Finite Group Databasebeta

← #11808797

Subgroups — #11808797

Order 1152.

1349 conjugacy classes of subgroups.

The subgroup lattice has 636 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64090C211yesmaximal, characteristic
2C2×#63843C211yesmaximal, characteristic, complemented
3C3×#4953C211yesmaximal, characteristic, complemented
4C3×#4947C211yesmaximal, characteristic, complemented
5#10591712C212yesmaximal
6#10591705C212yesmaximal, complemented
7#10591326C211yesmaximal, characteristic, complemented
8#10591310C211yesmaximal, characteristic, complemented
9#10591260C212yesmaximal, complemented
10#10591252C211yesmaximal, characteristic, complemented
11#10591210C212yesmaximal, complemented
12#77460—31nomaximal
13#76779—31nomaximal
14C22×#638C2211yescharacteristic
15C23×C3⋊Dic3C2211yescharacteristic
16C22×C4×C3⋊D3C2211yescharacteristic
17C22×C3×Dic6C2211yescharacteristic
18C2×C32×C22⋊C4C2211yescharacteristic
19C2×#3752C2211yescharacteristic
20C2×#3750C2211yescharacteristic
21C2×C4×C3⋊Dic3C2211yescharacteristic
22#64090—24no—
23C2×C3×#217C2212yes—
24C2×C3×#217C2212yes—
25C2×C3×C4⋊Dic3C2211yescharacteristic
26C2×Dic3⋊Dic3C2212yes—
27C2×#3722C2212yes—
28C2×#3722C2212yes—
29C2×Dic32C2212yes—
30C2×Dic32C2212yes—
31#63843—24no—
32C3×C3⋊#95C2211yescharacteristic
33C3×C3⋊#95C2211yescharacteristic
34C3×C3⋊#95C2212yes—
35C3×C3⋊#95C2212yes—
36#63579C2212yes—
37#63579C2212yes—
38#63579C2212yes—
39C2×Q8×Dic3—31no—
40C2×#887—31no—
41C2×#67⋊C4—31no—
42C2×#67⋊C4—31no—
43C2×#67⋊C4—61no—
44C3×#397—31no—
45C3×#393—31no—
46#5231—31no—
47#4992—31no—
48#4961—32no—
49#4959—32no—
50#4953D311yescharacteristic, complemented
51#4947D311yescharacteristic, complemented
52Dic3×C22⋊C4—32no—
53Dic3×C22⋊C4—32no—
54#4674—31no—
55#4673—31no—
56#4666—32no—
57#4666—32no—
58#4660—32no—
59#4658—32no—
60#4648—31no—
61#4648—31no—
62C24×C32C2311yescharacteristic
63C23×C3⋊D3C2311yescharacteristic
64C22×C32×C4C2311yescharacteristic
65C22×C32×C4C2311yescharacteristic
66C2×#638—22no—
67C2×#638—22no—
68C2×#638—22no—
69C22×C3⋊Dic3—22no—
70C22×C3⋊Dic3—24no—
71C22×C3⋊Dic3C2311yescharacteristic
72C22×C3⋊Dic3C2311yescharacteristic
73C22×C3⋊Dic3C2311yescharacteristic
74C2×C4×C3⋊D3—22no—
75C2×C4×C3⋊D3—24no—
76C22×C3×Dic3C2312yes—
77C22×C3×Dic3C2312yes—
78C22×C3×Dic3C2312yes—
79C22×C3×Dic3C2312yes—
80C2×C3×Dic6—22no—
81C2×C3×Dic6—24no—
82C32×C22⋊C4—22no—
83#3752—22no—
84#3750—22no—
85C4×C3⋊Dic3D414yes—
86C3×#217—24no—
87C3×#217—24no—
88C3×C4⋊Dic3—22no—
89Dic3⋊Dic3—24no—
90#3722—24no—
91#3722—24no—
92Dic32—24no—
93Dic32—24no—
94#2398—91noSylow
95C22×C3×Q8—31no—
96C22×#67—31no—
97C22×#67—31no—
98C22×#67—61no—
99C23×Dic3—31no—
100C23×Dic3—31no—
101C23×Dic3—61no—
102C22×C4×D3—31no—
