Finite Group Databasebeta

← #11802768

Subgroups — #11802768

Order 1152.

1473 conjugacy classes of subgroups.

The subgroup lattice has 558 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63921C211yesmaximal, characteristic
2C4×#3752C211yesmaximal, characteristic, complemented
3C3×#4940C212yesmaximal, complemented
4#10591399C212yesmaximal
5#10591367C212yesmaximal, complemented
6#10591286C212yesmaximal, complemented
7#10591285C212yesmaximal, complemented
8#10591284C212yesmaximal, complemented
9#10591260C211yesmaximal, characteristic, complemented
10#75825—32nomaximal
11C23×D32C2211yescharacteristic
12C22×C4×C3⋊D3C2211yescharacteristic
13C22×#624C2211yescharacteristic
14C2×C32×C42C2211yescharacteristic, complemented
15C2×#3752C2212yes—
16C2×C4×C3⋊Dic3C2211yescharacteristic, complemented
17C2×C3×(C2×D3)⋊C4C2212yes—
18C2×C3×(C2×D3)⋊C4C2212yes—
19C2×C3×(C2×D3)⋊C4C2212yes—
20C2×C3×Dic3⋊C4C2212yescomplemented
21C2×Dic3⋊Dic3C2212yescomplemented
22C2×#3722C2212yes—
23C2×(C2×D3)⋊Dic3C2212yes—
24C2×(C2×D3)⋊Dic3C2212yes—
25C2×(C2×D3)⋊Dic3C2212yes—
26C2×Dic32C2211yescharacteristic, complemented
27C2×Dic32C2211yescharacteristic, complemented
28#63921C418yescomplemented
29#63658C2212yescomplemented
30C3×C3⋊#95C2212yescomplemented
31C3×C3⋊#95C2212yescomplemented
32#63579C2212yescomplemented
33C2×D3×C22⋊C4—32no—
34C3×#388—32no—
35#4990—32no—
36#4987—32no—
37#4955—32no—
38#4955—32no—
39#4951—32no—
40#4945—32no—
41#4944—32no—
42#4940D312yescomplemented
43C4×(C2×D3)⋊C4—32no—
44C4×(C2×D3)⋊C4—61no—
45#4670—32no—
46#4669—32no—
47#4667—32no—
48#4666—32no—
49C23×C3⋊D3C2311yescharacteristic
50C23×C3×D3C2312yes—
51C22×D32—24no—
52C22×D32—41no—
53C22×D32—42no—
54C22×D32—41no—
55C22×D32C2×C414yes—
56C22×C32×C4C2312yes—
57C22×C32×C4C2311yescharacteristic
58C22×C3⋊Dic3C2312yes—
59C22×C3⋊Dic3C2311yescharacteristic
60C2×C4×C3⋊D3—41no—
61C2×C4×C3⋊D3—41no—
62C2×C4×C3⋊D3C2×C414yes—
63C22×C3×Dic3C2312yes—
64C22×C3×Dic3C2312yes—
65C22×C3×Dic3C2312yes—
66C2×#624—42no—
67C2×#624C2×C414yes—
68C32×C42—41no—
69#3752—24no—
70C4×C3⋊Dic3—41no—
71C3×(C2×D3)⋊C4—42no—
72C3×(C2×D3)⋊C4—42no—
73C3×(C2×D3)⋊C4C2×C418yes—
74C3×Dic3⋊C4—42no—
75Dic3⋊Dic3—42no—
76#3722—24no—
77(C2×D3)⋊Dic3—42no—
78(C2×D3)⋊Dic3—42no—
79(C2×D3)⋊Dic3C2×C418yes—
80Dic32—41no—
81Dic32—41no—
82#2312—91noSylow
83C24×D3—32no—
84C22×C4×D3—32no—
85C22×C4×D3—32no—
86C22×C4×D3—61no—
87C2×C3×C4⋊C4—32no—
88C2×C3×C22⋊C4—32no—
