Finite Group Databasebeta

← D3×#4873 #11859955

Subgroups — D3×#4873 #11859955

Order 1152.

1031 conjugacy classes of subgroups.

The subgroup lattice has 514 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D3×Dic12C211yesmaximal, characteristic
2D3×#887C212yesmaximal
3#10592572C211yesmaximal, characteristic, complemented
4C3×D3×#107C211yesmaximal, characteristic
5C3×#4873C211yesmaximal, characteristic, complemented
6#10590818C211yesmaximal, characteristic, complemented
7#10590807C211yesmaximal, characteristic, complemented
8D3×C8×Dic3C211yesmaximal, characteristic
9D3×#810C212yesmaximal
10#10590482C212yesmaximal, complemented
11#10590481C212yesmaximal, complemented
12C4×D3×Q16—31nomaximal
13C2×#4873—31nomaximal
14C2×D3×Dic6C2212yes—
15C2×#3746C2211yescharacteristic
16#64096C2212yes—
17C2×C3×Dic12C2211yescharacteristic
18C2×C3×D3×C8C2211yescharacteristic
19C3×D3×C4⋊C4C2212yes—
20C3×#887C2212yes—
21D3×Dic3⋊C4—22no—
22C4×D3×Dic3—22no—
23C4×D3×Dic3C2211yescharacteristic
24#63844C2212yes—
25#63843C2212yes—
26#63838—22no—
27#63837—22no—
28C2×#3719C2212yes—
29C2×D3×C3⋊C8C2211yescharacteristic
30D3×Dic12C418yescomplemented
31C32×#107C2211yescharacteristic
32C8×C3⋊Dic3C2211yescharacteristic
33#63637C2212yes—
34C3×#818C2211yescharacteristic
35C3×C8×Dic3C2211yescharacteristic
36C3×#810C2212yes—
37C3×#807C2212yes—
38#63567C2212yes—
39#63565C2212yes—
40#63553C2211yescharacteristic
41Dic3×C3⋊C8C2211yescharacteristic
42C2×D3×Q16—31no—
43C22×Dic12—31no—
44C4×D3×Q8—32no—
45C2×#887—32no—
46C3×C4×Q16—31no—
47C2×C3×#107—31no—
48Dic3×Q16—31no—
49C2×C8×Dic3—31no—
50C4×#216—32no—
51C2×#810—32no—
52D3×#107D311yescharacteristic
53#4873—31no—
54#4873—32no—
55#4873—31no—
56#4873—31no—
57#4873—31no—
58#4873—32no—
59#4873—61no—
60#4873D311yescharacteristic, direct product factor
61D3×#103—32no—
62#4790—32no—
63C4×Dic12—31no—
64C4×D3×C8—31no—
65C2×#634C2312yes—
66C2×C3×C4×D3—22no—
67C2×C3×C4×D3C2311yescharacteristic
68C2×C3×Dic6C2312yes—
69C2×#627—22no—
70C2×D3×Dic3—22no—
71C2×D3×Dic3D411yescharacteristic
72C2×D3×Dic3D411yescharacteristic
73D3×Dic6—24no—
74D3×Dic6C2×C418yes—
75C2×C32×C8C2311yescharacteristic
76C32×C4⋊C4C2312yes—
77#3750—22no—
78C4×C3⋊Dic3—22no—
79C4×C3⋊Dic3C2311yescharacteristic
80C2×C3⋊(C3⋊C8)C2311yescharacteristic
81#3746C2×C414yescomplemented
82C3×C4⋊Dic3C2312yes—
83C3×Dic3⋊C4—22no—
84C3×Dic3⋊C4—22no—
85C3×C4×Dic3—22no—
