Finite Group Databasebeta

← C3⋊D3×#394 #11808131

Subgroups — C3⋊D3×#394 #11808131

Order 1152.

3756 conjugacy classes of subgroups.

The subgroup lattice has 552 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×D4×C3⋊D3C211yesmaximal, characteristic
2C2×C4⋊C4×C3⋊D3C211yesmaximal, characteristic, complemented
3C2×C22⋊C4×C3⋊D3C212yesmaximal, complemented
4C2×C22⋊C4×C3⋊D3C212yesmaximal, complemented
5C32×#394C211yesmaximal, characteristic, complemented
6#10592921C211yesmaximal, characteristic, complemented
7#10592690C211yesmaximal, characteristic, complemented
8#10592660C212yesmaximal, complemented
9#10592658C212yesmaximal, complemented
10#10592371C211yesmaximal, characteristic, complemented
11C3⋊D3×#95C211yesmaximal, characteristic, complemented
12D3×#394—34nomaximal
13C24×C3⋊D3C2212yes—
14C22×C32×D4C2211yescharacteristic
15C22×#638C2212yes—
16C2×D4×C3⋊D3—24no—
17C2×D4×C3⋊D3—28no—
18C22×C4⋊(C3⋊D3)C2211yescharacteristic
19C22×C4×C3⋊D3C2212yes—
20C22×C4×C3⋊D3C2211yescharacteristic
21C22×C4×C3⋊D3C2211yescharacteristic
22C22×C4×C3⋊D3C2211yescharacteristic
23C2×C32×C4⋊C4C2211yescharacteristic, complemented
24C2×C32×C22⋊C4C2212yescomplemented
25C2×C32×C22⋊C4C2212yescomplemented
26C2×#3757C2212yescomplemented
27C2×#3757C2212yescomplemented
28C2×#3752C2212yescomplemented
29C2×#3752C2212yescomplemented
30C2×#3752C2212yescomplemented
31C2×#3752C2212yescomplemented
32C2×C4⋊(C3⋊Dic3)C2211yescharacteristic, complemented
33C2×#3750C2211yescharacteristic, complemented
34C2×#3750C2211yescharacteristic, complemented
35C4⋊C4×C3⋊D3—24no—
36C22⋊C4×C3⋊D3—28no—
37C22⋊C4×C3⋊D3—28no—
38C32×#95C2211yescharacteristic, complemented
39#63658C2212yescomplemented
40#63658C2211yescharacteristic, complemented
41C22×D3×D4—34no—
42C2×D3×C4⋊C4—34no—
43C2×D3×C22⋊C4—38no—
44C2×D3×C22⋊C4—38no—
45C3×#394D314yescomplemented
46#5222—34no—
47#4991—34no—
48#4961—38no—
49#4959—38no—
50#4672—34no—
51D3×#95—34no—
52C24×C32C2312yes—
53C23×C3⋊D3—24no—
54C23×C3⋊D3—24no—
55C23×C3⋊D3—24no—
56C23×C3⋊D3—24no—
57C23×C3⋊D3—24no—
58C23×C3⋊D3—24no—
59C23×C3⋊D3D418yes—
60C23×C3⋊D3C2312yes—
61C23×C3⋊D3C2311yescharacteristic
62C2×C32×D4—24no—
63C2×C32×D4—22no—
64C22×C32×C4C2311yescharacteristic
65C22×C32×C4C2312yes—
66C22×C32×C4C2311yescharacteristic
67C22×C32×C4C2311yescharacteristic
68C2×#638—24no—
69C2×#638—24no—
70C2×#638—24no—
71C22×C3⋊Dic3C2311yescharacteristic
72C22×C3⋊Dic3C2312yes—
73C22×C3⋊Dic3C2311yescharacteristic
74C22×C3⋊Dic3C2311yescharacteristic
75D4×C3⋊D3—232no—
76C2×C4⋊(C3⋊D3)—24no—
77C2×C4⋊(C3⋊D3)—22no—
78C2×C4×C3⋊D3—22no—
79C2×C4×C3⋊D3—24no—
80C2×C4×C3⋊D3—22no—
81C2×C4×C3⋊D3—24no—
82C2×C4×C3⋊D3—24no—
83C2×C4×C3⋊D3—24no—
84C2×C4×C3⋊D3—22no—
85C2×C4×C3⋊D3—24no—
86C2×C4×C3⋊D3D414yes—
87C2×C4×C3⋊D3D414yescomplemented
88C32×C4⋊C4—22no—
89C32×C22⋊C4—24no—
90C32×C22⋊C4—24no—
91#3757—24no—
92#3757—24no—
93#3752—24no—
94#3752—24no—
95#3752—24no—
96#3752—24no—
97C4⋊(C3⋊Dic3)—22no—
98#3750—22no—
