Finite Group Databasebeta

← #14648211

Subgroups — #14648211

Order 2816.

644 conjugacy classes of subgroups; only the 147 normal subgroups are shown.

normal subgroups only

This group has 644 conjugacy classes of subgroups — too many to draw. Only its 147 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#13071681C211yesmaximal, characteristic
2#13069377C212yesmaximal, complemented
3C2×#10622182C211yesmaximal, characteristic
4#13066456C212yesmaximal, complemented
5C11×#1957C211yesmaximal, characteristic
6C2×C11×#127C2211yescharacteristic
7C2×D4×Dic11—22no—
8C2×C11×#102—22no—
9C2×C4×C8×C11C2211yescharacteristic
10C11×#384C2211yescharacteristic
11#10622834—22no—
12#10622833—22no—
13C2×#66872—22no—
14C4×C4⋊Dic11C2212yes—
15C2×C4⋊(C11⋊C8)C2212yes—
16#10622182C414yescomplemented
17#10622167—22no—
18C22×D4×C11—22no—
19C22×D4×C11D412yes—
20C23×Dic11—22no—
21C22×C8×C11—21no—
22C11×#127—22no—
23C11×#127C2×C412yes—
24C11×#127Q812yes—
25C2×C11×C4⋊C4—22no—
26C2×C11×C4⋊C4—21no—
27C2×C42×C11C2311yescharacteristic
28C2×C22⋊Dic11—24no—
29C2×C22⋊Dic11—22no—
30D4×Dic11—44no—
31D4×Dic11—44no—
32C2×C4⋊Dic11D412yes—
33C2×C4⋊Dic11D412yes—
34C2×C4×Dic11—22no—
35C22×C11⋊C8—22no—
36C11×#102—44no—
37C4×C8×C11—22no—
38C11⋊#95—22no—
39#66872—44no—
40C4⋊(C11⋊C8)—22no—
41C4⋊(C11⋊C8)C2×C414yescomplemented
42#8924—111nomaximal, Sylow
43C24×C11—22no—
44C2×D4×C11—24no—
45C2×D4×C11—24no—
46C2×D4×C11—22no—
47C2×D4×C11—42no—
48C2×D4×C11—42no—
49C2×D4×C11—42no—
50C2×D4×C11—42no—
51C2×D4×C11—42no—
52C2×D4×C11—42no—
53C2×D4×C11C4⋊C414yes—
54C22×C4×C11—41no—
55C22×C4×C11C2×D411yescharacteristic
56C22×C4×C11C2×D412yes—
57C22×Dic11—22no—
58C22×Dic11—22no—
59C22×Dic11—48no—
60C22×Dic11—82no—
61C2×C8×C11—22no—
62C2×C8×C11—41no—
63C2×C8×C11—41no—
64C11×C4⋊C4—42no—
65C11×C4⋊C4—42no—
66C11×C4⋊C4—42no—
67C42×C11C22×C411yescharacteristic
68C42×C11C2×Q811yescharacteristic
69C42×C11#4112yes—
70C22⋊Dic11—48no—
71C22⋊Dic11—82no—
72C4⋊Dic11—22no—
73C4⋊Dic11—22no—
74C4⋊Dic11—22no—
75C4⋊Dic11SD1614yes—
76C4×Dic11—42no—
77C4×Dic11—42no—
78C2×C11⋊C8—24no—
79C2×C11⋊C8—42no—
80C2×C11⋊C8—42no—
81#2366—111no—
82#1957D1111yescharacteristic
83#1948—112no—
84C2×#331—111no—
85#1279—112no—
86C23×C11—24no—
87C23×C11—44no—
88C23×C11—44no—
89C23×C11—42no—
90C23×C11—42no—
91C23×C11#12011yescharacteristic
92D4×C11—44no—
93D4×C11—44no—
94D4×C11—44no—
95D4×C11—44no—
96D4×C11—44no—
97D4×C11—82no—
98C2×C4×C11—21no—
99C2×C4×C11—21no—
100C2×C4×C11—82no—
101C2×C4×C11—81no—
102C2×C4×C11C2×C4⋊C411yescharacteristic
103C2×C4×C11C4×D412yes—
104C2×C4×C11C22⋊Q812yes—
105C2×C4×C11#12311yescharacteristic
106C2×C4×C11C2×SD1612yes—
107C2×C4×C11#13512yes—
108C2×C4×C11AGL(1,ℤ/8)12yes—
109C2×C4×C11AGL(1,ℤ/8)12yes—
110C2×Dic11—24no—
111C2×Dic11—42no—
112C2×Dic11—42no—
113C2×Dic11—42no—
114C2×Dic11—42no—
115C2×Dic11—42no—
116C2×Dic11—88no—
117C8×C11—42no—
118C11⋊C8—44no—
119C2×#127C2×D1111yescharacteristic
120C2×C4×D4—222no—
121C2×#106—222no—
122C2×C4⋊C8—112no—
123C2×#102—22no—
124C2×C4×C8C2×D1111yescharacteristic
125#390—222no—
126#386—222no—
127#384C2×D1111yescharacteristic
128C4×C4⋊C4—112no—
129#340—222no—
130#331—114no—
131C22×C11—44no—
132C22×C11—48no—
133C22×C11—82no—
134C22×C11—82no—
135C22×C11—84no—
136C22×C11#38511yescharacteristic
137C22×C11#44912yes—
138C22×C11#45012yes—
