Finite Group Databasebeta

← #14656379

Subgroups — #14656379

Order 2816.

574 conjugacy classes of subgroups; only the 139 normal subgroups are shown.

normal subgroups only

This group has 574 conjugacy classes of subgroups — too many to draw. Only its 139 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×#10622707C212yesmaximal
2#13069552C211yesmaximal, characteristic
3C2×#10622185C212yesmaximal
4#13066451C211yesmaximal, characteristic
5C2×C11×#494C211yesmaximal, characteristic
6C22×C11×Q16—22no—
7C2×C11×C4⋊Q8C2212yes—
8C2×C4×Dic22C2211yescharacteristic
9C11×#494—24no—
10C2×C4×C8×C11C2211yescharacteristic
11#10622707—24no—
12#10622707—24no—
13C2×#66874—22no—
14C2×#66872—22no—
15C2×C4⋊(C11⋊C8)C2211yescharacteristic
16C2×C4⋊(C11⋊C8)C2212yes—
17#10622188—22no—
18#10622185—24no—
19C22×Q8×C11—22no—
20C22×Dic22D411yescharacteristic
21C2×C11×Q16—28no—
22C2×C11×Q16—44no—
23C2×C11×Q16—44no—
24C22×C8×C11D412yes—
25C11×C4⋊Q8—22no—
26C11×C4⋊Q8—22no—
27C11×C4⋊Q8—22no—
28C11×C4⋊Q8D414yes—
29C2×C11×C4⋊C4—22no—
30C2×C11×C4⋊C4—22no—
31C2×C42×C11C2311yescharacteristic
32C2×C4⋊Dic11D411yescharacteristic
33C2×Dic11⋊C4—21no—
34C2×C4×Dic11—21no—
35C22×C11⋊C8—22no—
36C22×C11⋊C8—21no—
37C4×Dic22—22no—
38C4×Dic22—22no—
39C4×C8×C11—22no—
40#66874—28no—
41#66872—28no—
42C4⋊(C11⋊C8)—22no—
43C4⋊(C11⋊C8)—22no—
44C4⋊(C11⋊C8)D414yes—
45#10276—111nomaximal, Sylow
46C2×Q8×C11—24no—
47C2×Q8×C11—42no—
48C2×Q8×C11—44no—
49C2×Q8×C11—44no—
50C22×C4×C11—42no—
51C22×C4×C11C2×D411yescharacteristic
52C22×C4×C11C2×D411yescharacteristic
53C22×C4×C11#4111yescharacteristic
54C22×Dic11—21no—
55C22×Dic11—21no—
56C2×Dic22—22no—
57C2×Dic22—21no—
58C2×Dic22—22no—
59C2×Dic22Q1612yescomplemented
60C11×Q16—416no—
61C2×C8×C11—22no—
62C2×C8×C11—22no—
63C2×C8×C11SD1614yes—
64C11×C4⋊C4—24no—
65C11×C4⋊C4—24no—
66C11×C4⋊C4—42no—
67C11×C4⋊C4—42no—
68C42×C11C2×D412yes—
69C42×C11C2×D412yes—
70C4⋊Dic11—22no—
71Dic11⋊C4—42no—
72C4×Dic11—41no—
73C4×Dic11—41no—
74C2×C11⋊C8—24no—
75C2×C11⋊C8—41no—
76C2×C11⋊C8—42no—
77C2×C11⋊C8—42no—
78C2×C11⋊C8—42no—
79C2×#494D1111yescharacteristic
80C2×#475—112no—
81#1984—111no—
82C2×#332—112no—
83#1277—111no—
84C23×C11#12111yescharacteristic
85Q8×C11—48no—
86Q8×C11—82no—
87Q8×C11—82no—
88C2×C4×C11—22no—
89C2×C4×C11—44no—
90C2×C4×C11—84no—
91C2×C4×C11#12012yes—
92C2×C4×C11#12011yescharacteristic
93C2×C4×C11#12112yes—
94C2×C4×C11#12711yescharacteristic
95C2×C4×C11C2×SD1612yes—
96C2×C4×C11C2×Q1611yescharacteristic
97C2×C4×C11#13511yescharacteristic
98C2×C4×C11AGL(1,ℤ/8)12yes—
99C2×C4×C11#13712yes—
100C2×Dic11—22no—
101C2×Dic11—41no—
102C2×Dic11—41no—
103C2×Dic11—41no—
104C2×Dic11—42no—
105Dic22—24no—
106Dic22—42no—
107C8×C11—24no—
108C11⋊C8—44no—
109C11⋊C8—81no—
110C22×Q16—22no—
111C2×C4⋊Q8C2×D1112yes—
112C2×C4×Q8—111no—
113#494—24no—
114#475—224no—
115#475—224no—
116C2×#106—222no—
117C2×C4⋊C8—112no—
118C2×C4⋊C8—111no—
119C2×#103—222no—
120C2×C4×C8C2×D1111yescharacteristic
121#336—222no—
122#332—224no—
123C22×C11#39211yescharacteristic
124C22×C11#46012yes—
