Finite Group Databasebeta

← D3×#5183 #11874211

Subgroups — D3×#5183 #11874211

Order 1152.

1165 conjugacy classes of subgroups.

The subgroup lattice has 518 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×D3×Q16C211yesmaximal, characteristic
2D3×#944C212yesmaximal
3C2×D3×#216C212yesmaximal
4C2×D3×Dic12C211yesmaximal, characteristic
5#10592882C211yesmaximal, characteristic, complemented
6C3×#5183C211yesmaximal, characteristic, complemented
7#10591628C212yesmaximal, complemented
8#10591626C212yesmaximal, complemented
9#10590905C211yesmaximal, characteristic, complemented
10#10590896C211yesmaximal, characteristic, complemented
11D3×C8×Dic3C211yesmaximal, characteristic
12C2×#5183—31nomaximal
13D3×#494—31nomaximal
14C2×C3×D3×Q8C2212yes—
15C2×D3×Dic6C2212yes—
16C2×C32×Q16C2211yescharacteristic
17#64153C2212yes—
18C2×#3756C2212yes—
19C2×#3746C2211yescharacteristic
20C3×#944C2212yes—
21C2×C3×#216C2212yes—
22C2×C3×#216C2212yes—
23C3×D3×Q16—24no—
24C2×C3×Dic12C2211yescharacteristic
25C2×C3×Dic12C2211yescharacteristic
26C2×C3×D3×C8C2211yescharacteristic
27D3×#216—28no—
28D3×Dic3⋊C4—24no—
29C4×D3×Dic3C2211yescharacteristic
30#63873C2212yes—
31#63866C2212yes—
32#63839—24no—
33C2×#3719C2212yes—
34C2×#3719C2212yes—
35C2×#3718C2212yes—
36C2×D3×C3⋊C8C2211yescharacteristic
37D3×Dic12—24no—
38C8×C3⋊Dic3C2211yescharacteristic
39C3×C8×Dic3C2211yescharacteristic
40#63553C2211yescharacteristic
41Dic3×C3⋊C8C2211yescharacteristic
42C22×C3×Q16—31no—
43C2×#944—32no—
44C22×#216—32no—
45C2×D3×Q16—32no—
46C2×D3×Q16—31no—
47C2×D3×Q16D311yescharacteristic
48C22×Dic12—31no—
49D3×C4⋊Q8—32no—
50C3×#494—31no—
51#5183—31no—
52#5183—31no—
53#5183—32no—
54#5183—32no—
55#5183—32no—
56#5183—31no—
57#5183—31no—
58#5183—31no—
59#5183—61no—
60#5183D311yescharacteristic, direct product factor
61C2×C8×Dic3—31no—
62#5092—32no—
63#4699—31no—
64C4×D3×C8—31no—
65C2×C32×Q8C2312yes—
66C2×#634C2312yes—
67C3×D3×Q8—24no—
68C3×D3×Q8—24no—
69C2×C3×C4×D3—22no—
70C2×C3×C4×D3C2311yescharacteristic
71C2×C3×Dic6—22no—
72C2×C3×Dic6C2312yes—
73C2×C3×Dic6C2312yes—
74C2×#627—22no—
75C2×D3×Dic3—22no—
76C2×D3×Dic3D412yes—
77D3×Dic6—24no—
78D3×Dic6—24no—
79C32×Q16—22no—
80C2×C32×C8C2311yescharacteristic
81#3756—24no—
82#3750—24no—
83C4×C3⋊Dic3C2311yescharacteristic
84C2×C3⋊(C3⋊C8)C2311yescharacteristic
85#3746—22no—
86C3×#216—24no—
87C3×#216—24no—
88C3×Dic3⋊C4—24no—
89C3×C4×Dic3C2311yescharacteristic
90C2×C3×C3⋊C8C2311yescharacteristic
91C2×C3×C3⋊C8C2311yescharacteristic
92C3×Dic12—22no—
93C3×Dic12—22no—
94C3×D3×C8D414yes—
95#3724—24no—
96Dic3⋊Dic3—24no—
97Dic32D412yes—
98#3719—24no—
99#3719—24no—
100#3718—24no—
101D3×C3⋊C8D414yes—
102C2×#494—91noSylow
103C22×C3×Q8—32no—
104C2×D3×Q8—32no—
105C2×D3×Q8C2×D312yes—
106C22×Dic6—32no—
107C2×C3×Q16—21no—
108C2×C3×Q16—32no—
109C2×C3×Q16—32no—
110C2×C3×Q16—31no—
111C2×C3×Q16—31no—
