Finite Group Databasebeta

← #11921082

Subgroups — #11921082

Order 1152.

388 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 388 conjugacy classes of subgroups — too many to draw. Only its 59 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×#64265C211yesmaximal, characteristic
2C2×C3×#131⋊C3C211yesmaximal, characteristic
3#10593660C211yesmaximal, characteristic
4#73124—33nomaximal
5#72019—31nomaximal
6C2×C3×#41⋊C3C2211yescharacteristic
7#64265—21no—
8#64265C412yescomplemented
9C2×C3⋊#226—21no—
10C3×#131⋊C3—21no—
11C3⋊#859—21no—
12#63643—41nomaximal
13C2×#984—33no—
14C2×C3×#131D311yescharacteristic
15C2×#951—31no—
16C2×#131⋊C3D313yes—
17#5426—33no—
18#5232—31no—
19C2×#824—31no—
20C2×#816—31no—
21#4554—31no—
22#4552—31no—
23C2×#634—41no—
24C3×#41⋊C3C2×C411yescharacteristic
25C3×#41⋊C3D411yescharacteristic
26C2×C3×SL(2,𝔽3)D411yescharacteristic
27C3⋊#226—22no—
28C2×C32×C8—41no—
29C4⋊(C3⋊Dic3)—41no—
30#1908—91noSylow
31C2×C3×#41C2×D311yescharacteristic
32C22×Dic6—31no—
33C2×#41⋊C3C2×D313yes—
34#984—36no—
35#984—63no—
36C2×#226—63no—
37C3×#131—21no—
38C3×#131—61no—
39C2×C3×M16—31no—
40C22×C3×C8—31no—
41#951—32no—
42#951—32no—
43#951—61no—
44#951—61no—
45C2×#216—61no—
46C2×#214—61no—
47C2×C4⋊Dic3—31no—
48C2×#208—31no—
49C2×#208—31no—
50#131⋊C3—23no—
51#859—63no—
52#835—61no—
53#832—61no—
54#824—62no—
55#816—61no—
56#816—61no—
57#816—123no—
58C2×C32×C4—41no—
59C2×C3⋊Dic3—81no—
60C2×C3⋊Dic3—81no—
61#634—42no—
62#634—81no—
63C3×SL(2,𝔽3)C22⋊C411yescharacteristic
64C32×C8—81no—
65C2×#137—91no—
66C2×#131C3⋊D311yescharacteristic
67#417—91no—
68C2×#103—91no—
69C2×#101—91no—
70#343—91no—
71#341—91no—
72C3×#41—31no—
73C3×#41—31no—
74C3×#41C4×D311yescharacteristic
75C3×#41#6711yescharacteristic
76C2×C3×Q8D1211yescharacteristic
77C2×C3×D4—31no—
78C22×C3×C4—31no—
79C22×Dic3—61no—
80C22×Dic3—61no—
81C2×Dic6—32no—
82C2×Dic6—61no—
83C2×Dic6—61no—
84C2×Dic6—61no—
85C2×Dic6—61no—
86C2×Dic6—61no—
87C2×Dic6—123no—
88#41⋊C3C4×D313yes—
89#41⋊C3#6713yes—
90C2×SL(2,𝔽3)D1213yes—
91#226—66no—
92C3×M16—32no—
93C3×M16—61no—
94C2×C3×C8—31no—
95C2×C3×C8—43no—
96C2×C3×C8—61no—
97C2×C3×C8—61no—
98C2×C3×C8S411yescharacteristic
99#216—62no—
100#216—62no—
101#214—62no—
102#214—62no—
103C4⋊Dic3—61no—
104C4⋊Dic3—61no—
105C4⋊Dic3—123no—
106#208—32no—
107#208—61no—
108#208—61no—
109#208—61no—
110C2×C3⋊C8—61no—
111C2×C3⋊C8—61no—
112C22×C32—41no—
113C32×C4—41no—
114C32×C4—41no—
115C3⋊Dic3—82no—
116C3⋊Dic3—161no—
117C2×#41C2×C3⋊D311yescharacteristic
118C22×Q8—91no—
119#137—92no—
120#137—92no—
121#137—181no—
122#137—181no—
123C2×Q16—181no—
124C2×SD16—181no—
125#131—21no—
126#131—61no—
127C2×M16—31no—
128C2×M16—91no—
129C2×M16—91no—
130C22×C8—31no—
131C2×C4⋊C4—91no—
132#103—181no—
133#103—181no—
134#103—181no—
135#102—181no—
136#101—182no—
137C23×C3—31no—
138C3×Q8—31no—
139C3×Q8(C2×D3)⋊C411yescharacteristic
140C3×D4—31no—
141C3×D4—31no—
142C3×D4—61no—
143C2×C3×C4—31no—
