Finite Group Databasebeta

← #14907087

Subgroups — #14907087

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×#10622760C211yesmaximal, characteristic
2#13077387C211yesmaximal, characteristic, complemented
3C2×D8×Dic11C211yesmaximal, characteristic, complemented
4#13070489C212yesmaximal, complemented
5#13070477C212yesmaximal, complemented
6#13070471C212yesmaximal, complemented
7#13070460C212yesmaximal, complemented
8#13070405C211yesmaximal, characteristic, complemented
9#13070329C211yesmaximal, characteristic, complemented
10M32×Dic11C211yesmaximal, characteristic, complemented
11C11×#2140C211yesmaximal, characteristic, complemented
12C22×C11×D8C2211yescharacteristic
13C2×D4×Dic11—21no—
14C2×#66957C2211yescharacteristic
15#10623053—21no—
16C2×C11×M32C2211yescharacteristic
17C11×#427C2211yescharacteristic
18C2×#66896—21no—
19D8×Dic11—21no—
20D8×Dic11—21no—
21D8×Dic11C2212yes—
22D8×Dic11C2212yes—
23C2×#66891C2212yes—
24#10622760C418yescomplemented
25C2×#66890C2212yes—
26C2×#66882C2211yescharacteristic
27C2×C8×Dic11C2211yescharacteristic
28C2×#66876C2211yescharacteristic
29#10622615—21no—
30#10622486C2211yescharacteristic, complemented
31#10622486C2211yescharacteristic, complemented
32#10622485C2211yescharacteristic, complemented
33#10622485C2211yescharacteristic, complemented
34#10622465—21no—
35#10622465—21no—
36C11×#357C2212yes—
37C11×#357C2212yes—
38#10622147C2212yescomplemented
39#10622141C2212yescomplemented
40#10622140C2212yescomplemented
41C16×Dic11C2212yescomplemented
42#10622128C2212yescomplemented
43#10622127C2212yescomplemented
44C22×D4×C11—21no—
45C23×Dic11—41no—
46C2×#4339—21no—
47C2×C11×D8—21no—
48C2×C11×D8—22no—
49C2×C11×D8C2×C414yescomplemented
50C2×C11×D8C2312yes—
51C22×C8×C11C2311yescharacteristic
52C11×#117—21no—
53C2×C22⋊Dic11—41no—
54D4×Dic11—22no—
55D4×Dic11—22no—
56D4×Dic11—41no—
57D4×Dic11—41no—
58C2×C4⋊Dic11—21no—
59C2×C4×Dic11D411yescharacteristic
60C22×C11⋊C8D411yescharacteristic
61C2×Dic44C2311yescharacteristic
62#66957—22no—
63#66957C2×C414yescomplemented
64C2×D88C2311yescharacteristic
65C2×#4314—21no—
66#66946—21no—
67#66946—21no—
68#66940—21no—
69#66940—21no—
70(C22⋊D11)⋊C4—41no—
71(C22⋊D11)⋊C4—41no—
72#66925—41no—
73C42×D11—41no—
74C11×M32—22no—
75C2×C11×C16C2312yes—
76C11×#107C2311yescharacteristic
77C11×#107C2311yescharacteristic
78C11×#106—21no—
79#66896—22no—
80#66896—22no—
81#66891C2×C418yescomplemented
82#66890C2×C418yescomplemented
83#66882—21no—
84#66882C2312yes—
85C8×Dic11D411yescharacteristic
86C8×Dic11D411yescharacteristic
87C8×Dic11C2311yescharacteristic
88C8×Dic11C2311yescharacteristic
89#66876C2×C414yescomplemented
90C2×C11⋊C16C2312yes—
91#66874—21no—
92#66874—21no—
93#66873—21no—
94#66873—21no—
95C4×#509—111nomaximal, Sylow
96C24×C11—41no—
97C2×D4×C11—24no—
98C2×D4×C11—22no—
99C2×D4×C11—41no—
100C2×D4×C11—42no—
101C22×C4×C11C2×D411yescharacteristic
102C2×C22⋊D11—41no—
103C22×Dic11—42no—
104C22×Dic11—42no—
105C22×Dic11—41no—
106C22×Dic11—84no—
107C22×Dic11D811yescharacteristic
108C22×Dic11D811yescharacteristic
109#4339—24no—
110#4339—42no—
111C2×D44—21no—
112C2×C4×D11—41no—
113C2×C4×D11—41no—
114C2×C4×D11—41no—
115C2×Dic22—21no—
116C11×D8—24no—
117C11×D8—22no—
118C11×D8C22×C414yes—
119C2×C8×C11C22×C412yes—
120C2×C8×C11C2×D411yescharacteristic
121C2×C8×C11#4112yes—
122C2×C8×C11C2411yescharacteristic
123C11×C4⋊C4—21no—
124C11×C4⋊C4—21no—
125C11×C22⋊C4—41no—
126C42×C11—41no—
127C22⋊Dic11—42no—
128C22⋊Dic11—42no—
129(C2×D11)⋊C4—41no—
130(C2×D11)⋊C4—41no—
131C4⋊Dic11—22no—
132C4⋊Dic11—41no—
133Dic11⋊C4—41no—
134Dic11⋊C4—41no—
135C4×Dic11—41no—
136C4×Dic11—41no—
137C4×Dic11D811yescharacteristic
138C4×Dic11D811yescharacteristic
139C4×Dic11C2×D411yescharacteristic
140C4×Dic11C2×D411yescharacteristic
141C2×C11⋊C8—22no—
142C2×C11⋊C8C2×D411yescharacteristic
143C2×C11⋊C8C2×D411yescharacteristic
144Dic44—21no—
145Dic44C22×C412yescomplemented
146D88—21no—
147D88C22×C412yescomplemented
148#4314—24no—
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#2140D1111yescharacteristic, complemented
160#2139—111no—
161C4×M32—111no—
162C23×C11—42no—
163C23×C11—44no—
164C23×C11—82no—
165C23×C11—82no—
166C23×C11C2×D811yescharacteristic
167C22×D11—41no—
168D4×C11—24no—
169D4×C11—42no—
170D4×C11—44no—
171C2×C4×C11—41no—
172C2×C4×C11—41no—
173C2×C4×C11C4×D412yes—
174C2×C4×C11C2×D811yescharacteristic
175C2×C4×C11#13512yes—
176C2×C4×C11C22×D411yescharacteristic
177C22⋊D11—44no—
178C2×Dic11—22no—
179C2×Dic11—41no—
180C2×Dic11—41no—
181C2×Dic11—42no—
