Finite Group Databasebeta

← #14725230

Subgroups — #14725230

Order 2816.

638 conjugacy classes of subgroups.

The subgroup lattice has 570 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13077568C211yesmaximal, characteristic
2Q8×#4313C211yesmaximal, characteristic
3C4×Q16×D11C211yesmaximal, characteristic
4#13067511C211yesmaximal, characteristic, complemented
5#13067510C211yesmaximal, characteristic, complemented
6#13067468C211yesmaximal, characteristic, complemented
7#13067467C211yesmaximal, characteristic, complemented
8#13067465C211yesmaximal, characteristic, complemented
9C8×#4326C211yesmaximal, characteristic, complemented
10#13067420C211yesmaximal, characteristic, complemented
11#13067373C211yesmaximal, characteristic
12#13067043C211yesmaximal, characteristic
13#13067043C211yesmaximal, characteristic
14#13066895C211yesmaximal, characteristic
15C11×#1584C211yesmaximal, characteristic, complemented
16C2×Q16×D11C411yescharacteristic
17C4×Q8×D11C2211yescharacteristic
18C4×Q8×D11C2211yescharacteristic
19C11×#446C2211yescharacteristic
20C8×Q8×C11C2211yescharacteristic
21C4×C11×Q16C2211yescharacteristic
22Q16×Dic11C411yescharacteristic
23C4×#4326C2211yescharacteristic
24C4×#4326C2211yescharacteristic
25#10622637C2211yescharacteristic
26Q8×C11⋊C8C2211yescharacteristic
27D11×#107C411yescharacteristic
28#10622486C411yescharacteristic
29#10622450—21no—
30#10622450—21no—
31#10622450C2211yescharacteristic
32#10622450C2211yescharacteristic
33#10622444—21no—
34#10622444C2211yescharacteristic
35#10622443C2211yescharacteristic
36#10622441—21no—
37D11×#103C411yescharacteristic
38D11×#103C411yescharacteristic
39#10622403C411yescharacteristic
40#10622403C411yescharacteristic
41#10622320—21no—
42#10622314—21no—
43C4×Dic44C2211yescharacteristic
44C4×#4313—21no—
45C4×#4313C2211yescharacteristic
46#10622298C2211yescharacteristic
47C4×C8×D11C2211yescharacteristic
48#10622292—21no—
49#10622292C2211yescharacteristic
50C8×Dic22C2211yescharacteristic
51C11×#335C2211yescharacteristic
52C11×Q8⋊C8C2211yescharacteristic
53C11×Q8⋊C8C2211yescharacteristic
54C11×#322C2211yescharacteristic
55Q8⋊(C11⋊C8)C2211yescharacteristic
56Q8⋊(C11⋊C8)C2211yescharacteristic
57#10622122C2211yescharacteristic
58#10622122C2211yescharacteristic
59#10622117C2211yescharacteristic
60#10622117C2211yescharacteristic
61#10622096C2211yescharacteristic
62#10622094C2211yescharacteristic
63#10622094C2211yescharacteristic
64#10622092C2211yescharacteristic
65C8×C11⋊C8C2211yescharacteristic
66C8×C11⋊C8C2211yescharacteristic
67C2×Q8×D11C2×C411yescharacteristic
68C2×Q8×D11C2×C411yescharacteristic
69C2×C11×Q16C2×C411yescharacteristic
70C4×Q8×C11C2311yescharacteristic
71C4×Q8×C11C2311yescharacteristic
72Q8×Dic11C2×C411yescharacteristic
73Q8×Dic11C2×C411yescharacteristic
