Finite Group Databasebeta

← #11778467

Subgroups — #11778467

Order 1152.

684 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 684 conjugacy classes of subgroups — too many to draw. Only its 149 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
1C32×#543C211yesmaximal, characteristic
2#10592742C212yesmaximal, complemented
3#10592652C211yesmaximal, characteristic
4#10589404C212yesmaximal, complemented
5#10589391C211yesmaximal, characteristic
6#71890—34nomaximal
7C32×C22⋊Q8—22no—
8C32×C22⋊Q8—21no—
9C32×C22⋊Q8—22no—
10C32×C22⋊Q8C2212yes—
11C2×C32×C22⋊C4—21no—
12C2×C32×C22⋊C4C2211yescharacteristic
13C2×#3757—21no—
14C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
15#63662—22no—
16#63658—21no—
17#63658C2211yescharacteristic
18#63657C2212yes—
19#63635—22no—
20C3×#543D314yes—
21#5043—38no—
22#4953—34no—
23#4538—38no—
24#4525—34no—
25C24×C32D411yescharacteristic
26C2×C32×Q8—21no—
27C2×C32×Q8D412yes—
28C22×C32×C4—21no—
29C22×C32×C4—21no—
30C22×C32×C4D411yescharacteristic
31C22×C32×C4C2311yescharacteristic
32C22×C3⋊Dic3—21no—
33C22×C3⋊Dic3—21no—
34C32×C4⋊C4—21no—
35C32×C4⋊C4—22no—
36C32×C4⋊C4—22no—
37C32×C4⋊C4D412yes—
38C32×C22⋊C4—22no—
39C32×C22⋊C4—22no—
40C32×C22⋊C4—22no—
41#3757—42no—
42C4⋊(C3⋊Dic3)—22no—
43C2×C3⋊(C3⋊C8)—22no—
44#1608—91noSylow
45C3×C22⋊Q8—28no—
46C3×C22⋊Q8—24no—
47C3×C22⋊Q8—28no—
48C3×C22⋊Q8C2×D318yes—
49C2×C3×C22⋊C4—24no—
50C2×C3×C22⋊C4C2×D314yes—
51C2×#217—64no—
52C2×C4⋊Dic3—34no—
53#835—68no—
54C3⋊#95—34no—
55C3⋊#95—64no—
56#830—38no—
57#808—68no—
58C23×C32—21no—
59C23×C32—21no—
60C23×C32—41no—
61C23×C32—41no—
62C23×C32SD1612yes—
63C23×C32C2×D411yescharacteristic
64C32×Q8—42no—
65C32×Q8—81no—
66C2×C32×C4—22no—
67C2×C32×C4—21no—
68C2×C32×C4—22no—
69C2×C32×C4—41no—
70C2×C32×C4—41no—
71C2×C32×C4—81no—
72C2×C32×C4—81no—
73C2×C32×C4C2×D412yes—
74C2×C3⋊Dic3—41no—
75C2×C3⋊Dic3—41no—
76C2×C3⋊Dic3—41no—
77C2×C3⋊Dic3—41no—
78C2×C3⋊Dic3—41no—
79C2×C3⋊Dic3—41no—
80C3⋊(C3⋊C8)—42no—
81#543C3⋊D311yescharacteristic
82#483—92no—
83#397—91no—
84#328—92no—
85#323—91no—
86C24×C3#6714yes—
87C2×C3×Q8—24no—
88C2×C3×Q8#6718yes—
89C22×C3×C4—24no—
90C22×C3×C4—24no—
91C22×C3×C4#6714yes—
92C22×C3×C4C22×D314yes—
93C22×Dic3—64no—
94C22×Dic3—64no—
95C3×C4⋊C4—24no—
96C3×C4⋊C4—28no—
97C3×C4⋊C4—28no—
98C3×C4⋊C4#6718yes—
99C3×C22⋊C4—28no—
100C3×C22⋊C4—28no—
101C3×C22⋊C4—28no—
102#217—128no—
103C4⋊Dic3—68no—
104C2×C3⋊C8—68no—
105C22×C32—21no—
106C22×C32—21no—
107C22×C32—22no—
108C22×C32—42no—
109C22×C32—41no—
110C22×C32—41no—
111C22×C32—81no—
112C22×C32#12011yescharacteristic
113C22×C32C2×SD1611yescharacteristic
114C22×C32#13711yescharacteristic
115C32×C4—22no—
116C32×C4—41no—
117C32×C4—42no—
118C32×C4—42no—
119C3⋊Dic3—81no—
120C3⋊Dic3—81no—
121C22⋊Q8—22no—
122C22⋊Q8—21no—
123C22⋊Q8—22no—
124C22⋊Q8C2×C3⋊D312yes—
125C2×C4⋊C4—91no—
126C2×C22⋊C4—21no—
127C2×C22⋊C4—181no—
