Finite Group Databasebeta

← #11808305

Subgroups — #11808305

Order 1152.

1805 conjugacy classes of subgroups.

The subgroup lattice has 674 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63921C211yesmaximal, characteristic
2C2×#63921C211yesmaximal, characteristic
3C2×#63921C211yesmaximal, characteristic
4C2×#63883C211yesmaximal, characteristic, complemented
5C3⋊D3×#95C211yesmaximal, characteristic, complemented
6C3×#4675C212yesmaximal, complemented
7#10591370C211yesmaximal, characteristic, complemented
8#10591370C211yesmaximal, characteristic, complemented
9#10591301C212yesmaximal, complemented
10#10591297C212yesmaximal, complemented
11#10591296C212yesmaximal, complemented
12D3×#397—32nomaximal
13C23×D32C2211yescharacteristic
14C22×C4×C3⋊D3C2211yescharacteristic
15C22×C4×C3⋊D3C2211yescharacteristic
16C22×C4×C3⋊D3C2211yescharacteristic
17C22×#624C2211yescharacteristic
18C22×#624C2211yescharacteristic
19C22×#624C2211yescharacteristic
20C2×C3×(C2×D3)⋊C4C2212yes—
21C2×C3×(C2×D3)⋊C4C2212yes—
22C2×C3×(C2×D3)⋊C4C2212yes—
23C2×C3×Dic3⋊C4C2212yescomplemented
24C2×Dic3⋊Dic3C2212yescomplemented
25C2×(C2×D3)⋊Dic3C2212yes—
26C2×(C2×D3)⋊Dic3C2212yes—
27C2×(C2×D3)⋊Dic3C2212yes—
28#63921—24no—
29#63921—24no—
30#63921—24no—
31#63883—24no—
32C32×#95C2211yescharacteristic, complemented
33#63658C2211yescharacteristic, complemented
34#63658C2211yescharacteristic, complemented
35#63658C2211yescharacteristic, complemented
36C3×C3⋊#95C2212yescomplemented
37C3×C3⋊#95C2212yescomplemented
38#63579C2212yescomplemented
39#63579C2212yescomplemented
40C2×D3×C4⋊C4—32no—
41C2×D3×C22⋊C4—32no—
42C2×D3×C22⋊C4—32no—
43C2×D3×C22⋊C4—32no—
44C3×#397—32no—
45#4992—32no—
46#4953—32no—
47#4952—32no—
48#4952—32no—
49#4675—32no—
50#4675D312yescomplemented
51#4674—32no—
52D3×#95—32no—
53D3×#95—32no—
54D3×#95—32no—
55D3×#95—61no—
56C23×C3⋊D3C2311yescharacteristic
57C23×C3×D3C2312yes—
58C22×D32—22no—
59C22×D32—22no—
60C22×D32—22no—
61C22×D32—22no—
62C22×D32—22no—
63C22×D32—22no—
64C22×D32D414yes—
65C22×C32×C4C2311yescharacteristic
66C22×C32×C4C2311yescharacteristic
67C22×C32×C4C2311yescharacteristic
68C22×C3⋊Dic3C2311yescharacteristic
69C22×C3⋊Dic3C2311yescharacteristic
70C22×C3⋊Dic3C2311yescharacteristic
71C2×C4×C3⋊D3—22no—
72C2×C4×C3⋊D3—22no—
73C2×C4×C3⋊D3—22no—
74C2×C4×C3⋊D3—22no—
75C2×C4×C3⋊D3—22no—
76C2×C4×C3⋊D3—22no—
77C2×C4×C3⋊D3—22no—
78C2×C4×C3⋊D3—22no—
79C2×C4×C3⋊D3—22no—
80C22×C3×Dic3C2312yes—
81C22×C3×Dic3C2312yes—
82C22×C3×Dic3C2312yes—
83C2×#624—22no—
84C2×#624—22no—
85C2×#624—22no—
86C2×#624—22no—
87C2×#624—22no—
88C2×#624—22no—
89C2×#624—22no—
90C2×#624—22no—
91C2×#624D414yes—
92C3×(C2×D3)⋊C4—24no—
93C3×(C2×D3)⋊C4—24no—
94C3×(C2×D3)⋊C4—24no—
95C3×Dic3⋊C4—24no—
