Finite Group Databasebeta

← #14909433

Subgroups — #14909433

Order 2816.

496 conjugacy classes of subgroups.

The subgroup lattice has 472 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079276C211yesmaximal, characteristic, complemented
2#13079252C211yesmaximal, characteristic
3#13070903C211yesmaximal, characteristic, complemented
4#13070888C211yesmaximal, characteristic, complemented
5#13070844C211yesmaximal, characteristic, complemented
6#13070728C211yesmaximal, characteristic
7#13070723C211yesmaximal, characteristic, complemented
8#13070711C211yesmaximal, characteristic
9#13070706C211yesmaximal, characteristic, complemented
10#13070484C211yesmaximal, characteristic, complemented
11#13070477C211yesmaximal, characteristic, complemented
12#13070472C211yesmaximal, characteristic, complemented
13#13070471C211yesmaximal, characteristic, complemented
14#13070211C211yesmaximal, characteristic, complemented
15C11×#2242C211yesmaximal, characteristic, complemented
16#10623228—21no—
17#10623213—21no—
18C11×#499C2211yescharacteristic
19C11×#495C2211yescharacteristic
20#10622801C2211yescharacteristic
21Q16×Dic11C2211yescharacteristic
22C2×#66893C2211yescharacteristic
23C2×#66893C2211yescharacteristic
24#10622787—21no—
25#10622777—21no—
26#10622770C2211yescharacteristic
27D8×Dic11C2211yescharacteristic
28C2×#66891C2211yescharacteristic
29C2×#66891C2211yescharacteristic
30#10622682—21no—
31#10622668—21no—
32C2×#66862C2211yescharacteristic
33C2×C16×D11C2211yescharacteristic
34#10622500C2211yescharacteristic
35#10622500C2211yescharacteristic
36#10622486C2211yescharacteristic
37#10622486C2211yescharacteristic
38#10622481—21no—
39#10622466—21no—
40#10622312C2211yescharacteristic
41#10622302C2211yescharacteristic
42#10622295C2211yescharacteristic
43C11×#358C2211yescharacteristic
44C11×#358C2211yescharacteristic
45C11×#357C2211yescharacteristic
46C11×#357C2211yescharacteristic
47C4×C11×C16C2211yescharacteristic
48#10622141C2211yescharacteristic
49#10622141C2211yescharacteristic
50#10622141C2211yescharacteristic
51#10622141C2211yescharacteristic
52#10622140C2211yescharacteristic
53C16×Dic11C2211yescharacteristic
54#10622128C2211yescharacteristic
55#10622128C2211yescharacteristic
56#10622127C2211yescharacteristic
57#10622127C2211yescharacteristic
58#10622099C2211yescharacteristic
59C2×C11×Q16C2311yescharacteristic
60C2×C11×SD16—21no—
61C2×C11×D8C2311yescharacteristic
62C11×#125—21no—
63C11×#124—21no—
64#66999—21no—
65Q8×Dic11—21no—
66#66991—21no—
67D4×Dic11—21no—
68C2×Dic44—21no—
69C2×Dic44C2311yescharacteristic
70C2×Dic44C2311yescharacteristic
71C2×#4313D411yescharacteristic
72C2×C8×D11C2311yescharacteristic
73#66951—41no—
74#66951—41no—
75#66950—21no—
76#66950—21no—
77#66943—41no—
78#66943—41no—
79#66940—21no—
80#66940—21no—
81#66939—41no—
