Finite Group Databasebeta

← #11895710

Subgroups — #11895710

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
1C32×#550C211yesmaximal, characteristic, complemented
2#10596050C211yesmaximal, characteristic, complemented
3#10592771C211yesmaximal, characteristic, complemented
4#10592771C212yesmaximal, complemented
5#10592770C212yesmaximal, complemented
6#10592769C211yesmaximal, characteristic, complemented
7#10592723C211yesmaximal, characteristic, complemented
8#10592713C212yesmaximal, complemented
9C4×#3753C211yesmaximal, characteristic, complemented
10#10592708C212yesmaximal, complemented
11#10592707C211yesmaximal, characteristic, complemented
12#83581—34nomaximal
13C2×C32×#41—21no—
14C32×#127C2211yescharacteristic
15C32×#127C2212yes—
16C32×#121—21no—
17C32×#121—22no—
18C32×C4×Q8C2211yescharacteristic
19C32×C4×D4C2211yescharacteristic
20C32×C4×D4C2212yes—
21#64155—21no—
22C2×#3753C2211yescharacteristic
23C2×#3753C2212yes—
24#64105—22no—
25C4⋊C4×C3⋊D3—21no—
26C4×C4⋊(C3⋊D3)C2211yescharacteristic
27C4×C4⋊(C3⋊D3)C2212yes—
28#64079C2212yes—
29#64078C2211yescharacteristic
30#63659C2212yes—
31#63659C2212yes—
32#63659C2211yescharacteristic
33#63659C2212yes—
34#63659C2212yes—
35#63636C2211yescharacteristic
36#63635C2212yes—
37#63634C2211yescharacteristic
38C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
39C4⋊(C3⋊(C3⋊C8))C2212yes—
40#63630C2212yes—
41C4×C3⋊(C3⋊C8)C2211yescharacteristic
42C3×#550D314yescomplemented
43#5579—34no—
44#5072—34no—
45#5072—38no—
46#5071—38no—
47#5070—34no—
48#5024—34no—
49#5014—38no—
50C4×#213—34no—
51#5009—38no—
52#5008—34no—
53C32×#41—44no—
54C2×C32×Q8D411yescharacteristic
55C2×C32×D4—22no—
56C2×C32×D4—21no—
57C2×C32×D4—22no—
58C2×C32×D4—21no—
59C2×C32×D4C2311yescharacteristic
60C2×C32×D4C2312yes—
61C22×C32×C4—22no—
62C22×C32×C4—21no—
63C2×C4⋊(C3⋊D3)C2311yescharacteristic
64C2×C4×C3⋊D3—21no—
65C2×C4×C3⋊D3—22no—
66C2×#634—21no—
67C32×C4⋊C4D411yescharacteristic
68C32×C4⋊C4D412yes—
69C32×C4⋊C4C2311yescharacteristic
70C32×C22⋊C4—22no—
71C32×C22⋊C4—21no—
72C32×C42C2311yescharacteristic
73C32×C42C2312yes—
74#3753—22no—
75#3753—24no—
76#3752—21no—
77#3752—22no—
78C4⋊(C3⋊Dic3)—21no—
79C4⋊(C3⋊Dic3)C2312yes—
80C4⋊(C3⋊Dic3)C2311yescharacteristic
81#3750—22no—
82#3750—22no—
83C2×C3⋊(C3⋊C8)C2311yescharacteristic
84C2×C3⋊(C3⋊C8)C2312yes—
85C2×C3⋊(C3⋊C8)C2311yescharacteristic
86#3366—91noSylow
87C2×C3×#41—24no—
88C3×#127C2×D314yes—
89C3×#127C2×D318yes—
90C3×#121—24no—
91C3×#121—28no—
92C3×C4×Q8C2×D314yes—
93C3×C4×D4C2×D314yes—
94C3×C4×D4C2×D318yes—
95#946—64no—
96C2×#213—34no—
97C2×#213—38no—
98#896—68no—
99D3×C4⋊C4—64no—
100C4×D12—34no—
101C4×D12—38no—
102#870—38no—
103#869—34no—
104#832—38no—
105#832—38no—
106#832—38no—
107#832—34no—
108#832—38no—
109#809—34no—
110#808—38no—
111#807—34no—
112C4⋊(C3⋊C8)—34no—
113C4⋊(C3⋊C8)—38no—
114#803—38no—
115C4×C3⋊C8—34no—
116C23×C32—22no—
117C23×C32—21no—
118C22×C3⋊D3—21no—
119C32×Q8—22no—
120C32×D4—21no—
121C32×D4—22no—