103C22×C4×D3—31no—
104C22×C4×D3—61no—
105C22×Dic6C2×D311yescharacteristic
106C2×C3×C4⋊C4—31no—
107C2×C3×C22⋊C4—21no—
108C2×C3×C22⋊C4—32no—
109C2×C3×C22⋊C4—32no—
110C2×C3×C22⋊C4C2×D311yescharacteristic
111C2×C3×C22⋊C4C2×D311yescharacteristic
112C2×#217C2×D312yes—
113C2×#217C2×D312yes—
114Q8×Dic3—64no—
115C2×(C2×D3)⋊C4—31no—
116C2×(C2×D3)⋊C4—31no—
117C2×(C2×D3)⋊C4—32no—
118C2×(C2×D3)⋊C4—32no—
119C2×(C2×D3)⋊C4—32no—
120C2×(C2×D3)⋊C4—32no—
121C2×(C2×D3)⋊C4—61no—
122C2×C4⋊Dic3—32no—
123C2×C4⋊Dic3C2×D311yescharacteristic
124C2×Dic3⋊C4—31no—
125C2×Dic3⋊C4—31no—
126C2×Dic3⋊C4—32no—
127C2×Dic3⋊C4—61no—
128C2×C4×Dic3—31no—
129C2×C4×Dic3—31no—
130C2×C4×Dic3—32no—
131C2×C4×Dic3—32no—
132C2×C4×Dic3—32no—
133C2×C4×Dic3—32no—
134C2×C4×Dic3—61no—
135#887—64no—
136#67⋊C4—64no—
137#67⋊C4—64no—
138#67⋊C4—68no—
139C3×#95—31no—
140C3×#95—31no—
141C3×#95—32no—
142C3×#95—32no—
143C3⋊#95—32no—
144C3⋊#95—32no—
145C3⋊#95—32no—
146C3⋊#95—32no—
147C3⋊#95—32no—
148C3⋊#95—32no—
149C3⋊#95C2×D311yescharacteristic
150C3⋊#95C2×D311yescharacteristic
151C3⋊#95C2×D312yes—
152C3⋊#95C2×D312yes—
153C23×C32—21no—
154C23×C32—21no—
155C23×C32—22no—
156C23×C32—22no—
157C23×C32#4112yes—
158C23×C32C2411yescharacteristic
159C22×C3⋊D3—21no—
160C22×C3⋊D3—21no—
161C22×C3⋊D3—22no—
162C22×C3⋊D3—22no—
163C22×C3⋊D3#4112yes—
164C2×C32×C4—21no—
165C2×C32×C4—22no—
166C2×C32×C4—22no—
167C2×C32×C4C2×D412yes—
168#638—28no—
169C2×C3⋊Dic3—21no—
170C2×C3⋊Dic3—21no—
171C2×C3⋊Dic3—21no—
172C2×C3⋊Dic3—22no—
173C2×C3⋊Dic3—44no—
174C2×C3⋊Dic3C2×D412yes—
175C2×C3⋊Dic3C2×D412yes—
176C2×C3⋊Dic3#4114yes—
177C4×C3⋊D3—44no—
178C2×C3×Dic3—22no—
179C2×C3×Dic3—22no—
180C2×C3×Dic3—22no—
181C2×C3×Dic3—22no—
182C2×C3×Dic3—22no—
183C2×C3×Dic3—22no—
184C2×C3×Dic3—22no—
185C2×C3×Dic3—22no—
186C2×C3×Dic3—22no—
187C2×C3×Dic3—22no—
188C2×C3×Dic3—22no—
189C2×C3×Dic3#4114yes—
190C3×Dic6—28no—
191C2×C4×Q8—91no—
192C2×C4×D4—91no—
193#400—92no—
194#397—31no—
195#397—91no—
196#394—92no—
197#393—31no—
198#393—91no—
199C4×C22⋊C4—92no—
200C4×C22⋊C4—92no—
201#376—91no—
202C24×C3—21no—
203C24×C3C22×D311yescharacteristic
204C24×C3C22×D311yescharacteristic
205C23×D3—31no—
206C23×D3—31no—
207C23×D3—61no—
208C2×C3×Q8—64no—
209C2×C3×Q8—62no—
210C22×C3×C4—21no—
211C22×C3×C4—21no—
212C22×C3×C4—32no—
213C22×C3×C4—32no—
214C22×C3×C4—32no—
215C22×C3×C4—32no—
216C22×C3×C4C22×D311yescharacteristic
217C22×C3×C4C22×D311yescharacteristic
218C22×C3×C4C22×D311yescharacteristic
219C22×C3×C4C22×D311yescharacteristic
220C2×#67—62no—
221C2×#67—62no—
222C2×#67—62no—
223C2×#67—62no—
224C2×#67—64no—
225C2×#67—64no—
226C2×#67—64no—
227C2×#67—62no—
228C2×#67—62no—
229C22×Dic3—31no—
230C22×Dic3—31no—
231C22×Dic3—31no—
232C22×Dic3—31no—
233C22×Dic3—31no—
