Finite Group Databasebeta

← D4×C3⋊SL(2,ℤ/4) #11923039

Subgroups — D4×C3⋊SL(2,ℤ/4) #11923039

Order 1152.

1210 conjugacy classes of subgroups; only the 165 normal subgroups are shown.

normal subgroups only

This group has 1210 conjugacy classes of subgroups — too many to draw. Only its 165 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×D4×A4C211yesmaximal, characteristic
2C22×C3⋊SL(2,ℤ/4)C212yesmaximal, complemented
3#10593666C212yesmaximal, complemented
4C4⋊(C3⋊SL(2,ℤ/4))C211yesmaximal, characteristic, complemented
5C4×C3⋊SL(2,ℤ/4)C211yesmaximal, characteristic, complemented
6D4×SL(2,ℤ/4)—33nomaximal
7D4×#217—31nomaximal
8C23×C3×A4C2212yes—
9C3×D4×A4C414yescomplemented
10C2×C3×C4×A4C2211yescharacteristic
11C2×C3⋊SL(2,ℤ/4)—24no—
12C2×C3⋊SL(2,ℤ/4)C2211yescharacteristic
13C2×C3⋊SL(2,ℤ/4)C2212yes—
14C2×C3⋊SL(2,ℤ/4)C2211yescharacteristic
15D4×C3⋊Dic3—41nomaximal
16C23×C3×D4D311yescharacteristic
17C2×D4×A4D313yes—
18C22×SL(2,ℤ/4)—36no—
19C22×#217—32no—
20C2×D4×Dic3—31no—
21C2×D4×Dic3—31no—
22#5432—36no—
23C4⋊SL(2,ℤ/4)—33no—
24C4×SL(2,ℤ/4)—33no—
25#5247—32no—
26#5221—31no—
27#5221—31no—
28#5220—32no—
29#5220—32no—
30#5212—31no—
31C4×#217—31no—
32C22×C3×A4—22no—
33C22×C3×A4—22no—
34C22×C3×A4C2×C414yescomplemented
35C22×C3×A4C2311yescharacteristic
36C2×C32×D4—41no—
37C22×C3⋊Dic3—42no—
38C3×C4×A4C2×C412yescomplemented
39C3⋊SL(2,ℤ/4)—22no—
40C3⋊SL(2,ℤ/4)—21no—
41C3⋊SL(2,ℤ/4)D412yesdirect product factor
42#3757—42no—
43C4⋊(C3⋊Dic3)—41no—
44C4×C3⋊Dic3—41no—
45D4×C22⋊C4—91noSylow
46C25×C3C2×D312yes—
47C23×A4C2×D316yes—
48C22×C3×D4—31no—
49C22×C3×D4—34no—
50C22×C3×D4—32no—
51C22×C3×D4—31no—
52C22×C3×D4Dic314yescomplemented
53C23×C3×C4C2×D311yescharacteristic
54C23×Dic3—32no—
55C23×Dic3—32no—
56D4×A4Dic3112yescomplemented
57C2×C4×A4C2×D313yes—
58C2×SL(2,ℤ/4)—33no—
59C2×SL(2,ℤ/4)—33no—
60C2×SL(2,ℤ/4)—36no—
61C2×SL(2,ℤ/4)—612no—
62C2×#217—31no—
63C2×#217—32no—
64C2×#217—32no—
65C2×#217—32no—
66C2×#217—32no—
67C2×#217—31no—
68C2×#217—32no—
69C2×#217—32no—
70C2×#217—32no—
71C2×#217—64no—
72C2×#217—64no—
73D4×Dic3—64no—
74D4×Dic3—62no—
75D4×Dic3—61no—
76D4×Dic3—61no—
77D4×Dic3—123no—
78C2×C4⋊Dic3—31no—
79C2×C4⋊Dic3—31no—
80C2×C4×Dic3—31no—
81C2×C4×Dic3—31no—
82C3⋊#95—31no—
83C3⋊#95—31no—
84C3⋊#95—32no—
85C23×C32—42no—
86C2×C3×A4—24no—
87C2×C3×A4C22×C411yescharacteristic
88C2×C3×A4C2×D411yescharacteristic
89C2×C3×A4#4111yescharacteristic
90C32×D4—44no—
91C2×C32×C4—41no—
92C2×C3⋊Dic3—41no—
93C2×C3⋊Dic3—41no—
94C2×C3⋊Dic3—42no—
95C2×C3⋊Dic3—84no—
