Finite Group Databasebeta

← #14810470

Subgroups — #14810470

Order 2816.

1010 conjugacy classes of subgroups.

The subgroup lattice has 494 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622682C211yesmaximal, characteristic, complemented
2C2×#10622706C211yesmaximal, characteristic, complemented
3#13074382C211yesmaximal, characteristic
4#13069764C212yesmaximal, complemented
5#13069754C212yesmaximal, complemented
6#13069590C211yesmaximal, characteristic, complemented
7#13069582C211yesmaximal, characteristic, complemented
8#13068928C212yesmaximal
9#13068923C212yesmaximal
10#13068382C211yesmaximal, characteristic
11C2×C11×#544C211yesmaximal, characteristic
12C11×#544—24no—
13C11×#544—24no—
14C2×C11×C4⋊Q8—21no—
15C2×C11×C4⋊Q8C2211yescharacteristic
16C2×C11×C4⋊Q8C2211yescharacteristic
17C2×C11×#125—21no—
18C2×C11×#125C2211yescharacteristic
19C2×C11×#125C2211yescharacteristic
20C2×C11×C22⋊Q8—21no—
21C2×C11×C22⋊Q8—21no—
22C2×C11×#117C2211yescharacteristic
23C2×C11×#117C2211yescharacteristic
24C22×C11×C4⋊C4C2211yescharacteristic
25C2×#66977C2212yes—
26C2×#66922C2211yescharacteristic
27C2×C22⋊(C11⋊C8)C2212yes—
28#10622706—24no—
29#10622682—24no—
30#10622596—21no—
31#10622596—21no—
32C2×#66874C2212yes—
33C2×#66874C2212yes—
34C2×#66874C2212yes—
35C2×#66874C2212yes—
36#10622566—21no—
37#10622566—21no—
38#10622549C2211yescharacteristic
39#10622542C2212yes—
40C2×#66867C2211yescharacteristic
41C2×C4×C11⋊C8C2211yescharacteristic
42#10622167C2212yes—
43#10622167C2212yes—
44#10622167C2212yes—
45#10622167C2212yes—
46#10622162C2212yes—
47C22×Q8×C11—21no—
48C22×Q8×C11—21no—
49C23×C4×C11—21no—
50C23×C4×C11C2311yescharacteristic
51C22×Dic22C2312yes—
52C11×C4⋊Q8—28no—
53C11×C4⋊Q8—22no—
54C11×C4⋊Q8—22no—
55C11×C4⋊Q8—22no—
56C11×C4⋊Q8D414yes—
57C11×#125—28no—
58C11×#125—22no—
59C11×#125—22no—
60C11×#125—22no—
61C11×#125D414yes—
62C11×C22⋊Q8—28no—
63C11×C22⋊Q8—28no—
64C11×#117—22no—
65C11×#117—22no—
66C11×#117—22no—
67C11×#117—22no—
68C2×C11×C4⋊C4—21no—
69C2×C11×C4⋊C4—21no—
70C2×C11×C4⋊C4—21no—
71C2×C11×C4⋊C4—21no—
72C2×C11×C4⋊C4—21no—
73C2×C11×C4⋊C4—21no—
74C2×C11×C4⋊C4—21no—
75C2×C11×C4⋊C4—22no—
76C2×C11×C4⋊C4—22no—
77C2×C11×C4⋊C4D411yescharacteristic
78C2×C11×C4⋊C4D411yescharacteristic
79C2×C11×C4⋊C4C2311yescharacteristic
80C2×C11×C4⋊C4C2311yescharacteristic
81C2×C11×C4⋊C4C2311yescharacteristic
82C2×C11×C4⋊C4C2311yescharacteristic
83C2×C11×C22⋊C4—21no—
84C2×C11×C22⋊C4D411yescharacteristic
85C2×C11×C22⋊C4D411yescharacteristic
86C2×C42×C11—21no—
87C2×C42×C11C2311yescharacteristic
88C2×C42×C11C2311yescharacteristic
89C2×C22⋊Dic11—22no—
90C2×C4⋊Dic11—21no—
91C2×C4⋊Dic11—21no—
92C2×C4⋊Dic11C2312yes—
93#66977—28no—
94C2×Dic11⋊C4—22no—
95C22×C11⋊C8C2312yes—
96C22×C11⋊C8C2312yes—
97#66922—22no—
98#66922—22no—
99C11⋊#95—22no—
100C11⋊#95—22no—
101C11⋊#95—21no—
102C11⋊#95—21no—
