Finite Group Databasebeta

← #14664839

Subgroups — #14664839

Order 2816.

422 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 422 conjugacy classes of subgroups — too many to draw. Only its 103 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13078197C211yesmaximal, characteristic
2C2×C22⋊(C11⋊C16)C211yesmaximal, characteristic, complemented
3#13066627C212yesmaximal, complemented
4#13066624C212yesmaximal, complemented
5C11×#1807C211yesmaximal, characteristic, complemented
6C23×C8×C11C2211yescharacteristic
7#10623322—21no—
8C2×#66957C411yescharacteristic, complemented
9C2×C11×#106—21no—
10C11×#380—21no—
11#10622729C411yescharacteristic, complemented
12#10622729C2211yescharacteristic
13#10622728C411yescharacteristic, complemented
14#10622728C2211yescharacteristic
15#10622727—21no—
16#10622727—21no—
17#10622726—21no—
18#10622719C411yescharacteristic, complemented
19C22×C11⋊C16—21no—
20C11×#340C2212yes—
21C22⋊(C11⋊C16)—21no—
22C22⋊(C11⋊C16)C2212yes—
23C23×C4×C11D411yescharacteristic
24C2×#4339—21no—
25C22×C8×C11—42no—
26C22×C8×C11C2×C411yescharacteristic
27C22×C8×C11C2×C411yescharacteristic
28C22×C8×C11D411yescharacteristic
29C22×C8×C11D411yescharacteristic
30C22×C8×C11D411yescharacteristic
31C22×C8×C11C2311yescharacteristic
32C2×C11×C4⋊C4—22no—
33C2×C11×C22⋊C4—41no—
34#67006—41no—
35#66983—21no—
36#66983—21no—
37#66982—41no—
38C4×C22⋊D11—41no—
39C4×C22⋊D11—41no—
40#66979—21no—
41#66977—21no—
42#66977—21no—
43C2×Dic44C2×C411yescharacteristic
44#66957—42no—
45C2×D88C2×C411yescharacteristic
46C2×#4314—21no—
47C11×#106—42no—
48C11×#95—41no—
49#66885—21no—
50#66885—21no—
51#66882C2×C411yescharacteristic
52#66882C2×C411yescharacteristic
53#66881—21no—
54#66880—21no—
55#66880—21no—
56C2×C11⋊C16—22no—
57C2×C11⋊C16—42no—
58#11885—111nomaximal, Sylow
59C24×C11D811yescharacteristic
60C22×C4×C11—41no—
61C22×C4×C11—41no—
62C22×C4×C11—42no—
63C22×C4×C11C22⋊C411yescharacteristic
64C22×C4×C11C22⋊C411yescharacteristic
65C22×C4×C11D811yescharacteristic
66C22×C4×C11SD1611yescharacteristic
67C22×C4×C11SD1611yescharacteristic
68C22×C4×C11C2×D411yescharacteristic
69C2×C22⋊D11—41no—
70C2×C22⋊D11—41no—
71C2×C22⋊D11—41no—
72#4339—42no—
73#4339—42no—
74C2×D44—21no—
75C2×C4×D11—41no—
76C2×Dic22—21no—
77C2×C8×C11—22no—
78C2×C8×C11—22no—
79C2×C8×C11—22no—
80C2×C8×C11—41no—
81C2×C8×C11—41no—
82C2×C8×C11—41no—
83C2×C8×C11C22⋊C411yescharacteristic
84C2×C8×C11C22⋊C411yescharacteristic
85C2×C8×C11C22×C411yescharacteristic
86C2×C8×C11C2×D411yescharacteristic
87C11×C4⋊C4—42no—
88C11×C4⋊C4—42no—
89C11×C22⋊C4—82no—
90C22⋊Dic11—41no—
91C22⋊Dic11—41no—
92C22⋊Dic11—41no—
93(C2×D11)⋊C4—41no—
94(C2×D11)⋊C4—41no—
95C4⋊Dic11—21no—
96C4⋊Dic11—21no—
97Dic11⋊C4—41no—
98Dic11⋊C4—41no—
99C4×Dic11—41no—
100Dic44—41no—
101D88—41no—
