Finite Group Databasebeta

← #11865847

Subgroups — #11865847

Order 1152.

1644 conjugacy classes of subgroups.

The subgroup lattice has 483 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64123C212yesmaximal, complemented
2#10596196C211yesmaximal, characteristic, complemented
3C4×D4×C3⋊D3C211yesmaximal, characteristic, complemented
4C32×#461C211yesmaximal, characteristic, complemented
5#10592864C212yesmaximal, complemented
6#10592782C211yesmaximal, characteristic, complemented
7#10592714C211yesmaximal, characteristic, complemented
8#10592542C211yesmaximal, characteristic, complemented
9#10592536C211yesmaximal, characteristic, complemented
10#10592518C212yesmaximal, complemented
11#10592502C212yesmaximal, complemented
12#80428—34nomaximal
13C2×#3832C2212yes—
14C2×D4×C3⋊D3C2211yescharacteristic
15C22×C4×C3⋊D3—21no—
16C2×C32×SD16C2212yes—
17C32×C4⋊Q8C2211yescharacteristic, complemented
18C32×C4×D4C2211yescharacteristic
19#64156C2212yescomplemented
20C2×#3755C2212yes—
21D4×C3⋊Dic3C2211yescharacteristic
22C2×#3753C2212yes—
23C4×#638—21no—
24#64123—28no—
25C2×#3745C2212yes—
26C2×#3743C2212yes—
27#64104—21no—
28#64104—21no—
29#64102—21no—
30#64102—21no—
31#64102C2211yescharacteristic
32C4⋊C4×C3⋊D3C2211yescharacteristic
33#64090—21no—
34C22⋊C4×C3⋊D3—21no—
35#64083C2211yescharacteristic, complemented
36C4×C4⋊(C3⋊D3)C2211yescharacteristic
37C42×C3⋊D3C2211yescharacteristic
38C32×C4⋊C8C2211yescharacteristic, complemented
39C32×#103C2212yescomplemented
40#63662C2212yescomplemented
41#63648C2212yescomplemented
42#63641C2212yescomplemented
43#63636C2212yescomplemented
44C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic, complemented
45C2×#914—38no—
46#5725—34no—
47C4×D3×D4—34no—
48C3×#461D314yescomplemented
49#5165—38no—
50#5083—34no—
51#5015—34no—
52#4843—34no—
53#4837—34no—
54#4819—38no—
55#4803—38no—
56C23×C3⋊D3—21no—
57C2×C32×Q8C2312yes—
58C2×C32×D4C2311yescharacteristic
59C22×C32×C4—21no—
60C2×#638—21no—
61C22×C3⋊Dic3—21no—
62#3832—24no—
63#3832—24no—
64D4×C3⋊D3—22no—
65D4×C3⋊D3D414yescomplemented
66C2×C4⋊(C3⋊D3)—22no—
67C2×C4⋊(C3⋊D3)—21no—
68C2×C4⋊(C3⋊D3)—21no—
69C2×C4⋊(C3⋊D3)C2312yes—
70C2×C4⋊(C3⋊D3)C2311yescharacteristic
71C2×C4×C3⋊D3—21no—
72C2×C4×C3⋊D3—21no—
73C2×C4×C3⋊D3—21no—
74C2×C4×C3⋊D3—22no—
75C2×C4×C3⋊D3—44no—
76C2×C4×C3⋊D3D411yescharacteristic
77C2×C4×C3⋊D3D411yescharacteristic
78C2×C4×C3⋊D3C2311yescharacteristic
79C32×SD16—24no—
80C2×C32×C8C2312yes—
81C32×C4⋊C4—21no—
82C32×C4⋊C4—21no—
83C32×C4⋊C4C2311yescharacteristic
84C32×C22⋊C4—21no—
85C32×C42C2311yescharacteristic
86#3757—21no—
87#3755—24no—
88#3753—24no—
89#3752—21no—
90#3752—21no—
91#3752—22no—
92#3752—22no—
93C4⋊(C3⋊Dic3)C2311yescharacteristic
94#3750—21no—
95C4×C3⋊Dic3D411yescharacteristic
96C4×C3⋊Dic3D411yescharacteristic
97C4×C3⋊Dic3C2311yescharacteristic
98C2×C3⋊(C3⋊C8)C2312yes—
99#3745—24no—
100#3743—24no—
101#3036—91noSylow
102C2×#239—38no—
103C2×D3×D4—34no—
104C22×C4×D3—64no—
105C2×C3×SD16C2×D318yes—
106C3×C4⋊Q8C2×D314yescomplemented
107C3×C4×D4C2×D314yes—
108#947—38no—
109C2×#215—38no—
110D4×Dic3—34no—
111C2×#213—38no—
112C4×#67—64no—
113#914—632no—
114C2×D24—38no—
115C2×ΓL(1,𝔽25)—38no—
116#895—64no—
117#895—64no—
118#893—34no—
119#893—64no—
120#893—64no—
121D3×C4⋊C4—34no—
122#67⋊C4—64no—
123D3×C22⋊C4—64no—
124#874—34no—
125C4×D12—34no—
126C42×D3—34no—
127C3×C4⋊C8C2×D314yescomplemented
128C3×#103C2×D318yescomplemented