234C22×Dic3—31no—
235C22×Dic3—61no—
236C22×Dic3—61no—
237C22×Dic3—61no—
238C22×Dic3—62no—
239C22×Dic3—62no—
240C22×Dic3—64no—
241C22×Dic3—64no—
242C22×Dic3—64no—
243C22×Dic3—124no—
244C22×Dic3C22×D312yes—
245C22×Dic3C22×D312yes—
246C22×Dic3C22×D312yes—
247C22×Dic3C22×D312yes—
248C2×C4×D3—62no—
249C2×C4×D3—62no—
250C2×C4×D3—64no—
251C2×C4×D3—64no—
252C2×C4×D3—64no—
253C2×C4×D3—124no—
254C2×Dic6—22no—
255C2×Dic6—24no—
256C3×C4⋊C4—62no—
257C3×C22⋊C4—24no—
258C3×C22⋊C4—22no—
259C3×C22⋊C4—22no—
260C3×C22⋊C4—64no—
261C3×C22⋊C4—64no—
262#217—24no—
263#217—24no—
264(C2×D3)⋊C4—64no—
265(C2×D3)⋊C4—64no—
266(C2×D3)⋊C4—64no—
267(C2×D3)⋊C4—64no—
268(C2×D3)⋊C4—62no—
269(C2×D3)⋊C4—62no—
270(C2×D3)⋊C4—64no—
271C4⋊Dic3—22no—
272C4⋊Dic3—64no—
273Dic3⋊C4—64no—
274Dic3⋊C4—62no—
275Dic3⋊C4—62no—
276Dic3⋊C4—64no—
277C4×Dic3—34no—
278C4×Dic3—34no—
279C4×Dic3—64no—
280C4×Dic3—64no—
281C4×Dic3—64no—
282C4×Dic3—64no—
283C4×Dic3—64no—
284C22×C32—22no—
285C22×C32—24no—
286C22×C32—41no—
287C22×C32—41no—
288C22×C32—42no—
289C22×C32C22×D411yescharacteristic
290C22×C32C2×#4111yescharacteristic
291C22×C32C2×#4112yes—
292C22×C32C2×#4111yescharacteristic
293C22×C32C2×#4112yes—
294C2×C3⋊D3—22no—
295C2×C3⋊D3—24no—
296C2×C3⋊D3—41no—
297C2×C3⋊D3—41no—
298C2×C3⋊D3—42no—
299C32×C4—22no—
300C32×C4—41no—
301C3⋊Dic3—22no—
302C3⋊Dic3—41no—
303C3⋊Dic3#12414yes—
304C3×Dic3—24no—
305C3×Dic3—42no—
306C3×Dic3—42no—
307C3×Dic3—42no—
308C22×Q8—31no—
309C22×D4—91no—
310C23×C4—91no—
311C23×C4—91no—
312C4×Q8—184no—
313C4×D4—184no—
314C2×C4⋊C4—31no—
315C2×C4⋊C4—92no—
316C2×C4⋊C4—91no—
317C2×C22⋊C4—32no—
318C2×C22⋊C4—32no—
319C2×C22⋊C4—92no—
320C2×C22⋊C4—92no—
321C2×C22⋊C4—91no—
322C2×C22⋊C4D3211yescharacteristic
323C2×C42—91no—
324C2×C42—92no—
325C2×C42—92no—
326#95—31no—
327#95—31no—
328#95—32no—
329#95—32no—
330#95—92no—
331#95—92no—
332#95—92no—
333C23×C3—22no—
334C23×C3—22no—
335C23×C3—21no—
336C23×C3—21no—
337C23×C3—22no—
338C23×C3—22no—
339C23×C3—22no—
340C23×C3—22no—
341C23×C3—21no—
342C23×C3—21no—
343C23×C3—21no—
344C23×C3—22no—
345C23×C3—42no—
346C23×C3—42no—
347C23×C3#23712yes—
348C23×C3#23912yes—
349C23×C3C23×D311yescharacteristic
350C23×C3C23×D311yescharacteristic
351C22×D3—32no—
352C22×D3—32no—
353C22×D3—62no—
354C22×D3—62no—
355C22×D3—62no—
356C22×D3—61no—
357C22×D3—61no—
358C22×D3—62no—
359C22×D3—61no—
360C22×D3—61no—
361C22×D3—62no—
362C22×D3—62no—
363C22×D3—62no—
364C22×D3—122no—
365C22×D3—122no—
366C3×Q8—68no—
367C2×C3×C4—22no—
368C2×C3×C4—22no—
369C2×C3×C4—22no—
370C2×C3×C4—21no—
371C2×C3×C4—21no—
372C2×C3×C4—22no—
373C2×C3×C4—22no—
374C2×C3×C4—22no—
375C2×C3×C4—34no—
376C2×C3×C4—42no—
377C2×C3×C4—42no—
378C2×C3×C4—62no—
379C2×C3×C4—62no—
380C2×C3×C4—62no—
