Finite Group Databasebeta

← #14668196

Subgroups — #14668196

Order 2816.

234 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 234 conjugacy classes of subgroups — too many to draw. Only its 63 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
2#13070435C211yesmaximal, characteristic, complemented
3#13068016C211yesmaximal, characteristic, complemented
4#13067968C211yesmaximal, characteristic
5#13066689C211yesmaximal, characteristic, complemented
6#13066673C211yesmaximal, characteristic, complemented
7C11×#1361C211yesmaximal, characteristic, complemented
8C11×#493C2211yescharacteristic
9#10622685—21no—
10C2×C16×D11—21no—
11#10622455—21no—
12C8×D44C2211yescharacteristic
13#10622295C2211yescharacteristic
14C11×C4⋊C16C2211yescharacteristic
15C11×#335C2211yescharacteristic
16#10622200—21no—
17#10622200—21no—
18#10622182—21no—
19(C2×D11)⋊C16—21no—
20#10622119—21no—
21C4×C11⋊C16C2211yescharacteristic
22#10622096C2211yescharacteristic
23C2×C11×D8—21no—
24C2×C11×D8—21no—
25C11×#127—21no—
26C2×#4323—41no—
27C2×C8×D11—21no—
28C4×D44D411yescharacteristic
29#66922—21no—
30C2×C11×C16—21no—
31C11×C4⋊C8—21no—
32C4×C8×C11C2311yescharacteristic
33#66896—41no—
34#66885—41no—
35(C2×D11)⋊C8—21no—
36#66882—21no—
37#66882—21no—
38#66881—41no—
39C2×C11⋊C16D411yescharacteristic
40C2×C11⋊C16D411yescharacteristic
41C4⋊(C11⋊C8)—21no—
42C4⋊(C11⋊C8)D411yescharacteristic
43C16×D11—42no—
44#12468—111nomaximal, Sylow
45C2×D4×C11—41no—
46C2×D4×C11—41no—
47C2×D4×C11—41no—
48C2×D44D811yescharacteristic
49C2×C4×D11—21no—
50C2×Dic22—41no—
51C11×D8—41no—
52C11×D8—41no—
53C11×D8—81no—
54C2×C8×C11—41no—
55C2×C8×C11C2×D411yescharacteristic
56C2×C8×C11#4111yescharacteristic
57C42×C11C2×D411yescharacteristic
58#4323—82no—
59(C2×D11)⋊C4—21no—
60C4⋊Dic11—41no—
61C4⋊Dic11—41no—
62C4⋊Dic11D811yescharacteristic
63C2×C11⋊C8—21no—
64C2×C11⋊C8—41no—
65C8×D11—41no—
66C8×D11—41no—
67C11×C16—41no—
68C11⋊C16—21no—
69C11⋊C16—21no—
70#2240—111no—
71D4×C16—111no—
72#1675—111no—
73#1667—111no—
74#1372—111no—
75#1365—111no—
76#1361D1111yescharacteristic, complemented
77C23×C11—81no—
78C22×D11—21no—
79D4×C11—81no—
80D4×C11—81no—
81D4×C11—81no—
82D4×C11—81no—
83D4×C11—161no—
84C2×C4×C11#12111yescharacteristic
85C2×C4×C11C2×D811yescharacteristic
86C2×C4×C11#13511yescharacteristic
87C2×Dic11—21no—
88C2×Dic11—81no—
89D44—21no—
90D44SD3212yes—
91C4×D11—41no—
92C4×D11—41no—
93Dic22—161no—
94C8×C11—21no—
95C8×C11—81no—
96C8×C11#13511yescharacteristic
97C8×C11AGL(1,ℤ/8)11yescharacteristic
98C11⋊C8—41no—
99C11⋊C8—81no—
100C22×C16—221no—
101#500—111no—
102#493C2×D1111yescharacteristic
103#476—221no—
104#459—221no—
105C8×D4—111no—
106C4⋊C16C2×D1111yescharacteristic
107#357—221no—
108#357—221no—
109C22⋊C16—221no—
110C4×C16—111no—
111#335—111no—
112#335C2×D1111yescharacteristic
113#333—221no—
114#331—221no—
115C22×C11—161no—
