Finite Group Databasebeta

← #14773519

Subgroups — #14773519

Order 2816.

934 conjugacy classes of subgroups.

The subgroup lattice has 356 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13071565C212yesmaximal, complemented
2#13069483C212yesmaximal
3#13069238C214yesmaximal, complemented
4#13068776C211yesmaximal, characteristic, complemented
5#13068616C212yesmaximal, complemented
6#107×Dic11C212yesmaximal, complemented
7C8×C4⋊Dic11C211yesmaximal, characteristic, complemented
8C2×C4×C11×D8C211yesmaximal, characteristic
9C22×C11×D8C2211yescharacteristic
10C2×C4×D4×C11C2212yes—
11C2×#66979—22no—
12C4×C11×D8C418yescomplemented
13C2×C11×#107C2211yescharacteristic
14C2×C11×#102C2212yes—
15C2×C4×C8×C11C2211yescharacteristic
16#10622834C2214yes—
17C2×#66896C2214yes—
18#10622825—22no—
19C2×#66882C2212yes—
20C2×#66882C2212yes—
21C2×C8×Dic11C2212yes—
22C4⋊C4×Dic11C2214yes—
23#10622564—24no—
24#10622548C2212yes—
25C4×C4⋊Dic11C2211yescharacteristic
26C2×C4⋊(C11⋊C8)C2211yescharacteristic
27#10622188C2212yes—
28#10622167C2214yes—
29C22×D4×C11C2312yes—
30C23×C4×C11—22no—
31C2×C11×D8—22no—
32C2×C11×D8—22no—
33C2×C11×D8C2×C414yes—
34C22×C8×C11C2311yescharacteristic
35C22×C8×C11C2311yescharacteristic
36C4×D4×C11—24no—
37C4×D4×C11C2×C418yes—
38C2×C11×C4⋊C4C2312yes—
39C2×C11×C22⋊C4—22no—
40C2×C42×C11C2311yescharacteristic
41C2×C22⋊Dic11—24no—
42C2×C22⋊Dic11—24no—
43#66979—48no—
44C2×C4⋊Dic11—22no—
45C2×C4⋊Dic11—22no—
46C2×C4⋊Dic11D411yescharacteristic
47C2×C4⋊Dic11D411yescharacteristic
48C2×C4⋊Dic11C2314yes—
49C2×C4×Dic11—24no—
50C2×C4×Dic11C2312yes—
51C22×C11⋊C8C2312yes—
52C11×#107C2×C414yes—
53C11×#102C2×C418yes—
54C4×C8×C11C2×C414yes—
55#66896—44no—
56C11⋊#95—24no—
57C11⋊#95D412yes—
58#66882—24no—
59#66882—42no—
60C8×Dic11—24no—
61C4⋊(C11⋊C8)—22no—
62#22807—111nomaximal, Sylow
63C24×C11—22no—
64C2×D4×C11—22no—
65C2×D4×C11—22no—
66C2×D4×C11—22no—
67C2×D4×C11—22no—
68C2×D4×C11—22no—
69C2×D4×C11C22×C414yes—
70C22×C4×C11—22no—
71C22×C4×C11—28no—
72C22×C4×C11—44no—
73C22×C4×C11—44no—
74C22×C4×C11C2×D411yescharacteristic
75C22×C4×C11C2×D411yescharacteristic
76C22×C4×C11C2411yescharacteristic
77C22×Dic11—24no—
78C22×Dic11C2×D412yes—
79C22×Dic11C2×D412yes—
80C11×D8—28no—
81C2×C8×C11—21no—
82C2×C8×C11—21no—
83C2×C8×C11C22×C412yes—
84C2×C8×C11C22×C412yes—
85C2×C8×C11#4112yes—
86C2×C8×C11#4112yes—
87C11×C4⋊C4—22no—
88C11×C4⋊C4C22×C414yes—
89C11×C22⋊C4—28no—
90C42×C11C22×C412yes—
91C42×C11#4112yes—
92C22⋊Dic11—48no—
93C22⋊Dic11—84no—
94C4⋊Dic11—22no—
95C4⋊Dic11—24no—
96C4⋊Dic11—24no—
97C4⋊Dic11—44no—
98C4⋊Dic11—82no—
99C4⋊Dic11D814yescomplemented
100C4×Dic11—22no—
101C4×Dic11—22no—
102C4×Dic11—48no—
103C2×C11⋊C8—22no—
104C2×C11⋊C8—22no—
105C2×C11⋊C8—22no—
106C2×C4×D8D1111yescharacteristic
107#2354—112no—
108#1970—112no—
109#1925—114no—
110#1845—111no—
111#1802—112no—
112C4×#107—112no—
113C8×C4⋊C4—111no—
114C23×C11—24no—
115C23×C11—42no—
116C23×C11—42no—
117C23×C11—42no—
118C23×C11—42no—
119C23×C11—42no—
120C23×C11—42no—
