Finite Group Databasebeta

← #25099838

Subgroups — #25099838

Order 11008.

780 conjugacy classes of subgroups.

The subgroup lattice has 682 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19143395C211yesmaximal, characteristic
2#19143245C211yesmaximal, characteristic, complemented
3#19143022C211yesmaximal, 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#19134399C211yesmaximal, characteristic, complemented
13#19134399C211yesmaximal, characteristic, complemented
14#19134342C211yesmaximal, 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#14582955—21no—
32#14582955—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—
47M16×Dic43C2211yescharacteristic
48M16×Dic43C2211yescharacteristic
49C4×#10621872—21no—
50C2×#13063235C2211yescharacteristic
51C2×#13063235C2211yescharacteristic
52#97×D43—21no—
53C42×Dic43C2211yescharacteristic
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×Dic43—21no—
102C2×C4×Dic43—21no—
103C2×C4×Dic43C2311yescharacteristic
104C2×C4×Dic43C2311yescharacteristic
105C42×D43—21no—
106C42×D43—21no—
107#13063260—22no—
108#13063260—22no—
109C4⋊(C43⋊C8)—21no—
110C4⋊(C43⋊C8)—21no—
111#13063253—22no—
112#13063253—22no—
113#13063251—22no—
114#13063251—22no—
115#13063248C2×C411yescharacteristic
116#13063248C2×C411yescharacteristic
117#13063248C2×C411yescharacteristic
118#13063248C2×C411yescharacteristic
119#13063245C2×C411yescharacteristic
120#13063245C2×C411yescharacteristic
121#13063245C2×C411yescharacteristic
122#13063245C2×C411yescharacteristic
123(C2×D43)⋊C8—21no—
124(C2×D43)⋊C8—21no—
125(C2×D43)⋊C8—21no—
126(C2×D43)⋊C8—21no—
127#13063236—21no—
128#13063235—21no—
129#13063235—21no—
130#13063235C2×C411yescharacteristic
131#13063235C2×C411yescharacteristic
132#13063235C2×C411yescharacteristic
133#13063235C2×C411yescharacteristic
134#13063235D411yescharacteristic
135#13063235D411yescharacteristic
136#13063235D411yescharacteristic
137#13063235D411yescharacteristic
138C4×C43⋊C8—21no—
139C8×Dic43—21no—
140C8×Dic43—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×Dic43—42no—
220C4×Dic43—42no—
221C4×Dic43C22×C411yescharacteristic
222C4×Dic43C22×C411yescharacteristic
223C4×Dic43C2×D411yescharacteristic
224C4×Dic43C2×D411yescharacteristic
225#10621877—21no—
226#10621877—21no—
227#10621877—21no—
228#10621877#4112yes—
229C2×C43⋊C8—21no—
230C2×C43⋊C8—21no—
231C2×C43⋊C8—21no—
232C2×C43⋊C8—21no—
233C2×C43⋊C8—21no—
234C2×C43⋊C8—21no—
235C2×C43⋊C8C22×C411yescharacteristic
236C2×C43⋊C8C22×C411yescharacteristic
237C2×C43⋊C8C2×D411yescharacteristic
238C2×C43⋊C8C2×D411yescharacteristic
239Dic172—22no—
240D344—22no—
241#10621873—22no—
242#10621873—22no—
243#10621872—24no—
244#10621872—24no—
245C8×D43—24no—
246C8×D43—24no—
247C23×C43C2×#4111yescharacteristic
248C22×D43—21no—
249C22×D43—21no—
250C2×C4×C43—22no—
251C2×C4×C43—21no—
252C2×C4×C43—21no—
253C2×C4×C43—21no—
254C2×C4×C43—21no—
255C2×C4×C43—41no—
256C2×C4×C43—41no—
257C2×C4×C43C23×C411yescharacteristic
