Finite Group Databasebeta

← #25106608

Subgroups — #25106608

Order 11008.

1106 conjugacy classes of subgroups.

The subgroup lattice has 686 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19147892C211yesmaximal, characteristic
2#19143226C211yesmaximal, characteristic, complemented
3#19136999C211yesmaximal, characteristic, complemented
4#19135540C211yesmaximal, characteristic, complemented
5#19135514C211yesmaximal, characteristic, complemented
6#19135513C211yesmaximal, characteristic, complemented
7#19135042C214yesmaximal, complemented
8#19134614C214yesmaximal, complemented
9C43×#1986C211yesmaximal, characteristic, complemented
10#14583454C411yescharacteristic, complemented
11#14583454C411yescharacteristic, complemented
12#14583450C411yescharacteristic, complemented
13#14583450C411yescharacteristic, complemented
14#14583449C2211yescharacteristic
15#14583436—21no—
16#14583436—21no—
17#14583435—21no—
18#14583435—21no—
19#14583434C412yescomplemented
20#14583434C412yescomplemented
21#14583412—21no—
22#14583412—21no—
23#14583411C2212yes—
24C4×#10621902—21no—
25C4×#10621902—21no—
26#14583367C2212yes—
27C2×#13063282C2212yes—
28C2×C42×D43C2211yescharacteristic
29#14582954—21no—
30#14582954—21no—
31#14582950—21no—
32#14582950—21no—
33#14582922C2212yes—
34C2×#13063253C2214yes—
35C2×#13063251C2214yes—
36#14582862C2212yes—
37C4×#10621877C2211yescharacteristic
38#14582768—21no—
39#14582763—21no—
40#14582758—21no—
41#14582756—21no—
42C4×Dic43⋊C4C2212yes—
43C4×C4⋊Dic43C2211yescharacteristic
44#14582658C2214yes—
45C43×#533C2211yescharacteristic
46C4×M16×C43C2211yescharacteristic
47C4×C4⋊C4×C43C2211yescharacteristic
48C43×#339C2214yes—
49C2×#10621902—21no—
50C2×#10621902—21no—
51C2×#10621898C2312yes—
52C22×C4×D43D411yescharacteristic
53C22×C4×D43D411yescharacteristic
54C22×C4×D43C2311yescharacteristic
55C2×#10621877C2312yes—
56#13063325C2×C411yescharacteristic
57#13063322C2×C411yescharacteristic
58#13063320—22no—
59#13063320—22no—
60#13063316—21no—
61#13063316—21no—
62#13063314—21no—
63#13063314—21no—
64#13063313C2×C412yes—
65#13063310—22no—
66#13063310—22no—
67#13063309—22no—
68#13063305C2×C412yes—
69#13063305C2×C412yes—
70#13063301—21no—
71#13063301—21no—
72#13063300—21no—
73#13063300—21no—
74#13063300C2×C412yes—
75#13063300C2×C412yes—
76#13063299—21no—
77#13063299—21no—
78#13063295—22no—
79Q8×Dic43—21no—
80Q8×Dic43—21no—
81#13063290C2×C412yes—
82#13063290C2×C412yes—
83C4×D172—22no—
84C4×D172—22no—
85C4×D172—21no—
86C4×D172—21no—
87#13063287—22no—
88#13063287—22no—
89#13063287—21no—
90#13063287—21no—
91#13063287C2×C412yes—
92#13063287C2×C412yes—
93(C22⋊D43)⋊C4—22no—
94(C22⋊D43)⋊C4—22no—
95#13063283—21no—
96#13063283—21no—
97#13063283—22no—
98#13063283—22no—
99#13063282—22no—
100#13063282—44no—
101C2×C4⋊Dic43—21no—
102C2×Dic43⋊C4—22no—
103C2×Dic43⋊C4—22no—
104C2×(C2×D43)⋊C4—22no—
105C2×C4×Dic43D411yescharacteristic
106C2×C4×Dic43D411yescharacteristic
107C2×C4×Dic43C2312yes—
