Finite Group Databasebeta

← #11778700

Subgroups — #11778700

Order 1152.

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

normal subgroups only

This group has 708 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#10595954C211yesmaximal, characteristic
2#10592648C211yesmaximal, characteristic
3#10592421C212yesmaximal, complemented
4C32×#323C211yesmaximal, characteristic
5#10589333C212yesmaximal, complemented
6#68117—34nomaximal
7C2×C32×C22⋊C4C2211yescharacteristic
8C2×#3757—21no—
9C2×#3757—21no—
10C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
11#64133—21no—
12#64133C2212yes—
13C2×#3750—21no—
14#64087—22no—
15#64087—22no—
16C32×C22⋊C8C2212yes—
17#63658C2211yescharacteristic
18#63645—22no—
19#63643—22no—
20#5483—34no—
21#4949—34no—
22#4722—38no—
23C3×#323D314yes—
24#4467—38no—
25C24×C32D411yescharacteristic
26C22×C32×C4D411yescharacteristic
27C22×C32×C4C2311yescharacteristic
28C22×C3⋊Dic3—21no—
29C22×C3⋊Dic3—21no—
30C22×C3⋊Dic3—21no—
31C22×C3⋊Dic3—21no—
32C2×#634—21no—
33C2×#634D412yes—
34C2×C32×C8—22no—
35C32×C22⋊C4—22no—
36#3757—22no—
37#3757—22no—
38#3757—42no—
39C4⋊(C3⋊Dic3)—21no—
40C4⋊(C3⋊Dic3)—22no—
41C4⋊(C3⋊Dic3)D412yes—
42#3750—22no—
43#3750—22no—
44#3750—42no—
45#1614—91noSylow
46C2×C3×C22⋊C4C2×D314yes—
47C2×#217—64no—
48C2×#217—64no—
49C2×C4⋊Dic3—34no—
50#924—38no—
51#924—64no—
52C2×Dic3⋊C4—64no—
53#878—68no—
54#878—68no—
55C3×C22⋊C8C2×D318yes—
56C3⋊#95—34no—
57#818—68no—
58#816—68no—
59C23×C32—21no—
60C23×C32—21no—
61C23×C32—41no—
62C23×C32—41no—
63C23×C32Q1612yes—
64C23×C32C2×D411yescharacteristic
65C2×C32×C4—21no—
66C2×C32×C4—41no—
67C2×C32×C4—41no—
68C2×C32×C4C2×D412yes—
69C2×C3⋊Dic3—22no—
70C2×C3⋊Dic3—22no—
71C2×C3⋊Dic3—22no—
72C2×C3⋊Dic3—41no—
73C2×C3⋊Dic3—41no—
74C2×C3⋊Dic3—41no—
75C2×C3⋊Dic3—41no—
76C2×C3⋊Dic3—41no—
77C2×C3⋊Dic3—81no—
78C2×C3⋊Dic3—81no—
79#634—42no—
80#634—81no—
81C32×C8—42no—
82#543—91no—
83#484—92no—
84#399—91no—
85#328—92no—
86#323C3⋊D311yescharacteristic
87C24×C3D1214yes—
88C22×C3×C4D1214yes—
89C22×C3×C4C22×D314yes—
90C22×Dic3—64no—
91C22×Dic3—64no—
92C22×Dic3—64no—
93C22×Dic3—64no—
94C2×Dic6—38no—
95C2×Dic6—64no—
96C2×C3×C8—28no—
97C3×C22⋊C4—28no—
98#217—68no—
99#217—68no—
100#217—128no—
101C4⋊Dic3—38no—
102C4⋊Dic3—64no—
103C4⋊Dic3—68no—
104Dic3⋊C4—68no—
105Dic3⋊C4—68no—
106Dic3⋊C4—128no—
107C22×C32—21no—
108C22×C32—21no—
109C22×C32—22no—
110C22×C32—42no—
111C22×C32—41no—
112C22×C32—41no—
113C22×C32—81no—
114C22×C32#12011yescharacteristic
115C22×C32C2×Q1611yescharacteristic
116C22×C32#13711yescharacteristic
117C32×C4—22no—
118C32×C4—41no—
119C3⋊Dic3—42no—
120C3⋊Dic3—42no—
121C3⋊Dic3—42no—
122C3⋊Dic3—81no—
123C22⋊Q8—92no—
124C22⋊Q8—182no—
125C22⋊Q8—182no—
126C22⋊Q8—181no—
127C2×C4⋊C4—91no—
128C2×C4⋊C4—181no—
129C2×C22⋊C4—181no—
130C2×C22⋊C4—181no—
131C2×C22⋊C4C2×C3⋊D311yescharacteristic
132#107—182no—
