Finite Group Databasebeta

← #14764093

Subgroups — #14764093

Order 2816.

1010 conjugacy classes of subgroups.

The subgroup lattice has 656 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622739C211yesmaximal, characteristic
2C2×#10622339C211yesmaximal, characteristic
3D11×#407C211yesmaximal, characteristic
4#13068823C211yesmaximal, characteristic, complemented
5#13068822C212yesmaximal, complemented
6#13068821C211yesmaximal, characteristic, complemented
7#13068820C211yesmaximal, characteristic, complemented
8#13068819C212yesmaximal, complemented
9#13068657C212yesmaximal, complemented
10#13068655C212yesmaximal, complemented
11C11×#1855C211yesmaximal, characteristic, complemented
12C23×C4×D11C2211yescharacteristic
13C22×C11×M16C2211yescharacteristic
14C22×#4318C2211yescharacteristic
15C2×M16×D11C2211yescharacteristic
16C2×M16×D11C2211yescharacteristic
17C22×#4313C2212yes—
18C2×C11×#108C2212yescomplemented
19C11×#407C2211yescharacteristic
20C2×C11×C22⋊C8C2211yescharacteristic
21#10622820C2211yescharacteristic
22C2×C22⋊(C11⋊C8)C2211yescharacteristic
23#10622739—21no—
24#10622739—21no—
25#10622739C2212yes—
26#10622739C2211yescharacteristic
27#10622739C2211yescharacteristic
28#10622739C2212yes—
29C2×#66886C2212yescomplemented
30C2×#66886C2212yescomplemented
31C2×(C2×D11)⋊C8—21no—
32C2×(C2×D11)⋊C8—21no—
33C2×(C2×D11)⋊C8C2212yes—
34C2×#66883C2212yescomplemented
35#10622339—21no—
36#10622339—21no—
37#10622339C412yes—
38#10622339C412yes—
39#10622339C412yes—
40#10622339C412yes—
41D11×C22⋊C8—21no—
42D11×C22⋊C8—21no—
43C11×#341C2212yescomplemented
44#10622196C2212yescomplemented
45#10622196C2212yescomplemented
46#10622190C2212yescomplemented
47C24×D11Q811yescharacteristic
48C23×C4×C11C2311yescharacteristic
49C23×Dic11Q811yescharacteristic
50C22×C4×D11—42no—
51C22×C4×D11—42no—
52C22×C4×D11C2×C411yescharacteristic
53C22×C4×D11C2×C411yescharacteristic
54C22×C4×D11C2×C411yescharacteristic
55C22×C4×D11C2×C411yescharacteristic
56C22×C4×D11D411yescharacteristic
57C22×C4×D11D411yescharacteristic
58C22×C4×D11D411yescharacteristic
59C22×C4×D11D411yescharacteristic
60C22×C4×D11Q811yescharacteristic
61C22×C4×D11Q811yescharacteristic
62C22×C4×D11C2311yescharacteristic
63C22×C4×D11C2311yescharacteristic
64C2×C11×M16—21no—
65C2×C11×M16—42no—
66C2×C11×M16C2311yescharacteristic
67C2×C11×M16C2312yes—
68C2×C11×M16C2311yescharacteristic
69C22×C8×C11—21no—
70C22×C8×C11C2312yes—
71C2×#4318—21no—
72C2×#4318—42no—
73C2×#4318C2311yescharacteristic
74C2×#4318C2312yes—
75C2×#4318C2311yescharacteristic
76C22×C11⋊C8—21no—
77C22×C11⋊C8C2312yes—
78M16×D11—42no—
79M16×D11—42no—
80C2×#4313—21no—
81C2×#4313—21no—
82C2×#4313—42no—
83C2×#4313—42no—
84C2×#4313C2×C414yes—
85C2×#4313C2×C414yes—
86C2×C8×D11—21no—
87C2×C8×D11—21no—
88C11×#108—42no—
89C11×C22⋊C8—21no—
90C11×C22⋊C8—21no—
91C11×C22⋊C8C2×C412yes—
92C11×C22⋊C8C2×C412yes—
93C22⋊(C11⋊C8)—21no—
94C22⋊(C11⋊C8)—21no—
95C22⋊(C11⋊C8)C2×C412yes—
