Finite Group Databasebeta

← #26217932

Subgroups — #26217932

Order 12032.

1700 conjugacy classes of subgroups.

The subgroup lattice has 822 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689889C211yesmaximal, characteristic, complemented
2#20256717C211yesmaximal, characteristic
3C2×#15689105C211yesmaximal, characteristic, complemented
4#20251833C211yesmaximal, characteristic, complemented
5#20243803C218yesmaximal, complemented
6C2×#15688895C211yesmaximal, characteristic, complemented
7C2×#15688894C211yesmaximal, characteristic, complemented
8C47×#2879C211yesmaximal, characteristic, complemented
9C22×#10625350C2211yescharacteristic
10#15689889—22no—
11#15689889—22no—
12#15689889—22no—
13#15689889C2214yes—
14C2×#13094032—22no—
15C2×#13094030—22no—
16C22×#10625329C2211yescharacteristic
17C22×#10625329C2211yescharacteristic
18C2×M16×D47—22no—
19#15689701—22no—
20#15689697C412yes—
21#15689694—21no—
22#15689690C412yes—
23#15689687—21no—
24#15689682C414yes—
25#15689669—22no—
26#15689634C2214yes—
27#15689630—22no—
28C2×#13093983C2211yescharacteristic
29#15689105—22no—
30#15689105C2214yes—
31C2×#13093942—21no—
32C2×#13093940—21no—
33#15689090—22no—
34#15689090—22no—
35#15689087C2214yescomplemented
36#15688895C2214yescomplemented
37#15688894C2214yescomplemented
38C22×#41×C47C2211yescharacteristic
39C22×M16×C47C2211yescharacteristic
40C22×M16×C47C2211yescharacteristic
41C47×#408—22no—
42C47×#408—22no—
43C47×#407C2214yescomplemented
44C2×#10625350—21no—
45C2×#10625350—21no—
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×#10625350C2312yes—
56C22×Dic94D411yescharacteristic
57C22×D188D411yescharacteristic
58C22×C22⋊D47C2×C412yes—
59C22×C4×D47D412yes—
60#13094032—28no—
61#13094032—28no—
62#13094030—28no—
63#13094030—28no—
64C2×#10625329—21no—
65C2×#10625329—21no—
66C2×#10625329—21no—
67C2×#10625329—21no—
68C2×#10625329—21no—
69C2×#10625329—21no—
70C2×#10625329—21no—
71C2×#10625329—21no—
72C2×#10625329—21no—
73C2×#10625329D412yescomplemented
74C2×#10625329C2312yes—
75C2×#10625329C2312yes—
76C2×#10625324—24no—
77M16×D47—28no—
78M16×D47—28no—
79C22×C47⋊C8—21no—
80C22×C47⋊C8D412yescomplemented
81C2×C8×D47—24no—
82#13094022—22no—
83#13094020—22no—
84#13094013—22no—
85#13094011—22no—
86#13094007C2×C418yes—
87#13094005—24no—
88#13094003—24no—
89#13094000—24no—
90#13093998—24no—
91#13093996—28no—
92#13093995—24no—
93#13093993C2×C418yes—
94#13093992—24no—
95C4×C22⋊D47—28no—
96#13093983—21no—
97#13093983—21no—
98#13093983C2×C412yes—
99#13093983C2312yes—
100C2×C4⋊Dic47—21no—
101C2×C22⋊Dic47C2×C412yes—
102C2×C4×Dic47—21no—
103#13093942—24no—
104#13093940—24no—
105C22⋊(C47⋊C8)—28no—
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×C47—21no—
