Finite Group Databasebeta

← #14909556

Subgroups — #14909556

Order 2816.

636 conjugacy classes of subgroups.

The subgroup lattice has 456 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D11×#467C211yesmaximal, characteristic, complemented
2C2×#10622496C211yesmaximal, characteristic
3#13070818C211yesmaximal, characteristic, complemented
4#13070798C212yesmaximal, complemented
5#13070732C212yesmaximal, complemented
6#13070730C212yesmaximal, complemented
7#13070547C211yesmaximal, characteristic, complemented
8#13070544C211yesmaximal, characteristic, complemented
9#13070534C212yesmaximal, complemented
10#13070225C211yesmaximal, characteristic, complemented
11C11×#2236C211yesmaximal, characteristic, complemented
12C2×Q16×D11C2211yescharacteristic, complemented
13C22×D88C2211yescharacteristic
14C22×C8×D11C2211yescharacteristic
15D11×C22⋊Q8—21no—
16C2×#66948—21no—
17C11×#467C2211yescharacteristic
18C2×C11×#107C2211yescharacteristic
19#10622801C2211yescharacteristic, complemented
20C2×#66892C2212yescomplemented
21#10622729C2211yescharacteristic
22#10622664—21no—
23C2×#66873—21no—
24C2×#66864C2212yescomplemented
25C2×#66862C2212yescomplemented
26#10622500C2211yescharacteristic, complemented
27#10622496—21no—
28#10622496—21no—
29#10622496C2212yes—
30#10622496C2212yes—
31D11×#107C2211yescharacteristic, complemented
32#10622426—21no—
33D11×#103—21no—
34C11×#366C2212yescomplemented
35C11×#358C2212yescomplemented
36C11×C22⋊C16C2211yescharacteristic
37C22⋊(C11⋊C16)C2211yescharacteristic
38#10622147C2212yescomplemented
39(C2×D11)⋊C16C2212yescomplemented
40#10622130C2212yescomplemented
41#10622129C2212yescomplemented
42#10622127C2212yescomplemented
43C2×Q8×D11—21no—
44C22×D44—21no—
45C22×D44—41no—
46C22×C4×D11D411yescharacteristic
47C2×C11×Q16C2311yescharacteristic
48C22×C8×C11C2311yescharacteristic
49C11×C22⋊Q8—21no—
50C2×C11×C4⋊C4—21no—
51#66999—21no—
52C2×#4326—21no—
53C2×(C2×D11)⋊C4—41no—
54#66977—21no—
55C22×C11⋊C8D411yescharacteristic
56Q16×D11—42no—
57C2×Dic44C2311yescharacteristic
58C2×D88—21no—
59C2×D88—42no—
60C2×D88C2312yes—
61C2×C8×D11—42no—
62C2×C8×D11D411yescharacteristic
63C2×C8×D11D411yescharacteristic
64C2×C8×D11C2311yescharacteristic
65C2×C8×D11C2311yescharacteristic
66#66950—21no—
67#66949—41no—
68#66948—22no—
69#66948—22no—
70#66948—41no—
71#66948—41no—
72C4⋊C4×D11—21no—
73C4⋊C4×D11—41no—
74C22⋊C4×D11—41no—
75#66931—41no—
76C2×C11×C16C2312yes—
77C11×#107—21no—
78C11×#107C2311yescharacteristic
79C11×#107C2312yes—
80C11×#103—21no—
81#66899—21no—
82#66892—42no—
83#66882C2311yescharacteristic
84#66880—21no—
85C2×C11⋊C16C2312yes—
86#66874—21no—
87#66873—22no—
88#66873—22no—
89#66871—21no—
90#66864—42no—
