Finite Group Databasebeta

← #11801360

Subgroups — #11801360

Order 1152.

1589 conjugacy classes of subgroups.

The subgroup lattice has 586 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63900C211yesmaximal, characteristic
2C2×#63883C211yesmaximal, characteristic
3C2×C4×#624C211yesmaximal, characteristic
4C3⋊D3×#95C211yesmaximal, characteristic
5C3×#4653C212yesmaximal, complemented
6#10591370C211yesmaximal, characteristic
7#10591370C211yesmaximal, characteristic
8#10591370C211yesmaximal, characteristic
9#10591270C212yesmaximal, complemented
10#10591249C212yesmaximal, complemented
11#10591193C212yesmaximal, complemented
12D3×#387—32nomaximal
13C22×C4×C3⋊D3C2211yescharacteristic
14C22×C4×C3⋊D3C2211yescharacteristic
15C22×C4×C3⋊D3C2211yescharacteristic
16C22×#624C2211yescharacteristic
17C22×#624C2211yescharacteristic
18C22×#624C2211yescharacteristic
19C22×#624C2211yescharacteristic
20C2×C3×C4⋊Dic3C2212yes—
21C2×C3×Dic3⋊C4C2212yes—
22C2×C3×C4×Dic3C2212yes—
23C2×#3724C2212yes—
24C2×Dic3⋊Dic3C2212yes—
25C2×Dic32C2212yes—
26#63900C418yescomplemented
27#63883—24no—
28C4×#624—24no—
29C32×#95C2211yescharacteristic
30#63658C2211yescharacteristic
31#63658C2211yescharacteristic
32#63658C2211yescharacteristic
33C3×C3⋊#95C2212yes—
34C3×C3⋊#95C2212yes—
35C3×C3⋊#95C2212yes—
36#63579C2212yes—
37#63579C2212yes—
38#63579C2212yes—
39C2×D3×C4⋊C4—32no—
40C2×D3×C4⋊C4—32no—
41C2×C42×D3—32no—
42C3×#387—32no—
43#4980—32no—
44#4978—32no—
45#4933—32no—
46D3×#95—32no—
47D3×#95—32no—
48D3×#95—32no—
49D3×#95—32no—
50D3×#95—61no—
51#4655—32no—
52#4654—32no—
53#4653D312yescomplemented
54#4652—32no—
55C23×C3⋊D3C2311yescharacteristic
56C22×C32×C4C2311yescharacteristic
57C22×C32×C4C2311yescharacteristic
58C22×C32×C4C2311yescharacteristic
59C22×C3⋊Dic3C2311yescharacteristic
60C22×C3⋊Dic3C2311yescharacteristic
61C22×C3⋊Dic3C2311yescharacteristic
62C2×C4×C3⋊D3—22no—
63C2×C4×C3⋊D3—22no—
64C2×C4×C3⋊D3—22no—
65C2×C4×C3⋊D3—22no—
66C2×C4×C3⋊D3—22no—
67C2×C4×C3⋊D3—22no—
68C2×C4×C3⋊D3—22no—
69C2×C4×C3⋊D3C2×C414yes—
70C2×C4×C3⋊D3D414yes—
71C22×C3×Dic3C2312yes—
72C22×C3×Dic3C2312yes—
73C22×C3×Dic3C2312yes—
74C22×C3×Dic3C2312yes—
75C2×#624—22no—
76C2×#624—22no—
77C2×#624—22no—
78C2×#624—22no—
79C2×#624—22no—
80C2×#624—22no—
81C2×#624—22no—
82C2×#624—22no—
83C2×#624—22no—
84C2×#624C2×C414yes—
85C2×#624C2×C414yes—
86C2×#624Q814yes—
87C3×C4⋊Dic3C2×C418yescomplemented
88C3×Dic3⋊C4—24no—
89C3×C4×Dic3—24no—
90#3724C2×C418yescomplemented
91Dic3⋊Dic3—24no—
92Dic32—24no—
