Finite Group Databasebeta

← #14673599

Subgroups — #14673599

Order 2816.

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

normal subgroups only

This group has 338 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×#10622133C212yesmaximal
2#13069492C211yesmaximal, characteristic
3#13066716C212yesmaximal, complemented
4#13066700C211yesmaximal, characteristic, complemented
5C11×#1849C211yesmaximal, characteristic, complemented
6C22×D88C2211yescharacteristic
7C2×C11×#108—21no—
8C2×C11×#108C2212yes—
9C11×#423—21no—
10C2×C11×#97C2211yescharacteristic
11C2×#66885—21no—
12C2×#66881C2211yescharacteristic
13C2×#66876C2212yes—
14#10622552—21no—
15#10622133—24no—
16C22×D44—21no—
17C2×C11×M16—22no—
18C22×C8×C11D411yescharacteristic
19C22×C8×C11C2311yescharacteristic
20C2×C42×C11D411yescharacteristic
21C2×(C2×D11)⋊C4—42no—
22C2×C4⋊Dic11—21no—
23C2×D88—22no—
24C2×D88—22no—
25C2×D88—21no—
26C2×D88D412yes—
27C11×#108—22no—
28C11×#108—22no—
29C11×#108—42no—
30C11×C4⋊C8—42no—
31C11×#97—22no—
32#66885—42no—
33#66881—22no—
34#66876—22no—
35#66876—22no—
36C2×C11⋊C16—22no—
37#13487—111nomaximal, Sylow
38C23×D11—41no—
39C22×C4×C11SD1612yes—
40C22×C4×C11C2×D411yescharacteristic
41C22×Dic11—41no—
42C2×D44—22no—
43C2×D44—41no—
44C2×D44—41no—
45C2×D44—41no—
46C2×D44—41no—
47C2×D44—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—
60(C2×D11)⋊C4—84no—
61C4⋊Dic11—41no—
62C4⋊Dic11—41no—
63D88—24no—
64D88—42no—
65C11⋊C16—42no—
66C2×#361—112no—
67#1972—111no—
68#1849D1111yescharacteristic, complemented
69#1383—112no—
70#1377—111no—
71C23×C11C2×SD1611yescharacteristic
72C22×D11—42no—
73C22×D11—82no—
74C22×D11—82no—
75C22×D11—81no—
76C22×D11—81no—
77C2×C4×C11—22no—
78C2×C4×C11—42no—
79C2×C4×C11#12111yescharacteristic
80C2×C4×C11#12311yescharacteristic
81C2×C4×C11#12411yescharacteristic
82C2×C4×C11C2×D811yescharacteristic
83C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
84C2×C4×C11#13711yescharacteristic
85C2×Dic11—82no—
86C2×Dic11—81no—
87D44—42no—
88D44—42no—
89D44—81no—
90D44—81no—
91C8×C11—22no—
92C8×C11—82no—
93C8×C11#12312yes—
94C8×C11#12612yes—
95C22×D8—111no—
96C2×M32—112no—
97C2×#108—21no—
98C2×#108C2×D1112yes—
99C2×#106—111no—
100#423—21no—
101C2×#102—221no—
102C2×#97C2×D1111yescharacteristic
103#390—221no—
104#361—224no—
105C22×C11—22no—
106C22×C11#46111yescharacteristic
107C22×C11#48111yescharacteristic
108C22×C11#48611yescharacteristic
109C2×D11—84no—
110C2×D11—82no—
111C2×D11—161no—
112C2×D11—161no—
113C2×D11—162no—
114C4×C11—42no—
115C4×C11#39711yescharacteristic
116C4×C11#45911yescharacteristic
117C4×C11#48011yescharacteristic
118C4×C11#48911yescharacteristic
119Dic11—161no—
120C22×D4—221no—
121C2×D8—112no—
122C2×D8—222no—
123C2×D8—221no—
124C2×D8—222no—
125C2×M16—22no—
126C22×C8C22⋊D1111yescharacteristic
127C22×C8C22×D1111yescharacteristic
128C2×C4⋊C4—221no—
129C2×C22⋊C4—442no—
130C2×C42C22⋊D1111yescharacteristic
131M32—222no—
132M32—222no—
133C2×C16—222no—
134#108—22no—
135#108—22no—
136#108—42no—
137#106—222no—
138C4⋊C8—42no—
139#102—442no—
140#97—22no—
141C2×C11—21no—
142C2×C11—21no—
143C2×C11#207111yescharacteristic
144C2×C11#223812yes—
145D11—162no—
146C24—441no—
147C2×D4—222no—
148C2×D4—441no—
149C2×D4—441no—
150C2×D4—441no—
151C2×D4—441no—
152C2×D4—441no—
153C22×C4—441no—
154C22×C4#432512yes—
155C22×C4C2×C22⋊D1111yescharacteristic
156D8—224no—
157D8—442no—
158M16—42no—
159M16—42no—
160C2×C8—21no—
161C2×C8—21no—
162C2×C8—42no—
163C2×C8#432312yes—
164C2×C8#433912yes—
165C2×C8D4×D1111yescharacteristic
166C2×C8#434111yescharacteristic
167C2×C8#434312yes—
168C4⋊C4—441no—
169C4⋊C4—441no—
170C22⋊C4—884no—
171C42—21no—
172C42—21no—
173C16—442no—
174C11#1348711yescharacteristic, complemented, Sylow
175C23—442no—
176C23—882no—
177C23—882no—
178C23—881no—
179C23—881no—
180C23C2×#432511yescharacteristic
181D4—442no—
182D4—442no—
183D4—881no—
184D4—881no—
185C2×C4—22no—
186C2×C4—42no—
187C2×C4—882no—
188C2×C4—881no—
189C2×C4#6698211yescharacteristic
190C2×C4C2×#432311yescharacteristic
191C2×C4#6698511yescharacteristic
192C2×C4#6699111yescharacteristic
193C2×C4#6699511yescharacteristic
194C2×C4#6700011yescharacteristic
195C8—22no—
196C8—82no—
197C8#6694712yes—
198C8#6695112yes—
199C22—22no—
200C22—884no—
201C22—882no—
202C22—1761no—
203C22—1761no—
204C22—1762no—
205C22#1062258111yescharacteristic
206C22#1062269611yescharacteristic
207C22#1062270111yescharacteristic
208C4—42no—
209C4—1761no—
210C4#1062258011yescharacteristic
211C4#1062260611yescharacteristic
212C4#1062268511yescharacteristic
213C4#1062270211yescharacteristic
214C2—21no—
215C2—21no—
216C2—1762no—
217C2#1307002011yescharacteristic
218C2#1307083012yes—
subgroupG/H
centerC22#10622581
commutator, cosocleC22×C8×C11C23
FrattiniC22×C8C22×D11
FittingC11×#1849C2
socleC22×C11#481
prime radicalC22×D88C22
hypercenter#1849D11
hypocenterC11#13487
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
3. #13066716C2semidirect
4. #13066700C2semidirect
5. C11×#1849C2semidirect
68. #1849D11semidirect
174. C11#13487semidirect

Maximal subgroups

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

subgroupindex
C2×#106221332
#130694922
#130667162
#130667002
C11×#18492
#1348711