Finite Group Databasebeta

← #14909354

Subgroups — #14909354

Order 2816.

510 conjugacy classes of subgroups.

The subgroup lattice has 382 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079200C211yesmaximal, characteristic, complemented
2#13079183C211yesmaximal, characteristic
3#13070902C211yesmaximal, characteristic, complemented
4#13070861C211yesmaximal, characteristic, complemented
5#13070852C211yesmaximal, characteristic, complemented
6#13070726C212yesmaximal
7#13070721C212yesmaximal, complemented
8Q32×Dic11C212yesmaximal, complemented
9SD32×Dic11C212yesmaximal, complemented
10#13070209C211yesmaximal, characteristic, complemented
11C11×#2251C211yesmaximal, characteristic, complemented
12#10623259—21no—
13#10623211—21no—
14C2×C11×Q32C2212yes—
15C2×C11×SD32C2212yes—
16C11×#495C2211yescharacteristic
17C11×#494C2211yescharacteristic
18#10622801—21no—
19#10622801C2211yescharacteristic
20#10622801C2212yes—
21Q16×Dic11—21no—
22Q16×Dic11C2212yes—
23Q16×Dic11C2211yescharacteristic
24#10622784—21no—
25SD16×Dic11—21no—
26#10622770C2211yescharacteristic
27D8×Dic11C2211yescharacteristic
28#10622694—21no—
29#10622669—21no—
30C2×#66862C2212yes—
31C4×C8×D11C2211yescharacteristic
32#10622296C2211yescharacteristic
33#10622295C2211yescharacteristic
34C11×#346C2211yescharacteristic
35#10622202C2212yes—
36#10622202C2212yes—
37#10622202C2212yes—
38#10622200C2212yes—
39#10622143C2212yes—
40#10622142C2212yes—
41C16×Dic11C2212yes—
42#10622099C2211yescharacteristic
43C2×C11×Q16—21no—
44C2×C11×Q16C2312yes—
45C2×C11×Q16C2311yescharacteristic
46C2×C11×SD16—21no—
47C2×C11×D8C2311yescharacteristic
48C11×C4⋊Q8—21no—
49C11×#124—21no—
50#66999—22no—
51#66999—21no—
52Q8×Dic11—22no—
53Q8×Dic11—21no—
54#66991—21no—
55D4×Dic11—21no—
56C2×C8×D11D411yescharacteristic
57C2×C8×D11C2311yescharacteristic
58#66950—41no—
59#66945—41no—
60#66943—41no—
61#66940—41no—
62#66936—41no—
63(C22⋊D11)⋊C4—41no—
64#66932—41no—
65#66930—41no—
66C42×D11D411yescharacteristic
67#66923—21no—
68#66922—21no—
69C11×Q32—24no—
70C11×SD32—24no—
71C2×C11×C16C2312yes—
72C4×C8×C11C2311yescharacteristic
73#66899—21no—
74#66899—21no—
75#66899—22no—
76#66899—22no—
77#66896—21no—
78#66896—21no—
79#66882—21no—
80#66882C2311yescharacteristic
81#66882C2311yescharacteristic
82#66882C2312yes—
83#66881—21no—
84C8×Dic11D411yescharacteristic
85C8×Dic11C2311yescharacteristic
86C2×C11⋊C16C2312yes—
87C4×C11⋊C8D411yescharacteristic
88#66862—24no—
89#33738—111nomaximal, Sylow
90C2×Q8×C11—21no—
91C2×Q8×C11—22no—
92C2×D4×C11—21no—
93C2×C22⋊D11—41no—
94C22×Dic11—41no—
95C2×C4×D11D811yescharacteristic
96C2×C4×D11D811yescharacteristic
97C2×C4×D11C2×D411yescharacteristic
98C2×Dic22—41no—
99C11×Q16—22no—
100C11×Q16—22no—
101C11×Q16—22no—
102C11×Q16—42no—
103C11×SD16—42no—
104C11×D8—22no—
105C2×C8×C11C2×D411yescharacteristic
106C2×C8×C11C2411yescharacteristic
107C11×C4⋊C4—41no—
108C11×C4⋊C4—41no—
109C11×C22⋊C4—41no—
110C11×C22⋊C4—41no—
