Finite Group Databasebeta

← #14786756

Subgroups — #14786756

Order 2816.

1344 conjugacy classes of subgroups.

The subgroup lattice has 616 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622647C211yesmaximal, characteristic, complemented
2C22×#66899C211yesmaximal, characteristic, complemented
3#13072933C211yesmaximal, characteristic, complemented
4#13069852C212yesmaximal, complemented
5#13069809C212yesmaximal, complemented
6#13069045C211yesmaximal, characteristic, complemented
7#13068909C211yesmaximal, characteristic, complemented
8#13068884C212yesmaximal, complemented
9#13068556C212yesmaximal, complemented
10#13068551C211yesmaximal, characteristic, complemented
11C2×C11×#548C211yesmaximal, characteristic
12C22×C11×#41C2211yescharacteristic
13C23×Q8×C11C2211yescharacteristic
14C11×#548—24no—
15C11×#548—24no—
16C2×C11×#124—21no—
17C2×C11×#124C2211yescharacteristic
18C2×C11×C22⋊Q8—21no—
19C2×C11×C22⋊Q8C2211yescharacteristic
20C2×C11×#121—21no—
21C2×C11×#121C2211yescharacteristic
22C2×C4×Q8×C11C2211yescharacteristic
23C2×C4×D4×C11—21no—
24C2×C4×D4×C11C2211yescharacteristic
25C22×C4⋊Dic11C2211yescharacteristic
26C23×C11⋊C8C2211yescharacteristic
27C2×#66899—24no—
28C2×#66899C2212yes—
29C2×#66899C2212yes—
30C2×#66899C2212yes—
31C2×#66899C2212yes—
32#10622833—21no—
33C2×#66896C2212yes—
34C2×#66896C2212yes—
35#10622825C2211yescharacteristic
36#10622825C2212yes—
37C2×C22⋊(C11⋊C8)C2211yescharacteristic
38C2×C22⋊(C11⋊C8)C2212yes—
39#10622647—24no—
40#10622599—21no—
41C2×#66872C2212yes—
42#10622562—21no—
43#10622559—21no—
44#10622541C2212yes—
45#10622167C2212yes—
46#10622162C2212yes—
47C2×C11×#41—22no—
48C2×C11×#41—22no—
49C2×C11×#41—24no—
50C2×C11×#41—42no—
51C22×Q8×C11—21no—
52C22×Q8×C11—22no—
53C22×Q8×C11—24no—
54C22×Q8×C11—42no—
55C22×Q8×C11D414yes—
56C22×Q8×C11C2311yescharacteristic
57C22×Q8×C11C2311yescharacteristic
58C22×D4×C11—21no—
59C22×D4×C11—21no—
60C22×D4×C11D411yescharacteristic
61C22×D4×C11C2311yescharacteristic
62C23×C4×C11—21no—
63C23×C4×C11—21no—
64C23×C4×C11C2311yescharacteristic
65C23×C4×C11C2311yescharacteristic
66C23×Dic11—21no—
67C11×#124—28no—
68C11×#124—22no—
69C11×#124—22no—
70C11×C22⋊Q8—28no—
71C11×C22⋊Q8—22no—
72C11×C22⋊Q8—22no—
73C11×#121—28no—
74C11×#121—22no—
75C11×#121D414yes—
76C4×Q8×C11—22no—
77C4×Q8×C11—22no—
78C4×D4×C11—28no—
79C4×D4×C11—22no—
80C4×D4×C11—22no—
81C2×C11×C4⋊C4—21no—
82C2×C11×C4⋊C4—21no—
83C2×C11×C4⋊C4D411yescharacteristic
84C2×C11×C4⋊C4C2311yescharacteristic
85C2×C11×C22⋊C4—21no—
86C2×C11×C22⋊C4—21no—
87C2×C11×C22⋊C4—21no—
88C2×C11×C22⋊C4—21no—
89C2×C11×C22⋊C4D411yescharacteristic
90C2×C11×C22⋊C4D411yescharacteristic
91C2×C42×C11—21no—
92C2×C42×C11C2311yescharacteristic
93C2×C22⋊Dic11—21no—
