Finite Group Databasebeta

← #14673604

Subgroups — #14673604

Order 2816.

302 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 302 conjugacy classes of subgroups — too many to draw. Only its 93 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
1C2×#10622134C212yesmaximal
2#13069487C211yesmaximal, characteristic
3#13066716C212yesmaximal
4#13066700C211yesmaximal, characteristic
5C11×#1849C211yesmaximal, characteristic
6C22×Dic44C2211yescharacteristic
7C2×C11×#108—21no—
8C2×C11×#108C2212yes—
9C11×#423—21no—
10C2×C11×#97C2211yescharacteristic
11C2×#66881C2211yescharacteristic
12C2×#66880—21no—
13C2×#66876C2212yes—
14#10622542—21no—
15#10622134—24no—
16C22×Dic22—21no—
17C2×C11×M16—22no—
18C22×C8×C11D411yescharacteristic
19C22×C8×C11C2311yescharacteristic
20C2×C42×C11D411yescharacteristic
21C2×C4⋊Dic11—21no—
22C2×Dic44—22no—
23C2×Dic44—22no—
24C2×Dic44—21no—
25C2×Dic44D412yes—
26C11×#108—22no—
27C11×#108—22no—
28C11×#108—42no—
29C11×C4⋊C8—42no—
30C11×#97—22no—
31C11⋊#95—42no—
32#66881—22no—
33#66880—42no—
34#66876—22no—
35#66876—22no—
36C2×C11⋊C16—22no—
37#13488—111nomaximal, Sylow
38C22×C4×C11SD1612yes—
39C22×C4×C11C2×D411yescharacteristic
40C22×Dic11—41no—
41C22×Dic11—41no—
42C2×Dic22—22no—
43C2×Dic22—41no—
44C2×Dic22—41no—
45C2×Dic22—41no—
46C2×Dic22—41no—
47C2×Dic22—41no—
48C11×M16—42no—
49C11×M16—42no—
50C2×C8×C11—21no—
51C2×C8×C11—21no—
52C2×C8×C11—42no—
53C2×C8×C11D812yes—
54C2×C8×C11C2×D411yescharacteristic
55C2×C8×C11#4111yescharacteristic
56C2×C8×C11#4112yes—
57C2×C8×C11#4112yes—
58C42×C11—21no—
59C42×C11—21no—
60C4⋊Dic11—41no—
61C4⋊Dic11—41no—
62Dic44—24no—
63Dic44—42no—
64C11⋊C16—42no—
65C2×#362—112no—
66#1971—111no—
67#1849D1111yescharacteristic
68#1383—112no—
69#1377—111no—
70C23×C11C2×SD1611yescharacteristic
71C2×C4×C11—22no—
72C2×C4×C11—42no—
73C2×C4×C11#12111yescharacteristic
74C2×C4×C11#12311yescharacteristic
75C2×C4×C11#12411yescharacteristic
76C2×C4×C11C2×D811yescharacteristic
77C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
78C2×C4×C11#13711yescharacteristic
79C2×Dic11—42no—
80C2×Dic11—81no—
81C2×Dic11—81no—
82C2×Dic11—82no—
83C2×Dic11—81no—
84Dic22—42no—
85Dic22—42no—
86Dic22—81no—
87Dic22—81no—
88C8×C11—22no—
89C8×C11—82no—
90C8×C11#12312yes—
91C8×C11#12612yes—
92C22×Q16—111no—
93C2×M32—112no—
94C2×#108—21no—
95C2×#108C2×D1112yes—
96C2×#106—111no—
97#423—21no—
98C2×#103—221no—
99C2×#97C2×D1111yescharacteristic
100#391—221no—
101#362—224no—
102C22×C11—22no—
103C22×C11#46111yescharacteristic
104C22×C11#48111yescharacteristic
105C22×C11#48611yescharacteristic
106C4×C11—42no—
107C4×C11#39711yescharacteristic
108C4×C11#45911yescharacteristic
109C4×C11#48011yescharacteristic
110C4×C11#48911yescharacteristic
111Dic11—82no—
112Dic11—161no—
113C22×Q8—221no—
114C2×Q16—112no—
115C2×Q16—222no—
116C2×Q16—221no—
117C2×Q16—222no—
118C2×M16—22no—
119C22×C8C22⋊D1111yescharacteristic
120C22×C8C22×D1111yescharacteristic
121C2×C4⋊C4—221no—
122C2×C42C22⋊D1111yescharacteristic
123M32—222no—
124M32—222no—
125C2×C16—222no—
126#108—22no—
127#108—22no—
128#108—42no—
129#106—222no—
130C4⋊C8—42no—
131#103—442no—
132#97—22no—
133#95—442no—
134C2×C11—21no—
135C2×C11—21no—
136C2×C11#207111yescharacteristic
137C2×C11#223912yes—
138C2×Q8—222no—
139C2×Q8—441no—
140C2×Q8—441no—
141C2×Q8—441no—
142C2×Q8—441no—
143C2×Q8—441no—
144C22×C4—441no—
145C22×C4—441no—
146C22×C4#432512yes—
147C22×C4C2×C22⋊D1111yescharacteristic
148Q16—224no—
149Q16—442no—
150M16—42no—
151M16—42no—
152C2×C8—21no—
153C2×C8—21no—
154C2×C8—42no—
155C2×C8#432312yes—
156C2×C8#433912yes—
157C2×C8D4×D1111yescharacteristic
158C2×C8#434111yescharacteristic
159C2×C8#434312yes—
160C4⋊C4—441no—
161C4⋊C4—441no—
162C42—21no—
163C42—21no—
164C16—442no—
165C11#1348811yescharacteristic, complemented, Sylow
166C23C2×#432511yescharacteristic
167Q8—442no—
168Q8—442no—
169Q8—881no—
170Q8—881no—
171C2×C4—22no—
172C2×C4—42no—
173C2×C4—442no—
174C2×C4—881no—
175C2×C4—881no—
176C2×C4—882no—
177C2×C4—881no—
178C2×C4#6698211yescharacteristic
179C2×C4C2×#432311yescharacteristic
180C2×C4#6698511yescharacteristic
181C2×C4#6699111yescharacteristic
182C2×C4#6699511yescharacteristic
183C2×C4#6700011yescharacteristic
184C8—22no—
185C8—82no—
186C8#6694712yes—
187C8#6695112yes—
188C22—22no—
189C22#1062258111yescharacteristic
190C22#1062269611yescharacteristic
191C22#1062270111yescharacteristic
192C4—42no—
193C4—882no—
194C4—1761no—
195C4#1062258011yescharacteristic
196C4#1062260611yescharacteristic
197C4#1062268511yescharacteristic
198C4#1062270211yescharacteristic
199C2—21no—
200C2—21no—
201C2#1307002011yescharacteristic
202C2#1307083512yes—
subgroupG/H
centerC22#10622581
commutator, cosocleC22×C8×C11C23
FrattiniC22×C8C22×D11
FittingC11×#1849C2
socleC22×C11#481
prime radicalC23×C11C2×SD16
hypercenter#1849D11
hypocenterC11#13488
LCSG ▷ C22×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#97 ◁ #1849

Complements

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

NH ≅ G/Ntype
165. C11#13488semidirect

Maximal subgroups

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

subgroupindex
C2×#106221342
#130694872
#130667162
#130667002
C11×#18492
#1348811