Finite Group Databasebeta

← #25079829

Subgroups — #25079829

Order 11008.

594 conjugacy classes of subgroups.

The subgroup lattice has 554 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19145745C211yesmaximal, characteristic
2#19145542C211yesmaximal, characteristic
3#498×D43C211yesmaximal, characteristic
4#19143524C211yesmaximal, characteristic
5#19134104C211yesmaximal, characteristic, complemented
6#19134103C211yesmaximal, characteristic, complemented
7#19134100C211yesmaximal, characteristic, complemented
8#19134099C211yesmaximal, characteristic, complemented
9#19133978C211yesmaximal, characteristic, complemented
10#19133977C211yesmaximal, characteristic, complemented
11#19133974C211yesmaximal, characteristic, complemented
12#19133340C211yesmaximal, characteristic
13#19133278C211yesmaximal, characteristic
14#19133274C211yesmaximal, characteristic
15C43×#1672C211yesmaximal, characteristic, complemented
16#14583453C2211yescharacteristic
17C4⋊Q8×D43C2211yescharacteristic
18C4⋊Q8×D43C2211yescharacteristic
19#14583303—21no—
20#14583297C2211yescharacteristic
21#14583296—21no—
22#14583296—21no—
23#14583295C2211yescharacteristic
24#14583295C2211yescharacteristic
25#14583277—21no—
26#14583248—21no—
27#14583248—21no—
28#14583236—21no—
29#14583233—21no—
30#14583195C2211yescharacteristic
31#14583194C2211yescharacteristic
32#14583191C2211yescharacteristic
33#14583110C2211yescharacteristic
34#14583109C2211yescharacteristic
35#14583106C2211yescharacteristic
36#14583056—21no—
37#14583053—21no—
38#14583030C2211yescharacteristic
39#14583028—21no—
40#14583026C2211yescharacteristic
41C8×Dic86—21no—
42C8×Dic86C2211yescharacteristic
43#14582951C2211yescharacteristic
44#14582951C2211yescharacteristic
45#106×D43—21no—
46#106×D43—21no—
47#14582924—21no—
48#14582921C2211yescharacteristic
49#14582853—21no—
50C4×C8×D43C2211yescharacteristic
51#14582651C2211yescharacteristic
52#14582651C2211yescharacteristic
53#14582650C2211yescharacteristic
54#14582648C2211yescharacteristic
55#14582647C2211yescharacteristic
56#14582647C2211yescharacteristic
57#14582646C2211yescharacteristic
58#14582645C2211yescharacteristic
59#14582644C2211yescharacteristic
60C43×#498C2211yescharacteristic
61C43×#477C2211yescharacteristic
62C43×#462C2211yescharacteristic
63C8×Q8×C43C2211yescharacteristic
64C43×#334C2211yescharacteristic
65C43×#333C2211yescharacteristic
66C43×#332C2211yescharacteristic
67C2×Q8×D43—21no—
68C2×Q8×D43—21no—
69C2×Dic172—21no—
70C2×#10621885—21no—
71C2×#10621885—21no—
72C2×#10621872—21no—
73C2×C8×D43D411yescharacteristic
74C2×C8×D43D411yescharacteristic
75#13063325C2311yescharacteristic
76#13063325C2311yescharacteristic
77#13063324—21no—
78#13063324—21no—
79#13063324—21no—
80#13063324—21no—
81#13063324D411yescharacteristic
82#13063323—21no—
83#13063323—21no—
84#13063323D411yescharacteristic
85#13063315—21no—
86#13063305D411yescharacteristic
87#13063303—21no—
88#13063301D411yescharacteristic
89C4×Dic86—21no—
90C4×Dic86C2311yescharacteristic
91#13063282—21no—
92C4⋊C4×D43—21no—
93C4⋊C4×D43—21no—
94C4⋊C4×D43—21no—
95C4⋊C4×D43—21no—
