Finite Group Databasebeta

← #11870423

Subgroups — #11870423

Order 1152.

1476 conjugacy classes of subgroups.

The subgroup lattice has 465 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596196C211yesmaximal, characteristic, complemented
2C4×D4×C3⋊D3C211yesmaximal, characteristic, complemented
3C32×#474C211yesmaximal, characteristic, complemented
4#10592786C211yesmaximal, characteristic, complemented
5#10592714C211yesmaximal, characteristic, complemented
6#10592581C212yesmaximal, complemented
7#10592571C212yesmaximal, complemented
8#10592542C211yesmaximal, characteristic, complemented
9#10592532C211yesmaximal, characteristic, complemented
10#10592472C212yesmaximal, complemented
11#10592455C212yesmaximal, complemented
12#80948—34nomaximal
13C2×#3832—21no—
14C2×D4×C3⋊D3C2211yescharacteristic
15C22×C4×C3⋊D3—21no—
16C32×C4⋊Q8C2211yescharacteristic, complemented
17C32×C4×D4C2211yescharacteristic
18#64156—21no—
19D4×C3⋊Dic3C2211yescharacteristic
20C2×#3753C2212yes—
21C4×#638—21no—
22C2×#3745C2212yes—
23#64104—21no—
24#64104C2212yes—
25#64102—21no—
26#64102C2211yescharacteristic
27#64102C2212yescomplemented
28C4⋊C4×C3⋊D3C2211yescharacteristic
29#64090—21no—
30C22⋊C4×C3⋊D3—21no—
31#64083C2211yescharacteristic, complemented
32C4×C4⋊(C3⋊D3)C2211yescharacteristic
33C42×C3⋊D3C2211yescharacteristic
34C32×#107C2212yescomplemented
35C32×C4⋊C8C2211yescharacteristic, complemented
36C32×#102C2212yes—
37#63648C2212yescomplemented
38#63647C2212yes—
39C8×C3⋊Dic3C2212yescomplemented
40#63636C2212yes—
41#63636C2212yescomplemented
42#63634C2212yescomplemented
43C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic, complemented
44#5725—34no—
45C4×D3×D4—34no—
46C3×#474D314yescomplemented
47#5087—34no—
48#5015—34no—
49#4882—38no—
50#4872—38no—
51#4843—34no—
52#4833—34no—
53#4773—38no—
54#4756—38no—
55C23×C3⋊D3—21no—
56C2×C32×Q8—21no—
57C2×C32×D4C2311yescharacteristic
58C22×C32×C4—21no—
59C2×#638—21no—
60C22×C3⋊Dic3—21no—
61#3832—44no—
62D4×C3⋊D3—22no—
63D4×C3⋊D3—22no—
64C2×C4⋊(C3⋊D3)—22no—
65C2×C4⋊(C3⋊D3)—21no—
66C2×C4⋊(C3⋊D3)—21no—
67C2×C4⋊(C3⋊D3)C2312yes—
68C2×C4⋊(C3⋊D3)C2311yescharacteristic
69C2×C4×C3⋊D3—21no—
70C2×C4×C3⋊D3—21no—
71C2×C4×C3⋊D3—21no—
72C2×C4×C3⋊D3—22no—
73C2×C4×C3⋊D3—44no—
74C2×C4×C3⋊D3D411yescharacteristic
75C2×C4×C3⋊D3D411yescharacteristic
76C2×C4×C3⋊D3C2311yescharacteristic
77C2×C32×C8C2312yes—
78C32×C4⋊C4—21no—
79C32×C4⋊C4C2311yescharacteristic
80C32×C4⋊C4C2312yes—
81C32×C22⋊C4—21no—
82C32×C42C2311yescharacteristic
83#3757—21no—
84#3753—24no—
85#3752—21no—
86#3752—21no—
87#3752—22no—
88#3752—22no—
89C4⋊(C3⋊Dic3)C2311yescharacteristic
90#3750—21no—
91C4×C3⋊Dic3D411yescharacteristic
92C4×C3⋊Dic3D411yescharacteristic
93C4×C3⋊Dic3C2311yescharacteristic
94C2×C3⋊(C3⋊C8)C2312yes—
95#3745—24no—
96#3100—91noSylow
97C2×#239—64no—
98C2×D3×D4—34no—
99C22×C4×D3—64no—
100C3×C4⋊Q8C2×D314yescomplemented
101C3×C4×D4C2×D314yes—
102#947—64no—
103D4×Dic3—34no—
104C2×#213—38no—
105C4×#67—64no—
106C2×D24—38no—
107#895—38no—
108#895—64no—
109#893—34no—
110#893—38no—
111#893—64no—
112D3×C4⋊C4—34no—
113#67⋊C4—64no—
114D3×C22⋊C4—64no—
115#874—34no—
116C4×D12—34no—
117C42×D3—34no—
118C3×#107C2×D318yescomplemented
119C3×C4⋊C8C2×D314yescomplemented
120C3×#102C2×D318yes—
121#821—38no—
122(C2×D3)⋊C8—38no—
123C8×Dic3—38no—
