Finite Group Databasebeta

← #14763530

Subgroups — #14763530

Order 2816.

1086 conjugacy classes of subgroups.

The subgroup lattice has 510 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623153C211yesmaximal, characteristic
2C2×#10622332C211yesmaximal, characteristic
3#13071019C211yesmaximal, characteristic
4#13069587C212yesmaximal, complemented
5#13069434C212yesmaximal, complemented
6#13068929C211yesmaximal, characteristic
7#13068928C211yesmaximal, characteristic
8#13068926C211yesmaximal, characteristic
9#13068620C212yesmaximal, complemented
10#13068619C212yesmaximal, complemented
11C11×#1873C211yesmaximal, characteristic
12C2×C11×C22⋊Q8C2211yescharacteristic
13C2×C11×#117C2211yescharacteristic
14C2×Q8×Dic11C2211yescharacteristic
15C2×#66997C2211yescharacteristic
16C2×#66979C2211yescharacteristic
17C2×#66977C2211yescharacteristic
18C22×C4×Dic11C2211yescharacteristic
19#10623153—24no—
20#10623153C418yescomplemented
21C2×#66942—21no—
22C2×#66941C2211yescharacteristic
23C2×#66940—21no—
24C2×#66940C2211yescharacteristic
25C2×#66931—21no—
26C2×#66930—21no—
27C2×C11×#103C2212yes—
28C2×C11×C22⋊C8C2211yescharacteristic
29C2×#66899C2212yes—
30C2×C22⋊(C11⋊C8)C2211yescharacteristic
31C2×#66880C2212yes—
32C2×#66879C2212yes—
33C2×Dic11⋊C8C2212yes—
34#10622590C2212yes—
35#10622589C2212yes—
36C2×#66874C2212yes—
37#10622555—21no—
38#10622555—21no—
39C4×Dic11⋊C4—21no—
40C4×Dic11⋊C4—21no—
41#10622332—24no—
42C11×#340C2212yes—
43#10622189C2212yes—
44#10622167C2212yes—
45#10622167C2212yes—
46C22×Q8×C11C2311yescharacteristic
47C23×C4×C11C2311yescharacteristic
48C23×Dic11D411yescharacteristic
49C23×Dic11D411yescharacteristic
50C22×Dic22—21no—
51C22×Dic22C2311yescharacteristic
52C22×C8×C11C2312yes—
53C11×C22⋊Q8—22no—
54C11×C22⋊Q8C2×C414yes—
55C11×#117—42no—
56C2×C11×C4⋊C4—21no—
57C2×C11×C4⋊C4C2312yes—
58C2×C11×C4⋊C4C2311yescharacteristic
59C2×C11×C22⋊C4—21no—
60C2×C11×C22⋊C4—21no—
61C2×C42×C11—21no—
62C2×C22⋊Dic11—21no—
63C2×C22⋊Dic11—21no—
64Q8×Dic11—22no—
65Q8×Dic11C2×C414yes—
66#66997—22no—
67#66997C2×C414yes—
68#66979—42no—
69C2×C4⋊Dic11—21no—
70C2×C4⋊Dic11C2312yes—
71C2×C4⋊Dic11C2311yescharacteristic
72#66977—22no—
73#66977C2×C414yes—
74C2×Dic11⋊C4—21no—
75C2×Dic11⋊C4—21no—
76C2×Dic11⋊C4—21no—
77C2×Dic11⋊C4—21no—
78C2×Dic11⋊C4—21no—
79C2×Dic11⋊C4—22no—
80C2×Dic11⋊C4—22no—
81C2×C4×Dic11—21no—
82C2×C4×Dic11—21no—
83C2×C4×Dic11—21no—
84C2×C4×Dic11C2×C414yes—
85C2×C4×Dic11D411yescharacteristic
86C2×C4×Dic11D411yescharacteristic
87C2×C4×Dic11D414yes—
88C2×C4×Dic11C2311yescharacteristic
89C2×C4×Dic11C2311yescharacteristic
90C22×C11⋊C8C2312yes—
91#66942—28no—
92#66941—22no—
93#66941C2×C414yes—
94#66940—28no—
95#66940—22no—
96#66940C2×C414yes—
97#66931—28no—
98#66930—28no—
99C11×#103—42no—
100C11×C22⋊C8—22no—
101#66899—42no—
102C11⋊#95—22no—
103C11⋊#95—22no—
104C22⋊(C11⋊C8)—22no—
