Finite Group Databasebeta

← #11901738

Subgroups — #11901738

Order 1152.

3120 conjugacy classes of subgroups.

The subgroup lattice has 609 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#10596054C212yesmaximal, complemented
5#10596053C212yesmaximal, complemented
6#10596035C214yesmaximal, complemented
7#10596033C212yesmaximal, complemented
8#10596032C212yesmaximal, complemented
9#10596031C214yesmaximal, complemented
10#10595999C214yesmaximal, complemented
11#10595995C211yesmaximal, characteristic, complemented
12#10595988C211yesmaximal, characteristic, complemented
13#10595950C214yesmaximal, complemented
14C4×#3828C211yesmaximal, characteristic, complemented
15C2×#64081C211yesmaximal, characteristic, complemented
16#85837—34nomaximal
17C2×C32×#41C2211yescharacteristic
18C2×#3828C2211yescharacteristic
19C22×C4×C3⋊D3C2211yescharacteristic
20C32×C4×Q8C2212yescomplemented
21C32×C4×D4C2214yes—
22C32×C4×D4C2212yescomplemented
23C32×#117C2211yescharacteristic
24C32×#117C2212yescomplemented
25C2×C32×C42C2211yescharacteristic
26C2×C32×C42C2212yescomplemented
27#64156C2211yescharacteristic, complemented
28#64155C2212yes—
29#64153C2211yescharacteristic, complemented
30#64149C2211yescharacteristic, complemented
31#64148C2214yes—
32#64147C2212yes—
33#64146C2212yes—
34#64145C2211yescharacteristic, complemented
35#64144C2212yes—
36#64139C2214yes—
37#64138C2214yes—
38#64138C2214yescomplemented
39C4×#638C2214yes—
40C4×#638C2214yes—
41C4×#638C2214yescomplemented
42C2×#3752C2212yes—
43#64135C2211yescharacteristic
44#64133C2214yescomplemented
45C2×#3750C2212yes—
46C2×C4×C3⋊Dic3C2211yescharacteristic
47#64107C2214yes—
48#64106C2212yes—
49#64105C2214yescomplemented
50#64104C2212yes—
51#64103C2214yes—
52#64099C2212yescomplemented
53#64098C2214yescomplemented
54#64097C2212yescomplemented
55#64095C2212yes—
56#64094C2214yes—
57#64093C2214yes—
58#64092C2214yescomplemented
59#64091C2212yes—
60#64088C2214yescomplemented
61#64087C2214yes—
62#64085C2214yes—
63#64085C2214yescomplemented
64#64084C2214yes—
65C4×C4⋊(C3⋊D3)C2214yes—
66C4×C4⋊(C3⋊D3)C2212yescomplemented
67#64081C2212yes—
68#64081C2212yes—
69#64081C2212yes—
70#64081C2212yes—
71#64081C2212yescomplemented
72C42×C3⋊D3C2212yescomplemented
73#64079C2214yescomplemented
74C4×#634C2212yescomplemented
75C4×#634C2214yescomplemented
76C3×C4×#41D314yescomplemented
77#5832—34no—
78#5828—34no—
79#5583—38no—
80#5582—38no—
81#5564—316no—
82#5562—38no—
83#5561—38no—
84#5560—316no—
85#5528—316no—
86#5524—34no—
87#5517—34no—
88#5479—316no—
89C4×#235—34no—
90C2×#872—34no—
91C23×C3⋊D3C2311yescharacteristic
92C32×#41—24no—
93C2×C32×Q8C2311yescharacteristic
94C2×C32×D4C2312yes—
95C2×C32×D4C2311yescharacteristic
96C22×C32×C4C2312yes—
97C22×C32×C4C2312yes—
98C22×C32×C4C2314yes—
99C22×C32×C4C2311yescharacteristic
