Finite Group Databasebeta

← #11922854

Subgroups — #11922854

Order 1152.

622 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 622 conjugacy classes of subgroups — too many to draw. Only its 85 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
1C3×A4×C4⋊C4C211yesmaximal, characteristic
2C4⋊(C3⋊SL(2,ℤ/4))C211yesmaximal, characteristic
3#10593645C211yesmaximal, characteristic
4#10593645C211yesmaximal, characteristic
5#10593645C211yesmaximal, characteristic
6#10593645C211yesmaximal, characteristic
7C4×C3⋊SL(2,ℤ/4)C211yesmaximal, characteristic
8#85304—33nomaximal
9#82174—31nomaximal
10C2×C3×C4×A4C2211yescharacteristic
11C2×C3×C4×A4C2211yescharacteristic
12C2×C3×C4×A4C2211yescharacteristic
13C2×C3⋊SL(2,ℤ/4)C2211yescharacteristic
14C2×C3⋊SL(2,ℤ/4)C2211yescharacteristic
15C2×C3⋊SL(2,ℤ/4)C2211yescharacteristic
16C2×C3⋊SL(2,ℤ/4)C2211yescharacteristic
17#64098—41nomaximal
18C22×C3×C4⋊C4D311yescharacteristic
19C2×#889—31no—
20A4×C4⋊C4D313yes—
21C4⋊SL(2,ℤ/4)—33no—
22SL(2,ℤ/4)⋊C4—33no—
23SL(2,ℤ/4)⋊C4—33no—
24SL(2,ℤ/4)⋊C4—33no—
25SL(2,ℤ/4)⋊C4—33no—
26C4×SL(2,ℤ/4)—33no—
27#5212—31no—
28#5210—31no—
29#5210—31no—
30#5210—31no—
31#5210—31no—
32C4×#217—31no—
33#4985—31no—
34#4983—31no—
35#4982—31no—
36#4981—31no—
37#4980—31no—
38#4978—31no—
39#4976—31no—
40C22×C3×A4C2311yescharacteristic
41C3×C4×A4—21no—
42C3×C4×A4—21no—
43C3×C4×A4—21no—
44C3⋊SL(2,ℤ/4)—21no—
45C3⋊SL(2,ℤ/4)—21no—
46C3⋊SL(2,ℤ/4)—21no—
47C3⋊SL(2,ℤ/4)Q812yes—
48C32×C4⋊C4—41no—
49C4⋊(C3⋊Dic3)—41no—
50#3750—41no—
51#3750—41no—
52#3750—41no—
53#3750—41no—
54C4×C3⋊Dic3—41no—
55#2473—91noSylow
56C23×C3×C4C2×D311yescharacteristic
57C23×C3×C4C2×D311yescharacteristic
58C23×C3×C4C2×D311yescharacteristic
59C2×C4×A4C2×D313yes—
60C2×C4×A4C2×D313yes—
61C2×C4×A4C2×D313yes—
62C2×SL(2,ℤ/4)—33no—
63C2×SL(2,ℤ/4)—33no—
64C2×SL(2,ℤ/4)—33no—
65C2×SL(2,ℤ/4)—33no—
66C2×C3×C4⋊C4—31no—
67C2×C3×C4⋊C4—31no—
68C2×C3×C4⋊C4—31no—
69C2×C3×C4⋊C4—31no—
70C2×#217—31no—
71C2×#217—31no—
72C2×#217—31no—
73C2×#217—31no—
74C2×C4⋊Dic3—31no—
75C2×C4⋊Dic3—31no—
76C2×Dic3⋊C4—31no—
77C2×Dic3⋊C4—31no—
78C2×Dic3⋊C4—31no—
79C2×Dic3⋊C4—31no—
80C2×Dic3⋊C4—31no—
81C2×Dic3⋊C4—31no—
82C2×Dic3⋊C4—31no—
83C2×Dic3⋊C4—31no—
84C2×C4×Dic3—31no—
85C2×C4×Dic3—31no—
86#889—61no—
87#889—61no—
88#889—61no—
89#889—61no—
90#889—123no—
91C3⋊#95—31no—
92C3⋊#95—31no—
93C3⋊#95—31no—
94C3⋊#95—31no—
95C3⋊#95—31no—
96C3⋊#95—31no—
97C3⋊#95—31no—
98C3⋊#95—31no—
99C3⋊#95—31no—
100C3⋊#95—31no—
101C3⋊#95—31no—
102C3⋊#95—31no—
103C2×C3×A4C2×Q811yescharacteristic
