Finite Group Databasebeta

← #14650526

Subgroups — #14650526

Order 2816.

488 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#13078413C211yesmaximal, characteristic
2#13077640C211yesmaximal, characteristic
3#13067179C211yesmaximal, characteristic, complemented
4#13067018C211yesmaximal, characteristic, complemented
5#13066513C211yesmaximal, characteristic, complemented
6#13066474C211yesmaximal, characteristic, complemented
7C11×#1804C211yesmaximal, characteristic
8C2×C4×D4×C11C2211yescharacteristic
9#10623001C2211yescharacteristic
10C2×C11×C4⋊C8C2211yescharacteristic
11C2×C11×#102—21no—
12C11×#382C2211yescharacteristic
13#10622828—21no—
14C2×C22⋊(C11⋊C8)—22no—
15D4×C11⋊C8—22no—
16D4×C11⋊C8—22no—
17#10622622—22no—
18#10622621C412yescomplemented
19#10622620C412yescomplemented
20#10622577—21no—
21#10622538C2211yescharacteristic
22#10622538C2211yescharacteristic
23#10622537C2211yescharacteristic
24C11×#340—21no—
25#10622122—22no—
26#10622090—22no—
27C22×D4×C11D411yescharacteristic
28C23×C4×C11—21no—
29C22×C8×C11—21no—
30C4×D4×C11—21no—
31C4×D4×C11—21no—
32C4×D4×C11C2×C412yes—
33C4×D4×C11D412yes—
34C2×C11×C4⋊C4—21no—
35C2×C11×C4⋊C4D411yescharacteristic
36C2×C11×C22⋊C4—21no—
37C2×C42×C11C2311yescharacteristic
38#66979—21no—
39#66977—21no—
40#66977—21no—
41C2×#4318—21no—
42C22×C11⋊C8—24no—
43#66923—21no—
44#66922C2×C411yescharacteristic
45#66922C2×C411yescharacteristic
46C4×Dic22—21no—
47C4×Dic22—21no—
48C11×C4⋊C8—21no—
49C11×C4⋊C8—21no—
50C11×#102—42no—
51C11×#95—21no—
52C11×#95—21no—
53#66896—22no—
54#66896—22no—
55C22⋊(C11⋊C8)—24no—
56C22⋊(C11⋊C8)—21no—
57C22⋊(C11⋊C8)D412yes—
58#66872—22no—
59#66871—22no—
60C4⋊(C11⋊C8)—21no—
61C4⋊(C11⋊C8)—21no—
62C4⋊(C11⋊C8)—21no—
63C4⋊(C11⋊C8)C2×C412yes—
64C4×C11⋊C8—21no—
65C4×C11⋊C8D412yes—
66#9303—111nomaximal, Sylow
67C24×C11—21no—
68C2×D4×C11—21no—
69C2×D4×C11—21no—
70C2×D4×C11—21no—
71C2×D4×C11C22⋊C412yes—
72C2×D4×C11SD1612yes—
73C2×D4×C11Q1612yes—
74C22×C4×C11—21no—
75C22×C4×C11—22no—
76C22×C4×C11—22no—
77C22×C4×C11—41no—
78C22×C4×C11—82no—
79C22×C4×C11C2×D411yescharacteristic
80C22×C4×C11C2×D411yescharacteristic
81C22×C4×C11#4111yescharacteristic
82C2×Dic22—21no—
83C2×Dic22—21no—
84C2×C8×C11—41no—
85C2×C8×C11—41no—
86C2×C8×C11—41no—
87C11×C4⋊C4—21no—
88C11×C4⋊C4—41no—
89C11×C4⋊C4—41no—
90C11×C4⋊C4C22⋊C412yes—
91C11×C22⋊C4—22no—
92C11×C22⋊C4—22no—
93C42×C11C22×C411yescharacteristic
94C42×C11C2×D411yescharacteristic
95C42×C11C2×D411yescharacteristic
96C42×C11#4111yescharacteristic
97C22⋊Dic11—41no—
98C4⋊Dic11—21no—
99C4⋊Dic11—21no—
100C4⋊Dic11—21no—
101C4⋊Dic11—21no—
102Dic11⋊C4—41no—
103Dic11⋊C4—41no—
104C4×Dic11—41no—
105#4318—41no—
106#4318—41no—
107C2×C11⋊C8—22no—
108C2×C11⋊C8—22no—
109C2×C11⋊C8—22no—
110C2×C11⋊C8—84no—
111#3077—111no—
112#2972—111no—
113#1804D1111yescharacteristic
