Finite Group Databasebeta

← D3×#4697 #11873441

Subgroups — D3×#4697 #11873441

Order 1152.

872 conjugacy classes of subgroups.

The subgroup lattice has 496 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D3×#875C211yesmaximal, characteristic
2D3×#870C211yesmaximal, characteristic, complemented
3#10592396C211yesmaximal, characteristic, complemented
4C3×#4697C211yesmaximal, characteristic, complemented
5C3×C4×D3×C8C211yesmaximal, characteristic, complemented
6D3×#821C212yesmaximal
7#10590872C212yesmaximal, complemented
8#10590863C212yesmaximal, complemented
9D3×#816C212yesmaximal, complemented
10#10590293C211yesmaximal, characteristic, complemented
11#10590274C211yesmaximal, characteristic, complemented
12D3×#488—31nomaximal
13C2×#4697—31nomaximal
14C2×D3×D12C2211yescharacteristic
15C2×D3×Dic6C2211yescharacteristic
16#64084C2211yescharacteristic
17#64079C2211yescharacteristic, complemented
18C2×C3×D3×C8C2212yes—
19C3×#875C2211yescharacteristic
20C3×C42×D3C2211yescharacteristic
21C3×#870C2211yescharacteristic, complemented
22D3×(C2×D3)⋊C4—22no—
23D3×C4⋊Dic3C2212yes—
24D3×Dic3⋊C4—22no—
25#63869C2212yescomplemented
26#63867—22no—
27#63864C2211yescharacteristic
28#63860C2211yescharacteristic
29#63852—22no—
30C32×C4×C8C2211yescharacteristic, complemented
31#63648C2212yes—
32#63643C2212yescomplemented
33C3×#821C2212yes—
34C3×#816C2212yescomplemented
35C3×C8×Dic3C2212yescomplemented
36C3×C4×C3⋊C8C2211yescharacteristic, complemented
37#63567C2212yescomplemented
38#63566C2212yescomplemented
39#63564C2212yes—
40#63563C2212yes—
41D3×#125—31no—
42D3×#124—31no—
43C2×#875—31no—
44C2×#870—31no—
45C3×#488—31no—
46C2×C3×C4×C8—31no—
47C2×#821—32no—
48C2×#816—32no—
49#5068—31no—
50#5056—31no—
51D3×#103—32no—
52#4800—32no—
53D3×#102—32no—
54#4768—32no—
55#4697—31no—
56#4697—31no—
57#4697—31no—
58#4697—31no—
59#4697—32no—
60#4697—32no—
61#4697—61no—
62#4697D311yescharacteristic, direct product factor
63C4×D3×C8D311yescharacteristic, complemented
64C22×D32—21no—
65C2×C4⋊(C3⋊D3)C2311yescharacteristic
66C2×#634C2311yescharacteristic
67C2×C3×D12C2311yescharacteristic
68C2×C3×C4×D3D412yes—
69C2×C3×C4×D3C2311yescharacteristic
70C2×C3×Dic6C2311yescharacteristic
71C2×#627—21no—
72C2×#626—21no—
73C2×D3×Dic3—21no—
74C2×D3×Dic3—22no—
75D3×D12—24no—
76D3×Dic6—24no—
77C2×C32×C8C2312yes—
78C32×C42C2311yescharacteristic
79#3752—22no—
80C4⋊(C3⋊Dic3)C2312yes—
81#3750—22no—
82C3×(C2×D3)⋊C4—22no—
83C3×C4⋊Dic3C2312yes—
84C3×Dic3⋊C4—22no—
85C3×C4×Dic3D412yes—
86C3×C4×Dic3C2311yescharacteristic
87C2×C3×C3⋊C8C2312yes—
88C3×D3×C8—24no—
89#3724—22no—
90Dic3⋊Dic3—22no—
91Dic3⋊Dic3—22no—
92#3722—22no—
93(C2×D3)⋊Dic3—22no—
94C2×#488—91noSylow
95C2×D3×Q8—31no—
96C2×D3×D4—31no—
97C22×D12—31no—
98C22×Dic6—31no—
99C22×C3×C8—32no—
100C3×#125—31no—
101C3×#124—31no—
102C2×C3×C42—31no—
103#947—31no—
104#936—31no—
105C2×(C2×D3)⋊C4—62no—
106C2×C4⋊Dic3—32no—
107C2×Dic3⋊C4—62no—
108C2×D3×C8C2×D312yes—
109D3×C4⋊C4—32no—
110D3×C4⋊C4—62no—
111#890—32no—
112#889—62no—
113#885—62no—
114D3×C22⋊C4—62no—
115#875—31no—
116#875—31no—
117#875—31no—
118#875—31no—
119#875—61no—
120#875—62no—
121#875C2×D311yescharacteristic
122C42×D3C2×D311yescharacteristic
123#870—31no—
124#870—31no—
125#870—32no—
126#870—61no—
127#870—62no—
128#870C2×D311yescharacteristic, complemented
129C3×#103—32no—
130C3×#102—32no—
131C3×C4×C8—21no—
132C3×C4×C8—32no—
133C3×C4×C8—31no—
134C3×C4×C8C2×D311yescharacteristic, complemented
