Finite Group Databasebeta

← #14640839

Subgroups — #14640839

Order 2816.

248 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 248 conjugacy classes of subgroups — too many to draw. Only its 79 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#13070230C211yesmaximal, characteristic
2#13068666C211yesmaximal, characteristic
3C11×#1812C211yesmaximal, characteristic
4C2×C11×#131C2211yescharacteristic
5C11×#427—21no—
6C11×#410—21no—
7#10622850—21no—
8C2×#66883—21no—
9C2×#66876C411yescharacteristic, complemented
10C22×C11⋊C16C411yescharacteristic, complemented
11C11×H(3,ℤ/4)C412yes—
12C11⋊#338C412yescomplemented
13C22⋊(C11⋊C16)—21no—
14C22⋊(C11⋊C16)—21no—
15C2×C11×#41D411yescharacteristic
16C11×#131—41no—
17C11×#131—41no—
18C2×C11×M16C2×C411yescharacteristic
19C2×C11×M16C2×C411yescharacteristic
20C2×C11×M16Q811yescharacteristic
21C22×C8×C11C2×C411yescharacteristic
22C22×C8×C11D411yescharacteristic
23C22×C8×C11D411yescharacteristic
24C11×#117—22no—
25C2×#4318—22no—
26C11×#107—41no—
27C11×#106—41no—
28C11×#99—41no—
29C11×#99—41no—
30#66900—41no—
31#66897—41no—
32#66883—41no—
33#66883—41no—
34#66876—41no—
35C2×C11⋊C16—21no—
36C2×C11⋊C16—21no—
37C2×C11⋊C16—41no—
38#7227—111nomaximal, Sylow
39C11×#41—41no—
40C11×#41—41no—
41C2×Q8×C11SD1611yescharacteristic
42C2×D4×C11D811yescharacteristic
43C2×D4×C11SD1611yescharacteristic
44C2×D4×C11Q1611yescharacteristic
45C22×C4×C11C22⋊C411yescharacteristic
46C22×C4×C11C22⋊C411yescharacteristic
47C22×C4×C11C4⋊C411yescharacteristic
48C11×M16—41no—
49C11×M16—41no—
50C11×M16—41no—
51C2×C8×C11—21no—
52C2×C8×C11—21no—
53C2×C8×C11—21no—
54C2×C8×C11—21no—
55C2×C8×C11—21no—
56C2×C8×C11—21no—
57C2×C8×C11C4211yescharacteristic
58C2×C8×C11C22⋊C411yescharacteristic
59C2×C8×C11C4⋊C411yescharacteristic
60C2×C8×C11C4⋊C411yescharacteristic
61C11×C4⋊C4—42no—
62C11×C22⋊C4—42no—
63C42×C11—42no—
64#4318—42no—
65#4318—42no—
66C2×C11⋊C8—42no—
67C11⋊C16—41no—
68C11⋊C16—41no—
69#2113—111no—
70#1813—111no—
71#1812D1111yescharacteristic
72C23×C11#10211yescharacteristic
73C23×C11#10311yescharacteristic
74C23×C11#10711yescharacteristic
75Q8×C11—41no—
76D4×C11—41no—
77D4×C11—41no—
78D4×C11—41no—
79C2×C4×C11—21no—
80C2×C4×C11—21no—
81C2×C4×C11—21no—
82C2×C4×C11—21no—
83C2×C4×C11—21no—
84C2×C4×C11—21no—
85C2×C4×C11—82no—
86C2×C4×C11#9511yescharacteristic
87C2×C4×C11#10211yescharacteristic
88C2×C4×C11#10311yescharacteristic
89C2×C4×C11#10611yescharacteristic
90C8×C11—21no—
91C8×C11—21no—
92C8×C11—21no—
93C8×C11#9911yescharacteristic
94C8×C11#9911yescharacteristic
95C11⋊C8—82no—
96C2×#131C2×D1111yescharacteristic
97C2×M32—111no—
98C22×C16—111no—
99C2×#108—221no—
100#427—21no—
101#413—221no—
102#410—21no—
103C22⋊C16—221no—
104C22⋊C16—221no—
105#338—112no—
106H(3,ℤ/4)Dic1112yes—
107C22×C11—21no—
108C22×C11—21no—
109C22×C11—21no—
110C22×C11—41no—
111C22×C11—41no—
112C22×C11—41no—
113C22×C11#34011yescharacteristic