129#835—38no—
130#821—38no—
131Dic3⋊C8—38no—
132#809—38no—
133C4⋊(C3⋊C8)—34no—
134C23×C32—21no—
135C22×C3⋊D3—21no—
136C22×C3⋊D3—24no—
137C22×C3⋊D3—22no—
138C22×C3⋊D3—42no—
139C22×C3⋊D3—42no—
140C22×C3⋊D3C2×D411yescharacteristic
141C32×Q8—22no—
142C32×Q8—22no—
143C32×D4—21no—
144C32×D4C2×D412yes—
145C2×C32×C4—21no—
146C2×C32×C4—22no—
147C2×C32×C4—42no—
148C2×C32×C4C2×D411yescharacteristic
149C2×C32×C4C2×D411yescharacteristic
150C2×C32×C4C2411yescharacteristic
151#638—24no—
152C2×C3⋊Dic3—21no—
153C2×C3⋊Dic3—42no—
154C2×C3⋊Dic3C2×D411yescharacteristic
155C2×C3⋊Dic3C2×D411yescharacteristic
156C2×C3⋊Dic3C2×D411yescharacteristic
157C4⋊(C3⋊D3)—22no—
158C4⋊(C3⋊D3)—21no—
159C4⋊(C3⋊D3)—22no—
160C4⋊(C3⋊D3)—42no—
161C4⋊(C3⋊D3)—44no—
162C4⋊(C3⋊D3)—42no—
163C4⋊(C3⋊D3)C2×D412yes—
164C4×C3⋊D3—22no—
165C4×C3⋊D3—41no—
166C4×C3⋊D3—42no—
167C4×C3⋊D3—42no—
168C4×C3⋊D3—42no—
169C4×C3⋊D3—44no—
170C4×C3⋊D3C2×D412yes—
171C4×C3⋊D3#4112yes—
172C32×C8—22no—
173C3⋊(C3⋊C8)—22no—
174C2×AGL(1,ℤ/8)—92no—
175#532—91no—
176C2×C4×D4—91no—
177#463—92no—
178#463—92no—
179#461—91no—
180#461C3⋊D311yescharacteristic, complemented
181#459—91no—
182#459—91no—
183#423—91no—
184#417—92no—
185C23×D3—64no—
186C2×C3×Q8C22×D318yes—
187C2×C3×D4C22×D314yes—
188C22×C3×C4—24no—
189C2×#67—64no—
190C22×Dic3—64no—
191#239—616no—
192#239—616no—
193D3×D4—316no—
194D3×D4—68no—
195C2×D12—34no—
196C2×D12—38no—
197C2×D12—68no—
198C2×D12—64no—
199C2×D12—64no—
200C2×C4×D3—34no—
201C2×C4×D3—34no—
202C2×C4×D3—34no—
203C2×C4×D3—64no—
204C2×C4×D3—68no—
205C2×C4×D3—64no—
206C2×C4×D3—64no—
207C2×C4×D3—1216no—
208C3×SD16—216no—
209C2×C3×C8C22×D318yes—
210C3×C4⋊C4—24no—
211C3×C4⋊C4—24no—
212C3×C4⋊C4C22×D314yes—
213C3×C22⋊C4—24no—
214C3×C42C22×D314yes—
215#217—64no—
216#215—616no—
217#213—616no—
218(C2×D3)⋊C4—64no—
219(C2×D3)⋊C4—68no—
220(C2×D3)⋊C4—68no—
221(C2×D3)⋊C4—64no—
222C4⋊Dic3—34no—
223Dic3⋊C4—64no—
224C4×Dic3—34no—
225C4×Dic3—34no—
226C4×Dic3—34no—
227C2×C3⋊C8—38no—
228D24—616no—
229ΓL(1,𝔽25)—616no—
230C22×C32—22no—
231C22×C32—41no—
232C22×C32—41no—
233C22×C32C22×D411yescharacteristic
234C2×C3⋊D3—21no—
235C2×C3⋊D3—21no—
236C2×C3⋊D3—22no—
237C2×C3⋊D3—48no—
238C2×C3⋊D3—41no—
239C2×C3⋊D3—41no—
240C2×C3⋊D3—42no—
241C2×C3⋊D3—42no—
242C2×C3⋊D3—42no—
243C2×C3⋊D3#12112yes—
244C32×C4—21no—
245C32×C4—42no—
246C32×C4—41no—
247C32×C4AGL(1,ℤ/8)12yescomplemented
248C32×C4C22×D411yescharacteristic
249C32×C4C2×#4111yescharacteristic
250C3⋊Dic3—21no—
251C3⋊Dic3—21no—
252C3⋊Dic3—41no—
253C3⋊Dic3#12112yes—
254C2×#41—92no—
255C22×D4—91no—
256C23×C4—181no—
257AGL(1,ℤ/8)—188no—
258C2×SD16—92no—
259C2×SD16C2×C3⋊D312yes—
260C2×D8—92no—
261C2×D8—92no—
262C2×M16—92no—
263C4⋊Q8C2×C3⋊D311yescharacteristic, complemented
264#127—91no—
265#124—92no—
266#121—181no—
267#121—181no—
268C4×D4—91no—
269C4×D4—91no—
270C4×D4—91no—
271C4×D4—181no—
272C4×D4—181no—
273C4×D4—181no—
274C4×D4—181no—
275C4×D4C2×C3⋊D311yescharacteristic
276C2×C4⋊C4—91no—
277C2×C22⋊C4—181no—
278C2×C42—91no—
279C4⋊C8—92no—
280C4⋊C8—91no—
281C4⋊C8C2×C3⋊D311yescharacteristic, complemented
282#103—92no—
283#103C2×C3⋊D312yescomplemented
284#102—92no—
285#102—92no—
286C23×C3—24no—
287C22×D3—34no—
288C22×D3—616no—
289C22×D3—64no—
290C22×D3—68no—
291C22×D3—128no—
292C22×D3—128no—
293C3×Q8—28no—
294C3×Q8—28no—
295C3×D4—24no—
296C3×D4D3×D418yes—
297C2×C3×C4—24no—
298C2×C3×C4—28no—
299C2×C3×C4—48no—
300C2×C3×C4D3×D414yes—
301C2×C3×C4D3×D414yes—
