Finite Group Databasebeta

← #11884830

Subgroups — #11884830

Order 1152.

1464 conjugacy classes of subgroups.

The subgroup lattice has 624 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C32×#550C211yesmaximal, characteristic, complemented
2C2×#64160C211yesmaximal, characteristic, complemented
3C2×#64159C211yesmaximal, characteristic, complemented
4#10596023C211yesmaximal, characteristic, complemented
5#10592938C211yesmaximal, characteristic, complemented
6#10592937C211yesmaximal, characteristic, complemented
7#10592774C211yesmaximal, characteristic, complemented
8#10592773C211yesmaximal, characteristic, complemented
9#10592740C211yesmaximal, characteristic, complemented
10#10592739C211yesmaximal, characteristic, complemented
11#10592738C211yesmaximal, characteristic, complemented
12#10592736C211yesmaximal, characteristic, complemented
13#10592729C211yesmaximal, characteristic, complemented
14#10592727C211yesmaximal, characteristic, complemented
15#10592710C211yesmaximal, characteristic, complemented
16#83583—34nomaximal
17C2×C32×#41C2211yescharacteristic
18C2×C32×#41C2211yescharacteristic
19C2×#3828C2211yescharacteristic
20C22×#634C2211yescharacteristic
21C32×#127—21no—
22C32×#127C2211yescharacteristic
23C32×#121—21no—
24C32×#121—21no—
25C32×#121C2211yescharacteristic
26C32×#121C2211yescharacteristic
27C32×C4×Q8C2211yescharacteristic
28C32×C4×D4—21no—
29C32×C4×D4C2211yescharacteristic
30#64160—24no—
31#64159—24no—
32C2×#3756C2211yescharacteristic
33C2×#3756C2211yescharacteristic
34C2×#3755C2211yescharacteristic
35#64148—21no—
36C2×#3754C2211yescharacteristic
37C2×#3754C2211yescharacteristic
38C2×#3754C2211yescharacteristic
39C2×#3754C2211yescharacteristic
40C2×#3753C2211yescharacteristic
41C2×#3753C2211yescharacteristic
42#64139C2211yescharacteristic
43#64133C2211yescharacteristic
44C2×#3748C2211yescharacteristic
45C22×C3⋊(C3⋊C8)C2211yescharacteristic
46#64105—21no—
47#64094—21no—
48#64090—21no—
49#64084C2211yescharacteristic
50C4×#634C2211yescharacteristic
51#63662C2211yescharacteristic
52#63659C2211yescharacteristic
53#63659C2211yescharacteristic
54#63657C2211yescharacteristic
55#63657C2211yescharacteristic
56#63637C2211yescharacteristic
57#63637C2211yescharacteristic
58#63636C2211yescharacteristic
59#63635C2211yescharacteristic
60C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
61#63630C2211yescharacteristic
62C3×#550D314yescomplemented
63C2×#951—34no—
64C2×#950—34no—
65#5552—34no—
66#5239—34no—
67#5238—34no—
68#5075—34no—
69#5074—34no—
70#5041—34no—
71#5040—34no—
72#5039—34no—
73#5037—34no—
74#5030—34no—
75#5028—34no—
76#5011—34no—
77C32×#41—22no—
78C32×#41—22no—
79C32×#41—41no—
80C32×#41—41no—
81C2×C32×Q8C2311yescharacteristic
82C2×C32×D4—21no—
83C2×C32×D4—21no—
84C2×C32×D4—21no—
