Finite Group Databasebeta

← #11900868

Subgroups — #11900868

Order 1152.

3636 conjugacy classes of subgroups.

The subgroup lattice has 627 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C32×C4×#41C211yesmaximal, characteristic, complemented
2#10596303C211yesmaximal, characteristic, complemented
3#10596299C211yesmaximal, characteristic, complemented
4#10596051C212yesmaximal, complemented
5#10596049C212yesmaximal, complemented
6#10596028C212yesmaximal, complemented
7#10596019C212yesmaximal, complemented
8#10596018C214yesmaximal, complemented
9#10596009C214yesmaximal, complemented
10#10595999C214yesmaximal, complemented
11#10595995C211yesmaximal, characteristic, complemented
12#10595988C211yesmaximal, characteristic, complemented
13C4×#3828C214yesmaximal, complemented
14C4×#3828C211yesmaximal, characteristic, complemented
15C2×C42×C3⋊D3C211yesmaximal, characteristic, complemented
16#85836—34nomaximal
17C2×C32×#41C2211yescharacteristic
18C2×#3828C2211yescharacteristic
19C2×#3828C2214yes—
20C22×C4×C3⋊D3C2211yescharacteristic
21C22×C4×C3⋊D3C2212yes—
22C32×C4×Q8C2212yescomplemented
23C32×C4×D4C2214yes—
24C32×C4×D4C2212yescomplemented
25C32×#117C2211yescharacteristic
26C32×#117C2212yescomplemented
27C2×C32×C42C2211yescharacteristic
28C2×C32×C42C2212yescomplemented
29#64156C2211yescharacteristic, complemented
30#64155C2212yes—
31#64153C2211yescharacteristic, complemented
32#64149C2211yescharacteristic, complemented
33#64148C2214yes—
34#64147C2212yes—
35#64146C2212yes—
36#64145C2211yescharacteristic, complemented
37#64144C2212yes—
38C4×#638C2214yes—
39C4×#638C2214yes—
40C4×#638C2214yes—
41C4×#638C2214yescomplemented
42C4×#638C2214yescomplemented
43#64135C2211yescharacteristic
44#64135C2214yescomplemented
45C2×C4×C3⋊Dic3C2211yescharacteristic
46C2×C4×C3⋊Dic3C2212yes—
47#64107C2214yescomplemented
48#64106C2212yes—
49#64105C2214yes—
50#64104C2212yes—
51#64103C2214yes—
52#64099C2212yescomplemented
53#64098C2214yescomplemented
54#64097C2212yescomplemented
55#64095C2212yes—
56#64094C2214yescomplemented
57#64093C2214yes—
58#64092C2214yes—
59#64091C2212yes—
60#64088C2214yescomplemented
61#64087C2214yes—
62C4×C4⋊(C3⋊D3)C2214yes—
63C4×C4⋊(C3⋊D3)C2214yes—
64C4×C4⋊(C3⋊D3)C2212yescomplemented
65#64081C2214yes—
66#64081C2212yescomplemented
67#64081C2214yescomplemented
68C42×C3⋊D3C2212yes—
69C42×C3⋊D3C2212yes—
70C42×C3⋊D3C2212yes—
71C42×C3⋊D3C2212yes—
72C42×C3⋊D3C2212yescomplemented
73C4×#634C2214yescomplemented
74C4×#634C2214yescomplemented
75C4×#634C2212yescomplemented
76C3×C4×#41D314yescomplemented
77#5832—34no—
78#5828—34no—
79#5580—38no—
80#5578—38no—
81#5557—38no—
