Finite Group Databasebeta

← #25067796

Subgroups — #25067796

Order 11008.

600 conjugacy classes of subgroups.

The subgroup lattice has 566 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19144671C211yesmaximal, characteristic
2#19143755C211yesmaximal, characteristic
3#19143685C211yesmaximal, characteristic, complemented
4#19133489C211yesmaximal, characteristic, complemented
5#19133488C211yesmaximal, characteristic, complemented
6#19133476C211yesmaximal, characteristic, complemented
7#19133469C211yesmaximal, characteristic, complemented
8#19133463C211yesmaximal, characteristic, complemented
9#19133449C211yesmaximal, characteristic, complemented
10#19133399C211yesmaximal, characteristic, complemented
11#19133398C211yesmaximal, characteristic, complemented
12#19133381C211yesmaximal, characteristic, complemented
13C2×#14582631C211yesmaximal, characteristic, complemented
14#19132878C211yesmaximal, characteristic, complemented
15C43×#1494C211yesmaximal, characteristic
16C2×C4×Dic86C2211yescharacteristic
17#14583227C411yescharacteristic
18#14583210C411yescharacteristic
19#14583203C411yescharacteristic
20#14583203C411yescharacteristic
21#14583118C411yescharacteristic
22#14583118C411yescharacteristic
23#14583054C411yescharacteristic
24#14583037C411yescharacteristic
25#14583030C2211yescharacteristic
26#14583027—21no—
27#14583027—21no—
28#14583026C2211yescharacteristic
29#14583026C2211yescharacteristic
30Q8×C43⋊C8C2211yescharacteristic
31#14583023C2211yescharacteristic
32#14583023C2211yescharacteristic
33C4×#10621885C2211yescharacteristic
34C4×#10621885C2211yescharacteristic
35C4×#10621883C2211yescharacteristic
36C4×#10621883C2211yescharacteristic
37#14582977C2211yescharacteristic
38#14582971—21no—
39D4×C43⋊C8—21no—
40D4×C43⋊C8C2211yescharacteristic
41#14582960—21no—
42#14582953—21no—
43#14582952C2211yescharacteristic
44#14582952C2211yescharacteristic
45#14582949—21no—
46#14582926—21no—
47C2×C4⋊(C43⋊C8)C2211yescharacteristic
48#14582651C2211yescharacteristic
49#14582651C2211yescharacteristic
50#14582649C2211yescharacteristic
51#14582649C2211yescharacteristic
52#14582631C2211yescharacteristic
53#14582631C2211yescharacteristic
54#14582631C2211yescharacteristic
55#14582631C2211yescharacteristic
56#14582620C2211yescharacteristic
57#14582620C2211yescharacteristic
58C8×C43⋊C8C2211yescharacteristic
59C8×C43⋊C8C2211yescharacteristic
60C43×#529C2211yescharacteristic
61C43×#432C2211yescharacteristic
62C2×C4×C8×C43C2211yescharacteristic
63C43×Q8⋊C8C2211yescharacteristic
64C43×Q8⋊C8C2211yescharacteristic
65C43×D4⋊C8C2211yescharacteristic
66C43×D4⋊C8C2211yescharacteristic
67C22×Dic86C2×C411yescharacteristic
68C2×#10621885C2×C411yescharacteristic
69C2×#10621885C2×C411yescharacteristic
70C2×#10621883C2×C411yescharacteristic
71C2×#10621883C2×C411yescharacteristic
