Finite Group Databasebeta

← #14724921

Subgroups — #14724921

Order 2816.

592 conjugacy classes of subgroups.

The subgroup lattice has 568 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13078683C211yesmaximal, characteristic
2#13077632C211yesmaximal, characteristic
3#13077564C211yesmaximal, characteristic, complemented
4#13067509C211yesmaximal, characteristic, complemented
5#13067492C211yesmaximal, characteristic, complemented
6#13067485C211yesmaximal, characteristic, complemented
7#13067465C211yesmaximal, characteristic, complemented
8#13067460C211yesmaximal, characteristic, complemented
9#13067436C211yesmaximal, characteristic, complemented
10#13067420C211yesmaximal, characteristic, complemented
11#13067400C211yesmaximal, characteristic, complemented
12#13067087C211yesmaximal, characteristic, complemented
13#13067000C211yesmaximal, characteristic
14#13066912C211yesmaximal, characteristic, complemented
15C11×#1592C211yesmaximal, characteristic, complemented
16#10623109C2211yescharacteristic
17C4×#4341C2211yescharacteristic
18C11×#446C2211yescharacteristic
19C4×C11×SD16C2211yescharacteristic
20C11×#436C2211yescharacteristic
21#10622786C411yescharacteristic
22#10622775C411yescharacteristic
23#10622741—21no—
24M16×Dic11—21no—
25C4×#4326C2211yescharacteristic
26Q8×C11⋊C8C2211yescharacteristic
27C4×#4324C2211yescharacteristic
28#10622625C2211yescharacteristic
29#10622480C411yescharacteristic
30#10622467C411yescharacteristic
31#10622452—21no—
32#10622448C2211yescharacteristic
33D11×C4⋊C8C2211yescharacteristic
34#10622444—21no—
35#10622444C2211yescharacteristic
36#10622443C2211yescharacteristic
37#10622427C411yescharacteristic
38#10622406C411yescharacteristic
39#10622396C411yescharacteristic
40#10622372C411yescharacteristic
41#10622342—21no—
42#10622332—21no—
43#10622321—21no—
44#10622314—21no—
45C4×Dic44C2211yescharacteristic
46C4×#4313C2211yescharacteristic
47#10622298C2211yescharacteristic
48#10622298C2211yescharacteristic
49C8×Dic22C2211yescharacteristic
50C8×Dic22C2211yescharacteristic
51C11×#335C2211yescharacteristic
52C11×Q8⋊C8C2211yescharacteristic
53C11×D4⋊C8C2211yescharacteristic
54C11×#322C2211yescharacteristic
55Q8⋊(C11⋊C8)C2211yescharacteristic
56D4⋊(C11⋊C8)C2211yescharacteristic
57#10622122C2211yescharacteristic
58#10622122C2211yescharacteristic
59#10622118C2211yescharacteristic
60#10622117C2211yescharacteristic
61#10622095C2211yescharacteristic
62#10622094C2211yescharacteristic
63#10622094C2211yescharacteristic
64#10622092C2211yescharacteristic
65#10622092C2211yescharacteristic
66C8×C11⋊C8C2211yescharacteristic
67C2×#4341C2×C411yescharacteristic
68C2×C11×SD16C2×C411yescharacteristic
69C2×C11×M16—21no—
70C4×Q8×C11C2311yescharacteristic
71C4×D4×C11C2311yescharacteristic
72#66999C2×C411yescharacteristic
