Finite Group Databasebeta

← #25084564

Subgroups — #25084564

Order 11008.

698 conjugacy classes of subgroups.

The subgroup lattice has 502 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19145747C211yesmaximal, characteristic
2#19145539C211yesmaximal, characteristic
3#19145180C211yesmaximal, characteristic
4#19145136C211yesmaximal, characteristic
5#19145136C211yesmaximal, characteristic
6#487×D43C211yesmaximal, characteristic
7#19134271C211yesmaximal, characteristic, complemented
8#19134270C211yesmaximal, characteristic, complemented
9#19134269C211yesmaximal, characteristic, complemented
10#19134269C211yesmaximal, characteristic, complemented
11#19134205C211yesmaximal, characteristic, complemented
12#19134203C211yesmaximal, characteristic, complemented
13#19134191C211yesmaximal, characteristic, complemented
14C8×#10621872C211yesmaximal, characteristic
15C43×#1707C211yesmaximal, characteristic, complemented
16#14583454C2211yescharacteristic
17#14583454C2211yescharacteristic
18C4⋊Q8×D43C2211yescharacteristic
19C4⋊Q8×D43C2211yescharacteristic
20#14583306—22no—
21#14583306—22no—
22#14583304C2211yescharacteristic
23#14583304C2211yescharacteristic
24#14583302C2211yescharacteristic
25#14583302C2211yescharacteristic
26#14583302C2211yescharacteristic
27#14583302C2211yescharacteristic
28#14583295C2211yescharacteristic
29#14583295C2211yescharacteristic
30#14583278C2211yescharacteristic
31#14583278C2211yescharacteristic
32#14583251C2211yescharacteristic
33#14583251C2211yescharacteristic
34#14583250C2211yescharacteristic
35#14583250C2211yescharacteristic
36#14583250C2211yescharacteristic
37#14583250C2211yescharacteristic
38#14583249C2211yescharacteristic
39#14583249C2211yescharacteristic
40#14583248—22no—
41#14583236—22no—
42#14583193—22no—
43#14583139—22no—
44#14583107—22no—
45#14583053—22no—
46#14582991—22no—
47#14582950C2211yescharacteristic
48#14582938—22no—
49#14582938—22no—
50#103×D43—22no—
51C4×#10621872C2211yescharacteristic
52C4×C8×D43C2211yescharacteristic
53#14582621C2211yescharacteristic
54#14582620C2211yescharacteristic
55C8×C43⋊C8C2211yescharacteristic
56C43×#500C2211yescharacteristic
57C43×#498C2211yescharacteristic
58C43×#498C2211yescharacteristic
59C43×#494C2211yescharacteristic
60C43×#487C2211yescharacteristic
61C43×#487C2211yescharacteristic
62C82×C43C2211yescharacteristic
63C2×Q8×D43—21no—
64C2×Q8×D43—21no—
65C2×#10621885—22no—
66C2×#10621885—22no—
67C2×#10621872D412yes—
68C2×C8×D43D412yes—
69#13063325C2311yescharacteristic
70#13063325C2311yescharacteristic
71#13063325C2311yescharacteristic
72#13063325C2311yescharacteristic
73#13063324—21no—
74#13063324—21no—
75#13063324—21no—
76#13063324—21no—
77#13063323—21no—
78#13063323—21no—
79#13063316—21no—
80#13063316—21no—
81#13063305—21no—
82#13063305—21no—
83#13063301—21no—
84#13063301—21no—
85Q8×Dic43—21no—
86Q8×Dic43—21no—
87#13063290—21no—
88#13063290—21no—
89#13063283—21no—
90#13063283—21no—
91C4⋊C4×D43—21no—
92C4⋊C4×D43—21no—
93C4⋊C4×D43—21no—
94C4⋊C4×D43—21no—
95C42×D43C2311yescharacteristic
96#13063259—22no—
97#13063259—22no—
98#13063258—22no—
99#13063258—22no—
100#13063258—22no—
101#13063258—22no—
102#13063256—22no—
103#13063256—22no—
104Dic43⋊C8D412yes—
105#13063250—22no—
106#13063250—22no—
107#13063250—22no—
108#13063250—22no—
109#13063249—22no—
110#13063249—22no—
111#13063248—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#106×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—44no—
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(C2×D43)⋊C4—41no—
