Finite Group Databasebeta

← #14660243

Subgroups — #14660243

Order 2816.

926 conjugacy classes of subgroups.

The subgroup lattice has 618 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622853C211yesmaximal, characteristic
2C2×#10622847C211yesmaximal, characteristic
3C2×#10622735C211yesmaximal, characteristic, complemented
4C2×#10622197C211yesmaximal, characteristic, complemented
5C2×#10622197C211yesmaximal, characteristic, complemented
6#13068314C211yesmaximal, characteristic, complemented
7C2×C11×#413C211yesmaximal, characteristic
8C22×C11×#41C2211yescharacteristic
9C22×C11×M16C2211yescharacteristic
10C22×C11×M16C2211yescharacteristic
11C2×#66979C2211yescharacteristic
12C2×#66979C2211yescharacteristic
13C22×#4318C2211yescharacteristic
14C23×C11⋊C8C2211yescharacteristic
15C11×#413—22no—
16C11×#413—22no—
17C2×C11×#101C412yescomplemented
18C2×C11×#100C412yescomplemented
19#10622853—22no—
20#10622853—22no—
21#10622847—22no—
22#10622847—21no—
23#10622847—21no—
24C2×#66898C414yes—
25C2×C22⋊(C11⋊C8)C414yescomplemented
26#10622735—22no—
27#10622735—22no—
28C2×#66879—21no—
29C2×C8×Dic11—21no—
30#10622197—22no—
31#10622197—22no—
32#10622188—22no—
33C2×C11×#41—21no—
34C2×C11×#41—21no—
35C2×C11×#41—21no—
36C2×C11×#41—21no—
37C2×C11×#41—21no—
38C2×C11×#41—21no—
39C2×C11×#41—21no—
40C2×C11×#41—21no—
41C2×C11×#41—21no—
42C2×C11×#41—21no—
43C2×C11×#41—21no—
44C2×C11×#41—21no—
45C22×Q8×C11C2×C411yescharacteristic
46C22×D4×C11C2×C412yes—
47C22×D4×C11C2×C411yescharacteristic
48C23×C4×C11C2×C412yes—
49C23×C4×C11C2311yescharacteristic
50C2×C11×M16—21no—
51C2×C11×M16—21no—
52C2×C11×M16—21no—
53C2×C11×M16—21no—
54C2×C11×M16—21no—
55C2×C11×M16—21no—
56C2×C11×M16—21no—
57C2×C11×M16—21no—
58C2×C11×M16C2×C412yes—
59C2×C11×M16C2×C412yes—
60C2×C11×M16D412yes—
61C2×C11×M16D412yes—
62C22×C8×C11—21no—
63C22×C8×C11—21no—
64C2×C22⋊Dic11C2×C412yes—
65C2×C22⋊Dic11C2×C412yes—
66#66979—21no—
67#66979—21no—
68#66979—21no—
69#66979—21no—
70#66979—21no—
71#66979—21no—
72#66979D412yes—
73#66979D412yes—
74C2×C4⋊Dic11—21no—
75C2×C4⋊Dic11—21no—
76C2×C4×Dic11—21no—
77C2×C4×Dic11—21no—
78C2×#4318—21no—
79C2×#4318—21no—
80C2×#4318—21no—
81C2×#4318—21no—
82C2×#4318—21no—
83C2×#4318—21no—
84C22×C11⋊C8—21no—
85C22×C11⋊C8—21no—
86C22×C11⋊C8—21no—
87C22×C11⋊C8—21no—
88C22×C11⋊C8C2×C412yes—
89C22×C11⋊C8C2×C412yes—
90C22×C11⋊C8D412yes—
91C22×C11⋊C8D411yescharacteristic
92C22×C11⋊C8D411yescharacteristic
93C11×#101—24no—
94C11×#100—24no—
95#66898—28no—
96C22⋊(C11⋊C8)—24no—
97C22⋊(C11⋊C8)—24no—
98#66879—24no—
99C8×Dic11—24no—
100#10961—111nomaximal, Sylow
101C24×C11C4212yes—
102C24×C11C22×C411yescharacteristic
103C11×#41—41no—
104C11×#41—41no—
105C11×#41—41no—
106C11×#41—41no—
107C11×#41—41no—
108C11×#41—41no—
109C11×#41—41no—
110C11×#41—41no—
111C11×#41—41no—
112C11×#41—41no—
113C11×#41—41no—
114C11×#41—41no—
115C11×#41—41no—
116C11×#41—41no—
117C11×#41—41no—
118C11×#41—41no—
119C2×Q8×C11—21no—
