Finite Group Databasebeta

← #25104442

Subgroups — #25104442

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#19144383C211yesmaximal, characteristic
2#19143532C211yesmaximal, characteristic, complemented
3#19143023C211yesmaximal, characteristic
4#19135538C211yesmaximal, characteristic, complemented
5#19135368C211yesmaximal, characteristic, complemented
6#19135192C211yesmaximal, characteristic, complemented
7#19135192C211yesmaximal, characteristic, complemented
8#19134868C211yesmaximal, characteristic
9#19134868C211yesmaximal, characteristic
10#19134478C211yesmaximal, characteristic, complemented
11#19134473C211yesmaximal, characteristic, complemented
12#19134470C211yesmaximal, characteristic, complemented
13#19134440C211yesmaximal, characteristic
14#19134433C211yesmaximal, characteristic
15C43×#1806C211yesmaximal, characteristic
16C2×#13063332C2211yescharacteristic
17C2×#13063332C2211yescharacteristic
18#14583456C2211yescharacteristic
19#14583206C411yescharacteristic, complemented
20#14583206C411yescharacteristic, complemented
21#14583199C411yescharacteristic, complemented
22#14583199C411yescharacteristic, complemented
23#14583194C411yescharacteristic, complemented
24#14583189C411yescharacteristic, complemented
25#14583184C411yescharacteristic, complemented
26#14583179C411yescharacteristic, complemented
27#14583028—21no—
28#14583028—21no—
29#14583028—21no—
30#14583028—21no—
31C2×#13063260C2211yescharacteristic
32C2×#13063260C2211yescharacteristic
33#14582935C2211yescharacteristic
34#14582935C2211yescharacteristic
35#14582927C2211yescharacteristic
36#14582927C2211yescharacteristic
37C2×C4⋊(C43⋊C8)C2211yescharacteristic
38#14582895C2211yescharacteristic
39#14582895C2211yescharacteristic
40#14582857C2211yescharacteristic
41#14582857C2211yescharacteristic
42#14582855—21no—
43#14582855—21no—
44#14582855C2211yescharacteristic
45#14582855C2211yescharacteristic
46C4×#10621877—21no—
47C4×#10621877C2211yescharacteristic
48C2×#13063236—21no—
49C2×#13063236C2211yescharacteristic
50C2×#13063236C2211yescharacteristic
51C2×C4×C43⋊C8C2211yescharacteristic
52#14582663C2211yescharacteristic
53#14582663C2211yescharacteristic
54#14582659C2211yescharacteristic
55#14582659C2211yescharacteristic
56#14582659C2211yescharacteristic
57#14582659C2211yescharacteristic
58#14582654C2211yescharacteristic
59#14582654C2211yescharacteristic
60C4×#41×C43C2211yescharacteristic
61C43×#423C2211yescharacteristic
62C2×#104×C43C2211yescharacteristic
63C2×#104×C43C2211yescharacteristic
64C4×C4⋊C4×C43C2211yescharacteristic
65C43×#339C2211yescharacteristic
66C43×#339C2211yescharacteristic
67#13063332—22no—
68#13063332—22no—
69#13063332—22no—
70#13063332Q814yescomplemented
71C2×#10621877—21no—
72C2×#10621877—21no—
73C2×#10621877C2311yescharacteristic
74C2×#10621877C2311yescharacteristic
75C22×C43⋊C8—21no—
76C22×C43⋊C8—21no—
77C22×C43⋊C8C2311yescharacteristic
78C22×C43⋊C8C2311yescharacteristic
79C22×C43⋊C8C2311yescharacteristic
80C22×C43⋊C8C2311yescharacteristic
81#13063325C2×C411yescharacteristic
