Finite Group Databasebeta

← #11801987

Subgroups — #11801987

Order 1152.

3672 conjugacy classes of subgroups.

The subgroup lattice has 531 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C4×C3⋊D3C211yesmaximal, characteristic, complemented
2C2×#64146C211yesmaximal, characteristic
3C2×D4×C3⋊Dic3C211yesmaximal, characteristic, complemented
4C2×#64090C212yesmaximal, complemented
5C32×#386C211yesmaximal, characteristic, complemented
6#10592909C211yesmaximal, characteristic, complemented
7#10592655C212yesmaximal, complemented
8#10592654C211yesmaximal, characteristic, complemented
9C22⋊C4×C3⋊Dic3C211yesmaximal, characteristic, complemented
10#10592367C212yesmaximal, complemented
11#10592365C212yesmaximal, complemented
12#74659—34nomaximal
13C24×C3⋊D3C2211yescharacteristic
14C22×C32×D4C2211yescharacteristic
15C23×C32×C4C2211yescharacteristic
16C22×#638C2212yes—
17C23×C3⋊Dic3C2211yescharacteristic
18C23×C3⋊Dic3C2211yescharacteristic, complemented
19C22×C4×C3⋊D3—24no—
20C22×C4×C3⋊D3—28no—
21C22×C4×C3⋊D3C2212yes—
22C22×C4×C3⋊D3C2212yes—
23C2×C32×C22⋊C4C2211yescharacteristic
24C2×C32×C22⋊C4C2212yescomplemented
25C2×#3757C2211yescharacteristic
26C2×#3757C2211yescharacteristic
27C2×#3757C2211yescharacteristic, complemented
28#64146C418yescomplemented
29D4×C3⋊Dic3—24no—
30C2×#3752C2212yes—
31C2×#3752C2212yes—
32C2×#3752C2212yes—
33C2×C4⋊(C3⋊Dic3)C2211yescharacteristic, complemented
34C2×#3750C2212yescomplemented
35C2×C4×C3⋊Dic3C2211yescharacteristic, complemented
36C2×C4×C3⋊Dic3C2212yescomplemented
37#64090—28no—
38C32×#95C2212yescomplemented
39#63658C2212yescomplemented
40#63658C2212yescomplemented
41C23×C4×D3—34no—
42C2×#937—34no—
43C2×D4×Dic3—34no—
44C2×#67⋊C4—38no—
45C3×#386D314yescomplemented
46#5210—34no—
47#4956—38no—
48#4955—34no—
49Dic3×C22⋊C4—34no—
50#4668—38no—
51#4666—38no—
52C24×C32C2311yescharacteristic
53C24×C32C2311yescharacteristic
54C23×C3⋊D3—22no—
55C23×C3⋊D3—22no—
56C23×C3⋊D3—24no—
57C23×C3⋊D3—24no—
58C23×C3⋊D3C2×C414yescomplemented
59C23×C3⋊D3C2312yes—
60C2×C32×D4—22no—
61C2×C32×D4—22no—
62C2×C32×D4C2×C414yescomplemented
63C22×C32×C4—22no—
64C22×C32×C4—24no—
65C22×C32×C4C2312yes—
66C22×C32×C4C2311yescharacteristic
67C22×C32×C4C2312yes—
68C2×#638—24no—
69C2×#638—24no—
70C2×#638C2×C418yescomplemented
71C22×C3⋊Dic3—24no—
72C22×C3⋊Dic3—24no—
73C22×C3⋊Dic3—22no—
74C22×C3⋊Dic3D414yescomplemented
75C22×C3⋊Dic3C2311yescharacteristic
76C22×C3⋊Dic3C2311yescharacteristic
77C22×C3⋊Dic3C2312yes—
78C22×C3⋊Dic3C2311yescharacteristic
79C22×C3⋊Dic3C2311yescharacteristic
80C2×C4×C3⋊D3—232no—
81C2×C4×C3⋊D3—24no—
82C2×C4×C3⋊D3—24no—
83C2×C4×C3⋊D3—24no—
84C2×C4×C3⋊D3—24no—
85C2×C4×C3⋊D3—24no—
86C2×C4×C3⋊D3D418yescomplemented
87C32×C22⋊C4—22no—
88C32×C22⋊C4—24no—
89#3757—22no—
90#3757—22no—
91#3757C2×C414yescomplemented
92#3752—24no—
93#3752—24no—
94#3752C2×C418yescomplemented
95C4⋊(C3⋊Dic3)—22no—
