Finite Group Databasebeta

← #11797745

Subgroups — #11797745

Order 1152.

250 conjugacy classes of subgroups; only the 48 normal subgroups are shown.

normal subgroups only

This group has 250 conjugacy classes of subgroups — too many to draw. Only its 48 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
1Q16×#157C211yesmaximal, characteristic, complemented
2D8×#157C211yesmaximal, characteristic
3C3⋊D3×SD32C211yesmaximal, characteristic
4#10590197C211yesmaximal, characteristic, complemented
5#10590193C211yesmaximal, characteristic
6#10590138C211yesmaximal, characteristic, complemented
7#10590135C211yesmaximal, characteristic, complemented
8Q8×#157—21no—
9D4×#157—21no—
10Q16×C3⋊D3C2211yescharacteristic
11D8×C3⋊D3C2211yescharacteristic
12#63784—21no—
13#63782—21no—
14#63769C2211yescharacteristic
15#63769C2211yescharacteristic
16C8×#157C2211yescharacteristic
17#63764C2211yescharacteristic
18C32×SD32C411yescharacteristic, complemented
19#63655C411yescharacteristic, complemented
20#63654C411yescharacteristic, complemented
21#63627C411yescharacteristic, complemented
22C16×C3⋊D3C2211yescharacteristic
23D3×SD32—62no—
24C22×#157—41no—
25Q8×C3⋊D3—21no—
26D4×C3⋊D3—21no—
27C22⋊#157—41no—
28C4⋊#157—21no—
29C4⋊#157—21no—
30C4⋊#157—41no—
31C4×#157—41no—
32C4×#157D411yescharacteristic
33#3787D411yescharacteristic
34C32×Q16C2×C411yescharacteristic, complemented
35C32×D8C2×C411yescharacteristic
36#3756—21no—
37#3753—21no—
38#3746C2×C411yescharacteristic, complemented
39#3745C2×C411yescharacteristic
40C8×C3⋊D3C2311yescharacteristic
41#3708—21no—
42C32×C16C2×C411yescharacteristic, complemented
43C3⋊(C3⋊C16)C2×C411yescharacteristic, complemented
44#2175—91nomaximal, Sylow
45D3×Q16—62no—
46D3×D8—62no—
47C3×SD32—22no—
48#828—62no—
49#827—62no—
50#800—62no—
51D3×C16—62no—
52C22×C3⋊D3—41no—
53C2×#157—41no—
54C2×#157—41no—
55C2×#157—82no—
56C2×#157D811yescharacteristic
57C2×#157D811yescharacteristic
58C32×Q8—21no—
59C32×D4—21no—
60#638—41no—
61C4⋊(C3⋊D3)—21no—
62C4×C3⋊D3—41no—
63C4×C3⋊D3C2×D411yescharacteristic
64#634—21no—
65#634—41no—
66#622—21no—
67C32×C8C22×C411yescharacteristic
68C3⋊(C3⋊C8)#4111yescharacteristic
69C2×SD32—91no—
70C4×Q16—91no—
71C4×D8—91no—
72#366—91no—
73#358—91no—
74#357—91no—
75#346—91no—
76D3×Q8—122no—
77D3×D4—122no—
78C3×Q16—22no—
79C3×D8—22no—
80#216—122no—
81#213—122no—
82Dic12—62no—
83D24—62no—
84D3×C8—62no—
85C3×C16—22no—
86C3⋊C16—62no—
87C22×C32—41no—
88C2×C3⋊D3—41no—
89C2×C3⋊D3—81no—
90C2×C3⋊D3—81no—
91C2×C3⋊D3C2×D811yescharacteristic
92#157—21no—
93#157—21no—
94#157—81no—
95#157—81no—
96C32×C4—41no—
97C32×C4C4×D411yescharacteristic
98C3⋊Dic3—41no—
99C3⋊Dic3#13511yescharacteristic