93C2×#387—91noSylow
94C22×C4×D3—32no—
95C22×C4×D3—32no—
96C22×C4×D3—32no—
97C22×C4×D3—32no—
98C22×C4×D3—32no—
99C22×C4×D3—32no—
100C22×C4×D3—32no—
101C22×C4×D3—61no—
102C22×C4×D3—61no—
103C22×C4×D3—61no—
104C2×C3×C4⋊C4—32no—
105C2×C3×C4⋊C4—32no—
106C2×C3×C42—32no—
107C2×C4⋊Dic3—32no—
108C2×C4⋊Dic3C2×D312yes—
109C2×Dic3⋊C4—32no—
110C2×Dic3⋊C4—32no—
111C2×Dic3⋊C4—32no—
112C2×Dic3⋊C4C2×D312yes—
113C2×C4×Dic3—32no—
114C2×C4×Dic3—32no—
115C2×C4×Dic3C2×D312yes—
116D3×C4⋊C4—316no—
117D3×C4⋊C4—68no—
118C42×D3—68no—
119C3×#95—21no—
120C3×#95—32no—
121C3×#95—32no—
122C3×#95—32no—
123C3×#95C2×D312yes—
124C3⋊#95—32no—
125C3⋊#95—32no—
126C3⋊#95—32no—
127C3⋊#95—32no—
128C3⋊#95—32no—
129C3⋊#95—32no—
130C3⋊#95—32no—
131C3⋊#95—32no—
132C3⋊#95—32no—
133C3⋊#95—61no—
134C3⋊#95—61no—
135C3⋊#95—61no—
136C3⋊#95C2×D312yes—
137C3⋊#95C2×D312yes—
138C3⋊#95C2×D312yes—
139C23×C32C2411yescharacteristic
140C22×C3⋊D3C22×C412yes—
141C22×C3⋊D3C2×D412yes—
142C22×C3⋊D3C2×Q812yes—
143C22×C3⋊D3#4112yes—
144C22×C3⋊D3#4112yes—
145C22×C3⋊D3#4112yes—
146C22×C3⋊D3#4112yes—
147C2×C32×C4—21no—
148C2×C32×C4—21no—
149C2×C32×C4—21no—
150C2×C32×C4—21no—
151C2×C32×C4—21no—
152C2×C32×C4—21no—
153C2×C32×C4—21no—
154C2×C32×C4C22×C412yes—
155C2×C32×C4C2×D412yes—
156C2×C3⋊Dic3—21no—
157C2×C3⋊Dic3—21no—
158C2×C3⋊Dic3—21no—
159C2×C3⋊Dic3—21no—
160C2×C3⋊Dic3—21no—
161C2×C3⋊Dic3—21no—
162C2×C3⋊Dic3—21no—
163C2×C3⋊Dic3C22×C412yes—
164C2×C3⋊Dic3C2×D412yes—
165C4×C3⋊D3—28no—
166C4×C3⋊D3—28no—
167C4×C3⋊D3—44no—
168C2×C3×Dic3—22no—
169C2×C3×Dic3—22no—
170C2×C3×Dic3—22no—
171C2×C3×Dic3—22no—
172C2×C3×Dic3—22no—
173C2×C3×Dic3—22no—
174C2×C3×Dic3—22no—
175C2×C3×Dic3—22no—
176C2×C3×Dic3—22no—
177C2×C3×Dic3C22×C414yes—
178C2×C3×Dic3C22×C414yes—
179C2×C3×Dic3C2×Q814yes—
180#624—28no—
181#624—28no—
182#624—28no—
183#624—44no—
184C22×C4⋊C4—91no—
185C22×C4⋊C4—91no—
186C22×C42—91no—
187#387—32no—
188#387—92no—
189#387—92no—
190#387—92no—
191C2×#95—91no—
192C2×#95—91no—
193C2×#95—91no—
194C2×#95—91no—
195C23×D3—32no—
196C23×D3—61no—
197C22×C3×C4—21no—
198C22×C3×C4—21no—
199C22×C3×C4—21no—
200C22×C3×C4—32no—
201C22×C3×C4—32no—
202C22×C3×C4—32no—
203C22×C3×C4—32no—
204C22×C3×C4C22×D312yes—
205C22×C3×C4C22×D312yes—
206C22×C3×C4C22×D312yes—
207C22×Dic3—32no—
208C22×Dic3—32no—
209C22×Dic3—32no—
210C22×Dic3—61no—
211C22×Dic3—61no—
212C22×Dic3—61no—
213C22×Dic3C22×D312yes—
214C22×Dic3C22×D312yes—
215C22×Dic3C22×D312yes—
216C22×Dic3C22×D312yes—
217C2×C4×D3—38no—
218C2×C4×D3—38no—
219C2×C4×D3—38no—
220C2×C4×D3—38no—