165(C2×D43)⋊C4—41no—
166C4⋊Dic43—21no—
167C4⋊Dic43—21no—
168C4⋊Dic43—21no—
169C4⋊Dic43—21no—
170C4⋊Dic43—21no—
171C4⋊Dic43—21no—
172C4⋊Dic43—21no—
173C4⋊Dic43—21no—
174C4⋊Dic43—41no—
175C4⋊Dic43—41no—
176Dic43⋊C4—41no—
177Dic43⋊C4—41no—
178Dic43⋊C4—41no—
179Dic43⋊C4—41no—
180Dic43⋊C4—41no—
181Dic43⋊C4—41no—
182C4×Dic43—41no—
183C4×Dic43—41no—
184C4×Dic43C2×D411yescharacteristic
185C4×Dic43C2×D411yescharacteristic
186C4×Dic43C2×D411yescharacteristic
187C2×C43⋊C8C2×D412yes—
188C2×C43⋊C8C2×D412yes—
189C2×C43⋊C8C2×D412yes—
190#10621872Q1618yescomplemented
191C8×D43—42no—
192C22×D43#12711yescharacteristic
193Q8×C43—42no—
194Q8×C43—42no—
195Q8×C43—42no—
196Q8×C43—42no—
197C2×C4×C43—41no—
198C2×C4×C43—41no—
199C2×C4×C43—41no—
200C2×C4×C43—41no—
201C2×C4×C43C22×D411yescharacteristic
202C2×C4×C43C22×D411yescharacteristic
203C2×C4×C43C22×D411yescharacteristic
204C2×Dic43—41no—
205C2×Dic43—41no—
206C2×Dic43—41no—
207C2×Dic43—41no—
208C2×Dic43#12711yescharacteristic
209C2×Dic43#12711yescharacteristic
210C2×Dic43#12711yescharacteristic
211C4×D43—22no—
212C4×D43—22no—
213C4×D43—82no—
214C4×D43—82no—
215C4×D43C2×Q1614yes—
216Dic86—42no—
217Dic86—42no—
218Dic86—42no—
219Dic86—42no—
220Dic86—82no—
221Dic86—82no—
222C8×C43—22no—
223C8×C43—22no—
224C8×C43C2×Q1614yes—
225C43⋊C8—22no—
226C43⋊C8—22no—
227C43⋊C8C2×Q1614yes—
228#19634—431nomaximal, Sylow
229C22×C43C2×#12711yescharacteristic
230C2×D43—21no—
231C2×D43—21no—
232C2×D43#49412yes—
233C4×C43—81no—
234C4×C43—81no—
235C4×C43—81no—
236C4×C43—81no—
237C4×C43C22×Q1612yes—
238C4×C43#57512yes—
239C4×C43#57712yes—
240Dic43—21no—
241Dic43—21no—
242Dic43—81no—
243Dic43—81no—
244Dic43—81no—
245Dic43—81no—
246Dic43#49412yes—
247#3230—431no—
248#3209—431no—
249#3170—431no—
250#3165—431no—
251#3165—431no—
252C2×#487—431no—
253#1723—431no—
254#1723—431no—
255#1723—431no—
256#1723—431no—
257#1710—431no—
258#1710—431no—
259#1707—431no—
260#1707D4311yescharacteristic, complemented
261C8×M16—431no—
262C2×C43C2×#49411yescharacteristic
263C2×C43#315311yescharacteristic
264C2×C43#315411yescharacteristic
265D43—22no—
266#533—431no—
267#533—431no—
268C2×C4⋊Q8—431no—
269C2×C4⋊Q8—431no—
270#501—862no—
271#501—862no—
272#500—431no—
273#500—431no—
274#500—431no—
275#500—431no—
276#500—431no—
277#500—431no—
278#500C2×D4311yescharacteristic
279#498—431no—
280#498—431no—
281#498C2×D4311yescharacteristic
282#498C2×D4311yescharacteristic
283#494—431no—
284#494—431no—
285#494C2×D4311yescharacteristic
286#487—431no—
287#487—431no—
288#487—431no—
289#487—431no—
290#487—431no—
291#487—431no—
292#487—431no—
293#487—431no—
294#487—862no—
295#487C2×D4311yescharacteristic
296#487C2×D4311yescharacteristic
297#484—862no—
298#477—862no—
299#467—862no—
300#462—862no—
301#451—862no—
302C4×Q16—862no—
303#431—431no—
304#428—862no—
305#428—862no—
306C2×#103—862no—
307C4×M16—431no—
308C2×C4×C8—431no—
309#322—431no—
310#322—431no—
311C82—431no—
312C82C2×D4311yescharacteristic
313C43#1963411yescharacteristic, complemented, Sylow
314C22×Q8—861no—
315C22×Q8—861no—
316C2×Q16—22no—
317C2×Q16—862no—
318C2×Q16—862no—
319C2×M16—432no—
320C22×C8—432no—
321C4⋊Q8—431no—
322C4⋊Q8—431no—
323C4⋊Q8—431no—
324C4⋊Q8—431no—
325C4⋊Q8—861no—
326C4⋊Q8—861no—
327C4⋊Q8—861no—
328C4⋊Q8—861no—
329C4⋊Q8—861no—
330C4⋊Q8—861no—
331C4⋊Q8C22×D4311yescharacteristic
332C4⋊Q8C22×D4311yescharacteristic
333C4⋊Q8C22×D4311yescharacteristic
334C4⋊Q8C22×D4311yescharacteristic
335#125—861no—
336#125—861no—
337C22⋊Q8—861no—
338C22⋊Q8—861no—
339C22⋊Q8—861no—
340C22⋊Q8—861no—
341C4×Q8—861no—
342C4×Q8—861no—