104C2×C3×A4#4111yescharacteristic
105C2×C3×A4#4111yescharacteristic
106C2×C32×C4—41no—
107C2×C32×C4—41no—
108C2×C32×C4—41no—
109C2×C3⋊Dic3—41no—
110C2×C3⋊Dic3—41no—
111C2×C3⋊Dic3—41no—
112C2×C3⋊Dic3—41no—
113C2×#125—91no—
114C22×C4⋊C4C3⋊D311yescharacteristic
115#400—91no—
116#398—91no—
117#398—91no—
118#398—91no—
119#389—91no—
120#387—91no—
121#387—91no—
122#385—91no—
123#385—91no—
124#385—91no—
125#385—91no—
126#380—91no—
127C4×C22⋊C4—91no—
128C24×C3C22×D311yescharacteristic
129C22×A4C22×D313yes—
130C22×C3×C4—21no—
131C22×C3×C4—21no—
132C22×C3×C4—21no—
133C22×C3×C4—31no—
134C22×C3×C4—31no—
135C22×C3×C4—31no—
136C22×C3×C4—31no—
137C22×C3×C4—31no—
138C22×C3×C4—31no—
139C22×C3×C4—61no—
140C22×C3×C4—61no—
141C22×C3×C4—61no—
142C22×Dic3—31no—
143C22×Dic3—31no—
144C22×Dic3—31no—
145C22×Dic3—31no—
146C22×Dic3—31no—
147C22×Dic3—31no—
148C22×Dic3—31no—
149C22×Dic3—31no—
150C4×A4—23no—
151C4×A4—23no—
152C4×A4—23no—
153SL(2,ℤ/4)—36no—
154SL(2,ℤ/4)—63no—
155SL(2,ℤ/4)—63no—
156SL(2,ℤ/4)—63no—
157C3×C4⋊C4—31no—
158C3×C4⋊C4—31no—
159C3×C4⋊C4—31no—
160C3×C4⋊C4—43no—
161C3×C4⋊C4—61no—
162C3×C4⋊C4S411yescharacteristic
163#217—32no—
164#217—32no—
165#217—61no—
166#217—61no—
167#217—61no—
168#217—61no—
169#217—61no—
170#217—61no—
171C4⋊Dic3—61no—
172C4⋊Dic3—61no—
173C4⋊Dic3—123no—
174C4⋊Dic3—121no—
175Dic3⋊C4—61no—
176Dic3⋊C4—61no—
177Dic3⋊C4—61no—
178Dic3⋊C4—61no—
179Dic3⋊C4—62no—
180Dic3⋊C4—62no—
181Dic3⋊C4—61no—
182Dic3⋊C4—61no—
183Dic3⋊C4—61no—
184Dic3⋊C4—61no—
185Dic3⋊C4—123no—
186Dic3⋊C4—123no—
187Dic3⋊C4—123no—
188Dic3⋊C4—123no—
189Dic3⋊C4—121no—
190Dic3⋊C4—121no—
191C4×Dic3—61no—
192C4×Dic3—61no—
193C4×Dic3—123no—
194C4×Dic3—121no—
195C22×C32—41no—
196C3×A4#12511yescharacteristic, complemented
197C32×C4—81no—
198C32×C4—81no—
199C32×C4—81no—
200C3⋊Dic3—42no—
201C3⋊Dic3—81no—
202C3⋊Dic3—81no—
203C3⋊Dic3—81no—
204C23×C4C2×C3⋊D311yescharacteristic
205C23×C4C2×C3⋊D311yescharacteristic
206C23×C4C2×C3⋊D311yescharacteristic
207#125—181no—
208#125—181no—
209#125—181no—
210#125—181no—
211C2×C4⋊C4—31no—
212C2×C4⋊C4—31no—
213C2×C4⋊C4—31no—
214C2×C4⋊C4—31no—
215C2×C4⋊C4—91no—
216C2×C4⋊C4—91no—
217C2×C4⋊C4—91no—
218C2×C4⋊C4—91no—
219C2×C4⋊C4—91no—
220C2×C4⋊C4—91no—
221C2×C4⋊C4—91no—
222C2×C4⋊C4—91no—
223C2×C4⋊C4—91no—
224C2×C4⋊C4—91no—
225C2×C22⋊C4—91no—
226C2×C22⋊C4—91no—
227C2×C22⋊C4—91no—
228C2×C22⋊C4—91no—
229C2×C42—91no—
230C2×C42—91no—
231#95—91no—
232#95—91no—
233#95—91no—
234#95—91no—
235#95—91no—
236#95—91no—
237#95—91no—
238#95—91no—
239#95—91no—
