Finite Group Databasebeta

← #11783355

Subgroups — #11783355

Order 1152.

1697 conjugacy classes of subgroups.

The subgroup lattice has 604 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C22⋊C4×C3⋊D3C211yesmaximal, characteristic
2C2×#63974C211yesmaximal, characteristic
3C2×#63974C211yesmaximal, characteristic
4C3×#4527C212yesmaximal, complemented
5#10589186C212yesmaximal, complemented
6D3×#342—32nomaximal
7C24×C3⋊D3C2211yescharacteristic
8C22×C4×C3⋊D3—21no—
9C22×#624—21no—
10C22×#624C412yescomplemented
11C2×C32×C22⋊C4C2211yescharacteristic
12C2×#3757C2211yescharacteristic
13C2×#3752—21no—
14C22⋊C4×C3⋊D3—22no—
15C22⋊C4×C3⋊D3C414yescomplemented
16C2×C3×#217C2212yes—
17C2×C3×#217C2212yes—
18#63974—21no—
19#63974—21no—
20#63974—22no—
21#63974—21no—
22#63974—21no—
23#63974C414yescomplemented
24C2×#3722—21no—
25C2×#3722C412yescomplemented
26C2×D3×C22⋊C4—32no—
27C2×D3×C22⋊C4—32no—
28C2×D3×C22⋊C4—32no—
29C2×D3×C22⋊C4—61no—
30C3×#342—32no—
31#4527—32no—
32#4527D312yescomplemented
33#4526—32no—
34C24×C32C2311yescharacteristic
35C23×C3⋊D3—44no—
36C23×C3⋊D3C2×C411yescharacteristic
37C23×C3⋊D3C2×C412yes—
38C23×C3⋊D3C2×C411yescharacteristic
39C23×C3⋊D3C2×C412yes—
40C23×C3⋊D3D411yescharacteristic
41C23×C3⋊D3D411yescharacteristic
42C23×C3⋊D3D412yes—
43C23×C3⋊D3D411yescharacteristic
44C23×C3⋊D3D411yescharacteristic
45C23×C3⋊D3Q812yes—
46C22×C32×C4—21no—
47C22×C3⋊Dic3—21no—
48C2×C4×C3⋊D3—24no—
49C2×C4×C3⋊D3—44no—
50C22×C3×Dic3—22no—
51C22×C3×Dic3C2×C414yescomplemented
52C2×#624—24no—
53C2×#624—22no—
54C2×#624—22no—
55C2×#624—44no—
56C2×#624—44no—
57C32×C22⋊C4—21no—
58C32×C22⋊C4C2×C412yescomplemented
59#3757—21no—
60#3757C2×C412yescomplemented
61#3752—24no—
62C3×#217—22no—
63C3×#217—22no—
64C3×#217—22no—
65C3×#217C2×C414yescomplemented
66#3722—24no—
67#3722—22no—
68#3722—22no—
69C2×#342—91noSylow
70C24×D3—32no—
71C24×D3—61no—
72C22×C4×D3—34no—
73C22×C4×D3—62no—
74C22×C4×D3—62no—
75C22×C4×D3—62no—
76C2×C3×C22⋊C4—21no—
77C2×C3×C22⋊C4—32no—
78C2×C3×C22⋊C4—32no—
79C2×C3×C22⋊C4C2×D312yes—
80C2×#217—32no—
81C2×#217—61no—
82C2×#217C2×D312yes—
83C2×#217C2×D312yes—
84C2×(C2×D3)⋊C4—34no—
85C2×(C2×D3)⋊C4—62no—
86C2×(C2×D3)⋊C4—62no—
87C2×(C2×D3)⋊C4—62no—
88D3×C22⋊C4—38no—
89D3×C22⋊C4—38no—
90D3×C22⋊C4—64no—
91D3×C22⋊C4—64no—
92D3×C22⋊C4—62no—
93D3×C22⋊C4—62no—
94D3×C22⋊C4—62no—
95D3×C22⋊C4—62no—
96D3×C22⋊C4—64no—
97D3×C22⋊C4—64no—
98C23×C32—42no—
99C23×C32C22×C411yescharacteristic
100C23×C32C22×C411yescharacteristic
101C23×C32C22×C411yescharacteristic