120C2×Q8×C11—21no—
121C2×Q8×C11—21no—
122C2×Q8×C11—21no—
123C2×Q8×C11—21no—
124C2×Q8×C11—21no—
125C2×D4×C11—22no—
126C2×D4×C11—22no—
127C2×D4×C11—22no—
128C2×D4×C11—22no—
129C2×D4×C11—22no—
130C2×D4×C11—22no—
131C2×D4×C11—21no—
132C2×D4×C11—21no—
133C2×D4×C11—21no—
134C2×D4×C11—21no—
135C2×D4×C11—21no—
136C2×D4×C11—21no—
137C22×C4×C11—22no—
138C22×C4×C11—22no—
139C22×C4×C11—22no—
140C22×C4×C11—22no—
141C22×C4×C11—22no—
142C22×C4×C11—22no—
143C22×C4×C11C4212yes—
144C22×C4×C11C22×C411yescharacteristic
145C22×C4×C11C22×C411yescharacteristic
146C22×C4×C11C2×D411yescharacteristic
147C22×C4×C11C2×D411yescharacteristic
148C22×C4×C11C2×D411yescharacteristic
149C22×C4×C11C2×D411yescharacteristic
150C22×C4×C11C2×D411yescharacteristic
151C22×C4×C11C2×D411yescharacteristic
152C22×C4×C11#4111yescharacteristic
153C22×C4×C11#4111yescharacteristic
154C22×C4×C11#4111yescharacteristic
155C22×C4×C11#4111yescharacteristic
156C22×C4×C11#4111yescharacteristic
157C22×C4×C11#4111yescharacteristic
158C22×Dic11—22no—
159C22×Dic11—22no—
160C11×M16—22no—
161C11×M16—22no—
162C11×M16—22no—
163C11×M16—22no—
164C11×M16—22no—
165C11×M16—41no—
166C11×M16—41no—
167C11×M16C22⋊C414yes—
168C2×C8×C11—22no—
169C2×C8×C11—22no—
170C2×C8×C11—22no—
171C2×C8×C11—22no—
172C2×C8×C11—41no—
173C2×C8×C11—41no—
174C22⋊Dic11—22no—
175C22⋊Dic11—22no—
176C22⋊Dic11—22no—
177C22⋊Dic11C22⋊C414yes—
178C4⋊Dic11—22no—
179C4⋊Dic11—22no—
180C4⋊Dic11—41no—
181C4⋊Dic11—41no—
182C4×Dic11—22no—
183C4×Dic11—22no—
184C4×Dic11—41no—
185C4×Dic11—41no—
186#4318—41no—
187#4318—41no—
188#4318—41no—
189#4318—41no—
190C2×C11⋊C8—22no—
191C2×C11⋊C8—22no—
192C2×C11⋊C8—22no—
193C2×C11⋊C8—22no—
194C2×C11⋊C8—22no—
195C2×C11⋊C8—21no—
196C2×C11⋊C8—21no—
197C2×C11⋊C8—22no—
198C2×C11⋊C8—22no—
199C2×C11⋊C8—21no—
200C2×C11⋊C8—21no—
201C2×C11⋊C8C22⋊C412yes—
202C2×C11⋊C8C22⋊C412yes—
203C2×#413D1111yescharacteristic
204C2×#410—111no—
205C2×#408—111no—
206C2×#405—111no—
207C2×#344—111no—
208C2×#344—111no—
209#1729—111no—
210C23×C11—22no—
211C23×C11—22no—
212C23×C11—22no—
213C23×C11—42no—
214C23×C11—44no—
215C23×C11C2×C4211yescharacteristic
216C23×C11C2×C22⋊C411yescharacteristic
217C23×C11#11711yescharacteristic
218C23×C11C4×D411yescharacteristic
219C23×C11C4×D411yescharacteristic
220C23×C11C4×D411yescharacteristic
221C23×C11C4×D411yescharacteristic
222Q8×C11—41no—
223Q8×C11—41no—
224Q8×C11—41no—
225Q8×C11—41no—
226D4×C11—42no—
227D4×C11—42no—
228D4×C11—42no—
229D4×C11—42no—
230D4×C11—41no—
231D4×C11—41no—
232D4×C11—41no—
233D4×C11—41no—
234C2×C4×C11—22no—
235C2×C4×C11—22no—
236C2×C4×C11—22no—
237C2×C4×C11—42no—
238C2×C4×C11—42no—
239C2×C4×C11—42no—
240C2×C4×C11—42no—
241C2×C4×C11C2×C22⋊C411yescharacteristic
242C2×C4×C11C2×C22⋊C411yescharacteristic
243C2×C4×C11#11711yescharacteristic
244C2×C4×C11#11711yescharacteristic
245C2×C4×C11C4×D411yescharacteristic
246C2×C4×C11C4×D411yescharacteristic
247C2×C4×C11C4×D411yescharacteristic
248C2×C4×C11C4×D411yescharacteristic
