Finite Group Databasebeta

← #14908251

Subgroups — #14908251

Order 2816.

738 conjugacy classes of subgroups.

The subgroup lattice has 492 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622521C211yesmaximal, characteristic, complemented
2C2×D11×M32C211yesmaximal, characteristic, complemented
3#13078198C211yesmaximal, characteristic, complemented
4C2×#10622496C211yesmaximal, characteristic, complemented
5#13070730C212yesmaximal, complemented
6#13070720C212yesmaximal, complemented
7#13070713C212yesmaximal, complemented
8#13070703C212yesmaximal, complemented
9#13070331C211yesmaximal, characteristic, complemented
10#13070326C211yesmaximal, characteristic, complemented
11C11×#2159C211yesmaximal, characteristic, complemented
12C2×#66957C2211yescharacteristic
13C22×D88C2211yescharacteristic
14C22×C8×D11C2211yescharacteristic
15#10623055—21no—
16C2×#66948—21no—
17C2×C11×M32C2211yescharacteristic
18C11×#427C2211yescharacteristic
19C2×C11×#107C2211yescharacteristic
20C2×#66876C2211yescharacteristic
21#10622615—21no—
22C2×#66873—21no—
23#10622521—24no—
24D11×M32—24no—
25C2×#66864C2212yescomplemented
26C2×D176C2212yescomplemented
27C2×#66862C2212yescomplemented
28C2×C16×D11C2212yescomplemented
29#10622500C2211yescharacteristic, complemented
30#10622500C2211yescharacteristic, complemented
31#10622496—21no—
32#10622496—21no—
33#10622496C2212yes—
34#10622496C2212yes—
35#10622496C2211yescharacteristic, complemented
36#10622496C2211yescharacteristic, complemented
37#10622477—21no—
38#10622477—21no—
39C11×#367C2212yescomplemented
40C11×#366C2212yescomplemented
41#10622130C2212yescomplemented
42#10622129C2212yescomplemented
43#10622129C2212yescomplemented
44#10622129C2212yescomplemented
45C2×#4339—21no—
46C22×D44—21no—
47C22×D44—41no—
48C22×C4×D11D411yescharacteristic
49C22×C8×C11C2311yescharacteristic
50C11×#117—21no—
51C2×C11×C4⋊C4—21no—
52C2×(C2×D11)⋊C4—41no—
53C22×C11⋊C8D411yescharacteristic
54C2×Dic44C2311yescharacteristic
55#66957—22no—
56#66957—22no—
57C2×D88—22no—
58C2×D88—22no—
59C2×D88—21no—
60C2×D88C2312yes—
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#66948—21no—
72#66948—21no—
73#66948—22no—
74#66948—22no—
75#66948—41no—
76#66948—41no—
77#66939—41no—
78#66935—41no—
79C4×D44—41no—
80C4×D44—41no—
81C11×M32D414yescomplemented
82C2×C11×C16C2312yes—
83C11×#107—21no—
84C11×#107C2312yes—
85C11×#107C2311yescharacteristic
86C11×#107C2311yescharacteristic
87C11×#106—21no—
88#66876—22no—
89C2×C11⋊C16C2312yes—
90#66874—21no—
91#66874—21no—
92#66873—21no—
93#66873—21no—
94#66873—22no—
95#66873—22no—
96#66864—24no—
97D176—24no—
98#66862—24no—
99C16×D11—24no—
100#33605—111nomaximal, Sylow
101C23×D11—41no—
102C23×D11D811yescharacteristic
103C22×C4×C11—41no—
104C22×C4×C11C2×D411yescharacteristic
105C2×C22⋊D11—41no—
106C22×Dic11D811yescharacteristic
