Finite Group Databasebeta

← #14724951

Subgroups — #14724951

Order 2816.

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#13078685C211yesmaximal, characteristic
2#13077740C211yesmaximal, characteristic
3#13077716C211yesmaximal, characteristic, complemented
4#13067513C211yesmaximal, characteristic, complemented
5#13067511C211yesmaximal, characteristic, complemented
6#13067490C211yesmaximal, characteristic, complemented
7#13067476C211yesmaximal, characteristic, complemented
8#13067475C211yesmaximal, characteristic, complemented
9C8×#4325C211yesmaximal, characteristic, complemented
10#13067415C211yesmaximal, characteristic, complemented
11#13067403C211yesmaximal, characteristic, complemented
12#13067069C211yesmaximal, characteristic, complemented
13#13066997C211yesmaximal, characteristic
14#13066901C211yesmaximal, characteristic, complemented
15C11×#1587C211yesmaximal, characteristic, complemented
16#10623109C2211yescharacteristic
17C4×#4343C2211yescharacteristic
18C11×#446C2211yescharacteristic
19C8×Q8×C11C2211yescharacteristic
20C4×C11×Q16C2211yescharacteristic
21#10622800C411yescharacteristic
22#10622795C411yescharacteristic
23C4×#4326C2211yescharacteristic
24C4×#4325C2211yescharacteristic
25#10622637C2211yescharacteristic
26#10622637C2211yescharacteristic
27#10622503C411yescharacteristic
28#10622501C411yescharacteristic
29#10622453—21no—
30#10622450C2211yescharacteristic
31#10622449—21no—
32#10622447C2211yescharacteristic
33#10622446C2211yescharacteristic
34D11×C4⋊C8—21no—
35#10622443C2211yescharacteristic
36#10622441—21no—
37#10622431C411yescharacteristic
38#10622428C411yescharacteristic
39#10622423C411yescharacteristic
40#10622404C411yescharacteristic
41#10622319—21no—
42#10622318—21no—
43C4×#4314C2211yescharacteristic
44#10622303—21no—
45C8×D44C2211yescharacteristic
46#10622298C2211yescharacteristic
47#10622298C2211yescharacteristic
48C4×C8×D11C2211yescharacteristic
49#10622292C2211yescharacteristic
50C8×Dic22—21no—
51C11×#334C2211yescharacteristic
52C11×Q8⋊C8C2211yescharacteristic
53C11×Q8⋊C8C2211yescharacteristic
54C11×#322C2211yescharacteristic
55Q8⋊(C11⋊C8)C2211yescharacteristic
56Q8⋊(C11⋊C8)C2211yescharacteristic
57#10622122C2211yescharacteristic
58#10622121C2211yescharacteristic
59#10622118C2211yescharacteristic
60#10622117C2211yescharacteristic
61#10622097C2211yescharacteristic
62#10622096C2211yescharacteristic
63#10622094C2211yescharacteristic
64#10622093C2211yescharacteristic
65C8×C11⋊C8C2211yescharacteristic
66C8×C11⋊C8C2211yescharacteristic
67C2×#4343C2×C411yescharacteristic
68C2×C11×Q16C2×C411yescharacteristic
69C4×Q8×C11C2311yescharacteristic
70C4×Q8×C11C2311yescharacteristic
71#66999C2×C411yescharacteristic
72Q8×Dic11C2×C411yescharacteristic
73#66997C2×C411yescharacteristic