96Dic3⋊Dic3—24no—
97(C2×D3)⋊Dic3—24no—
98(C2×D3)⋊Dic3—24no—
99(C2×D3)⋊Dic3—24no—
100C2×#397—91noSylow
101C24×D3—32no—
102C22×C4×D3—32no—
103C22×C4×D3—32no—
104C22×C4×D3—32no—
105C22×C4×D3—32no—
106C22×C4×D3—32no—
107C22×C4×D3—32no—
108C22×C4×D3—61no—
109C22×C4×D3—61no—
110C22×C4×D3—61no—
111C2×C3×C4⋊C4—32no—
112C2×C3×C22⋊C4—32no—
113C2×C3×C22⋊C4—32no—
114C2×C3×C22⋊C4—32no—
115C2×#217—32no—
116C2×#217—32no—
117C2×#217—32no—
118C2×(C2×D3)⋊C4—32no—
119C2×(C2×D3)⋊C4—32no—
120C2×(C2×D3)⋊C4—32no—
121C2×(C2×D3)⋊C4C2×D312yes—
122C2×(C2×D3)⋊C4C2×D312yes—
123C2×(C2×D3)⋊C4C2×D312yes—
124C2×C4⋊Dic3—32no—
125C2×Dic3⋊C4—32no—
126C2×Dic3⋊C4C2×D312yescomplemented
127D3×C4⋊C4—68no—
128D3×C22⋊C4—68no—
129D3×C22⋊C4—68no—
130D3×C22⋊C4—68no—
131C3×#95—21no—
132C3×#95—32no—
133C3×#95—32no—
134C3×#95C2×D312yescomplemented
135C3⋊#95—32no—
136C3⋊#95—32no—
137C3⋊#95—32no—
138C3⋊#95—32no—
139C3⋊#95—32no—
140C3⋊#95—32no—
141C3⋊#95—32no—
142C3⋊#95—61no—
143C3⋊#95—61no—
144C3⋊#95—61no—
145C3⋊#95C2×D312yescomplemented
146C3⋊#95C2×D312yescomplemented
147C23×C32C2411yescharacteristic
148C22×C3⋊D3C2×D412yes—
149C22×C3⋊D3C2×D412yes—
150C22×C3⋊D3#4112yes—
151C22×C3⋊D3#4112yes—
152C22×C3⋊D3#4112yes—
153C22×C3⋊D3#4112yes—
154C22×C3⋊D3#4112yes—
155C22×C3×D3—22no—
156C22×C3×D3—22no—
157C22×C3×D3—22no—
158C22×C3×D3—22no—
159C22×C3×D3—22no—
160C22×C3×D3—22no—
161C22×C3×D3C2×D414yes—
162C2×D32—28no—
163C2×D32—28no—
164C2×D32—28no—
165C2×D32—44no—
166C2×D32—44no—
167C2×D32—44no—
168C2×D32—44no—
169C2×C32×C4—21no—
170C2×C32×C4—21no—
171C2×C32×C4—21no—
172C2×C32×C4—21no—
173C2×C32×C4—21no—
174C2×C32×C4—21no—
175C2×C32×C4—21no—
176C2×C32×C4—21no—
177C2×C32×C4—21no—
178C2×C3⋊Dic3—21no—
179C2×C3⋊Dic3—21no—
180C2×C3⋊Dic3—21no—
181C2×C3⋊Dic3—21no—
182C2×C3⋊Dic3—21no—
183C2×C3⋊Dic3—21no—
184C2×C3⋊Dic3—21no—
185C2×C3⋊Dic3—21no—
186C2×C3⋊Dic3—21no—
187C4×C3⋊D3—44no—
188C4×C3⋊D3—44no—
189C4×C3⋊D3—44no—
190C2×C3×Dic3—22no—
191C2×C3×Dic3—22no—
192C2×C3×Dic3—22no—
193C2×C3×Dic3—22no—
194C2×C3×Dic3—22no—
195C2×C3×Dic3—22no—
196C2×C3×Dic3—22no—
197C2×C3×Dic3—22no—
198C2×C3×Dic3C2×D414yes—
199#624—28no—
200#624—44no—
201#624—44no—
202C22×C4⋊C4—91no—
203C22×C22⋊C4—91no—
204C22×C22⋊C4—91no—
205C22×C22⋊C4—91no—
206#397—32no—
207#397—92no—
208#397—92no—
209#397—92no—
210C2×#95—91no—
211C2×#95—91no—
212C2×#95—91no—
213C24×C3—32no—
214C23×D3—32no—
215C23×D3—38no—
216C23×D3—61no—
217C23×D3—64no—
218C23×D3—64no—
219C23×D3—64no—
220C23×D3—64no—
221C23×D3—64no—
222C23×D3—64no—
223C23×D3C22×D312yes—
224C22×C3×C4—21no—
225C22×C3×C4—21no—
226C22×C3×C4—21no—
227C22×C3×C4—32no—
228C22×C3×C4—32no—
229C22×C3×C4—32no—
230C22×C3×C4C22×D312yes—
231C22×C3×C4C22×D312yes—
232C22×C3×C4C22×D312yes—
233C22×Dic3—32no—
234C22×Dic3—32no—
