Finite Group Databasebeta

← #14667923

Subgroups — #14667923

Order 2816.

218 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 218 conjugacy classes of subgroups — too many to draw. Only its 65 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
2#13070663C211yesmaximal, characteristic
3#13068210C211yesmaximal, characteristic
4#13067422C211yesmaximal, characteristic
5#13066679C211yesmaximal, characteristic
6#13066675C211yesmaximal, characteristic
7C11×#1362C211yesmaximal, characteristic
8C11×#494C2211yescharacteristic
9C2×#66893—21no—
10#10622706—21no—
11#10622692—21no—
12#10622443—21no—
13C4×Dic44C2211yescharacteristic
14#10622295C2211yescharacteristic
15C11×C4⋊C16C2211yescharacteristic
16C11×#335C2211yescharacteristic
17#10622202—21no—
18#10622142—21no—
19#10622141—21no—
20#10622122—21no—
21C4⋊(C11⋊C16)C2211yescharacteristic
22C8×C11⋊C8C2211yescharacteristic
23C2×C11×Q16—21no—
24C2×C11×Q16—21no—
25C11×C4⋊Q8—21no—
26C2×Dic44D411yescharacteristic
27#66922—21no—
28C4×Dic22—21no—
29C2×C11×C16—21no—
30C11×C4⋊C8—21no—
31C4×C8×C11C2311yescharacteristic
32#66893—42no—
33#66882—21no—
34#66882—21no—
35#66882D411yescharacteristic
36#66880—21no—
37Dic11⋊C8—41no—
38C8×Dic11—41no—
39C2×C11⋊C16—21no—
40#66874—42no—
41#66872—41no—
42#66872—41no—
43C4×C11⋊C8D411yescharacteristic
44C4×C11⋊C8D411yescharacteristic
45#12421—111nomaximal, Sylow
46C2×Q8×C11—41no—
47C2×Dic22—21no—
48C2×Dic22—41no—
49C11×Q16—41no—
50C11×Q16—41no—
51C11×Q16—81no—
52C2×C8×C11—41no—
53C2×C8×C11C2×D411yescharacteristic
54C2×C8×C11#4111yescharacteristic
55C11×C4⋊C4—41no—
56C11×C4⋊C4—41no—
57C42×C11C2×D411yescharacteristic
58C4⋊Dic11—21no—
59C4⋊Dic11—41no—
60C4⋊Dic11—41no—
61Dic11⋊C4—41no—
62C4×Dic11—41no—
63C2×C11⋊C8—21no—
64C2×C11⋊C8D811yescharacteristic
65C2×C11⋊C8D811yescharacteristic
66Dic44—21no—
67Dic44SD1612yes—
68C11×C16—41no—
69C11⋊C16—41no—
70#2227—111no—
71#2209—111no—
72#1707—111no—
73C8×Q16—111no—
74#1367—111no—
75#1365—111no—
76#1362D1111yescharacteristic
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—82no—
89C8×C11—21no—
90C8×C11—81no—
91C8×C11C2×SD1611yescharacteristic
92C8×C11#13511yescharacteristic
93C11⋊C8—21no—
94C11⋊C8—41no—
95C11⋊C8Q3212yescomplemented
96C2×Q32—221no—
97#500—111no—
98#498—221no—
99#494C2×D1111yescharacteristic
100#487—221no—
101C8×Q8—221no—
102C4×Q16—111no—
103#366—221no—
104C4⋊C16—111no—
105C4⋊C16C2×D1111yescharacteristic
106#358—221no—
107#358—221no—
108#335C2×D1111yescharacteristic
109Q8⋊C8—221no—
110C82—111no—
111C22×C11#45911yescharacteristic
112C4×C11—21no—
113C4×C11—161no—
114C4×C11#46511yescharacteristic
115C4×C11#47111yescharacteristic
116C4×C11C2×Q3211yescharacteristic
117C4×C11#51011yescharacteristic
118Dic11—42no—
119Dic11—81no—
120Dic11—161no—
121C2×Q16—21no—
122C2×Q16—21no—
123C2×Q16—111no—
124C4⋊Q8—21no—
125C4⋊Q8—221no—
126C4×Q8—221no—
127Q32—442no—
128C2×C16—21no—
129C2×C16—221no—
130#107—111no—
131#107—221no—
132#107—221no—
133#106—441no—
134#106—441no—
135C4⋊C8—21no—
136C4⋊C8—441no—
137#103—221no—
138#103—442no—
139C4×C8—111no—
140C4×C8—111no—
141C4×C8—441no—
142C4×C8C22×D1111yescharacteristic
143C2×C11#166511yescharacteristic
144C2×C11#220911yescharacteristic
145C2×C11#221211yescharacteristic
146C2×Q8—41no—
147C2×Q8—221no—
148C2×Q8—441no—
149Q16—41no—
150Q16—41no—
151Q16—81no—
152Q16—112no—
153Q16—221no—
154C2×C8—41no—
155C2×C8—111no—
156C2×C8—111no—
157C2×C8—221no—
158C2×C8#433911yescharacteristic
159C2×C8D4×D1111yescharacteristic
160C4⋊C4—41no—
161C4⋊C4—41no—
162C4⋊C4—221no—
163C4⋊C4—441no—
164C4⋊C4—441no—
165C4⋊C4—441no—
166C42—441no—
167C42D4×D1111yescharacteristic
168C16—41no—
169C16—441no—
170C11#1242111yescharacteristic, complemented, Sylow
171Q8—81no—
172Q8—81no—
173Q8—222no—
174Q8—441no—
175Q8—882no—
176C2×C4—81no—
177C2×C4—441no—
178C2×C4—441no—
179C2×C4—881no—
180C2×C4#6693711yescharacteristic
181C2×C4D8×D1111yescharacteristic
182C2×C4#6696711yescharacteristic
183C8—21no—
184C8—81no—
185C8—112no—
186C8—221no—
187C8—441no—
188C8#6696511yescharacteristic
189C8SD16×D1111yescharacteristic
190C22#1062239911yescharacteristic
191C4—21no—
192C4—161no—
193C4—442no—
194C4—881no—
195C4—1761no—
196C4#1062236111yescharacteristic
197C4#1062239111yescharacteristic
198C4#1062252811yescharacteristic
199C4D11×Q3211yescharacteristic
200C2#1306795611yescharacteristic
201C2#1307066511yescharacteristic
202C2#1307068811yescharacteristic
subgroupG/H
centerC22#10622399
commutator, cosocleC4×C8×C11C23
FrattiniC4×C8C22×D11
FittingC11×#1362C2
socle, prime radicalC22×C11#459
hypercenter#1362D11
hypocenterC11#12421
LCSG ▷ C4×C8×C11 ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #1362

Complements

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

NH ≅ G/Ntype
95. C11⋊C8Q32semidirect
170. C11#12421semidirect

Maximal subgroups

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

subgroupindex
#130707692
#130706632
#130682102
#130674222
#130666792
#130666752
C11×#13622
#1242111