Finite Group Databasebeta

← #14807121

Subgroups — #14807121

Order 2816.

1262 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×#10622680C211yesmaximal, characteristic, complemented
2C2×#10622640C211yesmaximal, characteristic, complemented
3#13073562C211yesmaximal, characteristic
4#13069617C212yesmaximal, complemented
5#13069617C212yesmaximal, complemented
6#13069574C211yesmaximal, characteristic, complemented
7#13069415C211yesmaximal, characteristic, complemented
8#13068938C212yesmaximal, complemented
9#13068933C212yesmaximal, complemented
10#13068446C211yesmaximal, characteristic, complemented
11C2×C11×#552C211yesmaximal, characteristic, complemented
12C11×#552—24no—
13C11×#552—24no—
14C2×C11×#126—21no—
15C2×C11×#125—21no—
16C2×C11×#125C2211yescharacteristic
17C2×C11×#123—21no—
18C2×C11×C22⋊Q8C2211yescharacteristic
19C2×C11×C22⋊Q8C2211yescharacteristic
20C2×C4×Q8×C11C2211yescharacteristic
21C2×C4×D4×C11C2211yescharacteristic
22C2×C11×#117—21no—
23C2×C11×#117C2211yescharacteristic
24C22×C11×C4⋊C4C2211yescharacteristic
25C22×#4325C2212yes—
26C2×#66993—21no—
27C2×#66983C2212yes—
28C2×#66983C2212yes—
29C2×#66927C2211yescharacteristic
30C2×#66899C2212yes—
31C2×C22⋊(C11⋊C8)C2212yes—
32C2×C22⋊(C11⋊C8)C2212yes—
33#10622680—24no—
34#10622640—24no—
35#10622601—21no—
36C2×#66873C2212yes—
37C2×#66873C2212yes—
38C2×#66873C2212yes—
39#10622573—21no—
40#10622573—21no—
41C4×C4⋊Dic11C2211yescharacteristic
42C2×C4⋊(C11⋊C8)C2211yescharacteristic
43C2×#66867C2211yescharacteristic
44#10622167C2212yes—
45#10622167C2212yes—
46#10622167C2212yes—
47C22×Q8×C11C2311yescharacteristic
48C22×D4×C11D411yescharacteristic
49C23×C4×C11—21no—
50C23×C4×C11C2311yescharacteristic
51C23×C4×C11C2311yescharacteristic
52C22×C22⋊D11—22no—
53C22×C22⋊D11—22no—
54C22×D44—21no—
55C22×D44—21no—
56C22×D44C2312yes—
57C11×#126—28no—
58C11×#125—28no—
59C11×#125—22no—
60C11×#125D414yescomplemented
61C11×#123—28no—
62C11×C22⋊Q8—22no—
63C11×C22⋊Q8—22no—
64C11×C22⋊Q8—22no—
65C11×C22⋊Q8—22no—
66C4×Q8×C11—22no—
67C4×Q8×C11D414yescomplemented
68C4×D4×C11—22no—
69C4×D4×C11—22no—
70C11×#117—28no—
71C11×#117—22no—
72C11×#117—22no—
73C2×C11×C4⋊C4—21no—
74C2×C11×C4⋊C4—21no—
75C2×C11×C4⋊C4—21no—
76C2×C11×C4⋊C4—21no—
77C2×C11×C4⋊C4—21no—
78C2×C11×C4⋊C4—21no—
79C2×C11×C4⋊C4—22no—
80C2×C11×C4⋊C4—22no—
81C2×C11×C4⋊C4D411yescharacteristic
82C2×C11×C4⋊C4C2311yescharacteristic
83C2×C11×C4⋊C4C2311yescharacteristic
84C2×C11×C4⋊C4C2311yescharacteristic
85C2×C11×C22⋊C4—21no—
86C2×C11×C22⋊C4—21no—
87C2×C11×C22⋊C4—21no—
88C2×C11×C22⋊C4D411yescharacteristic
89C2×C11×C22⋊C4D411yescharacteristic
90C2×C42×C11—21no—
91C2×C42×C11—21no—
92C2×C42×C11C2311yescharacteristic
93C2×#4325—24no—
94C2×#4325—42no—
95C2×#4325—42no—