102C23×C32C2×D411yescharacteristic
103C23×C32C2×D411yescharacteristic
104C23×C32C2×D411yescharacteristic
105C23×C32C2×Q811yescharacteristic
106C22×C3⋊D3—24no—
107C22×C3⋊D3—24no—
108C22×C3⋊D3—24no—
109C22×C3⋊D3—44no—
110C22×C3⋊D3—44no—
111C22×C3⋊D3—44no—
112C22×C3⋊D3—44no—
113C22×C3⋊D3—42no—
114C22×C3⋊D3—42no—
115C22×C3⋊D3—42no—
116C22×C3⋊D3C4212yes—
117C22×C3⋊D3C4212yes—
118C22×C3⋊D3C22⋊C411yescharacteristic
119C22×C3⋊D3C22⋊C411yescharacteristic
120C22×C3⋊D3C22⋊C411yescharacteristic
121C22×C3⋊D3C22⋊C412yes—
122C22×C3⋊D3C22⋊C412yes—
123C22×C3⋊D3C22⋊C412yes—
124C22×C3⋊D3C22⋊C412yes—
125C22×C3⋊D3C22⋊C411yescharacteristic
126C22×C3⋊D3C4⋊C412yes—
127C22×C3⋊D3C4⋊C412yes—
128C22×C3⋊D3C4⋊C412yes—
129C22×C3⋊D3C4⋊C412yes—
130C22×C3⋊D3C4⋊C412yes—
131C22×C3⋊D3C4⋊C412yes—
132C2×C32×C4—22no—
133C2×C32×C4—42no—
134C2×C3⋊Dic3—22no—
135C2×C3⋊Dic3—42no—
136C4×C3⋊D3—48no—
137C2×C3×Dic3—24no—
138C2×C3×Dic3—24no—
139C2×C3×Dic3—44no—
140C2×C3×Dic3—44no—
141#624—48no—
142#624—44no—
143#624—44no—
144C22×C22⋊C4—91no—
145C22×C22⋊C4—91no—
146C22×C22⋊C4—91no—
147#342—32no—
148#342—92no—
149C24×C3—21no—
150C24×C3C22×D312yes—
151C23×D3—32no—
152C23×D3—32no—
153C23×D3—32no—
154C23×D3—34no—
155C23×D3—34no—
156C23×D3—32no—
157C23×D3—34no—
158C23×D3—32no—
159C23×D3—32no—
160C23×D3—34no—
161C23×D3—61no—
162C23×D3—62no—
163C23×D3—61no—
164C23×D3—61no—
165C23×D3—62no—
166C23×D3—62no—
167C23×D3—61no—
168C23×D3—61no—
169C23×D3—61no—
170C23×D3—62no—
171C23×D3—128no—
172C23×D3—128no—
173C22×C3×C4—22no—
174C22×C3×C4—22no—
175C22×C3×C4—34no—
176C22×C3×C4—62no—
177C22×Dic3—22no—
178C22×Dic3—62no—
179C22×Dic3—62no—
180C22×Dic3C4×D314yescomplemented
181C2×C4×D3—68no—
182C2×C4×D3—64no—
183C2×C4×D3—64no—
184C2×C4×D3—68no—
185C2×C4×D3—68no—
186C2×C4×D3—128no—
187C2×C4×D3—128no—
188C2×C4×D3—128no—
189C2×C4×D3—128no—
190C3×C22⋊C4—22no—
191C3×C22⋊C4—22no—
192C3×C22⋊C4—22no—
193C3×C22⋊C4—34no—
194C3×C22⋊C4—62no—
195C3×C22⋊C4—62no—
196C3×C22⋊C4—62no—
197C3×C22⋊C4C4×D314yescomplemented
198#217—22no—
199#217—22no—
200#217—22no—
201#217—34no—
202#217—62no—
203#217—62no—
204#217—62no—
205#217C4×D314yescomplemented
206(C2×D3)⋊C4—68no—
207(C2×D3)⋊C4—64no—
208(C2×D3)⋊C4—64no—
209(C2×D3)⋊C4—68no—
210(C2×D3)⋊C4—68no—
211C22×C32—22no—
212C22×C32—22no—
213C22×C32—22no—
214C22×C32—41no—
215C22×C32—41no—
216C22×C32—41no—
217C22×C32—41no—
218C22×C32C2×C4211yescharacteristic
219C22×C32C2×C22⋊C411yescharacteristic
220C22×C32C2×C22⋊C411yescharacteristic
221C22×C32C2×C22⋊C411yescharacteristic
222C22×C32C2×C4⋊C411yescharacteristic
