Finite Group Databasebeta

← #14908646

Subgroups — #14908646

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#13078282C211yesmaximal, characteristic
2#13077213C211yesmaximal, characteristic, complemented
3#13070822C212yesmaximal, complemented
4#13070812C212yesmaximal, complemented
5#13070806C212yesmaximal, complemented
6#13070800C212yesmaximal, complemented
7#13070405C211yesmaximal, characteristic, complemented
8C2×#10622143C211yesmaximal, characteristic, complemented
9#13070328C211yesmaximal, characteristic, complemented
10#13070229C211yesmaximal, characteristic, complemented
11C11×#2138C211yesmaximal, characteristic, complemented
12C2×C11×#135C2211yescharacteristic
13#10623364—21no—
14C2×#66954C2211yescharacteristic
15#10623054—21no—
16C22×C11×C16C2211yescharacteristic
17C11×#427C2211yescharacteristic
18#10622845—21no—
19#10622801C2212yes—
20#10622787—22no—
21#10622770C2212yes—
22C2×#66882C2211yescharacteristic
23C2×#66882C2211yescharacteristic
24C2×#66876C2211yescharacteristic
25#10622608—21no—
26#10622493C2212yes—
27D11×#107C2212yes—
28#10622474—22no—
29C11×#358C2211yescharacteristic
30C11×#358C2211yescharacteristic
31C11×#357C2211yescharacteristic
32C11×#357C2211yescharacteristic
33#10622202C2212yes—
34#10622200C2212yes—
35(C2×D11)⋊C16C2212yes—
36(C2×D11)⋊C16C2212yes—
37#10622143C2212yes—
38#10622143C2212yes—
39#10622128C2212yes—
40#10622127C2212yes—
41C2×C11×#41—21no—
42C2×#4339D411yescharacteristic
43C11×#135—22no—
44C11×#135—22no—
45C2×C11×Q16C2311yescharacteristic
46C2×C11×SD16—21no—
47C2×C11×D8C2311yescharacteristic
48C22×C8×C11C2311yescharacteristic
49C11×#117—21no—
50#66999—22no—
51#66992—42no—
52#66991—22no—
53#66983—41no—
54C2×C4⋊Dic11—21no—
55C2×C4⋊Dic11—21no—
56#66977—41no—
57C2×#4318D411yescharacteristic
58#66954—22no—
59#66954—22no—
60C2×#4313D412yes—
61C2×C8×D11C2312yes—
62#66945—22no—
63C4⋊C4×D11—22no—
64(C22⋊D11)⋊C4—42no—
65C4×D44—41no—
66C4×Dic22—41no—
67C2×C11×C16—22no—
68C2×C11×C16C2311yescharacteristic
69C2×C11×C16C2311yescharacteristic
70C11×#107C2311yescharacteristic
71C11×#107C2311yescharacteristic
72C11×#106—21no—
73#66899—22no—
74#66896—22no—
75#66882—21no—
76#66882—21no—
77#66882C2312yes—
78#66882C2312yes—
79#66876—22no—
80C2×C11⋊C16C2312yes—
81#66872—22no—
82#66871—22no—
83#33653—111nomaximal, Sylow
84C11×#41—42no—
85C11×#41—42no—
86C2×Q8×C11—21no—
87C2×D4×C11—21no—
88C2×D4×C11—41no—
89C22×C4×C11—41no—
90C22×C4×C11C2×D411yescharacteristic
91C2×C22⋊D11—42no—
92C2×C22⋊D11D812yes—
93C22×Dic11—41no—
94C22×Dic11—41no—
95#4339—22no—
96#4339—22no—
97C2×D44D811yescharacteristic
98C2×C4×D11—42no—
99C2×C4×D11C2×D412yes—
100C2×Dic22D811yescharacteristic
101C11×Q16—21no—
102C11×Q16—21no—
103C11×SD16—42no—
104C11×D8—21no—
105C11×D8—21no—
106C2×C8×C11C2×D411yescharacteristic
