Finite Group Databasebeta

← #11800033

Subgroups — #11800033

Order 1152.

230 conjugacy classes of subgroups; only the 35 normal subgroups are shown.

normal subgroups only

This group has 230 conjugacy classes of subgroups — too many to draw. Only its 35 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#10590914C211yesmaximal, characteristic
2#10590856C211yesmaximal, characteristic
3#10590180C211yesmaximal, characteristic
4#10590067C212yesmaximal, complemented
5#10590066C212yesmaximal, complemented
6C2×#3743C2211yescharacteristic
7#63871—21no—
8C2×#3718C2211yescharacteristic
9#63818—21no—
10#63773C2212yes—
11C3×#819—21no—
12C3×#816—21no—
13#63578C2212yes—
14#63574C2211yescharacteristic
15#4893—61no—
16#4816—61no—
17C2×C4×C3⋊D3D411yescharacteristic
18C2×C3×Dic6—21no—
19C2×C32×C8D411yescharacteristic
20C2×C3⋊(C3⋊C8)C2311yescharacteristic
21#3743—22no—
22C3×C4⋊Dic3—21no—
23C3×#208—22no—
24Dic3⋊Dic3—41no—
25#3722—41no—
26#3718—22no—
27#3712—41no—
28#3710—41no—
29#3708—22no—
30#2239—91nomaximal, Sylow
31#946—61no—
32C2×#216—61no—
33D3×M16—62no—
34C2×ΓL(1,𝔽25)—61no—
35C2×ΓL(1,𝔽25)—61no—
36#897—61no—
37C3×#108—61no—
38C3×#103—61no—
39#822—62no—
40#819—21no—
41#816—21no—
42#808—61no—
43C22×C3⋊D3SD1611yescharacteristic
44C2×C32×C4C2×D411yescharacteristic
45C2×C3⋊Dic3SD1611yescharacteristic
46C4×C3⋊D3—21no—
47C4×C3⋊D3—21no—
48C2×C3×Dic3—41no—
49C2×C3×Dic3—41no—
50C3×Dic6—41no—
51C3×Dic6—41no—
52C32×C8—21no—
53C3⋊(C3⋊C8)#4112yes—
54C3×C3⋊C8—42no—
55#470—91no—
56#430—91no—
57#365—92no—
58#362—92no—
59#349—91no—
60C2×C3×Q8—61no—
61C2×C4×D3—61no—
62C2×C4×D3—61no—
63C2×Dic6—21no—
64C3×M16—62no—
65C2×C3×C8—21no—
66C2×C3×C8—21no—
67C3×C4⋊C4—61no—
68#216—122no—
69(C2×D3)⋊C4—121no—
70(C2×D3)⋊C4—121no—
71C4⋊Dic3—21no—
72C4⋊Dic3—121no—
73Dic3⋊C4—121no—
74#208—22no—
75C2×C3⋊C8—61no—
76C2×C3⋊C8—61no—
77ΓL(1,𝔽25)—64no—
78ΓL(1,𝔽25)—122no—
79ΓL(1,𝔽25)—122no—
80D3×C8—122no—
81C22×C32C2×SD1611yescharacteristic
82C2×C3⋊D3—21no—
83C2×C3⋊D3—41no—
84C32×C4#12311yescharacteristic
85C32×C4AGL(1,ℤ/8)11yescharacteristic
86C3⋊Dic3—21no—
87C3×Dic3—81no—
88C3×Dic3—81no—
89C2×Q16—91no—
90C2×M16—91no—
91C2×M16—181no—
92C22⋊Q8—181no—
93M32—92no—
94#108—61no—
95#108—92no—
96#106—91no—
97#103—61no—
98C22×D3—61no—
99C22×D3—61no—
100C3×Q8—121no—
101C3×Q8—121no—
102C2×C3×C4—21no—
103C2×C3×C4—21no—
104C2×C3×C4—121no—
105C2×C3×C4—121no—
106C2×Dic3—41no—
107C2×Dic3—41no—
108C2×Dic3—61no—
109C2×Dic3—61no—
110C4×D3—62no—
111C4×D3—62no—
112C4×D3—121no—
113C4×D3—121no—
114Dic6—41no—
115Dic6—41no—
116C3×C8—22no—
117C3×C8—41no—
118C3×C8—122no—
119C3⋊C8—42no—
120C3⋊C8—62no—
121C3⋊C8—62no—
122C2×C32—21no—
123C2×C32#48111yescharacteristic
124C3⋊D3—41no—
125C2×Q8—61no—
126C22×C4—91no—
127Q16—182no—
128M16—62no—
129M16—182no—
130M16—361no—
131C2×C8—91no—
132C2×C8—361no—
133C2×C8GO+(4,𝔽2)11yescharacteristic
134C4⋊C4—61no—
135C4⋊C4—361no—
136C22⋊C4—361no—
137C16—182no—
138C22×C3—21no—
139C22×C3—21no—
140C2×D3—62no—
141C2×D3—121no—
142C2×D3—121no—
143C2×D3—121no—
144C2×D3—241no—
145C3×C4—21no—
146C3×C4—21no—
147C3×C4—21no—
148C3×C4—21no—
149C3×C4—241no—
150C3×C4—241no—
151Dic3—62no—
152Dic3—81no—
153Dic3—81no—
154Dic3—121no—
155C32#223911yescharacteristic, complemented, Sylow
156C23—91no—
157Q8—121no—
158Q8—121no—
159C2×C4—91no—
160C2×C4—121no—
161C2×C4—121no—
162C2×C4—181no—
163C2×C4—181no—
164C2×C4C2×GO+(4,𝔽2)11yescharacteristic
165C8—21no—
166C8—92no—
167C8—122no—
168C2×C3—21no—
169C2×C3—21no—
170C2×C3—21no—
171C2×C3—21no—
172C2×C3—41no—
173D3—122no—
174D3—241no—
175C22—181no—
176C22—361no—
177C22#6422711yescharacteristic
178C4—181no—
179C4—241no—
180C4—241no—
181C4#6422411yescharacteristic
182C4#6423311yescharacteristic
183C3—21no—
184C3—21no—
185C2—21no—
186C2—361no—
187C2#1059336111yescharacteristic
subgroupG/H
centerC2#10593361
commutator, cosocleC2×C3⋊(C3⋊C8)C23
FrattiniC2×C4C2×GO+(4,𝔽2)
FittingC2×C32×C8D4
socleC2×C32#481
prime radicalC22×C3⋊D3SD16
hypercenterC2×C8GO+(4,𝔽2)
hypocenterC32#2239
LCSG ▷ C2×C3⋊(C3⋊C8) ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8

Complements

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

NH ≅ G/Ntype
4. #10590067C2semidirect
5. #10590066C2semidirect
155. C32#2239semidirect

Maximal subgroups

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

subgroupindex
#105909142
#105908562
#105901802
#105900672
#105900662
#22399