223C22×C32C2×C4⋊C411yescharacteristic
224C22×C32C2×C4⋊C411yescharacteristic
225C2×C3⋊D3—22no—
226C2×C3⋊D3—24no—
227C2×C3⋊D3—24no—
228C2×C3⋊D3—22no—
229C2×C3⋊D3—22no—
230C2×C3⋊D3—24no—
231C2×C3⋊D3—24no—
232C2×C3⋊D3—24no—
233C2×C3⋊D3—24no—
234C2×C3⋊D3—42no—
235C2×C3⋊D3—42no—
236C2×C3⋊D3—42no—
237C2×C3⋊D3—42no—
238C2×C3⋊D3—42no—
239C2×C3⋊D3—42no—
240C2×C3⋊D3#9512yes—
241C2×C3⋊D3#9512yes—
242C2×C3⋊D3#9512yes—
243C2×C3⋊D3#9512yes—
244C2×C3⋊D3#9914yes—
245C32×C4—42no—
246C3⋊Dic3—42no—
247C3×Dic3—44no—
248C3×Dic3—44no—
249C25—91no—
250C23×C4—92no—
251C23×C4—181no—
252C23×C4—181no—
253C2×C22⋊C4—32no—
254C2×C22⋊C4—32no—
255C2×C22⋊C4—94no—
256C2×C22⋊C4—91no—
257C2×C22⋊C4—94no—
258C2×C22⋊C4—92no—
259C2×C22⋊C4—182no—
260C2×C22⋊C4—181no—
261C2×C22⋊C4—181no—
262C2×C22⋊C4—182no—
263C2×C22⋊C4—181no—
264C2×C22⋊C4—181no—
265C2×C22⋊C4—181no—
266C2×C22⋊C4—181no—
267C2×C22⋊C4D3211yescharacteristic
268C23×C3—21no—
269C23×C3—21no—
270C23×C3—21no—
271C23×C3—21no—
272C23×C3—21no—
273C23×C3—21no—
274C23×C3—21no—
275C23×C3—44no—
276C23×C3—44no—
277C23×C3C2×C4×D312yes—
278C23×C3C2×C4×D312yes—
279C23×C3C2×C4×D312yes—
280C23×C3D3×D412yes—
281C23×C3D3×D412yes—
282C23×C3D3×D412yes—
283C23×C3D3×Q812yes—
284C22×D3—32no—
285C22×D3—34no—
286C22×D3—32no—
287C22×D3—32no—
288C22×D3—34no—
289C22×D3—32no—
290C22×D3—34no—
291C22×D3—34no—
292C22×D3—34no—
293C22×D3—34no—
294C22×D3—34no—
295C22×D3—34no—
296C22×D3—34no—
297C22×D3—34no—
298C22×D3—34no—
299C22×D3—34no—
300C22×D3—62no—
301C22×D3—61no—
302C22×D3—61no—
303C22×D3—62no—
304C22×D3—62no—
305C22×D3—62no—
306C22×D3—62no—
307C22×D3—62no—
308C22×D3—61no—
309C22×D3—61no—
310C22×D3—62no—
311C22×D3—62no—
312C22×D3—62no—
313C22×D3—62no—
314C22×D3—62no—
315C22×D3—62no—
316C22×D3—68no—
317C22×D3—68no—
318C22×D3—68no—
319C22×D3—68no—
320C22×D3—124no—
321C22×D3—124no—
322C22×D3—128no—
323C22×D3—128no—
324C22×D3—128no—
325C22×D3—128no—
326C22×D3—124no—
327C22×D3—124no—
328C22×D3—124no—
329C22×D3—124no—
330C22×D3—124no—
331C22×D3—128no—
332C22×D3—128no—
333C22×D3—128no—
334C22×D3—128no—
335C22×D3—124no—
336C2×C3×C4—24no—
337C2×C3×C4—24no—
338C2×C3×C4—44no—
339C2×C3×C4—44no—
340C2×C3×C4—64no—
341C2×C3×C4—64no—
342C2×C3×C4—124no—
343C2×C3×C4—124no—
344C2×Dic3—24no—
345C2×Dic3—24no—
346C2×Dic3—44no—
347C2×Dic3—44no—
348C2×Dic3—64no—
349C2×Dic3—64no—
350C2×Dic3—124no—
351C2×Dic3—124no—
352C4×D3—128no—
353C4×D3—1216no—
354C4×D3—128no—
355C4×D3—1216no—
356C4×D3—1216no—
357C2×C32—21no—
358C2×C32—21no—
359C2×C32—21no—
360C2×C32—21no—
