Finite Group Databasebeta

← D3×C4⋊SL(2,ℤ/4) #11922008

Subgroups — D3×C4⋊SL(2,ℤ/4) #11922008

Order 1152.

1024 conjugacy classes of subgroups; only the 119 normal subgroups are shown.

normal subgroups only

This group has 1024 conjugacy classes of subgroups — too many to draw. Only its 119 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×C4×D3×A4C211yesmaximal, characteristic
2C2×D3×SL(2,ℤ/4)C212yesmaximal
3C4⋊(C3⋊SL(2,ℤ/4))C211yesmaximal, characteristic, complemented
4C3×C4⋊SL(2,ℤ/4)C211yesmaximal, characteristic, complemented
5Dic3⋊SL(2,ℤ/4)C212yesmaximal, complemented
6C2×C4⋊SL(2,ℤ/4)—31nomaximal
7D3×#380—31nomaximal
8C22×D3×A4C2211yescharacteristic
9C2×C3×C4×A4C2211yescharacteristic
10C2×Dic3×A4C2211yescharacteristic
11C4×D3×A4C414yescomplemented
12C2×C3⋊SL(2,ℤ/4)C2212yes—
13C2×C3×SL(2,ℤ/4)C2212yes—
14D3×SL(2,ℤ/4)—24no—
15D3×C4⋊Dic3—41nomaximal
16C23×C4×D3D311yescharacteristic
17C22×C4×A4—31no—
18C22×SL(2,ℤ/4)—32no—
19C2×D3×C4⋊C4—31no—
20C2×D3×C4⋊C4—31no—
21C2×D3×C22⋊C4—32no—
22C4⋊SL(2,ℤ/4)—31no—
23C4⋊SL(2,ℤ/4)—32no—
24C4⋊SL(2,ℤ/4)—61no—
25C4⋊SL(2,ℤ/4)D311yescharacteristic, direct product factor
26C3×#380—31no—
27#5212—31no—
28#4987—31no—
29#4987—31no—
30#4942—32no—
31#4667—32no—
32D3×#95—32no—
33C22×C3×A4C2311yescharacteristic
34C2×D3×A4C2×C412yes—
35C2×D3×A4D412yes—
36C2×D3×A4Q812yes—
37C2×C3×C4×D3—41no—
38C3×C4×A4C2×C412yescomplemented
39C2×D3×Dic3—42no—
40Dic3×A4C2×C412yescomplemented
41C3⋊SL(2,ℤ/4)—22no—
42C3×SL(2,ℤ/4)—22no—
43C4⋊(C3⋊Dic3)—41no—
44C3×C4⋊Dic3—41no—
45Dic3⋊Dic3—42no—
46C2×#380—91noSylow
47C24×D3C2×D311yescharacteristic
48C23×A4—31no—
49C23×C3×C4C2×D311yescharacteristic
50C23×Dic3C2×D311yescharacteristic
51C22×C4×D3—31no—
52C22×C4×D3—31no—
53C22×C4×D3—31no—
54C22×C4×D3—34no—
55C22×C4×D3—31no—
56C22×C4×D3—32no—
57C22×C4×D3—32no—
58C22×C4×D3Dic314yescomplemented
59C2×C4×A4—21no—
60C2×C4×A4—31no—
61C2×C4×A4—34no—
62C2×C4×A4C2×D311yescharacteristic
63C2×SL(2,ℤ/4)—32no—
64C2×SL(2,ℤ/4)—62no—
65C2×SL(2,ℤ/4)—64no—
66C2×SL(2,ℤ/4)C2×D312yes—
67C2×C3×C4⋊C4—31no—
68C2×C3×C4⋊C4—31no—
69C2×C3×C22⋊C4—32no—
70C2×#217—32no—
71C2×(C2×D3)⋊C4—32no—
72C2×(C2×D3)⋊C4—32no—
73C2×C4⋊Dic3—31no—
74C2×C4⋊Dic3—31no—
75C2×C4⋊Dic3—121no—
76C2×Dic3⋊C4—32no—
77C2×Dic3⋊C4—32no—
78D3×C4⋊C4—61no—
79D3×C4⋊C4—64no—
80D3×C4⋊C4—61no—
81D3×C4⋊C4—61no—
82D3×C4⋊C4—61no—
83D3×C22⋊C4—64no—
84D3×C22⋊C4—64no—
85C3×#95—32no—
86C3⋊#95—32no—
87C3⋊#95—32no—
88C3⋊#95—32no—
89C22×C3×D3—41no—
90C2×C3×A4C22×C411yescharacteristic
91C2×C3×A4C2×D411yescharacteristic
92C2×C3×A4C2×Q811yescharacteristic
93D3×A4C4⋊C414yescomplemented
94C2×C32×C4—41no—
95C2×C3⋊Dic3—42no—
96C2×C3×Dic3—42no—
97C2×C3×Dic3—41no—
98C3×C4×D3—44no—
