Finite Group Databasebeta

← #11807756

Subgroups — #11807756

Order 1152.

1269 conjugacy classes of subgroups.

The subgroup lattice has 574 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#930C211yesmaximal, characteristic
2#10592911C211yesmaximal, characteristic, complemented
3C3×#5211C211yesmaximal, characteristic, complemented
4#10591721C212yesmaximal, complemented
5#10591707C212yesmaximal, complemented
6#10591379C212yesmaximal, complemented
7#10591376C212yesmaximal, complemented
8#10591316C212yesmaximal, complemented
9#10591270C212yesmaximal, complemented
10#82639—31nomaximal
11#74124—31nomaximal
12C23×C32×C4C2211yescharacteristic
13C22×C3×#67C2212yes—
14C22×C3×D12C2211yescharacteristic
15C22×D3×Dic3C2212yes—
16C2×#3757C2211yescharacteristic
17C2×#3757C2211yescharacteristic
18C2×C4⋊(C3⋊Dic3)C2212yes—
19C2×C3×#217C2212yes—
20C3×#930C418yescomplemented
21C2×C3×(C2×D3)⋊C4C2212yes—
22C2×C3×C4⋊Dic3C2211yescharacteristic
23C2×Dic3⋊Dic3C2212yes—
24C2×(C2×D3)⋊Dic3C2212yes—
25C2×(C2×D3)⋊Dic3C2212yes—
26C2×(C2×D3)⋊Dic3C2212yes—
27C2×Dic32C2212yes—
28#63658C2212yes—
29C3×C3⋊#95C2212yes—
30C3×C3⋊#95C2211yescharacteristic
31C3×C3⋊#95C2211yescharacteristic
32#63579C2212yes—
33#63579C2212yes—
34C2×C3×#121—31no—
35C2×#930D311yescharacteristic
36C3×#381—31no—
37#5221—32no—
38#5220—32no—
39#5220—32no—
40#5212—31no—
41#5212—31no—
42#5212—61no—
43#5211D311yescharacteristic, complemented
44#4980—32no—
45#4957—32no—
46#4956—32no—
47#4951—32no—
48#4950—32no—
49#4670—32no—
50#4668—32no—
51#4665—32no—
52#4654—32no—
53C24×C32C2311yescharacteristic
54C23×C3×D3C2312yes—
55C22×C32×C4—42no—
56C22×C32×C4C2×C414yescomplemented
57C22×C32×C4C2311yescharacteristic
58C22×C32×C4C2311yescharacteristic
59C22×C3⋊Dic3C2312yes—
60C22×C3⋊Dic3C2312yes—
61C2×C3×#67—42no—
62C2×C3×#67—42no—
63C2×C3×#67C2×C418yescomplemented
64C22×C3×Dic3C2312yes—
65C22×C3×Dic3C2312yes—
66C22×C3×Dic3C2312yes—
67C2×C3×D12—42no—
68C2×C3×D12C2×C414yes—
69C2×D3×Dic3—42no—
70C2×D3×Dic3—42no—
71C2×D3×Dic3—42no—
72#3757—41no—
73#3757—41no—
74C4⋊(C3⋊Dic3)—42no—
75C3×#217—42no—
76C3×(C2×D3)⋊C4C2×C418yescomplemented
77C3×C4⋊Dic3C2×C414yescomplemented
78Dic3⋊Dic3—42no—
79(C2×D3)⋊Dic3—42no—
80(C2×D3)⋊Dic3—42no—
81(C2×D3)⋊Dic3—42no—
82Dic32—42no—
83#2377—91noSylow
84C22×C3×D4—32no—
85C22×C3×D4—31no—
86C23×C3×C4—21no—
87C23×C3×C4C2×D311yescharacteristic
88C23×C3×C4C2×D311yescharacteristic
89C22×#67C2×D312yes—
90C23×Dic3—32no—
91C22×D12C2×D311yescharacteristic
92C22×C4×D3—32no—
93C3×#121—38no—
94C2×C3×C4⋊C4—31no—
95C2×C3×C22⋊C4—32no—
