Finite Group Databasebeta

← #11921953

Subgroups — #11921953

Order 1152.

668 conjugacy classes of subgroups; only the 77 normal subgroups are shown.

normal subgroups only

This group has 668 conjugacy classes of subgroups — too many to draw. Only its 77 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×#64204C211yesmaximal, characteristic
2A4×Dic3⋊C4C211yesmaximal, characteristic
3C4×C3⋊SL(2,ℤ/4)C211yesmaximal, characteristic
4C3×SL(2,ℤ/4)⋊C4C211yesmaximal, characteristic
5#10593238C211yesmaximal, characteristic
6Dic3×SL(2,ℤ/4)C211yesmaximal, characteristic
7Dic3×SL(2,ℤ/4)C211yesmaximal, characteristic
8#85302—31nomaximal
9#74396—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#64204C414yescomplemented
18#63838—41nomaximal
19C2×A4⋊Q8—31no—
20C22×Dic3⋊C4D311yescharacteristic
21C2×#887—31no—
22C2×#878—31no—
23A4×C4⋊C4—31no—
24SL(2,ℤ/4)⋊C4—31no—
25SL(2,ℤ/4)⋊C4D311yescharacteristic
26C4×SL(2,ℤ/4)—31no—
27C4×SL(2,ℤ/4)—31no—
28C4×SL(2,ℤ/4)—31no—
29C4×SL(2,ℤ/4)—61no—
30C3×#385—31no—
31C4×#217—31no—
32#4976—31no—
33#4976—31no—
34#4972—31no—
35#4946—31no—
36Dic3×C22⋊C4—31no—
37Dic3×C22⋊C4—31no—
38#4653—31no—
39#4652—31no—
40#4649—31no—
41#4646—31no—
42C22×C3×A4C2311yescharacteristic
43C3×C4×A4—21no—
44C2×#627—41no—
45Dic3×A4—21no—
46Dic3×A4C2×C412yes—
47C3⋊SL(2,ℤ/4)C2×C412yes—
48C3⋊SL(2,ℤ/4)Q812yescomplemented
49C3×SL(2,ℤ/4)—21no—
50C3×SL(2,ℤ/4)C2×C412yes—
51C4×C3⋊Dic3—41no—
52C3×Dic3⋊C4—41no—
53C3×Dic3⋊C4—41no—
54#3724—41no—
55Dic32—41no—
56Dic32—41no—
57#2360—91noSylow
58C23×C3×C4C2×D311yescharacteristic
59C23×Dic3C2×D311yescharacteristic
60C23×Dic3C2×D311yescharacteristic
61C22×Dic6—31no—
62C2×C4×A4—21no—
63C2×C4×A4—31no—
64C2×C4×A4—31no—
65C2×C4×A4C2×D311yescharacteristic
66C2×SL(2,ℤ/4)—31no—
67C2×SL(2,ℤ/4)—31no—
68C2×SL(2,ℤ/4)—61no—
69C2×SL(2,ℤ/4)—61no—
70C2×SL(2,ℤ/4)C2×D311yescharacteristic
71C2×SL(2,ℤ/4)C2×D311yescharacteristic
72A4⋊Q8—34no—
73C2×C3×C4⋊C4—31no—
74C2×C3×C4⋊C4—31no—
75C2×C3×C22⋊C4—31no—
76C2×C3×C22⋊C4—31no—
77C2×#217—31no—
78C2×#217—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×C4×Dic3—31no—
89C2×C4×Dic3—31no—
90C2×C4×Dic3—31no—
91C2×C4×Dic3—31no—
92C2×C4×Dic3—31no—
93C2×C4×Dic3—31no—
94#887—61no—
95#887—61no—
96#887—61no—
97#887—61no—
98#887—121no—
99#878—34no—
100#878—34no—
101C3×#95—31no—
102C3×#95—31no—
103C3⋊#95—31no—
104C3⋊#95—31no—
105C3⋊#95—31no—
106C3⋊#95—31no—
107C3⋊#95—31no—
108C3⋊#95—31no—
109C3⋊#95—31no—
110C3⋊#95—31no—
111C2×C3×A4C22×C411yescharacteristic
112C2×C3×A4C2×Q811yescharacteristic
113C2×C3×A4#4111yescharacteristic
114C2×C32×C4—41no—
115C2×C3⋊Dic3—41no—
116C2×C3⋊Dic3—41no—
117C2×C3×Dic3—41no—
118C2×C3×Dic3—41no—
