Finite Group Databasebeta

← #14908262

Subgroups — #14908262

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×#10622522C211yesmaximal, characteristic, complemented
2C2×D11×M32C211yesmaximal, characteristic, complemented
3#13078198C211yesmaximal, characteristic
4C2×#10622500C211yesmaximal, characteristic, complemented
5#13070730C212yesmaximal, complemented
6#13070725C212yesmaximal, complemented
7#13070713C212yesmaximal, complemented
8#13070708C212yesmaximal, complemented
9#13070335C211yesmaximal, characteristic, complemented
10#13070326C211yesmaximal, characteristic, complemented
11C11×#2159C211yesmaximal, characteristic, complemented
12C22×Dic44C2211yescharacteristic
13C2×#66957C2211yescharacteristic
14C22×C8×D11C2211yescharacteristic
15#10623055—21no—
16C2×#66950—21no—
17C2×C11×M32C2211yescharacteristic
18C11×#427C2211yescharacteristic
19C2×C11×#107C2211yescharacteristic
20C2×#66876C2211yescharacteristic
21#10622615—21no—
22C2×#66874—21no—
23#10622522—24no—
24D11×M32—24no—
25C2×Dic88C2212yescomplemented
26C2×#66864C2212yescomplemented
27C2×#66862C2212yes—
28C2×C16×D11C2212yes—
29#10622500—21no—
30#10622500—21no—
31#10622500C2211yescharacteristic
32#10622500C2212yes—
33#10622500C2211yescharacteristic
34#10622500C2212yes—
35#10622496C2211yescharacteristic
36#10622496C2211yescharacteristic
37#10622477—21no—
38#10622477—21no—
39C11×#367C2212yescomplemented
40C11×#366C2212yescomplemented
41#10622130C2212yescomplemented
42#10622130C2212yescomplemented
43#10622130C2212yescomplemented
44#10622129C2212yescomplemented
45C2×#4339—21no—
46C22×C4×D11D411yescharacteristic
47C22×Dic22—21no—
48C22×C8×C11C2311yescharacteristic
49C11×#117—21no—
50C2×C11×C4⋊C4—21no—
51C2×(C2×D11)⋊C4—41no—
52C2×C4⋊Dic11—41no—
53C22×C11⋊C8D411yescharacteristic
54C2×Dic44—22no—
55C2×Dic44—22no—
56C2×Dic44—21no—
57C2×Dic44C2311yescharacteristic
58C2×Dic44C2312yes—
59#66957—22no—
60#66957—22no—
61C2×D88C2311yescharacteristic
62C2×#4314—21no—
63C2×C8×D11—22no—
64C2×C8×D11—22no—
65C2×C8×D11D411yescharacteristic
66C2×C8×D11D411yescharacteristic
67C2×C8×D11C2311yescharacteristic
68C2×C8×D11C2311yescharacteristic
69#66950—21no—
70#66950—21no—
71#66950—22no—
72#66950—22no—
73#66950—41no—
74#66950—41no—
75#66948—21no—
76#66948—21no—
77#66939—41no—
78#66935—41no—
79C4×D44—41no—
80C4×D44—41no—
81C11×M32D414yescomplemented
82C2×C11×C16C2312yes—
83C11×#107—21no—
84C11×#107C2311yescharacteristic
85C11×#107C2311yescharacteristic
86C11×#107C2312yes—
87C11×#106—21no—
88#66876—22no—
89C2×C11⋊C16C2312yes—
90#66874—21no—
91#66874—21no—
92#66874—22no—
93#66874—22no—
94#66873—21no—
95#66873—21no—
96Dic88—24no—
97#66864—24no—
98#66862—24no—
99C16×D11—24no—
100#33606—111nomaximal, Sylow
101C23×D11D811yescharacteristic
102C22×C4×C11—41no—
103C22×C4×C11C2×D411yescharacteristic
104C2×C22⋊D11—41no—
105C22×Dic11—41no—
106C22×Dic11D811yescharacteristic
107#4339—42no—
108#4339—42no—
109C2×D44—21no—
110C2×D44—41no—
111C2×D44—41no—
112C2×C4×D11—22no—
113C2×C4×D11—22no—
114C2×C4×D11—41no—
115C2×C4×D11D811yescharacteristic
