Finite Group Databasebeta

← #14672878

Subgroups — #14672878

Order 2816.

402 conjugacy classes of subgroups; only the 101 normal subgroups are shown.

normal subgroups only

This group has 402 conjugacy classes of subgroups — too many to draw. Only its 101 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×#10622126C212yesmaximal
2#13069504C211yesmaximal, characteristic
3#13066714C212yesmaximal, complemented
4#13066698C211yesmaximal, characteristic, complemented
5C2×C11×#498C211yesmaximal, characteristic, complemented
6C2×C11×C4⋊Q8—21no—
7C2×#66957C2211yescharacteristic
8C11×#498—24no—
9C2×C11×#106—21no—
10C2×C11×#106C2212yes—
11C2×C4×C8×C11C2211yescharacteristic
12#10622723—21no—
13C2×#66883C2211yescharacteristic
14C2×#66876C2212yes—
15C2×#66869—21no—
16#10622126—24no—
17C22×Q8×C11—41no—
18C2×#4339—21no—
19C22×C8×C11D411yescharacteristic
20C22×C8×C11C2311yescharacteristic
21C11×C4⋊Q8—24no—
22C11×C4⋊Q8—42no—
23C2×C11×C4⋊C4—22no—
24C2×C11×C4⋊C4—41no—
25C2×C42×C11D411yescharacteristic
26C2×#4318—21no—
27C2×Dic44Q811yescharacteristic, complemented
28#66957—22no—
29#66957—22no—
30C2×D88Q811yescharacteristic, complemented
31C2×#4314—21no—
32C11×#106—24no—
33C11×#106—22no—
34C11×#106D414yes—
35C4×C8×C11—22no—
36(C2×D11)⋊C8—42no—
37#66883—22no—
38#66876—22no—
39#66876—22no—
40C2×C11⋊C16—22no—
41#66869—42no—
42#13371—111nomaximal, Sylow
43C2×Q8×C11—44no—
44C2×Q8×C11—84no—
45C22×C4×C11—21no—
46C22×C4×C11—42no—
47C22×C4×C11C2×D411yescharacteristic
48C2×C22⋊D11—41no—
49#4339—41no—
50#4339—41no—
51#4339—41no—
52#4339—41no—
53C2×D44—21no—
54C2×C4×D11—41no—
55C2×Dic22—21no—
56C2×C8×C11—21no—
57C2×C8×C11—21no—
58C2×C8×C11SD1612yes—
59C2×C8×C11C2×D412yes—
60C2×C8×C11C2×Q811yescharacteristic
61C2×C8×C11#4111yescharacteristic
62C2×C8×C11#4112yes—
63C11×C4⋊C4—24no—
64C11×C4⋊C4—44no—
65C11×C4⋊C4—42no—
66C42×C11—21no—
67C42×C11D812yes—
68#4318—41no—
69#4318—41no—
70C2×C11⋊C8—41no—
71Dic44—22no—
72D88—22no—
73#4314—42no—
74C11⋊C16—42no—
75C2×#498D1111yescharacteristic, complemented
76C2×#360—112no—
77#1974—111no—
78#1383—112no—
79#1376—111no—
80C23×C11AGL(1,ℤ/8)11yescharacteristic
81C22×D11—41no—
82Q8×C11—88no—
83C2×C4×C11—24no—
84C2×C4×C11—22no—
85C2×C4×C11—44no—
86C2×C4×C11—84no—
87C2×C4×C11#12011yescharacteristic
88C2×C4×C11C22⋊Q811yescharacteristic
89C2×C4×C11#12411yescharacteristic
90C2×C4×C11C2×D811yescharacteristic
91C2×C4×C11C2×SD1611yescharacteristic
92C2×C4×C11#13711yescharacteristic
93C22⋊D11—81no—
94C22⋊D11—81no—
95C2×Dic11—41no—
96D44—41no—
97D44—41no—
98C4×D11—81no—
99C4×D11—81no—
100Dic22—41no—
101Dic22—41no—
102C8×C11—22no—
103C8×C11C22⋊Q812yes—
104C8×C11#12412yes—
105C11⋊C8—81no—
106C2×#135—111no—
107C2×C4⋊Q8—21no—
108C2×M32—112no—
109#498—24no—
110C2×#108—111no—
111C2×#106—21no—
112C2×#106C2×D1112yes—
113C2×#104—221no—
114#408—221no—
115C2×C4×C8C2×D1111yescharacteristic
116#360—224no—
117C22×C11—22no—
118C22×C11#44711yescharacteristic
119C22×C11#47611yescharacteristic
120C22×C11#48911yescharacteristic
121C2×D11—82no—
