Finite Group Databasebeta

← #15617595

Subgroups — #15617595

Order 2816.

2038 conjugacy classes of subgroups.

The subgroup lattice has 642 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13081815C211yesmaximal, characteristic
2#13077284C213yesmaximal, complemented
3#13077281C213yesmaximal, complemented
4#13077273C213yesmaximal, complemented
5#13077273C213yesmaximal, complemented
6#13077266C213yesmaximal, complemented
7#13077259C213yesmaximal, complemented
8#13077253C213yesmaximal, complemented
9C2×#10622453C213yesmaximal, complemented
10#13077184C211yesmaximal, characteristic, complemented
11#13077063C211yesmaximal, characteristic
12#13077063C211yesmaximal, characteristic
13#13077042C211yesmaximal, characteristic, complemented
14#131×Dic11C211yesmaximal, characteristic, complemented
15C11×#2906C211yesmaximal, characteristic, complemented
16C2×#41×D11C2211yescharacteristic
17C2×C11×#131C2211yescharacteristic
18C2×C11×#131C2211yescharacteristic
19C4×C11×#41C2211yescharacteristic
20#41×Dic11C2211yescharacteristic
21C2×#67001C2211yescharacteristic
22C2×#67001C2211yescharacteristic
23#10623105C411yescharacteristic
24#10623105C411yescharacteristic
25#10623103C411yescharacteristic
26#10623103C411yescharacteristic
27#10623077C413yes—
28#10623077C413yes—
29#10623076C413yes—
30#10623076C413yes—
31#10623053C2213yes—
32D11×#117C2213yes—
33C4×#4339C2213yes—
34C2×#66925C2213yes—
35C11×#424C2213yescomplemented
36C11×#424C2213yescomplemented
37C11×#423C2213yescomplemented
38C2×C11×C4⋊C8C2213yescomplemented
39#10622742C2213yes—
40#10622742C2213yes—
41#10622739C2213yes—
42#10622739C2213yes—
43#10622735C2213yescomplemented
44#10622735C2213yescomplemented
45M16×Dic11C2213yescomplemented
46M16×Dic11C2213yescomplemented
47#10622723C2213yes—
48#10622723C2213yes—
49C2×(C2×D11)⋊C8C2213yes—
50C2×(C2×D11)⋊C8C2213yes—
51#10622714C2213yescomplemented
52#10622714C2213yescomplemented
53C2×#66879C2213yescomplemented
54C2×C8×Dic11C2213yescomplemented
55#10622612C2213yescomplemented
56#10622612C2213yescomplemented
57#10622537C2213yescomplemented
58C2×C4⋊(C11⋊C8)C2213yescomplemented
59#10622453C2213yes—
60#10622453C2216yes—
61#10622453C2213yes—
62#10622453C2213yes—
63#10622453C2211yescharacteristic
64#10622453C2216yescomplemented
65#10622453C2216yescomplemented
66#10622453C2213yescomplemented
67#10622453C2213yescomplemented
68#10622453C2213yescomplemented
69#10622453C2213yescomplemented
70#10622448C2216yescomplemented
71#10622448C2216yescomplemented
72#10622446C2216yescomplemented
73#10622446C2216yescomplemented
74C2×C11×#41C2311yescharacteristic
75#41×D11—24no—
76#41×D11—24no—
77C2×#4343C2×C411yescharacteristic
78C2×Q8×D11C2×C411yescharacteristic
79C2×#4341C2×C413yes—
80C2×D4×D11C2×C413yes—
81C2×#4339C2313yes—
82C22×C4×D11C2313yes—
83C11×#131—24no—
84C11×#131—24no—
85C2×C11×M16C2313yes—
86C2×C11×M16C2313yes—
87C22×C8×C11C2313yes—