108C2×C4×Dic43C2311yescharacteristic
109C42×D43—22no—
110C42×D43C2×C411yescharacteristic
111C42×D43C2×C411yescharacteristic
112C42×D43C2×C411yescharacteristic
113C42×D43C2×C411yescharacteristic
114C42×D43D411yescharacteristic
115C42×D43D411yescharacteristic
116C42×D43D411yescharacteristic
117C42×D43D411yescharacteristic
118Dic43⋊C8—22no—
119Dic43⋊C8—22no—
120#13063253—44no—
121#13063251—44no—
122(C2×D43)⋊C8—22no—
123(C2×D43)⋊C8—22no—
124#13063236—21no—
125C4×C43⋊C8—21no—
126C43⋊#95—21no—
127C43⋊#95—22no—
128C2×M16×C43C2312yes—
129C4⋊Q8×C43C2×C411yescharacteristic
130C4⋊Q8×C43C2×C411yescharacteristic
131#125×C43C2×C412yes—
132C22⋊Q8×C43—21no—
133C22⋊Q8×C43—21no—
134C4×Q8×C43—21no—
135C4×Q8×C43—21no—
136#117×C43C2312yes—
137C2×C4⋊C4×C43—21no—
138C2×C42×C43C2312yes—
139C2×C42×C43C2311yescharacteristic
140#97×C43—21no—
141C4×C8×C43—21no—
142#95×C43—21no—
143C23×D43C2×D411yescharacteristic
144C2×Q8×C43—21no—
145C2×Q8×C43—21no—
146C22×C4×C43—22no—
147C22×C4×C43C2×D411yescharacteristic
148C22×C4×C43C2×D411yescharacteristic
149C22×C4×C43C2411yescharacteristic
150C2×C22⋊D43—22no—
151C22×Dic43—22no—
152C22×Dic43C2×D411yescharacteristic
153C22×Dic43C2×D411yescharacteristic
154C22×Dic43C2×D411yescharacteristic
155#10621902—44no—
156#10621902—44no—
157#10621898—24no—
158#10621898—24no—
159C2×D172—21no—
160C2×D172—21no—
161C2×D172—22no—
162C2×D172—22no—
163C2×D172C22×C412yes—
164C2×C4×D43—22no—
165C2×C4×D43—22no—
166C2×C4×D43—22no—
167C2×C4×D43—22no—
168C2×C4×D43—22no—
169C2×C4×D43—42no—
170C2×C4×D43—42no—
171C2×C4×D43C22⋊C411yescharacteristic
172C2×C4×D43C22⋊C411yescharacteristic
173C2×C4×D43C22⋊C411yescharacteristic
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×D43C2×D411yescharacteristic
182C2×C4×D43C2×D411yescharacteristic
183C2×Dic86C22×C412yes—
184M16×C43—22no—
185M16×C43—22no—
186C2×C8×C43—22no—
187C4⋊C4×C43—22no—
188C4⋊C4×C43—22no—
189C4⋊C4×C43—21no—
190C4⋊C4×C43—21no—
191C4⋊C4×C43—42no—
192C4⋊C4×C43C22×C412yes—
193C4⋊C4×C43C22×C412yes—
194C22⋊C4×C43—22no—
195C42×C43—22no—
196C42×C43—24no—
197C42×C43C22×C411yescharacteristic
198C42×C43C22×C411yescharacteristic
199C42×C43C2×D411yescharacteristic
200C42×C43C2×D411yescharacteristic
201(C2×D43)⋊C4—22no—
202(C2×D43)⋊C4—22no—
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—44no—
210C4⋊Dic43—21no—
211C4⋊Dic43—21no—
212C4⋊Dic43—22no—
213C4⋊Dic43—22no—
214C4⋊Dic43—42no—
215Dic43⋊C4—22no—
216Dic43⋊C4—22no—
217Dic43⋊C4—44no—
218Dic43⋊C4—44no—
219C4×Dic43—22no—
220C4×Dic43—22no—
221C4×Dic43—24no—
222C4×Dic43C22⋊C411yescharacteristic
223C4×Dic43C22⋊C411yescharacteristic
224C4×Dic43C22⋊C411yescharacteristic
225C4×Dic43C22⋊C411yescharacteristic
226C4×Dic43C22⋊C411yescharacteristic
227C4×Dic43C22⋊C411yescharacteristic
228C4×Dic43C22⋊C411yescharacteristic
229C4×Dic43C22⋊C411yescharacteristic
230C4×Dic43C22×C411yescharacteristic
231C4×Dic43C22×C411yescharacteristic
232C4×Dic43C2×D411yescharacteristic
233C4×Dic43C2×D411yescharacteristic
