Finite Group Databasebeta

← #14751940

Subgroups — #14751940

Order 2816.

930 conjugacy classes of subgroups.

The subgroup lattice has 342 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622332C212yesmaximal
2#117×Dic11C211yesmaximal, characteristic
3#13068476C211yesmaximal, characteristic, complemented
4#13068474C211yesmaximal, characteristic, complemented
5#13068472C212yesmaximal, complemented
6#13068384C212yesmaximal
7#13068382C211yesmaximal, characteristic
8#13068363C212yesmaximal, complemented
9C4×#66879C211yesmaximal, characteristic, complemented
10#97×Dic11C211yesmaximal, characteristic, complemented
11C11×#1750C211yesmaximal, characteristic
12C2×C11×#117C2211yescharacteristic
13C2×#66979C2211yescharacteristic
14C22×C4×Dic11C2211yescharacteristic
15C2×C11×C22⋊C8C2212yes—
16C2×C11×#97C2211yescharacteristic
17C2×C4×C8×C11C2211yescharacteristic
18C2×C22⋊(C11⋊C8)C2212yes—
19C2×#66879C2212yes—
20C2×#66879C2212yes—
21C2×#66879C2212yes—
22C2×Dic11⋊C8C2212yes—
23C2×Dic11⋊C8C2212yes—
24C2×C8×Dic11C2212yes—
25C4⋊C4×Dic11C414yes—
26C22⋊C4×Dic11C414yes—
27#10622545C2211yescharacteristic
28#10622545C2211yescharacteristic
29C42×Dic11C2211yescharacteristic
30C42×Dic11C2211yescharacteristic
31C2×#66867C2211yescharacteristic
32C2×C4×C11⋊C8C2211yescharacteristic
33#10622332C4116yescomplemented
34C11×#336C2212yes—
35#10622188C2212yes—
36#10622188C2212yes—
37#10622162C2212yes—
38C23×C4×C11C2311yescharacteristic
39C23×Dic11C2×C412yes—
40C22×C8×C11C2312yes—
41C22×C8×C11C2312yes—
42C11×#117—22no—
43C11×#117—22no—
44C2×C11×C4⋊C4C2×C412yes—
45C2×C11×C22⋊C4C2×C412yes—
46C2×C42×C11C2311yescharacteristic
47C2×C42×C11C2311yescharacteristic
48C2×C22⋊Dic11C2×C412yes—
49#66979—24no—
50C2×C4⋊Dic11C2×C412yes—
51C2×C4×Dic11C2×C414yes—
52C2×C4×Dic11C2×C414yes—
53C2×C4×Dic11C2×C412yes—
54C2×C4×Dic11C2×C418yes—
55C2×C4×Dic11C2311yescharacteristic
56C2×C4×Dic11C2311yescharacteristic
57C2×C4×Dic11C2311yescharacteristic
58C2×C4×Dic11C2311yescharacteristic
59C22×C11⋊C8C2312yes—
60C22×C11⋊C8C2312yes—
61C11×C22⋊C8C2×C418yes—
62C11×#97—22no—
63C4×C8×C11—22no—
64C11⋊#95C2×C414yes—
65C11⋊#95C2×C414yes—
66C22⋊(C11⋊C8)C2×C418yes—
67#66879—24no—
68#66879C2×C418yes—
69#66879C2×C418yes—
70Dic11⋊C8C2×C418yes—
71Dic11⋊C8C2×C418yes—
72C8×Dic11—24no—
73#66867—22no—
74C4×C11⋊C8—22no—
75#20467—111nomaximal, Sylow
76C24×C11C22×C411yescharacteristic
77C22×C4×C11—22no—
78C22×C4×C11—21no—
79C22×C4×C11—21no—
80C22×C4×C11C22×C412yes—
81C22×C4×C11C22×C411yescharacteristic
82C22×C4×C11C22×C414yes—
83C22×C4×C11C22×C412yes—
84C22×C4×C11C2411yescharacteristic
85C22×Dic11—44no—
86C22×Dic11C4218yes—
87C22×Dic11C22×C412yes—
88C22×Dic11C22×C412yes—
89C22×Dic11C22×C412yes—
90C22×Dic11C22×C412yes—
91C2×C8×C11—22no—
92C2×C8×C11—22no—
93C2×C8×C11—22no—
94C2×C8×C11—22no—