111C42×C11C2×D411yescharacteristic
112C22⋊Dic11—41no—
113C22⋊Dic11—41no—
114(C2×D11)⋊C4—41no—
115(C2×D11)⋊C4—42no—
116C4⋊Dic11—21no—
117C4⋊Dic11—21no—
118C4⋊Dic11—22no—
119C4⋊Dic11—41no—
120C4⋊Dic11—42no—
121C4⋊Dic11—41no—
122Dic11⋊C4—41no—
123Dic11⋊C4—42no—
124Dic11⋊C4—41no—
125Dic11⋊C4—41no—
126C4×Dic11—41no—
127C4×Dic11—42no—
128C4×Dic11D811yescharacteristic
129C4×Dic11D811yescharacteristic
130C4×Dic11C2×D411yescharacteristic
131C2×C11⋊C8C2×D411yescharacteristic
132C2×C11⋊C8C2×D411yescharacteristic
133C8×D11—22no—
134C8×D11—22no—
135C11×C16#4114yes—
136C11⋊C16—22no—
137#3170—111no—
138#3168—111no—
139#2255—111no—
140#2251D1111yescharacteristic, complemented
141#2245—111no—
142#2243—111no—
143#2220—112no—
144#2219—112no—
145C4×Q32—112no—
146C4×SD32—112no—
147C4×M32—111no—
148C23×C11—41no—
149C22×D11C2×D811yescharacteristic
150Q8×C11—42no—
151Q8×C11—41no—
152Q8×C11—41no—
153Q8×C11—42no—
154D4×C11—41no—
155D4×C11—41no—
156C2×C4×C11—41no—
157C2×C4×C11—42no—
158C2×C4×C11C2×D811yescharacteristic
159C2×C4×C11C2×D811yescharacteristic
160C2×C4×C11C22×D411yescharacteristic
161C22⋊D11—82no—
162C2×Dic11—41no—
163C2×Dic11—42no—
164C2×Dic11—41no—
165C2×Dic11—82no—
166C2×Dic11C2×D811yescharacteristic
167C2×Dic11C2×D811yescharacteristic
168C2×Dic11C2×D811yescharacteristic
169C4×D11—21no—
170C4×D11—21no—
171C4×D11—22no—
172C4×D11—41no—
173Dic22—82no—
174C8×C11#13512yes—
175C8×C11C2×#4112yes—
176C11⋊C8—21no—
177C11⋊C8—21no—
178#533—221no—
179#529—221no—
180C2×Q32C2×D1112yes—
181C2×SD32C2×D1112yes—
182C2×M32—112no—
183#500—111no—
184#499—111no—
185#495C2×D1111yescharacteristic
186#494C2×D1111yescharacteristic
187#488—221no—
188#487—221no—
189#467—111no—
190#467—112no—
191#467—221no—
192#466—111no—
193#465—221no—
194C4×Q16—111no—
195C4×Q16—112no—
196C4×Q16—221no—
197C4×SD16—221no—
198C4×D8—111no—
199C2×C4×C8—111no—
200#367—112no—
201#366—112no—
202#358—112no—
203#358—112no—
204#358—112no—
205#357—112no—
206#346—111no—
207#346C2×D1111yescharacteristic
208C4×C16—112no—
209C22×C11—81no—
210C22×C11—81no—
211C22×C11—81no—
212C22×C11C22×D811yescharacteristic
213C2×D11—21no—
214C2×D11—21no—
215C2×D11—21no—
216C4×C11—21no—
217C4×C11—21no—
218C4×C11—81no—
219C4×C11—82no—
220C4×C11#53211yescharacteristic
221C4×C11C2×#13511yescharacteristic
222Dic11—21no—
223Dic11—21no—
224Dic11—81no—
225Dic11—82no—
226Dic11—81no—
227Dic11#51012yes—
228C2×Q16—21no—
229C2×Q16C22×D1112yes—
230C2×Q16C22×D1111yescharacteristic
231C2×SD16—21no—
232C2×D8C22×D1111yescharacteristic
233C22×C8—111no—
234C22×C8—111no—
235C4⋊Q8—21no—
236C4⋊Q8—221no—
237#126—441no—
238#125—221no—
239#125—441no—
240#124—21no—
241#123—441no—
242C22⋊Q8—221no—
243C22⋊Q8—222no—
244C22⋊Q8—441no—
245#121—221no—
246C4×Q8—221no—
247C4×Q8—222no—
248C4×Q8—441no—
249C4×D4—221no—
250C4×D4—441no—
251#117—441no—
252#117—441no—
253C2×C42—111no—
254Q32—24no—
255SD32—24no—
256M32—224no—
257C2×C16—112no—
258C2×C16C22×D1112yes—
259#107—112no—