221C2×C4×D3—38no—
222C2×C4×D3—64no—
223C2×C4×D3—64no—
224C2×C4×D3—64no—
225C2×C4×D3—64no—
226C2×C4×D3—64no—
227C2×C4×D3—64no—
228C2×C4×D3—64no—
229C2×C4×D3—64no—
230C2×C4×D3—64no—
231C2×C4×D3—64no—
232C2×C4×D3—64no—
233C2×C4×D3—64no—
234C2×C4×D3—64no—
235C2×C4×D3—64no—
236C2×C4×D3—64no—
237C2×C4×D3—64no—
238C2×C4×D3—64no—
239C2×C4×D3—64no—
240C2×C4×D3—64no—
241C2×C4×D3—122no—
242C2×C4×D3—122no—
243C2×C4×D3—122no—
244C2×C4×D3—122no—
245C2×C4×D3—122no—
246C2×C4×D3—122no—
247C3×C4⋊C4—38no—
248C3×C4⋊C4—64no—
249C3×C42—64no—
250C4⋊Dic3—64no—
251C4⋊Dic3C4×D318yescomplemented
252Dic3⋊C4—24no—
253Dic3⋊C4—38no—
254Dic3⋊C4—38no—
255Dic3⋊C4—64no—
256C4×Dic3—24no—
257C4×Dic3—64no—
258C4×Dic3—64no—
259C22×C32C23×C411yescharacteristic
260C22×C32C22×D411yescharacteristic
261C22×C32C22×Q811yescharacteristic
262C22×C32C2×#4111yescharacteristic
263C22×C32C2×#4111yescharacteristic
264C22×C32C2×#4111yescharacteristic
265C22×C32C2×#4111yescharacteristic
266C2×C3⋊D3#11714yes—
267C2×C3⋊D3C4×D414yes—
268C2×C3⋊D3C4×Q814yes—
269C2×C3⋊D3C22⋊Q814yes—
270C2×C3⋊D3#12314yes—
271C2×C3⋊D3#12514yes—
272C2×C3⋊D3#12614yes—
273C32×C4—22no—
274C32×C4—22no—
275C32×C4—41no—
276C3⋊Dic3—22no—
277C3⋊Dic3—22no—
278C3⋊Dic3—41no—
279C3×Dic3—24no—
280C3×Dic3—24no—
281C3×Dic3—24no—
282C3×Dic3—42no—
283C23×C4—91no—
284C23×C4—91no—
285C23×C4—91no—
286C23×C4—91no—
287C23×C4—91no—
288C23×C4—91no—
289C23×C4—91no—
290C2×C4⋊C4—32no—
291C2×C4⋊C4—32no—
292C2×C4⋊C4—98no—
293C2×C4⋊C4—92no—
294C2×C4⋊C4—92no—
295C2×C4⋊C4—184no—
296C2×C42—32no—
297C2×C42—92no—
298C2×C42—184no—
299#95—32no—
300#95—32no—
301#95—32no—
302#95—92no—
303#95—92no—
304#95—92no—
305#95—91no—
306#95—91no—
307#95—91no—
308#95D3211yescharacteristic
309C23×C3—21no—
310C23×C3C23×D312yes—
311C22×D3—34no—
312C22×D3—34no—
313C22×D3—34no—
314C22×D3—34no—
315C22×D3—34no—
316C22×D3—34no—
317C22×D3—34no—
318C22×D3—62no—
319C22×D3—62no—
320C22×D3—62no—
321C22×D3—62no—
322C22×D3—62no—
323C22×D3—62no—
324C22×D3—62no—
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—22no—
332C2×C3×C4—22no—
333C2×C3×C4—22no—
334C2×C3×C4—22no—
335C2×C3×C4—34no—
336C2×C3×C4—34no—
337C2×C3×C4—34no—
338C2×C3×C4—41no—
339C2×C3×C4—41no—
340C2×C3×C4—41no—
341C2×C3×C4—41no—
342C2×C3×C4—41no—
343C2×C3×C4—41no—
344C2×C3×C4—62no—
345C2×C3×C4—62no—
346C2×C3×C4—62no—
347C2×C3×C4—62no—
348C2×C3×C4—62no—
349C2×C3×C4—62no—
350C2×C3×C4—62no—
351C2×C3×C4—62no—
352C2×C3×C4—62no—
353C2×C3×C4C2×C4×D314yes—
354C2×C3×C4D3×D414yes—
355C2×Dic3—22no—