96C22⋊(C11⋊C8)C2×C412yes—
97#66886—42no—
98#66886—42no—
99(C2×D11)⋊C8—22no—
100(C2×D11)⋊C8—22no—
101(C2×D11)⋊C8—22no—
102(C2×D11)⋊C8—22no—
103(C2×D11)⋊C8—21no—
104(C2×D11)⋊C8—21no—
105(C2×D11)⋊C8—21no—
106(C2×D11)⋊C8—21no—
107(C2×D11)⋊C8C2×C414yes—
108(C2×D11)⋊C8C2×C414yes—
109#66883—42no—
110#21949—111nomaximal, Sylow
111C24×C11C2×Q811yescharacteristic
112C23×D11—42no—
113C23×D11—42no—
114C23×D11—42no—
115C23×D11C4⋊C411yescharacteristic
116C23×D11C4⋊C411yescharacteristic
117C23×D11C4⋊C411yescharacteristic
118C23×D11C4⋊C411yescharacteristic
119C23×D11C2×Q811yescharacteristic
120C23×D11C2×Q811yescharacteristic
121C22×C4×C11—22no—
122C22×C4×C11—22no—
123C22×C4×C11C22×C411yescharacteristic
124C22×C4×C11C22×C411yescharacteristic
125C22×C4×C11C2×D411yescharacteristic
126C22×C4×C11C2×D411yescharacteristic
127C22×C4×C11C2×Q811yescharacteristic
128C22×C4×C11C2411yescharacteristic
129C22×Dic11—42no—
130C22×Dic11C4⋊C411yescharacteristic
131C22×Dic11C4⋊C411yescharacteristic
132C22×Dic11C4⋊C411yescharacteristic
133C22×Dic11C4⋊C411yescharacteristic
134C22×Dic11C2×Q811yescharacteristic
135C22×Dic11C2×Q811yescharacteristic
136C2×C4×D11—22no—
137C2×C4×D11—22no—
138C2×C4×D11—22no—
139C2×C4×D11—22no—
140C2×C4×D11—42no—
141C2×C4×D11—42no—
142C2×C4×D11—42no—
143C2×C4×D11—42no—
144C2×C4×D11—42no—
145C2×C4×D11—42no—
146C2×C4×D11—41no—
147C2×C4×D11—41no—
148C2×C4×D11—41no—
149C2×C4×D11—41no—
150C2×C4×D11—41no—
151C2×C4×D11—41no—
152C2×C4×D11—41no—
153C2×C4×D11—41no—
154C2×C4×D11C4⋊C411yescharacteristic
155C2×C4×D11C4⋊C411yescharacteristic
156C2×C4×D11C4⋊C411yescharacteristic
157C2×C4×D11C4⋊C411yescharacteristic
158C2×C4×D11C4⋊C411yescharacteristic
159C2×C4×D11C4⋊C411yescharacteristic
160C2×C4×D11C4⋊C411yescharacteristic
161C2×C4×D11C4⋊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
170C11×M16—22no—
171C11×M16—22no—
172C11×M16—22no—
173C11×M16—22no—
174C11×M16—42no—
175C2×C8×C11—22no—
176C2×C8×C11—21no—
177C2×C8×C11—21no—
178C2×C8×C11—22no—
179C2×C8×C11—22no—
180C2×C8×C11—42no—
181C2×C8×C11C22×C414yes—
182#4318—22no—
183#4318—22no—
184#4318—22no—
185#4318—22no—
186#4318—42no—
187C2×C11⋊C8—22no—
188C2×C11⋊C8—21no—
189C2×C11⋊C8—21no—
190C2×C11⋊C8—22no—
191C2×C11⋊C8—22no—
192C2×C11⋊C8—42no—
193C2×C11⋊C8C22×C414yes—
194#4313—44no—
195#4313—44no—
196#4313—42no—
197#4313—42no—
198C8×D11—42no—
199C8×D11—42no—
200C2×#407—111no—
201C2×#407—111no—
202C2×#407—111no—
203#1855—112no—
204#1855—111no—
205#1855—111no—
206#1855—112no—
207#1855—111no—
208#1855D1111yescharacteristic, complemented
209#1811—112no—
210#1811—112no—
211C23×C11—22no—
212C23×C11—22no—
213C23×C11—41no—
214C23×C11C2×C4⋊C411yescharacteristic
215C23×C11C2×C4⋊C411yescharacteristic
216C23×C11C22×Q811yescharacteristic
217C22×D11—22no—
218C22×D11—22no—
219C22×D11—22no—
220C22×D11—22no—
221C22×D11—22no—
222C22×D11—22no—
223C22×D11—22no—
224C22×D11—41no—
225C22×D11—41no—
226C22×D11—41no—
227C22×D11—41no—
228C22×D11—41no—