258C2×C4×C43C22×D411yescharacteristic
259C2×C4×C43C2×#4111yescharacteristic
260C2×C4×C43C2×#4111yescharacteristic
261C2×C4×C43C2×#4111yescharacteristic
262C2×C4×C43C2×#4111yescharacteristic
263C22⋊D43—22no—
264C22⋊D43—22no—
265C22⋊D43—41no—
266C22⋊D43—41no—
267C2×Dic43—21no—
268C2×Dic43—22no—
269C2×Dic43—21no—
270C2×Dic43—41no—
271C2×Dic43—41no—
272C2×Dic43—41no—
273C2×Dic43—41no—
274C2×Dic43C4×D411yescharacteristic
275C2×Dic43C4×D411yescharacteristic
276C2×Dic43C4×D411yescharacteristic
277C2×Dic43C4×D411yescharacteristic
278D172—21no—
279D172—21no—
280D172—21no—
281D172#11712yes—
282C4×D43—22no—
283C4×D43—22no—
284C4×D43—41no—
285C4×D43—41no—
286C4×D43—81no—
287C4×D43—81no—
288C4×D43—81no—
289C4×D43—81no—
290Dic86—21no—
291Dic86—21no—
292Dic86—21no—
293Dic86#11712yes—
294C8×C43—21no—
295C8×C43—21no—
296C8×C43—21no—
297C8×C43—22no—
298C8×C43—21no—
299C8×C43—41no—
300C43⋊C8—21no—
301C43⋊C8—21no—
302C43⋊C8—21no—
303C43⋊C8—22no—
304C43⋊C8—21no—
305C43⋊C8—41no—
306#21139—431nomaximal, Sylow
307C22×C43—21no—
308C22×C43—21no—
309C22×C43C2×C4×D411yescharacteristic
310C22×C43#52911yescharacteristic
311C22×C43#52911yescharacteristic
312C2×D43—22no—
313C2×D43—41no—
314C2×D43—41no—
315C2×D43—41no—
316C2×D43—41no—
317C2×D43—41no—
318C4×C43—42no—
319C4×C43—41no—
320C4×C43—41no—
321C4×C43—41no—
322C4×C43—41no—
323C4×C43C2×#11711yescharacteristic
324C4×C43C4×#4111yescharacteristic
325C4×C43#52511yescharacteristic
326C4×C43#52511yescharacteristic
327Dic43—21no—
328Dic43—21no—
329Dic43—21no—
330Dic43—21no—
331Dic43—22no—
332Dic43—42no—
333Dic43—41no—
334#2943—431no—
335#2923—431no—
336#2875—431no—
337#1929—431no—
338#1929—431no—
339#1922—431no—
340#1922D4311yescharacteristic, complemented
341#1876—431no—
342#1876—431no—
343#1866—431no—
344#1866—431no—
345#1778—431no—
346C4×#104—431no—
347C4×#104—431no—
348#1745—431no—
349C2×C43—21no—
350C2×C43—21no—
351C2×C43#229011yescharacteristic
352C2×C43#295611yescharacteristic
353C2×C43#295611yescharacteristic
354D43—42no—
355D43—81no—
356C2×#135—431no—
357C2×#131—431no—
358C2×#131—431no—
359C4×#41—431no—
360C4×#41—431no—
361#442—431no—
362#442—431no—
363#441—431no—
364#441—431no—
365#440—431no—
366#440—431no—
367#440—431no—
368#440—431no—
369#433—861no—
370#433—861no—
371#432—861no—
372#432—861no—
373C2×#108—431no—
374C2×#108—431no—
375#427C2×D4311yescharacteristic
376#424—431no—
377#424C2×D4311yescharacteristic
378C2×#104—431no—
379C2×#104—431no—
380C2×#104—431no—
381C2×#104—431no—
382#416—431no—
383#416—431no—
384#408—431no—
385#408—431no—
386#405—431no—
387#405—861no—
388#405—861no—
389#405C2×D4311yescharacteristic
390C4×M16—431no—
391C4×M16—431no—
392C4×M16—861no—
393C2×#97—431no—
394C2×#97—431no—
395C2×#97—861no—
396C43—431no—
397#341—431no—
398#341C2×D4311yescharacteristic
399#339—431no—
400#339—431no—
401#339C2×D4311yescharacteristic
402#339C2×D4311yescharacteristic
403#336—431no—
404#336—431no—
405#336—431no—
406#336C2×D4311yescharacteristic