361C2×C32—21no—
362C2×C32—21no—
363C2×C32C2×#9511yescharacteristic
364C2×C32C2×#9912yes—
365C3⋊D3—22no—
366C3⋊D3—22no—
367C3⋊D3—22no—
368C3⋊D3#34214yescomplemented
369C24—91no—
370C24—91no—
371C24—91no—
372C24—92no—
373C24—92no—
374C24—91no—
375C24—91no—
376C24—92no—
377C24—92no—
378C24—91no—
379C24—364no—
380C24C2×D3211yescharacteristic
381C22×C4—21no—
382C22×C4—34no—
383C22×C4—62no—
384C22×C4—184no—
385C22×C4—184no—
386C22×C4—182no—
387C22×C4—182no—
388C22×C4—181no—
389C22×C4—364no—
390C22×C4—364no—
391C22×C4—364no—
392C22⋊C4—21no—
393C22⋊C4—34no—
394C22⋊C4—62no—
395C22⋊C4—62no—
396C22⋊C4—62no—
397C22⋊C4—92no—
398C22⋊C4—184no—
399C22⋊C4—184no—
400C22⋊C4—182no—
401C22⋊C4—182no—
402C22⋊C4—181no—
403C22⋊C4#62412yescomplemented
404C22×C3—24no—
405C22×C3—24no—
406C22×C3—24no—
407C22×C3—24no—
408C22×C3—21no—
409C22×C3—21no—
410C22×C3—21no—
411C22×C3—21no—
412C22×C3—21no—
413C22×C3—21no—
414C22×C3—21no—
415C22×C3—42no—
416C22×C3—42no—
417C22×C3—42no—
418C22×C3—42no—
419C22×C3—42no—
420C22×C3—42no—
421C22×C3—42no—
422C22×C3—42no—
423C22×C3—42no—
424C22×C3—42no—
425C22×C3C42×D312yes—
426C22×C3D3×C22⋊C412yes—
427C22×C3D3×C22⋊C412yes—
428C22×C3D3×C22⋊C412yes—
429C22×C3D3×C4⋊C412yes—
430C22×C3D3×C4⋊C412yes—
431C22×C3D3×C4⋊C412yes—
432C2×D3—34no—
433C2×D3—38no—
434C2×D3—34no—
435C2×D3—34no—
436C2×D3—34no—
437C2×D3—62no—
438C2×D3—62no—
439C2×D3—64no—
440C2×D3—62no—
441C2×D3—62no—
442C2×D3—68no—
443C2×D3—68no—
444C2×D3—68no—
445C2×D3—68no—
446C2×D3—68no—
447C2×D3—68no—
448C2×D3—68no—
449C2×D3—68no—
450C2×D3—64no—
451C2×D3—64no—
452C2×D3—64no—
453C2×D3—64no—
454C2×D3—124no—
455C2×D3—124no—
456C2×D3—124no—
457C2×D3—124no—
458C2×D3—122no—
459C2×D3—122no—
460C2×D3—124no—
461C2×D3—124no—
462C2×D3—124no—
463C2×D3—124no—
464C2×D3—124no—
465C2×D3—124no—
466C2×D3—124no—
467C2×D3—124no—
468C2×D3—124no—
469C2×D3—124no—
470C2×D3—124no—
471C2×D3—124no—
472C3×C4—44no—
473C3×C4—44no—
474C3×C4—124no—
475C3×C4—124no—
476Dic3—44no—
477Dic3—44no—
478Dic3—124no—
479Dic3—124no—
480C32C2×#34211yescharacteristic, complemented, Sylow
481C23—42no—
482C23—91no—
483C23—92no—
484C23—92no—
485C23—92no—
486C23—92no—
487C23—92no—
488C23—91no—
489C23—91no—
490C23—91no—
491C23—92no—
492C23—92no—
493C23—92no—
494C23—92no—
495C23—92no—
496C23—92no—
497C23—92no—
498C23—184no—
499C23—184no—
500C23—184no—
501C23—362no—
502C23—362no—
503C23—362no—
504C23—364no—
505C23—364no—
506C23—364no—
507C23—364no—
508C23#379711yescharacteristic
509C23C4×D3211yescharacteristic
510C23C4×D3211yescharacteristic