100C2×#638C2312yes—
101C2×#638C2314yes—
102C2×#638C2314yes—
103C22×C3⋊Dic3C2311yescharacteristic
104C22×C3⋊Dic3C2312yes—
105#3828—24no—
106C2×C4⋊(C3⋊D3)C2311yescharacteristic
107C2×C4⋊(C3⋊D3)C2314yes—
108C2×C4×C3⋊D3—24no—
109C2×C4×C3⋊D3C2312yes—
110C2×C4×C3⋊D3C2312yes—
111C2×C4×C3⋊D3C2312yes—
112C2×C4×C3⋊D3C2314yes—
113C2×#634C2311yescharacteristic
114C2×#634C2314yes—
115C32×C4⋊C4C2312yes—
116C32×C4⋊C4C2314yes—
117C32×C22⋊C4C2312yes—
118C32×C22⋊C4C2314yes—
119C32×C42C2312yes—
120C32×C42C2312yes—
121C32×C42C2314yes—
122C32×C42C2311yescharacteristic
123C32×C42C2311yescharacteristic
124#3757C2312yes—
125#3757C2314yes—
126#3757C2314yes—
127#3752C2312yes—
128#3752C2312yes—
129#3752C2312yes—
130#3752C2312yes—
131#3752C2314yes—
132#3752C2314yes—
133#3752C2314yes—
134#3752C2314yes—
135#3752C2314yes—
136C4⋊(C3⋊Dic3)C2314yes—
137C4⋊(C3⋊Dic3)C2312yes—
138C4⋊(C3⋊Dic3)C2314yes—
139#3750C2314yes—
140#3750C2314yes—
141#3750C2314yes—
142#3750C2312yes—
143#3750C2314yes—
144#3750C2314yes—
145#3750C2312yes—
146#3750C2312yes—
147#3750C2312yes—
148C4×C3⋊Dic3C2312yes—
149C4×C3⋊Dic3C2312yes—
150C4×C3⋊Dic3C2314yes—
151C4×C3⋊Dic3C2311yescharacteristic
152C4×C3⋊Dic3C2311yescharacteristic
153#3455—91noSylow
154C2×C3×#41C2×D314yes—
155C2×#235—34no—
156C22×C4×D3—34no—
157C3×C4×Q8C2×D318yescomplemented
158C3×C4×D4C2×D3116yes—
159C3×C4×D4C2×D318yescomplemented
160C3×#117C2×D314yes—
161C3×#117C2×D318yescomplemented
162C2×C3×C42C2×D314yes—
163C2×C3×C42C2×D318yescomplemented
164#947—34no—
165#946—38no—
166#944—34no—
167#940—34no—
168#939—316no—
169#938—38no—
170#937—38no—
171#936—34no—
172#935—38no—
173#930—316no—
174#929—316no—
175#929—316no—
176C4×#67—316no—
177C4×#67—316no—
178C4×#67—316no—
179C2×(C2×D3)⋊C4—38no—
180#926—34no—
181#924—316no—
182C2×Dic3⋊C4—38no—
183C2×C4×Dic3—34no—
184#898—316no—
185#897—38no—
186#896—316no—
187#895—38no—
188#894—316no—
189#890—38no—
190#889—316no—
191#888—38no—
192#886—38no—
193#885—316no—
194#884—316no—
195#883—316no—
196#882—38no—
197#879—316no—
198#878—316no—
199#876—316no—
200#876—316no—
201#875—316no—
202C4×D12—316no—
203C4×D12—38no—
204#872—38no—
205#872—38no—
206#872—38no—
207#872—38no—
208#872—38no—
209C42×D3—38no—
210#870—316no—
211C4×Dic6—38no—
212C4×Dic6—316no—
213C23×C32C2412yes—
214C23×C32C2411yescharacteristic
215C22×C3⋊D3—22no—
216C22×C3⋊D3—42no—
217C22×C3⋊D3C2412yes—
218C22×C3⋊D3C2412yes—
219C32×Q8—22no—
220C32×D4—24no—
221C32×D4—22no—
222C2×C32×C4—24no—
223C2×C32×C4—44no—
224C2×C32×C4—42no—
225C2×C32×C4#4114yes—
226C2×C32×C4C2412yes—
227C2×C32×C4C2412yes—
228C2×C32×C4C2412yes—
229C2×C32×C4C2414yes—
230C2×C32×C4C2411yescharacteristic
231C2×C32×C4C2411yescharacteristic
232#638—24no—
233#638—44no—
234#638—44no—
235C2×C3⋊Dic3—22no—
236C2×C3⋊Dic3—42no—
237C2×C3⋊Dic3C2412yes—
238C2×C3⋊Dic3C2412yes—
