Finite Group Databasebeta

← #14650515

Subgroups — #14650515

Order 2816.

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

normal subgroups only

This group has 492 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#13079543C211yesmaximal, characteristic
2#13071362C211yesmaximal, characteristic, complemented
3#13069447C211yesmaximal, characteristic
4#13067298C211yesmaximal, 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#10622454—22no—
20#10622351—22no—
21#10622306C412yescomplemented
22#10622294C412yescomplemented
23#10622266—22no—
24#10622259—22no—
25#10622119—22no—
26#10622089—22no—
27C2×#4339—21no—
28C22×Dic22D412yes—
29C2×C11×M16—21no—
30C2×C11×C4⋊C4—21no—
31C2×C42×C11C2311yescharacteristic
32#66983—21no—
33#66983—21no—
34C2×C4⋊Dic11—21no—
35C2×C4⋊Dic11—21no—
36C2×Dic11⋊C4—22no—
37C2×C4×Dic11—22no—
38C2×C4×Dic11D411yescharacteristic
39C2×C4×Dic11D411yescharacteristic
40C2×#4314—24no—
41#66928—21no—
42#66927C2×C411yescharacteristic
43C4×D44—21no—
44C4×D44—21no—
45#66922—21no—
46#66922—21no—
47#66922C2×C411yescharacteristic
48#66922C2×C412yes—
49#66922D412yes—
50C11×C4⋊C8—21no—
51C11×C4⋊C8—21no—
52C11×C4⋊C8—21no—
53C11×C22⋊C8—21no—
54C4×C8×C11C2×C412yes—
55C11×#95—21no—
56C11×#95D412yes—
57C11⋊#95—22no—
58C11⋊#95—22no—
59C11⋊#95—21no—
60C11⋊#95—21no—
61C22⋊(C11⋊C8)—21no—
62#66889—42no—
63#66889—42no—
64#66880—24no—
65C4⋊(C11⋊C8)—21no—
66C4×C11⋊C8—21no—
67#9301—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—82no—
87C2×Dic22C22⋊C414yes—
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—22no—
103C4⋊Dic11—21no—
104C4⋊Dic11—22no—
105C4⋊Dic11—22no—
106Dic11⋊C4—82no—
107C4×Dic11—21no—
108C4×Dic11—21no—
109C4×Dic11—21no—
110C4×Dic11—82no—
111C4×Dic11SD1612yescomplemented
112C2×C11⋊C8—41no—
113#4314—84no—
114#3206—111no—
115#2331—111no—
116#1963—111no—
117#1548—111no—
118#1517—111no—
119#1286D1111yescharacteristic, complemented
120#1274—111no—
121C23×C11#12011yescharacteristic
122C22×D11—41no—
123C2×C4×C11—41no—
124C2×C4×C11—41no—
125C2×C4×C11—42no—
126C2×C4×C11—42no—
127C2×C4×C11—42no—
128C2×C4×C11C2×C22⋊C411yescharacteristic
129C2×C4×C11C4×D411yescharacteristic
130C2×C4×C11C4×D411yescharacteristic
131C2×C4×C11#12111yescharacteristic
132C2×C4×C11#12111yescharacteristic
133C2×C4×C11#12311yescharacteristic
134C2×C4×C11C2×SD1611yescharacteristic
135C2×C4×C11#13511yescharacteristic
136C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
137C2×C4×C11#13711yescharacteristic
138C22⋊D11—81no—
139C22⋊D11—81no—
140C2×Dic11—24no—
141C2×Dic11—22no—
142C2×Dic11—41no—
143C2×Dic11—42no—
144C2×Dic11—42no—
145C2×Dic11—41no—
146C2×Dic11—41no—
147C2×Dic11—41no—
148C2×Dic11—41no—
149C2×Dic11—41no—
150D44—42no—
151D44—41no—
152D44—41no—
153D44—81no—
154C4×D11—81no—
155C4×D11—81no—
156Dic22—44no—
157Dic22—41no—
158Dic22—41no—
159Dic22—82no—
160C8×C11—42no—
161C8×C11—81no—
162C11⋊C8—81no—
163#532—111no—
164C2×C4⋊Q8—111no—
165#492—112no—
166#487—112no—
167#461—222no—
168#448—222no—
169#431—111no—
170#431C2×D1111yescharacteristic
171#423C2×D1111yescharacteristic
172C2×#104—221no—
173C2×#104—221no—
174#391—222no—
175#389—221no—
176#387—222no—
177#382C2×D1111yescharacteristic
178C4×C4⋊C4—221no—
179#376—111no—
180#333—222no—
181#327—222no—
182C22×C11—21no—
183C22×C11—21no—
184C22×C11#38611yescharacteristic
185C22×C11#44811yescharacteristic
186C22×C11#44911yescharacteristic
187C2×D11—81no—
188C2×D11—81no—
189C2×D11—81no—
190C4×C11—21no—
191C4×C11—21no—
192C4×C11—21no—
193C4×C11—21no—
194C4×C11—82no—
195C4×C11C4×SD1611yescharacteristic
196C4×C11#44011yescharacteristic
197C4×C11#46011yescharacteristic
198C4×C11#46411yescharacteristic
199Dic11—42no—
200Dic11—44no—
201Dic11—81no—
202Dic11—81no—
203C2×#41—221no—
204C22×Q8—112no—
