Finite Group Databasebeta

← #11895734

Subgroups — #11895734

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#10596189C211yesmaximal, characteristic, complemented
2#10596014C211yesmaximal, characteristic, complemented
3C32×#459C211yesmaximal, characteristic, complemented
4#10592851C212yesmaximal, complemented
5#10592849C212yesmaximal, complemented
6#10592769C211yesmaximal, characteristic, complemented
7C4×#3753C211yesmaximal, characteristic, complemented
8#10592541C211yesmaximal, characteristic, complemented
9#10592530C211yesmaximal, characteristic, complemented
10#10592463C212yesmaximal, complemented
11#10592462C212yesmaximal, complemented
12#80320—34nomaximal
13C2×#3830—21no—
14C2×C32×D8C2212yes—
15C32×#127C2211yescharacteristic
16C32×C4×D4C2211yescharacteristic
17#64149C2212yes—
18#64148—22no—
19#64147—21no—
20D4×C3⋊Dic3C2212yes—
21D4×C3⋊Dic3C2212yes—
22C2×#3753C2211yescharacteristic
23C2×C4⋊(C3⋊Dic3)—21no—
24#64133—21no—
25#64099C2212yes—
26#64087—22no—
27C4×C4⋊(C3⋊D3)C2211yescharacteristic
28#64078C2211yescharacteristic
29C4×#634C2211yescharacteristic
30C32×C4⋊C8C2211yescharacteristic
31C32×#102C2212yes—
32#63659C2212yes—
33#63659C2212yes—
34#63659C2211yescharacteristic
35#63648C2212yes—
36#63644C2212yes—
37#63642C2212yes—
38#63641C2212yes—
39#63636C2211yescharacteristic
40#63634C2211yescharacteristic
41C4×C3⋊(C3⋊C8)C2211yescharacteristic
42#5718—34no—
43#5543—34no—
44C3×#459D314yescomplemented
45#5152—38no—
46#5150—38no—
47#5070—34no—
48C4×#213—34no—
49#4842—34no—
50#4831—34no—
51#4764—38no—
52#4763—38no—
53C2×C32×D4—21no—
54C2×C32×D4—21no—
55C2×C32×D4C2312yes—
56C2×C32×D4C2311yescharacteristic
57C22×C32×C4—21no—
58C2×#638—22no—
59C2×#638—22no—
60C22×C3⋊Dic3—22no—
61C22×C3⋊Dic3—22no—
62#3830—44no—
63C2×C4⋊(C3⋊D3)C2311yescharacteristic
64C2×C4×C3⋊D3—21no—
65C2×#634—21no—
66C2×#634D411yescharacteristic
67C32×D8—24no—
68C2×C32×C8C2312yes—
69C32×C4⋊C4C2311yescharacteristic
70C32×C22⋊C4—21no—
71C32×C42C2311yescharacteristic
72#3757—22no—
73#3757—22no—
74#3753—22no—
75#3752—21no—
76C4⋊(C3⋊Dic3)—21no—
77C4⋊(C3⋊Dic3)—22no—
78C4⋊(C3⋊Dic3)D411yescharacteristic
79C4⋊(C3⋊Dic3)C2312yes—
80C4⋊(C3⋊Dic3)C2311yescharacteristic
81#3750—22no—
82#3750D412yes—
83C4×C3⋊Dic3C2312yes—
84C2×C3⋊(C3⋊C8)C2311yescharacteristic
85C2×C3⋊(C3⋊C8)C2311yescharacteristic
86#3366—91noSylow
87C2×#237—64no—
88C2×C3×D8C2×D318yes—
89C3×#127C2×D314yes—
90C3×C4×D4C2×D314yes—
91#940—38no—
92#939—68no—
93#938—64no—
94D4×Dic3—38no—
95D4×Dic3—38no—
96C2×#213—34no—
97C2×C4⋊Dic3—64no—
98#924—64no—
99#890—38no—
100#878—68no—
101C4×D12—34no—
102#869—34no—
103C4×Dic6—34no—
104C3×C4⋊C8C2×D314yes—
105C3×#102C2×D318yes—
106#832—38no—
107#832—34no—
108#832—38no—
109#821—38no—
110#817—38no—
111#815—38no—
112Dic3⋊C8—38no—
113#809—34no—
114#807—34no—
115C4×C3⋊C8—34no—
116C23×C32—21no—
117C23×C32—22no—
118C22×C3⋊D3—21no—
119C32×D4—22no—
