Finite Group Databasebeta

← #14724671

Subgroups — #14724671

Order 2816.

680 conjugacy classes of subgroups.

The subgroup lattice has 602 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13078622C211yesmaximal, characteristic
2#13077564C211yesmaximal, characteristic, complemented
3D4×#4313C211yesmaximal, characteristic
4#13067506C211yesmaximal, characteristic, complemented
5#13067505C211yesmaximal, characteristic, complemented
6#13067461C211yesmaximal, characteristic, complemented
7#13067456C211yesmaximal, characteristic, complemented
8#13067449C211yesmaximal, characteristic, complemented
9SD16×C11⋊C8C211yesmaximal, characteristic, complemented
10C8×#4324C211yesmaximal, characteristic, complemented
11#13067385C211yesmaximal, characteristic, complemented
12#13067069C211yesmaximal, characteristic, complemented
13D11×D4⋊C8C211yesmaximal, characteristic
14#13066895C211yesmaximal, characteristic, complemented
15C11×#1582C211yesmaximal, characteristic, complemented
16C22×#4313—21no—
17#10623109C2211yescharacteristic
18C4×D4×D11C2211yescharacteristic
19C11×#446C2211yescharacteristic, complemented
20C4×C11×SD16C2211yescharacteristic
21C8×D4×C11C2211yescharacteristic
22#10622782C411yescharacteristic
23#10622775C411yescharacteristic
24#10622724—21no—
25C4×#4325C2211yescharacteristic
26Q8×C11⋊C8C2211yescharacteristic, complemented
27C4×#4324C2211yescharacteristic
28D4×C11⋊C8C2211yescharacteristic
29#10622483C411yescharacteristic
30#10622475C411yescharacteristic
31#10622452—21no—
32#10622451C2211yescharacteristic
33#10622450C2211yescharacteristic
34D11×C4⋊C8C2211yescharacteristic
35#10622444—21no—
36#10622444C2211yescharacteristic, complemented
37#10622431C411yescharacteristic
38#10622418C411yescharacteristic
39#10622389C411yescharacteristic
40#10622374C411yescharacteristic
41#10622343—21no—
42#10622339—21no—
43#10622321—21no—
44#10622314—21no—
45C4×#4314C2211yescharacteristic
46#10622301C2211yescharacteristic
47C4×#4313C2211yescharacteristic
48#10622298C2211yescharacteristic
49C4×C8×D11C2211yescharacteristic
50C8×Dic22C2211yescharacteristic, complemented
51C11×#334C2211yescharacteristic, complemented
52C11×Q8⋊C8C2211yescharacteristic, complemented
53C11×D4⋊C8C2211yescharacteristic
54C11×#322C2211yescharacteristic, complemented
55Q8⋊(C11⋊C8)C2211yescharacteristic, complemented
56D4⋊(C11⋊C8)C2211yescharacteristic
57#10622122C2211yescharacteristic, complemented
58#10622121C2211yescharacteristic
59#10622118C2211yescharacteristic, complemented
60#10622118C2211yescharacteristic, complemented
61#10622097C2211yescharacteristic
62#10622095C2211yescharacteristic, complemented
63#10622094C2211yescharacteristic, complemented
64#10622092C2211yescharacteristic, complemented
65C8×C11⋊C8C2211yescharacteristic, complemented
66C8×C11⋊C8C2211yescharacteristic, complemented
67C2×D4×D11C2×C411yescharacteristic
68C22×C4×D11—21no—
69C2×C11×SD16C2×C411yescharacteristic
70C22×C8×C11—21no—
71C4×Q8×C11C2311yescharacteristic
72C4×D4×C11C2311yescharacteristic
73#66999C2×C411yescharacteristic
74#66997C2×C411yescharacteristic
75C2×#4325C2×C411yescharacteristic
76D4×Dic11C2×C411yescharacteristic
77C2×#4324C2×C411yescharacteristic
78C4×C22⋊D11—21no—
79C22×C11⋊C8—21no—
80C2×#4314C2×C411yescharacteristic
81C2×#4313—21no—
82C2×#4313—21no—
83C2×#4313—21no—
84C2×#4313—44no—
85C2×#4313D411yescharacteristic
86C2×#4313D411yescharacteristic
87C2×C8×D11—21no—
88C2×C8×D11—21no—
89#66950C2×C411yescharacteristic
90#66949—21no—
91#66946C2×C411yescharacteristic
92C4⋊C4×D11C2×C411yescharacteristic
93#66942—21no—