381C2×C3×C4—62no—
382C2×C3×C4—62no—
383C2×C3×C4—62no—
384C2×C3×C4—62no—
385C2×C3×C4—62no—
386C2×C3×C4—62no—
387C2×C3×C4—62no—
388C2×C3×C4—62no—
389C2×C3×C4D3×D412yes—
390C2×C3×C4D3×D412yes—
391#67—616no—
392#67—68no—
393#67—68no—
394C2×Dic3—22no—
395C2×Dic3—22no—
396C2×Dic3—22no—
397C2×Dic3—22no—
398C2×Dic3—22no—
399C2×Dic3—22no—
400C2×Dic3—22no—
401C2×Dic3—22no—
402C2×Dic3—22no—
403C2×Dic3—22no—
404C2×Dic3—22no—
405C2×Dic3—32no—
406C2×Dic3—32no—
407C2×Dic3—34no—
408C2×Dic3—34no—
409C2×Dic3—32no—
410C2×Dic3—32no—
411C2×Dic3—62no—
412C2×Dic3—62no—
413C2×Dic3—64no—
414C2×Dic3—62no—
415C2×Dic3—62no—
416C2×Dic3—61no—
417C2×Dic3—61no—
418C2×Dic3—61no—
419C2×Dic3—61no—
420C2×Dic3—62no—
421C2×Dic3—61no—
422C2×Dic3—61no—
423C2×Dic3—62no—
424C2×Dic3—62no—
425C2×Dic3—122no—
426C2×Dic3—124no—
427C2×Dic3—124no—
428C2×Dic3—128no—
429C2×Dic3#23714yes—
430C4×D3—124no—
431C4×D3—124no—
432C4×D3—128no—
433Dic6—28no—
434C2×C32—42no—
435C2×C32#52511yescharacteristic
436C2×C32#52511yescharacteristic
437C2×C32C2×#12411yescharacteristic
438C2×C32#52912yes—
439C2×C32#52912yes—
440C3⋊D3—42no—
441C24—91no—
442C24C2×D3211yescharacteristic
443C2×Q8—64no—
444C2×Q8—62no—
445C2×D4—182no—
446C2×D4—182no—
447C2×D4—182no—
448C22×C4—32no—
449C22×C4—32no—
450C22×C4—32no—
451C22×C4—32no—
452C22×C4—91no—
453C22×C4—91no—
454C22×C4—91no—
455C22×C4—182no—
456C22×C4—184no—
457C22×C4—182no—
458C22×C4—184no—
459C22×C4C2×D3211yescharacteristic
460C22×C4C2×D3211yescharacteristic
461C4⋊C4—62no—
462C4⋊C4—182no—
463C4⋊C4—184no—
464C22⋊C4—22no—
465C22⋊C4—64no—
466C22⋊C4—64no—
467C22⋊C4—184no—
468C22⋊C4—184no—
469C22⋊C4—182no—
470C42—94no—
471C42—184no—
472C42—184no—
473C22×C3—24no—
474C22×C3—24no—
475C22×C3—22no—
476C22×C3—24no—
477C22×C3—22no—
478C22×C3—21no—
479C22×C3—21no—
480C22×C3—22no—
481C22×C3—22no—
482C22×C3—21no—
483C22×C3—44no—
484C22×C3—42no—
485C22×C3—42no—
486C22×C3—44no—
487C22×C3—41no—
488C22×C3—41no—
489C22×C3—41no—
490C22×C3—42no—
491C22×C3—42no—
492C22×C3—41no—
493C22×C3C2×D3×D411yescharacteristic
494C22×C3C2×D3×D411yescharacteristic
495C22×C3C2×#23711yescharacteristic
496C22×C3C2×#23712yes—
497C22×C3C2×#23911yescharacteristic
498C22×C3D3×#4111yescharacteristic
499C22×C3D3×#4111yescharacteristic
500C22×C3D3×#4112yes—
501C22×C3D3×#4112yes—
502C22×C3D3×#4112yes—
503C2×D3—64no—
504C2×D3—64no—
505C2×D3—64no—
506C2×D3—62no—
507C2×D3—62no—
508C2×D3—124no—
509C2×D3—122no—
510C2×D3—122no—
511C2×D3—124no—
512C2×D3—122no—
513C2×D3—121no—
514C2×D3—121no—
515C2×D3—121no—
516C2×D3—121no—
517C2×D3—122no—
518C3×C4—22no—
519C3×C4—22no—
520C3×C4—42no—
521C3×C4—42no—
522C3×C4—41no—
523C3×C4—41no—
524C3×C4—64no—
525C3×C4—122no—
526C3×C4—122no—
527C3×C4—122no—
528Dic3—24no—
