Finite Group Databasebeta

← #14672153

Subgroups — #14672153

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×#10622143C211yesmaximal, characteristic, complemented
3C2×#10622141C211yesmaximal, characteristic, complemented
4C2×#10622147C211yesmaximal, characteristic
5#13069482C211yesmaximal, characteristic
6#13069477C211yesmaximal, characteristic, complemented
7C2×C4×C11×C16C211yesmaximal, characteristic, complemented
8C22×Dic44C2211yescharacteristic
9C22×D88C2211yescharacteristic
10C22×C11×C16C2211yescharacteristic
11C22×C11×C16C2211yescharacteristic
12C2×C4×C8×C11C2211yescharacteristic
13C2×#66885—21no—
14C2×#66882C2211yescharacteristic
15C2×#66882C2211yescharacteristic
16C2×#66880—21no—
17#10622552—21no—
18#10622542—21no—
19C2×#66864—22no—
20C2×#66864—22no—
21C2×#66864C414yescomplemented
22C4×C11×C16—22no—
23#10622147—22no—
24#10622143—22no—
25#10622141—22no—
26C22×D44—21no—
27C22×Dic22—21no—
28C22×C8×C11D411yescharacteristic
29C22×C8×C11C2311yescharacteristic
30C2×C42×C11D411yescharacteristic
31C2×(C2×D11)⋊C4—42no—
32C2×C4⋊Dic11—21no—
33C2×C4⋊Dic11—21no—
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×C16—21no—
47C2×C11×C16—21no—
48C2×C11×C16C2×C412yes—
49C2×C11×C16D412yes—
50C2×C11×C16D412yes—
51C2×C11×C16D412yes—
52C4×C8×C11—21no—
53C4×C8×C11—21no—
54C11⋊#95—42no—
55#66885—42no—
56#66882—21no—
57#66882—21no—
58#66882—21no—
59#66882—21no—
60#66880—42no—
61#66864—28no—
62#13237—111nomaximal, Sylow
63C23×D11—41no—
64C22×C4×C11D812yes—
65C22×C4×C11C2×D411yescharacteristic
66C22×Dic11—41no—
67C22×Dic11—41no—
68C22×Dic11—41no—
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×C11—21no—
82C2×C8×C11—21no—
83C2×C8×C11D812yes—
84C2×C8×C11C22×C411yescharacteristic
85C2×C8×C11C2×D411yescharacteristic
86C2×C8×C11C2×D411yescharacteristic
87C2×C8×C11C2×D411yescharacteristic
88C2×C8×C11#4111yescharacteristic
89C2×C8×C11#4111yescharacteristic
90C42×C11—21no—
91C42×C11—21no—
92(C2×D11)⋊C4—84no—
93C4⋊Dic11—41no—
94C4⋊Dic11—41no—
95C4⋊Dic11—41no—
96C4⋊Dic11—41no—
97Dic44—22no—
98Dic44—22no—
99Dic44—41no—
100Dic44—41no—
101D88—22no—
102D88—22no—
103D88—41no—
104D88—41no—
105C11×C16—22no—
106C11×C16C22⋊C414yescomplemented
107C22×SD32—111no—
108C2×#367—111no—
109C2×#358—111no—
110C2×#357—111no—
111C2×C4×C16D1111yescharacteristic, complemented
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—22no—
121C2×C4×C11—22no—
122C2×C4×C11SD3214yescomplemented
123C2×C4×C11C4×D411yescharacteristic
124C2×C4×C11#12111yescharacteristic
125C2×C4×C11#12711yescharacteristic
126C2×C4×C11C2×D811yescharacteristic
127C2×C4×C11#13511yescharacteristic
128C2×C4×C11#13511yescharacteristic
129C2×Dic11—42no—
130C2×Dic11—81no—
131C2×Dic11—81no—
132C2×Dic11—81no—
133C2×Dic11—81no—
134C2×Dic11—82no—
135C2×Dic11—82no—
136D44—42no—
137D44—42no—
138D44—81no—
139D44—81no—
140Dic22—42no—
141Dic22—42no—
142Dic22—81no—
143Dic22—81no—
144C8×C11—22no—
145C8×C11C2×C22⋊C411yescharacteristic
146C8×C11C4×D411yescharacteristic
147C8×C11#12111yescharacteristic
148C8×C11#12411yescharacteristic
149C22×Q16—111no—
150C22×D8—111no—
151C2×SD32—114no—
152C2×SD32—222no—
153C2×SD32—222no—
154C22×C16C2×D1111yescharacteristic
155C22×C16C2×D1111yescharacteristic
156C2×#107—111no—
157C2×#107—111no—
158C2×#103—221no—
159C2×#102—221no—
160C2×C4×C8C2×D1111yescharacteristic
161#391—221no—
162#390—221no—
163#367—222no—
164#358—222no—
165#357—222no—
166C4×C16—22no—
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—24no—
178C4×C11#39011yescharacteristic
