Finite Group Databasebeta

← #14907096

Subgroups — #14907096

Order 2816.

738 conjugacy classes of subgroups.

The subgroup lattice has 436 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622806C211yesmaximal, characteristic
2#135×Dic11C211yesmaximal, characteristic, complemented
3C2×#10622485C211yesmaximal, characteristic, complemented
4#13070489C212yesmaximal, complemented
5#13070483C212yesmaximal, complemented
6#13070465C212yesmaximal, complemented
7#13070460C212yesmaximal, complemented
8#13070402C211yesmaximal, characteristic, complemented
9#13070333C211yesmaximal, characteristic, complemented
10M32×Dic11C211yesmaximal, characteristic, complemented
11C11×#2139C211yesmaximal, characteristic, complemented
12C2×C11×#135C2211yescharacteristic
13#41×Dic11—21no—
14C22×D88C2211yescharacteristic
15C2×#66946—21no—
16C2×C11×M32C2211yescharacteristic
17C2×C11×#107C2211yescharacteristic
18#10622846—21no—
19#10622806C418yescomplemented
20Q16×Dic11C2211yescharacteristic, complemented
21Q16×Dic11C2211yescharacteristic, complemented
22C2×#66892C2212yes—
23SD16×Dic11—21no—
24SD16×Dic11—21no—
25D8×Dic11C2211yescharacteristic, complemented
26D8×Dic11C2211yescharacteristic, complemented
27C2×#66890C2212yes—
28#10622719C2211yescharacteristic
29C2×C8×Dic11C2211yescharacteristic
30C2×#66876C2211yescharacteristic
31C2×#66873—21no—
32#10622485—21no—
33#10622485—21no—
34#10622485C2212yes—
35#10622485C2212yes—
36C11×#358C2212yescomplemented
37C11×#357C2212yescomplemented
38#10622147C2212yes—
39#10622147C2212yes—
40#10622140C2212yescomplemented
41C16×Dic11C2212yescomplemented
42#10622128C2212yescomplemented
43#10622127C2212yescomplemented
44C2×C11×#41—21no—
45C22×D44—21no—
46C22×C4×D11—41no—
47C11×#135—22no—
48C11×#135C2×C414yescomplemented
49C2×C11×Q16C2311yescharacteristic
50C2×C11×SD16—21no—
51C2×C11×D8C2311yescharacteristic
52C22×C8×C11C2311yescharacteristic
53C2×C11×C4⋊C4—21no—
54Q8×Dic11—21no—
55Q8×Dic11—21no—
56D4×Dic11—21no—
57D4×Dic11—21no—
58D4×Dic11—41no—
59D4×Dic11—41no—
60C2×(C2×D11)⋊C4—41no—
61#66979—21no—
62#66979—41no—
63C2×C4×Dic11—41no—
64C2×C4×Dic11D411yescharacteristic
65C22×C11⋊C8D411yescharacteristic
66C2×D88—21no—
67C2×D88—22no—
68C2×D88C2×C414yescomplemented
69C2×D88C2312yes—
70#66946—22no—
71#66946—22no—
72#66946—41no—
73#66946—41no—
74C11×M32—22no—
75C2×C11×C16C2312yes—
76C11×#107—21no—
77C11×#107C2312yes—
78#66899—21no—
79#66899—21no—
80#66896—21no—
81#66896—21no—
82#66892C2×C418yescomplemented
83#66890C2×C418yescomplemented
84#66882C2311yescharacteristic
85#66882C2311yescharacteristic
86#66881—21no—
87C8×Dic11D411yescharacteristic
88C8×Dic11D411yescharacteristic
89C8×Dic11C2311yescharacteristic
90C8×Dic11C2311yescharacteristic
91#66876C2×C414yescomplemented
92C2×C11⋊C16C2312yes—
93#66873—22no—
94#66873—22no—
95C4×#509—111nomaximal, Sylow
96C23×D11—41no—
97C11×#41—24no—
98C11×#41—42no—
99C2×Q8×C11—21no—
100C2×D4×C11—21no—
101C2×D4×C11—41no—
102C22×C4×C11—41no—
103C22×C4×C11—41no—
104C22×C4×C11C2×D411yescharacteristic
105C22×Dic11—41no—
106C22×Dic11—41no—
107C22×Dic11D811yescharacteristic
108C22×Dic11D811yescharacteristic
109C2×D44—24no—
110C2×D44—22no—
111C2×D44—41no—
112C2×D44—42no—
113C2×C4×D11—42no—
114C2×C4×D11—42no—
115C2×C4×D11—84no—
116C11×Q16—21no—
