Finite Group Databasebeta

← #14788853

Subgroups — #14788853

Order 2816.

1482 conjugacy classes of subgroups.

The subgroup lattice has 660 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623008C211yesmaximal, characteristic
2C2×#10622644C211yesmaximal, characteristic, complemented
3C2×#10622640C211yesmaximal, characteristic, complemented
4C2×#10622660C212yesmaximal, complemented
5#13069857C212yesmaximal, complemented
6#13069709C212yesmaximal, complemented
7#13069543C211yesmaximal, characteristic, complemented
8#13069539C211yesmaximal, characteristic, complemented
9#13068596C211yesmaximal, characteristic, complemented
10#13068554C212yesmaximal, complemented
11C4×C11×C22⋊Q8C211yesmaximal, characteristic, complemented
12C22×#4339C2212yes—
13C2×C11×C22⋊Q8C2211yescharacteristic
14C2×C4×Q8×C11C2211yescharacteristic
15C22×C42×C11C2211yescharacteristic
16C22×#4326C2212yes—
17C22×#4325C2212yes—
18C2×#66983—21no—
19C2×#66983—21no—
20#10623008—24no—
21#10623008—24no—
22C2×#66928C2212yes—
23C2×#66927C2211yescharacteristic
24C2×C4×D44—21no—
25C2×C4×D44—21no—
26C2×#66922C2211yescharacteristic
27C11×#391C2211yescharacteristic
28C11×#389C2211yescharacteristic
29C11×#387—21no—
30C11×#385—21no—
31C11×#380C2211yescharacteristic
32C4×C11×C4⋊C4—21no—
33C4×C11×C4⋊C4C2211yescharacteristic
34C4×C11×C22⋊C4—21no—
35C2×C22⋊(C11⋊C8)C2212yes—
36#10622660—28no—
37#10622644—24no—
38#10622640—24no—
39C2×#66874C2212yes—
40C2×#66874C2212yes—
41C2×#66874C2212yes—
42C2×#66873C2212yes—
43C2×#66873C2212yes—
44C2×#66873C2212yes—
45C2×C4⋊(C11⋊C8)C2211yescharacteristic
46C2×C4⋊(C11⋊C8)C2211yescharacteristic
47#10622162C2212yes—
48C22×Q8×C11C2311yescharacteristic
49C23×C4×C11D411yescharacteristic
50C23×C4×C11D411yescharacteristic
51C23×C4×C11C2311yescharacteristic
52C22×C22⋊D11—22no—
53C2×#4339—24no—
54C2×#4339—24no—
55C2×#4339—24no—
56C2×#4339—24no—
57C2×#4339—42no—
58C2×#4339—42no—
59C22×D44—21no—
60C22×D44—21no—
61C22×D44C2312yes—
62C22×C4×D11—22no—
63C22×Dic22C2312yes—
64C11×C22⋊Q8—22no—
65C11×C22⋊Q8D414yescomplemented
66C4×Q8×C11—22no—
67C4×Q8×C11—22no—
68C2×C11×C4⋊C4—21no—
69C2×C11×C4⋊C4—21no—
70C2×C11×C4⋊C4—21no—
71C2×C11×C4⋊C4C2311yescharacteristic
72C2×C11×C4⋊C4C2311yescharacteristic
73C2×C11×C4⋊C4C2311yescharacteristic
74C2×C11×C22⋊C4—21no—
75C2×C11×C22⋊C4—21no—
76C2×C42×C11—22no—
77C2×C42×C11—22no—
78C2×C42×C11—21no—
79C2×C42×C11—21no—
80C2×C42×C11D411yescharacteristic
81C2×C42×C11D411yescharacteristic
82C2×C42×C11C2311yescharacteristic
