Finite Group Databasebeta

← #14765971

Subgroups — #14765971

Order 2816.

740 conjugacy classes of subgroups.

The subgroup lattice has 588 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622621C211yesmaximal, characteristic
2#13071362C211yesmaximal, characteristic, complemented
3#13071259C211yesmaximal, characteristic
4#13069567C211yesmaximal, characteristic, complemented
5#13069382C211yesmaximal, characteristic, complemented
6#13069358C211yesmaximal, characteristic, complemented
7#13069343C211yesmaximal, characteristic, complemented
8#13069310C211yesmaximal, characteristic
9#13069296C211yesmaximal, characteristic
10#13069246C211yesmaximal, characteristic
11#13069239C211yesmaximal, characteristic
12#13069204C211yesmaximal, characteristic, complemented
13#13069197C211yesmaximal, characteristic, complemented
14#13068475C211yesmaximal, characteristic, complemented
15C11×#1804C211yesmaximal, characteristic
16C2×C4×D4×C11C2211yescharacteristic
17C2×#66922C2211yescharacteristic
18C2×C11×C4⋊C8C2211yescharacteristic
19C2×C11×#102C2211yescharacteristic
20C2×C11×#102C2211yescharacteristic
21C11×#382C2211yescharacteristic
22#10622834C2211yescharacteristic
23#10622834C2211yescharacteristic
24C2×#66896C2211yescharacteristic
25C2×#66896C2211yescharacteristic
26#10622825—21no—
27#10622824—21no—
28C2×#66879C2211yescharacteristic
29C2×C8×Dic11C2211yescharacteristic
30#10622621C418yescomplemented
31#10622598C2211yescharacteristic
32#10622598C2211yescharacteristic
33C4⋊C4×Dic11C2211yescharacteristic
34C4⋊C4×Dic11C2211yescharacteristic
35#10622586C2211yescharacteristic
36#10622586C2211yescharacteristic
37C2×#66872C2211yescharacteristic
38C2×#66872C2211yescharacteristic
39C2×#66872C2211yescharacteristic
40C2×#66871C2211yescharacteristic
41#10622564—21no—
42#10622564—21no—
43C4×C4⋊Dic11C2211yescharacteristic
44#10622545C2211yescharacteristic
45C2×C4⋊(C11⋊C8)C2211yescharacteristic
46#10622266—21no—
47#10622266—21no—
48#10622259—21no—
49#10622259—21no—
50C11×#340C2211yescharacteristic
51C11×#340C2211yescharacteristic
52#10622189C2211yescharacteristic
53#10622189C2211yescharacteristic
54#10622189C2211yescharacteristic
55#10622189C2211yescharacteristic
56#10622188C2211yescharacteristic
57#10622188C2211yescharacteristic
58#10622167C2211yescharacteristic
59#10622167C2211yescharacteristic
60C22×D4×C11C2311yescharacteristic
61C23×C4×C11—21no—
62C22×Dic22—21no—
63C22×C8×C11C2311yescharacteristic
64C22×C8×C11C2311yescharacteristic
65C4×D4×C11—22no—
66C4×D4×C11C2×C414yes—
67C2×C11×C4⋊C4C2311yescharacteristic
68C2×C11×C4⋊C4C2311yescharacteristic
69C2×C11×C4⋊C4C2311yescharacteristic
70C2×C11×C22⋊C4—21no—
