Finite Group Databasebeta

← #14771505

Subgroups — #14771505

Order 2816.

782 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
1#13071501C211yesmaximal, characteristic
2#13071493C211yesmaximal, characteristic
3#13069355C211yesmaximal, characteristic, complemented
4#13069350C211yesmaximal, characteristic, complemented
5#13069210C211yesmaximal, characteristic, complemented
6#13069203C211yesmaximal, characteristic, complemented
7#13069196C211yesmaximal, characteristic, complemented
8#13069189C211yesmaximal, characteristic, complemented
9#13068711C211yesmaximal, characteristic
10#13068702C211yesmaximal, characteristic
11#13068649C211yesmaximal, characteristic
12#13068516C211yesmaximal, characteristic, complemented
13#106×Dic11C211yesmaximal, characteristic, complemented
14#13068397C211yesmaximal, characteristic
15C2×C11×#428C211yesmaximal, characteristic
16C22×C11×M16C2211yescharacteristic
17C2×C11×#117C2211yescharacteristic
18C22×C11×C4⋊C4C2211yescharacteristic
19C11×#428C418yescomplemented
20C2×C11×#107C2211yescharacteristic
21C2×C11×#107C2211yescharacteristic
22C2×C11×#106C2211yescharacteristic
23C2×C11×#106C2211yescharacteristic
24#10622825—21no—
25#10622825C2211yescharacteristic
26#10622825C2211yescharacteristic
27C4×C22⋊Dic11—21no—
28C4×C22⋊Dic11C2211yescharacteristic
29C2×C22⋊(C11⋊C8)C2211yescharacteristic
30C2×#66882C2211yescharacteristic
31C2×#66881C2211yescharacteristic
32C2×#66879C2211yescharacteristic
33C2×C8×Dic11C2211yescharacteristic
34#10622598C2211yescharacteristic
35#10622598C2211yescharacteristic
36#10622598C2211yescharacteristic
37#10622598C2211yescharacteristic
38#10622594—21no—
39#10622594—21no—
40C4⋊C4×Dic11C2211yescharacteristic
41C4⋊C4×Dic11C2211yescharacteristic
42C4⋊C4×Dic11C2211yescharacteristic
43C4⋊C4×Dic11C2211yescharacteristic
44#10622564—21no—
45#10622564—21no—
46#10622549—21no—
47#10622545—21no—
48#10622189C2211yescharacteristic
49#10622189C2211yescharacteristic
50#10622188C2211yescharacteristic
51#10622188C2211yescharacteristic
52#10622167C2211yescharacteristic
53#10622167C2211yescharacteristic
54#10622167C2211yescharacteristic
55#10622167C2211yescharacteristic
56#10622167C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622167C2211yescharacteristic
59#10622167C2211yescharacteristic
60C23×C4×C11—21no—
61C23×C4×C11C2311yescharacteristic
62C2×C11×M16—22no—
63C2×C11×M16—22no—
64C2×C11×M16C2×C414yes—
65C22×C8×C11C2311yescharacteristic
66C22×C8×C11C2311yescharacteristic
67C11×#117—22no—
68C11×#117C2×C414yes—
69C2×C11×C4⋊C4—21no—
70C2×C11×C4⋊C4—22no—
71C2×C11×C4⋊C4C2×C414yes—
72C2×C11×C4⋊C4C2311yescharacteristic
73C2×C11×C4⋊C4C2311yescharacteristic
