Finite Group Databasebeta

← #11865841

Subgroups — #11865841

Order 1152.

1644 conjugacy classes of subgroups.

The subgroup lattice has 501 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596303C211yesmaximal, characteristic, complemented
2C2×#64158C211yesmaximal, characteristic, complemented
3C2×#64117C211yesmaximal, characteristic, complemented
4C2×#64102C211yesmaximal, characteristic, complemented
5C32×#417C211yesmaximal, characteristic, complemented
6#10592817C211yesmaximal, characteristic, complemented
7#10592665C211yesmaximal, characteristic, complemented
8#10592518C212yesmaximal, complemented
9#10592517C212yesmaximal, complemented
10#10592486C212yesmaximal, complemented
11#10592485C212yesmaximal, complemented
12#78910—34nomaximal
13C2×C32×#41C2211yescharacteristic
14C2×#3828C2211yescharacteristic
15C22×C4⋊(C3⋊D3)C2211yescharacteristic
16C22×C4×C3⋊D3—21no—
17C2×C32×M16C2211yescharacteristic
18C2×C32×C4⋊C4C2211yescharacteristic
19#64158—24no—
20#64156C2211yescharacteristic, complemented
21#64153C2211yescharacteristic, complemented
22C2×#3755C2212yes—
23#64149C2211yescharacteristic, complemented
24#64148—21no—
25#64148—21no—
26#64145C2211yescharacteristic, complemented
27C2×#3753C2212yes—
28C4×#638—21no—
29C4×#638—21no—
30C2×#3752—21no—
31C2×C4×C3⋊Dic3C2211yescharacteristic
32C2×#3748C2211yescharacteristic
33#64117—24no—
34C2×#3745C2212yes—
35C2×#3744C2212yes—
36#64102—21no—
37#64102—21no—
38#64102C2212yes—
39#64102C2212yes—
40C32×#103C2212yescomplemented
41C32×#102C2212yescomplemented
42#63641C2212yescomplemented
43#63641C2212yescomplemented
44#63637C2212yescomplemented
45#63636C2212yescomplemented
46#5832—34no—
47C2×#949—34no—
48C2×#908—34no—
49C2×#893—34no—
50C3×#417D314yescomplemented
51#5118—34no—
52#4966—34no—
53#4819—38no—
54#4818—38no—
55#4787—38no—
56#4786—38no—
57C23×C3⋊D3—21no—
58C32×#41—22no—
59C32×#41—22no—
60C2×C32×Q8C2311yescharacteristic
61C2×C32×D4—21no—
62C2×C32×D4C2311yescharacteristic
63C22×C32×C4—21no—
64C22×C32×C4—21no—
65C22×C32×C4C2311yescharacteristic
66C2×#638—21no—
67C2×#638—21no—
68C2×#638—21no—
69C22×C3⋊Dic3D411yescharacteristic
70C22×C3⋊Dic3D411yescharacteristic
71#3828—22no—
72#3828—22no—
73C2×C4⋊(C3⋊D3)—21no—
74C2×C4⋊(C3⋊D3)—22no—
75C2×C4⋊(C3⋊D3)D414yescomplemented
76C2×C4⋊(C3⋊D3)C2311yescharacteristic
77C2×C4⋊(C3⋊D3)C2312yes—
78C2×C4×C3⋊D3—21no—
79C2×C4×C3⋊D3—22no—
80C2×C4×C3⋊D3—22no—
81C2×C4×C3⋊D3—44no—
82C2×#634C2311yescharacteristic
83C32×M16—22no—
84C2×C32×C8C2312yes—
85C32×C4⋊C4—21no—
86C32×C4⋊C4C2312yes—
87#3757—21no—
88#3757—21no—
89#3755—24no—
90#3753—24no—
91#3752—22no—
92#3752—22no—
93#3752—21no—
94#3752—21no—
95#3750—21no—
96#3750—21no—
97C4×C3⋊Dic3D411yescharacteristic
98C4×C3⋊Dic3D411yescharacteristic
99C4×C3⋊Dic3C2311yescharacteristic
100C4×C3⋊Dic3C2311yescharacteristic
101#3748—22no—
102C2×C3⋊(C3⋊C8)C2312yes—
103#3745—24no—
104#3744—24no—
105#3036—91noSylow
106C2×C3×#41C2×D314yes—
107C2×#235—34no—
108C22×D12—34no—
109C22×C4×D3—64no—
110C2×C3×M16C2×D314yes—
111C2×C3×C4⋊C4C2×D314yes—
112#949—616no—
113#947—34no—
114#944—34no—
115C2×#215—38no—
116#940—34no—
117#939—64no—
118#939—64no—
119#936—34no—
120C2×#213—38no—
121C4×#67—64no—
122C4×#67—64no—
123C2×(C2×D3)⋊C4—64no—
124C2×C4×Dic3—34no—
125C2×#208—34no—
126#908—616no—
127C2×D24—38no—
128C2×#204—38no—
129#893—38no—
130#893—38no—
131#893—64no—
132#893—64no—
133C3×#103C2×D318yescomplemented
134C3×#102C2×D318yescomplemented
135Dic3⋊C8—38no—
136Dic3⋊C8—38no—
