Finite Group Databasebeta

← #25084558

Subgroups — #25084558

Order 11008.

710 conjugacy classes of subgroups.

The subgroup lattice has 506 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19145544C211yesmaximal, characteristic
2#19145539C211yesmaximal, characteristic
3#19145180C211yesmaximal, characteristic
4#19145138C211yesmaximal, characteristic
5#19145136C211yesmaximal, characteristic
6#500×D43C211yesmaximal, characteristic
7#19134275C211yesmaximal, characteristic, complemented
8#19134272C211yesmaximal, characteristic, complemented
9#19134271C211yesmaximal, characteristic, complemented
10#19134212C211yesmaximal, characteristic, complemented
11#19134211C211yesmaximal, characteristic, complemented
12#19134191C211yesmaximal, characteristic, complemented
13#19134190C211yesmaximal, characteristic, complemented
14#19132874C211yesmaximal, characteristic
15C43×#1723C211yesmaximal, characteristic, complemented
16#14583454C2211yescharacteristic
17#14583454C2211yescharacteristic
18C4⋊Q8×D43C2211yescharacteristic
19C4⋊Q8×D43C2211yescharacteristic
20#14583307—22no—
21#14583306—22no—
22#14583304C2211yescharacteristic
23#14583304C2211yescharacteristic
24#14583303—22no—
25#14583302C2211yescharacteristic
26#14583302C2211yescharacteristic
27#14583302C2211yescharacteristic
28#14583302C2211yescharacteristic
29#14583302C2211yescharacteristic
30#14583297C2211yescharacteristic
31#14583295C2211yescharacteristic
32#14583295C2211yescharacteristic
33#14583279C2211yescharacteristic
34#14583278C2211yescharacteristic
35#14583278C2211yescharacteristic
36#14583278C2211yescharacteristic
37#14583251C2211yescharacteristic
38#14583250C2211yescharacteristic
39#14583250C2211yescharacteristic
40#14583249C2211yescharacteristic
41#14583139—22no—
42#14583108—22no—
43#14583107—22no—
44#14583056—22no—
45#14583053—22no—
46#14582991—22no—
47#14582950C2211yescharacteristic
48#14582940—22no—
49#14582938—22no—
50#107×D43—22no—
51C4×#10621872C2211yescharacteristic
52C4×C8×D43C2211yescharacteristic
53#14582621C2211yescharacteristic
54C8×C43⋊C8C2211yescharacteristic
55C8×C43⋊C8C2211yescharacteristic
56C43×#500C2211yescharacteristic
57C43×#500C2211yescharacteristic
58C43×#498C2211yescharacteristic
59C43×#494C2211yescharacteristic
60C43×#487C2211yescharacteristic
61C43×#487C2211yescharacteristic
62C43×#322C2211yescharacteristic
63C2×Q8×D43—21no—
64C2×Q8×D43—21no—
65C2×Dic172—22no—
66C2×#10621885—22no—
67C2×#10621885—22no—
68C2×#10621885—22no—
69C2×#10621872D412yes—
70C2×C8×D43D412yes—
71#13063325C2311yescharacteristic
72#13063325C2311yescharacteristic
73#13063325C2311yescharacteristic
74#13063325C2311yescharacteristic
75#13063324—21no—
76#13063324—21no—
77#13063324—21no—
78#13063324—21no—
79#13063323—21no—
80#13063323—21no—
81#13063316—21no—
82#13063316—21no—
83#13063305—21no—
84#13063305—21no—
85#13063301—21no—
86#13063301—21no—
87Q8×Dic43—21no—
88Q8×Dic43—21no—
89#13063290—21no—
90#13063290—21no—