82#13063325C2×C411yescharacteristic
83#13063317C2×C411yescharacteristic
84#13063317C2×C411yescharacteristic
85#13063304—21no—
86#13063304—21no—
87C4×Dic86—21no—
88C4×Dic86—21no—
89#13063284C2311yescharacteristic
90#13063284C2311yescharacteristic
91#13063260—22no—
92#13063260—22no—
93#13063258C2×C411yescharacteristic
94#13063258C2×C411yescharacteristic
95#13063258C2×C411yescharacteristic
96#13063258C2×C411yescharacteristic
97#13063256C2×C411yescharacteristic
98#13063256C2×C411yescharacteristic
99#13063256C2×C411yescharacteristic
100#13063256C2×C411yescharacteristic
101C4⋊(C43⋊C8)C2×C411yescharacteristic
102C4⋊(C43⋊C8)C2×C411yescharacteristic
103C4⋊(C43⋊C8)C2×C411yescharacteristic
104C4⋊(C43⋊C8)C2×C411yescharacteristic
105Dic43⋊C8—21no—
106Dic43⋊C8—21no—
107Dic43⋊C8—21no—
108Dic43⋊C8—21no—
109#13063249C2×C411yescharacteristic
110#13063249C2×C411yescharacteristic
111#13063249C2×C411yescharacteristic
112#13063249C2×C411yescharacteristic
113#13063246C2×C411yescharacteristic
114#13063246C2×C411yescharacteristic
115#13063246C2×C411yescharacteristic
116#13063246C2×C411yescharacteristic
117#13063236—21no—
118#13063236—21no—
119#13063236—21no—
120#13063236—22no—
121#13063236D411yescharacteristic
122#13063236D411yescharacteristic
123#13063236D411yescharacteristic
124#13063236D411yescharacteristic
125#13063235—21no—
126#13063235—21no—
127C4×C43⋊C8—21no—
128C4×C43⋊C8—21no—
129C4×C43⋊C8—21no—
130C4×C43⋊C8—22no—
131C8×Dic43—21no—
132C8×Dic43—21no—
133C2×#41×C43C2311yescharacteristic
134C2×M16×C43C2311yescharacteristic
135C2×M16×C43C2311yescharacteristic
136C4×Q8×C43C2×C411yescharacteristic
137C4×Q8×C43C2×C411yescharacteristic
138C4×D4×C43—21no—
139C4×D4×C43—21no—
140C4×D4×C43C2×C411yescharacteristic
141C4×D4×C43C2×C411yescharacteristic
142#117×C43—21no—
143#117×C43C2311yescharacteristic
144C2×C4⋊C4×C43—21no—
145C2×C42×C43—21no—
146C2×C42×C43C2311yescharacteristic
147C2×C42×C43C2311yescharacteristic
148C2×C42×C43C2311yescharacteristic
149C4⋊C8×C43—21no—
150C4⋊C8×C43—21no—
151#104×C43—22no—
152#104×C43—22no—
153#95×C43—21no—
154#41×C43—21no—
155#41×C43—21no—
156#41×C43C2×Q812yes—
157#41×C43#4112yes—
158C2×Q8×C43C22×C411yescharacteristic
159C2×D4×C43—21no—
160C2×D4×C43C22×C411yescharacteristic
161C22×C4×C43—21no—
162C22×C4×C43—21no—
163C22×C4×C43—21no—
164C22×C4×C43—21no—
165C22×C4×C43—21no—
166C22×C4×C43#4111yescharacteristic
167C22×C4×C43#4111yescharacteristic
168C22×C4×C43C2411yescharacteristic
169C2×Dic86—21no—
170C2×Dic86—21no—
171M16×C43—21no—
172M16×C43—21no—
173M16×C43—21no—
174M16×C43—21no—
175C2×C8×C43—21no—
176C2×C8×C43—21no—
177C4⋊C4×C43—21no—
178C4⋊C4×C43—21no—
179C4⋊C4×C43—42no—
180C4⋊C4×C43C22×C411yescharacteristic
181C4⋊C4×C43C22×C411yescharacteristic
182C22⋊C4×C43—21no—
183C22⋊C4×C43—21no—
184C22⋊C4×C43—21no—
185C42×C43—21no—
186C42×C43—21no—
187C42×C43—21no—
188C42×C43—21no—
189C42×C43—21no—
190C42×C43—21no—
191C42×C43—21no—
192C42×C43C22×C411yescharacteristic
193C42×C43C22×C411yescharacteristic
194C42×C43C2×D411yescharacteristic
195C42×C43C2×D411yescharacteristic
196C22⋊Dic43—21no—
