Finite Group Databasebeta

← #25964305

Subgroups — #25964305

Order 11008.

1970 conjugacy classes of subgroups.

The subgroup lattice has 614 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#13063372C211yesmaximal, characteristic
2#19144453C213yesmaximal, complemented
3#19144442C213yesmaximal, complemented
4#19144431C213yesmaximal, complemented
5#19144431C213yesmaximal, complemented
6#19144413C213yesmaximal, complemented
7#19144396C213yesmaximal, complemented
8#19144377C213yesmaximal, complemented
9C2×#14583203C213yesmaximal, complemented
10#19143193C211yesmaximal, characteristic, complemented
11#19143188C211yesmaximal, characteristic, complemented
12#19143163C211yesmaximal, characteristic, complemented
13#19143125C211yesmaximal, characteristic
14#19143125C211yesmaximal, characteristic
15C43×#3504C211yesmaximal, characteristic, complemented
16C2×#13063372C2211yescharacteristic
17C2×#13063332C2211yescharacteristic
18C2×#13063332C2211yescharacteristic
19#14583382C2211yescharacteristic
20#14583379C2213yes—
21#14583378—23no—
22#14583376C2213yes—
23#14583375—21no—
24C4×#10621898C2213yes—
25C4×#10621900—23no—
26C2×C4×Dic86C2213yes—
27C4×Q8×D43—21no—
28#14583203C2216yes—
29#14583203C2213yes—
30#14583203C2216yes—
31#14583203C2216yes—
32#14583203C2213yes—
33#14583203C2216yes—
34#14583196C2216yes—
35#14583196C2211yescharacteristic
36#14583196C2213yes—
37#14583191C2213yes—
38#14583191C2216yes—
39#14583186C2213yes—
40#14583181C2216yes—
41#14583181C2213yes—
42#14583176C2213yes—
43#14582942C2213yes—
44#14582942C2213yes—
45#14582939C2213yes—
46#14582939C2213yes—
47#14582935C2213yes—
48#14582935C2213yes—
49C2×#13063258C2213yes—
50C2×#13063256C2213yes—
51#14582926C2213yes—
52#14582926C2213yes—
53#14582923C2213yes—
54C2×C4⋊(C43⋊C8)C2213yes—
55#14582907C2213yes—
56#14582907C2213yes—
57#14582898C2213yes—
58#14582898C2213yes—
59#14582893C2213yes—
60#14582893C2213yes—
61C2×#13063248C2213yes—
62C2×#13063248C2213yes—
63C43×#557—21no—
64C43×#557—21no—
65C43×#554—23no—
66C43×#554—23no—
67C43×#544C2213yes—
68C43×#544C2213yes—
69C43×#533C2213yes—
70C2×#125×C43C2213yes—
71C43×#520C2211yescharacteristic
72C43×#520C2211yescharacteristic
73C4×#41×C43C2211yescharacteristic
74#13063372—24no—
75#13063372Q818yescomplemented
76C2×#10621898C2313yes—
77C2×#10621900—23no—
78C22×Dic86C2313yes—
79C2×Q8×D43—21no—
80#13063332—24no—
81#13063332—24no—
82C2×#10621877C2313yes—
83C2×#10621877C2313yes—
84C22×C43⋊C8C2313yes—
85C22×C43⋊C8C2313yes—
86Q8×Dic43—21no—
87C4×Dic86—23no—
88C4×Dic86—23no—
89C4×Dic86C2313yes—
90C4×Dic86C2316yes—
91C4×Dic86C2313yes—
92#13063290—23no—
93#13063290—23no—
94C4×D172C2311yescharacteristic
95C4×D172C2313yes—
96D4×Dic43—23no—
97C4×C22⋊D43—23no—
98C4×C22⋊D43—23no—
99(C22⋊D43)⋊C4—26no—
100#13063284C2313yes—
