Finite Group Databasebeta

← #11901963

Subgroups — #11901963

Order 1152.

3480 conjugacy classes of subgroups.

The subgroup lattice has 612 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C32×#534C211yesmaximal, characteristic, complemented
2#10596275C212yesmaximal, complemented
3C2×D4×C3⋊Dic3C212yesmaximal, complemented
4#10596136C214yesmaximal, complemented
5#10596120C214yesmaximal, complemented
6#10596088C212yesmaximal, complemented
7#10596077C212yesmaximal, complemented
8#10596073C212yesmaximal, complemented
9#10596071C212yesmaximal, complemented
10#10596064C214yesmaximal, complemented
11#10596057C214yesmaximal, complemented
12C2×#64090C211yesmaximal, characteristic, complemented
13#10595954C211yesmaximal, characteristic, complemented
14#86295—34nomaximal
15C22×C32×D4C2212yes—
16C22×#638C2211yescharacteristic
17C23×C3⋊Dic3C2211yescharacteristic
18C23×C3⋊Dic3C2212yescomplemented
19C2×#3830C2212yescomplemented
20C22×C4×C3⋊D3C2211yescharacteristic, complemented
21C32×#123C2214yescomplemented
22C32×#121C2212yes—
23C32×#121C2212yes—
24C32×#120C2214yescomplemented
25C2×C32×C22⋊C4C2211yescharacteristic
26#64162C2214yescomplemented
27C2×#3757C2212yes—
28C2×#3757C2212yescomplemented
29#64148C2214yes—
30#64148C2214yes—
31#64148C2214yescomplemented
32#64147C2212yescomplemented
33#64146C2214yescomplemented
34#64145C2212yescomplemented
35#64144C2214yescomplemented
36#64144C2214yescomplemented
37D4×C3⋊Dic3C2214yescomplemented
38D4×C3⋊Dic3C2214yescomplemented
39D4×C3⋊Dic3C2214yescomplemented
40D4×C3⋊Dic3C2214yescomplemented
41D4×C3⋊Dic3C2212yescomplemented
42#64138C2214yescomplemented
43C2×#3752C2211yescharacteristic, complemented
44C2×C4⋊(C3⋊Dic3)C2212yescomplemented
45#64133C2212yescomplemented
46#64133C2212yescomplemented
47C2×#3750C2211yescharacteristic, complemented
48C2×C4×C3⋊Dic3C2212yescomplemented
49C2×C4×C3⋊Dic3C2211yescharacteristic, complemented
50#64107C2214yescomplemented
51#64106C2212yescomplemented
52#64101C2212yescomplemented
53#64099C2212yescomplemented
54#64098C2214yescomplemented
55#64096C2212yescomplemented
56#64095C2214yescomplemented
57#64094C2214yescomplemented
58#64092C2214yescomplemented
59#64090C2214yescomplemented
60#64090C2214yescomplemented
61#64090C2214yescomplemented
62#64088C2214yescomplemented
63#64088C2214yescomplemented
64#64087C2214yescomplemented
65#64087C2214yescomplemented
66#64087C2214yescomplemented
67#64086C2214yescomplemented
68C3×#534D314yescomplemented
69#5804—38no—
70C2×D4×Dic3—38no—
71#5665—316no—
72#5649—316no—
73#5617—38no—
