Finite Group Databasebeta

← #11803868

Subgroups — #11803868

Order 1152.

1557 conjugacy classes of subgroups.

The subgroup lattice has 534 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#893C211yesmaximal, characteristic, complemented
2C2×#63914C211yesmaximal, characteristic
3C2×Dic3×D12C211yesmaximal, characteristic, complemented
4#10592676C211yesmaximal, characteristic, complemented
5C3×#4988C211yesmaximal, characteristic, complemented
6#10591381C214yesmaximal, complemented
7#10591363C214yesmaximal, complemented
8#10591318C211yesmaximal, characteristic, complemented
9#10591222C211yesmaximal, characteristic, complemented
10#82329—31nomaximal
11#76298—31nomaximal
12C22×C3×D12C2211yescharacteristic
13C22×C3×D12C2211yescharacteristic
14C22×C3×C4×D3C2212yes—
15C22×#625C2214yes—
16C22×D3×Dic3C2212yes—
17C2×C32×C4⋊C4C2211yescharacteristic
18C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
19C2×C4×C3⋊Dic3C2211yescharacteristic
20C2×C3×(C2×D3)⋊C4C2212yes—
21C2×C3×(C2×D3)⋊C4C2214yes—
22C2×C3×C4×Dic3C2211yescharacteristic
23C2×C3×C4×Dic3C2211yescharacteristic
24C3×#893—24no—
25C2×(C2×D3)⋊Dic3C2212yes—
26C2×(C2×D3)⋊Dic3C2214yes—
27#63914C418yescomplemented
28Dic3×D12—24no—
29#63658C2214yes—
30#63579C2212yes—
31#63579C2212yes—
32C2×C3×C4×D4—31no—
33C2×#940—31no—
34C2×#940—31no—
35C2×D4×Dic3—31no—
36C2×#893D311yescharacteristic, complemented
37C2×C4×D12—31no—
38C3×#390—31no—
39#5221—31no—
40#5213—34no—
41#4988D311yescharacteristic, complemented
42#4977—31no—
43#4977—31no—
44#4977—61no—
45#4958—34no—
46#4956—34no—
47#4956—34no—
48#4939—31no—
49#4932—31no—
50#4932—31no—
51C23×C3×D3C2312yes—
52C23×C3×D3C2312yes—
53C22×C32×C4C2312yes—
54C22×C32×C4C2311yescharacteristic
55C22×C3⋊Dic3C2312yes—
56C22×C3⋊Dic3C2312yes—
57C22×C3×Dic3C2312yes—
58C22×C3×Dic3C2311yescharacteristic
59C22×C3×Dic3C2311yescharacteristic
60C2×C3×D12—22no—
61C2×C3×D12—22no—
62C2×C3×D12—22no—
63C2×C3×D12—22no—
64C2×C3×D12C2×C414yescomplemented
65C2×C3×D12C2×C414yescomplemented
66C2×C3×C4×D3—24no—
67C2×C3×C4×D3—44no—
68C2×#625—44no—
69C2×#625—44no—
70C2×#625C2×C4116yescomplemented
71C2×D3×Dic3—24no—
72C2×D3×Dic3—44no—
73C32×C4⋊C4—22no—
74C4⋊(C3⋊Dic3)—22no—
75C4×C3⋊Dic3C2×C414yescomplemented
76C3×(C2×D3)⋊C4—24no—
77C3×(C2×D3)⋊C4—44no—
78C3×C4×Dic3—22no—
79C3×C4×Dic3D414yescomplemented
80(C2×D3)⋊Dic3—24no—
81(C2×D3)⋊Dic3—44no—
82#2328—91noSylow
83C22×C3×D4—31no—