249C2×C4×C11C4×D411yescharacteristic
250C2×C4×C11C4×D411yescharacteristic
251C2×C4×C11C4×D411yescharacteristic
252C2×C4×C11C4×D411yescharacteristic
253C2×C4×C11#12011yescharacteristic
254C2×C4×C11#12111yescharacteristic
255C2×C4×C11#12111yescharacteristic
256C2×C4×C11#12111yescharacteristic
257C2×C4×C11#12111yescharacteristic
258C2×C4×C11#12111yescharacteristic
259C2×C4×C11#12111yescharacteristic
260C2×C4×C11#12311yescharacteristic
261C2×C4×C11#12311yescharacteristic
262C2×C4×C11#12311yescharacteristic
263C2×C4×C11#12411yescharacteristic
264C2×C4×C11#12411yescharacteristic
265C2×C4×C11#12411yescharacteristic
266C2×C4×C11#12611yescharacteristic
267C2×C4×C11#12611yescharacteristic
268C2×C4×C11#12711yescharacteristic
269C2×Dic11—24no—
270C2×Dic11—44no—
271C2×Dic11—44no—
272C2×Dic11—42no—
273C8×C11—24no—
274C8×C11—42no—
275C11⋊C8—22no—
276C11⋊C8—22no—
277C11⋊C8—42no—
278C22×#41C2×D1111yescharacteristic
279C22×M16—111no—
280C22×M16C2×D1111yescharacteristic
281C22×M16C2×D1111yescharacteristic
282C23×C8—111no—
283C2×#117—111no—
284C2×#117—111no—
285#413—22no—
286#413—22no—
287C2×#101Dic1112yescomplemented
288C2×#100Dic1112yescomplemented
289#410—222no—
290#410—222no—
291C2×#99—114no—
292#408—222no—
293#408—221no—
294#408—221no—
295C2×C22⋊C8—114no—
296#405—222no—
297#405—222no—
298C2×#97—221no—
299C2×C4×C8—221no—
300#344—222no—
301#344—222no—
302#336—222no—
303C22×C11—22no—
304C22×C11—22no—
305C22×C11—22no—
306C22×C11—41no—
307C22×C11—41no—
308C22×C11—41no—
309C22×C11—41no—
310C22×C11—42no—
311C22×C11—44no—
312C22×C11—82no—
313C22×C11—82no—
314C22×C11C4×C22⋊C411yescharacteristic
315C22×C11C4×C22⋊C411yescharacteristic
316C22×C11C4×C22⋊C411yescharacteristic
317C22×C11#38611yescharacteristic
318C22×C11#38811yescharacteristic
319C22×C11#38811yescharacteristic
320C22×C11#39011yescharacteristic
321C4×C11—42no—
322C4×C11#38611yescharacteristic
323C4×C11#38611yescharacteristic
324C4×C11#38811yescharacteristic
325C4×C11#38811yescharacteristic
326C4×C11#38811yescharacteristic
327C4×C11#38811yescharacteristic
328C4×C11#39011yescharacteristic
329C4×C11#39011yescharacteristic
330Dic11—44no—
331Dic11—82no—
332C2×#41—21no—
333C2×#41—21no—
334C2×#41—21no—
335C2×#41—21no—
336C2×#41—21no—
337C2×#41—21no—
338C2×#41—21no—
339C2×#41—21no—
340C2×#41—21no—
341C2×#41—21no—
342C2×#41—21no—
343C2×#41—21no—
344C22×Q8C2×Dic1111yescharacteristic
345C22×D4C4×D1112yes—
346C22×D4C2×Dic1111yescharacteristic
347C23×C4C4×D1112yes—
348C23×C4C22×D1111yescharacteristic
349C2×M16—21no—
350C2×M16—21no—
351C2×M16—21no—
352C2×M16—21no—
353C2×M16—21no—
354C2×M16—21no—
355C2×M16—21no—
356C2×M16—21no—
357C2×M16—221no—
358C2×M16—221no—
359C2×M16—221no—
360C2×M16—221no—
361C2×M16—221no—
362C2×M16—221no—
363C2×M16C2×Dic1112yes—
364C2×M16C2×Dic1112yes—
365C2×M16C22⋊D1112yes—
366C2×M16C22⋊D1112yes—
367C22×C8—21no—
368C22×C8—21no—
369C22×C8—112no—
370C22×C8—112no—
371C22×C8—111no—
372C22×C8—111no—
373C22×C8—112no—
