Finite Group Databasebeta

← #11921907

Subgroups — #11921907

Order 1152.

536 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 536 conjugacy classes of subgroups — too many to draw. Only its 63 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
1A4×Dic3⋊C4C211yesmaximal, characteristic
2#10593645C211yesmaximal, characteristic
3C3×C4×SL(2,ℤ/4)C211yesmaximal, characteristic
4Dic3⋊SL(2,ℤ/4)C211yesmaximal, characteristic
5SL(2,ℤ/4)⋊Dic3C211yesmaximal, characteristic
6SL(2,ℤ/4)⋊Dic3C211yesmaximal, characteristic
7#10593238C211yesmaximal, characteristic
8#85304—31nomaximal
9#73501—31nomaximal
10C2×C3×C4×A4C2211yescharacteristic
11C2×Dic3×A4C2211yescharacteristic
12C2×Dic3×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#63867—41nomaximal
18C22×Dic3⋊C4D311yescharacteristic
19C2×#870—31no—
20A4×C4⋊C4—31no—
21C4⋊SL(2,ℤ/4)—31no—
22SL(2,ℤ/4)⋊C4—31no—
23SL(2,ℤ/4)⋊C4—31no—
24SL(2,ℤ/4)⋊C4—31no—
25SL(2,ℤ/4)⋊C4—31no—
26SL(2,ℤ/4)⋊C4—61no—
27C4×SL(2,ℤ/4)D311yescharacteristic
28C3×C4×C22⋊C4—31no—
29#5210—31no—
30#4950—31no—
31#4950—31no—
32#4946—31no—
33#4942—31no—
34#4933—31no—
35#4933—31no—
36#4928—31no—
37#4660—31no—
38#4657—31no—
39#4657—31no—
40#4657—31no—
41C22×C3×A4C2311yescharacteristic
42C3×C4×A4—21no—
43Dic3×A4—21no—
44Dic3×A4—21no—
45C3⋊SL(2,ℤ/4)—21no—
46C3⋊SL(2,ℤ/4)—21no—
47C3×SL(2,ℤ/4)—21no—
48C3×SL(2,ℤ/4)Q812yes—
49#3750—41no—
50C3×Dic3⋊C4—41no—
51C3×C4×Dic3—41no—
52#3724—41no—
53Dic3⋊Dic3—41no—
54Dic3⋊Dic3—41no—
55Dic3⋊Dic3—41no—
56#2473—91noSylow
57C23×C3×C4C2×D311yescharacteristic
58C23×Dic3C2×D311yescharacteristic
59C23×Dic3C2×D311yescharacteristic
60C2×C4×A4—21no—
61C2×C4×A4—31no—
62C2×C4×A4—31no—
63C2×C4×A4C2×D311yescharacteristic
64C2×SL(2,ℤ/4)—31no—
65C2×SL(2,ℤ/4)—31no—
66C2×SL(2,ℤ/4)—61no—
67C2×SL(2,ℤ/4)—61no—
68C2×SL(2,ℤ/4)C2×D311yescharacteristic
69C2×SL(2,ℤ/4)C2×D311yescharacteristic
70C2×C3×C22⋊C4—31no—
71C2×C3×C22⋊C4—31no—
72C2×C3×C42—31no—
73C2×C3×C42—31no—
74C2×#217—31no—
75C2×#217—31no—
76C2×C4⋊Dic3—31no—
77C2×C4⋊Dic3—31no—
78C2×C4⋊Dic3—31no—
79C2×C4⋊Dic3—31no—
80C2×Dic3⋊C4—31no—
81C2×Dic3⋊C4—31no—
82C2×Dic3⋊C4—31no—
83C2×Dic3⋊C4—31no—
84C2×Dic3⋊C4—31no—
85C2×Dic3⋊C4—31no—
86C2×Dic3⋊C4—31no—
87C2×Dic3⋊C4—31no—
88C2×Dic3⋊C4—31no—
89C2×Dic3⋊C4—31no—
90#889—121no—
91#870—61no—
92#870—61no—
93#870—61no—
94#870—61no—
95C3×#95—31no—
96C3×#95—31no—
97C3⋊#95—31no—
98C3⋊#95—31no—
99C3⋊#95—31no—
100C3⋊#95—31no—
101C3⋊#95—31no—
102C3⋊#95—31no—
103C3⋊#95—31no—
104C3⋊#95—31no—
105C3⋊#95—31no—
106C3⋊#95—31no—
107C2×C3×A4C2×Q811yescharacteristic
108C2×C3×A4#4111yescharacteristic
109C2×C3×A4#4111yescharacteristic
