22no—
277C2×C47⋊C8C22×C414yes—
278C2×C47⋊C8C2×D414yes—
279#10625324—216no—
280C8×D47—216no—
281C23×C47—22no—
282C23×C47—41no—
283C23×C47—41no—
284C23×C47—81no—
285C23×C47—82no—
286C23×C47C4×D411yescharacteristic
287C23×C47C4×D411yescharacteristic
288C23×C47#12111yescharacteristic
289C23×C47#12111yescharacteristic
290C23×C47#12311yescharacteristic
291C23×C47#12311yescharacteristic
292C23×C47C2×#4111yescharacteristic
293C22×D47—22no—
294C22×D47—22no—
295C22×D47—22no—
296C22×D47—82no—
297Q8×C47—22no—
298Q8×C47—22no—
299Q8×C47—41no—
300Q8×C47—41no—
301D4×C47—22no—
302D4×C47—22no—
303D4×C47—42no—
304D4×C47—42no—
305D4×C47—42no—
306D4×C47—42no—
307D4×C47—41no—
308D4×C47—41no—
309C2×C4×C47—22no—
310C2×C4×C47—41no—
311C2×C4×C47—41no—
312C2×C4×C47—42no—
313C2×C4×C47—42no—
314C2×C4×C47—42no—
315C2×C4×C47—42no—
316C2×C4×C47C2×C22⋊C411yescharacteristic
317C2×C4×C47C2×C22⋊C411yescharacteristic
318C2×C4×C47C2×C22⋊C411yescharacteristic
319C2×C4×C47C2×C22⋊C411yescharacteristic
320C2×C4×C47C4×D411yescharacteristic
321C2×C4×C47C4×D411yescharacteristic
322C2×C4×C47C4×D411yescharacteristic
323C2×C4×C47C4×D411yescharacteristic
324C2×C4×C47C4×D411yescharacteristic
325C2×C4×C47C4×D411yescharacteristic
326C2×C4×C47#12011yescharacteristic
327C2×C4×C47#12011yescharacteristic
328C2×C4×C47#12011yescharacteristic
329C2×C4×C47#12011yescharacteristic
330C2×C4×C47#12111yescharacteristic
331C2×C4×C47#12111yescharacteristic
332C2×C4×C47#12111yescharacteristic
333C2×C4×C47#12111yescharacteristic
334C2×C4×C47#12111yescharacteristic
335C2×C4×C47#12111yescharacteristic
336C2×C4×C47#12311yescharacteristic
337C2×C4×C47#12311yescharacteristic
338C2×C4×C47C23×C411yescharacteristic
339C2×C4×C47C22×D411yescharacteristic
340C2×C4×C47C22×D411yescharacteristic
341C2×C4×C47C22×D411yescharacteristic
342C2×C4×C47C22×D411yescharacteristic
343C2×C4×C47C2×#4111yescharacteristic
344C22⋊D47—24no—
345C22⋊D47—24no—
346C22⋊D47—24no—
347C22⋊D47—24no—
348C2×Dic47—22no—
349C2×Dic47—22no—
350C2×Dic47—22no—
351C2×Dic47—42no—
352C2×Dic47—82no—
353D188—22no—
354D188—22no—
355D188—22no—
356D188C2×C22⋊C414yes—
357C4×D47—24no—
358C4×D47—24no—
359C4×D47—24no—
360C4×D47—24no—
361Dic94—22no—
362Dic94—22no—
363Dic94—22no—
364Dic94C2×C22⋊C414yes—
365C8×C47—24no—
366C8×C47—42no—
367C47⋊C8—24no—
368C47⋊C8—24no—
369#20995—471nomaximal, Sylow
370C22×C47—41no—
371C22×C47—41no—
372C22×C47—41no—
373C22×C47—41no—
374C22×C47—41no—
375C22×C47—41no—
376C22×C47—41no—
377C22×C47—42no—
378C22×C47—82no—
379C22×C47—82no—
380C22×C47—82no—
381C22×C47#38611yescharacteristic
382C22×C47#38611yescharacteristic
383C22×C47#38611yescharacteristic
384C22×C47#38611yescharacteristic
385C22×C47C2×C4×D411yescharacteristic
386C22×C47C2×#12111yescharacteristic
387C22×C47C2×#12311yescharacteristic
388C2×D47—24no—
389C2×D47—44no—
390C2×D47—82no—
391C2×D47—82no—
392C4×C47—42no—
393C4×C47#38611yescharacteristic
394C4×C47#38611yescharacteristic
395C4×C47#38611yescharacteristic
396C4×C47#38611yescharacteristic
397C4×C47C22×C22⋊C411yescharacteristic
398C4×C47C2×C4×D411yescharacteristic
399C4×C47C2×#12011yescharacteristic
400C4×C47C2×#12111yescharacteristic
401Dic47—24no—
402Dic47—82no—
403C2×#575—471no—