101#13063283—23no—
102#13063282—23no—
103#13063281—26no—
104C2×C4⋊Dic43C2313yes—
105C2×Dic43⋊C4—23no—
106C4⋊C4×D43—23no—
107C2×C4×Dic43—23no—
108C42×D43—23no—
109#13063258C2313yes—
110#13063258C2313yes—
111#13063258C2316yes—
112#13063258C2311yescharacteristic
113#13063258C2313yes—
114#13063256C2311yescharacteristic
115#13063256C2313yes—
116#13063256C2316yes—
117#13063256C2313yes—
118#13063256C2313yes—
119C4⋊(C43⋊C8)C2311yescharacteristic
120C4⋊(C43⋊C8)C2313yes—
121C4⋊(C43⋊C8)C2313yes—
122C4⋊(C43⋊C8)C2313yes—
123C4⋊(C43⋊C8)C2316yes—
124#13063248C2313yes—
125#13063248C2313yes—
126#13063248C2316yes—
127#13063248C2316yes—
128#13063248C2313yes—
129#13063248C2313yes—
130#13063245C2311yescharacteristic
131#13063245C2311yescharacteristic
132#13063245C2313yes—
133#13063245C2313yes—
134C2×#41×C43C2311yescharacteristic
135C4⋊Q8×C43—23no—
136C4⋊Q8×C43—23no—
137C4⋊Q8×C43C2313yes—
138C4⋊Q8×C43C2313yes—
139#125×C43—23no—
140#125×C43—23no—
141#125×C43—23no—
142#125×C43—23no—
143#125×C43C2313yes—
144#125×C43C2316yes—
145#125×C43C2311yescharacteristic
146C22⋊Q8×C43—23no—
147C22⋊Q8×C43—23no—
148C22⋊Q8×C43—26no—
149C22⋊Q8×C43—26no—
150C4×Q8×C43—21no—
151C4×Q8×C43—21no—
152C4×Q8×C43—23no—
153C4×Q8×C43—23no—
154C4×Q8×C43D411yescharacteristic
155C4×Q8×C43D411yescharacteristic
156C4×D4×C43—23no—
157C4×D4×C43—23no—
158C4×D4×C43D413yes—
159C4×D4×C43D413yes—
160#117×C43C2313yes—
161#117×C43C2313yes—
162#117×C43C2313yes—
163C2×C4⋊C4×C43—23no—
164C2×C4⋊C4×C43—23no—
165C2×C4⋊C4×C43C2313yes—
166C2×C4⋊C4×C43C2313yes—
167C2×C42×C43C2313yes—
168#41×C43C2×Q814yes—
169#41×C43#4114yes—
170C2×Q8×C43—23no—
171C2×Q8×C43—23no—
172C2×Q8×C43C2×D411yescharacteristic
173C2×D4×C43C2×D413yes—
174C22×C4×C43—23no—
175C22×C4×C43—23no—
176C22×C4×C43C2×D413yes—
177C22×C4×C43C2×D413yes—
178C22×C4×C43C2413yes—
179C2×C22⋊D43—23no—
180C22×Dic43—23no—
181C22×Dic43—23no—
182Q8×D43—28no—
183#10621900—224no—
184#10621898—26no—
185#10621898C2×Q8112yes—
186C2×D172C2411yescharacteristic
187C2×C4×D43—23no—
188C2×C4×D43—21no—
189C2×C4×D43—23no—
190C2×Dic86—23no—
191C2×Dic86—26no—
192C2×Dic86C2×Q8112yes—
193C2×Dic86C2413yes—
194C4⋊C4×C43—23no—
195C4⋊C4×C43—23no—
196C4⋊C4×C43—26no—
197C4⋊C4×C43—26no—
198C4⋊C4×C43—23no—
199C4⋊C4×C43—23no—
200C4⋊C4×C43—21no—
201C4⋊C4×C43—21no—
202C4⋊C4×C43—23no—
203C4⋊C4×C43—23no—
204C4⋊C4×C43C2×D413yes—
205C4⋊C4×C43C2×D413yes—
206C4⋊C4×C43C2413yes—
207C4⋊C4×C43C2413yes—
208C4⋊C4×C43C2411yescharacteristic
209C4⋊C4×C43C2411yescharacteristic
210C22⋊C4×C43—23no—
211C22⋊C4×C43—23no—
212C22⋊C4×C43C2×D416yes—
213C42×C43—23no—
214C42×C43—23no—
215C42×C43C2×D413yes—
216C42×C43C2×D413yes—
217C42×C43C2411yescharacteristic
218C42×C43C2413yes—
219C22⋊Dic43—23no—
220(C2×D43)⋊C4—21no—
221(C2×D43)⋊C4—23no—
222C4⋊Dic43—23no—