74C2×C11×C4⋊C4C2311yescharacteristic
75C2×C11×C4⋊C4C2311yescharacteristic
76C2×C11×C22⋊C4—21no—
77C2×C42×C11—21no—
78C2×C22⋊Dic11—21no—
79C2×C22⋊Dic11—21no—
80C2×C22⋊Dic11D411yescharacteristic
81C2×C22⋊Dic11D411yescharacteristic
82C2×C4⋊Dic11—21no—
83C2×C4⋊Dic11—21no—
84C2×C4⋊Dic11—21no—
85C2×C4⋊Dic11—21no—
86C2×C4⋊Dic11C2311yescharacteristic
87C2×C4⋊Dic11C2311yescharacteristic
88C2×C4⋊Dic11C2311yescharacteristic
89C2×C4⋊Dic11C2311yescharacteristic
90C2×C4×Dic11—21no—
91C2×C4×Dic11—21no—
92C2×C4×Dic11—21no—
93C2×C4×Dic11—21no—
94C2×C4×Dic11C2311yescharacteristic
95C2×C4×Dic11C2311yescharacteristic
96C22×C11⋊C8C2311yescharacteristic
97C22×C11⋊C8C2311yescharacteristic
98C11×#107C2×C414yes—
99C11×#107C2×C414yes—
100C11×#106C2×C414yes—
101C11×#106C2×C414yes—
102C11⋊#95—21no—
103C11⋊#95—21no—
104C11⋊#95—21no—
105C11⋊#95—21no—
106C11⋊#95—21no—
107C11⋊#95—21no—
108C11⋊#95—21no—
109C11⋊#95—21no—
110C11⋊#95—21no—
111C11⋊#95—21no—
112C11⋊#95D411yescharacteristic
113C11⋊#95D411yescharacteristic
114C22⋊(C11⋊C8)—22no—
115#66882—22no—
116#66881—22no—
117#66879—22no—
118C8×Dic11—22no—
119#22621—111nomaximal, Sylow
120C24×C11C2×D411yescharacteristic
121C22×C4×C11—21no—
122C22×C4×C11—21no—
123C22×C4×C11—21no—
124C22×C4×C11—21no—
125C22×C4×C11—21no—
126C22×C4×C11—21no—
127C22×C4×C11—21no—
128C22×C4×C11—21no—
129C22×C4×C11—24no—
130C22×C4×C11—81no—
131C22×C4×C11—81no—
132C22×C4×C11C22×C412yes—
133C22×C4×C11C2×D411yescharacteristic
134C22×C4×C11#4112yes—
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
144C11×M16—28no—
145C2×C8×C11—21no—
146C2×C8×C11—21no—
147C2×C8×C11C22×C412yes—
148C2×C8×C11C22×C412yes—
149C2×C8×C11#4112yes—
150C2×C8×C11#4112yes—
151C11×C4⋊C4—24no—
152C11×C4⋊C4—21no—
153C11×C4⋊C4—21no—
154C11×C4⋊C4—21no—
155C11×C4⋊C4—21no—
156C11×C4⋊C4C22×C412yes—
157C11×C4⋊C4C22×C412yes—
158C11×C4⋊C4C22×C412yes—
159C11×C4⋊C4C22×C412yes—
160C11×C22⋊C4—24no—
161C42×C11—24no—
162C22⋊Dic11—22no—
163C22⋊Dic11—41no—
164C22⋊Dic11—42no—
165C22⋊Dic11—81no—
166C4⋊Dic11—21no—
167C4⋊Dic11—21no—
168C4⋊Dic11—21no—
169C4⋊Dic11—21no—
170C4⋊Dic11—21no—
171C4⋊Dic11—21no—
172C4⋊Dic11—21no—
173C4⋊Dic11—21no—
174C4⋊Dic11—81no—
175C4⋊Dic11—81no—
176C4⋊Dic11—81no—
177C4⋊Dic11—81no—
178C4×Dic11—21no—
179C4×Dic11—21no—
180C4×Dic11—21no—
181C4×Dic11—21no—
182C4×Dic11—42no—
183C4×Dic11—42no—
184C4×Dic11—81no—
185C4×Dic11—81no—
186C2×C11⋊C8—21no—
187C2×C11⋊C8—21no—
188C2×C11⋊C8—21no—
189C2×C11⋊C8—21no—
190C2×C11⋊C8—21no—
191C2×C11⋊C8—21no—
192C2×#428D1111yescharacteristic
193#2346—111no—
194#2345—111no—
195#1943—111no—
196#1942—111no—
197#1921—111no—
198#1920—111no—
199#1919—111no—
200#1918—111no—
201#1825—111no—
202#1823—111no—
203#1809—111no—