96C2×C3×C22⋊C4—32no—
97C2×#217—31no—
98C2×#217—31no—
99C2×#217—31no—
100C2×#217—31no—
101C2×#217—32no—
102C2×#217—32no—
103C2×#217—32no—
104C2×#217—61no—
105C2×#217—61no—
106C2×#217C2×D312yes—
107#930Dic318yescomplemented
108C2×(C2×D3)⋊C4—32no—
109C2×(C2×D3)⋊C4—32no—
110C2×(C2×D3)⋊C4—32no—
111C2×(C2×D3)⋊C4C2×D312yes—
112C2×C4⋊Dic3—32no—
113C2×C4⋊Dic3—32no—
114C2×C4⋊Dic3—32no—
115C2×C4⋊Dic3—62no—
116C2×C4⋊Dic3C2×D311yescharacteristic
117C2×Dic3⋊C4—32no—
118C2×C4×Dic3—32no—
119C2×C4×Dic3—32no—
120C3×#95—32no—
121C3×#95—31no—
122C3×#95—31no—
123C3⋊#95—32no—
124C3⋊#95—32no—
125C3⋊#95—32no—
126C3⋊#95—32no—
127C3⋊#95—32no—
128C3⋊#95—32no—
129C3⋊#95—62no—
130C3⋊#95C2×D311yescharacteristic
131C3⋊#95C2×D311yescharacteristic
132C3⋊#95C2×D312yes—
133C23×C32—21no—
134C23×C32—21no—
135C23×C32—22no—
136C23×C32—22no—
137C23×C32C22×C412yes—
138C23×C32C2411yescharacteristic
139C22×C3×D3—22no—
140C22×C3×D3—22no—
141C22×C3×D3—22no—
142C22×C3×D3—22no—
143C22×C3×D3—22no—
144C22×C3×D3—22no—
145C22×C3×D3C22×C414yes—
146C2×C32×C4—22no—
147C2×C32×C4—22no—
148C2×C32×C4—44no—
149C2×C32×C4C22×C412yes—
150C2×C32×C4C22×C412yes—
151C2×C3⋊Dic3—22no—
152C2×C3⋊Dic3—22no—
153C2×C3⋊Dic3—22no—
154C2×C3⋊Dic3—22no—
155C2×C3⋊Dic3—22no—
156C2×C3⋊Dic3—22no—
157C3×#67—48no—
158C2×C3×Dic3—22no—
159C2×C3×Dic3—22no—
160C2×C3×Dic3—22no—
161C2×C3×Dic3—22no—
162C2×C3×Dic3—22no—
163C2×C3×Dic3—22no—
164C2×C3×Dic3—22no—
165C2×C3×Dic3—22no—
166C2×C3×Dic3C22×C414yes—
167C3×D12—44no—
168D3×Dic3—48no—
169C2×#121—31no—
170#390—92no—
171#388—92no—
172#387—92no—
173#386—92no—
174#386—92no—
175#385—92no—
176#381—31no—
177#380—91no—
178C24×C3—21no—
179C24×C3—32no—
180C24×C3C22×D311yescharacteristic
181C24×C3C22×D311yescharacteristic
182C23×D3C22×D312yes—
183C2×C3×D4—38no—
184C2×C3×D4—34no—
185C2×C3×D4—122no—
186C2×C3×D4—122no—
187C2×C3×D4—122no—
188C22×C3×C4—24no—
189C22×C3×C4—21no—
190C22×C3×C4—21no—
191C22×C3×C4—32no—
192C22×C3×C4—32no—
193C22×C3×C4—32no—
194C22×C3×C4—42no—
195C22×C3×C4—42no—
196C22×C3×C4—44no—
197C22×C3×C4C4×D314yescomplemented
198C22×C3×C4C2×Dic314yescomplemented
199C22×C3×C4C22×D311yescharacteristic
200C22×C3×C4C22×D311yescharacteristic
201C22×C3×C4C22×D311yescharacteristic
202C22×C3×C4C22×D311yescharacteristic
203C2×#67—42no—
204C2×#67—42no—
205C2×#67C2×Dic318yescomplemented
206C22×Dic3—32no—
207C22×Dic3—32no—
208C22×Dic3—32no—
209C22×Dic3—32no—
210C22×Dic3—62no—
211C22×Dic3—62no—
212C22×Dic3—122no—
213C22×Dic3—122no—
214C22×Dic3—122no—
215C22×Dic3C22×D312yes—
216C22×Dic3C22×D312yes—
217C22×Dic3C22×D312yes—