71C2×C42×C11C2311yescharacteristic
72C2×C22⋊Dic11—21no—
73C2×C22⋊Dic11—21no—
74C2×C22⋊Dic11—21no—
75C2×C22⋊Dic11—21no—
76C2×C4⋊Dic11—21no—
77C2×C4⋊Dic11—21no—
78C2×C4⋊Dic11—21no—
79C2×C4⋊Dic11C2311yescharacteristic
80C2×C4⋊Dic11C2311yescharacteristic
81C2×C4⋊Dic11C2311yescharacteristic
82C2×C4⋊Dic11C2311yescharacteristic
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#66922—22no—
93#66922C2×C414yes—
94C11×C4⋊C8—22no—
95C11×#102—41no—
96C11×#102—41no—
97C11×#95—21no—
98C11×#95—21no—
99#66896C2×C414yes—
100#66896C2×C414yes—
101C11⋊#95—21no—
102C11⋊#95—21no—
103C11⋊#95—21no—
104C11⋊#95—21no—
105C11⋊#95—21no—
106C11⋊#95—21no—
107C11⋊#95—21no—
108C11⋊#95D411yescharacteristic
109C11⋊#95D411yescharacteristic
110C11⋊#95D411yescharacteristic
111C11⋊#95D411yescharacteristic
112#66879—41no—
113C8×Dic11—41no—
114#66872—41no—
115#66872C2×C414yes—
116#66872C2×C414yes—
117#66871—41no—
118C4⋊(C11⋊C8)C2×C414yes—
119#22123—111nomaximal, Sylow
120C24×C11—21no—
121C2×D4×C11—21no—
122C2×D4×C11—21no—
123C2×D4×C11—21no—
124C2×D4×C11—21no—
125C2×D4×C11—21no—
126C2×D4×C11C22×C412yes—
127C22×C4×C11—21no—
128C22×C4×C11—24no—
129C22×C4×C11—21no—
130C22×C4×C11—21no—
131C22×C4×C11—81no—
132C22×C4×C11—81no—
133C22×C4×C11C2×D411yescharacteristic
134C22×C4×C11C2×D411yescharacteristic
135C22×C4×C11C2411yescharacteristic
136C22×Dic11—21no—
137C22×Dic11—21no—
138C22×Dic11—21no—
139C22×Dic11—21no—
140C22×Dic11C2×D411yescharacteristic
141C22×Dic11C2×D411yescharacteristic
142C22×Dic11C2×D411yescharacteristic
143C22×Dic11C2×D411yescharacteristic
144C2×Dic22—24no—
145C2×Dic22—81no—
146C2×Dic22—81no—
147C2×C8×C11—21no—
148C2×C8×C11—21no—
149C2×C8×C11—21no—
150C2×C8×C11—21no—
151C2×C8×C11—21no—
152C2×C8×C11—21no—
153C11×C4⋊C4—21no—
154C11×C4⋊C4—21no—
155C11×C4⋊C4—21no—
156C11×C4⋊C4—21no—
157C11×C4⋊C4—21no—
158C11×C4⋊C4C22×C412yes—
159C11×C22⋊C4—24no—
160C42×C11C22×C412yes—
161C42×C11#4112yes—
162C22⋊Dic11—81no—
163C22⋊Dic11—81no—
164C22⋊Dic11—81no—
165C22⋊Dic11—81no—
166C4⋊Dic11—24no—
167C4⋊Dic11—21no—
168C4⋊Dic11—21no—
169C4⋊Dic11—21no—
170C4⋊Dic11—21no—
171C4⋊Dic11—21no—
172C4⋊Dic11—21no—
173C4⋊Dic11—81no—
174C4⋊Dic11—81no—
175C4⋊Dic11C22×C412yes—
176C4⋊Dic11C22×C412yes—
177Dic11⋊C4—81no—
178Dic11⋊C4—81no—
179C4×Dic11—21no—
180C4×Dic11—21no—
181C4×Dic11—21no—
182C4×Dic11—21no—
183C4×Dic11—81no—
184C4×Dic11—81no—
185C4×Dic11—81no—
186C2×C11⋊C8—21no—
187C2×C11⋊C8—21no—
188C2×C11⋊C8—21no—
189C2×C11⋊C8—21no—
190C2×C11⋊C8C22×C412yes—
191C2×C11⋊C8C22×C412yes—
192C2×#476—111no—
193#2331—111no—
194#2319—111no—
195#1988—111no—
196#1949—111no—
197#1944—111no—
198#1941—111no—
199#1936—111no—
200#1934—111no—
201#1926—111no—
