Finite Group Databasebeta

← #25081962

Subgroups — #25081962

Order 11008.

598 conjugacy classes of subgroups.

The subgroup lattice has 560 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19145732C211yesmaximal, characteristic
2#19144719C211yesmaximal, characteristic
3#19144633C211yesmaximal, characteristic, complemented
4#19143674C211yesmaximal, characteristic, complemented
5#19134042C211yesmaximal, characteristic, complemented
6#19134041C211yesmaximal, characteristic, complemented
7#19134012C211yesmaximal, characteristic, complemented
8#19134011C211yesmaximal, characteristic, complemented
9#19133998C211yesmaximal, characteristic, complemented
10#19133997C211yesmaximal, characteristic, complemented
11#19133974C211yesmaximal, characteristic, complemented
12#19133372C211yesmaximal, characteristic, complemented
13#19133302C211yesmaximal, characteristic, complemented
14#19133256C211yesmaximal, characteristic
15C43×#1672C211yesmaximal, characteristic, complemented
16#14583454C2211yescharacteristic
17#14583450C2211yescharacteristic
18C4×Q8×D43C2211yescharacteristic
19#14583302C2211yescharacteristic
20#14583247C2211yescharacteristic
21#14583246C2211yescharacteristic
22#14583233—21no—
23#14583225—21no—
24#14583225—21no—
25#14583214—21no—
26#14583198—21no—
27#14583198—21no—
28#14583195C2211yescharacteristic
29#14583194C2211yescharacteristic
30#14583191C2211yescharacteristic
31#14583106C2211yescharacteristic
32#14583100C2211yescharacteristic
33#14583099C2211yescharacteristic
34#14583053—21no—
35#14583039—21no—
36Q8×C43⋊C8C2211yescharacteristic
37C8×Dic86—21no—
38C8×Dic86C2211yescharacteristic
39#14583023—21no—
40#14583023C2211yescharacteristic
41#14583002—21no—
42#14582998—21no—
43Q16×Dic43—21no—
44#14582991—21no—
45#14582955C2211yescharacteristic
46#14582951—21no—
47#14582951C2211yescharacteristic
48#14582951C2211yescharacteristic
49#14582950—21no—
50#14582950C2211yescharacteristic
51#14582651C2211yescharacteristic
52#14582651C2211yescharacteristic
53#14582650C2211yescharacteristic
54#14582648C2211yescharacteristic
55#14582647C2211yescharacteristic
56#14582647C2211yescharacteristic
57#14582645C2211yescharacteristic
58#14582642C2211yescharacteristic
59#14582642C2211yescharacteristic
60C43×#498C2211yescharacteristic
61C43×#477C2211yescharacteristic
62C43×#462C2211yescharacteristic
63C8×Q8×C43C2211yescharacteristic
64C43×#334C2211yescharacteristic
65C43×#333C2211yescharacteristic
66C43×#332C2211yescharacteristic
67C2×#10621902—21no—
68C2×Q8×D43D411yescharacteristic
69C2×#10621885—21no—
70C2×#10621873—21no—
71C2×#10621884—21no—
72#13063325C2311yescharacteristic
73#13063322C2311yescharacteristic
74#13063316—21no—
75#13063314—21no—
76#13063305—21no—
77#13063301—21no—
78#13063300—21no—
79#13063300—21no—
80Q8×Dic43—21no—
81Q8×Dic43D411yescharacteristic
82C4×Dic86—21no—
83C4×Dic86C2311yescharacteristic
84#13063290—21no—
85#13063290—21no—
86#13063290D411yescharacteristic
87#13063287—21no—
88#13063287—21no—
89#13063283—21no—
90C4⋊C4×D43—21no—
91C4⋊C4×D43D411yescharacteristic
92C42×D43—21no—
93C42×D43C2311yescharacteristic
94#13063259—21no—
95#13063258—21no—
96#13063258—21no—
97#13063258—21no—
98#13063258—21no—
99C4⋊(C43⋊C8)—21no—
100C4⋊(C43⋊C8)C2311yescharacteristic
101C4⋊(C43⋊C8)C2311yescharacteristic