95C2×C8×C11C22×C414yes—
96C2×C8×C11C22×C414yes—
97C11×C4⋊C4—24no—
98C11×C22⋊C4—24no—
99C42×C11—21no—
100C42×C11—21no—
101C42×C11#4112yes—
102C42×C11#4112yes—
103C22⋊Dic11—24no—
104C4⋊Dic11—24no—
105C4×Dic11—22no—
106C4×Dic11—44no—
107C4×Dic11—44no—
108C4×Dic11C4218yes—
109C4×Dic11C22×C414yes—
110C4×Dic11C22×C414yes—
111C4×Dic11#4114yes—
112C2×C11⋊C8—22no—
113C2×C11⋊C8—22no—
114C2×C11⋊C8—22no—
115C2×C11⋊C8—22no—
116C2×C11⋊C8C22×C414yes—
117C2×C11⋊C8C22×C414yes—
118C2×#432—112no—
119C4×#117—111no—
120#1768—111no—
121#1768—111no—
122#1768—112no—
123#1750—112no—
124#1750—111no—
125#1750D1111yescharacteristic
126#1745—112no—
127C4×#97—111no—
128C4×#97—111no—
129C23×C11—21no—
130C23×C11—21no—
131C23×C11—24no—
132C23×C11C2×C4212yes—
133C23×C11C23×C411yescharacteristic
134C2×C4×C11—21no—
135C2×C4×C11—21no—
136C2×C4×C11—24no—
137C2×C4×C11—24no—
138C2×C4×C11—24no—
139C2×C4×C11—22no—
140C2×C4×C11—24no—
141C2×C4×C11C2×C4212yes—
142C2×C4×C11#11714yes—
143C2×C4×C11C23×C412yes—
144C2×C4×C11C2×#4111yescharacteristic
145C2×C4×C11C2×#4111yescharacteristic
146C2×C4×C11C2×#4112yes—
147C2×Dic11—24no—
148C2×Dic11—24no—
149C2×Dic11—24no—
150C2×Dic11—22no—
151C2×Dic11—24no—
152C2×Dic11—48no—
153C2×Dic11C2×C4214yes—
154C2×Dic11C2×C4214yes—
155C2×Dic11#11714yes—
156C8×C11—24no—
157C8×C11—24no—
158C11⋊C8—24no—
159C11⋊C8—24no—
160C2×#117—111no—
161C2×#117C2×D1111yescharacteristic
162C22×C42—111no—
163#432—1116no—
164C2×C4⋊C8—112no—
165C2×C4⋊C8—112no—
166C2×C22⋊C8—112no—
167C2×C22⋊C8C2×D1112yes—
168C2×#97—112no—
169C2×#97—112no—
170C2×#97—112no—
171C2×#97—111no—
172C2×#97C2×D1111yescharacteristic
173C2×C4×C8—112no—
174C2×C4×C8—111no—
175C2×C4×C8C2×D1111yescharacteristic
176C4×C4⋊C4—114no—
177C4×C22⋊C4—114no—
178#376—111no—
179#376—111no—
180C43—111no—
181C43—111no—
182#336—112no—
183#336—112no—
184#336—112no—
185#336C2×D1112yes—
186C22×C11—24no—
187C22×C11—22no—
188C22×C11—42no—
189C22×C11—42no—
190C22×C11C22×C4211yescharacteristic
191C22×C11C2×#11711yescharacteristic
192C22×C11C2×#11711yescharacteristic
193C22×C11#56814yes—
194C4×C11—24no—
195C4×C11—22no—
196C4×C11—42no—
197C4×C11C4×#4112yes—
198C4×C11C4×#4112yes—
199Dic11—24no—
200Dic11—24no—
201Dic11—24no—
202Dic11—42no—
203C23×C4—112no—
204C23×C4C22×D1111yescharacteristic
205C22×C8—112no—
206C22×C8—112no—
207C22×C8C22×D1112yes—
208C22×C8C22×D1112yes—
209#117—22no—
210#117—22no—
211#117—224no—
212C2×C4⋊C4—112no—
213C2×C4⋊C4C4×D1112yes—
214C2×C22⋊C4—112no—
215C2×C22⋊C4C4×D1112yes—
216C2×C42—112no—
217C2×C42—118no—
218C2×C42—111no—
219C2×C42—111no—
220C2×C42—111no—
221C2×C42—111no—
222C2×C42—114no—
223C2×C42—114no—
224C2×C42C22×D1111yescharacteristic
225C2×C42C22×D1111yescharacteristic
226C4⋊C8—118no—
227C4⋊C8—118no—
228C22⋊C8—118no—
229C22⋊C8C4×D1118yes—
230#97—22no—
231#97—118no—
232#97—118no—