82#5548—38no—
83#5547—316no—
84#5538—316no—
85#5528—316no—
86#5524—34no—
87#5517—34no—
88C4×#235—34no—
89C4×#235—316no—
90C2×C42×D3—34no—
91C23×C3⋊D3C2311yescharacteristic
92C32×#41—24no—
93C2×C32×Q8C2311yescharacteristic
94C2×C32×D4C2312yes—
95C2×C32×D4C2311yescharacteristic
96C22×C32×C4C2312yes—
97C22×C32×C4C2314yes—
98C22×C32×C4C2312yes—
99C22×C32×C4C2311yescharacteristic
100C2×#638C2312yes—
101C2×#638C2314yes—
102C2×#638C2314yes—
103C22×C3⋊Dic3C2312yes—
104C22×C3⋊Dic3C2311yescharacteristic
105#3828—24no—
106#3828—216no—
107C2×C4⋊(C3⋊D3)C2314yes—
108C2×C4⋊(C3⋊D3)C2311yescharacteristic
109C2×C4×C3⋊D3—24no—
110C2×C4×C3⋊D3—28no—
111C2×C4×C3⋊D3C2312yes—
112C2×C4×C3⋊D3C2312yes—
113C2×C4×C3⋊D3C2312yes—
114C2×C4×C3⋊D3C2312yes—
115C2×C4×C3⋊D3C2312yes—
116C2×C4×C3⋊D3C2312yes—
117C2×C4×C3⋊D3C2314yes—
118C2×C4×C3⋊D3C2312yes—
119C2×#634C2314yes—
120C2×#634C2311yescharacteristic
121C32×C4⋊C4C2312yes—
122C32×C4⋊C4C2314yes—
123C32×C22⋊C4C2312yes—
124C32×C22⋊C4C2314yes—
125C32×C42C2312yes—
126C32×C42C2312yes—
127C32×C42C2314yes—
128C32×C42C2311yescharacteristic
129C32×C42C2311yescharacteristic
130#3757C2312yes—
131#3757C2314yes—
132#3757C2314yes—
133#3752C2314yes—
134#3752C2314yes—
135#3752C2314yes—
136#3752C2314yes—
137#3752C2314yes—
138C4⋊(C3⋊Dic3)C2314yes—
139C4⋊(C3⋊Dic3)C2314yes—
140C4⋊(C3⋊Dic3)C2312yes—
141#3750C2314yes—
142#3750C2314yes—
143#3750C2314yes—
144#3750C2314yes—
145#3750C2314yes—
146C4×C3⋊Dic3C2312yes—
147C4×C3⋊Dic3C2312yes—
148C4×C3⋊Dic3C2314yes—
149C4×C3⋊Dic3C2312yes—
150C4×C3⋊Dic3C2312yes—
151C4×C3⋊Dic3C2312yes—
152C4×C3⋊Dic3C2312yes—
153C4×C3⋊Dic3C2311yescharacteristic
154C4×C3⋊Dic3C2311yescharacteristic
155#3444—91noSylow
156C2×C3×#41C2×D314yes—
157C2×#235—34no—
158C2×#235—316no—
159C22×C4×D3—34no—
160C22×C4×D3—38no—
161C3×C4×Q8C2×D318yescomplemented
162C3×C4×D4C2×D3116yes—
163C3×C4×D4C2×D318yescomplemented
164C3×#117C2×D314yes—
165C3×#117C2×D318yescomplemented
166C2×C3×C42C2×D314yes—
167C2×C3×C42C2×D318yescomplemented
168#947—34no—
169#946—38no—
170#944—34no—
171#940—34no—
172#939—316no—
173#938—38no—
174#937—38no—
175#936—34no—
176#935—38no—
177C4×#67—316no—
178C4×#67—316no—
179C4×#67—316no—
180C4×#67—316no—
181C4×#67—316no—
182#926—34no—
183#926—316no—
184C2×C4×Dic3—34no—
185C2×C4×Dic3—38no—
186#898—316no—
187#897—38no—
188#896—316no—
189#895—38no—
190#894—316no—
191#890—38no—
192#889—316no—
193#888—38no—
194#886—38no—
195#885—316no—
196#884—316no—
197#883—316no—
198#882—38no—
199#879—316no—
200#878—316no—
201C4×D12—316no—
202C4×D12—316no—
203C4×D12—38no—
204#872—316no—
205#872—38no—
206#872—316no—
207C42×D3—38no—
208C42×D3—38no—
209C42×D3—38no—
210C42×D3—38no—
