Finite Group Databasebeta

← #14754347

Subgroups — #14754347

Order 2816.

810 conjugacy classes of subgroups.

The subgroup lattice has 590 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622735C211yesmaximal, characteristic
2#13071223C211yesmaximal, characteristic
3#13071223C211yesmaximal, characteristic
4#13068783C211yesmaximal, characteristic, complemented
5#13068781C211yesmaximal, characteristic, complemented
6#13068745C211yesmaximal, characteristic, complemented
7#13068742C211yesmaximal, characteristic, complemented
8#13068649C211yesmaximal, characteristic
9#13068643C211yesmaximal, characteristic
10#13068639C211yesmaximal, characteristic
11#13068512C211yesmaximal, characteristic, complemented
12#13068512C211yesmaximal, characteristic, complemented
13#107×Dic11C211yesmaximal, characteristic, complemented
14#106×Dic11C211yesmaximal, characteristic, complemented
15C11×#1809C211yesmaximal, characteristic
16C22×C11×M16C2211yescharacteristic
17C2×#66979C2211yescharacteristic
18C23×C11⋊C8C2211yescharacteristic
19C2×C11×#107C2211yescharacteristic
20C2×C11×#106C2211yescharacteristic
21C11×#380C2211yescharacteristic
22C11×#380C2211yescharacteristic
23#10622825C2211yescharacteristic
24#10622825C2211yescharacteristic
25#10622735C418yescomplemented
26C2×#66882C2211yescharacteristic
27C2×#66881C2211yescharacteristic
28C2×#66879C2211yescharacteristic
29C2×#66879C2211yescharacteristic
30C2×C8×Dic11C2211yescharacteristic
31C2×C8×Dic11C2211yescharacteristic
32#10622590C2211yescharacteristic
33#10622590C2211yescharacteristic
34#10622589C2211yescharacteristic
35#10622589C2211yescharacteristic
36C4⋊C4×Dic11C2211yescharacteristic
37C4⋊C4×Dic11C2211yescharacteristic
38C4⋊C4×Dic11C2211yescharacteristic
39C4⋊C4×Dic11C2211yescharacteristic
40C2×#66872C2211yescharacteristic
41C2×#66872C2211yescharacteristic
42C2×#66871C2211yescharacteristic
43C2×#66871C2211yescharacteristic
44#10622558—21no—
45#10622558—21no—
46#10622557—21no—
47#10622557—21no—
48#10622267—21no—
49#10622267—21no—
50#10622266—21no—
51#10622266—21no—
52C11×#340C2211yescharacteristic
53C11×#340C2211yescharacteristic
54#10622189C2211yescharacteristic
55#10622189C2211yescharacteristic
56#10622167C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622167C2211yescharacteristic
59#10622167C2211yescharacteristic
60C23×C4×C11C2311yescharacteristic
61C2×C11×M16—22no—
62C2×C11×M16—22no—
63C2×C11×M16C2×C414yes—
64C22×C8×C11C2311yescharacteristic
65C22×C8×C11C2311yescharacteristic
66C2×C11×C4⋊C4C2311yescharacteristic
67C2×C11×C4⋊C4C2311yescharacteristic
68C2×C11×C4⋊C4C2311yescharacteristic
69C2×C11×C4⋊C4C2311yescharacteristic
