Finite Group Databasebeta

← #11802164

Subgroups — #11802164

Order 1152.

1589 conjugacy classes of subgroups.

The subgroup lattice has 660 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D4×C3⋊Dic3C211yesmaximal, characteristic
2C2×C3×#935C211yesmaximal, characteristic
3C22×Dic32C211yesmaximal, characteristic, complemented
4C3×#5220C211yesmaximal, characteristic
5#10591718C211yesmaximal, characteristic, complemented
6#10591705C211yesmaximal, characteristic, complemented
7#10591705C212yesmaximal, complemented
8#10591702C212yesmaximal, complemented
9#10591696C211yesmaximal, characteristic, complemented
10#10591272C212yesmaximal, complemented
11#10591241C212yesmaximal, complemented
12Dic3×#123—31nomaximal
13#74661—31nomaximal
14C22×C32×D4C2211yescharacteristic
15C23×C3⋊Dic3C2211yescharacteristic
16C23×C3⋊Dic3C2211yescharacteristic
17C23×C3×Dic3C2211yescharacteristic
18C23×C3×Dic3C2211yescharacteristic
19C2×#3757C2211yescharacteristic
20C2×#3757C2211yescharacteristic
21D4×C3⋊Dic3—24no—
22C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
23C2×C4×C3⋊Dic3C2211yescharacteristic
24C2×C3×#217C2211yescharacteristic
25C2×C3×#217C2212yes—
26C2×C3×#217C2212yes—
27C2×C3×#217C2211yescharacteristic
28C3×#935C418yescomplemented
29C2×C3×Dic3⋊C4C2212yes—
30C2×Dic3⋊Dic3C2212yes—
31C2×Dic32—24no—
32C2×Dic32C2212yes—
33C2×Dic32C2212yes—
34C2×Dic32C2212yes—
35C3×C3⋊#95C2212yes—
36#63579C2212yes—
37#63579C2212yes—
38#63579C2212yes—
39#63579C2212yes—
40C2×C3×#123—31no—
41C2×#935D311yescharacteristic
42C2×D4×Dic3—31no—
43C2×D4×Dic3—31no—
44C2×D4×Dic3—61no—
45C22×C4×Dic3—31no—
46C22×C4×Dic3—31no—
47C3×#386—31no—
48#5220D311yescharacteristic
49#5211—31no—
50#5210—31no—
51#4980—32no—
52Dic3×C4⋊C4—32no—
53#4951—32no—
54#4950—31no—
55#4945—32no—
56#4943—31no—
57Dic3×C22⋊C4—32no—
58Dic3×C22⋊C4—31no—
59Dic3×C22⋊C4—32no—
60Dic3×C22⋊C4—31no—
61#4655—32no—
62#4649—32no—
63C24×C32C2311yescharacteristic
64C24×C32C2311yescharacteristic
65C2×C32×D4—22no—
66C2×C32×D4—22no—
67C2×C32×D4C2×C414yes—
68C22×C32×C4C2311yescharacteristic
69C22×C3⋊Dic3—24no—
70C22×C3⋊Dic3—22no—
71C22×C3⋊Dic3—24no—
72C22×C3⋊Dic3D414yes—
73C22×C3⋊Dic3C2311yescharacteristic
74C22×C3⋊Dic3C2311yescharacteristic
75C22×C3⋊Dic3C2311yescharacteristic
76C22×C3⋊Dic3C2311yescharacteristic
77C22×C3×Dic3—22no—
78C22×C3×Dic3—22no—
79C22×C3×Dic3—22no—
80C22×C3×Dic3—24no—
81C22×C3×Dic3C2×C414yescomplemented
