Finite Group Databasebeta

← #14724970

Subgroups — #14724970

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#13078698C211yesmaximal, characteristic
2#13077778C211yesmaximal, characteristic
3#13077703C211yesmaximal, characteristic, complemented
4#13067514C211yesmaximal, characteristic, complemented
5#13067508C211yesmaximal, characteristic, complemented
6#13067496C211yesmaximal, characteristic, complemented
7#13067489C211yesmaximal, characteristic, complemented
8#13067489C211yesmaximal, characteristic, complemented
9#13067475C211yesmaximal, characteristic, complemented
10C8×Dic44C211yesmaximal, characteristic, complemented
11C8×#4314C211yesmaximal, characteristic, complemented
12#13067401C211yesmaximal, characteristic, complemented
13#13067077C211yesmaximal, characteristic
14C2×#10622094C211yesmaximal, characteristic, complemented
15C11×#1450C211yesmaximal, characteristic, complemented
16#10623010C2211yescharacteristic
17C2×C4×Dic22C2211yescharacteristic
18C11×#431C2211yescharacteristic
19C11×#431C2211yescharacteristic
20C2×C4×C8×C11C2211yescharacteristic
21#10622539C2211yescharacteristic
22C2×C4⋊(C11⋊C8)C2211yescharacteristic
23#10622458C411yescharacteristic
24#10622458C411yescharacteristic
25#10622453—21no—
26#10622452—21no—
27#10622442C411yescharacteristic
28#10622442C411yescharacteristic
29#10622441—21no—
30#10622441—21no—
31#10622352C411yescharacteristic
32#10622351C411yescharacteristic
33#10622349C411yescharacteristic
34#10622343—21no—
35(C22⋊D11)⋊C8—21no—
36#10622334C411yescharacteristic
37#10622332—21no—
38#10622331—21no—
39C4×Dic44C2211yescharacteristic
40C4×Dic44C2211yescharacteristic
41C4×#4314C2211yescharacteristic
42C4×#4314C2211yescharacteristic
43#10622301C2211yescharacteristic
44C8×D44C2211yescharacteristic
45#10622292C2211yescharacteristic
46#10622292C2211yescharacteristic
47#10622292C2211yescharacteristic
48C8×Dic22C2211yescharacteristic
49C8×Dic22C2211yescharacteristic
50C8×Dic22C2211yescharacteristic
51C11×#322C2211yescharacteristic
52C11×#322C2211yescharacteristic
53C82×C11C2211yescharacteristic
54C82×C11C2211yescharacteristic
55#10622097C2211yescharacteristic
56#10622097C2211yescharacteristic
57#10622096C2211yescharacteristic
58#10622096C2211yescharacteristic
59#10622095C2211yescharacteristic
60#10622095C2211yescharacteristic
61#10622094C2211yescharacteristic
62#10622094C2211yescharacteristic
63#10622094C2211yescharacteristic
64#10622094C2211yescharacteristic
65#10622094C2211yescharacteristic
66#10622094C2211yescharacteristic
67C22×Dic22C2×C411yescharacteristic
68C22×C8×C11—21no—
69C2×C42×C11C2311yescharacteristic
70#66983C2×C411yescharacteristic
71#66982—21no—
72C4×C22⋊D11—21no—
73C2×C4⋊Dic11C2×C411yescharacteristic
74#66977C2×C411yescharacteristic
75C2×Dic11⋊C4—21no—
76C2×C4×Dic11—21no—
77C22×C11⋊C8—21no—
