Finite Group Databasebeta

← #11887542

Subgroups — #11887542

Order 1152.

986 conjugacy classes of subgroups.

The subgroup lattice has 579 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596026C211yesmaximal, characteristic
2C3×D4×Dic6C211yesmaximal, characteristic, complemented
3C3×D4×C3⋊C8C211yesmaximal, characteristic, complemented
4#10591177C212yesmaximal, complemented
5#10591174C212yesmaximal, complemented
6#10591126C212yesmaximal, complemented
7C2×#63566C212yesmaximal, complemented
8#10590379C211yesmaximal, characteristic, complemented
9C4×#3717C211yesmaximal, characteristic, complemented
10#10590301C211yesmaximal, characteristic, complemented
11#10590287C211yesmaximal, characteristic, complemented
12#83550—31nomaximal
13#79447—31nomaximal
14C2×#3830—21no—
15C22×C3×Dic6C2212yes—
16C32×C4×D4C2211yescharacteristic
17#64139C2212yes—
18C2×C4⋊(C3⋊Dic3)C2212yes—
19#64106—21no—
20#64095—22no—
21C4×C4⋊(C3⋊D3)C2211yescharacteristic
22#64078C2211yescharacteristic
23C3×D4×Dic3—21no—
24C3×#924C2212yes—
25C22×C3×C3⋊C8C2212yes—
26C3×#888—21no—
27C3×#878—22no—
28C3×#869C2211yescharacteristic
29C3×C4×Dic6C2211yescharacteristic
30C2×#3717C2211yescharacteristic
31C2×#3717C2212yes—
32C3×#830C2212yes—
33C3×C4⋊(C3⋊C8)C2211yescharacteristic
34C3×C4×C3⋊C8C2211yescharacteristic
35#63573C2212yes—
36#63573C2211yescharacteristic
37#63566C2212yes—
38#63566C2212yes—
39#63566C2212yes—
40#63566C2211yescharacteristic
41#63566C2212yes—
42#63564C2211yescharacteristic
43C3×D4×Q8—31no—
44#5555—31no—
45#5555—31no—
46#5555—61no—
47D4×Dic6D311yescharacteristic, complemented
48C3×C8×D4—31no—
49#5227—32no—
50C2×#835—32no—
51#5114—32no—
52C2×#816—32no—
53#5083—31no—
54#5079—31no—
55#5048—32no—
56#5043—32no—
57C4×#215—31no—
58#5020—31no—
59D4×C3⋊C8D311yescharacteristic, complemented
60#4851—31no—
61#4841—31no—
62#4738—32no—
63#4721—32no—
64C4×#204—31no—
65#4681—31no—
66C2×C32×D4D411yescharacteristic
67C22×C32×C4C2312yes—
68C2×#638—22no—
69C22×C3⋊Dic3—22no—
70#3830—44no—
71C2×C4⋊(C3⋊D3)C2311yescharacteristic
72C2×C4×C3⋊D3—21no—
73C2×#634—21no—
74C22×C3×Dic3—22no—
75C2×C3×Dic6—24no—
76C2×C3×Dic6—22no—
77C2×C3×Dic6—42no—
78C2×C3×Dic6C2312yes—
79C2×C3×Dic6C2311yescharacteristic
80C32×C4⋊C4D411yescharacteristic
81C32×C22⋊C4D412yes—
82C32×C42C2311yescharacteristic
83#3752—21no—
84#3752—22no—
85C4⋊(C3⋊Dic3)—21no—
86C4⋊(C3⋊Dic3)—22no—
87C4⋊(C3⋊Dic3)C2312yes—
88C4⋊(C3⋊Dic3)C2311yescharacteristic
89C3×#217—22no—
90C3×C4⋊Dic3—21no—
91C3×C4⋊Dic3—21no—
92C3×C4⋊Dic3C2311yescharacteristic
93C3×Dic3⋊C4—21no—
94C3×Dic3⋊C4—22no—
