Finite Group Databasebeta

← #14658442

Subgroups — #14658442

Order 2816.

306 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 306 conjugacy classes of subgroups — too many to draw. Only its 99 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#13069391C211yesmaximal, characteristic
2#13067388C211yesmaximal, characteristic
3#13067368C211yesmaximal, characteristic
4#13067297C211yesmaximal, characteristic
5C2×#10622184C211yesmaximal, characteristic
6#13066490C211yesmaximal, characteristic
7C11×#1997C211yesmaximal, characteristic
8C2×C11×C4⋊Q8C2211yescharacteristic
9C11×#423C2211yescharacteristic
10C4×C11×M16C2211yescharacteristic
11C2×#66886—21no—
12#10622538C2211yescharacteristic
13#10622537C2211yescharacteristic
14C2×C4⋊(C11⋊C8)C2211yescharacteristic
15C2×C4⋊(C11⋊C8)C2211yescharacteristic
16C11×#343—21no—
17C11×#343—21no—
18#10622196—21no—
19#10622184—22no—
20#10622184—21no—
21#10622184—21no—
22#10622118—22no—
23#10622096—21no—
24#10622095—21no—
25C22×Q8×C11Q812yes—
26C2×C11×M16—21no—
27C2×C11×M16D411yescharacteristic
28C2×C11×M16D411yescharacteristic
29C11×C4⋊Q8—21no—
30C11×C4⋊Q8—21no—
31C11×C4⋊Q8—21no—
32C11×C4⋊Q8—21no—
33C2×C11×C4⋊C4—21no—
34C2×C11×C4⋊C4—21no—
35C2×C42×C11C2311yescharacteristic
36C2×#4318—21no—
37C22×C11⋊C8—21no—
38C22×C11⋊C8—21no—
39C11×C4⋊C8—21no—
40C11×C4⋊C8—21no—
41C11×#97—21no—
42C4×C8×C11—21no—
43C22⋊(C11⋊C8)—21no—
44#66886—42no—
45C4⋊(C11⋊C8)—21no—
46C4⋊(C11⋊C8)—21no—
47C4⋊(C11⋊C8)—21no—
48C4⋊(C11⋊C8)—21no—
49C4⋊(C11⋊C8)—21no—
50C4⋊(C11⋊C8)D412yes—
51C4⋊(C11⋊C8)D411yescharacteristic
52C4⋊(C11⋊C8)D411yescharacteristic
53C4×C11⋊C8—21no—
54#10609—111nomaximal, Sylow
55C2×Q8×C11—22no—
56C2×Q8×C11—22no—
57C2×Q8×C11—82no—
58C22×C4×C11—22no—
59C22×C4×C11C2×D411yescharacteristic
60C22×C4×C11C2×Q811yescharacteristic
61C22×C4×C11#4111yescharacteristic
62C11×M16—21no—
63C11×M16—21no—
64C11×M16—21no—
65C11×M16—41no—
66C11×M16—41no—
67C11×M16SD1612yes—
68C2×C8×C11—21no—
69C2×C8×C11—21no—
70C2×C8×C11—41no—
71C11×C4⋊C4—41no—
72C11×C4⋊C4—41no—
73C11×C4⋊C4—41no—
74C11×C4⋊C4—41no—
75C42×C11C2×D411yescharacteristic
76C42×C11C2×D411yescharacteristic
77C42×C11#4111yescharacteristic
78C42×C11#4111yescharacteristic
79#4318—41no—
80#4318—41no—
81C2×C11⋊C8—21no—
82C2×C11⋊C8—21no—
83C2×C11⋊C8—22no—
84C2×C11⋊C8—41no—
85C2×C11⋊C8—41no—
86C2×C11⋊C8—41no—
87C2×C11⋊C8—41no—
88C2×C11⋊C8—81no—
89#1997D1111yescharacteristic
90#1950—111no—
91#1570—111no—
92#1565—111no—
93#1548—111no—
94C2×#333—111no—
95#1292—111no—
96C23×C11C22⋊Q811yescharacteristic
97Q8×C11—82no—
98Q8×C11—82no—
99C2×C4×C11—21no—
100C2×C4×C11—21no—
101C2×C4×C11—41no—
102C2×C4×C11—42no—
103C2×C4×C11—82no—
104C2×C4×C11#12111yescharacteristic
105C2×C4×C11#12111yescharacteristic
106C2×C4×C11#12111yescharacteristic
107C2×C4×C11C22⋊Q811yescharacteristic
108C2×C4×C11C22⋊Q811yescharacteristic
109C2×C4×C11#12611yescharacteristic
110C2×C4×C11C2×SD1611yescharacteristic
111C2×C4×C11#13511yescharacteristic
112C2×C4×C11#13711yescharacteristic
113C2×C4×C11#13711yescharacteristic
114C8×C11—22no—
115C8×C11—41no—
116C8×C11—81no—
117C11⋊C8—42no—
118C11⋊C8—41no—
119C11⋊C8—41no—
120C11⋊C8—81no—
121C11⋊C8—81no—
122C2×C4⋊Q8C2×D1111yescharacteristic
123#431—111no—
124C2×#108—221no—
125#423—111no—
126#423C2×D1111yescharacteristic
127C2×C4⋊C8—111no—
128C2×C4⋊C8—111no—
129C4×M16C2×D1111yescharacteristic
130#343—21no—
131#343—21no—
132#341—221no—
133#335—221no—
134#334—221no—
135#334—222no—
