Finite Group Databasebeta

← #11780269

Subgroups — #11780269

Order 1152.

702 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 702 conjugacy classes of subgroups — too many to draw. Only its 133 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#10596198C211yesmaximal, characteristic
2C32×#498C211yesmaximal, characteristic, complemented
3#10592793C211yesmaximal, characteristic, complemented
4#10592782C211yesmaximal, characteristic
5#10589413C211yesmaximal, characteristic, complemented
6#10589325C211yesmaximal, characteristic
7#10589322C211yesmaximal, characteristic, complemented
8#71342—34nomaximal
9C2×Q8×C3⋊D3—21no—
10C32×C4⋊Q8C2211yescharacteristic
11C32×C4⋊Q8C2211yescharacteristic
12#64155—21no—
13C2×#3755—21no—
14#64105—22no—
15#64102—21no—
16#64097—21no—
17C4×C4⋊(C3⋊D3)C2211yescharacteristic
18C4×#634C2211yescharacteristic
19C32×#106—22no—
20C32×C4×C8C2211yescharacteristic
21#63662—21no—
22#63637—21no—
23#63635—21no—
24C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
25C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
26#5727—34no—
27C3×#498D314yescomplemented
28#5094—34no—
29#5083—34no—
30#4547—34no—
31#4459—34no—
32#4456—34no—
33C2×C32×Q8—21no—
34C2×C32×Q8—21no—
35Q8×C3⋊D3—42no—
36Q8×C3⋊D3—42no—
37C2×C4⋊(C3⋊D3)D411yescharacteristic
38C2×C4×C3⋊D3—22no—
39C2×C4×C3⋊D3—21no—
40C2×#634—22no—
41C2×#634D411yescharacteristic
42C2×C32×C8—21no—
43C32×C4⋊C4—21no—
44C32×C4⋊C4—21no—
45C32×C4⋊C4—21no—
46C32×C4⋊C4D412yes—
47C32×C42C2311yescharacteristic
48#3755—42no—
49#3752—22no—
50#3752—21no—
51C4⋊(C3⋊Dic3)D411yescharacteristic
52C4⋊(C3⋊Dic3)D411yescharacteristic
53#3750—22no—
54#3750—21no—
55C4×C3⋊Dic3—21no—
56C2×C3⋊(C3⋊C8)—21no—
57C2×C3⋊(C3⋊C8)—21no—
58#1651—91noSylow
59C2×D3×Q8—64no—
60C3×C4⋊Q8C2×D314yes—
61C3×C4⋊Q8C2×D314yes—
62#946—64no—
63C2×#215—64no—
64#896—68no—
65#893—64no—
66#888—64no—
67C4×D12—34no—
68C4×Dic6—34no—
69C3×#106—28no—
70C3×C4×C8C2×D314yes—
71#835—64no—
72#810—64no—
73#808—64no—
74C4⋊(C3⋊C8)—34no—
75C4⋊(C3⋊C8)—34no—
76C22×C3⋊D3—21no—
77C32×Q8—41no—
78C32×Q8—41no—
79C32×Q8—41no—
80C32×Q8—41no—
81C2×C32×C4—22no—
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—21no—
89C4⋊(C3⋊D3)—21no—
90C4⋊(C3⋊D3)SD1612yes—
91C4×C3⋊D3—44no—
92C4×C3⋊D3—41no—
93C4×C3⋊D3—41no—
94#634—21no—
95#634—44no—
96#634SD1612yescomplemented
97C32×C8—22no—
98C3⋊(C3⋊C8)—41no—
99C3⋊(C3⋊C8)—41no—
100D4×Q8—91no—
101#498C3⋊D311yescharacteristic, complemented
102#475—91no—
103#461—91no—
104#332—91no—
105Q8⋊C8—91no—
106D4⋊C8—91no—
107C2×C3×Q8—24no—
108C2×C3×Q8—24no—
109D3×Q8—128no—
110D3×Q8—128no—
111C2×D12—34no—
112C2×C4×D3—68no—
113C2×C4×D3—64no—
114C2×Dic6—34no—
115C2×Dic6—68no—
116C2×C3×C8—24no—
117C3×C4⋊C4—24no—
118C3×C4⋊C4—24no—
119C3×C4⋊C4—24no—
120C3×C4⋊C4#6718yes—
121C3×C42C22×D314yes—
122#215—128no—
123(C2×D3)⋊C4—68no—
124(C2×D3)⋊C4—64no—
125C4⋊Dic3—34no—
126C4⋊Dic3—34no—
127Dic3⋊C4—68no—
128Dic3⋊C4—64no—
129C4×Dic3—64no—
130C2×C3⋊C8—64no—
131C2×C3⋊C8—64no—
132C22×C32#12011yescharacteristic
133C2×C3⋊D3—22no—
134C2×C3⋊D3—41no—
135C2×C3⋊D3—41no—
136C32×C4—21no—
137C32×C4—42no—
138C32×C4—81no—
139C32×C4C2×SD1611yescharacteristic
140C32×C4C2×SD1611yescharacteristic
141C32×C4AGL(1,ℤ/8)11yescharacteristic
142C32×C4#13711yescharacteristic