182C2×Dic11—84no—
183C2×Dic11—82no—
184C2×Dic11—84no—
185C2×Dic11C2×D811yescharacteristic
186C2×Dic11C2×D811yescharacteristic
187C2×Dic11C2×D811yescharacteristic
188C2×Dic11C2×D811yescharacteristic
189D44—22no—
190D44—41no—
191C4×D11—44no—
192C4×D11—82no—
193C4×D11—82no—
194Dic22—22no—
195Dic22—41no—
196C8×C11C4×D412yes—
197C8×C11C23×C411yescharacteristic
198C8×C11C2×#4111yescharacteristic
199C11⋊C8—21no—
200C11⋊C8—21no—
201C2×#135—111no—
202C22×D8C2×D1111yescharacteristic
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—112no—
215C4×D8—112no—
216C4×D8—111no—
217C4×D8—111no—
218C4×D8—221no—
219C4×D8—221no—
220#427C2×D1111yescharacteristic
221C2×#107—111no—
222#416—221no—
223C2×#102—221no—
224C2×C4×C8—111no—
225#367—112no—
226#366—112no—
227#358—112no—
228#357—112no—
229#357C2×D1112yes—
230#357C2×D1112yes—
231#346—112no—
232C4×C16—112no—
233C22×C11—21no—
234C22×C11—21no—
235C22×C11—44no—
236C22×C11—88no—
237C22×C11—82no—
238C22×C11—82no—
239C22×C11C4×D812yes—
240C22×C11C22×D811yescharacteristic
241C2×D11—42no—
242C2×D11—81no—
243C2×D11—81no—
244C4×C11—81no—
245C4×C11—81no—
246C4×C11C4×D812yes—
247C4×C11C2×C4×D411yescharacteristic
248C4×C11C2×#13511yescharacteristic
249Dic11—21no—
250Dic11—21no—
251Dic11—21no—
252Dic11—42no—
253Dic11—82no—
254Dic11#50912yescomplemented
255C2×#41—221no—
256C22×D4—21no—
257C23×C4—441no—
258#135—114no—
259#135—222no—
260C2×Q16—111no—
261C2×SD16—221no—
262C2×D8—21no—
263C2×D8—22no—
264C2×D8—111no—
265C2×D8C4×D1114yescomplemented
266C2×D8C22×D1112yes—
267C22×C8—111no—
268C22×C8C22×D1111yescharacteristic
269C4×Q8—221no—
270C4×Q8—221no—
271C4×D4—221no—
272C4×D4—221no—
273C4×D4—222no—
274C4×D4—222no—
275C4×D4—441no—
276C4×D4—441no—
277C4×D4—441no—
278C4×D4—441no—
279#117—21no—
280#117—441no—
281C2×C4⋊C4—221no—
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—112no—
292#107—221no—
293#107C22×D1111yescharacteristic
294#107C22×D1111yescharacteristic
295#106—21no—
296#103—221no—
297#103—221no—
298#102—221no—
299#102—221no—
300#102—222no—
301#102—222no—
302C4×C8—111no—
303C4×C8—111no—
304C4×C8—111no—
305C4×C8—111no—
306C2×C11—22no—
307C2×C11—84no—
308C2×C11C2×C4×D811yescharacteristic
309C2×C11C2×#50911yescharacteristic
310C2×C11#341411yescharacteristic
311D11—82no—
312C24—41no—
313#41—224no—
314#41—442no—
315C2×Q8—221no—
316C2×D4—24no—
317C2×D4—22no—
318C2×D4—41no—
319C2×D4—42no—
320C2×D4—221no—
321C2×D4—441no—
322C22×C4—111no—
323C22×C4—111no—
324C22×C4—441no—
325C22×C4—441no—
326C22×C4—442no—
327C22×C4—442no—
328C22×C4—441no—
329C22×C4—441no—
330C22×C4—884no—
331C22×C4D4×D1111yescharacteristic
332Q16—112no—
333Q16—221no—
334SD16—224no—
335D8—24no—
336D8—22no—
337D8—112no—
338D8—221no—
339D8C2×C4×D1114yes—
340C2×C8—111no—
341C2×C8—111no—
342C2×C8—222no—
343C2×C8C2×C4×D1112yes—
344C2×C8D4×D1111yescharacteristic
345C2×C8#434112yes—
346C2×C8C23×D1111yescharacteristic
347C4⋊C4—21no—
348C4⋊C4—21no—
349C4⋊C4—222no—
350C4⋊C4—441no—
351C4⋊C4—441no—
352C4⋊C4—441no—
353C22⋊C4—41no—
354C22⋊C4—441no—
355C22⋊C4—441no—
356C22⋊C4—442no—
357C22⋊C4—442no—
358C42—41no—
359C42—111no—
360C42—111no—
361C42—111no—
362C42—111no—
363C42—441no—
364C42—441no—
365C16—22no—
366C16—114no—
367C11C4×#50911yescharacteristic, complemented, Sylow
368C23—42no—
369C23—44no—
370C23—82no—
371C23—82no—
372C23—441no—
373C23D8×D1111yescharacteristic
374Q8—222no—
375Q8—441no—
376D4—24no—
377D4—42no—
378D4—44no—
379D4—222no—
380D4—444no—
381D4—441no—
382C2×C4—41no—
383C2×C4—41no—
384C2×C4—111no—
385C2×C4—111no—
386C2×C4—111no—
387C2×C4—111no—
388C2×C4—222no—
389C2×C4—441no—
390C2×C4—441no—
391C2×C4—444no—
392C2×C4—442no—
393C2×C4—882no—
394C2×C4—882no—
395C2×C4—884no—
396C2×C4—884no—
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—44no—
410C22—88no—
411C22—82no—
412C22—82no—
413C22—442no—
414C22—881no—
415C22—881no—
416C22#1062236912yes—
417C22C2×D8×D1111yescharacteristic
418C4—81no—
419C4—81no—
420C4—112no—
421C4—221no—
422C4—221no—
423C4—221no—
424C4—442no—
425C4—882no—
426C4#1062236912yes—
427C4C2×(C22⋊D11)⋊C411yescharacteristic
428C4C2×#6696911yescharacteristic
429C2—22no—
430C2—84no—
431C2—882no—
432C2C2×#1062236911yescharacteristic
433C2D11×#50911yescharacteristic
434C2#1308174811yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutatorC8×C11C23×C4
FrattiniC2×C8C23×D11
FittingC11×#2140C2
socleC22×C11C22×D8
prime radicalC2×#10622760C2
cosocleC2×C8×C11C24
hypercenter#2140D11
hypocenterC11C4×#509
LCSG ▷ C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #2140