83C2×C42×C11C2311yescharacteristic
84C2×#4326—24no—
85C2×#4326—24no—
86C2×#4326—42no—
87C2×#4325—24no—
88C2×#4325—24no—
89C2×#4325—42no—
90#66983—28no—
91#66983—28no—
92C2×(C2×D11)⋊C4—22no—
93C2×(C2×D11)⋊C4—22no—
94C2×C4⋊Dic11—21no—
95C2×C4⋊Dic11—21no—
96C22×C11⋊C8C2312yes—
97C22×C11⋊C8C2312yes—
98#66928—24no—
99#66928—24no—
100#66927—22no—
101#66927D414yes—
102C4×D44—28no—
103C4×D44—28no—
104#66922—22no—
105#66922D414yes—
106C11×#95—21no—
107C11×#95—21no—
108C11×#95—21no—
109C11×#95—21no—
110C11×#95—21no—
111C22⋊(C11⋊C8)—24no—
112#66874—24no—
113#66874—24no—
114#66874—42no—
115#66873—24no—
116#66873—24no—
117#66873—42no—
118C4⋊(C11⋊C8)—22no—
119C4⋊(C11⋊C8)—22no—
120#24213—111nomaximal, Sylow
121C24×C11C2×D411yescharacteristic
122C23×D11—22no—
123C2×Q8×C11—21no—
124C2×Q8×C11—21no—
125C2×Q8×C11—21no—
126C2×Q8×C11—21no—
127C2×Q8×C11—21no—
128C2×Q8×C11C2×D412yes—
129C22×C4×C11—21no—
130C22×C4×C11—21no—
131C22×C4×C11—21no—
132C22×C4×C11—21no—
133C22×C4×C11—21no—
134C22×C4×C11—21no—
135C22×C4×C11—22no—
136C22×C4×C11—22no—
137C22×C4×C11—22no—
138C22×C4×C11—22no—
139C22×C4×C11—21no—
140C22×C4×C11—21no—
141C22×C4×C11—41no—
142C22×C4×C11—41no—
143C22×C4×C11C2×D411yescharacteristic
144C22×C4×C11C2×D411yescharacteristic
145C22×C4×C11C2×D411yescharacteristic
146C22×C4×C11C2×D411yescharacteristic
147C22×C4×C11C2×D412yes—
148C22×C4×C11C2×D411yescharacteristic
149C22×C4×C11#4112yes—
150C22×C4×C11C2411yescharacteristic
151C2×C22⋊D11—28no—
152C2×C22⋊D11—44no—
153C2×C22⋊D11—44no—
154C22×Dic11—22no—
155#4339—48no—
156#4339—48no—
157#4339—48no—
158#4339—48no—
159C2×D44—24no—
160C2×D44—24no—
161C2×D44—22no—
162C2×D44—22no—
163C2×D44—22no—
164C2×D44—22no—
165C2×D44—22no—
166C2×D44—42no—
167C2×D44—42no—
168C2×D44—42no—
169C2×D44—42no—
170C2×D44C2×D414yes—
171C2×C4×D11—28no—
172C2×C4×D11—44no—
173C2×C4×D11—44no—
174C2×Dic22—22no—
175C2×Dic22—22no—
176C2×Dic22—22no—
177C2×Dic22—22no—
178C2×Dic22—22no—
179C2×Dic22C2×D414yes—
180C11×C4⋊C4—24no—
181C11×C4⋊C4—21no—
182C11×C4⋊C4—21no—
183C11×C4⋊C4—21no—
184C11×C4⋊C4—21no—
185C11×C4⋊C4—21no—
186C11×C4⋊C4—42no—
187C11×C4⋊C4—42no—
188C11×C4⋊C4C2×D412yes—
189C11×C22⋊C4—24no—
190C11×C22⋊C4—42no—
191C42×C11—22no—
192C42×C11—22no—
193C42×C11—21no—
194C42×C11—21no—
195C42×C11—42no—
196C42×C11—42no—
197C42×C11C2×D412yes—
198C42×C11C2×D412yes—
199#4326—48no—
200#4325—48no—
201(C2×D11)⋊C4—28no—
202(C2×D11)⋊C4—28no—
203C4⋊Dic11—24no—
204C4⋊Dic11—24no—
205C2×C11⋊C8—22no—
206C2×C11⋊C8—22no—