302C2×C3×C4C23×D314yes—
303#67—616no—
304C2×Dic3—34no—
305C2×Dic3—34no—
306C2×Dic3—34no—
307C2×Dic3—64no—
308C2×Dic3—128no—
309D12—38no—
310D12—68no—
311D12—64no—
312D12—68no—
313D12—128no—
314D12—1216no—
315D12—128no—
316C4×D3—38no—
317C4×D3—38no—
318C4×D3—68no—
319C4×D3—1216no—
320C4×D3—124no—
321C4×D3—128no—
322C4×D3—128no—
323C4×D3—128no—
324C3×C8—28no—
325C3⋊C8—68no—
326C2×C32—42no—
327C2×C32C2×#12111yescharacteristic
328C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
329C2×C32#57511yescharacteristic
330C3⋊D3—22no—
331C3⋊D3—42no—
332C3⋊D3—82no—
333C24—181no—
334#41—184no—
335#41—184no—
336C2×Q8C22×C3⋊D312yes—
337C2×D4—94no—
338C2×D4—91no—
339C2×D4—92no—
340C2×D4—182no—
341C2×D4—182no—
342C2×D4—181no—
343C2×D4—181no—
344C2×D4—181no—
345C2×D4C22×C3⋊D311yescharacteristic
346C22×C4—21no—
347C22×C4—91no—
348C22×C4—91no—
349C22×C4—91no—
350C22×C4—181no—
351C22×C4—182no—
352C22×C4—181no—
353C22×C4—181no—
354C22×C4—181no—
355C22×C4—364no—
356SD16—24no—
357SD16—184no—
358D8—184no—
359D8—184no—
360M16—184no—
361C2×C8—92no—
362C2×C8C22×C3⋊D312yes—
363C4⋊C4—21no—
364C4⋊C4—21no—
365C4⋊C4—91no—
366C4⋊C4—181no—
367C4⋊C4C22×C3⋊D311yescharacteristic
368C22⋊C4—21no—
369C22⋊C4—181no—
370C22⋊C4—182no—
371C22⋊C4—182no—
372C22⋊C4—181no—
373C22⋊C4—181no—
374C42—91no—
375C42—91no—
376C42—91no—
377C42C22×C3⋊D311yescharacteristic
378C22×C3—28no—
379C22×C3—44no—
380C22×C3—44no—
381C22×C3C2×D3×D414yes—
382C2×D3—38no—
383C2×D3—64no—
384C2×D3—64no—
385C2×D3—68no—
386C2×D3—1232no—
387C2×D3—124no—
388C2×D3—124no—
389C2×D3—128no—
390C2×D3—128no—
391C2×D3—128no—
392C3×C4—24no—
393C3×C4—44no—
394C3×C4—48no—
395C3×C4#91418yescomplemented
396C3×C4C2×D3×D414yes—
397C3×C4D3×#4114yes—
398Dic3—38no—
399Dic3—64no—
400Dic3—64no—
401Dic3—124no—
402C32#303611yescharacteristic, complemented, Sylow
403C23—21no—
404C23—91no—
405C23—184no—
406C23—181no—
407C23—182no—
408C23—362no—
409C23—362no—
410Q8—22no—
411Q8—22no—
412D4—21no—
413D4—92no—
414D4—184no—
415D4—182no—
416D4—181no—
417D4—182no—
418D4—362no—
419D4—364no—
420D4—362no—
421D4D4×C3⋊D312yes—
422C2×C4—21no—
423C2×C4—22no—
424C2×C4—42no—
425C2×C4—91no—
426C2×C4—92no—
427C2×C4—92no—
428C2×C4—91no—
429C2×C4—91no—
430C2×C4—182no—
431C2×C4—181no—
432C2×C4—361no—
433C2×C4—364no—
434C2×C4—362no—
435C2×C4—362no—
436C2×C4—362no—
437C2×C4—362no—
438C2×C4D4×C3⋊D311yescharacteristic
439C2×C4D4×C3⋊D311yescharacteristic
440C2×C4C23×C3⋊D311yescharacteristic
441C8—22no—
442C8—182no—
443C2×C3—48no—
444C2×C3D3×#12114yes—
445C2×C3C2×#91414yes—
446C2×C3#577714yes—
447D3—68no—
448D3—128no—
449D3—248no—
450C22—22no—
451C22—41no—
452C22—41no—
453C22—92no—
454C22—181no—
455C22—181no—
456C22—182no—
457C22—368no—
458C22—361no—
459C22—361no—
460C22—362no—
461C22—362no—
462C22—362no—
463C22C2×D4×C3⋊D311yescharacteristic
464C4—21no—
465C4—41no—
466C4—42no—
467C4—92no—
468C4—181no—
469C4—181no—
470C4—361no—
471C4#6412312yescomplemented
472C4C2×D4×C3⋊D311yescharacteristic
473C4#41×C3⋊D311yescharacteristic
474C3#8042814yescomplemented
475C2—42no—
476C2—182no—
477C2—362no—
478C2—722no—
479C2C3⋊D3×#12111yescharacteristic
480C2C2×#6412311yescharacteristic
481C2#1059624811yescharacteristic
subgroupG/H
centerC22C2×D4×C3⋊D3
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C23×C3⋊D3
FittingC32×#461C2
socleC22×C32C22×D4
hypercenter#461C3⋊D3
hypocenterC32#3036
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ #461

