Finite Group Databasebeta

← #14766015

Subgroups — #14766015

Order 2816.

732 conjugacy classes of subgroups.

The subgroup lattice has 586 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622484C211yesmaximal, characteristic
2#13071356C211yesmaximal, characteristic, complemented
3#13071255C211yesmaximal, characteristic
4#13069570C211yesmaximal, characteristic, complemented
5#13069371C211yesmaximal, characteristic, complemented
6#13069346C211yesmaximal, characteristic, complemented
7#13069313C211yesmaximal, characteristic
8#13069298C211yesmaximal, characteristic
9#13069235C211yesmaximal, characteristic
10#13069234C211yesmaximal, characteristic
11#13069211C211yesmaximal, characteristic, complemented
12#13069196C211yesmaximal, characteristic, complemented
13#13068615C211yesmaximal, characteristic
14#13068476C211yesmaximal, characteristic, complemented
15C11×#1944C211yesmaximal, characteristic, complemented
16C2×#66946C2211yescharacteristic
17C2×#66943C2211yescharacteristic
18C2×C11×#107C2211yescharacteristic
19C2×C11×#106C2211yescharacteristic
20C2×C11×#97C2211yescharacteristic
21C11×#389C2211yescharacteristic
22C11×#389C2211yescharacteristic
23C2×#66885C2211yescharacteristic
24C2×#66885C2211yescharacteristic
25C2×Dic11⋊C8C2211yescharacteristic
26C2×Dic11⋊C8C2211yescharacteristic
27#10622603—21no—
28#10622601C2211yescharacteristic
29#10622600—21no—
30#10622598C2211yescharacteristic
31#10622589C2211yescharacteristic
32C4⋊C4×Dic11C2211yescharacteristic
33C4⋊C4×Dic11C2211yescharacteristic
34C4⋊C4×Dic11C2211yescharacteristic
35#10622586—21no—
36#10622585—21no—
37C2×#66873C2211yescharacteristic
38C2×#66873C2211yescharacteristic
39C2×#66871C2211yescharacteristic
40C2×#66871C2211yescharacteristic
41#10622552C2211yescharacteristic
42#10622545C2211yescharacteristic
43#10622541C2211yescharacteristic
44C2×C4×C11⋊C8C2211yescharacteristic
45#10622484C418yescomplemented
46#10622283—21no—
47#10622277—21no—
48#10622266—21no—
49#10622265—21no—
50C11×#340C2211yescharacteristic
51C11×#340C2211yescharacteristic
52#10622189C2211yescharacteristic
53#10622189C2211yescharacteristic
54#10622188C2211yescharacteristic
55#10622188C2211yescharacteristic
56#10622167C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622167C2211yescharacteristic
59#10622167C2211yescharacteristic
60C22×D44C2311yescharacteristic
61C22×C4×D11—21no—
62C22×C8×C11C2311yescharacteristic
63C22×C8×C11C2311yescharacteristic
64C2×C11×C4⋊C4—21no—
65C2×C11×C4⋊C4—21no—
66C2×C11×C4⋊C4C2311yescharacteristic
67C2×C11×C4⋊C4C2311yescharacteristic
68C2×C11×C4⋊C4C2311yescharacteristic
69C2×C11×C4⋊C4C2311yescharacteristic
70C2×C42×C11C2311yescharacteristic
71C2×(C2×D11)⋊C4—21no—
72C2×(C2×D11)⋊C4—21no—
73C2×(C2×D11)⋊C4—21no—
74C2×(C2×D11)⋊C4—21no—
75C2×(C2×D11)⋊C4—21no—
