Finite Group Databasebeta

← #11802174

Subgroups — #11802174

Order 1152.

1547 conjugacy classes of subgroups.

The subgroup lattice has 649 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64138C211yesmaximal, characteristic
2C22×C3×C4×Dic3C211yesmaximal, characteristic, complemented
3C2×#63952C211yesmaximal, characteristic
4C3×#5211C211yesmaximal, characteristic, complemented
5#10591711C211yesmaximal, characteristic
6Dic3×#217C211yesmaximal, characteristic, complemented
7#10591693C211yesmaximal, characteristic, complemented
8#10591243C212yesmaximal, complemented
9#10591233C212yesmaximal, complemented
10#10591202C212yesmaximal, complemented
11#10591197C212yesmaximal, complemented
12C4×#929—31nomaximal
13#74052—31nomaximal
14C23×C32×C4C2211yescharacteristic
15C22×#638C2211yescharacteristic
16C23×C3×Dic3C2211yescharacteristic
17C23×C3×Dic3C2211yescharacteristic
18C22×#624C2211yescharacteristic
19C2×#3757C2211yescharacteristic
20#64138C418yescomplemented
21C2×#3752C2212yes—
22C2×#3750C2212yes—
23C2×C3×#217C2211yescharacteristic
24C2×C3×#217C2211yescharacteristic
25C2×C3×C4×Dic3—24no—
26C2×C3×C4×Dic3C2212yes—
27C2×C3×C4×Dic3C2212yes—
28C2×#3724C2212yes—
29C2×#3724C2211yescharacteristic
30C2×#3722C2212yes—
31C2×#3722C2211yescharacteristic
32C2×Dic32C2212yes—
33C2×Dic32C2211yescharacteristic
34#63952—24no—
35C3×C3⋊#95C2212yes—
36C3×C3⋊#95C2212yes—
37#63579C2212yes—
38#63579C2212yes—
39#63579C2212yes—
40C22×C3×C42—31no—
41C2×#929—31no—
42C2×#929—31no—
43C2×#929—61no—
44C2×C4×#67—31no—
45C22×C4×Dic3D311yescharacteristic, complemented
46C2×#67⋊C4—31no—
47C3×#381—31no—
48#5213—31no—
49#5211D311yescharacteristic, complemented
50#5210—31no—
51C4×#217—31no—
52#4958—31no—
53#4946—31no—
54Dic3×C22⋊C4—31no—
55#4940—32no—
56C4×(C2×D3)⋊C4—32no—
57#4933—32no—
58C4×Dic3⋊C4—32no—
59#4669—32no—
60#4666—32no—
61#4652—32no—
62#4649—32no—
63C24×C32C2311yescharacteristic
64C23×C3⋊D3C2311yescharacteristic
65C22×C32×C4—22no—
66C22×C32×C4—22no—
67C22×C32×C4C2×C414yescomplemented
68C22×C32×C4C2312yes—
69C2×#638—22no—
70C2×#638—22no—
71C2×#638C2×C414yes—
72C22×C3⋊Dic3C2311yescharacteristic
73C22×C3⋊Dic3C2312yes—
74C22×C3×Dic3—22no—
75C22×C3×Dic3—24no—
76C22×C3×Dic3—24no—
77C22×C3×Dic3D414yes—
78C22×C3×Dic3C2311yescharacteristic
79C22×C3×Dic3C2312yes—
80C22×C3×Dic3C2311yescharacteristic
81C22×C3×Dic3C2311yescharacteristic