88C22×C8×C11C2313yes—
89C4×Q8×C11C2×C411yescharacteristic
90C4×Q8×C11C2×C411yescharacteristic
91C4×D4×C11C2×C413yes—
92C4×D4×C11C2×C413yes—
93C11×#117C2313yes—
94C2×C42×C11C2313yes—
95#67001—24no—
96#67001—24no—
97Q8×Dic11C2×C411yescharacteristic
98Q8×Dic11C2×C411yescharacteristic
99D4×Dic11C2×C413yes—
100D4×Dic11C2×C413yes—
101C4×C22⋊D11C2×C416yes—
102C4×C22⋊D11C2×C416yes—
103C2×(C2×D11)⋊C4C2×C413yes—
104C2×(C2×D11)⋊C4C2×C413yes—
105#66979C2313yes—
106C2×Dic11⋊C4C2×C413yes—
107C2×Dic11⋊C4C2×C413yes—
108C2×C4×Dic11C2313yes—
109C2×#4318C2313yes—
110C2×#4318C2313yes—
111C22×C11⋊C8C2313yes—
112C22×C11⋊C8C2313yes—
113#66946C2×C413yes—
114#66946C2×C413yes—
115#66945C2×C413yes—
116#66945C2×C413yes—
117C4⋊C4×D11C2×C413yes—
118C4⋊C4×D11C2×C413yes—
119#66940C2×C413yes—
120#66940C2×C413yes—
121(C22⋊D11)⋊C4C2×C416yes—
122(C22⋊D11)⋊C4C2×C416yes—
123C22⋊C4×D11C2×C416yes—
124#66930C2×C416yes—
125C4×D44C2×C413yes—
126C4×D44C2×C413yes—
127#66925C2×C413yes—
128#66925C2×C413yes—
129#66925C2×C413yes—
130#66925C2×C413yes—
131#66925C2311yescharacteristic
132#66925C2313yes—
133#66925C2313yes—
134#66925C2313yes—
135C42×D11C2316yes—
136C4×Dic22C2×C413yes—
137C4×Dic22C2×C413yes—
138C11×C4⋊C8C2311yescharacteristic
139C11×C4⋊C8C2313yes—
140C11×C4⋊C8C2313yes—
141C11×C4⋊C8C2313yes—
142C11×C4⋊C8C2316yes—
143(C2×D11)⋊C8C2311yescharacteristic
144(C2×D11)⋊C8C2311yescharacteristic
145(C2×D11)⋊C8C2313yes—
146(C2×D11)⋊C8C2313yes—
147(C2×D11)⋊C8C2313yes—
148(C2×D11)⋊C8C2313yes—
149(C2×D11)⋊C8C2313yes—
150(C2×D11)⋊C8C2313yes—
151(C2×D11)⋊C8C2316yes—
152(C2×D11)⋊C8C2316yes—
153#66879C2313yes—
154#66879C2316yes—
155#66879C2313yes—
156#66879C2313yes—
157#66879C2311yescharacteristic
158C8×Dic11C2313yes—
159C8×Dic11C2316yes—
160C8×Dic11C2313yes—
161C8×Dic11C2313yes—
162C8×Dic11C2311yescharacteristic
163C4⋊(C11⋊C8)C2311yescharacteristic
164C4⋊(C11⋊C8)C2313yes—
165C4⋊(C11⋊C8)C2313yes—
166C4⋊(C11⋊C8)C2313yes—
167C4⋊(C11⋊C8)C2316yes—
168#60129—111nomaximal, Sylow
169C23×D11C22×C413yes—
170C11×#41#4114yes—
171C11×#41#4114yes—
172C2×Q8×C11C22×C411yescharacteristic
173C2×D4×C11C22×C413yes—
174C22×C4×C11C22×C413yes—
175C22×C4×C11C22×C413yes—
176C22×C4×C11C2413yes—
177C2×C22⋊D11C22×C416yes—
178C22×Dic11C22×C413yes—
179C22×Dic11C22×C413yes—
180C22×Dic11C22×C413yes—
181#4343—24no—
182Q8×D11—24no—
183#4341—212no—
184D4×D11—212no—
185#4339—26no—
186#4339—26no—
187C2×D44C22×C413yes—
188C2×C4×D11—26no—
189C2×C4×D11—26no—
190C2×C4×D11C22×C413yes—
191C2×C4×D11C22×C413yes—
192C2×C4×D11C22×C416yes—
193C2×C4×D11C22×C416yes—
194C2×C4×D11C2413yes—
195C2×C4×D11C2411yescharacteristic
196C2×Dic22C22×C413yes—
197C11×M16—26no—
198C11×M16—26no—
199C2×C8×C11—26no—
200C2×C8×C11—26no—
201C2×C8×C11C2411yescharacteristic
202C2×C8×C11C2413yes—
203C2×C8×C11C2413yes—
204C2×C8×C11C2411yescharacteristic
205C11×C4⋊C4C22×C413yes—
206C11×C4⋊C4C22×C413yes—
207C11×C22⋊C4C22×C416yes—
