Finite Group Databasebeta

← #11909867

Subgroups — #11909867

Order 1152.

2976 conjugacy classes of subgroups.

The subgroup lattice has 633 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C32×#556C211yesmaximal, characteristic, complemented
2#10596199C211yesmaximal, characteristic, complemented
3#10596192C211yesmaximal, characteristic, complemented
4#10596179C214yesmaximal, complemented
5#10596172C214yesmaximal, complemented
6#10596151C212yesmaximal
7#10596142C212yesmaximal, complemented
8#10596103C212yesmaximal, complemented
9#10596096C212yesmaximal, complemented
10#10596049C212yesmaximal, complemented
11C4×Q8×C3⋊D3C211yesmaximal, characteristic, complemented
12#10596040C212yesmaximal, complemented
13#10596038C211yesmaximal, characteristic, complemented
14#10596028C211yesmaximal, characteristic
15D4×#634C211yesmaximal, characteristic, complemented
16#10596000C212yesmaximal, complemented
17#10595987C212yesmaximal, complemented
18#86993—34nomaximal
19C2×Q8×C3⋊D3C2211yescharacteristic
20C22×#634C2212yes—
21C32×C4⋊Q8C2211yescharacteristic
22C32×#126C2214yes—
23C32×#124C2212yes—
24C32×C22⋊Q8C2212yes—
25C32×C4×Q8C2211yescharacteristic
26C32×C4×Q8C2212yes—
27C32×C4×D4C2211yescharacteristic
28C32×#117C2212yes—
29#64155C2212yes—
30Q8×C3⋊Dic3C2211yescharacteristic
31Q8×C3⋊Dic3C2212yes—
32Q8×C3⋊Dic3C2212yes—
33#64153C2212yes—
34#64153C2212yes—
35#64147C2211yescharacteristic
36#64145C2211yescharacteristic
37D4×C3⋊Dic3C2212yes—
38C4×#638C2212yes—
39#64135C2212yes—
40#64133C2212yes—
41#64106C2212yes—
42#64106C2211yescharacteristic
43#64105C2214yes—
44#64101C2212yes—
45C4⋊C4×C3⋊D3C2212yes—
46C4⋊C4×C3⋊D3C2211yescharacteristic
47#64099C2214yes—
48#64099C2212yes—
49#64099C2212yes—
50#64099C2211yescharacteristic
51#64098C2214yes—
52#64098C2214yes—
53#64098C2214yes—
54#64097C2214yes—
55#64097C2212yes—
56#64096C2212yes—
57#64096C2212yes—
58#64096C2212yes—
59#64096C2211yescharacteristic
60#64096C2212yes—
61#64092C2214yes—
62#64092C2212yes—
63#64090C2214yes—
64#64088C2214yes—
65#64088C2214yes—
66#64088C2214yes—
67#64088C2212yes—
68#64087C2214yes—
69#64087C2214yes—
70#64086C2214yes—
71#64086C2214yes—
72#64081C2214yes—
73C42×C3⋊D3C2212yes—
74C42×C3⋊D3C2211yescharacteristic
75#64079C2212yes—
76#64079C2214yes—
77#64078C2211yescharacteristic
78C4×#634C2212yes—
79C4×#634C2212yes—
80C4×#634C2214yes—
81C4×#634C2214yes—
82C4×#634C2211yescharacteristic
83C4×#634C2211yescharacteristic
84C3×#556D314yescomplemented
85#5728—34no—
86#5721—34no—
87#5708—316no—
88#5701—316no—
89#5680—38no—
90#5671—38no—
91#5632—38no—
92#5625—38no—
93#5578—38no—
94C4×D3×Q8—34no—
95#5569—38no—
96#5567—34no—
97#5557—34no—
98D4×Dic6—34no—
99#5529—38no—
100#5516—38no—
101C2×C32×Q8C2311yescharacteristic
102C2×C32×Q8C2312yes—
