Finite Group Databasebeta

← #11923029

Subgroups — #11923029

Order 1152.

946 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 946 conjugacy classes of subgroups — too many to draw. Only its 115 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
1C22×C3×C4×A4C211yesmaximal, characteristic
2C2×#64259C211yesmaximal, characteristic, complemented
3#10593666C212yesmaximal
4C4⋊(C3⋊SL(2,ℤ/4))C211yesmaximal, characteristic, complemented
5#10593645C212yesmaximal, complemented
6#85480—33nomaximal
7#84031—31nomaximal
8C23×C3×A4C2211yescharacteristic
9C2×C3×C4×A4—22no—
10C2×C3×C4×A4C2211yescharacteristic
11C2×C3×C4×A4C2211yescharacteristic
12C2×C3⋊SL(2,ℤ/4)C2212yes—
13C2×C3⋊SL(2,ℤ/4)C2212yes—
14#64259—22no—
15#64133—41nomaximal
16C24×C3×C4D311yescharacteristic
17C22×C4×A4D313yes—
18C2×A4⋊Q8—33no—
19C2×#924—31no—
20C2×#924—31no—
21C2×#924—31no—
22#5432—36no—
23C4⋊SL(2,ℤ/4)—33no—
24SL(2,ℤ/4)⋊C4—36no—
25#5247—32no—
26#5212—31no—
27#5212—31no—
28#5212—31no—
29#5210—32no—
30#5210—32no—
31#5210—32no—
32C22×C3×A4—21no—
33C22×C3×A4—21no—
34C22×C3×A4Q812yescomplemented
35C22×C3×A4C2311yescharacteristic
36C22×C32×C4—41no—
37C2×#634—41no—
38C3×C4×A4—21no—
39C3×C4×A4D412yes—
40C3⋊SL(2,ℤ/4)—22no—
41C3⋊SL(2,ℤ/4)—22no—
42#3757—42no—
43C4⋊(C3⋊Dic3)—41no—
44#3750—42no—
45#2848—91noSylow
46C25×C3C2×D311yescharacteristic
47C23×A4C2×D313yes—
48C23×C3×C4—22no—
49C23×C3×C4—31no—
50C23×C3×C4—31no—
51C23×C3×C4—31no—
52C23×C3×C4—31no—
53C23×C3×C4—62no—
54C23×C3×C4C2×D311yescharacteristic
55C23×C3×C4C2×D311yescharacteristic
56C22×Dic6—31no—
57C2×C4×A4—26no—
58C2×C4×A4C2×D313yes—
59C2×C4×A4C2×D313yes—
60C2×SL(2,ℤ/4)—36no—
61C2×SL(2,ℤ/4)—36no—
62A4⋊Q8—66no—
63C2×#217—32no—
64C2×#217—32no—
65C2×#217—32no—
66C2×#217—32no—
67C2×#217—32no—
68C2×#217—32no—
69C2×C4⋊Dic3—31no—
70C2×C4⋊Dic3—31no—
71C2×C4⋊Dic3—31no—
72#924—62no—
73#924—64no—
74#924—61no—
75#924—61no—
76#924—61no—
77#924—62no—
78#924—61no—
79#924—123no—
80C2×Dic3⋊C4—32no—
81C2×Dic3⋊C4—32no—
82C2×Dic3⋊C4—32no—
83C3⋊#95—32no—
84C3⋊#95—32no—
85C3⋊#95—32no—
86C23×C32—41no—
87C2×C3×A4—22no—
88C2×C3×A4C2×D411yescharacteristic
89C2×C3×A4C2×Q811yescharacteristic
90C2×C3×A4#4111yescharacteristic
91C2×C32×C4—41no—
92C2×C32×C4—41no—
93C2×C32×C4—82no—
94C2×C3⋊Dic3—42no—
95C2×C3⋊Dic3—42no—
96#634—82no—
97C24×C4C3⋊D311yescharacteristic
98C2×C22⋊Q8—91no—
99C2×C22⋊Q8—91no—
100C2×C22⋊Q8—91no—
101#385—92no—
102#385—92no—
103#385—92no—
104#380—91no—
105#380—91no—
106#380—91no—
107#379—92no—
108C24×C3—21no—
109C24×C3—21no—
110C24×C3—31no—
111C24×C3—31no—
112C24×C3—32no—
113C24×C3—61no—
114C24×C3—61no—
