Finite Group Databasebeta

← #14723877

Subgroups — #14723877

Order 2816.

598 conjugacy classes of subgroups.

The subgroup lattice has 564 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13078685C211yesmaximal, characteristic
2#13077726C211yesmaximal, characteristic
3#13077712C211yesmaximal, characteristic, complemented
4#13067475C211yesmaximal, characteristic, complemented
5#13067466C211yesmaximal, characteristic, complemented
6#13067450C211yesmaximal, characteristic, complemented
7#13067432C211yesmaximal, characteristic, complemented
8#13067431C211yesmaximal, characteristic, complemented
9Q16×C11⋊C8C211yesmaximal, characteristic, complemented
10#13067415C211yesmaximal, characteristic, complemented
11#13067398C211yesmaximal, characteristic, complemented
12#13067049C211yesmaximal, characteristic
13#13067017C211yesmaximal, characteristic, complemented
14#13066917C211yesmaximal, 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
25Q8×C11⋊C8C2211yescharacteristic
26Q8×C11⋊C8C2211yescharacteristic
27#10622503C411yescharacteristic
28#10622501C411yescharacteristic
29#10622453—21no—
30#10622448C2211yescharacteristic
31#10622447—21no—
32#10622447C2211yescharacteristic
33D11×C4⋊C8—21no—
34D11×C4⋊C8C2211yescharacteristic
35#10622444—21no—
36#10622443C2211yescharacteristic
37#10622431C411yescharacteristic
38#10622428C411yescharacteristic
39#10622423C411yescharacteristic
40#10622404C411yescharacteristic
41#10622322—21no—
42#10622314—21no—
43C4×#4314C2211yescharacteristic
44C8×D44—21no—
45C8×D44C2211yescharacteristic
46#10622298—21no—
47#10622298C2211yescharacteristic
48#10622298C2211yescharacteristic
49#10622298C2211yescharacteristic
50#10622292C2211yescharacteristic
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
65#10622092C2211yescharacteristic
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×C8×D11—21no—
78C2×C8×D11—21no—
79C2×C8×D11—21no—
80#66950C2×C411yescharacteristic
81#66949—21no—
82#66946—21no—
83#66946C2×C411yescharacteristic
84#66945—21no—
85#66945C2×C411yescharacteristic
86#66942—21no—
87#66941C2×C411yescharacteristic
88C4×D44—21no—
89C4×D44C2311yescharacteristic
90#66925—21no—
91C42×D11—21no—
92C42×D11C2311yescharacteristic
93C4×Dic22—21no—
94C4×Dic22C2311yescharacteristic
95C11×#107C2×C411yescharacteristic
96C11×C4⋊C8—21no—
97C11×C4⋊C8—21no—
98C11×C4⋊C8C2311yescharacteristic
99C11×C4⋊C8C2311yescharacteristic
100C11×#103C2×C411yescharacteristic
101C11×#103C2×C411yescharacteristic
102C11×#97—21no—
103C4×C8×C11—21no—
104C4×C8×C11C2311yescharacteristic
105C4×C8×C11C2311yescharacteristic
106C4×C8×C11C2311yescharacteristic
107#66899C2×C411yescharacteristic
108#66899C2×C411yescharacteristic
109#66885C2×C411yescharacteristic
110(C2×D11)⋊C8—21no—