103C2×C32×D4C2311yescharacteristic
104C22×C32×C4C2312yes—
105C2×#638C2312yes—
106C22×C3⋊Dic3C2314yes—
107Q8×C3⋊D3—24no—
108C2×C4×C3⋊D3C2311yescharacteristic
109C2×C4×C3⋊D3C2312yes—
110C2×C4×C3⋊D3C2312yes—
111C2×C4×C3⋊D3C2311yescharacteristic
112C2×C4×C3⋊D3C2311yescharacteristic
113C2×#634—28no—
114C2×#634C2311yescharacteristic
115C2×#634C2314yes—
116C2×#634C2312yes—
117C2×#634C2312yes—
118C2×#634C2311yescharacteristic
119C32×C4⋊C4C2311yescharacteristic
120C32×C4⋊C4C2312yes—
121C32×C4⋊C4C2312yes—
122C32×C4⋊C4C2311yescharacteristic
123C32×C4⋊C4C2314yes—
124C32×C4⋊C4C2312yes—
125C32×C22⋊C4C2314yes—
126C32×C22⋊C4C2312yes—
127C32×C22⋊C4C2314yes—
128C32×C42C2311yescharacteristic
129C32×C42C2312yes—
130C32×C42C2314yes—
131#3757C2312yes—
132#3757C2312yes—
133#3757C2312yes—
134#3757C2314yes—
135#3752C2312yes—
136#3752C2314yes—
137C4⋊(C3⋊Dic3)C2312yes—
138C4⋊(C3⋊Dic3)C2312yes—
139C4⋊(C3⋊Dic3)C2312yes—
140C4⋊(C3⋊Dic3)C2311yescharacteristic
141C4⋊(C3⋊Dic3)C2312yes—
142C4⋊(C3⋊Dic3)C2311yescharacteristic
143C4⋊(C3⋊Dic3)C2312yes—
144C4⋊(C3⋊Dic3)C2314yes—
145C4⋊(C3⋊Dic3)C2314yes—
146#3750C2312yes—
147#3750C2314yes—
148#3750C2312yes—
149#3750C2314yes—
150#3750C2314yes—
151#3750C2312yes—
152#3750C2314yes—
153#3750C2312yes—
154#3750C2312yes—
155#3750C2314yes—
156#3750C2314yes—
157#3750C2314yes—
158C4×C3⋊Dic3C2312yes—
159C4×C3⋊Dic3C2312yes—
160C4×C3⋊Dic3C2311yescharacteristic
161C4×C3⋊Dic3C2314yes—
162C4×C3⋊Dic3C2314yes—
163C4×C3⋊Dic3C2314yes—
164C4×C3⋊Dic3C2312yes—
165C4×C3⋊Dic3C2311yescharacteristic
166C4×C3⋊Dic3C2312yes—
167C4×C3⋊Dic3C2311yescharacteristic
168#3523—91noSylow
169C2×D3×Q8—34no—
170C22×Dic6—38no—
171C3×C4⋊Q8C2×D314yes—
172C3×#126C2×D3116yes—
173C3×#124C2×D318yes—
174C3×C22⋊Q8C2×D318yes—
175C3×C4×Q8C2×D314yes—
176C3×C4×Q8C2×D318yes—
177C3×C4×D4C2×D314yes—
178C3×#117C2×D318yes—
179#946—38no—
180Q8×Dic3—38no—
181Q8×Dic3—38no—
182Q8×Dic3—34no—
183#944—38no—
184#944—38no—
185#938—34no—
186#936—34no—
187D4×Dic3—38no—
188C4×#67—38no—
189#926—38no—
190#924—38no—
191#897—38no—
192#897—34no—
193#896—316no—
194#892—38no—
195D3×C4⋊C4—38no—
196D3×C4⋊C4—34no—
197#890—38no—
198#890—316no—
199#890—38no—
200#890—34no—
201#889—316no—
202#889—316no—
203#889—316no—
204#888—316no—
205#888—38no—
206#887—38no—
207#887—38no—
208#887—38no—
209#887—34no—
210#887—38no—
211#883—316no—
212#883—38no—
213#67⋊C4—316no—
214#879—316no—
215#879—316no—
216#879—316no—
217#879—38no—
218#878—316no—
219#878—316no—
220#877—316no—
221#877—316no—
222#872—316no—
223C42×D3—38no—
224C42×D3—34no—
225#870—38no—
226#870—316no—
227#869—34no—
228C4×Dic6—38no—
229C4×Dic6—38no—
230C4×Dic6—316no—
231C4×Dic6—316no—
232C4×Dic6—34no—
233C4×Dic6—34no—
234C23×C32C2412yes—
235C22×C3⋊D3C2411yescharacteristic
236C32×Q8—22no—
237C32×Q8—24no—
238C32×D4—22no—
