Finite Group Databasebeta

← #11808064

Subgroups — #11808064

Order 1152.

1035 conjugacy classes of subgroups; only the 244 normal subgroups are shown.

normal subgroups only

This group has 1035 conjugacy classes of subgroups — too many to draw. Only its 244 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×#64085C211yesmaximal, characteristic
2C3×#4937C211yesmaximal, characteristic, complemented
3C3×#4935C211yesmaximal, characteristic, complemented
4#10591378C213yesmaximal
5#10591266C213yesmaximal
6#10591264C213yesmaximal, complemented
7#10591263C213yesmaximal, complemented
8#74361—31nomaximal
9#74299—31nomaximal
10C22×#624C2211yescharacteristic
11C2×C32×C42C2211yescharacteristic
12C2×#3752C2213yes—
13C2×#3750C2213yes—
14#64085C418yescomplemented
15C2×C3×C4⋊Dic3C2213yes—
16C2×C3×C4⋊Dic3C2213yes—
17C2×#3724C2213yes—
18C2×#3722C2213yes—
19C2×Dic32C2213yes—
20C3×C3⋊#95C2213yes—
21C3×C3⋊#95C2213yes—
22#63579C2213yes—
23#63579C2213yes—
24C2×#876—31no—
25C2×#876—31no—
26C2×#876—61no—
27C3×#384—31no—
28C3×#383—31no—
29#4990—33no—
30#4989—33no—
31#4978—33no—
32#4976—33no—
33#4937D311yescharacteristic, complemented
34#4935D311yescharacteristic, complemented
35#4670—33no—
36#4668—33no—
37#4655—33no—
38#4647—33no—
39C23×C3⋊D3C2311yescharacteristic
40C22×C32×C4C2313yes—
41C22×C3⋊Dic3C2313yes—
42C22×C3×Dic3C2311yescharacteristic
43C22×C3×Dic3C2313yes—
44C22×C3×Dic3C2311yescharacteristic
45C22×C3×Dic3C2313yes—
46C2×#624—43no—
47C32×C42C2×C414yescomplemented
48#3752C2×C4112yes—
49#3750C2×C4112yescomplemented
50C3×C4⋊Dic3—43no—
51C3×C4⋊Dic3—43no—
52#3724—43no—
53#3722—43no—
54Dic32—43no—
55#2383—91noSylow
56C22×C4×D3—31no—
57C22×C4×D3—31no—
58C2×C3×C4⋊C4—33no—
59C2×C3×C4⋊C4—33no—
60C2×C3×C42—21no—
61C2×C3×C42C2×D311yescharacteristic
62C2×C3×C42C2×D311yescharacteristic
63C2×(C2×D3)⋊C4—33no—
64C2×(C2×D3)⋊C4—33no—
65C2×(C2×D3)⋊C4—33no—
66C2×(C2×D3)⋊C4—33no—
67C2×(C2×D3)⋊C4—63no—
68C2×C4⋊Dic3C2×D313yes—
69C2×C4⋊Dic3C2×D313yes—
70C2×Dic3⋊C4—33no—
71C2×Dic3⋊C4—33no—
72C2×Dic3⋊C4—33no—
73C2×Dic3⋊C4—33no—
74C2×Dic3⋊C4—63no—
75C2×C4×Dic3—33no—
76C2×C4×Dic3—33no—
77#876—38no—
78#876—38no—
79#876—68no—
80C3×#95—33no—
81C3×#95—33no—
82C3⋊#95—33no—
83C3⋊#95—33no—
84C3⋊#95—33no—
85C3⋊#95—33no—
86C3⋊#95C2×D313yes—
87C3⋊#95C2×D313yes—
88C23×C32C2411yescharacteristic
89C22×C3⋊D3—23no—
90C22×C3⋊D3—23no—
91C22×C3⋊D3C22×C412yes—
92C2×C32×C4—23no—
93C2×C32×C4—23no—
94C2×C32×C4C22×C416yes—
95C2×C3⋊Dic3—23no—
96C2×C3⋊Dic3—23no—
97C2×C3⋊Dic3C22×C416yes—
98C2×C3×Dic3—23no—