78C2×Dic44C2×C411yescharacteristic
79C2×Dic44C2×C411yescharacteristic
80C2×#4314C2×C411yescharacteristic
81C2×#4314C2×C411yescharacteristic
82C2×#4313—21no—
83C2×C8×D11—21no—
84#66929—21no—
85#66928C2×C411yescharacteristic
86C4×D44C2311yescharacteristic
87#66925—21no—
88#66923C2×C411yescharacteristic
89C4×Dic22—21no—
90C4×Dic22—21no—
91C4×Dic22C2×C411yescharacteristic
92C4×Dic22C2×C411yescharacteristic
93C4×Dic22C2311yescharacteristic
94C4×Dic22C2311yescharacteristic
95C4×Dic22C2311yescharacteristic
96C11×C4⋊C8C2×C411yescharacteristic
97C11×C4⋊C8C2×C411yescharacteristic
98C11×C4⋊C8D411yescharacteristic
99C11×C4⋊C8D411yescharacteristic
100C11×C22⋊C8C2×C411yescharacteristic
101C11×C22⋊C8C2×C411yescharacteristic
102C11×C22⋊C8D411yescharacteristic
103C11×C22⋊C8D411yescharacteristic
104C4×C8×C11—21no—
105C4×C8×C11C2311yescharacteristic
106C4×C8×C11C2311yescharacteristic
107C4×C8×C11C2311yescharacteristic
108C4×C8×C11C2311yescharacteristic
109C4×C8×C11C2311yescharacteristic
110C4×C8×C11C2311yescharacteristic
111C22⋊(C11⋊C8)—21no—
112#66885C2×C411yescharacteristic
113#66885C2×C411yescharacteristic
114(C2×D11)⋊C8—21no—
115(C2×D11)⋊C8—21no—
116#66882C2×C411yescharacteristic
117#66882C2×C411yescharacteristic
118#66881C2×C411yescharacteristic
119#66881C2×C411yescharacteristic
120#66880C2×C411yescharacteristic
121#66880C2×C411yescharacteristic
122#66880C2×C411yescharacteristic
123#66880C2×C411yescharacteristic
124#66880C2×C411yescharacteristic
125#66880C2×C411yescharacteristic
126#66879—21no—
127#66879—21no—
128#66879—21no—
129Dic11⋊C8—21no—
130Dic11⋊C8—21no—
131Dic11⋊C8—21no—
132Dic11⋊C8—21no—
133Dic11⋊C8—21no—
134Dic11⋊C8—21no—
135C8×Dic11—21no—
136C8×Dic11—21no—
137C8×Dic11—21no—
138C4⋊(C11⋊C8)—21no—
139C4⋊(C11⋊C8)C2311yescharacteristic
140C4⋊(C11⋊C8)C2311yescharacteristic
141C4⋊(C11⋊C8)C2311yescharacteristic
142C4⋊(C11⋊C8)C2311yescharacteristic
143#66867—21no—
144#18017—111nomaximal, Sylow
145C22×C4×C11C22×C411yescharacteristic
146C22×C4×C11C2×D411yescharacteristic
147C22×C4×C11#4111yescharacteristic
148C2×C22⋊D11—21no—
149C22×Dic11—21no—
150C22×Dic11—21no—
151C2×D44C22×C411yescharacteristic
152C2×C4×D11—21no—
153C2×Dic22—22no—
154C2×Dic22—21no—
155C2×Dic22—41no—
156C2×Dic22C22×C411yescharacteristic
157C2×Dic22C22×C411yescharacteristic
158C2×Dic22C22×C411yescharacteristic
159C2×C8×C11—24no—
160C2×C8×C11—21no—
161C2×C8×C11—21no—
162C2×C8×C11C22×C411yescharacteristic
163C2×C8×C11C22×C411yescharacteristic
164C2×C8×C11C22×C411yescharacteristic
165C2×C8×C11C22×C411yescharacteristic
166C2×C8×C11C2×D411yescharacteristic
167C2×C8×C11C2×D411yescharacteristic
168C2×C8×C11C2×D411yescharacteristic
169C2×C8×C11C2×D411yescharacteristic
170C42×C11C22×C411yescharacteristic
171C42×C11C2×D411yescharacteristic
172C42×C11#4111yescharacteristic
173C42×C11C2411yescharacteristic
174C22⋊Dic11—21no—
