Finite Group Databasebeta

← #14673603

Subgroups — #14673603

Order 2816.

302 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 302 conjugacy classes of subgroups — too many to draw. Only its 95 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×#10622203C212yesmaximal
2#13068791C211yesmaximal, characteristic
3#13066714C212yesmaximal
4#13066700C211yesmaximal, characteristic
5C11×#1971C211yesmaximal, characteristic
6C22×C11×Q16C2211yescharacteristic
7C2×C11×#106C2211yescharacteristic
8C2×C11×#103—21no—
9C2×C11×#97C2211yescharacteristic
10C11×#391—21no—
11C2×#66883—21no—
12C2×#66883C2212yes—
13C2×#66876C2212yes—
14#10622537—21no—
15#10622203—24no—
16C22×Q8×C11—21no—
17C2×C11×Q16—22no—
18C2×C11×Q16—22no—
19C2×C11×Q16—21no—
20C2×C11×Q16D412yes—
21C22×C8×C11D411yescharacteristic
22C22×C8×C11C2311yescharacteristic
23C2×C11×C4⋊C4—21no—
24C2×C42×C11D411yescharacteristic
25C2×#4318—22no—
26C11×#106—22no—
27C11×#103—42no—
28C11×#97—22no—
29C11×#95—42no—
30#66883—22no—
31#66883—22no—
32#66883—42no—
33#66876—22no—
34#66876—22no—
35C2×C11⋊C16—22no—
36C4⋊(C11⋊C8)—42no—
37#13488—111nomaximal, Sylow
38C2×Q8×C11—22no—
39C2×Q8×C11—41no—
40C2×Q8×C11—41no—
41C2×Q8×C11—41no—
42C2×Q8×C11—41no—
43C2×Q8×C11—41no—
44C22×C4×C11—41no—
45C22×C4×C11—41no—
46C22×C4×C11SD1612yes—
47C22×C4×C11C2×D411yescharacteristic
48C11×Q16—24no—
49C11×Q16—42no—
50C2×C8×C11—21no—
51C2×C8×C11—21no—
52C2×C8×C11D812yes—
53C2×C8×C11C2×D411yescharacteristic
54C2×C8×C11#4111yescharacteristic
55C2×C8×C11#4112yes—
56C2×C8×C11#4112yes—
57C11×C4⋊C4—41no—
58C11×C4⋊C4—41no—
59C42×C11—21no—
60C42×C11—21no—
61#4318—42no—
62#4318—42no—
63C2×C11⋊C8—42no—
64C11⋊C16—42no—
65C2×#362—112no—
66#1971D1111yescharacteristic
67#1849—111no—
68#1383—112no—
69#1377—111no—
70C23×C11C2×SD1611yescharacteristic
71Q8×C11—42no—
72Q8×C11—42no—
73Q8×C11—81no—
74Q8×C11—81no—
75C2×C4×C11—22no—
76C2×C4×C11—42no—
77C2×C4×C11—42no—
78C2×C4×C11—81no—
79C2×C4×C11—81no—
80C2×C4×C11—82no—
81C2×C4×C11—81no—
82C2×C4×C11#12111yescharacteristic
83C2×C4×C11#12311yescharacteristic
84C2×C4×C11#12411yescharacteristic
85C2×C4×C11C2×D811yescharacteristic
86C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
87C2×C4×C11#13711yescharacteristic
88C8×C11—22no—
89C8×C11#12312yes—
90C8×C11#12612yes—
91C11⋊C8—82no—
92C22×Q16C2×D1111yescharacteristic
93C2×M32—112no—
94C2×#108—112no—
95C2×#108—221no—
96C2×#106C2×D1111yescharacteristic
97#423—221no—
98C2×#103—21no—
99C2×#97C2×D1111yescharacteristic
100#391—21no—
101#362—224no—
102C22×C11—22no—
103C22×C11#46111yescharacteristic
104C22×C11#48111yescharacteristic
105C22×C11#48611yescharacteristic
106C4×C11—42no—
107C4×C11—82no—
108C4×C11—161no—
109C4×C11#39711yescharacteristic
110C4×C11#45911yescharacteristic
111C4×C11#48011yescharacteristic
112C4×C11#48911yescharacteristic
113C22×Q8—21no—
114C2×Q16—21no—
115C2×Q16—22no—
116C2×Q16—22no—
117C2×Q16D4412yes—
118C2×M16—222no—
119C22×C8C22⋊D1111yescharacteristic
120C22×C8C22×D1111yescharacteristic
121C2×C4⋊C4—21no—
122C2×C42C22⋊D1111yescharacteristic
123M32—222no—
124M32—222no—
125C2×C16—222no—
126#108—222no—
127#108—222no—
128#108—442no—
129#106—22no—
130C4⋊C8—442no—
131#103—42no—
132#97—22no—
133#95—42no—
134C2×C11—21no—
135C2×C11—21no—
136C2×C11#207111yescharacteristic
137C2×C11#223912yes—
138C2×Q8—22no—
139C2×Q8—41no—
140C2×Q8—41no—
141C2×Q8—41no—
142C2×Q8—41no—
143C2×Q8—41no—
144C22×C4—41no—
145C22×C4—41no—
146C22×C4#432412yes—
147C22×C4C2×C22⋊D1111yescharacteristic
148Q16—24no—
149Q16—42no—
150M16—442no—
151M16—442no—
152C2×C8—21no—
153C2×C8—21no—
154C2×C8—442no—
155C2×C8#432312yes—
156C2×C8C2×D4411yescharacteristic
157C2×C8#433911yescharacteristic
158C2×C8#434112yes—
159C2×C8#434112yes—
160C4⋊C4—41no—
161C4⋊C4—41no—
162C42—21no—
163C42—21no—
164C16—442no—
165C11#1348811yescharacteristic, complemented, Sylow
166C23C2×#432411yescharacteristic
167Q8—42no—
168Q8—42no—
169Q8—81no—
170Q8—81no—
171C2×C4—22no—
172C2×C4—42no—
173C2×C4—42no—
174C2×C4—81no—
175C2×C4—81no—
176C2×C4—82no—
177C2×C4—81no—
178C2×C4#6698311yescharacteristic
179C2×C4C2×#432311yescharacteristic
180C2×C4#6698811yescharacteristic
181C2×C4#6698911yescharacteristic
182C2×C4#6700211yescharacteristic
183C2×C4#6700411yescharacteristic
184C8—22no—
185C8—882no—
186C8#6693212yes—
187C8#6693912yes—
188C22—22no—
189C22#1062263211yescharacteristic
190C22#1062264711yescharacteristic
191C22#1062268311yescharacteristic
192C4—42no—
193C4—82no—
194C4—161no—
195C4#1062256611yescharacteristic
196C4#1062262811yescharacteristic
197C4#1062264611yescharacteristic
198C4#1062266811yescharacteristic
199C2—21no—
200C2—21no—
201C2#1307001911yescharacteristic
202C2#1307083312yes—
subgroupG/H
centerC22#10622647
commutator, cosocleC22×C8×C11C23
FrattiniC22×C8C22×D11
FittingC11×#1971C2
socleC22×C11#481
prime radicalC23×C11C2×SD16
hypercenter#1971D11
hypocenterC11#13488
LCSG ▷ C22×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#97 ◁ #1971

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×#106222032
#130687912
#130667142
#130667002
C11×#19712
#1348811