Finite Group Databasebeta

← #11921084

Subgroups — #11921084

Order 1152.

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

normal subgroups only

This group has 424 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×#64267C211yesmaximal, characteristic
2C2×C3×#131⋊C3C211yesmaximal, characteristic, complemented
3#10593660C211yesmaximal, characteristic, complemented
4#73128—33nomaximal
5#72018—31nomaximal
6C2×C3×#41⋊C3C2211yescharacteristic
7#64267—21no—
8#64267C412yescomplemented
9C2×C3⋊GL(2,𝔽3)—21no—
10C3×#131⋊C3—21no—
11C3⋊#859—21no—
12#63648—41nomaximal
13C2×#986—33no—
14C2×C3×#131D311yescharacteristic, complemented
15C2×#949—31no—
16C2×#131⋊C3D313yescomplemented
17#5426—33no—
18#5232—31no—
19C2×#823—31no—
20C2×#821—31no—
21#4554—31no—
22#4552—31no—
23C2×C4⋊(C3⋊D3)—41no—
24C3×#41⋊C3C2×C411yescharacteristic
25C3×#41⋊C3D411yescharacteristic
26C2×C3×SL(2,𝔽3)D411yescharacteristic
27C3⋊GL(2,𝔽3)—22no—
28C2×C32×C8—41no—
29C4⋊(C3⋊Dic3)—41no—
30#1907—91noSylow
31C2×C3×#41C2×D311yescharacteristic
32C22×D12—31no—
33C2×#41⋊C3C2×D313yes—
34#986—36no—
35#986—63no—
36C2×GL(2,𝔽3)—63no—
37C3×#131—21no—
38C3×#131—61no—
39C2×C3×M16—31no—
40C22×C3×C8—31no—
41#949—32no—
42#949—32no—
43#949—61no—
44#949—61no—
45C2×#215—61no—
46C2×#213—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#823—62no—
55#821—61no—
56#821—61no—
57#821—123no—
58C22×C3⋊D3—81no—
59C2×C32×C4—41no—
60C2×C3⋊Dic3—81no—
61C4⋊(C3⋊D3)—42no—
62C4⋊(C3⋊D3)—81no—
63C3×SL(2,𝔽3)C22⋊C411yescharacteristic
64C32×C8—81no—
65C2×AGL(1,ℤ/8)—91no—
66C2×#131C3⋊D311yescharacteristic, complemented
67#417—91no—
68C2×#102—91no—
69C2×#100—91no—
70#343—91no—
71#341—91no—
72C23×D3—61no—
73C3×#41—31no—
74C3×#41—31no—
75C3×#41C4×D311yescharacteristic
76C3×#41#6711yescharacteristic
77C2×C3×Q8D1211yescharacteristic
78C2×C3×D4—31no—
79C22×C3×C4—31no—
80C22×Dic3—61no—
81C2×D12—32no—
82C2×D12—61no—
83C2×D12—61no—
84C2×D12—61no—
85C2×D12—61no—
86C2×D12—61no—
87C2×D12—123no—
88#41⋊C3C4×D313yes—
89#41⋊C3#6713yes—
90C2×SL(2,𝔽3)D1213yes—
91GL(2,𝔽3)—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#215—62no—
100#215—62no—
101#213—62no—
102#213—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—
113C2×C3⋊D3—82no—
114C2×C3⋊D3—161no—
115C2×C3⋊D3—161no—
116C32×C4—41no—
117C32×C4—41no—
118C3⋊Dic3—161no—
119C2×#41C2×C3⋊D311yescharacteristic
120C22×D4—91no—
121AGL(1,ℤ/8)—92no—
122AGL(1,ℤ/8)—92no—
123AGL(1,ℤ/8)—181no—
124AGL(1,ℤ/8)—181no—
125C2×SD16—181no—
126C2×D8—181no—
127#131—21no—
128#131—61no—
129C2×M16—31no—
130C2×M16—91no—
131C2×M16—91no—
132C22×C8—31no—
133C2×C4⋊C4—91no—
134#103—181no—
135#102—181no—
136#102—181no—
137#102—181no—
138#100—182no—
139C23×C3—31no—
140C22×D3—62no—
141C22×D3—121no—
142C22×D3—121no—
143C22×D3—243no—
144C22×D3—241no—
145C22×D3—241no—
146C3×Q8—31no—
147C3×Q8(C2×D3)⋊C411yescharacteristic
148C3×D4—31no—
149C3×D4—31no—
150C3×D4—61no—
151C2×C3×C4—31no—
152C2×C3×C4—31no—
153C2×C3×C4—31no—
154C2×C3×C4—31no—
155C2×C3×C4—31no—
