Finite Group Databasebeta

← #11870449

Subgroups — #11870449

Order 1152.

1043 conjugacy classes of subgroups.

The subgroup lattice has 498 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#3802C211yesmaximal, characteristic, complemented
2#10593972C211yesmaximal, characteristic, complemented
3#10592384C211yesmaximal, characteristic, complemented
4C3×C4×D24C212yesmaximal, complemented
5#10590945C212yesmaximal, complemented
6#10590778C212yesmaximal, complemented
7#10590749C212yesmaximal, complemented
8#10590650C212yesmaximal, complemented
9C4×#3713C212yesmaximal, complemented
10#79590—32nomaximal
11C2×#3802C2211yescharacteristic
12C2×C4×D32—21no—
13C2×#3798—21no—
14C42×C3⋊D3C2211yescharacteristic
15C2×C3×D24C2212yes—
16C3×C4×D12C2212yes—
17C3×C4×D12C2212yescomplemented
18#63921—21no—
19#63919C2211yescharacteristic, complemented
20#63916C2212yes—
21#63915—21no—
22#63914C2211yescharacteristic, complemented
23#63912—21no—
24#63902—21no—
25C4×#625—21no—
26C4×#625—21no—
27#63900C2211yescharacteristic
28#63898C2212yes—
29C2×#3713C2212yes—
30C32×C4×C8C2211yescharacteristic, complemented
31#63647C2212yes—
32#63641C2212yescomplemented
33C4×C3⋊(C3⋊C8)C2211yescharacteristic, complemented
34C3×#821C2212yes—
35C3×#821C2212yescomplemented
36C3×#818C2212yescomplemented
37#63576C2212yescomplemented
38#63562C2212yes—
39#63562C2212yescomplemented
40#5548—32no—
41C4×D3×D4—32no—
42C3×C4×D8—32no—
43#5156—32no—
44#5150—32no—
45C4×#213—32no—
46C4×#213—32no—
47#4890—32no—
48#4882—32no—
49#4786—32no—
50#4774—32no—
51#4773—32no—
52#4759—32no—
53C4×D24D312yescomplemented
54#4685—32no—
55#4685—61no—
56C22×D32—21no—
57C2×C4×C3⋊D3D411yescharacteristic
58C2×C4×C3⋊D3D411yescharacteristic
59C2×C4×C3⋊D3C2311yescharacteristic
60C2×C3×D12C2312yes—
61C2×C3×D12C2312yes—
62C2×C3×C4×D3—22no—
63C2×C3×C4×D3—22no—
64C2×#627—21no—
65C2×#626—22no—
66C2×#625—21no—
67C2×#625—21no—
68C2×#625—21no—
69C2×#624—21no—
70C2×D3×Dic3—22no—
71#3802—24no—
72C4×D32—44no—
73#3798—44no—
74C2×C32×C8C2312yes—
75C32×C42C2311yescharacteristic
76C4×C3⋊Dic3D411yescharacteristic
77C4×C3⋊Dic3D411yescharacteristic
78C4×C3⋊Dic3C2311yescharacteristic
79C2×C3⋊(C3⋊C8)C2312yes—
80C3×(C2×D3)⋊C4—22no—
81C3×(C2×D3)⋊C4—22no—
82C3×C4⋊Dic3C2312yes—
83C3×C4⋊Dic3C2312yes—
84C3×D24—24no—
85#3724—21no—
86#3724—21no—
87(C2×D3)⋊Dic3—22no—
88(C2×D3)⋊Dic3—22no—
89#3713—24no—
90#3100—91noSylow
91C2×D3×D4—32no—
92C2×#235—62no—
93C22×C4×D3—62no—
94C2×C3×D8—32no—
95C3×C4×D4—32no—
96C3×C4×D4—32no—
97#940—32no—
98#938—32no—
99D4×Dic3—32no—
100C2×#213—32no—
101C2×#213—32no—
102C4×#67—62no—
103C4×#67—62no—
104C2×D24C2×D312yes—
105#895—32no—
106#893—32no—
107D3×C4⋊C4—32no—
108#888—32no—
109#885—62no—
110#884—62no—
111#67⋊C4—62no—
112D3×C22⋊C4—62no—
113C4×D12C2×D312yes—
114C4×D12C2×D312yescomplemented
115C42×D3—32no—
116C42×D3—61no—
117C3×#107—32no—
118C3×#102—32no—
119C3×#102—32no—
120C3×C4×C8—21no—
121C3×C4×C8C2×D312yescomplemented
122#832—32no—
123#832—32no—
124#821C2×D312yes—
125#821C2×D312yescomplemented
126(C2×D3)⋊C8—32no—
127(C2×D3)⋊C8—32no—
128(C2×D3)⋊C8—62no—
129#818C2×D312yescomplemented
130Dic3⋊C8—32no—
131Dic3⋊C8—32no—
132Dic3⋊C8—62no—
133#809—32no—
134#809—32no—
135#807—32no—
136#807—32no—
137C4×C3⋊C8—32no—
138C4×C3⋊C8—61no—
