Finite Group Databasebeta

← #14667970

Subgroups — #14667970

Order 2816.

240 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 240 conjugacy classes of subgroups — too many to draw. Only its 67 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#13070666C211yesmaximal, characteristic, complemented
2#13068221C211yesmaximal, characteristic
3Q16×C11⋊C8C211yesmaximal, characteristic, complemented
4#13066685C211yesmaximal, characteristic, complemented
5#13066666C211yesmaximal, characteristic, complemented
6#13066662C211yesmaximal, characteristic
7C11×#2207C211yesmaximal, characteristic
8C2×C11×SD32—21no—
9C11×#493C2211yescharacteristic
10C4×C11×Q16C2211yescharacteristic
11C2×#66893—21no—
12#10622683—21no—
13#10622683—21no—
14Q8×C11⋊C8—21no—
15#10622312C2211yescharacteristic
16C11×C4⋊C16C2211yescharacteristic
17C11×#357—21no—
18Q8⋊(C11⋊C8)—21no—
19#10622130—21no—
20C4⋊(C11⋊C16)C2211yescharacteristic
21#10622096C2211yescharacteristic
22C8×C11⋊C8C2211yescharacteristic
23C2×C11×Q16D411yescharacteristic
24C2×C11×D8—21no—
25C2×C11×D8—21no—
26C11×#127—21no—
27C4×Q8×C11—21no—
28C2×Dic44—21no—
29C2×Dic44—21no—
30#66922—21no—
31C11×SD32—42no—
32C2×C11×C16—21no—
33C11×#107D411yescharacteristic
34C11×#103—21no—
35C4×C8×C11C2311yescharacteristic
36#66896—42no—
37#66896—41no—
38#66896—41no—
39#66893—42no—
40C2×C11⋊C16—21no—
41C4⋊(C11⋊C8)—21no—
42C4⋊(C11⋊C8)—41no—
43C4×C11⋊C8—41no—
44C4×C11⋊C8D411yescharacteristic
45C4×C11⋊C8D411yescharacteristic
46#12429—111nomaximal, Sylow
47C2×Q8×C11—21no—
48C2×D4×C11—41no—
49C2×D4×C11—41no—
50C2×D4×C11—41no—
51C2×Dic22—41no—
52C11×Q16—21no—
53C11×Q16D812yes—
54C11×D8—41no—
55C11×D8—41no—
56C11×D8—81no—
57C2×C8×C11C2×D411yescharacteristic
58C2×C8×C11#4111yescharacteristic
59C11×C4⋊C4—21no—
60C11×C4⋊C4—41no—
61C42×C11—41no—
62C42×C11C2×D411yescharacteristic
63C4⋊Dic11—41no—
64C4⋊Dic11—41no—
65C2×C11⋊C8—21no—
66C2×C11⋊C8—41no—
67C2×C11⋊C8D811yescharacteristic
68C2×C11⋊C8D811yescharacteristic
69Dic44—41no—
70Dic44—41no—
71Dic44—81no—
72C11×C16—41no—
73C11⋊C16—41no—
74#2209—111no—
75#2207D1111yescharacteristic
76#1709—111no—
77C8×Q16—111no—
78#1370—111no—
79#1362—111no—
80#1361—111no—
81C23×C11—81no—
82Q8×C11—22no—
83Q8×C11—41no—
84D4×C11—82no—
85D4×C11—81no—
86D4×C11—81no—
87D4×C11—81no—
88D4×C11—81no—
89C2×C4×C11—41no—
90C2×C4×C11—41no—
91C2×C4×C11#12111yescharacteristic
92C2×C4×C11C2×D811yescharacteristic
93C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
94C2×Dic11—81no—
95Dic22—81no—
96Dic22—81no—
97C8×C11—21no—
98C8×C11C2×D811yescharacteristic
99C8×C11#13511yescharacteristic
100C11⋊C8—21no—
101C11⋊C8—21no—
102C11⋊C8—41no—
103C11⋊C8—81no—
104C2×Q32—221no—
105C2×SD32—21no—
106#494—111no—
107#493C2×D1111yescharacteristic
108#486—221no—
109#486—221no—
110C8×Q8—221no—
111C4×Q16C2×D1111yescharacteristic
112C4⋊C16—111no—
113C4⋊C16C2×D1111yescharacteristic
