Finite Group Databasebeta

← #11874320

Subgroups — #11874320

Order 1152.

1209 conjugacy classes of subgroups.

The subgroup lattice has 540 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63808C211yesmaximal, characteristic, complemented
2C2×#63807C211yesmaximal, characteristic, complemented
3C2×#63806C212yesmaximal, complemented
4#10593969C212yesmaximal, complemented
5#10592395C211yesmaximal, characteristic, complemented
6C3×#4696C211yesmaximal, characteristic, complemented
7C3×C4×D3×C8C211yesmaximal, characteristic, complemented
8#10590896C211yesmaximal, characteristic, complemented
9#10590880C211yesmaximal, characteristic, complemented
10#10590877C212yesmaximal, complemented
11#10590370C212yesmaximal, complemented
12#81820—31nomaximal
13#78467—31nomaximal
14C2×#3799C2212yes—
15C2×#3795C2212yes—
16C2×#3746C2211yescharacteristic
17C2×#3745C2211yescharacteristic
18C2×#3744C2212yes—
19#64084C2212yes—
20C2×C3×Dic12C2211yescharacteristic
21C2×C3×D24C2211yescharacteristic
22C2×C3×#204C2212yes—
23C2×C3×D3×C8C2211yescharacteristic
24C2×C3×D3×C8C2211yescharacteristic
25C3×#875C2212yes—
26C3×C42×D3C2211yescharacteristic
27#63911C2212yes—
28#63906—24no—
29#63880—24no—
30#63866C2212yes—
31C2×#3719C2212yes—
32C2×#3717C2212yes—
33C2×#3716C2212yes—
34C2×#3714C2212yes—
35#63808—24no—
36#63807—24no—
37#63806—28no—
38C32×C4×C8C2211yescharacteristic
39C3×C8×Dic3C2211yescharacteristic
40C3×C8×Dic3C2211yescharacteristic
41C3×C4×C3⋊C8C2211yescharacteristic
42C2×#919—31no—
43C2×#916—32no—
44C2×#912—31no—
45C2×#904—31no—
46C2×#904—31no—
47C2×#904—32no—
48#5668—32no—
49#5477—32no—
50C3×#495—31no—
51C2×C3×C4×C8—31no—
52#5183—31no—
53#5175—32no—
54#5151—31no—
55#5059—32no—
56#4699—31no—
57#4696—32no—
58#4696—31no—
59#4696—31no—
60#4696—61no—
61#4696D311yescharacteristic, complemented
62#4695—31no—
63#4693—32no—
64C4×D3×C8D311yescharacteristic, complemented
65C2×C4⋊(C3⋊D3)C2312yes—
66C2×#634C2312yes—
67C2×C3×D12C2312yes—
68C2×C3×C4×D3D412yes—
69C2×C3×C4×D3C2311yescharacteristic
70C2×C3×Dic6C2312yes—
71C2×#626—22no—
72C2×#626—24no—
73C2×#625—22no—
74C2×#624—22no—
75C2×D3×Dic3—22no—
76#3799—24no—
77#3799—24no—
78#3795—24no—
79#3795—24no—
80C2×C32×C8C2311yescharacteristic
81C2×C32×C8C2311yescharacteristic
82C32×C42C2311yescharacteristic
83#3752—24no—
84#3746—22no—
85#3745—22no—
86#3744—24no—
87C3×(C2×D3)⋊C4—24no—
88C3×C4×Dic3D412yes—
89C3×C4×Dic3C2311yescharacteristic
90C2×C3×C3⋊C8C2311yescharacteristic
91C2×C3×C3⋊C8C2311yescharacteristic
92C3×Dic12—22no—
93C3×D24—22no—
94C3×#204—24no—
95C3×D3×C8D414yescomplemented
96C3×D3×C8D414yescomplemented
97Dic3⋊Dic3—24no—
98#3719—24no—
99#3717—24no—
100#3716—24no—
101#3714—24no—
102#3147—91noSylow
103C2×#239—32no—
104C2×#237—32no—
105C2×#235—32no—
106C2×#235—32no—
107C2×C3×Q16—31no—
108C2×C3×SD16—32no—
109C2×C3×D8—31no—
110C22×C3×C8—31no—
111C22×C3×C8—31no—
112C3×#124—32no—
113C2×C3×C42—31no—
114#944—32no—
115C2×#216—32no—
116C2×#215—32no—
117#940—32no—
118C2×#214—32no—