234#10621877—22no—
235#10621877—22no—
236C2×C43⋊C8—22no—
237C23×C43C22×D411yescharacteristic
238C22×D43—21no—
239C22×D43—21no—
240C22×D43—22no—
241C22×D43—41no—
242C22×D43—41no—
243C22×D43C2×C22⋊C411yescharacteristic
244C22×D43C2×C22⋊C411yescharacteristic
245Q8×C43—42no—
246Q8×C43—42no—
247C2×C4×C43—22no—
248C2×C4×C43—22no—
249C2×C4×C43—22no—
250C2×C4×C43—41no—
251C2×C4×C43—42no—
252C2×C4×C43—42no—
253C2×C4×C43—42no—
254C2×C4×C43C2×C22⋊C411yescharacteristic
255C2×C4×C43C2×C22⋊C411yescharacteristic
256C2×C4×C43C2×C22⋊C411yescharacteristic
257C2×C4×C43C2×C22⋊C411yescharacteristic
258C2×C4×C43C23×C411yescharacteristic
259C2×C4×C43C22×D411yescharacteristic
260C2×C4×C43H(5,𝔽2)12yes—
261C2×C4×C432−1+412yes—
262C22⋊D43—42no—
263C22⋊D43—42no—
264C2×Dic43—21no—
265C2×Dic43—21no—
266C2×Dic43—22no—
267C2×Dic43—22no—
268C2×Dic43—41no—
269C2×Dic43—42no—
270C2×Dic43—42no—
271C2×Dic43—42no—
272C2×Dic43C2×C22⋊C411yescharacteristic
273C2×Dic43C2×C22⋊C411yescharacteristic
274C2×Dic43C2×C22⋊C411yescharacteristic
275C2×Dic43C2×C22⋊C411yescharacteristic
276C2×Dic43C2×C22⋊C411yescharacteristic
277C2×Dic43C2×C22⋊C411yescharacteristic
278D172—24no—
279D172—42no—
280D172—44no—
281D172—44no—
282D172—42no—
283C4×D43—22no—
284C4×D43—22no—
285C4×D43—22no—
286C4×D43—22no—
287C4×D43—22no—
288C4×D43—22no—
289C4×D43—22no—
290C4×D43—22no—
291C4×D43—41no—
292C4×D43—41no—
293C4×D43—41no—
294C4×D43—41no—
295C4×D43—44no—
296C4×D43—44no—
297C4×D43—44no—
298Dic86—24no—
299C8×C43—42no—
300C43⋊C8—42no—
301#21900—431nomaximal, Sylow
302C22×C43—21no—
303C22×C43—21no—
304C22×C43C22×C22⋊C411yescharacteristic
305C22×C43#53511yescharacteristic
306C22×C43#53611yescharacteristic
307C2×D43—21no—
308C2×D43—21no—
309C2×D43—21no—
310C2×D43—21no—
311C2×D43—21no—
312C2×D43—21no—
313C2×D43—42no—
314C2×D43—42no—
315C2×D43—42no—
316C2×D43—42no—
317C2×D43—42no—
318C4×C43—21no—
319C4×C43—21no—
320C4×C43—21no—
321C4×C43—42no—
322C4×C43—42no—
323C4×C43—82no—
324C4×C43#42112yes—
325C4×C43#52012yes—
326C4×C43#53712yes—
327Dic43—21no—
328Dic43—21no—
329Dic43—21no—
330Dic43—21no—
331Dic43—21no—
332Dic43—42no—
333Dic43—82no—
334Dic43#42112yes—
335#3444—431no—
336#2920—431no—
337#2285—431no—
338#1986—431no—
339#1986D4311yescharacteristic, complemented
340#1980—431no—
341#1980—431no—
342#1897—434no—
343#1806—434no—
344C2×C43—21no—
345C2×C43—21no—
346C2×C43#231111yescharacteristic
347C2×C43C2×#42111yescharacteristic
348C2×C43C2×#42111yescharacteristic
349D43—41no—
350D43—41no—
351D43—82no—
352#533—431no—
353#533—431no—
354#533C2×D4311yescharacteristic
355#532—431no—
356#532—431no—
357#532—431no—
358#529—432no—
359#529—432no—
360#529—861no—
361#529—861no—
362#529—861no—
363#529—861no—
364#525—432no—
365#525—861no—
366#525—861no—
367C4×#41—432no—
368C4×#41—861no—
369C4×#41—861no—
370C2×#117—432no—
371C22×C42—431no—
372#432—861no—
373#432—861no—
374#431—861no—
375#431—861no—
376#423—432no—
377C2×#104—434no—
378C2×#104—434no—
