Finite Group Databasebeta

← #14908648

Subgroups — #14908648

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#13078286C211yesmaximal, characteristic
2#13070824C212yesmaximal, complemented
3#13070813C212yesmaximal, complemented
4#13070807C212yesmaximal, complemented
5#13070801C212yesmaximal, complemented
6#13070405C211yesmaximal, characteristic, complemented
7C2×#10622128C211yesmaximal, characteristic, complemented
8#13070326C211yesmaximal, characteristic, complemented
9#13070321C211yesmaximal, characteristic, complemented
10#13070230C211yesmaximal, characteristic, complemented
11C11×#2913C211yesmaximal, characteristic, complemented
12C2×C11×#131C2211yescharacteristic
13C11×#520—21no—
14#10623364—21no—
15C2×#66957C2211yescharacteristic
16C11×#428—21no—
17C11×#428—22no—
18C11×#427C2211yescharacteristic
19C11×#427C2212yes—
20C2×C11×#107C2211yescharacteristic
21C2×C11×#107C2212yes—
22#10622747—22no—
23#10622746—21no—
24#10622729C2212yes—
25#10622728C2212yes—
26C2×#66882C2211yescharacteristic
27C2×#66876C2211yescharacteristic
28C22×C11⋊C16C2211yescharacteristic
29C22⋊(C11⋊C16)C2212yes—
30C22⋊(C11⋊C16)C2212yes—
31#10622130C2211yescharacteristic
32#10622130C2212yes—
33#10622130C2211yescharacteristic
34#10622129C2211yescharacteristic
35#10622129C2212yes—
36#10622129C2211yescharacteristic
37#10622128C2212yes—
38#10622128C2212yes—
39#10622128C2212yes—
40#10622127C2212yes—
41C2×C11×#41D411yescharacteristic
42C2×#4339—21no—
43C11×#131—22no—
44C11×#131—22no—
45C2×C11×M16D411yescharacteristic
46C2×C11×M16D412yes—
47C22×C8×C11C2312yes—
48C22×C8×C11C2311yescharacteristic
49C4×Q8×C11—41no—
50C4×D4×C11—41no—
51C4×D4×C11—42no—
52C11×#117—22no—
53C11×#117—21no—
54C2×C11×C4⋊C4—22no—
55C2×C11×C4⋊C4—21no—
56#66999—41no—
57#66992—42no—
58#66991—41no—
59#66983—22no—
60C2×C4⋊Dic11—21no—
61#66977—22no—
62C2×Dic44C2311yescharacteristic
63#66957—22no—
64#66957—22no—
65C2×D88C2311yescharacteristic
66C2×#4314—21no—
67C11×#107—22no—
68C11×#107—21no—
69C11×#107C2311yescharacteristic
70C11×#107C2312yes—
71C11×#107C2311yescharacteristic
72C11×#106—22no—
73C11×#106—21no—
74#66885—22no—
75#66882—21no—
76#66882C2312yes—
77#66880—22no—
78#66876—22no—
79C2×C11⋊C16—22no—
80C2×C11⋊C16C2312yes—
81C2×C11⋊C16C2311yescharacteristic
82C2×C11⋊C16C2311yescharacteristic
83#33653—111nomaximal, Sylow
84C11×#41—22no—
85C11×#41—22no—
86C2×Q8×C11D811yescharacteristic
87C2×D4×C11D811yescharacteristic
88C2×D4×C11D812yes—
89C22×C4×C11—42no—
90C22×C4×C11—41no—
91C22×C4×C11C2×D412yes—
92C22×C4×C11C2×D411yescharacteristic
93C2×C22⋊D11—41no—
94C2×C22⋊D11—42no—
95C22×Dic11—41no—
96#4339—42no—
97#4339—42no—
98C2×D44—21no—
99C2×C4×D11—41no—
100C2×Dic22—21no—
101C11×M16—24no—
102C11×M16—22no—
103C2×C8×C11—22no—
104C2×C8×C11—22no—
105C2×C8×C11C2×D412yes—
106C2×C8×C11C2×D411yescharacteristic
107C2×C8×C11#4112yes—
108C2×C8×C11#4112yes—
109C2×C8×C11C2411yescharacteristic
110C11×C4⋊C4—21no—
