Finite Group Databasebeta

← #14908259

Subgroups — #14908259

Order 2816.

686 conjugacy classes of subgroups.

The subgroup lattice has 474 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622792C211yesmaximal, characteristic, complemented
2C2×D11×M32C211yesmaximal, characteristic, complemented
3#13078198C211yesmaximal, characteristic
4C2×#10622801C211yesmaximal, characteristic, complemented
5#13070732C212yesmaximal, complemented
6#13070723C212yesmaximal, complemented
7#13070715C212yesmaximal, complemented
8#13070706C212yesmaximal, complemented
9#13070405C211yesmaximal, characteristic, complemented
10#13070329C211yesmaximal, characteristic, complemented
11C11×#2141C211yesmaximal, characteristic, complemented
12C22×C11×Q16C2211yescharacteristic
13C2×#66999—21no—
14C2×#66957C2211yescharacteristic
15C22×C8×D11C2211yescharacteristic
16#10623055—21no—
17C2×C11×M32C2211yescharacteristic
18C11×#427C2211yescharacteristic
19C2×#66899—21no—
20#10622801—21no—
21#10622801—21no—
22#10622801C2212yes—
23#10622801C2212yes—
24C2×#66893C2212yescomplemented
25#10622792—24no—
26C2×#66892C2212yescomplemented
27C2×#66882C2211yescharacteristic
28C2×#66876C2211yescharacteristic
29#10622615—21no—
30D11×M32—24no—
31C2×#66862C2212yes—
32C2×C16×D11C2212yes—
33#10622500C2211yescharacteristic
34#10622500C2211yescharacteristic
35#10622496C2211yescharacteristic
36#10622496C2211yescharacteristic
37#10622477—21no—
38#10622477—21no—
39C11×#358C2212yescomplemented
40C11×#358C2212yescomplemented
41#10622147C2212yescomplemented
42#10622141C2212yescomplemented
43#10622128C2212yescomplemented
44#10622127C2212yescomplemented
45C22×Q8×C11—21no—
46C2×#4339—21no—
47C22×C4×D11D411yescharacteristic
48C2×C11×Q16—22no—
49C2×C11×Q16—21no—
50C2×C11×Q16—22no—
51C2×C11×Q16C2312yes—
52C22×C8×C11C2311yescharacteristic
53C11×#117—21no—
54#66999—22no—
55#66999—22no—
56#66999—41no—
57#66999—41no—
58C2×(C2×D11)⋊C4—41no—
59C2×C4⋊Dic11—21no—
60C2×Dic11⋊C4—41no—
61C22×C11⋊C8D411yescharacteristic
62C2×Dic44C2311yescharacteristic
63#66957—22no—
64#66957—22no—
65C2×D88C2311yescharacteristic
66C2×#4314—21no—
67C2×C8×D11—22no—
68C2×C8×D11—22no—
69C2×C8×D11D411yescharacteristic
70C2×C8×D11D411yescharacteristic
71C2×C8×D11C2311yescharacteristic
72C2×C8×D11C2311yescharacteristic
73#66950—21no—
74#66950—21no—
75#66948—21no—
76#66948—21no—
77#66939—41no—
78#66935—41no—
79C4×D44—41no—
80C4×D44—41no—
81C11×M32—22no—
82C2×C11×C16C2312yes—
83C11×#107C2311yescharacteristic
84C11×#107C2311yescharacteristic
85C11×#106—21no—
86#66899—22no—
87#66899—22no—
88#66893—24no—
89#66892—24no—
90#66882—21no—
91#66882C2312yes—
92#66876D414yescomplemented
93C2×C11⋊C16C2312yes—
94#66874—21no—
95#66874—21no—
96#66873—21no—
97#66873—21no—
98#66862—24no—