91#66862—42no—
92#33759—111nomaximal, Sylow
93C23×D11—41no—
94C23×D11D811yescharacteristic
95C2×Q8×C11—21no—
96C22×C4×C11—41no—
97C22×C4×C11C2×D411yescharacteristic
98C22×Dic11D811yescharacteristic
99Q8×D11—42no—
100Q8×D11—42no—
101C2×D44—22no—
102C2×D44—42no—
103C2×D44—42no—
104C2×D44—42no—
105C2×D44—42no—
106C2×D44—41no—
107C2×D44—84no—
108C2×C4×D11—41no—
109C2×C4×D11—41no—
110C2×C4×D11—41no—
111C2×C4×D11—41no—
112C2×C4×D11D811yescharacteristic
113C2×C4×D11D811yescharacteristic
114C2×C4×D11C2×D411yescharacteristic
115C2×C4×D11C2×D411yescharacteristic
116C2×Dic22—21no—
117C2×Dic22—41no—
118C11×Q16—22no—
119C2×C8×C11—22no—
120C2×C8×C11C2×D411yescharacteristic
121C2×C8×C11C2411yescharacteristic
122C11×C4⋊C4—21no—
123C11×C4⋊C4—22no—
124C11×C4⋊C4—41no—
125C11×C4⋊C4—41no—
126C11×C22⋊C4—41no—
127C22⋊Dic11—41no—
128#4326—42no—
129(C2×D11)⋊C4—42no—
130(C2×D11)⋊C4—42no—
131(C2×D11)⋊C4—41no—
132(C2×D11)⋊C4—41no—
133C4⋊Dic11—21no—
134C4⋊Dic11—41no—
135Dic11⋊C4—41no—
136Dic11⋊C4—41no—
137Dic11⋊C4—41no—
138C2×C11⋊C8—41no—
139C2×C11⋊C8C2×D411yescharacteristic
140C2×C11⋊C8C2×D411yescharacteristic
141Dic44—22no—
142D88—22no—
143D88—22no—
144D88—42no—
145C8×D11—22no—
146C8×D11—22no—
147C8×D11—41no—
148C8×D11—41no—
149C11×C16—22no—
150C11⋊C16—22no—
151C2×#467—111no—
152C2×#466—111no—
153#2236—111no—
154#2236D1111yescharacteristic, complemented
155#2232—112no—
156#2220—112no—
157#2220—112no—
158#2187—111no—
159#2187—111no—
160#2185—112no—
161#2112—111no—
162C23×C11C2×D811yescharacteristic
163C22×D11—22no—
164C22×D11—22no—
165C22×D11—41no—
166C22×D11—42no—
167C22×D11—82no—
168C22×D11—82no—
169C22×D11—82no—
170C22×D11C2×D811yescharacteristic
171C22×D11C2×D811yescharacteristic
172Q8×C11—41no—
173Q8×C11—41no—
174C2×C4×C11—21no—
175C2×C4×C11—21no—
176C2×C4×C11—41no—
177C2×C4×C11—41no—
178C2×C4×C11—42no—
179C2×C4×C11—82no—
180C2×C4×C11C2×D811yescharacteristic
181C2×C4×C11C22×D411yescharacteristic
182C2×Dic11—41no—
183C2×Dic11—41no—
184C2×Dic11—41no—
185C2×Dic11C2×D811yescharacteristic
186C2×Dic11C2×D811yescharacteristic
187D44—42no—
188D44—42no—
189D44—82no—
190D44—84no—
191D44—84no—
192C4×D11—21no—
193C4×D11—21no—
194C4×D11—21no—
195C4×D11—21no—
196C4×D11—41no—
197C4×D11—41no—
198C4×D11—82no—
199C4×D11—82no—
200Dic22—41no—
201Dic22—41no—
202Dic22—82no—
203C8×C11—21no—
204C8×C11H(5,𝔽2)12yes—
205C11⋊C8—21no—
206C11⋊C8—21no—
207C22×Q16—111no—
208C22×D8—111no—
209C23×C8—111no—
210C2×C22⋊Q8—221no—
211C2×#121—221no—
212C2×SD32—112no—
213C2×SD32—112no—
214C2×M32—112no—
215#467—111no—
216#467—111no—
217#467—111no—
218#467—221no—
219#467—221no—
220#467C2×D1111yescharacteristic
221#466—112no—
222#466—112no—
223#466—221no—