239C2×C32×C4—24no—
240C2×C32×C4C2412yes—
241C2×C32×C4C2414yes—
242C2×C32×C4C2411yescharacteristic
243C2×C32×C4C2412yes—
244C2×C32×C4C2412yes—
245C2×C32×C4C2411yescharacteristic
246C2×C32×C4C2411yescharacteristic
247#638—24no—
248C2×C3⋊Dic3—28no—
249C2×C3⋊Dic3C2411yescharacteristic
250C2×C3⋊Dic3C2411yescharacteristic
251C2×C3⋊Dic3C2412yes—
252C2×C3⋊Dic3C2412yes—
253C2×C3⋊Dic3C2412yes—
254C2×C3⋊Dic3C2414yes—
255C2×C3⋊Dic3C2411yescharacteristic
256C2×C3⋊Dic3C2412yes—
257C4×C3⋊D3—24no—
258C4×C3⋊D3—22no—
259C4×C3⋊D3—22no—
260C4×C3⋊D3—22no—
261C4×C3⋊D3—24no—
262#634—24no—
263#634—22no—
264#634—28no—
265#634—24no—
266#634#4114yes—
267#557—91no—
268#557—91no—
269#557—92no—
270#556—92no—
271#556C3⋊D311yescharacteristic, complemented
272#552—94no—
273#552—92no—
274D4×Q8—92no—
275D4×Q8—91no—
276#541—94no—
277#541—92no—
278#533—91no—
279#533—92no—
280#529—92no—
281#529—91no—
282#519—92no—
283C2×C4×Q8—91no—
284C2×C3×Q8C22×D314yes—
285C2×C3×Q8C22×D318yes—
286C2×C3×D4C22×D314yes—
287C22×C3×C4C22×D318yes—
288C2×#67—38no—
289C22×Dic3—316no—
290D3×Q8—616no—
291C2×C4×D3—34no—
292C2×C4×D3—38no—
293C2×C4×D3—38no—
294C2×C4×D3—34no—
295C2×C4×D3—34no—
296C2×Dic6—34no—
297C2×Dic6—34no—
298C2×Dic6—316no—
299C2×Dic6—38no—
300C2×Dic6—38no—
301C2×Dic6—632no—
302C3×C4⋊C4C22×D314yes—
303C3×C4⋊C4C22×D318yes—
304C3×C4⋊C4C22×D318yes—
305C3×C4⋊C4C22×D314yes—
306C3×C4⋊C4C22×D3116yes—
307C3×C4⋊C4C22×D318yes—
308C3×C22⋊C4C22×D3116yes—
309C3×C22⋊C4C22×D318yes—
310C3×C22⋊C4C22×D3116yes—
311C3×C42C22×D314yes—
312C3×C42C22×D318yes—
313C3×C42C22×D3116yes—
314#217—38no—
315#217—38no—
316#217—38no—
317#217—316no—
318(C2×D3)⋊C4—38no—
319(C2×D3)⋊C4—316no—
320C4⋊Dic3—38no—
321C4⋊Dic3—38no—
322C4⋊Dic3—38no—
323C4⋊Dic3—34no—
324C4⋊Dic3—38no—
325C4⋊Dic3—34no—
326C4⋊Dic3—38no—
327C4⋊Dic3—316no—
328C4⋊Dic3—316no—
329Dic3⋊C4—38no—
330Dic3⋊C4—316no—
331Dic3⋊C4—38no—
332Dic3⋊C4—316no—
333Dic3⋊C4—316no—
334Dic3⋊C4—38no—
335Dic3⋊C4—316no—
336Dic3⋊C4—38no—
337Dic3⋊C4—38no—
338Dic3⋊C4—316no—
339Dic3⋊C4—316no—
340Dic3⋊C4—316no—
341C4×Dic3—38no—
342C4×Dic3—38no—
343C4×Dic3—34no—
344C4×Dic3—316no—
345C4×Dic3—316no—
346C4×Dic3—316no—
347C4×Dic3—38no—
348C4×Dic3—34no—
349C4×Dic3—38no—
350C4×Dic3—34no—
351C22×C32—22no—
352C22×C32—22no—
353C22×C32—22no—
354C22×C32C2511yescharacteristic
355C2×C3⋊D3—21no—
356C2×C3⋊D3—21no—
357C2×C3⋊D32−1+412yes—
358C32×C4—22no—
359C32×C4—22no—
360C32×C4—22no—
361C32×C4—21no—
362C32×C4—24no—
363C32×C4C2×#4112yes—
364C32×C42−1+412yes—
365C3⋊Dic3—21no—
366C3⋊Dic3—24no—
367C3⋊Dic3—22no—
368C3⋊Dic3—21no—
369C3⋊Dic3—21no—
370C3⋊Dic3—22no—
371C3⋊Dic3—22no—
372C3⋊Dic3C2×#4114yes—
373C22×Q8—91no—
374C22×Q8—92no—
375C4⋊Q8—92no—
376C4⋊Q8—92no—
377C4⋊Q8—92no—
378C4⋊Q8—94no—
379C4⋊Q8—91no—
380C4⋊Q8C2×C3⋊D311yescharacteristic
381#126—94no—