86C3×C4×Dic3C2311yescharacteristic
87C2×C3×C3⋊C8C2311yescharacteristic
88C2×C3×C3⋊C8C2311yescharacteristic
89C3×Dic12C2×C414yescomplemented
90C3×D3×C8C2×C414yes—
91#3724—22no—
92Dic3⋊Dic3—22no—
93Dic32—22no—
94Dic32—22no—
95Dic32D411yescharacteristic
96Dic32D411yescharacteristic
97#3719C2×C418yescomplemented
98D3×C3⋊C8—22no—
99C2×C4×Q16—91noSylow
100C2×D3×Q8—32no—
101C22×Dic6—32no—
102C2×C3×Q16—31no—
103C22×C3×C8—31no—
104C3×C4×Q8—32no—
105C2×C3×C4⋊C4—32no—
106Q8×Dic3—32no—
107C2×#216—32no—
108C2×Dic3⋊C4—62no—
109C2×C4×Dic3—31no—
110C2×C4×Dic3—62no—
111C22×C3⋊C8—31no—
112D3×Q16—38no—
113C2×Dic12—32no—
114C2×Dic12—31no—
115C2×Dic12—31no—
116C2×Dic12—38no—
117C2×Dic12—61no—
118C2×Dic12C2×D311yescharacteristic
119C2×D3×C8—31no—
120C2×D3×C8C2×D311yescharacteristic
121D3×C4⋊C4—62no—
122D3×C4⋊C4C2×D312yes—
123#887—32no—
124#887—32no—
125#887—32no—
126#887—32no—
127#887—62no—
128#887—62no—
129#887—62no—
130#887—62no—
131#887C2×D312yes—
132C42×D3—31no—
133C42×D3—62no—
134C4×Dic6—32no—
135C4×Dic6—62no—
136C3×#107—21no—
137C3×#107—31no—
138C3×#107—32no—
139C3×#107C2×D311yescharacteristic
140C3×#107C2×D311yescharacteristic
141C3×#103—32no—
142C3×C4×C8—31no—
143#835—32no—
144#818C2×D311yescharacteristic
145#816—32no—
146C8×Dic3—31no—
147C8×Dic3—31no—
148C8×Dic3—31no—
149C8×Dic3—31no—
150C8×Dic3—31no—
151C8×Dic3—61no—
152C8×Dic3C2×D311yescharacteristic
153#810—32no—
154#810—32no—
155#810—32no—
156#810—32no—
157#810—62no—
158#810C2×D312yes—
159#807C2×D312yes—
160C4×C3⋊C8—31no—
161C22×C3×D3C2×D411yescharacteristic
162C2×C32×C4—22no—
163C2×C32×C4C2411yescharacteristic
164C2×C3⋊Dic3—22no—
165C2×C3⋊Dic3C2×D411yescharacteristic
166C2×C3⋊Dic3C2×D411yescharacteristic
167#634—22no—
168#634C22×C414yes—
169C2×C3×Dic3—22no—
170C2×C3×Dic3—22no—
171C2×C3×Dic3C2×D411yescharacteristic
172C2×C3×Dic3C2×D411yescharacteristic
173C2×C3×Dic3C2×D411yescharacteristic
174C3×C4×D3—44no—
175C3×C4×D3C22×C412yes—
176C3×C4×D3#4112yes—
177C3×Dic6—22no—
178C3×Dic6C22×C414yes—
179#627—28no—
180D3×Dic3—28no—
181D3×Dic3—22no—
182D3×Dic3Q1614yescomplemented
183C32×C8C22×C412yes—
184C3⋊(C3⋊C8)—21no—
185C3×C3⋊C8—21no—
186C3×C3⋊C8C22×C412yes—
187C22×Q16—91no—
188C2×C4×Q8—92no—
189C4×Q16—31no—
190C4×Q16—91no—
191C4×Q16—92no—
192C4×Q16—92no—
193C4×Q16—91no—
194C4×Q16—91no—
195C2×#107—31no—
196C2×#103—92no—
197C2×C4×C8—91no—
198C2×C3×Q8—32no—
199C22×C3×C4—31no—
200C22×C3×C4—62no—
