Finite Group Databasebeta

← #25079479

Subgroups — #25079479

Order 11008.

596 conjugacy classes of subgroups.

The subgroup lattice has 550 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19145136C211yesmaximal, characteristic
2#19144633C211yesmaximal, characteristic
3#477×D43C211yesmaximal, characteristic
4Q8×#10621872C211yesmaximal, characteristic
5#19134124C211yesmaximal, characteristic, complemented
6#19134122C211yesmaximal, characteristic, complemented
7#19134100C211yesmaximal, characteristic, complemented
8#19134098C211yesmaximal, characteristic, complemented
9#19133999C211yesmaximal, characteristic, complemented
10#19133997C211yesmaximal, characteristic, complemented
11#19133975C211yesmaximal, characteristic, complemented
12#19133344C211yesmaximal, characteristic
13#19133284C211yesmaximal, characteristic
14#19133274C211yesmaximal, characteristic
15C43×#1672C211yesmaximal, characteristic, complemented
16#14583454C2211yescharacteristic
17C4⋊Q8×D43C2211yescharacteristic
18C4×Q8×D43C2211yescharacteristic
19#14583306—21no—
20#14583306—21no—
21#14583304C2211yescharacteristic
22#14583302C2211yescharacteristic
23#14583295C2211yescharacteristic
24#14583233—21no—
25#14583195C2211yescharacteristic
26#14583195C2211yescharacteristic
27#14583194C2211yescharacteristic
28#14583194C2211yescharacteristic
29#14583193—21no—
30#14583192—21no—
31#14583191C2211yescharacteristic
32#14583106C2211yescharacteristic
33#14583053—21no—
34#14583029—21no—
35#14583029C2211yescharacteristic
36#14583026—21no—
37#14583026C2211yescharacteristic
38Q8×C43⋊C8C2211yescharacteristic
39Q16×Dic43—21no—
40#14582991—21no—
41#14582951C2211yescharacteristic
42#14582938—21no—
43#14582938—21no—
44#107×D43—21no—
45#14582921—21no—
46#14582921C2211yescharacteristic
47C4⋊C8×D43C2211yescharacteristic
48#103×D43—21no—
49C4×#10621872—21no—
50C4×#10621872C2211yescharacteristic
51#14582652C2211yescharacteristic
52#14582651C2211yescharacteristic
53#14582649C2211yescharacteristic
54#14582648C2211yescharacteristic
55#14582647C2211yescharacteristic
56#14582647C2211yescharacteristic
57#14582647C2211yescharacteristic
58#14582647C2211yescharacteristic
59#14582645C2211yescharacteristic
60C43×#498C2211yescharacteristic
61C43×#477C2211yescharacteristic
62C43×#462C2211yescharacteristic
63C8×Q8×C43C2211yescharacteristic
64C43×#334C2211yescharacteristic
65C43×#333C2211yescharacteristic
66C43×#332C2211yescharacteristic
67C2×Q8×D43—21no—
68C2×Q8×D43D411yescharacteristic
69C2×#10621885—21no—
70C2×#10621872—21no—
71C2×#10621872D411yescharacteristic
72C2×#10621872D411yescharacteristic
73C2×C8×D43—21no—
74#13063325C2311yescharacteristic
75#13063325C2311yescharacteristic
76#13063324—21no—
77#13063324—21no—
78#13063323—21no—
79#13063316—21no—
80#13063305—21no—
81#13063301—21no—
82Q8×Dic43—21no—
83Q8×Dic43D411yescharacteristic
84C4×Dic86—21no—
85C4×Dic86C2311yescharacteristic
86#13063290—21no—
87#13063290—21no—
88#13063290D411yescharacteristic