382#126—92no—
383#126—94no—
384#126—94no—
385#126C2×C3⋊D314yes—
386#125—91no—
387#125—94no—
388#125—92no—
389#125—94no—
390#125—94no—
391#125—94no—
392#125—92no—
393#125—92no—
394#125—94no—
395#124—91no—
396#124C2×C3⋊D312yes—
397#123—92no—
398#123—94no—
399C22⋊Q8—92no—
400C22⋊Q8—92no—
401C22⋊Q8—91no—
402C22⋊Q8—94no—
403C22⋊Q8—92no—
404C22⋊Q8—94no—
405C22⋊Q8—94no—
406C22⋊Q8C2×C3⋊D312yes—
407#121—91no—
408C4×Q8—91no—
409C4×Q8—92no—
410C4×Q8—92no—
411C4×Q8—91no—
412C4×Q8—92no—
413C4×Q8—92no—
414C4×Q8—92no—
415C4×Q8—92no—
416C4×Q8—91no—
417C4×Q8—92no—
418C4×Q8—94no—
419C4×Q8—94no—
420C4×Q8—91no—
421C4×Q8—92no—
422C4×Q8C2×C3⋊D311yescharacteristic
423C4×Q8C2×C3⋊D312yes—
424C4×D4—92no—
425C4×D4—92no—
426C4×D4—94no—
427C4×D4C2×C3⋊D311yescharacteristic
428#117—92no—
429#117—92no—
430#117—94no—
431#117—94no—
432#117—94no—
433#117C2×C3⋊D312yes—
434C2×C4⋊C4—92no—
435C2×C4⋊C4—91no—
436C2×C42—92no—
437C2×C42—91no—
438C23×C3C23×D318yes—
439C22×D3—34no—
440C3×Q8—28no—
441C3×Q8—216no—
442C3×D4—28no—
443C2×C3×C4—216no—
444C2×C3×C4C23×D318yes—
445C2×C3×C4C23×D3116yes—
446C2×C3×C4C23×D314yes—
447C2×C3×C4C23×D318yes—
448C2×C3×C4C23×D318yes—
449C2×C3×C4C23×D314yes—
450C2×C3×C4C23×D314yes—
451#67—616no—
452C2×Dic3—38no—
453C2×Dic3—34no—
454C2×Dic3—34no—
455C2×Dic3—38no—
456C2×Dic3—38no—
457C2×Dic3—38no—
458C2×Dic3—316no—
459C2×Dic3—34no—
460C2×Dic3—632no—
461C4×D3—616no—
462C4×D3—616no—
463C4×D3—68no—
464C4×D3—68no—
465C4×D3—68no—
466Dic6—316no—
467Dic6—632no—
468Dic6—616no—
469Dic6—616no—
470Dic6—68no—
471C2×C32—42no—
472C2×C32C22×#4111yescharacteristic
473C2×C32C2×2−1+411yescharacteristic
474C2×C32C2×2−1+411yescharacteristic
475C3⋊D3—22no—
476C2×Q8—91no—
477C2×Q8—91no—
478C2×Q8—92no—
479C2×Q8—94no—
480C2×Q8—92no—
481C2×Q8—188no—
482C2×Q8—184no—
483C2×Q8C22×C3⋊D312yes—
484C2×Q8C22×C3⋊D311yescharacteristic
485C2×D4—92no—
486C2×D4C22×C3⋊D311yescharacteristic
487C22×C4—94no—
488C22×C4—91no—
489C22×C4—91no—
490C22×C4—92no—
491C22×C4—92no—
492C22×C4—91no—
493C22×C4C22×C3⋊D312yes—
494C4⋊C4—92no—
495C4⋊C4—92no—
496C4⋊C4—91no—
497C4⋊C4—92no—
498C4⋊C4—92no—
499C4⋊C4—94no—
500C4⋊C4—94no—
501C4⋊C4—92no—
502C4⋊C4—94no—
503C4⋊C4—92no—
504C4⋊C4—94no—
505C4⋊C4—92no—
506C4⋊C4—94no—
507C4⋊C4—92no—
508C4⋊C4—94no—
509C4⋊C4—92no—
510C4⋊C4—91no—
511C4⋊C4—94no—
512C4⋊C4—94no—
513C4⋊C4—92no—
514C4⋊C4—94no—
515C4⋊C4C22×C3⋊D311yescharacteristic
516C4⋊C4C22×C3⋊D312yes—
517C4⋊C4C22×C3⋊D312yes—
518C4⋊C4C22×C3⋊D312yes—
519C4⋊C4C22×C3⋊D311yescharacteristic
520C4⋊C4C22×C3⋊D314yes—
521C22⋊C4—92no—
522C22⋊C4—92no—
523C22⋊C4—94no—
524C22⋊C4—92no—
525C22⋊C4—92no—
526C22⋊C4—94no—
527C22⋊C4C22×C3⋊D314yes—
528C22⋊C4C22×C3⋊D314yes—
529C22⋊C4C22×C3⋊D312yes—
530C42—92no—
531C42—91no—
532C42—92no—
533C42—91no—
534C42—92no—
535C42—91no—
536C42—94no—
