Finite Group Databasebeta

← #11869527

Subgroups — #11869527

Order 1152.

913 conjugacy classes of subgroups.

The subgroup lattice has 501 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595429C211yesmaximal, characteristic
2#10594602C211yesmaximal, characteristic
3C3⋊D3×#103C211yesmaximal, characteristic, complemented
4C3×#4814C212yesmaximal, complemented
5#10591559C212yesmaximal, complemented
6#10591552C211yesmaximal, characteristic, complemented
7#10590935C211yesmaximal, characteristic
8#10590708C212yesmaximal, complemented
9#10590687C211yesmaximal, characteristic, complemented
10#10590575C211yesmaximal, characteristic, complemented
11#10590428C212yesmaximal, complemented
12D3×#485—32nomaximal
13C2×Q8×C3⋊D3C2211yescharacteristic
14C2×C4×D32C2211yescharacteristic
15C2×C8×C3⋊D3C2211yescharacteristic
16C4⋊C4×C3⋊D3C2211yescharacteristic
17C3×#946C2212yes—
18C3×#892C2212yes—
19#63921—21no—
20#63921—21no—
21#63900C2211yescharacteristic
22#63900C2211yescharacteristic
23#63896—22no—
24#63883—21no—
25C4×#624—21no—
26#63877—22no—
27#63857C2212yes—
28#63841C2212yes—
29C2×#3710C2211yescharacteristic
30C32×#103C2211yescharacteristic, complemented
31#63662C2211yescharacteristic, complemented
32#63643C2211yescharacteristic, complemented
33#63637C2211yescharacteristic, complemented
34C3×#835C2212yescomplemented
35C3×(C2×D3)⋊C8C2212yes—
36C3×#818C2212yescomplemented
37C3×#808C2212yescomplemented
38#63576C2212yescomplemented
39#63573C2212yescomplemented
40#63567C2212yescomplemented
41(C2×D3)⋊(C3⋊C8)C2212yes—
42D3×C22⋊Q8—32no—
43D3×#117—32no—
44C3×#485—32no—
45#5045—32no—
46#4996—32no—
47#4888—32no—
48D3×#107—32no—
49#4868—32no—
50D3×#106—32no—
51#4815—32no—
52#4814D312yescomplemented
53D3×#103—32no—
54D3×#103—32no—
55D3×#103—61no—
56D3×C22⋊C8—32no—
57#4723—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×D3C2312yes—
68C2×#624—21no—
69C2×#624—21no—
70C2×#624D411yescharacteristic
71C2×D3×Dic3D412yes—
72C4×D32—22no—
73C4×D32—22no—
74C2×C32×C8C2311yescharacteristic
75C32×C4⋊C4C2311yescharacteristic
76C4⋊(C3⋊Dic3)C2311yescharacteristic
77#3750—21no—
78C2×C3⋊(C3⋊C8)C2311yescharacteristic
79C8×C3⋊D3—22no—
80C3×(C2×D3)⋊C4—22no—
81C3×(C2×D3)⋊C4—22no—
82C3×C4⋊Dic3C2312yes—
83C3×C4⋊Dic3C2312yes—
84C3×Dic3⋊C4—22no—
85C3×C4×Dic3—22no—
86C2×C3×C3⋊C8C2312yes—
87#3724—21no—
88#3724—21no—
89Dic3⋊Dic3—22no—
90(C2×D3)⋊Dic3—22no—
91(C2×D3)⋊Dic3—22no—
92Dic32—22no—
93#3710—22no—
94C2×#485—91noSylow
95C2×D3×Q8—32no—
96C2×D3×Q8—61no—
97C22×C4×D3—32no—
98C3×C22⋊Q8—32no—
99C3×#117—32no—
100#946C2×D312yes—
101#926—32no—
102#924—32no—
103C2×D3×C8—32no—
104C2×D3×C8—32no—
105C2×D3×C8—61no—
106#897—32no—
107#896—62no—
108#892—32no—