85C2×C32×D4—21no—
86C2×C32×D4—21no—
87C2×C32×D4—21no—
88C2×C32×D4D411yescharacteristic
89C2×C32×D4C2311yescharacteristic
90C2×C32×D4C2311yescharacteristic
91C22×C32×C4—21no—
92C22×C32×C4—21no—
93C22×C32×C4C2311yescharacteristic
94C22×C32×C4C2311yescharacteristic
95C2×#638—21no—
96C2×#638—21no—
97C22×C3⋊Dic3—21no—
98#3828—22no—
99#3828—41no—
100C2×C4⋊(C3⋊D3)C2311yescharacteristic
101C2×C4×C3⋊D3—21no—
102C2×#634—22no—
103C2×#634—21no—
104C2×#634—41no—
105C2×#634C2311yescharacteristic
106C2×#634C2311yescharacteristic
107C32×C4⋊C4—21no—
108C32×C4⋊C4D411yescharacteristic
109C32×C4⋊C4C2311yescharacteristic
110C32×C22⋊C4—21no—
111C32×C22⋊C4—21no—
112C32×C22⋊C4D411yescharacteristic
113C32×C22⋊C4D411yescharacteristic
114C32×C42—21no—
115C32×C42C2311yescharacteristic
116#3757—21no—
117#3756—22no—
118#3756D414yescomplemented
119#3755—22no—
120#3754—22no—
121#3754—22no—
122#3754—22no—
123#3754—41no—
124#3753—22no—
125#3753—41no—
126#3752—21no—
127#3752—21no—
128#3752—21no—
129C4⋊(C3⋊Dic3)C2311yescharacteristic
130#3750—21no—
131#3750—21no—
132C4×C3⋊Dic3—21no—
133#3748—22no—
134C2×C3⋊(C3⋊C8)—22no—
135C2×C3⋊(C3⋊C8)C2311yescharacteristic
136C2×C3⋊(C3⋊C8)C2311yescharacteristic
137C2×C3⋊(C3⋊C8)C2311yescharacteristic
138C2×C3⋊(C3⋊C8)C2311yescharacteristic
139#3271—91noSylow
140C2×C3×#41C2×D314yes—
141C2×C3×#41C2×D314yes—
142C2×#235—34no—
143C22×Dic6—34no—
144C3×#127—24no—
145C3×#127C2×D314yes—
146C3×#121—24no—
147C3×#121—24no—
148C3×#121C2×D314yes—
149C3×#121C2×D314yes—
150C3×C4×Q8C2×D314yes—
151C3×C4×D4—24no—
152C3×C4×D4C2×D314yes—
153#951—616no—
154#950—616no—
155C2×#216—34no—
156C2×#216—34no—
157C2×#215—34no—
158#939—64no—
159C2×#214—34no—
160C2×#214—34no—
161C2×#214—34no—
162C2×#214—34no—
163C2×#213—34no—
164C2×#213—34no—
165#930—34no—
166#924—34no—
167C2×#208—34no—
168C22×C3⋊C8—34no—
169#896—64no—
170#885—64no—
171#67⋊C4—64no—
172#875—34no—
173C4×Dic6—34no—
174#835—34no—
175#832—34no—
176#832—34no—
177#830—34no—
178#830—34no—
179#810—34no—
180#810—34no—
181#809—34no—
182#808—34no—
183C4⋊(C3⋊C8)—34no—
184#803—34no—
185C23×C32—21no—
186C23×C32—21no—
187C23×C32C2×D411yescharacteristic
188C23×C32C2×D411yescharacteristic
189C22×C3⋊D3—21no—
190C32×Q8—21no—
191C32×Q8C2×D412yes—
192C32×D4—21no—
193C32×D4—21no—
194C32×D4—21no—
195C32×D4—21no—
196C32×D4—41no—
197C32×D4—42no—
198C32×D4—42no—
199C32×D4—42no—
200C32×D4—81no—
201C32×D4—81no—
202C32×D4—81no—
203C2×C32×C4—21no—
204C2×C32×C4—21no—
205C2×C32×C4—21no—
206C2×C32×C4—21no—
207C2×C32×C4—21no—
208C2×C32×C4—21no—
209C2×C32×C4—42no—
210C2×C32×C4—42no—
211C2×C32×C4C2×D411yescharacteristic
212C2×C32×C4C2×D411yescharacteristic
213C2×C32×C4C2×D411yescharacteristic
214C2×C32×C4C2×D411yescharacteristic
215C2×C32×C4C2411yescharacteristic
216#638—42no—
217#638—42no—
218C2×C3⋊Dic3—21no—