105#66880—42no—
106#66879—24no—
107Dic11⋊C8—24no—
108#66874—42no—
109#21870—111nomaximal, Sylow
110C24×C11C2×D411yescharacteristic
111C2×Q8×C11—21no—
112C2×Q8×C11—22no—
113C2×Q8×C11—22no—
114C2×Q8×C11C22×C412yes—
115C22×C4×C11—22no—
116C22×C4×C11—22no—
117C22×C4×C11—21no—
118C22×C4×C11—21no—
119C22×C4×C11—22no—
120C22×C4×C11C22×C412yes—
121C22×C4×C11C2×D411yescharacteristic
122C22×C4×C11C2×D412yes—
123C22×C4×C11C2411yescharacteristic
124C22×Dic11—24no—
125C22×Dic11—21no—
126C22×Dic11—21no—
127C22×Dic11—22no—
128C22×Dic11—42no—
129C22×Dic11C22⋊C414yes—
130C22×Dic11C22⋊C414yes—
131C22×Dic11C2×D411yescharacteristic
132C22×Dic11C2×D411yescharacteristic
133C22×Dic11C2×D411yescharacteristic
134C22×Dic11C2×D411yescharacteristic
135C2×Dic22—24no—
136C2×Dic22—21no—
137C2×Dic22—22no—
138C2×Dic22—22no—
139C2×Dic22—44no—
140C2×Dic22C22×C412yes—
141C2×C8×C11—22no—
142C2×C8×C11—22no—
143C2×C8×C11—22no—
144C11×C4⋊C4—24no—
145C11×C4⋊C4—21no—
146C11×C4⋊C4—22no—
147C11×C4⋊C4—22no—
148C11×C4⋊C4C22×C412yes—
149C11×C22⋊C4—24no—
150C11×C22⋊C4—42no—
151C42×C11—42no—
152C22⋊Dic11—24no—
153C22⋊Dic11—42no—
154C4⋊Dic11—24no—
155C4⋊Dic11—21no—
156C4⋊Dic11—22no—
157C4⋊Dic11—22no—
158C4⋊Dic11C22×C412yes—
159Dic11⋊C4—24no—
160Dic11⋊C4—24no—
161Dic11⋊C4—24no—
162Dic11⋊C4—24no—
163Dic11⋊C4—24no—
164Dic11⋊C4—44no—
165Dic11⋊C4—44no—
166C4×Dic11—24no—
167C4×Dic11—24no—
168C4×Dic11—42no—
169C4×Dic11C22⋊C414yes—
170C4×Dic11C22⋊C414yes—
171C4×Dic11C22×C412yes—
172C4×Dic11C22×C412yes—
173C4×Dic11C2×D412yes—
174C4×Dic11C2×D412yes—
175C2×C11⋊C8—22no—
176C2×C11⋊C8—22no—
177C2×C11⋊C8—22no—
178C2×#533—111no—
179C2×#432—111no—
180#2285—111no—
181#1993—112no—
182#1960—112no—
183#1873—111no—
184#1873—111no—
185#1873—111no—
186#1873D1111yescharacteristic
187#1803—112no—
188#1803—112no—
189C23×C11—21no—
190C23×C11—21no—
191C23×C11—22no—
192C23×C11—22no—
193C23×C11C2×C22⋊C412yes—
194C23×C11C22×D411yescharacteristic
195Q8×C11—24no—
196Q8×C11—42no—
197C2×C4×C11—21no—
198C2×C4×C11—21no—
199C2×C4×C11—24no—
200C2×C4×C11—24no—
201C2×C4×C11—22no—
202C2×C4×C11—22no—
203C2×C4×C11—41no—
204C2×C4×C11—41no—
205C2×C4×C11—42no—
206C2×C4×C11—42no—
207C2×C4×C11—42no—
208C2×C4×C11—42no—
209C2×C4×C11C2×C22⋊C412yes—
210C2×C4×C11C23×C411yescharacteristic
211C2×C4×C11C22×D411yescharacteristic
212C2×C4×C11H(5,𝔽2)12yes—
213C2×C4×C112−1+412yes—
214C2×Dic11—22no—
215C2×Dic11—22no—
216C2×Dic11—22no—
217C2×Dic11—28no—
218C2×Dic11—22no—
219C2×Dic11—22no—
220C2×Dic11—44no—
221C2×Dic11—41no—
222C2×Dic11—41no—
223C2×Dic11—42no—
224C2×Dic11—42no—
225C2×Dic11—42no—
226C2×Dic11—42no—
227C2×Dic11C2×C22⋊C412yes—
228C2×Dic11C2×C22⋊C412yes—
229C2×Dic11C2×C22⋊C412yes—
230C2×Dic11C2×C22⋊C412yes—
231C2×Dic11#13714yes—
232Dic22—24no—
233Dic22—48no—
234Dic22—42no—
235C8×C11—42no—
236C11⋊C8—42no—
237#533—118no—
238#533—224no—
239C2×C4⋊Q8—111no—
