Finite Group Databasebeta

← #11802787

Subgroups — #11802787

Order 1152.

1461 conjugacy classes of subgroups.

The subgroup lattice has 544 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63921C211yesmaximal, characteristic
2#10592366C211yesmaximal, characteristic, complemented
3C3×#4670C212yesmaximal, complemented
4#10591399C212yesmaximal
5#10591325C211yesmaximal, characteristic, complemented
6#10591307C212yesmaximal, complemented
7#10591281C212yesmaximal, complemented
8#10591280C212yesmaximal, complemented
9#10591233C212yesmaximal, complemented
10#75825—32nomaximal
11C23×D32C2211yescharacteristic
12C22×C4×C3⋊D3C2211yescharacteristic
13C22×#624C2211yescharacteristic
14C2×#3752C2212yes—
15C2×#3750C2212yescomplemented
16C2×C3×(C2×D3)⋊C4C2212yes—
17C2×C3×(C2×D3)⋊C4C2212yes—
18C2×C3×(C2×D3)⋊C4C2212yes—
19C2×C3×C4⋊Dic3C2212yescomplemented
20C2×C3×C4×Dic3C2212yescomplemented
21C2×#3722C2212yes—
22C2×(C2×D3)⋊Dic3C2212yes—
23C2×(C2×D3)⋊Dic3C2212yes—
24C2×(C2×D3)⋊Dic3C2212yes—
25C2×Dic32C2212yescomplemented
26#63921C418yescomplemented
27C32×#95C2211yescharacteristic, complemented
28#63658C2211yescharacteristic, complemented
29C3×C3⋊#95C2212yescomplemented
30#63579C2212yescomplemented
31#63579C2211yescharacteristic, complemented
32#63579C2211yescharacteristic, complemented
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#4940—32no—
43C4×(C2×D3)⋊C4—32no—
44#4670D312yescomplemented
45#4669—32no—
46#4667—32no—
47#4667—61no—
48#4666—32no—
49C23×C3⋊D3C2311yescharacteristic
50C23×C3×D3C2312yes—
51C22×D32—22no—
52C22×D32—22no—
53C22×D32—42no—
54C22×D32—42no—
55C22×D32C2×C414yes—
56C22×C32×C4C2312yes—
57C22×C32×C4C2311yescharacteristic
58C22×C3⋊Dic3C2312yes—
59C22×C3⋊Dic3C2311yescharacteristic
60C2×C4×C3⋊D3—42no—
61C2×C4×C3⋊D3C2×C414yes—
62C22×C3×Dic3C2312yes—
63C22×C3×Dic3C2312yes—
64C22×C3×Dic3C2312yes—
65C2×#624—42no—
66C2×#624C2×C414yes—
67#3752—24no—
68#3750—42no—
69C3×(C2×D3)⋊C4—42no—
70C3×(C2×D3)⋊C4—42no—
71C3×(C2×D3)⋊C4C2×C418yes—
72C3×C4⋊Dic3—42no—
73C3×C4×Dic3—42no—
74#3722—24no—
75(C2×D3)⋊Dic3—42no—
76(C2×D3)⋊Dic3—42no—
77(C2×D3)⋊Dic3C2×C418yes—
78Dic32—42no—
79#2312—91noSylow
80C24×D3—32no—
81C22×C4×D3—32no—
82C22×C4×D3—32no—
83C22×C4×D3—61no—
84C2×C3×C4⋊C4—32no—
85C2×C3×C22⋊C4—32no—
86C2×C3×C22⋊C4—32no—
87C2×C3×C22⋊C4—32no—
88C2×C3×C42—32no—
89C2×#217—32no—
90C2×#217—32no—