529Dic3—34no—
530Dic3—34no—
531Dic3—42no—
532Dic3—42no—
533Dic3—42no—
534Dic3—64no—
535Dic3—64no—
536Dic3—62no—
537Dic3—62no—
538Dic3—122no—
539Dic3—121no—
540Dic3—121no—
541C32#239811yescharacteristic, complemented, Sylow
542C23—21no—
543C23—22no—
544C23—22no—
545C23—21no—
546C23—92no—
547C23—181no—
548C23—182no—
549C23—182no—
550C23—181no—
551C23#379612yes—
552C23C22×D3211yescharacteristic
553Q8—68no—
554D4—188no—
555C2×C4—22no—
556C2×C4—22no—
557C2×C4—21no—
558C2×C4—34no—
559C2×C4—62no—
560C2×C4—62no—
561C2×C4—62no—
562C2×C4—62no—
563C2×C4—62no—
564C2×C4—62no—
565C2×C4—62no—
566C2×C4—62no—
567C2×C4—62no—
568C2×C4—62no—
569C2×C4—62no—
570C2×C4—94no—
571C2×C4—92no—
572C2×C4—92no—
573C2×C4—181no—
574C2×C4—181no—
575C2×C4—182no—
576C2×C4—181no—
577C2×C4—364no—
578C2×C4—364no—
579C2×C4#381112yes—
580C2×C3—21no—
581C2×C3—22no—
582C2×C3—22no—
583C2×C3—21no—
584C2×C3—21no—
585C2×C3—44no—
586C2×C3—42no—
587C2×C3—42no—
588C2×C3#558611yescharacteristic
589C2×C3#560611yescharacteristic
590C2×C3#562412yes—
591C2×C3#562711yescharacteristic
592C2×C3#564912yes—
593C2×C3#565611yescharacteristic
594C2×C3D3×#12411yescharacteristic
595C2×C3D3×#12411yescharacteristic
596C2×C3#568012yes—
597C2×C3#570612yes—
598D3—124no—
599D3—122no—
600D3—122no—
601C22—24no—
602C22—22no—
603C22—41no—
604C22—42no—
605C22—41no—
606C22—184no—
607C22—182no—
608C22—361no—
609C22—362no—
610C22—361no—
611C22C2×#379611yescharacteristic
612C22#6430611yescharacteristic
613C22D3×#23712yes—
614C22#6431212yes—
615C22C2×#381111yescharacteristic
616C4—22no—
617C4—41no—
618C4—64no—
619C4—94no—
620C4—122no—
621C4—122no—
622C4—122no—
623C4—182no—
624C4—361no—
625C3—21no—
626C3#7677911yescharacteristic, complemented
627C3#7746011yescharacteristic, complemented
628C2—42no—
629C2—362no—
630C2#1059413712yes—
631C2#1059414412yes—
632C2#1059492211yescharacteristic
633C2#1059516011yescharacteristic
634C2#1059517011yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutator, socle, cosocleC23×C32C24
FittingC2×C32×C22⋊C4C22
prime radicalC22×#638C22
hypercenterC2×C22⋊C4D32
hypocenterC32#2398
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×#63843C2semidirect
3. C3×#4953C2semidirect
4. C3×#4947C2semidirect
6. #10591705C2semidirect
7. #10591326C2semidirect
8. #10591310C2semidirect
9. #10591260C2semidirect
10. #10591252C2semidirect
11. #10591210C2semidirect
50. #4953D3semidirect
51. #4947D3semidirect
541. C32#2398semidirect
626. C3#76779semidirect
627. C3#77460semidirect

Maximal subgroups

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

subgroupindex
C2×#640902
C2×#638432
C3×#49532
C3×#49472
#105917122
#105917052
#105913262
#105913102
#105912602
#105912522
#105912102
#774603
#767793