356C2×Dic3—22no—
357C2×Dic3—22no—
358C2×Dic3—22no—
359C2×Dic3—22no—
360C2×Dic3—22no—
361C2×Dic3—22no—
362C2×Dic3—22no—
363C2×Dic3—22no—
364C2×Dic3—34no—
365C2×Dic3—34no—
366C2×Dic3—62no—
367C2×Dic3—62no—
368C2×Dic3—62no—
369C2×Dic3—62no—
370C2×Dic3—62no—
371C2×Dic3—62no—
372C2×Dic3—62no—
373C2×Dic3—62no—
374C2×Dic3—62no—
375C2×Dic3—62no—
376C2×Dic3—121no—
377C2×Dic3—121no—
378C2×Dic3—121no—
379C2×Dic3—121no—
380C2×Dic3—121no—
381C2×Dic3—121no—
382C2×Dic3C2×C4×D314yes—
383C2×Dic3C2×C4×D314yes—
384C2×Dic3D3×Q814yes—
385C4×D3—616no—
386C4×D3—616no—
387C4×D3—616no—
388C4×D3—616no—
389C4×D3—616no—
390C4×D3—128no—
391C4×D3—128no—
392C4×D3—128no—
393C4×D3—128no—
394C4×D3—128no—
395C2×C32C2×#11711yescharacteristic
396C2×C32C2×C4×D411yescharacteristic
397C2×C32C2×C4×Q811yescharacteristic
398C2×C32C2×C22⋊Q811yescharacteristic
399C2×C32C2×#12311yescharacteristic
400C2×C32C2×#12511yescharacteristic
401C2×C32C2×#12611yescharacteristic
402C3⋊D3#38718yescomplemented
403C24—91no—
404C22×C4—32no—
405C22×C4—32no—
406C22×C4—32no—
407C22×C4—32no—
408C22×C4—94no—
409C22×C4—94no—
410C22×C4—94no—
411C22×C4—91no—
412C22×C4—91no—
413C22×C4—94no—
414C22×C4—94no—
415C22×C4—91no—
416C22×C4—182no—
417C22×C4—182no—
418C22×C4—182no—
419C22×C4—182no—
420C22×C4—182no—
421C22×C4—182no—
422C22×C4—182no—
423C22×C4—182no—
424C22×C4—182no—
425C22×C4—182no—
426C22×C4—182no—
427C22×C4—182no—
428C22×C4—182no—
429C22×C4—182no—
430C22×C4—182no—
431C22×C4—182no—
432C22×C4C2×D3211yescharacteristic
433C22×C4C2×D3211yescharacteristic
434C22×C4C2×D3211yescharacteristic
435C4⋊C4—38no—
436C4⋊C4—64no—
437C4⋊C4—98no—
438C4⋊C4—184no—
439C42—64no—
440C42—184no—
441C22×C3—21no—
442C22×C3—21no—
443C22×C3—21no—
444C22×C3—21no—
445C22×C3—21no—
446C22×C3—21no—
447C22×C3—21no—
448C22×C3C22×C4×D312yes—
449C22×C3C2×D3×D412yes—
450C22×C3C2×D3×Q812yes—
451C22×C3D3×#4112yes—
452C22×C3D3×#4112yes—
453C22×C3D3×#4112yes—
454C22×C3D3×#4112yes—
455C2×D3—38no—
456C2×D3—38no—
457C2×D3—38no—
458C2×D3—38no—
459C2×D3—38no—
460C2×D3—38no—
461C2×D3—38no—
462C2×D3—64no—
463C2×D3—64no—
464C2×D3—64no—
465C2×D3—64no—
466C2×D3—64no—
467C2×D3—64no—
468C2×D3—64no—
469C3×C4—24no—
470C3×C4—24no—
471C3×C4—42no—
472C3×C4—42no—
473C3×C4—42no—
474C3×C4—42no—
475C3×C4—64no—
476C3×C4—64no—
477C3×C4—64no—
478C3×C4—122no—
479Dic3—24no—
480Dic3—24no—
481Dic3—24no—
482Dic3—42no—
483Dic3—64no—
484Dic3—64no—
485Dic3—122no—
486Dic3—122no—
487Dic3—122no—
488Dic3—122no—
489C32C2×#38711yescharacteristic, complemented, Sylow
