Finite Group Databasebeta

← #11865829

Subgroups — #11865829

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×#64120C212yesmaximal, complemented
2#10596187C211yesmaximal, characteristic, complemented
3C4×D4×C3⋊D3C211yesmaximal, characteristic, complemented
4C32×#459C211yesmaximal, characteristic, complemented
5#10592852C212yesmaximal, complemented
6#10592771C211yesmaximal, characteristic, complemented
7#10592718C211yesmaximal, characteristic, complemented
8#10592540C211yesmaximal, characteristic, complemented
9#10592536C211yesmaximal, characteristic, complemented
10#10592486C212yesmaximal, complemented
11#10592470C212yesmaximal, complemented
12#80332—34nomaximal
13C2×#3830C2212yes—
14C2×D4×C3⋊D3C2211yescharacteristic
15C22×C4×C3⋊D3—21no—
16C2×C32×D8C2212yes—
17C32×#127C2211yescharacteristic, complemented
18C32×C4×D4C2211yescharacteristic
19#64147—21no—
20#64147—21no—
21#64145C2212yescomplemented
22D4×C3⋊Dic3—21no—
23D4×C3⋊Dic3—21no—
24D4×C3⋊Dic3C2211yescharacteristic
25C2×#3754C2212yes—
26C2×#3753C2212yes—
27C4×#638—21no—
28#64120—28no—
29C2×#3744C2212yes—
30C2×#3743C2212yes—
31#64102C2211yescharacteristic
32C4⋊C4×C3⋊D3C2211yescharacteristic
33#64090—21no—
34C22⋊C4×C3⋊D3—21no—
35C4×C4⋊(C3⋊D3)C2211yescharacteristic
36C42×C3⋊D3C2211yescharacteristic
37#64078C2211yescharacteristic, complemented
38C32×C4⋊C8C2211yescharacteristic, complemented
39C32×#102C2212yescomplemented
40#63659C2212yescomplemented
41#63643C2212yescomplemented
42#63641C2212yescomplemented
43#63637C2212yescomplemented
44C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic, complemented
45C2×#911—38no—
46#5716—34no—
47C4×D3×D4—34no—
48C3×#459D314yescomplemented
49#5153—38no—
50#5072—34no—
51#5019—34no—
52#4841—34no—
53#4837—34no—
54#4787—38no—
55#4771—38no—
56C23×C3⋊D3—21no—
57C2×C32×D4—21no—
58C2×C32×D4—21no—
59C2×C32×D4C2312yes—
60C2×C32×D4C2311yescharacteristic
61C22×C32×C4—21no—
62C2×#638—22no—
63C2×#638—21no—
64C22×C3⋊Dic3—21no—
65C22×C3⋊Dic3—22no—
66#3830—24no—
67#3830—24no—
68D4×C3⋊D3—22no—
69D4×C3⋊D3D414yescomplemented
70C2×C4⋊(C3⋊D3)C2311yescharacteristic
71C2×C4×C3⋊D3—21no—
72C2×C4×C3⋊D3—21no—
73C2×C4×C3⋊D3—21no—
74C2×C4×C3⋊D3—44no—
75C2×C4×C3⋊D3D411yescharacteristic
76C2×C4×C3⋊D3D411yescharacteristic
77C2×C4×C3⋊D3C2311yescharacteristic
78C2×#634C2312yes—
79C32×D8—24no—
80C2×C32×C8C2312yes—
81C32×C4⋊C4C2311yescharacteristic
82C32×C22⋊C4—21no—
83C32×C42C2311yescharacteristic
84#3757—21no—
85#3757—22no—
86#3757—22no—
87#3754—24no—
88#3753—24no—
89#3752—21no—
90#3752—21no—
91C4⋊(C3⋊Dic3)—21no—
92C4⋊(C3⋊Dic3)—21no—
93C4⋊(C3⋊Dic3)C2311yescharacteristic
94#3750—21no—
95C4×C3⋊Dic3D411yescharacteristic
96C4×C3⋊Dic3D411yescharacteristic
