Finite Group Databasebeta

← #14810409

Subgroups — #14810409

Order 2816.

1104 conjugacy classes of subgroups.

The subgroup lattice has 464 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623048C211yesmaximal, characteristic, complemented
2C2×#10622413C212yesmaximal, complemented
3#13076919C211yesmaximal, characteristic
4#13069755C212yesmaximal, complemented
5#13069751C212yesmaximal, complemented
6#13069579C212yesmaximal, complemented
7#13068938C211yesmaximal, characteristic
8#13068936C211yesmaximal, characteristic
9#13068929C211yesmaximal, characteristic, complemented
10C22⋊C8×Dic11C211yesmaximal, characteristic, complemented
11C11×#1873C211yesmaximal, characteristic, complemented
12C2×C11×C22⋊Q8C2211yescharacteristic
13C2×C11×#117C2211yescharacteristic
14C2×#67000C2211yescharacteristic
15C2×#66983C2211yescharacteristic
16C2×#66979C2211yescharacteristic
17C22×C4×Dic11C2211yescharacteristic
18#10623048—28no—
19C2×#66943C2212yes—
20C2×#66941C2212yes—
21C2×#66931—22no—
22C2×C4×Dic22—22no—
23C2×C11×#103C2212yes—
24C2×C11×C22⋊C8C2211yescharacteristic
25#10622843C2211yescharacteristic
26C2×#66899C2212yes—
27C2×C22⋊(C11⋊C8)C2211yescharacteristic
28C2×#66885C2212yes—
29C2×C8×Dic11C2212yes—
30#10622603—22no—
31#10622601C2211yescharacteristic
32#10622590C2211yescharacteristic
33C2×#66873C2212yes—
34#10622571—22no—
35#10622413—28no—
36C11×#340C2212yes—
37#10622189C2212yes—
38#10622188C2212yes—
39#10622167C2212yes—
40#10622167C2212yes—
41C22×Q8×C11C2311yescharacteristic
42C23×C4×C11C2311yescharacteristic
43C22×C22⋊D11—21no—
44C23×Dic11D412yes—
45C22×D44C2311yescharacteristic
46C22×Dic22—22no—
47C22×C8×C11C2312yes—
48C11×C22⋊Q8—22no—
49C11×C22⋊Q8—22no—
50C11×#117—24no—
51C2×C11×C4⋊C4—21no—
52C2×C11×C4⋊C4C2311yescharacteristic
53C2×C11×C4⋊C4C2312yes—
54C2×C11×C22⋊C4—21no—
55C2×C11×C22⋊C4—21no—
56C2×C42×C11—21no—
57C2×C22⋊Dic11—21no—
58#67000—24no—
59#66983—22no—
60#66983—22no—
61C2×(C2×D11)⋊C4—21no—
62C2×(C2×D11)⋊C4—22no—
63C2×(C2×D11)⋊C4—22no—
64#66979—24no—
65C2×C4⋊Dic11—22no—
66C2×C4⋊Dic11C2311yescharacteristic
67C2×C4⋊Dic11C2312yes—
68C2×Dic11⋊C4—22no—
69C2×Dic11⋊C4—22no—
70C2×C4×Dic11—21no—
71C2×C4×Dic11—24no—
72C2×C4×Dic11D412yes—
73C2×C4×Dic11C2311yescharacteristic
74C2×C4×Dic11C2311yescharacteristic
75C22×C11⋊C8C2312yes—
76#66943—24no—
77#66943D418yescomplemented
78#66941—24no—
79#66941—24no—
80#66931—216no—
81C4×Dic22—216no—
82C11×#103—24no—
83C11×C22⋊C8—22no—
84#66899—24no—
85C11⋊#95—22no—
86C11⋊#95—22no—
87C22⋊(C11⋊C8)—22no—
88#66885—24no—
89C8×Dic11—24no—
90#66873—24no—
91#25906—111nomaximal, Sylow
92C24×C11C2×D411yescharacteristic
