Finite Group Databasebeta

← #25065009

Subgroups — #25065009

Order 11008.

994 conjugacy classes of subgroups.

The subgroup lattice has 680 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19147892C211yesmaximal, characteristic
2#19143227C211yesmaximal, characteristic, complemented
3C2×#14582951C211yesmaximal, characteristic, complemented
4#19133304C212yesmaximal, complemented
5#19133299C212yesmaximal, complemented
6#19133285C211yesmaximal, characteristic, complemented
7#19133273C211yesmaximal, characteristic, complemented
8#19133270C211yesmaximal, characteristic, complemented
9#19133258C212yesmaximal, complemented
10#19133256C212yesmaximal, complemented
11C43×#1550C211yesmaximal, characteristic, complemented
12#14583454C2211yescharacteristic
13#14583454C2211yescharacteristic
14#14583450C2211yescharacteristic
15#14583450C2211yescharacteristic
16#14583449C2211yescharacteristic
17#14583436—21no—
18#14583436C412yes—
19#14583435—21no—
20#14583435C412yes—
21#14583434—21no—
22#14583434—21no—
23#14583412—21no—
24#14583412C412yes—
25#14583411—21no—
26C4×#10621902—21no—
27C4×#10621902C412yes—
28#14583367—21no—
29C2×C42×D43C2211yescharacteristic
30#14582955—21no—
31#14582955C2212yes—
32#14582951—21no—
33#14582951—21no—
34#14582951—21no—
35#14582951C2212yes—
36#14582951C2212yes—
37#14582951C2212yes—
38#14582923C2211yescharacteristic
39C2×C4⋊(C43⋊C8)C2211yescharacteristic
40#14582862—21no—
41C2×(C2×D43)⋊C8—21no—
42M16×Dic43—21no—
43C2×C8×Dic43—21no—
44#14582648C2212yescomplemented
45#14582646C2212yescomplemented
46#14582645C2212yescomplemented
47#14582644C2212yescomplemented
48#14582642C2212yescomplemented
49#14582642C2212yescomplemented
50C43×#533C2211yescharacteristic
51C43×#423C2211yescharacteristic
52C2×C4⋊C8×C43C2211yescharacteristic
53C43×#333C2212yescomplemented
54C43×#332C2212yescomplemented
55C2×#10621902—21no—
56C2×#10621902C2×C412yes—
57C2×#10621898—21no—
58C22×C4×D43C2×C411yescharacteristic
59C22×C4×D43D411yescharacteristic
60C22×C4×D43D411yescharacteristic
61C2×#10621877—21no—
62C22×C43⋊C8—21no—
63#13063325C2311yescharacteristic
64#13063322C2311yescharacteristic
65#13063320—22no—
66#13063320—22no—
67#13063316—21no—
68#13063316C2×C412yes—
69#13063314—21no—
70#13063314C2×C412yes—
71#13063313—21no—
72#13063310—22no—
73#13063310—22no—
74#13063309—22no—
75#13063305—21no—
76#13063305—21no—
77#13063301—21no—
78#13063301C2×C412yes—
79#13063300—21no—
80#13063300—21no—
81#13063300—21no—
82#13063300C2×C412yes—
83#13063299—21no—
84#13063299C2×C412yes—
85#13063295—22no—
86Q8×Dic43—21no—
87Q8×Dic43C2×C412yes—
88#13063290—21no—
89#13063290—21no—
90C4×D172—22no—
