Finite Group Databasebeta

← #14668199

Subgroups — #14668199

Order 2816.

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

normal subgroups only

This group has 234 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#13070841C211yesmaximal, characteristic, complemented
2D4×C11⋊C16C211yesmaximal, characteristic, complemented
3#13067971C211yesmaximal, characteristic
4#13066689C211yesmaximal, characteristic, complemented
5#13066674C211yesmaximal, characteristic, complemented
6#13066661C211yesmaximal, characteristic, complemented
7C11×#1675C211yesmaximal, characteristic, complemented
8C11×#500C2211yescharacteristic
9C11×#476—21no—
10C8×D4×C11C2211yescharacteristic
11C22×C11⋊C16—21no—
12#10622628—21no—
13#10622308C2211yescharacteristic
14C11×#335C2211yescharacteristic
15C11×#333—21no—
16C22⋊(C11⋊C16)—21no—
17#10622129—21no—
18#10622129—21no—
19#10622123—21no—
20C4⋊(C11⋊C16)C2211yescharacteristic
21C4×C11⋊C16C2211yescharacteristic
22#10622096C2211yescharacteristic
23C22×C8×C11—21no—
24C11×C4⋊Q8—21no—
25C4×D4×C11D411yescharacteristic
26C2×#4323—41no—
27C2×D88—21no—
28C2×D88—21no—
29#66927—21no—
30C11×#107—21no—
31C11×#107—21no—
32C11×#106—41no—
33C11×C4⋊C8—21no—
34C11×C4⋊C8D411yescharacteristic
35C11×#102—41no—
36C11×C22⋊C8—21no—
37C4×C8×C11C2311yescharacteristic
38C2×C11⋊C16—21no—
39C2×C11⋊C16—42no—
40C2×C11⋊C16D411yescharacteristic
41C2×C11⋊C16D411yescharacteristic
42#66873—41no—
43C4⋊(C11⋊C8)—21no—
44#12468—111nomaximal, Sylow
45C2×Q8×C11—41no—
46C2×D4×C11D811yescharacteristic
47C22×C4×C11—21no—
48C2×D44—41no—
49C2×D44—41no—
50C2×D44—41no—
51C2×C8×C11—21no—
52C2×C8×C11—41no—
53C2×C8×C11—41no—
54C2×C8×C11—41no—
55C2×C8×C11C2×D411yescharacteristic
56C2×C8×C11#4111yescharacteristic
57C11×C4⋊C4—41no—
58C11×C4⋊C4—41no—
59C11×C4⋊C4D811yescharacteristic
60C11×C22⋊C4—21no—
61C42×C11C2×D411yescharacteristic
62#4323—82no—
63C2×C11⋊C8—41no—
64D88—41no—
65D88—41no—
66D88—81no—
67C11⋊C16—21no—
68C11⋊C16—21no—
69C11⋊C16—41no—
70#2240—111no—
71D4×C16—111no—
72#1675D1111yescharacteristic, complemented
73#1667—111no—
74#1372—111no—
75#1365—111no—
76#1361—111no—
77C23×C11—21no—
78C22×D11—81no—
79Q8×C11—161no—
80D4×C11—21no—
81D4×C11SD3212yes—
82C2×C4×C11—21no—
83C2×C4×C11—41no—
84C2×C4×C11—41no—
85C2×C4×C11—81no—
86C2×C4×C11#12111yescharacteristic
87C2×C4×C11C2×D811yescharacteristic
88C2×C4×C11#13511yescharacteristic
89D44—81no—
90D44—81no—
91D44—81no—
92D44—81no—
93D44—161no—
94C8×C11—21no—
95C8×C11—41no—
96C8×C11—81no—
97C8×C11#13511yescharacteristic
98C8×C11AGL(1,ℤ/8)11yescharacteristic
99C11⋊C8—81no—
100C22×C16—221no—
101#500C2×D1111yescharacteristic
102#493—111no—
103#476—21no—
104#459—221no—
105C8×D4C2×D1111yescharacteristic
106C4⋊C16—111no—
107#357—221no—
108#357—221no—
109C22⋊C16—221no—
110C4×C16—111no—
111#335—111no—
112#335C2×D1111yescharacteristic
113#333—21no—
114#331—221no—
115C22×C11—22no—
116C22×C11—41no—