84C22×C3×D4—31no—
85C23×C3×C4—32no—
86C22×#67—34no—
87C22×#67—34no—
88C23×Dic3—32no—
89C22×D12C2×D311yescharacteristic
90C22×D12C2×D311yescharacteristic
91C22×C4×D3—32no—
92C22×C4×D3C2×D312yes—
93C3×C4×D4—64no—
94C2×C3×C4⋊C4—21no—
95C2×C3×C4⋊C4C2×D311yescharacteristic
96C2×C3×C4⋊C4C2×D311yescharacteristic
97C2×C3×C22⋊C4—32no—
98C2×C3×C22⋊C4—34no—
99C2×C3×C42—31no—
100C2×C3×C42—31no—
101C2×#217—32no—
102C2×#217—34no—
103#940—38no—
104#940—38no—
105D4×Dic3—64no—
106C2×(C2×D3)⋊C4—32no—
107C2×(C2×D3)⋊C4—34no—
108C2×(C2×D3)⋊C4C2×D312yes—
109C2×(C2×D3)⋊C4C2×D314yes—
110C2×C4⋊Dic3—31no—
111C2×C4⋊Dic3—31no—
112C2×C4⋊Dic3—61no—
113C2×C4×Dic3—31no—
114C2×C4×Dic3—31no—
115C2×C4×Dic3—61no—
116C2×C4×Dic3C2×D311yescharacteristic
117C2×C4×Dic3C2×D311yescharacteristic
118#893—24no—
119C4×D12—64no—
120C3⋊#95—34no—
121C3⋊#95—34no—
122C3⋊#95—32no—
123C3⋊#95—32no—
124C3⋊#95—32no—
125C3⋊#95—32no—
126C3⋊#95—64no—
127C23×C32C2411yescharacteristic
128C22×C3×D3—22no—
129C22×C3×D3—22no—
130C22×C3×D3—22no—
131C22×C3×D3—22no—
132C22×C3×D3—24no—
133C22×C3×D3—24no—
134C22×C3×D3—24no—
135C22×C3×D3—24no—
136C22×C3×D3C22×C414yes—
137C22×C3×D3C22×C414yes—
138C2×C32×C4—22no—
139C2×C32×C4—24no—
140C2×C32×C4C22×C412yes—
141C2×C32×C4C2×D412yes—
142C2×C32×C4#4112yes—
143C2×C3⋊Dic3—22no—
144C2×C3⋊Dic3—22no—
145C2×C3⋊Dic3—22no—
146C2×C3⋊Dic3—24no—
147C2×C3⋊Dic3C22×C414yes—
148C2×C3×Dic3—22no—
149C2×C3×Dic3—22no—
150C2×C3×Dic3—22no—
151C2×C3×Dic3—22no—
152C2×C3×Dic3—22no—
153C2×C3×Dic3C2×D412yes—
154C2×C3×Dic3C2×D412yes—
155C3×D12—28no—
156C3×D12—28no—
157C3×C4×D3—48no—
158#625—416no—
159D3×Dic3—48no—
160C2×#127—91no—
161C2×C4×D4—31no—
162C2×C4×D4—91no—
163#390—31no—
164#390—91no—
165#386—94no—
166#386—94no—
167#382—91no—
168#376—91no—
169C24×C3—32no—
170C24×C3—32no—
171C23×D3C22×D312yes—
172C23×D3C22×D312yes—
173C2×C3×D4—34no—
174C2×C3×D4—34no—
175C2×C3×D4—62no—
176C2×C3×D4—62no—
177C2×C3×D4—62no—
178C2×C3×D4—62no—
179C22×C3×C4—21no—
180C22×C3×C4—22no—
181C22×C3×C4—31no—
182C22×C3×C4—31no—
183C22×C3×C4—32no—
184C22×C3×C4—64no—
185C22×C3×C4—124no—
186C22×C3×C4C22×D312yes—
187C22×C3×C4C22×D312yes—
188C22×C3×C4C22×D311yescharacteristic
189C22×C3×C4C22×D311yescharacteristic
190C2×#67—316no—
191C2×#67—316no—
192C2×#67—124no—
193C2×#67—124no—
194C2×#67—124no—
195C2×#67—124no—
196C22×Dic3—32no—
197C22×Dic3—32no—
198C22×Dic3—32no—
199C22×Dic3—32no—
200C22×Dic3—62no—
201C22×Dic3—62no—
