Finite Group Databasebeta

← #25063751

Subgroups — #25063751

Order 11008.

1150 conjugacy classes of subgroups.

The subgroup lattice has 658 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19147890C211yesmaximal, characteristic
2#19143225C211yesmaximal, characteristic, complemented
3#376×D43C211yesmaximal, characteristic, complemented
4#19133108C211yesmaximal, characteristic, complemented
5#19133106C211yesmaximal, characteristic, complemented
6#19133103C211yesmaximal, characteristic, complemented
7#19133096C214yesmaximal, complemented
8#19133078C214yesmaximal, complemented
9C43×#1505C211yesmaximal, characteristic, complemented
10#14583456C2211yescharacteristic
11#14583454C411yescharacteristic, complemented
12#14583454C411yescharacteristic, complemented
13#14583447C411yescharacteristic, complemented
14#14583447C411yescharacteristic, complemented
15#14583431—21no—
16#14583431C412yescomplemented
17#14583430—21no—
18#14583430C2212yes—
19#14583428—21no—
20#14583428—21no—
21#14583409—21no—
22#14583409C2212yes—
23#14583406—21no—
24#41×Dic43—21no—
25C4×#10621900—21no—
26C4×#10621900C412yescomplemented
27C2×C42×D43—21no—
28C2×C42×D43C2211yescharacteristic
29#14582956C2211yescharacteristic
30#14582954—21no—
31#14582951—21no—
32#14582949C2212yes—
33#14582921—21no—
34#14582861C2212yes—
35#14582851—21no—
36#14582745—21no—
37#14582745C2211yescharacteristic
38#14582744—21no—
39#14582744C2212yes—
40#95×D43—21no—
41#95×D43C2212yes—
42#14582637C2214yes—
43#14582635C2214yes—
44#14582633C2214yes—
45C43×#532C2211yescharacteristic
46C43×#432C2211yescharacteristic
47C43×#376C2211yescharacteristic
48C43×#327C2214yes—
49C2×#10621900—21no—
50C2×#10621900C2×C412yes—
51C22×C4×D43—22no—
52C22×C4×D43D411yescharacteristic
53C22×C4×D43D411yescharacteristic
54C22×C4×D43C2311yescharacteristic
55C2×#10621872—22no—
56#13063325C2×C411yescharacteristic, complemented
57#13063325C2×C411yescharacteristic, complemented
58#13063318—22no—
59#13063318—22no—
60#13063317—21no—
61#13063316—21no—
62#13063316C2×C412yescomplemented
63#13063312—21no—
64#13063312C2×C412yescomplemented
65#13063307—22no—
66#13063307—22no—
67#13063306—22no—
68#13063305—21no—
69#13063305C2×C412yes—
70#13063304—21no—
71#13063304C2312yes—
72#13063301—21no—
73#13063301—21no—
74#13063296—21no—
75#13063296—21no—
76#13063296—21no—
77#13063296C2×C412yes—
78#13063293—22no—
79Q8×Dic43—21no—
80Q8×Dic43—21no—
81C4×Dic86—21no—
82C4×Dic86C2×C412yescomplemented
83#13063290—21no—
84#13063290C2×C412yescomplemented
85D4×Dic43—22no—
86D4×Dic43—22no—
87D4×Dic43—21no—
88D4×Dic43—21no—
89D4×Dic43—21no—
90D4×Dic43C2×C412yescomplemented
91C4×C22⋊D43—22no—
92C4×C22⋊D43—22no—
93(C22⋊D43)⋊C4—22no—
94(C22⋊D43)⋊C4—22no—
95#13063284—21no—
96#13063284—22no—
97#13063283—21no—
98#13063283C2×C412yes—
99#13063281—22no—
100#13063281—22no—
101C2×C4×Dic43—21no—
102C2×C4×Dic43—22no—
103C2×C4×Dic43—22no—
104C2×C4×Dic43D411yescharacteristic
105C2×C4×Dic43D411yescharacteristic
106C2×C4×Dic43C2311yescharacteristic
107C42×D43—28no—
108C42×D43C2×C411yescharacteristic
109C42×D43C2×C411yescharacteristic
110C42×D43C2×C411yescharacteristic
111C42×D43C2×C411yescharacteristic
112C42×D43D411yescharacteristic
113C42×D43D411yescharacteristic
114C42×D43D411yescharacteristic
115C42×D43D411yescharacteristic
116C4⋊(C43⋊C8)—21no—
117Dic43⋊C8—22no—
118C22⋊(C43⋊C8)C2312yes—
119(C2×D43)⋊C8—22no—
120#13063236—21no—
121C8×Dic43—22no—
122C43⋊#95—21no—
123C43⋊#95—22no—
124C43⋊#95—22no—
125C43⋊#95C2312yes—
126C2×#41×C43—21no—
