Finite Group Databasebeta

← #14729978

Subgroups — #14729978

Order 2816.

1146 conjugacy classes of subgroups.

The subgroup lattice has 478 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079158C211yesmaximal, characteristic, complemented
2#13078746C211yesmaximal, characteristic, complemented
3#13078715C211yesmaximal, characteristic
4#13067879C214yesmaximal, complemented
5#13067865C214yesmaximal, complemented
6#13067333C211yesmaximal, characteristic, complemented
7#13067063C211yesmaximal, characteristic, complemented
8#13067059C211yesmaximal, characteristic
9C2×D4×Q8×C11C211yesmaximal, characteristic
10C23×Q8×C11—21no—
11D4×Q8×C11—22no—
12D4×Q8×C11—22no—
13D4×Q8×C11—22no—
14D4×Q8×C11C2214yes—
15C2×C11×C4⋊Q8—21no—
16C2×C11×C4⋊Q8C2211yescharacteristic
17C2×C11×C22⋊Q8—21no—
18C2×C11×C22⋊Q8—22no—
19C2×C4×Q8×C11C2211yescharacteristic
20C2×C4×D4×C11—21no—
21C2×C4×D4×C11C2211yescharacteristic
22#10623001C2211yescharacteristic
23#10622841—21no—
24#10622831—21no—
25#10622693—22no—
26#10622692C2212yescomplemented
27#10622691C2212yescomplemented
28#10622644C2212yescomplemented
29#10622643—22no—
30#10622633C2212yescomplemented
31#10622632C2212yes—
32#10622631—22no—
33#10622620C2212yes—
34#10622584—21no—
35#10622583—21no—
36#10622577—22no—
37#10622539C2211yescharacteristic
38#10622539C2211yescharacteristic
39C4×#4318C2211yescharacteristic
40#10622185C2214yescomplemented
41Q8⋊(C11⋊C8)C2214yescomplemented
42D4⋊(C11⋊C8)C2214yes—
43C22×Q8×C11—22no—
44C22×Q8×C11—24no—
45C22×Q8×C11—24no—
46C22×Q8×C11—21no—
47C22×Q8×C11—48no—
48C22×Q8×C11D411yescharacteristic
49C22×D4×C11D411yescharacteristic
50C23×C4×C11—22no—
51C23×C4×C11—21no—
52C11×C4⋊Q8—24no—
53C11×C4⋊Q8—24no—
54C11×C4⋊Q8—21no—
55C11×C4⋊Q8—21no—
56C11×C4⋊Q8D412yes—
57C11×C4⋊Q8C2312yes—
58C11×C22⋊Q8—24no—
59C11×C22⋊Q8—28no—
60C11×C22⋊Q8—24no—
61C11×C22⋊Q8—28no—
62C4×Q8×C11—21no—
63C4×Q8×C11—21no—
64C4×Q8×C11D412yes—
65C4×Q8×C11C2312yes—
66C4×D4×C11—24no—
67C4×D4×C11—24no—
68C4×D4×C11—21no—
69C4×D4×C11—21no—
70C4×D4×C11D412yes—
71C4×D4×C11C2312yes—
72C2×C11×C4⋊C4—22no—
73C2×C11×C4⋊C4—21no—
74C2×C11×C4⋊C4—21no—
75C2×C11×C4⋊C4D412yes—
76C2×C11×C4⋊C4D411yescharacteristic
77C2×C11×C4⋊C4D411yescharacteristic
78C2×C11×C22⋊C4—22no—
79C2×C11×C22⋊C4—21no—
80C2×C42×C11—21no—
81C2×C42×C11C2311yescharacteristic
82C2×#4326—22no—
83C2×#4324—22no—
84#66979—21no—
85#66977—21no—
86#66977—21no—
87C2×#4318—21no—
88#66923—21no—
89#66922C2311yescharacteristic
90#66922C2311yescharacteristic
91C4×Dic22—21no—
92C4×Dic22—21no—
93#66899—22no—
94#66896—22no—
95C22⋊(C11⋊C8)—21no—
96C22⋊(C11⋊C8)—21no—
97#66874—22no—
98#66874—22no—
99#66872—24no—
100#66872—22no—
101#66871—24no—
102#66871—22no—
103C4⋊(C11⋊C8)C2312yes—
