Finite Group Databasebeta

← #11895719

Subgroups — #11895719

Order 1152.

1188 conjugacy classes of subgroups.

The subgroup lattice has 390 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596201C211yesmaximal, characteristic, complemented
2#10596024C211yesmaximal, characteristic, complemented
3C32×#476C211yesmaximal, characteristic, complemented
4#10592787C211yesmaximal, characteristic, complemented
5C4×#3753C211yesmaximal, characteristic, complemented
6#10592570C212yesmaximal, complemented
7#10592568C212yesmaximal, complemented
8#10592542C211yesmaximal, characteristic, complemented
9#10592530C211yesmaximal, characteristic, complemented
10#10592485C212yesmaximal, complemented
11#10592463C212yesmaximal, complemented
12#81088—34nomaximal
13C2×#3828—21no—
14C32×C4⋊Q8C2211yescharacteristic
15C32×C4×D4C2211yescharacteristic
16#64155—22no—
17#64149C2212yes—
18C2×#3753C2211yescharacteristic
19#64139—21no—
20C2×#3745C2212yes—
21#64106—21no—
22#64102C2212yes—
23#64102C2212yes—
24C4⋊C4×C3⋊D3—21no—
25#64099C2212yes—
26#64093—22no—
27#64083C2211yescharacteristic
28C4×C4⋊(C3⋊D3)C2211yescharacteristic
29C4×#634C2211yescharacteristic
30C32×#106C2212yes—
31C32×C4⋊C8C2211yescharacteristic
32C32×#102C2212yes—
33#63659C2211yescharacteristic
34#63648C2212yes—
35#63642C2212yes—
36#63641C2212yes—
37#63636C2212yes—
38#63636C2212yes—
39#63636C2211yescharacteristic
40#63634C2211yescharacteristic
41C4×C3⋊(C3⋊C8)C2211yescharacteristic
42#5730—34no—
43#5553—34no—
44C3×#476D314yescomplemented
45#5088—34no—
46C4×#213—34no—
47#4871—38no—
48#4869—38no—
49#4843—34no—
50#4831—34no—
51#4786—38no—
52#4764—38no—
53C2×C32×Q8—21no—
54C2×C32×D4C2311yescharacteristic
55C22×C32×C4—21no—
56C2×#638—22no—
57C2×#638—22no—
58#3828—44no—
59C2×C4⋊(C3⋊D3)—21no—
60C2×C4⋊(C3⋊D3)—21no—
61C2×C4⋊(C3⋊D3)C2312yes—
62C2×C4⋊(C3⋊D3)C2311yescharacteristic
63C2×C4×C3⋊D3—21no—
64C2×C4×C3⋊D3—22no—
65C2×C4×C3⋊D3—22no—
66C2×#634D411yescharacteristic
67C2×C32×C8C2312yes—
68C32×C4⋊C4—21no—
69C32×C4⋊C4C2312yes—
70C32×C4⋊C4C2311yescharacteristic
71C32×C22⋊C4—21no—
72C32×C42C2311yescharacteristic
73#3753—22no—
74#3752—21no—
75#3752—22no—
76#3752—22no—
77C4⋊(C3⋊Dic3)—22no—
78C4⋊(C3⋊Dic3)D411yescharacteristic
79C4⋊(C3⋊Dic3)C2311yescharacteristic
80#3750—22no—
81#3750D412yes—
82C4×C3⋊Dic3C2312yes—
83C2×C3⋊(C3⋊C8)C2311yescharacteristic
84C2×C3⋊(C3⋊C8)C2311yescharacteristic
85#3745—24no—
86#3366—91noSylow
87C2×#235—64no—
88C3×C4⋊Q8C2×D314yes—
89C3×C4×D4C2×D314yes—
90#946—68no—
91#940—38no—
92C2×#213—34no—
93#930—64no—
94C2×D24—38no—
95#897—64no—
96#893—38no—
97#893—38no—
98D3×C4⋊C4—64no—
99#890—38no—
100#884—68no—
101#874—34no—
102C4×D12—34no—
103C4×Dic6—34no—
104C3×#106C2×D318yes—
105C3×C4⋊C8C2×D314yes—
106C3×#102C2×D318yes—
107#832—34no—
108#821—38no—
109#815—38no—
110Dic3⋊C8—38no—
111#809—34no—
112#809—38no—
113#809—38no—
114#807—34no—
115C4×C3⋊C8—34no—
116C23×C32—21no—
117C22×C3⋊D3—21no—
118C22×C3⋊D3—22no—
119C32×Q8—81no—
120C32×D4—21no—
