Finite Group Databasebeta

← #14908653

Subgroups — #14908653

Order 2816.

568 conjugacy classes of subgroups.

The subgroup lattice has 378 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13078288C211yesmaximal, characteristic
2#13077212C211yesmaximal, characteristic, complemented
3#13070827C212yesmaximal, complemented
4#13070815C212yesmaximal, complemented
5#13070809C212yesmaximal, complemented
6#13070803C212yesmaximal, complemented
7#13070402C211yesmaximal, characteristic, complemented
8#13070326C211yesmaximal, characteristic, complemented
9#13070324C211yesmaximal, characteristic, complemented
10#13070229C211yesmaximal, characteristic, complemented
11C2×C11×#367C211yesmaximal, characteristic, complemented
12C2×#66957C2211yescharacteristic
13C2×#66954C2211yescharacteristic
14#10623041—21no—
15#10623035—21no—
16C22×C11×C16C2211yescharacteristic
17C2×C11×#107C2211yescharacteristic
18C2×C11×#107C2211yescharacteristic
19#10622719C2211yescharacteristic
20C2×#66876C2211yescharacteristic
21#10622579—21no—
22#10622577—21no—
23#10622500C2212yes—
24#10622499—22no—
25#10622496C2212yes—
26#10622494—22no—
27#10622493C2212yes—
28D11×#107C2212yes—
29C11×#367C2212yes—
30C11×#367C2212yes—
31#10622147C2211yescharacteristic
32#10622147C2211yescharacteristic
33(C2×D11)⋊C16C2212yes—
34(C2×D11)⋊C16C2212yes—
35#10622141C2211yescharacteristic
36#10622141C2211yescharacteristic
37#10622130C2212yes—
38#10622129C2212yes—
39#10622128C2212yes—
40#10622127C2212yes—
41C2×#4339—21no—
42C2×#4339D411yescharacteristic
43C22×C8×C11C2311yescharacteristic
44C2×C11×C4⋊C4—21no—
45C2×C11×C4⋊C4—21no—
46#66983—42no—
47C4×C22⋊D11—42no—
48#66979—21no—
49C2×#4318D411yescharacteristic
50C2×Dic44C2311yescharacteristic
51#66957—22no—
52#66957—22no—
53C2×D88C2311yescharacteristic
54C2×#4314—21no—
55#66954—22no—
56#66954—22no—
57C2×#4313D412yes—
58C2×C8×D11C2312yes—
59#66950—22no—
60#66950—41no—
61#66948—22no—
62#66948—41no—
63#66946—41no—
64#66945—22no—
65C4⋊C4×D11—22no—
66#66940—41no—
67C2×C11×C16—22no—
68C2×C11×C16C2311yescharacteristic
69C2×C11×C16C2311yescharacteristic
70C11×#107—21no—
71C11×#107—21no—
72C11×#107C2312yes—
73C11×#107C2312yes—
74#66882C2311yescharacteristic
75#66882C2311yescharacteristic
76#66881—21no—
77#66876—22no—
78C2×C11⋊C16C2312yes—
79#66874—22no—
80#66873—22no—
81#66872—22no—
82#66871—22no—
83#33653—111nomaximal, Sylow
84C22×C4×C11—41no—
85C22×C4×C11—41no—
86C22×C4×C11C2×D411yescharacteristic
87C2×C22⋊D11—41no—
88C2×C22⋊D11D812yes—
89#4339—22no—
90#4339—22no—
91#4339—42no—
92#4339—42no—
93C2×D44—21no—
94C2×D44—42no—
95C2×D44D811yescharacteristic
96C2×C4×D11—42no—
97C2×C4×D11—41no—
98C2×C4×D11C2×D412yes—
99C2×Dic22—21no—
100C2×Dic22D811yescharacteristic
101C2×C8×C11C2×D411yescharacteristic
102C2×C8×C11#4112yes—
103C2×C8×C11#4112yes—
104C2×C8×C11C2411yescharacteristic
105C11×C4⋊C4—22no—
106C11×C4⋊C4—22no—
107C11×C4⋊C4—41no—
108C11×C4⋊C4—41no—
