Finite Group Databasebeta

← #14667941

Subgroups — #14667941

Order 2816.

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

normal subgroups only

This group has 218 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#13070755C211yesmaximal, characteristic
2#13070667C211yesmaximal, characteristic
3#13068214C211yesmaximal, characteristic
4#13067422C211yesmaximal, characteristic
5#13066679C211yesmaximal, characteristic
6#13066664C211yesmaximal, characteristic
7C11×#1364C211yesmaximal, characteristic
8C11×#500C2211yescharacteristic
9#10622694—21no—
10#10622692—21no—
11C2×Dic88—21no—
12#10622443—21no—
13#10622312C2211yescharacteristic
14C4×Dic44C2211yescharacteristic
15C11×C4⋊C16C2211yescharacteristic
16C11×#335C2211yescharacteristic
17#10622141—21no—
18#10622130—21no—
19#10622128—21no—
20#10622122—21no—
21C4⋊(C11⋊C16)C2211yescharacteristic
22C8×C11⋊C8C2211yescharacteristic
23C11×C4⋊Q8—21no—
24C2×Dic44—21no—
25C2×Dic44—21no—
26C2×Dic44D411yescharacteristic
27#66922—21no—
28C4×Dic22—21no—
29C2×C11×C16—21no—
30C11×#107—21no—
31C11×#107—21no—
32C11×C4⋊C8—21no—
33C4×C8×C11C2311yescharacteristic
34#66899—41no—
35#66899—41no—
36#66882D411yescharacteristic
37#66880—21no—
38Dic11⋊C8—41no—
39C8×Dic11—41no—
40C2×C11⋊C16—21no—
41#66872—42no—
42C4×C11⋊C8D411yescharacteristic
43C4×C11⋊C8D411yescharacteristic
44Dic88—42no—
45#12423—111nomaximal, Sylow
46C2×Q8×C11—41no—
47C2×Dic22—21no—
48C2×Dic22—41no—
49C2×C8×C11—41no—
50C2×C8×C11C2×D411yescharacteristic
51C2×C8×C11#4111yescharacteristic
52C11×C4⋊C4—41no—
53C11×C4⋊C4—41no—
54C42×C11C2×D411yescharacteristic
55C4⋊Dic11—21no—
56C4⋊Dic11—41no—
57C4⋊Dic11—41no—
58Dic11⋊C4—41no—
59C4×Dic11—41no—
60C2×C11⋊C8—21no—
61C2×C11⋊C8D811yescharacteristic
62C2×C11⋊C8D811yescharacteristic
63Dic44—21no—
64Dic44—41no—
65Dic44—41no—
66Dic44—81no—
67Dic44SD1612yes—
68C11×C16—41no—
69C11⋊C16—41no—
70#2225—111no—
71#2209—111no—
72#1707—111no—
73C8×Q16—111no—
74#1367—111no—
75#1364D1111yescharacteristic
76#1362—111no—
77Q8×C11—81no—
78Q8×C11—81no—
79C2×C4×C11—81no—
80C2×C4×C11#12111yescharacteristic
81C2×C4×C11C2×D811yescharacteristic
82C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
83C2×Dic11—41no—
84C2×Dic11—41no—
85C2×Dic11—81no—
86Dic22—22no—
87Dic22—41no—
88Dic22—81no—
89Dic22—81no—
90C8×C11—21no—
91C8×C11—81no—
92C8×C11C2×SD1611yescharacteristic
93C8×C11#13511yescharacteristic
94C11⋊C8—22no—
95C11⋊C8—21no—
96C11⋊C8—21no—
97C2×Q32—221no—
98#500C2×D1111yescharacteristic
99#498—221no—
100#494—111no—
101#487—221no—
102C8×Q8—221no—
103C4×Q16—111no—
104#367—221no—
105C4⋊C16—111no—
106C4⋊C16C2×D1111yescharacteristic
107#358—221no—
108#358—221no—
109#335C2×D1111yescharacteristic
110Q8⋊C8—221no—
111C82—111no—
112C22×C11#45911yescharacteristic
113C4×C11—21no—
114C4×C11—161no—
115C4×C11#46511yescharacteristic
116C4×C11#47111yescharacteristic
117C4×C11#50811yescharacteristic
118C4×C11#51011yescharacteristic
119Dic11—42no—
120Dic11—81no—
121Dic11—161no—
122C2×Q16—111no—
123C2×Q16—221no—
124C2×Q16—221no—
125C4⋊Q8—21no—
126C4⋊Q8—221no—
127C4×Q8—221no—
128Q32—442no—
129C2×C16—21no—
130C2×C16—221no—
131#107—21no—
132#107—21no—
133#107—111no—
134#106—442no—
135C4⋊C8—21no—
136C4⋊C8—441no—
137#103—221no—
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—41no—
148C2×Q8—221no—
149C2×Q8—441no—
150Q16—112no—
151Q16—221no—
152Q16—441no—
153Q16—441no—
154Q16—881no—
155C2×C8—41no—
156C2×C8—111no—
157C2×C8—111no—
158C2×C8—221no—
159C2×C8#433911yescharacteristic
160C2×C8D4×D1111yescharacteristic
161C4⋊C4—41no—
162C4⋊C4—41no—
163C4⋊C4—221no—
164C4⋊C4—441no—
165C4⋊C4—441no—
166C4⋊C4—441no—
167C42—441no—
168C42D4×D1111yescharacteristic
169C16—41no—
170C16—441no—
171C11#1242311yescharacteristic, complemented, Sylow
172Q8—81no—
173Q8—81no—
174Q8—222no—
175Q8—441no—
176Q8—881no—
177Q8—881no—
178C2×C4—81no—
179C2×C4—441no—
180C2×C4—441no—
181C2×C4—881no—
182C2×C4#6693711yescharacteristic
183C2×C4D8×D1111yescharacteristic
184C2×C4#6696711yescharacteristic
185C8—21no—
186C8—81no—
187C8—222no—
188C8—221no—
189C8—221no—
190C8SD16×D1111yescharacteristic
191C8#6697211yescharacteristic
192C22#1062239911yescharacteristic
193C4—21no—
194C4—161no—
195C4—442no—
196C4—881no—
197C4—1761no—
198C4#1062236711yescharacteristic
199C4#1062242011yescharacteristic
200C4#1062252511yescharacteristic
201C4#1062252811yescharacteristic
202C2#1306796011yescharacteristic
203C2#1307067711yescharacteristic
204C2#1307069611yescharacteristic
subgroupG/H
centerC22#10622399
commutator, cosocleC4×C8×C11C23
FrattiniC4×C8C22×D11
FittingC11×#1364C2
socle, prime radicalC22×C11#459
hypercenter#1364D11
hypocenterC11#12423
LCSG ▷ C4×C8×C11 ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #1364

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
#130707552
#130706672
#130682142
#130674222
#130666792
#130666642
C11×#13642
#1242311