Finite Group Databasebeta

← #15620009

Subgroups — #15620009

Order 2816.

1930 conjugacy classes of subgroups.

The subgroup lattice has 620 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#67040C211yesmaximal, characteristic
2#13077742C213yesmaximal, complemented
3#13077740C213yesmaximal, complemented
4#13077730C213yesmaximal, complemented
5#13077726C211yesmaximal, characteristic, complemented
6#13077705C211yesmaximal, characteristic, complemented
7#13077704C211yesmaximal, characteristic, complemented
8#13077698C213yesmaximal, complemented
9#13077631C213yesmaximal, complemented
10#13077629C213yesmaximal, complemented
11#13077578C213yesmaximal, complemented
12C8×#4343C211yesmaximal, characteristic, complemented
13Q8×#4313C211yesmaximal, characteristic, complemented
14D11×#446C213yesmaximal, complemented
15Q8×C11×M16C211yesmaximal, characteristic, complemented
16C2×#67040C411yescharacteristic
17C2×C4×Q8×C11C2211yescharacteristic
18#10623343C411yescharacteristic
19#10623105C413yes—
20#10623105C411yescharacteristic
21C4×#4343C2211yescharacteristic
22C4×#4343C2213yes—
23#10623103C413yes—
24#10623103C411yescharacteristic
25C4×Q8×D11C2213yes—
26C4×Q8×D11C2211yescharacteristic
27#10623035C413yes—
28#10623035C413yes—
29C4×#4339C2213yes—
30C4×#4339C2213yes—
31C11×#446C2213yes—
32C11×#446C2213yes—
33C8×Q8×C11C2211yescharacteristic
34C8×Q8×C11C2211yescharacteristic
35C11×#423C2213yes—
36C4×C11×M16C2213yes—
37#10622741C2211yescharacteristic
38#10622741C2213yes—
39#10622740C2213yes—
40#10622740C2213yes—
41#10622740C2216yes—
42#10622637C2213yes—
43#10622637C2213yes—
44Q8×C11⋊C8C2211yescharacteristic
45Q8×C11⋊C8C2211yescharacteristic
46#10622539C2213yes—
47#10622538C2213yes—
48#10622450C2213yes—
49#10622449C2216yes—
50#10622448C2216yes—
51#10622448C2213yes—
52#10622447C2213yes—
53#10622447C2213yes—
54#10622446C2213yes—
55D11×C4⋊C8C2213yes—
56D11×C4⋊C8C2216yes—
57#10622444C2213yes—
58#10622444C2213yes—
59#10622441C2216yes—
60#10622319C2213yes—
61#10622319C2213yes—
62#10622318C2216yes—
63D11×#97C2216yes—
64#10622314C2213yes—
65#10622314C2213yes—
66C4×#4313C2213yes—
67C8×D44C2213yes—
68C8×D44C2213yes—
69#10622298C2213yes—
70#10622298C2213yes—
71C4×C8×D11C2213yes—
72#10622292C2213yes—
73#10622292C2213yes—
74C22×Q8×C11C2×C411yescharacteristic
75#67040—28no—
76C2×#4343C2×C413yes—
77C2×#4343C2×C411yescharacteristic
78C2×Q8×D11C2×C411yescharacteristic
79C2×Q8×D11C2×C413yes—
80C2×#4339C2×C413yes—
81C2×#4339C2×C413yes—
82C2×C11×M16C2311yescharacteristic
83C2×C11×M16C2313yes—
84C4×Q8×C11C2×C413yes—
85C4×Q8×C11C2×C411yescharacteristic
86C4×Q8×C11C2311yescharacteristic
87C4×Q8×C11C2313yes—
88C2×C11×C4⋊C4C2×C413yes—
89C2×C42×C11C2313yes—
90Q8×Dic11C2×C413yes—
91Q8×Dic11C2×C411yescharacteristic
92Q8×Dic11C2×C413yes—
93Q8×Dic11C2×C411yescharacteristic
94C4×C22⋊D11C2×C413yes—
95C4×C22⋊D11C2×C413yes—
96C4×C22⋊D11C2×C416yes—
