Finite Group Databasebeta

← #14788124

Subgroups — #14788124

Order 2816.

1394 conjugacy classes of subgroups.

The subgroup lattice has 628 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623008C211yesmaximal, characteristic
2C2×#10622633C211yesmaximal, characteristic, complemented
3C2×#10622640C211yesmaximal, characteristic, complemented
4#13069805C212yesmaximal, complemented
5#13069617C212yesmaximal, complemented
6#13069568C211yesmaximal, characteristic, complemented
7#13069543C211yesmaximal, characteristic, complemented
8#13068953C212yesmaximal, complemented
9#13068876C212yesmaximal, complemented
10#13068596C211yesmaximal, characteristic, complemented
11C4×C11×C22⋊Q8C211yesmaximal, characteristic, complemented
12C22×#4339—21no—
13C2×C11×C22⋊Q8C2211yescharacteristic
14C2×C4×Q8×C11C2211yescharacteristic
15C22×C42×C11C2211yescharacteristic
16C22×#4325C2212yes—
17C2×#66983—21no—
18C2×#66983C2212yes—
19#10623008—24no—
20#10623008—24no—
21C2×#66928—21no—
22C2×#66927C2211yescharacteristic
23C2×C4×D44—21no—
24C2×C4×D44C2212yes—
25C2×#66922C2211yescharacteristic
26C11×#391C2211yescharacteristic
27C11×#389C2211yescharacteristic
28C11×#387—21no—
29C11×#385—21no—
30C11×#380C2211yescharacteristic
31C4×C11×C4⋊C4—21no—
32C4×C11×C4⋊C4C2211yescharacteristic
33C4×C11×C22⋊C4—21no—
34C2×#66899C2212yes—
35C2×C22⋊(C11⋊C8)C2212yes—
36#10622640—24no—
37#10622633—24no—
38C2×#66873C2212yes—
39C2×#66873C2212yes—
40C2×#66873C2212yes—
41C2×#66872C2212yes—
42C2×C4⋊(C11⋊C8)C2211yescharacteristic
43C2×C4⋊(C11⋊C8)C2211yescharacteristic
44#10622167C2212yes—
45#10622167C2212yes—
46#10622162C2212yes—
47C22×Q8×C11C2311yescharacteristic
48C23×C4×C11D411yescharacteristic
49C23×C4×C11D411yescharacteristic
50C23×C4×C11C2311yescharacteristic
51C22×C22⋊D11—22no—
52C2×#4339—28no—
53C2×#4339—44no—
54C2×#4339—44no—
55C22×D44—21no—
56C22×D44—21no—
57C22×D44C2312yes—
58C22×C4×D11—22no—
59C22×Dic22—21no—
60C11×C22⋊Q8—22no—
61C11×C22⋊Q8—22no—
62C4×Q8×C11—22no—
63C4×Q8×C11—22no—
64C2×C11×C4⋊C4—21no—
65C2×C11×C4⋊C4—21no—
66C2×C11×C4⋊C4—21no—
67C2×C11×C4⋊C4C2311yescharacteristic
68C2×C11×C4⋊C4C2311yescharacteristic
69C2×C11×C4⋊C4C2311yescharacteristic
70C2×C11×C22⋊C4—21no—
71C2×C11×C22⋊C4—21no—
72C2×C42×C11—22no—
73C2×C42×C11—22no—
74C2×C42×C11—21no—
75C2×C42×C11—21no—
76C2×C42×C11D411yescharacteristic
77C2×C42×C11D411yescharacteristic
78C2×C42×C11C2311yescharacteristic
79C2×C42×C11C2311yescharacteristic
80C2×#4325—24no—
81C2×#4325—24no—
82C2×#4325—42no—
83#66983—28no—
84#66983—24no—
85#66983—24no—
86C2×(C2×D11)⋊C4—22no—
87C2×(C2×D11)⋊C4—22no—
88C2×C4⋊Dic11—21no—
89C2×C4⋊Dic11C2312yes—
90C22×C11⋊C8C2312yes—
91C22×C11⋊C8C2312yes—
92#66928—28no—
93#66927—22no—
94#66927D414yes—
95C4×D44—28no—
96C4×D44—24no—
97C4×D44—24no—
98#66922—22no—
99#66922D414yes—
100C11×#95—21no—
101C11×#95—21no—
102C11×#95—21no—
