Finite Group Databasebeta

← #26217821

Subgroups — #26217821

Order 12032.

1708 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×#15689889C211yesmaximal, characteristic, complemented
2#20256717C211yesmaximal, characteristic
3C2×#15689140C211yesmaximal, characteristic, complemented
4C2×#15689096C211yesmaximal, characteristic, complemented
5#20243768C218yesmaximal, complemented
6#20243099C211yesmaximal, characteristic, complemented
7#20243097C211yesmaximal, characteristic, complemented
8C2×C47×#421C211yesmaximal, characteristic, complemented
9C22×#10625350C2211yescharacteristic
10#15689889—22no—
11#15689889—22no—
12#15689889—22no—
13#15689889C2214yescomplemented
14C2×#13094032—22no—
15C2×#13094030—22no—
16C22×#10625329C2211yescharacteristic
17C2×M16×D47—22no—
18#15689701—22no—
19#15689697C412yescomplemented
20#15689694C412yescomplemented
21#15689690C412yescomplemented
22#15689687C412yescomplemented
23#15689682—22no—
24#15689669C2214yes—
25#15689634—22no—
26#15689630—22no—
27C2×#13093983C2211yescharacteristic
28C2×#13093983C2211yescharacteristic
29#15689140—22no—
30#15689140C2214yescomplemented
31C2×#13093951—22no—
32#15689096—22no—
33#15689096C2214yescomplemented
34C2×#13093938—22no—
35#15688884C2214yescomplemented
36#15688882C2214yescomplemented
37C22×#41×C47C2211yescharacteristic
38C22×M16×C47C2211yescharacteristic
39C2×#117×C47C2211yescharacteristic
40C47×#421—22no—
41C47×#421C2214yescomplemented
42C2×#104×C47—22no—
43C2×#10625350—21no—
44C2×#10625350—21no—
45C2×#10625350—21no—
46C2×#10625350—21no—
47C2×#10625350—21no—
48C2×#10625350—21no—
49C2×#10625350—21no—
50C2×#10625350—21no—
51C2×#10625350C2×C412yes—
52C2×#10625350D412yes—
53C2×#10625350D412yes—
54C2×#10625350C2312yes—
55C22×Dic94C2×C411yescharacteristic
56C22×D188C2×C411yescharacteristic
57C22×C22⋊D47D412yes—
58C22×C4×D47D412yes—
59#13094032—28no—
60#13094032—28no—
61#13094030—28no—
62#13094030—28no—
63C2×#10625329—21no—
64C2×#10625329—21no—
65C2×#10625329—21no—
66C2×#10625329D412yescomplemented
67C2×#10625329D412yescomplemented
68C2×#10625329C2312yes—
69C2×#10625324—24no—
70M16×D47—28no—
71M16×D47—28no—
72C22×C47⋊C8—21no—
73C2×C8×D47—24no—
74#13094022C2×C414yescomplemented
75#13094020C2×C414yescomplemented
76#13094013C2×C414yescomplemented
77#13094011C2×C414yescomplemented
78#13094007—24no—
79#13094005—24no—
80#13094003—24no—
81#13094000—24no—
82#13093998—24no—
83#13093996—28no—
84#13093995—24no—
85#13093993—24no—
86#13093992—24no—
87C4×C22⋊D47—28no—
88#13093983—21no—
89#13093983—21no—
90#13093983—21no—
91#13093983—21no—
92#13093983—21no—
93#13093983C2×C412yes—
94#13093983C2×C412yes—
95#13093983C2312yes—
96C2×C4⋊Dic47—21no—
97C2×C4⋊Dic47—21no—