96#66993—44no—
97#66983—24no—
98#66983—24no—
99#66983—42no—
100#66983—42no—
101C2×(C2×D11)⋊C4—22no—
102C2×(C2×D11)⋊C4—22no—
103C2×C4⋊Dic11C2312yes—
104C2×C4×Dic11—21no—
105C22×C11⋊C8C2312yes—
106C22×C11⋊C8C2312yes—
107#66927—22no—
108#66927—22no—
109#66899—24no—
110C11⋊#95—21no—
111C22⋊(C11⋊C8)—42no—
112C22⋊(C11⋊C8)—42no—
113#66873—24no—
114#66873—24no—
115#66873—24no—
116C4⋊(C11⋊C8)—22no—
117#66867—22no—
118#25583—111nomaximal, Sylow
119C24×C11C2×D411yescharacteristic
120C24×C11C2×D411yescharacteristic
121C23×D11—22no—
122C2×Q8×C11—21no—
123C2×Q8×C11—22no—
124C2×Q8×C11—22no—
125C2×Q8×C11C2×D412yes—
126C2×D4×C11—22no—
127C2×D4×C11—22no—
128C2×D4×C11—41no—
129C22×C4×C11—24no—
130C22×C4×C11—21no—
131C22×C4×C11—21no—
132C22×C4×C11—21no—
133C22×C4×C11—21no—
134C22×C4×C11—21no—
135C22×C4×C11—21no—
136C22×C4×C11—21no—
137C22×C4×C11—21no—
138C22×C4×C11—22no—
139C22×C4×C11—22no—
140C22×C4×C11—22no—
141C22×C4×C11—22no—
142C22×C4×C11—42no—
143C22×C4×C11—42no—
144C22×C4×C11C2×D411yescharacteristic
145C22×C4×C11C2×D411yescharacteristic
146C22×C4×C11C2×D411yescharacteristic
147C22×C4×C11C2×D411yescharacteristic
148C22×C4×C11C2411yescharacteristic
149C2×C22⋊D11—44no—
150C2×C22⋊D11—44no—
151C2×C22⋊D11—44no—
152C2×C22⋊D11—44no—
153C2×C22⋊D11—82no—
154C2×C22⋊D11—82no—
155C22×Dic11—22no—
156C2×D44—22no—
157C2×D44—22no—
158C2×D44—22no—
159C2×D44—22no—
160C2×D44—22no—
161C2×D44—22no—
162C2×D44—42no—
163C2×D44—42no—
164C2×D44—42no—
165C2×D44—42no—
166C2×D44—82no—
167C11×C4⋊C4—24no—
168C11×C4⋊C4—24no—
169C11×C4⋊C4—24no—
170C11×C4⋊C4—24no—
171C11×C4⋊C4—24no—
172C11×C4⋊C4—24no—
173C11×C4⋊C4—22no—
174C11×C4⋊C4—21no—
175C11×C4⋊C4—21no—
176C11×C4⋊C4—21no—
177C11×C4⋊C4C2×D412yes—
178C11×C4⋊C4C2×D412yes—
179C11×C4⋊C4C2×D412yes—
180C11×C22⋊C4—24no—
181C11×C22⋊C4—24no—
182C11×C22⋊C4—24no—
183C11×C22⋊C4—22no—
184C11×C22⋊C4—22no—
185C42×C11—24no—
186C42×C11—24no—
187C42×C11C2×D412yes—
188C42×C11C2×D412yes—
189#4325—48no—
190(C2×D11)⋊C4—44no—
191(C2×D11)⋊C4—44no—
192C4⋊Dic11—22no—
193C4⋊Dic11#4114yes—
194C4×Dic11—42no—
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×#552D1111yescharacteristic, complemented
202C2×#490—111no—
203C2×#460—111no—
204#2541—111no—
205#2000—112no—
206#2000—112no—
207#1989—111no—
208#1955—111no—
209#1875—112no—
210#1874—112no—
211#1763—111no—
212C23×C11—21no—
213C23×C11—22no—
214C23×C11—21no—
215C23×C11—22no—
216C23×C11—21no—
217C23×C11—22no—
218C23×C11—21no—
219C23×C11—21no—
220C23×C11—22no—
221C23×C11AGL(1,ℤ/8)12yes—
222C23×C11C22×D411yescharacteristic
223C22×D11—42no—
224C22×D11—42no—
225C22×D11—42no—
226C22×D11—42no—
227C22×D11—42no—
228C22×D11—42no—
229C22×D11—42no—
230Q8×C11—22no—
231Q8×C11—22no—
232Q8×C11—42no—
233D4×C11—44no—
234C2×C4×C11—21no—