197C22⋊Dic43—21no—
198C4⋊Dic43—21no—
199C4⋊Dic43—21no—
200C4⋊Dic43C22×C411yescharacteristic
201C4⋊Dic43C22×C411yescharacteristic
202C4⋊Dic43C22×C411yescharacteristic
203C4⋊Dic43C22×C411yescharacteristic
204Dic43⋊C4—21no—
205Dic43⋊C4—21no—
206Dic43⋊C4—21no—
207Dic43⋊C4—21no—
208C4×Dic43—21no—
209C4×Dic43—21no—
210#10621877—24no—
211#10621877—21no—
212#10621877—21no—
213#10621877—24no—
214#10621877C2×Q812yes—
215#10621877#4112yes—
216C2×C43⋊C8—24no—
217C2×C43⋊C8—21no—
218C2×C43⋊C8—21no—
219C2×C43⋊C8—21no—
220C2×C43⋊C8—21no—
221C2×C43⋊C8—21no—
222C2×C43⋊C8—21no—
223C2×C43⋊C8—21no—
224C2×C43⋊C8—21no—
225C2×C43⋊C8—24no—
226C2×C43⋊C8C22×C411yescharacteristic
227C2×C43⋊C8C22×C411yescharacteristic
228C2×C43⋊C8C22×C411yescharacteristic
229C2×C43⋊C8C22×C411yescharacteristic
230C2×C43⋊C8C2×D411yescharacteristic
231C2×C43⋊C8C2×D411yescharacteristic
232C2×C43⋊C8C2×D411yescharacteristic
233C2×C43⋊C8C2×D411yescharacteristic
234C2×C43⋊C8C2×Q812yes—
235C2×C43⋊C8#4112yes—
236C23×C43—21no—
237C23×C43C2×#4111yescharacteristic
238Q8×C43—21no—
239Q8×C43C4×Q812yes—
240D4×C43—22no—
241D4×C43—22no—
242D4×C43—21no—
243D4×C43C4×Q812yes—
244C2×C4×C43—21no—
245C2×C4×C43—22no—
246C2×C4×C43—22no—
247C2×C4×C43—22no—
248C2×C4×C43—21no—
249C2×C4×C43—21no—
250C2×C4×C43—41no—
251C2×C4×C43—41no—
252C2×C4×C43—41no—
253C2×C4×C43—41no—
254C2×C4×C43—41no—
255C2×C4×C43—41no—
256C2×C4×C43—41no—
257C2×C4×C43—81no—
258C2×C4×C43—81no—
259C2×C4×C43C4×D411yescharacteristic
260C2×C4×C43C4×D411yescharacteristic
261C2×C4×C43C4×D411yescharacteristic
262C2×C4×C43C4×D411yescharacteristic
263C2×C4×C43C23×C411yescharacteristic
264C2×C4×C43C22×D411yescharacteristic
265C2×C4×C43C22×Q811yescharacteristic
266C2×C4×C43C2×#4111yescharacteristic
267C2×C4×C43C2×#4111yescharacteristic
268C2×C4×C43C2×#4111yescharacteristic
269C2×Dic43—21no—
270C2×Dic43—21no—
271C2×Dic43—21no—
272C2×Dic43—21no—
273Dic86—81no—
274Dic86—81no—
275C8×C43—41no—
276C8×C43—41no—
277C43⋊C8—21no—
278C43⋊C8—21no—
279C43⋊C8—21no—
280C43⋊C8—21no—
281C43⋊C8—22no—
282C43⋊C8—21no—
283C43⋊C8—22no—
284C43⋊C8—21no—
285C43⋊C8C22⋊Q812yes—
286C43⋊C8C22⋊Q812yes—
287#21629—431nomaximal, Sylow
288C22×C43—21no—
289C22×C43—21no—
290C22×C43—22no—
291C22×C43—41no—
292C22×C43—41no—
293C22×C43C2×C4×D411yescharacteristic
294C22×C43#52911yescharacteristic
295C22×C43#53311yescharacteristic
296C4×C43—21no—
297C4×C43—21no—
298C4×C43—21no—
299C4×C43—21no—
300C4×C43—22no—
301C4×C43—42no—
302C4×C43—41no—
303C4×C43—41no—
304C4×C43—81no—
305C4×C43C2×C4×Q811yescharacteristic
306C4×C43C4×#4111yescharacteristic
307C4×C43C2×C22⋊Q811yescharacteristic
308C4×C43#52511yescharacteristic
309Dic43—41no—
310Dic43—41no—
311Dic43—41no—
312Dic43—41no—
313#3076—431no—
314#2961—431no—
315#2875—431no—
316#1986—431no—
317#1950—431no—
318#1922—431no—
319#1922—431no—
320#1866—431no—
321#1866—431no—
322#1806D4311yescharacteristic
323#1773—431no—
324#1772—431no—
325#1771—431no—
326#1765—431no—
327#1764—431no—
328C2×C43—21no—
329C2×C43—21no—
330C2×C43—42no—
331C2×C43C4×C22⋊Q811yescharacteristic