175(C2×D11)⋊C4—21no—
176(C2×D11)⋊C4—21no—
177(C2×D11)⋊C4—21no—
178(C2×D11)⋊C4—21no—
179C4⋊Dic11—21no—
180C4⋊Dic11C22×C411yescharacteristic
181C4⋊Dic11C22×C411yescharacteristic
182C4⋊Dic11C22×C411yescharacteristic
183C4⋊Dic11C22×C411yescharacteristic
184Dic11⋊C4—21no—
185Dic11⋊C4—21no—
186Dic11⋊C4—21no—
187Dic11⋊C4—21no—
188Dic11⋊C4—21no—
189Dic11⋊C4—21no—
190Dic11⋊C4—21no—
191Dic11⋊C4—21no—
192C4×Dic11—21no—
193C4×Dic11—21no—
194C4×Dic11—21no—
195C4×Dic11—21no—
196C4×Dic11—21no—
197C2×C11⋊C8—21no—
198C2×C11⋊C8—21no—
199C2×C11⋊C8—21no—
200C2×C11⋊C8—21no—
201C2×C11⋊C8—81no—
202Dic44—22no—
203Dic44—41no—
204#4314—22no—
205#4314—41no—
206#4313—81no—
207C8×D11—81no—
208#3108—111no—
209#2994—111no—
210#2984—111no—
211#1591—111no—
212#1590—111no—
213#1588—111no—
214#1587—111no—
215#1587—111no—
216#1585—111no—
217C8×Q16—111no—
218C8×SD16—111no—
219#1573—111no—
220#1494—111no—
221C2×Q8⋊C8—111no—
222#1450D1111yescharacteristic, complemented
223C23×C11C4×D411yescharacteristic
224C22×D11—21no—
225C2×C4×C11—22no—
226C2×C4×C11—21no—
227C2×C4×C11—21no—
228C2×C4×C11—21no—
229C2×C4×C11—21no—
230C2×C4×C11C4×D411yescharacteristic
231C2×C4×C11C4×D411yescharacteristic
232C2×C4×C11C4×D411yescharacteristic
233C2×C4×C11C23×C411yescharacteristic
234C2×C4×C11C22×D411yescharacteristic
235C2×C4×C11C2×#4111yescharacteristic
236C22⋊D11—42no—
237C2×Dic11—21no—
238C2×Dic11—21no—
239C2×Dic11—21no—
240C2×Dic11—21no—
241C2×Dic11—21no—
242C2×Dic11—21no—
243C2×Dic11—21no—
244C2×Dic11—42no—
245C2×Dic11—42no—
246D44—21no—
247D44—21no—
248C4×D11—41no—
249C4×D11—41no—
250Dic22—21no—
251Dic22—21no—
252Dic22—21no—
253Dic22—21no—
254Dic22—21no—
255Dic22—42no—
256Dic22#13112yes—
257C8×C11—22no—
258C8×C11—22no—
259C8×C11—21no—
260C8×C11—21no—
261C8×C11—21no—
262C8×C11—21no—
263C8×C11—21no—
264C8×C11—21no—
265C8×C11—21no—
266C8×C11—21no—
267C11⋊C8—41no—
268C11⋊C8—41no—
269C11⋊C8—41no—
270C11⋊C8—41no—
271#529—111no—
272C2×C4×Q8—111no—
273#483—111no—
274#480—111no—
275#479—111no—
276#479—111no—
277#464—111no—
278#464—111no—
279#451—111no—
280#448—111no—
281#446—111no—
282#446—111no—
283#446—111no—
284#446—221no—
285#446—221no—
286C8×Q8—111no—
287C8×Q8—111no—
288C8×Q8—111no—
289C4×Q16—111no—
290C4×Q16—111no—
291C4×SD16—111no—
292C4×SD16—111no—
293#436—111no—
294#435—221no—
295C8×D4—111no—
296C8×D4—221no—
297#433—221no—
298#432—111no—
299#432—221no—
300#431—221no—
301#431C2×D1111yescharacteristic
302#431C2×D1111yescharacteristic
303#424—221no—
304C2×C4⋊C8—111no—
305C2×C4×C8C2×D1111yescharacteristic
306#335—111no—
307#335—111no—
308#334—111no—
309#334—111no—
310Q8⋊C8—111no—
311Q8⋊C8—111no—
312Q8⋊C8—111no—
313Q8⋊C8—111no—
314Q8⋊C8—111no—
315Q8⋊C8—111no—
316D4⋊C8—111no—
317D4⋊C8—111no—
318#322C2×D1111yescharacteristic
319#322C2×D1111yescharacteristic
320C82C2×D1111yescharacteristic
321C82C2×D1111yescharacteristic