82C22×C3×Dic3C2312yes—
83C22×C3×Dic3C2311yescharacteristic
84C2×#624—22no—
85C2×#624—24no—
86#3757C2×C414yescomplemented
87#3752C2×C418yescomplemented
88#3750C2×C418yescomplemented
89C3×#217—22no—
90C3×#217—22no—
91C3×C4×Dic3—24no—
92C3×C4×Dic3—24no—
93#3724—22no—
94#3724—24no—
95#3722—22no—
96#3722—24no—
97Dic32—22no—
98Dic32—24no—
99C4×#123—91noSylow
100C23×C3×C4—21no—
101C23×C3×C4—31no—
102C23×C3×C4—31no—
103C23×C3×C4C2×D311yescharacteristic
104C23×C3×C4C2×D311yescharacteristic
105C22×#67—31no—
106C22×#67—31no—
107C22×#67—61no—
108C23×Dic3C2×D311yescharacteristic
109C23×Dic3C2×D311yescharacteristic
110C22×C4×D3—31no—
111C22×C4×D3—31no—
112C2×C3×C22⋊C4—31no—
113C2×C3×C22⋊C4—31no—
114C2×C3×C42—32no—
115C2×C3×C42—32no—
116C2×C3×C42—64no—
117C2×#217—31no—
118C2×#217—31no—
119C2×#217—61no—
120C2×#217C2×D311yescharacteristic
121C2×#217C2×D311yescharacteristic
122#929—38no—
123#929—38no—
124#929—68no—
125C4×#67—64no—
126C2×(C2×D3)⋊C4—32no—
127C2×(C2×D3)⋊C4—32no—
128C2×(C2×D3)⋊C4—32no—
129C2×(C2×D3)⋊C4—31no—
130C2×(C2×D3)⋊C4—32no—
131C2×(C2×D3)⋊C4—31no—
132C2×(C2×D3)⋊C4—62no—
133C2×Dic3⋊C4—32no—
134C2×Dic3⋊C4—32no—
135C2×Dic3⋊C4—32no—
136C2×Dic3⋊C4—31no—
137C2×Dic3⋊C4—32no—
138C2×Dic3⋊C4—31no—
139C2×Dic3⋊C4—62no—
140C2×C4×Dic3—24no—
141C2×C4×Dic3—31no—
142C2×C4×Dic3—32no—
143C2×C4×Dic3—31no—
144C2×C4×Dic3—32no—
145C2×C4×Dic3C2×D312yes—
146C2×C4×Dic3C2×D312yes—
147#67⋊C4—64no—
148C3×#95—32no—
149C3×#95—32no—
150C3⋊#95—32no—
151C3⋊#95—32no—
152C3⋊#95—32no—
153C3⋊#95—32no—
154C3⋊#95—32no—
155C3⋊#95—32no—
156C3⋊#95C2×D312yes—
157C3⋊#95C2×D312yes—
158C23×C32—22no—
159C23×C32—22no—
160C23×C32C22×C412yes—
161C23×C32C2×D412yes—
162C23×C32#4112yes—
163C23×C32C2411yescharacteristic
164C22×C3⋊D3—21no—
165C22×C3⋊D3—22no—
166C22×C3⋊D3—22no—
167C22×C3⋊D3—21no—
168C22×C3⋊D3C22×C412yes—
169C2×C32×C4—28no—
170C2×C32×C4—22no—
171C2×C32×C4—22no—
172C2×C32×C4C22×C414yes—
173#638—28no—
174C2×C3⋊Dic3—21no—
175C2×C3⋊Dic3—22no—
176C2×C3⋊Dic3—22no—
177C2×C3⋊Dic3—21no—
178C2×C3⋊Dic3C22×C412yes—
179C2×C3⋊Dic3C22×C414yes—
180C2×C3×Dic3—28no—
181C2×C3×Dic3—22no—
182C2×C3×Dic3—22no—
183C2×C3×Dic3—22no—
184C2×C3×Dic3—28no—
185C2×C3×Dic3—21no—
186C2×C3×Dic3—21no—
187C2×C3×Dic3—22no—
188C2×C3×Dic3—22no—
189C2×C3×Dic3—22no—
190C2×C3×Dic3—22no—
191C2×C3×Dic3—22no—
192C2×C3×Dic3C2×D412yes—
193C2×C3×Dic3C2×D412yes—
194C2×C3×Dic3#4114yes—