89#13063283—21no—
90C4⋊C4×D43—21no—
91C4⋊C4×D43—21no—
92C4⋊C4×D43—21no—
93C4⋊C4×D43D411yescharacteristic
94C42×D43—21no—
95C42×D43C2311yescharacteristic
96#13063259—21no—
97#13063259—21no—
98#13063259—21no—
99#13063259—21no—
100#13063258—21no—
101#13063258—21no—
102#13063258—21no—
103#13063258—21no—
104#13063258—21no—
105#13063256—21no—
106#13063256—21no—
107C4⋊(C43⋊C8)—21no—
108C4⋊(C43⋊C8)C2311yescharacteristic
109C4⋊(C43⋊C8)C2311yescharacteristic
110C4⋊(C43⋊C8)C2311yescharacteristic
111Dic43⋊C8—21no—
112Dic43⋊C8—21no—
113Dic43⋊C8—21no—
114Dic43⋊C8—21no—
115#13063250—21no—
116#13063250—21no—
117#13063249—21no—
118#13063249—21no—
119#13063249—21no—
120#13063248—21no—
121(C2×D43)⋊C8—21no—
122#13063235—21no—
123#13063235—21no—
124#13063235D411yescharacteristic
125#13063235D411yescharacteristic
126C4×C43⋊C8—21no—
127C4×C43⋊C8C2311yescharacteristic
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
147Q8×D43—22no—
148Q8×D43—41no—
149Q8×D43—82no—
150C2×C4×D43—21no—
151C2×C4×D43—21no—
152C2×C4×D43—41no—
153C2×C4×D43C2×D411yescharacteristic
154C2×C4×D43C2×D411yescharacteristic
155C2×C4×D43#4111yescharacteristic
156C2×Dic86—21no—
157C2×Dic86—21no—
158C2×Dic86—21no—
159C2×Dic86—41no—
160C2×Dic86C2×D411yescharacteristic
161Q16×C43—42no—
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—42no—
176(C2×D43)⋊C4—41no—
177C4⋊Dic43—21no—
178C4⋊Dic43—21no—
179C4⋊Dic43—21no—
180C4⋊Dic43—21no—
181C4⋊Dic43—21no—
182C4⋊Dic43—41no—
183C4⋊Dic43C2×D411yescharacteristic
184Dic43⋊C4—21no—
185Dic43⋊C4—21no—
186Dic43⋊C4—21no—
187Dic43⋊C4—41no—
188Dic43⋊C4—41no—
189Dic43⋊C4—41no—
190C4×Dic43—21no—
191C4×Dic43—21no—
192C4×Dic43—21no—
193C4×Dic43—41no—
194C4×Dic43C2×D411yescharacteristic
195C4×Dic43C2×D411yescharacteristic
196C4×Dic43#4111yescharacteristic
197C2×C43⋊C8—21no—
198C2×C43⋊C8—21no—
199C2×C43⋊C8—21no—
200C2×C43⋊C8C2×D411yescharacteristic
201C2×C43⋊C8C2×D411yescharacteristic
202#10621872—22no—
203#10621872—42no—
204#10621872Q1614yescomplemented
205C8×D43—42no—
206C22×D43#12111yescharacteristic
207Q8×C43—21no—
208Q8×C43—41no—
209Q8×C43—41no—
210Q8×C43—81no—
211Q8×C43#13712yes—
212C2×C4×C43—21no—
213C2×C4×C43—21no—
214C2×C4×C43—41no—
215C2×C4×C43—41no—
216C2×C4×C43C22×D411yescharacteristic
217C2×C4×C43C22×D411yescharacteristic
218C2×C4×C43C2×#4111yescharacteristic
219C2×Dic43—21no—
220C2×Dic43—21no—
221C2×Dic43—41no—
222C2×Dic43—41no—
223C2×Dic43#12111yescharacteristic
224C2×Dic43#12111yescharacteristic
225C2×Dic43#12111yescharacteristic
226C4×D43—21no—
227C4×D43—21no—
228C4×D43—41no—
229C4×D43—42no—
230C4×D43—81no—
231C4×D43—82no—
232C4×D43C2×Q1612yes—
233C4×D43#13712yes—
234Dic86—21no—
235Dic86—21no—
236Dic86—42no—
237Dic86—82no—
238Dic86—81no—
239Dic86—81no—
240C8×C43—21no—
241C8×C43—41no—
242C8×C43—41no—
243C8×C43—41no—
244C8×C43C2×Q1612yes—
245C43⋊C8—21no—
246C43⋊C8—41no—
247C43⋊C8—41no—
248C43⋊C8—41no—
249C43⋊C8C2×Q1612yes—
250#19173—431nomaximal, Sylow
251C22×C43C2×#12111yescharacteristic