116C22×C11—161no—
117C22×C11—161no—
118C22×C11#46611yescharacteristic
119C2×D11—22no—
120C2×D11—41no—
121C2×D11—41no—
122C4×C11—21no—
123C4×C11#46311yescharacteristic
124C4×C11#47111yescharacteristic
125C4×C11C2×SD3211yescharacteristic
126C4×C11#50811yescharacteristic
127Dic11—41no—
128Dic11—161no—
129C2×D8—21no—
130C2×D8—21no—
131C2×D8—441no—
132C22×C8—221no—
133C4⋊Q8—221no—
134#127—21no—
135C4×D4—111no—
136C2×C16—21no—
137C2×C16—111no—
138C2×C16—111no—
139C2×C16—442no—
140#107—221no—
141#107—221no—
142#106—441no—
143C4⋊C8—21no—
144C4⋊C8—111no—
145C4⋊C8—221no—
146#102—441no—
147#102—441no—
148C22⋊C8—221no—
149C4×C8C22×D1111yescharacteristic
150C2×C11—321no—
151C2×C11#168111yescharacteristic
152C2×C11#221711yescharacteristic
153C2×C11#222111yescharacteristic
154D11—42no—
155C2×Q8—441no—
156C2×D4—41no—
157C2×D4—41no—
158C2×D4—41no—
159C2×D4—111no—
160C22×C4—221no—
161D8—41no—
162D8—41no—
163D8—81no—
164D8—882no—
165C2×C8—41no—
166C2×C8—221no—
167C2×C8—441no—
168C2×C8—441no—
169C2×C8—441no—
170C2×C8#433911yescharacteristic
171C2×C8D4×D1111yescharacteristic
172C4⋊C4—111no—
173C4⋊C4—441no—
174C4⋊C4—441no—
175C22⋊C4—221no—
176C42D4×D1111yescharacteristic
177C16—41no—
178C16—221no—
179C16—221no—
180C11#1246811yescharacteristic, complemented, Sylow
181C23—81no—
182C23—221no—
183Q8—1761no—
184D4—81no—
185D4—81no—
186D4—81no—
187D4—81no—
188D4—112no—
189D4—161no—
190D4—221no—
191C2×C4—221no—
192C2×C4—441no—
193C2×C4—441no—
194C2×C4—881no—
195C2×C4#6693711yescharacteristic
196C2×C4D8×D1111yescharacteristic
197C2×C4#6696911yescharacteristic
198C8—21no—
199C8—81no—
200C8—441no—
201C8—881no—
202C8#6696411yescharacteristic
203C8#6696911yescharacteristic
204C22—161no—
205C22—161no—
206C22—161no—
207C22—222no—
208C22—441no—
209C22—441no—
210C22#1062238811yescharacteristic
211C4—21no—
212C4—441no—
213C4—1761no—
214C4#1062236111yescharacteristic
215C4#1062240011yescharacteristic
216C4#1062252511yescharacteristic
217C4D11×SD3211yescharacteristic
218C2—321no—
219C2—442no—
220C2#1306805211yescharacteristic
221C2#1307071111yescharacteristic
222C2#1307073511yescharacteristic
subgroupG/H
centerC22#10622388
commutator, cosocleC4×C8×C11C23
FrattiniC4×C8C22×D11
FittingC11×#1361C2
socleC22×C11#466
prime radical#13067968C2
hypercenter#1361D11
hypocenterC11#12468
LCSG ▷ C4×C8×C11 ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #1361

Complements

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

NH ≅ G/Ntype
1. #13070839C2semidirect
2. #13070435C2semidirect
3. #13068016C2semidirect
5. #13066689C2semidirect
6. #13066673C2semidirect
7. C11×#1361C2semidirect
76. #1361D11semidirect
180. C11#12468semidirect

Maximal subgroups

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

subgroupindex
#130708392
#130704352
#130680162
#130679682
#130666892
#130666732
C11×#13612
#1246811