Finite Group Databasebeta

← #25106607

Subgroups — #25106607

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#19147890C211yesmaximal, characteristic
2#19143226C211yesmaximal, characteristic, complemented
3#19136999C211yesmaximal, characteristic, complemented
4#19135539C211yesmaximal, characteristic, complemented
5#19135538C211yesmaximal, characteristic, complemented
6#19135515C211yesmaximal, characteristic, complemented
7#19135040C214yesmaximal, complemented
8#19134613C214yesmaximal, complemented
9C43×#1980C211yesmaximal, characteristic, complemented
10#14583456C2211yescharacteristic
11#14583454C411yescharacteristic, complemented
12#14583454C411yescharacteristic, complemented
13#14583447C411yescharacteristic, complemented
14#14583447C411yescharacteristic, complemented
15#14583431—21no—
16#14583431—21no—
17#14583430—21no—
18#14583430—21no—
19#14583428C412yescomplemented
20#14583428C412yescomplemented
21#14583409—21no—
22#14583409—21no—
23#14583406C2212yes—
24#41×Dic43C2212yes—
25C4×#10621900—21no—
26C4×#10621900—21no—
27C2×#13063282C2212yes—
28C2×C42×D43C2211yescharacteristic
29#14582954—21no—
30#14582954—21no—
31#14582950—21no—
32#14582950—21no—
33#14582922C2212yes—
34C2×#13063252C2214yes—
35#14582862C2212yes—
36C4×#10621877C2211yescharacteristic
37#14582768—21no—
38#14582763—21no—
39#14582758—21no—
40#14582756—21no—
41C4×Dic43⋊C4C2212yes—
42C4×C4⋊Dic43C2211yescharacteristic
43#14582660C2214yes—
44#14582659C2214yes—
45C43×#532C2211yescharacteristic
46C2×#104×C43C2214yes—
47C4×M16×C43C2211yescharacteristic
48C4×C4⋊C4×C43C2211yescharacteristic
49C2×#10621900—21no—
50C2×#10621900—21no—
51C22×C4×D43D411yescharacteristic
52C22×C4×D43D411yescharacteristic
53C22×C4×D43C2311yescharacteristic
54C2×#10621877C2312yes—
55#13063325C2×C411yescharacteristic
56#13063325C2×C411yescharacteristic
57#13063318—22no—
58#13063318—22no—
59#13063317C2×C412yes—
60#13063316—21no—
61#13063316—21no—
62#13063312—21no—
63#13063312—21no—
64#13063307—22no—
65#13063307—22no—
66#13063306—22no—
67#13063305—21no—
68#13063305—21no—
69#13063304—21no—
70#13063304—21no—
71#13063301C2×C412yes—
72#13063301C2×C412yes—
73#13063296—21no—
74#13063296—21no—
75#13063296C2×C412yes—
76#13063296C2×C412yes—
77#13063293—22no—
78Q8×Dic43C2×C412yes—
79Q8×Dic43C2×C412yes—
80C4×Dic86—21no—
81C4×Dic86—21no—
82#13063290—21no—
83#13063290—21no—
84D4×Dic43—22no—
85D4×Dic43—22no—
86D4×Dic43—21no—
87D4×Dic43—21no—
88D4×Dic43C2×C412yes—
89D4×Dic43C2×C412yes—
90C4×C22⋊D43—22no—
91C4×C22⋊D43—22no—
92(C22⋊D43)⋊C4—22no—
93(C22⋊D43)⋊C4—22no—
94#13063284—22no—
95#13063284C2312yes—
96#13063283—21no—
97#13063283—21no—
98#13063282—44no—
99#13063281—22no—
100#13063281—22no—
101C2×C4⋊Dic43—21no—
102C2×Dic43⋊C4—22no—
103C2×Dic43⋊C4—22no—
104C2×(C2×D43)⋊C4—22no—
105C2×C4×Dic43—22no—
106C2×C4×Dic43D411yescharacteristic
107C2×C4×Dic43D411yescharacteristic
108C2×C4×Dic43C2312yes—
109C2×C4×Dic43C2311yescharacteristic
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#13063252—44no—
121(C2×D43)⋊C8—22no—
122(C2×D43)⋊C8—22no—
123#13063236—21no—
124C4×C43⋊C8—21no—