70C2×C11×C22⋊C4—21no—
71C2×C11×C22⋊C4—21no—
72C2×C22⋊Dic11—21no—
73C2×C22⋊Dic11—21no—
74C2×C22⋊Dic11D411yescharacteristic
75C2×C22⋊Dic11D411yescharacteristic
76#66979C2×C414yes—
77#66979Q814yes—
78C2×C4⋊Dic11D411yescharacteristic
79C2×C4⋊Dic11D411yescharacteristic
80C2×C4⋊Dic11C2311yescharacteristic
81C2×C4⋊Dic11C2311yescharacteristic
82C2×C4⋊Dic11C2311yescharacteristic
83C2×C4⋊Dic11C2311yescharacteristic
84C2×Dic11⋊C4—21no—
85C2×Dic11⋊C4—21no—
86C2×Dic11⋊C4—21no—
87C2×Dic11⋊C4—21no—
88C2×C4×Dic11—21no—
89C2×C4×Dic11—21no—
90C2×C4×Dic11—21no—
91C2×C4×Dic11—21no—
92C2×C4×Dic11C2311yescharacteristic
93C2×C4×Dic11C2311yescharacteristic
94C22×C11⋊C8—22no—
95C22×C11⋊C8—22no—
96C22×C11⋊C8C2×C414yes—
97C22×C11⋊C8C2311yescharacteristic
98C22×C11⋊C8C2311yescharacteristic
99C11×#107—22no—
100C11×#106—22no—
101C11×#95—21no—
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⋊#95—21no—
113#66882—22no—
114#66881—22no—
115#66879C2×C414yes—
116#66879C2×C414yes—
117C8×Dic11C2×C414yes—
118C8×Dic11C2×C414yes—
119#66872—22no—
120#66872—22no—
121#66871—22no—
122#66871—22no—
123#20822—111nomaximal, Sylow
124C24×C11C2×D411yescharacteristic
125C22×C4×C11—21no—
126C22×C4×C11—21no—
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×C11C22×C412yes—
134C22×C4×C11C2×D411yescharacteristic
135C22×C4×C11C2×Q812yes—
136C22×C4×C11C2411yescharacteristic
137C22×Dic11—21no—
138C22×Dic11—21no—
139C22×Dic11—21no—
140C22×Dic11—21no—
141C22×Dic11C2×D411yescharacteristic
142C22×Dic11C2×D411yescharacteristic
143C22×Dic11C2×D411yescharacteristic
144C22×Dic11C2×D411yescharacteristic
145C11×M16—28no—
146C2×C8×C11—21no—
147C2×C8×C11—21no—
148C2×C8×C11C22×C412yes—
149C2×C8×C11C22×C412yes—
150C2×C8×C11#4112yes—
151C2×C8×C11#4112yes—
152C11×C4⋊C4—21no—
153C11×C4⋊C4—21no—
154C11×C4⋊C4—21no—
155C11×C4⋊C4—21no—
156C11×C4⋊C4—21no—
157C11×C4⋊C4—21no—
158C11×C4⋊C4—21no—
159C11×C4⋊C4—21no—
160C11×C22⋊C4—81no—
161C11×C22⋊C4—81no—
162C22⋊Dic11—81no—
163C22⋊Dic11—81no—
164C22⋊Dic11C4⋊C414yes—
165C22⋊Dic11C4⋊C414yes—
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⋊Dic11C4⋊C414yes—
175C4⋊Dic11C4⋊C414yes—
176Dic11⋊C4—81no—
177Dic11⋊C4—81no—
178Dic11⋊C4—81no—
179Dic11⋊C4—81no—
180C4×Dic11—81no—
181C4×Dic11—81no—
182C4×Dic11—81no—
183C4×Dic11—81no—
184C4×Dic11C22×C412yes—
185C4×Dic11C22×C412yes—
186C4×Dic11C2×Q812yes—
187C4×Dic11C2×Q812yes—
188C2×C11⋊C8—28no—
189C2×C11⋊C8—21no—
190C2×C11⋊C8—21no—
191C2×C11⋊C8C22×C412yes—
192C2×C11⋊C8C22×C412yes—
193C2×C11⋊C8#4112yes—
194C2×C11⋊C8#4112yes—
195C2×#405—111no—
196#2314—111no—
197#2314—111no—
198#1847—111no—
199#1847—111no—
200#1835—111no—
201#1834—111no—
202#1809—111no—