121C32×D4—21no—
122C2×C32×C4—22no—
123C2×C32×C4—21no—
124C2×C32×C4—42no—
125C2×C32×C4C2×D411yescharacteristic
126C2×C32×C4C2×D411yescharacteristic
127C2×C32×C4C2411yescharacteristic
128#638—44no—
129#638—82no—
130C2×C3⋊Dic3—21no—
131C2×C3⋊Dic3C2×D412yes—
132C2×C3⋊Dic3C2×D412yes—
133C4⋊(C3⋊D3)—22no—
134C4⋊(C3⋊D3)—21no—
135C4⋊(C3⋊D3)—22no—
136C4⋊(C3⋊D3)—42no—
137C4⋊(C3⋊D3)—81no—
138C4⋊(C3⋊D3)#4112yescomplemented
139C4×C3⋊D3—44no—
140C4×C3⋊D3—42no—
141C4×C3⋊D3—82no—
142#634—22no—
143C32×C8—22no—
144C3⋊(C3⋊C8)—21no—
145C3⋊(C3⋊C8)—21no—
146#554—91no—
147#550—91no—
148#490—92no—
149#486—91no—
150#478—92no—
151#476C3⋊D311yescharacteristic, complemented
152#459—91no—
153#459—92no—
154#446—91no—
155#442—92no—
156C4×D8—91no—
157C2×C3×Q8—24no—
158C2×C3×D4C22×D314yes—
159C22×C3×C4—24no—
160C2×#67—68no—
161C2×#67—68no—
162#235—1216no—
163C2×D12—34no—
164C2×D12—38no—
165C2×D12—64no—
166C2×D12—64no—
167C2×C4×D3—68no—
168C2×C4×D3—64no—
169C2×C4×D3—68no—
170C2×Dic6—34no—
171C2×C3×C8C22×D318yes—
172C3×C4⋊C4—24no—
173C3×C4⋊C4C22×D314yes—
174C3×C4⋊C4C22×D318yes—
175C3×C22⋊C4—24no—
176C3×C42C22×D314yes—
177#213—68no—
178(C2×D3)⋊C4—68no—
179(C2×D3)⋊C4—68no—
180(C2×D3)⋊C4—64no—
181C4⋊Dic3—34no—
182C4⋊Dic3—34no—
183C4⋊Dic3—68no—
184Dic3⋊C4—38no—
185Dic3⋊C4—68no—
186C4×Dic3—38no—
187C2×C3⋊C8—34no—
188C2×C3⋊C8—34no—
189D24—616no—
190C22×C32—41no—
191C22×C32—41no—
192C22×C32—41no—
193C22×C32C22×D411yescharacteristic
194C2×C3⋊D3—22no—
195C2×C3⋊D3—41no—
196C2×C3⋊D3—41no—
197C2×C3⋊D3—42no—
198C2×C3⋊D3—42no—
199C2×C3⋊D3—42no—
200C32×C4—21no—
201C32×C4—41no—
202C32×C4—42no—
203C32×C4AGL(1,ℤ/8)12yes—
204C32×C4C2×#4111yescharacteristic
205C32×C42−1+411yescharacteristic
206C3⋊Dic3—22no—
207C3⋊Dic3—22no—
208C3⋊Dic3—41no—
209C2×#41—181no—
210C2×D8—91no—
211C2×D8—92no—
212C4⋊Q8C2×C3⋊D311yescharacteristic
213#127—92no—
214#127—91no—
215#125—92no—
216C22⋊Q8—181no—
217C22⋊Q8—182no—
218#121—182no—
219#121—181no—
220C4×Q8—91no—
221C4×D4—92no—
222C4×D4—92no—
223C4×D4—91no—
224C4×D4C2×C3⋊D311yescharacteristic
225C2×C4⋊C4—181no—
226#107—91no—
227#106C2×C3⋊D312yes—
228C4⋊C8—92no—
229C4⋊C8C2×C3⋊D311yescharacteristic
230#102—91no—
231#102—92no—
232#102—91no—
233#102—92no—
234#102—92no—
235#102C2×C3⋊D312yes—
236#97—92no—
237C4×C8—91no—
238C23×C3—24no—
239C22×D3—64no—
240C22×D3—68no—
241C3×Q8—84no—
242C3×D4—24no—
243C3×D4—24no—
244C2×C3×C4—28no—
245C2×C3×C4—24no—
246C2×C3×C4—48no—
247C2×C3×C4D3×D414yes—
248C2×C3×C4D3×D414yes—
249C2×C3×C4C23×D314yes—
250#67—1216no—
251#67—248no—
252C2×Dic3—38no—
253C2×Dic3—38no—
254C2×Dic3—64no—
255D12—38no—
256D12—64no—
257D12—68no—
258D12—68no—
259D12—128no—
260D12—244no—
261C4×D3—1216no—
262C4×D3—128no—
263C4×D3—248no—
264Dic6—68no—
265C3×C8—28no—
266C3⋊C8—64no—
267C3⋊C8—64no—
268C2×C32—81no—
269C2×C32#54811yescharacteristic
270C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
271C2×C32#57611yescharacteristic
272C3⋊D3—42no—
273C3⋊D3—82no—
274#41—364no—
275C2×Q8—21no—
