Finite Group Databasebeta

← #14667909

Subgroups — #14667909

Order 2816.

240 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 240 conjugacy classes of subgroups — too many to draw. Only its 63 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#13070769C211yesmaximal, characteristic, complemented
2#13070653C211yesmaximal, characteristic
3#13068205C211yesmaximal, characteristic
4#13067422C211yesmaximal, characteristic, complemented
5#13066679C211yesmaximal, characteristic, complemented
6#13066675C211yesmaximal, characteristic, complemented
7C11×#1361C211yesmaximal, characteristic
8C11×#493C2211yescharacteristic
9C2×#66891—21no—
10#10622689—21no—
11#10622683—21no—
12#10622443—21no—
13C4×Dic44C2211yescharacteristic
14#10622295C2211yescharacteristic
15C11×C4⋊C16C2211yescharacteristic
16C11×#335C2211yescharacteristic
17#10622200—21no—
18#10622142—21no—
19#10622141—21no—
20#10622122—21no—
21C4⋊(C11⋊C16)C2211yescharacteristic
22C8×C11⋊C8C2211yescharacteristic
23C2×C11×D8—21no—
24C2×C11×D8—21no—
25C11×#127—21no—
26C2×#4324—42no—
27C2×Dic44D411yescharacteristic
28#66922—21no—
29C4×Dic22—21no—
30C2×C11×C16—21no—
31C11×C4⋊C8—21no—
32C4×C8×C11C2311yescharacteristic
33#66896—41no—
34#66896—41no—
35#66891—42no—
36#66882—21no—
37#66882—21no—
38#66882D411yescharacteristic
39#66880—21no—
40Dic11⋊C8—41no—
41C8×Dic11—41no—
42C2×C11⋊C16—21no—
43C4×C11⋊C8D411yescharacteristic
44C4×C11⋊C8D411yescharacteristic
45#12419—111nomaximal, Sylow
46C2×D4×C11—41no—
47C2×D4×C11—41no—
48C2×D4×C11—41no—
49C2×Dic22—21no—
50C2×Dic22—41no—
51C11×D8—41no—
52C11×D8—41no—
53C11×D8—81no—
54C2×C8×C11—41no—
55C2×C8×C11C2×D411yescharacteristic
56C2×C8×C11#4111yescharacteristic
57C42×C11C2×D411yescharacteristic
58#4324—84no—
59C4⋊Dic11—21no—
60C4⋊Dic11—41no—
61C4⋊Dic11—41no—
62Dic11⋊C4—41no—
63C4×Dic11—41no—
64C2×C11⋊C8—21no—
65C2×C11⋊C8D811yescharacteristic
66C2×C11⋊C8D811yescharacteristic
67Dic44—21no—
68Dic44SD1612yescomplemented
69C11×C16—41no—
70C11⋊C16—41no—
71#2227—111no—
72#2207—111no—
73#1706—111no—
74C8×Q16—111no—
75#1367—111no—
76#1365—111no—
77#1361D1111yescharacteristic
78C23×C11—81no—
79D4×C11—82no—
80D4×C11—81no—
81D4×C11—81no—
82D4×C11—81no—
83D4×C11—81no—
84C2×C4×C11#12111yescharacteristic
85C2×C4×C11C2×D811yescharacteristic
86C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
87C2×Dic11—41no—
88C2×Dic11—41no—
89C2×Dic11—81no—
90Dic22—22no—
91Dic22—41no—
92Dic22—82no—
93C8×C11—21no—
94C8×C11—81no—
95C8×C11C2×SD1611yescharacteristic
96C8×C11#13511yescharacteristic
97C11⋊C8—22no—
98C11⋊C8—21no—
99C11⋊C8—21no—
100C2×SD32—221no—
101#500—111no—
102#493C2×D1111yescharacteristic
103#492—221no—
104#486—221no—
105C8×Q8—221no—
106C4×Q16—111no—
107#366—221no—
108C4⋊C16—111no—
109C4⋊C16C2×D1111yescharacteristic
110#358—221no—
