Finite Group Databasebeta

← #14724933

Subgroups — #14724933

Order 2816.

650 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#13078665C211yesmaximal, characteristic
2#13077778C211yesmaximal, characteristic, complemented
3#13077650C211yesmaximal, characteristic, complemented
4#13067508C211yesmaximal, characteristic, complemented
5#13067502C211yesmaximal, characteristic, complemented
6#13067496C211yesmaximal, characteristic, complemented
7#13067482C211yesmaximal, characteristic, complemented
8#13067482C211yesmaximal, characteristic, complemented
9#13067475C211yesmaximal, characteristic, complemented
10C8×#4314C211yesmaximal, characteristic, complemented
11C8×D88C211yesmaximal, characteristic, complemented
12#13067401C211yesmaximal, characteristic, complemented
13#13067077C211yesmaximal, characteristic, complemented
14C2×#10622097C211yesmaximal, characteristic, complemented
15C11×#1450C211yesmaximal, characteristic, complemented
16#10623010C2211yescharacteristic
17C2×C4×D44C2211yescharacteristic
18C11×#431C2211yescharacteristic
19C11×#431C2211yescharacteristic
20C2×C4×C8×C11C2211yescharacteristic
21#10622539C2211yescharacteristic
22C2×C4⋊(C11⋊C8)C2211yescharacteristic
23#10622460C411yescharacteristic
24#10622460C411yescharacteristic
25#10622457C411yescharacteristic
26#10622457C411yescharacteristic
27#10622453—21no—
28#10622452—21no—
29#10622449—21no—
30#10622449—21no—
31#10622348C411yescharacteristic
32#10622345C411yescharacteristic
33#10622344C411yescharacteristic
34#10622343—21no—
35#10622339—21no—
36(C22⋊D11)⋊C8—21no—
37D11×C22⋊C8—21no—
38#10622335C411yescharacteristic
39C4×D88C2211yescharacteristic
40C4×D88C2211yescharacteristic
41C4×#4314C2211yescharacteristic
42C4×#4314C2211yescharacteristic
43#10622301C2211yescharacteristic
44#10622301C2211yescharacteristic
45#10622301C2211yescharacteristic, complemented
46C8×D44C2211yescharacteristic
47C8×D44C2211yescharacteristic
48C8×D44C2211yescharacteristic, complemented
49#10622292C2211yescharacteristic, complemented
50C8×Dic22C2211yescharacteristic, complemented
51C11×#322C2211yescharacteristic, complemented
52C11×#322C2211yescharacteristic, complemented
53C82×C11C2211yescharacteristic, complemented
54C82×C11C2211yescharacteristic, complemented
55#10622097C2211yescharacteristic
56#10622097C2211yescharacteristic
57#10622097C2211yescharacteristic
58#10622097C2211yescharacteristic
59#10622097C2211yescharacteristic, complemented
60#10622097C2211yescharacteristic, complemented
61#10622096C2211yescharacteristic, complemented
62#10622096C2211yescharacteristic, complemented
63#10622095C2211yescharacteristic, complemented
64#10622095C2211yescharacteristic, complemented
65#10622094C2211yescharacteristic, complemented
66#10622094C2211yescharacteristic, complemented
67C22×D44C2×C411yescharacteristic
68C22×C4×D11—21no—
69C22×C8×C11—21no—
70C2×C42×C11C2311yescharacteristic
71#66983C2×C411yescharacteristic
72#66982—21no—
73C4×C22⋊D11—21no—
74C2×(C2×D11)⋊C4—21no—
75C2×C4⋊Dic11C2×C411yescharacteristic
76#66977C2×C411yescharacteristic
77C22×C11⋊C8—21no—
78C2×D88C2×C411yescharacteristic
79C2×D88C2×C411yescharacteristic
80C2×#4314C2×C411yescharacteristic
81C2×#4314C2×C411yescharacteristic
82C2×#4313—21no—
83C2×#4313—21no—
84C2×#4313—21no—
85C2×C8×D11—21no—
86C2×C8×D11—21no—
87C2×C8×D11—21no—
88#66929—21no—
89#66928C2×C411yescharacteristic
90C4×D44—21no—
91C4×D44—21no—
92C4×D44C2×C411yescharacteristic
93C4×D44C2×C411yescharacteristic
94C4×D44C2311yescharacteristic
95C4×D44C2311yescharacteristic
96C4×D44C2311yescharacteristic
97#66925—21no—
98#66923C2×C411yescharacteristic