98C2×C22⋊Dic47—21no—
99C2×C22⋊Dic47—21no—
100C2×C4×Dic47—21no—
101C2×C4×Dic47C2312yes—
102#13093951—28no—
103#13093938—28no—
104C2×#41×C47—21no—
105C2×#41×C47—21no—
106C2×#41×C47—21no—
107C2×#41×C47—21no—
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×C47C2×C412yes—
115C2×#41×C47C2312yes—
116C22×Q8×C47C2×C411yescharacteristic
117C22×D4×C47—21no—
118C22×D4×C47C2×C411yescharacteristic
119C23×C4×C47—21no—
120C23×C4×C47C2311yescharacteristic
121C2×M16×C47—21no—
122C2×M16×C47—21no—
123C2×M16×C47—21no—
124C2×M16×C47D412yescomplemented
125C2×M16×C47D412yescomplemented
126C2×M16×C47C2312yes—
127C22×C8×C47—21no—
128#117×C47—21no—
129#117×C47—21no—
130#117×C47—21no—
131#117×C47C2312yes—
132C2×C4⋊C4×C47—21no—
133C2×C22⋊C4×C47—21no—
134C2×C42×C47—21no—
135#104×C47—28no—
136C24×C47—21no—
137C24×C47C2×D411yescharacteristic
138C23×D47C22⋊C412yes—
139#41×C47—22no—
140#41×C47—22no—
141#41×C47—22no—
142#41×C47—22no—
143#41×C47—22no—
144#41×C47—22no—
145#41×C47—22no—
146#41×C47—22no—
147#41×C47—41no—
148#41×C47—41no—
149#41×C47—41no—
150#41×C47—41no—
151#41×C47—41no—
152#41×C47—41no—
153#41×C47—41no—
154#41×C47—41no—
155C2×Q8×C47—21no—
156C2×Q8×C47—21no—
157C2×Q8×C47—21no—
158C2×Q8×C47—21no—
159C2×Q8×C47—21no—
160C2×Q8×C47C22×C412yes—
161C2×D4×C47—22no—
162C2×D4×C47—22no—
163C2×D4×C47—21no—
164C2×D4×C47—21no—
165C2×D4×C47—21no—
166C2×D4×C47—21no—
167C2×D4×C47—21no—
168C2×D4×C47—41no—
169C2×D4×C47—41no—
170C2×D4×C47—41no—
171C2×D4×C47—41no—
172C2×D4×C47C22×C412yes—
173C22×C4×C47—21no—
174C22×C4×C47—22no—
175C22×C4×C47—22no—
176C22×C4×C47—41no—
177C22×C4×C47—41no—
178C22×C4×C47—41no—
179C22×C4×C47—41no—
180C22×C4×C47—41no—
181C22×C4×C47C22×C411yescharacteristic
182C22×C4×C47C22×C411yescharacteristic
183C22×C4×C47C2×D411yescharacteristic
184C22×C4×C47C2×D411yescharacteristic
185C22×C4×C47C2×D411yescharacteristic
186C22×C4×C47C2×D411yescharacteristic
187C22×C4×C47C2×D411yescharacteristic
188C22×C4×C47C2×D411yescharacteristic
189C22×C4×C47C2×D411yescharacteristic
190C22×C4×C47#4111yescharacteristic
191C22×C4×C47#4111yescharacteristic
192C22×C4×C47#4111yescharacteristic
193C22×C4×C47#4111yescharacteristic
194C22×C4×C47C2411yescharacteristic
195C2×C22⋊D47—22no—
196C2×C22⋊D47—22no—
197C2×C22⋊D47—22no—
198C2×C22⋊D47—22no—
199C2×C22⋊D47—28no—
200C2×C22⋊D47C22⋊C414yes—
201C2×C22⋊D47C2×D414yes—
202C22×Dic47—22no—
203C22×Dic47—41no—
204C22×Dic47C22⋊C412yes—
205#10625350—22no—
206#10625350—22no—
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#10625350—22no—
220#10625350—22no—
221C2×D188—21no—
222C2×D188—21no—
223C2×D188—21no—
224C2×D188—21no—
225C2×D188C22⋊C412yes—
226C2×D188C22×C412yes—
227C2×C4×D47—22no—
228C2×C4×D47—22no—