74C2×#4326C2×C411yescharacteristic
75C2×#4325C2×C411yescharacteristic
76C2×#4314C2×C411yescharacteristic
77C2×#4313—21no—
78C2×C8×D11—21no—
79C2×C8×D11—21no—
80C2×C8×D11—21no—
81#66950C2×C411yescharacteristic
82#66949—21no—
83#66946—21no—
84#66946C2×C411yescharacteristic
85#66945—21no—
86#66945C2×C411yescharacteristic
87#66942—21no—
88#66941C2×C411yescharacteristic
89C4×D44—21no—
90C4×D44C2311yescharacteristic
91#66925—21no—
92C42×D11—21no—
93C42×D11C2311yescharacteristic
94C4×Dic22—21no—
95C4×Dic22C2311yescharacteristic
96C11×#107C2×C411yescharacteristic
97C11×C4⋊C8—21no—
98C11×C4⋊C8—21no—
99C11×C4⋊C8C2311yescharacteristic
100C11×C4⋊C8C2311yescharacteristic
101C11×#103C2×C411yescharacteristic
102C11×#103C2×C411yescharacteristic
103C11×#97—21no—
104C4×C8×C11—21no—
105C4×C8×C11C2311yescharacteristic
106C4×C8×C11C2311yescharacteristic
107C4×C8×C11C2311yescharacteristic
108#66899C2×C411yescharacteristic
109#66899C2×C411yescharacteristic
110#66885C2×C411yescharacteristic
111(C2×D11)⋊C8—21no—
112(C2×D11)⋊C8—21no—
113(C2×D11)⋊C8—21no—
114(C2×D11)⋊C8C2×C411yescharacteristic
115(C2×D11)⋊C8C2×C411yescharacteristic
116(C2×D11)⋊C8D411yescharacteristic
117(C2×D11)⋊C8D411yescharacteristic
118#66881C2×C411yescharacteristic
119#66880C2×C411yescharacteristic
120#66879—21no—
121Dic11⋊C8—21no—
122Dic11⋊C8—21no—
123Dic11⋊C8—21no—
124Dic11⋊C8C2×C411yescharacteristic
125Dic11⋊C8C2×C411yescharacteristic
126Dic11⋊C8D411yescharacteristic
127Dic11⋊C8D411yescharacteristic
128C8×Dic11—21no—
129C8×Dic11—21no—
130C8×Dic11—21no—
131#66874C2×C411yescharacteristic
132#66873C2×C411yescharacteristic
133#66872C2×C411yescharacteristic
134#66871C2×C411yescharacteristic
135C4⋊(C11⋊C8)—21no—
136C4⋊(C11⋊C8)—21no—
137C4⋊(C11⋊C8)C2311yescharacteristic
138C4⋊(C11⋊C8)C2311yescharacteristic
139#66867—21no—
140#66867—21no—
141C4×C11⋊C8C2311yescharacteristic
142C4×C11⋊C8C2311yescharacteristic
143C4×C11⋊C8C2311yescharacteristic
144#18016—111nomaximal, Sylow
145C2×Q8×C11C22×C411yescharacteristic
146C2×Q8×C11C22×C411yescharacteristic
147#4343—22no—
148#4343—41no—
149C2×D44—21no—
150C2×D44C22×C411yescharacteristic
151C2×C4×D11—21no—
152C2×C4×D11—21no—
153C2×C4×D11—21no—
154C2×C4×D11C22×C411yescharacteristic
155C2×C4×D11C2×D411yescharacteristic
156C2×C4×D11#4111yescharacteristic
157C2×Dic22—21no—
158C2×Dic22C22×C411yescharacteristic
159C11×Q16—41no—
160C2×C8×C11—21no—
161C2×C8×C11—21no—
162C2×C8×C11—21no—
163C2×C8×C11C22×C411yescharacteristic
164C2×C8×C11C22×C411yescharacteristic
165C2×C8×C11C2×D411yescharacteristic
166C2×C8×C11C2×D411yescharacteristic
167C11×C4⋊C4—21no—
168C11×C4⋊C4—21no—
169C11×C4⋊C4C22×C411yescharacteristic
170C11×C4⋊C4C22×C411yescharacteristic
171C42×C11—21no—
172C42×C11—21no—
173C42×C11C2411yescharacteristic
174#4326—41no—
175#4325—22no—