208C42×C11C22×C413yes—
209C42×C11C22×C413yes—
210C42×C11C2413yes—
211C42×C11C2411yescharacteristic
212C22⋊Dic11C22×C416yes—
213(C2×D11)⋊C4C22×C411yescharacteristic
214(C2×D11)⋊C4C22×C411yescharacteristic
215(C2×D11)⋊C4C22×C413yes—
216(C2×D11)⋊C4C22×C413yes—
217(C2×D11)⋊C4C22×C413yes—
218(C2×D11)⋊C4C22×C413yes—
219(C2×D11)⋊C4C22×C413yes—
220(C2×D11)⋊C4C22×C413yes—
221C4⋊Dic11C22×C413yes—
222C4⋊Dic11C22×C413yes—
223Dic11⋊C4C22×C413yes—
224Dic11⋊C4C22×C413yes—
225Dic11⋊C4C22×C411yescharacteristic
226Dic11⋊C4C22×C411yescharacteristic
227Dic11⋊C4C22×C413yes—
228Dic11⋊C4C22×C413yes—
229Dic11⋊C4C22×C413yes—
230Dic11⋊C4C22×C413yes—
231C4×Dic11C22×C416yes—
232C4×Dic11C22×C416yes—
233C4×Dic11C22×C413yes—
234C4×Dic11C22×C413yes—
235C4×Dic11C2413yes—
236C4×Dic11C2411yescharacteristic
237#4318—26no—
238#4318—26no—
239C2×C11⋊C8—26no—
240C2×C11⋊C8—26no—
241C2×C11⋊C8C2411yescharacteristic
242C2×C11⋊C8C2413yes—
243C2×C11⋊C8C2413yes—
244C2×C11⋊C8C2411yescharacteristic
245#3428—111no—
246#2925—113no—
247#2925—113no—
248#2924—113no—
249#2924—113no—
250#2923—113no—
251#2922—113no—
252#2921—113no—
253C2×#433—113no—
254#2906—111no—
255#2906D1111yescharacteristic, complemented
256#2880—111no—
257#2880—111no—
258#2875—111no—
259C4×#131—111no—
260C23×C11C23×C413yes—
261C22×D11—26no—
262C22×D11—43no—
263C22×D11—43no—
264C22×D11C23×C411yescharacteristic
265C22×D11C23×C413yes—
266Q8×C11#11714yes—
267D4×C11#117112yes—
268C2×C4×C11—43no—
269C2×C4×C11—43no—
270C2×C4×C11C23×C413yes—
271C2×C4×C11C23×C413yes—
272C2×C4×C11C23×C411yescharacteristic
273C2×C4×C11C23×C411yescharacteristic
274C2×C4×C11C23×C413yes—
275C2×C4×C11C2×#4116yes—
276C2×C4×C11C2×#4116yes—
277C2×C4×C11C2511yescharacteristic
278C22⋊D11—212no—
279C2×Dic11—26no—
280C2×Dic11—43no—
281C2×Dic11—43no—
282C2×Dic11C23×C413yes—
283C2×Dic11C23×C411yescharacteristic
284C2×Dic11C23×C411yescharacteristic
285C2×Dic11C23×C413yes—
286C2×Dic11C23×C413yes—
287C2×Dic11C23×C411yescharacteristic
288D44—26no—
289C4×D11—26no—
290C4×D11—26no—
291C4×D11—21no—
292C4×D11—21no—
293C4×D11—23no—
294C4×D11—23no—
295C4×D11—46no—
296C4×D11—46no—
297Dic22—26no—
298C8×C11—21no—
299C8×C11—21no—
300C8×C11—23no—
301C8×C11—23no—
302C11⋊C8—21no—
303C11⋊C8—21no—
304C11⋊C8—23no—
305C11⋊C8—23no—
306C22×#41—111no—
307C2×#131—111no—
308C2×#131—111no—
309C2×#131C2×D1111yescharacteristic
310C2×#131C2×D1111yescharacteristic
311#520—111no—
312#520—111no—
313#520—113no—
314#520—113no—
315#519—111no—
316#519—111no—
317#518—113no—
318#518—113no—
319C4×#41—111no—
320C4×#41—113no—
321C4×#41—113no—
322C4×#41C2×D1111yescharacteristic
323C2×#117—113no—
324C2×#117—113no—
325#433—111no—
326#433—113no—
327#433—113no—
328#433—113no—
329#433—113no—
330#433—113no—
331#433—113no—
332#433—113no—
333#433—116no—
334#433—116no—
335#433—116no—
336#432—116no—
337#432—116no—
338#431—116no—
339#431—116no—
340#424—113no—
341#424—113no—