137#810—38no—
138#809—38no—
139C23×C32—21no—
140C23×C32C2×D411yescharacteristic
141C22×C3⋊D3—24no—
142C22×C3⋊D3—22no—
143C22×C3⋊D3—21no—
144C22×C3⋊D3—42no—
145C22×C3⋊D3—42no—
146C32×Q8—21no—
147C32×Q8—21no—
148C32×D4—21no—
149C32×D4—21no—
150C32×D4—42no—
151C2×C32×C4—21no—
152C2×C32×C4—22no—
153C2×C32×C4—42no—
154C2×C32×C4—42no—
155C2×C32×C4C2×D411yescharacteristic
156C2×C32×C4C2×D412yes—
157C2×C32×C4#4112yes—
158C2×C32×C4C2411yescharacteristic
159#638—42no—
160#638—42no—
161#638—42no—
162C2×C3⋊Dic3—22no—
163C2×C3⋊Dic3—21no—
164C2×C3⋊Dic3—41no—
165C2×C3⋊Dic3C2×D411yescharacteristic
166C2×C3⋊Dic3C2×D411yescharacteristic
167C2×C3⋊Dic3C2×D411yescharacteristic
168C2×C3⋊Dic3C2×D411yescharacteristic
169C4⋊(C3⋊D3)—24no—
170C4⋊(C3⋊D3)—21no—
171C4⋊(C3⋊D3)—22no—
172C4⋊(C3⋊D3)—21no—
173C4⋊(C3⋊D3)C2×D414yes—
174C4×C3⋊D3—44no—
175C4×C3⋊D3—42no—
176C4×C3⋊D3—44no—
177#634—21no—
178#634—21no—
179C32×C8—22no—
180C3⋊(C3⋊C8)—22no—
181C2×AGL(1,ℤ/8)—91no—
182C2×AGL(1,ℤ/8)—91no—
183#532—91no—
184C2×C4×D4—91no—
185#463—92no—
186#463—92no—
187#461—92no—
188#459—92no—
189#423—91no—
190#417—91no—
191#417C3⋊D311yescharacteristic, complemented
192C23×D3—64no—
193C3×#41—28no—
194C3×#41—28no—
195C2×C3×Q8C22×D314yes—
196C2×C3×D4—24no—
197C2×C3×D4C22×D314yes—
198C22×C3×C4—24no—
199C22×C3×C4—24no—
200C22×C3×C4C22×D314yes—
201C2×#67—64no—
202C2×#67—64no—
203C2×#67—64no—
204C22×Dic3—34no—
205C22×Dic3—34no—
206#235—68no—
207#235—68no—
208C2×D12—316no—
209C2×D12—38no—
210C2×D12—34no—
211C2×D12—68no—
212C2×D12—64no—
213C2×C4×D3—68no—
214C2×C4×D3—68no—
215C2×C4×D3—64no—
216C2×C4×D3—1216no—
217C2×Dic6—34no—
218C3×M16—28no—
219C2×C3×C8C22×D318yes—
220C3×C4⋊C4—24no—
221C3×C4⋊C4C22×D318yes—
222#217—64no—
223#217—64no—
224#215—616no—
225#213—616no—
226(C2×D3)⋊C4—68no—
227(C2×D3)⋊C4—68no—
228(C2×D3)⋊C4—64no—
229(C2×D3)⋊C4—64no—
230Dic3⋊C4—64no—
231Dic3⋊C4—64no—
232C4×Dic3—34no—
233C4×Dic3—34no—
234C4×Dic3—34no—
235C4×Dic3—34no—
236#208—68no—
237C2×C3⋊C8—38no—
238D24—616no—
239#204—616no—
240C22×C32—21no—
241C22×C32—21no—
242C22×C32—41no—
243C22×C32—41no—
244C22×C32—41no—
245C22×C32#12112yes—
246C22×C32C22×D411yescharacteristic
247C2×C3⋊D3—24no—
248C2×C3⋊D3—48no—
249C2×C3⋊D3—42no—
250C2×C3⋊D3—42no—
251C2×C3⋊D3—41no—
252C2×C3⋊D3—41no—
253C2×C3⋊D3—41no—
254C32×C4—41no—
255C32×C4—42no—
256C32×C4#12112yes—
257C32×C4C22×D411yescharacteristic
258C32×C4C2×#4111yescharacteristic
259C3⋊Dic3—21no—
260C3⋊Dic3—21no—
261C3⋊Dic3—21no—
262C3⋊Dic3—41no—
263C3⋊Dic3AGL(1,ℤ/8)12yescomplemented
264C2×#41—91no—
265C2×#41C2×C3⋊D311yescharacteristic
266C22×D4—91no—
267C23×C4—181no—
268AGL(1,ℤ/8)—184no—
269AGL(1,ℤ/8)—184no—
270C2×SD16—92no—
271C2×SD16—92no—
272C2×D8—92no—
273C2×D8—92no—
274C2×M16—91no—
275C2×M16C2×C3⋊D311yescharacteristic
276C4⋊Q8—91no—
277#127—91no—
278#124—91no—
279#124—91no—
280#121—181no—
281#121—181no—
282C4×D4—92no—
283C4×D4—92no—
284C4×D4—181no—
285C4×D4—181no—
286C4×D4—181no—
287C4×D4—181no—
288C2×C4⋊C4C2×C3⋊D311yescharacteristic
289C2×C22⋊C4—181no—
290C2×C42—91no—
291C4⋊C8—92no—
292C4⋊C8—92no—
293#103—92no—
294#103C2×C3⋊D312yescomplemented
295#102—92no—
296#102C2×C3⋊D312yescomplemented
297C23×C3—24no—
298C23×C3D3×D414yes—
299C22×D3—616no—
300C22×D3—68no—
301C22×D3—64no—
302C22×D3—128no—
303C22×D3—128no—
304C3×Q8—24no—
305C3×Q8—24no—
306C3×D4—24no—
307C3×D4—24no—
308C3×D4—48no—
309C2×C3×C4—24no—
310C2×C3×C4—28no—
311C2×C3×C4—48no—
312C2×C3×C4—48no—
313C2×C3×C4#23518yes—
314C2×C3×C4D3×D414yes—
315C2×C3×C4D3×D418yes—
