Finite Group Databasebeta

← #11801963

Subgroups — #11801963

Order 1152.

1213 conjugacy classes of subgroups.

The subgroup lattice has 350 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64081C211yesmaximal, characteristic
2C3×#4932C211yesmaximal, characteristic, complemented
3C3×C42×Dic3C211yesmaximal, characteristic, complemented
4C4×#3724C212yesmaximal, complemented
5C4×#3722C212yesmaximal
6#10591202C214yesmaximal
7#10591197C214yesmaximal, complemented
8#73385—31nomaximal
9#73301—31nomaximal
10C22×C4×C3⋊D3C2211yescharacteristic
11C2×C32×C42C2211yescharacteristic
12C2×#3752C2212yes—
13C2×#3750C2212yes—
14C2×C4×C3⋊Dic3C2211yescharacteristic
15#64081C418yescomplemented
16C2×C3×C4×Dic3C2212yes—
17C2×C3×C4×Dic3C2214yes—
18C2×C3×C4×Dic3C2212yes—
19C2×#3724C2214yes—
20C2×#3722C2214yes—
21C3×C3⋊#95C2214yes—
22#63579C2214yes—
23#63579C2214yes—
24C2×#872—31no—
25C2×#872—31no—
26C2×#872—61no—
27C3×#376—31no—
28C3×C43—31no—
29#4940—34no—
30C4×(C2×D3)⋊C4—32no—
31C4×(C2×D3)⋊C4—32no—
32#4933—34no—
33#4932D311yescharacteristic, complemented
34C4×Dic3⋊C4—32no—
35C4×Dic3⋊C4—32no—
36C42×Dic3D311yescharacteristic, complemented
37#4669—34no—
38#4652—34no—
39C23×C3⋊D3C2311yescharacteristic
40C22×C32×C4C2312yes—
41C22×C32×C4C2311yescharacteristic
42C22×C3⋊Dic3C2311yescharacteristic
43C22×C3⋊Dic3C2312yes—
44C2×C4×C3⋊D3—24no—
45C2×C4×C3⋊D3C2×C414yes—
46C22×C3×Dic3C2314yes—
47C22×C3×Dic3C2314yes—
48C32×C42C2×C414yes—
49#3752C2×C418yes—
50#3750C2×C418yes—
51C4×C3⋊Dic3C2×C414yes—
52C3×C4×Dic3—24no—
53C3×C4×Dic3—24no—
54C3×C4×Dic3—28no—
55#3724—28no—
56#3722—28no—
57#2298—91noSylow
58C22×C4×D3—31no—
59C22×C4×D3—31no—
60C22×C4×D3—61no—
61C2×C3×C42—21no—
62C2×C3×C42—32no—
63C2×C3×C42—32no—
64C2×C3×C42—34no—
65C2×C3×C42C2×D311yescharacteristic
66C2×C3×C42C2×D311yescharacteristic
67C2×(C2×D3)⋊C4—32no—
68C2×(C2×D3)⋊C4—32no—
69C2×(C2×D3)⋊C4—34no—
70C2×(C2×D3)⋊C4—34no—
71C2×(C2×D3)⋊C4—62no—
72C2×Dic3⋊C4—32no—
73C2×Dic3⋊C4—32no—
74C2×Dic3⋊C4—34no—
75C2×Dic3⋊C4—34no—
76C2×Dic3⋊C4—62no—
77C2×C4×Dic3—31no—
78C2×C4×Dic3—31no—
79C2×C4×Dic3—61no—
80C2×C4×Dic3C2×D314yes—
81C2×C4×Dic3C2×D312yes—
82C2×C4×Dic3C2×D312yes—
83#872—38no—
84#872—38no—
85#872—68no—
86C3×#95—34no—
87C3⋊#95—34no—
88C3⋊#95—34no—
89C3⋊#95—34no—
90C3⋊#95—34no—
91C3⋊#95C2×D314yes—
92C23×C32C2411yescharacteristic
93C22×C3⋊D3—22no—
94C22×C3⋊D3—24no—
95C22×C3⋊D3C22×C412yes—
96C2×C32×C4—24no—
97C2×C32×C4C22×C414yes—
98C2×C32×C4C22×C412yes—
99C2×C32×C4#4114yes—
100C2×C3⋊Dic3—22no—
101C2×C3⋊Dic3—24no—
102C2×C3⋊Dic3C22×C414yes—
103C2×C3⋊Dic3C22×C412yes—
104C4×C3⋊D3—28no—
105C2×C3×Dic3—24no—
106C2×C3×Dic3—24no—
107C2×C3×Dic3—24no—