240C2×C4⋊Q8—111no—
241C2×#125—221no—
242C2×C22⋊Q8—111no—
243C2×C22⋊Q8—221no—
244C2×C22⋊Q8C2×D1111yescharacteristic
245C2×C4×Q8—111no—
246C2×C4×Q8—111no—
247C2×C4×Q8—221no—
248C2×#117—111no—
249C2×#117—221no—
250C2×#117C2×D1111yescharacteristic
251C22×C42—111no—
252#432—224no—
253C2×C4⋊C8—112no—
254C2×#103—112no—
255C2×#103—112no—
256C2×#103—112no—
257C2×#103C2×D1112yes—
258C2×C22⋊C8—111no—
259C2×C22⋊C8C2×D1111yescharacteristic
260C2×#97—112no—
261#384—112no—
262#382—112no—
263#380—221no—
264#380—221no—
265C4×C4⋊C4—221no—
266C4×C4⋊C4—221no—
267#340—112no—
268#340—112no—
269#340—112no—
270#340C2×D1112yes—
271C22×C11—22no—
272C22×C11—22no—
273C22×C11—22no—
274C22×C11—42no—
275C22×C11—42no—
276C22×C11C22×C22⋊C411yescharacteristic
277C22×C11#53511yescharacteristic
278C22×C11#53611yescharacteristic
279C22×C11C2×#13712yes—
280C22×C11#57512yes—
281C4×C11—22no—
282C4×C11—42no—
283C4×C11—42no—
284C4×C11—82no—
285C4×C11#52012yes—
286C4×C11#53712yes—
287Dic11—22no—
288Dic11—22no—
289Dic11—22no—
290Dic11—42no—
291Dic11—42no—
292Dic11—82no—
293Dic11#41914yes—
294C22×Q8—111no—
295C22×Q8—221no—
296C22×Q8C22×D1111yescharacteristic
297C23×C4—111no—
298C23×C4—111no—
299C23×C4C22×D1111yescharacteristic
300C22×C8—112no—
301C22×C8C22×D1112yes—
302C4⋊Q8—114no—
303C4⋊Q8—114no—
304C4⋊Q8—222no—
305C4⋊Q8—222no—
306#125—228no—
307C22⋊Q8—22no—
308C22⋊Q8—114no—
309C22⋊Q8—228no—
310C22⋊Q8—222no—
311C22⋊Q8C4×D1114yes—
312C4×Q8—114no—
313C4×Q8—114no—
314C4×Q8—222no—
315C4×Q8—228no—
316C4×Q8—222no—
317#117—42no—
318#117—228no—
319#117—442no—
320C2×C4⋊C4—21no—
321C2×C4⋊C4—111no—
322C2×C4⋊C4—112no—
323C2×C4⋊C4—221no—
324C2×C4⋊C4—221no—
325C2×C4⋊C4—221no—
326C2×C4⋊C4—221no—
327C2×C4⋊C4—221no—
328C2×C4⋊C4—221no—
329C2×C4⋊C4—222no—
330C2×C4⋊C4—222no—
331C2×C4⋊C4C22×D1112yes—
332C2×C4⋊C4C22×D1111yescharacteristic
333C2×C22⋊C4—21no—
334C2×C22⋊C4—21no—
335C2×C22⋊C4—221no—
336C2×C22⋊C4—221no—
337C2×C42—21no—
338C2×C42—114no—
339C2×C42—111no—
340C2×C42—111no—
341C2×C42—114no—
342C2×C42—111no—
343C2×C42—111no—
344C2×C42—221no—
345C2×C42—221no—
346C2×C42—221no—
347C4⋊C8—224no—
348#103—42no—
349#103—442no—
350#103—442no—
351#103—442no—
352C22⋊C8—22no—
353C22⋊C8—222no—
354#97—224no—
355#95—222no—
356#95—222no—
357C2×C11—42no—
358C2×C11#231111yescharacteristic
359C2×C11C2×#41911yescharacteristic
360C2×C11#289611yescharacteristic
361C2×C11#321612yes—
362C2×C11#323712yes—
363C24D4×D1111yescharacteristic
364C2×Q8—21no—
365C2×Q8—22no—
366C2×Q8—22no—
367C2×Q8—112no—
368C2×Q8—224no—
369C2×Q8—221no—
370C2×Q8—222no—
371C2×Q8—222no—
372C2×Q8—444no—
373C2×Q8C2×C4×D1112yes—
374C22×C4—22no—
375C22×C4—22no—
376C22×C4—21no—
377C22×C4—21no—
378C22×C4—22no—
379C22×C4—111no—
380C22×C4—114no—
381C22×C4—111no—
382C22×C4—111no—
383C22×C4—111no—
384C22×C4—114no—
385C22×C4—224no—
386C22×C4—221no—
387C22×C4—221no—
388C22×C4—222no—