99D3×Dic3—84no—
100C24×C4—31no—
101C22×C4⋊C4—91no—
102C22×C4⋊C4—91no—
103C22×C22⋊C4—92no—
104#380—31no—
105#380—92no—
106#380—92no—
107#380—91no—
108#380—91no—
109#380—91no—
110C2×#95—92no—
111C24×C3C22×D311yescharacteristic
112C23×D3—31no—
113C23×D3—32no—
114C23×D3—31no—
115C23×D3—32no—
116C23×D3—32no—
117C23×D3Dic612yes—
118C23×D3D1212yes—
119C23×D3C2×Dic312yes—
120C22×A4—21no—
121C22×A4—32no—
122C22×A4—32no—
123C22×A4—32no—
124C22×A4C22×D311yescharacteristic
125C22×C3×C4—31no—
126C22×C3×C4—31no—
127C22×C3×C4—32no—
128C22×C3×C4—32no—
129C22×C3×C4—32no—
130C22×C3×C4—121no—
131C22×C3×C4C2×Dic312yescomplemented
132C22×Dic3—31no—
133C22×Dic3—31no—
134C22×Dic3—32no—
135C22×Dic3—32no—
136C22×Dic3—32no—
137C22×Dic3—122no—
138C22×Dic3C2×Dic312yescomplemented
139C2×C4×D3—31no—
140C2×C4×D3—31no—
141C2×C4×D3—31no—
142C2×C4×D3—34no—
143C2×C4×D3—34no—
144C2×C4×D3—34no—
145C2×C4×D3—34no—
146C2×C4×D3—34no—
147C2×C4×D3—62no—
148C2×C4×D3—62no—
149C2×C4×D3—62no—
150C2×C4×D3—61no—
151C2×C4×D3—64no—
152C2×C4×D3—64no—
153C2×C4×D3—64no—
154C2×C4×D3—62no—
155C2×C4×D3—64no—
156C2×C4×D3—64no—
157C2×C4×D3—62no—
158C2×C4×D3S411yescharacteristic
159C4×A4—22no—
160C4×A4—32no—
161C4×A4C4×D312yescomplemented
162SL(2,ℤ/4)—22no—
163SL(2,ℤ/4)—62no—
164SL(2,ℤ/4)—122no—
165C3×C4⋊C4—61no—
166C3×C4⋊C4—62no—
167C3×C4⋊C4—61no—
168C3×C22⋊C4—62no—
169C3×C22⋊C4—62no—
170#217—62no—
171#217—62no—
172(C2×D3)⋊C4—64no—
173(C2×D3)⋊C4—64no—
174C4⋊Dic3—41no—
175C4⋊Dic3—62no—
176C4⋊Dic3—61no—
177C4⋊Dic3—61no—
178C4⋊Dic3—122no—
179C4⋊Dic3—121no—
180C4⋊Dic3—241no—
181Dic3⋊C4—62no—
182Dic3⋊C4—64no—
183Dic3⋊C4—62no—
184C22×C32—41no—
185C2×C3×D3—42no—
186C2×C3×D3—42no—
187C2×C3×D3—42no—
188C3×A4C2×C4⋊C411yescharacteristic, complemented
189C32×C4—42no—
190C3⋊Dic3—82no—
191C3×Dic3—42no—
192C3×Dic3—82no—
193C25—31no—
194C23×C4—31no—
195C23×C4—34no—
196C23×C4—91no—
197C23×C4—91no—
198C23×C4—91no—
199C23×C4—91no—
200C23×C4—94no—
201C23×C4—92no—
202C23×C4—92no—
203C23×C4D3211yescharacteristic
204C2×C4⋊C4—31no—
205C2×C4⋊C4—31no—
206C2×C4⋊C4—92no—
207C2×C4⋊C4—92no—
208C2×C4⋊C4—91no—
209C2×C4⋊C4—91no—
210C2×C4⋊C4—181no—
211C2×C4⋊C4—181no—
212C2×C4⋊C4—184no—
213C2×C4⋊C4—181no—
214C2×C4⋊C4—181no—
215C2×C22⋊C4—32no—
216C2×C22⋊C4—92no—
217C2×C22⋊C4—92no—
218C2×C22⋊C4—92no—
219C2×C22⋊C4—184no—
220C2×C22⋊C4—184no—
221#95—32no—
222#95—92no—
223#95—92no—
224#95—92no—
225C23×C3—31no—
226C23×C3—31no—
227C23×C3—31no—
228C23×C3—31no—
229C23×C3—121no—
230C23×C3C2×Dic611yescharacteristic
231C23×C3C2×D1211yescharacteristic
232C23×C3C22×Dic311yescharacteristic
233C22×D3—31no—
234C22×D3—32no—
235C22×D3—32no—
236C22×D3—32no—
237C22×D3—32no—
238C22×D3—32no—
239C22×D3—32no—
