Finite Group Databasebeta

← #14720540

Subgroups — #14720540

Order 2816.

960 conjugacy classes of subgroups.

The subgroup lattice has 624 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623109C211yesmaximal, characteristic
2#13077247C211yesmaximal, characteristic
3D11×#432C211yesmaximal, characteristic
4#13067087C214yesmaximal, complemented
5#13067064C211yesmaximal, characteristic, complemented
6#13067063C211yesmaximal, characteristic, complemented
7#13067062C211yesmaximal, characteristic, complemented
8#13067017C214yesmaximal, complemented
9C11×#1491C211yesmaximal, characteristic, complemented
10C2×C4×Q8×C11C2211yescharacteristic
11C2×#66999C411yescharacteristic
12C2×#66997C411yescharacteristic
13#10623109—21no—
14#10623109—21no—
15#10623109—21no—
16#10623109—21no—
17#10623109C412yes—
18#10623109C412yes—
19#10623109C2212yes—
20#10623109C2212yes—
21C2×#66950C411yescharacteristic
22C2×#66949—21no—
23C2×#66942—21no—
24C2×#66941C411yescharacteristic
25C2×#66925—21no—
26C2×C42×D11C2211yescharacteristic
27C2×C4×Dic22—21no—
28C2×C4×Dic22C2211yescharacteristic
29C11×#432C2211yescharacteristic
30C4×C11×M16C2211yescharacteristic
31#10622739—21no—
32#10622731—21no—
33#10622539C2211yescharacteristic
34C4×#4318C2211yescharacteristic
35#10622448C2212yes—
36D11×C4⋊C8C2212yes—
37D11×C22⋊C8—21no—
38#10622332—21no—
39#10622318—21no—
40#10622318—21no—
41#10622318—21no—
42D11×#97—21no—
43#10622298C2212yes—
44#10622298C2212yes—
45C11×Q8⋊C8C2214yescomplemented
46Q8⋊(C11⋊C8)C2214yescomplemented
47#10622122C2214yescomplemented
48#10622094C2214yescomplemented
49C22×Q8×C11C2×C411yescharacteristic
50C22×C4×D11C2×C411yescharacteristic
51C22×C4×D11D411yescharacteristic
52C22×C4×D11D411yescharacteristic
53C22×Dic22—21no—
54C22×Dic22C2×C411yescharacteristic
55C2×C11×M16—21no—
56C4×Q8×C11—21no—
57C4×Q8×C11—21no—
58C4×Q8×C11C2×C412yes—
59C4×Q8×C11C2312yes—
60C2×C11×C4⋊C4—21no—
61C2×C11×C4⋊C4C2×C411yescharacteristic
62C2×C42×C11—21no—
63C2×C42×C11C2311yescharacteristic
64#66999—21no—
65#66999—21no—
66#66999C2×C412yes—
67#66999C2×C412yes—
68#66997—21no—
69#66997—21no—
70#66997C2×C412yes—
71#66997C2×C412yes—
72C2×(C2×D11)⋊C4—21no—
73C2×(C2×D11)⋊C4—21no—
74C2×C4⋊Dic11—21no—
75C2×C4⋊Dic11C2×C411yescharacteristic
76C2×Dic11⋊C4—21no—
77C2×Dic11⋊C4—21no—
78C2×Dic11⋊C4—21no—
79C2×Dic11⋊C4—21no—
80C2×Dic11⋊C4—21no—
81C2×C4×Dic11—21no—
82C2×C4×Dic11C2×C411yescharacteristic
83C2×C4×Dic11D411yescharacteristic
84C2×C4×Dic11D411yescharacteristic
85C2×#4318—21no—
86C2×C8×D11—22no—
87#66950—21no—
88#66950—21no—
89#66950C2×C412yes—
90#66950C2×C412yes—
91#66949—22no—
92#66949—22no—
93#66949—22no—
94#66949—22no—
95#66942—22no—
96#66942—22no—
97#66942—22no—
98#66942—22no—
99#66941—21no—
100#66941—21no—
101#66941C2×C412yes—
102#66941C2×C412yes—
103#66925—22no—
104#66925—22no—
105#66925—22no—
106#66925—22no—
