Finite Group Databasebeta

← D3×#5086 #11874391

Subgroups — D3×#5086 #11874391

Order 1152.

1190 conjugacy classes of subgroups.

The subgroup lattice has 564 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×D3×C4⋊Q8C211yesmaximal, characteristic, complemented
2C2×D3×#216C212yesmaximal, complemented
3C2×D3×#215C212yesmaximal
4D3×#875C211yesmaximal, characteristic
5#10592785C211yesmaximal, characteristic, complemented
6C3×#5086C211yesmaximal, characteristic, complemented
7#10591608C212yesmaximal, complemented
8#10591605C212yesmaximal, complemented
9#10590376C211yesmaximal, characteristic, complemented
10#10590374C211yesmaximal, characteristic, complemented
11D3×#803C211yesmaximal, characteristic, complemented
12C2×#5086—31nomaximal
13D3×#497—31nomaximal
14C2×C3×D3×Q8C2212yes—
15C2×D3×D12C2211yescharacteristic
16C2×D3×Dic6C2211yescharacteristic
17C32×C4⋊Q8C2211yescharacteristic, complemented
18C2×#3756C2212yescomplemented
19C2×#3755C2212yes—
20#64084C2211yescharacteristic
21C3×#944C2212yescomplemented
22C2×C3×#216C2212yescomplemented
23C2×C3×#215C2212yes—
24C3×D3×C4⋊C4—22no—
25C3×#888—22no—
26C3×#875C2211yescharacteristic
27C3×C42×D3C2211yescharacteristic
28C3×#869C2211yescharacteristic, complemented
29D3×#216—28no—
30D3×#215—28no—
31D3×(C2×D3)⋊C4—22no—
32#63864C2211yescharacteristic
33#63860C2211yescharacteristic
34#63852—22no—
35C2×#3719C2212yescomplemented
36C2×#3718C2212yescomplemented
37C2×#3717C2212yes—
38C2×#3715C2212yes—
39C2×D3×C3⋊C8C2212yes—
40#63630C2211yescharacteristic, complemented
41C3×#803C2211yescharacteristic, complemented
42#63554C2212yescomplemented
43C2×C3×C4⋊Q8—31no—
44C22×#216—32no—
45C22×#215—32no—
46C2×D3×Q16—32no—
47C2×D3×SD16—32no—
48D3×C4⋊Q8D311yescharacteristic, complemented
49D3×#124—31no—
50C2×#875—31no—
51C3×#497—31no—
52#5190—32no—
53#5167—32no—
54#5086—31no—
55#5086—31no—
56#5086—32no—
57#5086—32no—
58#5086—31no—
59#5086—31no—
60#5086—61no—
61#5086D311yescharacteristic, direct product factor
62#5060—31no—
63C2×#803—31no—
64#4715—31no—
65D3×#97—31no—
66C22×D32—21no—
67C2×C32×Q8C2312yes—
68C2×C4⋊(C3⋊D3)C2311yescharacteristic
69C2×#634C2311yescharacteristic
70C3×D3×Q8—24no—
71C3×D3×Q8—24no—
72C2×C3×D12C2311yescharacteristic
73C2×C3×C4×D3—22no—
74C2×C3×C4×D3D412yes—
75C2×C3×C4×D3C2311yescharacteristic
76C2×C3×Dic6—22no—
77C2×C3×Dic6C2311yescharacteristic
78C2×C3×Dic6C2312yes—
79C2×#627—21no—
80C2×#626—21no—
81C2×D3×Dic3—21no—
82D3×D12—24no—
83D3×Dic6—24no—
84C32×C4⋊C4—22no—
85C32×C42C2311yescharacteristic
86#3756—24no—
87#3755—24no—
88#3752—22no—
89C2×C3⋊(C3⋊C8)C2312yes—
90C3×#216—24no—
91C3×#215—24no—
92C3×(C2×D3)⋊C4—22no—
93C3×C4⋊Dic3—22no—
94C3×Dic3⋊C4—24no—
95C3×C4×Dic3D412yes—
96C3×C4×Dic3C2311yescharacteristic
97C2×C3×C3⋊C8C2312yes—
98#3722—22no—
99(C2×D3)⋊Dic3—22no—
100#3719—24no—
101#3718—24no—
102#3717—24no—
103#3715—24no—
