Finite Group Databasebeta

← #11865882

Subgroups — #11865882

Order 1152.

1309 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
1C2×#64102C211yesmaximal, characteristic, complemented
2#10595032C211yesmaximal, characteristic, complemented
3C2×#63825C212yesmaximal, complemented
4C3×#4966C212yesmaximal, complemented
5#10591120C211yesmaximal, characteristic, complemented
6#10590565C212yesmaximal, complemented
7#10590551C212yesmaximal, complemented
8#10590540C214yesmaximal, complemented
9#78910—32nomaximal
10C22×C4⋊(C3⋊D3)C2211yescharacteristic
11C22×C4×C3⋊D3—21no—
12C2×C3×#235C2212yes—
13C2×C32×C4⋊C4C2211yescharacteristic
14C2×#3752—21no—
15C2×C4×C3⋊Dic3C2211yescharacteristic
16#64102—21no—
17#64102—21no—
18#64102C2212yes—
19#64102C2212yes—
20C2×C3×#208C2212yes—
21#63980—21no—
22#63980—21no—
23#63914C2211yescharacteristic, complemented
24C4×#625—21no—
25C4×#625—21no—
26#63873C2211yescharacteristic, complemented
27#63863C2212yescomplemented
28C2×#3717C2214yes—
29#63825—28no—
30C2×#3714C2214yes—
31C3×#810C2214yescomplemented
32C3×#809C2214yescomplemented
33#63572C2212yescomplemented
34#63572C2212yescomplemented
35#5832—32no—
36C2×#949—32no—
37C2×#908—32no—
38C2×#893—32no—
39C2×#893—61no—
40C3×#417—32no—
41#5118—32no—
42#4966D312yescomplemented
43#4819—34no—
44#4818—34no—
45#4787—34no—
46#4786—34no—
47C23×C3⋊D3—21no—
48C22×C32×C4—21no—
49C22×C32×C4C2311yescharacteristic
50C22×C3⋊Dic3D411yescharacteristic
51C22×C3⋊Dic3D411yescharacteristic
52C2×C4⋊(C3⋊D3)—21no—
53C2×C4⋊(C3⋊D3)—22no—
54C2×C4⋊(C3⋊D3)D414yescomplemented
55C2×C4⋊(C3⋊D3)C2312yes—
56C2×C4×C3⋊D3—22no—
57C2×C4×C3⋊D3—22no—
58C2×C4×C3⋊D3—44no—
59C2×C3×#67—22no—
60C3×#235—24no—
61C3×#235—24no—
62C2×C3×D12C2312yes—
63C2×C3×C4×D3—22no—
64C2×C3×Dic6C2312yes—
65C2×#625—21no—
66C2×#625—21no—
67C32×C4⋊C4—21no—
68C32×C4⋊C4C2312yes—
69#3752—22no—
70#3752—22no—
71C4×C3⋊Dic3D411yescharacteristic
72C4×C3⋊Dic3D411yescharacteristic
73C4×C3⋊Dic3C2311yescharacteristic
74C4×C3⋊Dic3C2311yescharacteristic
75C3×#208—24no—
76C2×C3×C3⋊C8C2314yes—
77#3724—21no—
78#3724—21no—
79(C2×D3)⋊Dic3—22no—
80(C2×D3)⋊Dic3—22no—
81#3717—28no—
82#3714—28no—
83#3036—91noSylow
84C2×C3×#41—32no—
85C2×#235C2×D312yes—
86C22×D12—32no—
87C22×D12—61no—
88C22×C4×D3—62no—
89C22×C4×D3—62no—
90C2×C3×M16—32no—
91C2×C3×C4⋊C4—21no—
92C2×C3×C4⋊C4C2×D312yes—
93#949—68no—
94#947—32no—
95#944—32no—
96C2×#215—34no—
97#940—32no—
98#939—62no—
99#939—62no—
100#936—32no—
101C2×#213—34no—
102C4×#67—62no—
103C4×#67—62no—
104C2×(C2×D3)⋊C4—62no—
105C2×(C2×D3)⋊C4—62no—
106C2×C4×Dic3—32no—
107C2×C4×Dic3—61no—
108C2×#208C2×D312yes—
109#908—68no—
110C2×D24—34no—
111C2×#204—34no—
