Finite Group Databasebeta

← #25084585

Subgroups — #25084585

Order 11008.

686 conjugacy classes of subgroups.

The subgroup lattice has 498 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19145740C211yesmaximal, characteristic
2#19145735C211yesmaximal, characteristic
3#19145180C211yesmaximal, characteristic
4#500×D43C211yesmaximal, characteristic
5#19144972C211yesmaximal, characteristic
6#19144972C211yesmaximal, characteristic
7#19134244C211yesmaximal, characteristic, complemented
8#19134241C211yesmaximal, characteristic, complemented
9#19134240C211yesmaximal, characteristic, complemented
10#19134203C211yesmaximal, characteristic, complemented
11#19134203C211yesmaximal, characteristic, complemented
12#19134191C211yesmaximal, characteristic, complemented
13#19134190C211yesmaximal, characteristic, complemented
14#19132874C211yesmaximal, characteristic
15C43×#1718C211yesmaximal, characteristic, complemented
16#14583454C2211yescharacteristic
17#14583454C2211yescharacteristic
18C4⋊Q8×D43C2211yescharacteristic
19C4⋊Q8×D43C2211yescharacteristic
20#14583304C2211yescharacteristic
21#14583303—22no—
22#14583302C2211yescharacteristic
23#14583302C2211yescharacteristic
24#14583302C2211yescharacteristic
25#14583297C2211yescharacteristic
26#14583295C2211yescharacteristic
27#14583295C2211yescharacteristic
28#14583278C2211yescharacteristic
29#14583266—22no—
30#14583266—22no—
31#14583251C2211yescharacteristic
32#14583251C2211yescharacteristic
33#14583251C2211yescharacteristic
34#14583250C2211yescharacteristic
35#14583250C2211yescharacteristic
36#14583250C2211yescharacteristic
37#14583250C2211yescharacteristic
38#14583249C2211yescharacteristic
39#14583249C2211yescharacteristic
40#14583249C2211yescharacteristic
41#14583231—22no—
42#14583228—22no—
43#14583183—22no—
44#14583182—22no—
45#14583139—22no—
46#14582991—22no—
47#14582950C2211yescharacteristic
48#107×D43—22no—
49#14582906—22no—
50#14582906—22no—
51C4×#10621872C2211yescharacteristic
52C4×C8×D43C2211yescharacteristic
53#14582621C2211yescharacteristic
54C8×C43⋊C8C2211yescharacteristic
55C8×C43⋊C8C2211yescharacteristic
56C43×#500C2211yescharacteristic
57C43×#498C2211yescharacteristic
58C43×#487C2211yescharacteristic
59C43×#487C2211yescharacteristic
60C43×#487C2211yescharacteristic
61C43×#487C2211yescharacteristic
62C43×#322C2211yescharacteristic
63C2×Q8×D43—21no—
64C2×Q8×D43—21no—
65C2×#10621885—22no—
66C2×#10621872D412yes—
67C2×C8×D43D412yes—
68#13063325C2311yescharacteristic
69#13063325C2311yescharacteristic
70#13063325C2311yescharacteristic
71#13063325C2311yescharacteristic
72#13063324—21no—
73#13063324—21no—
74#13063324—21no—
75#13063324—21no—
76#13063323—21no—
77#13063323—21no—
78#13063316—21no—
79#13063316—21no—
80#13063305—21no—
81#13063305—21no—