229C2×C4×D47—22no—
230C2×C4×D47—22no—
231C2×C4×D47C22⋊C414yes—
232C2×C4×D47C2×D414yes—
233C2×Dic94—21no—
234C2×Dic94—21no—
235C2×Dic94—21no—
236C2×Dic94—21no—
237C2×Dic94C22⋊C412yes—
238C2×Dic94C22×C412yes—
239M16×C47—22no—
240M16×C47—22no—
241M16×C47—22no—
242M16×C47C2×D414yes—
243C2×C8×C47—22no—
244C2×C8×C47—22no—
245C2×C8×C47—22no—
246C4⋊C4×C47—22no—
247C4⋊C4×C47—41no—
248C22⋊C4×C47—22no—
249C22⋊C4×C47—41no—
250C42×C47—22no—
251C42×C47—41no—
252C22⋊Dic47—22no—
253C22⋊Dic47—22no—
254C22⋊Dic47—28no—
255C22⋊Dic47—22no—
256C22⋊Dic47—41no—
257(C2×D47)⋊C4—28no—
258C4⋊Dic47—22no—
259C4⋊Dic47—22no—
260C4⋊Dic47—22no—
261C4⋊Dic47—41no—
262Dic47⋊C4—28no—
263C4×Dic47—22no—
264C4×Dic47—22no—
265C4×Dic47—41no—
266C4×Dic47C22×C414yes—
267#10625329—22no—
268#10625329—22no—
269#10625329—22no—
270#10625329C2×D414yes—
271C2×C47⋊C8—22no—
272C2×C47⋊C8—22no—
273C2×C47⋊C8—22no—
274#10625324—216no—
275C8×D47—216no—
276C23×C47—22no—
277C23×C47—41no—
278C23×C47—41no—
279C23×C47—81no—
280C23×C47—82no—
281C23×C47C2×C22⋊C411yescharacteristic
282C23×C47C2×C22⋊C411yescharacteristic
283C23×C47#12111yescharacteristic
284C23×C47#12111yescharacteristic
285C23×C47#12111yescharacteristic
286C23×C47#12111yescharacteristic
287C23×C47C22×D411yescharacteristic
288C22×D47—22no—
289C22×D47—22no—
290C22×D47—82no—
291C22×D47C2×C22⋊C414yes—
292Q8×C47—22no—
293Q8×C47—22no—
294Q8×C47—41no—
295Q8×C47—41no—
296D4×C47—22no—
297D4×C47—22no—
298D4×C47—42no—
299D4×C47—42no—
300D4×C47—42no—
301D4×C47—42no—
302D4×C47—41no—
303D4×C47—41no—
304C2×C4×C47—22no—
305C2×C4×C47—41no—
306C2×C4×C47—41no—
307C2×C4×C47—42no—
308C2×C4×C47—42no—
309C2×C4×C47—42no—
310C2×C4×C47—42no—
311C2×C4×C47—42no—
312C2×C4×C47—82no—
313C2×C4×C47C2×C22⋊C411yescharacteristic
314C2×C4×C47C2×C22⋊C411yescharacteristic
315C2×C4×C47C4×D411yescharacteristic
316C2×C4×C47C4×D411yescharacteristic
317C2×C4×C47C4×D411yescharacteristic
318C2×C4×C47C4×D411yescharacteristic
319C2×C4×C47C4×D411yescharacteristic
320C2×C4×C47C4×D411yescharacteristic
321C2×C4×C47C4×D411yescharacteristic
322C2×C4×C47C4×D411yescharacteristic
323C2×C4×C47#12011yescharacteristic
324C2×C4×C47#12011yescharacteristic
325C2×C4×C47#12011yescharacteristic
326C2×C4×C47#12011yescharacteristic
327C2×C4×C47#12111yescharacteristic
328C2×C4×C47#12111yescharacteristic
329C2×C4×C47#12111yescharacteristic
330C2×C4×C47#12111yescharacteristic
331C2×C4×C47#12311yescharacteristic
332C2×C4×C47#12311yescharacteristic
333C2×C4×C47#12311yescharacteristic
334C2×C4×C47#12311yescharacteristic
335C2×C4×C47C23×C411yescharacteristic
336C2×C4×C47C22×D411yescharacteristic
337C2×C4×C47C22×D411yescharacteristic
338C2×C4×C47C22×D411yescharacteristic
