Finite Group Databasebeta

← C3⋊D3×#385 #11801243

Subgroups — C3⋊D3×#385 #11801243

Order 1152.

3696 conjugacy classes of subgroups.

The subgroup lattice has 513 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C4×C3⋊D3C211yesmaximal, characteristic
2C2×C4⋊C4×C3⋊D3C212yesmaximal, complemented
3C2×C22⋊C4×C3⋊D3C211yesmaximal, characteristic
4C2×C22⋊C4×C3⋊D3C211yesmaximal, characteristic
5C32×#385C211yesmaximal, characteristic, complemented
6#10592909C211yesmaximal, characteristic, complemented
7#10592688C212yesmaximal, complemented
8#10592649C211yesmaximal, characteristic, complemented
9#10592645C211yesmaximal, characteristic, complemented
10#10592367C212yesmaximal, complemented
11C3⋊D3×#95C212yesmaximal, complemented
12D3×#385—34nomaximal
13C24×C3⋊D3C2211yescharacteristic
14C23×C32×C4C2211yescharacteristic
15C23×C3⋊Dic3C2211yescharacteristic
16C22×C4×C3⋊D3—28no—
17C22×C4×C3⋊D3—24no—
18C22×C4×C3⋊D3C2211yescharacteristic
19C22×C4×C3⋊D3C2212yes—
20C22×C4×C3⋊D3C2211yescharacteristic
21C22×C4×C3⋊D3C2212yes—
22C22×C4×C3⋊D3C2212yes—
23C2×C32×C4⋊C4C2212yescomplemented
24C2×C32×C22⋊C4C2211yescharacteristic
25C2×C32×C22⋊C4C2211yescharacteristic
26C2×#3757C2211yescharacteristic
27C2×#3757C2211yescharacteristic
28C2×#3752C2211yescharacteristic
29C2×#3752C2211yescharacteristic
30C2×#3752C2212yes—
31C2×C4⋊(C3⋊Dic3)C2212yescomplemented
32C2×#3750C2212yescomplemented
33C2×#3750C2212yescomplemented
34C4⋊C4×C3⋊D3—28no—
35C22⋊C4×C3⋊D3—24no—
36C22⋊C4×C3⋊D3C418yescomplemented
37C32×#95C2212yescomplemented
38#63658C2212yescomplemented
39#63658C2212yescomplemented
40#63658C2212yescomplemented
41C23×C4×D3—34no—
42C2×D3×C4⋊C4—38no—
43C2×D3×C22⋊C4—34no—
44C2×D3×C22⋊C4—34no—
45C3×#385D314yescomplemented
46#5210—34no—
47#4989—38no—
48#4950—34no—
49#4946—34no—
50#4668—38no—
51D3×#95—38no—
52C24×C32C2311yescharacteristic
53C23×C3⋊D3—24no—
54C23×C3⋊D3—24no—
55C23×C3⋊D3C2×C414yes—
56C23×C3⋊D3D414yes—
57C23×C3⋊D3Q814yes—
58C23×C3⋊D3C2311yescharacteristic
59C23×C3⋊D3C2311yescharacteristic
60C22×C32×C4—22no—
61C22×C32×C4—24no—
62C22×C32×C4C2311yescharacteristic
63C22×C32×C4C2311yescharacteristic
64C22×C32×C4C2312yes—
65C22×C32×C4C2312yes—
66C22×C3⋊Dic3—22no—
67C22×C3⋊Dic3—24no—
68C22×C3⋊Dic3C2311yescharacteristic
69C22×C3⋊Dic3C2311yescharacteristic
70C22×C3⋊Dic3C2312yes—
71C22×C3⋊Dic3C2312yes—
72C2×C4×C3⋊D3—232no—
73C2×C4×C3⋊D3—24no—
74C2×C4×C3⋊D3—24no—
75C2×C4×C3⋊D3—24no—
76C2×C4×C3⋊D3—24no—
77C2×C4×C3⋊D3—24no—
78C2×C4×C3⋊D3—24no—
79C2×C4×C3⋊D3—24no—
80C2×C4×C3⋊D3—22no—
81C2×C4×C3⋊D3—22no—
82C2×C4×C3⋊D3—24no—
83C2×C4×C3⋊D3—24no—
84C2×C4×C3⋊D3C2×C418yescomplemented
85C2×C4×C3⋊D3D418yes—
86C32×C4⋊C4—24no—
87C32×C22⋊C4—22no—
88C32×C22⋊C4C2×C414yescomplemented
89#3757—22no—
90#3757C2×C414yescomplemented
91#3752—22no—
92#3752—22no—
93#3752C2×C418yescomplemented