107C42×D11C2×C411yescharacteristic
108C42×D11C2×C411yescharacteristic
109C42×D11D411yescharacteristic
110C42×D11D411yescharacteristic
111C42×D11D411yescharacteristic
112C42×D11D411yescharacteristic
113C42×D11C2311yescharacteristic
114C42×D11C2311yescharacteristic
115C4×Dic22—21no—
116C4×Dic22—21no—
117C4×Dic22—22no—
118C4×Dic22—22no—
119C4×Dic22—22no—
120C4×Dic22—22no—
121C4×Dic22C2×C412yes—
122C4×Dic22C2312yes—
123C11×C4⋊C8C2312yes—
124C11×C22⋊C8—21no—
125C11×#97—21no—
126C11×#97—21no—
127C4×C8×C11C2312yes—
128C22⋊(C11⋊C8)—21no—
129(C2×D11)⋊C8—22no—
130(C2×D11)⋊C8—22no—
131(C2×D11)⋊C8—22no—
132#66879—22no—
133Dic11⋊C8—22no—
134Dic11⋊C8—22no—
135Dic11⋊C8—22no—
136C4⋊(C11⋊C8)C2312yes—
137#66867—21no—
138#66867—21no—
139C4×C11⋊C8C2312yes—
140#17496—111nomaximal, Sylow
141C23×D11C22⋊C411yescharacteristic
142C2×Q8×C11—21no—
143C2×Q8×C11—42no—
144C2×Q8×C11C22×C412yes—
145C22×C4×C11—21no—
146C22×C4×C11—21no—
147C22×C4×C11C22×C411yescharacteristic
148C22×C4×C11C2×D411yescharacteristic
149C22×C4×C11C2×D411yescharacteristic
150C22×Dic11—21no—
151C22×Dic11—21no—
152C22×Dic11C22⋊C411yescharacteristic
153C22×Dic11C22⋊C411yescharacteristic
154C22×Dic11C22⋊C411yescharacteristic
155C2×C4×D11—24no—
156C2×C4×D11—42no—
157C2×C4×D11—42no—
158C2×C4×D11C22⋊C411yescharacteristic
159C2×C4×D11C22⋊C411yescharacteristic
160C2×C4×D11C22⋊C411yescharacteristic
161C2×C4×D11C22⋊C411yescharacteristic
162C2×C4×D11C22⋊C411yescharacteristic
163C2×C4×D11C22⋊C411yescharacteristic
164C2×C4×D11C22×C411yescharacteristic
165C2×C4×D11C22×C411yescharacteristic
166C2×C4×D11C2×D411yescharacteristic
167C2×C4×D11C2×D411yescharacteristic
168C2×C4×D11C2×D411yescharacteristic
169C2×C4×D11C2×D411yescharacteristic
170C2×Dic22—22no—
171C2×Dic22—22no—
172C2×Dic22—21no—
173C2×Dic22—42no—
174C2×Dic22—44no—
175C2×Dic22C22×C412yes—
176C11×M16—42no—
177C2×C8×C11—22no—
178C2×C8×C11—22no—
179C11×C4⋊C4—21no—
180C11×C4⋊C4—22no—
181C11×C4⋊C4—22no—
182C11×C4⋊C4C22×C412yes—
183C42×C11—22no—
184C42×C11—22no—
185C42×C11C22×C411yescharacteristic
186C42×C11C2×D411yescharacteristic
187C42×C11C2×D411yescharacteristic
188C42×C11C2411yescharacteristic
189(C2×D11)⋊C4—22no—
190(C2×D11)⋊C4—22no—
191(C2×D11)⋊C4—22no—
192(C2×D11)⋊C4—22no—
193C4⋊Dic11—22no—
194C4⋊Dic11—22no—
195C4⋊Dic11—21no—
196C4⋊Dic11C22×C412yes—
197Dic11⋊C4—22no—
198Dic11⋊C4—22no—
199Dic11⋊C4—22no—
200Dic11⋊C4—22no—
201Dic11⋊C4—22no—
202Dic11⋊C4—22no—
203Dic11⋊C4—22no—
204Dic11⋊C4—22no—
205Dic11⋊C4—22no—
206Dic11⋊C4—22no—
207C4×Dic11—22no—
208C4×Dic11—22no—
209C4×Dic11C22⋊C411yescharacteristic
210C4×Dic11C22⋊C411yescharacteristic
211C4×Dic11C22⋊C411yescharacteristic
212C4×Dic11C22⋊C411yescharacteristic
213C4×Dic11C22⋊C411yescharacteristic
214C4×Dic11C22⋊C411yescharacteristic
215C4×Dic11C22×C411yescharacteristic
216C4×Dic11C22×C411yescharacteristic