374C22×C8—221no—
375C22×C8—221no—
376C22×C8—221no—
377C22×C8—221no—
378#117—112no—
379#117—112no—
380#117—221no—
381#117—221no—
382#117—221no—
383#117—221no—
384#117—221no—
385#117—221no—
386C2×C4⋊C4—221no—
387C2×C4⋊C4—221no—
388C2×C22⋊C4—112no—
389C2×C22⋊C4—112no—
390C2×C42—221no—
391C2×C42—221no—
392#101—24no—
393#100—24no—
394#99—228no—
395C22⋊C8—224no—
396C22⋊C8—224no—
397#97—224no—
398C4×C8—224no—
399C2×C11—21no—
400C2×C11—21no—
401C2×C11—21no—
402C2×C11—21no—
403C2×C11—21no—
404C2×C11—21no—
405C2×C11—82no—
406C2×C11#143711yescharacteristic
407C2×C11#175712yes—
408C24C4×Dic1112yes—
409C24C2×C4×D1111yescharacteristic
410#41—41no—
411#41—41no—
412#41—41no—
413#41—41no—
414#41—41no—
415#41—41no—
416#41—41no—
417#41—41no—
418#41—41no—
419#41—41no—
420#41—41no—
421#41—41no—
422#41—41no—
423#41—41no—
424#41—41no—
425#41—41no—
426C2×Q8—21no—
427C2×Q8—21no—
428C2×Q8—21no—
429C2×Q8—21no—
430C2×Q8—21no—
431C2×Q8—21no—
432C2×D4—22no—
433C2×D4—22no—
434C2×D4—22no—
435C2×D4—22no—
436C2×D4—22no—
437C2×D4—22no—
438C2×D4—21no—
439C2×D4—21no—
440C2×D4—21no—
441C2×D4—21no—
442C2×D4—21no—
443C2×D4—21no—
444C22×C4—22no—
445C22×C4—22no—
446C22×C4—22no—
447C22×C4—22no—
448C22×C4—22no—
449C22×C4—22no—
450C22×C4—222no—
451C22×C4—222no—
452C22×C4C4×Dic1112yes—
453C22×C4C2×C4×D1111yescharacteristic
454C22×C4#433911yescharacteristic
455C22×C4#433911yescharacteristic
456C22×C4D4×D1111yescharacteristic
457C22×C4D4×D1111yescharacteristic
458C22×C4D4×D1111yescharacteristic
459C22×C4D4×D1111yescharacteristic
460C22×C4#434111yescharacteristic
461C22×C4#434111yescharacteristic
462C22×C4#434111yescharacteristic
463C22×C4#434111yescharacteristic
464C22×C4C22×Dic1111yescharacteristic
465C22×C4C2×C22⋊D1111yescharacteristic
466C22×C4C2×C22⋊D1111yescharacteristic
467M16—22no—
468M16—22no—
469M16—22no—
470M16—22no—
471M16—22no—
472M16—41no—
473M16—41no—
474M16—441no—
475M16—441no—
476M16—441no—
477M16—441no—
478M16C22⋊Dic1114yes—
479C2×C8—22no—
480C2×C8—22no—
481C2×C8—22no—
482C2×C8—22no—
483C2×C8—41no—
484C2×C8—41no—
485C2×C8—112no—
486C2×C8—112no—
487C2×C8—222no—
488C2×C8—221no—
489C2×C8—221no—
490C2×C8—222no—
491C2×C8—222no—
492C2×C8—221no—
493C2×C8—221no—
494C2×C8—222no—
495C2×C8—222no—
496C2×C8—222no—
497C2×C8—222no—
498C4⋊C4—222no—
499C4⋊C4—222no—
500C4⋊C4—441no—
501C4⋊C4—441no—
502C22⋊C4—114no—
503C22⋊C4—222no—
504C22⋊C4—222no—
505C22⋊C4—222no—
506C42—222no—
507C42—222no—
508C42—441no—
509C42—441no—
510C11#1096111yescharacteristic, complemented, Sylow
511C23—22no—
512C23—22no—
513C23—22no—
514C23—42no—
515C23—44no—
516C23#6693011yescharacteristic
517C23C22⋊C4×D1111yescharacteristic
518C23(C22⋊D11)⋊C411yescharacteristic
519C23(C22⋊D11)⋊C411yescharacteristic
520C23C2×C4×Dic1111yescharacteristic
521C23C4×C22⋊D1111yescharacteristic
522C23C4×C22⋊D1111yescharacteristic
523Q8—41no—
524Q8—41no—
525Q8—41no—
526Q8—41no—
527D4—42no—
528D4—42no—
529D4—42no—
530D4—42no—
531D4—41no—
532D4—41no—