96C23×D4C3⋊D311yescharacteristic
97C2×C4×D4—91no—
98C2×C4×D4—91no—
99C22×C22⋊C4—92no—
100#390—91no—
101#390—91no—
102#386—92no—
103#386—92no—
104#380—91no—
105#379—92no—
106C4×C22⋊C4—91no—
107C24×C3—22no—
108C24×C3—22no—
109C24×C3—32no—
110C24×C3—32no—
111C24×C3—34no—
112C24×C3—62no—
113C24×C3—62no—
114C24×C3C2×Dic314yescomplemented
115C24×C3C22×D311yescharacteristic
116C22×A4—26no—
117C22×A4—26no—
118C22×A4C2×Dic3112yescomplemented
119C22×A4C22×D313yes—
120C2×C3×D4—32no—
121C2×C3×D4—34no—
122C2×C3×D4—34no—
123C2×C3×D4—34no—
124C2×C3×D4—38no—
125C2×C3×D4—31no—
126C2×C3×D4—43no—
127C2×C3×D4—62no—
128C2×C3×D4—61no—
129C2×C3×D4—64no—
130C2×C3×D4S411yescharacteristic
131C22×C3×C4—31no—
132C22×C3×C4—31no—
133C22×C3×C4—32no—
134C22×C3×C4C2×Dic312yescomplemented
135C22×Dic3—31no—
136C22×Dic3—31no—
137C22×Dic3—31no—
138C22×Dic3—31no—
139C22×Dic3—32no—
140C22×Dic3—32no—
141C22×Dic3—64no—
142C22×Dic3—64no—
143C22×Dic3—64no—
144C22×Dic3—62no—
145C22×Dic3—62no—
146C22×Dic3—126no—
147C22×Dic3—122no—
148C22×Dic3—122no—
149C4×A4C2×Dic316yescomplemented
150SL(2,ℤ/4)—36no—
151SL(2,ℤ/4)—66no—
152SL(2,ℤ/4)—63no—
153#217—32no—
154#217—32no—
155#217—64no—
156#217—64no—
157#217—64no—
158#217—62no—
159#217—61no—
160#217—62no—
161#217—62no—
162#217—61no—
163#217—62no—
164#217—126no—
165#217—122no—
166#217—122no—
167C4⋊Dic3—62no—
168C4⋊Dic3—61no—
169C4⋊Dic3—61no—
170C4⋊Dic3—123no—
171C4×Dic3—62no—
172C4×Dic3—61no—
173C4×Dic3—61no—
174C4×Dic3—123no—
175C22×C32—44no—
176C22×C32—41no—
177C22×C32—82no—
178C22×C32—82no—
179C3×A4C4×D411yescharacteristic, complemented
180C32×C4—42no—
181C3⋊Dic3—42no—
182C3⋊Dic3—82no—
183C3⋊Dic3—81no—
184C25C2×C3⋊D312yes—
185C22×D4—31no—
186C22×D4—32no—
187C22×D4—31no—
188C22×D4—34no—
189C22×D4C3⋊Dic314yescomplemented
190C23×C4—92no—
191C23×C4—92no—
192C23×C4C2×C3⋊D311yescharacteristic
193C4×D4—184no—
194C4×D4—182no—
195C4×D4—181no—
196C4×D4—181no—
197C2×C4⋊C4—91no—
198C2×C4⋊C4—91no—
199C2×C22⋊C4—91no—
200C2×C22⋊C4—92no—
201C2×C22⋊C4—92no—
202C2×C22⋊C4—92no—
203C2×C22⋊C4—92no—
204C2×C22⋊C4—92no—
205C2×C22⋊C4—91no—
206C2×C22⋊C4—92no—
207C2×C22⋊C4—92no—
208C2×C22⋊C4—184no—
209C2×C22⋊C4—184no—
210C2×C42—91no—
211C2×C42—91no—
212#95—91no—
213#95—91no—
214#95—92no—
215C23×C3—24no—
216C23×C3—31no—
217C23×C3—31no—
218C23×C3—31no—
219C23×C3—31no—
220C23×C3—34no—
221C23×C3—34no—
222C23×C3—34no—
223C23×C3—32no—
224C23×C3—46no—
225C23×C3—62no—
226C23×C3—62no—
227C23×C3—62no—
228C23×C3—62no—
229C23×C3—62no—
230C23×C3—64no—
231C23×C3—62no—
232C23×C3—62no—
233C23×C3—62no—
