Finite Group Databasebeta

← #14790028

Subgroups — #14790028

Order 2816.

1078 conjugacy classes of subgroups.

The subgroup lattice has 452 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13078409C212yesmaximal, complemented
2#13071338C211yesmaximal, characteristic
3#13069963C212yesmaximal, complemented
4#13069769C212yesmaximal, complemented
5#13069598C212yesmaximal, complemented
6#13069014C212yesmaximal
7#13068826C212yesmaximal, complemented
8#13068608C211yesmaximal, characteristic, complemented
9C11×#3501C211yesmaximal, characteristic, complemented
10C11×#554—22no—
11C11×#554—24no—
12D4×Q8×C11—22no—
13C11×#544C2212yes—
14C11×#543—22no—
15C11×#533C2212yes—
16C2×C11×C22⋊Q8—22no—
17C11×#518C2212yes—
18C2×C4×D4×C11C2211yescharacteristic
19C2×#66993C2211yescharacteristic
20C2×C4×D44C2211yescharacteristic
21#10622834C2211yescharacteristic
22C2×#66897C2212yes—
23#10622826—22no—
24#10622700—22no—
25#10622697—22no—
26#10622679—24no—
27#10622614C2214yes—
28#10622608C2214yes—
29#10622601C2211yescharacteristic
30#10622590C2211yescharacteristic
31#10622569—22no—
32#10622545C2211yescharacteristic
33#10622537C2212yes—
34#10622170C2214yes—
35#10622170C2214yes—
36#10622168C2212yes—
37C22×Q8×C11—22no—
38C22×D4×C11C2311yescharacteristic
39C23×C4×C11D412yes—
40C22×C22⋊D11—22no—
41C22×D44C2311yescharacteristic
42C22×C4×D11—21no—
43C11×C4⋊Q8—24no—
44C11×C4⋊Q8D412yescomplemented
45C11×C4⋊Q8D412yescomplemented
46C11×#125—24no—
47C11×#125D414yescomplemented
48C11×C22⋊Q8—24no—
49C11×C22⋊Q8—24no—
50C11×C22⋊Q8—28no—
51C11×C22⋊Q8—28no—
52C11×C22⋊Q8—22no—
53C11×C22⋊Q8—24no—
54C11×C22⋊Q8—22no—
55C4×Q8×C11—22no—
56C4×Q8×C11—22no—
57C4×D4×C11—24no—
58C4×D4×C11—24no—
59C4×D4×C11—22no—
60C4×D4×C11—22no—
61C11×#117C2314yes—
62C2×C11×C4⋊C4—22no—
63C2×C11×C4⋊C4—24no—
64C2×C11×C4⋊C4C2311yescharacteristic
65C2×C11×C22⋊C4—24no—
66C2×C11×C22⋊C4D412yes—
67C2×C42×C11C2311yescharacteristic
68C2×C22⋊Dic11—22no—
69#66993—22no—
70#66993Q814yescomplemented
71C2×(C2×D11)⋊C4—21no—
72C2×(C2×D11)⋊C4—22no—
73C2×C4⋊Dic11C2311yescharacteristic
74C2×C4×Dic11C2311yescharacteristic
75C2×C4×Dic11C2311yescharacteristic
76C2×#4318C2314yes—
77C4×D44—22no—
78C4×D44—22no—
79#66897—24no—
80C11⋊#95—21no—
81C11⋊#95—21no—
82C11⋊#95—22no—
83#66873—24no—
84#66873—24no—
85#66872—24no—
86#66871—24no—
87C4⋊(C11⋊C8)—22no—
88C4⋊(C11⋊C8)—22no—
89#24316—111nomaximal, Sylow
90C24×C11C2×D412yes—
91C23×D11—21no—
92C2×Q8×C11—24no—
93C2×Q8×C11—22no—
94C2×Q8×C11—22no—
95C2×Q8×C11—84no—
96C2×D4×C11—22no—
97C2×D4×C11—22no—
98C2×D4×C11C2×Q812yes—
99C2×D4×C11#4112yes—
