Finite Group Databasebeta

← #11798894

Subgroups — #11798894

Order 1152.

310 conjugacy classes of subgroups; only the 43 normal subgroups are shown.

normal subgroups only

This group has 310 conjugacy classes of subgroups — too many to draw. Only its 43 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
2#10590886C211yesmaximal, characteristic
3#10590790C211yesmaximal, characteristic, complemented
4#10590177C211yesmaximal, characteristic, complemented
5#10590061C212yesmaximal, complemented
6C2×C3×D24—21no—
7#63914—21no—
8#63843—21no—
9C2×#3718C2211yescharacteristic
10C2×#3713C2212yes—
11C2×#3708C2212yes—
12#63735—24no—
13C8×C3⋊Dic3C2211yescharacteristic
14C3×#816—21no—
15#63576C2211yescharacteristic
16#5151—61no—
17#4790—61no—
18C2×C3×D12—22no—
19C2×C3×Dic6—21no—
20C2×#625—41no—
21C2×#625—41no—
22C2×C32×C8D411yescharacteristic
23C4×C3⋊Dic3D411yescharacteristic
24C2×C3⋊(C3⋊C8)C2311yescharacteristic
25C3×C4⋊Dic3—21no—
26C3×D24—42no—
27Dic3⋊Dic3—41no—
28Dic32—41no—
29#3718—21no—
30#3718D412yescomplemented
31#3713—22no—
32#3713—22no—
33#3708—22no—
34#2207—91nomaximal, Sylow
35C2×C3×D8—61no—
36Q8×Dic3—61no—
37C2×#216—61no—
38#940—62no—
39C2×#213—62no—
40C2×D24—21no—
41#887—61no—
42C3×#103—61no—
43#816—21no—
44C8×Dic3—61no—
45C8×Dic3—61no—
46#807—61no—
47C22×C3×D3—42no—
48C2×C32×C4C2×D411yescharacteristic
49C2×C3⋊Dic3D811yescharacteristic
50C2×C3⋊Dic3D811yescharacteristic
51C2×C3×Dic3—41no—
52C2×C3×Dic3—41no—
53C3×D12—42no—
54C3×D12—42no—
55C3×Dic6—22no—
56C3×Dic6—41no—
57#625—82no—
58#625—82no—
59C32×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×#67—122no—
70C2×#67—122no—
71C2×D12—22no—
72C2×Dic6—21no—
73C3×D8—122no—
74C2×C3×C8—21no—
75C2×C3×C8—21no—
76C3×C4⋊C4—61no—
77#216—62no—
78#216—62no—
79#213—122no—
80#213—122no—
81C4⋊Dic3—21no—
82C4⋊Dic3—121no—
83Dic3⋊C4—121no—
84C4×Dic3—61no—
85C4×Dic3—61no—
86C4×Dic3—121no—
87C4×Dic3—121no—
88C2×C3⋊C8—61no—
89C2×C3⋊C8—61no—
90D24—42no—
91C22×C32C2×D811yescharacteristic
92C2×C3×D3—82no—
93C2×C3×D3—82no—
94C2×C3×D3—82no—
95C32×C4#12111yescharacteristic
96C32×C4AGL(1,ℤ/8)11yescharacteristic
97C3⋊Dic3—21no—
98C3⋊Dic3SD3212yescomplemented
99C3×Dic3—42no—
100C3×Dic3—81no—
101C2×Q16—91no—
102C2×D8—61no—
103C2×D8—92no—
104#127—181no—
105C4×Q8—181no—
106SD32—184no—
107C2×C16—92no—
108#107—91no—
109#103—61no—
110C4×C8—91no—
111C23×C3—122no—
112C22×D3—42no—
113C3×Q8—62no—
114C3×Q8—121no—
115C3×D4—122no—
116C3×D4—122no—
117C2×C3×C4—21no—
118C2×C3×C4—21no—
119C2×C3×C4—121no—
120C2×C3×C4—121no—
121#67—244no—
122#67—244no—
123C2×Dic3—41no—
124C2×Dic3—41no—
125C2×Dic3—61no—
126C2×Dic3—61no—
127C2×Dic3—61no—
128C2×Dic3—61no—
129D12—42no—
130D12—42no—
131Dic6—22no—
132Dic6—41no—
133C3×C8—22no—
134C3×C8—41no—
135C3⋊C8—61no—
136C3⋊C8—61no—
137C3⋊C8—61no—
138C3⋊C8—61no—
139C2×C32#45911yescharacteristic
140C2×C32C2×SD3211yescharacteristic
141C2×C32#50911yescharacteristic
142C3×D3—162no—
143C2×Q8—61no—
144C2×D4—62no—
145C2×D4—361no—
146C2×D4—361no—
147Q16—92no—
148Q16—181no—
149D8—122no—
150D8—182no—
151D8—182no—
152C2×C8—91no—
153C2×C8GO+(4,𝔽2)11yescharacteristic
154C4⋊C4—61no—
155C4⋊C4—361no—
156C42—91no—
157C42—361no—
158C16—182no—
159C22×C3—21no—
160C22×C3—21no—
161C22×C3—242no—
162C22×C3—242no—
163C22×C3—242no—
164C2×D3—82no—
165C2×D3—82no—
166C2×D3—82no—
167C3×C4—21no—
168C3×C4—21no—
169C3×C4—21no—
170C3×C4—21no—
171C3×C4—122no—
172C3×C4—241no—
173Dic3—42no—
174Dic3—62no—
175Dic3—62no—
176Dic3—62no—
177Dic3—81no—
178Dic3—121no—
179C32#220711yescharacteristic, complemented, Sylow
180C23—122no—
181Q8—62no—
182Q8—121no—
183D4—122no—
184D4—122no—
185D4—722no—
186D4—722no—
187C2×C4—91no—
188C2×C4—91no—
189C2×C4—121no—
190C2×C4—121no—
191C2×C4C2×GO+(4,𝔽2)11yescharacteristic
192C8—21no—
193C8—91no—
194C8—91no—
195C2×C3—21no—
196C2×C3—21no—
197C2×C3—21no—
198C2×C3—21no—
199C2×C3—21no—
200C2×C3—21no—
201C2×C3—482no—
202D3—162no—
203C22—242no—
204C22—242no—
205C22—242no—
206C22#6422511yescharacteristic
207C4—92no—
208C4—122no—
209C4—181no—
210C4—241no—
211C4#6423011yescharacteristic
212C4#6423611yescharacteristic
213C3—21no—
214C3—21no—
215C2—482no—
216C2#1059327711yescharacteristic
217C2#1059327811yescharacteristic
218C2#1059342611yescharacteristic
subgroupG/H
centerC22#64225
commutator, cosocleC2×C3⋊(C3⋊C8)C23
FrattiniC2×C4C2×GO+(4,𝔽2)
FittingC2×C32×C8D4
socleC22×C32C2×D8
prime radical#10590886C2
hypercenterC2×C8GO+(4,𝔽2)
hypocenterC32#2207
LCSG ▷ C2×C3⋊(C3⋊C8) ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8

Complements

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

NH ≅ G/Ntype
1. C2×#63735C2semidirect
3. #10590790C2semidirect
4. #10590177C2semidirect
5. #10590061C2semidirect
30. #3718D4semidirect
98. C3⋊Dic3SD32semidirect
179. C32#2207semidirect

Maximal subgroups

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

subgroupindex
C2×#637352
#105908862
#105907902
#105901772
#105900612
#22079