93C23×D11—21no—
94C2×Q8×C11—22no—
95C2×Q8×C11—21no—
96C2×Q8×C11—21no—
97C2×Q8×C11—22no—
98C22×C4×C11—22no—
99C22×C4×C11—22no—
100C22×C4×C11—22no—
101C22×C4×C11—21no—
102C22×C4×C11—21no—
103C22×C4×C11C2×D411yescharacteristic
104C22×C4×C11#4112yes—
105C22×C4×C11#4112yes—
106C22×C4×C11C2411yescharacteristic
107C2×C22⋊D11—44no—
108C2×C22⋊D11—42no—
109C22×Dic11—24no—
110C22×Dic11—24no—
111C22×Dic11—22no—
112C22×Dic11—21no—
113C22×Dic11—42no—
114C22×Dic11C2×D412yes—
115C22×Dic11C2×D412yes—
116C2×D44—22no—
117C2×D44—21no—
118C2×D44—21no—
119C2×D44—22no—
120C2×Dic22—28no—
121C2×Dic22—44no—
122C2×Dic22—44no—
123C2×C8×C11—22no—
124C2×C8×C11—22no—
125C2×C8×C11—22no—
126C11×C4⋊C4—22no—
127C11×C4⋊C4—21no—
128C11×C4⋊C4—21no—
129C11×C4⋊C4—42no—
130C11×C4⋊C4C2×D414yes—
131C11×C22⋊C4—24no—
132C11×C22⋊C4—42no—
133C42×C11—24no—
134C22⋊Dic11—24no—
135(C2×D11)⋊C4—44no—
136(C2×D11)⋊C4—44no—
137(C2×D11)⋊C4—42no—
138C4⋊Dic11—28no—
139C4⋊Dic11—22no—
140C4⋊Dic11—21no—
141C4⋊Dic11—21no—
142C4⋊Dic11C2×D414yes—
143Dic11⋊C4—28no—
144Dic11⋊C4—28no—
145C4×Dic11—24no—
146C4×Dic11—24no—
147C4×Dic11—22no—
148C4×Dic11C2×D414yes—
149C2×C11⋊C8—22no—
150C2×C11⋊C8—22no—
151C2×C11⋊C8—22no—
152C2×#533—111no—
153C2×#488—112no—
154#2850—111no—
155#2024—112no—
156#2023—112no—
157#1991—112no—
158#1875—111no—
159#1875—111no—
160#1873—111no—
161#1873D1111yescharacteristic, complemented
162C4×C22⋊C8—111no—
163C23×C11—21no—
164C23×C11—21no—
165C23×C11—22no—
166C23×C11—22no—
167C23×C11#12412yes—
168C23×C11C22×D411yescharacteristic
169C22×D11—41no—
170C22×D11—41no—
171C22×D11—41no—
172C22×D11—42no—
173C22×D11—42no—
174Q8×C11—42no—
175Q8×C11—42no—
176C2×C4×C11—21no—
177C2×C4×C11—21no—
178C2×C4×C11—24no—
179C2×C4×C11—24no—
180C2×C4×C11—24no—
181C2×C4×C11—42no—
182C2×C4×C11—42no—
183C2×C4×C11—41no—
184C2×C4×C11—41no—
185C2×C4×C11—41no—
186C2×C4×C11—41no—
187C2×C4×C11—42no—
188C2×C4×C11#12412yes—
189C2×C4×C11C22×D412yes—
190C2×C4×C11C2×#4111yescharacteristic
191C2×C4×C11C2×#4111yescharacteristic
192C2×C4×C112−1+412yes—
193C22⋊D11—84no—
194C2×Dic11—22no—
195C2×Dic11—22no—
196C2×Dic11—22no—
197C2×Dic11—22no—
198C2×Dic11—24no—
199C2×Dic11—48no—
200C2×Dic11—42no—
201C2×Dic11—42no—
202C2×Dic11—41no—
203C2×Dic11—42no—
204C2×Dic11#12014yes—
205C2×Dic11#13514yes—
206D44—42no—
207D44—42no—
208Dic22—416no—
209C8×C11—42no—
210C11⋊C8—42no—
211#533—228no—
212C2×C4⋊Q8—112no—
213C2×#125—112no—
214C2×#124—111no—
215C2×C22⋊Q8—222no—
216C2×C22⋊Q8C2×D1111yescharacteristic
217C2×#121—111no—
218C2×C4×Q8—222no—
219C2×#117—111no—
220C2×#117C2×D1111yescharacteristic
221C22×C42—111no—