115C24×C3Dic612yescomplemented
116C24×C3C22×D311yescharacteristic
117C22×A4—23no—
118C22×A4—23no—
119C22×A4Dic616yescomplemented
120C22×A4C22×D313yes—
121C22×C3×C4—21no—
122C22×C3×C4—31no—
123C22×C3×C4—31no—
124C22×C3×C4—31no—
125C22×C3×C4—32no—
126C22×C3×C4—34no—
127C22×C3×C4—31no—
128C22×C3×C4—31no—
129C22×C3×C4—31no—
130C22×C3×C4—31no—
131C22×C3×C4—43no—
132C22×C3×C4—62no—
133C22×C3×C4—62no—
134C22×C3×C4—61no—
135C22×C3×C4—61no—
136C22×C3×C4—62no—
137C22×C3×C4—62no—
138C22×C3×C4—62no—
139C22×C3×C4—62no—
140C22×C3×C4—62no—
141C22×C3×C4#6712yes—
142C22×C3×C4S411yescharacteristic
143C22×Dic3—32no—
144C22×Dic3—32no—
145C22×Dic3—32no—
146C22×Dic3—32no—
147C2×Dic6—61no—
148C2×Dic6—62no—
149C2×Dic6—62no—
150C2×Dic6—61no—
151C2×Dic6—123no—
152C4×A4—23no—
153C4×A4#6716yes—
154SL(2,ℤ/4)—66no—
155SL(2,ℤ/4)—66no—
156#217—62no—
157#217—64no—
158#217—62no—
159#217—62no—
160#217—64no—
161#217—64no—
162#217—62no—
163#217—62no—
164#217—62no—
165#217—126no—
166C4⋊Dic3—62no—
167C4⋊Dic3—62no—
168C4⋊Dic3—61no—
169C4⋊Dic3—61no—
170C4⋊Dic3—123no—
171Dic3⋊C4—64no—
172Dic3⋊C4—64no—
173Dic3⋊C4—62no—
174Dic3⋊C4—62no—
175Dic3⋊C4—126no—
176C22×C32—42no—
177C22×C32—41no—
178C22×C32—81no—
179C22×C32—81no—
180C3×A4C22⋊Q811yescharacteristic, complemented
181C32×C4—42no—
182C32×C4—81no—
183C3⋊Dic3—82no—
184C3⋊Dic3—82no—
185C25C2×C3⋊D311yescharacteristic
186C22×Q8—91no—
187C23×C4—22no—
188C23×C4—31no—
189C23×C4—31no—
190C23×C4—31no—
191C23×C4—31no—
192C23×C4—62no—
193C23×C4C2×C3⋊D311yescharacteristic
194C23×C4C2×C3⋊D311yescharacteristic
195C22⋊Q8—182no—
196C22⋊Q8—184no—
197C22⋊Q8—181no—
198C22⋊Q8—181no—
199C22⋊Q8—181no—
200C22⋊Q8—182no—
201C22⋊Q8—181no—
202C2×C4⋊C4—91no—
203C2×C4⋊C4—91no—
204C2×C4⋊C4—91no—
205C2×C4⋊C4—92no—
206C2×C4⋊C4—92no—
207C2×C4⋊C4—92no—
208C2×C22⋊C4—92no—
209C2×C22⋊C4—92no—
210C2×C22⋊C4—92no—
211C2×C22⋊C4—92no—
212C2×C22⋊C4—92no—
213C2×C22⋊C4—92no—
214#95—92no—
215#95—92no—
216#95—92no—
217C23×C3—22no—
218C23×C3—31no—
219C23×C3—31no—
220C23×C3—31no—
221C23×C3—32no—
222C23×C3—31no—
223C23×C3—32no—
224C23×C3—32no—
225C23×C3—32no—
226C23×C3—32no—
227C23×C3—31no—
228C23×C3—43no—
229C23×C3—61no—
230C23×C3—61no—
231C23×C3—61no—
232C23×C3—61no—
233C23×C3—62no—
234C23×C3—61no—
235C23×C3—61no—
236C23×C3—62no—
237C23×C3—62no—
238C23×C3—61no—
239C23×C3—64no—
240C23×C3C2×Dic611yescharacteristic
241C23×C3#23511yescharacteristic
242C23×C3C2×#6711yescharacteristic
243C23×C3C2×S411yescharacteristic
244C2×A4—26no—
245C2×A4C2×Dic613yes—
246C2×A4#23513yes—
247C2×A4C2×#6713yes—
248C2×C3×C4—22no—
249C2×C3×C4—31no—
250C2×C3×C4—32no—
251C2×C3×C4—32no—