102C4⋊(C43⋊C8)C2311yescharacteristic
103Dic43⋊C8—21no—
104Dic43⋊C8—21no—
105Dic43⋊C8D411yescharacteristic
106Dic43⋊C8D411yescharacteristic
107#13063250—21no—
108#13063249—21no—
109#13063249—21no—
110#13063248—21no—
111#13063247—21no—
112#13063247—21no—
113#13063247—21no—
114#13063245—21no—
115#13063245—21no—
116#13063245—21no—
117(C2×D43)⋊C8—21no—
118(C2×D43)⋊C8—21no—
119(C2×D43)⋊C8—21no—
120(C2×D43)⋊C8D411yescharacteristic
121(C2×D43)⋊C8D411yescharacteristic
122#13063235—21no—
123C4×C43⋊C8—21no—
124C4×C43⋊C8C2311yescharacteristic
125C8×Dic43—21no—
126C8×Dic43—21no—
127C8×Dic43—21no—
128C8×Dic43—21no—
129C2×Q16×C43—21no—
130C4⋊Q8×C43C2311yescharacteristic
131C4⋊Q8×C43C2311yescharacteristic
132C4×Q8×C43C2311yescharacteristic
133#107×C43—21no—
134#106×C43—21no—
135#106×C43—21no—
136C4⋊C8×C43—21no—
137C4⋊C8×C43C2311yescharacteristic
138C4⋊C8×C43C2311yescharacteristic
139C4⋊C8×C43C2311yescharacteristic
140#103×C43—21no—
141#103×C43—21no—
142C4×C8×C43—21no—
143C4×C8×C43C2311yescharacteristic
144C2×Q8×C43—21no—
145C2×Q8×C43—21no—
146C2×Q8×C43C2×D411yescharacteristic
147#10621902—82no—
148Q8×D43—22no—
149Q8×D43—22no—
150C2×D172—21no—
151C2×D172—21no—
152C2×D172—21no—
153C2×D172—41no—
154C2×C4×D43—21no—
155C2×C4×D43—21no—
156C2×C4×D43—41no—
157C2×C4×D43C2×D411yescharacteristic
158C2×C4×D43C2×D411yescharacteristic
159C2×C4×D43#4111yescharacteristic
160C2×Dic86—21no—
161C2×Dic86—21no—
162C2×Dic86C2×D411yescharacteristic
163Q16×C43—42no—
164C2×C8×C43—21no—
165C2×C8×C43—21no—
166C2×C8×C43—21no—
167C2×C8×C43C2×D411yescharacteristic
168C2×C8×C43C2×D411yescharacteristic
169C4⋊C4×C43—21no—
170C4⋊C4×C43—21no—
171C4⋊C4×C43—21no—
172C4⋊C4×C43—21no—
173C4⋊C4×C43—21no—
174C4⋊C4×C43C2×D411yescharacteristic
175C42×C43—21no—
176C42×C43C2411yescharacteristic
177#10621885—42no—
178#10621884—42no—
179(C2×D43)⋊C4—41no—
180(C2×D43)⋊C4—41no—
181(C2×D43)⋊C4—41no—
182C4⋊Dic43—21no—
183C4⋊Dic43—21no—
184C4⋊Dic43—21no—
185C4⋊Dic43—41no—
186C4⋊Dic43C2×D411yescharacteristic
187Dic43⋊C4—21no—
188Dic43⋊C4—21no—
189Dic43⋊C4—21no—
190Dic43⋊C4—41no—
191C4×Dic43—21no—
192C4×Dic43—21no—
193C4×Dic43—21no—
194C4×Dic43—41no—
195C4×Dic43C2×D411yescharacteristic
196C4×Dic43C2×D411yescharacteristic
197C4×Dic43#4111yescharacteristic
198C2×C43⋊C8—21no—
199C2×C43⋊C8—21no—
200C2×C43⋊C8—21no—
201C2×C43⋊C8C2×D411yescharacteristic
202C2×C43⋊C8C2×D411yescharacteristic
203#10621873—42no—
204C22×D43—41no—
205C22×D43#12111yescharacteristic
206Q8×C43—21no—
207Q8×C43—41no—
208Q8×C43—41no—
209Q8×C43—81no—
210Q8×C43#13512yes—
211C2×C4×C43—21no—
212C2×C4×C43—21no—
213C2×C4×C43—41no—
214C2×C4×C43—41no—
215C2×C4×C43C22×D411yescharacteristic
216C2×C4×C43C22×D411yescharacteristic
217C2×C4×C43C2×#4111yescharacteristic
218C2×Dic43—21no—
219C2×Dic43—21no—
220C2×Dic43—41no—
221C2×Dic43#12111yescharacteristic
222C2×Dic43#12111yescharacteristic
223C2×Dic43#12111yescharacteristic
224D172—41no—
225D172—41no—
226D172—41no—
227D172—41no—
228D172—81no—
229D172—82no—
230C4×D43—24no—
231C4×D43—21no—
232C4×D43—21no—
233C4×D43—21no—
234C4×D43—21no—
235C4×D43—41no—
236C4×D43—82no—
237C4×D43—81no—
238Dic86—24no—
239Dic86—21no—
240Dic86—81no—
241Dic86#13512yes—
242C8×C43—21no—
243C8×C43—21no—
244C8×C43—41no—
245C8×C43—41no—
246C8×C43—41no—
247C43⋊C8—21no—
248C43⋊C8—21no—