218C2×D12—42no—
219C2×D12C2×Dic314yes—
220C2×C4×D3—122no—
221C2×C4×D3—122no—
222C2×C4×D3—122no—
223C3×C4⋊C4—34no—
224C3×C22⋊C4—38no—
225C3×C22⋊C4—122no—
226#217—42no—
227#217—122no—
228#217—122no—
229#217—122no—
230#217—121no—
231#217—121no—
232#217—121no—
233#217—121no—
234#217—122no—
235#217—122no—
236(C2×D3)⋊C4—122no—
237(C2×D3)⋊C4—122no—
238(C2×D3)⋊C4—122no—
239(C2×D3)⋊C4C2×Dic318yescomplemented
240C4⋊Dic3—122no—
241C4⋊Dic3—122no—
242C4⋊Dic3—122no—
243C4⋊Dic3—124no—
244C4⋊Dic3C2×Dic314yescomplemented
245Dic3⋊C4—122no—
246C4×Dic3—122no—
247C4×Dic3—122no—
248C22×C32—22no—
249C22×C32—22no—
250C22×C32—22no—
251C22×C32—42no—
252C22×C32—42no—
253C22×C32C23×C411yescharacteristic
254C22×C32H(5,𝔽2)12yes—
255C22×C32H(5,𝔽2)12yes—
256C22×C32H(5,𝔽2)11yescharacteristic
257C22×C322−1+411yescharacteristic
258C2×C3×D3—24no—
259C2×C3×D3—24no—
260C2×C3×D3—24no—
261C2×C3×D3—42no—
262C2×C3×D3—42no—
263C2×C3×D3—42no—
264C2×C3×D3—42no—
265C32×C4—22no—
266C32×C4—22no—
267C3⋊Dic3—42no—
268C3⋊Dic3—42no—
269C3×Dic3—24no—
270C3×Dic3—42no—
271C3×Dic3—42no—
272C22×D4—32no—
273C22×D4—31no—
274C23×C4—92no—
275C23×C4D3211yescharacteristic
276#121—38no—
277C2×C4⋊C4—31no—
278C2×C4⋊C4—92no—
279C2×C4⋊C4—92no—
280C2×C22⋊C4—32no—
281C2×C22⋊C4—32no—
282C2×C22⋊C4—92no—
283C2×C22⋊C4—92no—
284C2×C22⋊C4—92no—
285C2×C22⋊C4—91no—
286C2×C22⋊C4—91no—
287C2×C42—92no—
288#95—31no—
289#95—32no—
290#95—31no—
291#95—92no—
292#95—92no—
293#95—92no—
294C23×C3—22no—
295C23×C3—22no—
296C23×C3—22no—
297C23×C3—22no—
298C23×C3—22no—
299C23×C3—21no—
300C23×C3—21no—
301C23×C3—22no—
302C23×C3—21no—
303C23×C3—21no—
304C23×C3—21no—
305C23×C3—22no—
306C23×C3—34no—
307C23×C3—42no—
308C23×C3—42no—
309C23×C3—62no—
310C23×C3—62no—
311C23×C3—62no—
312C23×C3—62no—
313C23×C3—62no—
314C23×C3—62no—
315C23×C3C2×C4×D312yes—
316C23×C3C22×Dic312yes—
317C23×C3C23×D311yescharacteristic
318C23×C3C23×D311yescharacteristic
319C22×D3—22no—
320C22×D3—22no—
321C22×D3—22no—
322C22×D3—22no—
323C22×D3—22no—
324C22×D3—22no—
325C22×D3C22×Dic314yes—
326C3×D4—124no—
327C3×D4—128no—
328C2×C3×C4—24no—
329C2×C3×C4—22no—
330C2×C3×C4—22no—
331C2×C3×C4—22no—
332C2×C3×C4—22no—
333C2×C3×C4—22no—
334C2×C3×C4—22no—
335C2×C3×C4—34no—
336C2×C3×C4—42no—
337C2×C3×C4—44no—
338C2×C3×C4—44no—
339C2×C3×C4—48no—
340C2×C3×C4—62no—
341C2×C3×C4—62no—
342C2×C3×C4—62no—
343C2×C3×C4—62no—
344C2×C3×C4—62no—
345C2×C3×C4—62no—
346C2×C3×C4—62no—
347C2×C3×C4—62no—
348C2×C3×C4C2×C4×D312yes—
349C2×C3×C4C2×C4×D312yes—
350C2×C3×C4C22×Dic312yes—
351C2×C3×C4C22×Dic312yes—
352#67—48no—
353C2×Dic3—22no—