114#1518—111no—
115#1481—111no—
116#1301—111no—
117#1286—111no—
118C23×C11—22no—
119C23×C11—22no—
120C23×C11—22no—
121C23×C11—81no—
122C23×C11—81no—
123C23×C11#12111yescharacteristic
124D4×C11—22no—
125D4×C11—22no—
126D4×C11—22no—
127D4×C11#10314yes—
128C2×C4×C11—22no—
129C2×C4×C11—41no—
130C2×C4×C11—41no—
131C2×C4×C11—44no—
132C2×C4×C11—82no—
133C2×C4×C11—81no—
134C2×C4×C11—81no—
135C2×C4×C11—81no—
136C2×C4×C11—81no—
137C2×C4×C11C2×C22⋊C411yescharacteristic
138C2×C4×C11C4×D411yescharacteristic
139C2×C4×C11C4×D411yescharacteristic
140C2×C4×C11#12011yescharacteristic
141C2×C4×C11#12111yescharacteristic
142C2×C4×C11#12311yescharacteristic
143C2×C4×C11C2×SD1611yescharacteristic
144C2×C4×C11C2×Q1611yescharacteristic
145C2×C4×C11#13511yescharacteristic
146C2×C4×C11#13511yescharacteristic
147C2×Dic11—41no—
148C2×Dic11—41no—
149Dic22—42no—
150Dic22—81no—
151C8×C11—81no—
152C11⋊C8—42no—
153C11⋊C8—42no—
154C11⋊C8—42no—
155#533—111no—
156C2×C4×D4C2×D1111yescharacteristic
157#478—222no—
158#476—112no—
159#474—112no—
160C8×D4—222no—
161C8×D4—222no—
162#431—111no—
163#431—111no—
164#428—221no—
165#423—111no—
166C2×C4⋊C8C2×D1111yescharacteristic
167#418—221no—
168C2×#102—21no—
169C2×C22⋊C8—222no—
170#382C2×D1111yescharacteristic
171#340—21no—
172#328—222no—
173Q8⋊C8—222no—
174C22×C11—21no—
175C22×C11—21no—
176C22×C11—24no—
177C22×C11—42no—
178C22×C11—42no—
179C22×C11—82no—
180C22×C11—82no—
181C22×C11#38611yescharacteristic
182C22×C11#46511yescharacteristic
183C22×C11#46711yescharacteristic
184C4×C11—21no—
185C4×C11—21no—
186C4×C11—21no—
187C4×C11—21no—
188C4×C11—42no—
189C4×C11—161no—
190C4×C11C2×#10311yescharacteristic
191C4×C11#41611yescharacteristic
192C4×C11#46511yescharacteristic
193C4×C11#46711yescharacteristic
194Dic11—81no—
195Dic11—81no—
196C22×D4C22⋊D1111yescharacteristic
197C23×C4—21no—
198C2×M16—221no—
199C22×C8—21no—
200C22×C8—224no—
201C4⋊Q8—111no—
202C4⋊Q8—111no—
203#125—221no—
204C22⋊Q8—221no—
205C22⋊Q8—221no—
206C4×Q8—221no—
207C4×Q8—221no—
208C4×D4—21no—
209C4×D4—21no—
210C4×D4C4×D1112yes—
211C4×D4D4412yes—
212#117—221no—
213C2×C4⋊C4—21no—
214C2×C4⋊C4C22⋊D1111yescharacteristic
215C2×C22⋊C4—21no—
216C2×C42C22×D1111yescharacteristic
217#107—222no—
218#106—222no—
219C4⋊C8—21no—
220C4⋊C8—21no—
221C4⋊C8—112no—
222C4⋊C8—221no—
223C4⋊C8—221no—
224C4⋊C8—221no—
225#102—42no—
226#102—222no—
227#102—222no—
228C22⋊C8—112no—
229C22⋊C8—224no—
230C22⋊C8—221no—
231C4×C8—112no—
232C4×C8—221no—
233#95—21no—
234#95—21no—
235C2×C11—21no—
236C2×C11—21no—
237C2×C11—44no—
238C2×C11#188111yescharacteristic
239C2×C11#189211yescharacteristic
240C2×C11#190411yescharacteristic
241C24—21no—
242C2×Q8—221no—
243C2×Q8—221no—
244C2×D4—21no—
245C2×D4—21no—
246C2×D4—21no—
247C2×D4(C2×D11)⋊C412yes—
248C2×D4#432412yes—
249C2×D4#432612yes—