207C2×C11⋊C8—22no—
208C2×C11⋊C8—22no—
209C2×C11⋊C8—22no—
210C2×C11⋊C8—22no—
211C2×#532—111no—
212C2×#462—111no—
213C2×#460—111no—
214C2×#452—112no—
215C4×C22⋊Q8D1111yescharacteristic, complemented
216#2042—112no—
217#2015—112no—
218#1982—111no—
219#1981—111no—
220#1797—111no—
221#1788—112no—
222C23×C11—21no—
223C23×C11—21no—
224C23×C11—21no—
225C23×C11—21no—
226C23×C11—21no—
227C23×C11—21no—
228C23×C11#12112yes—
229C23×C11C22×D411yescharacteristic
230C22×D11—24no—
231C22×D11—42no—
232C22×D11—42no—
233C22×D11—42no—
234C22×D11—42no—
235C22×D11—42no—
236C22×D11—42no—
237Q8×C11—22no—
238Q8×C11—22no—
239Q8×C11—41no—
240Q8×C11—41no—
241C2×C4×C11—21no—
242C2×C4×C11—21no—
243C2×C4×C11—21no—
244C2×C4×C11—21no—
245C2×C4×C11—22no—
246C2×C4×C11—22no—
247C2×C4×C11—22no—
248C2×C4×C11—22no—
249C2×C4×C11—21no—
250C2×C4×C11—21no—
251C2×C4×C11—22no—
252C2×C4×C11—22no—
253C2×C4×C11—21no—
254C2×C4×C11—21no—
255C2×C4×C11—21no—
256C2×C4×C11—21no—
257C2×C4×C11—44no—
258C2×C4×C11—41no—
259C2×C4×C11—41no—
260C2×C4×C11—41no—
261C2×C4×C11—41no—
262C2×C4×C11—44no—
263C2×C4×C11—41no—
264C2×C4×C11—41no—
265C2×C4×C11—41no—
266C2×C4×C11—41no—
267C2×C4×C11—41no—
268C2×C4×C11—41no—
269C2×C4×C11#12012yes—
270C2×C4×C11#12012yes—
271C2×C4×C11#12112yes—
272C2×C4×C11#13512yes—
273C2×C4×C11#13712yes—
274C2×C4×C11C22×D411yescharacteristic
275C2×C4×C11C22×D411yescharacteristic
276C2×C4×C11C22×D411yescharacteristic
277C2×C4×C11C2×#4111yescharacteristic
278C2×C4×C11H(5,𝔽2)11yescharacteristic
279C2×C4×C11H(5,𝔽2)11yescharacteristic
280C22⋊D11—416no—
281C2×Dic11—24no—
282C2×Dic11—42no—
283C2×Dic11—42no—
284D44—24no—
285D44—24no—
286D44—48no—
287D44—42no—
288D44—42no—
289D44—48no—
290C4×D11—416no—
291Dic22—24no—
292Dic22—24no—
293Dic22—42no—
294Dic22—42no—
295C11⋊C8—42no—
296C11⋊C8—42no—
297C22×#41—112no—
298C22×Q16—112no—
299C22×SD16—112no—
300#532—224no—
301#532—224no—
302C2×C4⋊Q8—111no—
303C2×#127—111no—
304C2×#124—112no—
305C2×C22⋊Q8C2×D1111yescharacteristic
306C2×#121—221no—
307C2×#121—221no—
308C2×C4×Q8C2×D1111yescharacteristic
309C2×C4×D4—221no—
310C2×C4×D4—221no—
311C22×C42C2×D1111yescharacteristic
312#462—224no—
313#460—224no—
314#452—228no—
315C2×C4⋊C8—111no—
316C2×C4⋊C8—111no—
317C2×#103—112no—
318C2×#103—112no—
319C2×#103—112no—
320C2×#102—112no—
321C2×#102—112no—
322C2×#102—112no—
323C2×C22⋊C8—112no—
324#391C2×D1111yescharacteristic
325#389C2×D1111yescharacteristic
326#387—21no—
327#385—21no—
328#380C2×D1111yescharacteristic
329C4×C4⋊C4—21no—
