Finite Group Databasebeta

← #14673460

Subgroups — #14673460

Order 2816.

384 conjugacy classes of subgroups; only the 81 normal subgroups are shown.

normal subgroups only

This group has 384 conjugacy classes of subgroups — too many to draw. Only its 81 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#13068830C212yesmaximal
2#13068830C211yesmaximal, characteristic
3#13066743C211yesmaximal, characteristic
4#13066743C212yesmaximal
5C11×#2809C211yesmaximal, characteristic
6#10623343C2211yescharacteristic
7C11×#400—21no—
8C11×#398—22no—
9C11×#391C2211yescharacteristic
10C11×#391C2212yes—
11C11×#389—21no—
12C11×#387—22no—
13C2×#66900C2212yes—
14C2×#66900C2211yescharacteristic
15#10622577—22no—
16#10622577—21no—
17#10622161—22no—
18#10622161—21no—
19C22×Q8×C11C2311yescharacteristic
20C2×C11×C4⋊C4—22no—
21C2×C11×C4⋊C4—21no—
22C2×C11×C4⋊C4—21no—
23C2×C11×C4⋊C4—21no—
24C2×C11×C4⋊C4D412yes—
25C2×C11×C4⋊C4D411yescharacteristic
26C2×C42×C11D412yes—
27C2×C42×C11D411yescharacteristic
28Q8×Dic11—41no—
29Q8×Dic11—41no—
30#66979—22no—
31#66979—21no—
32C2×#4318—22no—
33C2×#4318—21no—
34C11×#95—21no—
35C11×#95—22no—
36C11×#95—22no—
37C11×#95—22no—
38C11×#95—22no—
39#66900—22no—
40#66900—21no—
41#66900Q814yes—
42#66900Q812yes—
43#66872—42no—
44#66872—41no—
45#66871—42no—
46#66871—41no—
47#13465—111nomaximal, Sylow
48C2×Q8×C11—41no—
49C2×Q8×C11—41no—
50C2×Q8×C11C2×Q812yes—
51C2×Q8×C11C2×Q811yescharacteristic
52C2×Q8×C11#4111yescharacteristic
53C22×C4×C11—21no—
54C22×C4×C11—21no—
55C22×C4×C11—22no—
56C22×C4×C11—22no—
57C22×C4×C11C2×D412yes—
58C22×C4×C11C2×D411yescharacteristic
59C11×C4⋊C4—44no—
60C11×C4⋊C4—42no—
61C11×C4⋊C4—42no—
62C11×C4⋊C4—41no—
63C11×C4⋊C4—81no—
64C11×C4⋊C4—81no—
65C42×C11—41no—
66C42×C11—42no—
67C22⋊Dic11—41no—
68C4⋊Dic11—21no—
69C4⋊Dic11—22no—
70C4⋊Dic11—22no—
71C4⋊Dic11—21no—
72C4×Dic11—42no—
73C4×Dic11—41no—
74#4318—24no—
75#4318—22no—
76#4318—41no—
77#4318—42no—
78C2×C11⋊C8—42no—
79C2×C11⋊C8—41no—
80#2809D1111yescharacteristic
81#1857—112no—
82#1857—111no—
83#1394—111no—
84#1394—112no—
85C23×C11#12011yescharacteristic
86Q8×C11—42no—
87Q8×C11—41no—
88Q8×C11—41no—
89C2×C4×C11—22no—
90C2×C4×C11—21no—
91C2×C4×C11—21no—
92C2×C4×C11—22no—
93C2×C4×C11—22no—
94C2×C4×C11—41no—
95C2×C4×C11—41no—
96C2×C4×C11—42no—
97C2×C4×C11—42no—
98C2×C4×C11—42no—
99C2×C4×C11—42no—
100C2×C4×C11—42no—
101C2×C4×C11—41no—
102C2×C4×C11—42no—
103C2×C4×C11—42no—
104C2×C4×C11C22⋊Q812yes—
105C2×C4×C11C22⋊Q811yescharacteristic
106C2×C4×C11C4⋊Q812yes—
107C2×C4×C11C4⋊Q811yescharacteristic
108C2×Dic11—41no—
109C2×Dic11—41no—
110C11⋊C8—44no—
111C11⋊C8—42no—
112#519—111no—
113#428—222no—
114#428—221no—
115C2×#101—112no—
116C2×#101—111no—
117#400—21no—
118#398—22no—
119#391C2×D1111yescharacteristic
120#391C2×D1112yes—
121#389—21no—
122#387—22no—
123#339—222no—
124#339—221no—
125C22×C11—21no—
126C22×C11—21no—
127C22×C11#39511yescharacteristic
