Finite Group Databasebeta

← D3×#5101 #11857196

Subgroups — D3×#5101 #11857196

Order 1152.

1249 conjugacy classes of subgroups.

The subgroup lattice has 531 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×D3×C8C211yesmaximal, characteristic
2D3×#926C211yesmaximal, characteristic
3C2×D3×#208C211yesmaximal, characteristic
4#10592800C211yesmaximal, characteristic, complemented
5C3×#5101C211yesmaximal, characteristic, complemented
6#10591059C211yesmaximal, characteristic, complemented
7#10591055C211yesmaximal, characteristic, complemented
8#10590693C212yesmaximal, complemented
9#10590692C212yesmaximal, complemented
10D3×#815C212yesmaximal, complemented
11D3×C8×Dic3C212yesmaximal, complemented
12C2×#5101—31nomaximal
13D3×#405—31nomaximal
14C22×C3×C4×D3C2211yescharacteristic
15C22×C32×C8C2211yescharacteristic
16#64135C2211yescharacteristic
17C2×#3748C2211yescharacteristic
18C3×#926C2211yescharacteristic
19C2×C3×#208C2211yescharacteristic
20C22×C3×C3⋊C8C2211yescharacteristic
21C2×C3×D3×C8C418yescomplemented
22C2×C3×D3×C8C2211yescharacteristic
23C2×C3×D3×C8C2211yescharacteristic
24C2×C3×D3×C8C2211yescharacteristic
25C2×C3×D3×C8C2211yescharacteristic
26D3×#217C412yes—
27#63955C412yes—
28D3×C4⋊Dic3C412yes—
29C4×D3×Dic3C2212yes—
30#63855C2212yes—
31#63841C412yes—
32C2×#3711C2212yes—
33D3×#208C418yescomplemented
34C2×D3×C3⋊C8C2212yes—
35#63642C2212yescomplemented
36C8×C3⋊Dic3C2212yescomplemented
37C3×#815C2212yescomplemented
38C3×C8×Dic3C2212yescomplemented
39#63555C2212yescomplemented
40#63554C2212yescomplemented
41#63553C2212yescomplemented
42Dic3×C3⋊C8C2212yescomplemented
43C23×C3×C8—31no—
44C2×#926—31no—
45C22×#208—31no—
46C2×D3×M16—31no—
47C22×D3×C8D311yescharacteristic
48D3×#117—31no—
49C3×#405—31no—
50#5122—31no—
51#5101—31no—
52#5101—31no—
53#5101—31no—
54#5101—31no—
55#5101—32no—
56#5101—32no—
57#5101—61no—
58#5101D311yescharacteristic, direct product factor
59C2×#815—32no—
60C2×C8×Dic3—32no—
61#4997—31no—
62#4708—32no—
63D3×#97—32no—
64#4689—32no—
65C4×D3×C8—32no—
66C23×C3×D3C2×C411yescharacteristic
67C22×C32×C4C2311yescharacteristic
68C22×C3×Dic3C2×C411yescharacteristic
69C2×C3×C4×D3C2×C411yescharacteristic
70C2×C3×C4×D3C2×C411yescharacteristic
71C2×C3×C4×D3C2×C414yes—
72C2×C3×C4×D3C2×C414yes—
73C2×C3×C4×D3C2311yescharacteristic
74C2×C3×C4×D3C2311yescharacteristic
75C2×D3×Dic3C2×C414yes—
76C2×C32×C8C2×C414yescomplemented
77C2×C32×C8C2311yescharacteristic
78C2×C32×C8C2311yescharacteristic
79#3757C2×C412yes—
80C4⋊(C3⋊Dic3)C2×C412yes—
81C4×C3⋊Dic3C2312yes—
82#3748C2×C414yescomplemented
83C2×C3⋊(C3⋊C8)C2312yes—
84C3×#217C2×C412yes—
85C3×C4⋊Dic3C2×C412yes—
86C3×C4×Dic3C2312yes—
87C3×#208C2×C414yescomplemented
88C2×C3×C3⋊C8C2×C414yescomplemented
89C2×C3×C3⋊C8C2311yescharacteristic
90C2×C3×C3⋊C8C2311yescharacteristic
91C2×C3×C3⋊C8C2312yes—
92C3×D3×C8C2×C414yes—
93C3×D3×C8C2×C414yes—
94C3×D3×C8C2×C414yescomplemented
95C3×D3×C8C2×C414yescomplemented
96Dic3⋊Dic3C2×C414yes—
97(C2×D3)⋊Dic3C2×C414yes—
98Dic32C2×C414yes—
99#3711C2×C418yescomplemented
100D3×C3⋊C8C2×C418yes—
101C2×#405—91noSylow
102C23×C3×C4—31no—