211C42×D3—38no—
212C4×Dic6—316no—
213C4×Dic6—316no—
214C4×Dic6—38no—
215C23×C32C2412yes—
216C23×C32C2411yescharacteristic
217C22×C3⋊D3—22no—
218C22×C3⋊D3—24no—
219C22×C3⋊D3C2412yes—
220C22×C3⋊D3C2412yes—
221C32×Q8—22no—
222C32×D4—24no—
223C32×D4—22no—
224C2×C32×C4—24no—
225C2×C32×C4—28no—
226C2×C32×C4—24no—
227C2×C32×C4#4114yescomplemented
228C2×C32×C4C2412yes—
229C2×C32×C4C2412yes—
230C2×C32×C4C2414yes—
231C2×C32×C4C2411yescharacteristic
232C2×C32×C4C2412yes—
233C2×C32×C4C2411yescharacteristic
234#638—24no—
235#638—28no—
236#638—28no—
237C2×C3⋊Dic3—22no—
238C2×C3⋊Dic3—24no—
239C2×C3⋊Dic3C2412yes—
240C2×C3⋊Dic3C2412yes—
241C2×C3⋊Dic3C2412yes—
242C2×C3⋊Dic3C2414yes—
243C2×C3⋊Dic3C2412yes—
244C4⋊(C3⋊D3)—28no—
245C4⋊(C3⋊D3)—22no—
246C4×C3⋊D3—24no—
247C4×C3⋊D3—24no—
248C4×C3⋊D3—24no—
249C4×C3⋊D3—24no—
250C4×C3⋊D3—24no—
251C4×C3⋊D3—28no—
252C4×C3⋊D3—24no—
253C4×C3⋊D3#4118yescomplemented
254#634—22no—
255#634—28no—
256#533—92no—
257#533—91no—
258#532—91no—
259#532—92no—
260#529—92no—
261#529—94no—
262#529—92no—
263#529—94no—
264#525—91no—
265#525—94no—
266#525—91no—
267C4×#41—91no—
268C4×#41—94no—
269C4×#41C3⋊D311yescharacteristic, complemented
270C22×C42—91no—
271C23×D3—34no—
272C3×#41—216no—
273C2×C3×Q8C22×D314yes—
274C2×C3×D4C22×D318yes—
275C2×C3×D4C22×D314yes—
276C22×C3×C4C22×D318yes—
277C22×C3×C4C22×D3116yes—
278C22×C3×C4C22×D318yes—
279C22×C3×C4C22×D314yes—
280C2×#67—38no—
281C2×#67—316no—
282C2×#67—316no—
283C22×Dic3—38no—
284C22×Dic3—34no—
285#235—664no—
286#235—616no—
287C2×D12—316no—
288C2×D12—34no—
289C2×C4×D3—38no—
290C2×C4×D3—38no—
291C2×C4×D3—38no—
292C2×C4×D3—38no—
293C2×C4×D3—38no—
294C2×C4×D3—38no—
295C2×C4×D3—38no—
296C2×C4×D3—316no—
297C2×C4×D3—632no—
298C2×C4×D3—616no—
299C2×Dic6—316no—
300C2×Dic6—34no—
301C3×C4⋊C4C22×D318yes—
302C3×C4⋊C4C22×D3116yes—
303C3×C22⋊C4C22×D318yes—
304C3×C22⋊C4C22×D3116yes—
305C3×C42C22×D318yes—
306C3×C42C22×D318yes—
307C3×C42C22×D3116yes—
308C3×C42C22×D314yes—
309C3×C42C22×D314yes—
310#217—38no—
311#217—316no—
312#217—316no—
313(C2×D3)⋊C4—316no—
314(C2×D3)⋊C4—316no—
315(C2×D3)⋊C4—316no—
316(C2×D3)⋊C4—316no—
317(C2×D3)⋊C4—316no—
318C4⋊Dic3—316no—
319C4⋊Dic3—316no—
320C4⋊Dic3—38no—
321Dic3⋊C4—316no—
322Dic3⋊C4—316no—
323Dic3⋊C4—316no—
324Dic3⋊C4—316no—
325Dic3⋊C4—316no—
326C4×Dic3—38no—
327C4×Dic3—38no—
328C4×Dic3—38no—
329C4×Dic3—316no—
330C4×Dic3—38no—
331C4×Dic3—38no—
332C4×Dic3—38no—
333C4×Dic3—34no—
334C4×Dic3—34no—
335C22×C32—22no—
336C22×C32—24no—
337C22×C32—22no—
338C22×C32C2×#4112yes—
339C22×C32C2511yescharacteristic
340C2×C3⋊D3—28no—
341C2×C3⋊D3—22no—
342C2×C3⋊D3—22no—
343C2×C3⋊D3—22no—
344C2×C3⋊D3—24no—