111#357—221no—
112#335C2×D1111yescharacteristic
113Q8⋊C8—221no—
114C82—111no—
115C22×C11—161no—
116C22×C11—161no—
117C22×C11—161no—
118C22×C11#45911yescharacteristic
119C4×C11—21no—
120C4×C11#46511yescharacteristic
121C4×C11#47111yescharacteristic
122C4×C11#50811yescharacteristic
123C4×C11#51011yescharacteristic
124Dic11—42no—
125Dic11—81no—
126Dic11—161no—
127C2×Q16—111no—
128C2×SD16—442no—
129C2×D8—21no—
130C2×D8—21no—
131C4⋊Q8—221no—
132#127—21no—
133C4×Q8—221no—
134SD32—442no—
135C2×C16—21no—
136C2×C16—221no—
137#107—111no—
138#107—221no—
139#107—221no—
140C4⋊C8—21no—
141C4⋊C8—441no—
142#103—221no—
143#102—441no—
144#102—441no—
145C4×C8—111no—
146C4×C8—111no—
147C4×C8—441no—
148C4×C8C22×D1111yescharacteristic
149C2×C11—321no—
150C2×C11#166511yescharacteristic
151C2×C11#221111yescharacteristic
152C2×C11#221311yescharacteristic
153C2×Q8—221no—
154C2×Q8—441no—
155C2×D4—41no—
156C2×D4—41no—
157C2×D4—41no—
158Q16—112no—
159Q16—221no—
160SD16—884no—
161D8—41no—
162D8—41no—
163D8—81no—
164C2×C8—41no—
165C2×C8—111no—
166C2×C8—111no—
167C2×C8—221no—
168C2×C8#433911yescharacteristic
169C2×C8D4×D1111yescharacteristic
170C4⋊C4—221no—
171C4⋊C4—441no—
172C4⋊C4—441no—
173C4⋊C4—441no—
174C42—441no—
175C42D4×D1111yescharacteristic
176C16—41no—
177C16—441no—
178C11#1241911yescharacteristic, complemented, Sylow
179C23—81no—
180Q8—222no—
181Q8—441no—
182Q8—882no—
183D4—82no—
184D4—81no—
185D4—81no—
186D4—81no—
187D4—81no—
188C2×C4—441no—
189C2×C4—441no—
190C2×C4—881no—
191C2×C4#6693711yescharacteristic
192C2×C4D8×D1111yescharacteristic
193C2×C4#6696711yescharacteristic
194C8—21no—
195C8—81no—
196C8—222no—
197C8—221no—
198C8—221no—
199C8#6696511yescharacteristic
200C8SD16×D1111yescharacteristic
201C22—161no—
202C22—161no—
203C22—161no—
204C22#1062239911yescharacteristic
205C4—21no—
206C4—442no—
207C4—881no—
208C4—1761no—
209C4#1062236111yescharacteristic
210C4#1062239111yescharacteristic
211C4#1062252511yescharacteristic
212C4#1062252811yescharacteristic
213C2—321no—
214C2#1306795611yescharacteristic
215C2#1307067711yescharacteristic
216C2#1307069111yescharacteristic
subgroupG/H
centerC22#10622399
commutator, cosocleC4×C8×C11C23
FrattiniC4×C8C22×D11
FittingC11×#1361C2
socleC22×C11#459
prime radicalC11×#493C22
hypercenter#1361D11
hypocenterC11#12419
LCSG ▷ C4×C8×C11 ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #1361

Complements

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

NH ≅ G/Ntype
1. #13070769C2semidirect
4. #13067422C2semidirect
5. #13066679C2semidirect
6. #13066675C2semidirect
68. Dic44SD16semidirect
178. C11#12419semidirect

Maximal subgroups

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

subgroupindex
#130707692
#130706532
#130682052
#130674222
#130666792
#130666752
C11×#13612
#1241911