96#3750—24no—
97C4×C3⋊Dic3—24no—
98C4×C3⋊Dic3—22no—
99C4×#120—91noSylow
100C24×D3—34no—
101C22×C3×D4C2×D314yes—
102C23×C3×C4C2×D314yes—
103C22×#67—38no—
104C23×Dic3—34no—
105C23×Dic3—34no—
106C22×C4×D3—38no—
107C22×C4×D3—38no—
108C22×C4×D3—632no—
109C22×C4×D3—616no—
110C2×C3×C22⋊C4C2×D314yes—
111C2×C3×C22⋊C4C2×D318yescomplemented
112C2×#217—34no—
113C2×#217—34no—
114C2×#217—34no—
115#937—332no—
116D4×Dic3—616no—
117C2×(C2×D3)⋊C4—38no—
118C2×(C2×D3)⋊C4—38no—
119C2×(C2×D3)⋊C4—38no—
120C2×C4⋊Dic3—34no—
121C2×Dic3⋊C4—38no—
122C2×C4×Dic3—34no—
123C2×C4×Dic3—38no—
124#67⋊C4—632no—
125C3×#95C2×D318yescomplemented
126C3⋊#95—38no—
127C3⋊#95—38no—
128C23×C32—22no—
129C23×C32—22no—
130C23×C32—21no—
131C23×C32—22no—
132C23×C32—22no—
133C23×C32—21no—
134C23×C32C22×C412yes—
135C23×C32C22×C412yescomplemented
136C23×C32C2×D412yes—
137C23×C32#4112yes—
138C23×C32C2411yescharacteristic
139C22×C3⋊D3—216no—
140C22×C3⋊D3—28no—
141C22×C3⋊D3—28no—
142C22×C3⋊D3—28no—
143C22×C3⋊D3—22no—
144C22×C3⋊D3—22no—
145C22×C3⋊D3—22no—
146C22×C3⋊D3—22no—
147C22×C3⋊D3—216no—
148C22×C3⋊D3C22×C414yes—
149C22×C3⋊D3C2×D414yes—
150C22×C3⋊D3#4114yes—
151C32×D4—28no—
152C2×C32×C4—28no—
153C2×C32×C4—21no—
154C2×C32×C4—22no—
155C2×C32×C4—22no—
156C2×C32×C4—21no—
157C2×C32×C4—22no—
158C2×C32×C4—22no—
159C2×C32×C4—22no—
160C2×C32×C4C22×C412yescomplemented
161C2×C32×C4C2×D414yes—
162#638—216no—
163C2×C3⋊Dic3—22no—
164C2×C3⋊Dic3—22no—
165C2×C3⋊Dic3—22no—
166C2×C3⋊Dic3—28no—
167C2×C3⋊Dic3—21no—
168C2×C3⋊Dic3—22no—
169C2×C3⋊Dic3—21no—
170C2×C3⋊Dic3—22no—
171C2×C3⋊Dic3—44no—
172C2×C3⋊Dic3C22×C414yescomplemented
173C2×C3⋊Dic3C2×D412yes—
174C2×C3⋊Dic3C2×D412yes—
175C2×C3⋊Dic3C2×D414yes—
176C4×C3⋊D3—216no—
177C4×C3⋊D3—216no—
178C24×C4—91no—
179C2×#120—91no—
180C2×C4×D4—91no—
181C2×C4×D4—92no—
182#386—92no—
183#386C3⋊D311yescharacteristic, complemented
184#385—91no—
185#385—92no—
186#379—91no—
187C4×C22⋊C4—91no—
188C4×C22⋊C4—92no—
189C24×C3C22×D314yes—
190C24×C3C22×D314yes—
191C23×D3—38no—
192C23×D3—316no—
193C23×D3—616no—
194C23×D3—616no—
195C23×D3—68no—
196C23×D3—68no—
197C2×C3×D4—28no—
198C2×C3×D4—28no—
199C2×C3×D4C4×D3116yescomplemented
200C22×C3×C4—28no—
201C22×C3×C4—216no—
202C22×C3×C4C22×D318yes—
203C22×C3×C4C22×D314yes—
204C22×C3×C4C22×D318yes—
205C2×#67—332no—
206C2×#67—616no—
207C2×#67—616no—
208C22×Dic3—34no—
209C22×Dic3—316no—
210C22×Dic3—38no—
211C22×Dic3—34no—
212C22×Dic3—34no—
213C22×Dic3—34no—
214C22×Dic3—616no—
215C22×Dic3—616no—
216C22×Dic3—68no—
217C2×C4×D3—332no—
218C2×C4×D3—616no—
219C2×C4×D3—616no—
220C2×C4×D3—616no—
221C2×C4×D3—616no—
222C2×C4×D3—6128no—
223C2×C4×D3—616no—
224C3×C22⋊C4—28no—
225C3×C22⋊C4—216no—
226#217—316no—
227#217—68no—
228#217—68no—
229(C2×D3)⋊C4—332no—
230(C2×D3)⋊C4—616no—
231(C2×D3)⋊C4—616no—
232C4⋊Dic3—68no—
233Dic3⋊C4—616no—
234C4×Dic3—616no—
235C4×Dic3—68no—
236C22×C32—24no—
237C22×C32—22no—
