Finite Group Databasebeta

← #25106600

Subgroups — #25106600

Order 11008.

1242 conjugacy classes of subgroups.

The subgroup lattice has 694 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19147890C211yesmaximal, characteristic
2#19143226C211yesmaximal, characteristic, complemented
3C4×C4⋊C4×D43C211yesmaximal, characteristic, complemented
4#19135539C211yesmaximal, characteristic, complemented
5#19135538C211yesmaximal, characteristic, complemented
6#19135515C211yesmaximal, characteristic, complemented
7#19135035C214yesmaximal, 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×C4⋊C4×D43—21no—
28C2×C42×D43C2212yes—
29C2×C42×D43C2211yescharacteristic
30#14582954—21no—
31#14582954—21no—
32#14582950—21no—
33#14582950—21no—
34#14582922C2212yes—
35C2×#13063252C2214yes—
36#14582862C2212yes—
37C4×#10621877C2211yescharacteristic
38C4⋊C4×Dic43—21no—
39C4×Dic43⋊C4C2212yes—
40C4×C4⋊Dic43C2211yescharacteristic
41#14582750—21no—
42#95×D43—21no—
43#14582660C2214yes—
44#14582659C2214yes—
45C43×#532C2211yescharacteristic
46C2×#104×C43C2214yes—
47C4×M16×C43C2211yescharacteristic
48C4×C4⋊C4×C43C2211yescharacteristic
49C2×#10621900—21no—
50C2×#10621900—21no—
51C22×C4×D43—22no—
52C22×C4×D43D411yescharacteristic
53C22×C4×D43D411yescharacteristic
54C22×C4×D43C2311yescharacteristic
55C2×#10621877C2312yes—
56#13063325C2×C411yescharacteristic, complemented
57#13063325C2×C411yescharacteristic, complemented
58#13063318—22no—
59#13063318—22no—
60#13063317C2×C412yescomplemented
61#13063316—21no—
62#13063316—21no—
63#13063312—21no—
64#13063312—21no—
65#13063307—22no—
66#13063307—22no—
67#13063306—22no—
68#13063305—21no—
69#13063305—21no—
70#13063304—21no—
71#13063304—21no—
72#13063301C2×C412yes—
73#13063301C2×C412yes—
74#13063296—21no—
75#13063296—21no—
76#13063296C2×C412yes—
77#13063296C2×C412yes—
78#13063293—22no—
79Q8×Dic43C2×C412yescomplemented
80Q8×Dic43C2×C412yescomplemented
81C4×Dic86—21no—
82C4×Dic86—21no—
83#13063290—21no—
84#13063290—21no—
85D4×Dic43—22no—
86D4×Dic43—22no—
87D4×Dic43—21no—
88D4×Dic43—21no—
89D4×Dic43C2×C412yescomplemented
90D4×Dic43C2×C412yescomplemented
91C4×C22⋊D43—22no—
92C4×C22⋊D43—22no—
93(C22⋊D43)⋊C4—22no—
94(C22⋊D43)⋊C4—22no—
95#13063284—22no—
96#13063284C2312yes—
97#13063283—21no—
98#13063283—21no—
99#13063281—22no—
100#13063281—22no—
101C2×C4⋊Dic43—21no—
102C2×Dic43⋊C4—22no—
103C4⋊C4×D43—28no—
104C2×C4×Dic43—22no—
105C2×C4×Dic43—22no—
106C2×C4×Dic43D411yescharacteristic
107C2×C4×Dic43D411yescharacteristic
108C2×C4×Dic43C2312yes—
109C2×C4×Dic43C2311yescharacteristic
110C42×D43—44no—
111C42×D43C2×C411yescharacteristic
112C42×D43C2×C411yescharacteristic
113C42×D43C2×C411yescharacteristic
114C42×D43C2×C411yescharacteristic
115C42×D43D411yescharacteristic
116C42×D43D411yescharacteristic
117C42×D43D411yescharacteristic
118C42×D43D411yescharacteristic
119Dic43⋊C8—22no—
120Dic43⋊C8—22no—
121#13063252—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×#41×C43C2312yes—
129C2×M16×C43C2312yes—