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—
121#66879—21no—
122Dic11⋊C8—21no—
123Dic11⋊C8—21no—
124Dic11⋊C8—21no—
125Dic11⋊C8—21no—
126Dic11⋊C8C2×C411yescharacteristic
127Dic11⋊C8C2×C411yescharacteristic
128Dic11⋊C8D411yescharacteristic
129Dic11⋊C8D411yescharacteristic
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
139C4×C11⋊C8—21no—
140C4×C11⋊C8—21no—
141C4×C11⋊C8C2311yescharacteristic
142C4×C11⋊C8C2311yescharacteristic
143C4×C11⋊C8C2311yescharacteristic
144#17921—111nomaximal, Sylow
145C2×Q8×C11C22×C411yescharacteristic
146C2×Q8×C11C22×C411yescharacteristic
147#4343—22no—
148#4343—22no—
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—22no—
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—22no—
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—
204C8×D11—81no—
205C8×D11—81no—
206C8×D11—81no—
207#3107—111no—
208#2988—111no—
209#2985—111no—
210#1587D1111yescharacteristic, complemented
211#1585—111no—
212#1584—111no—
213#1582—111no—
214#1579—111no—
215SD16⋊C8—111no—
216C8×Q16—111no—
217C8×SD16—111no—
218#1573—111no—
219#1488—111no—
220#1481—111no—
221#1454—111no—
222C22×D11—21no—
223C22×D11C4×D411yescharacteristic
224Q8×C11—21no—
225Q8×C11—21no—
226Q8×C11—21no—
227Q8×C11#13112yes—
228C2×C4×C11—21no—
229C2×C4×C11—21no—
230C2×C4×C11—21no—
231C2×C4×C11—21no—
232C2×C4×C11C23×C411yescharacteristic
233C2×C4×C11C22×D411yescharacteristic
234C2×C4×C11C2×#4111yescharacteristic
235C2×Dic11—21no—
236C2×Dic11—21no—
237C2×Dic11—21no—
238C2×Dic11C4×D411yescharacteristic
239C2×Dic11C4×D411yescharacteristic
240C2×Dic11C4×D411yescharacteristic
241D44—24no—
242D44—21no—
243D44#13112yes—
244C4×D11—24no—
245C4×D11—21no—
246C4×D11—21no—
247C4×D11—21no—
248C4×D11—21no—
249C4×D11—41no—
250C4×D11—41no—
251C4×D11—41no—
252C4×D11—81no—
253Dic22—21no—
254Dic22—21no—
255Dic22—81no—
256C8×C11—21no—
257C8×C11—21no—
258C8×C11—21no—
259C8×C11—21no—
260C8×C11—41no—
261C8×C11—41no—
262C8×C11—41no—
263C11⋊C8—21no—
264C11⋊C8—21no—
265C11⋊C8—21no—
266C11⋊C8—21no—
267C11⋊C8—41no—
268C11⋊C8—41no—
269C11⋊C8—41no—
270#533—111no—
271C4×#41—111no—
272#485—111no—
273#485—111no—
274#475—111no—
275#474—111no—
276#462—111no—
277#461—111no—
278#452—111no—
279#452—111no—
280#446—111no—
281#446—221no—
282#446—221no—
283#446C2×D1111yescharacteristic
284C8×Q8—111no—
285C8×Q8—111no—
286C8×Q8—111no—
287C8×Q8C2×D1111yescharacteristic
288C4×Q16—111no—
289C4×Q16C2×D1111yescharacteristic
290C4×SD16—111no—
291C4×SD16—111no—
292C8×D4—111no—
293C8×D4—111no—
294C8×D4—221no—
295C8×D4—221no—
296#433—221no—
297#433—221no—
298#432—111no—
299#431—111no—
300#431—111no—
301#431—111no—
302#431—221no—
303C2×C4⋊C8—111no—
304C2×C4⋊C8—221no—
305#335—111no—
306#335—111no—
307#334—111no—
308#334C2×D1111yescharacteristic