234C23×C3—64no—
235C23×C3—64no—
236C23×C3—62no—
237C23×C3—124no—
238C23×C3D3×D411yescharacteristic
239C23×C3#23711yescharacteristic
240C23×C3C22×Dic311yescharacteristic
241C23×C3C2×S412yes—
242C2×A4—212no—
243C2×A4D3×D413yes—
244C2×A4#23713yes—
245C2×A4C22×Dic313yes—
246C3×D4—38no—
247C3×D4—34no—
248C3×D4—412no—
249C3×D4—64no—
250C3×D4SL(2,ℤ/4)14yescomplemented
251C2×C3×C4—31no—
252C2×C3×C4—32no—
253C2×C3×C4—32no—
254C2×C3×C4—32no—
255C2×C3×C4—43no—
256C2×C3×C4—61no—
257C2×C3×C4C2×S411yescharacteristic
258C2×Dic3—32no—
259C2×Dic3—32no—
260C2×Dic3—61no—
261C2×Dic3—61no—
262C2×Dic3—61no—
263C2×Dic3—61no—
264C2×Dic3—61no—
265C2×Dic3—62no—
266C2×Dic3—62no—
267C2×Dic3—62no—
268C2×Dic3—61no—
269C2×Dic3—61no—
270C2×Dic3—61no—
271C2×Dic3—61no—
272C2×Dic3—62no—
273C2×Dic3—62no—
274C2×Dic3—61no—
275C2×Dic3—62no—
276C2×Dic3—123no—
277C2×Dic3—123no—
278C2×Dic3—126no—
279C2×Dic3—124no—
280C2×Dic3—128no—
281C2×Dic3—124no—
282C2×Dic3—2412no—
283C2×C32—41no—
284C2×C32—41no—
285C2×C32—41no—
286C2×C32—84no—
287C24—22no—
288C24—22no—
289C24—32no—
290C24—32no—
291C24—34no—
292C24—62no—
293C24—62no—
294C24C2×C3⋊Dic314yescomplemented
295C24C22×C3⋊D311yescharacteristic
296C2×D4—32no—
297C2×D4—34no—
298C2×D4—34no—
299C2×D4—34no—
300C2×D4—38no—
301C2×D4—31no—
302C2×D4—62no—
303C2×D4—61no—
304C2×D4—64no—
305C2×D4C3⋊S411yescharacteristic
306C22×C4—31no—
307C22×C4—31no—
308C22×C4—32no—
309C22×C4—91no—
310C22×C4—91no—
311C22×C4—91no—
312C22×C4—91no—
313C22×C4—92no—
314C22×C4—92no—
315C22×C4—184no—
316C22×C4—184no—
317C22×C4—184no—
318C22×C4—182no—
319C22×C4—182no—
320C22×C4—362no—
321C22×C4—362no—
322C22×C4C2×C3⋊Dic312yescomplemented
323C4⋊C4—181no—
324C4⋊C4—182no—
325C4⋊C4—181no—
326C22⋊C4—92no—
327C22⋊C4—92no—
328C22⋊C4—184no—
329C22⋊C4—184no—
330C22⋊C4—182no—
331C22⋊C4—184no—
332C22⋊C4—182no—
333C22⋊C4—181no—
334C22⋊C4—182no—
335C22⋊C4—182no—
336C22⋊C4—181no—
337C22⋊C4—362no—
338C22⋊C4—362no—
339C42—181no—
340C42—182no—
341C42—181no—
342C22×C3—22no—
343C22×C3—22no—
344C22×C3—31no—
345C22×C3—31no—
346C22×C3—31no—
347C22×C3—31no—
348C22×C3—31no—
349C22×C3—31no—
350C22×C3—31no—
351C22×C3—31no—
352C22×C3—31no—
353C22×C3—34no—
354C22×C3—412no—
355C22×C3—43no—
356C22×C3—64no—
357C22×C3—64no—
358C22×C3—64no—
359C22×C3—64no—
360C22×C3—61no—
361C22×C3—64no—
362C22×C3—64no—
363C22×C3—62no—
364C22×C3—62no—
365C22×C3—86no—
366C22×C3—86no—
367C22×C3—122no—
368C22×C3—122no—
369C22×C3D4×Dic311yescharacteristic, complemented
370C22×C3C2×SL(2,ℤ/4)14yescomplemented
371C22×C3C22×S411yescharacteristic