109#892C2×D312yes—
110D3×C4⋊C4—32no—
111D3×C4⋊C4—32no—
112D3×C4⋊C4—32no—
113D3×C4⋊C4—61no—
114D3×C4⋊C4—62no—
115D3×C22⋊C4—62no—
116D3×C22⋊C4—62no—
117#878—62no—
118#877—62no—
119#872—62no—
120C42×D3—62no—
121C3×#107—32no—
122C3×#106—32no—
123C3×#103—21no—
124C3×#103—32no—
125C3×#103C2×D312yescomplemented
126C3×C22⋊C8—32no—
127#835—32no—
128#835—61no—
129#835C2×D312yescomplemented
130#830—32no—
131(C2×D3)⋊C8—32no—
132(C2×D3)⋊C8C2×D312yes—
133#818C2×D312yescomplemented
134#817—32no—
135#816—32no—
136#816—32no—
137#816—61no—
138#810—32no—
139#810—32no—
140#810—61no—
141#808—32no—
142#808C2×D312yescomplemented
143#807—32no—
144#807—32no—
145C22×C3⋊D3C2×D411yescharacteristic
146C22×C3×D3C2×D412yes—
147C2×D32—22no—
148C2×D32—22no—
149C2×D32—22no—
150C32×Q8—21no—
151C32×Q8—21no—
152C2×C32×C4—21no—
153C2×C32×C4—21no—
154C2×C32×C4C2411yescharacteristic
155C2×C3⋊Dic3—21no—
156C2×C3⋊Dic3—21no—
157C2×C3⋊Dic3C2×D411yescharacteristic
158C4×C3⋊D3—42no—
159C4×C3⋊D3—42no—
160C4×C3⋊D3#4112yes—
161C4×C3⋊D3#4112yes—
162#634—21no—
163#634—21no—
164#634—42no—
165C2×C3×Dic3—22no—
166C2×C3×Dic3—22no—
167C2×C3×Dic3C2×D412yes—
168C3×C4×D3—22no—
169C3×C4×D3—22no—
170#624—22no—
171#624—42no—
172#624—42no—
173D3×Dic3—24no—
174C32×C8—21no—
175C3⋊(C3⋊C8)—21no—
176C3×C3⋊C8—22no—
177C2×C22⋊Q8—91no—
178C2×#117—91no—
179#485—32no—
180#485—92no—
181#485—92no—
182#485—92no—
183C2×#107—91no—
184C2×#106—91no—
185C2×#103—91no—
186C2×#103—91no—
187C2×C22⋊C8—91no—
188C23×D3—32no—
189C2×C3×Q8—21no—
190C2×C3×Q8C22×D312yes—
191C22×C3×C4—32no—
192C22×Dic3—32no—
193D3×Q8—64no—
194D3×Q8—64no—
195D3×Q8—64no—
196D3×Q8—122no—
197C2×C4×D3—32no—
198C2×C4×D3—32no—
199C2×C4×D3—32no—
200C2×C4×D3—61no—
201C2×C4×D3—64no—
202C2×C4×D3—64no—
203C2×C4×D3—62no—
204C2×C4×D3—62no—
205C2×C4×D3—62no—
206C2×C4×D3—62no—
207C2×C4×D3—121no—
208C2×C4×D3—121no—
209C2×C4×D3C22×D312yes—
210C2×Dic6—32no—
211C2×Dic6—61no—
212C2×Dic6—62no—
213C2×Dic6—121no—
214C2×C3×C8—21no—
215C2×C3×C8—32no—
216C2×C3×C8C22×D312yes—
217C3×C4⋊C4—21no—
218C3×C4⋊C4—32no—
219C3×C4⋊C4—32no—
220C3×C4⋊C4—62no—
221C3×C4⋊C4C22×D312yes—
222C3×C22⋊C4—62no—
223C3×C22⋊C4—62no—
224C3×C42—62no—
225#217—62no—
226#217—62no—
227(C2×D3)⋊C4—22no—
228(C2×D3)⋊C4—22no—
229(C2×D3)⋊C4—62no—
230(C2×D3)⋊C4—62no—
231C4⋊Dic3—32no—
232C4⋊Dic3—61no—
233C4⋊Dic3—62no—
234C4⋊Dic3C22×D312yes—
235C4⋊Dic3C22×D312yes—
236Dic3⋊C4—22no—
237Dic3⋊C4—62no—
238Dic3⋊C4—62no—
239Dic3⋊C4—62no—
240Dic3⋊C4—62no—
241Dic3⋊C4—121no—
242C4×Dic3—22no—
243C4×Dic3—62no—
244C4×Dic3—62no—
245C2×C3⋊C8—32no—
246C2×C3⋊C8—61no—
247C2×C3⋊C8C22×D312yes—
248D3×C8—64no—
249D3×C8—64no—
250D3×C8—122no—
251C22×C32C22×D411yescharacteristic