99C16×D11—24no—
100#33606—111nomaximal, Sylow
101C23×D11D811yescharacteristic
102C2×Q8×C11—22no—
103C2×Q8×C11—41no—
104C2×Q8×C11—42no—
105C2×Q8×C11—42no—
106C22×C4×C11—41no—
107C22×C4×C11C2×D411yescharacteristic
108C2×C22⋊D11—41no—
109C22×Dic11—41no—
110C22×Dic11D811yescharacteristic
111#4339—42no—
112#4339—42no—
113C2×D44—21no—
114C2×D44—41no—
115C2×D44—41no—
116C2×C4×D11—22no—
117C2×C4×D11—22no—
118C2×C4×D11—41no—
119C2×C4×D11D811yescharacteristic
120C2×C4×D11D811yescharacteristic
121C2×C4×D11C2×D411yescharacteristic
122C2×C4×D11C2×D411yescharacteristic
123C2×Dic22—21no—
124C11×Q16—22no—
125C11×Q16—22no—
126C11×Q16—42no—
127C2×C8×C11C2×D412yes—
128C2×C8×C11C2×D411yescharacteristic
129C2×C8×C11#4112yes—
130C2×C8×C11C2411yescharacteristic
131C11×C4⋊C4—21no—
132C11×C4⋊C4—21no—
133C11×C22⋊C4—41no—
134C42×C11—41no—
135(C2×D11)⋊C4—41no—
136(C2×D11)⋊C4—41no—
137(C2×D11)⋊C4—41no—
138(C2×D11)⋊C4—41no—
139(C2×D11)⋊C4—42no—
140(C2×D11)⋊C4—42no—
141C4⋊Dic11—22no—
142C4⋊Dic11—41no—
143C4⋊Dic11—41no—
144C4⋊Dic11—41no—
145Dic11⋊C4—42no—
146Dic11⋊C4—42no—
147C2×C11⋊C8—22no—
148C2×C11⋊C8C2×D411yescharacteristic
149C2×C11⋊C8C2×D411yescharacteristic
150Dic44—21no—
151Dic44—21no—
152D88—21no—
153D88—21no—
154#4314—42no—
155C8×D11—22no—
156C8×D11—22no—
157C8×D11—21no—
158C8×D11—21no—
159C8×D11—21no—
160C8×D11—21no—
161C11×C16—22no—
162C11⋊C16C2×D414yes—
163C2×#510—111no—
164C22×M32—111no—
165#3050—111no—
166C2×#467—111no—
167#2220—112no—
168#2219—112no—
169#2217—112no—
170#2216—112no—
171#2159—111no—
172#2141D1111yescharacteristic, complemented
173#2139—111no—
174C23×C11C2×D811yescharacteristic
175C22×D11—22no—
176C22×D11—22no—
177C22×D11—41no—
178C22×D11—41no—
179C22×D11C2×D811yescharacteristic
180C22×D11C2×D811yescharacteristic
181Q8×C11—42no—
182Q8×C11—42no—
183Q8×C11—82no—
184C2×C4×C11—42no—
185C2×C4×C11—41no—
186C2×C4×C11—41no—
187C2×C4×C11—82no—
188C2×C4×C11#12112yes—
189C2×C4×C11C2×D811yescharacteristic
190C2×C4×C11#13512yes—
191C2×C4×C11C22×D411yescharacteristic
192C22⋊D11—82no—
193C2×Dic11—22no—
194C2×Dic11—42no—
195C2×Dic11—41no—
196C2×Dic11—82no—
197C2×Dic11C2×D811yescharacteristic
198C2×Dic11C2×D811yescharacteristic
199D44—41no—
200D44—41no—
201D44—82no—
202D44—82no—
203C4×D11—21no—
204C4×D11—21no—
205C4×D11—21no—
206C4×D11—21no—
207C4×D11—22no—
208C4×D11—22no—
209C4×D11—82no—
210Dic22—41no—
211Dic22—41no—
212C8×C11#12112yes—
213C8×C11C22×D411yescharacteristic
214C8×C11C2×#4111yescharacteristic
215C11⋊C8—21no—
216C11⋊C8—21no—
217C2×#135—111no—
218C22×Q16C2×D1111yescharacteristic
219C23×C8—111no—
220#525—221no—
221C2×C22⋊Q8—221no—
222#510—224no—
223C2×Q32—112no—
224C2×SD32—112no—
225C2×M32—111no—
226C2×M32—112no—
227C2×M32—224no—
228C2×M32C2×D1111yescharacteristic
229C22×C16—112no—