99C2×C3×Dic3—23no—
100C2×C3×Dic3—23no—
101C2×C3×Dic3—23no—
102C2×C3×Dic3—23no—
103C2×C3×Dic3—23no—
104C2×C3×Dic3—26no—
105#624—44no—
106C2×#126—91no—
107#389—93no—
108#388—93no—
109#387—93no—
110#385—93no—
111#384—31no—
112#383—31no—
113C23×D3—31no—
114C23×D3—31no—
115C23×D3—61no—
116C22×C3×C4—23no—
117C22×C3×C4—31no—
118C22×C3×C4—33no—
119C22×C3×C4—33no—
120C22×C3×C4—31no—
121C22×C3×C4C22×D313yes—
122C22×C3×C4C22×D313yes—
123C22×Dic3—33no—
124C22×Dic3—33no—
125C22×Dic3—63no—
126C22×Dic3C22×D311yescharacteristic
127C22×Dic3C22×D313yes—
128C22×Dic3C22×D313yes—
129C22×Dic3C22×D311yescharacteristic
130C2×C4×D3—123no—
131C2×C4×D3—123no—
132C3×C4⋊C4—123no—
133C3×C4⋊C4—123no—
134C3×C42—24no—
135C3×C42C4×D314yescomplemented
136C3×C42C4×D314yescomplemented
137(C2×D3)⋊C4—312no—
138(C2×D3)⋊C4—312no—
139(C2×D3)⋊C4—612no—
140(C2×D3)⋊C4—123no—
141(C2×D3)⋊C4—123no—
142C4⋊Dic3—43no—
143C4⋊Dic3—43no—
144Dic3⋊C4—312no—
145Dic3⋊C4—312no—
146Dic3⋊C4—612no—
147Dic3⋊C4—123no—
148Dic3⋊C4—123no—
149C4×Dic3—123no—
150C4×Dic3—123no—
151C22×C32C23×C411yescharacteristic
152C22×C32H(5,𝔽2)13yes—
153C22×C322−1+413yes—
154C2×C3⋊D3—26no—
155C2×C3⋊D3—41no—
156C2×C3⋊D3—43no—
157C32×C4—26no—
158C3⋊Dic3—26no—
159C3×Dic3—41no—
160C3×Dic3—41no—
161C3×Dic3—43no—
162C3×Dic3—43no—
163C23×C4—91no—
164#126—98no—
165C2×C4⋊C4—33no—
166C2×C4⋊C4—33no—
167C2×C4⋊C4—93no—
168C2×C4⋊C4—93no—
169C2×C22⋊C4—93no—
170C2×C22⋊C4—93no—
171C2×C42—93no—
172C2×C42D3211yescharacteristic
173#95—33no—
174#95—33no—
175#95—93no—
176#95—93no—
177C23×C3—21no—
178C23×C3C23×D311yescharacteristic
179C23×C3C23×D311yescharacteristic
180C22×D3—32no—
181C22×D3—32no—
182C22×D3—62no—
183C22×D3—63no—
184C22×D3—63no—
185C22×D3—63no—
186C22×D3—63no—
187C22×D3—123no—
188C22×D3—123no—
189C2×C3×C4—23no—
190C2×C3×C4—23no—
191C2×C3×C4—23no—
192C2×C3×C4—23no—
193C2×C3×C4—26no—
194C2×C3×C4—43no—
195C2×C3×C4—43no—
196C2×C3×C4—63no—
197C2×C3×C4—63no—
198C2×C3×C4—66no—
199C2×C3×C4—63no—
200C2×C3×C4—63no—
201C2×C3×C4—63no—
202C2×C3×C4—63no—
203C2×C3×C4C2×C4×D316yes—
204C2×C3×C4C2×C4×D316yes—
205C2×Dic3—23no—
206C2×Dic3—23no—
207C2×Dic3—23no—
208C2×Dic3—23no—
209C2×Dic3—23no—
210C2×Dic3—23no—
211C2×Dic3—26no—
212C2×Dic3—36no—
213C2×Dic3—36no—
214C2×Dic3—66no—
215C2×Dic3—63no—
216C2×Dic3—63no—
217C2×Dic3—63no—
218C2×Dic3—63no—
219C2×Dic3—123no—
220C2×Dic3—123no—
221C4×D3—124no—
222C4×D3—124no—
223C2×C32#52013yes—
224C2×C32#56011yescharacteristic
225C2×C32#56313yes—
226C3⋊D3—42no—
227C24—91no—
228C22×C4—33no—
229C22×C4—31no—
230C22×C4—31no—
