Finite Group Databasebeta

← #14650522

Subgroups — #14650522

Order 2816.

480 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 480 conjugacy classes of subgroups — too many to draw. Only its 107 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#13079746C211yesmaximal, characteristic
2#13071362C211yesmaximal, characteristic, complemented
3#13069447C211yesmaximal, characteristic
4#13067302C211yesmaximal, characteristic, complemented
5#13067175C211yesmaximal, characteristic
6#13066444C211yesmaximal, characteristic, complemented
7C11×#1286C211yesmaximal, characteristic, complemented
8#10623008C2211yescharacteristic
9C2×#66922C2211yescharacteristic
10C11×#431C2211yescharacteristic
11C11×#423C2211yescharacteristic
12C11×#382C2211yescharacteristic
13C2×#66889—21no—
14C2×#66889—21no—
15C4⋊C4×Dic11—21no—
16#10622586—21no—
17#10622545C2211yescharacteristic
18#10622538C2211yescharacteristic
19#10622455—22no—
20#10622348—22no—
21#10622307C412yescomplemented
22#10622293C412yescomplemented
23#10622266—22no—
24#10622259—22no—
25#10622124—22no—
26#10622089—22no—
27C2×#4339—21no—
28C22×Dic22—21no—
29C2×C11×M16—21no—
30C2×C11×C4⋊C4—21no—
31C2×C42×C11C2311yescharacteristic
32#66983—21no—
33#66983—21no—
34C2×C4⋊Dic11—21no—
35C2×C4⋊Dic11D412yes—
36C2×Dic11⋊C4—22no—
37C2×C4×Dic11—22no—
38C2×C4×Dic11D411yescharacteristic
39C2×C4×Dic11D411yescharacteristic
40#66928—21no—
41#66927C2×C411yescharacteristic
42C4×D44—21no—
43C4×D44—21no—
44#66922—21no—
45#66922—21no—
46#66922C2×C411yescharacteristic
47#66922C2×C412yes—
48#66922D412yes—
49C11×C4⋊C8—21no—
50C11×C4⋊C8—21no—
51C11×C4⋊C8—21no—
52C11×C22⋊C8—21no—
53C4×C8×C11C2×C412yes—
54C11×#95—21no—
55C11×#95D412yes—
56C11⋊#95—22no—
57C11⋊#95—22no—
58C11⋊#95—21no—
59C11⋊#95—21no—
60C22⋊(C11⋊C8)—21no—
61#66889—42no—
62#66889—42no—
63#66885—24no—
64#66881—24no—
65C4⋊(C11⋊C8)—21no—
66C4×C11⋊C8—21no—
67#9302—111nomaximal, Sylow
68C22×C4×C11—22no—
69C22×C4×C11C2×D411yescharacteristic
70C22×C4×C11C2×D411yescharacteristic
71C22×C4×C11C2×D411yescharacteristic
72C2×C22⋊D11—41no—
73C22×Dic11—21no—
74C22×Dic11—22no—
75C22×Dic11—21no—
76#4339—41no—
77#4339—41no—
78#4339—41no—
79#4339—41no—
80C2×D44—21no—
81C2×D44—21no—
82C2×D44—21no—
83C2×C4×D11—41no—
84C2×Dic22—21no—
85C2×Dic22—22no—
86C2×Dic22—22no—
87C2×Dic22—82no—
88C11×M16—41no—
89C11×M16—41no—
90C2×C8×C11—22no—
91C2×C8×C11—41no—
92C11×C4⋊C4—41no—
93C11×C4⋊C4—41no—
94C42×C11C22×C411yescharacteristic
95C42×C11C2×D411yescharacteristic
96C42×C11#4111yescharacteristic
97C42×C11#4111yescharacteristic
98(C2×D11)⋊C4—41no—
99(C2×D11)⋊C4—41no—
100C4⋊Dic11—21no—
101C4⋊Dic11—22no—
102C4⋊Dic11—21no—
103C4⋊Dic11—22no—
104C4⋊Dic11—22no—
105C4⋊Dic11C22⋊C414yes—
106Dic11⋊C4—82no—
107C4×Dic11—21no—
108C4×Dic11—21no—
109C4×Dic11—21no—
110C4×Dic11—82no—
111C4×Dic11SD1612yes—
112C2×C11⋊C8—41no—
113#3227—111no—
114#2331—111no—
