Finite Group Databasebeta

← #14913909

Subgroups — #14913909

Order 2816.

2250 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
1C22×Q8×Dic11C211yesmaximal, characteristic
2#13071580C218yesmaximal, complemented
3#13071572C218yesmaximal, complemented
4#13071217C214yesmaximal
5#13071202C211yesmaximal, characteristic
6#13071019C212yesmaximal
7#13071007C214yesmaximal
8#13070972C212yesmaximal
9C11×#2310C211yesmaximal, characteristic
10C23×Q8×C11C2211yescharacteristic
11C2×C11×#117C2212yes—
12C2×Q8×Dic11C4116yescomplemented
13C2×Q8×Dic11C2214yes—
14C2×Q8×Dic11C2214yes—
15C2×#66979C2212yes—
16C22×C4⋊Dic11C2212yes—
17C22×C4⋊Dic11C2211yescharacteristic
18C22×C4×Dic11C2212yes—
19C22×C4×Dic11C2211yescharacteristic
20C11×#391C2218yes—
21C11×#381C2214yes—
22#10622843C2218yes—
23#10622824C2214yes—
24#10622590C2214yes—
25#10622589C2214yes—
26C4⋊C4×Dic11C2218yes—
27#10622555C2214yes—
28#10622555C2214yes—
29C22⋊C4×Dic11C2218yes—
30C4×C4⋊Dic11C2218yes—
31C4×Dic11⋊C4C2214yes—
32C4×Dic11⋊C4C2214yes—
33#10622267C22116yes—
34#10622266C22116yes—
35#10622264C2218yes—
36#10622263C2218yes—
37#10622262C2218yes—
38#10622261C2218yes—
39C22×Q8×C11—28no—
40C22×Q8×C11C2×C418yes—
41C22×Q8×C11C2314yes—
42C23×C4×C11C2312yes—
43C23×C4×C11C2311yescharacteristic
44C23×Dic11C2311yescharacteristic
45C23×Dic11C2312yes—
46C23×Dic11C2311yescharacteristic
47C11×#117—28no—
48C2×C11×C4⋊C4C2314yes—
49C2×C11×C22⋊C4C2314yes—
50C2×C42×C11C2314yes—
51C2×C22⋊Dic11C2314yes—
52Q8×Dic11C2×C4132yes—
53Q8×Dic11C2×C4132yes—
54#66979—28no—
55C2×C4⋊Dic11C2×C4116yes—
56C2×C4⋊Dic11C2×C418yes—
57C2×C4⋊Dic11C2314yes—
58C2×C4⋊Dic11C2318yes—
59C2×C4⋊Dic11C2314yes—
60C2×Dic11⋊C4C2318yes—
61C2×Dic11⋊C4C2318yes—
62C2×C4×Dic11C2×C4116yes—
63C2×C4×Dic11C2×C418yes—
64C2×C4×Dic11C2314yes—
65C2×C4×Dic11C23116yes—
66C2×C4×Dic11C2314yes—
67C2×C4×Dic11C2314yes—
68C2×C4×Dic11C2312yes—
69C2×C4×Dic11C2312yes—
70C11×#95C2318yes—
71C11×#95C2318yes—
72C11⋊#95C2318yes—
73C11⋊#95C2318yes—
74C11⋊#95C2318yes—
75C11⋊#95C23116yes—
76C11⋊#95C2318yes—
77#34187—111nomaximal, Sylow
78C24×C11C2411yescharacteristic
79C2×Q8×C11—232no—
80C2×Q8×C11—28no—
81C2×Q8×C11—28no—
82C2×Q8×C11C22×C4116yes—
83C22×C4×C11—28no—
84C22×C4×C11C22×C418yes—
85C22×C4×C11C22×C414yes—
86C22×C4×C11#4118yes—
87C22×C4×C11C2418yes—
88C22×C4×C11C2414yes—
89C22×C4×C11C2412yes—
90C22×Dic11—24no—
91C22×Dic11—44no—
92C22×Dic11—42no—
93C22×Dic11C22×C414yes—
94C22×Dic11C22×C418yes—
95C22×Dic11C22×C414yes—
96C22×Dic11C2418yes—
97C22×Dic11C2411yescharacteristic
98C22×Dic11C2414yes—
99C22×Dic11C2412yes—
100C22×Dic11C2411yescharacteristic
