Finite Group Databasebeta

← #14653271

Subgroups — #14653271

Order 2816.

454 conjugacy classes of subgroups; only the 113 normal subgroups are shown.

normal subgroups only

This group has 454 conjugacy classes of subgroups — too many to draw. Only its 113 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×#10622705C211yesmaximal, characteristic
2#13068753C211yesmaximal, characteristic
3#13067289C211yesmaximal, characteristic
4#13067288C211yesmaximal, characteristic
5#13067287C211yesmaximal, characteristic
6#13066909C211yesmaximal, characteristic
7C11×#1546C211yesmaximal, characteristic
8C2×C11×C4⋊Q8C2211yescharacteristic
9C22×#4326—22no—
10C2×#66922C2211yescharacteristic
11C11×#431C2211yescharacteristic
12C11×#423C2211yescharacteristic
13#10622705—21no—
14#10622705—21no—
15#10622705C414yes—
16#10622538C2211yescharacteristic
17#10622537C2211yescharacteristic
18C2×C4×C11⋊C8C2211yescharacteristic
19C11×#332—22no—
20#10622196—22no—
21#10622185—22no—
22#10622124—22no—
23#10622120—22no—
24#10622093—21no—
25#10622092—21no—
26C22×Q8×C11—21no—
27C22×Dic22—21no—
28C2×C11×M16—21no—
29C11×C4⋊Q8—21no—
30C11×C4⋊Q8—21no—
31C11×C4⋊Q8—21no—
32C11×C4⋊Q8C2×C412yes—
33C2×C11×C4⋊C4—21no—
34C2×C11×C4⋊C4—21no—
35C2×C42×C11C2311yescharacteristic
36C2×#4326—24no—
37C2×#4326—24no—
38C2×#4326—44no—
39C2×#4326—44no—
40C2×C4⋊Dic11—21no—
41C2×C4⋊Dic11—21no—
42C2×#4318—21no—
43C22×C11⋊C8D412yes—
44#66922—21no—
45#66922—21no—
46#66922—21no—
47#66922C2×C412yes—
48C11×C4⋊C8—21no—
49C11×C4⋊C8—21no—
50C11×C4⋊C8D412yes—
51C11×C22⋊C8—21no—
52C4×C8×C11—21no—
53C22⋊(C11⋊C8)—21no—
54C4⋊(C11⋊C8)—21no—
55C4⋊(C11⋊C8)—21no—
56C4⋊(C11⋊C8)D412yes—
57C4×C11⋊C8—21no—
58C4×C11⋊C8C2×C412yes—
59C4×C11⋊C8D411yescharacteristic
60C4×C11⋊C8D411yescharacteristic
61#9779—111nomaximal, Sylow
62C2×Q8×C11—22no—
63C2×Q8×C11—41no—
64C2×Q8×C11—42no—
65C2×Q8×C11—42no—
66C22×C4×C11—41no—
67C22×C4×C11C2×D411yescharacteristic
68C22×C4×C11#4111yescharacteristic
69C22×C4×C11#4111yescharacteristic
70C22×Dic11—41no—
71C2×Dic22—22no—
72C2×Dic22—41no—
73C2×Dic22—42no—
74C2×Dic22—42no—
75C11×M16—42no—
76C2×C8×C11—22no—
77C2×C8×C11—41no—
78C11×C4⋊C4—22no—
79C11×C4⋊C4—22no—
80C11×C4⋊C4—41no—
81C11×C4⋊C4—41no—
82C42×C11C22×C411yescharacteristic
83C42×C11C2×D411yescharacteristic
84C42×C11C2×D411yescharacteristic
85C42×C11C2×D411yescharacteristic
86#4326—48no—
87#4326—48no—
88C4⋊Dic11—22no—
89C4⋊Dic11—22no—
90C4⋊Dic11—41no—
91C4⋊Dic11—41no—
92#4318—42no—
93C2×C11⋊C8—22no—
94C2×C11⋊C8—22no—
95C2×C11⋊C8—22no—
96C2×C11⋊C8—41no—
97C2×C11⋊C8C22⋊C412yes—
98C2×C11⋊C8C22⋊C412yes—
99C2×#494—111no—
100#1837—111no—
101#1546—111no—
102#1546—111no—
103#1546—111no—
104#1546D1111yescharacteristic
105#1452—111no—
106C23×C11#12411yescharacteristic
107Q8×C11—44no—
108Q8×C11—81no—
109Q8×C11—81no—
110C2×C4×C11—22no—
111C2×C4×C11—22no—
112C2×C4×C11—42no—
113C2×C4×C11—82no—
114C2×C4×C11C2×C22⋊C411yescharacteristic
115C2×C4×C11C4×D411yescharacteristic
116C2×C4×C11C4×D411yescharacteristic
117C2×C4×C11#12111yescharacteristic
118C2×C4×C11#12111yescharacteristic
119C2×C4×C11#12711yescharacteristic
120C2×C4×C11AGL(1,ℤ/8)12yes—
121C2×C4×C11AGL(1,ℤ/8)12yes—
122C2×Dic11—42no—
123C2×Dic11—82no—
124Dic22—44no—
125Dic22—81no—
126Dic22—81no—
127C8×C11—42no—
128C8×C11—81no—
129C11⋊C8—22no—
130C11⋊C8—22no—
131C11⋊C8—42no—
132C11⋊C8—81no—
133C22×Q16—222no—
134C2×C4⋊Q8—111no—
135C2×C4⋊Q8C2×D1111yescharacteristic
136#494—114no—
