Finite Group Databasebeta

← #14737880

Subgroups — #14737880

Order 2816.

586 conjugacy classes of subgroups.

The subgroup lattice has 334 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079202C211yesmaximal, characteristic
2#13078747C212yesmaximal
3C2×#10622292C211yesmaximal, characteristic
4#13068171C214yesmaximal, complemented
5#13068135C212yesmaximal, complemented
6#13068111C212yesmaximal, complemented
7#13067317C212yesmaximal
8C11×#1568C211yesmaximal, characteristic
9#10623001C2212yes—
10C2×C4×Dic22C2211yescharacteristic
11C11×#432C2212yes—
12C2×C4×C8×C11C2211yescharacteristic
13#10622729—21no—
14#10622729—21no—
15C2×#66879—21no—
16C2×Dic11⋊C8—21no—
17C2×C4⋊(C11⋊C8)C2211yescharacteristic
18#10622464C2214yes—
19#10622462C2214yes—
20#10622352—22no—
21#10622334—22no—
22#10622329—24no—
23#10622312C2211yescharacteristic
24C4×Dic44—21no—
25C4×Dic44—21no—
26#10622295C2211yescharacteristic
27#10622294C2212yes—
28#10622292—21no—
29#10622292—21no—
30#10622292C2212yes—
31#10622292C2212yes—
32C11×#335C2212yes—
33C11×#334C2212yes—
34#10622124C2214yes—
35#10622120C2214yes—
36C22×Dic22D411yescharacteristic
37C22×C8×C11D411yescharacteristic
38C22×C8×C11D411yescharacteristic
39C2×C42×C11C2311yescharacteristic
40#66979—22no—
41C2×C4⋊Dic11D411yescharacteristic
42#66977—22no—
43#66977—22no—
44C2×Dic11⋊C4—21no—
45C2×C4×Dic11—21no—
46C22×C11⋊C8—21no—
47C2×Dic44—24no—
48C2×Dic44—21no—
49C2×Dic44—21no—
50#66923—22no—
51#66922C2312yes—
52#66922C2312yes—
53C4×Dic22—21no—
54C4×Dic22—21no—
55C4×Dic22—22no—
56C4×Dic22—22no—
57C4×Dic22D412yes—
58C4×Dic22C2312yes—
59C11×C4⋊C8C2314yes—
60C11×C22⋊C8—22no—
61C11×#97—22no—
62C4×C8×C11D411yescharacteristic
63C4×C8×C11D411yescharacteristic
64C4×C8×C11C2311yescharacteristic
65C4×C8×C11C2311yescharacteristic
66#66882—21no—
67#66882—21no—
68#66881—24no—
69#66880—24no—
70#66880—22no—
71#66880—22no—
72#66880—24no—
73#66879—22no—
74#66879—22no—
75Dic11⋊C8—22no—
76Dic11⋊C8—22no—
77C4⋊(C11⋊C8)—21no—
78C4⋊(C11⋊C8)C2312yes—
79#19290—111nomaximal, Sylow
80C22×C4×C11C2×D411yescharacteristic
81C22×C4×C11C2×D411yescharacteristic
82C22×C4×C11#4111yescharacteristic
83C22×Dic11—21no—
84C22×Dic11—21no—
85C2×Dic22—21no—
86C2×Dic22—22no—
87C2×Dic22—22no—
88C2×Dic22—42no—
89C2×Dic22C2×D412yes—
90C2×C8×C11—22no—
91C2×C8×C11—24no—
92C2×C8×C11—41no—
93C2×C8×C11C2×D411yescharacteristic
94C2×C8×C11C2×D411yescharacteristic
95C2×C8×C11C2×D411yescharacteristic
96C2×C8×C11C2×D411yescharacteristic
97C42×C11C2×D411yescharacteristic
98C42×C11C2×D411yescharacteristic
99C42×C11#4111yescharacteristic
100C42×C11C2411yescharacteristic
101C22⋊Dic11—42no—
