Finite Group Databasebeta

← #14907126

Subgroups — #14907126

Order 2816.

660 conjugacy classes of subgroups.

The subgroup lattice has 372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622792C211yesmaximal, characteristic
2#13077493C211yesmaximal, characteristic
3#13070485C212yesmaximal, complemented
4#13070478C212yesmaximal, complemented
5C4×#66893C212yesmaximal, complemented
6C4×#66892C212yesmaximal, complemented
7#13070405C211yesmaximal, characteristic, complemented
8#13070321C211yesmaximal, characteristic
9C2×#10622202C211yesmaximal, characteristic, complemented
10#13070213C211yesmaximal, characteristic, complemented
11C11×#2950C211yesmaximal, characteristic, complemented
12C22×C11×Q16C2211yescharacteristic
13C11×#519—21no—
14C2×#66957C2211yescharacteristic
15#10623054—21no—
16C11×#441—22no—
17C4×C11×Q16C2212yes—
18C4×C11×Q16C2212yes—
19C11×#427C2211yescharacteristic
20C11×#419—21no—
21C11×#405C2211yescharacteristic
22C2×#66893C2212yes—
23#10622792C418yescomplemented
24C2×#66892C2212yes—
25#10622746—21no—
26C2×#66882C2211yescharacteristic
27C2×#66876C2211yescharacteristic
28C22×C11⋊C16C2211yescharacteristic
29#10622323—22no—
30C4×Dic44C2212yes—
31C4×D88C2212yes—
32#10622202C2212yes—
33#10622202C2212yes—
34#10622130C2211yescharacteristic
35#10622130C2211yescharacteristic
36#10622129C2211yescharacteristic
37#10622129C2211yescharacteristic
38#10622128C2212yes—
39#10622127C2212yes—
40#10622099C2212yes—
41C4×C11⋊C16C2212yes—
42C22×Q8×C11—21no—
43C2×#4339—21no—
44C2×C11×Q16—21no—
45C2×C11×Q16—22no—
46C2×C11×Q16C2×C414yescomplemented
47C2×C11×Q16C2312yes—
48C2×C11×M16D411yescharacteristic
49C22×C8×C11C2311yescharacteristic
50C4×Q8×C11—22no—
51C4×Q8×C11—22no—
52C4×Q8×C11—41no—
53C4×Q8×C11—41no—
54C11×#117—21no—
55C11×#117—42no—
56C11×#117D411yescharacteristic
57C2×C4⋊Dic11—21no—
58C2×Dic44C2311yescharacteristic
59#66957—22no—
60#66957C2×C414yes—
61C2×D88C2311yescharacteristic
62C2×#4314—21no—
63#66945—41no—
64C4⋊C4×D11—41no—
65(C22⋊D11)⋊C4—42no—
66C4×D44—22no—
67C4×Dic22—22no—
68C11×#107C2311yescharacteristic
69C11×#107C2311yescharacteristic
70C11×#106—21no—
71C11×#103—22no—
72C11×#103—22no—
73C11×#97D412yes—
74C4×C8×C11C2312yes—
75#66893C2×C418yescomplemented
76#66892C2×C418yescomplemented
77#66885—22no—
78#66882—21no—
79#66882C2312yes—
80#66880—22no—
81#66876C2×C414yescomplemented
82C2×C11⋊C16—22no—
83C2×C11⋊C16C2311yescharacteristic
84C2×C11⋊C16C2311yescharacteristic
85C2×C11⋊C16C2312yes—
86#33455—111nomaximal, Sylow
87C2×Q8×C11—24no—
88C2×Q8×C11—22no—
89C2×Q8×C11—41no—
90C2×Q8×C11—42no—
91C22×C4×C11—41no—
92C22×C4×C11C2×D411yescharacteristic
93C2×C22⋊D11—41no—
94C22×Dic11—41no—
95#4339—24no—
96#4339—42no—
97C2×D44—21no—
98C2×C4×D11—41no—
99C2×C4×D11—42no—
100C2×Dic22—21no—
101C11×Q16—24no—
102C11×Q16—22no—
103C11×Q16C22×C414yes—
104C11×M16—22no—
105C2×C8×C11C22×C412yes—
106C2×C8×C11C2×D412yes—
107C2×C8×C11C2×D411yescharacteristic
108C2×C8×C11#4112yes—
109C2×C8×C11C2411yescharacteristic
110C11×C4⋊C4—21no—
111C11×C4⋊C4—21no—
112C11×C4⋊C4—42no—