120C32×D4—21no—
121C32×D4—22no—
122C32×D4—42no—
123C32×D4—81no—
124C32×D4#4112yescomplemented
125C2×C32×C4—21no—
126C2×C32×C4—42no—
127C2×C32×C4C2×D411yescharacteristic
128C2×C32×C4C2×D411yescharacteristic
129C2×C32×C4C2411yescharacteristic
130#638—44no—
131#638—82no—
132C2×C3⋊Dic3—22no—
133C2×C3⋊Dic3—21no—
134C2×C3⋊Dic3—44no—
135C2×C3⋊Dic3—82no—
136C2×C3⋊Dic3C2×D412yes—
137C2×C3⋊Dic3C2×D412yes—
138C4⋊(C3⋊D3)—21no—
139C4⋊(C3⋊D3)—21no—
140C4×C3⋊D3—42no—
141#634—22no—
142#634—81no—
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#476—91no—
152#459—92no—
153#459C3⋊D311yescharacteristic, complemented
154#446—91no—
155#442—92no—
156C4×D8—91no—
157C2×C3×D4—24no—
158C2×C3×D4—24no—
159C2×C3×D4C22×D318yes—
160C2×C3×D4C22×D314yes—
161C22×C3×C4—24no—
162C2×#67—68no—
163C2×#67—68no—
164C22×Dic3—68no—
165C22×Dic3—68no—
166#237—1216no—
167C2×D12—34no—
168C2×C4×D3—64no—
169C2×Dic6—34no—
170C2×Dic6—64no—
171C3×D8—216no—
172C2×C3×C8C22×D318yes—
173C3×C4⋊C4C22×D314yes—
174C3×C22⋊C4—24no—
175C3×C42C22×D314yes—
176#217—68no—
177#217—68no—
178#213—68no—
179(C2×D3)⋊C4—64no—
180C4⋊Dic3—34no—
181C4⋊Dic3—34no—
182C4⋊Dic3—38no—
183C4⋊Dic3—68no—
184C4⋊Dic3—64no—
185Dic3⋊C4—38no—
186Dic3⋊C4—68no—
187C4×Dic3—38no—
188C2×C3⋊C8—34no—
189C2×C3⋊C8—34no—
190C22×C32—22no—
191C22×C32—41no—
192C22×C32—41no—
193C22×C32—42no—
194C22×C32—42no—
195C22×C32—42no—
196C22×C32C22×D411yescharacteristic
197C2×C3⋊D3—41no—
198C2×C3⋊D3—41no—
199C2×C3⋊D3—41no—
200C32×C4—21no—
201C32×C4—41no—
202C32×C4AGL(1,ℤ/8)12yes—
203C32×C4C2×#4111yescharacteristic
204C32×C42−1+411yescharacteristic
205C3⋊Dic3—22no—
206C3⋊Dic3—22no—
207C3⋊Dic3—41no—
208C3⋊Dic3—42no—
209C2×#41—181no—
210C2×D8—91no—
211C2×D8C2×C3⋊D312yes—
212C4⋊Q8—91no—
213#127—92no—
214#127C2×C3⋊D311yescharacteristic
215#125—92no—
216C22⋊Q8—182no—
217C22⋊Q8—181no—
218#121—181no—
219#121—182no—
220C4×Q8—91no—
221C4×D4—92no—
222C4×D4—92no—
223C4×D4—91no—
224C4×D4C2×C3⋊D311yescharacteristic
225C2×C4⋊C4—181no—
226#107—91no—
227#106—92no—
228C4⋊C8—92no—
229C4⋊C8C2×C3⋊D311yescharacteristic
230#102—91no—
231#102—92no—
232#102—92no—
233#102—92no—
234#102—91no—
235#102C2×C3⋊D312yes—
236#97—92no—
237C4×C8—91no—
238C23×C3—24no—
239C23×C3—28no—
240C22×D3—64no—
241C3×D4—28no—
242C3×D4—24no—
243C3×D4—28no—
244C3×D4—48no—
245C3×D4—84no—
246C3×D4#23718yescomplemented
247C2×C3×C4—24no—
248C2×C3×C4—48no—
249C2×C3×C4D3×D414yes—
250C2×C3×C4D3×D414yes—
251C2×C3×C4C23×D314yes—
252#67—1216no—
253#67—248no—
254C2×Dic3—38no—
255C2×Dic3—38no—
256C2×Dic3—68no—
257C2×Dic3—64no—
258C2×Dic3—1216no—
259C2×Dic3—248no—
260D12—64no—
261D12—64no—
262C4×D3—128no—
263Dic6—68no—
264Dic6—244no—
265C3×C8—28no—
266C3⋊C8—64no—
267C3⋊C8—64no—
268C2×C32—42no—
269C2×C32—82no—
270C2×C32#54811yescharacteristic
271C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
272C2×C32#57611yescharacteristic
273C3⋊D3—81no—
274#41—364no—