202C22×Dic3—64no—
203C22×Dic3—124no—
204C22×Dic3C22×D312yes—
205C22×Dic3C22×D311yescharacteristic
206C22×Dic3C22×D311yescharacteristic
207C2×D12—22no—
208C2×D12—22no—
209C2×D12—22no—
210C2×D12—22no—
211C2×D12C4×D314yescomplemented
212C2×D12C4×D314yescomplemented
213C2×C4×D3—24no—
214C2×C4×D3—44no—
215C2×C4×D3—64no—
216C2×C4×D3—124no—
217C3×C4⋊C4—22no—
218C3×C4⋊C4—22no—
219C3×C4⋊C4—42no—
220C3×C22⋊C4—64no—
221C3×C22⋊C4—124no—
222C3×C42—34no—
223C3×C42—62no—
224#217—64no—
225#217—124no—
226(C2×D3)⋊C4—24no—
227(C2×D3)⋊C4—44no—
228(C2×D3)⋊C4—64no—
229(C2×D3)⋊C4—124no—
230C4⋊Dic3—62no—
231C4⋊Dic3—62no—
232C4⋊Dic3—122no—
233C4×Dic3—22no—
234C4×Dic3—34no—
235C4×Dic3—34no—
236C4×Dic3—64no—
237C4×Dic3#6714yescomplemented
238C22×C32C23×C411yescharacteristic
239C22×C32C22×D411yescharacteristic
240C22×C32C2×#4111yescharacteristic
241C22×C32H(5,𝔽2)12yes—
242C22×C32H(5,𝔽2)12yes—
243C2×C3×D3—24no—
244C2×C3×D3—24no—
245C2×C3×D3—28no—
246C2×C3×D3—28no—
247C2×C3×D3—42no—
248C2×C3×D3—42no—
249C2×C3×D3—42no—
250C2×C3×D3—42no—
251C2×C3×D3—44no—
252C2×C3×D3—44no—
253C32×C4—42no—
254C32×C4C4×D414yes—
255C3⋊Dic3—24no—
256C3⋊Dic3—42no—
257C3×Dic3—22no—
258C3×Dic3—22no—
259C3×Dic3—42no—
260C22×D4—31no—
261C22×D4—31no—
262C22×D4—94no—
263C23×C4—32no—
264C23×C4—92no—
265#127—98no—
266C4×D4—64no—
267C4×D4—184no—
268C2×C4⋊C4—91no—
269C2×C4⋊C4D3211yescharacteristic
270C2×C22⋊C4—32no—
271C2×C22⋊C4—34no—
272C2×C22⋊C4—92no—
273C2×C22⋊C4—94no—
274C2×C42—31no—
275C2×C42—31no—
276C2×C42—91no—
277#95—92no—
278#95—92no—
279#95—94no—
280C23×C3—21no—
281C23×C3—34no—
282C23×C3—34no—
283C23×C3—62no—
284C23×C3—62no—
285C23×C3—62no—
286C23×C3—64no—
287C23×C3—64no—
288C23×C3—64no—
289C23×C3—64no—
290C23×C3—62no—
291C23×C3C23×D311yescharacteristic
292C23×C3C23×D311yescharacteristic
293C22×D3—22no—
294C22×D3—22no—
295C22×D3—22no—
296C22×D3—24no—
297C22×D3—24no—
298C22×D3—24no—
299C22×D3—24no—
300C22×D3—22no—
301C22×D3C2×C4×D314yes—
302C22×D3C2×C4×D314yes—
303C3×D4—68no—
304C3×D4—68no—
305C2×C3×C4—22no—
306C2×C3×C4—24no—
307C2×C3×C4—24no—
308C2×C3×C4—22no—
309C2×C3×C4—22no—
310C2×C3×C4—22no—
311C2×C3×C4—22no—
312C2×C3×C4—32no—
313C2×C3×C4—32no—
314C2×C3×C4—42no—
315C2×C3×C4—44no—
316C2×C3×C4—62no—
317C2×C3×C4—62no—
318C2×C3×C4—62no—
319C2×C3×C4—62no—
320C2×C3×C4—62no—
321C2×C3×C4—128no—
322C2×C3×C4C2×C4×D312yes—
323C2×C3×C4C2×C4×D312yes—
324C2×C3×C4#23512yes—
325C2×C3×C4D3×D412yes—
