Finite Group Databasebeta

← #14673464

Subgroups — #14673464

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#13076604C211yesmaximal, characteristic
2#13068833C212yesmaximal
3#13068830C211yesmaximal, characteristic
4#13066742C212yesmaximal
5C11×#1394C211yesmaximal, characteristic
6#10623343C2211yescharacteristic
7C2×C11×#101C2212yes—
8C11×#391C2211yescharacteristic
9#10622843C2212yes—
10C2×#66900C2211yescharacteristic
11#10622734—22no—
12#10622599—21no—
13#10622577—21no—
14#10622541—21no—
15#10622274—22no—
16#10622268—22no—
17#10622193—22no—
18#10622161—21no—
19C22×Q8×C11C2311yescharacteristic
20C2×C11×M16—22no—
21C2×C11×C4⋊C4D411yescharacteristic
22C2×C42×C11D411yescharacteristic
23Q8×Dic11—41no—
24Q8×Dic11—41no—
25#66979—22no—
26#66979—21no—
27C2×C4⋊Dic11—21no—
28C2×C4⋊Dic11—21no—
29C2×C4⋊Dic11—21no—
30C2×C4⋊Dic11D412yes—
31C2×Dic11⋊C4—22no—
32C2×C4×Dic11D412yes—
33C2×#4318—21no—
34C11×#101—22no—
35C11×#101Q814yes—
36C11×#95—22no—
37#66900—21no—
38#66900Q812yes—
39C11⋊#95—21no—
40C11⋊#95—22no—
41C11⋊#95—22no—
42C11⋊#95—22no—
43#66882—42no—
44#66881—42no—
45#66872—41no—
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×C11C2×D411yescharacteristic
56C22×C4×C11C2×D412yes—
57C22×Dic11—22no—
58C22×Dic11—22no—
59C11×M16—24no—
60C11×M16—42no—
61C2×C8×C11—42no—
62C11×C4⋊C4—41no—
63C42×C11—41no—
64C22⋊Dic11—41no—
65C4⋊Dic11—21no—
66C4⋊Dic11—21no—
67C4⋊Dic11—22no—
68C4⋊Dic11—22no—
69C4⋊Dic11—42no—
70C4⋊Dic11—42no—
71C4⋊Dic11—81no—
72C4⋊Dic11—81no—
73Dic11⋊C4—44no—
74C4×Dic11—42no—
75C4×Dic11—41no—
76C4×Dic11—42no—
77#4318—22no—
78#4318—41no—
79C2×C11⋊C8—41no—
80#2809—111no—
81#1857—112no—
82#1857—111no—
83#1394—112no—
84#1394D1111yescharacteristic
85C23×C11#12011yescharacteristic
86Q8×C11—42no—
87Q8×C11—41no—
88Q8×C11—41no—
89C2×C4×C11—21no—
90C2×C4×C11—22no—
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—41no—
98C2×C4×C11C22⋊Q812yes—
99C2×C4×C11C22⋊Q811yescharacteristic
100C2×C4×C11C4⋊Q811yescharacteristic
101C2×C4×C11C4⋊Q812yes—
102C2×Dic11—42no—
103C2×Dic11—42no—
104C2×Dic11—42no—
105C2×Dic11—42no—
106C2×Dic11—41no—
107C2×Dic11—41no—
108C2×Dic11—42no—
109C2×Dic11—42no—
110C8×C11—44no—
111C11⋊C8—42no—
112#519—111no—
113#428—222no—
114#428—221no—
115C2×#101—111no—
116C2×#101C2×D1112yes—
117#400—221no—
118#398—222no—
119#391—112no—
120#391C2×D1111yescharacteristic
121#389—221no—
122#387—222no—
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—21no—
131C4×C11—22no—
132C4×C11—21no—
133C4×C11—22no—
134C4×C11—42no—
135C4×C11—81no—
136Dic11—82no—
137Dic11—81no—