91C4×D172—22no—
92C4×D172—21no—
93C4×D172C2×C412yes—
94#13063287—22no—
95#13063287—22no—
96#13063287—21no—
97#13063287—21no—
98#13063287—21no—
99#13063287C2×C412yes—
100(C22⋊D43)⋊C4—22no—
101(C22⋊D43)⋊C4—22no—
102#13063283—21no—
103#13063283—22no—
104#13063283—22no—
105#13063283C2×C412yes—
106#13063282—22no—
107C2×C4×Dic43C2×C411yescharacteristic
108C2×C4×Dic43D411yescharacteristic
109C2×C4×Dic43D411yescharacteristic
110C42×D43—22no—
111C42×D43C2×C411yescharacteristic
112C42×D43C2×C411yescharacteristic
113C42×D43D411yescharacteristic
114C42×D43D411yescharacteristic
115C42×D43D411yescharacteristic
116C42×D43D411yescharacteristic
117C42×D43C2311yescharacteristic
118C42×D43C2311yescharacteristic
119C4⋊(C43⋊C8)—21no—
120C4⋊(C43⋊C8)—21no—
121C4⋊(C43⋊C8)C2312yes—
122C4⋊(C43⋊C8)C2312yes—
123(C2×D43)⋊C8—22no—
124(C2×D43)⋊C8—22no—
125(C2×D43)⋊C8—22no—
126(C2×D43)⋊C8—22no—
127#13063235—22no—
128C8×Dic43—22no—
129C8×Dic43—22no—
130C8×Dic43—22no—
131C2×M16×C43—21no—
132C22×C8×C43—21no—
133C4⋊Q8×C43C2311yescharacteristic
134C4⋊Q8×C43C2311yescharacteristic
135#125×C43—21no—
136C22⋊Q8×C43—21no—
137C22⋊Q8×C43C2×C412yes—
138C4×Q8×C43—21no—
139C4×Q8×C43C2×C412yes—
140#117×C43—21no—
141C2×C42×C43C2311yescharacteristic
142C4⋊C8×C43—21no—
143C4⋊C8×C43—21no—
144C4⋊C8×C43C2312yes—
145C4⋊C8×C43C2312yes—
146C23×D43C22⋊C411yescharacteristic
147C2×Q8×C43—21no—
148C2×Q8×C43C22×C412yes—
149C22×C4×C43C22×C411yescharacteristic
150C22×C4×C43C2×D411yescharacteristic
151C22×C4×C43C2×D411yescharacteristic
152C2×C22⋊D43—22no—
153C22×Dic43C22⋊C411yescharacteristic
154C22×Dic43C22⋊C411yescharacteristic
155C22×Dic43C22⋊C411yescharacteristic
156#10621902—42no—
157#10621902—42no—
158#10621902—44no—
159#10621898—42no—
160#10621898—42no—
161C2×D172—21no—
162C2×D172—21no—
163C2×D172—22no—
164C2×D172—22no—
165C2×D172C22×C412yes—
166C2×C4×D43—22no—
167C2×C4×D43—22no—
168C2×C4×D43—22no—
169C2×C4×D43—22no—
170C2×C4×D43—22no—
171C2×C4×D43—42no—
172C2×C4×D43—41no—
173C2×C4×D43—41no—
174C2×C4×D43C22⋊C411yescharacteristic
175C2×C4×D43C22⋊C411yescharacteristic
176C2×C4×D43C22⋊C411yescharacteristic
177C2×C4×D43C22⋊C411yescharacteristic
178C2×C4×D43C22⋊C411yescharacteristic
179C2×C4×D43C22⋊C411yescharacteristic
180C2×C4×D43C22×C411yescharacteristic
181C2×C4×D43C22×C411yescharacteristic
182C2×C4×D43C2×D411yescharacteristic
183C2×C4×D43C2×D411yescharacteristic
184C2×C4×D43C2×D411yescharacteristic
185C2×C4×D43C2×D411yescharacteristic
186C2×Dic86—21no—
187M16×C43—42no—
188C2×C8×C43—22no—
189C2×C8×C43—22no—
190C2×C8×C43—42no—
191C4⋊C4×C43—22no—
192C4⋊C4×C43—22no—
193C4⋊C4×C43—21no—
194C4⋊C4×C43—21no—
195C4⋊C4×C43—21no—