389C22×C4—442no—
390C22×C4C2×C4×D1112yes—
391C22×C4D4×D1111yescharacteristic
392C22×C4D4×D1112yes—
393C22×C4C23×D1111yescharacteristic
394C2×C8—22no—
395C2×C8—22no—
396C2×C8—22no—
397C2×C8—222no—
398C2×C8—222no—
399C2×C8—222no—
400C4⋊C4—24no—
401C4⋊C4—21no—
402C4⋊C4—22no—
403C4⋊C4—22no—
404C4⋊C4—112no—
405C4⋊C4—224no—
406C4⋊C4—224no—
407C4⋊C4—224no—
408C4⋊C4—224no—
409C4⋊C4—224no—
410C4⋊C4—224no—
411C4⋊C4—221no—
412C4⋊C4—222no—
413C4⋊C4—222no—
414C4⋊C4—444no—
415C4⋊C4—444no—
416C4⋊C4C2×C4×D1112yes—
417C22⋊C4—24no—
418C22⋊C4—42no—
419C22⋊C4—224no—
420C22⋊C4—442no—
421C42—42no—
422C42—114no—
423C42—114no—
424C42—112no—
425C42—112no—
426C42—112no—
427C42—112no—
428C42—224no—
429C42—224no—
430C42—442no—
431C11#2187011yescharacteristic, complemented, Sylow
432C23—22no—
433C23—22no—
434C23—21no—
435C23—21no—
436C23C22⋊C4×D1112yes—
437C23C2×D4×D1111yescharacteristic
438Q8—24no—
439Q8—42no—
440Q8—224no—
441Q8—448no—
442Q8—442no—
443C2×C4—21no—
444C2×C4—21no—
445C2×C4—24no—
446C2×C4—24no—
447C2×C4—22no—
448C2×C4—22no—
449C2×C4—42no—
450C2×C4—41no—
451C2×C4—41no—
452C2×C4—42no—
453C2×C4—42no—
454C2×C4—42no—
455C2×C4—112no—
456C2×C4—114no—
457C2×C4—112no—
458C2×C4—112no—
459C2×C4—112no—
460C2×C4—228no—
461C2×C4—222no—
462C2×C4—222no—
463C2×C4—222no—
464C2×C4—222no—
465C2×C4—222no—
466C2×C4—444no—
467C2×C4—442no—
468C2×C4—441no—
469C2×C4—441no—
470C2×C4—442no—
471C2×C4—442no—
472C2×C4—442no—
473C2×C4C22⋊C4×D1112yes—
474C2×C4C22×C4×D1111yescharacteristic
475C2×C4C2×D4×D1111yescharacteristic
476C2×C4#6703712yes—
477C2×C4#6704312yes—
478C8—42no—
479C8—442no—
480C22—22no—
481C22—22no—
482C22—22no—
483C22—42no—
484C22—42no—
485C22C2×C22⋊C4×D1111yescharacteristic
486C22#1062312311yescharacteristic
487C22#1062317911yescharacteristic
488C22#1062329912yes—
489C22D11×#13712yes—
490C4—22no—
491C4—42no—
492C4—42no—
493C4—82no—
494C4—114no—
495C4—222no—
496C4—222no—
497C4—222no—
498C4—442no—
499C4—442no—
500C4—882no—
501C4#1062307712yes—
502C4#1062312812yes—
503C2—42no—
504C2#1307120311yescharacteristic
505C2D11×#41911yescharacteristic
506C2#1307713111yescharacteristic
507C2#1307962412yes—
508C2#1307982712yes—
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1873C2
socleC23×C11C22×D4
prime radicalC24×C11C2×D4
cosocleC22×C4×C11C24
hypercenter#1873D11
hypocenterC11#21870
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1873

Complements

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

NH ≅ G/Ntype
4. #13069587C2semidirect
5. #13069434C2semidirect
9. #13068620C2semidirect
10. #13068619C2semidirect
20. #10623153C4semidirect
431. C11#21870semidirect

Maximal subgroups

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

subgroupindex
C2×#106231532
C2×#106223322
#130710192
#130695872
#130694342
#130689292
#130689282
#130689262
#130686202
#130686192
C11×#18732
#2187011