102C4⋊Dic11—21no—
103C4⋊Dic11—22no—
104C4⋊Dic11—22no—
105C4⋊Dic11—22no—
106C4⋊Dic11—22no—
107C4⋊Dic11C2×D412yes—
108Dic11⋊C4—22no—
109Dic11⋊C4—22no—
110Dic11⋊C4—42no—
111Dic11⋊C4—42no—
112C4×Dic11—22no—
113C4×Dic11—22no—
114C4×Dic11—42no—
115C2×C11⋊C8—22no—
116C2×C11⋊C8—42no—
117Dic44—42no—
118Dic44—48no—
119Dic44—42no—
120#3170—111no—
121#3113—112no—
122C2×#446—111no—
123#1700—114no—
124#1694—112no—
125#1690—112no—
126#1568D1111yescharacteristic
127#1552—112no—
128C23×C11#12111yescharacteristic
129C2×C4×C11—22no—
130C2×C4×C11—21no—
131C2×C4×C11—21no—
132C2×C4×C11—22no—
133C2×C4×C11#12111yescharacteristic
134C2×C4×C11#12111yescharacteristic
135C2×C4×C11#12111yescharacteristic
136C2×C4×C11C22×D411yescharacteristic
137C2×C4×C11C22×D411yescharacteristic
138C2×C4×C11C2×#4111yescharacteristic
139C2×Dic11—22no—
140C2×Dic11—22no—
141C2×Dic11—42no—
142C2×Dic11—42no—
143C2×Dic11—42no—
144C2×Dic11—42no—
145Dic22—24no—
146Dic22—42no—
147Dic22—42no—
148Dic22—42no—
149Dic22—44no—
150C8×C11—21no—
151C8×C11—21no—
152C8×C11—21no—
153C8×C11—44no—
154C8×C11#13712yes—
155C11⋊C8—42no—
156#533—112no—
157C2×C4×Q8—111no—
158#500—111no—
159#494—111no—
160#487—112no—
161#483—222no—
162#475—114no—
163#467—221no—
164#467—221no—
165#462—114no—
166#451—222no—
167#446—112no—
168#446—112no—
169#446—221no—
170#446—221no—
171#441—224no—
172C4×Q16—221no—
173C4×Q16—221no—
174#432C2×D1112yes—
175C2×C4⋊C8—111no—
176C2×C4⋊C8—221no—
177C2×#97—221no—
178C2×C4×C8C2×D1111yescharacteristic
179#335C2×D1112yes—
180#334C2×D1112yes—
181#332—114no—
182#332—114no—
183C22×C11—21no—
184C22×C11—21no—
185C22×C11#47312yes—
186C22×C11C2×#12111yescharacteristic
187C4×C11—21no—
188C4×C11—21no—
189C4×C11—21no—
190C4×C11—21no—
191C4×C11C2×#13711yescharacteristic
192C4×C11#57511yescharacteristic
193C4×C11#57512yes—
194Dic11—42no—
195Dic11—42no—
196Dic11—82no—
197Dic11—82no—
198C22×Q8—111no—
199C2×Q16—224no—
200C2×Q16—221no—
201C2×Q16—221no—
202C22×C8—221no—
203C22×C8D4411yescharacteristic
204C22×C8D4411yescharacteristic
205C4⋊Q8—112no—
206C4⋊Q8—112no—
207#125—222no—
208C22⋊Q8—222no—
209C22⋊Q8—222no—
210C4×Q8—112no—
211C4×Q8—112no—
212C4×Q8—221no—
213C4×Q8—221no—
214C4×Q8—222no—
215C4×Q8—222no—
216#117—222no—
217C2×C4⋊C4—111no—
218C2×C4⋊C4—221no—
219C2×C42—221no—
220C2×C42C22×D1111yescharacteristic
221#107—221no—
222#107—221no—
223#106—224no—
224C4⋊C8—112no—
225C4⋊C8—222no—
226C4⋊C8—222no—
227C4⋊C8—221no—
228C4⋊C8C22×D1114yes—
229#103—224no—
230#103—224no—
231#103—222no—
232#103—222no—
233C22⋊C8—22no—
234#97—22no—
235#97—222no—
236#97—222no—
237C4×C8D4411yescharacteristic
238C4×C8D4411yescharacteristic
