Finite Group Databasebeta

← #11868130

Subgroups — #11868130

Order 1152.

1061 conjugacy classes of subgroups.

The subgroup lattice has 652 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596216C211yesmaximal, characteristic, complemented
2#10594795C211yesmaximal, characteristic, complemented
3C2×#63830C211yesmaximal, characteristic, complemented
4C2×#63823C211yesmaximal, characteristic, complemented
5C3×#5132C211yesmaximal, characteristic, complemented
6C2×C3×#823C211yesmaximal, characteristic, complemented
7#10591143C211yesmaximal, characteristic, complemented
8#10590991C214yesmaximal, complemented
9#10590988C214yesmaximal, complemented
10#78720—31nomaximal
11#78703—31nomaximal
12C2×#3828C2211yescharacteristic
13C2×C3×#235C2211yescharacteristic
14C22×C3×D12C2211yescharacteristic
15C2×C32×M16C2211yescharacteristic
16C2×#3748C2211yescharacteristic
17#64116C2214yescomplemented
18M16×C3⋊D3—22no—
19#64110—22no—
20C2×C3×#208C2211yescharacteristic
21C2×C3×#208C2211yescharacteristic
22#63833C2212yescomplemented
23#63831—21no—
24#63830—22no—
25#63830C2214yes—
26#63830C2212yescomplemented
27#63829—22no—
28C2×#3716—21no—
29C2×#3715C2212yescomplemented
30#63825—21no—
31C2×#3714—21no—
32#63823—22no—
33#63823—22no—
34C2×#3713C2212yescomplemented
35C3×#824C2212yescomplemented
36C3×#823C2212yescomplemented
37C3×#823C2214yescomplemented
38#63578C2214yescomplemented
39#5822—31no—
40C2×#949—31no—
41C2×#932—31no—
42C2×#932—31no—
43#5748—31no—
44C2×#908—31no—
45#5745—31no—
46#5745—31no—
47#5745—61no—
48C3×#413—31no—
49C2×C3×#100—31no—
50#5132D311yescharacteristic, complemented
51C2×#823D311yescharacteristic, complemented
52#5124—31no—
53#5124—31no—
54#4754—34no—
55#4749—34no—
56#4749—34no—
57#4748—34no—
58C23×C3×D3—21no—
59C22×C32×C4C2311yescharacteristic
60C2×#638—21no—
61#3828—21no—
62#3828—21no—
63#3828D412yes—
64#3828C2312yes—
65C2×C4⋊(C3⋊D3)D411yescharacteristic
66C2×C4×C3⋊D3—21no—
67C2×#634D411yescharacteristic
68C2×C3×#67—21no—
69C3×#235—21no—
70C3×#235—21no—
71C3×#235—21no—
72C3×#235—21no—
73C2×C3×D12—21no—
74C2×C3×D12—21no—
75C2×C3×D12—21no—
76C2×C3×D12—21no—
77C2×C3×D12—21no—
78C2×C3×D12C2311yescharacteristic
79C2×C3×D12C2312yes—
80C2×C3×C4×D3—21no—
81C2×C3×Dic6C2311yescharacteristic
82C32×M16—21no—
83C32×M16C2312yes—
84C2×C32×C8—21no—
85#3748D412yes—
86#3748D412yes—
87C2×C3⋊(C3⋊C8)C2312yes—
88#3743—24no—
89C8×C3⋊D3—24no—
90C3×#208—21no—
91C3×#208—21no—
92C3×#208C2312yes—
93C3×#208C2312yes—
94C2×C3×C3⋊C8—21no—
95C2×C3×C3⋊C8—21no—
96#3719—22no—
97#3717—22no—
98#3716—24no—
99#3716—22no—
100#3715—24no—
101#3714—24no—
102#3714—22no—
103#3713—24no—
104#3068—91noSylow
105C2×C3×#41—31no—
106C22×C3×D4—31no—
107C2×#235—31no—
108C2×#235—31no—
109C2×#235—61no—
110C2×#235C2×D311yescharacteristic