100C22×C4×C11—24no—
101C22×C4×C11—24no—
102C22×C4×C11—22no—
103C22×C4×C11—22no—
104C22×C4×C11—82no—
105C22×C4×C11C2×D412yes—
106C22×C4×C11C2×D411yescharacteristic
107C22×C4×C11C2×D411yescharacteristic
108C22×C4×C11C2411yescharacteristic
109C2×C22⋊D11—28no—
110C2×C22⋊D11—82no—
111C2×C22⋊D11—82no—
112C22×Dic11—21no—
113C22×Dic11—21no—
114C22×Dic11—21no—
115C2×D44—22no—
116C2×D44—21no—
117C2×D44—22no—
118C2×D44C2×Q812yescomplemented
119C2×C4×D11—42no—
120C2×C4×D11—82no—
121C11×C4⋊C4—24no—
122C11×C4⋊C4—28no—
123C11×C4⋊C4—24no—
124C11×C4⋊C4—22no—
125C11×C4⋊C4—24no—
126C11×C4⋊C4—22no—
127C11×C4⋊C4—22no—
128C11×C4⋊C4C2×D414yes—
129C11×C4⋊C4C2×D414yes—
130C11×C22⋊C4—28no—
131C11×C22⋊C4—24no—
132C11×C22⋊C4—24no—
133C42×C11—24no—
134C42×C11C2×D412yes—
135C42×C11C2×D412yes—
136C22⋊Dic11—82no—
137(C2×D11)⋊C4—41no—
138(C2×D11)⋊C4—41no—
139(C2×D11)⋊C4—82no—
140C4⋊Dic11—22no—
141C4×Dic11—21no—
142C4×Dic11—22no—
143C4×Dic11C2×Q812yescomplemented
144#4318—24no—
145#4318—24no—
146C2×C11⋊C8—24no—
147#3501D1111yescharacteristic, complemented
148#3077—112no—
149#2328—111no—
150#2061—112no—
151#2027—112no—
152#1995—112no—
153#1887—112no—
154#1856—112no—
155#1800—111no—
156C23×C11—22no—
157C23×C11—22no—
158C23×C11—42no—
159C23×C11—42no—
160C23×C11C22⋊Q814yes—
161C23×C11C22×D411yescharacteristic
162C22×D11—22no—
163C22×D11—42no—
164C22×D11—42no—
165C22×D11—41no—
166C22×D11—41no—
167Q8×C11—44no—
168Q8×C11—82no—
169Q8×C11—84no—
170D4×C11—24no—
171D4×C11—24no—
172C2×C4×C11—24no—
173C2×C4×C11—24no—
174C2×C4×C11—22no—
175C2×C4×C11—41no—
176C2×C4×C11—41no—
177C2×C4×C11—44no—
178C2×C4×C11—42no—
179C2×C4×C11—82no—
180C2×C4×C11—84no—
181C2×C4×C11—84no—
182C2×C4×C11#12011yescharacteristic
183C2×C4×C11#12011yescharacteristic
184C2×C4×C11#12012yes—
185C2×C4×C11C22×D412yes—
186C2×C4×C11C22×Q811yescharacteristic
187C2×C4×C11C2×#4111yescharacteristic
188C2×C4×C112−1+412yes—
189C22⋊D11—88no—
190C2×Dic11—22no—
191C2×Dic11—41no—
192C2×Dic11—41no—
193C2×Dic11—41no—
194C2×Dic11—41no—
195C2×Dic11—42no—
196C2×Dic11—41no—
197C2×Dic11—41no—
198D44—24no—
199D44—42no—
200C4×D11—84no—
201C11⋊C8—44no—
202#554—22no—
203#554—24no—
204D4×Q8—22no—
205#544C2×D1112yes—
206#543—22no—
207#533C2×D1112yes—
208C2×#127—111no—
209C2×C22⋊Q8—22no—
210#518C2×D1112yes—
211C2×C4×D4—111no—
212C2×C4×D4C2×D1111yescharacteristic
213#478—224no—
214#476—222no—
215#474—222no—
216#428—114no—
217#423—112no—
218#418—114no—
219C2×#100—112no—
220#390—111no—
221#390—111no—
222#386—222no—
223#386—222no—
224#382—111no—
225#376—111no—
226#343—112no—
227#339—114no—