112#893—34no—
113#893—34no—
114#893—62no—
115#893—62no—
116#893—62no—
117#893—62no—
118#893—62no—
119#893—62no—
120C3×#103—34no—
121C3×#102—34no—
122Dic3⋊C8—34no—
123Dic3⋊C8—34no—
124#810C2×D314yescomplemented
125#809C2×D314yescomplemented
126C23×C32C2×D411yescharacteristic
127C22×C3⋊D3—24no—
128C22×C3⋊D3—22no—
129C22×C3⋊D3—42no—
130C22×C3⋊D3—42no—
131C22×C3×D3—22no—
132C2×C32×C4—22no—
133C2×C32×C4—42no—
134C2×C32×C4C2×D411yescharacteristic
135C2×C32×C4C2×D412yes—
136C2×C32×C4#4112yes—
137C2×C32×C4C2411yescharacteristic
138C2×C3⋊Dic3—22no—
139C2×C3⋊Dic3—41no—
140C2×C3⋊Dic3C2×D411yescharacteristic
141C2×C3⋊Dic3C2×D411yescharacteristic
142C2×C3⋊Dic3C2×D411yescharacteristic
143C2×C3⋊Dic3C2×D411yescharacteristic
144C4⋊(C3⋊D3)—24no—
145C4⋊(C3⋊D3)—22no—
146C4⋊(C3⋊D3)C2×D414yes—
147C4×C3⋊D3—44no—
148C4×C3⋊D3—44no—
149C3×#67—44no—
150C2×C3×Dic3—22no—
151C3×D12—22no—
152C3×D12—22no—
153C3×C4×D3—44no—
154C3×Dic6—22no—
155C3×Dic6—22no—
156#625—42no—
157#625—42no—
158C3×C3⋊C8—24no—
159C2×AGL(1,ℤ/8)—92no—
160#532—91no—
161C2×C4×D4—91no—
162#463—94no—
163#461—92no—
164#459—92no—
165#423—91no—
166#417—32no—
167C23×D3—62no—
168C23×D3—62no—
169C3×#41—64no—
170C3×#41—64no—
171C2×C3×Q8—32no—
172C2×C3×D4—32no—
173C2×C3×D4—62no—
174C22×C3×C4—22no—
175C22×C3×C4—22no—
176C22×C3×C4—21no—
177C22×C3×C4—62no—
178C22×C3×C4C22×D312yes—
179C2×#67—22no—
180C2×#67—62no—
181C2×#67—62no—
182C22×Dic3—32no—
183C22×Dic3—32no—
184C22×Dic3—61no—
185C22×Dic3—61no—
186#235—24no—
187#235—24no—
188C2×D12—38no—
189C2×D12—34no—
190C2×D12—62no—
191C2×D12—64no—
192C2×D12—62no—
193C2×D12—64no—
194C2×D12—64no—
195C2×D12—62no—
196C2×D12C22×D312yes—
197C2×C4×D3—22no—
198C2×C4×D3—64no—
199C2×C4×D3—64no—
200C2×C4×D3—64no—
201C2×C4×D3—64no—
202C2×C4×D3—128no—
203C2×C4×D3—128no—
204C2×Dic6C22×D312yes—
205C3×M16—64no—
206C2×C3×C8—34no—
207C3×C4⋊C4—22no—
208C3×C4⋊C4—22no—
209C3×C4⋊C4—22no—
210C3×C4⋊C4C22×D314yes—
211#217—62no—
212#217—62no—
213#215—68no—
214#213—68no—
215(C2×D3)⋊C4—64no—
216(C2×D3)⋊C4—64no—
217(C2×D3)⋊C4—62no—
218(C2×D3)⋊C4—62no—
219(C2×D3)⋊C4—64no—
220(C2×D3)⋊C4—64no—
221Dic3⋊C4—62no—
222Dic3⋊C4—62no—
223C4×Dic3—32no—
224C4×Dic3—32no—
225C4×Dic3—32no—
226C4×Dic3—32no—
227C4×Dic3—61no—
228C4×Dic3—61no—
229C4×Dic3—61no—
230C4×Dic3—61no—
231#208—24no—
232C2×C3⋊C8C22×D314yes—
233D24—68no—
234#204—68no—
235C22×C32—21no—
236C22×C32—21no—
237C22×C32#12112yes—
238C22×C32C22×D411yescharacteristic
239C2×C3⋊D3—24no—
240C2×C3⋊D3—48no—
241C2×C3⋊D3—42no—
242C2×C3⋊D3—42no—
243C2×C3×D3—42no—
244C2×C3×D3—42no—
245C2×C3×D3—42no—
246C32×C4—42no—
247C32×C4#12112yes—
248C32×C4C22×D411yescharacteristic