217C4×Dic11C2×D411yescharacteristic
218C4×Dic11C2×D411yescharacteristic
219C4×Dic11C2×D411yescharacteristic
220C4×Dic11C2×D411yescharacteristic
221#4318—42no—
222C2×C11⋊C8—22no—
223C2×C11⋊C8—22no—
224C8×D11—44no—
225C2×#533—111no—
226#2920—111no—
227C2×#432—111no—
228#1497—114no—
229#1491—111no—
230#1491—111no—
231#1491—111no—
232#1491D1111yescharacteristic, complemented
233#1481—114no—
234C23×C11C2×C22⋊C411yescharacteristic
235C22×D11—22no—
236C22×D11—22no—
237C22×D11—41no—
238C22×D11C2×C22⋊C411yescharacteristic
239C22×D11C2×C22⋊C411yescharacteristic
240Q8×C11—24no—
241Q8×C11—42no—
242C2×C4×C11—22no—
243C2×C4×C11—22no—
244C2×C4×C11—22no—
245C2×C4×C11—22no—
246C2×C4×C11—22no—
247C2×C4×C11—42no—
248C2×C4×C11—42no—
249C2×C4×C11C2×C22⋊C411yescharacteristic
250C2×C4×C11C2×C22⋊C411yescharacteristic
251C2×C4×C11C2×C22⋊C411yescharacteristic
252C2×C4×C11C23×C411yescharacteristic
253C2×C4×C11C22×D411yescharacteristic
254C2×C4×C11C22×D411yescharacteristic
255C2×Dic11—22no—
256C2×Dic11—22no—
257C2×Dic11—22no—
258C2×Dic11—22no—
259C2×Dic11—41no—
260C2×Dic11—42no—
261C2×Dic11—42no—
262C2×Dic11C2×C22⋊C411yescharacteristic
263C2×Dic11C2×C22⋊C411yescharacteristic
264C2×Dic11C2×C22⋊C411yescharacteristic
265C2×Dic11C2×C22⋊C411yescharacteristic
266C2×Dic11C2×C22⋊C411yescharacteristic
267C2×Dic11C2×C22⋊C411yescharacteristic
268C4×D11—22no—
269C4×D11—22no—
270C4×D11—22no—
271C4×D11—22no—
272C4×D11—22no—
273C4×D11—41no—
274C4×D11—41no—
275C4×D11—41no—
276C4×D11—41no—
277C4×D11—41no—
278C4×D11—41no—
279C4×D11#13714yes—
280Dic22—24no—
281Dic22—44no—
282Dic22—44no—
283Dic22—42no—
284C8×C11—42no—
285C8×C11—42no—
286C11⋊C8—42no—
287C11⋊C8—42no—
288#533—112no—
289#533—112no—
290#533—112no—
291#533—112no—
292#533—221no—
293#533—221no—
294#533—221no—
295#533—221no—
296C2×C4⋊Q8—111no—
297C2×C4⋊Q8—111no—
298C2×#125—221no—
299C2×C22⋊Q8—111no—
300C2×C22⋊Q8—111no—
301C2×C22⋊Q8—221no—
302C2×C4×Q8—111no—
303C2×C4×Q8—221no—
304C2×C4×Q8C2×D1111yescharacteristic
305C2×#117—221no—
306C22×C42—111no—
307#432—111no—
308#432—112no—
309#432—221no—
310#432—221no—
311#432—221no—
312#432—221no—
313#432C2×D1111yescharacteristic
314#431—112no—
315#431—112no—
316#423—221no—
317C2×C4⋊C8—112no—
318#407—221no—
319C2×C22⋊C8—221no—
320C4×M16—111no—
321C4×M16C2×D1111yescharacteristic
322C2×#97—221no—
323Q8⋊C8—114no—
324Q8⋊C8—114no—
325Q8⋊C8—114no—
326Q8⋊C8C2×D1114yescomplemented
327C22×C11—21no—
328C22×C11—21no—
329C22×C11#42112yes—
330C22×C11C22×C22⋊C411yescharacteristic
331C2×D11—21no—
332C2×D11—21no—
333C2×D11—21no—
334C2×D11—21no—
335C2×D11—21no—
336C2×D11—44no—
337C2×D11#41912yes—
338C4×C11—21no—
339C4×C11—21no—
340C4×C11—21no—
341C4×C11—21no—
342C4×C11—42no—
343C4×C11—42no—
344C4×C11#56812yes—
345C4×C11C2×#13712yes—
346Dic11—21no—
347Dic11—21no—
348Dic11—21no—
349Dic11—21no—
350Dic11—21no—
351Dic11—42no—
352Dic11—42no—
