Finite Group Databasebeta

← #14781069

Subgroups — #14781069

Order 2816.

1294 conjugacy classes of subgroups.

The subgroup lattice has 466 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623219C211yesmaximal, characteristic, complemented
2C2×#10622417C212yesmaximal
3#13071105C211yesmaximal, characteristic
4#13069767C211yesmaximal, characteristic, complemented
5#13069763C211yesmaximal, characteristic, complemented
6#13069759C211yesmaximal, characteristic, complemented
7#13069755C212yesmaximal, complemented
8#13069751C212yesmaximal, complemented
9#13068331C212yesmaximal, complemented
10D11×#336C211yesmaximal, characteristic, complemented
11C11×#2026C211yesmaximal, characteristic, complemented
12C22×#4343C2211yescharacteristic
13C2×C11×#125C2211yescharacteristic
14C22×C8×D11C2212yes—
15#10623219—28no—
16C2×#66949—22no—
17C2×#66945C2211yescharacteristic
18C2×#66945C2212yes—
19C2×#66941C2212yes—
20C2×#66940—22no—
21C2×C42×D11C2211yescharacteristic
22C2×#66923C2211yescharacteristic
23C2×C11×#103C2212yes—
24C11×#391C2211yescharacteristic
25#10622843C2211yescharacteristic
26C2×#66899C2212yes—
27C2×#66885C2212yes—
28#10622601C2211yescharacteristic
29C2×#66873C2212yes—
30#10622552C2211yescharacteristic
31#10622417—28no—
32#10622279—22no—
33#10622278—22no—
34C11×#340C2212yes—
35C11×#336C2211yescharacteristic
36#10622189C2212yes—
37#10622188C2212yes—
38#10622167C2212yes—
39#10622167C2212yes—
40#10622162C2211yescharacteristic
41C22×Q8×C11C2311yescharacteristic
42C2×#4343—22no—
43C2×#4343—24no—
44C2×#4343—24no—
45C2×#4343Q814yescomplemented
46C22×D44—21no—
47C22×D44C2311yescharacteristic
48C22×C4×D11—21no—
49C22×C4×D11D412yes—
50C22×C4×D11C2311yescharacteristic
51C22×Dic22—22no—
52C22×C8×C11C2312yes—
53C11×#125—24no—
54C2×C11×C4⋊C4—22no—
55C2×C11×C4⋊C4C2311yescharacteristic
56C2×C11×C4⋊C4C2312yes—
57C2×C42×C11C2311yescharacteristic
58C2×(C2×D11)⋊C4—22no—
59C2×(C2×D11)⋊C4—21no—
60C2×(C2×D11)⋊C4—22no—
61C2×(C2×D11)⋊C4—22no—
62C2×C4⋊Dic11C2311yescharacteristic
63C2×C4⋊Dic11C2312yes—
64C2×Dic11⋊C4—22no—
65C2×Dic11⋊C4—22no—
66C2×C4×Dic11—22no—
67C2×C4×Dic11—21no—
68C2×C4×Dic11D412yes—
69C2×C4×Dic11C2311yescharacteristic
70C22×C11⋊C8C2312yes—
71C2×C8×D11—24no—
72C2×C8×D11—24no—
73C2×C8×D11—24no—
74#66949—216no—
75#66945—24no—
76#66945—24no—
77#66945D418yes—
78#66941—24no—
79#66941—24no—
80#66940—216no—
81C42×D11—24no—
82#66923—24no—
83C11×#103—24no—
84C11×#95—22no—
85#66899—24no—
86C11⋊#95—22no—
87#66885—24no—
88#66873—24no—
89#23451—111nomaximal, Sylow
90C23×D11—21no—
91C23×D11C2×D411yescharacteristic
92C2×Q8×C11—21no—
93C2×Q8×C11—22no—
