Finite Group Databasebeta

← #14657007

Subgroups — #14657007

Order 2816.

414 conjugacy classes of subgroups; only the 77 normal subgroups are shown.

normal subgroups only

This group has 414 conjugacy classes of subgroups — too many to draw. Only its 77 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#13068716C212yesmaximal
2#13068691C211yesmaximal, characteristic
3#13066524C211yesmaximal, characteristic
4#13066469C212yesmaximal
5C11×#2607C211yesmaximal, characteristic
6C2×#66979C2211yescharacteristic
7C11×#399—21no—
8C11×#393—21no—
9C11×#391—22no—
10C11×#387—22no—
11C11×#381C2211yescharacteristic
12C4×C11×C22⋊C4C2212yes—
13#10622824C2211yescharacteristic
14#10622820C2212yes—
15#10622165—21no—
16#10622165—21no—
17#10622161—22no—
18#10622161—22no—
19C22×Q8×C11—21no—
20C23×C4×C11C2311yescharacteristic
21C2×C11×C4⋊C4—22no—
22C2×C11×C4⋊C4—21no—
23C2×C11×C22⋊C4—22no—
24C2×C11×C22⋊C4D411yescharacteristic
25C2×C11×C22⋊C4D411yescharacteristic
26C2×C42×C11D412yes—
27C2×C42×C11D412yes—
28C2×C22⋊Dic11—21no—
29C2×C22⋊Dic11—21no—
30#66979—22no—
31#66979—22no—
32C2×C4⋊Dic11Q812yescomplemented
33C2×C4×Dic11—21no—
34C2×#4318—22no—
35C11×#95—21no—
36C11×#95—22no—
37C11×#95—21no—
38C11×#95—22no—
39C11×#95—22no—
40C11⋊#95—22no—
41C22⋊(C11⋊C8)—22no—
42C22⋊(C11⋊C8)—22no—
43#10387—111nomaximal, Sylow
44C24×C11C2×D411yescharacteristic
45C2×Q8×C11—44no—
46C2×Q8×C11—81no—
47C22×C4×C11—22no—
48C22×C4×C11—21no—
49C22×C4×C11—22no—
50C22×C4×C11—21no—
51C22×C4×C11—41no—
52C22×C4×C11—41no—
53C22×C4×C11C2×D412yes—
54C22×C4×C11C2×Q811yescharacteristic
55C22×C4×C11#4112yes—
56C22×C4×C11#4111yescharacteristic
57C22×Dic11—22no—
58C22×Dic11—41no—
59C11×C4⋊C4—44no—
60C11×C4⋊C4—81no—
61C11×C22⋊C4—44no—
62C11×C22⋊C4—41no—
63C11×C22⋊C4—41no—
64C42×C11—42no—
65C42×C11—42no—
66C22⋊Dic11—41no—
67C22⋊Dic11—41no—
68C22⋊Dic11—41no—
69C22⋊Dic11—41no—
70C4⋊Dic11—24no—
71C4×Dic11—42no—
72#4318—42no—
73#4318—42no—
74C2×C11⋊C8—42no—
75#2607D1111yescharacteristic
76#1826—112no—
77#1820—111no—
78#1306—111no—
79#1284—112no—
80C23×C11—21no—
81C23×C11—21no—
82C23×C11—42no—
83C23×C11#12011yescharacteristic
84C23×C11C22⋊Q811yescharacteristic
85C23×C11#12411yescharacteristic
86Q8×C11—84no—
87C2×C4×C11—22no—
88C2×C4×C11—22no—
89C2×C4×C11—24no—
90C2×C4×C11—41no—
91C2×C4×C11—42no—
92C2×C4×C11—41no—
93C2×C4×C11—42no—
94C2×C4×C11—42no—
95C2×C4×C11—42no—
96C2×C4×C11—42no—
97C2×C4×C11—42no—
98C2×C4×C11—42no—
99C2×C4×C11—42no—
100C2×C4×C11—41no—
101C2×C4×C11—41no—
102C2×C4×C11C22⋊Q812yes—
103C2×C4×C11#12412yes—
104C2×Dic11—42no—
105C2×Dic11—82no—
106C2×Dic11—81no—
107C2×Dic11—82no—
108C11⋊C8—82no—
109C2×#117—111no—
110#407—112no—
111#399—21no—
112#393—21no—
113#391—22no—
114#387—22no—
115#381—111no—
116#381C2×D1111yescharacteristic
117C4×C22⋊C4C2×D1112yes—
118#342—221no—
119#342—221no—
120#339—222no—
121#339—222no—
122C22×C11—22no—
123C22×C11—21no—
124C22×C11—21no—
125C22×C11—22no—
126C22×C11—22no—
