Finite Group Databasebeta

← #25099827

Subgroups — #25099827

Order 11008.

772 conjugacy classes of subgroups.

The subgroup lattice has 678 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19143395C211yesmaximal, characteristic
2#19143238C211yesmaximal, characteristic, complemented
3#19143017C211yesmaximal, characteristic, complemented
4#19135243C211yesmaximal, characteristic, complemented
5#19135241C211yesmaximal, characteristic, complemented
6#19135196C211yesmaximal, characteristic, complemented
7#19134923C211yesmaximal, characteristic
8#19134921C211yesmaximal, characteristic
9#19134871C211yesmaximal, characteristic, complemented
10#19134869C211yesmaximal, characteristic, complemented
11#19134500C211yesmaximal, characteristic, complemented
12#19134404C211yesmaximal, characteristic, complemented
13#19134404C211yesmaximal, characteristic, complemented
14#19134345C211yesmaximal, characteristic, complemented
15C43×#1922C211yesmaximal, characteristic, complemented
16C2×#13063347C2211yescharacteristic
17C2×#13063333C2211yescharacteristic
18C2×#13063331C2211yescharacteristic
19#14583367C2211yescharacteristic
20#14583367C2211yescharacteristic
21#14583010C411yescharacteristic, complemented
22#14583010C411yescharacteristic, complemented
23#14583005C411yescharacteristic, complemented
24#14583005C411yescharacteristic, complemented
25#14582998C411yescharacteristic, complemented
26#14582998C411yescharacteristic, complemented
27#14582998C411yescharacteristic, complemented
28#14582998C411yescharacteristic, complemented
29#14582959—21no—
30#14582959—21no—
31#14582951—21no—
32#14582951—21no—
33C2×#13063260C2211yescharacteristic
34C2×#13063260C2211yescharacteristic
35#14582926C2211yescharacteristic
36C2×#13063253C2211yescharacteristic
37C2×#13063253C2211yescharacteristic
38C2×#13063251C2211yescharacteristic
39C2×#13063251C2211yescharacteristic
40#14582893C2211yescharacteristic
41#14582893C2211yescharacteristic
42#14582867C2211yescharacteristic
43#14582865C2211yescharacteristic
44#14582856—21no—
45#14582855C2211yescharacteristic
46#14582853—21no—
47#14582851—21no—
48M16×Dic43C2211yescharacteristic
49M16×Dic43C2211yescharacteristic
50C2×#13063235C2211yescharacteristic
51C2×C8×Dic43C2211yescharacteristic
52C4×C8×D43—21no—
53#14582745C2211yescharacteristic
54#14582664C2211yescharacteristic
55#14582658C2211yescharacteristic
56#14582658C2211yescharacteristic
57#14582654C2211yescharacteristic
58#14582653C2211yescharacteristic
59#14582653C2211yescharacteristic
60C43×#427C2211yescharacteristic
61C43×#424C2211yescharacteristic
62C43×#405C2211yescharacteristic
63C43×#341C2211yescharacteristic
64C43×#339C2211yescharacteristic
65C43×#339C2211yescharacteristic
66C43×#336C2211yescharacteristic
67C2×#10621898C2311yescharacteristic