94#66941C2×C411yescharacteristic
95(C22⋊D11)⋊C4—21no—
96C22⋊C4×D11—21no—
97C4×D44C2311yescharacteristic
98#66925—21no—
99C42×D11C2311yescharacteristic
100C4×Dic22—21no—
101C4×Dic22C2311yescharacteristic
102C11×#106C2×C411yescharacteristic
103C11×C4⋊C8—21no—
104C11×C4⋊C8C2311yescharacteristic
105C11×C4⋊C8C2311yescharacteristic
106C11×#103C2×C411yescharacteristic
107C11×#102C2×C411yescharacteristic
108C11×C22⋊C8—21no—
109C11×#97—21no—
110C4×C8×C11C2311yescharacteristic
111C4×C8×C11C2311yescharacteristic
112C4×C8×C11C2311yescharacteristic
113#66899C2×C411yescharacteristic
114#66896C2×C411yescharacteristic
115C22⋊(C11⋊C8)—21no—
116#66885C2×C411yescharacteristic
117(C2×D11)⋊C8—21no—
118(C2×D11)⋊C8—21no—
119(C2×D11)⋊C8C2×C411yescharacteristic
120(C2×D11)⋊C8C2×C411yescharacteristic
121#66881C2×C411yescharacteristic
122#66880C2×C411yescharacteristic
123#66879—21no—
124#66879D411yescharacteristic
125#66879D411yescharacteristic
126Dic11⋊C8—21no—
127Dic11⋊C8—21no—
128Dic11⋊C8—21no—
129Dic11⋊C8—21no—
130Dic11⋊C8C2×C411yescharacteristic
131Dic11⋊C8C2×C411yescharacteristic
132C8×Dic11—21no—
133C8×Dic11—21no—
134#66874C2×C411yescharacteristic
135#66873C2×C411yescharacteristic
136#66872C2×C411yescharacteristic
137#66872C2×C411yescharacteristic
138C4⋊(C11⋊C8)—21no—
139C4⋊(C11⋊C8)C2311yescharacteristic
140C4⋊(C11⋊C8)C2311yescharacteristic
141C4×C11⋊C8—21no—
142C4×C11⋊C8C2311yescharacteristic
143C4×C11⋊C8C2311yescharacteristic
144C4×C11⋊C8C2311yescharacteristic
145#17995—111nomaximal, Sylow
146C23×D11—21no—
147C2×Q8×C11C22×C411yescharacteristic
148C2×D4×C11C22×C411yescharacteristic
149C22×C4×C11—21no—
150C2×C22⋊D11—21no—
151C22×Dic11—21no—
152D4×D11—22no—
153D4×D11—41no—
154C2×D44C22×C411yescharacteristic
155C2×C4×D11—21no—
156C2×C4×D11—21no—
157C2×C4×D11—21no—
158C2×C4×D11—42no—
159C2×C4×D11—42no—
160C2×C4×D11C22×C411yescharacteristic
161C2×C4×D11C2×D411yescharacteristic
162C2×C4×D11#4111yescharacteristic
163C2×Dic22—21no—
164C2×Dic22C22×C411yescharacteristic
165C11×SD16—22no—
166C2×C8×C11—21no—
167C2×C8×C11—21no—
168C2×C8×C11—21no—
169C2×C8×C11—42no—
170C2×C8×C11C22×C411yescharacteristic
171C2×C8×C11C22×C411yescharacteristic
172C2×C8×C11C2×D411yescharacteristic
173C2×C8×C11C2×D411yescharacteristic
174C11×C4⋊C4—21no—
175C11×C4⋊C4C22×C411yescharacteristic
176C11×C4⋊C4C22×C411yescharacteristic
177C11×C22⋊C4—21no—
178C42×C11—21no—
179C42×C11C2411yescharacteristic
180C22⋊Dic11—21no—
181#4325—41no—
182#4324—22no—
183(C2×D11)⋊C4—21no—
184(C2×D11)⋊C4—21no—
185(C2×D11)⋊C4—21no—
186(C2×D11)⋊C4—21no—
187C4⋊Dic11—21no—
188C4⋊Dic11C22×C411yescharacteristic
189C4⋊Dic11C22×C411yescharacteristic
190Dic11⋊C4—21no—
191Dic11⋊C4—21no—
192Dic11⋊C4—21no—
193Dic11⋊C4—21no—
194Dic11⋊C4—21no—
195Dic11⋊C4—21no—
196C4×Dic11—21no—
197C4×Dic11C22×C411yescharacteristic
198C4×Dic11C2×D411yescharacteristic
199C4×Dic11#4111yescharacteristic
200C2×C11⋊C8—21no—
201C2×C11⋊C8—21no—
202C2×C11⋊C8—21no—
203C2×C11⋊C8—42no—
204C2×C11⋊C8C22×C411yescharacteristic
205C2×C11⋊C8C22×C411yescharacteristic
206C2×C11⋊C8C2×D411yescharacteristic
207C2×C11⋊C8C2×D411yescharacteristic
208#4314—41no—
209#4313—22no—
210#4313—42no—
211#4313—42no—
212#4313—42no—
213#4313SD1614yescomplemented
214C8×D11—42no—
215C8×D11—42no—
216#3101—111no—
217#2962—111no—
218D4×M16—111no—
219#1590—111no—
220#1590—111no—
221#1583—111no—
222#1583—111no—
223#1582—111no—
224#1582D1111yescharacteristic, complemented
225C8×SD16—111no—
226C8×SD16—111no—
227#1570—111no—
228#1493—111no—
229C2×D4⋊C8—111no—
230C8×M16—111no—
231C23×C11—21no—
232C22×D11—21no—
233C22×D11—42no—