102#4314—42no—
103C11⋊C16—42no—
104#3050—111no—
105C2×C22⋊C16—111no—
106#1807D1111yescharacteristic, complemented
107#1348—112no—
108#1347—112no—
109C23×C11—22no—
110C23×C11—22no—
111C23×C11—41no—
112C23×C11#10211yescharacteristic
113C23×C11#10211yescharacteristic
114C23×C11C2×D811yescharacteristic
115C22×D11—41no—
116C2×C4×C11—21no—
117C2×C4×C11—21no—
118C2×C4×C11—21no—
119C2×C4×C11—21no—
120C2×C4×C11—21no—
121C2×C4×C11—21no—
122C2×C4×C11—41no—
123C2×C4×C11—41no—
124C2×C4×C11—41no—
125C2×C4×C11—82no—
126C2×C4×C11—82no—
127C2×C4×C11—82no—
128C2×C4×C11#10211yescharacteristic
129C2×C4×C11#10211yescharacteristic
130C2×C4×C11C2×C22⋊C411yescharacteristic
131C2×C4×C11C2×SD1611yescharacteristic
132C22⋊D11—82no—
133C22⋊D11—82no—
134C22⋊D11—82no—
135C2×Dic11—41no—
136C2×Dic11—41no—
137C2×Dic11—41no—
138D44—41no—
139D44—41no—
140C4×D11—82no—
141Dic22—41no—
142Dic22—41no—
143C8×C11—21no—
144C8×C11—21no—
145C8×C11—21no—
146C8×C11#9912yes—
147C2×#135—111no—
148C23×C8C2×D1111yescharacteristic
149#525—221no—
150C22×C16—221no—
151#467—111no—
152#467—111no—
153#466—111no—
154#466—111no—
155#465—221no—
156#465—221no—
157#427—111no—
158C2×#106—21no—
159#416—221no—
160#380—21no—
161C22⋊C16—112no—
162C22⋊C16—221no—
163#340C2×D1112yes—
164C22×C11—21no—
165C22×C11—21no—
166C22×C11—21no—
167C22×C11—21no—
168C22×C11—21no—
169C22×C11—21no—
170C22×C11—21no—
171C22×C11—44no—
172C22×C11#36012yes—
173C22×C11C2×#10211yescharacteristic
174C22×C11#50812yes—
175C2×D11—81no—
176C2×D11—81no—
177C2×D11—81no—
178C4×C11—21no—
179C4×C11—21no—
180C4×C11—21no—
181C4×C11—162no—
182C4×C11C2×#9911yescharacteristic
183C4×C11#42111yescharacteristic
184Dic11—81no—
185Dic11—81no—
186Dic11—81no—
187C2×#41—221no—
188C23×C4C22⋊D1111yescharacteristic
189#135—442no—
190C2×Q16—111no—
191C2×SD16—221no—
192C2×D8—111no—
193C22×C8—42no—
194C22×C8C4×D1111yescharacteristic
195C22×C8C4×D1111yescharacteristic
196C22×C8D4411yescharacteristic
197C22×C8D4411yescharacteristic
198C22×C8C22⋊D1111yescharacteristic
199C22×C8C22×D1111yescharacteristic
200#123—441no—
201C22⋊Q8—221no—
202C22⋊Q8—221no—
203#121—221no—
204#121—221no—
205#120—441no—
206C4×D4—441no—
207C4×D4—441no—
208#117—221no—
209C2×C4⋊C4—22no—
210C2×C22⋊C4—41no—
211C2×C16—222no—
212C2×C16—442no—
213#107—111no—
214#107—111no—
215#106—42no—
216#106—221no—
217#103—221no—
218#103—221no—
219#102—221no—
220#102—221no—
221#95—41no—
222C2×C11—22no—
223C2×C11—22no—
224C2×C11—41no—
225C2×C11#151911yescharacteristic
226C2×C11#213811yescharacteristic
227C2×C11C2×#36011yescharacteristic
228D11—161no—
229C24#432311yescharacteristic
230#41—442no—
231#41—442no—
232C2×Q8—221no—
233C2×D4—221no—
234C2×D4—441no—
235C2×D4—441no—
236C2×D4—441no—
237C22×C4—41no—
238C22×C4—41no—
239C22×C4—42no—
240C22×C4—441no—