82C22×C3×Dic3C2312yes—
83C22×C3×Dic3C2312yes—
84C22×C3×Dic3C2312yes—
85C22×C3×Dic3C2312yes—
86#3757—22no—
87#3757—22no—
88C4⋊(C3⋊Dic3)—22no—
89C4×C3⋊Dic3—22no—
90C3×#217—22no—
91C3×#217—24no—
92C3×#217C2×C414yescomplemented
93C3×#217C2×C418yescomplemented
94C3×Dic3⋊C4C2×C418yescomplemented
95Dic3⋊Dic3—24no—
96Dic32—24no—
97Dic32—24no—
98Dic32—24no—
99C4×#123—91noSylow
100C22×C3×D4—21no—
101C22×C3×D4C2×D311yescharacteristic
102C22×C3×D4C2×D311yescharacteristic
103C23×C3×C4—31no—
104C23×C3×C4—31no—
105C23×Dic3—31no—
106C23×Dic3—31no—
107C23×Dic3—31no—
108C23×Dic3—31no—
109C23×Dic3—61no—
110C23×Dic3—61no—
111C23×Dic3C2×D311yescharacteristic
112C23×Dic3C2×D311yescharacteristic
113C3×#123—38no—
114C2×C3×C4⋊C4—32no—
115C2×C3×C22⋊C4—31no—
116C2×C3×C22⋊C4—32no—
117C2×C3×C22⋊C4—31no—
118C2×C3×C22⋊C4—32no—
119C2×#217—31no—
120C2×#217—31no—
121C2×#217—31no—
122C2×#217—31no—
123C2×#217—61no—
124C2×#217—61no—
125C2×#217C2×D312yes—
126C2×#217C2×D311yescharacteristic
127C2×#217C2×D312yes—
128C2×#217C2×D311yescharacteristic
129#935Dic318yescomplemented
130D4×Dic3—64no—
131D4×Dic3—64no—
132D4×Dic3—68no—
133C2×C4⋊Dic3—31no—
134C2×C4⋊Dic3—31no—
135C2×C4⋊Dic3—32no—
136C2×C4⋊Dic3—61no—
137C2×Dic3⋊C4—32no—
138C2×Dic3⋊C4C2×D312yes—
139C2×C4×Dic3—31no—
140C2×C4×Dic3—31no—
141C2×C4×Dic3—32no—
142C2×C4×Dic3—32no—
143C2×C4×Dic3—32no—
144C2×C4×Dic3—32no—
145C2×C4×Dic3—32no—
146C2×C4×Dic3—32no—
147C2×C4×Dic3—61no—
148C2×C4×Dic3—64no—
149C2×C4×Dic3—64no—
150C3×#95—32no—
151C3⋊#95—32no—
152C3⋊#95—32no—
153C3⋊#95—32no—
154C3⋊#95—32no—
155C3⋊#95—32no—
156C3⋊#95—32no—
157C3⋊#95—32no—
158C3⋊#95—32no—
159C3⋊#95C2×D312yes—
160C23×C32—21no—
161C23×C32—21no—
162C23×C32—22no—
163C23×C32—22no—
164C23×C32—22no—
165C23×C32—22no—
166C23×C32C22×C412yes—
167C23×C32C22×C412yes—
168C23×C32C2×D412yes—
169C23×C32#4112yes—
170C23×C32C2411yescharacteristic
171C32×D4—28no—
172C2×C32×C4—21no—
173C2×C32×C4—21no—
174C2×C32×C4C22×C412yes—
175C2×C3⋊Dic3—21no—
176C2×C3⋊Dic3—21no—
177C2×C3⋊Dic3—22no—
178C2×C3⋊Dic3—28no—
179C2×C3⋊Dic3—22no—
180C2×C3⋊Dic3—22no—
181C2×C3⋊Dic3—44no—
182C2×C3⋊Dic3C2×D412yes—
183C2×C3⋊Dic3C2×D412yes—
184C2×C3⋊Dic3#4114yes—
185C2×C3×Dic3—28no—
186C2×C3×Dic3—28no—
187C2×C3×Dic3—22no—
188C2×C3×Dic3—22no—
189C2×C3×Dic3—22no—
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×Dic3C22×C414yes—
197C2×C3×Dic3C22×C414yes—
198C2×C3×Dic3#4114yes—
199C2×#123—31no—