97C4×C3⋊Dic3C2311yescharacteristic
98C2×C3⋊(C3⋊C8)C2312yes—
99#3744—24no—
100#3743—24no—
101#3036—91noSylow
102C2×#237—38no—
103C2×D3×D4—34no—
104C22×C4×D3—64no—
105C2×C3×D8C2×D318yes—
106C3×#127C2×D314yescomplemented
107C3×C4×D4C2×D314yes—
108#938—64no—
109#938—64no—
110#936—38no—
111D4×Dic3—34no—
112D4×Dic3—64no—
113D4×Dic3—64no—
114C2×#214—38no—
115C2×#213—38no—
116C4×#67—64no—
117#911—632no—
118C2×#204—38no—
119C2×ΓL(1,𝔽25)—38no—
120#893—34no—
121D3×C4⋊C4—34no—
122#67⋊C4—64no—
123D3×C22⋊C4—64no—
124C4×D12—34no—
125C42×D3—34no—
126#869—34no—
127C3×C4⋊C8C2×D314yescomplemented
128C3×#102C2×D318yescomplemented
129#832—38no—
130#816—38no—
131Dic3⋊C8—38no—
132#810—38no—
133C4⋊(C3⋊C8)—34no—
134C23×C32—21no—
135C23×C32—22no—
136C22×C3⋊D3—21no—
137C22×C3⋊D3—24no—
138C22×C3⋊D3—42no—
139C22×C3⋊D3—42no—
140C22×C3⋊D3C2×D411yescharacteristic
141C32×D4—22no—
142C32×D4—21no—
143C32×D4—22no—
144C32×D4—42no—
145C32×D4—42no—
146C32×D4C2×D412yes—
147C2×C32×C4—21no—
148C2×C32×C4—42no—
149C2×C32×C4C2×D411yescharacteristic
150C2×C32×C4C2×D411yescharacteristic
151C2×C32×C4C2411yescharacteristic
152#638—24no—
153#638—44no—
154C2×C3⋊Dic3—21no—
155C2×C3⋊Dic3—22no—
156C2×C3⋊Dic3—42no—
157C2×C3⋊Dic3—44no—
158C2×C3⋊Dic3C2×D411yescharacteristic
159C2×C3⋊Dic3C2×D411yescharacteristic
160C2×C3⋊Dic3C2×D411yescharacteristic
161C4⋊(C3⋊D3)—21no—
162C4⋊(C3⋊D3)C2×D412yes—
163C4×C3⋊D3—22no—
164C4×C3⋊D3—41no—
165C4×C3⋊D3—42no—
166C4×C3⋊D3—42no—
167C4×C3⋊D3—42no—
168C4×C3⋊D3C2×D412yes—
169C4×C3⋊D3#4112yes—
170#634—22no—
171#634—22no—
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#461—91no—
181#459—91no—
182#459C3⋊D311yescharacteristic, complemented
183#423—91no—
184#417—92no—
185C23×D3—64no—
186C2×C3×D4—24no—
187C2×C3×D4—24no—
188C2×C3×D4C22×D318yes—
189C2×C3×D4C22×D314yes—
190C22×C3×C4—24no—
191C2×#67—64no—
192C2×#67—68no—
193C22×Dic3—64no—
194C22×Dic3—68no—
195#237—616no—
196#237—616no—
197D3×D4—316no—
198D3×D4—68no—
199C2×D12—34no—
200C2×C4×D3—34no—
201C2×C4×D3—34no—
202C2×C4×D3—34no—
203C2×C4×D3—64no—
204C2×C4×D3—64no—
205C2×C4×D3—64no—
206C2×C4×D3—1216no—
207C2×Dic6—38no—
208C3×D8—216no—
209C2×C3×C8C22×D318yes—
210C3×C4⋊C4C22×D314yes—
211C3×C22⋊C4—24no—
212C3×C42C22×D314yes—
213#217—64no—
214#217—68no—
215#217—68no—
216#214—616no—
217#213—616no—
218(C2×D3)⋊C4—64no—
219(C2×D3)⋊C4—64no—
220C4⋊Dic3—34no—
221C4⋊Dic3—64no—
222C4⋊Dic3—64no—
223Dic3⋊C4—64no—
224C4×Dic3—34no—
225C4×Dic3—34no—
226C4×Dic3—34no—
227C2×C3⋊C8—38no—
228#204—616no—
229ΓL(1,𝔽25)—616no—
230C22×C32—22no—
231C22×C32—41no—
232C22×C32—41no—
233C22×C32—42no—
234C22×C32—42no—
235C22×C32—42no—
236C22×C32C22×D411yescharacteristic
237C2×C3⋊D3—21no—
238C2×C3⋊D3—21no—