111C22×D12C2×D311yescharacteristic
112C2×C3×M16—21no—
113C2×C3×M16—31no—
114C2×C3×M16—31no—
115C2×C3×M16C2×D311yescharacteristic
116C2×C3×M16C2×D311yescharacteristic
117#951—61no—
118#950—62no—
119#949—61no—
120#949—62no—
121#949—62no—
122#942—32no—
123C2×#215—32no—
124C2×#214—32no—
125C2×#214—61no—
126#932—34no—
127#932—32no—
128#932—62no—
129#932—62no—
130#932—62no—
131C2×#213—32no—
132C2×#213—32no—
133C2×#213—61no—
134C2×#208—31no—
135C2×#208—31no—
136C2×#208—61no—
137C2×#208C2×D311yescharacteristic
138C2×#208C2×D311yescharacteristic
139#909—32no—
140#909—61no—
141#908—34no—
142#908—32no—
143#908—62no—
144#908—61no—
145#907—34no—
146#907—34no—
147#907—64no—
148D3×M16—62no—
149D3×M16—62no—
150D3×M16—64no—
151#904—62no—
152C2×D24—61no—
153C2×#204—61no—
154#901—62no—
155#901—62no—
156#901—64no—
157C3×#101—32no—
158C3×#100—34no—
159C3×#100—32no—
160#824C2×D312yescomplemented
161#823C2×D314yescomplemented
162#823C2×D312yescomplemented
163#822—34no—
164#822—34no—
165C23×C32#4111yescharacteristic
166C22×C3⋊D3—21no—
167C22×C3×D3—22no—
168C22×C3×D3—21no—
169C22×C3×D3—41no—
170C22×C3×D3—41no—
171C22×C3×D3—82no—
172C2×C32×C4C2×D411yescharacteristic
173C2×C32×C4C2×D411yescharacteristic
174C2×C32×C4C2×D411yescharacteristic
175C2×C32×C4C2×D411yescharacteristic
176C2×C32×C4#4111yescharacteristic
177C2×C32×C4C2411yescharacteristic
178#638—22no—
179#638—22no—
180C2×C3⋊Dic3—21no—
181C4⋊(C3⋊D3)—21no—
182C4⋊(C3⋊D3)C2×D412yes—
183C4×C3⋊D3—22no—
184C4×C3⋊D3—22no—
185#634—21no—
186#634C2×D412yes—
187C3×#67—41no—
188C3×#67—41no—
189C2×C3×Dic3—21no—
190C3×D12—21no—
191C3×D12—22no—
192C3×D12—22no—
193C3×D12—21no—
194C3×D12—41no—
195C3×D12—41no—
196C3×C4×D3—41no—
197C3×C4×D3—41no—
198C3×Dic6—21no—
199C3×Dic6—21no—
200C32×C8—22no—
201C3⋊(C3⋊C8)C2×D414yes—
202C3×C3⋊C8—22no—
203C3×C3⋊C8—22no—
204#575—91no—
205C2×AGL(1,ℤ/8)—91no—
206C2×AGL(1,ℤ/8)—91no—
207#568—91no—
208#472—94no—
209#471—94no—
210#430—91no—
211#413—31no—
212C2×#100—31no—
213C24×C3—61no—
214C23×D3—21no—
215C3×#41—61no—
216C3×#41—61no—
217C3×#41—61no—
218C3×#41—61no—
219C2×C3×Q8—31no—
220C2×C3×D4—31no—
221C2×C3×D4—32no—
222C2×C3×D4—61no—
223C2×C3×D4—61no—
224C2×C3×D4—61no—
225C2×C3×D4—61no—
226C2×C3×D4—61no—
227C2×C3×D4—61no—
228C22×C3×C4—21no—
229C22×C3×C4—61no—
230C22×C3×C4C22×D311yescharacteristic
231C22×C3×C4C22×D311yescharacteristic
232C2×#67—21no—
233C2×#67—62no—
234C2×#67—61no—
235C2×#67—61no—
236#235—21no—
237#235—21no—
238#235—21no—
239#235—21no—
240#235—32no—
241#235—32no—
242#235—32no—
243#235—32no—
244#235—62no—
245#235—62no—
246#235—62no—
247#235—62no—
248#235—61no—
249#235—61no—
250#235—61no—
251#235—61no—
252C2×D12—21no—
253C2×D12—21no—
254C2×D12—21no—
255C2×D12—21no—
256C2×D12—21no—
257C2×D12—31no—
258C2×D12—31no—
259C2×D12—61no—
