Finite Group Databasebeta

← #106×#157 #11784440

Subgroups — #106×#157 #11784440

Order 1152.

410 conjugacy classes of subgroups; only the 106 normal subgroups are shown.

normal subgroups only

This group has 410 conjugacy classes of subgroups — too many to draw. Only its 106 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×#63768C211yesmaximal, characteristic
2C2×C8×#157C211yesmaximal, characteristic
3C4⋊C4×#157C212yesmaximal
4C3⋊D3×#106C211yesmaximal, characteristic
5#10590163C212yesmaximal
6C2×C4⋊#157C2212yes—
7C2×C4×#157—22no—
8C2×C4×#157C2211yescharacteristic
9C2×#3787C2211yescharacteristic
10C2×C8×C3⋊D3C2211yescharacteristic
11C4⋊C4×C3⋊D3C2212yes—
12#63781—22no—
13#63768C414yescomplemented
14C8×#157C414yescomplemented
15C32×#106C411yescharacteristic, complemented
16#63644C411yescharacteristic, complemented
17#63635C412yescomplemented
18D3×#106—62no—
19C22×#157—22no—
20C22×#157D411yescharacteristic
21C22×#157D411yescharacteristic
22C2×C4×C3⋊D3—22no—
23C2×C4×C3⋊D3C2311yescharacteristic
24C2×#622—21no—
25C4⋊#157—22no—
26C4⋊#157C2×C414yes—
27C4×#157—44no—
28C4×#157C2×C412yes—
29C4×#157Q812yes—
30#3787—21no—
31#3787C2×C412yes—
32C2×C32×C8C2×C411yescharacteristic
33C32×C4⋊C4C2×C412yes—
34C4⋊(C3⋊Dic3)C2×C412yes—
35#3750—22no—
36C2×C3⋊(C3⋊C8)C2×C411yescharacteristic
37C8×C3⋊D3C2×C412yes—
38C8×C3⋊D3C2×C412yes—
39C4×#106—91nomaximal, Sylow
40C2×D3×C8—62no—
41D3×C4⋊C4—64no—
42C3×#106—22no—
43#817—62no—
44#808—64no—
45C22×C3⋊D3C2×D411yescharacteristic
46C2×#157—22no—
47C2×#157—24no—
48C2×#157—42no—
49C2×#157—42no—
50C2×#157C4⋊C412yes—
51C2×#157C4⋊C412yes—
52C2×#157SD1614yes—
53C2×C32×C4—22no—
54C2×C32×C4C22×C411yescharacteristic
55C2×C3⋊Dic3—22no—
56C2×C3⋊Dic3#4111yescharacteristic
57C4×C3⋊D3—42no—
58C4×C3⋊D3—42no—
59C4×C3⋊D3C22×C411yescharacteristic
60C4×C3⋊D3C22×C411yescharacteristic
61C4×C3⋊D3C2×Q811yescharacteristic
62C4×C3⋊D3#4111yescharacteristic
63#622—22no—
64C32×C8C4212yescomplemented
65C3⋊(C3⋊C8)C4212yescomplemented
66C2×#106—91no—
67C2×#106—91no—
68C2×C4×C8—91no—
69C4×C4⋊C4—92no—
70#340—92no—
71C2×C4×D3—62no—
72C2×C4×D3—124no—
73C2×C3×C8—22no—
74C3×C4⋊C4—24no—
75C4⋊Dic3—64no—
76Dic3⋊C4—124no—
77C2×C3⋊C8—62no—
78D3×C8—64no—
79D3×C8—64no—
80C22×C32C4×D411yescharacteristic
81C2×C3⋊D3C2×C4⋊C411yescharacteristic
82C2×C3⋊D3C4×D411yescharacteristic
83C2×C3⋊D3C2×SD1612yes—
84C2×C3⋊D3#13512yes—
85#157—22no—
86#157—44no—
87#157#10614yesdirect product factor
88C32×C4—42no—
89C32×C4C2×C4211yescharacteristic
90C32×C4C4×Q811yescharacteristic
91C3⋊Dic3—42no—
92C3⋊Dic3#11711yescharacteristic
93C3⋊Dic3C4×Q811yescharacteristic
94C22×C8—91no—
95C22×C8—91no—
96C2×C4⋊C4—92no—