74#5606—38no—
75#5602—38no—
76#5600—38no—
77#5593—316no—
78#5586—316no—
79C2×#67⋊C4—34no—
80#5483—34no—
81C24×C32C2312yes—
82C24×C32C2311yescharacteristic
83C23×C3⋊D3C2311yescharacteristic
84C2×C32×D4—28no—
85C2×C32×D4C2314yes—
86C2×C32×D4C2314yes—
87C2×C32×D4C2312yes—
88C2×C32×D4C2312yes—
89C22×C32×C4C2312yes—
90C22×C32×C4C2311yescharacteristic
91C22×C32×C4C2311yescharacteristic
92C2×#638—24no—
93C2×#638C2314yes—
94C2×#638C2314yes—
95C2×#638C2314yes—
96C22×C3⋊Dic3—42no—
97C22×C3⋊Dic3—44no—
98C22×C3⋊Dic3C2314yes—
99C22×C3⋊Dic3C2312yes—
100C22×C3⋊Dic3C2311yescharacteristic
101C22×C3⋊Dic3C2311yescharacteristic
102C22×C3⋊Dic3C2312yes—
103C22×C3⋊Dic3C2312yes—
104C22×C3⋊Dic3C2314yes—
105C22×C3⋊Dic3C2312yes—
106C22×C3⋊Dic3C2311yescharacteristic
107#3830—44no—
108C2×C4×C3⋊D3—42no—
109C2×C4×C3⋊D3C2312yes—
110C2×C4×C3⋊D3C2312yes—
111C2×#634C2312yes—
112C2×#634C2312yes—
113C32×C4⋊C4C2312yes—
114C32×C4⋊C4C2312yes—
115C32×C22⋊C4C2314yes—
116C32×C22⋊C4C2314yes—
117C32×C22⋊C4C2314yes—
118#3757C2314yes—
119#3757C2314yes—
120#3757C2314yes—
121#3757C2314yes—
122#3757C2314yes—
123#3757C2314yes—
124#3752C2314yes—
125#3752C2314yes—
126#3752C2314yes—
127C4⋊(C3⋊Dic3)C2312yes—
128C4⋊(C3⋊Dic3)C2312yes—
129C4⋊(C3⋊Dic3)C2314yes—
130C4⋊(C3⋊Dic3)C2314yes—
131#3750C2314yes—
132#3750C2314yes—
133#3750C2314yes—
134#3750C2314yes—
135#3750C2314yes—
136C4×C3⋊Dic3C2312yes—
137C4×C3⋊Dic3C2314yes—
138C4×C3⋊Dic3C2312yes—
139C4×C3⋊Dic3C2314yes—
140#3459—91noSylow
141C22×C3×D4C2×D318yes—
142C22×#67—34no—
143C23×Dic3—34no—
144C23×Dic3—38no—
145C2×#237—38no—
146C22×C4×D3—34no—
147C3×#123C2×D3116yescomplemented
148C3×#121C2×D318yes—
149C3×#121C2×D318yes—
150C3×#120C2×D3116yescomplemented
151C2×C3×C22⋊C4C2×D314yes—
152#953—316no—
153C2×#217—38no—
154C2×#217—38no—
155#939—316no—
156#939—316no—
157#939—316no—
158#938—38no—
159#937—316no—
160#936—38no—
161#935—316no—
162#935—316no—
163D4×Dic3—316no—
164D4×Dic3—316no—
165D4×Dic3—316no—
166D4×Dic3—316no—
167D4×Dic3—38no—
168#929—316no—
169C2×(C2×D3)⋊C4—34no—
170C2×C4⋊Dic3—38no—
171#924—38no—
172#924—38no—
173C2×Dic3⋊C4—34no—
174C2×C4×Dic3—38no—
175C2×C4×Dic3—34no—
176#898—316no—
177#897—38no—
178#892—38no—
179#890—38no—
180#889—316no—
181#887—38no—
182#886—316no—
183#885—316no—
184#883—316no—
185#67⋊C4—316no—
186#67⋊C4—316no—
187#67⋊C4—316no—
188#879—316no—
189#879—316no—
190#878—316no—
191#878—316no—
192#878—316no—
193#877—316no—
194C23×C32—24no—
195C23×C32—41no—
196C23×C32—42no—
197C23×C32—41no—
198C23×C32—42no—
199C23×C32#4114yescomplemented
200C23×C32C2414yes—
201C23×C32C2411yescharacteristic