136#333—222no—
137#333—221no—
138#333—221no—
139C22×C11—21no—
140C22×C11—21no—
141C22×C11#39611yescharacteristic
142C22×C11#47511yescharacteristic
143C22×C11#47911yescharacteristic
144C4×C11—21no—
145C4×C11—21no—
146C4×C11—21no—
147C4×C11—82no—
148C4×C11#46111yescharacteristic
149C4×C11#46411yescharacteristic
150C4×C11#46511yescharacteristic
151C4×C11#47011yescharacteristic
152C4×C11#47111yescharacteristic
153C4×C11#47311yescharacteristic
154C22×Q8Dic2212yes—
155C2×M16—21no—
156C2×M16—221no—
157C2×M16C22⋊D1111yescharacteristic
158C2×M16C22⋊D1111yescharacteristic
159C22×C8—221no—
160C22×C8—221no—
161C4⋊Q8—21no—
162C4⋊Q8—21no—
163C4⋊Q8—21no—
164C4⋊Q8—21no—
165C2×C4⋊C4—21no—
166C2×C4⋊C4—21no—
167C2×C42C22×D1111yescharacteristic
168#108—442no—
169C4⋊C8—21no—
170C4⋊C8—21no—
171C4⋊C8—112no—
172C4⋊C8—111no—
173C4⋊C8—111no—
174C4⋊C8—221no—
175C4⋊C8—221no—
176C4⋊C8—221no—
177C4⋊C8—221no—
178C4⋊C8—221no—
179C22⋊C8—221no—
180#97—21no—
181C4×C8—21no—
182C4×C8—221no—
183C2×C11—21no—
184C2×C11—21no—
185C2×C11#206411yescharacteristic
186C2×C11#206611yescharacteristic
187C2×C11#206911yescharacteristic
188C2×Q8—22no—
189C2×Q8—22no—
190C2×Q8—82no—
191C22×C4—22no—
192C22×C4C2×Dic2211yescharacteristic
193C22×C4#433911yescharacteristic
194C22×C4C2×C22⋊D1111yescharacteristic
195M16—21no—
196M16—21no—
197M16—21no—
198M16—41no—
199M16—41no—
200M16—441no—
201M16—441no—
202M16#432512yes—
203C2×C8—21no—
204C2×C8—21no—
205C2×C8—41no—
206C2×C8—221no—
207C2×C8—221no—
208C2×C8—222no—
209C2×C8—441no—
210C2×C8—441no—
211C2×C8—441no—
212C2×C8—441no—
213C2×C8—881no—
214C4⋊C4—41no—
215C4⋊C4—41no—
216C4⋊C4—41no—
217C4⋊C4—41no—
218C42D4×D1111yescharacteristic
219C42D4×D1111yescharacteristic
220C42#434111yescharacteristic
221C42#434111yescharacteristic
222C11#1060911yescharacteristic, complemented, Sylow
223C23#6697711yescharacteristic
224Q8—82no—
225Q8—82no—
226C2×C4—21no—
227C2×C4—21no—
228C2×C4—41no—
229C2×C4—42no—
230C2×C4—82no—
231C2×C4#6693111yescharacteristic
232C2×C4#6693111yescharacteristic
233C2×C4#6693211yescharacteristic
234C2×C4#6693711yescharacteristic
235C2×C4#6699111yescharacteristic
236C2×C4#6699211yescharacteristic
237C2×C4C2×#432511yescharacteristic
238C2×C4#6699511yescharacteristic
239C2×C4#6700311yescharacteristic
240C2×C4#6700411yescharacteristic
241C8—22no—
242C8—41no—
243C8—81no—
244C8—441no—
245C8—441no—
246C8—442no—
247C8—881no—
248C8—881no—
249C22—21no—
250C22—21no—
251C22#1062256111yescharacteristic
252C22#1062263311yescharacteristic
253C22#1062263511yescharacteristic
254C4—21no—
255C4—21no—
256C4—21no—
257C4—82no—
258C4#1062236711yescharacteristic
259C4#1062236811yescharacteristic
260C4#1062266111yescharacteristic
261C4#1062266511yescharacteristic
262C4#1062266711yescharacteristic
263C4#1062269611yescharacteristic
264C2—21no—
265C2—21no—
266C2#1306997911yescharacteristic
267C2#1306999711yescharacteristic
268C2#1307001411yescharacteristic
subgroupG/H
centerC22#10622561
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1997C2
socleC22×C11#396
prime radicalC23×C11C22⋊Q8
hypercenter#1997D11
hypocenterC11#10609
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1997

Complements

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

NH ≅ G/Ntype
222. C11#10609semidirect

Maximal subgroups

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

subgroupindex
#130693912
#130673882
#130673682
#130672972
C2×#106221842
#130664902
C11×#19972
#1060911