72C2×#10621877—21no—
73C22×C43⋊C8—21no—
74C22×C43⋊C8—21no—
75C4×Dic86—21no—
76C4×Dic86—21no—
77C4×Dic86C2×C411yescharacteristic
78C4×Dic86C2×C411yescharacteristic
79C4×Dic86C2311yescharacteristic
80C4×Dic86C2311yescharacteristic
81C2×C4⋊Dic43C2×C411yescharacteristic
82C2×Dic43⋊C4—21no—
83C2×C4×Dic43—21no—
84#13063258C2×C411yescharacteristic
85#13063258C2×C411yescharacteristic
86#13063256C2×C411yescharacteristic
87#13063256C2×C411yescharacteristic
88C4⋊(C43⋊C8)—21no—
89C4⋊(C43⋊C8)—21no—
90C4⋊(C43⋊C8)—21no—
91C4⋊(C43⋊C8)C2×C411yescharacteristic
92C4⋊(C43⋊C8)C2×C411yescharacteristic
93C4⋊(C43⋊C8)D411yescharacteristic
94C4⋊(C43⋊C8)D411yescharacteristic
95C4⋊(C43⋊C8)C2311yescharacteristic
96C4⋊(C43⋊C8)C2311yescharacteristic
97Dic43⋊C8—21no—
98Dic43⋊C8—21no—
99Dic43⋊C8—21no—
100Dic43⋊C8—21no—
101#13063249C2×C411yescharacteristic
102#13063249C2×C411yescharacteristic
103#13063248C2×C411yescharacteristic
104#13063248C2×C411yescharacteristic
105#13063248C2×C411yescharacteristic
106#13063248C2×C411yescharacteristic
107#13063246C2×C411yescharacteristic
108#13063246C2×C411yescharacteristic
109C22⋊(C43⋊C8)—21no—
110C22⋊(C43⋊C8)—21no—
111C22⋊(C43⋊C8)C2×C411yescharacteristic
112C22⋊(C43⋊C8)C2×C411yescharacteristic
113C22⋊(C43⋊C8)D411yescharacteristic
114C22⋊(C43⋊C8)D411yescharacteristic
115#13063236—21no—
116#13063235—21no—
117#13063235—21no—
118C4×C43⋊C8—21no—
119C4×C43⋊C8C2311yescharacteristic
120C4×C43⋊C8C2311yescharacteristic
121C4×C43⋊C8C2311yescharacteristic
122C4×C43⋊C8C2311yescharacteristic
123C8×Dic43—21no—
124C8×Dic43—21no—
125C22×C8×C43—21no—
126#126×C43—21no—
127#125×C43C2×C411yescharacteristic
128#124×C43C2×C411yescharacteristic
129#123×C43—21no—
130C22⋊Q8×C43C2×C411yescharacteristic
131#121×C43C2×C411yescharacteristic
132C4×Q8×C43C2311yescharacteristic
133C4×D4×C43—21no—
134C4×D4×C43C2311yescharacteristic
135#117×C43—21no—
136C2×C42×C43C2311yescharacteristic
137C4⋊C8×C43C2311yescharacteristic
138C4⋊C8×C43C2311yescharacteristic
139C22⋊C8×C43—21no—
140#97×C43—21no—
141C4×C8×C43—21no—
142C4×C8×C43C2311yescharacteristic
143C4×C8×C43C2311yescharacteristic
144C2×Q8×C43C22×C411yescharacteristic
145C2×D4×C43—21no—
146C2×D4×C43C22×C411yescharacteristic
147C22×C4×C43—21no—
148C22×C4×C43C22×C411yescharacteristic
149C22×C4×C43C2×D411yescharacteristic
150C22×C4×C43#4111yescharacteristic
151C22×Dic43—21no—
152C22×Dic43—21no—
153C2×Dic86—22no—
154C2×Dic86—21no—
155C2×Dic86—41no—
156C2×Dic86C22×C411yescharacteristic
157C2×Dic86C22×C411yescharacteristic
158C2×C8×C43—24no—
159C2×C8×C43—21no—
160C2×C8×C43—21no—
161C2×C8×C43—21no—
162C2×C8×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—
171C22⋊C4×C43—21no—
172C22⋊C4×C43—21no—
173C22⋊C4×C43—21no—
174C42×C43—21no—
175C42×C43C22×C411yescharacteristic
176C42×C43C2×D411yescharacteristic