339C2×C4×C47C2×#4111yescharacteristic
340C2×C4×C47C2×#4111yescharacteristic
341C22⋊D47—24no—
342C22⋊D47—24no—
343C22⋊D47—24no—
344C22⋊D47—24no—
345C22⋊D47—88no—
346C2×Dic47—22no—
347C2×Dic47—22no—
348C2×Dic47—24no—
349C2×Dic47—42no—
350C2×Dic47—82no—
351C2×Dic47—82no—
352C2×Dic47C2×C22⋊C414yes—
353D188—22no—
354D188—22no—
355D188—22no—
356D188—22no—
357C4×D47—24no—
358C4×D47—24no—
359C4×D47—24no—
360C4×D47—24no—
361Dic94—22no—
362Dic94—22no—
363Dic94—22no—
364Dic94—22no—
365C8×C47—24no—
366C47⋊C8—24no—
367#20947—471nomaximal, Sylow
368C22×C47—41no—
369C22×C47—41no—
370C22×C47—41no—
371C22×C47—41no—
372C22×C47—41no—
373C22×C47—41no—
374C22×C47—41no—
375C22×C47—44no—
376C22×C47—42no—
377C22×C47—82no—
378C22×C47—82no—
379C22×C47#38611yescharacteristic
380C22×C47#38611yescharacteristic
381C22×C47#38611yescharacteristic
382C22×C47#38611yescharacteristic
383C22×C47C22×C22⋊C411yescharacteristic
384C22×C47C2×#12111yescharacteristic
385C22×C47C2×#12111yescharacteristic
386C2×D47—24no—
387C2×D47—44no—
388C2×D47—44no—
389C2×D47—82no—
390C4×C47—42no—
391C4×C47—82no—
392C4×C47#38611yescharacteristic
393C4×C47#38611yescharacteristic
394C4×C47#38611yescharacteristic
395C4×C47#38611yescharacteristic
396C4×C47C2×C4×D411yescharacteristic
397C4×C47C2×C4×D411yescharacteristic
398C4×C47C2×#12011yescharacteristic
399C4×C47C2×#12311yescharacteristic
400Dic47—24no—
401Dic47—44no—
402Dic47—82no—
403C2×#568—471no—
404#3449—471no—
405C2×#421—471no—
406C2×#421D4711yescharacteristic, complemented
407C2×#410—471no—
408#1884—478no—
409#1733—471no—
410#1733—471no—
411C2×C47—21no—
412C2×C47—21no—
413C2×C47—21no—
414C2×C47—21no—
415C2×C47—21no—
416C2×C47—21no—
417C2×C47—21no—
418C2×C47—82no—
419C2×C47C2×#38611yescharacteristic
420D47—44no—
421C22×#41—471no—
422C22×#41C2×D4711yescharacteristic
423#568—474no—
424#568—942no—
425#568—942no—
426#568—942no—
427C2×#131—942no—
428C2×#131—942no—
429C22×M16—471no—
430C22×M16—942no—
431C22×M16C2×D4711yescharacteristic
432#537—942no—
433#536—472no—
434#536—472no—
435#535—472no—
436#535—472no—
437#534—942no—
438#532—474no—
439#525—942no—
440#525—942no—
441C2×#117—471no—
442C2×#117—471no—
443C2×#117C2×D4711yescharacteristic
444#421—22no—
445#421—474no—
446#421—942no—
447#421C2×D4714yescomplemented
448C2×#104—22no—
449C2×#104—942no—
450#410—474no—
451#410—942no—
452C2×#99—942no—
453#339—474no—
454#339—474no—
455C47#2094711yescharacteristic, complemented, Sylow
456C2×#41—21no—
457C2×#41—21no—
458C2×#41—21no—
459C2×#41—21no—
460C2×#41—21no—
461C2×#41—21no—
462C2×#41—21no—
463C2×#41—21no—
464C2×#41—21no—
465C2×#41—21no—
466C2×#41—472no—
467C2×#41—472no—
468C2×#41—472no—
469C2×#41—472no—
470C2×#41—941no—
471C2×#41—941no—
472C2×#41—941no—