176(C2×D11)⋊C4—21no—
177(C2×D11)⋊C4—21no—
178(C2×D11)⋊C4—21no—
179(C2×D11)⋊C4—21no—
180(C2×D11)⋊C4—21no—
181C4⋊Dic11—21no—
182C4⋊Dic11—21no—
183C4⋊Dic11C22×C411yescharacteristic
184C4⋊Dic11C22×C411yescharacteristic
185Dic11⋊C4—21no—
186Dic11⋊C4—21no—
187Dic11⋊C4—21no—
188Dic11⋊C4—21no—
189Dic11⋊C4—21no—
190C4×Dic11—21no—
191C4×Dic11—21no—
192C4×Dic11—21no—
193C4×Dic11C22×C411yescharacteristic
194C4×Dic11C2×D411yescharacteristic
195C4×Dic11#4111yescharacteristic
196C2×C11⋊C8—21no—
197C2×C11⋊C8—21no—
198C2×C11⋊C8—21no—
199C2×C11⋊C8C22×C411yescharacteristic
200C2×C11⋊C8C22×C411yescharacteristic
201C2×C11⋊C8C2×D411yescharacteristic
202C2×C11⋊C8C2×D411yescharacteristic
203#4314—22no—
204#4313—81no—
205C8×D11—24no—
206C8×D11—81no—
207C8×D11—81no—
208#3107—111no—
209#2990—111no—
210#2986—111no—
211#1591—111no—
212#1591—111no—
213#1587—111no—
214#1587D1111yescharacteristic, complemented
215#1585—111no—
216#1585—111no—
217C8×SD16—111no—
218C8×SD16—111no—
219#1574—111no—
220#1493—111no—
221#1476—111no—
222#1450—111no—
223C22×D11—21no—
224C22×D11C4×D411yescharacteristic
225Q8×C11—21no—
226Q8×C11—21no—
227Q8×C11—21no—
228Q8×C11—21no—
229C2×C4×C11—21no—
230C2×C4×C11—21no—
231C2×C4×C11—21no—
232C2×C4×C11—21no—
233C2×C4×C11C23×C411yescharacteristic
234C2×C4×C11C22×D411yescharacteristic
235C2×C4×C11C2×#4111yescharacteristic
236C2×Dic11—21no—
237C2×Dic11—21no—
238C2×Dic11—21no—
239C2×Dic11C4×D411yescharacteristic
240C2×Dic11C4×D411yescharacteristic
241C2×Dic11C4×D411yescharacteristic
242D44—21no—
243D44—42no—
244D44#13112yes—
245C4×D11—21no—
246C4×D11—21no—
247C4×D11—21no—
248C4×D11—21no—
249C4×D11—22no—
250C4×D11—42no—
251C4×D11—41no—
252C4×D11—41no—
253C4×D11—42no—
254Dic22—21no—
255Dic22—21no—
256Dic22—42no—
257C8×C11—22no—
258C8×C11—21no—
259C8×C11—21no—
260C8×C11—21no—
261C8×C11—21no—
262C8×C11—41no—
263C8×C11—41no—
264C11⋊C8—22no—
265C11⋊C8—21no—
266C11⋊C8—21no—
267C11⋊C8—21no—
268C11⋊C8—21no—
269C11⋊C8—41no—
270C11⋊C8—41no—
271#533—111no—
272C4×#41—111no—
273#485—111no—
274#485—111no—
275#475—111no—
276#474—111no—
277#462—111no—
278#461—111no—
279#452—111no—
280#452—111no—
281#446—111no—
282#446—111no—
283#446—111no—
284#446—221no—
285#446C2×D1111yescharacteristic
286C8×Q8—111no—
287C8×Q8—221no—
288C8×Q8C2×D1111yescharacteristic
289C4×Q16—111no—
290C4×Q16C2×D1111yescharacteristic
291C4×SD16—111no—
292C4×SD16—111no—
293#435—221no—
294#435—221no—
295C8×D4—111no—
296C8×D4—111no—
297#433—221no—
298#433—221no—
299#432—221no—
300#431—111no—
301#431—111no—
302#431—111no—
303#423—111no—
304C2×C4⋊C8—221no—
305C2×C4×C8—111no—
306#335—111no—
307#335—111no—
308#334—111no—
309#334C2×D1111yescharacteristic
310Q8⋊C8—111no—
311Q8⋊C8—111no—
312Q8⋊C8—111no—
313Q8⋊C8—111no—
314Q8⋊C8C2×D1111yescharacteristic
315Q8⋊C8C2×D1111yescharacteristic
