Finite Group Databasebeta

← #14667913

Subgroups — #14667913

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#13070765C211yesmaximal, characteristic, complemented
2#13070657C211yesmaximal, characteristic
3#13068209C211yesmaximal, characteristic
4#13067422C211yesmaximal, characteristic, complemented
5#13066679C211yesmaximal, characteristic, complemented
6#13066661C211yesmaximal, characteristic
7C11×#1365C211yesmaximal, characteristic, complemented
8C11×#500C2211yescharacteristic
9#10622701—21no—
10#10622698—21no—
11C2×#66864—21no—
12#10622443—21no—
13C4×Dic44C2211yescharacteristic
14#10622308C2211yescharacteristic
15C11×C4⋊C16C2211yescharacteristic
16C11×#335C2211yescharacteristic
17#10622147—21no—
18#10622130—21no—
19#10622127—21no—
20#10622122—21no—
21C4⋊(C11⋊C16)C2211yescharacteristic
22C8×C11⋊C8C2211yescharacteristic
23C11×C4⋊Q8—21no—
24C2×#4325—42no—
25C2×Dic44D411yescharacteristic
26C2×D88—21no—
27C2×D88—21no—
28#66927—21no—
29C4×Dic22—21no—
30C2×C11×C16—21no—
31C11×#107—21no—
32C11×#107—21no—
33C11×C4⋊C8—21no—
34C4×C8×C11C2311yescharacteristic
35#66882D411yescharacteristic
36#66880—21no—
37Dic11⋊C8—41no—
38C8×Dic11—41no—
39C2×C11⋊C16—21no—
40#66873—41no—
41#66873—41no—
42C4×C11⋊C8D411yescharacteristic
43C4×C11⋊C8D411yescharacteristic
44#66864—42no—
45#12419—111nomaximal, Sylow
46C2×Q8×C11—41no—
47C2×D44—41no—
48C2×D44—41no—
49C2×D44—41no—
50C2×Dic22—21no—
51C2×C8×C11—41no—
52C2×C8×C11C2×D411yescharacteristic
53C2×C8×C11#4111yescharacteristic
54C11×C4⋊C4—41no—
55C11×C4⋊C4—41no—
56C42×C11C2×D411yescharacteristic
57#4325—84no—
58C4⋊Dic11—21no—
59Dic11⋊C4—41no—
60C4×Dic11—41no—
61C2×C11⋊C8—21no—
62C2×C11⋊C8D811yescharacteristic
63C2×C11⋊C8D811yescharacteristic
64Dic44—21no—
65Dic44SD1612yescomplemented
66D88—41no—
67D88—41no—
68D88—81no—
69C11×C16—41no—
70C11⋊C16—41no—
71#2227—111no—
72#2207—111no—
73#1706—111no—
74C8×Q16—111no—
75#1367—111no—
76#1365D1111yescharacteristic, complemented
77#1361—111no—
78C22×D11—81no—
79Q8×C11—82no—
80C2×C4×C11—81no—
81C2×C4×C11#12111yescharacteristic
82C2×C4×C11C2×D811yescharacteristic
83C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
84C2×Dic11—41no—
85C2×Dic11—41no—
86D44—82no—
87D44—81no—
88D44—81no—
89D44—81no—
90D44—81no—
91Dic22—22no—
92Dic22—41no—
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#500C2×D1111yescharacteristic
102#493—111no—
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#45911yescharacteristic
116C2×D11—161no—
117C2×D11—161no—
118C2×D11—161no—
119C4×C11—21no—
120C4×C11—161no—
121C4×C11#46511yescharacteristic
122C4×C11#47111yescharacteristic
123C4×C11#50811yescharacteristic
124C4×C11#51011yescharacteristic
125Dic11—42no—
126Dic11—81no—
127C2×Q16—111no—
128C2×SD16—442no—
129C2×D8—221no—
130C2×D8—221no—
131C4⋊Q8—21no—
132#127—221no—
133C4×Q8—221no—
134SD32—442no—
135C2×C16—21no—
136C2×C16—221no—
137#107—21no—
138#107—21no—
139#107—111no—
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#166511yescharacteristic
150C2×C11#221111yescharacteristic
151C2×C11#221311yescharacteristic
152D11—321no—
153C2×Q8—41no—
154C2×Q8—221no—
155C2×D4—441no—
156C2×D4—441no—
157C2×D4—441no—
158Q16—112no—
159Q16—221no—
160SD16—884no—
161D8—441no—
162D8—441no—
163D8—881no—
164C2×C8—41no—
165C2×C8—111no—
166C2×C8—111no—
167C2×C8—221no—
168C2×C8#433911yescharacteristic
169C2×C8D4×D1111yescharacteristic
170C4⋊C4—41no—
171C4⋊C4—41no—
172C4⋊C4—221no—
173C4⋊C4—441no—
174C42—441no—
175C42D4×D1111yescharacteristic
176C16—41no—
177C16—441no—
178C11#1241911yescharacteristic, complemented, Sylow
179C23—881no—
180Q8—82no—
181Q8—222no—
182Q8—441no—
183D4—882no—
184D4—881no—
185D4—881no—
186D4—881no—
187D4—881no—
188C2×C4—81no—
189C2×C4—441no—
190C2×C4—441no—
191C2×C4#6693711yescharacteristic
192C2×C4D8×D1111yescharacteristic
193C2×C4#6696711yescharacteristic
194C8—21no—
195C8—81no—
196C8—222no—
197C8—221no—
198C8—221no—
199C8SD16×D1111yescharacteristic
200C8#6697211yescharacteristic
201C22—1761no—
202C22—1761no—
203C22—1761no—
204C22#1062239911yescharacteristic
205C4—21no—
206C4—161no—
207C4—442no—
208C4—881no—
209C4#1062236711yescharacteristic
210C4#1062242011yescharacteristic
211C4#1062252911yescharacteristic
212C4#1062253111yescharacteristic
213C2—3521no—
214C2#1306796011yescharacteristic
215C2#1307068111yescharacteristic
216C2#1307069111yescharacteristic
subgroupG/H
centerC22#10622399
commutator, cosocleC4×C8×C11C23
FrattiniC4×C8C22×D11
FittingC11×#1365C2
socleC22×C11#459
prime radical#10622308C22
hypercenter#1365D11
hypocenterC11#12419
LCSG ▷ C4×C8×C11 ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #1365

Complements

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

NH ≅ G/Ntype
1. #13070765C2semidirect
4. #13067422C2semidirect
5. #13066679C2semidirect
7. C11×#1365C2semidirect
65. Dic44SD16semidirect
76. #1365D11semidirect
178. C11#12419semidirect

Maximal subgroups

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

subgroupindex
#130707652
#130706572
#130682092
#130674222
#130666792
#130666612
C11×#13652
#1241911