238C22×C32—22no—
239C22×C32—24no—
240C22×C32—24no—
241C22×C32—22no—
242C22×C32—41no—
243C22×C32—41no—
244C22×C32—42no—
245C22×C32C4×D414yescomplemented
246C22×C32C23×C411yescharacteristic
247C22×C32C22×D412yes—
248C22×C32C22×D411yescharacteristic
249C22×C32C2×#4111yescharacteristic
250C22×C32C2×#4112yes—
251C2×C3⋊D3—232no—
252C2×C3⋊D3—24no—
253C2×C3⋊D3—24no—
254C2×C3⋊D3—24no—
255C2×C3⋊D3—24no—
256C2×C3⋊D3—24no—
257C2×C3⋊D3—24no—
258C2×C3⋊D3C4×D418yescomplemented
259C32×C4—22no—
260C32×C4—24no—
261C32×C4—42no—
262C3⋊Dic3—24no—
263C3⋊Dic3—22no—
264C3⋊Dic3—41no—
265C3⋊Dic3—41no—
266C3⋊Dic3#12014yescomplemented
267C25—91no—
268C22×D4—92no—
269C22×D4C2×C3⋊D311yescharacteristic
270C23×C4—91no—
271C23×C4—92no—
272C23×C4—91no—
273C23×C4—92no—
274C23×C4—184no—
275C23×C4—188no—
276C23×C4C2×C3⋊D311yescharacteristic
277#120—98no—
278C4×D4—188no—
279C4×D4—184no—
280C2×C4⋊C4—92no—
281C2×C4⋊C4—91no—
282C2×C22⋊C4—91no—
283C2×C22⋊C4—92no—
284C2×C22⋊C4—91no—
285C2×C22⋊C4—91no—
286C2×C22⋊C4—92no—
287C2×C22⋊C4—92no—
288C2×C22⋊C4C2×C3⋊D311yescharacteristic
289C2×C22⋊C4C2×C3⋊D312yescomplemented
290C2×C42—92no—
291C2×C42—91no—
292#95—92no—
293#95—92no—
294#95C2×C3⋊D312yescomplemented
295C23×C3—28no—
296C23×C3—28no—
297C23×C3—24no—
298C23×C3—28no—
299C23×C3—24no—
300C23×C3—28no—
301C23×C3C2×C4×D318yes—
302C23×C3C2×C4×D318yescomplemented
303C23×C3D3×D418yes—
304C23×C3#23718yes—
305C23×C3C23×D314yes—
306C22×D3—316no—
307C22×D3—316no—
308C22×D3—316no—
309C22×D3—664no—
310C22×D3—632no—
311C22×D3—632no—
312C22×D3—664no—
313C22×D3—632no—
314C22×D3—68no—
315C22×D3—68no—
316C22×D3—68no—
317C22×D3—68no—
318C3×D4—232no—
319C2×C3×C4—232no—
320C2×C3×C4—24no—
321C2×C3×C4—28no—
322C2×C3×C4—28no—
323C2×C3×C4—24no—
324C2×C3×C4—28no—
325C2×C3×C4—28no—
326C2×C3×C4—28no—
327C2×C3×C4C2×C4×D318yescomplemented
328C2×C3×C4D3×D4116yes—
329#67—664no—
330C2×Dic3—316no—
331C2×Dic3—38no—
332C2×Dic3—316no—
333C2×Dic3—38no—
334C2×Dic3—632no—
335C2×Dic3—68no—
336C2×Dic3—68no—
337C2×Dic3—68no—
338C2×Dic3—64no—
339C2×Dic3—68no—
340C2×Dic3—64no—
341C2×Dic3—68no—
342C2×Dic3—1216no—
343C4×D3—664no—
344C4×D3—664no—
345C2×C32—24no—
346C2×C32—42no—
347C2×C32C2×C4×D411yescharacteristic
348C2×C32C2×C4×D412yes—
349C2×C32C2×#12011yescharacteristic
350C2×C32#52511yescharacteristic
351C2×C32#52512yes—
352C3⋊D3—28no—
353C24—92no—
354C24—94no—
355C24—184no—
356C24—184no—
357C24—182no—
358C24—182no—
359C24C22×C3⋊D311yescharacteristic
360C24C22×C3⋊D311yescharacteristic
361C2×D4—22no—
362C2×D4—22no—
363C2×D4—98no—
364C2×D4—184no—
365C2×D4—184no—
366C2×D4C4×C3⋊D314yescomplemented
367C22×C4—22no—
368C22×C4—24no—
369C22×C4—91no—
370C22×C4—92no—
371C22×C4—91no—
372C22×C4—94no—
373C22×C4—98no—
374C22×C4—91no—
375C22×C4—91no—
376C22×C4—184no—
377C22×C4—184no—
378C22×C4—184no—
379C22×C4—184no—
380C22×C4—1832no—
381C22×C4—184no—
382C22×C4—184no—
383C22×C4—182no—