228#339—114no—
229C22×C11—21no—
230C22×C11—21no—
231C22×C11—24no—
232C22×C11—44no—
233C22×C11—42no—
234C22×C11—42no—
235C22×C11—82no—
236C22×C11C2×#12011yescharacteristic
237C22×C11C2×C22⋊Q811yescharacteristic
238C22×C11#53611yescharacteristic
239C2×D11—44no—
240C2×D11—42no—
241C2×D11—82no—
242C2×D11—81no—
243C2×D11—81no—
244C4×C11—21no—
245C4×C11—21no—
246C4×C11—22no—
247C4×C11—42no—
248C4×C11—44no—
249C4×C11—44no—
250C4×C11#54812yes—
251C4×C11D4×Q812yes—
252Dic11—42no—
253Dic11—81no—
254Dic11—81no—
255C22×Q8—22no—
256C22×D4—111no—
257C22×D4—222no—
258C22×D4C22×D1111yescharacteristic
259C23×C4—221no—
260C23×C4C22⋊D1112yes—
261C2×M16—114no—
262C4⋊Q8—24no—
263C4⋊Q8C22⋊D1112yescomplemented
264C4⋊Q8C22⋊D1112yescomplemented
265#127—114no—
266#127—222no—
267#125—24no—
268#125C22⋊D1114yescomplemented
269C22⋊Q8—24no—
270C22⋊Q8—24no—
271C22⋊Q8—28no—
272C22⋊Q8—28no—
273C22⋊Q8—22no—
274C22⋊Q8—24no—
275C22⋊Q8—22no—
276C4×Q8—22no—
277C4×Q8—22no—
278C4×D4—24no—
279C4×D4—24no—
280C4×D4—22no—
281C4×D4—22no—
282C4×D4—222no—
283C4×D4—222no—
284#117C22×D1114yes—
285C2×C4⋊C4—22no—
286C2×C4⋊C4—24no—
287C2×C4⋊C4—111no—
288C2×C4⋊C4C22×D1111yescharacteristic
289C2×C22⋊C4—24no—
290C2×C22⋊C4—221no—
291C2×C22⋊C4—222no—
292C2×C22⋊C4—222no—
293C2×C22⋊C4C22⋊D1112yes—
294C2×C42—111no—
295C2×C42—111no—
296C2×C42C22×D1111yescharacteristic
297#107—224no—
298#106—224no—
299C4⋊C8—222no—
300C4⋊C8—222no—
301#102—224no—
302#102—224no—
303#100—224no—
304#95—221no—
305#95—221no—
306#95—222no—
307C2×C11—21no—
308C2×C11—21no—
309C2×C11—44no—
310C2×C11#240911yescharacteristic
311C2×C11#301911yescharacteristic
312C2×C11#302111yescharacteristic
313D11—82no—
314C24—221no—
315C24C2×C22⋊D1112yes—
316C2×Q8—24no—
317C2×Q8—22no—
318C2×Q8—22no—
319C2×Q8—84no—
320C2×D4—22no—
321C2×D4—22no—
322C2×D4—112no—
323C2×D4—228no—
324C2×D4—221no—
325C2×D4—222no—
326C2×D4—222no—
327C2×D4—882no—
328C2×D4—882no—
329C2×D4Q8×D1112yes—
330C2×D4#434312yes—
331C22×C4—24no—
332C22×C4—24no—
333C22×C4—22no—
334C22×C4—22no—
335C22×C4—82no—
336C22×C4—221no—
337C22×C4—221no—
338C22×C4—221no—
339C22×C4—442no—
340C22×C4—882no—
341C22×C4C2×C22⋊D1112yes—
342C22×C4C2×C22⋊D1111yescharacteristic
343C22×C4C2×C22⋊D1111yescharacteristic
344C22×C4C23×D1111yescharacteristic
345M16—224no—
346M16—224no—
347C2×C8—224no—
348C4⋊C4—24no—
349C4⋊C4—28no—
350C4⋊C4—24no—
351C4⋊C4—22no—
352C4⋊C4—24no—
353C4⋊C4—22no—
354C4⋊C4—22no—
355C4⋊C4—222no—
356C4⋊C4C2×C22⋊D1114yes—
357C4⋊C4C2×C22⋊D1114yes—
358C22⋊C4—28no—
359C22⋊C4—24no—
360C22⋊C4—24no—
361C22⋊C4—441no—
362C22⋊C4—441no—
