Finite Group Databasebeta

← #14653210

Subgroups — #14653210

Order 2816.

530 conjugacy classes of subgroups; only the 129 normal subgroups are shown.

normal subgroups only

This group has 530 conjugacy classes of subgroups — too many to draw. Only its 129 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
1C2×#10622698C211yesmaximal, characteristic
2#13068787C211yesmaximal, characteristic, complemented
3#13067288C211yesmaximal, characteristic, complemented
4#13067285C211yesmaximal, characteristic
5#13067283C211yesmaximal, characteristic
6#13066900C211yesmaximal, characteristic, complemented
7C11×#1546C211yesmaximal, characteristic, complemented
8C2×C11×C4⋊Q8C2211yescharacteristic
9C22×#4325—22no—
10C2×#66927C2211yescharacteristic
11C11×#431C2211yescharacteristic
12C11×#423C2211yescharacteristic
13C2×#66886—22no—
14#10622698—21no—
15#10622698—21no—
16#10622698C414yes—
17#10622538C2211yescharacteristic
18#10622537C2211yescharacteristic
19C2×C4×C11⋊C8C2211yescharacteristic
20C11×#332—22no—
21#10622185—22no—
22#10622123—22no—
23#10622123—22no—
24#10622092—21no—
25C8×C11⋊C8—21no—
26C22×Q8×C11—21no—
27C22×D44—21no—
28C22×D44—21no—
29C22×D44—21no—
30C2×C11×M16—21no—
31C11×C4⋊Q8—21no—
32C11×C4⋊Q8—21no—
33C11×C4⋊Q8—21no—
34C11×C4⋊Q8C2×C412yes—
35C2×C11×C4⋊C4—21no—
36C2×C11×C4⋊C4—21no—
37C2×C42×C11C2311yescharacteristic
38C2×#4325—24no—
39C2×#4325—24no—
40C2×#4325—44no—
41C2×#4325—44no—
42C2×#4318—21no—
43C22×C11⋊C8D412yes—
44#66927—21no—
45#66927—21no—
46#66927—21no—
47#66927C2×C412yes—
48C11×C4⋊C8—21no—
49C11×C4⋊C8—21no—
50C11×C4⋊C8D412yes—
51C11×C22⋊C8—21no—
52C4×C8×C11—21no—
53C22⋊(C11⋊C8)—21no—
54#66886—44no—
55C4⋊(C11⋊C8)—21no—
56C4⋊(C11⋊C8)—21no—
57C4⋊(C11⋊C8)D412yes—
58C4×C11⋊C8—21no—
59C4×C11⋊C8C2×C412yes—
60C4×C11⋊C8D411yescharacteristic
61C4×C11⋊C8D411yescharacteristic
62#9768—111nomaximal, Sylow
63C23×D11—41no—
64C2×Q8×C11—22no—
65C2×Q8×C11—41no—
66C2×Q8×C11—42no—
67C2×Q8×C11—42no—
68C22×C4×C11—41no—
69C22×C4×C11C2×D411yescharacteristic
70C22×C4×C11#4111yescharacteristic
71C22×C4×C11#4111yescharacteristic
72C2×D44—22no—
73C2×D44—22no—
74C2×D44—22no—
75C2×D44—41no—
76C2×D44—41no—
77C2×D44—41no—
78C2×D44—42no—
79C2×D44—42no—
80C2×D44—82no—
81C2×D44—82no—
82C11×M16—42no—
83C2×C8×C11—22no—
84C2×C8×C11—41no—
85C11×C4⋊C4—22no—
86C11×C4⋊C4—22no—
87C11×C4⋊C4—41no—
88C11×C4⋊C4—41no—
89C42×C11C22×C411yescharacteristic
90C42×C11C2×D411yescharacteristic
91C42×C11C2×D411yescharacteristic
92C42×C11C2×D411yescharacteristic
93#4325—48no—
94#4325—48no—
95#4318—42no—
96C2×C11⋊C8—22no—
97C2×C11⋊C8—41no—
98C2×C11⋊C8C22⋊C412yes—
99C2×C11⋊C8C22⋊C412yes—
100C2×C11⋊C8D814yes—
101C2×C11⋊C8SD1614yes—
102C2×#492—111no—
103#1848—111no—
104#1546—111no—
105#1546D1111yescharacteristic, complemented
106#1545—111no—
107#1545—111no—
108#1450—111no—
109C23×C11#12411yescharacteristic
110C22×D11—42no—
111C22×D11—82no—
112C22×D11—82no—
113C22×D11—82no—
114Q8×C11—44no—
115Q8×C11—81no—
116Q8×C11—81no—
117C2×C4×C11—22no—
118C2×C4×C11—22no—
119C2×C4×C11—42no—
120C2×C4×C11—82no—
121C2×C4×C11C2×C22⋊C411yescharacteristic
122C2×C4×C11C4×D411yescharacteristic
123C2×C4×C11C4×D411yescharacteristic
124C2×C4×C11#12111yescharacteristic
125C2×C4×C11#12111yescharacteristic
126C2×C4×C11#12711yescharacteristic
127C2×C4×C11C2×D812yes—
128C2×C4×C11C2×SD1612yes—
129D44—44no—
130D44—82no—
131D44—82no—
132D44—82no—
133D44—82no—
134D44—81no—
135D44—81no—
136C8×C11—42no—
137C8×C11—81no—
138C11⋊C8—42no—
139C11⋊C8—81no—
140C11⋊C8#10214yes—
141C11⋊C8#10214yes—
142C22×SD16—222no—
143C2×C4⋊Q8C2×D1111yescharacteristic
144C2×#127—111no—
145#492—114no—
146#492—221no—
147#492—221no—
148#431—111no—
149#431C2×D1111yescharacteristic
150C2×#108—222no—
151#423—111no—
152#423C2×D1111yescharacteristic