223C4⋊Dic43C2413yes—
224C4⋊Dic43C2411yescharacteristic
225Dic43⋊C4—26no—
226Dic43⋊C4—23no—
227Dic43⋊C4—23no—
228C4×Dic43—23no—
229C4×Dic43—23no—
230C4×Dic43—23no—
231C4×Dic43—26no—
232#10621877—26no—
233#10621877—26no—
234C2×C43⋊C8—26no—
235C2×C43⋊C8—26no—
236C2×C43⋊C8C2411yescharacteristic
237C2×C43⋊C8C2413yes—
238C2×C43⋊C8C2413yes—
239C2×C43⋊C8C2411yescharacteristic
240C23×C43C22×D413yes—
241C22×D43—21no—
242Q8×C43—83no—
243Q8×C43—83no—
244Q8×C43C22⋊Q814yes—
245D4×C43C22⋊Q8112yes—
246C2×C4×C43—21no—
247C2×C4×C43—21no—
248C2×C4×C43—23no—
249C2×C4×C43—23no—
250C2×C4×C43—43no—
251C2×C4×C43—43no—
252C2×C4×C43—83no—
253C2×C4×C43—83no—
254C2×C4×C43C22×D411yescharacteristic
255C2×C4×C43C22×D413yes—
256C2×C4×C43C22×D413yes—
257C2×C4×C43C22×D411yescharacteristic
258C2×C4×C43C22×D413yes—
259C2×C4×C43C22×Q816yes—
260C2×C4×C43C2×#4116yes—
261C2×C4×C43C2511yescharacteristic
262C22⋊D43—212no—
263C2×Dic43—212no—
264C2×Dic43—23no—
265C2×Dic43—21no—
266C2×Dic43—23no—
267C2×Dic43—83no—
268D172—21no—
269D172C22×Q812yes—
270C4×D43—212no—
271C4×D43—42no—
272C4×D43—83no—
273Dic86—212no—
274Dic86—23no—
275Dic86C22×Q816yes—
276C43⋊C8—21no—
277C43⋊C8—21no—
278C43⋊C8—23no—
279C43⋊C8—23no—
280#60499—431nomaximal, Sylow
281C22×C43—23no—
282C22×C43—23no—
283C22×C43C2×C22⋊Q816yes—
284C22×C43C23×D411yescharacteristic
285C2×D43—22no—
286C2×D43—41no—
287C2×D43—41no—
288C4×C43—23no—
289C4×C43—21no—
290C4×C43—21no—
291C4×C43—23no—
292C4×C43—43no—
293C4×C43—41no—
294C4×C43—43no—
295C4×C43—41no—
296C4×C43C2×C22⋊Q816yes—
297C4×C43C23×Q811yescharacteristic
298C4×C43C22×#4111yescharacteristic
299Dic43—26no—
300Dic43—43no—
301Dic43—41no—
302#3504D4311yescharacteristic, complemented
303C4×2−1+4—431no—
304#3084—433no—
305#3083—433no—
306#3082—433no—
307#3082—433no—
308#3080—433no—
309#3078—433no—
310#3076—433no—
311C2×#479—433no—
312#2913—431no—
313#2912—431no—
314#2906—431no—
315#2898—431no—
316#2898—431no—
317C2×C43—26no—
318C2×C43C22×C22⋊Q811yescharacteristic
319C2×C43#358411yescharacteristic
320C2×C43#358611yescharacteristic
321D43—42no—
322C2×2−1+4—431no—
323C2×#131—431no—
324C2×#131—431no—
325#557—21no—
326#557—21no—
327#554—23no—
328#554—23no—
329#544C2×D4313yes—
330#544C2×D4313yes—
331#533C2×D4313yes—
332C2×#125C2×D4313yes—
333#520—431no—
334#520—433no—
335#520—863no—
336#520C2×D4311yescharacteristic
337#520C2×D4311yescharacteristic
338#519—433no—
339#519—861no—
340C4×#41—433no—
341C4×#41—863no—
342C4×#41C2×D4311yescharacteristic
343C2×C4×Q8—433no—
344C2×C4×Q8—861no—
345#479—433no—
346#479—436no—
347#479—436no—
348#479—436no—
349#479—433no—
350#479—436no—
351#478—431no—
352#478—433no—
353#478—436no—
354#477—433no—
355#477—436no—
356#476—433no—
357#475—433no—
358#475—436no—
359#474—433no—
360#428—433no—
361#428—433no—