113C11×C4⋊C4—42no—
114C11×C4⋊C4D811yescharacteristic
115C11×C4⋊C4D811yescharacteristic
116C11×C22⋊C4—41no—
117C11×C22⋊C4D812yes—
118C42×C11—41no—
119C42×C11—42no—
120C42×C11—42no—
121C42×C11C2×D412yes—
122(C2×D11)⋊C4—42no—
123C4⋊Dic11—22no—
124C4⋊Dic11—41no—
125Dic11⋊C4—42no—
126C4×Dic11—42no—
127Dic44—21no—
128Dic44C22×C412yes—
129D88—21no—
130D88C22×C412yes—
131#4314—24no—
132C11⋊C16—21no—
133C11⋊C16—21no—
134C11⋊C16C22×C414yes—
135C2×#510—111no—
136#2951—111no—
137#2950D1111yescharacteristic, complemented
138#2176—112no—
139#2175—112no—
140C4×Q32—112no—
141C4×SD32—112no—
142#2159—111no—
143#2138—111no—
144C2×#358—111no—
145#2108—111no—
146C23×C11C2×D811yescharacteristic
147C22×D11—41no—
148Q8×C11—24no—
149Q8×C11—42no—
150Q8×C11—44no—
151C2×C4×C11—42no—
152C2×C4×C11—44no—
153C2×C4×C11—41no—
154C2×C4×C11—41no—
155C2×C4×C11C4×D412yes—
156C2×C4×C11C2×D812yes—
157C2×C4×C11C2×D812yes—
158C2×C4×C11C2×D811yescharacteristic
159C2×C4×C11#13512yes—
160C2×C4×C11C22×D411yescharacteristic
161C22⋊D11—44no—
162C2×Dic11—41no—
163C2×Dic11—42no—
164C2×Dic11—161no—
165D44—22no—
166D44—41no—
167C4×D11—44no—
168C4×D11—162no—
169Dic22—22no—
170Dic22—41no—
171C8×C11—22no—
172C8×C11C4×D412yes—
173C8×C11C23×C411yescharacteristic
174C8×C11C2×#4111yescharacteristic
175C2×#135—111no—
176C22×Q16C2×D1111yescharacteristic
177#520—221no—
178#519—21no—
179#510—118no—
180C2×Q32—112no—
181C2×SD32—112no—
182C2×M32—111no—
183C22×C16—111no—
184#441—22no—
185#440—222no—
186C4×Q16—112no—
187C4×Q16C2×D1112yes—
188C4×Q16C2×D1112yes—
189C4×D8—112no—
190#427C2×D1111yescharacteristic
191C2×#107—111no—
192#419—21no—
193#417—221no—
194#405C2×D1111yescharacteristic
195#367—112no—
196#366—112no—
197#358—112no—
198#358—112no—
199#358—111no—
200#358—111no—
201#357—111no—
202#357—111no—
203#346—112no—
204C4×C16—112no—
205C22×C11—21no—
206C22×C11—21no—
207C22×C11C4×D812yes—
208C22×C11C22×D811yescharacteristic
209C2×D11—42no—
210C2×D11—81no—
211C2×D11—81no—
212C4×C11—22no—
213C4×C11—22no—
214C4×C11—44no—
215C4×C11—81no—
216C4×C11—81no—
217C4×C11C4×D812yes—
218C4×C11C2×C4×D411yescharacteristic
219C4×C11C2×#13511yescharacteristic
220Dic11—42no—
221Dic11—82no—
222C2×#41—221no—
223C22×Q8—21no—
224#135—114no—
225#135—222no—
226C2×Q16—22no—
227C2×Q16—21no—
228C2×Q16—111no—
229C2×Q16C4×D1114yescomplemented
230C2×Q16C22×D1112yes—
231C2×SD16—221no—
232C2×D8—111no—
233C2×M16C22⋊D1111yescharacteristic
234C22×C8C22×D1111yescharacteristic
235C4×Q8—22no—
236C4×Q8—22no—
237C4×Q8—41no—
238C4×Q8—41no—
239C4×Q8—222no—
240C4×D4—222no—
241C4×D4—442no—
242#117—21no—
243#117—42no—
244#117—441no—
245#117C22⋊D1111yescharacteristic
246C2×C4⋊C4—221no—
247C2×C4⋊C4—441no—
248Q32—118no—
249SD32—118no—
250M32—114no—
251C2×C16—112no—
252C2×C16—111no—
253C2×C16—111no—
254C2×C16—222no—
255#107—112no—
256#107—221no—
257#107C22×D1111yescharacteristic
258#107C22×D1111yescharacteristic
259#106—21no—
260#103—22no—
261#103—22no—
262#103—222no—
263#102—222no—
264#97C22⋊D1112yes—
265C4×C8C22×D1112yes—
266C2×C11—22no—
267C2×C11C2×C4×D811yescharacteristic