250C22×C4—21no—
251C22×C4—22no—
252C22×C4—22no—
253C22×C4—41no—
254C22×C4—82no—
255C22×C4D4×D1111yescharacteristic
256C22×C4#434111yescharacteristic
257C22×C4C2×C22⋊D1111yescharacteristic
258M16—441no—
259M16—441no—
260C2×C8—41no—
261C2×C8—41no—
262C2×C8—41no—
263C2×C8—222no—
264C2×C8—222no—
265C2×C8—222no—
266C2×C8—884no—
267C4⋊C4—21no—
268C4⋊C4—41no—
269C4⋊C4—41no—
270C4⋊C4—221no—
271C4⋊C4—221no—
272C4⋊C4—221no—
273C4⋊C4—221no—
274C4⋊C4—441no—
275C4⋊C4—441no—
276C4⋊C4(C2×D11)⋊C412yes—
277C22⋊C4—22no—
278C22⋊C4—22no—
279C22⋊C4—441no—
280C42—441no—
281C42C2×C4×D1111yescharacteristic
282C42C2×D4411yescharacteristic
283C42D4×D1111yescharacteristic
284C42#434111yescharacteristic
285C11#930311yescharacteristic, complemented, Sylow
286C23—22no—
287C23—22no—
288C23—22no—
289C23—81no—
290C23—81no—
291C23#6699211yescharacteristic
292Q8—442no—
293Q8—881no—
294D4—22no—
295D4—22no—
296D4—22no—
297D4#6687414yes—
298C2×C4—22no—
299C2×C4—41no—
300C2×C4—41no—
301C2×C4—44no—
302C2×C4—82no—
303C2×C4—81no—
304C2×C4—81no—
305C2×C4—81no—
306C2×C4—81no—
307C2×C4—441no—
308C2×C4—441no—
309C2×C4(C22⋊D11)⋊C411yescharacteristic
310C2×C4(C22⋊D11)⋊C411yescharacteristic
311C2×C4#6693511yescharacteristic
312C2×C4#6693911yescharacteristic
313C2×C4C2×(C2×D11)⋊C411yescharacteristic
314C2×C4C2×#432411yescharacteristic
315C2×C4#6699211yescharacteristic
316C2×C4C2×#432611yescharacteristic
317C2×C4#6700311yescharacteristic
318C2×C4#6700311yescharacteristic
319C8—81no—
320C8—442no—
321C8—442no—
322C8—442no—
323C22—21no—
324C22—21no—
325C22—24no—
326C22—42no—
327C22—42no—
328C22—82no—
329C22—82no—
330C22#1062257111yescharacteristic
331C22#1062265411yescharacteristic
332C22#1062266411yescharacteristic
333C4—21no—
334C4—21no—
335C4—21no—
336C4—21no—
337C4—42no—
338C4—161no—
339C4—881no—
340C4—881no—
341C4C2×#6687411yescharacteristic
342C4#1062261511yescharacteristic
343C4#1062265411yescharacteristic
344C4#1062266411yescharacteristic
345C2—21no—
346C2—21no—
347C2—44no—
348C2#1306897611yescharacteristic
349C2#1306903711yescharacteristic
350C2#1306910111yescharacteristic
subgroupG/H
centerC22#10622571
commutatorC42×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1804C2
socleC22×C11#386
prime radicalC22×D4×C11D4
cosocleC2×C42×C11C23
hypercenter#1804D11
hypocenterC11#9303
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1804

Complements

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

NH ≅ G/Ntype
3. #13067179C2semidirect
4. #13067018C2semidirect
5. #13066513C2semidirect
6. #13066474C2semidirect
18. #10622621C4semidirect
19. #10622620C4semidirect
285. C11#9303semidirect

Maximal subgroups

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

subgroupindex
#130784132
#130776402
#130671792
#130670182
#130665132
#130664742
C11×#18042
#930311