316C2×C3×C4C23×D314yes—
317#67—128no—
318#67—128no—
319#67—128no—
320C2×Dic3—34no—
321C2×Dic3—34no—
322C2×Dic3—34no—
323C2×Dic3—34no—
324C2×Dic3—68no—
325C2×Dic3—64no—
326C2×Dic3—124no—
327D12—316no—
328D12—616no—
329D12—68no—
330D12—64no—
331D12—64no—
332C4×D3—1216no—
333C4×D3—1216no—
334C4×D3—128no—
335Dic6—64no—
336Dic6—64no—
337C3×C8—28no—
338C3⋊C8—68no—
339C2×C32—22no—
340C2×C32—81no—
341C2×C32C2×#12111yescharacteristic
342C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
343C2×C32#57511yescharacteristic
344C3⋊D3—44no—
345C3⋊D3—81no—
346C24—181no—
347#41—22no—
348#41—22no—
349#41—182no—
350#41—182no—
351C2×Q8—91no—
352C2×Q8C22×C3⋊D311yescharacteristic
353C2×D4—21no—
354C2×D4—92no—
355C2×D4—91no—
356C2×D4—94no—
357C2×D4—181no—
358C2×D4—181no—
359C2×D4—181no—
360C2×D4—182no—
361C2×D4—181no—
362C2×D4C22×C3⋊D311yescharacteristic
363C22×C4—21no—
364C22×C4—21no—
365C22×C4—91no—
366C22×C4—91no—
367C22×C4—182no—
368C22×C4—182no—
369C22×C4—181no—
370C22×C4—364no—
371C22×C4C22×C3⋊D311yescharacteristic
372SD16—184no—
373SD16—184no—
374D8—184no—
375D8—184no—
376M16—22no—
377M16—182no—
378C2×C8—92no—
379C2×C8C22×C3⋊D312yes—
380C4⋊C4—21no—
381C4⋊C4—181no—
382C4⋊C4—181no—
383C4⋊C4C22×C3⋊D312yes—
384C22⋊C4—182no—
385C22⋊C4—182no—
386C22⋊C4—181no—
387C22⋊C4—181no—
388C22⋊C4—181no—
389C22⋊C4—181no—
390C42—91no—
391C42—91no—
392C42—91no—
393C42—91no—
394C22×C3—24no—
395C22×C3—24no—
396C22×C3—44no—
397C22×C3—44no—
398C22×C3—44no—
399C22×C3#88418yes—
400C22×C3C2×D3×D414yes—
401C2×D3—616no—
402C2×D3—1232no—
403C2×D3—128no—
404C2×D3—128no—
405C2×D3—124no—
406C2×D3—124no—
407C2×D3—124no—
408C3×C4—44no—
409C3×C4—48no—
410C3×C4#88418yes—
411C3×C4C2×#23514yes—
412C3×C4C2×D3×D414yes—
413Dic3—38no—
414Dic3—64no—
415Dic3—64no—
416Dic3—64no—
417Dic3—124no—
418C32#303611yescharacteristic, complemented, Sylow
419C23—21no—
420C23—184no—
421C23—182no—
422C23—181no—
423C23—362no—
424C23—362no—
425C23D4×C3⋊D311yescharacteristic
426Q8—21no—
427Q8—21no—
428Q8—181no—
429Q8—181no—
430D4—21no—
431D4—21no—
432D4—42no—
433D4—94no—
434D4—184no—
435D4—182no—
436D4—181no—
437D4—181no—
438D4—362no—
439D4—362no—
440D4—362no—
441C2×C4—22no—
442C2×C4—21no—
443C2×C4—42no—
444C2×C4—42no—
445C2×C4—91no—
446C2×C4—91no—
447C2×C4—91no—
448C2×C4—91no—
449C2×C4—182no—
450C2×C4—181no—
451C2×C4—364no—
452C2×C4—364no—
453C2×C4—361no—
454C2×C4—362no—
455C2×C4#382812yes—
456C2×C4D4×C3⋊D311yescharacteristic
457C2×C4D4×C3⋊D312yes—
458C2×C4C23×C3⋊D311yescharacteristic
459C8—22no—
460C8—182no—
461C2×C3—28no—
462C2×C3—84no—
463C2×C3C2×#88414yes—
464C2×C3D3×AGL(1,ℤ/8)14yes—
465C2×C3#577714yes—
466D3—1216no—
467D3—244no—
468C22—21no—
469C22—21no—
470C22—41no—
471C22—41no—
472C22—41no—
473C22—184no—
474C22—368no—
475C22—362no—
476C22—362no—
477C22—361no—
478C22—361no—
479C22—361no—
480C22#6409312yes—
481C22C2×D4×C3⋊D311yescharacteristic
482C4—41no—
483C4—42no—
484C4—92no—
485C4—181no—
486C4—181no—
487C4—181no—
488C4—361no—
489C4#6409312yes—
490C4C2×#382811yescharacteristic
491C4C2×D4×C3⋊D311yescharacteristic
492C3#7891014yescomplemented
493C2—22no—
494C2—81no—
495C2—364no—
496C2—721no—
497C2C2×#6409311yescharacteristic
498C2C3⋊D3×AGL(1,ℤ/8)11yescharacteristic
499C2#1059624811yescharacteristic
subgroupG/H
centerC22C2×D4×C3⋊D3
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C23×C3⋊D3
FittingC32×#417C2
socleC22×C32C22×D4
hypercenter#417C3⋊D3
hypocenterC32#3036
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ #417