153C2×C4×C8—111no—
154#332—22no—
155#332—222no—
156#331—222no—
157#331—222no—
158#322—221no—
159C82—221no—
160C22×C11—21no—
161C22×C11—21no—
162C22×C11#39011yescharacteristic
163C22×C11#48612yes—
164C2×D11—82no—
165C2×D11—82no—
166C2×D11—82no—
167C2×D11—164no—
168C4×C11—21no—
169C4×C11—21no—
170C4×C11—82no—
171C4×C11C2×#10212yes—
172C4×C11#47112yes—
173C4×C11#47112yes—
174C4×C11#49211yescharacteristic
175C4×C11#49311yescharacteristic
176C22×Q8—21no—
177C22×D4—221no—
178C22×D4—221no—
179C22×D4—221no—
180C2×SD16—224no—
181C2×SD16—224no—
182C2×SD16—444no—
183C2×SD16—444no—
184C2×M16—21no—
185C2×M16—221no—
186C22×C8—112no—
187C4⋊Q8—21no—
188C4⋊Q8—21no—
189C4⋊Q8—21no—
190C4⋊Q8C4×D1112yes—
191#127—112no—
192#127—221no—
193#127—221no—
194#127—221no—
195C2×C4⋊C4—21no—
196C2×C4⋊C4—21no—
197C2×C42C22×D1111yescharacteristic
198#108—444no—
199C4⋊C8—21no—
200C4⋊C8—21no—
201C4⋊C8—112no—
202C4⋊C8—221no—
203C4⋊C8—221no—
204C4⋊C8C22⋊D1112yes—
205C22⋊C8—21no—
206C22⋊C8—221no—
207C4×C8—21no—
208C4×C8—112no—
209C4×C8—111no—
210C4×C8—111no—
211C4×C8—221no—
212C2×C11—22no—
213C2×C11#195711yescharacteristic
214C2×C11#197711yescharacteristic
215C2×C11#197711yescharacteristic
216D11—162no—
217C24—441no—
218C2×Q8—22no—
219C2×Q8—41no—
220C2×Q8—42no—
221C2×Q8—42no—
222C2×D4—222no—
223C2×D4—222no—
224C2×D4—222no—
225C2×D4—441no—
226C2×D4—442no—
227C2×D4—442no—
228C2×D4—441no—
229C2×D4—441no—
230C2×D4—882no—
231C2×D4—882no—
232C22×C4—41no—
233C22×C4#433911yescharacteristic
234C22×C4D4×D1111yescharacteristic
235C22×C4#434111yescharacteristic
236SD16—448no—
237SD16—448no—
238M16—42no—
239M16—442no—
240C2×C8—22no—
241C2×C8—41no—
242C2×C8—112no—
243C2×C8—112no—
244C2×C8—114no—
245C2×C8—114no—
246C2×C8—222no—
247C2×C8—441no—
248C4⋊C4—22no—
249C4⋊C4—22no—
250C4⋊C4—41no—
251C4⋊C4—41no—
252C42C2×C4×D1111yescharacteristic
253C42D4×D1111yescharacteristic
254C42D4×D1111yescharacteristic
255C42C2×C22⋊D1111yescharacteristic
256C11#976811yescharacteristic, complemented, Sylow
257C23—442no—
258C23—882no—
259C23—882no—
260C23—882no—
261C23#6693811yescharacteristic
262Q8—44no—
263Q8—81no—
264Q8—81no—
265D4—444no—
266D4—882no—
267D4—882no—
268D4—881no—
269D4—881no—
270D4—882no—
271D4—882no—
272C2×C4—22no—
273C2×C4—22no—
274C2×C4—42no—
275C2×C4—82no—
276C2×C4C22⋊C4×D1111yescharacteristic
277C2×C4(C22⋊D11)⋊C411yescharacteristic
278C2×C4#6693711yescharacteristic
279C2×C4D8×D1112yes—
280C2×C4SD16×D1112yes—
281C2×C4C4×C22⋊D1111yescharacteristic
282C2×C4#6699211yescharacteristic
283C2×C4#6699311yescharacteristic
284C8—42no—
285C8—81no—
286C8—114no—
287C8—114no—
288C8—442no—
289C8—881no—
290C22—21no—
291C22—21no—
292C22—882no—
293C22—882no—
294C22—882no—
295C22—1764no—
296C22#1062237312yes—
297C22#1062257011yescharacteristic
298C4—21no—
299C4—21no—
300C4—82no—
301C4#1062236712yes—
302C4D11×#10212yes—
303C4#1062276411yescharacteristic
304C4#1062278811yescharacteristic
305C4#1062281612yes—
306C2—22no—
307C2—1762no—
308C2#1306942011yescharacteristic
309C2#1306951811yescharacteristic
310C2#1306952011yescharacteristic
subgroupG/H
centerC22#10622570
commutatorC42×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1546C2
socleC22×C11#390
prime radicalC2×#66927C22
cosocleC2×C42×C11C23
hypercenter#1546D11
hypocenterC11#9768
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1546

Complements

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

NH ≅ G/Ntype
2. #13068787C2semidirect
3. #13067288C2semidirect
6. #13066900C2semidirect
7. C11×#1546C2semidirect
105. #1546D11semidirect
256. C11#9768semidirect

Maximal subgroups

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

subgroupindex
C2×#106226982
#130687872
#130672882
#130672852
#130672832
#130669002
C11×#15462
#976811