177C42×C43#4111yescharacteristic
178C42×C43C2411yescharacteristic
179#10621885—22no—
180#10621885—41no—
181#10621883—22no—
182#10621883—41no—
183C4⋊Dic43—21no—
184C4⋊Dic43C22×C411yescharacteristic
185C4⋊Dic43C22×C411yescharacteristic
186Dic43⋊C4—21no—
187Dic43⋊C4—21no—
188Dic43⋊C4—21no—
189Dic43⋊C4—21no—
190C4×Dic43—21no—
191C4×Dic43—21no—
192C4×Dic43—21no—
193C4×Dic43—21no—
194#10621877—81no—
195C2×C43⋊C8—21no—
196C2×C43⋊C8—21no—
197C2×C43⋊C8—81no—
198C2×C43⋊C8—81no—
199C2×C43⋊C8C22×C411yescharacteristic
200C2×C43⋊C8C22×C411yescharacteristic
201C2×C43⋊C8C22×C411yescharacteristic
202C2×C43⋊C8C22×C411yescharacteristic
203C2×C43⋊C8C2×D411yescharacteristic
204C2×C43⋊C8C2×D411yescharacteristic
205C2×C43⋊C8C2×D411yescharacteristic
206C2×C43⋊C8C2×D411yescharacteristic
207C23×C43—21no—
208C23×C43C4×D411yescharacteristic
209Q8×C43—21no—
210Q8×C43—21no—
211D4×C43—21no—
212D4×C43—21no—
213D4×C43—42no—
214C2×C4×C43—22no—
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×C43—41no—
224C2×C4×C43C4×D411yescharacteristic
225C2×C4×C43C4×D411yescharacteristic
226C2×C4×C43C4×D411yescharacteristic
227C2×C4×C43C23×C411yescharacteristic
228C2×C4×C43C22×D411yescharacteristic
229C2×C4×C43C2×#4111yescharacteristic
230C2×Dic43—21no—
231C2×Dic43—21no—
232C2×Dic43—21no—
233C2×Dic43—21no—
234C2×Dic43—42no—
235C2×Dic43—42no—
236Dic86—21no—
237Dic86—21no—
238Dic86—21no—
239Dic86—42no—
240Dic86#13112yes—
241C8×C43—22no—
242C8×C43—22no—
243C8×C43—41no—
244C8×C43—41no—
245C43⋊C8—21no—
246C43⋊C8—21no—
247C43⋊C8—21no—
248C43⋊C8—21no—
249C43⋊C8—21no—
250C43⋊C8—21no—
251C43⋊C8—21no—
252C43⋊C8—21no—
253C43⋊C8—41no—
254C43⋊C8—41no—
255#18017—431nomaximal, Sylow
256C22×C43—21no—
257C22×C43—21no—
258C22×C43—41no—
259C22×C43—41no—
260C22×C43—41no—
261C22×C43#44312yes—
262C22×C43C2×C4×D411yescharacteristic
263C4×C43—21no—
264C4×C43—21no—
265C4×C43—21no—
266C4×C43—21no—
267C4×C43—41no—
268C4×C43—41no—
269C4×C43—41no—
270C4×C43C2×#13111yescharacteristic
271C4×C43#56811yescharacteristic
272C4×C43#57711yescharacteristic
273C4×C43#57811yescharacteristic
274Dic43—22no—
275Dic43—41no—
276Dic43—41no—
277Dic43—41no—
278#3108—431no—
279#2994—431no—
280#2984—431no—
281#1591—431no—
282#1590—431no—
283#1588—431no—
284#1587—431no—
285#1587—431no—
286#1585—431no—
287C8×Q16—431no—
288C8×SD16—431no—
289#1573—431no—
290#1494D4311yescharacteristic
291C2×Q8⋊C8—431no—
292#1450—431no—
293C2×C43—22no—
294C2×C43—81no—
295C2×C43#293311yescharacteristic
296C2×C43#294711yescharacteristic
297C2×C43C2×#44311yescharacteristic
298#529C2×D4311yescharacteristic
299C2×C4×Q8—431no—
300#483—431no—
301#480—431no—
302#479—431no—
303#479—431no—
304#464—431no—
305#464—431no—
306#451—431no—
307#448—431no—
308#446—431no—
309#446—431no—
310#446—431no—
311#446—861no—
312#446—861no—
313C8×Q8—431no—
314C8×Q8—431no—