195C2×C3×Dic3#4114yes—
196#624—44no—
197C2×#123—91no—
198C2×C4×D4—91no—
199C22×C42—31no—
200#388—92no—
201#387—92no—
202#386—91no—
203#385—91no—
204#381—31no—
205C4×C4⋊C4—92no—
206C4×C22⋊C4—92no—
207C4×C22⋊C4—91no—
208C24×C3—21no—
209C24×C3C22×D311yescharacteristic
210C24×C3C22×D311yescharacteristic
211C23×D3—31no—
212C23×D3—31no—
213C23×D3—61no—
214C22×C3×C4—22no—
215C22×C3×C4—22no—
216C22×C3×C4—22no—
217C22×C3×C4—22no—
218C22×C3×C4—24no—
219C22×C3×C4—22no—
220C22×C3×C4—31no—
221C22×C3×C4—34no—
222C22×C3×C4—31no—
223C22×C3×C4—32no—
224C22×C3×C4—32no—
225C22×C3×C4—31no—
226C22×C3×C4—31no—
227C22×C3×C4—42no—
228C22×C3×C4—42no—
229C22×C3×C4—64no—
230C22×C3×C4—64no—
231C22×C3×C4—62no—
232C22×C3×C4C4×D314yescomplemented
233C22×C3×C4C4×D314yescomplemented
234C22×C3×C4C22×D312yes—
235C22×C3×C4C22×D312yes—
236C2×#67—34no—
237C2×#67—34no—
238C2×#67—64no—
239C2×#67—62no—
240C2×#67—62no—
241C2×#67—62no—
242C2×#67—62no—
243C2×#67—122no—
244C2×#67—122no—
245C22×Dic3—22no—
246C22×Dic3—24no—
247C22×Dic3—24no—
248C22×Dic3—31no—
249C22×Dic3—31no—
250C22×Dic3—32no—
251C22×Dic3—32no—
252C22×Dic3—61no—
253C22×Dic3—62no—
254C22×Dic3#6714yes—
255C22×Dic3C22×D312yes—
256C22×Dic3C22×D311yescharacteristic
257C22×Dic3C22×D311yescharacteristic
258C22×Dic3C22×D312yes—
259C22×Dic3C22×D311yescharacteristic
260C22×Dic3C22×D311yescharacteristic
261C2×C4×D3—62no—
262C2×C4×D3—64no—
263C2×C4×D3—64no—
264C2×C4×D3—62no—
265C3×C22⋊C4—62no—
266C3×C22⋊C4—62no—
267C3×C42—64no—
268C3×C42—64no—
269#217—22no—
270#217—22no—
271#217—34no—
272#217—34no—
273#217—64no—
274(C2×D3)⋊C4—38no—
275(C2×D3)⋊C4—38no—
276(C2×D3)⋊C4—68no—
277(C2×D3)⋊C4—64no—
278(C2×D3)⋊C4—62no—
279(C2×D3)⋊C4—64no—
280(C2×D3)⋊C4—62no—
281Dic3⋊C4—38no—
282Dic3⋊C4—38no—
283Dic3⋊C4—68no—
284Dic3⋊C4—64no—
285Dic3⋊C4—62no—
286Dic3⋊C4—64no—
287Dic3⋊C4—62no—
288C4×Dic3—24no—
289C4×Dic3—24no—
290C4×Dic3—64no—
291C4×Dic3—62no—
292C4×Dic3—64no—
293C4×Dic3—62no—
294C22×C32—24no—
295C22×C32—22no—
296C22×C32—22no—
297C22×C32—24no—
298C22×C32C4×D414yes—
299C22×C32C23×C411yescharacteristic
300C22×C32C22×D411yescharacteristic
301C22×C32C2×#4111yescharacteristic
302C22×C32C2×#4112yes—
303C22×C32C2×#4112yes—
304C2×C3⋊D3—22no—
305C2×C3⋊D3—24no—
306C2×C3⋊D3—41no—
307C2×C3⋊D3—41no—
308C2×C3⋊D3—42no—
309C32×C4—24no—
310C3⋊Dic3—22no—
311C3⋊Dic3—24no—
312C3×Dic3—22no—
313C3×Dic3—24no—
