Finite Group Databasebeta

← #14658845

Subgroups — #14658845

Order 2816.

494 conjugacy classes of subgroups; only the 147 normal subgroups are shown.

normal subgroups only

This group has 494 conjugacy classes of subgroups — too many to draw. Only its 147 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#13069423C212yesmaximal
2#13068773C211yesmaximal, characteristic, complemented
3#13068743C212yesmaximal, complemented
4C11⋊#1273C211yesmaximal, characteristic, complemented
5C11×#1957C211yesmaximal, characteristic
6C2×C11×#127C2211yescharacteristic
7C2×C11×#102—22no—
8C2×C4×C8×C11C2211yescharacteristic
9C11×#384C2211yescharacteristic
10C2×#66896—24no—
11C2×#66881—22no—
12#10622548C2212yes—
13C2×C4×C11⋊C8C2212yes—
14#10622167—24no—
15C22×D4×C11—22no—
16C22×D4×C11—21no—
17C22×C8×C11D412yes—
18C11×#127—21no—
19C11×#127—22no—
20C11×#127Q812yes—
21C2×C11×C4⋊C4—21no—
22C2×C11×C4⋊C4—22no—
23C2×C42×C11C2311yescharacteristic
24C2×C4⋊Dic11—22no—
25C2×C4⋊Dic11—22no—
26C2×C4⋊Dic11—22no—
27C22×C11⋊C8D414yes—
28C11×#102—44no—
29C4×C8×C11—22no—
30#66896—48no—
31#66881—44no—
32C4×C11⋊C8—22no—
33C4×C11⋊C8—22no—
34#10677—111nomaximal, Sylow
35C24×C11—41no—
36C2×D4×C11—24no—
37C2×D4×C11—22no—
38C2×D4×C11—42no—
39C2×D4×C11—41no—
40C2×D4×C11—42no—
41C2×D4×C11—44no—
42C2×D4×C11—44no—
43C2×D4×C11—42no—
44C22×C4×C11—41no—
45C22×C4×C11C2×D411yescharacteristic
46C22×C4×C11C2×D412yes—
47C22×Dic11—42no—
48C2×C8×C11—22no—
49C2×C8×C11—22no—
50C2×C8×C11SD1614yes—
51C11×C4⋊C4—42no—
52C11×C4⋊C4—44no—
53C42×C11C2×Q811yescharacteristic
54C42×C11#4111yescharacteristic
55C42×C11#4112yes—
56C4⋊Dic11—44no—
57C4⋊Dic11—44no—
58C4⋊Dic11—44no—
59C2×C11⋊C8—24no—
60C2×C11⋊C8—24no—
61C2×C11⋊C8—24no—
62#1957—112no—
63#1957D1111yescharacteristic
64#1844—111no—
65#1834—112no—
66#1273—111no—
67C23×C11—42no—
68C23×C11—81no—
69C23×C11—82no—
70C23×C11—82no—
71C23×C11—81no—
72C23×C11#12711yescharacteristic
73D4×C11—44no—
74D4×C11—48no—
75D4×C11—82no—
76D4×C11—84no—
77C2×C4×C11—81no—
78C2×C4×C11—82no—
79C2×C4×C11C22⋊Q812yes—
80C2×C4×C11C22⋊Q811yescharacteristic
81C2×C4×C11#12312yes—
82C2×C4×C11#12311yescharacteristic
83C2×C4×C11C2×SD1612yes—
84C2×C4×C11#13514yes—
85C2×C4×C11AGL(1,ℤ/8)14yes—
86C2×C4×C11AGL(1,ℤ/8)12yes—
87C2×Dic11—82no—
88C2×Dic11—82no—
89C2×Dic11—82no—
90C8×C11—24no—
91C11⋊C8—44no—
92C2×#127C2×D1111yescharacteristic
93C2×#106—222no—
94C2×#102—22no—
95C2×#102—224no—
96C2×C4×C8—112no—
97C2×C4×C8C2×D1111yescharacteristic
98#384—112no—
99#384C2×D1111yescharacteristic
100#340—224no—
101C22×C11—84no—
102C22×C11—82no—
103C22×C11—161no—
104C22×C11—161no—
105C22×C11—162no—
106C22×C11#39911yescharacteristic
107C22×C11#49211yescharacteristic
108C22×C11#49512yes—
109C22×C11#49612yes—