96C42×D43C2311yescharacteristic
97#13063259—21no—
98#13063258—21no—
99#13063258—21no—
100#13063257—21no—
101#13063257—21no—
102#13063256—21no—
103#13063256—21no—
104#13063256—21no—
105#13063256—21no—
106C4⋊(C43⋊C8)—21no—
107C4⋊(C43⋊C8)C2311yescharacteristic
108C4⋊(C43⋊C8)C2311yescharacteristic
109C4⋊(C43⋊C8)C2311yescharacteristic
110Dic43⋊C8—21no—
111Dic43⋊C8—21no—
112Dic43⋊C8—21no—
113#13063250—21no—
114#13063250—21no—
115#13063249—21no—
116#13063249—21no—
117#13063248—21no—
118#13063248—21no—
119(C2×D43)⋊C8—21no—
120(C2×D43)⋊C8—21no—
121#13063236—21no—
122#13063235—21no—
123C4×C43⋊C8C2311yescharacteristic
124C8×Dic43—21no—
125C8×Dic43—21no—
126C8×Dic43—21no—
127C8×Dic43D411yescharacteristic
128C8×Dic43D411yescharacteristic
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
147Q8×D43—81no—
148Q8×D43—81no—
149Q8×D43—82no—
150C2×C4×D43—41no—
151C2×C4×D43—41no—
152C2×C4×D43C2×D411yescharacteristic
153C2×C4×D43C2×D411yescharacteristic
154C2×C4×D43#4111yescharacteristic
155C2×Dic86—21no—
156C2×Dic86—21no—
157C2×Dic86—21no—
158C2×Dic86—41no—
159C2×Dic86—41no—
160C2×Dic86C2×D411yescharacteristic
161Q16×C43—81no—
162C2×C8×C43—21no—
163C2×C8×C43—21no—
164C2×C8×C43—21no—
165C2×C8×C43C2×D411yescharacteristic
166C2×C8×C43C2×D411yescharacteristic
167C4⋊C4×C43—21no—
168C4⋊C4×C43—21no—
169C4⋊C4×C43—21no—
170C4⋊C4×C43—21no—
171C4⋊C4×C43—21no—
172C4⋊C4×C43C2×D411yescharacteristic
173C42×C43—21no—
174C42×C43C2411yescharacteristic
175#10621885—81no—
176#10621885—81no—
177(C2×D43)⋊C4—21no—
178(C2×D43)⋊C4—21no—
179C4⋊Dic43—21no—
180C4⋊Dic43—21no—
181C4⋊Dic43—21no—
182C4⋊Dic43—21no—
183C4⋊Dic43—21no—
184C4⋊Dic43C2×D411yescharacteristic
185Dic43⋊C4—21no—
186Dic43⋊C4—21no—
187Dic43⋊C4—21no—
188Dic43⋊C4—21no—
189Dic43⋊C4—21no—
190Dic43⋊C4—41no—
191Dic43⋊C4—41no—
192Dic43⋊C4—41no—
193Dic43⋊C4—41no—
194C4×Dic43—21no—
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
203Dic172—81no—
204#10621872—42no—
205C8×D43—22no—
206C8×D43Q1614yescomplemented
207C22×D43#12111yescharacteristic
208Q8×C43—21no—
209Q8×C43—21no—
210Q8×C43—41no—
211Q8×C43—41no—
212Q8×C43—81no—
213C2×C4×C43—21no—
214C2×C4×C43—21no—
215C2×C4×C43—41no—
216C2×C4×C43—41no—
217C2×C4×C43C22×D411yescharacteristic
218C2×C4×C43C22×D411yescharacteristic
219C2×C4×C43C2×#4111yescharacteristic
220C2×Dic43—21no—
221C2×Dic43—21no—
222C2×Dic43—41no—
223C2×Dic43—41no—
224C2×Dic43#12111yescharacteristic
225C2×Dic43#12111yescharacteristic
226C2×Dic43#12111yescharacteristic
227C4×D43—21no—
228C4×D43—21no—
229C4×D43—22no—
230C4×D43—82no—
231C4×D43—82no—
232C4×D43C2×Q1612yes—
233C4×D43#13712yes—
234Dic86—21no—
235Dic86—21no—
236Dic86—42no—
237Dic86—41no—
238Dic86—41no—
239Dic86—82no—
240Dic86—82no—
241Dic86—81no—
242C8×C43—21no—
243C8×C43—41no—
244C8×C43—41no—
245C8×C43—41no—
246C8×C43C2×Q1612yes—
247C43⋊C8—21no—
248C43⋊C8—41no—
249C43⋊C8—41no—
250C43⋊C8—41no—
251C43⋊C8C2×Q1612yes—
252#19207—431nomaximal, Sylow
253C22×C43C2×#12111yescharacteristic
254C2×D43—21no—
255C2×D43—21no—
256C2×D43#46212yes—
257C4×C43—21no—
258C4×C43—41no—
259C4×C43—41no—
260C4×C43—81no—
261C4×C43—81no—