252C2×C3⋊D3#12312yes—
253C2×C3⋊D3#13512yes—
254C2×C3⋊D3#13712yes—
255C2×C3×D3—22no—
256C2×C3×D3—22no—
257C2×C3×D3—22no—
258D32—44no—
259C32×C4—41no—
260C32×C4—41no—
261C32×C4C2×#4111yescharacteristic
262C32×C4C2×#4111yescharacteristic
263C3⋊Dic3—41no—
264C3⋊Dic3—41no—
265C3⋊Dic3#12312yes—
266C3×Dic3—22no—
267C3×Dic3—42no—
268C3×Dic3—42no—
269C22×Q8—91no—
270C23×C4—91no—
271C22×C8—91no—
272C22×C8—91no—
273C22⋊Q8—32no—
274C22⋊Q8—92no—
275C22⋊Q8—182no—
276#117—32no—
277#117—92no—
278#117—182no—
279C2×C4⋊C4—91no—
280C2×C4⋊C4—91no—
281C2×C4⋊C4—91no—
282C2×C4⋊C4—181no—
283C2×C22⋊C4—181no—
284C2×C22⋊C4—181no—
285C2×C42—181no—
286#107—32no—
287#107—92no—
288#106—32no—
289#106—92no—
290#103—32no—
291#103—92no—
292#103—91no—
293#103—91no—
294#103—91no—
295#103D3211yescharacteristic, complemented
296C22⋊C8—32no—
297C22⋊C8—92no—
298C23×C3—32no—
299C22×D3—32no—
300C22×D3—61no—
301C22×D3—64no—
302C22×D3—64no—
303C22×D3—64no—
304C22×D3D3×D412yes—
305C3×Q8—22no—
306C3×Q8—22no—
307C3×Q8—22no—
308C3×Q8—41no—
309C2×C3×C4—22no—
310C2×C3×C4—22no—
311C2×C3×C4—21no—
312C2×C3×C4—32no—
313C2×C3×C4—41no—
314C2×C3×C4—41no—
315C2×C3×C4—62no—
316C2×C3×C4—62no—
317C2×C3×C4—62no—
318C2×C3×C4—62no—
319C2×C3×C4C23×D312yes—
320C2×Dic3—22no—
321C2×Dic3—22no—
322C2×Dic3—32no—
323C2×Dic3—61no—
324C2×Dic3—64no—
325C2×Dic3—62no—
326C2×Dic3—62no—
327C2×Dic3—121no—
328C2×Dic3—121no—
329C2×Dic3D3×D412yes—
330C4×D3—22no—
331C4×D3—22no—
332C4×D3—34no—
333C4×D3—34no—
334C4×D3—62no—
335C4×D3—62no—
336C4×D3—64no—
337C4×D3—64no—
338C4×D3—124no—
339C4×D3—124no—
340C4×D3—124no—
341C4×D3—124no—
342C4×D3—124no—
343C4×D3—242no—
344Dic6—62no—
345Dic6—62no—
346Dic6—62no—
347Dic6—121no—
348Dic6—124no—
349Dic6—124no—
350C3×C8—22no—
351C3×C8—41no—
352C3×C8—62no—
353C3⋊C8—22no—
354C3⋊C8—62no—
355C3⋊C8—121no—
356C2×C32C2×#12311yescharacteristic
357C2×C32C2×#13511yescharacteristic
358C2×C32C2×#13711yescharacteristic
359C3⋊D3#48514yescomplemented
360C3×D3—42no—
361C24—91no—
362C2×Q8—91no—
363C2×Q8—181no—
364C2×Q8—182no—
365C2×Q8—182no—
366C2×Q8C2×D3211yescharacteristic
367C22×C4—32no—
368C22×C4—91no—
369C22×C4—92no—
370C22×C4—91no—
371C22×C4—181no—
372C22×C4—181no—
373C22×C4—182no—
374C22×C4—182no—
375C22×C4—181no—
376C22×C4—181no—
377C2×C8—32no—
378C2×C8—91no—
379C2×C8—182no—
380C2×C8—182no—
381C2×C8C2×D3211yescharacteristic
382C4⋊C4—32no—
383C4⋊C4—32no—
384C4⋊C4—62no—
385C4⋊C4—91no—
386C4⋊C4—181no—
387C4⋊C4—182no—
388C4⋊C4—181no—
389C4⋊C4—181no—
390C4⋊C4C2×D3211yescharacteristic
391C22⋊C4—62no—
392C22⋊C4—62no—
393C22⋊C4—182no—
394C22⋊C4—182no—
395C42—62no—
396C42—182no—
397C22×C3—21no—
398C22×C3—62no—
399C22×C3—62no—
400C22×C3—62no—
401C22×C3C2×D3×D412yes—
402C2×D3—22no—