404C2×#568—471no—
405C2×#421—471no—
406#2896—471no—
407C2×#413D4711yescharacteristic, complemented
408#1903—474no—
409#1902—474no—
410C2×#344—471no—
411C2×#338—471no—
412C2×C47—21no—
413C2×C47—21no—
414C2×C47—21no—
415C2×C47—21no—
416C2×C47—21no—
417C2×C47—21no—
418C2×C47—21no—
419C2×C47—82no—
420C2×C47C2×#38611yescharacteristic
421D47—44no—
422C22×#41—471no—
423C22×#41C2×D4711yescharacteristic
424#575—942no—
425#575—942no—
426#575—942no—
427#575—942no—
428C2×#137—472no—
429C2×#137—472no—
430C2×AGL(1,ℤ/8)—472no—
431C2×AGL(1,ℤ/8)—472no—
432C2×#135—474no—
433#568—474no—
434#568—942no—
435#568—942no—
436#568—942no—
437C2×#131—942no—
438C2×#131—942no—
439C22×M16—471no—
440C22×M16—471no—
441C22×M16—942no—
442C22×M16C2×D4711yescharacteristic
443C22×M16C2×D4711yescharacteristic
444C2×#117—471no—
445#421—474no—
446#421—942no—
447C2×#104—942no—
448#419—472no—
449#418—472no—
450#417—942no—
451#416—942no—
452#413—22no—
453#413—22no—
454C2×#101C2×D4712yescomplemented
455C2×#100C2×D4712yescomplemented
456#344—474no—
457#338—474no—
458C47#2099511yescharacteristic, complemented, Sylow
459C2×#41—21no—
460C2×#41—21no—
461C2×#41—21no—
462C2×#41—21no—
463C2×#41—21no—
464C2×#41—21no—
465C2×#41—21no—
466C2×#41—21no—
467C2×#41—21no—
468C2×#41—21no—
469C2×#41—472no—
470C2×#41—472no—
471C2×#41—472no—
472C2×#41—472no—
473C2×#41—472no—
474C2×#41—472no—
475C2×#41—941no—
476C2×#41—941no—
477C2×#41—941no—
478C2×#41—941no—
479C2×#41—941no—
480C2×#41—941no—
481C2×#41C4×D4712yes—
482C2×#41C4×D4712yes—
483C22×Q8—471no—
484C22×Q8C22×D4711yescharacteristic
485C22×D4—21no—
486C22×D4—471no—
487C22×D4—941no—
488C22×D4C22×D4711yescharacteristic
489C23×C4—21no—
490C23×C4—941no—
491C23×C4C22×D4711yescharacteristic
492#137—944no—
493#137—944no—
494#137—944no—
495#137—944no—
496AGL(1,ℤ/8)—944no—
497AGL(1,ℤ/8)—944no—
498AGL(1,ℤ/8)—944no—
499AGL(1,ℤ/8)—944no—
500#135—948no—
501#135—948no—
502C2×Q16—474no—
503C2×SD16—474no—
504C2×SD16—474no—
505C2×D8—474no—
506#131—948no—
507#131—948no—
508#131—948no—
509#131—948no—
510C2×M16—21no—
511C2×M16—21no—
512C2×M16—21no—
513C2×M16—21no—
514C2×M16—21no—
515C2×M16—21no—
516C2×M16—21no—
517C2×M16—21no—
518C2×M16—472no—
519C2×M16—472no—
520C2×M16—472no—
521C2×M16—472no—
522C2×M16—944no—
523C2×M16—948no—
524C2×M16—941no—
525C2×M16—941no—
526C2×M16—941no—
527C2×M16—941no—
528C2×M16—941no—
529C2×M16—941no—
530C2×M16—941no—
531C2×M16—941no—
532C2×M16—948no—
533C2×M16C22⋊D4712yes—
534C2×M16C22⋊D4712yes—
535C2×M16C22×D4712yes—
536C2×M16C22×D4712yes—
537C22×C8—21no—
538C22×C8—21no—
539C22×C8—472no—
540C22×C8—472no—
541C22×C8—944no—
542#117—472no—
543#117—941no—
544#117—941no—
545#117—941no—
546C2×C4⋊C4—941no—
547C2×C22⋊C4—941no—
548C2×C42—941no—
549#104—948no—
550#103—944no—
551#102—944no—
552#101—24no—
553#100—24no—
554C24—21no—
555C24—941no—
556C24#1062535011yescharacteristic
557#41—22no—
558#41—22no—
559#41—22no—
560#41—22no—
561#41—22no—
562#41—22no—
563#41—22no—
564#41—22no—
565#41—41no—
566#41—41no—
567#41—41no—
568#41—41no—
569#41—41no—
570#41—41no—
571#41—41no—
572#41—41no—
573#41—474no—
574#41—474no—
575#41—474no—
576#41—474no—
577#41—942no—
578#41—942no—
579#41—942no—
580#41—942no—