196C4⋊C4×C43C22×C412yes—
197C22⋊C4×C43—22no—
198C42×C43—22no—
199C42×C43C22×C411yescharacteristic
200C42×C43C2×D411yescharacteristic
201C42×C43C2×D411yescharacteristic
202C42×C43C2411yescharacteristic
203(C2×D43)⋊C4—22no—
204(C2×D43)⋊C4—22no—
205(C2×D43)⋊C4—22no—
206(C2×D43)⋊C4—22no—
207(C2×D43)⋊C4—22no—
208(C2×D43)⋊C4—22no—
209(C2×D43)⋊C4—22no—
210(C2×D43)⋊C4—22no—
211C4⋊Dic43—21no—
212C4⋊Dic43—22no—
213C4⋊Dic43—22no—
214C4⋊Dic43C22×C412yes—
215Dic43⋊C4—22no—
216Dic43⋊C4—22no—
217C4×Dic43—22no—
218C4×Dic43—22no—
219C4×Dic43C22⋊C411yescharacteristic
220C4×Dic43C22⋊C411yescharacteristic
221C4×Dic43C22⋊C411yescharacteristic
222C4×Dic43C22⋊C411yescharacteristic
223C4×Dic43C22⋊C411yescharacteristic
224C4×Dic43C22⋊C411yescharacteristic
225C4×Dic43C22×C411yescharacteristic
226C4×Dic43C22×C411yescharacteristic
227C4×Dic43C2×D411yescharacteristic
228C4×Dic43C2×D411yescharacteristic
229C4×Dic43C2×D411yescharacteristic
230C4×Dic43C2×D411yescharacteristic
231#10621877—42no—
232C2×C43⋊C8—22no—
233C2×C43⋊C8—22no—
234C2×C43⋊C8—42no—
235C23×C43C2×C22⋊C411yescharacteristic
236C22×D43—22no—
237C22×D43—22no—
238C22×D43—41no—
239C22×D43—41no—
240C22×D43C2×C22⋊C411yescharacteristic
241C22×D43C2×C22⋊C411yescharacteristic
242Q8×C43—42no—
243Q8×C43—41no—
244Q8×C43—41no—
245C2×C4×C43—21no—
246C2×C4×C43—21no—
247C2×C4×C43—22no—
248C2×C4×C43—22no—
249C2×C4×C43—41no—
250C2×C4×C43C2×C22⋊C411yescharacteristic
251C2×C4×C43C2×C22⋊C411yescharacteristic
252C2×C4×C43C2×C22⋊C411yescharacteristic
253C2×C4×C43#13512yes—
254C2×C4×C43#13512yes—
255C2×C4×C43C23×C411yescharacteristic
256C2×C4×C43C22×D411yescharacteristic
257C2×C4×C43C22×D411yescharacteristic
258C22⋊D43—44no—
259C2×Dic43—22no—
260C2×Dic43—22no—
261C2×Dic43—22no—
262C2×Dic43—41no—
263C2×Dic43C2×C22⋊C411yescharacteristic
264C2×Dic43C2×C22⋊C411yescharacteristic
265C2×Dic43C2×C22⋊C411yescharacteristic
266C2×Dic43C2×C22⋊C411yescharacteristic
267C2×Dic43C2×C22⋊C411yescharacteristic
268C2×Dic43C2×C22⋊C411yescharacteristic
269D172—42no—
270D172—44no—
271D172—44no—
272D172—41no—
273D172—41no—
274D172—41no—
275D172—41no—
276C4×D43—21no—
277C4×D43—21no—
278C4×D43—21no—
279C4×D43—21no—
280C4×D43—21no—
281C4×D43—21no—
282C4×D43—21no—
283C4×D43—21no—
284C4×D43—22no—
285C4×D43—22no—
286C4×D43—22no—
287C4×D43—22no—
288C4×D43—41no—
289C4×D43—41no—
290C4×D43—41no—
291C4×D43—41no—
292C4×D43—44no—
293C4×D43—44no—
294C4×D43—44no—
295Dic86—41no—
296Dic86—41no—
297C8×C43—42no—
298C8×C43—42no—
299C43⋊C8—42no—
300C43⋊C8—42no—
301#17716—431nomaximal, Sylow
302C22×C43—21no—
303C22×C43—21no—
304C22×C43#41612yes—
305C22×C43C22×C22⋊C411yescharacteristic
