Finite Group Databasebeta

← #25104456

Subgroups — #25104456

Order 11008.

730 conjugacy classes of subgroups.

The subgroup lattice has 638 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19144381C211yesmaximal, characteristic
2#19143534C211yesmaximal, characteristic, complemented
3#19143022C211yesmaximal, characteristic
4#19135537C211yesmaximal, characteristic, complemented
5#19135369C211yesmaximal, characteristic, complemented
6#19135194C211yesmaximal, characteristic, complemented
7#19134873C211yesmaximal, characteristic
8#19134869C211yesmaximal, characteristic
9#19134614C211yesmaximal, characteristic
10#19134481C211yesmaximal, characteristic, complemented
11#19134473C211yesmaximal, characteristic, complemented
12#19134466C211yesmaximal, characteristic, complemented
13#19134438C211yesmaximal, characteristic
14#19134429C211yesmaximal, characteristic
15C43×#1922C211yesmaximal, characteristic, complemented
16C2×#13063333C2211yescharacteristic
17C2×#13063331C2211yescharacteristic
18#14583452C2211yescharacteristic
19#14583367C2211yescharacteristic
20#14583209C411yescharacteristic, complemented
21#14583205C411yescharacteristic, complemented
22#14583202C411yescharacteristic, complemented
23#14583198C411yescharacteristic, complemented
24#14583193C411yescharacteristic, complemented
25#14583188C411yescharacteristic, complemented
26#14583183C411yescharacteristic, complemented
27#14583178C411yescharacteristic, complemented
28#14583028—21no—
29#14583028—21no—
30#14583026—21no—
31#14583026—21no—
32C2×#13063261C2211yescharacteristic
33C2×#13063260C2211yescharacteristic
34#14582935C2211yescharacteristic
35#14582925C2211yescharacteristic
36#14582922C2211yescharacteristic
37C2×Dic43⋊C8C2211yescharacteristic
38C2×#13063253C2211yescharacteristic
39C2×#13063251C2211yescharacteristic
40#14582896C2211yescharacteristic
41#14582893C2211yescharacteristic
42#14582857C2211yescharacteristic
43#14582856—21no—
44#14582855C2211yescharacteristic
45#14582855C2211yescharacteristic
46#14582853—21no—
47M16×Dic43C2211yescharacteristic
48C4×#10621872—21no—
49C2×#13063235C2211yescharacteristic
50C2×#13063235C2211yescharacteristic
51#97×D43—21no—
52C2×C4×C43⋊C8C2211yescharacteristic
53C4×Dic43⋊C4C2211yescharacteristic
54#14582663C2211yescharacteristic
55#14582660C2211yescharacteristic
56#14582659C2211yescharacteristic
57#14582658C2211yescharacteristic
58#14582658C2211yescharacteristic
59#14582653C2211yescharacteristic
60C43×#427C2211yescharacteristic
61C43×#424C2211yescharacteristic
62C43×#405C2211yescharacteristic
63C43×#341C2211yescharacteristic
64C43×#339C2211yescharacteristic
65C43×#339C2211yescharacteristic
66C43×#336C2211yescharacteristic
67C2×#10621898C2311yescharacteristic
68#13063333—22no—
69#13063333Q814yescomplemented
70#13063331—22no—
71#13063331—22no—
72C2×#10621877C2311yescharacteristic
73C2×#10621877C2311yescharacteristic
74C2×#10621872—21no—
75C2×#10621872—21no—
76C22×C43⋊C8C2311yescharacteristic
77C22×C43⋊C8C2311yescharacteristic
78C2×C8×D43—21no—
79C2×C8×D43—21no—
80#13063324C2×C411yescharacteristic
81#13063324C2×C411yescharacteristic
82#13063316C2×C411yescharacteristic