314C3×Dic3—41no—
315C3×Dic3—41no—
316C3×Dic3—42no—
317C3×Dic3#12314yescomplemented
318C22×D4—91no—
319C23×C4—31no—
320C23×C4—31no—
321C23×C4—91no—
322C23×C4D3211yescharacteristic
323#123—98no—
324C4×D4—184no—
325C2×C4⋊C4—92no—
326C2×C4⋊C4—91no—
327C2×C4⋊C4—92no—
328C2×C22⋊C4—31no—
329C2×C22⋊C4—31no—
330C2×C22⋊C4—91no—
331C2×C22⋊C4—92no—
332C2×C22⋊C4—91no—
333C2×C22⋊C4—92no—
334C2×C42—32no—
335C2×C42—32no—
336C2×C42—64no—
337C2×C42—91no—
338C2×C42—92no—
339#95—32no—
340#95—32no—
341#95—92no—
342#95—92no—
343#95—92no—
344C23×C3—22no—
345C23×C3—22no—
346C23×C3—22no—
347C23×C3—22no—
348C23×C3—21no—
349C23×C3—22no—
350C23×C3—22no—
351C23×C3—22no—
352C23×C3—42no—
353C23×C3—42no—
354C23×C3C2×C4×D312yes—
355C23×C3C2×C4×D312yes—
356C23×C3#23512yes—
357C23×C3D3×D412yes—
358C23×C3#23712yes—
359C23×C3C2×#6712yes—
360C23×C3C23×D311yescharacteristic
361C23×C3C23×D311yescharacteristic
362C22×D3—32no—
363C22×D3—32no—
364C22×D3—62no—
365C22×D3—62no—
366C22×D3—62no—
367C22×D3—61no—
368C22×D3—61no—
369C22×D3—61no—
370C22×D3—62no—
371C22×D3—62no—
372C22×D3—61no—
373C22×D3—121no—
374C22×D3—121no—
375C22×D3—122no—
376C22×D3—122no—
377C2×C3×C4—28no—
378C2×C3×C4—28no—
379C2×C3×C4—22no—
380C2×C3×C4—22no—
381C2×C3×C4—22no—
382C2×C3×C4—22no—
383C2×C3×C4—24no—
384C2×C3×C4—32no—
385C2×C3×C4—34no—
386C2×C3×C4—32no—
387C2×C3×C4—34no—
388C2×C3×C4—42no—
389C2×C3×C4—42no—
390C2×C3×C4—48no—
391C2×C3×C4—68no—
392C2×C3×C4—68no—
393C2×C3×C4—62no—
394C2×C3×C4—62no—
395C2×C3×C4—62no—
396C2×C3×C4—62no—
397C2×C3×C4—62no—
398C2×C3×C4—62no—
399C2×C3×C4—62no—
400C2×C3×C4—62no—
401C2×C3×C4—61no—
402C2×C3×C4—61no—
403C2×C3×C4C2×C4×D314yes—
404C2×C3×C4C2×C4×D314yes—
405#67—68no—
406#67—68no—
407#67—128no—
408C2×Dic3—28no—
409C2×Dic3—22no—
410C2×Dic3—22no—
411C2×Dic3—22no—
412C2×Dic3—28no—
413C2×Dic3—21no—
414C2×Dic3—21no—
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—62no—
425C2×Dic3—64no—
426C2×Dic3—62no—
427C2×Dic3—62no—
428C2×Dic3—61no—
429C2×Dic3—61no—
430C2×Dic3—61no—
431C2×Dic3—62no—
432C2×Dic3—62no—
433C2×Dic3—61no—
434C2×Dic3—122no—
435C2×Dic3—122no—
436C2×Dic3—121no—
437C2×Dic3—121no—
438C2×Dic3#23514yes—
439C2×Dic3#23514yes—
440C2×Dic3C2×#6712yes—
441C2×Dic3C2×#6712yes—
442C4×D3—124no—
443C4×D3—124no—
444C2×C32—24no—
445C2×C32C2×C4×D411yescharacteristic
446C2×C32C4×#4112yes—
447C2×C32C2×#12311yescharacteristic