222#488—228no—
223C2×#103—112no—
224C2×#103C2×D1112yes—
225C2×#102—112no—
226C2×#102—112no—
227C2×C22⋊C8—111no—
228C2×C22⋊C8C2×D1111yescharacteristic
229C2×C4×C8—112no—
230#391—111no—
231#390—111no—
232#388—222no—
233#386—222no—
234#382—111no—
235#340—112no—
236#340—112no—
237#340—112no—
238#340C2×D1112yes—
239#336—112no—
240C22×C11—22no—
241C22×C11—22no—
242C22×C11—22no—
243C22×C11—42no—
244C22×C11—42no—
245C22×C11C2×#12011yescharacteristic
246C22×C11C2×#12411yescharacteristic
247C22×C11#53611yescharacteristic
248C22×C11C2×#13512yes—
249C22×C11#57512yes—
250C2×D11—81no—
251C2×D11—81no—
252C2×D11—81no—
253C2×D11—82no—
254C2×D11—82no—
255C4×C11—22no—
256C4×C11—44no—
257C4×C11—81no—
258C4×C11—81no—
259C4×C11#54812yes—
260C4×C11#54812yes—
261Dic11—24no—
262Dic11—24no—
263Dic11—44no—
264Dic11—81no—
265C22×Q8—222no—
266C22×Q8C22×D1111yescharacteristic
267C22×D4—111no—
268C22×D4—221no—
269C23×C4—112no—
270C23×C4C22×D1111yescharacteristic
271C22×C8—112no—
272C22×C8C22×D1112yes—
273C4⋊Q8—224no—
274C4⋊Q8—224no—
275#125—118no—
276#125—224no—
277#124—224no—
278C22⋊Q8—22no—
279C22⋊Q8—22no—
280C22⋊Q8—2216no—
281#121—222no—
282#121—222no—
283C4×Q8—2216no—
284#117—24no—
285#117—224no—
286C2×C4⋊C4—21no—
287C2×C4⋊C4—112no—
288C2×C4⋊C4—111no—
289C2×C4⋊C4—222no—
290C2×C4⋊C4—222no—
291C2×C4⋊C4—222no—
292C2×C4⋊C4C22×D1111yescharacteristic
293C2×C4⋊C4C22×D1112yes—
294C2×C22⋊C4—21no—
295C2×C22⋊C4—21no—
296C2×C22⋊C4—221no—
297C2×C22⋊C4—222no—
298C2×C22⋊C4—222no—
299C2×C22⋊C4—221no—
300C2×C42—21no—
301C2×C42—111no—
302C2×C42—112no—
303C2×C42—111no—
304C2×C42—224no—
305C2×C42—221no—
306#103—24no—
307#103—224no—
308#102—224no—
309#102—224no—
310C22⋊C8—22no—
311C22⋊C8—222no—
312C4×C8—224no—
313#95—222no—
314#95—222no—
315C2×C11—42no—
316C2×C11#243611yescharacteristic
317C2×C11#300212yes—
318C2×C11#313111yescharacteristic
319C2×C11#314011yescharacteristic
320C2×C11#323312yes—
321D11—161no—
322C24—221no—
323C24D4×D1111yescharacteristic
324C2×Q8—21no—
325C2×Q8—22no—
326C2×Q8—21no—
327C2×Q8—22no—
328C2×Q8—228no—
329C2×Q8—444no—
330C2×Q8—444no—
331C2×D4—221no—
332C2×D4—222no—
333C2×D4—221no—
334C2×D4—222no—
335C2×D4—444no—
336C2×D4—442no—
337C22×C4—22no—
338C22×C4—22no—
339C22×C4—22no—
340C22×C4—21no—
341C22×C4—21no—
342C22×C4—112no—
343C22×C4—112no—
344C22×C4—224no—
345C22×C4—224no—
346C22×C4—222no—
347C22×C4—221no—
348C22×C4—442no—
349C22×C4#433912yes—
350C22×C4D4×D1111yescharacteristic
351C22×C4#434112yes—
352C22×C4C23×D1111yescharacteristic
353C2×C8—22no—
354C2×C8—22no—
355C2×C8—22no—
356C2×C8—222no—
357C2×C8—222no—
358C2×C8—222no—
359C4⋊C4—22no—
360C4⋊C4—21no—