229C22×D11—41no—
230C22×D11—41no—
231C22×D11—41no—
232C22×D11—41no—
233C22×D11—41no—
234C22×D11—41no—
235C22×D11—416no—
236C22×D11C2×C4⋊C411yescharacteristic
237C22×D11C2×C4⋊C411yescharacteristic
238C22×D11C2×C4⋊C411yescharacteristic
239C22×D11C2×C4⋊C411yescharacteristic
240C2×C4×C11—22no—
241C2×C4×C11—22no—
242C2×C4×C11—22no—
243C2×C4×C11—21no—
244C2×C4×C11—21no—
245C2×C4×C11—21no—
246C2×C4×C11—21no—
247C2×C4×C11C2×C4⋊C411yescharacteristic
248C2×C4×C11C2×C4⋊C411yescharacteristic
249C2×C4×C11C23×C411yescharacteristic
250C2×C4×C11C22×D411yescharacteristic
251C2×C4×C11H(5,𝔽2)12yes—
252C2×C4×C11H(5,𝔽2)12yes—
253C2×Dic11—22no—
254C2×Dic11—22no—
255C2×Dic11—41no—
256C2×Dic11—41no—
257C2×Dic11—41no—
258C2×Dic11—41no—
259C2×Dic11C2×C4⋊C411yescharacteristic
260C2×Dic11C2×C4⋊C411yescharacteristic
261C2×Dic11C2×C4⋊C411yescharacteristic
262C2×Dic11C2×C4⋊C411yescharacteristic
263C4×D11—22no—
264C4×D11—22no—
265C4×D11—22no—
266C4×D11—22no—
267C4×D11—21no—
268C4×D11—21no—
269C4×D11—21no—
270C4×D11—21no—
271C4×D11—21no—
272C4×D11—21no—
273C4×D11—21no—
274C4×D11—21no—
275C4×D11—41no—
276C4×D11—41no—
277C4×D11—41no—
278C4×D11—41no—
279C4×D11—41no—
280C4×D11—41no—
281C4×D11—41no—
282C4×D11—41no—
283C8×C11—24no—
284C8×C11—41no—
285C8×C11—41no—
286C8×C11—42no—
287C11⋊C8—24no—
288C11⋊C8—41no—
289C11⋊C8—41no—
290C11⋊C8—42no—
291C24×C4—111no—
292C22×M16—112no—
293C22×M16—111no—
294C22×M16—111no—
295C22×M16—111no—
296C22×M16C2×D1111yescharacteristic
297C2×#108—112no—
298C2×#108—112no—
299C2×#108—112no—
300C2×#108C2×D1112yescomplemented
301#407—112no—
302#407—112no—
303#407—112no—
304#407—112no—
305#407—111no—
306#407—111no—
307#407—111no—
308#407—112no—
309#407—112no—
310#407—221no—
311#407—221no—
312#407—221no—
313#407—221no—
314#407C2×D1111yescharacteristic
315C2×C22⋊C8—111no—
316C2×C22⋊C8—112no—
317C2×C22⋊C8—221no—
318C2×C22⋊C8—221no—
319C2×C22⋊C8—221no—
320C2×C22⋊C8—221no—
321C2×C22⋊C8C2×D1111yescharacteristic
322#341—112no—
323#341—112no—
324#341—112no—
325#341C2×D1112yescomplemented
326C22×C11—21no—
327C22×C11—21no—
328C22×C11—21no—
329C22×C11—21no—
330C22×C11—21no—
331C22×C11—21no—
332C22×C11—21no—
333C22×C11—44no—
334C22×C11#43012yes—
335C22×C11C22×C4⋊C411yescharacteristic
336C22×C11#54312yes—
337C2×D11—21no—
338C2×D11—21no—
339C2×D11—21no—
340C2×D11—21no—
341C2×D11—21no—
342C2×D11—21no—
343C2×D11—21no—
344C2×D11—21no—
345C2×D11—21no—
346C2×D11—21no—
347C2×D11—21no—
348C2×D11—44no—
349C2×D11—44no—
350C2×D11—44no—
351C2×D11—44no—
352C2×D11—44no—
353C2×D11—44no—
354C2×D11#43012yes—
355C4×C11—21no—
356C4×C11—21no—
357C4×C11#51812yes—
358C4×C11#53411yescharacteristic
359C4×C11#53411yescharacteristic
360Dic11—21no—
361Dic11—21no—
362Dic11—21no—
363Dic11—21no—
364C25—111no—
365C23×C4—111no—
366C23×C4—111no—
367C23×C4—111no—
368C23×C4—111no—
369C23×C4—111no—
370C23×C4—111no—
371C23×C4—111no—
372C23×C4—111no—
373C23×C4—111no—
374C23×C4—111no—
375C23×C4—111no—
376C23×C4—111no—