99#3750—22no—
100C2×#394—91noSylow
101C24×D3—38no—
102C22×C3×D4C2×D314yes—
103C22×#67—38no—
104C2×D3×D4—616no—
105C2×D3×D4—632no—
106C22×D12—34no—
107C22×C4×D3—34no—
108C22×C4×D3—34no—
109C22×C4×D3—38no—
110C22×C4×D3—34no—
111C2×C3×C4⋊C4C2×D314yescomplemented
112C2×C3×C22⋊C4C2×D318yescomplemented
113C2×C3×C22⋊C4C2×D318yescomplemented
114C2×#217—38no—
115C2×#217—38no—
116C2×(C2×D3)⋊C4—38no—
117C2×(C2×D3)⋊C4—38no—
118C2×(C2×D3)⋊C4—38no—
119C2×(C2×D3)⋊C4—38no—
120C2×C4⋊Dic3—34no—
121C2×Dic3⋊C4—34no—
122C2×Dic3⋊C4—34no—
123D3×C4⋊C4—616no—
124D3×C22⋊C4—632no—
125D3×C22⋊C4—632no—
126C3×#95C2×D314yescomplemented
127C3⋊#95—38no—
128C3⋊#95—34no—
129C23×C32—22no—
130C23×C32—22no—
131C23×C32—22no—
132C23×C32—22no—
133C23×C32—22no—
134C23×C32—22no—
135C23×C32C2×D414yes—
136C23×C32C2411yescharacteristic
137C22×C3⋊D3—22no—
138C22×C3⋊D3—22no—
139C22×C3⋊D3—22no—
140C22×C3⋊D3—22no—
141C22×C3⋊D3—22no—
142C22×C3⋊D3—22no—
143C22×C3⋊D3—216no—
144C22×C3⋊D3—216no—
145C22×C3⋊D3—216no—
146C22×C3⋊D3—48no—
147C22×C3⋊D3—48no—
148C22×C3⋊D3—48no—
149C22×C3⋊D3—48no—
150C22×C3⋊D3C2×D414yes—
151C22×C3⋊D3C2×D414yes—
152C22×C3⋊D3C2×D412yes—
153C22×C3⋊D3C2×D412yes—
154C22×C3⋊D3#4112yes—
155C22×C3⋊D3#4114yes—
156C32×D4—28no—
157C2×C32×C4—21no—
158C2×C32×C4—22no—
159C2×C32×C4—21no—
160C2×C32×C4—21no—
161C2×C32×C4—22no—
162C2×C32×C4—22no—
163C2×C32×C4—22no—
164C2×C32×C4—22no—
165C2×C32×C4C2×D412yes—
166C2×C32×C4C2×D412yescomplemented
167#638—216no—
168C2×C3⋊Dic3—21no—
169C2×C3⋊Dic3—22no—
170C2×C3⋊Dic3—21no—
171C2×C3⋊Dic3—21no—
172C2×C3⋊Dic3—22no—
173C2×C3⋊Dic3—22no—
174C2×C3⋊Dic3—22no—
175C2×C3⋊Dic3—22no—
176C2×C3⋊Dic3C2×D412yes—
177C2×C3⋊Dic3C2×D412yescomplemented
178C4⋊(C3⋊D3)—28no—
179C4×C3⋊D3—28no—
180C4×C3⋊D3—28no—
181C4×C3⋊D3—44no—
182C4×C3⋊D3—48no—
183C23×D4—91no—
184C22×C4⋊C4—91no—
185C22×C22⋊C4—92no—
186C22×C22⋊C4—92no—
187#394—91no—
188#394—91no—
189#394—92no—
190#394—92no—
191#394—91no—
192#394C3⋊D311yescharacteristic, direct product factor
193C2×#95—91no—
194C24×C3C22×D318yes—
195C23×D3—34no—
196C23×D3—332no—
197C23×D3—38no—
198C23×D3—616no—
199C23×D3—616no—
200C23×D3—616no—
201C23×D3—616no—
202C23×D3—616no—
203C23×D3—616no—
204C2×C3×D4—216no—
205C2×C3×D4—28no—
206C22×C3×C4C22×D318yes—
207C22×C3×C4C22×D314yes—
208C22×C3×C4C22×D314yes—
209C22×C3×C4C22×D314yes—
210C2×#67—616no—
211C2×#67—616no—
212C2×#67—616no—
213C22×Dic3—34no—
214C22×Dic3—34no—
215C22×Dic3—38no—
216C22×Dic3—34no—
217D3×D4—6128no—
218C2×D12—616no—
219C2×D12—68no—
220C2×C4×D3—316no—
221C2×C4×D3—316no—
222C2×C4×D3—68no—
223C2×C4×D3—616no—
224C2×C4×D3—68no—
225C2×C4×D3—616no—
226C2×C4×D3—616no—
227C2×C4×D3—616no—
228C2×C4×D3—68no—
229C2×C4×D3—616no—
230C3×C4⋊C4—28no—
231C3×C22⋊C4—216no—
232C3×C22⋊C4—216no—
233#217—616no—
234#217—616no—
235(C2×D3)⋊C4—616no—
236(C2×D3)⋊C4—616no—
237(C2×D3)⋊C4—616no—
238(C2×D3)⋊C4—616no—
239C4⋊Dic3—68no—
240Dic3⋊C4—68no—
241Dic3⋊C4—68no—
242C22×C32—24no—
243C22×C32—24no—
244C22×C32—24no—