117C11×Q16C22×C412yescomplemented
118C11×SD16—24no—
119C11×D8—21no—
120C11×D8C22×C412yescomplemented
121C2×C8×C11C22×C412yes—
122C2×C8×C11C2×D411yescharacteristic
123C2×C8×C11#4112yes—
124C2×C8×C11C2411yescharacteristic
125C11×C4⋊C4—22no—
126C11×C4⋊C4—41no—
127C22⋊Dic11—41no—
128C22⋊Dic11—41no—
129C22⋊Dic11—41no—
130(C2×D11)⋊C4—42no—
131(C2×D11)⋊C4—42no—
132C4⋊Dic11—21no—
133C4⋊Dic11—21no—
134C4⋊Dic11—41no—
135C4⋊Dic11—41no—
136C4×Dic11—41no—
137C4×Dic11—41no—
138C4×Dic11—41no—
139C4×Dic11D811yescharacteristic
140C4×Dic11D811yescharacteristic
141C4×Dic11C2×D411yescharacteristic
142C4×Dic11C2×D411yescharacteristic
143C2×C11⋊C8—22no—
144C2×C11⋊C8C2×D411yescharacteristic
145C2×C11⋊C8C2×D411yescharacteristic
146D88—24no—
147D88—22no—
148D88C22×C414yes—
149C11×C16—22no—
150C11⋊C16C22×C414yescomplemented
151C2×#509—111no—
152C4×#135—111no—
153C2×C4×D8—111no—
154#2177—112no—
155#2175—112no—
156C4×SD32—112no—
157C4×D16—112no—
158#2159—111no—
159#2140—111no—
160#2139D1111yescharacteristic, complemented
161C4×M32—111no—
162C23×C11—41no—
163C23×C11C2×D811yescharacteristic
164C22×D11—42no—
165C22×D11—44no—
166C22×D11—82no—
167C22×D11—82no—
168Q8×C11—22no—
169Q8×C11—41no—
170D4×C11—22no—
171D4×C11—44no—
172D4×C11—41no—
173C2×C4×C11—41no—
174C2×C4×C11—44no—
175C2×C4×C11—42no—
176C2×C4×C11—82no—
177C2×C4×C11C4×D412yes—
178C2×C4×C11C2×D811yescharacteristic
179C2×C4×C11#13512yes—
180C2×C4×C11C22×D411yescharacteristic
181C2×Dic11—22no—
182C2×Dic11—41no—
183C2×Dic11—41no—
184C2×Dic11—41no—
185C2×Dic11—82no—
186C2×Dic11—82no—
187C2×Dic11C2×D811yescharacteristic
188C2×Dic11C2×D811yescharacteristic
189C2×Dic11C2×D811yescharacteristic
190C2×Dic11C2×D811yescharacteristic
191D44—24no—
192D44—42no—
193D44—44no—
194C4×D11—84no—
195C4×D11—84no—
196C8×C11C4×D412yes—
197C8×C11C23×C411yescharacteristic
198C8×C11C2×#4111yescharacteristic
199C11⋊C8—21no—
200C11⋊C8—21no—
201C2×#135C2×D1111yescharacteristic
202C22×D8—111no—
203C4×#41—221no—
204C2×C4×D4—221no—
205#509—118no—
206C2×SD32—112no—
207C2×D16—112no—
208C2×M32—111no—
209C2×M32C2×D1111yescharacteristic
210C4×Q16—111no—
211C4×Q16—111no—
212C4×SD16—221no—
213C4×SD16—221no—
214C4×D8—111no—
215C4×D8—111no—
216C4×D8—112no—
217C4×D8—112no—
218C4×D8—221no—
219C4×D8—221no—
220#427—111no—
221C2×#107C2×D1111yescharacteristic
222#416—221no—
223C2×#102—221no—
224C2×C4×C8—111no—
225#367—112no—
226#366—112no—
227#358C2×D1112yescomplemented
228#357—112no—
229#357—112no—
230#357C2×D1112yescomplemented
231#346—112no—
232C4×C16—112no—
233C22×C11—21no—
234C22×C11—21no—
235C22×C11—42no—
236C22×C11—81no—
237C22×C11—81no—
238C22×C11C4×D812yes—
239C22×C11C22×D811yescharacteristic
240C2×D11—44no—
241C2×D11—88no—
242C2×D11—82no—
243C2×D11—82no—
244C4×C11—42no—
245C4×C11—82no—
246C4×C11C4×D812yes—
247C4×C11C2×C4×D411yescharacteristic
248C4×C11C2×#13511yescharacteristic
249Dic11—21no—
250Dic11—21no—
251Dic11—21no—
252Dic11—81no—
253Dic11—81no—
254Dic11#50912yescomplemented
255C2×#41—21no—
256C22×D4—221no—
257C23×C4—441no—
258#135—22no—
259#135C4×D1114yescomplemented
260C2×Q16C22×D1111yescharacteristic
261C2×SD16—21no—
262C2×D8—114no—
263C2×D8—112no—
264C2×D8—221no—
265C2×D8—222no—
266C2×D8C22×D1111yescharacteristic
267C22×C8—111no—
268C22×C8C22×D1111yescharacteristic