103C22×C4×D3C2×D311yescharacteristic
104C2×C3×M16—31no—
105C22×C3×C8—21no—
106C22×C3×C8—31no—
107C22×C3×C8—38no—
108C22×C3×C8—31no—
109C22×C3×C8—31no—
110C22×C3×C8—31no—
111C22×C3×C8—31no—
112C22×C3×C8C2×D311yescharacteristic
113C22×C3×C8C2×D311yescharacteristic
114C3×#117—31no—
115C2×#217—32no—
116#926—31no—
117#926—31no—
118#926—32no—
119#926—32no—
120#926—32no—
121#926—61no—
122#926C2×D311yescharacteristic
123C2×C4⋊Dic3—32no—
124C2×C4×Dic3—32no—
125C2×#208—31no—
126C2×#208—31no—
127C2×#208—38no—
128C2×#208—32no—
129C2×#208—61no—
130C2×#208C2×D311yescharacteristic
131C22×C3⋊C8—32no—
132C22×C3⋊C8C2×D311yescharacteristic
133D3×M16—38no—
134C2×ΓL(1,𝔽25)—32no—
135C2×D3×C8—32no—
136C2×D3×C8Dic318yescomplemented
137C2×D3×C8C2×D311yescharacteristic
138C2×D3×C8C2×D311yescharacteristic
139C2×D3×C8C2×D311yescharacteristic
140C2×D3×C8C2×D311yescharacteristic
141#892—32no—
142D3×C4⋊C4—32no—
143D3×C22⋊C4—32no—
144#877—32no—
145#872—32no—
146C42×D3—32no—
147C3×#97—32no—
148C3×C4×C8—32no—
149#815—32no—
150#815—32no—
151#815—32no—
152#815—32no—
153#815—32no—
154#815—62no—
155#815C2×D312yescomplemented
156C8×Dic3—32no—
157C8×Dic3—32no—
158C8×Dic3—32no—
159C8×Dic3—32no—
160C8×Dic3—32no—
161C8×Dic3—62no—
162C8×Dic3C2×D312yescomplemented
163#803—32no—
164C4×C3⋊C8—32no—
165C23×C32C22×C411yescharacteristic
166C22×C3×D3—24no—
167C22×C3×D3C4214yes—
168C22×C3×D3C22×C411yescharacteristic
169C22×C3×D3C22×C411yescharacteristic
170C2×C32×C4C22×C411yescharacteristic
171C2×C32×C4C22×C412yes—
172C2×C32×C4C22×C412yes—
173C2×C32×C4C2411yescharacteristic
174C2×C3⋊Dic3C22×C414yes—
175C2×C3×Dic3C4214yes—
176C2×C3×Dic3C22×C414yes—
177C2×C3×Dic3C22×C411yescharacteristic
178C2×C3×Dic3C22×C411yescharacteristic
179C3×C4×D3C4214yes—
180C3×C4×D3C4214yes—
181C3×C4×D3C22×C412yes—
182C3×C4×D3C22×C412yes—
183C3×C4×D3C22×C412yes—
184C3×C4×D3C22×C412yes—
185D3×Dic3—28no—
186C32×C8C22×C412yes—
187C32×C8C22×C412yes—
188C3⋊(C3⋊C8)C22×C414yes—
189C3×C3⋊C8C22×C414yes—
190C3×C3⋊C8C22×C412yes—
191C3×C3⋊C8C22×C412yes—
192C22×M16—91no—
193C23×C8—31no—
194C2×#117—91no—
195#405—31no—
196#405—92no—
197#405—92no—
198#405—91no—
199#405—91no—
200#405—91no—
201C2×#97—92no—
202C2×C4×C8—92no—
203C24×C3—31no—
204C23×D3C4×D311yescharacteristic
205C22×C3×C4—21no—
206C22×C3×C4—31no—
207C22×C3×C4—34no—
208C22×C3×C4—31no—
209C22×C3×C4—31no—
210C22×C3×C4—34no—
211C22×C3×C4—31no—
212C22×C3×C4—31no—
213C22×C3×C4C22×D311yescharacteristic
214C22×C3×C4C22×D311yescharacteristic
215C22×Dic3—34no—
216C22×Dic3C4×D311yescharacteristic
217C2×C4×D3—34no—
218C2×C4×D3C4×D311yescharacteristic
219C2×C4×D3C4×D311yescharacteristic
220C2×C4×D3C4×D314yes—
221C2×C4×D3C2×Dic314yes—
222C2×C4×D3C22×D311yescharacteristic
223C2×C4×D3C22×D311yescharacteristic
224C3×M16—34no—
225C2×C3×C8—24no—
226C2×C3×C8—21no—
227C2×C3×C8—21no—
228C2×C3×C8—34no—
229C2×C3×C8—31no—
230C2×C3×C8—32no—
231C2×C3×C8—31no—
232C2×C3×C8—34no—
233C2×C3×C8—34no—
234C2×C3×C8—34no—
235C2×C3×C8—34no—
236C2×C3×C8C4×D314yescomplemented
237C2×C3×C8C2×Dic314yescomplemented
238C2×C3×C8C22×D311yescharacteristic
239C2×C3×C8C22×D311yescharacteristic