202C23×C32C2412yes—
203C22×C3⋊D3—22no—
204C22×C3⋊D3—41no—
205C22×C3⋊D3—41no—
206C22×C3⋊D3C2412yes—
207C32×D4—28no—
208C32×D4—28no—
209C32×D4—42no—
210C32×D4—42no—
211C2×C32×C4—24no—
212C2×C32×C4—41no—
213C2×C32×C4—41no—
214C2×C32×C4C2414yes—
215C2×C32×C4C2412yes—
216C2×C32×C4C2412yes—
217#638—28no—
218#638—44no—
219#638—44no—
220C2×C3⋊Dic3—22no—
221C2×C3⋊Dic3—22no—
222C2×C3⋊Dic3—28no—
223C2×C3⋊Dic3—24no—
224C2×C3⋊Dic3—42no—
225C2×C3⋊Dic3—44no—
226C2×C3⋊Dic3—42no—
227C2×C3⋊Dic3—41no—
228C2×C3⋊Dic3—42no—
229C2×C3⋊Dic3C2412yes—
230C2×C3⋊Dic3C2414yes—
231C2×C3⋊Dic3C2412yes—
232C2×C3⋊Dic3C2411yescharacteristic
233C2×C3⋊Dic3C2414yes—
234C2×C3⋊Dic3C2411yescharacteristic
235C4×C3⋊D3—24no—
236C4×C3⋊D3—42no—
237#634—42no—
238#634—42no—
239#543—91no—
240#539—94no—
241#539—92no—
242#538—92no—
243#538—94no—
244#534—92no—
245#534C3⋊D311yescharacteristic, complemented
246#529—94no—
247#529—92no—
248#525—92no—
249#525—94no—
250C2×C4×D4—92no—
251C2×C4×D4—91no—
252C24×C3C22×D318yes—
253C24×C3C22×D314yes—
254C23×D3—34no—
255C2×C3×D4—232no—
256C2×C3×D4C22×D3116yes—
257C2×C3×D4C22×D3116yes—
258C2×C3×D4C22×D318yes—
259C2×C3×D4C22×D318yes—
260C22×C3×C4C22×D318yes—
261C22×C3×C4C22×D314yes—
262C22×C3×C4C22×D314yes—
263C2×#67—316no—
264C2×#67—316no—
265C2×#67—316no—
266C2×#67—616no—
267C22×Dic3—316no—
268C22×Dic3—38no—
269C22×Dic3—34no—
270C22×Dic3—34no—
271C22×Dic3—38no—
272C22×Dic3—38no—
273C22×Dic3—316no—
274C22×Dic3—38no—
275C22×Dic3—34no—
276C22×Dic3—128no—
277C22×Dic3—1216no—
278#237—1216no—
279C2×C4×D3—38no—
280C2×C4×D3—38no—
281C2×C4×D3—128no—
282C2×Dic6—38no—
283C2×Dic6—38no—
284C3×C4⋊C4C22×D318yes—
285C3×C4⋊C4C22×D318yes—
286C3×C22⋊C4C22×D3116yes—
287C3×C22⋊C4C22×D3116yes—
288C3×C22⋊C4C22×D3116yes—
289#217—316no—
290#217—316no—
291#217—316no—
292#217—316no—
293#217—316no—
294#217—316no—
295(C2×D3)⋊C4—316no—
296(C2×D3)⋊C4—316no—
297(C2×D3)⋊C4—316no—
298C4⋊Dic3—38no—
299C4⋊Dic3—38no—
300C4⋊Dic3—316no—
301C4⋊Dic3—316no—
302Dic3⋊C4—316no—
303Dic3⋊C4—316no—
304Dic3⋊C4—316no—
305Dic3⋊C4—316no—
306Dic3⋊C4—316no—
307C4×Dic3—38no—
308C4×Dic3—316no—
309C4×Dic3—38no—
310C4×Dic3—316no—
311C22×C32—22no—
312C22×C32—21no—
313C22×C32—22no—
314C22×C32—21no—
315C22×C32—24no—
316C22×C32—24no—
317C22×C32—24no—
318C22×C32—44no—
319C22×C32—48no—
320C22×C32C2×#4112yes—
321C22×C32C2×#4114yes—
322C22×C32C2511yescharacteristic
323C2×C3⋊D3—22no—
324C2×C3⋊D3—22no—
325C2×C3⋊D3—22no—
326C2×C3⋊D3—44no—
327C32×C4—24no—
328C32×C4—22no—
329C32×C4—22no—
330C3⋊Dic3—22no—
331C3⋊Dic3—24no—
332C3⋊Dic3—21no—
333C3⋊Dic3—22no—