95C3×C4×Dic3—21no—
96C2×C3×C3⋊C8—42no—
97C2×C3×C3⋊C8C2311yescharacteristic
98C2×C3×C3⋊C8C2312yes—
99C2×C3×C3⋊C8C2311yescharacteristic
100#3717—22no—
101#3717—42no—
102#3298—91noSylow
103C22×C3×Q8—32no—
104C2×#237—62no—
105C2×#237—61no—
106C2×#237—61no—
107C22×Dic6C2×D312yes—
108C22×C3×C8—32no—
109C3×C4⋊Q8—31no—
110C3×C4⋊Q8—61no—
111C3×C22⋊Q8—32no—
112C3×C22⋊Q8—62no—
113C3×C4×Q8—31no—
114C3×C4×D4—21no—
115C3×C4×D4—61no—
116C3×C4×D4C2×D311yescharacteristic
117C3×C4×D4C2×D311yescharacteristic
118C2×#215—31no—
119C2×#215—32no—
120D4×Dic3—21no—
121#930—32no—
122#930—32no—
123#930—62no—
124C2×C4⋊Dic3—32no—
125C2×C4⋊Dic3—32no—
126C2×C4⋊Dic3—62no—
127#924C2×D312yes—
128C22×C3⋊C8C2×D312yes—
129C2×#204—31no—
130C2×#204—32no—
131#897—62no—
132#897—61no—
133#897—61no—
134#888—21no—
135#886—64no—
136#886—62no—
137#886—62no—
138#878—22no—
139C4×D12—31no—
140C4×D12—31no—
141C4×D12—61no—
142#869—31no—
143#869—31no—
144#869—61no—
145#869C2×D311yescharacteristic
146C4×Dic6C2×D311yescharacteristic
147C3×C4⋊C8—31no—
148C3×C22⋊C8—32no—
149C3×C4×C8—31no—
150#835—31no—
151#835—32no—
152#835—32no—
153#835—32no—
154#835—32no—
155#830C2×D312yes—
156#821—31no—
157#817—31no—
158#817—32no—
159#816—32no—
160#816—32no—
161#816—31no—
162#816—32no—
163#816—32no—
164#809—31no—
165#808—32no—
166#808—31no—
167C4⋊(C3⋊C8)C2×D311yescharacteristic
168C4×C3⋊C8C2×D311yescharacteristic
169C23×C32C2×D412yes—
170C22×C3⋊D3—21no—
171C32×D4SD1614yescomplemented
172C2×C32×C4—22no—
173C2×C32×C4—22no—
174C2×C32×C4C2×D411yescharacteristic
175C2×C32×C4C2×D412yes—
176C2×C32×C4C2×D411yescharacteristic
177C2×C32×C4C2411yescharacteristic
178#638—44no—
179C2×C3⋊Dic3—22no—
180C2×C3⋊Dic3—21no—
181C2×C3⋊Dic3—44no—
182C4⋊(C3⋊D3)—21no—
183C4⋊(C3⋊D3)—21no—
184C4×C3⋊D3—42no—
185#634—42no—
186C2×C3×Dic3—21no—
187C2×C3×Dic3—21no—
188C2×C3×Dic3—22no—
189C2×C3×Dic3—44no—
190C3×Dic6—21no—
191C3×Dic6—22no—
192C3×Dic6—22no—
193C3×Dic6—44no—
194C3×Dic6#4112yescomplemented
195C3×C3⋊C8—21no—
196C3×C3⋊C8—22no—
197C3×C3⋊C8—21no—
198D4×Q8—31no—
199#547—91no—
200#487—91no—
201#483—92no—
202#475—91no—
203#465—92no—
204#461—91no—
205#448—92no—
206C4×SD16—91no—
207C8×D4—31no—
208C2×#103—92no—
209C2×C3×Q8—31no—
210C2×C3×Q8—32no—
211C2×C3×Q8—64no—
212C2×C3×Q8—62no—
213C2×C3×Q8—122no—
214C2×C3×D4—21no—
215C2×C3×D4D1211yescharacteristic
216C2×C3×D4#6711yescharacteristic
217C22×C3×C4—22no—
218C22×C3×C4—62no—
219C22×C3×C4C22×D312yes—
220C22×C3×C4C22×D312yes—
221C2×#67—64no—
222C2×#67—62no—
223C2×#67—62no—
224C22×Dic3—22no—
225C22×Dic3—64no—
226C22×Dic3—62no—
227C22×Dic3—62no—