448C2×C32#52511yescharacteristic
449C2×C32#52912yes—
450C3⋊D3—42no—
451C24—91no—
452C24C2×D3211yescharacteristic
453C2×D4—94no—
454C2×D4—182no—
455C2×D4—182no—
456C22×C4—22no—
457C22×C4—22no—
458C22×C4—31no—
459C22×C4—32no—
460C22×C4—31no—
461C22×C4—34no—
462C22×C4—32no—
463C22×C4—31no—
464C22×C4—31no—
465C22×C4—64no—
466C22×C4—64no—
467C22×C4—62no—
468C22×C4—92no—
469C22×C4—91no—
470C22×C4—182no—
471C22×C4—184no—
472C22×C4#62414yescomplemented
473C22×C4C2×D3212yes—
474C4⋊C4—98no—
475C4⋊C4—182no—
476C4⋊C4—184no—
477C22⋊C4—62no—
478C22⋊C4—62no—
479C22⋊C4—94no—
480C22⋊C4—98no—
481C22⋊C4—182no—
482C22⋊C4—184no—
483C42—64no—
484C42—64no—
485C42—182no—
486C42—184no—
487C22×C3—24no—
488C22×C3—22no—
489C22×C3—22no—
490C22×C3—24no—
491C22×C3—24no—
492C22×C3—24no—
493C22×C3—22no—
494C22×C3—22no—
495C22×C3—22no—
496C22×C3—22no—
497C22×C3—21no—
498C22×C3—21no—
499C22×C3—21no—
500C22×C3—24no—
501C22×C3—42no—
502C22×C3—44no—
503C22×C3—44no—
504C22×C3—42no—
505C22×C3#67⋊C414yes—
506C22×C3C4×#6714yes—
507C22×C3C22×C4×D311yescharacteristic
508C22×C3C22×C4×D311yescharacteristic
509C22×C3C2×#23512yes—
510C22×C3C2×#23512yes—
511C22×C3C2×#23511yescharacteristic
512C22×C3C2×D3×D411yescharacteristic
513C22×C3C2×#23711yescharacteristic
514C22×C3D3×#4112yes—
515C22×C3D3×#4112yes—
516C22×C3C22×#6711yescharacteristic
517C2×D3—64no—
518C2×D3—62no—
519C2×D3—64no—
520C2×D3—62no—
521C2×D3—122no—
522C2×D3—124no—
523C2×D3—122no—
524C2×D3—121no—
525C2×D3—121no—
526C2×D3—122no—
527C2×D3—121no—
528C2×D3—121no—
529C2×D3—241no—
530C2×D3—242no—
531C2×D3—241no—
532C3×C4—24no—
533C3×C4—24no—
534C3×C4—34no—
535C3×C4—44no—
536C3×C4—62no—
537C3×C4—64no—
538C3×C4—122no—
539C3×C4—121no—
540C3×C4—121no—
541Dic3—22no—
542Dic3—24no—
543Dic3—42no—
544Dic3—41no—
545Dic3—41no—
546Dic3—64no—
547Dic3—62no—
548Dic3—64no—
549Dic3—62no—
550Dic3—122no—
551Dic3—124no—
552Dic3#92914yescomplemented
553C32C4×#12311yescharacteristic, complemented, Sylow
554C23—22no—
555C23—22no—
556C23—92no—
557C23—182no—
558C23—182no—
559C23—181no—
560C23—181no—
561C23#380412yes—
562C23C2×#62412yes—
563C23D3×#6712yes—
564C23C22×D3211yescharacteristic
565D4—188no—
566C2×C4—22no—
567C2×C4—22no—
568C2×C4—28no—
569C2×C4—34no—
570C2×C4—32no—
571C2×C4—34no—
572C2×C4—32no—
573C2×C4—68no—
574C2×C4—68no—
575C2×C4—62no—
576C2×C4—62no—
577C2×C4—62no—
578C2×C4—62no—
579C2×C4—62no—
580C2×C4—62no—