309Q8⋊C8—111no—
310Q8⋊C8—111no—
311Q8⋊C8—111no—
312Q8⋊C8—111no—
313Q8⋊C8C2×D1111yescharacteristic
314Q8⋊C8C2×D1111yescharacteristic
315D4⋊C8—111no—
316D4⋊C8—111no—
317#322—111no—
318#322—111no—
319#322C2×D1111yescharacteristic
320C82—111no—
321C22×C11C2×C4×D411yescharacteristic
322C2×D11—22no—
323C2×D11—21no—
324C2×D11—21no—
325C2×D11—21no—
326C2×D11—41no—
327C2×D11—41no—
328C4×C11—22no—
329C4×C11—21no—
330C4×C11—41no—
331C4×C11—41no—
332C4×C11—41no—
333C4×C11C2×#13111yescharacteristic
334C4×C11C2×#13111yescharacteristic
335C4×C11#57711yescharacteristic
336C4×C11#57811yescharacteristic
337Dic11—21no—
338Dic11—21no—
339Dic11—21no—
340Dic11—41no—
341Dic11—41no—
342Dic11—41no—
343C2×#41—111no—
344C2×Q16—111no—
345C2×Q16C4×D1111yescharacteristic
346C2×SD16—111no—
347C2×SD16—111no—
348C22×C8—221no—
349C22×C8—221no—
350C22×C8—221no—
351C4⋊Q8—111no—
352C4⋊Q8—111no—
353#125—221no—
354C22⋊Q8—111no—
355C22⋊Q8—111no—
356C22⋊Q8—221no—
357C4×Q8—111no—
358C4×Q8—111no—
359C4×Q8—221no—
360C4×Q8C22×D1111yescharacteristic
361C4×Q8C22×D1111yescharacteristic
362C4×D4—111no—
363C4×D4—111no—
364C4×D4—221no—
365C4×D4—221no—
366#117—111no—
367#117—221no—
368#117—221no—
369C2×C42—111no—
370C2×C42—221no—
371#107—111no—
372#107C4×D1111yescharacteristic
373#106—111no—
374#106—111no—
375C4⋊C8—21no—
376C4⋊C8—21no—
377C4⋊C8—111no—
378C4⋊C8—111no—
379C4⋊C8—111no—
380C4⋊C8—111no—
381C4⋊C8—111no—
382C4⋊C8—111no—
383C4⋊C8—221no—
384C4⋊C8—221no—
385C4⋊C8—221no—
386C4⋊C8—221no—
387C4⋊C8—221no—
388C4⋊C8—221no—
389C4⋊C8C22×D1111yescharacteristic
390C4⋊C8C22×D1111yescharacteristic
391#103—111no—
392#103—111no—
393#103—111no—
394#103—111no—
395#103C4×D1111yescharacteristic
396#103C4×D1111yescharacteristic
397#102—111no—
398#102—111no—
399C22⋊C8—111no—
400C22⋊C8—111no—
401C22⋊C8—111no—
402C22⋊C8—111no—
403C22⋊C8—221no—
404C22⋊C8—221no—
405C22⋊C8—221no—
406C22⋊C8—221no—
407#97—21no—
408#97—221no—
409#97—221no—
410C4×C8—21no—
411C4×C8—111no—
412C4×C8—111no—
413C4×C8—111no—
414C4×C8—221no—
415C4×C8—221no—
416C4×C8—221no—
417C4×C8C22×D1111yescharacteristic
418C4×C8C22×D1111yescharacteristic
419C4×C8C22×D1111yescharacteristic
420C2×C11#292911yescharacteristic
421C2×C11#294711yescharacteristic
422C2×C11#295711yescharacteristic
423D11—41no—
424D11—42no—
425#41—222no—
426#41—222no—
427C2×Q8—111no—
428C2×Q8—221no—
429C2×Q8C2×C4×D1111yescharacteristic
430C2×Q8C2×C4×D1111yescharacteristic
431C2×D4—111no—
432C2×D4—221no—
433C22×C4—111no—
434C22×C4—111no—
435C22×C4—111no—
436C22×C4—221no—
437C22×C4—221no—
438C22×C4—221no—
439Q16—22no—
440Q16—222no—
441SD16—222no—
442SD16—222no—
443C2×C8—21no—
444C2×C8—21no—
445C2×C8—21no—
446C2×C8—111no—
447C2×C8—111no—
448C2×C8—111no—
449C2×C8—111no—
450C2×C8—221no—
451C2×C8—221no—