94C2×C22⋊Dic11—22no—
95C2×C4⋊Dic11—22no—
96C2×C4⋊Dic11—22no—
97C2×C4⋊Dic11—21no—
98C2×C4⋊Dic11C2312yes—
99C2×C4⋊Dic11C2312yes—
100C2×Dic11⋊C4—22no—
101C22×C11⋊C8—22no—
102C22×C11⋊C8—42no—
103C22×C11⋊C8C2312yes—
104C22×C11⋊C8C2312yes—
105#66899—24no—
106#66899—24no—
107#66899—24no—
108#66899—42no—
109#66896—24no—
110#66896—42no—
111C11⋊#95—22no—
112C11⋊#95—22no—
113C11⋊#95—21no—
114C22⋊(C11⋊C8)—22no—
115C22⋊(C11⋊C8)—42no—
116#66872—24no—
117#24036—111nomaximal, Sylow
118C24×C11—21no—
119C24×C11C2×D411yescharacteristic
120C24×C11C2×D411yescharacteristic
121C11×#41—48no—
122C11×#41—44no—
123C11×#41—44no—
124C2×Q8×C11—24no—
125C2×Q8×C11—21no—
126C2×Q8×C11—21no—
127C2×Q8×C11—22no—
128C2×Q8×C11—28no—
129C2×Q8×C11—22no—
130C2×Q8×C11—22no—
131C2×Q8×C11—44no—
132C2×Q8×C11—44no—
133C2×Q8×C11—48no—
134C2×Q8×C11C2×D412yes—
135C2×Q8×C11C2×D412yes—
136C2×Q8×C11#4114yes—
137C2×D4×C11—24no—
138C2×D4×C11—22no—
139C2×D4×C11—24no—
140C2×D4×C11—22no—
141C2×D4×C11—22no—
142C2×D4×C11—21no—
143C2×D4×C11—22no—
144C2×D4×C11—22no—
145C2×D4×C11—44no—
146C2×D4×C11—42no—
147C2×D4×C11—42no—
148C2×D4×C11C2×D412yes—
149C22×C4×C11—21no—
150C22×C4×C11—22no—
151C22×C4×C11—22no—
152C22×C4×C11—24no—
153C22×C4×C11—24no—
154C22×C4×C11—21no—
155C22×C4×C11—21no—
156C22×C4×C11—21no—
157C22×C4×C11—21no—
158C22×C4×C11—22no—
159C22×C4×C11—22no—
160C22×C4×C11—44no—
161C22×C4×C11—44no—
162C22×C4×C11C2×D411yescharacteristic
163C22×C4×C11C2×D411yescharacteristic
164C22×C4×C11C2×D411yescharacteristic
165C22×C4×C11C2×D411yescharacteristic
166C22×C4×C11C2×D412yes—
167C22×C4×C11C2×D412yes—
168C22×C4×C11C2411yescharacteristic
169C22×Dic11—22no—
170C22×Dic11—22no—
171C22×Dic11—42no—
172C22×Dic11—82no—
173C11×C4⋊C4—24no—
174C11×C4⋊C4—24no—
175C11×C4⋊C4—22no—
176C11×C4⋊C4—21no—
177C11×C4⋊C4C2×D412yes—
178C11×C22⋊C4—24no—
179C11×C22⋊C4—24no—
180C11×C22⋊C4—24no—
181C11×C22⋊C4—22no—
182C11×C22⋊C4—24no—
183C11×C22⋊C4—22no—
184C42×C11—24no—
185C42×C11—21no—
186C42×C11—21no—
187C22⋊Dic11—42no—
188C22⋊Dic11—82no—
189C4⋊Dic11—22no—
190C4⋊Dic11—22no—
191C4⋊Dic11—22no—
192C4⋊Dic11—22no—
193C4⋊Dic11—42no—
194Dic11⋊C4—82no—
195C2×C11⋊C8—22no—
196C2×C11⋊C8—22no—
197C2×C11⋊C8—22no—
198C2×C11⋊C8—22no—
199C2×C11⋊C8—22no—
200C2×C11⋊C8—22no—
201C2×C11⋊C8—44no—
202C2×#548D1111yescharacteristic
203C2×#481—111no—
204C22×#103—111no—
205#2487—111no—
206#2042—112no—
207#2035—112no—
208#1893—111no—
209#1869—111no—
210#1865—112no—
211#1788—112no—
212#1787—111no—
213C23×C11—22no—
214C23×C11—22no—
215C23×C11—21no—
216C23×C11—22no—
217C23×C11—22no—
218C23×C11—21no—
219C23×C11—21no—
220C23×C11—22no—
221C23×C11—42no—
222C23×C11—41no—
223C23×C11—41no—
224C23×C11—42no—
225C23×C11#12012yes—
226C23×C11#13512yes—
227C23×C11#13712yes—