326C2×C3×C4#23712yes—
327C2×C3×C4C2×#6712yes—
328#67—1216no—
329#67—1216no—
330C2×Dic3—22no—
331C2×Dic3—22no—
332C2×Dic3—22no—
333C2×Dic3—22no—
334C2×Dic3—22no—
335C2×Dic3—34no—
336C2×Dic3—34no—
337C2×Dic3—64no—
338C2×Dic3—62no—
339C2×Dic3—62no—
340C2×Dic3—62no—
341C2×Dic3—62no—
342C2×Dic3—62no—
343C2×Dic3—64no—
344C2×Dic3—64no—
345C2×Dic3—62no—
346C2×Dic3—122no—
347C2×Dic3—122no—
348C2×Dic3—122no—
349C2×Dic3—124no—
350C2×Dic3—128no—
351C2×Dic3C2×#6712yes—
352C2×Dic3C2×#6712yes—
353D12—28no—
354D12—28no—
355C4×D3—48no—
356C4×D3—128no—
357C2×C32C2×C4×D411yescharacteristic
358C2×C32#51812yes—
359C2×C32#53511yescharacteristic
360C2×C32#53511yescharacteristic
361C2×C32#54012yes—
362C3×D3—44no—
363C3×D3—44no—
364C24—32no—
365C24—32no—
366C2×D4—34no—
367C2×D4—34no—
368C2×D4—62no—
369C2×D4—62no—
370C2×D4—62no—
371C2×D4—62no—
372C2×D4—916no—
373C2×D4—364no—
374C2×D4—364no—
375C22×C4—31no—
376C22×C4—31no—
377C22×C4—32no—
378C22×C4—64no—
379C22×C4—92no—
380C22×C4—92no—
381C22×C4—124no—
382C22×C4—184no—
383C22×C4—364no—
384C22×C4C2×D3212yes—
385C22×C4C2×D3211yescharacteristic
386C4⋊C4—22no—
387C4⋊C4—182no—
388C22⋊C4—64no—
389C22⋊C4—124no—
390C22⋊C4—184no—
391C22⋊C4—364no—
392C42—34no—
393C42—62no—
394C42—94no—
395C22×C3—21no—
396C22×C3—21no—
397C22×C3—22no—
398C22×C3—22no—
399C22×C3—21no—
400C22×C3—64no—
401C22×C3—64no—
402C22×C3—68no—
403C22×C3—68no—
404C22×C3—122no—
405C22×C3—122no—
406C22×C3—122no—
407C22×C3—124no—
408C22×C3—122no—
409C22×C3—124no—
410C22×C3C22×C4×D311yescharacteristic
411C22×C3C22×C4×D311yescharacteristic
412C22×C3C2×#23511yescharacteristic
413C22×C3C2×D3×D411yescharacteristic
414C22×C3C2×#23711yescharacteristic
415C22×C3#100412yes—
416C22×C3#100412yes—
417C22×C3#100912yes—
418C22×C3#100912yes—
419C22×C3C22×#6711yescharacteristic
420C2×D3—24no—
421C2×D3—24no—
422C2×D3—28no—
423C2×D3—28no—
424C2×D3—42no—
425C2×D3—42no—
426C2×D3—42no—
427C2×D3—44no—
428C2×D3—42no—
429C2×D3—44no—
430C3×C4—24no—
431C3×C4—42no—
432C3×C4—42no—
433C3×C4—62no—
434C3×C4—62no—
435C3×C4—82no—
436C3×C4—122no—
437C3×C4#67⋊C414yes—
438C3×C4C4×#6714yes—
439Dic3—22no—
440Dic3—22no—
441Dic3—42no—
442Dic3—64no—
443Dic3—64no—
444Dic3—124no—
445Dic3—122no—
446Dic3—122no—
447Dic3—242no—
448C32#232811yescharacteristic, complemented, Sylow
449C23—34no—
450C23—34no—
451C23—62no—
452C23—62no—
453C23—64no—
454C23—64no—
455C23—64no—
456C23—64no—
