Finite Group Databasebeta

← #11778548

Subgroups — #11778548

Order 1152.

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

normal subgroups only

This group has 762 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×#537C211yesmaximal, characteristic
2#10592732C212yesmaximal, complemented
3#10592680C211yesmaximal, characteristic, complemented
4#10589403C212yesmaximal, complemented
5#10589394C211yesmaximal, characteristic, complemented
6#71874—34nomaximal
7C2×C32×#41—21no—
8C32×C22⋊Q8—22no—
9C32×#121—22no—
10C32×#121—21no—
11C32×#121C2212yes—
12C2×C32×C4⋊C4C2211yescharacteristic
13C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
14C2×#3750—21no—
15#63659—22no—
16#63658—21no—
17#63658C2211yescharacteristic
18#63657C2212yes—
19#63634—22no—
20C3×#537D314yes—
21#5033—38no—
22#4981—34no—
23#4537—38no—
24#4528—34no—
25C32×#41—42no—
26C32×#41—42no—
27C2×C32×Q8—21no—
28C2×C32×D4—21no—
29C2×C32×D4—22no—
30C2×C32×D4—21no—
31C2×C32×D4D412yes—
32C22×C32×C4—22no—
33C22×C32×C4D411yescharacteristic
34C22×C32×C4D411yescharacteristic
35C22×C32×C4C2311yescharacteristic
36C22×C3⋊Dic3—21no—
37C22×C3⋊Dic3—21no—
38C32×C4⋊C4—21no—
39C32×C4⋊C4—22no—
40C32×C4⋊C4D412yes—
41C32×C22⋊C4—22no—
42C32×C22⋊C4—22no—
43C4⋊(C3⋊Dic3)—22no—
44#3750—42no—
45C2×C3⋊(C3⋊C8)—22no—
46#1610—91noSylow
47C2×C3×#41—24no—
48C3×C22⋊Q8—28no—
49C3×#121—28no—
50C3×#121—24no—
51C3×#121C2×D318yes—
52C2×C3×C4⋊C4C2×D314yes—
53C2×C4⋊Dic3—34no—
54C2×Dic3⋊C4—64no—
55#832—68no—
56C3⋊#95—34no—
57C3⋊#95—64no—
58#830—38no—
59#807—68no—
60C23×C32—22no—
61C23×C32C2×D411yescharacteristic
62C32×Q8—42no—
63C32×D4—42no—
64C32×D4—42no—
65C32×D4—42no—
66C32×D4—42no—
67C32×D4—81no—
68C2×C32×C4—21no—
69C2×C32×C4—21no—
70C2×C32×C4—21no—
71C2×C32×C4—22no—
72C2×C32×C4—41no—
73C2×C32×C4—44no—
74C2×C32×C4—41no—
75C2×C32×C4D812yes—
76C2×C32×C4C2×D412yes—
77C2×C3⋊Dic3—22no—
78C2×C3⋊Dic3—41no—
79C2×C3⋊Dic3—41no—
80C2×C3⋊Dic3—41no—
81C2×C3⋊Dic3—41no—
82C2×C3⋊Dic3—41no—
83C3⋊(C3⋊C8)—42no—
84#537C3⋊D311yescharacteristic
85#480—92no—
86#398—91no—
87#327—92no—
88#324—91no—
89C3×#41—48no—
90C3×#41—48no—
91C2×C3×Q8—24no—
92C2×C3×D4—24no—
93C2×C3×D4—28no—
94C2×C3×D4—24no—
95C2×C3×D4#6718yes—
96C22×C3×C4—28no—
97C22×C3×C4#6714yes—
98C22×C3×C4#6714yes—
99C22×C3×C4C22×D314yes—
100C22×Dic3—64no—
101C22×Dic3—64no—
102C3×C4⋊C4—24no—
103C3×C4⋊C4—28no—
104C3×C4⋊C4#6718yes—
105C3×C22⋊C4—28no—
106C3×C22⋊C4—28no—
107C4⋊Dic3—68no—
108Dic3⋊C4—128no—
109C2×C3⋊C8—68no—
110C22×C32—21no—
111C22×C32—21no—
112C22×C32—42no—
113C22×C32—42no—
114C22×C32—42no—
115C22×C32#12011yescharacteristic
116C22×C32C2×D811yescharacteristic
117C22×C32AGL(1,ℤ/8)11yescharacteristic
118C32×C4—22no—
119C32×C4—22no—
120C32×C4—42no—
121C32×C4—41no—
122C3⋊Dic3—42no—
123C3⋊Dic3—81no—
124C2×#41—21no—
125C22⋊Q8—22no—
126#121—22no—
127#121—21no—
128#121C2×C3⋊D312yes—
129C2×C4⋊C4—91no—
130C2×C4⋊C4—181no—
131C2×C4⋊C4C2×C3⋊D311yescharacteristic