228C23×C11C22×D411yescharacteristic
229Q8×C11—22no—
230Q8×C11—24no—
231Q8×C11—22no—
232Q8×C11—22no—
233Q8×C11—48no—
234Q8×C11—42no—
235Q8×C11#12314yes—
236D4×C11—24no—
237D4×C11—48no—
238D4×C11—44no—
239D4×C11—48no—
240D4×C11—41no—
241D4×C11—41no—
242C2×C4×C11—22no—
243C2×C4×C11—22no—
244C2×C4×C11—24no—
245C2×C4×C11—22no—
246C2×C4×C11—22no—
247C2×C4×C11—24no—
248C2×C4×C11—21no—
249C2×C4×C11—21no—
250C2×C4×C11—22no—
251C2×C4×C11—22no—
252C2×C4×C11—21no—
253C2×C4×C11—22no—
254C2×C4×C11—21no—
255C2×C4×C11—21no—
256C2×C4×C11—22no—
257C2×C4×C11—48no—
258C2×C4×C11—48no—
259C2×C4×C11—42no—
260C2×C4×C11—41no—
261C2×C4×C11—41no—
262C2×C4×C11—41no—
263C2×C4×C11—41no—
264C2×C4×C11—42no—
265C2×C4×C11#12012yes—
266C2×C4×C11C22×D411yescharacteristic
267C2×C4×C11C22×D411yescharacteristic
268C2×C4×C11C2×#4112yes—
269C2×C4×C11H(5,𝔽2)12yes—
270C2×Dic11—42no—
271C2×Dic11—42no—
272C2×Dic11—42no—
273C2×Dic11—42no—
274C2×Dic11—42no—
275C2×Dic11—42no—
276C2×Dic11—84no—
277C11⋊C8—42no—
278C11⋊C8—42no—
279C22×#41C2×D1111yescharacteristic
280C23×Q8C2×D1111yescharacteristic
281C23×C8—111no—
282#548—24no—
283#548—24no—
284C2×#124—21no—
285C2×#124C2×D1111yescharacteristic
286C2×C22⋊Q8—21no—
287C2×C22⋊Q8C2×D1111yescharacteristic
288C2×#121—21no—
289C2×#121C2×D1111yescharacteristic
290C2×C4×Q8C2×D1111yescharacteristic
291C2×C4×D4—21no—
292C2×C4×D4C2×D1111yescharacteristic
293C22×C4⋊C4—111no—
294#481—224no—
295C2×#106—112no—
296C2×#103—112no—
297C2×#103—112no—
298C2×#103—112no—
299C2×#103—112no—
300C2×#103—224no—
301C2×#102—112no—
302C2×#102—112no—
303C2×C22⋊C8—111no—
304C2×C22⋊C8—112no—
305#400—221no—
306#399—221no—
307#389—112no—
308#386—221no—
309#385—221no—
310#380—111no—
311#380—112no—
312#340—112no—
313#336—112no—
314C22×C11—22no—
315C22×C11—22no—
316C22×C11—24no—
317C22×C11—24no—
318C22×C11—42no—
319C22×C11—41no—
320C22×C11—41no—
321C22×C11—42no—
322C22×C11—41no—
323C22×C11—42no—
324C22×C11—42no—
325C22×C11—42no—
326C22×C11—82no—
327C22×C11—82no—
328C22×C11#45214yes—
329C22×C11C2×#12011yescharacteristic
330C22×C11#54612yes—
331C22×C11C2×#13511yescharacteristic
332C22×C11C2×#13711yescharacteristic
333C22×C11#57712yes—
334C4×C11—22no—
335C4×C11—24no—
336C4×C11—41no—
337C4×C11—42no—
338C4×C11—41no—
339C4×C11—42no—
340C4×C11—41no—
341C4×C11C2×#12311yescharacteristic
342C4×C11#53411yescharacteristic
343C4×C11#54612yes—
344Dic11—82no—
345Dic11—82no—
346C2×#41—22no—
347C2×#41—22no—
348C2×#41—24no—
349C2×#41—42no—
350C22×Q8—21no—
351C22×Q8—22no—
352C22×Q8—24no—
353C22×Q8—42no—
354C22×Q8C22⋊D1114yes—
355C22×Q8C22×D1111yescharacteristic
356C22×Q8C22×D1111yescharacteristic
357C22×D4—21no—
358C22×D4—21no—
359C22×D4C22⋊D1111yescharacteristic
360C22×D4C22×D1111yescharacteristic
361C23×C4—21no—