249C32×C4C2×#4111yescharacteristic
250C3⋊Dic3—21no—
251C3⋊Dic3—21no—
252C3⋊Dic3—21no—
253C3⋊Dic3AGL(1,ℤ/8)12yescomplemented
254C3×Dic3—42no—
255C2×#41—32no—
256C22×D4—91no—
257C23×C4—181no—
258AGL(1,ℤ/8)—188no—
259C2×SD16—94no—
260C2×D8—94no—
261C2×M16—32no—
262C4⋊Q8—91no—
263#127—91no—
264#124—92no—
265#121—181no—
266#121—181no—
267C4×D4—92no—
268C4×D4—92no—
269C4×D4—181no—
270C4×D4—181no—
271C4×D4—181no—
272C4×D4—181no—
273C2×C4⋊C4D3211yescharacteristic
274C2×C22⋊C4—181no—
275C2×C42—91no—
276C4⋊C8—92no—
277C4⋊C8—92no—
278#103—34no—
279#102—34no—
280C23×C3—21no—
281C23×C3—62no—
282C23×C3D3×D412yes—
283C22×D3—22no—
284C22×D3—64no—
285C22×D3—68no—
286C22×D3—68no—
287C22×D3—64no—
288C22×D3—124no—
289C22×D3—124no—
290C22×D3—124no—
291C22×D3—124no—
292C3×Q8—62no—
293C3×Q8—62no—
294C3×D4—62no—
295C3×D4—62no—
296C3×D4—124no—
297C2×C3×C4—24no—
298C2×C3×C4—24no—
299C2×C3×C4—21no—
300C2×C3×C4—22no—
301C2×C3×C4—22no—
302C2×C3×C4—21no—
303C2×C3×C4—44no—
304C2×C3×C4—44no—
305C2×C3×C4—62no—
306C2×C3×C4—124no—
307C2×C3×C4#23514yes—
308C2×C3×C4D3×D414yes—
309C2×C3×C4D3×D412yes—
310C2×C3×C4C23×D312yes—
311#67—44no—
312#67—124no—
313#67—124no—
314C2×Dic3—22no—
315C2×Dic3—32no—
316C2×Dic3—32no—
317C2×Dic3—32no—
318C2×Dic3—32no—
319C2×Dic3—61no—
320C2×Dic3—61no—
321C2×Dic3—61no—
322C2×Dic3—61no—
323C2×Dic3—64no—
324C2×Dic3—64no—
325C2×Dic3—122no—
326C2×Dic3—122no—
327D12—22no—
328D12—22no—
329D12—38no—
330D12—64no—
331D12—64no—
332D12—68no—
333D12—68no—
334D12—64no—
335C4×D3—44no—
336C4×D3—128no—
337C4×D3—128no—
338C4×D3—128no—
339C4×D3—128no—
340Dic6—22no—
341Dic6—22no—
342C3×C8—64no—
343C3⋊C8—24no—
344C2×C32—22no—
345C2×C32C2×#12111yescharacteristic
346C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
347C2×C32#57511yescharacteristic
348C3⋊D3—44no—
349C3×D3—82no—
350C24—181no—
351#41—64no—
352#41—64no—
353C2×Q8—32no—
354C2×D4—32no—
355C2×D4—62no—
356C2×D4—92no—
357C2×D4—94no—
358C2×D4—181no—
359C2×D4—181no—
360C2×D4—182no—
361C2×D4—181no—
362C22×C4—21no—
363C22×C4—62no—
364C22×C4—91no—
365C22×C4—91no—
366C22×C4—182no—
367C22×C4—182no—
368C22×C4—364no—
369C22×C4C2×D3211yescharacteristic
370SD16—188no—
371D8—188no—
372M16—64no—
373C2×C8—34no—
374C4⋊C4—21no—
375C4⋊C4—181no—
376C4⋊C4—181no—
377C4⋊C4C2×D3212yes—
378C22⋊C4—182no—
379C22⋊C4—182no—
380C22⋊C4—182no—
381C22⋊C4—182no—
382C42—91no—
383C42—91no—
384C42—91no—
385C42—91no—
386C22×C3—22no—
387C22×C3—22no—
388C22×C3—22no—
389C22×C3—22no—
390C22×C3—21no—
391C22×C3—22no—
392C22×C3—122no—
393C22×C3—122no—
394C22×C3—122no—
395C22×C3#88414yes—
396C22×C3C2×D3×D412yes—
397C2×D3—42no—
398C2×D3—42no—
399C2×D3—42no—
400C2×D3—68no—
401C2×D3—68no—