200C2×C4×D4—91no—
201C22×C42—91no—
202#388—92no—
203#387—92no—
204#386—31no—
205#385—91no—
206#381—91no—
207C4×C4⋊C4—92no—
208C4×C22⋊C4—92no—
209C4×C22⋊C4—91no—
210C24×C3—21no—
211C24×C3—21no—
212C24×C3C22×D311yescharacteristic
213C24×C3C22×D311yescharacteristic
214C24×C3C22×D311yescharacteristic
215C24×C3C22×D311yescharacteristic
216C2×C3×D4—24no—
217C2×C3×D4—24no—
218C2×C3×D4—22no—
219C2×C3×D4—22no—
220C2×C3×D4—22no—
221C2×C3×D4—22no—
222C2×C3×D4—24no—
223C2×C3×D4C4×D314yes—
224C2×C3×D4C2×Dic314yes—
225C22×C3×C4—21no—
226C22×C3×C4—34no—
227C22×C3×C4—32no—
228C22×C3×C4—32no—
229C22×C3×C4—32no—
230C22×C3×C4—32no—
231C22×C3×C4—64no—
232C22×C3×C4—62no—
233C22×C3×C4—62no—
234C22×C3×C4—62no—
235C22×C3×C4C22×D311yescharacteristic
236C22×C3×C4C22×D311yescharacteristic
237C22×Dic3—22no—
238C22×Dic3—22no—
239C22×Dic3—22no—
240C22×Dic3—24no—
241C22×Dic3—31no—
242C22×Dic3—31no—
243C22×Dic3—34no—
244C22×Dic3—34no—
245C22×Dic3—31no—
246C22×Dic3—31no—
247C22×Dic3—31no—
248C22×Dic3—31no—
249C22×Dic3—31no—
250C22×Dic3—31no—
251C22×Dic3—61no—
252C22×Dic3—61no—
253C22×Dic3—61no—
254C22×Dic3—61no—
255C22×Dic3—64no—
256C22×Dic3—64no—
257C22×Dic3—64no—
258C22×Dic3—62no—
259C22×Dic3—62no—
260C22×Dic3—64no—
261C22×Dic3—64no—
262C22×Dic3—64no—
263C22×Dic3—124no—
264C22×Dic3—124no—
265C22×Dic3C2×Dic314yescomplemented
266C22×Dic3C22×D312yes—
267C22×Dic3C22×D312yes—
268C22×Dic3C22×D312yes—
269C22×Dic3C22×D312yes—
270C3×C4⋊C4—38no—
271C3×C22⋊C4—34no—
272C3×C22⋊C4—38no—
273C3×C22⋊C4—64no—
274C3×C22⋊C4—62no—
275#217—22no—
276#217—24no—
277#217—62no—
278#217—62no—
279#217—64no—
280#217—64no—
281#217—62no—
282#217—62no—
283#217C2×Dic314yescomplemented
284#217C2×Dic318yescomplemented
285C4⋊Dic3—62no—
286C4⋊Dic3—62no—
287C4⋊Dic3—64no—
288C4⋊Dic3—64no—
289Dic3⋊C4—64no—
290Dic3⋊C4C2×Dic318yescomplemented
291C4×Dic3—64no—
292C4×Dic3—64no—
293C4×Dic3—64no—
294C4×Dic3—64no—
295C4×Dic3—64no—
296C4×Dic3—64no—
297C4×Dic3—62no—
298C4×Dic3—62no—
299C4×Dic3—64no—
300C22×C32—22no—
301C22×C32—24no—
302C22×C32—22no—
303C22×C32—22no—
304C22×C32—24no—
305C22×C32—24no—
306C22×C32—41no—
307C22×C32—41no—
308C22×C32—42no—
309C22×C32C4×D414yes—
310C22×C32C23×C411yescharacteristic
311C22×C32C22×D411yescharacteristic
312C22×C32C2×#4111yescharacteristic
313C22×C32C2×#4112yes—
314C22×C32C2×#4112yes—
315C32×C4—22no—
316C3⋊Dic3—22no—
317C3⋊Dic3—41no—
318C3⋊Dic3—41no—
319C3⋊Dic3#12314yescomplemented