130C4⋊Q8×C43C2×C411yescharacteristic, complemented
131#127×C43C2×C411yescharacteristic, complemented
132#124×C43C2×C412yescomplemented
133#121×C43—21no—
134#121×C43—21no—
135C4×D4×C43—21no—
136C4×D4×C43—21no—
137C2×C4⋊C4×C43—21no—
138C2×C42×C43C2312yes—
139C2×C42×C43C2311yescharacteristic
140#104×C43—44no—
141#97×C43—21no—
142C4×C8×C43—21no—
143#95×C43—21no—
144C23×D43C2×D411yescharacteristic
145#41×C43—24no—
146#41×C43—24no—
147C2×Q8×C43C22×C412yes—
148C2×D4×C43—21no—
149C2×D4×C43—21no—
150C2×D4×C43—22no—
151C2×D4×C43C22×C412yes—
152C22×C4×C43—22no—
153C22×C4×C43—22no—
154C22×C4×C43C2×D411yescharacteristic
155C22×C4×C43C2×D411yescharacteristic
156C22×C4×C43C2411yescharacteristic
157C2×C22⋊D43—22no—
158C2×C22⋊D43—22no—
159C22×Dic43—22no—
160C22×Dic43—22no—
161C22×Dic43—22no—
162C22×Dic43C2×D411yescharacteristic
163C22×Dic43C2×D411yescharacteristic
164C22×Dic43C2×D411yescharacteristic
165#10621900—44no—
166#10621900—44no—
167C2×C4×D43—22no—
168C2×C4×D43—22no—
169C2×C4×D43—24no—
170C2×C4×D43—28no—
171C2×C4×D43—42no—
172C2×C4×D43—44no—
173C2×C4×D43—44no—
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×D43C22×C411yescharacteristic
183C2×C4×D43C22×C411yescharacteristic
184C2×C4×D43C2×D411yescharacteristic
185C2×C4×D43C2×D411yescharacteristic
186C2×Dic86—21no—
187C2×Dic86—21no—
188M16×C43—22no—
189M16×C43—22no—
190C2×C8×C43—22no—
191C4⋊C4×C43—24no—
192C4⋊C4×C43—21no—
193C4⋊C4×C43—21no—
194C22⋊C4×C43—22no—
195C22⋊C4×C43—22no—
196C42×C43—24no—
197C42×C43C22×C411yescharacteristic
198C42×C43C22×C411yescharacteristic
199C42×C43C2×D411yescharacteristic
200C42×C43C2×D411yescharacteristic
201C22⋊Dic43—22no—
202C22⋊Dic43—22no—
203C22⋊Dic43—22no—
204C22⋊Dic43—22no—
205C22⋊Dic43—22no—
206(C2×D43)⋊C4—22no—
207(C2×D43)⋊C4—22no—
208C4⋊Dic43—24no—
209C4⋊Dic43—21no—
210C4⋊Dic43—21no—
211C4⋊Dic43—22no—
212C4⋊Dic43—22no—
213C4⋊Dic43C22×C412yes—
214C4⋊Dic43C22×C412yes—
215Dic43⋊C4—28no—
216Dic43⋊C4—22no—
217Dic43⋊C4—22no—
218Dic43⋊C4—22no—
219Dic43⋊C4—22no—
220C4×Dic43—22no—
221C4×Dic43—22no—
222C4×Dic43—22no—
223C4×Dic43—24no—
224C4×Dic43—44no—
225C4×Dic43C22⋊C411yescharacteristic
226C4×Dic43C22⋊C411yescharacteristic
227C4×Dic43C22⋊C411yescharacteristic
228C4×Dic43C22⋊C411yescharacteristic
229C4×Dic43C22⋊C411yescharacteristic
230C4×Dic43C22⋊C411yescharacteristic
231C4×Dic43C22⋊C411yescharacteristic
232C4×Dic43C22⋊C411yescharacteristic
233C4×Dic43C22×C411yescharacteristic
234C4×Dic43C22×C411yescharacteristic
235C4×Dic43C2×D411yescharacteristic
236C4×Dic43C2×D411yescharacteristic
237#10621877—22no—
238#10621877—22no—
239C2×C43⋊C8—22no—
240C23×C43—22no—
241C23×C43C22×D411yescharacteristic
242C22×D43—21no—
243C22×D43—21no—
244C22×D43—22no—
245C22×D43—22no—
246C22×D43C2×C22⋊C411yescharacteristic
247C22×D43C2×C22⋊C411yescharacteristic
248Q8×C43—24no—
249D4×C43—24no—
250D4×C43—42no—
251D4×C43—42no—
252D4×C43—42no—
253D4×C43—42no—
254C2×C4×C43—22no—
255C2×C4×C43—24no—
256C2×C4×C43—22no—
257C2×C4×C43—41no—
258C2×C4×C43—42no—