228#237—128no—
229#237—124no—
230#237—124no—
231C2×D12—31no—
232C2×D12—31no—
233C2×D12—61no—
234C2×C4×D3—62no—
235C2×C4×D3—61no—
236C2×C4×D3—61no—
237C2×Dic6—24no—
238C2×Dic6—22no—
239C2×Dic6—42no—
240C2×Dic6—62no—
241C2×Dic6—61no—
242C2×Dic6—61no—
243C2×Dic6C22×D312yes—
244C2×Dic6C22×D311yescharacteristic
245C2×C3×C8—31no—
246C2×C3×C8—31no—
247C2×C3×C8—32no—
248C2×C3×C8—122no—
249C3×C4⋊C4—21no—
250C3×C4⋊C4—31no—
251C3×C4⋊C4—61no—
252C3×C4⋊C4—62no—
253C3×C4⋊C4—61no—
254C3×C4⋊C4—61no—
255C3×C4⋊C4D1211yescharacteristic
256C3×C4⋊C4#6711yescharacteristic
257C3×C22⋊C4—22no—
258C3×C22⋊C4—62no—
259C3×C22⋊C4D1212yes—
260C3×C22⋊C4#6712yes—
261C3×C42—21no—
262C3×C42—61no—
263C3×C42C22×D311yescharacteristic
264C3×C42C22×D311yescharacteristic
265#217—22no—
266#215—62no—
267#215—122no—
268(C2×D3)⋊C4—62no—
269(C2×D3)⋊C4—64no—
270(C2×D3)⋊C4—61no—
271(C2×D3)⋊C4—62no—
272(C2×D3)⋊C4—61no—
273(C2×D3)⋊C4—62no—
274C4⋊Dic3—21no—
275C4⋊Dic3—21no—
276C4⋊Dic3—32no—
277C4⋊Dic3—31no—
278C4⋊Dic3—32no—
279C4⋊Dic3—31no—
280C4⋊Dic3—62no—
281C4⋊Dic3—61no—
282C4⋊Dic3—62no—
283C4⋊Dic3—64no—
284C4⋊Dic3—61no—
285C4⋊Dic3—62no—
286C4⋊Dic3—61no—
287C4⋊Dic3—62no—
288C4⋊Dic3C22×D311yescharacteristic
289Dic3⋊C4—21no—
290Dic3⋊C4—22no—
291C4×Dic3—21no—
292C2×C3⋊C8—42no—
293C2×C3⋊C8C22×D311yescharacteristic
294C2×C3⋊C8C22×D311yescharacteristic
295C2×C3⋊C8C22×D312yes—
296#204—62no—
297#204—122no—
298C22×C32—22no—
299C22×C32—22no—
300C22×C32C2×SD1614yes—
301C22×C32C22×D411yescharacteristic
302C2×C3⋊D3—41no—
303C2×C3⋊D3—41no—
304C2×C3⋊D3—41no—
305C32×C4—22no—
306C32×C4—21no—
307C32×C4C2×SD1612yes—
308C32×C4C2×#4111yescharacteristic
309C32×C4H(5,𝔽2)11yescharacteristic
310C3⋊Dic3—42no—
311C3⋊Dic3—41no—
312C3×Dic3—22no—
313C3×Dic3—42no—
314C3×Dic3—41no—
315C2×#41—181no—
316C22×Q8—32no—
317C2×SD16—91no—
318C2×SD16—92no—
319C22×C8—32no—
320C4⋊Q8—31no—
321C4⋊Q8—61no—
322C4⋊Q8—91no—
323#123—182no—
324C22⋊Q8—32no—
325C22⋊Q8—62no—
326C22⋊Q8—181no—
327#121—92no—
328C4×Q8—31no—
329C4×D4—61no—
330C4×D4—91no—
331C4×D4D3211yescharacteristic
332C2×C4⋊C4—92no—
333#106—91no—
334#106—92no—
335C4⋊C8—31no—
336#103—91no—
337#103—92no—
338#103—92no—
339#103—92no—
340#103—92no—
341#102—91no—
342C22⋊C8—32no—
343C4×C8—31no—
344C23×C3—22no—
345C23×C3C2×D1212yes—
346C23×C3C2×#6712yes—
347C22×D3—62no—
348C22×D3—61no—
349C22×D3—61no—
350C3×Q8—32no—
351C3×Q8—61no—
352C3×Q8—62no—
353C3×Q8—62no—
354C3×Q8—124no—
355C3×D4—24no—
356C3×D4#20414yescomplemented
357C3×D4#21514yescomplemented
358C2×C3×C4—22no—
359C2×C3×C4—22no—
360C2×C3×C4—22no—
361C2×C3×C4—22no—
362C2×C3×C4—21no—