103C11×#95—21no—
104C11×#95—21no—
105#66899—24no—
106C22⋊(C11⋊C8)—42no—
107#66873—24no—
108#66873—24no—
109#66873—42no—
110#66872—24no—
111C4⋊(C11⋊C8)—22no—
112C4⋊(C11⋊C8)—22no—
113#24154—111nomaximal, Sylow
114C24×C11C2×D411yescharacteristic
115C23×D11—22no—
116C2×Q8×C11—21no—
117C2×Q8×C11—21no—
118C2×Q8×C11—21no—
119C2×Q8×C11—21no—
120C2×Q8×C11—21no—
121C2×Q8×C11#4112yescomplemented
122C22×C4×C11—22no—
123C22×C4×C11—22no—
124C22×C4×C11—21no—
125C22×C4×C11—21no—
126C22×C4×C11—22no—
127C22×C4×C11—21no—
128C22×C4×C11—21no—
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—41no—
136C22×C4×C11—41no—
137C22×C4×C11SD1614yescomplemented
138C22×C4×C11C2×D411yescharacteristic
139C22×C4×C11C2×D411yescharacteristic
140C22×C4×C11C2×D411yescharacteristic
141C22×C4×C11C2×D411yescharacteristic
142C22×C4×C11C2×D411yescharacteristic
143C22×C4×C11C2411yescharacteristic
144C2×C22⋊D11—28no—
145C2×C22⋊D11—44no—
146C2×C22⋊D11—44no—
147C22×Dic11—22no—
148#4339—432no—
149C2×D44—24no—
150C2×D44—24no—
151C2×D44—22no—
152C2×D44—22no—
153C2×D44—22no—
154C2×D44—22no—
155C2×D44—22no—
156C2×D44—42no—
157C2×D44—42no—
158C2×D44—42no—
159C2×D44—42no—
160C2×D44C2×D414yes—
161C2×C4×D11—28no—
162C2×C4×D11—44no—
163C2×C4×D11—44no—
164C2×Dic22—24no—
165C2×Dic22—42no—
166C2×Dic22—42no—
167C11×C4⋊C4—24no—
168C11×C4⋊C4—21no—
169C11×C4⋊C4—21no—
170C11×C4⋊C4—21no—
171C11×C4⋊C4—21no—
172C11×C4⋊C4—21no—
173C11×C4⋊C4—42no—
174C11×C4⋊C4—42no—
175C11×C4⋊C4#4112yescomplemented
176C11×C22⋊C4—24no—
177C11×C22⋊C4—42no—
178C42×C11—22no—
179C42×C11—22no—
180C42×C11—21no—
181C42×C11—21no—
182C42×C11—42no—
183C42×C11—42no—
184C42×C11C2×D412yes—
185C42×C11C2×D412yes—
186#4325—48no—
187(C2×D11)⋊C4—28no—
188(C2×D11)⋊C4—28no—
189C4⋊Dic11—24no—
190C4⋊Dic11—22no—
191C4⋊Dic11C2×D414yes—
192C2×C11⋊C8—22no—
193C2×C11⋊C8—22no—
194C2×C11⋊C8—22no—
195C2×C11⋊C8—22no—
196C2×C11⋊C8—22no—
197C2×C11⋊C8—22no—
198C2×#532—111no—
199C2×#475—111no—
200C2×#460—111no—
201C4×C22⋊Q8D1111yescharacteristic, complemented
202#2034—112no—
203#2000—112no—
204#1988—111no—
205#1982—111no—
206#1877—112no—
207#1864—112no—
208#1797—111no—
209C23×C11—21no—
210C23×C11—21no—
211C23×C11—21no—
212C23×C11—21no—
213C23×C11—21no—
214C23×C11—21no—
215C23×C11C2×SD1612yes—
216C23×C11C22×D411yescharacteristic
217C22×D11—24no—
218C22×D11—42no—
219C22×D11—42no—
220C22×D11—42no—
221C22×D11—42no—
222C22×D11—42no—
223C22×D11—42no—
224Q8×C11—22no—
225Q8×C11—22no—
226Q8×C11—41no—
227Q8×C11—41no—
228C2×C4×C11—21no—
229C2×C4×C11—21no—
230C2×C4×C11—21no—
231C2×C4×C11—21no—
232C2×C4×C11—28no—
233C2×C4×C11—21no—
234C2×C4×C11—21no—
235C2×C4×C11—22no—
236C2×C4×C11—22no—
237C2×C4×C11—21no—
238C2×C4×C11—21no—
239C2×C4×C11—21no—
240C2×C4×C11—21no—
241C2×C4×C11—44no—
242C2×C4×C11—41no—
243C2×C4×C11—41no—
244C2×C4×C11—41no—
245C2×C4×C11—41no—
246C2×C4×C11—41no—