74C2×#4326C2×C411yescharacteristic
75C2×#4326C2×C411yescharacteristic
76Q16×D11—24no—
77C2×Dic44C2×C411yescharacteristic
78C2×#4313—21no—
79C2×#4313—21no—
80C2×#4313D411yescharacteristic
81C2×#4313D411yescharacteristic
82C2×C8×D11C2×C411yescharacteristic
83C2×C8×D11C2×C411yescharacteristic
84C4⋊C4×D11—21no—
85C4⋊C4×D11—21no—
86C4⋊C4×D11C2×C411yescharacteristic
87C4⋊C4×D11C2×C411yescharacteristic
88#66940—21no—
89#66940—21no—
90#66940C2×C411yescharacteristic
91#66940C2×C411yescharacteristic
92C42×D11—21no—
93C42×D11—21no—
94C42×D11C2311yescharacteristic
95C4×Dic22—21no—
96C4×Dic22—21no—
97C4×Dic22C2311yescharacteristic
98C4×Dic22C2311yescharacteristic
99C11×#107C2×C411yescharacteristic
100C11×C4⋊C8—21no—
101C11×C4⋊C8—21no—
102C11×C4⋊C8C2311yescharacteristic
103C11×C4⋊C8C2311yescharacteristic
104C11×#103C2×C411yescharacteristic
105C11×#103C2×C411yescharacteristic
106C11×#97—21no—
107C4×C8×C11—21no—
108C4×C8×C11C2311yescharacteristic
109C4×C8×C11C2311yescharacteristic
110C4×C8×C11C2311yescharacteristic
111#66899C2×C411yescharacteristic
112#66899C2×C411yescharacteristic
113(C2×D11)⋊C8—21no—
114#66882C2×C411yescharacteristic
115#66880C2×C411yescharacteristic
116#66880C2×C411yescharacteristic
117#66879—21no—
118#66879—21no—
119#66879D411yescharacteristic
120#66879D411yescharacteristic
121Dic11⋊C8—21no—
122Dic11⋊C8—21no—
123Dic11⋊C8—21no—
124Dic11⋊C8—21no—
125Dic11⋊C8—21no—
126Dic11⋊C8—21no—
127Dic11⋊C8—21no—
128C8×Dic11—21no—
129C8×Dic11—21no—
130C8×Dic11C2×C411yescharacteristic
131C8×Dic11C2×C411yescharacteristic
132#66874C2×C411yescharacteristic
133#66874C2×C411yescharacteristic
134#66871C2×C411yescharacteristic
135#66871C2×C411yescharacteristic
136C4⋊(C11⋊C8)—21no—
137C4⋊(C11⋊C8)—21no—
138C4⋊(C11⋊C8)C2311yescharacteristic
139C4⋊(C11⋊C8)C2311yescharacteristic
140#66867—21no—
141C4×C11⋊C8—21no—
142C4×C11⋊C8C2311yescharacteristic
143C4×C11⋊C8C2311yescharacteristic
144C4×C11⋊C8C2311yescharacteristic
145M16×Q16—111nomaximal, Sylow
146C2×Q8×C11C22×C411yescharacteristic
147C2×Q8×C11C22×C411yescharacteristic
148Q8×D11—22no—
149Q8×D11—22no—
150Q8×D11—41no—
151Q8×D11—41no—
152C2×C4×D11—21no—
153C2×C4×D11—21no—
154C2×C4×D11—21no—
155C2×C4×D11—21no—
156C2×C4×D11C22×C411yescharacteristic
157C2×C4×D11C2×D411yescharacteristic
158C2×C4×D11#4111yescharacteristic
159C2×Dic22—21no—
160C2×Dic22—21no—
161C2×Dic22C22×C411yescharacteristic
162C2×Dic22C22×C411yescharacteristic
163C11×Q16—22no—
164C2×C8×C11—21no—
165C2×C8×C11—21no—
166C2×C8×C11—21no—
167C2×C8×C11C22×C411yescharacteristic
168C2×C8×C11C22×C411yescharacteristic
169C2×C8×C11C2×D411yescharacteristic
170C2×C8×C11C2×D411yescharacteristic
171C11×C4⋊C4—21no—
172C11×C4⋊C4—21no—
173C11×C4⋊C4C22×C411yescharacteristic
174C11×C4⋊C4C22×C411yescharacteristic
175C42×C11—21no—
176C42×C11—21no—
177C42×C11C2411yescharacteristic