101C11×C4⋊C4—28no—
102C11×C22⋊C4—28no—
103C42×C11—28no—
104C22⋊Dic11—28no—
105C4⋊Dic11—28no—
106C4⋊Dic11C22×C4132yes—
107C4⋊Dic11C22×C4116yes—
108Dic11⋊C4—216no—
109Dic11⋊C4—48no—
110C4×Dic11—28no—
111C4×Dic11—416no—
112C4×Dic11C22×C4116yes—
113C4×Dic11C22×C4116yes—
114C4×Dic11C22×C418yes—
115C4×Dic11C22×C418yes—
116C22×C4×Q8—111no—
117#2356—118no—
118#2355—118no—
119#2313—114no—
120#2310—111no—
121#2310D1111yescharacteristic
122#2285—112no—
123#2283—114no—
124#2274—112no—
125C23×C11—22no—
126C23×C11—22no—
127C23×C11C23×C412yes—
128C23×C11C2×#4114yes—
129C23×C11C2511yescharacteristic
130Q8×C11—232no—
131C2×C4×C11—216no—
132C2×C4×C11—28no—
133C2×C4×C11—28no—
134C2×C4×C11—28no—
135C2×C4×C11—28no—
136C2×C4×C11#117116yes—
137C2×C4×C11C23×C418yes—
138C2×C4×C11C23×C414yes—
139C2×C4×C11C2×#4114yes—
140C2×C4×C11C2×#4114yes—
141C2×Dic11—22no—
142C2×Dic11—28no—
143C2×Dic11—24no—
144C2×Dic11—28no—
145C2×Dic11—28no—
146C2×Dic11—28no—
147C2×Dic11—28no—
148C2×Dic11—48no—
149C2×Dic11—44no—
150C2×Dic11C23×C412yes—
151C2×Dic11C23×C418yes—
152C2×Dic11C23×C414yes—
153C2×Dic11C23×C412yes—
154C2×Dic112−1+414yes—
155C23×Q8C2×D1111yescharacteristic
156C2×C4×Q8—114no—
157C2×C4×Q8—114no—
158C2×C4×Q8—1116no—
159C2×#117—112no—
160C2×#117C2×D1112yes—
161C22×C4⋊C4—112no—
162C22×C4⋊C4—111no—
163C22×C42—112no—
164C22×C42—111no—
165#391—118no—
166#391C2×D1118yes—
167#387—1116no—
168#387—1116no—
169#384—114no—
170#383—118no—
171#382—114no—
172#382—118no—
173#381—114no—
174#381C2×D1114yes—
175#380—114no—
176#380—114no—
177C4×C4⋊C4—118no—
178C4×C4⋊C4—114no—
179C4×C4⋊C4—118no—
180C4×C4⋊C4—114no—
181C4×C4⋊C4—118no—
182C4×C22⋊C4—118no—
183#376—118no—
184C22×C11—22no—
185C22×C11—22no—
186C22×C11—28no—
187C22×C11C2×#11714yes—
188C22×C11C24×C411yescharacteristic
189C22×C11C22×#4112yes—
190C22×C11C2×2−1+412yes—
191C22×C11#58512yes—
192C4×C11—28no—
193C4×C11—48no—
194C4×C11C2×#11718yes—
195Dic11—22no—
196Dic11—28no—
197Dic11—24no—
198Dic11—48no—
199Dic11#51914yes—
200C22×Q8—28no—
201C22×Q8C4×D1118yes—
202C22×Q8C22×D1114yes—
203C23×C4—111no—
204C23×C4—112no—
205C23×C4—111no—
206C23×C4C22×D1112yes—
207C23×C4C22×D1111yescharacteristic
208C4×Q8—1132no—
209C4×Q8—1132no—
210#117—28no—
211#117—228no—
212C2×C4⋊C4—1116no—
213C2×C4⋊C4—118no—
214C2×C4⋊C4—114no—
215C2×C4⋊C4—118no—
216C2×C4⋊C4—114no—
217C2×C4⋊C4—118no—
218C2×C4⋊C4—118no—
219C2×C4⋊C4C22×D1114yes—
220C2×C22⋊C4—114no—
221C2×C22⋊C4C22×D1114yes—
222C2×C42—1116no—
223C2×C42—118no—
224C2×C42—114no—
225C2×C42—114no—
226C2×C42—112no—
227C2×C42—112no—
228C2×C42—114no—
229C2×C42—1116no—
230C2×C42C22×D1114yes—