82#13063301—21no—
83#13063301—21no—
84Q8×Dic43—21no—
85Q8×Dic43—21no—
86#13063290—21no—
87#13063290—21no—
88#13063283—21no—
89#13063283—21no—
90C4⋊C4×D43—21no—
91C4⋊C4×D43—21no—
92C4⋊C4×D43—21no—
93C4⋊C4×D43—21no—
94C42×D43C2311yescharacteristic
95#13063259—22no—
96#13063258—22no—
97#13063258—22no—
98#13063258—22no—
99#13063257—22no—
100#13063256—22no—
101#13063256—22no—
102Dic43⋊C8D412yes—
103#13063250—22no—
104#13063250—22no—
105#13063250—22no—
106#13063250—22no—
107#13063249—22no—
108#13063249—22no—
109#13063249—22no—
110#13063248—22no—
111#13063248—22no—
112#13063248—22no—
113(C2×D43)⋊C8D412yes—
114#13063235D412yes—
115C4×C43⋊C8C2311yescharacteristic
116C4×C43⋊C8C2311yescharacteristic
117C4×C43⋊C8C2311yescharacteristic
118C8×Dic43D412yes—
119C4⋊Q8×C43C2311yescharacteristic
120C4⋊Q8×C43C2311yescharacteristic
121C4⋊Q8×C43C2311yescharacteristic
122C4⋊Q8×C43C2311yescharacteristic
123#107×C43—22no—
124#106×C43—22no—
125#103×C43—22no—
126#103×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—44no—
137Q8×D43—44no—
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—
149C2×C8×C43C2×D412yes—
150C2×C8×C43C2×D412yes—
151C2×C8×C43C2×D412yes—
152C4⋊C4×C43—21no—
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—
160C42×C43C2411yescharacteristic
161#10621885—44no—
162(C2×D43)⋊C4—41no—
163(C2×D43)⋊C4—41no—
164C4⋊Dic43—21no—
165C4⋊Dic43—21no—
166C4⋊Dic43—21no—
167C4⋊Dic43—21no—
168C4⋊Dic43—21no—
169C4⋊Dic43—21no—
170C4⋊Dic43—21no—
171C4⋊Dic43—21no—
172C4⋊Dic43—41no—
173C4⋊Dic43—41no—
174Dic43⋊C4—41no—
175Dic43⋊C4—41no—
176Dic43⋊C4—41no—
177Dic43⋊C4—41no—
178Dic43⋊C4—41no—
179Dic43⋊C4—41no—
180C4×Dic43—41no—
181C4×Dic43—41no—
182C4×Dic43C2×D411yescharacteristic
183C4×Dic43C2×D411yescharacteristic
184C4×Dic43C2×D411yescharacteristic
185C2×C43⋊C8C2×D412yes—
186C2×C43⋊C8C2×D412yes—
187C2×C43⋊C8C2×D412yes—
188#10621872—24no—
189C8×D43—24no—
190C22×D43#12711yescharacteristic
191Q8×C43—42no—
192Q8×C43—42no—
193Q8×C43—42no—
194Q8×C43—42no—
195C2×C4×C43—41no—
196C2×C4×C43—41no—
197C2×C4×C43—41no—
198C2×C4×C43—41no—
199C2×C4×C43C22×D411yescharacteristic
200C2×C4×C43C22×D411yescharacteristic
201C2×C4×C43C22×D411yescharacteristic
202C2×Dic43—41no—
203C2×Dic43—41no—
204C2×Dic43—41no—
205C2×Dic43—41no—
206C2×Dic43#12711yescharacteristic
207C2×Dic43#12711yescharacteristic
208C2×Dic43#12711yescharacteristic
209C4×D43—22no—
210C4×D43—22no—
211C4×D43—82no—
212C4×D43—82no—
213C4×D43#13514yes—
214Dic86—42no—
215Dic86—42no—
216Dic86—42no—
217Dic86—42no—
218Dic86—82no—
219Dic86—82no—
220C8×C43—22no—
221C8×C43—22no—
222C8×C43—22no—
223C43⋊C8—22no—
224C43⋊C8—22no—
225C43⋊C8#13714yes—
226#19636—431nomaximal, Sylow
227C22×C43C2×#12711yescharacteristic
228C2×D43—21no—
229C2×D43—21no—
230C2×D43#49512yes—
231C4×C43—81no—