Complements

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

NH ≅ G/Ntype
1. C2×#64123C2semidirect
2. #10596196C2semidirect
3. C4×D4×C3⋊D3C2semidirect
4. C32×#461C2semidirect
5. #10592864C2semidirect
6. #10592782C2semidirect
7. #10592714C2semidirect
8. #10592542C2semidirect
9. #10592536C2semidirect
10. #10592518C2semidirect
11. #10592502C2semidirect
17. C32×C4⋊Q8C22semidirect
19. #64156C22semidirect
35. #64083C22semidirect
38. C32×C4⋊C8C22semidirect
39. C32×#103C22semidirect
40. #63662C22semidirect
41. #63648C22semidirect
42. #63641C22semidirect
43. #63636C22semidirect
44. C4⋊(C3⋊(C3⋊C8))C22semidirect
48. C3×#461D3semidirect
65. D4×C3⋊D3D4semidirect
106. C3×C4⋊Q8C2×D3semidirect
127. C3×C4⋊C8C2×D3semidirect
128. C3×#103C2×D3semidirect
180. #461C3⋊D3semidirect
247. C32×C4AGL(1,ℤ/8)semidirect
263. C4⋊Q8C2×C3⋊D3semidirect
281. C4⋊C8C2×C3⋊D3semidirect
283. #103C2×C3⋊D3semidirect
395. C3×C4#914semidirect
402. C32#3036semidirect
471. C4#64123semidirect
474. C3#80428semidirect

Maximal subgroups

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

subgroupindex
C2×#641232
#105961962
C4×D4×C3⋊D32
C32×#4612
#105928642
#105927822
#105927142
#105925422
#105925362
#105925182
#105925022
#804283