Finite Group Databasebeta

← #14657692

Subgroups — #14657692

Order 2816.

366 conjugacy classes of subgroups; only the 81 normal subgroups are shown.

normal subgroups only

This group has 366 conjugacy classes of subgroups — too many to draw. Only its 81 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#13079739C211yesmaximal, characteristic
2#13069605C211yesmaximal, characteristic, complemented
3#13067404C211yesmaximal, characteristic, complemented
4#13067349C211yesmaximal, characteristic
5#13067302C211yesmaximal, characteristic, complemented
6#13067034C211yesmaximal, characteristic
7C11×#1299C211yesmaximal, characteristic, complemented
8#10623008C2211yescharacteristic
9C2×#66922C2211yescharacteristic
10C11×#431C2211yescharacteristic
11C11×#423C2211yescharacteristic
12C4×C11×M16C2211yescharacteristic
13#10622538C2211yescharacteristic
14#10622537C2211yescharacteristic
15#10622459—21no—
16#10622459—21no—
17#10622349—22no—
18#10622307—21no—
19#10622295—21no—
20#10622192—22no—
21#10622124—22no—
22#10622123—21no—
23#10622119—21no—
24#10622118—21no—
25#10622117—21no—
26#10622097—22no—
27C2×#4339—21no—
28C22×Dic22—21no—
29C2×C11×M16—21no—
30C2×C11×M16—21no—
31C2×C42×C11C2311yescharacteristic
32#66983—21no—
33#66983—21no—
34C2×C4⋊Dic11—21no—
35C2×C4⋊Dic11D412yes—
36C2×#4318—21no—
37#66928—21no—
38#66927D411yescharacteristic
39C4×D44—21no—
40C4×D44—21no—
41#66922—21no—
42#66922—21no—
43#66922—21no—
44#66922—21no—
45#66922D411yescharacteristic
46C11×C4⋊C8—21no—
47C11×C4⋊C8—21no—
48C11×C4⋊C8D411yescharacteristic
49C11×C4⋊C8D411yescharacteristic
50C11×C22⋊C8—21no—
51C11×#97—21no—
52C4×C8×C11—21no—
53C4×C8×C11—21no—
54C22⋊(C11⋊C8)—21no—
55#66885—22no—
56#66885—22no—
57#66882—22no—
58#66882—22no—
59C4⋊(C11⋊C8)—21no—
60C4⋊(C11⋊C8)—21no—
61C4⋊(C11⋊C8)D412yes—
62C4×C11⋊C8—21no—
63#10490—111nomaximal, Sylow
64C22×C4×C11C2×D411yescharacteristic
65C22×C4×C11#4111yescharacteristic
66C22×C4×C11#4111yescharacteristic
67C2×C22⋊D11—41no—
68C22×Dic11—22no—
69#4339—82no—
70C2×D44—21no—
71C2×D44—21no—
72C2×D44—21no—
73C2×C4×D11—41no—
74C2×Dic22—21no—
75C2×Dic22—41no—
76C2×Dic22—41no—
77C2×Dic22—82no—
78C11×M16—22no—
79C11×M16—41no—
80C11×M16—81no—
81C2×C8×C11—21no—
82C2×C8×C11—21no—
83C2×C8×C11—41no—
84C2×C8×C11—41no—
85C42×C11C2×D411yescharacteristic
86C42×C11C2×D411yescharacteristic
87C42×C11C2×D411yescharacteristic
88C42×C11#4111yescharacteristic
89(C2×D11)⋊C4—41no—
90(C2×D11)⋊C4—41no—
91C4⋊Dic11—21no—
92C4⋊Dic11—22no—
93C4⋊Dic11—22no—
94C4⋊Dic11—21no—
95C4⋊Dic11—41no—
96C4⋊Dic11—41no—
97#4318—42no—
98C2×C11⋊C8—22no—
99C2×C11⋊C8—41no—
100#3226—111no—
101#1997—111no—
102#1574—111no—
103#1560—111no—
104#1549—111no—
105#1484—111no—
106#1299D1111yescharacteristic, complemented
107C23×C11#12311yescharacteristic
108C22×D11—41no—
109C2×C4×C11—21no—
110C2×C4×C11—21no—
111C2×C4×C11—21no—
112C2×C4×C11—22no—
113C2×C4×C11—21no—
114C2×C4×C11#12011yescharacteristic
115C2×C4×C11#12111yescharacteristic
116C2×C4×C11#12111yescharacteristic
117C2×C4×C11#12111yescharacteristic
118C2×C4×C11#12311yescharacteristic
119C2×C4×C11#12411yescharacteristic
120C22⋊D11—82no—
121C2×Dic11—42no—
122C2×Dic11—41no—
123C2×Dic11—82no—
124D44—41no—
125D44—41no—
126D44—41no—
127D44—41no—
128D44—81no—
129C4×D11—82no—
130Dic22—82no—
131Dic22—82no—
132Dic22—81no—
133C8×C11—42no—
134C8×C11—41no—
135C8×C11—41no—
136C8×C11—81no—
137C11⋊C8—42no—
138C11⋊C8—81no—
139#532—111no—
140C2×C4⋊Q8—111no—
141#500—221no—
142#486—221no—
143#480—222no—
144#474—221no—
145#474—221no—
146#431—111no—
147#431C2×D1111yescharacteristic
148#423—111no—
149#423C2×D1111yescharacteristic
150C4×M16C2×D1111yescharacteristic
151#343—222no—
152#335—221no—
