Finite Group Databasebeta

← #14730664

Subgroups — #14730664

Order 2816.

910 conjugacy classes of subgroups.

The subgroup lattice has 516 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079826C211yesmaximal, characteristic, complemented
2#13079357C211yesmaximal, characteristic, complemented
3#13078624C211yesmaximal, characteristic
4#13067879C212yesmaximal, complemented
5#13067823C212yesmaximal, complemented
6#13067781C212yesmaximal, complemented
7#13067750C212yesmaximal, complemented
8#13067326C211yesmaximal, characteristic, complemented
9#13067059C211yesmaximal, characteristic
10#13067037C211yesmaximal, characteristic, complemented
11C11×#3501C211yesmaximal, characteristic
12C11×#554—21no—
13C11×#554—22no—
14C11×#554—22no—
15C11×#554C2212yes—
16D4×Q8×C11—21no—
17D4×Q8×C11C2212yes—
18C11×#544—21no—
19C11×#543—22no—
20C11×#533C2211yescharacteristic
21C11×#533C2211yescharacteristic
22C2×C11×C22⋊Q8—22no—
23C11×#518—21no—
24C2×C4×D4×C11C2211yescharacteristic
25#10623001C2211yescharacteristic
26#10622831—21no—
27#10622706C2211yescharacteristic, complemented
28#10622705C2211yescharacteristic, complemented
29#10622695—21no—
30#10622694C2211yescharacteristic, complemented
31#10622693—21no—
32#10622692C2211yescharacteristic, complemented
33#10622665—22no—
34#10622658—22no—
35#10622643—22no—
36#10622634C2212yescomplemented
37#10622633C2212yescomplemented
38#10622632C2212yes—
39C4×#4324—22no—
40#10622621C2212yes—
41#10622584—21no—
42#10622539C2211yescharacteristic
43#10622538C2211yescharacteristic
44C4×#4318C2211yescharacteristic
45#10622185C2212yescomplemented
46#10622184C2212yescomplemented
47Q8⋊(C11⋊C8)C2212yescomplemented
48Q8⋊(C11⋊C8)C2212yescomplemented
49D4⋊(C11⋊C8)C2212yes—
50D4⋊(C11⋊C8)C2212yes—
51C22×Q8×C11—22no—
52C22×D4×C11D411yescharacteristic
53C23×C4×C11—21no—
54C11×C4⋊Q8—22no—
55C11×C4⋊Q8—22no—
56C11×C4⋊Q8D411yescharacteristic
57C11×C4⋊Q8D411yescharacteristic
58C11×C4⋊Q8C2311yescharacteristic
59C11×C4⋊Q8C2311yescharacteristic
60C11×#125—22no—
61C11×#125—22no—
62C11×#125—21no—
63C11×#125—21no—
64C11×C22⋊Q8—24no—
65C11×C22⋊Q8—24no—
66C11×C22⋊Q8—24no—
67C11×C22⋊Q8—24no—
68C11×C22⋊Q8—22no—
69C11×C22⋊Q8—24no—
70C11×C22⋊Q8—21no—
71C11×C22⋊Q8—21no—
72C11×C22⋊Q8—22no—
73C11×C22⋊Q8—24no—
74C11×C22⋊Q8D412yes—
75C11×C22⋊Q8D412yes—
76C4×Q8×C11—21no—
77C4×Q8×C11—21no—
78C4×Q8×C11D412yes—
79C4×Q8×C11C2312yes—
80C4×D4×C11—22no—
81C4×D4×C11—22no—
82C4×D4×C11—22no—
83C4×D4×C11—22no—
84C4×D4×C11—21no—
85C4×D4×C11—21no—
86C4×D4×C11D412yes—
87C4×D4×C11C2312yes—
88C11×#117—21no—
89C11×#117—21no—
90C2×C11×C4⋊C4—24no—
91C2×C11×C4⋊C4—22no—
92C2×C11×C4⋊C4D411yescharacteristic
93C2×C11×C22⋊C4—24no—
94C2×C11×C22⋊C4—21no—
95C2×C42×C11C2311yescharacteristic
96C2×#4326—22no—
97C2×#4324—22no—
98#66979—21no—
99#66977—21no—
100#66977—21no—
101C2×#4318—21no—
102#66923—21no—
103#66922C2311yescharacteristic
104#66922C2311yescharacteristic
105C4×Dic22—21no—