269C4×Q8—221no—
270C4×Q8—221no—
271C4×D4—222no—
272C4×D4—222no—
273C4×D4—221no—
274C4×D4—221no—
275C4×D4—441no—
276C4×D4—441no—
277C4×D4—441no—
278C4×D4—441no—
279#117—221no—
280#117—441no—
281C2×C4⋊C4—21no—
282C2×C22⋊C4—441no—
283C2×C42—111no—
284C2×C42—441no—
285SD32—118no—
286D16—118no—
287M32—22no—
288M32—114no—
289C2×C16—112no—
290C2×C16C22×D1112yes—
291#107—21no—
292#107—111no—
293#107—111no—
294#107C22×D1112yes—
295#106—221no—
296#103—221no—
297#103—221no—
298#102—222no—
299#102—222no—
300#102—221no—
301#102—221no—
302C4×C8—111no—
303C4×C8—111no—
304C4×C8—111no—
305C4×C8—111no—
306C2×C11—22no—
307C2×C11—82no—
308C2×C11C2×C4×D811yescharacteristic
309C2×C11C2×#50911yescharacteristic
310C2×C11#341411yescharacteristic
311D11—84no—
312C24—441no—
313#41—24no—
314#41—42no—
315C2×Q8—21no—
316C2×D4—21no—
317C2×D4—41no—
318C2×D4—224no—
319C2×D4—222no—
320C2×D4—441no—
321C2×D4—442no—
322C22×C4—41no—
323C22×C4—41no—
324C22×C4—111no—
325C22×C4—111no—
326C22×C4—442no—
327C22×C4—442no—
328C22×C4—441no—
329C22×C4—441no—
330C22×C4—884no—
331C22×C4D4×D1111yescharacteristic
332Q16—21no—
333Q16C2×C4×D1112yescomplemented
334SD16—24no—
335D8—21no—
336D8—114no—
337D8—224no—
338D8—222no—
339D8C2×C4×D1112yescomplemented
340C2×C8—111no—
341C2×C8—111no—
342C2×C8—222no—
343C2×C8C2×C4×D1112yes—
344C2×C8D4×D1111yescharacteristic
345C2×C8#434112yes—
346C2×C8C23×D1111yescharacteristic
347C4⋊C4—22no—
348C4⋊C4—41no—
349C4⋊C4—221no—
350C4⋊C4—221no—
351C4⋊C4—441no—
352C4⋊C4—441no—
353C22⋊C4—442no—
354C22⋊C4—442no—
355C22⋊C4—441no—
356C22⋊C4—441no—
357C22⋊C4—441no—
358C42—111no—
359C42—111no—
360C42—111no—
361C42—111no—
362C42—441no—
363C42—441no—
364C42—441no—
365C16—22no—
366C16—114no—
367C11C4×#50911yescharacteristic, complemented, Sylow
368C23—41no—
369C23—442no—
370C23—444no—
371C23—882no—
372C23—882no—
373C23D8×D1111yescharacteristic
374Q8—22no—
375Q8—41no—
376D4—22no—
377D4—44no—
378D4—41no—
379D4—224no—
380D4—442no—
381D4—444no—
382C2×C4—41no—
383C2×C4—44no—
384C2×C4—42no—
385C2×C4—82no—
386C2×C4—111no—
387C2×C4—111no—
388C2×C4—111no—
389C2×C4—111no—
390C2×C4—222no—
391C2×C4—441no—
392C2×C4—441no—
393C2×C4—441no—
394C2×C4—884no—
395C2×C4—884no—
396C2×C4—882no—
397C2×C4—882no—
398C2×C4(C22⋊D11)⋊C412yes—
399C2×C4D8×D1111yescharacteristic
400C2×C4#6696912yes—
401C2×C4C2×D4×D1111yescharacteristic
402C8—221no—
403C8—221no—
404C8(C22⋊D11)⋊C412yes—
405C8C22×C4×D1111yescharacteristic
406C8C2×#434111yescharacteristic
407C22—21no—
408C22—21no—
409C22—42no—
410C22—81no—
411C22—81no—
412C22—444no—
413C22—888no—
414C22—882no—
415C22—882no—
416C22#1062236912yes—
417C22C2×D8×D1111yescharacteristic
418C4—42no—
419C4—82no—
420C4—112no—
421C4—221no—
422C4—221no—
423C4—221no—
424C4—881no—
425C4—881no—
426C4#1062236912yes—
427C4C2×(C22⋊D11)⋊C411yescharacteristic
428C4C2×#6696911yescharacteristic
429C2—22no—
430C2—82no—
431C2—884no—
432C2C2×#1062236911yescharacteristic
433C2D11×#50911yescharacteristic
434C2#1308175111yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutatorC8×C11C23×C4
FrattiniC2×C8C23×D11
FittingC11×#2139C2
socleC22×C11C22×D8
prime radicalC2×#10622806C2
cosocleC2×C8×C11C24
hypercenter#2139D11
hypocenterC11C4×#509
LCSG ▷ C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #2139