119C2×C3×Dic3—41no—
120C2×C3×Dic3—41no—
121#627—44no—
122C2×C22⋊Q8—91no—
123C2×C4×Q8—91no—
124C22×C4⋊C4—31no—
125#391—91no—
126#389—91no—
127#389—91no—
128#389—91no—
129#387—91no—
130#387—91no—
131#385—31no—
132#385—91no—
133C4×C4⋊C4—91no—
134C4×C22⋊C4—91no—
135C4×C22⋊C4—91no—
136C4×C22⋊C4—91no—
137C24×C3C22×D311yescharacteristic
138C22×A4—21no—
139C22×A4C22×D311yescharacteristic
140C22×C3×C4—21no—
141C22×C3×C4—31no—
142C22×C3×C4—31no—
143C22×C3×C4—31no—
144C22×C3×C4—31no—
145C22×C3×C4—31no—
146C22×C3×C4—31no—
147C22×C3×C4—61no—
148C22×Dic3—21no—
149C22×Dic3—31no—
150C22×Dic3—31no—
151C22×Dic3—32no—
152C22×Dic3—31no—
153C22×Dic3—31no—
154C22×Dic3—31no—
155C22×Dic3—31no—
156C22×Dic3—31no—
157C22×Dic3—31no—
158C22×Dic3—61no—
159C22×Dic3C4×D312yes—
160C2×Dic6—34no—
161C2×Dic6—61no—
162C2×Dic6—62no—
163C2×Dic6—61no—
164C2×Dic6—121no—
165C4×A4—22no—
166C4×A4—21no—
167C4×A4—32no—
168C4×A4—61no—
169SL(2,ℤ/4)—21no—
170SL(2,ℤ/4)—32no—
171SL(2,ℤ/4)—32no—
172SL(2,ℤ/4)—62no—
173SL(2,ℤ/4)—62no—
174SL(2,ℤ/4)C4×D312yes—
175C3×C4⋊C4—61no—
176C3×C4⋊C4—61no—
177C3×C4⋊C4—121no—
178C3×C4⋊C4—121no—
179C3×C22⋊C4—32no—
180C3×C22⋊C4—32no—
181C3×C22⋊C4—61no—
182C3×C22⋊C4—61no—
183#217—32no—
184#217—32no—
185#217—32no—
186#217—32no—
187C4⋊Dic3—34no—
188Dic3⋊C4—34no—
189Dic3⋊C4—34no—
190Dic3⋊C4—31no—
191Dic3⋊C4—31no—
192Dic3⋊C4—31no—
193Dic3⋊C4—41no—
194Dic3⋊C4—61no—
195Dic3⋊C4—61no—
196Dic3⋊C4—61no—
197Dic3⋊C4—121no—
198Dic3⋊C4—121no—
199Dic3⋊C4S411yescharacteristic
200C4×Dic3—61no—
201C4×Dic3—61no—
202C4×Dic3—62no—
203C4×Dic3—61no—
204C4×Dic3—61no—
205C4×Dic3—61no—
206C4×Dic3—61no—
207C4×Dic3—121no—
208C4×Dic3—121no—
209C4×Dic3—121no—
210C4×Dic3—121no—
211C4×Dic3—121no—
212C4×Dic3—241no—
213C22×C32—41no—
214C3×A4C4×Q811yescharacteristic, complemented
215C32×C4—81no—
216C3⋊Dic3—42no—
217C3⋊Dic3—42no—
218C3×Dic3—42no—
219C3×Dic3—42no—
220C3×Dic3—81no—
221C3×Dic3—81no—
222C22×Q8—91no—
223C23×C4—31no—
224C23×C4—31no—
225C23×C4D3211yescharacteristic
226C22⋊Q8—94no—
227C22⋊Q8—94no—
228C4×Q8—181no—
229C4×Q8—181no—
230C4×Q8—181no—
231C4×Q8—181no—
232C2×C4⋊C4—31no—
233C2×C4⋊C4—31no—
234C2×C4⋊C4—91no—
235C2×C4⋊C4—91no—
236C2×C4⋊C4—91no—
237C2×C4⋊C4—91no—
238C2×C4⋊C4—91no—
239C2×C4⋊C4—91no—
240C2×C4⋊C4—91no—
241C2×C4⋊C4—91no—
242C2×C4⋊C4—91no—
243C2×C22⋊C4—31no—
244C2×C22⋊C4—31no—
245C2×C22⋊C4—91no—
246C2×C22⋊C4—91no—
247C2×C42—91no—
248C2×C42—91no—
249C2×C42—91no—
250C2×C42—91no—
251C2×C42—91no—
252C2×C42—91no—
253#95—31no—
254#95—31no—
255#95—91no—
256#95—91no—
257#95—91no—
258#95—91no—
259#95—91no—
260#95—91no—
261#95—91no—
262#95—91no—
263C23×C3—31no—
264C23×C3—31no—
265C23×C3—31no—
266C23×C3—31no—