203#1809D1111yescharacteristic
204#1808—111no—
205#1807—111no—
206#1776—111no—
207#1776—111no—
208C4×#107—111no—
209C4×#106—111no—
210C23×C11—21no—
211C23×C11—21no—
212C23×C11—21no—
213C23×C11—21no—
214C23×C11—21no—
215C23×C11—21no—
216C23×C11C2×C4⋊C412yes—
217C23×C11C22×D411yescharacteristic
218C2×C4×C11—21no—
219C2×C4×C11—21no—
220C2×C4×C11—22no—
221C2×C4×C11—22no—
222C2×C4×C11—22no—
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—41no—
233C2×C4×C11—41no—
234C2×C4×C11—41no—
235C2×C4×C11—41no—
236C2×C4×C11C2×C4⋊C412yes—
237C2×C4×C11C23×C411yescharacteristic
238C2×C4×C11C22×Q811yescharacteristic
239C2×C4×C11C2×#4111yescharacteristic
240C2×C4×C11C2×#4111yescharacteristic
241C2×C4×C11C2×#4111yescharacteristic
242C2×C4×C11C2×#4111yescharacteristic
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—41no—
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×Dic11C2×C4⋊C412yes—
264C2×Dic11C2×C4⋊C412yes—
265C2×Dic11C2×C4⋊C412yes—
266C2×Dic11C2×C4⋊C412yes—
267C8×C11—22no—
268C8×C11#11714yes—
269C11⋊C8—22no—
270C11⋊C8#11714yes—
271C22×M16C2×D1111yescharacteristic
272C23×C8—111no—
273C2×#117—111no—
274C2×#107—111no—
275C2×#107—111no—
276C2×#107—111no—
277C2×#107C2×D1111yescharacteristic
278C2×#106—111no—
279C2×#106—111no—
280C2×#106—111no—
281C2×#106C2×D1111yescharacteristic
282#405—118no—
283C2×#97—111no—
284C2×#97—111no—
285C2×C4×C8—111no—
286C2×C4×C8—111no—
287#388—221no—
288#388—221no—
289#388—221no—
290#388—221no—
291#387—221no—
292#387—221no—
293#387—221no—
294#387—221no—
295#384—111no—
296#384—111no—
297#382—111no—
298#382—111no—
299#380—111no—
300#380—111no—
301#380C2×D1111yescharacteristic
302#380C2×D1111yescharacteristic
303C4×C4⋊C4—111no—
304C4×C4⋊C4—111no—
305C4×C4⋊C4—111no—
306C4×C4⋊C4—111no—
307#340—111no—
308#340—111no—
309#340—111no—
310#340—111no—
311#340—111no—
312#340—111no—
313#340C2×D1111yescharacteristic
314#340C2×D1111yescharacteristic
315C22×C11—22no—
316C22×C11—22no—
317C22×C11—22no—
318C22×C11—41no—
319C22×C11—41no—
320C22×C11—41no—
321C22×C11—41no—
322C22×C11C22×C4⋊C411yescharacteristic
323C22×C11#53211yescharacteristic
324C22×C11#53211yescharacteristic
325C22×C11#57611yescharacteristic
326C22×C11#57711yescharacteristic
327C22×C11#57711yescharacteristic
328C22×C11#57811yescharacteristic
329C4×C11—22no—
330C4×C11—81no—
331C4×C11—81no—
332C4×C11—81no—
333C4×C11—81no—
334C4×C11C2×#11711yescharacteristic
335C4×C11C2×#11711yescharacteristic
336C4×C11#53311yescharacteristic
337C4×C11#53311yescharacteristic
338Dic11—22no—
339Dic11—22no—
340Dic11—22no—
341Dic11—22no—
342Dic11—81no—
343Dic11—81no—
344Dic11—81no—
345Dic11—81no—
346C23×C4C22×D1111yescharacteristic