103C22⋊(C11⋊C8)—24no—
104#66874—24no—
105#66874—24no—
106#66874—24no—
107#66874—24no—
108#66867—22no—
109C4×C11⋊C8—22no—
110#25914—111nomaximal, Sylow
111C24×C11C2×D411yescharacteristic
112C2×Q8×C11—24no—
113C2×Q8×C11—24no—
114C2×Q8×C11—82no—
115C2×Q8×C11—82no—
116C22×C4×C11—21no—
117C22×C4×C11—21no—
118C22×C4×C11—22no—
119C22×C4×C11—21no—
120C22×C4×C11—21no—
121C22×C4×C11—21no—
122C22×C4×C11—21no—
123C22×C4×C11—24no—
124C22×C4×C11—82no—
125C22×C4×C11C2×D411yescharacteristic
126C22×C4×C11C2×D411yescharacteristic
127C22×C4×C11C2×D411yescharacteristic
128C22×C4×C11C2×D411yescharacteristic
129C22×C4×C11C2×D411yescharacteristic
130C22×C4×C11#4114yes—
131C22×C4×C11C2411yescharacteristic
132C22×Dic11—22no—
133C22×Dic11—22no—
134C2×Dic22—22no—
135C2×Dic22—22no—
136C2×Dic22—24no—
137C2×Dic22—24no—
138C11×C4⋊C4—24no—
139C11×C4⋊C4—24no—
140C11×C4⋊C4—24no—
141C11×C4⋊C4—24no—
142C11×C4⋊C4—24no—
143C11×C4⋊C4—24no—
144C11×C4⋊C4—24no—
145C11×C4⋊C4—22no—
146C11×C4⋊C4—22no—
147C11×C4⋊C4—21no—
148C11×C4⋊C4—21no—
149C11×C4⋊C4—21no—
150C11×C4⋊C4—21no—
151C11×C4⋊C4C2×D412yes—
152C11×C4⋊C4C2×D412yes—
153C11×C4⋊C4C2×D412yes—
154C11×C4⋊C4C2×D412yes—
155C11×C22⋊C4—24no—
156C11×C22⋊C4—22no—
157C11×C22⋊C4—22no—
158C42×C11—24no—
159C42×C11—21no—
160C42×C11—21no—
161C42×C11C2×D412yes—
162C42×C11C2×D412yes—
163C22⋊Dic11—44no—
164C4⋊Dic11—24no—
165C4⋊Dic11—42no—
166C4⋊Dic11—42no—
167Dic11⋊C4—44no—
168C2×C11⋊C8—22no—
169C2×C11⋊C8—22no—
170C2×C11⋊C8—22no—
171C2×C11⋊C8—22no—
172C2×C11⋊C8—22no—
173C2×C11⋊C8—22no—
174C2×#544D1111yescharacteristic
175C2×#491—111no—
176C2×#487—111no—
177#2621—111no—
178#2026—112no—
179#2024—112no—
180#1993—111no—
181#1991—111no—
182#1873—112no—
183#1872—112no—
184#1750—111no—
185C23×C11—21no—
186C23×C11—21no—
187C23×C11—22no—
188C23×C11—22no—
189C23×C11#12412yes—
190C23×C11C22×D411yescharacteristic
191Q8×C11—84no—
192Q8×C11—84no—
193C2×C4×C11—21no—
194C2×C4×C11—21no—
195C2×C4×C11—22no—
196C2×C4×C11—22no—
197C2×C4×C11—24no—
198C2×C4×C11—24no—
199C2×C4×C11—21no—
200C2×C4×C11—22no—
201C2×C4×C11—21no—
202C2×C4×C11—22no—
203C2×C4×C11—22no—
204C2×C4×C11—22no—
205C2×C4×C11—22no—
206C2×C4×C11—22no—
207C2×C4×C11—42no—
208C2×C4×C11—42no—
209C2×C4×C11—42no—
210C2×C4×C11—42no—
211C2×C4×C11—84no—
212C2×C4×C11#12012yes—
213C2×C4×C11#12012yes—
214C2×C4×C11#12412yes—
215C2×C4×C11C22×D411yescharacteristic
216C2×C4×C11C22×D411yescharacteristic
217C2×C4×C11C2×#4112yes—
218C2×C4×C112−1+412yes—
219C2×Dic11—42no—
220C2×Dic11—42no—
221C2×Dic11—42no—
222C2×Dic11—42no—
223C2×Dic11—42no—
224C2×Dic11—42no—
225Dic22—44no—
226Dic22—44no—
227C11⋊C8—42no—
228C11⋊C8—42no—
229#544—24no—
230#544—24no—
231C2×C4⋊Q8—21no—
232C2×C4⋊Q8—111no—
233C2×C4⋊Q8C2×D1111yescharacteristic
234C2×C4⋊Q8C2×D1111yescharacteristic
235C2×#125—21no—
236C2×#125C2×D1111yescharacteristic
237C2×#125C2×D1111yescharacteristic