330C4×C4⋊C4C2×D1111yescharacteristic
331C4×C22⋊C4—21no—
332#336—112no—
333C22×C11—22no—
334C22×C11—22no—
335C22×C11—22no—
336C22×C11—41no—
337C22×C11—41no—
338C22×C11—41no—
339C22×C11—41no—
340C22×C11C2×#12011yescharacteristic
341C22×C11C2×#12111yescharacteristic
342C22×C11#53511yescharacteristic
343C22×C11C2×#13511yescharacteristic
344C22×C11C2×#13711yescharacteristic
345C22×C11#57511yescharacteristic
346C22×C11#57511yescharacteristic
347C2×D11—44no—
348C2×D11—44no—
349C2×D11—44no—
350C2×D11—82no—
351C2×D11—82no—
352C2×D11—82no—
353C2×D11—82no—
354C4×C11—22no—
355C4×C11—22no—
356C4×C11—42no—
357C4×C11—41no—
358C4×C11—41no—
359C4×C11—42no—
360C4×C11—81no—
361C4×C11—81no—
362C4×C11#45214yescomplemented
363C4×C11D4211yescharacteristic
364C4×C11D4211yescharacteristic
365C4×C11#54611yescharacteristic
366C4×C11#54611yescharacteristic
367Dic11—44no—
368C2×#41—224no—
369C2×#41—224no—
370C2×#41—224no—
371C2×#41—224no—
372C2×#41—442no—
373C2×#41—442no—
374C22×Q8—112no—
375C22×Q8C22×D1111yescharacteristic
376C22×D4—112no—
377C22×D4—222no—
378C22×D4—221no—
379C22×D4—221no—
380C23×C4—222no—
381C23×C4C22⋊D1111yescharacteristic
382C23×C4C22⋊D1111yescharacteristic
383C23×C4C22×D1111yescharacteristic
384C2×Q16—224no—
385C2×Q16—224no—
386C2×Q16—442no—
387C2×SD16—224no—
388C2×SD16—224no—
389C2×SD16—442no—
390C22×C8—112no—
391C22×C8—112no—
392C4⋊Q8—114no—
393C4⋊Q8—222no—
394#127—114no—
395#127—222no—
396#124—224no—
397#124—224no—
398C22⋊Q8—22no—
399C22⋊Q8D4414yescomplemented
400#121—228no—
401#121—228no—
402C4×Q8—22no—
403C4×Q8—22no—
404C4×D4—228no—
405C4×D4—228no—
406C2×C4⋊C4—21no—
407C2×C4⋊C4—21no—
408C2×C4⋊C4—21no—
409C2×C4⋊C4—221no—
410C2×C4⋊C4—221no—
411C2×C4⋊C4C22×D1111yescharacteristic
412C2×C4⋊C4C22×D1111yescharacteristic
413C2×C4⋊C4C22×D1111yescharacteristic
414C2×C22⋊C4—21no—
415C2×C22⋊C4—21no—
416C2×C22⋊C4—222no—
417C2×C22⋊C4—222no—
418C2×C42—22no—
419C2×C42—22no—
420C2×C42—21no—
421C2×C42—21no—
422C2×C42C22⋊D1111yescharacteristic
423C2×C42C22⋊D1111yescharacteristic
424C2×C42C22×D1111yescharacteristic
425C2×C42C22×D1111yescharacteristic
426C4⋊C8—222no—
427C4⋊C8—222no—
428#103—224no—
429#103—224no—
430#103—442no—
431#102—224no—
432#102—224no—
433#102—442no—
434C22⋊C8—224no—
435#95—21no—
436#95—21no—
437#95—21no—
438#95—21no—
439#95—21no—
440C2×C11—42no—
441C2×C11#240811yescharacteristic
442C2×C11C2×#45211yescharacteristic
443C2×C11#300511yescharacteristic
444C2×C11#303511yescharacteristic
445C2×C11#303711yescharacteristic