232C4×C43—81no—
233C4×C43—81no—
234C4×C43—81no—
235C4×C43C2×#13512yes—
236C4×C43C2×#13712yes—
237C4×C43#57812yes—
238Dic43—21no—
239Dic43—21no—
240Dic43—81no—
241Dic43—81no—
242Dic43—81no—
243Dic43—81no—
244Dic43#49512yes—
245#3229—431no—
246#3229—431no—
247#3170—431no—
248C2×#500—431no—
249#3139—431no—
250#3139—431no—
251#1718—431no—
252#1718—431no—
253#1718—431no—
254#1718D4311yescharacteristic, complemented
255#1710—431no—
256#1710—431no—
257#1707—431no—
258#1707—431no—
259C8×M16—431no—
260C2×C43C2×#49511yescharacteristic
261C2×C43#315211yescharacteristic
262C2×C43#315611yescharacteristic
263D43—22no—
264#533—431no—
265#533—431no—
266C2×C4⋊Q8—431no—
267C2×C4⋊Q8—431no—
268#500—431no—
269#500—431no—
270#500—431no—
271#500—431no—
272#500—862no—
273#500C2×D4311yescharacteristic
274#498—431no—
275#498—431no—
276#498—431no—
277#498C2×D4311yescharacteristic
278#494—431no—
279#491—862no—
280#491—862no—
281#487—431no—
282#487—431no—
283#487—431no—
284#487—431no—
285#487—431no—
286#487—431no—
287#487—431no—
288#487—431no—
289#487—431no—
290#487—431no—
291#487C2×D4311yescharacteristic
292#487C2×D4311yescharacteristic
293#487C2×D4311yescharacteristic
294#487C2×D4311yescharacteristic
295#483—862no—
296#483—862no—
297#475—862no—
298#475—862no—
299#467—862no—
300C4×Q16—862no—
301#431—431no—
302C2×#107—862no—
303#419—862no—
304#419—862no—
305C4×M16—431no—
306C2×C4×C8—431no—
307#322—431no—
308#322C2×D4311yescharacteristic
309C82—431no—
310C82—431no—
311C43#1963611yescharacteristic, complemented, Sylow
312C22×Q8—861no—
313C22×Q8—861no—
314C2×Q16—862no—
315C2×M16—432no—
316C22×C8—432no—
317C4⋊Q8—431no—
318C4⋊Q8—431no—
319C4⋊Q8—431no—
320C4⋊Q8—431no—
321C4⋊Q8—861no—
322C4⋊Q8—861no—
323C4⋊Q8—861no—
324C4⋊Q8—861no—
325C4⋊Q8—861no—
326C4⋊Q8—861no—
327C4⋊Q8C22×D4311yescharacteristic
328C4⋊Q8C22×D4311yescharacteristic
329C4⋊Q8C22×D4311yescharacteristic
330C4⋊Q8C22×D4311yescharacteristic
331#125—861no—
332#125—861no—
333C22⋊Q8—861no—
334C22⋊Q8—861no—
335C22⋊Q8—861no—
336C22⋊Q8—861no—
337C4×Q8—861no—
338C4×Q8—861no—
339C4×Q8—861no—
340C4×Q8—861no—
341#117—861no—
342#117—861no—
343C2×C4⋊C4—861no—
344C2×C4⋊C4—861no—
345C2×C4⋊C4—861no—
346C2×C4⋊C4—861no—
347C2×C42—431no—
348#107—22no—
349#107—862no—
350#107—862no—
351#107—862no—
352#107—862no—
353#106—22no—
354#106—862no—
355#106—862no—
356#106—862no—
357C4⋊C8—432no—
358#103—22no—
359#103—22no—
360#103—22no—
361#103—22no—
362#103—862no—
363#103—862no—
364#103—862no—
365#103—862no—
366#103—862no—
367#103—862no—
368#103—862no—
369#103—862no—
370#103—862no—
371#103—862no—
372C22⋊C8—432no—
373#97—432no—
374C4×C8—432no—
375C4×C8—431no—
376C4×C8—431no—
377C4×C8—431no—
378C4×C8C22×D4311yescharacteristic
379C4×C8C22×D4311yescharacteristic
380C4×C8C22×D4311yescharacteristic
381C2×Q8—21no—