239C2×C3⋊D3—22no—
240C2×C3⋊D3—48no—
241C2×C3⋊D3—41no—
242C2×C3⋊D3—41no—
243C2×C3⋊D3#12112yes—
244C32×C4—21no—
245C32×C4—41no—
246C32×C4AGL(1,ℤ/8)12yescomplemented
247C32×C4C22×D411yescharacteristic
248C32×C4C2×#4111yescharacteristic
249C3⋊Dic3—21no—
250C3⋊Dic3—21no—
251C3⋊Dic3—42no—
252C3⋊Dic3—41no—
253C3⋊Dic3#12112yes—
254C2×#41—92no—
255C22×D4—91no—
256C23×C4—181no—
257AGL(1,ℤ/8)—188no—
258C2×SD16—92no—
259C2×SD16—92no—
260C2×D8—92no—
261C2×D8C2×C3⋊D312yes—
262C2×M16—92no—
263C4⋊Q8—91no—
264#127C2×C3⋊D311yescharacteristic, complemented
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#103—92no—
284#102—92no—
285#102C2×C3⋊D312yescomplemented
286C23×C3—24no—
287C23×C3—28no—
288C22×D3—34no—
289C22×D3—616no—
290C22×D3—64no—
291C22×D3—128no—
292C22×D3—128no—
293C3×D4—28no—
294C3×D4—24no—
295C3×D4—28no—
296C3×D4—48no—
297C3×D4—48no—
298C3×D4D3×D418yes—
299C2×C3×C4—24no—
300C2×C3×C4—48no—
301C2×C3×C4D3×D414yes—
302C2×C3×C4D3×D414yes—
303C2×C3×C4C23×D314yes—
304#67—616no—
305#67—1216no—
306C2×Dic3—34no—
307C2×Dic3—34no—
308C2×Dic3—34no—
309C2×Dic3—64no—
310C2×Dic3—68no—
311C2×Dic3—1216no—
312C2×Dic3—128no—
313D12—38no—
314D12—64no—
315C4×D3—38no—
316C4×D3—38no—
317C4×D3—68no—
318C4×D3—124no—
319C4×D3—128no—
320C4×D3—128no—
321C4×D3—128no—
322Dic6—68no—
323Dic6—68no—
324C3×C8—28no—
325C3⋊C8—68no—
326C2×C32—42no—
327C2×C32—82no—
328C2×C32C2×#12111yescharacteristic
329C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
330C2×C32#57511yescharacteristic
331C3⋊D3—22no—
332C3⋊D3—42no—
333C24—181no—
334#41—184no—
335#41—184no—
336C2×Q8—92no—
337C2×D4—21no—
338C2×D4—21no—
339C2×D4—94no—
340C2×D4—91no—
341C2×D4—182no—
342C2×D4—181no—
343C2×D4—182no—
344C2×D4C22×C3⋊D312yes—
345C2×D4C22×C3⋊D311yescharacteristic
346C22×C4—21no—
347C22×C4—91no—
348C22×C4—91no—
349C22×C4—91no—
350C22×C4—181no—
351C22×C4—181no—
352C22×C4—181no—
353C22×C4—182no—
354C22×C4—181no—
355C22×C4—364no—
356SD16—184no—
357SD16—184no—
358D8—24no—
359D8—184no—
360M16—184no—
361C2×C8—92no—
362C2×C8C22×C3⋊D312yes—
363C4⋊C4—91no—
364C4⋊C4—181no—
365C4⋊C4—181no—
366C4⋊C4—181no—
367C4⋊C4C22×C3⋊D311yescharacteristic
368C22⋊C4—21no—
369C22⋊C4—181no—
370C22⋊C4—181no—
371C22⋊C4—182no—
372C22⋊C4—182no—
373C22⋊C4—181no—
374C42—91no—
375C42—91no—
376C42—91no—
377C42C22×C3⋊D311yescharacteristic
378C22×C3—28no—
379C22×C3—44no—
380C22×C3—44no—
381C22×C3—48no—
382C22×C3—48no—
383C22×C3—48no—
384C22×C3C2×D3×D414yes—
385C2×D3—38no—
386C2×D3—64no—
387C2×D3—64no—
388C2×D3—68no—
389C2×D3—1232no—
390C2×D3—124no—
391C2×D3—124no—
392C3×C4—24no—
393C3×C4—44no—
394C3×C4#91118yescomplemented
395C3×C4C2×D3×D414yes—
396C3×C4D3×#4114yes—
397Dic3—38no—
398Dic3—64no—