82#66938—41no—
83#66932—41no—
84#66931—41no—
85#66925D411yescharacteristic
86#66922—21no—
87#66922—21no—
88C2×C11×C16C2311yescharacteristic
89C2×C11×C16C2311yescharacteristic
90C11×#107C2311yescharacteristic
91C11×#107C2311yescharacteristic
92C11×#106—21no—
93C4×C8×C11C2311yescharacteristic
94#66899—21no—
95#66899—21no—
96#66896—21no—
97#66896—21no—
98#66893—22no—
99#66893—22no—
100#66891—22no—
101#66891—22no—
102#66882—21no—
103#66882C2311yescharacteristic
104#66882C2311yescharacteristic
105#66879D411yescharacteristic
106C8×Dic11C2311yescharacteristic
107C2×C11⋊C16C2311yescharacteristic
108C2×C11⋊C16C2311yescharacteristic
109#66874—21no—
110#66874—21no—
111#66874—21no—
112#66874—21no—
113#66867D411yescharacteristic
114#66862—22no—
115C16×D11—22no—
116#33745—111nomaximal, Sylow
117C2×Q8×C11—21no—
118C2×D4×C11—21no—
119C2×C22⋊D11—41no—
120C22×Dic11—41no—
121C2×C4×D11C2×D411yescharacteristic
122C2×Dic22—21no—
123C2×Dic22—21no—
124C2×Dic22—41no—
125C11×Q16—21no—
126C11×Q16—21no—
127C11×SD16—42no—
128C11×D8—21no—
129C11×D8—21no—
130C2×C8×C11C2×D411yescharacteristic
131C2×C8×C11C2411yescharacteristic
132C11×C4⋊C4—21no—
133C11×C4⋊C4—21no—
134C11×C4⋊C4—41no—
135C11×C4⋊C4—41no—
136C11×C22⋊C4—41no—
137C11×C22⋊C4—41no—
138C42×C11C2×D411yescharacteristic
139C22⋊Dic11—41no—
140C22⋊Dic11—41no—
141(C2×D11)⋊C4—41no—
142(C2×D11)⋊C4—41no—
143(C2×D11)⋊C4—41no—
144(C2×D11)⋊C4D811yescharacteristic
145(C2×D11)⋊C4D811yescharacteristic
146C4⋊Dic11—21no—
147C4⋊Dic11—21no—
148C4⋊Dic11—41no—
149C4⋊Dic11—41no—
150C4⋊Dic11—41no—
151C4⋊Dic11—41no—
152C4⋊Dic11—41no—
153C4⋊Dic11—41no—
154Dic11⋊C4—41no—
155Dic11⋊C4—41no—
156Dic11⋊C4—41no—
157Dic11⋊C4D811yescharacteristic
158Dic11⋊C4D811yescharacteristic
159C4×Dic11—41no—
160C4×Dic11—41no—
161C4×Dic11—41no—
162C4×Dic11C2×D411yescharacteristic
163C2×C11⋊C8C2×D411yescharacteristic
164C2×C11⋊C8C2×D411yescharacteristic
165Dic44—21no—
166Dic44—21no—
167Dic44—21no—
168Dic44—21no—
169Dic44—42no—
170#4313—22no—
171C8×D11—21no—
172C8×D11—21no—
173C11×C16—21no—
174C11×C16—21no—
175C11⋊C16#4112yes—
176C11⋊C16#4112yes—
177#3177—111no—
178#3175—111no—
179#2255—111no—
180#2251—111no—
181#2242D1111yescharacteristic, complemented
182#2241—111no—
183#2220—111no—
184#2219—111no—
185#2217—111no—
186#2216—111no—
187#2176—111no—
188#2175—111no—
189C4×Q32—111no—
190C4×SD32—111no—
191#2108—111no—
192C23×C11—41no—
193C22×D11C2×D811yescharacteristic
194Q8×C11—41no—
195Q8×C11—41no—
196D4×C11—41no—
197D4×C11—41no—
198C2×C4×C11—41no—
199C2×C4×C11—41no—
200C2×C4×C11—41no—
201C2×C4×C11C2×D811yescharacteristic
202C2×C4×C11C2×D811yescharacteristic
203C2×C4×C11C22×D411yescharacteristic
204C22⋊D11—161no—
205C2×Dic11—41no—
206C2×Dic11—41no—
207C2×Dic11—41no—
208C2×Dic11—41no—
209C2×Dic11—161no—
210C2×Dic11C2×D811yescharacteristic
211C2×Dic11C2×D811yescharacteristic
