Finite Group Databasebeta

← #14672151

Subgroups — #14672151

Order 2816.

474 conjugacy classes of subgroups.

The subgroup lattice has 332 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66864C211yesmaximal, characteristic
2C2×#10622130C211yesmaximal, characteristic, complemented
3C2×#10622129C211yesmaximal, characteristic
4C2×C16×Dic11C211yesmaximal, characteristic, complemented
5#13069480C211yesmaximal, characteristic
6#13069475C211yesmaximal, characteristic, complemented
7C2×C11×#367C211yesmaximal, characteristic, complemented
8C22×Dic44C2211yescharacteristic
9C22×D88C2211yescharacteristic
10C22×C11×C16C2211yescharacteristic
11C2×C11×#107C2211yescharacteristic
12C2×C11×#107C2211yescharacteristic
13C2×C8×Dic11C2211yescharacteristic
14C22×C11⋊C16C2211yescharacteristic
15#10622601—21no—
16#10622587—21no—
17C2×#66874—21no—
18C2×#66873—21no—
19C2×#66864—22no—
20C2×#66864—22no—
21C2×#66864C414yescomplemented
22C11×#367—22no—
23C16×Dic11—22no—
24#10622130—22no—
25#10622129—22no—
26C22×D44—21no—
27C22×Dic22—21no—
28C22×C8×C11C2311yescharacteristic
29C2×C11×C4⋊C4—21no—
30C2×C11×C4⋊C4—21no—
31C2×(C2×D11)⋊C4—42no—
32C2×C4×Dic11D411yescharacteristic
33C22×C11⋊C8D411yescharacteristic
34C2×Dic44—21no—
35C2×Dic44—21no—
36C2×Dic44—21no—
37C2×Dic44—21no—
38C2×Dic44—21no—
39C2×Dic44C2×C412yes—
40C2×D88—21no—
41C2×D88—21no—
42C2×D88—21no—
43C2×D88—21no—
44C2×D88—21no—
45C2×D88C2×C412yes—
46C2×C11×C16C2×C412yes—
47C2×C11×C16D412yes—
48C2×C11×C16D412yes—
49C11×#107—21no—
50C11×#107—21no—
51C11×#107—21no—
52C11×#107—21no—
53C11⋊#95—42no—
54C8×Dic11—21no—
55C8×Dic11—21no—
56C2×C11⋊C16—21no—
57C2×C11⋊C16—21no—
58C2×C11⋊C16D412yes—
59#66874—42no—
60#66873—42no—
61#66864—28no—
62#13237—111nomaximal, Sylow
63C23×D11—41no—
64C22×C4×C11—41no—
65C22×C4×C11—41no—
66C22×C4×C11C2×D411yescharacteristic
67C22×Dic11—41no—
68C22×Dic11D812yes—
69C2×D44—22no—
70C2×D44—41no—
71C2×D44—41no—
72C2×D44—41no—
73C2×D44—41no—
74C2×D44—41no—
75C2×Dic22—22no—
76C2×Dic22—41no—
77C2×Dic22—41no—
78C2×Dic22—41no—
79C2×Dic22—41no—
80C2×Dic22—41no—
81C2×C8×C11C22×C411yescharacteristic
82C2×C8×C11C2×D411yescharacteristic
83C2×C8×C11C2×D411yescharacteristic
84C2×C8×C11C2×D411yescharacteristic
85C2×C8×C11#4111yescharacteristic
86C2×C8×C11#4111yescharacteristic
87C11×C4⋊C4—41no—
88C11×C4⋊C4—41no—
89C11×C4⋊C4—41no—
90C11×C4⋊C4—41no—
91(C2×D11)⋊C4—84no—
92C4×Dic11—21no—
93C4×Dic11—21no—
94C2×C11⋊C8—21no—
95C2×C11⋊C8—21no—
96C2×C11⋊C8D812yes—
97Dic44—22no—
98Dic44—22no—
99Dic44—41no—
100Dic44—41no—
101D88—22no—
102D88—22no—
103D88—41no—
104D88—41no—
105C11×C16C22⋊C414yescomplemented
106C11⋊C16—22no—
107C22×SD32—111no—
108C2×#367D1111yescharacteristic, complemented
109C2×#358—111no—
110C2×#357—111no—