94C2×Q8×C11—22no—
95C2×Q8×C11C2×Q812yes—
96C22×C4×C11—21no—
97C22×C4×C11—22no—
98C22×C4×C11—21no—
99C22×C4×C11C2×D412yes—
100C22×C4×C11C2411yescharacteristic
101C22×Dic11—22no—
102C22×Dic11—21no—
103C22×Dic11C2×D412yes—
104C22×Dic11C2×D411yescharacteristic
105#4343—216no—
106#4343—48no—
107C2×D44—24no—
108C2×D44—22no—
109C2×D44—21no—
110C2×D44—22no—
111C2×D44—42no—
112C2×D44—42no—
113C2×D44C2×Q812yes—
114C2×C4×D11—24no—
115C2×C4×D11—24no—
116C2×C4×D11—24no—
117C2×C4×D11—42no—
118C2×C4×D11—42no—
119C2×C4×D11—42no—
120C2×C4×D11C2×D414yes—
121C2×C4×D11C2×Q812yes—
122C2×C4×D11#4112yes—
123C2×C4×D11#4114yes—
124C2×Dic22—28no—
125C2×Dic22—44no—
126C2×Dic22—44no—
127C2×C8×C11—22no—
128C2×C8×C11—22no—
129C2×C8×C11—22no—
130C11×C4⋊C4—28no—
131C11×C4⋊C4—22no—
132C11×C4⋊C4—22no—
133C11×C4⋊C4C2×D414yes—
134C42×C11—22no—
135(C2×D11)⋊C4—28no—
136(C2×D11)⋊C4—44no—
137(C2×D11)⋊C4—44no—
138(C2×D11)⋊C4—42no—
139C4⋊Dic11—22no—
140C4⋊Dic11—22no—
141C4⋊Dic11C2×D414yes—
142Dic11⋊C4—28no—
143Dic11⋊C4—28no—
144C4×Dic11—24no—
145C4×Dic11—28no—
146C4×Dic11—22no—
147C4×Dic11—42no—
148C2×C11⋊C8—22no—
149C2×C11⋊C8—22no—
150C2×C11⋊C8—22no—
151C8×D11—48no—
152C2×#533—111no—
153C2×#416—112no—
154#2297—111no—
155#2026—111no—
156#2026D1111yescharacteristic, complemented
157#2025—111no—
158#2025—111no—
159#2024—112no—
160#2023—112no—
161#1735—112no—
162C2×#336—111no—
163C23×C11C22×D411yescharacteristic
164C22×D11—22no—
165C22×D11—22no—
166C22×D11—22no—
167C22×D11—41no—
168C22×D11—41no—
169C22×D11—42no—
170C22×D11—42no—
171C22×D11#12012yes—
172C22×D11C22⋊Q812yes—
173C22×D11#12412yes—
174Q8×C11—24no—
175Q8×C11—42no—
176C2×C4×C11—22no—
177C2×C4×C11—24no—
178C2×C4×C11—22no—
179C2×C4×C11—22no—
180C2×C4×C11—22no—
181C2×C4×C11—41no—
182C2×C4×C11—41no—
183C2×C4×C11—42no—
184C2×C4×C11—42no—
185C2×C4×C11—41no—
186C2×C4×C11—42no—
187C2×C4×C11C22×D412yes—
188C2×C4×C11C22×Q811yescharacteristic
189C2×C4×C11C2×#4112yes—
190C2×C4×C11C2×#4111yescharacteristic
191C2×Dic11—22no—
192C2×Dic11—22no—
193C2×Dic11—24no—
194C2×Dic11—42no—
195C2×Dic11—42no—
196C2×Dic11—41no—
197C2×Dic11—42no—
198C2×Dic11#12012yes—
199C2×Dic11C22⋊Q812yes—
200C2×Dic11#12412yes—
201C2×Dic11#13514yes—
202D44—24no—
203D44—48no—
204D44—42no—
205C4×D11—48no—
206C4×D11—48no—
207C4×D11C22⋊Q818yes—
208C4×D11#12418yes—
209Dic22—416no—
210C8×C11—42no—
211C11⋊C8—42no—
212C22×#41—111no—
213C23×C8—112no—
214#533—228no—
215C2×C4⋊Q8—112no—
216C2×#125—111no—
217C2×#125C2×D1111yescharacteristic
218C2×C22⋊Q8—222no—
219C2×C4×Q8—222no—
220C2×#117—112no—
221C2×#117—111no—
222C22×C42—111no—
223#416—228no—
