Finite Group Databasebeta

← D3×#5078 #11874948

Subgroups — D3×#5078 #11874948

Order 1152.

897 conjugacy classes of subgroups.

The subgroup lattice has 471 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×D3×C4⋊Q8C211yesmaximal, characteristic
2D3×#869C211yesmaximal, characteristic
3#10592777C211yesmaximal, characteristic, complemented
4C3×#5078C211yesmaximal, characteristic, complemented
5D3×#807C214yesmaximal
6#10590411C214yesmaximal, complemented
7C4×D3×C3⋊C8C211yesmaximal, characteristic
8#10590312C211yesmaximal, characteristic, complemented
9#10590311C211yesmaximal, characteristic, complemented
10C2×#5078—31nomaximal
11D3×#500—31nomaximal
12C2×C3×D3×Q8—21no—
13C2×D3×Dic6—21no—
14C32×C4⋊Q8C2211yescharacteristic
15#64078C2211yescharacteristic
16C3×#944—21no—
17C3×D3×C4⋊C4—21no—
18C3×D3×C4⋊C4C2212yes—
19C3×#888—21no—
20C3×#888C2212yes—
21C3×C42×D3C2211yescharacteristic
22C3×#869C2211yescharacteristic
23C3×#869C2211yescharacteristic
24#63918—21no—
25#63918C2212yes—
26D3×C4⋊Dic3—21no—
27D3×C4⋊Dic3C2212yes—
28#63866—21no—
29C2×D3×C3⋊C8C2212yes—
30#63634C2214yes—
31C4×C3⋊(C3⋊C8)C2211yescharacteristic
32C3×#807C2214yes—
33C3×C4×C3⋊C8C2211yescharacteristic
34#63576C2214yes—
35#63575C2214yes—
36Dic3×C3⋊C8C2212yes—
37C2×C3×C4⋊Q8—31no—
38D3×C4⋊Q8—31no—
39D3×C4⋊Q8D311yescharacteristic
40C2×#869—31no—
41C3×#500—31no—
42#5078—31no—
43#5078—31no—
44#5078—31no—
45#5078—31no—
46#5078—34no—
47#5078—31no—
48#5078—61no—
49#5078D311yescharacteristic, direct product factor
50C2×#807—34no—
51C2×C4×C3⋊C8—31no—
52D3×#107—34no—
53#4874—34no—
54C4×D3×C8—31no—
55#4682—31no—
56C2×C32×Q8—21no—
57C2×#634—21no—
58C3×D3×Q8—44no—
59C2×C3×C4×D3—22no—
60C2×C3×C4×D3D411yescharacteristic
61C2×C3×C4×D3D411yescharacteristic
62C2×C3×C4×D3C2311yescharacteristic
63C2×C3×Dic6—21no—
64C2×C3×Dic6—21no—
65C2×C3×Dic6—22no—
66C2×#627—22no—
67C2×D3×Dic3—22no—
68D3×Dic6—44no—
69C32×C4⋊C4—21no—
70C32×C4⋊C4C2312yes—
71C32×C42C2311yescharacteristic
72C4⋊(C3⋊Dic3)—21no—
73C4⋊(C3⋊Dic3)C2312yes—
74C2×C3⋊(C3⋊C8)C2312yes—
75C3×C4⋊Dic3—21no—
76C3×C4⋊Dic3—21no—
77C3×C4⋊Dic3C2312yes—
78C3×C4⋊Dic3C2312yes—
79C3×Dic3⋊C4—22no—
80C3×Dic3⋊C4—22no—
81C3×C4×Dic3D411yescharacteristic
82C3×C4×Dic3D411yescharacteristic
83C3×C4×Dic3C2311yescharacteristic
84C2×C3×C3⋊C8C2312yes—
85Dic3⋊Dic3—22no—
86Dic3⋊Dic3—22no—
87D3×C3⋊C8Q818yescomplemented
88C2×#500—91noSylow
89C22×C3×Q8—61no—
90C2×D3×Q8—21no—
91C2×D3×Q8—61no—
92C22×Dic6—61no—
93C3×C4⋊Q8—21no—
94C3×C4⋊Q8—32no—
95C3×C4⋊Q8—31no—
96C3×C4⋊Q8—31no—
97C3×C4⋊Q8—61no—
98C3×C4⋊Q8—61no—
99C3×C4⋊Q8C2×D311yescharacteristic
100C3×C4⋊Q8C2×D311yescharacteristic
101C2×C3×C4⋊C4—32no—
102C2×C3×C4⋊C4—61no—
103C2×C3×C42—31no—
104#944—21no—
