Finite Group Databasebeta

← #14653228

Subgroups — #14653228

Order 2816.

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

normal subgroups only

This group has 398 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×#10622694C211yesmaximal, characteristic
2#13068753C211yesmaximal, characteristic
3#13067302C211yesmaximal, characteristic
4#13067296C211yesmaximal, characteristic
5#13067288C211yesmaximal, characteristic
6#13066900C211yesmaximal, characteristic
7C11×#1546C211yesmaximal, characteristic
8C2×C11×C4⋊Q8C2211yescharacteristic
9C2×#66922C2211yescharacteristic
10C11×#431C2211yescharacteristic
11C11×#423C2211yescharacteristic
12C2×#66899—22no—
13#10622694—21no—
14#10622694—21no—
15#10622694C414yes—
16#10622538C2211yescharacteristic
17#10622537C2211yescharacteristic
18C2×C4×C11⋊C8C2211yescharacteristic
19C11×#332—22no—
20#10622196—22no—
21#10622185—22no—
22#10622124—22no—
23#10622119—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×C4⋊Dic11—21no—
37C2×C4⋊Dic11—21no—
38C2×#4318—21no—
39C22×C11⋊C8D412yes—
40#66922—21no—
41#66922—21no—
42#66922—21no—
43#66922C2×C412yes—
44C11×C4⋊C8—21no—
45C11×C4⋊C8—21no—
46C11×C4⋊C8D412yes—
47C11×C22⋊C8—21no—
48C4×C8×C11—21no—
49#66899—24no—
50#66899—24no—
51C22⋊(C11⋊C8)—21no—
52C4⋊(C11⋊C8)—21no—
53C4⋊(C11⋊C8)—21no—
54C4⋊(C11⋊C8)D412yes—
55C4×C11⋊C8—21no—
56C4×C11⋊C8C2×C412yes—
57C4×C11⋊C8D411yescharacteristic
58C4×C11⋊C8D411yescharacteristic
59#9770—111nomaximal, Sylow
60C2×Q8×C11—22no—
61C2×Q8×C11—41no—
62C2×Q8×C11—42no—
63C2×Q8×C11—42no—
64C22×C4×C11—41no—
65C22×C4×C11C2×D411yescharacteristic
66C22×C4×C11#4111yescharacteristic
67C22×C4×C11#4111yescharacteristic
68C22×Dic11—41no—
69C2×Dic22—22no—
70C2×Dic22—41no—
71C2×Dic22—82no—
72C11×M16—42no—
73C2×C8×C11—22no—
74C2×C8×C11—41no—
75C11×C4⋊C4—22no—
76C11×C4⋊C4—22no—
77C11×C4⋊C4—41no—
78C11×C4⋊C4—41no—
79C42×C11C22×C411yescharacteristic
80C42×C11C2×D411yescharacteristic
81C42×C11C2×D411yescharacteristic
82C42×C11C2×D411yescharacteristic
83C4⋊Dic11—22no—
84C4⋊Dic11—22no—
85C4⋊Dic11—41no—
86C4⋊Dic11—41no—
87#4318—42no—
88C2×C11⋊C8—22no—
89C2×C11⋊C8—22no—
90C2×C11⋊C8—22no—
91C2×C11⋊C8—41no—
92C2×C11⋊C8C22⋊C412yes—
93C2×C11⋊C8C22⋊C412yes—
94C2×#487—111no—
95#1837—111no—
96#1549—111no—
97#1548—111no—
98#1546—111no—
99#1546D1111yescharacteristic
100#1450—111no—
101C23×C11#12411yescharacteristic
102Q8×C11—44no—
103Q8×C11—81no—
104Q8×C11—81no—
105C2×C4×C11—22no—
106C2×C4×C11—22no—
107C2×C4×C11—42no—
108C2×C4×C11—82no—
109C2×C4×C11C2×C22⋊C411yescharacteristic
110C2×C4×C11C4×D411yescharacteristic
111C2×C4×C11C4×D411yescharacteristic
112C2×C4×C11#12111yescharacteristic
113C2×C4×C11#12111yescharacteristic
114C2×C4×C11#12711yescharacteristic
115C2×C4×C11#13512yes—
116C2×C4×C11#13512yes—
117C2×Dic11—42no—
118C2×Dic11—82no—
119Dic22—82no—
120Dic22—82no—
121C8×C11—42no—
122C8×C11—81no—
123C11⋊C8—22no—
124C11⋊C8—22no—
125C11⋊C8—42no—
126C11⋊C8—81no—
127C2×C4⋊Q8—111no—
128C2×C4⋊Q8C2×D1111yescharacteristic
129#487—114no—
130#487—221no—
131#487—221no—
132#431—111no—
133#431C2×D1111yescharacteristic