260C2×D12C22×D311yescharacteristic
261C2×D12C22×D312yes—
262C2×C4×D3—21no—
263C2×C4×D3—62no—
264C2×C4×D3—61no—
265C2×C4×D3—61no—
266C2×Dic6—31no—
267C2×Dic6—31no—
268C2×Dic6—61no—
269C2×Dic6C22×D311yescharacteristic
270C3×M16—22no—
271C3×M16—21no—
272C3×M16—21no—
273C3×M16—22no—
274C3×M16—32no—
275C3×M16—32no—
276C3×M16—61no—
277C3×M16—61no—
278C3×M16C22×D312yes—
279C3×M16C22×D312yes—
280C2×C3×C8—22no—
281C2×C3×C8—21no—
282C2×C3×C8—21no—
283C2×C3×C8—61no—
284C2×C3×C8—61no—
285#216—62no—
286#215—62no—
287#215—64no—
288#214—64no—
289#214—62no—
290#214—64no—
291#213—64no—
292#213—62no—
293#213—64no—
294#213—64no—
295#208—21no—
296#208—21no—
297#208—32no—
298#208—32no—
299#208—32no—
300#208—32no—
301#208—62no—
302#208—62no—
303#208C22×D312yes—
304#208C22×D312yes—
305C2×C3⋊C8—21no—
306C2×C3⋊C8—21no—
307C2×C3⋊C8—32no—
308C2×C3⋊C8—32no—
309C2×C3⋊C8—62no—
310Dic12—62no—
311D24—64no—
312D24—62no—
313#204—62no—
314#204—64no—
315#204—62no—
316ΓL(1,𝔽25)—64no—
317ΓL(1,𝔽25)—64no—
318ΓL(1,𝔽25)—68no—
319D3×C8—64no—
320D3×C8—64no—
321D3×C8—68no—
322C22×C32—41no—
323C22×C32#12111yescharacteristic
324C22×C32#12111yescharacteristic
325C22×C32C2×#4111yescharacteristic
326C2×C3⋊D3—22no—
327C2×C3⋊D3—81no—
328C2×C3×D3—41no—
329C2×C3×D3—42no—
330C2×C3×D3—82no—
331C2×C3×D3—82no—
332C2×C3×D3—81no—
333C2×C3×D3—82no—
334C32×C4#12111yescharacteristic
335C32×C4#12111yescharacteristic
336C32×C4C22×D411yescharacteristic
337C32×C4C22×D411yescharacteristic
338C3⋊Dic3—22no—
339C3×Dic3—41no—
340C2×#41—31no—
341C2×#41—91no—
342C22×D4—31no—
343#137—92no—
344#137—181no—
345AGL(1,ℤ/8)—94no—
346AGL(1,ℤ/8)—92no—
347AGL(1,ℤ/8)—182no—
348AGL(1,ℤ/8)—181no—
349AGL(1,ℤ/8)—182no—
350AGL(1,ℤ/8)—182no—
351#135—182no—
352C2×SD16—92no—
353C2×SD16—181no—
354C2×D8—92no—
355C2×D8—181no—
356#131—94no—
357#131—182no—
358C2×M16—31no—
359C2×M16—31no—
360C2×M16—91no—
361C2×M16—182no—
362C2×M16D3211yescharacteristic
363#108—94no—
364#101—32no—
365#100—34no—
366#100—32no—
367C23×C3—21no—
368C23×C3—61no—
369C23×C3—62no—
370C23×C3—121no—
371C23×C3—121no—
372C23×C3—242no—
373C23×C3#23511yescharacteristic
374C23×C3#23511yescharacteristic
375C22×D3—21no—
376C22×D3—22no—
377C22×D3—41no—
378C22×D3—41no—
379C22×D3—62no—
380C22×D3—61no—
381C22×D3—61no—
382C22×D3—82no—
383C3×Q8—61no—
384C3×Q8—61no—
385C3×D4—61no—
386C3×D4—62no—
387C3×D4—62no—
388C3×D4—61no—
389C3×D4—121no—
390C3×D4—121no—
391C3×D4—121no—
392C3×D4—121no—
393C2×C3×C4—21no—
394C2×C3×C4—21no—
395C2×C3×C4—21no—
396C2×C3×C4—21no—
397C2×C3×C4—21no—
398C2×C3×C4—21no—
399C2×C3×C4—61no—
400C2×C3×C4—121no—
401C2×C3×C4—121no—
402C2×C3×C4#23511yescharacteristic
403C2×C3×C4#23511yescharacteristic
404C2×C3×C4D3×D411yescharacteristic
405C2×C3×C4D3×D411yescharacteristic
406C2×C3×C4D3×D411yescharacteristic