68C2×#10621898C2311yescharacteristic
69#13063347—22no—
70#13063347—22no—
71C2×Dic172C2×C411yescharacteristic
72C2×#10621873C2×C411yescharacteristic
73C2×#10621873C2×C411yescharacteristic
74C2×D344C2×C411yescharacteristic
75#13063333—22no—
76#13063333—22no—
77#13063331—22no—
78#13063331—22no—
79C2×#10621877C2311yescharacteristic
80C2×#10621877C2311yescharacteristic
81C2×#10621872—21no—
82C2×#10621872—21no—
83C22×C43⋊C8C2311yescharacteristic
84C22×C43⋊C8C2311yescharacteristic
85C2×C8×D43—21no—
86C2×C8×D43—21no—
87#13063290C2×C411yescharacteristic
88#13063290C2×C411yescharacteristic
89#13063290C2×C411yescharacteristic
90#13063290C2×C411yescharacteristic
91#13063287C2×C411yescharacteristic
92#13063287C2×C411yescharacteristic
93#13063287C2×C411yescharacteristic
94#13063287C2×C411yescharacteristic
95(C22⋊D43)⋊C4—21no—
96(C22⋊D43)⋊C4—21no—
97(C22⋊D43)⋊C4—21no—
98(C22⋊D43)⋊C4—21no—
99#13063282—21no—
100#13063282—21no—
101C2×C4×Dic43C2311yescharacteristic
102C2×C4×Dic43C2311yescharacteristic
103C42×D43—21no—
104C42×D43—21no—
105#13063260—22no—
106#13063260—22no—
107C4⋊(C43⋊C8)—21no—
108C4⋊(C43⋊C8)—21no—
109#13063253—22no—
110#13063253—22no—
111#13063251—22no—
112#13063251—22no—
113#13063248C2×C411yescharacteristic
114#13063248C2×C411yescharacteristic
115#13063248C2×C411yescharacteristic
116#13063248C2×C411yescharacteristic
117#13063245C2×C411yescharacteristic
118#13063245C2×C411yescharacteristic
119#13063245C2×C411yescharacteristic
120#13063245C2×C411yescharacteristic
121(C2×D43)⋊C8—21no—
122(C2×D43)⋊C8—21no—
123(C2×D43)⋊C8—21no—
124(C2×D43)⋊C8—21no—
125#13063236—21no—
126#13063235—21no—
127#13063235—21no—
128#13063235C2×C411yescharacteristic
129#13063235C2×C411yescharacteristic
130#13063235C2×C411yescharacteristic
131#13063235C2×C411yescharacteristic
132C4×C43⋊C8—21no—
133C8×Dic43—21no—
134C8×Dic43—21no—
135C8×Dic43D411yescharacteristic
136C8×Dic43D411yescharacteristic
137C8×Dic43D411yescharacteristic
138C8×Dic43D411yescharacteristic
139C43⋊#95—21no—
140C43⋊#95—21no—
141C2×M16×C43C2311yescharacteristic
142C2×M16×C43C2311yescharacteristic
143C22×C8×C43C2311yescharacteristic
144C22×C8×C43C2311yescharacteristic
145#117×C43C2311yescharacteristic
146#117×C43C2311yescharacteristic
147C2×C42×C43C2311yescharacteristic
148#107×C43C2×C411yescharacteristic
149#107×C43C2×C411yescharacteristic
150#106×C43C2×C411yescharacteristic
151#106×C43C2×C411yescharacteristic
152C4⋊C8×C43—21no—
153C4⋊C8×C43—21no—
154#97×C43—21no—
155C4×C8×C43—21no—
156C22×C4×C43—21no—
157C22×C4×C43C2411yescharacteristic
158C2×C22⋊D43—21no—
159C2×C22⋊D43—21no—
160C22×Dic43—21no—
161C22×Dic43#4111yescharacteristic
162C22×Dic43#4111yescharacteristic
163#10621898—21no—
164#10621898—21no—
165#10621898—21no—
166#10621898—21no—
167#10621898—21no—
