Finite Group Databasebeta

← #14909143

Subgroups — #14909143

Order 2816.

622 conjugacy classes of subgroups.

The subgroup lattice has 426 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D11×#500C211yesmaximal, characteristic, complemented
2#13079041C211yesmaximal, characteristic
3#13070855C211yesmaximal, characteristic, complemented
4#13070853C211yesmaximal, characteristic, complemented
5#13070852C211yesmaximal, characteristic, complemented
6#13070842C212yesmaximal, complemented
7#13070838C212yesmaximal, complemented
8#13070327C212yesmaximal, complemented
9#13070325C212yesmaximal, complemented
10#13070209C211yesmaximal, characteristic, complemented
11C11×#2243C211yesmaximal, characteristic, complemented
12C2×#66972C2211yescharacteristic
13C2×#66969—21no—
14C2×#66965C2211yescharacteristic
15D11×C4⋊Q8—21no—
16#10623199—21no—
17C11×#500C2211yescharacteristic
18C11×#495C2211yescharacteristic
19#10622794C2211yescharacteristic
20#10622788—21no—
21#10622764C2211yescharacteristic
22#10622691—21no—
23#10622672—21no—
24C2×#66862C2212yes—
25D11×#107—21no—
26D11×#107C2212yes—
27#10622487—21no—
28#10622487C2212yes—
29#10622309C2211yescharacteristic
30C4×C8×D11C2211yescharacteristic
31#10622295C2211yescharacteristic
32C11×#358C2212yes—
33C11×#357C2212yes—
34C11×#346C2211yescharacteristic
35#10622202C2212yes—
36#10622200C2212yes—
37#10622147C2212yes—
38#10622141C2212yes—
39C16×Dic11C2212yes—
40#10622130C2212yes—
41#10622129C2212yes—
42#10622099C2211yescharacteristic
43C2×#4343—21no—
44C2×Q8×D11—41no—
45C2×#4341—21no—
46C2×C11×Q16C2311yescharacteristic
47C2×C11×SD16—21no—
48C2×C11×D8C2311yescharacteristic
49C11×C4⋊Q8—21no—
50C11×#124—21no—
51#66997—21no—
52#66997—41no—
53C2×#4326—21no—
54C2×#4325—21no—
55#66993—21no—
56C2×#4324—21no—
57C2×#4323—21no—
58#66972—24no—
59#66969—44no—
60#66965—24no—
61C2×Dic44C2311yescharacteristic
62C2×D88C2311yescharacteristic
63C2×#4314—21no—
64C2×C8×D11D411yescharacteristic
65C2×C8×D11C2311yescharacteristic
66C4⋊C4×D11—22no—
67C4⋊C4×D11—41no—
68#66941—22no—
69#66941—41no—
70#66937—41no—
71#66937—41no—
72(C22⋊D11)⋊C4—41no—
73(C22⋊D11)⋊C4—41no—
74#66928—21no—
75C42×D11D411yescharacteristic
76#66922—21no—
77C2×C11×C16C2312yes—
78C11×#107—21no—
79C11×#107C2312yes—
80C4×C8×C11C2311yescharacteristic
81#66882—21no—
82#66882C2312yes—
83C8×Dic11D411yescharacteristic
84C8×Dic11C2311yescharacteristic
85C2×C11⋊C16C2312yes—
86#66871—22no—
87#66871—22no—
88C4×C11⋊C8D411yescharacteristic
89#66862—24no—
90#33707—111nomaximal, Sylow
91C2×Q8×C11—21no—
92C2×Q8×C11—41no—
93C2×D4×C11—21no—
94C2×C22⋊D11—41no—
95C2×C22⋊D11—41no—
96C2×C22⋊D11—41no—
97C22×Dic11—41no—
98#4343—42no—
99#4343—42no—
100Q8×D11—84no—
101#4341—42no—
102#4341—42no—
103C2×D44—21no—
104C2×D44—41no—
105C2×C4×D11—41no—
106C2×C4×D11—42no—
107C2×C4×D11D811yescharacteristic
108C2×C4×D11D811yescharacteristic
109C2×C4×D11C2×D411yescharacteristic
110C2×Dic22—21no—
111C2×Dic22—42no—
112C2×Dic22—41no—
113C11×Q16—22no—
114C11×SD16—42no—
115C11×D8—22no—
116C2×C8×C11C2×D411yescharacteristic
117C2×C8×C11C2411yescharacteristic
118C11×C4⋊C4—22no—
119C11×C4⋊C4—41no—
120C11×C22⋊C4—41no—
121C11×C22⋊C4—41no—
122C42×C11C2×D411yescharacteristic
