Finite Group Databasebeta

← #11865877

Subgroups — #11865877

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×D4×C3⋊Dic3C211yesmaximal, characteristic, complemented
2C2×C3×#932C212yesmaximal, complemented
3#10595032C211yesmaximal, characteristic, complemented
4#10591497C212yesmaximal, complemented
5#10591486C212yesmaximal, complemented
6#10591476C214yesmaximal, complemented
7#10591120C211yesmaximal, characteristic, complemented
8#10591088C212yesmaximal, complemented
9#83931—32nomaximal
10C22×C32×D4C2211yescharacteristic
11C23×C3⋊Dic3—21no—
12C2×C3×#235C2212yes—
13C2×#3757—21no—
14D4×C3⋊Dic3—21no—
15D4×C3⋊Dic3—21no—
16D4×C3⋊Dic3C2212yes—
17D4×C3⋊Dic3C2212yes—
18C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
19C2×C4×C3⋊Dic3C2211yescharacteristic
20C2×C3×#214C2214yes—
21C3×#932—28no—
22C2×C3×#213C2214yes—
23C2×C3×#208C2212yes—
24#63980—21no—
25#63980—21no—
26#63914C2211yescharacteristic, complemented
27C4×#625—21no—
28C4×#625—21no—
29#63873C2211yescharacteristic, complemented
30#63863C2212yescomplemented
31#63572C2212yescomplemented
32#63572C2212yescomplemented
33#63566C2214yescomplemented
34#63563C2214yescomplemented
35C2×C3×AGL(1,ℤ/8)—32no—
36#5832—32no—
37C2×D4×Dic3—32no—
38C2×D4×Dic3—61no—
39C2×#932D312yescomplemented
40#5232—32no—
41#5165—34no—
42#5162—34no—
43#5153—34no—
44#5150—34no—
45#5133—32no—
46#5118—32no—
47C24×C32—21no—
48C2×C32×D4—21no—
49C2×C32×D4—22no—
50C2×C32×D4D414yescomplemented
51C2×C32×D4C2312yes—
52C22×C32×C4C2311yescharacteristic
53C22×C3⋊Dic3—21no—
54C22×C3⋊Dic3—22no—
55C22×C3⋊Dic3—22no—
56C22×C3⋊Dic3—44no—
57C22×C3⋊Dic3D411yescharacteristic
58C22×C3⋊Dic3D411yescharacteristic
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—
67#3757—22no—
68#3757—22no—
69C4⋊(C3⋊Dic3)—21no—
70C4⋊(C3⋊Dic3)C2312yes—
71C4×C3⋊Dic3D411yescharacteristic
72C4×C3⋊Dic3D411yescharacteristic
73C4×C3⋊Dic3C2311yescharacteristic
74C4×C3⋊Dic3C2311yescharacteristic
75C3×#214—28no—
76C3×#213—28no—
77C3×#208—24no—
78C2×C3×C3⋊C8C2314yes—
79#3724—21no—
80#3724—21no—
81(C2×D3)⋊Dic3—22no—
82(C2×D3)⋊Dic3—22no—
83#3036—91noSylow
84C2×C3×#41—32no—
85C22×C3×D4—21no—
86C22×C3×D4C2×D312yes—
87C23×Dic3—62no—
88C23×Dic3—62no—
89C2×#235C2×D312yes—
90C3×AGL(1,ℤ/8)—68no—
91C2×C3×SD16—34no—
92C2×C3×D8—34no—
93C2×C3×M16—32no—
94C2×#217—62no—
95C2×#217—62no—
96#947—32no—
97#944—32no—
98#940—32no—
99#939—62no—
100#939—62no—
101#936—32no—
102D4×Dic3—34no—
103D4×Dic3—34no—
104D4×Dic3—62no—
105D4×Dic3—62no—
106D4×Dic3—62no—
107D4×Dic3—62no—