219C2×C3⋊Dic3—21no—
220C2×C3⋊Dic3—21no—
221C2×C3⋊Dic3—42no—
222C4⋊(C3⋊D3)—21no—
223C4⋊(C3⋊D3)—21no—
224C4×C3⋊D3—42no—
225#634—21no—
226#634—21no—
227#634—21no—
228#634—42no—
229#634C2×D412yes—
230C3⋊(C3⋊C8)—21no—
231C3⋊(C3⋊C8)—21no—
232C3⋊(C3⋊C8)—21no—
233C3⋊(C3⋊C8)C2×D412yes—
234C2×#137—91no—
235C2×#135—91no—
236#550C3⋊D311yescharacteristic, complemented
237#548—91no—
238#496—91no—
239#469—91no—
240#465—91no—
241#464—91no—
242#460—91no—
243#452—91no—
244#449—91no—
245#449—91no—
246#448—91no—
247#441—91no—
248#435—91no—
249C3×#41—28no—
250C3×#41—28no—
251C3×#41—44no—
252C3×#41—44no—
253C2×C3×Q8C22×D314yes—
254C2×C3×D4—24no—
255C2×C3×D4—24no—
256C2×C3×D4—24no—
257C2×C3×D4—24no—
258C2×C3×D4—24no—
259C2×C3×D4—24no—
260C2×C3×D4#6714yes—
261C2×C3×D4C22×D314yes—
262C2×C3×D4C22×D314yes—
263C22×C3×C4—24no—
264C22×C3×C4—24no—
265C22×C3×C4C22×D314yes—
266C22×C3×C4C22×D314yes—
267C2×#67—64no—
268C2×#67—64no—
269C22×Dic3—64no—
270#235—68no—
271#235—124no—
272C2×D12—34no—
273C2×C4×D3—64no—
274C2×Dic6—34no—
275C2×Dic6—34no—
276C2×Dic6—68no—
277C2×Dic6—64no—
278C2×Dic6—124no—
279C3×C4⋊C4—24no—
280C3×C4⋊C4#6714yes—
281C3×C4⋊C4C22×D314yes—
282C3×C22⋊C4—24no—
283C3×C22⋊C4—24no—
284C3×C22⋊C4#6714yes—
285C3×C22⋊C4#6714yes—
286C3×C42—24no—
287C3×C42C22×D314yes—
288#217—64no—
289#216—316no—
290#216—68no—
291#215—68no—
292#214—68no—
293#214—68no—
294#214—68no—
295#214—124no—
296#213—68no—
297#213—124no—
298(C2×D3)⋊C4—64no—
299(C2×D3)⋊C4—64no—
300(C2×D3)⋊C4—64no—
301C4⋊Dic3—34no—
302Dic3⋊C4—64no—
303Dic3⋊C4—64no—
304C4×Dic3—64no—
305#208—68no—
306C2×C3⋊C8—34no—
307C2×C3⋊C8—34no—
308C2×C3⋊C8—34no—
309C2×C3⋊C8—34no—
310C2×C3⋊C8—68no—
311C22×C32—21no—
312C22×C32—21no—
313C22×C32—21no—
314C22×C32—21no—
315C22×C32—21no—
316C22×C32—21no—
317C22×C32—41no—
318C22×C32—41no—
319C22×C32—41no—
320C22×C32—41no—
321C22×C32—41no—
322C22×C32—41no—
323C22×C32C22×D411yescharacteristic
324C2×C3⋊D3—41no—
325C2×C3⋊D3—41no—
326C2×C3⋊D3—41no—
327C32×C4—21no—
328C32×C4—21no—
329C32×C4—22no—
330C32×C4—21no—
331C32×C4—21no—
332C32×C4—41no—
333C32×C4C22×D411yescharacteristic
334C32×C4H(5,𝔽2)11yescharacteristic
335C3⋊Dic3—22no—
336C3⋊Dic3—41no—
337C3⋊Dic3—41no—
338C2×#41—91no—
339C2×#41C2×C3⋊D311yescharacteristic
340C2×#41C2×C3⋊D311yescharacteristic
341C22×Q8—91no—
342#137—184no—
343#135—184no—
344C2×Q16—91no—
345C2×Q16—91no—
346C2×SD16—91no—
347C2×SD16—91no—
348C2×SD16—91no—
349C2×SD16—91no—
350C2×SD16—91no—
351C2×D8—91no—
352C2×D8—91no—
353C2×M16—91no—
354C22×C8—91no—
355#127—21no—
356#127C2×C3⋊D311yescharacteristic
357#124—91no—
358#124—181no—
359C22⋊Q8—91no—
360C22⋊Q8—181no—
361#121—21no—
362#121—21no—
363#121—91no—
364#121—181no—
365#121C2×C3⋊D311yescharacteristic
366#121C2×C3⋊D311yescharacteristic
367C4×Q8—91no—
368C4×Q8C2×C3⋊D311yescharacteristic