122C32×D4—21no—
123C32×D4—22no—
124C32×D4—44no—
125C32×D4—42no—
126C32×D4—81no—
127C32×D4—82no—
128C2×C32×C4—21no—
129C2×C32×C4—44no—
130C2×C32×C4—42no—
131C2×C32×C4C2×D412yes—
132C2×C32×C4C2×D412yes—
133C2×C32×C4C2×D411yescharacteristic
134C2×C32×C4C2×D411yescharacteristic
135C2×C32×C4C2411yescharacteristic
136C2×C3⋊Dic3—21no—
137C2×C3⋊Dic3—22no—
138C4⋊(C3⋊D3)—21no—
139C4⋊(C3⋊D3)#4112yescomplemented
140C4×C3⋊D3—42no—
141C4×C3⋊D3—82no—
142#634—81no—
143C3⋊(C3⋊C8)—21no—
144C3⋊(C3⋊C8)—22no—
145C3⋊(C3⋊C8)—21no—
146#554—91no—
147#550C3⋊D311yescharacteristic, complemented
148#490—92no—
149#486—91no—
150#478—92no—
151#476—91no—
152#459—92no—
153#459—91no—
154#446—91no—
155#442—92no—
156C4×D8—91no—
157C3×#41—416no—
158C2×C3×Q8#6714yes—
159C2×C3×D4—28no—
160C2×C3×D4—24no—
161C2×C3×D4—28no—
162C2×C3×D4—24no—
163C2×C3×D4C22×D314yes—
164C2×C3×D4C22×D318yes—
165C22×C3×C4—28no—
166C22×C3×C4—24no—
167C2×D12—34no—
168C2×C4×D3—64no—
169C2×C4×D3—68no—
170C2×Dic6—64no—
171C3×C4⋊C4#6714yes—
172C3×C4⋊C4#6718yes—
173C3×C4⋊C4C22×D314yes—
174C3×C22⋊C4—28no—
175C3×C22⋊C4—24no—
176C3×C42C22×D314yes—
177C3×C42C22×D318yes—
178#213—68no—
179#213—616no—
180(C2×D3)⋊C4—64no—
181(C2×D3)⋊C4—68no—
182C4⋊Dic3—34no—
183C4⋊Dic3—38no—
184C4⋊Dic3—64no—
185Dic3⋊C4—68no—
186Dic3⋊C4—68no—
187C2×C3⋊C8—34no—
188C2×C3⋊C8—34no—
189C2×C3⋊C8—38no—
190C22×C32—42no—
191C22×C32—41no—
192C22×C32—42no—
193C22×C32—41no—
194C22×C32—42no—
195C22×C32—41no—
196C22×C32C22×D411yescharacteristic
197C2×C3⋊D3—22no—
198C2×C3⋊D3—41no—
199C2×C3⋊D3—41no—
200C32×C4—22no—
201C32×C4—21no—
202C32×C4—22no—
203C32×C4—41no—
204C32×C4AGL(1,ℤ/8)12yes—
205C32×C4C2×#4111yescharacteristic
206C32×C42−1+411yescharacteristic
207C3⋊Dic3—41no—
208C3⋊Dic3—42no—
209C2×#41—21no—
210C2×D8—91no—
211C2×D8—92no—
212C4⋊Q8—91no—
213#127C2×C3⋊D311yescharacteristic
214#127C2×C3⋊D312yes—
215#125—92no—
216C22⋊Q8—181no—
217C22⋊Q8—182no—
218#121—21no—
219#121—22no—
220C4×Q8C2×C3⋊D311yescharacteristic
221C4×D4—91no—
222C4×D4—92no—
223C4×D4C2×C3⋊D311yescharacteristic
224C4×D4C2×C3⋊D312yes—
225C2×C4⋊C4—181no—
226#107—91no—
227#106—92no—
228C4⋊C8—91no—
229C4⋊C8—92no—
230#102—91no—
231#102—92no—
232#102—92no—
233#102—92no—
234#102—92no—
235#102—91no—
236#97—92no—
237C4×C8—91no—
238C23×C3—28no—
239C23×C3—24no—
240C22×D3—64no—
241C3×Q8—28no—
242C3×D4—24no—
243C3×D4—28no—
244C3×D4—24no—
245C3×D4—28no—
246C3×D4—416no—
247C3×D4—48no—
248C3×D4—84no—
249C3×D4—88no—
250C2×C3×C4—24no—
251C2×C3×C4—416no—
252C2×C3×C4—48no—
253C2×C3×C4C2×#6718yes—
254C2×C3×C4C2×#6718yes—
255C2×C3×C4C2×#6714yes—
256C2×C3×C4C2×#6714yes—
257C2×C3×C4C23×D314yes—
258C2×Dic3—64no—
259C2×Dic3—68no—
260D12—38no—
261D12—64no—
262C4×D3—128no—
263C4×D3—248no—
264Dic6—244no—
265C3⋊C8—64no—
266C3⋊C8—68no—
267C3⋊C8—64no—
268C2×C32—82no—
269C2×C32—81no—
270C2×C32#54811yescharacteristic
271C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
272C2×C32#57611yescharacteristic
273C3⋊D3—42no—
274#41—44no—
275C2×Q8—181no—
276C2×Q8#63811yescharacteristic