99C4×Dic22C2311yescharacteristic
100C11×C4⋊C8C2×C411yescharacteristic
101C11×C4⋊C8C2×C411yescharacteristic
102C11×C4⋊C8D411yescharacteristic
103C11×C4⋊C8D411yescharacteristic
104C11×C22⋊C8C2×C411yescharacteristic
105C11×C22⋊C8C2×C411yescharacteristic
106C11×C22⋊C8D411yescharacteristic
107C11×C22⋊C8D411yescharacteristic
108C4×C8×C11—21no—
109C4×C8×C11C2311yescharacteristic
110C4×C8×C11C2311yescharacteristic
111C4×C8×C11C2311yescharacteristic
112C4×C8×C11C2311yescharacteristic
113C4×C8×C11C2311yescharacteristic
114C4×C8×C11C2311yescharacteristic
115C22⋊(C11⋊C8)—21no—
116#66885C2×C411yescharacteristic
117#66885C2×C411yescharacteristic
118#66885C2×C411yescharacteristic
119#66885C2×C411yescharacteristic
120#66885C2×C411yescharacteristic
121#66885C2×C411yescharacteristic
122(C2×D11)⋊C8—21no—
123(C2×D11)⋊C8—21no—
124(C2×D11)⋊C8—21no—
125(C2×D11)⋊C8—21no—
126(C2×D11)⋊C8—21no—
127(C2×D11)⋊C8—21no—
128#66882C2×C411yescharacteristic
129#66882C2×C411yescharacteristic
130#66881C2×C411yescharacteristic
131#66881C2×C411yescharacteristic
132#66880C2×C411yescharacteristic
133#66880C2×C411yescharacteristic
134#66879—21no—
135Dic11⋊C8—21no—
136Dic11⋊C8—21no—
137C8×Dic11—21no—
138C4⋊(C11⋊C8)—21no—
139C4⋊(C11⋊C8)C2311yescharacteristic
140C4⋊(C11⋊C8)C2311yescharacteristic
141C4⋊(C11⋊C8)C2311yescharacteristic
142C4⋊(C11⋊C8)C2311yescharacteristic
143#66867—21no—
144#18014—111nomaximal, Sylow
145C23×D11—21no—
146C22×C4×C11C22×C411yescharacteristic
147C22×C4×C11C2×D411yescharacteristic
148C22×C4×C11#4111yescharacteristic
149C2×C22⋊D11—21no—
150C22×Dic11—21no—
151C2×D44—22no—
152C2×D44—21no—
153C2×D44—41no—
154C2×D44C22×C411yescharacteristic
155C2×D44C22×C411yescharacteristic
156C2×D44C22×C411yescharacteristic
157C2×C4×D11—21no—
158C2×C4×D11—21no—
159C2×C4×D11—21no—
160C2×C4×D11—21no—
161C2×C4×D11—21no—
162C2×C4×D11—81no—
163C2×C4×D11—81no—
164C2×Dic22C22×C411yescharacteristic
165C2×C8×C11—24no—
166C2×C8×C11—21no—
167C2×C8×C11—21no—
168C2×C8×C11C22×C411yescharacteristic
169C2×C8×C11C22×C411yescharacteristic
170C2×C8×C11C22×C411yescharacteristic
171C2×C8×C11C22×C411yescharacteristic
172C2×C8×C11C2×D411yescharacteristic
173C2×C8×C11C2×D411yescharacteristic
174C2×C8×C11C2×D411yescharacteristic
175C2×C8×C11C2×D411yescharacteristic
176C42×C11C22×C411yescharacteristic
177C42×C11C2×D411yescharacteristic
178C42×C11#4111yescharacteristic
179C42×C11C2411yescharacteristic
180C22⋊Dic11—21no—
181(C2×D11)⋊C4—21no—
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
192C4⋊Dic11C22×C411yescharacteristic
193C4⋊Dic11C22×C411yescharacteristic
194Dic11⋊C4—21no—
195Dic11⋊C4—21no—
196Dic11⋊C4—21no—
197Dic11⋊C4—21no—
198C4×Dic11—21no—
199C2×C11⋊C8—21no—
200C2×C11⋊C8—21no—
201C2×C11⋊C8—21no—
202C2×C11⋊C8—21no—
203C2×C11⋊C8—81no—
204D88—22no—
205D88—41no—
206#4314—22no—
207#4314—41no—
208#4313—81no—
209#4313—81no—
210#4313—81no—
211C8×D11—81no—
212C8×D11—81no—
213C8×D11—81no—
214#3105—111no—
215#2994—111no—
216#2974—111no—
217#1590—111no—
218#1589—111no—
219#1588—111no—
220#1586—111no—
221#1586—111no—
222#1585—111no—
223C8×SD16—111no—
224C8×D8—111no—
225#1573—111no—
226#1494—111no—
227C2×D4⋊C8—111no—
228#1450D1111yescharacteristic, complemented
229C23×C11C4×D411yescharacteristic
230C22×D11—21no—
231C22×D11—21no—
232C22×D11—21no—
233C22×D11—42no—
234C22×D11—42no—
235C22×D11—81no—
236C2×C4×C11—22no—
237C2×C4×C11—21no—
238C2×C4×C11—21no—
239C2×C4×C11—21no—
240C2×C4×C11—21no—
241C2×C4×C11C4×D411yescharacteristic
242C2×C4×C11C4×D411yescharacteristic
243C2×C4×C11C4×D411yescharacteristic
244C2×C4×C11C23×C411yescharacteristic