362C23×C4—21no—
363C23×C4—221no—
364C23×C4C22×D1111yescharacteristic
365C23×C4C22×D1111yescharacteristic
366C22×C8—112no—
367C22×C8—112no—
368C22×C8—222no—
369C22×C8—442no—
370#124—28no—
371#124—22no—
372#124—22no—
373C22⋊Q8—28no—
374C22⋊Q8—22no—
375C22⋊Q8—22no—
376#121—28no—
377#121—22no—
378#121C22⋊D1114yes—
379C4×Q8—22no—
380C4×Q8—22no—
381C4×D4—28no—
382C4×D4—22no—
383C4×D4—22no—
384C2×C4⋊C4—21no—
385C2×C4⋊C4—21no—
386C2×C4⋊C4—112no—
387C2×C4⋊C4—112no—
388C2×C4⋊C4—222no—
389C2×C4⋊C4—222no—
390C2×C4⋊C4—221no—
391C2×C4⋊C4—222no—
392C2×C4⋊C4C22⋊D1111yescharacteristic
393C2×C4⋊C4C22×D1111yescharacteristic
394C2×C22⋊C4—21no—
395C2×C22⋊C4—21no—
396C2×C22⋊C4—21no—
397C2×C22⋊C4—21no—
398C2×C22⋊C4—221no—
399C2×C22⋊C4—222no—
400C2×C22⋊C4C22⋊D1111yescharacteristic
401C2×C22⋊C4C22⋊D1111yescharacteristic
402C2×C42—21no—
403C2×C42C22×D1111yescharacteristic
404#106—224no—
405#103—224no—
406#103—224no—
407#103—224no—
408#103—442no—
409#102—224no—
410#102—442no—
411C22⋊C8—222no—
412C22⋊C8—442no—
413#95—222no—
414#95—221no—
415#95—222no—
416C2×C11—24no—
417C2×C11—81no—
418C2×C11—82no—
419C2×C11#240511yescharacteristic
420C2×C11C2×#45211yescharacteristic
421C2×C11#301011yescharacteristic
422C2×C11#330112yes—
423C2×C11#331612yes—
424C24—21no—
425C24C2×C22⋊D1111yescharacteristic
426C24C2×C22⋊D1111yescharacteristic
427#41—48no—
428#41—44no—
429#41—44no—
430C2×Q8—24no—
431C2×Q8—22no—
432C2×Q8—21no—
433C2×Q8—21no—
434C2×Q8—28no—
435C2×Q8—22no—
436C2×Q8—22no—
437C2×Q8—44no—
438C2×Q8—44no—
439C2×Q8—48no—
440C2×Q8#434114yes—
441C2×Q8C2×C22⋊D1112yes—
442C2×Q8C2×C22⋊D1112yes—
443C2×D4—24no—
444C2×D4—22no—
445C2×D4—22no—
446C2×D4—22no—
447C2×D4—24no—
448C2×D4—22no—
449C2×D4—22no—
450C2×D4—21no—
451C2×D4—44no—
452C2×D4—42no—
453C2×D4—42no—
454C2×D4C2×C22⋊D1112yes—
455C22×C4—21no—
456C22×C4—22no—
457C22×C4—22no—
458C22×C4—24no—
459C22×C4—24no—
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—22no—
463C22×C4—22no—
464C22×C4—21no—
465C22×C4—21no—
466C22×C4—44no—
467C22×C4—44no—
468C22×C4—222no—
469C22×C4—222no—
470C22×C4—442no—
471C22×C4—882no—
472C22×C4C2×C22⋊D1111yescharacteristic
473C22×C4C2×C22⋊D1111yescharacteristic
474C22×C4C2×C22⋊D1111yescharacteristic
475C22×C4C2×C22⋊D1111yescharacteristic
476C22×C4C2×C22⋊D1112yes—
477C22×C4C2×C22⋊D1112yes—
478C22×C4C23×D1111yescharacteristic
479C2×C8—222no—
480C2×C8—222no—
481C2×C8—222no—
482C2×C8—222no—
483C2×C8—222no—
484C2×C8—222no—
485C2×C8—444no—
486C4⋊C4—24no—
487C4⋊C4—24no—
488C4⋊C4—22no—
489C4⋊C4—21no—
490C4⋊C4—222no—
491C4⋊C4—222no—
492C4⋊C4—222no—
493C4⋊C4—222no—
494C4⋊C4—442no—
495C4⋊C4—882no—
496C4⋊C4C2×C22⋊D1112yes—
497C22⋊C4—24no—
498C22⋊C4—24no—
499C22⋊C4—24no—
500C22⋊C4—22no—
501C22⋊C4—24no—
502C22⋊C4—22no—