259C2×C4×C43—42no—
260C2×C4×C43—44no—
261C2×C4×C43C2×C22⋊C411yescharacteristic
262C2×C4×C43C2×C22⋊C411yescharacteristic
263C2×C4×C43C2×C22⋊C411yescharacteristic
264C2×C4×C43C2×C22⋊C411yescharacteristic
265C2×C4×C43C23×C411yescharacteristic
266C2×C4×C43C22×D411yescharacteristic
267C2×C4×C43H(5,𝔽2)12yes—
268C2×C4×C432−1+412yes—
269C22⋊D43—44no—
270C22⋊D43—44no—
271C2×Dic43—21no—
272C2×Dic43—21no—
273C2×Dic43—22no—
274C2×Dic43—24no—
275C2×Dic43—22no—
276C2×Dic43—22no—
277C2×Dic43—41no—
278C2×Dic43—44no—
279C2×Dic43—42no—
280C2×Dic43—42no—
281C2×Dic43—44no—
282C2×Dic43C2×C22⋊C411yescharacteristic
283C2×Dic43C2×C22⋊C411yescharacteristic
284C2×Dic43C2×C22⋊C411yescharacteristic
285C2×Dic43C2×C22⋊C411yescharacteristic
286C2×Dic43C2×C22⋊C411yescharacteristic
287C2×Dic43C2×C22⋊C411yescharacteristic
288C4×D43—22no—
289C4×D43—22no—
290C4×D43—22no—
291C4×D43—22no—
292C4×D43—22no—
293C4×D43—22no—
294C4×D43—22no—
295C4×D43—22no—
296C4×D43—22no—
297C4×D43—41no—
298C4×D43—41no—
299C4×D43—416no—
300C4×D43#10414yescomplemented
301Dic86—42no—
302Dic86—42no—
303C8×C43—42no—
304C43⋊C8—42no—
305#21899—431nomaximal, Sylow
306C22×C43—21no—
307C22×C43—21no—
308C22×C43—42no—
309C22×C43—42no—
310C22×C43—42no—
311C22×C43C22×C22⋊C411yescharacteristic
312C22×C43#53511yescharacteristic
313C22×C43#53611yescharacteristic
314C2×D43—24no—
315C2×D43—24no—
316C2×D43—21no—
317C2×D43—21no—
318C2×D43—21no—
319C2×D43—21no—
320C2×D43C2×#10412yes—
321C2×D43#42112yes—
322C4×C43—21no—
323C4×C43—21no—
324C4×C43—21no—
325C4×C43—44no—
326C4×C43—42no—
327C4×C43C2×#10412yes—
328C4×C43#52012yes—
329C4×C43#53712yes—
330Dic43—21no—
331Dic43—21no—
332Dic43—21no—
333Dic43—21no—
334Dic43—21no—
335Dic43—44no—
336Dic43—42no—
337Dic43—42no—
338Dic43C2×#10412yes—
339#3444—431no—
340#2920—431no—
341C2×C4×C4⋊C4—431no—
342#1986—431no—
343#1986—431no—
344#1980—431no—
345#1980D4311yescharacteristic, complemented
346#1896—434no—
347#1806—434no—
348C2×C43—21no—
349C2×C43—21no—
350C2×C43—82no—
351C2×C43#231111yescharacteristic
352C2×C43C22×#10411yescharacteristic
353C2×C43C2×#42111yescharacteristic
354D43—22no—
355D43—22no—
356#533—431no—
357#533—431no—
358#533—431no—
359#532—431no—
360#532—431no—
361#532C2×D4311yescharacteristic
362#529—432no—
363#529—432no—
364#529—861no—
365#529—861no—
366#529—861no—
367#529—861no—
368#525—432no—
369#525—861no—
370#525—861no—
371C4×#41—432no—
372C4×#41—861no—
373C4×#41—861no—
374C22×C4⋊C4—861no—
375C22×C42—431no—
376C22×C42—432no—
377#432—861no—
378#432—861no—
379#431—861no—
380#431—861no—
381#423—432no—
382C2×#104—434no—
383C2×#104C2×D4314yes—
384#407—432no—
385C4×M16—431no—
386C4×M16C2×D4311yescharacteristic
387C4×C4⋊C4—432no—
388C4×C4⋊C4—431no—
389C4×C4⋊C4—861no—
390C4×C4⋊C4—861no—
391C4×C4⋊C4C2×D4311yescharacteristic
392C2×#95—861no—
393#339—434no—
394#339—434no—
395C43#2189911yescharacteristic, complemented, Sylow
396C2×#41—861no—
397C2×#41—861no—
398C2×#41C22×D4312yes—
399C23×C4—431no—
400C23×C4—431no—
401C23×C4—431no—