122C2×D11—81no—
123C4×C11—24no—
124C4×C11—84no—
125C4×C11#39311yescharacteristic
126C4×C11#44811yescharacteristic
127C4×C11#47411yescharacteristic
128C4×C11#48611yescharacteristic
129Dic11—81no—
130C2×#41—221no—
131C22×Q8—41no—
132#135—222no—
133#135—222no—
134C2×Q16—111no—
135C2×SD16—221no—
136C2×D8—111no—
137C2×M16—221no—
138C22×C8C22⋊D1111yescharacteristic
139C22×C8C22×D1111yescharacteristic
140C4⋊Q8—24no—
141C4⋊Q8—42no—
142C2×C4⋊C4—22no—
143C2×C4⋊C4—41no—
144C2×C42C22⋊D1111yescharacteristic
145M32—222no—
146M32—222no—
147C2×C16—222no—
148#108—222no—
149#106—24no—
150#106—22no—
151#106C22⋊D1114yes—
152#104—442no—
153C22⋊C8—442no—
154C4×C8—22no—
155C2×C11—21no—
156C2×C11—21no—
157C2×C11#202311yescharacteristic
158C2×C11#223012yes—
159D11—161no—
160#41—441no—
161#41—441no—
162#41—441no—
163#41—441no—
164C2×Q8—44no—
165C2×Q8—84no—
166C2×Q8—221no—
167C2×D4—221no—
168C2×D4—441no—
169C22×C4—21no—
170C22×C4—42no—
171C22×C4—441no—
172C22×C4C2×C22⋊D1111yescharacteristic
173Q16—222no—
174SD16—442no—
175D8—222no—
176M16—441no—
177M16—441no—
178C2×C8—21no—
179C2×C8—21no—
180C2×C8—441no—
181C2×C8#432512yes—
182C2×C8Q8×D1111yescharacteristic
183C2×C8#434312yes—
184C2×C8#434311yescharacteristic
185C2×C8C2×C22⋊D1112yes—
186C4⋊C4—24no—
187C4⋊C4—44no—
188C4⋊C4—42no—
189C42—21no—
190C42#432312yes—
191C16—442no—
192C11#1337111yescharacteristic, complemented, Sylow
193C23—441no—
194C23#6698511yescharacteristic
195Q8—88no—
196Q8—441no—
197Q8—441no—
198D4—441no—
199D4—441no—
200D4—881no—
201D4—881no—
202C2×C4—24no—
203C2×C4—22no—
204C2×C4—44no—
205C2×C4—84no—
206C2×C4—441no—
207C2×C4—881no—
208C2×C4—881no—
209C2×C4C2×#432311yescharacteristic
210C2×C4C2×#432511yescharacteristic
211C2×C4#6699511yescharacteristic
212C2×C4#6699911yescharacteristic
213C2×C4#6700011yescharacteristic
214C2×C4#6700611yescharacteristic
215C8—22no—
216C8—881no—
217C8#6699912yes—
218C8#6700012yes—
219C22—22no—
220C22—881no—
221C22—882no—
222C22#1062269711yescharacteristic
223C22#1062270211yescharacteristic
224C22#1062283011yescharacteristic
225C4—24no—
226C4—84no—
227C4—881no—
228C4#1062270011yescharacteristic
229C4#1062270111yescharacteristic
230C4#1062284011yescharacteristic
231C4#1062284411yescharacteristic
232C2—21no—
233C2—21no—
234C2—1761no—
235C2#1306974911yescharacteristic
236C2#1307078412yes—
subgroupG/H
centerC22#10622697
commutator, cosocleC22×C8×C11C23
FrattiniC22×C8C22×D11
FittingC2×C11×#498C2
socleC22×C11#476
prime radicalC2×#66957C22
hypercenterC2×#498D11
hypocenterC11#13371
LCSG ▷ C22×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×C8 ◁ C2×#498

Complements

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

NH ≅ G/Ntype
3. #13066714C2semidirect
4. #13066698C2semidirect
5. C2×C11×#498C2semidirect
27. C2×Dic44Q8semidirect
30. C2×D88Q8semidirect
75. C2×#498D11semidirect
192. C11#13371semidirect

Maximal subgroups

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

subgroupindex
C2×#106221262
#130695042
#130667142
#130666982
C2×C11×#4982
#1337111