322C22×C11—21no—
323C22×C11—21no—
324C22×C11#44312yes—
325C22×C11C2×C4×D411yescharacteristic
326C2×D11—41no—
327C2×D11—41no—
328C2×D11—41no—
329C4×C11—21no—
330C4×C11—21no—
331C4×C11—21no—
332C4×C11—21no—
333C4×C11C2×#13111yescharacteristic
334C4×C11#56811yescharacteristic
335C4×C11#57711yescharacteristic
336C4×C11#57811yescharacteristic
337Dic11—22no—
338Dic11—41no—
339Dic11—41no—
340Dic11—41no—
341Dic11—41no—
342Dic11—41no—
343Dic11—41no—
344C22×Q8—111no—
345C2×Q16—111no—
346C2×Q16—111no—
347C2×SD16—111no—
348C2×SD16—111no—
349C2×M16—221no—
350C22×C8—21no—
351C22×C8—221no—
352C22×C8—221no—
353#126—221no—
354#125—111no—
355#124—111no—
356#123—221no—
357C22⋊Q8—111no—
358#121—111no—
359C4×Q8—111no—
360C4×Q8—111no—
361C4×Q8—111no—
362C4×Q8—111no—
363C4×Q8—111no—
364C4×Q8—221no—
365C4×Q8—221no—
366C4×D4—111no—
367C4×D4—221no—
368#117—221no—
369C2×C4⋊C4—111no—
370C2×C4⋊C4—221no—
371C2×C42—221no—
372C2×C42C22×D1111yescharacteristic
373#107—111no—
374#107—111no—
375#106—111no—
376#106—111no—
377C4⋊C8—111no—
378C4⋊C8—111no—
379C4⋊C8—111no—
380C4⋊C8—111no—
381C4⋊C8—221no—
382C4⋊C8—221no—
383C4⋊C8—221no—
384C4⋊C8—221no—
385C4⋊C8—221no—
386C4⋊C8—221no—
387C4⋊C8—221no—
388C4⋊C8C4×D1111yescharacteristic
389C4⋊C8C4×D1111yescharacteristic
390C4⋊C8D4411yescharacteristic
391C4⋊C8D4411yescharacteristic
392#103—111no—
393#103—111no—
394#103—111no—
395#103—111no—
396#103—111no—
397#103—111no—
398#102—111no—
399#102—111no—
400C22⋊C8—221no—
401C22⋊C8—221no—
402C22⋊C8—221no—
403C22⋊C8C4×D1111yescharacteristic
404C22⋊C8C4×D1111yescharacteristic
405C22⋊C8D4411yescharacteristic
406C22⋊C8D4411yescharacteristic
407#97—221no—
408#97—221no—
409#97—221no—
410#97—221no—
411C4×C8—21no—
412C4×C8—221no—
413C4×C8—221no—
414C4×C8—221no—
415C4×C8C22×D1111yescharacteristic
416C4×C8C22×D1111yescharacteristic
417C4×C8C22×D1111yescharacteristic
418C4×C8C22×D1111yescharacteristic
419C4×C8C22×D1111yescharacteristic
420C4×C8C22×D1111yescharacteristic
421C2×C11—22no—
422C2×C11#293311yescharacteristic
423C2×C11#294711yescharacteristic
424C2×C11C2×#44311yescharacteristic
425D11—81no—
426C2×Q8—111no—
427C2×Q8—111no—
428C2×Q8—111no—
429C2×Q8—222no—
430C2×Q8—221no—
431C2×Q8—441no—
432C2×D4—111no—
433C2×D4—221no—
434C22×C4—221no—
435C22×C4—221no—
436C22×C4—221no—
437C22×C4C2×C4×D1111yescharacteristic
438C22×C4C2×D4411yescharacteristic
439C22×C4#433911yescharacteristic
440Q16—222no—
441Q16—441no—
442SD16—222no—
443SD16—441no—
444M16—881no—
445C2×C8—24no—
446C2×C8—21no—
447C2×C8—21no—
448C2×C8—221no—
449C2×C8—221no—
450C2×C8—221no—
451C2×C8—221no—
452C2×C8—881no—
453C2×C8—881no—
454C2×C8C2×C4×D1111yescharacteristic
455C2×C8C2×C4×D1111yescharacteristic
456C2×C8C2×C4×D1111yescharacteristic
457C2×C8C2×C4×D1111yescharacteristic
458C2×C8C2×D4411yescharacteristic
459C2×C8C2×D4411yescharacteristic