252C2×C3×C4—32no—
253C2×C3×C4—32no—
254C2×C3×C4—31no—
255C2×C3×C4—43no—
256C2×C3×C4—43no—
257C2×C3×C4—62no—
258C2×C3×C4—61no—
259C2×C3×C4—61no—
260C2×C3×C4—61no—
261C2×C3×C4—62no—
262C2×C3×C4—64no—
263C2×C3×C4—62no—
264C2×C3×C4—61no—
265C2×C3×C4—86no—
266C2×C3×C4C2×S411yescharacteristic
267C2×C3×C4C2×S411yescharacteristic
268C2×Dic3—62no—
269C2×Dic3—62no—
270C2×Dic3—62no—
271C2×Dic3—62no—
272C2×Dic3—62no—
273C2×Dic3—62no—
274C2×Dic3—62no—
275C2×Dic3—62no—
276C2×Dic3—62no—
277C2×Dic3—62no—
278C2×Dic3—62no—
279C2×Dic3—62no—
280C2×Dic3—126no—
281C2×Dic3—126no—
282Dic6—122no—
283Dic6—122no—
284Dic6—246no—
285C2×C32—41no—
286C2×C32—41no—
287C2×C32—41no—
288C2×C32—82no—
289C24—21no—
290C24—21no—
291C24—31no—
292C24—31no—
293C24—32no—
294C24—61no—
295C24—61no—
296C24#63412yescomplemented
297C24C22×C3⋊D311yescharacteristic
298C2×Q8—181no—
299C2×Q8—182no—
300C2×Q8—182no—
301C2×Q8—181no—
302C22×C4—21no—
303C22×C4—31no—
304C22×C4—31no—
305C22×C4—31no—
306C22×C4—32no—
307C22×C4—34no—
308C22×C4—31no—
309C22×C4—31no—
310C22×C4—31no—
311C22×C4—31no—
312C22×C4—62no—
313C22×C4—62no—
314C22×C4—61no—
315C22×C4—61no—
316C22×C4—62no—
317C22×C4—62no—
318C22×C4—62no—
319C22×C4—62no—
320C22×C4—62no—
321C22×C4—92no—
322C22×C4—92no—
323C22×C4—92no—
324C22×C4—92no—
325C22×C4#63812yes—
326C22×C4C3⋊S411yescharacteristic
327C4⋊C4—184no—
328C4⋊C4—184no—
329C4⋊C4—182no—
330C4⋊C4—181no—
331C4⋊C4—182no—
332C4⋊C4—182no—
333C4⋊C4—182no—
334C4⋊C4—181no—
335C22⋊C4—182no—
336C22⋊C4—184no—
337C22⋊C4—182no—
338C22⋊C4—182no—
339C22⋊C4—184no—
340C22⋊C4—184no—
341C22⋊C4—182no—
342C22⋊C4—182no—
343C22⋊C4—182no—
344C22×C3—21no—
345C22×C3—21no—
346C22×C3—31no—
347C22×C3—31no—
348C22×C3—31no—
349C22×C3—31no—
350C22×C3—31no—
351C22×C3—31no—
352C22×C3—31no—
353C22×C3—31no—
354C22×C3—31no—
355C22×C3—34no—
356C22×C3—32no—
357C22×C3—46no—
358C22×C3—43no—
359C22×C3—62no—
360C22×C3—62no—
361C22×C3—62no—
362C22×C3—62no—
363C22×C3—61no—
364C22×C3—62no—
365C22×C3—62no—
366C22×C3—62no—
367C22×C3—61no—
368C22×C3—61no—
369C22×C3—83no—
370C22×C3—83no—
371C22×C3#92411yescharacteristic, complemented
372C22×C3A4⋊Q812yescomplemented
373C22×C3C22×S411yescharacteristic
374A4#92413yescomplemented
375C3×C4—21no—
376C3×C4—32no—
377C3×C4—46no—
378C3×C4—61no—
379C3×C4—83no—
380C3×C4GL(2,ℤ/4)12yes—
381Dic3—122no—
382Dic3—122no—
383Dic3—122no—
384Dic3—122no—
385Dic3—246no—
386Dic3—246no—
387C32—41noSylow
388C23—22no—
389C23—31no—
390C23—31no—
391C23—31no—
392C23—32no—
393C23—31no—
394C23—32no—
395C23—32no—
396C23—32no—
397C23—32no—
398C23—31no—
399C23—61no—
400C23—61no—
401C23—61no—
