Finite Group Databasebeta

← #14907124

Subgroups — #14907124

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×#10622522C211yesmaximal, characteristic
2#13077490C211yesmaximal, characteristic
3#13077483C211yesmaximal, characteristic, complemented
4#13070486C212yesmaximal, complemented
5#13070479C212yesmaximal, complemented
6#13070474C212yesmaximal, complemented
7#13070467C212yesmaximal, complemented
8#13070321C211yesmaximal, characteristic
9C2×#10622130C211yesmaximal, characteristic, complemented
10#13070215C211yesmaximal, characteristic, complemented
11C11×#2159C211yesmaximal, characteristic, complemented
12C22×Dic44C2211yescharacteristic
13C2×#66957C2211yescharacteristic
14#10623047—21no—
15#10623035—21no—
16C2×C11×M32C2211yescharacteristic
17C11×#427C2211yescharacteristic
18C2×C11×#107C2211yescharacteristic
19#10622714C2211yescharacteristic
20C22×C11⋊C16C2211yescharacteristic
21#10622617—21no—
22#10622579—21no—
23#10622522C418yescomplemented
24C2×Dic88C2212yes—
25C2×#66864C2212yes—
26#10622502—22no—
27#10622486C2212yes—
28#10622486C2212yes—
29#10622486C2212yes—
30#10622485C2212yes—
31#10622466—22no—
32C11×#367C2212yes—
33C11×#366C2212yes—
34#10622140C2212yes—
35C16×Dic11C2212yes—
36#10622130C2212yes—
37#10622130C2211yescharacteristic
38#10622130C2212yes—
39#10622130C2211yescharacteristic
40#10622129C2211yescharacteristic
41#10622129C2211yescharacteristic
42C2×#4339—21no—
43C22×Dic22—21no—
44C22×C8×C11C2311yescharacteristic
45C11×#117—21no—
46C2×C11×C4⋊C4—21no—
47C4×C22⋊D11—42no—
48#66979D411yescharacteristic
49C2×#4318D411yescharacteristic
50C2×Dic44—21no—
51C2×Dic44—22no—
52C2×Dic44C2×C414yescomplemented
53C2×Dic44C2311yescharacteristic
54C2×Dic44C2312yes—
55#66957—22no—
56#66957C2×C414yes—
57C2×D88C2311yescharacteristic
58C2×#4314—21no—
59#66946—22no—
60#66945—41no—
61C4⋊C4×D11—41no—
62#66940—22no—
63#66940—22no—
64#66940—22no—
65#66930—42no—
66C4×Dic22—41no—
67C4×Dic22—41no—
68C11×M32C2×C414yescomplemented
69C2×C11×C16C2312yes—
70C11×#107—21no—
71C11×#107C2312yes—
72C11×#107C2311yescharacteristic
73C11×#107C2311yescharacteristic
74C11×#106—21no—
75#66879D412yes—
76C8×Dic11C2312yes—
77C2×C11⋊C16—22no—
78C2×C11⋊C16C2311yescharacteristic
79C2×C11⋊C16C2311yescharacteristic
80#66874—22no—
81#66874—22no—
82#66874—22no—
83#66873—22no—
84Dic88C2×C418yescomplemented
85#66864C2×C418yescomplemented
86#33455—111nomaximal, Sylow
87C22×C4×C11—41no—
88C22×C4×C11C2×D411yescharacteristic
89C2×C22⋊D11—41no—
90C22×Dic11—41no—
91#4339—24no—
92#4339—42no—
93C2×D44—21no—
94C2×C4×D11—42no—
95C2×C4×D11—41no—
96C2×Dic22—24no—
97C2×Dic22—21no—
98C2×Dic22—22no—
99C2×Dic22—41no—
100C2×Dic22—42no—
101C2×C8×C11C22×C412yes—
102C2×C8×C11C2×D411yescharacteristic
103C2×C8×C11#4112yes—
104C2×C8×C11C2411yescharacteristic
105C11×C4⋊C4—22no—
106C11×C4⋊C4—21no—
107C11×C4⋊C4—21no—
108C11×C4⋊C4—41no—