235C22×Dic3—32no—
236C22×Dic3—61no—
237C22×Dic3—61no—
238C22×Dic3—61no—
239C22×Dic3C22×D312yes—
240C22×Dic3C22×D312yes—
241C22×Dic3C22×D312yes—
242C2×C4×D3—38no—
243C2×C4×D3—64no—
244C2×C4×D3—64no—
245C2×C4×D3—64no—
246C2×C4×D3—64no—
247C2×C4×D3—64no—
248C2×C4×D3—64no—
249C2×C4×D3—64no—
250C2×C4×D3—64no—
251C2×C4×D3—64no—
252C2×C4×D3—64no—
253C2×C4×D3—64no—
254C2×C4×D3—64no—
255C2×C4×D3—64no—
256C2×C4×D3—64no—
257C2×C4×D3—64no—
258C2×C4×D3—64no—
259C2×C4×D3—64no—
260C2×C4×D3—64no—
261C2×C4×D3—64no—
262C2×C4×D3—64no—
263C2×C4×D3—122no—
264C2×C4×D3—122no—
265C2×C4×D3—122no—
266C2×C4×D3—122no—
267C2×C4×D3—122no—
268C2×C4×D3—122no—
269C3×C4⋊C4—64no—
270C3×C22⋊C4—64no—
271C3×C22⋊C4—64no—
272C3×C22⋊C4—64no—
273#217—64no—
274#217—64no—
275#217—64no—
276(C2×D3)⋊C4—24no—
277(C2×D3)⋊C4—24no—
278(C2×D3)⋊C4—24no—
279(C2×D3)⋊C4—64no—
280(C2×D3)⋊C4—64no—
281(C2×D3)⋊C4—64no—
282C4⋊Dic3—64no—
283Dic3⋊C4—24no—
284Dic3⋊C4—64no—
285C22×C32C22×D411yescharacteristic
286C22×C32C22×D411yescharacteristic
287C22×C32C2×#4111yescharacteristic
288C22×C32C2×#4111yescharacteristic
289C22×C32C2×#4111yescharacteristic
290C22×C32C2×#4111yescharacteristic
291C22×C32C2×#4111yescharacteristic
292C2×C3⋊D3#12114yes—
293C2×C3⋊D3#12314yes—
294C2×C3⋊D3#12314yes—
295C2×C3⋊D3#12314yes—
296C2×C3⋊D3#12414yes—
297C2×C3⋊D3#12614yes—
298C2×C3⋊D3#12614yes—
299C2×C3×D3—24no—
300C2×C3×D3—24no—
301C2×C3×D3—24no—
302C2×C3×D3—42no—
303C2×C3×D3—42no—
304C2×C3×D3—42no—
305C2×C3×D3—42no—
306D32—416no—
307C32×C4—41no—
308C32×C4—41no—
309C32×C4—41no—
310C3⋊Dic3—41no—
311C3⋊Dic3—41no—
312C3⋊Dic3—41no—
313C3×Dic3—24no—
314C3×Dic3—42no—
315C3×Dic3—42no—
316C25—91no—
317C23×C4—91no—
318C23×C4—91no—
319C23×C4—91no—
320C23×C4—91no—
321C23×C4—91no—
322C23×C4—91no—
323C2×C4⋊C4—32no—
324C2×C4⋊C4—92no—
325C2×C4⋊C4—184no—
326C2×C22⋊C4—32no—
327C2×C22⋊C4—32no—
328C2×C22⋊C4—32no—
329C2×C22⋊C4—92no—
330C2×C22⋊C4—92no—
331C2×C22⋊C4—92no—
332C2×C22⋊C4—184no—
333C2×C22⋊C4—184no—
334C2×C22⋊C4—184no—
335#95—32no—
336#95—32no—
337#95—92no—
338#95—92no—
339#95—91no—
340#95—91no—
341#95—91no—
342#95D3211yescharacteristic, complemented
343C23×C3—21no—
344C23×C3—34no—
345C23×C3—62no—
346C23×C3—62no—
347C23×C3—62no—
348C23×C3—62no—
349C23×C3—62no—
350C23×C3—62no—
351C23×C3C23×D312yes—
352C22×D3—22no—
353C22×D3—22no—
354C22×D3—22no—
355C22×D3—22no—
356C22×D3—22no—
357C22×D3—22no—
358C22×D3—34no—
359C22×D3—34no—
360C22×D3—34no—
361C22×D3—34no—
362C22×D3—34no—
363C22×D3—34no—
364C22×D3—34no—
365C22×D3—62no—
366C22×D3—62no—
367C22×D3—62no—
368C22×D3—62no—
369C22×D3—62no—
370C22×D3—62no—
371C22×D3—62no—
372C22×D3—616no—
373C22×D3—616no—
374C22×D3—616no—
375C22×D3—128no—
376C22×D3—128no—
377C22×D3—128no—
378C22×D3—128no—
379C22×D3D3×D414yes—