125C43⋊#95—21no—
126C43⋊#95—22no—
127C2×#41×C43C2312yes—
128C2×M16×C43C2312yes—
129C4⋊Q8×C43C2×C411yescharacteristic
130#127×C43C2×C411yescharacteristic
131#124×C43C2×C412yes—
132#121×C43—21no—
133#121×C43—21no—
134C4×D4×C43—21no—
135C4×D4×C43—21no—
136C2×C4⋊C4×C43—21no—
137C2×C42×C43C2312yes—
138C2×C42×C43C2311yescharacteristic
139#104×C43—44no—
140#97×C43—21no—
141C4×C8×C43—21no—
142#95×C43—21no—
143C23×D43C2×D411yescharacteristic
144#41×C43—24no—
145#41×C43—24no—
146C2×Q8×C43C22×C412yes—
147C2×D4×C43—21no—
148C2×D4×C43—21no—
149C2×D4×C43—22no—
150C2×D4×C43C22×C412yes—
151C22×C4×C43—22no—
152C22×C4×C43—22no—
153C22×C4×C43C2×D411yescharacteristic
154C22×C4×C43C2×D411yescharacteristic
155C22×C4×C43C2411yescharacteristic
156C2×C22⋊D43—22no—
157C2×C22⋊D43—22no—
158C22×Dic43—22no—
159C22×Dic43—22no—
160C22×Dic43—22no—
161C22×Dic43C2×D411yescharacteristic
162C22×Dic43C2×D411yescharacteristic
163C22×Dic43C2×D411yescharacteristic
164#10621900—44no—
165#10621900—44no—
166C2×C4×D43—22no—
167C2×C4×D43—22no—
168C2×C4×D43—42no—
169C2×C4×D43—42no—
170C2×C4×D43C22⋊C411yescharacteristic
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×D43C2×D411yescharacteristic
181C2×C4×D43C2×D411yescharacteristic
182C2×Dic86—21no—
183C2×Dic86—21no—
184M16×C43—22no—
185M16×C43—22no—
186C2×C8×C43—22no—
187C4⋊C4×C43—21no—
188C4⋊C4×C43—21no—
189C4⋊C4×C43—42no—
190C22⋊C4×C43—22no—
191C22⋊C4×C43—22no—
192C42×C43—24no—
193C42×C43C22×C411yescharacteristic
194C42×C43C22×C411yescharacteristic
195C42×C43C2×D411yescharacteristic
196C42×C43C2×D411yescharacteristic
197C22⋊Dic43—22no—
198C22⋊Dic43—22no—
199C22⋊Dic43—22no—
200C22⋊Dic43—22no—
201C22⋊Dic43—22no—
202(C2×D43)⋊C4—22no—
203(C2×D43)⋊C4—22no—
204(C2×D43)⋊C4—44no—
205C4⋊Dic43—21no—
206C4⋊Dic43—21no—
207C4⋊Dic43—22no—
208C4⋊Dic43—22no—
209C4⋊Dic43—42no—
210C4⋊Dic43C22×C412yes—
211C4⋊Dic43C22×C412yes—
212Dic43⋊C4—22no—
213Dic43⋊C4—22no—
214Dic43⋊C4—22no—
215Dic43⋊C4—22no—
216Dic43⋊C4—44no—
217Dic43⋊C4—44no—
218C4×Dic43—22no—
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×C43—22no—
238C23×C43C22×D411yescharacteristic
239C22×D43—21no—
240C22×D43—21no—
241C22×D43—41no—
242C22×D43—41no—
243C22×D43C2×C22⋊C411yescharacteristic
244C22×D43C2×C22⋊C411yescharacteristic
245Q8×C43—24no—
246D4×C43—24no—
247D4×C43—42no—
248D4×C43—42no—
249D4×C43—42no—
250D4×C43—42no—
251C2×C4×C43—22no—
252C2×C4×C43—22no—
253C2×C4×C43—41no—
254C2×C4×C43—44no—
255C2×C4×C43—42no—
256C2×C4×C43—42no—
257C2×C4×C43—42no—
258C2×C4×C43C2×C22⋊C411yescharacteristic
259C2×C4×C43C2×C22⋊C411yescharacteristic
260C2×C4×C43C2×C22⋊C411yescharacteristic
261C2×C4×C43C2×C22⋊C411yescharacteristic
262C2×C4×C43C23×C411yescharacteristic
263C2×C4×C43C22×D411yescharacteristic
264C2×C4×C43H(5,𝔽2)12yes—
265C2×C4×C432−1+412yes—
266C22⋊D43—44no—
267C22⋊D43—44no—
268C2×Dic43—21no—
269C2×Dic43—21no—
270C2×Dic43—22no—
271C2×Dic43—22no—
272C2×Dic43—22no—
273C2×Dic43—41no—
274C2×Dic43—44no—
275C2×Dic43—44no—
276C2×Dic43—42no—
277C2×Dic43—42no—
278C2×Dic43—42no—
279C2×Dic43C2×C22⋊C411yescharacteristic
280C2×Dic43C2×C22⋊C411yescharacteristic