345C2×C3⋊D3C2×#4114yes—
346C32×C4—24no—
347C32×C4—22no—
348C32×C4—22no—
349C32×C4C2×#4112yes—
350C32×C4C2×#4112yes—
351C32×C4C2×#4114yes—
352C3⋊Dic3—22no—
353C3⋊Dic3—24no—
354C3⋊Dic3—22no—
355C3⋊Dic3—22no—
356C3⋊Dic3C2×#4114yes—
357C2×#41—94no—
358C2×#41—91no—
359C2×#41C2×C3⋊D311yescharacteristic
360C23×C4—92no—
361C23×C4—91no—
362C4⋊Q8—91no—
363C4⋊Q8—92no—
364#127—91no—
365#126—94no—
366#126—94no—
367#125—94no—
368#125—92no—
369#124—91no—
370#124—91no—
371#124—94no—
372#123—92no—
373#123—94no—
374#123—94no—
375#123—92no—
376C22⋊Q8—92no—
377C22⋊Q8—94no—
378C22⋊Q8—92no—
379C22⋊Q8—94no—
380#121—92no—
381#121—94no—
382#121—92no—
383#121—94no—
384#120—92no—
385#120—92no—
386C4×Q8—94no—
387C4×Q8—94no—
388C4×Q8—92no—
389C4×Q8C2×C3⋊D312yescomplemented
390C4×D4—94no—
391C4×D4—94no—
392C4×D4—94no—
393C4×D4—94no—
394C4×D4—94no—
395C4×D4—94no—
396C4×D4—94no—
397C4×D4—92no—
398C4×D4C2×C3⋊D314yes—
399C4×D4C2×C3⋊D312yescomplemented
400#117—91no—
401#117—94no—
402#117—94no—
403#117—94no—
404#117—92no—
405#117C2×C3⋊D311yescharacteristic
406#117C2×C3⋊D312yescomplemented
407C2×C42—92no—
408C2×C42—91no—
409C2×C42—92no—
410C2×C42—92no—
411C2×C42—92no—
412C2×C42—92no—
413C2×C42—92no—
414C2×C42C2×C3⋊D311yescharacteristic
415C2×C42C2×C3⋊D312yescomplemented
416C23×C3C23×D318yes—
417C23×C3C23×D314yes—
418C22×D3—38no—
419C22×D3—38no—
420C22×D3—616no—
421C22×D3—68no—
422C3×Q8—28no—
423C3×D4—216no—
424C3×D4—28no—
425C2×C3×C4—216no—
426C2×C3×C4—216no—
427C2×C3×C4—232no—
428C2×C3×C4#235116yescomplemented
429C2×C3×C4C23×D318yes—
430C2×C3×C4C23×D318yes—
431C2×C3×C4C23×D3116yes—
432C2×C3×C4C23×D314yes—
433C2×C3×C4C23×D314yes—
434C2×C3×C4C23×D318yes—
435#67—632no—
436#67—632no—
437#67—616no—
438C2×Dic3—38no—
439C2×Dic3—38no—
440C2×Dic3—38no—
441C2×Dic3—38no—
442C2×Dic3—316no—
443C2×Dic3—616no—
444C2×Dic3—68no—
445D12—632no—
446D12—68no—
447C4×D3—332no—
448C4×D3—616no—
449C4×D3—616no—
450C4×D3—616no—
451C4×D3—616no—
452C4×D3—616no—
453C4×D3—616no—
454C4×D3—632no—
455Dic6—632no—
456Dic6—68no—
457C2×C32—22no—
458C2×C32—42no—
459C2×C32C22×#4111yescharacteristic
460C2×C32C22×#4112yes—
461C3⋊D3—24no—
462C3⋊D3—42no—
463C24—91no—
464#41—24no—
465#41—1816no—
466#41—184no—
467C2×Q8—94no—
468C2×Q8—91no—
469C2×Q8C22×C3⋊D311yescharacteristic
470C2×D4—94no—
471C2×D4—92no—
472C2×D4—94no—
473C2×D4—94no—
474C2×D4—91no—
475C2×D4C22×C3⋊D312yes—
476C2×D4C22×C3⋊D311yescharacteristic
477C22×C4—92no—
478C22×C4—92no—
479C22×C4—91no—
480C22×C4—92no—
481C22×C4—92no—
482C22×C4—92no—
483C22×C4—92no—
484C22×C4—92no—
485C22×C4—92no—
486C22×C4—94no—
487C22×C4—188no—
488C22×C4—184no—
489C22×C4C22×C3⋊D312yes—
490C22×C4C22×C3⋊D314yes—