320C3×Dic3—24no—
321C3×Dic3—24no—
322C3×Dic3—24no—
323C3×Dic3—42no—
324C22×D4D3211yescharacteristic
325C23×C4—31no—
326C23×C4—31no—
327C23×C4—91no—
328C23×C4—91no—
329#123—38no—
330C4×D4—184no—
331C2×C4⋊C4—32no—
332C2×C4⋊C4—92no—
333C2×C4⋊C4—91no—
334C2×C22⋊C4—31no—
335C2×C22⋊C4—32no—
336C2×C22⋊C4—31no—
337C2×C22⋊C4—32no—
338C2×C22⋊C4—91no—
339C2×C22⋊C4—91no—
340C2×C42—92no—
341C2×C42—92no—
342C2×C42—92no—
343C2×C42—91no—
344C2×C42—184no—
345#95—32no—
346#95—92no—
347#95—92no—
348#95—92no—
349#95—92no—
350C23×C3—22no—
351C23×C3—22no—
352C23×C3—22no—
353C23×C3—22no—
354C23×C3—22no—
355C23×C3—22no—
356C23×C3—21no—
357C23×C3—21no—
358C23×C3—22no—
359C23×C3—21no—
360C23×C3—21no—
361C23×C3—22no—
362C23×C3—22no—
363C23×C3—22no—
364C23×C3—21no—
365C23×C3—22no—
366C23×C3—22no—
367C23×C3—22no—
368C23×C3—22no—
369C23×C3—42no—
370C23×C3—42no—
371C23×C3—42no—
372C23×C3—42no—
373C23×C3C2×C4×D312yes—
374C23×C3C2×C4×D312yes—
375C23×C3D3×D412yes—
376C23×C3D3×D412yes—
377C23×C3#23712yes—
378C23×C3#23712yes—
379C23×C3C22×Dic312yes—
380C23×C3C22×Dic312yes—
381C23×C3C23×D311yescharacteristic
382C23×C3C23×D311yescharacteristic
383C3×D4—216no—
384C3×D4—28no—
385C3×D4—28no—
386C2×C3×C4—22no—
387C2×C3×C4—22no—
388C2×C3×C4—21no—
389C2×C3×C4—21no—
390C2×C3×C4—21no—
391C2×C3×C4—21no—
392C2×C3×C4—22no—
393C2×C3×C4—34no—
394C2×C3×C4—34no—
395C2×C3×C4—34no—
396C2×C3×C4—68no—
397C2×C3×C4—68no—
398C2×C3×C4—62no—
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×C3×C4C2×C4×D312yes—
408C2×C3×C4C22×Dic312yes—
409C2×Dic3—28no—
410C2×Dic3—28no—
411C2×Dic3—22no—
412C2×Dic3—22no—
413C2×Dic3—22no—
414C2×Dic3—22no—
415C2×Dic3—22no—
416C2×Dic3—22no—
417C2×Dic3—22no—
418C2×Dic3—22no—
419C2×Dic3—22no—
420C2×Dic3—32no—
421C2×Dic3—32no—
422C2×Dic3—34no—
423C2×Dic3—34no—
424C2×Dic3—32no—
425C2×Dic3—32no—
426C2×Dic3—62no—
427C2×Dic3—64no—
428C2×Dic3—62no—
429C2×Dic3—68no—
430C2×Dic3—68no—
431C2×Dic3—62no—
432C2×Dic3—62no—
433C2×Dic3—62no—
434C2×Dic3—62no—
435C2×Dic3—61no—
436C2×Dic3—61no—
437C2×Dic3—61no—
438C2×Dic3—61no—
439C2×Dic3—62no—
440C2×Dic3—62no—
441C2×Dic3—62no—
442C2×Dic3—62no—
443C2×Dic3—128no—
444C2×Dic3—122no—
445C2×Dic3—122no—
446C2×Dic3—122no—
447C2×Dic3—124no—
448C2×Dic3—124no—
449C2×Dic3—128no—
450C2×Dic3#23714yes—
451C2×Dic3C22×Dic314yes—
452C2×Dic3C22×Dic314yes—
453C2×C32—24no—
454C2×C32—42no—
455C2×C32C2×C4×D411yescharacteristic
456C2×C32C4×#4112yes—
