Finite Group Databasebeta

← #14731412

Subgroups — #14731412

Order 2816.

882 conjugacy classes of subgroups.

The subgroup lattice has 532 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079932C211yesmaximal, characteristic
2#13079198C211yesmaximal, characteristic, complemented
3#13078421C211yesmaximal, characteristic, complemented
4#13067872C212yesmaximal, complemented
5#13067823C212yesmaximal, complemented
6#13067788C212yesmaximal, complemented
7#13067750C212yesmaximal, complemented
8#13067306C211yesmaximal, characteristic, complemented
9#13067067C211yesmaximal, characteristic
10C2×Q8⋊(C11⋊C8)C211yesmaximal, characteristic, complemented
11C11×#3507C211yesmaximal, characteristic
12C11×#559—21no—
13C11×#557—21no—
14C11×#556—22no—
15C11×#556C2212yes—
16C11×#554C2212yes—
17C11×#552—22no—
18C11×#539—22no—
19C11×#536—21no—
20C11×#533C2211yescharacteristic
21C11×#532C2211yescharacteristic
22C11×#529—22no—
23C11×#520—21no—
24C2×C4×Q8×C11C2211yescharacteristic
25#10623001C2211yescharacteristic
26#10622838—21no—
27#10622707—21no—
28#10622706C2211yescharacteristic
29#10622705C2211yescharacteristic
30#10622694C2211yescharacteristic
31#10622691C2211yescharacteristic
32#10622688—21no—
33#10622664—22no—
34#10622654—22no—
35C4×#4326—22no—
36#10622635—22no—
37#10622634C2212yes—
38#10622633C2212yes—
39#10622632C2212yes—
40#10622621C2212yes—
41#10622577—21no—
42#10622537C2211yescharacteristic
43C2×C4⋊(C11⋊C8)C2211yescharacteristic
44C2×C4×C11⋊C8C2211yescharacteristic
45#10622185C2212yes—
46#10622184C2212yes—
47Q8⋊(C11⋊C8)C2212yes—
48Q8⋊(C11⋊C8)C2212yes—
49D4⋊(C11⋊C8)C2212yes—
50D4⋊(C11⋊C8)C2212yes—
51C2×C11×#41—21no—
52C22×Q8×C11D411yescharacteristic
53C11×C4⋊Q8—22no—
54C11×C4⋊Q8D411yescharacteristic
55C11×C4⋊Q8C2311yescharacteristic
56C11×C4⋊Q8C2311yescharacteristic
57C11×#127D411yescharacteristic
58C11×#126—24no—
59C11×#126—24no—
60C11×#125—24no—
61C11×#125—22no—
62C11×#125—21no—
63C11×#124—22no—
64C11×#124—22no—
65C11×#124—21no—
66C11×#123—24no—
67C11×#123—24no—
68C11×C22⋊Q8—22no—
69C11×C22⋊Q8—22no—
70C11×C22⋊Q8—24no—
71C11×C22⋊Q8—21no—
72C11×C22⋊Q8D412yes—
73C11×#121—21no—
74C11×#121D412yes—
75C4×Q8×C11—22no—
76C4×Q8×C11—22no—
77C4×Q8×C11—21no—
78C4×Q8×C11—21no—
79C4×Q8×C11—21no—
80C4×Q8×C11D412yes—
81C4×Q8×C11D412yes—
82C4×Q8×C11C2312yes—
83C4×D4×C11—24no—
84C4×D4×C11—22no—
85C4×D4×C11—22no—
86C4×D4×C11—21no—
87C4×D4×C11C2312yes—
88C11×#117—24no—
89C11×#117—21no—
90C11×#117—22no—
91C2×C11×C4⋊C4—21no—
92C2×C11×C4⋊C4—22no—
93C2×C11×C4⋊C4D411yescharacteristic
94C2×C42×C11—21no—
95C2×C42×C11C2311yescharacteristic
96C2×#4326—22no—
97C2×#4324—22no—
98#66979—21no—
99#66977—21no—
100#66977—21no—
101C2×#4318—21no—
102C22×C11⋊C8—21no—
103C22×C11⋊C8—21no—
104#66923—21no—
105#66922C2311yescharacteristic
106#66922C2311yescharacteristic
107C4×Dic22—21no—
108C4×Dic22—21no—
109#66899—22no—
110#66899—22no—
111#66899—22no—
112#66896—22no—
113#66874—22no—
114#66874—22no—
115#66872—22no—