128C2×C22⋊C4C2×C3⋊D311yescharacteristic
129#106—182no—
130#103—182no—
131C22⋊C8—92no—
132#95—91no—
133#95—181no—
134C23×C3—24no—
135C23×C3—24no—
136C23×C3—44no—
137C23×C3—44no—
138C23×C3#21518yes—
139C23×C3C2×#6714yes—
140C3×Q8—48no—
141C3×Q8—84no—
142C2×C3×C4—28no—
143C2×C3×C4—24no—
144C2×C3×C4—28no—
145C2×C3×C4—44no—
146C2×C3×C4—44no—
147C2×C3×C4—84no—
148C2×C3×C4—84no—
149C2×C3×C4C2×#6718yes—
150C2×Dic3—124no—
151C2×Dic3—124no—
152C2×Dic3—124no—
153C2×Dic3—124no—
154C2×Dic3—124no—
155C2×Dic3—124no—
156C3⋊C8—128no—
157C2×C32—21no—
158C2×C32—21no—
159C2×C32—42no—
160C2×C32#44811yescharacteristic
161C2×C32#45511yescharacteristic
162C2×C32#45811yescharacteristic
163C24#63811yescharacteristic
164C2×Q8—21no—
165C2×Q8#63812yes—
166C22×C4—21no—
167C22×C4—21no—
168C22×C4—181no—
169C22×C4—181no—
170C22×C4#63811yescharacteristic
171C22×C4C22×C3⋊D311yescharacteristic
172C2×C8—182no—
173C4⋊C4—21no—
174C4⋊C4—22no—
175C4⋊C4—22no—
176C4⋊C4—182no—
177C4⋊C4#63812yes—
178C22⋊C4—22no—
179C22⋊C4—22no—
180C22⋊C4—22no—
181C22⋊C4—362no—
182C22×C3—24no—
183C22×C3—24no—
184C22×C3—28no—
185C22×C3—48no—
186C22×C3—44no—
187C22×C3—44no—
188C22×C3—84no—
189C22×C3C2×#21514yes—
190C22×C3#94214yes—
191C22×C3#95314yes—
192C3×C4—28no—
193C3×C4—44no—
194C3×C4—48no—
195C3×C4—48no—
196Dic3—244no—
197Dic3—244no—
198C32#160811yescharacteristic, complemented, Sylow
199C23—21no—
200C23—21no—
201C23—41no—
202C23—41no—
203C23#375512yes—
204C23C2×#63811yescharacteristic
205Q8—42no—
206Q8—81no—
207C2×C4—22no—
208C2×C4—21no—
209C2×C4—22no—
210C2×C4—41no—
211C2×C4—41no—
212C2×C4—81no—
213C2×C4—81no—
214C2×C4—361no—
215C2×C4—361no—
216C2×C4—361no—
217C2×C4—361no—
218C2×C4—361no—
219C2×C4—361no—
220C2×C4C2×#63812yes—
221C8—362no—
222C2×C3—24no—
223C2×C3—24no—
224C2×C3—48no—
225C2×C3#522714yes—
226C2×C3#524214yes—
227C2×C3#524314yes—
228C22—21no—
229C22—21no—
230C22—22no—
231C22—42no—
232C22—41no—
233C22—41no—
234C22—81no—
235C22C2×#375511yescharacteristic
236C22#6415111yescharacteristic
237C22#6416211yescharacteristic
238C4—22no—
239C4—41no—
240C4—42no—
241C4—42no—
242C4—721no—
243C4—721no—
244C3#7189014yescomplemented
245C2—21no—
246C2—21no—
247C2—42no—
248C2#1059292611yescharacteristic
249C2#1059294111yescharacteristic
250C2#1059294211yescharacteristic
subgroupG/H
centerC22#64162
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C22×C3⋊D3
FittingC32×#543C2
socleC22×C32#120
prime radicalC24×C32D4
hypercenter#543C3⋊D3
hypocenterC32#1608
LCSG ▷ C22×C32×C4 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ #543

Complements

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

NH ≅ G/Ntype
2. #10592742C2semidirect
4. #10589404C2semidirect
198. C32#1608semidirect
244. C3#71890semidirect

Maximal subgroups

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

subgroupindex
C32×#5432
#105927422
#105926522
#105894042
#105893912
#718903