354C2×Dic3—22no—
355C2×Dic3—22no—
356C2×Dic3—22no—
357C2×Dic3—22no—
358C2×Dic3—22no—
359C2×Dic3—22no—
360C2×Dic3—22no—
361C2×Dic3—62no—
362C2×Dic3—62no—
363C2×Dic3—62no—
364C2×Dic3—62no—
365C2×Dic3—62no—
366C2×Dic3—62no—
367C2×Dic3—62no—
368C2×Dic3—62no—
369C2×Dic3—62no—
370C2×Dic3—62no—
371C2×Dic3—62no—
372C2×Dic3—62no—
373C2×Dic3—122no—
374C2×Dic3—122no—
375C2×Dic3—122no—
376C2×Dic3—122no—
377C2×Dic3—122no—
378C2×Dic3—122no—
379C2×Dic3—128no—
380C2×Dic3C22×Dic314yes—
381D12—44no—
382C4×D3—128no—
383C2×C32—42no—
384C2×C32#51811yescharacteristic
385C2×C32#51811yescharacteristic
386C2×C32#52011yescharacteristic
387C2×C32#56012yes—
388C2×C32#56212yes—
389C3×D3—44no—
390C24—32no—
391C24C2×D3211yescharacteristic
392C2×D4—38no—
393C2×D4—34no—
394C2×D4—122no—
395C2×D4—122no—
396C2×D4—122no—
397C22×C4—32no—
398C22×C4—32no—
399C22×C4—32no—
400C22×C4—42no—
401C22×C4—92no—
402C22×C4—92no—
403C22×C4—362no—
404C22×C4—362no—
405C22×C4—362no—
406C22×C4D3×Dic314yescomplemented
407C22×C4C2×D3211yescharacteristic
408C22×C4C2×D3211yescharacteristic
409C4⋊C4—34no—
410C4⋊C4—362no—
411C4⋊C4—362no—
412C22⋊C4—38no—
413C22⋊C4—122no—
414C22⋊C4—362no—
415C22⋊C4—362no—
416C22⋊C4—362no—
417C22⋊C4—361no—
418C22⋊C4—361no—
419C42—362no—
420C22×C3—24no—
421C22×C3—22no—
422C22×C3—22no—
423C22×C3—22no—
424C22×C3—22no—
425C22×C3—22no—
426C22×C3—22no—
427C22×C3—21no—
428C22×C3—22no—
429C22×C3—21no—
430C22×C3—21no—
431C22×C3—22no—
432C22×C3—42no—
433C22×C3—42no—
434C22×C3—44no—
435C22×C3—44no—
436C22×C3—42no—
437C22×C3—42no—
438C22×C3—42no—
439C22×C3—42no—
440C22×C3—64no—
441C22×C3—64no—
442C22×C3—64no—
443C22×C3—122no—
444C22×C3—122no—
445C22×C3—122no—
446C22×C3—122no—
447C22×C3C22×C4×D311yescharacteristic
448C22×C3#100412yes—
449C22×C3#100412yes—
450C22×C3#100412yes—
451C22×C3#100912yes—
452C22×C3#100911yescharacteristic
453C22×C3#100911yescharacteristic
454C22×C3#101011yescharacteristic
455C22×C3#101011yescharacteristic
456C22×C3C23×Dic311yescharacteristic
457C2×D3—24no—
458C2×D3—24no—
459C2×D3—24no—
460C2×D3—42no—
461C2×D3—42no—
462C2×D3—42no—
463C2×D3—42no—
464C3×C4—24no—
465C3×C4—22no—
466C3×C4—22no—
467C3×C4—22no—
468C3×C4—22no—
469C3×C4—42no—
470C3×C4—64no—
471C3×C4—122no—
472C3×C4—122no—
473Dic3—24no—
474Dic3—42no—
475Dic3—42no—
476Dic3—122no—
477Dic3—122no—
478Dic3—122no—
479Dic3—122no—
480Dic3—242no—
481Dic3—242no—
482C32#237711yescharacteristic, complemented, Sylow
483C23—21no—
484C23—22no—
485C23—21no—
486C23—22no—
487C23—34no—
488C23—62no—
489C23—62no—
490C23—62no—
491C23—62no—
492C23—62no—