121C23×C11C22×D411yescharacteristic
122D4×C11—24no—
123D4×C11—24no—
124D4×C11—42no—
125D4×C11—42no—
126C2×C4×C11—21no—
127C2×C4×C11—21no—
128C2×C4×C11—24no—
129C2×C4×C11—42no—
130C2×C4×C11—42no—
131C2×C4×C11—416no—
132C2×C4×C11C4×D412yes—
133C2×C4×C11C4×D412yes—
134C2×C4×C11C2×D812yes—
135C2×C4×C11#13512yes—
136C2×C4×C11C23×C411yescharacteristic
137C2×C4×C11C2×#4111yescharacteristic
138C2×C4×C11C2×#4111yescharacteristic
139C2×C4×C11C2×#4111yescharacteristic
140C2×C4×C11H(5,𝔽2)11yescharacteristic
141C2×C4×C112−1+411yescharacteristic
142C2×Dic11—22no—
143C2×Dic11—22no—
144C2×Dic11—22no—
145C2×Dic11—22no—
146C2×Dic11—22no—
147C2×Dic11—44no—
148C2×Dic11—44no—
149C2×Dic11—44no—
150C2×Dic11C2×D814yes—
151C8×C11—22no—
152C8×C11#11714yescomplemented
153C11⋊C8—42no—
154C22×D8C2×D1111yescharacteristic
155C2×C4×D4C2×D1112yes—
156C2×#117—222no—
157C4×D8Dic1118yescomplemented
158C2×#107—112no—
159C2×#107—112no—
160C2×#107C2×D1111yescharacteristic
161C2×C4⋊C8—111no—
162C2×#102—114no—
163C2×#102C2×D1112yes—
164C2×C4×C8—112no—
165C2×C4×C8C2×D1111yescharacteristic
166#390—114no—
167#388—224no—
168#384—112no—
169#380—222no—
170C4×C4⋊C4—111no—
171C4×C4⋊C4—114no—
172#340—114no—
173#336—112no—
174C22×C11—44no—
175C22×C11—44no—
176C22×C11—44no—
177C22×C11—82no—
178C22×C11—82no—
179C22×C11—82no—
180C22×C11—82no—
181C22×C11C2×C4×D411yescharacteristic
182C22×C11#54711yescharacteristic
183C22×C11#55011yescharacteristic
184C22×C11C22×D811yescharacteristic
185C22×C11C2×#13511yescharacteristic
186C22×C11#57611yescharacteristic
187C22×C11#57811yescharacteristic
188C4×C11—22no—
189C4×C11—44no—
190C4×C11C4×D814yes—
191C4×C11C2×#11711yescharacteristic
192C4×C11#52011yescharacteristic
193C4×C11#55511yescharacteristic
194C4×C11#55611yescharacteristic
195Dic11—24no—
196Dic11—42no—
197Dic11—84no—
198C22×D4C22×D1112yes—
199C23×C4—22no—
200C2×D8—22no—
201C2×D8—22no—
202C2×D8C2×Dic1114yes—
203C22×C8—112no—
204C22×C8C22×D1111yescharacteristic
205C22×C8C22×D1111yescharacteristic
206C4×D4—24no—
207C4×D4C2×Dic1118yes—
208#117—448no—
209C2×C4⋊C4—111no—
210C2×C4⋊C4—111no—
211C2×C4⋊C4—114no—
212C2×C4⋊C4—222no—
213C2×C4⋊C4—222no—
214C2×C4⋊C4C22×D1112yes—
215C2×C22⋊C4—22no—
216C2×C22⋊C4—224no—
217C2×C22⋊C4—224no—
218C2×C42—112no—
219C2×C42—224no—
220C2×C42C22×D1111yescharacteristic
221#107—224no—
222#107—442no—
223#107C2×Dic1114yes—
224C4⋊C8—222no—
225#102—444no—
226#102C2×Dic1118yes—
227C4×C8—224no—
228C4×C8C2×Dic1114yes—
229#95—112no—
230#95—224no—
231C2×C11—84no—
232C2×C11#235411yescharacteristic
233C2×C11C2×C4×D811yescharacteristic
234C2×C11#295111yescharacteristic
235C2×C11#333411yescharacteristic
236C2×C11#334111yescharacteristic
237C2×C11#339111yescharacteristic
238C2×C11#339311yescharacteristic
239C24—22no—
240C2×D4—22no—
241C2×D4—22no—
242C2×D4—22no—
243C2×D4—22no—
244C2×D4—22no—
245C2×D4C22×Dic1114yes—
246C22×C4—22no—
247C22×C4—28no—
248C22×C4—44no—
249C22×C4—44no—
250C22×C4—112no—
251C22×C4—112no—
252C22×C4—224no—
253C22×C4D4×D1111yescharacteristic