342#424C2×D1113yescomplemented
343#424C2×D1113yescomplemented
344#423—113no—
345#423C2×D1113yescomplemented
346C2×C4⋊C8—113no—
347C2×C4⋊C8C2×D1113yescomplemented
348#408—113no—
349#408—113no—
350#408—113no—
351#408—113no—
352#407—113no—
353#407—113no—
354C2×C22⋊C8—113no—
355C2×C22⋊C8—113no—
356#405—113no—
357#405—113no—
358#405—113no—
359#405—113no—
360C4×M16—113no—
361C4×M16—113no—
362C2×#97—113no—
363C2×C4×C8—113no—
364C22×C11—23no—
365C22×C11—23no—
366C22×C11C2×#11716yes—
367C22×C11C24×C411yescharacteristic
368C2×D11—21no—
369C2×D11—23no—
370C2×D11—21no—
371C2×D11—21no—
372C2×D11—23no—
373C2×D11—23no—
374C2×D11—86no—
375C4×C11—21no—
376C4×C11—21no—
377C4×C11—23no—
378C4×C11—23no—
379C4×C11C2×#11716yes—
380C4×C11C22×#4111yescharacteristic
381C4×C11C22×#4111yescharacteristic
382Dic11—23no—
383Dic11—21no—
384Dic11—23no—
385Dic11—23no—
386Dic11—21no—
387Dic11—21no—
388C2×#41—111no—
389C2×#41—113no—
390C2×#41—113no—
391C2×#41—224no—
392C2×#41—224no—
393C2×#41C22×D1111yescharacteristic
394C22×Q8—111no—
395C22×D4—113no—
396C23×C4—113no—
397#131—24no—
398#131—24no—
399#131—224no—
400#131—224no—
401C2×M16—113no—
402C2×M16—113no—
403C2×M16C22×D1113yes—
404C2×M16C22×D1113yes—
405C22×C8—113no—
406C22×C8—113no—
407C22×C8C22×D1113yes—
408C22×C8C22×D1113yes—
409C4×Q8—111no—
410C4×Q8—111no—
411C4×Q8—113no—
412C4×Q8—113no—
413C4×Q8—113no—
414C4×Q8—113no—
415C4×Q8C4×D1111yescharacteristic
416C4×Q8C4×D1111yescharacteristic
417C4×D4—113no—
418C4×D4—113no—
419C4×D4—116no—
420C4×D4—116no—
421C4×D4—113no—
422C4×D4—113no—
423C4×D4—116no—
424C4×D4—116no—
425C4×D4—113no—
426C4×D4—113no—
427C4×D4C4×D1113yes—
428C4×D4C4×D1113yes—
429#117—113no—
430#117—113no—
431#117—113no—
432#117—116no—
433#117—113no—
434#117—113no—
435#117—113no—
436#117—113no—
437#117—113no—
438#117—111no—
439#117—113no—
440#117—113no—
441#117C22×D1113yes—
442C2×C4⋊C4—113no—
443C2×C4⋊C4—113no—
444C2×C4⋊C4—113no—
445C2×C4⋊C4—113no—
446C2×C22⋊C4—113no—
447C2×C22⋊C4—113no—
448C2×C22⋊C4—116no—
449C2×C42—113no—
450C2×C42—116no—
451C2×C42C22×D1113yes—
452C4⋊C8—111no—
453C4⋊C8—113no—
454C4⋊C8—113no—
455C4⋊C8—113no—
456C4⋊C8—116no—
457C4⋊C8C22×D1111yescharacteristic
458C4⋊C8C22×D1113yes—
459C4⋊C8C22×D1113yes—
460C4⋊C8C22×D1113yes—
461C4⋊C8C22×D1116yes—
462C22⋊C8—111no—
463C22⋊C8—111no—
464C22⋊C8—113no—
465C22⋊C8—113no—
466C22⋊C8—113no—
467C22⋊C8—113no—
468C22⋊C8—113no—
469C22⋊C8—113no—
470C22⋊C8—116no—
471C22⋊C8—116no—
472#97—111no—
473#97—113no—
474#97—113no—
475#97—113no—
476#97—116no—
477C4×C8—111no—
478C4×C8—113no—
479C4×C8—113no—
480C4×C8—113no—
481C4×C8—116no—
482C2×C11—26no—
483C2×C11C22×#11711yescharacteristic
484C2×C11#357311yescharacteristic
485C2×C11#357311yescharacteristic
486D11—43no—
487D11—41no—
488C24—113no—
489#41—224no—
490#41—2212no—
491#41—226no—
492#41—226no—
493#41#434114yes—
494#41#434314yes—
495C2×Q8—113no—
496C2×Q8—224no—