100C2×Q16—91no—
101C2×D8—91no—
102C4×Q8—181no—
103C4×D4—181no—
104SD32—91no—
105SD32—91no—
106SD32—91no—
107SD32#15711yescharacteristic, complemented
108C2×C16—91no—
109C2×C16—91no—
110#107—91no—
111#107—91no—
112#103—181no—
113#102—181no—
114C4×C8—91no—
115C22×D3—242no—
116C3×Q8—42no—
117C3×D4—42no—
118#67—242no—
119D12—122no—
120C4×D3—62no—
121C4×D3—242no—
122Dic6—122no—
123Dic6—242no—
124C3×C8—22no—
125C3⋊C8—62no—
126C2×C32—81no—
127C2×C32C4×D811yescharacteristic
128C3⋊D3—81no—
129C3⋊D3#50911yescharacteristic
130C3⋊D3#51011yescharacteristic
131C2×Q8—181no—
132C2×D4—181no—
133C22×C4—361no—
134Q16—91no—
135Q16—181no—
136Q16C2×#15711yescharacteristic, complemented
137D8—91no—
138D8—181no—
139D8C2×#15711yescharacteristic
140C2×C8—91no—
141C2×C8—91no—
142C4⋊C4—181no—
143C4⋊C4—181no—
144C4⋊C4—361no—
145C22⋊C4—361no—
146C42—91no—
147C42—361no—
148C16—91no—
149C16—181no—
150C16C2×#15711yescharacteristic, complemented
151C22×C3—82no—
152C2×D3—62no—
153C2×D3—242no—
154C2×D3—482no—
155C2×D3—482no—
156C3×C4—22no—
157C3×C4—82no—
158Dic3—62no—
159Dic3—242no—
160C32#217511yescharacteristic, complemented, Sylow
161C23—361no—
162Q8—21no—
163Q8—181no—
164Q8—361no—
165D4—21no—
166D4—181no—
167D4—361no—
168C2×C4—91no—
169C2×C4—91no—
170C2×C4—91no—
171C2×C4—361no—
172C2×C4—361no—
173C2×C4—361no—
174C2×C4—722no—
175C8—91no—
176C8—181no—
177C8C22×#15711yescharacteristic
178C2×C3—22no—
179C2×C3—162no—
180D3—62no—
181D3—62no—
182D3—482no—
183C22—41no—
184C22—91no—
185C22—361no—
186C22—721no—
187C22—721no—
188C4—41no—
189C4—91no—
190C4—181no—
191C4—181no—
192C4—361no—
193C4—721no—
194C4—721no—
195C4D4×#15711yescharacteristic
196C3—22no—
197C2—81no—
198C2—91no—
199C2—91no—
200C2—721no—
201C2D8×#15711yescharacteristic
subgroupG/H
centerC2D8×#157
commutatorC32×C8C22×C4
FrattiniC8C22×#157
FittingC32×SD32C4
socleC2×C32C4×D8
prime radicalD8×C3⋊D3C22
cosocleC8×C3⋊D3C23
hypercenterSD32#157
hypocenterC32#2175
LCSG ▷ C32×C8 ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C4 ◁ C8 ◁ SD32

Complements

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

NH ≅ G/Ntype
1. Q16×#157C2semidirect
4. #10590197C2semidirect
6. #10590138C2semidirect
7. #10590135C2semidirect
18. C32×SD32C4semidirect
19. #63655C4semidirect
20. #63654C4semidirect
21. #63627C4semidirect
34. C32×Q16C2×C4semidirect
38. #3746C2×C4semidirect
42. C32×C16C2×C4semidirect
43. C3⋊(C3⋊C16)C2×C4semidirect
107. SD32#157semidirect
136. Q16C2×#157semidirect
150. C16C2×#157semidirect
160. C32#2175semidirect

Maximal subgroups

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

subgroupindex
Q16×#1572
D8×#1572
C3⋊D3×SD322
#105901972
#105901932
#105901382
#105901352
#21759