239C2×C3⋊Dic3C2414yes—
240C2×C3⋊Dic3C2412yes—
241C2×C3⋊Dic3C2412yes—
242C4⋊(C3⋊D3)—22no—
243C4⋊(C3⋊D3)—44no—
244C4×C3⋊D3—24no—
245C4×C3⋊D3—24no—
246C4×C3⋊D3—24no—
247C4×C3⋊D3—44no—
248#634—22no—
249#634—44no—
250#542—92no—
251#542—92no—
252#541—92no—
253#540—92no—
254#539—94no—
255#538—94no—
256#533—91no—
257#532—91no—
258#529—94no—
259#529—94no—
260#525—91no—
261#525—91no—
262C4×#41—91no—
263C4×#41C3⋊D311yescharacteristic, complemented
264C2×#117—91no—
265C23×D3—34no—
266C3×#41—216no—
267C2×C3×Q8C22×D314yes—
268C2×C3×D4C22×D318yes—
269C2×C3×D4C22×D314yes—
270C22×C3×C4C22×D318yes—
271C22×C3×C4C22×D318yes—
272C22×C3×C4C22×D3116yes—
273C22×C3×C4C22×D314yes—
274C2×#67—38no—
275C2×#67—316no—
276C2×#67—316no—
277C22×Dic3—34no—
278C22×Dic3—38no—
279#235—616no—
280C2×D12—34no—
281C2×D12—316no—
282C2×C4×D3—38no—
283C2×C4×D3—38no—
284C2×C4×D3—38no—
285C2×C4×D3—316no—
286C2×C4×D3—616no—
287C2×Dic6—34no—
288C2×Dic6—316no—
289C3×C4⋊C4C22×D318yes—
290C3×C4⋊C4C22×D3116yes—
291C3×C22⋊C4C22×D318yes—
292C3×C22⋊C4C22×D3116yes—
293C3×C42C22×D318yes—
294C3×C42C22×D318yes—
295C3×C42C22×D3116yes—
296C3×C42C22×D314yes—
297C3×C42C22×D314yes—
298#217—38no—
299#217—316no—
300#217—316no—
301(C2×D3)⋊C4—38no—
302(C2×D3)⋊C4—38no—
303(C2×D3)⋊C4—38no—
304(C2×D3)⋊C4—38no—
305(C2×D3)⋊C4—316no—
306(C2×D3)⋊C4—316no—
307(C2×D3)⋊C4—316no—
308(C2×D3)⋊C4—316no—
309(C2×D3)⋊C4—316no—
310C4⋊Dic3—316no—
311C4⋊Dic3—38no—
312C4⋊Dic3—316no—
313Dic3⋊C4—316no—
314Dic3⋊C4—316no—
315Dic3⋊C4—316no—
316Dic3⋊C4—38no—
317Dic3⋊C4—316no—
318Dic3⋊C4—316no—
319Dic3⋊C4—38no—
320Dic3⋊C4—38no—
321Dic3⋊C4—38no—
322C4×Dic3—38no—
323C4×Dic3—38no—
324C4×Dic3—316no—
325C4×Dic3—34no—
326C4×Dic3—34no—
327C22×C32—22no—
328C22×C32—22no—
329C22×C32—24no—
330C22×C32C2×#4112yes—
331C22×C32C2511yescharacteristic
332C2×C3⋊D3—22no—
333C2×C3⋊D3—22no—
334C2×C3⋊D3—24no—
335C2×C3⋊D3—22no—
336C2×C3⋊D3—22no—
337C2×C3⋊D3—44no—
338C32×C4—22no—
339C32×C4—24no—
340C32×C4—22no—
341C32×C4—22no—
342C32×C4C2×#4112yes—
343C32×C4C2×#4112yes—
344C3⋊Dic3—22no—
345C3⋊Dic3—22no—
346C3⋊Dic3—22no—
347C3⋊Dic3—24no—
348C3⋊Dic3—22no—
349C2×#41—91no—
350C2×#41C2×C3⋊D311yescharacteristic
351C23×C4—91no—
352C4⋊Q8—91no—
353C4⋊Q8—92no—
354#127—91no—
355#126—94no—
356#126—94no—
357#126—94no—
358#126—94no—
359#125—94no—
360#125—92no—
361#125—94no—
362#124—91no—
363#124—91no—
364#124—94no—
365#124—94no—
366#123—92no—
367#123—94no—
368#123—94no—
369#123—94no—
370#123—92no—
371#123—94no—
372C22⋊Q8—92no—
373C22⋊Q8—94no—
374C22⋊Q8—92no—
375C22⋊Q8—94no—
376C22⋊Q8—94no—
377#121—92no—
378#121—94no—
379#121—94no—
380#121—92no—
381#121—94no—
382#120—92no—
383#120—92no—
384C4×Q8—92no—
385C4×Q8—94no—
386C4×Q8C2×C3⋊D312yescomplemented
387C4×D4—94no—
388C4×D4—94no—
389C4×D4—94no—
390C4×D4—92no—
391C4×D4—94no—
392C4×D4C2×C3⋊D314yes—
393C4×D4C2×C3⋊D312yescomplemented