490C23—92no—
491C23—92no—
492C23—92no—
493C23—92no—
494C23—92no—
495C23—92no—
496C23—92no—
497C23C22×D3211yescharacteristic
498C2×C4—21no—
499C2×C4—21no—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—34no—
506C2×C4—34no—
507C2×C4—34no—
508C2×C4—62no—
509C2×C4—62no—
510C2×C4—62no—
511C2×C4—62no—
512C2×C4—62no—
513C2×C4—62no—
514C2×C4—62no—
515C2×C4—62no—
516C2×C4—62no—
517C2×C4—92no—
518C2×C4—92no—
519C2×C4—188no—
520C2×C4—188no—
521C2×C4—188no—
522C2×C4—188no—
523C2×C4—188no—
524C2×C4—181no—
525C2×C4—181no—
526C2×C4—181no—
527C2×C4—181no—
528C2×C4—181no—
529C2×C4—181no—
530C2×C4—181no—
531C2×C4—364no—
532C2×C4—364no—
533C2×C4C4×D3212yes—
534C2×C4#380212yes—
535C2×C3—21no—
536C2×C3—21no—
537C2×C3—21no—
538C2×C3—21no—
539C2×C3—21no—
540C2×C3—21no—
541C2×C3—21no—
542C2×C3D3×#11712yes—
543C2×C3C4×D3×D412yes—
544C2×C3C4×D3×Q812yes—
545C2×C3D3×C22⋊Q812yes—
546C2×C3D3×#12312yes—
547C2×C3D3×#12512yes—
548C2×C3D3×#12612yes—
549D3—316no—
550D3—68no—
551C22—94no—
552C22—94no—
553C22—94no—
554C22—94no—
555C22—94no—
556C22—94no—
557C22—94no—
558C22C2×C4×D3211yescharacteristic
559C22C2×#380211yescharacteristic
560C22#6430611yescharacteristic
561C22#6431211yescharacteristic
562C22#6431211yescharacteristic
563C22#6431211yescharacteristic
564C22D32×Q811yescharacteristic
565C4—22no—
566C4—22no—
567C4—41no—
568C4—64no—
569C4—64no—
570C4—64no—
571C4—122no—
572C4—182no—
573C4—182no—
574C4—361no—
575C3—21no—
576C3D3×#38712yescomplemented
577C2—98no—
578C2C4×#380211yescharacteristic
579C2#1059405211yescharacteristic
580C2#1059415411yescharacteristic
581C2#1059429511yescharacteristic
582C2#1059436311yescharacteristic
583C2#1059439911yescharacteristic
584C2#1059463111yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC32×#95C22
socle, cosocleC23×C32C24
prime radicalC23×C3⋊D3C23
hypercenter#95D32
hypocenterC32C2×#387
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ #95

Complements

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

NH ≅ G/Ntype
5. C3×#4653C2semidirect
9. #10591270C2semidirect
10. #10591249C2semidirect
11. #10591193C2semidirect
26. #63900C4semidirect
53. #4653D3semidirect
87. C3×C4⋊Dic3C2×C4semidirect
90. #3724C2×C4semidirect
251. C4⋊Dic3C4×D3semidirect
402. C3⋊D3#387semidirect
489. C32C2×#387semidirect
576. C3D3×#387semidirect

Maximal subgroups

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

subgroupindex
C2×#639002
C2×#638832
C2×C4×#6242
C3⋊D3×#952
C3×#46532
#105913702
#105912702
#105912492
#105911932
D3×#3873