Finite Group Databasebeta

← #14667007

Subgroups — #14667007

Order 2816.

338 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 338 conjugacy classes of subgroups — too many to draw. Only its 59 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#13079481C211yesmaximal, characteristic
2#13070801C211yesmaximal, characteristic, complemented
3#13070796C211yesmaximal, characteristic, complemented
4#13066630C211yesmaximal, characteristic, complemented
5#13066630C211yesmaximal, characteristic, complemented
6#13066542C211yesmaximal, characteristic, complemented
7C11×#2078C211yesmaximal, characteristic, complemented
8#10623361—21no—
9C2×C11×#107C2211yescharacteristic, complemented
10C11×#417—21no—
11C11×#408C2211yescharacteristic
12#10622748—21no—
13#10622728C2211yescharacteristic
14#10622728C2211yescharacteristic
15#10622350—21no—
16#10622350—21no—
17#10622345—21no—
18#10622345—21no—
19C11×#343—21no—
20C11×#341C2211yescharacteristic, complemented
21C22⋊(C11⋊C16)C2211yescharacteristic, complemented
22C22⋊(C11⋊C16)C2211yescharacteristic, complemented
23#10622129—21no—
24#10622129—21no—
25#10622128—21no—
26#10622127—21no—
27C2×C11×#41D411yescharacteristic
28C22×D44—21no—
29C2×C11×M16—21no—
30C2×C11×M16D411yescharacteristic
31C22×C8×C11C2311yescharacteristic
32C2×C11×C4⋊C4—21no—
33#67000—41no—
34#66993—41no—
35#66990—41no—
36#66990—41no—
37#66983—21no—
38#66983—21no—
39#66983—21no—
40#66983—21no—
41#66979—21no—
42C2×D88—21no—
43C2×D88D411yescharacteristic
44C2×D88D411yescharacteristic
45C11×#107—21no—
46C11×#107—21no—
47C11×#103—41no—
48C11×#102—41no—
49C11×C22⋊C8—21no—
50C11×C22⋊C8—21no—
51#66885—21no—
52#66885—21no—
53#66885—21no—
54#66885—21no—
55#66882D411yescharacteristic
56#66882D411yescharacteristic
57#66881—21no—
58C2×C11⋊C16—21no—
59C2×C11⋊C16—21no—
60#12284—111nomaximal, Sylow
61C23×D11—41no—
62C11×#41—41no—
63C11×#41—41no—
64C2×Q8×C11D811yescharacteristic
65C2×D4×C11—21no—
66C2×D4×C11D811yescharacteristic
67C22×C4×C11—21no—
68C22×C4×C11—41no—
69C22×C4×C11C2×D411yescharacteristic
70C2×C22⋊D11—41no—
71C2×C22⋊D11—41no—
72C2×C22⋊D11—41no—
73C2×C22⋊D11—41no—
74C2×D44—21no—
75C2×D44—21no—
76C2×D44—41no—
77C2×D44—81no—
78C2×D44—81no—
79C11×M16—41no—
80C11×M16—41no—
81C11×M16—41no—
82C2×C8×C11—21no—
83C2×C8×C11—41no—
84C2×C8×C11—41no—
85C2×C8×C11C2×D411yescharacteristic
86C2×C8×C11C2×D411yescharacteristic
87C11×C4⋊C4—41no—
88C11×C4⋊C4—41no—
89C22⋊Dic11—41no—
90(C2×D11)⋊C4—41no—
91(C2×D11)⋊C4—41no—
92(C2×D11)⋊C4—41no—
93(C2×D11)⋊C4—41no—
94C4⋊Dic11—21no—
95C4⋊Dic11—21no—
96C4×Dic11—41no—
97D88—41no—
98D88—41no—
99D88—81no—
100C11⋊C16—41no—
101C11⋊C16—41no—
102#3199—111no—
103#2233—111no—
104#2232—111no—
105#2078D1111yescharacteristic, complemented
106#1349—111no—
107#1349—111no—
108#1315—111no—
109C23×C11—21no—
110C23×C11AGL(1,ℤ/8)11yescharacteristic
111C22×D11—41no—
112C22×D11—41no—
113C22×D11—82no—
114C22×D11—161no—
115C22×D11—161no—
116Q8×C11—41no—
117D4×C11—41no—
118D4×C11—81no—
119C2×C4×C11—21no—
120C2×C4×C11—21no—
121C2×C4×C11—21no—
122C2×C4×C11—41no—
123C2×C4×C11—41no—
124C2×C4×C11—81no—
125C2×C4×C11—161no—
126C2×C4×C11#12011yescharacteristic
127C2×C4×C11C2×D811yescharacteristic
128C22⋊D11—161no—
129C22⋊D11—161no—
130C22⋊D11—161no—
131C22⋊D11—161no—
132C2×Dic11—41no—
133C2×Dic11—41no—
134D44—41no—
135D44—41no—
136D44—41no—
137D44—41no—
138D44—82no—
139C8×C11—21no—
140C8×C11—21no—
141C8×C11—41no—
142C8×C11—81no—
143#535—221no—
144#482—221no—
145#482—221no—
146#469—221no—
147#466—111no—
148#466—111no—
149#447—221no—
150#447—221no—
151C2×#107C2×D1111yescharacteristic, complemented
152#417—21no—
153#408C2×D1111yescharacteristic
154#367—221no—
155#366—221no—
156#357—221no—
157#357—221no—
158C22⋊C16—111no—
159C22⋊C16—111no—
160#343—21no—
161#341C2×D1111yescharacteristic, complemented
162C22×C11—21no—
163C22×C11—21no—