240C2×C3×C8C22×D311yescharacteristic
241C2×C3×C8C22×D311yescharacteristic
242C3×C4⋊C4—32no—
243C3×C22⋊C4—32no—
244C3×C42—32no—
245#217—32no—
246#217—32no—
247#217—34no—
248#217—62no—
249#217C4×D312yes—
250(C2×D3)⋊C4—34no—
251C4⋊Dic3—32no—
252C4⋊Dic3—32no—
253C4⋊Dic3—34no—
254C4⋊Dic3—62no—
255C4⋊Dic3C4×D312yes—
256Dic3⋊C4—34no—
257C4×Dic3—32no—
258C4×Dic3—32no—
259C4×Dic3—34no—
260C4×Dic3—34no—
261C4×Dic3—62no—
262C4×Dic3C22×D312yes—
263#208—34no—
264#208—34no—
265#208—38no—
266#208—64no—
267#208C4×D314yescomplemented
268C2×C3⋊C8—32no—
269C2×C3⋊C8—32no—
270C2×C3⋊C8—38no—
271C2×C3⋊C8—62no—
272C2×C3⋊C8C2×Dic314yescomplemented
273C2×C3⋊C8C22×D312yes—
274C2×C3⋊C8C22×D311yescharacteristic
275C2×C3⋊C8C22×D311yescharacteristic
276ΓL(1,𝔽25)—38no—
277D3×C8—38no—
278D3×C8C2×Dic314yes—
279D3×C8C2×Dic314yes—
280D3×C8C2×Dic314yescomplemented
281D3×C8C2×Dic314yescomplemented
282C22×C32—22no—
283C22×C32C2×C4212yes—
284C22×C32C23×C411yescharacteristic
285C2×C3×D3—22no—
286C2×C3×D3—28no—
287C2×C3×D3C2×C4212yes—
288C2×C3×D3C2×C4212yes—
289C2×C3×D3#13114yes—
290C32×C4C2×C4212yes—
291C32×C4C23×C411yescharacteristic
292C32×C4C23×C411yescharacteristic
293C3⋊Dic3—24no—
294C3×Dic3—24no—
295C3×Dic3C2×C4212yes—
296C3×Dic3C2×C4212yes—
297C23×C4—31no—
298C2×M16—31no—
299C2×M16—92no—
300C2×M16—98no—
301C2×M16—91no—
302C22×C8—31no—
303C22×C8—38no—
304C22×C8—31no—
305C22×C8—31no—
306C22×C8—31no—
307C22×C8—31no—
308C22×C8—92no—
309C22×C8D3211yescharacteristic
310#117—31no—
311#117—92no—
312#117—92no—
313#117—92no—
314#117—91no—
315C2×C4⋊C4—92no—
316C2×C22⋊C4—92no—
317C2×C42—92no—
318#97—32no—
319#97—92no—
320#97—92no—
321#97—92no—
322C4×C8—32no—
323C4×C8—92no—
324C4×C8—92no—
325C4×C8—92no—
326C23×C3—21no—
327C23×C3—31no—
328C23×C3—34no—
329C23×C3—31no—
330C23×C3—64no—
331C23×C3C2×C4×D311yescharacteristic
332C23×C3C2×C4×D311yescharacteristic
333C22×D3—24no—
334C22×D3C4×Dic314yes—
335C22×D3C2×C4×D311yescharacteristic
336C22×D3C2×C4×D311yescharacteristic
337C2×C3×C4—21no—
338C2×C3×C4—22no—
339C2×C3×C4—21no—
340C2×C3×C4—22no—
341C2×C3×C4—34no—
342C2×C3×C4—31no—
343C2×C3×C4—31no—
344C2×C3×C4—34no—
345C2×C3×C4—34no—
346C2×C3×C4—32no—
347C2×C3×C4—32no—
348C2×C3×C4—32no—
349C2×C3×C4—32no—
350C2×C3×C4—34no—
351C2×C3×C4C2×C4×D311yescharacteristic
352C2×C3×C4C2×C4×D312yes—
353C2×C3×C4C2×C4×D311yescharacteristic
354C2×C3×C4C2×C4×D312yes—
355C2×C3×C4C2×C4×D312yes—
356C2×C3×C4C22×Dic312yes—
357C2×C3×C4C23×D311yescharacteristic
358C2×C3×C4C23×D311yescharacteristic
359C2×Dic3—34no—
360C2×Dic3—34no—
361C2×Dic3—64no—
362C2×Dic3—68no—
363C2×Dic3C4×Dic314yes—
364C2×Dic3C2×C4×D314yes—
365C2×Dic3C2×C4×D311yescharacteristic
366C2×Dic3C2×C4×D311yescharacteristic
367C4×D3—68no—
368C4×D3C4×Dic314yes—
369C4×D3C4×Dic314yes—
370C4×D3C2×C4×D312yes—
371C4×D3C2×C4×D312yes—
372C4×D3C22×Dic312yes—
373C4×D3C22×Dic312yes—
374C3×C8—22no—
375C3×C8—22no—
376C3×C8—34no—
377C3×C8—32no—
378C3×C8—32no—
379C3×C8C2×C4×D312yes—
380C3×C8C2×C4×D312yes—
381C3×C8C22×Dic312yes—
382C3×C8C22×Dic312yes—
383C3⋊C8—34no—
384C3⋊C8—34no—
385C3⋊C8—64no—
386C3⋊C8C2×C4×D314yes—
387C3⋊C8C22×Dic312yes—