115C2×#41×C47—21no—
116C2×#41×C47—21no—
117C2×#41×C47—21no—
118C22×Q8×C47C2×C411yescharacteristic
119C22×D4×C47C2×C412yes—
120C22×D4×C47C2×C411yescharacteristic
121C23×C4×C47C2312yes—
122C23×C4×C47C2311yescharacteristic
123C2×M16×C47—21no—
124C2×M16×C47—21no—
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×C47D412yescomplemented
133C2×M16×C47C2312yes—
134C2×M16×C47C2312yes—
135C22×C8×C47—21no—
136C22×C8×C47D412yescomplemented
137C22⋊C8×C47—28no—
138C24×C47C22×C412yes—
139C24×C47C22×C411yescharacteristic
140C23×D47C22⋊C412yes—
141#41×C47—41no—
142#41×C47—41no—
143#41×C47—41no—
144#41×C47—41no—
145#41×C47—41no—
146#41×C47—41no—
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—
155#41×C47—41no—
156#41×C47—41no—
157C2×Q8×C47—21no—
158C2×Q8×C47—21no—
159C2×Q8×C47—21no—
160C2×Q8×C47—21no—
161C2×Q8×C47—21no—
162C2×Q8×C47—21no—
163C2×D4×C47—22no—
164C2×D4×C47—22no—
165C2×D4×C47—22no—
166C2×D4×C47—22no—
167C2×D4×C47—22no—
168C2×D4×C47—22no—
169C2×D4×C47—21no—
170C2×D4×C47—21no—
171C2×D4×C47—21no—
172C2×D4×C47—21no—
173C2×D4×C47—21no—
174C2×D4×C47—21no—
175C22×C4×C47—22no—
176C22×C4×C47—22no—
177C22×C4×C47—22no—
178C22×C4×C47—22no—
179C22×C4×C47—22no—
180C22×C4×C47—22no—
181C22×C4×C47C22×C412yes—
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×C47C2×D411yescharacteristic
191C22×C4×C47#4111yescharacteristic
192C22×C4×C47#4111yescharacteristic
193C22×C4×C47#4111yescharacteristic
194C22×C4×C47#4111yescharacteristic
195C22×C4×C47C2411yescharacteristic
196C2×C22⋊D47—22no—
197C2×C22⋊D47—22no—
198C2×C22⋊D47—22no—
199C2×C22⋊D47—22no—
200C2×C22⋊D47—28no—
201C2×C22⋊D47C22⋊C414yes—
202C2×C22⋊D47C22×C414yes—
203C22×Dic47—22no—
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×D188C2×D412yes—
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×Dic94C2×D412yes—
239M16×C47—22no—
240M16×C47—22no—
241M16×C47—22no—
242M16×C47—22no—
243M16×C47—22no—
244M16×C47—22no—
245M16×C47—41no—
246M16×C47—41no—
247C2×C8×C47—22no—
248C2×C8×C47—22no—
249C2×C8×C47—22no—
250C2×C8×C47—41no—
251C2×C8×C47—41no—
252C2×C8×C47C2×D414yes—
253C22⋊Dic47—22no—
254C22⋊Dic47—28no—
255C22⋊Dic47C22×C414yes—
256(C2×D47)⋊C4—28no—
257C4⋊Dic47—22no—
258C4⋊Dic47—22no—
259Dic47⋊C4—28no—
260C4×Dic47—22no—
261C4×Dic47—22no—
262#10625329—22no—
263#10625329—22no—
264#10625329—22no—
265#10625329—22no—
266#10625329—22no—
267#10625329—22no—
268#10625329—41no—
269#10625329—41no—
270C2×C47⋊C8—22no—
271C2×C47⋊C8—22no—
272C2×C47⋊C8—22no—
273C2×C47⋊C8—41no—
274C2×C47⋊C8—41no—
275C2×C47⋊C8C2×D414yes—
276#10625324—216no—
277C8×D47—216no—
278C23×C47—22no—
279C23×C47—22no—
280C23×C47—22no—
281C23×C47—81no—
282C23×C47—82no—
283C23×C47C2×C22⋊C411yescharacteristic