104D3×C3⋊C8D418yes—
105C2×#497—91noSylow
106C22×C3×Q8—32no—
107C2×D3×Q8—31no—
108C2×D3×Q8C2×D312yes—
109C2×D3×D4—31no—
110C22×D12—31no—
111C22×Dic6—31no—
112C2×C3×Q16—32no—
113C2×C3×SD16—32no—
114C3×C4⋊Q8—21no—
115C3×C4⋊Q8—32no—
116C3×C4⋊Q8—31no—
117C3×C4⋊Q8—62no—
118C3×C4⋊Q8C2×D311yescharacteristic, complemented
119C3×C4⋊Q8C2×D311yescharacteristic, complemented
120C3×#124—31no—
121C2×C3×C4⋊C4—62no—
122C2×C3×C42—31no—
123#947—31no—
124#944C2×D312yescomplemented
125C2×#216—32no—
126C2×#216—32no—
127C2×#216—32no—
128C2×#216—32no—
129C2×#216—32no—
130C2×#216—62no—
131C2×#216—68no—
132C2×#216C2×D312yescomplemented
133C2×#215—32no—
134C2×#215—32no—
135C2×#215—32no—
136C2×#215—32no—
137C2×#215—62no—
138C2×#215—68no—
139C2×#215C2×D312yes—
140#936—31no—
141C2×#214—32no—
142C2×(C2×D3)⋊C4—62no—
143C22×C3⋊C8—32no—
144D3×Q16—68no—
145D3×SD16—68no—
146C2×Dic12—32no—
147C2×#204—32no—
148C2×D3×C8—32no—
149D3×C4⋊C4—22no—
150#888—22no—
151#885—62no—
152D3×C22⋊C4—62no—
153#875—31no—
154#875—31no—
155#875—31no—
156#875—31no—
157#875—61no—
158#875—62no—
159#875C2×D311yescharacteristic
160C42×D3C2×D311yescharacteristic
161#869C2×D311yescharacteristic, complemented
162C3×#97—31no—
163#815—32no—
164#803—31no—
165#803—31no—
166#803—32no—
167#803—61no—
168#803C2×D311yescharacteristic, complemented
169C22×C3⋊D3—21no—
170C22×C3×D3—21no—
171C22×C3×D3C2×D411yescharacteristic
172C2×D32—42no—
173C2×D32—44no—
174C32×Q8—22no—
175C32×Q8—22no—
176C2×C32×C4—22no—
177C2×C32×C4C2×D412yes—
178C2×C32×C4C2411yescharacteristic
179C2×C3⋊Dic3—21no—
180C4⋊(C3⋊D3)—22no—
181#634—22no—
182C2×C3×Dic3—21no—
183C2×C3×Dic3—22no—
184C2×C3×Dic3C2×D412yes—
185C2×C3×Dic3C2×D411yescharacteristic
186C3×D12—22no—
187C3×C4×D3—24no—
188C3×C4×D3—44no—
189C3×C4×D3C2×D414yes—
190C3×Dic6—22no—
191C3×Dic6—22no—
192C3×Dic6—22no—
193C3×Dic6—44no—
194#627—42no—
195#626—42no—
196D3×Dic3—42no—
197C3⋊(C3⋊C8)C2×D414yes—
198C3×C3⋊C8C2×D414yes—
199C22×Q16—92no—
200C22×SD16—92no—
201C2×C4⋊Q8—31no—
202C2×#124—91no—
203#497—31no—
204#497—91no—
205#497—91no—
206#497—92no—
207#497—92no—
208#497—91no—
209C2×#97—91no—
210C23×D3—61no—
211C23×D3—61no—
212C2×C3×Q8—22no—
213C2×C3×Q8—32no—
214C2×C3×Q8—31no—
215C2×C3×Q8—62no—
216C2×C3×Q8—64no—
217C2×C3×Q8—64no—
218C2×C3×Q8C22×D312yes—
219C2×C3×Q8C22×D312yes—
220C2×C3×D4—31no—
221C22×C3×C4—31no—
222C22×C3×C4—32no—
223C22×C3×C4—62no—
224C2×#67—61no—
225C22×Dic3—61no—
226D3×Q8—24no—
227D3×Q8—24no—
228D3×Q8—64no—
229D3×D4—64no—
230C2×D12—31no—
231C2×D12—31no—
232C2×D12—61no—
233C2×D12—64no—
234C2×D12—61no—
235C2×D12C22×D311yescharacteristic
236C2×C4×D3—22no—
237C2×C4×D3—61no—
238C2×C4×D3#6712yes—
239C2×C4×D3C22×D311yescharacteristic
240C2×Dic6—22no—
241C2×Dic6—31no—
242C2×Dic6—31no—
243C2×Dic6—61no—
244C2×Dic6—64no—
245C2×Dic6—61no—
246C2×Dic6—61no—
247C2×Dic6C22×D312yes—
248C2×Dic6C22×D311yescharacteristic
249C3×Q16—64no—