94C4⋊(C3⋊Dic3)—24no—
95#3750—24no—
96#3750—24no—
97C2×#385—91noSylow
98C24×D3—34no—
99C23×C3×C4C2×D314yes—
100C23×Dic3—34no—
101C22×C4×D3—38no—
102C22×C4×D3—38no—
103C22×C4×D3—34no—
104C22×C4×D3—38no—
105C22×C4×D3—34no—
106C22×C4×D3—632no—
107C22×C4×D3—616no—
108C2×C3×C4⋊C4C2×D318yescomplemented
109C2×C3×C22⋊C4C2×D314yes—
110C2×C3×C22⋊C4C2×D314yes—
111C2×#217—34no—
112C2×#217—34no—
113C2×(C2×D3)⋊C4—38no—
114C2×(C2×D3)⋊C4—34no—
115C2×(C2×D3)⋊C4—34no—
116C2×C4⋊Dic3—38no—
117C2×Dic3⋊C4—38no—
118C2×Dic3⋊C4—38no—
119D3×C4⋊C4—632no—
120D3×C22⋊C4—332no—
121D3×C22⋊C4—616no—
122C3×#95C2×D318yescomplemented
123C3⋊#95—38no—
124C3⋊#95—38no—
125C3⋊#95—38no—
126C23×C32—22no—
127C23×C32—22no—
128C23×C32C22×C412yes—
129C23×C32C2×D412yes—
130C23×C32C2×Q812yes—
131C23×C32C2411yescharacteristic
132C22×C3⋊D3—22no—
133C22×C3⋊D3—22no—
134C22×C3⋊D3—216no—
135C22×C3⋊D3—28no—
136C22×C3⋊D3—216no—
137C22×C3⋊D3—28no—
138C22×C3⋊D3C4⋊C4116yescomplemented
139C22×C3⋊D3C22×C412yes—
140C22×C3⋊D3C22×C412yes—
141C22×C3⋊D3C2×D412yes—
142C22×C3⋊D3C2×D412yes—
143C22×C3⋊D3C2×D414yes—
144C22×C3⋊D3C2×Q812yes—
145C22×C3⋊D3C2×Q812yes—
146C22×C3⋊D3#4114yes—
147C2×C32×C4—28no—
148C2×C32×C4—22no—
149C2×C32×C4—22no—
150C2×C32×C4—22no—
151C2×C32×C4—22no—
152C2×C32×C4—22no—
153C2×C32×C4—21no—
154C2×C32×C4—21no—
155C2×C32×C4—22no—
156C2×C32×C4C22×C414yescomplemented
157C2×C32×C4C2×D414yes—
158C2×C3⋊Dic3—28no—
159C2×C3⋊Dic3—22no—
160C2×C3⋊Dic3—22no—
161C2×C3⋊Dic3—22no—
162C2×C3⋊Dic3—22no—
163C2×C3⋊Dic3—22no—
164C2×C3⋊Dic3—21no—
165C2×C3⋊Dic3—21no—
166C2×C3⋊Dic3—22no—
167C2×C3⋊Dic3C22×C414yescomplemented
168C2×C3⋊Dic3C2×D414yes—
169C4×C3⋊D3—216no—
170C4×C3⋊D3—216no—
171C4×C3⋊D3—216no—
172C4×C3⋊D3—44no—
173C4×C3⋊D3—44no—
174C24×C4—91no—
175C22×C4⋊C4—92no—
176C22×C22⋊C4—91no—
177C22×C22⋊C4—91no—
178#385—91no—
179#385—92no—
180#385—91no—
181#385—91no—
182#385—92no—
183#385C3⋊D311yescharacteristic, direct product factor
184C2×#95—92no—
185C24×C3C22×D314yes—
186C23×D3—34no—
187C23×D3—316no—
188C23×D3—316no—
189C23×D3—316no—
190C23×D3—34no—
191C23×D3—616no—
192C23×D3—616no—
193C22×C3×C4—28no—
194C22×C3×C4—216no—
195C22×C3×C4C22×D314yes—
196C22×C3×C4C22×D314yes—
197C22×C3×C4C22×D318yes—
198C22×C3×C4C22×D318yes—
199C22×Dic3—38no—
200C22×Dic3—38no—
201C22×Dic3—34no—
202C22×Dic3—34no—
203C22×Dic3—616no—
204C22×Dic3—68no—
205C2×C4×D3—332no—
206C2×C4×D3—332no—
207C2×C4×D3—616no—
208C2×C4×D3—616no—
209C2×C4×D3—616no—
210C2×C4×D3—616no—
211C2×C4×D3—616no—
212C2×C4×D3—616no—
213C2×C4×D3—6128no—
214C2×C4×D3—616no—
215C2×C4×D3—68no—
216C2×C4×D3—68no—
217C2×C4×D3—616no—
218C2×C4×D3—616no—
219C3×C4⋊C4—216no—
220C3×C22⋊C4—28no—
221C3×C22⋊C4C4×D3116yescomplemented
222#217—316no—
223#217—68no—
224(C2×D3)⋊C4—332no—
225(C2×D3)⋊C4—68no—
226(C2×D3)⋊C4—68no—
227C4⋊Dic3—616no—
228Dic3⋊C4—616no—
229Dic3⋊C4—616no—
230C22×C32—24no—
