Finite Group Databasebeta

← #11780228

Subgroups — #11780228

Order 1152.

600 conjugacy classes of subgroups; only the 129 normal subgroups are shown.

normal subgroups only

This group has 600 conjugacy classes of subgroups — too many to draw. Only its 129 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#10596055C211yesmaximal, characteristic
2C32×#475C211yesmaximal, characteristic, complemented
3#10592782C211yesmaximal, characteristic
4#10592777C211yesmaximal, characteristic, complemented
5#10589401C211yesmaximal, characteristic, complemented
6#10589352C211yesmaximal, characteristic, complemented
7#10589349C211yesmaximal, characteristic
8#71126—34nomaximal
9C32×C4⋊Q8C2211yescharacteristic
10C32×C4×Q8C2211yescharacteristic
11#64155—21no—
12C2×#3755—21no—
13#64107—22no—
14#64101—21no—
15#64084—21no—
16C4×C4⋊(C3⋊D3)C2211yescharacteristic
17#64078C2211yescharacteristic
18C4×#634—21no—
19C32×#106—21no—
20C32×C4⋊C8C2211yescharacteristic
21C32×#103—21no—
22#63662—21no—
23#63634—22no—
24C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
25C4×C3⋊(C3⋊C8)C2211yescharacteristic
26#5584—34no—
27C3×#475D314yescomplemented
28#5083—34no—
29#5078—34no—
30#4535—34no—
31#4486—34no—
32#4483—34no—
33C2×C32×Q8—21no—
34C2×C32×Q8D411yescharacteristic
35C2×C4⋊(C3⋊D3)D411yescharacteristic
36C2×C4×C3⋊D3—21no—
37C2×#634—21no—
38C2×C32×C8—21no—
39C32×C4⋊C4—21no—
40C32×C4⋊C4—21no—
41C32×C4⋊C4—21no—
42C32×C4⋊C4D411yescharacteristic
43C32×C42—21no—
44C32×C42C2311yescharacteristic
45#3755—42no—
46#3752—22no—
47#3752—22no—
48#3752—21no—
49C4⋊(C3⋊Dic3)—21no—
50C4⋊(C3⋊Dic3)D411yescharacteristic
51C4⋊(C3⋊Dic3)D412yes—
52#3750—22no—
53C4×C3⋊Dic3—22no—
54C2×C3⋊(C3⋊C8)—21no—
55C2×C3⋊(C3⋊C8)—21no—
56#1650—91noSylow
57C3×C4⋊Q8C2×D314yes—
58C3×C4×Q8C2×D314yes—
59#946—64no—
60C2×#215—64no—
61#898—68no—
62#892—64no—
63#875—64no—
64C4×D12—34no—
65#869—34no—
66C4×Dic6—64no—
67C3×#106—24no—
68C3×C4⋊C8C2×D314yes—
69C3×#103—24no—
70#835—64no—
71#807—68no—
72C4⋊(C3⋊C8)—34no—
73C4×C3⋊C8—34no—
74C22×C3⋊D3—21no—
75C32×Q8—21no—
76C32×Q8—21no—
77C32×Q8—41no—
78C32×Q8—41no—
79C2×C32×C4—21no—
80C2×C32×C4—21no—
81C2×C32×C4—41no—
82C2×C32×C4C2×D411yescharacteristic
83C2×C32×C4C2×D411yescharacteristic
84C2×C32×C4C2×D411yescharacteristic
85C2×C3⋊Dic3—21no—
86C2×C3⋊Dic3—22no—
87C4⋊(C3⋊D3)—21no—
88C4⋊(C3⋊D3)—21no—
89C4×C3⋊D3—41no—
90C4×C3⋊D3—41no—
91#634—41no—
92#634—41no—
93C32×C8—41no—
94C3⋊(C3⋊C8)—22no—
95C3⋊(C3⋊C8)—41no—
96#556—91no—
97#500—91no—
98#475C3⋊D311yescharacteristic, complemented
99#461—91no—
100#332—91no—
101Q8⋊C8—91no—
102D4⋊C8—91no—
103C2×C3×Q8—24no—
104C2×C3×Q8#6714yes—
105C2×D12—34no—
106C2×C4×D3—64no—
107C2×Dic6—64no—
108C2×C3×C8—24no—
109C3×C4⋊C4—24no—
110C3×C4⋊C4—24no—
111C3×C4⋊C4—24no—
112C3×C4⋊C4#6714yes—
113C3×C42—24no—
114C3×C42C22×D314yes—
115#215—128no—
116(C2×D3)⋊C4—68no—
117(C2×D3)⋊C4—68no—
118(C2×D3)⋊C4—64no—
119C4⋊Dic3—38no—
120C4⋊Dic3—34no—
121C4⋊Dic3—64no—
122Dic3⋊C4—68no—
123C4×Dic3—68no—
124C2×C3⋊C8—64no—
125C2×C3⋊C8—64no—
126C22×C32#12011yescharacteristic
127C2×C3⋊D3—41no—
128C2×C3⋊D3—41no—
129C2×C3⋊D3—41no—
130C32×C4—21no—
131C32×C4—41no—
132C32×C4—41no—
133C32×C4—81no—
134C32×C4#13511yescharacteristic
135C32×C4#13511yescharacteristic