116#66872—22no—
117#66871—22no—
118#66871—22no—
119C4⋊(C11⋊C8)—21no—
120C4⋊(C11⋊C8)—21no—
121C4⋊(C11⋊C8)C2312yes—
122C4⋊(C11⋊C8)C2312yes—
123C4×C11⋊C8—21no—
124C4×C11⋊C8C2311yescharacteristic
125C4×C11⋊C8C2311yescharacteristic
126#18669—111nomaximal, Sylow
127C11×#41—42no—
128C11×#41—42no—
129C2×Q8×C11—21no—
130C2×Q8×C11—21no—
131C2×Q8×C11—21no—
132C2×Q8×C11—22no—
133C2×Q8×C11—22no—
134C2×Q8×C11C2×D412yes—
135C2×Q8×C11C2×D412yes—
136C2×D4×C11—22no—
137C2×D4×C11—21no—
138C2×D4×C11—21no—
139C2×D4×C11C2×D412yes—
140C22×C4×C11—21no—
141C22×C4×C11—24no—
142C22×C4×C11—21no—
143C22×C4×C11—22no—
144C22×C4×C11C2×D411yescharacteristic
145C22×C4×C11C2×D411yescharacteristic
146C22×C4×C11C2×D411yescharacteristic
147C2×Dic22—21no—
148C2×Dic22—21no—
149C11×C4⋊C4—24no—
150C11×C4⋊C4—24no—
151C11×C4⋊C4—24no—
152C11×C4⋊C4—22no—
153C11×C4⋊C4—21no—
154C11×C4⋊C4—22no—
155C11×C4⋊C4—21no—
156C11×C4⋊C4—22no—
157C11×C4⋊C4—21no—
158C11×C4⋊C4—22no—
159C11×C4⋊C4—21no—
160C11×C4⋊C4—21no—
161C11×C4⋊C4C2×D412yes—
162C11×C4⋊C4C2×D412yes—
163C11×C4⋊C4C2×D412yes—
164C11×C22⋊C4—24no—
165C11×C22⋊C4—24no—
166C11×C22⋊C4—24no—
167C11×C22⋊C4—22no—
168C11×C22⋊C4—22no—
169C11×C22⋊C4—22no—
170C42×C11—24no—
171C42×C11—22no—
172C42×C11—22no—
173C42×C11—22no—
174C42×C11C2×D411yescharacteristic
175C42×C11C2×D411yescharacteristic
176C42×C11C2×D411yescharacteristic
177C42×C11C2411yescharacteristic
178C22⋊Dic11—41no—
179#4326—44no—
180#4324—82no—
181C4⋊Dic11—21no—
182C4⋊Dic11—21no—
183C4⋊Dic11—21no—
184C4⋊Dic11—21no—
185Dic11⋊C4—41no—
186Dic11⋊C4—41no—
187C4×Dic11—41no—
188#4318—42no—
189C2×C11⋊C8—21no—
190C2×C11⋊C8—21no—
191C2×C11⋊C8—22no—
192C2×C11⋊C8—22no—
193C2×C11⋊C8—42no—
194C2×C11⋊C8—81no—
195#3507D1111yescharacteristic
196#3246—111no—
197#3170—111no—
198#3078—111no—
199#1650—112no—
200#1643—112no—
201#1638—112no—
202#1632—112no—
203#1550—111no—
204#1492—111no—
205C2×Q8⋊C8—111no—
206C23×C11—22no—
207C23×C11#12011yescharacteristic
208Q8×C11—22no—
209Q8×C11—22no—
210Q8×C11—42no—
211Q8×C11—41no—
212Q8×C11—41no—
213Q8×C11—42no—
214Q8×C11—42no—
215D4×C11—22no—
216D4×C11—22no—
217D4×C11—44no—
218D4×C11—42no—
219D4×C11—81no—
220C2×C4×C11—21no—
221C2×C4×C11—21no—
222C2×C4×C11—22no—
223C2×C4×C11—22no—
224C2×C4×C11—22no—
225C2×C4×C11—22no—
226C2×C4×C11—22no—
227C2×C4×C11—41no—
228C2×C4×C11—42no—
229C2×C4×C11—42no—
230C2×C4×C11—42no—
231C2×C4×C11—81no—
232C2×C4×C11—84no—
233C2×C4×C11#12011yescharacteristic
234C2×C4×C11#12011yescharacteristic
235C2×C4×C11#12011yescharacteristic
236C2×C4×C11#13512yes—
237C2×C4×C11#13712yes—
238C2×C4×C11C22×D411yescharacteristic
239C2×C4×C11C22×D411yescharacteristic
240C2×C4×C11C22×D411yescharacteristic
241C2×Dic11—41no—
242C2×Dic11—41no—
243Dic22—42no—
244Dic22—41no—
245Dic22—41no—
246C11⋊C8—22no—
247C11⋊C8—41no—
248C11⋊C8—42no—
249C11⋊C8—42no—
250#559—21no—
251#557—21no—
252#556—22no—
253#556C2×D1112yes—
254#554C2×D1112yes—
255#552—22no—
256#539—22no—
257#536—21no—
258#533—111no—
