Finite Group Databasebeta

← #14644841

Subgroups — #14644841

Order 2816.

482 conjugacy classes of subgroups.

The subgroup lattice has 338 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13077328C211yesmaximal, characteristic
2C4⋊C4×C11⋊C8C211yesmaximal, characteristic, complemented
3#13067265C211yesmaximal, characteristic
4#13066900C211yesmaximal, characteristic, complemented
5#13066519C211yesmaximal, characteristic, complemented
6#13066512C211yesmaximal, characteristic, complemented
7C11×#1502C211yesmaximal, characteristic
8C11×#532C2211yescharacteristic
9C2×#67001—21no—
10C11×#431C2211yescharacteristic
11C4×C11×C4⋊C4C2211yescharacteristic
12#10622847—21no—
13#10622625—21no—
14#10622625C412yescomplemented
15D4×C11⋊C8—21no—
16D4×C11⋊C8C412yescomplemented
17#10622538C2211yescharacteristic
18#10622537C2211yescharacteristic
19C2×C4⋊(C11⋊C8)C2211yescharacteristic
20C2×C4×C11⋊C8—21no—
21C2×C4×C11⋊C8C2211yescharacteristic
22C11×#327C414yes—
23#10622185C412yescomplemented
24#10622182C412yescomplemented
25#10622162—21no—
26#10622092—21no—
27C8×C11⋊C8—21no—
28C2×C11×#41—21no—
29C11×C4⋊Q8C2×C411yescharacteristic
30C11×#127C2×C411yescharacteristic
31C11×#124—21no—
32C11×#121—21no—
33C11×#121C2×C412yes—
34C4×D4×C11—21no—
35C4×D4×C11C2×C412yes—
36C2×C11×C4⋊C4—21no—
37C2×C42×C11—21no—
38C2×C42×C11C2311yescharacteristic
39#67001—42no—
40#67001—42no—
41C2×#4318—21no—
42C2×#4318—22no—
43C22×C11⋊C8—21no—
44C22×C11⋊C8—22no—
45C22×C11⋊C8D411yescharacteristic
46C22×C11⋊C8D411yescharacteristic
47C11×C4⋊C8—21no—
48C11×C22⋊C8C2×C412yes—
49C4×C8×C11—21no—
50C11×#95C2×C412yes—
51C22⋊(C11⋊C8)—21no—
52C22⋊(C11⋊C8)—22no—
53C22⋊(C11⋊C8)—22no—
54C4⋊(C11⋊C8)—21no—
55C4⋊(C11⋊C8)—21no—
56C4⋊(C11⋊C8)C2×C412yes—
57C4⋊(C11⋊C8)C2×C412yes—
58C4⋊(C11⋊C8)C2×C412yes—
59C4×C11⋊C8—21no—
60C4×C11⋊C8—42no—
61C4×C11⋊C8C2×C411yescharacteristic
62C4×C11⋊C8C2×C411yescharacteristic
63C4×C11⋊C8D411yescharacteristic
64C4×C11⋊C8D411yescharacteristic
65#8251—111nomaximal, Sylow
66C11×#41—41no—
67C11×#41—41no—
68C11×#41—41no—
69C11×#41—41no—
70C2×Q8×C11—21no—
71C2×D4×C11—22no—
72C2×D4×C11—21no—
73C2×D4×C11—21no—
74C2×D4×C11C4212yes—
75C22×C4×C11—22no—
76C22×C4×C11—22no—
77C22×C4×C11C22×C411yescharacteristic
78C22×C4×C11C2×D411yescharacteristic
79C22×C4×C11#4111yescharacteristic
80C2×C8×C11—22no—
81C11×C4⋊C4—24no—
82C11×C4⋊C4—21no—
83C11×C4⋊C4C4212yes—
84C11×C22⋊C4—22no—
85C11×C22⋊C4—22no—
86C42×C11—41no—
87C42×C11—41no—
88C42×C11C22×C411yescharacteristic
89C42×C11C22×C411yescharacteristic
90C42×C11C2×D411yescharacteristic
91C42×C11#4111yescharacteristic
92#4318—44no—
93#4318—41no—
94#4318—41no—
95C2×C11⋊C8—22no—
96C2×C11⋊C8—22no—
97C2×C11⋊C8—22no—
98C2×C11⋊C8—21no—
99C2×C11⋊C8—21no—
100C2×C11⋊C8—44no—
101C2×C11⋊C8—41no—
102C2×C11⋊C8—41no—
103C2×C11⋊C8C22⋊C411yescharacteristic
104C2×C11⋊C8C22⋊C411yescharacteristic