388C3⋊C8C22×Dic312yes—
389C2×C32—22no—
390C2×C32C22×C4211yescharacteristic
391C2×C32C2×#13112yes—
392C3×D3—22no—
393C3×D3#40514yescomplemented
394C24—31no—
395C22×C4—31no—
396C22×C4—31no—
397C22×C4—31no—
398C22×C4—31no—
399C22×C4—31no—
400C22×C4—34no—
401C22×C4—34no—
402C22×C4—94no—
403C22×C4C2×D3211yescharacteristic
404M16—34no—
405M16—98no—
406M16—94no—
407C2×C8—32no—
408C2×C8—31no—
409C2×C8—31no—
410C2×C8—34no—
411C2×C8—34no—
412C2×C8—34no—
413C2×C8—34no—
414C2×C8—34no—
415C2×C8—98no—
416C2×C8—92no—
417C2×C8D3×Dic314yescomplemented
418C2×C8C2×D3211yescharacteristic
419C2×C8C2×D3211yescharacteristic
420C4⋊C4—32no—
421C4⋊C4—94no—
422C4⋊C4—92no—
423C22⋊C4—32no—
424C22⋊C4—94no—
425C22⋊C4—92no—
426C42—32no—
427C42—94no—
428C42—92no—
429C22×C3—22no—
430C22×C3—22no—
431C22×C3—21no—
432C22×C3—22no—
433C22×C3—32no—
434C22×C3—34no—
435C22×C3—32no—
436C22×C3—42no—
437C22×C3—68no—
438C22×C3—62no—
439C22×C3C42×D312yes—
440C22×C3C2×C4×Dic312yes—
441C22×C3C22×C4×D311yescharacteristic
442C22×C3C22×C4×D311yescharacteristic
443C2×D3—22no—
444C2×D3—28no—
445C2×D3#90114yes—
446C2×D3C2×C4×Dic312yes—
447C2×D3C2×C4×Dic312yes—
448C3×C4—21no—
449C3×C4—21no—
450C3×C4—22no—
451C3×C4—32no—
452C3×C4—32no—
453C3×C4—64no—
454C3×C4C42×D312yes—
455C3×C4C2×C4×Dic312yes—
456C3×C4C22×C4×D311yescharacteristic
457C3×C4C22×C4×D311yescharacteristic
458C3×C4C22×C4×D311yescharacteristic
459C3×C4C23×Dic311yescharacteristic
460Dic3—24no—
461Dic3—64no—
462Dic3—64no—
463Dic3—124no—
464Dic3C2×C4×Dic312yes—
465Dic3C2×C4×Dic312yes—
466C32C2×#40511yescharacteristic, complemented, Sylow
467C23—31no—
468C23—31no—
469C23—34no—
470C23—64no—
471C23C4×D3211yescharacteristic
472C2×C4—31no—
473C2×C4—31no—
474C2×C4—34no—
475C2×C4—32no—
476C2×C4—32no—
477C2×C4—32no—
478C2×C4—32no—
479C2×C4—34no—
480C2×C4—34no—
481C2×C4—34no—
482C2×C4—94no—
483C2×C4—188no—
484C2×C4C4×D3212yes—
485C2×C4C4×D3211yescharacteristic
486C2×C4C2×D3×Dic312yes—
487C2×C4C22×D3211yescharacteristic
488C8—34no—
489C8—32no—
490C8—32no—
491C8—94no—
492C8C2×D3×Dic312yes—
493C8C2×D3×Dic312yes—
494C2×C3—22no—
495C2×C3—22no—
496C2×C3—21no—
497C2×C3—22no—
498C2×C3—34no—
499C2×C3—42no—
500C2×C3—62no—
501C2×C3C2×C42×D311yescharacteristic
502C2×C3C2×#90112yes—
503C2×C3D3×#13112yes—
504C2×C3C22×C4×Dic311yescharacteristic
505D3—22no—
506D3#510114yesdirect product factor
507C22—22no—
508C22—32no—
509C22—34no—
510C22—32no—
511C22—68no—
512C22—62no—
513C22C4×D3×Dic312yes—
514C22C2×C4×D3211yescharacteristic
515C4—32no—
516C4—32no—
517C4—64no—
518C4—184no—
519C4C4×D3×Dic312yes—
520C4C2×C4×D3211yescharacteristic
521C4C22×D3×Dic311yescharacteristic
522C3—21no—
523C3D3×#40511yescharacteristic, complemented
524C3C2×#510111yescharacteristic, complemented
525C2—22no—
526C2—34no—
527C2—62no—
528C2D3×#90112yes—
529C2C2×C4×D3×Dic311yescharacteristic
subgroupG/H
centerC2×C8C2×D32
commutatorC2×C32C22×C42
FrattiniC2×C4C22×D32
FittingC22×C32×C8C22
socleC22×C32C23×C4
prime radicalC23×C3×D3C2×C4
cosocleC2×C32×C4C24
hypercenterC22×C8D32
hypocenterC32C2×#405
LCSG ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C8 ◁ C22×C8