108D4×Dic3—62no—
109D4×Dic3—62no—
110C2×#214C2×D314yes—
111#932—28no—
112C2×#213C2×D314yes—
113C4×#67—62no—
114C4×#67—62no—
115C2×C4⋊Dic3—32no—
116C2×C4⋊Dic3—61no—
117C2×C4×Dic3—32no—
118C2×C4×Dic3—61no—
119C2×#208C2×D312yes—
120#835—34no—
121#832—34no—
122#821—34no—
123#816—34no—
124Dic3⋊C8—34no—
125Dic3⋊C8—34no—
126C23×C32—24no—
127C23×C32—22no—
128C23×C32—42no—
129C23×C32—42no—
130C23×C32C2×D411yescharacteristic
131C22×C3×D3—22no—
132C32×D4—24no—
133C32×D4—22no—
134C32×D4C2×D414yes—
135C2×C32×C4C2×D411yescharacteristic
136C2×C32×C4C2×D412yes—
137C2×C32×C4#4112yes—
138C2×C32×C4C2411yescharacteristic
139C2×C3⋊Dic3—22no—
140C2×C3⋊Dic3—22no—
141C2×C3⋊Dic3—41no—
142C2×C3⋊Dic3—44no—
143C2×C3⋊Dic3—42no—
144C2×C3⋊Dic3—44no—
145C2×C3⋊Dic3C2×D411yescharacteristic
146C2×C3⋊Dic3C2×D411yescharacteristic
147C2×C3⋊Dic3C2×D411yescharacteristic
148C2×C3⋊Dic3C2×D411yescharacteristic
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)—32no—
160#532—91no—
161C2×C4×D4—91no—
162#463—94no—
163#461—92no—
164#459—92no—
165#423—91no—
166#417—92no—
167C24×C3—22no—
168C24×C3—22no—
169C3×#41—64no—
170C3×#41—64no—
171C2×C3×Q8—32no—
172C2×C3×D4—22no—
173C2×C3×D4—24no—
174C2×C3×D4—22no—
175C2×C3×D4—24no—
176C2×C3×D4—24no—
177C2×C3×D4—22no—
178C2×C3×D4—32no—
179C2×C3×D4—62no—
180C2×C3×D4#6718yescomplemented
181C2×C3×D4C22×D314yes—
182C22×C3×C4—21no—
183C22×C3×C4—62no—
184C22×C3×C4C22×D312yes—
185C2×#67—22no—
186C2×#67—62no—
187C2×#67—62no—
188C22×Dic3—32no—
189C22×Dic3—32no—
190C22×Dic3—61no—
191C22×Dic3—61no—
192C22×Dic3—64no—
193C22×Dic3—64no—
194C22×Dic3—62no—
195C22×Dic3—64no—
196C22×Dic3—64no—
197C22×Dic3—62no—
198C22×Dic3—128no—
199C22×Dic3—128no—
200#235—24no—
201#235—24no—
202C2×D12C22×D312yes—
203C2×C4×D3—22no—
204C2×Dic6C22×D312yes—
205C3×SD16—68no—
206C3×D8—68no—
207C3×M16—64no—
208C2×C3×C8—34no—
209#217—62no—
210#217—62no—
211#217—64no—
212#217—64no—
213#217—64no—
214#217—64no—
215#214—28no—
216#213—28no—
217(C2×D3)⋊C4—62no—
218(C2×D3)⋊C4—62no—
219C4⋊Dic3—34no—
220C4⋊Dic3—62no—
221C4⋊Dic3—62no—
222C4⋊Dic3—62no—
223Dic3⋊C4—62no—
224Dic3⋊C4—62no—
225C4×Dic3—32no—
226C4×Dic3—32no—
227C4×Dic3—32no—
228C4×Dic3—32no—
229C4×Dic3—61no—
230C4×Dic3—61no—
231C4×Dic3—61no—
232C4×Dic3—61no—
233#208—24no—
234C2×C3⋊C8C22×D314yes—
235C22×C32—21no—
236C22×C32—21no—
237C22×C32—24no—
238C22×C32—48no—
239C22×C32—42no—
240C22×C32—42no—
241C22×C32#12112yes—
242C22×C32C22×D411yescharacteristic
243C2×C3×D3—42no—
244C2×C3×D3—42no—
245C2×C3×D3—42no—
246C32×C4#12112yes—