245C2×C4×C11C22×D411yescharacteristic
246C2×C4×C11C2×#4111yescharacteristic
247C22⋊D11—42no—
248C2×Dic11—21no—
249C2×Dic11—21no—
250C2×Dic11—21no—
251C2×Dic11—21no—
252C2×Dic11—21no—
253C2×Dic11—81no—
254D44—21no—
255D44—21no—
256D44—21no—
257D44—21no—
258D44—21no—
259D44—42no—
260D44#13112yes—
261C4×D11—41no—
262C4×D11—41no—
263C4×D11—41no—
264C4×D11—41no—
265C4×D11—41no—
266C4×D11—41no—
267C4×D11—81no—
268C4×D11—81no—
269Dic22—21no—
270Dic22—21no—
271C8×C11—22no—
272C8×C11—22no—
273C8×C11—21no—
274C8×C11—21no—
275C8×C11—21no—
276C8×C11—21no—
277C8×C11—21no—
278C8×C11—21no—
279C8×C11—21no—
280C8×C11—21no—
281C11⋊C8—41no—
282C11⋊C8—41no—
283C11⋊C8—41no—
284C11⋊C8—41no—
285#529—111no—
286C2×C4×D4—111no—
287#484—111no—
288#481—111no—
289#478—111no—
290#478—111no—
291#463—111no—
292#463—111no—
293#450—111no—
294#447—111no—
295#446—111no—
296C8×Q8—111no—
297C4×SD16—111no—
298C4×SD16—111no—
299C4×D8—111no—
300C4×D8—111no—
301#436—111no—
302#436—111no—
303#436—111no—
304#435—221no—
305#435—221no—
306#435—221no—
307C8×D4—111no—
308C8×D4—111no—
309C8×D4—111no—
310C8×D4—221no—
311#433—221no—
312#432—111no—
313#431C2×D1111yescharacteristic
314#431C2×D1111yescharacteristic
315#424—221no—
316C2×C4⋊C8—111no—
317#407—221no—
318C2×C22⋊C8—221no—
319C2×C4×C8C2×D1111yescharacteristic
320#335—111no—
321#335—111no—
322#334—111no—
323#334—111no—
324Q8⋊C8—111no—
325Q8⋊C8—111no—
326D4⋊C8—111no—
327D4⋊C8—111no—
328D4⋊C8—111no—
329D4⋊C8—111no—
330D4⋊C8—111no—
331D4⋊C8—111no—
332#322C2×D1111yescharacteristic, complemented
333#322C2×D1111yescharacteristic, complemented
334C82C2×D1111yescharacteristic, complemented
335C82C2×D1111yescharacteristic, complemented
336C22×C11—21no—
337C22×C11—21no—
338C22×C11#44312yes—
339C22×C11C2×C4×D411yescharacteristic
340C2×D11—22no—
341C2×D11—41no—
342C2×D11—41no—
343C2×D11—41no—
344C2×D11—41no—
345C2×D11—41no—
346C2×D11—41no—
347C2×D11—41no—
348C2×D11—41no—
349C2×D11—84no—
350C4×C11—21no—
351C4×C11—21no—
352C4×C11—21no—
353C4×C11—21no—
354C4×C11C2×#13111yescharacteristic
355C4×C11#56811yescharacteristic
356C4×C11#57611yescharacteristic
357C4×C11#57711yescharacteristic
358Dic11—41no—
359Dic11—41no—
360Dic11—41no—
361Dic11—41no—
362Dic11—41no—
363C22×D4—111no—
364C23×C4—221no—
365C2×SD16—111no—
366C2×SD16—111no—
367C2×D8—111no—
368C2×D8—111no—
369C2×M16—221no—
370C2×M16—221no—
371C2×M16—221no—
372C22×C8—21no—
373C22×C8—221no—
374C22×C8—221no—
375C22×C8—221no—
376C22×C8—221no—
377#126—221no—
378#125—111no—
379#124—111no—
380#123—221no—
381C22⋊Q8—111no—
382#121—111no—
383C4×Q8—111no—
384C4×D4—111no—
385C4×D4—111no—
386C4×D4—111no—
387C4×D4—111no—
388C4×D4—111no—
389C4×D4—221no—
390C4×D4—221no—
391C4×D4—221no—
392#117—221no—
393C2×C4⋊C4—111no—
394C2×C22⋊C4—221no—
395C2×C42C22×D1111yescharacteristic
396#107—111no—
397#107—111no—
398#106—111no—
399#106—111no—
400C4⋊C8—111no—
401C4⋊C8—111no—
402C4⋊C8—111no—
403C4⋊C8—111no—
404C4⋊C8—221no—
405C4⋊C8—221no—
406C4⋊C8—221no—
407C4⋊C8C4×D1111yescharacteristic
408C4⋊C8C4×D1111yescharacteristic
409C4⋊C8D4411yescharacteristic
410C4⋊C8D4411yescharacteristic
411#103—111no—
412#103—111no—
413#102—111no—
414#102—111no—
415#102—111no—
416#102—111no—
417#102—111no—
418#102—111no—
419C22⋊C8—221no—
420C22⋊C8—221no—
421C22⋊C8—221no—
422C22⋊C8—221no—
423C22⋊C8—221no—
424C22⋊C8—221no—
425C22⋊C8—221no—
426C22⋊C8C4×D1111yescharacteristic
427C22⋊C8C4×D1111yescharacteristic
428C22⋊C8D4411yescharacteristic
429C22⋊C8D4411yescharacteristic
430#97—221no—
431#97—221no—
432C4×C8—21no—
433C4×C8—221no—
434C4×C8C22×D1111yescharacteristic
435C4×C8C22×D1111yescharacteristic