105#944—61no—
106C2×C4⋊Dic3—32no—
107C2×C4⋊Dic3—61no—
108C22×C3⋊C8—32no—
109C2×D3×C8—32no—
110D3×C4⋊C4—21no—
111D3×C4⋊C4—32no—
112D3×C4⋊C4—61no—
113D3×C4⋊C4C2×D312yes—
114#888—21no—
115#888—32no—
116#888—61no—
117#888C2×D312yes—
118C42×D3C2×D311yescharacteristic
119#869—31no—
120#869—31no—
121#869—32no—
122#869—61no—
123#869—61no—
124#869—61no—
125#869C2×D311yescharacteristic
126#869C2×D311yescharacteristic
127C3×#107—34no—
128C3×C4×C8—31no—
129#818—34no—
130C8×Dic3—32no—
131#807—34no—
132#807—34no—
133#807—34no—
134#807—34no—
135#807—34no—
136#807—64no—
137#807C2×D314yes—
138C4×C3⋊C8—31no—
139C4×C3⋊C8—31no—
140C4×C3⋊C8—32no—
141C4×C3⋊C8—61no—
142C4×C3⋊C8C2×D311yescharacteristic
143C22×C3×D3C2×D411yescharacteristic
144C32×Q8—42no—
145C2×C32×C4—22no—
146C2×C32×C4C2×D411yescharacteristic
147C2×C32×C4C2×D411yescharacteristic
148C2×C32×C4C2411yescharacteristic
149C2×C3⋊Dic3—22no—
150#634—42no—
151C2×C3×Dic3—22no—
152C2×C3×Dic3—22no—
153C2×C3×Dic3C2×D411yescharacteristic
154C2×C3×Dic3C2×D411yescharacteristic
155C2×C3×Dic3C2×D411yescharacteristic
156C3×C4×D3—44no—
157C3×C4×D3D814yes—
158C3×C4×D3Q1614yes—
159C3×C4×D3C2×Q814yes—
160C3×Dic6—42no—
161C3×Dic6—42no—
162C3×Dic6—44no—
163#627—44no—
164D3×Dic3—44no—
165C3⋊(C3⋊C8)C2×Q814yescomplemented
166C3×C3⋊C8C2×Q814yescomplemented
167C2×C4⋊Q8—31no—
168C2×C4⋊Q8—91no—
169#500—31no—
170#500—91no—
171#500—94no—
172#500—91no—
173#500—91no—
174C2×#107—94no—
175C2×C4×C8—91no—
176C2×C3×Q8—21no—
177C2×C3×Q8—21no—
178C2×C3×Q8—41no—
179C2×C3×Q8—62no—
180C2×C3×Q8—61no—
181C2×C3×Q8—61no—
182C2×C3×Q8—124no—
183C22×C3×C4—31no—
184C22×C3×C4—31no—
185C22×C3×C4—31no—
186C22×C3×C4—62no—
187C22×Dic3—62no—
188D3×Q8—44no—
189D3×Q8—124no—
190C2×C4×D3—22no—
191C2×C4×D3—62no—
192C2×C4×D3#6711yescharacteristic
193C2×C4×D3#6711yescharacteristic
194C2×C4×D3C22×D311yescharacteristic
195C2×Dic6—21no—
196C2×Dic6—21no—
197C2×Dic6—22no—
198C2×Dic6—62no—
199C2×Dic6—61no—
200C2×Dic6—61no—
201C2×Dic6—62no—
202C2×Dic6—121no—
203C2×Dic6—124no—
204C2×C3×C8—32no—
205C3×C4⋊C4—21no—
206C3×C4⋊C4—21no—
207C3×C4⋊C4—22no—
208C3×C4⋊C4—32no—
209C3×C4⋊C4—32no—
210C3×C4⋊C4—41no—
211C3×C4⋊C4—62no—
212C3×C4⋊C4—62no—
213C3×C4⋊C4—61no—
214C3×C4⋊C4—61no—
215C3×C4⋊C4C22×D312yes—
216C3×C4⋊C4C22×D312yes—
217C3×C42—21no—
218C3×C42—31no—
219C3×C42—31no—
220C3×C42—31no—
221C3×C42C22×D311yescharacteristic
222C3×C42C22×D311yescharacteristic
223C4⋊Dic3—21no—
224C4⋊Dic3—21no—
225C4⋊Dic3—32no—
226C4⋊Dic3—32no—
227C4⋊Dic3—62no—
228C4⋊Dic3—62no—
229C4⋊Dic3—62no—
230C4⋊Dic3—61no—
231C4⋊Dic3—61no—
232C4⋊Dic3—121no—
233C4⋊Dic3C22×D312yes—
234C4⋊Dic3C22×D312yes—
235Dic3⋊C4—22no—
236Dic3⋊C4—22no—
237Dic3⋊C4—62no—
238Dic3⋊C4—62no—