247C32×C4C22×D411yescharacteristic
248C32×C4C2×#4111yescharacteristic
249C3⋊Dic3—21no—
250C3⋊Dic3—21no—
251C3⋊Dic3—21no—
252C3⋊Dic3—42no—
253C3⋊Dic3AGL(1,ℤ/8)12yescomplemented
254C3×Dic3—42no—
255C2×#41—32no—
256C22×D4D3211yescharacteristic
257C23×C4—181no—
258AGL(1,ℤ/8)—68no—
259C2×SD16—34no—
260C2×D8—34no—
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⋊C4—91no—
274C2×C22⋊C4—181no—
275C2×C42—91no—
276C4⋊C8—92no—
277C4⋊C8—92no—
278#103—94no—
279#102—94no—
280C23×C3—24no—
281C23×C3—28no—
282C23×C3—28no—
283C23×C3—24no—
284C23×C3—21no—
285C23×C3—44no—
286C23×C3—44no—
287C23×C3—44no—
288C23×C3—44no—
289C23×C3—62no—
290C23×C3D3×D412yes—
291C22×D3—22no—
292C3×Q8—62no—
293C3×Q8—62no—
294C3×D4—24no—
295C3×D4—28no—
296C3×D4—28no—
297C3×D4—24no—
298C3×D4—24no—
299C3×D4—62no—
300C3×D4—62no—
301C3×D4—124no—
302C3×D4C2×#6718yes—
303C2×C3×C4—21no—
304C2×C3×C4—22no—
305C2×C3×C4—22no—
306C2×C3×C4—21no—
307C2×C3×C4—62no—
308C2×C3×C4—124no—
309C2×C3×C4D3×D412yes—
310C2×C3×C4#23714yes—
311C2×C3×C4C2×#6714yes—
312C2×C3×C4C23×D312yes—
313#67—44no—
314#67—124no—
315#67—124no—
316C2×Dic3—22no—
317C2×Dic3—32no—
318C2×Dic3—32no—
319C2×Dic3—32no—
320C2×Dic3—32no—
321C2×Dic3—61no—
322C2×Dic3—61no—
323C2×Dic3—61no—
324C2×Dic3—61no—
325C2×Dic3—64no—
326C2×Dic3—64no—
327C2×Dic3—64no—
328C2×Dic3—64no—
329C2×Dic3—128no—
330C2×Dic3—122no—
331C2×Dic3—128no—
332C2×Dic3—128no—
333C2×Dic3—128no—
334C2×Dic3—122no—
335C2×Dic3—124no—
336C2×Dic3—124no—
337D12—22no—
338D12—22no—
339C4×D3—44no—
340Dic6—22no—
341Dic6—22no—
342C3×C8—64no—
343C3⋊C8—24no—
344C2×C32—22no—
345C2×C32—44no—
346C2×C32C2×#12111yescharacteristic
347C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
348C2×C32#57511yescharacteristic
349C3×D3—82no—
350C24—21no—
351#41—64no—
352#41—64no—
353C2×Q8—32no—
354C2×D4—22no—
355C2×D4—21no—
356C2×D4—32no—
357C2×D4—62no—
358C2×D4—181no—
359C2×D4—181no—
360C2×D4#62514yescomplemented
361C2×D4C2×D3212yes—
362C22×C4—62no—
363C22×C4—91no—
364C22×C4—91no—
365C22×C4—182no—
366C22×C4—182no—
367C22×C4—181no—
368C22×C4—364no—
369C22×C4C2×D3211yescharacteristic
370SD16—68no—
371D8—68no—
372M16—64no—
373C2×C8—34no—
374C4⋊C4—92no—
375C4⋊C4—181no—
376C4⋊C4—181no—
377C4⋊C4—181no—
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—28no—
391C22×C3—28no—
392C22×C3—21no—
393C22×C3—22no—
394C22×C3—44no—
395C22×C3—416no—
396C22×C3—416no—
397C22×C3—44no—
398C22×C3—44no—
399C22×C3—44no—
400C22×C3—122no—
401C22×C3—122no—
402C22×C3—122no—
403C22×C3#93914yes—
404C22×C3C2×D3×D412yes—