402C23×C4—862no—
403C2×M16—432no—
404C2×M16C22×D4312yes—
405C4⋊Q8—431no—
406C4⋊Q8—431no—
407C4⋊Q8C4×D4311yescharacteristic, complemented
408#127C4×D4311yescharacteristic, complemented
409#126—862no—
410#126—862no—
411#125—432no—
412#125—861no—
413#125—861no—
414#124—861no—
415#124—861no—
416#124C4×D4312yescomplemented
417#123—862no—
418#123—862no—
419#123—862no—
420C22⋊Q8—432no—
421C22⋊Q8—432no—
422C22⋊Q8—861no—
423C22⋊Q8—861no—
424C22⋊Q8—861no—
425C22⋊Q8—861no—
426#121—21no—
427#121—21no—
428#121—432no—
429#121—432no—
430#121—861no—
431#121—861no—
432#120—862no—
433C4×Q8—432no—
434C4×Q8—432no—
435C4×Q8—861no—
436C4×Q8—861no—
437C4×Q8—861no—
438C4×Q8—861no—
439C4×D4—21no—
440C4×D4—21no—
441C4×D4—432no—
442C4×D4—432no—
443C4×D4—861no—
444C4×D4—861no—
445C4×D4—862no—
446C4×D4—862no—
447C4×D4—862no—
448C4×D4—862no—
449C4×D4—862no—
450C4×D4—862no—
451#117—432no—
452#117—862no—
453#117—862no—
454#117—862no—
455#117—861no—
456#117—861no—
457C2×C4⋊C4—21no—
458C2×C4⋊C4—868no—
459C2×C4⋊C4—862no—
460C2×C4⋊C4—861no—
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—431no—
470C2×C42—431no—
471C2×C42—431no—
472C2×C42—432no—
473C2×C42—862no—
474C2×C42—862no—
475C2×C42—1724no—
476C2×C42C22×D4312yes—
477C2×C42C22×D4311yescharacteristic
478C4⋊C8—862no—
479C4⋊C8—862no—
480#104—44no—
481#104—1724no—
482C22⋊C8—862no—
483C22⋊C8—862no—
484#97—21no—
485#97—861no—
486C4×C8—21no—
487C4×C8—861no—
488#95—21no—
489#95—862no—
490#95—861no—
491C24—431no—
492#41—24no—
493#41—24no—
494#41—1724no—
495#41—1724no—
496C2×Q8—861no—
497C2×Q8—861no—
498C2×Q8C2×C4×D4312yes—
499C2×D4—22no—
500C2×D4—21no—
501C2×D4—21no—
502C2×D4—862no—
503C2×D4—862no—
504C2×D4C2×C4×D4312yes—
505C22×C4—22no—
506C22×C4—22no—
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—431no—
518C22×C4—431no—
519C22×C4—431no—
520C22×C4—431no—
521C22×C4—431no—
522C22×C4—864no—
523C22×C4—868no—
524C22×C4—862no—
525C22×C4—862no—
526C22×C4—862no—
527C22×C4—862no—
528C22×C4—862no—
529C22×C4—1722no—
530C22×C4—1724no—
531C22×C4—1724no—
532C22×C4D4×D4311yescharacteristic
533C22×C4D4×D4311yescharacteristic
534C22×C4C23×D4311yescharacteristic
535M16—22no—
536M16—22no—
537M16—862no—
538M16—862no—
539C2×C8—22no—
540C2×C8—862no—
541C4⋊C4—24no—
542C4⋊C4—21no—
543C4⋊C4—21no—
544C4⋊C4—432no—
545C4⋊C4—432no—
546C4⋊C4—862no—
547C4⋊C4—862no—
548C4⋊C4—862no—
549C4⋊C4—862no—
550C4⋊C4—868no—
551C4⋊C4—864no—
552C4⋊C4—861no—
553C4⋊C4—861no—
554C4⋊C4—862no—
555C4⋊C4—862no—
556C22⋊C4—22no—
557C22⋊C4—22no—
558C22⋊C4—862no—
559C22⋊C4—862no—
560C22⋊C4—862no—
561C22⋊C4—862no—
562C22⋊C4—862no—
563C22⋊C4—862no—
564C22⋊C4—862no—
565C42—24no—
566C42—431no—
567C42—431no—
568C42—431no—
569C42—431no—
570C42—431no—
571C42—431no—
572C42—431no—
573C42—431no—
574C42—431no—
575C42—431no—
576C42—431no—
577C42—431no—
578C42—862no—
579C42—862no—
580C42—862no—
581C42—864no—
582C42—1724no—
583C42C2×C4×D4311yescharacteristic
584C42C2×C4×D4311yescharacteristic
585C42D4×D4311yescharacteristic