245C22×C32—42no—
246C22×C32—42no—
247C22×C32—42no—
248C22×C32—42no—
249C22×C32C22×D412yes—
250C22×C32C22×D411yescharacteristic
251C22×C32C22×D411yescharacteristic
252C22×C32C2×#4111yescharacteristic
253C22×C32C2×#4112yes—
254C2×C3⋊D3—24no—
255C2×C3⋊D3—24no—
256C2×C3⋊D3—24no—
257C2×C3⋊D3—42no—
258C2×C3⋊D3—42no—
259C2×C3⋊D3—42no—
260C2×C3⋊D3—42no—
261C2×C3⋊D3—432no—
262C2×C3⋊D3#12014yes—
263C2×C3⋊D3#12114yes—
264C2×C3⋊D3#12118yes—
265C2×C3⋊D3#12318yes—
266C2×C3⋊D3#12414yes—
267C32×C4—22no—
268C32×C4—22no—
269C32×C4—41no—
270C32×C4—42no—
271C3⋊Dic3—22no—
272C3⋊Dic3—22no—
273C3⋊Dic3—41no—
274C3⋊Dic3—42no—
275C25—92no—
276C22×D4—92no—
277C22×D4—91no—
278C22×D4—184no—
279C22×D4—188no—
280C22×D4C2×C3⋊D311yescharacteristic
281C23×C4—91no—
282C23×C4—91no—
283C23×C4—91no—
284C23×C4—92no—
285C2×C4⋊C4—91no—
286C2×C4⋊C4—91no—
287C2×C4⋊C4—91no—
288C2×C4⋊C4—184no—
289C2×C4⋊C4C2×C3⋊D311yescharacteristic, complemented
290C2×C22⋊C4—92no—
291C2×C22⋊C4—92no—
292C2×C22⋊C4—92no—
293C2×C22⋊C4—92no—
294C2×C22⋊C4—92no—
295C2×C22⋊C4—92no—
296C2×C22⋊C4—188no—
297C2×C22⋊C4—188no—
298C2×C22⋊C4C2×C3⋊D312yescomplemented
299C2×C22⋊C4C2×C3⋊D312yescomplemented
300#95—92no—
301#95—91no—
302#95C2×C3⋊D311yescharacteristic, complemented
303C23×C3—28no—
304C23×C3—28no—
305C23×C3—28no—
306C23×C3—28no—
307C23×C3—28no—
308C23×C3—28no—
309C23×C3D3×D4116yes—
310C23×C3C23×D314yes—
311C22×D3—38no—
312C22×D3—38no—
313C22×D3—316no—
314C22×D3—38no—
315C22×D3—316no—
316C22×D3—316no—
317C22×D3—664no—
318C22×D3—664no—
319C22×D3—664no—
320C22×D3—68no—
321C22×D3—68no—
322C22×D3—68no—
323C22×D3—68no—
324C22×D3—68no—
325C22×D3—68no—
326C22×D3—1232no—
327C22×D3—1232no—
328C22×D3—1232no—
329C22×D3—1232no—
330C3×D4—232no—
331C2×C3×C4—24no—
332C2×C3×C4—28no—
333C2×C3×C4—24no—
334C2×C3×C4—24no—
335C2×C3×C4—28no—
336C2×C3×C4—28no—
337C2×C3×C4—28no—
338C2×C3×C4—28no—
339C2×C3×C4D3×D418yes—
340C2×C3×C4D3×D418yescomplemented
341#67—664no—
342C2×Dic3—38no—
343C2×Dic3—38no—
344C2×Dic3—64no—
345C2×Dic3—68no—
346C2×Dic3—64no—
347C2×Dic3—64no—
348C2×Dic3—68no—
349C2×Dic3—68no—
350C2×Dic3—68no—
351C2×Dic3—68no—
352D12—632no—
353C4×D3—632no—
354C4×D3—632no—
355C4×D3—1216no—
356C4×D3—1232no—
357C2×C32—44no—
358C2×C32C2×#12011yescharacteristic
359C2×C32C2×#12111yescharacteristic
360C2×C32C2×#12112yes—
361C2×C32C2×#12312yes—
362C2×C32C2×#12411yescharacteristic
363C3⋊D3—44no—
364C3⋊D3#39418yesdirect product factor
365C24—91no—
366C24—92no—
367C24—98no—
368C24—184no—
369C24—184no—
370C24—184no—
371C24—184no—
372C24—184no—
373C24—184no—
374C24C22×C3⋊D312yes—
375C2×D4—24no—
376C2×D4—22no—
377C2×D4—184no—
378C2×D4—184no—
379C2×D4—1832no—
380C2×D4—184no—
381C2×D4—184no—
382C2×D4—182no—
383C22×C4—91no—
384C22×C4—91no—
385C22×C4—94no—
386C22×C4—94no—
387C22×C4—92no—
388C22×C4—91no—
389C22×C4—182no—
390C22×C4—184no—
391C22×C4—182no—
392C22×C4—184no—
393C22×C4—184no—
394C22×C4—184no—
395C22×C4—182no—
396C22×C4—184no—