405C2×D3—42no—
406C2×D3—42no—
407C2×D3—42no—
408C3×C4—21no—
409C3×C4—21no—
410C3×C4—22no—
411C3×C4—122no—
412C3×C4#93914yes—
413C3×C4C2×#23712yes—
414C3×C4C22×#6712yes—
415Dic3—34no—
416Dic3—42no—
417Dic3—62no—
418Dic3—62no—
419Dic3—62no—
420Dic3—62no—
421Dic3—62no—
422Dic3—121no—
423Dic3—121no—
424Dic3—124no—
425Dic3—124no—
426C32#303611yescharacteristic, complemented, Sylow
427C23—22no—
428C23—24no—
429C23—42no—
430C23—42no—
431C23—62no—
432C23#381111yescharacteristic
433Q8—62no—
434Q8—62no—
435D4—22no—
436D4—24no—
437D4—62no—
438D4—62no—
439D4—124no—
440D4—362no—
441D4—362no—
442D4C2×#62514yes—
443C2×C4—62no—
444C2×C4—91no—
445C2×C4—91no—
446C2×C4—91no—
447C2×C4—91no—
448C2×C4—124no—
449C2×C4—182no—
450C2×C4—182no—
451C2×C4—364no—
452C2×C4—361no—
453C2×C4—364no—
454C2×C4—362no—
455C2×C4#380512yes—
456C2×C4C2×#62512yes—
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—48no—
466C2×C3—48no—
467C2×C3—242no—
468C2×C3D3×AGL(1,ℤ/8)12yes—
469C2×C3#577312yes—
470C2×C3C2×#93912yes—
471D3—82no—
472C22—21no—
473C22—21no—
474C22—24no—
475C22—48no—
476C22—42no—
477C22—42no—
478C22—122no—
479C22—122no—
480C22—122no—
481C22#6398012yes—
482C22C2×#381111yescharacteristic
483C4—92no—
484C4—122no—
485C4—181no—
486C4—181no—
487C4—181no—
488C4—362no—
489C4#6398012yes—
490C4C2×#380511yescharacteristic
491C4C22×#62511yescharacteristic
492C3—21no—
493C3#8393112yescomplemented
494C2—22no—
495C2—44no—
496C2—242no—
497C2#1059510011yescharacteristic
498C2#1059510111yescharacteristic
499C2C2×#6398011yescharacteristic
subgroupG/H
centerC22C2×#3811
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC22×C32×D4C22
socleC22×C32C22×D4
hypercenterC22×D4D32
hypocenterC32#3036
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
1. C2×D4×C3⋊Dic3C2semidirect
2. C2×C3×#932C2semidirect
3. #10595032C2semidirect
4. #10591497C2semidirect
5. #10591486C2semidirect
6. #10591476C2semidirect
7. #10591120C2semidirect
8. #10591088C2semidirect
26. #63914C22semidirect
29. #63873C22semidirect
30. #63863C22semidirect
31. #63572C22semidirect
32. #63572C22semidirect
33. #63566C22semidirect
34. #63563C22semidirect
39. C2×#932D3semidirect
50. C2×C32×D4D4semidirect
180. C2×C3×D4#67semidirect
253. C3⋊Dic3AGL(1,ℤ/8)semidirect
360. C2×D4#625semidirect
426. C32#3036semidirect
493. C3#83931semidirect

Maximal subgroups

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

subgroupindex
C2×D4×C3⋊Dic32
C2×C3×#9322
#105950322
#105914972
#105914862
#105914762
#105911202
#105910882
#839313