Finite Group Databasebeta

← #10596126

Subgroups — #10596126

Order 576.

876 conjugacy classes of subgroups.

The subgroup lattice has 348 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3830C211yesmaximal, characteristic, complemented
2C2×#3828C211yesmaximal, characteristic, complemented
3C32×#123C211yesmaximal, characteristic, complemented
4#64148C211yesmaximal, characteristic, complemented
5C2×#3750C211yesmaximal, characteristic, complemented
6#64105C211yesmaximal, characteristic, complemented
7#64103C211yesmaximal, characteristic, complemented
8C4⋊C4×C3⋊D3C211yesmaximal, characteristic, complemented
9#64097C211yesmaximal, characteristic, complemented
10#64095C211yesmaximal, characteristic, complemented
11#64093C211yesmaximal, characteristic, complemented
12#64092C211yesmaximal, characteristic, complemented
13#64090C211yesmaximal, characteristic, complemented
14#64090C211yesmaximal, characteristic, complemented
15#64087C211yesmaximal, characteristic, complemented
16#5655—34nomaximal
17C2×C32×D4C2211yescharacteristic
18C22×C32×C4C2211yescharacteristic
19C2×#638C2211yescharacteristic
20C2×#638C2211yescharacteristic
21C2×#638C2211yescharacteristic
22C2×#638C2211yescharacteristic
23C22×C3⋊Dic3C2211yescharacteristic
24C22×C3⋊Dic3C2211yescharacteristic
25C22×C3⋊Dic3C2211yescharacteristic
26#3830—24no—
27#3828—24no—
28C2×C4⋊(C3⋊D3)C2211yescharacteristic
29C2×C4×C3⋊D3C2211yescharacteristic
30C2×C4×C3⋊D3C2211yescharacteristic
31C2×C4×C3⋊D3C2211yescharacteristic
32C2×C4×C3⋊D3C2211yescharacteristic
33C2×#634C2211yescharacteristic
34C2×#634C2211yescharacteristic
35C32×C4⋊C4C2211yescharacteristic
36C32×C4⋊C4C2211yescharacteristic
37C32×C22⋊C4C2211yescharacteristic
38C32×C22⋊C4C2211yescharacteristic
39C32×C22⋊C4C2211yescharacteristic
40#3757C2211yescharacteristic
41#3752C2211yescharacteristic
42#3752C2211yescharacteristic
43#3752C2211yescharacteristic
44#3752C2211yescharacteristic
45C4⋊(C3⋊Dic3)C2211yescharacteristic
46C4⋊(C3⋊Dic3)C2211yescharacteristic
47#3750C2211yescharacteristic
48#3750C2211yescharacteristic
49#3750C2211yescharacteristic
50#3750C2211yescharacteristic
51#3750C2211yescharacteristic
52#3750C2211yescharacteristic
53C4×C3⋊Dic3C2211yescharacteristic
54C2×#237—34no—
55C2×#235—34no—
56C3×#123D314yescomplemented
57#939—34no—
58C2×Dic3⋊C4—34no—
59#896—34no—
60#894—34no—
61D3×C4⋊C4—34no—
62#888—34no—
63#886—34no—
64#884—34no—
65#883—34no—
66#67⋊C4—34no—
67#67⋊C4—34no—
68#878—34no—
69C23×C32C2311yescharacteristic
70C23×C32C2311yescharacteristic
71C22×C3⋊D3C2311yescharacteristic
72C22×C3⋊D3C2311yescharacteristic
73C32×D4—22no—
74C2×C32×C4—22no—
75C2×C32×C4C2311yescharacteristic
76C2×C32×C4C2311yescharacteristic
77C2×C32×C4C2311yescharacteristic
78C2×C32×C4C2311yescharacteristic
79C2×C32×C4C2311yescharacteristic
80#638—22no—
81#638—22no—
82#638—22no—
83#638D414yescomplemented
84C2×C3⋊Dic3—22no—
85C2×C3⋊Dic3—22no—
86C2×C3⋊Dic3—22no—