Complements

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

NH ≅ G/Ntype
4. #10592800C2semidirect
5. C3×#5101C2semidirect
6. #10591059C2semidirect
7. #10591055C2semidirect
8. #10590693C2semidirect
9. #10590692C2semidirect
10. D3×#815C2semidirect
11. D3×C8×Dic3C2semidirect
21. C2×C3×D3×C8C4semidirect
33. D3×#208C4semidirect
35. #63642C22semidirect
36. C8×C3⋊Dic3C22semidirect
37. C3×#815C22semidirect
38. C3×C8×Dic3C22semidirect
39. #63555C22semidirect
40. #63554C22semidirect
41. #63553C22semidirect
42. Dic3×C3⋊C8C22semidirect
58. #5101D3direct (N × H)
76. C2×C32×C8C2×C4semidirect
82. #3748C2×C4semidirect
87. C3×#208C2×C4semidirect
88. C2×C3×C3⋊C8C2×C4semidirect
94. C3×D3×C8C2×C4semidirect
95. C3×D3×C8C2×C4semidirect
99. #3711C2×C4semidirect
136. C2×D3×C8Dic3semidirect
155. #815C2×D3semidirect
162. C8×Dic3C2×D3semidirect
236. C2×C3×C8C4×D3semidirect
237. C2×C3×C8C2×Dic3semidirect
267. #208C4×D3semidirect
272. C2×C3⋊C8C2×Dic3semidirect
280. D3×C8C2×Dic3semidirect
281. D3×C8C2×Dic3semidirect
393. C3×D3#405semidirect
417. C2×C8D3×Dic3semidirect
466. C32C2×#405semidirect
506. D3#5101direct (N × H)
523. C3D3×#405semidirect
524. C3C2×#5101semidirect

Maximal subgroups

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

subgroupindex
C22×C3×D3×C82
D3×#9262
C2×D3×#2082
#105928002
C3×#51012
#105910592
#105910552
#105906932
#105906922
D3×#8152
D3×C8×Dic32
C2×#51013
D3×#4053