267C23×C3C2×C4×D311yescharacteristic
268C23×C3#23711yescharacteristic
269C23×C3D3×Q811yescharacteristic
270C2×A4—21no—
271C2×A4—21no—
272C2×A4—21no—
273C2×A4C2×C4×D311yescharacteristic
274C2×A4#23711yescharacteristic
275C2×A4D3×Q811yescharacteristic
276C2×C3×C4—32no—
277C2×C3×C4—32no—
278C2×C3×C4—31no—
279C2×C3×C4—41no—
280C2×C3×C4—61no—
281C2×C3×C4—61no—
282C2×C3×C4—61no—
283C2×C3×C4—61no—
284C2×C3×C4—61no—
285C2×C3×C4—61no—
286C2×C3×C4—61no—
287C2×C3×C4—61no—
288C2×C3×C4—61no—
289C2×C3×C4—61no—
290C2×C3×C4—61no—
291C2×C3×C4—61no—
292C2×C3×C4—61no—
293C2×C3×C4—61no—
294C2×C3×C4—81no—
295C2×C3×C4—121no—
296C2×C3×C4—121no—
297C2×C3×C4C2×S411yescharacteristic
298C2×Dic3—31no—
299C2×Dic3—32no—
300C2×Dic3—32no—
301C2×Dic3—32no—
302C2×Dic3—32no—
303C2×Dic3—32no—
304C2×Dic3—32no—
305C2×Dic3—32no—
306C2×Dic3—31no—
307C2×Dic3—41no—
308C2×Dic3—41no—
309C2×Dic3—61no—
310C2×Dic3—61no—
311C2×Dic3—61no—
312C2×Dic3—61no—
313C2×Dic3—61no—
314C2×Dic3—61no—
315C2×Dic3—61no—
316C2×Dic3—61no—
317C2×Dic3—61no—
318C2×Dic3—61no—
319C2×Dic3—61no—
320C2×Dic3—61no—
321C2×Dic3—61no—
322C2×Dic3—121no—
323C2×Dic3—121no—
324C2×Dic3—241no—
325C2×Dic3—241no—
326C2×Dic3C2×S411yescharacteristic
327C2×Dic3C2×S411yescharacteristic
328Dic6—64no—
329Dic6—64no—
330Dic6—124no—
331C2×C32—41no—
332C2×C32—41no—
333C2×C32—41no—
334C24C2×D3211yescharacteristic
335C2×Q8—94no—
336C2×Q8—181no—
337C2×Q8—181no—
338C2×Q8—182no—
339C22×C4—21no—
340C22×C4—31no—
341C22×C4—31no—
342C22×C4—31no—
343C22×C4—31no—
344C22×C4—31no—
345C22×C4—31no—
346C22×C4—32no—
347C22×C4—61no—
348C22×C4—61no—
349C22×C4—91no—
350C22×C4—91no—
351C22×C4—91no—
352C22×C4—92no—
353C22×C4—91no—
354C22×C4—91no—
355C22×C4—91no—
356C22×C4—91no—
357C22×C4—91no—
358C22×C4—181no—
359C4⋊C4—31no—
360C4⋊C4—61no—
361C4⋊C4—61no—
362C4⋊C4—91no—
363C4⋊C4—91no—
364C4⋊C4—94no—
365C4⋊C4—94no—
366C4⋊C4—94no—
367C4⋊C4—91no—
368C4⋊C4—121no—
369C4⋊C4—181no—
370C4⋊C4—181no—
371C4⋊C4—181no—
372C4⋊C4—361no—
373C22⋊C4—32no—
374C22⋊C4—32no—
375C22⋊C4—61no—
376C22⋊C4—61no—
377C22⋊C4—92no—
378C22⋊C4—92no—
379C22⋊C4—92no—
380C22⋊C4—92no—
381C42—181no—
382C42—181no—
383C42—181no—
384C42—181no—
385C42—181no—
386C42—182no—
387C42—181no—
388C42—361no—
389C42—361no—
390C22×C3—31no—
391C22×C3—31no—
392C22×C3—31no—
393C22×C3—31no—
394C22×C3—31no—
395C22×C3—31no—
396C22×C3—31no—
397C22×C3—31no—
398C22×C3—31no—
399C22×C3—41no—
400C22×C3—61no—
401C22×C3—81no—
402C22×C3#88711yescharacteristic, complemented
403C22×C3C22×S411yescharacteristic
404A4—21no—
405A4#88711yescharacteristic, complemented
406C3×C4—21no—
407C3×C4—62no—
408C3×C4—62no—
409C3×C4—61no—
410C3×C4—81no—
411C3×C4—82no—
412C3×C4—122no—
413C3×C4—121no—