247C2×C4×C11—41no—
248C2×C4×C11—41no—
249C2×C4×C11—41no—
250C2×C4×C11—41no—
251C2×C4×C11—41no—
252C2×C4×C11—41no—
253C2×C4×C11—41no—
254C2×C4×C11—41no—
255C2×C4×C11—41no—
256C2×C4×C11#12012yes—
257C2×C4×C11#12012yes—
258C2×C4×C11C2×SD1612yes—
259C2×C4×C11C2×SD1612yes—
260C2×C4×C11AGL(1,ℤ/8)12yes—
261C2×C4×C11C22×D411yescharacteristic
262C2×C4×C11C22×D411yescharacteristic
263C2×C4×C11C2×#4111yescharacteristic
264C2×C4×C11C2×#4111yescharacteristic
265C2×C4×C11H(5,𝔽2)11yescharacteristic
266C2×C4×C112−1+411yescharacteristic
267C22⋊D11—416no—
268C2×Dic11—24no—
269C2×Dic11—42no—
270C2×Dic11—42no—
271D44—24no—
272D44—24no—
273D44—48no—
274D44—42no—
275D44—42no—
276D44—48no—
277C4×D11—416no—
278Dic22—48no—
279C11⋊C8—42no—
280C11⋊C8—42no—
281C22×#41—221no—
282C22×SD16—112no—
283#532—224no—
284#532—224no—
285C2×C4⋊Q8—111no—
286C2×#127—111no—
287C2×#124—221no—
288C2×C22⋊Q8C2×D1111yescharacteristic
289C2×#121—112no—
290C2×#121—221no—
291C2×C4×Q8C2×D1111yescharacteristic
292C2×C4×D4—112no—
293C2×C4×D4—221no—
294C22×C42C2×D1111yescharacteristic
295#475—224no—
296#460—224no—
297C2×#106—112no—
298C2×C4⋊C8—111no—
299C2×C4⋊C8—111no—
300C2×#103—112no—
301C2×#102—112no—
302C2×#102—112no—
303C2×#102—112no—
304C2×C22⋊C8—112no—
305#391C2×D1111yescharacteristic
306#389C2×D1111yescharacteristic
307#387—21no—
308#385—21no—
309#380C2×D1111yescharacteristic
310C4×C4⋊C4—21no—
311C4×C4⋊C4C2×D1111yescharacteristic
312C4×C22⋊C4—21no—
313#340—112no—
314#340—112no—
315#336—112no—
316C22×C11—22no—
317C22×C11—22no—
318C22×C11—22no—
319C22×C11—41no—
320C22×C11—41no—
321C22×C11—41no—
322C22×C11—41no—
323C22×C11C2×#12011yescharacteristic
324C22×C11#52511yescharacteristic
325C22×C11#53711yescharacteristic
326C22×C11C22×SD1611yescharacteristic
327C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
328C22×C11#57511yescharacteristic
329C22×C11#57511yescharacteristic
330C2×D11—44no—
331C2×D11—44no—
332C2×D11—44no—
333C2×D11—82no—
334C2×D11—82no—
335C2×D11—82no—
336C2×D11—82no—
337C4×C11—22no—
338C4×C11—22no—
339C4×C11—42no—
340C4×C11—41no—
341C4×C11—42no—
342C4×C11—41no—
343C4×C11—81no—
344C4×C11—81no—
345C4×C11#45014yes—
346C4×C11#54611yescharacteristic
347C4×C11#54711yescharacteristic
348C4×C11#54811yescharacteristic
349C4×C11#55011yescharacteristic
350Dic11—44no—
351C2×#41—228no—
352C2×#41—444no—
353C2×#41—444no—
354C22×Q8—221no—
355C22×Q8C22×D1111yescharacteristic
356C22×D4—112no—
357C22×D4—222no—
358C22×D4—221no—
359C22×D4—221no—
360C23×C4—222no—
361C23×C4C22⋊D1111yescharacteristic
362C23×C4C22⋊D1111yescharacteristic
363C23×C4C22×D1111yescharacteristic
364C2×SD16—224no—
365C2×SD16—224no—
366C2×SD16—442no—
367C22×C8—112no—
368C22×C8—112no—
369C4⋊Q8—114no—
370C4⋊Q8—222no—
371#127—114no—
372#127—222no—
373#124—228no—
374C22⋊Q8—22no—
375C22⋊Q8—22no—
376#121—224no—
377#121—224no—
378#121—228no—
379C4×Q8—22no—