407C43#2113911yescharacteristic, complemented, Sylow
408C2×#41—431no—
409C2×#41—431no—
410#135—862no—
411#135—862no—
412C2×Q16—431no—
413C2×SD16—431no—
414C2×SD16—431no—
415C2×D8—431no—
416#131—862no—
417#131—862no—
418#131—862no—
419#131—862no—
420C2×M16—431no—
421C2×M16—431no—
422C2×M16—861no—
423C2×M16—861no—
424C2×M16C22×D4311yescharacteristic
425C2×M16C22×D4311yescharacteristic
426C22×C8—431no—
427C22×C8—431no—
428C22×C8—861no—
429C22×C8—861no—
430C22×C8C22×D4311yescharacteristic
431C22×C8C22×D4311yescharacteristic
432C4×Q8—431no—
433C4×Q8—431no—
434C4×Q8—431no—
435C4×Q8—431no—
436C4×D4—431no—
437C4×D4—431no—
438C4×D4—431no—
439C4×D4—431no—
440C4×D4—861no—
441C4×D4—861no—
442C4×D4—861no—
443C4×D4—861no—
444#117—861no—
445#117—861no—
446#117C22×D4311yescharacteristic
447#117C22×D4311yescharacteristic
448C2×C42—431no—
449C2×C42—431no—
450C2×C42—861no—
451C2×C42—861no—
452C2×C42—861no—
453C2×C42—861no—
454C2×C42C22×D4311yescharacteristic
455#108—862no—
456#108—862no—
457#107C4×D4311yescharacteristic
458#107C4×D4311yescharacteristic
459#106C4×D4311yescharacteristic
460#106C4×D4311yescharacteristic
461C4⋊C8—21no—
462C4⋊C8—21no—
463C4⋊C8—861no—
464C4⋊C8—861no—
465#104—862no—
466#104—862no—
467#104—862no—
468#104—862no—
469#103—431no—
470#103—431no—
471#103—431no—
472#103—431no—
473#102—431no—
474#102—431no—
475#102—431no—
476#102—431no—
477C22⋊C8—861no—
478C22⋊C8—861no—
479C22⋊C8—861no—
480C22⋊C8—861no—
481#97—21no—
482#97—431no—
483#97—431no—
484#97—431no—
485#97—431no—
486#97—431no—
487#97—431no—
488#97—431no—
489#97—431no—
490#97—861no—
491#97—861no—
492#97—861no—
493C4×C8—21no—
494C4×C8—861no—
495C4×C8—861no—
496C4×C8—861no—
497#41—432no—
498#41—432no—
499#41—861no—
500#41—861no—
501#41—861no—
502#41—861no—
503#41—861no—
504#41—861no—
505C2×Q8—431no—
506C2×Q8—431no—
507C2×D4—431no—
508C2×D4—431no—
509C2×D4—861no—
510C2×D4—861no—
511C22×C4—21no—
512C22×C4—431no—
513C22×C4—431no—
514C22×C4—861no—
515C22×C4—861no—
516C22×C4—861no—
517C22×C4—861no—
518C22×C4—861no—
519C22×C4—861no—
520C22×C4—861no—
521C22×C4C23×D4311yescharacteristic
522Q16—862no—
523SD16—862no—
524SD16—862no—
525D8—862no—
526M16—21no—
527M16—21no—
528M16—21no—
529M16—432no—
530M16—864no—
531M16—864no—
532M16—861no—
533M16—861no—
534M16—861no—
535M16#1062190212yes—
536C2×C8—21no—
537C2×C8—21no—
538C2×C8—21no—
539C2×C8—21no—
540C2×C8—21no—
541C2×C8—21no—
542C2×C8—431no—
543C2×C8—431no—
544C2×C8—431no—
545C2×C8—431no—
546C2×C8—864no—
547C2×C8—864no—
548C2×C8—861no—
549C2×C8—861no—
550C2×C8—861no—
551C2×C8—861no—
552C2×C8—861no—
553C2×C8—861no—
554C2×C8C2×C4×D4311yescharacteristic
555C2×C8C2×C4×D4311yescharacteristic
556C2×C8D4×D4311yescharacteristic
557C2×C8D4×D4311yescharacteristic
558C4⋊C4—861no—
559C4⋊C4—861no—
560C4⋊C4—861no—
561C4⋊C4—861no—
562C4⋊C4C2×C4×D4311yescharacteristic
563C4⋊C4C2×C4×D4311yescharacteristic
564C4⋊C4C2×C4×D4311yescharacteristic
565C4⋊C4C2×C4×D4311yescharacteristic
