Finite Group Databasebeta

← #11920708

Subgroups — #11920708

Order 1152.

383 conjugacy classes of subgroups; only the 45 normal subgroups are shown.

normal subgroups only

This group has 383 conjugacy classes of subgroups — too many to draw. Only its 45 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⋊C3)C211yesmaximal, characteristic, complemented
3C3×#5426C211yesmaximal, characteristic, complemented
4#73128—31nomaximal
5#70303—31nomaximal
6C2×C3×#41⋊C3C2211yescharacteristic
7#64267—21no—
8#64267C412yescomplemented
9C2×C3⋊GL(2,𝔽3)—21no—
10C3⋊(#131⋊C3)—21no—
11C3×#859—21no—
12#63564—41nomaximal
13C2×#986—31no—
14C2×#986—61no—
15C2×#949—31no—
16C2×#948D311yescharacteristic, complemented
17C2×#131⋊C3—31no—
18#5426D311yescharacteristic, complemented
19C3×#417—31no—
20C2×#823—31no—
21C2×#809—31no—
22#4558—31no—
23#4530—31no—
24C2×C4⋊(C3⋊D3)—41no—
25C3×#41⋊C3C2×C411yescharacteristic
26C3×#41⋊C3D411yescharacteristic
27C2×C3×SL(2,𝔽3)D411yescharacteristic
28C3⋊GL(2,𝔽3)—22no—
29C3×C4⋊Dic3—41no—
30C2×C3×C3⋊C8—41no—
31#1907—91noSylow
32C2×C3×#41C2×D311yescharacteristic
33C22×D12—31no—
34C2×#41⋊C3—21no—
35C2×#41⋊C3C2×D311yescharacteristic
36#986—32no—
37#986—62no—
38#986—62no—
39#986—61no—
40C2×GL(2,𝔽3)—62no—
41C2×GL(2,𝔽3)—61no—
42C2×C3×M16—31no—
43C2×C3×C4⋊C4—31no—
44#949—32no—
45#949—32no—
46#949—61no—
47#949—61no—
48#948—21no—
49#948—61no—
50C2×#215—61no—
51C2×#213—61no—
52C2×#208—31no—
53C2×#208—31no—
54C22×C3⋊C8—31no—
55#131⋊C3—61no—
56#859—21no—
57C3×#103—61no—
58C3×#102—61no—
59#823—62no—
60#821—121no—
61#809—61no—
62#809—61no—
63C22×C3⋊D3—81no—
64C2×C32×C4—41no—
65C4⋊(C3⋊D3)—42no—
66C4⋊(C3⋊D3)—81no—
67C2×C3×Dic3—81no—
68C3×SL(2,𝔽3)C22⋊C411yescharacteristic
69C3×C3⋊C8—81no—
70C2×AGL(1,ℤ/8)—91no—
71C2×#131—31no—
72#417—31no—
73C2×#102—91no—
74C2×#100—91no—
75#343—91no—
76#341—91no—
77C23×D3—61no—
78C3×#41—31no—
79C3×#41—31no—
80C3×#41C4×D311yescharacteristic
81C3×#41#6711yescharacteristic
82C2×C3×Q8D1211yescharacteristic
83C2×C3×D4—31no—
84C22×C3×C4—31no—
85C22×C3×C4—61no—
86C2×D12—32no—
87C2×D12—61no—
88C2×D12—61no—
89C2×D12—61no—
90C2×D12—61no—
91C2×D12—61no—
92C2×D12—121no—
93C2×D12—241no—
94#41⋊C3—21no—
95#41⋊C3—21no—
96#41⋊C3C4×D311yescharacteristic
97#41⋊C3D1211yescharacteristic
98C2×SL(2,𝔽3)—21no—
99C2×SL(2,𝔽3)#6711yescharacteristic
100GL(2,𝔽3)—64no—
101GL(2,𝔽3)—62no—
102C3×M16—61no—
103C3×M16—61no—
104C2×C3×C8—61no—
105C2×C3×C8—121no—
106C3×C4⋊C4—61no—
107C3×C4⋊C4—61no—
108#215—62no—
109#215—62no—
110#213—62no—
111#213—62no—
112C4⋊Dic3—41no—
113#208—32no—
114#208—32no—
115#208—61no—
116#208—61no—
117C2×C3⋊C8—31no—
118C2×C3⋊C8—61no—
119C2×C3⋊C8—61no—
120C2×C3⋊C8—61no—
121C2×C3⋊C8S411yescharacteristic
122C22×C32—41no—
123C2×C3⋊D3—82no—
124C2×C3⋊D3—161no—
125C2×C3⋊D3—161no—
126C32×C4—41no—
127C32×C4—41no—
128C3×Dic3—161no—
129C2×#41D3211yescharacteristic
130C22×D4—91no—
131AGL(1,ℤ/8)—92no—
132AGL(1,ℤ/8)—92no—
133AGL(1,ℤ/8)—181no—
134AGL(1,ℤ/8)—181no—
135C2×SD16—181no—
136C2×D8—181no—
137#131—61no—
138#131—181no—
139C2×M16—31no—
140C2×M16—91no—
141C2×M16—91no—
142C22×C8—91no—
143C2×C4⋊C4—31no—
144#103—61no—
145#102—61no—
146#102—181no—
147#102—181no—
148#100—182no—
149C23×C3—31no—
150C22×D3—62no—
151C22×D3—121no—
152C22×D3—121no—
153C22×D3—241no—
154C22×D3—242no—
155C22×D3—241no—
156C22×D3—241no—
157C3×Q8—31no—
158C3×Q8(C2×D3)⋊C411yescharacteristic