268C2×C11#341611yescharacteristic
269C2×C11#341711yescharacteristic
270D11—82no—
271#41—224no—
272#41—442no—
273C2×Q8—24no—
274C2×Q8—22no—
275C2×Q8—41no—
276C2×Q8—42no—
277C2×Q8—221no—
278C2×D4—221no—
279C2×D4—441no—
280C22×C4—41no—
281C22×C4—441no—
282C22×C4—441no—
283C22×C4—442no—
284C22×C4C2×C22⋊D1111yescharacteristic
285Q16—24no—
286Q16—22no—
287Q16—112no—
288Q16—221no—
289Q16C2×C4×D1114yes—
290SD16—224no—
291D8—112no—
292D8—221no—
293M16—22no—
294C2×C8C2×C4×D1112yes—
295C2×C8#433912yes—
296C2×C8C2×C22⋊D1112yes—
297C2×C8C2×C22⋊D1111yescharacteristic
298C2×C8C23×D1111yescharacteristic
299C4⋊C4—21no—
300C4⋊C4—21no—
301C4⋊C4—42no—
302C4⋊C4—42no—
303C4⋊C4—222no—
304C4⋊C4—441no—
305C4⋊C4—442no—
306C4⋊C4#432311yescharacteristic
307C4⋊C4#432311yescharacteristic
308C22⋊C4—41no—
309C22⋊C4—442no—
310C22⋊C4#432312yes—
311C42—41no—
312C42—42no—
313C42—42no—
314C42—442no—
315C42C2×C22⋊D1112yes—
316C16—114no—
317C16—221no—
318C16—221no—
319C11#3345511yescharacteristic, complemented, Sylow
320C23—441no—
321C23C2×#432311yescharacteristic
322Q8—24no—
323Q8—42no—
324Q8—44no—
325Q8—222no—
326Q8—441no—
327D4—222no—
328D4—444no—
329D4—441no—
330C2×C4—42no—
331C2×C4—44no—
332C2×C4—41no—
333C2×C4—41no—
334C2×C4—441no—
335C2×C4—444no—
336C2×C4—442no—
337C2×C4—1762no—
338C2×C4—1761no—
339C2×C4C4×C22⋊D1112yes—
340C2×C4C2×#432312yes—
341C2×C4C2×#432312yes—
342C2×C4C2×#432311yescharacteristic
343C2×C4#6700312yes—
344C2×C4C22×C22⋊D1111yescharacteristic
345C8—22no—
346C8C4×C22⋊D1112yes—
347C8C22×C4×D1111yescharacteristic
348C8C2×#433911yescharacteristic
349C22—21no—
350C22—21no—
351C22—442no—
352C22—881no—
353C22—881no—
354C22C4×#432312yes—
355C22C22×#432311yescharacteristic
356C4—22no—
357C4—22no—
358C4—44no—
359C4—81no—
360C4—81no—
361C4—442no—
362C4—882no—
363C4C4×#432312yes—
364C4C2×C4×C22⋊D1111yescharacteristic
365C4C2×#6700311yescharacteristic
366C2—22no—
367C2—882no—
368C2C2×C4×#432311yescharacteristic
369C2#1308176011yescharacteristic
370C2#1308176711yescharacteristic
subgroupG/H
centerC22C22×#4323
commutatorC8×C11C23×C4
FrattiniC2×C8C23×D11
FittingC11×#2950C2
socleC22×C11C22×D8
prime radicalC2×#66957C22
cosocleC2×C8×C11C24
hypercenter#2950D11
hypocenterC11#33455
LCSG ▷ C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ #117 ◁ #405 ◁ #2950

Complements

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

NH ≅ G/Ntype
3. #13070485C2semidirect
4. #13070478C2semidirect
5. C4×#66893C2semidirect
6. C4×#66892C2semidirect
7. #13070405C2semidirect
9. C2×#10622202C2semidirect
10. #13070213C2semidirect
11. C11×#2950C2semidirect
23. #10622792C4semidirect
46. C2×C11×Q16C2×C4semidirect
75. #66893C2×C4semidirect
76. #66892C2×C4semidirect
81. #66876C2×C4semidirect
137. #2950D11semidirect
229. C2×Q16C4×D11semidirect
319. C11#33455semidirect

Maximal subgroups

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

subgroupindex
C2×#106227922
#130774932
#130704852
#130704782
C4×#668932
C4×#668922
#130704052
#130703212
C2×#106222022
#130702132
C11×#29502
#3345511