332C2×C43#295611yescharacteristic
333C2×C43#295711yescharacteristic
334C2×#131—431no—
335C2×#131—431no—
336#533—431no—
337C4×#41C2×D4311yescharacteristic
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#427—431no—
354#424—431no—
355#424—431no—
356#423C2×D4311yescharacteristic
357C2×C4⋊C8—431no—
358C2×#104C2×D4311yescharacteristic
359C2×#104C2×D4311yescharacteristic
360#416—431no—
361#416—431no—
362#405—431no—
363#405—431no—
364#405—431no—
365#405—431no—
366#405—861no—
367#405—861no—
368C4×M16—431no—
369C4×M16—861no—
370C2×#97—431no—
371C2×#97—431no—
372C2×#97—861no—
373C2×C4×C8—431no—
374C4×C4⋊C4C2×D4311yescharacteristic
375#341—431no—
376#341—431no—
377#339—431no—
378#339—431no—
379#339—431no—
380#339—431no—
381#339C2×D4311yescharacteristic
382#339C2×D4311yescharacteristic
383#336—431no—
384#336—431no—
385C43#2162911yescharacteristic, complemented, Sylow
386C2×#41C22×D4311yescharacteristic
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—431no—
400C22×C8—431no—
401C22×C8—861no—
402C22×C8—861no—
403C4⋊Q8—431no—
404C4⋊Q8—431no—
405#125—431no—
406#125—431no—
407C22⋊Q8—861no—
408C22⋊Q8—861no—
409C4×Q8—861no—
410C4×Q8—861no—
411C4×Q8C4×D4311yescharacteristic
412C4×Q8C4×D4311yescharacteristic
413C4×D4—21no—
414C4×D4—21no—
415C4×D4C4×D4311yescharacteristic
416C4×D4C4×D4311yescharacteristic
417#117—21no—
418#117—431no—
419#117—431no—
420#117C22×D4311yescharacteristic
421C2×C4⋊C4—21no—
422C2×C42—21no—
423C2×C42C22×D4311yescharacteristic
424C2×C42C22×D4311yescharacteristic
425C2×C42C22×D4311yescharacteristic
426#108—862no—
427#108—862no—
428#107—431no—
429#107—431no—
430#107—431no—
431#107—431no—
432#106—431no—
433#106—431no—
434#106—431no—
435#106—431no—
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—22no—
447#104—22no—
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—431no—
457#97—431no—
458#97—431no—
459#97—431no—
460#97—862no—
461#97—861no—
462#97—861no—
463#97—861no—
464#97—861no—
465#97—861no—
466C4×C8—862no—
467C4×C8—861no—
468C4×C8—861no—
469C4×C8—861no—
470C4×C8—861no—
471C4×C8—861no—
472#95—21no—
473#41—21no—
474#41—21no—
475#41#1062190012yes—
476#41Q8×D4312yes—
477C2×Q8—861no—
478C2×Q8—861no—
479C2×Q8C2×C4×D4311yescharacteristic
480C2×D4—21no—
481C2×D4C2×C4×D4311yescharacteristic
482C22×C4—21no—
483C22×C4—21no—
484C22×C4—21no—
485C22×C4—21no—
486C22×C4—21no—
487C22×C4#1062190011yescharacteristic
488C22×C4#1062190011yescharacteristic
489C22×C4C23×D4311yescharacteristic
490M16—21no—
491M16—21no—
492M16—21no—
493M16—21no—
494M16—432no—
495M16—432no—
496M16—864no—
497M16—864no—
498M16—861no—
499M16—861no—
500C2×C8—21no—
501C2×C8—21no—
502C2×C8—431no—
503C2×C8—431no—
504C2×C8—432no—
505C2×C8—432no—
506C2×C8—431no—
507C2×C8—431no—
508C2×C8—431no—
509C2×C8—431no—
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×C8—861no—
519C2×C8—861no—
520C2×C8—861no—
521C2×C8—861no—
522C4⋊C4—21no—
523C4⋊C4—21no—
524C4⋊C4—42no—
525C4⋊C4—431no—
526C4⋊C4—431no—
527C4⋊C4—431no—
528C4⋊C4—431no—
529C4⋊C4—861no—
530C4⋊C4—861no—
531C4⋊C4—861no—
532C4⋊C4—861no—
533C4⋊C4—861no—