316D4⋊C8—111no—
317D4⋊C8—111no—
318#322—111no—
319#322C2×D1111yescharacteristic
320C82—111no—
321C82—111no—
322C22×C11C2×C4×D411yescharacteristic
323C2×D11—22no—
324C2×D11—21no—
325C2×D11—21no—
326C2×D11—21no—
327C2×D11—41no—
328C2×D11—41no—
329C4×C11—21no—
330C4×C11—41no—
331C4×C11—41no—
332C4×C11—41no—
333C4×C11—41no—
334C4×C11C2×#13111yescharacteristic
335C4×C11#56811yescharacteristic
336C4×C11#57711yescharacteristic
337C4×C11#57811yescharacteristic
338Dic11—21no—
339Dic11—21no—
340Dic11—41no—
341Dic11—41no—
342Dic11—41no—
343Dic11#44312yes—
344C2×#41—111no—
345C2×Q16—111no—
346C2×Q16C4×D1111yescharacteristic
347C2×SD16—111no—
348C2×SD16—111no—
349C2×M16—221no—
350C22×C8—221no—
351C22×C8—221no—
352C22×C8—221no—
353C4⋊Q8—111no—
354C4⋊Q8—111no—
355#125—221no—
356C22⋊Q8—111no—
357C22⋊Q8—111no—
358C22⋊Q8—221no—
359C4×Q8—111no—
360C4×Q8—111no—
361C4×Q8—221no—
362C4×Q8C22×D1111yescharacteristic
363C4×Q8C22×D1111yescharacteristic
364C4×D4—111no—
365C4×D4—111no—
366C4×D4—221no—
367C4×D4—221no—
368#117—111no—
369#117—221no—
370#117—221no—
371C2×C42—111no—
372C2×C42—221no—
373#107—111no—
374#107C4×D1111yescharacteristic
375#106—111no—
376#106—111no—
377C4⋊C8—21no—
378C4⋊C8—21no—
379C4⋊C8—111no—
380C4⋊C8—111no—
381C4⋊C8—111no—
382C4⋊C8—111no—
383C4⋊C8—111no—
384C4⋊C8—111no—
385C4⋊C8—221no—
386C4⋊C8—221no—
387C4⋊C8—221no—
388C4⋊C8—221no—
389C4⋊C8—221no—
390C4⋊C8C22×D1111yescharacteristic
391C4⋊C8C22×D1111yescharacteristic
392#103—111no—
393#103—111no—
394#103—111no—
395#103—111no—
396#103C4×D1111yescharacteristic
397#103C4×D1111yescharacteristic
398#102—111no—
399#102—111no—
400C22⋊C8—111no—
401C22⋊C8—111no—
402C22⋊C8—111no—
403C22⋊C8—111no—
404C22⋊C8—221no—
405C22⋊C8—221no—
406C22⋊C8—221no—
407#97—21no—
408#97—221no—
409#97—221no—
410#97—221no—
411C4×C8—21no—
412C4×C8—111no—
413C4×C8—111no—
414C4×C8—111no—
415C4×C8—221no—
416C4×C8—221no—
417C4×C8—221no—
418C4×C8C22×D1111yescharacteristic
419C4×C8C22×D1111yescharacteristic
420C4×C8C22×D1111yescharacteristic
421C2×C11#293311yescharacteristic
422C2×C11#294711yescharacteristic
423C2×C11C2×#44311yescharacteristic
424D11—41no—
425D11—42no—
426#41—222no—
427#41—441no—
428C2×Q8—111no—
429C2×Q8—221no—
430C2×Q8C2×C4×D1111yescharacteristic
431C2×Q8C2×C4×D1111yescharacteristic
432C2×D4—111no—
433C2×D4—221no—
434C22×C4—111no—
435C22×C4—111no—
436C22×C4—111no—
437C22×C4—221no—
438C22×C4—221no—
439C22×C4—221no—
440Q16—41no—
441Q16—441no—
442SD16—222no—
443SD16—222no—
444M16—881no—
445C2×C8—21no—
446C2×C8—21no—
447C2×C8—21no—
448C2×C8—111no—
449C2×C8—111no—
450C2×C8—111no—
451C2×C8—111no—
452C2×C8—224no—
453C2×C8—221no—
454C2×C8—221no—
455C2×C8—221no—
456C2×C8—881no—
457C2×C8—881no—
458C2×C8C2×C4×D1111yescharacteristic
459C2×C8C2×C4×D1111yescharacteristic