Complements

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

NH ≅ G/Ntype
1. #10596303C2semidirect
2. C2×#64158C2semidirect
3. C2×#64117C2semidirect
4. C2×#64102C2semidirect
5. C32×#417C2semidirect
6. #10592817C2semidirect
7. #10592665C2semidirect
8. #10592518C2semidirect
9. #10592517C2semidirect
10. #10592486C2semidirect
11. #10592485C2semidirect
20. #64156C22semidirect
21. #64153C22semidirect
23. #64149C22semidirect
26. #64145C22semidirect
40. C32×#103C22semidirect
41. C32×#102C22semidirect
42. #63641C22semidirect
43. #63641C22semidirect
44. #63637C22semidirect
45. #63636C22semidirect
50. C3×#417D3semidirect
75. C2×C4⋊(C3⋊D3)D4semidirect
133. C3×#103C2×D3semidirect
134. C3×#102C2×D3semidirect
191. #417C3⋊D3semidirect
263. C3⋊Dic3AGL(1,ℤ/8)semidirect
294. #103C2×C3⋊D3semidirect
296. #102C2×C3⋊D3semidirect
418. C32#3036semidirect
492. C3#78910semidirect

Maximal subgroups

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

subgroupindex
#105963032
C2×#641582
C2×#641172
C2×#641022
C32×#4172
#105928172
#105926652
#105925182
#105925172
#105924862
#105924852
#789103