240#95—91no—
241#95—91no—
242#95—91no—
243C23×C3—31no—
244C23×C3—31no—
245C23×C3—31no—
246C23×C3—31no—
247C23×C3#23511yescharacteristic
248C23×C3#23711yescharacteristic
249C23×C3D3×Q811yescharacteristic
250C2×A4#23513yes—
251C2×A4#23713yes—
252C2×A4D3×Q813yes—
253C2×C3×C4—32no—
254C2×C3×C4—31no—
255C2×C3×C4—31no—
256C2×C3×C4—31no—
257C2×C3×C4—43no—
258C2×C3×C4—43no—
259C2×C3×C4—43no—
260C2×C3×C4—61no—
261C2×C3×C4—61no—
262C2×C3×C4—61no—
263C2×C3×C4—61no—
264C2×C3×C4—61no—
265C2×C3×C4—61no—
266C2×C3×C4—61no—
267C2×C3×C4—61no—
268C2×C3×C4—61no—
269C2×C3×C4—61no—
270C2×C3×C4—61no—
271C2×C3×C4C2×S411yescharacteristic
272C2×C3×C4C2×S411yescharacteristic
273C2×C3×C4C2×S411yescharacteristic
274C2×Dic3—32no—
275C2×Dic3—32no—
276C2×Dic3—61no—
277C2×Dic3—61no—
278C2×Dic3—61no—
279C2×Dic3—61no—
280C2×Dic3—61no—
281C2×Dic3—61no—
282C2×Dic3—61no—
283C2×Dic3—61no—
284C2×Dic3—61no—
285C2×Dic3—61no—
286C2×Dic3—61no—
287C2×Dic3—61no—
288C2×Dic3—61no—
289C2×Dic3—61no—
290C2×Dic3—61no—
291C2×Dic3—61no—
292C2×Dic3—61no—
293C2×Dic3—61no—
294C2×Dic3—61no—
295C2×Dic3—61no—
296C2×Dic3—61no—
297C2×Dic3—61no—
298C2×Dic3—123no—
299C2×Dic3—123no—
300C2×Dic3—123no—
301C2×Dic3—123no—
302C2×C32—41no—
303C2×C32—41no—
304C2×C32—41no—
305C24C22×C3⋊D311yescharacteristic
306C22×C4—21no—
307C22×C4—21no—
308C22×C4—21no—
309C22×C4—31no—
310C22×C4—31no—
311C22×C4—31no—
312C22×C4—31no—
313C22×C4—31no—
314C22×C4—31no—
315C22×C4—61no—
316C22×C4—61no—
317C22×C4—61no—
318C22×C4—91no—
319C22×C4—91no—
320C22×C4—91no—
321C22×C4—91no—
322C22×C4—91no—
323C22×C4—91no—
324C22×C4—91no—
325C22×C4—91no—
326C4⋊C4—31no—
327C4⋊C4—31no—
328C4⋊C4—31no—
329C4⋊C4—61no—
330C4⋊C4—181no—
331C4⋊C4—181no—
332C4⋊C4—181no—
333C4⋊C4—181no—
334C4⋊C4—181no—
335C4⋊C4—182no—
336C4⋊C4—182no—
337C4⋊C4—181no—
338C4⋊C4—181no—
339C4⋊C4—181no—
340C4⋊C4—181no—
341C4⋊C4—181no—
342C4⋊C4—361no—
343C4⋊C4—361no—
344C4⋊C4—361no—
345C4⋊C4C3⋊S411yescharacteristic
346C22⋊C4—92no—
347C22⋊C4—92no—
348C22⋊C4—181no—
349C22⋊C4—181no—
350C22⋊C4—181no—
351C22⋊C4—181no—
352C22⋊C4—181no—
353C22⋊C4—181no—
354C42—181no—
355C42—181no—
356C42—361no—
357C22×C3—31no—
358C22×C3—31no—
359C22×C3—31no—
360C22×C3—31no—
361C22×C3—31no—
362C22×C3—31no—
363C22×C3—31no—
364C22×C3—31no—
365C22×C3—31no—
366C22×C3—43no—
367C22×C3—61no—
368C22×C3#88911yescharacteristic, complemented
369C22×C3C22×S411yescharacteristic
370A4#88913yescomplemented
371C3×C4—21no—
372C3×C4—21no—
373C3×C4—21no—
374C3×C4—61no—
375C3×C4—61no—
376C3×C4—61no—
377C3×C4—83no—