581#41—942no—
582#41—942no—
583#41—942no—
584#41—942no—
585#41—942no—
586#41—942no—
587#41—942no—
588#41—942no—
589C2×Q8—21no—
590C2×Q8—21no—
591C2×Q8—21no—
592C2×Q8—21no—
593C2×Q8—21no—
594C2×Q8—472no—
595C2×Q8—472no—
596C2×Q8—472no—
597C2×Q8—941no—
598C2×Q8—941no—
599C2×Q8—941no—
600C2×Q8C2×C4×D4712yes—
601C2×D4—22no—
602C2×D4—22no—
603C2×D4—21no—
604C2×D4—21no—
605C2×D4—21no—
606C2×D4—21no—
607C2×D4—21no—
608C2×D4—41no—
609C2×D4—41no—
610C2×D4—41no—
611C2×D4—41no—
612C2×D4—472no—
613C2×D4—472no—
614C2×D4—472no—
615C2×D4—942no—
616C2×D4—942no—
617C2×D4—942no—
618C2×D4—942no—
619C2×D4—942no—
620C2×D4—942no—
621C2×D4—941no—
622C2×D4—941no—
623C2×D4—941no—
624C2×D4C2×C4×D4712yes—
625C22×C4—21no—
626C22×C4—22no—
627C22×C4—22no—
628C22×C4—41no—
629C22×C4—41no—
630C22×C4—41no—
631C22×C4—41no—
632C22×C4—941no—
633C22×C4—942no—
634C22×C4—942no—
635C22×C4—942no—
636C22×C4—942no—
637C22×C4—942no—
638C22×C4—942no—
639C22×C4—1881no—
640C22×C4C2×C4×D4711yescharacteristic
641C22×C4C2×C4×D4711yescharacteristic
642C22×C4#1062535011yescharacteristic
643C22×C4D4×D4711yescharacteristic
644C22×C4D4×D4711yescharacteristic
645C22×C4D4×D4711yescharacteristic
646C22×C4D4×D4711yescharacteristic
647C22×C4D4×D4711yescharacteristic
648C22×C4D4×D4711yescharacteristic
649C22×C4#1062535211yescharacteristic
650C22×C4#1062535211yescharacteristic
651C22×C4C2×C22⋊D4711yescharacteristic
652C22×C4C2×C22⋊D4711yescharacteristic
653C22×C4C23×D4711yescharacteristic
654Q16—948no—
655SD16—948no—
656SD16—948no—
657D8—948no—
658M16—22no—
659M16—22no—
660M16—22no—
661M16—22no—
662M16—22no—
663M16—41no—
664M16—41no—
665M16—9416no—
666M16—942no—
667M16—942no—
668M16—942no—
669M16—942no—
670M16—942no—
671M16—942no—
672M16—942no—
673M16—942no—
674M16C2×C22⋊D4714yes—
675C2×C8—22no—
676C2×C8—22no—
677C2×C8—22no—
678C2×C8—22no—
679C2×C8—41no—
680C2×C8—41no—
681C2×C8—474no—
682C2×C8—474no—
683C2×C8—9416no—
684C2×C8—942no—
685C2×C8—942no—
686C2×C8—942no—
687C2×C8—942no—
688C4⋊C4—942no—
689C4⋊C4—1881no—
690C22⋊C4—942no—
691C22⋊C4—1881no—
692C42—942no—
693C42—1881no—
694C23—22no—
695C23—41no—
696C23—41no—
697C23—81no—
698C23—82no—
699C23—942no—
700C23—942no—
701C23—942no—
702C23—3762no—
703C23C4×C22⋊D4711yescharacteristic
704C23C4×C22⋊D4711yescharacteristic
705C23#1309399711yescharacteristic
706C23#1309399711yescharacteristic
707C23#1309400611yescharacteristic
708C23#1309400611yescharacteristic
709C23C2×#1062535011yescharacteristic
710Q8—22no—
711Q8—22no—
712Q8—41no—
713Q8—41no—
714Q8—474no—
715Q8—942no—
716Q8—942no—
717Q8—942no—
718D4—22no—
719D4—22no—
720D4—42no—
721D4—42no—
722D4—42no—
723D4—42no—
724D4—41no—
725D4—41no—
726D4—474no—
727D4—944no—
728D4—944no—
729D4—944no—
730D4—944no—
731D4—942no—
732D4—942no—
733D4—942no—
734C2×C4—22no—
735C2×C4—41no—
736C2×C4—41no—
737C2×C4—42no—
738C2×C4—42no—
739C2×C4—42no—
740C2×C4—42no—
741C2×C4—942no—
742C2×C4—942no—
743C2×C4—942no—
744C2×C4—944no—
745C2×C4—944no—
746C2×C4—944no—
747C2×C4—944no—
748C2×C4—3762no—
749C2×C4—1882no—
750C2×C4C22⋊C4×D4711yescharacteristic
751C2×C4C22⋊C4×D4711yescharacteristic
752C2×C4C22⋊C4×D4711yescharacteristic
753C2×C4C22⋊C4×D4711yescharacteristic
754C2×C4(C22⋊D47)⋊C411yescharacteristic