91C2×#217—32no—
92C2×(C2×D3)⋊C4—32no—
93C2×(C2×D3)⋊C4—32no—
94C2×(C2×D3)⋊C4—32no—
95C2×(C2×D3)⋊C4—32no—
96C2×(C2×D3)⋊C4—32no—
97C2×(C2×D3)⋊C4—32no—
98C2×(C2×D3)⋊C4—32no—
99C2×(C2×D3)⋊C4—62no—
100C2×(C2×D3)⋊C4C2×D312yes—
101C2×(C2×D3)⋊C4C2×D312yes—
102C2×(C2×D3)⋊C4C2×D312yes—
103C2×C4⋊Dic3C2×D312yescomplemented
104C2×Dic3⋊C4—32no—
105C2×Dic3⋊C4—32no—
106C2×Dic3⋊C4—62no—
107C2×C4×Dic3—32no—
108C2×C4×Dic3—32no—
109C2×C4×Dic3C2×D312yescomplemented
110D3×C22⋊C4—316no—
111C3×#95—21no—
112C3×#95—32no—
113C3×#95C2×D312yescomplemented
114C3⋊#95—32no—
115C3⋊#95—32no—
116C3⋊#95—32no—
117C3⋊#95—32no—
118C3⋊#95—32no—
119C3⋊#95—61no—
120C3⋊#95C2×D312yescomplemented
121C23×C32C2411yescharacteristic
122C22×C3⋊D3—22no—
123C22×C3⋊D3—22no—
124C22×C3⋊D3C22×C412yes—
125C22×C3⋊D3#4112yes—
126C22×C3⋊D3#4112yes—
127C22×C3×D3—22no—
128C22×C3×D3—22no—
129C22×C3×D3—22no—
130C22×C3×D3—22no—
131C22×C3×D3—22no—
132C22×C3×D3—22no—
133C22×C3×D3C22×C414yes—
134C2×D32—28no—
135C2×D32—44no—
136C2×D32—44no—
137C2×D32—48no—
138C2×D32—48no—
139C2×C32×C4—22no—
140C2×C32×C4—22no—
141C2×C32×C4—22no—
142C2×C32×C4—22no—
143C2×C32×C4C22×C412yes—
144C2×C3⋊Dic3—22no—
145C2×C3⋊Dic3—22no—
146C2×C3⋊Dic3—22no—
147C2×C3⋊Dic3—22no—
148C2×C3⋊Dic3C22×C412yes—
149C4×C3⋊D3—44no—
150C2×C3×Dic3—22no—
151C2×C3×Dic3—22no—
152C2×C3×Dic3—22no—
153C2×C3×Dic3—22no—
154C2×C3×Dic3—22no—
155C2×C3×Dic3—22no—
156C2×C3×Dic3—22no—
157C2×C3×Dic3—22no—
158C2×C3×Dic3C22×C414yes—
159#624—44no—
160C22×C22⋊C4—91no—
161#388—32no—
162#388—92no—
163#388—92no—
164#388—92no—
165#380—91no—
166#380—91no—
167#379—92no—
168C4×C22⋊C4—92no—
169C24×C3—32no—
170C23×D3—32no—
171C23×D3—38no—
172C23×D3—61no—
173C23×D3—64no—
174C23×D3—64no—
175C23×D3—122no—
176C23×D3—122no—
177C23×D3—122no—
178C23×D3—122no—
179C23×D3C22×D312yes—
180C22×C3×C4—21no—
181C22×C3×C4—22no—
182C22×C3×C4—32no—
183C22×C3×C4—32no—
184C22×C3×C4—32no—
185C22×C3×C4C22×D312yes—
186C22×C3×C4C22×D312yes—
187C22×C3×C4C22×D312yes—
188C22×Dic3—32no—
189C22×Dic3—32no—
190C22×Dic3—32no—
191C22×Dic3—61no—
192C22×Dic3—62no—
193C22×Dic3C22×D312yes—
194C22×Dic3C22×D312yes—
195C22×Dic3C22×D312yes—
196C2×C4×D3—38no—
197C2×C4×D3—38no—
198C2×C4×D3—64no—
199C2×C4×D3—122no—
200C2×C4×D3—122no—
201C2×C4×D3—122no—
202C2×C4×D3—122no—
203C2×C4×D3—124no—
204C3×C4⋊C4—122no—
205C3×C22⋊C4—38no—
206C3×C22⋊C4—122no—
207C3×C22⋊C4—122no—
208C3×C42—122no—
