Finite Group Databasebeta

← #14908586

Subgroups — #14908586

Order 2816.

628 conjugacy classes of subgroups.

The subgroup lattice has 430 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13078199C211yesmaximal, characteristic
2C2×D11×#107C211yesmaximal, characteristic, complemented
3#13070816C211yesmaximal, characteristic, complemented
4#13070812C212yesmaximal, complemented
5#13070802C211yesmaximal, characteristic, complemented
6#13070801C211yesmaximal, characteristic, complemented
7#13070798C212yesmaximal, complemented
8#13070401C212yesmaximal, complemented
9#13070327C212yesmaximal, complemented
10#13070225C211yesmaximal, characteristic, complemented
11C11×#2236C211yesmaximal, characteristic, complemented
12C2×#66972C2211yescharacteristic
13C22×C8×D11C2211yescharacteristic
14#10623158—21no—
15C2×C4⋊C4×D11—21no—
16C11×#467C2211yescharacteristic
17C2×C11×#107C2211yescharacteristic
18#10622801C2211yescharacteristic
19#10622728C2211yescharacteristic
20C2×#66882C2211yescharacteristic
21#10622661—21no—
22C2×#66871—21no—
23C2×#66862C2212yes—
24#10622496C2211yescharacteristic
25#10622493C2211yescharacteristic
26D11×#107—21no—
27D11×#107—21no—
28D11×#107C2212yes—
29D11×#107C2212yes—
30#10622420—21no—
31#10622417—21no—
32C11×#366C2212yescomplemented
33C11×#358C2212yescomplemented
34C11×C22⋊C16C2211yescharacteristic
35#10622202C2212yescomplemented
36C22⋊(C11⋊C16)C2211yescharacteristic
37#10622147C2212yescomplemented
38(C2×D11)⋊C16C2212yes—
39#10622143C2212yescomplemented
40#10622129C2212yescomplemented
41#10622128C2212yescomplemented
42#10622127C2212yescomplemented
43C2×#4343—21no—
44C22×C4×D11—41no—
45C22×C4×D11D411yescharacteristic
46C2×C11×Q16C2311yescharacteristic
47C22×C8×C11C2311yescharacteristic
48C11×C22⋊Q8—21no—
49C2×C11×C4⋊C4—21no—
50#66999—21no—
51C2×#4325—21no—
52#66983—21no—
53C2×C4⋊Dic11—21no—
54C2×Dic11⋊C4—41no—
55C22×C11⋊C8D411yescharacteristic
56#66972—24no—
57C2×D88C2311yescharacteristic
58C2×C8×D11—24no—
59C2×C8×D11D411yescharacteristic
60C2×C8×D11D411yescharacteristic
61C2×C8×D11C2311yescharacteristic
62C2×C8×D11C2311yescharacteristic
63#66948—21no—
64#66947—41no—
65#66946—41no—
66#66945—21no—
67C4⋊C4×D11—22no—
68C4⋊C4×D11—22no—
69C4⋊C4×D11—41no—
70C4⋊C4×D11—41no—
71#66935—41no—
72(C22⋊D11)⋊C4—41no—
73C2×C11×C16C2312yes—
74C11×#107—21no—
75C11×#107C2312yes—
76C11×#107C2311yescharacteristic
77C11×#103—21no—
78#66899—21no—
79#66885—21no—
80#66882—21no—
81#66882C2311yescharacteristic
82#66882C2312yes—
83C2×C11⋊C16C2312yes—
84#66873—21no—
85#66872—21no—
86#66871—22no—
87#66871—22no—
88#66862—24no—
89#33646—111nomaximal, Sylow
90C23×D11D811yescharacteristic
91C2×Q8×C11—21no—
92C22×C4×C11—41no—
93C22×C4×C11C2×D411yescharacteristic
94C2×C22⋊D11—41no—
95C22×Dic11—41no—
96C22×Dic11D811yescharacteristic
97#4343—42no—
98#4343—42no—
99C2×D44—21no—
100C2×D44—41no—
101C2×D44—41no—
102C2×C4×D11—22no—
103C2×C4×D11—22no—
104C2×C4×D11—41no—
105C2×C4×D11—42no—
106C2×C4×D11—42no—
107C2×C4×D11—84no—
108C2×C4×D11D811yescharacteristic
109C2×C4×D11D811yescharacteristic
110C2×C4×D11C2×D411yescharacteristic
111C2×C4×D11C2×D411yescharacteristic
112C11×Q16—22no—
113C2×C8×C11—22no—
114C2×C8×C11C2×D411yescharacteristic
115C2×C8×C11C2411yescharacteristic
116C11×C4⋊C4—22no—
117C11×C4⋊C4—21no—
118C11×C4⋊C4—41no—
119C11×C4⋊C4—41no—
120C11×C22⋊C4—41no—
121#4325—42no—
122(C2×D11)⋊C4—41no—