446C2×C11#321211yescharacteristic
447C2×C11#321611yescharacteristic
448D11—84no—
449C24—222no—
450C24C2×C22⋊D1111yescharacteristic
451#41—448no—
452#41—448no—
453#41—448no—
454#41—448no—
455C2×Q8—21no—
456C2×Q8—21no—
457C2×Q8—21no—
458C2×Q8—21no—
459C2×Q8—21no—
460C2×Q8—114no—
461C2×Q8—222no—
462C2×Q8—222no—
463C2×Q8—222no—
464C2×Q8—222no—
465C2×Q8—222no—
466C2×Q8C2×D4412yes—
467C2×D4—114no—
468C2×D4—228no—
469C2×D4—224no—
470C2×D4—224no—
471C2×D4—222no—
472C2×D4—222no—
473C2×D4—222no—
474C2×D4—222no—
475C2×D4—222no—
476C2×D4—442no—
477C2×D4—442no—
478C2×D4—444no—
479C2×D4—444no—
480C2×D4—442no—
481C2×D4—442no—
482C22×C4—21no—
483C22×C4—21no—
484C22×C4—21no—
485C22×C4—21no—
486C22×C4—21no—
487C22×C4—21no—
488C22×C4—22no—
489C22×C4—22no—
490C22×C4—22no—
491C22×C4—22no—
492C22×C4—21no—
493C22×C4—21no—
494C22×C4—41no—
495C22×C4—41no—
496C22×C4—228no—
497C22×C4—222no—
498C22×C4—444no—
499C22×C4—444no—
500C22×C4C2×D4412yes—
501C22×C4#433912yes—
502C22×C4C2×C22⋊D1111yescharacteristic
503C22×C4C2×C22⋊D1111yescharacteristic
504C22×C4C2×C22⋊D1111yescharacteristic
505C22×C4C2×C22⋊D1111yescharacteristic
506C22×C4C2×C22⋊D1111yescharacteristic
507C22×C4C23×D1111yescharacteristic
508Q16—448no—
509SD16—448no—
510C2×C8—222no—
511C2×C8—222no—
512C2×C8—222no—
513C2×C8—222no—
514C2×C8—222no—
515C2×C8—222no—
516C4⋊C4—24no—
517C4⋊C4—21no—
518C4⋊C4—21no—
519C4⋊C4—21no—
520C4⋊C4—21no—
521C4⋊C4—21no—
522C4⋊C4—42no—
523C4⋊C4—42no—
524C4⋊C4—224no—
525C4⋊C4—224no—
526C4⋊C4C2×D4412yes—
527C22⋊C4—24no—
528C22⋊C4—42no—
529C22⋊C4—228no—
530C22⋊C4—228no—
531C42—22no—
532C42—22no—
533C42—21no—
534C42—21no—
535C42—42no—
536C42—42no—
537C42D4×D1112yes—
538C42D4×D1112yes—
539C11#2421311yescharacteristic, complemented, Sylow
540C23—21no—
541C23—21no—
542C23—21no—
543C23—21no—
544C23—21no—
545C23—21no—
546C23—224no—
547C23—442no—
548C23—442no—
549C23—442no—
550C23—442no—
551C23—442no—
552C23—442no—
553C23#6698312yes—
554C23C22×C22⋊D1111yescharacteristic
555Q8—22no—
556Q8—22no—
557Q8—41no—
558Q8—41no—
559Q8—224no—
560Q8—224no—
561Q8—442no—
562Q8—442no—
563D4—224no—
564D4—224no—
565D4—448no—
566D4—4416no—
567D4—442no—
568D4—442no—
569D4—448no—
570C2×C4—21no—
571C2×C4—21no—
572C2×C4—21no—
573C2×C4—21no—
574C2×C4—22no—
575C2×C4—22no—
576C2×C4—22no—
577C2×C4—22no—
578C2×C4—22no—
579C2×C4—22no—
580C2×C4—21no—
581C2×C4—21no—
582C2×C4—21no—
583C2×C4—21no—
584C2×C4—21no—
585C2×C4—21no—
586C2×C4—44no—
587C2×C4—41no—
588C2×C4—41no—
589C2×C4—41no—