460C2×C8C2×D4411yescharacteristic
461C2×C8C2×D4411yescharacteristic
462C4⋊C4—111no—
463C4⋊C4—111no—
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⋊C4—221no—
474C4⋊C4—221no—
475C22⋊C4—221no—
476C22⋊C4—221no—
477C22⋊C4—221no—
478C22⋊C4—221no—
479C22⋊C4—221no—
480C42—221no—
481C42—221no—
482C42—221no—
483C42—221no—
484C42—221no—
485C42C2×C4×D1111yescharacteristic
486C42C2×D4411yescharacteristic
487C42#433911yescharacteristic
488C42C23×D1111yescharacteristic
489C11#1801711yescharacteristic, complemented, Sylow
490C23—221no—
491C23C4×D4411yescharacteristic
492Q8—112no—
493Q8—221no—
494Q8—221no—
495Q8—221no—
496Q8—221no—
497Q8—221no—
498Q8—442no—
499D4—221no—
500D4—221no—
501D4—442no—
502C2×C4—22no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—221no—
508C2×C4—221no—
509C2×C4—221no—
510C2×C4—221no—
511C2×C4—221no—
512C2×C4—221no—
513C2×C4—221no—
514C2×C4—442no—
515C2×C4—442no—
516C2×C4—441no—
517C2×C4—441no—
518C2×C4C4×D4411yescharacteristic
519C2×C4C4×D4411yescharacteristic
520C2×C4C4×D4411yescharacteristic
521C2×C4C22×C4×D1111yescharacteristic
522C2×C4C22×D4411yescharacteristic
523C2×C4C2×#433911yescharacteristic
524C8—22no—
525C8—22no—
526C8—21no—
527C8—21no—
528C8—21no—
529C8—21no—
530C8—21no—
531C8—21no—
532C8—21no—
533C8—21no—
534C8—441no—
535C8—441no—
536C8—441no—
537C8—441no—
538C22—21no—
539C22—21no—
540C22—441no—
541C22—441no—
542C22—441no—
543C22#1062231312yes—
544C22C2×C4×D4411yescharacteristic
545C4—21no—
546C4—21no—
547C4—21no—
548C4—21no—
549C4—222no—
550C4—441no—
551C4—441no—
552C4—441no—
553C4—441no—
554C4—441no—
555C4—441no—
556C4D11×#13111yescharacteristic
557C4#1062328111yescharacteristic
558C4#1062328211yescharacteristic
559C4#1062328411yescharacteristic
560C2—22no—
561C2—881no—
562C2#1307734411yescharacteristic
563C2#1307746111yescharacteristic
564C2C2×#1062231311yescharacteristic
subgroupG/H
centerC2×C4C22×D44
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
FittingC11×#1450C2
socleC22×C11C2×C4×D4
prime radical#66983C2×C4
cosocleC42×C11C24
hypercenter#1450D11
hypocenterC11#18017
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ #431 ◁ #1450

Complements

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

NH ≅ G/Ntype
3. #13077703C2semidirect
4. #13067514C2semidirect
5. #13067508C2semidirect
6. #13067496C2semidirect
7. #13067489C2semidirect
8. #13067489C2semidirect
9. #13067475C2semidirect
10. C8×Dic44C2semidirect
11. C8×#4314C2semidirect
12. #13067401C2semidirect
14. C2×#10622094C2semidirect
15. C11×#1450C2semidirect
222. #1450D11semidirect
489. C11#18017semidirect

Maximal subgroups

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

subgroupindex
#130786982
#130777782
#130777032
#130675142
#130675082
#130674962
#130674892
#130674752
C8×Dic442
C8×#43142
#130674012
#130670772
C2×#106220942
C11×#14502
#1801711