123(C2×D11)⋊C4—41no—
124(C2×D11)⋊C4—41no—
125(C2×D11)⋊C4—41no—
126C4⋊Dic11—22no—
127C4⋊Dic11—21no—
128C4⋊Dic11—41no—
129Dic11⋊C4—41no—
130Dic11⋊C4—42no—
131Dic11⋊C4—42no—
132C4×Dic11—41no—
133C2×C11⋊C8—22no—
134C2×C11⋊C8C2×D411yescharacteristic
135C2×C11⋊C8C2×D411yescharacteristic
136D88—22no—
137C8×D11—22no—
138C8×D11—22no—
139C8×D11—22no—
140C8×D11#4114yes—
141C11×C16—22no—
142C11⋊C16—22no—
143#3050—111no—
144C22×#107—111no—
145#2236—111no—
146#2236D1111yescharacteristic, complemented
147#2235—112no—
148#2233—111no—
149#2233—111no—
150#2232—112no—
151#2159—112no—
152#2139—112no—
153#2112—111no—
154C23×C11C2×D811yescharacteristic
155C22×D11—22no—
156C22×D11—22no—
157C22×D11—22no—
158C22×D11—41no—
159C22×D11C2×D811yescharacteristic
160C22×D11C2×D811yescharacteristic
161Q8×C11—41no—
162Q8×C11—41no—
163C2×C4×C11—21no—
164C2×C4×C11—21no—
165C2×C4×C11—41no—
166C2×C4×C11—42no—
167C2×C4×C11—41no—
168C2×C4×C11—82no—
169C2×C4×C11C2×D811yescharacteristic
170C2×C4×C11C22×D411yescharacteristic
171C22⋊D11—82no—
172C2×Dic11—22no—
173C2×Dic11—41no—
174C2×Dic11—42no—
175C2×Dic11—82no—
176C2×Dic11C2×D811yescharacteristic
177C2×Dic11C2×D811yescharacteristic
178D44—41no—
179D44—41no—
180D44—82no—
181D44—82no—
182C4×D11—22no—
183C4×D11—21no—
184C4×D11—21no—
185C4×D11—22no—
186C4×D11—84no—
187C4×D11—84no—
188C4×D11—82no—
189C4×D11#12312yes—
190C4×D11#13712yes—
191C8×C11—21no—
192C8×C11C2×#4112yes—
193C11⋊C8—21no—
194C11⋊C8#12312yes—
195C2×#135—111no—
196C23×C8—111no—
197#525—221no—
198C22×C4⋊C4—221no—
199C2×M32—112no—
200#467—111no—
201#467C2×D1111yescharacteristic
202#466—111no—
203#466—111no—
204#465—221no—
205#465—221no—
206#427—111no—
207C2×#107—111no—
208C2×#107—112no—
209C2×#107—112no—
210C2×#107—221no—
211C2×#107—221no—
212C2×#107—221no—
213C2×#107C2×D1111yescharacteristic
214#416—221no—
215#367—112no—
216#367—112no—
217#366—112no—
218#366C2×D1112yescomplemented
219#358—112no—
220#358C2×D1112yescomplemented
221#357—112no—
222#357—112no—
223C22⋊C16—111no—
224C22⋊C16—112no—
225C22⋊C16C2×D1111yescharacteristic
226C22×C11—21no—
227C22×C11—21no—
228C22×C11#51012yes—
229C22×C11C22×D811yescharacteristic
230C2×D11—28no—
231C2×D11—21no—
232C2×D11—21no—
233C2×D11—21no—
234C2×D11—21no—
235C2×D11—81no—
236C2×D11—81no—
237C2×D11—81no—
238C2×D11#48012yes—
239C2×D11#50912yes—
240C4×C11—21no—
241C4×C11—81no—
242C4×C11—82no—
243C4×C11—81no—
244C4×C11C2×#12311yescharacteristic
245C4×C11C2×#13711yescharacteristic
246Dic11—21no—
247Dic11—82no—
248Dic11—81no—
249Dic11#48012yes—
250C2×#41—221no—
251C23×C4—111no—
252C23×C4—441no—
253#135—224no—
254C2×Q16C22×D1111yescharacteristic
255C2×SD16—221no—
256C2×D8—111no—
257C22×C8—111no—
258C22×C8—111no—
259C22×C8—111no—
260C22×C8—111no—
261C22×C8—111no—
262C22×C8—224no—
263C22×C8C22×D1111yescharacteristic
264#123—441no—
265C22⋊Q8—21no—
266C22⋊Q8—221no—
267#121—221no—
268#121—221no—
269#120—441no—
270C4×D4—441no—
271C4×D4—441no—
272#117—221no—
273C2×C4⋊C4—21no—
274C2×C4⋊C4—222no—
275C2×C4⋊C4—222no—
276C2×C4⋊C4—221no—
277C2×C4⋊C4—441no—
278C2×C4⋊C4—441no—
279C2×C4⋊C4—441no—
280M32—224no—
281C2×C16—112no—
282C2×C16C22×D1112yes—
283#107—21no—
284#107—112no—
285#107—111no—
286#107—222no—
287#107—222no—
288#107—221no—
289#107C22×D1112yes—
290#107C22×D1111yescharacteristic
291#106—221no—
292#103—21no—
293#103—221no—
294#102—221no—
295#102—221no—
296C2×C11—22no—
297C2×C11C2×#48011yescharacteristic