382C2×Q8—21no—
383C2×Q8—21no—
384C2×Q8—21no—
385C2×Q8—861no—
386C2×Q8—861no—
387C2×Q8—861no—
388C2×Q8—861no—
389C2×Q8—1721no—
390C2×Q8—1721no—
391C2×Q8—1724no—
392C2×Q8—1724no—
393C22×C4—431no—
394C22×C4—431no—
395C22×C4—431no—
396C22×C4—1721no—
397C22×C4—1721no—
398Q16—1724no—
399M16—864no—
400C2×C8—432no—
401C2×C8—432no—
402C2×C8—432no—
403C2×C8—864no—
404C2×C8D4×D4312yes—
405C2×C8D4×D4312yes—
406C2×C8D4×D4312yes—
407C4⋊C4—21no—
408C4⋊C4—21no—
409C4⋊C4—21no—
410C4⋊C4—21no—
411C4⋊C4—21no—
412C4⋊C4—21no—
413C4⋊C4—21no—
414C4⋊C4—21no—
415C4⋊C4—861no—
416C4⋊C4—861no—
417C4⋊C4—861no—
418C4⋊C4—861no—
419C4⋊C4—861no—
420C4⋊C4—861no—
421C4⋊C4—861no—
422C4⋊C4—861no—
423C4⋊C4—1721no—
424C4⋊C4—1721no—
425C4⋊C4—1721no—
426C4⋊C4—1721no—
427C4⋊C4—1721no—
428C4⋊C4—1721no—
429C4⋊C4—1721no—
430C4⋊C4—1721no—
431C22⋊C4—1721no—
432C22⋊C4—1721no—
433C42—431no—
434C42—431no—
435C42—431no—
436C42—1721no—
437C42—1721no—
438C42C23×D4311yescharacteristic
439C23—431no—
440Q8—42no—
441Q8—42no—
442Q8—42no—
443Q8—42no—
444Q8—3442no—
445Q8—3442no—
446Q8—1722no—
447Q8—1722no—
448Q8—1722no—
449Q8—1722no—
450C2×C4—41no—
451C2×C4—41no—
452C2×C4—41no—
453C2×C4—41no—
454C2×C4—431no—
455C2×C4—434no—
456C2×C4—431no—
457C2×C4—431no—
458C2×C4—862no—
459C2×C4—862no—
460C2×C4—3442no—
461C2×C4—3442no—
462C2×C4—1721no—
463C2×C4—1721no—
464C2×C4—1721no—
465C2×C4—1721no—
466C2×C4C2×D4×D4311yescharacteristic
467C2×C4C2×D4×D4311yescharacteristic
468C2×C4C2×D4×D4311yescharacteristic
469C8—22no—
470C8—22no—
471C8—22no—
472C8—434no—
473C8—862no—
474C8—862no—
475C22—432no—
476C22—861no—
477C22—861no—
478C22#127×D4311yescharacteristic
479C4—81no—
480C4—81no—
481C4—81no—
482C4—81no—
483C4—432no—
484C4—861no—
485C4—861no—
486C4—3441no—
487C4—3441no—
488C4—3441no—
489C4—3441no—
490C4#135×D4312yes—
491C4#137×D4312yes—
492C4#1458371512yes—
493C2—862no—
494C2#495×D4311yescharacteristic
495C2#1914505111yescharacteristic
496C2#1914508711yescharacteristic
subgroupG/H
centerC22#127×D43
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#1718C2
socleC22×C43C2×#127
prime radicalC22×D43#127
hypercenter#1718D43
hypocenterC43#19636
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #1718

Complements

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

NH ≅ G/Ntype
7. #19134244C2semidirect
8. #19134241C2semidirect
9. #19134240C2semidirect
10. #19134203C2semidirect
11. #19134203C2semidirect
12. #19134191C2semidirect
13. #19134190C2semidirect
15. C43×#1718C2semidirect
254. #1718D43semidirect
311. C43#19636semidirect

Maximal subgroups

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

subgroupindex
#191457402
#191457352
#191451802
#500×D432
#191449722
#191342442
#191342412
#191342402
#191342032
#191341912
#191341902
#191328742
C43×#17182
#1963643