Finite Group Databasebeta

← #14913905

Subgroups — #14913905

Order 2816.

2250 conjugacy classes of subgroups.

The subgroup lattice has 336 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66940C211yesmaximal, characteristic
2#13071577C218yesmaximal, complemented
3#13071569C218yesmaximal, complemented
4#13071216C214yesmaximal
5#13071200C212yesmaximal
6#13071019C212yesmaximal
7#13071010C214yesmaximal
8#13070973C211yesmaximal, characteristic
9C11×#2274C211yesmaximal, characteristic
10C23×Dic22C2211yescharacteristic
11C2×C11×#117C2212yes—
12C22×C11×C4⋊C4C2211yescharacteristic
13C2×#66979C2212yes—
14C22×Dic11⋊C4C2212yes—
15C22×C4×Dic11C2212yes—
16C22×C4×Dic11C2211yescharacteristic
17C2×#66940C4116yescomplemented
18C2×#66940C2214yes—
19C2×#66940C2214yes—
20C4×C11×C4⋊C4C2218yes—
21C4×C11×C22⋊C4C2214yes—
22C4×C22⋊Dic11C2214yes—
23#10622590C2214yes—
24#10622589C2214yes—
25C4⋊C4×Dic11C2218yes—
26#10622587C2218yes—
27#10622556C2218yes—
28#10622555C2214yes—
29#10622555C2214yes—
30#10622546C22116yes—
31#10622545C2218yes—
32C4×Dic11⋊C4C2218yes—
33C4×Dic11⋊C4C2214yes—
34C4×Dic11⋊C4C2214yes—
35#10622542C2218yes—
36#10622265C22116yes—
37#10622264C2218yes—
38#10622263C2218yes—
39C23×C4×C11C2312yes—
40C23×C4×C11C2311yescharacteristic
41C23×Dic11C2311yescharacteristic
42C23×Dic11C2312yes—
43C23×Dic11C2311yescharacteristic
44C22×Dic22—28no—
45C22×Dic22C2×C418yes—
46C22×Dic22C2314yes—
47C11×#117—28no—
48C2×C11×C4⋊C4C2×C418yes—
49C2×C11×C4⋊C4C2314yes—
50C2×C11×C4⋊C4C2314yes—
51C2×C11×C22⋊C4C2314yes—
52C2×C42×C11C2314yes—
53C2×C42×C11C2318yes—
54C2×C22⋊Dic11C2314yes—
55#66979—28no—
56C2×C4⋊Dic11C2314yes—
57C2×Dic11⋊C4C2×C4116yes—
58C2×Dic11⋊C4C2318yes—
59C2×Dic11⋊C4C2318yes—
60C2×Dic11⋊C4C2318yes—
61C2×C4×Dic11C2×C4116yes—
62C2×C4×Dic11C2×C418yes—
63C2×C4×Dic11C2314yes—
64C2×C4×Dic11C2318yes—
65C2×C4×Dic11C2314yes—
66C2×C4×Dic11C2314yes—
67C2×C4×Dic11C2312yes—
68C2×C4×Dic11C2312yes—
69#66940C2×C4132yes—
70#66940C2×C4132yes—
71C11×#95C2318yes—
72C11⋊#95C2318yes—
73C11⋊#95C23116yes—
74C11⋊#95C2318yes—
75C11⋊#95C23116yes—
76C11⋊#95C2318yes—
77#34187—111nomaximal, Sylow
78C24×C11C2411yescharacteristic
79C22×C4×C11—44no—
80C22×C4×C11C22×C418yes—
81C22×C4×C11C22×C414yes—
82C22×C4×C11#4118yes—
83C22×C4×C11C2418yes—
84C22×C4×C11C2414yes—
85C22×C4×C11C2412yes—
86C22×Dic11—24no—
87C22×Dic11—28no—
88C22×Dic11—42no—
89C22×Dic11C22×C414yes—
90C22×Dic11C22×C418yes—
91C22×Dic11C22×C414yes—
92C22×Dic11C2418yes—
93C22×Dic11C2411yescharacteristic
94C22×Dic11C2414yes—
95C22×Dic11C2412yes—
96C22×Dic11C2411yescharacteristic
97C2×Dic22—232no—
98C2×Dic22—28no—
99C2×Dic22—28no—