497C2×Q8C2×C4×D1111yescharacteristic
498C2×D4—116no—
499C2×D4—113no—
500C2×D4—2212no—
501C2×D4C2×C4×D1113yes—
502C22×C4—113no—
503C22×C4—113no—
504C22×C4—113no—
505C22×C4—113no—
506C22×C4—113no—
507C22×C4—113no—
508C22×C4—111no—
509C22×C4—116no—
510C22×C4—116no—
511C22×C4—226no—
512C22×C4—226no—
513C22×C4C2×C4×D1113yes—
514C22×C4C2×C4×D1113yes—
515C22×C4C23×D1113yes—
516M16—26no—
517M16—26no—
518M16—226no—
519M16—226no—
520C2×C8—26no—
521C2×C8—26no—
522C2×C8—111no—
523C2×C8—113no—
524C2×C8—113no—
525C2×C8—111no—
526C2×C8—226no—
527C2×C8—226no—
528C2×C8C23×D1111yescharacteristic
529C2×C8C23×D1113yes—
530C2×C8C23×D1113yes—
531C2×C8C23×D1111yescharacteristic
532C4⋊C4—113no—
533C4⋊C4—113no—
534C4⋊C4—111no—
535C4⋊C4—111no—
536C4⋊C4—113no—
537C4⋊C4—113no—
538C4⋊C4—113no—
539C4⋊C4—113no—
540C4⋊C4—113no—
541C4⋊C4—113no—
542C4⋊C4C2×C4×D1113yes—
543C4⋊C4C2×C4×D1113yes—
544C22⋊C4—116no—
545C22⋊C4—113no—
546C22⋊C4—113no—
547C22⋊C4—111no—
548C22⋊C4—111no—
549C22⋊C4—113no—
550C22⋊C4—113no—
551C22⋊C4—113no—
552C22⋊C4—113no—
553C22⋊C4C2×C4×D1116yes—
554C42—113no—
555C42—113no—
556C42—116no—
557C42—116no—
558C42—111no—
559C42—113no—
560C42C2×C4×D1113yes—
561C42C2×C4×D1113yes—
562C42C23×D1113yes—
563C42C23×D1111yescharacteristic
564C11#6012911yescharacteristic, complemented, Sylow
565C23—111no—
566C23—113no—
567C23—226no—
568C23—443no—
569C23—443no—
570C23C22×C4×D1113yes—
571Q8—226no—
572Q8#6694514yes—
573D4—2212no—
574D4—226no—
575D4#66945112yes—
576C2×C4—43no—
577C2×C4—43no—
578C2×C4—113no—
579C2×C4—111no—
580C2×C4—113no—
581C2×C4—111no—
582C2×C4—113no—
583C2×C4—111no—
584C2×C4—226no—
585C2×C4—226no—
586C2×C4—226no—
587C2×C4—221no—
588C2×C4—223no—
589C2×C4—221no—
590C2×C4—223no—
591C2×C4—446no—
592C2×C4—446no—
593C2×C4—443no—
594C2×C4—443no—
595C2×C4C22×C4×D1113yes—
596C2×C4C22×C4×D1113yes—
597C2×C4C22×C4×D1111yescharacteristic
598C2×C4C22×C4×D1111yescharacteristic
599C2×C4C22×C4×D1113yes—
600C2×C4C2×#434116yes—
601C2×C4C2×#434316yes—
602C2×C4C24×D1111yescharacteristic
603C8—21no—
604C8—21no—
605C8—23no—
606C8—23no—
607C8—221no—
608C8—221no—
609C8—223no—
610C8—223no—
611C22—23no—
612C22—23no—
613C22—221no—
614C22—223no—
615C22—223no—
616C22—221no—
617C22—223no—
618C22—221no—
619C22—886no—
620C22C2×#6694516yes—
621C22C23×C4×D1111yescharacteristic
622C4—21no—
623C4—23no—
624C4—21no—
625C4—23no—
626C4—221no—
627C4—223no—
628C4—223no—
629C4—221no—
630C4—223no—
631C4—221no—
632C4C2×#6694516yes—
633C4C22×#434111yescharacteristic
634C4C22×#434311yescharacteristic
635C2—26no—
636C2—441no—
637C2—443no—
638C2C22×#6694511yescharacteristic
639C2#1308332711yescharacteristic
640C2#1308332911yescharacteristic
subgroupG/H
center, FrattiniC2×C4C24×D11
commutator, socleC22×C11C24×C4
FittingC11×#2906C2
prime radicalC2×#41×D11C22
cosocleC2×C4×C11C25
hypercenter#2906D11
hypocenterC11#60129
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ #2906