Complements

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

NH ≅ G/Ntype
2. #135×Dic11C2semidirect
3. C2×#10622485C2semidirect
4. #13070489C2semidirect
5. #13070483C2semidirect
6. #13070465C2semidirect
7. #13070460C2semidirect
8. #13070402C2semidirect
9. #13070333C2semidirect
10. M32×Dic11C2semidirect
11. C11×#2139C2semidirect
19. #10622806C4semidirect
20. Q16×Dic11C22semidirect
21. Q16×Dic11C22semidirect
25. D8×Dic11C22semidirect
26. D8×Dic11C22semidirect
36. C11×#358C22semidirect
37. C11×#357C22semidirect
40. #10622140C22semidirect
41. C16×Dic11C22semidirect
42. #10622128C22semidirect
43. #10622127C22semidirect
48. C11×#135C2×C4semidirect
68. C2×D88C2×C4semidirect
82. #66892C2×C4semidirect
83. #66890C2×C4semidirect
91. #66876C2×C4semidirect
117. C11×Q16C22×C4semidirect
120. C11×D8C22×C4semidirect
150. C11⋊C16C22×C4semidirect
160. #2139D11semidirect
227. #358C2×D11semidirect
230. #357C2×D11semidirect
254. Dic11#509semidirect
259. #135C4×D11semidirect
333. Q16C2×C4×D11semidirect
339. D8C2×C4×D11semidirect
367. C11C4×#509semidirect

Maximal subgroups

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

subgroupindex
C2×#106228062
#135×Dic112
C2×#106224852
#130704892
#130704832
#130704652
#130704602
#130704022
#130703332
M32×Dic112
C11×#21392
C4×#50911