135C3×C4×C8C2×D311yescharacteristic, complemented
136#835—32no—
137#832—32no—
138#821—32no—
139#821—32no—
140#821—32no—
141#821—32no—
142#821—62no—
143#821C2×D312yes—
144#816—32no—
145#816—32no—
146#816—32no—
147#816—32no—
148#816—62no—
149#816C2×D312yescomplemented
150C8×Dic3C2×D312yescomplemented
151#810—32no—
152#809—32no—
153C4×C3⋊C8C2×D311yescharacteristic, complemented
154C22×C3⋊D3—21no—
155C22×C3×D3—21no—
156C22×C3×D3C2×D411yescharacteristic
157C2×D32—42no—
158C2×D32—44no—
159C2×C32×C4C2×D412yes—
160C2×C32×C4C2411yescharacteristic
161C2×C3⋊Dic3—21no—
162C2×C3⋊Dic3—22no—
163C4⋊(C3⋊D3)—22no—
164#634—22no—
165C2×C3×Dic3—21no—
166C2×C3×Dic3—22no—
167C2×C3×Dic3C2×D412yes—
168C2×C3×Dic3C2×D411yescharacteristic
169C3×D12—22no—
170C3×C4×D3—24no—
171C3×C4×D3#4114yes—
172C3×Dic6—22no—
173#627—42no—
174#626—42no—
175D3×Dic3—42no—
176D3×Dic3—44no—
177C32×C8—22no—
178C3×C3⋊C8—22no—
179C2×#125—91no—
180C2×#124—91no—
181#488—31no—
182#488—92no—
183#488—92no—
184#488—91no—
185#488—91no—
186#488—91no—
187C2×#103—92no—
188C2×#102—92no—
189C2×C4×C8—31no—
190C23×D3—61no—
191C23×D3—61no—
192C2×C3×Q8—31no—
193C2×C3×D4—31no—
194C22×C3×C4—31no—
195C22×C3×C4—32no—
196C2×#67—61no—
197C22×Dic3—62no—
198C22×Dic3—61no—
199D3×Q8—64no—
200D3×D4—64no—
201C2×D12—31no—
202C2×D12—31no—
203C2×D12—61no—
204C2×D12—64no—
205C2×D12—61no—
206C2×D12C22×D311yescharacteristic
207C2×C4×D3—61no—
208C2×C4×D3—62no—
209C2×C4×D3D1212yes—
210C2×C4×D3C22×D311yescharacteristic
211C2×Dic6—31no—
212C2×Dic6—31no—
213C2×Dic6—61no—
214C2×Dic6—64no—
215C2×Dic6—61no—
216C2×Dic6—61no—
217C2×Dic6C22×D311yescharacteristic
218C2×C3×C8—22no—
219C2×C3×C8—32no—
220C2×C3×C8—64no—
221C2×C3×C8C22×D312yes—
222C2×C3×C8C22×D312yes—
223C3×C4⋊C4—32no—
224C3×C4⋊C4—62no—
225C3×C22⋊C4—62no—
226C3×C42—21no—
227C3×C42—32no—
228C3×C42—31no—
229C3×C42C22×D311yescharacteristic
230C3×C42C22×D311yescharacteristic
231#217—62no—
232(C2×D3)⋊C4—22no—
233(C2×D3)⋊C4—62no—
234(C2×D3)⋊C4—62no—
235(C2×D3)⋊C4—62no—
236(C2×D3)⋊C4—62no—
237(C2×D3)⋊C4—62no—
238(C2×D3)⋊C4—122no—
239C4⋊Dic3—32no—
240C4⋊Dic3—32no—
241C4⋊Dic3—62no—
242C4⋊Dic3—62no—
243C4⋊Dic3—62no—
244C4⋊Dic3C22×D312yes—
245Dic3⋊C4—22no—
246Dic3⋊C4—62no—
247Dic3⋊C4—62no—
248Dic3⋊C4—62no—
249Dic3⋊C4—62no—
250Dic3⋊C4—62no—
251Dic3⋊C4—62no—
252Dic3⋊C4—122no—
253C4×Dic3D1212yes—
254C4×Dic3C22×D311yescharacteristic
255C2×C3⋊C8C22×D312yes—
256D3×C8—24no—
257C22×C32C22×D411yescharacteristic
258C2×C3⋊D3—41no—
259C2×C3⋊D3—42no—
260C2×C3×D3—41no—
261C2×C3×D3—42no—
262C2×C3×D3#12412yes—
263C2×C3×D3#13514yes—
264D32—84no—
265C32×C4—22no—
266C32×C4C2×#4112yes—
267C3⋊Dic3—41no—
268C3⋊Dic3—42no—
269C3×Dic3—22no—
270C3×Dic3—41no—
271C3×Dic3—42no—
272C3×Dic3#12412yes—
273C22×Q8—91no—
274C22×D4—91no—
275C22×C8—32no—
276#125—31no—
277#125—92no—
278#125—91no—
279#125—182no—
280#124—31no—
281#124—91no—
282#124—91no—
283#124—91no—
284#124—182no—
285C2×C4⋊C4—92no—
286C2×C4⋊C4—182no—
287C2×C22⋊C4—182no—
288C2×C42—31no—
289#103—32no—
290#103—92no—
291#103—92no—
292#103—92no—
293#102—32no—
294#102—92no—
295#102—92no—
296#102—92no—
297C4×C8—32no—
298C4×C8—31no—
299C4×C8D3211yescharacteristic, complemented
300C23×C3—31no—
301C23×C3—61no—
302C22×D3—21no—
303C22×D3—61no—
304C22×D3—61no—
305C22×D3—121no—
306C22×D3—122no—
307C22×D3—124no—
308C22×D3—122no—
309C22×D3—124no—
310C22×D3C2×D1211yescharacteristic
311C3×Q8—62no—
312C3×D4—62no—
313C2×C3×C4—21no—
314C2×C3×C4—22no—
315C2×C3×C4—31no—