105C2×C11⋊C8C22⋊C411yescharacteristic
106C2×C11⋊C8C22⋊C411yescharacteristic
107C2×C11⋊C8D812yes—
108C2×C11⋊C8SD1612yes—
109#2931—111no—
110C8×C4⋊C4—111no—
111#1540—111no—
112#1502D1111yescharacteristic
113#1450—111no—
114#1303—111no—
115#1301—111no—
116C23×C11—22no—
117C23×C11C4×D411yescharacteristic
118Q8×C11—41no—
119Q8×C11—41no—
120D4×C11—42no—
121D4×C11—42no—
122D4×C11—42no—
123D4×C11—41no—
124D4×C11—41no—
125D4×C11—42no—
126C2×C4×C11—22no—
127C2×C4×C11—24no—
128C2×C4×C11—22no—
129C2×C4×C11—41no—
130C2×C4×C11—42no—
131C2×C4×C11—42no—
132C2×C4×C11—42no—
133C2×C4×C11—42no—
134C2×C4×C11C2×C4211yescharacteristic
135C2×C4×C11C2×C22⋊C411yescharacteristic
136C2×C4×C11#11711yescharacteristic
137C2×C4×C11C4×D411yescharacteristic
138C2×C4×C11C4×D411yescharacteristic
139C2×C4×C11C4×D411yescharacteristic
140C2×C4×C11C2×D811yescharacteristic
141C2×C4×C11C2×SD1611yescharacteristic
142C2×C4×C11#13511yescharacteristic
143C2×C4×C11#13511yescharacteristic
144C8×C11—42no—
145C11⋊C8—21no—
146C11⋊C8—21no—
147C11⋊C8—42no—
148C11⋊C8—42no—
149C11⋊C8—42no—
150C11⋊C8#10212yes—
151C11⋊C8#10212yes—
152C2×#131—221no—
153#532C2×D1111yescharacteristic
154#436—112no—
155#436—221no—
156C8×D4—112no—
157C8×D4—221no—
158#431—111no—
159#431C2×D1111yescharacteristic
160#423—111no—
161C2×C4⋊C8—111no—
162#408—221no—
163C2×C4×C8—111no—
164C2×C4×C8—221no—
165C4×C4⋊C4C2×D1111yescharacteristic
166#336—221no—
167#332—112no—
168#331—112no—
169#327Dic1114yes—
170#322—221no—
171C82—221no—
172C22×C11—21no—
173C22×C11—21no—
174C22×C11—42no—
175C22×C11—42no—
176C22×C11—42no—
177C22×C11C4×C22⋊C411yescharacteristic
178C22×C11C4×D811yescharacteristic
179C22×C11C4×SD1611yescharacteristic
180C4×C11—21no—
181C4×C11—21no—
182C4×C11—21no—
183C4×C11—44no—
184C4×C11—42no—
185C4×C11C2×#10211yescharacteristic
186C4×C11#41611yescharacteristic
187C4×C11C4×D811yescharacteristic
188C4×C11C4×SD1611yescharacteristic
189C4×C11#44312yes—
190C2×#41—21no—
191#131—442no—
192#131—442no—
193C2×M16—222no—
194C2×M16—221no—
195C22×C8—111no—
196C22×C8—111no—
197C22×C8—222no—
198C22×C8—221no—
199C4⋊Q8C4×D1111yescharacteristic
200#127C4×D1111yescharacteristic
201#124—21no—
202#121—21no—
203#121C2×Dic1112yes—
204C4×D4—21no—
205C4×D4C4×D1112yes—
206C2×C4⋊C4—21no—
207C2×C42—21no—
208C2×C42C22×D1111yescharacteristic
209C4⋊C8—21no—
210C4⋊C8—112no—
211C4⋊C8—112no—
212C4⋊C8—112no—
213C4⋊C8—221no—
214C4⋊C8—221no—
215C22⋊C8—222no—
216C22⋊C8—222no—
217C22⋊C8—221no—
218C22⋊C8C2×Dic1112yes—
219C4×C8—21no—
220C4×C8—111no—
221C4×C8—111no—
222C4×C8—111no—
223C4×C8—111no—
224C4×C8—221no—
225C4×C8—442no—
226#95C2×Dic1112yes—
227C2×C11—21no—
228C2×C11—21no—
229C2×C11—82no—
230C2×C11#175711yescharacteristic
231C2×C11C4×#10211yescharacteristic
232C2×C11#176411yescharacteristic
233#41—41no—
234#41—41no—
235#41—41no—
236#41—41no—
237C2×Q8—21no—