399Dic3—64no—
400Dic3—124no—
401Dic3—128no—
402C32#303611yescharacteristic, complemented, Sylow
403C23—21no—
404C23—22no—
405C23—91no—
406C23—184no—
407C23—181no—
408C23—362no—
409C23—362no—
410Q8—182no—
411Q8—182no—
412D4—22no—
413D4—21no—
414D4—22no—
415D4—42no—
416D4—42no—
417D4—92no—
418D4—184no—
419D4—181no—
420D4—364no—
421D4D4×C3⋊D312yes—
422C2×C4—21no—
423C2×C4—42no—
424C2×C4—91no—
425C2×C4—92no—
426C2×C4—92no—
427C2×C4—91no—
428C2×C4—91no—
429C2×C4—182no—
430C2×C4—181no—
431C2×C4—182no—
432C2×C4—361no—
433C2×C4—362no—
434C2×C4—362no—
435C2×C4—364no—
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×C3—88no—
445C2×C3D3×#12114yes—
446C2×C3C2×#91114yes—
447C2×C3#577314yes—
448D3—68no—
449D3—128no—
450C22—22no—
451C22—41no—
452C22—41no—
453C22—42no—
454C22—42no—
455C22—42no—
456C22—92no—
457C22—181no—
458C22—181no—
459C22—182no—
460C22—368no—
461C22—361no—
462C22—361no—
463C22C2×D4×C3⋊D311yescharacteristic
464C4—21no—
465C4—41no—
466C4—92no—
467C4—181no—
468C4—181no—
469C4—361no—
470C4—362no—
471C4#6412012yescomplemented
472C4C2×D4×C3⋊D311yescharacteristic
473C4#41×C3⋊D311yescharacteristic
474C3#8033214yescomplemented
475C2—42no—
476C2—82no—
477C2—182no—
478C2—362no—
479C2C3⋊D3×#12111yescharacteristic
480C2C2×#6412011yescharacteristic
481C2#1059624411yescharacteristic
subgroupG/H
centerC22C2×D4×C3⋊D3
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C23×C3⋊D3
FittingC32×#459C2
socleC22×C32C22×D4
hypercenter#459C3⋊D3
hypocenterC32#3036
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. C2×#64120C2semidirect
2. #10596187C2semidirect
3. C4×D4×C3⋊D3C2semidirect
4. C32×#459C2semidirect
5. #10592852C2semidirect
6. #10592771C2semidirect
7. #10592718C2semidirect
8. #10592540C2semidirect
9. #10592536C2semidirect
10. #10592486C2semidirect
11. #10592470C2semidirect
17. C32×#127C22semidirect
21. #64145C22semidirect
37. #64078C22semidirect
38. C32×C4⋊C8C22semidirect
39. C32×#102C22semidirect
40. #63659C22semidirect
41. #63643C22semidirect
42. #63641C22semidirect
43. #63637C22semidirect
44. C4⋊(C3⋊(C3⋊C8))C22semidirect
48. C3×#459D3semidirect
69. D4×C3⋊D3D4semidirect
106. C3×#127C2×D3semidirect
127. C3×C4⋊C8C2×D3semidirect
128. C3×#102C2×D3semidirect
182. #459C3⋊D3semidirect
246. C32×C4AGL(1,ℤ/8)semidirect
264. #127C2×C3⋊D3semidirect
281. C4⋊C8C2×C3⋊D3semidirect
285. #102C2×C3⋊D3semidirect
394. C3×C4#911semidirect
402. C32#3036semidirect
471. C4#64120semidirect
474. C3#80332semidirect

Maximal subgroups

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

subgroupindex
C2×#641202
#105961872
C4×D4×C3⋊D32
C32×#4592
#105928522
#105927712
#105927182
#105925402
#105925362
#105924862
#105924702
#803323