491C22×C4C22×C3⋊D312yes—
492C22×C4C22×C3⋊D311yescharacteristic
493C4⋊C4—94no—
494C4⋊C4—94no—
495C4⋊C4—92no—
496C4⋊C4—94no—
497C4⋊C4—94no—
498C4⋊C4—94no—
499C4⋊C4—94no—
500C4⋊C4—94no—
501C4⋊C4C22×C3⋊D312yes—
502C4⋊C4C22×C3⋊D314yes—
503C22⋊C4—92no—
504C22⋊C4—94no—
505C22⋊C4—94no—
506C22⋊C4—94no—
507C22⋊C4—94no—
508C22⋊C4—94no—
509C22⋊C4—94no—
510C22⋊C4—94no—
511C22⋊C4C22×C3⋊D312yes—
512C22⋊C4C22×C3⋊D314yes—
513C42—92no—
514C42—92no—
515C42—92no—
516C42—92no—
517C42—91no—
518C42—92no—
519C42—91no—
520C42—92no—
521C42—94no—
522C42C22×C3⋊D311yescharacteristic
523C42C22×C3⋊D312yes—
524C42C22×C3⋊D314yes—
525C42C22×C3⋊D312yes—
526C42C22×C3⋊D311yescharacteristic
527C22×C3—28no—
528C22×C3—28no—
529C22×C3—216no—
530C22×C3C2×#23518yes—
531C22×C3C24×D314yes—
532C2×D3—316no—
533C2×D3—632no—
534C2×D3—68no—
535C2×D3—68no—
536C2×D3—68no—
537C2×D3—616no—
538C3×C4—28no—
539C3×C4—216no—
540C3×C4—28no—
541C3×C4C2×#23518yes—
542C3×C4C2×#23518yes—
543C3×C4D3×#41116yes—
544Dic3—316no—
545Dic3—68no—
546Dic3—68no—
547Dic3—616no—
548Dic3—68no—
549C32#344411yescharacteristic, complemented, Sylow
550C23—92no—
551C23—92no—
552C23—184no—
553C23—182no—
554C23C23×C3⋊D312yes—
555C23C23×C3⋊D311yescharacteristic
556Q8—22no—
557Q8—188no—
558Q8—182no—
559D4—24no—
560D4—22no—
561D4—188no—
562D4—188no—
563D4—188no—
564D4—184no—
565D4—182no—
566C2×C4—24no—
567C2×C4—24no—
568C2×C4—28no—
569C2×C4—92no—
570C2×C4—98no—
571C2×C4—92no—
572C2×C4—92no—
573C2×C4—92no—
574C2×C4—94no—
575C2×C4—184no—
576C2×C4—184no—
577C2×C4—184no—
578C2×C4—182no—
579C2×C4—184no—
580C2×C4—184no—
581C2×C4—184no—
582C2×C4—184no—
583C2×C4—188no—
584C2×C4#382814yescomplemented
585C2×C4C23×C3⋊D312yes—
586C2×C4C23×C3⋊D312yes—
587C2×C4C23×C3⋊D314yes—
588C2×C4C23×C3⋊D311yescharacteristic
589C2×C4C23×C3⋊D311yescharacteristic
590C2×C4C23×C3⋊D312yes—
591C2×C3—28no—
592C2×C3—48no—
593C2×C3C22×#23514yes—
594C2×C3C2×D3×#4118yes—
595D3—616no—
596D3—128no—
597C22—22no—
598C22—22no—
599C22—24no—
600C22—94no—
601C22—188no—
602C22—182no—
603C22—182no—
604C22—182no—
605C22—184no—
606C22C2×#382812yes—
607C22C24×C3⋊D311yescharacteristic
608C4—22no—
609C4—22no—
610C4—24no—
611C4—94no—
612C4—182no—
613C4—182no—
614C4—182no—
615C4—184no—
616C4C2×#382812yes—
617C4C2×#382812yes—
618C4#41×C3⋊D314yes—
619C3#8583614yescomplemented
620C2—22no—
621C2—42no—
622C2—184no—
623C2—362no—
624C2C22×#382811yescharacteristic
625C2C2×#41×C3⋊D312yes—
subgroupG/H
centerC42C22×C3⋊D3
commutator, socle, cosocleC22×C32C25
FrattiniC22C24×C3⋊D3
FittingC32×C4×#41C2
hypercenterC4×#41C3⋊D3
hypocenterC32#3444
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C42 ◁ C4×#41