97C4×C22⋊D11C2313yes—
98C4×C22⋊D11C2311yescharacteristic
99#66979C2×C413yes—
100#66979C2×C413yes—
101C2×#4313C2311yescharacteristic
102C2×#4313C2313yes—
103C2×C8×D11C2313yes—
104C2×C8×D11C2313yes—
105C2×C8×D11C2316yes—
106#66946C2×C416yes—
107#66946C2×C413yes—
108#66946C2×C413yes—
109#66945C2×C416yes—
110#66945C2×C413yes—
111#66945C2×C413yes—
112C4⋊C4×D11C2×C416yes—
113C4⋊C4×D11C2×C413yes—
114C4⋊C4×D11C2×C413yes—
115#66940C2×C413yes—
116#66940C2×C416yes—
117#66940C2×C413yes—
118C4×D44C2×C413yes—
119C4×D44C2×C413yes—
120C4×D44C2313yes—
121C4×D44C2313yes—
122#66925C2×C413yes—
123#66925C2×C416yes—
124#66925C2×C413yes—
125C42×D11C2313yes—
126C42×D11C2313yes—
127C42×D11C2316yes—
128C4×Dic22C2×C413yes—
129C4×Dic22C2×C413yes—
130C4×Dic22C2313yes—
131C4×Dic22C2313yes—
132C11×C4⋊C8C2313yes—
133C11×C4⋊C8C2313yes—
134C11×C4⋊C8C2316yes—
135C11×#97C2313yes—
136C11×#97C2313yes—
137C4×C8×C11C2313yes—
138C4×C8×C11C2313yes—
139C22⋊(C11⋊C8)C2311yescharacteristic
140C22⋊(C11⋊C8)C2313yes—
141(C2×D11)⋊C8C2313yes—
142(C2×D11)⋊C8C2313yes—
143(C2×D11)⋊C8C2316yes—
144(C2×D11)⋊C8C2311yescharacteristic
145(C2×D11)⋊C8C2313yes—
146#66879C2313yes—
147#66879C2316yes—
148#66879C2313yes—
149Dic11⋊C8C2313yes—
150Dic11⋊C8C2316yes—
151Dic11⋊C8C2313yes—
152Dic11⋊C8C2311yescharacteristic
153Dic11⋊C8C2313yes—
154C8×Dic11C2311yescharacteristic
155C8×Dic11C2313yes—
156C4⋊(C11⋊C8)C2313yes—
157C4⋊(C11⋊C8)C2313yes—
158C4⋊(C11⋊C8)C2313yes—
159C4⋊(C11⋊C8)C2313yes—
160#66867C2316yes—
161C4×C11⋊C8C2313yes—
162C4×C11⋊C8C2313yes—
163#60343—111nomaximal, Sylow
164C2×Q8×C11—24no—
165C2×Q8×C11C22×C413yes—
166C2×Q8×C11C22×C411yescharacteristic
167C22×C4×C11C22×C413yes—
168C22×C4×C11C22×C413yes—
169C22×C4×C11C2411yescharacteristic
170C2×C22⋊D11C22×C411yescharacteristic
171C2×C22⋊D11C22×C413yes—
172#4343—212no—
173#4343M1618yescomplemented
174Q8×D11—212no—
175Q8×D11—24no—
176#4339—212no—
177#4339—212no—
178C2×D44C22×C413yes—
179C2×D44C22×C413yes—
180C2×C4×D11C22×C416yes—
181C2×C4×D11C22×C413yes—
182C2×C4×D11C22×C413yes—
183C2×C4×D11C22×C413yes—
184C2×C4×D11C22×C416yes—
185C2×C4×D11C22×C413yes—
186C2×C4×D11C2413yes—
187C2×C4×D11C2411yescharacteristic
188C2×Dic22C22×C413yes—
189C2×Dic22C22×C413yes—
190C11×M16—22no—
191C11×M16—43no—
192C2×C8×C11C2413yes—
193C2×C8×C11C2411yescharacteristic
194C2×C8×C11C2413yes—
195C2×C8×C11C2411yescharacteristic
196C11×C4⋊C4C22×C416yes—
197C11×C4⋊C4C22×C413yes—
198C11×C4⋊C4C22×C413yes—
199C42×C11C22×C413yes—
200C42×C11C22×C413yes—
201C42×C11C2413yes—
202C42×C11C2413yes—
203C22⋊Dic11C22×C413yes—
204C22⋊Dic11C22×C411yescharacteristic
205(C2×D11)⋊C4C22×C411yescharacteristic
206(C2×D11)⋊C4C22×C413yes—
207(C2×D11)⋊C4C22×C413yes—
208(C2×D11)⋊C4C22×C416yes—
209(C2×D11)⋊C4C22×C413yes—
210C4⋊Dic11C22×C413yes—
211C4⋊Dic11C22×C413yes—
212C4⋊Dic11C22×C413yes—
213C4⋊Dic11C22×C413yes—
214Dic11⋊C4C22×C413yes—
215Dic11⋊C4C22×C411yescharacteristic
216Dic11⋊C4C22×C416yes—
