Finite Group Databasebeta

← #14653234

Subgroups — #14653234

Order 2816.

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

normal subgroups only

This group has 478 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×#10622705C211yesmaximal, characteristic
2#13068787C211yesmaximal, characteristic
3#13067289C211yesmaximal, characteristic
4#13067288C211yesmaximal, characteristic
5#13067287C211yesmaximal, characteristic
6#13066900C211yesmaximal, characteristic
7C11×#1546C211yesmaximal, characteristic
8C2×C11×C4⋊Q8C2211yescharacteristic
9C22×#4326—22no—
10C2×#66922C2211yescharacteristic
11C11×#431C2211yescharacteristic
12C11×#423C2211yescharacteristic
13C2×#66886—22no—
14#10622705—21no—
15#10622705—21no—
16#10622705C414yes—
17#10622538C2211yescharacteristic
18#10622537C2211yescharacteristic
19C2×C4×C11⋊C8C2211yescharacteristic
20C11×#332—22no—
21#10622185—22no—
22#10622124—22no—
23#10622120—22no—
24#10622092—21no—
25C8×C11⋊C8—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—
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#9772—111nomaximal, Sylow
63C2×Q8×C11—22no—
64C2×Q8×C11—41no—
65C2×Q8×C11—42no—
66C2×Q8×C11—42no—
67C22×C4×C11—41no—
68C22×C4×C11C2×D411yescharacteristic
69C22×C4×C11#4111yescharacteristic
70C22×C4×C11#4111yescharacteristic
71C22×Dic11—41no—
72C2×Dic22—22no—
73C2×Dic22—41no—
74C2×Dic22—42no—
75C2×Dic22—42no—
76C11×M16—42no—
77C2×C8×C11—22no—
78C2×C8×C11—41no—
79C11×C4⋊C4—22no—
80C11×C4⋊C4—22no—
81C11×C4⋊C4—41no—
82C11×C4⋊C4—41no—
83C42×C11C22×C411yescharacteristic
84C42×C11C2×D411yescharacteristic
85C42×C11C2×D411yescharacteristic
86C42×C11C2×D411yescharacteristic
87#4326—48no—
88#4326—48no—
89C4⋊Dic11—22no—
90C4⋊Dic11—22no—
91C4⋊Dic11—41no—
92C4⋊Dic11—41no—
93#4318—42no—
94C2×C11⋊C8—22no—
95C2×C11⋊C8—41no—
96C2×C11⋊C8C22⋊C412yes—
97C2×C11⋊C8C22⋊C412yes—
98C2×C11⋊C8D814yes—
99C2×C11⋊C8SD1614yes—
100C2×#494—111no—
101#1848—111no—
102#1546—111no—
103#1546—111no—
104#1546—111no—
105#1546D1111yescharacteristic
106#1450—111no—
107C23×C11#12411yescharacteristic
108Q8×C11—44no—
109Q8×C11—81no—
110Q8×C11—81no—
111C2×C4×C11—22no—
112C2×C4×C11—22no—
113C2×C4×C11—42no—
114C2×C4×C11—82no—
115C2×C4×C11C2×C22⋊C411yescharacteristic
116C2×C4×C11C4×D411yescharacteristic
117C2×C4×C11C4×D411yescharacteristic
118C2×C4×C11#12111yescharacteristic
119C2×C4×C11#12111yescharacteristic
120C2×C4×C11#12711yescharacteristic
121C2×C4×C11C2×D812yes—
122C2×C4×C11C2×SD1612yes—
123C2×Dic11—42no—
124C2×Dic11—82no—
125Dic22—44no—
126Dic22—81no—
127Dic22—81no—
128C8×C11—42no—
129C8×C11—81no—
130C11⋊C8—42no—
131C11⋊C8—81no—
132C11⋊C8#10214yes—
133C11⋊C8#10214yes—
134C22×Q16—222no—
135C2×C4⋊Q8—111no—
136C2×C4⋊Q8C2×D1111yescharacteristic
137#494—114no—
138#494—221no—
139#494—221no—
140#431—111no—
141#431C2×D1111yescharacteristic
142C2×#108—222no—
143#423—111no—
144#423C2×D1111yescharacteristic
145C2×C4×C8—111no—
146#332—22no—
147#332—222no—
148#332—222no—
149#332—222no—
150#322—221no—
151C82—221no—
152C22×C11—21no—