107C2×C8×C11#4112yes—
108C2×C8×C11#4112yes—
109C2×C8×C11C2411yescharacteristic
110C11×C4⋊C4—21no—
111C11×C4⋊C4—21no—
112C11×C22⋊C4—41no—
113C42×C11—41no—
114C22⋊Dic11—42no—
115(C2×D11)⋊C4—42no—
116(C2×D11)⋊C4—42no—
117C4⋊Dic11—22no—
118C4⋊Dic11—22no—
119C4⋊Dic11—41no—
120C4⋊Dic11—41no—
121Dic11⋊C4—42no—
122Dic11⋊C4—42no—
123C4×Dic11—42no—
124#4318—22no—
125C2×C11⋊C8C2×D412yes—
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×#367—111no—
140#2139—111no—
141#2138D1111yescharacteristic, complemented
142#2113—111no—
143C23×C11—41no—
144C23×C11C2×D811yescharacteristic
145C22×D11C2×D812yes—
146Q8×C11—41no—
147Q8×C11—41no—
148D4×C11—41no—
149D4×C11—41no—
150D4×C11—82no—
151C2×C4×C11—41no—
152C2×C4×C11—41no—
153C2×C4×C11—41no—
154C2×C4×C11—82no—
155C2×C4×C11#12312yes—
156C2×C4×C11C2×D811yescharacteristic
157C2×C4×C11#13712yes—
158C2×C4×C11C22×D411yescharacteristic
159C22⋊D11—24no—
160C22⋊D11—162no—
161C2×Dic11—42no—
162C2×Dic11—42no—
163C2×Dic11—161no—
164C2×Dic11—161no—
165C2×Dic11C2×D812yes—
166D44—22no—
167C4×D11—22no—
168C4×D11—22no—
169C4×D11—162no—
170Dic22—22no—
171C8×C11#12312yes—
172C8×C11C2×#4111yescharacteristic
173C8×C11C2×#4111yescharacteristic
174C11⋊C8—22no—
175C2×#135C2×D1111yescharacteristic
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—112no—
187#427C2×D1111yescharacteristic
188C2×#107—111no—
189C2×#107—111no—
190C2×#107—112no—
191#417—221no—
192#367—112no—
193#367—112no—
194#367—112no—
195#366—112no—
196#358—112no—
197#358C2×D1111yescharacteristic
198#358C2×D1111yescharacteristic
199#357—112no—
200#357C2×D1111yescharacteristic
201#357C2×D1111yescharacteristic
202C22⋊C16—112no—
203C22⋊C16—112no—
204C22×C11—21no—
205C22×C11—21no—
206C22×C11—81no—
207C22×C11—81no—
208C22×C11—81no—
209C22×C11#48012yes—
210C22×C11C22×D811yescharacteristic
211C2×D11—22no—
212C2×D11—22no—
213C2×D11—22no—
214C4×C11—81no—
215C4×C11—81no—
216C4×C11—81no—
217C4×C11#48012yes—
218C4×C11C2×#12311yescharacteristic
219C4×C11C2×#13711yescharacteristic
220Dic11—22no—
221Dic11—82no—
222Dic11—82no—
223C2×#41—21no—
224C2×#41—111no—
225#135—22no—
226#135—22no—
227C2×Q16C22×D1111yescharacteristic
228C2×SD16—21no—
229C2×D8C22×D1111yescharacteristic
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—21no—
245#117—222no—
246C2×C4⋊C4—222no—
247C2×C4⋊C4—221no—
248C2×C4⋊C4—221no—
249M32—222no—
250C2×C16—22no—
251C2×C16—112no—
252C2×C16C22×D1111yescharacteristic
253C2×C16C22×D1111yescharacteristic
254#107—112no—
255#107—112no—
256#107—222no—
257#107—221no—
258#107—221no—
259#107C22×D1111yescharacteristic
260#107C22×D1111yescharacteristic
261#106—21no—
262#106—222no—
263#103—222no—
264#102—222no—
265C2×C11—22no—
266C2×C11—161no—
267C2×C11C2×#48011yescharacteristic
268C2×C11#341611yescharacteristic