231C22×C32—22no—
232C22×C32—24no—
233C22×C32—22no—
234C22×C32C2×C4⋊C414yescomplemented
235C22×C32C23×C411yescharacteristic
236C22×C32C22×D411yescharacteristic
237C22×C32C22×D412yes—
238C22×C32C22×Q811yescharacteristic
239C22×C32C2×#4112yes—
240C2×C3⋊D3—24no—
241C2×C3⋊D3—22no—
242C2×C3⋊D3—24no—
243C2×C3⋊D3—22no—
244C2×C3⋊D3—232no—
245C2×C3⋊D3C2×C4⋊C414yes—
246C2×C3⋊D3C2×C4⋊C414yescomplemented
247C2×C3⋊D3C4×D418yes—
248C2×C3⋊D3#12014yes—
249C2×C3⋊D3C22⋊Q818yes—
250C2×C3⋊D3#12314yes—
251C32×C4—24no—
252C32×C4—24no—
253C32×C4—41no—
254C32×C4—41no—
255C3⋊Dic3—24no—
256C3⋊Dic3—24no—
257C3⋊Dic3—41no—
258C3⋊Dic3—41no—
259C25—91no—
260C23×C4—92no—
261C23×C4—92no—
262C23×C4—91no—
263C23×C4—91no—
264C23×C4—91no—
265C23×C4—92no—
266C23×C4—188no—
267C23×C4—184no—
268C23×C4C2×C3⋊D311yescharacteristic
269C2×C4⋊C4—92no—
270C2×C4⋊C4—92no—
271C2×C4⋊C4—92no—
272C2×C4⋊C4—188no—
273C2×C4⋊C4C2×C3⋊D312yescomplemented
274C2×C22⋊C4—91no—
275C2×C22⋊C4—92no—
276C2×C22⋊C4—98no—
277C2×C22⋊C4—91no—
278C2×C22⋊C4—91no—
279C2×C22⋊C4—91no—
280C2×C22⋊C4—184no—
281C2×C22⋊C4C2×C3⋊D311yescharacteristic
282C2×C22⋊C4C2×C3⋊D311yescharacteristic
283#95—92no—
284#95—92no—
285#95—92no—
286#95C2×C3⋊D312yescomplemented
287C23×C3—28no—
288C23×C3—28no—
289C23×C3C2×C4×D318yes—
290C23×C3D3×D418yes—
291C23×C3D3×Q818yes—
292C23×C3C23×D314yes—
293C22×D3—38no—
294C22×D3—316no—
295C22×D3—38no—
296C22×D3—38no—
297C22×D3—316no—
298C22×D3—364no—
299C22×D3—38no—
300C22×D3—38no—
301C22×D3—38no—
302C22×D3—632no—
303C22×D3—632no—
304C22×D3—664no—
305C22×D3—664no—
306C22×D3—68no—
307C22×D3—68no—
308C2×C3×C4—232no—
309C2×C3×C4—28no—
310C2×C3×C4—28no—
311C2×C3×C4—28no—
312C2×C3×C4—28no—
313C2×C3×C4—28no—
314C2×C3×C4—24no—
315C2×C3×C4—24no—
316C2×C3×C4—28no—
317C2×C3×C4C2×C4×D3116yescomplemented
318C2×C3×C4D3×D4116yes—
319C2×Dic3—316no—
320C2×Dic3—316no—
321C2×Dic3—632no—
322C2×Dic3—68no—
323C2×Dic3—68no—
324C2×Dic3—68no—
325C2×Dic3—68no—
326C2×Dic3—68no—
327C2×Dic3—64no—
328C2×Dic3—64no—
329C2×Dic3—68no—
330C4×D3—664no—
331C4×D3—664no—
332C4×D3—664no—
333C4×D3—1216no—
334C4×D3—1216no—
335C2×C32—24no—
336C2×C32C22×C4⋊C411yescharacteristic
337C2×C32C2×C4×D412yes—
338C2×C32C2×#12011yescharacteristic
339C2×C32C2×C22⋊Q812yes—
340C2×C32C2×#12311yescharacteristic
341C3⋊D3—24no—
342C3⋊D3#38518yesdirect product factor
343C24—91no—
344C24—91no—
345C24—94no—
346C24—94no—
347C24—94no—
348C24—184no—
349C24—184no—
350C24C22×C3⋊D311yescharacteristic
351C22×C4—22no—
352C22×C4—24no—
353C22×C4—92no—
354C22×C4—92no—
355C22×C4—98no—
356C22×C4—98no—
357C22×C4—91no—
358C22×C4—91no—
359C22×C4—184no—
360C22×C4—184no—
361C22×C4—184no—
362C22×C4—184no—
363C22×C4—184no—
364C22×C4—184no—
365C22×C4—1832no—
366C22×C4—182no—
367C22×C4—182no—
368C22×C4—184no—
369C22×C4—184no—
370C22×C4—184no—
371C22×C4—182no—
372C22×C4—184no—