407C2×C3×C4D3×D411yescharacteristic
408C2×C3×C4D3×D411yescharacteristic
409C2×C3×C4D3×D411yescharacteristic
410C2×C3×C4D3×D411yescharacteristic
411C2×C3×C4D3×D411yescharacteristic
412C2×C3×C4C23×D311yescharacteristic
413C2×C3×C4C23×D311yescharacteristic
414#67—41no—
415#67—41no—
416#67—64no—
417#67—64no—
418#67—62no—
419#67—62no—
420#67—62no—
421#67—62no—
422C2×Dic3—21no—
423C2×Dic3—62no—
424C2×Dic3—61no—
425C2×Dic3—61no—
426D12—22no—
427D12—21no—
428D12—21no—
429D12—22no—
430D12—32no—
431D12—32no—
432D12—41no—
433D12—41no—
434D12—62no—
435D12—62no—
436D12—61no—
437D12—61no—
438C4×D3—41no—
439C4×D3—41no—
440C4×D3—64no—
441C4×D3—64no—
442C4×D3—62no—
443C4×D3—62no—
444C4×D3—62no—
445C4×D3—62no—
446Dic6—21no—
447Dic6—21no—
448Dic6—32no—
449Dic6—32no—
450Dic6—62no—
451Dic6—62no—
452Dic6—61no—
453Dic6—61no—
454C3×C8—24no—
455C3×C8—22no—
456C3×C8—22no—
457C3×C8—62no—
458C3×C8—62no—
459C3⋊C8—22no—
460C3⋊C8—22no—
461C3⋊C8—34no—
462C3⋊C8—34no—
463C3⋊C8—64no—
464C2×C32—21no—
465C2×C32—21no—
466C2×C32—21no—
467C2×C32C2×#12111yescharacteristic
468C3⋊D3—42no—
469C3×D3—81no—
470C3×D3—82no—
471C24—61no—
472#41—61no—
473#41—61no—
474#41—61no—
475#41—61no—
476#41—92no—
477#41—92no—
478#41—181no—
479#41—181no—
480C2×Q8—31no—
481C2×Q8—91no—
482C2×D4—31no—
483C2×D4—32no—
484C2×D4—61no—
485C2×D4—61no—
486C2×D4—61no—
487C2×D4—61no—
488C2×D4—61no—
489C2×D4—61no—
490C2×D4—91no—
491C2×D4—181no—
492C22×C4—61no—
493C22×C4—181no—
494C22×C4C2×D3211yescharacteristic
495Q16—182no—
496SD16—184no—
497SD16—182no—
498SD16—182no—
499SD16—184no—
500D8—184no—
501D8—182no—
502D8—184no—
503M16—21no—
504M16—32no—
505M16—32no—
506M16—61no—
507M16—61no—
508M16—92no—
509M16—92no—
510M16—184no—
511M16C2×D3212yes—
512C2×C8—21no—
513C2×C8—61no—
514C2×C8—61no—
515C2×C8—92no—
516C2×C8—184no—
517C22×C3—21no—
518C22×C3—21no—
519C22×C3—21no—
520C22×C3—41no—
521C22×C3—41no—
522C22×C3—81no—
523C22×C3—121no—
524C22×C3—122no—
525C22×C3—242no—
526C22×C3—241no—
527C22×C3—242no—
528C22×C3—242no—
529C22×C3#88411yescharacteristic
530C22×C3#88411yescharacteristic
531C22×C3#88411yescharacteristic
532C22×C3#88411yescharacteristic
533C22×C3C2×#23511yescharacteristic
534C22×C3C2×#23511yescharacteristic
535C2×D3—41no—
536C2×D3—42no—
537C2×D3—64no—
538C2×D3—62no—
539C2×D3—62no—
540C2×D3—82no—
541C2×D3—82no—
542C2×D3—82no—
543C2×D3—81no—
544C2×D3—241no—
545C2×D3—241no—
546C2×D3—242no—
547C3×C4—21no—
548C3×C4—21no—
549C3×C4—21no—
550C3×C4—21no—
551C3×C4—121no—
552C3×C4#88411yescharacteristic
553C3×C4#88411yescharacteristic
554C3×C4#88411yescharacteristic
555C3×C4#88411yescharacteristic
556C3×C4C2×D3×D411yescharacteristic
557C3×C4C2×D3×D411yescharacteristic
558C3×C4C2×D3×D411yescharacteristic
559C3×C4C2×D3×D411yescharacteristic
560Dic3—41no—
561Dic3—64no—
562Dic3—62no—