269C2×C11#341611yescharacteristic
270D11—42no—
271#41—42no—
272#41—42no—
273#41—222no—
274#41—222no—
275C2×Q8—21no—
276C2×Q8—111no—
277C2×D4—21no—
278C2×D4—41no—
279C2×D4—112no—
280C2×D4—111no—
281C2×D4—442no—
282C22×C4—41no—
283C22×C4—112no—
284C22×C4—442no—
285C22×C4—441no—
286C22×C4—441no—
287C22×C4D4×D1111yescharacteristic
288Q16—21no—
289Q16—21no—
290SD16—42no—
291D8—21no—
292D8—21no—
293M16—222no—
294M16—224no—
295C2×C8—112no—
296C2×C8—222no—
297C2×C8—222no—
298C2×C8#433912yes—
299C2×C8D4×D1111yescharacteristic
300C2×C8#434112yes—
301C2×C8C23×D1111yescharacteristic
302C4⋊C4—21no—
303C4⋊C4—21no—
304C4⋊C4—222no—
305C4⋊C4—222no—
306C4⋊C4—442no—
307C4⋊C4—442no—
308C4⋊C4—441no—
309C4⋊C4—441no—
310C22⋊C4—41no—
311C22⋊C4—442no—
312C22⋊C4—442no—
313C22⋊C4—442no—
314C42—41no—
315C42—442no—
316C16—21no—
317C16—21no—
318C16—222no—
319C11#3365311yescharacteristic, complemented, Sylow
320C23—41no—
321C23—112no—
322C23D8×D1111yescharacteristic
323Q8—41no—
324Q8—41no—
325Q8—222no—
326D4—41no—
327D4—41no—
328D4—82no—
329D4—224no—
330D4—222no—
331D4—1762no—
332C2×C4—41no—
333C2×C4—41no—
334C2×C4—41no—
335C2×C4—82no—
336C2×C4—112no—
337C2×C4—222no—
338C2×C4—222no—
339C2×C4—442no—
340C2×C4—442no—
341C2×C4—1762no—
342C2×C4—1761no—
343C2×C4—1761no—
344C2×C4#6693612yes—
345C2×C4D8×D1111yescharacteristic
346C2×C4#6696812yes—
347C2×C4C2×D4×D1111yescharacteristic
348C8—222no—
349C8#6693612yes—
350C8C2×#433911yescharacteristic
351C8C2×#434111yescharacteristic
352C22—21no—
353C22—21no—
354C22—81no—
355C22—81no—
356C22—81no—
357C22—222no—
358C22—222no—
359C22—222no—
360C22#1062238712yes—
361C22C2×D8×D1111yescharacteristic
362C4—81no—
363C4—81no—
364C4—81no—
365C4—222no—
366C4—882no—
367C4—882no—
368C4#1062238712yes—
369C4C2×#6693611yescharacteristic
370C4C2×#6696811yescharacteristic
371C2—22no—
372C2—161no—
373C2—442no—
374C2C2×#1062238711yescharacteristic
375C2#1308175911yescharacteristic
376C2#1308175911yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2138C2
socleC22×C11C22×D8
prime radical#13078282C2
hypercenter#2138D11
hypocenterC11#33653
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #2138

Complements

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

NH ≅ G/Ntype
2. #13077213C2semidirect
3. #13070822C2semidirect
4. #13070812C2semidirect
5. #13070806C2semidirect
6. #13070800C2semidirect
7. #13070405C2semidirect
8. C2×#10622143C2semidirect
9. #13070328C2semidirect
10. #13070229C2semidirect
11. C11×#2138C2semidirect
141. #2138D11semidirect
319. C11#33653semidirect

Maximal subgroups

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

subgroupindex
#130782822
#130772132
#130708222
#130708122
#130708062
#130708002
#130704052
C2×#106221432
#130703282
#130702292
C11×#21382
#3365311