Finite Group Databasebeta

← #14650393

Subgroups — #14650393

Order 2816.

396 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 396 conjugacy classes of subgroups — too many to draw. Only its 95 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#13079752C211yesmaximal, characteristic
2#13077711C211yesmaximal, characteristic, complemented
3#13067226C211yesmaximal, characteristic
4#13067084C211yesmaximal, characteristic
5#13066479C211yesmaximal, characteristic, complemented
6#13066447C211yesmaximal, characteristic, complemented
7C11×#1531C211yesmaximal, characteristic, complemented
8C11×#533C2211yescharacteristic
9#10623008C2211yescharacteristic
10C11×#432C2211yescharacteristic
11C2×C11×#97C2211yescharacteristic
12#10622701C411yescharacteristic
13#10622701C411yescharacteristic
14#10622692C411yescharacteristic
15#10622691C411yescharacteristic
16#10622679—22no—
17#10622637—22no—
18#10622637—21no—
19Q8×C11⋊C8—21no—
20#10622616—22no—
21#10622613—22no—
22#10622539C2211yescharacteristic
23#10622538C2211yescharacteristic
24#10622538C2211yescharacteristic
25C11×#330—22no—
26#10622121—21no—
27#10622121—21no—
28#10622102—22no—
29C2×#4339—21no—
30C22×C8×C11—21no—
31C11×C4⋊Q8C2×C411yescharacteristic
32C11×C4⋊Q8C2×C411yescharacteristic
33C11×#125D412yes—
34C11×C22⋊Q8—21no—
35C11×C22⋊Q8—21no—
36C4×Q8×C11—21no—
37C4×Q8×C11—21no—
38C11×#117D412yes—
39C2×C42×C11C2311yescharacteristic
40#66983—21no—
41#66983—21no—
42#66928—21no—
43#66927C2×C411yescharacteristic
44C4×D44—21no—
45C4×D44—21no—
46#66922C2×C411yescharacteristic
47C11×C4⋊C8—21no—
48C11×C22⋊C8—21no—
49C11×#97—21no—
50C11×#97—21no—
51C11×#97—21no—
52C22⋊(C11⋊C8)—21no—
53C22⋊(C11⋊C8)—21no—
54C22⋊(C11⋊C8)—21no—
55#66873—22no—
56#66873—22no—
57#66872—22no—
58#66871—22no—
59C4⋊(C11⋊C8)—22no—
60C4⋊(C11⋊C8)—22no—
61C4⋊(C11⋊C8)—21no—
62C4⋊(C11⋊C8)—21no—
63C4⋊(C11⋊C8)—21no—
64#66867—22no—
65#66867D412yes—
66C4×C11⋊C8—22no—
67C4×C11⋊C8C2×C411yescharacteristic
68C4×C11⋊C8C2×C411yescharacteristic
69C4×C11⋊C8D411yescharacteristic
70C4×C11⋊C8D411yescharacteristic
71#9284—111nomaximal, Sylow
72C2×Q8×C11—21no—
73C2×Q8×C11—21no—
74C22×C4×C11C2×D411yescharacteristic
75C22×C4×C11#4111yescharacteristic
76C22×C4×C11#4111yescharacteristic
77C2×C22⋊D11—41no—
78#4339—82no—
79C2×D44—21no—
80C2×D44—21no—
81C2×D44—21no—
82C2×C4×D11—41no—
83C2×Dic22—21no—
84C2×C8×C11—22no—
85C2×C8×C11—41no—
86C2×C8×C11—41no—
87C2×C8×C11—41no—
88C11×C4⋊C4—21no—
89C11×C4⋊C4—21no—
90C11×C4⋊C4—22no—
91C11×C4⋊C4—22no—
92C11×C4⋊C4C22⋊C412yes—
93C11×C4⋊C4C22⋊C412yes—
94C11×C22⋊C4—22no—
95C42×C11—22no—
96C42×C11C22×C411yescharacteristic
97C42×C11C2×D411yescharacteristic
98C42×C11C2×D411yescharacteristic
99C42×C11C2×D411yescharacteristic
100(C2×D11)⋊C4—41no—
101(C2×D11)⋊C4—41no—
102C4⋊Dic11—21no—
103C4⋊Dic11—21no—
104C2×C11⋊C8—21no—
105C2×C11⋊C8—21no—
106C2×C11⋊C8—21no—
107C2×C11⋊C8—22no—
108C2×C11⋊C8—21no—
109#3228—111no—
110#2985—111no—
111#1531D1111yescharacteristic, complemented
112#1530—111no—
113#1496—111no—
114#1287—111no—
115#1275—111no—
116C23×C11#12311yescharacteristic
117C22×D11—41no—
118Q8×C11—41no—
119Q8×C11—41no—
120Q8×C11—81no—
121C2×C4×C11—21no—
122C2×C4×C11—21no—
123C2×C4×C11—22no—
124C2×C4×C11—22no—
125C2×C4×C11—41no—
126C2×C4×C11—41no—
127C2×C4×C11C2×C22⋊C411yescharacteristic
128C2×C4×C11C4×D411yescharacteristic
129C2×C4×C11C4×D411yescharacteristic
130C2×C4×C11#12011yescharacteristic
131C2×C4×C11#12111yescharacteristic
132C2×C4×C11#12111yescharacteristic
133C22⋊D11—82no—
134C2×Dic11—41no—
135D44—42no—
136D44—41no—
137D44—41no—
138D44—81no—
139C4×D11—82no—
140Dic22—81no—
141C8×C11—42no—
142C8×C11—81no—
143C11⋊C8—41no—
144C11⋊C8—41no—
145C11⋊C8—41no—
146C11⋊C8—42no—
147C11⋊C8—41no—
148#533C2×D1111yescharacteristic
149#532—111no—
150#500—111no—
151#498—111no—
152#486—111no—
153#486—111no—
154#482—222no—
155#478—222no—
156#446—221no—
157#446—222no—