566C22⋊C4—21no—
567C22⋊C4—21no—
568C22⋊C4—861no—
569C22⋊C4—861no—
570C22⋊C4—861no—
571C22⋊C4—861no—
572C42—21no—
573C42—21no—
574C42—21no—
575C42—21no—
576C42—431no—
577C42—431no—
578C42—431no—
579C42—431no—
580C42—861no—
581C42—861no—
582C42—861no—
583C42—861no—
584C42—861no—
585C42—861no—
586C42—1722no—
587C42—1722no—
588C23—861no—
589C23—861no—
590C23#41×D4311yescharacteristic
591Q8—432no—
592Q8—861no—
593Q8—861no—
594Q8—861no—
595D4—432no—
596D4—862no—
597D4—862no—
598D4—861no—
599D4—861no—
600D4—861no—
601D4—1721no—
602D4—1721no—
603C2×C4—22no—
604C2×C4—21no—
605C2×C4—21no—
606C2×C4—21no—
607C2×C4—21no—
608C2×C4—41no—
609C2×C4—41no—
610C2×C4—431no—
611C2×C4—431no—
612C2×C4—431no—
613C2×C4—431no—
614C2×C4—861no—
615C2×C4—862no—
616C2×C4—862no—
617C2×C4—862no—
618C2×C4—861no—
619C2×C4—3441no—
620C2×C4—3441no—
621C2×C4—3441no—
622C2×C4—3441no—
623C2×C4—1721no—
624C2×C4—1721no—
625C2×C4—1721no—
626C2×C4—1721no—
627C2×C4—1721no—
628C2×C4—1721no—
629C2×C4C22×C4×D4311yescharacteristic
630C2×C4C2×D4×D4311yescharacteristic
631C2×C4#41×D4311yescharacteristic
632C2×C4#41×D4311yescharacteristic
633C2×C4#41×D4311yescharacteristic
634C2×C4C2×#1062190211yescharacteristic
635C8—21no—
636C8—21no—
637C8—21no—
638C8—21no—
639C8—22no—
640C8—41no—
641C8—861no—
642C8—861no—
643C8—862no—
644C8—861no—
645C8—861no—
646C8—1721no—
647C22—21no—
648C22—21no—
649C22—862no—
650C22—1721no—
651C22—1721no—
652C22—1721no—
653C22—1721no—
654C22—1721no—
655C22C4×D4×D4311yescharacteristic
656C22#1458343211yescharacteristic
657C22#1458343411yescharacteristic
658C4—42no—
659C4—41no—
660C4—41no—
661C4—41no—
662C4—41no—
663C4—862no—
664C4—861no—
665C4—861no—
666C4—861no—
667C4—861no—
668C4—1722no—
669C4—1721no—
670C4#117×D4311yescharacteristic
671C4C4×#1062190211yescharacteristic
672C4#1458340711yescharacteristic
673C4#1458341211yescharacteristic
674C2—21no—
675C2—21no—
676C2—3441no—
677C2—1722no—
678C2#1913703311yescharacteristic
679C2#1914350011yescharacteristic
680C2#1914350311yescharacteristic
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#21139
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. #19143245C2semidirect
3. #19143022C2semidirect
4. #19135243C2semidirect
5. #19135241C2semidirect
6. #19135196C2semidirect
9. #19134871C2semidirect
10. #19134869C2semidirect
11. #19134500C2semidirect
12. #19134399C2semidirect
13. #19134399C2semidirect
14. #19134342C2semidirect
15. C43×#1922C2semidirect
21. #14583010C4semidirect
22. #14583010C4semidirect
23. #14583005C4semidirect
24. #14583005C4semidirect
25. #14582998C4semidirect
26. #14582998C4semidirect
27. #14582998C4semidirect
28. #14582998C4semidirect
340. #1922D43semidirect
407. C43#21139semidirect

Maximal subgroups

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

subgroupindex
#191433952
#191432452
#191430222
#191352432
#191352412
#191351962
#191349232
#191349212
#191348712
#191348692
#191345002
#191343992
#191343422
C43×#19222
#2113943