Finite Group Databasebeta

← #25067236

Subgroups — #25067236

Order 11008.

582 conjugacy classes of subgroups.

The subgroup lattice has 562 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19145195C211yesmaximal, characteristic
2#19143740C211yesmaximal, characteristic
3#19143690C211yesmaximal, characteristic, complemented
4#19133501C211yesmaximal, characteristic, complemented
5#19133500C211yesmaximal, characteristic, complemented
6#19133489C211yesmaximal, characteristic, complemented
7#19133482C211yesmaximal, characteristic, complemented
8#19133411C211yesmaximal, characteristic, complemented
9#19133410C211yesmaximal, characteristic, complemented
10#19133399C211yesmaximal, characteristic, complemented
11#19133392C211yesmaximal, characteristic, complemented
12#19133360C211yesmaximal, characteristic, complemented
13#19133056C211yesmaximal, characteristic
14C8×#10621877C211yesmaximal, characteristic, complemented
15C43×#1493C211yesmaximal, characteristic, complemented
16#14583433C2211yescharacteristic
17#14583305C411yescharacteristic
18#14583291C411yescharacteristic
19#14583267C411yescharacteristic
20#14583261C411yescharacteristic
21#14583155C411yescharacteristic
22#14583155C411yescharacteristic
23#14583147C411yescharacteristic
24#14583147C411yescharacteristic
25#14583030—21no—
26#14583030—21no—
27#14583030C2211yescharacteristic
28#14583030C2211yescharacteristic
29#14583026C2211yescharacteristic
30Q8×C43⋊C8C2211yescharacteristic
31Q8×C43⋊C8C2211yescharacteristic
32#14583023C2211yescharacteristic
33C4×#10621885C2211yescharacteristic
34C4×#10621885C2211yescharacteristic
35C4×#10621884C2211yescharacteristic
36C4×#10621884C2211yescharacteristic
37#14582976C2211yescharacteristic
38#14582975—21no—
39#14582968—21no—
40#14582964C2211yescharacteristic
41#14582960—21no—
42#14582960—21no—
43#14582959—21no—
44#14582956C2211yescharacteristic
45#14582952C2211yescharacteristic
46#14582924—21no—
47C4×#10621877C2211yescharacteristic
48#14582651C2211yescharacteristic
49#14582651C2211yescharacteristic
50#14582649C2211yescharacteristic
51#14582649C2211yescharacteristic
52#14582631C2211yescharacteristic
53#14582631C2211yescharacteristic
54#14582628C2211yescharacteristic
55#14582628C2211yescharacteristic
56#14582621C2211yescharacteristic
57#14582621C2211yescharacteristic
58C8×C43⋊C8C2211yescharacteristic
59C8×C43⋊C8C2211yescharacteristic
60C43×#533C2211yescharacteristic
61C43×#423C2211yescharacteristic
62C2×C4×C8×C43C2211yescharacteristic
63C43×Q8⋊C8C2211yescharacteristic
64C43×Q8⋊C8C2211yescharacteristic
65C43×Q8⋊C8C2211yescharacteristic
66C43×Q8⋊C8C2211yescharacteristic
67C2×#10621885C2×C411yescharacteristic
68C2×#10621885C2×C411yescharacteristic
69C2×#10621884C2×C411yescharacteristic
70C2×#10621884C2×C411yescharacteristic
71C2×#10621877C2×C411yescharacteristic
72C2×#10621877C2×C411yescharacteristic