116C2×C4×D11D811yescharacteristic
117C2×C4×D11C2×D411yescharacteristic
118C2×C4×D11C2×D411yescharacteristic
119C2×Dic22—21no—
120C2×Dic22—22no—
121C2×Dic22—42no—
122C2×Dic22—41no—
123C2×Dic22—42no—
124C2×C8×C11C2×D412yes—
125C2×C8×C11C2×D411yescharacteristic
126C2×C8×C11#4112yes—
127C2×C8×C11C2411yescharacteristic
128C11×C4⋊C4—21no—
129C11×C4⋊C4—21no—
130C11×C4⋊C4—22no—
131C11×C4⋊C4—41no—
132C11×C22⋊C4—41no—
133C42×C11—41no—
134(C2×D11)⋊C4—41no—
135(C2×D11)⋊C4—41no—
136(C2×D11)⋊C4—41no—
137(C2×D11)⋊C4—41no—
138(C2×D11)⋊C4—42no—
139(C2×D11)⋊C4—42no—
140C4⋊Dic11—41no—
141C4⋊Dic11—41no—
142C4⋊Dic11—42no—
143C4⋊Dic11—42no—
144C2×C11⋊C8—22no—
145C2×C11⋊C8C2×D411yescharacteristic
146C2×C11⋊C8C2×D411yescharacteristic
147Dic44—22no—
148Dic44—21no—
149Dic44—21no—
150Dic44—22no—
151Dic44—42no—
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×C16C2×D414yes—
162C11⋊C16—22no—
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#2159D1111yescharacteristic, complemented
172#2141—111no—
173#2139—111no—
174C23×C11C2×D811yescharacteristic
175C22×D11—22no—
176C22×D11—22no—
177C22×D11—41no—
178C22×D11—41no—
179C22×D11C2×D811yescharacteristic
180C22×D11C2×D811yescharacteristic
181C2×C4×C11—42no—
182C2×C4×C11—41no—
183C2×C4×C11—41no—
184C2×C4×C11—82no—
185C2×C4×C11#12112yes—
186C2×C4×C11C2×D811yescharacteristic
187C2×C4×C11#13512yes—
188C2×C4×C11C22×D411yescharacteristic
189C22⋊D11—82no—
190C2×Dic11—22no—
191C2×Dic11—42no—
192C2×Dic11—41no—
193C2×Dic11—82no—
194C2×Dic11C2×D811yescharacteristic
195C2×Dic11C2×D811yescharacteristic
196D44—41no—
197D44—41no—
198D44—82no—
199D44—82no—
200C4×D11—21no—
201C4×D11—21no—
202C4×D11—21no—
203C4×D11—21no—
204C4×D11—22no—
205C4×D11—22no—
206C4×D11—82no—
207Dic22—41no—
208Dic22—42no—
209Dic22—42no—
210Dic22—41no—
211Dic22—82no—
212C8×C11#12112yes—
213C8×C11C22×D411yescharacteristic
214C8×C11C2×#4111yescharacteristic
215C11⋊C8—21no—
216C11⋊C8—21no—
217C2×#135—111no—
218C22×Q16—111no—
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—111no—
231#467—112no—
232#467—111no—
233#467—112no—
234#467—221no—
235#467—221no—
236#466—111no—
237#466—111no—
238#465—221no—
239#465—221no—
240#427C2×D1111yescharacteristic
241C2×#107C2×D1111yescharacteristic
242#416—221no—
243C2×#103—221no—
244#367C2×D1112yescomplemented
245#366C2×D1112yescomplemented
246#358—112no—
247#358—112no—
248#358—112no—
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—82no—
266C4×C11—81no—
267C4×C11#46612yes—
268C4×C11C2×#12111yescharacteristic
269C4×C11C2×#13511yescharacteristic
270Dic11—21no—
271Dic11—21no—
272Dic11—82no—
273Dic11—81no—
274C2×#41—221no—
275C22×Q8—221no—
276C23×C4—111no—
277#135—222no—
278#135—222no—
279C2×Q16—112no—
280C2×Q16—111no—
281C2×Q16—222no—
282C2×Q16—221no—
283C2×Q16—222no—
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—222no—
296C22⋊Q8—222no—
297C22⋊Q8—221no—
298C22⋊Q8—221no—
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—21no—
308C2×C4⋊C4—441no—
309C2×C22⋊C4—441no—
310Q32—224no—
311SD32—224no—
312M32—222no—
313M32—224no—
314M32D4414yescomplemented
315C2×C16—112no—