250C3×SD16—64no—
251C2×C3×C8—32no—
252C3×C4⋊C4—22no—
253C3×C4⋊C4—22no—
254C3×C4⋊C4—42no—
255C3×C4⋊C4—64no—
256C3×C4⋊C4—62no—
257C3×C22⋊C4—62no—
258C3×C42—21no—
259C3×C42—32no—
260C3×C42—31no—
261C3×C42C22×D311yescharacteristic
262C3×C42C22×D311yescharacteristic
263#217—62no—
264#216—24no—
265#216—64no—
266#216—64no—
267#216—64no—
268#216—64no—
269#216—64no—
270#216—124no—
271#215—24no—
272#215—64no—
273#215—64no—
274#215—64no—
275#215—64no—
276#215—124no—
277#214—64no—
278(C2×D3)⋊C4—22no—
279(C2×D3)⋊C4—62no—
280(C2×D3)⋊C4—62no—
281(C2×D3)⋊C4—62no—
282(C2×D3)⋊C4—62no—
283(C2×D3)⋊C4—62no—
284(C2×D3)⋊C4—122no—
285C4⋊Dic3—22no—
286Dic3⋊C4—24no—
287C4×Dic3#6712yes—
288C4×Dic3C22×D311yescharacteristic
289C2×C3⋊C8—32no—
290C2×C3⋊C8—32no—
291C2×C3⋊C8—38no—
292C2×C3⋊C8—62no—
293C2×C3⋊C8C22×D312yes—
294Dic12—64no—
295#204—64no—
296D3×C8—38no—
297C22×C32C22×D411yescharacteristic
298C2×C3⋊D3—41no—
299C2×C3⋊D3—42no—
300C2×C3×D3—41no—
301C2×C3×D3—42no—
302C2×C3×D3#12712yes—
303C2×C3×D3#13714yes—
304D32—84no—
305C32×C4—22no—
306C32×C4—42no—
307C32×C4C22×D412yes—
308C3⋊Dic3—41no—
309C3×Dic3—22no—
310C3×Dic3—41no—
311C3×Dic3—42no—
312C3×Dic3#12712yes—
313C22×Q8—32no—
314C22×Q8—91no—
315C22×D4—91no—
316C2×Q16—32no—
317C2×Q16—92no—
318C2×Q16—92no—
319C2×Q16—92no—
320C2×Q16—188no—
321C2×SD16—32no—
322C2×SD16—92no—
323C2×SD16—92no—
324C2×SD16—92no—
325C2×SD16—188no—
326C22×C8—92no—
327C4⋊Q8—32no—
328C4⋊Q8—31no—
329C4⋊Q8—62no—
330C4⋊Q8D3211yescharacteristic, complemented
331#124—31no—
332#124—91no—
333#124—91no—
334#124—91no—
335#124—182no—
336C2×C4⋊C4—62no—
337C2×C22⋊C4—182no—
338C2×C42—31no—
339#97—31no—
340#97—92no—
341#97—91no—
342C23×C3—31no—
343C23×C3—61no—
344C22×D3—21no—
345C22×D3—61no—
346C22×D3—61no—
347C22×D3—121no—
348C22×D3—122no—
349C22×D3—124no—
350C22×D3—122no—
351C22×D3—124no—
352C22×D3C2×#6711yescharacteristic
353C3×Q8—22no—
354C3×Q8—22no—
355C3×Q8—22no—
356C3×Q8—22no—
357C3×Q8—42no—
358C3×Q8—42no—
359C3×Q8—62no—
360C3×Q8—62no—
361C3×Q8—62no—
362C3×Q8—124no—
363C3×D4—62no—
364C2×C3×C4—22no—
365C2×C3×C4—22no—
366C2×C3×C4—21no—
367C2×C3×C4—22no—
368C2×C3×C4—31no—
369C2×C3×C4—34no—
370C2×C3×C4—32no—
371C2×C3×C4—42no—
372C2×C3×C4—64no—
373C2×C3×C4—62no—
374C2×C3×C4—61no—
375C2×C3×C4—124no—
376C2×C3×C4D3×D412yes—
377C2×C3×C4C2×#6712yes—
378C2×C3×C4C23×D311yescharacteristic
379C2×C3×C4C23×D311yescharacteristic
380#67—122no—
381C2×Dic3—21no—
382C2×Dic3—22no—
383C2×Dic3—61no—
384C2×Dic3—61no—
385C2×Dic3—121no—
386C2×Dic3—122no—
387C2×Dic3C2×#6712yes—
388C2×Dic3C2×#6711yescharacteristic
389D12—22no—
390D12—62no—
391D12—62no—
392D12—122no—
393D12—122no—
394C4×D3—24no—
395C4×D3—44no—
396C4×D3—122no—
397C4×D3D3×D414yes—
398Dic6—22no—
399Dic6—22no—
400Dic6—22no—
401Dic6—44no—
402Dic6—62no—
403Dic6—62no—
404Dic6—122no—
405Dic6—122no—
406Dic6—122no—
407C3×C8—34no—
408C3⋊C8—34no—
409C3⋊C8—34no—
