Finite Group Databasebeta

← M16×C3⋊S4 #11922990

Subgroups — M16×C3⋊S4 #11922990

Order 1152.

730 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 730 conjugacy classes of subgroups — too many to draw. Only its 93 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×C3⋊S4C211yesmaximal, characteristic
2C3×A4×M16C211yesmaximal, characteristic, complemented
3#10593643C211yesmaximal, characteristic, complemented
4#10593634C212yesmaximal, complemented
5C8×C3⋊S4C212yesmaximal, complemented
6M16×S4—33nomaximal
7M16×#67—31nomaximal
8C22×C3⋊S4C411yescharacteristic
9C2×C3×C4×A4C2211yescharacteristic
10C2×C3⋊SL(2,ℤ/4)C411yescharacteristic
11C4×C3⋊S4C411yescharacteristic
12C4×C3⋊S4C411yescharacteristic
13C4×C3⋊S4C2211yescharacteristic
14C4×C3⋊S4C2211yescharacteristic
15M16×C3⋊D3—41nomaximal
16C3×C8×A4C2212yescomplemented
17C3⋊(A4⋊C8)C2212yescomplemented
18C2×C4×S4—33no—
19C22×C3×M16D311yescharacteristic, complemented
20C2×C4×#67—31no—
21C2×D3×M16—31no—
22A4×M16D313yescomplemented
23#5409—33no—
24#5400—36no—
25C8×S4—36no—
26#5207—31no—
27#5128—32no—
28#5127—32no—
29#5126—31no—
30#5118—31no—
31Dic3×M16—31no—
32#5111—32no—
33C8×#67—32no—
34C22×C3×A4C2×C411yescharacteristic
35C2×C3⋊S4—22no—
36C2×C3⋊S4C2×C411yescharacteristic
37C2×C3⋊S4C2×C411yescharacteristic
38C2×C4×C3⋊D3—41no—
39C3×C4×A4C2×C411yescharacteristic
40C3×C4×A4C2311yescharacteristic
41C3⋊SL(2,ℤ/4)C2×C411yescharacteristic
42C3⋊SL(2,ℤ/4)C2×C411yescharacteristic
43C32×M16—41no—
44#3748—41no—
45#3743—42no—
46C8×C3⋊D3—42no—
47D4×M16—91noSylow
48C22×S4—33no—
49C23×C3×C4C2×D311yescharacteristic
50C22×#67—31no—
51C22×C4×D3—31no—
52C2×C4×A4C2×D313yes—
53C2×SL(2,ℤ/4)—33no—
54C4×S4—33no—
55C4×S4—33no—
56C4×S4—33no—
57C4×S4—33no—
58C2×C3×M16—31no—
59C2×C3×M16—31no—
60C2×C3×M16—32no—
61C22×C3×C8C2×D312yescomplemented
62C2×#217—31no—
63C4×#67—31no—
64C4×#67—31no—
65C4×#67—31no—
66C4×#67—31no—
67C4×#67—31no—
68C4×#67—31no—
69C4×#67—31no—
70C4×#67—31no—
71C2×(C2×D3)⋊C4—31no—
72C2×Dic3⋊C4—31no—
73C2×C4×Dic3—31no—
74C2×#208—31no—
75C2×#208—31no—
76D3×M16—61no—
77D3×M16—62no—
78D3×M16—61no—
79D3×M16—123no—
80C2×ΓL(1,𝔽25)—32no—
81C2×D3×C8—32no—
82C8×A4C2×D316yescomplemented
83A4⋊C8—36no—
84#830—32no—
85#830—32no—
86(C2×D3)⋊C8—32no—
87(C2×D3)⋊C8—32no—
88#815—32no—
89Dic3⋊C8—32no—
90Dic3⋊C8—32no—
91C8×Dic3—32no—
92C22×C3⋊D3—41no—
93C2×C3×A4—21no—
94C2×C3×A4C22×C411yescharacteristic
95C3⋊S4—21no—
96C3⋊S4M1612yesdirect product factor
97C2×C32×C4—41no—
98C2×C3⋊Dic3—41no—
99C4×C3⋊D3—41no—
100C4×C3⋊D3—41no—
101C4×C3⋊D3—41no—
102C4×C3⋊D3—41no—
103C32×C8—42no—
