Finite Group Databasebeta

← #14907239

Subgroups — #14907239

Order 2816.

632 conjugacy classes of subgroups.

The subgroup lattice has 352 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622522C211yesmaximal, characteristic
2#13077532C211yesmaximal, characteristic
3#13077483C211yesmaximal, characteristic, complemented
4#13070506C218yesmaximal, complemented
5C2×#10622134C211yesmaximal, characteristic, complemented
6#13070351C211yesmaximal, characteristic
7#13070220C211yesmaximal, characteristic, complemented
8C11×#2155C211yesmaximal, characteristic, complemented
9#10623276—21no—
10C22×Dic44C2211yescharacteristic
11C2×#66957C2211yescharacteristic
12#10623047—21no—
13C2×C11×M32C2211yescharacteristic
14C2×C11×#108C2211yescharacteristic
15C11×#427C2211yescharacteristic
16#10622752—21no—
17#10622714C2211yescharacteristic
18C2×#66876C2211yescharacteristic
19#10622617—21no—
20#10622522C414yescomplemented
21#10622522C2214yes—
22C2×Dic88C412yescomplemented
23C2×#66864C412yescomplemented
24#10622508—22no—
25#10622507C2214yes—
26#10622486—22no—
27#10622466C2214yescomplemented
28C11×#365C2214yescomplemented
29#10622150C2214yescomplemented
30#10622134C2214yescomplemented
31#10622126C2214yes—
32C2×#4339—21no—
33C22×Dic22—21no—
34C2×C11×M16—21no—
35C22×C8×C11C2311yescharacteristic
36C11×#117—21no—
37#66979D411yescharacteristic
38C2×#4318D411yescharacteristic
39#66960—24no—
40M16×D11—42no—
41C2×Dic44—21no—
42C2×Dic44—21no—
43C2×Dic44—21no—
44C2×Dic44C2×C411yescharacteristic
45C2×Dic44C2×C412yes—
46C2×Dic44C2×C412yes—
47C2×Dic44C2312yes—
48#66957—21no—
49#66957—21no—
50#66957C2×C412yes—
51#66957C2312yes—
52C2×D88C2×C411yescharacteristic
53C2×#4314—21no—
54#66954—42no—
55#66940—24no—
56#66930—42no—
57C4×Dic22—42no—
58C11×M32C2×C412yes—
59C11×M32C2312yes—
60C2×C11×C16C2×C412yes—
61C11×#108—21no—
62C11×#108C2312yes—
63C11×#107—21no—
64C11×#106C2312yes—
65#66889—24no—
66#66879C2312yes—
67C8×Dic11D412yes—
68#66876—21no—
69#66876C2312yes—
70C2×C11⋊C16—21no—
71#66874—24no—
72Dic88C2×C418yes—
73#66864C2×C418yes—
74#33470—111nomaximal, Sylow
75C22×C4×C11C2×D411yescharacteristic
76C2×C22⋊D11—41no—
77C22×Dic11—41no—
78#4339—22no—
79#4339—22no—
80#4339—41no—
81#4339—41no—
82C2×D44—21no—
83C2×C4×D11—41no—
84C2×Dic22—21no—
85C2×Dic22—22no—
86C2×Dic22—22no—
87C2×Dic22—22no—
88C2×Dic22—41no—
89C2×Dic22—41no—
90C2×Dic22—41no—
91C11×M16—22no—
92C11×M16—41no—
93C2×C8×C11—41no—
94C2×C8×C11C22×C411yescharacteristic
95C2×C8×C11C22×C411yescharacteristic
96C2×C8×C11C2×D411yescharacteristic
97C2×C8×C11#4111yescharacteristic
98C2×C8×C11#4111yescharacteristic
99C2×C8×C11C2411yescharacteristic
100C11×C4⋊C4—22no—
101C11×C22⋊C4—41no—
102C42×C11—41no—
103C22⋊Dic11—21no—
104C4⋊Dic11—21no—
105Dic11⋊C4—44no—
106C4×Dic11—44no—
107C4×Dic11C2×D412yes—
108#4318—21no—
109#4318—21no—
110C2×C11⋊C8C2×D412yes—
111Dic44—21no—
112Dic44—22no—
113Dic44—22no—
114Dic44—22no—