239C4×C8C22×D1111yescharacteristic
240C4×C8C22×D1111yescharacteristic
241C2×C11—22no—
242C2×C11#303711yescharacteristic
243C2×C11#305411yescharacteristic
244C2×C11C2×#47311yescharacteristic
245C2×Q8—112no—
246C2×Q8—221no—
247C2×Q8—222no—
248C2×Q8—222no—
249C2×Q8—442no—
250C22×C4—221no—
251C22×C4—221no—
252C22×C4C2×D4411yescharacteristic
253C22×C4D4×D1111yescharacteristic
254C22×C4#434311yescharacteristic
255Q16—442no—
256Q16—448no—
257Q16—442no—
258C2×C8—22no—
259C2×C8—24no—
260C2×C8—41no—
261C2×C8—222no—
262C2×C8—442no—
263C2×C8C2×D4411yescharacteristic
264C2×C8C2×D4411yescharacteristic
265C2×C8C2×D4411yescharacteristic
266C2×C8C2×D4411yescharacteristic
267C4⋊C4—112no—
268C4⋊C4—221no—
269C4⋊C4—222no—
270C4⋊C4—222no—
271C4⋊C4—222no—
272C4⋊C4—222no—
273C4⋊C4—222no—
274C4⋊C4—222no—
275C4⋊C4—442no—
276C4⋊C4—442no—
277C22⋊C4—442no—
278C42—222no—
279C42—222no—
280C42—442no—
281C42C2×D4411yescharacteristic
282C42D4×D1111yescharacteristic
283C42#434311yescharacteristic
284C42C23×D1111yescharacteristic
285C11#1929011yescharacteristic, complemented, Sylow
286C23#6694811yescharacteristic
287Q8—224no—
288Q8—442no—
289Q8—442no—
290Q8—442no—
291Q8—444no—
292C2×C4—22no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—22no—
296C2×C4—222no—
297C2×C4—222no—
298C2×C4—442no—
299C2×C4—442no—
300C2×C4—442no—
301C2×C4—442no—
302C2×C4#6694811yescharacteristic
303C2×C4#6694811yescharacteristic
304C2×C4#6694811yescharacteristic
305C2×C4C22×D4411yescharacteristic
306C2×C4C2×D4×D1111yescharacteristic
307C2×C4C2×#434311yescharacteristic
308C8—21no—
309C8—21no—
310C8—21no—
311C8—44no—
312C8—442no—
313C8#6696212yes—
314C22—21no—
315C22—21no—
316C22#1062250912yes—
317C22C2×#6694811yescharacteristic
318C4—21no—
319C4—21no—
320C4—21no—
321C4—21no—
322C4—442no—
323C4—442no—
324C4—882no—
325C4—882no—
326C4C2×#6696211yescharacteristic
327C4#1062327911yescharacteristic
328C4#1062329912yes—
329C2—22no—
330C2#1307809011yescharacteristic
331C2#1307822611yescharacteristic
332C2C2×#1062250911yescharacteristic
subgroupG/H
centerC22C2×#66948
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#1568C2
socleC22×C11C2×#121
prime radicalC23×C11#121
hypercenter#1568D11
hypocenterC11#19290
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1568

Complements

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

NH ≅ G/Ntype
4. #13068171C2semidirect
5. #13068135C2semidirect
6. #13068111C2semidirect
285. C11#19290semidirect

Maximal subgroups

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

subgroupindex
#130792022
#130787472
C2×#106222922
#130681712
#130681352
#130681112
#130673172
C11×#15682
#1929011