89C2×C3×C22⋊C4—32no—
90C2×C3×C22⋊C4—32no—
91C2×C3×C42—21no—
92C2×C3×C42C2×D312yescomplemented
93C2×#217—32no—
94C2×#217—32no—
95C2×#217—32no—
96C2×(C2×D3)⋊C4—32no—
97C2×(C2×D3)⋊C4—32no—
98C2×(C2×D3)⋊C4—32no—
99C2×(C2×D3)⋊C4—32no—
100C2×(C2×D3)⋊C4—32no—
101C2×(C2×D3)⋊C4—32no—
102C2×(C2×D3)⋊C4—32no—
103C2×(C2×D3)⋊C4—62no—
104C2×(C2×D3)⋊C4C2×D312yes—
105C2×(C2×D3)⋊C4C2×D312yes—
106C2×(C2×D3)⋊C4C2×D312yes—
107C2×C4⋊Dic3—32no—
108C2×Dic3⋊C4—32no—
109C2×Dic3⋊C4C2×D312yescomplemented
110C2×C4×Dic3—32no—
111C2×C4×Dic3—32no—
112C2×C4×Dic3—32no—
113C2×C4×Dic3—61no—
114D3×C22⋊C4—316no—
115C3×#95—32no—
116C3×#95—32no—
117C3⋊#95—32no—
118C3⋊#95—32no—
119C3⋊#95—32no—
120C3⋊#95—32no—
121C3⋊#95—62no—
122C3⋊#95C2×D312yescomplemented
123C3⋊#95C2×D312yescomplemented
124C23×C32C2411yescharacteristic
125C22×C3⋊D3—22no—
126C22×C3⋊D3—21no—
127C22×C3⋊D3—21no—
128C22×C3⋊D3C22×C412yes—
129C22×C3⋊D3#4114yes—
130C22×C3×D3—22no—
131C22×C3×D3—22no—
132C22×C3×D3—22no—
133C22×C3×D3—22no—
134C22×C3×D3—22no—
135C22×C3×D3—22no—
136C22×C3×D3C22×C414yes—
137C2×D32—28no—
138C2×D32—44no—
139C2×D32—44no—
140C2×D32—48no—
141C2×D32—48no—
142C2×C32×C4—21no—
143C2×C32×C4—21no—
144C2×C32×C4—22no—
145C2×C32×C4—22no—
146C2×C32×C4—22no—
147C2×C32×C4C22×C412yes—
148C2×C3⋊Dic3—22no—
149C2×C3⋊Dic3—21no—
150C2×C3⋊Dic3—21no—
151C2×C3⋊Dic3—22no—
152C2×C3⋊Dic3—22no—
153C2×C3⋊Dic3C22×C412yes—
154C4×C3⋊D3—44no—
155C2×C3×Dic3—22no—
156C2×C3×Dic3—22no—
157C2×C3×Dic3—22no—
158C2×C3×Dic3—22no—
159C2×C3×Dic3—22no—
160C2×C3×Dic3—22no—
161C2×C3×Dic3—22no—
162C2×C3×Dic3—22no—
163C2×C3×Dic3C22×C414yes—
164#624—44no—
165C22×C22⋊C4—91no—
166#388—32no—
167#388—92no—
168#388—92no—
169#388—92no—
170#380—92no—
171#379—92no—
172C4×C22⋊C4—91no—
173C4×C22⋊C4—91no—
174C24×C3—32no—
175C23×D3—32no—
176C23×D3—38no—
177C23×D3—61no—
178C23×D3—64no—
179C23×D3—64no—
180C23×D3—122no—
181C23×D3—122no—
182C23×D3—122no—
183C23×D3—122no—
184C23×D3C22×D312yes—
185C22×C3×C4—21no—
186C22×C3×C4—22no—
187C22×C3×C4—32no—
188C22×C3×C4—32no—
189C22×C3×C4—32no—
190C22×C3×C4C22×D312yes—
191C22×C3×C4C22×D312yes—
192C22×C3×C4C22×D312yes—
193C22×Dic3—32no—
194C22×Dic3—32no—
195C22×Dic3—32no—
196C22×Dic3—61no—
197C22×Dic3—62no—
198C22×Dic3C22×D312yes—
199C22×Dic3C22×D312yes—
200C22×Dic3C22×D312yes—
201C2×C4×D3—38no—
202C2×C4×D3—38no—
203C2×C4×D3—64no—
204C2×C4×D3—122no—
205C2×C4×D3—122no—
206C2×C4×D3—122no—
207C2×C4×D3—122no—
208C2×C4×D3—122no—