362#428—433no—
363#428—433no—
364#427—433no—
365#427—433no—
366C2×#107—433no—
367C2×#106—433no—
368#424—433no—
369#424—433no—
370#423—433no—
371C2×C4⋊C8—433no—
372#419—433no—
373#419—433no—
374#417—433no—
375#417—433no—
376#416—433no—
377#416—433no—
378C2×#103—433no—
379C2×#103—433no—
380C43#6049911yescharacteristic, complemented, Sylow
3812−1+4—438no—
3822−1+4—864no—
383C2×#41—433no—
384C2×#41—863no—
385C2×#41C22×D4311yescharacteristic
386C22×Q8—433no—
387C22×Q8—861no—
388#131—864no—
389#131—864no—
390C2×M16—433no—
391C2×M16—433no—
392C22×C8—433no—
393C22×C8—433no—
394C4⋊Q8—23no—
395C4⋊Q8—23no—
396C4⋊Q8C22×D4313yes—
397C4⋊Q8C22×D4313yes—
398#125—23no—
399#125—23no—
400#125—23no—
401#125—23no—
402#125C22×D4313yes—
403#125C22×D4316yes—
404#125C22×D4311yescharacteristic
405C22⋊Q8—23no—
406C22⋊Q8—23no—
407C22⋊Q8—26no—
408C22⋊Q8—26no—
409C4×Q8—21no—
410C4×Q8—21no—
411C4×Q8—23no—
412C4×Q8—23no—
413C4×Q8—433no—
414C4×Q8—436no—
415C4×Q8—433no—
416C4×Q8—861no—
417C4×Q8—863no—
418C4×Q8—863no—
419C4×Q8—863no—
420C4×Q8—863no—
421C4×Q8C22⋊D4311yescharacteristic
422C4×Q8C22⋊D4311yescharacteristic
423C4×D4—23no—
424C4×D4—23no—
425C4×D4—431no—
426C4×D4—433no—
427C4×D4—863no—
428C4×D4—863no—
429C4×D4—863no—
430C4×D4—866no—
431C4×D4C22⋊D4313yes—
432C4×D4C22⋊D4313yes—
433#117—433no—
434#117—863no—
435#117—866no—
436#117—863no—
437#117C22×D4313yes—
438#117C22×D4313yes—
439#117C22×D4313yes—
440C2×C4⋊C4—23no—
441C2×C4⋊C4—23no—
442C2×C4⋊C4—433no—
443C2×C4⋊C4—863no—
444C2×C4⋊C4—863no—
445C2×C4⋊C4C22×D4313yes—
446C2×C4⋊C4C22×D4313yes—
447C2×C42—863no—
448C2×C42—863no—
449C2×C42C22×D4313yes—
450#107—433no—
451#107—436no—
452#107—431no—
453#107—433no—
454#107—433no—
455#106—433no—
456#106—436no—
457#106—431no—
458#106—433no—
459#106—433no—
460C4⋊C8—431no—
461C4⋊C8—433no—
462C4⋊C8—433no—
463C4⋊C8—433no—
464C4⋊C8—436no—
465#103—433no—
466#103—433no—
467#103—436no—
468#103—436no—
469#103—433no—
470#103—433no—
471#102—431no—
472#102—431no—
473#102—433no—
474#102—433no—
475#41—4312no—
476#41—8624no—
477#41—866no—
478#41Q8×D4314yes—
479#41#1062190214yes—
480C2×Q8—23no—
481C2×Q8—23no—
482C2×Q8—4312no—
483C2×Q8—433no—
484C2×Q8—868no—
485C2×Q8—863no—
486C2×Q8—866no—
487C2×Q8C2×C22⋊D4311yescharacteristic
488C2×D4—431no—
489C2×D4—863no—
490C2×D4C2×C22⋊D4313yes—
491C22×C4—23no—
492C22×C4—23no—
493C22×C4—863no—
494C22×C4—863no—
495C22×C4—863no—
496C22×C4—863no—
497C22×C4—861no—
498C22×C4C2×C22⋊D4313yes—
499C22×C4C2×C22⋊D4313yes—
500C22×C4C23×D4313yes—
501M16—866no—
502M16—866no—
503C2×C8—431no—
504C2×C8—433no—
505C2×C8—433no—
506C2×C8—431no—
507C2×C8—866no—
508C2×C8—866no—
509C4⋊C4—23no—
510C4⋊C4—23no—
511C4⋊C4—26no—
512C4⋊C4—26no—
513C4⋊C4—23no—
514C4⋊C4—23no—
515C4⋊C4—21no—
516C4⋊C4—21no—
517C4⋊C4—23no—
518C4⋊C4—23no—