110C22×C11#49611yescharacteristic
111C4×C11—161no—
112C4×C11#47612yes—
113C4×C11#47814yes—
114C4×C11#48112yes—
115C4×C11#48214yes—
116Dic11—162no—
117C22×D4—22no—
118C22×D4—21no—
119C22×C8—114no—
120C22×C8C22⋊D1112yes—
121#127—21no—
122#127—22no—
123#127Dic2212yes—
124C2×C4⋊C4—22no—
125C2×C4⋊C4—21no—
126C2×C4⋊C4—222no—
127C2×C4⋊C4—222no—
128C2×C4⋊C4—222no—
129C2×C42C22×D1111yescharacteristic
130#106—444no—
131#102—44no—
132#102—448no—
133C4×C8—22no—
134C4×C8—222no—
135C4×C8—222no—
136C2×C11—162no—
137C2×C11#170811yescharacteristic
138C2×C11#171511yescharacteristic
139C2×C11#171712yes—
140C2×C11#209212yes—
141C2×C11#209411yescharacteristic
142C24—41no—
143C2×D4—24no—
144C2×D4—22no—
145C2×D4—42no—
146C2×D4—44no—
147C2×D4—44no—
148C2×D4—42no—
149C2×D4—41no—
150C2×D4—42no—
151C22×C4—41no—
152C22×C4—442no—
153C22×C4D4×D1112yes—
154C22×C4C2×C22⋊D1111yescharacteristic
155C2×C8—22no—
156C2×C8—22no—
157C2×C8—224no—
158C2×C8—224no—
159C2×C8—224no—
160C2×C8#432414yes—
161C4⋊C4—44no—
162C4⋊C4—42no—
163C4⋊C4—444no—
164C4⋊C4—444no—
165C4⋊C4—444no—
166C42C2×Dic2211yescharacteristic
167C42#433911yescharacteristic
168C42#434112yes—
169C11#1067711yescharacteristic, complemented, Sylow
170C23—42no—
171C23—82no—
172C23—82no—
173C23—81no—
174C23—81no—
175C23#6699311yescharacteristic
176D4—44no—
177D4—48no—
178D4—82no—
179D4—84no—
180C2×C4—82no—
181C2×C4—81no—
182C2×C4—882no—
183C2×C4—882no—
184C2×C4—882no—
185C2×C4#6693112yes—
186C2×C4#6693612yes—
187C2×C4#6696414yes—
188C2×C4#6696914yes—
189C2×C4#6697711yescharacteristic
190C2×C4C2×#432412yes—
191C2×C4#6698811yescharacteristic
192C2×C4#6700212yes—
193C8—24no—
194C8—444no—
195C22—84no—
196C22—82no—
197C22—161no—
198C22—161no—
199C22—162no—
200C22#1062256211yescharacteristic
201C22#1062267111yescharacteristic
202C22#1062268911yescharacteristic
203C22#1062276712yes—
204C22#1062278112yes—
205C4—161no—
206C4—1762no—
207C4#1062237614yes—
208C4#1062239214yes—
209C4#1062262112yes—
210C4#1062264712yes—
211C2—162no—
212C2#1306821511yescharacteristic
213C2#1306824211yescharacteristic
214C2#1306825712yes—
215C2#1307013912yes—
216C2#1307014911yescharacteristic
subgroupG/H
centerC23#66993
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1957C2
socleC23×C11#127
prime radicalC2×C11×#127C22
hypercenter#1957D11
hypocenterC11#10677
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1957

Complements

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

NH ≅ G/Ntype
2. #13068773C2semidirect
3. #13068743C2semidirect
4. C11⋊#1273C2semidirect
169. C11#10677semidirect

Maximal subgroups

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

subgroupindex
#130694232
#130687732
#130687432
C11⋊#12732
C11×#19572
#1067711