137#494—221no—
138#494—221no—
139#431—111no—
140#431C2×D1111yescharacteristic
141#423—111no—
142#423C2×D1111yescharacteristic
143C2×C4×C8—111no—
144#341—222no—
145#332—22no—
146#332—222no—
147#332—222no—
148#332—222no—
149#322—221no—
150#322—221no—
151C22×C11—21no—
152C22×C11—21no—
153C22×C11#39011yescharacteristic
154C22×C11#49012yes—
155C4×C11—21no—
156C4×C11—21no—
157C4×C11—82no—
158C4×C11#41812yes—
159C4×C11#47312yes—
160C4×C11#47312yes—
161C4×C11#49611yescharacteristic
162C4×C11#49611yescharacteristic
163Dic11—82no—
164C22×Q8—21no—
165C22×Q8—221no—
166C2×Q16—224no—
167C2×Q16—224no—
168C2×Q16—444no—
169C2×Q16—444no—
170C2×M16—21no—
171C2×M16—221no—
172C22×C8—112no—
173C4⋊Q8—21no—
174C4⋊Q8—21no—
175C4⋊Q8—21no—
176C4⋊Q8—112no—
177C4⋊Q8—221no—
178C4⋊Q8—221no—
179C4⋊Q8—221no—
180C4⋊Q8C4×D1112yes—
181C2×C4⋊C4—21no—
182C2×C4⋊C4—21no—
183C2×C4⋊C4—221no—
184C2×C4⋊C4—221no—
185C2×C42C22×D1111yescharacteristic
186C4⋊C8—21no—
187C4⋊C8—21no—
188C4⋊C8—112no—
189C4⋊C8—221no—
190C4⋊C8—221no—
191C4⋊C8C22⋊D1112yes—
192C22⋊C8—21no—
193C22⋊C8—221no—
194C4×C8—21no—
195C4×C8—112no—
196C4×C8—111no—
197C4×C8—111no—
198C4×C8—221no—
199C2×C11—22no—
200C2×C11#196111yescharacteristic
201C2×C11#197911yescharacteristic
202C2×C11#197911yescharacteristic
203C2×Q8—22no—
204C2×Q8—41no—
205C2×Q8—42no—
206C2×Q8—42no—
207C2×Q8—222no—
208C2×Q8—441no—
209C2×Q8—442no—
210C2×Q8—442no—
211C22×C4—41no—
212C22×C4—441no—
213C22×C4#433911yescharacteristic
214C22×C4D4×D1111yescharacteristic
215C22×C4#434111yescharacteristic
216Q16—448no—
217Q16—448no—
218M16—42no—
219M16—442no—
220C2×C8—22no—
221C2×C8—41no—
222C2×C8—112no—
223C2×C8—112no—
224C2×C8—222no—
225C2×C8—222no—
226C2×C8—222no—
227C2×C8—441no—
228C4⋊C4—22no—
229C4⋊C4—22no—
230C4⋊C4—41no—
231C4⋊C4—41no—
232C4⋊C4—222no—
233C4⋊C4—222no—
234C4⋊C4—441no—
235C4⋊C4—441no—
236C42C2×C4×D1111yescharacteristic
237C42D4×D1111yescharacteristic
238C42D4×D1111yescharacteristic
239C42C2×C22⋊D1111yescharacteristic
240C11#977911yescharacteristic, complemented, Sylow
241C23#6693811yescharacteristic
242Q8—44no—
243Q8—81no—
244Q8—81no—
245Q8—444no—
246Q8—881no—
247Q8—881no—
248C2×C4—22no—
249C2×C4—22no—
250C2×C4—42no—
251C2×C4—82no—
252C2×C4—442no—
253C2×C4—882no—
254C2×C4C22⋊C4×D1111yescharacteristic
255C2×C4(C22⋊D11)⋊C411yescharacteristic
256C2×C4#6693711yescharacteristic
257C2×C4#6696412yes—
258C2×C4#6696712yes—
259C2×C4C4×C22⋊D1111yescharacteristic
260C2×C4#6699211yescharacteristic
261C2×C4#6699311yescharacteristic
262C8—42no—
263C8—81no—
264C8—222no—
265C8—222no—
266C8—442no—
267C8—881no—
268C22—21no—
269C22—21no—
270C22#1062237712yes—
271C22#1062257011yescharacteristic
272C4—21no—
273C4—21no—
274C4—82no—
275C4—882no—
276C4#1062236812yes—
277C4#1062238312yes—
278C4#1062276711yescharacteristic
279C4#1062278911yescharacteristic
280C4#1062281712yes—
281C2—22no—
282C2#1306943811yescharacteristic
283C2#1306952811yescharacteristic
284C2#1306953011yescharacteristic
subgroupG/H
centerC22#10622570
commutatorC42×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1546C2
socleC22×C11#390
prime radicalC23×C11#124
cosocleC2×C42×C11C23
hypercenter#1546D11
hypocenterC11#9779
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
240. C11#9779semidirect

Maximal subgroups

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

subgroupindex
C2×#106227052
#130687532
#130672892
#130672882
#130672872
#130669092
C11×#15462
#977911