Finite Group Databasebeta

← #11781193

Subgroups — #11781193

Order 1152.

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

normal subgroups only

This group has 268 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
1D4×#622C211yesmaximal, characteristic
2#10593395C211yesmaximal, characteristic, complemented
3#10591495C212yesmaximal
4#10590042C211yesmaximal, characteristic, complemented
5#10590040C212yesmaximal, complemented
6C22×#622—21no—
7D4×C3⋊Dic3C2211yescharacteristic
8#63919C2212yes—
9C22⋊#622—21no—
10C4⋊#622C2211yescharacteristic
11C4×#622C2211yescharacteristic
12#63743—21no—
13#63743—21no—
14C3×#832—22no—
15#63573—22no—
16#63572C2212yes—
17#4761—62no—
18C2×C32×D4D411yescharacteristic
19C22×C3⋊Dic3—21no—
20C2×#627—22no—
21C2×#622—21no—
22C2×#622—42no—
23C2×#622D411yescharacteristic
24C2×#622D411yescharacteristic
25#3757—21no—
26C4⋊(C3⋊Dic3)D411yescharacteristic
27C4×C3⋊Dic3C2311yescharacteristic
28C3×C4⋊Dic3—22no—
29C2×C3×C3⋊C8—22no—
30#3724—22no—
31#1675—91nomaximal, Sylow
32D4×Dic3—62no—
33#888—62no—
34C3×#102—62no—
35#832—22no—
36#817—62no—
37Dic3⋊C8—62no—
38#808—62no—
39C23×C32—21no—
40C32×D4—21no—
41C32×D4Q1612yes—
42C2×C32×C4C2×D411yescharacteristic
43C2×C3⋊Dic3—21no—
44C2×C3⋊Dic3—41no—
45C2×C3⋊Dic3—41no—
46C2×C3⋊Dic3C2×D411yescharacteristic
47C2×C3⋊Dic3#4111yescharacteristic
48C2×C3×Dic3—42no—
49#627—82no—
50#622—21no—
51#622—41no—
52#622SD1612yes—
53C3×C3⋊C8—42no—
54#500—91no—
55#476—92no—
56C8×D4—91no—
57#335—91no—
58#333—92no—
59C2×C3×D4—22no—
60C22×Dic3—122no—
61C2×Dic6—122no—
62C2×C3×C8—62no—
63C3×C4⋊C4—62no—
64#217—122no—
65C4⋊Dic3—22no—
66C4⋊Dic3—62no—
67Dic3⋊C4—122no—
68C4×Dic3—62no—
69C2×C3⋊C8—22no—
70C22×C32—22no—
71C22×C32—41no—
72C22×C32—41no—
73C22×C32#12111yescharacteristic
74C32×C4C2×Q1611yescharacteristic
75C32×C4#13511yescharacteristic
76C3⋊Dic3—21no—
77C3⋊Dic3—41no—
78C3⋊Dic3C2×SD1611yescharacteristic
79C3⋊Dic3#13711yescharacteristic
80C3×Dic3—82no—
81C22×C8—181no—
82C4⋊Q8—92no—
83C4×D4—91no—
84#107—181no—
85#107—181no—
86#106—182no—
87C4⋊C8—92no—
88C4⋊C8—91no—
89#102—62no—
90C22⋊C8—181no—
91C4×C8—91no—
92C23×C3—42no—
93C3×D4—24no—
94C3×D4—42no—
95C2×C3×C4—22no—
96C2×C3×C4—122no—
97C2×Dic3—42no—
98C2×Dic3—62no—
99C2×Dic3—62no—
100C2×Dic3—122no—
101C2×Dic3—242no—
102C2×Dic3—242no—
103Dic6—244no—
104C3×C8—122no—
105C3⋊C8—42no—
106C2×C32—42no—
107C2×C32#46111yescharacteristic
108C2×C32#46711yescharacteristic
109C2×C32#47211yescharacteristic
110C2×Q8—182no—
111C2×D4GO+(4,𝔽2)11yescharacteristic
112C22×C4—181no—
113C2×C8—62no—
114C2×C8—91no—
115C2×C8—91no—
116C2×C8—181no—
117C2×C8—362no—
118C4⋊C4—62no—
119C4⋊C4—91no—
120C4⋊C4—182no—
121C22⋊C4—181no—
122C42—91no—
123C22×C3—22no—
124C22×C3—44no—
125C22×C3—82no—
126C22×C3—82no—
127C3×C4—22no—
128C3×C4—22no—
129C3×C4—242no—
130Dic3—62no—
131Dic3—62no—
132Dic3—82no—
133Dic3—122no—
134Dic3—242no—
135C32#167511yescharacteristic, complemented, Sylow
136C23—21no—
137Q8—722no—
138D4—21no—
139D4#377612yes—
140C2×C4—91no—
141C2×C4—91no—
142C2×C4—122no—
143C2×C4—181no—
144C2×C4—361no—
145C2×C4—361no—
146C2×C4C2×GO+(4,𝔽2)11yescharacteristic
147C8—92no—
148C8—122no—
149C8—181no—
150C8—361no—
151C2×C3—22no—
152C2×C3—22no—
153C2×C3—22no—
154C2×C3—84no—
155C22—22no—
156C22—41no—
157C22—41no—
158C22#6424211yescharacteristic
159C4—91no—
160C4—91no—
161C4—181no—
162C4—242no—
163C4—361no—
164C4#6423711yescharacteristic
165C4C2×#377611yescharacteristic
166C3—22no—
167C2—42no—
168C2#1059346511yescharacteristic
169C2#1059346611yescharacteristic
170C2#1059352711yescharacteristic
subgroupG/H
centerC22#64242
commutator, cosocleC4×C3⋊Dic3C23
FrattiniC2×C4C2×GO+(4,𝔽2)
Fitting, prime radicalC2×C32×D4D4
socleC22×C32#121
hypercenterC2×D4GO+(4,𝔽2)
hypocenterC32#1675
LCSG ▷ C4×C3⋊Dic3 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×D4

Complements

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

NH ≅ G/Ntype
2. #10593395C2semidirect
4. #10590042C2semidirect
5. #10590040C2semidirect
135. C32#1675semidirect

Maximal subgroups

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

subgroupindex
D4×#6222
#105933952
#105914952
#105900422
#105900402
#16759