106C4×Dic22—21no—
107#66899—22no—
108#66899—22no—
109#66899—22no—
110#66896—22no—
111C22⋊(C11⋊C8)—21no—
112C22⋊(C11⋊C8)—21no—
113#66874—22no—
114#66874—22no—
115#66872—22no—
116#66872—22no—
117#66872—22no—
118#66871—22no—
119C4⋊(C11⋊C8)C2312yes—
120C4⋊(C11⋊C8)C2312yes—
121#66867—21no—
122#66867—21no—
123C4×C11⋊C8—21no—
124C4×C11⋊C8C2311yescharacteristic
125C4×C11⋊C8C2311yescharacteristic
126#18601—111nomaximal, Sylow
127C24×C11—21no—
128C2×Q8×C11—24no—
129C2×Q8×C11—21no—
130C2×Q8×C11—21no—
131C2×Q8×C11—84no—
132C2×Q8×C11C2×D412yes—
133C2×Q8×C11C2×D412yes—
134C2×D4×C11—24no—
135C2×D4×C11—21no—
136C2×D4×C11C2×D412yes—
137C22×C4×C11—24no—
138C22×C4×C11—24no—
139C22×C4×C11—21no—
140C22×C4×C11—22no—
141C22×C4×C11—22no—
142C22×C4×C11—82no—
143C22×C4×C11C2×D411yescharacteristic
144C22×C4×C11C2×D411yescharacteristic
145C22×C4×C11C2×D411yescharacteristic
146C2×Dic22—21no—
147C2×Dic22—21no—
148C11×C4⋊C4—24no—
149C11×C4⋊C4—24no—
150C11×C4⋊C4—24no—
151C11×C4⋊C4—22no—
152C11×C4⋊C4—22no—
153C11×C4⋊C4—21no—
154C11×C4⋊C4—21no—
155C11×C4⋊C4—21no—
156C11×C4⋊C4—21no—
157C11×C4⋊C4—22no—
158C11×C4⋊C4—21no—
159C11×C4⋊C4—21no—
160C11×C4⋊C4—21no—
161C11×C4⋊C4—22no—
162C11×C4⋊C4C2×D412yes—
163C11×C4⋊C4C2×D412yes—
164C11×C4⋊C4C2×D412yes—
165C11×C22⋊C4—24no—
166C11×C22⋊C4—24no—
167C11×C22⋊C4—22no—
168C11×C22⋊C4—22no—
169C11×C22⋊C4—22no—
170C11×C22⋊C4—22no—
171C42×C11—22no—
172C42×C11—22no—
173C42×C11C2×D411yescharacteristic
174C42×C11C2×D411yescharacteristic
175C42×C11C2×D411yescharacteristic
176C42×C11C2411yescharacteristic
177C22⋊Dic11—41no—
178#4326—44no—
179#4324—44no—
180C4⋊Dic11—21no—
181C4⋊Dic11—21no—
182C4⋊Dic11—21no—
183C4⋊Dic11—21no—
184Dic11⋊C4—41no—
185Dic11⋊C4—41no—
186C4×Dic11—41no—
187#4318—42no—
188C2×C11⋊C8—21no—
189C2×C11⋊C8—22no—
190C2×C11⋊C8—21no—
191C2×C11⋊C8—22no—
192#3501D1111yescharacteristic
193#3237—111no—
194#3185—111no—
195#3101—111no—
196#1651—112no—
197#1643—112no—
198#1637—112no—
199#1632—112no—
200#1554—111no—
201#1490—111no—
202#1485—111no—
203C23×C11—24no—
204C23×C11—22no—
205C23×C11—81no—
206C23×C11—81no—
207C23×C11#12011yescharacteristic
208Q8×C11—24no—
209Q8×C11—42no—
210Q8×C11—42no—
211Q8×C11—81no—
212Q8×C11—84no—
213D4×C11—24no—
214D4×C11—22no—
215D4×C11#13714yes—
216C2×C4×C11—22no—
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—41no—
224C2×C4×C11—44no—
225C2×C4×C11—82no—
226C2×C4×C11—81no—
227C2×C4×C11—84no—
228C2×C4×C11—84no—
229C2×C4×C11#12011yescharacteristic
230C2×C4×C11#12011yescharacteristic
231C2×C4×C11#12011yescharacteristic
232C2×C4×C11C22×D411yescharacteristic
233C2×C4×C11C22×D411yescharacteristic
234C2×C4×C11C22×D411yescharacteristic
235C2×Dic11—41no—
236C2×Dic11—41no—
237Dic22—42no—
238Dic22—42no—
239C11⋊C8—22no—
240C11⋊C8—41no—
241C11⋊C8—42no—
242C11⋊C8—42no—
243#554—21no—
244#554—22no—
245#554—22no—
246#554C2×D1112yes—
247D4×Q8—21no—
248D4×Q8C2×D1112yes—
249#544—21no—
250#543—22no—
251#533—111no—
252#533C2×D1111yescharacteristic