132#107—182no—
133#102—182no—
134C22⋊C8—92no—
135#95—91no—
136#95—181no—
137C23×C3—28no—
138C23×C3C2×#6714yes—
139C3×Q8—48no—
140C3×D4—48no—
141C3×D4—48no—
142C3×D4—48no—
143C3×D4—48no—
144C3×D4—84no—
145C2×C3×C4—24no—
146C2×C3×C4—24no—
147C2×C3×C4—24no—
148C2×C3×C4—28no—
149C2×C3×C4—44no—
150C2×C3×C4—416no—
151C2×C3×C4—44no—
152C2×C3×C4#21318yes—
153C2×C3×C4C2×#6718yes—
154C2×Dic3—68no—
155C2×Dic3—124no—
156C2×Dic3—124no—
157C2×Dic3—124no—
158C2×Dic3—124no—
159C2×Dic3—124no—
160C3⋊C8—128no—
161C2×C32—21no—
162C2×C32—21no—
163C2×C32—82no—
164C2×C32#44711yescharacteristic
165C2×C32#45611yescharacteristic
166C2×C32#45811yescharacteristic
167#41—42no—
168#41—42no—
169C2×Q8—21no—
170C2×D4—21no—
171C2×D4—22no—
172C2×D4—21no—
173C2×D4#63812yes—
174C22×C4—22no—
175C22×C4—181no—
176C22×C4—181no—
177C22×C4#63811yescharacteristic
178C22×C4#63811yescharacteristic
179C22×C4C22×C3⋊D311yescharacteristic
180C2×C8—182no—
181C4⋊C4—21no—
182C4⋊C4—22no—
183C4⋊C4—182no—
184C4⋊C4—362no—
185C4⋊C4#63812yes—
186C22⋊C4—22no—
187C22⋊C4—22no—
188C22×C3—24no—
189C22×C3—24no—
190C22×C3—48no—
191C22×C3—48no—
192C22×C3—48no—
193C22×C3C2×#21314yes—
194C22×C3#93214yes—
195C22×C3#95314yes—
196C3×C4—28no—
197C3×C4—28no—
198C3×C4—48no—
199C3×C4—44no—
200Dic3—128no—
201Dic3—244no—
202C32#161011yescharacteristic, complemented, Sylow
203C23—22no—
204C23C2×#63811yescharacteristic
205Q8—42no—
206D4—42no—
207D4—42no—
208D4—42no—
209D4—42no—
210D4—81no—
211C2×C4—21no—
212C2×C4—21no—
213C2×C4—21no—
214C2×C4—22no—
215C2×C4—41no—
216C2×C4—44no—
217C2×C4—41no—
218C2×C4—182no—
219C2×C4—361no—
220C2×C4—361no—
221C2×C4—361no—
222C2×C4—361no—
223C2×C4—361no—
224C2×C4#375312yes—
225C2×C4C2×#63812yes—
226C8—362no—
227C2×C3—24no—
228C2×C3—24no—
229C2×C3—88no—
230C2×C3#521714yes—
231C2×C3#524314yes—
232C2×C3#524614yes—
233C22—21no—
234C22—21no—
235C22—42no—
236C22—42no—
237C22—42no—
238C22C2×#375311yescharacteristic
239C22#6414111yescharacteristic
240C22#6416211yescharacteristic
241C4—22no—
242C4—22no—
243C4—42no—
244C4—41no—
245C4—362no—
246C4—721no—
247C3#7187414yescomplemented
248C2—21no—
249C2—21no—
250C2—82no—
251C2#1059291611yescharacteristic
252C2#1059294211yescharacteristic
253C2#1059294511yescharacteristic
subgroupG/H
centerC22#64162
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C22×C3⋊D3
Fitting, prime radicalC32×#537C2
socleC22×C32#120
hypercenter#537C3⋊D3
hypocenterC32#1610
LCSG ▷ C22×C32×C4 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ #537

Complements

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

NH ≅ G/Ntype
2. #10592732C2semidirect
3. #10592680C2semidirect
4. #10589403C2semidirect
5. #10589394C2semidirect
202. C32#1610semidirect
247. C3#71874semidirect

Maximal subgroups

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

subgroupindex
C32×#5372
#105927322
#105926802
#105894032
#105893942
#718743