231C22×C4—33no—
232C22×C4—93no—
233C22×C4—363no—
234C22×C4C2×D3213yes—
235C4⋊C4—912no—
236C4⋊C4—123no—
237C4⋊C4—123no—
238C4⋊C4—363no—
239C22⋊C4—912no—
240C22⋊C4—363no—
241C42—363no—
242C42#62414yescomplemented
243C22×C3—23no—
244C22×C3—23no—
245C22×C3—21no—
246C22×C3C22×C4×D311yescharacteristic
247C22×C3C22×C4×D311yescharacteristic
248C22×C3#100413yes—
249C22×C3#100713yes—
250C22×C3#100913yes—
251C22×C3#101013yes—
252C2×D3—66no—
253C2×D3—66no—
254C2×D3—126no—
255C2×D3—121no—
256C2×D3—123no—
257C2×D3—121no—
258C2×D3—123no—
259C2×D3—243no—
260C2×D3—241no—
261C3×C4—26no—
262C3×C4—26no—
263C3×C4—46no—
264C3×C4—121no—
265C3×C4—123no—
266C3×C4—121no—
267C3×C4—123no—
268Dic3—41no—
269Dic3—43no—
270Dic3—41no—
271Dic3—43no—
272Dic3—66no—
273Dic3—66no—
274Dic3—126no—
275C32#238311yescharacteristic, complemented, Sylow
276C23—92no—
277C23—183no—
278C23—183no—
279C23C22×D3211yescharacteristic
280C2×C4—23no—
281C2×C4—23no—
282C2×C4—66no—
283C2×C4—63no—
284C2×C4—63no—
285C2×C4—63no—
286C2×C4—63no—
287C2×C4—63no—
288C2×C4—63no—
289C2×C4—96no—
290C2×C4—183no—
291C2×C4—183no—
292C2×C4—364no—
293C2×C4C2×#62416yes—
294C2×C3—23no—
295C2×C3—23no—
296C2×C3—21no—
297C2×C3#550413yes—
298C2×C3#552313yes—
299C2×C3#571111yescharacteristic
300C2×C3#571213yes—
301C2×C3#572011yescharacteristic
302C2×C3#573513yes—
303D3—122no—
304D3—122no—
305D3—242no—
306C22—186no—
307C22—363no—
308C22—361no—
309C22#6429713yes—
310C22#6430713yes—
311C22C22×#62411yescharacteristic
312C4—26no—
313C4—123no—
314C4—121no—
315C4—121no—
316C4—123no—
317C4—186no—
318C3—21no—
319C3#7429911yescharacteristic, complemented
320C3#7436111yescharacteristic, complemented
321C2—362no—
322C2#1059395713yes—
323C2#1059402211yescharacteristic
324C2#1059499013yes—
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC2×C32×C42C22
socle, cosocleC23×C32C24
prime radicalC23×C3⋊D3C23
hypercenterC2×C42D32
hypocenterC32#2383
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
2. C3×#4937C2semidirect
3. C3×#4935C2semidirect
6. #10591264C2semidirect
7. #10591263C2semidirect
14. #64085C4semidirect
33. #4937D3semidirect
34. #4935D3semidirect
47. C32×C42C2×C4semidirect
49. #3750C2×C4semidirect
135. C3×C42C4×D3semidirect
136. C3×C42C4×D3semidirect
242. C42#624semidirect
275. C32#2383semidirect
319. C3#74299semidirect
320. C3#74361semidirect

Maximal subgroups

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

subgroupindex
C2×#640852
C3×#49372
C3×#49352
#105913782
#105912662
#105912642
#105912632
#743613
#742993