Finite Group Databasebeta

← #11869529

Subgroups — #11869529

Order 1152.

897 conjugacy classes of subgroups.

The subgroup lattice has 490 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10594631C211yesmaximal, characteristic
2#10594602C211yesmaximal, characteristic
3C3⋊D3×#106C211yesmaximal, characteristic, complemented
4C3×#4868C212yesmaximal, complemented
5#10590935C211yesmaximal, characteristic
6#10590711C212yesmaximal, complemented
7#10590672C211yesmaximal, characteristic, complemented
8#10590601C211yesmaximal, characteristic, complemented
9#10590573C211yesmaximal, characteristic, complemented
10#10590519C212yesmaximal, complemented
11#10590448C212yesmaximal, complemented
12D3×#485—32nomaximal
13C2×C4×D32C2211yescharacteristic
14C2×#3797C2211yescharacteristic
15C2×C8×C3⋊D3C2211yescharacteristic
16C4⋊C4×C3⋊D3C2211yescharacteristic
17C4⋊C4×C3⋊D3C2211yescharacteristic
18C3×#897C2212yes—
19C3×#892C2212yes—
20#63921—21no—
21#63921—21no—
22#63900—21no—
23#63900C2211yescharacteristic
24#63899—22no—
25C4×#624—21no—
26#63877—22no—
27#63856C2212yes—
28#63841C2212yes—
29C2×#3710C2211yescharacteristic
30C32×#106C2211yescharacteristic, complemented
31#63644C2211yescharacteristic, complemented
32#63635C2211yescharacteristic, complemented
33#63635C2211yescharacteristic, complemented
34C3×(C2×D3)⋊C8C2212yes—
35C3×#816C2212yescomplemented
36C3×#810C2212yescomplemented
37C3×#807C2212yescomplemented
38#63575C2212yescomplemented
39#63566C2212yescomplemented
40#63565C2212yescomplemented
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#4868D312yescomplemented
50D3×#106—32no—
51D3×#106—61no—
52#4815—32no—
53#4814—32no—
54D3×#103—32no—
55D3×#103—32no—
56D3×C22⋊C8—32no—
57#4723—32no—
58C22×D32D411yescharacteristic
59C2×C4×C3⋊D3—21no—
60C2×C4×C3⋊D3—21no—
61C2×C4×C3⋊D3C2311yescharacteristic
62C2×C3×C4×D3C2312yes—
63C2×C3×Dic6C2312yes—
64C2×#627—21no—
65C2×#624—21no—
66C2×#624—21no—
67C2×#624D411yescharacteristic
68C2×D3×Dic3D412yes—
69C4×D32—22no—
70C4×D32—22no—
71#3797—22no—
72#3797—22no—
73C2×C32×C8C2311yescharacteristic
74C32×C4⋊C4C2311yescharacteristic
75C32×C4⋊C4C2311yescharacteristic
76C4⋊(C3⋊Dic3)C2311yescharacteristic
77C4⋊(C3⋊Dic3)C2311yescharacteristic
78#3750—21no—
79#3750—21no—
80C2×C3⋊(C3⋊C8)C2311yescharacteristic
81C8×C3⋊D3—22no—
82C3×(C2×D3)⋊C4—22no—
83C3×(C2×D3)⋊C4—22no—
84C3×C4⋊Dic3—22no—
85C3×C4⋊Dic3C2312yes—
86C3×C4×Dic3—22no—
87C2×C3×C3⋊C8C2312yes—
88#3724—21no—
89#3724—22no—
90(C2×D3)⋊Dic3—22no—
91(C2×D3)⋊Dic3—22no—
92Dic32—22no—
93#3710—22no—
94C2×#485—91noSylow
95C2×D3×Q8—32no—
96C22×C4×D3—32no—
97C3×C22⋊Q8—32no—
98C3×#117—32no—
99#946—32no—
100#926—32no—
101#924—32no—