97C2×C4⋊C4—92no—
98C2×C42—91no—
99C2×C42—182no—
100#106—94no—
101#106—91no—
102#106—92no—
103#106#15711yescharacteristic, direct product factor
104C4×C8—94no—
105#95—182no—
106C22×D3—62no—
107C2×C3×C4—22no—
108C2×C3×C4—44no—
109C2×Dic3—62no—
110C2×Dic3—124no—
111C4×D3—62no—
112C4×D3—62no—
113C4×D3—62no—
114C4×D3—62no—
115C4×D3—244no—
116C4×D3—244no—
117C3×C8—24no—
118C3⋊C8—64no—
119C2×C32C4×C4⋊C411yescharacteristic
120C2×C32C4×SD1612yes—
121C3⋊D3C2×#10611yescharacteristic
122C3⋊D3#42711yescharacteristic
123C3⋊D3C4×SD1612yes—
124C22×C4—91no—
125C22×C4—91no—
126C22×C4—91no—
127C22×C4—182no—
128C22×C4—182no—
129C2×C8—91no—
130C2×C8—92no—
131C2×C8—92no—
132C2×C8—92no—
133C2×C8—181no—
134C2×C8—181no—
135C2×C8C2×#15711yescharacteristic
136C4⋊C4—94no—
137C4⋊C4—92no—
138C4⋊C4—182no—
139C4⋊C4—182no—
140C4⋊C4C2×#15712yes—
141C42—92no—
142C42—92no—
143C42—364no—
144C22×C3—22no—
145C2×D3—62no—
146C2×D3—62no—
147C2×D3—64no—
148C2×D3—64no—
149C3×C4—22no—
150C3×C4—22no—
151C3×C4—84no—
152Dic3—62no—
153Dic3—62no—
154Dic3—244no—
155C32C4×#10611yescharacteristic, complemented, Sylow
156C23—91no—
157C2×C4—22no—
158C2×C4—92no—
159C2×C4—94no—
160C2×C4—91no—
161C2×C4—91no—
162C2×C4—91no—
163C2×C4—91no—
164C2×C4—91no—
165C2×C4—92no—
166C2×C4—182no—
167C2×C4—184no—
168C2×C4—182no—
169C2×C4—362no—
170C2×C4—362no—
171C2×C4—362no—
172C2×C4—362no—
173C2×C4C22×#15711yescharacteristic
174C8—92no—
175C8—182no—
176C8C4×#15712yescomplemented
177C2×C3—22no—
178C2×C3—24no—
179D3—62no—
180D3—62no—
181D3—64no—
182C22—91no—
183C22—91no—
184C22—92no—
185C22—92no—
186C22D4×#15711yescharacteristic
187C4—42no—
188C4—94no—
189C4—91no—
190C4—91no—
191C4—182no—
192C4—364no—
193C4—362no—
194C4C2×C4×#15711yescharacteristic
195C4Q8×#15711yescharacteristic
196C3—22no—
197C2—91no—
198C2—91no—
199C2—92no—
200C2C4⋊C4×#15711yescharacteristic
201C2SD16×#15712yes—
subgroupG/H
centerC22D4×#157
commutatorC32×C4C2×C42
FrattiniC2×C4C22×#157
FittingC32×#106C4
socleC22×C32C4×D4
prime radicalC22×C3⋊D3C2×D4
cosocleC2×C4×C3⋊D3C23
hypercenter#106#157
hypocenterC32C4×#106
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ #106

Complements

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

NH ≅ G/Ntype
13. #63768C4semidirect
14. C8×#157C4semidirect
15. C32×#106C4semidirect
16. #63644C4semidirect
17. #63635C4semidirect
64. C32×C8C42semidirect
65. C3⋊(C3⋊C8)C42semidirect
87. #157#106direct (N × H)
103. #106#157direct (N × H)
155. C32C4×#106semidirect
176. C8C4×#157semidirect

Maximal subgroups

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

subgroupindex
C2×#637682
C2×C8×#1572
C4⋊C4×#1572
C3⋊D3×#1062
#105901632
C4×#1069