457C2×C32C2×#12311yescharacteristic
458C2×C32#52511yescharacteristic
459C2×C32#52912yes—
460C24C2×D3211yescharacteristic
461C24C2×D3211yescharacteristic
462C2×D4—22no—
463C2×D4—22no—
464C2×D4D3×Dic314yes—
465C22×C4—32no—
466C22×C4—32no—
467C22×C4—32no—
468C22×C4—34no—
469C22×C4—32no—
470C22×C4—64no—
471C22×C4—62no—
472C22×C4—62no—
473C22×C4—62no—
474C22×C4—91no—
475C22×C4—91no—
476C22×C4—94no—
477C22×C4—91no—
478C22×C4—91no—
479C22×C4—184no—
480C22×C4—182no—
481C22×C4—184no—
482C22×C4C2×D3211yescharacteristic
483C4⋊C4—38no—
484C4⋊C4—182no—
485C4⋊C4—184no—
486C22⋊C4—34no—
487C22⋊C4—38no—
488C22⋊C4—64no—
489C22⋊C4—62no—
490C22⋊C4—182no—
491C22⋊C4—182no—
492C42—182no—
493C42—184no—
494C42—184no—
495C42—184no—
496C22×C3—24no—
497C22×C3—22no—
498C22×C3—22no—
499C22×C3—22no—
500C22×C3—24no—
501C22×C3—24no—
502C22×C3—22no—
503C22×C3—24no—
504C22×C3—24no—
505C22×C3—22no—
506C22×C3—24no—
507C22×C3—22no—
508C22×C3—24no—
509C22×C3—22no—
510C22×C3—22no—
511C22×C3—21no—
512C22×C3—21no—
513C22×C3—21no—
514C22×C3—24no—
515C22×C3—42no—
516C22×C3—42no—
517C22×C3—44no—
518C22×C3—44no—
519C22×C3—44no—
520C22×C3—42no—
521C22×C3—42no—
522C22×C3—44no—
523C22×C3—42no—
524C22×C3—41no—
525C22×C3—41no—
526C22×C3—41no—
527C22×C3—41no—
528C22×C3—42no—
529C22×C3#67⋊C414yes—
530C22×C3D4×Dic314yes—
531C22×C3C22×C4×D311yescharacteristic
532C22×C3C2×D3×D411yescharacteristic
533C22×C3C2×D3×D411yescharacteristic
534C22×C3C2×#23712yes—
535C22×C3C2×#23711yescharacteristic
536C22×C3C2×#23711yescharacteristic
537C22×C3D3×#4112yes—
538C22×C3D3×#4112yes—
539C22×C3D3×#4112yes—
540C22×C3C23×Dic311yescharacteristic
541C3×C4—24no—
542C3×C4—22no—
543C3×C4—22no—
544C3×C4—64no—
545C3×C4—64no—
546C3×C4—64no—
547C3×C4—122no—
548Dic3—24no—
549Dic3—24no—
550Dic3—24no—
551Dic3—34no—
552Dic3—34no—
553Dic3—42no—
554Dic3—64no—
555Dic3—62no—
556Dic3—62no—
557Dic3—122no—
558Dic3—122no—
559Dic3—122no—
560Dic3—121no—
561Dic3—121no—
562Dic3—121no—
563Dic3—121no—
564C32C4×#12311yescharacteristic, complemented, Sylow
565C23—22no—
566C23—22no—
567C23—22no—
568C23—22no—
569C23—21no—
570C23—21no—
571C23C2×D3×Dic312yes—
572C23C2×D3×Dic312yes—
573C23#380512yes—
574C23#381112yes—
575C23C22×D3211yescharacteristic
576D4—28no—
577C2×C4—21no—
578C2×C4—21no—
579C2×C4—34no—
580C2×C4—34no—
581C2×C4—34no—
582C2×C4—68no—
583C2×C4—62no—
584C2×C4—62no—
585C2×C4—62no—
586C2×C4—62no—
587C2×C4—62no—
588C2×C4—62no—