110C2×C32×C4—41no—
111C2×C3⋊Dic3—41no—
112C2×C3⋊Dic3—41no—
113C2×C3×Dic3—41no—
114C2×C3×Dic3—41no—
115C2×C3×Dic3—41no—
116C2×C3×Dic3—41no—
117C2×#125—91no—
118C22×C4⋊C4—31no—
119#400—91no—
120#398—91no—
121#398—91no—
122#398—91no—
123#389—91no—
124#387—91no—
125#387—91no—
126#385—91no—
127#385—91no—
128#385—91no—
129#385—91no—
130#380—91no—
131C4×C22⋊C4—31no—
132C24×C3C22×D311yescharacteristic
133C22×A4—21no—
134C22×A4C22×D311yescharacteristic
135C22×C3×C4—21no—
136C22×C3×C4—31no—
137C22×C3×C4—31no—
138C22×C3×C4—31no—
139C22×C3×C4—31no—
140C22×C3×C4—31no—
141C22×C3×C4—31no—
142C22×C3×C4—61no—
143C22×Dic3—21no—
144C22×Dic3—21no—
145C22×Dic3—31no—
146C22×Dic3—31no—
147C22×Dic3—31no—
148C22×Dic3—31no—
149C22×Dic3—31no—
150C22×Dic3—31no—
151C22×Dic3—31no—
152C22×Dic3—31no—
153C22×Dic3—61no—
154C22×Dic3—61no—
155C4×A4—21no—
156C4×A4—41no—
157C4×A4—61no—
158C4×A4—61no—
159SL(2,ℤ/4)—21no—
160SL(2,ℤ/4)—62no—
161SL(2,ℤ/4)—61no—
162SL(2,ℤ/4)—61no—
163SL(2,ℤ/4)—121no—
164SL(2,ℤ/4)Dic612yes—
165C3×C4⋊C4—121no—
166C3×C22⋊C4—32no—
167C3×C22⋊C4—32no—
168C3×C22⋊C4—61no—
169C3×C22⋊C4—61no—
170C3×C42—61no—
171C3×C42—61no—
172C3×C42—121no—
173#217—61no—
174#217—61no—
175#217—61no—
176#217—61no—
177C4⋊Dic3—61no—
178C4⋊Dic3—61no—
179C4⋊Dic3—62no—
180C4⋊Dic3—61no—
181C4⋊Dic3—61no—
182C4⋊Dic3—121no—
183C4⋊Dic3—121no—
184Dic3⋊C4—31no—
185Dic3⋊C4—31no—
186Dic3⋊C4—31no—
187Dic3⋊C4—61no—
188Dic3⋊C4—61no—
189Dic3⋊C4—61no—
190Dic3⋊C4—62no—
191Dic3⋊C4—61no—
192Dic3⋊C4—61no—
193Dic3⋊C4—61no—
194Dic3⋊C4—61no—
195Dic3⋊C4—121no—
196Dic3⋊C4—121no—
197Dic3⋊C4—121no—
198Dic3⋊C4—121no—
199Dic3⋊C4—121no—
200Dic3⋊C4—121no—
201Dic3⋊C4—241no—
202Dic3⋊C4S411yescharacteristic
203C4×Dic3—41no—
204C22×C32—41no—
205C3×A4#12511yescharacteristic, complemented
206C32×C4—81no—
207C3⋊Dic3—81no—
208C3⋊Dic3—81no—
209C3×Dic3—42no—
210C3×Dic3—81no—
211C3×Dic3—81no—
212C3×Dic3—81no—
213C23×C4—31no—
214C23×C4—31no—
215C23×C4D3211yescharacteristic
216#125—181no—
217#125—181no—
218#125—181no—
219#125—181no—
220C2×C4⋊C4—91no—
221C2×C4⋊C4—91no—
222C2×C4⋊C4—91no—
223C2×C4⋊C4—91no—
224C2×C4⋊C4—91no—
225C2×C4⋊C4—91no—
226C2×C4⋊C4—91no—
227C2×C4⋊C4—91no—
228C2×C4⋊C4—91no—
229C2×C4⋊C4—91no—
230C2×C4⋊C4—91no—
231C2×C4⋊C4—91no—
232C2×C4⋊C4—91no—
233C2×C4⋊C4—91no—
234C2×C22⋊C4—31no—
235C2×C22⋊C4—31no—
236C2×C22⋊C4—91no—
237C2×C22⋊C4—91no—
238C2×C42—31no—
239C2×C42—31no—
240#95—31no—
241#95—31no—
242#95—91no—
243#95—91no—
244#95—91no—
245#95—91no—
246#95—91no—
247#95—91no—
248#95—91no—
249#95—91no—
250#95—91no—
251#95—91no—
252C23×C3—31no—
253C23×C3—31no—