377C23×C4—111no—
378C23×C4—442no—
379C23×C4—442no—
380C23×C4C22×D1111yescharacteristic
381C2×M16—21no—
382C2×M16—42no—
383C2×M16—114no—
384C2×M16—114no—
385C2×M16—111no—
386C2×M16—112no—
387C2×M16—111no—
388C2×M16—221no—
389C2×M16—221no—
390C2×M16—221no—
391C2×M16—442no—
392C2×M16—442no—
393C2×M16—442no—
394C2×M16—442no—
395C2×M16—442no—
396C2×M16C22×D1111yescharacteristic
397C2×M16C22×D1111yescharacteristic
398C2×M16C22×D1112yes—
399C22×C8—21no—
400C22×C8—112no—
401C22×C8—221no—
402C22×C8—221no—
403C22×C8—221no—
404C22×C8C22×D1112yes—
405#108—42no—
406#108—442no—
407#108—442no—
408#108—442no—
409C22⋊C8—21no—
410C22⋊C8—21no—
411C22⋊C8—112no—
412C22⋊C8—112no—
413C22⋊C8—114no—
414C22⋊C8—114no—
415C22⋊C8—221no—
416C22⋊C8—221no—
417C22⋊C8—221no—
418C22⋊C8—221no—
419C22⋊C8—222no—
420C22⋊C8—222no—
421C22⋊C8—222no—
422C22⋊C8—222no—
423C22⋊C8—221no—
424C22⋊C8—221no—
425C22⋊C8C4×D1112yes—
426C22⋊C8C4×D1112yes—
427C2×C11—22no—
428C2×C11—22no—
429C2×C11—41no—
430C2×C11#231511yescharacteristic
431C2×C11C2×#43011yescharacteristic
432C2×C11C2×#43011yescharacteristic
433D11—22no—
434D11—41no—
435D11—41no—
436D11—41no—
437C24—111no—
438C24—111no—
439C24—111no—
440C24—111no—
441C24—111no—
442C24—111no—
443C24—442no—
444C24—442no—
445C24—442no—
446C24Q8×D1111yescharacteristic
447C22×C4—22no—
448C22×C4—22no—
449C22×C4—111no—
450C22×C4—111no—
451C22×C4—111no—
452C22×C4—111no—
453C22×C4—111no—
454C22×C4—111no—
455C22×C4—111no—
456C22×C4—111no—
457C22×C4—111no—
458C22×C4—111no—
459C22×C4—111no—
460C22×C4—111no—
461C22×C4—111no—
462C22×C4—111no—
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—222no—
472C22×C4—222no—
473C22×C4—222no—
474C22×C4—222no—
475C22×C4—442no—
476C22×C4—442no—
477C22×C4—442no—
478C22×C4—442no—
479C22×C4—441no—
480C22×C4—441no—
481C22×C4—441no—
482C22×C4—441no—
483C22×C4—441no—
484C22×C4—441no—
485C22×C4—441no—
486C22×C4—441no—
487C22×C4—442no—
488C22×C4—442no—
489C22×C4—442no—
490C22×C4C2×C4×D1111yescharacteristic
491C22×C4C2×C4×D1111yescharacteristic
492C22×C4D4×D1111yescharacteristic
493C22×C4D4×D1111yescharacteristic
494C22×C4Q8×D1111yescharacteristic
495C22×C4C23×D1111yescharacteristic
496M16—22no—
497M16—22no—
498M16—22no—
499M16—22no—
500M16—42no—
501M16—222no—
502M16—222no—
503M16—222no—
504M16—222no—
505M16—444no—
506M16—444no—
507M16—442no—
508M16—442no—
509M16—442no—
510C2×C8—22no—
511C2×C8—22no—
512C2×C8—21no—
513C2×C8—21no—
514C2×C8—22no—
515C2×C8—42no—
516C2×C8—114no—
517C2×C8—222no—
518C2×C8—222no—
519C2×C8—221no—
520C2×C8—222no—
521C2×C8—221no—
522C2×C8—442no—
523C2×C8—442no—
524C2×C8—442no—
525C2×C8C2×C4×D1114yes—
526C11#2194911yescharacteristic, complemented, Sylow
527C23—22no—
528C23—22no—
529C23—41no—
530C23—111no—
531C23—111no—
532C23—111no—
533C23—111no—
534C23—222no—
535C23—222no—
536C23—222no—
537C23—222no—
538C23—222no—
539C23—222no—
540C23—222no—
541C23—441no—
542C23—441no—
543C23—441no—
544C23—441no—
545C23—441no—