234C22×D11—42no—
235C22×D11—81no—
236C22×D11C4×D411yescharacteristic
237Q8×C11—21no—
238Q8×C11—21no—
239D4×C11—21no—
240D4×C11#13112yes—
241C2×C4×C11—21no—
242C2×C4×C11—21no—
243C2×C4×C11—21no—
244C2×C4×C11—41no—
245C2×C4×C11—41no—
246C2×C4×C11C23×C411yescharacteristic
247C2×C4×C11C22×D411yescharacteristic
248C2×C4×C11C2×#4111yescharacteristic
249C22⋊D11—42no—
250C2×Dic11—21no—
251C2×Dic11—21no—
252C2×Dic11—21no—
253C2×Dic11—42no—
254C2×Dic11C4×D411yescharacteristic
255C2×Dic11C4×D411yescharacteristic
256C2×Dic11C4×D411yescharacteristic
257D44—21no—
258D44—21no—
259C4×D11—21no—
260C4×D11—21no—
261C4×D11—41no—
262C4×D11—42no—
263C4×D11—41no—
264C4×D11—41no—
265C4×D11—42no—
266C4×D11C2×SD1612yes—
267C4×D11#13512yes—
268Dic22—21no—
269Dic22—21no—
270Dic22—81no—
271C8×C11—21no—
272C8×C11—21no—
273C8×C11—21no—
274C8×C11—41no—
275C8×C11—41no—
276C8×C11—41no—
277C8×C11C2×SD1612yes—
278C11⋊C8—22no—
279C11⋊C8—21no—
280C11⋊C8—21no—
281C11⋊C8—21no—
282C11⋊C8—41no—
283C11⋊C8—41no—
284C11⋊C8C2×SD1612yes—
285C22×M16—221no—
286#533—111no—
287C2×C4×D4—111no—
288#483—111no—
289#483—111no—
290#476—111no—
291#476—111no—
292#461—111no—
293#461—111no—
294#450—111no—
295#450—111no—
296#446—111no—
297#446—221no—
298#446—221no—
299#446C2×D1111yescharacteristic, complemented
300C8×Q8—111no—
301C8×Q8—111no—
302C4×SD16—111no—
303C4×SD16—111no—
304C4×SD16—111no—
305C4×SD16C2×D1111yescharacteristic
306#436—111no—
307#436—111no—
308#435—221no—
309#435—221no—
310C8×D4—111no—
311C8×D4C2×D1111yescharacteristic
312#431—111no—
313#424—221no—
314#423—111no—
315C2×C4⋊C8—111no—
316#407—221no—
317#405—221no—
318C4×M16—111no—
319C2×C4×C8—111no—
320#334—111no—
321#334—111no—
322#334—111no—
323#334C2×D1111yescharacteristic, complemented
324Q8⋊C8—111no—
325Q8⋊C8—111no—
326Q8⋊C8—111no—
327Q8⋊C8C2×D1111yescharacteristic, complemented
328D4⋊C8—111no—
329D4⋊C8—111no—
330D4⋊C8—111no—
331D4⋊C8C2×D1111yescharacteristic
332#322—111no—
333#322C2×D1111yescharacteristic, complemented
334C82—111no—
335C82—111no—
336C22×C11—22no—
337C22×C11—41no—
338C22×C11—41no—
339C22×C11C2×C4×D411yescharacteristic
340C2×D11—21no—
341C2×D11—21no—
342C2×D11—41no—
343C2×D11—41no—
344C2×D11—41no—
345C2×D11—84no—
346C2×D11C4×SD1612yes—
347C4×C11—21no—
348C4×C11—41no—
349C4×C11—41no—
350C4×C11—41no—
351C4×C11C2×#13111yescharacteristic
352C4×C11#56811yescharacteristic
353C4×C11C22×SD1611yescharacteristic
354C4×C11C2×#13511yescharacteristic
355Dic11—21no—
356Dic11—21no—
357Dic11—41no—
358Dic11—41no—
359Dic11—41no—
360Dic11C4×SD1612yes—
361C22×D4—111no—
362C23×C4—221no—
363C2×SD16—111no—
364C2×SD16—111no—
365C2×SD16—111no—
366C2×SD16C4×D1111yescharacteristic
367C2×M16—111no—
368C2×M16—111no—
369C2×M16—221no—
370C2×M16—221no—
371C2×M16—221no—
372C2×M16—444no—
373C22×C8—21no—
374C22×C8—221no—
375C22×C8—221no—
376C22×C8—221no—
377C4⋊Q8—111no—
378C4⋊Q8—111no—
379#125—221no—
380C22⋊Q8—111no—
381C22⋊Q8—111no—
382C22⋊Q8—221no—
383C4×Q8—111no—
384C4×Q8—221no—
385C4×Q8C22×D1111yescharacteristic
386C4×D4—111no—
387C4×D4—111no—
388C4×D4—111no—
389C4×D4—221no—
390C4×D4—221no—
391C4×D4C22×D1111yescharacteristic
392#117—221no—
393C2×C4⋊C4—111no—
394C2×C22⋊C4—221no—
395C2×C42—111no—
396#106—111no—
397#106—111no—
398#106—111no—
399#106C4×D1111yescharacteristic
400C4⋊C8—21no—
401C4⋊C8—111no—
402C4⋊C8—111no—
403C4⋊C8—111no—
404C4⋊C8—111no—
405C4⋊C8—221no—
406C4⋊C8—221no—
407C4⋊C8—221no—
408C4⋊C8—221no—
409C4⋊C8—221no—
410C4⋊C8C22×D1111yescharacteristic
411C4⋊C8C22×D1111yescharacteristic
412#103—111no—
413#103—111no—
414#103—111no—
415#103C4×D1111yescharacteristic
