Finite Group Databasebeta

← #11780225

Subgroups — #11780225

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#10596013C211yesmaximal, characteristic
2C32×#461C211yesmaximal, characteristic
3#10592793C211yesmaximal, characteristic, complemented
4#10592777C211yesmaximal, characteristic, complemented
5D4⋊(C3⋊(C3⋊C8))C211yesmaximal, characteristic
6#10589350C211yesmaximal, characteristic, complemented
7#10589348C211yesmaximal, characteristic, complemented
8#71049—34nomaximal
9C2×C32×SD16—21no—
10C32×C4⋊Q8C2211yescharacteristic
11C32×C4×D4C2211yescharacteristic
12#64145—21no—
13#64135—21no—
14#64133—21no—
15#64096—21no—
16#64088—22no—
17#64078C2211yescharacteristic
18C4×#634C2211yescharacteristic
19C32×C4⋊C8C2211yescharacteristic
20C32×#103—21no—
21#63637—21no—
22#63635—21no—
23#63634—22no—
24C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
25C4×C3⋊(C3⋊C8)C2211yescharacteristic
26#5542—34no—
27C3×#461D314yes—
28#5094—34no—
29#5078—34no—
30D4⋊(C3⋊C8)—34no—
31#4484—34no—
32#4482—34no—
33C2×C32×Q8—21no—
34C2×C32×D4D411yescharacteristic
35C22×C32×C4—21no—
36C2×#634—21no—
37C2×#634D411yescharacteristic
38C32×SD16—42no—
39C2×C32×C8—21no—
40C32×C4⋊C4—21no—
41C32×C4⋊C4—21no—
42C32×C4⋊C4D411yescharacteristic
43C32×C22⋊C4—21no—
44C32×C42C2311yescharacteristic
45#3757—22no—
46#3757—22no—
47C4⋊(C3⋊Dic3)—21no—
48C4⋊(C3⋊Dic3)D411yescharacteristic
49C4⋊(C3⋊Dic3)D412yes—
50#3750—22no—
51#3750—21no—
52C4×C3⋊Dic3—22no—
53C4×C3⋊Dic3—21no—
54C2×C3⋊(C3⋊C8)—21no—
55C2×C3⋊(C3⋊C8)—21no—
56#1650—91noSylow
57C2×C3×SD16—24no—
58C3×C4⋊Q8C2×D314yes—
59C3×C4×D4C2×D314yes—
60#936—64no—
61#926—64no—
62#924—64no—
63#887—64no—
64#879—68no—
65#869—34no—
66C4×Dic6—34no—
67C3×C4⋊C8C2×D314yes—
68C3×#103—24no—
69#810—64no—
70#808—64no—
71#807—68no—
72C4⋊(C3⋊C8)—34no—
73C4×C3⋊C8—34no—
74C23×C32—21no—
75C32×Q8—41no—
76C32×Q8—41no—
77C32×D4—21no—
78C32×D4—21no—
79C2×C32×C4—21no—
80C2×C32×C4—41no—
81C2×C32×C4—41no—
82C2×C32×C4—41no—
83C2×C32×C4C2×D411yescharacteristic
84C2×C32×C4C2×D411yescharacteristic
85C2×C32×C4C2×D411yescharacteristic
86C2×C3⋊Dic3—21no—
87C2×C3⋊Dic3—21no—
88C2×C3⋊Dic3—22no—
89#634—21no—
90#634—21no—
91#634—41no—
92#634—41no—
93C32×C8—41no—
94C3⋊(C3⋊C8)—22no—
95C3⋊(C3⋊C8)—41no—
96#556—91no—
97#500—91no—
98#475—91no—
99#461C3⋊D311yescharacteristic
100#332—91no—
101Q8⋊C8—91no—
102D4⋊C8—91no—
103C2×C3×Q8—24no—
104C2×C3×D4#6714yes—
105C22×C3×C4—24no—
106C2×Dic6—34no—
107C2×Dic6—64no—
108C3×SD16—48no—
109C2×C3×C8—24no—
110C3×C4⋊C4—24no—
111C3×C4⋊C4—24no—
112C3×C4⋊C4#6714yes—
113C3×C22⋊C4—24no—
114C3×C42C22×D314yes—
115#217—68no—
116#217—68no—
117C4⋊Dic3—38no—
118C4⋊Dic3—34no—
119C4⋊Dic3—64no—
120Dic3⋊C4—68no—
121Dic3⋊C4—64no—
122C4×Dic3—68no—
123C4×Dic3—64no—
124C2×C3⋊C8—64no—
125C2×C3⋊C8—64no—
126C22×C32—41no—
127C22×C32—41no—
128C22×C32—41no—
129C22×C32#12011yescharacteristic
130C32×C4—21no—
131C32×C4—41no—
132C32×C4—81no—
133C32×C4#13511yescharacteristic
134C32×C4#13511yescharacteristic
135C32×C4AGL(1,ℤ/8)11yescharacteristic
136C32×C4#13711yescharacteristic
137C3⋊Dic3—42no—
138C3⋊Dic3—41no—