124#809—38no—
125#809—38no—
126#807—38no—
127C4⋊(C3⋊C8)—34no—
128C23×C32—21no—
129C22×C3⋊D3—24no—
130C22×C3⋊D3—21no—
131C22×C3⋊D3—22no—
132C22×C3⋊D3—42no—
133C22×C3⋊D3—42no—
134C22×C3⋊D3C2×D411yescharacteristic
135C32×Q8—42no—
136C32×D4—21no—
137C32×D4#4112yescomplemented
138C2×C32×C4—21no—
139C2×C32×C4—22no—
140C2×C32×C4—42no—
141C2×C32×C4C2×D411yescharacteristic
142C2×C32×C4C2×D411yescharacteristic
143C2×C32×C4C2411yescharacteristic
144#638—24no—
145C2×C3⋊Dic3—21no—
146C2×C3⋊Dic3—42no—
147C2×C3⋊Dic3C2×D411yescharacteristic
148C2×C3⋊Dic3C2×D411yescharacteristic
149C2×C3⋊Dic3C2×D411yescharacteristic
150C4⋊(C3⋊D3)—21no—
151C4⋊(C3⋊D3)—22no—
152C4⋊(C3⋊D3)—22no—
153C4⋊(C3⋊D3)—42no—
154C4⋊(C3⋊D3)—44no—
155C4⋊(C3⋊D3)—42no—
156C4⋊(C3⋊D3)#4112yescomplemented
157C4×C3⋊D3—21no—
158C4×C3⋊D3—21no—
159C4×C3⋊D3—41no—
160C4×C3⋊D3—42no—
161C4×C3⋊D3—42no—
162C4×C3⋊D3—42no—
163C4×C3⋊D3—44no—
164C4×C3⋊D3D814yescomplemented
165C32×C8—22no—
166C3⋊(C3⋊C8)—22no—
167#532—91no—
168C2×C4×D4—91no—
169#480—92no—
170#474—91no—
171#474C3⋊D311yescharacteristic, complemented
172#459—91no—
173#459—91no—
174#447—92no—
175C4×D8—92no—
176C4×D8—92no—
177#431—91no—
178C23×D3—64no—
179C2×C3×Q8—24no—
180C2×C3×D4C22×D314yes—
181C22×C3×C4—24no—
182C2×#67—64no—
183C22×Dic3—64no—
184#239—1216no—
185D3×D4—68no—
186D3×D4—68no—
187C2×D12—34no—
188C2×D12—38no—
189C2×D12—68no—
190C2×D12—64no—
191C2×D12—64no—
192C2×C4×D3—34no—
193C2×C4×D3—34no—
194C2×C4×D3—34no—
195C2×C4×D3—64no—
196C2×C4×D3—68no—
197C2×C4×D3—64no—
198C2×C4×D3—64no—
199C2×C4×D3—1216no—
200C2×C3×C8C22×D318yes—
201C3×C4⋊C4—24no—
202C3×C4⋊C4C22×D318yes—
203C3×C4⋊C4C22×D314yes—
204C3×C22⋊C4—24no—
205C3×C42C22×D314yes—
206#217—64no—
207#213—616no—
208(C2×D3)⋊C4—64no—
209(C2×D3)⋊C4—68no—
210(C2×D3)⋊C4—68no—
211(C2×D3)⋊C4—64no—
212C4⋊Dic3—34no—
213Dic3⋊C4—64no—
214C4×Dic3—34no—
215C4×Dic3—34no—
216C4×Dic3—34no—
217C2×C3⋊C8—38no—
218D24—616no—
219C22×C32—22no—
220C22×C32—41no—
221C22×C32—41no—
222C22×C32C22×D411yescharacteristic
223C2×C3⋊D3—21no—
224C2×C3⋊D3—21no—
225C2×C3⋊D3—22no—
226C2×C3⋊D3—48no—
227C2×C3⋊D3—41no—
228C2×C3⋊D3—41no—
229C2×C3⋊D3—42no—
230C2×C3⋊D3—42no—
231C2×C3⋊D3—42no—
232C2×C3⋊D3C2×D812yes—
233C32×C4—21no—
234C32×C4—41no—
235C32×C4—42no—
236C32×C4C2×D812yes—
237C32×C4C2×#4111yescharacteristic
238C32×C4C2×#4111yescharacteristic
239C3⋊Dic3—21no—
240C3⋊Dic3—21no—
241C3⋊Dic3—41no—
242C3⋊Dic3C2×D812yes—
243C2×#41—181no—
244C22×D4—91no—
245C23×C4—181no—
246C2×D8—92no—
247C2×D8—92no—
248C4⋊Q8C2×C3⋊D311yescharacteristic, complemented
249#127—91no—
250#124—181no—
251#121—92no—
252#121—181no—
253C4×D4—91no—
254C4×D4—91no—
255C4×D4—92no—
256C4×D4—91no—
257C4×D4—181no—
258C4×D4—181no—
259C4×D4—181no—
260C4×D4C2×C3⋊D311yescharacteristic
261C2×C4⋊C4—91no—
262C2×C22⋊C4—181no—
263C2×C42—91no—
264#107—92no—
265#107C2×C3⋊D312yescomplemented
266C4⋊C8—91no—
267C4⋊C8C2×C3⋊D311yescharacteristic, complemented
268#102—92no—
269#102—92no—
270#102—92no—
271#102C2×C3⋊D312yes—
272C22⋊C8—92no—
273C4×C8—92no—
274C23×C3—24no—
275C22×D3—34no—
276C22×D3—616no—
277C22×D3—64no—
278C22×D3—68no—
279C22×D3—128no—
280C22×D3—128no—
281C3×Q8—48no—
282C3×D4—24no—
283C3×D4#23918yescomplemented
284C2×C3×C4—24no—
285C2×C3×C4—28no—
286C2×C3×C4—48no—
287C2×C3×C4D3×D414yes—
288C2×C3×C4D3×D414yes—