384C22×C4—184no—
385C22×C4C22×C3⋊D312yes—
386C22×C4C22×C3⋊D311yescharacteristic
387C22×C4C22×C3⋊D312yes—
388C4⋊C4—182no—
389C4⋊C4—184no—
390C22⋊C4—22no—
391C22⋊C4—24no—
392C22⋊C4—94no—
393C22⋊C4—98no—
394C22⋊C4—184no—
395C22⋊C4—184no—
396C22⋊C4—182no—
397C22⋊C4—182no—
398C42—182no—
399C42—184no—
400C22×C3—28no—
401C22×C3—216no—
402C22×C3—28no—
403C22×C3—216no—
404C22×C3—28no—
405C22×C3—216no—
406C22×C3—44no—
407C22×C3—44no—
408C22×C3—48no—
409C22×C3#67⋊C4116yescomplemented
410C22×C3C22×C4×D314yes—
411C22×C3C2×D3×D414yes—
412C22×C3C2×D3×D418yes—
413C22×C3C2×#23714yes—
414C22×C3D3×#4118yes—
415C2×D3—332no—
416C2×D3—6128no—
417C2×D3—616no—
418C2×D3—616no—
419C2×D3—616no—
420C2×D3—616no—
421C2×D3—616no—
422C2×D3—616no—
423C3×C4—28no—
424C3×C4—216no—
425C3×C4—48no—
426Dic3—316no—
427Dic3—616no—
428Dic3—68no—
429Dic3—124no—
430Dic3—124no—
431C32C4×#12011yescharacteristic, complemented, Sylow
432C23—22no—
433C23—22no—
434C23—22no—
435C23—21no—
436C23—21no—
437C23—22no—
438C23—94no—
439C23—94no—
440C23—94no—
441C23—1816no—
442C23—188no—
443C23—188no—
444C23—1816no—
445C23—188no—
446C23—182no—
447C23—182no—
448C23—182no—
449C23—182no—
450C23C2×C4×C3⋊D312yes—
451C23C2×C4×C3⋊D312yescomplemented
452C23D4×C3⋊D312yes—
453C23#383012yes—
454C23C23×C3⋊D311yescharacteristic
455D4—28no—
456D4—1816no—
457C2×C4—28no—
458C2×C4—21no—
459C2×C4—22no—
460C2×C4—22no—
461C2×C4—21no—
462C2×C4—22no—
463C2×C4—22no—
464C2×C4—22no—
465C2×C4—92no—
466C2×C4—94no—
467C2×C4—94no—
468C2×C4—92no—
469C2×C4—1816no—
470C2×C4—1816no—
471C2×C4—188no—
472C2×C4—182no—
473C2×C4—182no—
474C2×C4—182no—
475C2×C4—181no—
476C2×C4—181no—
477C2×C4—182no—
478C2×C4—182no—
479C2×C4—364no—
480C2×C4C2×C4×C3⋊D312yescomplemented
481C2×C4D4×C3⋊D314yes—
482C2×C3—216no—
483C2×C3—48no—
484C2×C3C2×#67⋊C414yes—
485C2×C3C4×D3×D418yes—
486C2×C3D3×#12014yes—
487C2×C3#560618yes—
488C2×C3#565614yes—
489D3—632no—
490C22—22no—
491C22—24no—
492C22—22no—
493C22—24no—
494C22—22no—
495C22—24no—
496C22—41no—
497C22—41no—
498C22—42no—
499C22—98no—
500C22—1832no—
501C22—184no—
502C22—184no—
503C22—184no—
504C22—184no—
505C22—184no—
506C22—184no—
507C22#6409014yescomplemented
508C22C22×C4×C3⋊D311yescharacteristic
509C22C2×D4×C3⋊D311yescharacteristic
510C22C2×D4×C3⋊D312yes—
511C22C2×#383011yescharacteristic
512C22#41×C3⋊D312yes—
513C4—22no—
514C4—24no—
515C4—42no—
516C4—94no—
517C4—184no—
518C4—182no—
519C4—361no—
520C4—361no—
521C3#7465914yescomplemented
522C2—24no—
523C2—42no—
524C2—188no—
525C2C2×#6409011yescharacteristic
526C2C4×D4×C3⋊D312yes—
527C2C3⋊D3×#12011yescharacteristic
528C2#1059607712yes—
529C2#1059612711yescharacteristic
subgroupG/H
center, FrattiniC23C23×C3⋊D3
commutatorC22×C32C23×C4
FittingC32×#386C2
socle, cosocleC23×C32C24
prime radicalC2×#64146C2
hypercenter#386C3⋊D3
hypocenterC32C4×#120
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ #386