109C11×C22⋊C4—41no—
110C42×C11—41no—
111C22⋊Dic11D812yes—
112(C2×D11)⋊C4—42no—
113C4⋊Dic11D811yescharacteristic
114C4⋊Dic11D811yescharacteristic
115Dic11⋊C4—42no—
116Dic11⋊C4—42no—
117Dic11⋊C4—42no—
118C4×Dic11—42no—
119C4×Dic11—42no—
120C4×Dic11—42no—
121C4×Dic11C2×D412yes—
122#4318—22no—
123C2×C11⋊C8C2×D412yes—
124Dic44—24no—
125Dic44—21no—
126Dic44—22no—
127Dic44C22×C414yes—
128Dic44C22×C412yes—
129D88—21no—
130D88C22×C412yes—
131#4314—24no—
132C11×C16C22×C414yes—
133C11⋊C16—21no—
134C11⋊C16—21no—
135C2×#510—111no—
136#2951—111no—
137#2950—111no—
138#2176—112no—
139#2175—112no—
140C4×Q32—112no—
141C4×SD32—112no—
142#2159D1111yescharacteristic, complemented
143#2138—111no—
144C2×#358—111no—
145#2108—111no—
146C23×C11C2×D811yescharacteristic
147C22×D11—41no—
148C2×C4×C11—41no—
149C2×C4×C11—41no—
150C2×C4×C11—42no—
151C2×C4×C11—161no—
152C2×C4×C11C4×D412yes—
153C2×C4×C11C2×D811yescharacteristic
154C2×C4×C11#13512yes—
155C2×C4×C11C22×D411yescharacteristic
156C22⋊D11—44no—
157C2×Dic11—42no—
158C2×Dic11—41no—
159C2×Dic11—44no—
160C2×Dic11C2×D812yes—
161C2×Dic11C2×D812yes—
162D44—22no—
163D44—41no—
164C4×D11—44no—
165C4×D11—162no—
166Dic22—22no—
167Dic22—24no—
168Dic22—42no—
169Dic22—41no—
170Dic22—44no—
171C8×C11C4×D412yes—
172C8×C11C23×C411yescharacteristic
173C8×C11C2×#4111yescharacteristic
174C11⋊C8—22no—
175C2×#135—111no—
176C22×Q16—111no—
177#520—221no—
178#519—221no—
179#510—118no—
180C2×Q32—112no—
181C2×SD32—112no—
182C2×M32C2×D1111yescharacteristic
183C22×C16—111no—
184#441—222no—
185#440—222no—
186C4×Q16—112no—
187C4×Q16—112no—
188C4×Q16—112no—
189C4×D8—112no—
190#427C2×D1111yescharacteristic
191C2×#107C2×D1111yescharacteristic
192#419—221no—
193#417—221no—
194#405—111no—
195#367C2×D1112yes—
196#366C2×D1112yes—
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—81no—
213C4×C11—82no—
214C4×C11—81no—
215C4×C11C4×D812yes—
216C4×C11C2×C4×D411yescharacteristic
217C4×C11C2×#13511yescharacteristic
218Dic11—22no—
219Dic11—22no—
220Dic11—44no—
221Dic11—42no—
222C2×#41—221no—
223C22×Q8—221no—
224#135—114no—
225#135—222no—
226C2×Q16—114no—
227C2×Q16—112no—
228C2×Q16—111no—
229C2×Q16—221no—
230C2×Q16—222no—
231C2×SD16—221no—
232C2×D8—111no—
233C2×M16—111no—
234C22×C8C22×D1111yescharacteristic
235C4×Q8—222no—
236C4×Q8—222no—
237C4×Q8—222no—
238C4×Q8—441no—
239C4×Q8—441no—
240C4×D4—222no—
241C4×D4—442no—
242#117—21no—
243#117—111no—
244#117—442no—
245#117—441no—
246C2×C4⋊C4—21no—
247C2×C4⋊C4—441no—
248Q32—118no—
249SD32—118no—
250M32C4×D1114yescomplemented
251C2×C16—111no—
252C2×C16—111no—
253C2×C16—222no—
254C2×C16C22×D1112yes—
255#107—21no—
256#107C22×D1111yescharacteristic
257#107C22×D1111yescharacteristic
258#107C22×D1112yes—
259#106—21no—
260#103—222no—
261#103—222no—
262#103—222no—
263#102—222no—
264#97—112no—
265C4×C8—112no—
266C2×C11—22no—
267C2×C11C2×C4×D811yescharacteristic