107#4339—42no—
108#4339—42no—
109C2×D44—21no—
110C2×D44—22no—
111C2×D44—41no—
112C2×D44—41no—
113C2×D44—42no—
114C2×D44—42no—
115C2×D44—42no—
116C2×D44—41no—
117C2×D44—42no—
118C2×D44—84no—
119C2×C4×D11—22no—
120C2×C4×D11—22no—
121C2×C4×D11—41no—
122C2×C4×D11D811yescharacteristic
123C2×C4×D11D811yescharacteristic
124C2×C4×D11C2×D411yescharacteristic
125C2×C4×D11C2×D411yescharacteristic
126C2×Dic22—21no—
127C2×C8×C11C2×D412yes—
128C2×C8×C11C2×D411yescharacteristic
129C2×C8×C11#4112yes—
130C2×C8×C11C2411yescharacteristic
131C11×C4⋊C4—22no—
132C11×C4⋊C4—21no—
133C11×C4⋊C4—21no—
134C11×C4⋊C4—41no—
135C11×C22⋊C4—41no—
136C42×C11—41no—
137(C2×D11)⋊C4—41no—
138(C2×D11)⋊C4—41no—
139(C2×D11)⋊C4—42no—
140(C2×D11)⋊C4—42no—
141(C2×D11)⋊C4—41no—
142(C2×D11)⋊C4—41no—
143C4⋊Dic11—41no—
144C4⋊Dic11—41no—
145C2×C11⋊C8—22no—
146C2×C11⋊C8C2×D411yescharacteristic
147C2×C11⋊C8C2×D411yescharacteristic
148Dic44—21no—
149Dic44—21no—
150D88—21no—
151D88—22no—
152D88—22no—
153D88—21no—
154D88—42no—
155#4314—42no—
156C8×D11—22no—
157C8×D11—22no—
158C8×D11—21no—
159C8×D11—21no—
160C8×D11—21no—
161C8×D11—21no—
162C11×C16C2×D414yescomplemented
163C11⋊C16—22no—
164C2×#509—111no—
165C22×M32—111no—
166#3050—111no—
167C2×#466—111no—
168#2220—112no—
169#2218—112no—
170#2217—112no—
171#2215—112no—
172#2159D1111yescharacteristic, complemented
173#2140—111no—
174#2139—111no—
175C23×C11C2×D811yescharacteristic
176C22×D11—22no—
177C22×D11—22no—
178C22×D11—41no—
179C22×D11—41no—
180C22×D11—42no—
181C22×D11—82no—
182C22×D11—82no—
183C22×D11—82no—
184C22×D11C2×D811yescharacteristic
185C22×D11C2×D811yescharacteristic
186C2×C4×C11—41no—
187C2×C4×C11—41no—
188C2×C4×C11—42no—
189C2×C4×C11—82no—
190C2×C4×C11#12112yes—
191C2×C4×C11C2×D811yescharacteristic
192C2×C4×C11#13512yes—
193C2×C4×C11C22×D411yescharacteristic
194C22⋊D11—82no—
195C2×Dic11—22no—
196C2×Dic11—41no—
197C2×Dic11C2×D811yescharacteristic
198C2×Dic11C2×D811yescharacteristic
199D44—41no—
200D44—42no—
201D44—42no—
202D44—41no—
203D44—82no—
204D44—84no—
205D44—82no—
206D44—84no—
207D44—82no—
208C4×D11—21no—
209C4×D11—21no—
210C4×D11—21no—
211C4×D11—21no—
212C4×D11—22no—
213C4×D11—22no—
214C4×D11—82no—
215Dic22—41no—
216Dic22—41no—
217C8×C11#12112yes—
218C8×C11C22×D411yescharacteristic
219C8×C11C2×#4111yescharacteristic
220C11⋊C8—21no—
221C11⋊C8—21no—
222C2×#135—111no—
223C22×D8—111no—
224C23×C8—111no—
225#525—221no—
226C2×#121—221no—
227#509—224no—
228C2×SD32—112no—
229C2×D16—112no—
230C2×M32—111no—
231C2×M32—112no—
232C2×M32—224no—
233C2×M32C2×D1111yescharacteristic
234C22×C16—112no—
235#467—111no—
236#467—111no—
237#466—112no—
238#466—112no—
239#466—111no—
240#466—111no—
241#466—221no—
242#466—221no—
243#465—221no—
244#465—221no—
245#427C2×D1111yescharacteristic
246C2×#107C2×D1111yescharacteristic
247#416—221no—