168#10621898—21no—
169#10621898#4112yes—
170#10621898#4112yes—
171C2×D172C22×C411yescharacteristic
172C2×D172C22×C411yescharacteristic
173C2×C4×D43—21no—
174C2×C4×D43—21no—
175C2×C4×D43—21no—
176C2×C4×D43—21no—
177C2×C4×D43—21no—
178C2×C4×D43—21no—
179C2×Dic86C22×C411yescharacteristic
180C2×Dic86C22×C411yescharacteristic
181M16×C43—21no—
182M16×C43—21no—
183M16×C43—21no—
184M16×C43#4112yes—
185C2×C8×C43—21no—
186C2×C8×C43—21no—
187C2×C8×C43—21no—
188C2×C8×C43—21no—
189C2×C8×C43—21no—
190C2×C8×C43—21no—
191C2×C8×C43C22×C411yescharacteristic
192C2×C8×C43C22×C411yescharacteristic
193C2×C8×C43C2×D411yescharacteristic
194C2×C8×C43C2×D411yescharacteristic
195C4⋊C4×C43C22×C411yescharacteristic
196C4⋊C4×C43C22×C411yescharacteristic
197C4⋊C4×C43C22×C411yescharacteristic
198C4⋊C4×C43C22×C411yescharacteristic
199C22⋊C4×C43—21no—
200C22⋊C4×C43—21no—
201C42×C43—21no—
202C42×C43—21no—
203C42×C43—21no—
204C42×C43—21no—
205(C2×D43)⋊C4—21no—
206(C2×D43)⋊C4—21no—
207(C2×D43)⋊C4—21no—
208(C2×D43)⋊C4—21no—
209Dic43⋊C4—21no—
210Dic43⋊C4—21no—
211Dic43⋊C4—21no—
212Dic43⋊C4—21no—
213C4×Dic43—21no—
214C4×Dic43—21no—
215C4×Dic43—21no—
216C4×Dic43—21no—
217C4×Dic43—21no—
218C4×Dic43—21no—
219C4×Dic43C22×C411yescharacteristic
220C4×Dic43C22×C411yescharacteristic
221C4×Dic43C2×D411yescharacteristic
222C4×Dic43C2×D411yescharacteristic
223#10621877—21no—
224#10621877—21no—
225#10621877—21no—
226#10621877#4112yes—
227C2×C43⋊C8—21no—
228C2×C43⋊C8—21no—
229C2×C43⋊C8—21no—
230C2×C43⋊C8—21no—
231C2×C43⋊C8—21no—
232C2×C43⋊C8—21no—
233C2×C43⋊C8C22×C411yescharacteristic
234C2×C43⋊C8C22×C411yescharacteristic
235C2×C43⋊C8C2×D411yescharacteristic
236C2×C43⋊C8C2×D411yescharacteristic
237Dic172—22no—
238D344—22no—
239#10621873—22no—
240#10621873—22no—
241#10621872—24no—
242#10621872—24no—
243C8×D43—24no—
244C8×D43—24no—
245C23×C43C2×#4111yescharacteristic
246C22×D43—21no—
247C22×D43—21no—
248C2×C4×C43—21no—
249C2×C4×C43—21no—
250C2×C4×C43—21no—
251C2×C4×C43—21no—
252C2×C4×C43—41no—
253C2×C4×C43—41no—
254C2×C4×C43—41no—
255C2×C4×C43C23×C411yescharacteristic
256C2×C4×C43C22×D411yescharacteristic
257C2×C4×C43C2×#4111yescharacteristic
258C2×C4×C43C2×#4111yescharacteristic
259C2×C4×C43C2×#4111yescharacteristic
260C2×C4×C43C2×#4111yescharacteristic
261C22⋊D43—22no—
262C22⋊D43—22no—
263C22⋊D43—41no—
264C22⋊D43—41no—
265C2×Dic43—21no—
266C2×Dic43—21no—
267C2×Dic43—41no—
268C2×Dic43—41no—
269C2×Dic43—41no—
270C2×Dic43—41no—
271C2×Dic43—41no—
272C2×Dic43C4×D411yescharacteristic
273C2×Dic43C4×D411yescharacteristic
274C2×Dic43C4×D411yescharacteristic
275C2×Dic43C4×D411yescharacteristic
276D172—21no—
277D172—21no—
278D172—21no—
279D172#11712yes—
280C4×D43—22no—
281C4×D43—22no—
282C4×D43—42no—
283C4×D43—42no—
284C4×D43—42no—
285C4×D43—42no—