347C2×M16—22no—
348C2×M16—22no—
349C2×M16C4×D1114yes—
350C22×C8—111no—
351C22×C8—114no—
352C22×C8—111no—
353C22×C8—222no—
354C22×C8—222no—
355C22×C8C22×D1111yescharacteristic
356C22×C8C22×D1111yescharacteristic
357#117—114no—
358#117—114no—
359C2×C4⋊C4—111no—
360C2×C4⋊C4—111no—
361C2×C4⋊C4—111no—
362C2×C4⋊C4—111no—
363C2×C4⋊C4—111no—
364C2×C4⋊C4—111no—
365C2×C4⋊C4—221no—
366C2×C4⋊C4—221no—
367C2×C4⋊C4—221no—
368C2×C4⋊C4—221no—
369C2×C4⋊C4C22×D1111yescharacteristic
370C2×C4⋊C4C22×D1111yescharacteristic
371C2×C4⋊C4C22×D1111yescharacteristic
372C2×C4⋊C4C22×D1111yescharacteristic
373C2×C22⋊C4—21no—
374C2×C22⋊C4—21no—
375C2×C22⋊C4—111no—
376C2×C22⋊C4—111no—
377C2×C22⋊C4—221no—
378C2×C22⋊C4—221no—
379C2×C42—111no—
380C2×C42—111no—
381C2×C42—221no—
382C2×C42—221no—
383C2×C42—221no—
384C2×C42—221no—
385#107—22no—
386#107—222no—
387#107—222no—
388#107—222no—
389#106—22no—
390#106—222no—
391#106—222no—
392#106—222no—
393#97—114no—
394#97—114no—
395C4×C8—114no—
396C4×C8—114no—
397#95—21no—
398#95—21no—
399#95—221no—
400#95—221no—
401#95—221no—
402#95—221no—
403#95—221no—
404#95—221no—
405#95—221no—
406#95—221no—
407#95—221no—
408#95—221no—
409C2×C11—42no—
410C2×C11#228511yescharacteristic
411C2×C11#291211yescharacteristic
412C2×C11#291311yescharacteristic
413C2×C11#317811yescharacteristic
414C2×C11#317811yescharacteristic
415C2×C11#317911yescharacteristic
416C2×C11#317911yescharacteristic
417C24D4×D1111yescharacteristic
418C22×C4—21no—
419C22×C4—21no—
420C22×C4—21no—
421C22×C4—21no—
422C22×C4—21no—
423C22×C4—21no—
424C22×C4—21no—
425C22×C4—21no—
426C22×C4—111no—
427C22×C4—111no—
428C22×C4—111no—
429C22×C4—111no—
430C22×C4—221no—
431C22×C4—221no—
432C22×C4—221no—
433C22×C4—221no—
434C22×C4C2×C4×D1112yes—
435C22×C4D4×D1111yescharacteristic
436C22×C4Q8×D1112yes—
437C22×C4C23×D1111yescharacteristic
438M16—28no—
439C2×C8—21no—
440C2×C8—21no—
441C2×C8—112no—
442C2×C8—112no—
443C2×C8—112no—
444C2×C8—112no—
445C2×C8—228no—
446C2×C8—221no—
447C2×C8—221no—
448C2×C8C2×C4×D1112yes—
449C2×C8C2×C4×D1112yes—
450C2×C8#434112yes—
451C2×C8#434112yes—
452C4⋊C4—21no—
453C4⋊C4—21no—
454C4⋊C4—21no—
455C4⋊C4—21no—
456C4⋊C4—21no—
457C4⋊C4—21no—
458C4⋊C4—21no—
459C4⋊C4—21no—
460C4⋊C4—114no—
461C4⋊C4—114no—
462C4⋊C4—221no—
463C4⋊C4—221no—
464C4⋊C4—221no—
465C4⋊C4—221no—
466C4⋊C4—221no—
467C4⋊C4—221no—
468C4⋊C4—221no—
469C4⋊C4—221no—
470C4⋊C4—881no—
471C4⋊C4—881no—
472C4⋊C4—881no—
473C4⋊C4—881no—
474C22⋊C4—81no—
475C22⋊C4—81no—
476C22⋊C4—114no—
477C22⋊C4—114no—
478C22⋊C4—881no—
479C22⋊C4—881no—
480C42—112no—
481C42—112no—
482C42—112no—
483C42—112no—
484C42—881no—
485C42—881no—
486C42—881no—
487C42—881no—
