Finite Group Databasebeta

← #11865858

Subgroups — #11865858

Order 1152.

1251 conjugacy classes of subgroups; only the 176 normal subgroups are shown.

normal subgroups only

This group has 1251 conjugacy classes of subgroups — too many to draw. Only its 176 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596196C211yesmaximal, characteristic, complemented
2C2×#63941C212yesmaximal, complemented
3C4×#3802C211yesmaximal, characteristic, complemented
4C3×#5083C212yesmaximal, complemented
5#10591570C214yesmaximal, complemented
6#10591554C212yesmaximal, complemented
7#10590349C212yesmaximal, complemented
8#10590340C211yesmaximal, characteristic, complemented
9#80428—32nomaximal
10C2×#3832C2212yes—
11C2×#3802C2211yescharacteristic
12C2×C4×D32—21no—
13C32×C4⋊Q8C2211yescharacteristic, complemented
14#64156C2212yescomplemented
15#64104—21no—
16#64104—21no—
17#64102—21no—
18#64102—21no—
19#64083C2211yescharacteristic, complemented
20C42×C3⋊D3C2211yescharacteristic
21C2×C3×#215C2214yes—
22C3×C4×D12C2212yes—
23#63941—28no—
24#63921—21no—
25#63902—21no—
26C4×#625—21no—
27#63900C2211yescharacteristic
28#63898C2212yes—
29C2×#3714C2214yes—
30C2×#3712C2212yes—
31C3×#835C2214yescomplemented
32C3×C4⋊(C3⋊C8)C2212yescomplemented
33#63572C2212yescomplemented
34#63564C2214yescomplemented
35C2×#914—34no—
36#5725—32no—
37#5725—61no—
38C4×D3×D4—32no—
39C3×#461—32no—
40#5165—34no—
41#5083D312yescomplemented
42#5015—32no—
43#4843—32no—
44#4837—32no—
45#4819—34no—
46#4803—34no—
47C22×D32—21no—
48C2×C32×Q8C2312yes—
49#3832—24no—
50#3832—24no—
51C2×C4⋊(C3⋊D3)—22no—
52C2×C4⋊(C3⋊D3)—21no—
53C2×C4⋊(C3⋊D3)—21no—
54C2×C4⋊(C3⋊D3)C2312yes—
55C2×C4×C3⋊D3—22no—
56C2×C4×C3⋊D3D411yescharacteristic
57C2×C4×C3⋊D3D411yescharacteristic
58C2×C4×C3⋊D3C2311yescharacteristic
59C2×C3×D12C2312yes—
60C2×C3×C4×D3—22no—
61C2×#625—21no—
62C2×#624—21no—
63C2×D3×Dic3—22no—
64#3802—22no—
65#3802D414yescomplemented
66C4×D32—44no—
67C32×C4⋊C4—21no—
68C32×C4⋊C4—21no—
69C32×C42C2311yescharacteristic
70#3752—22no—
71#3752—22no—
72C4×C3⋊Dic3D411yescharacteristic
73C4×C3⋊Dic3D411yescharacteristic
74C4×C3⋊Dic3C2311yescharacteristic
75C3×#215—28no—
76C3×(C2×D3)⋊C4—22no—
77C3×C4⋊Dic3C2312yes—
78C2×C3×C3⋊C8C2314yes—
79#3724—21no—
80(C2×D3)⋊Dic3—22no—
81#3714—28no—
82#3712—24no—
83#3036—91noSylow
84C2×#239—34no—
85C2×#239—62no—
86C2×D3×D4—32no—
87C22×C4×D3—62no—
88C2×C3×SD16—34no—
89C3×C4⋊Q8—21no—
90C3×C4⋊Q8C2×D312yescomplemented
91C3×C4×D4—32no—
92#947—34no—
93#947—62no—
94C2×#215C2×D314yes—
95D4×Dic3—32no—
96C2×#213—34no—
97C4×#67—62no—
98#914—616no—
99C2×D24—34no—
100C2×ΓL(1,𝔽25)—34no—
101#895—62no—
102#895—62no—
103#895—62no—
104#895—62no—
105#893—32no—