104C3⋊(C3⋊C8)—42no—
105C22×M16—91no—
106C22×M16C3⋊D311yescharacteristic, complemented
107C2×C4×D4—91no—
108#436—92no—
109#435—92no—
110#435—92no—
111C8×D4—92no—
112#423—91no—
113#407—91no—
114#407—91no—
115C4×M16—91no—
116C24×C3C4×D311yescharacteristic
117C23×D3—31no—
118C22×A4C4×D313yes—
119C2×S4—33no—
120C2×S4—33no—
121C2×S4—66no—
122C22×C3×C4—31no—
123C22×C3×C4—31no—
124C22×C3×C4—31no—
125C22×C3×C4—31no—
126C22×C3×C4C4×D311yescharacteristic
127C22×C3×C4C22×D311yescharacteristic
128C2×#67—31no—
129C2×#67—31no—
130C2×#67—31no—
131C2×#67—31no—
132C2×#67—62no—
133C2×#67—62no—
134C22×Dic3—31no—
135C22×Dic3—31no—
136C22×Dic3—31no—
137C2×C4×D3—31no—
138C2×C4×D3—31no—
139C2×C4×D3—31no—
140C2×C4×D3—31no—
141C2×C4×D3—61no—
142C2×C4×D3—61no—
143C2×C4×D3—61no—
144C2×C4×D3—61no—
145C2×C4×D3—123no—
146C4×A4C4×D313yes—
147C4×A4C22×D313yes—
148SL(2,ℤ/4)—33no—
149SL(2,ℤ/4)—33no—
150C3×M16—31no—
151C3×M16—32no—
152C3×M16—43no—
153C3×M16—61no—
154C3×M16S411yescharacteristic, complemented
155C2×C3×C8—32no—
156C2×C3×C8—32no—
157#217—31no—
158#217—31no—
159#217—31no—
160#217—31no—
161(C2×D3)⋊C4—31no—
162(C2×D3)⋊C4—31no—
163(C2×D3)⋊C4—31no—
164(C2×D3)⋊C4—31no—
165Dic3⋊C4—31no—
166Dic3⋊C4—31no—
167Dic3⋊C4—31no—
168Dic3⋊C4—31no—
169C4×Dic3—31no—
170C4×Dic3—31no—
171C4×Dic3—31no—
172C4×Dic3—31no—
173#208—61no—
174#208—61no—
175#208—61no—
176#208—61no—
177#208—123no—
178C2×C3⋊C8—32no—
179C2×C3⋊C8—32no—
180ΓL(1,𝔽25)—62no—
181ΓL(1,𝔽25)—62no—
182ΓL(1,𝔽25)—126no—
183D3×C8—62no—
184D3×C8—62no—
185D3×C8—126no—
186C22×C32—41no—
187C2×C3⋊D3—41no—
188C2×C3⋊D3—41no—
189C2×C3⋊D3—82no—
190C3×A4C2×M1611yescharacteristic, complemented
191C32×C4—41no—
192C32×C4—41no—
193C3⋊Dic3—41no—
194C3⋊Dic3—41no—
195C22×D4—91no—
196C23×C4—91no—
197C23×C4C2×C3⋊D311yescharacteristic
198C2×M16—31no—
199C2×M16—31no—
200C2×M16—32no—
201C2×M16—92no—
202C2×M16—91no—
203C2×M16—91no—
204C2×M16—181no—
205C2×M16—182no—
206C2×M16—181no—
207C22×C8—92no—
208C22×C8C2×C3⋊D312yescomplemented
209C4×D4—91no—
210C4×D4—91no—
211C4×D4—91no—
212C4×D4—91no—
213C4×D4—91no—
214C4×D4—91no—
215C4×D4—91no—
216C4×D4—91no—
217C2×C4⋊C4—91no—
218C2×C22⋊C4—91no—
219C2×C22⋊C4—91no—
220C2×C42—91no—
221C4⋊C8—92no—
222C4⋊C8—92no—
223C22⋊C8—92no—
224C22⋊C8—92no—
225C22⋊C8—92no—
226C22⋊C8—92no—
227#97—92no—
228C4×C8—92no—
229C23×C3—21no—
230C23×C3—31no—
231C23×C3—31no—
232C23×C3—61no—
233C23×C3C2×C4×D311yescharacteristic
234C22×D3—31no—
235C22×D3—31no—
236C22×D3—62no—
237C22×D3—61no—
238C22×D3—61no—
239C22×D3—123no—
240C22×D3—121no—
241C2×A4—23no—
242C2×A4C2×C4×D313yes—
243S4—36no—