402C2×D3—124no—
403C2×D3—1216no—
404C2×D3—1216no—
405C2×D3—124no—
406C2×D3—124no—
407C2×D3—124no—
408C3×C4—21no—
409C3×C4—21no—
410C3×C4—22no—
411C3×C4—44no—
412C3×C4—44no—
413C3×C4—122no—
414C3×C4#88414yes—
415C3×C4C2×#23512yes—
416C3×C4C2×D3×D412yes—
417Dic3—34no—
418Dic3—42no—
419Dic3—62no—
420Dic3—62no—
421Dic3—62no—
422Dic3—62no—
423Dic3—62no—
424Dic3—121no—
425Dic3—121no—
426C32#303611yescharacteristic, complemented, Sylow
427C23—62no—
428C23—182no—
429C23—184no—
430C23—362no—
431C23—362no—
432C23#381111yescharacteristic
433Q8—62no—
434Q8—62no—
435D4—62no—
436D4—62no—
437D4—94no—
438D4—124no—
439D4—182no—
440D4—184no—
441D4—362no—
442D4—362no—
443C2×C4—22no—
444C2×C4—42no—
445C2×C4—62no—
446C2×C4—91no—
447C2×C4—91no—
448C2×C4—91no—
449C2×C4—91no—
450C2×C4—124no—
451C2×C4—182no—
452C2×C4—364no—
453C2×C4—364no—
454C2×C4—361no—
455C2×C4#379812yes—
456C2×C4#380212yes—
457C2×C4#381111yescharacteristic
458C2×C4C22×D3211yescharacteristic
459C8—64no—
460C2×C3—24no—
461C2×C3—24no—
462C2×C3—21no—
463C2×C3—21no—
464C2×C3—21no—
465C2×C3—242no—
466C2×C3C2×#88412yes—
467C2×C3D3×AGL(1,ℤ/8)12yes—
468C2×C3#577712yes—
469D3—82no—
470D3—128no—
471D3—128no—
472C22—21no—
473C22—21no—
474C22—122no—
475C22—122no—
476C22—122no—
477C22—184no—
478C22—368no—
479C22—362no—
480C22—362no—
481C22#6391212yes—
482C22C2×#381111yescharacteristic
483C4—42no—
484C4—92no—
485C4—122no—
486C4—181no—
487C4—181no—
488C4—181no—
489C4#6391212yes—
490C4C2×#379811yescharacteristic
491C4C2×#380211yescharacteristic
492C3—21no—
493C3#7891012yescomplemented
494C2—22no—
495C2—242no—
496C2—364no—
497C2C2×#6391211yescharacteristic
498C2#1059510011yescharacteristic
499C2#1059532311yescharacteristic
subgroupG/H
centerC22C2×#3811
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×C4⋊C4C22
socleC22×C32C22×D4
hypercenterC2×C4⋊C4D32
hypocenterC32#3036
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×#64102C2semidirect
2. #10595032C2semidirect
3. C2×#63825C2semidirect
4. C3×#4966C2semidirect
5. #10591120C2semidirect
6. #10590565C2semidirect
7. #10590551C2semidirect
8. #10590540C2semidirect
23. #63914C22semidirect
26. #63873C22semidirect
27. #63863C22semidirect
31. C3×#810C22semidirect
32. C3×#809C22semidirect
33. #63572C22semidirect
34. #63572C22semidirect
42. #4966D3semidirect
54. C2×C4⋊(C3⋊D3)D4semidirect
124. #810C2×D3semidirect
125. #809C2×D3semidirect
253. C3⋊Dic3AGL(1,ℤ/8)semidirect
426. C32#3036semidirect
493. C3#78910semidirect

Maximal subgroups

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

subgroupindex
C2×#641022
#105950322
C2×#638252
C3×#49662
#105911202
#105905652
#105905512
#105905402
#789103