123#4326—42no—
124#4325—42no—
125#4324—42no—
126#4323—42no—
127(C2×D11)⋊C4—41no—
128(C2×D11)⋊C4—41no—
129C4⋊Dic11—22no—
130C4⋊Dic11—41no—
131Dic11⋊C4—41no—
132Dic11⋊C4—41no—
133Dic11⋊C4—42no—
134Dic11⋊C4—42no—
135C4×Dic11D811yescharacteristic
136C4×Dic11D811yescharacteristic
137C4×Dic11C2×D411yescharacteristic
138C2×C11⋊C8C2×D411yescharacteristic
139C2×C11⋊C8C2×D411yescharacteristic
140Dic44—22no—
141D88—22no—
142#4314—42no—
143C8×D11SD1614yes—
144C8×D11#4114yes—
145C11×C16—22no—
146C11⋊C16—22no—
147C2×#500—111no—
148#3147—111no—
149#2243—111no—
150#2243—111no—
151#2243—111no—
152#2243D1111yescharacteristic, complemented
153#2241—112no—
154#2240—112no—
155#2139—112no—
156#2139—112no—
157C4×M32—111no—
158C23×C11—41no—
159C22×D11—41no—
160C22×D11C2×D811yescharacteristic
161Q8×C11—41no—
162Q8×C11—41no—
163Q8×C11—82no—
164D4×C11—41no—
165D4×C11—41no—
166C2×C4×C11—41no—
167C2×C4×C11—42no—
168C2×C4×C11C2×D811yescharacteristic
169C2×C4×C11C2×D811yescharacteristic
170C2×C4×C11C22×D411yescharacteristic
171C22⋊D11—82no—
172C22⋊D11—82no—
173C22⋊D11—82no—
174C2×Dic11—42no—
175C2×Dic11—41no—
176C2×Dic11—82no—
177C2×Dic11C2×D811yescharacteristic
178C2×Dic11C2×D811yescharacteristic
179C2×Dic11C2×D811yescharacteristic
180D44—41no—
181D44—41no—
182D44—82no—
183C4×D11—22no—
184C4×D11—22no—
185C4×D11—84no—
186C4×D11—82no—
187C4×D11#12412yes—
188C4×D11C2×SD1612yes—
189Dic22—41no—
190Dic22—41no—
191Dic22—82no—
192Dic22—84no—
193C8×C11C2×SD1612yes—
194C8×C11C2×#4112yes—
195C11⋊C8#12412yes—
196C11⋊C8C2×SD1612yes—
197C2×#135—111no—
198C2×#135—111no—
199C2×#135—221no—
200#532—221no—
201C2×C4⋊Q8—221no—
202C2×M32—112no—
203#500—112no—
204#500—111no—
205#500—221no—
206#500—221no—
207#500C2×D1111yescharacteristic
208#495—111no—
209#495—221no—
210#495C2×D1111yescharacteristic
211#494—111no—
212#493—111no—
213#492—221no—
214C2×#107—112no—
215C2×#107—221no—
216C2×C4×C8—111no—
217#358—112no—
218#358—112no—
219#358—112no—
220#358C2×D1112yes—
221#357—112no—
222#357—112no—
223#357—112no—
224#357C2×D1112yes—
225#346—111no—
226#346C2×D1111yescharacteristic
227C4×C16—112no—
228C22×C11—81no—
229C22×C11—81no—
230C22×C11—81no—
231C22×C11C22×D811yescharacteristic
232C2×D11—21no—
233C2×D11—21no—
234C2×D11—81no—
235C2×D11—81no—
236C2×D11—81no—
237C2×D11#48612yes—
238C4×C11—21no—
239C4×C11—21no—
240C4×C11—81no—
241C4×C11—82no—
242C4×C11C2×#12411yescharacteristic
243C4×C11C22×SD1611yescharacteristic
244Dic11—81no—
245Dic11—82no—
246Dic11#48612yes—
247Dic11#50912yes—
248Dic11#51012yes—
249C2×#41—221no—
250C2×#41—221no—
251C22×Q8—441no—
252#135—224no—
253#135—224no—
254#135—444no—
255C2×Q16—111no—
256C2×Q16—221no—
257C2×Q16C22×D1111yescharacteristic
258C2×SD16—21no—
259C2×SD16—221no—
260C2×SD16—221no—
261C2×SD16—221no—
262C2×D8—111no—
263C2×D8—221no—
264C2×D8C22×D1111yescharacteristic
265C22×C8—111no—
266C22×C8—111no—
267C4⋊Q8—21no—
268C4⋊Q8—222no—
269C4⋊Q8—221no—
270C4⋊Q8—221no—
271C4⋊Q8—441no—
272C4⋊Q8—441no—
273#127—221no—
274#124—21no—
275#124—221no—
276#121—441no—
277#121—441no—
278C4×D4—441no—
279C4×D4—441no—
280C2×C4⋊C4—222no—
281C2×C4⋊C4—441no—
282C2×C42—111no—
283M32—224no—
284C2×C16—112no—
285C2×C16C22×D1112yes—
286#107—21no—
287#107—112no—