416#102—111no—
417#102—111no—
418#102—111no—
419#102C4×D1111yescharacteristic
420C22⋊C8—21no—
421C22⋊C8—111no—
422C22⋊C8—111no—
423C22⋊C8—221no—
424C22⋊C8—221no—
425C22⋊C8—221no—
426#97—21no—
427#97—111no—
428#97—111no—
429#97—221no—
430C4×C8—111no—
431C4×C8—111no—
432C4×C8—111no—
433C4×C8—221no—
434C4×C8—221no—
435C4×C8—221no—
436C4×C8C22×D1111yescharacteristic
437C4×C8C22×D1111yescharacteristic
438C4×C8C22×D1111yescharacteristic
439C2×C11—42no—
440C2×C11#293311yescharacteristic
441C2×C11C2×C4×SD1611yescharacteristic
442C2×C11#295611yescharacteristic
443D11—22no—
444D11—81no—
445C24—221no—
446C2×Q8—111no—
447C2×Q8—221no—
448C2×Q8C2×C4×D1111yescharacteristic
449C2×D4—111no—
450C2×D4—221no—
451C2×D4—222no—
452C2×D4—441no—
453C2×D4C2×C4×D1111yescharacteristic
454C22×C4—21no—
455C22×C4—111no—
456C22×C4—111no—
457C22×C4—111no—
458C22×C4—221no—
459C22×C4—221no—
460C22×C4—221no—
461C22×C4—221no—
462C22×C4—442no—
463C22×C4—442no—
464SD16—22no—
465SD16—222no—
466SD16—441no—
467SD16—441no—
468M16—114no—
469M16—222no—
470M16—442no—
471M16—442no—
472M16—442no—
473C2×C8—21no—
474C2×C8—21no—
475C2×C8—21no—
476C2×C8—42no—
477C2×C8—111no—
478C2×C8—111no—
479C2×C8—111no—
480C2×C8—111no—
481C2×C8—221no—
482C2×C8—221no—
483C2×C8—221no—
484C2×C8—442no—
485C2×C8—442no—
486C2×C8—442no—
487C2×C8C2×C4×D1111yescharacteristic
488C2×C8C2×C4×D1111yescharacteristic
489C2×C8D4×D1111yescharacteristic
490C2×C8D4×D1111yescharacteristic
491C4⋊C4—21no—
492C4⋊C4—111no—
493C4⋊C4—111no—
494C4⋊C4—221no—
495C4⋊C4—221no—
496C4⋊C4—221no—
497C4⋊C4—221no—
498C4⋊C4—221no—
499C4⋊C4—221no—
500C4⋊C4—221no—
501C4⋊C4C2×C4×D1111yescharacteristic
502C4⋊C4C2×C4×D1111yescharacteristic
503C22⋊C4—21no—
504C22⋊C4—221no—
505C22⋊C4—221no—
506C22⋊C4—221no—
507C22⋊C4—221no—
508C22⋊C4—221no—
509C42—21no—
510C42—111no—
511C42—111no—
512C42—111no—
513C42—221no—
514C42C23×D1111yescharacteristic
515C11#1799511yescharacteristic, complemented, Sylow
516C23—21no—
517C23—111no—
518C23—221no—
519C23—442no—
520C23—442no—
521C23—881no—
522Q8—21no—
523Q8—21no—
524Q8—221no—
525Q8—221no—
526Q8—881no—
527D4—21no—
528D4—221no—
529D4—221no—
530D4—442no—
531D4#6696012yes—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—111no—
538C2×C4—112no—
539C2×C4—112no—
540C2×C4—111no—
541C2×C4—111no—
542C2×C4—221no—
543C2×C4—221no—
544C2×C4—221no—
545C2×C4—221no—
546C2×C4—221no—
547C2×C4—441no—
548C2×C4—442no—
549C2×C4—442no—
550C2×C4—442no—
551C2×C4—441no—
552C2×C4—441no—
553C2×C4C22×C4×D1111yescharacteristic
554C2×C4C2×D4×D1111yescharacteristic
555C2×C4#41×D1111yescharacteristic
556C8—21no—
557C8—21no—
558C8—21no—
559C8—41no—
560C8—41no—
561C8—41no—
562C8—112no—
563C8—222no—
564C8—221no—
565C8—221no—
566C8—221no—
567C8—441no—
568C8—441no—
569C8SD16×D1112yes—
570C22—22no—
571C22—41no—
572C22—41no—
573C22—112no—
574C22—221no—
575C22—221no—
576C22—441no—
577C22—441no—
578C22—441no—
579C22—884no—
580C22C4×D4×D1111yescharacteristic
581C4—21no—
582C4—41no—
583C4—41no—
584C4—41no—
585C4—112no—
586C4—221no—
587C4—221no—
588C4—441no—
589C4—441no—
590C4—441no—
591C4C2×#6696011yescharacteristic
592C4#1062328111yescharacteristic
593C4C2×SD16×D1111yescharacteristic
594C4D11×#13511yescharacteristic
595C2—42no—
596C2—222no—
597C2—881no—
598C2#1307734211yescharacteristic
599C2C4×SD16×D1111yescharacteristic
600C2#1307752411yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
FittingC11×#1582C2
socleC22×C11C2×C4×D4
prime radicalC2×D4×D11C2×C4
cosocleC42×C11C24
hypercenter#1582D11
hypocenterC11#17995
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ #1582