209C2×C4×D3—122no—
210C3×C4⋊C4—122no—
211C3×C22⋊C4—38no—
212C3×C22⋊C4—122no—
213C3×C22⋊C4—122no—
214C3×C42—42no—
215C3×C42—42no—
216#217—38no—
217#217—122no—
218#217—122no—
219(C2×D3)⋊C4—38no—
220(C2×D3)⋊C4—42no—
221(C2×D3)⋊C4—42no—
222(C2×D3)⋊C4—64no—
223(C2×D3)⋊C4—64no—
224(C2×D3)⋊C4—64no—
225(C2×D3)⋊C4—64no—
226(C2×D3)⋊C4—68no—
227(C2×D3)⋊C4—122no—
228(C2×D3)⋊C4—122no—
229(C2×D3)⋊C4C4×D318yes—
230C4⋊Dic3—122no—
231Dic3⋊C4—42no—
232Dic3⋊C4—122no—
233C4×Dic3—122no—
234C4×Dic3—122no—
235C4×Dic3—122no—
236C4×Dic3—122no—
237C22×C32C23×C411yescharacteristic
238C22×C32C2×#4112yes—
239C22×C32H(5,𝔽2)11yescharacteristic
240C22×C32H(5,𝔽2)12yes—
241C22×C32H(5,𝔽2)11yescharacteristic
242C2×C3⋊D3—22no—
243C2×C3⋊D3—22no—
244C2×C3⋊D3—24no—
245C2×C3⋊D3—24no—
246C2×C3⋊D3#11714yes—
247C2×C3×D3—24no—
248C2×C3×D3—24no—
249C2×C3×D3—24no—
250C2×C3×D3—42no—
251C2×C3×D3—42no—
252C2×C3×D3—42no—
253C2×C3×D3—42no—
254D32—416no—
255C32×C4—22no—
256C32×C4—42no—
257C3⋊Dic3—22no—
258C3⋊Dic3—42no—
259C3×Dic3—24no—
260C3×Dic3—42no—
261C3×Dic3—42no—
262C25—91no—
263C23×C4—91no—
264C23×C4—91no—
265C2×C4⋊C4—32no—
266C2×C4⋊C4—92no—
267C2×C22⋊C4—32no—
268C2×C22⋊C4—32no—
269C2×C22⋊C4—32no—
270C2×C22⋊C4—98no—
271C2×C22⋊C4—92no—
272C2×C22⋊C4—92no—
273C2×C22⋊C4—92no—
274C2×C22⋊C4—92no—
275C2×C22⋊C4—92no—
276C2×C42—91no—
277C2×C42—91no—
278C2×C42—91no—
279C2×C42D3211yescharacteristic, complemented
280#95—32no—
281#95—32no—
282#95—92no—
283#95—92no—
284C23×C3—21no—
285C23×C3—34no—
286C23×C3—62no—
287C23×C3—62no—
288C23×C3—62no—
289C23×C3—62no—
290C23×C3—62no—
291C23×C3—62no—
292C23×C3C23×D312yes—
293C22×D3—22no—
294C22×D3—22no—
295C22×D3—22no—
296C22×D3—22no—
297C22×D3—22no—
298C22×D3—22no—
299C22×D3—34no—
300C22×D3—34no—
301C22×D3—34no—
302C22×D3—62no—
303C22×D3—64no—
304C22×D3—616no—
305C22×D3—62no—
306C22×D3—62no—
307C22×D3—62no—
308C22×D3—62no—
309C22×D3—121no—
310C22×D3—121no—
311C22×D3—122no—
312C22×D3—128no—
313C22×D3—128no—
314C22×D3—128no—
315C22×D3—128no—
316C22×D3—128no—
317C22×D3—128no—
318C22×D3C2×C4×D314yes—
319C2×C3×C4—22no—
320C2×C3×C4—22no—
321C2×C3×C4—22no—
322C2×C3×C4—22no—
323C2×C3×C4—24no—
324C2×C3×C4—22no—
325C2×C3×C4—22no—
326C2×C3×C4—22no—
327C2×C3×C4—22no—
328C2×C3×C4—22no—
329C2×C3×C4—22no—
330C2×C3×C4—22no—
331C2×C3×C4—34no—
332C2×C3×C4—42no—
333C2×C3×C4—42no—
334C2×C3×C4—62no—
335C2×C3×C4—62no—
336C2×C3×C4—62no—
337C2×C3×C4—62no—
338C2×C3×C4—62no—
339C2×C3×C4—62no—
