Finite Group Databasebeta

← #14907241

Subgroups — #14907241

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
1#13077533C211yesmaximal, characteristic
2#13077484C211yesmaximal, characteristic, complemented
3#13070508C218yesmaximal, complemented
4#13070389C211yesmaximal, characteristic, complemented
5C2×#10622203C211yesmaximal, characteristic, complemented
6#13070352C211yesmaximal, characteristic
7#13070220C211yesmaximal, characteristic, complemented
8C2×C11×#510C211yesmaximal, characteristic
9C2×C11×#135C2211yescharacteristic
10C22×C11×Q16C2211yescharacteristic
11#10623350—21no—
12#10623343—21no—
13C11×#510C414yescomplemented
14C11×#510C2214yes—
15C2×C11×Q32C412yescomplemented
16C2×C11×SD32C412yescomplemented
17C2×C11×M32C2211yescharacteristic
18#10622849—21no—
19#10622838—21no—
20#10622810C2214yes—
21#10622809—22no—
22#10622797C2214yescomplemented
23Q16×Dic11—22no—
24C2×#66883C2211yescharacteristic
25#10622719C2211yescharacteristic
26#10622714C2211yescharacteristic
27C2×#66876C2211yescharacteristic
28#10622204C2214yes—
29#10622203C2214yescomplemented
30#10622151C2214yescomplemented
31#10622150C2214yescomplemented
32C2×C11×#41—21no—
33C22×Q8×C11—21no—
34C11×#135—21no—
35C11×#135—21no—
36C11×#135C2×C412yes—
37C11×#135C2312yes—
38C2×C11×Q16—21no—
39C2×C11×Q16—21no—
40C2×C11×Q16—21no—
41C2×C11×Q16C2×C412yes—
42C2×C11×Q16C2×C411yescharacteristic
43C2×C11×Q16C2×C412yes—
44C2×C11×Q16C2312yes—
45C2×C11×SD16—21no—
46C2×C11×D8C2×C411yescharacteristic
47C22×C8×C11C2311yescharacteristic
48#67001—24no—
49#67001—42no—
50Q8×Dic11—24no—
51Q8×Dic11—42no—
52#66979—21no—
53#66979—42no—
54#66979D411yescharacteristic
55C2×#4318—21no—
56C2×#4318—42no—
57C2×#4318D411yescharacteristic
58C11×Q32C2×C418yes—
59C11×SD32C2×C418yes—
60C11×M32C2×C412yes—
61C11×M32C2312yes—
62C2×C11×C16C2×C412yes—
63#66901—24no—
64#66899—24no—
65#66883—21no—
66#66883C2312yes—
67#66882—21no—
68#66881C2312yes—
69#66879C2312yes—
70C8×Dic11D412yes—
71#66876—21no—
72#66876C2312yes—
73C2×C11⋊C16—21no—
74#33470—111nomaximal, Sylow
75C11×#41—22no—
76C11×#41—22no—
77C11×#41—41no—
78C11×#41—41no—
79C2×Q8×C11—21no—
80C2×Q8×C11—22no—
81C2×Q8×C11—22no—
82C2×Q8×C11—22no—
83C2×Q8×C11—41no—
84C2×Q8×C11—41no—
85C2×Q8×C11—41no—
86C2×D4×C11—21no—
87C2×D4×C11—41no—
88C22×C4×C11—41no—
89C22×C4×C11—41no—
90C22×C4×C11C2×D411yescharacteristic
91C11×Q16—22no—
92C11×Q16—22no—
93C11×Q16—21no—
94C11×Q16—22no—
95C11×Q16C22×C414yes—
96C11×Q16C22×C412yes—
97C11×SD16—22no—
98C11×SD16—22no—
99C11×D8—21no—
100C11×D8C22×C412yes—
101C2×C8×C11C22×C411yescharacteristic
102C2×C8×C11C22×C411yescharacteristic
103C2×C8×C11C2×D411yescharacteristic
104C2×C8×C11#4111yescharacteristic
105C2×C8×C11#4111yescharacteristic
106C2×C8×C11C2411yescharacteristic
107C22⋊Dic11—21no—
108C22⋊Dic11—41no—
109C4⋊Dic11—21no—
110C4⋊Dic11—22no—
111C4⋊Dic11—44no—
112C4×Dic11—44no—
113C4×Dic11—41no—
114C4×Dic11C2×D412yes—