563Dic3—62no—
564C32#306811yescharacteristic, complemented, Sylow
565C23—61no—
566C23—62no—
567C23—121no—
568C23—121no—
569C23—181no—
570C23—242no—
571C23#379811yescharacteristic
572Q8—61no—
573Q8—61no—
574Q8—92no—
575Q8—181no—
576D4—62no—
577D4—61no—
578D4—61no—
579D4—62no—
580D4—92no—
581D4—121no—
582D4—121no—
583D4—121no—
584D4—121no—
585D4—182no—
586D4—182no—
587D4—181no—
588C2×C4—61no—
589C2×C4—121no—
590C2×C4—121no—
591C2×C4—181no—
592C2×C4—182no—
593C2×C4—182no—
594C2×C4#379811yescharacteristic
595C2×C4#380211yescharacteristic
596C2×C4#380211yescharacteristic
597C2×C4#381111yescharacteristic
598C2×C4#381111yescharacteristic
599C2×C4C22×D3211yescharacteristic
600C8—22no—
601C8—62no—
602C8—62no—
603C8—94no—
604C2×C3—21no—
605C2×C3—21no—
606C2×C3—21no—
607C2×C3—21no—
608C2×C3—21no—
609C2×C3—21no—
610C2×C3—21no—
611C2×C3—41no—
612C2×C3—41no—
613C2×C3—41no—
614C2×C3—241no—
615C2×C3—242no—
616C2×C3C2×#88411yescharacteristic
617C2×C3C2×#88411yescharacteristic
618D3—82no—
619D3—81no—
620D3—124no—
621D3—122no—
622D3—122no—
623C22—41no—
624C22—121no—
625C22—122no—
626C22—182no—
627C22—242no—
628C22—241no—
629C22—242no—
630C22—242no—
631C22—721no—
632C22#6391211yescharacteristic
633C22#6391211yescharacteristic
634C22C2×#379811yescharacteristic
635C4—121no—
636C4—182no—
637C4#6391211yescharacteristic
638C4#6391211yescharacteristic
639C4C2×#380211yescharacteristic
640C4C2×#381111yescharacteristic
641C3—21no—
642C3#7870311yescharacteristic, complemented
643C3#7872011yescharacteristic, complemented
644C2—21no—
645C2—21no—
646C2—21no—
647C2—242no—
648C2—241no—
649C2—362no—
650C2C2×#6391211yescharacteristic
subgroupG/H
centerC2C2×#63912
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×M16C22
socleC2×C32C2×#121
hypercenterC2×M16D32
hypocenterC32#3068
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C22×C4 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
1. #10596216C2semidirect
2. #10594795C2semidirect
3. C2×#63830C2semidirect
4. C2×#63823C2semidirect
5. C3×#5132C2semidirect
6. C2×C3×#823C2semidirect
7. #10591143C2semidirect
8. #10590991C2semidirect
9. #10590988C2semidirect
17. #64116C22semidirect
22. #63833C22semidirect
26. #63830C22semidirect
29. C2×#3715C22semidirect
34. C2×#3713C22semidirect
35. C3×#824C22semidirect
36. C3×#823C22semidirect
37. C3×#823C22semidirect
38. #63578C22semidirect
50. #5132D3semidirect
51. C2×#823D3semidirect
160. #824C2×D3semidirect
161. #823C2×D3semidirect
162. #823C2×D3semidirect
564. C32#3068semidirect
642. C3#78703semidirect
643. C3#78720semidirect

Maximal subgroups

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

subgroupindex
#105962162
#105947952
C2×#638302
C2×#638232
C3×#51322
C2×C3×#8232
#105911432
#105909912
#105909882
#787203
#787033