127C4⋊Q8×C43C2×C411yescharacteristic, complemented
128#127×C43C2×C411yescharacteristic, complemented
129#124×C43—21no—
130#121×C43—21no—
131#121×C43C2312yes—
132C4×D4×C43—21no—
133C4×D4×C43C2×C412yescomplemented
134C2×C42×C43—21no—
135C2×C42×C43C2311yescharacteristic
136C4⋊C8×C43—21no—
137C22⋊C8×C43C2312yes—
138#97×C43—21no—
139#95×C43—21no—
140#95×C43C2312yes—
141C23×D43C2×D411yescharacteristic
142#41×C43—44no—
143C2×Q8×C43—21no—
144C2×D4×C43—21no—
145C2×D4×C43—21no—
146C2×D4×C43—22no—
147C2×D4×C43C22×C412yes—
148C22×C4×C43—22no—
149C22×C4×C43—22no—
150C22×C4×C43C2×D411yescharacteristic
151C22×C4×C43C2×D411yescharacteristic
152C22×C4×C43C2411yescharacteristic
153C2×C22⋊D43—22no—
154C2×C22⋊D43—22no—
155C22×Dic43—22no—
156C22×Dic43—22no—
157C22×Dic43—22no—
158C22×Dic43C2×D411yescharacteristic
159C22×Dic43C2×D411yescharacteristic
160C22×Dic43C2×D411yescharacteristic
161#10621900—44no—
162#10621900—44no—
163C2×C4×D43—24no—
164C2×C4×D43—28no—
165C2×C4×D43—42no—
166C2×C4×D43—42no—
167C2×C4×D43—44no—
168C2×C4×D43—44no—
169C2×C4×D43C22⋊C411yescharacteristic
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×D43C2×D411yescharacteristic
180C2×C4×D43C2×D411yescharacteristic
181C2×Dic86—21no—
182C2×Dic86C22×C412yes—
183C2×C8×C43—22no—
184C4⋊C4×C43—21no—
185C4⋊C4×C43C22×C412yes—
186C22⋊C4×C43—22no—
187C22⋊C4×C43—22no—
188C42×C43—24no—
189C42×C43C22×C411yescharacteristic
190C42×C43C22×C411yescharacteristic
191C42×C43C2×D411yescharacteristic
192C42×C43C2×D411yescharacteristic
193C22⋊Dic43—22no—
194C22⋊Dic43—22no—
195C22⋊Dic43—22no—
196C22⋊Dic43—22no—
197C22⋊Dic43—22no—
198(C2×D43)⋊C4—22no—
199(C2×D43)⋊C4—22no—
200C4⋊Dic43—21no—
201C4⋊Dic43—21no—
202C4⋊Dic43—21no—
203C4⋊Dic43—22no—
204C4⋊Dic43—22no—
205C4⋊Dic43C22×C412yes—
206Dic43⋊C4—22no—
207Dic43⋊C4—22no—
208Dic43⋊C4—22no—
209Dic43⋊C4—22no—
210C4×Dic43—28no—
211C4×Dic43—24no—
212C4×Dic43—22no—
213C4×Dic43—22no—
214C4×Dic43—22no—
215C4×Dic43C22⋊C411yescharacteristic
216C4×Dic43C22⋊C411yescharacteristic
217C4×Dic43C22⋊C411yescharacteristic
218C4×Dic43C22⋊C411yescharacteristic
219C4×Dic43C22⋊C411yescharacteristic
220C4×Dic43C22⋊C411yescharacteristic
221C4×Dic43C22⋊C411yescharacteristic
222C4×Dic43C22⋊C411yescharacteristic
223C4×Dic43C22×C411yescharacteristic
224C4×Dic43C22×C411yescharacteristic
225C4×Dic43C2×D411yescharacteristic
226C4×Dic43C2×D411yescharacteristic
227C2×C43⋊C8—22no—
228#10621872—44no—
229C23×C43—22no—
230C23×C43C22×D411yescharacteristic
231C22×D43—22no—
232C22×D43—22no—
233C22×D43—22no—
234C22×D43C2×C22⋊C411yescharacteristic
235C22×D43C2×C22⋊C411yescharacteristic
236Q8×C43—42no—
237D4×C43—42no—
238D4×C43—42no—
239D4×C43—44no—
240D4×C43—42no—
241C2×C4×C43—22no—
242C2×C4×C43—22no—
243C2×C4×C43—24no—
244C2×C4×C43—22no—
245C2×C4×C43—41no—
246C2×C4×C43—44no—
247C2×C4×C43—42no—
248C2×C4×C43—42no—
249C2×C4×C43C2×C22⋊C411yescharacteristic
250C2×C4×C43C2×C22⋊C411yescharacteristic
251C2×C4×C43C2×C22⋊C411yescharacteristic
252C2×C4×C43C2×C22⋊C411yescharacteristic
253C2×C4×C43C23×C411yescharacteristic
254C2×C4×C43C22×D411yescharacteristic
255C22⋊D43—44no—
256C22⋊D43—44no—
257C2×Dic43—22no—
258C2×Dic43—22no—
259C2×Dic43—24no—
260C2×Dic43—22no—
261C2×Dic43—22no—
262C2×Dic43—41no—
263C2×Dic43—44no—
264C2×Dic43—42no—
265C2×Dic43—42no—
266C2×Dic43—44no—
267C2×Dic43C2×C22⋊C411yescharacteristic
268C2×Dic43C2×C22⋊C411yescharacteristic
269C2×Dic43C2×C22⋊C411yescharacteristic
270C2×Dic43C2×C22⋊C411yescharacteristic
271C2×Dic43C2×C22⋊C411yescharacteristic
272C2×Dic43C2×C22⋊C411yescharacteristic
