Finite Group Databasebeta

← #14907243

Subgroups — #14907243

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×#10622792C211yesmaximal, characteristic
2#13077532C211yesmaximal, characteristic
3#13077484C211yesmaximal, characteristic, complemented
4#13070510C218yesmaximal, complemented
5#13070390C211yesmaximal, characteristic, complemented
6#13070353C211yesmaximal, characteristic
7#13070220C211yesmaximal, characteristic, complemented
8C2×C11×#362C211yesmaximal, characteristic, complemented
9C22×C11×Q16C2211yescharacteristic
10#10623343—21no—
11#10623276—21no—
12C2×#66957C2211yescharacteristic
13C2×C11×M32C2211yescharacteristic
14C2×C11×#108C2211yescharacteristic
15#10622838—21no—
16#10622797C2214yescomplemented
17Q16×Dic11—22no—
18C2×#66893C412yescomplemented
19#10622792C414yescomplemented
20#10622792C2214yes—
21C2×#66892C412yescomplemented
22#10622752—21no—
23#10622719C2211yescharacteristic
24#10622714C2211yescharacteristic
25C2×#66876C2211yescharacteristic
26#10622508—22no—
27#10622507C2214yes—
28C11×#362C2214yescomplemented
29#10622156C2214yes—
30#10622150C2214yescomplemented
31#10622132C2214yescomplemented
32C22×Q8×C11—21no—
33C2×#4339—21no—
34C2×C11×Q16—21no—
35C2×C11×Q16—21no—
36C2×C11×Q16—21no—
37C2×C11×Q16C2×C412yes—
38C2×C11×Q16C2×C412yes—
39C2×C11×Q16C2312yes—
40C2×C11×M16—21no—
41C22×C8×C11C2311yescharacteristic
42Q8×Dic11—24no—
43Q8×Dic11—42no—
44#66979—21no—
45#66979—42no—
46#66979D411yescharacteristic
47C2×#4318D411yescharacteristic
48#66960—24no—
49M16×D11—42no—
50C2×Dic44C2×C411yescharacteristic
51#66957—21no—
52#66957—21no—
53#66957C2×C412yes—
54#66957C2312yes—
55C2×D88C2×C411yescharacteristic
56C2×#4314—21no—
57#66954—42no—
58C11×M32—21no—
59C11×M32C2312yes—
60C2×C11×C16—21no—
61C11×#108—21no—
62C11×#108C2312yes—
63#66899—24no—
64#66893C2×C418yes—
65#66892C2×C418yes—
66#66889—24no—
67#66882—21no—
68#66881C2312yes—
69#66879C2312yes—
70C8×Dic11D412yes—
71#66876C2×C412yes—
72#66876C2312yes—
73C2×C11⋊C16C2×C412yes—
74#33470—111nomaximal, Sylow
75C2×Q8×C11—22no—
76C2×Q8×C11—22no—
77C2×Q8×C11—22no—
78C2×Q8×C11—41no—
79C2×Q8×C11—41no—
80C2×Q8×C11—41no—
81C22×C4×C11—41no—
82C22×C4×C11C2×D411yescharacteristic
83C2×C22⋊D11—41no—
84#4339—22no—
85#4339—22no—
86#4339—41no—
87#4339—41no—
88C2×D44—21no—
89C2×C4×D11—41no—
90C2×Dic22—21no—
91C11×Q16—22no—
92C11×Q16—22no—
93C11×Q16—22no—
94C11×Q16C22×C414yes—
95C11×M16—22no—
96C11×M16—41no—
97C2×C8×C11—41no—
98C2×C8×C11C22×C411yescharacteristic
99C2×C8×C11C22×C411yescharacteristic
100C2×C8×C11C2×D411yescharacteristic
101C2×C8×C11#4111yescharacteristic
102C2×C8×C11#4111yescharacteristic
103C2×C8×C11C2411yescharacteristic
104C22⋊Dic11—21no—
105C22⋊Dic11—41no—
106C4⋊Dic11—21no—
107C4⋊Dic11—22no—
108C4⋊Dic11—44no—
109C4×Dic11—44no—
110C4×Dic11—41no—
111C4×Dic11C2×D412yes—
112#4318—21no—
113#4318—21no—
114C2×C11⋊C8C2×D412yes—
115Dic44—21no—
116Dic44C22×C412yes—
117D88—21no—
118D88C22×C412yes—
119#4314—22no—
120#4314—22no—
121#4313—44no—
122C8×D11—44no—
123C11×C16—22no—
124C11⋊C16C22×C414yes—
125C2×#510—111no—
126#2957—111no—
127#2950—111no—
128#2180—118no—
129#2155—111no—
130C2×#362D1111yescharacteristic, complemented
131#2145—111no—
132#2110—111no—
133C23×C11AGL(1,ℤ/8)11yescharacteristic
134C22×D11—41no—
135Q8×C11—24no—
136Q8×C11—42no—
137Q8×C11—42no—
138Q8×C11—42no—
139C2×C4×C11—42no—
140C2×C4×C11—42no—
141C2×C4×C11—42no—
142C2×C4×C11C4×D411yescharacteristic
143C2×C4×C11C4×D411yescharacteristic
144C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
145C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
146C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
147C2×C4×C11C22×D411yescharacteristic
148C22⋊D11—42no—
149C22⋊D11—42no—
150C2×Dic11—22no—
151C2×Dic11—41no—
152C2×Dic11—42no—
153D44—22no—
154D44—41no—
155C4×D11—42no—
156C4×D11—42no—
157Dic22—22no—
158Dic22—41no—
159C8×C11—42no—