284C23×C47C2×C22⋊C411yescharacteristic
285C23×C47C4×D411yescharacteristic
286C23×C47C4×D411yescharacteristic
287C23×C47C4×D411yescharacteristic
288C23×C47C4×D411yescharacteristic
289C23×C47C23×C411yescharacteristic
290C22×D47—22no—
291C22×D47—22no—
292C22×D47—82no—
293C22×D47C2×C22⋊C414yes—
294Q8×C47—41no—
295Q8×C47—41no—
296Q8×C47—41no—
297Q8×C47—41no—
298D4×C47—42no—
299D4×C47—42no—
300D4×C47—42no—
301D4×C47—42no—
302D4×C47—41no—
303D4×C47—41no—
304D4×C47—41no—
305D4×C47—41no—
306C2×C4×C47—22no—
307C2×C4×C47—22no—
308C2×C4×C47—22no—
309C2×C4×C47—42no—
310C2×C4×C47—42no—
311C2×C4×C47—42no—
312C2×C4×C47—42no—
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×C47#12011yescharacteristic
320C2×C4×C47#12011yescharacteristic
321C2×C4×C47#12011yescharacteristic
322C2×C4×C47#12011yescharacteristic
323C2×C4×C47#12111yescharacteristic
324C2×C4×C47#12111yescharacteristic
325C2×C4×C47#12111yescharacteristic
326C2×C4×C47#12111yescharacteristic
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×C47C22×D411yescharacteristic
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—82no—
350C2×Dic47C2×C22⋊C414yes—
351D188—22no—
352D188—22no—
353D188—22no—
354D188—22no—
355C4×D47—24no—
356C4×D47—24no—
357C4×D47—24no—
358C4×D47—24no—
359Dic94—22no—
360Dic94—22no—
361Dic94—22no—
362Dic94—22no—
363C8×C47—24no—
364C8×C47—42no—
365C47⋊C8—24no—
366C47⋊C8—42no—
367#20964—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—44no—
377C22×C47—44no—
378C22×C47—42no—
379C22×C47#38611yescharacteristic
380C22×C47#38611yescharacteristic
381C22×C47#38611yescharacteristic
382C22×C47#38611yescharacteristic
383C22×C47C22×C22⋊C411yescharacteristic
384C22×C47C2×C4×D411yescharacteristic
385C22×C47C2×C4×D411yescharacteristic
386C2×D47—24no—
387C2×D47—44no—
388C2×D47—44no—
389C2×D47—82no—
390C4×C47—42no—
391C4×C47#38611yescharacteristic
392C4×C47#38611yescharacteristic
393C4×C47#38611yescharacteristic
394C4×C47#38611yescharacteristic
395C4×C47C2×#12011yescharacteristic
396C4×C47C2×#12111yescharacteristic
397C4×C47C2×#12111yescharacteristic
398C4×C47C2×#12311yescharacteristic
399Dic47—24no—
400Dic47—44no—
401C2×#568—471no—
402#3449—471no—
403C2×#413—471no—
404#2879—471no—
405#2879D4711yescharacteristic, complemented
406#1891—478no—
407C2×#344—471no—
408C2×#344—471no—
409C2×C47—21no—
410C2×C47—21no—
411C2×C47—21no—
412C2×C47—21no—
413C2×C47—21no—
414C2×C47—21no—
415C2×C47—21no—
416C2×C47—82no—
417C2×C47C2×#38611yescharacteristic
418D47—44no—
419C22×#41—471no—
420C22×#41C2×D4711yescharacteristic
421#568—474no—
422#568—942no—
423#568—942no—
424#568—942no—
425C2×#131—942no—
426C2×#131—942no—
427C22×M16—471no—
428C22×M16—471no—
429C22×M16—942no—
