Finite Group Databasebeta

← #11797597

Subgroups — #11797597

Order 1152.

250 conjugacy classes of subgroups; only the 58 normal subgroups are shown.

normal subgroups only

This group has 250 conjugacy classes of subgroups — too many to draw. Only its 58 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#10593838C211yesmaximal, characteristic, complemented
2#10593772C211yesmaximal, characteristic, complemented
3#10592523C211yesmaximal, characteristic
4#10590221C211yesmaximal, characteristic, complemented
5#10590187C211yesmaximal, characteristic, complemented
6#10590150C211yesmaximal, characteristic, complemented
7#10590148C211yesmaximal, characteristic, complemented
8#64159C411yescharacteristic
9#64157C2211yescharacteristic
10#64116C2211yescharacteristic
11#63773—21no—
12#63773C2211yescharacteristic
13#63773C2211yescharacteristic
14C2×#3708—21no—
15C2×#3708C2211yescharacteristic
16C2×#3708C2211yescharacteristic
17#63765—21no—
18#63764—21no—
19C32×#104C411yescharacteristic
20#63649C411yescharacteristic
21#63632C411yescharacteristic
22C4×C3⋊(C3⋊C8)C2211yescharacteristic
23#4824—62no—
24C32×#41C2×C411yescharacteristic
25#3828C2×C411yescharacteristic
26C32×M16C2×C411yescharacteristic
27C32×C42C2×C411yescharacteristic
28#3756C811yescharacteristic
29#3755C811yescharacteristic
30#3754C811yescharacteristic
31#3753C811yescharacteristic
32#3748—21no—
33#3748C2×C411yescharacteristic
34C2×C3⋊(C3⋊C8)—21no—
35C2×C3⋊(C3⋊C8)C2×C411yescharacteristic
36C2×C3⋊(C3⋊C8)C2311yescharacteristic
37#3743—21no—
38C8×C3⋊D3—21no—
39#3708—21no—
40#3708—21no—
41#3708—21no—
42#3708D411yescharacteristic
43#3708D411yescharacteristic
44#2171—91nomaximal, Sylow
45#950—62no—
46#948—62no—
47#907—62no—
48C3×#104—22no—
49#822—62no—
50#805—62no—
51C4×C3⋊C8—62no—
52C32×Q8C2×C811yescharacteristic
53C32×D4—21no—
54C32×D4C2×C811yescharacteristic
55C2×C32×C4—21no—
56C2×C32×C4—21no—
57C2×C32×C4C22×C411yescharacteristic
58#638—21no—
59C4⋊(C3⋊D3)C2×C811yescharacteristic
60C4×C3⋊D3—21no—
61#634C2×C811yescharacteristic
62C32×C8—21no—
63C3⋊(C3⋊C8)—21no—
64C3⋊(C3⋊C8)C2×C811yescharacteristic
65C3⋊(C3⋊C8)C2×C811yescharacteristic
66C3⋊(C3⋊C8)C2×D411yescharacteristic
67C3⋊(C3⋊C8)#4111yescharacteristic
68#504—91no—
69#504—91no—
70#443—91no—
71#364—91no—
72#350—91no—
73#350—91no—
74#346—91no—
75C3×#41—22no—
76#235—62no—
77C3×M16—22no—
78C3×C42—22no—
79#216—62no—
80#215—62no—
81#214—62no—
82#213—62no—
83#208—62no—
84#208—122no—
85C2×C3⋊C8—62no—
86C2×C3⋊C8—62no—
87C2×C3⋊C8—122no—
88ΓL(1,𝔽25)—122no—
89D3×C8—122no—
90C22×C32—21no—
91C22×C32#13111yescharacteristic
92C2×C3⋊D3—21no—
93C32×C4—21no—
94C32×C4—41no—
95C32×C4C4×D411yescharacteristic
96C32×C4C22×C811yescharacteristic
97C3⋊Dic3—21no—
98#135—91no—
99#131—91no—
100#131—91no—
101M32—91no—
102M32—91no—
103M32—181no—
104M32—181no—
105C2×C16—91no—
106C2×C16—91no—
107C2×C16—181no—
108C2×C16—181no—
109#108—91no—
110#104—91no—
111#104#15711yescharacteristic
112C4×C8—91no—
113C3×Q8—22no—
114C3×D4—22no—
115C3×D4—42no—
116C2×C3×C4—22no—
117C2×C3×C4—42no—
118C2×C3×C4—42no—
119#67—122no—
120D12—62no—
121C4×D3—122no—
122Dic6—62no—
123C3×C8—42no—
124C3⋊C8—62no—
125C3⋊C8—62no—
126C3⋊C8—62no—
127C3⋊C8—62no—
128C3⋊C8—122no—
129C2×C32—21no—
130C2×C32—41no—
131C2×C32C8×D411yescharacteristic
132C3⋊D3—41no—
133#41—91no—
134#41C2×#15711yescharacteristic
135Q16—91no—
136SD16—91no—
137SD16—91no—
138D8—91no—
139M16—91no—
140M16—181no—
141M16—181no—
142M16C2×#15711yescharacteristic
143C2×C8—91no—
144C2×C8—91no—
145C2×C8—181no—
146C2×C8—181no—
147C42C2×#15711yescharacteristic
148C16—91no—
149C16—91no—
150C16—181no—
151C16—181no—
152C16—181no—
153C22×C3—22no—
154C22×C3—42no—
155C2×D3—122no—
156C3×C4—22no—
157C3×C4—22no—
158C3×C4—42no—
159C3×C4—44no—
160Dic3—122no—
161C32#217111yescharacteristic, complemented, Sylow
162Q8—91no—
163Q8#378711yescharacteristic
164D4—21no—
165D4—91no—
166D4—181no—
167D4#378711yescharacteristic
168C2×C4—21no—
169C2×C4—21no—
170C2×C4—181no—
171C2×C4C22×#15711yescharacteristic
172C8—21no—
173C8—91no—
174C8—91no—
175C8—91no—
176C8—91no—
177C8—181no—
178C2×C3—22no—
179C2×C3—42no—
180C2×C3—82no—
181D3—242no—
182C22—21no—
183C22—181no—
184C22#6428711yescharacteristic
185C4—21no—
186C4—41no—
187C4—181no—
188C4C2×#378711yescharacteristic
189C4D4×#15711yescharacteristic
190C3—22no—
191C2—21no—
192C2—41no—
193C2—361no—
194C2#1059373911yescharacteristic
subgroupG/H
centerC4D4×#157
commutatorC32×C4C22×C8
FrattiniC2×C4C22×#157
FittingC32×#104C4
socleC2×C32C8×D4
prime radical#64159C4
cosocleC2×C3⋊(C3⋊C8)C23
hypercenter#104#157
hypocenterC32#2171
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C4 ◁ C2×C4 ◁ #104

Complements

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

NH ≅ G/Ntype
1. #10593838C2semidirect
2. #10593772C2semidirect
4. #10590221C2semidirect
5. #10590187C2semidirect
6. #10590150C2semidirect
7. #10590148C2semidirect
161. C32#2171semidirect

Maximal subgroups

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

subgroupindex
#105938382
#105937722
#105925232
#105902212
#105901872
#105901502
#105901482
#21719