115#4318—21no—
116#4318—21no—
117#4318—22no—
118#4318—44no—
119#4318—41no—
120C2×C11⋊C8—44no—
121C2×C11⋊C8—41no—
122C2×C11⋊C8C2×D412yes—
123C11×C16C22×C414yes—
124C11⋊C16—22no—
125C2×#510D1111yescharacteristic
126#2957—111no—
127#2950—111no—
128#2180—118no—
129#2155—111no—
130C2×#362—111no—
131#2145—111no—
132#2110—111no—
133C23×C11—41no—
134C23×C11AGL(1,ℤ/8)11yescharacteristic
135Q8×C11—22no—
136Q8×C11—24no—
137Q8×C11—42no—
138Q8×C11—42no—
139Q8×C11—42no—
140Q8×C11—41no—
141D4×C11—22no—
142D4×C11—42no—
143D4×C11—42no—
144D4×C11—41no—
145C2×C4×C11—42no—
146C2×C4×C11—41no—
147C2×C4×C11—42no—
148C2×C4×C11—42no—
149C2×C4×C11—42no—
150C2×C4×C11—42no—
151C2×C4×C11C4×D411yescharacteristic
152C2×C4×C11C4×D411yescharacteristic
153C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
154C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
155C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
156C2×C4×C11C22×D411yescharacteristic
157C2×Dic11—22no—
158C2×Dic11—42no—
159C8×C11C4×D411yescharacteristic
160C8×C11C4×D411yescharacteristic
161C8×C11C23×C411yescharacteristic
162C8×C11C2×#4111yescharacteristic
163C11⋊C8—22no—
164C11⋊C8—42no—
165C2×#135C2×D1111yescharacteristic
166C22×Q16C2×D1111yescharacteristic
167#568—221no—
168#519—221no—
169#510Dic1114yescomplemented
170#510C2×D1114yes—
171C2×Q32Dic1112yescomplemented
172C2×SD32Dic1112yescomplemented
173C2×M32—111no—
174C2×M32C2×D1111yescharacteristic
175#444—114no—
176#443—222no—
177#441—114no—
178C4×Q16—222no—
179C2×#108—111no—
180#427—111no—
181#421—221no—
182#419—221no—
183#405—111no—
184#365—114no—
185#362—114no—
186#360—114no—
187#347—114no—
188C22×C11—41no—
189C22×C11—42no—
190C22×C11—161no—
191C22×C11#44211yescharacteristic
192C22×C11#44211yescharacteristic
193C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
194C4×C11—42no—
195C4×C11—44no—
196C4×C11#44211yescharacteristic
197C4×C11#44211yescharacteristic
198C4×C11C2×C4×D411yescharacteristic
199C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
200Dic11—42no—
201Dic11—82no—
202C2×#41—21no—
203C22×Q8—21no—
204#135—21no—
205#135—21no—
206#135C2×Dic1112yes—
207#135C22×D1112yes—
208C2×Q16—21no—
209C2×Q16—21no—
210C2×Q16—21no—
211C2×Q16C2×Dic1112yes—
212C2×Q16C2×Dic1112yes—
213C2×Q16C2×Dic1111yescharacteristic
214C2×Q16C22×D1112yes—
215C2×SD16—21no—
216C2×D8C2×Dic1111yescharacteristic
217#131—224no—
218#131—442no—
219C2×M16—111no—
220C2×M16—221no—
221C2×M16—442no—
222C22×C8C22×D1111yescharacteristic
223C4×Q8—224no—
224C4×Q8—442no—
225#117—111no—
226#117—221no—
227#117—442no—
228Q32C2×Dic1118yes—
229SD32C2×Dic1118yes—
230M32—112no—
231M32—221no—
232M32C2×Dic1112yes—
233M32C22×D1112yes—
234C2×C16—221no—
235C2×C16C2×Dic1112yes—
236#108—112no—
237#108—221no—
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×C11—82no—
248C2×C11C2×#44211yescharacteristic
249#41—22no—
250#41—22no—
251#41—41no—