112C2×C3×Q16—64no—
113C2×C3×Q16C2×D311yescharacteristic
114C2×C3×Q16C2×D311yescharacteristic
115C22×C3×C8—31no—
116C3×C4⋊Q8—32no—
117#944—32no—
118#944—32no—
119#944—32no—
120#944—32no—
121#944—32no—
122#944—62no—
123#944—64no—
124#944C2×D312yes—
125C2×#216—32no—
126C2×#216—32no—
127C2×#216—32no—
128C2×#216—32no—
129C2×#216—32no—
130C2×#216—32no—
131C2×#216—62no—
132C2×#216—68no—
133C2×#216C2×D312yes—
134C2×#216C2×D312yes—
135C2×Dic3⋊C4—64no—
136C2×C4×Dic3—31no—
137C22×C3⋊C8—31no—
138D3×Q16—24no—
139D3×Q16—68no—
140D3×Q16—64no—
141C2×Dic12—32no—
142C2×Dic12—32no—
143C2×Dic12—31no—
144C2×Dic12—31no—
145C2×Dic12—61no—
146C2×Dic12—64no—
147C2×Dic12C2×D311yescharacteristic
148C2×Dic12C2×D311yescharacteristic
149C2×D3×C8—31no—
150C2×D3×C8C2×D311yescharacteristic
151D3×C4⋊C4—64no—
152#888—64no—
153C42×D3—31no—
154#869—32no—
155C3×C4×C8—31no—
156C8×Dic3—31no—
157C8×Dic3—31no—
158C8×Dic3—31no—
159C8×Dic3—31no—
160C8×Dic3—31no—
161C8×Dic3—61no—
162C8×Dic3C2×D311yescharacteristic
163C4×C3⋊C8—31no—
164C22×C3×D3C2×D411yescharacteristic
165C32×Q8—22no—
166C32×Q8—22no—
167C2×C32×C4—22no—
168C2×C32×C4C2411yescharacteristic
169C2×C3⋊Dic3—22no—
170C2×C3⋊Dic3C2×D412yes—
171#634—22no—
172#634—22no—
173C2×C3×Dic3—22no—
174C2×C3×Dic3—22no—
175C2×C3×Dic3C2×D411yescharacteristic
176C2×C3×Dic3C2×D412yes—
177C3×C4×D3—44no—
178C3×C4×D3C2×D412yes—
179C3×C4×D3C2×D412yes—
180C3×Dic6—22no—
181C3×Dic6—22no—
182C3×Dic6—22no—
183C3×Dic6—22no—
184C3×Dic6—44no—
185#627—44no—
186D3×Dic3—44no—
187D3×Dic3Q1618yescomplemented
188C32×C8C2×D412yes—
189C3⋊(C3⋊C8)C2×D412yes—
190C3×C3⋊C8C2×D412yes—
191C3×C3⋊C8C2×D412yes—
192C22×Q16—31no—
193C22×Q16—91no—
194C22×Q16—92no—
195C2×C4⋊Q8—92no—
196#494—31no—
197#494—91no—
198#494—92no—
199#494—92no—
200#494—91no—
201#494—91no—
202C2×C4×C8—91no—
203C2×C3×Q8—22no—
204C2×C3×Q8—32no—
205C2×C3×Q8—32no—
206C2×C3×Q8—62no—
207C2×C3×Q8—64no—
208C2×C3×Q8—64no—
209C2×C3×Q8C22×D312yes—
210C2×C3×Q8C22×D312yes—
211C22×C3×C4—31no—
212C22×C3×C4—62no—
213C22×Dic3—32no—
214C22×Dic3—62no—
215D3×Q8—24no—
216D3×Q8—24no—
217D3×Q8—64no—
218D3×Q8—64no—
219C2×C4×D3—22no—
220C2×C4×D3—32no—
221C2×C4×D3—62no—
222C2×C4×D3C22×D311yescharacteristic
223C2×Dic6—22no—
224C2×Dic6—32no—
225C2×Dic6—32no—
226C2×Dic6—62no—
227C2×Dic6—64no—
228C2×Dic6—64no—
229C2×Dic6—62no—
230C2×Dic6—62no—
231C2×Dic6C22×D312yes—
232C2×Dic6C22×D312yes—
233C3×Q16—22no—
234C3×Q16—22no—
235C3×Q16—42no—
236C3×Q16—64no—
237C3×Q16—64no—
238C3×Q16—62no—
239C3×Q16—62no—
240C2×C3×C8—21no—
241C2×C3×C8—31no—
242C2×C3×C8—31no—
243C2×C3×C8—34no—
244C2×C3×C8C22×D311yescharacteristic
245C2×C3×C8C22×D311yescharacteristic
246C3×C4⋊C4—64no—
247C3×C42—31no—
248#216—24no—
249#216—24no—
250#216—64no—
251#216—64no—
252#216—64no—
253#216—64no—
254#216—64no—
255#216—64no—
256#216—124no—
257C4⋊Dic3—64no—
258Dic3⋊C4—24no—
259Dic3⋊C4—64no—
260Dic3⋊C4—64no—