353Dic11#41912yes—
354C22×Q8—111no—
355C22×Q8—221no—
356C22×Q8C4×D1111yescharacteristic
357C23×C4—111no—
358C23×C4—111no—
359C23×C4—111no—
360C2×M16—21no—
361C2×M16—221no—
362C22×C8—222no—
363C4⋊Q8—112no—
364C4⋊Q8—112no—
365C4⋊Q8—112no—
366C4⋊Q8—112no—
367C4⋊Q8—221no—
368C4⋊Q8—221no—
369C4⋊Q8—221no—
370C4⋊Q8—221no—
371#125—222no—
372#125—222no—
373#125—222no—
374#125—222no—
375C22⋊Q8—112no—
376C22⋊Q8—112no—
377C22⋊Q8—112no—
378C22⋊Q8—112no—
379C22⋊Q8—221no—
380C22⋊Q8—221no—
381C22⋊Q8—222no—
382C22⋊Q8—222no—
383C22⋊Q8—222no—
384C22⋊Q8—222no—
385C22⋊Q8—221no—
386C22⋊Q8—221no—
387C4×Q8—21no—
388C4×Q8—21no—
389C4×Q8—112no—
390C4×Q8—112no—
391C4×Q8—222no—
392C4×Q8—222no—
393C4×Q8—222no—
394C4×Q8—222no—
395C4×Q8—221no—
396C4×Q8—221no—
397C4×Q8C4×D1112yes—
398C4×Q8C22×D1112yes—
399#117—222no—
400#117—222no—
401#117—222no—
402#117—222no—
403C2×C4⋊C4—21no—
404C2×C4⋊C4—111no—
405C2×C4⋊C4—221no—
406C2×C4⋊C4—221no—
407C2×C4⋊C4—221no—
408C2×C4⋊C4—221no—
409C2×C4⋊C4—221no—
410C2×C4⋊C4—221no—
411C2×C4⋊C4C4×D1111yescharacteristic
412C2×C22⋊C4—221no—
413C2×C22⋊C4—221no—
414C2×C42—21no—
415C2×C42—111no—
416C2×C42—111no—
417C2×C42—111no—
418C2×C42—111no—
419C2×C42—111no—
420C2×C42—111no—
421C2×C42—111no—
422C2×C42—111no—
423C2×C42—111no—
424C2×C42—111no—
425C2×C42—111no—
426C2×C42—221no—
427C2×C42C22×D1111yescharacteristic
428C4⋊C8—112no—
429C4⋊C8—222no—
430C4⋊C8—222no—
431C4⋊C8—222no—
432C4⋊C8C22×D1112yes—
433C22⋊C8—21no—
434C22⋊C8—222no—
435C22⋊C8—222no—
436C22⋊C8—222no—
437C22⋊C8—221no—
438#97—21no—
439#97—21no—
440#97—222no—
441#97—221no—
442#97—221no—
443C4×C8—112no—
444C4×C8C22×D1112yes—
445C2×C11—22no—
446C2×C11#287911yescharacteristic
447C2×C11C2×#41911yescharacteristic
448C2×C11C2×#42111yescharacteristic
449D11—22no—
450D11—41no—
451C24—111no—
452C2×Q8—21no—
453C2×Q8—42no—
454C2×Q8—112no—
455C2×Q8—222no—
456C2×Q8—222no—
457C2×Q8—221no—
458C2×Q8—442no—
459C2×Q8—444no—
460C2×Q8C2×C4×D1112yes—
461C22×C4—21no—
462C22×C4—21no—
463C22×C4—111no—
464C22×C4—111no—
465C22×C4—111no—
466C22×C4—111no—
467C22×C4—111no—
468C22×C4—111no—
469C22×C4—111no—
470C22×C4—111no—
471C22×C4—111no—
472C22×C4—111no—
473C22×C4—111no—
474C22×C4—111no—
475C22×C4—111no—
476C22×C4—111no—
477C22×C4—111no—
478C22×C4—224no—
479C22×C4—221no—
480C22×C4—221no—
481C22×C4—442no—
482C22×C4—442no—
483C22×C4C2×C4×D1111yescharacteristic
484C22×C4D4×D1111yescharacteristic
485C22×C4D4×D1111yescharacteristic
486M16—42no—
487M16—442no—
488C2×C8—22no—
489C2×C8—22no—
490C2×C8—222no—
491C2×C8—222no—
492C2×C8—444no—
493C4⋊C4—22no—
494C4⋊C4—21no—
495C4⋊C4—22no—
496C4⋊C4—112no—
497C4⋊C4—222no—
498C4⋊C4—222no—
499C4⋊C4—222no—
500C4⋊C4—222no—
501C4⋊C4—222no—
502C4⋊C4—222no—
503C4⋊C4—222no—
504C4⋊C4—222no—
505C4⋊C4—222no—
506C4⋊C4—222no—
507C4⋊C4—221no—
508C4⋊C4—222no—
509C4⋊C4—222no—
510C4⋊C4C2×C4×D1112yes—
511C22⋊C4—222no—