115#1963—111no—
116#1549—111no—
117#1517—111no—
118#1286D1111yescharacteristic, complemented
119#1274—111no—
120C23×C11#12011yescharacteristic
121C22×D11—41no—
122C2×C4×C11—41no—
123C2×C4×C11—41no—
124C2×C4×C11—42no—
125C2×C4×C11—42no—
126C2×C4×C11—42no—
127C2×C4×C11C2×C22⋊C411yescharacteristic
128C2×C4×C11C4×D411yescharacteristic
129C2×C4×C11C4×D411yescharacteristic
130C2×C4×C11#12111yescharacteristic
131C2×C4×C11#12111yescharacteristic
132C2×C4×C11#12311yescharacteristic
133C2×C4×C11C2×SD1611yescharacteristic
134C2×C4×C11#13511yescharacteristic
135C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
136C2×C4×C11#13711yescharacteristic
137C22⋊D11—81no—
138C22⋊D11—81no—
139C2×Dic11—24no—
140C2×Dic11—22no—
141C2×Dic11—41no—
142C2×Dic11—42no—
143C2×Dic11—42no—
144C2×Dic11—41no—
145C2×Dic11—41no—
146C2×Dic11—41no—
147C2×Dic11—41no—
148C2×Dic11—41no—
149D44—42no—
150D44—41no—
151D44—41no—
152D44—81no—
153C4×D11—81no—
154C4×D11—81no—
155Dic22—41no—
156Dic22—41no—
157Dic22—82no—
158Dic22—82no—
159C8×C11—42no—
160C8×C11—81no—
161C11⋊C8—81no—
162#532—111no—
163C2×C4⋊Q8—111no—
164#498—112no—
165#486—112no—
166#481—222no—
167#476—222no—
168#431—111no—
169#431C2×D1111yescharacteristic
170#423C2×D1111yescharacteristic
171C2×#104—221no—
172C2×#104—221no—
173#391—222no—
174#389—221no—
175#387—222no—
176#382C2×D1111yescharacteristic
177C4×C4⋊C4—221no—
178#376—111no—
179#332—222no—
180#327—222no—
181C22×C11—21no—
182C22×C11—21no—
183C22×C11#38611yescharacteristic
184C22×C11#44811yescharacteristic
185C22×C11#44911yescharacteristic
186C2×D11—81no—
187C2×D11—81no—
188C2×D11—81no—
189C4×C11—21no—
190C4×C11—21no—
191C4×C11—21no—
192C4×C11—21no—
193C4×C11—82no—
194C4×C11C4×SD1611yescharacteristic
195C4×C11#44011yescharacteristic
196C4×C11#46011yescharacteristic
197C4×C11#46411yescharacteristic
198Dic11—42no—
199Dic11—44no—
200Dic11—81no—
201Dic11—81no—
202C2×#41—221no—
203C22×Q8—221no—
204C2×M16—21no—
205C4⋊Q8—112no—
206C4⋊Q8—111no—
207C4⋊Q8—112no—
208C4⋊Q8—221no—
209C4⋊Q8—221no—
210#127—111no—
211#124—221no—
212#121—221no—
213#121—221no—
214C4×D4—221no—
215C4×D4—221no—
216C2×C4⋊C4—21no—
217C2×C4⋊C4—112no—
218C2×C4⋊C4—221no—
219C2×C4⋊C4—222no—
220C2×C42—111no—
221C2×C42—111no—
222C2×C42—222no—
223C2×C42C22×D1111yescharacteristic
224#106—224no—
225C4⋊C8—21no—
226C4⋊C8—21no—
227C4⋊C8—21no—
228C4⋊C8—221no—
229#104—442no—
230#104—442no—
231#102—224no—
232C22⋊C8—21no—
233C22⋊C8—221no—
234C4×C8—221no—
235C4×C8C4×D1112yes—
236#95—21no—
237#95—222no—
238#95—222no—
239#95—221no—
240#95—221no—
241#95D4412yes—
242C2×C11—21no—
243C2×C11—21no—
244C2×C11#188011yescharacteristic
245C2×C11#190411yescharacteristic
246C2×C11#191211yescharacteristic
247D11—161no—
248#41—441no—
249#41—441no—
250#41—441no—
251#41—441no—
252C2×Q8—222no—
253C2×Q8—222no—
254C2×Q8—221no—
255C2×Q8—882no—
256C2×D4—221no—
257C2×D4—221no—
