Finite Group Databasebeta

← #14725626

Subgroups — #14725626

Order 2816.

656 conjugacy classes of subgroups.

The subgroup lattice has 608 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079207C211yesmaximal, characteristic
2#13077619C211yesmaximal, characteristic, complemented
3#13077355C211yesmaximal, characteristic, complemented
4#13067531C211yesmaximal, characteristic, complemented
5#13067507C211yesmaximal, characteristic, complemented
6#13067494C211yesmaximal, characteristic, complemented
7#13067480C211yesmaximal, characteristic, complemented
8#13067455C211yesmaximal, characteristic, complemented
9#13067448C211yesmaximal, characteristic, complemented
10#13067410C211yesmaximal, characteristic, complemented
11#13067367C211yesmaximal, characteristic, complemented
12#13067031C211yesmaximal, characteristic, complemented
13#13067028C211yesmaximal, characteristic, complemented
14#13066920C211yesmaximal, characteristic, complemented
15C11×SD16⋊C8C211yesmaximal, characteristic, complemented
16C2×#66954—21no—
17#10623111C2211yescharacteristic
18#10623079C2211yescharacteristic
19C8×Q8×C11C2211yescharacteristic
20C4×C11×SD16C2211yescharacteristic
21C8×D4×C11C2211yescharacteristic
22#10622789C411yescharacteristic
23#10622787C411yescharacteristic
24#10622724—21no—
25C4×#4325C2211yescharacteristic
26#10622637C2211yescharacteristic
27C4×#4323C2211yescharacteristic
28#10622625C2211yescharacteristic
29#10622478C411yescharacteristic
30#10622469C411yescharacteristic
31#10622453—21no—
32#10622449—21no—
33#10622447C2211yescharacteristic
34#10622447C2211yescharacteristic
35#10622446C2211yescharacteristic
36D11×C4⋊C8C2211yescharacteristic
37#10622425C411yescharacteristic
38#10622408C411yescharacteristic
39#10622395C411yescharacteristic
40#10622377C411yescharacteristic
41#10622341—21no—
42#10622340—21no—
43C4×D88C2211yescharacteristic
44#10622302—21no—
45#10622301—21no—
46#10622301C2211yescharacteristic
47#10622301C2211yescharacteristic
48C4×#4313C2211yescharacteristic
49C4×#4313C2211yescharacteristic
50C4×#4313C2211yescharacteristic
51C11×#335C2211yescharacteristic
52C11×Q8⋊C8C2211yescharacteristic
53C11×D4⋊C8C2211yescharacteristic
54C11×#322C2211yescharacteristic
55Q8⋊(C11⋊C8)C2211yescharacteristic
56D4⋊(C11⋊C8)C2211yescharacteristic
57#10622121C2211yescharacteristic
58#10622121C2211yescharacteristic
59#10622118C2211yescharacteristic
60#10622117C2211yescharacteristic
61#10622097C2211yescharacteristic
62#10622097C2211yescharacteristic
63#10622095C2211yescharacteristic
64#10622092C2211yescharacteristic
65#10622092C2211yescharacteristic
66C8×C11⋊C8C2211yescharacteristic
67C2×#4339—21no—
68C2×C11×SD16C2×C411yescharacteristic
69C22×C8×C11—21no—
70C4×Q8×C11C2311yescharacteristic
71C4×D4×C11C2311yescharacteristic
72#67000C2×C411yescharacteristic
73#66999C2×C411yescharacteristic
74C2×#4325C2×C411yescharacteristic
75#66993C2×C411yescharacteristic
76#66991C2×C411yescharacteristic