111C2×C4×C16—111no—
112#1970—111no—
113#1969—111no—
114C23×C11C2×D811yescharacteristic
115C22×D11—42no—
116C22×D11—81no—
117C22×D11—81no—
118C22×D11—82no—
119C22×D11—82no—
120C2×C4×C11—81no—
121C2×C4×C11—81no—
122C2×C4×C11—82no—
123C2×C4×C11—82no—
124C2×C4×C11C4×D411yescharacteristic
125C2×C4×C11#12111yescharacteristic
126C2×C4×C11#12711yescharacteristic
127C2×C4×C11C2×D811yescharacteristic
128C2×C4×C11#13511yescharacteristic
129C2×C4×C11#13511yescharacteristic
130C2×Dic11—22no—
131C2×Dic11—22no—
132C2×Dic11—42no—
133C2×Dic11—81no—
134C2×Dic11—81no—
135C2×Dic11SD3214yescomplemented
136D44—42no—
137D44—42no—
138D44—81no—
139D44—81no—
140Dic22—42no—
141Dic22—42no—
142Dic22—81no—
143Dic22—81no—
144C8×C11C2×C22⋊C411yescharacteristic
145C8×C11C4×D411yescharacteristic
146C8×C11#12111yescharacteristic
147C8×C11#12411yescharacteristic
148C11⋊C8—22no—
149C22×Q16—111no—
150C22×D8—111no—
151C2×SD32—114no—
152C2×SD32—222no—
153C2×SD32—222no—
154C22×C16—111no—
155C22×C16C2×D1111yescharacteristic
156C2×#107C2×D1111yescharacteristic
157C2×#107C2×D1111yescharacteristic
158C2×#103—221no—
159C2×#102—221no—
160C2×C4×C8—111no—
161#391—221no—
162#390—221no—
163#367—22no—
164#358—222no—
165#357—222no—
166C4×C16—222no—
167C22×C11C4×D811yescharacteristic
168C22×C11#46611yescharacteristic
169C22×C11#49311yescharacteristic
170C22×C11C2×SD3212yes—
171C22×C11#50812yes—
172C2×D11—84no—
173C2×D11—82no—
174C2×D11—162no—
175C2×D11—161no—
176C2×D11—161no—
177C4×C11—161no—
178C4×C11—161no—
179C4×C11#39011yescharacteristic
180C4×C11C4×D811yescharacteristic
181C4×C11#46611yescharacteristic
182C4×C11#49511yescharacteristic
183Dic11—24no—
184Dic11—82no—
185C22×Q8—221no—
186C22×D4—221no—
187C2×Q16—112no—
188C2×Q16—221no—
189C2×Q16—221no—
190C2×Q16—221no—
191C2×Q16—221no—
192C2×Q16—221no—
193C2×D8—112no—
194C2×D8—221no—
195C2×D8—221no—
196C2×D8—221no—
197C2×D8—221no—
198C2×D8—221no—
199C22×C8—111no—
200C22×C8C22×D1111yescharacteristic
201C2×C4⋊C4—21no—
202C2×C4⋊C4—21no—
203C2×C22⋊C4—442no—
204C2×C42—111no—
205SD32—228no—
206C2×C16—112no—
207C2×C16—221no—
208C2×C16—221no—
209C2×C16C4×D1112yes—
210C2×C16D4412yes—
211C2×C16C22⋊D1112yes—
212#107—21no—
213#107—21no—
214#107—21no—
215#107—21no—
216#103—442no—
217#102—442no—
218C4×C8—221no—
219C4×C8—221no—
220#95—442no—
221C2×C11#197011yescharacteristic
222C2×C11C4×SD3212yes—
223C2×C11#221712yes—
224C2×C11#224811yescharacteristic
225C2×C11#224911yescharacteristic
226D11—162no—
227C24—441no—
228C2×Q8—222no—
229C2×Q8—441no—
230C2×Q8—441no—
231C2×Q8—441no—
232C2×Q8—441no—
233C2×Q8—441no—
234C2×D4—222no—
235C2×D4—441no—
236C2×D4—441no—
237C2×D4—441no—
238C2×D4—441no—
239C2×D4—441no—
240C22×C4—41no—
241C22×C4—41no—
242C22×C4—112no—
243C22×C4—441no—