134#423—111no—
135#423C2×D1111yescharacteristic
136C2×#103—222no—
137C2×C4×C8—111no—
138#341—222no—
139#333—222no—
140#332—22no—
141#332—222no—
142#332—222no—
143#322—221no—
144C82—221no—
145C22×C11—21no—
146C22×C11—21no—
147C22×C11#39011yescharacteristic
148C22×C11#48812yes—
149C4×C11—21no—
150C4×C11—21no—
151C4×C11—82no—
152C4×C11#41612yes—
153C4×C11#47112yes—
154C4×C11#47312yes—
155C4×C11#49511yescharacteristic
156C4×C11#49511yescharacteristic
157Dic11—82no—
158C22×Q8—21no—
159C22×Q8—221no—
160C2×M16—21no—
161C2×M16—221no—
162C22×C8—112no—
163C4⋊Q8—21no—
164C4⋊Q8—21no—
165C4⋊Q8—21no—
166C4⋊Q8—112no—
167C4⋊Q8—221no—
168C4⋊Q8—221no—
169C4⋊Q8—221no—
170C4⋊Q8C4×D1112yes—
171C2×C4⋊C4—21no—
172C2×C4⋊C4—21no—
173C2×C4⋊C4—221no—
174C2×C4⋊C4—221no—
175C2×C42C22×D1111yescharacteristic
176C4⋊C8—21no—
177C4⋊C8—21no—
178C4⋊C8—112no—
179C4⋊C8—221no—
180C4⋊C8—221no—
181C4⋊C8C22⋊D1112yes—
182#103—224no—
183#103—224no—
184C22⋊C8—21no—
185C22⋊C8—221no—
186C4×C8—21no—
187C4×C8—112no—
188C4×C8—111no—
189C4×C8—111no—
190C4×C8—221no—
191C2×C11—22no—
192C2×C11#195811yescharacteristic
193C2×C11#197711yescharacteristic
194C2×C11#197911yescharacteristic
195C2×Q8—22no—
196C2×Q8—41no—
197C2×Q8—42no—
198C2×Q8—42no—
199C2×Q8—222no—
200C2×Q8—441no—
201C2×Q8—882no—
202C22×C4—41no—
203C22×C4—441no—
204C22×C4#433911yescharacteristic
205C22×C4D4×D1111yescharacteristic
206C22×C4#434111yescharacteristic
207M16—42no—
208M16—442no—
209C2×C8—22no—
210C2×C8—41no—
211C2×C8—112no—
212C2×C8—112no—
213C2×C8—222no—
214C2×C8—222no—
215C2×C8—222no—
216C2×C8—441no—
217C4⋊C4—22no—
218C4⋊C4—22no—
219C4⋊C4—41no—
220C4⋊C4—41no—
221C4⋊C4—222no—
222C4⋊C4—222no—
223C4⋊C4—441no—
224C4⋊C4—441no—
225C42C2×C4×D1111yescharacteristic
226C42D4×D1111yescharacteristic
227C42D4×D1111yescharacteristic
228C42C2×C22⋊D1111yescharacteristic
229C11#977011yescharacteristic, complemented, Sylow
230C23#6693811yescharacteristic
231Q8—44no—
232Q8—81no—
233Q8—81no—
234Q8—882no—
235Q8—882no—
236C2×C4—22no—
237C2×C4—22no—
238C2×C4—42no—
239C2×C4—82no—
240C2×C4—442no—
241C2×C4—882no—
242C2×C4C22⋊C4×D1111yescharacteristic
243C2×C4(C22⋊D11)⋊C411yescharacteristic
244C2×C4#6693711yescharacteristic
245C2×C4#6696512yes—
246C2×C4#6696912yes—
247C2×C4C4×C22⋊D1111yescharacteristic
248C2×C4#6699211yescharacteristic
249C2×C4#6699311yescharacteristic
250C8—42no—
251C8—81no—
252C8—222no—
253C8—222no—
254C8—442no—
255C8—881no—
256C22—21no—
257C22—21no—
258C22#1062238112yes—
259C22#1062257011yescharacteristic
260C4—21no—
261C4—21no—
262C4—82no—
263C4—882no—
264C4#1062236712yes—
265C4#1062238512yes—
266C4#1062276811yescharacteristic
267C4#1062278111yescharacteristic
268C4#1062281712yes—
269C2—22no—
270C2#1306942611yescharacteristic
271C2#1306952011yescharacteristic
272C2#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#9770
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
229. C11#9770semidirect

Maximal subgroups

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

subgroupindex
C2×#106226942
#130687532
#130673022
#130672962
#130672882
#130669002
C11×#15462
#977011