91#13063283—21no—
92#13063283—21no—
93C4⋊C4×D43—21no—
94C4⋊C4×D43—21no—
95C4⋊C4×D43—21no—
96C4⋊C4×D43—21no—
97C42×D43C2311yescharacteristic
98#13063259—22no—
99#13063259—22no—
100#13063258—22no—
101#13063258—22no—
102#13063258—22no—
103#13063258—22no—
104#13063258—22no—
105#13063257—22no—
106#13063256—22no—
107#13063256—22no—
108Dic43⋊C8D412yes—
109#13063250—22no—
110#13063250—22no—
111#13063249—22no—
112#13063248—22no—
113(C2×D43)⋊C8D412yes—
114#13063235D412yes—
115C4×C43⋊C8C2311yescharacteristic
116C4×C43⋊C8C2311yescharacteristic
117C4×C43⋊C8C2311yescharacteristic
118C8×Dic43D412yes—
119C2×Q16×C43—22no—
120C4⋊Q8×C43C2311yescharacteristic
121C4⋊Q8×C43C2311yescharacteristic
122C4⋊Q8×C43C2311yescharacteristic
123C4⋊Q8×C43C2311yescharacteristic
124#107×C43—22no—
125#107×C43—22no—
126#106×C43—22no—
127#103×C43—22no—
128#103×C43—22no—
129C4×C8×C43C2311yescharacteristic
130C4×C8×C43C2311yescharacteristic
131C4×C8×C43C2311yescharacteristic
132C2×Q8×C43—21no—
133C2×Q8×C43—21no—
134C2×Q8×C43—21no—
135C2×Q8×C43—21no—
136Q8×D43—82no—
137Q8×D43—82no—
138C2×C4×D43—41no—
139C2×C4×D43—41no—
140C2×C4×D43C2×D411yescharacteristic
141C2×C4×D43C2×D411yescharacteristic
142C2×C4×D43C2×D411yescharacteristic
143C2×Dic86—21no—
144C2×Dic86—21no—
145C2×Dic86—21no—
146C2×Dic86—21no—
147C2×Dic86—41no—
148C2×Dic86—41no—
149Q16×C43—82no—
150C2×C8×C43C2×D412yes—
151C2×C8×C43C2×D412yes—
152C2×C8×C43C2×D412yes—
153C4⋊C4×C43—21no—
154C4⋊C4×C43—21no—
155C4⋊C4×C43—21no—
156C4⋊C4×C43—21no—
157C4⋊C4×C43—21no—
158C4⋊C4×C43—21no—
159C4⋊C4×C43—21no—
160C4⋊C4×C43—21no—
161C42×C43C2411yescharacteristic
162#10621885—44no—
163#10621885—82no—
164#10621885—82no—
165(C2×D43)⋊C4—41no—
166(C2×D43)⋊C4—41no—
167C4⋊Dic43—21no—
168C4⋊Dic43—21no—
169C4⋊Dic43—21no—
170C4⋊Dic43—21no—
171C4⋊Dic43—21no—
172C4⋊Dic43—21no—
173C4⋊Dic43—21no—
174C4⋊Dic43—21no—
175C4⋊Dic43—41no—
176C4⋊Dic43—41no—
177Dic43⋊C4—41no—
178Dic43⋊C4—41no—
179Dic43⋊C4—41no—
180Dic43⋊C4—41no—
181Dic43⋊C4—41no—
182Dic43⋊C4—41no—
183C4×Dic43—41no—
184C4×Dic43—41no—
185C4×Dic43C2×D411yescharacteristic
186C4×Dic43C2×D411yescharacteristic
187C4×Dic43C2×D411yescharacteristic
188C2×C43⋊C8C2×D412yes—
189C2×C43⋊C8C2×D412yes—
190C2×C43⋊C8C2×D412yes—
191Dic172—82no—
192#10621872Q1618yescomplemented
193C8×D43—24no—
194C22×D43#12711yescharacteristic
195Q8×C43—42no—
196Q8×C43—42no—
197Q8×C43—42no—
198Q8×C43—42no—
199C2×C4×C43—41no—
200C2×C4×C43—41no—
201C2×C4×C43—41no—
202C2×C4×C43—41no—
203C2×C4×C43C22×D411yescharacteristic
204C2×C4×C43C22×D411yescharacteristic
205C2×C4×C43C22×D411yescharacteristic
206C2×Dic43—41no—
207C2×Dic43—41no—
208C2×Dic43—41no—
209C2×Dic43—41no—
210C2×Dic43#12711yescharacteristic
211C2×Dic43#12711yescharacteristic
212C2×Dic43#12711yescharacteristic
213C4×D43—22no—
214C4×D43—22no—
215C4×D43—82no—
216C4×D43—82no—
217C4×D43C2×Q1614yes—
218Dic86—42no—
219Dic86—42no—
220Dic86—42no—
221Dic86—42no—
222Dic86—82no—
223Dic86—82no—
224C8×C43—22no—
225C8×C43—22no—