286C4×D43—41no—
287C4×D43—41no—
288Dic86—21no—
289Dic86—21no—
290Dic86—21no—
291Dic86#11712yes—
292C8×C43—21no—
293C8×C43—21no—
294C8×C43—21no—
295C8×C43—22no—
296C8×C43—21no—
297C8×C43—41no—
298C43⋊C8—21no—
299C43⋊C8—21no—
300C43⋊C8—21no—
301C43⋊C8—22no—
302C43⋊C8—21no—
303C43⋊C8—41no—
304#21138—431nomaximal, Sylow
305C22×C43—21no—
306C22×C43—21no—
307C22×C43C2×C4×D411yescharacteristic
308C22×C43#52911yescharacteristic
309C22×C43#52911yescharacteristic
310C2×D43—22no—
311C2×D43—41no—
312C2×D43—41no—
313C2×D43—41no—
314C2×D43—41no—
315C2×D43—41no—
316C4×C43—41no—
317C4×C43—41no—
318C4×C43—41no—
319C4×C43—41no—
320C4×C43—81no—
321C4×C43C2×#11711yescharacteristic
322C4×C43C4×#4111yescharacteristic
323C4×C43#52511yescharacteristic
324C4×C43#52511yescharacteristic
325Dic43—21no—
326Dic43—21no—
327Dic43—21no—
328Dic43—21no—
329Dic43—22no—
330Dic43—41no—
331Dic43—81no—
332#2943—431no—
333#2922—431no—
334C4×#131—431no—
335#1929—431no—
336#1929—431no—
337#1922—431no—
338#1922D4311yescharacteristic, complemented
339#1876—431no—
340#1876—431no—
341#1866—431no—
342#1866—431no—
343#1778—431no—
344#1759—431no—
345#1759—431no—
346#1746—431no—
347C2×C43—21no—
348C2×C43—21no—
349C2×C43#229011yescharacteristic
350C2×C43#295511yescharacteristic
351C2×C43#295511yescharacteristic
352D43—42no—
353D43—81no—
354C2×#135—431no—
355C2×#131—431no—
356C2×#131—431no—
357C4×#41—431no—
358C4×#41—431no—
359#442—431no—
360#442—431no—
361#441—431no—
362#441—431no—
363#440—431no—
364#440—431no—
365#440—431no—
366#440—431no—
367#433—861no—
368#433—861no—
369#431—861no—
370#431—861no—
371C2×#108—431no—
372C2×#108—431no—
373#427C2×D4311yescharacteristic
374#424—431no—
375#424C2×D4311yescharacteristic
376C2×#104—431no—
377C2×#104—431no—
378C2×#104—431no—
379C2×#104—431no—
380#416—431no—
381#416—431no—
382#408—431no—
383#408—431no—
384#405—431no—
385#405—861no—
386#405—861no—
387#405C2×D4311yescharacteristic
388C4×M16—431no—
389C4×M16—431no—
390C4×M16—861no—
391C2×#97—431no—
392C2×C4×C8—431no—
393C2×C4×C8—861no—
394#376—431no—
395#341—431no—
396#341C2×D4311yescharacteristic
397#339—431no—
398#339—431no—
399#339C2×D4311yescharacteristic
400#339C2×D4311yescharacteristic
401#336—431no—
402#336—431no—
403#336—431no—
404#336C2×D4311yescharacteristic
405C43#2113811yescharacteristic, complemented, Sylow
406C2×#41—431no—
407C2×#41—431no—
408#135—862no—
409#135—862no—
410C2×Q16—431no—
411C2×SD16—431no—
412C2×SD16—431no—
413C2×D8—431no—
414#131—862no—
415#131—862no—
416#131—862no—
417#131—862no—
418C2×M16—431no—
419C2×M16—431no—
420C2×M16—861no—
421C2×M16—861no—
422C2×M16C22×D4311yescharacteristic
423C2×M16C22×D4311yescharacteristic
424C22×C8—431no—
425C22×C8—431no—
426C22×C8—861no—
427C22×C8—861no—
428C22×C8C22×D4311yescharacteristic