239C4×Dic3#6711yescharacteristic
240C4×Dic3#6711yescharacteristic
241C4×Dic3C22×D311yescharacteristic
242C2×C3⋊C8—32no—
243C2×C3⋊C8—32no—
244C2×C3⋊C8—38no—
245C2×C3⋊C8—62no—
246C2×C3⋊C8C22×D312yes—
247D3×C8—38no—
248C22×C32C22×D411yescharacteristic
249C2×C3×D3C4⋊Q812yes—
250C2×C3×D3C2×D812yes—
251C2×C3×D3C2×Q1612yes—
252C32×C4—42no—
253C32×C4C2×D812yes—
254C32×C4C2×Q1612yes—
255C32×C4C22×Q812yes—
256C3⋊Dic3—42no—
257C3×Dic3—42no—
258C3×Dic3—42no—
259C3×Dic3C4⋊Q812yes—
260C3×Dic3C2×D812yes—
261C3×Dic3C2×Q1612yes—
262C22×Q8—61no—
263C22×Q8—181no—
264C22×C8—92no—
265C4⋊Q8—32no—
266C4⋊Q8—31no—
267C4⋊Q8—31no—
268C4⋊Q8—61no—
269C4⋊Q8—61no—
270C4⋊Q8—92no—
271C4⋊Q8—91no—
272C4⋊Q8—181no—
273C4⋊Q8—181no—
274C4⋊Q8D3211yescharacteristic
275C2×C4⋊C4—32no—
276C2×C4⋊C4—61no—
277C2×C4⋊C4—92no—
278C2×C4⋊C4—181no—
279C2×C42—31no—
280#107—34no—
281#107—94no—
282#107—94no—
283#107—94no—
284C4×C8—31no—
285C4×C8—92no—
286C4×C8—91no—
287C23×C3—31no—
288C22×D3C2×#6711yescharacteristic
289C3×Q8—42no—
290C3×Q8—42no—
291C3×Q8—82no—
292C3×Q8—124no—
293C3×Q8—122no—
294C3×Q8—122no—
295C2×C3×C4—22no—
296C2×C3×C4—22no—
297C2×C3×C4—21no—
298C2×C3×C4—21no—
299C2×C3×C4—21no—
300C2×C3×C4—31no—
301C2×C3×C4—31no—
302C2×C3×C4—31no—
303C2×C3×C4—34no—
304C2×C3×C4—34no—
305C2×C3×C4—34no—
306C2×C3×C4—42no—
307C2×C3×C4—62no—
308C2×C3×C4—62no—
309C2×C3×C4—124no—
310C2×C3×C4D3×D411yescharacteristic
311C2×C3×C4D3×D411yescharacteristic
312C2×C3×C4C2×#6711yescharacteristic
313C2×C3×C4C2×#6711yescharacteristic
314C2×C3×C4C23×D311yescharacteristic
315C2×C3×C4C23×D311yescharacteristic
316C2×Dic3—22no—
317C2×Dic3—22no—
318C2×Dic3—62no—
319C2×Dic3—62no—
320C2×Dic3—122no—
321C2×Dic3—124no—
322C2×Dic3C2×#6711yescharacteristic
323C2×Dic3C2×#6711yescharacteristic
324C2×Dic3C2×#6711yescharacteristic
325C4×D3—44no—
326C4×D3—124no—
327C4×D3#21314yes—
328C4×D3#21614yes—
329C4×D3D3×Q814yes—
330Dic6—42no—
331Dic6—42no—
332Dic6—44no—
333Dic6—124no—
334Dic6—122no—
335Dic6—122no—
336Dic6—124no—
337Dic6—242no—
338C3×C8—34no—
339C3⋊C8—34no—
340C3⋊C8—34no—
341C3⋊C8—64no—
342C3⋊C8D3×Q814yescomplemented
343C2×C32C2×C4⋊Q811yescharacteristic
344C2×C32C22×D811yescharacteristic
345C2×C32C22×Q1611yescharacteristic
346C3×D3#50014yescomplemented
347C2×Q8—21no—
348C2×Q8—62no—
349C2×Q8—61no—
350C2×Q8—61no—
351C2×Q8—124no—
352C2×Q8—182no—
353C2×Q8—181no—
354C2×Q8—364no—
355C22×C4—31no—
356C22×C4—31no—
357C22×C4—31no—
358C22×C4—62no—
359C22×C4—182no—
360C2×C8—32no—
361C2×C8—98no—
362C2×C8—92no—
363C4⋊C4—21no—
364C4⋊C4—32no—
365C4⋊C4—32no—
366C4⋊C4—62no—
367C4⋊C4—62no—
368C4⋊C4—61no—
369C4⋊C4—61no—
370C4⋊C4—92no—
371C4⋊C4—182no—
372C4⋊C4—182no—
373C4⋊C4—181no—
374C4⋊C4C2×D3212yes—
375C42—31no—
376C42—31no—