281C2×Dic43C2×C22⋊C411yescharacteristic
282C2×Dic43C2×C22⋊C411yescharacteristic
283C2×Dic43C2×C22⋊C411yescharacteristic
284C2×Dic43C2×C22⋊C411yescharacteristic
285C4×D43—22no—
286C4×D43—22no—
287C4×D43—22no—
288C4×D43—22no—
289C4×D43—22no—
290C4×D43—22no—
291C4×D43—22no—
292C4×D43—22no—
293C4×D43—41no—
294C4×D43—41no—
295C4×D43—41no—
296C4×D43—41no—
297Dic86—42no—
298Dic86—42no—
299C8×C43—42no—
300C43⋊C8—42no—
301#21900—431nomaximal, Sylow
302C22×C43—21no—
303C22×C43—21no—
304C22×C43—42no—
305C22×C43—42no—
306C22×C43—42no—
307C22×C43C22×C22⋊C411yescharacteristic
308C22×C43#53511yescharacteristic
309C22×C43#53611yescharacteristic
310C2×D43—21no—
311C2×D43—21no—
312C2×D43—21no—
313C2×D43—21no—
314C2×D43—21no—
315C2×D43—21no—
316C2×D43—42no—
317C2×D43—42no—
318C4×C43—21no—
319C4×C43—21no—
320C4×C43—21no—
321C4×C43—42no—
322C4×C43—82no—
323C4×C43#42112yes—
324C4×C43#52012yes—
325C4×C43#53712yes—
326Dic43—21no—
327Dic43—21no—
328Dic43—21no—
329Dic43—21no—
330Dic43—21no—
331Dic43—42no—
332Dic43—42no—
333Dic43—82no—
334Dic43#42112yes—
335#3444—431no—
336#2920—431no—
337#2285—431no—
338#1986—431no—
339#1986—431no—
340#1980—431no—
341#1980D4311yescharacteristic, complemented
342#1897—434no—
343#1806—434no—
344C2×C43—21no—
345C2×C43—21no—
346C2×C43—82no—
347C2×C43#231111yescharacteristic
348C2×C43C2×#42111yescharacteristic
349C2×C43C2×#42111yescharacteristic
350D43—41no—
351D43—41no—
352#533—431no—
353#533—431no—
354#533—431no—
355#532—431no—
356#532—431no—
357#532C2×D4311yescharacteristic
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×#104C2×D4314yes—
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#339—434no—
391C43#2190011yescharacteristic, complemented, Sylow
392C2×#41—861no—
393C2×#41—861no—
394C2×#41C22×D4312yes—
395C23×C4—431no—
396C23×C4—431no—
397C23×C4—431no—
398C2×M16—432no—
399C2×M16C22×D4312yes—
400C4⋊Q8—431no—
401C4⋊Q8—431no—
402C4⋊Q8C4×D4311yescharacteristic
403#127C4×D4311yescharacteristic
404#126—862no—
405#126—862no—
406#125—432no—
407#125—861no—
408#125—861no—
409#124—861no—
410#124—861no—
411#124C4×D4312yes—
412#123—862no—
413#123—862no—
414#123—862no—
415C22⋊Q8—432no—
416C22⋊Q8—432no—
417C22⋊Q8—861no—
418C22⋊Q8—861no—
419C22⋊Q8—861no—
420C22⋊Q8—861no—
421#121—21no—
422#121—21no—
423#121—432no—
424#121—432no—
425#121—861no—
426#121—861no—
427#120—862no—
428C4×Q8—432no—
429C4×Q8—432no—
430C4×Q8—861no—
431C4×Q8—861no—
432C4×Q8—861no—
433C4×Q8—861no—
434C4×D4—21no—
435C4×D4—21no—
436C4×D4—432no—
437C4×D4—432no—
438C4×D4—861no—
439C4×D4—861no—
440C4×D4—862no—
441C4×D4—862no—
442C4×D4—862no—
443C4×D4—862no—
444C4×D4—862no—
445C4×D4—862no—
446#117—432no—
447#117—862no—
448#117—862no—
449#117—862no—
450#117—861no—
451#117—861no—
452#117—1724no—
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—44no—
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—24no—
488#41—24no—
489#41—1724no—
490#41—1724no—
491C2×Q8—861no—
492C2×Q8—861no—
493C2×Q8C2×C4×D4312yes—
494C2×D4—22no—
495C2×D4—21no—
496C2×D4—21no—
497C2×D4—862no—
498C2×D4—862no—
499C2×D4C2×C4×D4312yes—
500C22×C4—22no—
501C22×C4—22no—
