Finite Group Databasebeta

← #11796741

Subgroups — #11796741

Order 1152.

569 conjugacy classes of subgroups; only the 100 normal subgroups are shown.

normal subgroups only

This group has 569 conjugacy classes of subgroups — too many to draw. Only its 100 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
1C2×Q16×C3⋊D3C211yesmaximal, characteristic
2#10590714C211yesmaximal, characteristic
3C2×#63544C211yesmaximal, characteristic
4C3×#4564C212yesmaximal, complemented
5#10589119C212yesmaximal, complemented
6#69222—32nomaximal
7C2×Q8×C3⋊D3—21no—
8C2×C32×Q16C2211yescharacteristic
9C2×#3756—21no—
10Q16×C3⋊D3—22no—
11Q16×C3⋊D3C414yescomplemented
12C2×#3746C2211yescharacteristic
13C2×C8×C3⋊D3C2211yescharacteristic
14#63849—21no—
15C3×#818C2212yes—
16C2×C3×C3⋊C16C2212yes—
17#63574—21no—
18#63544—22no—
19C2×D3×Q16—32no—
20C2×D3×Q16—61no—
21C2×#798—32no—
22#4880—32no—
23C3×#358—32no—
24#4564D312yescomplemented
25#4503—32no—
26#4492—32no—
27C2×C32×Q8—21no—
28Q8×C3⋊D3—24no—
29Q8×C3⋊D3—42no—
30C2×C4×C3⋊D3—41no—
31C2×C4×C3⋊D3D411yescharacteristic
32C2×#634—21no—
33C2×#634—41no—
34C32×Q16—21no—
35C32×Q16C2×C412yes—
36C2×C32×C8C2311yescharacteristic
37#3756—24no—
38C2×C3⋊(C3⋊C8)D411yescharacteristic
39#3746—21no—
40#3746C2×C412yes—
41C8×C3⋊D3C2×C412yes—
42C8×C3⋊D3D412yes—
43C3×C4⋊Dic3—22no—
44#3722—41no—
45Dic32—41no—
46C3×C3⋊C16—22no—
47#2141—91noSylow
48C2×D3×Q8—62no—
49C2×D3×Q8—62no—
50C2×C3×Q16—21no—
51C2×C3×Q16C2×D312yes—
52C2×#216—62no—
53C2×#216—62no—
54D3×Q16—38no—
55D3×Q16—64no—
56D3×Q16—64no—
57D3×Q16—64no—
58C2×Dic12—32no—
59C2×Dic12—61no—
60C2×D3×C8—32no—
61C2×D3×C8—61no—
62#892—62no—
63C2×C3×C16—32no—
64C3×#107—32no—
65#818C2×D312yes—
66C2×C3⋊C16C2×D312yes—
67#808—62no—
68#798—64no—
69C22×C3⋊D3D811yescharacteristic
70C32×Q8—22no—
71C32×Q8—41no—
72C2×C32×C4—41no—
73C2×C32×C4C2×D411yescharacteristic
74C2×C3⋊Dic3—41no—
75C2×C3⋊Dic3D811yescharacteristic
76C4×C3⋊D3—44no—
77C4×C3⋊D3C22⋊C412yes—
78C4×C3⋊D3SD1612yes—
79#634—22no—
80#634—41no—
81#634—44no—
82C2×C3×Dic3—42no—
83C32×C8C22×C411yescharacteristic
84C32×C8C2×D411yescharacteristic
85C3⋊(C3⋊C8)C22⋊C412yes—
86C22×Q16—91no—
87C2×M32—91no—
88#427—91no—
89#358—32no—
90#358—92no—
91C2×C3×Q8—22no—
92C2×C3×Q8—22no—
93D3×Q8—68no—
94D3×Q8—68no—
95D3×Q8—124no—
96D3×Q8—124no—
97C2×C4×D3—32no—
98C2×C4×D3—61no—
99C2×C4×D3—122no—
100C2×C4×D3—122no—
101C2×Dic6—62no—
102C2×Dic6—62no—
103C2×Dic6—122no—
104C2×Dic6—122no—
105C3×Q16—22no—
106C3×Q16—22no—
107C3×Q16—22no—
108C3×Q16C4×D314yes—
109C2×C3×C8—21no—
110C2×C3×C8C22×D312yes—
111C3×C4⋊C4—62no—
112#216—68no—
113#216—68no—
114(C2×D3)⋊C4—122no—
115C4⋊Dic3—22no—
116C4×Dic3—122no—
117C2×C3⋊C8—32no—
118C2×C3⋊C8—61no—
119Dic12—34no—
120Dic12—62no—
121Dic12—62no—
122Dic12—62no—
123D3×C8—34no—
124D3×C8—34no—
125D3×C8—62no—
126D3×C8—62no—
127C3×C16—62no—
128C3⋊C16—22no—
129C22×C32C2×D811yescharacteristic
130C2×C3⋊D3—22no—
131C2×C3⋊D3#10212yes—
132C32×C4—42no—
133C32×C4C2×C22⋊C411yescharacteristic