83#13063316C2×C411yescharacteristic
84#13063302—21no—
85#13063302—21no—
86C4×Dic86—21no—
87C4×Dic86—21no—
88#13063290C2×C411yescharacteristic
89#13063290C2×C411yescharacteristic
90#13063287C2×C411yescharacteristic
91#13063287C2×C411yescharacteristic
92(C22⋊D43)⋊C4—21no—
93(C22⋊D43)⋊C4—21no—
94#13063284C2311yescharacteristic
95#13063282—21no—
96C2×Dic43⋊C4—21no—
97C2×C4×Dic43C2311yescharacteristic
98C2×C4×Dic43C2311yescharacteristic
99C42×D43—21no—
100#13063261—22no—
101#13063260—22no—
102#13063258C2×C411yescharacteristic
103#13063258C2×C411yescharacteristic
104#13063256C2×C411yescharacteristic
105#13063256C2×C411yescharacteristic
106Dic43⋊C8—21no—
107Dic43⋊C8—21no—
108Dic43⋊C8—21no—
109Dic43⋊C8—21no—
110Dic43⋊C8C2×C411yescharacteristic
111Dic43⋊C8C2×C411yescharacteristic
112Dic43⋊C8C2×C411yescharacteristic
113Dic43⋊C8C2×C411yescharacteristic
114#13063253—22no—
115#13063251—22no—
116#13063250C2×C411yescharacteristic
117#13063250C2×C411yescharacteristic
118#13063248C2×C411yescharacteristic
119#13063248C2×C411yescharacteristic
120#13063247C2×C411yescharacteristic
121#13063247C2×C411yescharacteristic
122#13063245C2×C411yescharacteristic
123#13063245C2×C411yescharacteristic
124#13063236—21no—
125#13063236—21no—
126#13063235—21no—
127#13063235—21no—
128#13063235—22no—
129#13063235D411yescharacteristic
130#13063235D411yescharacteristic
131#13063235D411yescharacteristic
132#13063235D411yescharacteristic
133C4×C43⋊C8—21no—
134C4×C43⋊C8—21no—
135C4×C43⋊C8—22no—
136C8×Dic43—21no—
137C8×Dic43—21no—
138C43⋊#95—21no—
139C2×M16×C43C2311yescharacteristic
140C2×M16×C43C2311yescharacteristic
141C22×C8×C43C2311yescharacteristic
142C22×C8×C43C2311yescharacteristic
143#117×C43C2311yescharacteristic
144#117×C43C2311yescharacteristic
145C2×C42×C43C2311yescharacteristic
146#107×C43C2×C411yescharacteristic
147#107×C43C2×C411yescharacteristic
148#106×C43C2×C411yescharacteristic
149#106×C43C2×C411yescharacteristic
150C4⋊C8×C43—21no—
151C4⋊C8×C43—21no—
152#97×C43—21no—
153C4×C8×C43—21no—
154C22×C4×C43—21no—
155C22×C4×C43C2411yescharacteristic
156C2×C22⋊D43—21no—
157C22×Dic43—21no—
158C22×Dic43#4111yescharacteristic
159C22×Dic43#4111yescharacteristic
160#10621898—21no—
161#10621898—21no—
162#10621898C2×Q812yes—
163#10621898#4112yes—
164C2×D172C22×C411yescharacteristic
165C2×C4×D43—21no—
166C2×C4×D43—21no—
167C2×C4×D43—21no—
168C2×Dic86—21no—
169C2×Dic86—21no—
170C2×Dic86C22×C411yescharacteristic
171M16×C43—21no—
172M16×C43—21no—
173M16×C43—21no—
174M16×C43C2×Q812yes—
175C2×C8×C43—21no—
176C2×C8×C43—21no—
177C2×C8×C43—21no—
178C2×C8×C43—21no—
179C2×C8×C43—21no—
180C2×C8×C43—21no—
181C2×C8×C43C22×C411yescharacteristic
182C2×C8×C43C22×C411yescharacteristic
183C2×C8×C43C2×D411yescharacteristic
184C2×C8×C43C2×D411yescharacteristic
185C4⋊C4×C43C22×C411yescharacteristic
186C4⋊C4×C43C22×C411yescharacteristic
187C4⋊C4×C43C22×C411yescharacteristic
188C4⋊C4×C43C22×C411yescharacteristic
189C22⋊C4×C43—21no—
190C22⋊C4×C43—21no—
191C42×C43—21no—
192C42×C43—21no—
193C42×C43—21no—
194C42×C43—21no—
195C22⋊Dic43—21no—
196(C2×D43)⋊C4—21no—
197(C2×D43)⋊C4—21no—
198C4⋊Dic43—21no—
199C4⋊Dic43—21no—
200C4⋊Dic43C22×C411yescharacteristic