340C2×C3×C4—62no—
341C2×C3×C4—62no—
342C2×C3×C4C2×C4×D314yes—
343C2×Dic3—22no—
344C2×Dic3—22no—
345C2×Dic3—22no—
346C2×Dic3—22no—
347C2×Dic3—22no—
348C2×Dic3—22no—
349C2×Dic3—22no—
350C2×Dic3—22no—
351C2×Dic3—34no—
352C2×Dic3—62no—
353C2×Dic3—62no—
354C2×Dic3—62no—
355C2×Dic3—64no—
356C2×Dic3—62no—
357C2×Dic3—62no—
358C2×Dic3—62no—
359C2×Dic3—62no—
360C2×Dic3—62no—
361C2×Dic3—62no—
362C2×Dic3—122no—
363C2×Dic3—121no—
364C2×Dic3—121no—
365C2×Dic3—122no—
366C2×Dic3C2×C4×D314yes—
367C4×D3—128no—
368C4×D3—128no—
369C4×D3—128no—
370C2×C32C2×#11711yescharacteristic
371C2×C32#51811yescharacteristic
372C2×C32#51811yescharacteristic
373C2×C32#53812yes—
374C2×C32#53812yes—
375C3⋊D3—24no—
376C3×D3—44no—
377C24—32no—
378C24—94no—
379C24—91no—
380C24—184no—
381C24—362no—
382C24—361no—
383C24—361no—
384C22×C4—32no—
385C22×C4—32no—
386C22×C4—32no—
387C22×C4—94no—
388C22×C4—91no—
389C22×C4—94no—
390C22×C4—92no—
391C22×C4—361no—
392C22×C4—361no—
393C22×C4—362no—
394C22×C4C2×D3212yes—
395C22×C4C2×D3211yescharacteristic
396C4⋊C4—122no—
397C4⋊C4—362no—
398C22⋊C4—38no—
399C22⋊C4—98no—
400C22⋊C4—122no—
401C22⋊C4—122no—
402C22⋊C4—184no—
403C22⋊C4—184no—
404C22⋊C4—362no—
405C22⋊C4—362no—
406C42—41no—
407C42—361no—
408C42—361no—
409C42—361no—
410C22×C3—21no—
411C22×C3—22no—
412C22×C3—22no—
413C22×C3—21no—
414C22×C3—21no—
415C22×C3—64no—
416C22×C3—64no—
417C22×C3—64no—
418C22×C3—122no—
419C22×C3—122no—
420C22×C3—122no—
421C22×C3—122no—
422C22×C3C22×C4×D312yes—
423C22×C3#100412yes—
424C22×C3#100412yes—
425C22×C3D3×#4112yes—
426C22×C3D3×#4112yes—
427C22×C3#100912yes—
428C22×C3#100912yes—
429C2×D3—24no—
430C2×D3—24no—
431C2×D3—24no—
432C2×D3—38no—
433C2×D3—42no—
434C2×D3—42no—
435C2×D3—42no—
436C2×D3—42no—
437C2×D3—64no—
438C2×D3—64no—
439C2×D3—64no—
440C2×D3—64no—
441C2×D3—64no—
442C2×D3—64no—
443C2×D3—64no—
444C2×D3—122no—
445C2×D3—124no—
446C2×D3—122no—
447C2×D3—124no—
448C2×D3—1232no—
449C3×C4—24no—
450C3×C4—24no—
451C3×C4—44no—
452C3×C4—42no—
453C3×C4—42no—
454C3×C4—64no—
455C3×C4—122no—
456C3×C4—122no—
457Dic3—24no—
458Dic3—42no—
459Dic3—42no—
460Dic3—64no—
461Dic3—122no—
462Dic3—124no—
463Dic3—122no—
464Dic3—122no—
465C32#231211yescharacteristic, complemented, Sylow
466C23—34no—
467C23—62no—
468C23—62no—
469C23—62no—
470C23—62no—
471C23—62no—
472C23—62no—
473C23—92no—
474C23—94no—
475C23—188no—
476C23—182no—
477C23—181no—
478C23—181no—
479C23—364no—
480C23—364no—