238C2×C22⋊Q8—21no—
239C2×C22⋊Q8—21no—
240C2×C22⋊Q8—112no—
241C2×#117C2×D1111yescharacteristic
242C2×#117C2×D1111yescharacteristic
243C22×C4⋊C4C2×D1111yescharacteristic
244#491—224no—
245#487—224no—
246C2×#103—112no—
247C2×#103—112no—
248C2×#103—112no—
249C2×#103—112no—
250C2×C22⋊C8—112no—
251C2×#97—111no—
252C2×C4×C8—111no—
253#398—221no—
254#398—221no—
255#397—221no—
256#397—221no—
257#391—112no—
258#382—111no—
259#340—112no—
260#340—112no—
261#340—112no—
262#340—112no—
263#336—112no—
264C22×C11—24no—
265C22×C11—22no—
266C22×C11—42no—
267C22×C11—41no—
268C22×C11—41no—
269C22×C11C2×#12011yescharacteristic
270C22×C11C2×#12411yescharacteristic
271C22×C11#53611yescharacteristic
272C22×C11#57712yes—
273C22×C11#57812yes—
274C4×C11—22no—
275C4×C11—22no—
276C4×C11—22no—
277C4×C11—41no—
278C4×C11—42no—
279C4×C11—42no—
280C4×C11—42no—
281C4×C11—41no—
282C4×C11—42no—
283C4×C11#54812yes—
284C4×C11#54812yes—
285Dic11—82no—
286Dic11—82no—
287C22×Q8—21no—
288C22×Q8—21no—
289C22×Q8—112no—
290C23×C4—21no—
291C23×C4C22×D1111yescharacteristic
292C22×C8—112no—
293C22×C8—112no—
294C4⋊Q8—28no—
295C4⋊Q8—22no—
296C4⋊Q8—22no—
297C4⋊Q8—22no—
298C4⋊Q8—222no—
299C4⋊Q8—222no—
300C4⋊Q8C22⋊D1114yes—
301#125—28no—
302#125—22no—
303#125—22no—
304#125—22no—
305#125C22⋊D1114yes—
306C22⋊Q8—28no—
307C22⋊Q8—28no—
308C22⋊Q8—228no—
309#117—22no—
310#117—22no—
311#117—22no—
312#117—22no—
313C2×C4⋊C4—21no—
314C2×C4⋊C4—21no—
315C2×C4⋊C4—21no—
316C2×C4⋊C4—21no—
317C2×C4⋊C4—21no—
318C2×C4⋊C4—21no—
319C2×C4⋊C4—21no—
320C2×C4⋊C4—22no—
321C2×C4⋊C4—22no—
322C2×C4⋊C4—112no—
323C2×C4⋊C4—222no—
324C2×C4⋊C4—221no—
325C2×C4⋊C4—221no—
326C2×C4⋊C4C22⋊D1111yescharacteristic
327C2×C4⋊C4C22⋊D1111yescharacteristic
328C2×C4⋊C4C22×D1111yescharacteristic
329C2×C4⋊C4C22×D1111yescharacteristic
330C2×C4⋊C4C22×D1111yescharacteristic
331C2×C4⋊C4C22×D1111yescharacteristic
332C2×C22⋊C4—21no—
333C2×C22⋊C4—222no—
334C2×C22⋊C4C22⋊D1111yescharacteristic
335C2×C22⋊C4C22⋊D1111yescharacteristic
336C2×C42—21no—
337C2×C42C22×D1111yescharacteristic
338C2×C42C22×D1111yescharacteristic
339#103—224no—
340#103—224no—
341#103—224no—
342#103—224no—
343C22⋊C8—224no—
344#97—222no—
345C4×C8—222no—
346#95—221no—
347#95—221no—
348#95—222no—
349#95—222no—
350C2×C11—42no—
351C2×C11#243611yescharacteristic
352C2×C11#300911yescharacteristic
353C2×C11#301111yescharacteristic
354C2×C11#313712yes—
355C2×C11#324212yes—
356C24C2×C22⋊D1111yescharacteristic
357C2×Q8—24no—
358C2×Q8—24no—
359C2×Q8—82no—
360C2×Q8—82no—
361C2×Q8—224no—
362C2×Q8—224no—
363C2×Q8—222no—
364C2×Q8—222no—
365C22×C4—22no—
366C22×C4—21no—
367C22×C4—21no—
368C22×C4—21no—
369C22×C4—21no—
370C22×C4—21no—
371C22×C4—21no—
372C22×C4—24no—
373C22×C4—82no—
374C22×C4—222no—
375C22×C4—222no—
376C22×C4#434314yes—
377C22×C4C2×C22⋊D1111yescharacteristic
378C22×C4C2×C22⋊D1111yescharacteristic