276C2×Q8—91no—
277C2×D4—91no—
278C2×D4—92no—
279C2×D4—182no—
280C2×D4—182no—
281C2×D4—181no—
282C2×D4—181no—
283C2×D4C22×C3⋊D311yescharacteristic
284C22×C4—21no—
285C22×C4—182no—
286C22×C4—182no—
287C22×C4—181no—
288D8—184no—
289D8—182no—
290C2×C8—91no—
291C2×C8—91no—
292C2×C8C22×C3⋊D312yes—
293C4⋊C4—21no—
294C4⋊C4—91no—
295C4⋊C4—92no—
296C4⋊C4—91no—
297C4⋊C4—182no—
298C4⋊C4—182no—
299C4⋊C4C22×C3⋊D312yes—
300C4⋊C4C22×C3⋊D311yescharacteristic
301C22⋊C4—21no—
302C22⋊C4—182no—
303C22⋊C4—182no—
304C22⋊C4—181no—
305C42—92no—
306C42C22×C3⋊D311yescharacteristic
307C22×C3—44no—
308C22×C3—44no—
309C22×C3—44no—
310C22×C3C2×D3×D414yes—
311C2×D3—68no—
312C2×D3—124no—
313C2×D3—124no—
314C2×D3—128no—
315C2×D3—128no—
316C2×D3—128no—
317C3×C4—24no—
318C3×C4—44no—
319C3×C4—48no—
320C3×C4#91418yes—
321C3×C4#100714yes—
322C3×C4D3×#4114yes—
323Dic3—68no—
324Dic3—68no—
325Dic3—124no—
326C32#336611yescharacteristic, complemented, Sylow
327C23—21no—
328C23—181no—
329C23—182no—
330Q8—81no—
331Q8—182no—
332D4—21no—
333D4—21no—
334D4—92no—
335D4—181no—
336D4—182no—
337D4—182no—
338D4—364no—
339D4—362no—
340D4—721no—
341D4—722no—
342C2×C4—21no—
343C2×C4—22no—
344C2×C4—42no—
345C2×C4—92no—
346C2×C4—92no—
347C2×C4—181no—
348C2×C4—364no—
349C2×C4—362no—
350C2×C4—722no—
351C2×C4D4×C3⋊D311yescharacteristic
352C2×C4D4×C3⋊D311yescharacteristic
353C2×C4C23×C3⋊D311yescharacteristic
354C8—22no—
355C8—181no—
356C8—181no—
357C2×C3—84no—
358C2×C3#563314yes—
359C2×C3C2×#91414yes—
360C2×C3#577414yes—
361D3—128no—
362D3—248no—
363C22—41no—
364C22—41no—
365C22—41no—
366C22—182no—
367C22—361no—
368C22—361no—
369C22—362no—
370C22—362no—
371C22—362no—
372C22C2×D4×C3⋊D311yescharacteristic
373C4—21no—
374C4—41no—
375C4—42no—
376C4—182no—
377C4—182no—
378C4—361no—
379C4#6412312yes—
380C4#6436411yescharacteristic
381C4#41×C3⋊D311yescharacteristic
382C3#8108814yescomplemented
383C2—81no—
384C2—362no—
385C2—722no—
386C2#1059610411yescharacteristic
387C2C2×#6412311yescharacteristic
388C2#1059624511yescharacteristic
subgroupG/H
centerC22C2×D4×C3⋊D3
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C23×C3⋊D3
FittingC32×#476C2
socleC22×C32C22×D4
hypercenter#476C3⋊D3
hypocenterC32#3366
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ #476

Complements

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

NH ≅ G/Ntype
1. #10596201C2semidirect
2. #10596024C2semidirect
3. C32×#476C2semidirect
4. #10592787C2semidirect
5. C4×#3753C2semidirect
6. #10592570C2semidirect
7. #10592568C2semidirect
8. #10592542C2semidirect
9. #10592530C2semidirect
10. #10592485C2semidirect
11. #10592463C2semidirect
44. C3×#476D3semidirect
138. C4⋊(C3⋊D3)#41semidirect
151. #476C3⋊D3semidirect
326. C32#3366semidirect
382. C3#81088semidirect

Maximal subgroups

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

subgroupindex
#105962012
#105960242
C32×#4762
#105927872
C4×#37532
#105925702
#105925682
#105925422
#105925302
#105924852
#105924632
#810883