436C4×C8C22×D1111yescharacteristic
437C4×C8C22×D1111yescharacteristic
438C4×C8C22×D1111yescharacteristic
439C4×C8C22×D1111yescharacteristic
440C2×C11—22no—
441C2×C11#293311yescharacteristic
442C2×C11#294611yescharacteristic
443C2×C11C2×#44311yescharacteristic
444D11—42no—
445D11—81no—
446D11—81no—
447C24—221no—
448C2×Q8—111no—
449C2×D4—111no—
450C2×D4—111no—
451C2×D4—111no—
452C2×D4—222no—
453C2×D4—221no—
454C2×D4—221no—
455C2×D4—441no—
456C22×C4—221no—
457C22×C4—221no—
458C22×C4—221no—
459C22×C4—221no—
460C22×C4—221no—
461C22×C4—221no—
462C22×C4—881no—
463C22×C4—881no—
464C22×C4C2×C4×D1111yescharacteristic
465C22×C4C2×D4411yescharacteristic
466C22×C4#433911yescharacteristic
467SD16—222no—
468SD16—441no—
469D8—222no—
470D8—441no—
471M16—881no—
472M16—881no—
473M16—881no—
474C2×C8—24no—
475C2×C8—21no—
476C2×C8—21no—
477C2×C8—221no—
478C2×C8—221no—
479C2×C8—221no—
480C2×C8—221no—
481C2×C8—881no—
482C2×C8—881no—
483C2×C8—881no—
484C2×C8—881no—
485C2×C8C2×C4×D1111yescharacteristic
486C2×C8C2×C4×D1111yescharacteristic
487C2×C8C2×C4×D1111yescharacteristic
488C2×C8C2×C4×D1111yescharacteristic
489C2×C8C2×D4411yescharacteristic
490C2×C8C2×D4411yescharacteristic
491C2×C8C2×D4411yescharacteristic
492C2×C8C2×D4411yescharacteristic
493C4⋊C4—111no—
494C4⋊C4—111no—
495C4⋊C4—111no—
496C4⋊C4—111no—
497C4⋊C4—221no—
498C4⋊C4—221no—
499C4⋊C4—221no—
500C4⋊C4—221no—
501C4⋊C4—221no—
502C22⋊C4—221no—
503C22⋊C4—221no—
504C22⋊C4—221no—
505C22⋊C4—221no—
506C22⋊C4—221no—
507C22⋊C4—221no—
508C22⋊C4—221no—
509C22⋊C4—221no—
510C22⋊C4—221no—
511C42—221no—
512C42C2×C4×D1111yescharacteristic
513C42C2×D4411yescharacteristic
514C42#433911yescharacteristic
515C42C23×D1111yescharacteristic
516C11#1801411yescharacteristic, complemented, Sylow
517C23—221no—
518C23—221no—
519C23—221no—
520C23—442no—
521C23—442no—
522C23—881no—
523C23C4×D4411yescharacteristic
524Q8—221no—
525Q8—221no—
526D4—112no—
527D4—221no—
528D4—221no—
529D4—221no—
530D4—221no—
531D4—221no—
532D4—442no—
533D4—442no—
534C2×C4—22no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—21no—
539C2×C4—221no—
540C2×C4—221no—
541C2×C4—221no—
542C2×C4—221no—
543C2×C4—221no—
544C2×C4—441no—
545C2×C4—441no—
546C2×C4—441no—
547C2×C4—441no—
548C2×C4—441no—
549C2×C4—441no—
550C2×C4—881no—
551C2×C4—881no—
552C2×C4—881no—
553C2×C4C4×D4411yescharacteristic
554C2×C4C4×D4411yescharacteristic
555C2×C4C4×D4411yescharacteristic
556C2×C4C22×C4×D1111yescharacteristic
557C2×C4C22×D4411yescharacteristic
558C2×C4C2×#433911yescharacteristic
559C8—22no—
560C8—22no—
561C8—21no—
562C8—21no—
563C8—21no—
564C8—21no—
565C8—21no—
566C8—21no—
567C8—21no—
568C8—21no—
569C8—441no—
570C8—441no—
571C8—441no—
572C8—441no—
573C22—21no—
574C22—21no—
575C22—222no—
576C22—441no—
577C22—441no—
578C22—441no—
579C22—441no—
580C22—441no—
581C22—441no—
582C22—441no—
583C22—441no—
584C22—884no—
585C22#1062231312yes—
586C22C2×C4×D4411yescharacteristic
587C4—21no—
588C4—21no—
589C4—21no—
590C4—21no—
591C4—441no—
592C4—441no—
593C4—441no—
594C4—441no—
595C4—441no—
596C4D11×#13111yescharacteristic
597C4#1062328111yescharacteristic
598C4#1062328211yescharacteristic
599C4#1062328311yescharacteristic
600C2—22no—
601C2—442no—
602C2—881no—
603C2—881no—
604C2#1307734411yescharacteristic
605C2#1307745011yescharacteristic
606C2C2×#1062231311yescharacteristic
subgroupG/H
centerC2×C4C22×D44
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
FittingC11×#1450C2
socleC22×C11C2×C4×D4
prime radical#10622345C4
cosocleC42×C11C24
hypercenter#1450D11
hypocenterC11#18014
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ #431 ◁ #1450

