Finite Group Databasebeta

← #11869387

Subgroups — #11869387

Order 1152.

1001 conjugacy classes of subgroups.

The subgroup lattice has 512 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595429C211yesmaximal, characteristic
2D32×C4⋊C4C211yesmaximal, characteristic
3C3⋊D3×#103C211yesmaximal, characteristic, complemented
4C3×#4805C212yesmaximal, complemented
5#10591552C211yesmaximal, characteristic, complemented
6#10591549C212yesmaximal, complemented
7#10590935C211yesmaximal, characteristic
8#10590685C211yesmaximal, characteristic, complemented
9#10590674C212yesmaximal, complemented
10#10590575C211yesmaximal, characteristic, complemented
11#10590426C212yesmaximal, complemented
12D3×#483—32nomaximal
13C2×Q8×C3⋊D3C2211yescharacteristic
14C2×C4×D32—21no—
15C2×C4×D32C2211yescharacteristic
16C2×C8×C3⋊D3C2211yescharacteristic
17C4⋊C4×C3⋊D3C2211yescharacteristic
18C3×#946C2212yes—
19C3×D3×C4⋊C4C2212yes—
20#63921—21no—
21#63900C2211yescharacteristic
22#63900C2211yescharacteristic
23#63896—22no—
24D3×C4⋊Dic3C2212yes—
25#63883—21no—
26#63883—21no—
27D3×Dic3⋊C4—22no—
28#63857C2212yes—
29C2×#3710C2211yescharacteristic
30C32×#103C2211yescharacteristic, complemented
31#63662C2211yescharacteristic, complemented
32#63643C2211yescharacteristic, complemented
33#63637C2211yescharacteristic, complemented
34C3×#835C2212yescomplemented
35C3×(C2×D3)⋊C8C2212yes—
36C3×#817C2212yescomplemented
37C3×#808C2212yescomplemented
38#63574C2212yescomplemented
39#63573C2212yescomplemented
40#63567C2212yescomplemented
41(C2×D3)⋊(C3⋊C8)C2212yes—
42D3×C22⋊Q8—32no—
43C2×D3×C4⋊C4—32no—
44C3×#483—32no—
45#5043—32no—
46#4971—32no—
47#4862—32no—
48#4862—32no—
49D3×#106—32no—
50D3×#106—32no—
51#4805—32no—
52#4805D312yescomplemented
53D3×#103—32no—
54D3×#103—32no—
55D3×#103—61no—
56D3×C22⋊C8—32no—
57#4721—32no—
58C22×D32D411yescharacteristic
59C2×C32×Q8C2311yescharacteristic
60Q8×C3⋊D3—22no—
61Q8×C3⋊D3—22no—
62C2×C4×C3⋊D3—21no—
63C2×C4×C3⋊D3—21no—
64C2×C4×C3⋊D3C2311yescharacteristic
65C2×#634—21no—
66C2×#634C2311yescharacteristic
67C2×C3×C4×D3—22no—
68C2×C3×C4×D3C2312yes—
69C2×#624—21no—
70C2×#624—21no—
71C2×#624D411yescharacteristic
72C2×D3×Dic3—22no—
73C2×D3×Dic3D412yes—
74C4×D32—22no—
75C4×D32—22no—
76C4×D32—44no—
77C2×C32×C8C2311yescharacteristic
78C32×C4⋊C4C2311yescharacteristic
79C4⋊(C3⋊Dic3)C2311yescharacteristic
80#3750—21no—
81C2×C3⋊(C3⋊C8)C2311yescharacteristic
82C8×C3⋊D3—22no—
83C3×(C2×D3)⋊C4—22no—
84C3×C4⋊Dic3C2312yes—
85C3×C4⋊Dic3C2312yes—
86C3×Dic3⋊C4—22no—
87C3×Dic3⋊C4—22no—
88C2×C3×C3⋊C8C2312yes—
89#3724—21no—
90#3724—21no—
91Dic3⋊Dic3—22no—
92Dic3⋊Dic3—22no—
93(C2×D3)⋊Dic3—22no—
94#3710—22no—
95C2×#483—91noSylow
96C2×D3×Q8—32no—
97C2×D3×Q8—61no—
98C22×C4×D3—32no—
99C22×C4×D3—62no—
100C3×C22⋊Q8—32no—
101C2×C3×C4⋊C4—32no—
102#946C2×D312yes—
103C2×C4⋊Dic3—32no—