114C4×C11—21no—
115C4×C11—21no—
116C4×C11—21no—
117C4×C11—162no—
118C4×C11H(3,ℤ/4)11yescharacteristic
119C4×C11#34211yescharacteristic
120C2×#41C22⋊D1111yescharacteristic
121#131—41no—
122#131—41no—
123C2×M16—222no—
124C2×M16Dic2211yescharacteristic
125C2×M16C4×D1111yescharacteristic
126C2×M16C2×Dic1111yescharacteristic
127C22×C8C4×D1111yescharacteristic
128C22×C8D4411yescharacteristic
129C22×C8C22⋊D1111yescharacteristic
130#117—22no—
131M32—441no—
132C2×C16—221no—
133C2×C16—221no—
134C2×C16—441no—
135#108—441no—
136#108—441no—
137#107—41no—
138#106—41no—
139#101—441no—
140#100—441no—
141#99—41no—
142#99—41no—
143C2×C11—21no—
144C2×C11—41no—
145C2×C11—41no—
146C2×C11—41no—
147C2×C11#128911yescharacteristic
148#41—41no—
149#41—41no—
150C2×Q8#432511yescharacteristic
151C2×D4#432311yescharacteristic
152C2×D4#432411yescharacteristic
153C2×D4#432611yescharacteristic
154C22×C4Dic11⋊C411yescharacteristic
155C22×C4(C2×D11)⋊C411yescharacteristic
156C22×C4C22⋊Dic1111yescharacteristic
157M16—41no—
158M16—41no—
159M16—41no—
160M16—442no—
161M16—442no—
162C2×C8—21no—
163C2×C8—21no—
164C2×C8—21no—
165C2×C8—21no—
166C2×C8—21no—
167C2×C8—21no—
168C2×C8—442no—
169C2×C8C4×Dic1111yescharacteristic
170C2×C8Dic11⋊C411yescharacteristic
171C2×C8C4⋊Dic1111yescharacteristic
172C2×C8(C2×D11)⋊C411yescharacteristic
173C4⋊C4—42no—
174C22⋊C4—42no—
175C42—42no—
176C16—441no—
177C16—441no—
178C11#722711yescharacteristic, complemented, Sylow
179C23#6687111yescharacteristic
180C23#6687411yescharacteristic
181C23#6689611yescharacteristic
182Q8—41no—
183D4—41no—
184D4—41no—
185D4—41no—
186C2×C4—21no—
187C2×C4—21no—
188C2×C4—21no—
189C2×C4—21no—
190C2×C4—21no—
191C2×C4—21no—
192C2×C4—82no—
193C2×C4#6687211yescharacteristic
194C2×C4#6687311yescharacteristic
195C2×C4C11⋊#9511yescharacteristic
196C2×C4#6689911yescharacteristic
197C8—21no—
198C8—21no—
199C8—21no—
200C8—882no—
201C8#6687011yescharacteristic
202C8#6687011yescharacteristic
203C22—21no—
204C22—21no—
205C22—21no—
206C22—41no—
207C22—41no—
208C22—41no—
209C22#1062216711yescharacteristic
210C4—21no—
211C4—21no—
212C4—21no—
213C4—162no—
214C4#1062216511yescharacteristic
215C4#1062216911yescharacteristic
216C2—21no—
217C2—41no—
218C2—41no—
219C2—41no—
220C2#1306648311yescharacteristic
subgroupG/H
centerC4#10622169
commutatorC2×C8×C11C42
FrattiniC2×#131C2×D11
FittingC11×#1812C2
socleC2×C11#1289
prime radicalC2×C11×#41D4
cosocleC2×C11×#131C22
hypercenter#1812D11
hypocenterC11#7227
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C11
UCSC1 ◁ C4 ◁ C2×C8 ◁ #1812

Complements

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

NH ≅ G/Ntype
9. C2×#66876C4semidirect
10. C22×C11⋊C16C4semidirect
12. C11⋊#338C4semidirect
178. C11#7227semidirect

Maximal subgroups

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

subgroupindex
#130702302
#130686662
C11×#18122
#722711