159C3×D4—31no—
160C3×D4—31no—
161C3×D4—61no—
162C2×C3×C4—31no—
163C2×C3×C4—31no—
164C2×C3×C4—31no—
165C2×C3×C4—31no—
166C2×C3×C4—31no—
167C2×C3×C4—41no—
168C2×C3×C4—81no—
169C2×C3×C4—121no—
170C2×C3×C4—241no—
171C2×C3×C4C2×S411yescharacteristic
172C2×Dic3—81no—
173D12—62no—
174D12—62no—
175D12—122no—
176D12—121no—
177D12—121no—
178D12—242no—
179D12—241no—
180D12—242no—
181SL(2,𝔽3)—21no—
182SL(2,𝔽3)(C2×D3)⋊C411yescharacteristic
183C3×C8—121no—
184C3×C8—241no—
185C3⋊C8—21no—
186C3⋊C8—62no—
187C3⋊C8—61no—
188C2×C32—41no—
189C2×C32—41no—
190C2×C32—41no—
191C3⋊D3—162no—
192C24—181no—
193#41—31no—
194#41—31no—
195#41#62411yescharacteristic
196#41#62611yescharacteristic
197C2×Q8#62611yescharacteristic
198C2×D4—31no—
199C2×D4—92no—
200C2×D4—181no—
201C2×D4—181no—
202C2×D4—181no—
203C2×D4—181no—
204C2×D4—181no—
205C22×C4—31no—
206C22×C4—61no—
207SD16—182no—
208SD16—182no—
209D8—182no—
210D8—182no—
211M16—61no—
212M16—61no—
213M16—92no—
214M16—92no—
215M16—181no—
216M16—181no—
217C2×C8—31no—
218C2×C8—61no—
219C2×C8—91no—
220C2×C8—181no—
221C2×C8—181no—
222C2×C8—181no—
223C4⋊C4—61no—
224C4⋊C4—61no—
225C22×C3—31no—
226C22×C3—31no—
227C22×C3—41no—
228C22×C3—61no—
229C22×C3—61no—
230C22×C3—81no—
231C22×C3C4⋊S411yescharacteristic
232C2×D3—122no—
233C2×D3—242no—
234C2×D3—244no—
235C2×D3—242no—
236C2×D3—241no—
237C2×D3—241no—
238C2×D3—242no—
239C2×D3—481no—
240C2×D3—481no—
241C2×D3—482no—
242C2×D3—482no—
243C3×C4—31no—
244C3×C4—31no—
245C3×C4—41no—
246C3×C4—41no—
247C3×C4—81no—
248C3×C4—81no—
249C3×C4—241no—
250C3×C4C4×S411yescharacteristic
251C3×C4GL(2,ℤ/4)11yescharacteristic
252Dic3—161no—
253C32—41noSylow
254C23—31no—
255C23—182no—
256C23—361no—
257C23—361no—
258C23—721no—
259C23—721no—
260Q8—31no—
261Q8#372211yescharacteristic
262D4—31no—
263D4—31no—
264D4—61no—
265D4—182no—
266D4—182no—
267D4—361no—
268D4—361no—
269C2×C4—31no—
270C2×C4—31no—
271C2×C4—31no—
272C2×C4—31no—
273C2×C4—31no—
274C2×C4—121no—
275C2×C4—241no—
276C2×C4D3×S411yescharacteristic
277C8—61no—
278C8—121no—
279C8—182no—
280C8—181no—
281C2×C3—41no—
282C2×C3—41no—
283C2×C3—41no—
284C2×C3—61no—
285C2×C3—61no—
286C2×C3—81no—
287C2×C3—81no—
288C2×C3—81no—
289C2×C3#540611yescharacteristic
290C2×C3#540711yescharacteristic
291C2×C3(C2×S4)⋊C411yescharacteristic
292D3—242no—
293D3—482no—
294D3—484no—
295C22—31no—
296C22—31no—
297C22—61no—
298C22—61no—
299C22—362no—
300C22—722no—
301C22—722no—
302C22—721no—
303C22—721no—
304C22#6420711yescharacteristic
305C4—31no—
306C4—31no—
307C4—241no—
308C4(C3⋊S4)⋊C411yescharacteristic
309C4#6421011yescharacteristic
310C3—41no—
311C3—81no—
312C3#7312811yescharacteristic, complemented
313C2—61no—
314C2—61no—
315C2—722no—
316C2#1059322411yescharacteristic
317C2#1059322511yescharacteristic
318C2#1059324211yescharacteristic
subgroupG/H
centerC22#64207
commutatorC3×#41⋊C3C2×C4
Frattini, hypercenterC2×C4D3×S4
FittingC2×C3×#41C2×D3
socleC22×C3C4⋊S4
prime radicalC2×#64267C2
cosocleC2×C3×#41⋊C3C22
hypocenterC3×SL(2,𝔽3)C22⋊C4
LCSG ▷ C3×#41⋊C3 ▷ C3×SL(2,𝔽3)
UCSC1 ◁ C22 ◁ C2×C4

Complements

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

NH ≅ G/Ntype
2. C2×C3⋊(#131⋊C3)C2semidirect
3. C3×#5426C2semidirect
8. #64267C4semidirect
16. C2×#948D3semidirect
18. #5426D3semidirect
312. 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⋊C3)2
C3×#54262
#731283
#703033
#635644