77C2×#4323C2×C411yescharacteristic
78C4×C22⋊D11—21no—
79C2×#4318—21no—
80C2×D88C2×C411yescharacteristic
81#66954—44no—
82C2×#4313—21no—
83C2×#4313—21no—
84C2×#4313—21no—
85C2×#4313C2×C411yescharacteristic
86C2×#4313C2×C411yescharacteristic
87C2×#4313D411yescharacteristic
88C2×#4313D411yescharacteristic
89C2×C8×D11—21no—
90C2×C8×D11—21no—
91C2×C8×D11—21no—
92#66951—21no—
93#66948C2×C411yescharacteristic
94#66948C2×C411yescharacteristic
95#66947—21no—
96#66943C2×C411yescharacteristic
97#66941C2×C411yescharacteristic
98#66938—21no—
99#66937—21no—
100C4×D44—21no—
101C4×D44C2311yescharacteristic
102C4×D44C2311yescharacteristic
103#66925—21no—
104C42×D11C2311yescharacteristic
105C11×#106C2×C411yescharacteristic
106C11×C4⋊C8—21no—
107C11×C4⋊C8C2311yescharacteristic
108C11×C4⋊C8C2311yescharacteristic
109C11×#103C2×C411yescharacteristic
110C11×#102C2×C411yescharacteristic
111C11×C22⋊C8—21no—
112C4×C8×C11—21no—
113C4×C8×C11C2311yescharacteristic
114C4×C8×C11C2311yescharacteristic
115C4×C8×C11C2311yescharacteristic
116#66899C2×C411yescharacteristic
117#66896C2×C411yescharacteristic
118C22⋊(C11⋊C8)—21no—
119#66885C2×C411yescharacteristic
120#66885C2×C411yescharacteristic
121(C2×D11)⋊C8—21no—
122(C2×D11)⋊C8—21no—
123(C2×D11)⋊C8—21no—
124(C2×D11)⋊C8—21no—
125(C2×D11)⋊C8—21no—
126#66882C2×C411yescharacteristic
127#66879—21no—
128#66879C2×C411yescharacteristic
129#66879C2×C411yescharacteristic
130#66879D411yescharacteristic
131#66879D411yescharacteristic
132Dic11⋊C8—21no—
133C8×Dic11—21no—
134#66873C2×C411yescharacteristic
135#66873C2×C411yescharacteristic
136#66872C2×C411yescharacteristic
137#66871C2×C411yescharacteristic
138C4⋊(C11⋊C8)—21no—
139C4⋊(C11⋊C8)C2311yescharacteristic
140C4⋊(C11⋊C8)C2311yescharacteristic
141#66867—21no—
142C4×C11⋊C8C2311yescharacteristic
143C4×C11⋊C8C2311yescharacteristic
144C4×C11⋊C8C2311yescharacteristic
145#18076—111nomaximal, Sylow
146C2×Q8×C11C22×C411yescharacteristic
147C2×D4×C11C22×C411yescharacteristic
148C22×C4×C11—21no—
149C2×C22⋊D11—21no—
150C2×C22⋊D11—21no—
151C2×C22⋊D11—21no—
152#4339—42no—
153#4339—42no—
154C2×D44—21no—
155C2×D44—21no—
156C2×D44C22×C411yescharacteristic
157C2×D44C22×C411yescharacteristic
158C2×C4×D11—21no—
159C2×C4×D11—21no—
160C2×C4×D11C22×C411yescharacteristic
161C2×C4×D11C2×D411yescharacteristic
162C2×C4×D11#4111yescharacteristic
163C2×Dic22—21no—
164C11×SD16—22no—
165C2×C8×C11—21no—
166C2×C8×C11—21no—
167C2×C8×C11—21no—
168C2×C8×C11—42no—
169C2×C8×C11C22×C411yescharacteristic
170C2×C8×C11C22×C411yescharacteristic
171C2×C8×C11C2×D411yescharacteristic
172C2×C8×C11C2×D411yescharacteristic
173C11×C4⋊C4—21no—
174C11×C4⋊C4C22×C411yescharacteristic
175C11×C4⋊C4C22×C411yescharacteristic
176C11×C22⋊C4—21no—
177C42×C11—21no—
178C42×C11C2411yescharacteristic
179C22⋊Dic11—21no—
180#4325—41no—
181#4323—41no—
182(C2×D11)⋊C4—21no—
183(C2×D11)⋊C4—21no—
184(C2×D11)⋊C4—21no—
185(C2×D11)⋊C4—21no—
186(C2×D11)⋊C4—21no—