363C2×C3×C4—21no—
364C2×C3×C4—21no—
365C2×C3×C4—22no—
366C2×C3×C4—42no—
367C2×C3×C4—42no—
368C2×C3×C4—61no—
369C2×C3×C4—61no—
370C2×C3×C4—62no—
371C2×C3×C4—124no—
372C2×C3×C4C2×D1211yescharacteristic
373C2×C3×C4C2×D1212yes—
374C2×C3×C4C2×D1211yescharacteristic
375C2×C3×C4C2×#6711yescharacteristic
376C2×C3×C4C2×#6712yes—
377C2×C3×C4C2×#6711yescharacteristic
378C2×C3×C4C23×D311yescharacteristic
379C2×C3×C4C23×D311yescharacteristic
380#67—128no—
381#67—124no—
382#67—124no—
383C2×Dic3—21no—
384C2×Dic3—21no—
385C2×Dic3—22no—
386C2×Dic3—44no—
387C2×Dic3—64no—
388C2×Dic3—62no—
389C2×Dic3—62no—
390C2×Dic3—61no—
391C2×Dic3—62no—
392C2×Dic3—61no—
393C2×Dic3—128no—
394C2×Dic3—124no—
395C2×Dic3—124no—
396D12—61no—
397D12—61no—
398D12—61no—
399D12—61no—
400D12—121no—
401D12—121no—
402C4×D3—124no—
403C4×D3—122no—
404C4×D3—122no—
405Dic6—21no—
406Dic6—22no—
407Dic6—22no—
408Dic6—44no—
409Dic6—124no—
410Dic6—122no—
411Dic6—122no—
412Dic6#23712yescomplemented
413C3×C8—61no—
414C3×C8—62no—
415C3×C8—61no—
416C3⋊C8—21no—
417C3⋊C8—22no—
418C3⋊C8—21no—
419C2×C32—24no—
420C2×C32#54611yescharacteristic
421C2×C32C22×SD1611yescharacteristic
422C2×C32#57811yescharacteristic
423C3⋊D3—81no—
424#41—364no—
425C2×Q8—31no—
426C2×Q8—32no—
427C2×Q8—64no—
428C2×Q8—62no—
429C2×Q8—122no—
430C2×Q8—181no—
431C2×D4—91no—
432C2×D4—182no—
433C2×D4#62611yescharacteristic
434C22×C4—62no—
435C22×C4—182no—
436C22×C4—181no—
437C22×C4C2×D3212yes—
438SD16—182no—
439SD16—362no—
440C2×C8—31no—
441C2×C8—31no—
442C2×C8—32no—
443C2×C8—122no—
444C4⋊C4—31no—
445C4⋊C4—61no—
446C4⋊C4—61no—
447C4⋊C4—62no—
448C4⋊C4—61no—
449C4⋊C4—91no—
450C4⋊C4—92no—
451C4⋊C4—182no—
452C4⋊C4—181no—
453C4⋊C4#62611yescharacteristic
454C22⋊C4—62no—
455C22⋊C4—181no—
456C22⋊C4—182no—
457C22⋊C4#62612yes—
458C42—61no—
459C42C2×D3211yescharacteristic
460C22×C3—22no—
461C22×C3—22no—
462C22×C3—22no—
463C22×C3—22no—
464C22×C3—21no—
465C22×C3—24no—
466C22×C3—42no—
467C22×C3—42no—
468C22×C3C2×#20414yes—
469C22×C3C2×#21514yes—
470C22×C3C22×D1211yescharacteristic
471C22×C3C22×#6711yescharacteristic
472C2×D3—122no—
473C2×D3—122no—
474C2×D3—122no—
475C2×D3—121no—
476C2×D3—121no—
477C2×D3—121no—
478C2×D3—121no—
479C2×D3—121no—
480C2×D3—121no—
481C3×C4—21no—
482C3×C4—22no—
483C3×C4—22no—
484C3×C4—21no—
485C3×C4—21no—
486C3×C4—21no—
487C3×C4—22no—
488C3×C4—42no—
489C3×C4—41no—
490C3×C4—62no—
491C3×C4—121no—
492C3×C4—122no—
493C3×C4C2×#20412yes—
494C3×C4C2×#21512yes—
495C3×C4C2×#23711yescharacteristic
496C3×C4#100411yescharacteristic
497C3×C4#100411yescharacteristic
