Finite Group Databasebeta

← #13070565

Subgroups — #13070565

Order 1408.

216 conjugacy classes of subgroups; only the 47 normal subgroups are shown.

normal subgroups only

This group has 216 conjugacy classes of subgroups — too many to draw. Only its 47 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#10623299C211yesmaximal, characteristic
2C11×#510C211yesmaximal, characteristic, complemented
3#10622802C211yesmaximal, characteristic, complemented
4#10622792C211yesmaximal, characteristic, complemented
5#10622204C211yesmaximal, characteristic, complemented
6#10622156C211yesmaximal, characteristic, complemented
7#10622152C211yesmaximal, characteristic, complemented
8#41×D11—21no—
9C11×#135C2211yescharacteristic
10C2×C11×Q16C2211yescharacteristic, complemented
11#67003—21no—
12#66999—21no—
13#66971—21no—
14#66968—21no—
15#66967—21no—
16#66964—21no—
17#66957C2211yescharacteristic
18C2×#4313C2211yescharacteristic
19C11×Q32—21no—
20C11×SD32—21no—
21C11×M32C2211yescharacteristic, complemented
22#66899—21no—
23#66893—21no—
24#66892—21no—
25#66881C2211yescharacteristic, complemented
26#66876C2211yescharacteristic, complemented
27C11×#41—21no—
28C2×Q8×C11—21no—
29#4343—21no—
30Q8×D11—21no—
31#4341—21no—
32#4341—41no—
33D4×D11—21no—
34D4×D11—41no—
35#4339—21no—
36#4339—41no—
37C2×C4×D11—41no—
38C2×C4×D11D411yescharacteristic
39C11×Q16—21no—
40C11×Q16—21no—
41C11×Q16D411yescharacteristic
42C11×SD16—21no—
43C11×D8D411yescharacteristic
44C2×C8×C11C2311yescharacteristic
45#4326—21no—
46#4325—21no—
47#4324—21no—
48#4323—21no—
49(C2×D11)⋊C4—41no—
50C4⋊Dic11—21no—
51Dic11⋊C4—41no—
52C2×C11⋊C8D411yescharacteristic
53Dic44D411yescharacteristic
54D88D411yescharacteristic
55#4314—21no—
56#4313—21no—
57#4313—21no—
58C11×C16—21no—
59C11⋊C16—21no—
60#2191—111nomaximal, Sylow
61C22×D11—41no—
62C22×D11D811yescharacteristic
63Q8×C11—21no—
64Q8×C11—41no—
65Q8×C11—41no—
66D4×C11—21no—
67D4×C11—41no—
68C2×C4×C11—41no—
69C2×C4×C11—41no—
70C2×C4×C11C2×D411yescharacteristic
71C22⋊D11—41no—
72C22⋊D11—41no—
73C22⋊D11—41no—
74C2×Dic11—41no—
75C2×Dic11—41no—
76C2×Dic11D811yescharacteristic
77D44—21no—
78D44—41no—
79C4×D11—21no—
80C4×D11—21no—
81C4×D11—41no—
82C4×D11—41no—
83C4×D11—41no—
84Dic22—21no—
85Dic22—41no—
86C8×C11C2×D411yescharacteristic
87C8×C11C2×D411yescharacteristic
88C11⋊C8—21no—
89#575—111no—
90#510—111no—
91#510D1111yescharacteristic, complemented
92#470—111no—
93#360—111no—
94#360—111no—
95#349—111no—
96C22×C11—41no—
97C22×C11C2×D811yescharacteristic
98C2×D11—21no—
99C2×D11—41no—
100C2×D11—41no—
101C2×D11—82no—
102C4×C11—41no—
103C4×C11—81no—
104C4×C11#12011yescharacteristic
105C4×C11AGL(1,ℤ/8)11yescharacteristic
106Dic11—21no—
107Dic11—41no—
108Dic11—81no—
109C2×#41—221no—
110#137—221no—
111#137—221no—
112AGL(1,ℤ/8)—221no—
113AGL(1,ℤ/8)—221no—
114#135—111no—
115#135—221no—
116#135C2×D1111yescharacteristic
117C2×Q16C2×D1111yescharacteristic, complemented
118C2×M16—111no—
119C22⋊Q8—221no—
120Q32—21no—
121Q32—221no—
122SD32—21no—
123SD32—221no—
124M32—111no—
125M32C2×D1111yescharacteristic, complemented
126#106—111no—
127#103—221no—
128C2×C11—21no—
129C2×C11—81no—
130C2×C11#44711yescharacteristic
131D11—41no—
132D11—81no—
133#41—21no—
134#41—221no—
135#41—221no—
136#41—221no—
137#41—441no—
138#41—441no—
139C2×Q8—21no—
140C2×Q8—221no—
141C2×D4—221no—
142C2×D4—441no—
143C22×C4—111no—
144C22×C4—441no—
145Q16—21no—
146Q16—21no—
147Q16—111no—
148Q16—221no—
149Q16C22⋊D1111yescharacteristic
150SD16—21no—
151SD16—221no—
152SD16—221no—
153SD16—221no—
154D8—111no—
155D8—221no—
156D8C22⋊D1111yescharacteristic
157M16—221no—
158M16—221no—
159C2×C8—111no—
160C2×C8C22×D1111yescharacteristic
161C4⋊C4—221no—
162C4⋊C4—441no—
163C22⋊C4—441no—
164C16—21no—
165C16—221no—
166C11#219111yescharacteristic, complemented, Sylow
167C23—111no—
168C23—441no—
169Q8—21no—
170Q8—41no—
171Q8—41no—
172Q8—221no—
173Q8—441no—
174D4—21no—
175D4—41no—
176D4—221no—
177D4—441no—
178D4—441no—
179D4—441no—
180D4—441no—
181C2×C4—41no—
182C2×C4—41no—
183C2×C4—111no—
184C2×C4—221no—
185C2×C4—221no—
186C2×C4—441no—
187C2×C4—441no—
188C2×C4—441no—
189C2×C4—441no—
190C2×C4—441no—
191C2×C4D4×D1111yescharacteristic
192C8—221no—
193C8D4×D1111yescharacteristic
194C8C2×C22⋊D1111yescharacteristic
195C22—41no—
196C22—221no—
197C22—441no—
198C22—441no—
199C22—882no—
200C22D8×D1111yescharacteristic
201C4—41no—
202C4—81no—
203C4—221no—
204C4—441no—
205C4—881no—
206C4#6696411yescharacteristic
207C4#6699011yescharacteristic
208C2—21no—
209C2—81no—
210C2—441no—
211C2—881no—
212C2#1062276911yescharacteristic
subgroupG/H
centerC2#10622769
commutator, cosocleC2×C8×C11C23
FrattiniC2×C8C22×D11
FittingC11×#510C2
socleC2×C11#447
prime radical#10623299C2
hypercenter#510D11
hypocenterC11#2191
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ #510

Complements

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

NH ≅ G/Ntype
2. C11×#510C2semidirect
3. #10622802C2semidirect
4. #10622792C2semidirect
5. #10622204C2semidirect
6. #10622156C2semidirect
7. #10622152C2semidirect
10. C2×C11×Q16C22semidirect
21. C11×M32C22semidirect
25. #66881C22semidirect
26. #66876C22semidirect
91. #510D11semidirect
117. C2×Q16C2×D11semidirect
125. M32C2×D11semidirect
166. C11#2191semidirect

Maximal subgroups

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

subgroupindex
#106232992
C11×#5102
#106228022
#106227922
#106222042
#106221562
#106221522
#219111