104C4⋊(C11⋊C8)C2312yes—
105#66867—21no—
106#66867—21no—
107#66867—21no—
108C4×C11⋊C8C2312yes—
109#18540—111nomaximal, Sylow
110C24×C11—21no—
111C2×Q8×C11—24no—
112C2×Q8×C11—28no—
113C2×Q8×C11—21no—
114C2×Q8×C11—22no—
115C2×Q8×C11—22no—
116C2×Q8×C11—48no—
117C2×Q8×C11—44no—
118C2×Q8×C11—416no—
119C2×Q8×C11—48no—
120C2×Q8×C11—48no—
121C2×Q8×C11C2×D412yes—
122C2×D4×C11—24no—
123C2×D4×C11—21no—
124C2×D4×C11C2×D412yes—
125C22×C4×C11—21no—
126C22×C4×C11—28no—
127C22×C4×C11—21no—
128C22×C4×C11—22no—
129C22×C4×C11—21no—
130C22×C4×C11—22no—
131C22×C4×C11—22no—
132C22×C4×C11—48no—
133C22×C4×C11—44no—
134C22×C4×C11C2×D411yescharacteristic
135C22×C4×C11C2×D411yescharacteristic
136C22×C4×C11C2×D411yescharacteristic
137C2×Dic22—21no—
138C2×Dic22—21no—
139C11×C4⋊C4—28no—
140C11×C4⋊C4—22no—
141C11×C4⋊C4—22no—
142C11×C4⋊C4—21no—
143C11×C4⋊C4—21no—
144C11×C4⋊C4—22no—
145C11×C4⋊C4—22no—
146C11×C4⋊C4—22no—
147C11×C4⋊C4C2×D414yes—
148C11×C4⋊C4C2×D412yes—
149C11×C4⋊C4C2×D412yes—
150C11×C22⋊C4—28no—
151C11×C22⋊C4—22no—
152C11×C22⋊C4—22no—
153C42×C11—22no—
154C42×C11—22no—
155C42×C11C2×D411yescharacteristic
156C42×C11C2×D411yescharacteristic
157C42×C11C2×D411yescharacteristic
158C42×C11C2411yescharacteristic
159C22⋊Dic11—41no—
160#4326—44no—
161#4324—44no—
162C4⋊Dic11—21no—
163C4⋊Dic11—21no—
164C4⋊Dic11—21no—
165C4⋊Dic11—21no—
166Dic11⋊C4—41no—
167Dic11⋊C4—41no—
168C4×Dic11—41no—
169#4318—24no—
170C2×C11⋊C8—22no—
171C2×C11⋊C8—22no—
172C2×C11⋊C8—22no—
173C2×D4×Q8D1111yescharacteristic
174#3165—111no—
175#3113—111no—
176#3110—111no—
177#1651—114no—
178#1649—114no—
179#1556—111no—
180#1491—111no—
181#1490—111no—
182C23×C11—24no—
183C23×C11—22no—
184C23×C11—42no—
185C23×C11—42no—
186C23×C11#12011yescharacteristic
187Q8×C11—24no—
188Q8×C11—22no—
189Q8×C11—416no—
190Q8×C11—44no—
191Q8×C11—44no—
192Q8×C11AGL(1,ℤ/8)14yes—
193D4×C11—24no—
194D4×C11—22no—
195D4×C11#13714yes—
196C2×C4×C11—24no—
197C2×C4×C11—22no—
198C2×C4×C11—22no—
199C2×C4×C11—22no—
200C2×C4×C11—22no—
201C2×C4×C11—22no—
202C2×C4×C11—24no—
203C2×C4×C11—22no—
204C2×C4×C11—416no—
205C2×C4×C11—44no—
206C2×C4×C11—44no—
207C2×C4×C11—42no—
208C2×C4×C11—42no—
209C2×C4×C11—44no—
210C2×C4×C11#12011yescharacteristic
211C2×C4×C11#12011yescharacteristic
212C2×C4×C11#12011yescharacteristic
213C2×C4×C11C22×D411yescharacteristic
214C2×C4×C11C22×D411yescharacteristic
215C2×C4×C11C22×D411yescharacteristic
216C2×Dic11—41no—
217C2×Dic11—41no—
218Dic22—42no—
219Dic22—42no—
220C11⋊C8—24no—
221C11⋊C8—42no—
222C11⋊C8—42no—
223C23×Q8—21no—
224D4×Q8—22no—
225D4×Q8—22no—
226D4×Q8—22no—
227D4×Q8C2×D1114yes—
228#533—111no—
229C2×C4⋊Q8—21no—
230C2×C4⋊Q8C2×D1111yescharacteristic
231C2×C22⋊Q8—21no—
232C2×C22⋊Q8—22no—