380C2×C3×C4—22no—
381C2×C3×C4—22no—
382C2×C3×C4—22no—
383C2×C3×C4—22no—
384C2×C3×C4—22no—
385C2×C3×C4—22no—
386C2×C3×C4—22no—
387C2×C3×C4—22no—
388C2×C3×C4—22no—
389C2×C3×C4—22no—
390C2×C3×C4—22no—
391C2×C3×C4—22no—
392C2×C3×C4—34no—
393C2×C3×C4—41no—
394C2×C3×C4—41no—
395C2×C3×C4—41no—
396C2×C3×C4—41no—
397C2×C3×C4—41no—
398C2×C3×C4—41no—
399C2×C3×C4—62no—
400C2×C3×C4—62no—
401C2×C3×C4—62no—
402C2×C3×C4—62no—
403C2×C3×C4—62no—
404C2×C3×C4—62no—
405C2×C3×C4—62no—
406C2×C3×C4—62no—
407C2×Dic3—22no—
408C2×Dic3—22no—
409C2×Dic3—22no—
410C2×Dic3—22no—
411C2×Dic3—22no—
412C2×Dic3—22no—
413C2×Dic3—22no—
414C2×Dic3—22no—
415C2×Dic3—62no—
416C2×Dic3—62no—
417C2×Dic3—62no—
418C2×Dic3—62no—
419C2×Dic3—62no—
420C2×Dic3—62no—
421C2×Dic3—62no—
422C2×Dic3—62no—
423C2×Dic3—62no—
424C2×Dic3—62no—
425C2×Dic3—62no—
426C2×Dic3—62no—
427C2×Dic3—121no—
428C2×Dic3—121no—
429C2×Dic3—121no—
430C2×Dic3—121no—
431C2×Dic3—121no—
432C2×Dic3—121no—
433C2×Dic3D3×D414yes—
434C4×D3—616no—
435C4×D3—128no—
436C4×D3—128no—
437C4×D3—128no—
438C4×D3—128no—
439C4×D3—128no—
440C4×D3—128no—
441C4×D3—128no—
442C4×D3—128no—
443C2×C32C2×#12111yescharacteristic
444C2×C32C2×#12311yescharacteristic
445C2×C32C2×#12311yescharacteristic
446C2×C32C2×#12311yescharacteristic
447C2×C32C2×#12411yescharacteristic
448C2×C32C2×#12611yescharacteristic
449C2×C32C2×#12611yescharacteristic
450C3⋊D3#39718yescomplemented
451C3×D3—44no—
452C24—32no—
453C24—94no—
454C24—91no—
455C24—182no—
456C24—182no—
457C24—182no—
458C24—182no—
459C24—182no—
460C24—182no—
461C22×C4—32no—
462C22×C4—32no—
463C22×C4—32no—
464C22×C4—94no—
465C22×C4—91no—
466C22×C4—91no—
467C22×C4—91no—
468C22×C4—182no—
469C22×C4—182no—
470C22×C4—182no—
471C22×C4—182no—
472C22×C4—182no—
473C22×C4—182no—
474C22×C4—182no—
475C22×C4—182no—
476C22×C4—182no—
477C22×C4—182no—
478C22×C4—182no—
479C22×C4—182no—
480C22×C4—182no—
481C22×C4—182no—
482C22×C4—182no—
483C22×C4—182no—
484C22×C4—182no—
485C22×C4C2×D3211yescharacteristic
486C22×C4C2×D3211yescharacteristic
487C22×C4C2×D3211yescharacteristic
488C4⋊C4—64no—
489C4⋊C4—184no—
490C22⋊C4—64no—
491C22⋊C4—64no—
492C22⋊C4—64no—
493C22⋊C4—184no—
494C22⋊C4—184no—
495C22⋊C4—184no—
496C22×C3—21no—
497C22×C3—21no—
498C22×C3—21no—
499C22×C3—21no—
500C22×C3—21no—
501C22×C3—21no—
502C22×C3—21no—
503C22×C3—64no—
504C22×C3—64no—
505C22×C3—64no—
506C22×C3—122no—
507C22×C3—122no—
508C22×C3—122no—
509C22×C3—122no—
510C22×C3C2×D3×D412yes—
511C22×C3C2×D3×D412yes—
512C22×C3D3×#4112yes—
513C22×C3D3×#4112yes—
514C22×C3D3×#4112yes—
515C22×C3D3×#4112yes—
516C22×C3D3×#4112yes—
517C2×D3—24no—
518C2×D3—24no—
519C2×D3—24no—
520C2×D3—38no—
521C2×D3—38no—
522C2×D3—38no—
523C2×D3—38no—
524C2×D3—38no—
525C2×D3—38no—
526C2×D3—38no—