429C22×C8C22×D4311yescharacteristic
430C4×Q8—431no—
431C4×Q8—431no—
432C4×Q8—431no—
433C4×Q8—431no—
434C4×D4—431no—
435C4×D4—431no—
436C4×D4—431no—
437C4×D4—431no—
438C4×D4—861no—
439C4×D4—861no—
440C4×D4—861no—
441C4×D4—861no—
442#117—861no—
443#117—861no—
444#117C22×D4311yescharacteristic
445#117C22×D4311yescharacteristic
446C2×C42—431no—
447C2×C42—431no—
448C2×C42—861no—
449C2×C42—861no—
450C2×C42C22×D4311yescharacteristic
451#108—862no—
452#108—862no—
453#107C4×D4311yescharacteristic
454#107C4×D4311yescharacteristic
455#106C4×D4311yescharacteristic
456#106C4×D4311yescharacteristic
457C4⋊C8—21no—
458C4⋊C8—21no—
459C4⋊C8—861no—
460C4⋊C8—861no—
461#104—862no—
462#104—862no—
463#104—862no—
464#104—862no—
465#103—431no—
466#103—431no—
467#103—431no—
468#103—431no—
469#102—431no—
470#102—431no—
471#102—431no—
472#102—431no—
473C22⋊C8—861no—
474C22⋊C8—861no—
475C22⋊C8—861no—
476C22⋊C8—861no—
477#97—21no—
478#97—431no—
479#97—431no—
480#97—431no—
481#97—431no—
482#97—861no—
483#97—861no—
484#97—861no—
485C4×C8—21no—
486C4×C8—431no—
487C4×C8—431no—
488C4×C8—431no—
489C4×C8—431no—
490C4×C8—861no—
491C4×C8—861no—
492C4×C8—861no—
493#95—861no—
494#95—861no—
495#41—432no—
496#41—432no—
497#41—861no—
498#41—861no—
499#41—861no—
500#41—861no—
501#41—861no—
502#41—861no—
503C2×Q8—431no—
504C2×Q8—431no—
505C2×D4—431no—
506C2×D4—431no—
507C2×D4—861no—
508C2×D4—861no—
509C22×C4—21no—
510C22×C4—431no—
511C22×C4—431no—
512C22×C4—861no—
513C22×C4—861no—
514C22×C4—861no—
515C22×C4—861no—
516C22×C4—861no—
517C22×C4—861no—
518C22×C4—861no—
519C22×C4C23×D4311yescharacteristic
520Q16—862no—
521SD16—862no—
522SD16—862no—
523D8—862no—
524M16—21no—
525M16—21no—
526M16—21no—
527M16—432no—
528M16—864no—
529M16—864no—
530M16—861no—
531M16—861no—
532M16—861no—
533M16#1062190212yes—
534C2×C8—21no—
535C2×C8—21no—
536C2×C8—21no—
537C2×C8—21no—
538C2×C8—21no—
539C2×C8—21no—
540C2×C8—431no—
541C2×C8—431no—
542C2×C8—431no—
543C2×C8—431no—
544C2×C8—864no—
545C2×C8—864no—
546C2×C8—861no—
547C2×C8—861no—
548C2×C8—861no—
549C2×C8—861no—
550C2×C8—861no—
551C2×C8—861no—
552C2×C8C2×C4×D4311yescharacteristic
553C2×C8C2×C4×D4311yescharacteristic
554C2×C8D4×D4311yescharacteristic
555C2×C8D4×D4311yescharacteristic
556C4⋊C4—861no—
557C4⋊C4—861no—
558C4⋊C4—861no—
559C4⋊C4—861no—
560C4⋊C4C2×C4×D4311yescharacteristic
561C4⋊C4C2×C4×D4311yescharacteristic
562C4⋊C4C2×C4×D4311yescharacteristic
563C4⋊C4C2×C4×D4311yescharacteristic
564C22⋊C4—21no—
565C22⋊C4—21no—
566C22⋊C4—861no—
567C22⋊C4—861no—
568C22⋊C4—861no—
569C22⋊C4—861no—
570C42—21no—
571C42—21no—
572C42—21no—
573C42—21no—
574C42—431no—
575C42—431no—
576C42—431no—
577C42—431no—
578C42—861no—
579C42—861no—
580C42—861no—
581C42—861no—
582C42—861no—
583C42—861no—
584C23—861no—
585C23—861no—
586C23#41×D4311yescharacteristic