233C2×C4×Q8C2×D1111yescharacteristic
234C2×C4×D4—21no—
235C2×C4×D4C2×D1111yescharacteristic
236#501—222no—
237#500—112no—
238#498—112no—
239#484—221no—
240#483—221no—
241#475—112no—
242#474—112no—
243#462—112no—
244#461—112no—
245#451—221no—
246#450—221no—
247#441—222no—
248#440—222no—
249#432—111no—
250#432—111no—
251#428—222no—
252C4×M16—111no—
253#332—114no—
254Q8⋊C8—114no—
255D4⋊C8—114no—
256C22×C11—21no—
257C22×C11—21no—
258C22×C11—24no—
259C22×C11—48no—
260C22×C11—42no—
261C22×C11—42no—
262C22×C11#45612yes—
263C22×C11C2×#12011yescharacteristic
264C4×C11—24no—
265C4×C11—21no—
266C4×C11—21no—
267C4×C11—21no—
268C4×C11—21no—
269C4×C11—44no—
270C4×C11—42no—
271C4×C11—42no—
272C4×C11C2×AGL(1,ℤ/8)12yes—
273C4×C11C2×#13712yes—
274Dic11—81no—
275Dic11—81no—
276C22×Q8—22no—
277C22×Q8—24no—
278C22×Q8—24no—
279C22×Q8—21no—
280C22×Q8—48no—
281C22×Q8C22⋊D1111yescharacteristic
282C22×D4C22⋊D1111yescharacteristic
283C23×C4—22no—
284C23×C4—21no—
285C2×Q16—222no—
286C2×SD16—222no—
287C2×M16—221no—
288C4⋊Q8—24no—
289C4⋊Q8—24no—
290C4⋊Q8—21no—
291C4⋊Q8—21no—
292C4⋊Q8—111no—
293C4⋊Q8—111no—
294C4⋊Q8C22⋊D1112yes—
295C4⋊Q8C22×D1112yes—
296#125—221no—
297C22⋊Q8—24no—
298C22⋊Q8—28no—
299C22⋊Q8—24no—
300C22⋊Q8—28no—
301C22⋊Q8—221no—
302C22⋊Q8—221no—
303C4×Q8—21no—
304C4×Q8—21no—
305C4×Q8—221no—
306C4×Q8—221no—
307C4×Q8C22⋊D1112yes—
308C4×Q8C22×D1112yes—
309C4×D4—24no—
310C4×D4—24no—
311C4×D4—21no—
312C4×D4—21no—
313C4×D4C22⋊D1112yes—
314C4×D4C22×D1112yes—
315#117—221no—
316C2×C4⋊C4—22no—
317C2×C4⋊C4—21no—
318C2×C4⋊C4—21no—
319C2×C4⋊C4C22⋊D1111yescharacteristic
320C2×C4⋊C4C22⋊D1111yescharacteristic
321C2×C4⋊C4C22⋊D1112yes—
322C2×C22⋊C4—22no—
323C2×C22⋊C4—21no—
324C2×C42—21no—
325C2×C42C22×D1111yescharacteristic
326#107—224no—
327#107—222no—
328#106—224no—
329#106—222no—
330C4⋊C8—112no—
331C4⋊C8—112no—
332#103—222no—
333#103—222no—
334#103—222no—
335#102—222no—
336C22⋊C8—221no—
337C22⋊C8—221no—
338#97—221no—
339#97—221no—
340#97—221no—
341C4×C8—112no—
342C2×C11—22no—
343C2×C11—44no—
344C2×C11#300311yescharacteristic
345C2×C11#300411yescharacteristic
346C2×C11C2×#45611yescharacteristic
347C24—21no—
348C2×Q8—24no—
349C2×Q8—28no—
350C2×Q8—21no—
351C2×Q8—22no—
352C2×Q8—22no—
353C2×Q8—48no—
354C2×Q8—44no—
355C2×Q8—416no—
356C2×Q8—48no—
357C2×Q8—48no—
358C2×Q8—221no—
359C2×Q8—221no—
360C2×Q8C2×C22⋊D1112yes—
361C2×D4—24no—
362C2×D4—21no—
363C2×D4C2×C22⋊D1112yes—
364C22×C4—21no—
365C22×C4—28no—
366C22×C4—21no—
367C22×C4—22no—
368C22×C4—21no—
369C22×C4—22no—
370C22×C4—22no—
371C22×C4—48no—
372C22×C4—44no—
373C22×C4C2×C22⋊D1111yescharacteristic
374C22×C4C2×C22⋊D1111yescharacteristic
375C22×C4C2×C22⋊D1111yescharacteristic
376Q16—444no—
377SD16—444no—
378M16—224no—