534C4⋊C4—861no—
535C4⋊C4C2×C4×D4311yescharacteristic
536C4⋊C4C2×C4×D4311yescharacteristic
537C22⋊C4—21no—
538C22⋊C4—21no—
539C22⋊C4—21no—
540C22⋊C4—861no—
541C22⋊C4—861no—
542C42—21no—
543C42—21no—
544C42—21no—
545C42—21no—
546C42—21no—
547C42—21no—
548C42—21no—
549C42—861no—
550C42—861no—
551C42C2×C4×D4311yescharacteristic
552C42C2×C4×D4311yescharacteristic
553C42D4×D4311yescharacteristic
554C42D4×D4311yescharacteristic
555C23—21no—
556C23C2×#1062190011yescharacteristic
557Q8—21no—
558Q8—3441no—
559Q8—3441no—
560Q8#1306329012yes—
561D4—22no—
562D4—22no—
563D4—21no—
564D4#1306329012yes—
565C2×C4—21no—
566C2×C4—22no—
567C2×C4—22no—
568C2×C4—22no—
569C2×C4—21no—
570C2×C4—21no—
571C2×C4—41no—
572C2×C4—41no—
573C2×C4—41no—
574C2×C4—41no—
575C2×C4—41no—
576C2×C4—41no—
577C2×C4—41no—
578C2×C4—81no—
579C2×C4—81no—
580C2×C4—861no—
581C2×C4—861no—
582C2×C4—861no—
583C2×C4—861no—
584C2×C4(C22⋊D43)⋊C411yescharacteristic
585C2×C4(C22⋊D43)⋊C411yescharacteristic
586C2×C4(C22⋊D43)⋊C411yescharacteristic
587C2×C4(C22⋊D43)⋊C411yescharacteristic
588C2×C4C22×C4×D4311yescharacteristic
589C2×C4C2×D4×D4311yescharacteristic
590C2×C4C2×Q8×D4311yescharacteristic
591C2×C4#41×D4311yescharacteristic
592C2×C4#41×D4311yescharacteristic
593C2×C4C2×#1062190011yescharacteristic
594C8—41no—
595C8—41no—
596C8—432no—
597C8—432no—
598C8—861no—
599C8—861no—
600C8—861no—
601C8—861no—
602C8—862no—
603C8—861no—
604C8—861no—
605C8—862no—
606C22—21no—
607C22—21no—
608C22—22no—
609C22—41no—
610C22—41no—
611C22C2×(C22⋊D43)⋊C411yescharacteristic
612C22#1458343011yescharacteristic
613C22#1458345111yescharacteristic
614C4—21no—
615C4—21no—
616C4—21no—
617C4—21no—
618C4—22no—
619C4—42no—
620C4—41no—
621C4—41no—
622C4—81no—
623C4—1721no—
624C4—1721no—
625C4—1721no—
626C4—1721no—
627C4C2×#1306329011yescharacteristic
628C4#1458336711yescharacteristic
629C4C22⋊Q8×D4311yescharacteristic
630C4#1458340911yescharacteristic
631C2—21no—
632C2—21no—
633C2—42no—
634C2#1913712311yescharacteristic
635C2#1914350111yescharacteristic
636C2#1914350811yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1806C2
socleC22×C43C2×C4×D4
prime radicalC2×#41×C43C23
cosocleC22×C4×C43C24
hypercenter#1806D43
hypocenterC43#21629
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1806

Complements

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

NH ≅ G/Ntype
2. #19143532C2semidirect
4. #19135538C2semidirect
5. #19135368C2semidirect
6. #19135192C2semidirect
7. #19135192C2semidirect
10. #19134478C2semidirect
11. #19134473C2semidirect
12. #19134470C2semidirect
19. #14583206C4semidirect
20. #14583206C4semidirect
21. #14583199C4semidirect
22. #14583199C4semidirect
23. #14583194C4semidirect
24. #14583189C4semidirect
25. #14583184C4semidirect
26. #14583179C4semidirect
70. #13063332Q8semidirect
385. C43#21629semidirect

Maximal subgroups

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

subgroupindex
#191443832
#191435322
#191430232
#191355382
#191353682
#191351922
#191348682
#191344782
#191344732
#191344702
#191344402
#191344332
C43×#18062
#2162943