202#1925—111no—
203#1920—111no—
204#1919—111no—
205#1804D1111yescharacteristic
206#1768—111no—
207C23×C11—22no—
208C23×C11—41no—
209C23×C11—41no—
210C23×C11—41no—
211C23×C11—41no—
212C23×C11—41no—
213C23×C11—41no—
214C23×C11C22×D411yescharacteristic
215D4×C11—22no—
216D4×C11—22no—
217D4×C11—41no—
218D4×C11—41no—
219C2×C4×C11—21no—
220C2×C4×C11—21no—
221C2×C4×C11—21no—
222C2×C4×C11—21no—
223C2×C4×C11—22no—
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—84no—
233C2×C4×C11C4×D412yes—
234C2×C4×C11C4×D412yes—
235C2×C4×C11C23×C411yescharacteristic
236C2×C4×C11C2×#4111yescharacteristic
237C2×C4×C11H(5,𝔽2)11yescharacteristic
238C2×C4×C112−1+411yescharacteristic
239C2×C4×C112−1+411yescharacteristic
240C2×C4×C112−1+411yescharacteristic
241C2×Dic11—22no—
242C2×Dic11—22no—
243C2×Dic11—21no—
244C2×Dic11—21no—
245C2×Dic11—21no—
246C2×Dic11—21no—
247C2×Dic11—21no—
248C2×Dic11—21no—
249C2×Dic11—21no—
250C2×Dic11—21no—
251C2×Dic11—21no—
252C2×Dic11—21no—
253C2×Dic11—21no—
254C2×Dic11—21no—
255C2×Dic11—41no—
256C2×Dic11—41no—
257C2×Dic11—41no—
258C2×Dic11—41no—
259C2×Dic11—41no—
260C2×Dic11—41no—
261C2×Dic11—41no—
262C2×Dic11—41no—
263C2×Dic11—41no—
264C2×Dic11—41no—
265Dic22—84no—
266C8×C11—41no—
267C8×C11—41no—
268C11⋊C8—22no—
269C11⋊C8—22no—
270C2×C4⋊Q8—111no—
271C2×C4×D4C2×D1111yescharacteristic
272#476—118no—
273C2×#107—111no—
274C2×#106—111no—
275C2×#106—111no—
276C2×#106—111no—
277C2×C4⋊C8—111no—
278C2×C4⋊C8C2×D1111yescharacteristic
279C2×#102—111no—
280C2×#102—111no—
281C2×#102C2×D1111yescharacteristic
282C2×#102C2×D1111yescharacteristic
283C2×#97—111no—
284C2×C4×C8—111no—
285#391—221no—
286#391—221no—
287#390—111no—
288#390—111no—
289#389—111no—
290#389—111no—
291#389—111no—
292#389—111no—
293#388—221no—
294#388—221no—
295#387—221no—
296#387—221no—
297#382C2×D1111yescharacteristic
298#381—221no—
299#380—221no—
300C4×C4⋊C4—111no—
301C4×C4⋊C4—111no—
302C4×C4⋊C4—111no—
303#376—111no—
304#340—111no—
305#340—111no—
306#340—111no—
307#340—111no—
308#340—111no—
309#340—111no—
310#340C2×D1111yescharacteristic
311#340C2×D1111yescharacteristic
312#336—111no—
313#336—111no—
314C22×C11—42no—
315C22×C11—42no—
316C22×C11—42no—
317C22×C11—81no—
318C22×C11—81no—
319C22×C11—81no—
320C22×C11—81no—
321C22×C11C2×C4×D411yescharacteristic
322C22×C11#53611yescharacteristic
323C22×C11#53711yescharacteristic
324C22×C11#57611yescharacteristic
325C22×C11#57711yescharacteristic
326C22×C11#57711yescharacteristic
327C22×C11#57711yescharacteristic
328C4×C11—22no—
329C4×C11—22no—
330C4×C11—42no—
331C4×C11—81no—
332C4×C11—81no—
333C4×C11#51911yescharacteristic
334C4×C11#52011yescharacteristic
