Finite Group Databasebeta

← #14668188

Subgroups — #14668188

Order 2816.

240 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 240 conjugacy classes of subgroups — too many to draw. Only its 69 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#13070839C211yesmaximal, characteristic, complemented
2D4×C11⋊C16C211yesmaximal, characteristic, complemented
3#13068005C211yesmaximal, characteristic, complemented
4#13066687C211yesmaximal, characteristic, complemented
5#13066672C211yesmaximal, characteristic, complemented
6#13066662C211yesmaximal, characteristic, complemented
7C11×#1667C211yesmaximal, characteristic
8C11×#493C2211yescharacteristic
9C11×#459—21no—
10C8×D4×C11C2211yescharacteristic
11C22×C11⋊C16—21no—
12#10622632—21no—
13#10622295C2211yescharacteristic
14C11×#335C2211yescharacteristic
15C11×#331—21no—
16#10622200—21no—
17#10622200—21no—
18C22⋊(C11⋊C16)—21no—
19#10622124—21no—
20C4⋊(C11⋊C16)C2211yescharacteristic
21C4×C11⋊C16C2211yescharacteristic
22#10622096C2211yescharacteristic
23C2×C11×D8—21no—
24C2×C11×D8—21no—
25C2×C11×D8—41no—
26C22×C8×C11—21no—
27C11×#127—21no—
28C4×D4×C11D411yescharacteristic
29C2×#4324—41no—
30#66922—21no—
31C11×C4⋊C8—21no—
32C11×C4⋊C8D411yescharacteristic
33C11×#102—41no—
34C11×C22⋊C8—21no—
35C4×C8×C11C2311yescharacteristic
36#66882—21no—
37#66882—21no—
38C2×C11⋊C16—21no—
39C2×C11⋊C16—42no—
40C2×C11⋊C16D411yescharacteristic
41C2×C11⋊C16D411yescharacteristic
42#66874—41no—
43C4⋊(C11⋊C8)—21no—
44#12467—111nomaximal, Sylow
45C2×D4×C11—41no—
46C2×D4×C11—41no—
47C2×D4×C11—41no—
48C2×D4×C11D811yescharacteristic
49C22×C4×C11—21no—
50C2×Dic22—41no—
51C11×D8—41no—
52C11×D8—41no—
53C11×D8—82no—
54C11×D8—81no—
55C2×C8×C11—21no—
56C2×C8×C11—41no—
57C2×C8×C11—41no—
58C2×C8×C11—41no—
59C2×C8×C11C2×D411yescharacteristic
60C2×C8×C11#4111yescharacteristic
61C11×C4⋊C4D811yescharacteristic
62C11×C22⋊C4—21no—
63C42×C11C2×D411yescharacteristic
64#4324—82no—
65C4⋊Dic11—41no—
66C4⋊Dic11—41no—
67C2×C11⋊C8—41no—
68C11⋊C16—21no—
69C11⋊C16—21no—
70C11⋊C16—41no—
71#2240—111no—
72D4×C16—111no—
73#1673—111no—
74#1667D1111yescharacteristic
75#1371—111no—
76#1364—111no—
77#1361—111no—
78C23×C11—21no—
79C23×C11—81no—
80D4×C11—21no—
81D4×C11—81no—
82D4×C11—81no—
83D4×C11—81no—
84D4×C11—81no—
85D4×C11—161no—
86D4×C11D1612yes—
87C2×C4×C11—21no—
88C2×C4×C11—41no—
89C2×C4×C11—41no—
90C2×C4×C11#12111yescharacteristic
91C2×C4×C11C2×D811yescharacteristic
92C2×C4×C11#13511yescharacteristic
93C2×Dic11—81no—
94Dic22—81no—
95Dic22—81no—
96C8×C11—21no—
97C8×C11—41no—
98C8×C11—81no—
99C8×C11#13511yescharacteristic
100C8×C11AGL(1,ℤ/8)11yescharacteristic
101C11⋊C8—81no—
102C22×C16—221no—
103#500—111no—
104#493C2×D1111yescharacteristic
105#461—221no—
106#459—21no—
107C8×D4C2×D1111yescharacteristic
108C4⋊C16—111no—
109#357—221no—
110#357—221no—
111C22⋊C16—221no—
112C4×C16—111no—
113#335—111no—
114#335C2×D1111yescharacteristic
115#332—221no—
116#331—21no—