102C2×D3×C8—32no—
103C2×D3×C8—32no—
104C2×D3×C8—61no—
105#897C2×D312yes—
106#896—62no—
107#892—32no—
108#892C2×D312yes—
109D3×C4⋊C4—32no—
110D3×C4⋊C4—32no—
111D3×C4⋊C4—32no—
112D3×C4⋊C4—61no—
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—21no—
123C3×#106C2×D312yescomplemented
124C3×#103—32no—
125C3×#103—32no—
126C3×C22⋊C8—32no—
127#835—32no—
128#835—32no—
129#830—32no—
130(C2×D3)⋊C8—32no—
131(C2×D3)⋊C8C2×D312yes—
132#818—32no—
133#817—32no—
134#817—61no—
135#816—32no—
136#816C2×D312yescomplemented
137#810—32no—
138#810C2×D312yescomplemented
139#808—32no—
140#808—32no—
141#808—61no—
142#808—61no—
143#807—32no—
144#807C2×D312yescomplemented
145C22×C3⋊D3C2×D411yescharacteristic
146C22×C3×D3C2×D412yes—
147C2×D32—22no—
148C2×D32—22no—
149C2×D32—22no—
150C2×C32×C4—21no—
151C2×C32×C4—21no—
152C2×C32×C4C2411yescharacteristic
153C2×C3⋊Dic3—21no—
154C2×C3⋊Dic3—21no—
155C2×C3⋊Dic3C2×D411yescharacteristic
156C4×C3⋊D3—42no—
157C4×C3⋊D3—42no—
158C4×C3⋊D3#4112yes—
159C4×C3⋊D3#4112yes—
160C2×C3×Dic3—22no—
161C2×C3×Dic3—22no—
162C2×C3×Dic3C2×D412yes—
163C3×C4×D3—22no—
164C3×C4×D3—22no—
165C3×Dic6—22no—
166C3×Dic6—22no—
167#627—42no—
168#624—22no—
169#624—42no—
170#624—42no—
171D3×Dic3—24no—
172C32×C8—21no—
173C3⋊(C3⋊C8)—21no—
174C3×C3⋊C8—22no—
175C2×C22⋊Q8—91no—
176C2×#117—91no—
177#485—32no—
178#485—92no—
179#485—92no—
180#485—92no—
181C2×#107—91no—
182C2×#106—91no—
183C2×#103—91no—
184C2×#103—91no—
185C2×C22⋊C8—91no—
186C23×D3—32no—
187C2×C3×Q8—32no—
188C22×C3×C4—32no—
189C22×Dic3—32no—
190D3×Q8—64no—
191D3×Q8—64no—
192C2×C4×D3—32no—
193C2×C4×D3—32no—
194C2×C4×D3—32no—
195C2×C4×D3—61no—
196C2×C4×D3—64no—
197C2×C4×D3—64no—
198C2×C4×D3—62no—
199C2×C4×D3—62no—
200C2×C4×D3—62no—
201C2×C4×D3—62no—
202C2×C4×D3—121no—
203C2×C4×D3—121no—
204C2×C4×D3C22×D312yes—
205C2×Dic6—62no—
206C2×Dic6C22×D312yes—
207C2×C3×C8—21no—
208C2×C3×C8—32no—
209C2×C3×C8C22×D312yes—
210C3×C4⋊C4—21no—
211C3×C4⋊C4—21no—
212C3×C4⋊C4—32no—
213C3×C4⋊C4—62no—
214C3×C4⋊C4C22×D312yes—
215C3×C4⋊C4C22×D312yes—
216C3×C22⋊C4—62no—
217C3×C22⋊C4—62no—
218C3×C42—62no—
219#217—62no—
220#217—62no—
221(C2×D3)⋊C4—22no—
222(C2×D3)⋊C4—22no—
223(C2×D3)⋊C4—62no—
224(C2×D3)⋊C4—62no—
225C4⋊Dic3—22no—
226C4⋊Dic3—32no—
227C4⋊Dic3—32no—
228C4⋊Dic3—61no—
229C4⋊Dic3—61no—
230C4⋊Dic3C22×D312yes—
231Dic3⋊C4—62no—
232Dic3⋊C4—62no—
233Dic3⋊C4—62no—
234Dic3⋊C4—62no—
235Dic3⋊C4—62no—
236Dic3⋊C4—121no—
237Dic3⋊C4—121no—
238C4×Dic3—22no—
239C4×Dic3—62no—
240C4×Dic3—62no—
241C2×C3⋊C8—32no—
242C2×C3⋊C8—61no—
243C2×C3⋊C8C22×D312yes—
244D3×C8—64no—
245D3×C8—64no—
246D3×C8—64no—
247C22×C32C22×D411yescharacteristic
248C2×C3⋊D3#12312yes—
249C2×C3⋊D3#13512yes—