587Q8—432no—
588Q8—861no—
589Q8—861no—
590Q8—861no—
591D4—432no—
592D4—862no—
593D4—862no—
594D4—861no—
595D4—861no—
596D4—861no—
597D4—1721no—
598D4—1721no—
599C2×C4—21no—
600C2×C4—21no—
601C2×C4—21no—
602C2×C4—21no—
603C2×C4—41no—
604C2×C4—41no—
605C2×C4—41no—
606C2×C4—431no—
607C2×C4—431no—
608C2×C4—431no—
609C2×C4—431no—
610C2×C4—861no—
611C2×C4—862no—
612C2×C4—862no—
613C2×C4—861no—
614C2×C4—1722no—
615C2×C4—1722no—
616C2×C4—1722no—
617C2×C4—1722no—
618C2×C4—1721no—
619C2×C4—1721no—
620C2×C4—1721no—
621C2×C4—1721no—
622C2×C4—1721no—
623C2×C4—1721no—
624C2×C4—1721no—
625C2×C4C22×C4×D4311yescharacteristic
626C2×C4C2×D4×D4311yescharacteristic
627C2×C4#41×D4311yescharacteristic
628C2×C4#41×D4311yescharacteristic
629C2×C4#41×D4311yescharacteristic
630C2×C4C2×#1062190211yescharacteristic
631C8—21no—
632C8—21no—
633C8—21no—
634C8—21no—
635C8—22no—
636C8—41no—
637C8—861no—
638C8—861no—
639C8—862no—
640C8—861no—
641C8—861no—
642C8—1721no—
643C22—21no—
644C22—21no—
645C22—862no—
646C22—1721no—
647C22—1721no—
648C22—1721no—
649C22—1721no—
650C22—1721no—
651C22C4×D4×D4311yescharacteristic
652C22#1458343211yescharacteristic
653C22#1458343411yescharacteristic
654C4—41no—
655C4—41no—
656C4—41no—
657C4—41no—
658C4—81no—
659C4—862no—
660C4—861no—
661C4—861no—
662C4—861no—
663C4—861no—
664C4—3441no—
665C4—1721no—
666C4#117×D4311yescharacteristic
667C4C4×#1062190211yescharacteristic
668C4#1458340711yescharacteristic
669C4#1458341211yescharacteristic
670C2—21no—
671C2—21no—
672C2—3441no—
673C2—1722no—
674C2#1913703311yescharacteristic
675C2#1914349311yescharacteristic
676C2#1914349511yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1922C2
socleC22×C43C2×C4×D4
prime radicalC2×#13063347C22
cosocleC22×C4×C43C24
hypercenter#1922D43
hypocenterC43#21138
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C22×C8 ◁ #1922

Complements

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

NH ≅ G/Ntype
2. #19143238C2semidirect
3. #19143017C2semidirect
4. #19135243C2semidirect
5. #19135241C2semidirect
6. #19135196C2semidirect
9. #19134871C2semidirect
10. #19134869C2semidirect
11. #19134500C2semidirect
12. #19134404C2semidirect
13. #19134404C2semidirect
14. #19134345C2semidirect
15. C43×#1922C2semidirect
21. #14583010C4semidirect
22. #14583010C4semidirect
23. #14583005C4semidirect
24. #14583005C4semidirect
25. #14582998C4semidirect
26. #14582998C4semidirect
27. #14582998C4semidirect
28. #14582998C4semidirect
338. #1922D43semidirect
405. C43#21138semidirect

Maximal subgroups

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

subgroupindex
#191433952
#191432382
#191430172
#191352432
#191352412
#191351962
#191349232
#191349212
#191348712
#191348692
#191345002
#191344042
#191343452
C43×#19222
#2113843