394#117—91no—
395#117—92no—
396#117—92no—
397#117—92no—
398#117—92no—
399#117—92no—
400#117C2×C3⋊D311yescharacteristic
401#117C2×C3⋊D312yescomplemented
402C2×C4⋊C4—92no—
403C2×C22⋊C4—92no—
404C2×C42—91no—
405C2×C42—92no—
406C2×C42C2×C3⋊D311yescharacteristic
407C2×C42C2×C3⋊D312yescomplemented
408C23×C3C23×D318yes—
409C23×C3C23×D314yes—
410C22×D3—38no—
411C22×D3—38no—
412C22×D3—68no—
413C22×D3—128no—
414C3×Q8—28no—
415C3×D4—216no—
416C3×D4—28no—
417C2×C3×C4—216no—
418C2×C3×C4—416no—
419C2×C3×C4—48no—
420C2×C3×C4#235116yes—
421C2×C3×C4C23×D318yes—
422C2×C3×C4C23×D318yes—
423C2×C3×C4C23×D318yes—
424C2×C3×C4C23×D3116yes—
425C2×C3×C4C23×D314yes—
426C2×C3×C4C23×D314yes—
427#67—616no—
428#67—1216no—
429#67—1216no—
430C2×Dic3—38no—
431C2×Dic3—38no—
432C2×Dic3—316no—
433C2×Dic3—38no—
434C2×Dic3—38no—
435C2×Dic3—68no—
436C2×Dic3—128no—
437D12—68no—
438D12—1216no—
439C4×D3—616no—
440C4×D3—616no—
441C4×D3—616no—
442C4×D3—1216no—
443Dic6—68no—
444Dic6—1216no—
445C2×C32—22no—
446C2×C32—42no—
447C2×C32C22×#4111yescharacteristic
448C2×C32#58512yes—
449C3⋊D3—42no—
450C3⋊D3—42no—
451C24—91no—
452#41—24no—
453#41—184no—
454C2×Q8—91no—
455C2×Q8—94no—
456C2×Q8C22×C3⋊D311yescharacteristic
457C2×D4—92no—
458C2×D4—94no—
459C2×D4—94no—
460C2×D4—91no—
461C2×D4—94no—
462C2×D4C22×C3⋊D312yes—
463C2×D4C22×C3⋊D311yescharacteristic
464C22×C4—91no—
465C22×C4—92no—
466C22×C4—92no—
467C22×C4—92no—
468C22×C4—92no—
469C22×C4—94no—
470C22×C4—184no—
471C22×C4C22×C3⋊D312yes—
472C22×C4C22×C3⋊D312yes—
473C22×C4C22×C3⋊D314yes—
474C22×C4C22×C3⋊D311yescharacteristic
475C4⋊C4—92no—
476C4⋊C4—92no—
477C4⋊C4—92no—
478C4⋊C4—92no—
479C4⋊C4—92no—
480C4⋊C4—94no—
481C4⋊C4—94no—
482C4⋊C4—94no—
483C4⋊C4—94no—
484C4⋊C4—94no—
485C4⋊C4—94no—
486C4⋊C4—94no—
487C4⋊C4C22×C3⋊D312yes—
488C4⋊C4C22×C3⋊D314yes—
489C22⋊C4—92no—
490C22⋊C4—94no—
491C22⋊C4—94no—
492C22⋊C4—92no—
493C22⋊C4—92no—
494C22⋊C4—92no—
495C22⋊C4—92no—
496C22⋊C4—94no—
497C22⋊C4—94no—
498C22⋊C4—94no—
499C22⋊C4—94no—
500C22⋊C4—94no—
501C22⋊C4C22×C3⋊D312yes—
502C22⋊C4C22×C3⋊D314yes—
503C42—91no—
504C42—91no—
505C42—94no—
506C42—92no—
507C42—92no—
508C42C22×C3⋊D312yes—
509C42C22×C3⋊D314yes—
510C42C22×C3⋊D311yescharacteristic
511C42C22×C3⋊D311yescharacteristic
512C42C22×C3⋊D312yes—
513C22×C3—28no—
514C22×C3—28no—
515C22×C3—216no—
516C22×C3C2×#23518yes—
517C22×C3C24×D314yes—
518C2×D3—68no—
519C2×D3—68no—
520C2×D3—616no—
521C2×D3—68no—
522C2×D3—68no—
523C2×D3—1216no—
524C3×C4—28no—
525C3×C4—216no—
526C3×C4—28no—
527C3×C4—28no—
528C3×C4C2×#23518yes—
529C3×C4C2×#23518yes—
530Dic3—68no—
531Dic3—68no—
532Dic3—68no—
533Dic3—616no—
534Dic3—68no—
535C32#345511yescharacteristic, complemented, Sylow
536C23—92no—
537C23—92no—
538C23—182no—
539C23—362no—
540C23C23×C3⋊D312yes—
541C23C23×C3⋊D311yescharacteristic
542Q8—22no—