363C22⋊C4—882no—
364C22⋊C4—882no—
365C42—24no—
366C42—112no—
367C42—221no—
368C42—222no—
369C42C2×C22⋊D1112yes—
370C42C2×C22⋊D1112yes—
371C11#2431611yescharacteristic, complemented, Sylow
372C23—22no—
373C23—22no—
374C23—42no—
375C23—42no—
376C23—222no—
377C23—442no—
378C23—442no—
379C23—441no—
380C23—441no—
381C23#6699914yes—
382C23C22×C22⋊D1111yescharacteristic
383Q8—44no—
384Q8—82no—
385Q8—84no—
386D4—24no—
387D4—24no—
388D4—224no—
389D4—442no—
390D4—888no—
391C2×C4—24no—
392C2×C4—24no—
393C2×C4—22no—
394C2×C4—41no—
395C2×C4—41no—
396C2×C4—44no—
397C2×C4—42no—
398C2×C4—82no—
399C2×C4—84no—
400C2×C4—84no—
401C2×C4—222no—
402C2×C4—441no—
403C2×C4—441no—
404C2×C4—441no—
405C2×C4—441no—
406C2×C4—442no—
407C2×C4—441no—
408C2×C4—441no—
409C2×C4—884no—
410C2×C4#6700612yes—
411C2×C4#6700611yescharacteristic
412C2×C4#6700611yescharacteristic
413C2×C4C2×Q8×D1111yescharacteristic
414C2×C4C2×#434311yescharacteristic
415C2×C4#6704012yes—
416C2×C4C22×C22⋊D1112yes—
417C8—444no—
418C22—21no—
419C22—21no—
420C22—24no—
421C22—44no—
422C22—42no—
423C22—42no—
424C22—82no—
425C22—444no—
426C22—442no—
427C22—882no—
428C22—881no—
429C22—881no—
430C22C2×#6699911yescharacteristic
431C22#1062334711yescharacteristic
432C22C2×#6700611yescharacteristic
433C4—21no—
434C4—21no—
435C4—22no—
436C4—42no—
437C4—44no—
438C4—44no—
439C4—442no—
440C4—881no—
441C4—881no—
442C4Q8×C22⋊D1112yes—
443C4#1062334812yes—
444C2—21no—
445C2—21no—
446C2—44no—
447C2—882no—
448C2#1307197511yescharacteristic
449C2#1307797311yescharacteristic
450C2#1307798811yescharacteristic
subgroupG/H
centerC22C2×#67006
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#3501C2
socleC22×C11C2×#120
prime radicalC2×#66993C22
hypercenter#3501D11
hypocenterC11#24316
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3501

Complements

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

NH ≅ G/Ntype
1. #13078409C2semidirect
3. #13069963C2semidirect
4. #13069769C2semidirect
5. #13069598C2semidirect
7. #13068826C2semidirect
8. #13068608C2semidirect
9. C11×#3501C2semidirect
44. C11×C4⋊Q8D4semidirect
45. C11×C4⋊Q8D4semidirect
47. C11×#125D4semidirect
70. #66993Q8semidirect
118. C2×D44C2×Q8semidirect
143. C4×Dic11C2×Q8semidirect
147. #3501D11semidirect
263. C4⋊Q8C22⋊D11semidirect
264. C4⋊Q8C22⋊D11semidirect
268. #125C22⋊D11semidirect
371. C11#24316semidirect

Maximal subgroups

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

subgroupindex
#130784092
#130713382
#130699632
#130697692
#130695982
#130690142
#130688262
#130686082
C11×#35012
#2431611