139C3⋊Dic3—41no—
140C2×SD16—21no—
141C4⋊Q8—91no—
142C4⋊Q8C2×C3⋊D311yescharacteristic
143#126—182no—
144#124—181no—
145C22⋊Q8—181no—
146C4×Q8—91no—
147C4×Q8—181no—
148C4×D4C2×C3⋊D311yescharacteristic
149#117—181no—
150#107—182no—
151#106—181no—
152C4⋊C8—91no—
153C4⋊C8C2×C3⋊D311yescharacteristic
154#103—21no—
155#103—181no—
156C4×C8—91no—
157C23×C3—24no—
158C3×Q8—44no—
159C3×Q8—44no—
160C3×D4—24no—
161C3×D4—24no—
162C2×C3×C4—24no—
163C2×C3×C4—44no—
164C2×C3×C4—44no—
165C2×C3×C4—44no—
166C2×C3×C4D3×D414yes—
167C2×C3×C4D3×D414yes—
168C2×C3×C4C2×#6714yes—
169C2×Dic3—64no—
170C2×Dic3—64no—
171C2×Dic3—68no—
172Dic6—64no—
173Dic6—64no—
174Dic6—124no—
175Dic6—124no—
176C3×C8—44no—
177C3⋊C8—68no—
178C3⋊C8—124no—
179C2×C32—81no—
180C2×C32#44911yescharacteristic
181C2×C32#45211yescharacteristic
182C2×C32#45611yescharacteristic
183C2×Q8—21no—
184C2×Q8—91no—
185C2×Q8—181no—
186C2×D4#63811yescharacteristic
187C22×C4—21no—
188SD16—42no—
189C2×C8—21no—
190C2×C8—181no—
191C2×C8—181no—
192C4⋊C4—21no—
193C4⋊C4—21no—
194C4⋊C4—91no—
195C4⋊C4—92no—
196C4⋊C4—182no—
197C4⋊C4—181no—
198C4⋊C4—181no—
199C4⋊C4#63811yescharacteristic
200C22⋊C4—21no—
201C22⋊C4—182no—
202C22⋊C4—182no—
203C42—182no—
204C42—181no—
205C42C22×C3⋊D311yescharacteristic
206C22×C3—44no—
207C22×C3—44no—
208C22×C3—44no—
209C22×C3#93714yes—
210C3×C4—24no—
211C3×C4—44no—
212C3×C4—84no—
213C3×C4#91514yes—
214C3×C4#91614yes—
215C3×C4#93214yes—
216C3×C4#95014yes—
217Dic3—124no—
218Dic3—124no—
219Dic3—128no—
220C32#165011yescharacteristic, complemented, Sylow
221C23—21no—
222Q8—41no—
223Q8—41no—
224Q8—181no—
225Q8—181no—
226Q8—361no—
227Q8—361no—
228D4—21no—
229D4—21no—
230C2×C4—21no—
231C2×C4—41no—
232C2×C4—41no—
233C2×C4—41no—
234C2×C4—181no—
235C2×C4—182no—
236C2×C4—181no—
237C2×C4D4×C3⋊D311yescharacteristic
238C2×C4D4×C3⋊D311yescharacteristic
239C2×C4C2×#63811yescharacteristic
240C8—41no—
241C8—182no—
242C8—361no—
243C2×C3—84no—
244C2×C3#503714yes—
245C2×C3#517314yes—
246C2×C3#520514yes—
247C22—41no—
248C22—41no—
249C22—41no—
250C22#6414611yescharacteristic
251C4—21no—
252C4—41no—
253C4—81no—
254C4—361no—
255C4—361no—
256C4—362no—
257C4#6412411yescharacteristic
258C4#6412511yescharacteristic
259C4#6414111yescharacteristic
260C4#6415911yescharacteristic
261C3#7104914yescomplemented
262C2—81no—
263C2#1059273611yescharacteristic
264C2#1059287211yescharacteristic
265C2#1059290411yescharacteristic
subgroupG/H
centerC22#64146
commutator, cosocleC32×C42C23
FrattiniC42C22×C3⋊D3
FittingC32×#461C2
socleC22×C32#120
prime radicalC2×C32×D4D4
hypercenter#461C3⋊D3
hypocenterC32#1650
LCSG ▷ C32×C42 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ #461

Complements

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

NH ≅ G/Ntype
3. #10592793C2semidirect
4. #10592777C2semidirect
6. #10589350C2semidirect
7. #10589348C2semidirect
220. C32#1650semidirect
261. C3#71049semidirect

Maximal subgroups

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

subgroupindex
#105960132
C32×#4612
#105927932
#105927772
D4⋊(C3⋊(C3⋊C8))2
#105893502
#105893482
#710493