244S4—63no—
245C2×C3×C4—31no—
246C2×C3×C4—31no—
247C2×C3×C4—31no—
248C2×C3×C4—31no—
249C2×C3×C4—31no—
250C2×C3×C4—31no—
251C2×C3×C4—31no—
252C2×C3×C4—43no—
253C2×C3×C4—61no—
254C2×C3×C4C2×S411yescharacteristic
255#67—32no—
256#67—32no—
257#67—62no—
258#67—62no—
259#67—61no—
260#67—61no—
261C2×Dic3—31no—
262C2×Dic3—31no—
263C2×Dic3—31no—
264C2×Dic3—31no—
265C2×Dic3—31no—
266C2×Dic3—31no—
267C2×Dic3—62no—
268C2×Dic3—61no—
269C2×Dic3—61no—
270C2×Dic3—123no—
271C2×Dic3—121no—
272C4×D3—61no—
273C4×D3—61no—
274C4×D3—61no—
275C4×D3—61no—
276C4×D3—61no—
277C4×D3—61no—
278C4×D3—61no—
279C4×D3—61no—
280C4×D3—123no—
281C4×D3—123no—
282C4×D3—123no—
283C4×D3—123no—
284C3×C8—32no—
285C3×C8—46no—
286C3×C8C2×S412yescomplemented
287C3⋊C8—62no—
288C3⋊C8—62no—
289C3⋊C8—126no—
290C2×C32—41no—
291C2×C32—81no—
292C3⋊D3—42no—
293C3⋊D3—81no—
294C24—91no—
295C24C4×C3⋊D311yescharacteristic
296C2×D4—91no—
297C2×D4—91no—
298C2×D4—91no—
299C2×D4—91no—
300C2×D4—182no—
301C2×D4—182no—
302C22×C4—31no—
303C22×C4—31no—
304C22×C4—31no—
305C22×C4—31no—
306C22×C4—91no—
307C22×C4—91no—
308C22×C4—91no—
309C22×C4—91no—
310C22×C4—91no—
311C22×C4—91no—
312C22×C4—91no—
313C22×C4—181no—
314C22×C4—181no—
315C22×C4—181no—
316C22×C4—181no—
317C22×C4C4×C3⋊D311yescharacteristic
318C22×C4C22×C3⋊D311yescharacteristic
319M16—31no—
320M16—32no—
321M16—61no—
322M16—182no—
323M16—181no—
324M16—181no—
325M16—181no—
326M16—181no—
327M16—182no—
328M16C3⋊S411yescharacteristic, direct product factor
329C2×C8—32no—
330C2×C8—32no—
331C2×C8—92no—
332C2×C8—92no—
333C2×C8—182no—
334C2×C8—182no—
335C4⋊C4—91no—
336C4⋊C4—91no—
337C4⋊C4—91no—
338C4⋊C4—91no—
339C22⋊C4—91no—
340C22⋊C4—91no—
341C22⋊C4—91no—
342C22⋊C4—91no—
343C22⋊C4—91no—
344C22⋊C4—91no—
345C22⋊C4—91no—
346C22⋊C4—91no—
347C42—91no—
348C42—91no—
349C42—91no—
350C42—91no—
351C22×C3—31no—
352C22×C3—31no—
353C22×C3—31no—
354C22×C3—43no—
355C22×C3—61no—
356C22×C3—61no—
357C22×C3—61no—
358C22×C3—61no—
359C22×C3D3×M1611yescharacteristic, complemented
360C22×C3C4×S411yescharacteristic
361C2×D3—32no—
362C2×D3—61no—
363C2×D3—61no—
364C2×D3—61no—
365C2×D3—61no—
366C2×D3—61no—
367C2×D3—123no—
368C2×D3—123no—
369C2×D3—122no—
370C2×D3—122no—
371C2×D3—246no—
372A4D3×M1613yescomplemented
373C3×C4—31no—
374C3×C4—31no—
375C3×C4—43no—
376C3×C4—43no—
377C3×C4C4×S411yescharacteristic
378C3×C4C22×S411yescharacteristic
379Dic3—32no—
380Dic3—61no—
381Dic3—61no—
382Dic3—61no—
383Dic3—61no—
384Dic3—61no—
385Dic3—123no—
386Dic3—123no—
387C32—41noSylow
388C23—21no—
389C23—31no—
390C23—31no—
391C23—61no—
392C23—91no—
393C23—91no—