201C22×Dic3—31no—
202C22×Dic3—31no—
203C22×Dic3—62no—
204D3×Q8—38no—
205D3×Q8—64no—
206C2×C4×D3—22no—
207C2×C4×D3—31no—
208C2×C4×D3—31no—
209C2×C4×D3—62no—
210C2×C4×D3C22×D311yescharacteristic
211C2×Dic6—32no—
212C2×Dic6—32no—
213C2×Dic6—38no—
214C2×Dic6—62no—
215C2×Dic6—64no—
216C2×Dic6—62no—
217C2×Dic6—62no—
218C2×Dic6C22×D312yes—
219C3×Q16—34no—
220C2×C3×C8—21no—
221C2×C3×C8—31no—
222C2×C3×C8—34no—
223C2×C3×C8—31no—
224C2×C3×C8C22×D311yescharacteristic
225C2×C3×C8C22×D311yescharacteristic
226C3×C4⋊C4—22no—
227C3×C4⋊C4—32no—
228C3×C4⋊C4—62no—
229C3×C4⋊C4—62no—
230C3×C4⋊C4C22×D312yes—
231C3×C4⋊C4C22×D312yes—
232C3×C42—31no—
233C3×C42—62no—
234#216—38no—
235C4⋊Dic3—62no—
236C4⋊Dic3C22×D312yes—
237Dic3⋊C4—22no—
238Dic3⋊C4—22no—
239Dic3⋊C4—62no—
240Dic3⋊C4—62no—
241Dic3⋊C4—62no—
242Dic3⋊C4—62no—
243Dic3⋊C4—62no—
244Dic3⋊C4—122no—
245C4×Dic3—22no—
246C4×Dic3—31no—
247C4×Dic3—31no—
248C4×Dic3—31no—
249C4×Dic3—31no—
250C4×Dic3—31no—
251C4×Dic3—31no—
252C4×Dic3—61no—
253C4×Dic3—62no—
254C4×Dic3—62no—
255C4×Dic3—62no—
256C4×Dic3—62no—
257C4×Dic3—62no—
258C4×Dic3—62no—
259C4×Dic3—122no—
260C4×Dic3C22×D311yescharacteristic
261C2×C3⋊C8—31no—
262C2×C3⋊C8—31no—
263C2×C3⋊C8—61no—
264C2×C3⋊C8—62no—
265C2×C3⋊C8C22×D311yescharacteristic
266C2×C3⋊C8C22×D311yescharacteristic
267Dic12—38no—
268Dic12—34no—
269Dic12—34no—
270Dic12—64no—
271Dic12C4×D314yescomplemented
272D3×C8—62no—
273D3×C8C4×D314yes—
274C22×C32C22×D411yescharacteristic
275C2×C3×D3C4×D412yes—
276C2×C3×D3C2×Q1612yes—
277C2×C3×D3#13512yes—
278C32×C4—42no—
279C32×C4C23×C411yescharacteristic
280C32×C4C2×#4111yescharacteristic
281C3⋊Dic3—24no—
282C3⋊Dic3—21no—
283C3⋊Dic3C2×Q1612yescomplemented
284C3×Dic3—24no—
285C3×Dic3—21no—
286C3×Dic3—42no—
287C3×Dic3C4×D412yes—
288C3×Dic3C2×Q1612yescomplemented
289C22×Q8—92no—
290C2×Q16—31no—
291C2×Q16—98no—
292C2×Q16—92no—
293C2×Q16—91no—
294C22×C8—31no—
295C22×C8—91no—
296C4×Q8—32no—
297C4×Q8—92no—
298C4×Q8—92no—
299C4×Q8—92no—
300C4×Q8—182no—
301C4×Q8—182no—
302C2×C4⋊C4—32no—
303C2×C4⋊C4—182no—
304C2×C42—91no—
305C2×C42—182no—
306#107—31no—
307#107—32no—
308#107D3211yescharacteristic
309#103—32no—
310#103—92no—
311#103—92no—
312#103—92no—
313C4×C8—31no—
314C4×C8—91no—
315C4×C8—91no—
316C4×C8—91no—
317C23×C3—31no—
318C22×D3D3×D411yescharacteristic
319C3×Q8—34no—
320C3×Q8—62no—
321C2×C3×C4—22no—
322C2×C3×C4—22no—
323C2×C3×C4—21no—