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—431no—
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—42no—
536C4⋊C4—432no—
537C4⋊C4—432no—
538C4⋊C4—862no—
539C4⋊C4—862no—
540C4⋊C4—862no—
541C4⋊C4—862no—
542C4⋊C4—861no—
543C4⋊C4—861no—
544C4⋊C4—862no—
545C4⋊C4—862no—
546C4⋊C4—1722no—
547C4⋊C4—1724no—
548C4⋊C4—1724no—
549C22⋊C4—22no—
550C22⋊C4—22no—
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—24no—
560C42—431no—
561C42—431no—
562C42—431no—
563C42—431no—
564C42—431no—
565C42—431no—
566C42—431no—
567C42—431no—
568C42—431no—
569C42—431no—
570C42—431no—
571C42—431no—
572C42—862no—
573C42—862no—
574C42—862no—
575C42—864no—
576C42C2×C4×D4311yescharacteristic
577C42C2×C4×D4311yescharacteristic
578C42D4×D4311yescharacteristic
579C42D4×D4311yescharacteristic
580C23—22no—
581C23—431no—
582C23—431no—
583C23—861no—
584C23—861no—
585C23—1721no—
586C23—1721no—
587C23C2×D4×D4311yescharacteristic
588Q8—24no—
589Q8—1722no—
590Q8—1722no—
591D4—24no—
592D4—42no—
593D4—42no—
594D4—42no—
595D4—42no—
596D4—1724no—
597D4—1724no—
598C2×C4—22no—
599C2×C4—22no—
600C2×C4—41no—
601C2×C4—44no—
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—862no—
624C2×C4—1721no—
625C2×C4—1721no—
626C2×C4—1721no—
627C2×C4—1721no—
628C2×C4—1724no—
629C2×C4—1721no—
630C2×C4—1724no—
631C2×C4—1722no—
632C2×C4—1722no—
633C2×C4—1722no—
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#1306337012yes—
641C2×C4#1306337212yes—
642C8—42no—
643C8—1722no—
644C22—21no—
645C22—21no—
646C22—42no—
647C22—42no—
648C22—42no—
649C22—861no—
650C22—861no—
651C22—861no—
652C22—861no—
653C22—861no—
654C22—861no—
655C22—1722no—
656C22—1722no—
657C22C2×C22⋊C4×D4311yescharacteristic
658C22#1458346211yescharacteristic
659C22#1458346911yescharacteristic
660C4—21no—
661C4—21no—
662C4—21no—
663C4—42no—
664C4—82no—
665C4—432no—
666C4—861no—
667C4—861no—
668C4—861no—
669C4—861no—
670C4—861no—
671C4—3442no—
672C4—1722no—
673C4—1722no—
674C4#1458291412yes—
675C4#1458337812yes—
676C4#1458347812yes—
677C2—21no—
678C2—21no—
679C2—82no—
680C2—1721no—
681C2—1721no—
682C2#1913718511yescharacteristic
683C2#421×D4311yescharacteristic
684C2C2×#1458291411yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1980C2
socleC22×C43C22×C22⋊C4
prime radical#19147890C2
cosocleC22×C4×C43C24
hypercenter#1980D43
hypocenterC43#21900
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1980

Complements

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

NH ≅ G/Ntype
2. #19143226C2semidirect
3. #19136999C2semidirect
4. #19135539C2semidirect
5. #19135538C2semidirect
6. #19135515C2semidirect
7. #19135040C2semidirect
8. #19134613C2semidirect
9. C43×#1980C2semidirect
11. #14583454C4semidirect
12. #14583454C4semidirect
13. #14583447C4semidirect
14. #14583447C4semidirect
19. #14583428C4semidirect
20. #14583428C4semidirect
341. #1980D43semidirect
391. C43#21900semidirect

Maximal subgroups

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

subgroupindex
#191478902
#191432262
#191369992
#191355392
#191355382
#191355152
#191350402
#191346132
C43×#19802
#2190043