Finite Group Databasebeta

← #14909136

Subgroups — #14909136

Order 2816.

598 conjugacy classes of subgroups.

The subgroup lattice has 422 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079127C211yesmaximal, characteristic, complemented
2D11×#495C211yesmaximal, characteristic
3#13070855C211yesmaximal, characteristic, complemented
4#13070853C211yesmaximal, characteristic, complemented
5#13070852C211yesmaximal, characteristic, complemented
6#13070849C212yesmaximal, complemented
7#13070846C212yesmaximal, complemented
8#13070334C212yesmaximal, complemented
9#13070330C212yesmaximal
10#13070209C211yesmaximal, characteristic, complemented
11C11×#2243C211yesmaximal, characteristic, complemented
12C2×Q16×D11C2211yescharacteristic
13C2×SD16×D11—21no—
14C2×D8×D11C2211yescharacteristic
15#10623259—21no—
16D11×#124—21no—
17C11×#500C2211yescharacteristic, complemented
18C11×#495C2211yescharacteristic
19#10622804C2211yescharacteristic
20#10622781—21no—
21#10622768C2211yescharacteristic
22#10622692—21no—
23#10622672—21no—
24C2×#66862C2212yes—
25#10622493—21no—
26#10622493C2212yes—
27#10622491—21no—
28#10622491C2212yescomplemented
29#10622309C2211yescharacteristic
30C4×C8×D11C2211yescharacteristic
31#10622295C2211yescharacteristic, complemented
32C11×#358C2212yescomplemented
33C11×#357C2212yes—
34C11×#346C2211yescharacteristic, complemented
35#10622202C2212yescomplemented
36#10622200C2212yes—
37#10622147C2212yes—
38#10622141C2212yescomplemented
39C16×Dic11C2212yescomplemented
40#10622130C2212yescomplemented
41#10622129C2212yes—
42#10622099C2211yescharacteristic, complemented
43C2×Q8×D11—21no—
44C2×D4×D11—21no—
45C2×C11×Q16C2311yescharacteristic
46C2×C11×SD16—21no—
47C2×C11×D8C2311yescharacteristic
48C11×C4⋊Q8—21no—
49C11×#124—21no—
50#67000—21no—
51#66999—41no—
52Q8×Dic11—41no—
53C2×#4326—21no—
54C2×#4325—21no—
55#66989—21no—
56C2×#4324—21no—
57C2×#4323—21no—
58Q16×D11—24no—
59SD16×D11—44no—
60D8×D11—24no—
61C2×Dic44C2311yescharacteristic
62C2×D88C2311yescharacteristic
63C2×#4314—21no—
64C2×C8×D11D411yescharacteristic
65C2×C8×D11C2311yescharacteristic
66#66950—41no—
67#66945—22no—
68#66943—22no—
69#66940—41no—
70#66938—41no—
71#66938—41no—
72C22⋊C4×D11—41no—
73C22⋊C4×D11—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#66872—22no—
87#66872—22no—
88C4×C11⋊C8D411yescharacteristic
89#66862—24no—
90#33706—111nomaximal, Sylow
91C23×D11—41no—
92C2×Q8×C11—21no—
93C2×Q8×C11—41no—
94C2×D4×C11—21no—
95C2×C22⋊D11—41no—
96Q8×D11—42no—
97Q8×D11—42no—
98D4×D11—42no—
99D4×D11—42no—
100C2×D44—21no—
101C2×C4×D11—41no—
102C2×C4×D11D811yescharacteristic
103C2×C4×D11D811yescharacteristic
104C2×C4×D11C2×D411yescharacteristic
105C2×Dic22—21no—
106C2×Dic22—41no—
107C2×Dic22—41no—
108C11×Q16—22no—
109C11×SD16—42no—
110C11×D8—22no—
111C2×C8×C11C2×D411yescharacteristic
112C2×C8×C11C2411yescharacteristic
113C11×C4⋊C4—22no—
114C11×C4⋊C4—41no—
115C11×C22⋊C4—41no—
116C11×C22⋊C4—41no—
117C42×C11C2×D411yescharacteristic
118C22⋊Dic11—41no—
119C22⋊Dic11—41no—
120#4326—42no—
121#4325—42no—
122#4324—42no—
123#4323—42no—
124(C2×D11)⋊C4—41no—
125(C2×D11)⋊C4—41no—
126(C2×D11)⋊C4—42no—
127(C2×D11)⋊C4—41no—
128(C2×D11)⋊C4—41no—
129C4⋊Dic11—22no—
130C4⋊Dic11—42no—