473C2×#41—941no—
474C2×#41—941no—
475C2×#41—941no—
476C2×#41—941no—
477C2×#41—941no—
478C2×#41C4×D4712yes—
479C2×#41C22×D4712yes—
480C22×Q8—471no—
481C22×Q8C4×D4711yescharacteristic
482C22×D4—21no—
483C22×D4—472no—
484C22×D4—471no—
485C22×D4C4×D4711yescharacteristic
486C23×C4—21no—
487C23×C4—472no—
488C23×C4C22×D4711yescharacteristic
489#131—948no—
490#131—948no—
491#131—948no—
492#131—948no—
493C2×M16—21no—
494C2×M16—21no—
495C2×M16—21no—
496C2×M16—472no—
497C2×M16—472no—
498C2×M16—472no—
499C2×M16—944no—
500C2×M16—948no—
501C2×M16—948no—
502C2×M16—941no—
503C2×M16—941no—
504C2×M16—941no—
505C2×M16C22⋊D4712yescomplemented
506C2×M16C22⋊D4712yescomplemented
507C2×M16C22×D4712yes—
508C22×C8—21no—
509C22×C8—944no—
510C22×C8—941no—
511C4⋊Q8—474no—
512#127—474no—
513#124—474no—
514#124—474no—
515#123—944no—
516#123—944no—
517C22⋊Q8—944no—
518C22⋊Q8—944no—
519#121—944no—
520#121—944no—
521#121—948no—
522#120—944no—
523#120—944no—
524C4×D4—948no—
525#117—21no—
526#117—21no—
527#117—21no—
528#117—472no—
529#117—472no—
530#117—472no—
531#117—941no—
532#117—941no—
533#117—941no—
534#117—941no—
535#117—941no—
536#117C22×D4712yes—
537C2×C4⋊C4—21no—
538C2×C4⋊C4—941no—
539C2×C4⋊C4—941no—
540C2×C22⋊C4—21no—
541C2×C22⋊C4—941no—
542C2×C22⋊C4—941no—
543C2×C42—21no—
544C2×C42—472no—
545C2×C42—941no—
546#104—28no—
547#104—948no—
548#99—948no—
549C24—21no—
550C24—472no—
551C24D4×D4711yescharacteristic
552#41—22no—
553#41—22no—
554#41—22no—
555#41—22no—
556#41—22no—
557#41—22no—
558#41—22no—
559#41—22no—
560#41—41no—
561#41—41no—
562#41—41no—
563#41—41no—
564#41—41no—
565#41—41no—
566#41—41no—
567#41—41no—
568#41—942no—
569#41—942no—
570#41—942no—
571#41—942no—
572#41—942no—
573#41—942no—
574#41—942no—
575#41—942no—
576#41—942no—
577#41—942no—
578#41—942no—
579#41—942no—
580#41—942no—
581#41—942no—
582#41—942no—
583#41—942no—
584C2×Q8—21no—
585C2×Q8—21no—
586C2×Q8—21no—
587C2×Q8—21no—
588C2×Q8—21no—
589C2×Q8—472no—
590C2×Q8—472no—
591C2×Q8—941no—
592C2×Q8—941no—
593C2×Q8—941no—
594C2×Q8—941no—
595C2×Q8C2×C4×D4712yes—
596C2×D4—22no—
597C2×D4—22no—
598C2×D4—21no—
599C2×D4—21no—
600C2×D4—21no—
601C2×D4—21no—
602C2×D4—21no—
603C2×D4—41no—
604C2×D4—41no—
605C2×D4—41no—
606C2×D4—41no—
607C2×D4—474no—
608C2×D4—474no—
609C2×D4—472no—
610C2×D4—472no—
611C2×D4—942no—
612C2×D4—942no—
613C2×D4—942no—
614C2×D4—942no—
615C2×D4—948no—
616C2×D4—941no—
617C2×D4—941no—
618C2×D4—941no—
619C2×D4—941no—
620C2×D4C2×C4×D4712yes—
621C22×C4—21no—
622C22×C4—22no—
623C22×C4—22no—
624C22×C4—41no—
625C22×C4—41no—
626C22×C4—41no—
627C22×C4—41no—
628C22×C4—41no—
629C22×C4—472no—
630C22×C4—474no—
631C22×C4—474no—
632C22×C4—942no—
633C22×C4—942no—
634C22×C4—942no—