394C23—181no—
395C23—182no—
396C23—181no—
397C23—361no—
398C23C2×C4×C3⋊D311yescharacteristic
399D4—92no—
400D4—92no—
401D4—182no—
402D4—181no—
403D4—182no—
404D4—181no—
405C2×C4—31no—
406C2×C4—31no—
407C2×C4—31no—
408C2×C4—31no—
409C2×C4—31no—
410C2×C4—31no—
411C2×C4—31no—
412C2×C4—61no—
413C2×C4—91no—
414C2×C4—91no—
415C2×C4—91no—
416C2×C4—91no—
417C2×C4—91no—
418C2×C4—91no—
419C2×C4—181no—
420C2×C4—181no—
421C2×C4—181no—
422C2×C4—181no—
423C2×C4—182no—
424C2×C4—181no—
425C2×C4—181no—
426C2×C4—181no—
427C2×C4—181no—
428C2×C4—181no—
429C2×C4—181no—
430C2×C4—361no—
431C2×C4C2×C3⋊S411yescharacteristic
432C8—32no—
433C8—182no—
434C8—182no—
435C8C2×C3⋊S412yescomplemented
436C2×C3—21no—
437C2×C3—31no—
438C2×C3—31no—
439C2×C3—43no—
440C2×C3—61no—
441C2×C3—83no—
442C2×C3C2×C4×S411yescharacteristic
443D3—62no—
444D3—126no—
445D3—121no—
446D3—243no—
447C22—31no—
448C22—31no—
449C22—31no—
450C22—61no—
451C22—61no—
452C22—61no—
453C22—61no—
454C22—92no—
455C22—181no—
456C22—181no—
457C22—181no—
458C22—181no—
459C22—181no—
460C22—362no—
461C22—362no—
462C22M16×C3⋊D311yescharacteristic, complemented
463C22C4×C3⋊S411yescharacteristic
464C4—31no—
465C4—31no—
466C4—92no—
467C4—181no—
468C4—181no—
469C4—181no—
470C4—181no—
471C4—181no—
472C4C4×C3⋊S411yescharacteristic
473C4C22×C3⋊S411yescharacteristic
474C3—43no—
475C3M16×S411yescharacteristic, complemented
476C2—21no—
477C2—31no—
478C2—31no—
479C2—61no—
480C2—182no—
481C2—361no—
482C2C2×C4×C3⋊S411yescharacteristic
subgroupG/H
center, FrattiniC4C22×C3⋊S4
commutatorC2×C3×A4C22×C4
FittingC22×C3×M16D3
socleC23×C3C2×C4×D3
prime radicalC22×C3⋊S4C4
cosocleC3×C4×A4C23
hypercenterM16C3⋊S4
hypocenterC3×A4C2×M16
LCSG ▷ C2×C3×A4 ▷ C3×A4
UCSC1 ◁ C4 ◁ M16

Complements

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

NH ≅ G/Ntype
2. C3×A4×M16C2semidirect
3. #10593643C2semidirect
4. #10593634C2semidirect
5. C8×C3⋊S4C2semidirect
16. C3×C8×A4C22semidirect
17. C3⋊(A4⋊C8)C22semidirect
19. C22×C3×M16D3semidirect
22. A4×M16D3semidirect
61. C22×C3×C8C2×D3semidirect
82. C8×A4C2×D3semidirect
96. C3⋊S4M16direct (N × H)
106. C22×M16C3⋊D3semidirect
154. C3×M16S4semidirect
190. C3×A4C2×M16semidirect
208. C22×C8C2×C3⋊D3semidirect
286. C3×C8C2×S4semidirect
328. M16C3⋊S4direct (N × H)
359. C22×C3D3×M16semidirect
372. A4D3×M16semidirect
435. C8C2×C3⋊S4semidirect
462. C22M16×C3⋊D3semidirect
475. C3M16×S4semidirect

Maximal subgroups

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

subgroupindex
C2×C4×C3⋊S42
C3×A4×M162
#105936432
#105936342
C8×C3⋊S42
M16×S43
M16×#673
M16×C3⋊D34