Complements

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

NH ≅ G/Ntype
2. #13077284C2semidirect
3. #13077281C2semidirect
4. #13077273C2semidirect
5. #13077273C2semidirect
6. #13077266C2semidirect
7. #13077259C2semidirect
8. #13077253C2semidirect
9. C2×#10622453C2semidirect
10. #13077184C2semidirect
13. #13077042C2semidirect
14. #131×Dic11C2semidirect
15. C11×#2906C2semidirect
35. C11×#424C22semidirect
36. C11×#424C22semidirect
37. C11×#423C22semidirect
38. C2×C11×C4⋊C8C22semidirect
43. #10622735C22semidirect
44. #10622735C22semidirect
45. M16×Dic11C22semidirect
46. M16×Dic11C22semidirect
51. #10622714C22semidirect
52. #10622714C22semidirect
53. C2×#66879C22semidirect
54. C2×C8×Dic11C22semidirect
55. #10622612C22semidirect
56. #10622612C22semidirect
57. #10622537C22semidirect
58. C2×C4⋊(C11⋊C8)C22semidirect
64. #10622453C22semidirect
65. #10622453C22semidirect
66. #10622453C22semidirect
67. #10622453C22semidirect
68. #10622453C22semidirect
69. #10622453C22semidirect
70. #10622448C22semidirect
71. #10622448C22semidirect
72. #10622446C22semidirect
73. #10622446C22semidirect
255. #2906D11semidirect
342. #424C2×D11semidirect
343. #424C2×D11semidirect
345. #423C2×D11semidirect
347. C2×C4⋊C8C2×D11semidirect
564. C11#60129semidirect

Maximal subgroups

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

subgroupindex
#130818152
#130772842
#130772812
#130772732
#130772662
#130772592
#130772532
C2×#106224532
#130771842
#130770632
#130770422
#131×Dic112
C11×#29062
#6012911