187(C2×D11)⋊C4—21no—
188(C2×D11)⋊C4—21no—
189C4⋊Dic11—21no—
190C4⋊Dic11C22×C411yescharacteristic
191C4⋊Dic11C22×C411yescharacteristic
192Dic11⋊C4—21no—
193Dic11⋊C4—21no—
194Dic11⋊C4—21no—
195C4×Dic11C22×C411yescharacteristic
196C4×Dic11C2×D411yescharacteristic
197C4×Dic11#4111yescharacteristic
198#4318—42no—
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
206D88—22no—
207#4313—22no—
208#4313—22no—
209#4313—41no—
210#4313—41no—
211#4313—42no—
212#4313—42no—
213#4313—42no—
214C8×D11—42no—
215C8×D11—42no—
216C8×D11—42no—
217#3171—111no—
218#2969—111no—
219#2935—111no—
220#1594—111no—
221#1590—111no—
222#1588—111no—
223#1586—111no—
224#1582—111no—
225#1581—111no—
226SD16⋊C8D1111yescharacteristic, complemented
227C8×D8—111no—
228#1565—111no—
229#1484—111no—
230#1483—111no—
231#1455—111no—
232C23×C11—21no—
233C22×D11—21no—
234C22×D11—21no—
235C22×D11C4×D411yescharacteristic
236Q8×C11—21no—
237Q8×C11—21no—
238D4×C11—21no—
239D4×C11—21no—
240C2×C4×C11—21no—
241C2×C4×C11—21no—
242C2×C4×C11—21no—
243C2×C4×C11—41no—
244C2×C4×C11—41no—
245C2×C4×C11C23×C411yescharacteristic
246C2×C4×C11C22×D411yescharacteristic
247C2×C4×C11C2×#4111yescharacteristic
248C22⋊D11—42no—
249C22⋊D11—42no—
250C22⋊D11—81no—
251C2×Dic11—21no—
252C2×Dic11—21no—
253C2×Dic11C4×D411yescharacteristic
254C2×Dic11C4×D411yescharacteristic
255C2×Dic11C4×D411yescharacteristic
256D44—21no—
257D44—21no—
258D44—21no—
259D44—21no—
260D44—42no—
261D44—81no—
262C4×D11—21no—
263C4×D11—21no—
264C4×D11—21no—
265C4×D11—21no—
266C4×D11—41no—
267C4×D11—41no—
268C4×D11—41no—
269C4×D11—41no—
270C4×D11—41no—
271Dic22—42no—
272C8×C11—21no—
273C8×C11—21no—
274C8×C11—21no—
275C8×C11—41no—
276C8×C11—41no—
277C8×C11—41no—
278C8×C11#13112yescomplemented
279C11⋊C8—22no—
280C11⋊C8—21no—
281C11⋊C8—21no—
282C11⋊C8—21no—
283C11⋊C8—41no—
284C11⋊C8—41no—
285C11⋊C8AGL(1,ℤ/8)12yes—
286C2×#131—221no—
287#532—111no—
288#529—111no—
289#501—111no—
290#496—111no—
291#490—111no—
292#489—111no—
293#469—111no—
294#469—111no—
295#468—111no—
296#468—111no—
297#446—111no—
298C8×Q8C2×D1111yescharacteristic
299C4×SD16—111no—
300C4×SD16C2×D1111yescharacteristic
301C4×D8—111no—
302C4×D8—111no—
303#436—111no—
304#436—111no—
305#436—111no—
306#436—221no—
307#435—221no—
308#435—221no—
309#435—221no—
310C8×D4—111no—
311C8×D4—111no—
312C8×D4C2×D1111yescharacteristic
313#433—221no—
314#431—111no—
315C2×C4⋊C8—111no—
316#408—221no—
317#405—221no—
318C4×M16—111no—
319C4×M16—111no—
320C4×M16—111no—
321#335—111no—
322#335C2×D1111yescharacteristic
323#334—111no—
324#334—111no—
325Q8⋊C8—111no—
326Q8⋊C8C2×D1111yescharacteristic
327D4⋊C8—111no—
328D4⋊C8—111no—
329D4⋊C8—111no—
330D4⋊C8—111no—
331D4⋊C8—111no—
332D4⋊C8C2×D1111yescharacteristic
333#322—111no—
334#322—111no—
335#322C2×D1111yescharacteristic
336C82—111no—
337C22×C11—41no—
338C22×C11—41no—
339C22×C11—41no—
340C22×C11C2×C4×D411yescharacteristic
341C2×D11—21no—
342C2×D11—21no—
343C2×D11—21no—