224C2×#103—112no—
225C2×#103C2×D1112yes—
226C2×#102—112no—
227C2×#102—112no—
228#391—111no—
229#391C2×D1111yescharacteristic
230#390—111no—
231#390—111no—
232#386—222no—
233C4×C22⋊C4—222no—
234#340—112no—
235#340—112no—
236#340—112no—
237#340C2×D1112yes—
238#336—112no—
239#336—111no—
240#336C2×D1111yescharacteristic
241C22×C11C2×#12011yescharacteristic
242C22×C11C2×C22⋊Q811yescharacteristic
243C22×C11C2×#12411yescharacteristic
244C22×C11C2×#13512yes—
245C22×C11#57512yes—
246C2×D11—24no—
247C2×D11—22no—
248C2×D11—22no—
249C2×D11—24no—
250C2×D11—44no—
251C2×D11—42no—
252C2×D11—81no—
253C2×D11—81no—
254C2×D11—82no—
255C2×D11#39314yes—
256C4×C11—42no—
257C4×C11—42no—
258C4×C11—44no—
259C4×C11—81no—
260C4×C11C2×C22⋊Q812yes—
261C4×C11C2×#12412yes—
262Dic11—24no—
263Dic11—44no—
264Dic11—81no—
265Dic11#39314yes—
266C2×#41—114no—
267C2×#41—222no—
268C2×#41—224no—
269C2×#41—224no—
270C22×Q8—222no—
271C22×Q8C22×D1111yescharacteristic
272C22×D4—111no—
273C22×D4—221no—
274C23×C4—111no—
275C23×C4—112no—
276C23×C4—221no—
277C22×C8—112no—
278C22×C8—224no—
279C22×C8—224no—
280C22×C8—224no—
281C22×C8C22×D1112yes—
282C4⋊Q8—224no—
283C4⋊Q8—224no—
284#125—24no—
285#125—224no—
286C22⋊Q8—2216no—
287C4×Q8—2216no—
288#117—118no—
289#117—224no—
290#117—224no—
291C2×C4⋊C4—22no—
292C2×C4⋊C4—112no—
293C2×C4⋊C4—111no—
294C2×C4⋊C4—222no—
295C2×C4⋊C4—222no—
296C2×C4⋊C4C22×D1111yescharacteristic
297C2×C4⋊C4C22×D1112yes—
298C2×C22⋊C4—222no—
299C2×C22⋊C4—222no—
300C2×C22⋊C4—221no—
301C2×C22⋊C4—222no—
302C2×C42—112no—
303C2×C42—111no—
304C2×C42—224no—
305C2×C42—222no—
306C2×C42—221no—
307C2×C42C22×D1111yescharacteristic
308#103—24no—
309#103—224no—
310#102—224no—
311#102—224no—
312#95—22no—
313#95—222no—
314C2×C11C2×#39311yescharacteristic
315C2×C11#300212yes—
316C2×C11#307612yes—
317C2×C11#313111yescharacteristic
318C2×C11#313511yescharacteristic
319D11—24no—
320D11—82no—
321C24—111no—
322C24—221no—
323#41—2216no—
324#41—448no—
325C2×Q8—21no—
326C2×Q8—22no—
327C2×Q8—22no—
328C2×Q8—228no—
329C2×Q8—444no—
330C2×Q8—444no—
331C2×Q8Q8×D1112yes—
332C2×D4—112no—
333C2×D4—224no—
334C2×D4—222no—
335C2×D4—222no—
336C2×D4—221no—
337C2×D4—442no—
338C2×D4—442no—
339C22×C4—21no—
340C22×C4—22no—
341C22×C4—21no—
342C22×C4—111no—
343C22×C4—114no—
344C22×C4—112no—
345C22×C4—114no—
346C22×C4—112no—
347C22×C4—112no—
348C22×C4—224no—
349C22×C4—224no—
350C22×C4—224no—
351C22×C4—222no—
352C22×C4—221no—
353C22×C4—442no—
354C22×C4—442no—
355C22×C4—442no—
356C22×C4D4×D1112yes—
357C22×C4C23×D1111yescharacteristic
358C2×C8—22no—
359C2×C8—22no—
360C2×C8—22no—
361C2×C8—222no—
362C2×C8—222no—