204#1776—111no—
205C4×#106—111no—
206#1753—111no—
207C23×C11—21no—
208C23×C11—21no—
209C23×C11—21no—
210C23×C11—21no—
211C23×C11—21no—
212C23×C11—21no—
213C23×C11C4×D412yes—
214C23×C11C22×D411yescharacteristic
215C2×C4×C11—21no—
216C2×C4×C11—21no—
217C2×C4×C11—22no—
218C2×C4×C11—22no—
219C2×C4×C11—22no—
220C2×C4×C11—22no—
221C2×C4×C11—22no—
222C2×C4×C11—22no—
223C2×C4×C11—22no—
224C2×C4×C11—22no—
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×C11—84no—
234C2×C4×C11C4×D412yes—
235C2×C4×C11C23×C411yescharacteristic
236C2×C4×C11C2×#4111yescharacteristic
237C2×C4×C11C2×#4111yescharacteristic
238C2×C4×C11C2×#4111yescharacteristic
239C2×C4×C112−1+411yescharacteristic
240C2×C4×C112−1+411yescharacteristic
241C2×Dic11—21no—
242C2×Dic11—21no—
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—41no—
253C2×Dic11—41no—
254C2×Dic11—41no—
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#13712yes—
265C8×C11—22no—
266C8×C11#11714yes—
267C11⋊C8—41no—
268C11⋊C8—41no—
269C22×M16C2×D1111yescharacteristic
270C2×#117C2×D1111yescharacteristic
271C22×C4⋊C4C2×D1111yescharacteristic
272#428Dic1118yescomplemented
273C2×#107—111no—
274C2×#107C2×D1111yescharacteristic
275C2×#107C2×D1111yescharacteristic
276C2×#106—111no—
277C2×#106C2×D1111yescharacteristic
278C2×#106C2×D1111yescharacteristic
279C2×C22⋊C8—111no—
280C2×#97—111no—
281C2×C4×C8—111no—
282#389—111no—
283#389—111no—
284#389—111no—
285#389—111no—
286#388—221no—
287#388—221no—
288#387—221no—
289#387—221no—
290#382—221no—
291#380—111no—
292#380—111no—
293#380—221no—
294C4×C4⋊C4—111no—
295C4×C4⋊C4—111no—
296C4×C4⋊C4—111no—
297C4×C4⋊C4—111no—
298C4×C22⋊C4—111no—
299C4×C22⋊C4—221no—
300#376—221no—
301#340—111no—
302#340—111no—
303#340—111no—
304#340—111no—
305#340—111no—
306#340—111no—
307#340—111no—
308#340—111no—
309#340—111no—
310#340—111no—
311#336—111no—
312#336—111no—
313C22×C11—22no—
314C22×C11—22no—
315C22×C11—22no—
316C22×C11—41no—
317C22×C11—41no—
318C22×C11—41no—
319C22×C11—41no—
320C22×C11C2×C4×D411yescharacteristic
321C22×C11#54711yescharacteristic
322C22×C11#54711yescharacteristic
323C22×C11C2×#13711yescharacteristic
324C22×C11#57511yescharacteristic
325C22×C11#57611yescharacteristic
326C22×C11#57711yescharacteristic
327C4×C11—22no—
328C4×C11—42no—
329C4×C11—42no—
330C4×C11—42no—
331C4×C11—42no—
332C4×C11C2×#11711yescharacteristic
333C4×C11#51911yescharacteristic
334C4×C11#55211yescharacteristic
335C4×C11#55211yescharacteristic
336Dic11—22no—
337Dic11—41no—
338Dic11—41no—
339Dic11—41no—
340Dic11—81no—
341Dic11—81no—
342Dic11—81no—
343Dic11—81no—
344C23×C4—21no—
345C23×C4C22×D1111yescharacteristic
346C2×M16—22no—
347C2×M16—22no—