109C22⋊Dic11—41no—
110(C2×D11)⋊C4—42no—
111(C2×D11)⋊C4—42no—
112(C2×D11)⋊C4—42no—
113C4⋊Dic11—21no—
114C4⋊Dic11—21no—
115C4⋊Dic11—42no—
116Dic11⋊C4—42no—
117C4×Dic11—42no—
118C4×Dic11—41no—
119#4318—22no—
120C2×C11⋊C8C2×D412yes—
121Dic44—21no—
122Dic44—21no—
123D88—21no—
124D88—21no—
125#4314—42no—
126#4313—24no—
127C8×D11—22no—
128C8×D11—22no—
129C11×C16—21no—
130C11×C16—21no—
131C11⋊C16—22no—
132#3061—111no—
133#2913—111no—
134#2237—112no—
135#2235—112no—
136#2234—112no—
137#2233—112no—
138#2159—111no—
139C2×#367D1111yescharacteristic, complemented
140#2139—111no—
141#2138—111no—
142#2113—111no—
143C23×C11C2×D811yescharacteristic
144C22×D11—41no—
145C22×D11C2×D812yes—
146C2×C4×C11—42no—
147C2×C4×C11—42no—
148C2×C4×C11—161no—
149C2×C4×C11—161no—
150C2×C4×C11#12312yes—
151C2×C4×C11C2×D811yescharacteristic
152C2×C4×C11#13712yes—
153C2×C4×C11C22×D411yescharacteristic
154C22⋊D11—24no—
155C22⋊D11—82no—
156C2×Dic11—41no—
157C2×Dic11—41no—
158C2×Dic11—41no—
159C2×Dic11C2×D812yes—
160D44—22no—
161D44—41no—
162D44—41no—
163D44—162no—
164C4×D11—22no—
165C4×D11—22no—
166C4×D11—82no—
167C4×D11—162no—
168Dic22—22no—
169Dic22—41no—
170Dic22—41no—
171C8×C11#12312yes—
172C8×C11C2×#4111yescharacteristic
173C8×C11C2×#4111yescharacteristic
174C11⋊C8—22no—
175C2×#135—111no—
176C2×#131—111no—
177#537—221no—
178#520—221no—
179C2×M32—111no—
180C22×C16C2×D1111yescharacteristic
181#468—222no—
182#467—112no—
183#466—112no—
184#428—222no—
185#428—221no—
186#427—111no—
187#427—112no—
188C2×#107—112no—
189C2×#107C2×D1111yescharacteristic
190C2×#107C2×D1111yescharacteristic
191#417—221no—
192#367—112no—
193#367C2×D1112yes—
194#367C2×D1112yes—
195#366—112no—
196#358—111no—
197#358—111no—
198#358—112no—
199#357—111no—
200#357—111no—
201#357—112no—
202C22⋊C16—112no—
203C22⋊C16—112no—
204C22×C11—21no—
205C22×C11—21no—
206C22×C11#48012yes—
207C22×C11C22×D811yescharacteristic
208C2×D11—22no—
209C2×D11—22no—
210C2×D11—22no—
211C2×D11—81no—
212C2×D11—81no—
213C2×D11—81no—
214C4×C11—82no—
215C4×C11—82no—
216C4×C11#48012yes—
217C4×C11C2×#12311yescharacteristic
218C4×C11C2×#13711yescharacteristic
219Dic11—22no—
220Dic11—81no—
221Dic11—81no—
222Dic11—81no—
223C2×#41—111no—
224C2×#41—221no—
225#135—222no—
226#135—222no—
227C2×Q16—111no—
228C2×SD16—221no—
229C2×D8—111no—
230#131—222no—
231#131—222no—
232C2×M16—111no—
233C2×M16—112no—
234C22×C8—112no—
235C22×C8C22×D1111yescharacteristic
236C22⋊Q8—222no—
237C22⋊Q8—441no—
238#121—222no—
239#121—441no—
240#121—442no—
241C4×Q8—441no—
242C4×D4—441no—
243C4×D4—442no—
244#117—222no—
245#117—221no—
246C2×C4⋊C4—21no—
247C2×C4⋊C4—21no—
248C2×C4⋊C4—222no—
249M32—222no—
250C2×C16—22no—
251C2×C16—112no—
252C2×C16C22×D1111yescharacteristic
253C2×C16C22×D1111yescharacteristic
254#107—21no—
255#107—21no—
256#107—111no—
257#107—111no—
258#107—222no—
259#107C22×D1112yes—
260#107C22×D1112yes—
261#106—222no—
262#106—221no—
263#103—222no—