259#533C2×D1111yescharacteristic
260#532C2×D1111yescharacteristic
261#529—22no—
262#520—21no—
263C2×C4×Q8C2×D1111yescharacteristic
264#500—111no—
265#494—111no—
266#487—111no—
267#487—111no—
268#479—222no—
269#477—112no—
270#476—112no—
271#475—112no—
272#475—221no—
273#467—222no—
274#465—222no—
275#461—112no—
276#460—221no—
277C4×Q16—222no—
278#428—221no—
279#423—111no—
280C2×C4⋊C8—111no—
281#419—221no—
282C2×C4×C8—111no—
283#333—112no—
284#332—112no—
285Q8⋊C8—112no—
286Q8⋊C8—112no—
287D4⋊C8—112no—
288D4⋊C8—112no—
289C22×C11—21no—
290C22×C11—21no—
291C22×C11—42no—
292C22×C11—42no—
293C22×C11—42no—
294C22×C11#45212yes—
295C22×C11C2×#12011yescharacteristic
296C4×C11—21no—
297C4×C11—21no—
298C4×C11—21no—
299C4×C11—42no—
300C4×C11—42no—
301C4×C11—42no—
302C4×C11—42no—
303C4×C11—42no—
304C4×C11#45212yes—
305C4×C11C2×#13511yescharacteristic
306C4×C11C2×#13711yescharacteristic
307C4×C11#57711yescharacteristic
308C4×C11#57811yescharacteristic
309Dic11—81no—
310Dic11—81no—
311C2×#41—21no—
312C22×Q8C22⋊D1111yescharacteristic
313C2×Q16—222no—
314C2×SD16—222no—
315C2×M16—221no—
316C22×C8—221no—
317C22×C8—221no—
318C4⋊Q8—22no—
319C4⋊Q8—111no—
320C4⋊Q8—111no—
321C4⋊Q8C22⋊D1111yescharacteristic
322C4⋊Q8C22×D1111yescharacteristic
323C4⋊Q8C22×D1111yescharacteristic
324#127C22⋊D1111yescharacteristic
325#126—24no—
326#126—24no—
327#125—24no—
328#125—22no—
329#125—21no—
330#125—221no—
331#124—22no—
332#124—22no—
333#124—21no—
334#123—24no—
335#123—24no—
336C22⋊Q8—22no—
337C22⋊Q8—22no—
338C22⋊Q8—24no—
339C22⋊Q8—21no—
340C22⋊Q8—221no—
341C22⋊Q8—221no—
342C22⋊Q8C22⋊D1112yes—
343#121—21no—
344#121C22⋊D1112yes—
345C4×Q8—22no—
346C4×Q8—22no—
347C4×Q8—21no—
348C4×Q8—21no—
349C4×Q8—21no—
350C4×Q8—221no—
351C4×Q8—221no—
352C4×Q8C22⋊D1112yes—
353C4×Q8C22⋊D1112yes—
354C4×Q8C22×D1112yes—
355C4×D4—24no—
356C4×D4—22no—
357C4×D4—22no—
358C4×D4—21no—
359C4×D4C22×D1112yes—
360#117—24no—
361#117—21no—
362#117—22no—
363#117—221no—
364C2×C4⋊C4—21no—
365C2×C4⋊C4—22no—
366C2×C4⋊C4C22⋊D1111yescharacteristic
367C2×C42—21no—
368C2×C42C22×D1111yescharacteristic
369#107—222no—
370#107—222no—
371#106—222no—
372#106—222no—
373C4⋊C8—112no—
374C4⋊C8—112no—
375C4⋊C8—221no—
376C4⋊C8—221no—
377#103—222no—
378#103—222no—
379#103—222no—
380#103—222no—
381#103—222no—
382#102—222no—
383C4×C8—111no—
384C4×C8—111no—
385C4×C8—221no—
386C2×C11—22no—
387C2×C11—82no—
388C2×C11C2×#45211yescharacteristic
389C2×C11#301311yescharacteristic
390C2×C11#301811yescharacteristic
391#41—42no—
392#41—42no—
393C2×Q8—21no—
394C2×Q8—21no—
395C2×Q8—21no—
396C2×Q8—22no—
397C2×Q8—22no—
398C2×Q8—221no—
399C2×Q8—221no—
400C2×Q8C2×C22⋊D1112yes—
401C2×Q8C2×C22⋊D1112yes—
402C2×D4—22no—
403C2×D4—21no—
404C2×D4—21no—
405C2×D4C2×C22⋊D1112yes—
406C22×C4—21no—
407C22×C4—24no—
408C22×C4—21no—
409C22×C4—22no—
410C22×C4C2×C22⋊D1111yescharacteristic
411C22×C4C2×C22⋊D1111yescharacteristic
412C22×C4C2×C22⋊D1111yescharacteristic
413Q16—444no—