493C23—62no—
494C23C2×D3×Dic312yes—
495C23C22×D3211yescharacteristic
496D4—124no—
497D4—128no—
498C2×C4—22no—
499C2×C4—22no—
500C2×C4—34no—
501C2×C4—44no—
502C2×C4—62no—
503C2×C4—62no—
504C2×C4—62no—
505C2×C4—62no—
506C2×C4—62no—
507C2×C4—62no—
508C2×C4—62no—
509C2×C4—62no—
510C2×C4—182no—
511C2×C4—182no—
512C2×C4—182no—
513C2×C4—182no—
514C2×C4—182no—
515C2×C4—182no—
516C2×C4—368no—
517C2×C4C2×D3×Dic312yes—
518C2×C4C2×D3×Dic312yes—
519C2×C3—22no—
520C2×C3—22no—
521C2×C3—21no—
522C2×C3—21no—
523C2×C3—21no—
524C2×C3—44no—
525C2×C3—42no—
526C2×C3—42no—
527C2×C3—124no—
528C2×C3#548611yescharacteristic
529C2×C3#552111yescharacteristic
530C2×C3#552311yescharacteristic
531C2×C3#562012yes—
532C2×C3#562112yes—
533C2×C3#566612yes—
534C2×C3#566712yes—
535C2×C3#579811yescharacteristic
536C2×C3#579811yescharacteristic
537C2×C3#582711yescharacteristic
538D3—44no—
539C22—22no—
540C22—22no—
541C22—22no—
542C22—42no—
543C22—42no—
544C22—64no—
545C22—64no—
546C22—64no—
547C22—122no—
548C22—122no—
549C22—122no—
550C22—122no—
551C22#6429811yescharacteristic
552C22#6430712yes—
553C22#6430811yescharacteristic
554C22C22×D3×Dic311yescharacteristic
555C22#6433012yes—
556C4—22no—
557C4—22no—
558C4—64no—
559C4—122no—
560C4—122no—
561C4—362no—
562C4—362no—
563C3—21no—
564C3#7412411yescharacteristic, complemented
565C3#8263911yescharacteristic, complemented
566C2—42no—
567C2—124no—
568C2#1059497512yes—
569C2#1059498211yescharacteristic
570C2#1059499211yescharacteristic
571C2#1059509012yes—
572C2#1059550611yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC23×C32×C4C22
socle, cosocleC23×C32C24
prime radicalC2×C3×#930C2
hypercenterC23×C4D32
hypocenterC32#2377
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
2. #10592911C2semidirect
3. C3×#5211C2semidirect
4. #10591721C2semidirect
5. #10591707C2semidirect
6. #10591379C2semidirect
7. #10591376C2semidirect
8. #10591316C2semidirect
9. #10591270C2semidirect
20. C3×#930C4semidirect
43. #5211D3semidirect
56. C22×C32×C4C2×C4semidirect
63. C2×C3×#67C2×C4semidirect
76. C3×(C2×D3)⋊C4C2×C4semidirect
77. C3×C4⋊Dic3C2×C4semidirect
107. #930Dic3semidirect
197. C22×C3×C4C4×D3semidirect
198. C22×C3×C4C2×Dic3semidirect
205. C2×#67C2×Dic3semidirect
239. (C2×D3)⋊C4C2×Dic3semidirect
244. C4⋊Dic3C2×Dic3semidirect
406. C22×C4D3×Dic3semidirect
482. C32#2377semidirect
564. C3#74124semidirect
565. C3#82639semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#9302
#105929112
C3×#52112
#105917212
#105917072
#105913792
#105913762
#105913162
#105912702
#826393
#741243