158C8×Q8—221no—
159#433—222no—
160#432—111no—
161#432C2×D1111yescharacteristic
162#431—111no—
163#431—111no—
164C2×#97C2×D1111yescharacteristic
165#330—22no—
166#329—222no—
167D4⋊C8—221no—
168D4⋊C8—221no—
169C22×C11—21no—
170C22×C11—21no—
171C22×C11—21no—
172C22×C11#38611yescharacteristic
173C2×D11—81no—
174C2×D11—81no—
175C2×D11—81no—
176C4×C11—21no—
177C4×C11—21no—
178C4×C11—21no—
179C4×C11—21no—
180C4×C11—21no—
181C4×C11—42no—
182C4×C11—42no—
183C4×C11#44311yescharacteristic
184C4×C11#44411yescharacteristic
185Dic11—81no—
186C2×#41—221no—
187C22×C8—21no—
188C4⋊Q8—111no—
189C4⋊Q8C4×D1111yescharacteristic
190C4⋊Q8C4×D1111yescharacteristic
191#127—111no—
192#125C22⋊D1112yes—
193#124—221no—
194C22⋊Q8—21no—
195C22⋊Q8—21no—
196#121—221no—
197#121—221no—
198C4×Q8—21no—
199C4×Q8—21no—
200C4×D4—221no—
201C4×D4—221no—
202#117D4412yes—
203C2×C42C22×D1111yescharacteristic
204#107—222no—
205#106—222no—
206C4⋊C8—21no—
207C4⋊C8—222no—
208C4⋊C8—222no—
209C4⋊C8—221no—
210C4⋊C8—221no—
211C4⋊C8—221no—
212#102—222no—
213#102—222no—
214C22⋊C8—21no—
215C22⋊C8—221no—
216C22⋊C8—221no—
217C22⋊C8—221no—
218#97—21no—
219#97—21no—
220#97—21no—
221#97—112no—
222#97—222no—
223C4×C8—111no—
224C4×C8—111no—
225C4×C8—111no—
226C4×C8—111no—
227C4×C8—222no—
228C2×C11—41no—
229C2×C11#187611yescharacteristic
230C2×C11#190311yescharacteristic
231C2×C11#191211yescharacteristic
232D11—161no—
233#41—882no—
234C2×Q8—21no—
235C2×Q8—21no—
236C2×Q8—221no—
237C2×D4—221no—
238C2×D4—221no—
239C2×D4—221no—
240C2×D4—441no—
241C22×C4—441no—
242C22×C4C2×D4411yescharacteristic
243C22×C4#434111yescharacteristic
244C22×C4#434111yescharacteristic
245C2×C8—22no—
246C2×C8—41no—
247C2×C8—41no—
248C2×C8—41no—
249C2×C8—221no—
250C2×C8—221no—
251C2×C8—222no—
252C2×C8—221no—
253C2×C8—221no—
254C4⋊C4—21no—
255C4⋊C4—21no—
256C4⋊C4—22no—
257C4⋊C4—22no—
258C4⋊C4—221no—
259C4⋊C4—221no—
260C4⋊C4(C2×D11)⋊C412yes—
261C4⋊C4(C2×D11)⋊C412yes—
262C22⋊C4—22no—
263C22⋊C4—441no—
264C22⋊C4—441no—
265C42—22no—
266C42C2×C4×D1111yescharacteristic
267C42D4×D1111yescharacteristic
268C42D4×D1111yescharacteristic
269C42C2×C22⋊D1111yescharacteristic
270C11#928411yescharacteristic, complemented, Sylow
271C23—441no—
272C23#6693911yescharacteristic
273Q8—41no—
274Q8—41no—
275Q8—81no—
276Q8—881no—
277D4—442no—
278D4—441no—
279D4—441no—
280D4—881no—
281D4—882no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—22no—
285C2×C4—22no—
286C2×C4—41no—
287C2×C4—41no—
288C2×C4—441no—
289C2×C4—882no—
290C2×C4(C22⋊D11)⋊C411yescharacteristic
291C2×C4(C22⋊D11)⋊C411yescharacteristic
292C2×C4#6693511yescharacteristic
293C2×C4C2×(C2×D11)⋊C411yescharacteristic
294C2×C4#6699211yescharacteristic
295C2×C4#6699211yescharacteristic
296C8—42no—
297C8—81no—
298C8—441no—
299C8—441no—
300C8—442no—
301C8—441no—
302C8—441no—
303C22—21no—
304C22—21no—
305C22—21no—
306C22—881no—
307C22—881no—
308C22—881no—
309C22#1062257111yescharacteristic
310C4—21no—
311C4—21no—
312C4—21no—
313C4—21no—
314C4—21no—
315C4—42no—
316C4—42no—
317C4—881no—
318C4#1062243611yescharacteristic
319C4#1062243711yescharacteristic
320C2—41no—
321C2—1761no—
322C2#1306894111yescharacteristic
323C2#1306909411yescharacteristic
324C2#1306915111yescharacteristic
subgroupG/H
centerC22#10622571
commutatorC42×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1531C2
socleC22×C11#386
prime radical#10623008C22
cosocleC2×C42×C11C23
hypercenter#1531D11
hypocenterC11#9284
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1531

Complements

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

NH ≅ G/Ntype
2. #13077711C2semidirect
5. #13066479C2semidirect
6. #13066447C2semidirect
7. C11×#1531C2semidirect
111. #1531D11semidirect
270. C11#9284semidirect

Maximal subgroups

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

subgroupindex
#130797522
#130777112
#130672262
#130670842
#130664792
#130664472
C11×#15312
#928411