324C2×C3×C4—31no—
325C2×C3×C4—31no—
326C2×C3×C4—32no—
327C2×C3×C4—32no—
328C2×C3×C4—31no—
329C2×C3×C4—42no—
330C2×C3×C4—62no—
331C2×C3×C4—62no—
332C2×C3×C4—124no—
333C2×C3×C4C23×D311yescharacteristic
334C2×C3×C4C23×D311yescharacteristic
335C2×Dic3—22no—
336C2×Dic3—22no—
337C2×Dic3—31no—
338C2×Dic3—31no—
339C2×Dic3—34no—
340C2×Dic3—31no—
341C2×Dic3—31no—
342C2×Dic3—61no—
343C2×Dic3—61no—
344C2×Dic3—68no—
345C2×Dic3—62no—
346C2×Dic3—62no—
347C2×Dic3—62no—
348C2×Dic3—122no—
349C2×Dic3D3×D411yescharacteristic
350C2×Dic3D3×D411yescharacteristic
351C2×Dic3D3×D411yescharacteristic
352C4×D3—34no—
353C4×D3—44no—
354C4×D3—68no—
355C4×D3—62no—
356C4×D3C2×C4×D312yes—
357C4×D3#23912yes—
358Dic6—22no—
359Dic6—34no—
360Dic6—34no—
361Dic6—64no—
362Dic6—68no—
363Dic6—62no—
364Dic6—62no—
365Dic6—68no—
366Dic6—122no—
367Dic6C2×C4×D314yes—
368C3×C8—22no—
369C3×C8—32no—
370C3×C8—61no—
371C3×C8C2×C4×D312yes—
372C3×C8C2×C4×D312yes—
373C3⋊C8—21no—
374C3⋊C8—61no—
375C3⋊C8—61no—
376C3⋊C8—121no—
377C3⋊C8C2×C4×D312yes—
378C2×C32C2×C4×D411yescharacteristic
379C2×C32C22×Q1611yescharacteristic
380C2×C32C2×#13511yescharacteristic
381C3×D3C4×Q1614yescomplemented
382C2×Q8—32no—
383C2×Q8—98no—
384C2×Q8—92no—
385C2×Q8—182no—
386C2×Q8—184no—
387C22×C4—31no—
388C22×C4—62no—
389C22×C4—91no—
390C22×C4—91no—
391C22×C4—182no—
392Q16—34no—
393Q16—98no—
394Q16—94no—
395C2×C8—31no—
396C2×C8—34no—
397C2×C8—31no—
398C2×C8—91no—
399C2×C8—182no—
400C2×C8C2×D3211yescharacteristic
401C4⋊C4—32no—
402C4⋊C4—62no—
403C4⋊C4—62no—
404C4⋊C4—182no—
405C4⋊C4—182no—
406C4⋊C4—182no—
407C4⋊C4C2×D3212yes—
408C42—31no—
409C42—62no—
410C42—91no—
411C42—91no—
412C42—91no—
413C42—182no—
414C42—182no—
415C42—182no—
416C22×C3—21no—
417C22×C3—32no—
418C22×C3—32no—
419C22×C3—32no—
420C22×C3C2×D3×D411yescharacteristic
421C22×C3C2×D3×D411yescharacteristic
422C2×D3#89312yes—
423C2×D3#91212yes—
424C2×D3D3×Q1612yes—
425C3×C4—21no—
426C3×C4—21no—
427C3×C4—32no—
428C3×C4—32no—
429C3×C4—42no—
430C3×C4—42no—
431C3×C4—61no—
432C3×C4—64no—
433C3×C4—82no—
434C3×C4—122no—
435C3×C4C22×C4×D311yescharacteristic
436C3×C4C22×C4×D311yescharacteristic
437C3×C4C2×#23911yescharacteristic
438C3×C4D3×#4111yescharacteristic
439Dic3—21no—
440Dic3—24no—
441Dic3—32no—
442Dic3—32no—
443Dic3—42no—
444Dic3—62no—
445Dic3—61no—
446Dic3—64no—
447Dic3—61no—
448Dic3—64no—
449Dic3—124no—
450Dic3—121no—
451Dic3#89312yes—
452Dic3D3×Q1612yescomplemented