252C2×D43—21no—
253C2×D43—21no—
254C2×D43#46212yes—
255C4×C43—22no—
256C4×C43—21no—
257C4×C43—41no—
258C4×C43—81no—
259C4×C43—81no—
260C4×C43C22×Q1611yescharacteristic
261C4×C43C2×#13711yescharacteristic
262C4×C43C2×#13711yescharacteristic
263C4×C43#57511yescharacteristic
264Dic43—21no—
265Dic43—21no—
266Dic43—41no—
267Dic43—41no—
268Dic43—81no—
269Dic43—81no—
270Dic43#46212yes—
271#3165—431no—
272#3104—431no—
273C2×#477—431no—
274Q8×M16—431no—
275#1696—431no—
276#1696—431no—
277#1692—431no—
278#1692—431no—
279#1676—431no—
280#1676—431no—
281#1672—431no—
282#1672D4311yescharacteristic, complemented
283#1565—431no—
284#1550—431no—
285#1548—431no—
286C2×C43C2×#46211yescharacteristic
287C2×C43#305611yescharacteristic
288C2×C43#306811yescharacteristic
289D43—22no—
290#533—431no—
291C2×C4⋊Q8—431no—
292C2×C4×Q8—431no—
293#501—861no—
294#501—861no—
295#500—431no—
296#500—431no—
297#498—431no—
298#498C2×D4311yescharacteristic
299#484—861no—
300#477—431no—
301#477—431no—
302#477—431no—
303#477—431no—
304#477—431no—
305#477—861no—
306#477—861no—
307#477C2×D4311yescharacteristic
308#462—431no—
309#462C2×D4311yescharacteristic
310#451—861no—
311#446—431no—
312#446—431no—
313#446—861no—
314#446—861no—
315C8×Q8—431no—
316C8×Q8C2×D4311yescharacteristic
317C4×Q16—861no—
318C4×Q16—861no—
319#431—431no—
320#428—861no—
321#428—861no—
322C2×#107—861no—
323#423—431no—
324#423—861no—
325C2×C4⋊C8—431no—
326C2×#103—861no—
327C4×M16—431no—
328C4×M16—861no—
329#335—431no—
330#335—431no—
331#334—431no—
332#334C2×D4311yescharacteristic
333#333—431no—
334#333—431no—
335#333—431no—
336#333—431no—
337#333—431no—
338#333C2×D4311yescharacteristic
339#332—431no—
340#332C2×D4311yescharacteristic
341C43#1917311yescharacteristic, complemented, Sylow
342C22×Q8—431no—
343C22×Q8—861no—
344C2×Q16—21no—
345C2×Q16—861no—
346C2×M16—431no—
347C2×M16—431no—
348C2×M16—861no—
349C22×C8—861no—
350C4⋊Q8—431no—
351C4⋊Q8—431no—
352C4⋊Q8—861no—
353C4⋊Q8—861no—
354C4⋊Q8—861no—
355C4⋊Q8C22×D4311yescharacteristic
356C4⋊Q8C22×D4311yescharacteristic
357#125—861no—
358C22⋊Q8—861no—
359C22⋊Q8—861no—
360C4×Q8—431no—
361C4×Q8—431no—
362C4×Q8—431no—
363C4×Q8—861no—
364C4×Q8—861no—
365C4×Q8—861no—
366C4×Q8—861no—
367C4×Q8C22×D4311yescharacteristic
368#117—861no—
369C2×C4⋊C4—431no—
370C2×C4⋊C4—861no—
371C2×C4⋊C4—861no—
372C2×C4⋊C4—861no—
373C2×C42—431no—
374C2×C42—861no—
375#107—21no—
376#107—861no—
377#107—861no—
378#107—861no—
379#107—861no—
380#107—861no—
381#107—861no—
382#107—861no—
383#107—861no—
384#107—861no—
385#106—21no—
386#106—21no—
387#106—861no—
388#106—861no—
389C4⋊C8—21no—
390C4⋊C8—431no—
391C4⋊C8—431no—
392C4⋊C8—431no—
393C4⋊C8—861no—
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—
410#97—431no—
411#97—431no—
412#97—861no—
413#97—861no—
414C4×C8—21no—
415C4×C8—431no—
416C4×C8—861no—
417C4×C8—861no—
418C4×C8C22×D4311yescharacteristic
419C2×Q8—21no—
420C2×Q8—21no—
421C2×Q8—431no—
422C2×Q8—861no—
423C2×Q8—862no—
424C2×Q8—861no—