252#41—41no—
253C2×Q8—21no—
254C2×Q8—22no—
255C2×Q8—22no—
256C2×Q8—22no—
257C2×Q8—41no—
258C2×Q8—41no—
259C2×Q8—41no—
260C2×D4—21no—
261C2×D4—41no—
262C22×C4—41no—
263C22×C4—41no—
264C22×C4D4×D1111yescharacteristic
265Q16—22no—
266Q16—22no—
267Q16—21no—
268Q16—22no—
269Q16C22×Dic1114yes—
270Q16C22×Dic1112yes—
271SD16—22no—
272SD16—22no—
273D8—21no—
274D8C22×Dic1112yes—
275M16—221no—
276M16—221no—
277M16—222no—
278M16—444no—
279M16—441no—
280C2×C8—112no—
281C2×C8—444no—
282C2×C8—441no—
283C2×C8D4×D1111yescharacteristic
284C2×C8#434111yescharacteristic
285C2×C8#434111yescharacteristic
286C2×C8C22×Dic1111yescharacteristic
287C2×C8C22×Dic1111yescharacteristic
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—222no—
298C16C22×Dic1114yes—
299C11#3347011yescharacteristic, complemented, Sylow
300C23—41no—
301C23#6696411yescharacteristic
302Q8—22no—
303Q8—24no—
304Q8—42no—
305Q8—42no—
306Q8—41no—
307Q8—42no—
308D4—22no—
309D4—42no—
310D4—42no—
311D4—41no—
312C2×C4—41no—
313C2×C4—42no—
314C2×C4—42no—
315C2×C4—42no—
316C2×C4—42no—
317C2×C4—42no—
318C2×C4—222no—
319C2×C4—442no—
320C2×C4#6696411yescharacteristic
321C2×C4#6696411yescharacteristic
322C2×C4#6696411yescharacteristic
323C2×C4D4×Dic1111yescharacteristic
324C2×C4D4×Dic1111yescharacteristic
325C2×C4C2×D4×D1111yescharacteristic
326C8—222no—
327C8—442no—
328C8D4×Dic1111yescharacteristic
329C8D4×Dic1111yescharacteristic
330C8C2×#434111yescharacteristic
331C8C23×Dic1111yescharacteristic
332C22—41no—
333C22—42no—
334C22—161no—
335C22#1062276511yescharacteristic
336C22#1062276511yescharacteristic
337C22C2×#6696411yescharacteristic
338C4—42no—
339C4—44no—
340C4—442no—
341C4—882no—
342C4#1062276511yescharacteristic
343C4#1062276511yescharacteristic
344C4C2×#6696411yescharacteristic
345C4C2×D4×Dic1111yescharacteristic
346C2—21no—
347C2—21no—
348C2—21no—
349C2—82no—
350C2C2×#1062276511yescharacteristic
subgroupG/H
centerC2C2×#10622765
commutatorC8×C11C23×C4
FrattiniC2×C8C23×D11
FittingC2×C11×#510C2
socleC2×C11C2×#442
prime radicalC2×C11×#135C22
cosocleC2×C8×C11C24
hypercenterC2×#510D11
hypocenterC11#33470
LCSG ▷ C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2 ◁ C22×C4 ◁ C22×C8 ◁ C2×#510

Complements

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

NH ≅ G/Ntype
2. #13077484C2semidirect
3. #13070508C2semidirect
4. #13070389C2semidirect
5. C2×#10622203C2semidirect
7. #13070220C2semidirect
13. C11×#510C4semidirect
15. C2×C11×Q32C4semidirect
16. C2×C11×SD32C4semidirect
22. #10622797C22semidirect
29. #10622203C22semidirect
30. #10622151C22semidirect
31. #10622150C22semidirect
169. #510Dic11semidirect
171. C2×Q32Dic11semidirect
172. C2×SD32Dic11semidirect
299. C11#33470semidirect

Maximal subgroups

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

subgroupindex
#130775332
#130774842
#130705082
#130703892
C2×#106222032
#130703522
#130702202
C2×C11×#5102
#3347011