378C3×C4—83no—
379C3×C4—83no—
380Dic3—62no—
381Dic3—62no—
382Dic3—126no—
383Dic3—121no—
384Dic3—121no—
385Dic3—121no—
386Dic3—121no—
387Dic3—121no—
388Dic3—121no—
389Dic3—243no—
390Dic3—243no—
391Dic3—243no—
392C32—41noSylow
393C23—31no—
394C23—31no—
395C23—31no—
396C23—31no—
397C23#382811yescharacteristic
398C23#383011yescharacteristic
399C23Q8×C3⋊D311yescharacteristic
400C2×C4—32no—
401C2×C4—31no—
402C2×C4—31no—
403C2×C4—31no—
404C2×C4—61no—
405C2×C4—61no—
406C2×C4—61no—
407C2×C4—61no—
408C2×C4—61no—
409C2×C4—61no—
410C2×C4—61no—
411C2×C4—61no—
412C2×C4—61no—
413C2×C4—61no—
414C2×C4—61no—
415C2×C4—92no—
416C2×C4—92no—
417C2×C4—181no—
418C2×C4—181no—
419C2×C4—181no—
420C2×C4—181no—
421C2×C4—181no—
422C2×C4—181no—
423C2×C4—181no—
424C2×C4—181no—
425C2×C4—181no—
426C2×C4—181no—
427C2×C4—181no—
428C2×C4—181no—
429C2×C4—181no—
430C2×C4—181no—
431C2×C4—181no—
432C2×C4—181no—
433C2×C4—181no—
434C2×C4—181no—
435C2×C4—181no—
436C2×C4—181no—
437C2×C4—181no—
438C2×C4—181no—
439C2×C4C2×C3⋊S411yescharacteristic
440C2×C4C2×C3⋊S411yescharacteristic
441C2×C4C2×C3⋊S411yescharacteristic
442C2×C3—31no—
443C2×C3—31no—
444C2×C3—31no—
445C2×C3—31no—
446C2×C3—43no—
447C2×C3—43no—
448C2×C3—43no—
449C2×C3#591211yescharacteristic
450C2×C3#591411yescharacteristic
451C2×C3Q8×S411yescharacteristic
452C22—31no—
453C22—31no—
454C22—31no—
455C22—31no—
456C22—31no—
457C22—31no—
458C22—31no—
459C22—31no—
460C22—31no—
461C22—61no—
462C22#6409811yescharacteristic, complemented
463C22C22×C3⋊S411yescharacteristic
464C4—21no—
465C4—21no—
466C4—21no—
467C4—61no—
468C4—61no—
469C4—61no—
470C4—182no—
471C4—182no—
472C4—361no—
473C4—361no—
474C4—361no—
475C4—361no—
476C4—361no—
477C4—361no—
478C3—43no—
479C3#8530411yescharacteristic, complemented
480C2—31no—
481C2—31no—
482C2—31no—
483C2—31no—
484C2#1059657511yescharacteristic
485C2#1059657711yescharacteristic
486C2Q8×C3⋊S411yescharacteristic
subgroupG/H
center, FrattiniC22C22×C3⋊S4
commutator, prime radical, cosocleC22×C3×A4C23
FittingC22×C3×C4⋊C4D3
socleC24×C3C22×D3
hypercenterC4⋊C4C3⋊S4
hypocenterC3×A4#125
LCSG ▷ C22×C3×A4 ▷ C3×A4
UCSC1 ◁ C22 ◁ C4⋊C4

Complements

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

NH ≅ G/Ntype
196. C3×A4#125semidirect
368. C22×C3#889semidirect
370. A4#889semidirect
462. C22#64098semidirect
479. C3#85304semidirect

Maximal subgroups

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

subgroupindex
C3×A4×C4⋊C42
C4⋊(C3⋊SL(2,ℤ/4))2
#105936452
C4×C3⋊SL(2,ℤ/4)2
#853043
#821743
#640984