273C4×D43—22no—
274C4×D43—22no—
275C4×D43—22no—
276C4×D43—22no—
277C4×D43—22no—
278C4×D43—41no—
279C4×D43—41no—
280C4×D43—41no—
281C4×D43—41no—
282C4×D43—41no—
283C4×D43—41no—
284C4×D43—416no—
285C4×D43#10414yes—
286Dic86—42no—
287Dic86—42no—
288C8×C43—42no—
289C43⋊C8—42no—
290#17541—431nomaximal, Sylow
291C22×C43—21no—
292C22×C43—21no—
293C22×C43—42no—
294C22×C43—42no—
295C22×C43—42no—
296C22×C43C22×C22⋊C411yescharacteristic
297C22×C43#57512yes—
298C2×D43—28no—
299C2×D43—21no—
300C2×D43—21no—
301C2×D43—21no—
302C2×D43—21no—
303C2×D43#41012yes—
304C2×D43C2×#10412yes—
305C4×C43—21no—
306C4×C43—21no—
307C4×C43—21no—
308C4×C43—21no—
309C4×C43—21no—
310C4×C43—44no—
311C4×C43—42no—
312C4×C43C2×#10412yes—
313Dic43—21no—
314Dic43—21no—
315Dic43—21no—
316Dic43—21no—
317Dic43—21no—
318Dic43—44no—
319Dic43—42no—
320Dic43—42no—
321Dic43C2×#10412yes—
322#3444—431no—
323#2920—431no—
324C2×#376—431no—
325#1506—431no—
326#1506—431no—
327#1505—431no—
328#1505D4311yescharacteristic, complemented
329#1504—434no—
330#1500—434no—
331C2×C43—22no—
332C2×C43—82no—
333C2×C43C2×#41011yescharacteristic
334C2×C43#289611yescharacteristic
335C2×C43C22×#10411yescharacteristic
336D43—22no—
337D43—22no—
338#533—431no—
339#533—431no—
340#533—431no—
341#532—431no—
342#532—431no—
343#532C2×D4311yescharacteristic
344#529—432no—
345#529—432no—
346#529—861no—
347#529—861no—
348#529—861no—
349#529—861no—
350#525—432no—
351#525—861no—
352#525—861no—
353C4×#41—432no—
354C4×#41—861no—
355C4×#41—861no—
356C22×C42—431no—
357C22×C42—861no—
358#432—431no—
359#432—861no—
360#432C2×D4311yescharacteristic
361#431—432no—
362#431—861no—
363#423—861no—
364#407—432no—
365C4×M16—861no—
366#376—431no—
367#376—432no—
368#376—861no—
369#376—861no—
370#376C2×D4311yescharacteristic
371C2×#95—432no—
372C2×#95—861no—
373#328—434no—
374#328—434no—
375#327—434no—
376#327C2×D4314yes—
377C43#1754111yescharacteristic, complemented, Sylow
378C2×#41—21no—
379C2×#41—432no—
380C2×#41—861no—
381C23×C4—431no—
382C23×C4—431no—
383C23×C4—431no—
384C23×C4—862no—
385C2×M16—862no—
386C4⋊Q8—431no—
387C4⋊Q8—431no—
388C4⋊Q8C4×D4311yescharacteristic, complemented
389#127C4×D4311yescharacteristic, complemented
390#126—862no—
391#126—862no—
392#125—432no—
393#125—861no—
394#125—861no—
395#124—21no—
396#124—432no—
397#124—861no—
398#123—862no—
399#123—862no—
400#123—862no—
401C22⋊Q8—432no—
402C22⋊Q8—432no—
403C22⋊Q8—861no—
404C22⋊Q8—861no—
405C22⋊Q8—861no—
406C22⋊Q8—861no—
407#121—21no—
408#121—432no—
409#121—861no—
410#121—861no—
411#121—861no—
412#121C22×D4312yes—
413#120—862no—
414C4×Q8—432no—
415C4×Q8—432no—
416C4×Q8—861no—
417C4×Q8—861no—
418C4×Q8—861no—
419C4×Q8—861no—
420C4×D4—21no—
421C4×D4—432no—
422C4×D4—861no—
423C4×D4—861no—
424C4×D4—861no—
425C4×D4—862no—
426C4×D4—862no—
427C4×D4—862no—
428C4×D4—862no—
429C4×D4—862no—
430C4×D4—862no—
431C4×D4C4×D4312yescomplemented
432#117—432no—
433#117—862no—
434#117—862no—
435#117—862no—
436#117—861no—
437#117—861no—
438C2×C42—21no—
439C2×C42—431no—
440C2×C42—431no—
441C2×C42—431no—
442C2×C42—431no—
443C2×C42—431no—
444C2×C42—431no—
445C2×C42—431no—
446C2×C42—431no—
447C2×C42—431no—
448C2×C42—431no—
449C2×C42—431no—
450C2×C42—868no—
451C2×C42—862no—
452C2×C42—862no—
453C2×C42—861no—
454C2×C42C22×D4311yescharacteristic
455C4⋊C8—21no—
456C4⋊C8—862no—
457C4⋊C8—861no—
458C22⋊C8—432no—
459C22⋊C8—862no—
460C22⋊C8C22×D4312yes—
461#97—21no—
462#97—861no—
463C4×C8—862no—
464#95—21no—
465#95—432no—
466#95—862no—
467#95—862no—
468#95—861no—