258C2×D4—221no—
259C2×D4—441no—
260C22×C4—22no—
261C22×C4—221no—
262C22×C4—222no—
263C22×C4—221no—
264C22×C4—441no—
265C22×C4C2×D4411yescharacteristic
266C22×C4D4×D1111yescharacteristic
267C22×C4D4×D1111yescharacteristic
268M16—41no—
269M16—41no—
270C2×C8—22no—
271C2×C8—41no—
272C2×C8—441no—
273C4⋊C4—41no—
274C4⋊C4—41no—
275C4⋊C4—114no—
276C4⋊C4—222no—
277C4⋊C4—222no—
278C4⋊C4—222no—
279C4⋊C4—221no—
280C4⋊C4—221no—
281C4⋊C4—882no—
282C22⋊C4—441no—
283C22⋊C4—441no—
284C42—112no—
285C42—221no—
286C42—221no—
287C42—221no—
288C42—882no—
289C42C2×C4×D1111yescharacteristic
290C42#433911yescharacteristic
291C42D4×D1111yescharacteristic
292C42#434311yescharacteristic
293C11#930211yescharacteristic, complemented, Sylow
294C23—441no—
295C23#6693511yescharacteristic
296Q8—441no—
297Q8—441no—
298Q8—882no—
299Q8—882no—
300D4—442no—
301D4—441no—
302D4—441no—
303D4—881no—
304D4—881no—
305D4—881no—
306C2×C4—41no—
307C2×C4—41no—
308C2×C4—42no—
309C2×C4—42no—
310C2×C4—42no—
311C2×C4—224no—
312C2×C4—222no—
313C2×C4—441no—
314C2×C4—442no—
315C2×C4—442no—
316C2×C4—441no—
317C2×C4—441no—
318C2×C4—441no—
319C2×C4—441no—
320C2×C4—441no—
321C2×C4—881no—
322C2×C4—881no—
323C2×C4C4×D4411yescharacteristic
324C2×C4C22⋊C4×D1111yescharacteristic
325C2×C4#6693711yescharacteristic
326C2×C4#6694611yescharacteristic
327C2×C4#6694711yescharacteristic
328C2×C4#6694811yescharacteristic
329C2×C4#6696411yescharacteristic
330C2×C4SD16×D1111yescharacteristic
331C2×C4#6696911yescharacteristic
332C2×C4#6697111yescharacteristic
333C8—42no—
334C8—81no—
335C8—881no—
336C22—21no—
337C22—21no—
338C22—881no—
339C22—881no—
340C22—881no—
341C22#1062227811yescharacteristic
342C22#1062239411yescharacteristic
343C22#1062241911yescharacteristic
344C4—21no—
345C4—21no—
346C4—21no—
347C4—21no—
348C4—82no—
349C4—442no—
350C4—444no—
351C4—881no—
352C4—881no—
353C4#1062237511yescharacteristic
354C4#1062241111yescharacteristic
355C4#1062246511yescharacteristic
356C4#1062250211yescharacteristic
357C2—21no—
358C2—21no—
359C2—1761no—
360C2#1306897211yescharacteristic
361C2#1306910211yescharacteristic
362C2#1306915211yescharacteristic
subgroupG/H
centerC22#10622278
commutatorC42×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1286C2
socleC22×C11#386
prime radical#10623008C22
cosocleC2×C42×C11C23
hypercenter#1286D11
hypocenterC11#9302
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1286

Complements

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

NH ≅ G/Ntype
2. #13071362C2semidirect
4. #13067302C2semidirect
6. #13066444C2semidirect
7. C11×#1286C2semidirect
21. #10622307C4semidirect
22. #10622293C4semidirect
118. #1286D11semidirect
293. C11#9302semidirect

Maximal subgroups

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

subgroupindex
#130797462
#130713622
#130694472
#130673022
#130671752
#130664442
C11×#12862
#930211