Finite Group Databasebeta

← #11798893

Subgroups — #11798893

Order 1152.

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

normal subgroups only

This group has 310 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
1C2×#63735C212yesmaximal, complemented
2C4×#3718C211yesmaximal, characteristic, complemented
3#10590352C211yesmaximal, characteristic
4C4⋊#3708C211yesmaximal, characteristic, complemented
5#10590061C212yesmaximal, complemented
6C3×#874—21no—
7C3×C4×Dic6—21no—
8C2×#3718C2211yescharacteristic
9C2×#3713—21no—
10C2×#3713C2212yes—
11C2×#3708C2212yes—
12#63735—24no—
13C4×C3⋊(C3⋊C8)C2211yescharacteristic
14#63576C2211yescharacteristic
15#63565—21no—
16#5073—61no—
17C4×#216—61no—
18C2×C3×D12—22no—
19C2×C3×D12—41no—
20C2×C3×D12—41no—
21C2×C3×Dic6—21no—
22C32×C42D411yescharacteristic
23C2×C3⋊(C3⋊C8)D411yescharacteristic
24C2×C3⋊(C3⋊C8)C2311yescharacteristic
25C3×C4⋊Dic3—21no—
26C3×Dic3⋊C4—41no—
27C3×C4×Dic3—41no—
28#3718—21no—
29#3718D412yescomplemented
30#3713—22no—
31#3713—22no—
32#3713—42no—
33#3708—22no—
34#2207—91nomaximal, Sylow
35C3×#127—61no—
36C3×C4×Q8—61no—
37C2×#216—61no—
38C2×#213—62no—
39C2×#213—62no—
40#874—21no—
41C4×Dic6—21no—
42#835—61no—
43#810—61no—
44#807—61no—
45C4×C3⋊C8—61no—
46C4×C3⋊C8—61no—
47C22×C3×D3—42no—
48C2×C32×C4D811yescharacteristic
49C2×C32×C4D811yescharacteristic
50C2×C32×C4C2×D411yescharacteristic
51C2×C3×Dic3—41no—
52C2×C3×Dic3—41no—
53C3×D12—42no—
54C3×D12—42no—
55C3×D12—82no—
56C3×D12—82no—
57C3×Dic6—22no—
58C3×Dic6—41no—
59C3⋊(C3⋊C8)—21no—
60C3⋊(C3⋊C8)C2×D411yescharacteristic
61C3⋊(C3⋊C8)#4111yescharacteristic
62C2×SD32—92no—
63#493—91no—
64C4×Q16—91no—
65C4⋊C16—91no—
66#357—92no—
67C2×C3×Q8—61no—
68C2×C3×D4—62no—
69C2×C3×D4—121no—
70C2×C3×D4—121no—
71C2×D12—22no—
72C2×D12—41no—
73C2×D12—41no—
74C2×Dic6—21no—
75C3×C4⋊C4—61no—
76C3×C4⋊C4—121no—
77C3×C42—21no—
78C3×C42—21no—
79C3×C42—121no—
80#216—62no—
81#216—62no—
82#213—122no—
83#213—122no—
84#213—124no—
85C4⋊Dic3—21no—
86Dic3⋊C4—41no—
87C4×Dic3—41no—
88C2×C3⋊C8—61no—
89C2×C3⋊C8—61no—
90C2×C3⋊C8—61no—
91C2×C3⋊C8—61no—
92C22×C32C2×D811yescharacteristic
93C2×C3×D3—82no—
94C2×C3×D3—82no—
95C2×C3×D3—82no—
96C32×C4—21no—
97C32×C4SD3212yescomplemented
98C32×C4#12111yescharacteristic
99C32×C4AGL(1,ℤ/8)11yescharacteristic
100C3×Dic3—42no—
101C3×Dic3—81no—
102C2×Q16—91no—
103C2×D8—92no—
104C2×D8—181no—
105#127—61no—
106C4×Q8—61no—
107SD32—184no—
108C2×C16—92no—
109#107—91no—
110#103—181no—
111C4×C8—91no—
112C23×C3—122no—
113C22×D3—42no—
114C3×Q8—62no—
115C3×Q8—121no—
116C3×D4—122no—
117C3×D4—122no—