Complements

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

NH ≅ G/Ntype
2. #13077564C2semidirect
4. #13067506C2semidirect
5. #13067505C2semidirect
6. #13067461C2semidirect
7. #13067456C2semidirect
8. #13067449C2semidirect
9. SD16×C11⋊C8C2semidirect
10. C8×#4324C2semidirect
11. #13067385C2semidirect
12. #13067069C2semidirect
14. #13066895C2semidirect
15. C11×#1582C2semidirect
19. C11×#446C22semidirect
26. Q8×C11⋊C8C22semidirect
36. #10622444C22semidirect
50. C8×Dic22C22semidirect
51. C11×#334C22semidirect
52. C11×Q8⋊C8C22semidirect
54. C11×#322C22semidirect
55. Q8⋊(C11⋊C8)C22semidirect
57. #10622122C22semidirect
59. #10622118C22semidirect
60. #10622118C22semidirect
62. #10622095C22semidirect
63. #10622094C22semidirect
64. #10622092C22semidirect
65. C8×C11⋊C8C22semidirect
66. C8×C11⋊C8C22semidirect
213. #4313SD16semidirect
224. #1582D11semidirect
299. #446C2×D11semidirect
323. #334C2×D11semidirect
327. Q8⋊C8C2×D11semidirect
333. #322C2×D11semidirect
515. C11#17995semidirect

Maximal subgroups

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

subgroupindex
#130786222
#130775642
D4×#43132
#130675062
#130675052
#130674612
#130674562
#130674492
SD16×C11⋊C82
C8×#43242
#130673852
#130670692
D11×D4⋊C82
#130668952
C11×#15822
#1799511