425C2×Q8—861no—
426C2×Q8—3442no—
427C2×Q8—1721no—
428C2×Q8—1721no—
429C2×Q8D4×D4311yescharacteristic
430C22×C4—431no—
431C22×C4—431no—
432C22×C4—431no—
433C22×C4—861no—
434C22×C4—861no—
435C22×C4—1721no—
436Q16—42no—
437Q16—1722no—
438M16—434no—
439M16—862no—
440M16—1722no—
441C2×C8—21no—
442C2×C8—21no—
443C2×C8—21no—
444C2×C8—431no—
445C2×C8—431no—
446C2×C8—861no—
447C2×C8—861no—
448C2×C8—861no—
449C2×C8—1722no—
450C2×C8D4×D4311yescharacteristic
451C2×C8D4×D4311yescharacteristic
452C4⋊C4—21no—
453C4⋊C4—21no—
454C4⋊C4—21no—
455C4⋊C4—21no—
456C4⋊C4—21no—
457C4⋊C4—431no—
458C4⋊C4—861no—
459C4⋊C4—861no—
460C4⋊C4—861no—
461C4⋊C4—861no—
462C4⋊C4—861no—
463C4⋊C4—861no—
464C4⋊C4—861no—
465C4⋊C4—861no—
466C4⋊C4—1721no—
467C4⋊C4—1721no—
468C4⋊C4—1721no—
469C4⋊C4—1721no—
470C4⋊C4D4×D4311yescharacteristic
471C22⋊C4—1721no—
472C42—21no—
473C42—431no—
474C42—431no—
475C42—431no—
476C42—861no—
477C42—861no—
478C42—861no—
479C42—1721no—
480C42C23×D4311yescharacteristic
481C23—431no—
482Q8—21no—
483Q8—41no—
484Q8—41no—
485Q8—81no—
486Q8—861no—
487Q8—861no—
488Q8—3441no—
489Q8—3441no—
490Q8—3442no—
491Q8—1722no—
492Q8#1306335412yes—
493C2×C4—21no—
494C2×C4—21no—
495C2×C4—41no—
496C2×C4—41no—
497C2×C4—431no—
498C2×C4—432no—
499C2×C4—432no—
500C2×C4—431no—
501C2×C4—431no—
502C2×C4—861no—
503C2×C4—861no—
504C2×C4—861no—
505C2×C4—861no—
506C2×C4—3441no—
507C2×C4—3442no—
508C2×C4—1721no—
509C2×C4—1722no—
510C2×C4—1721no—
511C2×C4—1721no—
512C2×C4C2×D4×D4311yescharacteristic
513C2×C4C2×D4×D4311yescharacteristic
514C2×C4#41×D4311yescharacteristic
515C8—21no—
516C8—41no—
517C8—41no—
518C8—41no—
519C8—432no—
520C8—861no—
521C8—1721no—
522C8—1721no—
523C8—1721no—
524C8Q16×D4312yes—
525C22—432no—
526C22—861no—
527C22—861no—
528C22#121×D4311yescharacteristic
529C4—22no—
530C4—21no—
531C4—41no—
532C4—81no—
533C4—81no—
534C4—432no—
535C4—861no—
536C4—861no—
537C4—3441no—
538C4—3441no—
539C4—1721no—
540C4—1721no—
541C4C2×Q16×D4311yescharacteristic
542C4#137×D4311yescharacteristic
543C4C2×#1306335411yescharacteristic
544C4#1458369611yescharacteristic
545C2—862no—
546C2#462×D4311yescharacteristic
547C2#1914421811yescharacteristic
548C2#1914431811yescharacteristic
subgroupG/H
centerC22#121×D43
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#1672C2
socleC22×C43C2×#121
prime radicalC22×D43#121
hypercenter#1672D43
hypocenterC43#19173
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. #19134124C2semidirect
6. #19134122C2semidirect
7. #19134100C2semidirect
8. #19134098C2semidirect
9. #19133999C2semidirect
10. #19133997C2semidirect
11. #19133975C2semidirect
15. C43×#1672C2semidirect
204. #10621872Q16semidirect
282. #1672D43semidirect
341. C43#19173semidirect

Maximal subgroups

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

subgroupindex
#191451362
#191446332
#477×D432
Q8×#106218722
#191341242
#191341222
#191341002
#191340982
#191339992
#191339972
#191339752
#191333442
#191332842
#191332742
C43×#16722
#1917343