268C2×C11#341611yescharacteristic
269C2×C11#341711yescharacteristic
270D11—82no—
271#41—224no—
272#41—442no—
273C2×Q8—224no—
274C2×Q8—221no—
275C2×Q8—222no—
276C2×Q8—441no—
277C2×Q8—442no—
278C2×D4—221no—
279C2×D4—441no—
280C22×C4—41no—
281C22×C4—442no—
282C22×C4—441no—
283C22×C4—441no—
284C22×C4D4×D1111yescharacteristic
285Q16—114no—
286Q16—112no—
287Q16—224no—
288Q16—222no—
289Q16—221no—
290SD16—224no—
291D8—112no—
292D8—221no—
293M16—222no—
294C2×C8—112no—
295C2×C8C2×C4×D1112yes—
296C2×C8D4×D1111yescharacteristic
297C2×C8#434312yes—
298C2×C8C23×D1111yescharacteristic
299C4⋊C4—22no—
300C4⋊C4—21no—
301C4⋊C4—21no—
302C4⋊C4—41no—
303C4⋊C4—111no—
304C4⋊C4—111no—
305C4⋊C4—442no—
306C4⋊C4—442no—
307C4⋊C4—442no—
308C22⋊C4—41no—
309C22⋊C4—112no—
310C22⋊C4—442no—
311C42—41no—
312C42—112no—
313C42—442no—
314C42—442no—
315C42—442no—
316C16—221no—
317C16—221no—
318C16C2×C4×D1114yes—
319C11#3345511yescharacteristic, complemented, Sylow
320C23—441no—
321C23D8×D1111yescharacteristic
322Q8—222no—
323Q8—224no—
324Q8—444no—
325Q8—442no—
326Q8—441no—
327D4—222no—
328D4—444no—
329D4—441no—
330C2×C4—41no—
331C2×C4—41no—
332C2×C4—42no—
333C2×C4—112no—
334C2×C4—112no—
335C2×C4—161no—
336C2×C4—444no—
337C2×C4—441no—
338C2×C4—442no—
339C2×C4—444no—
340C2×C4—1762no—
341C2×C4#6694612yes—
342C2×C4D8×D1111yescharacteristic
343C2×C4#6697212yes—
344C2×C4C2×D4×D1111yescharacteristic
345C8—222no—
346C8#6694612yes—
347C8C22×C4×D1111yescharacteristic
348C8C2×#434311yescharacteristic
349C22—21no—
350C22—21no—
351C22—442no—
352C22—881no—
353C22—881no—
354C22#1062248512yes—
355C22C2×D8×D1111yescharacteristic
356C4—82no—
357C4—81no—
358C4—81no—
359C4—222no—
360C4—222no—
361C4—442no—
362C4—444no—
363C4#1062248512yes—
364C4C2×#6694611yescharacteristic
365C4C2×#6697211yescharacteristic
366C2—22no—
367C2—882no—
368C2C2×#1062248511yescharacteristic
369C2#1308176211yescharacteristic
370C2#1308176811yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutatorC8×C11C23×C4
FrattiniC2×C8C23×D11
FittingC11×#2159C2
socleC22×C11C22×D8
prime radicalC2×#66957C22
cosocleC2×C8×C11C24
hypercenter#2159D11
hypocenterC11#33455
LCSG ▷ C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #2159

Complements

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

NH ≅ G/Ntype
3. #13077483C2semidirect
4. #13070486C2semidirect
5. #13070479C2semidirect
6. #13070474C2semidirect
7. #13070467C2semidirect
9. C2×#10622130C2semidirect
10. #13070215C2semidirect
11. C11×#2159C2semidirect
23. #10622522C4semidirect
52. C2×Dic44C2×C4semidirect
68. C11×M32C2×C4semidirect
84. Dic88C2×C4semidirect
85. #66864C2×C4semidirect
142. #2159D11semidirect
250. M32C4×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×#106225222
#130774902
#130774832
#130704862
#130704792
#130704742
#130704672
#130703212
C2×#106221302
#130702152
C11×#21592
#3345511