289C2×C3×C4C23×D314yes—
290#67—616no—
291C2×Dic3—34no—
292C2×Dic3—34no—
293C2×Dic3—34no—
294C2×Dic3—64no—
295C2×Dic3—128no—
296D12—38no—
297D12—64no—
298D12—68no—
299D12—68no—
300D12—128no—
301D12—1216no—
302D12—128no—
303C4×D3—316no—
304C4×D3—64no—
305C4×D3—64no—
306C4×D3—128no—
307C4×D3—1216no—
308C4×D3—124no—
309C4×D3—128no—
310C4×D3—128no—
311C3×C8—28no—
312C3⋊C8—68no—
313C2×C32—42no—
314C2×C32#52511yescharacteristic
315C2×C32C22×D811yescharacteristic
316C2×C32#57511yescharacteristic
317C3⋊D3—22no—
318C3⋊D3—42no—
319C3⋊D3—82no—
320C24—181no—
321#41—364no—
322C2×Q8—21no—
323C2×D4—91no—
324C2×D4—92no—
325C2×D4—182no—
326C2×D4—181no—
327C2×D4—182no—
328C2×D4—182no—
329C2×D4—181no—
330C2×D4—181no—
331C2×D4C22×C3⋊D311yescharacteristic
332C22×C4—21no—
333C22×C4—91no—
334C22×C4—91no—
335C22×C4—91no—
336C22×C4—181no—
337C22×C4—182no—
338C22×C4—181no—
339C22×C4—181no—
340C22×C4—181no—
341C22×C4—364no—
342D8—184no—
343D8—184no—
344C2×C8—92no—
345C2×C8C22×C3⋊D312yes—
346C4⋊C4—21no—
347C4⋊C4—91no—
348C4⋊C4—181no—
349C4⋊C4C22×C3⋊D311yescharacteristic
350C4⋊C4C22×C3⋊D312yes—
351C22⋊C4—21no—
352C22⋊C4—181no—
353C22⋊C4—182no—
354C22⋊C4—182no—
355C22⋊C4—181no—
356C22⋊C4—181no—
357C42—91no—
358C42—91no—
359C42—91no—
360C42C22×C3⋊D311yescharacteristic
361C22×C3—28no—
362C22×C3—44no—
363C22×C3—44no—
364C22×C3C2×D3×D414yes—
365C2×D3—38no—
366C2×D3—64no—
367C2×D3—64no—
368C2×D3—68no—
369C2×D3—1232no—
370C2×D3—124no—
371C2×D3—124no—
372C2×D3—128no—
373C2×D3—128no—
374C2×D3—128no—
375C3×C4—24no—
376C3×C4—44no—
377C3×C4—48no—
378C3×C4D3×D818yes—
379C3×C4C2×#23914yes—
380C3×C4D3×#4114yes—
381Dic3—38no—
382Dic3—64no—
383Dic3—64no—
384Dic3—124no—
385C32#310011yescharacteristic, complemented, Sylow
386C23—21no—
387C23—91no—
388C23—184no—
389C23—181no—
390C23—182no—
391C23—362no—
392C23—362no—
393Q8—42no—
394D4—21no—
395D4—92no—
396D4—184no—
397D4—181no—
398D4—182no—
399D4—182no—
400D4—362no—
401D4—364no—
402D4—362no—
403D4#383212yescomplemented
404C2×C4—21no—
405C2×C4—22no—
406C2×C4—42no—
407C2×C4—91no—
408C2×C4—94no—
409C2×C4—91no—
410C2×C4—91no—
411C2×C4—181no—
412C2×C4—181no—
413C2×C4—181no—
414C2×C4—361no—
415C2×C4—362no—
416C2×C4—364no—
417C2×C4—362no—
418C2×C4—362no—
419C2×C4—362no—
420C2×C4D4×C3⋊D311yescharacteristic
421C2×C4D4×C3⋊D311yescharacteristic
422C2×C4C23×C3⋊D311yescharacteristic
423C8—22no—
424C8—182no—
425C2×C3—48no—
426C2×C3#562714yes—
427C2×C3C2×D3×D814yes—
428C2×C3#577714yes—
429D3—68no—
430D3—128no—
431D3—248no—
432C22—22no—
433C22—41no—
434C22—41no—
435C22—92no—
436C22—181no—
437C22—181no—
438C22—182no—
439C22—368no—
440C22—361no—
441C22—361no—
442C22—362no—
443C22—362no—
444C22—362no—
445C22C2×D4×C3⋊D311yescharacteristic
446C4—21no—
447C4—41no—
448C4—42no—
449C4—92no—
450C4—181no—
451C4—181no—
452C4—361no—
453C4D8×C3⋊D312yes—
454C4C2×#383211yescharacteristic
455C4#41×C3⋊D311yescharacteristic
456C3#8094814yescomplemented
457C2—42no—
458C2—182no—
459C2—362no—
460C2—722no—
461C2#1059609811yescharacteristic
462C2C2×D8×C3⋊D311yescharacteristic
463C2#1059624811yescharacteristic
subgroupG/H
centerC22C2×D4×C3⋊D3
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C23×C3⋊D3
FittingC32×#474C2
socleC22×C32C22×D4
hypercenter#474C3⋊D3
hypocenterC32#3100
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ #474