334C3⋊Dic3—24no—
335C3⋊Dic3H(5,𝔽2)12yes—
336C2×#41—92no—
337C22×D4—91no—
338C22×D4C2×C3⋊D312yes—
339C23×C4—91no—
340C23×C4—92no—
341C23×C4—91no—
342#126—94no—
343#126—94no—
344#126—94no—
345#125—94no—
346#125—92no—
347#124—92no—
348#124—94no—
349#123—94no—
350#123—94no—
351#123—94no—
352#123—94no—
353#123—94no—
354#123C2×C3⋊D314yescomplemented
355C22⋊Q8—92no—
356C22⋊Q8—92no—
357C22⋊Q8—92no—
358C22⋊Q8—94no—
359C22⋊Q8—94no—
360C22⋊Q8—94no—
361#121—94no—
362#121—92no—
363#121—94no—
364#121—94no—
365#121C2×C3⋊D312yes—
366#121C2×C3⋊D312yes—
367#120—94no—
368#120—94no—
369#120C2×C3⋊D314yescomplemented
370C4×Q8—92no—
371C4×D4—94no—
372C4×D4—94no—
373C4×D4—94no—
374C4×D4—94no—
375C4×D4—92no—
376C4×D4—94no—
377C4×D4—94no—
378C4×D4—94no—
379#117—92no—
380#117—94no—
381C2×C4⋊C4—91no—
382C2×C4⋊C4—92no—
383C2×C22⋊C4—92no—
384C2×C22⋊C4—92no—
385C2×C22⋊C4—91no—
386C2×C22⋊C4C2×C3⋊D311yescharacteristic
387C2×C42—91no—
388C2×C42—92no—
389C23×C3—216no—
390C23×C3—44no—
391C23×C3—48no—
392C23×C3—44no—
393C23×C3—48no—
394C23×C3#237116yescomplemented
395C23×C3C23×D3116yes—
396C23×C3C23×D314yes—
397C23×C3C23×D318yes—
398C22×D3—38no—
399C22×D3—68no—
400C22×D3—124no—
401C22×D3—124no—
402C3×D4—232no—
403C3×D4—232no—
404C3×D4—48no—
405C3×D4—48no—
406C2×C3×C4—216no—
407C2×C3×C4—44no—
408C2×C3×C4—44no—
409C2×C3×C4C23×D3116yes—
410C2×C3×C4C23×D318yes—
411C2×C3×C4C23×D318yes—
412#67—632no—
413#67—1216no—
414#67—1216no—
415C2×Dic3—34no—
416C2×Dic3—38no—
417C2×Dic3—316no—
418C2×Dic3—38no—
419C2×Dic3—34no—
420C2×Dic3—316no—
421C2×Dic3—68no—
422C2×Dic3—632no—
423C2×Dic3—616no—
424C2×Dic3—68no—
425C2×Dic3—128no—
426C2×Dic3—128no—
427C2×Dic3—1216no—
428C2×Dic3—128no—
429C2×Dic3—124no—
430C4×D3—616no—
431C4×D3—128no—
432Dic6—128no—
433Dic6—128no—
434C2×C32—22no—
435C2×C32—24no—
436C2×C32—44no—
437C2×C32C22×#4111yescharacteristic
438C2×C32C2×H(5,𝔽2)11yescharacteristic
439C2×C32#58511yescharacteristic
440C3⋊D3—42no—
441C24—91no—
442C24C22×C3⋊D312yes—
443C24C22×C3⋊D311yescharacteristic
444#41—364no—
445C2×Q8—92no—
446C2×Q8—92no—
447C2×D4—28no—
448C2×D4—94no—
449C2×D4—94no—
450C2×D4—94no—
451C2×D4—184no—
452C2×D4C22×C3⋊D314yes—
453C2×D4C22×C3⋊D314yes—
454C2×D4C22×C3⋊D312yes—
455C2×D4C22×C3⋊D312yes—
456C22×C4—91no—
457C22×C4—91no—
458C22×C4—92no—
459C22×C4—94no—
460C22×C4—92no—
461C22×C4—91no—
462C22×C4—92no—
463C22×C4—92no—
464C22×C4—94no—
465C22×C4—92no—
466C22×C4—92no—
467C22×C4—362no—
468C22×C4—362no—
469C22×C4—364no—
470C22×C4C22×C3⋊D312yes—
471C22×C4C22×C3⋊D311yescharacteristic
472C22×C4C22×C3⋊D311yescharacteristic