Complements

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

NH ≅ G/Ntype
2. #13077387C2semidirect
3. C2×D8×Dic11C2semidirect
4. #13070489C2semidirect
5. #13070477C2semidirect
6. #13070471C2semidirect
7. #13070460C2semidirect
8. #13070405C2semidirect
9. #13070329C2semidirect
10. M32×Dic11C2semidirect
11. C11×#2140C2semidirect
24. #10622760C4semidirect
30. #10622486C22semidirect
31. #10622486C22semidirect
32. #10622485C22semidirect
33. #10622485C22semidirect
38. #10622147C22semidirect
39. #10622141C22semidirect
40. #10622140C22semidirect
41. C16×Dic11C22semidirect
42. #10622128C22semidirect
43. #10622127C22semidirect
49. C2×C11×D8C2×C4semidirect
63. #66957C2×C4semidirect
81. #66891C2×C4semidirect
82. #66890C2×C4semidirect
89. #66876C2×C4semidirect
145. Dic44C22×C4semidirect
147. D88C22×C4semidirect
150. C11⋊C16C22×C4semidirect
159. #2140D11semidirect
254. Dic11#509semidirect
265. C2×D8C4×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×#106227602
#130773872
C2×D8×Dic112
#130704892
#130704772
#130704712
#130704602
#130704052
#130703292
M32×Dic112
C11×#21402
C4×#50911