178#4326—22no—
179#4326M1614yescomplemented
180C4⋊Dic11—21no—
181C4⋊Dic11—21no—
182C4⋊Dic11C22×C411yescharacteristic
183C4⋊Dic11C22×C411yescharacteristic
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×Dic11—21no—
195C4×Dic11—21no—
196C4×Dic11C22×C411yescharacteristic
197C4×Dic11C2×D411yescharacteristic
198C4×Dic11#4111yescharacteristic
199C2×C11⋊C8—21no—
200C2×C11⋊C8—21no—
201C2×C11⋊C8—21no—
202C2×C11⋊C8C22×C411yescharacteristic
203C2×C11⋊C8C22×C411yescharacteristic
204C2×C11⋊C8C2×D411yescharacteristic
205C2×C11⋊C8C2×D411yescharacteristic
206Dic44—22no—
207#4313—22no—
208#4313—42no—
209#4313—42no—
210#4313Q1614yescomplemented
211C8×D11—22no—
212C8×D11—41no—
213Q8×M16—111no—
214Q8×M16—111no—
215C2×C4×Q16—111no—
216#1591—111no—
217#1591—111no—
218#1584—111no—
219#1584—111no—
220#1584—111no—
221#1584D1111yescharacteristic, complemented
222C8×Q16—111no—
223C8×Q16—111no—
224#1567—111no—
225#1487—111no—
226#1487—111no—
227C8×M16—111no—
228C22×D11C4×D411yescharacteristic
229Q8×C11—21no—
230Q8×C11—21no—
231Q8×C11—21no—
232Q8×C11C2×M1612yes—
233C2×C4×C11—21no—
234C2×C4×C11—21no—
235C2×C4×C11—21no—
236C2×C4×C11—21no—
237C2×C4×C11C23×C411yescharacteristic
238C2×C4×C11C22×D411yescharacteristic
239C2×C4×C11C2×#4111yescharacteristic
240C2×Dic11—21no—
241C2×Dic11—21no—
242C2×Dic11—21no—
243C2×Dic11—21no—
244C2×Dic11C4×D411yescharacteristic
245C2×Dic11C4×D411yescharacteristic
246C2×Dic11C4×D411yescharacteristic
247C4×D11—21no—
248C4×D11—21no—
249C4×D11—41no—
250C4×D11—42no—
251C4×D11—42no—
252C4×D11—81no—
253C4×D11—81no—
254C4×D11C2×Q1612yes—
255C4×D11#13512yes—
256Dic22—21no—
257Dic22—21no—
258Dic22—21no—
259Dic22—42no—
260Dic22—42no—
261Dic22C2×M1612yes—
262C8×C11—21no—
263C8×C11—21no—
264C8×C11—21no—
265C8×C11—41no—
266C8×C11—41no—
267C8×C11—41no—
268C8×C11C2×Q1612yescomplemented
269C11⋊C8—21no—
270C11⋊C8—21no—
271C11⋊C8—41no—
272C11⋊C8—41no—
273C11⋊C8—41no—
274C11⋊C8C2×M1612yes—
275C11⋊C8C2×Q1612yescomplemented
276C22×Q16—111no—
277C2×C4×Q8—111no—
278C2×C4×Q8—111no—
279#446—111no—
280#446—111no—
281#446—111no—
282#446—221no—
283#446—221no—
284#446—221no—
285#446—221no—
286#446C2×D1111yescharacteristic
287C8×Q8—111no—
288C8×Q8—111no—
289C8×Q8—111no—
290C8×Q8C2×D1111yescharacteristic
291C4×Q16—111no—
292C4×Q16—111no—
293C4×Q16—111no—
294C4×Q16—111no—
295C4×Q16—111no—
296C4×Q16—111no—
297C4×Q16—111no—
298C4×Q16C2×D1111yescharacteristic
299#431—111no—
300C2×#107—111no—
301#423—111no—
302#423—111no—
303#423—221no—
304#423—221no—
305C2×#103—111no—
306C2×#103—111no—
307C4×M16—111no—
308C4×M16—221no—
309C4×M16—221no—
310C2×C4×C8—111no—
311#335—111no—
312#335—111no—
313#335—111no—
314#335C2×D1111yescharacteristic
315Q8⋊C8—111no—
316Q8⋊C8—111no—
317Q8⋊C8—111no—
318Q8⋊C8—111no—
319Q8⋊C8—111no—
320Q8⋊C8—111no—
321Q8⋊C8C2×D1111yescharacteristic
