Finite Group Databasebeta

← #14673584

Subgroups — #14673584

Order 2816.

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

normal subgroups only

This group has 330 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
1#13070326C212yesmaximal
2#13069504C211yesmaximal, characteristic
3#13066724C212yesmaximal, complemented
4#13066698C211yesmaximal, characteristic, complemented
5C11×#1845C211yesmaximal, characteristic, complemented
6C2×#66957C2211yescharacteristic
7C2×C11×#107—21no—
8C2×C11×#107C2212yes—
9C2×C4×C8×C11C2211yescharacteristic
10C11×#384—21no—
11#10622723—21no—
12C2×#66883C2211yescharacteristic
13C2×#66876C2212yes—
14C2×#66869—21no—
15#10622130—22no—
16#10622129—22no—
17C2×#4339—21no—
18C22×C8×C11D411yescharacteristic
19C22×C8×C11C2311yescharacteristic
20C2×C11×C4⋊C4—22no—
21C2×C11×C4⋊C4—42no—
22C2×C42×C11D411yescharacteristic
23C2×#4318—21no—
24C2×Dic44D411yescharacteristic
25#66957—22no—
26#66957—22no—
27C2×D88D411yescharacteristic
28C2×#4314—21no—
29C11×#107—22no—
30C11×#107—22no—
31C11×#107—42no—
32C4×C8×C11—22no—
33(C2×D11)⋊C8—42no—
34#66883—22no—
35#66876—22no—
36#66876—22no—
37C2×C11⋊C16—22no—
38#66869—42no—
39#13484—111nomaximal, Sylow
40C22×C4×C11—21no—
41C22×C4×C11—42no—
42C22×C4×C11C2×D411yescharacteristic
43C2×C22⋊D11—41no—
44#4339—41no—
45#4339—41no—
46#4339—41no—
47#4339—41no—
48C2×D44—21no—
49C2×C4×D11—41no—
50C2×Dic22—21no—
51C2×C8×C11—21no—
52C2×C8×C11—21no—
53C2×C8×C11D812yes—
54C2×C8×C11C2×D411yescharacteristic
55C2×C8×C11#4111yescharacteristic
56C2×C8×C11#4112yes—
57C2×C8×C11#4112yes—
58C11×C4⋊C4—42no—
59C11×C4⋊C4—42no—
60C11×C4⋊C4—84no—
61C42×C11—21no—
62C42×C11SD1612yes—
63#4318—41no—
64#4318—41no—
65C2×C11⋊C8—41no—
66Dic44—22no—
67D88—22no—
68#4314—42no—
69C11⋊C16—42no—
70#2139—112no—
71#1974—111no—
72#1845D1111yescharacteristic, complemented
73#1387—112no—
74#1376—111no—
75C23×C11AGL(1,ℤ/8)11yescharacteristic
76C22×D11—41no—
77C2×C4×C11—22no—
78C2×C4×C11—22no—
79C2×C4×C11—22no—
80C2×C4×C11—84no—
81C2×C4×C11—82no—
82C2×C4×C11#12111yescharacteristic
83C2×C4×C11#12311yescharacteristic
84C2×C4×C11#12411yescharacteristic
85C2×C4×C11C2×D811yescharacteristic
86C2×C4×C11C2×SD1611yescharacteristic
87C2×C4×C11#13711yescharacteristic
88C22⋊D11—81no—
89C22⋊D11—81no—
90C2×Dic11—41no—
91D44—41no—
92D44—41no—
93C4×D11—81no—
94C4×D11—81no—
95Dic22—41no—
96Dic22—41no—
97C8×C11—22no—
98C8×C11#12312yes—
99C8×C11#12612yes—
100C11⋊C8—81no—
101C2×#135—111no—
102C2×M32—112no—
103C2×#108—111no—
104C2×#107—21no—
105C2×#107C2×D1112yes—
106C2×#104—221no—
107#408—221no—
108C2×C4×C8C2×D1111yescharacteristic
109#384—21no—
110#358—222no—
111#357—222no—
112C22×C11—21no—
113C22×C11—21no—
114C22×C11#45911yescharacteristic
115C22×C11#48111yescharacteristic
116C22×C11#48911yescharacteristic
117C2×D11—81no—
118C2×D11—81no—
119C2×D11—81no—
120C4×C11—24no—
121C4×C11—162no—
122C4×C11#39711yescharacteristic