139C22×C3⋊D3C2×D411yescharacteristic
140C22×C3×D3—22no—
141C22×C3×D3—22no—
142C2×D32—24no—
143C2×D32—42no—
144C2×D32—42no—
145C2×C32×C4C2×D411yescharacteristic
146C2×C32×C4C2×D411yescharacteristic
147C2×C32×C4C2411yescharacteristic
148C2×C3⋊Dic3C2×D411yescharacteristic
149C2×C3⋊Dic3C2×D411yescharacteristic
150C2×C3⋊Dic3C2×D411yescharacteristic
151C4×C3⋊D3—22no—
152C4×C3⋊D3—41no—
153C4×C3⋊D3D814yescomplemented
154C2×C3×Dic3—22no—
155C2×C3×Dic3—22no—
156C3×D12—22no—
157C3×D12—22no—
158C3×D12—22no—
159C3×D12#4114yescomplemented
160C3×C4×D3—44no—
161C3×C4×D3—44no—
162#627—42no—
163#626—44no—
164#625—24no—
165#625—42no—
166#625—42no—
167#624—42no—
168D3×Dic3—44no—
169C32×C8—22no—
170C3⋊(C3⋊C8)—22no—
171#532—91no—
172C2×C4×D4—91no—
173#480—92no—
174#474—92no—
175#459—92no—
176#447—92no—
177C4×D8—32no—
178C4×D8—92no—
179#431—91no—
180C23×D3—62no—
181C2×C3×D4—32no—
182C2×C3×D4—32no—
183C22×C3×C4—62no—
184C22×C3×C4—62no—
185C2×#67—62no—
186C2×#67—62no—
187C2×#67—62no—
188C2×#67—62no—
189C22×Dic3—62no—
190D3×D4—64no—
191D3×D4—64no—
192#235—128no—
193C2×D12—62no—
194C2×D12C22×D312yes—
195C2×D12C22×D312yes—
196C2×C4×D3—22no—
197C2×C4×D3—22no—
198C2×C4×D3—32no—
199C2×C4×D3—32no—
200C2×C4×D3—32no—
201C2×C4×D3—61no—
202C2×C4×D3—61no—
203C2×C4×D3—61no—
204C2×C4×D3—62no—
205C2×C4×D3—62no—
206C2×C4×D3—128no—
207C2×Dic6—62no—
208C3×D8—64no—
209C2×C3×C8—22no—
210C2×C3×C8C22×D312yes—
211C2×C3×C8C22×D312yes—
212C3×C4⋊C4—32no—
213C3×C4⋊C4—32no—
214C3×C22⋊C4—62no—
215C3×C22⋊C4—62no—
216C3×C42—21no—
217C3×C42C22×D312yes—
218#217—62no—
219#217—62no—
220#213—64no—
221#213—64no—
222(C2×D3)⋊C4—22no—
223(C2×D3)⋊C4—22no—
224(C2×D3)⋊C4—62no—
225(C2×D3)⋊C4—62no—
226C4⋊Dic3C22×D312yes—
227C4⋊Dic3C22×D312yes—
228Dic3⋊C4—62no—
229Dic3⋊C4—62no—
230C4×Dic3—32no—
231C4×Dic3—32no—
232C4×Dic3—32no—
233C4×Dic3—61no—
234C4×Dic3—61no—
235C4×Dic3—61no—
236C2×C3⋊C8—32no—
237C2×C3⋊C8—32no—
238C2×C3⋊C8—62no—
239D24—24no—
240C22×C32C22×D411yescharacteristic
241C2×C3⋊D3—21no—
242C2×C3⋊D3—21no—
243C2×C3⋊D3C2×D812yes—
244C2×C3×D3—24no—
245C2×C3×D3—42no—
246C2×C3×D3—42no—
247C2×C3×D3—42no—
248C2×C3×D3—42no—
249C2×C3×D3—42no—
250D32—48no—
251C32×C4—21no—
252C32×C4C2×D812yes—
253C32×C4C2×#4112yes—
254C3⋊Dic3—21no—
255C3⋊Dic3—21no—
256C3⋊Dic3C2×D812yes—
257C3×Dic3—42no—
258C3×Dic3—42no—
259C2×#41—181no—
260C22×D4—91no—
261C23×C4—181no—
262C2×D8—32no—
263C2×D8—92no—
264C4⋊Q8—91no—
265#127—91no—
266#124—181no—
267#121—92no—
268#121—181no—
269C4×D4—32no—
270C4×D4—32no—
271C4×D4—92no—
272C4×D4—181no—
273C4×D4—181no—
274C4×D4—181no—
275C2×C4⋊C4—91no—
276C2×C22⋊C4—181no—
277C2×C42—91no—
278#107—32no—
279#107—92no—
280C4⋊C8—92no—
281#102—32no—
282#102—32no—
283#102—92no—
284#102—92no—
285C22⋊C8—92no—
286C4×C8—91no—
287C4×C8D3211yescharacteristic, complemented
288C23×C3—62no—
289C23×C3—62no—
290C22×D3—22no—
291C22×D3—22no—
292C22×D3—32no—
293C22×D3—61no—
294C22×D3—68no—
295C22×D3—124no—
296C22×D3—124no—
297C3×D4—34no—
298C3×D4—62no—
299C3×D4—62no—
300C3×D4—62no—
301C2×C3×C4—21no—
302C2×C3×C4—21no—
303C2×C3×C4—21no—
304C2×C3×C4—62no—
305C2×C3×C4—62no—
306C2×C3×C4—124no—
307C2×C3×C4—124no—
308C2×C3×C4D3×D412yes—
309C2×C3×C4D3×D412yes—
310C2×C3×C4C23×D312yes—
311#67—68no—
312#67—124no—
313#67—124no—
314#67—124no—
315C2×Dic3—22no—