201C4⋊Dic43C22×C411yescharacteristic
202Dic43⋊C4—21no—
203Dic43⋊C4—21no—
204Dic43⋊C4—21no—
205Dic43⋊C4—21no—
206Dic43⋊C4—21no—
207Dic43⋊C4—21no—
208Dic43⋊C4—42no—
209C4×Dic43—21no—
210C4×Dic43—21no—
211C4×Dic43—21no—
212C4×Dic43—21no—
213C4×Dic43—21no—
214C4×Dic43C22×C411yescharacteristic
215C4×Dic43C22×C411yescharacteristic
216C4×Dic43C2×D411yescharacteristic
217C4×Dic43C2×D411yescharacteristic
218#10621877—21no—
219#10621877—21no—
220#10621877—21no—
221#10621877#4112yes—
222C2×C43⋊C8—21no—
223C2×C43⋊C8—21no—
224C2×C43⋊C8—21no—
225C2×C43⋊C8—21no—
226C2×C43⋊C8C22×C411yescharacteristic
227C2×C43⋊C8C22×C411yescharacteristic
228C2×C43⋊C8C2×D411yescharacteristic
229C2×C43⋊C8C2×D411yescharacteristic
230C2×C43⋊C8C2×Q812yes—
231C2×C43⋊C8#4112yes—
232#10621872—24no—
233#10621872—24no—
234C8×D43—24no—
235C8×D43—24no—
236C23×C43C2×#4111yescharacteristic
237C22×D43—21no—
238C2×C4×C43—22no—
239C2×C4×C43—21no—
240C2×C4×C43—21no—
241C2×C4×C43—21no—
242C2×C4×C43—21no—
243C2×C4×C43—41no—
244C2×C4×C43—41no—
245C2×C4×C43C23×C411yescharacteristic
246C2×C4×C43C22×D411yescharacteristic
247C2×C4×C43C22×Q811yescharacteristic
248C2×C4×C43C2×#4111yescharacteristic
249C2×C4×C43C2×#4111yescharacteristic
250C2×C4×C43C2×#4111yescharacteristic
251C22⋊D43—22no—
252C22⋊D43—22no—
253C2×Dic43—21no—
254C2×Dic43—21no—
255C2×Dic43—21no—
256C2×Dic43—41no—
257C2×Dic43—41no—
258C2×Dic43—41no—
259C2×Dic43—41no—
260C2×Dic43—41no—
261C2×Dic43C4×D411yescharacteristic
262C2×Dic43C4×D411yescharacteristic
263C2×Dic43C4×D411yescharacteristic
264C2×Dic43C4×D411yescharacteristic
265D172—21no—
266D172C4×Q812yes—
267C4×D43—22no—
268C4×D43—22no—
269C4×D43—81no—
270C4×D43—81no—
271Dic86—21no—
272Dic86—81no—
273Dic86—81no—
274Dic86C4×Q812yes—
275C8×C43—21no—
276C8×C43—21no—
277C8×C43—22no—
278C8×C43—21no—
279C8×C43—21no—
280C8×C43—41no—
281C43⋊C8—21no—
282C43⋊C8—21no—
283C43⋊C8—22no—
284C43⋊C8—41no—
285C43⋊C8C22⋊Q812yes—
286C43⋊C8C22⋊Q812yes—
287#21629—431nomaximal, Sylow
288C22×C43—21no—
289C22×C43—21no—
290C22×C43C2×C4×D411yescharacteristic
291C22×C43#52911yescharacteristic
292C22×C43#53311yescharacteristic
293C2×D43—22no—
294C2×D43—41no—
295C2×D43—41no—
296C4×C43—42no—
297C4×C43—41no—
298C4×C43—41no—
299C4×C43—41no—
300C4×C43—41no—
301C4×C43C2×C4×Q811yescharacteristic
302C4×C43C4×#4111yescharacteristic
303C4×C43C2×C22⋊Q811yescharacteristic
304C4×C43#52511yescharacteristic
305Dic43—21no—
306Dic43—21no—
307Dic43—21no—
308Dic43—21no—
309Dic43—22no—
310Dic43—41no—
311Dic43—41no—
312Dic43—81no—
313#3076—431no—
314#2961—431no—
315#2875—431no—
316#1986—431no—
317#1950—431no—
318#1922—431no—
319#1922D4311yescharacteristic, complemented
320#1866—431no—
321#1866—431no—
322#1806—431no—
323#1773—431no—
324#1772—431no—
325#1771—431no—
326#1765—431no—
327#1764—431no—
328C2×C43—21no—
329C2×C43—21no—
330C2×C43C4×C22⋊Q811yescharacteristic
331C2×C43#295611yescharacteristic
332C2×C43#295711yescharacteristic
333D43—42no—
334C2×#131—431no—
335C2×#131—431no—
336#533—431no—
337C4×#41—431no—
338#479—431no—
339#479—431no—
340#478—431no—
341#478—431no—
342#477—431no—
343#476—431no—
344#475—431no—
345#474—431no—
346#446—861no—