533D4—41no—
534D4—41no—
535C2×C4—22no—
536C2×C4—22no—
537C2×C4—22no—
538C2×C4—42no—
539C2×C4—42no—
540C2×C4—42no—
541C2×C4—42no—
542C2×C4—224no—
543C2×C4—444no—
544C2×C4—444no—
545C2×C4—442no—
546C2×C4#6693011yescharacteristic
547C2×C4#6693211yescharacteristic
548C2×C4#6693211yescharacteristic
549C2×C4C22⋊C4×D1111yescharacteristic
550C2×C4(C22⋊D11)⋊C411yescharacteristic
551C2×C4(C22⋊D11)⋊C411yescharacteristic
552C2×C4#6693611yescharacteristic
553C2×C4#6693611yescharacteristic
554C2×C4#6693711yescharacteristic
555C2×C4#6693711yescharacteristic
556C2×C4#6693811yescharacteristic
557C2×C4#6693811yescharacteristic
558C2×C4#6697911yescharacteristic
559C2×C4C4×C22⋊D1111yescharacteristic
560C2×C4C4×C22⋊D1111yescharacteristic
561C2×C4D4×Dic1111yescharacteristic
562C2×C4D4×Dic1111yescharacteristic
563C2×C4D4×Dic1111yescharacteristic
564C2×C4D4×Dic1111yescharacteristic
565C2×C4#6698811yescharacteristic
566C2×C4#6698911yescharacteristic
567C2×C4#6699011yescharacteristic
568C2×C4#6699111yescharacteristic
569C2×C4#6699111yescharacteristic
570C2×C4#6699211yescharacteristic
571C2×C4#6699211yescharacteristic
572C2×C4#6699311yescharacteristic
573C2×C4C2×C22⋊Dic1111yescharacteristic
574C8—24no—
575C8—42no—
576C8—222no—
577C8—222no—
578C8—442no—
579C22—22no—
580C22—22no—
581C22—22no—
582C22—41no—
583C22—41no—
584C22—41no—
585C22—41no—
586C22—42no—
587C22—44no—
588C22—82no—
589C22—82no—
590C22C22⋊C4×Dic1111yescharacteristic
591C22C22⋊C4×Dic1111yescharacteristic
592C22#1062255711yescharacteristic
593C22#1062255811yescharacteristic
594C22#1062256911yescharacteristic
595C22#1062257011yescharacteristic
596C22C4×C22⋊Dic1111yescharacteristic
597C4—42no—
598C4—444no—
599C4—882no—
600C4#1062255711yescharacteristic
601C4#1062255811yescharacteristic
602C4#1062256411yescharacteristic
603C4#1062256411yescharacteristic
604C4#1062256911yescharacteristic
605C4#1062257011yescharacteristic
606C4#1062283311yescharacteristic
607C4#1062283411yescharacteristic
608C2—21no—
609C2—21no—
610C2—21no—
611C2—21no—
612C2—21no—
613C2—21no—
614C2—82no—
615C2#1306685311yescharacteristic
616C2#1306841912yes—
subgroupG/H
centerC2×C4C22⋊C4×D11
commutatorC23×C11C2×C42
FrattiniC23×C4C22×D11
FittingC2×C11×#413C2
socleC22×C11C4×C22⋊C4
prime radicalC22×C11×#41C22
cosocleC23×C4×C11C23
hypercenterC2×#413D11
hypocenterC11#10961
LCSG ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C2×#413

Complements

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

NH ≅ G/Ntype
3. C2×#10622735C2semidirect
4. C2×#10622197C2semidirect
5. C2×#10622197C2semidirect
6. #13068314C2semidirect
17. C2×C11×#101C4semidirect
18. C2×C11×#100C4semidirect
25. C2×C22⋊(C11⋊C8)C4semidirect
287. C2×#101Dic11semidirect
288. C2×#100Dic11semidirect
510. C11#10961semidirect

Maximal subgroups

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

subgroupindex
C2×#106228532
C2×#106228472
C2×#106227352
C2×#106221972
#130683142
C2×C11×#4132
#1096111