306C2×D43—21no—
307C2×D43—21no—
308C2×D43—21no—
309C2×D43—21no—
310C2×D43—21no—
311C2×D43—21no—
312C2×D43—44no—
313C2×D43—42no—
314C2×D43—42no—
315C2×D43—42no—
316C4×C43—21no—
317C4×C43—21no—
318C4×C43—21no—
319C4×C43—42no—
320C4×C43—42no—
321C4×C43#41612yes—
322C4×C43C2×#13511yescharacteristic
323C4×C43C2×#13511yescharacteristic
324C4×C43#57511yescharacteristic
325C4×C43#57511yescharacteristic
326Dic43—21no—
327Dic43—21no—
328Dic43—21no—
329Dic43—21no—
330Dic43—21no—
331Dic43—42no—
332Dic43#41312yes—
333#3444—431no—
334#2920—431no—
335C2×#431—431no—
336#1554—432no—
337#1553—432no—
338#1550—431no—
339#1550D4311yescharacteristic, complemented
340#1547—431no—
341#1547—431no—
342#1544—432no—
343#1543—432no—
344C2×C43—22no—
345C2×C43C2×#41311yescharacteristic
346C2×C43C2×#41611yescharacteristic
347C2×C43#289611yescharacteristic
348D43—41no—
349D43—41no—
350D43—82no—
351#533—431no—
352#533—431no—
353#533C2×D4311yescharacteristic
354#532—431no—
355#532—431no—
356#532—431no—
357#529—432no—
358#529—432no—
359#529—861no—
360#529—861no—
361#529—861no—
362#529—861no—
363#525—432no—
364#525—861no—
365#525—861no—
366C4×#41—432no—
367C4×#41—861no—
368C4×#41—861no—
369C22×C42—431no—
370#432—432no—
371#432—861no—
372#431—432no—
373#431—432no—
374#431—432no—
375#431—861no—
376#431—861no—
377#431—861no—
378#423—431no—
379#423C2×D4311yescharacteristic
380C2×C4⋊C8—431no—
381C2×C4⋊C8C2×D4311yescharacteristic
382#407—861no—
383C2×C22⋊C8—861no—
384C4×M16—861no—
385C2×C4×C8—861no—
386#333—432no—
387#333C2×D4312yescomplemented
388#332—432no—
389#332—432no—
390#332—432no—
391#332C2×D4312yescomplemented
392#331—432no—
393#331—432no—
394C43#1771611yescharacteristic, complemented, Sylow
395C2×#41—432no—
396C2×#41—861no—
397C2×#41—861no—
398C23×C4—431no—
399C23×C4—431no—
400C23×C4—431no—
401C2×M16—21no—
402C2×M16—861no—
403C22×C8—21no—
404C22×C8—861no—
405C4⋊Q8—431no—
406C4⋊Q8C22×D4311yescharacteristic
407C4⋊Q8C22×D4311yescharacteristic
408#127—431no—
409#126—862no—
410#126—862no—
411#125—21no—
412#125—432no—
413#125—861no—
414#124—432no—
415#124—861no—
416#124—861no—
417#123—862no—
418#123—862no—
419#123—862no—
420C22⋊Q8—21no—
421C22⋊Q8—432no—
422C22⋊Q8—861no—
423C22⋊Q8—861no—
424C22⋊Q8—861no—
425C22⋊Q8C4×D4312yes—
426#121—432no—
427#121—432no—
428#121—861no—
429#121—861no—
430#121—861no—
431#121—861no—
432#120—862no—
433C4×Q8—21no—
434C4×Q8—432no—
435C4×Q8—861no—
436C4×Q8—861no—
437C4×Q8—861no—
438C4×Q8C4×D4312yes—
439C4×D4—432no—
440C4×D4—432no—
441C4×D4—862no—
442C4×D4—862no—
443C4×D4—861no—
444C4×D4—861no—
445C4×D4—861no—
446C4×D4—862no—
447C4×D4—862no—
448C4×D4—862no—