136C32×C4AGL(1,ℤ/8)11yescharacteristic
137C32×C4#13711yescharacteristic
138C3⋊Dic3—42no—
139C3⋊Dic3—41no—
140C2×SD16—181no—
141C4⋊Q8—91no—
142C4⋊Q8C2×C3⋊D311yescharacteristic
143#126—182no—
144#124—181no—
145C22⋊Q8—181no—
146C4×Q8—181no—
147C4×Q8C2×C3⋊D311yescharacteristic
148C4×D4—91no—
149#117—181no—
150#107—182no—
151#106—21no—
152C4⋊C8—91no—
153C4⋊C8C2×C3⋊D311yescharacteristic
154#103—21no—
155#103—181no—
156C4×C8—91no—
157C22×D3—64no—
158C3×Q8—24no—
159C3×Q8—24no—
160C3×Q8—44no—
161C3×Q8—44no—
162C2×C3×C4—24no—
163C2×C3×C4—24no—
164C2×C3×C4—44no—
165C2×C3×C4D3×D414yes—
166C2×C3×C4D3×D414yes—
167C2×C3×C4C2×#6714yes—
168C2×Dic3—64no—
169C2×Dic3—68no—
170D12—64no—
171D12—64no—
172C4×D3—124no—
173C4×D3—124no—
174Dic6—124no—
175Dic6—124no—
176C3×C8—44no—
177C3⋊C8—68no—
178C3⋊C8—124no—
179C2×C32#44911yescharacteristic
180C2×C32#45211yescharacteristic
181C2×C32#45611yescharacteristic
182C3⋊D3—81no—
183C2×Q8—21no—
184C2×Q8—181no—
185C2×Q8#63811yescharacteristic
186C2×D4—91no—
187C22×C4—181no—
188SD16—362no—
189C2×C8—21no—
190C2×C8—181no—
191C2×C8—181no—
192C4⋊C4—21no—
193C4⋊C4—21no—
194C4⋊C4—21no—
195C4⋊C4—91no—
196C4⋊C4—92no—
197C4⋊C4—182no—
198C4⋊C4—181no—
199C4⋊C4#63811yescharacteristic
200C22⋊C4—182no—
201C22⋊C4—182no—
202C22⋊C4—181no—
203C42—21no—
204C42—182no—
205C42C22×C3⋊D311yescharacteristic
206C22×C3#93714yes—
207C2×D3—124no—
208C2×D3—124no—
209C2×D3—124no—
210C3×C4—24no—
211C3×C4—44no—
212C3×C4—44no—
213C3×C4—84no—
214C3×C4#91414yes—
215C3×C4#91614yes—
216C3×C4#94214yes—
217C3×C4#95014yes—
218Dic3—128no—
219Dic3—124no—
220C32#165011yescharacteristic, complemented, Sylow
221C23—181no—
222Q8—21no—
223Q8—21no—
224Q8—41no—
225Q8—41no—
226Q8—361no—
227Q8—361no—
228D4—181no—
229D4—181no—
230C2×C4—21no—
231C2×C4—21no—
232C2×C4—41no—
233C2×C4—181no—
234C2×C4—182no—
235C2×C4—361no—
236C2×C4—361no—
237C2×C4D4×C3⋊D311yescharacteristic
238C2×C4D4×C3⋊D311yescharacteristic
239C2×C4C2×#63811yescharacteristic
240C8—41no—
241C8—182no—
242C8—361no—
243C2×C3#504714yes—
244C2×C3#517214yes—
245C2×C3#520514yes—
246D3—244no—
247C22—361no—
248C22—361no—
249C22—361no—
250C22#6414611yescharacteristic
251C4—21no—
252C4—41no—
253C4—41no—
254C4—81no—
255C4—362no—
256C4—361no—
257C4#6412311yescharacteristic
258C4#6412511yescharacteristic
259C4#6415111yescharacteristic
260C4#6415911yescharacteristic
261C3#7112614yescomplemented
262C2—721no—
263C2#1059274611yescharacteristic
264C2#1059287111yescharacteristic
265C2#1059290411yescharacteristic
subgroupG/H
centerC22#64146
commutator, cosocleC32×C42C23
FrattiniC42C22×C3⋊D3
FittingC32×#475C2
socleC22×C32#120
prime radicalC2×C4⋊(C3⋊D3)D4
hypercenter#475C3⋊D3
hypocenterC32#1650
LCSG ▷ C32×C42 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ #475

Complements

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

NH ≅ G/Ntype
2. C32×#475C2semidirect
4. #10592777C2semidirect
5. #10589401C2semidirect
6. #10589352C2semidirect
27. C3×#475D3semidirect
98. #475C3⋊D3semidirect
220. C32#1650semidirect
261. C3#71126semidirect

Maximal subgroups

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

subgroupindex
#105960552
C32×#4752
#105927822
#105927772
#105894012
#105893522
#105893492
#711263