250C2×C3⋊D3#13712yes—
251C2×C3×D3—22no—
252C2×C3×D3—22no—
253C2×C3×D3—22no—
254D32—44no—
255C32×C4—41no—
256C32×C4—41no—
257C32×C4C2×#4111yescharacteristic
258C32×C4C2×#4111yescharacteristic
259C3⋊Dic3—41no—
260C3⋊Dic3—41no—
261C3⋊Dic3#12312yes—
262C3×Dic3—22no—
263C3×Dic3—42no—
264C3×Dic3—42no—
265C22×Q8—91no—
266C23×C4—91no—
267C22×C8—91no—
268C22×C8—91no—
269C22⋊Q8—32no—
270C22⋊Q8—92no—
271C22⋊Q8—182no—
272#117—32no—
273#117—92no—
274#117—182no—
275C2×C4⋊C4—91no—
276C2×C4⋊C4—91no—
277C2×C4⋊C4—91no—
278C2×C4⋊C4—181no—
279C2×C22⋊C4—181no—
280C2×C22⋊C4—181no—
281C2×C42—181no—
282#107—32no—
283#107—92no—
284#106—91no—
285#106—91no—
286#106—91no—
287#106D3211yescharacteristic, complemented
288#103—32no—
289#103—32no—
290#103—92no—
291#103—92no—
292C22⋊C8—32no—
293C22⋊C8—92no—
294C23×C3—32no—
295C22×D3—32no—
296C22×D3—61no—
297C22×D3—64no—
298C22×D3—64no—
299C22×D3—64no—
300C22×D3D3×D412yes—
301C3×Q8—62no—
302C3×Q8—62no—
303C2×C3×C4—22no—
304C2×C3×C4—22no—
305C2×C3×C4—21no—
306C2×C3×C4—32no—
307C2×C3×C4—41no—
308C2×C3×C4—41no—
309C2×C3×C4—62no—
310C2×C3×C4—62no—
311C2×C3×C4—62no—
312C2×C3×C4—62no—
313C2×C3×C4C23×D312yes—
314C2×Dic3—22no—
315C2×Dic3—22no—
316C2×Dic3—32no—
317C2×Dic3—61no—
318C2×Dic3—64no—
319C2×Dic3—62no—
320C2×Dic3—62no—
321C2×Dic3—121no—
322C2×Dic3—121no—
323C2×Dic3D3×D412yes—
324C4×D3—22no—
325C4×D3—22no—
326C4×D3—34no—
327C4×D3—34no—
328C4×D3—62no—
329C4×D3—62no—
330C4×D3—64no—
331C4×D3—64no—
332C4×D3—124no—
333C4×D3—124no—
334C4×D3—124no—
335C4×D3—124no—
336C4×D3—242no—
337C4×D3—242no—
338Dic6—22no—
339Dic6—22no—
340Dic6—124no—
341C3×C8—22no—
342C3×C8—22no—
343C3×C8—62no—
344C3⋊C8—22no—
345C3⋊C8—62no—
346C3⋊C8—62no—
347C2×C32C2×#12311yescharacteristic
348C2×C32C2×#13511yescharacteristic
349C2×C32C2×#13711yescharacteristic
350C3⋊D3#48514yescomplemented
351C3×D3—42no—
352C24—91no—
353C2×Q8—32no—
354C2×Q8—181no—
355C2×Q8—182no—
356C2×Q8—182no—
357C22×C4—32no—
358C22×C4—91no—
359C22×C4—92no—
360C22×C4—91no—
361C22×C4—181no—
362C22×C4—181no—
363C22×C4—182no—
364C22×C4—182no—
365C22×C4—181no—
366C22×C4—181no—
367C2×C8—32no—
368C2×C8—91no—
369C2×C8—182no—
370C2×C8—182no—
371C2×C8C2×D3211yescharacteristic
372C4⋊C4—32no—
373C4⋊C4—62no—
374C4⋊C4—91no—
375C4⋊C4—91no—
376C4⋊C4—181no—
377C4⋊C4—181no—
378C4⋊C4—182no—
379C4⋊C4—181no—
380C4⋊C4C2×D3211yescharacteristic
381C4⋊C4C2×D3211yescharacteristic
382C22⋊C4—62no—
383C22⋊C4—62no—
384C22⋊C4—182no—
385C22⋊C4—182no—
386C42—62no—
387C42—182no—
388C22×C3—21no—
389C22×C3—62no—
390C22×C3—62no—
391C22×C3—62no—
392C22×C3C2×D3×D412yes—
393C2×D3—22no—
394C2×D3—22no—
395C2×D3—22no—
396C2×D3—34no—
397C2×D3—34no—
398C2×D3—34no—
399C2×D3—62no—