586C42D4×D4311yescharacteristic
587C23—22no—
588C23—431no—
589C23—431no—
590C23—862no—
591C23—862no—
592C23—861no—
593C23—861no—
594C23C2×D4×D4311yescharacteristic
595Q8—24no—
596Q8—1722no—
597Q8—1722no—
598D4—24no—
599D4—42no—
600D4—42no—
601D4—42no—
602D4—42no—
603D4—1724no—
604D4—1724no—
605C2×C4—22no—
606C2×C4—24no—
607C2×C4—22no—
608C2×C4—41no—
609C2×C4—42no—
610C2×C4—42no—
611C2×C4—44no—
612C2×C4—431no—
613C2×C4—434no—
614C2×C4—431no—
615C2×C4—431no—
616C2×C4—431no—
617C2×C4—431no—
618C2×C4—431no—
619C2×C4—862no—
620C2×C4—862no—
621C2×C4—862no—
622C2×C4—862no—
623C2×C4—862no—
624C2×C4—861no—
625C2×C4—861no—
626C2×C4—862no—
627C2×C4—862no—
628C2×C4—862no—
629C2×C4—862no—
630C2×C4—862no—
631C2×C4—864no—
632C2×C4—862no—
633C2×C4—862no—
634C2×C4—1721no—
635C2×C4—1721no—
636C2×C4—17216no—
637C2×C4—1724no—
638C2×C4—1721no—
639C2×C4—1724no—
640C2×C4—1722no—
641C2×C4—1722no—
642C2×C4C22⋊C4×D4311yescharacteristic
643C2×C4C22⋊C4×D4311yescharacteristic
644C2×C4C22⋊C4×D4311yescharacteristic
645C2×C4C22⋊C4×D4311yescharacteristic
646C2×C4C22×C4×D4311yescharacteristic
647C2×C4C2×D4×D4311yescharacteristic
648C2×C4#1306337012yes—
649C2×C4#1306337212yes—
650C8—42no—
651C8—1722no—
652C22—21no—
653C22—21no—
654C22—42no—
655C22—42no—
656C22—42no—
657C22—432no—
658C22—432no—
659C22—864no—
660C22—864no—
661C22—861no—
662C22—861no—
663C22—861no—
664C22—861no—
665C22C2×C22⋊C4×D4311yescharacteristic
666C22#1458346211yescharacteristic
667C22#1458346911yescharacteristic
668C4—21no—
669C4—21no—
670C4—21no—
671C4—44no—
672C4—42no—
673C4—432no—
674C4—861no—
675C4—861no—
676C4—861no—
677C4—861no—
678C4—861no—
679C4—1724no—
680C4—1722no—
681C4—1722no—
682C4#104×D4312yes—
683C4#1458337812yes—
684C4#1458347812yes—
685C2—21no—
686C2—21no—
687C2—82no—
688C2—862no—
689C2—862no—
690C2#1913718511yescharacteristic
691C2C2×#104×D4311yescharacteristic
692C2#421×D4311yescharacteristic
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#21899
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. C4×C4⋊C4×D43C2semidirect
4. #19135539C2semidirect
5. #19135538C2semidirect
6. #19135515C2semidirect
7. #19135035C2semidirect
8. #19134613C2semidirect
9. C43×#1980C2semidirect
11. #14583454C4semidirect
12. #14583454C4semidirect
13. #14583447C4semidirect
14. #14583447C4semidirect
19. #14583428C4semidirect
20. #14583428C4semidirect
56. #13063325C2×C4semidirect
57. #13063325C2×C4semidirect
60. #13063317C2×C4semidirect
79. Q8×Dic43C2×C4semidirect
80. Q8×Dic43C2×C4semidirect
89. D4×Dic43C2×C4semidirect
90. D4×Dic43C2×C4semidirect
130. C4⋊Q8×C43C2×C4semidirect
131. #127×C43C2×C4semidirect
132. #124×C43C2×C4semidirect
300. C4×D43#104semidirect
345. #1980D43semidirect
395. C43#21899semidirect
407. C4⋊Q8C4×D43semidirect
408. #127C4×D43semidirect
416. #124C4×D43semidirect

Maximal subgroups

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

subgroupindex
#191478902
#191432262
C4×C4⋊C4×D432
#191355392
#191355382
#191355152
#191350352
#191346132
C43×#19802
#2189943