363C2×C8—222no—
364C2×C8—448no—
365C4⋊C4—28no—
366C4⋊C4—22no—
367C4⋊C4—22no—
368C4⋊C4—114no—
369C4⋊C4—228no—
370C4⋊C4—228no—
371C4⋊C4—222no—
372C4⋊C4—222no—
373C4⋊C4D4×D1114yes—
374C22⋊C4—228no—
375C22⋊C4—444no—
376C22⋊C4—444no—
377C22⋊C4—442no—
378C42—22no—
379C42—224no—
380C42—228no—
381C42—222no—
382C42—442no—
383C11#2345111yescharacteristic, complemented, Sylow
384C23—112no—
385C23—112no—
386C23—112no—
387C23—222no—
388C23—222no—
389C23—222no—
390C23—442no—
391C23—442no—
392C23—441no—
393C23—441no—
394C23C2×D4×D1111yescharacteristic
395Q8—24no—
396Q8—42no—
397Q8—4416no—
398D4—224no—
399D4—448no—
400D4—442no—
401C2×C4—22no—
402C2×C4—22no—
403C2×C4—22no—
404C2×C4—24no—
405C2×C4—22no—
406C2×C4—42no—
407C2×C4—42no—
408C2×C4—41no—
409C2×C4—41no—
410C2×C4—42no—
411C2×C4—41no—
412C2×C4—112no—
413C2×C4—112no—
414C2×C4—112no—
415C2×C4—118no—
416C2×C4—118no—
417C2×C4—114no—
418C2×C4—222no—
419C2×C4—222no—
420C2×C4—224no—
421C2×C4—448no—
422C2×C4—448no—
423C2×C4—442no—
424C2×C4—442no—
425C2×C4—442no—
426C2×C4—441no—
427C2×C4C2×D4×D1112yes—
428C2×C4C2×Q8×D1111yescharacteristic
429C2×C4#41×D1112yes—
430C2×C4#41×D1111yescharacteristic
431C8—42no—
432C8—442no—
433C22—114no—
434C22—224no—
435C22—224no—
436C22—222no—
437C22—222no—
438C22—444no—
439C22—442no—
440C22—882no—
441C22—881no—
442C22—881no—
443C22D11×#12011yescharacteristic
444C22D11×C22⋊Q811yescharacteristic
445C22D11×#12411yescharacteristic
446C22D11×#13512yes—
447C22#1062330812yes—
448C4—42no—
449C4—44no—
450C4—42no—
451C4—81no—
452C4—114no—
453C4—224no—
454C4—444no—
455C4—881no—
456C4D11×C22⋊Q812yes—
457C4D11×#12412yes—
458C2—224no—
459C2—882no—
460C2D11×#39311yescharacteristic
461C2#1307783712yes—
462C2#1307840312yes—
463C2#1307893711yescharacteristic
464C2#1307896311yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2026C2
socleC23×C11C22×D4
prime radicalC22×#4343C22
hypercenter#2026D11
hypocenterC11#23451
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2026

Complements

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

NH ≅ G/Ntype
1. C2×#10623219C2semidirect
4. #13069767C2semidirect
5. #13069763C2semidirect
6. #13069759C2semidirect
7. #13069755C2semidirect
8. #13069751C2semidirect
9. #13068331C2semidirect
10. D11×#336C2semidirect
11. C11×#2026C2semidirect
45. C2×#4343Q8semidirect
156. #2026D11semidirect
383. C11#23451semidirect

Maximal subgroups

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

subgroupindex
C2×#106232192
C2×#106224172
#130711052
#130697672
#130697632
#130697592
#130697552
#130697512
#130683312
D11×#3362
C11×#20262
#2345111