Finite Group Databasebeta

← #14667912

Subgroups — #14667912

Order 2816.

240 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 240 conjugacy classes of subgroups — too many to draw. Only its 67 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#13070656C211yesmaximal, characteristic
2#13068209C211yesmaximal, characteristic
3Q16×C11⋊C8C211yesmaximal, characteristic, complemented
4#13066679C211yesmaximal, characteristic, complemented
5#13066674C211yesmaximal, characteristic, complemented
6#13066663C211yesmaximal, characteristic
7C11×#2227C211yesmaximal, characteristic, complemented
8C11×#500C2211yescharacteristic
9C4×C11×Q16C2211yescharacteristic
10C2×#66892—21no—
11#10622701—21no—
12#10622698—21no—
13Q8×C11⋊C8—21no—
14#10622308C2211yescharacteristic
15C11×#366—21no—
16C11×C4⋊C16C2211yescharacteristic
17C11×#358—21no—
18Q8⋊(C11⋊C8)—21no—
19#10622129—21no—
20C4⋊(C11⋊C16)C2211yescharacteristic
21#10622096C2211yescharacteristic
22C8×C11⋊C8C2211yescharacteristic
23C2×C11×Q16D411yescharacteristic
24C11×C4⋊Q8—21no—
25C4×Q8×C11—21no—
26C2×#4325—42no—
27C2×D88—21no—
28C2×D88—21no—
29#66927—21no—
30C2×C11×C16—21no—
31C11×#107—21no—
32C11×#107—21no—
33C11×#107D411yescharacteristic
34C11×#103—21no—
35C4×C8×C11C2311yescharacteristic
36#66892—42no—
37C2×C11⋊C16—21no—
38#66873—41no—
39#66873—41no—
40C4⋊(C11⋊C8)—21no—
41C4⋊(C11⋊C8)—41no—
42C4×C11⋊C8—41no—
43C4×C11⋊C8D411yescharacteristic
44C4×C11⋊C8D411yescharacteristic
45#12419—111nomaximal, Sylow
46C2×Q8×C11—21no—
47C2×Q8×C11—41no—
48C2×D44—41no—
49C2×D44—41no—
50C2×D44—41no—
51C11×Q16—21no—
52C11×Q16SD1612yescomplemented
53C2×C8×C11C2×D411yescharacteristic
54C2×C8×C11#4111yescharacteristic
55C11×C4⋊C4—21no—
56C11×C4⋊C4—41no—
57C11×C4⋊C4—41no—
58C11×C4⋊C4—41no—
59C42×C11—41no—
60C42×C11C2×D411yescharacteristic
61#4325—84no—
62C2×C11⋊C8—21no—
63C2×C11⋊C8—41no—
64C2×C11⋊C8D811yescharacteristic
65C2×C11⋊C8D811yescharacteristic
66D88—41no—
67D88—41no—
68D88—81no—
69C11×C16—41no—
70C11⋊C16—41no—
71#2227D1111yescharacteristic, complemented
72#2207—111no—
73#1706—111no—
74C8×Q16—111no—
75#1367—111no—
76#1365—111no—
77#1361—111no—
78C22×D11—81no—
79Q8×C11—22no—
80Q8×C11—41no—
81Q8×C11—82no—
82C2×C4×C11—41no—
83C2×C4×C11—41no—
84C2×C4×C11—81no—
85C2×C4×C11#12111yescharacteristic
86C2×C4×C11C2×D811yescharacteristic
87C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
88D44—82no—
89D44—81no—
90D44—81no—
91D44—81no—
92D44—81no—
93C8×C11—21no—
94C8×C11C2×SD1611yescharacteristic
95C8×C11#13511yescharacteristic
96C11⋊C8—22no—
97C11⋊C8—21no—
98C11⋊C8—21no—
99C11⋊C8—81no—
100C2×SD32—221no—
101#500C2×D1111yescharacteristic
102#493—111no—
103#492—221no—
104#486—221no—
105C8×Q8—221no—
106C4×Q16C2×D1111yescharacteristic
107#366—21no—