106#893—62no—
107#893—62no—
108#893—62no—
109#893—62no—
110D3×C4⋊C4—32no—
111#67⋊C4—62no—
112D3×C22⋊C4—62no—
113#874—32no—
114#874—61no—
115C4×D12C2×D312yes—
116C42×D3—32no—
117C42×D3—61no—
118C3×C4⋊C8—32no—
119C3×#103—34no—
120#835C2×D314yescomplemented
121#821—34no—
122Dic3⋊C8—34no—
123#809—34no—
124C4⋊(C3⋊C8)C2×D312yescomplemented
125C22×C3⋊D3—22no—
126C22×C3⋊D3C2×D411yescharacteristic
127C22×C3×D3—22no—
128C2×D32—24no—
129C2×D32—42no—
130C2×D32—42no—
131C32×Q8—22no—
132C32×Q8—22no—
133C2×C32×C4—22no—
134C2×C32×C4C2×D411yescharacteristic
135C2×C32×C4C2×D411yescharacteristic
136C2×C32×C4C2411yescharacteristic
137C2×C3⋊Dic3C2×D411yescharacteristic
138C2×C3⋊Dic3C2×D411yescharacteristic
139C2×C3⋊Dic3C2×D411yescharacteristic
140C4⋊(C3⋊D3)—22no—
141C4⋊(C3⋊D3)—22no—
142C4⋊(C3⋊D3)—42no—
143C4⋊(C3⋊D3)—44no—
144C4⋊(C3⋊D3)—42no—
145C4×C3⋊D3—22no—
146C4×C3⋊D3—41no—
147C4×C3⋊D3—44no—
148C4×C3⋊D3C2×D412yes—
149C4×C3⋊D3#4112yes—
150C2×C3×Dic3—22no—
151C3×D12—22no—
152C3×D12C2×D414yes—
153C3×C4×D3—44no—
154#625—24no—
155#624—42no—
156D3×Dic3—44no—
157C3×C3⋊C8—24no—
158C2×AGL(1,ℤ/8)—92no—
159#532—91no—
160C2×C4×D4—91no—
161#463—94no—
162#461—32no—
163#459—92no—
164#423—91no—
165#417—92no—
166C23×D3—62no—
167C2×C3×Q8—22no—
168C2×C3×Q8C22×D314yes—
169C2×C3×D4—32no—
170C22×C3×C4—62no—
171C2×#67—62no—
172C22×Dic3—62no—
173#239—68no—
174#239—68no—
175#239—124no—
176#239—124no—
177D3×D4—38no—
178D3×D4—64no—
179C2×D12—34no—
180C2×D12—62no—
181C2×D12—64no—
182C2×D12—62no—
183C2×D12—62no—
184C2×D12—64no—
185C2×D12—62no—
186C2×D12—62no—
187C2×D12C22×D312yes—
188C2×C4×D3—22no—
189C2×C4×D3—32no—
190C2×C4×D3—32no—
191C2×C4×D3—32no—
192C2×C4×D3—61no—
193C2×C4×D3—61no—
194C2×C4×D3—61no—
195C2×C4×D3—62no—
196C2×C4×D3—64no—
197C2×C4×D3—62no—
198C2×C4×D3—64no—
199C2×C4×D3—128no—
200C3×SD16—68no—
201C2×C3×C8—34no—
202C3×C4⋊C4—22no—
203C3×C4⋊C4—22no—
204C3×C4⋊C4—22no—
205C3×C4⋊C4—22no—
206C3×C4⋊C4—32no—
207C3×C22⋊C4—62no—
208C3×C42—21no—
209C3×C42C22×D312yes—
210#217—62no—
211#215—28no—
212#213—68no—
213(C2×D3)⋊C4—22no—
214(C2×D3)⋊C4—64no—
215(C2×D3)⋊C4—64no—
216(C2×D3)⋊C4—62no—
217(C2×D3)⋊C4—64no—
218(C2×D3)⋊C4—64no—
219C4⋊Dic3C22×D312yes—
220Dic3⋊C4—62no—
221C4×Dic3—32no—
222C4×Dic3—32no—
223C4×Dic3—32no—
224C4×Dic3—61no—
225C4×Dic3—61no—
226C4×Dic3—61no—
227C2×C3⋊C8C22×D314yes—
228D24—68no—
229ΓL(1,𝔽25)—68no—
230C22×C32C22×D411yescharacteristic
231C2×C3⋊D3—21no—
232C2×C3⋊D3—21no—
233C2×C3⋊D3—42no—
234C2×C3⋊D3—42no—
235C2×C3⋊D3—42no—
236C2×C3⋊D3#12112yes—
237C2×C3×D3—24no—
238C2×C3×D3—42no—
239C2×C3×D3—42no—
240D32—48no—
241C32×C4—21no—
242C32×C4—42no—
243C32×C4AGL(1,ℤ/8)12yescomplemented
244C32×C4C22×D411yescharacteristic