254C23×C3—31no—
255C23×C3—31no—
256C23×C3#23511yescharacteristic
257C23×C3#23711yescharacteristic
258C23×C3D3×Q811yescharacteristic
259C2×A4—21no—
260C2×A4—21no—
261C2×A4—21no—
262C2×A4C2×Dic611yescharacteristic
263C2×A4#23511yescharacteristic
264C2×A4#23511yescharacteristic
265C2×C3×C4—32no—
266C2×C3×C4—32no—
267C2×C3×C4—31no—
268C2×C3×C4—41no—
269C2×C3×C4—61no—
270C2×C3×C4—61no—
271C2×C3×C4—61no—
272C2×C3×C4—61no—
273C2×C3×C4—61no—
274C2×C3×C4—61no—
275C2×C3×C4—61no—
276C2×C3×C4—61no—
277C2×C3×C4—61no—
278C2×C3×C4—61no—
279C2×C3×C4—61no—
280C2×C3×C4—61no—
281C2×C3×C4—61no—
282C2×C3×C4—61no—
283C2×C3×C4—81no—
284C2×C3×C4—121no—
285C2×C3×C4—121no—
286C2×C3×C4C2×S411yescharacteristic
287C2×Dic3—32no—
288C2×Dic3—31no—
289C2×Dic3—31no—
290C2×Dic3—41no—
291C2×Dic3—41no—
292C2×Dic3—61no—
293C2×Dic3—61no—
294C2×Dic3—61no—
295C2×Dic3—61no—
296C2×Dic3—61no—
297C2×Dic3—61no—
298C2×Dic3—61no—
299C2×Dic3—61no—
300C2×Dic3—61no—
301C2×Dic3—61no—
302C2×Dic3—61no—
303C2×Dic3—61no—
304C2×Dic3—61no—
305C2×Dic3—61no—
306C2×Dic3—61no—
307C2×Dic3—61no—
308C2×Dic3—61no—
309C2×Dic3—61no—
310C2×Dic3—61no—
311C2×Dic3—121no—
312C2×Dic3—121no—
313C2×Dic3—241no—
314C2×Dic3—241no—
315C2×Dic3C2×S411yescharacteristic
316C2×Dic3C2×S411yescharacteristic
317C2×C32—41no—
318C2×C32—41no—
319C2×C32—41no—
320C24C2×D3211yescharacteristic
321C22×C4—21no—
322C22×C4—31no—
323C22×C4—31no—
324C22×C4—31no—
325C22×C4—31no—
326C22×C4—31no—
327C22×C4—31no—
328C22×C4—61no—
329C22×C4—61no—
330C22×C4—61no—
331C22×C4—91no—
332C22×C4—91no—
333C22×C4—91no—
334C22×C4—91no—
335C22×C4—91no—
336C22×C4—91no—
337C22×C4—91no—
338C22×C4—91no—
339C22×C4—181no—
340C22×C4—181no—
341C4⋊C4—31no—
342C4⋊C4—91no—
343C4⋊C4—91no—
344C4⋊C4—91no—
345C4⋊C4—181no—
346C4⋊C4—181no—
347C4⋊C4—181no—
348C4⋊C4—181no—
349C4⋊C4—181no—
350C4⋊C4—181no—
351C4⋊C4—181no—
352C4⋊C4—181no—
353C4⋊C4—181no—
354C4⋊C4—181no—
355C4⋊C4—182no—
356C4⋊C4—182no—
357C4⋊C4—181no—
358C4⋊C4—361no—
359C4⋊C4—361no—
360C4⋊C4—361no—
361C22⋊C4—32no—
362C22⋊C4—32no—
363C22⋊C4—61no—
364C22⋊C4—61no—
365C22⋊C4—181no—
366C22⋊C4—181no—
367C22⋊C4—181no—
368C22⋊C4—181no—
369C42—61no—
370C42—61no—
371C42—121no—
372C22×C3—31no—
373C22×C3—31no—
374C22×C3—31no—
375C22×C3—31no—
376C22×C3—31no—
377C22×C3—31no—
378C22×C3—31no—
379C22×C3—31no—
380C22×C3—31no—
381C22×C3—41no—
382C22×C3—61no—
383C22×C3—81no—
384C22×C3#88911yescharacteristic, complemented
385C22×C3C22×S411yescharacteristic
386A4—21no—
387A4#87011yescharacteristic, complemented
388C3×C4—21no—
389C3×C4—62no—
390C3×C4—61no—
391C3×C4—62no—
392C3×C4—81no—
393C3×C4—121no—
394C3×C4—121no—