205C2×SD16—224no—
206C2×M16—21no—
207C4⋊Q8—112no—
208C4⋊Q8—111no—
209C4⋊Q8—112no—
210C4⋊Q8—221no—
211C4⋊Q8—221no—
212#127—111no—
213#124—221no—
214#121—221no—
215#121—221no—
216C4×D4—221no—
217C4×D4—221no—
218C2×C4⋊C4—21no—
219C2×C4⋊C4—221no—
220C2×C4⋊C4—221no—
221C2×C4⋊C4—222no—
222C2×C42—111no—
223C2×C42—111no—
224C2×C42—222no—
225C2×C42C22×D1111yescharacteristic
226C4⋊C8—21no—
227C4⋊C8—21no—
228C4⋊C8—21no—
229C4⋊C8—221no—
230#104—442no—
231#104—442no—
232#103—224no—
233C22⋊C8—21no—
234C22⋊C8—221no—
235C4×C8—221no—
236C4×C8C4×D1112yes—
237#95—21no—
238#95—222no—
239#95—222no—
240#95—221no—
241#95—221no—
242#95D4412yes—
243C2×C11—21no—
244C2×C11—21no—
245C2×C11#188011yescharacteristic
246C2×C11#190511yescharacteristic
247C2×C11#191111yescharacteristic
248D11—161no—
249#41—441no—
250#41—441no—
251#41—441no—
252#41—441no—
253C2×Q8—114no—
254C2×Q8—222no—
255C2×Q8—221no—
256C2×Q8—882no—
257C2×D4—221no—
258C2×D4—221no—
259C2×D4—221no—
260C2×D4—441no—
261C22×C4—22no—
262C22×C4—221no—
263C22×C4—222no—
264C22×C4—221no—
265C22×C4—441no—
266C22×C4C2×D4411yescharacteristic
267C22×C4D4×D1111yescharacteristic
268C22×C4D4×D1111yescharacteristic
269SD16—884no—
270M16—41no—
271M16—41no—
272C2×C8—22no—
273C2×C8—41no—
274C2×C8—441no—
275C4⋊C4—41no—
276C4⋊C4—41no—
277C4⋊C4—222no—
278C4⋊C4—222no—
279C4⋊C4—222no—
280C4⋊C4—222no—
281C4⋊C4—221no—
282C4⋊C4—221no—
283C4⋊C4—882no—
284C22⋊C4—441no—
285C22⋊C4—441no—
286C42—112no—
287C42—221no—
288C42—221no—
289C42—221no—
290C42—882no—
291C42C2×C4×D1111yescharacteristic
292C42#433911yescharacteristic
293C42D4×D1111yescharacteristic
294C42#434311yescharacteristic
295C11#930111yescharacteristic, complemented, Sylow
296C23—441no—
297C23#6693511yescharacteristic
298Q8—444no—
299Q8—441no—
300Q8—441no—
301Q8—882no—
302D4—442no—
303D4—441no—
304D4—441no—
305D4—881no—
306D4—881no—
307D4—881no—
308C2×C4—41no—
309C2×C4—41no—
310C2×C4—42no—
311C2×C4—42no—
312C2×C4—42no—
313C2×C4—224no—
314C2×C4—222no—
315C2×C4—441no—
316C2×C4—442no—
317C2×C4—442no—
318C2×C4—441no—
319C2×C4—441no—
320C2×C4—441no—
321C2×C4—441no—
322C2×C4—441no—
323C2×C4—881no—
324C2×C4—881no—
325C2×C4C4×D4411yescharacteristic
326C2×C4C22⋊C4×D1111yescharacteristic
327C2×C4#6693711yescharacteristic
328C2×C4#6694611yescharacteristic
329C2×C4#6694711yescharacteristic
330C2×C4#6694811yescharacteristic
331C2×C4#6696411yescharacteristic
332C2×C4SD16×D1111yescharacteristic
333C2×C4#6696911yescharacteristic
334C2×C4#6697111yescharacteristic
335C8—42no—
336C8—81no—
337C8—881no—
338C22—21no—
339C22—21no—
340C22—881no—
341C22—881no—
342C22—881no—
343C22#1062227811yescharacteristic
344C22#1062239411yescharacteristic
345C22#1062241911yescharacteristic
346C4—21no—
347C4—21no—
348C4—21no—
349C4—21no—
350C4—82no—
351C4—442no—
352C4—444no—
353C4—881no—
354C4—881no—
355C4#1062237511yescharacteristic
356C4#1062241111yescharacteristic
357C4#1062246511yescharacteristic
358C4#1062250211yescharacteristic
359C2—21no—
360C2—21no—
361C2—1761no—
362C2#1306897211yescharacteristic
363C2#1306910911yescharacteristic
364C2#1306914711yescharacteristic
subgroupG/H
centerC22#10622278
commutatorC42×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1286C2
socleC22×C11#386
prime radical#10623008C22
cosocleC2×C42×C11C23
hypercenter#1286D11
hypocenterC11#9301
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. #13067298C2semidirect
6. #13066444C2semidirect
7. C11×#1286C2semidirect
21. #10622306C4semidirect
22. #10622294C4semidirect
111. C4×Dic11SD16semidirect
119. #1286D11semidirect
295. C11#9301semidirect

Maximal subgroups

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

subgroupindex
#130795432
#130713622
#130694472
#130672982
#130671752
#130664442
C11×#12862
#930111