379C22×C4C2×C22⋊D1111yescharacteristic
380C22×C4C2×C22⋊D1111yescharacteristic
381C22×C4C2×C22⋊D1111yescharacteristic
382C22×C4C23×D1111yescharacteristic
383C2×C8—222no—
384C2×C8—222no—
385C2×C8—222no—
386C2×C8—222no—
387C2×C8—222no—
388C2×C8—222no—
389C4⋊C4—24no—
390C4⋊C4—24no—
391C4⋊C4—24no—
392C4⋊C4—24no—
393C4⋊C4—24no—
394C4⋊C4—24no—
395C4⋊C4—24no—
396C4⋊C4—22no—
397C4⋊C4—22no—
398C4⋊C4—21no—
399C4⋊C4—21no—
400C4⋊C4—21no—
401C4⋊C4—21no—
402C4⋊C4—224no—
403C4⋊C4—444no—
404C4⋊C4—442no—
405C4⋊C4—442no—
406C4⋊C4C2×C22⋊D1112yes—
407C4⋊C4C2×C22⋊D1112yes—
408C4⋊C4C2×C22⋊D1112yes—
409C4⋊C4C2×C22⋊D1112yes—
410C22⋊C4—24no—
411C22⋊C4—22no—
412C22⋊C4—22no—
413C22⋊C4—444no—
414C42—24no—
415C42—21no—
416C42—21no—
417C42C2×C22⋊D1112yes—
418C42C2×C22⋊D1112yes—
419C11#2591411yescharacteristic, complemented, Sylow
420C23—21no—
421C23—22no—
422C23—22no—
423C23—21no—
424C23#6700012yes—
425C23C22×C22⋊D1111yescharacteristic
426Q8—84no—
427Q8—84no—
428Q8—444no—
429Q8—444no—
430C2×C4—21no—
431C2×C4—22no—
432C2×C4—22no—
433C2×C4—21no—
434C2×C4—24no—
435C2×C4—24no—
436C2×C4—22no—
437C2×C4—22no—
438C2×C4—21no—
439C2×C4—22no—
440C2×C4—21no—
441C2×C4—22no—
442C2×C4—22no—
443C2×C4—22no—
444C2×C4—42no—
445C2×C4—42no—
446C2×C4—42no—
447C2×C4—42no—
448C2×C4—84no—
449C2×C4—442no—
450C2×C4—442no—
451C2×C4—442no—
452C2×C4—442no—
453C2×C4—442no—
454C2×C4—442no—
455C2×C4#6700012yes—
456C2×C4#6700612yes—
457C2×C4#6700612yes—
458C2×C4C2×#434312yes—
459C2×C4#6704012yes—
460C2×C4C22×C22⋊D1111yescharacteristic
461C2×C4C22×C22⋊D1111yescharacteristic
462C8—442no—
463C8—442no—
464C22—22no—
465C22—24no—
466C22—42no—
467C22—41no—
468C22—41no—
469C22C2×#6700011yescharacteristic
470C22#1062334711yescharacteristic
471C22#1062336712yes—
472C22#1062336912yes—
473C22C2×#6700611yescharacteristic
474C4—22no—
475C4—22no—
476C4—22no—
477C4—41no—
478C4—42no—
479C4—42no—
480C4—42no—
481C4—41no—
482C4—42no—
483C4—882no—
484C4—882no—
485C4#1062334812yes—
486C4#1062334812yes—
487C2—42no—
488C2#1307227011yescharacteristic
489C2#1307789311yescharacteristic
490C2#1307791111yescharacteristic
491C2#1307898612yes—
492C2#1307988412yes—
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C11×#544C2
socleC23×C11C22×D4
prime radicalC24×C11C2×D4
hypercenterC2×#544D11
hypocenterC11#25914
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×#117 ◁ C2×#544

Complements

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

NH ≅ G/Ntype
1. C2×#10622682C2semidirect
2. C2×#10622706C2semidirect
4. #13069764C2semidirect
5. #13069754C2semidirect
6. #13069590C2semidirect
7. #13069582C2semidirect
419. C11#25914semidirect

Maximal subgroups

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

subgroupindex
C2×#106226822
C2×#106227062
#130743822
#130697642
#130697542
#130695902
#130695822
#130689282
#130689232
#130683822
C2×C11×#5442
#2591411