119C2×#213—32no—
120#930—64no—
121#919—64no—
122#916—68no—
123#912—64no—
124C2×Dic12—32no—
125C2×Dic12—31no—
126C2×Dic12—31no—
127C2×Dic12—61no—
128C2×Dic12C2×D311yescharacteristic
129#904—68no—
130#904—64no—
131#904—64no—
132C2×D24—32no—
133C2×D24—31no—
134C2×D24—31no—
135C2×D24—61no—
136C2×D24C2×D311yescharacteristic
137C2×#204—32no—
138C2×#204—32no—
139C2×#204—32no—
140C2×#204—32no—
141C2×#204—62no—
142C2×#204C2×D312yes—
143C2×D3×C8C2×D311yescharacteristic
144C2×D3×C8C2×D311yescharacteristic
145#884—64no—
146#67⋊C4—64no—
147#875—32no—
148#875—32no—
149#875—62no—
150#875C2×D312yes—
151#874—32no—
152C4×D12—64no—
153C42×D3C2×D311yescharacteristic
154#869—32no—
155C3×C4×C8—21no—
156C3×C4×C8—31no—
157C3×C4×C8—31no—
158C3×C4×C8—31no—
159C3×C4×C8C2×D311yescharacteristic
160C3×C4×C8C2×D311yescharacteristic
161C8×Dic3C2×D311yescharacteristic
162C8×Dic3C2×D311yescharacteristic
163C4×C3⋊C8C2×D311yescharacteristic
164C22×C3⋊D3—22no—
165C22×C3×D3—22no—
166C22×C3×D3C2×D411yescharacteristic
167C2×C32×C4C2×D412yes—
168C2×C32×C4C2411yescharacteristic
169C2×C3⋊Dic3—22no—
170C4⋊(C3⋊D3)—22no—
171C4⋊(C3⋊D3)—22no—
172#634—22no—
173#634—22no—
174C2×C3×Dic3—22no—
175C2×C3×Dic3C2×D411yescharacteristic
176C2×C3×Dic3C2×D412yes—
177C3×D12—22no—
178C3×D12—22no—
179C3×C4×D3—24no—
180C3×C4×D3C2×D412yes—
181C3×C4×D3C2×D412yes—
182C3×Dic6—22no—
183C3×Dic6—22no—
184#626—44no—
185#626—48no—
186#625—44no—
187#624—44no—
188D3×Dic3—44no—
189C32×C8C2×D412yes—
190C32×C8C2×D412yes—
191C3×C3⋊C8C2×D412yes—
192C3×C3⋊C8C2×D412yes—
193C2×#135—91no—
194C2×#135—92no—
195C2×#135—91no—
196#532—92no—
197#495—31no—
198#495—92no—
199#495—91no—
200#494—91no—
201#493—91no—
202#492—92no—
203C2×C4×C8—31no—
204C2×C3×Q8—32no—
205C2×C3×D4—32no—
206C22×C3×C4—31no—
207C22×C3×C4—32no—
208C2×#67—62no—
209C2×#67—62no—
210C2×#67—62no—
211C2×#67—64no—
212C22×Dic3—62no—
213#239—64no—
214#239—64no—
215#237—64no—
216#237—64no—
217#235—64no—
218#235—64no—
219#235—64no—
220#235—64no—
221C2×D12—32no—
222C2×D12—32no—
223C2×D12—62no—
224C2×D12—64no—
225C2×D12—62no—
226C2×D12C22×D312yes—
227C2×C4×D3—62no—
228C2×C4×D3—62no—
229C2×C4×D3—62no—
230C2×C4×D3D1212yes—
231C2×C4×D3C22×D311yescharacteristic
232C2×Dic6—32no—
233C2×Dic6—32no—
234C2×Dic6—62no—
235C2×Dic6C22×D312yes—
236C3×Q16—62no—
237C3×SD16—64no—
238C3×D8—62no—
239C2×C3×C8—21no—
240C2×C3×C8—21no—
241C2×C3×C8—31no—
242C2×C3×C8—31no—
243C2×C3×C8—34no—
244C2×C3×C8—34no—
245C2×C3×C8C22×D311yescharacteristic
246C2×C3×C8C22×D311yescharacteristic
247C2×C3×C8C22×D311yescharacteristic
248C2×C3×C8C22×D311yescharacteristic
249C3×C22⋊C4—64no—
250C3×C42—21no—
251C3×C42—32no—
252C3×C42—31no—
253C3×C42C22×D311yescharacteristic
254C3×C42C22×D311yescharacteristic
255#216—64no—
256#215—64no—
257#214—64no—
258#213—64no—
259(C2×D3)⋊C4—24no—
260(C2×D3)⋊C4—64no—
261(C2×D3)⋊C4—64no—
262(C2×D3)⋊C4—124no—
263C4⋊Dic3—64no—
264Dic3⋊C4—64no—
265C4×Dic3D1212yes—
266C4×Dic3C22×D311yescharacteristic
267C2×C3⋊C8C22×D311yescharacteristic