117C22×C11—41no—
118C22×C11#46611yescharacteristic
119C2×D11—161no—
120C2×D11—161no—
121C2×D11—161no—
122C4×C11—21no—
123C4×C11—41no—
124C4×C11—161no—
125C4×C11#46311yescharacteristic
126C4×C11#47111yescharacteristic
127C4×C11C2×SD3211yescharacteristic
128C4×C11#50811yescharacteristic
129C2×D8—221no—
130C2×D8—221no—
131C2×D8—441no—
132C22×C8—21no—
133C4⋊Q8—21no—
134#127—221no—
135C4×D4C22⋊D1111yescharacteristic
136C2×C16—111no—
137C2×C16—111no—
138C2×C16—221no—
139C2×C16—442no—
140#107—21no—
141#107—21no—
142#106—41no—
143C4⋊C8—21no—
144C4⋊C8—221no—
145C4⋊C8C22⋊D1111yescharacteristic
146#102—41no—
147#102—441no—
148C22⋊C8—21no—
149C4×C8C22×D1111yescharacteristic
150C2×C11—42no—
151C2×C11#168111yescharacteristic
152C2×C11#221711yescharacteristic
153C2×C11#222111yescharacteristic
154D11—321no—
155C2×Q8—41no—
156C2×D4—441no—
157C2×D4—441no—
158C2×D4—441no—
159C2×D4#432311yescharacteristic
160C22×C4—21no—
161D8—441no—
162D8—441no—
163D8—881no—
164D8—882no—
165C2×C8—21no—
166C2×C8—41no—
167C2×C8—41no—
168C2×C8—41no—
169C2×C8—441no—
170C2×C8D4×D1111yescharacteristic
171C2×C8#434111yescharacteristic
172C4⋊C4—41no—
173C4⋊C4—41no—
174C4⋊C4#432311yescharacteristic
175C22⋊C4—21no—
176C42C2×C22⋊D1111yescharacteristic
177C16—221no—
178C16—221no—
179C16—441no—
180C11#1246811yescharacteristic, complemented, Sylow
181C23—21no—
182C23—881no—
183Q8—161no—
184D4—21no—
185D4—881no—
186D4—881no—
187D4—881no—
188D4—881no—
189D4—1761no—
190D4#6689212yes—
191C2×C4—21no—
192C2×C4—41no—
193C2×C4—41no—
194C2×C4—81no—
195C2×C4C2×#432311yescharacteristic
196C2×C4#6699211yescharacteristic
197C2×C4#6700311yescharacteristic
198C8—21no—
199C8—41no—
200C8—81no—
201C8—881no—
202C8#6696711yescharacteristic
203C8#6696911yescharacteristic
204C22—22no—
205C22—41no—
206C22—41no—
207C22—1761no—
208C22—1761no—
209C22—1761no—
210C22#1062265111yescharacteristic
211C4—21no—
212C4—41no—
213C4—161no—
214C4#1062277811yescharacteristic
215C4C2×#6689211yescharacteristic
216C4#1062280711yescharacteristic
217C4#1062281611yescharacteristic
218C2—42no—
219C2—3521no—
220C2#1306805511yescharacteristic
221C2#1307071411yescharacteristic
222C2#1307073411yescharacteristic
subgroupG/H
centerC22#10622651
commutator, cosocleC4×C8×C11C23
FrattiniC4×C8C22×D11
FittingC11×#1675C2
socleC22×C11#466
prime radical#13067971C2
hypercenter#1675D11
hypocenterC11#12468
LCSG ▷ C4×C8×C11 ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ C8×D4 ◁ #1675

Complements

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

NH ≅ G/Ntype
1. #13070841C2semidirect
2. D4×C11⋊C16C2semidirect
4. #13066689C2semidirect
5. #13066674C2semidirect
6. #13066661C2semidirect
7. C11×#1675C2semidirect
72. #1675D11semidirect
180. C11#12468semidirect

Maximal subgroups

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

subgroupindex
#130708412
D4×C11⋊C162
#130679712
#130666892
#130666742
#130666612
C11×#16752
#1246811