118C3×D4—242no—
119C3×D4—242no—
120C2×C3×C4—21no—
121C2×C3×C4—21no—
122C2×C3×C4—21no—
123C2×C3×C4—21no—
124C2×C3×C4—21no—
125C2×C3×C4—21no—
126C2×C3×C4—121no—
127C2×C3×C4—121no—
128C2×Dic3—41no—
129C2×Dic3—41no—
130D12—42no—
131D12—42no—
132D12—82no—
133D12—82no—
134Dic6—22no—
135Dic6—41no—
136C3⋊C8—61no—
137C3⋊C8—61no—
138C3⋊C8—61no—
139C3⋊C8—61no—
140C3⋊C8—62no—
141C3⋊C8—121no—
142C2×C32#45911yescharacteristic
143C2×C32C2×SD3211yescharacteristic
144C2×C32#50911yescharacteristic
145C3×D3—162no—
146C2×Q8—61no—
147C2×D4—62no—
148C2×D4—121no—
149C2×D4—121no—
150Q16—92no—
151Q16—181no—
152D8—182no—
153D8—182no—
154D8—362no—
155C2×C8—91no—
156C2×C8—91no—
157C4⋊C4—61no—
158C4⋊C4—121no—
159C42—121no—
160C42GO+(4,𝔽2)11yescharacteristic
161C16—182no—
162C22×C3—21no—
163C22×C3—21no—
164C22×C3—242no—
165C22×C3—242no—
166C22×C3—242no—
167C2×D3—82no—
168C2×D3—82no—
169C2×D3—82no—
170C3×C4—22no—
171C3×C4—21no—
172C3×C4—21no—
173C3×C4—21no—
174C3×C4—21no—
175C3×C4—22no—
176C3×C4—22no—
177C3×C4—41no—
178C3×C4—122no—
179C3×C4—241no—
180Dic3—42no—
181Dic3—81no—
182C32#220711yescharacteristic, complemented, Sylow
183C23—122no—
184Q8—62no—
185Q8—121no—
186D4—122no—
187D4—122no—
188D4—242no—
189D4—242no—
190C2×C4—121no—
191C2×C4—121no—
192C2×C4#377411yescharacteristic
193C2×C4#377411yescharacteristic
194C2×C4C2×GO+(4,𝔽2)11yescharacteristic
195C8—91no—
196C8—91no—
197C8—181no—
198C2×C3—21no—
199C2×C3—21no—
200C2×C3—21no—
201C2×C3—21no—
202C2×C3—21no—
203C2×C3—21no—
204C2×C3—482no—
205D3—162no—
206C22—242no—
207C22—242no—
208C22—242no—
209C22C2×#377411yescharacteristic
210C4—21no—
211C4—122no—
212C4—241no—
213C4#6373512yescomplemented
214C4#6422411yescharacteristic
215C4#6423011yescharacteristic
216C3—21no—
217C3—21no—
218C2—482no—
219C2#1059333411yescharacteristic
220C2C2×#6373511yescharacteristic
221C2#1059341711yescharacteristic
subgroupG/H
centerC22C2×#3774
commutator, cosocleC2×C3⋊(C3⋊C8)C23
FrattiniC2×C4C2×GO+(4,𝔽2)
FittingC32×C42D4
socleC22×C32C2×D8
prime radical#10590352C2
hypercenterC42GO+(4,𝔽2)
hypocenterC32#2207
LCSG ▷ C2×C3⋊(C3⋊C8) ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42

Complements

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

NH ≅ G/Ntype
1. C2×#63735C2semidirect
2. C4×#3718C2semidirect
4. C4⋊#3708C2semidirect
5. #10590061C2semidirect
29. #3718D4semidirect
97. C32×C4SD32semidirect
182. C32#2207semidirect
213. C4#63735semidirect

Maximal subgroups

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

subgroupindex
C2×#637352
C4×#37182
#105903522
C4⋊#37082
#105900612
#22079