316C2×C3×C4—34no—
317C2×C3×C4—32no—
318C2×C3×C4—64no—
319C2×C3×C4—62no—
320C2×C3×C4—61no—
321C2×C3×C4C2×D1212yes—
322C2×C3×C4D3×D412yes—
323C2×C3×C4C23×D311yescharacteristic
324C2×C3×C4C23×D311yescharacteristic
325#67—122no—
326C2×Dic3—22no—
327C2×Dic3—21no—
328C2×Dic3—62no—
329C2×Dic3—61no—
330C2×Dic3—62no—
331C2×Dic3—61no—
332C2×Dic3—122no—
333C2×Dic3—121no—
334C2×Dic3—122no—
335C2×Dic3—124no—
336C2×Dic3C2×D1212yes—
337C2×Dic3C2×D1211yescharacteristic
338D12—22no—
339D12—62no—
340D12—62no—
341D12—122no—
342D12—122no—
343C4×D3—24no—
344C4×D3—122no—
345C4×D3—124no—
346C4×D3#23514yes—
347Dic6—22no—
348Dic6—62no—
349Dic6—62no—
350Dic6—122no—
351Dic6—122no—
352Dic6—122no—
353C3×C8—22no—
354C3×C8—22no—
355C3×C8—42no—
356C3×C8—62no—
357C3⋊C8—22no—
358C2×C32C2×#12411yescharacteristic
359C2×C32C2×#13512yes—
360C3⋊D3—81no—
361C3×D3—81no—
362C3×D3#48814yescomplemented
363C24—181no—
364C2×Q8—31no—
365C2×Q8—91no—
366C2×Q8—181no—
367C2×Q8—184no—
368C2×D4—31no—
369C2×D4—91no—
370C2×D4—184no—
371C2×D4—181no—
372C22×C4—31no—
373C22×C4—32no—
374C22×C4—181no—
375C22×C4—182no—
376C2×C8—32no—
377C2×C8—64no—
378C2×C8C2×D3212yes—
379C4⋊C4—32no—
380C4⋊C4—62no—
381C4⋊C4—92no—
382C4⋊C4—182no—
383C4⋊C4—182no—
384C4⋊C4—182no—
385C4⋊C4—182no—
386C22⋊C4—62no—
387C22⋊C4—182no—
388C22⋊C4—182no—
389C22⋊C4—182no—
390C42—31no—
391C42—32no—
392C42C2×D3211yescharacteristic
393C22×C3—21no—
394C22×C3—32no—
395C22×C3—34no—
396C22×C3—121no—
397C22×C3—122no—
398C22×C3C22×D1211yescharacteristic
399C22×C3C2×D3×D411yescharacteristic
400C2×D3—41no—
401C2×D3—42no—
402C2×D3—121no—
403C2×D3—121no—
404C2×D3—122no—
405C2×D3—122no—
406C2×D3—241no—
407C2×D3—242no—
408C2×D3—244no—
409C2×D3—244no—
410C2×D3#87512yes—
411C2×D3#90414yes—
412C3×C4—22no—
413C3×C4—22no—
414C3×C4—22no—
415C3×C4—32no—
416C3×C4—42no—
417C3×C4—62no—
418C3×C4—121no—
419C3×C4—122no—
420C3×C4C2×#23512yes—
421C3×C4D3×#4112yes—
422Dic3—22no—
423Dic3—41no—
424Dic3—42no—
425Dic3—121no—
426Dic3—121no—
427Dic3—122no—
428Dic3—122no—
429Dic3—241no—
430Dic3—242no—
431Dic3#87512yes—
432C32C2×#48811yescharacteristic, complemented, Sylow
433C23—31no—
434C23—61no—
435C23—181no—
436C23—362no—
437C23—364no—
438Q8—62no—
439Q8—182no—
440Q8—362no—
441D4—62no—
442D4—182no—
443D4—362no—
444C2×C4—31no—
445C2×C4—34no—
446C2×C4—32no—
447C2×C4—64no—
448C2×C4—61no—
449C2×C4—62no—
450C2×C4—181no—
451C2×C4—182no—
452C2×C4—362no—
453C2×C4—364no—
454C2×C4D3×D1212yes—
455C2×C4C22×D3211yescharacteristic
456C8—22no—
457C8—62no—
458C2×C3—22no—
459C2×C3—21no—
460C2×C3—34no—
461C2×C3—241no—
462C2×C3C2×#87511yescharacteristic
463C2×C3D3×#12411yescharacteristic
464C2×C3C2×#90412yes—
465C2×C3D3×#13512yes—
466D3—81no—
467D3—241no—
468D3—241no—
469D3—481no—
470D3#469714yesdirect product factor
471C22—34no—
472C22—32no—
473C22—122no—
474C22—121no—
475C22—362no—
476C22—361no—
477C22—724no—
478C22C2×D3×D1211yescharacteristic
479C4—22no—
480C4—32no—
481C4—62no—
482C4—122no—
483C4—121no—
484C4—362no—
485C4—361no—
486C4D3×#23512yes—
487C3—21no—
488C3C2×#469711yescharacteristic, complemented
489C3D3×#48811yescharacteristic, complemented
490C2—34no—
491C2—241no—
492C2—721no—
493C2D3×#87511yescharacteristic
494C2D3×#90412yes—
subgroupG/H
centerC22C2×D3×D12
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4×C8C22
socleC22×C32C22×D4
prime radicalC2×D3×D12C22
hypercenterC4×C8D32
hypocenterC32C2×#488
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8