261Dic3⋊C4—64no—
262Dic3⋊C4—64no—
263Dic3⋊C4—64no—
264Dic3⋊C4—124no—
265C4×Dic3—31no—
266C4×Dic3—31no—
267C4×Dic3—32no—
268C4×Dic3—32no—
269C4×Dic3—61no—
270C4×Dic3C22×D311yescharacteristic
271C2×C3⋊C8—31no—
272C2×C3⋊C8—31no—
273C2×C3⋊C8—34no—
274C2×C3⋊C8—61no—
275C2×C3⋊C8C22×D311yescharacteristic
276C2×C3⋊C8C22×D311yescharacteristic
277Dic12—22no—
278Dic12—22no—
279Dic12—64no—
280Dic12—64no—
281Dic12—62no—
282Dic12—62no—
283Dic12—122no—
284D3×C8—34no—
285D3×C8#6714yes—
286C22×C32C22×D411yescharacteristic
287C2×C3×D3#12712yes—
288C2×C3×D3C2×Q1614yes—
289C32×C4—42no—
290C32×C4C22×D411yescharacteristic
291C32×C4C22×D411yescharacteristic
292C3⋊Dic3—42no—
293C3⋊Dic3C2×Q1614yescomplemented
294C3×Dic3—42no—
295C3×Dic3—42no—
296C3×Dic3#12712yes—
297C3×Dic3C2×Q1614yescomplemented
298C22×Q8—32no—
299C22×Q8—92no—
300C2×Q16—32no—
301C2×Q16—32no—
302C2×Q16—31no—
303C2×Q16—31no—
304C2×Q16—64no—
305C2×Q16—92no—
306C2×Q16—92no—
307C2×Q16—92no—
308C2×Q16—92no—
309C2×Q16—91no—
310C2×Q16—184no—
311C2×Q16—188no—
312C2×Q16D3211yescharacteristic
313C22×C8—31no—
314C22×C8—91no—
315C4⋊Q8—32no—
316C4⋊Q8—92no—
317C4⋊Q8—92no—
318C4⋊Q8—92no—
319C4⋊Q8—184no—
320C2×C4⋊C4—184no—
321C2×C42—91no—
322C4×C8—31no—
323C4×C8—91no—
324C4×C8—91no—
325C4×C8—91no—
326C23×C3—31no—
327C22×D3D3×D411yescharacteristic
328C3×Q8—22no—
329C3×Q8—22no—
330C3×Q8—22no—
331C3×Q8—22no—
332C3×Q8—42no—
333C3×Q8—42no—
334C3×Q8—62no—
335C3×Q8—62no—
336C3×Q8—62no—
337C3×Q8—62no—
338C3×Q8—124no—
339C2×C3×C4—22no—
340C2×C3×C4—22no—
341C2×C3×C4—21no—
342C2×C3×C4—31no—
343C2×C3×C4—32no—
344C2×C3×C4—32no—
345C2×C3×C4—32no—
346C2×C3×C4—42no—
347C2×C3×C4—62no—
348C2×C3×C4—62no—
349C2×C3×C4—124no—
350C2×C3×C4C23×D311yescharacteristic
351C2×C3×C4C23×D311yescharacteristic
352C2×Dic3—22no—
353C2×Dic3—22no—
354C2×Dic3—32no—
355C2×Dic3—32no—
356C2×Dic3—38no—
357C2×Dic3—62no—
358C2×Dic3—62no—
359C2×Dic3—62no—
360C2×Dic3—122no—
361C2×Dic3—124no—
362C2×Dic3D3×D412yes—
363C2×Dic3D3×D411yescharacteristic
364C4×D3—38no—
365C4×D3—44no—
366C4×D3—124no—
367C4×D3D3×D412yes—
368C4×D3C2×#6712yes—
369Dic6—22no—
370Dic6—22no—
371Dic6—22no—
372Dic6—22no—
373Dic6—44no—
374Dic6—62no—
375Dic6—62no—
376Dic6—62no—
377Dic6—62no—
378Dic6—122no—
379Dic6—122no—
380Dic6—124no—
381Dic6—124no—
382C3×C8—22no—
383C3×C8—32no—
384C3×C8—32no—
385C3×C8D3×D412yes—
386C3×C8C2×#6712yes—
387C3⋊C8—32no—
388C3⋊C8—32no—
389C3⋊C8—62no—
390C3⋊C8D3×D412yes—
391C3⋊C8C2×#6712yes—
392C2×C32C2×#12711yescharacteristic
393C2×C32C22×Q1612yes—
394C3×D3#49414yescomplemented
395C2×Q8—32no—
396C2×Q8—32no—
397C2×Q8—62no—
398C2×Q8—64no—
399C2×Q8—64no—
400C2×Q8—92no—
401C2×Q8—182no—
402C2×Q8—184no—
403C2×Q8—184no—
404C2×Q8C2×D3212yes—
405C22×C4—31no—
406C22×C4—62no—
407C22×C4—92no—
408C22×C4—182no—
409Q16—22no—
410Q16—64no—
411Q16—64no—
412Q16—62no—
413Q16—62no—
414Q16—184no—
415Q16—184no—