315C8×Q8—431no—
316C4×Q16—431no—
317C4×Q16—431no—
318C4×SD16—431no—
319C4×SD16—431no—
320#436—431no—
321#435—861no—
322C8×D4—431no—
323C8×D4—861no—
324#433—861no—
325#432—861no—
326#432C2×D4311yescharacteristic
327#431—431no—
328#431—431no—
329#431—861no—
330#424—861no—
331C2×C4⋊C8—431no—
332C2×C4×C8C2×D4311yescharacteristic
333#335—431no—
334#335—431no—
335#334—431no—
336#334—431no—
337Q8⋊C8—431no—
338Q8⋊C8—431no—
339Q8⋊C8—431no—
340Q8⋊C8—431no—
341Q8⋊C8C2×D4311yescharacteristic
342Q8⋊C8C2×D4311yescharacteristic
343D4⋊C8C2×D4311yescharacteristic
344D4⋊C8C2×D4311yescharacteristic
345#322—431no—
346#322—431no—
347C82—431no—
348C82—431no—
349C43#1801711yescharacteristic, complemented, Sylow
350C22×Q8—431no—
351C2×Q16—431no—
352C2×Q16—431no—
353C2×SD16—431no—
354C2×SD16—431no—
355C2×M16—861no—
356C22×C8—21no—
357C22×C8—861no—
358C22×C8—861no—
359#126—21no—
360#125C4×D4311yescharacteristic
361#124C4×D4311yescharacteristic
362#123—21no—
363C22⋊Q8C4×D4311yescharacteristic
364#121C4×D4311yescharacteristic
365C4×Q8—431no—
366C4×Q8—431no—
367C4×Q8—431no—
368C4×Q8—431no—
369C4×Q8—861no—
370C4×Q8—861no—
371C4×Q8C22×D4311yescharacteristic
372C4×D4—21no—
373C4×D4C22×D4311yescharacteristic
374#117—21no—
375C2×C4⋊C4—431no—
376C2×C4⋊C4—861no—
377C2×C42—861no—
378C2×C42C22×D4311yescharacteristic
379#107—431no—
380#107—431no—
381#106—431no—
382#106—431no—
383C4⋊C8—431no—
384C4⋊C8—431no—
385C4⋊C8—431no—
386C4⋊C8—431no—
387C4⋊C8—431no—
388C4⋊C8—431no—
389C4⋊C8—861no—
390C4⋊C8—861no—
391C4⋊C8—861no—
392C4⋊C8—861no—
393C4⋊C8—861no—
394C4⋊C8—861no—
395C4⋊C8—861no—
396C4⋊C8C22×D4311yescharacteristic
397C4⋊C8C22×D4311yescharacteristic
398#103—431no—
399#103—431no—
400#103—431no—
401#103—431no—
402#103—431no—
403#103—431no—
404#102—431no—
405#102—431no—
406C22⋊C8—21no—
407C22⋊C8—431no—
408C22⋊C8—431no—
409C22⋊C8—431no—
410C22⋊C8—431no—
411C22⋊C8—861no—
412C22⋊C8—861no—
413#97—21no—
414#97—861no—
415#97—861no—
416#97—861no—
417C4×C8—21no—
418C4×C8—431no—
419C4×C8—431no—
420C4×C8—431no—
421C4×C8—431no—
422C4×C8—861no—
423C4×C8—861no—
424C4×C8—861no—
425C4×C8C22×D4311yescharacteristic
426C4×C8C22×D4311yescharacteristic
427C2×Q8—431no—
428C2×Q8—431no—
429C2×Q8—862no—
430C2×Q8—861no—
431C2×Q8—1721no—
432C2×Q8C2×C4×D4311yescharacteristic
433C2×D4—21no—
434C2×D4C2×C4×D4311yescharacteristic
435C22×C4—21no—
436C22×C4—861no—
437C22×C4—861no—
438C22×C4C2×C4×D4311yescharacteristic
439C22×C4D4×D4311yescharacteristic
440C22×C4#1062190011yescharacteristic
441Q16—862no—
442Q16—1721no—
443SD16—862no—
444SD16—1721no—
445M16—3441no—
446C2×C8—24no—
447C2×C8—21no—
448C2×C8—21no—
449C2×C8—21no—
450C2×C8—21no—
451C2×C8—431no—
452C2×C8—431no—
453C2×C8—431no—
454C2×C8—431no—
455C2×C8—431no—
456C2×C8—431no—
457C2×C8—431no—
458C2×C8—431no—
459C2×C8—861no—
460C2×C8—861no—