348C2×M16C2×Dic1114yes—
349C22×C8—111no—
350C22×C8—111no—
351C22×C8C22×D1111yescharacteristic
352C22×C8C22×D1111yescharacteristic
353#117—22no—
354#117C2×Dic1114yes—
355C2×C4⋊C4—21no—
356C2×C4⋊C4—22no—
357C2×C4⋊C4—111no—
358C2×C4⋊C4—111no—
359C2×C4⋊C4—111no—
360C2×C4⋊C4—111no—
361C2×C4⋊C4—221no—
362C2×C4⋊C4—221no—
363C2×C4⋊C4—221no—
364C2×C4⋊C4—221no—
365C2×C4⋊C4C2×Dic1114yes—
366C2×C4⋊C4C22×D1111yescharacteristic
367C2×C4⋊C4C22×D1111yescharacteristic
368C2×C4⋊C4C22×D1111yescharacteristic
369C2×C4⋊C4C22×D1111yescharacteristic
370C2×C22⋊C4—21no—
371C2×C22⋊C4—111no—
372C2×C22⋊C4—111no—
373C2×C22⋊C4—221no—
374C2×C22⋊C4—221no—
375C2×C42—21no—
376C2×C42—111no—
377C2×C42—111no—
378C2×C42—221no—
379C2×C42—221no—
380C2×C42—221no—
381C2×C42—221no—
382#107—222no—
383#107C2×Dic1114yes—
384#107C2×Dic1114yes—
385#106—222no—
386#106C2×Dic1114yes—
387#106C2×Dic1114yes—
388C22⋊C8—222no—
389#97—222no—
390C4×C8—222no—
391#95—111no—
392#95—111no—
393#95—221no—
394#95—221no—
395#95—221no—
396#95—221no—
397#95—221no—
398#95—221no—
399#95—221no—
400#95—221no—
401#95—221no—
402#95—221no—
403C2×C11—42no—
404C2×C11#234411yescharacteristic
405C2×C11C4×#13711yescharacteristic
406C2×C11#294611yescharacteristic
407C2×C11#334411yescharacteristic
408C2×C11#334711yescharacteristic
409C2×C11#335111yescharacteristic
410C2×C11#335711yescharacteristic
411C24D4×D1111yescharacteristic
412C22×C4—21no—
413C22×C4—21no—
414C22×C4—21no—
415C22×C4—21no—
416C22×C4—21no—
417C22×C4—21no—
418C22×C4—21no—
419C22×C4—21no—
420C22×C4—24no—
421C22×C4—81no—
422C22×C4—81no—
423C22×C4—111no—
424C22×C4—111no—
425C22×C4—111no—
426C22×C4—111no—
427C22×C4—221no—
428C22×C4—221no—
429C22×C4—221no—
430C22×C4—221no—
431C22×C4D4×D1111yescharacteristic
432C22×C4#434112yes—
433C22×C4C22×Dic1112yes—
434C22×C4C23×D1111yescharacteristic
435M16—28no—
436C2×C8—21no—
437C2×C8—21no—
438C2×C8—221no—
439C2×C8—221no—
440C2×C8—221no—
441C2×C8—221no—
442C2×C8—221no—
443C2×C8—221no—
444C2×C8#433912yes—
445C2×C8#433912yes—
446C2×C8C22×Dic1112yes—
447C2×C8C22×Dic1112yes—
448C4⋊C4—24no—
449C4⋊C4—21no—
450C4⋊C4—21no—
451C4⋊C4—21no—
452C4⋊C4—21no—
453C4⋊C4—221no—
454C4⋊C4—221no—
455C4⋊C4—221no—
456C4⋊C4—221no—
457C4⋊C4—221no—
458C4⋊C4—221no—
459C4⋊C4—221no—
460C4⋊C4—221no—
461C4⋊C4—881no—
462C4⋊C4—881no—
463C4⋊C4—881no—
464C4⋊C4—881no—
465C4⋊C4C22×Dic1112yes—
466C4⋊C4C22×Dic1112yes—
467C4⋊C4C22×Dic1112yes—
468C4⋊C4C22×Dic1112yes—
469C22⋊C4—24no—
470C22⋊C4—222no—
471C22⋊C4—441no—
472C22⋊C4—442no—
473C22⋊C4—881no—
474C42—24no—
475C42—221no—
476C42—221no—
477C42—221no—
478C42—221no—
479C42—442no—
480C42—442no—
481C42—881no—
482C42—881no—
483C11#2262111yescharacteristic, complemented, Sylow