275C2×Q8—91no—
276C2×Q8—181no—
277C2×D4—21no—
278C2×D4—21no—
279C2×D4—91no—
280C2×D4—182no—
281C2×D4—182no—
282C2×D4C22×C3⋊D312yes—
283C2×D4C22×C3⋊D311yescharacteristic
284C22×C4—21no—
285C22×C4—182no—
286C22×C4—182no—
287C22×C4—181no—
288D8—24no—
289D8—182no—
290C2×C8—91no—
291C2×C8—91no—
292C2×C8C22×C3⋊D312yes—
293C4⋊C4—91no—
294C4⋊C4—92no—
295C4⋊C4—92no—
296C4⋊C4—91no—
297C4⋊C4—182no—
298C4⋊C4—182no—
299C4⋊C4—181no—
300C4⋊C4C22×C3⋊D311yescharacteristic
301C22⋊C4—21no—
302C22⋊C4—182no—
303C22⋊C4—182no—
304C22⋊C4—181no—
305C42—92no—
306C42C22×C3⋊D311yescharacteristic
307C22×C3—28no—
308C22×C3—44no—
309C22×C3—44no—
310C22×C3—48no—
311C22×C3—48no—
312C22×C3—48no—
313C22×C3C2×D3×D414yes—
314C2×D3—124no—
315C2×D3—124no—
316C2×D3—124no—
317C3×C4—24no—
318C3×C4—44no—
319C3×C4#91118yes—
320C3×C4C2×#23714yes—
321C3×C4#101014yes—
322Dic3—68no—
323Dic3—68no—
324Dic3—124no—
325Dic3—128no—
326C32#336611yescharacteristic, complemented, Sylow
327C23—21no—
328C23—22no—
329C23—181no—
330Q8—182no—
331Q8—721no—
332D4—22no—
333D4—21no—
334D4—22no—
335D4—42no—
336D4—81no—
337D4—181no—
338D4—181no—
339D4—364no—
340D4—722no—
341D4#383012yescomplemented
342C2×C4—21no—
343C2×C4—42no—
344C2×C4—92no—
345C2×C4—92no—
346C2×C4—181no—
347C2×C4—182no—
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—48no—
358C2×C3—88no—
359C2×C3#559814yes—
360C2×C3C2×#91114yes—
361C2×C3#577414yes—
362D3—244no—
363C22—22no—
364C22—41no—
365C22—41no—
366C22—42no—
367C22—42no—
368C22—42no—
369C22—361no—
370C22—361no—
371C22—361no—
372C22C2×D4×C3⋊D311yescharacteristic
373C4—21no—
374C4—41no—
375C4—182no—
376C4—182no—
377C4—361no—
378C4—362no—
379C4#6412012yes—
380C4C2×#383011yescharacteristic
381C4#6436711yescharacteristic
382C3#8032014yescomplemented
383C2—42no—
384C2—82no—
385C2—721no—
386C2#1059606911yescharacteristic
387C2C2×#6412011yescharacteristic
388C2#1059624511yescharacteristic
subgroupG/H
centerC22C2×D4×C3⋊D3
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C23×C3⋊D3
FittingC32×#459C2
socleC22×C32C22×D4
hypercenter#459C3⋊D3
hypocenterC32#3366
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ #459

Complements

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

NH ≅ G/Ntype
1. #10596189C2semidirect
2. #10596014C2semidirect
3. C32×#459C2semidirect
4. #10592851C2semidirect
5. #10592849C2semidirect
6. #10592769C2semidirect
7. C4×#3753C2semidirect
8. #10592541C2semidirect
9. #10592530C2semidirect
10. #10592463C2semidirect
11. #10592462C2semidirect
44. C3×#459D3semidirect
124. C32×D4#41semidirect
153. #459C3⋊D3semidirect
246. C3×D4#237semidirect
326. C32#3366semidirect
341. D4#3830semidirect
382. C3#80320semidirect

Maximal subgroups

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

subgroupindex
#105961892
#105960142
C32×#4592
#105928512
#105928492
#105927692
C4×#37532
#105925412
#105925302
#105924632
#105924622
#803203