416Q16—184no—
417Q16—184no—
418Q16—182no—
419C2×C8—31no—
420C2×C8—31no—
421C2×C8—34no—
422C2×C8—94no—
423C2×C8—91no—
424C2×C8C2×D3211yescharacteristic
425C4⋊C4—64no—
426C4⋊C4—184no—
427C4⋊C4—184no—
428C4⋊C4—184no—
429C42—31no—
430C42—92no—
431C42—91no—
432C22×C3—21no—
433C22×C3—32no—
434C22×C3—34no—
435C22×C3C2×D3×D411yescharacteristic
436C22×C3C2×D3×D411yescharacteristic
437C2×D3D3×Q1614yes—
438C2×D3#94012yes—
439C3×C4—21no—
440C3×C4—21no—
441C3×C4—32no—
442C3×C4—34no—
443C3×C4—42no—
444C3×C4—42no—
445C3×C4—82no—
446C3×C4—122no—
447C3×C4—122no—
448C3×C4C2×D3×D411yescharacteristic
449C3×C4C2×D3×D411yescharacteristic
450C3×C4C2×D3×D411yescharacteristic
451C3×C4C22×#6711yescharacteristic
452Dic3—34no—
453Dic3—34no—
454Dic3—42no—
455Dic3—42no—
456Dic3—64no—
457Dic3—122no—
458Dic3—122no—
459Dic3—242no—
460Dic3D3×Q1614yescomplemented
461Dic3#94012yes—
462C32C2×#49411yescharacteristic, complemented, Sylow
463C23—31no—
464Q8—22no—
465Q8—22no—
466Q8—62no—
467Q8—62no—
468Q8—62no—
469Q8—62no—
470Q8—124no—
471Q8—182no—
472Q8—182no—
473Q8—364no—
474C2×C4—22no—
475C2×C4—32no—
476C2×C4—31no—
477C2×C4—32no—
478C2×C4—32no—
479C2×C4—62no—
480C2×C4—62no—
481C2×C4—98no—
482C2×C4—92no—
483C2×C4—124no—
484C2×C4—182no—
485C2×C4—364no—
486C2×C4C22×D3211yescharacteristic
487C8—32no—
488C8—32no—
489C8—92no—
490C8D3×#6712yes—
491C2×C3—22no—
492C2×C3—21no—
493C2×C3—34no—
494C2×C3D3×#12711yescharacteristic
495C2×C3C2×D3×Q1612yes—
496C2×C3C2×D3×Q1612yes—
497C2×C3C2×#94011yescharacteristic
498D3#518314yesdirect product factor
499C22—34no—
500C22—32no—
501C22D32×D411yescharacteristic
502C4—34no—
503C4—32no—
504C4—42no—
505C4—94no—
506C4—122no—
507C4—122no—
508C4—362no—
509C4D32×D411yescharacteristic
510C4C2×D3×#6711yescharacteristic
511C3—21no—
512C3D3×#49411yescharacteristic, complemented
513C3C2×#518311yescharacteristic, complemented
514C2—34no—
515C2D32×Q1612yes—
516C2D3×#94011yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×Q16C22
socleC22×C32C22×D4
prime radicalC22×C3×D3C2×D4
hypercenterC2×Q16D32
hypocenterC32C2×#494
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×Q16

Complements

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

NH ≅ G/Ntype
5. #10592882C2semidirect
6. C3×#5183C2semidirect
7. #10591628C2semidirect
8. #10591626C2semidirect
9. #10590905C2semidirect
10. #10590896C2semidirect
60. #5183D3direct (N × H)
187. D3×Dic3Q16semidirect
293. C3⋊Dic3C2×Q16semidirect
297. C3×Dic3C2×Q16semidirect
394. C3×D3#494semidirect
460. Dic3D3×Q16semidirect
462. C32C2×#494semidirect
498. D3#5183direct (N × H)
512. C3D3×#494semidirect
513. C3C2×#5183semidirect

Maximal subgroups

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

subgroupindex
C2×C3×D3×Q162
D3×#9442
C2×D3×#2162
C2×D3×Dic122
#105928822
C3×#51832
#105916282
#105916262
#105909052
#105908962
D3×C8×Dic32
C2×#51833
D3×#4943