457C23—62no—
458C23—62no—
459C23C22×D3211yescharacteristic
460D4—68no—
461D4—68no—
462D4—3616no—
463C2×C4—24no—
464C2×C4—22no—
465C2×C4—32no—
466C2×C4—32no—
467C2×C4—62no—
468C2×C4—62no—
469C2×C4—62no—
470C2×C4—62no—
471C2×C4—62no—
472C2×C4—94no—
473C2×C4—128no—
474C2×C4—182no—
475C2×C4—182no—
476C2×C4—184no—
477C2×C4—182no—
478C2×C4—368no—
479C2×C4#379512yes—
480C2×C4C4×D3212yes—
481C2×C4D3×#6712yes—
482C2×C3—22no—
483C2×C3—21no—
484C2×C3—21no—
485C2×C3—21no—
486C2×C3—22no—
487C2×C3—124no—
488C2×C3—124no—
489C2×C3C2×#67⋊C411yescharacteristic
490C2×C3#554512yes—
491C2×C3#554512yes—
492C2×C3#556212yes—
493C2×C3#561912yes—
494C2×C3#567411yescharacteristic
495C2×C3#571511yescharacteristic
496C2×C3C2×C4×#6711yescharacteristic
497C2×C3#580511yescharacteristic
498C2×C3#583011yescharacteristic
499D3—44no—
500D3—44no—
501C22—68no—
502C22—68no—
503C22—64no—
504C22—64no—
505C22—122no—
506C22—122no—
507C22—122no—
508C22—122no—
509C22—124no—
510C22—124no—
511C22C2×#379511yescharacteristic
512C22C2×C4×D3211yescharacteristic
513C22#6431312yes—
514C22#6432012yes—
515C22C2×D3×#6711yescharacteristic
516C4—42no—
517C4—62no—
518C4—62no—
519C4—122no—
520C4—184no—
521C4—362no—
522C4#6387914yes—
523C3—21no—
524C3#7629811yescharacteristic, complemented
525C3#8232911yescharacteristic, complemented
526C2—124no—
527C2—124no—
528C2#1059449612yes—
529C2#1059460612yes—
530C2C2×#6387911yescharacteristic
531C2#1059523311yescharacteristic
532C2#1059542611yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC2×C32×C4⋊C4C22
socle, cosocleC23×C32C24
prime radicalC2×#63914C2
hypercenterC2×C4⋊C4D32
hypocenterC32#2328
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×C3×#893C2semidirect
3. C2×Dic3×D12C2semidirect
4. #10592676C2semidirect
5. C3×#4988C2semidirect
6. #10591381C2semidirect
7. #10591363C2semidirect
8. #10591318C2semidirect
9. #10591222C2semidirect
27. #63914C4semidirect
36. C2×#893D3semidirect
41. #4988D3semidirect
64. C2×C3×D12C2×C4semidirect
65. C2×C3×D12C2×C4semidirect
70. C2×#625C2×C4semidirect
75. C4×C3⋊Dic3C2×C4semidirect
79. C3×C4×Dic3D4semidirect
211. C2×D12C4×D3semidirect
212. C2×D12C4×D3semidirect
237. C4×Dic3#67semidirect
448. C32#2328semidirect
524. C3#76298semidirect
525. C3#82329semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#8932
C2×#639142
C2×Dic3×D122
#105926762
C3×#49882
#105913812
#105913632
#105913182
#105912222
#823293
#762983