73C2×#10621872—21no—
74C2×C8×D43—21no—
75#13063319—21no—
76#13063317C2×C411yescharacteristic
77#13063313C2×C411yescharacteristic
78#13063308—21no—
79#13063304C2×C411yescharacteristic
80#13063299C2×C411yescharacteristic
81C4×Dic86C2311yescharacteristic
82C4×D172C2311yescharacteristic
83C4×C22⋊D43—21no—
84#13063282—21no—
85#13063258C2×C411yescharacteristic
86#13063258C2×C411yescharacteristic
87#13063256C2×C411yescharacteristic
88#13063256C2×C411yescharacteristic
89C4⋊(C43⋊C8)—21no—
90C4⋊(C43⋊C8)—21no—
91C4⋊(C43⋊C8)—21no—
92C4⋊(C43⋊C8)—21no—
93C4⋊(C43⋊C8)D411yescharacteristic
94C4⋊(C43⋊C8)D411yescharacteristic
95C4⋊(C43⋊C8)C2311yescharacteristic
96C4⋊(C43⋊C8)C2311yescharacteristic
97Dic43⋊C8—21no—
98Dic43⋊C8—21no—
99#13063249C2×C411yescharacteristic
100#13063249C2×C411yescharacteristic
101#13063249C2×C411yescharacteristic
102#13063249C2×C411yescharacteristic
103#13063248C2×C411yescharacteristic
104#13063248C2×C411yescharacteristic
105#13063245C2×C411yescharacteristic
106#13063245C2×C411yescharacteristic
107C22⋊(C43⋊C8)—21no—
108C22⋊(C43⋊C8)D411yescharacteristic
109C22⋊(C43⋊C8)D411yescharacteristic
110(C2×D43)⋊C8—21no—
111(C2×D43)⋊C8—21no—
112#13063236—21no—
113#13063236—21no—
114#13063236—21no—
115#13063236C2×C411yescharacteristic
116#13063236C2×C411yescharacteristic
117#13063235—21no—
118C4×C43⋊C8—21no—
119C4×C43⋊C8—21no—
120C4×C43⋊C8C2311yescharacteristic
121C4×C43⋊C8C2311yescharacteristic
122C4×C43⋊C8C2311yescharacteristic
123C4×C43⋊C8C2311yescharacteristic
124C8×Dic43—21no—
125C2×M16×C43—21no—
126C22×C8×C43—21no—
127C4⋊Q8×C43C2×C411yescharacteristic
128C4⋊Q8×C43C2×C411yescharacteristic
129#125×C43—21no—
130C22⋊Q8×C43—21no—
131C22⋊Q8×C43C2×C411yescharacteristic
132C22⋊Q8×C43C2×C411yescharacteristic
133C4×Q8×C43—21no—
134C4×Q8×C43C2311yescharacteristic
135C4×Q8×C43C2311yescharacteristic
136#117×C43—21no—
137C2×C42×C43C2311yescharacteristic
138C4⋊C8×C43—21no—
139C4⋊C8×C43C2311yescharacteristic
140C4⋊C8×C43C2311yescharacteristic
141C4×C8×C43—21no—
142C4×C8×C43C2311yescharacteristic
143C4×C8×C43C2311yescharacteristic
144C2×Q8×C43—21no—
145C2×Q8×C43C22×C411yescharacteristic
146C2×Q8×C43C22×C411yescharacteristic
147C22×C4×C43C22×C411yescharacteristic
148C22×C4×C43C2×D411yescharacteristic
149C22×C4×C43#4111yescharacteristic
150C2×C22⋊D43—21no—
151C2×D172C22×C411yescharacteristic
152C2×C4×D43—21no—
153C2×Dic86C22×C411yescharacteristic
154M16×C43—81no—
155C2×C8×C43—21no—
156C2×C8×C43—21no—
157C2×C8×C43—21no—
158C2×C8×C43—21no—
159C2×C8×C43—42no—
160C4⋊C4×C43—21no—
161C4⋊C4×C43—21no—
162C4⋊C4×C43—21no—
163C4⋊C4×C43—21no—
164C4⋊C4×C43—21no—
165C4⋊C4×C43—21no—
166C4⋊C4×C43—21no—
167C4⋊C4×C43C22×C411yescharacteristic
168C4⋊C4×C43C22×C411yescharacteristic
169C22⋊C4×C43—21no—
170C22⋊C4×C43—21no—
171C42×C43—21no—
172C42×C43—21no—
173C42×C43C22×C411yescharacteristic