484C23—21no—
485C23—21no—
486C23—21no—
487C23—21no—
488C23—21no—
489C23—21no—
490C23D4×Dic1112yes—
491C23C2×D4×D1111yescharacteristic
492C2×C4—21no—
493C2×C4—21no—
494C2×C4—22no—
495C2×C4—22no—
496C2×C4—22no—
497C2×C4—22no—
498C2×C4—22no—
499C2×C4—22no—
500C2×C4—22no—
501C2×C4—22no—
502C2×C4—41no—
503C2×C4—41no—
504C2×C4—41no—
505C2×C4—41no—
506C2×C4—41no—
507C2×C4—41no—
508C2×C4—41no—
509C2×C4—41no—
510C2×C4—84no—
511C2×C4—112no—
512C2×C4—221no—
513C2×C4—221no—
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—441no—
524C2×C4—441no—
525C2×C4—441no—
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×C4D4×Dic1112yes—
536C2×C4C2×#433911yescharacteristic
537C2×C4C2×#433911yescharacteristic
538C2×C4C2×#434111yescharacteristic
539C2×C4#6704011yescharacteristic
540C2×C4#6704011yescharacteristic
541C2×C4C23×Dic1111yescharacteristic
542C8—22no—
543C8—441no—
544C8—441no—
545C8#6697914yes—
546C22—22no—
547C22—22no—
548C22—22no—
549C22—41no—
550C22—41no—
551C22—41no—
552C22—41no—
553C22#1062303811yescharacteristic
554C22#1062303811yescharacteristic
555C22#1062330511yescharacteristic
556C22#1062330611yescharacteristic
557C22D11×#13711yescharacteristic
558C22#1062330811yescharacteristic
559C22C2×D4×Dic1111yescharacteristic
560C4—22no—
561C4—42no—
562C4—42no—
563C4—42no—
564C4—42no—
565C4—222no—
566C4—441no—
567C4—441no—
568C4—441no—
569C4—881no—
570C4—881no—
571C4—881no—
572C4—881no—
573C4#1062304411yescharacteristic
574C4#1062304411yescharacteristic
575C4C2×#6697911yescharacteristic
576C4#1062334311yescharacteristic
577C2—42no—
578C2#1307148511yescharacteristic
579C2#137×Dic1111yescharacteristic
580C2#1307744911yescharacteristic
581C2#1308107211yescharacteristic
582C2#1308111711yescharacteristic
583C2#1308117711yescharacteristic
584C2#1308123811yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC2×C11×#428C2
socleC23×C11C22×D4
prime radicalC24×C11C2×D4
cosocleC22×C4×C11C24
hypercenterC2×#428D11
hypocenterC11#22621
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#428

Complements

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

NH ≅ G/Ntype
3. #13069355C2semidirect
4. #13069350C2semidirect
5. #13069210C2semidirect
6. #13069203C2semidirect
7. #13069196C2semidirect
8. #13069189C2semidirect
12. #13068516C2semidirect
13. #106×Dic11C2semidirect
19. C11×#428C4semidirect
272. #428Dic11semidirect
483. C11#22621semidirect

Maximal subgroups

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

subgroupindex
#130715012
#130714932
#130693552
#130693502
#130692102
#130692032
#130691962
#130691892
#130687112
#130687022
#130686492
#130685162
#106×Dic112
#130683972
C2×C11×#4282
#2262111