481C23—368no—
482C23—368no—
483C23C22×D3211yescharacteristic
484C2×C4—21no—
485C2×C4—21no—
486C2×C4—22no—
487C2×C4—22no—
488C2×C4—22no—
489C2×C4—34no—
490C2×C4—62no—
491C2×C4—62no—
492C2×C4—62no—
493C2×C4—62no—
494C2×C4—62no—
495C2×C4—62no—
496C2×C4—62no—
497C2×C4—62no—
498C2×C4—92no—
499C2×C4—181no—
500C2×C4—181no—
501C2×C4—182no—
502C2×C4—182no—
503C2×C4—182no—
504C2×C4—364no—
505C2×C4—364no—
506C2×C4C4×D3212yes—
507C2×C3—22no—
508C2×C3—21no—
509C2×C3—21no—
510C2×C3—22no—
511C2×C3—21no—
512C2×C3—124no—
513C2×C3D3×#11712yes—
514C2×C3#554512yes—
515C2×C3#554512yes—
516C2×C3#561312yes—
517C2×C3#565712yes—
518C2×C3#567812yes—
519C2×C3#570412yes—
520D3—44no—
521D3—68no—
522D3—124no—
523C22—64no—
524C22—64no—
525C22—64no—
526C22—94no—
527C22—122no—
528C22—122no—
529C22—122no—
530C22—122no—
531C22—184no—
532C22—182no—
533C22—184no—
534C22—182no—
535C22—3616no—
536C22C2×C4×D3211yescharacteristic
537C22#6430612yes—
538C22#6430712yes—
539C22#6430811yescharacteristic
540C22#6433011yescharacteristic
541C4—22no—
542C4—42no—
543C4—64no—
544C4—122no—
545C4—122no—
546C4—182no—
547C4—362no—
548C3—21no—
549C3#7582512yescomplemented
550C2—124no—
551C2—184no—
552C2#1059399211yescharacteristic
553C2#1059399611yescharacteristic
554C2#1059401912yes—
555C2#1059505811yescharacteristic
556C2#1059508912yes—
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC2×C32×C42C22
socle, cosocleC23×C32C24
prime radicalC23×D32C22
hypercenterC2×C42D32
hypocenterC32#2312
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
2. C4×#3752C2semidirect
3. C3×#4940C2semidirect
5. #10591367C2semidirect
6. #10591286C2semidirect
7. #10591285C2semidirect
8. #10591284C2semidirect
9. #10591260C2semidirect
14. C2×C32×C42C22semidirect
16. C2×C4×C3⋊Dic3C22semidirect
20. C2×C3×Dic3⋊C4C22semidirect
21. C2×Dic3⋊Dic3C22semidirect
26. C2×Dic32C22semidirect
27. C2×Dic32C22semidirect
28. #63921C4semidirect
29. #63658C22semidirect
30. C3×C3⋊#95C22semidirect
31. C3×C3⋊#95C22semidirect
32. #63579C22semidirect
42. #4940D3semidirect
92. C2×C3×C42C2×D3semidirect
109. C2×Dic3⋊C4C2×D3semidirect
122. C3⋊#95C2×D3semidirect
123. C3⋊#95C2×D3semidirect
279. C2×C42D32semidirect
465. C32#2312semidirect
549. C3#75825semidirect

Maximal subgroups

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

subgroupindex
C2×#639212
C4×#37522
C3×#49402
#105913992
#105913672
#105912862
#105912852
#105912842
#105912602
#758253