Complements

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

NH ≅ G/Ntype
1. C32×C4×#41C2semidirect
2. #10596303C2semidirect
3. #10596299C2semidirect
4. #10596051C2semidirect
5. #10596049C2semidirect
6. #10596028C2semidirect
7. #10596019C2semidirect
8. #10596018C2semidirect
9. #10596009C2semidirect
10. #10595999C2semidirect
11. #10595995C2semidirect
12. #10595988C2semidirect
13. C4×#3828C2semidirect
14. C4×#3828C2semidirect
15. C2×C42×C3⋊D3C2semidirect
22. C32×C4×Q8C22semidirect
24. C32×C4×D4C22semidirect
26. C32×#117C22semidirect
28. C2×C32×C42C22semidirect
29. #64156C22semidirect
31. #64153C22semidirect
32. #64149C22semidirect
36. #64145C22semidirect
41. C4×#638C22semidirect
42. C4×#638C22semidirect
44. #64135C22semidirect
47. #64107C22semidirect
52. #64099C22semidirect
53. #64098C22semidirect
54. #64097C22semidirect
56. #64094C22semidirect
60. #64088C22semidirect
64. C4×C4⋊(C3⋊D3)C22semidirect
66. #64081C22semidirect
67. #64081C22semidirect
72. C42×C3⋊D3C22semidirect
73. C4×#634C22semidirect
74. C4×#634C22semidirect
75. C4×#634C22semidirect
76. C3×C4×#41D3semidirect
161. C3×C4×Q8C2×D3semidirect
163. C3×C4×D4C2×D3semidirect
165. C3×#117C2×D3semidirect
167. C2×C3×C42C2×D3semidirect
227. C2×C32×C4#41semidirect
253. C4×C3⋊D3#41semidirect
269. C4×#41C3⋊D3semidirect
389. C4×Q8C2×C3⋊D3semidirect
399. C4×D4C2×C3⋊D3semidirect
406. #117C2×C3⋊D3semidirect
415. C2×C42C2×C3⋊D3semidirect
428. C2×C3×C4#235semidirect
549. C32#3444semidirect
584. C2×C4#3828semidirect
619. C3#85836semidirect

Maximal subgroups

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

subgroupindex
C32×C4×#412
#105963032
#105962992
#105960512
#105960492
#105960282
#105960192
#105960182
#105960092
#105959992
#105959952
#105959882
C4×#38282
C2×C42×C3⋊D32
#858363