253#533C2×D1111yescharacteristic
254C2×C22⋊Q8—22no—
255#518—21no—
256C2×C4×D4C2×D1111yescharacteristic
257#501—221no—
258#498—111no—
259#494—111no—
260#491—221no—
261#487—111no—
262#487—111no—
263#485—222no—
264#483—221no—
265#477—112no—
266#476—112no—
267#475—112no—
268#470—222no—
269#461—112no—
270#450—221no—
271#441—222no—
272C4×SD16—222no—
273#432—111no—
274#431—111no—
275C4×M16—111no—
276#333—112no—
277#332—112no—
278Q8⋊C8—112no—
279Q8⋊C8—112no—
280D4⋊C8—112no—
281D4⋊C8—112no—
282C22×C11—21no—
283C22×C11—24no—
284C22×C11—21no—
285C22×C11—21no—
286C22×C11—42no—
287C22×C11—42no—
288C22×C11—84no—
289C22×C11C2×#12011yescharacteristic
290C4×C11—21no—
291C4×C11—21no—
292C4×C11—21no—
293C4×C11—21no—
294C4×C11—42no—
295C4×C11—42no—
296C4×C11—42no—
297C4×C11—42no—
298C4×C11—42no—
299C4×C11C2×#13712yes—
300C4×C11#57712yes—
301Dic11—81no—
302Dic11—81no—
303C22×Q8—22no—
304C22×D4C22⋊D1111yescharacteristic
305C23×C4—21no—
306C2×Q16—222no—
307C2×SD16—222no—
308C2×M16—221no—
309C4⋊Q8—22no—
310C4⋊Q8—22no—
311C4⋊Q8—111no—
312C4⋊Q8—111no—
313C4⋊Q8C22⋊D1111yescharacteristic
314C4⋊Q8C22⋊D1111yescharacteristic
315C4⋊Q8C22×D1111yescharacteristic
316C4⋊Q8C22×D1111yescharacteristic
317#125—22no—
318#125—22no—
319#125—21no—
320#125—21no—
321#125—221no—
322C22⋊Q8—24no—
323C22⋊Q8—24no—
324C22⋊Q8—24no—
325C22⋊Q8—24no—
326C22⋊Q8—22no—
327C22⋊Q8—24no—
328C22⋊Q8—21no—
329C22⋊Q8—21no—
330C22⋊Q8—22no—
331C22⋊Q8—24no—
332C22⋊Q8—221no—
333C22⋊Q8—221no—
334C22⋊Q8C22⋊D1112yes—
335C22⋊Q8C22⋊D1112yes—
336C4×Q8—21no—
337C4×Q8—21no—
338C4×Q8—221no—
339C4×Q8—221no—
340C4×Q8C22⋊D1112yes—
341C4×Q8C22×D1112yes—
342C4×D4—22no—
343C4×D4—22no—
344C4×D4—22no—
345C4×D4—22no—
346C4×D4—21no—
347C4×D4—21no—
348C4×D4C22⋊D1112yes—
349C4×D4C22×D1112yes—
350#117—21no—
351#117—21no—
352#117—221no—
353C2×C4⋊C4—24no—
354C2×C4⋊C4—22no—
355C2×C4⋊C4C22⋊D1111yescharacteristic
356C2×C22⋊C4—24no—
357C2×C22⋊C4—21no—
358C2×C42C22×D1111yescharacteristic
359#107—222no—
360#106—222no—
361#106—222no—
362#106—222no—
363C4⋊C8—112no—
364C4⋊C8—112no—
365#103—222no—
366#103—222no—
367#103—222no—
368#103—222no—
369#103—222no—
370#102—222no—
371C22⋊C8—221no—
372C22⋊C8—221no—
373#97—221no—
374#97—221no—
375C4×C8—111no—
376C4×C8—111no—
377C4×C8—221no—
378C2×C11—41no—
379C2×C11—44no—
380C2×C11#300411yescharacteristic
381C2×C11#300911yescharacteristic
382C2×C11#301811yescharacteristic
383C24—21no—
384C2×Q8—24no—
385C2×Q8—21no—
386C2×Q8—21no—
387C2×Q8—84no—
388C2×Q8—221no—
389C2×Q8—221no—
390C2×Q8C2×C22⋊D1112yes—
391C2×Q8C2×C22⋊D1112yes—
392C2×D4—24no—
393C2×D4—21no—
394C2×D4C2×C22⋊D1112yes—
395C22×C4—24no—
396C22×C4—24no—
397C22×C4—21no—
398C22×C4—22no—
399C22×C4—22no—
400C22×C4—82no—
401C22×C4C2×C22⋊D1111yescharacteristic
402C22×C4C2×C22⋊D1111yescharacteristic
403C22×C4C2×C22⋊D1111yescharacteristic
404Q16—444no—
405SD16—444no—
406M16—442no—
407C2×C8—221no—
408C2×C8—221no—
409C2×C8—222no—
410C2×C8—222no—