527C2×D3—42no—
528C2×D3—42no—
529C2×D3—42no—
530C2×D3—42no—
531C2×D3—64no—
532C2×D3—64no—
533C2×D3—64no—
534C2×D3—64no—
535C2×D3—64no—
536C2×D3—64no—
537C2×D3—64no—
538C2×D3—1232no—
539C3×C4—42no—
540C3×C4—42no—
541C3×C4—42no—
542C3×C4—42no—
543C3×C4—42no—
544C3×C4—42no—
545C3×C4—64no—
546C3×C4—122no—
547C3×C4—122no—
548Dic3—24no—
549Dic3—42no—
550Dic3—42no—
551Dic3—122no—
552Dic3—122no—
553Dic3—122no—
554Dic3—122no—
555Dic3—122no—
556Dic3—122no—
557C32C2×#39711yescharacteristic, complemented, Sylow
558C23—34no—
559C23—62no—
560C23—62no—
561C23—62no—
562C23—62no—
563C23—62no—
564C23—62no—
565C23—92no—
566C23—92no—
567C23—92no—
568C23—92no—
569C23—92no—
570C23—92no—
571C23—92no—
572C23—188no—
573C23—188no—
574C23—188no—
575C23—364no—
576C23—364no—
577C23—364no—
578C23—364no—
579C23C22×D3211yescharacteristic
580C2×C4—21no—
581C2×C4—21no—
582C2×C4—21no—
583C2×C4—21no—
584C2×C4—21no—
585C2×C4—21no—
586C2×C4—21no—
587C2×C4—21no—
588C2×C4—21no—
589C2×C4—34no—
590C2×C4—62no—
591C2×C4—62no—
592C2×C4—62no—
593C2×C4—62no—
594C2×C4—62no—
595C2×C4—62no—
596C2×C4—62no—
597C2×C4—62no—
598C2×C4—188no—
599C2×C4—181no—
600C2×C4—181no—
601C2×C4—181no—
602C2×C4—181no—
603C2×C4—181no—
604C2×C4—181no—
605C2×C4—181no—
606C2×C4—181no—
607C2×C4—181no—
608C2×C4—364no—
609C2×C4—364no—
610C2×C4—364no—
611C2×C4—364no—
612C2×C4—364no—
613C2×C3—21no—
614C2×C3—21no—
615C2×C3—21no—
616C2×C3—21no—
617C2×C3—21no—
618C2×C3—21no—
619C2×C3—21no—
620C2×C3—124no—
621C2×C3D3×#12112yes—
622C2×C3D3×#12312yes—
623C2×C3D3×#12312yes—
624C2×C3D3×#12312yes—
625C2×C3D3×#12412yes—
626C2×C3D3×#12612yes—
627C2×C3D3×#12612yes—
628D3—316no—
629D3—44no—
630D3—68no—
631C22—64no—
632C22—64no—
633C22—64no—
634C22—94no—
635C22—94no—
636C22—94no—
637C22—94no—
638C22—94no—
639C22—94no—
640C22—94no—
641C22—122no—
642C22—122no—
643C22—122no—
644C22—122no—
645C22—3616no—
646C22#6430611yescharacteristic
647C22#6430611yescharacteristic
648C22#6430611yescharacteristic
649C22D32×D411yescharacteristic
650C22D32×D411yescharacteristic
651C22#6431211yescharacteristic
652C22#6431911yescharacteristic
653C4—41no—
654C4—41no—
655C4—41no—
656C4—64no—
657C4—122no—
658C4—122no—
659C4—361no—
660C4—361no—
661C4—361no—
662C3—21no—
663C3D3×#39712yescomplemented
664C2—98no—
665C2—124no—
666C2#1059402011yescharacteristic
667C2#1059426011yescharacteristic
668C2#1059426511yescharacteristic
669C2#1059428811yescharacteristic
670C2#1059460811yescharacteristic
671C2#1059460811yescharacteristic
672C2#1059465611yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutator, socle, cosocleC23×C32C24
FittingC32×#95C22
prime radicalC23×D32C22
hypercenter#95D32
hypocenterC32C2×#397
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C23 ◁ #95