238C2×D4—22no—
239C2×D4—21no—
240C2×D4—21no—
241C2×D4C4×Dic1112yes—
242C22×C4—22no—
243C22×C4—22no—
244C22×C4D4×D1111yescharacteristic
245C22×C4#434111yescharacteristic
246C22×C4C22×Dic1111yescharacteristic
247M16—444no—
248M16—441no—
249M16—441no—
250C2×C8—22no—
251C2×C8—111no—
252C2×C8—111no—
253C2×C8—112no—
254C2×C8—112no—
255C2×C8—111no—
256C2×C8—111no—
257C2×C8—221no—
258C2×C8—221no—
259C2×C8—222no—
260C2×C8—222no—
261C2×C8—222no—
262C2×C8—444no—
263C2×C8—441no—
264C2×C8—441no—
265C4⋊C4—24no—
266C4⋊C4—21no—
267C4⋊C4C4×Dic1112yes—
268C22⋊C4—22no—
269C22⋊C4—22no—
270C42—41no—
271C42—41no—
272C42C2×C4×D1111yescharacteristic
273C42C2×C4×D1111yescharacteristic
274C42D4×D1111yescharacteristic
275C42#434111yescharacteristic
276C11#825111yescharacteristic, complemented, Sylow
277C23—22no—
278C23D4×Dic1111yescharacteristic
279Q8—41no—
280Q8—41no—
281D4—42no—
282D4—42no—
283D4—42no—
284D4—41no—
285D4—41no—
286D4—42no—
287C2×C4—22no—
288C2×C4—24no—
289C2×C4—22no—
290C2×C4—41no—
291C2×C4—42no—
292C2×C4—42no—
293C2×C4—42no—
294C2×C4—42no—
295C2×C4#6693011yescharacteristic
296C2×C4C22⋊C4×D1111yescharacteristic
297C2×C4(C22⋊D11)⋊C411yescharacteristic
298C2×C4(C22⋊D11)⋊C411yescharacteristic
299C2×C4D8×D1111yescharacteristic
300C2×C4#6696511yescharacteristic
301C2×C4SD16×D1111yescharacteristic
302C2×C4#6696911yescharacteristic
303C2×C4C2×C4×Dic1111yescharacteristic
304C2×C4D4×Dic1111yescharacteristic
305C8—42no—
306C8—112no—
307C8—112no—
308C8—221no—
309C8—221no—
310C8—442no—
311C8—442no—
312C8—442no—
313C22—21no—
314C22—21no—
315C22—42no—
316C22—42no—
317C22—42no—
318C22C22⋊C4×Dic1111yescharacteristic
319C22D8×Dic1111yescharacteristic
320C22SD16×Dic1111yescharacteristic
321C4—21no—
322C4—21no—
323C4—21no—
324C4—44no—
325C4—42no—
326C4#1062236911yescharacteristic
327C4#1062237111yescharacteristic
328C4D11×#10211yescharacteristic
329C4#1062238511yescharacteristic
330C4#1062243712yes—
331C2—21no—
332C2—21no—
333C2—82no—
334C2#1306841811yescharacteristic
335C2#102×Dic1111yescharacteristic
336C2#1306845411yescharacteristic
subgroupG/H
centerC2×C4C22⋊C4×D11
commutatorC2×C4×C11C2×C42
FrattiniC2×C42C22×D11
FittingC11×#1502C2
socleC22×C11C4×C22⋊C4
prime radicalC11×#532C22
cosocleC2×C42×C11C23
hypercenter#1502D11
hypocenterC11#8251
LCSG ▷ C2×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1502

Complements

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

NH ≅ G/Ntype
2. C4⋊C4×C11⋊C8C2semidirect
4. #13066900C2semidirect
5. #13066519C2semidirect
6. #13066512C2semidirect
14. #10622625C4semidirect
16. D4×C11⋊C8C4semidirect
23. #10622185C4semidirect
24. #10622182C4semidirect
276. C11#8251semidirect

Maximal subgroups

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

subgroupindex
#130773282
C4⋊C4×C11⋊C82
#130672652
#130669002
#130665192
#130665122
C11×#15022
#825111