262C4×C43C22×Q1611yescharacteristic
263C4×C43C2×#13711yescharacteristic
264C4×C43#57711yescharacteristic
265C4×C43#57711yescharacteristic
266Dic43—21no—
267Dic43—41no—
268Dic43—41no—
269Dic43—81no—
270Dic43—81no—
271Dic43#46212yes—
272Dic43#47112yes—
273#3230—431no—
274#3209—431no—
275C2×#498—431no—
276#2960—431no—
277#1692—431no—
278#1692—431no—
279#1692—431no—
280#1692—431no—
281#1672—431no—
282#1672—431no—
283#1672—431no—
284#1672D4311yescharacteristic, complemented
285#1564—431no—
286#1549—431no—
287#1548—431no—
288C2×C43C2×#46211yescharacteristic
289C2×C43#305711yescharacteristic
290C2×C43C2×#47111yescharacteristic
291D43—22no—
292#533—431no—
293C2×C4⋊Q8—431no—
294C2×C4⋊Q8—431no—
295#500—861no—
296#498—431no—
297#498—431no—
298#498—431no—
299#498—861no—
300#498—861no—
301#498C2×D4311yescharacteristic
302#494—861no—
303#487—861no—
304#487—861no—
305#484—861no—
306#484—861no—
307#477—431no—
308#477—431no—
309#477—431no—
310#477C2×D4311yescharacteristic
311#462—431no—
312#462—431no—
313#462—431no—
314#462C2×D4311yescharacteristic
315#451—861no—
316#451—861no—
317#446—431no—
318#446—431no—
319#446—861no—
320C8×Q8—431no—
321C8×Q8—861no—
322C8×Q8C2×D4311yescharacteristic
323#431—431no—
324#431—431no—
325C2×#106—861no—
326C2×#106—861no—
327#424—861no—
328#423—431no—
329#405—861no—
330C2×C4×C8—431no—
331#335—431no—
332#335—431no—
333#334—431no—
334#334C2×D4311yescharacteristic
335#333—431no—
336#333—431no—
337#333—431no—
338#333C2×D4311yescharacteristic
339#332—431no—
340#332—431no—
341#332—431no—
342#332C2×D4311yescharacteristic
343C43#1920711yescharacteristic, complemented, Sylow
344C22×Q8—861no—
345C22×Q8—861no—
346C2×Q16—21no—
347C2×Q16—861no—
348C2×Q16—861no—
349C2×Q16—861no—
350C2×M16—861no—
351C22×C8—431no—
352C22×C8—431no—
353C4⋊Q8—431no—
354C4⋊Q8—431no—
355C4⋊Q8—431no—
356C4⋊Q8—431no—
357C4⋊Q8—861no—
358C4⋊Q8—861no—
359C4⋊Q8—861no—
360C4⋊Q8—861no—
361C4⋊Q8—861no—
362C4⋊Q8—861no—
363C4⋊Q8C22×D4311yescharacteristic
364C4⋊Q8C22×D4311yescharacteristic
365#125—861no—
366C22⋊Q8—431no—
367C22⋊Q8—431no—
368C22⋊Q8—861no—
369C4×Q8—431no—
370C4×Q8—861no—
371C4×Q8C22×D4311yescharacteristic
372#117—861no—
373C2×C4⋊C4—861no—
374C2×C4⋊C4—861no—
375C2×C4⋊C4—861no—
376C2×C4⋊C4—861no—
377C2×C42—431no—
378#107—21no—
379#107—861no—
380#107—861no—
381#107—861no—
382#106—21no—
383#106—21no—
384#106—861no—
385#106—861no—
386#106—861no—
387#106—861no—
388#106—861no—
389#106—861no—
390C4⋊C8—21no—
391C4⋊C8—431no—
392C4⋊C8—431no—
393C4⋊C8—431no—
394C4⋊C8—861no—
395C4⋊C8—861no—
396C4⋊C8—861no—
397C4⋊C8—861no—
398C4⋊C8C22×D4311yescharacteristic
399C4⋊C8C22×D4311yescharacteristic
400C4⋊C8C22×D4311yescharacteristic
401#103—21no—
402#103—21no—
403#103—861no—
404#103—861no—
405#103—861no—
406#103—861no—
407#103—861no—
408#103—861no—
409C22⋊C8—861no—
410C22⋊C8—861no—
411#97—861no—
412#97—861no—
413C4×C8—21no—
414C4×C8—431no—
415C4×C8—431no—
416C4×C8—431no—
417C4×C8—861no—
418C4×C8—861no—
419C4×C8—861no—
420C4×C8C22×D4311yescharacteristic
421C2×Q8—21no—
422C2×Q8—21no—
423C2×Q8—431no—
424C2×Q8—861no—
425C2×Q8—861no—