Complements

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

NH ≅ G/Ntype
2. #13077778C2semidirect
3. #13077650C2semidirect
4. #13067508C2semidirect
5. #13067502C2semidirect
6. #13067496C2semidirect
7. #13067482C2semidirect
8. #13067482C2semidirect
9. #13067475C2semidirect
10. C8×#4314C2semidirect
11. C8×D88C2semidirect
12. #13067401C2semidirect
13. #13067077C2semidirect
14. C2×#10622097C2semidirect
15. C11×#1450C2semidirect
45. #10622301C22semidirect
48. C8×D44C22semidirect
49. #10622292C22semidirect
50. C8×Dic22C22semidirect
51. C11×#322C22semidirect
52. C11×#322C22semidirect
53. C82×C11C22semidirect
54. C82×C11C22semidirect
59. #10622097C22semidirect
60. #10622097C22semidirect
61. #10622096C22semidirect
62. #10622096C22semidirect
63. #10622095C22semidirect
64. #10622095C22semidirect
65. #10622094C22semidirect
66. #10622094C22semidirect
228. #1450D11semidirect
332. #322C2×D11semidirect
333. #322C2×D11semidirect
334. C82C2×D11semidirect
335. C82C2×D11semidirect
516. C11#18014semidirect

Maximal subgroups

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

subgroupindex
#130786652
#130777782
#130776502
#130675082
#130675022
#130674962
#130674822
#130674752
C8×#43142
C8×D882
#130674012
#130670772
C2×#106220972
C11×#14502
#1801411