104#924—32no—
105C2×Dic3⋊C4—62no—
106C2×D3×C8—32no—
107C2×D3×C8—32no—
108C2×D3×C8—61no—
109#897—32no—
110#896—62no—
111D3×C4⋊C4—32no—
112D3×C4⋊C4—32no—
113D3×C4⋊C4—32no—
114D3×C4⋊C4—32no—
115D3×C4⋊C4—61no—
116D3×C4⋊C4—62no—
117D3×C4⋊C4—62no—
118D3×C4⋊C4—62no—
119D3×C4⋊C4C2×D312yes—
120D3×C22⋊C4—62no—
121#878—62no—
122C3×#106—32no—
123C3×#106—32no—
124C3×#103—21no—
125C3×#103—32no—
126C3×#103C2×D312yescomplemented
127C3×C22⋊C8—32no—
128#835—32no—
129#835—61no—
130#835C2×D312yescomplemented
131#830—32no—
132(C2×D3)⋊C8—32no—
133(C2×D3)⋊C8C2×D312yes—
134#817—32no—
135#817C2×D312yescomplemented
136#816—32no—
137#816—32no—
138#816—61no—
139#810—32no—
140#810—32no—
141#810—61no—
142#808—32no—
143#808—32no—
144#808—32no—
145#808C2×D312yescomplemented
146C22×C3⋊D3C2×D411yescharacteristic
147C22×C3×D3C2×D412yes—
148C2×D32—22no—
149C2×D32—22no—
150C2×D32SD1614yes—
151C32×Q8—21no—
152C32×Q8—21no—
153C2×C32×C4—21no—
154C2×C32×C4—21no—
155C2×C32×C4C2411yescharacteristic
156C2×C3⋊Dic3—21no—
157C2×C3⋊Dic3—21no—
158C2×C3⋊Dic3C2×D411yescharacteristic
159C4×C3⋊D3—42no—
160C4×C3⋊D3—42no—
161C4×C3⋊D3#4112yes—
162C4×C3⋊D3#4112yes—
163#634—21no—
164#634—21no—
165#634—42no—
166C2×C3×Dic3—22no—
167C2×C3×Dic3—22no—
168C2×C3×Dic3C2×D412yes—
169C3×C4×D3—22no—
170C3×C4×D3—22no—
171C3×C4×D3—44no—
172#624—22no—
173#624—42no—
174#624—42no—
175D3×Dic3—24no—
176D3×Dic3—44no—
177C32×C8—21no—
178C3⋊(C3⋊C8)—21no—
179C3×C3⋊C8—22no—
180C2×C22⋊Q8—91no—
181C22×C4⋊C4—91no—
182#483—32no—
183#483—92no—
184#483—92no—
185#483—92no—
186C2×#106—91no—
187C2×#106—91no—
188C2×#103—91no—
189C2×#103—91no—
190C2×C22⋊C8—91no—
191C23×D3—32no—
192C2×C3×Q8—21no—
193C2×C3×Q8C22×D312yes—
194C22×C3×C4—32no—
195C22×C3×C4—62no—
196C22×Dic3—32no—
197C22×Dic3—62no—
198D3×Q8—64no—
199D3×Q8—64no—
200D3×Q8—64no—
201D3×Q8—122no—
202C2×C4×D3—22no—
203C2×C4×D3—32no—
204C2×C4×D3—32no—
205C2×C4×D3—32no—
206C2×C4×D3—61no—
207C2×C4×D3—64no—
208C2×C4×D3—64no—
209C2×C4×D3—62no—
210C2×C4×D3—62no—
211C2×C4×D3—62no—
212C2×C4×D3—62no—
213C2×C4×D3—62no—
214C2×C4×D3—121no—
215C2×C4×D3—121no—
216C2×C4×D3—128no—
217C2×C4×D3C22×D312yes—
218C2×Dic6—32no—
219C2×Dic6—61no—
220C2×Dic6—62no—
221C2×Dic6—121no—
222C2×C3×C8—21no—
223C2×C3×C8—32no—
224C2×C3×C8C22×D312yes—
225C3×C4⋊C4—21no—
226C3×C4⋊C4—32no—
227C3×C4⋊C4—32no—
228C3×C4⋊C4—62no—
229C3×C4⋊C4—62no—
230C3×C4⋊C4C22×D312yes—
231C3×C22⋊C4—62no—
232#217—62no—
233(C2×D3)⋊C4—22no—
234(C2×D3)⋊C4—62no—
235C4⋊Dic3—32no—
236C4⋊Dic3—61no—
237C4⋊Dic3—62no—
238C4⋊Dic3—62no—
239C4⋊Dic3C22×D312yes—
240C4⋊Dic3C22×D312yes—
241Dic3⋊C4—22no—
242Dic3⋊C4—22no—
243Dic3⋊C4—62no—
244Dic3⋊C4—62no—
245Dic3⋊C4—62no—
246Dic3⋊C4—62no—
247Dic3⋊C4—62no—
248Dic3⋊C4—121no—
249C2×C3⋊C8—32no—
250C2×C3⋊C8—61no—
251C2×C3⋊C8C22×D312yes—
252D3×C8—64no—
253D3×C8—64no—
254D3×C8—122no—
255C22×C32C22×D411yescharacteristic