179C4×C11C4×D811yescharacteristic
180C4×C11#46611yescharacteristic
181C4×C11#49511yescharacteristic
182Dic11—82no—
183Dic11—161no—
184Dic11—161no—
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×C8D4411yescharacteristic
200C22×C8C22×D1111yescharacteristic
201C2×C4⋊C4—221no—
202C2×C4⋊C4—221no—
203C2×C22⋊C4—442no—
204C2×C42D4411yescharacteristic
205SD32—228no—
206C2×C16—21no—
207C2×C16—21no—
208C2×C16C4×D1112yes—
209C2×C16D4412yes—
210C2×C16D4412yes—
211C2×C16C22⋊D1112yes—
212#107—221no—
213#107—221no—
214#107—221no—
215#107—221no—
216#103—442no—
217#102—442no—
218C4×C8—21no—
219C4×C8—21no—
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—441no—
241C22×C4—441no—
242C22×C4—441no—
243C22×C4D8812yes—
244C22×C4C2×D4411yescharacteristic
245Q16—222no—
246Q16—222no—
247Q16—441no—
248Q16—441no—
249D8—222no—
250D8—222no—
251D8—441no—
252D8—441no—
253C2×C8—21no—
254C2×C8—21no—
255C2×C8D8812yes—
256C2×C8C2×C4×D1111yescharacteristic
257C2×C8C2×D4411yescharacteristic
258C2×C8C2×D4411yescharacteristic
259C2×C8#433911yescharacteristic
260C2×C8#433911yescharacteristic
261C2×C8C2×C22⋊D1111yescharacteristic
262C4⋊C4—441no—
263C4⋊C4—441no—
264C4⋊C4—441no—
265C4⋊C4—441no—
266C22⋊C4—884no—
267C42—21no—
268C42—21no—
269C16—22no—
270C16(C2×D11)⋊C414yescomplemented
271C11#1323711yescharacteristic, complemented, Sylow
272C23—442no—
273C23—881no—
274C23—882no—
275C23—882no—
276C23—881no—
277C23C2×D8811yescharacteristic
278Q8—442no—
279Q8—442no—
280Q8—881no—
281Q8—881no—
282D4—442no—
283D4—442no—
284D4—881no—
285D4—881no—
286C2×C4—22no—
287C2×C4—22no—
288C2×C4—442no—
289C2×C4—881no—
290C2×C4—881no—
291C2×C4—882no—
292C2×C4—882no—
293C2×C4—881no—
294C2×C4—881no—
295C2×C4#6686414yescomplemented
296C2×C4C4×D4411yescharacteristic
297C2×C4#6692711yescharacteristic
298C2×C4C2×D8811yescharacteristic
299C2×C4#6695711yescharacteristic
300C2×C4#6695711yescharacteristic
301C2×C4#6698311yescharacteristic
302C8—22no—
303C8C4×D4411yescharacteristic
304C8#6692811yescharacteristic
305C8C2×(C2×D11)⋊C411yescharacteristic
306C8#6698311yescharacteristic
307C22—884no—
308C22—882no—
309C22—1761no—
310C22—1761no—
311C22—1762no—
312C22C4×D8811yescharacteristic
313C22#1062230811yescharacteristic
314C22C2×#6686412yes—
315C22#1062251712yes—
316C22#1062272811yescharacteristic
317C4—24no—
318C4—882no—
319C4—1761no—
320C4—1761no—
321C4C4×D8811yescharacteristic
322C4#1062230911yescharacteristic
323C4#1062255211yescharacteristic
324C4#1062272811yescharacteristic
325C2—1762no—
326C2#1306948211yescharacteristic
327C2C4×#6686412yes—
328C2#1307071212yes—
329C2#1307087211yescharacteristic
330C2#1307087711yescharacteristic
subgroupG/H
centerC23C2×D88
commutatorC2×C8×C11C22×C4
FrattiniC22×C8C22×D11
FittingC2×C4×C11×C16C2
socleC23×C11C2×D8
prime radicalC22×D88C22
cosocleC22×C8×C11C23
hypercenterC2×C4×C16D11
hypocenterC11#13237
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4×C8 ◁ C2×C4×C16

Complements

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

NH ≅ G/Ntype
2. C2×#10622143C2semidirect
3. C2×#10622141C2semidirect
6. #13069477C2semidirect
7. C2×C4×C11×C16C2semidirect
21. C2×#66864C4semidirect
106. C11×C16C22⋊C4semidirect
111. C2×C4×C16D11semidirect
122. C2×C4×C11SD32semidirect
270. C16(C2×D11)⋊C4semidirect
271. C11#13237semidirect
295. C2×C4#66864semidirect

Maximal subgroups

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

subgroupindex
C22×#668642
C2×#106221432
C2×#106221412
C2×#106221472
#130694822
#130694772
C2×C4×C11×C162
#1323711