380C4×Q8—22no—
381C4×D4—224no—
382C4×D4—224no—
383C4×D4—228no—
384C2×C4⋊C4—21no—
385C2×C4⋊C4—21no—
386C2×C4⋊C4—21no—
387C2×C4⋊C4—112no—
388C2×C4⋊C4—221no—
389C2×C4⋊C4C22×D1111yescharacteristic
390C2×C4⋊C4C22×D1111yescharacteristic
391C2×C4⋊C4C22×D1111yescharacteristic
392C2×C22⋊C4—21no—
393C2×C22⋊C4—21no—
394C2×C22⋊C4—222no—
395C2×C22⋊C4—222no—
396C2×C42—22no—
397C2×C42—22no—
398C2×C42—21no—
399C2×C42—21no—
400C2×C42C22⋊D1111yescharacteristic
401C2×C42C22⋊D1111yescharacteristic
402C2×C42C22×D1111yescharacteristic
403C2×C42C22×D1111yescharacteristic
404#106—224no—
405C4⋊C8—222no—
406C4⋊C8—222no—
407#103—224no—
408#102—224no—
409#102—224no—
410#102—442no—
411C22⋊C8—442no—
412#95—21no—
413#95—21no—
414#95—21no—
415#95—21no—
416#95—21no—
417C2×C11—42no—
418C2×C11#240711yescharacteristic
419C2×C11C2×#45011yescharacteristic
420C2×C11#300511yescharacteristic
421C2×C11#310311yescharacteristic
422C2×C11#311511yescharacteristic
423C2×C11#324611yescharacteristic
424C2×C11#325111yescharacteristic
425D11—84no—
426C24—222no—
427C24C2×C22⋊D1111yescharacteristic
428#41—4432no—
429C2×Q8—21no—
430C2×Q8—21no—
431C2×Q8—21no—
432C2×Q8—21no—
433C2×Q8—21no—
434C2×Q8—224no—
435C2×Q8—442no—
436C2×Q8—442no—
437C2×Q8#433912yescomplemented
438C2×D4—114no—
439C2×D4—228no—
440C2×D4—224no—
441C2×D4—224no—
442C2×D4—222no—
443C2×D4—222no—
444C2×D4—222no—
445C2×D4—222no—
446C2×D4—222no—
447C2×D4—442no—
448C2×D4—442no—
449C2×D4—444no—
450C2×D4—444no—
451C2×D4—442no—
452C2×D4—442no—
453C22×C4—22no—
454C22×C4—22no—
455C22×C4—21no—
456C22×C4—21no—
457C22×C4—22no—
458C22×C4—21no—
459C22×C4—21no—
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—21no—
463C22×C4—21no—
464C22×C4—21no—
465C22×C4—21no—
466C22×C4—41no—
467C22×C4—41no—
468C22×C4—228no—
469C22×C4—222no—
470C22×C4—444no—
471C22×C4—444no—
472C22×C4#432514yescomplemented
473C22×C4C2×C22⋊D1111yescharacteristic
474C22×C4C2×C22⋊D1111yescharacteristic
475C22×C4C2×C22⋊D1111yescharacteristic
476C22×C4C2×C22⋊D1111yescharacteristic
477C22×C4C2×C22⋊D1111yescharacteristic
478C22×C4C23×D1111yescharacteristic
479SD16—448no—
480C2×C8—222no—
481C2×C8—222no—
482C2×C8—222no—
483C2×C8—222no—
484C2×C8—222no—
485C2×C8—222no—
486C4⋊C4—24no—
487C4⋊C4—21no—
488C4⋊C4—21no—
489C4⋊C4—21no—
490C4⋊C4—21no—
491C4⋊C4—21no—
492C4⋊C4—42no—
493C4⋊C4—42no—
494C4⋊C4—114no—
495C4⋊C4—224no—
496C4⋊C4—222no—
497C4⋊C4#433912yescomplemented
498C22⋊C4—24no—
499C22⋊C4—42no—
500C22⋊C4—228no—
501C22⋊C4—228no—
502C42—22no—
503C42—22no—
504C42—21no—
505C42—21no—
506C42—42no—
507C42—42no—
508C42D4×D1112yes—
509C42D4×D1112yes—
510C11#2415411yescharacteristic, complemented, Sylow
511C23—21no—
512C23—21no—
513C23—21no—
514C23—21no—
515C23—21no—
516C23—21no—
517C23—224no—
518C23—442no—
519C23—442no—
520C23—442no—
521C23—442no—
522C23—442no—
523C23—442no—
524C23C2×#432512yes—