73#66997C2×C411yescharacteristic
74C2×#4326C2×C411yescharacteristic
75D4×Dic11C2×C411yescharacteristic
76C2×#4324C2×C411yescharacteristic
77C4×C22⋊D11—21no—
78C2×C4×Dic11—21no—
79C2×#4318—21no—
80C2×Dic44C2×C411yescharacteristic
81C2×#4313D411yescharacteristic
82C2×#4313D411yescharacteristic
83C2×C8×D11—21no—
84#66950C2×C411yescharacteristic
85#66949—21no—
86#66945C2×C411yescharacteristic
87#66942—21no—
88#66941C2×C411yescharacteristic
89#66940C2×C411yescharacteristic
90(C22⋊D11)⋊C4—21no—
91#66930—21no—
92#66925—21no—
93C42×D11C2311yescharacteristic
94C4×Dic22—21no—
95C4×Dic22C2311yescharacteristic
96C4×Dic22C2311yescharacteristic
97C11×#106C2×C411yescharacteristic
98C11×C4⋊C8—21no—
99C11×C4⋊C8C2311yescharacteristic
100C11×C4⋊C8C2311yescharacteristic
101C11×#103C2×C411yescharacteristic
102C11×#102C2×C411yescharacteristic
103C11×C22⋊C8—21no—
104C11×#97—21no—
105C4×C8×C11C2311yescharacteristic
106C4×C8×C11C2311yescharacteristic
107C4×C8×C11C2311yescharacteristic
108#66899C2×C411yescharacteristic
109#66896C2×C411yescharacteristic
110C22⋊(C11⋊C8)—21no—
111(C2×D11)⋊C8—21no—
112(C2×D11)⋊C8—21no—
113(C2×D11)⋊C8C2×C411yescharacteristic
114(C2×D11)⋊C8C2×C411yescharacteristic
115#66882C2×C411yescharacteristic
116#66880C2×C411yescharacteristic
117#66880C2×C411yescharacteristic
118#66879—21no—
119#66879—21no—
120#66879D411yescharacteristic
121#66879D411yescharacteristic
122Dic11⋊C8—21no—
123Dic11⋊C8—21no—
124Dic11⋊C8—21no—
125Dic11⋊C8—21no—
126Dic11⋊C8—21no—
127Dic11⋊C8—21no—
128Dic11⋊C8C2×C411yescharacteristic
129Dic11⋊C8C2×C411yescharacteristic
130C8×Dic11—21no—
131C8×Dic11—21no—
132C8×Dic11—21no—
133#66874C2×C411yescharacteristic
134#66874C2×C411yescharacteristic
135#66872C2×C411yescharacteristic
136#66871C2×C411yescharacteristic
137C4⋊(C11⋊C8)—21no—
138C4⋊(C11⋊C8)C2311yescharacteristic
139C4⋊(C11⋊C8)C2311yescharacteristic
140C4×C11⋊C8—21no—
141C4×C11⋊C8C2311yescharacteristic
142C4×C11⋊C8C2311yescharacteristic
143C4×C11⋊C8C2311yescharacteristic
144#18013—111nomaximal, Sylow
145C2×Q8×C11C22×C411yescharacteristic
146C2×D4×C11C22×C411yescharacteristic
147C22×C4×C11—21no—
148C2×C22⋊D11—21no—
149C22×Dic11—21no—
150C22×Dic11—21no—
151#4341—22no—
152#4341—41no—
153C2×C4×D11C22×C411yescharacteristic
154C2×C4×D11C2×D411yescharacteristic
155C2×C4×D11#4111yescharacteristic
156C2×Dic22—21no—
157C2×Dic22C22×C411yescharacteristic
158C2×Dic22C22×C411yescharacteristic
159C11×SD16—41no—
160C11×M16—42no—
161C2×C8×C11—21no—
162C2×C8×C11—21no—
163C2×C8×C11—21no—
164C2×C8×C11C22×C411yescharacteristic
165C2×C8×C11C22×C411yescharacteristic
166C2×C8×C11C2×D411yescharacteristic
167C2×C8×C11C2×D411yescharacteristic
168C11×C4⋊C4—21no—
169C11×C4⋊C4C22×C411yescharacteristic
170C11×C4⋊C4C22×C411yescharacteristic
171C11×C22⋊C4—21no—