87C2×C3⋊Dic3C2311yescharacteristic
88C2×C3⋊Dic3C2311yescharacteristic
89C2×C3⋊Dic3C2311yescharacteristic
90C2×C3⋊Dic3C2311yescharacteristic
91C2×C3⋊Dic3C2311yescharacteristic
92C2×C3⋊Dic3C2311yescharacteristic
93C4⋊(C3⋊D3)—22no—
94C4×C3⋊D3—22no—
95C4×C3⋊D3—22no—
96C4×C3⋊D3—22no—
97C4×C3⋊D3—22no—
98#634—22no—
99#634—22no—
100#547—91noSylow
101C2×C3×D4C2×D314yes—
102C22×C3×C4C2×D314yes—
103C2×#67—34no—
104C2×#67—34no—
105C2×#67—34no—
106C2×#67—34no—
107C22×Dic3—34no—
108C22×Dic3—34no—
109C22×Dic3—34no—
110#237—616no—
111#235—616no—
112C2×D12—34no—
113C2×C4×D3—34no—
114C2×C4×D3—34no—
115C2×C4×D3—34no—
116C2×C4×D3—34no—
117C2×Dic6—34no—
118C2×Dic6—34no—
119C3×C4⋊C4C2×D314yes—
120C3×C4⋊C4C2×D314yes—
121C3×C22⋊C4C2×D314yes—
122C3×C22⋊C4C2×D314yes—
123C3×C22⋊C4C2×D314yes—
124#217—34no—
125(C2×D3)⋊C4—34no—
126(C2×D3)⋊C4—34no—
127(C2×D3)⋊C4—34no—
128(C2×D3)⋊C4—34no—
129C4⋊Dic3—34no—
130C4⋊Dic3—34no—
131Dic3⋊C4—34no—
132Dic3⋊C4—34no—
133Dic3⋊C4—34no—
134Dic3⋊C4—34no—
135Dic3⋊C4—34no—
136Dic3⋊C4—34no—
137C4×Dic3—34no—
138C22×C32—21no—
139C22×C32—21no—
140C22×C32—21no—
141C22×C32—21no—
142C22×C32—21no—
143C22×C32C2×D412yes—
144C22×C32C2411yescharacteristic
145C2×C3⋊D3—21no—
146C2×C3⋊D3—21no—
147C2×C3⋊D3—21no—
148C2×C3⋊D3—21no—
149C2×C3⋊D3—21no—
150C2×C3⋊D3C2×D412yes—
151C32×C4—21no—
152C32×C4—21no—
153C32×C4—21no—
154C32×C4—21no—
155C32×C4—21no—
156C3⋊Dic3—21no—
157C3⋊Dic3—21no—
158C3⋊Dic3—21no—
159C3⋊Dic3—21no—
160C3⋊Dic3C2×D412yes—
161C3⋊Dic3#4112yescomplemented
162C2×#41—91no—
163C2×#41—91no—
164C4⋊Q8—91no—
165#123—91no—
166#123—91no—
167#123—91no—
168#123C3⋊D311yescharacteristic, complemented
169C22⋊Q8—91no—
170C22⋊Q8—91no—
171#121—91no—
172#121—91no—
173C4×D4—91no—
174C4×D4—91no—
175C2×C4⋊C4—91no—
176C2×C4⋊C4—91no—
177C23×C3C22×D314yes—
178C23×C3C22×D314yes—
179C22×D3—34no—
180C22×D3—34no—
181C3×D4—28no—
182C2×C3×C4—28no—
183C2×C3×C4C22×D314yes—
184C2×C3×C4C22×D314yes—
185C2×C3×C4C22×D314yes—
186C2×C3×C4C22×D314yes—
187C2×C3×C4C22×D314yes—
188#67—316no—
189#67—68no—
190#67—68no—
191#67—68no—
192C2×Dic3—34no—
193C2×Dic3—34no—
194C2×Dic3—34no—
195C2×Dic3—34no—
196C2×Dic3—34no—
197C2×Dic3—34no—
198C2×Dic3—68no—
199C2×Dic3—68no—
200C2×Dic3—68no—
201D12—68no—
202C4×D3—68no—
203C4×D3—68no—
204C4×D3—68no—
205C4×D3—68no—
206Dic6—68no—
207Dic6—68no—
208C2×C32—22no—
209C2×C32—41no—
210C2×C32C22×D411yescharacteristic
211C2×C32C2×#4111yescharacteristic
212C2×C322−1+411yescharacteristic
213C3⋊D3—22no—
214C3⋊D3—41no—
215#41—184no—
216#41—184no—
217C2×Q8—91no—
218C2×Q8—91no—
219C2×D4—91no—
220C2×D4—91no—
221C2×D4—91no—
222C2×D4—91no—
223C2×D4—91no—
224C2×D4C2×C3⋊D311yescharacteristic
225C22×C4—91no—
226C22×C4—91no—
227C22×C4—91no—
228C22×C4—91no—
229C22×C4—91no—
230C22×C4—91no—
231C22×C4—91no—
232C22×C4C2×C3⋊D311yescharacteristic
233C4⋊C4—91no—
234C4⋊C4—91no—
235C4⋊C4—91no—
236C4⋊C4—91no—
237C4⋊C4—91no—
238C4⋊C4—91no—
239C4⋊C4—91no—
240C4⋊C4—91no—
241C4⋊C4C2×C3⋊D311yescharacteristic