131C4⋊Dic11—41no—
132Dic11⋊C4—42no—
133C4×Dic11—42no—
134C4×Dic11D811yescharacteristic
135C4×Dic11D811yescharacteristic
136C4×Dic11C2×D411yescharacteristic
137C2×C11⋊C8C2×D411yescharacteristic
138C2×C11⋊C8C2×D411yescharacteristic
139Dic44—22no—
140D88—22no—
141#4314—42no—
142C8×D11SD1614yes—
143C8×D11#4114yes—
144C11×C16—22no—
145C11⋊C16—22no—
146#3160—111no—
147C2×#495—111no—
148#2243—111no—
149#2243—111no—
150#2243—111no—
151#2243D1111yescharacteristic, complemented
152#2242—112no—
153#2242—112no—
154#2141—112no—
155#2140—112no—
156C4×M32—111no—
157C23×C11—41no—
158C22×D11—41no—
159C22×D11—82no—
160C22×D11—82no—
161C22×D11—82no—
162C22×D11C2×D811yescharacteristic
163Q8×C11—41no—
164Q8×C11—41no—
165Q8×C11—82no—
166D4×C11—41no—
167D4×C11—41no—
168C2×C4×C11—42no—
169C2×C4×C11—41no—
170C2×C4×C11C2×D811yescharacteristic
171C2×C4×C11C2×D811yescharacteristic
172C2×C4×C11C22×D411yescharacteristic
173C22⋊D11—82no—
174C2×Dic11—42no—
175C2×Dic11—41no—
176C2×Dic11C2×D811yescharacteristic
177C2×Dic11C2×D811yescharacteristic
178C2×Dic11C2×D811yescharacteristic
179D44—41no—
180D44—41no—
181C4×D11—41no—
182C4×D11—41no—
183C4×D11—82no—
184C4×D11#12412yes—
185C4×D11C2×SD1612yes—
186Dic22—41no—
187Dic22—41no—
188Dic22—82no—
189Dic22—82no—
190C8×C11C2×SD1612yes—
191C8×C11C2×#4112yes—
192C11⋊C8#12412yes—
193C11⋊C8C2×SD1612yes—
194C22×Q16—111no—
195C22×SD16—221no—
196C22×D8—111no—
197#533—221no—
198C2×#124—221no—
199C2×M32—112no—
200#500—111no—
201#500C2×D1111yescharacteristic, complemented
202#499—112no—
203#499—221no—
204#498—221no—
205#495—111no—
206#495—111no—
207#495—111no—
208#495—221no—
209#495—221no—
210#495C2×D1111yescharacteristic
211#427—112no—
212#427—221no—
213C2×C4×C8—111no—
214#358—112no—
215#358—112no—
216#358—112no—
217#358C2×D1112yescomplemented
218#357—112no—
219#357—112no—
220#357—112no—
221#357C2×D1112yes—
222#346—111no—
223#346C2×D1111yescharacteristic, complemented
224C4×C16—112no—
225C22×C11—81no—
226C22×C11—81no—
227C22×C11—81no—
228C22×C11C22×D811yescharacteristic
229C2×D11—21no—
230C2×D11—21no—
231C2×D11—81no—
232C2×D11—81no—
233C2×D11—81no—
234C2×D11—164no—
235C2×D11#48612yes—
236C4×C11—21no—
237C4×C11—21no—
238C4×C11—81no—
239C4×C11—82no—
240C4×C11C2×#12411yescharacteristic
241C4×C11C22×SD1611yescharacteristic
242Dic11—21no—
243Dic11—21no—
244Dic11—81no—
245Dic11—82no—
246Dic11#48612yes—
247C22×Q8—221no—
248C22×D4—221no—
249C2×Q16—111no—
250C2×Q16—224no—
251C2×Q16—221no—
252C2×Q16C22×D1111yescharacteristic
253C2×SD16—21no—
254C2×SD16—221no—
255C2×SD16—221no—
256C2×SD16—221no—
257C2×SD16—444no—
258C2×D8—111no—
259C2×D8—224no—
260C2×D8—221no—
261C2×D8C22×D1111yescharacteristic
262C22×C8—111no—
263C22×C8—111no—
264C4⋊Q8—21no—
265C4⋊Q8—221no—
266#125—222no—
267#124—21no—
268#124—221no—
269#124—221no—
270#124—221no—
271#124—441no—
272#124—441no—
273C22⋊Q8—441no—
274C22⋊Q8—441no—
275C4×Q8—441no—
276C4×Q8—441no—
277#117—222no—
278C2×C22⋊C4—441no—
279C2×C22⋊C4—441no—
280C2×C42—111no—
281M32—224no—
282C2×C16—112no—
283C2×C16C22×D1112yes—
284#107—21no—
285#107—112no—
286#107—221no—
287#107C22×D1112yes—
288#106—222no—
289#106—222no—
290C4×C8—111no—
291C4×C8—111no—
292C4×C8—111no—
293C4×C8C22×D1111yescharacteristic
294C2×C11—161no—