235C2×C4×C11—21no—
236C2×C4×C11—22no—
237C2×C4×C11—21no—
238C2×C4×C11—22no—
239C2×C4×C11—22no—
240C2×C4×C11—22no—
241C2×C4×C11—21no—
242C2×C4×C11—22no—
243C2×C4×C11—22no—
244C2×C4×C11—22no—
245C2×C4×C11—48no—
246C2×C4×C11—42no—
247C2×C4×C11—41no—
248C2×C4×C11—41no—
249C2×C4×C11—41no—
250C2×C4×C11—41no—
251C2×C4×C11—42no—
252C2×C4×C11—41no—
253C2×C4×C11—41no—
254C2×C4×C11—41no—
255C2×C4×C11—41no—
256C2×C4×C11—42no—
257C2×C4×C11—42no—
258C2×C4×C11#12012yes—
259C2×C4×C11#12012yes—
260C2×C4×C11C22×D411yescharacteristic
261C2×C4×C11C22×D411yescharacteristic
262C2×C4×C11C2×#4112yes—
263C2×C4×C11H(5,𝔽2)12yes—
264C22⋊D11—88no—
265C22⋊D11—88no—
266C2×Dic11—24no—
267C2×Dic11—42no—
268C2×Dic11—42no—
269D44—42no—
270D44—42no—
271D44—42no—
272D44—42no—
273D44—84no—
274D44—84no—
275C11⋊C8—42no—
276C11⋊C8—42no—
277C22×SD16—112no—
278#552—24no—
279#552—24no—
280C2×#127—111no—
281C2×#127—221no—
282C2×#126—21no—
283C2×#125—21no—
284C2×#125C2×D1111yescharacteristic
285C2×#123—21no—
286C2×C22⋊Q8C2×D1111yescharacteristic
287C2×C22⋊Q8C2×D1111yescharacteristic
288C2×#121—112no—
289C2×#121—112no—
290C2×C4×Q8C2×D1111yescharacteristic
291C2×C4×D4C2×D1111yescharacteristic
292C2×#117—21no—
293C2×#117C2×D1111yescharacteristic
294C22×C4⋊C4C2×D1111yescharacteristic
295#490—224no—
296#460—224no—
297C2×C4⋊C8—111no—
298C2×#103—112no—
299C2×#102—112no—
300C2×#102—112no—
301C2×#102—112no—
302C2×C22⋊C8—112no—
303C2×C22⋊C8—112no—
304C2×#97—111no—
305#392—221no—
306#392—221no—
307#390—221no—
308C4×C4⋊C4—111no—
309#340—112no—
310#340—112no—
311#340—112no—
312C22×C11—22no—
313C22×C11—24no—
314C22×C11—41no—
315C22×C11—41no—
316C22×C11—42no—
317C22×C11—41no—
318C22×C11—41no—
319C22×C11—41no—
320C22×C11—42no—
321C22×C11—42no—
322C22×C11C2×#12011yescharacteristic
323C22×C11#54612yes—
324C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
325C22×C11#57511yescharacteristic
326C22×C11#57712yes—
327C2×D11—82no—
328C2×D11—82no—
329C2×D11—82no—
330C2×D11—82no—
331C2×D11—82no—
332C2×D11—82no—
333C2×D11—82no—
334C4×C11—22no—
335C4×C11—22no—
336C4×C11—41no—
337C4×C11—41no—
338C4×C11—42no—
339C4×C11—42no—
340C4×C11—42no—
341C4×C11—42no—
342C4×C11#53211yescharacteristic
343C4×C11#53511yescharacteristic
344C4×C11#55012yes—
345Dic11—44no—
346C22×Q8C22×D1111yescharacteristic
347C22×D4—112no—
348C22×D4—222no—
349C22×D4—222no—
350C22×D4—221no—
351C22×D4—221no—
352C22×D4C22⋊D1111yescharacteristic
353C23×C4—21no—
354C23×C4C22×D1111yescharacteristic
355C23×C4C22×D1111yescharacteristic
356C2×SD16—224no—
357C2×SD16—442no—
358C2×SD16—442no—
359C22×C8—112no—
360C22×C8—112no—
361#127—222no—
362#127—222no—
363#127—444no—
364#126—28no—
365#125—28no—
366#125—22no—
367#125C22⋊D1114yescomplemented
368#123—28no—