397C22×C4C22×C3⋊D312yes—
398C22×C4C22×C3⋊D311yescharacteristic
399C22×C4C22×C3⋊D311yescharacteristic
400C22×C4C22×C3⋊D311yescharacteristic
401C4⋊C4—22no—
402C4⋊C4—182no—
403C4⋊C4—182no—
404C4⋊C4—182no—
405C22⋊C4—24no—
406C22⋊C4—24no—
407C22⋊C4—184no—
408C22⋊C4—184no—
409C22⋊C4—184no—
410C22⋊C4—184no—
411C22⋊C4—184no—
412C22⋊C4—184no—
413C22×C3—216no—
414C22×C3—216no—
415C22×C3—216no—
416C22×C3—48no—
417C22×C3—48no—
418C22×C3—48no—
419C22×C3—48no—
420C22×C3C2×D3×D418yes—
421C22×C3C2×D3×D414yes—
422C22×C3C2×D3×D414yes—
423C22×C3D3×#4114yes—
424C22×C3D3×#4118yes—
425C2×D3—332no—
426C2×D3—316no—
427C2×D3—316no—
428C2×D3—316no—
429C2×D3—332no—
430C2×D3—616no—
431C2×D3—616no—
432C2×D3—616no—
433C2×D3—12128no—
434C2×D3—128no—
435C2×D3—128no—
436C2×D3—128no—
437C2×D3—128no—
438C3×C4—28no—
439C3×C4—28no—
440C3×C4—44no—
441C3×C4—48no—
442Dic3—68no—
443Dic3—68no—
444Dic3—124no—
445Dic3—128no—
446C32C2×#39411yescharacteristic, complemented, Sylow
447C23—22no—
448C23—22no—
449C23—22no—
450C23—22no—
451C23—22no—
452C23—22no—
453C23—92no—
454C23—92no—
455C23—94no—
456C23—92no—
457C23—94no—
458C23—94no—
459C23—1816no—
460C23—1816no—
461C23—1816no—
462C23—182no—
463C23—182no—
464C23—182no—
465C23—182no—
466C23—182no—
467C23—182no—
468C23—368no—
469C23—368no—
470C23—368no—
471C23—368no—
472C23D4×C3⋊D314yes—
473C23C23×C3⋊D311yescharacteristic
474D4—28no—
475D4—188no—
476D4—1816no—
477C2×C4—21no—
478C2×C4—22no—
479C2×C4—21no—
480C2×C4—22no—
481C2×C4—22no—
482C2×C4—22no—
483C2×C4—21no—
484C2×C4—22no—
485C2×C4—92no—
486C2×C4—92no—
487C2×C4—188no—
488C2×C4—188no—
489C2×C4—181no—
490C2×C4—182no—
491C2×C4—181no—
492C2×C4—182no—
493C2×C4—182no—
494C2×C4—182no—
495C2×C4—181no—
496C2×C4—182no—
497C2×C4—364no—
498C2×C4—368no—
499C2×C4D4×C3⋊D312yes—
500C2×C4D4×C3⋊D312yescomplemented
501C2×C3—416no—
502C2×C3D3×#12014yes—
503C2×C3D3×#12114yes—
504C2×C3D3×#12118yes—
505C2×C3D3×#12318yes—
506C2×C3D3×#12414yes—
507D3—332no—
508D3—1216no—
509C22—24no—
510C22—24no—
511C22—24no—
512C22—42no—
513C22—42no—
514C22—42no—
515C22—42no—
516C22—98no—
517C22—94no—
518C22—94no—
519C22—94no—
520C22—98no—
521C22—184no—
522C22—184no—
523C22—184no—
524C22—3632no—
525C22—362no—
526C22—362no—
527C22—362no—
528C22—362no—
529C22C2×D4×C3⋊D312yes—
530C22C2×D4×C3⋊D311yescharacteristic
531C22C2×D4×C3⋊D311yescharacteristic
532C22#41×C3⋊D311yescharacteristic
533C22#41×C3⋊D312yes—
534C4—22no—
535C4—22no—
536C4—41no—
537C4—42no—
538C4—182no—
539C4—182no—
540C4—361no—
541C4—362no—
542C3D3×#39414yescomplemented
543C2—44no—
544C2—98no—
545C2—364no—
546C2C3⋊D3×#12011yescharacteristic
547C2C3⋊D3×#12111yescharacteristic
548C2C3⋊D3×#12112yes—
549C2C3⋊D3×#12312yes—
550C2C3⋊D3×#12411yescharacteristic
subgroupG/H
center, FrattiniC23C23×C3⋊D3
commutator, socle, cosocleC23×C32C24
FittingC32×#394C2
prime radicalC22×D4×C3⋊D3C2
hypercenter#394C3⋊D3
hypocenterC32C2×#394
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C23 ◁ #394