512C22⋊C4—222no—
513C22⋊C4—222no—
514C22⋊C4—222no—
515C42—22no—
516C42—22no—
517C42—111no—
518C42—111no—
519C42—111no—
520C42—111no—
521C42—111no—
522C42—111no—
523C42—111no—
524C42—111no—
525C42—111no—
526C42—111no—
527C42—111no—
528C42—111no—
529C42—222no—
530C42—222no—
531C42C2×C4×D1111yescharacteristic
532C42D4×D1111yescharacteristic
533C42D4×D1111yescharacteristic
534C42C23×D1111yescharacteristic
535C11#1749611yescharacteristic, complemented, Sylow
536C23—111no—
537C23—111no—
538C23—222no—
539C23—222no—
540C23—441no—
541C23C22⋊C4×D1111yescharacteristic
542Q8—24no—
543Q8—42no—
544Q8—224no—
545Q8—442no—
546Q8—444no—
547Q8—444no—
548C2×C4—22no—
549C2×C4—22no—
550C2×C4—22no—
551C2×C4—22no—
552C2×C4—22no—
553C2×C4—42no—
554C2×C4—42no—
555C2×C4—111no—
556C2×C4—114no—
557C2×C4—111no—
558C2×C4—111no—
559C2×C4—111no—
560C2×C4—111no—
561C2×C4—111no—
562C2×C4—222no—
563C2×C4—222no—
564C2×C4—222no—
565C2×C4—222no—
566C2×C4—222no—
567C2×C4—222no—
568C2×C4—222no—
569C2×C4—222no—
570C2×C4—222no—
571C2×C4—441no—
572C2×C4—441no—
573C2×C4—441no—
574C2×C4—441no—
575C2×C4—441no—
576C2×C4—441no—
577C2×C4—441no—
578C2×C4—442no—
579C2×C4—442no—
580C2×C4C22⋊C4×D1111yescharacteristic
581C2×C4C22⋊C4×D1111yescharacteristic
582C2×C4C22⋊C4×D1111yescharacteristic
583C2×C4C22×C4×D1111yescharacteristic
584C2×C4C2×D4×D1111yescharacteristic
585C2×C4C2×D4×D1111yescharacteristic
586C8—42no—
587C8—42no—
588C8—442no—
589C8—442no—
590C22—21no—
591C22—21no—
592C22—112no—
593C22—221no—
594C22—221no—
595C22—221no—
596C22—221no—
597C22—221no—
598C22—444no—
599C22#1062243412yes—
600C22C2×C22⋊C4×D1111yescharacteristic
601C4—21no—
602C4—21no—
603C4—21no—
604C4—21no—
605C4—42no—
606C4—42no—
607C4—112no—
608C4—221no—
609C4—221no—
610C4—221no—
611C4—221no—
612C4—221no—
613C4—442no—
614C4—442no—
615C4#1062327612yes—
616C4D11×#13712yes—
617C2—22no—
618C2—222no—
619C2—441no—
620C2#1307705911yescharacteristic
621C2D11×#41911yescharacteristic
622C2C2×#1062243411yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
FittingC11×#1491C2
socleC22×C11C22×C22⋊C4
prime radicalC23×D11C22⋊C4
cosocleC42×C11C24
hypercenter#1491D11
hypocenterC11#17496
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1491

Complements

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

NH ≅ G/Ntype
4. #13067087C2semidirect
5. #13067064C2semidirect
6. #13067063C2semidirect
7. #13067062C2semidirect
8. #13067017C2semidirect
9. C11×#1491C2semidirect
45. C11×Q8⋊C8C22semidirect
46. Q8⋊(C11⋊C8)C22semidirect
47. #10622122C22semidirect
48. #10622094C22semidirect
232. #1491D11semidirect
326. Q8⋊C8C2×D11semidirect
535. C11#17496semidirect

Maximal subgroups

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

subgroupindex
C2×#106231092
#130772472
D11×#4322
#130670872
#130670642
#130670632
#130670622
#130670172
C11×#14912
#1749611