452C2×C8—221no—
453C2×C8—881no—
454C2×C8—881no—
455C2×C8—881no—
456C2×C8C2×C4×D1111yescharacteristic
457C2×C8C2×C4×D1111yescharacteristic
458C2×C8D4×D1111yescharacteristic
459C2×C8D4×D1111yescharacteristic
460C4⋊C4—21no—
461C4⋊C4—21no—
462C4⋊C4—111no—
463C4⋊C4—111no—
464C4⋊C4—221no—
465C4⋊C4—221no—
466C4⋊C4—221no—
467C4⋊C4—221no—
468C4⋊C4—221no—
469C4⋊C4—221no—
470C4⋊C4—221no—
471C4⋊C4C2×C4×D1111yescharacteristic
472C4⋊C4C2×C4×D1111yescharacteristic
473C22⋊C4—221no—
474C22⋊C4—221no—
475C22⋊C4—221no—
476C22⋊C4—221no—
477C22⋊C4—221no—
478C42—21no—
479C42—21no—
480C42—111no—
481C42—111no—
482C42—111no—
483C42—221no—
484C42—221no—
485C42—221no—
486C42C23×D1111yescharacteristic
487C11#1792111yescharacteristic, complemented, Sylow
488C23—111no—
489C23—221no—
490Q8—21no—
491Q8—21no—
492Q8—21no—
493Q8—221no—
494Q8—221no—
495Q8—881no—
496Q8#6696012yes—
497D4—112no—
498D4—224no—
499D4—221no—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—111no—
505C2×C4—111no—
506C2×C4—111no—
507C2×C4—224no—
508C2×C4—221no—
509C2×C4—221no—
510C2×C4—221no—
511C2×C4—221no—
512C2×C4—221no—
513C2×C4—221no—
514C2×C4—221no—
515C2×C4—441no—
516C2×C4—441no—
517C2×C4—441no—
518C2×C4—881no—
519C2×C4C22×C4×D1111yescharacteristic
520C2×C4C2×D4×D1111yescharacteristic
521C2×C4#41×D1111yescharacteristic
522C8—21no—
523C8—21no—
524C8—21no—
525C8—21no—
526C8—41no—
527C8—41no—
528C8—41no—
529C8—221no—
530C8—221no—
531C8—221no—
532C8—221no—
533C8—441no—
534C8—441no—
535C8—441no—
536C22—221no—
537C22—222no—
538C22—221no—
539C22—221no—
540C22—441no—
541C22—441no—
542C22C4×D4×D1111yescharacteristic
543C4—21no—
544C4—22no—
545C4—41no—
546C4—41no—
547C4—41no—
548C4—221no—
549C4—221no—
550C4—221no—
551C4—441no—
552C4—441no—
553C4—441no—
554C4C2×#6696011yescharacteristic
555C4D11×#13111yescharacteristic
556C4#1062330911yescharacteristic
557C4#1062331011yescharacteristic
558C2—441no—
559C2—442no—
560C2#1307730711yescharacteristic
561C2#1307745811yescharacteristic
562C2#1307752811yescharacteristic
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#17921
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. #13077712C2semidirect
4. #13067475C2semidirect
5. #13067466C2semidirect
6. #13067450C2semidirect
7. #13067432C2semidirect
8. #13067431C2semidirect
9. Q16×C11⋊C8C2semidirect
10. #13067415C2semidirect
11. #13067398C2semidirect
13. #13067017C2semidirect
14. #13066917C2semidirect
15. C11×#1587C2semidirect
210. #1587D11semidirect
487. C11#17921semidirect

Maximal subgroups

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

subgroupindex
#130786852
#130777262
#130777122
#130674752
#130674662
#130674502
#130674322
#130674312
Q16×C11⋊C82
#130674152
#130673982
#130670492
#130670172
#130669172
C11×#15872
#1792111