469#95C22×D4312yes—
470C24—431no—
471#41—44no—
472#41—1724no—
473#41—1724no—
474C2×Q8—21no—
475C2×Q8—432no—
476C2×Q8—861no—
477C2×D4—22no—
478C2×D4—21no—
479C2×D4—21no—
480C2×D4—862no—
481C2×D4—862no—
482C2×D4C2×C4×D4312yes—
483C22×C4—22no—
484C22×C4—22no—
485C22×C4—431no—
486C22×C4—431no—
487C22×C4—431no—
488C22×C4—431no—
489C22×C4—431no—
490C22×C4—431no—
491C22×C4—431no—
492C22×C4—431no—
493C22×C4—431no—
494C22×C4—431no—
495C22×C4—431no—
496C22×C4—431no—
497C22×C4—431no—
498C22×C4—431no—
499C22×C4—431no—
500C22×C4—864no—
501C22×C4—868no—
502C22×C4—862no—
503C22×C4—862no—
504C22×C4—862no—
505C22×C4—1722no—
506C22×C4—1722no—
507C22×C4—1724no—
508C22×C4—1724no—
509C22×C4D4×D4311yescharacteristic
510C22×C4D4×D4311yescharacteristic
511C22×C4C23×D4311yescharacteristic
512M16—1724no—
513C2×C8—22no—
514C2×C8—862no—
515C4⋊C4—21no—
516C4⋊C4—432no—
517C4⋊C4—862no—
518C4⋊C4—862no—
519C4⋊C4—862no—
520C4⋊C4—862no—
521C4⋊C4—862no—
522C4⋊C4—861no—
523C4⋊C4—861no—
524C4⋊C4—861no—
525C4⋊C4—862no—
526C4⋊C4C2×C4×D4312yes—
527C22⋊C4—22no—
528C22⋊C4—22no—
529C22⋊C4—862no—
530C22⋊C4—862no—
531C22⋊C4—862no—
532C22⋊C4—862no—
533C22⋊C4—862no—
534C22⋊C4—862no—
535C22⋊C4—862no—
536C42—24no—
537C42—431no—
538C42—431no—
539C42—431no—
540C42—431no—
541C42—431no—
542C42—431no—
543C42—431no—
544C42—431no—
545C42—431no—
546C42—431no—
547C42—431no—
548C42—431no—
549C42—862no—
550C42—862no—
551C42—864no—
552C42—868no—
553C42—862no—
554C42C2×C4×D4311yescharacteristic
555C42C2×C4×D4311yescharacteristic
556C42D4×D4311yescharacteristic
557C42D4×D4311yescharacteristic
558C23—22no—
559C23—431no—
560C23—431no—
561C23—862no—
562C23—862no—
563C23—862no—
564C23C2×D4×D4311yescharacteristic
565Q8—42no—
566Q8—1722no—
567Q8—1722no—
568D4—42no—
569D4—42no—
570D4—44no—
571D4—42no—
572D4—1724no—
573D4—1724no—
574C2×C4—22no—
575C2×C4—22no—
576C2×C4—24no—
577C2×C4—22no—
578C2×C4—41no—
579C2×C4—44no—
580C2×C4—42no—
581C2×C4—42no—
582C2×C4—431no—
583C2×C4—434no—
584C2×C4—431no—
585C2×C4—431no—
586C2×C4—431no—
587C2×C4—431no—
588C2×C4—431no—
589C2×C4—862no—
590C2×C4—862no—
591C2×C4—862no—
592C2×C4—862no—
593C2×C4—862no—
594C2×C4—862no—
595C2×C4—862no—
596C2×C4—864no—
597C2×C4—862no—
598C2×C4—862no—
599C2×C4—1721no—
600C2×C4—1721no—
601C2×C4—1721no—
602C2×C4—1721no—
603C2×C4—1721no—
604C2×C4—1721no—
605C2×C4—17216no—
606C2×C4—1724no—
607C2×C4—1721no—
608C2×C4—1724no—
609C2×C4—1722no—
610C2×C4—1722no—
611C2×C4C22⋊C4×D4311yescharacteristic
612C2×C4C22⋊C4×D4311yescharacteristic
613C2×C4C22⋊C4×D4311yescharacteristic
614C2×C4C22⋊C4×D4311yescharacteristic
615C2×C4C22×C4×D4311yescharacteristic
616C2×C4C2×D4×D4311yescharacteristic
617C8—42no—
618C8—1722no—
619C22—21no—
620C22—21no—
621C22—42no—
622C22—42no—
623C22—42no—
624C22—432no—
625C22—432no—
626C22—868no—
627C22—861no—
628C22—861no—
629C22—861no—
630C22—861no—
631C22C2×C22⋊C4×D4311yescharacteristic
632C22#1458369512yes—
633C4—21no—
634C4—21no—
635C4—21no—
636C4—21no—
637C4—21no—
638C4—44no—
639C4—42no—
640C4—432no—
641C4—861no—
642C4—861no—
643C4—861no—
644C4—861no—
645C4—861no—
646C4—1724no—
647C4—1722no—
648C4—1722no—
649C4#104×D4312yes—
650C2—22no—
651C2—82no—
652C2—862no—
653C2—862no—
654C2#410×D4311yescharacteristic
655C2#1914310911yescharacteristic
656C2C2×#104×D4311yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1505C2
socleC22×C43C22×C22⋊C4
prime radical#19147890C2
cosocleC22×C4×C43C24
hypercenter#1505D43
hypocenterC43#17541
LCSG ▷ C2×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1505