335C4×C11#54111yescharacteristic
336C4×C11#54211yescharacteristic
337Dic11—42no—
338Dic11—42no—
339Dic11—41no—
340Dic11—41no—
341Dic11—41no—
342Dic11—41no—
343Dic11—81no—
344Dic11—81no—
345C22×Q8—221no—
346C22×D4C22×D1111yescharacteristic
347C23×C4—21no—
348C22×C8—111no—
349C22×C8—111no—
350C22×C8C22×D1111yescharacteristic
351C22×C8C22×D1111yescharacteristic
352C4⋊Q8—114no—
353C4⋊Q8—222no—
354C4×D4—22no—
355C4×D4C4×D1114yes—
356C2×C4⋊C4—111no—
357C2×C4⋊C4—111no—
358C2×C4⋊C4—111no—
359C2×C4⋊C4—111no—
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×C22⋊C4—21no—
369C2×C22⋊C4—221no—
370C2×C22⋊C4—221no—
371C2×C22⋊C4—221no—
372C2×C22⋊C4—221no—
373C2×C42—111no—
374C2×C42—111no—
375C2×C42—221no—
376C2×C42—221no—
377C2×C42—221no—
378C2×C42C22×D1111yescharacteristic
379#107—441no—
380#106—114no—
381#106—114no—
382#106—441no—
383C4⋊C8—22no—
384C4⋊C8—114no—
385#102—41no—
386#102—41no—
387#102—114no—
388#102—114no—
389#97—441no—
390C4×C8—441no—
391#95—21no—
392#95—21no—
393#95—111no—
394#95—111no—
395#95—111no—
396#95—111no—
397#95—221no—
398#95—221no—
399#95—221no—
400#95—221no—
401#95—221no—
402#95—221no—
403#95—221no—
404C2×C11—82no—
405C2×C11#232311yescharacteristic
406C2×C11#294611yescharacteristic
407C2×C11#294911yescharacteristic
408C2×C11#324111yescharacteristic
409C2×C11#324411yescharacteristic
410C2×C11#325711yescharacteristic
411C2×C11#326311yescharacteristic
412C24—21no—
413C2×Q8—224no—
414C2×Q8—881no—
415C2×Q8—881no—
416C2×D4—21no—
417C2×D4—21no—
418C2×D4—21no—
419C2×D4—21no—
420C2×D4—21no—
421C2×D4C2×C4×D1112yes—
422C22×C4—21no—
423C22×C4—24no—
424C22×C4—21no—
425C22×C4—21no—
426C22×C4—81no—
427C22×C4—81no—
428C22×C4—111no—
429C22×C4—111no—
430C22×C4—111no—
431C22×C4—111no—
432C22×C4—221no—
433C22×C4—221no—
434C22×C4—221no—
435C22×C4—221no—
436C22×C4D4×D1111yescharacteristic
437C22×C4D4×D1111yescharacteristic
438C22×C4C23×D1111yescharacteristic
439C2×C8—21no—
440C2×C8—21no—
441C2×C8—21no—
442C2×C8—21no—
443C2×C8—21no—
444C2×C8—21no—
445C2×C8—112no—
446C2×C8—112no—
447C2×C8—221no—
448C2×C8—221no—
449C2×C8—221no—
450C2×C8—221no—
451C4⋊C4—21no—
452C4⋊C4—21no—
453C4⋊C4—21no—
454C4⋊C4—21no—
455C4⋊C4—21no—
456C4⋊C4—112no—
457C4⋊C4—112no—
458C4⋊C4—224no—
459C4⋊C4—221no—
460C4⋊C4—221no—
461C4⋊C4—221no—
462C4⋊C4—221no—
463C4⋊C4—221no—
464C4⋊C4—221no—
465C4⋊C4—881no—
466C4⋊C4—881no—
467C4⋊C4—881no—
468C4⋊C4—881no—
469C4⋊C4C2×C4×D1112yes—
470C22⋊C4—24no—
471C22⋊C4—881no—
472C22⋊C4—881no—
473C22⋊C4—881no—
474C22⋊C4—881no—
475C42—221no—
476C42—221no—
477C42—221no—
478C42—221no—
479C42—881no—
480C42—881no—
481C42—881no—
482C42C2×C4×D1112yes—
483C42#434112yes—
484C11#2212311yescharacteristic, complemented, Sylow