230#467—112no—
231#467—112no—
232#467—111no—
233#467—111no—
234#467—221no—
235#467—221no—
236#466—111no—
237#466—111no—
238#465—221no—
239#465—221no—
240#427C2×D1111yescharacteristic
241C2×#107—111no—
242#416—221no—
243C2×#103—221no—
244#367—112no—
245#366—112no—
246#358—112no—
247#358C2×D1112yescomplemented
248#358C2×D1112yescomplemented
249#357—112no—
250C22×C11—21no—
251C22×C11—21no—
252C22×C11#46612yes—
253C22×C11C22×D811yescharacteristic
254C2×D11—21no—
255C2×D11—21no—
256C2×D11—21no—
257C2×D11—21no—
258C2×D11—21no—
259C2×D11—44no—
260C2×D11—81no—
261C2×D11—81no—
262C2×D11—81no—
263C2×D11#51012yescomplemented
264C4×C11—81no—
265C4×C11—81no—
266C4×C11—82no—
267C4×C11#46612yes—
268C4×C11C2×#12111yescharacteristic
269C4×C11C2×#13511yescharacteristic
270Dic11—21no—
271Dic11—21no—
272Dic11—82no—
273Dic11—81no—
274C2×#41—221no—
275C22×Q8—21no—
276C23×C4—111no—
277#135—222no—
278#135—222no—
279C2×Q16—22no—
280C2×Q16—22no—
281C2×Q16—21no—
282C2×Q16—111no—
283C2×Q16C22×D1112yes—
284C2×SD16—221no—
285C2×D8—111no—
286C22×C8—111no—
287C22×C8—111no—
288C22×C8—111no—
289C22×C8—111no—
290C22×C8—111no—
291C22×C8—222no—
292C22×C8—222no—
293C22×C8C22×D1111yescharacteristic
294#123—441no—
295C22⋊Q8—221no—
296C22⋊Q8—221no—
297C22⋊Q8—222no—
298C22⋊Q8—222no—
299C22⋊Q8—441no—
300C22⋊Q8—441no—
301#121—221no—
302#121—221no—
303#120—441no—
304C4×D4—441no—
305C4×D4—441no—
306#117—21no—
307C2×C4⋊C4—221no—
308C2×C4⋊C4—441no—
309C2×C22⋊C4—441no—
310Q32—224no—
311SD32—224no—
312M32—22no—
313M32—114no—
314M32—224no—
315C2×C16—112no—
316C2×C16—224no—
317C2×C16C22×D1112yes—
318#107—112no—
319#107—221no—
320#107C22×D1111yescharacteristic
321#107C22×D1111yescharacteristic
322#106—21no—
323#103—221no—
324#103—221no—
325#103—222no—
326#103—222no—
327#102—221no—
328#102—221no—
329C2×C11—22no—
330C2×C11C2×#46611yescharacteristic
331C2×C11C2×#51011yescharacteristic
332C2×C11#341411yescharacteristic
333D11—22no—
334D11—41no—
335D11—161no—
336C24—111no—
337#41—442no—
338#41—442no—
339C2×Q8—22no—
340C2×Q8—41no—
341C2×Q8—42no—
342C2×Q8—42no—
343C2×Q8—221no—
344C2×D4—221no—
345C2×D4—441no—
346C2×D4—441no—
347C2×D4—441no—
348C22×C4—41no—
349C22×C4—111no—
350C22×C4—111no—
351C22×C4—111no—
352C22×C4—111no—
353C22×C4—111no—
354C22×C4—222no—
355C22×C4—222no—
356C22×C4—441no—
357C22×C4—441no—
358C22×C4D4×D1111yescharacteristic
359Q16—22no—
360Q16—22no—
361Q16—42no—
362Q16—221no—
363Q16—221no—
364SD16—442no—
365D8—221no—
366D8—221no—
367C2×C8—111no—
368C2×C8—111no—
369C2×C8—222no—
370C2×C8—222no—
371C2×C8—222no—
372C2×C8—221no—
373C2×C8—221no—
374C2×C8—221no—
375C2×C8—221no—
376C2×C8#433912yes—
377C2×C8D4×D1111yescharacteristic
378C2×C8D4×D1112yes—
379C2×C8C23×D1111yescharacteristic
380C4⋊C4—21no—
381C4⋊C4—21no—