372A4D4×Dic313yescomplemented
373C3×C4—32no—
374C3×C4—46no—
375C3×C4C2×SL(2,ℤ/4)12yescomplemented
376Dic3—62no—
377Dic3—62no—
378Dic3—126no—
379Dic3—121no—
380Dic3—122no—
381Dic3—122no—
382Dic3—121no—
383Dic3—246no—
384Dic3—243no—
385C32—41noSylow
386C23—24no—
387C23—31no—
388C23—31no—
389C23—31no—
390C23—31no—
391C23—34no—
392C23—34no—
393C23—34no—
394C23—32no—
395C23—62no—
396C23—62no—
397C23—62no—
398C23—62no—
399C23—62no—
400C23—64no—
401C23—62no—
402C23—62no—
403C23—62no—
404C23—64no—
405C23—64no—
406C23—62no—
407C23—124no—
408C23D4×C3⋊D311yescharacteristic
409C23#383011yescharacteristic
410C23C22×C3⋊Dic311yescharacteristic
411C23C2×C3⋊S412yes—
412D4—38no—
413D4—34no—
414D4—64no—
415D4C3⋊SL(2,ℤ/4)14yesdirect product factor
416C2×C4—31no—
417C2×C4—32no—
418C2×C4—32no—
419C2×C4—32no—
420C2×C4—61no—
421C2×C4—92no—
422C2×C4—92no—
423C2×C4—181no—
424C2×C4—181no—
425C2×C4—181no—
426C2×C4—181no—
427C2×C4—181no—
428C2×C4—182no—
429C2×C4—182no—
430C2×C4—182no—
431C2×C4—181no—
432C2×C4—181no—
433C2×C4—181no—
434C2×C4—181no—
435C2×C4—182no—
436C2×C4—182no—
437C2×C4—181no—
438C2×C4—182no—
439C2×C4—364no—
440C2×C4—368no—
441C2×C4—364no—
442C2×C4C2×C3⋊S411yescharacteristic
443C2×C3—24no—
444C2×C3—31no—
445C2×C3—31no—
446C2×C3—31no—
447C2×C3—31no—
448C2×C3—43no—
449C2×C3—43no—
450C2×C3—43no—
451C2×C3—64no—
452C2×C3—812no—
453C2×C3D4×S411yescharacteristic
454C2×C3#591411yescharacteristic
455C2×C3C22×SL(2,ℤ/4)11yescharacteristic
456C22—22no—
457C22—22no—
458C22—31no—
459C22—31no—
460C22—31no—
461C22—31no—
462C22—31no—
463C22—31no—
464C22—31no—
465C22—31no—
466C22—31no—
467C22—34no—
468C22—64no—
469C22—64no—
470C22—64no—
471C22—64no—
472C22—61no—
473C22—64no—
474C22—64no—
475C22—62no—
476C22—62no—
477C22—122no—
478C22—122no—
479C22D4×C3⋊Dic311yescharacteristic, complemented
480C22C2×C3⋊SL(2,ℤ/4)14yescomplemented
481C22C22×C3⋊S411yescharacteristic
482C4—32no—
483C4—182no—
484C4—182no—
485C4—362no—
486C4—361no—
487C4—362no—
488C4—361no—
489C4C2×C3⋊SL(2,ℤ/4)12yescomplemented
490C3—43no—
491C3D4×SL(2,ℤ/4)11yescharacteristic, complemented
492C2—24no—
493C2—31no—
494C2—31no—
495C2—31no—
496C2—31no—
497C2—64no—
498C2D4×C3⋊S411yescharacteristic
499C2#1059657711yescharacteristic
500C2C22×C3⋊SL(2,ℤ/4)11yescharacteristic
subgroupG/H
center, FrattiniC22C22×C3⋊S4
commutatorC2×C3×A4C22×C4
FittingC23×C3×D4D3
socleC24×C3C22×D3
prime radicalC2×C3×D4×A4C2
cosocleC22×C3×A4C23
hypercenterC2×D4C3⋊S4
hypocenterC3×A4C4×D4
LCSG ▷ C2×C3×A4 ▷ C3×A4
UCSC1 ◁ C22 ◁ C2×D4