209#217—38no—
210#217—122no—
211#217—122no—
212(C2×D3)⋊C4—38no—
213(C2×D3)⋊C4—42no—
214(C2×D3)⋊C4—42no—
215(C2×D3)⋊C4—64no—
216(C2×D3)⋊C4—64no—
217(C2×D3)⋊C4—64no—
218(C2×D3)⋊C4—64no—
219(C2×D3)⋊C4—124no—
220(C2×D3)⋊C4—122no—
221(C2×D3)⋊C4—122no—
222(C2×D3)⋊C4C4×D318yes—
223C4⋊Dic3—42no—
224Dic3⋊C4—122no—
225Dic3⋊C4—122no—
226Dic3⋊C4—124no—
227C4×Dic3—42no—
228C4×Dic3—122no—
229C4×Dic3—122no—
230C22×C32C23×C411yescharacteristic
231C22×C32C2×#4111yescharacteristic
232C22×C32C2×#4111yescharacteristic
233C22×C32H(5,𝔽2)12yes—
234C22×C32H(5,𝔽2)12yes—
235C2×C3⋊D3—22no—
236C2×C3⋊D3—22no—
237C2×C3⋊D3—24no—
238C2×C3⋊D3—24no—
239C2×C3⋊D3#11714yes—
240C2×C3×D3—24no—
241C2×C3×D3—24no—
242C2×C3×D3—24no—
243C2×C3×D3—42no—
244C2×C3×D3—42no—
245C2×C3×D3—42no—
246C2×C3×D3—42no—
247D32—416no—
248C32×C4—22no—
249C32×C4—42no—
250C3⋊Dic3—22no—
251C3⋊Dic3—42no—
252C3×Dic3—24no—
253C3×Dic3—42no—
254C3×Dic3—42no—
255C25—91no—
256C23×C4—91no—
257C23×C4—91no—
258C2×C4⋊C4—32no—
259C2×C4⋊C4—92no—
260C2×C22⋊C4—32no—
261C2×C22⋊C4—32no—
262C2×C22⋊C4—32no—
263C2×C22⋊C4—98no—
264C2×C22⋊C4—92no—
265C2×C22⋊C4—92no—
266C2×C22⋊C4—92no—
267C2×C22⋊C4—92no—
268C2×C22⋊C4—92no—
269C2×C42—32no—
270C2×C42—92no—
271#95—32no—
272#95—92no—
273#95—91no—
274#95—91no—
275#95—91no—
276#95D3211yescharacteristic, complemented
277C23×C3—21no—
278C23×C3—34no—
279C23×C3—62no—
280C23×C3—62no—
281C23×C3—62no—
282C23×C3—62no—
283C23×C3—62no—
284C23×C3—62no—
285C23×C3C23×D312yes—
286C22×D3—22no—
287C22×D3—22no—
288C22×D3—22no—
289C22×D3—22no—
290C22×D3—22no—
291C22×D3—22no—
292C22×D3—34no—
293C22×D3—34no—
294C22×D3—34no—
295C22×D3—62no—
296C22×D3—62no—
297C22×D3—62no—
298C22×D3—616no—
299C22×D3—62no—
300C22×D3—62no—
301C22×D3—62no—
302C22×D3—62no—
303C22×D3—122no—
304C22×D3—122no—
305C22×D3—128no—
306C22×D3—128no—
307C22×D3—128no—
308C22×D3—128no—
309C22×D3—128no—
310C22×D3—128no—
311C22×D3C2×C4×D314yes—
312C2×C3×C4—22no—
313C2×C3×C4—22no—
314C2×C3×C4—22no—
315C2×C3×C4—22no—
316C2×C3×C4—22no—
317C2×C3×C4—22no—
318C2×C3×C4—22no—
319C2×C3×C4—22no—
320C2×C3×C4—22no—
321C2×C3×C4—34no—
322C2×C3×C4—42no—
323C2×C3×C4—42no—
324C2×C3×C4—42no—
325C2×C3×C4—42no—
326C2×C3×C4—62no—
327C2×C3×C4—62no—
328C2×C3×C4—62no—
329C2×C3×C4—62no—
330C2×C3×C4—62no—
331C2×C3×C4—62no—
332C2×C3×C4—62no—
333C2×C3×C4—62no—
334C2×C3×C4C2×C4×D314yes—
335C2×Dic3—22no—