755C2×C4(C22⋊D47)⋊C411yescharacteristic
756C2×C4(C22⋊D47)⋊C411yescharacteristic
757C2×C4(C22⋊D47)⋊C411yescharacteristic
758C2×C4C4×C22⋊D4711yescharacteristic
759C2×C4C4×C22⋊D4711yescharacteristic
760C2×C4#1309399211yescharacteristic
761C2×C4#1309399211yescharacteristic
762C2×C4#1309399211yescharacteristic
763C2×C4#1309399211yescharacteristic
764C2×C4#1309399511yescharacteristic
765C2×C4#1309399511yescharacteristic
766C2×C4#1309399511yescharacteristic
767C2×C4#1309399511yescharacteristic
768C2×C4#1309399711yescharacteristic
769C2×C4#1309399711yescharacteristic
770C2×C4#1309400611yescharacteristic
771C2×C4#1309400611yescharacteristic
772C2×C4C22×C4×D4711yescharacteristic
773C2×C4C2×D4×D4711yescharacteristic
774C2×C4C2×D4×D4711yescharacteristic
775C2×C4C2×D4×D4711yescharacteristic
776C2×C4C22×C22⋊D4711yescharacteristic
777C2×C4C2×#1062535211yescharacteristic
778C8—24no—
779C8—42no—
780C8—944no—
781C8—944no—
782C22—41no—
783C22—41no—
784C22—41no—
785C22—41no—
786C22—41no—
787C22—41no—
788C22—41no—
789C22—42no—
790C22—82no—
791C22—82no—
792C22—82no—
793C22—944no—
794C22—3762no—
795C22—3762no—
796C22—1884no—
797C22#1568899911yescharacteristic
798C22#1568899911yescharacteristic
799C22#1568899911yescharacteristic
800C22#1568899911yescharacteristic
801C22C2×C4×C22⋊D4711yescharacteristic
802C22C2×#1309399711yescharacteristic
803C22C2×#1309400611yescharacteristic
804C4—42no—
805C4—944no—
806C4—3762no—
807C4#1568899911yescharacteristic
808C4#1568899911yescharacteristic
809C4#1568899911yescharacteristic
810C4#1568899911yescharacteristic
811C4C2×C22⋊C4×D4711yescharacteristic
812C4C2×(C22⋊D47)⋊C411yescharacteristic
813C4C2×#1309399211yescharacteristic
814C4C2×#1309399511yescharacteristic
815C2—21no—
816C2—21no—
817C2—21no—
818C2—21no—
819C2—21no—
820C2—21no—
821C2—21no—
822C2—82no—
823C2—1884no—
824C2C2×#1568899911yescharacteristic
subgroupG/H
centerC4#15688999
commutatorC2×C4×C47C23×C4
FrattiniC22×C4C23×D47
FittingC2×C47×#413C2
socleC2×C47C2×#386
prime radicalC2×#15689921C2
cosocleC22×C4×C47C24
hypercenterC2×#413D47
hypocenterC47#20995
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C4 ◁ C23×C4 ◁ C2×#413

Complements

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

NH ≅ G/Ntype
2. C2×#15689889C2semidirect
3. C2×#15689139C2semidirect
4. #20251907C2semidirect
5. #20243871C2semidirect
6. #20243864C2semidirect
7. C2×#15688895C2semidirect
8. C2×C47⋊#338C2semidirect
9. C2×C47×#413C2semidirect
16. C2×#13094054C4semidirect
18. C2×#13094049C4semidirect
19. C2×#13094044C4semidirect
33. #15689132C22semidirect
34. #15689128C22semidirect
37. #15688895C22semidirect
38. C47⋊#338C22semidirect
44. C2×#101×C47C22semidirect
45. C2×#100×C47C22semidirect
72. C2×#10625337C2×C4semidirect
73. C2×#10625335C2×C4semidirect
74. C2×#10625336C2×C4semidirect
75. C2×#10625334C2×C4semidirect
407. C2×#413D47semidirect
454. C2×#101C2×D47semidirect
455. C2×#100C2×D47semidirect
458. C47#20995semidirect

Maximal subgroups

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

subgroupindex
C2×#156899212
C2×#156898892
C2×#156891392
#202519072
#202438712
#202438642
C2×#156888952
C2×C47⋊#3382
C2×C47×#4132
#2099547