240C22×D3—32no—
241C22×D3—32no—
242C22×D3—32no—
243C22×D3—34no—
244C22×D3—34no—
245C22×D3—34no—
246C22×D3—64no—
247C22×D3—61no—
248C22×D3—61no—
249C22×D3—61no—
250C22×D3C4⋊Dic314yescomplemented
251C22×D3C2×S411yescharacteristic
252C2×A4—21no—
253C2×A4—21no—
254C2×A4—21no—
255C2×A4—34no—
256C2×A4C2×C4×D311yescharacteristic
257C2×A4D3×D411yescharacteristic
258C2×A4D3×Q811yescharacteristic
259C2×C3×C4—31no—
260C2×C3×C4—32no—
261C2×C3×C4—32no—
262C2×C3×C4—32no—
263C2×C3×C4—41no—
264C2×C3×C4—61no—
265C2×C3×C4—62no—
266C2×C3×C4—62no—
267C2×C3×C4—62no—
268C2×C3×C4—62no—
269C2×C3×C4—62no—
270C2×C3×C4—62no—
271C2×C3×C4—81no—
272C2×C3×C4—124no—
273C2×C3×C4—121no—
274C2×C3×C4C2×S411yescharacteristic
275C2×Dic3—31no—
276C2×Dic3—32no—
277C2×Dic3—32no—
278C2×Dic3—32no—
279C2×Dic3—42no—
280C2×Dic3—61no—
281C2×Dic3—62no—
282C2×Dic3—62no—
283C2×Dic3—62no—
284C2×Dic3—62no—
285C2×Dic3—62no—
286C2×Dic3—62no—
287C2×Dic3—122no—
288C2×Dic3—242no—
289C2×Dic3—244no—
290C2×Dic3C2×S411yescharacteristic
291C4×D3—34no—
292C4×D3—34no—
293C4×D3—34no—
294C4×D3—64no—
295C4×D3—128no—
296C4×D3—124no—
297C4×D3—124no—
298C4×D3SL(2,ℤ/4)14yescomplemented
299C2×C32—41no—
300C2×C32—41no—
301C2×C32—41no—
302C3×D3—44no—
303C24—32no—
304C24—32no—
305C24—32no—
306C24—91no—
307C24—91no—
308C24—92no—
309C24—92no—
310C24—92no—
311C24C2×D3211yescharacteristic
312C22×C4—31no—
313C22×C4—31no—
314C22×C4—31no—
315C22×C4—32no—
316C22×C4—32no—
317C22×C4—32no—
318C22×C4—32no—
319C22×C4—91no—
320C22×C4—94no—
321C22×C4—94no—
322C22×C4—91no—
323C22×C4—91no—
324C22×C4—94no—
325C22×C4—94no—
326C22×C4—94no—
327C22×C4—91no—
328C22×C4—91no—
329C22×C4—92no—
330C22×C4—92no—
331C22×C4—92no—
332C22×C4—182no—
333C22×C4—181no—
334C22×C4—182no—
335C22×C4—182no—
336C22×C4—182no—
337C22×C4—184no—
338C22×C4—184no—
339C22×C4—184no—
340C22×C4—182no—
341C22×C4—184no—
342C22×C4—184no—
343C22×C4D3×Dic312yescomplemented
344C4⋊C4—61no—
345C4⋊C4—62no—
346C4⋊C4—61no—
347C4⋊C4—182no—
348C4⋊C4—181no—
349C4⋊C4—182no—
350C4⋊C4—184no—
351C4⋊C4—182no—
352C4⋊C4—181no—
353C22⋊C4—62no—
354C22⋊C4—62no—
355C22⋊C4—184no—
356C22⋊C4—184no—
357C22⋊C4—182no—
358C22⋊C4—182no—
359C22×C3—31no—
360C22×C3—31no—
361C22×C3—31no—
362C22×C3—31no—
363C22×C3—31no—
364C22×C3—31no—
365C22×C3—31no—
366C22×C3—31no—
367C22×C3—31no—
368C22×C3—41no—
369C22×C3—61no—
370C22×C3—81no—
371C22×C3—122no—
372C22×C3—122no—
373C22×C3—122no—
374C22×C3C2×C4⋊Dic311yescharacteristic, complemented
375C22×C3C22×S411yescharacteristic
376C2×D3—32no—
377C2×D3—32no—
378C2×D3—32no—
379C2×D3—34no—
380C2×D3—34no—
381C2×D3—34no—
382C2×D3—34no—
383C2×D3—34no—
384C2×D3—62no—
385C2×D3—62no—
386C2×D3—62no—
387C2×D3A4⋊Q812yes—