134C32×C4C2×SD1611yescharacteristic
135C3⋊Dic3—42no—
136C3⋊Dic3#10212yes—
137C3×Dic3—82no—
138C22×Q8—181no—
139C2×Q16—94no—
140C2×Q16—91no—
141C2×Q16—182no—
142C2×Q16—181no—
143C2×Q16D3211yescharacteristic
144C22×C8—91no—
145#117—181no—
146M32—182no—
147C2×C16—32no—
148#107—32no—
149#106—181no—
150C22×D3—32no—
151C22×D3—61no—
152C3×Q8—24no—
153C3×Q8—24no—
154C3×Q8—42no—
155C3×Q8—42no—
156C2×C3×C4—21no—
157C2×C3×C4—42no—
158C2×C3×C4—42no—
159C2×C3×C4—122no—
160C2×C3×C4D3×D412yes—
161C2×Dic3—32no—
162C2×Dic3—42no—
163C2×Dic3—61no—
164C2×Dic3—122no—
165C2×Dic3—122no—
166C4×D3—34no—
167C4×D3—34no—
168C4×D3—62no—
169C4×D3—62no—
170C4×D3—128no—
171C4×D3—128no—
172Dic6—64no—
173Dic6—64no—
174Dic6—128no—
175Dic6—128no—
176Dic6—122no—
177Dic6—122no—
178C3×C8—21no—
179C3×C8—21no—
180C3×C8C2×C4×D312yes—
181C3×C8D3×D412yes—
182C3⋊C8—34no—
183C3⋊C8—62no—
184C2×C32C2×#10211yescharacteristic
185C2×C32#51012yes—
186C3⋊D3—22no—
187C2×Q8—21no—
188C2×Q8—184no—
189C2×Q8—181no—
190C2×Q8—361no—
191C2×Q8—362no—
192C22×C4—91no—
193C22×C4—361no—
194Q16—21no—
195Q16—92no—
196Q16—184no—
197Q16—181no—
198Q16#62412yes—
199C2×C8—91no—
200C2×C8—92no—
201C2×C8—92no—
202C2×C8C2×D3211yescharacteristic
203C4⋊C4—62no—
204C22⋊C4—361no—
205C42—361no—
206C16—62no—
207C22×C3—21no—
208C22×C3D3×D812yes—
209C2×D3—34no—
210C2×D3—62no—
211C2×D3—64no—
212C2×D3—62no—
213C2×D3—62no—
214C3×C4—21no—
215C3×C4—21no—
216C3×C4—44no—
217C3×C4—44no—
218C3×C4—242no—
219C3×C4D3×C22⋊C412yes—
220C3×C4D3×SD1612yes—
221Dic3—34no—
222Dic3—62no—
223Dic3—82no—
224Dic3—124no—
225Dic3—124no—
226C32#214111yescharacteristic, complemented, Sylow
227C23—91no—
228Q8—22no—
229Q8—41no—
230Q8—182no—
231Q8—364no—
232Q8—361no—
233C2×C4—41no—
234C2×C4—91no—
235C2×C4—92no—
236C2×C4—92no—
237C2×C4—122no—
238C2×C4—364no—
239C2×C4—361no—
240C2×C4#381111yescharacteristic
241C8—92no—
242C8C2×#62411yescharacteristic
243C8#381111yescharacteristic
244C2×C3—22no—
245C2×C3—21no—
246C2×C3D3×#10212yes—
247C2×C3#491512yes—
248C2×C3#491812yes—
249D3—64no—
250D3—64no—
251C22—92no—
252C22—182no—
253C22#6392611yescharacteristic
254C4—42no—
255C4—92no—
256C4—242no—
257C4—362no—
258C4#6393011yescharacteristic
259C4#6397411yescharacteristic
260C3—21no—
261C3#6922212yescomplemented
262C2—182no—
263C2#1059105012yes—
264C2#1059141611yescharacteristic
subgroupG/H
centerC22#63926
commutatorC32×C8C22×C4
FrattiniC2×C8C2×D32
FittingC2×C32×Q16C22
socleC22×C32C2×D8
prime radicalC22×C3⋊D3D8
cosocleC2×C32×C8C23
hypercenterC2×Q16D32
hypocenterC32#2141
LCSG ▷ C32×C8 ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ C2×Q16

Complements

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

NH ≅ G/Ntype
4. C3×#4564C2semidirect
5. #10589119C2semidirect
11. Q16×C3⋊D3C4semidirect
24. #4564D3semidirect
226. C32#2141semidirect
261. C3#69222semidirect

Maximal subgroups

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

subgroupindex
C2×Q16×C3⋊D32
#105907142
C2×#635442
C3×#45642
#105891192
#692223