395C3×C4—161no—
396C3×C4—241no—
397C3×C4—241no—
398Dic3—21no—
399Dic3—21no—
400Dic3—42no—
401Dic3—61no—
402Dic3—61no—
403Dic3—81no—
404Dic3—121no—
405Dic3—121no—
406Dic3—121no—
407Dic3—121no—
408Dic3—241no—
409Dic3—241no—
410Dic3—242no—
411Dic3—481no—
412C32—41noSylow
413C23—31no—
414C23—31no—
415C23—31no—
416C23—31no—
417C23D3×Dic611yescharacteristic
418C23#379811yescharacteristic
419C23#380411yescharacteristic
420C2×C4—32no—
421C2×C4—32no—
422C2×C4—31no—
423C2×C4—31no—
424C2×C4—31no—
425C2×C4—61no—
426C2×C4—61no—
427C2×C4—61no—
428C2×C4—61no—
429C2×C4—61no—
430C2×C4—61no—
431C2×C4—61no—
432C2×C4—61no—
433C2×C4—61no—
434C2×C4—61no—
435C2×C4—61no—
436C2×C4—61no—
437C2×C4—61no—
438C2×C4—61no—
439C2×C4—92no—
440C2×C4—91no—
441C2×C4—91no—
442C2×C4—181no—
443C2×C4—181no—
444C2×C4—181no—
445C2×C4—181no—
446C2×C4—181no—
447C2×C4—181no—
448C2×C4—181no—
449C2×C4—181no—
450C2×C4—181no—
451C2×C4—181no—
452C2×C4—181no—
453C2×C4—181no—
454C2×C4—181no—
455C2×C4—181no—
456C2×C4—181no—
457C2×C4—181no—
458C2×C4—181no—
459C2×C4—181no—
460C2×C4—181no—
461C2×C4D3×S411yescharacteristic
462C2×C3—31no—
463C2×C3—31no—
464C2×C3—31no—
465C2×C3—31no—
466C2×C3—41no—
467C2×C3—41no—
468C2×C3—41no—
469C2×C3—81no—
470C2×C3—81no—
471C2×C3—81no—
472C2×C3#591211yescharacteristic
473C2×C3#591411yescharacteristic
474C2×C3Q8×S411yescharacteristic
475C22—31no—
476C22—31no—
477C22—31no—
478C22—31no—
479C22—31no—
480C22—31no—
481C22—31no—
482C22—31no—
483C22—31no—
484C22—61no—
485C22#6386711yescharacteristic, complemented
486C22C2×D3×S411yescharacteristic
487C4—21no—
488C4—62no—
489C4—62no—
490C4—61no—
491C4—61no—
492C4—61no—
493C4—121no—
494C4—121no—
495C4—181no—
496C4—181no—
497C4—361no—
498C4—361no—
499C4—361no—
500C4—361no—
501C3—41no—
502C3—81no—
503C3#8530411yescharacteristic, complemented
504C2—31no—
505C2—31no—
506C2—31no—
507C2—31no—
508C2Dic6×S411yescharacteristic
509C2#1059642611yescharacteristic
510C2#1059646711yescharacteristic
subgroupG/H
center, FrattiniC22C2×D3×S4
commutator, prime radical, cosocleC22×C3×A4C23
FittingC23×C3×C4C2×D3
socleC24×C3C22×D3
hypercenterC2×C4D3×S4
hypocenterC3×A4#125
LCSG ▷ C22×C3×A4 ▷ C3×A4
UCSC1 ◁ C22 ◁ C2×C4

Complements

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

NH ≅ G/Ntype
205. C3×A4#125semidirect
384. C22×C3#889semidirect
387. A4#870semidirect
485. C22#63867semidirect
503. C3#85304semidirect

Maximal subgroups

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

subgroupindex
A4×Dic3⋊C42
#105936452
C3×C4×SL(2,ℤ/4)2
Dic3⋊SL(2,ℤ/4)2
SL(2,ℤ/4)⋊Dic32
#105932382
#853043
#735013
#638674