212C2×Dic11C2×D811yescharacteristic
213C4×D11—21no—
214C4×D11—21no—
215Dic22—41no—
216Dic22—41no—
217Dic22—41no—
218Dic22—41no—
219Dic22—161no—
220C8×C11#13512yes—
221C8×C11C2×#4111yescharacteristic
222C8×C11C2×#4111yescharacteristic
223C11⋊C8—21no—
224C11⋊C8—21no—
225#542—221no—
226#541—221no—
227C2×Q32—111no—
228C2×Q32—111no—
229C2×SD32—111no—
230C2×SD32—111no—
231C2×M32—111no—
232C22×C16—111no—
233#500—111no—
234#499C2×D1111yescharacteristic
235#495C2×D1111yescharacteristic
236#494—111no—
237#491—221no—
238#489—221no—
239#470—221no—
240#468—221no—
241#467—111no—
242#467—111no—
243#467—111no—
244#466—111no—
245#441—221no—
246#440—221no—
247C4×Q16—111no—
248C4×Q16—111no—
249C4×Q16—111no—
250C4×D8—111no—
251#405—111no—
252#367—111no—
253#367—111no—
254#366—111no—
255#366—111no—
256#358—111no—
257#358—111no—
258#358—111no—
259#358—111no—
260#358C2×D1111yescharacteristic
261#358C2×D1111yescharacteristic
262#357C2×D1111yescharacteristic
263#357C2×D1111yescharacteristic
264#346—111no—
265#346—111no—
266C4×C16—111no—
267C4×C16C2×D1111yescharacteristic
268C22×C11—81no—
269C22×C11—81no—
270C22×C11—81no—
271C22×C11C22×D811yescharacteristic
272C2×D11—21no—
273C2×D11—21no—
274C2×D11—21no—
275C4×C11—21no—
276C4×C11—21no—
277C4×C11—81no—
278C4×C11—81no—
279C4×C11—81no—
280C4×C11#53211yescharacteristic
281C4×C11C2×#13511yescharacteristic
282Dic11—21no—
283Dic11—21no—
284Dic11—21no—
285Dic11—81no—
286Dic11—81no—
287Dic11—81no—
288Dic11—81no—
289C2×Q16—111no—
290C2×Q16—111no—
291C2×Q16—221no—
292C2×Q16C22×D1111yescharacteristic
293C2×SD16—21no—
294C2×D8C22×D1111yescharacteristic
295C2×M16—111no—
296C22×C8—111no—
297C4⋊Q8—221no—
298C4⋊Q8—221no—
299#126—441no—
300#126—441no—
301#126—441no—
302#125—21no—
303#125—441no—
304#125—441no—
305#124—21no—
306#124—441no—
307#123—441no—
308C22⋊Q8—221no—
309C22⋊Q8—221no—
310C22⋊Q8—221no—
311C22⋊Q8—441no—
312#121—221no—
313C4×Q8—221no—
314C4×Q8—221no—
315C4×Q8—221no—
316C4×D4—221no—
317#117—111no—
318Q32—222no—
319Q32—222no—
320SD32—222no—
321SD32—222no—
322M32—222no—
323C2×C16—111no—
324C2×C16—111no—
325C2×C16—222no—
326C2×C16C22×D1111yescharacteristic
327C2×C16C22×D1111yescharacteristic
328#107—111no—
329#107—111no—
330#107—221no—
331#107C22×D1111yescharacteristic
332#107C22×D1111yescharacteristic
333#106—21no—
334#103—221no—
335#103—221no—
336#103—221no—
337#103—221no—
338#103—221no—
339#103—221no—
340#102—221no—
341#102—221no—
342#97—111no—
343#97—111no—
344C4×C8—111no—
345C4×C8C22×D1111yescharacteristic
346C2×C11—161no—
347C2×C11#316911yescharacteristic
348C2×C11#341611yescharacteristic
349C2×C11#341711yescharacteristic
350D11—41no—
351C2×Q8—21no—
352C2×Q8—221no—
353C2×Q8—221no—
354C2×Q8—441no—
355C2×D4—21no—
356C2×D4—441no—
357C22×C4—111no—
358C22×C4—441no—
359Q16—21no—
360Q16—21no—
361Q16—221no—