473C4⋊C4—94no—
474C4⋊C4—94no—
475C4⋊C4—94no—
476C4⋊C4—94no—
477C4⋊C4—92no—
478C4⋊C4—94no—
479C4⋊C4—94no—
480C4⋊C4—92no—
481C4⋊C4—94no—
482C4⋊C4C22×C3⋊D312yes—
483C4⋊C4C22×C3⋊D312yes—
484C22⋊C4—94no—
485C22⋊C4—94no—
486C22⋊C4—94no—
487C22⋊C4—94no—
488C22⋊C4—94no—
489C22⋊C4—94no—
490C22⋊C4—94no—
491C22⋊C4—94no—
492C22⋊C4—94no—
493C22⋊C4C22×C3⋊D314yes—
494C22⋊C4C22×C3⋊D314yes—
495C22⋊C4C22×C3⋊D314yes—
496C42—94no—
497C42—92no—
498C42—94no—
499C42—92no—
500C22×C3—28no—
501C22×C3—24no—
502C22×C3—28no—
503C22×C3—24no—
504C22×C3—216no—
505C22×C3—216no—
506C22×C3—216no—
507C22×C3—416no—
508C22×C3—432no—
509C22×C3C2×#23718yes—
510C22×C3C2×#237116yes—
511C22×C3C24×D314yes—
512C2×D3—68no—
513C2×D3—68no—
514C2×D3—68no—
515C2×D3—1216no—
516C3×C4—216no—
517C3×C4—28no—
518C3×C4—28no—
519Dic3—38no—
520Dic3—68no—
521Dic3—616no—
522Dic3—64no—
523Dic3—68no—
524Dic3—616no—
525C32#345911yescharacteristic, complemented, Sylow
526C23—24no—
527C23—41no—
528C23—42no—
529C23—41no—
530C23—42no—
531C23—92no—
532C23—182no—
533C23—361no—
534C23—361no—
535C23#383014yescomplemented
536C23C23×C3⋊D314yes—
537C23C23×C3⋊D311yescharacteristic
538C23C23×C3⋊D312yes—
539Q8—362no—
540Q8—362no—
541D4—28no—
542D4—28no—
543D4—42no—
544D4—42no—
545D4—188no—
546D4—364no—
547D4—364no—
548C2×C4—24no—
549C2×C4—41no—
550C2×C4—41no—
551C2×C4—91no—
552C2×C4—94no—
553C2×C4—92no—
554C2×C4—91no—
555C2×C4—92no—
556C2×C4—94no—
557C2×C4—184no—
558C2×C4—182no—
559C2×C4—184no—
560C2×C4—188no—
561C2×C4—182no—
562C2×C4—362no—
563C2×C4—361no—
564C2×C4—362no—
565C2×C4—364no—
566C2×C4—362no—
567C2×C4—362no—
568C2×C4C23×C3⋊D312yes—
569C2×C4C23×C3⋊D314yes—
570C2×C4C23×C3⋊D312yes—
571C2×C3—28no—
572C2×C3—216no—
573C2×C3—416no—
574C2×C3C22×#23714yes—
575C2×C3D3×H(5,𝔽2)14yes—
576C2×C3#596614yes—
577D3—128no—
578C22—21no—
579C22—22no—
580C22—21no—
581C22—22no—
582C22—24no—
583C22—24no—
584C22—24no—
585C22—44no—
586C22—48no—
587C22—182no—
588C22—182no—
589C22—182no—
590C22—364no—
591C22C2×#383014yes—
592C22C2×#383012yes—
593C22C24×C3⋊D311yescharacteristic
594C4—24no—
595C4—22no—
596C4—22no—
597C4—92no—
598C4—182no—
599C4—181no—
600C4—182no—
601C4—184no—
602C4—184no—
603C3#8629514yescomplemented
604C2—24no—
605C2—22no—
606C2—44no—
607C2—362no—
608C2C22×#383011yescharacteristic
609C2C3⋊D3×H(5,𝔽2)11yescharacteristic
610C2#1059675811yescharacteristic
subgroupG/H
center, FrattiniC22C24×C3⋊D3
commutator, socle, cosocleC22×C32C25
FittingC32×#534C2
hypercenter#534C3⋊D3
hypocenterC32#3459
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ #534