316C2×Dic3—22no—
317C2×Dic3—32no—
318C2×Dic3—32no—
319C2×Dic3—32no—
320C2×Dic3—61no—
321C2×Dic3—61no—
322C2×Dic3—61no—
323C2×Dic3—124no—
324D12—22no—
325D12—22no—
326D12—22no—
327D12—124no—
328D12#23514yescomplemented
329C4×D3—38no—
330C4×D3—44no—
331C4×D3—44no—
332C4×D3—64no—
333C4×D3—62no—
334C4×D3—62no—
335C4×D3—122no—
336C4×D3—124no—
337C4×D3—124no—
338C4×D3—122no—
339C4×D3—122no—
340Dic6—124no—
341C3×C8—22no—
342C3×C8—22no—
343C3×C8—42no—
344C3⋊C8—62no—
345C3⋊C8—62no—
346C3⋊C8—122no—
347C2×C32#52511yescharacteristic
348C2×C32C22×D811yescharacteristic
349C2×C32#57511yescharacteristic
350C3⋊D3—22no—
351C3×D3—44no—
352C3×D3—82no—
353C24—181no—
354#41—364no—
355C2×Q8—181no—
356C2×D4—32no—
357C2×D4—32no—
358C2×D4—182no—
359C2×D4—181no—
360C2×D4—181no—
361C2×D4—181no—
362C2×D4—184no—
363C22×C4—62no—
364C22×C4—62no—
365C22×C4—91no—
366C22×C4—91no—
367C22×C4—91no—
368C22×C4—181no—
369C22×C4—182no—
370C22×C4—364no—
371D8—64no—
372D8—184no—
373C2×C8—92no—
374C2×C8C2×D3212yes—
375C4⋊C4—32no—
376C4⋊C4—32no—
377C4⋊C4—181no—
378C4⋊C4—181no—
379C22⋊C4—62no—
380C22⋊C4—62no—
381C22⋊C4—182no—
382C22⋊C4—182no—
383C42—91no—
384C42—91no—
385C42—91no—
386C42C2×D3211yescharacteristic
387C22×C3—21no—
388C22×C3—64no—
389C22×C3—122no—
390C22×C3—122no—
391C22×C3—122no—
392C22×C3—122no—
393C22×C3—122no—
394C22×C3C2×D3×D412yes—
395C2×D3—24no—
396C2×D3—34no—
397C2×D3—42no—
398C2×D3—42no—
399C2×D3—42no—
400C2×D3—42no—
401C2×D3—42no—
402C2×D3—62no—
403C2×D3—62no—
404C2×D3—62no—
405C2×D3—121no—
406C2×D3—121no—
407C2×D3—1216no—
408C3×C4—22no—
409C3×C4—22no—
410C3×C4—22no—
411C3×C4—22no—
412C3×C4—122no—
413C3×C4—122no—
414C3×C4D3×D814yes—
415C3×C4C2×#23512yes—
416C3×C4D3×#4112yes—
417Dic3—34no—
418Dic3—42no—
419Dic3—42no—
420Dic3—62no—
421Dic3—62no—
422Dic3—62no—
423Dic3—121no—
424Dic3—121no—
425C32#310011yescharacteristic, complemented, Sylow
426C23—62no—
427C23—62no—
428C23—91no—
429C23—184no—
430C23—362no—
431C23—362no—
432Q8—362no—
433D4—34no—
434D4—62no—
435D4—62no—
436D4—62no—
437D4—184no—
438D4—362no—
439D4—364no—
440D4—362no—
441C2×C4—62no—
442C2×C4—62no—
443C2×C4—91no—
444C2×C4—94no—
445C2×C4—91no—
446C2×C4—91no—
447C2×C4—124no—
448C2×C4—124no—
449C2×C4—182no—
450C2×C4—361no—
451C2×C4—364no—
452C2×C4—362no—
453C2×C4#380211yescharacteristic
454C2×C4#380211yescharacteristic
455C2×C4C22×D3211yescharacteristic
456C8—22no—
457C8—182no—
458C2×C3—21no—
459C2×C3—21no—
460C2×C3—21no—
461C2×C3—124no—
462C2×C3—242no—
463C2×C3#554712yes—
464C2×C3C2×D3×D812yes—
465C2×C3#576812yes—
466D3—44no—
467D3—64no—
468D3—82no—
469D3—122no—
470C22—64no—
471C22—92no—
472C22—122no—
473C22—122no—
474C22—122no—
475C22—122no—
476C22—122no—
477C22—181no—
478C22—181no—
479C22—368no—
480C22C2×#380211yescharacteristic
481C4—21no—
482C4—92no—
483C4—122no—
484C4—122no—
485C4—181no—
486C4—181no—
487C4#6379712yes—
488C4D3×#23512yes—
489C3—21no—
490C3#7959012yescomplemented
491C2—124no—
492C2—182no—
493C2—242no—
494C2#1059400611yescharacteristic
495C2C2×#6379711yescharacteristic
496C2#1059468511yescharacteristic
subgroupG/H
centerC2×C4#3802
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4×C8C22
socleC22×C32C22×D4
hypercenterC4×C8D32
hypocenterC32#3100
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C42 ◁ C4×C8