322Q8⋊C8C2×D1111yescharacteristic
323#322—111no—
324#322C2×D1111yescharacteristic
325C82—111no—
326C82—111no—
327C22×C11C2×C4×D411yescharacteristic
328C2×D11—21no—
329C2×D11—21no—
330C2×D11C4×Q1612yes—
331C4×C11—22no—
332C4×C11—21no—
333C4×C11—41no—
334C4×C11—41no—
335C4×C11—41no—
336C4×C11C22×M1611yescharacteristic
337C4×C11#56811yescharacteristic
338C4×C11C22×Q1611yescharacteristic
339C4×C11C2×#13511yescharacteristic
340Dic11—22no—
341Dic11—21no—
342Dic11—21no—
343Dic11—41no—
344Dic11—41no—
345Dic11—41no—
346Dic11C4×Q1612yes—
347C22×Q8—111no—
348C22×Q8—111no—
349C2×Q16—111no—
350C2×Q16—111no—
351C2×Q16—111no—
352C2×Q16—224no—
353C2×Q16C4×D1111yescharacteristic
354C2×M16—111no—
355C2×M16—111no—
356C2×M16—221no—
357C2×M16—221no—
358C22×C8—111no—
359C22×C8—111no—
360C4×Q8—111no—
361C4×Q8—111no—
362C4×Q8—111no—
363C4×Q8—111no—
364C4×Q8—111no—
365C4×Q8—111no—
366C4×Q8—221no—
367C4×Q8—221no—
368C4×Q8—221no—
369C4×Q8—221no—
370C4×Q8C22×D1111yescharacteristic
371C4×Q8C22×D1111yescharacteristic
372C2×C4⋊C4—111no—
373C2×C4⋊C4—111no—
374C2×C4⋊C4—221no—
375C2×C4⋊C4—221no—
376C2×C42—111no—
377C2×C42—221no—
378C2×C42—221no—
379#107—111no—
380#107—111no—
381#107—111no—
382#107C4×D1111yescharacteristic
383C4⋊C8—21no—
384C4⋊C8—21no—
385C4⋊C8—111no—
386C4⋊C8—111no—
387C4⋊C8—221no—
388C4⋊C8—221no—
389C4⋊C8—221no—
390C4⋊C8—221no—
391C4⋊C8—221no—
392C4⋊C8—221no—
393C4⋊C8—221no—
394C4⋊C8—221no—
395C4⋊C8—221no—
396C4⋊C8C22×D1111yescharacteristic
397C4⋊C8C22×D1111yescharacteristic
398#103—111no—
399#103—111no—
400#103—111no—
401#103—111no—
402#103—111no—
403#103—111no—
404#103C4×D1111yescharacteristic
405#103C4×D1111yescharacteristic
406C22⋊C8—221no—
407#97—21no—
408#97—111no—
409#97—111no—
410#97—221no—
411#97—221no—
412#97—221no—
413C4×C8—21no—
414C4×C8—111no—
415C4×C8—111no—
416C4×C8—111no—
417C4×C8—111no—
418C4×C8—111no—
419C4×C8—221no—
420C4×C8—221no—
421C4×C8—221no—
422C4×C8C22×D1111yescharacteristic
423C4×C8C22×D1111yescharacteristic
424C4×C8C22×D1111yescharacteristic
425C2×C11D4×M1611yescharacteristic
426C2×C11C2×C4×Q1611yescharacteristic
427C2×C11#295711yescharacteristic
428D11—22no—
429C2×Q8—111no—
430C2×Q8—111no—
431C2×Q8—221no—
432C2×Q8—221no—
433C2×Q8—222no—
434C2×Q8—222no—
435C2×Q8—441no—
436C2×Q8—441no—
437C2×Q8C2×C4×D1111yescharacteristic
438C2×Q8C2×C4×D1111yescharacteristic
439C22×C4—111no—
440C22×C4—111no—
441C22×C4—111no—
442C22×C4—221no—
443C22×C4—221no—
444C22×C4—221no—
445C22×C4—221no—
446Q16—22no—
447Q16—114no—
448Q16—222no—
449Q16—222no—
450M16—114no—
451M16—222no—
452M16—442no—
453M16—442no—
454C2×C8—21no—
455C2×C8—21no—
456C2×C8—21no—
457C2×C8—111no—
458C2×C8—111no—
459C2×C8—111no—
460C2×C8—111no—
461C2×C8—222no—
462C2×C8—221no—
463C2×C8—221no—
464C2×C8—221no—
465C2×C8—441no—
466C2×C8C2×C4×D1111yescharacteristic