256C2×C3⋊D3#12312yes—
257C2×C3⋊D3C2×SD1612yes—
258C2×C3⋊D3#13712yes—
259C2×C3×D3—22no—
260C2×C3×D3—22no—
261C2×C3×D3C2×SD1614yes—
262D32—28no—
263C32×C4—41no—
264C32×C4—41no—
265C32×C4C2×#4111yescharacteristic
266C32×C4C2×#4111yescharacteristic
267C3⋊Dic3—41no—
268C3⋊Dic3—41no—
269C3⋊Dic3#12312yes—
270C3×Dic3—22no—
271C3×Dic3—42no—
272C3×Dic3—42no—
273C22×Q8—91no—
274C23×C4—91no—
275C23×C4—181no—
276C22×C8—91no—
277C22×C8—91no—
278C22⋊Q8—32no—
279C22⋊Q8—92no—
280C22⋊Q8—182no—
281C2×C4⋊C4—32no—
282C2×C4⋊C4—91no—
283C2×C4⋊C4—91no—
284C2×C4⋊C4—92no—
285C2×C4⋊C4—91no—
286C2×C4⋊C4—181no—
287C2×C4⋊C4—181no—
288C2×C4⋊C4—182no—
289C2×C22⋊C4—181no—
290#106—32no—
291#106—32no—
292#106—92no—
293#106—92no—
294#103—32no—
295#103—92no—
296#103—91no—
297#103—91no—
298#103—91no—
299#103D3211yescharacteristic, complemented
300C22⋊C8—32no—
301C22⋊C8—92no—
302C23×C3—32no—
303C22×D3—32no—
304C22×D3—38no—
305C22×D3—61no—
306C22×D3—64no—
307C22×D3—64no—
308C22×D3D3×D412yes—
309C3×Q8—22no—
310C3×Q8—22no—
311C3×Q8—22no—
312C3×Q8—41no—
313C2×C3×C4—22no—
314C2×C3×C4—22no—
315C2×C3×C4—21no—
316C2×C3×C4—32no—
317C2×C3×C4—41no—
318C2×C3×C4—41no—
319C2×C3×C4—62no—
320C2×C3×C4—62no—
321C2×C3×C4—62no—
322C2×C3×C4—62no—
323C2×C3×C4—124no—
324C2×C3×C4C23×D312yes—
325C2×Dic3—22no—
326C2×Dic3—22no—
327C2×Dic3—32no—
328C2×Dic3—61no—
329C2×Dic3—64no—
330C2×Dic3—62no—
331C2×Dic3—62no—
332C2×Dic3—121no—
333C2×Dic3—121no—
334C2×Dic3—124no—
335C2×Dic3D3×D412yes—
336C4×D3—22no—
337C4×D3—22no—
338C4×D3—34no—
339C4×D3—34no—
340C4×D3—44no—
341C4×D3—62no—
342C4×D3—62no—
343C4×D3—64no—
344C4×D3—64no—
345C4×D3—124no—
346C4×D3—124no—
347C4×D3—124no—
348C4×D3—124no—
349C4×D3—124no—
350C4×D3—124no—
351C4×D3—242no—
352Dic6—62no—
353Dic6—62no—
354Dic6—62no—
355Dic6—121no—
356Dic6—124no—
357Dic6—124no—
358C3×C8—22no—
359C3×C8—41no—
360C3×C8—62no—
361C3⋊C8—22no—
362C3⋊C8—62no—
363C3⋊C8—121no—
364C2×C32C2×#12311yescharacteristic
365C2×C32C22×SD1611yescharacteristic
366C2×C32C2×#13711yescharacteristic
367C3⋊D3#48314yescomplemented
368C3×D3—24no—
369C24—91no—
370C2×Q8—91no—
371C2×Q8—181no—
372C2×Q8—182no—
373C2×Q8—182no—
374C2×Q8C2×D3211yescharacteristic
375C22×C4—32no—
376C22×C4—62no—
377C22×C4—91no—
378C22×C4—92no—
379C22×C4—91no—
380C22×C4—181no—
381C22×C4—181no—
382C22×C4—182no—
383C22×C4—182no—
384C22×C4—181no—
385C22×C4—181no—
386C22×C4—182no—
387C22×C4—364no—
388C2×C8—32no—
389C2×C8—91no—
390C2×C8—182no—
391C2×C8—182no—
392C2×C8C2×D3211yescharacteristic
393C4⋊C4—32no—
394C4⋊C4—32no—
395C4⋊C4—62no—
396C4⋊C4—62no—
397C4⋊C4—91no—
398C4⋊C4—181no—
399C4⋊C4—182no—
400C4⋊C4—182no—
401C4⋊C4—181no—
402C4⋊C4—181no—
403C4⋊C4C2×D3211yescharacteristic
404C22⋊C4—62no—
405C22⋊C4—182no—
406C22×C3—21no—
407C22×C3—34no—
408C22×C3—62no—
409C22×C3—62no—
410C22×C3C2×D3×D412yes—
411C2×D3—22no—