125C22×C11#46711yescharacteristic
126C22×C11#47011yescharacteristic
127C22×C11#47312yes—
128C4×C11—22no—
129C4×C11—84no—
130C4×C11#45012yes—
131C4×C11#45112yes—
132C4×C11#45212yes—
133C4×C11#49211yescharacteristic
134C4×C11#49611yescharacteristic
135Dic11—42no—
136Dic11—81no—
137C22×Q8—22no—
138C22×Q8—111no—
139C2×Q16—28no—
140C2×Q16—44no—
141C2×Q16—44no—
142C22×C8—222no—
143C22×C8—221no—
144C22×C8C22⋊D1112yes—
145C4⋊Q8—22no—
146C4⋊Q8—22no—
147C4⋊Q8—22no—
148C4⋊Q8C22⋊D1114yes—
149C4×Q8—222no—
150C4×Q8—222no—
151C2×C4⋊C4—22no—
152C2×C4⋊C4—22no—
153C2×C4⋊C4—111no—
154C2×C4⋊C4—221no—
155C2×C42—221no—
156C2×C42C22×D1111yescharacteristic
157#106—228no—
158C4⋊C8—114no—
159C4⋊C8—222no—
160C4⋊C8—222no—
161#103—228no—
162C4×C8—22no—
163C2×C11#167012yes—
164C2×C11#169012yes—
165C2×C11#200111yescharacteristic
166C2×C11#201411yescharacteristic
167C2×C11#202011yescharacteristic
168C2×Q8—24no—
169C2×Q8—42no—
170C2×Q8—44no—
171C2×Q8—44no—
172C2×Q8—112no—
173C2×Q8—221no—
174C2×Q8—222no—
175C2×Q8—222no—
176C22×C4—42no—
177C22×C4—221no—
178C22×C4—221no—
179C22×C4D4×D1111yescharacteristic
180C22×C4#434111yescharacteristic
181C22×C4C2×C22⋊D1111yescharacteristic
182Q16—416no—
183C2×C8—22no—
184C2×C8—22no—
185C2×C8—224no—
186C2×C8—442no—
187C2×C8—442no—
188C2×C8—442no—
189C2×C8—441no—
190C2×C8#432414yes—
191C4⋊C4—24no—
192C4⋊C4—24no—
193C4⋊C4—42no—
194C4⋊C4—42no—
195C4⋊C4—222no—
196C4⋊C4—442no—
197C42—441no—
198C42—441no—
199C42D4×D1112yes—
200C42C2×C22⋊D1112yes—
201C11#1027611yescharacteristic, complemented, Sylow
202C23#6699111yescharacteristic
203Q8—48no—
204Q8—82no—
205Q8—82no—
206Q8—224no—
207Q8—442no—
208C2×C4—22no—
209C2×C4—44no—
210C2×C4—84no—
211C2×C4—222no—
212C2×C4—441no—
213C2×C4—441no—
214C2×C4—442no—
215C2×C4—441no—
216C2×C4Q16×D1111yescharacteristic
217C2×C4#6697112yes—
218C2×C4#6697211yescharacteristic
219C2×C4#6698512yes—
220C2×C4C2×#432412yes—
221C2×C4#6699012yes—
222C2×C4#6699212yes—
223C2×C4#6699311yescharacteristic
224C2×C4#6700611yescharacteristic
225C8—24no—
226C8—444no—
227C8—881no—
228C22#1062268812yes—
229C22#1062280111yescharacteristic
230C22#1062280211yescharacteristic
231C22#1062280512yes—
232C22#1062283611yescharacteristic
233C4—22no—
234C4—84no—
235C4—442no—
236C4—881no—
237C4#1062268711yescharacteristic
238C4#1062268911yescharacteristic
239C4#1062279912yes—
240C4#1062280012yes—
241C4#1062283112yes—
242C2#1306798312yes—
243C2#1306810712yes—
244C2#1306962311yescharacteristic
245C2#1306970411yescharacteristic
246C2#1306973511yescharacteristic
subgroupG/H
centerC23#66991
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC2×C11×#494C2
socle, prime radicalC23×C11#121
hypercenterC2×#494D11
hypocenterC11#10276
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#494

Complements

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

NH ≅ G/Ntype
59. C2×Dic22Q16semidirect
201. C11#10276semidirect

Maximal subgroups

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

subgroupindex
C2×#106227072
#130695522
C2×#106221852
#130664512
C2×C11×#4942
#1027611