Finite Group Databasebeta

← #14667940

Subgroups — #14667940

Order 2816.

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

normal subgroups only

This group has 218 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#13070666C211yesmaximal, characteristic
2#13068214C211yesmaximal, characteristic
3Q16×C11⋊C8C211yesmaximal, characteristic
4#13066679C211yesmaximal, characteristic
5#13066671C211yesmaximal, characteristic
6#13066666C211yesmaximal, characteristic
7C11×#2225C211yesmaximal, characteristic
8C11×#500C2211yescharacteristic
9C4×C11×Q16C2211yescharacteristic
10C2×#66893—21no—
11#10622694—21no—
12#10622692—21no—
13Q8×C11⋊C8—21no—
14#10622312C2211yescharacteristic
15C11×#367—21no—
16C11×C4⋊C16C2211yescharacteristic
17C11×#358—21no—
18Q8⋊(C11⋊C8)—21no—
19#10622130—21no—
20C4⋊(C11⋊C16)C2211yescharacteristic
21#10622096C2211yescharacteristic
22C8×C11⋊C8C2211yescharacteristic
23C2×C11×Q16D411yescharacteristic
24C11×C4⋊Q8—21no—
25C4×Q8×C11—21no—
26C2×Dic44—21no—
27C2×Dic44—21no—
28#66922—21no—
29C2×C11×C16—21no—
30C11×#107—21no—
31C11×#107—21no—
32C11×#107D411yescharacteristic
33C11×#103—21no—
34C4×C8×C11C2311yescharacteristic
35#66899—41no—
36#66899—41no—
37#66893—42no—
38C2×C11⋊C16—21no—
39#66872—42no—
40C4⋊(C11⋊C8)—21no—
41C4⋊(C11⋊C8)—41no—
42C4×C11⋊C8—41no—
43C4×C11⋊C8D411yescharacteristic
44C4×C11⋊C8D411yescharacteristic
45#12423—111nomaximal, Sylow
46C2×Q8×C11—21no—
47C2×Q8×C11—41no—
48C2×Dic22—41no—
49C11×Q16—21no—
50C11×Q16SD1612yes—
51C2×C8×C11C2×D411yescharacteristic
52C2×C8×C11#4111yescharacteristic
53C11×C4⋊C4—21no—
54C11×C4⋊C4—41no—
55C11×C4⋊C4—41no—
56C11×C4⋊C4—41no—
57C42×C11—41no—
58C42×C11C2×D411yescharacteristic
59C4⋊Dic11—41no—
60C4⋊Dic11—41no—
61C2×C11⋊C8—21no—
62C2×C11⋊C8—41no—
63C2×C11⋊C8D811yescharacteristic
64C2×C11⋊C8D811yescharacteristic
65Dic44—41no—
66Dic44—41no—
67Dic44—81no—
68C11×C16—41no—
69C11⋊C16—41no—
70#2225D1111yescharacteristic
71#2209—111no—
72#1707—111no—
73C8×Q16—111no—
74#1367—111no—
75#1364—111no—
76#1362—111no—
77Q8×C11—22no—
78Q8×C11—41no—
79Q8×C11—81no—
80Q8×C11—81no—
81C2×C4×C11—41no—
82C2×C4×C11—41no—
83C2×C4×C11—81no—
84C2×C4×C11#12111yescharacteristic
85C2×C4×C11C2×D811yescharacteristic
86C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
87C2×Dic11—81no—
88Dic22—81no—
89Dic22—81no—
90C8×C11—21no—
91C8×C11C2×SD1611yescharacteristic
92C8×C11#13511yescharacteristic
93C11⋊C8—22no—
94C11⋊C8—21no—
95C11⋊C8—21no—
96C11⋊C8—81no—
97C2×Q32—221no—
98#500C2×D1111yescharacteristic
99#498—221no—
100#494—111no—
101#487—221no—
102C8×Q8—221no—
103C4×Q16C2×D1111yescharacteristic
104#367—21no—
105C4⋊C16—111no—
106C4⋊C16C2×D1111yescharacteristic
107#358—21no—
108#358—221no—
109#335—111no—
110Q8⋊C8—221no—
111C82—111no—
112C22×C11#45911yescharacteristic
113C4×C11—21no—
114C4×C11—42no—
115C4×C11—81no—
116C4×C11—161no—
117C4×C11#46511yescharacteristic
118C4×C11#47111yescharacteristic
119C4×C11#50811yescharacteristic
120C4×C11#51011yescharacteristic
121Dic11—161no—
122C2×Q16—221no—
123C2×Q16—221no—
124C2×Q16C22⋊D1111yescharacteristic
125C4⋊Q8—21no—
126C4⋊Q8—221no—
127C4×Q8—21no—
128Q32—442no—
129C2×C16—21no—
130C2×C16—221no—
131#107—21no—
132#107—21no—
133#107C22⋊D1111yescharacteristic
134#106—442no—
135C4⋊C8—221no—
136C4⋊C8—441no—
137#103—21no—
138#103—441no—
139#103—441no—
140C4×C8—111no—
141C4×C8—111no—
142C4×C8—441no—
143C4×C8C22×D1111yescharacteristic
144C2×C11#166511yescharacteristic
145C2×C11#221111yescharacteristic
146C2×C11#221411yescharacteristic
147C2×Q8—21no—
148C2×Q8—41no—
149C2×Q8—441no—
150Q16—21no—
151Q16—441no—
152Q16—441no—
153Q16—881no—
154Q16#432512yes—
155C2×C8—111no—
156C2×C8—111no—
157C2×C8—221no—
158C2×C8—441no—
159C2×C8#434111yescharacteristic
160C2×C8C2×C22⋊D1111yescharacteristic
161C4⋊C4—21no—
162C4⋊C4—41no—
163C4⋊C4—41no—
164C4⋊C4—41no—
165C4⋊C4—441no—
166C4⋊C4—441no—
167C42—41no—
168C42D4×D1111yescharacteristic
169C16—41no—
170C16—441no—
171C11#1242311yescharacteristic, complemented, Sylow
172Q8—22no—
173Q8—41no—
174Q8—81no—
175Q8—81no—
176Q8—881no—
177Q8—881no—
178C2×C4—41no—
179C2×C4—41no—
180C2×C4—81no—
181C2×C4—881no—
182C2×C4D8×D1111yescharacteristic
183C2×C4#6696411yescharacteristic
184C2×C4#6699211yescharacteristic
185C8—21no—
186C8—222no—
187C8—221no—
188C8—221no—
189C8—881no—
190C8C2×#432511yescharacteristic
191C8#6700311yescharacteristic
192C22#1062276311yescharacteristic
193C4—21no—
194C4—42no—
195C4—81no—
196C4—161no—
197C4—1761no—
198C4#1062252811yescharacteristic
199C4#1062252911yescharacteristic
200C4#1062266111yescharacteristic
201C4#1062281611yescharacteristic
202C2#1306795911yescharacteristic
203C2#1307067611yescharacteristic
204C2#1307069511yescharacteristic
subgroupG/H
centerC22#10622763
commutator, cosocleC4×C8×C11C23
FrattiniC4×C8C22×D11
FittingC11×#2225C2
socle, prime radicalC22×C11#459
hypercenter#2225D11
hypocenterC11#12423
LCSG ▷ C4×C8×C11 ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #2225

Complements

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

NH ≅ G/Ntype
171. C11#12423semidirect

Maximal subgroups

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

subgroupindex
#130706662
#130682142
Q16×C11⋊C82
#130666792
#130666712
#130666662
C11×#22252
#1242311