153C22×C11—21no—
154C22×C11#39011yescharacteristic
155C22×C11#48612yes—
156C4×C11—21no—
157C4×C11—21no—
158C4×C11—82no—
159C4×C11C2×#10212yes—
160C4×C11#47312yes—
161C4×C11#47312yes—
162C4×C11#49211yescharacteristic
163C4×C11#49311yescharacteristic
164Dic11—82no—
165C22×Q8—21no—
166C22×Q8—221no—
167C2×Q16—224no—
168C2×Q16—224no—
169C2×Q16—444no—
170C2×Q16—444no—
171C2×M16—21no—
172C2×M16—221no—
173C22×C8—112no—
174C4⋊Q8—21no—
175C4⋊Q8—21no—
176C4⋊Q8—21no—
177C4⋊Q8—112no—
178C4⋊Q8—221no—
179C4⋊Q8—221no—
180C4⋊Q8—221no—
181C4⋊Q8C4×D1112yes—
182C2×C4⋊C4—21no—
183C2×C4⋊C4—21no—
184C2×C4⋊C4—221no—
185C2×C4⋊C4—221no—
186C2×C42C22×D1111yescharacteristic
187#108—444no—
188C4⋊C8—21no—
189C4⋊C8—21no—
190C4⋊C8—112no—
191C4⋊C8—221no—
192C4⋊C8—221no—
193C4⋊C8C22⋊D1112yes—
194C22⋊C8—21no—
195C22⋊C8—221no—
196C4×C8—21no—
197C4×C8—112no—
198C4×C8—111no—
199C4×C8—111no—
200C4×C8—221no—
201C2×C11—22no—
202C2×C11#195711yescharacteristic
203C2×C11#197911yescharacteristic
204C2×C11#197911yescharacteristic
205C2×Q8—22no—
206C2×Q8—41no—
207C2×Q8—42no—
208C2×Q8—42no—
209C2×Q8—222no—
210C2×Q8—441no—
211C2×Q8—442no—
212C2×Q8—442no—
213C22×C4—41no—
214C22×C4—441no—
215C22×C4#433911yescharacteristic
216C22×C4D4×D1111yescharacteristic
217C22×C4#434111yescharacteristic
218Q16—448no—
219Q16—448no—
220M16—42no—
221M16—442no—
222C2×C8—22no—
223C2×C8—41no—
224C2×C8—112no—
225C2×C8—112no—
226C2×C8—114no—
227C2×C8—114no—
228C2×C8—222no—
229C2×C8—441no—
230C4⋊C4—22no—
231C4⋊C4—22no—
232C4⋊C4—41no—
233C4⋊C4—41no—
234C4⋊C4—222no—
235C4⋊C4—222no—
236C4⋊C4—441no—
237C4⋊C4—441no—
238C42C2×C4×D1111yescharacteristic
239C42D4×D1111yescharacteristic
240C42D4×D1111yescharacteristic
241C42C2×C22⋊D1111yescharacteristic
242C11#977211yescharacteristic, complemented, Sylow
243C23#6693811yescharacteristic
244Q8—44no—
245Q8—81no—
246Q8—81no—
247Q8—444no—
248Q8—881no—
249Q8—881no—
250C2×C4—22no—
251C2×C4—22no—
252C2×C4—42no—
253C2×C4—82no—
254C2×C4—442no—
255C2×C4—882no—
256C2×C4C22⋊C4×D1111yescharacteristic
257C2×C4(C22⋊D11)⋊C411yescharacteristic
258C2×C4#6693711yescharacteristic
259C2×C4D8×D1112yes—
260C2×C4SD16×D1112yes—
261C2×C4C4×C22⋊D1111yescharacteristic
262C2×C4#6699211yescharacteristic
263C2×C4#6699311yescharacteristic
264C8—42no—
265C8—81no—
266C8—114no—
267C8—114no—
268C8—442no—
269C8—881no—
270C22—21no—
271C22—21no—
272C22#1062237312yes—
273C22#1062257011yescharacteristic
274C4—21no—
275C4—21no—
276C4—82no—
277C4—882no—
278C4#1062236812yes—
279C4D11×#10212yes—
280C4#1062276411yescharacteristic
281C4#1062278811yescharacteristic
282C4#1062281712yes—
283C2—22no—
284C2#1306942011yescharacteristic
285C2#1306952811yescharacteristic
286C2#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#9772
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
242. C11#9772semidirect

Maximal subgroups

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

subgroupindex
C2×#106227052
#130687872
#130672892
#130672882
#130672872
#130669002
C11×#15462
#977211