589C2×C4—68no—
590C2×C4—62no—
591C2×C4—62no—
592C2×C4—62no—
593C2×C4—94no—
594C2×C4—92no—
595C2×C4—92no—
596C2×C4—188no—
597C2×C4—182no—
598C2×C4—182no—
599C2×C4—182no—
600C2×C4—181no—
601C2×C4—181no—
602C2×C4—364no—
603C2×C4C2×D3×Dic312yes—
604C2×C3—24no—
605C2×C3—24no—
606C2×C3—21no—
607C2×C3—21no—
608C2×C3—22no—
609C2×C3—22no—
610C2×C3—21no—
611C2×C3—44no—
612C2×C3—44no—
613C2×C3—42no—
614C2×C3—42no—
615C2×C3C2×#67⋊C411yescharacteristic
616C2×C3C4×#23712yes—
617C2×C3#558611yescharacteristic
618C2×C3#560012yes—
619C2×C3#564912yes—
620C2×C3D3×#12311yescharacteristic
621C2×C3D3×#12311yescharacteristic
622C2×C3#565611yescharacteristic
623C2×C3C2×D4×Dic311yescharacteristic
624C2×C3Dic3×#4112yes—
625C22—22no—
626C22—22no—
627C22—24no—
628C22—24no—
629C22—24no—
630C22—22no—
631C22—41no—
632C22—41no—
633C22—42no—
634C22#67⋊Dic314yes—
635C22D3×#23712yes—
636C22#6431212yes—
637C22C22×D3×Dic311yescharacteristic
638C22C2×#380511yescharacteristic
639C22C2×#381111yescharacteristic
640C4—22no—
641C4—64no—
642C4—64no—
643C4—64no—
644C4—94no—
645C4—122no—
646C4—182no—
647C4—361no—
648C4—361no—
649C3—21no—
650C3#7466111yescharacteristic, complemented
651C3Dic3×#12311yescharacteristic, complemented
652C2—24no—
653C2—42no—
654C2#1059516011yescharacteristic
655C2#1059516911yescharacteristic
656C2Dic3×#23712yes—
657C2#1059520212yes—
658C2C2×#67⋊Dic311yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
Fitting, prime radicalC22×C32×D4C22
socle, cosocleC23×C32C24
hypercenterC22×D4D32
hypocenterC32C4×#123
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
3. C22×Dic32C2semidirect
5. #10591718C2semidirect
6. #10591705C2semidirect
7. #10591705C2semidirect
8. #10591702C2semidirect
9. #10591696C2semidirect
10. #10591272C2semidirect
11. #10591241C2semidirect
28. C3×#935C4semidirect
81. C22×C3×Dic3C2×C4semidirect
92. C3×#217C2×C4semidirect
93. C3×#217C2×C4semidirect
94. C3×Dic3⋊C4C2×C4semidirect
129. #935Dic3semidirect
265. C22×Dic3C2×Dic3semidirect
283. #217C2×Dic3semidirect
284. #217C2×Dic3semidirect
290. Dic3⋊C4C2×Dic3semidirect
319. C3⋊Dic3#123semidirect
564. C32C4×#123semidirect
650. C3#74661semidirect
651. C3Dic3×#123semidirect

Maximal subgroups

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

subgroupindex
C2×D4×C3⋊Dic32
C2×C3×#9352
C22×Dic322
C3×#52202
#105917182
#105917052
#105917022
#105916962
#105912722
#105912412
Dic3×#1233
#746613