410C3⋊C8—64no—
411C3⋊C8D3×D414yes—
412C2×C32C2×#12711yescharacteristic
413C2×C32C2×#13712yes—
414C3⋊D3—81no—
415C3×D3—81no—
416C3×D3#49714yescomplemented
417C24—181no—
418C2×Q8—31no—
419C2×Q8—32no—
420C2×Q8—62no—
421C2×Q8—64no—
422C2×Q8—64no—
423C2×Q8—91no—
424C2×Q8—181no—
425C2×Q8—184no—
426C2×Q8C2×D3212yes—
427C2×D4—31no—
428C2×D4—91no—
429C2×D4—184no—
430C2×D4—181no—
431C22×C4—31no—
432C22×C4—32no—
433C22×C4—62no—
434C22×C4—181no—
435Q16—64no—
436Q16—184no—
437Q16—184no—
438Q16—184no—
439SD16—64no—
440SD16—184no—
441SD16—184no—
442SD16—184no—
443C2×C8—32no—
444C2×C8—98no—
445C2×C8—92no—
446C4⋊C4—22no—
447C4⋊C4—64no—
448C4⋊C4—62no—
449C22⋊C4—62no—
450C22⋊C4—182no—
451C22⋊C4—182no—
452C22⋊C4—182no—
453C42—31no—
454C42—32no—
455C42C2×D3211yescharacteristic
456C22×C3—21no—
457C22×C3—32no—
458C22×C3—34no—
459C22×C3—121no—
460C22×C3—122no—
461C22×C3C2×D3×D411yescharacteristic
462C22×C3C22×#6711yescharacteristic
463C2×D3—41no—
464C2×D3—42no—
465C2×D3—121no—
466C2×D3—122no—
467C2×D3—121no—
468C2×D3—122no—
469C2×D3—241no—
470C2×D3—242no—
471C2×D3—244no—
472C2×D3—244no—
473C2×D3#94012yes—
474C2×D3#94214yes—
475C3×C4—22no—
476C3×C4—22no—
477C3×C4—22no—
478C3×C4—32no—
479C3×C4—42no—
480C3×C4—42no—
481C3×C4—42no—
482C3×C4—62no—
483C3×C4—82no—
484C3×C4—122no—
485C3×C4—121no—
486C3×C4C2×D3×D412yes—
487C3×C4C2×D3×D412yes—
488Dic3—22no—
489Dic3—41no—
490Dic3—42no—
491Dic3—121no—
492Dic3—121no—
493Dic3—241no—
494Dic3#94012yes—
495C32C2×#49711yescharacteristic, complemented, Sylow
496C23—31no—
497C23—61no—
498C23—181no—
499C23—362no—
500C23—364no—
501Q8—22no—
502Q8—22no—
503Q8—62no—
504Q8—62no—
505Q8—62no—
506Q8—124no—
507Q8—182no—
508Q8—362no—
509D4—62no—
510D4—182no—
511D4—362no—
512C2×C4—22no—
513C2×C4—31no—
514C2×C4—34no—
515C2×C4—32no—
516C2×C4—64no—
517C2×C4—61no—
518C2×C4—62no—
519C2×C4—124no—
520C2×C4—181no—
521C2×C4—362no—
522C2×C4D3×#6712yes—
523C2×C4C22×D3211yescharacteristic
524C8—34no—
525C8—94no—
526C2×C3—21no—
527C2×C3—22no—
528C2×C3—34no—
529C2×C3—241no—
530C2×C3D3×#12711yescharacteristic
531C2×C3D3×#13712yes—
532C2×C3C2×#94011yescharacteristic
533C2×C3C2×#94212yes—
534D3—81no—
535D3—241no—
536D3—241no—
537D3—481no—
538D3#508614yesdirect product factor
539C22—32no—
540C22—34no—
541C22—121no—
542C22—122no—
543C22—361no—
544C22—362no—
545C22—724no—
546C22C2×D3×#6711yescharacteristic
547C4—22no—
548C4—32no—
549C4—42no—
550C4—62no—
551C4—122no—
552C4—121no—
553C4—361no—
554C4D32×D412yes—
555C3—21no—
556C3D3×#49711yescharacteristic, complemented
557C3C2×#508611yescharacteristic, complemented
558C2—34no—
559C2—241no—
560C2—721no—
561C2D3×#94011yescharacteristic
562C2D3×#94212yes—
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4⋊Q8C22
socleC22×C32C22×D4
prime radicalC2×D3×D12C22
hypercenterC4⋊Q8D32
hypocenterC32C2×#497
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊Q8