100C2×Dic22C22×C4116yes—
101C11×C4⋊C4—28no—
102C11×C4⋊C4C22×C4116yes—
103C11×C22⋊C4—28no—
104C42×C11—28no—
105C42×C11—48no—
106C22⋊Dic11—28no—
107C4⋊Dic11—28no—
108Dic11⋊C4—216no—
109Dic11⋊C4—48no—
110Dic11⋊C4C22×C4132yes—
111C4×Dic11—28no—
112C4×Dic11—48no—
113C4×Dic11C22×C4116yes—
114C4×Dic11C22×C4116yes—
115C4×Dic11C22×C418yes—
116C4×Dic11C22×C418yes—
117C22×C4×Q8—111no—
118#2356—118no—
119#2355—118no—
120#2313—114no—
121#2310—112no—
122#2285—112no—
123#2283—114no—
124#2274—111no—
125#2274D1111yescharacteristic
126C23×C11—22no—
127C23×C11—22no—
128C23×C11C23×C412yes—
129C23×C11C2×#4114yes—
130C23×C11C2511yescharacteristic
131C2×C4×C11—28no—
132C2×C4×C11—28no—
133C2×C4×C11—28no—
134C2×C4×C11—28no—
135C2×C4×C11—48no—
136C2×C4×C11#117116yes—
137C2×C4×C11C23×C418yes—
138C2×C4×C11C23×C414yes—
139C2×C4×C11C2×#4114yes—
140C2×C4×C11C2×#4114yes—
141C2×Dic11—216no—
142C2×Dic11—28no—
143C2×Dic11—22no—
144C2×Dic11—24no—
145C2×Dic11—28no—
146C2×Dic11—28no—
147C2×Dic11—28no—
148C2×Dic11—28no—
149C2×Dic11—44no—
150C2×Dic11C23×C412yes—
151C2×Dic11C23×C414yes—
152C2×Dic11C23×C418yes—
153C2×Dic11C23×C412yes—
154C2×Dic112−1+414yes—
155Dic22—232no—
156C23×Q8—111no—
157C2×C4×Q8—114no—
158C2×C4×Q8—114no—
159C2×C4×Q8—1116no—
160C2×#117—112no—
161C2×#117C2×D1112yes—
162C22×C4⋊C4—112no—
163C22×C4⋊C4C2×D1111yescharacteristic
164C22×C42—112no—
165C22×C42—111no—
166#391—118no—
167#391—118no—
168#387—1116no—
169#387—1116no—
170#384—114no—
171#383—118no—
172#382—114no—
173#382—118no—
174#381—118no—
175#380—114no—
176#380—114no—
177C4×C4⋊C4—118no—
178C4×C4⋊C4—118no—
179C4×C4⋊C4—114no—
180C4×C4⋊C4—114no—
181C4×C4⋊C4C2×D1118yes—
182C4×C22⋊C4—114no—
183C4×C22⋊C4C2×D1114yes—
184#376—118no—
185C22×C11—22no—
186C22×C11—22no—
187C22×C11—28no—
188C22×C11C2×#11714yes—
189C22×C11C24×C411yescharacteristic
190C22×C11C22×#4112yes—
191C22×C11C2×2−1+412yes—
192C22×C11#58512yes—
193C4×C11—28no—
194C4×C11—48no—
195C4×C11C2×#11718yes—
196Dic11—28no—
197Dic11—22no—
198Dic11—24no—
199Dic11—48no—
200Dic11#51914yes—
201C22×Q8—118no—
202C22×Q8—114no—
203C22×Q8—228no—
204C23×C4—112no—
205C23×C4—111no—
206C23×C4—111no—
207C23×C4C22×D1112yes—
208C23×C4C22×D1111yescharacteristic
209C4×Q8—1132no—
210C4×Q8—1132no—
211#117—28no—
212#117—228no—
213C2×C4⋊C4—1116no—
214C2×C4⋊C4—118no—
215C2×C4⋊C4—114no—
216C2×C4⋊C4—118no—
217C2×C4⋊C4—118no—
218C2×C4⋊C4C4×D1118yes—
219C2×C4⋊C4C22×D1114yes—
220C2×C4⋊C4C22×D1114yes—
221C2×C22⋊C4—114no—
222C2×C22⋊C4C22×D1114yes—
223C2×C42—1116no—
224C2×C42—118no—
225C2×C42—114no—
226C2×C42—114no—
227C2×C42—112no—
228C2×C42—112no—
229C2×C42—114no—
230C2×C42—118no—