123C4×C11#46111yescharacteristic
124C4×C11#48011yescharacteristic
125C4×C11#48611yescharacteristic
126Dic11—81no—
127C2×#41—221no—
128#135—222no—
129#135—222no—
130C2×Q16—111no—
131C2×SD16—221no—
132C2×D8—111no—
133C2×M16—221no—
134C22×C8C22⋊D1111yescharacteristic
135C22×C8C22×D1111yescharacteristic
136C2×C4⋊C4—22no—
137C2×C4⋊C4—42no—
138C2×C42C22⋊D1111yescharacteristic
139M32—222no—
140M32—222no—
141C2×C16—222no—
142#108—222no—
143#107—22no—
144#107—22no—
145#107—42no—
146#104—442no—
147C22⋊C8—442no—
148C4×C8—22no—
149C2×C11—21no—
150C2×C11—21no—
151C2×C11#207111yescharacteristic
152C2×C11#221311yescharacteristic
153C2×C11#221411yescharacteristic
154D11—161no—
155#41—441no—
156#41—441no—
157#41—441no—
158#41—441no—
159C2×Q8—221no—
160C2×D4—221no—
161C2×D4—441no—
162C22×C4—21no—
163C22×C4—42no—
164C22×C4—441no—
165C22×C4C2×C22⋊D1111yescharacteristic
166Q16—222no—
167SD16—442no—
168D8—222no—
169M16—441no—
170M16—441no—
171C2×C8—21no—
172C2×C8—21no—
173C2×C8—441no—
174C2×C8#432312yes—
175C2×C8#433912yes—
176C2×C8D4×D1111yescharacteristic
177C2×C8#434111yescharacteristic
178C2×C8#434312yes—
179C4⋊C4—42no—
180C4⋊C4—42no—
181C4⋊C4—84no—
182C42—21no—
183C42#432512yes—
184C16—442no—
185C11#1348411yescharacteristic, complemented, Sylow
186C23—441no—
187C23#6698511yescharacteristic
188Q8—441no—
189Q8—441no—
190D4—441no—
191D4—441no—
192D4—881no—
193D4—881no—
194C2×C4—22no—
195C2×C4—22no—
196C2×C4—22no—
197C2×C4—84no—
198C2×C4—82no—
199C2×C4—441no—
200C2×C4—881no—
201C2×C4—881no—
202C2×C4#6698211yescharacteristic
203C2×C4C2×#432311yescharacteristic
204C2×C4#6699111yescharacteristic
205C2×C4C2×#432511yescharacteristic
206C2×C4#6699511yescharacteristic
207C2×C4#6700011yescharacteristic
208C8—22no—
209C8—881no—
210C8#6694712yes—
211C8#6695112yes—
212C22—21no—
213C22—21no—
214C22—881no—
215C22—881no—
216C22—881no—
217C22#1062258111yescharacteristic
218C22#1062268511yescharacteristic
219C22#1062270211yescharacteristic
220C4—24no—
221C4—162no—
222C4—881no—
223C4#1062258011yescharacteristic
224C4#1062260611yescharacteristic
225C4#1062269611yescharacteristic
226C4#1062270111yescharacteristic
227C2—21no—
228C2—21no—
229C2—1761no—
230C2#1307002011yescharacteristic
231C2#1307068911yescharacteristic
232C2#1307069411yescharacteristic
subgroupG/H
centerC22#10622685
commutator, cosocleC22×C8×C11C23
FrattiniC22×C8C22×D11
FittingC11×#1845C2
socleC22×C11#459
prime radicalC2×#66957C22
hypercenter#1845D11
hypocenterC11#13484
LCSG ▷ C22×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×C8 ◁ #1845

Complements

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

NH ≅ G/Ntype
3. #13066724C2semidirect
4. #13066698C2semidirect
5. C11×#1845C2semidirect
72. #1845D11semidirect
185. C11#13484semidirect

Maximal subgroups

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

subgroupindex
#130703262
#130695042
#130667242
#130666982
C11×#18452
#1348411