430C22×M16C2×D4711yescharacteristic
431C22×M16C2×D4711yescharacteristic
432#537—942no—
433#536—472no—
434#536—941no—
435#535—472no—
436#535—941no—
437#534—474no—
438#532—942no—
439#525—474no—
440#525—942no—
441C2×#117—471no—
442#413—474no—
443#413—942no—
444C2×#101—941no—
445C2×#100—941no—
446#408—22no—
447#408—22no—
448#408—942no—
449#408—942no—
450#407—474no—
451#407C2×D4714yescomplemented
452#344—474no—
453#344—474no—
454C47#2096411yescharacteristic, complemented, Sylow
455C2×#41—21no—
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—21no—
467C2×#41—472no—
468C2×#41—472no—
469C2×#41—472no—
470C2×#41—472no—
471C2×#41—941no—
472C2×#41—941no—
473C2×#41—941no—
474C2×#41—941no—
475C2×#41—941no—
476C2×#41—941no—
477C2×#41—941no—
478C2×#41—941no—
479C22×Q8—471no—
480C22×Q8C4×D4711yescharacteristic
481C22×D4—472no—
482C22×D4—471no—
483C22×D4C4×D4712yes—
484C22×D4C4×D4711yescharacteristic
485C23×C4—472no—
486C23×C4C22×D4712yes—
487C23×C4C22×D4711yescharacteristic
488#131—948no—
489#131—948no—
490#131—948no—
491#131—948no—
492C2×M16—21no—
493C2×M16—21no—
494C2×M16—21no—
495C2×M16—21no—
496C2×M16—21no—
497C2×M16—21no—
498C2×M16—21no—
499C2×M16—21no—
500C2×M16—21no—
501C2×M16—472no—
502C2×M16—472no—
503C2×M16—472no—
504C2×M16—944no—
505C2×M16—948no—
506C2×M16—948no—
507C2×M16—941no—
508C2×M16—941no—
509C2×M16—941no—
510C2×M16—941no—
511C2×M16—941no—
512C2×M16—941no—
513C2×M16—941no—
514C2×M16—941no—
515C2×M16—941no—
516C2×M16C22⋊D4712yescomplemented
517C2×M16C22×D4712yes—
518C2×M16C22×D4712yes—
519C22×C8—21no—
520C22×C8—472no—
521C22×C8—944no—
522C22×C8—941no—
523C22×C8C22⋊D4712yescomplemented
524C4⋊Q8—942no—
525#127—942no—
526#124—942no—
527#124—942no—
528#123—478no—
529#123—944no—
530C22⋊Q8—944no—
531C22⋊Q8—944no—
532#121—944no—
533#121—944no—
534#121—948no—
535#120—478no—
536#120—944no—
537C4×D4—948no—
538#117—472no—
539#117—472no—
540#117—941no—
541#117—941no—
542C2×C4⋊C4—941no—
543C2×C22⋊C4—472no—
544C2×C42—941no—
545#101—944no—
546#100—944no—
547C22⋊C8—28no—
548C22⋊C8—948no—
549C24—472no—
550C24C2×C4×D4712yes—
551C24C2×C4×D4711yescharacteristic
552#41—41no—
553#41—41no—
554#41—41no—
555#41—41no—
556#41—41no—
557#41—41no—
558#41—41no—
559#41—41no—
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—21no—
590C2×Q8—472no—
591C2×Q8—472no—
592C2×Q8—941no—
593C2×Q8—941no—
594C2×Q8—941no—
595C2×Q8—941no—
596C2×D4—22no—
597C2×D4—22no—
598C2×D4—22no—
599C2×D4—22no—
600C2×D4—22no—
601C2×D4—22no—
602C2×D4—21no—
603C2×D4—21no—
604C2×D4—21no—
605C2×D4—21no—
606C2×D4—21no—
607C2×D4—21no—
608C2×D4—474no—
609C2×D4—474no—
610C2×D4—472no—
611C2×D4—472no—
612C2×D4—942no—
613C2×D4—942no—
614C2×D4—942no—
615C2×D4—942no—
616C2×D4—948no—