581C2×C4—62no—
582C2×C4—62no—
583C2×C4—61no—
584C2×C4—61no—
585C2×C4—94no—
586C2×C4—92no—
587C2×C4—182no—
588C2×C4—182no—
589C2×C4—181no—
590C2×C4—181no—
591C2×C4—364no—
592C2×C4C2×#62414yes—
593C2×C3—24no—
594C2×C3—24no—
595C2×C3—21no—
596C2×C3—22no—
597C2×C3—22no—
598C2×C3—21no—
599C2×C3—21no—
600C2×C3—44no—
601C2×C3C4×#23512yes—
602C2×C3#547912yes—
603C2×C3C2×#67⋊C411yescharacteristic
604C2×C3#552212yes—
605C2×C3#564912yes—
606C2×C3D3×#12311yescharacteristic
607C2×C3#565611yescharacteristic
608C2×C3C2×C4×#6711yescharacteristic
609C2×C3C2×#92911yescharacteristic
610C2×C3#579111yescharacteristic
611D3—122no—
612D3—122no—
613D3—242no—
614C22—22no—
615C22—24no—
616C22—24no—
617C22—22no—
618C22—184no—
619C22—182no—
620C22—361no—
621C22—362no—
622C22—361no—
623C22#6395214yes—
624C22D3×#23512yes—
625C22D3×#23512yes—
626C22C2×#380411yescharacteristic
627C22C22×#62411yescharacteristic
628C22C2×D3×#6711yescharacteristic
629C4—24no—
630C4—34no—
631C4—64no—
632C4—62no—
633C4—121no—
634C4—122no—
635C4—121no—
636C4—184no—
637C4—182no—
638C3—21no—
639C3#7405211yescharacteristic, complemented
640C3C4×#92911yescharacteristic, complemented
641C2—24no—
642C2—362no—
643C2#1059489611yescharacteristic
644C2#1059494812yes—
645C2#1059495412yes—
646C2D3×#92911yescharacteristic
647C2C2×#6395211yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC23×C32×C4C22
socle, cosocleC23×C32C24
prime radicalC22×#638C22
hypercenterC23×C4D32
hypocenterC32C4×#123
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
2. C22×C3×C4×Dic3C2semidirect
4. C3×#5211C2semidirect
6. Dic3×#217C2semidirect
7. #10591693C2semidirect
8. #10591243C2semidirect
9. #10591233C2semidirect
10. #10591202C2semidirect
11. #10591197C2semidirect
20. #64138C4semidirect
45. C22×C4×Dic3D3semidirect
49. #5211D3semidirect
67. C22×C32×C4C2×C4semidirect
86. #3757C2×C4semidirect
87. #3752C2×C4semidirect
88. #3750C2×C4semidirect
232. C22×C3×C4C4×D3semidirect
233. C22×C3×C4C4×D3semidirect
317. C3×Dic3#123semidirect
472. C22×C4#624semidirect
552. Dic3#929semidirect
553. C32C4×#123semidirect
639. C3#74052semidirect
640. C3C4×#929semidirect

Maximal subgroups

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

subgroupindex
C2×#641382
C22×C3×C4×Dic32
C2×#639522
C3×#52112
#105917112
Dic3×#2172
#105916932
#105912432
#105912332
#105912022
#105911972
C4×#9293
#740523