347#446—861no—
348#446—861no—
349#446—861no—
350C2×#108—431no—
351C2×#108—431no—
352#427—431no—
353#427C2×D4311yescharacteristic
354#424—431no—
355#424C2×D4311yescharacteristic
356#423—431no—
357C2×C4⋊C8—431no—
358C2×#104—431no—
359C2×#104—431no—
360#416—431no—
361#416—431no—
362#405—431no—
363#405—431no—
364#405—431no—
365#405—861no—
366#405—861no—
367#405C2×D4311yescharacteristic
368C4×M16—431no—
369C4×M16—861no—
370C2×#97—431no—
371C2×#97—431no—
372C2×#97—861no—
373C2×C4×C8—431no—
374C4×C4⋊C4—431no—
375#341—431no—
376#341C2×D4311yescharacteristic
377#339—431no—
378#339—431no—
379#339—431no—
380#339—431no—
381#339C2×D4311yescharacteristic
382#339C2×D4311yescharacteristic
383#336—431no—
384#336C2×D4311yescharacteristic
385C43#2162911yescharacteristic, complemented, Sylow
386C2×#41—431no—
387#131—434no—
388#131—862no—
389#131—862no—
390#131—862no—
391C2×M16—431no—
392C2×M16—431no—
393C2×M16—861no—
394C2×M16—861no—
395C2×M16C22×D4311yescharacteristic
396C2×M16C22×D4311yescharacteristic
397C22×C8—431no—
398C22×C8—431no—
399C22×C8—861no—
400C22×C8—861no—
401C22×C8C22×D4311yescharacteristic
402C22×C8C22×D4311yescharacteristic
403C4⋊Q8—431no—
404C4⋊Q8—431no—
405#125—431no—
406#125—431no—
407C22⋊Q8—861no—
408C22⋊Q8—861no—
409C4×Q8—431no—
410C4×Q8—431no—
411C4×Q8—861no—
412C4×Q8—861no—
413C4×D4—431no—
414C4×D4—431no—
415C4×D4—861no—
416C4×D4—861no—
417#117—431no—
418#117—861no—
419#117C22×D4311yescharacteristic
420#117C22×D4311yescharacteristic
421C2×C4⋊C4—861no—
422C2×C42—431no—
423C2×C42—431no—
424C2×C42—861no—
425C2×C42C22×D4311yescharacteristic
426#108—862no—
427#108—862no—
428#107—431no—
429#107—431no—
430#107C4×D4311yescharacteristic
431#107C4×D4311yescharacteristic
432#106—431no—
433#106—431no—
434#106C4×D4311yescharacteristic
435#106C4×D4311yescharacteristic
436C4⋊C8—21no—
437C4⋊C8—21no—
438C4⋊C8—431no—
439C4⋊C8—431no—
440C4⋊C8—431no—
441C4⋊C8—431no—
442C4⋊C8—861no—
443C4⋊C8—861no—
444C4⋊C8—861no—
445C4⋊C8—861no—
446#104—862no—
447#104—862no—
448#103—431no—
449#103—431no—
450#103—431no—
451#103—431no—
452#102—431no—
453#102—431no—
454#102—431no—
455#102—431no—
456#97—21no—
457#97—431no—
458#97—431no—
459#97—431no—
460#97—431no—
461#97—861no—
462#97—861no—
463#97—861no—
464#97—862no—
465#97—861no—
466C4×C8—21no—
467C4×C8—862no—
468C4×C8—861no—
469C4×C8—861no—
470C4×C8—861no—
471C4×C8—861no—
472#95—861no—
473#41—432no—
474#41—432no—
475#41—861no—
476#41—861no—
477C2×Q8—431no—
478C2×Q8—861no—
479C2×Q8—861no—
480C2×D4—431no—
481C2×D4—861no—
482C22×C4—21no—
483C22×C4—431no—
484C22×C4—431no—
485C22×C4—861no—
486C22×C4—861no—
487C22×C4—861no—
488C22×C4—861no—
489C22×C4C23×D4311yescharacteristic
490M16—21no—
491M16—21no—
492M16—21no—
493M16—432no—
494M16—864no—
495M16—864no—
496M16—861no—
497M16—861no—
498M16—861no—
499M16Q8×D4312yes—
500C2×C8—21no—
501C2×C8—21no—
502C2×C8—21no—
503C2×C8—21no—
504C2×C8—21no—
505C2×C8—21no—
506C2×C8—431no—
507C2×C8—431no—
508C2×C8—432no—
509C2×C8—432no—
510C2×C8—431no—
511C2×C8—431no—
512C2×C8—864no—
513C2×C8—864no—
514C2×C8—861no—
515C2×C8—861no—
516C2×C8—861no—
517C2×C8—861no—
518C2×C8C2×C4×D4311yescharacteristic
519C2×C8C2×C4×D4311yescharacteristic