411C4⋊C4—24no—
412C4⋊C4—24no—
413C4⋊C4—24no—
414C4⋊C4—22no—
415C4⋊C4—22no—
416C4⋊C4—21no—
417C4⋊C4—21no—
418C4⋊C4—21no—
419C4⋊C4—21no—
420C4⋊C4—22no—
421C4⋊C4—21no—
422C4⋊C4—21no—
423C4⋊C4—21no—
424C4⋊C4—22no—
425C4⋊C4—221no—
426C4⋊C4—221no—
427C4⋊C4—221no—
428C4⋊C4—221no—
429C4⋊C4—441no—
430C4⋊C4—441no—
431C4⋊C4C2×C22⋊D1112yes—
432C4⋊C4C2×C22⋊D1112yes—
433C4⋊C4C2×C22⋊D1112yes—
434C22⋊C4—24no—
435C22⋊C4—24no—
436C22⋊C4—22no—
437C22⋊C4—22no—
438C22⋊C4—22no—
439C22⋊C4—22no—
440C22⋊C4—441no—
441C42—22no—
442C42—22no—
443C42—441no—
444C42C2×C22⋊D1111yescharacteristic
445C42C2×C22⋊D1111yescharacteristic
446C42C2×C22⋊D1111yescharacteristic
447C42C23×D1111yescharacteristic
448C11#1860111yescharacteristic, complemented, Sylow
449C23—24no—
450C23—22no—
451C23—81no—
452C23—81no—
453C23#6700611yescharacteristic
454Q8—24no—
455Q8—42no—
456Q8—42no—
457Q8—81no—
458Q8—84no—
459Q8—442no—
460Q8—442no—
461D4—24no—
462D4—22no—
463D4#6699514yes—
464C2×C4—22no—
465C2×C4—22no—
466C2×C4—22no—
467C2×C4—22no—
468C2×C4—22no—
469C2×C4—22no—
470C2×C4—22no—
471C2×C4—41no—
472C2×C4—44no—
473C2×C4—82no—
474C2×C4—81no—
475C2×C4—84no—
476C2×C4—84no—
477C2×C4—441no—
478C2×C4—441no—
479C2×C4#6700611yescharacteristic
480C2×C4#6700611yescharacteristic
481C2×C4#6700611yescharacteristic
482C2×C4C22×C22⋊D1111yescharacteristic
483C2×C4C22×C22⋊D1111yescharacteristic
484C2×C4C22×C22⋊D1111yescharacteristic
485C8—222no—
486C8—441no—
487C8—442no—
488C8—442no—
489C22—21no—
490C22—24no—
491C22—21no—
492C22—21no—
493C22—42no—
494C22—42no—
495C22—84no—
496C22C2×#6700611yescharacteristic
497C4—21no—
498C4—21no—
499C4—21no—
500C4—21no—
501C4—42no—
502C4—42no—
503C4—42no—
504C4—42no—
505C4—42no—
506C4—881no—
507C4—881no—
508C4C2×#6699512yes—
509C4#1062336712yes—
510C2—41no—
511C2—44no—
512C2#1307785011yescharacteristic
513C2#1307789311yescharacteristic
514C2#1307796511yescharacteristic
subgroupG/H
centerC22C2×#67006
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#3501C2
socleC22×C11C2×#120
prime radicalC22×D4×C11D4
hypercenter#3501D11
hypocenterC11#18601
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3501

Complements

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

NH ≅ G/Ntype
1. #13079826C2semidirect
2. #13079357C2semidirect
4. #13067879C2semidirect
5. #13067823C2semidirect
6. #13067781C2semidirect
7. #13067750C2semidirect
8. #13067326C2semidirect
10. #13067037C2semidirect
27. #10622706C22semidirect
28. #10622705C22semidirect
30. #10622694C22semidirect
32. #10622692C22semidirect
36. #10622634C22semidirect
37. #10622633C22semidirect
45. #10622185C22semidirect
46. #10622184C22semidirect
47. Q8⋊(C11⋊C8)C22semidirect
48. Q8⋊(C11⋊C8)C22semidirect
448. C11#18601semidirect

Maximal subgroups

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

subgroupindex
#130798262
#130793572
#130786242
#130678792
#130678232
#130677812
#130677502
#130673262
#130670592
#130670372
C11×#35012
#1860111