76C2×C4⋊Dic11—21no—
77C2×C4⋊Dic11—21no—
78C2×C4⋊Dic11C2311yescharacteristic
79C2×C4⋊Dic11C2311yescharacteristic
80C2×C4⋊Dic11C2311yescharacteristic
81C2×Dic11⋊C4—21no—
82C2×Dic11⋊C4—21no—
83C2×Dic11⋊C4—21no—
84C2×Dic11⋊C4—21no—
85C2×C4×Dic11—21no—
86C2×C4×Dic11—21no—
87C2×C4×Dic11—21no—
88C2×C4×Dic11C2311yescharacteristic
89C2×C4×Dic11C2311yescharacteristic
90C22×C11⋊C8C2311yescharacteristic
91C22×C11⋊C8C2311yescharacteristic
92#66946—22no—
93#66946C2×C414yes—
94#66943—22no—
95#66943C2×C414yes—
96C11×#107—41no—
97C11×#106C2×C414yes—
98C11×#97—41no—
99C11×#95—21no—
100C11×#95—21no—
101C11⋊#95—21no—
102C11⋊#95—21no—
103C11⋊#95—21no—
104C11⋊#95—21no—
105C11⋊#95—21no—
106C11⋊#95D411yescharacteristic
107C11⋊#95D411yescharacteristic
108C11⋊#95D411yescharacteristic
109C11⋊#95D411yescharacteristic
110#66885—41no—
111#66885C2×C414yes—
112Dic11⋊C8—22no—
113Dic11⋊C8C2×C414yes—
114#66873—41no—
115#66873C2×C414yes—
116#66871—41no—
117#66871C2×C414yes—
118C4×C11⋊C8—41no—
119#22126—111nomaximal, Sylow
120C23×D11—21no—
121C22×C4×C11—21no—
122C22×C4×C11—21no—
123C22×C4×C11—21no—
124C22×C4×C11—21no—
125C22×C4×C11C2×D411yescharacteristic
126C22×C4×C11C2×D411yescharacteristic
127C22×C4×C11C2411yescharacteristic
128C22×Dic11—21no—
129C22×Dic11—21no—
130C22×Dic11—21no—
131C22×Dic11C2×D411yescharacteristic
132C22×Dic11C2×D411yescharacteristic
133C22×Dic11C2×D411yescharacteristic
134C22×Dic11C2×D411yescharacteristic
135C2×D44—21no—
136C2×D44—21no—
137C2×D44—21no—
138C2×D44—21no—
139C2×D44—21no—
140C2×D44C22×C412yes—
141C2×C4×D11—24no—
142C2×C4×D11—81no—
143C2×C4×D11—81no—
144C2×C8×C11—21no—
145C2×C8×C11—21no—
146C2×C8×C11—21no—
147C2×C8×C11—21no—
148C2×C8×C11—21no—
149C2×C8×C11C22×C412yes—
150C11×C4⋊C4—21no—
151C11×C4⋊C4—21no—
152C11×C4⋊C4—21no—
153C11×C4⋊C4—21no—
154C11×C4⋊C4—21no—
155C11×C4⋊C4—21no—
156C11×C4⋊C4—81no—
157C11×C4⋊C4—81no—
158C11×C4⋊C4C22×C412yes—
159C11×C4⋊C4C22×C412yes—
160C42×C11—21no—
161C42×C11—21no—
162(C2×D11)⋊C4—24no—
163(C2×D11)⋊C4—81no—
164(C2×D11)⋊C4—81no—
165(C2×D11)⋊C4—81no—
166(C2×D11)⋊C4—81no—
167C4⋊Dic11—24no—
168C4⋊Dic11—21no—
169C4⋊Dic11—21no—
170C4⋊Dic11—21no—
171C4⋊Dic11—21no—
172C4⋊Dic11—21no—
173C4⋊Dic11—81no—
174C4⋊Dic11C22×C412yes—
175Dic11⋊C4—24no—
176Dic11⋊C4—81no—
177Dic11⋊C4—81no—
178Dic11⋊C4—81no—
179C4×Dic11—21no—
180C4×Dic11—21no—
181C4×Dic11—81no—
182C4×Dic11—81no—
183C4×Dic11—81no—
184C4×Dic11C22×C412yes—
185C4×Dic11#4112yes—
186C2×C11⋊C8—21no—
187C2×C11⋊C8—21no—
188C2×C11⋊C8—21no—
189C2×C11⋊C8—21no—
190C2×C11⋊C8—21no—
191C2×C11⋊C8C22×C412yes—
192C2×#478—111no—
193#2330—111no—
194#2319—111no—
195#1989—111no—
196#1947—111no—
197#1944D1111yescharacteristic, complemented
198#1942—111no—
199#1936—111no—
200#1934—111no—
201#1925—111no—
202#1925—111no—
203#1921—111no—
204#1919—111no—