Complements

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

NH ≅ G/Ntype
4. C2×#63883C2semidirect
5. C3⋊D3×#95C2semidirect
6. C3×#4675C2semidirect
7. #10591370C2semidirect
8. #10591370C2semidirect
9. #10591301C2semidirect
10. #10591297C2semidirect
11. #10591296C2semidirect
23. C2×C3×Dic3⋊C4C22semidirect
24. C2×Dic3⋊Dic3C22semidirect
32. C32×#95C22semidirect
33. #63658C22semidirect
34. #63658C22semidirect
35. #63658C22semidirect
36. C3×C3⋊#95C22semidirect
37. C3×C3⋊#95C22semidirect
38. #63579C22semidirect
39. #63579C22semidirect
50. #4675D3semidirect
126. C2×Dic3⋊C4C2×D3semidirect
134. C3×#95C2×D3semidirect
145. C3⋊#95C2×D3semidirect
146. C3⋊#95C2×D3semidirect
342. #95D32semidirect
450. C3⋊D3#397semidirect
557. C32C2×#397semidirect
663. C3D3×#397semidirect

Maximal subgroups

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

subgroupindex
C2×#639212
C2×#638832
C3⋊D3×#952
C3×#46752
#105913702
#105913012
#105912972
#105912962
D3×#3973