414SD16—882no—
415M16—442no—
416C2×C8—221no—
417C2×C8—221no—
418C2×C8—222no—
419C2×C8—222no—
420C2×C8—442no—
421C2×C8—881no—
422C4⋊C4—24no—
423C4⋊C4—24no—
424C4⋊C4—24no—
425C4⋊C4—22no—
426C4⋊C4—21no—
427C4⋊C4—22no—
428C4⋊C4—21no—
429C4⋊C4—22no—
430C4⋊C4—21no—
431C4⋊C4—22no—
432C4⋊C4—21no—
433C4⋊C4—21no—
434C4⋊C4—221no—
435C4⋊C4—221no—
436C4⋊C4—221no—
437C4⋊C4—221no—
438C4⋊C4—441no—
439C4⋊C4—441no—
440C4⋊C4C2×C22⋊D1112yes—
441C4⋊C4C2×C22⋊D1112yes—
442C4⋊C4C2×C22⋊D1112yes—
443C22⋊C4—24no—
444C22⋊C4—24no—
445C22⋊C4—24no—
446C22⋊C4—22no—
447C22⋊C4—22no—
448C22⋊C4—22no—
449C22⋊C4—441no—
450C42—24no—
451C42—22no—
452C42—22no—
453C42—22no—
454C42—441no—
455C42C2×C22⋊D1111yescharacteristic
456C42C2×C22⋊D1111yescharacteristic
457C42C2×C22⋊D1111yescharacteristic
458C42C23×D1111yescharacteristic
459C11#1866911yescharacteristic, complemented, Sylow
460C23—22no—
461C23#6700611yescharacteristic
462Q8—22no—
463Q8—22no—
464Q8—42no—
465Q8—42no—
466Q8—42no—
467Q8—41no—
468Q8—41no—
469Q8—442no—
470Q8—441no—
471Q8—441no—
472D4—22no—
473D4—22no—
474D4—44no—
475D4—42no—
476D4—81no—
477C2×C4—21no—
478C2×C4—21no—
479C2×C4—22no—
480C2×C4—22no—
481C2×C4—22no—
482C2×C4—22no—
483C2×C4—22no—
484C2×C4—41no—
485C2×C4—42no—
486C2×C4—42no—
487C2×C4—42no—
488C2×C4—81no—
489C2×C4—84no—
490C2×C4—441no—
491C2×C4—441no—
492C2×C4#6700312yes—
493C2×C4#6700412yes—
494C2×C4#6700611yescharacteristic
495C2×C4#6700611yescharacteristic
496C2×C4#6700611yescharacteristic
497C2×C4C22×C22⋊D1111yescharacteristic
498C2×C4C22×C22⋊D1111yescharacteristic
499C2×C4C22×C22⋊D1111yescharacteristic
500C8—222no—
501C8—441no—
502C8—442no—
503C8—442no—
504C22—21no—
505C22—21no—
506C22—42no—
507C22—42no—
508C22—42no—
509C22#1062285212yes—
510C22C2×#6700611yescharacteristic
511C4—21no—
512C4—21no—
513C4—21no—
514C4—42no—
515C4—42no—
516C4—42no—
517C4—42no—
518C4—42no—
519C4—881no—
520C4—881no—
521C4#1062285212yes—
522C4C2×#6700311yescharacteristic
523C4C2×#6700411yescharacteristic
524C4#1062336811yescharacteristic
525C4#1062336911yescharacteristic
526C2—22no—
527C2—82no—
528C2C2×#1062285211yescharacteristic
529C2#1307793111yescharacteristic
530C2#1307796511yescharacteristic
subgroupG/H
centerC22C2×#67006
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#3507C2
socleC22×C11C2×#120
prime radicalC11×#532C22
hypercenter#3507D11
hypocenterC11#18669
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3507

Complements

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

NH ≅ G/Ntype
2. #13079198C2semidirect
3. #13078421C2semidirect
4. #13067872C2semidirect
5. #13067823C2semidirect
6. #13067788C2semidirect
7. #13067750C2semidirect
8. #13067306C2semidirect
10. C2×Q8⋊(C11⋊C8)C2semidirect
459. C11#18669semidirect

Maximal subgroups

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

subgroupindex
#130799322
#130791982
#130784212
#130678722
#130678232
#130677882
#130677502
#130673062
#130670672
C2×Q8⋊(C11⋊C8)2
C11×#35072
#1866911