467C2×C8C2×C4×D1111yescharacteristic
468C2×C8D4×D1111yescharacteristic
469C2×C8D4×D1111yescharacteristic
470C4⋊C4—21no—
471C4⋊C4—21no—
472C4⋊C4—111no—
473C4⋊C4—111no—
474C4⋊C4—221no—
475C4⋊C4—221no—
476C4⋊C4—221no—
477C4⋊C4—221no—
478C4⋊C4—221no—
479C4⋊C4—221no—
480C4⋊C4—221no—
481C4⋊C4—221no—
482C4⋊C4C2×C4×D1111yescharacteristic
483C4⋊C4C2×C4×D1111yescharacteristic
484C42—21no—
485C42—21no—
486C42—111no—
487C42—111no—
488C42—111no—
489C42—221no—
490C42—221no—
491C42—221no—
492C42—221no—
493C42—221no—
494C42—221no—
495C42C23×D1111yescharacteristic
496C11M16×Q1611yescharacteristic, complemented, Sylow
497C23—111no—
498Q8—21no—
499Q8—21no—
500Q8—21no—
501Q8—112no—
502Q8—221no—
503Q8—221no—
504Q8—221no—
505Q8—442no—
506Q8—442no—
507Q8M16×D1112yes—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—111no—
513C2×C4—112no—
514C2×C4—112no—
515C2×C4—111no—
516C2×C4—111no—
517C2×C4—221no—
518C2×C4—221no—
519C2×C4—221no—
520C2×C4—221no—
521C2×C4—221no—
522C2×C4—221no—
523C2×C4—441no—
524C2×C4—442no—
525C2×C4—442no—
526C2×C4—881no—
527C2×C4—881no—
528C2×C4C22×C4×D1111yescharacteristic
529C2×C4C2×D4×D1111yescharacteristic
530C2×C4#41×D1111yescharacteristic
531C8—21no—
532C8—21no—
533C8—21no—
534C8—41no—
535C8—41no—
536C8—41no—
537C8—112no—
538C8—112no—
539C8—221no—
540C8—221no—
541C8—441no—
542C8—441no—
543C8—441no—
544C8Q16×D1112yescomplemented
545C22—112no—
546C22—221no—
547C22—221no—
548C22C4×D4×D1111yescharacteristic
549C4—21no—
550C4—22no—
551C4—41no—
552C4—41no—
553C4—41no—
554C4—112no—
555C4—221no—
556C4—221no—
557C4—222no—
558C4—441no—
559C4—441no—
560C4—441no—
561C4C2×M16×D1111yescharacteristic
562C4#1062328111yescharacteristic
563C4C2×Q16×D1111yescharacteristic
564C4D11×#13511yescharacteristic
565C2—222no—
566C2#1307734911yescharacteristic
567C2C4×Q16×D1111yescharacteristic
568C2#1307753011yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
FittingC11×#1584C2
socleC22×C11C2×C4×D4
prime radicalC22×D11C4×D4
cosocleC42×C11C24
hypercenter#1584D11
hypocenterC11M16×Q16
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ #1584

Complements

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

NH ≅ G/Ntype
4. #13067511C2semidirect
5. #13067510C2semidirect
6. #13067468C2semidirect
7. #13067467C2semidirect
8. #13067465C2semidirect
9. C8×#4326C2semidirect
10. #13067420C2semidirect
15. C11×#1584C2semidirect
179. #4326M16semidirect
210. #4313Q16semidirect
221. #1584D11semidirect
268. C8×C11C2×Q16semidirect
275. C11⋊C8C2×Q16semidirect
496. C11M16×Q16semidirect
544. C8Q16×D11semidirect

Maximal subgroups

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

subgroupindex
#130775682
Q8×#43132
C4×Q16×D112
#130675112
#130675102
#130674682
#130674672
#130674652
C8×#43262
#130674202
#130673732
#130670432
#130668952
C11×#15842
M16×Q1611