248C2×#102—221no—
249#367C2×D1112yescomplemented
250#366C2×D1112yescomplemented
251#358—112no—
252#357—112no—
253#357—112no—
254#357—112no—
255C22×C11—21no—
256C22×C11—21no—
257C22×C11#46612yes—
258C22×C11C22×D811yescharacteristic
259C2×D11—21no—
260C2×D11—21no—
261C2×D11—21no—
262C2×D11—21no—
263C2×D11—21no—
264C2×D11—44no—
265C2×D11—82no—
266C2×D11—81no—
267C2×D11—82no—
268C2×D11—81no—
269C2×D11—82no—
270C2×D11—81no—
271C2×D11—164no—
272C2×D11#50912yescomplemented
273C4×C11—82no—
274C4×C11—81no—
275C4×C11—81no—
276C4×C11#46612yes—
277C4×C11C2×#12111yescharacteristic
278C4×C11C2×#13511yescharacteristic
279Dic11—21no—
280Dic11—21no—
281Dic11—81no—
282C2×#41—221no—
283C22×D4—221no—
284C22×D4—441no—
285C23×C4—111no—
286#135—222no—
287#135—222no—
288C2×Q16—111no—
289C2×SD16—221no—
290C2×D8—112no—
291C2×D8—111no—
292C2×D8—222no—
293C2×D8—221no—
294C2×D8—222no—
295C22×C8—111no—
296C22×C8—111no—
297C22×C8—111no—
298C22×C8—111no—
299C22×C8—111no—
300C22×C8—222no—
301C22×C8—222no—
302C22×C8C22×D1111yescharacteristic
303#123—441no—
304C22⋊Q8—221no—
305C22⋊Q8—221no—
306#121—222no—
307#121—222no—
308#121—221no—
309#121—221no—
310#121—441no—
311#121—441no—
312#120—441no—
313C4×D4—441no—
314C4×D4—441no—
315#117—21no—
316C2×C4⋊C4—21no—
317C2×C22⋊C4—441no—
318SD32—224no—
319D16—224no—
320M32—222no—
321M32—224no—
322M32D4414yescomplemented
323C2×C16—112no—
324C2×C16—224no—
325C2×C16C22×D1112yes—
326#107—21no—
327#107C22×D1111yescharacteristic
328#107C22×D1111yescharacteristic
329#107C22×D1112yes—
330#106—21no—
331#103—221no—
332#103—221no—
333#102—222no—
334#102—222no—
335#102—221no—
336#102—221no—
337C2×C11—22no—
338C2×C11C2×#46611yescharacteristic
339C2×C11C2×#50911yescharacteristic
340C2×C11#341411yescharacteristic
341D11—22no—
342D11—41no—
343D11—161no—
344D11—162no—
345C24—111no—
346C24—441no—
347#41—442no—
348#41—442no—
349C2×Q8—221no—
350C2×D4—222no—
351C2×D4—221no—
352C2×D4—441no—
353C2×D4—441no—
354C2×D4—442no—
355C2×D4—442no—
356C2×D4—441no—
357C2×D4—442no—
358C2×D4—441no—
359C2×D4—442no—
360C2×D4—884no—
361C22×C4—41no—
362C22×C4—111no—
363C22×C4—111no—
364C22×C4—111no—
365C22×C4—111no—
366C22×C4—111no—
367C22×C4—222no—
368C22×C4—222no—
369C22×C4—441no—
370C22×C4D4×D1111yescharacteristic
371Q16—221no—
372Q16—221no—
373SD16—442no—
374D8—221no—
375D8—222no—
376D8—222no—
377D8—221no—
378D8—442no—
379C2×C8—111no—
380C2×C8—111no—
381C2×C8—222no—
382C2×C8—222no—
383C2×C8—222no—
384C2×C8—221no—
385C2×C8—221no—
386C2×C8—221no—
387C2×C8—221no—
388C2×C8C2×D4412yes—
389C2×C8D4×D1111yescharacteristic
390C2×C8#434312yes—
391C2×C8C23×D1111yescharacteristic
392C4⋊C4—22no—
393C4⋊C4—21no—
394C4⋊C4—21no—
395C4⋊C4—41no—
396C4⋊C4—441no—
397C4⋊C4—441no—
398C22⋊C4—41no—
399C22⋊C4—442no—
400C22⋊C4—442no—
401C22⋊C4—441no—
402C22⋊C4—441no—
403C22⋊C4—441no—
