Finite Group Databasebeta

← #14667151

Subgroups — #14667151

Order 2816.

318 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 318 conjugacy classes of subgroups — too many to draw. Only its 55 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#13079997C211yesmaximal, characteristic
2#13070831C212yesmaximal, complemented
3#13070191C211yesmaximal, characteristic, complemented
4#13066602C212yesmaximal, complemented
5C11×#1327C211yesmaximal, characteristic, complemented
6#10623008—21no—
7C11×#423C2211yescharacteristic
8#10622748—21no—
9#10622748C2212yes—
10#10622738C2211yescharacteristic
11#10622456—22no—
12#10622455—22no—
13C11×#349C2212yes—
14#10622197—21no—
15#10622195C2211yescharacteristic
16#10622161—21no—
17#10622154—22no—
18#10622151—22no—
19C2×#4339—41no—
20C2×C11×M16D411yescharacteristic
21C2×C11×M16C2311yescharacteristic
22C2×C42×C11D411yescharacteristic
23#66983—22no—
24#66983—41no—
25#66979—21no—
26C2×#4318—21no—
27C2×D88—21no—
28C2×D88D412yes—
29#66928—41no—
30#66927—21no—
31C4×D44—22no—
32C4×D44—41no—
33#66922—21no—
34C11×M32—22no—
35C11×C4⋊C8—22no—
36#66885—22no—
37#66885—22no—
38#66883—22no—
39#66881—21no—
40#66881D412yes—
41#12307—111nomaximal, Sylow
42C22×C4×C11—21no—
43C22×C4×C11C2×D411yescharacteristic
44C2×C22⋊D11—42no—
45#4339—84no—
46C2×D44—22no—
47C2×D44—41no—
48C2×D44—41no—
49C2×C4×D11—42no—
50C2×Dic22—41no—
51C11×M16—41no—
52C11×M16—41no—
53C2×C8×C11—21no—
54C2×C8×C11C2×D412yes—
55C42×C11—21no—
56C42×C11SD1611yescharacteristic
57C42×C11SD1611yescharacteristic
58C22⋊Dic11—41no—
59(C2×D11)⋊C4—42no—
60(C2×D11)⋊C4—42no—
61C4⋊Dic11—22no—
62C4⋊Dic11—41no—
63C4⋊Dic11—41no—
64C4×Dic11—41no—
65#4318—41no—
66#4318—41no—
67C2×C11⋊C8—41no—
68D88—42no—
69D88—81no—
70C11×C16—42no—
71#3253—111no—
72#2238—112no—
73#2102—111no—
74#1339—112no—
75#1327D1111yescharacteristic, complemented
76C23×C11AGL(1,ℤ/8)11yescharacteristic
77C22×D11—42no—
78C2×C4×C11—21no—
79C2×C4×C11—21no—
80C2×C4×C11—21no—
81C2×C4×C11—21no—
82C2×C4×C11—42no—
83C2×C4×C11#12011yescharacteristic
84C2×C4×C11C2×SD1611yescharacteristic
85C22⋊D11—84no—
86C2×Dic11—42no—
87C2×Dic11—81no—
88D44—42no—
89D44—42no—
90D44—82no—
91D44—82no—
92C4×D11—84no—
93Dic22—82no—
94C8×C11—22no—
95C8×C11—41no—
96C11⋊C8—81no—
97#532—221no—
98#476—222no—
99#469—112no—
100#469—221no—
101#459—222no—
102#430—111no—
103#423C2×D1111yescharacteristic
104#365—222no—
105#361—222no—
106#349C2×D1112yes—
107#344—221no—
108#339—221no—
109H(3,ℤ/4)—111no—
110C22×C11—21no—
111C22×C11—41no—
112C22×C11#45011yescharacteristic
113C2×D11—82no—
114C2×D11—82no—
115C2×D11—82no—
116C4×C11—22no—
117C4×C11—21no—
118C4×C11—41no—
119C4×C11#45411yescharacteristic
120C4×C11#45811yescharacteristic
121Dic11—82no—
122Dic11—161no—
123C2×#41—441no—
124C2×D8—112no—
125C2×D8—221no—
126C2×M16—221no—
127C2×M16D4411yescharacteristic
128C2×M16C22×D1111yescharacteristic
129C4⋊Q8—221no—
130#127—221no—
131#124—441no—
132#121—222no—
133#121—441no—
134C4×D4—222no—
135C4×D4—441no—
136#117—221no—
137C2×C42D4411yescharacteristic
138M32—22no—
139#108—222no—
140#106—112no—
141#106—221no—
142C4⋊C8—22no—
143#102—222no—
144#102—222no—
145C2×C11—21no—
146C2×C11—41no—
147C2×C11#161611yescharacteristic
148D11—162no—
149#41—884no—
150C2×Q8—441no—
151C2×D4—222no—
152C2×D4—441no—
153C2×D4—441no—
154C2×D4—442no—
155C22×C4—21no—
156C22×C4—442no—
157C22×C4C2×D4411yescharacteristic
158D8—442no—
159D8—881no—
160M16—41no—
161M16—41no—
162M16—441no—
163M16—441no—
164C2×C8—21no—
165C2×C8—441no—
166C2×C8D4×D1112yes—
167C4⋊C4—222no—
168C4⋊C4—441no—
169C4⋊C4—441no—
170C22⋊C4—442no—
171C22⋊C4—442no—
172C22⋊C4—441no—
173C42—21no—
174C42—441no—
175C42#431411yescharacteristic
176C42#431411yescharacteristic
177C16—42no—
178C11#1230711yescharacteristic, complemented, Sylow
179C23—442no—
180C23#6696111yescharacteristic
181Q8—882no—
182D4—442no—
183D4—442no—
184D4—882no—
185D4—882no—
186D4—884no—
187C2×C4—21no—
188C2×C4—21no—
189C2×C4—21no—
190C2×C4—21no—
191C2×C4—42no—
192C2×C4—442no—
193C2×C4—884no—
194C2×C4—881no—
195C2×C4#6693511yescharacteristic
196C2×C4C2×#431411yescharacteristic
197C8—22no—
198C8—41no—
199C8—881no—
200C22—21no—
201C22—41no—
202C22—882no—
203C22—882no—
204C22—882no—
205C22#1062234411yescharacteristic
206C4—22no—
207C4—21no—
208C4—41no—
209C4—882no—
210C4—1761no—
211C4#1062235511yescharacteristic
212C4#1062236611yescharacteristic
213C2—21no—
214C2—41no—
215C2—1762no—
216C2#1306765511yescharacteristic
subgroupG/H
centerC2#13067655
commutator, cosocleC2×C11×M16C23
FrattiniC2×M16C22×D11
FittingC11×#1327C2
socleC2×C11#1616
prime radical#13079997C2
hypercenter#1327D11
hypocenterC11#12307
LCSG ▷ C2×C11×M16 ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×M16 ◁ #1327

Complements

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

NH ≅ G/Ntype
2. #13070831C2semidirect
3. #13070191C2semidirect
4. #13066602C2semidirect
5. C11×#1327C2semidirect
75. #1327D11semidirect
178. C11#12307semidirect

Maximal subgroups

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

subgroupindex
#130799972
#130708312
#130701912
#130666022
C11×#13272
#1230711