Complements

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

NH ≅ G/Ntype
2. C22×C3⋊SL(2,ℤ/4)C2semidirect
3. #10593666C2semidirect
4. C4⋊(C3⋊SL(2,ℤ/4))C2semidirect
5. C4×C3⋊SL(2,ℤ/4)C2semidirect
9. C3×D4×A4C4semidirect
34. C22×C3×A4C2×C4semidirect
38. C3×C4×A4C2×C4semidirect
41. C3⋊SL(2,ℤ/4)D4direct (N × H)
52. C22×C3×D4Dic3semidirect
56. D4×A4Dic3semidirect
114. C24×C3C2×Dic3semidirect
118. C22×A4C2×Dic3semidirect
134. C22×C3×C4C2×Dic3semidirect
149. C4×A4C2×Dic3semidirect
179. C3×A4C4×D4semidirect
189. C22×D4C3⋊Dic3semidirect
250. C3×D4SL(2,ℤ/4)semidirect
294. C24C2×C3⋊Dic3semidirect
322. C22×C4C2×C3⋊Dic3semidirect
369. C22×C3D4×Dic3semidirect
370. C22×C3C2×SL(2,ℤ/4)semidirect
372. A4D4×Dic3semidirect
375. C3×C4C2×SL(2,ℤ/4)semidirect
415. D4C3⋊SL(2,ℤ/4)direct (N × H)
479. C22D4×C3⋊Dic3semidirect
480. C22C2×C3⋊SL(2,ℤ/4)semidirect
489. C4C2×C3⋊SL(2,ℤ/4)semidirect
491. C3D4×SL(2,ℤ/4)semidirect

Maximal subgroups

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

subgroupindex
C2×C3×D4×A42
C22×C3⋊SL(2,ℤ/4)2
#105936662
C4⋊(C3⋊SL(2,ℤ/4))2
C4×C3⋊SL(2,ℤ/4)2
D4×SL(2,ℤ/4)3
D4×#2173
D4×C3⋊Dic34