205#1802—111no—
206#1768—111no—
207C23×C11C22×D411yescharacteristic
208C22×D11—22no—
209C22×D11—41no—
210C22×D11—41no—
211C22×D11—41no—
212C22×D11—41no—
213C22×D11—41no—
214C22×D11—41no—
215C2×C4×C11—22no—
216C2×C4×C11—22no—
217C2×C4×C11—21no—
218C2×C4×C11—21no—
219C2×C4×C11—21no—
220C2×C4×C11—21no—
221C2×C4×C11—21no—
222C2×C4×C11—21no—
223C2×C4×C11—41no—
224C2×C4×C11—41no—
225C2×C4×C11—41no—
226C2×C4×C11—41no—
227C2×C4×C11—41no—
228C2×C4×C11—41no—
229C2×C4×C11—41no—
230C2×C4×C11—41no—
231C2×C4×C11—41no—
232C2×C4×C11—41no—
233C2×C4×C11C23×C411yescharacteristic
234C2×C4×C11C2×#4111yescharacteristic
235C2×C4×C11H(5,𝔽2)11yescharacteristic
236C2×C4×C112−1+411yescharacteristic
237C2×C4×C112−1+411yescharacteristic
238C2×C4×C112−1+411yescharacteristic
239C2×Dic11—21no—
240C2×Dic11—21no—
241C2×Dic11—21no—
242C2×Dic11—21no—
243C2×Dic11—22no—
244C2×Dic11—21no—
245C2×Dic11—21no—
246C2×Dic11—21no—
247C2×Dic11—21no—
248C2×Dic11—21no—
249C2×Dic11—21no—
250C2×Dic11—41no—
251C2×Dic11—41no—
252C2×Dic11—41no—
253C2×Dic11—41no—
254C2×Dic11—41no—
255C2×Dic11—41no—
256C2×Dic11—41no—
257C2×Dic11—41no—
258C2×Dic11C4×D412yes—
259C2×Dic11C4×D412yes—
260D44—22no—
261D44—22no—
262D44—41no—
263D44—41no—
264C4×D11—84no—
265C8×C11—22no—
266C8×C11—41no—
267C11⋊C8—22no—
268C11⋊C8—41no—
269C2×#125—111no—
270C2×C4×D4—111no—
271#478—118no—
272C2×#107—111no—
273C2×#107—111no—
274C2×#107C2×D1111yescharacteristic
275C2×#106C2×D1111yescharacteristic
276C2×C4⋊C8—111no—
277C2×C4⋊C8—111no—
278C2×#102—111no—
279C2×#102—111no—
280C2×#102—111no—
281C2×#102—111no—
282C2×#97C2×D1111yescharacteristic
283C2×C4×C8—111no—
284#390—111no—
285#390—111no—
286#389—111no—
287#389—111no—
288#389—221no—
289#389—221no—
290#389C2×D1111yescharacteristic
291#389C2×D1111yescharacteristic
292#388—221no—
293#388—221no—
294#387—221no—
295#387—221no—
296#384—111no—
297#381—221no—
298#380—221no—
299C4×C4⋊C4—111no—
300C4×C4⋊C4—111no—
301C4×C4⋊C4—111no—
302#376—111no—
303#340—111no—
304#340—111no—
305#340—111no—
306#340—111no—
307#340—111no—
308#340—111no—
309#340C2×D1111yescharacteristic
310#340C2×D1111yescharacteristic
311#336—111no—
312#336—111no—
313C22×C11C2×C4×D411yescharacteristic
314C22×C11#53611yescharacteristic
315C22×C11#53711yescharacteristic
316C22×C11#57611yescharacteristic
317C22×C11#57611yescharacteristic
318C22×C11#57711yescharacteristic
319C22×C11#57811yescharacteristic
320C2×D11—42no—
321C2×D11—42no—
322C2×D11—42no—
323C2×D11—81no—
324C2×D11—81no—
325C2×D11—81no—
326C2×D11—81no—
327C4×C11—42no—
328C4×C11—42no—
329C4×C11—41no—
330C4×C11—41no—
331C4×C11—81no—
332C4×C11—81no—
333C4×C11#51911yescharacteristic
334C4×C11#52011yescharacteristic
335C4×C11#54111yescharacteristic
336C4×C11#54211yescharacteristic
337Dic11—22no—
338Dic11—22no—
339Dic11—42no—