369C4×D4—21no—
370C4×D4—181no—
371C4×D4C2×C3⋊D311yescharacteristic
372#106—91no—
373C4⋊C8—91no—
374#103—91no—
375#103—91no—
376#103—91no—
377#102—91no—
378#102—91no—
379#102—91no—
380C22⋊C8—91no—
381C22⋊C8—91no—
382#97—91no—
383C23×C3—24no—
384C23×C3—24no—
385C23×C3C2×#6714yes—
386C23×C3C2×#6714yes—
387C22×D3—64no—
388C3×Q8—24no—
389C3×Q8D3×D418yes—
390C3×D4—24no—
391C3×D4—24no—
392C3×D4—24no—
393C3×D4—24no—
394C3×D4—44no—
395C3×D4—48no—
396C3×D4—48no—
397C3×D4—48no—
398C3×D4—84no—
399C3×D4—84no—
400C3×D4—84no—
401C2×C3×C4—24no—
402C2×C3×C4—24no—
403C2×C3×C4—24no—
404C2×C3×C4—24no—
405C2×C3×C4—24no—
406C2×C3×C4—24no—
407C2×C3×C4—48no—
408C2×C3×C4—48no—
409C2×C3×C4C2×#6714yes—
410C2×C3×C4C2×#6714yes—
411C2×C3×C4C2×#6714yes—
412C2×C3×C4C2×#6714yes—
413C2×C3×C4C23×D314yes—
414#67—128no—
415#67—128no—
416C2×Dic3—64no—
417C2×Dic3—64no—
418C2×Dic3—64no—
419C2×Dic3—128no—
420D12—64no—
421D12—64no—
422C4×D3—128no—
423Dic6—38no—
424Dic6—64no—
425Dic6—64no—
426Dic6—64no—
427Dic6—128no—
428C3⋊C8—38no—
429C3⋊C8—64no—
430C3⋊C8—64no—
431C3⋊C8—64no—
432C2×C32—41no—
433C2×C32—41no—
434C2×C32—81no—
435C2×C32—81no—
436C2×C32D4211yescharacteristic
437C2×C32#57511yescharacteristic
438C2×C32#57711yescharacteristic
439C3⋊D3—81no—
440#41—22no—
441#41—22no—
442#41—41no—
443#41—41no—
444#41—182no—
445#41—361no—
446C2×Q8—91no—
447C2×Q8—91no—
448C2×Q8—182no—
449C2×Q8—181no—
450C2×Q8—361no—
451C2×Q8C22×C3⋊D311yescharacteristic
452C2×D4—21no—
453C2×D4—21no—
454C2×D4—21no—
455C2×D4—21no—
456C2×D4—21no—
457C2×D4—21no—
458C2×D4—91no—
459C2×D4—181no—
460C2×D4—181no—
461C2×D4#63811yescharacteristic
462C2×D4C22×C3⋊D311yescharacteristic
463C2×D4C22×C3⋊D311yescharacteristic
464C22×C4—21no—
465C22×C4—21no—
466C22×C4—181no—
467C22×C4—181no—
468C22×C4C22×C3⋊D311yescharacteristic
469C22×C4C22×C3⋊D311yescharacteristic
470Q16—94no—
471Q16—182no—
472SD16—182no—
473SD16—182no—
474SD16—182no—
475SD16—182no—
476SD16—361no—
477D8—182no—
478D8—361no—
479M16—182no—
480C2×C8—91no—
481C2×C8—91no—
482C2×C8—91no—
483C2×C8—91no—
484C2×C8—182no—
485C4⋊C4—21no—
486C4⋊C4—91no—
487C4⋊C4—181no—
488C4⋊C4—181no—
489C4⋊C4#63811yescharacteristic
490C4⋊C4C22×C3⋊D311yescharacteristic
491C22⋊C4—21no—
492C22⋊C4—21no—
493C22⋊C4—181no—
494C22⋊C4—181no—
495C22⋊C4—181no—
496C22⋊C4—181no—
497C22⋊C4#63811yescharacteristic
498C22⋊C4#63811yescharacteristic
499C42—21no—
500C42—181no—
501C42C22×C3⋊D311yescharacteristic
502C22×C3—24no—
503C22×C3—24no—
504C22×C3—24no—
505C22×C3—24no—
506C22×C3—24no—
507C22×C3—24no—
508C22×C3—44no—
509C22×C3—44no—
510C22×C3—44no—
511C22×C3—44no—
512C22×C3—44no—
513C22×C3—44no—
514C22×C3C22×#6714yes—
515C2×D3—124no—
516C2×D3—124no—
517C2×D3—124no—
518C3×C4—24no—
519C3×C4—24no—
520C3×C4—28no—
521C3×C4—24no—
522C3×C4—24no—
523C3×C4—44no—
524C3×C4C2×D3×D414yes—