114#358—221no—
115#357—21no—
116#335—111no—
117Q8⋊C8—221no—
118C82—111no—
119C22×C11—161no—
120C22×C11—161no—
121C22×C11—161no—
122C22×C11#45911yescharacteristic
123C4×C11—21no—
124C4×C11—42no—
125C4×C11—81no—
126C4×C11#46611yescharacteristic
127C4×C11#47211yescharacteristic
128C4×C11#50811yescharacteristic
129C4×C11#51011yescharacteristic
130Dic11—161no—
131C2×Q16—221no—
132C2×Q16—221no—
133C2×Q16C22⋊D1111yescharacteristic
134C2×D8—21no—
135C2×D8—21no—
136C4⋊Q8—221no—
137#127—21no—
138C4×Q8—21no—
139Q32—442no—
140SD32—42no—
141C2×C16—21no—
142C2×C16—221no—
143#107C22⋊D1111yescharacteristic
144C4⋊C8—221no—
145C4⋊C8—441no—
146#103—21no—
147#102—441no—
148#102—441no—
149#102—442no—
150C4×C8—111no—
151C4×C8—111no—
152C4×C8—441no—
153C4×C8C22×D1111yescharacteristic
154C2×C11—321no—
155C2×C11#166711yescharacteristic
156C2×C11#221111yescharacteristic
157C2×C11#221211yescharacteristic
158C2×Q8—21no—
159C2×Q8—441no—
160C2×D4—41no—
161C2×D4—41no—
162C2×D4—41no—
163Q16—21no—
164Q16—441no—
165Q16—441no—
166Q16—881no—
167Q16#432312yes—
168D8—41no—
169D8—41no—
170D8—81no—
171C2×C8—111no—
172C2×C8—111no—
173C2×C8—221no—
174C2×C8—441no—
175C2×C8#434111yescharacteristic
176C2×C8C2×C22⋊D1111yescharacteristic
177C4⋊C4—21no—
178C4⋊C4—41no—
179C4⋊C4—441no—
180C4⋊C4—441no—
181C42—41no—
182C42D4×D1111yescharacteristic
183C16—41no—
184C16—441no—
185C11#1242911yescharacteristic, complemented, Sylow
186C23—81no—
187Q8—22no—
188Q8—41no—
189Q8—881no—
190Q8—881no—
191D4—82no—
192D4—81no—
193D4—81no—
194D4—81no—
195D4—81no—
196C2×C4—41no—
197C2×C4—41no—
198C2×C4—881no—
199C2×C4D8×D1111yescharacteristic
200C2×C4#6696411yescharacteristic
201C2×C4#6699211yescharacteristic
202C8—21no—
203C8—221no—
204C8—221no—
205C8—441no—
206C8—881no—
207C8C2×#432311yescharacteristic
208C8#6700311yescharacteristic
209C22—161no—
210C22—161no—
211C22—161no—
212C22#1062276311yescharacteristic
213C4—21no—
214C4—42no—
215C4—81no—
216C4—1761no—
217C4#1062252811yescharacteristic
218C4#1062252911yescharacteristic
219C4#1062265111yescharacteristic
220C4#1062281211yescharacteristic
221C2—321no—
222C2#1306796911yescharacteristic
223C2#1307067611yescharacteristic
224C2#1307068311yescharacteristic
subgroupG/H
centerC22#10622763
commutator, cosocleC4×C8×C11C23
FrattiniC4×C8C22×D11
FittingC11×#2207C2
socleC22×C11#459
prime radicalC11×#493C22
hypercenter#2207D11
hypocenterC11#12429
LCSG ▷ C4×C8×C11 ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #2207

Complements

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

NH ≅ G/Ntype
1. #13070666C2semidirect
3. Q16×C11⋊C8C2semidirect
4. #13066685C2semidirect
5. #13066666C2semidirect
185. C11#12429semidirect

Maximal subgroups

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

subgroupindex
#130706662
#130682212
Q16×C11⋊C82
#130666852
#130666662
#130666622
C11×#22072
#1242911