Finite Group Databasebeta

← #11779752

Subgroups — #11779752

Order 1152.

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

normal subgroups only

This group has 636 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#10596056C211yesmaximal, characteristic
2C32×#462C211yesmaximal, characteristic, complemented
3#10592793C211yesmaximal, characteristic, complemented
4#10592787C211yesmaximal, characteristic
5#10589401C211yesmaximal, characteristic, complemented
6#10589351C211yesmaximal, characteristic
7#10589350C211yesmaximal, characteristic, complemented
8#71060—34nomaximal
9C2×C32×Q16—21no—
10C32×C4⋊Q8C2211yescharacteristic
11C32×C4×Q8C2211yescharacteristic
12#64156—21no—
13#64103—22no—
14#64102—21no—
15#64084—21no—
16#64083C2211yescharacteristic
17C4×C4⋊(C3⋊D3)—21no—
18C4×#634C2211yescharacteristic
19C32×C4⋊C8C2211yescharacteristic
20C32×#103—21no—
21#63637—21no—
22#63636—22no—
23#63635—21no—
24C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
25C4×C3⋊(C3⋊C8)C2211yescharacteristic
26#5585—34no—
27C3×#462D314yescomplemented
28#5094—34no—
29#5088—34no—
30#4535—34no—
31#4485—34no—
32#4484—34no—
33C2×C32×Q8—21no—
34C2×C32×Q8D411yescharacteristic
35C2×C4⋊(C3⋊D3)—21no—
36C2×C4⋊(C3⋊D3)—21no—
37C2×C4⋊(C3⋊D3)D412yes—
38C2×C4×C3⋊D3—22no—
39C2×#634D411yescharacteristic
40C32×Q16—42no—
41C2×C32×C8—21no—
42C32×C4⋊C4—21no—
43C32×C4⋊C4—21no—
44C32×C4⋊C4—21no—
45C32×C4⋊C4D411yescharacteristic
46C32×C42—21no—
47C32×C42C2311yescharacteristic
48#3752—22no—
49#3752—22no—
50#3752—22no—
51C4⋊(C3⋊Dic3)D411yescharacteristic
52#3750—21no—
53C4×C3⋊Dic3—21no—
54C2×C3⋊(C3⋊C8)—21no—
55C2×C3⋊(C3⋊C8)—21no—
56#1640—91noSylow
57C2×C3×Q16—24no—
58C3×C4⋊Q8C2×D314yes—
59C3×C4×Q8C2×D314yes—
60#947—64no—
61#894—68no—
62#893—64no—
63#875—64no—
64#874—34no—
65C4×D12—64no—
66C4×Dic6—34no—
67C3×C4⋊C8C2×D314yes—
68C3×#103—24no—
69#810—64no—
70#809—68no—
71#808—64no—
72C4⋊(C3⋊C8)—34no—
73C4×C3⋊C8—34no—
74C22×C3⋊D3—22no—
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—21no—
87C4⋊(C3⋊D3)—42no—
88C4⋊(C3⋊D3)—41no—
89C4⋊(C3⋊D3)—41no—
90C4⋊(C3⋊D3)—41no—
91C4⋊(C3⋊D3)—41no—
92C4×C3⋊D3—82no—
93#634—21no—
94#634—21no—
95C32×C8—41no—
96C3⋊(C3⋊C8)—41no—
97C3⋊(C3⋊C8)—41no—
98#559—91no—
99#486—91no—
100#475—91no—
101#462C3⋊D311yescharacteristic, complemented
102#331—91no—
103Q8⋊C8—91no—
104Q8⋊C8—91no—
105C2×C3×Q8—24no—
106C2×C3×Q8#6714yes—
107C2×D12—38no—
108C2×D12—64no—
109C2×D12—64no—
110C2×C4×D3—68no—
111C2×Dic6—34no—
112C3×Q16—48no—
113C2×C3×C8—24no—
114C3×C4⋊C4—24no—
115C3×C4⋊C4—24no—
116C3×C4⋊C4—24no—
117C3×C4⋊C4#6714yes—
118C3×C42—24no—
119C3×C42C22×D314yes—
120(C2×D3)⋊C4—68no—
121(C2×D3)⋊C4—68no—
122(C2×D3)⋊C4—68no—
123C4⋊Dic3—34no—
124Dic3⋊C4—64no—
125C4×Dic3—64no—
126C2×C3⋊C8—64no—
127C2×C3⋊C8—64no—
128C22×C32#12011yescharacteristic
129C2×C3⋊D3—42no—
130C2×C3⋊D3—42no—
131C2×C3⋊D3—42no—
132C32×C4—21no—
133C32×C4—41no—
134C32×C4—41no—
135C32×C4—81no—
136C32×C4#13511yescharacteristic
137C32×C4#13511yescharacteristic
138C32×C4AGL(1,ℤ/8)11yescharacteristic
139C32×C4#13711yescharacteristic
140C3⋊Dic3—41no—
141C3⋊Dic3—41no—
142C2×Q16—21no—