369C22⋊Q8—22no—
370C22⋊Q8—22no—
371C22⋊Q8—22no—
372C22⋊Q8—22no—
373#121—224no—
374#121—224no—
375#121—442no—
376#121—442no—
377C4×Q8—22no—
378C4×Q8C22⋊D1114yescomplemented
379C4×D4—22no—
380C4×D4—22no—
381#117—28no—
382#117—22no—
383#117—22no—
384C2×C4⋊C4—21no—
385C2×C4⋊C4—21no—
386C2×C4⋊C4—21no—
387C2×C4⋊C4—21no—
388C2×C4⋊C4—21no—
389C2×C4⋊C4—21no—
390C2×C4⋊C4—22no—
391C2×C4⋊C4—22no—
392C2×C4⋊C4—112no—
393C2×C4⋊C4C22⋊D1111yescharacteristic
394C2×C4⋊C4C22×D1111yescharacteristic
395C2×C4⋊C4C22×D1111yescharacteristic
396C2×C4⋊C4C22×D1111yescharacteristic
397C2×C22⋊C4—21no—
398C2×C22⋊C4—21no—
399C2×C22⋊C4—21no—
400C2×C22⋊C4—222no—
401C2×C22⋊C4—222no—
402C2×C22⋊C4C22⋊D1111yescharacteristic
403C2×C22⋊C4C22⋊D1111yescharacteristic
404C2×C42—21no—
405C2×C42—21no—
406C2×C42—221no—
407C2×C42C22×D1111yescharacteristic
408C4⋊C8—222no—
409#103—224no—
410#102—224no—
411#102—224no—
412#102—224no—
413C22⋊C8—442no—
414C22⋊C8—442no—
415#97—222no—
416#95—221no—
417C2×C11—42no—
418C2×C11—81no—
419C2×C11#243111yescharacteristic
420C2×C11#300611yescharacteristic
421C2×C11#301011yescharacteristic
422C2×C11#331012yes—
423C2×C11#331712yes—
424D11—162no—
425C24—222no—
426C24C2×C22⋊D1111yescharacteristic
427C24C2×C22⋊D1111yescharacteristic
428C2×Q8—21no—
429C2×Q8—22no—
430C2×Q8—22no—
431C2×Q8C2×C22⋊D1112yes—
432C2×D4—22no—
433C2×D4—22no—
434C2×D4—41no—
435C2×D4—222no—
436C2×D4—222no—
437C2×D4—222no—
438C2×D4—222no—
439C2×D4—222no—
440C2×D4—222no—
441C2×D4—442no—
442C2×D4—442no—
443C2×D4—444no—
444C2×D4—444no—
445C2×D4—444no—
446C2×D4—444no—
447C2×D4—442no—
448C2×D4—442no—
449C2×D4—882no—
450C2×D4—882no—
451C2×D4—882no—
452C22×C4—24no—
453C22×C4—21no—
454C22×C4—21no—
455C22×C4—21no—
456C22×C4—21no—
457C22×C4—22no—
458C22×C4—22no—
459C22×C4—22no—
460C22×C4—22no—
461C22×C4—21no—
462C22×C4—21no—
463C22×C4—21no—
464C22×C4—21no—
465C22×C4—42no—
466C22×C4—42no—
467C22×C4—222no—
468C22×C4C2×C22⋊D1111yescharacteristic
469C22×C4C2×C22⋊D1111yescharacteristic
470C22×C4C2×C22⋊D1111yescharacteristic
471C22×C4C2×C22⋊D1111yescharacteristic
472C22×C4C23×D1111yescharacteristic
473SD16—448no—
474C2×C8—222no—
475C2×C8—222no—
476C2×C8—222no—
477C2×C8—222no—
478C2×C8—222no—
479C2×C8—222no—
480C4⋊C4—24no—
481C4⋊C4—24no—
482C4⋊C4—24no—
483C4⋊C4—24no—
484C4⋊C4—24no—
485C4⋊C4—24no—
486C4⋊C4—22no—
487C4⋊C4—21no—
488C4⋊C4—21no—
489C4⋊C4—21no—
490C4⋊C4—114no—
491C4⋊C4—222no—
492C4⋊C4C2×C22⋊D1112yes—
493C4⋊C4C2×C22⋊D1112yes—
494C4⋊C4C2×C22⋊D1112yes—
495C22⋊C4—24no—
496C22⋊C4—24no—
497C22⋊C4—24no—
498C22⋊C4—22no—
499C22⋊C4—22no—
500C22⋊C4—444no—
501C22⋊C4—444no—
502C42—24no—
503C42—24no—
504C42—442no—
505C42C2×C22⋊D1112yes—
506C42C2×C22⋊D1112yes—
507C11#2558311yescharacteristic, complemented, Sylow
508C23—21no—
