Finite Group Databasebeta

← #11790508

Subgroups — #11790508

Order 1152.

314 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 314 conjugacy classes of subgroups — too many to draw. Only its 65 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#10593748C211yesmaximal, characteristic
2#10593396C211yesmaximal, characteristic
3C2×#63733C211yesmaximal, characteristic
4#10590584C212yesmaximal
5#10590052C212yesmaximal
6C2×#3788C2211yescharacteristic
7C2×#3787C2211yescharacteristic
8#64101C2211yescharacteristic
9#63900C2212yes—
10C2×#3712C2212yes—
11#63777—21no—
12C4×#622—21no—
13#63743—21no—
14#63743—21no—
15#63733C414yescomplemented
16C3×#808—22no—
17#63575—22no—
18#4861—62no—
19C2×C4×C3⋊D3C2311yescharacteristic
20C2×#624—22no—
21C2×#622—21no—
22C2×#622D411yescharacteristic
23C2×#622D411yescharacteristic
24#3788—21no—
25#3788Q812yes—
26#3787C2×C412yes—
27#3787Q812yes—
28C32×C4⋊C4D411yescharacteristic
29#3752—21no—
30C4⋊(C3⋊Dic3)D411yescharacteristic
31C4×C3⋊Dic3—21no—
32C3×C4⋊Dic3—22no—
33C2×C3×C3⋊C8—22no—
34#3724—22no—
35#3712—22no—
36#3712C2×C414yes—
37#1952—91nomaximal, Sylow
38C2×ΓL(1,𝔽25)—62no—
39#892—62no—
40D3×C4⋊C4—62no—
41C3×#106—62no—
42#818—62no—
43#808—22no—
44#807—62no—
45C22×C3⋊D3#4111yescharacteristic
46C2×C32×C4—21no—
47C2×C32×C4C2×D411yescharacteristic
48C2×C3⋊Dic3—21no—
49C2×C3⋊Dic3C2×D411yescharacteristic
50C4×C3⋊D3C22×C411yescharacteristic
51C4×C3⋊D3C2×Q811yescharacteristic
52C4×C3⋊D3C2×Q811yescharacteristic
53C4×C3⋊D3#4111yescharacteristic
54C2×C3×Dic3—42no—
55#624—82no—
56#622—22no—
57#622C4⋊C412yes—
58#622C4⋊C412yes—
59C3×C3⋊C8—24no—
60C2×#108—91no—
61#428—92no—
62C2×#107—91no—
63#405—91no—
64#343—92no—
65C2×C4×D3—62no—
66C2×C4×D3—122no—
67C2×C3×C8—62no—
68C3×C4⋊C4—22no—
69C3×C4⋊C4—62no—
70(C2×D3)⋊C4—122no—
71C4⋊Dic3—22no—
72C4⋊Dic3—62no—
73Dic3⋊C4—122no—
74C4×Dic3—122no—
75C2×C3⋊C8—22no—
76ΓL(1,𝔽25)—64no—
77ΓL(1,𝔽25)—64no—
78C22×C32#12111yescharacteristic
79C2×C3⋊D3—21no—
80C2×C3⋊D3—21no—
81C2×C3⋊D3C4×Q811yescharacteristic
82C2×C3⋊D3#12511yescharacteristic
83C32×C4—41no—
84C32×C4C4×D411yescharacteristic
85C32×C4C4⋊Q811yescharacteristic
86C3⋊Dic3—41no—
87C3⋊Dic3C2×C4⋊C411yescharacteristic
88C3⋊Dic3C22⋊Q811yescharacteristic
89C3×Dic3—82no—
90C2×M16—92no—
91C2×M16—91no—
92C22×C8—91no—
93#117—91no—
94C2×C4⋊C4—92no—
95#108—94no—
96#107—182no—
97#107—181no—
98#107—181no—
99#106—62no—
100#97—181no—
101C4×C8—181no—
102C22×D3—62no—
103C2×C3×C4—22no—
104C2×C3×C4—42no—
105C2×C3×C4—122no—
106C2×Dic3—42no—
107C2×Dic3—62no—
108C2×Dic3—122no—
109C4×D3—62no—
110C4×D3—62no—
111C4×D3—62no—
112C4×D3—62no—
113C4×D3—244no—
114C3×C8—64no—
115C3⋊C8—24no—
116C2×C32#38911yescharacteristic
117C2×C32#47211yescharacteristic
118C2×C32#47311yescharacteristic
119C3⋊D3—21no—
120C3⋊D3—21no—
121C22×C4—91no—
122C22×C4—182no—
123M16—94no—
124M16—92no—
125M16—182no—
126M16—181no—
127C2×C8—62no—
128C2×C8—91no—
129C2×C8—91no—
130C2×C8—92no—
131C2×C8—92no—
132C2×C8—181no—
133C4⋊C4—62no—
134C4⋊C4—91no—
135C4⋊C4—182no—
136C4⋊C4GO+(4,𝔽2)11yescharacteristic
137C22⋊C4—181no—
138C42—181no—
139C22×C3—22no—
140C2×D3—62no—
141C2×D3—62no—
142C2×D3—122no—
143C2×D3—122no—
144C3×C4—22no—
145C3×C4—22no—
146C3×C4—82no—
147C3×C4—242no—
148Dic3—62no—
149Dic3—62no—
150Dic3—82no—
151Dic3—242no—
152C32#195211yescharacteristic, complemented, Sylow
153C23—91no—
154C2×C4—21no—
155C2×C4—91no—
156C2×C4—91no—
157C2×C4—91no—
158C2×C4—91no—
159C2×C4—91no—
160C2×C4—122no—
161C2×C4—181no—
162C2×C4—722no—
163C2×C4C2×GO+(4,𝔽2)11yescharacteristic
164C8—64no—
165C8—92no—
166C8—92no—
167C8—182no—
168C2×C3—22no—
169C2×C3—22no—
170C2×C3—22no—
171D3—122no—
172D3—122no—
173C22—91no—
174C22—91no—
175C22—181no—
176C22—181no—
177C22#6424211yescharacteristic
178C4—41no—
179C4—91no—
180C4—91no—
181C4—242no—
182C4—361no—
183C4#6422211yescharacteristic
184C4C4×GO+(4,𝔽2)11yescharacteristic
185C3—22no—
186C2—181no—
187C2—181no—
188C2#1059341011yescharacteristic
189C2#1059346811yescharacteristic
190C2#1059347911yescharacteristic
subgroupG/H
centerC22#64242
commutatorC4×C3⋊D3C22×C4
FrattiniC2×C4C2×GO+(4,𝔽2)
FittingC32×C4⋊C4D4
socleC22×C32#121
prime radicalC22×C3⋊D3#41
cosocleC2×C4×C3⋊D3C23
hypercenterC4⋊C4GO+(4,𝔽2)
hypocenterC32#1952
LCSG ▷ C4×C3⋊D3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ C4⋊C4

Complements

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

NH ≅ G/Ntype
15. #63733C4semidirect
152. C32#1952semidirect

Maximal subgroups

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

subgroupindex
#105937482
#105933962
C2×#637332
#105905842
#105900522
#19529