426C2×Q8—861no—
427C2×Q8—3441no—
428C2×Q8—3441no—
429C2×Q8—3442no—
430C2×Q8—1721no—
431C2×Q8—1721no—
432C2×Q8D4×D4311yescharacteristic
433C22×C4—431no—
434C22×C4—431no—
435C22×C4—431no—
436C22×C4—1721no—
437C22×C4—1721no—
438Q16—81no—
439Q16—3441no—
440Q16—3441no—
441Q16—3441no—
442M16—1722no—
443C2×C8—21no—
444C2×C8—21no—
445C2×C8—21no—
446C2×C8—431no—
447C2×C8—434no—
448C2×C8—431no—
449C2×C8—862no—
450C2×C8—861no—
451C2×C8—861no—
452C2×C8—861no—
453C2×C8D4×D4311yescharacteristic
454C2×C8D4×D4311yescharacteristic
455C4⋊C4—21no—
456C4⋊C4—21no—
457C4⋊C4—21no—
458C4⋊C4—21no—
459C4⋊C4—21no—
460C4⋊C4—431no—
461C4⋊C4—861no—
462C4⋊C4—861no—
463C4⋊C4—861no—
464C4⋊C4—861no—
465C4⋊C4—861no—
466C4⋊C4—861no—
467C4⋊C4—861no—
468C4⋊C4—861no—
469C4⋊C4—861no—
470C4⋊C4—861no—
471C4⋊C4—1721no—
472C4⋊C4—1721no—
473C4⋊C4—1721no—
474C4⋊C4—1721no—
475C4⋊C4D4×D4311yescharacteristic
476C22⋊C4—861no—
477C22⋊C4—861no—
478C42—21no—
479C42—431no—
480C42—431no—
481C42—431no—
482C42—861no—
483C42C23×D4311yescharacteristic
484C23—431no—
485Q8—21no—
486Q8—21no—
487Q8—41no—
488Q8—41no—
489Q8—81no—
490Q8—861no—
491Q8—861no—
492Q8—3441no—
493Q8—3442no—
494Q8—3442no—
495Q8—1722no—
496Q8—1721no—
497Q8—1721no—
498C2×C4—21no—
499C2×C4—21no—
500C2×C4—41no—
501C2×C4—41no—
502C2×C4—431no—
503C2×C4—431no—
504C2×C4—432no—
505C2×C4—432no—
506C2×C4—431no—
507C2×C4—862no—
508C2×C4—861no—
509C2×C4—861no—
510C2×C4—861no—
511C2×C4—861no—
512C2×C4—3442no—
513C2×C4—3442no—
514C2×C4—1721no—
515C2×C4—1721no—
516C2×C4C2×D4×D4311yescharacteristic
517C2×C4C2×D4×D4311yescharacteristic
518C2×C4#41×D4311yescharacteristic
519C8—21no—
520C8—41no—
521C8—41no—
522C8—41no—
523C8—432no—
524C8—861no—
525C8—1721no—
526C8—1721no—
527C8—1721no—
528C8Q16×D4312yes—
529C22—432no—
530C22—861no—
531C22—861no—
532C22#121×D4311yescharacteristic
533C4—21no—
534C4—41no—
535C4—41no—
536C4—81no—
537C4—81no—
538C4—432no—
539C4—432no—
540C4—861no—
541C4—3441no—
542C4—3441no—
543C4—1721no—
544C4—1721no—
545C4C2×Q16×D4311yescharacteristic
546C4#137×D4311yescharacteristic
547C4#1458370511yescharacteristic
548C4#1458370611yescharacteristic
549C2—862no—
550C2#462×D4311yescharacteristic
551C2#1914422911yescharacteristic
552C2#471×D4311yescharacteristic
subgroupG/H
centerC22#121×D43
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#1672C2
socleC22×C43C2×#121
prime radicalC22×D43#121
hypercenter#1672D43
hypocenterC43#19207
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #1672

Complements

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

NH ≅ G/Ntype
5. #19134104C2semidirect
6. #19134103C2semidirect
7. #19134100C2semidirect
8. #19134099C2semidirect
9. #19133978C2semidirect
10. #19133977C2semidirect
11. #19133974C2semidirect
15. C43×#1672C2semidirect
206. C8×D43Q16semidirect
284. #1672D43semidirect
343. C43#19207semidirect

Maximal subgroups

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

subgroupindex
#191457452
#191455422
#498×D432
#191435242
#191341042
#191341032
#191341002
#191340992
#191339782
#191339772
#191339742
#191333402
#191332782
#191332742
C43×#16722
#1920743