Complements

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

NH ≅ G/Ntype
2. D3×#870C2semidirect
3. #10592396C2semidirect
4. C3×#4697C2semidirect
5. C3×C4×D3×C8C2semidirect
7. #10590872C2semidirect
8. #10590863C2semidirect
9. D3×#816C2semidirect
10. #10590293C2semidirect
11. #10590274C2semidirect
17. #64079C22semidirect
21. C3×#870C22semidirect
25. #63869C22semidirect
30. C32×C4×C8C22semidirect
32. #63643C22semidirect
34. C3×#816C22semidirect
35. C3×C8×Dic3C22semidirect
36. C3×C4×C3⋊C8C22semidirect
37. #63567C22semidirect
38. #63566C22semidirect
62. #4697D3direct (N × H)
63. C4×D3×C8D3semidirect
128. #870C2×D3semidirect
134. C3×C4×C8C2×D3semidirect
135. C3×C4×C8C2×D3semidirect
149. #816C2×D3semidirect
150. C8×Dic3C2×D3semidirect
153. C4×C3⋊C8C2×D3semidirect
299. C4×C8D32semidirect
362. C3×D3#488semidirect
432. C32C2×#488semidirect
470. D3#4697direct (N × H)
488. C3C2×#4697semidirect
489. C3D3×#488semidirect

Maximal subgroups

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

subgroupindex
D3×#8752
D3×#8702
#105923962
C3×#46972
C3×C4×D3×C82
D3×#8212
#105908722
#105908632
D3×#8162
#105902932
#105902742
D3×#4883
C2×#46973