264#102—222no—
265C2×C11—22no—
266C2×C11C2×#48011yescharacteristic
267C2×C11#341611yescharacteristic
268C2×C11#341611yescharacteristic
269D11—42no—
270D11—161no—
271#41—222no—
272#41—222no—
273#41—442no—
274#41—442no—
275C2×Q8—111no—
276C2×Q8—221no—
277C2×D4—112no—
278C2×D4—111no—
279C2×D4—221no—
280C2×D4—442no—
281C2×D4—441no—
282C22×C4—41no—
283C22×C4—41no—
284C22×C4—112no—
285C22×C4—442no—
286C22×C4—441no—
287C22×C4D4×D1111yescharacteristic
288Q16—221no—
289Q16—221no—
290SD16—442no—
291D8—221no—
292D8—221no—
293M16—222no—
294M16—224no—
295C2×C8—112no—
296C2×C8—222no—
297C2×C8—222no—
298C2×C8#433912yes—
299C2×C8D4×D1111yescharacteristic
300C2×C8#434312yes—
301C2×C8C23×D1111yescharacteristic
302C4⋊C4—22no—
303C4⋊C4—22no—
304C4⋊C4—41no—
305C4⋊C4—41no—
306C4⋊C4—221no—
307C4⋊C4—221no—
308C4⋊C4—442no—
309C4⋊C4—442no—
310C22⋊C4—442no—
311C22⋊C4—442no—
312C22⋊C4—442no—
313C22⋊C4—441no—
314C42—442no—
315C42—441no—
316C16—21no—
317C16—21no—
318C16—222no—
319C11#3365311yescharacteristic, complemented, Sylow
320C23—112no—
321C23—441no—
322C23D8×D1111yescharacteristic
323Q8—222no—
324Q8—441no—
325Q8—441no—
326D4—224no—
327D4—222no—
328D4—441no—
329D4—441no—
330D4—882no—
331D4—1762no—
332C2×C4—42no—
333C2×C4—42no—
334C2×C4—112no—
335C2×C4—161no—
336C2×C4—161no—
337C2×C4—222no—
338C2×C4—222no—
339C2×C4—441no—
340C2×C4—441no—
341C2×C4—441no—
342C2×C4—882no—
343C2×C4—1762no—
344C2×C4#6694712yes—
345C2×C4D8×D1111yescharacteristic
346C2×C4#6697112yes—
347C2×C4C2×D4×D1111yescharacteristic
348C8—222no—
349C8#6694712yes—
350C8C2×#433911yescharacteristic
351C8C2×#434311yescharacteristic
352C22—21no—
353C22—21no—
354C22—222no—
355C22—222no—
356C22—222no—
357C22—881no—
358C22—881no—
359C22—881no—
360C22#1062249512yes—
361C22C2×D8×D1111yescharacteristic
362C4—82no—
363C4—82no—
364C4—222no—
365C4—881no—
366C4—881no—
367C4—881no—
368C4#1062249512yes—
369C4C2×#6694711yescharacteristic
370C4C2×#6697111yescharacteristic
371C2—22no—
372C2—442no—
373C2—1761no—
374C2C2×#1062249511yescharacteristic
375C2#1308175811yescharacteristic
376C2#1308175811yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC2×C11×#367C2
socleC22×C11C22×D8
prime radical#13078288C2
hypercenterC2×#367D11
hypocenterC11#33653
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ C2×#367

Complements

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

NH ≅ G/Ntype
2. #13077212C2semidirect
3. #13070827C2semidirect
4. #13070815C2semidirect
5. #13070809C2semidirect
6. #13070803C2semidirect
7. #13070402C2semidirect
8. #13070326C2semidirect
9. #13070324C2semidirect
10. #13070229C2semidirect
11. C2×C11×#367C2semidirect
139. C2×#367D11semidirect
319. C11#33653semidirect

Maximal subgroups

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

subgroupindex
#130782882
#130772122
#130708272
#130708152
#130708092
#130708032
#130704022
#130703262
#130703242
#130702292
C2×C11×#3672
#3365311