115Dic44C22×C414yes—
116Dic44C22×C412yes—
117D88—21no—
118D88C22×C412yes—
119#4314—22no—
120#4314—22no—
121#4313—44no—
122C8×D11—44no—
123C11×C16C22×C414yes—
124C11⋊C16—22no—
125C2×#510—111no—
126#2957—111no—
127#2950—111no—
128#2180—118no—
129#2155D1111yescharacteristic, complemented
130C2×#362—111no—
131#2145—111no—
132#2110—111no—
133C23×C11AGL(1,ℤ/8)11yescharacteristic
134C22×D11—41no—
135C2×C4×C11—42no—
136C2×C4×C11C4×D411yescharacteristic
137C2×C4×C11C4×D411yescharacteristic
138C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
139C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
140C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
141C2×C4×C11C22×D411yescharacteristic
142C22⋊D11—42no—
143C22⋊D11—42no—
144C2×Dic11—22no—
145C2×Dic11—42no—
146C2×Dic11—42no—
147C2×Dic11—42no—
148C2×Dic11—41no—
149D44—22no—
150D44—41no—
151C4×D11—42no—
152C4×D11—42no—
153Dic22—22no—
154Dic22—24no—
155Dic22—42no—
156Dic22—42no—
157Dic22—42no—
158Dic22—41no—
159C8×C11—42no—
160C8×C11C4×D411yescharacteristic
161C8×C11C4×D411yescharacteristic
162C8×C11C23×C411yescharacteristic
163C8×C11C2×#4111yescharacteristic
164C11⋊C8—22no—
165C2×#135—111no—
166C22×Q16—111no—
167#568—221no—
168#519—221no—
169#510—114no—
170#510—114no—
171C2×Q32—112no—
172C2×SD32—112no—
173C2×M32—111no—
174C2×M32C2×D1111yescharacteristic
175#444—114no—
176#443—222no—
177#441—114no—
178C4×Q16—222no—
179C2×#108C2×D1111yescharacteristic
180#427C2×D1111yescharacteristic
181#421—221no—
182#419—221no—
183#405—111no—
184#365C2×D1114yescomplemented
185#362—114no—
186#360—114no—
187#347—114no—
188C22×C11—41no—
189C22×C11#44211yescharacteristic
190C22×C11#44211yescharacteristic
191C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
192C2×D11—42no—
193C2×D11—161no—
194C4×C11—82no—
195C4×C11#44211yescharacteristic
196C4×C11#44211yescharacteristic
197C4×C11C2×C4×D411yescharacteristic
198C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
199Dic11—42no—
200Dic11—44no—
201Dic11—42no—
202C2×#41—221no—
203C22×Q8—221no—
204#135—112no—
205#135—112no—
206#135—221no—
207#135—221no—
208C2×Q16—112no—
209C2×Q16—112no—
210C2×Q16—111no—
211C2×Q16—112no—
212C2×Q16—221no—
213C2×Q16—221no—
214C2×Q16—221no—
215C2×SD16—221no—
216C2×D8—111no—
217#131—224no—
218#131—442no—
219C2×M16—21no—
220C2×M16—111no—
221C2×M16—442no—
222C22×C8C22×D1111yescharacteristic
223C4×Q8—224no—
224C4×Q8—442no—
225#117—21no—
226#117—111no—
227#117—442no—
228Q32—118no—
229SD32—118no—
230M32—112no—
231M32—221no—
232M32C4×D1112yes—
233M32C22×D1112yes—
234C2×C16—221no—
235C2×C16C4×D1112yes—
236#108—21no—
237#108C22×D1112yes—
238#107—21no—
239#106C22×D1112yes—
240#104—224no—
241#103—224no—
242#97—112no—
243C4×C8—112no—
244C2×C11—21no—
245C2×C11—21no—
246C2×C11—21no—
247C2×C11C2×#44211yescharacteristic
248D11—82no—
249#41—222no—
250#41—222no—
251#41—441no—
252#41—441no—
253C2×Q8—221no—
254C2×Q8—222no—
255C2×Q8—222no—