295C2×C11C2×#48611yescharacteristic
296C2×C11#341411yescharacteristic
297C2×C11#341411yescharacteristic
298D11—22no—
299D11—161no—
300C24—441no—
301C2×Q8—21no—
302C2×Q8—41no—
303C2×Q8—221no—
304C2×Q8—441no—
305C2×Q8—442no—
306C2×Q8—442no—
307C2×Q8—441no—
308C2×D4—21no—
309C2×D4—221no—
310C2×D4—442no—
311C2×D4—442no—
312C2×D4—441no—
313C22×C4—111no—
314C22×C4—111no—
315C22×C4—111no—
316C22×C4—441no—
317Q16—22no—
318Q16—222no—
319Q16—442no—
320SD16—42no—
321SD16—442no—
322SD16—442no—
323SD16—442no—
324D8—22no—
325D8—222no—
326D8—442no—
327C2×C8—111no—
328C2×C8—111no—
329C2×C8—114no—
330C2×C8—114no—
331C2×C8D4×D1111yescharacteristic
332C2×C8C23×D1111yescharacteristic
333C4⋊C4—22no—
334C4⋊C4—41no—
335C4⋊C4—222no—
336C4⋊C4—442no—
337C4⋊C4—442no—
338C4⋊C4—441no—
339C22⋊C4—41no—
340C22⋊C4—41no—
341C22⋊C4—441no—
342C22⋊C4—441no—
343C22⋊C4—442no—
344C22⋊C4—441no—
345C22⋊C4—441no—
346C22⋊C4—441no—
347C22⋊C4—441no—
348C42—111no—
349C42—111no—
350C42—111no—
351C42—442no—
352C42D4×D1111yescharacteristic
353C16—22no—
354C16—222no—
355C11#3370611yescharacteristic, complemented, Sylow
356C23—41no—
357C23—111no—
358C23—441no—
359C23—882no—
360C23—882no—
361C23—882no—
362Q8—41no—
363Q8—41no—
364Q8—82no—
365Q8—441no—
366Q8—441no—
367Q8—882no—
368Q8—882no—
369D4—41no—
370D4—41no—
371D4—441no—
372D4—441no—
373D4—882no—
374C2×C4—42no—
375C2×C4—41no—
376C2×C4—111no—
377C2×C4—112no—
378C2×C4—112no—
379C2×C4—111no—
380C2×C4—111no—
381C2×C4—441no—
382C2×C4—441no—
383C2×C4—442no—
384C2×C4—441no—
385C2×C4—882no—
386C2×C4D8×D1111yescharacteristic
387C2×C4D8×D1111yescharacteristic
388C2×C4C2×D4×D1111yescharacteristic
389C8—112no—
390C8—112no—
391C8SD16×D1112yes—
392C8#41×D1112yes—
393C22—81no—
394C22—81no—
395C22—81no—
396C22—112no—
397C22—221no—
398C22—221no—
399C22—881no—
400C22—881no—
401C22—881no—
402C22—1764no—
403C22C2×D8×D1111yescharacteristic
404C4—21no—
405C4—21no—
406C4—81no—
407C4—82no—
408C4—112no—
409C4—221no—
410C4—221no—
411C4—881no—
412C4—882no—
413C4D11×#12411yescharacteristic
414C4C2×SD16×D1111yescharacteristic
415C2—161no—
416C2—222no—
417C2—1761no—
418C2D11×#48611yescharacteristic
419C2#1308174811yescharacteristic
420C2#1308175111yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2243C2
socleC22×C11C22×D8
prime radicalC2×D8×D11C22
hypercenter#2243D11
hypocenterC11#33706
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. #13079127C2semidirect
3. #13070855C2semidirect
4. #13070853C2semidirect
5. #13070852C2semidirect
6. #13070849C2semidirect
7. #13070846C2semidirect
8. #13070334C2semidirect
10. #13070209C2semidirect
11. C11×#2243C2semidirect
17. C11×#500C22semidirect
28. #10622491C22semidirect
31. #10622295C22semidirect
32. C11×#358C22semidirect
34. C11×#346C22semidirect
35. #10622202C22semidirect
38. #10622141C22semidirect
39. C16×Dic11C22semidirect
40. #10622130C22semidirect
42. #10622099C22semidirect
151. #2243D11semidirect
201. #500C2×D11semidirect
217. #358C2×D11semidirect
223. #346C2×D11semidirect
355. C11#33706semidirect

Maximal subgroups

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

subgroupindex
#130791272
D11×#4952
#130708552
#130708532
#130708522
#130708492
#130708462
#130703342
#130703302
#130702092
C11×#22432
#3370611