139C22×C11#45311yescharacteristic
140C22×C11#45511yescharacteristic
141C4×C11—21no—
142C4×C11—21no—
143C4×C11—161no—
144C4×C11C4×SD1612yes—
145C4×C11#44212yes—
146C4×C11#47612yes—
147C4×C11#47812yes—
148Dic11—44no—
149Dic11—82no—
150C22×D4—22no—
151C22×D4C22⋊D1112yes—
152C23×C4—222no—
153C22×C8—21no—
154C22×C8—222no—
155#127—22no—
156#127Dic2212yes—
157#127C4×D1112yes—
158C4×D4—444no—
159C4×D4—444no—
160C2×C4⋊C4—22no—
161C2×C4⋊C4—21no—
162C2×C4⋊C4—112no—
163C2×C4⋊C4—112no—
164C2×C22⋊C4—224no—
165C2×C22⋊C4—222no—
166C2×C42—222no—
167C2×C42C22×D1111yescharacteristic
168#106—444no—
169C4⋊C8—114no—
170C4⋊C8—222no—
171#102—44no—
172C4×C8—22no—
173#95—222no—
174C2×C11—84no—
175C2×C11#162011yescharacteristic
176C2×C11#162911yescharacteristic
177C2×C11#164212yes—
178C2×C11#185611yescharacteristic
179C2×C11#186412yes—
180C24—22no—
181C2×D4—24no—
182C2×D4—24no—
183C2×D4—22no—
184C2×D4—42no—
185C2×D4—42no—
186C2×D4—42no—
187C2×D4—42no—
188C2×D4—42no—
189C2×D4—42no—
190C2×D4Dic11⋊C414yes—
191C22×C4—41no—
192C22×C4—222no—
193C22×C4—222no—
194C22×C4—448no—
195C22×C4—882no—
196C22×C4D4×D1112yes—
197C22×C4C2×C22⋊D1111yescharacteristic
198C2×C8—22no—
199C2×C8—41no—
200C2×C8—41no—
201C2×C8—224no—
202C2×C8—442no—
203C2×C8—442no—
204C4⋊C4—42no—
205C4⋊C4—42no—
206C4⋊C4—42no—
207C4⋊C4—114no—
208C4⋊C4—222no—
209C4⋊C4—222no—
210C4⋊C4—222no—
211C22⋊C4—448no—
212C22⋊C4—882no—
213C42—442no—
214C42—442no—
215C42C2×Dic2211yescharacteristic
216C42C2×C4×D1111yescharacteristic
217C42#434112yes—
218C11#892411yescharacteristic, complemented, Sylow
219C23—24no—
220C23—44no—
221C23—44no—
222C23—42no—
223C23—42no—
224C23#6699011yescharacteristic
225D4—44no—
226D4—44no—
227D4—44no—
228D4—44no—
229D4—44no—
230D4—82no—
231C2×C4—21no—
232C2×C4—21no—
233C2×C4—82no—
234C2×C4—81no—
235C2×C4—224no—
236C2×C4—442no—
237C2×C4—442no—
238C2×C4—442no—
239C2×C4—442no—
240C2×C4—442no—
241C2×C4—888no—
242C2×C4#6693112yes—
243C2×C4(C22⋊D11)⋊C412yes—
244C2×C4#6696412yes—
245C2×C4#6696512yes—
246C2×C4SD16×D1112yes—
247C2×C4#6696712yes—
248C2×C4C2×Dic11⋊C411yescharacteristic
249C2×C4#6698811yescharacteristic
250C8—42no—
251C8—444no—
252C22—44no—
253C22—48no—
254C22—84no—
255C22—82no—
256C22—82no—
257C22#1062255911yescharacteristic
258C22#1062267411yescharacteristic
259C22#1062269011yescharacteristic
260C22#1062277112yes—
261C22#1062278212yes—
262C4—21no—
263C4—21no—
264C4—161no—
265C4—444no—
266C4—882no—
267C4#1062237112yes—
268C4#1062237412yes—
269C4#1062237912yes—
270C4#1062239812yes—
271C2—84no—
272C2#1306767311yescharacteristic
273C2#1306773011yescharacteristic
274C2#1306781312yes—
275C2#1306882511yescharacteristic
276C2#1306887512yes—
subgroupG/H
centerC23#66990
commutatorC42×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1957C2
socleC23×C11#120
prime radicalC2×C11×#127C22
cosocleC2×C42×C11C23
hypercenter#1957D11
hypocenterC11#8924
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1957

Complements

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

NH ≅ G/Ntype
2. #13069377C2semidirect
4. #13066456C2semidirect
16. #10622182C4semidirect
41. C4⋊(C11⋊C8)C2×C4semidirect
218. C11#8924semidirect

Maximal subgroups

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

subgroupindex
#130716812
#130693772
C2×#106221822
#130664562
C11×#19572
#892411