402C23—61no—
403C23—62no—
404C23—61no—
405C23—61no—
406C23—62no—
407C23—62no—
408C23—61no—
409C23—64no—
410C23C2×#63411yescharacteristic
411C23#382811yescharacteristic
412C23C2×#63811yescharacteristic
413C23C2×C3⋊S411yescharacteristic
414Q8—362no—
415Q8—362no—
416C2×C4—22no—
417C2×C4—31no—
418C2×C4—32no—
419C2×C4—32no—
420C2×C4—32no—
421C2×C4—32no—
422C2×C4—31no—
423C2×C4—62no—
424C2×C4—61no—
425C2×C4—61no—
426C2×C4—61no—
427C2×C4—62no—
428C2×C4—64no—
429C2×C4—62no—
430C2×C4—61no—
431C2×C4—182no—
432C2×C4—182no—
433C2×C4—182no—
434C2×C4—182no—
435C2×C4—182no—
436C2×C4—182no—
437C2×C4—182no—
438C2×C4—182no—
439C2×C4—182no—
440C2×C4—182no—
441C2×C4—182no—
442C2×C4—182no—
443C2×C4C2×C3⋊S411yescharacteristic
444C2×C4C2×C3⋊S411yescharacteristic
445C2×C3—22no—
446C2×C3—31no—
447C2×C3—31no—
448C2×C3—31no—
449C2×C3—31no—
450C2×C3—43no—
451C2×C3—43no—
452C2×C3—43no—
453C2×C3—62no—
454C2×C3—86no—
455C2×C3C2×A4⋊Q811yescharacteristic
456C2×C3#591211yescharacteristic
457C2×C3C2×GL(2,ℤ/4)11yescharacteristic
458C22—21no—
459C22—21no—
460C22—31no—
461C22—31no—
462C22—31no—
463C22—31no—
464C22—31no—
465C22—31no—
466C22—31no—
467C22—31no—
468C22—31no—
469C22—34no—
470C22—32no—
471C22—62no—
472C22—62no—
473C22—62no—
474C22—62no—
475C22—61no—
476C22—62no—
477C22—62no—
478C22—62no—
479C22—61no—
480C22—61no—
481C22#6413311yescharacteristic, complemented
482C22#6425912yescomplemented
483C22C22×C3⋊S411yescharacteristic
484C4—21no—
485C4—32no—
486C4—61no—
487C4—362no—
488C4—362no—
489C4—362no—
490C4—362no—
491C4#6426912yes—
492C3—43no—
493C3#8548011yescharacteristic, complemented
494C2—22no—
495C2—31no—
496C2—31no—
497C2—31no—
498C2—31no—
499C2—62no—
500C2C2×#6425911yescharacteristic
501C2#1059657511yescharacteristic
502C2C2×#6426911yescharacteristic
subgroupG/H
center, FrattiniC22C22×C3⋊S4
commutator, cosocleC22×C3×A4C23
FittingC24×C3×C4D3
socleC24×C3C22×D3
prime radicalC23×C3×A4C22
hypercenterC22×C4C3⋊S4
hypocenterC3×A4C22⋊Q8
LCSG ▷ C22×C3×A4 ▷ C3×A4
UCSC1 ◁ C22 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
2. C2×#64259C2semidirect
4. C4⋊(C3⋊SL(2,ℤ/4))C2semidirect
5. #10593645C2semidirect
34. C22×C3×A4Q8semidirect
115. C24×C3Dic6semidirect
119. C22×A4Dic6semidirect
180. C3×A4C22⋊Q8semidirect
296. C24#634semidirect
371. C22×C3#924semidirect
372. C22×C3A4⋊Q8semidirect
374. A4#924semidirect
481. C22#64133semidirect
482. C22#64259semidirect
493. C3#85480semidirect

Maximal subgroups

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

subgroupindex
C22×C3×C4×A42
C2×#642592
#105936662
C4⋊(C3⋊SL(2,ℤ/4))2
#105936452
#854803
#840313
#641334