617C2×D4—941no—
618C2×D4—941no—
619C2×D4—941no—
620C2×D4—941no—
621C22×C4—22no—
622C22×C4—22no—
623C22×C4—22no—
624C22×C4—22no—
625C22×C4—22no—
626C22×C4—22no—
627C22×C4—472no—
628C22×C4—474no—
629C22×C4—474no—
630C22×C4—942no—
631C22×C4—942no—
632C22×C4—942no—
633C22×C4—942no—
634C22×C4—942no—
635C22×C4C2×C4×D4712yes—
636C22×C4C2×C4×D4711yescharacteristic
637C22×C4#1062535011yescharacteristic
638C22×C4#1062535011yescharacteristic
639C22×C4D4×D4711yescharacteristic
640C22×C4D4×D4711yescharacteristic
641C22×C4D4×D4711yescharacteristic
642C22×C4D4×D4711yescharacteristic
643C22×C4D4×D4711yescharacteristic
644C22×C4D4×D4711yescharacteristic
645C22×C4#1062535211yescharacteristic
646C22×C4#1062535211yescharacteristic
647C22×C4C2×C22⋊D4711yescharacteristic
648C22×C4C2×C22⋊D4711yescharacteristic
649C22×C4C23×D4711yescharacteristic
650M16—22no—
651M16—22no—
652M16—22no—
653M16—22no—
654M16—22no—
655M16—22no—
656M16—41no—
657M16—41no—
658M16—9416no—
659M16—942no—
660M16—942no—
661M16—942no—
662M16—942no—
663M16—942no—
664M16—942no—
665M16—1881no—
666M16—1881no—
667C2×C8—22no—
668C2×C8—22no—
669C2×C8—22no—
670C2×C8—41no—
671C2×C8—41no—
672C2×C8—474no—
673C2×C8—9416no—
674C2×C8—942no—
675C2×C8—942no—
676C2×C8—942no—
677C2×C8—1881no—
678C2×C8—1881no—
679C2×C8C2×C22⋊D4714yes—
680C4⋊C4—948no—
681C4⋊C4—942no—
682C4⋊C4—942no—
683C22⋊C4—474no—
684C22⋊C4—948no—
685C22⋊C4—948no—
686C22⋊C4—942no—
687C42—942no—
688C42—942no—
689C23—22no—
690C23—22no—
691C23—22no—
692C23—81no—
693C23—82no—
694C23—474no—
695C23—942no—
696C23—942no—
697C23—3762no—
698C23C22⋊C4×D4711yescharacteristic
699C23C22⋊C4×D4711yescharacteristic
700C23(C22⋊D47)⋊C411yescharacteristic
701C23(C22⋊D47)⋊C411yescharacteristic
702C23C4×C22⋊D4711yescharacteristic
703C23C4×C22⋊D4711yescharacteristic
704C23C22×C4×D4711yescharacteristic
705Q8—41no—
706Q8—41no—
707Q8—41no—
708Q8—41no—
709Q8—942no—
710Q8—942no—
711Q8—942no—
712Q8—942no—
713D4—42no—
714D4—42no—
715D4—42no—
716D4—42no—
717D4—41no—
718D4—41no—
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—22no—
732C2×C4—22no—
733C2×C4—42no—
734C2×C4—42no—
735C2×C4—42no—
736C2×C4—42no—
737C2×C4—474no—
738C2×C4—942no—
739C2×C4—942no—
740C2×C4—944no—
741C2×C4—944no—
742C2×C4—944no—
743C2×C4—944no—
744C2×C4—944no—
745C2×C4—3762no—
746C2×C4C22⋊C4×D4711yescharacteristic
747C2×C4C22⋊C4×D4711yescharacteristic
748C2×C4(C22⋊D47)⋊C411yescharacteristic
749C2×C4(C22⋊D47)⋊C411yescharacteristic
750C2×C4C4×C22⋊D4711yescharacteristic
751C2×C4C4×C22⋊D4711yescharacteristic
752C2×C4#1309399211yescharacteristic
753C2×C4#1309399211yescharacteristic
754C2×C4#1309399211yescharacteristic
755C2×C4#1309399211yescharacteristic
756C2×C4#1309399511yescharacteristic