388C2×D3C4⋊S412yes—
389C2×D3C2×SL(2,ℤ/4)12yes—
390A4—21no—
391A4D3×C4⋊C411yescharacteristic, complemented
392C3×C4—32no—
393C3×C4—42no—
394C3×C4—82no—
395C3×C4—122no—
396C3×C4—122no—
397C3×C4—122no—
398C3×C4C2×SL(2,ℤ/4)12yescomplemented
399Dic3—32no—
400Dic3—82no—
401Dic3—122no—
402Dic3—122no—
403Dic3—242no—
404Dic3—482no—
405Dic3C2×SL(2,ℤ/4)12yescomplemented
406C32—41noSylow
407C23—31no—
408C23—31no—
409C23—31no—
410C23—31no—
411C23—31no—
412C23—34no—
413C23—92no—
414C23—92no—
415C23—92no—
416C23—92no—
417C23—92no—
418C23—92no—
419C23—92no—
420C23—92no—
421C23—94no—
422C23—94no—
423C23—94no—
424C23—92no—
425C23—91no—
426C23—181no—
427C23—181no—
428C23—181no—
429C23—184no—
430C23D3×Dic611yescharacteristic
431C23D3×D1211yescharacteristic
432C23C2×D3×Dic311yescharacteristic
433C2×C4—31no—
434C2×C4—31no—
435C2×C4—32no—
436C2×C4—32no—
437C2×C4—34no—
438C2×C4—32no—
439C2×C4—61no—
440C2×C4—62no—
441C2×C4—62no—
442C2×C4—62no—
443C2×C4—62no—
444C2×C4—62no—
445C2×C4—62no—
446C2×C4—94no—
447C2×C4—92no—
448C2×C4—92no—
449C2×C4—94no—
450C2×C4—91no—
451C2×C4—94no—
452C2×C4—92no—
453C2×C4—184no—
454C2×C4—181no—
455C2×C4—182no—
456C2×C4—182no—
457C2×C4—182no—
458C2×C4—182no—
459C2×C4—182no—
460C2×C4—182no—
461C2×C4—364no—
462C2×C4—368no—
463C2×C4—364no—
464C2×C4D3×S411yescharacteristic
465C2×C3—31no—
466C2×C3—31no—
467C2×C3—31no—
468C2×C3—31no—
469C2×C3—41no—
470C2×C3—41no—
471C2×C3—41no—
472C2×C3—81no—
473C2×C3—81no—
474C2×C3—81no—
475C2×C3—124no—
476C2×C3C2×A4⋊Q811yescharacteristic
477C2×C3C2×C4⋊S411yescharacteristic
478C2×C3C22×SL(2,ℤ/4)11yescharacteristic
479D3—34no—
480D3C4⋊SL(2,ℤ/4)14yesdirect product factor
481C22—31no—
482C22—31no—
483C22—31no—
484C22—31no—
485C22—31no—
486C22—32no—
487C22—31no—
488C22—31no—
489C22—32no—
490C22—31no—
491C22—31no—
492C22—32no—
493C22—61no—
494C22—94no—
495C22—94no—
496C22—94no—
497C22—94no—
498C22—94no—
499C22—92no—
500C22—92no—
501C22—92no—
502C22—182no—
503C22—182no—
504C22—182no—
505C22D3×C4⋊Dic311yescharacteristic, complemented
506C22C2×D3×S411yescharacteristic
507C4—32no—
508C4—32no—
509C4—92no—
510C4—122no—
511C4—122no—
512C4—362no—
513C4—362no—
514C4D3×SL(2,ℤ/4)12yescomplemented
515C3—41no—
516C3—81no—
517C3C2×C4⋊SL(2,ℤ/4)11yescharacteristic, complemented
518C2—31no—
519C2—31no—
520C2—31no—
521C2—31no—
522C2—34no—
523C2—94no—
524C2D3×A4⋊Q811yescharacteristic
525C2D3×C4⋊S411yescharacteristic
526C2C2×D3×SL(2,ℤ/4)11yescharacteristic
subgroupG/H
center, FrattiniC22C2×D3×S4
commutatorC2×C3×A4C22×C4
FittingC23×C3×C4C2×D3
socleC24×C3C22×D3
prime radicalC22×D3×A4C22
cosocleC22×C3×A4C23
hypercenterC2×C4D3×S4
hypocenterC3×A4C2×C4⋊C4
LCSG ▷ C2×C3×A4 ▷ C3×A4
UCSC1 ◁ C22 ◁ C2×C4