277C2×D4—22no—
278C2×D4—21no—
279C2×D4—21no—
280C2×D4—22no—
281C2×D4—91no—
282C2×D4C22×C3⋊D311yescharacteristic
283C2×D4C22×C3⋊D312yes—
284C22×C4—22no—
285C22×C4—21no—
286C22×C4—181no—
287C22×C4—182no—
288D8—182no—
289D8—184no—
290C2×C8—91no—
291C2×C8—91no—
292C2×C8—92no—
293C4⋊C4—92no—
294C4⋊C4—91no—
295C4⋊C4—182no—
296C4⋊C4—181no—
297C4⋊C4—182no—
298C4⋊C4#63811yescharacteristic
299C4⋊C4#63812yes—
300C4⋊C4C22×C3⋊D311yescharacteristic
301C22⋊C4—21no—
302C22⋊C4—22no—
303C22⋊C4—181no—
304C22⋊C4—182no—
305C42C22×C3⋊D311yescharacteristic
306C42C22×C3⋊D312yes—
307C22×C3—48no—
308C22×C3—44no—
309C22×C3—48no—
310C22×C3—44no—
311C22×C3—48no—
312C22×C3—44no—
313C22×C3C22×#6714yes—
314C2×D3—68no—
315C2×D3—124no—
316C2×D3—124no—
317C3×C4—28no—
318C3×C4—24no—
319C3×C4—28no—
320C3×C4—44no—
321C3×C4#93218yes—
322C3×C4D3×#4114yes—
323C3×C4#101014yes—
324Dic3—124no—
325Dic3—128no—
326C32#336611yescharacteristic, complemented, Sylow
327C23—22no—
328C23—21no—
329C23—181no—
330Q8—22no—
331Q8—721no—
332D4—21no—
333D4—22no—
334D4—21no—
335D4—22no—
336D4—44no—
337D4—42no—
338D4—82no—
339D4—81no—
340D4—92no—
341D4—181no—
342C2×C4—21no—
343C2×C4—44no—
344C2×C4—42no—
345C2×C4—181no—
346C2×C4—182no—
347C2×C4—362no—
348C2×C4—722no—
349C2×C4C2×#63811yescharacteristic
350C2×C4C2×#63812yes—
351C2×C4C2×#63812yes—
352C2×C4C2×#63811yescharacteristic
353C2×C4C23×C3⋊D311yescharacteristic
354C8—181no—
355C8—182no—
356C8—181no—
357C2×C3—88no—
358C2×C3—84no—
359C2×C3C2×#93214yes—
360C2×C3#583114yes—
361C2×C3#583514yes—
362D3—128no—
363C22—42no—
364C22—41no—
365C22—42no—
366C22—41no—
367C22—41no—
368C22—42no—
369C22—182no—
370C22—361no—
371C22—361no—
372C22C22×#63811yescharacteristic
373C4—22no—
374C4—22no—
375C4—21no—
376C4—41no—
377C4—361no—
378C4—362no—
379C4#6414112yes—
380C4#41×C3⋊D311yescharacteristic
381C4#6436711yescharacteristic
382C3#8358114yescomplemented
383C2—82no—
384C2—81no—
385C2—362no—
386C2C2×#6414111yescharacteristic
387C2#1059630211yescharacteristic
388C2#1059630611yescharacteristic
subgroupG/H
centerC22C22×#638
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C23×C3⋊D3
FittingC32×#550C2
socleC22×C32C22×D4
hypercenter#550C3⋊D3
hypocenterC32#3366
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C4×Q8 ◁ #550

Complements

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

NH ≅ G/Ntype
1. C32×#550C2semidirect
2. #10596050C2semidirect
3. #10592771C2semidirect
4. #10592771C2semidirect
5. #10592770C2semidirect
6. #10592769C2semidirect
7. #10592723C2semidirect
8. #10592713C2semidirect
9. C4×#3753C2semidirect
10. #10592708C2semidirect
11. #10592707C2semidirect
42. C3×#550D3semidirect
139. C4⋊(C3⋊D3)#41semidirect
147. #550C3⋊D3semidirect
326. C32#3366semidirect
382. C3#83581semidirect

Maximal subgroups

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

subgroupindex
C32×#5502
#105960502
#105927712
#105927702
#105927692
#105927232
#105927132
C4×#37532
#105927082
#105927072
#835813