340Dic11—41no—
341Dic11—41no—
342Dic11—81no—
343Dic11—81no—
344C22×D4—111no—
345C23×C4—221no—
346C22×C8—111no—
347C22×C8—111no—
348C22×C8C22×D1111yescharacteristic
349C22×C8C22×D1111yescharacteristic
350#125—114no—
351#125—222no—
352C4×D4—114no—
353C4×D4—222no—
354C2×C4⋊C4—21no—
355C2×C4⋊C4—21no—
356C2×C4⋊C4—111no—
357C2×C4⋊C4—111no—
358C2×C4⋊C4—111no—
359C2×C4⋊C4—221no—
360C2×C4⋊C4—221no—
361C2×C4⋊C4—221no—
362C2×C4⋊C4—221no—
363C2×C4⋊C4—221no—
364C2×C4⋊C4—221no—
365C2×C4⋊C4C22×D1111yescharacteristic
366C2×C4⋊C4C22×D1111yescharacteristic
367C2×C4⋊C4C22×D1111yescharacteristic
368C2×C4⋊C4C22×D1111yescharacteristic
369C2×C22⋊C4—221no—
370C2×C22⋊C4—221no—
371C2×C22⋊C4—221no—
372C2×C22⋊C4—221no—
373C2×C22⋊C4—221no—
374C2×C42—111no—
375C2×C42—111no—
376C2×C42—221no—
377C2×C42—221no—
378C2×C42—221no—
379C2×C42C22×D1111yescharacteristic
380#107—41no—
381#107—114no—
382#107—441no—
383#106C4×D1114yes—
384C4⋊C8—114no—
385C4⋊C8—222no—
386#102—114no—
387#102—114no—
388#102—441no—
389#102—441no—
390#97—41no—
391C4×C8—441no—
392#95—21no—
393#95—21no—
394#95—111no—
395#95—111no—
396#95—111no—
397#95—111no—
398#95—221no—
399#95—221no—
400#95—221no—
401#95—221no—
402#95—221no—
403C2×C11#232311yescharacteristic
404C2×C11#294611yescharacteristic
405C2×C11#295111yescharacteristic
406C2×C11#324111yescharacteristic
407C2×C11#324311yescharacteristic
408C2×C11#325811yescharacteristic
409C2×C11#325911yescharacteristic
410D11—82no—
411C24—221no—
412C2×D4—112no—
413C2×D4—221no—
414C2×D4—221no—
415C2×D4—221no—
416C2×D4—221no—
417C2×D4—221no—
418C22×C4—21no—
419C22×C4—21no—
420C22×C4—21no—
421C22×C4—21no—
422C22×C4—111no—
423C22×C4—111no—
424C22×C4—111no—
425C22×C4—111no—
426C22×C4—224no—
427C22×C4—221no—
428C22×C4—221no—
429C22×C4—221no—
430C22×C4—881no—
431C22×C4—881no—
432C22×C4D4×D1111yescharacteristic
433C22×C4D4×D1111yescharacteristic
434C22×C4C23×D1111yescharacteristic
435C2×C8—21no—
436C2×C8—21no—
437C2×C8—21no—
438C2×C8—21no—
439C2×C8—21no—
440C2×C8—112no—
441C2×C8—221no—
442C2×C8—221no—
443C2×C8—221no—
444C2×C8—221no—
445C2×C8—221no—
446C2×C8C2×C4×D1112yes—
447C4⋊C4—21no—
448C4⋊C4—21no—
449C4⋊C4—21no—
450C4⋊C4—21no—
451C4⋊C4—21no—
452C4⋊C4—21no—
453C4⋊C4—81no—
454C4⋊C4—81no—
455C4⋊C4—112no—
456C4⋊C4—224no—
457C4⋊C4—224no—
458C4⋊C4—221no—
459C4⋊C4—221no—
460C4⋊C4—221no—
461C4⋊C4—221no—
462C4⋊C4—221no—
463C4⋊C4—881no—
464C4⋊C4—881no—
465C4⋊C4—881no—
466C4⋊C4—881no—
467C4⋊C4C2×C4×D1112yes—
468C4⋊C4C2×C4×D1112yes—
469C22⋊C4—224no—
470C22⋊C4—881no—
471C22⋊C4—881no—
472C22⋊C4—881no—
473C22⋊C4—881no—
474C42—21no—
475C42—21no—
476C42—112no—
477C42—112no—
478C42—221no—
479C42—221no—
480C42—881no—
481C42—881no—
482C42—881no—
483C11#2212611yescharacteristic, complemented, Sylow
484C23—222no—
485C23—441no—
486C23—441no—
487C23—441no—