461C2×C8—3441no—
462C2×C8—3441no—
463C4⋊C4—21no—
464C4⋊C4—21no—
465C4⋊C4—21no—
466C4⋊C4—21no—
467C4⋊C4—431no—
468C4⋊C4—431no—
469C4⋊C4—861no—
470C4⋊C4—861no—
471C4⋊C4—861no—
472C4⋊C4—861no—
473C4⋊C4—861no—
474C4⋊C4C2×C4×D4311yescharacteristic
475C4⋊C4C2×C4×D4311yescharacteristic
476C22⋊C4—21no—
477C22⋊C4—21no—
478C22⋊C4—21no—
479C22⋊C4—21no—
480C22⋊C4—21no—
481C42—21no—
482C42—861no—
483C42—861no—
484C42—861no—
485C42—861no—
486C42C2×C4×D4311yescharacteristic
487C42D4×D4311yescharacteristic
488C42#1062190011yescharacteristic
489C42C23×D4311yescharacteristic
490C23—21no—
491C23(C22⋊D43)⋊C411yescharacteristic
492Q8—21no—
493Q8—21no—
494Q8—432no—
495Q8—861no—
496Q8—861no—
497Q8—861no—
498Q8—1722no—
499D4—21no—
500D4—21no—
501D4—42no—
502C2×C4—22no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—41no—
511C2×C4—41no—
512C2×C4—861no—
513C2×C4—861no—
514C2×C4—861no—
515C2×C4—861no—
516C2×C4—1722no—
517C2×C4—1722no—
518C2×C4(C22⋊D43)⋊C411yescharacteristic
519C2×C4(C22⋊D43)⋊C411yescharacteristic
520C2×C4(C22⋊D43)⋊C411yescharacteristic
521C2×C4C22×C4×D4311yescharacteristic
522C2×C4C2×D4×D4311yescharacteristic
523C2×C4C2×#1062190011yescharacteristic
524C8—22no—
525C8—22no—
526C8—41no—
527C8—41no—
528C8—861no—
529C8—861no—
530C8—861no—
531C8—861no—
532C8—861no—
533C8—861no—
534C8—861no—
535C8—861no—
536C8—1721no—
537C8—1721no—
538C22—21no—
539C22—21no—
540C22—41no—
541C22—41no—
542C22—41no—
543C22#1458301312yes—
544C22C2×(C22⋊D43)⋊C411yescharacteristic
545C4—21no—
546C4—21no—
547C4—21no—
548C4—21no—
549C4—41no—
550C4—41no—
551C4—41no—
552C4—862no—
553C4—1721no—
554C4—1721no—
555C4—1721no—
556C4#131×D4311yescharacteristic
557C4#1458366411yescharacteristic
558C4#1458370611yescharacteristic
559C4#1458371311yescharacteristic
560C2—22no—
561C2—81no—
562C2#1914332511yescharacteristic
563C2#1914344111yescharacteristic
564C2C2×#1458301311yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC42C23×D43
FittingC43×#1494C2
socleC22×C43C2×C4×D4
prime radical#121×C43C2×C4
cosocleC42×C43C24
hypercenter#1494D43
hypocenterC43#18017
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1494

Complements

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

NH ≅ G/Ntype
3. #19143685C2semidirect
4. #19133489C2semidirect
5. #19133488C2semidirect
6. #19133476C2semidirect
7. #19133469C2semidirect
8. #19133463C2semidirect
9. #19133449C2semidirect
10. #19133399C2semidirect
11. #19133398C2semidirect
12. #19133381C2semidirect
13. C2×#14582631C2semidirect
14. #19132878C2semidirect
349. C43#18017semidirect

Maximal subgroups

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

subgroupindex
#191446712
#191437552
#191436852
#191334892
#191334882
#191334762
#191334692
#191334632
#191334492
#191333992
#191333982
#191333812
C2×#145826312
#191328782
C43×#14942
#1801743