217Dic11⋊C4C22×C413yes—
218Dic11⋊C4C22×C413yes—
219C4×Dic11C22×C413yes—
220C4×Dic11C22×C416yes—
221C4×Dic11C22×C413yes—
222C4×Dic11C22×C416yes—
223C4×Dic11C22×C413yes—
224C4×Dic11C22×C413yes—
225C4×Dic11C2411yescharacteristic
226C4×Dic11C2413yes—
227C2×C11⋊C8C2411yescharacteristic
228C2×C11⋊C8C2411yescharacteristic
229C2×C11⋊C8C2413yes—
230C2×C11⋊C8C2413yes—
231#4313—22no—
232#4313—43no—
233C8×D11—26no—
234C8×D11—43no—
235C8×D11—46no—
236C4×2−1+4—111no—
237#2990—113no—
238#2990—113no—
239#2989—113no—
240#2988—111no—
241#2984—111no—
242#2984—111no—
243#2983—113no—
244#2970—113no—
245#2970—113no—
246#2965—113no—
247C8×#41—111no—
248Q8×M16—111no—
249Q8×M16D1111yescharacteristic, complemented
250C2×#446—113no—
251C23×C11C23×C411yescharacteristic
252C22×D11C23×C411yescharacteristic
253C22×D11C23×C413yes—
254Q8×C11—26no—
255Q8×C11C2×M1614yes—
256C2×C4×C11—26no—
257C2×C4×C11—21no—
258C2×C4×C11—21no—
259C2×C4×C11—43no—
260C2×C4×C11C23×C413yes—
261C2×C4×C11C23×C413yes—
262C2×C4×C11C23×C413yes—
263C2×C4×C11C23×C411yescharacteristic
264C2×C4×C11C23×C413yes—
265C2×C4×C11C2511yescharacteristic
266C22⋊D11—26no—
267C22⋊D11—22no—
268C2×Dic11C23×C413yes—
269C2×Dic11C23×C411yescharacteristic
270C2×Dic11C23×C413yes—
271C2×Dic11C23×C411yescharacteristic
272C2×Dic11C23×C413yes—
273C2×Dic11C23×C411yescharacteristic
274D44—26no—
275D44C2×M16112yes—
276C4×D11—212no—
277C4×D11—26no—
278C4×D11—23no—
279C4×D11—21no—
280C4×D11—23no—
281C4×D11—21no—
282C4×D11—43no—
283C4×D11—46no—
284C4×D11—43no—
285C4×D11C2×M16112yes—
286Dic22—26no—
287Dic22—26no—
288C8×C11—21no—
289C8×C11—23no—
290C8×C11—23no—
291C8×C112−1+412yescomplemented
292C11⋊C8—23no—
293C11⋊C8—21no—
294C11⋊C8—21no—
295C11⋊C8—23no—
296C2×2−1+4—111no—
297#520—111no—
298#520—113no—
299#520—113no—
300#520—113no—
301#519—111no—
302#519—113no—
303#519—111no—
304C4×#41—111no—
305C4×#41—113no—
306C4×#41—113no—
307C4×#41—113no—
308C2×C4×Q8—113no—
309C2×C4×Q8—111no—
310C2×C4×Q8C2×D1111yescharacteristic
311#446—113no—
312#446—113no—
313#446—116no—
314#446—113no—
315#446—113no—
316#446—113no—
317#446—113no—
318#446—113no—
319#446—113no—
320#446C2×D1113yes—
321#446C2×D1113yes—
322C8×Q8—111no—
323C8×Q8—111no—
324C8×Q8C2×D1111yescharacteristic
325C8×Q8C2×D1111yescharacteristic
326#436—111no—
327#436—113no—
328#435—113no—
329#435—113no—
330#435—116no—
331#435—116no—
332#435—113no—
333#435—113no—
334C8×D4—113no—
335C8×D4—113no—
336C8×D4—113no—
337C8×D4—113no—
338#432—113no—
339#432—116no—
340#432—113no—
341#432—116no—
342#431—113no—
343#431—113no—
344#431—113no—
345#431—113no—
346#423—113no—
347#423C2×D1113yes—
348C2×C4⋊C8—113no—
349C2×C4⋊C8—116no—
350C4×M16—113no—
351C4×M16C2×D1113yes—
352C2×#97—116no—
353C2×C4×C8—113no—
354C22×C11—21no—
355C22×C11—21no—
356C22×C11—21no—
357C22×C11C24×C411yescharacteristic
358C2×D11—23no—
359C2×D11—23no—
360C2×D11—21no—
361C2×D11—21no—
362C2×D11—21no—