316C2×C16—224no—
317C2×C16C22×D1112yes—
318#107—21no—
319#107C22×D1112yes—
320#107C22×D1111yescharacteristic
321#107C22×D1111yescharacteristic
322#106—21no—
323#103—222no—
324#103—222no—
325#103—221no—
326#103—221no—
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—221no—
340C2×Q8—222no—
341C2×Q8—441no—
342C2×Q8—442no—
343C2×Q8—442no—
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—222no—
360Q16—221no—
361Q16—222no—
362Q16—221no—
363Q16—442no—
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×C8C2×D4412yes—
377C2×C8D4×D1111yescharacteristic
378C2×C8#434312yes—
379C2×C8C23×D1111yescharacteristic
380C4⋊C4—21no—
381C4⋊C4—21no—
382C4⋊C4—22no—
383C4⋊C4—41no—
384C4⋊C4—442no—
385C4⋊C4—442no—
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—222no—
397C16C2×D4414yes—
398C11#3360611yescharacteristic, complemented, Sylow
399C23—111no—
400C23—111no—
401C23—222no—
402C23—222no—
403C23—441no—
404C23—441no—
405C23D8×D1111yescharacteristic
406Q8—441no—
407Q8—442no—
408Q8—442no—
409Q8—441no—
410Q8—882no—
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—222no—
424C2×C4—222no—
425C2×C4—221no—
426C2×C4—221no—
427C2×C4—221no—
428C2×C4—221no—
429C2×C4—441no—
430C2×C4—442no—
431C2×C4—882no—
432C2×C4—882no—
433C2×C4#6694812yes—
434C2×C4D8×D1111yescharacteristic
435C2×C4#6697212yes—
436C2×C4C2×D4×D1111yescharacteristic
437C8—221no—
438C8—221no—
439C8#6694812yes—
440C8C22×D4411yescharacteristic
441C8C2×#434311yescharacteristic
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#1062249612yes—
455C22C2×D8×D1111yescharacteristic
456C4—81no—
457C4—82no—
458C4—81no—
459C4—221no—
460C4—221no—
461C4—881no—
462C4—882no—
463C4#1062249612yes—
464C4C2×#6694811yescharacteristic
465C4C2×#6697211yescharacteristic
466C2—22no—
467C2—222no—
468C2—441no—
469C2—1761no—
470C2C2×#1062249611yescharacteristic
471C2D11×#51011yescharacteristic
472C2#1308174811yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2159C2
socleC22×C11C22×D8
prime radical#13078198C2
hypercenter#2159D11
hypocenterC11#33606
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #2159

Complements

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

NH ≅ G/Ntype
1. C2×#10622522C2semidirect
2. C2×D11×M32C2semidirect
4. C2×#10622500C2semidirect
5. #13070730C2semidirect
6. #13070725C2semidirect
7. #13070713C2semidirect
8. #13070708C2semidirect
9. #13070335C2semidirect
10. #13070326C2semidirect
11. C11×#2159C2semidirect
25. C2×Dic88C22semidirect
26. C2×#66864C22semidirect
39. C11×#367C22semidirect
40. C11×#366C22semidirect
41. #10622130C22semidirect
42. #10622130C22semidirect
43. #10622130C22semidirect
44. #10622129C22semidirect
81. C11×M32D4semidirect
171. #2159D11semidirect
244. #367C2×D11semidirect
245. #366C2×D11semidirect
263. C2×D11#510semidirect
314. M32D44semidirect
398. C11#33606semidirect

Maximal subgroups

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

subgroupindex
C2×#106225222
C2×D11×M322
#130781982
C2×#106225002
#130707302
#130707252
#130707132
#130707082
#130703352
#130703262
C11×#21592
#3360611