224#466—221no—
225C2×#107—111no—
226C2×#107C2×D1111yescharacteristic
227C2×#103—221no—
228C2×#102—221no—
229#366—112no—
230#366C2×D1112yescomplemented
231#358—112no—
232#358C2×D1112yescomplemented
233#357—112no—
234#357—112no—
235C22⋊C16—111no—
236C22⋊C16—112no—
237C22⋊C16C2×D1111yescharacteristic
238C22×C11—21no—
239C22×C11—21no—
240C22×C11#51012yes—
241C22×C11C22×D811yescharacteristic
242C2×D11—21no—
243C2×D11—21no—
244C2×D11—21no—
245C2×D11—21no—
246C2×D11—21no—
247C2×D11—44no—
248C2×D11—82no—
249C2×D11—82no—
250C2×D11—82no—
251C2×D11—164no—
252C2×D11#50912yes—
253C4×C11—21no—
254C4×C11—82no—
255C4×C11—81no—
256C4×C11—81no—
257C4×C11#53411yescharacteristic
258C4×C11#57511yescharacteristic
259Dic11—21no—
260Dic11—21no—
261Dic11—81no—
262Dic11—81no—
263C22×Q8—221no—
264C22×D4—221no—
265C22×D4—441no—
266C23×C4—111no—
267C2×Q16—111no—
268C2×Q16—221no—
269C2×Q16—442no—
270C2×Q16C22×D1111yescharacteristic
271C2×D8—112no—
272C2×D8—221no—
273C2×D8—442no—
274C22×C8—111no—
275C22×C8—111no—
276C22×C8—111no—
277C22×C8—111no—
278C22×C8—111no—
279C22×C8—442no—
280C22×C8C22×D1111yescharacteristic
281C22⋊Q8—21no—
282C22⋊Q8—221no—
283C22⋊Q8—221no—
284C22⋊Q8—221no—
285C22⋊Q8—441no—
286C22⋊Q8—441no—
287#121—222no—
288#121—222no—
289#121—441no—
290#121—441no—
291C2×C4⋊C4—21no—
292C2×C4⋊C4—221no—
293C2×C4⋊C4—441no—
294C2×C22⋊C4—441no—
295C2×C22⋊C4—441no—
296SD32—442no—
297SD32—442no—
298M32—442no—
299C2×C16—112no—
300C2×C16C22×D1112yes—
301#107—21no—
302#107—111no—
303#107—221no—
304#107C22×D1111yescharacteristic
305#107C22×D1112yes—
306#103—21no—
307#103—221no—
308#103—221no—
309#103—221no—
310#102—222no—
311#102—222no—
312C2×C11—22no—
313C2×C11#318611yescharacteristic
314C2×C11C2×#50911yescharacteristic
315C2×C11C2×#51011yescharacteristic
316D11—22no—
317D11—41no—
318D11—162no—
319C24—111no—
320C24—441no—
321C2×Q8—21no—
322C2×Q8—221no—
323C2×Q8—441no—
324C2×Q8—442no—
325C2×Q8—442no—
326C2×D4—222no—
327C2×D4—442no—
328C2×D4—442no—
329C2×D4—442no—
330C2×D4—442no—
331C2×D4—441no—
332C2×D4—884no—
333C22×C4—41no—
334C22×C4—111no—
335C22×C4—111no—
336C22×C4—111no—
337C22×C4—111no—
338C22×C4—111no—
339C22×C4—441no—
340C22×C4—441no—
341C22×C4—441no—
342C22×C4—441no—
343C22×C4D4×D1111yescharacteristic
344Q16—22no—
345Q16—222no—
346Q16—442no—
347D8—222no—
348D8—222no—
349D8—442no—
350C2×C8—22no—
351C2×C8—111no—
352C2×C8—111no—
353C2×C8—222no—
354C2×C8—222no—
355C2×C8—441no—
356C2×C8—441no—
357C2×C8—441no—
358C2×C8D4×D1111yescharacteristic
359C2×C8C23×D1111yescharacteristic
360C4⋊C4—22no—
361C4⋊C4—21no—
362C4⋊C4—41no—
363C4⋊C4—41no—
364C4⋊C4—221no—
365C4⋊C4—441no—
366C4⋊C4—441no—
367C4⋊C4—441no—
368C4⋊C4—441no—
369C22⋊C4—41no—
370C22⋊C4—442no—