160C8×C11C4×D411yescharacteristic
161C8×C11C4×D411yescharacteristic
162C8×C11C23×C411yescharacteristic
163C8×C11C2×#4111yescharacteristic
164C11⋊C8—22no—
165C2×#135—111no—
166C22×Q16C2×D1111yescharacteristic
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#427—111no—
181#421—221no—
182#419—221no—
183#405—111no—
184#365—114no—
185#362C2×D1114yescomplemented
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—44no—
195C4×C11#44211yescharacteristic
196C4×C11#44211yescharacteristic
197C4×C11C2×C4×D411yescharacteristic
198C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
199Dic11—42no—
200Dic11—42no—
201Dic11—82no—
202C2×#41—221no—
203C22×Q8—21no—
204#135—112no—
205#135—112no—
206#135—221no—
207#135—221no—
208C2×Q16—21no—
209C2×Q16—21no—
210C2×Q16—21no—
211C2×Q16—111no—
212C2×Q16C4×D1112yes—
213C2×Q16C4×D1112yes—
214C2×Q16C22×D1112yes—
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—111no—
226#117—221no—
227#117—442no—
228Q32—118no—
229SD32—118no—
230M32—21no—
231M32—112no—
232M32—112no—
233M32C22×D1112yes—
234C2×C16—21no—
235C2×C16—112no—
236#108—21no—
237#108C22×D1112yes—
238#107—221no—
239#106—112no—
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—22no—
254C2×Q8—22no—
255C2×Q8—22no—
256C2×Q8—41no—
257C2×Q8—41no—
258C2×Q8—41no—
259C2×Q8—221no—
260C2×D4—221no—
261C2×D4—441no—
262C22×C4—41no—
263C22×C4—441no—
264C22×C4D4×D1111yescharacteristic
265Q16—22no—
266Q16—22no—
267Q16—22no—
268Q16—112no—
269Q16—221no—
270Q16C2×C4×D1114yes—
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#434111yescharacteristic
287C2×C8#434111yescharacteristic
288C2×C8C23×D1111yescharacteristic
289C4⋊C4—221no—
290C4⋊C4—222no—
291C4⋊C4—444no—
292C22⋊C4—221no—
293C22⋊C4—441no—
294C42—112no—
295C42—444no—
296C42—441no—
297C16—22no—
298C16—114no—
299C11#3347011yescharacteristic, complemented, Sylow
300C23—441no—
301C23#6696711yescharacteristic
302Q8—24no—
303Q8—42no—
304Q8—42no—
305Q8—42no—
306Q8—222no—
307Q8—441no—
308D4—222no—
309D4—442no—
310D4—442no—
311D4—441no—
312C2×C4—42no—
313C2×C4—42no—
314C2×C4—42no—
315C2×C4—222no—
316C2×C4—441no—
317C2×C4—442no—
318C2×C4—442no—
319C2×C4—442no—
320C2×C4(C22⋊D11)⋊C411yescharacteristic
321C2×C4(C22⋊D11)⋊C411yescharacteristic
322C2×C4#6696411yescharacteristic
323C2×C4#6696411yescharacteristic
324C2×C4#6696711yescharacteristic
325C2×C4C2×D4×D1111yescharacteristic
326C8—42no—
327C8—222no—
328C8(C22⋊D11)⋊C411yescharacteristic
329C8(C22⋊D11)⋊C411yescharacteristic
330C8C22×C4×D1111yescharacteristic
331C8C2×#434111yescharacteristic
332C22—41no—
333C22—442no—
334C22—1761no—
335C22#1062239811yescharacteristic
336C22#1062239811yescharacteristic
337C22C2×#6696711yescharacteristic
338C4—44no—
339C4—442no—
340C4—442no—
341C4—882no—
342C4#1062239811yescharacteristic
343C4#1062239811yescharacteristic
344C4C2×(C22⋊D11)⋊C411yescharacteristic
345C4C2×#6696411yescharacteristic
346C2—21no—
347C2—21no—
348C2—21no—
349C2—882no—
350C2C2×#1062239811yescharacteristic
subgroupG/H
centerC2C2×#10622398
commutatorC8×C11C23×C4
FrattiniC2×C8C23×D11
FittingC2×C11×#362C2
socleC2×C11C2×#442
prime radicalC2×#66957C22
cosocleC2×C8×C11C24
hypercenterC2×#362D11
hypocenterC11#33470
LCSG ▷ C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2 ◁ C22×C4 ◁ C22×C8 ◁ C2×#362

Complements

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

NH ≅ G/Ntype
3. #13077484C2semidirect
4. #13070510C2semidirect
5. #13070390C2semidirect
7. #13070220C2semidirect
8. C2×C11×#362C2semidirect
16. #10622797C22semidirect
18. C2×#66893C4semidirect
19. #10622792C4semidirect
21. C2×#66892C4semidirect
28. C11×#362C22semidirect
30. #10622150C22semidirect
31. #10622132C22semidirect
130. C2×#362D11semidirect
185. #362C2×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×#106227922
#130775322
#130774842
#130705102
#130703902
#130703532
#130702202
C2×C11×#3622
#3347011