249C43⋊C8—41no—
250C43⋊C8—41no—
251C43⋊C8—41no—
252#19406—431nomaximal, Sylow
253C22×C43C2×#12111yescharacteristic
254C2×D43—21no—
255C2×D43—21no—
256C2×D43—21no—
257C2×D43—81no—
258C2×D43—81no—
259C2×D43—81no—
260C4×C43—22no—
261C4×C43—21no—
262C4×C43—41no—
263C4×C43—81no—
264C4×C43—81no—
265C4×C43C2×#13511yescharacteristic
266C4×C43C2×#13511yescharacteristic
267C4×C43#57811yescharacteristic
268C4×C43#57811yescharacteristic
269Dic43—21no—
270Dic43—21no—
271Dic43—22no—
272Dic43—21no—
273Dic43—41no—
274Dic43—81no—
275#3228—431no—
276#3112—431no—
277#3104—431no—
278#2982—431no—
279#1682—431no—
280#1682—431no—
281#1678—431no—
282#1678—431no—
283#1676—431no—
284#1676—431no—
285#1672—431no—
286#1672D4311yescharacteristic, complemented
287#1572—431no—
288#1554—431no—
289#1543—431no—
290C2×C43#304411yescharacteristic
291C2×C43#305011yescharacteristic
292C2×C43#306811yescharacteristic
293D43—41no—
294D43—161no—
295#533—431no—
296#532—431no—
297C2×C4×Q8—431no—
298#500—431no—
299#498C2×D4311yescharacteristic
300#486—431no—
301#486—431no—
302#484—861no—
303#482—861no—
304#482—861no—
305#480—861no—
306#478—861no—
307#478—861no—
308#477—431no—
309#477—431no—
310#477—431no—
311#477C2×D4311yescharacteristic
312#462—431no—
313#462C2×D4311yescharacteristic
314#460—431no—
315#460—431no—
316#451—861no—
317#448—861no—
318C8×Q8—431no—
319C8×Q8—431no—
320C8×Q8—431no—
321C8×Q8—861no—
322C8×Q8—861no—
323C8×Q8C2×D4311yescharacteristic
324#440—861no—
325#440—861no—
326C4×Q16—861no—
327C4×Q16—861no—
328#432—431no—
329#431—431no—
330#431—431no—
331#431—431no—
332#431—861no—
333#431—861no—
334#335—431no—
335#335—431no—
336#334—431no—
337#334C2×D4311yescharacteristic
338#333—431no—
339#333—431no—
340#333—431no—
341#333C2×D4311yescharacteristic
342#332—431no—
343#332C2×D4311yescharacteristic
344#331—431no—
345#331—431no—
346C43#1940611yescharacteristic, complemented, Sylow
347C2×#41—861no—
348C22×Q8—431no—
349C2×Q16—21no—
350C2×Q16—861no—
351C2×SD16—861no—
352C2×SD16—861no—
353C4⋊Q8—431no—
354C4⋊Q8C22×D4311yescharacteristic
355C4⋊Q8C22×D4311yescharacteristic
356#127—431no—
357#125—861no—
358#124—861no—
359C22⋊Q8—861no—
360C22⋊Q8—861no—
361#121—861no—
362#121—861no—
363C4×Q8—431no—
364C4×Q8—431no—
365C4×Q8—431no—
366C4×Q8—861no—
367C4×Q8—861no—
368C4×Q8—861no—
369C4×Q8—861no—
370C4×Q8C22×D4311yescharacteristic
371C4×D4—861no—
372C4×D4—861no—
373#117—861no—
374C2×C4⋊C4—431no—
375C2×C4⋊C4—861no—
376C2×C42—431no—
377C2×C42—861no—
378#107—21no—
379#107—861no—
380#107—861no—
381#107—861no—
382#107—861no—
383#107—861no—
384#106—21no—
385#106—21no—
386C4⋊C8—21no—
387C4⋊C8—431no—
388C4⋊C8—431no—
389C4⋊C8—431no—
390C4⋊C8—431no—
391C4⋊C8—431no—
392C4⋊C8—861no—
393C4⋊C8—861no—
394C4⋊C8—861no—
395C4⋊C8C22×D4311yescharacteristic
396C4⋊C8C22×D4311yescharacteristic
397C4⋊C8C22×D4311yescharacteristic
398#103—21no—
399#103—21no—
400#103—861no—
401#103—861no—
402#103—861no—
403#103—861no—
404#102—861no—
405#102—861no—
406#102—861no—
407#102—861no—
408#102—861no—
409#102—861no—
410C22⋊C8—431no—
411C22⋊C8—431no—
412C22⋊C8—861no—
413C22⋊C8—861no—
414C22⋊C8—861no—
415#97—861no—
416C4×C8—21no—
417C4×C8—431no—
418C4×C8—861no—
419C4×C8—861no—
420C4×C8—861no—
421C4×C8—861no—
422C4×C8—861no—
423C4×C8C22×D4311yescharacteristic
424#41—3442no—