111C11×C4⋊C4—22no—
112C11×C4⋊C4—21no—
113C11×C4⋊C4—42no—
114C11×C4⋊C4—41no—
115C11×C22⋊C4—42no—
116C11×C22⋊C4—41no—
117C42×C11—42no—
118C42×C11—41no—
119C22⋊Dic11—42no—
120(C2×D11)⋊C4—42no—
121C4⋊Dic11—22no—
122C4⋊Dic11—41no—
123Dic11⋊C4—42no—
124Dic44—21no—
125Dic44—21no—
126D88—21no—
127D88—21no—
128#4314—42no—
129C11⋊C16—21no—
130C11⋊C16—21no—
131C11⋊C16—22no—
132#3061—111no—
133#2913D1111yescharacteristic, complemented
134#2237—112no—
135#2235—112no—
136#2234—112no—
137#2233—112no—
138#2159—111no—
139C2×#367—111no—
140#2139—111no—
141#2138—111no—
142#2113—111no—
143C23×C11C2×D812yes—
144C23×C11C2×D811yescharacteristic
145C22×D11—41no—
146Q8×C11—22no—
147D4×C11—24no—
148D4×C11—22no—
149C2×C4×C11—22no—
150C2×C4×C11—22no—
151C2×C4×C11—41no—
152C2×C4×C11—42no—
153C2×C4×C11—41no—
154C2×C4×C11—161no—
155C2×C4×C11—162no—
156C2×C4×C11#12312yes—
157C2×C4×C11C2×D812yes—
158C2×C4×C11C2×D811yescharacteristic
159C2×C4×C11#13712yes—
160C2×C4×C11C22×D411yescharacteristic
161C22⋊D11—82no—
162C22⋊D11—162no—
163C2×Dic11—41no—
164C2×Dic11—42no—
165C2×Dic11—161no—
166D44—41no—
167D44—41no—
168C4×D11—82no—
169Dic22—41no—
170Dic22—41no—
171C8×C11—22no—
172C8×C11#12312yes—
173C8×C11C2×#4111yescharacteristic
174C8×C11C2×#4111yescharacteristic
175C2×#135—111no—
176C2×#131C2×D1111yescharacteristic
177#537—221no—
178#520—21no—
179C2×M32—111no—
180C22×C16—111no—
181#468—222no—
182#467—112no—
183#466—112no—
184#428—21no—
185#428—22no—
186#427C2×D1111yescharacteristic
187#427C2×D1112yes—
188C2×#107—111no—
189C2×#107C2×D1111yescharacteristic
190C2×#107C2×D1112yes—
191#417—221no—
192#367—112no—
193#367—112no—
194#367—112no—
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—22no—
207C22×C11—22no—
208C22×C11—22no—
209C22×C11#48012yes—
210C22×C11C22×D811yescharacteristic
211C2×D11—81no—
212C2×D11—81no—
213C2×D11—81no—
214C4×C11—22no—
215C4×C11—81no—
216C4×C11—82no—
217C4×C11—81no—
218C4×C11#48012yes—
219C4×C11C2×#12311yescharacteristic
220C4×C11C2×#13711yescharacteristic
221Dic11—81no—
222Dic11—82no—
223C2×#41—221no—
224C2×#41C22⋊D1111yescharacteristic
225#135—222no—
226#135—222no—
227C2×Q16—111no—
228C2×SD16—221no—
229C2×D8—111no—
230#131—22no—
231#131—22no—
232C2×M16C22⋊D1111yescharacteristic
233C2×M16C22⋊D1112yes—
234C22×C8C22×D1112yes—
235C22×C8C22×D1111yescharacteristic
236C22⋊Q8—222no—
237C22⋊Q8—441no—
238#121—222no—
239#121—441no—
240#121—442no—
241C4×Q8—41no—
242C4×D4—42no—
243C4×D4—41no—
244#117—22no—
245#117—21no—
246C2×C4⋊C4—22no—
247C2×C4⋊C4—21no—
248C2×C4⋊C4—221no—
249M32—222no—
250C2×C16—112no—
251C2×C16—111no—
252C2×C16—111no—
253C2×C16—222no—
254#107—22no—
255#107—21no—
256#107—112no—
257#107—221no—
258#107C22×D1111yescharacteristic
259#107C22×D1111yescharacteristic
260#107C22×D1112yes—
261#106—22no—
262#106—21no—
263#103—222no—
264#102—222no—
265C2×C11—22no—
266C2×C11—42no—
267C2×C11C2×#48011yescharacteristic
268C2×C11#341611yescharacteristic