231C2×C42C22×D1114yes—
232C2×C42C22×D1118yes—
233#95—118no—
234#95—1116no—
235#95—118no—
236#95—118no—
237#95—1116no—
238#95C22×D1118yes—
239C2×C11—24no—
240C2×C11C22×#11711yescharacteristic
241C2×C11C2×#51911yescharacteristic
242C2×C11#342811yescharacteristic
243C2×C11#350714yes—
244C24C23×D1111yescharacteristic
245C2×Q8—1116no—
246C2×Q8—2232no—
247C2×Q8—228no—
248C2×Q8—228no—
249C22×C4—44no—
250C22×C4—111no—
251C22×C4—114no—
252C22×C4—118no—
253C22×C4—111no—
254C22×C4—114no—
255C22×C4—112no—
256C22×C4—114no—
257C22×C4—118no—
258C22×C4—224no—
259C22×C4—228no—
260C22×C4—442no—
261C22×C4C2×C4×D1118yes—
262C22×C4C2×C4×D1114yes—
263C22×C4#433918yes—
264C22×C4C23×D1118yes—
265C22×C4C23×D1114yes—
266C22×C4C23×D1112yes—
267C4⋊C4—28no—
268C4⋊C4—1132no—
269C4⋊C4—2216no—
270C4⋊C4—228no—
271C4⋊C4—448no—
272C4⋊C4C2×C4×D11116yes—
273C22⋊C4—28no—
274C22⋊C4—228no—
275C42—28no—
276C42—48no—
277C42—118no—
278C42—1116no—
279C42—118no—
280C42—1116no—
281C42—228no—
282C42—448no—
283C11#3418711yescharacteristic, complemented, Sylow
284C23—22no—
285C23—22no—
286C23C22×C4×D1112yes—
287C23C2×#433914yes—
288C23C24×D1111yescharacteristic
289Q8—2232no—
290C2×C4—28no—
291C2×C4—28no—
292C2×C4—28no—
293C2×C4—28no—
294C2×C4—48no—
295C2×C4—112no—
296C2×C4—114no—
297C2×C4—112no—
298C2×C4—114no—
299C2×C4—118no—
300C2×C4—228no—
301C2×C4—2216no—
302C2×C4—228no—
303C2×C4—224no—
304C2×C4—222no—
305C2×C4—228no—
306C2×C4—228no—
307C2×C4—228no—
308C2×C4—444no—
309C2×C4#66925116yes—
310C2×C4C22×C4×D1118yes—
311C2×C4C22×C4×D1114yes—
312C2×C4C2×#433914yes—
313C2×C4C2×#433914yes—
314C22—28no—
315C22—22no—
316C22—22no—
317C22C2×#6692514yes—
318C22C23×C4×D1111yescharacteristic
319C22C22×#433912yes—
320C22#1062345512yes—
321C22D11×2−1+412yes—
322C4—28no—
323C4—48no—
324C4—114no—
325C4—228no—
326C4—222no—
327C4—224no—
328C4—448no—
329C4C2×#6692518yes—
330C2—24no—
331C2C22×#6692511yescharacteristic
332C2D11×#51911yescharacteristic
333C2#1308181411yescharacteristic
334C2#1308247414yes—
subgroupG/H
center, FrattiniC23C24×D11
commutatorC22×C11C24×C4
FittingC11×#2274C2
socle, cosocleC23×C11C25
prime radicalC24×C11C24
hypercenter#2274D11
hypocenterC11#34187
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2274

Complements

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

NH ≅ G/Ntype
2. #13071577C2semidirect
3. #13071569C2semidirect
17. C2×#66940C4semidirect
283. C11#34187semidirect

Maximal subgroups

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

subgroupindex
C22×#669402
#130715772
#130715692
#130712162
#130712002
#130710192
#130710102
#130709732
C11×#22742
#3418711