260#107—111no—
261#107—111no—
262#107—221no—
263#106—221no—
264#103—221no—
265#103—221no—
266#103—222no—
267#103—222no—
268#102—221no—
269#102—221no—
270C4×C8—111no—
271C4×C8—111no—
272C4×C8—111no—
273C4×C8C22×D1111yescharacteristic
274C2×C11—161no—
275C2×C11#316911yescharacteristic
276C2×C11C2×#51011yescharacteristic
277C2×C11#341411yescharacteristic
278D11—41no—
279C2×Q8—21no—
280C2×Q8—22no—
281C2×Q8—441no—
282C2×D4—21no—
283C2×D4—441no—
284C22×C4—111no—
285C22×C4—111no—
286C22×C4—111no—
287C22×C4—441no—
288Q16—22no—
289Q16—22no—
290Q16—22no—
291Q16—42no—
292SD16—42no—
293D8—22no—
294C2×C8—111no—
295C2×C8—111no—
296C2×C8—222no—
297C2×C8—222no—
298C2×C8D4×D1111yescharacteristic
299C2×C8C23×D1111yescharacteristic
300C4⋊C4—41no—
301C4⋊C4—41no—
302C4⋊C4—221no—
303C4⋊C4—221no—
304C4⋊C4—222no—
305C4⋊C4—441no—
306C4⋊C4—442no—
307C4⋊C4—441no—
308C4⋊C4—442no—
309C4⋊C4—441no—
310C4⋊C4—441no—
311C4⋊C4—441no—
312C22⋊C4—41no—
313C22⋊C4—41no—
314C22⋊C4—442no—
315C22⋊C4—441no—
316C22⋊C4—441no—
317C22⋊C4—441no—
318C42—111no—
319C42—111no—
320C42—111no—
321C42—441no—
322C42—442no—
323C42D4×D1111yescharacteristic
324C16—222no—
325C16#434114yes—
326C11#3373811yescharacteristic, complemented, Sylow
327C23—41no—
328C23—111no—
329Q8—42no—
330Q8—41no—
331Q8—41no—
332Q8—42no—
333Q8—882no—
334D4—41no—
335D4—41no—
336D4—882no—
337C2×C4—41no—
338C2×C4—42no—
339C2×C4—111no—
340C2×C4—111no—
341C2×C4—111no—
342C2×C4—222no—
343C2×C4—221no—
344C2×C4—221no—
345C2×C4—441no—
346C2×C4—441no—
347C2×C4—442no—
348C2×C4—441no—
349C2×C4—882no—
350C2×C4D8×D1111yescharacteristic
351C2×C4D8×D1111yescharacteristic
352C2×C4C2×D4×D1111yescharacteristic
353C8—221no—
354C8—221no—
355C8#6696512yes—
356C8C2×#434112yes—
357C22—81no—
358C22—81no—
359C22—81no—
360C22—221no—
361C22—221no—
362C22—221no—
363C22C2×D8×D1111yescharacteristic
364C4—21no—
365C4—21no—
366C4—81no—
367C4—82no—
368C4—112no—
369C4—221no—
370C4—221no—
371C4—881no—
372C4—881no—
373C4—882no—
374C4#1062324711yescharacteristic
375C4C2×#6696511yescharacteristic
376C2—161no—
377C2—441no—
378C2#1307919311yescharacteristic
379C2D11×#51011yescharacteristic
380C2#1308175111yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2251C2
socleC22×C11C22×D8
prime radical#10622770C22
hypercenter#2251D11
hypocenterC11#33738
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #2251

Complements

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

NH ≅ G/Ntype
1. #13079200C2semidirect
3. #13070902C2semidirect
4. #13070861C2semidirect
5. #13070852C2semidirect
7. #13070721C2semidirect
8. Q32×Dic11C2semidirect
9. SD32×Dic11C2semidirect
10. #13070209C2semidirect
11. C11×#2251C2semidirect
140. #2251D11semidirect
326. C11#33738semidirect

Maximal subgroups

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

subgroupindex
#130792002
#130791832
#130709022
#130708612
#130708522
#130707262
#130707212
Q32×Dic112
SD32×Dic112
#130702092
C11×#22512
#3373811