361C4⋊C4—21no—
362C4⋊C4—42no—
363C4⋊C4—114no—
364C4⋊C4—228no—
365C4⋊C4—228no—
366C4⋊C4—228no—
367C4⋊C4—222no—
368C4⋊C4—221no—
369C4⋊C4—221no—
370C4⋊C4D4×D1114yes—
371C22⋊C4—24no—
372C22⋊C4—42no—
373C22⋊C4—224no—
374C22⋊C4—444no—
375C22⋊C4—444no—
376C22⋊C4—442no—
377C42—24no—
378C42—114no—
379C42—224no—
380C42—224no—
381C42—222no—
382C11#2590611yescharacteristic, complemented, Sylow
383C23—22no—
384C23—22no—
385C23—21no—
386C23—21no—
387C23—441no—
388C23—442no—
389C23—442no—
390C23—441no—
391C23—441no—
392C23#6693812yes—
393C23C2×D4×D1111yescharacteristic
394Q8—42no—
395Q8—42no—
396Q8—4416no—
397D4—442no—
398D4—442no—
399D4—884no—
400C2×C4—21no—
401C2×C4—21no—
402C2×C4—24no—
403C2×C4—24no—
404C2×C4—24no—
405C2×C4—42no—
406C2×C4—42no—
407C2×C4—41no—
408C2×C4—41no—
409C2×C4—42no—
410C2×C4—41no—
411C2×C4—41no—
412C2×C4—114no—
413C2×C4—114no—
414C2×C4—222no—
415C2×C4—222no—
416C2×C4—222no—
417C2×C4—222no—
418C2×C4—224no—
419C2×C4—448no—
420C2×C4—442no—
421C2×C4—442no—
422C2×C4—441no—
423C2×C4—442no—
424C2×C4#6693812yes—
425C2×C4C2×#433911yescharacteristic
426C2×C4C2×D4×D1112yes—
427C2×C4C2×#434111yescharacteristic
428C2×C4#6704312yes—
429C8—42no—
430C8—442no—
431C22—22no—
432C22—22no—
433C22—22no—
434C22—42no—
435C22—42no—
436C22—882no—
437C22—881no—
438C22—881no—
439C22—881no—
440C22—882no—
441C22C2×#6693811yescharacteristic
442C22D11×#12011yescharacteristic
443C22#1062317911yescharacteristic
444C22D11×#13512yes—
445C22#1062330812yes—
446C4—22no—
447C4—44no—
448C4—81no—
449C4—81no—
450C4—224no—
451C4—224no—
452C4—444no—
453C4—881no—
454C4#1062308312yes—
455C4#1062312912yes—
456C2—42no—
457C2—1761no—
458C2#1307227211yescharacteristic
459C2#1307783712yes—
460C2#1307893611yescharacteristic
461C2#1307900411yescharacteristic
462C2#1307979812yes—
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#1873C2
socleC23×C11C22×D4
prime radicalC2×#66983C22
hypercenter#1873D11
hypocenterC11#25906
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1873

Complements

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

NH ≅ G/Ntype
1. C2×#10623048C2semidirect
2. C2×#10622413C2semidirect
4. #13069755C2semidirect
5. #13069751C2semidirect
6. #13069579C2semidirect
9. #13068929C2semidirect
10. C22⋊C8×Dic11C2semidirect
11. C11×#1873C2semidirect
77. #66943D4semidirect
161. #1873D11semidirect
382. C11#25906semidirect

Maximal subgroups

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

subgroupindex
C2×#106230482
C2×#106224132
#130769192
#130697552
#130697512
#130695792
#130689382
#130689362
#130689292
C22⋊C8×Dic112
C11×#18732
#2590611