128C22×C11B(4,𝔽2)11yescharacteristic
129C22×C11#45811yescharacteristic
130C4×C11—22no—
131C4×C11—21no—
132C4×C11—22no—
133C4×C11—21no—
134C4×C11—42no—
135C4×C11—82no—
136C4×C11—81no—
137C4×C11—82no—
138Dic11—81no—
139Dic11—81no—
140C22×Q8C22×D1111yescharacteristic
141C2×M16—222no—
142C2×M16—221no—
143C4×Q8—441no—
144C4×Q8—441no—
145#117—222no—
146#117—221no—
147C2×C4⋊C4—22no—
148C2×C4⋊C4—21no—
149C2×C4⋊C4—21no—
150C2×C4⋊C4—21no—
151C2×C4⋊C4C22⋊D1112yes—
152C2×C4⋊C4C22⋊D1111yescharacteristic
153C2×C42C22⋊D1112yes—
154C2×C42C22⋊D1111yescharacteristic
155#107—442no—
156#107—441no—
157#106—442no—
158#106—441no—
159#101—114no—
160#101—112no—
161#101—222no—
162#101—221no—
163#95—21no—
164#95—22no—
165#95—22no—
166#95—22no—
167#95—22no—
168C2×C11—21no—
169C2×C11—21no—
170C2×C11#206211yescharacteristic
171C2×C11#220311yescharacteristic
172C2×C11#220411yescharacteristic
173C2×Q8—41no—
174C2×Q8—41no—
175C2×Q8Q8×D1111yescharacteristic
176C2×Q8Q8×D1112yes—
177C2×Q8#434311yescharacteristic
178C22×C4—21no—
179C22×C4—21no—
180C22×C4—22no—
181C22×C4—22no—
182C22×C4C2×C22⋊D1112yes—
183C22×C4C2×C22⋊D1111yescharacteristic
184M16—224no—
185M16—222no—
186M16—441no—
187M16—442no—
188C2×C8—442no—
189C2×C8—441no—
190C4⋊C4—42no—
191C4⋊C4—41no—
192C4⋊C4—44no—
193C4⋊C4—42no—
194C4⋊C4—81no—
195C4⋊C4—81no—
196C4⋊C4—222no—
197C4⋊C4—221no—
198C4⋊C4—221no—
199C4⋊C4—222no—
200C22⋊C4—441no—
201C42—41no—
202C42—42no—
203C42—442no—
204C42—441no—
205C11#1346511yescharacteristic, complemented, Sylow
206C23#6700611yescharacteristic
207Q8—41no—
208Q8—42no—
209Q8—41no—
210C2×C4—21no—
211C2×C4—22no—
212C2×C4—22no—
213C2×C4—21no—
214C2×C4—22no—
215C2×C4—41no—
216C2×C4—41no—
217C2×C4—42no—
218C2×C4—42no—
219C2×C4—42no—
220C2×C4—42no—
221C2×C4—42no—
222C2×C4—42no—
223C2×C4—41no—
224C2×C4—42no—
225C2×C4—441no—
226C2×C4—441no—
227C2×C4#6699712yes—
228C2×C4#6699711yescharacteristic
229C2×C4#6699912yes—
230C2×C4#6699911yescharacteristic
231C8—442no—
232C8—444no—
233C22—21no—
234C22—21no—
235C22#1062284211yescharacteristic
236C22#1062285611yescharacteristic
237C22#1062285711yescharacteristic
238C4—21no—
239C4—22no—
240C4—21no—
241C4—22no—
242C4—42no—
243C4—82no—
244C4—81no—
245C4—82no—
246C4—881no—
247C4—881no—
248C2—21no—
249C2—21no—
250C2#1306996811yescharacteristic
251C2#1307063711yescharacteristic
252C2#1307064211yescharacteristic
subgroupG/H
centerC22#10622857
commutator, cosocleC22×Q8×C11C23
FrattiniC22×Q8C22×D11
FittingC11×#2809C2
socleC22×C11B(4,𝔽2)
prime radicalC23×C11#120
hypercenter#2809D11
hypocenterC11#13465
LCSG ▷ C22×Q8×C11 ▷ C22×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23 ◁ C22×Q8 ◁ #2809

Complements

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

NH ≅ G/Ntype
205. C11#13465semidirect

Maximal subgroups

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

subgroupindex
#130688302
#130667432
C11×#28092
#1346511