172C42×C11—21no—
173C42×C11C2411yescharacteristic
174C22⋊Dic11—21no—
175#4326—22no—
176#4324—41no—
177(C2×D11)⋊C4—21no—
178(C2×D11)⋊C4—21no—
179(C2×D11)⋊C4—21no—
180C4⋊Dic11—21no—
181C4⋊Dic11C22×C411yescharacteristic
182C4⋊Dic11C22×C411yescharacteristic
183Dic11⋊C4—21no—
184Dic11⋊C4—21no—
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×Dic11—21no—
194C4×Dic11C22×C411yescharacteristic
195C4×Dic11C2×D411yescharacteristic
196C4×Dic11#4111yescharacteristic
197#4318—42no—
198C2×C11⋊C8—21no—
199C2×C11⋊C8—21no—
200C2×C11⋊C8—21no—
201C2×C11⋊C8C22×C411yescharacteristic
202C2×C11⋊C8C22×C411yescharacteristic
203C2×C11⋊C8C2×D411yescharacteristic
204C2×C11⋊C8C2×D411yescharacteristic
205Dic44—22no—
206#4313—22no—
207#4313—41no—
208C8×D11—42no—
209#3107—111no—
210#2971—111no—
211#2962—111no—
212#1592D1111yescharacteristic, complemented
213#1590—111no—
214#1588—111no—
215#1587—111no—
216#1584—111no—
217#1583—111no—
218#1579—111no—
219C8×Q16—111no—
220#1573—111no—
221#1497—111no—
222#1477—111no—
223#1453—111no—
224C23×C11—21no—
225C22×D11C4×D411yescharacteristic
226Q8×C11—21no—
227Q8×C11—21no—
228D4×C11—21no—
229D4×C11—21no—
230C2×C4×C11—21no—
231C2×C4×C11—21no—
232C2×C4×C11—21no—
233C2×C4×C11—41no—
234C2×C4×C11—41no—
235C2×C4×C11C23×C411yescharacteristic
236C2×C4×C11C22×D411yescharacteristic
237C2×C4×C11C2×#4111yescharacteristic
238C22⋊D11—42no—
239C2×Dic11—21no—
240C2×Dic11—21no—
241C2×Dic11—21no—
242C2×Dic11—21no—
243C2×Dic11—42no—
244C2×Dic11—81no—
245C2×Dic11C4×D411yescharacteristic
246C2×Dic11C4×D411yescharacteristic
247C2×Dic11C4×D411yescharacteristic
248C4×D11—21no—
249C4×D11—21no—
250C4×D11—21no—
251C4×D11—21no—
252C4×D11—41no—
253Dic22—21no—
254Dic22—21no—
255Dic22—21no—
256Dic22—81no—
257Dic22#13112yes—
258C8×C11—21no—
259C8×C11—21no—
260C8×C11—21no—
261C8×C11—21no—
262C8×C11—41no—
263C8×C11—41no—
264C8×C11—41no—
265C11⋊C8—21no—
266C11⋊C8—21no—
267C11⋊C8—21no—
268C11⋊C8—41no—
269C11⋊C8—41no—
270C11⋊C8—41no—
271C11⋊C8#13712yes—
272#533—111no—
273C4×#41—111no—
274#485—111no—
275#485—111no—
276#475—111no—
277#474—111no—
278#462—111no—
279#461—111no—
280#452—111no—
281#452—111no—
282#446—111no—
283#446—221no—
284#446—221no—
285#446C2×D1111yescharacteristic
286C8×Q8—111no—
287C8×Q8—111no—
288C8×Q8—111no—
289C8×Q8—111no—
290C4×Q16—111no—
291C4×Q16—111no—
292C4×SD16—111no—
293C4×SD16C2×D1111yescharacteristic
294#436—111no—
295#436—221no—
296#436—221no—
297#436C2×D1111yescharacteristic
298#432—111no—
299#432—221no—
300#431—111no—
301#431—111no—
302#424—221no—
303C2×C4⋊C8—111no—
304#405—221no—
305C4×M16—111no—
306C4×M16—221no—
307#335—111no—
308#335C2×D1111yescharacteristic
309#334—111no—
310#334—111no—
311Q8⋊C8—111no—
312Q8⋊C8—111no—
313Q8⋊C8—111no—
314Q8⋊C8—111no—
315Q8⋊C8—111no—
316Q8⋊C8C2×D1111yescharacteristic
317D4⋊C8—111no—