138Dic11—81no—
139Dic11—82no—
140C22×Q8C22×D1111yescharacteristic
141C2×M16—22no—
142C2×M16—221no—
143C4×Q8—441no—
144C4×Q8—441no—
145#117—221no—
146#117—222no—
147C2×C4⋊C4—112no—
148C2×C4⋊C4—222no—
149C2×C4⋊C4—221no—
150C2×C4⋊C4—221no—
151C2×C4⋊C4—221no—
152C2×C4⋊C4D4411yescharacteristic
153C2×C42—112no—
154C2×C42D4411yescharacteristic
155#107—441no—
156#107—442no—
157#106—441no—
158#106—442no—
159#101—22no—
160#101—112no—
161#101—221no—
162#101Dic2214yes—
163#95—22no—
164#95—221no—
165#95—222no—
166#95—222no—
167#95—222no—
168C2×C11—21no—
169C2×C11—21no—
170C2×C11#206211yescharacteristic
171C2×C11#220311yescharacteristic
172C2×C11#220411yescharacteristic
173C2×Q8—41no—
174C2×Q8—41no—
175C2×Q8C2×Dic2212yes—
176C2×Q8#434111yescharacteristic
177C2×Q8Q8×D1111yescharacteristic
178C22×C4—21no—
179C22×C4—21no—
180C22×C4—222no—
181C22×C4—222no—
182C22×C4C2×D4411yescharacteristic
183C22×C4D4×D1112yes—
184M16—24no—
185M16—42no—
186M16—222no—
187M16—441no—
188C2×C8—42no—
189C2×C8—441no—
190C4⋊C4—41no—
191C4⋊C4—221no—
192C4⋊C4—222no—
193C4⋊C4—221no—
194C4⋊C4—222no—
195C4⋊C4—442no—
196C4⋊C4—444no—
197C4⋊C4—442no—
198C4⋊C4—881no—
199C4⋊C4—881no—
200C22⋊C4—441no—
201C42—41no—
202C42—442no—
203C42—441no—
204C42—442no—
205C11#1346511yescharacteristic, complemented, Sylow
206C23#6693511yescharacteristic
207Q8—42no—
208Q8—41no—
209Q8—41no—
210C2×C4—21no—
211C2×C4—22no—
212C2×C4—21no—
213C2×C4—22no—
214C2×C4—22no—
215C2×C4—41no—
216C2×C4—41no—
217C2×C4—42no—
218C2×C4—41no—
219C2×C4—442no—
220C2×C4—442no—
221C2×C4—442no—
222C2×C4—442no—
223C2×C4—441no—
224C2×C4—441no—
225C2×C4—442no—
226C2×C4—442no—
227C2×C4#6692211yescharacteristic
228C2×C4#6693112yes—
229C2×C4#6694112yes—
230C2×C4#6695011yescharacteristic
231C8—44no—
232C8—442no—
233C22—21no—
234C22—21no—
235C22#1062226911yescharacteristic
236C22#1062235411yescharacteristic
237C22#1062235511yescharacteristic
238C4—22no—
239C4—21no—
240C4—21no—
241C4—22no—
242C4—42no—
243C4—81no—
244C4—882no—
245C4—881no—
246C4—882no—
247C4—881no—
248C2—21no—
249C2—21no—
250C2#1306997011yescharacteristic
251C2#1307063911yescharacteristic
252C2#1307064411yescharacteristic
subgroupG/H
centerC22#10622354
commutator, cosocleC22×Q8×C11C23
FrattiniC22×Q8C22×D11
FittingC11×#1394C2
socleC22×C11B(4,𝔽2)
prime radicalC23×C11#120
hypercenter#1394D11
hypocenterC11#13465
LCSG ▷ C22×Q8×C11 ▷ C22×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23 ◁ C22×Q8 ◁ #1394

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
#130766042
#130688332
#130688302
#130667422
C11×#13942
#1346511