Complements

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

NH ≅ G/Ntype
1. C4×#3802C2semidirect
2. #10593972C2semidirect
3. #10592384C2semidirect
4. C3×C4×D24C2semidirect
5. #10590945C2semidirect
6. #10590778C2semidirect
7. #10590749C2semidirect
8. #10590650C2semidirect
9. C4×#3713C2semidirect
17. C3×C4×D12C22semidirect
19. #63919C22semidirect
22. #63914C22semidirect
30. C32×C4×C8C22semidirect
32. #63641C22semidirect
33. C4×C3⋊(C3⋊C8)C22semidirect
35. C3×#821C22semidirect
36. C3×#818C22semidirect
37. #63576C22semidirect
39. #63562C22semidirect
53. C4×D24D3semidirect
114. C4×D12C2×D3semidirect
121. C3×C4×C8C2×D3semidirect
125. #821C2×D3semidirect
129. #818C2×D3semidirect
153. C4×C3⋊D3D8semidirect
159. C3×D12#41semidirect
287. C4×C8D32semidirect
328. D12#235semidirect
425. C32#3100semidirect
490. C3#79590semidirect

Maximal subgroups

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

subgroupindex
C4×#38022
#105939722
#105923842
C3×C4×D242
#105909452
#105907782
#105907492
#105906502
C4×#37132
#795903