241C22×C4(C2×D11)⋊C411yescharacteristic
242C22×C4(C2×D11)⋊C411yescharacteristic
243C22×C4#432311yescharacteristic
244C22×C4#432511yescharacteristic
245C22×C4#432511yescharacteristic
246C22×C4C2×C22⋊D1111yescharacteristic
247Q16—441no—
248SD16—442no—
249D8—441no—
250C2×C8—22no—
251C2×C8—22no—
252C2×C8—22no—
253C2×C8—41no—
254C2×C8—41no—
255C2×C8—41no—
256C2×C8(C2×D11)⋊C411yescharacteristic
257C2×C8(C2×D11)⋊C411yescharacteristic
258C2×C8C2×C4×D1111yescharacteristic
259C2×C8C2×D4411yescharacteristic
260C4⋊C4—42no—
261C4⋊C4—42no—
262C4⋊C4—221no—
263C4⋊C4—221no—
264C4⋊C4—441no—
265C4⋊C4—441no—
266C22⋊C4—82no—
267C22⋊C4—441no—
268C22⋊C4—441no—
269C22⋊C4—441no—
270C22⋊C4—441no—
271C22⋊C4—441no—
272C42—441no—
273C16—442no—
274C11#1188511yescharacteristic, complemented, Sylow
275C23—22no—
276C23—22no—
277C23—41no—
278C23—441no—
279C23#6687311yescharacteristic
280C23#6687311yescharacteristic
281C23C2×#432311yescharacteristic
282Q8—441no—
283Q8—441no—
284D4—441no—
285D4—441no—
286D4—882no—
287D4—882no—
288D4—882no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—41no—
296C2×C4—41no—
297C2×C4—41no—
298C2×C4—82no—
299C2×C4—82no—
300C2×C4—82no—
301C2×C4—441no—
302C2×C4—441no—
303C2×C4—441no—
304C2×C4—882no—
305C2×C4#6687311yescharacteristic
306C2×C4#6687311yescharacteristic
307C2×C4C2×(C2×D11)⋊C411yescharacteristic
308C2×C4C2×#432511yescharacteristic
309C8—21no—
310C8—21no—
311C8—21no—
312C8#6687012yes—
313C22—21no—
314C22—21no—
315C22—21no—
316C22—21no—
317C22—21no—
318C22—21no—
319C22—21no—
320C22—44no—
321C22—881no—
322C22—881no—
323C22—881no—
324C22#1062212612yes—
325C22C2×#6687311yescharacteristic
326C22#1062280712yes—
327C4—21no—
328C4—21no—
329C4—21no—
330C4—162no—
331C4—881no—
332C4—881no—
333C4—881no—
334C4C2×#6687011yescharacteristic
335C4#1062261811yescharacteristic
336C2—22no—
337C2—22no—
338C2—41no—
339C2—1761no—
340C2#1306718311yescharacteristic
341C2#1307032111yescharacteristic
342C2C2×#1062212611yescharacteristic
subgroupG/H
centerC22C2×#66873
commutatorC2×C8×C11C22×C4
FrattiniC22×C8C22×D11
FittingC11×#1807C2
socleC22×C11C2×#102
prime radical#13078197C2
cosocleC22×C8×C11C23
hypercenter#1807D11
hypocenterC11#11885
LCSG ▷ C2×C8×C11 ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ C23×C8 ◁ #1807

Complements

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

NH ≅ G/Ntype
2. C2×C22⋊(C11⋊C16)C2semidirect
3. #13066627C2semidirect
4. #13066624C2semidirect
5. C11×#1807C2semidirect
8. C2×#66957C4semidirect
11. #10622729C4semidirect
13. #10622728C4semidirect
18. #10622719C4semidirect
106. #1807D11semidirect
274. C11#11885semidirect

Maximal subgroups

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

subgroupindex
#130781972
C2×C22⋊(C11⋊C16)2
#130666272
#130666242
C11×#18072
#1188511