127C22×C11—81no—
128C22×C11—81no—
129C22×C11#39311yescharacteristic
130C22×C11#45811yescharacteristic
131C22×C11#45811yescharacteristic
132C4×C11—22no—
133C4×C11—22no—
134C4×C11—44no—
135C4×C11—82no—
136C4×C11—81no—
137C4×C11—81no—
138Dic11—82no—
139Dic11—161no—
140C22×Q8—21no—
141C23×C4C22×D1111yescharacteristic
142C2×M16—222no—
143#117—222no—
144#117—222no—
145C2×C4⋊C4—22no—
146C2×C4⋊C4—21no—
147C2×C4⋊C4—112no—
148C2×C22⋊C4—22no—
149C2×C22⋊C4—221no—
150C2×C22⋊C4—221no—
151C2×C22⋊C4C22⋊D1111yescharacteristic
152C2×C22⋊C4C22⋊D1111yescharacteristic
153C2×C42—221no—
154C2×C42C22⋊D1112yes—
155C2×C42C22⋊D1112yes—
156C22⋊C8—222no—
157C22⋊C8—222no—
158#95—21no—
159#95—22no—
160#95—21no—
161#95—22no—
162#95—22no—
163#95—222no—
164C2×C11—21no—
165C2×C11—21no—
166C2×C11—41no—
167C2×C11—41no—
168C2×C11#203011yescharacteristic
169C2×C11#203112yes—
170C24C2×C22⋊D1111yescharacteristic
171C2×Q8—44no—
172C2×Q8—81no—
173C22×C4—22no—
174C22×C4—21no—
175C22×C4—22no—
176C22×C4—21no—
177C22×C4—41no—
178C22×C4—41no—
179C22×C4—222no—
180C22×C4—441no—
181C22×C4Q8×D1111yescharacteristic
182C22×C4#434312yes—
183C22×C4#434311yescharacteristic
184C22×C4C2×C22⋊D1112yes—
185M16—442no—
186M16—442no—
187C2×C8—442no—
188C4⋊C4—44no—
189C4⋊C4—81no—
190C4⋊C4—224no—
191C22⋊C4—44no—
192C22⋊C4—41no—
193C22⋊C4—41no—
194C22⋊C4—441no—
195C22⋊C4—441no—
196C22⋊C4—441no—
197C22⋊C4—441no—
198C42—42no—
199C42—42no—
200C42—442no—
201C11#1038711yescharacteristic, complemented, Sylow
202C23—21no—
203C23—21no—
204C23—42no—
205C23#6699911yescharacteristic
206C23#6700011yescharacteristic
207C23#6700611yescharacteristic
208Q8—84no—
209C2×C4—22no—
210C2×C4—22no—
211C2×C4—24no—
212C2×C4—41no—
213C2×C4—41no—
214C2×C4—42no—
215C2×C4—42no—
216C2×C4—42no—
217C2×C4—42no—
218C2×C4—42no—
219C2×C4—42no—
220C2×C4—42no—
221C2×C4—42no—
222C2×C4—41no—
223C2×C4—41no—
224C2×C4—442no—
225C2×C4—882no—
226C2×C4—881no—
227C2×C4—882no—
228C2×C4#6699912yes—
229C2×C4#6700012yes—
230C8—882no—
231C22—22no—
232C22—21no—
233C22—21no—
234C22—22no—
235C22—22no—
236C22—81no—
237C22—81no—
238C22#1062284411yescharacteristic
239C22#1062285611yescharacteristic
240C22#1062285611yescharacteristic
241C4—22no—
242C4—22no—
243C4—44no—
244C4—81no—
245C4—82no—
246C4—81no—
247C4—882no—
248C4—1761no—
249C2—21no—
250C2—21no—
251C2—41no—
252C2—41no—
253C2#1306978211yescharacteristic
254C2#1306978512yes—
subgroupG/H
centerC22#10622844
commutator, cosocleC23×C4×C11C23
FrattiniC23×C4C22×D11
FittingC11×#2607C2
socleC22×C11#393
prime radicalC24×C11C2×D4
hypercenter#2607D11
hypocenterC11#10387
LCSG ▷ C23×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ #2607

Complements

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

NH ≅ G/Ntype
32. C2×C4⋊Dic11Q8semidirect
201. C11#10387semidirect

Maximal subgroups

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

subgroupindex
#130687162
#130686912
#130665242
#130664692
C11×#26072
#1038711