373C22×C4C22×C3⋊D311yescharacteristic
374C22×C4C22×C3⋊D311yescharacteristic
375C22×C4C22×C3⋊D312yes—
376C22×C4C22×C3⋊D312yes—
377C4⋊C4—24no—
378C4⋊C4—184no—
379C4⋊C4—184no—
380C4⋊C4—184no—
381C22⋊C4—22no—
382C22⋊C4—94no—
383C22⋊C4—98no—
384C22⋊C4—182no—
385C22⋊C4—182no—
386C22⋊C4—182no—
387C22⋊C4C4×C3⋊D314yescomplemented
388C22×C3—28no—
389C22×C3—216no—
390C22×C3—28no—
391C22×C3—216no—
392C22×C3D3×C4⋊C4116yescomplemented
393C22×C3C22×C4×D314yes—
394C22×C3C2×D3×D414yes—
395C22×C3C2×D3×D418yes—
396C22×C3C2×D3×Q814yes—
397C22×C3D3×#4118yes—
398C2×D3—316no—
399C2×D3—316no—
400C2×D3—332no—
401C2×D3—316no—
402C2×D3—332no—
403C2×D3—316no—
404C2×D3—6128no—
405C2×D3—68no—
406C2×D3—616no—
407C2×D3—68no—
408C2×D3—616no—
409C3×C4—216no—
410C3×C4—216no—
411C3×C4—44no—
412C3×C4—44no—
413Dic3—616no—
414Dic3—616no—
415Dic3—124no—
416Dic3—124no—
417C32C2×#38511yescharacteristic, complemented, Sylow
418C23—22no—
419C23—22no—
420C23—92no—
421C23—94no—
422C23—92no—
423C23—92no—
424C23—94no—
425C23—916no—
426C23—92no—
427C23—92no—
428C23—92no—
429C23—188no—
430C23—1816no—
431C23—188no—
432C23—1816no—
433C23—182no—
434C23—182no—
435C23C2×C4×C3⋊D312yes—
436C23D4×C3⋊D312yes—
437C23Q8×C3⋊D312yes—
438C23C23×C3⋊D311yescharacteristic
439C2×C4—28no—
440C2×C4—22no—
441C2×C4—22no—
442C2×C4—22no—
443C2×C4—22no—
444C2×C4—21no—
445C2×C4—21no—
446C2×C4—22no—
447C2×C4—22no—
448C2×C4—94no—
449C2×C4—94no—
450C2×C4—1816no—
451C2×C4—1816no—
452C2×C4—1816no—
453C2×C4—188no—
454C2×C4—182no—
455C2×C4—182no—
456C2×C4—182no—
457C2×C4—182no—
458C2×C4—181no—
459C2×C4—181no—
460C2×C4—182no—
461C2×C4—182no—
462C2×C4—364no—
463C2×C4—364no—
464C2×C4C2×C4×C3⋊D314yescomplemented
465C2×C4D4×C3⋊D314yes—
466C2×C3—216no—
467C2×C3C2×D3×C4⋊C414yes—
468C2×C3C4×D3×D418yes—
469C2×C3D3×#12014yes—
470C2×C3D3×C22⋊Q818yes—
471C2×C3D3×#12314yes—
472D3—332no—
473D3—616no—
474C22—24no—
475C22—22no—
476C22—24no—
477C22—22no—
478C22—98no—
479C22—94no—
480C22—94no—
481C22—98no—
482C22—94no—
483C22—94no—
484C22—1832no—
485C22—184no—
486C22—182no—
487C22—184no—
488C22—182no—
489C22C4⋊C4×C3⋊D314yescomplemented
490C22C22×C4×C3⋊D311yescharacteristic
491C22C2×D4×C3⋊D312yes—
492C22C2×D4×C3⋊D311yescharacteristic
493C22C2×Q8×C3⋊D311yescharacteristic
494C22#41×C3⋊D312yes—
495C4—24no—
496C4—24no—
497C4—41no—
498C4—41no—
499C4—184no—
500C4—184no—
501C4—361no—
502C4—361no—
503C3D3×#38514yescomplemented
504C2—24no—
505C2—98no—
506C2—184no—
507C2C2×C4⋊C4×C3⋊D311yescharacteristic
508C2C4×D4×C3⋊D312yes—
509C2C3⋊D3×#12011yescharacteristic
510C2C3⋊D3×C22⋊Q812yes—
511C2C3⋊D3×#12311yescharacteristic
subgroupG/H
center, FrattiniC23C23×C3⋊D3
commutatorC22×C32C23×C4
FittingC32×#385C2
socle, cosocleC23×C32C24
prime radicalC24×C3⋊D3C22
hypercenter#385C3⋊D3
hypocenterC32C2×#385
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ #385