298C2×C11C2×#50911yescharacteristic
299C2×C11C2×#51011yescharacteristic
300D11—22no—
301D11—22no—
302D11—161no—
303C24—111no—
304#41—442no—
305#41—442no—
306C2×Q8—21no—
307C2×D4—221no—
308C2×D4—441no—
309C2×D4—441no—
310C2×D4—441no—
311C22×C4—41no—
312C22×C4—111no—
313C22×C4—111no—
314C22×C4—111no—
315C22×C4—111no—
316C22×C4—111no—
317C22×C4—222no—
318C22×C4—222no—
319C22×C4—441no—
320C22×C4—442no—
321C22×C4—442no—
322C22×C4—441no—
323C22×C4—884no—
324C22×C4D4×D1111yescharacteristic
325Q16—22no—
326SD16—442no—
327D8—222no—
328C2×C8—22no—
329C2×C8—111no—
330C2×C8—114no—
331C2×C8—111no—
332C2×C8—222no—
333C2×C8—222no—
334C2×C8—222no—
335C2×C8—222no—
336C2×C8D4×D1111yescharacteristic
337C2×C8C23×D1111yescharacteristic
338C4⋊C4—21no—
339C4⋊C4—22no—
340C4⋊C4—41no—
341C4⋊C4—41no—
342C4⋊C4—221no—
343C4⋊C4—222no—
344C4⋊C4—442no—
345C4⋊C4—442no—
346C4⋊C4—441no—
347C4⋊C4—441no—
348C22⋊C4—41no—
349C22⋊C4—441no—
350C22⋊C4—441no—
351C22⋊C4—441no—
352C22⋊C4—441no—
353C42—441no—
354C16—22no—
355C16—222no—
356C11#3364611yescharacteristic, complemented, Sylow
357C23—111no—
358C23—111no—
359C23—222no—
360C23—222no—
361C23—222no—
362C23—441no—
363C23D8×D1111yescharacteristic
364Q8—41no—
365Q8—41no—
366D4—441no—
367D4—441no—
368D4—882no—
369D4—882no—
370D4—882no—
371C2×C4—21no—
372C2×C4—21no—
373C2×C4—41no—
374C2×C4—41no—
375C2×C4—42no—
376C2×C4—82no—
377C2×C4—111no—
378C2×C4—112no—
379C2×C4—112no—
380C2×C4—111no—
381C2×C4—222no—
382C2×C4—222no—
383C2×C4—222no—
384C2×C4—221no—
385C2×C4—221no—
386C2×C4—441no—
387C2×C4—442no—
388C2×C4—882no—
389C2×C4—884no—
390C2×C4—884no—
391C2×C4—882no—
392C2×C4D8×D1111yescharacteristic
393C2×C4C2×D4×D1111yescharacteristic
394C8—21no—
395C8—112no—
396C8—221no—
397C8#41×D1112yes—
398C22—21no—
399C22—21no—
400C22—112no—
401C22—112no—
402C22—228no—
403C22—221no—
404C22—221no—
405C22—221no—
406C22—221no—
407C22—881no—
408C22—881no—
409C22—881no—
410C22#1062253112yes—
411C22C2×D8×D1111yescharacteristic
412C4—21no—
413C4—82no—
414C4—81no—
415C4—81no—
416C4—112no—
417C4—221no—
418C4—882no—
419C4—881no—
420C4D11×#12311yescharacteristic
421C4D11×#13711yescharacteristic
422C2—22no—
423C2—222no—
424C2—222no—
425C2—1761no—
426C2D11×#48011yescharacteristic
427C2D11×#50911yescharacteristic
428C2C2×#1062253111yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2236C2
socleC22×C11C22×D8
prime radical#13078199C2
hypercenter#2236D11
hypocenterC11#33646
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #2236

Complements

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

NH ≅ G/Ntype
2. C2×D11×#107C2semidirect
3. #13070816C2semidirect
4. #13070812C2semidirect
5. #13070802C2semidirect
6. #13070801C2semidirect
7. #13070798C2semidirect
8. #13070401C2semidirect
9. #13070327C2semidirect
10. #13070225C2semidirect
11. C11×#2236C2semidirect
32. C11×#366C22semidirect
33. C11×#358C22semidirect
35. #10622202C22semidirect
37. #10622147C22semidirect
39. #10622143C22semidirect
40. #10622129C22semidirect
41. #10622128C22semidirect
42. #10622127C22semidirect
146. #2236D11semidirect
218. #366C2×D11semidirect
220. #358C2×D11semidirect
356. C11#33646semidirect

Maximal subgroups

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

subgroupindex
#130781992
C2×D11×#1072
#130708162
#130708122
#130708022
#130708012
#130707982
#130704012
#130703272
#130702252
C11×#22362
#3364611