Finite Group Databasebeta

← #11800001

Subgroups — #11800001

Order 1152.

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

normal subgroups only

This group has 250 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, complemented
2#10590840C211yesmaximal, characteristic
3#10590180C211yesmaximal, characteristic, complemented
4#10590067C212yesmaximal, complemented
5#10590065C212yesmaximal, complemented
6C2×#3743C2211yescharacteristic
7#63916—21no—
8C2×#3713C2211yescharacteristic
9#63818—21no—
10#63773C2212yes—
11C3×#821—21no—
12C3×#819—21no—
13#63578C2212yes—
14#63574C2211yescharacteristic
15#4893—61no—
16#4782—61no—
17C2×C4×C3⋊D3D411yescharacteristic
18C2×C3×D12—21no—
19C2×#626—41no—
20C2×C32×C8D411yescharacteristic
21C2×C3⋊(C3⋊C8)C2311yescharacteristic
22#3743—22no—
23C3×C4⋊Dic3—21no—
24C3×#208—22no—
25(C2×D3)⋊Dic3—41no—
26#3713—22no—
27#3712—41no—
28#3710—41no—
29#3708—22no—
30#2238—91nomaximal, Sylow
31#938—61no—
32C2×#213—61no—
33D3×M16—62no—
34C2×ΓL(1,𝔽25)—61no—
35C2×ΓL(1,𝔽25)—61no—
36#895—61no—
37C3×#108—61no—
38C3×#102—61no—
39#822—62no—
40#821—21no—
41#819—21no—
42#808—61no—
43C22×C3⋊D3SD1611yescharacteristic
44C22×C3×D3—41no—
45C2×C32×C4C2×D411yescharacteristic
46C2×C3⋊Dic3SD1611yescharacteristic
47C4×C3⋊D3—21no—
48C4×C3⋊D3—21no—
49C2×C3×Dic3—41no—
50C3×D12—41no—
51C3×D12—41no—
52#626—82no—
53C32×C8—21no—
54C3⋊(C3⋊C8)#4112yes—
55C3×C3⋊C8—42no—
56#469—91no—
57#430—91no—
58#365—92no—
59#361—92no—
60#349—91no—
61C2×C3×D4—61no—
62C2×#67—121no—
63C2×D12—21no—
64C2×D12—121no—
65C2×C4×D3—61no—
66C2×C4×D3—61no—
67C3×M16—62no—
68C2×C3×C8—21no—
69C2×C3×C8—21no—
70C3×C4⋊C4—61no—
71#217—121no—
72#213—122no—
73(C2×D3)⋊C4—121no—
74C4⋊Dic3—21no—
75#208—22no—
76C2×C3⋊C8—61no—
77C2×C3⋊C8—61no—
78ΓL(1,𝔽25)—64no—
79ΓL(1,𝔽25)—122no—
80ΓL(1,𝔽25)—122no—
81D3×C8—122no—
82C22×C32C2×SD1611yescharacteristic
83C2×C3⋊D3—21no—
84C2×C3⋊D3—41no—
85C2×C3×D3—81no—
86C2×C3×D3—81no—
87C2×C3×D3—81no—
88C32×C4#12311yescharacteristic
89C32×C4AGL(1,ℤ/8)11yescharacteristic
90C3⋊Dic3—21no—
91C3×Dic3—81no—
92C2×D8—91no—
93C2×M16—91no—
94C2×M16—181no—
95#121—181no—
96M32—92no—
97#108—61no—
98#108—92no—
99#106—91no—
100#102—61no—
101C23×C3—121no—
102C22×D3—41no—
103C22×D3—61no—
104C22×D3—61no—
105C3×D4—121no—
106C3×D4—121no—
107C2×C3×C4—21no—
108C2×C3×C4—21no—
109C2×C3×C4—121no—
110#67—242no—
111C2×Dic3—41no—
112C2×Dic3—61no—
113C2×Dic3—61no—
114D12—41no—
115D12—41no—
116D12—242no—
117C4×D3—62no—
118C4×D3—62no—
119C4×D3—121no—
120C4×D3—121no—
121C3×C8—22no—
122C3×C8—41no—
123C3×C8—122no—
124C3⋊C8—42no—
125C3⋊C8—62no—
126C3⋊C8—62no—
127C2×C32—21no—
128C2×C32#48111yescharacteristic
129C3⋊D3—41no—
130C3×D3—161no—
131C2×D4—61no—
132C2×D4—361no—
133C22×C4—91no—
134D8—182no—
135M16—62no—
136M16—182no—
137M16—361no—
138C2×C8—91no—
139C2×C8—361no—
140C2×C8GO+(4,𝔽2)11yescharacteristic
141C4⋊C4—61no—
142C22⋊C4—361no—
143C16—182no—
144C22×C3—21no—
145C22×C3—21no—
146C22×C3—241no—
147C22×C3—241no—
148C22×C3—241no—
149C2×D3—62no—
150C2×D3—81no—
151C2×D3—81no—
152C2×D3—81no—
153C2×D3—121no—
154C2×D3—121no—
155C2×D3—121no—
156C2×D3—241no—
157C3×C4—21no—
158C3×C4—21no—
159C3×C4—21no—
160C3×C4—21no—
161C3×C4—241no—
162Dic3—62no—
163Dic3—81no—
164Dic3—121no—
165C32#223811yescharacteristic, complemented, Sylow
166C23—91no—
167C23—121no—
168D4—121no—
169D4—121no—
170D4—722no—
171C2×C4—91no—
172C2×C4—121no—
173C2×C4—181no—
174C2×C4—181no—
175C2×C4C2×GO+(4,𝔽2)11yescharacteristic
176C8—21no—
177C8—92no—
178C8—122no—
179C2×C3—21no—
180C2×C3—21no—
181C2×C3—21no—
182C2×C3—21no—
183C2×C3—41no—
184C2×C3—481no—
185D3—122no—
186D3—161no—
187D3—241no—
188C22—181no—
189C22—241no—
190C22—241no—
191C22—241no—
192C22—361no—
193C22#6422711yescharacteristic
194C4—181no—
195C4—241no—
196C4#6422411yescharacteristic
197C4#6423311yescharacteristic
198C3—21no—
199C3—21no—
200C2—21no—
201C2—361no—
202C2—481no—
203C2#1059336111yescharacteristic
subgroupG/H
centerC2#10593361
commutator, cosocleC2×C3⋊(C3⋊C8)C23
FrattiniC2×C4C2×GO+(4,𝔽2)
FittingC2×C32×C8D4
socleC2×C32#481
prime radical#10590840C2
hypercenterC2×C8GO+(4,𝔽2)
hypocenterC32#2238
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
1. #10590914C2semidirect
3. #10590180C2semidirect
4. #10590067C2semidirect
5. #10590065C2semidirect
165. C32#2238semidirect

Maximal subgroups

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

subgroupindex
#105909142
#105908402
#105901802
#105900672
#105900652
#22389