379C2×C8—222no—
380C2×C8—222no—
381C2×C8—222no—
382C4⋊C4—28no—
383C4⋊C4—22no—
384C4⋊C4—22no—
385C4⋊C4—21no—
386C4⋊C4—21no—
387C4⋊C4—22no—
388C4⋊C4—22no—
389C4⋊C4—22no—
390C4⋊C4—221no—
391C4⋊C4—221no—
392C4⋊C4—221no—
393C4⋊C4—221no—
394C4⋊C4—441no—
395C4⋊C4—441no—
396C4⋊C4C2×C22⋊D1112yes—
397C4⋊C4C2×C22⋊D1112yes—
398C4⋊C4C2×C22⋊D1114yes—
399C22⋊C4—28no—
400C22⋊C4—22no—
401C22⋊C4—22no—
402C22⋊C4—441no—
403C42—22no—
404C42—22no—
405C42—441no—
406C42C2×C22⋊D1111yescharacteristic
407C42C2×C22⋊D1111yescharacteristic
408C42C2×C22⋊D1111yescharacteristic
409C42C23×D1111yescharacteristic
410C11#1854011yescharacteristic, complemented, Sylow
411C23—24no—
412C23—22no—
413C23—42no—
414C23—42no—
415C23#6700611yescharacteristic
416Q8—24no—
417Q8—22no—
418Q8—416no—
419Q8—44no—
420Q8—44no—
421Q8—442no—
422Q8—442no—
423Q8#6698514yes—
424D4—24no—
425D4—22no—
426D4#6699514yes—
427C2×C4—24no—
428C2×C4—22no—
429C2×C4—22no—
430C2×C4—22no—
431C2×C4—22no—
432C2×C4—22no—
433C2×C4—24no—
434C2×C4—22no—
435C2×C4—416no—
436C2×C4—44no—
437C2×C4—44no—
438C2×C4—42no—
439C2×C4—42no—
440C2×C4—44no—
441C2×C4—441no—
442C2×C4—441no—
443C2×C4#6700611yescharacteristic
444C2×C4#6700611yescharacteristic
445C2×C4#6700611yescharacteristic
446C2×C4C22×C22⋊D1111yescharacteristic
447C2×C4C22×C22⋊D1111yescharacteristic
448C2×C4C22×C22⋊D1111yescharacteristic
449C8—224no—
450C8—442no—
451C8—442no—
452C22—21no—
453C22—21no—
454C22—24no—
455C22—48no—
456C22—42no—
457C22—42no—
458C22#1062285912yes—
459C22C2×#6700611yescharacteristic
460C4—24no—
461C4—21no—
462C4—21no—
463C4—21no—
464C4—21no—
465C4—44no—
466C4—42no—
467C4—42no—
468C4—881no—
469C4—881no—
470C4C2×#6698512yes—
471C4C2×#6699512yes—
472C2—22no—
473C2—44no—
474C2#1307784311yescharacteristic
475C2#1307785011yescharacteristic
476C2C2×#1062285911yescharacteristic
subgroupG/H
centerC22C2×#67006
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC2×D4×Q8×C11C2
socleC22×C11C2×#120
prime radicalC22×D4×C11D4
hypercenterC2×D4×Q8D11
hypocenterC11#18540
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×D4×Q8

Complements

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

NH ≅ G/Ntype
1. #13079158C2semidirect
2. #13078746C2semidirect
4. #13067879C2semidirect
5. #13067865C2semidirect
6. #13067333C2semidirect
7. #13067063C2semidirect
26. #10622692C22semidirect
27. #10622691C22semidirect
28. #10622644C22semidirect
30. #10622633C22semidirect
40. #10622185C22semidirect
41. Q8⋊(C11⋊C8)C22semidirect
410. C11#18540semidirect

Maximal subgroups

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

subgroupindex
#130791582
#130787462
#130787152
#130678792
#130678652
#130673332
#130670632
#130670592
C2×D4×Q8×C112
#1854011