143C4⋊Q8C2×C3⋊D311yescharacteristic
144#127—91no—
145#124—181no—
146#124—181no—
147#123—182no—
148C4×Q8—91no—
149C4×Q8C2×C3⋊D311yescharacteristic
150C4×D4—181no—
151C4×D4—181no—
152#106—181no—
153C4⋊C8—91no—
154C4⋊C8C2×C3⋊D311yescharacteristic
155#103—21no—
156#103—181no—
157#102—182no—
158C4×C8—91no—
159C22×D3—68no—
160C3×Q8—24no—
161C3×Q8—24no—
162C3×Q8—44no—
163C3×Q8—44no—
164C2×C3×C4—24no—
165C2×C3×C4—24no—
166C2×C3×C4—44no—
167C2×C3×C4D3×D414yes—
168C2×C3×C4D3×D414yes—
169C2×C3×C4C2×#6714yes—
170C2×Dic3—64no—
171C2×Dic3—64no—
172D12—128no—
173D12—124no—
174D12—124no—
175D12—124no—
176D12—124no—
177C4×D3—248no—
178Dic6—64no—
179Dic6—64no—
180C3×C8—44no—
181C3⋊C8—124no—
182C3⋊C8—124no—
183C2×C32#44911yescharacteristic
184C2×C32#45211yescharacteristic
185C2×C32#45511yescharacteristic
186C3⋊D3—82no—
187C2×Q8—21no—
188C2×Q8—91no—
189C2×Q8#63811yescharacteristic
190C2×D4—92no—
191C2×D4—181no—
192C2×D4—181no—
193C22×C4—182no—
194Q16—42no—
195C2×C8—21no—
196C2×C8—181no—
197C2×C8—181no—
198C4⋊C4—21no—
199C4⋊C4—21no—
200C4⋊C4—21no—
201C4⋊C4—91no—
202C4⋊C4—181no—
203C4⋊C4#63811yescharacteristic
204C22⋊C4—182no—
205C22⋊C4—182no—
206C22⋊C4—182no—
207C42—21no—
208C42—181no—
209C42C22×C3⋊D311yescharacteristic
210C22×C3#93714yes—
211C2×D3—128no—
212C2×D3—128no—
213C2×D3—128no—
214C3×C4—24no—
215C3×C4—44no—
216C3×C4—44no—
217C3×C4—84no—
218C3×C4#91814yes—
219C3×C4#91914yes—
220C3×C4#93214yes—
221C3×C4#95014yes—
222Dic3—124no—
223Dic3—124no—
224C32#164011yescharacteristic, complemented, Sylow
225C23—182no—
226Q8—21no—
227Q8—21no—
228Q8—41no—
229Q8—41no—
230Q8—181no—
231Q8—181no—
232D4—362no—
233D4—361no—
234D4—361no—
235D4—361no—
236D4—361no—
237C2×C4—21no—
238C2×C4—21no—
239C2×C4—41no—
240C2×C4—181no—
241C2×C4—181no—
242C2×C4—722no—
243C2×C4D4×C3⋊D311yescharacteristic
244C2×C4D4×C3⋊D311yescharacteristic
245C2×C4C2×#63811yescharacteristic
246C8—41no—
247C8—361no—
248C8—361no—
249C2×C3#503714yes—
250C2×C3#518714yes—
251C2×C3#520214yes—
252D3—248no—
253C22—362no—
254C22—362no—
255C22—362no—
256C22#6414611yescharacteristic
257C4—21no—
258C4—41no—
259C4—41no—
260C4—81no—
261C4—361no—
262C4—361no—
263C4#6412711yescharacteristic
264C4#6412811yescharacteristic
265C4#6414111yescharacteristic
266C4#6415911yescharacteristic
267C3#7106014yescomplemented
268C2—722no—
269C2#1059273611yescharacteristic
270C2#1059288611yescharacteristic
271C2#1059290111yescharacteristic
subgroupG/H
centerC22#64146
commutator, cosocleC32×C42C23
FrattiniC42C22×C3⋊D3
FittingC32×#462C2
socleC22×C32#120
prime radical#64083C22
hypercenter#462C3⋊D3
hypocenterC32#1640
LCSG ▷ C32×C42 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ #462

Complements

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

NH ≅ G/Ntype
2. C32×#462C2semidirect
3. #10592793C2semidirect
5. #10589401C2semidirect
7. #10589350C2semidirect
27. C3×#462D3semidirect
101. #462C3⋊D3semidirect
224. C32#1640semidirect
267. C3#71060semidirect

Maximal subgroups

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

subgroupindex
#105960562
C32×#4622
#105927932
#105927872
#105894012
#105893512
#105893502
#710603