Complements

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

NH ≅ G/Ntype
1. C23×C4×C3⋊D3C2semidirect
3. C2×D4×C3⋊Dic3C2semidirect
4. C2×#64090C2semidirect
5. C32×#386C2semidirect
6. #10592909C2semidirect
7. #10592655C2semidirect
8. #10592654C2semidirect
9. C22⋊C4×C3⋊Dic3C2semidirect
10. #10592367C2semidirect
11. #10592365C2semidirect
18. C23×C3⋊Dic3C22semidirect
24. C2×C32×C22⋊C4C22semidirect
27. C2×#3757C22semidirect
28. #64146C4semidirect
33. C2×C4⋊(C3⋊Dic3)C22semidirect
34. C2×#3750C22semidirect
35. C2×C4×C3⋊Dic3C22semidirect
36. C2×C4×C3⋊Dic3C22semidirect
38. C32×#95C22semidirect
39. #63658C22semidirect
40. #63658C22semidirect
45. C3×#386D3semidirect
58. C23×C3⋊D3C2×C4semidirect
62. C2×C32×D4C2×C4semidirect
70. C2×#638C2×C4semidirect
74. C22×C3⋊Dic3D4semidirect
86. C2×C4×C3⋊D3D4semidirect
91. #3757C2×C4semidirect
94. #3752C2×C4semidirect
111. C2×C3×C22⋊C4C2×D3semidirect
125. C3×#95C2×D3semidirect
135. C23×C32C22×C4semidirect
160. C2×C32×C4C22×C4semidirect
172. C2×C3⋊Dic3C22×C4semidirect
183. #386C3⋊D3semidirect
199. C2×C3×D4C4×D3semidirect
245. C22×C32C4×D4semidirect
258. C2×C3⋊D3C4×D4semidirect
266. C3⋊Dic3#120semidirect
289. C2×C22⋊C4C2×C3⋊D3semidirect
294. #95C2×C3⋊D3semidirect
302. C23×C3C2×C4×D3semidirect
327. C2×C3×C4C2×C4×D3semidirect
366. C2×D4C4×C3⋊D3semidirect
409. C22×C3#67⋊C4semidirect
431. C32C4×#120semidirect
451. C23C2×C4×C3⋊D3semidirect
480. C2×C4C2×C4×C3⋊D3semidirect
507. C22#64090semidirect
521. C3#74659semidirect

Maximal subgroups

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

subgroupindex
C23×C4×C3⋊D32
C2×#641462
C2×D4×C3⋊Dic32
C2×#640902
C32×#3862
#105929092
#105926552
#105926542
C22⋊C4×C3⋊Dic32
#105923672
#105923652
#746593