543Q8—182no—
544Q8—364no—
545D4—24no—
546D4—22no—
547D4—184no—
548D4—182no—
549D4—364no—
550D4—364no—
551D4—364no—
552C2×C4—24no—
553C2×C4—42no—
554C2×C4—44no—
555C2×C4—92no—
556C2×C4—92no—
557C2×C4—94no—
558C2×C4—92no—
559C2×C4—92no—
560C2×C4—182no—
561C2×C4—184no—
562C2×C4—184no—
563C2×C4—184no—
564C2×C4—364no—
565C2×C4—362no—
566C2×C4#382814yes—
567C2×C4C23×C3⋊D312yes—
568C2×C4C23×C3⋊D312yes—
569C2×C4C23×C3⋊D312yes—
570C2×C4C23×C3⋊D314yes—
571C2×C4C23×C3⋊D311yescharacteristic
572C2×C4C23×C3⋊D311yescharacteristic
573C2×C3—28no—
574C2×C3—48no—
575C2×C3C22×#23514yes—
576C2×C3#596418yes—
577D3—128no—
578D3—128no—
579C22—22no—
580C22—22no—
581C22—24no—
582C22—182no—
583C22—182no—
584C22—184no—
585C22—182no—
586C22—182no—
587C22—364no—
588C22C2×#382812yes—
589C22C24×C3⋊D311yescharacteristic
590C4—22no—
591C4—22no—
592C4—22no—
593C4—24no—
594C4—182no—
595C4—182no—
596C4—182no—
597C4—184no—
598C4—182no—
599C4C2×#382812yes—
600C4C2×#382812yes—
601C3#8583714yescomplemented
602C2—22no—
603C2—42no—
604C2—362no—
605C2—362no—
606C2C22×#382811yescharacteristic
607C2#1059675612yes—
subgroupG/H
centerC2×C4C23×C3⋊D3
commutator, socle, cosocleC22×C32C25
FrattiniC22C24×C3⋊D3
FittingC32×C4×#41C2
hypercenterC4×#41C3⋊D3
hypocenterC32#3455
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ 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. #10596054C2semidirect
5. #10596053C2semidirect
6. #10596035C2semidirect
7. #10596033C2semidirect
8. #10596032C2semidirect
9. #10596031C2semidirect
10. #10595999C2semidirect
11. #10595995C2semidirect
12. #10595988C2semidirect
13. #10595950C2semidirect
14. C4×#3828C2semidirect
15. C2×#64081C2semidirect
20. C32×C4×Q8C22semidirect
22. C32×C4×D4C22semidirect
24. C32×#117C22semidirect
26. C2×C32×C42C22semidirect
27. #64156C22semidirect
29. #64153C22semidirect
30. #64149C22semidirect
34. #64145C22semidirect
38. #64138C22semidirect
41. C4×#638C22semidirect
44. #64133C22semidirect
49. #64105C22semidirect
52. #64099C22semidirect
53. #64098C22semidirect
54. #64097C22semidirect
58. #64092C22semidirect
60. #64088C22semidirect
63. #64085C22semidirect
66. C4×C4⋊(C3⋊D3)C22semidirect
71. #64081C22semidirect
72. C42×C3⋊D3C22semidirect
73. #64079C22semidirect
74. C4×#634C22semidirect
75. C4×#634C22semidirect
76. C3×C4×#41D3semidirect
157. C3×C4×Q8C2×D3semidirect
159. C3×C4×D4C2×D3semidirect
161. C3×#117C2×D3semidirect
163. C2×C3×C42C2×D3semidirect
263. C4×#41C3⋊D3semidirect
386. C4×Q8C2×C3⋊D3semidirect
393. C4×D4C2×C3⋊D3semidirect
401. #117C2×C3⋊D3semidirect
407. C2×C42C2×C3⋊D3semidirect
535. C32#3455semidirect
601. C3#85837semidirect

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
#105960542
#105960532
#105960352
#105960332
#105960322
#105960312
#105959992
#105959952
#105959882
#105959502
C4×#38282
C2×#640812
#858373