226C8×C43C2×Q1614yes—
227C43⋊C8—22no—
228C43⋊C8C2×Q1614yes—
229C43⋊C8#13714yes—
230#19633—431nomaximal, Sylow
231C22×C43C2×#12711yescharacteristic
232C2×D43—21no—
233C2×D43—21no—
234C2×D43#49412yes—
235C4×C43—81no—
236C4×C43—81no—
237C4×C43—81no—
238C4×C43—81no—
239C4×C43C22×Q1612yes—
240C4×C43C2×#13712yes—
241C4×C43#57612yes—
242Dic43—21no—
243Dic43—21no—
244Dic43—81no—
245Dic43—81no—
246Dic43—81no—
247Dic43—81no—
248Dic43#49412yes—
249#3209—431no—
250#3209—431no—
251#3170—431no—
252#3165—431no—
253#3165—431no—
254C2×#500—431no—
255#1723—431no—
256#1723—431no—
257#1723—431no—
258#1723D4311yescharacteristic, complemented
259#1713—431no—
260#1713—431no—
261#1707—431no—
262#1707—431no—
263C8×M16—431no—
264C2×C43C2×#49411yescharacteristic
265C2×C43#315211yescharacteristic
266C2×C43#315511yescharacteristic
267D43—22no—
268#533—431no—
269#533—431no—
270C2×C4⋊Q8—431no—
271C2×C4⋊Q8—431no—
272#501—862no—
273#501—862no—
274#500—431no—
275#500—431no—
276#500—431no—
277#500—431no—
278#500—431no—
279#500—431no—
280#500—431no—
281#500—862no—
282#500C2×D4311yescharacteristic
283#500C2×D4311yescharacteristic
284#498—431no—
285#498—431no—
286#498—431no—
287#498C2×D4311yescharacteristic
288#494—431no—
289#494—431no—
290#494—431no—
291#494—431no—
292#494C2×D4311yescharacteristic
293#487—431no—
294#487—431no—
295#487—431no—
296#487—431no—
297#487C2×D4311yescharacteristic
298#487C2×D4311yescharacteristic
299#467—862no—
300#462—862no—
301#462—862no—
302#451—862no—
303#451—862no—
304C4×Q16—862no—
305#431—431no—
306#428—862no—
307#428—862no—
308C2×#107—862no—
309C4×M16—431no—
310C2×C4×C8—431no—
311#322—431no—
312#322C2×D4311yescharacteristic
313C82—431no—
314C82—431no—
315C43#1963311yescharacteristic, complemented, Sylow
316C22×Q8—861no—
317C22×Q8—861no—
318C2×Q16—22no—
319C2×Q16—862no—
320C2×Q16—862no—
321C2×Q16—862no—
322C2×Q16—862no—
323C2×M16—432no—
324C22×C8—432no—
325C4⋊Q8—431no—
326C4⋊Q8—431no—
327C4⋊Q8—431no—
328C4⋊Q8—431no—
329C4⋊Q8—861no—
330C4⋊Q8—861no—
331C4⋊Q8—861no—
332C4⋊Q8—861no—
333C4⋊Q8—861no—
334C4⋊Q8—861no—
335C4⋊Q8C22×D4311yescharacteristic
336C4⋊Q8C22×D4311yescharacteristic
337C4⋊Q8C22×D4311yescharacteristic
338C4⋊Q8C22×D4311yescharacteristic
339#125—861no—
340#125—861no—
341C22⋊Q8—861no—
342C22⋊Q8—861no—
343C22⋊Q8—861no—
344C22⋊Q8—861no—
345C4×Q8—861no—
346C4×Q8—861no—
347C4×Q8—861no—
348C4×Q8—861no—
349#117—861no—
350#117—861no—
351C2×C4⋊C4—861no—
352C2×C4⋊C4—861no—
353C2×C4⋊C4—861no—
354C2×C4⋊C4—861no—
355C2×C42—431no—
356#107—22no—
357#107—22no—
358#107—862no—
359#107—862no—
360#107—862no—
361#107—862no—
362#107—862no—
363#107—862no—
364#107—862no—
365#106—22no—
366#106—862no—
367#106—862no—
368#106—862no—
369C4⋊C8—432no—
370#103—22no—
371#103—22no—
372#103—862no—
373#103—862no—
374#103—862no—
375#103—862no—
376C22⋊C8—432no—
377#97—432no—
378C4×C8—432no—
379C4×C8—431no—
380C4×C8—431no—
381C4×C8—431no—
382C4×C8C22×D4311yescharacteristic
383C4×C8C22×D4311yescharacteristic