231#95—118no—
232#95—118no—
233#95—1116no—
234#95—118no—
235#95—118no—
236#95C22×D1118yes—
237#95C22×D1118yes—
238C2×C11—24no—
239C2×C11C22×#11711yescharacteristic
240C2×C11C2×#51911yescharacteristic
241C2×C11#342811yescharacteristic
242C2×C11#350714yes—
243C24C23×D1111yescharacteristic
244C2×Q8—232no—
245C2×Q8—28no—
246C2×Q8—28no—
247C2×Q8C2×C4×D11116yes—
248C22×C4—28no—
249C22×C4—111no—
250C22×C4—114no—
251C22×C4—111no—
252C22×C4—114no—
253C22×C4—112no—
254C22×C4—118no—
255C22×C4—114no—
256C22×C4—118no—
257C22×C4—224no—
258C22×C4—444no—
259C22×C4—442no—
260C22×C4C2×C4×D1118yes—
261C22×C4C2×C4×D1114yes—
262C22×C4#434118yes—
263C22×C4C23×D1118yes—
264C22×C4C23×D1114yes—
265C22×C4C23×D1112yes—
266C4⋊C4—28no—
267C4⋊C4—1132no—
268C4⋊C4—1116no—
269C4⋊C4—2216no—
270C4⋊C4—228no—
271C4⋊C4—448no—
272C22⋊C4—28no—
273C22⋊C4—228no—
274C42—28no—
275C42—1116no—
276C42—118no—
277C42—1116no—
278C42—118no—
279C42—228no—
280C42—4416no—
281C11#3418711yescharacteristic, complemented, Sylow
282C23—22no—
283C23—22no—
284C23C22×C4×D1112yes—
285C23C2×#434114yes—
286C23C24×D1111yescharacteristic
287Q8—232no—
288C2×C4—216no—
289C2×C4—28no—
290C2×C4—28no—
291C2×C4—28no—
292C2×C4—28no—
293C2×C4—112no—
294C2×C4—114no—
295C2×C4—112no—
296C2×C4—118no—
297C2×C4—114no—
298C2×C4—228no—
299C2×C4—222no—
300C2×C4—228no—
301C2×C4—224no—
302C2×C4—228no—
303C2×C4—228no—
304C2×C4—228no—
305C2×C4—448no—
306C2×C4—444no—
307C2×C4#66930116yes—
308C2×C4C22×C4×D1118yes—
309C2×C4C22×C4×D1114yes—
310C2×C4C2×#434114yes—
311C2×C4C2×#434114yes—
312C22—28no—
313C22—22no—
314C22—22no—
315C22C2×#6693014yes—
316C22C23×C4×D1111yescharacteristic
317C22C22×#434112yes—
318C22D11×2−1+412yes—
319C22#1062345712yes—
320C4—28no—
321C4—48no—
322C4—114no—
323C4—222no—
324C4—228no—
325C4—224no—
326C4—448no—
327C4C2×#6693018yes—
328C2—24no—
329C2C22×#6693011yescharacteristic
330C2D11×#51911yescharacteristic
331C2#1308181811yescharacteristic
332C2#1308248014yes—
subgroupG/H
center, FrattiniC23C24×D11
commutatorC22×C11C24×C4
FittingC11×#2310C2
socle, cosocleC23×C11C25
prime radicalC24×C11C24
hypercenter#2310D11
hypocenterC11#34187
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2310

Complements

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

NH ≅ G/Ntype
2. #13071580C2semidirect
3. #13071572C2semidirect
12. C2×Q8×Dic11C4semidirect
281. C11#34187semidirect

Maximal subgroups

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

subgroupindex
C22×Q8×Dic112
#130715802
#130715722
#130712172
#130712022
#130710192
#130710072
#130709722
C11×#23102
#3418711