108C4⋊C16—111no—
109C4⋊C16C2×D1111yescharacteristic
110#358—21no—
111#357—221no—
112#335—111no—
113Q8⋊C8—221no—
114C82—111no—
115C22×C11#45911yescharacteristic
116C2×D11—161no—
117C2×D11—161no—
118C2×D11—161no—
119C4×C11—21no—
120C4×C11—42no—
121C4×C11—81no—
122C4×C11—161no—
123C4×C11#46511yescharacteristic
124C4×C11#47111yescharacteristic
125C4×C11#50811yescharacteristic
126C4×C11#51011yescharacteristic
127C2×Q16C22⋊D1111yescharacteristic
128C2×SD16—442no—
129C2×D8—221no—
130C2×D8—221no—
131C4⋊Q8—21no—
132#127—221no—
133C4×Q8—21no—
134SD32—442no—
135C2×C16—21no—
136C2×C16—221no—
137#107—21no—
138#107—21no—
139#107C22⋊D1111yescharacteristic
140C4⋊C8—221no—
141C4⋊C8—441no—
142#103—21no—
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—21no—
154C2×Q8—41no—
155C2×D4—441no—
156C2×D4—441no—
157C2×D4—441no—
158Q16—21no—
159Q16#432512yescomplemented
160SD16—884no—
161D8—441no—
162D8—441no—
163D8—881no—
164C2×C8—111no—
165C2×C8—111no—
166C2×C8—221no—
167C2×C8—441no—
168C2×C8#434111yescharacteristic
169C2×C8C2×C22⋊D1111yescharacteristic
170C4⋊C4—21no—
171C4⋊C4—41no—
172C4⋊C4—41no—
173C4⋊C4—41no—
174C42—41no—
175C42D4×D1111yescharacteristic
176C16—41no—
177C16—441no—
178C11#1241911yescharacteristic, complemented, Sylow
179C23—881no—
180Q8—22no—
181Q8—41no—
182Q8—82no—
183D4—882no—
184D4—881no—
185D4—881no—
186D4—881no—
187D4—881no—
188C2×C4—41no—
189C2×C4—41no—
190C2×C4—81no—
191C2×C4D8×D1111yescharacteristic
192C2×C4#6696411yescharacteristic
193C2×C4#6699211yescharacteristic
194C8—21no—
195C8—222no—
196C8—221no—
197C8—221no—
198C8—881no—
199C8C2×#432511yescharacteristic
200C8#6700311yescharacteristic
201C22—1761no—
202C22—1761no—
203C22—1761no—
204C22#1062276311yescharacteristic
205C4—21no—
206C4—42no—
207C4—81no—
208C4—161no—
209C4#1062253111yescharacteristic
210C4#1062253211yescharacteristic
211C4#1062266111yescharacteristic
212C4#1062281611yescharacteristic
213C2—3521no—
214C2#1306795911yescharacteristic
215C2#1307068011yescharacteristic
216C2#1307069011yescharacteristic
subgroupG/H
centerC22#10622763
commutator, cosocleC4×C8×C11C23
FrattiniC4×C8C22×D11
FittingC11×#2227C2
socleC22×C11#459
prime radical#10622308C22
hypercenter#2227D11
hypocenterC11#12419
LCSG ▷ C4×C8×C11 ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #2227

Complements

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

NH ≅ G/Ntype
3. Q16×C11⋊C8C2semidirect
4. #13066679C2semidirect
5. #13066674C2semidirect
7. C11×#2227C2semidirect
52. C11×Q16SD16semidirect
71. #2227D11semidirect
159. Q16#4325semidirect
178. C11#12419semidirect

Maximal subgroups

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

subgroupindex
#130706562
#130682092
Q16×C11⋊C82
#130666792
#130666742
#130666632
C11×#22272
#1241911