488C11#2082211yescharacteristic, complemented, Sylow
489C23—21no—
490C23—21no—
491C23—21no—
492C23—21no—
493C23—21no—
494C23—21no—
495C23C4⋊C4×D1112yes—
496C23C2×D4×D1111yescharacteristic
497C2×C4—21no—
498C2×C4—21no—
499C2×C4—22no—
500C2×C4—22no—
501C2×C4—22no—
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—41no—
512C2×C4—41no—
513C2×C4—41no—
514C2×C4—41no—
515C2×C4—112no—
516C2×C4—112no—
517C2×C4—112no—
518C2×C4—112no—
519C2×C4—221no—
520C2×C4—221no—
521C2×C4—221no—
522C2×C4—221no—
523C2×C4—221no—
524C2×C4—221no—
525C2×C4—221no—
526C2×C4—221no—
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—441no—
537C2×C4—441no—
538C2×C4—441no—
539C2×C4C4⋊C4×D1112yes—
540C2×C4C22×C4×D1111yescharacteristic
541C2×C4C2×#434111yescharacteristic
542C2×C4C2×#434111yescharacteristic
543C2×C4C2×Q8×D1111yescharacteristic
544C2×C4#41×D1111yescharacteristic
545C2×C4#41×D1111yescharacteristic
546C8—22no—
547C8—114no—
548C8—222no—
549C8#6693014yes—
550C22—22no—
551C22—22no—
552C22—22no—
553C22—41no—
554C22—41no—
555C22—41no—
556C22—41no—
557C22C2×C4⋊C4×D1111yescharacteristic
558C22#1062312711yescharacteristic
559C22#1062312711yescharacteristic
560C22#1062330511yescharacteristic
561C22#1062330611yescharacteristic
562C22#1062330911yescharacteristic
563C22#1062331011yescharacteristic
564C4—22no—
565C4—81no—
566C4—81no—
567C4—81no—
568C4—81no—
569C4—222no—
570C4—222no—
571C4—222no—
572C4—222no—
573C4—881no—
574C4—881no—
575C4—881no—
576C4—881no—
577C4C2×#6693011yescharacteristic
578C4D11×#11711yescharacteristic
579C4#1062315311yescharacteristic
580C4#1062315311yescharacteristic
581C2—42no—
582C2#1307101811yescharacteristic
583C2#1307721011yescharacteristic
584C2#1307721511yescharacteristic
585C2#1307927711yescharacteristic
586C2#1307928511yescharacteristic
587C2#1307929211yescharacteristic
588C2#1307930011yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1809C2
socleC23×C11C22×D4
prime radicalC24×C11C2×D4
cosocleC22×C4×C11C24
hypercenter#1809D11
hypocenterC11#20822
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1809

Complements

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

NH ≅ G/Ntype
4. #13068783C2semidirect
5. #13068781C2semidirect
6. #13068745C2semidirect
7. #13068742C2semidirect
11. #13068512C2semidirect
12. #13068512C2semidirect
13. #107×Dic11C2semidirect
14. #106×Dic11C2semidirect
25. #10622735C4semidirect
488. C11#20822semidirect

Maximal subgroups

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

subgroupindex
C2×#106227352
#130712232
#130687832
#130687812
#130687452
#130687422
#130686492
#130686432
#130686392
#130685122
#107×Dic112
#106×Dic112
C11×#18092
#2082211