233#97—224no—
234#97—222no—
235C4×C8—22no—
236C4×C8—224no—
237C4×C8—222no—
238#95—114no—
239#95—114no—
240C2×C11—42no—
241C2×C11C4×#11711yescharacteristic
242C2×C11#287312yes—
243C2×C11#292312yes—
244C2×C11#292312yes—
245C24C2×C4×D1111yescharacteristic
246C22×C4—21no—
247C22×C4—21no—
248C22×C4—22no—
249C22×C4—112no—
250C22×C4—112no—
251C22×C4—112no—
252C22×C4—118no—
253C22×C4—112no—
254C22×C4—444no—
255C22×C4C2×C4×D1112yes—
256C22×C4C2×C4×D1111yescharacteristic
257C22×C4C2×C4×D1114yes—
258C22×C4C2×C4×D1112yes—
259C22×C4C23×D1111yescharacteristic
260C2×C8—22no—
261C2×C8—22no—
262C2×C8—22no—
263C2×C8—22no—
264C2×C8—114no—
265C2×C8—114no—
266C2×C8—222no—
267C2×C8—222no—
268C2×C8—222no—
269C2×C8—222no—
270C2×C8C2×C4×D1114yes—
271C2×C8C2×C4×D1114yes—
272C4⋊C4—24no—
273C4⋊C4—224no—
274C22⋊C4—24no—
275C22⋊C4—224no—
276C42—21no—
277C42—21no—
278C42—118no—
279C42—114no—
280C42—114no—
281C42—114no—
282C42—222no—
283C42—444no—
284C42—444no—
285C42#434112yes—
286C42#434112yes—
287C11#2046711yescharacteristic, complemented, Sylow
288C23—21no—
289C23—24no—
290C23—21no—
291C23C42×D1112yes—
292C23C22×C4×D1111yescharacteristic
293C2×C4—21no—
294C2×C4—24no—
295C2×C4—21no—
296C2×C4—24no—
297C2×C4—24no—
298C2×C4—22no—
299C2×C4—24no—
300C2×C4—114no—
301C2×C4—114no—
302C2×C4—114no—
303C2×C4—224no—
304C2×C4—224no—
305C2×C4—224no—
306C2×C4—224no—
307C2×C4—222no—
308C2×C4—448no—
309C2×C4C42×D1112yes—
310C2×C4#6693014yes—
311C2×C4C22×C4×D1112yes—
312C2×C4C2×#434111yescharacteristic
313C2×C4C2×#434111yescharacteristic
314C2×C4#41×D1112yes—
315C8—24no—
316C8—24no—
317C8—224no—
318C8—224no—
319C22—24no—
320C22—22no—
321C22—42no—
322C22—42no—
323C22C2×C42×D1111yescharacteristic
324C22C2×#6693011yescharacteristic
325C22D11×#11711yescharacteristic
326C22#1062328114yes—
327C4—24no—
328C4—22no—
329C4—42no—
330C4—224no—
331C4—224no—
332C4—224no—
333C4—442no—
334C4C4×#434112yes—
335C4C4×#434112yes—
336C2—42no—
337C2C4×#6693011yescharacteristic
338C2#1307703212yes—
339C2#1307726312yes—
340C2#1307726412yes—
subgroupG/H
center, FrattiniC22×C4C23×D11
commutatorC22×C11C22×C42
FittingC11×#1750C2
socleC23×C11C23×C4
prime radicalC24×C11C22×C4
cosocleC22×C4×C11C24
hypercenter#1750D11
hypocenterC11#20467
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ #1750

Complements

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

NH ≅ G/Ntype
3. #13068476C2semidirect
4. #13068474C2semidirect
5. #13068472C2semidirect
8. #13068363C2semidirect
9. C4×#66879C2semidirect
10. #97×Dic11C2semidirect
33. #10622332C4semidirect
287. C11#20467semidirect

Maximal subgroups

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

subgroupindex
C2×#106223322
#117×Dic112
#130684762
#130684742
#130684722
#130683842
#130683822
#130683632
C4×#668792
#97×Dic112
C11×#17502
#2046711