Complements

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

NH ≅ G/Ntype
2. #19143225C2semidirect
3. #376×D43C2semidirect
4. #19133108C2semidirect
5. #19133106C2semidirect
6. #19133103C2semidirect
7. #19133096C2semidirect
8. #19133078C2semidirect
9. C43×#1505C2semidirect
11. #14583454C4semidirect
12. #14583454C4semidirect
13. #14583447C4semidirect
14. #14583447C4semidirect
16. #14583431C4semidirect
26. C4×#10621900C4semidirect
56. #13063325C2×C4semidirect
57. #13063325C2×C4semidirect
62. #13063316C2×C4semidirect
64. #13063312C2×C4semidirect
82. C4×Dic86C2×C4semidirect
84. #13063290C2×C4semidirect
90. D4×Dic43C2×C4semidirect
127. C4⋊Q8×C43C2×C4semidirect
128. #127×C43C2×C4semidirect
133. C4×D4×C43C2×C4semidirect
328. #1505D43semidirect
377. C43#17541semidirect
388. C4⋊Q8C4×D43semidirect
389. #127C4×D43semidirect
431. C4×D4C4×D43semidirect

Maximal subgroups

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

subgroupindex
#191478902
#191432252
#376×D432
#191331082
#191331062
#191331032
#191330962
#191330782
C43×#15052
#1754143