256C2×Q8—222no—
257C2×Q8—441no—
258C2×Q8—441no—
259C2×Q8—441no—
260C2×D4—221no—
261C2×D4—441no—
262C22×C4—441no—
263C22×C4—441no—
264C22×C4D4×D1111yescharacteristic
265Q16—114no—
266Q16—112no—
267Q16—222no—
268Q16—222no—
269Q16—221no—
270Q16—222no—
271SD16—222no—
272SD16—222no—
273D8—112no—
274D8—221no—
275M16—22no—
276M16—41no—
277M16—221no—
278M16—221no—
279M16—444no—
280C2×C8—41no—
281C2×C8—112no—
282C2×C8—444no—
283C2×C8C2×C4×D1111yescharacteristic
284C2×C8C2×C4×D1111yescharacteristic
285C2×C8D4×D1111yescharacteristic
286C2×C8#434311yescharacteristic
287C2×C8#434311yescharacteristic
288C2×C8C23×D1111yescharacteristic
289C4⋊C4—22no—
290C4⋊C4—221no—
291C4⋊C4—444no—
292C22⋊C4—41no—
293C22⋊C4—221no—
294C42—41no—
295C42—112no—
296C42—444no—
297C16—222no—
298C16C2×C4×D1114yes—
299C11#3347011yescharacteristic, complemented, Sylow
300C23—441no—
301C23#6696711yescharacteristic
302Q8—222no—
303Q8—224no—
304Q8—442no—
305Q8—442no—
306Q8—441no—
307Q8—442no—
308D4—222no—
309D4—442no—
310D4—442no—
311D4—441no—
312C2×C4—42no—
313C2×C4—222no—
314C2×C4—441no—
315C2×C4—442no—
316C2×C4—442no—
317C2×C4—442no—
318C2×C4—442no—
319C2×C4—442no—
320C2×C4#6694611yescharacteristic
321C2×C4#6694611yescharacteristic
322C2×C4#6696711yescharacteristic
323C2×C4#6696711yescharacteristic
324C2×C4#6696711yescharacteristic
325C2×C4C2×D4×D1111yescharacteristic
326C8—42no—
327C8—222no—
328C8#6694611yescharacteristic
329C8#6694611yescharacteristic
330C8C22×C4×D1111yescharacteristic
331C8C2×#434311yescharacteristic
332C22—41no—
333C22—442no—
334C22—1761no—
335C22#1062248211yescharacteristic
336C22#1062248211yescharacteristic
337C22C2×#6696711yescharacteristic
338C4—82no—
339C4—442no—
340C4—442no—
341C4—444no—
342C4#1062248211yescharacteristic
343C4#1062248211yescharacteristic
344C4C2×#6694611yescharacteristic
345C4C2×#6696711yescharacteristic
346C2—21no—
347C2—21no—
348C2—21no—
349C2—882no—
350C2C2×#1062248211yescharacteristic
subgroupG/H
centerC2C2×#10622482
commutatorC8×C11C23×C4
FrattiniC2×C8C23×D11
FittingC11×#2155C2
socleC2×C11C2×#442
prime radicalC2×#66957C22
cosocleC2×C8×C11C24
hypercenter#2155D11
hypocenterC11#33470
LCSG ▷ C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2 ◁ C22×C4 ◁ C22×C8 ◁ #2155

Complements

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

NH ≅ G/Ntype
3. #13077483C2semidirect
4. #13070506C2semidirect
5. C2×#10622134C2semidirect
7. #13070220C2semidirect
8. C11×#2155C2semidirect
20. #10622522C4semidirect
22. C2×Dic88C4semidirect
23. C2×#66864C4semidirect
27. #10622466C22semidirect
28. C11×#365C22semidirect
29. #10622150C22semidirect
30. #10622134C22semidirect
129. #2155D11semidirect
184. #365C2×D11semidirect
299. C11#33470semidirect

Maximal subgroups

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

subgroupindex
C2×#106225222
#130775322
#130774832
#130705062
C2×#106221342
#130703512
#130702202
C11×#21552
#3347011