404C22⋊C4—441no—
405C42—41no—
406C16—222no—
407C16C2×D4414yescomplemented
408C11#3360511yescharacteristic, complemented, Sylow
409C23—111no—
410C23—111no—
411C23—222no—
412C23—222no—
413C23—441no—
414C23—441no—
415C23—442no—
416C23—882no—
417C23—882no—
418C23—882no—
419C23D8×D1111yescharacteristic
420Q8—441no—
421Q8—441no—
422D4—442no—
423D4—441no—
424D4—442no—
425D4—441no—
426D4—884no—
427D4—882no—
428D4—884no—
429D4—882no—
430D4—882no—
431D4—882no—
432C2×C4—41no—
433C2×C4—41no—
434C2×C4—42no—
435C2×C4—82no—
436C2×C4—111no—
437C2×C4—111no—
438C2×C4—222no—
439C2×C4—222no—
440C2×C4—222no—
441C2×C4—221no—
442C2×C4—221no—
443C2×C4—221no—
444C2×C4—221no—
445C2×C4—441no—
446C2×C4—882no—
447C2×C4#6694812yes—
448C2×C4D8×D1111yescharacteristic
449C2×C4#6697212yes—
450C2×C4C2×D4×D1111yescharacteristic
451C8—221no—
452C8—221no—
453C8#6694812yes—
454C8C22×D4411yescharacteristic
455C8C2×#434311yescharacteristic
456C22—21no—
457C22—21no—
458C22—112no—
459C22—221no—
460C22—221no—
461C22—221no—
462C22—221no—
463C22—221no—
464C22—444no—
465C22—882no—
466C22—881no—
467C22—881no—
468C22—882no—
469C22—881no—
470C22—882no—
471C22—1764no—
472C22#1062249612yes—
473C22C2×D8×D1111yescharacteristic
474C4—82no—
475C4—81no—
476C4—81no—
477C4—221no—
478C4—221no—
479C4—881no—
480C4#1062249612yes—
481C4C2×#6694811yescharacteristic
482C4C2×#6697211yescharacteristic
483C2—22no—
484C2—222no—
485C2—441no—
486C2—1762no—
487C2—1761no—
488C2C2×#1062249611yescharacteristic
489C2D11×#50911yescharacteristic
490C2#1308175111yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2159C2
socleC22×C11C22×D8
hypercenter#2159D11
hypocenterC11#33605
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×#10622521C2semidirect
2. C2×D11×M32C2semidirect
3. #13078198C2semidirect
4. C2×#10622496C2semidirect
5. #13070730C2semidirect
6. #13070720C2semidirect
7. #13070713C2semidirect
8. #13070703C2semidirect
9. #13070331C2semidirect
10. #13070326C2semidirect
11. C11×#2159C2semidirect
25. C2×#66864C22semidirect
26. C2×D176C22semidirect
27. C2×#66862C22semidirect
28. C2×C16×D11C22semidirect
29. #10622500C22semidirect
30. #10622500C22semidirect
35. #10622496C22semidirect
36. #10622496C22semidirect
39. C11×#367C22semidirect
40. C11×#366C22semidirect
41. #10622130C22semidirect
42. #10622129C22semidirect
43. #10622129C22semidirect
44. #10622129C22semidirect
81. C11×M32D4semidirect
162. C11×C16C2×D4semidirect
172. #2159D11semidirect
249. #367C2×D11semidirect
250. #366C2×D11semidirect
272. C2×D11#509semidirect
322. M32D44semidirect
407. C16C2×D44semidirect
408. C11#33605semidirect

Maximal subgroups

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

subgroupindex
C2×#106225212
C2×D11×M322
#130781982
C2×#106224962
#130707302
#130707202
#130707132
#130707032
#130703312
#130703262
C11×#21592
#3360511