244C22×C4D4×D1111yescharacteristic
245Q16—222no—
246Q16—222no—
247Q16—441no—
248Q16—441no—
249D8—222no—
250D8—222no—
251D8—441no—
252D8—441no—
253C2×C8—112no—
254C2×C8—221no—
255C2×C8—221no—
256C2×C8C2×C4×D1111yescharacteristic
257C2×C8C2×D4411yescharacteristic
258C2×C8D4×D1111yescharacteristic
259C2×C8#434311yescharacteristic
260C2×C8#434311yescharacteristic
261C2×C8C2×C22⋊D1111yescharacteristic
262C4⋊C4—41no—
263C4⋊C4—41no—
264C4⋊C4—41no—
265C4⋊C4—41no—
266C22⋊C4—884no—
267C42—221no—
268C42—221no—
269C16—222no—
270C16(C2×D11)⋊C414yescomplemented
271C11#1323711yescharacteristic, complemented, Sylow
272C23—442no—
273C23—881no—
274C23—881no—
275C23—882no—
276C23—882no—
277C23D8×D1111yescharacteristic
278Q8—442no—
279Q8—442no—
280Q8—881no—
281Q8—881no—
282D4—442no—
283D4—442no—
284D4—881no—
285D4—881no—
286C2×C4—81no—
287C2×C4—81no—
288C2×C4—82no—
289C2×C4—82no—
290C2×C4—114no—
291C2×C4—222no—
292C2×C4—222no—
293C2×C4—442no—
294C2×C4—881no—
295C2×C4—881no—
296C2×C4#6694611yescharacteristic
297C2×C4#6694811yescharacteristic
298C2×C4D8×D1111yescharacteristic
299C2×C4#6697211yescharacteristic
300C2×C4#6697211yescharacteristic
301C2×C4#6699311yescharacteristic
302C8—222no—
303C8#6694611yescharacteristic
304C8#6694811yescharacteristic
305C8C2×(C2×D11)⋊C411yescharacteristic
306C8#6700011yescharacteristic
307C22—884no—
308C22—882no—
309C22—1761no—
310C22—1761no—
311C22—1762no—
312C22#1062248511yescharacteristic
313C22#1062249611yescharacteristic
314C22D11×SD3212yes—
315C22#1062252912yes—
316C22#1062276411yescharacteristic
317C4—161no—
318C4—161no—
319C4—224no—
320C4—882no—
321C4#1062248511yescharacteristic
322C4#1062249611yescharacteristic
323C4#1062260111yescharacteristic
324C4#1062280411yescharacteristic
325C2—1762no—
326C2#1306948011yescharacteristic
327C2#1307046712yes—
328C2#1307071312yes—
329C2#1307087011yescharacteristic
330C2#1307087611yescharacteristic
subgroupG/H
centerC23D8×D11
commutatorC2×C8×C11C22×C4
FrattiniC22×C8C22×D11
FittingC2×C11×#367C2
socleC23×C11C2×D8
prime radicalC22×D88C22
cosocleC22×C8×C11C23
hypercenterC2×#367D11
hypocenterC11#13237
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×C8 ◁ C2×#367

Complements

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

NH ≅ G/Ntype
2. C2×#10622130C2semidirect
4. C2×C16×Dic11C2semidirect
6. #13069475C2semidirect
7. C2×C11×#367C2semidirect
21. C2×#66864C4semidirect
105. C11×C16C22⋊C4semidirect
108. C2×#367D11semidirect
135. C2×Dic11SD32semidirect
270. C16(C2×D11)⋊C4semidirect
271. C11#13237semidirect

Maximal subgroups

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

subgroupindex
C22×#668642
C2×#106221302
C2×#106221292
C2×C16×Dic112
#130694802
#130694752
C2×C11×#3672
#1323711