108C2×C3×Dic3—24no—
109C2×C3×Dic3—24no—
110C2×C3×Dic3#4118yes—
111C2×#117—91no—
112#388—94no—
113#387—94no—
114C4×C4⋊C4—92no—
115C4×C22⋊C4—92no—
116#376—31no—
117C43—31no—
118C23×D3—31no—
119C23×D3—31no—
120C23×D3—61no—
121C22×C3×C4—22no—
122C22×C3×C4—21no—
123C22×C3×C4—34no—
124C22×C3×C4—34no—
125C22×C3×C4C22×D312yes—
126C22×C3×C4C22×D312yes—
127C22×C3×C4C22×D311yescharacteristic
128C22×C3×C4C22×D311yescharacteristic
129C22×Dic3—31no—
130C22×Dic3—31no—
131C22×Dic3—32no—
132C22×Dic3—32no—
133C22×Dic3—61no—
134C22×Dic3—62no—
135C22×Dic3C22×D314yes—
136C22×Dic3C22×D314yes—
137C2×C4×D3—34no—
138C2×C4×D3—34no—
139C2×C4×D3—64no—
140C2×C4×D3—68no—
141C2×C4×D3—64no—
142C2×C4×D3—64no—
143C3×C42—24no—
144C3×C42—68no—
145C3×C42—64no—
146C3×C42—64no—
147C3×C42C4×D314yes—
148C3×C42C4×D314yes—
149(C2×D3)⋊C4—38no—
150(C2×D3)⋊C4—38no—
151(C2×D3)⋊C4—68no—
152(C2×D3)⋊C4—68no—
153(C2×D3)⋊C4—68no—
154Dic3⋊C4—38no—
155Dic3⋊C4—38no—
156Dic3⋊C4—68no—
157Dic3⋊C4—68no—
158Dic3⋊C4—68no—
159C4×Dic3—24no—
160C4×Dic3—24no—
161C4×Dic3—28no—
162C4×Dic3—34no—
163C4×Dic3—34no—
164C4×Dic3—64no—
165C22×C32C23×C411yescharacteristic
166C22×C32C2×#4112yes—
167C22×C32C2×#4114yes—
168C2×C3⋊D3—22no—
169C2×C3⋊D3—24no—
170C2×C3⋊D3—44no—
171C32×C4—24no—
172C32×C4#11714yes—
173C3⋊Dic3—22no—
174C3⋊Dic3—24no—
175C3×Dic3—28no—
176C3×Dic3—44no—
177C23×C4—91no—
178#117—98no—
179C2×C4⋊C4—92no—
180C2×C4⋊C4—94no—
181C2×C22⋊C4—92no—
182C2×C22⋊C4—94no—
183C2×C42—34no—
184C2×C42—32no—
185C2×C42—32no—
186C2×C42—91no—
187C2×C42D3211yescharacteristic
188#95—34no—
189#95—94no—
190#95—94no—
191C23×C3—21no—
192C23×C3C23×D311yescharacteristic
193C23×C3C23×D311yescharacteristic
194C22×D3—32no—
195C22×D3—32no—
196C22×D3—62no—
197C22×D3—64no—
198C22×D3—64no—
199C22×D3—62no—
200C22×D3—62no—
201C22×D3—64no—
202C22×D3—124no—
203C2×C3×C4—24no—
204C2×C3×C4—24no—
205C2×C3×C4—24no—
206C2×C3×C4—22no—
207C2×C3×C4—24no—
208C2×C3×C4—38no—
209C2×C3×C4—44no—
210C2×C3×C4—64no—
211C2×C3×C4—64no—
212C2×C3×C4—64no—
213C2×C3×C4—64no—
214C2×C3×C4—64no—
215C2×C3×C4C2×C4×D314yes—
216C2×C3×C4C2×C4×D314yes—
217C2×C3×C4C2×C4×D312yes—
218C2×C3×C4C2×C4×D312yes—
219C2×C3×C4#23514yes—
220C2×C3×C4#23514yes—
221C2×Dic3—24no—
222C2×Dic3—24no—
223C2×Dic3—24no—
224C2×Dic3—24no—
225C2×Dic3—24no—
226C2×Dic3—34no—
227C2×Dic3—34no—
228C2×Dic3—32no—
229C2×Dic3—32no—
230C2×Dic3—62no—
231C2×Dic3—64no—
232C2×Dic3—64no—
233C2×Dic3—64no—
234C2×Dic3—62no—
235C2×Dic3—62no—
236C2×Dic3—64no—
237C2×Dic3—124no—
238C2×Dic3#23518yes—
239C4×D3—616no—
240C4×D3—68no—
241C4×D3—68no—
242C2×C32C2×#11711yescharacteristic
243C2×C32C4×#4112yes—
244C2×C32#52914yes—
245C3⋊D3—42no—
246C24—91no—