414C3×C4—121no—
415C3×C4—241no—
416Dic3—21no—
417Dic3—32no—
418Dic3—42no—
419Dic3—62no—
420Dic3—62no—
421Dic3—62no—
422Dic3—61no—
423Dic3—62no—
424Dic3—81no—
425Dic3—122no—
426Dic3—122no—
427Dic3—242no—
428Dic3—242no—
429Dic3C4×S412yes—
430C32—41noSylow
431C23—31no—
432C23—31no—
433C23—31no—
434C23—31no—
435C23#379711yescharacteristic
436C23C4×D3211yescharacteristic
437C23#380511yescharacteristic
438Q8—184no—
439Q8—184no—
440C2×C4—31no—
441C2×C4—32no—
442C2×C4—32no—
443C2×C4—31no—
444C2×C4—31no—
445C2×C4—61no—
446C2×C4—61no—
447C2×C4—61no—
448C2×C4—61no—
449C2×C4—61no—
450C2×C4—61no—
451C2×C4—61no—
452C2×C4—61no—
453C2×C4—61no—
454C2×C4—61no—
455C2×C4—61no—
456C2×C4—61no—
457C2×C4—61no—
458C2×C4—61no—
459C2×C4—92no—
460C2×C4—92no—
461C2×C4—91no—
462C2×C4—92no—
463C2×C4—92no—
464C2×C4—92no—
465C2×C4—92no—
466C2×C4—92no—
467C2×C4—91no—
468C2×C4—181no—
469C2×C4—181no—
470C2×C4—181no—
471C2×C4—181no—
472C2×C4—181no—
473C2×C4—181no—
474C2×C4—181no—
475C2×C4—181no—
476C2×C4—181no—
477C2×C4—181no—
478C2×C4—181no—
479C2×C4—181no—
480C2×C4—181no—
481C2×C4D3×S411yescharacteristic
482C2×C3—31no—
483C2×C3—31no—
484C2×C3—31no—
485C2×C3—31no—
486C2×C3—41no—
487C2×C3—41no—
488C2×C3—41no—
489C2×C3—81no—
490C2×C3—81no—
491C2×C3—81no—
492C2×C3C2×C4×S411yescharacteristic
493C2×C3#591411yescharacteristic
494C2×C3Q8×S411yescharacteristic
495C22—31no—
496C22—31no—
497C22—31no—
498C22—31no—
499C22—31no—
500C22—31no—
501C22—31no—
502C22—31no—
503C22—31no—
504C22—61no—
505C22#6383811yescharacteristic, complemented
506C22C2×D3×S411yescharacteristic
507C4—21no—
508C4—32no—
509C4—62no—
510C4—62no—
511C4—61no—
512C4—61no—
513C4—92no—
514C4—121no—
515C4—121no—
516C4—182no—
517C4—182no—
518C4—182no—
519C4—182no—
520C4—181no—
521C3—41no—
522C3—81no—
523C3#8530211yescharacteristic, complemented
524C2—31no—
525C2—31no—
526C2—31no—
527C2—31no—
528C2(C3⋊S4)⋊Q811yescharacteristic
529C2C4×D3×S411yescharacteristic
530C2#1059646811yescharacteristic
subgroupG/H
center, FrattiniC22C2×D3×S4
commutatorC2×C3×A4C22×C4
FittingC23×C3×C4C2×D3
socleC24×C3C22×D3
prime radical, cosocleC22×C3×A4C23
hypercenterC2×C4D3×S4
hypocenterC3×A4C4×Q8
LCSG ▷ C2×C3×A4 ▷ C3×A4
UCSC1 ◁ C22 ◁ C2×C4

Complements

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

NH ≅ G/Ntype
17. #64204C4semidirect
48. C3⋊SL(2,ℤ/4)Q8semidirect
214. C3×A4C4×Q8semidirect
402. C22×C3#887semidirect
405. A4#887semidirect
505. C22#63838semidirect
523. C3#85302semidirect

Maximal subgroups

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

subgroupindex
C2×#642042
A4×Dic3⋊C42
C4×C3⋊SL(2,ℤ/4)2
C3×SL(2,ℤ/4)⋊C42
#105932382
Dic3×SL(2,ℤ/4)2
#853023
#743963
#638384