371C22⋊C4—442no—
372C22⋊C4—441no—
373C22⋊C4—441no—
374C22⋊C4—441no—
375C16—22no—
376C16—222no—
377C11#3375911yescharacteristic, complemented, Sylow
378C23—111no—
379C23—111no—
380C23—222no—
381C23—222no—
382C23—441no—
383C23—442no—
384C23—882no—
385C23—882no—
386C23—882no—
387C23D8×D1111yescharacteristic
388Q8—41no—
389Q8—41no—
390Q8—441no—
391Q8—441no—
392Q8—882no—
393D4—442no—
394D4—442no—
395D4—882no—
396D4—884no—
397D4—884no—
398C2×C4—21no—
399C2×C4—21no—
400C2×C4—41no—
401C2×C4—41no—
402C2×C4—42no—
403C2×C4—82no—
404C2×C4—111no—
405C2×C4—111no—
406C2×C4—221no—
407C2×C4—221no—
408C2×C4—221no—
409C2×C4—221no—
410C2×C4—441no—
411C2×C4—441no—
412C2×C4—441no—
413C2×C4—441no—
414C2×C4—441no—
415C2×C4—882no—
416C2×C4—882no—
417C2×C4D8×D1111yescharacteristic
418C2×C4C2×D4×D1111yescharacteristic
419C8—21no—
420C8—221no—
421C8—221no—
422C8#6704212yes—
423C22—21no—
424C22—21no—
425C22—112no—
426C22—221no—
427C22—221no—
428C22—221no—
429C22—221no—
430C22—221no—
431C22—444no—
432C22—882no—
433C22—882no—
434C22—882no—
435C22—1764no—
436C22#1062253112yes—
437C22C2×D8×D1111yescharacteristic
438C4—21no—
439C4—81no—
440C4—82no—
441C4—81no—
442C4—221no—
443C4—221no—
444C4—881no—
445C4—881no—
446C4#1062318411yescharacteristic
447C4#1062330811yescharacteristic
448C2—22no—
449C2—222no—
450C2—441no—
451C2—1762no—
452C2#1307936611yescharacteristic
453C2D11×#50911yescharacteristic
454C2C2×#1062253111yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2236C2
socleC22×C11C22×D8
prime radicalC2×#10622496C2
hypercenter#2236D11
hypocenterC11#33759
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #2236

Complements

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

NH ≅ G/Ntype
1. D11×#467C2semidirect
3. #13070818C2semidirect
4. #13070798C2semidirect
5. #13070732C2semidirect
6. #13070730C2semidirect
7. #13070547C2semidirect
8. #13070544C2semidirect
9. #13070534C2semidirect
10. #13070225C2semidirect
11. C11×#2236C2semidirect
12. C2×Q16×D11C22semidirect
19. #10622801C22semidirect
20. C2×#66892C22semidirect
24. C2×#66864C22semidirect
25. C2×#66862C22semidirect
26. #10622500C22semidirect
31. D11×#107C22semidirect
34. C11×#366C22semidirect
35. C11×#358C22semidirect
38. #10622147C22semidirect
39. (C2×D11)⋊C16C22semidirect
40. #10622130C22semidirect
41. #10622129C22semidirect
42. #10622127C22semidirect
154. #2236D11semidirect
230. #366C2×D11semidirect
232. #358C2×D11semidirect
377. C11#33759semidirect

Maximal subgroups

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

subgroupindex
D11×#4672
C2×#106224962
#130708182
#130707982
#130707322
#130707302
#130705472
#130705442
#130705342
#130702252
C11×#22362
#3375911