143C3⋊Dic3—22no—
144C3⋊Dic3—41no—
145C3⋊Dic3—41no—
146C22×Q8—181no—
147C2×SD16—181no—
148C4⋊Q8—181no—
149C4⋊Q8C2×C3⋊D311yescharacteristic
150C4⋊Q8C2×C3⋊D311yescharacteristic
151C22⋊Q8—181no—
152C22⋊Q8—182no—
153C4×Q8—91no—
154C4×D4—91no—
155C4×D4—181no—
156#106—22no—
157#106—181no—
158C4⋊C8—91no—
159C4⋊C8—91no—
160#103—181no—
161#103—181no—
162C4×C8C2×C3⋊D311yescharacteristic
163C22×D3—64no—
164C3×Q8—44no—
165C3×Q8—44no—
166C3×Q8—44no—
167C3×Q8—44no—
168C2×C3×C4—28no—
169C2×C3×C4—44no—
170C2×C3×C4D3×D414yes—
171C2×C3×C4D3×D414yes—
172C2×C3×C4C2×#6714yes—
173C2×Dic3—64no—
174C2×Dic3—64no—
175C2×Dic3—64no—
176D12—38no—
177D12—64no—
178C4×D3—1216no—
179C4×D3—124no—
180C4×D3—124no—
181Dic6—38no—
182Dic6—64no—
183Dic6—1216no—
184C3×C8—28no—
185C3⋊C8—124no—
186C3⋊C8—124no—
187C2×C32#44811yescharacteristic
188C2×C32#45011yescharacteristic
189C2×C32#45611yescharacteristic
190C3⋊D3—42no—
191C2×Q8—21no—
192C2×Q8—21no—
193C2×Q8—91no—
194C2×Q8—182no—
195C2×Q8—362no—
196C2×Q8—362no—
197C2×D4—91no—
198C22×C4—182no—
199C22×C4—181no—
200SD16—362no—
201C2×C8—21no—
202C2×C8—181no—
203C2×C8—181no—
204C4⋊C4—21no—
205C4⋊C4—21no—
206C4⋊C4—21no—
207C4⋊C4—91no—
208C4⋊C4—91no—
209C4⋊C4—182no—
210C4⋊C4—181no—
211C4⋊C4#63812yes—
212C22⋊C4—182no—
213C22⋊C4—181no—
214C42—181no—
215C42C22×C3⋊D311yescharacteristic
216C22×C3#93714yes—
217C2×D3—68no—
218C2×D3—124no—
219C2×D3—124no—
220C3×C4—24no—
221C3×C4—48no—
222C3×C4—84no—
223C3×C4D3×SD1614yes—
224C3×C4D3×SD1614yes—
225C3×C4#91414yes—
226C3×C4#91514yes—
227Dic3—68no—
228Dic3—124no—
229Dic3—124no—
230C32#165111yescharacteristic, complemented, Sylow
231C23—181no—
232Q8—41no—
233Q8—41no—
234Q8—41no—
235Q8—41no—
236Q8—92no—
237Q8—181no—
238Q8—364no—
239D4—92no—
240D4—181no—
241C2×C4—22no—
242C2×C4—41no—
243C2×C4—181no—
244C2×C4—181no—
245C2×C4—181no—
246C2×C4—364no—
247C2×C4—361no—
248C2×C4—361no—
249C2×C4D4×C3⋊D311yescharacteristic
250C2×C4D4×C3⋊D311yescharacteristic
251C2×C4C2×#63811yescharacteristic
252C8—22no—
253C8—361no—
254C8—361no—
255C2×C3#509514yes—
256C2×C3#516914yes—
257C2×C3#517014yes—
258D3—128no—
259C22—182no—
260C22—361no—
261C22—361no—
262C22#6414611yescharacteristic
263C4—21no—
264C4—42no—
265C4—81no—
266C4—182no—
267C4—361no—
268C4—361no—
269C4SD16×C3⋊D311yescharacteristic
270C4SD16×C3⋊D311yescharacteristic
271C4#6412311yescharacteristic
272C4#6412411yescharacteristic
273C3#7134214yescomplemented
274C2—362no—
275C2#1059279411yescharacteristic
276C2#1059286811yescharacteristic
277C2#1059286911yescharacteristic
subgroupG/H
centerC22#64146
commutator, cosocleC32×C42C23
FrattiniC42C22×C3⋊D3
FittingC32×#498C2
socleC22×C32#120
prime radicalC2×C4⋊(C3⋊D3)D4
hypercenter#498C3⋊D3
hypocenterC32#1651
LCSG ▷ C32×C42 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ #498

Complements

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

NH ≅ G/Ntype
2. C32×#498C2semidirect
3. #10592793C2semidirect
5. #10589413C2semidirect
7. #10589322C2semidirect
27. C3×#498D3semidirect
96. #634SD16semidirect
101. #498C3⋊D3semidirect
230. C32#1651semidirect
273. C3#71342semidirect

Maximal subgroups

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

subgroupindex
#105961982
C32×#4982
#105927932
#105927822
#105894132
#105893252
#105893222
#713423