268C2×C3⋊C8C22×D311yescharacteristic
269Dic12—22no—
270Dic12—64no—
271Dic12—62no—
272Dic12—62no—
273Dic12—122no—
274D24—22no—
275D24—64no—
276D24—62no—
277D24—62no—
278D24—122no—
279#204—24no—
280#204—64no—
281#204—64no—
282#204—64no—
283#204—64no—
284#204—124no—
285D3×C8D1214yescomplemented
286D3×C8D1214yescomplemented
287C22×C32C22×D411yescharacteristic
288C2×C3⋊D3—42no—
289C2×C3⋊D3—44no—
290C2×C3×D3—22no—
291C2×C3×D3—42no—
292C2×C3×D3—44no—
293C2×C3×D3#12712yes—
294C32×C4—22no—
295C32×C4C22×D411yescharacteristic
296C32×C4C22×D411yescharacteristic
297C3⋊Dic3—42no—
298C3×Dic3—42no—
299C3×Dic3#12712yes—
300C3×Dic3#13514yescomplemented
301C2×#41—92no—
302C2×#41—92no—
303#135—184no—
304#135—188no—
305#135—184no—
306C2×Q16—31no—
307C2×Q16—92no—
308C2×Q16—91no—
309C2×SD16—32no—
310C2×SD16—92no—
311C2×SD16—92no—
312C2×SD16—92no—
313C2×D8—31no—
314C2×D8—92no—
315C2×D8—91no—
316C22×C8—31no—
317C22×C8—31no—
318C4⋊Q8—92no—
319#127—92no—
320#124—32no—
321#124—92no—
322#121—184no—
323C4×D4—184no—
324C2×C42—31no—
325C4×C8—31no—
326C4×C8—31no—
327C4×C8—31no—
328C4×C8D3211yescharacteristic
329C23×C3—31no—
330C23×C3—62no—
331C22×D3—22no—
332C22×D3—62no—
333C22×D3—62no—
334C22×D3—122no—
335C22×D3C2×D1211yescharacteristic
336C3×Q8—62no—
337C3×Q8—62no—
338C3×D4—62no—
339C3×D4—62no—
340C2×C3×C4—21no—
341C2×C3×C4—22no—
342C2×C3×C4—32no—
343C2×C3×C4—31no—
344C2×C3×C4—32no—
345C2×C3×C4—32no—
346C2×C3×C4—64no—
347C2×C3×C4—62no—
348C2×C3×C4C2×D1212yes—
349C2×C3×C4D3×D412yes—
350C2×C3×C4C23×D311yescharacteristic
351C2×C3×C4C23×D311yescharacteristic
352#67—124no—
353#67—124no—
354#67—124no—
355#67—128no—
356C2×Dic3—22no—
357C2×Dic3—62no—
358C2×Dic3—62no—
359C2×Dic3—122no—
360C2×Dic3—124no—
361C2×Dic3C2×D1211yescharacteristic
362C2×Dic3C2×D1212yes—
363D12—22no—
364D12—22no—
365D12—62no—
366D12—62no—
367D12—62no—
368D12—62no—
369D12—122no—
370D12—122no—
371D12—128no—
372D12—124no—
373C4×D3—24no—
374C4×D3—124no—
375C4×D3—124no—
376C4×D3—124no—
377C4×D3C2×D1212yes—
378C4×D3C2×D1212yes—
379Dic6—22no—
380Dic6—22no—
381Dic6—62no—
382Dic6—62no—
383Dic6—62no—
384Dic6—62no—
385Dic6—122no—
386Dic6—122no—
387C3×C8—22no—
388C3×C8—22no—
389C3×C8—32no—
390C3×C8—32no—
391C3×C8C2×D1212yes—
392C3×C8C2×D1212yes—
393C3×C8D3×D412yes—
394C3×C8D3×D412yes—
395C3⋊C8C2×D1212yes—
396C3⋊C8C2×D1212yes—
397C2×C32C2×#12711yescharacteristic
398C2×C32C2×#13512yes—
399C3⋊D3—82no—
400C3×D3—22no—
401C3×D3—82no—
402#41—184no—
403#41—184no—
404#41—184no—
405#41—184no—
406C2×Q8—32no—
407C2×Q8—92no—
408C2×D4—32no—
409C2×D4—92no—
410C2×D4—184no—
411C2×D4—182no—
412C2×D4—182no—
413C22×C4—31no—
414C22×C4—32no—
415C22×C4—182no—
416C22×C4—182no—
417Q16—62no—
418Q16—184no—
419Q16—182no—
420SD16—64no—
421SD16—184no—
422SD16—184no—
423SD16—184no—
424D8—62no—
425D8—184no—
426D8—182no—
427C2×C8—31no—
428C2×C8—31no—
429C2×C8—34no—
430C2×C8—34no—
431C2×C8C2×D3211yescharacteristic
432C2×C8C2×D3211yescharacteristic
433C4⋊C4—184no—
434C22⋊C4—64no—
435C22⋊C4—184no—
436C42—31no—