242C4⋊C4C2×C3⋊D311yescharacteristic
243C22⋊C4—91no—
244C22⋊C4—91no—
245C22⋊C4—91no—
246C22⋊C4—91no—
247C22⋊C4—91no—
248C22⋊C4C2×C3⋊D311yescharacteristic
249C22⋊C4C2×C3⋊D311yescharacteristic
250C22⋊C4C2×C3⋊D311yescharacteristic
251C42—91no—
252C22×C3—24no—
253C22×C3—24no—
254C22×C3—24no—
255C22×C3—24no—
256C22×C3—24no—
257C22×C3D3×D418yes—
258C22×C3C23×D314yes—
259C2×D3—38no—
260C2×D3—64no—
261C2×D3—64no—
262C2×D3—64no—
263C2×D3—64no—
264C2×D3—64no—
265C3×C4—24no—
266C3×C4—24no—
267C3×C4—24no—
268C3×C4—24no—
269C3×C4—24no—
270Dic3—38no—
271Dic3—38no—
272Dic3—64no—
273Dic3—64no—
274Dic3—64no—
275Dic3—64no—
276C32#54711yescharacteristic, complemented, Sylow
277C23—91no—
278C23—91no—
279C23C22×C3⋊D311yescharacteristic
280C23C22×C3⋊D311yescharacteristic
281Q8—182no—
282Q8—182no—
283D4—22no—
284D4—94no—
285D4—182no—
286D4—182no—
287D4—182no—
288D4—182no—
289C2×C4—22no—
290C2×C4—91no—
291C2×C4—91no—
292C2×C4—91no—
293C2×C4—91no—
294C2×C4—91no—
295C2×C4—91no—
296C2×C4—182no—
297C2×C4—182no—
298C2×C4—182no—
299C2×C4—182no—
300C2×C4—182no—
301C2×C4—182no—
302C2×C4—182no—
303C2×C4C22×C3⋊D311yescharacteristic
304C2×C4C22×C3⋊D311yescharacteristic
305C2×C4C22×C3⋊D311yescharacteristic
306C2×C4C22×C3⋊D311yescharacteristic
307C2×C4C22×C3⋊D311yescharacteristic
308C2×C3—28no—
309C2×C3—44no—
310C2×C3C2×D3×D414yes—
311C2×C3D3×#4114yes—
312C2×C3#101014yes—
313D3—68no—
314D3—124no—
315C22—21no—
316C22—21no—
317C22—21no—
318C22—21no—
319C22—21no—
320C22—92no—
321C22—181no—
322C22—181no—
323C22—181no—
324C22—181no—
325C22—181no—
326C22D4×C3⋊D312yes—
327C22C23×C3⋊D311yescharacteristic
328C4—21no—
329C4—21no—
330C4—21no—
331C4—21no—
332C4—21no—
333C4—92no—
334C4—92no—
335C4—181no—
336C4—181no—
337C4—181no—
338C4—181no—
339C3#565514yescomplemented
340C2—22no—
341C2—41no—
342C2—182no—
343C2—361no—
344C2C2×D4×C3⋊D311yescharacteristic
345C2#41×C3⋊D311yescharacteristic
346C2#6436711yescharacteristic
subgroupG/H
center, FrattiniC22C23×C3⋊D3
commutator, socle, cosocleC22×C32C24
FittingC32×#123C2
hypercenter#123C3⋊D3
hypocenterC32#547
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ #123

Complements

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

NH ≅ G/Ntype
1. C2×#3830C2semidirect
2. C2×#3828C2semidirect
3. C32×#123C2semidirect
4. #64148C2semidirect
5. C2×#3750C2semidirect
6. #64105C2semidirect
7. #64103C2semidirect
8. C4⋊C4×C3⋊D3C2semidirect
9. #64097C2semidirect
10. #64095C2semidirect
11. #64093C2semidirect
12. #64092C2semidirect
13. #64090C2semidirect
14. #64090C2semidirect
15. #64087C2semidirect
56. C3×#123D3semidirect
83. #638D4semidirect
161. C3⋊Dic3#41semidirect
168. #123C3⋊D3semidirect
276. C32#547semidirect
339. C3#5655semidirect

Maximal subgroups

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

subgroupindex
C2×#38302
C2×#38282
C32×#1232
#641482
C2×#37502
#641052
#641032
C4⋊C4×C3⋊D32
#640972
#640952
#640932
#640922
#640902
#640872
#56553