400C2×D3—62no—
401C2×D3—62no—
402C2×D3—128no—
403C3×C4—21no—
404C3×C4—21no—
405C3×C4—42no—
406C3×C4—42no—
407C3×C4—62no—
408C3×C4—81no—
409C3×C4—81no—
410C3×C4—122no—
411C3×C4—122no—
412C3×C4D3×#4112yes—
413C3×C4D3×#4112yes—
414Dic3—22no—
415Dic3—34no—
416Dic3—42no—
417Dic3—42no—
418Dic3—62no—
419Dic3—122no—
420Dic3—122no—
421Dic3—241no—
422Dic3—241no—
423C32C2×#48511yescharacteristic, complemented, Sylow
424C23—32no—
425C23—91no—
426C23—182no—
427C23—182no—
428C23—182no—
429Q8—62no—
430Q8—62no—
431Q8—362no—
432C2×C4—21no—
433C2×C4—21no—
434C2×C4—32no—
435C2×C4—62no—
436C2×C4—62no—
437C2×C4—62no—
438C2×C4—62no—
439C2×C4—91no—
440C2×C4—92no—
441C2×C4—92no—
442C2×C4—182no—
443C2×C4—184no—
444C2×C4—181no—
445C2×C4—181no—
446C2×C4—362no—
447C2×C4—362no—
448C2×C4—362no—
449C2×C4—362no—
450C2×C4C22×D3211yescharacteristic
451C8—21no—
452C8—62no—
453C8—181no—
454C2×C3—21no—
455C2×C3—21no—
456C2×C3—21no—
457C2×C3—122no—
458C2×C3D3×#12312yes—
459C2×C3D3×#13512yes—
460C2×C3D3×#13712yes—
461D3—38no—
462D3—42no—
463D3—64no—
464C22—62no—
465C22—62no—
466C22—62no—
467C22—92no—
468C22—92no—
469C22—92no—
470C22—364no—
471C22D32×D411yescharacteristic
472C4—41no—
473C4—41no—
474C4—62no—
475C4—92no—
476C4—122no—
477C4—122no—
478C4—361no—
479C4—361no—
480C4#6430611yescharacteristic
481C4#6431911yescharacteristic
482C3—21no—
483C3D3×#48512yescomplemented
484C2—94no—
485C2—122no—
486C2#1059460811yescharacteristic
487C2#1059474211yescharacteristic
488C2#1059474711yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#106C22
socleC22×C32C22×D4
prime radicalC22×D32D4
hypercenter#106D32
hypocenterC32C2×#485
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ #106

Complements

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

NH ≅ G/Ntype
3. C3⋊D3×#106C2semidirect
4. C3×#4868C2semidirect
6. #10590711C2semidirect
7. #10590672C2semidirect
8. #10590601C2semidirect
9. #10590573C2semidirect
10. #10590519C2semidirect
11. #10590448C2semidirect
30. C32×#106C22semidirect
31. #63644C22semidirect
32. #63635C22semidirect
33. #63635C22semidirect
35. C3×#816C22semidirect
36. C3×#810C22semidirect
37. C3×#807C22semidirect
38. #63575C22semidirect
39. #63566C22semidirect
40. #63565C22semidirect
49. #4868D3semidirect
123. C3×#106C2×D3semidirect
136. #816C2×D3semidirect
138. #810C2×D3semidirect
144. #807C2×D3semidirect
287. #106D32semidirect
350. C3⋊D3#485semidirect
423. C32C2×#485semidirect
483. C3D3×#485semidirect

Maximal subgroups

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

subgroupindex
#105946312
#105946022
C3⋊D3×#1062
C3×#48682
#105909352
#105907112
#105906722
#105906012
#105905732
#105905192
#105904482
D3×#4853