164C22×C11—21no—
165C22×C11—41no—
166C22×C11—41no—
167C22×C11—41no—
168C22×C11#44711yescharacteristic
169C2×D11—81no—
170C2×D11—81no—
171C2×D11—81no—
172C2×D11—81no—
173C2×D11—81no—
174C2×D11—81no—
175C2×D11—164no—
176C4×C11—21no—
177C4×C11—41no—
178C4×C11—161no—
179C4×C11#45511yescharacteristic
180C4×C11#45811yescharacteristic
181Dic11—81no—
182Dic11—81no—
183C2×#41C22⋊D1111yescharacteristic
184C22×D4—221no—
185C2×D8—111no—
186C2×D8—111no—
187C2×D8—221no—
188C2×M16—21no—
189C2×M16C22⋊D1111yescharacteristic
190C22×C8C22×D1111yescharacteristic
191#127—441no—
192#124—441no—
193#121—221no—
194#121—221no—
195#121—221no—
196#121—221no—
197#120—441no—
198#120—441no—
199#117—221no—
200C2×C4⋊C4—21no—
201C2×C16—221no—
202C2×C16—221no—
203#107—21no—
204#107—21no—
205#107—111no—
206#107—111no—
207#106—221no—
208#103—41no—
209#102—41no—
210#102—221no—
211#102—221no—
212#102—221no—
213#102—221no—
214C22⋊C8—21no—
215C22⋊C8—21no—
216C2×C11—41no—
217C2×C11—81no—
218C2×C11#160711yescharacteristic
219C2×C11#219211yescharacteristic
220C2×C11#219411yescharacteristic
221D11—161no—
222D11—161no—
223C24—441no—
224#41—41no—
225#41—41no—
226C2×Q8#432311yescharacteristic
227C2×D4—21no—
228C2×D4—221no—
229C2×D4—221no—
230C2×D4—441no—
231C2×D4—441no—
232C2×D4—441no—
233C2×D4—441no—
234C2×D4—441no—
235C2×D4—881no—
236C2×D4—881no—
237C2×D4#432311yescharacteristic
238C22×C4—21no—
239C22×C4—41no—
240C22×C4C2×C22⋊D1111yescharacteristic
241D8—441no—
242D8—441no—
243D8—881no—
244M16—41no—
245M16—41no—
246M16—41no—
247C2×C8—21no—
248C2×C8—41no—
249C2×C8—41no—
250C2×C8D4×D1111yescharacteristic
251C2×C8D4×D1111yescharacteristic
252C4⋊C4—41no—
253C4⋊C4—41no—
254C4⋊C4—221no—
255C4⋊C4—221no—
256C22⋊C4—441no—
257C22⋊C4—441no—
258C22⋊C4—441no—
259C22⋊C4—441no—
260C22⋊C4—441no—
261C42—441no—
262C16—441no—
263C16—441no—
264C11#1228411yescharacteristic, complemented, Sylow
265C23—21no—
266C23—441no—
267C23—441no—
268C23—882no—
269C23—1761no—
270C23—1761no—
271C23#6700211yescharacteristic
272Q8—41no—
273D4—41no—
274D4—81no—
275D4—441no—
276D4—441no—
277D4—441no—
278D4—441no—
279D4—882no—
280D4—1761no—
281D4—1761no—
282D4—1761no—
283D4—1761no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—41no—
288C2×C4—41no—
289C2×C4—81no—
290C2×C4—161no—
291C2×C4—441no—
292C2×C4—441no—
293C2×C4C2×#432311yescharacteristic
294C2×C4#6699011yescharacteristic
295C8—21no—
296C8—21no—
297C8—41no—
298C8—81no—
299C22—21no—
300C22—21no—
301C22—21no—
302C22—41no—
303C22—41no—
304C22—41no—
305C22—881no—
306C22—881no—
307C22—881no—
308C22—881no—
309C22—881no—
310C22—881no—
311C22—1764no—
312C22#1062264911yescharacteristic
313C4—21no—
314C4—41no—
315C4—161no—
316C4—881no—
317C4—881no—
318C4#1062266611yescharacteristic
319C4#1062267411yescharacteristic
320C2—41no—
321C2—81no—
322C2—1761no—
323C2—1761no—
324C2#1306760111yescharacteristic
325C2#1307057111yescharacteristic
326C2#1307058511yescharacteristic
subgroupG/H
centerC22#10622649
commutator, cosocleC22×C8×C11C23
FrattiniC22×C8C22×D11
FittingC11×#2078C2
socleC22×C11#447
prime radical#13079481C2
hypercenter#2078D11
hypocenterC11#12284
LCSG ▷ C22×C8×C11 ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ #408 ◁ #2078

Complements

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

NH ≅ G/Ntype
2. #13070801C2semidirect
3. #13070796C2semidirect
4. #13066630C2semidirect
5. #13066630C2semidirect
6. #13066542C2semidirect
7. C11×#2078C2semidirect
9. C2×C11×#107C22semidirect
20. C11×#341C22semidirect
21. C22⋊(C11⋊C16)C22semidirect
22. C22⋊(C11⋊C16)C22semidirect
105. #2078D11semidirect
151. C2×#107C2×D11semidirect
161. #341C2×D11semidirect
264. C11#12284semidirect

Maximal subgroups

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

subgroupindex
#130794812
#130708012
#130707962
#130666302
#130665422
C11×#20782
#1228411