Complements

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

NH ≅ G/Ntype
1. #10596196C2semidirect
2. C4×D4×C3⋊D3C2semidirect
3. C32×#474C2semidirect
4. #10592786C2semidirect
5. #10592714C2semidirect
6. #10592581C2semidirect
7. #10592571C2semidirect
8. #10592542C2semidirect
9. #10592532C2semidirect
10. #10592472C2semidirect
11. #10592455C2semidirect
16. C32×C4⋊Q8C22semidirect
27. #64102C22semidirect
31. #64083C22semidirect
34. C32×#107C22semidirect
35. C32×C4⋊C8C22semidirect
37. #63648C22semidirect
39. C8×C3⋊Dic3C22semidirect
41. #63636C22semidirect
42. #63634C22semidirect
43. C4⋊(C3⋊(C3⋊C8))C22semidirect
46. C3×#474D3semidirect
100. C3×C4⋊Q8C2×D3semidirect
118. C3×#107C2×D3semidirect
119. C3×C4⋊C8C2×D3semidirect
137. C32×D4#41semidirect
156. C4⋊(C3⋊D3)#41semidirect
164. C4×C3⋊D3D8semidirect
171. #474C3⋊D3semidirect
248. C4⋊Q8C2×C3⋊D3semidirect
265. #107C2×C3⋊D3semidirect
267. C4⋊C8C2×C3⋊D3semidirect
283. C3×D4#239semidirect
385. C32#3100semidirect
403. D4#3832semidirect
456. C3#80948semidirect

Maximal subgroups

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

subgroupindex
#105961962
C4×D4×C3⋊D32
C32×#4742
#105927862
#105927142
#105925812
#105925712
#105925422
#105925322
#105924722
#105924552
#809483