245C32×C4C2×#4111yescharacteristic
246C3⋊Dic3—21no—
247C3⋊Dic3—21no—
248C3⋊Dic3#12112yes—
249C3×Dic3—42no—
250C2×#41—92no—
251C22×D4—91no—
252C23×C4—181no—
253AGL(1,ℤ/8)—188no—
254C2×SD16—34no—
255C2×D8—94no—
256C2×M16—92no—
257C4⋊Q8D3211yescharacteristic, complemented
258#127—91no—
259#124—92no—
260#121—181no—
261#121—181no—
262C4×D4—32no—
263C4×D4—92no—
264C4×D4—181no—
265C4×D4—181no—
266C4×D4—181no—
267C4×D4—181no—
268C2×C4⋊C4—91no—
269C2×C22⋊C4—181no—
270C2×C42—91no—
271C4⋊C8—32no—
272C4⋊C8—92no—
273#103—34no—
274#102—94no—
275C23×C3—62no—
276C22×D3—22no—
277C22×D3—32no—
278C22×D3—61no—
279C22×D3—68no—
280C22×D3—64no—
281C22×D3—64no—
282C22×D3—124no—
283C22×D3—124no—
284C3×Q8—24no—
285C3×Q8—24no—
286C3×Q8—42no—
287C3×Q8—42no—
288C3×D4—34no—
289C3×D4—62no—
290C2×C3×C4—24no—
291C2×C3×C4—24no—
292C2×C3×C4—21no—
293C2×C3×C4—21no—
294C2×C3×C4—21no—
295C2×C3×C4—62no—
296C2×C3×C4—124no—
297C2×C3×C4D3×D412yes—
298C2×C3×C4D3×D412yes—
299C2×C3×C4C23×D312yes—
300#67—68no—
301C2×Dic3—22no—
302C2×Dic3—32no—
303C2×Dic3—32no—
304C2×Dic3—32no—
305C2×Dic3—61no—
306C2×Dic3—61no—
307C2×Dic3—61no—
308C2×Dic3—124no—
309D12—22no—
310D12—64no—
311D12—64no—
312D12—122no—
313D12—122no—
314D12—124no—
315D12—124no—
316D12—124no—
317D12—128no—
318D12—128no—
319D12—124no—
320D12D3×D414yes—
321C4×D3—34no—
322C4×D3—34no—
323C4×D3—44no—
324C4×D3—62no—
325C4×D3—62no—
326C4×D3—64no—
327C4×D3—122no—
328C4×D3—128no—
329C4×D3—124no—
330C4×D3—122no—
331C4×D3—128no—
332C4×D3—124no—
333C4×D3—122no—
334C3×C8—64no—
335C3⋊C8—24no—
336C2×C32C2×#12111yescharacteristic
337C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
338C2×C32#57511yescharacteristic
339C3⋊D3—22no—
340C3⋊D3—82no—
341C3×D3—44no—
342C24—181no—
343#41—184no—
344#41—184no—
345C2×Q8C2×D3212yes—
346C2×D4—32no—
347C2×D4—94no—
348C2×D4—92no—
349C2×D4—182no—
350C2×D4—182no—
351C2×D4—181no—
352C2×D4—181no—
353C2×D4—181no—
354C22×C4—62no—
355C22×C4—91no—
356C22×C4—91no—
357C22×C4—91no—
358C22×C4—182no—
359C22×C4—181no—
360C22×C4—182no—
361C22×C4—364no—
362SD16—68no—
363D8—188no—
364M16—184no—
365C2×C8—34no—
366C4⋊C4—21no—
367C4⋊C4—21no—
368C4⋊C4—32no—
369C4⋊C4—181no—
370C22⋊C4—62no—
371C22⋊C4—182no—
372C22⋊C4—182no—
373C22⋊C4—182no—
374C42—91no—
375C42—91no—
376C42—91no—
377C42C2×D3211yescharacteristic
378C22×C3—21no—
379C22×C3—64no—
380C22×C3—122no—
381C22×C3—122no—
382C22×C3C2×D3×D412yes—
383C2×D3—24no—
384C2×D3—34no—
385C2×D3—42no—
386C2×D3—42no—
387C2×D3—62no—
388C2×D3—62no—
389C2×D3—62no—
390C2×D3—121no—
391C2×D3—121no—
392C2×D3—1216no—
393C2×D3—124no—
394C2×D3—124no—
395C2×D3—124no—
396C2×D3—124no—
397C2×D3—124no—
398C2×D3—124no—
399C3×C4—22no—
400C3×C4—22no—
401C3×C4—21no—
402C3×C4—21no—