384C4×C8C22×D4311yescharacteristic
385C2×Q8—21no—
386C2×Q8—21no—
387C2×Q8—21no—
388C2×Q8—21no—
389C2×Q8—861no—
390C2×Q8—861no—
391C2×Q8—861no—
392C2×Q8—861no—
393C2×Q8—3442no—
394C2×Q8—3442no—
395C2×Q8—1721no—
396C2×Q8—1721no—
397C22×C4—431no—
398C22×C4—431no—
399C22×C4—431no—
400C22×C4—1721no—
401C22×C4—1721no—
402Q16—82no—
403Q16—3442no—
404Q16—3442no—
405Q16—3442no—
406Q16—1724no—
407M16—438no—
408C2×C8—432no—
409C2×C8—432no—
410C2×C8—432no—
411C2×C8—864no—
412C2×C8D4×D4312yes—
413C2×C8D4×D4312yes—
414C2×C8D4×D4312yes—
415C4⋊C4—21no—
416C4⋊C4—21no—
417C4⋊C4—21no—
418C4⋊C4—21no—
419C4⋊C4—21no—
420C4⋊C4—21no—
421C4⋊C4—21no—
422C4⋊C4—21no—
423C4⋊C4—861no—
424C4⋊C4—861no—
425C4⋊C4—861no—
426C4⋊C4—861no—
427C4⋊C4—861no—
428C4⋊C4—861no—
429C4⋊C4—861no—
430C4⋊C4—861no—
431C4⋊C4—1721no—
432C4⋊C4—1721no—
433C4⋊C4—1721no—
434C4⋊C4—1721no—
435C4⋊C4—1721no—
436C4⋊C4—1721no—
437C4⋊C4—1721no—
438C4⋊C4—1721no—
439C22⋊C4—1721no—
440C22⋊C4—1721no—
441C42—431no—
442C42—431no—
443C42—431no—
444C42—1721no—
445C42—1721no—
446C42C23×D4311yescharacteristic
447C23—431no—
448Q8—42no—
449Q8—42no—
450Q8—42no—
451Q8—42no—
452Q8—3442no—
453Q8—3442no—
454Q8—1722no—
455Q8—1722no—
456Q8—1722no—
457Q8—1722no—
458C2×C4—41no—
459C2×C4—41no—
460C2×C4—41no—
461C2×C4—41no—
462C2×C4—431no—
463C2×C4—434no—
464C2×C4—431no—
465C2×C4—431no—
466C2×C4—862no—
467C2×C4—862no—
468C2×C4—3442no—
469C2×C4—3442no—
470C2×C4—1721no—
471C2×C4—1721no—
472C2×C4—1721no—
473C2×C4—1721no—
474C2×C4C2×D4×D4311yescharacteristic
475C2×C4C2×D4×D4311yescharacteristic
476C2×C4C2×D4×D4311yescharacteristic
477C8—22no—
478C8—22no—
479C8—434no—
480C8—434no—
481C8—862no—
482C8Q16×D4314yes—
483C22—432no—
484C22—861no—
485C22—861no—
486C22#127×D4311yescharacteristic
487C4—81no—
488C4—81no—
489C4—81no—
490C4—81no—
491C4—432no—
492C4—861no—
493C4—861no—
494C4—3441no—
495C4—3441no—
496C4—3441no—
497C4—3441no—
498C4C2×Q16×D4312yes—
499C4#137×D4312yes—
500C4#1458370312yes—
501C2—862no—
502C2#494×D4311yescharacteristic
503C2#1914505111yescharacteristic
504C2#1914507911yescharacteristic
subgroupG/H
centerC22#127×D43
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#1723C2
socleC22×C43C2×#127
prime radicalC22×D43#127
hypercenter#1723D43
hypocenterC43#19633
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #1723

Complements

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

NH ≅ G/Ntype
7. #19134275C2semidirect
8. #19134272C2semidirect
9. #19134271C2semidirect
10. #19134212C2semidirect
11. #19134211C2semidirect
12. #19134191C2semidirect
13. #19134190C2semidirect
15. C43×#1723C2semidirect
192. #10621872Q16semidirect
258. #1723D43semidirect
315. C43#19633semidirect

Maximal subgroups

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

subgroupindex
#191455442
#191455392
#191451802
#191451382
#191451362
#500×D432
#191342752
#191342722
#191342712
#191342122
#191342112
#191341912
#191341902
#191328742
C43×#17232
#1963343