Complements

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

NH ≅ G/Ntype
1. C32×#534C2semidirect
2. #10596275C2semidirect
3. C2×D4×C3⋊Dic3C2semidirect
4. #10596136C2semidirect
5. #10596120C2semidirect
6. #10596088C2semidirect
7. #10596077C2semidirect
8. #10596073C2semidirect
9. #10596071C2semidirect
10. #10596064C2semidirect
11. #10596057C2semidirect
12. C2×#64090C2semidirect
13. #10595954C2semidirect
18. C23×C3⋊Dic3C22semidirect
19. C2×#3830C22semidirect
20. C22×C4×C3⋊D3C22semidirect
21. C32×#123C22semidirect
24. C32×#120C22semidirect
26. #64162C22semidirect
28. C2×#3757C22semidirect
31. #64148C22semidirect
32. #64147C22semidirect
33. #64146C22semidirect
34. #64145C22semidirect
35. #64144C22semidirect
36. #64144C22semidirect
37. D4×C3⋊Dic3C22semidirect
38. D4×C3⋊Dic3C22semidirect
39. D4×C3⋊Dic3C22semidirect
40. D4×C3⋊Dic3C22semidirect
41. D4×C3⋊Dic3C22semidirect
42. #64138C22semidirect
43. C2×#3752C22semidirect
44. C2×C4⋊(C3⋊Dic3)C22semidirect
45. #64133C22semidirect
46. #64133C22semidirect
47. C2×#3750C22semidirect
48. C2×C4×C3⋊Dic3C22semidirect
49. C2×C4×C3⋊Dic3C22semidirect
50. #64107C22semidirect
51. #64106C22semidirect
52. #64101C22semidirect
53. #64099C22semidirect
54. #64098C22semidirect
55. #64096C22semidirect
56. #64095C22semidirect
57. #64094C22semidirect
58. #64092C22semidirect
59. #64090C22semidirect
60. #64090C22semidirect
61. #64090C22semidirect
62. #64088C22semidirect
63. #64088C22semidirect
64. #64087C22semidirect
65. #64087C22semidirect
66. #64087C22semidirect
67. #64086C22semidirect
68. C3×#534D3semidirect
147. C3×#123C2×D3semidirect
150. C3×#120C2×D3semidirect
199. C23×C32#41semidirect
245. #534C3⋊D3semidirect
354. #123C2×C3⋊D3semidirect
369. #120C2×C3⋊D3semidirect
394. C23×C3#237semidirect
525. C32#3459semidirect
535. C23#3830semidirect
603. C3#86295semidirect

Maximal subgroups

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

subgroupindex
C32×#5342
#105962752
C2×D4×C3⋊Dic32
#105961362
#105961202
#105960882
#105960772
#105960732
#105960712
#105960642
#105960572
C2×#640902
#105959542
#862953