546C23—441no—
547C23—441no—
548C23—441no—
549C23—441no—
550C23—441no—
551C23—441no—
552C23—4416no—
553C23C4⋊C4×D1111yescharacteristic
554C23C4⋊C4×D1111yescharacteristic
555C23C2×Q8×D1111yescharacteristic
556C2×C4—22no—
557C2×C4—22no—
558C2×C4—22no—
559C2×C4—21no—
560C2×C4—21no—
561C2×C4—21no—
562C2×C4—21no—
563C2×C4—111no—
564C2×C4—111no—
565C2×C4—111no—
566C2×C4—111no—
567C2×C4—222no—
568C2×C4—222no—
569C2×C4—222no—
570C2×C4—222no—
571C2×C4—222no—
572C2×C4—222no—
573C2×C4—221no—
574C2×C4—221no—
575C2×C4—221no—
576C2×C4—221no—
577C2×C4—221no—
578C2×C4—221no—
579C2×C4—221no—
580C2×C4—221no—
581C2×C4—441no—
582C2×C4—441no—
583C2×C4—441no—
584C2×C4—441no—
585C2×C4—441no—
586C2×C4—441no—
587C2×C4—441no—
588C2×C4—441no—
589C2×C4—441no—
590C2×C4—441no—
591C2×C4—441no—
592C2×C4—441no—
593C2×C4C4⋊C4×D1111yescharacteristic
594C2×C4C4⋊C4×D1111yescharacteristic
595C2×C4C22×C4×D1111yescharacteristic
596C2×C4C2×D4×D1111yescharacteristic
597C2×C4#6703712yes—
598C2×C4#6704212yes—
599C8—24no—
600C8—42no—
601C8—41no—
602C8—41no—
603C8—224no—
604C8—441no—
605C8—441no—
606C8—442no—
607C22—21no—
608C22—21no—
609C22—21no—
610C22—21no—
611C22—21no—
612C22—21no—
613C22—21no—
614C22—44no—
615C22—112no—
616C22—221no—
617C22—221no—
618C22—221no—
619C22—221no—
620C22—221no—
621C22—221no—
622C22—221no—
623C22—221no—
624C22—221no—
625C22—221no—
626C22—221no—
627C22—444no—
628C22—444no—
629C22—444no—
630C22—444no—
631C22—444no—
632C22—444no—
633C22#1062250612yes—
634C22C2×C4⋊C4×D1111yescharacteristic
635C22#1062316512yes—
636C4—21no—
637C4—21no—
638C4—221no—
639C4—221no—
640C4—221no—
641C4—221no—
642C4#1062307612yes—
643C4#1062312011yescharacteristic
644C4#1062318411yescharacteristic
645C2—22no—
646C2—22no—
647C2—41no—
648C2—222no—
649C2—441no—
650C2—441no—
651C2—441no—
652C2#1307122711yescharacteristic
653C2D11×#43011yescharacteristic
654C2C2×#1062250611yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1855C2
socleC22×C11C22×C4⋊C4
prime radicalC24×D11Q8
cosocleC22×C4×C11C24
hypercenter#1855D11
hypocenterC11#21949
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #1855

Complements

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

NH ≅ G/Ntype
4. #13068823C2semidirect
5. #13068822C2semidirect
6. #13068821C2semidirect
7. #13068820C2semidirect
8. #13068819C2semidirect
9. #13068657C2semidirect
10. #13068655C2semidirect
11. C11×#1855C2semidirect
18. C2×C11×#108C22semidirect
29. C2×#66886C22semidirect
30. C2×#66886C22semidirect
34. C2×#66883C22semidirect
43. C11×#341C22semidirect
44. #10622196C22semidirect
45. #10622196C22semidirect
46. #10622190C22semidirect
208. #1855D11semidirect
300. C2×#108C2×D11semidirect
325. #341C2×D11semidirect
526. C11#21949semidirect

Maximal subgroups

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

subgroupindex
C2×#106227392
C2×#106223392
D11×#4072
#130688232
#130688222
#130688212
#130688202
#130688192
#130686572
#130686552
C11×#18552
#2194911