519C4⋊C4—433no—
520C4⋊C4—431no—
521C4⋊C4—863no—
522C4⋊C4—866no—
523C4⋊C4—863no—
524C4⋊C4—863no—
525C4⋊C4C2×C22⋊D4313yes—
526C4⋊C4C2×C22⋊D4313yes—
527C4⋊C4C23×D4313yes—
528C4⋊C4C23×D4311yescharacteristic
529C4⋊C4C23×D4313yes—
530C4⋊C4C23×D4311yescharacteristic
531C22⋊C4—23no—
532C22⋊C4—23no—
533C22⋊C4—863no—
534C22⋊C4—861no—
535C22⋊C4—863no—
536C22⋊C4C2×C22⋊D4316yes—
537C42—23no—
538C42—23no—
539C42—863no—
540C42—863no—
541C42—863no—
542C42—866no—
543C42C2×C22⋊D4313yes—
544C42C2×C22⋊D4313yes—
545C42C23×D4311yescharacteristic
546C42C23×D4313yes—
547C23—861no—
548C23C22×C22⋊D4313yes—
549Q8—83no—
550Q8—83no—
551Q8—436no—
552Q8—8612no—
553Q8—863no—
554Q8#1306330114yes—
555D4—432no—
556D4—8612no—
557D4—861no—
558D4#13063301112yes—
559C2×C4—21no—
560C2×C4—21no—
561C2×C4—23no—
562C2×C4—23no—
563C2×C4—43no—
564C2×C4—43no—
565C2×C4—83no—
566C2×C4—83no—
567C2×C4—8612no—
568C2×C4—863no—
569C2×C4—8612no—
570C2×C4—861no—
571C2×C4—863no—
572C2×C4—3443no—
573C2×C4—3443no—
574C2×C4—1722no—
575C2×C4C22×C22⋊D4311yescharacteristic
576C2×C4C22×C22⋊D4313yes—
577C2×C4C22×C22⋊D4313yes—
578C2×C4C22×C22⋊D4311yescharacteristic
579C2×C4C22×C22⋊D4313yes—
580C2×C4C2×Q8×D4316yes—
581C2×C4C2×#1062190216yes—
582C2×C4C24×D4311yescharacteristic
583C8—861no—
584C8—861no—
585C8—863no—
586C8—863no—
587C22—23no—
588C22—23no—
589C22—862no—
590C22—1721no—
591C22—1721no—
592C22C2×#1306330116yes—
593C22C23×C22⋊D4311yescharacteristic
594C4—21no—
595C4—23no—
596C4—21no—
597C4—23no—
598C4—43no—
599C4—41no—
600C4—43no—
601C4—41no—
602C4—866no—
603C4—1723no—
604C4—1721no—
605C4C2×#1306330116yes—
606C4C22×Q8×D4311yescharacteristic
607C4C22×#1062190211yescharacteristic
608C2—26no—
609C2—1722no—
610C2C22×#1306330111yescharacteristic
611C2#1914936611yescharacteristic
612C2#1914938111yescharacteristic
subgroupG/H
centerC22C23×C22⋊D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC43×#3504C2
socleC22×C43C23×D4
prime radicalC2×#13063372C22
hypercenter#3504D43
hypocenterC43#60499
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C4×#41 ◁ #3504

Complements

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

NH ≅ G/Ntype
2. #19144453C2semidirect
3. #19144442C2semidirect
4. #19144431C2semidirect
5. #19144431C2semidirect
6. #19144413C2semidirect
7. #19144396C2semidirect
8. #19144377C2semidirect
9. C2×#14583203C2semidirect
10. #19143193C2semidirect
11. #19143188C2semidirect
12. #19143163C2semidirect
15. C43×#3504C2semidirect
75. #13063372Q8semidirect
302. #3504D43semidirect
380. C43#60499semidirect

Maximal subgroups

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

subgroupindex
C4×#130633722
#191444532
#191444422
#191444312
#191444132
#191443962
#191443772
C2×#145832032
#191431932
#191431882
#191431632
#191431252
C43×#35042
#6049943