336C2×Dic3—22no—
337C2×Dic3—22no—
338C2×Dic3—22no—
339C2×Dic3—22no—
340C2×Dic3—22no—
341C2×Dic3—22no—
342C2×Dic3—22no—
343C2×Dic3—34no—
344C2×Dic3—62no—
345C2×Dic3—64no—
346C2×Dic3—62no—
347C2×Dic3—62no—
348C2×Dic3—62no—
349C2×Dic3—62no—
350C2×Dic3—62no—
351C2×Dic3—62no—
352C2×Dic3—62no—
353C2×Dic3—62no—
354C2×Dic3—122no—
355C2×Dic3—122no—
356C2×Dic3—122no—
357C2×Dic3C2×C4×D314yes—
358C4×D3—128no—
359C4×D3—128no—
360C4×D3—128no—
361C2×C32C2×#11711yescharacteristic
362C2×C32#51811yescharacteristic
363C2×C32#51811yescharacteristic
364C2×C32#53812yes—
365C2×C32#53812yes—
366C3⋊D3—24no—
367C3×D3—44no—
368C24—32no—
369C24—94no—
370C24—91no—
371C24—182no—
372C24—182no—
373C24—362no—
374C24—362no—
375C22×C4—32no—
376C22×C4—32no—
377C22×C4—32no—
378C22×C4—94no—
379C22×C4—91no—
380C22×C4—94no—
381C22×C4—92no—
382C22×C4—362no—
383C22×C4—362no—
384C22×C4C2×D3212yes—
385C22×C4C2×D3211yescharacteristic
386C4⋊C4—122no—
387C4⋊C4—362no—
388C22⋊C4—38no—
389C22⋊C4—98no—
390C22⋊C4—122no—
391C22⋊C4—122no—
392C22⋊C4—184no—
393C22⋊C4—184no—
394C22⋊C4—362no—
395C22⋊C4—362no—
396C42—122no—
397C42—362no—
398C22×C3—21no—
399C22×C3—22no—
400C22×C3—21no—
401C22×C3—22no—
402C22×C3—21no—
403C22×C3—64no—
404C22×C3—64no—
405C22×C3—64no—
406C22×C3—122no—
407C22×C3—122no—
408C22×C3—122no—
409C22×C3—122no—
410C22×C3C22×C4×D312yes—
411C22×C3#100412yes—
412C22×C3#100412yes—
413C22×C3D3×#4112yes—
414C22×C3D3×#4112yes—
415C22×C3#100912yes—
416C22×C3#100912yes—
417C2×D3—24no—
418C2×D3—24no—
419C2×D3—24no—
420C2×D3—38no—
421C2×D3—42no—
422C2×D3—42no—
423C2×D3—42no—
424C2×D3—42no—
425C2×D3—64no—
426C2×D3—64no—
427C2×D3—64no—
428C2×D3—64no—
429C2×D3—64no—
430C2×D3—64no—
431C2×D3—64no—
432C2×D3—122no—
433C2×D3—124no—
434C2×D3—124no—
435C2×D3—122no—
436C2×D3—1232no—
437C3×C4—24no—
438C3×C4—42no—
439C3×C4—42no—
440C3×C4—42no—
441C3×C4—64no—
442C3×C4—82no—
443C3×C4—122no—
444C3×C4—122no—
445Dic3—24no—
446Dic3—42no—
447Dic3—42no—
448Dic3—64no—
449Dic3—64no—
450Dic3—122no—
451Dic3—122no—
452Dic3—242no—
453C32#231211yescharacteristic, complemented, Sylow
454C23—34no—
455C23—62no—
456C23—62no—
457C23—62no—
458C23—62no—
459C23—62no—
460C23—62no—
461C23—92no—
462C23—92no—
463C23—92no—
464C23—188no—
465C23—182no—
466C23—182no—
467C23—364no—
468C23—364no—
469C23—368no—
470C23—368no—
471C23C22×D3211yescharacteristic
472C2×C4—22no—
473C2×C4—22no—
