Finite Group Databasebeta

← #14667996

Subgroups — #14667996

Order 2816.

262 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 262 conjugacy classes of subgroups — too many to draw. Only its 71 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#13070866C211yesmaximal, characteristic, complemented
2#13067971C212yesmaximal, complemented
3#13066690C211yesmaximal, characteristic, complemented
4#13066663C212yesmaximal, complemented
5C11×#2169C211yesmaximal, characteristic, complemented
6C2×C11×M32—21no—
7C8×D4×C11C2211yescharacteristic
8#10622628—22no—
9C2×D176—21no—
10C2×D176—21no—
11#10622308C2212yes—
12C11×C4⋊C16C2211yescharacteristic
13C11×C22⋊C16—21no—
14C4×C11×C16C2211yescharacteristic
15#10622123—22no—
16#10622096C2212yes—
17C22×C8×C11—21no—
18C4×D4×C11D411yescharacteristic
19C2×#4323—42no—
20C2×D88—22no—
21C2×D88—22no—
22#66927—22no—
23C11×M32—42no—
24C2×C11×C16—21no—
25C2×C11×C16D411yescharacteristic
26C2×C11×C16D411yescharacteristic
27C11×C4⋊C8D411yescharacteristic
28C11×C22⋊C8—21no—
29C4×C8×C11C2311yescharacteristic
30#66873—42no—
31C4⋊(C11⋊C8)—22no—
32D176—42no—
33D176—42no—
34#12433—111nomaximal, Sylow
35C2×D4×C11D811yescharacteristic
36C22×C4×C11—21no—
37C2×D44—42no—
38C2×D44—42no—
39C2×D44—42no—
40C2×C8×C11—21no—
41C2×C8×C11—41no—
42C2×C8×C11—41no—
43C2×C8×C11C2×D411yescharacteristic
44C2×C8×C11#4111yescharacteristic
45C11×C4⋊C4D811yescharacteristic
46C11×C22⋊C4—21no—
47C42×C11C2×D411yescharacteristic
48#4323—84no—
49C2×C11⋊C8—42no—
50D88—42no—
51D88—42no—
52D88—82no—
53C11×C16—21no—
54C11×C16—41no—
55C11×C16D812yescomplemented
56#2246—111no—
57#2169D1111yescharacteristic, complemented
58#1667—112no—
59#1372—111no—
60#1361—112no—
61C23×C11—21no—
62C22×D11—82no—
63D4×C11—22no—
64C2×C4×C11—21no—
65C2×C4×C11—41no—
66C2×C4×C11—41no—
67C2×C4×C11#12111yescharacteristic
68C2×C4×C11C2×D811yescharacteristic
69C2×C4×C11#13511yescharacteristic
70D44—82no—
71D44—82no—
72D44—82no—
73D44—82no—
74D44—162no—
75C8×C11—21no—
76C8×C11—41no—
77C8×C11C2×D811yescharacteristic
78C8×C11AGL(1,ℤ/8)11yescharacteristic
79C11⋊C8—82no—
80C2×D16—221no—
81C2×D16—221no—
82C2×M32—21no—
83#493—112no—
84#459—222no—
85C8×D4C2×D1111yescharacteristic
86C4⋊C16C2×D1111yescharacteristic
87C22⋊C16—21no—
88C4×C16C2×D1111yescharacteristic
89#335—112no—
90#331—222no—
91C22×C11—41no—
92C22×C11—41no—
93C22×C11—41no—
94C22×C11#46611yescharacteristic
95C2×D11—162no—
96C2×D11—162no—
97C2×D11—162no—
98C4×C11—21no—
99C4×C11—41no—
100C4×C11#45911yescharacteristic
101C4×C11#47211yescharacteristic
102C4×C11#50912yes—
103C2×D8—222no—
104C2×D8—222no—
105C2×D8—442no—
106C22×C8—21no—
107#127—222no—
108C4×D4D4411yescharacteristic
109D16—442no—
110D16—442no—
111M32—42no—
112C2×C16—21no—
113C2×C16C22⋊D1111yescharacteristic
114C2×C16C22⋊D1111yescharacteristic
115C4⋊C8—222no—
116C4⋊C8D4411yescharacteristic
117#102—442no—
118C22⋊C8—21no—
119C4×C8C22×D1111yescharacteristic
120C2×C11—81no—
121C2×C11#166711yescharacteristic
122C2×C11#221811yescharacteristic
123C2×C11#222111yescharacteristic
124D11—322no—
125C2×D4—442no—
126C2×D4—442no—
127C2×D4—442no—
128C2×D4D8811yescharacteristic
129C22×C4—21no—
130D8—442no—
131D8—442no—
132D8—882no—
133D8—884no—
134C2×C8—21no—
135C2×C8—41no—
136C2×C8—41no—
137C2×C8—442no—
138C2×C8#433911yescharacteristic
139C2×C8C2×C22⋊D1111yescharacteristic
140C4⋊C4D8811yescharacteristic
141C22⋊C4—21no—
142C42C2×D4411yescharacteristic
143C16—21no—
144C16—41no—
145C16#432312yescomplemented
146C11#1243311yescharacteristic, complemented, Sylow
147C23—21no—
148C23—882no—
149D4—22no—
150D4—882no—
151D4—882no—
152D4—882no—
153D4—882no—
154D4—1762no—
155C2×C4—21no—
156C2×C4—41no—
157C2×C4—41no—
158C2×C4C2×D8811yescharacteristic
159C2×C4#6695711yescharacteristic
160C2×C4#6698311yescharacteristic
161C8—21no—
162C8—41no—
163C8—882no—
164C8C2×#432311yescharacteristic
165C8#6700211yescharacteristic
166C22—41no—
167C22—41no—
168C22—41no—
169C22—1762no—
170C22—1762no—
171C22—1762no—
172C22#1062272811yescharacteristic
173C4—21no—
174C4—41no—
175C4#1062252112yes—
176C4#1062262811yescharacteristic
177C4#1062275511yescharacteristic
178C2—81no—
179C2—3522no—
180C2#1306797111yescharacteristic
181C2#1307071911yescharacteristic
182C2#1307073611yescharacteristic
subgroupG/H
centerC22#10622728
commutator, cosocleC4×C8×C11C23
FrattiniC4×C8C22×D11
FittingC11×#2169C2
socleC22×C11#466
hypercenter#2169D11
hypocenterC11#12433
LCSG ▷ C4×C8×C11 ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ C8×D4 ◁ #2169

Complements

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

NH ≅ G/Ntype
1. #13070866C2semidirect
2. #13067971C2semidirect
3. #13066690C2semidirect
4. #13066663C2semidirect
5. C11×#2169C2semidirect
55. C11×C16D8semidirect
57. #2169D11semidirect
145. C16#4323semidirect
146. C11#12433semidirect

Maximal subgroups

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

subgroupindex
#130708662
#130679712
#130666902
#130666632
C11×#21692
#1243311