437C42—32no—
438C42C2×D3211yescharacteristic
439C22×C3—21no—
440C22×C3—32no—
441C22×C3—62no—
442C22×C3—122no—
443C22×C3—124no—
444C22×C3C22×D1211yescharacteristic
445C22×C3C2×D3×D411yescharacteristic
446C2×D3—22no—
447C2×D3—42no—
448C2×D3—44no—
449C2×D3—122no—
450C2×D3—122no—
451C2×D3—124no—
452C2×D3—124no—
453C2×D3—242no—
454C2×D3—244no—
455C2×D3#87412yes—
456C3×C4—22no—
457C3×C4—22no—
458C3×C4—21no—
459C3×C4—21no—
460C3×C4—32no—
461C3×C4—34no—
462C3×C4—42no—
463C3×C4—122no—
464C3×C4C22×D1211yescharacteristic
465C3×C4C22×D1211yescharacteristic
466C3×C4C2×D3×D411yescharacteristic
467C3×C4C2×D3×D411yescharacteristic
468Dic3—42no—
469Dic3—122no—
470Dic3—122no—
471Dic3—242no—
472Dic3#87412yes—
473Dic3#90414yescomplemented
474C32#314711yescharacteristic, complemented, Sylow
475C23—31no—
476C23—62no—
477C23—182no—
478Q8—62no—
479Q8—62no—
480Q8—182no—
481Q8—182no—
482D4—62no—
483D4—62no—
484D4—182no—
485D4—182no—
486D4—368no—
487D4—364no—
488D4—364no—
489C2×C4—32no—
490C2×C4—31no—
491C2×C4—32no—
492C2×C4—32no—
493C2×C4—64no—
494C2×C4—62no—
495C2×C4—182no—
496C2×C4—364no—
497C2×C4—364no—
498C2×C4D3×D1212yes—
499C2×C4C22×D3211yescharacteristic
500C8—32no—
501C8—32no—
502C8D3×D1212yes—
503C8D3×D1212yes—
504C2×C3—22no—
505C2×C3—21no—
506C2×C3—62no—
507C2×C3—242no—
508C2×C3C2×#87411yescharacteristic
509C2×C3D3×#12711yescharacteristic
510C2×C3C2×#90412yes—
511C2×C3D3×#13512yes—
512D3—22no—
513D3—82no—
514D3—242no—
515D3—242no—
516D3—482no—
517C22—32no—
518C22—62no—
519C22—124no—
520C22—122no—
521C22—364no—
522C22—362no—
523C22C2×D3×D1211yescharacteristic
524C4—22no—
525C4—34no—
526C4—32no—
527C4—122no—
528C4—362no—
529C4C2×D3×D1211yescharacteristic
530C4C2×D3×D1211yescharacteristic
531C3—21no—
532C3#7846711yescharacteristic, complemented
533C3#8182011yescharacteristic, complemented
534C2—62no—
535C2—242no—
536C2—722no—
537C2D3×#87411yescharacteristic
538C2D3×#90412yes—
subgroupG/H
centerC22C2×D3×D12
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4×C8C22
socleC22×C32C22×D4
hypercenterC4×C8D32
hypocenterC32#3147
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8

Complements

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

NH ≅ G/Ntype
1. C2×#63808C2semidirect
2. C2×#63807C2semidirect
3. C2×#63806C2semidirect
4. #10593969C2semidirect
5. #10592395C2semidirect
6. C3×#4696C2semidirect
7. C3×C4×D3×C8C2semidirect
8. #10590896C2semidirect
9. #10590880C2semidirect
10. #10590877C2semidirect
11. #10590370C2semidirect
61. #4696D3semidirect
64. C4×D3×C8D3semidirect
95. C3×D3×C8D4semidirect
96. C3×D3×C8D4semidirect
285. D3×C8D12semidirect
286. D3×C8D12semidirect
300. C3×Dic3#135semidirect
473. Dic3#904semidirect
474. C32#3147semidirect
532. C3#78467semidirect
533. C3#81820semidirect

Maximal subgroups

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

subgroupindex
C2×#638082
C2×#638072
C2×#638062
#105939692
#105923952
C3×#46962
C3×C4×D3×C82
#105908962
#105908802
#105908772
#105903702
#818203
#784673