474C2×C4—22no—
475C2×C4—22no—
476C2×C4—34no—
477C2×C4—62no—
478C2×C4—62no—
479C2×C4—62no—
480C2×C4—62no—
481C2×C4—62no—
482C2×C4—62no—
483C2×C4—62no—
484C2×C4—62no—
485C2×C4—92no—
486C2×C4—182no—
487C2×C4—182no—
488C2×C4—182no—
489C2×C4—182no—
490C2×C4—364no—
491C2×C4—364no—
492C2×C4C4×D3212yes—
493C2×C3—22no—
494C2×C3—21no—
495C2×C3—22no—
496C2×C3—21no—
497C2×C3—21no—
498C2×C3—124no—
499C2×C3D3×#11712yes—
500C2×C3#554512yes—
501C2×C3#554512yes—
502C2×C3#561312yes—
503C2×C3#565712yes—
504C2×C3#567812yes—
505C2×C3#570412yes—
506D3—44no—
507D3—68no—
508D3—124no—
509C22—64no—
510C22—64no—
511C22—64no—
512C22—94no—
513C22—122no—
514C22—122no—
515C22—122no—
516C22—122no—
517C22—184no—
518C22—184no—
519C22—182no—
520C22—182no—
521C22—3616no—
522C22C2×C4×D3211yescharacteristic
523C22#6430712yes—
524C22#6431211yescharacteristic
525C22#6431412yes—
526C22#6431911yescharacteristic
527C4—22no—
528C4—42no—
529C4—64no—
530C4—122no—
531C4—122no—
532C4—182no—
533C4—362no—
534C3—21no—
535C3#7582512yescomplemented
536C2—124no—
537C2—184no—
538C2#1059399611yescharacteristic
539C2#1059425611yescharacteristic
540C2#1059430712yes—
541C2#1059460211yescharacteristic
542C2#1059466012yes—
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC32×#95C22
socle, cosocleC23×C32C24
prime radicalC23×D32C22
hypercenter#95D32
hypocenterC32#2312
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ #95

Complements

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

NH ≅ G/Ntype
2. #10592366C2semidirect
3. C3×#4670C2semidirect
5. #10591325C2semidirect
6. #10591307C2semidirect
7. #10591281C2semidirect
8. #10591280C2semidirect
9. #10591233C2semidirect
15. C2×#3750C22semidirect
19. C2×C3×C4⋊Dic3C22semidirect
20. C2×C3×C4×Dic3C22semidirect
25. C2×Dic32C22semidirect
26. #63921C4semidirect
27. C32×#95C22semidirect
28. #63658C22semidirect
29. C3×C3⋊#95C22semidirect
30. #63579C22semidirect
31. #63579C22semidirect
32. #63579C22semidirect
44. #4670D3semidirect
103. C2×C4⋊Dic3C2×D3semidirect
109. C2×C4×Dic3C2×D3semidirect
113. C3×#95C2×D3semidirect
120. C3⋊#95C2×D3semidirect
276. #95D32semidirect
453. C32#2312semidirect
535. C3#75825semidirect

Maximal subgroups

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

subgroupindex
C2×#639212
#105923662
C3×#46702
#105913992
#105913252
#105913072
#105912812
#105912802
#105912332
#758253