254C22×C4D4×D1111yescharacteristic
255C22×C4C23×D1111yescharacteristic
256D8—28no—
257C2×C8—21no—
258C2×C8—21no—
259C2×C8—222no—
260C2×C8—222no—
261C2×C8—222no—
262C2×C8#433912yes—
263C2×C8#433912yes—
264C2×C8C22×Dic1112yes—
265C2×C8C22×Dic1112yes—
266C4⋊C4—22no—
267C4⋊C4—114no—
268C4⋊C4—222no—
269C4⋊C4—224no—
270C4⋊C4—224no—
271C4⋊C4—444no—
272C4⋊C4—882no—
273C4⋊C4C22×Dic1114yes—
274C22⋊C4—28no—
275C22⋊C4—448no—
276C22⋊C4—884no—
277C42—222no—
278C42—222no—
279C42—448no—
280C42#434112yes—
281C42C22×Dic1112yes—
282C11#2280711yescharacteristic, complemented, Sylow
283C23—24no—
284C23—42no—
285C23—42no—
286C23—42no—
287C23—42no—
288C23—42no—
289C23—42no—
290C23C2×D4×D1111yescharacteristic
291D4—24no—
292D4—24no—
293D4—42no—
294D4—42no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—24no—
298C2×C4—42no—
299C2×C4—42no—
300C2×C4—416no—
301C2×C4—114no—
302C2×C4—222no—
303C2×C4—222no—
304C2×C4—222no—
305C2×C4—222no—
306C2×C4—222no—
307C2×C4—444no—
308C2×C4—444no—
309C2×C4—444no—
310C2×C4D8×D1112yes—
311C2×C4#6696512yes—
312C2×C4D4×Dic1112yes—
313C2×C4D4×Dic1112yes—
314C2×C4C2×#433911yescharacteristic
315C2×C4C2×#433911yescharacteristic
316C2×C4C2×#434111yescharacteristic
317C2×C4#6704211yescharacteristic
318C2×C4#6704311yescharacteristic
319C2×C4C23×Dic1111yescharacteristic
320C8—22no—
321C8—442no—
322C8#6697914yescomplemented
323C22—44no—
324C22—44no—
325C22—44no—
326C22—82no—
327C22—82no—
328C22—82no—
329C22—82no—
330C22#1062308211yescharacteristic
331C22#1062308411yescharacteristic
332C22C2×D8×D1111yescharacteristic
333C22C2×#6696511yescharacteristic
334C22#1062330011yescharacteristic
335C22#1062330211yescharacteristic
336C22C2×D4×Dic1111yescharacteristic
337C4—22no—
338C4—44no—
339C4—224no—
340C4—442no—
341C4—884no—
342C4D8×Dic1114yes—
343C4#1062307311yescharacteristic
344C4#1062309411yescharacteristic
345C4C2×#6697911yescharacteristic
346C4#1062335811yescharacteristic
347C2—84no—
348C2#1307156511yescharacteristic
349C2C2×D8×Dic1111yescharacteristic
350C2#1307749211yescharacteristic
351C2#1308096511yescharacteristic
352C2#1308104011yescharacteristic
353C2#1308159011yescharacteristic
354C2#1308160211yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC2×C4×C11×D8C2
socleC23×C11C22×D4
prime radicalC22×C11×D8C22
cosocleC22×C4×C11C24
hypercenterC2×C4×D8D11
hypocenterC11#22807
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4×D8

Complements

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

NH ≅ G/Ntype
1. #13071565C2semidirect
3. #13069238C2semidirect
4. #13068776C2semidirect
5. #13068616C2semidirect
6. #107×Dic11C2semidirect
7. C8×C4⋊Dic11C2semidirect
12. C4×C11×D8C4semidirect
99. C4⋊Dic11D8semidirect
152. C8×C11#117semidirect
157. C4×D8Dic11semidirect
282. C11#22807semidirect
322. C8#66979semidirect

Maximal subgroups

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

subgroupindex
#130715652
#130694832
#130692382
#130687762
#130686162
#107×Dic112
C8×C4⋊Dic112
C2×C4×C11×D82
#2280711