449C4×D4—862no—
450C4×D4—861no—
451#117—21no—
452#117—432no—
453#117—862no—
454#117—862no—
455#117—862no—
456#117—861no—
457C2×C42—431no—
458C2×C42—431no—
459C2×C42—431no—
460C2×C42—431no—
461C2×C42—431no—
462C2×C42—431no—
463C2×C42—431no—
464C2×C42—431no—
465C2×C42—431no—
466C2×C42—431no—
467C2×C42—431no—
468C2×C42—862no—
469C2×C42C22×D4311yescharacteristic
470C4⋊C8—21no—
471C4⋊C8—21no—
472C4⋊C8—432no—
473C4⋊C8—432no—
474C4⋊C8—861no—
475C4⋊C8—861no—
476C4⋊C8C22×D4312yes—
477C4⋊C8C22×D4312yes—
478C22⋊C8—862no—
479C22⋊C8—862no—
480C22⋊C8—862no—
481C22⋊C8—862no—
482#97—862no—
483C4×C8—862no—
484C4×C8—862no—
485C4×C8—862no—
486C24—431no—
487#41—1722no—
488#41—1722no—
489#41—1724no—
490#41—1722no—
491#41—1722no—
492C2×Q8—21no—
493C2×Q8—861no—
494C2×Q8C2×C4×D4312yes—
495C2×D4—432no—
496C2×D4—862no—
497C2×D4—862no—
498C2×D4—862no—
499C2×D4—861no—
500C2×D4—861no—
501C22×C4—431no—
502C22×C4—431no—
503C22×C4—431no—
504C22×C4—431no—
505C22×C4—431no—
506C22×C4—431no—
507C22×C4—431no—
508C22×C4—431no—
509C22×C4—431no—
510C22×C4—431no—
511C22×C4—431no—
512C22×C4—431no—
513C22×C4—431no—
514C22×C4—431no—
515C22×C4—431no—
516C22×C4—862no—
517C22×C4—862no—
518C22×C4—862no—
519C22×C4—862no—
520C22×C4—862no—
521C22×C4—1721no—
522C22×C4—1721no—
523C22×C4—1722no—
524C22×C4C2×C4×D4311yescharacteristic
525C22×C4D4×D4311yescharacteristic
526C22×C4D4×D4311yescharacteristic
527M16—42no—
528M16—1722no—
529C2×C8—22no—
530C2×C8—22no—
531C2×C8—42no—
532C2×C8—862no—
533C2×C8—862no—
534C2×C8—1722no—
535C4⋊C4—22no—
536C4⋊C4—22no—
537C4⋊C4—21no—
538C4⋊C4—21no—
539C4⋊C4—21no—
540C4⋊C4—432no—
541C4⋊C4—862no—
542C4⋊C4—862no—
543C4⋊C4—862no—
544C4⋊C4—862no—
545C4⋊C4—861no—
546C4⋊C4C2×C4×D4312yes—
547C22⋊C4—22no—
548C22⋊C4—862no—
549C22⋊C4—862no—
550C22⋊C4—862no—
551C22⋊C4—862no—
552C22⋊C4—862no—
553C22⋊C4—862no—
554C22⋊C4—862no—
555C22⋊C4—862no—
556C42—22no—
557C42—431no—
558C42—431no—
559C42—431no—
560C42—431no—
561C42—431no—
562C42—431no—
563C42—431no—
564C42—431no—
565C42—431no—
566C42—431no—
567C42—431no—
568C42—431no—
569C42—862no—
570C42—862no—
571C42C2×C4×D4311yescharacteristic
572C42D4×D4311yescharacteristic
573C42D4×D4311yescharacteristic
574C42C23×D4311yescharacteristic
575C23—431no—
576C23—431no—
577C23—862no—
578C23—862no—
579C23—1721no—
580C23—1721no—
581C23C22⋊C4×D4311yescharacteristic
582Q8—42no—
583Q8—41no—
584Q8—41no—
585Q8—1721no—
586Q8—1721no—
587D4—1722no—
588D4—1724no—
589D4—1724no—
590D4—1724no—
591D4—1721no—
592D4—1721no—
593D4—1721no—
594D4—1721no—
595C2×C4—21no—
596C2×C4—21no—
597C2×C4—22no—
598C2×C4—22no—
599C2×C4—41no—
600C2×C4—431no—
601C2×C4—431no—
602C2×C4—431no—