635C22×C4—942no—
636C22×C4—942no—
637C22×C4—1881no—
638C22×C4C2×C4×D4711yescharacteristic
639C22×C4C2×C4×D4711yescharacteristic
640C22×C4#1062535011yescharacteristic
641C22×C4#1062535011yescharacteristic
642C22×C4D4×D4711yescharacteristic
643C22×C4D4×D4711yescharacteristic
644C22×C4D4×D4711yescharacteristic
645C22×C4D4×D4711yescharacteristic
646C22×C4D4×D4711yescharacteristic
647C22×C4#1062535211yescharacteristic
648C22×C4#1062535211yescharacteristic
649C22×C4C2×C22⋊D4711yescharacteristic
650C22×C4C2×C22⋊D4711yescharacteristic
651C22×C4C23×D4711yescharacteristic
652M16—22no—
653M16—22no—
654M16—22no—
655M16—474no—
656M16—9416no—
657M16—942no—
658M16—942no—
659M16—942no—
660M16C2×C22⋊D4714yes—
661C2×C8—22no—
662C2×C8—22no—
663C2×C8—22no—
664C2×C8—9416no—
665C2×C8—942no—
666C2×C8—942no—
667C2×C8—942no—
668C4⋊C4—22no—
669C4⋊C4—41no—
670C4⋊C4—948no—
671C4⋊C4—942no—
672C4⋊C4—942no—
673C4⋊C4—942no—
674C4⋊C4—1881no—
675C22⋊C4—22no—
676C22⋊C4—41no—
677C22⋊C4—948no—
678C22⋊C4—948no—
679C22⋊C4—942no—
680C22⋊C4—942no—
681C22⋊C4—942no—
682C22⋊C4—1881no—
683C42—22no—
684C42—41no—
685C42—474no—
686C42—942no—
687C42—942no—
688C42—1881no—
689C23—22no—
690C23—41no—
691C23—41no—
692C23—81no—
693C23—82no—
694C23—474no—
695C23—942no—
696C23—942no—
697C23—3762no—
698C23C22⋊C4×D4711yescharacteristic
699C23C22⋊C4×D4711yescharacteristic
700C23#1309399511yescharacteristic
701C23#1309399511yescharacteristic
702C23#1309399711yescharacteristic
703C23#1309399711yescharacteristic
704C23C2×D4×D4711yescharacteristic
705Q8—22no—
706Q8—22no—
707Q8—41no—
708Q8—41no—
709Q8—942no—
710Q8—942no—
711Q8—942no—
712Q8—942no—
713D4—22no—
714D4—22no—
715D4—42no—
716D4—42no—
717D4—42no—
718D4—42no—
719D4—41no—
720D4—41no—
721D4—944no—
722D4—944no—
723D4—944no—
724D4—944no—
725D4—942no—
726D4—942no—
727D4—942no—
728D4—942no—
729D4—3768no—
730C2×C4—22no—
731C2×C4—41no—
732C2×C4—41no—
733C2×C4—42no—
734C2×C4—42no—
735C2×C4—42no—
736C2×C4—42no—
737C2×C4—42no—
738C2×C4—82no—
739C2×C4—474no—
740C2×C4—942no—
741C2×C4—942no—
742C2×C4—944no—
743C2×C4—944no—
744C2×C4—944no—
745C2×C4—944no—
746C2×C4—944no—
747C2×C4—3762no—
748C2×C4—3762no—
749C2×C4—1882no—
750C2×C4C22⋊C4×D4711yescharacteristic
751C2×C4C22⋊C4×D4711yescharacteristic
752C2×C4(C22⋊D47)⋊C411yescharacteristic
753C2×C4(C22⋊D47)⋊C411yescharacteristic
754C2×C4(C22⋊D47)⋊C411yescharacteristic
755C2×C4(C22⋊D47)⋊C411yescharacteristic
756C2×C4C4×C22⋊D4711yescharacteristic
757C2×C4C4×C22⋊D4711yescharacteristic
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#1309399711yescharacteristic
767C2×C4#1309399711yescharacteristic
768C2×C4#1309400611yescharacteristic
769C2×C4#1309400611yescharacteristic