511C23#380211yescharacteristic
512C23C2×#62411yescharacteristic
513C23#381111yescharacteristic
514C23#381111yescharacteristic
515C2×C4—22no—
516C2×C4—42no—
517C2×C4—64no—
518C2×C4—64no—
519C2×C4—124no—
520C2×C4—124no—
521C2×C4—182no—
522C2×C4—368no—
523C2×C4—364no—
524C2×C4—368no—
525C2×C4—364no—
526C2×C4—362no—
527C2×C3—22no—
528C2×C3—22no—
529C2×C3—22no—
530C2×C3—22no—
531C2×C3—22no—
532C2×C3—22no—
533C2×C3—22no—
534C2×C3—22no—
535C2×C3—21no—
536C2×C3—22no—
537C2×C3—41no—
538C2×C3—41no—
539C2×C3—41no—
540C2×C3—41no—
541C2×C3D3×#9512yes—
542C2×C3D3×#9914yes—
543D3—38no—
544D3—64no—
545D3—64no—
546D3—64no—
547D3—64no—
548D3—64no—
549D3—122no—
550D3—122no—
551C22—22no—
552C22—22no—
553C22—22no—
554C22—41no—
555C22—41no—
556C22—41no—
557C22—41no—
558C22—92no—
559C22—94no—
560C22—92no—
561C22—92no—
562C22—92no—
563C22—184no—
564C22—184no—
565C22—184no—
566C22—184no—
567C22—184no—
568C22—184no—
569C22—182no—
570C22—182no—
571C22—182no—
572C22—362no—
573C22—362no—
574C22—362no—
575C22—362no—
576C22—362no—
577C22—362no—
578C22C4×#62411yescharacteristic
579C22#6388311yescharacteristic
580C22#6388311yescharacteristic
581C22#6390011yescharacteristic
582C22#6392111yescharacteristic
583C22#6392111yescharacteristic
584C22#6397411yescharacteristic
585C4—42no—
586C4—124no—
587C4—124no—
588C4—362no—
589C3—21no—
590C3D3×#34212yescomplemented
591C2—21no—
592C2—21no—
593C2—21no—
594C2—21no—
595C2—21no—
596C2—21no—
597C2—94no—
598C2—182no—
599C2—182no—
600C2—182no—
601C2#1059040412yes—
602C2#1059137011yescharacteristic
subgroupG/H
centerC22#63921
commutatorC22×C32C2×C42
FrattiniC24C2×D32
FittingC2×C32×C22⋊C4C22
socleC22×C32C2×C22⋊C4
prime radicalC24×C3⋊D3C22
cosocleC24×C32C23
hypercenterC2×C22⋊C4D32
hypocenterC32C2×#342
LCSG ▷ C22×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C24 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
4. C3×#4527C2semidirect
5. #10589186C2semidirect
10. C22×#624C4semidirect
15. C22⋊C4×C3⋊D3C4semidirect
23. #63974C4semidirect
25. C2×#3722C4semidirect
32. #4527D3semidirect
51. C22×C3×Dic3C2×C4semidirect
58. C32×C22⋊C4C2×C4semidirect
60. #3757C2×C4semidirect
65. C3×#217C2×C4semidirect
180. C22×Dic3C4×D3semidirect
197. C3×C22⋊C4C4×D3semidirect
205. #217C4×D3semidirect
368. C3⋊D3#342semidirect
403. C22⋊C4#624semidirect
480. C32C2×#342semidirect
590. C3D3×#342semidirect

Maximal subgroups

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

subgroupindex
C2×C22⋊C4×C3⋊D32
C2×#639742
C3×#45272
#105891862
D3×#3423