379#407—432no—
380C4×M16—431no—
381C4×M16C2×D4311yescharacteristic
382#384—861no—
383#382—861no—
384#380—861no—
385#380—861no—
386C4×C4⋊C4—432no—
387C4×C4⋊C4—431no—
388C4×C4⋊C4C2×D4311yescharacteristic
389#339—434no—
390#339C2×D4314yes—
391C43#2190011yescharacteristic, complemented, Sylow
392C2×#41—432no—
393C2×#41—861no—
394C2×#41—861no—
395C23×C4—431no—
396C23×C4—431no—
397C23×C4—431no—
398C2×M16—432no—
399C2×M16C22×D4312yes—
400C4⋊Q8—431no—
401C4⋊Q8C4×D4311yescharacteristic
402C4⋊Q8C4×D4311yescharacteristic
403#127—431no—
404#126—862no—
405#126—862no—
406#125—861no—
407#125—861no—
408#125C4×D4312yes—
409#124—432no—
410#124—861no—
411#124—861no—
412#123—862no—
413#123—862no—
414#123—862no—
415C22⋊Q8—21no—
416C22⋊Q8—21no—
417C22⋊Q8—432no—
418C22⋊Q8—432no—
419C22⋊Q8—861no—
420C22⋊Q8—861no—
421#121—432no—
422#121—432no—
423#121—861no—
424#121—861no—
425#121—861no—
426#121—861no—
427#120—862no—
428C4×Q8—21no—
429C4×Q8—21no—
430C4×Q8—432no—
431C4×Q8—432no—
432C4×Q8—861no—
433C4×Q8—861no—
434C4×D4—432no—
435C4×D4—432no—
436C4×D4—862no—
437C4×D4—862no—
438C4×D4—861no—
439C4×D4—861no—
440C4×D4—862no—
441C4×D4—862no—
442C4×D4—862no—
443C4×D4—862no—
444C4×D4—861no—
445C4×D4—861no—
446#117—862no—
447#117—862no—
448#117—862no—
449#117—861no—
450#117—861no—
451#117—1724no—
452#117C22×D4312yes—
453C2×C4⋊C4—21no—
454C2×C4⋊C4—862no—
455C2×C4⋊C4—862no—
456C2×C4⋊C4—861no—
457C2×C22⋊C4—862no—
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—431no—
469C2×C42—432no—
470C2×C42—862no—
471C2×C42C22×D4312yes—
472C2×C42C22×D4311yescharacteristic
473C4⋊C8—862no—
474C4⋊C8—862no—
475#104—1724no—
476#104—1724no—
477C22⋊C8—862no—
478C22⋊C8—862no—
479#97—21no—
480#97—861no—
481C4×C8—21no—
482C4×C8—861no—
483#95—21no—
484#95—862no—
485#95—861no—
486C24—431no—
487#41—864no—
488#41—864no—
489#41—1724no—
490#41—1724no—
491C2×Q8—21no—
492C2×Q8—21no—
493C2×Q8—432no—
494C2×D4—432no—
495C2×D4—862no—
496C2×D4—862no—
497C2×D4—862no—
498C2×D4—861no—
499C2×D4—861no—
500C22×C4—22no—
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—862no—
522C22×C4—1722no—
523C22×C4—1722no—
524C22×C4D4×D4311yescharacteristic
525C22×C4D4×D4311yescharacteristic
526C22×C4C23×D4311yescharacteristic
527M16—22no—
528M16—22no—
529M16—862no—
530M16—862no—
531C2×C8—22no—
532C2×C8—862no—
533C4⋊C4—21no—
534C4⋊C4—21no—
535C4⋊C4—22no—
536C4⋊C4—22no—
537C4⋊C4—42no—
538C4⋊C4—862no—
539C4⋊C4—862no—
540C4⋊C4—862no—
541C4⋊C4—862no—
542C4⋊C4—861no—
543C4⋊C4—861no—
544C4⋊C4—1722no—
545C4⋊C4—1724no—
546C4⋊C4—1724no—
547C4⋊C4C2×C4×D4312yes—
548C4⋊C4C2×C4×D4312yes—
549C22⋊C4—22no—
550C22⋊C4—862no—
551C22⋊C4—862no—
552C22⋊C4—862no—
553C22⋊C4—862no—
554C22⋊C4—862no—
555C22⋊C4—862no—
556C22⋊C4—862no—
557C22⋊C4—862no—
558C22⋊C4—1724no—
559C42—22no—
560C42—24no—
561C42—431no—
562C42—431no—
563C42—431no—
564C42—431no—
565C42—431no—
566C42—431no—
567C42—431no—
568C42—431no—
569C42—431no—
570C42—431no—
571C42—431no—
572C42—431no—
573C42—862no—