603C2×C4—431no—
604C2×C4—431no—
605C2×C4—431no—
606C2×C4—862no—
607C2×C4—862no—
608C2×C4—862no—
609C2×C4—862no—
610C2×C4—862no—
611C2×C4—862no—
612C2×C4—861no—
613C2×C4—861no—
614C2×C4—861no—
615C2×C4—861no—
616C2×C4—861no—
617C2×C4—861no—
618C2×C4—861no—
619C2×C4—861no—
620C2×C4—862no—
621C2×C4—1721no—
622C2×C4—1721no—
623C2×C4—1721no—
624C2×C4—1721no—
625C2×C4—1724no—
626C2×C4—1724no—
627C2×C4—1721no—
628C2×C4—1724no—
629C2×C4C22⋊C4×D4311yescharacteristic
630C2×C4C22⋊C4×D4311yescharacteristic
631C2×C4C22⋊C4×D4311yescharacteristic
632C2×C4#1306334612yes—
633C2×C4#1306334812yes—
634C2×C4C22×C4×D4311yescharacteristic
635C2×C4C2×D4×D4311yescharacteristic
636C2×C4C2×D4×D4311yescharacteristic
637C8—42no—
638C8—42no—
639C8—1722no—
640C8—1722no—
641C22—21no—
642C22—21no—
643C22—861no—
644C22—861no—
645C22—861no—
646C22—861no—
647C22—861no—
648C22—861no—
649C22—1724no—
650C22—1722no—
651C22—1722no—
652C22—1722no—
653C22#1458289412yes—
654C22C2×C22⋊C4×D4311yescharacteristic
655C4—21no—
656C4—21no—
657C4—21no—
658C4—42no—
659C4—42no—
660C4—432no—
661C4—861no—
662C4—861no—
663C4—861no—
664C4—861no—
665C4—861no—
666C4—1722no—
667C4#1458289412yes—
668C4C2×#1306334611yescharacteristic
669C4C2×#1306334811yescharacteristic
670C4#1458369511yescharacteristic
671C4#1458369811yescharacteristic
672C2—22no—
673C2—3442no—
674C2—1721no—
675C2—1721no—
676C2#413×D4311yescharacteristic
677C2C2×#1458289411yescharacteristic
678C2#1914311111yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D43
commutatorC2×C4×C43C23×C4
FrattiniC42C23×D43
FittingC43×#1550C2
socleC22×C43C22×C22⋊C4
prime radical#19147892C2
cosocleC42×C43C24
hypercenter#1550D43
hypocenterC43#17716
LCSG ▷ C2×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1550

Complements

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

NH ≅ G/Ntype
2. #19143227C2semidirect
3. C2×#14582951C2semidirect
4. #19133304C2semidirect
5. #19133299C2semidirect
6. #19133285C2semidirect
7. #19133273C2semidirect
8. #19133270C2semidirect
9. #19133258C2semidirect
10. #19133256C2semidirect
11. C43×#1550C2semidirect
44. #14582648C22semidirect
45. #14582646C22semidirect
46. #14582645C22semidirect
47. #14582644C22semidirect
48. #14582642C22semidirect
49. #14582642C22semidirect
53. C43×#333C22semidirect
54. C43×#332C22semidirect
339. #1550D43semidirect
387. #333C2×D43semidirect
391. #332C2×D43semidirect
394. C43#17716semidirect

Maximal subgroups

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

subgroupindex
#191478922
#191432272
C2×#145829512
#191333042
#191332992
#191332852
#191332732
#191332702
#191332582
#191332562
C43×#15502
#1771643