247C22×C4—34no—
248C22×C4—34no—
249C22×C4—91no—
250C22×C4—92no—
251C22×C4—94no—
252C22×C4—184no—
253C22×C4C2×D3212yes—
254C22×C4C2×D3211yescharacteristic
255C4⋊C4—98no—
256C4⋊C4—188no—
257C22⋊C4—98no—
258C22⋊C4—188no—
259C42—68no—
260C42—64no—
261C42—64no—
262C42—94no—
263C42#62414yes—
264C22×C3—22no—
265C22×C3—24no—
266C22×C3—21no—
267C22×C3C22×C4×D311yescharacteristic
268C22×C3C22×C4×D311yescharacteristic
269C22×C3C2×#23512yes—
270C22×C3C2×#23512yes—
271C22×C3C2×#23514yes—
272C22×C3D3×#4114yes—
273C2×D3—64no—
274C2×D3—62no—
275C2×D3—62no—
276C2×D3—64no—
277C2×D3—64no—
278C2×D3—124no—
279C2×D3—128no—
280C2×D3—124no—
281C2×D3—124no—
282C3×C4—24no—
283C3×C4—24no—
284C3×C4—24no—
285C3×C4—44no—
286C3×C4—68no—
287C3×C4—124no—
288C3×C4#87214yes—
289C3×C4#87214yes—
290Dic3—28no—
291Dic3—44no—
292Dic3—64no—
293Dic3—62no—
294Dic3—62no—
295Dic3—64no—
296Dic3—64no—
297Dic3—124no—
298C32#229811yescharacteristic, complemented, Sylow
299C23—92no—
300C23—182no—
301C23—184no—
302C23C22×D3211yescharacteristic
303C2×C4—24no—
304C2×C4—38no—
305C2×C4—64no—
306C2×C4—64no—
307C2×C4—64no—
308C2×C4—64no—
309C2×C4—64no—
310C2×C4—94no—
311C2×C4—92no—
312C2×C4—182no—
313C2×C4—184no—
314C2×C4—188no—
315C2×C4#379814yes—
316C2×C4C2×#62414yes—
317C2×C4C2×#62412yes—
318C2×C3—21no—
319C2×C3—22no—
320C2×C3—24no—
321C2×C3C2×#87211yescharacteristic
322C2×C3C2×#87211yescharacteristic
323C2×C3C4×#23512yes—
324C2×C3#547914yes—
325C2×C3#552212yes—
326C2×C3#552814yes—
327D3—124no—
328D3—122no—
329D3—122no—
330C22—182no—
331C22—184no—
332C22—364no—
333C22C2×#379812yes—
334C22D3×#23514yes—
335C22C22×#62411yescharacteristic
336C4—24no—
337C4—68no—
338C4—124no—
339C4—182no—
340C4—184no—
341C4#6387414yes—
342C3—21no—
343C3#7330111yescharacteristic, complemented
344C3#7338511yescharacteristic, complemented
345C2—362no—
346C2#1059397314yes—
347C2C2×#6387411yescharacteristic
348C2#1059495412yes—
subgroupG/H
centerC22×C4C2×D32
commutatorC22×C32C23×C4
FrattiniC23C22×D32
FittingC2×C32×C42C22
socle, cosocleC23×C32C24
prime radicalC23×C3⋊D3C23
hypercenterC2×C42D32
hypocenterC32#2298
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22×C4 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
2. C3×#4932C2semidirect
3. C3×C42×Dic3C2semidirect
4. C4×#3724C2semidirect
7. #10591197C2semidirect
15. #64081C4semidirect
33. #4932D3semidirect
36. C42×Dic3D3semidirect
298. C32#2298semidirect
343. C3#73301semidirect
344. C3#73385semidirect

Maximal subgroups

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

subgroupindex
C2×#640812
C3×#49322
C3×C42×Dic32
C4×#37242
C4×#37222
#105912022
#105911972
#733853
#733013