520C2×C8D4×D4311yescharacteristic
521C2×C8D4×D4311yescharacteristic
522C4⋊C4—431no—
523C4⋊C4—431no—
524C4⋊C4—861no—
525C4⋊C4—861no—
526C4⋊C4—861no—
527C4⋊C4—861no—
528C4⋊C4—861no—
529C4⋊C4—861no—
530C4⋊C4—861no—
531C4⋊C4—861no—
532C4⋊C4—1722no—
533C4⋊C4C2×C4×D4311yescharacteristic
534C4⋊C4C2×C4×D4311yescharacteristic
535C4⋊C4C2×C4×D4311yescharacteristic
536C4⋊C4C2×C4×D4311yescharacteristic
537C22⋊C4—21no—
538C22⋊C4—21no—
539C22⋊C4—861no—
540C22⋊C4—861no—
541C22⋊C4—861no—
542C42—21no—
543C42—21no—
544C42—21no—
545C42—21no—
546C42—431no—
547C42—431no—
548C42—431no—
549C42—431no—
550C42—861no—
551C42—861no—
552C42—861no—
553C42—861no—
554C42—861no—
555C23—861no—
556C23#41×D4311yescharacteristic
557Q8—432no—
558Q8—861no—
559Q8—3441no—
560Q8—3441no—
561D4—432no—
562D4—862no—
563D4—862no—
564D4—861no—
565C2×C4—22no—
566C2×C4—21no—
567C2×C4—21no—
568C2×C4—21no—
569C2×C4—21no—
570C2×C4—41no—
571C2×C4—41no—
572C2×C4—431no—
573C2×C4—431no—
574C2×C4—431no—
575C2×C4—431no—
576C2×C4—861no—
577C2×C4—862no—
578C2×C4—862no—
579C2×C4—861no—
580C2×C4—861no—
581C2×C4—3441no—
582C2×C4—3441no—
583C2×C4—1721no—
584C2×C4—1721no—
585C2×C4—1721no—
586C2×C4—1721no—
587C2×C4—1721no—
588C2×C4C22×C4×D4311yescharacteristic
589C2×C4C2×D4×D4311yescharacteristic
590C2×C4C2×Q8×D4311yescharacteristic
591C2×C4#41×D4311yescharacteristic
592C2×C4#41×D4311yescharacteristic
593C2×C4#41×D4311yescharacteristic
594C8—21no—
595C8—21no—
596C8—22no—
597C8—21no—
598C8—21no—
599C8—41no—
600C8—432no—
601C8—432no—
602C8—861no—
603C8—861no—
604C8—862no—
605C8—1721no—
606C22—21no—
607C22—21no—
608C22—862no—
609C22—1721no—
610C22—1721no—
611C22C4×D4×D4311yescharacteristic
612C22#1458343211yescharacteristic
613C22#1458345511yescharacteristic
614C4—42no—
615C4—41no—
616C4—41no—
617C4—41no—
618C4—41no—
619C4—861no—
620C4—861no—
621C4—861no—
622C4—861no—
623C4—862no—
624C4—3441no—
625C4—1721no—
626C4—1721no—
627C4C4×Q8×D4311yescharacteristic
628C4#1458336711yescharacteristic
629C4C22⋊Q8×D4311yescharacteristic
630C4#1458340711yescharacteristic
631C2—21no—
632C2—21no—
633C2—1722no—
634C2#1913712911yescharacteristic
635C2#1914350011yescharacteristic
636C2#1914350911yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1922C2
socleC22×C43C2×C4×D4
prime radicalC2×#10621898C23
cosocleC22×C4×C43C24
hypercenter#1922D43
hypocenterC43#21629
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. #19143534C2semidirect
4. #19135537C2semidirect
5. #19135369C2semidirect
6. #19135194C2semidirect
10. #19134481C2semidirect
11. #19134473C2semidirect
12. #19134466C2semidirect
15. C43×#1922C2semidirect
20. #14583209C4semidirect
21. #14583205C4semidirect
22. #14583202C4semidirect
23. #14583198C4semidirect
24. #14583193C4semidirect
25. #14583188C4semidirect
26. #14583183C4semidirect
27. #14583178C4semidirect
69. #13063333Q8semidirect
319. #1922D43semidirect
385. C43#21629semidirect

Maximal subgroups

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

subgroupindex
#191443812
#191435342
#191430222
#191355372
#191353692
#191351942
#191348732
#191348692
#191346142
#191344812
#191344732
#191344662
#191344382
#191344292
C43×#19222
#2162943