525C3×C4#100414yes—
526Dic3—68no—
527Dic3—124no—
528Dic3—124no—
529C32#327111yescharacteristic, complemented, Sylow
530C23—21no—
531C23—21no—
532C23—181no—
533C23C2×#63811yescharacteristic
534C23C2×#63811yescharacteristic
535Q8—21no—
536Q8—92no—
537Q8—181no—
538Q8—181no—
539Q8—181no—
540Q8—362no—
541Q8D4×C3⋊D312yes—
542D4—21no—
543D4—21no—
544D4—21no—
545D4—21no—
546D4—41no—
547D4—42no—
548D4—42no—
549D4—42no—
550D4—81no—
551D4—81no—
552D4—81no—
553D4—181no—
554D4—181no—
555D4—362no—
556D4—362no—
557C2×C4—21no—
558C2×C4—21no—
559C2×C4—21no—
560C2×C4—21no—
561C2×C4—21no—
562C2×C4—21no—
563C2×C4—42no—
564C2×C4—42no—
565C2×C4—181no—
566C2×C4—181no—
567C2×C4—181no—
568C2×C4—362no—
569C2×C4—362no—
570C2×C4C2×#63811yescharacteristic
571C2×C4C2×#63811yescharacteristic
572C2×C4C2×#63811yescharacteristic
573C2×C4C2×#63811yescharacteristic
574C2×C4C23×C3⋊D311yescharacteristic
575C8—92no—
576C8—181no—
577C8—181no—
578C8—181no—
579C2×C3—44no—
580C2×C3—44no—
581C2×C3—84no—
582C2×C3—84no—
583C2×C3D4×#6714yes—
584C2×C3#582214yes—
585C2×C3#583614yes—
586D3—244no—
587C22—21no—
588C22—21no—
589C22—21no—
590C22—21no—
591C22—21no—
592C22—21no—
593C22—41no—
594C22—41no—
595C22—41no—
596C22—41no—
597C22—41no—
598C22—41no—
599C22—361no—
600C22—361no—
601C22—361no—
602C22C22×#63811yescharacteristic
603C4—21no—
604C4—21no—
605C4—22no—
606C4—21no—
607C4—21no—
608C4—41no—
609C4—182no—
610C4—361no—
611C4—361no—
612C4C2×D4×C3⋊D311yescharacteristic
613C4#6436111yescharacteristic
614C3#8358314yescomplemented
615C2—41no—
616C2—41no—
617C2—81no—
618C2—81no—
619C2—721no—
620C2D4×#63811yescharacteristic
621C2#1059629311yescharacteristic
622C2#1059630711yescharacteristic
subgroupG/H
centerC22C22×#638
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C23×C3⋊D3
FittingC32×#550C2
socleC22×C32C22×D4
hypercenter#550C3⋊D3
hypocenterC32#3271
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C4×D4 ◁ #550

Complements

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

NH ≅ G/Ntype
1. C32×#550C2semidirect
2. C2×#64160C2semidirect
3. C2×#64159C2semidirect
4. #10596023C2semidirect
5. #10592938C2semidirect
6. #10592937C2semidirect
7. #10592774C2semidirect
8. #10592773C2semidirect
9. #10592740C2semidirect
10. #10592739C2semidirect
11. #10592738C2semidirect
12. #10592736C2semidirect
13. #10592729C2semidirect
14. #10592727C2semidirect
15. #10592710C2semidirect
62. C3×#550D3semidirect
118. #3756D4semidirect
236. #550C3⋊D3semidirect
529. C32#3271semidirect
614. C3#83583semidirect

Maximal subgroups

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

subgroupindex
C32×#5502
C2×#641602
C2×#641592
#105960232
#105929382
#105929372
#105927742
#105927732
#105927402
#105927392
#105927382
#105927362
#105927292
#105927272
#105927102
#835833