288#107—222no—
289#107—222no—
290#107—221no—
291#107C22×D1112yes—
292C4×C8—111no—
293C4×C8—111no—
294C4×C8—111no—
295C4×C8C22×D1111yescharacteristic
296C2×C11—161no—
297C2×C11C2×#48611yescharacteristic
298C2×C11C2×#50911yescharacteristic
299C2×C11C2×#51011yescharacteristic
300D11—22no—
301D11—161no—
302#41—442no—
303#41—442no—
304#41—442no—
305#41—442no—
306C2×Q8—21no—
307C2×Q8—41no—
308C2×Q8—221no—
309C2×Q8—442no—
310C2×Q8—441no—
311C2×Q8—884no—
312C2×D4—21no—
313C2×D4—221no—
314C2×D4—441no—
315C2×D4—441no—
316C2×D4—441no—
317C2×D4—441no—
318C22×C4—111no—
319C22×C4—111no—
320C22×C4—111no—
321C22×C4—441no—
322C22×C4—442no—
323C22×C4—441no—
324Q16—22no—
325Q16—222no—
326Q16—442no—
327SD16—42no—
328SD16—442no—
329SD16—442no—
330SD16—442no—
331D8—22no—
332D8—222no—
333D8—442no—
334C2×C8—111no—
335C2×C8—111no—
336C2×C8—114no—
337C2×C8—114no—
338C2×C8D4×D1111yescharacteristic
339C2×C8C23×D1111yescharacteristic
340C4⋊C4—22no—
341C4⋊C4—41no—
342C4⋊C4—222no—
343C4⋊C4—442no—
344C4⋊C4—442no—
345C4⋊C4—441no—
346C4⋊C4—441no—
347C4⋊C4—441no—
348C22⋊C4—41no—
349C22⋊C4—41no—
350C22⋊C4—441no—
351C22⋊C4—441no—
352C42—111no—
353C42—111no—
354C42—111no—
355C42D4×D1111yescharacteristic
356C16—22no—
357C16—222no—
358C11#3370711yescharacteristic, complemented, Sylow
359C23—41no—
360C23—111no—
361C23—441no—
362Q8—41no—
363Q8—41no—
364Q8—82no—
365Q8—441no—
366Q8—441no—
367Q8—882no—
368Q8—884no—
369D4—41no—
370D4—41no—
371D4—441no—
372D4—441no—
373D4—882no—
374D4—882no—
375D4—882no—
376D4—882no—
377C2×C4—41no—
378C2×C4—42no—
379C2×C4—111no—
380C2×C4—111no—
381C2×C4—111no—
382C2×C4—112no—
383C2×C4—112no—
384C2×C4—222no—
385C2×C4—222no—
386C2×C4—441no—
387C2×C4—442no—
388C2×C4—882no—
389C2×C4—884no—
390C2×C4—882no—
391C2×C4D8×D1111yescharacteristic
392C2×C4D8×D1111yescharacteristic
393C2×C4C2×D4×D1111yescharacteristic
394C8—112no—
395C8—112no—
396C8SD16×D1112yes—
397C8#41×D1112yes—
398C22—81no—
399C22—81no—
400C22—81no—
401C22—112no—
402C22—221no—
403C22—221no—
404C22—881no—
405C22—881no—
406C22—881no—
407C22C2×D8×D1111yescharacteristic
408C4—21no—
409C4—21no—
410C4—81no—
411C4—82no—
412C4—112no—
413C4—112no—
414C4—112no—
415C4—881no—
416C4—882no—
417C4D11×#12411yescharacteristic
418C4C2×SD16×D1111yescharacteristic
419C2—161no—
420C2—222no—
421C2—1761no—
422C2D11×#48611yescharacteristic
423C2D11×#50911yescharacteristic
424C2D11×#51011yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2243C2
socleC22×C11C22×D8
prime radical#13079041C2
hypercenter#2243D11
hypocenterC11#33707
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #2243

Complements

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

NH ≅ G/Ntype
1. D11×#500C2semidirect
3. #13070855C2semidirect
4. #13070853C2semidirect
5. #13070852C2semidirect
6. #13070842C2semidirect
7. #13070838C2semidirect
8. #13070327C2semidirect
9. #13070325C2semidirect
10. #13070209C2semidirect
11. C11×#2243C2semidirect
152. #2243D11semidirect
358. C11#33707semidirect

Maximal subgroups

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

subgroupindex
D11×#5002
#130790412
#130708552
#130708532
#130708522
#130708422
#130708382
#130703272
#130703252
#130702092
C11×#22432
#3370711