590C2×C4—41no—
591C2×C4—44no—
592C2×C4—41no—
593C2×C4—41no—
594C2×C4—41no—
595C2×C4—41no—
596C2×C4—41no—
597C2×C4—41no—
598C2×C4—224no—
599C2×C4—4416no—
600C2×C4—442no—
601C2×C4—442no—
602C2×C4#6698312yes—
603C2×C4#6699012yes—
604C2×C4#6699012yes—
605C2×C4#6699512yes—
606C2×C4#6700312yes—
607C2×C4C22×D4411yescharacteristic
608C2×C4C2×#433911yescharacteristic
609C2×C4C2×D4×D1111yescharacteristic
610C2×C4C2×D4×D1111yescharacteristic
611C2×C4#6704211yescharacteristic
612C2×C4#6704211yescharacteristic
613C8—442no—
614C8—442no—
615C22—22no—
616C22—22no—
617C22—22no—
618C22—41no—
619C22—41no—
620C22—41no—
621C22—41no—
622C22—444no—
623C22—444no—
624C22—444no—
625C22—882no—
626C22—882no—
627C22—882no—
628C22—882no—
629C22C2×#6698311yescharacteristic
630C22C2×#6699011yescharacteristic
631C22C2×#6699511yescharacteristic
632C22C2×#6700311yescharacteristic
633C22#1062335311yescharacteristic
634C22#1062335311yescharacteristic
635C22#1062336111yescharacteristic
636C4—22no—
637C4—22no—
638C4—42no—
639C4—41no—
640C4—41no—
641C4—42no—
642C4—81no—
643C4—81no—
644C4—444no—
645C4#1062266014yescomplemented
646C4D4×D4411yescharacteristic
647C4D4×D4411yescharacteristic
648C4#1062308111yescharacteristic
649C4#1062308111yescharacteristic
650C2—42no—
651C2—884no—
652C2#1307197211yescharacteristic
653C2C2×#1062266011yescharacteristic
654C2#1307785611yescharacteristic
655C2#1307807111yescharacteristic
656C2#1307808811yescharacteristic
657C2#1307958811yescharacteristic
658C2#1307962311yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC4×C11×C22⋊Q8C2
socleC23×C11C22×D4
prime radicalC2×#10623008C2
hypercenterC4×C22⋊Q8D11
hypocenterC11#24213
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×C42 ◁ C4×C22⋊Q8

Complements

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

NH ≅ G/Ntype
2. C2×#10622644C2semidirect
3. C2×#10622640C2semidirect
4. C2×#10622660C2semidirect
5. #13069857C2semidirect
6. #13069709C2semidirect
7. #13069543C2semidirect
8. #13069539C2semidirect
9. #13068596C2semidirect
10. #13068554C2semidirect
11. C4×C11×C22⋊Q8C2semidirect
65. C11×C22⋊Q8D4semidirect
215. C4×C22⋊Q8D11semidirect
362. C4×C11#452semidirect
399. C22⋊Q8D44semidirect
539. C11#24213semidirect
645. C4#10622660semidirect

Maximal subgroups

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

subgroupindex
C2×#106230082
C2×#106226442
C2×#106226402
C2×#106226602
#130698572
#130697092
#130695432
#130695392
#130685962
#130685542
C4×C11×C22⋊Q82
#2421311