117C22×C11—22no—
118C22×C11—41no—
119C22×C11—41no—
120C22×C11—161no—
121C22×C11—161no—
122C22×C11—161no—
123C22×C11#46611yescharacteristic
124C4×C11—21no—
125C4×C11—41no—
126C4×C11#46311yescharacteristic
127C4×C11#47111yescharacteristic
128C4×C11C2×D1611yescharacteristic
129C4×C11#50811yescharacteristic
130Dic11—161no—
131C2×SD16—441no—
132C2×D8—21no—
133C2×D8—21no—
134C2×D8—41no—
135C22×C8—21no—
136C4⋊Q8—221no—
137#127—21no—
138C4×D4C22⋊D1111yescharacteristic
139C2×C16—111no—
140C2×C16—111no—
141C2×C16—221no—
142C2×C16—442no—
143#107—221no—
144#107—221no—
145C4⋊C8—21no—
146C4⋊C8—221no—
147C4⋊C8C22⋊D1111yescharacteristic
148#103—441no—
149#102—41no—
150C22⋊C8—21no—
151C4×C8C22×D1111yescharacteristic
152C2×C11—42no—
153C2×C11—321no—
154C2×C11#168111yescharacteristic
155C2×C11#221511yescharacteristic
156C2×C11#222311yescharacteristic
157C2×Q8—441no—
158C2×D4—41no—
159C2×D4—41no—
160C2×D4—41no—
161C2×D4#432311yescharacteristic
162C22×C4—21no—
163SD16—882no—
164D8—41no—
165D8—41no—
166D8—81no—
167D8—82no—
168C2×C8—21no—
169C2×C8—41no—
170C2×C8—41no—
171C2×C8—41no—
172C2×C8—441no—
173C2×C8D4×D1111yescharacteristic
174C2×C8#434111yescharacteristic
175C4⋊C4—441no—
176C4⋊C4—441no—
177C4⋊C4#432311yescharacteristic
178C22⋊C4—21no—
179C42C2×C22⋊D1111yescharacteristic
180C16—221no—
181C16—221no—
182C16—441no—
183C11#1246711yescharacteristic, complemented, Sylow
184C23—21no—
185C23—81no—
186Q8—881no—
187Q8—881no—
188D4—21no—
189D4—81no—
190D4—81no—
191D4—81no—
192D4—81no—
193D4—161no—
194D4#6689012yes—
195C2×C4—21no—
196C2×C4—41no—
197C2×C4—41no—
198C2×C4—881no—
199C2×C4C2×#432311yescharacteristic
200C2×C4#6699211yescharacteristic
201C2×C4#6700311yescharacteristic
202C8—21no—
203C8—41no—
204C8—81no—
205C8—881no—
206C8#6696411yescharacteristic
207C8#6696511yescharacteristic
208C22—22no—
209C22—41no—
210C22—41no—
211C22—161no—
212C22—161no—
213C22—161no—
214C22#1062265111yescharacteristic
215C4—21no—
216C4—41no—
217C4—1761no—
218C4C2×#6689011yescharacteristic
219C4#1062276611yescharacteristic
220C4#1062280711yescharacteristic
221C4#1062281311yescharacteristic
222C2—42no—
223C2—321no—
224C2#1306805111yescharacteristic
225C2#1307070011yescharacteristic
226C2#1307074411yescharacteristic
subgroupG/H
centerC22#10622651
commutator, cosocleC4×C8×C11C23
FrattiniC4×C8C22×D11
Fitting, prime radicalC11×#1667C2
socleC22×C11#466
hypercenter#1667D11
hypocenterC11#12467
LCSG ▷ C4×C8×C11 ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ C8×D4 ◁ #1667

Complements

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

NH ≅ G/Ntype
1. #13070839C2semidirect
2. D4×C11⋊C16C2semidirect
3. #13068005C2semidirect
4. #13066687C2semidirect
5. #13066672C2semidirect
6. #13066662C2semidirect
183. C11#12467semidirect

Maximal subgroups

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

subgroupindex
#130708392
D4×C11⋊C162
#130680052
#130666872
#130666722
#130666622
C11×#16672
#1246711