537C42—94no—
538C42—94no—
539C42—92no—
540C42C22×C3⋊D311yescharacteristic
541C42C22×C3⋊D312yes—
542C42C22×C3⋊D314yes—
543C22×C3—28no—
544C22×C3—28no—
545C22×C3—28no—
546C22×C3C24×D314yes—
547C2×D3—38no—
548C2×D3—64no—
549C2×D3—64no—
550C3×C4—28no—
551C3×C4—28no—
552C3×C4—216no—
553C3×C4—28no—
554C3×C4—24no—
555C3×C4D3×#4118yes—
556C3×C4#101018yes—
557Dic3—316no—
558Dic3—64no—
559Dic3—616no—
560Dic3—68no—
561Dic3—64no—
562Dic3—64no—
563Dic3—68no—
564Dic3—68no—
565C32#352311yescharacteristic, complemented, Sylow
566C23—91no—
567C23C23×C3⋊D312yes—
568Q8—22no—
569Q8—24no—
570Q8—94no—
571Q8—188no—
572Q8—184no—
573Q8—184no—
574Q8—182no—
575D4—22no—
576D4—184no—
577C2×C4—24no—
578C2×C4—92no—
579C2×C4—91no—
580C2×C4—91no—
581C2×C4—92no—
582C2×C4—92no—
583C2×C4—92no—
584C2×C4—91no—
585C2×C4—94no—
586C2×C4—184no—
587C2×C4—184no—
588C2×C4—182no—
589C2×C4—188no—
590C2×C4—182no—
591C2×C4—182no—
592C2×C4C23×C3⋊D312yes—
593C2×C4C23×C3⋊D314yes—
594C2×C4C23×C3⋊D311yescharacteristic
595C2×C4C23×C3⋊D312yes—
596C2×C4C23×C3⋊D312yes—
597C2×C4C23×C3⋊D311yescharacteristic
598C2×C4C23×C3⋊D311yescharacteristic
599C2×C3—48no—
600C2×C3C2×D3×#4114yes—
601C2×C3C2×#101014yes—
602C2×C3D3×2−1+414yes—
603D3—68no—
604C22—22no—
605C22—22no—
606C22—22no—
607C22—92no—
608C22—181no—
609C22—181no—
610C22C24×C3⋊D311yescharacteristic
611C4—22no—
612C4—22no—
613C4—24no—
614C4—22no—
615C4—21no—
616C4—94no—
617C4—184no—
618C4—181no—
619C4—181no—
620C4—182no—
621C4—181no—
622C4—182no—
623C4—182no—
624C4#41×C3⋊D312yes—
625C4#6436712yes—
626C3#8699314yescomplemented
627C2—42no—
628C2—182no—
629C2C2×#41×C3⋊D311yescharacteristic
630C2C2×#6436711yescharacteristic
631C2C3⋊D3×2−1+411yescharacteristic
subgroupG/H
center, FrattiniC22C24×C3⋊D3
commutator, socle, cosocleC22×C32C25
FittingC32×#556C2
prime radical#64147C22
hypercenter#556C3⋊D3
hypocenterC32#3523
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ #556

Complements

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

NH ≅ G/Ntype
1. C32×#556C2semidirect
2. #10596199C2semidirect
3. #10596192C2semidirect
4. #10596179C2semidirect
5. #10596172C2semidirect
7. #10596142C2semidirect
8. #10596103C2semidirect
9. #10596096C2semidirect
10. #10596049C2semidirect
11. C4×Q8×C3⋊D3C2semidirect
12. #10596040C2semidirect
13. #10596038C2semidirect
15. D4×#634C2semidirect
16. #10596000C2semidirect
17. #10595987C2semidirect
84. C3×#556D3semidirect
271. #556C3⋊D3semidirect
565. C32#3523semidirect
626. C3#86993semidirect

Maximal subgroups

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

subgroupindex
C32×#5562
#105961992
#105961922
#105961792
#105961722
#105961512
#105961422
#105961032
#105960962
#105960492
C4×Q8×C3⋊D32
#105960402
#105960382
#105960282
D4×#6342
#105960002
#105959872
#869933