382C4⋊C4—222no—
383C4⋊C4—442no—
384C4⋊C4—442no—
385C4⋊C4—441no—
386C4⋊C4—441no—
387C4⋊C4—441no—
388C22⋊C4—41no—
389C22⋊C4—441no—
390C22⋊C4—441no—
391C22⋊C4—442no—
392C22⋊C4—442no—
393C22⋊C4—441no—
394C22⋊C4—441no—
395C42—41no—
396C16—22no—
397C16—114no—
398C11#3360611yescharacteristic, complemented, Sylow
399C23—111no—
400C23—111no—
401C23—222no—
402C23—222no—
403C23—441no—
404C23—441no—
405C23D8×D1111yescharacteristic
406Q8—42no—
407Q8—42no—
408Q8—82no—
409Q8—441no—
410Q8—441no—
411D4—441no—
412D4—441no—
413D4—882no—
414D4—882no—
415D4—882no—
416C2×C4—41no—
417C2×C4—41no—
418C2×C4—42no—
419C2×C4—82no—
420C2×C4—111no—
421C2×C4—111no—
422C2×C4—222no—
423C2×C4—221no—
424C2×C4—221no—
425C2×C4—221no—
426C2×C4—221no—
427C2×C4—222no—
428C2×C4—222no—
429C2×C4—442no—
430C2×C4—441no—
431C2×C4—882no—
432C2×C4—882no—
433C2×C4#6693712yes—
434C2×C4D8×D1111yescharacteristic
435C2×C4#6696912yes—
436C2×C4C2×D4×D1111yescharacteristic
437C8—221no—
438C8—221no—
439C8#6693712yes—
440C8C2×#433911yescharacteristic
441C8C2×D4×D1111yescharacteristic
442C22—21no—
443C22—21no—
444C22—112no—
445C22—221no—
446C22—221no—
447C22—221no—
448C22—221no—
449C22—221no—
450C22—444no—
451C22—881no—
452C22—881no—
453C22—881no—
454C22#1062238812yes—
455C22C2×D8×D1111yescharacteristic
456C4—81no—
457C4—81no—
458C4—82no—
459C4—221no—
460C4—221no—
461C4—882no—
462C4—881no—
463C4#1062238812yes—
464C4C2×#6693711yescharacteristic
465C4C2×#6696911yescharacteristic
466C2—22no—
467C2—222no—
468C2—441no—
469C2—1761no—
470C2C2×#1062238811yescharacteristic
471C2D11×#51011yescharacteristic
472C2#1308175111yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2141C2
socleC22×C11C22×D8
prime radical#13078198C2
hypercenter#2141D11
hypocenterC11#33606
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #2141

Complements

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

NH ≅ G/Ntype
1. C2×#10622792C2semidirect
2. C2×D11×M32C2semidirect
4. C2×#10622801C2semidirect
5. #13070732C2semidirect
6. #13070723C2semidirect
7. #13070715C2semidirect
8. #13070706C2semidirect
9. #13070405C2semidirect
10. #13070329C2semidirect
11. C11×#2141C2semidirect
24. C2×#66893C22semidirect
26. C2×#66892C22semidirect
39. C11×#358C22semidirect
40. C11×#358C22semidirect
41. #10622147C22semidirect
42. #10622141C22semidirect
43. #10622128C22semidirect
44. #10622127C22semidirect
92. #66876D4semidirect
172. #2141D11semidirect
247. #358C2×D11semidirect
248. #358C2×D11semidirect
263. C2×D11#510semidirect
398. C11#33606semidirect

Maximal subgroups

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

subgroupindex
C2×#106227922
C2×D11×M322
#130781982
C2×#106228012
#130707322
#130707232
#130707152
#130707062
#130704052
#130703292
C11×#21412
#3360611