133#103—182no—
134C22⋊C8C2×C3⋊D312yes—
135#95—91no—
136C23×C3—24no—
137C23×C3—24no—
138C23×C3—44no—
139C23×C3—44no—
140C23×C3Dic1218yes—
141C23×C3C2×D1214yes—
142C2×C3×C4—24no—
143C2×C3×C4—44no—
144C2×C3×C4—44no—
145C2×C3×C4D3×D418yes—
146C2×Dic3—68no—
147C2×Dic3—68no—
148C2×Dic3—68no—
149C2×Dic3—124no—
150C2×Dic3—124no—
151C2×Dic3—124no—
152C2×Dic3—124no—
153C2×Dic3—124no—
154C2×Dic3—244no—
155C2×Dic3—244no—
156Dic6—128no—
157Dic6—244no—
158C3×C8—48no—
159C2×C32—21no—
160C2×C32—21no—
161C2×C32—42no—
162C2×C32#45111yescharacteristic
163C2×C32#45311yescharacteristic
164C2×C32#45811yescharacteristic
165C24C4⋊(C3⋊D3)11yescharacteristic
166C2×Q8—92no—
167C2×Q8—181no—
168C22×C4—181no—
169C22×C4—181no—
170C22×C4—181no—
171C22×C4—181no—
172C22×C4C4⋊(C3⋊D3)11yescharacteristic
173C22×C4C22×C3⋊D311yescharacteristic
174C2×C8—22no—
175C4⋊C4—92no—
176C4⋊C4—182no—
177C4⋊C4—181no—
178C4⋊C4—182no—
179C4⋊C4—182no—
180C4⋊C4—362no—
181C22⋊C4—22no—
182C22⋊C4—182no—
183C22⋊C4—182no—
184C22⋊C4—362no—
185C22×C3—24no—
186C22×C3—24no—
187C22×C3—28no—
188C22×C3—48no—
189C22×C3—44no—
190C22×C3—44no—
191C22×C3—84no—
192C22×C3#88214yes—
193C22×C3C2×Dic1214yes—
194C22×C3#90914yes—
195C3×C4—28no—
196C3×C4—44no—
197Dic3—128no—
198Dic3—128no—
199Dic3—128no—
200Dic3—244no—
201C32#161411yescharacteristic, complemented, Sylow
202C23—21no—
203C23—21no—
204C23—41no—
205C23—41no—
206C23#374612yes—
207C23C2×C4⋊(C3⋊D3)11yescharacteristic
208Q8—362no—
209Q8—721no—
210C2×C4—21no—
211C2×C4—41no—
212C2×C4—41no—
213C2×C4—182no—
214C2×C4—182no—
215C2×C4—182no—
216C2×C4—361no—
217C2×C4—361no—
218C2×C4—361no—
219C2×C4—361no—
220C2×C4—361no—
221C2×C4—721no—
222C2×C4—721no—
223C2×C4D4×C3⋊D312yes—
224C8—42no—
225C2×C3—24no—
226C2×C3—24no—
227C2×C3—48no—
228C2×C3#473914yes—
229C2×C3#474214yes—
230C2×C3#474714yes—
231C22—21no—
232C22—21no—
233C22—22no—
234C22—42no—
235C22—41no—
236C22—41no—
237C22—81no—
238C22#6409111yescharacteristic
239C22C2×#374611yescharacteristic
240C22#6411811yescharacteristic
241C4—22no—
242C4—41no—
243C4—362no—
244C4—362no—
245C4—362no—
246C4—721no—
247C3#6811714yescomplemented
248C2—21no—
249C2—21no—
250C2—42no—
251C2#1059243811yescharacteristic
252C2#1059244111yescharacteristic
253C2#1059244611yescharacteristic
subgroupG/H
centerC22#64091
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C22×C3⋊D3
FittingC32×#323C2
socleC22×C32#120
prime radicalC24×C32D4
hypercenter#323C3⋊D3
hypocenterC32#1614
LCSG ▷ C22×C32×C4 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ #323

Complements

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

NH ≅ G/Ntype
3. #10592421C2semidirect
5. #10589333C2semidirect
201. C32#1614semidirect
247. C3#68117semidirect

Maximal subgroups

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

subgroupindex
#105959542
#105926482
#105924212
C32×#3232
#105893332
#681173