144C2×C3×C4—31no—
145C2×C3×C4—31no—
146C2×C3×C4—31no—
147C2×C3×C4—31no—
148C2×C3×C4—43no—
149C2×C3×C4C2×S411yescharacteristic
150C2×Dic3—62no—
151C2×Dic3—121no—
152C2×Dic3—121no—
153C2×Dic3—121no—
154C2×Dic3—243no—
155C2×Dic3—243no—
156C2×Dic3—241no—
157Dic6—62no—
158Dic6—62no—
159Dic6—126no—
160Dic6—121no—
161Dic6—121no—
162Dic6—243no—
163SL(2,𝔽3)(C2×D3)⋊C413yes—
164C3×C8—21no—
165C3×C8—61no—
166C3×C8—83no—
167C3⋊C8—62no—
168C3⋊C8—121no—
169C2×C32—41no—
170C2×C32—41no—
171C2×C32—41no—
172#41—31no—
173#41—31no—
174#41C4×C3⋊D311yescharacteristic
175#41#63811yescharacteristic
176C2×Q8—92no—
177C2×Q8—181no—
178C2×Q8—181no—
179C2×Q8—181no—
180C2×Q8—181no—
181C2×Q8—181no—
182C2×Q8C4⋊(C3⋊D3)11yescharacteristic
183C2×D4—31no—
184C22×C4—31no—
185C22×C4—181no—
186C22×C4—181no—
187Q16—182no—
188Q16—182no—
189SD16—182no—
190SD16—182no—
191M16—32no—
192M16—61no—
193M16—92no—
194M16—181no—
195M16—181no—
196M16—181no—
197C2×C8—31no—
198C2×C8—61no—
199C2×C8—61no—
200C2×C8—181no—
201C2×C8—181no—
202C2×C8C3⋊S411yescharacteristic
203C4⋊C4—181no—
204C4⋊C4—181no—
205C22×C3—31no—
206C22×C3—31no—
207C22×C3—43no—
208C22×C3—61no—
209C22×C3—61no—
210C22×C3C4⋊S411yescharacteristic
211C3×C4—31no—
212C3×C4—31no—
213C3×C4—43no—
214C3×C4—43no—
215C3×C4C4×S411yescharacteristic
216C3×C4GL(2,ℤ/4)11yescharacteristic
217Dic3—122no—
218Dic3—246no—
219Dic3—241no—
220Dic3—483no—
221C32—41noSylow
222C23—31no—
223Q8—31no—
224Q8—182no—
225Q8—182no—
226Q8—361no—
227Q8—361no—
228Q8#375211yescharacteristic
229D4—31no—
230D4—31no—
231D4—61no—
232C2×C4—31no—
233C2×C4—31no—
234C2×C4—31no—
235C2×C4—31no—
236C2×C4—31no—
237C2×C4—182no—
238C2×C4—361no—
239C2×C4—361no—
240C2×C4—361no—
241C2×C4—721no—
242C2×C4C2×C3⋊S411yescharacteristic
243C8—21no—
244C8—61no—
245C8—182no—
246C8—361no—
247C2×C3—43no—
248C2×C3—43no—
249C2×C3—43no—
250C2×C3—61no—
251C2×C3—61no—
252C2×C3#540311yescharacteristic
253C2×C3#540611yescharacteristic
254C2×C3(C2×S4)⋊C411yescharacteristic
255C22—31no—
256C22—31no—
257C22—61no—
258C22—61no—
259C22C4⋊(C3⋊S4)11yescharacteristic
260C4—31no—
261C4—31no—
262C4—362no—
263C4—721no—
264C4C4×C3⋊S411yescharacteristic
265C4#6426911yescharacteristic
266C3—43no—
267C3#7312411yescharacteristic, complemented
268C2—61no—
269C2—61no—
270C2#1059363711yescharacteristic
271C2#1059364011yescharacteristic
272C2#1059364711yescharacteristic
subgroupG/H
centerC22C4⋊(C3⋊S4)
commutatorC3×#41⋊C3C2×C4
FrattiniC2×C4C2×C3⋊S4
FittingC2×C3×#131D3
socleC22×C3C4⋊S4
prime radical, cosocleC2×C3×#41⋊C3C22
hypercenterC2×C8C3⋊S4
hypocenterC3×SL(2,𝔽3)C22⋊C4
LCSG ▷ C3×#41⋊C3 ▷ C3×SL(2,𝔽3)
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8

Complements

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

NH ≅ G/Ntype
8. #64265C4semidirect
267. C3#73124semidirect

Maximal subgroups

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

subgroupindex
C2×#642652
C2×C3×#131⋊C32
#105936602
#731243
#720193
#636434