344C2×D11—41no—
345C2×D11—41no—
346C2×D11—41no—
347C2×D11—41no—
348C2×D11—41no—
349C2×D11—41no—
350C4×C11—21no—
351C4×C11—41no—
352C4×C11—41no—
353C4×C11—41no—
354C4×C11C2×#13111yescharacteristic
355C4×C11#56811yescharacteristic
356C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
357C4×C11#57511yescharacteristic
358Dic11—21no—
359Dic11—21no—
360Dic11—21no—
361Dic11—41no—
362Dic11—41no—
363C2×#41—221no—
364C2×SD16—111no—
365C2×SD16C4×D1111yescharacteristic
366C2×D8—111no—
367C2×D8—111no—
368#131—444no—
369C2×M16—111no—
370C2×M16—111no—
371C2×M16—111no—
372C2×M16—111no—
373C2×M16—221no—
374C2×M16—221no—
375C2×M16—221no—
376C2×M16—221no—
377C22×C8—21no—
378C22×C8—221no—
379C22×C8—221no—
380C22×C8—221no—
381C4⋊Q8—111no—
382#127—111no—
383#126—221no—
384#125—111no—
385#124—111no—
386#124—221no—
387#123—221no—
388C22⋊Q8—111no—
389#121—111no—
390#121—111no—
391#121—111no—
392#121—221no—
393C4×Q8C22×D1111yescharacteristic
394C4×D4—111no—
395C4×D4—111no—
396C4×D4—221no—
397C4×D4—221no—
398C4×D4C22×D1111yescharacteristic
399#117—221no—
400C2×C42—111no—
401#107—111no—
402#107—111no—
403#106—111no—
404#106C4×D1111yescharacteristic
405C4⋊C8—21no—
406C4⋊C8—111no—
407C4⋊C8—111no—
408C4⋊C8—221no—
409C4⋊C8—221no—
410C4⋊C8C22×D1111yescharacteristic
411C4⋊C8C22×D1111yescharacteristic
412#103—111no—
413#103C4×D1111yescharacteristic
414#102—111no—
415#102—111no—
416#102—111no—
417#102—111no—
418#102—111no—
419#102C4×D1111yescharacteristic
420C22⋊C8—21no—
421C22⋊C8—221no—
422C22⋊C8—221no—
423C22⋊C8—221no—
424C22⋊C8—221no—
425C22⋊C8—221no—
426C22⋊C8—221no—
427#97—111no—
428#97—111no—
429#97—111no—
430#97—111no—
431#97—221no—
432#97—221no—
433C4×C8—21no—
434C4×C8—111no—
435C4×C8—111no—
436C4×C8—111no—
437C4×C8—221no—
438C4×C8C22×D1111yescharacteristic
439C4×C8C22×D1111yescharacteristic
440C4×C8C22×D1111yescharacteristic
441C2×C11—81no—
442C2×C11#293511yescharacteristic
443C2×C11C4×AGL(1,ℤ/8)11yescharacteristic
444C2×C11#295611yescharacteristic
445D11—41no—
446D11—81no—
447D11—81no—
448#41—442no—
449#41—442no—
450C2×Q8—221no—
451C2×Q8C2×C4×D1111yescharacteristic
452C2×D4—111no—
453C2×D4—111no—
454C2×D4—221no—
455C2×D4—221no—
456C2×D4—221no—
457C2×D4—221no—
458C2×D4—221no—
459C2×D4C2×C4×D1111yescharacteristic
460C22×C4—21no—
461C22×C4—111no—
462C22×C4—111no—
463C22×C4—111no—
464C22×C4—221no—
465C22×C4—221no—
466SD16—22no—
467SD16—441no—
468D8—222no—
469D8—441no—
470M16—222no—
471M16—222no—
472M16—441no—
473M16—441no—
474M16—442no—
475M16—442no—
476M16—442no—
477M16—442no—
478C2×C8—21no—
479C2×C8—21no—
480C2×C8—21no—
481C2×C8—42no—
482C2×C8—111no—
483C2×C8—111no—
484C2×C8—111no—
485C2×C8—111no—
486C2×C8—221no—
487C2×C8—221no—
488C2×C8—221no—
489C2×C8—442no—
490C2×C8—442no—
491C2×C8—442no—
492C2×C8C2×C4×D1111yescharacteristic
493C2×C8C2×C4×D1111yescharacteristic
494C2×C8D4×D1111yescharacteristic
495C2×C8D4×D1111yescharacteristic
496C4⋊C4—21no—
497C4⋊C4—111no—
498C4⋊C4—111no—