Complements

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

NH ≅ G/Ntype
2. C2×C4⋊C4×C3⋊D3C2semidirect
5. C32×#385C2semidirect
6. #10592909C2semidirect
7. #10592688C2semidirect
8. #10592649C2semidirect
9. #10592645C2semidirect
10. #10592367C2semidirect
11. C3⋊D3×#95C2semidirect
23. C2×C32×C4⋊C4C22semidirect
31. C2×C4⋊(C3⋊Dic3)C22semidirect
32. C2×#3750C22semidirect
33. C2×#3750C22semidirect
36. C22⋊C4×C3⋊D3C4semidirect
37. C32×#95C22semidirect
38. #63658C22semidirect
39. #63658C22semidirect
40. #63658C22semidirect
45. C3×#385D3semidirect
84. C2×C4×C3⋊D3C2×C4semidirect
88. C32×C22⋊C4C2×C4semidirect
90. #3757C2×C4semidirect
93. #3752C2×C4semidirect
108. C2×C3×C4⋊C4C2×D3semidirect
122. C3×#95C2×D3semidirect
138. C22×C3⋊D3C4⋊C4semidirect
156. C2×C32×C4C22×C4semidirect
167. C2×C3⋊Dic3C22×C4semidirect
183. #385C3⋊D3direct (N × H)
221. C3×C22⋊C4C4×D3semidirect
234. C22×C32C2×C4⋊C4semidirect
246. C2×C3⋊D3C2×C4⋊C4semidirect
273. C2×C4⋊C4C2×C3⋊D3semidirect
286. #95C2×C3⋊D3semidirect
317. C2×C3×C4C2×C4×D3semidirect
342. C3⋊D3#385direct (N × H)
387. C22⋊C4C4×C3⋊D3semidirect
392. C22×C3D3×C4⋊C4semidirect
417. C32C2×#385semidirect
464. C2×C4C2×C4×C3⋊D3semidirect
489. C22C4⋊C4×C3⋊D3semidirect
503. C3D3×#385semidirect

Maximal subgroups

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

subgroupindex
C23×C4×C3⋊D32
C2×C4⋊C4×C3⋊D32
C2×C22⋊C4×C3⋊D32
C32×#3852
#105929092
#105926882
#105926492
#105926452
#105923672
C3⋊D3×#952
D3×#3853