Finite Group Databasebeta

← #11783840

Subgroups — #11783840

Order 1152.

434 conjugacy classes of subgroups; only the 86 normal subgroups are shown.

normal subgroups only

This group has 434 conjugacy classes of subgroups — too many to draw. Only its 86 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
1C2×#64287C211yesmaximal, characteristic
2#10593818C211yesmaximal, characteristic
3#10593775C212yesmaximal, complemented
4#10592444C211yesmaximal, characteristic
5#10590191C212yesmaximal, complemented
6C2×#3830C2211yescharacteristic
7C2×#3792C412yescomplemented
8C22×#622C412yescomplemented
9#64287—22no—
10#64287—22no—
11#64286C2212yes—
12C2×#3788C2211yescharacteristic
13C2×#3787C2211yescharacteristic
14M16×C3⋊D3C2212yes—
15#63786C414yes—
16#63767—22no—
17C8×#157—22no—
18C32×#100C411yescharacteristic, complemented
19#63660C411yescharacteristic, complemented
20#63651C412yescomplemented
21#4745—62no—
22C2×C32×D4C2×C411yescharacteristic
23C2×#638C2×C412yes—
24C22×C3⋊Dic3C2×C412yes—
25#3830—22no—
26#3830—22no—
27C2×C4×C3⋊D3C2311yescharacteristic
28C2×#634C2×C411yescharacteristic
29C22⋊#157C2×C414yes—
30#3792—24no—
31C2×#622—22no—
32C2×#622—22no—
33C2×#622C2×C412yes—
34C2×#622C2×C411yescharacteristic
35C2×#622C2×C411yescharacteristic
36C4⋊#157—22no—
37C4×#157—22no—
38#3788—22no—
39#3787D412yes—
40#3787D412yes—
41C32×M16C2×C412yes—
42#3748C2×C412yes—
43#3743—22no—
44C8×C3⋊D3—22no—
45#1757—91nomaximal, Sylow
46C2×#237—62no—
47D3×M16—64no—
48C3×#100—22no—
49#833—62no—
50#824—64no—
51C23×C32C4212yes—
52C22×C3⋊D3C22×C411yescharacteristic
53C2×#157—24no—
54C32×D4—22no—
55C2×C32×C4C22×C411yescharacteristic
56#638—24no—
57C2×C3⋊Dic3—22no—
58C2×C3⋊Dic3—22no—
59C2×C3⋊Dic3C4212yes—
60C2×C3⋊Dic3C22×C411yescharacteristic
61C4×C3⋊D3C2×D412yes—
62C4×C3⋊D3#4112yes—
63#634—22no—
64#622—22no—
65#622C22⋊C411yescharacteristic
66#622C22⋊C411yescharacteristic
67#622C22⋊C412yes—
68C32×C8—22no—
69C3⋊(C3⋊C8)—22no—
70C2×#131—91no—
71#413—91no—
72#410—91no—
73#405—92no—
74#344—92no—
75C2×C3×D4—22no—
76C2×#67—64no—
77C22×Dic3—64no—
78#237—124no—
79#237—124no—
80C2×C4×D3—62no—
81C2×Dic6—62no—
82C3×M16—24no—
83#208—64no—
84ΓL(1,𝔽25)—124no—
85D3×C8—124no—
86C22×C32—22no—
87C22×C32—42no—
88C22×C32C2×C4211yescharacteristic
89C2×C3⋊D3—41no—
90C2×C3⋊D3C4×D412yes—
91#157—44no—
92C32×C4C4×D412yes—
93C3⋊Dic3—22no—
94C3⋊Dic3C2×C22⋊C411yescharacteristic
95C3⋊Dic3#11711yescharacteristic
96C2×#41—91no—
97#131—182no—
98#131—182no—
99C2×M16—91no—
100C2×M16—92no—
101C2×M16—92no—
102C22×C8—91no—
103C22×C8—92no—
104#117—92no—
105#101—92no—
106#100—91no—
107#100#15711yescharacteristic, complemented
108#99—94no—
109#97—182no—
110C4×C8—182no—
111C23×C3—24no—
112C22×D3—62no—
113C3×D4—44no—
114C2×C3×C4—22no—
115#67—128no—
116C2×Dic3—62no—
117C2×Dic3—64no—
118C2×Dic3—124no—
119C2×Dic3—124no—
120C4×D3—64no—
121C4×D3—64no—
122Dic6—124no—
123C3×C8—44no—
124C3⋊C8—124no—
125C2×C32—21no—
126C2×C32—42no—
127C2×C32C4×C22⋊C411yescharacteristic
128C3⋊D3—22no—
129#41—182no—
130#41—182no—
131C2×Q8—91no—
132C2×D4—92no—
133C2×D4C2×#15711yescharacteristic
134C22×C4—91no—
135C22×C4—92no—
136M16—92no—
137M16—182no—
138M16—184no—
139M16—182no—
140M16C2×#15712yes—
141C2×C8—92no—
142C2×C8—92no—
143C2×C8—91no—
144C2×C8—91no—
145C2×C8—92no—
146C2×C8—182no—
147C2×C8—182no—
148C2×C8—182no—
149C4⋊C4—182no—
150C22⋊C4—94no—
151C42—182no—
152C22×C3—22no—
153C22×C3—44no—
154C22×C3—84no—
155C2×D3—64no—
156C2×D3—242no—
157C3×C4—24no—
158Dic3—62no—
159Dic3—62no—
160Dic3—124no—
161C32#175711yescharacteristic, complemented, Sylow
162C23—91no—
163C23C4×#15712yes—
164Q8—182no—
165D4—22no—
166D4—184no—
167C2×C4—91no—
168C2×C4—92no—
169C2×C4—92no—
170C2×C4—92no—
171C2×C4—182no—
172C2×C4—182no—
173C2×C4—184no—
174C2×C4C22×#15711yescharacteristic
175C8—22no—
176C8—91no—
177C8—91no—
178C8—92no—
179C8—182no—
180C8—182no—
181C2×C3—22no—
182C2×C3—42no—
183C2×C3—84no—
184D3—124no—
185C22—22no—
186C22—42no—
187C22—92no—
188C22—361no—
189C22C2×C4×#15711yescharacteristic
190C4—91no—
191C4—91no—
192C4—182no—
193C4—364no—
194C4D4×#15712yes—
195C3—22no—
196C2—21no—
197C2—42no—
198C2—182no—
199C2C22⋊C4×#15711yescharacteristic
subgroupG/H
centerC2C22⋊C4×#157
commutatorC22×C32C2×C42
FrattiniC2×C4C22×#157
FittingC32×#100C4
socleC2×C32C4×C22⋊C4
prime radicalC2×#3830C22
cosocleC2×C4×C3⋊D3C23
hypercenter#100#157
hypocenterC32#1757
LCSG ▷ C22×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C2×C4 ◁ #100

Complements

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

NH ≅ G/Ntype
3. #10593775C2semidirect
5. #10590191C2semidirect
7. C2×#3792C4semidirect
8. C22×#622C4semidirect
18. C32×#100C4semidirect
19. #63660C4semidirect
20. #63651C4semidirect
107. #100#157semidirect
161. C32#1757semidirect

Maximal subgroups

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

subgroupindex
C2×#642872
#105938182
#105937752
#105924442
#105901912
#17579