153#334—221no—
154#333—221no—
155#332—222no—
156#331—221no—
157D4⋊C8—222no—
158C22×C11—21no—
159C22×C11—21no—
160C22×C11—21no—
161C22×C11#39411yescharacteristic
162C2×D11—81no—
163C2×D11—81no—
164C2×D11—81no—
165C4×C11—21no—
166C4×C11—21no—
167C4×C11—21no—
168C4×C11#45411yescharacteristic
169C4×C11#45611yescharacteristic
170C4×C11#47111yescharacteristic
171C4×C11#47212yes—
172C4×C11#47311yescharacteristic
173Dic11—82no—
174Dic11—81no—
175C2×#41—221no—
176C22×Q8—221no—
177C2×M16—21no—
178C2×M16—21no—
179C2×M16—221no—
180C4⋊Q8—111no—
181C4⋊Q8—221no—
182C4⋊Q8—221no—
183C4⋊Q8—221no—
184C4⋊Q8—221no—
185#127—111no—
186#124—221no—
187#121—221no—
188#121—221no—
189C4×D4—221no—
190C4×D4—221no—
191C2×C4⋊C4—112no—
192C2×C4⋊C4—221no—
193C2×C42C22×D1111yescharacteristic
194#107—222no—
195#107—222no—
196C4⋊C8—21no—
197C4⋊C8—21no—
198C4⋊C8—112no—
199C4⋊C8—221no—
200C4⋊C8—221no—
201C4⋊C8D4411yescharacteristic
202C4⋊C8D4411yescharacteristic
203#102—222no—
204#102—222no—
205C22⋊C8—21no—
206C22⋊C8—221no—
207#97—21no—
208C4×C8—21no—
209C4×C8—21no—
210C4×C8—221no—
211C2×C11—41no—
212C2×C11#203811yescharacteristic
213C2×C11#204511yescharacteristic
214C2×C11#205211yescharacteristic
215D11—161no—
216#41—882no—
217C2×Q8—221no—
218C2×Q8—441no—
219C2×Q8—441no—
220C2×Q8—882no—
221C2×D4—221no—
222C2×D4—221no—
223C2×D4—221no—
224C2×D4—441no—
225C22×C4—222no—
226C22×C4—441no—
227C22×C4#433911yescharacteristic
228C22×C4D4×D1111yescharacteristic
229C22×C4#434311yescharacteristic
230M16—22no—
231M16—41no—
232M16—81no—
233M16—442no—
234C2×C8—21no—
235C2×C8—21no—
236C2×C8—41no—
237C2×C8—41no—
238C2×C8—222no—
239C2×C8—441no—
240C4⋊C4—222no—
241C4⋊C4—221no—
242C4⋊C4—222no—
243C4⋊C4—221no—
244C4⋊C4—441no—
245C4⋊C4—441no—
246C22⋊C4—441no—
247C22⋊C4—441no—
248C42C2×D4411yescharacteristic
249C42#433911yescharacteristic
250C42D4×D1111yescharacteristic
251C42D4×D1111yescharacteristic
252C11#1049011yescharacteristic, complemented, Sylow
253C23—441no—
254C23#6694711yescharacteristic
255Q8—881no—
256Q8—882no—
257Q8—882no—
258D4—441no—
259D4—441no—
260D4—441no—
261D4—441no—
262D4—881no—
263D4—882no—
264C2×C4—22no—
265C2×C4—21no—
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—21no—
269C2×C4—441no—
270C2×C4—442no—
271C2×C4—882no—
272C2×C4—882no—
273C2×C4#6692811yescharacteristic
274C2×C4#6693511yescharacteristic
275C2×C4#6693711yescharacteristic
276C2×C4#6693711yescharacteristic
277C2×C4#6694711yescharacteristic
278C2×C4#6694811yescharacteristic
279C8—42no—
280C8—41no—
281C8—41no—
282C8—81no—
283C8—442no—
284C8—881no—
285C22—21no—
286C22—21no—
287C22—21no—
288C22—881no—
289C22—881no—
290C22—881no—
291C22#1062228511yescharacteristic
292C4—21no—
293C4—21no—
294C4—21no—
295C4—881no—
296C4—882no—
297C4#1062236111yescharacteristic
298C4#1062236811yescharacteristic
299C4#1062243911yescharacteristic
300C4#1062244011yescharacteristic
301C4#1062251012yes—
302C2—41no—
303C2—1761no—
304C2#1306983611yescharacteristic
305C2#1306987311yescharacteristic
306C2#1306991811yescharacteristic
subgroupG/H
centerC22#10622285
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1299C2
socleC22×C11#394
prime radical#10623008C22
hypercenter#1299D11
hypocenterC11#10490
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1299

Complements

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

NH ≅ G/Ntype
2. #13069605C2semidirect
3. #13067404C2semidirect
5. #13067302C2semidirect
7. C11×#1299C2semidirect
106. #1299D11semidirect
252. C11#10490semidirect

Maximal subgroups

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

subgroupindex
#130797392
#130696052
#130674042
#130673492
#130673022
#130670342
C11×#12992
#1049011