485C23—22no—
486C23—41no—
487C23—41no—
488C23—41no—
489C23—41no—
490C23—41no—
491C23—41no—
492C23C2×D4×D1111yescharacteristic
493Q8—884no—
494D4—22no—
495D4—22no—
496D4—41no—
497D4—41no—
498C2×C4—21no—
499C2×C4—21no—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—22no—
503C2×C4—41no—
504C2×C4—41no—
505C2×C4—41no—
506C2×C4—41no—
507C2×C4—41no—
508C2×C4—41no—
509C2×C4—41no—
510C2×C4—41no—
511C2×C4—84no—
512C2×C4—222no—
513C2×C4—222no—
514C2×C4—221no—
515C2×C4—221no—
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—441no—
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—441no—
536C2×C4(C22⋊D11)⋊C412yes—
537C2×C4(C22⋊D11)⋊C412yes—
538C2×C4C22×C4×D1111yescharacteristic
539C2×C4C2×#434111yescharacteristic
540C2×C4#6703711yescharacteristic
541C2×C4#6704011yescharacteristic
542C2×C4#6704311yescharacteristic
543C2×C4#6704311yescharacteristic
544C8—41no—
545C8—41no—
546C8—222no—
547C8—222no—
548C22—42no—
549C22—42no—
550C22—42no—
551C22—81no—
552C22—81no—
553C22—81no—
554C22—81no—
555C22C2×(C22⋊D11)⋊C411yescharacteristic
556C22#1062313911yescharacteristic
557C22#1062315911yescharacteristic
558C22#1062330011yescharacteristic
559C22#1062330111yescharacteristic
560C22#1062330611yescharacteristic
561C22#1062330611yescharacteristic
562C4—22no—
563C4—22no—
564C4—42no—
565C4—81no—
566C4—81no—
567C4—441no—
568C4—441no—
569C4—441no—
570C4—442no—
571C4—442no—
572C4—441no—
573C4—881no—
574C4—881no—
575C4#1062303511yescharacteristic
576C4#1062304711yescharacteristic
577C4#1062313411yescharacteristic
578C4#1062315611yescharacteristic
579C2—82no—
580C2#1307129411yescharacteristic
581C2#1307745111yescharacteristic
582C2#1307747811yescharacteristic
583C2#1307986611yescharacteristic
584C2#1307991311yescharacteristic
585C2#1308002411yescharacteristic
586C2#1308008311yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1804C2
socleC23×C11C22×D4
prime radicalC22×D4×C11C23
cosocleC22×C4×C11C24
hypercenter#1804D11
hypocenterC11#22123
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1804

Complements

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

NH ≅ G/Ntype
2. #13071362C2semidirect
4. #13069567C2semidirect
5. #13069382C2semidirect
6. #13069358C2semidirect
7. #13069343C2semidirect
12. #13069204C2semidirect
13. #13069197C2semidirect
14. #13068475C2semidirect
30. #10622621C4semidirect
484. C11#22123semidirect

Maximal subgroups

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

subgroupindex
C2×#106226212
#130713622
#130712592
#130695672
#130693822
#130693582
#130693432
#130693102
#130692962
#130692462
#130692392
#130692042
#130691972
#130684752
C11×#18042
#2212311