574C42—862no—
575C42—864no—
576C42C2×C4×D4311yescharacteristic
577C42C2×C4×D4311yescharacteristic
578C42D4×D4311yescharacteristic
579C42D4×D4311yescharacteristic
580C23—431no—
581C23—431no—
582C23—861no—
583C23—861no—
584C23—862no—
585C23—1721no—
586C23—1721no—
587C23C2×D4×D4311yescharacteristic
588Q8—42no—
589Q8—42no—
590Q8—864no—
591D4—864no—
592D4—1722no—
593D4—1724no—
594D4—1724no—
595D4—1722no—
596D4—1722no—
597D4—1722no—
598C2×C4—22no—
599C2×C4—22no—
600C2×C4—22no—
601C2×C4—41no—
602C2×C4—42no—
603C2×C4—42no—
604C2×C4—42no—
605C2×C4—431no—
606C2×C4—431no—
607C2×C4—431no—
608C2×C4—431no—
609C2×C4—431no—
610C2×C4—431no—
611C2×C4—862no—
612C2×C4—862no—
613C2×C4—862no—
614C2×C4—861no—
615C2×C4—861no—
616C2×C4—862no—
617C2×C4—862no—
618C2×C4—862no—
619C2×C4—862no—
620C2×C4—862no—
621C2×C4—862no—
622C2×C4—862no—
623C2×C4—1721no—
624C2×C4—1721no—
625C2×C4—1721no—
626C2×C4—1721no—
627C2×C4—1724no—
628C2×C4—1724no—
629C2×C4—1721no—
630C2×C4—1722no—
631C2×C4—1722no—
632C2×C4—1722no—
633C2×C4—1724no—
634C2×C4C22⋊C4×D4311yescharacteristic
635C2×C4C22⋊C4×D4311yescharacteristic
636C2×C4C22⋊C4×D4311yescharacteristic
637C2×C4C22⋊C4×D4311yescharacteristic
638C2×C4C22×C4×D4311yescharacteristic
639C2×C4C2×D4×D4311yescharacteristic
640C2×C4#1306337112yes—
641C2×C4#1306337312yes—
642C8—42no—
643C8—1722no—
644C22—21no—
645C22—21no—
646C22—861no—
647C22—861no—
648C22—861no—
649C22—861no—
650C22—861no—
651C22—861no—
652C22—1722no—
653C22—1722no—
654C22—1722no—
655C22—1722no—
656C22—1722no—
657C22C2×C22⋊C4×D4311yescharacteristic
658C22#1458346711yescharacteristic
659C22#1458347411yescharacteristic
660C4—21no—
661C4—21no—
662C4—21no—
663C4—42no—
664C4—42no—
665C4—82no—
666C4—432no—
667C4—861no—
668C4—861no—
669C4—861no—
670C4—861no—
671C4—861no—
672C4—3442no—
673C4—1722no—
674C4#1458291412yes—
675C4#1458338112yes—
676C4#1458347912yes—
677C2—21no—
678C2—21no—
679C2—3442no—
680C2—1721no—
681C2—1721no—
682C2#1913718611yescharacteristic
683C2#421×D4311yescharacteristic
684C2C2×#1458291411yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1986C2
socleC22×C43C22×C22⋊C4
prime radical#19147892C2
cosocleC22×C4×C43C24
hypercenter#1986D43
hypocenterC43#21900
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1986

Complements

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

NH ≅ G/Ntype
2. #19143226C2semidirect
3. #19136999C2semidirect
4. #19135540C2semidirect
5. #19135514C2semidirect
6. #19135513C2semidirect
7. #19135042C2semidirect
8. #19134614C2semidirect
9. C43×#1986C2semidirect
10. #14583454C4semidirect
11. #14583454C4semidirect
12. #14583450C4semidirect
13. #14583450C4semidirect
19. #14583434C4semidirect
20. #14583434C4semidirect
339. #1986D43semidirect
391. C43#21900semidirect

Maximal subgroups

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

subgroupindex
#191478922
#191432262
#191369992
#191355402
#191355142
#191355132
#191350422
#191346142
C43×#19862
#2190043