525C23C22×C22⋊D1111yescharacteristic
526Q8—22no—
527Q8—22no—
528Q8—41no—
529Q8—41no—
530Q8—448no—
531D4—224no—
532D4—224no—
533D4—448no—
534D4—4416no—
535D4—442no—
536D4—442no—
537D4—448no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—21no—
542C2×C4—28no—
543C2×C4—22no—
544C2×C4—22no—
545C2×C4—21no—
546C2×C4—21no—
547C2×C4—21no—
548C2×C4—21no—
549C2×C4—21no—
550C2×C4—21no—
551C2×C4—44no—
552C2×C4—41no—
553C2×C4—41no—
554C2×C4—41no—
555C2×C4—41no—
556C2×C4—41no—
557C2×C4—41no—
558C2×C4—41no—
559C2×C4—41no—
560C2×C4—41no—
561C2×C4—41no—
562C2×C4—41no—
563C2×C4—41no—
564C2×C4—41no—
565C2×C4—41no—
566C2×C4—224no—
567C2×C4—4416no—
568C2×C4—442no—
569C2×C4—442no—
570C2×C4#6699012yes—
571C2×C4#6699012yes—
572C2×C4C2×#432512yes—
573C2×C4C2×#432512yes—
574C2×C4#6700212yes—
575C2×C4C2×#433911yescharacteristic
576C2×C4C2×#433911yescharacteristic
577C2×C4C2×D4×D1111yescharacteristic
578C2×C4C2×D4×D1111yescharacteristic
579C2×C4#6704211yescharacteristic
580C2×C4#6704311yescharacteristic
581C8—442no—
582C8—442no—
583C22—22no—
584C22—22no—
585C22—22no—
586C22—41no—
587C22—41no—
588C22—41no—
589C22—41no—
590C22—444no—
591C22—444no—
592C22—444no—
593C22—882no—
594C22—882no—
595C22—882no—
596C22—882no—
597C22#1062332211yescharacteristic
598C22C2×#6699011yescharacteristic
599C22C22×#432511yescharacteristic
600C22C2×#6700211yescharacteristic
601C22#1062335311yescharacteristic
602C22#1062335311yescharacteristic
603C22#1062336411yescharacteristic
604C4—22no—
605C4—22no—
606C4—41no—
607C4—42no—
608C4—41no—
609C4—42no—
610C4—81no—
611C4—81no—
612C4—444no—
613C4#1062265914yes—
614C4#1062308111yescharacteristic
615C4#1062308211yescharacteristic
616C4#1062308311yescharacteristic
617C4#1062308411yescharacteristic
618C2—42no—
619C2—884no—
620C2#1307196111yescharacteristic
621C2C2×#1062265911yescharacteristic
622C2#1307785611yescharacteristic
623C2#1307864711yescharacteristic
624C2#1307876711yescharacteristic
625C2#1307992811yescharacteristic
626C2#1307997811yescharacteristic
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#24154
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×#10622633C2semidirect
3. C2×#10622640C2semidirect
4. #13069805C2semidirect
5. #13069617C2semidirect
6. #13069568C2semidirect
7. #13069543C2semidirect
8. #13068953C2semidirect
9. #13068876C2semidirect
10. #13068596C2semidirect
11. C4×C11×C22⋊Q8C2semidirect
121. C2×Q8×C11#41semidirect
137. C22×C4×C11SD16semidirect
175. C11×C4⋊C4#41semidirect
201. C4×C22⋊Q8D11semidirect
437. C2×Q8#4339semidirect
472. C22×C4#4325semidirect
497. C4⋊C4#4339semidirect
510. C11#24154semidirect

Maximal subgroups

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

subgroupindex
C2×#106230082
C2×#106226332
C2×#106226402
#130698052
#130696172
#130695682
#130695432
#130689532
#130688762
#130685962
C4×C11×C22⋊Q82
#2415411