Complements

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

NH ≅ G/Ntype
1. C3×D3×C4⋊Q8C2semidirect
2. C2×D3×#216C2semidirect
5. #10592785C2semidirect
6. C3×#5086C2semidirect
7. #10591608C2semidirect
8. #10591605C2semidirect
9. #10590376C2semidirect
10. #10590374C2semidirect
11. D3×#803C2semidirect
17. C32×C4⋊Q8C22semidirect
18. C2×#3756C22semidirect
21. C3×#944C22semidirect
22. C2×C3×#216C22semidirect
28. C3×#869C22semidirect
35. C2×#3719C22semidirect
36. C2×#3718C22semidirect
40. #63630C22semidirect
41. C3×#803C22semidirect
42. #63554C22semidirect
48. D3×C4⋊Q8D3semidirect
61. #5086D3direct (N × H)
118. C3×C4⋊Q8C2×D3semidirect
119. C3×C4⋊Q8C2×D3semidirect
124. #944C2×D3semidirect
132. C2×#216C2×D3semidirect
161. #869C2×D3semidirect
168. #803C2×D3semidirect
330. C4⋊Q8D32semidirect
416. C3×D3#497semidirect
495. C32C2×#497semidirect
538. D3#5086direct (N × H)
556. C3D3×#497semidirect
557. C3C2×#5086semidirect

Maximal subgroups

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

subgroupindex
C3×D3×C4⋊Q82
C2×D3×#2162
C2×D3×#2152
D3×#8752
#105927852
C3×#50862
#105916082
#105916052
#105903762
#105903742
D3×#8032
C2×#50863
D3×#4973