412C2×D3—22no—
413C2×D3—34no—
414C2×D3—34no—
415C2×D3—34no—
416C2×D3—62no—
417C2×D3—62no—
418C2×D3—62no—
419C2×D3—616no—
420C2×D3D3×SD1614yes—
421C3×C4—21no—
422C3×C4—21no—
423C3×C4—42no—
424C3×C4—42no—
425C3×C4—42no—
426C3×C4—62no—
427C3×C4—81no—
428C3×C4—122no—
429C3×C4—122no—
430C3×C4D3×#4112yes—
431C3×C4D3×#4112yes—
432Dic3—22no—
433Dic3—34no—
434Dic3—42no—
435Dic3—42no—
436Dic3—62no—
437Dic3—122no—
438Dic3—122no—
439Dic3—122no—
440Dic3—241no—
441C32C2×#48311yescharacteristic, complemented, Sylow
442C23—32no—
443C23—94no—
444C23—91no—
445C23—182no—
446C23—182no—
447Q8—21no—
448Q8—21no—
449Q8—181no—
450Q8—181no—
451Q8—362no—
452C2×C4—21no—
453C2×C4—21no—
454C2×C4—32no—
455C2×C4—62no—
456C2×C4—62no—
457C2×C4—62no—
458C2×C4—62no—
459C2×C4—91no—
460C2×C4—92no—
461C2×C4—92no—
462C2×C4—124no—
463C2×C4—182no—
464C2×C4—184no—
465C2×C4—181no—
466C2×C4—181no—
467C2×C4—362no—
468C2×C4—362no—
469C2×C4—362no—
470C2×C4—362no—
471C2×C4—364no—
472C2×C4C22×D3211yescharacteristic
473C8—21no—
474C8—62no—
475C8—181no—
476C2×C3—21no—
477C2×C3—21no—
478C2×C3—21no—
479C2×C3—64no—
480C2×C3D3×#12312yes—
481C2×C3C2×D3×SD1612yes—
482C2×C3D3×#13712yes—
483D3—24no—
484D3—38no—
485D3—64no—
486C22—34no—
487C22—62no—
488C22—62no—
489C22—92no—
490C22—92no—
491C22—92no—
492C22—188no—
493C22D32×D411yescharacteristic
494C4—41no—
495C4—41no—
496C4—62no—
497C4—92no—
498C4—122no—
499C4—122no—
500C4—361no—
501C4—361no—
502C4#6430611yescharacteristic
503C4#6431211yescharacteristic
504C3—21no—
505C3D3×#48312yescomplemented
506C2—64no—
507C2—94no—
508C2#1059426011yescharacteristic
509C2D32×SD1611yescharacteristic
510C2#1059476011yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#103C22
socleC22×C32C22×D4
prime radicalC22×D32D4
hypercenter#103D32
hypocenterC32C2×#483
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ #103

Complements

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

NH ≅ G/Ntype
3. C3⋊D3×#103C2semidirect
4. C3×#4805C2semidirect
5. #10591552C2semidirect
6. #10591549C2semidirect
8. #10590685C2semidirect
9. #10590674C2semidirect
10. #10590575C2semidirect
11. #10590426C2semidirect
30. C32×#103C22semidirect
31. #63662C22semidirect
32. #63643C22semidirect
33. #63637C22semidirect
34. C3×#835C22semidirect
36. C3×#817C22semidirect
37. C3×#808C22semidirect
38. #63574C22semidirect
39. #63573C22semidirect
40. #63567C22semidirect
52. #4805D3semidirect
126. C3×#103C2×D3semidirect
130. #835C2×D3semidirect
135. #817C2×D3semidirect
145. #808C2×D3semidirect
299. #103D32semidirect
367. C3⋊D3#483semidirect
441. C32C2×#483semidirect
505. C3D3×#483semidirect

Maximal subgroups

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

subgroupindex
#105954292
D32×C4⋊C42
C3⋊D3×#1032
C3×#48052
#105915522
#105915492
#105909352
#105906852
#105906742
#105905752
#105904262
D3×#4833