343C4×Q8—861no—
344C4×Q8—861no—
345#117—861no—
346#117—861no—
347C2×C4⋊C4—861no—
348C2×C4⋊C4—861no—
349C2×C4⋊C4—861no—
350C2×C4⋊C4—861no—
351C2×C42—431no—
352#107—22no—
353#107—862no—
354#107—862no—
355#107—862no—
356#107—862no—
357#107—862no—
358#107—862no—
359#106—22no—
360#106—22no—
361#106—862no—
362#106—862no—
363C4⋊C8—432no—
364#103—22no—
365#103—22no—
366#103—862no—
367#103—862no—
368#103—862no—
369#103—862no—
370#103—862no—
371#103—862no—
372#103—862no—
373#103—862no—
374C22⋊C8—432no—
375#97—432no—
376C4×C8—432no—
377C4×C8—431no—
378C4×C8—431no—
379C4×C8—431no—
380C4×C8C22×D4311yescharacteristic
381C4×C8C22×D4311yescharacteristic
382C4×C8C22×D4311yescharacteristic
383C2×Q8—21no—
384C2×Q8—21no—
385C2×Q8—21no—
386C2×Q8—21no—
387C2×Q8—861no—
388C2×Q8—861no—
389C2×Q8—861no—
390C2×Q8—861no—
391C2×Q8—3442no—
392C2×Q8—1721no—
393C2×Q8—1721no—
394C2×Q8—1724no—
395C22×C4—431no—
396C22×C4—431no—
397C22×C4—431no—
398C22×C4—1721no—
399C22×C4—1721no—
400Q16—82no—
401Q16—3442no—
402Q16—1724no—
403M16—438no—
404C2×C8—432no—
405C2×C8—432no—
406C2×C8—432no—
407C2×C8—1722no—
408C2×C8D4×D4312yes—
409C2×C8D4×D4312yes—
410C2×C8D4×D4312yes—
411C4⋊C4—21no—
412C4⋊C4—21no—
413C4⋊C4—21no—
414C4⋊C4—21no—
415C4⋊C4—21no—
416C4⋊C4—21no—
417C4⋊C4—21no—
418C4⋊C4—21no—
419C4⋊C4—861no—
420C4⋊C4—861no—
421C4⋊C4—861no—
422C4⋊C4—861no—
423C4⋊C4—861no—
424C4⋊C4—861no—
425C4⋊C4—861no—
426C4⋊C4—861no—
427C4⋊C4—1721no—
428C4⋊C4—1721no—
429C4⋊C4—1721no—
430C4⋊C4—1721no—
431C4⋊C4—1721no—
432C4⋊C4—1721no—
433C4⋊C4—1721no—
434C4⋊C4—1721no—
435C22⋊C4—1721no—
436C22⋊C4—1721no—
437C42—431no—
438C42—431no—
439C42—431no—
440C42—1721no—
441C42—1721no—
442C42C23×D4311yescharacteristic
443C23—431no—
444Q8—42no—
445Q8—42no—
446Q8—42no—
447Q8—42no—
448Q8—3442no—
449Q8—3442no—
450Q8—1722no—
451Q8—1722no—
452Q8—1722no—
453Q8—1722no—
454C2×C4—41no—
455C2×C4—41no—
456C2×C4—41no—
457C2×C4—41no—
458C2×C4—431no—
459C2×C4—434no—
460C2×C4—431no—
461C2×C4—431no—
462C2×C4—862no—
463C2×C4—862no—
464C2×C4—3442no—
465C2×C4—3442no—
466C2×C4—1721no—
467C2×C4—1721no—
468C2×C4—1721no—
469C2×C4—1721no—
470C2×C4C2×D4×D4311yescharacteristic
471C2×C4C2×D4×D4311yescharacteristic
472C2×C4C2×D4×D4311yescharacteristic
473C8—22no—
474C8—22no—
475C8—434no—
476C8—862no—
477C8—862no—
478C8Q16×D4314yes—
479C22—432no—
480C22—861no—
481C22—861no—
482C22#127×D4311yescharacteristic
483C4—81no—
484C4—81no—
485C4—81no—
486C4—81no—
487C4—432no—
488C4—861no—
489C4—861no—
490C4—3441no—
491C4—3441no—
492C4—3441no—
493C4—3441no—
494C4C2×Q16×D4312yes—
495C4#1458369612yes—
496C4#1458370512yes—
497C2—862no—
498C2#494×D4311yescharacteristic
499C2#1914505611yescharacteristic
500C2#1914506411yescharacteristic
subgroupG/H
centerC22#127×D43
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#1707C2
socleC22×C43C2×#127
prime radicalC22×D43#127
hypercenter#1707D43
hypocenterC43#19634
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #1707

Complements

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

NH ≅ G/Ntype
7. #19134271C2semidirect
8. #19134270C2semidirect
9. #19134269C2semidirect
10. #19134269C2semidirect
11. #19134205C2semidirect
12. #19134203C2semidirect
13. #19134191C2semidirect
15. C43×#1707C2semidirect
190. #10621872Q16semidirect
260. #1707D43semidirect
313. C43#19634semidirect

Maximal subgroups

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

subgroupindex
#191457472
#191455392
#191451802
#191451362
#487×D432
#191342712
#191342702
#191342692
#191342052
#191342032
#191341912
C8×#106218722
C43×#17072
#1963443