499C4⋊C4—221no—
500C4⋊C4—221no—
501C4⋊C4—221no—
502C4⋊C4—221no—
503C4⋊C4C2×C4×D1111yescharacteristic
504C4⋊C4C2×C4×D1111yescharacteristic
505C22⋊C4—21no—
506C22⋊C4—221no—
507C22⋊C4—221no—
508C22⋊C4—221no—
509C22⋊C4—221no—
510C22⋊C4—221no—
511C22⋊C4—221no—
512C22⋊C4—221no—
513C22⋊C4—221no—
514C42—21no—
515C42—111no—
516C42—111no—
517C42—111no—
518C42C23×D1111yescharacteristic
519C11#1807611yescharacteristic, complemented, Sylow
520C23—21no—
521C23—111no—
522C23—221no—
523C23—221no—
524Q8—21no—
525Q8—21no—
526Q8—442no—
527D4—21no—
528D4—21no—
529D4—221no—
530D4—221no—
531D4—221no—
532D4—221no—
533D4—442no—
534D4—442no—
535D4—442no—
536D4—881no—
537D4—881no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—41no—
542C2×C4—41no—
543C2×C4—111no—
544C2×C4—111no—
545C2×C4—111no—
546C2×C4—221no—
547C2×C4—221no—
548C2×C4—221no—
549C2×C4—221no—
550C2×C4—221no—
551C2×C4—221no—
552C2×C4—441no—
553C2×C4—441no—
554C2×C4—441no—
555C2×C4—441no—
556C2×C4—441no—
557C2×C4C22×C4×D1111yescharacteristic
558C2×C4C2×D4×D1111yescharacteristic
559C2×C4#41×D1111yescharacteristic
560C8—21no—
561C8—21no—
562C8—21no—
563C8—41no—
564C8—41no—
565C8—41no—
566C8—112no—
567C8—222no—
568C8—221no—
569C8—221no—
570C8—221no—
571C8—441no—
572C8—441no—
573C8#6695412yescomplemented
574C22—41no—
575C22—41no—
576C22—41no—
577C22—221no—
578C22—221no—
579C22—221no—
580C22—441no—
581C22—441no—
582C22—441no—
583C22—441no—
584C22—441no—
585C22—441no—
586C22C4×D4×D1111yescharacteristic
587C4—21no—
588C4—41no—
589C4—41no—
590C4—41no—
591C4—221no—
592C4—221no—
593C4—221no—
594C4—441no—
595C4—441no—
596C4C2×#6695411yescharacteristic
597C4#1062328111yescharacteristic
598C4D11×AGL(1,ℤ/8)11yescharacteristic
599C4#1062330811yescharacteristic
600C2—81no—
601C2—441no—
602C2—881no—
603C2—881no—
604C2#1307735511yescharacteristic
605C2#1307742111yescharacteristic
606C2#1307752411yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
FittingC11×SD16⋊C8C2
socleC22×C11C2×C4×D4
prime radical#13079207C2
cosocleC42×C11C24
hypercenterSD16⋊C8D11
hypocenterC11#18076
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ SD16⋊C8

Complements

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

NH ≅ G/Ntype
2. #13077619C2semidirect
3. #13077355C2semidirect
4. #13067531C2semidirect
5. #13067507C2semidirect
6. #13067494C2semidirect
7. #13067480C2semidirect
8. #13067455C2semidirect
9. #13067448C2semidirect
10. #13067410C2semidirect
11. #13067367C2semidirect
12. #13067031C2semidirect
13. #13067028C2semidirect
14. #13066920C2semidirect
15. C11×SD16⋊C8C2semidirect
226. SD16⋊C8D11semidirect
278. C8×C11#131semidirect
519. C11#18076semidirect
573. C8#66954semidirect

Maximal subgroups

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

subgroupindex
#130792072
#130776192
#130773552
#130675312
#130675072
#130674942
#130674802
#130674552
#130674482
#130674102
#130673672
#130670312
#130670282
#130669202
C11×SD16⋊C82
#1807611