503C22⋊C4—442no—
504C22⋊C4—882no—
505C42—24no—
506C42—21no—
507C42—21no—
508C11#2403611yescharacteristic, complemented, Sylow
509C23—22no—
510C23—22no—
511C23—22no—
512C23—21no—
513C23—21no—
514C23—22no—
515C23—21no—
516C23—22no—
517C23—42no—
518C23—41no—
519C23—41no—
520C23—42no—
521C23#6700312yes—
522C23#6700412yes—
523C23#6700612yes—
524C23C22×C22⋊D1111yescharacteristic
525Q8—22no—
526Q8—24no—
527Q8—22no—
528Q8—22no—
529Q8—48no—
530Q8—42no—
531Q8#6698814yes—
532D4—24no—
533D4—48no—
534D4—44no—
535D4—48no—
536D4—41no—
537D4—41no—
538C2×C4—22no—
539C2×C4—24no—
540C2×C4—22no—
541C2×C4—22no—
542C2×C4—22no—
543C2×C4—24no—
544C2×C4—22no—
545C2×C4—21no—
546C2×C4—21no—
547C2×C4—22no—
548C2×C4—21no—
549C2×C4—21no—
550C2×C4—22no—
551C2×C4—22no—
552C2×C4—21no—
553C2×C4—48no—
554C2×C4—48no—
555C2×C4—42no—
556C2×C4—41no—
557C2×C4—41no—
558C2×C4—41no—
559C2×C4—41no—
560C2×C4—42no—
561C2×C4—442no—
562C2×C4—442no—
563C2×C4—442no—
564C2×C4—442no—
565C2×C4—442no—
566C2×C4—442no—
567C2×C4—884no—
568C2×C4#6700612yes—
569C2×C4C2×#434112yes—
570C2×C4#6703712yes—
571C2×C4C22×C22⋊D1111yescharacteristic
572C2×C4C22×C22⋊D1111yescharacteristic
573C8—442no—
574C8—442no—
575C22—22no—
576C22—22no—
577C22—24no—
578C22—24no—
579C22—41no—
580C22—42no—
581C22—42no—
582C22—41no—
583C22—41no—
584C22—42no—
585C22—42no—
586C22—42no—
587C22—82no—
588C22—82no—
589C22#1062285214yes—
590C22#1062333712yes—
591C22C2×#6700311yescharacteristic
592C22C2×#6700411yescharacteristic
593C22#1062336812yes—
594C22C2×#6700611yescharacteristic
595C4—22no—
596C4—24no—
597C4—41no—
598C4—42no—
599C4—41no—
600C4—42no—
601C4—41no—
602C4—882no—
603C4—882no—
604C4C2×#6698811yescharacteristic
605C4#1062333511yescharacteristic
606C4#1062333712yes—
607C2—24no—
608C2—81no—
609C2—82no—
610C2#1307193911yescharacteristic
611C2C2×#1062285211yescharacteristic
612C2#1307790211yescharacteristic
613C2#1308051812yes—
614C2#1308072712yes—
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
Fitting, prime radicalC2×C11×#548C2
socleC23×C11C22×D4
hypercenterC2×#548D11
hypocenterC11#24036
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#548

Complements

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

NH ≅ G/Ntype
1. C2×#10622647C2semidirect
2. C22×#66899C2semidirect
3. #13072933C2semidirect
4. #13069852C2semidirect
5. #13069809C2semidirect
6. #13069045C2semidirect
7. #13068909C2semidirect
8. #13068884C2semidirect
9. #13068556C2semidirect
10. #13068551C2semidirect
508. C11#24036semidirect

Maximal subgroups

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

subgroupindex
C2×#106226472
C22×#668992
#130729332
#130698522
#130698092
#130690452
#130689092
#130688842
#130685562
#130685512
C2×C11×#5482
#2403611