174C42×C43C2×D411yescharacteristic
175C42×C43#4111yescharacteristic
176C42×C43C2411yescharacteristic
177C22⋊Dic43—21no—
178#10621885—22no—
179#10621885—22no—
180#10621884—22no—
181#10621884—22no—
182(C2×D43)⋊C4—21no—
183(C2×D43)⋊C4—21no—
184(C2×D43)⋊C4—21no—
185(C2×D43)⋊C4—21no—
186C4⋊Dic43C22×C411yescharacteristic
187C4⋊Dic43C22×C411yescharacteristic
188Dic43⋊C4—21no—
189Dic43⋊C4—21no—
190Dic43⋊C4—21no—
191Dic43⋊C4—21no—
192C4×Dic43—21no—
193#10621877—22no—
194#10621877—22no—
195C2×C43⋊C8—21no—
196C2×C43⋊C8—21no—
197C2×C43⋊C8C22×C411yescharacteristic
198C2×C43⋊C8C22×C411yescharacteristic
199C2×C43⋊C8C22×C411yescharacteristic
200C2×C43⋊C8C22×C411yescharacteristic
201C2×C43⋊C8C2×D411yescharacteristic
202C2×C43⋊C8C2×D411yescharacteristic
203C2×C43⋊C8C2×D411yescharacteristic
204C2×C43⋊C8C2×D411yescharacteristic
205#10621872—81no—
206C8×D43—81no—
207C23×C43C4×D411yescharacteristic
208C22×D43—21no—
209Q8×C43—21no—
210Q8×C43—21no—
211Q8×C43—21no—
212Q8×C43—21no—
213Q8×C43—81no—
214C2×C4×C43—21no—
215C2×C4×C43—21no—
216C2×C4×C43—21no—
217C2×C4×C43—21no—
218C2×C4×C43—21no—
219C2×C4×C43—21no—
220C2×C4×C43—21no—
221C2×C4×C43—21no—
222C2×C4×C43—41no—
223C2×C4×C43C4×D411yescharacteristic
224C2×C4×C43C4×D411yescharacteristic
225C2×C4×C43C4×D411yescharacteristic
226C2×C4×C43C23×C411yescharacteristic
227C2×C4×C43C22×D411yescharacteristic
228C2×C4×C43C2×#4111yescharacteristic
229C22⋊D43—81no—
230C2×Dic43—21no—
231C2×Dic43—21no—
232C2×Dic43—21no—
233D172—21no—
234D172—21no—
235C4×D43—41no—
236C4×D43—41no—
237Dic86—21no—
238Dic86—21no—
239C8×C43—22no—
240C8×C43—41no—
241C8×C43—41no—
242C8×C43—41no—
243C43⋊C8—21no—
244C43⋊C8—21no—
245C43⋊C8—21no—
246C43⋊C8—21no—
247C43⋊C8—21no—
248C43⋊C8—21no—
249C43⋊C8—41no—
250C43⋊C8—41no—
251C43⋊C8#13112yes—
252C43⋊C8#13112yes—
253#17969—431nomaximal, Sylow
254C22×C43—21no—
255C22×C43—21no—
256C22×C43—21no—
257C22×C43C2×C4×D411yescharacteristic
258C2×D43—41no—
259C2×D43—41no—
260C2×D43—41no—
261C4×C43—21no—
262C4×C43—21no—
263C4×C43—21no—
264C4×C43—21no—
265C4×C43—41no—
266C4×C43—41no—
267C4×C43—41no—
268C4×C43—41no—
269C4×C43C2×#13111yescharacteristic
270C4×C43C2×#13111yescharacteristic
271C4×C43#57711yescharacteristic
272C4×C43#57811yescharacteristic
273Dic43—41no—
274Dic43—41no—
275Dic43—41no—
276#3172—431no—
277#2993—431no—
278#2985—431no—
279#1593—431no—
280#1592—431no—
281#1591—431no—
282#1590—431no—
283#1579—431no—
284SD16⋊C8—431no—
285C8×Q16—431no—
286C8×SD16—431no—
287#1569—431no—
288#1494—431no—
289#1493D4311yescharacteristic, complemented
290C8×M16—431no—
291C2×C43—41no—
292C2×C43#293111yescharacteristic
293C2×C43#294711yescharacteristic
294C2×C43#295611yescharacteristic
295D43—81no—
296#533C2×D4311yescharacteristic
297#529—431no—
298#501—431no—
299#497—431no—
300#491—431no—
301#489—431no—
302#470—431no—
303#470—431no—
304#468—431no—