425C2×Q8—21no—
426C2×Q8—21no—
427C2×Q8—431no—
428C2×Q8—861no—
429C2×Q8—862no—
430C2×Q8—862no—
431C2×Q8—861no—
432C2×Q8D4×D4311yescharacteristic
433C2×D4—861no—
434C2×D4—861no—
435C2×D4—861no—
436C2×D4—1721no—
437C22×C4—431no—
438C22×C4—431no—
439C22×C4—431no—
440C22×C4—861no—
441C22×C4—861no—
442C22×C4—1721no—
443Q16—42no—
444Q16—1722no—
445SD16—1722no—
446SD16—1722no—
447C2×C8—21no—
448C2×C8—21no—
449C2×C8—21no—
450C2×C8—431no—
451C2×C8—431no—
452C2×C8—861no—
453C2×C8—861no—
454C2×C8—861no—
455C2×C8D4×D4311yescharacteristic
456C2×C8D4×D4311yescharacteristic
457C4⋊C4—21no—
458C4⋊C4—21no—
459C4⋊C4—21no—
460C4⋊C4—21no—
461C4⋊C4—21no—
462C4⋊C4—431no—
463C4⋊C4—861no—
464C4⋊C4—861no—
465C4⋊C4—861no—
466C4⋊C4—861no—
467C4⋊C4—861no—
468C4⋊C4—861no—
469C4⋊C4—1721no—
470C4⋊C4—1721no—
471C4⋊C4D4×D4311yescharacteristic
472C22⋊C4—1721no—
473C22⋊C4—1721no—
474C22⋊C4—1721no—
475C42—21no—
476C42—431no—
477C42—431no—
478C42—431no—
479C42—861no—
480C42—861no—
481C42—861no—
482C42—1721no—
483C42C23×D4311yescharacteristic
484C23—431no—
485C23—1721no—
486Q8—21no—
487Q8—41no—
488Q8—41no—
489Q8—81no—
490Q8—432no—
491Q8—864no—
492Q8—861no—
493Q8—3441no—
494Q8#1306334612yes—
495D4—3441no—
496D4—3442no—
497D4—1721no—
498D4—1721no—
499D4—1721no—
500D4—1721no—
501C2×C4—21no—
502C2×C4—21no—
503C2×C4—41no—
504C2×C4—41no—
505C2×C4—431no—
506C2×C4—431no—
507C2×C4—431no—
508C2×C4—864no—
509C2×C4—861no—
510C2×C4—861no—
511C2×C4—861no—
512C2×C4—861no—
513C2×C4—861no—
514C2×C4—861no—
515C2×C4—3441no—
516C2×C4—3442no—
517C2×C4—1721no—
518C2×C4—1721no—
519C2×C4C2×D4×D4311yescharacteristic
520C2×C4C2×D4×D4311yescharacteristic
521C2×C4#41×D4311yescharacteristic
522C8—21no—
523C8—21no—
524C8—41no—
525C8—41no—
526C8—41no—
527C8—861no—
528C8—861no—
529C8—1721no—
530C8—1721no—
531C8—1721no—
532C22—861no—
533C22—861no—
534C22—861no—
535C22—3441no—
536C22—3441no—
537C22—3441no—
538C22#121×D4311yescharacteristic
539C4—21no—
540C4—22no—
541C4—41no—
542C4—81no—
543C4—81no—
544C4—861no—
545C4—861no—
546C4—861no—
547C4—862no—
548C4—3441no—
549C4—1721no—
550C4#135×D4311yescharacteristic
551C4C2×#1306334611yescharacteristic
552C4#1458371211yescharacteristic
553C4#1458371511yescharacteristic
554C2—1721no—
555C2—6881no—
556C2#1914412011yescharacteristic
557C2#1914417111yescharacteristic
558C2#1914431811yescharacteristic
subgroupG/H
centerC22#121×D43
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#1672C2
socleC22×C43C2×#121
prime radical#14583450C22
hypercenter#1672D43
hypocenterC43#19406
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #1672

Complements

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

NH ≅ G/Ntype
3. #19144633C2semidirect
4. #19143674C2semidirect
5. #19134042C2semidirect
6. #19134041C2semidirect
7. #19134012C2semidirect
8. #19134011C2semidirect
9. #19133998C2semidirect
10. #19133997C2semidirect
11. #19133974C2semidirect
12. #19133372C2semidirect
13. #19133302C2semidirect
15. C43×#1672C2semidirect
286. #1672D43semidirect
346. C43#19406semidirect

Maximal subgroups

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

subgroupindex
#191457322
#191447192
#191446332
#191436742
#191340422
#191340412
#191340122
#191340112
#191339982
#191339972
#191339742
#191333722
#191333022
#191332562
C43×#16722
#1940643