Complements

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

NH ≅ G/Ntype
3. C4⋊(C3⋊SL(2,ℤ/4))C2semidirect
4. C3×C4⋊SL(2,ℤ/4)C2semidirect
5. Dic3⋊SL(2,ℤ/4)C2semidirect
11. C4×D3×A4C4semidirect
25. C4⋊SL(2,ℤ/4)D3direct (N × H)
38. C3×C4×A4C2×C4semidirect
40. Dic3×A4C2×C4semidirect
58. C22×C4×D3Dic3semidirect
93. D3×A4C4⋊C4semidirect
131. C22×C3×C4C2×Dic3semidirect
138. C22×Dic3C2×Dic3semidirect
161. C4×A4C4×D3semidirect
188. C3×A4C2×C4⋊C4semidirect
250. C22×D3C4⋊Dic3semidirect
298. C4×D3SL(2,ℤ/4)semidirect
343. C22×C4D3×Dic3semidirect
374. C22×C3C2×C4⋊Dic3semidirect
391. A4D3×C4⋊C4semidirect
398. C3×C4C2×SL(2,ℤ/4)semidirect
405. Dic3C2×SL(2,ℤ/4)semidirect
480. D3C4⋊SL(2,ℤ/4)direct (N × H)
505. C22D3×C4⋊Dic3semidirect
514. C4D3×SL(2,ℤ/4)semidirect
517. C3C2×C4⋊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×C4×D3×A42
C2×D3×SL(2,ℤ/4)2
C4⋊(C3⋊SL(2,ℤ/4))2
C3×C4⋊SL(2,ℤ/4)2
Dic3⋊SL(2,ℤ/4)2
C2×C4⋊SL(2,ℤ/4)3
D3×#3803
D3×C4⋊Dic34