403C2×D3—22no—
404C2×D3—22no—
405C2×D3—34no—
406C2×D3—34no—
407C2×D3—34no—
408C2×D3—62no—
409C2×D3—62no—
410C2×D3—62no—
411C2×D3—128no—
412C3×C4—21no—
413C3×C4—21no—
414C3×C4—42no—
415C3×C4—42no—
416C3×C4—42no—
417C3×C4—62no—
418C3×C4—81no—
419C3×C4—122no—
420C3×C4—122no—
421C3×C4D3×#4112yes—
422C3×C4D3×#4112yes—
423Dic3—22no—
424Dic3—34no—
425Dic3—42no—
426Dic3—42no—
427Dic3—62no—
428Dic3—122no—
429Dic3—122no—
430Dic3—122no—
431Dic3—241no—
432C32C2×#48511yescharacteristic, complemented, Sylow
433C23—32no—
434C23—91no—
435C23—182no—
436C23—182no—
437C23—182no—
438Q8—21no—
439Q8—21no—
440Q8—181no—
441Q8—181no—
442Q8—362no—
443C2×C4—21no—
444C2×C4—21no—
445C2×C4—32no—
446C2×C4—62no—
447C2×C4—62no—
448C2×C4—62no—
449C2×C4—62no—
450C2×C4—91no—
451C2×C4—92no—
452C2×C4—92no—
453C2×C4—182no—
454C2×C4—184no—
455C2×C4—181no—
456C2×C4—181no—
457C2×C4—362no—
458C2×C4—362no—
459C2×C4—362no—
460C2×C4—362no—
461C2×C4C22×D3211yescharacteristic
462C8—21no—
463C8—62no—
464C8—181no—
465C2×C3—21no—
466C2×C3—21no—
467C2×C3—21no—
468C2×C3—122no—
469C2×C3D3×#12312yes—
470C2×C3D3×#13512yes—
471C2×C3D3×#13712yes—
472D3—38no—
473D3—42no—
474D3—64no—
475C22—62no—
476C22—62no—
477C22—62no—
478C22—92no—
479C22—92no—
480C22—92no—
481C22—364no—
482C22D32×D411yescharacteristic
483C4—41no—
484C4—41no—
485C4—62no—
486C4—92no—
487C4—122no—
488C4—122no—
489C4—361no—
490C4—361no—
491C4#6430611yescharacteristic
492C4#6431211yescharacteristic
493C3—21no—
494C3D3×#48512yescomplemented
495C2—94no—
496C2—122no—
497C2#1059426011yescharacteristic
498C2#1059474211yescharacteristic
499C2#1059476411yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#103C22
socleC22×C32C22×D4
prime radicalC22×D32D4
hypercenter#103D32
hypocenterC32C2×#485
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×#4814C2semidirect
5. #10591559C2semidirect
6. #10591552C2semidirect
8. #10590708C2semidirect
9. #10590687C2semidirect
10. #10590575C2semidirect
11. #10590428C2semidirect
30. C32×#103C22semidirect
31. #63662C22semidirect
32. #63643C22semidirect
33. #63637C22semidirect
34. C3×#835C22semidirect
36. C3×#818C22semidirect
37. C3×#808C22semidirect
38. #63576C22semidirect
39. #63573C22semidirect
40. #63567C22semidirect
52. #4814D3semidirect
125. C3×#103C2×D3semidirect
129. #835C2×D3semidirect
133. #818C2×D3semidirect
142. #808C2×D3semidirect
295. #103D32semidirect
359. C3⋊D3#485semidirect
432. C32C2×#485semidirect
494. C3D3×#485semidirect

Maximal subgroups

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

subgroupindex
#105954292
#105946022
C3⋊D3×#1032
C3×#48142
#105915592
#105915522
#105909352
#105907082
#105906872
#105905752
#105904282
D3×#4853