Complements

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

NH ≅ G/Ntype
2. C2×C4⋊C4×C3⋊D3C2semidirect
3. C2×C22⋊C4×C3⋊D3C2semidirect
4. C2×C22⋊C4×C3⋊D3C2semidirect
5. C32×#394C2semidirect
6. #10592921C2semidirect
7. #10592690C2semidirect
8. #10592660C2semidirect
9. #10592658C2semidirect
10. #10592371C2semidirect
11. C3⋊D3×#95C2semidirect
23. C2×C32×C4⋊C4C22semidirect
24. C2×C32×C22⋊C4C22semidirect
25. C2×C32×C22⋊C4C22semidirect
26. C2×#3757C22semidirect
27. C2×#3757C22semidirect
28. C2×#3752C22semidirect
29. C2×#3752C22semidirect
30. C2×#3752C22semidirect
31. C2×#3752C22semidirect
32. C2×C4⋊(C3⋊Dic3)C22semidirect
33. C2×#3750C22semidirect
34. C2×#3750C22semidirect
38. C32×#95C22semidirect
39. #63658C22semidirect
40. #63658C22semidirect
45. C3×#394D3semidirect
87. C2×C4×C3⋊D3D4semidirect
111. C2×C3×C4⋊C4C2×D3semidirect
112. C2×C3×C22⋊C4C2×D3semidirect
113. C2×C3×C22⋊C4C2×D3semidirect
126. C3×#95C2×D3semidirect
166. C2×C32×C4C2×D4semidirect
177. C2×C3⋊Dic3C2×D4semidirect
192. #394C3⋊D3direct (N × H)
289. C2×C4⋊C4C2×C3⋊D3semidirect
298. C2×C22⋊C4C2×C3⋊D3semidirect
299. C2×C22⋊C4C2×C3⋊D3semidirect
302. #95C2×C3⋊D3semidirect
340. C2×C3×C4D3×D4semidirect
364. C3⋊D3#394direct (N × H)
446. C32C2×#394semidirect
500. C2×C4D4×C3⋊D3semidirect
542. C3D3×#394semidirect

Maximal subgroups

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

subgroupindex
C22×D4×C3⋊D32
C2×C4⋊C4×C3⋊D32
C2×C22⋊C4×C3⋊D32
C32×#3942
#105929212
#105926902
#105926602
#105926582
#105923712
C3⋊D3×#952
D3×#3943