156C2×C3×C4—43no—
157C2×C3×C4C2×S411yescharacteristic
158C2×Dic3—121no—
159C2×Dic3—243no—
160C2×Dic3—241no—
161D12—62no—
162D12—62no—
163D12—126no—
164D12—121no—
165D12—121no—
166D12—243no—
167SL(2,𝔽3)(C2×D3)⋊C413yes—
168C3×C8—21no—
169C3×C8—61no—
170C3×C8—83no—
171C3⋊C8—62no—
172C3⋊C8—121no—
173C2×C32—41no—
174C2×C32—41no—
175C2×C32—41no—
176C3⋊D3—162no—
177C24—181no—
178#41—31no—
179#41—31no—
180#41C4×C3⋊D311yescharacteristic
181#41#63811yescharacteristic
182C2×Q8C4⋊(C3⋊D3)11yescharacteristic
183C2×D4—31no—
184C2×D4—92no—
185C2×D4—181no—
186C2×D4—181no—
187C2×D4—181no—
188C2×D4—181no—
189C2×D4—181no—
190C22×C4—31no—
191C22×C4—181no—
192SD16—182no—
193SD16—182no—
194D8—182no—
195D8—182no—
196M16—32no—
197M16—61no—
198M16—92no—
199M16—181no—
200M16—181no—
201M16—181no—
202C2×C8—31no—
203C2×C8—61no—
204C2×C8—61no—
205C2×C8—181no—
206C2×C8—181no—
207C2×C8C3⋊S411yescharacteristic
208C4⋊C4—181no—
209C4⋊C4—181no—
210C22×C3—31no—
211C22×C3—31no—
212C22×C3—43no—
213C22×C3—61no—
214C22×C3—61no—
215C22×C3C4⋊S411yescharacteristic
216C2×D3—122no—
217C2×D3—246no—
218C2×D3—242no—
219C2×D3—241no—
220C2×D3—241no—
221C2×D3—242no—
222C2×D3—483no—
223C2×D3—483no—
224C3×C4—31no—
225C3×C4—31no—
226C3×C4—43no—
227C3×C4—43no—
228C3×C4C4×S411yescharacteristic
229C3×C4GL(2,ℤ/4)11yescharacteristic
230Dic3—241no—
231Dic3—483no—
232C32—41noSylow
233C23—31no—
234C23—182no—
235C23—361no—
236C23—361no—
237C23—721no—
238C23—721no—
239Q8—31no—
240Q8#375211yescharacteristic
241D4—31no—
242D4—31no—
243D4—61no—
244D4—182no—
245D4—182no—
246D4—361no—
247D4—361no—
248C2×C4—31no—
249C2×C4—31no—
250C2×C4—31no—
251C2×C4—31no—
252C2×C4—31no—
253C2×C4—361no—
254C2×C4—721no—
255C2×C4C2×C3⋊S411yescharacteristic
256C8—21no—
257C8—61no—
258C8—182no—
259C8—361no—
260C2×C3—43no—
261C2×C3—43no—
262C2×C3—43no—
263C2×C3—61no—
264C2×C3—61no—
265C2×C3#540611yescharacteristic
266C2×C3#540711yescharacteristic
267C2×C3(C2×S4)⋊C411yescharacteristic
268D3—242no—
269D3—486no—
270C22—31no—
271C22—31no—
272C22—61no—
273C22—61no—
274C22—362no—
275C22—722no—
276C22—722no—
277C22—721no—
278C22—721no—
279C22C4⋊(C3⋊S4)11yescharacteristic
280C4—31no—
281C4—31no—
282C4—721no—
283C4C4×C3⋊S411yescharacteristic
284C4#6426911yescharacteristic
285C3—43no—
286C3#7312811yescharacteristic, complemented
287C2—61no—
288C2—61no—
289C2—722no—
290C2#1059364011yescharacteristic
291C2#1059364111yescharacteristic
292C2#1059364711yescharacteristic
subgroupG/H
centerC22C4⋊(C3⋊S4)
commutatorC3×#41⋊C3C2×C4
FrattiniC2×C4C2×C3⋊S4
FittingC2×C3×#131D3
socleC22×C3C4⋊S4
prime radicalC2×#64267C2
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
2. C2×C3×#131⋊C3C2semidirect
3. #10593660C2semidirect
8. #64267C4semidirect
14. C2×C3×#131D3semidirect
16. C2×#131⋊C3D3semidirect
66. C2×#131C3⋊D3semidirect
286. C3#73128semidirect

Maximal subgroups

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

subgroupindex
C2×#642672
C2×C3×#131⋊C32
#105936602
#731283
#720183
#636484