403C3×C4—22no—
404C3×C4—44no—
405C3×C4—44no—
406C3×C4—122no—
407C3×C4#91414yescomplemented
408C3×C4C2×D3×D412yes—
409C3×C4D3×#4112yes—
410Dic3—34no—
411Dic3—42no—
412Dic3—62no—
413Dic3—62no—
414Dic3—62no—
415Dic3—121no—
416Dic3—121no—
417C32#303611yescharacteristic, complemented, Sylow
418C23—62no—
419C23—91no—
420C23—184no—
421C23—182no—
422C23—362no—
423C23—362no—
424Q8—22no—
425Q8—22no—
426D4—34no—
427D4—62no—
428D4—184no—
429D4—182no—
430D4—182no—
431D4—362no—
432D4—364no—
433D4—362no—
434C2×C4—22no—
435C2×C4—62no—
436C2×C4—91no—
437C2×C4—92no—
438C2×C4—92no—
439C2×C4—91no—
440C2×C4—91no—
441C2×C4—124no—
442C2×C4—182no—
443C2×C4—361no—
444C2×C4—364no—
445C2×C4—362no—
446C2×C4—364no—
447C2×C4#381111yescharacteristic
448C2×C4#381111yescharacteristic
449C2×C4C22×D3211yescharacteristic
450C8—64no—
451C2×C3—21no—
452C2×C3—21no—
453C2×C3—21no—
454C2×C3—124no—
455C2×C3D3×#12112yes—
456C2×C3C2×#91412yes—
457C2×C3#577712yes—
458D3—44no—
459D3—64no—
460D3—122no—
461D3—244no—
462D3—244no—
463C22—64no—
464C22—92no—
465C22—122no—
466C22—122no—
467C22—181no—
468C22—181no—
469C22—368no—
470C22—362no—
471C22—362no—
472C22—362no—
473C22C2×#381111yescharacteristic
474C4—21no—
475C4—42no—
476C4—92no—
477C4—122no—
478C4—181no—
479C4—181no—
480C4#6394112yescomplemented
481C4D32×D411yescharacteristic
482C4#6431211yescharacteristic
483C3—21no—
484C3#8042812yescomplemented
485C2—124no—
486C2—182no—
487C2—722no—
488C2#1059528211yescharacteristic
489C2C2×#6394111yescharacteristic
490C2#1059532311yescharacteristic
subgroupG/H
centerC22C2×#3811
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4⋊Q8C22
socleC22×C32C22×D4
hypercenterC4⋊Q8D32
hypocenterC32#3036
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊Q8

Complements

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

NH ≅ G/Ntype
1. #10596196C2semidirect
2. C2×#63941C2semidirect
3. C4×#3802C2semidirect
4. C3×#5083C2semidirect
5. #10591570C2semidirect
6. #10591554C2semidirect
7. #10590349C2semidirect
8. #10590340C2semidirect
13. C32×C4⋊Q8C22semidirect
14. #64156C22semidirect
19. #64083C22semidirect
31. C3×#835C22semidirect
32. C3×C4⋊(C3⋊C8)C22semidirect
33. #63572C22semidirect
34. #63564C22semidirect
41. #5083D3semidirect
65. #3802D4semidirect
90. C3×C4⋊Q8C2×D3semidirect
120. #835C2×D3semidirect
124. C4⋊(C3⋊C8)C2×D3semidirect
243. C32×C4AGL(1,ℤ/8)semidirect
257. C4⋊Q8D32semidirect
407. C3×C4#914semidirect
417. C32#3036semidirect
480. C4#63941semidirect
484. C3#80428semidirect

Maximal subgroups

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

subgroupindex
#105961962
C2×#639412
C4×#38022
C3×#50832
#105915702
#105915542
#105903492
#105903402
#804283