757C2×C4#1309399511yescharacteristic
758C2×C4#1309399511yescharacteristic
759C2×C4#1309399511yescharacteristic
760C2×C4#1309399711yescharacteristic
761C2×C4#1309399711yescharacteristic
762C2×C4#1309399711yescharacteristic
763C2×C4#1309399711yescharacteristic
764C2×C4#1309400611yescharacteristic
765C2×C4#1309400611yescharacteristic
766C2×C4#1309400611yescharacteristic
767C2×C4#1309400611yescharacteristic
768C2×C4C2×D4×D4711yescharacteristic
769C2×C4C2×D4×D4711yescharacteristic
770C2×C4C2×D4×D4711yescharacteristic
771C2×C4C22×C22⋊D4711yescharacteristic
772C2×C4C2×#1062535211yescharacteristic
773C2×C4C2×#1062535011yescharacteristic
774C8—24no—
775C8—42no—
776C8—944no—
777C8—1882no—
778C22—41no—
779C22—41no—
780C22—41no—
781C22—41no—
782C22—41no—
783C22—41no—
784C22—41no—
785C22—44no—
786C22—44no—
787C22—44no—
788C22—42no—
789C22—944no—
790C22—3762no—
791C22—1884no—
792C22—1884no—
793C22#1568899911yescharacteristic
794C22#1568899911yescharacteristic
795C22#1568899911yescharacteristic
796C22#1568899911yescharacteristic
797C22C2×C22⋊C4×D4711yescharacteristic
798C22C2×(C22⋊D47)⋊C411yescharacteristic
799C22C2×C4×C22⋊D4711yescharacteristic
800C4—42no—
801C4—944no—
802C4—1884no—
803C4#1568899911yescharacteristic
804C4#1568899911yescharacteristic
805C4#1568899911yescharacteristic
806C4#1568899911yescharacteristic
807C4C2×#1309399211yescharacteristic
808C4C2×#1309399511yescharacteristic
809C4C2×#1309399711yescharacteristic
810C4C2×#1309400611yescharacteristic
811C2—21no—
812C2—21no—
813C2—21no—
814C2—21no—
815C2—21no—
816C2—21no—
817C2—21no—
818C2—82no—
819C2—1884no—
820C2C2×#1568899911yescharacteristic
subgroupG/H
centerC4C2×#13093992
commutatorC23×C47C23×C4
FrattiniC22×C4C23×D47
FittingC47×#2879C2
socleC2×C47C2×#386
prime radical#20256717C2
cosocleC22×C4×C47C24
hypercenter#2879D47
hypocenterC47#20964
LCSG ▷ C23×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C4 ◁ C23×C4 ◁ #2879

Complements

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

NH ≅ G/Ntype
1. C2×#15689889C2semidirect
3. C2×#15689105C2semidirect
4. #20251833C2semidirect
5. #20243803C2semidirect
6. C2×#15688895C2semidirect
7. C2×#15688894C2semidirect
8. C47×#2879C2semidirect
35. #15689087C22semidirect
36. #15688895C22semidirect
37. #15688894C22semidirect
43. C47×#407C22semidirect
73. C2×#10625329D4semidirect
80. C22×C47⋊C8D4semidirect
132. C2×M16×C47D4semidirect
136. C22×C8×C47D4semidirect
405. #2879D47semidirect
451. #407C2×D47semidirect
454. C47#20964semidirect
516. C2×M16C22⋊D47semidirect
523. C22×C8C22⋊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×#156891052
#202518332
#202438032
C2×#156888952
C2×#156888942
C47×#28792
#2096447