305#468—431no—
306#446—431no—
307#446—431no—
308#446—431no—
309#446—861no—
310#446—861no—
311C8×Q8—431no—
312C8×Q8—431no—
313C8×Q8—431no—
314C4×Q16—431no—
315C4×Q16—431no—
316C4×SD16—431no—
317C4×SD16—431no—
318#436—431no—
319#436—861no—
320#435—861no—
321C8×D4—431no—
322#433—861no—
323#433—861no—
324#433—861no—
325#432—431no—
326#431—431no—
327#424—861no—
328#423C2×D4311yescharacteristic
329C4×M16—431no—
330C2×C4×C8C2×D4311yescharacteristic
331#335—431no—
332#335—431no—
333#334—431no—
334#334—431no—
335Q8⋊C8—431no—
336Q8⋊C8—431no—
337Q8⋊C8C2×D4311yescharacteristic
338Q8⋊C8C2×D4311yescharacteristic
339Q8⋊C8C2×D4311yescharacteristic
340Q8⋊C8C2×D4311yescharacteristic
341D4⋊C8—431no—
342D4⋊C8—431no—
343#322—431no—
344#322—431no—
345C82—431no—
346C82—431no—
347C43#1796911yescharacteristic, complemented, Sylow
348C2×Q16—431no—
349C2×Q16—431no—
350C2×SD16—431no—
351C2×SD16—431no—
352C2×M16—21no—
353C2×M16—431no—
354C2×M16—431no—
355C2×M16—861no—
356C22×C8—21no—
357C22×C8—861no—
358C4⋊Q8C4×D4311yescharacteristic
359C4⋊Q8C4×D4311yescharacteristic
360#126—861no—
361#125—21no—
362#125—431no—
363#124—431no—
364#123—861no—
365C22⋊Q8—21no—
366C22⋊Q8—431no—
367C22⋊Q8C4×D4311yescharacteristic
368C22⋊Q8C4×D4311yescharacteristic
369#121—431no—
370C4×Q8—21no—
371C4×Q8—431no—
372C4×Q8C22×D4311yescharacteristic
373C4×Q8C22×D4311yescharacteristic
374C4×D4—431no—
375C4×D4—861no—
376#117—21no—
377#117—861no—
378C2×C42C22×D4311yescharacteristic
379#107—431no—
380#107—431no—
381#106—431no—
382#106—431no—
383C4⋊C8—21no—
384C4⋊C8—431no—
385C4⋊C8—431no—
386C4⋊C8—431no—
387C4⋊C8—431no—
388C4⋊C8—861no—
389C4⋊C8—861no—
390C4⋊C8—861no—
391C4⋊C8—861no—
392C4⋊C8—861no—
393C4⋊C8—861no—
394C4⋊C8C22×D4311yescharacteristic
395C4⋊C8C22×D4311yescharacteristic
396#103—431no—
397#103—431no—
398#103—431no—
399#103—431no—
400#103—431no—
401#103—431no—
402#102—431no—
403#102—431no—
404C22⋊C8—431no—
405C22⋊C8—431no—
406C22⋊C8—861no—
407C22⋊C8—861no—
408C22⋊C8—861no—
409#97—431no—
410#97—431no—
411#97—861no—
412#97—861no—
413#97—861no—
414#97—861no—
415C4×C8—21no—
416C4×C8—431no—
417C4×C8—431no—
418C4×C8—431no—
419C4×C8—431no—
420C4×C8—861no—
421C4×C8—861no—
422C4×C8—861no—
423C4×C8C22×D4311yescharacteristic
424C4×C8C22×D4311yescharacteristic
425C2×Q8—21no—
426C2×Q8—431no—
427C2×Q8C2×C4×D4311yescharacteristic
428C2×Q8C2×C4×D4311yescharacteristic
429C2×D4—431no—
430C2×D4—861no—
431C22×C4—861no—
432C22×C4C2×C4×D4311yescharacteristic
433C22×C4D4×D4311yescharacteristic
434C22×C4#1062190011yescharacteristic
435Q16—862no—
436Q16—862no—
437SD16—862no—
438SD16—862no—
439M16—81no—
440M16—862no—
441M16—862no—
442M16—3441no—
443C2×C8—21no—
444C2×C8—21no—
445C2×C8—21no—
446C2×C8—21no—
447C2×C8—42no—
448C2×C8—431no—
449C2×C8—431no—
450C2×C8—431no—
451C2×C8—431no—
452C2×C8—431no—
453C2×C8—431no—
454C2×C8—431no—
455C2×C8—431no—