509C23—22no—
510C23—22no—
511C23—21no—
512C23—21no—
513C23—21no—
514C23—22no—
515C23—22no—
516C23—21no—
517C23—442no—
518C23—442no—
519C23—442no—
520C23—442no—
521C23—442no—
522C23—442no—
523C23—442no—
524C23#6700212yes—
525C23C22×C22⋊D1111yescharacteristic
526Q8—22no—
527Q8—22no—
528Q8—42no—
529D4—44no—
530D4—442no—
531D4—442no—
532D4—442no—
533D4—442no—
534D4—884no—
535D4—884no—
536D4—888no—
537D4—888no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—22no—
541C2×C4—22no—
542C2×C4—22no—
543C2×C4—21no—
544C2×C4—22no—
545C2×C4—22no—
546C2×C4—22no—
547C2×C4—21no—
548C2×C4—22no—
549C2×C4—48no—
550C2×C4—41no—
551C2×C4—41no—
552C2×C4—41no—
553C2×C4—41no—
554C2×C4—42no—
555C2×C4—42no—
556C2×C4—41no—
557C2×C4—41no—
558C2×C4—41no—
559C2×C4—41no—
560C2×C4—42no—
561C2×C4—42no—
562C2×C4—224no—
563C2×C4—442no—
564C2×C4—442no—
565C2×C4#6700612yes—
566C2×C4#6700612yes—
567C2×C4#41×D1112yes—
568C2×C4#6704212yes—
569C2×C4C22×C22⋊D1111yescharacteristic
570C2×C4C22×C22⋊D1111yescharacteristic
571C8—442no—
572C8—442no—
573C22—24no—
574C22—22no—
575C22—41no—
576C22—41no—
577C22—42no—
578C22—42no—
579C22—41no—
580C22—41no—
581C22—41no—
582C22—42no—
583C22—882no—
584C22—882no—
585C22—882no—
586C22—882no—
587C22—882no—
588C22—882no—
589C22—882no—
590C22C2×#6700211yescharacteristic
591C22#1062335311yescharacteristic
592C22#1062336012yes—
593C22#1062336812yes—
594C22C2×#6700611yescharacteristic
595C4—22no—
596C4—22no—
597C4—41no—
598C4—41no—
599C4—42no—
600C4—42no—
601C4—42no—
602C4—42no—
603C4—444no—
604C4#1062336111yescharacteristic
605C4#1062336311yescharacteristic
606C4#1062336512yes—
607C2—42no—
608C2—81no—
609C2—1762no—
610C2#1307223111yescharacteristic
611C2#1307786811yescharacteristic
612C2#1307790211yescharacteristic
613C2#1308063112yes—
614C2#1308073612yes—
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C11×#552C2
socleC23×C11C22×D4
prime radical#13073562C2
hypercenterC2×#552D11
hypocenterC11#25583
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#552

Complements

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

NH ≅ G/Ntype
1. C2×#10622680C2semidirect
2. C2×#10622640C2semidirect
4. #13069617C2semidirect
5. #13069617C2semidirect
6. #13069574C2semidirect
7. #13069415C2semidirect
8. #13068938C2semidirect
9. #13068933C2semidirect
10. #13068446C2semidirect
11. C2×C11×#552C2semidirect
60. C11×#125D4semidirect
67. C4×Q8×C11D4semidirect
201. C2×#552D11semidirect
367. #125C22⋊D11semidirect
378. C4×Q8C22⋊D11semidirect
507. C11#25583semidirect

Maximal subgroups

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

subgroupindex
C2×#106226802
C2×#106226402
#130735622
#130696172
#130695742
#130694152
#130689382
#130689332
#130684462
C2×C11×#5522
#2558311