770C2×C4#1309400611yescharacteristic
771C2×C4#1309400611yescharacteristic
772C2×C4C22×C4×D4711yescharacteristic
773C2×C4C2×D4×D4711yescharacteristic
774C2×C4C2×D4×D4711yescharacteristic
775C2×C4C22×C22⋊D4711yescharacteristic
776C2×C4C2×#1062535211yescharacteristic
777C2×C4C2×#1062535011yescharacteristic
778C8—24no—
779C8—944no—
780C22—41no—
781C22—41no—
782C22—41no—
783C22—41no—
784C22—41no—
785C22—41no—
786C22—41no—
787C22—44no—
788C22—42no—
789C22—82no—
790C22—82no—
791C22—944no—
792C22—3762no—
793C22—1884no—
794C22—1884no—
795C22#1568899911yescharacteristic
796C22#1568899911yescharacteristic
797C22#1568899911yescharacteristic
798C22#1568899911yescharacteristic
799C22C2×C22⋊C4×D4711yescharacteristic
800C22C2×#1309399511yescharacteristic
801C22C2×#1309399711yescharacteristic
802C4—42no—
803C4—82no—
804C4—944no—
805C4—3762no—
806C4—1884no—
807C4#1568899911yescharacteristic
808C4#1568899911yescharacteristic
809C4#1568899911yescharacteristic
810C4#1568899911yescharacteristic
811C4C2×(C22⋊D47)⋊C411yescharacteristic
812C4C2×C4×C22⋊D4711yescharacteristic
813C4C2×#1309399211yescharacteristic
814C4C2×#1309400611yescharacteristic
815C2—21no—
816C2—21no—
817C2—21no—
818C2—21no—
819C2—21no—
820C2—21no—
821C2—21no—
822C2—82no—
823C2—1884no—
824C2C2×#1568899911yescharacteristic
subgroupG/H
centerC4C2×#13093992
commutatorC2×C4×C47C23×C4
FrattiniC22×C4C23×D47
FittingC2×C47×#421C2
socleC2×C47C2×#386
prime radical#20256717C2
cosocleC22×C4×C47C24
hypercenterC2×#421D47
hypocenterC47#20947
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C4 ◁ C23×C4 ◁ C2×#421

Complements

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

NH ≅ G/Ntype
1. C2×#15689889C2semidirect
3. C2×#15689140C2semidirect
4. C2×#15689096C2semidirect
5. #20243768C2semidirect
6. #20243099C2semidirect
7. #20243097C2semidirect
8. C2×C47×#421C2semidirect
13. #15689889C22semidirect
19. #15689697C4semidirect
20. #15689694C4semidirect
21. #15689690C4semidirect
22. #15689687C4semidirect
30. #15689140C22semidirect
33. #15689096C22semidirect
35. #15688884C22semidirect
36. #15688882C22semidirect
41. C47×#421C22semidirect
66. C2×#10625329D4semidirect
67. C2×#10625329D4semidirect
74. #13094022C2×C4semidirect
75. #13094020C2×C4semidirect
76. #13094013C2×C4semidirect
77. #13094011C2×C4semidirect
124. C2×M16×C47D4semidirect
125. C2×M16×C47D4semidirect
406. C2×#421D47semidirect
447. #421C2×D47semidirect
455. C47#20947semidirect
505. C2×M16C22⋊D47semidirect
506. C2×M16C22⋊D47semidirect

Maximal subgroups

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

subgroupindex
C2×#156898892
#202567172
C2×#156891402
C2×#156890962
#202437682
#202430992
#202430972
C2×C47×#4212
#2094747