456C2×C8—861no—
457C2×C8—861no—
458C2×C8—3441no—
459C4⋊C4—21no—
460C4⋊C4—21no—
461C4⋊C4—21no—
462C4⋊C4—21no—
463C4⋊C4—21no—
464C4⋊C4—21no—
465C4⋊C4—21no—
466C4⋊C4—431no—
467C4⋊C4—431no—
468C4⋊C4—861no—
469C4⋊C4—861no—
470C4⋊C4—861no—
471C4⋊C4—861no—
472C4⋊C4C2×C4×D4311yescharacteristic
473C4⋊C4C2×C4×D4311yescharacteristic
474C22⋊C4—21no—
475C22⋊C4—21no—
476C22⋊C4—861no—
477C22⋊C4—861no—
478C22⋊C4—861no—
479C22⋊C4—861no—
480C22⋊C4—861no—
481C42—21no—
482C42—21no—
483C42—861no—
484C42C2×C4×D4311yescharacteristic
485C42D4×D4311yescharacteristic
486C42#1062190011yescharacteristic
487C42C23×D4311yescharacteristic
488C23—861no—
489C23(C22⋊D43)⋊C411yescharacteristic
490Q8—21no—
491Q8—21no—
492Q8—21no—
493Q8—21no—
494Q8—81no—
495Q8—861no—
496Q8—861no—
497D4—861no—
498D4—861no—
499D4—3441no—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—41no—
509C2×C4—861no—
510C2×C4—861no—
511C2×C4—861no—
512C2×C4—1721no—
513C2×C4—1721no—
514C2×C4(C22⋊D43)⋊C411yescharacteristic
515C2×C4(C22⋊D43)⋊C411yescharacteristic
516C2×C4(C22⋊D43)⋊C411yescharacteristic
517C2×C4C22×C4×D4311yescharacteristic
518C2×C4C2×D4×D4311yescharacteristic
519C2×C4C2×#1062190011yescharacteristic
520C8—22no—
521C8—41no—
522C8—41no—
523C8—41no—
524C8—432no—
525C8—432no—
526C8—861no—
527C8—861no—
528C8—861no—
529C8—861no—
530C8—861no—
531C8—861no—
532C8—1721no—
533C8—1721no—
534C22—21no—
535C22—21no—
536C22—21no—
537C22—1721no—
538C22—1721no—
539C22—1721no—
540C22C2×(C22⋊D43)⋊C411yescharacteristic
541C4—21no—
542C4—21no—
543C4—21no—
544C4—21no—
545C4—41no—
546C4—41no—
547C4—41no—
548C4—41no—
549C4—1721no—
550C4—1721no—
551C4—1721no—
552C4#131×D4311yescharacteristic
553C4#131×D4311yescharacteristic
554C4#1458370511yescharacteristic
555C4#1458371211yescharacteristic
556C2—41no—
557C2—3441no—
558C2#1914330311yescharacteristic
559C2#1914343211yescharacteristic
560C2#1914350111yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC42C23×D43
FittingC43×#1493C2
socleC22×C43C2×C4×D4
prime radical#13063299C2×C4
cosocleC42×C43C24
hypercenter#1493D43
hypocenterC43#17969
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1493

Complements

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

NH ≅ G/Ntype
3. #19143690C2semidirect
4. #19133501C2semidirect
5. #19133500C2semidirect
6. #19133489C2semidirect
7. #19133482C2semidirect
8. #19133411C2semidirect
9. #19133410C2semidirect
10. #19133399C2semidirect
11. #19133392C2semidirect
12. #19133360C2semidirect
14. C8×#10621877C2semidirect
15. C43×#1493C2semidirect
289. #1493D43semidirect
347. C43#17969semidirect

Maximal subgroups

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

subgroupindex
#191451952
#191437402
#191436902
#191335012
#191335002
#191334892
#191334822
#191334112
#191334102
#191333992
#191333922
#191333602
#191330562
C8×#106218772
C43×#14932
#1796943