488C23—441no—
489C23—441no—
490C23—441no—
491C23C2×D4×D1111yescharacteristic
492D4—222no—
493D4—222no—
494D4—441no—
495D4—441no—
496C2×C4—21no—
497C2×C4—21no—
498C2×C4—21no—
499C2×C4—21no—
500C2×C4—22no—
501C2×C4—22no—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—41no—
505C2×C4—41no—
506C2×C4—41no—
507C2×C4—41no—
508C2×C4—41no—
509C2×C4—41no—
510C2×C4—41no—
511C2×C4—41no—
512C2×C4—41no—
513C2×C4—41no—
514C2×C4—112no—
515C2×C4—112no—
516C2×C4—221no—
517C2×C4—221no—
518C2×C4—221no—
519C2×C4—221no—
520C2×C4—221no—
521C2×C4—221no—
522C2×C4—221no—
523C2×C4—221no—
524C2×C4—221no—
525C2×C4—221no—
526C2×C4—222no—
527C2×C4—441no—
528C2×C4—441no—
529C2×C4—441no—
530C2×C4—441no—
531C2×C4—441no—
532C2×C4—441no—
533C2×C4—441no—
534C2×C4—441no—
535C2×C4—884no—
536C2×C4C22×C4×D1111yescharacteristic
537C2×C4#6703711yescharacteristic
538C2×C4#6704011yescharacteristic
539C2×C4#6704011yescharacteristic
540C2×C4#41×D1111yescharacteristic
541C2×C4#6704311yescharacteristic
542C8—22no—
543C8—41no—
544C8—222no—
545C8—441no—
546C22—442no—
547C22—442no—
548C22—442no—
549C22—881no—
550C22—881no—
551C22—881no—
552C22—881no—
553C22C4×D4×D1111yescharacteristic
554C22#1062312811yescharacteristic
555C22#1062325511yescharacteristic
556C22#1062330511yescharacteristic
557C22#1062330511yescharacteristic
558C22#1062330911yescharacteristic
559C22#1062331011yescharacteristic
560C4—42no—
561C4—41no—
562C4—42no—
563C4—41no—
564C4—81no—
565C4—81no—
566C4—222no—
567C4—222no—
568C4—441no—
569C4—441no—
570C4—442no—
571C4—881no—
572C4—881no—
573C4#1062303511yescharacteristic
574C4#1062310311yescharacteristic
575C4#1062317111yescharacteristic
576C4#1062322711yescharacteristic
577C2—882no—
578C2#1307129311yescharacteristic
579C2#1307744711yescharacteristic
580C2#1307748811yescharacteristic
581C2#1307987011yescharacteristic
582C2#1307990011yescharacteristic
583C2#1308003711yescharacteristic
584C2#1308005211yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1944C2
socleC23×C11C22×D4
prime radicalC22×D44C23
cosocleC22×C4×C11C24
hypercenter#1944D11
hypocenterC11#22126
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1944

Complements

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

NH ≅ G/Ntype
2. #13071356C2semidirect
4. #13069570C2semidirect
5. #13069371C2semidirect
6. #13069346C2semidirect
11. #13069211C2semidirect
12. #13069196C2semidirect
14. #13068476C2semidirect
15. C11×#1944C2semidirect
45. #10622484C4semidirect
197. #1944D11semidirect
483. C11#22126semidirect

Maximal subgroups

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

subgroupindex
C2×#106224842
#130713562
#130712552
#130695702
#130693712
#130693462
#130693132
#130692982
#130692352
#130692342
#130692112
#130691962
#130686152
#130684762
C11×#19442
#2212611