318D4⋊C8C2×D1111yescharacteristic
319#322—111no—
320#322—111no—
321#322C2×D1111yescharacteristic
322C82—111no—
323C22×C11—41no—
324C22×C11—41no—
325C22×C11—41no—
326C22×C11C2×C4×D411yescharacteristic
327C2×D11—21no—
328C2×D11—21no—
329C2×D11—21no—
330C4×C11—21no—
331C4×C11—41no—
332C4×C11—41no—
333C4×C11—41no—
334C4×C11C2×#13111yescharacteristic
335C4×C11#56811yescharacteristic
336C4×C11C2×#13711yescharacteristic
337C4×C11#57511yescharacteristic
338Dic11—22no—
339Dic11—21no—
340Dic11—21no—
341Dic11—21no—
342Dic11—41no—
343Dic11—41no—
344Dic11—41no—
345C2×#41—111no—
346C2×Q16—111no—
347C2×Q16—111no—
348C2×SD16—111no—
349C2×SD16C4×D1111yescharacteristic
350C2×M16—21no—
351C2×M16—111no—
352C2×M16—111no—
353C2×M16—221no—
354C22×C8—221no—
355C4⋊Q8—111no—
356C4⋊Q8—111no—
357#125—221no—
358C22⋊Q8—111no—
359C22⋊Q8—111no—
360C22⋊Q8—221no—
361C4×Q8—111no—
362C4×Q8—111no—
363C4×Q8—111no—
364C4×Q8—221no—
365C4×Q8C22×D1111yescharacteristic
366C4×D4—111no—
367C4×D4—221no—
368C4×D4—221no—
369C4×D4C22×D1111yescharacteristic
370#117—111no—
371#117—221no—
372#117—221no—
373C2×C42—111no—
374C2×C42—221no—
375#107—111no—
376#107—111no—
377#106—111no—
378#106C4×D1111yescharacteristic
379C4⋊C8—21no—
380C4⋊C8—111no—
381C4⋊C8—111no—
382C4⋊C8—111no—
383C4⋊C8—111no—
384C4⋊C8—221no—
385C4⋊C8—221no—
386C4⋊C8—221no—
387C4⋊C8—221no—
388C4⋊C8—221no—
389C4⋊C8—221no—
390C4⋊C8—221no—
391C4⋊C8C22×D1111yescharacteristic
392C4⋊C8C22×D1111yescharacteristic
393#103—111no—
394#103—111no—
395#103—111no—
396#103—111no—
397#103—111no—
398#103C4×D1111yescharacteristic
399#102—111no—
400#102C4×D1111yescharacteristic
401C22⋊C8—21no—
402C22⋊C8—111no—
403C22⋊C8—111no—
404C22⋊C8—221no—
405C22⋊C8—221no—
406C22⋊C8—221no—
407#97—21no—
408#97—111no—
409#97—111no—
410#97—221no—
411#97—221no—
412C4×C8—111no—
413C4×C8—111no—
414C4×C8—111no—
415C4×C8—221no—
416C4×C8—221no—
417C4×C8—221no—
418C4×C8—221no—
419C4×C8C22×D1111yescharacteristic
420C4×C8C22×D1111yescharacteristic
421C4×C8C22×D1111yescharacteristic
422C2×C11—81no—
423C2×C11#293311yescharacteristic
424C2×C11C4×#13711yescharacteristic
425C2×C11#295711yescharacteristic
426D11—41no—
427#41—222no—
428#41—441no—
429C2×Q8—111no—
430C2×Q8—111no—
431C2×Q8—221no—
432C2×Q8C2×C4×D1111yescharacteristic
433C2×D4—221no—
434C2×D4C2×C4×D1111yescharacteristic
435C22×C4—21no—
436C22×C4—111no—
437C22×C4—111no—
438C22×C4—111no—
439C22×C4—221no—
440C22×C4—221no—
441Q16—222no—
442Q16—222no—
443SD16—41no—
444SD16—441no—
445M16—42no—
446M16—222no—
447M16—441no—
448M16—442no—
449C2×C8—21no—
450C2×C8—21no—
451C2×C8—21no—
452C2×C8—111no—
453C2×C8—111no—
454C2×C8—111no—
455C2×C8—111no—
456C2×C8—221no—
457C2×C8—221no—
458C2×C8—221no—
459C2×C8—442no—
460C2×C8C2×C4×D1111yescharacteristic
461C2×C8C2×C4×D1111yescharacteristic