363C2×D11C22×M1616yes—
364C4×C11—21no—
365C4×C11—23no—
366C4×C11—23no—
367C4×C11—23no—
368C4×C11C22×M1616yes—
369C4×C11C2×2−1+411yescharacteristic
370C4×C11#58511yescharacteristic
371Dic11—23no—
372Dic11—21no—
373Dic11—23no—
374Dic11—21no—
375Dic11—23no—
376Dic11C22×M1612yes—
3772−1+4—228no—
378C2×#41—111no—
379C2×#41—113no—
380C2×#41—113no—
381C2×#41—113no—
382C22×Q8—113no—
383C22×Q8—111no—
384C22×Q8C4×D1111yescharacteristic
385C2×M16—111no—
386C2×M16—113no—
387C2×M16C22×D1111yescharacteristic
388C2×M16C22×D1113yes—
389C22×C8—113no—
390C22×C8—113no—
391C22×C8—116no—
392C4×Q8—113no—
393C4×Q8—111no—
394C4×Q8—113no—
395C4×Q8—111no—
396C4×Q8—116no—
397C4×Q8—113no—
398C4×Q8—113no—
399C4×Q8—113no—
400C4×Q8—113no—
401C4×Q8—113no—
402C4×Q8—113no—
403C4×Q8C4×D1113yes—
404C4×Q8C4×D1111yescharacteristic
405C4×Q8C22×D1111yescharacteristic
406C4×Q8C22×D1113yes—
407C4×D4—113no—
408C4×D4—113no—
409C4×D4—116no—
410C4×D4—113no—
411C4×D4—111no—
412C4×D4—113no—
413C4×D4—113no—
414C4×D4—116no—
415C4×D4—113no—
416C4×D4—113no—
417C4×D4—113no—
418C4×D4—113no—
419#117—113no—
420#117—113no—
421#117—113no—
422#117—113no—
423#117—116no—
424#117—113no—
425#117—113no—
426#117—116no—
427C2×C4⋊C4—113no—
428C2×C4⋊C4—116no—
429C2×C4⋊C4—113no—
430C2×C4⋊C4C4×D1113yes—
431C2×C42—113no—
432C2×C42—116no—
433C2×C42—113no—
434C2×C42C22×D1113yes—
435C4⋊C8—113no—
436C4⋊C8—113no—
437C4⋊C8—116no—
438C4⋊C8—111no—
439C4⋊C8—113no—
440C4⋊C8—113no—
441C4⋊C8—113no—
442C4⋊C8—113no—
443C4⋊C8—113no—
444C4⋊C8C22×D1113yes—
445C4⋊C8C22×D1116yes—
446C4⋊C8C22×D1113yes—
447C22⋊C8—111no—
448C22⋊C8—113no—
449C22⋊C8—111no—
450C22⋊C8—113no—
451C22⋊C8—116no—
452C22⋊C8—113no—
453C22⋊C8—113no—
454#97—113no—
455#97—116no—
456#97—113no—
457#97—116no—
458#97C22×D1113yes—
459#97C22×D1113yes—
460C4×C8—111no—
461C4×C8—113no—
462C4×C8—113no—
463C4×C8—113no—
464C4×C8C22×D1113yes—
465C4×C8C22×D1113yes—
466C2×C11—41no—
467C2×C11C4×2−1+411yescharacteristic
468C2×C11C23×M1611yescharacteristic
469C2×C11#357311yescharacteristic
470D11—26no—
471D11—41no—
472#41—118no—
473#41—2212no—
474#41—2212no—
475#41—2212no—
476C2×Q8—24no—
477C2×Q8—113no—
478C2×Q8—113no—
479C2×Q8—2212no—
480C2×Q8—224no—
481C2×Q8C2×C4×D1113yes—
482C2×Q8C2×C4×D1111yescharacteristic
483C2×D4—111no—
484C2×D4—113no—
485C2×D4—113no—
486C2×D4—113no—
487C22×C4—113no—
488C22×C4—116no—
489C22×C4—113no—
490C22×C4—113no—
491C22×C4—111no—
492C22×C4—113no—
493C22×C4—116no—
494C22×C4—113no—
495C22×C4C2×C4×D1113yes—
496C22×C4C2×C4×D1113yes—
497C22×C4C23×D1111yescharacteristic
498M16—22no—
499M16—43no—
500M16—222no—
501M16—443no—
502C2×C8—111no—
503C2×C8—111no—
504C2×C8—113no—
505C2×C8—113no—
506C2×C8—226no—
507C2×C8—446no—
508C2×C8—443no—
509C2×C8C23×D1113yes—
510C2×C8C23×D1111yescharacteristic
511C2×C8C23×D1113yes—
512C2×C8C23×D1111yescharacteristic
513C4⋊C4—113no—
514C4⋊C4—113no—
515C4⋊C4—116no—
516C4⋊C4—113no—
517C4⋊C4—113no—