362Q16—221no—
363Q16—221no—
364Q16—221no—
365Q16—442no—
366SD16—42no—
367D8—21no—
368D8—21no—
369M16—222no—
370C2×C8—111no—
371C2×C8—111no—
372C2×C8—221no—
373C2×C8—221no—
374C2×C8D4×D1111yescharacteristic
375C2×C8C23×D1111yescharacteristic
376C4⋊C4—21no—
377C4⋊C4—21no—
378C4⋊C4—41no—
379C4⋊C4—41no—
380C4⋊C4—111no—
381C4⋊C4—111no—
382C4⋊C4—221no—
383C4⋊C4—221no—
384C4⋊C4—441no—
385C4⋊C4—441no—
386C4⋊C4—441no—
387C4⋊C4—441no—
388C4⋊C4—441no—
389C4⋊C4—441no—
390C4⋊C4—441no—
391C4⋊C4—441no—
392C4⋊C4—441no—
393C22⋊C4—41no—
394C22⋊C4—41no—
395C22⋊C4—111no—
396C22⋊C4—111no—
397C22⋊C4—441no—
398C22⋊C4—441no—
399C22⋊C4—441no—
400C22⋊C4—441no—
401C22⋊C4—441no—
402C42—111no—
403C42—441no—
404C42—441no—
405C42—441no—
406C42D4×D1111yescharacteristic
407C16—21no—
408C16—21no—
409C16—112no—
410C16—112no—
411C11#3374511yescharacteristic, complemented, Sylow
412C23—41no—
413C23—111no—
414Q8—41no—
415Q8—41no—
416Q8—441no—
417Q8—441no—
418Q8—441no—
419Q8—441no—
420Q8—1761no—
421D4—41no—
422D4—41no—
423D4—1761no—
424C2×C4—41no—
425C2×C4—41no—
426C2×C4—41no—
427C2×C4—111no—
428C2×C4—111no—
429C2×C4—111no—
430C2×C4—221no—
431C2×C4—221no—
432C2×C4—441no—
433C2×C4—441no—
434C2×C4—441no—
435C2×C4—441no—
436C2×C4—1761no—
437C2×C4D8×D1111yescharacteristic
438C2×C4D8×D1111yescharacteristic
439C2×C4C2×D4×D1111yescharacteristic
440C8—221no—
441C8—221no—
442C8#6696912yes—
443C8#41×D1111yescharacteristic
444C8#41×D1111yescharacteristic
445C22—81no—
446C22—81no—
447C22—81no—
448C22—221no—
449C22—221no—
450C22—221no—
451C22C2×D8×D1111yescharacteristic
452C4—21no—
453C4—21no—
454C4—81no—
455C4—81no—
456C4—81no—
457C4—221no—
458C4—221no—
459C4—221no—
460C4—881no—
461C4—881no—
462C4—881no—
463C4—881no—
464C4#1062319911yescharacteristic
465C4C2×#6696911yescharacteristic
466C2—161no—
467C2—441no—
468C2#1307919411yescharacteristic
469C2#1308175911yescharacteristic
470C2#1308176611yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2242C2
socleC22×C11C22×D8
prime radical#10622770C22
hypercenter#2242D11
hypocenterC11#33745
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #2242

Complements

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

NH ≅ G/Ntype
1. #13079276C2semidirect
3. #13070903C2semidirect
4. #13070888C2semidirect
5. #13070844C2semidirect
7. #13070723C2semidirect
9. #13070706C2semidirect
10. #13070484C2semidirect
11. #13070477C2semidirect
12. #13070472C2semidirect
13. #13070471C2semidirect
14. #13070211C2semidirect
15. C11×#2242C2semidirect
181. #2242D11semidirect
411. C11#33745semidirect

Maximal subgroups

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

subgroupindex
#130792762
#130792522
#130709032
#130708882
#130708442
#130707282
#130707232
#130707112
#130707062
#130704842
#130704772
#130704722
#130704712
#130702112
C11×#22422
#3374511