269C2×C11#341611yescharacteristic
270D11—161no—
271#41—22no—
272#41—22no—
273#41—442no—
274#41—442no—
275C2×Q8—221no—
276C2×Q8#432311yescharacteristic
277C2×D4—221no—
278C2×D4—441no—
279C2×D4—442no—
280C2×D4#432312yes—
281C2×D4#432311yescharacteristic
282C22×C4—42no—
283C22×C4—41no—
284C22×C4—441no—
285C22×C4—441no—
286C22×C4C2×C22⋊D1112yes—
287C22×C4C2×C22⋊D1111yescharacteristic
288Q16—221no—
289Q16—221no—
290SD16—442no—
291D8—221no—
292D8—221no—
293M16—22no—
294M16—24no—
295C2×C8—22no—
296C2×C8—22no—
297C2×C8#433912yes—
298C2×C8#433912yes—
299C2×C8C2×C22⋊D1112yes—
300C2×C8C2×C22⋊D1111yescharacteristic
301C2×C8C23×D1111yescharacteristic
302C4⋊C4—21no—
303C4⋊C4—22no—
304C4⋊C4—21no—
305C4⋊C4—42no—
306C4⋊C4—41no—
307C4⋊C4—222no—
308C4⋊C4—441no—
309C4⋊C4—442no—
310C22⋊C4—42no—
311C22⋊C4—41no—
312C22⋊C4—442no—
313C22⋊C4—442no—
314C42—42no—
315C42—41no—
316C16—221no—
317C16—221no—
318C16—222no—
319C11#3365311yescharacteristic, complemented, Sylow
320C23—441no—
321C23C2×#432312yes—
322C23C2×#432311yescharacteristic
323Q8—22no—
324Q8—441no—
325Q8—441no—
326D4—24no—
327D4—22no—
328D4—441no—
329D4—441no—
330D4—882no—
331D4—1762no—
332C2×C4—22no—
333C2×C4—22no—
334C2×C4—41no—
335C2×C4—42no—
336C2×C4—41no—
337C2×C4—161no—
338C2×C4—162no—
339C2×C4—442no—
340C2×C4—441no—
341C2×C4—882no—
342C2×C4—1761no—
343C2×C4#6698212yes—
344C2×C4C2×#432312yes—
345C2×C4C2×#432311yescharacteristic
346C2×C4#6699512yes—
347C2×C4C22×C22⋊D1111yescharacteristic
348C8—22no—
349C8#6698212yes—
350C8C2×#433911yescharacteristic
351C8C2×#433911yescharacteristic
352C22—21no—
353C22—21no—
354C22—22no—
355C22—22no—
356C22—22no—
357C22—881no—
358C22—881no—
359C22—881no—
360C22#1062258012yes—
361C22C22×#432311yescharacteristic
362C4—22no—
363C4—81no—
364C4—82no—
365C4—81no—
366C4—882no—
367C4—881no—
368C4#1062258012yes—
369C4C2×#6698211yescharacteristic
370C4C2×#6699511yescharacteristic
371C2—22no—
372C2—42no—
373C2—1761no—
374C2C2×#1062258011yescharacteristic
375C2#1308176011yescharacteristic
376C2#1308176311yescharacteristic
subgroupG/H
centerC22C22×#4323
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2913C2
socleC22×C11C22×D8
prime radical#13078286C2
hypercenter#2913D11
hypocenterC11#33653
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×#41 ◁ C2×#131 ◁ #2913

Complements

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

NH ≅ G/Ntype
2. #13070824C2semidirect
3. #13070813C2semidirect
4. #13070807C2semidirect
5. #13070801C2semidirect
6. #13070405C2semidirect
7. C2×#10622128C2semidirect
8. #13070326C2semidirect
9. #13070321C2semidirect
10. #13070230C2semidirect
11. C11×#2913C2semidirect
133. #2913D11semidirect
319. C11#33653semidirect

Maximal subgroups

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

subgroupindex
#130782862
#130708242
#130708132
#130708072
#130708012
#130704052
C2×#106221282
#130703262
#130703212
#130702302
C11×#29132
#3365311