453C32C2×C4×Q1611yescharacteristic, complemented, Sylow
454C23—31no—
455Q8—34no—
456Q8—62no—
457Q8—94no—
458Q8—188no—
459Q8—182no—
460C2×C4—22no—
461C2×C4—31no—
462C2×C4—31no—
463C2×C4—32no—
464C2×C4—32no—
465C2×C4—31no—
466C2×C4—62no—
467C2×C4—62no—
468C2×C4—94no—
469C2×C4—91no—
470C2×C4—91no—
471C2×C4—124no—
472C2×C4—182no—
473C2×C4—188no—
474C2×C4—182no—
475C2×C4C22×D3211yescharacteristic
476C8—32no—
477C8—61no—
478C8—181no—
479C8C4×D3212yes—
480C2×C3—21no—
481C2×C3—21no—
482C2×C3—21no—
483C2×C3—34no—
484C2×C3C2×#89311yescharacteristic
485C2×C3C4×D3×D411yescharacteristic
486C2×C3C2×#91211yescharacteristic
487C2×C3C2×D3×Q1611yescharacteristic
488C2×C3C2×D3×Q1611yescharacteristic
489C2×C3D3×#13511yescharacteristic
490D3#487314yesdirect product factor
491C22—32no—
492C22—32no—
493C22—32no—
494C22D32×D411yescharacteristic
495C4—32no—
496C4—32no—
497C4—42no—
498C4—64no—
499C4—61no—
500C4—92no—
501C4—122no—
502C4—184no—
503C4—181no—
504C4C2×C4×D3211yescharacteristic
505C4D3×#23911yescharacteristic
506C3—21no—
507C3C2×#487311yescharacteristic, complemented
508C3C4×D3×Q1611yescharacteristic, complemented
509C2—34no—
510C2D3×#89311yescharacteristic
511C2D3×#91211yescharacteristic
512C2D32×Q1611yescharacteristic
subgroupG/H
centerC22D32×D4
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC32×#107C22
socleC22×C32C22×D4
prime radicalC22×C3×D3C2×D4
cosocleC2×C32×C4C24
hypercenter#107D32
hypocenterC32C2×C4×Q16
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ #107

Complements

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

NH ≅ G/Ntype
3. #10592572C2semidirect
5. C3×#4873C2semidirect
6. #10590818C2semidirect
7. #10590807C2semidirect
10. #10590482C2semidirect
11. #10590481C2semidirect
30. D3×Dic12C4semidirect
60. #4873D3direct (N × H)
81. #3746C2×C4semidirect
89. C3×Dic12C2×C4semidirect
97. #3719C2×C4semidirect
182. D3×Dic3Q16semidirect
271. Dic12C4×D3semidirect
283. C3⋊Dic3C2×Q16semidirect
288. C3×Dic3C2×Q16semidirect
381. C3×D3C4×Q16semidirect
452. Dic3D3×Q16semidirect
453. C32C2×C4×Q16semidirect
490. D3#4873direct (N × H)
507. C3C2×#4873semidirect
508. C3C4×D3×Q16semidirect

Maximal subgroups

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

subgroupindex
C2×D3×Dic122
D3×#8872
#105925722
C3×D3×#1072
C3×#48732
#105908182
#105908072
D3×C8×Dic32
D3×#8102
#105904822
#105904812
C4×D3×Q163
C2×#48733