518C4⋊C4—111no—
519C4⋊C4—113no—
520C4⋊C4—113no—
521C4⋊C4—113no—
522C4⋊C4C2×C4×D1116yes—
523C4⋊C4C2×C4×D1113yes—
524C4⋊C4C2×C4×D1113yes—
525C22⋊C4—113no—
526C22⋊C4—111no—
527C22⋊C4—116no—
528C22⋊C4—113no—
529C22⋊C4—113no—
530C22⋊C4—113no—
531C22⋊C4—111no—
532C42—113no—
533C42—116no—
534C42—113no—
535C42—113no—
536C42—116no—
537C42—113no—
538C42—111no—
539C42—113no—
540C42C2×C4×D1113yes—
541C42C2×C4×D1113yes—
542C42C23×D1113yes—
543C42C23×D1113yes—
544C11#6034311yescharacteristic, complemented, Sylow
545C23—113no—
546C23—111no—
547C23C22×C4×D1111yescharacteristic
548Q8—26no—
549Q8—226no—
550Q8—226no—
551Q8M16×D1114yes—
552D4—1112no—
553D4—226no—
554D4—222no—
555D4—226no—
556C2×C4—26no—
557C2×C4—21no—
558C2×C4—21no—
559C2×C4—43no—
560C2×C4—111no—
561C2×C4—1112no—
562C2×C4—113no—
563C2×C4—111no—
564C2×C4—111no—
565C2×C4—113no—
566C2×C4—113no—
567C2×C4—2212no—
568C2×C4—226no—
569C2×C4—223no—
570C2×C4—221no—
571C2×C4—223no—
572C2×C4—221no—
573C2×C4—443no—
574C2×C4—446no—
575C2×C4—443no—
576C2×C4C22×C4×D1113yes—
577C2×C4C22×C4×D1113yes—
578C2×C4C22×C4×D1113yes—
579C2×C4C22×C4×D1111yescharacteristic
580C2×C4C22×C4×D1113yes—
581C2×C4C24×D1111yescharacteristic
582C8—21no—
583C8—23no—
584C8—23no—
585C8—223no—
586C8—221no—
587C8—221no—
588C8—223no—
589C8#6704012yescomplemented
590C22—21no—
591C22—21no—
592C22—21no—
593C22—116no—
594C22—223no—
595C22—223no—
596C22—221no—
597C22—221no—
598C22—221no—
599C22C23×C4×D1111yescharacteristic
600C4—23no—
601C4—23no—
602C4—23no—
603C4—21no—
604C4—112no—
605C4—223no—
606C4—221no—
607C4—223no—
608C4—223no—
609C4—221no—
610C4C2×M16×D1116yes—
611C4C2×#6704011yescharacteristic
612C4#1062345311yescharacteristic
613C2—41no—
614C2—226no—
615C2—441no—
616C2C4×#6704011yescharacteristic
617C2C22×M16×D1111yescharacteristic
618C2#1308332911yescharacteristic
subgroupG/H
center, FrattiniC2×C4C24×D11
commutator, socleC22×C11C24×C4
FittingQ8×C11×M16C2
prime radicalC2×#67040C4
cosocleC2×C4×C11C25
hypercenterQ8×M16D11
hypocenterC11#60343
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ Q8×M16

Complements

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

NH ≅ G/Ntype
2. #13077742C2semidirect
3. #13077740C2semidirect
4. #13077730C2semidirect
5. #13077726C2semidirect
6. #13077705C2semidirect
7. #13077704C2semidirect
8. #13077698C2semidirect
9. #13077631C2semidirect
10. #13077629C2semidirect
11. #13077578C2semidirect
12. C8×#4343C2semidirect
13. Q8×#4313C2semidirect
14. D11×#446C2semidirect
15. Q8×C11×M16C2semidirect
173. #4343M16semidirect
249. Q8×M16D11semidirect
291. C8×C112−1+4semidirect
544. C11#60343semidirect
589. C8#67040semidirect

Maximal subgroups

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

subgroupindex
C4×#670402
#130777422
#130777402
#130777302
#130777262
#130777052
#130777042
#130776982
#130776312
#130776292
#130775782
C8×#43432
Q8×#43132
D11×#4462
Q8×C11×M162
#6034311