462C2×C8D4×D1111yescharacteristic
463C2×C8D4×D1111yescharacteristic
464C4⋊C4—21no—
465C4⋊C4—111no—
466C4⋊C4—111no—
467C4⋊C4—221no—
468C4⋊C4—221no—
469C4⋊C4—221no—
470C4⋊C4—221no—
471C4⋊C4—221no—
472C4⋊C4—221no—
473C4⋊C4—221no—
474C4⋊C4—221no—
475C4⋊C4C2×C4×D1111yescharacteristic
476C4⋊C4C2×C4×D1111yescharacteristic
477C22⋊C4—21no—
478C22⋊C4—221no—
479C22⋊C4—221no—
480C22⋊C4—221no—
481C22⋊C4—221no—
482C42—21no—
483C42—111no—
484C42—111no—
485C42—111no—
486C42—221no—
487C42—221no—
488C42—221no—
489C42—221no—
490C42C23×D1111yescharacteristic
491C11#1801311yescharacteristic, complemented, Sylow
492C23—21no—
493C23—111no—
494Q8—21no—
495Q8—21no—
496Q8—112no—
497Q8—221no—
498Q8—221no—
499Q8—221no—
500Q8—881no—
501D4—21no—
502D4—21no—
503D4—442no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—41no—
508C2×C4—41no—
509C2×C4—111no—
510C2×C4—111no—
511C2×C4—111no—
512C2×C4—221no—
513C2×C4—221no—
514C2×C4—221no—
515C2×C4—221no—
516C2×C4—221no—
517C2×C4—221no—
518C2×C4—221no—
519C2×C4—221no—
520C2×C4—441no—
521C2×C4—442no—
522C2×C4—881no—
523C2×C4C22×C4×D1111yescharacteristic
524C2×C4C2×D4×D1111yescharacteristic
525C2×C4#41×D1111yescharacteristic
526C8—21no—
527C8—21no—
528C8—21no—
529C8—21no—
530C8—41no—
531C8—41no—
532C8—41no—
533C8—112no—
534C8—221no—
535C8—221no—
536C8—221no—
537C8—441no—
538C8—441no—
539C8—441no—
540C22—41no—
541C22—41no—
542C22—41no—
543C22—221no—
544C22—221no—
545C22—221no—
546C22C4×D4×D1111yescharacteristic
547C4—21no—
548C4—41no—
549C4—41no—
550C4—41no—
551C4—221no—
552C4—221no—
553C4—222no—
554C4—221no—
555C4—441no—
556C4—441no—
557C4—441no—
558C4#1062327611yescharacteristic
559C4D11×#13111yescharacteristic
560C4#1062330411yescharacteristic
561C4D11×#13711yescharacteristic
562C2—81no—
563C2—441no—
564C2#1307734511yescharacteristic
565C2#1307743811yescharacteristic
566C2#1307753011yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
FittingC11×#1592C2
socleC22×C11C2×C4×D4
prime radicalC2×#4341C2×C4
cosocleC42×C11C24
hypercenter#1592D11
hypocenterC11#18013
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ #1592

Complements

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

NH ≅ G/Ntype
3. #13077564C2semidirect
4. #13067509C2semidirect
5. #13067492C2semidirect
6. #13067485C2semidirect
7. #13067465C2semidirect
8. #13067460C2semidirect
9. #13067436C2semidirect
10. #13067420C2semidirect
11. #13067400C2semidirect
12. #13067087C2semidirect
14. #13066912C2semidirect
15. C11×#1592C2semidirect
212. #1592D11semidirect
491. C11#18013semidirect

Maximal subgroups

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

subgroupindex
#130786832
#130776322
#130775642
#130675092
#130674922
#130674852
#130674652
#130674602
#130674362
#130674202
#130674002
#130670872
#130670002
#130669122
C11×#15922
#1801311