498C3×C4D3×#4111yescharacteristic
499Dic3—22no—
500Dic3—42no—
501Dic3—41no—
502Dic3—124no—
503Dic3—122no—
504Dic3—122no—
505Dic3—121no—
506Dic3—122no—
507Dic3—121no—
508C32#329811yescharacteristic, complemented, Sylow
509C23—181no—
510C23C2×#62612yes—
511Q8—32no—
512Q8—61no—
513Q8—62no—
514Q8—62no—
515Q8—124no—
516Q8—362no—
517D4—181no—
518D4—181no—
519D4—364no—
520D4#371714yescomplemented
521C2×C4—22no—
522C2×C4—22no—
523C2×C4—61no—
524C2×C4—61no—
525C2×C4—62no—
526C2×C4—124no—
527C2×C4—181no—
528C2×C4—182no—
529C2×C4—364no—
530C2×C4—362no—
531C2×C4C2×#62611yescharacteristic
532C2×C4C2×#62612yes—
533C2×C4C2×#62611yescharacteristic
534C2×C4C22×D3211yescharacteristic
535C8—61no—
536C8—61no—
537C8—62no—
538C2×C3—24no—
539C2×C3—24no—
540C2×C3—21no—
541C2×C3—21no—
542C2×C3—21no—
543C2×C3—44no—
544C2×C3#555411yescharacteristic
545C2×C3C22×#20411yescharacteristic
546C2×C3#575311yescharacteristic
547C2×C3#580611yescharacteristic
548C2×C3C22×#21511yescharacteristic
549C2×C3#583811yescharacteristic
550D3—242no—
551D3—241no—
552D3—241no—
553C22—22no—
554C22—22no—
555C22—361no—
556C22—361no—
557C22—361no—
558C22C2×#371714yes—
559C22C22×#62611yescharacteristic
560C4—21no—
561C4—22no—
562C4—62no—
563C4—121no—
564C4—122no—
565C4—361no—
566C4—362no—
567C4C2×#371712yes—
568C4D3×#23711yescharacteristic
569C4#6431311yescharacteristic
570C3—21no—
571C3#7944711yescharacteristic, complemented
572C3#8355011yescharacteristic, complemented
573C2—24no—
574C2—721no—
575C2C22×#371711yescharacteristic
576C2#1059524611yescharacteristic
577C2#1059545011yescharacteristic
subgroupG/H
centerC22C22×#626
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4×D4C22
socleC22×C32C22×D4
prime radical#10596026C2
hypercenterC4×D4D32
hypocenterC32#3298
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
2. C3×D4×Dic6C2semidirect
3. C3×D4×C3⋊C8C2semidirect
4. #10591177C2semidirect
5. #10591174C2semidirect
6. #10591126C2semidirect
7. C2×#63566C2semidirect
8. #10590379C2semidirect
9. C4×#3717C2semidirect
10. #10590301C2semidirect
11. #10590287C2semidirect
47. D4×Dic6D3semidirect
59. D4×C3⋊C8D3semidirect
171. C32×D4SD16semidirect
194. C3×Dic6#41semidirect
356. C3×D4#204semidirect
357. C3×D4#215semidirect
412. Dic6#237semidirect
508. C32#3298semidirect
520. D4#3717semidirect
571. C3#79447semidirect
572. C3#83550semidirect

Maximal subgroups

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

subgroupindex
#105960262
C3×D4×Dic62
C3×D4×C3⋊C82
#105911772
#105911742
#105911262
C2×#635662
#105903792
C4×#37172
#105903012
#105902872
#835503
#794473