460C2×C8D4×D1111yescharacteristic
461C2×C8D4×D1111yescharacteristic
462C4⋊C4—21no—
463C4⋊C4—21no—
464C4⋊C4—111no—
465C4⋊C4—111no—
466C4⋊C4—221no—
467C4⋊C4—221no—
468C4⋊C4—221no—
469C4⋊C4—221no—
470C4⋊C4—221no—
471C4⋊C4—221no—
472C4⋊C4—221no—
473C4⋊C4C2×C4×D1111yescharacteristic
474C4⋊C4C2×C4×D1111yescharacteristic
475C22⋊C4—221no—
476C22⋊C4—221no—
477C22⋊C4—221no—
478C22⋊C4—221no—
479C22⋊C4—221no—
480C42—21no—
481C42—21no—
482C42—111no—
483C42—111no—
484C42—111no—
485C42—221no—
486C42—221no—
487C42—221no—
488C42C23×D1111yescharacteristic
489C11#1801611yescharacteristic, complemented, Sylow
490C23—111no—
491C23—221no—
492Q8—21no—
493Q8—21no—
494Q8—21no—
495Q8—21no—
496Q8—221no—
497Q8—221no—
498Q8—442no—
499D4—112no—
500D4—221no—
501D4—442no—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—111no—
507C2×C4—111no—
508C2×C4—111no—
509C2×C4—222no—
510C2×C4—221no—
511C2×C4—221no—
512C2×C4—221no—
513C2×C4—221no—
514C2×C4—221no—
515C2×C4—221no—
516C2×C4—221no—
517C2×C4—442no—
518C2×C4—442no—
519C2×C4—441no—
520C2×C4—441no—
521C2×C4C22×C4×D1111yescharacteristic
522C2×C4C2×D4×D1111yescharacteristic
523C2×C4#41×D1111yescharacteristic
524C8—22no—
525C8—21no—
526C8—21no—
527C8—21no—
528C8—21no—
529C8—41no—
530C8—41no—
531C8—222no—
532C8—221no—
533C8—221no—
534C8—221no—
535C8—221no—
536C8—441no—
537C8—441no—
538C22—221no—
539C22—222no—
540C22—221no—
541C22—221no—
542C22—441no—
543C22—441no—
544C22C4×D4×D1111yescharacteristic
545C4—21no—
546C4—41no—
547C4—41no—
548C4—41no—
549C4—41no—
550C4—112no—
551C4—221no—
552C4—221no—
553C4—441no—
554C4—441no—
555C4—441no—
556C4#1062327611yescharacteristic
557C4D11×#13111yescharacteristic
558C4#1062330911yescharacteristic
559C4#1062331011yescharacteristic
560C2—441no—
561C2—442no—
562C2#1307733911yescharacteristic
563C2#1307745811yescharacteristic
564C2D11×#44311yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
FittingC11×#1587C2
socleC22×C11C2×C4×D4
prime radicalC2×#4343C2×C4
cosocleC42×C11C24
hypercenter#1587D11
hypocenterC11#18016
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ #1587

Complements

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

NH ≅ G/Ntype
3. #13077716C2semidirect
4. #13067513C2semidirect
5. #13067511C2semidirect
6. #13067490C2semidirect
7. #13067476C2semidirect
8. #13067475C2semidirect
9. C8×#4325C2semidirect
10. #13067415C2semidirect
11. #13067403C2semidirect
12. #13067069C2semidirect
14. #13066901C2semidirect
15. C11×#1587C2semidirect
214. #1587D11semidirect
489. C11#18016semidirect

Maximal subgroups

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

subgroupindex
#130786852
#130777402
#130777162
#130675132
#130675112
#130674902
#130674762
#130674752
C8×#43252
#130674152
#130674032
#130670692
#130669972
#130669012
C11×#15872
#1801611