377C42—31no—
378C42C2×D3211yescharacteristic
379C22×C3—21no—
380C22×C3—32no—
381C22×C3—32no—
382C22×C3—32no—
383C22×C3C2×D3×D411yescharacteristic
384C22×C3C22×#6711yescharacteristic
385C2×D3C2×#21312yes—
386C2×D3C2×#21612yes—
387C2×D3#94412yes—
388C3×C4—22no—
389C3×C4—22no—
390C3×C4—22no—
391C3×C4—32no—
392C3×C4—32no—
393C3×C4—32no—
394C3×C4—42no—
395C3×C4—42no—
396C3×C4—82no—
397C3×C4—122no—
398C3×C4—122no—
399C3×C4D3×D812yes—
400C3×C4D3×Q1612yes—
401C3×C4C2×#21312yes—
402C3×C4C2×#21612yes—
403C3×C4C2×D3×Q812yes—
404C3×C4C2×D3×Q812yes—
405Dic3—42no—
406Dic3—42no—
407Dic3—122no—
408Dic3—122no—
409Dic3—242no—
410Dic3C2×#21312yes—
411Dic3C2×#21612yes—
412Dic3#94412yes—
413C32C2×#50011yescharacteristic, complemented, Sylow
414C23—31no—
415Q8—42no—
416Q8—124no—
417Q8—122no—
418Q8—122no—
419Q8—364no—
420Q8—362no—
421C2×C4—22no—
422C2×C4—31no—
423C2×C4—31no—
424C2×C4—31no—
425C2×C4—34no—
426C2×C4—34no—
427C2×C4—34no—
428C2×C4—62no—
429C2×C4—62no—
430C2×C4—124no—
431C2×C4—182no—
432C2×C4—364no—
433C2×C4D3×#6711yescharacteristic
434C2×C4D3×#6711yescharacteristic
435C2×C4C22×D3211yescharacteristic
436C8—34no—
437C8—94no—
438C2×C3—21no—
439C2×C3—21no—
440C2×C3—21no—
441C2×C3—34no—
442C2×C3D3×C4⋊Q811yescharacteristic
443C2×C3C2×D3×D811yescharacteristic
444C2×C3C2×D3×Q1611yescharacteristic
445C2×C3C22×#21311yescharacteristic
446C2×C3C22×#21611yescharacteristic
447C2×C3C2×#94411yescharacteristic
448D3#507814yesdirect product factor
449C22—32no—
450C22—32no—
451C22—32no—
452C22C2×D3×#6711yescharacteristic
453C4—32no—
454C4—32no—
455C4—32no—
456C4—42no—
457C4—122no—
458C4—122no—
459C4—362no—
460C4D3×#21312yes—
461C4D3×#21612yes—
462C4D32×Q812yes—
463C3—21no—
464C3D3×#50011yescharacteristic, complemented
465C3C2×#507811yescharacteristic, complemented
466C2—34no—
467C2C2×D3×#21311yescharacteristic
468C2C2×D3×#21611yescharacteristic
469C2D3×#94411yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4⋊Q8C22
socleC22×C32C22×D4
prime radicalC22×C3×D3C2×D4
hypercenterC4⋊Q8D32
hypocenterC32C2×#500
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
3. #10592777C2semidirect
4. C3×#5078C2semidirect
6. #10590411C2semidirect
8. #10590312C2semidirect
9. #10590311C2semidirect
49. #5078D3direct (N × H)
87. D3×C3⋊C8Q8semidirect
165. C3⋊(C3⋊C8)C2×Q8semidirect
166. C3×C3⋊C8C2×Q8semidirect
342. C3⋊C8D3×Q8semidirect
346. C3×D3#500semidirect
413. C32C2×#500semidirect
448. D3#5078direct (N × H)
464. C3D3×#500semidirect
465. C3C2×#5078semidirect

Maximal subgroups

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

subgroupindex
C3×D3×C4⋊Q82
D3×#8692
#105927772
C3×#50782
D3×#8072
#105904112
C4×D3×C3⋊C82
#105903122
#105903112
C2×#50783
D3×#5003