Finite Group Databasebeta

← #11923062

Subgroups — #11923062

Order 1152.

808 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 808 conjugacy classes of subgroups — too many to draw. Only its 83 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×#41C211yesmaximal, characteristic, complemented
2C2×C4⋊(C3⋊S4)C211yesmaximal, characteristic, complemented
3#10593651C212yesmaximal, complemented
4#10593649C212yesmaximal, complemented
5#10593643C211yesmaximal, characteristic, complemented
6#85513—33nomaximal
7#84082—31nomaximal
8C22×C3⋊S4—21no—
9C3×Q8×A4C2211yescharacteristic, complemented
10C3×D4×A4—21no—
11C3×D4×A4C2211yescharacteristic, complemented
12C2×C3×C4×A4—21no—
13C2×C3×C4×A4C2211yescharacteristic
14C4⋊(C3⋊S4)—21no—
15C4⋊(C3⋊S4)C2212yes—
16#64158—41nomaximal
17C3⋊(A4⋊C8)C2212yescomplemented
18C22×C3×#41D311yescharacteristic, complemented
19A4×#41D313yescomplemented
20C2×C4⋊S4—33no—
21C2×#949—31no—
22C2×#949—31no—
23C2×#930—31no—
24#5417—36no—
25#5415—36no—
26#5409—33no—
27#5238—32no—
28#5238—32no—
29#5232—31no—
30#5232—31no—
31#5227—32no—
32#5217—32no—
33#5207—31no—
34C22×C3×A4—21no—
35C22×C3×A4D411yescharacteristic
36C2×C3⋊S4—22no—
37C2×C3⋊S4—42no—
38C32×#41—41no—
39C2×C4⋊(C3⋊D3)—41no—
40C3×C4×A4—21no—
41C3×C4×A4D411yescharacteristic
42C3×C4×A4C2311yescharacteristic
43#3755—42no—
44#3753—42no—
45#3748—41no—
46#3006—91noSylow
47C22×S4—63no—
48C2×C3×#41—31no—
49C2×C3×#41—31no—
50C2×C3×#41—31no—
51C2×C3×#41—31no—
52C2×C3×#41—61no—
53C2×C3×#41—61no—
54C22×C3×Q8C2×D311yescharacteristic, complemented
55C22×C3×D4—21no—
56C22×C3×D4C2×D311yescharacteristic, complemented
57C23×C3×C4—21no—
58C23×C3×C4C2×D311yescharacteristic
59C22×#67—61no—
60C22×D12—31no—
61Q8×A4C2×D313yescomplemented
62D4×A4—23no—
63D4×A4C2×D313yescomplemented
64C2×C4×A4—23no—
65C2×C4×A4C2×D313yes—
66C4⋊S4—36no—
67C4⋊S4—63no—
68#949—62no—
69#949—62no—
70#949—61no—
71#949—61no—
72#949—61no—
73#949—61no—
74#949—123no—
75C2×#215—32no—
76C2×#215—32no—
77C2×#213—32no—
78C2×#213—32no—
79#930—32no—
80#930—32no—
81#930—61no—
82#930—61no—
83C2×(C2×D3)⋊C4—61no—
84C2×C4⋊Dic3—31no—
85C2×#208—31no—
86C2×#208—31no—
87A4⋊C8—36no—
88#835—32no—
89#835—32no—
90#832—32no—
91#832—32no—
92#830—32no—
93#830—32no—
94C22×C3⋊D3—81no—
95C2×C3×A4—21no—
96C2×C3×A4—41no—
97C2×C3×A4C2×D411yescharacteristic
98C3⋊S4—42no—
99C32×Q8—41no—
100C32×D4—41no—
101C32×D4—81no—
102C2×C32×C4—41no—
103C2×C32×C4—81no—
104C4⋊(C3⋊D3)—42no—
105C4⋊(C3⋊D3)—81no—
106C3⋊(C3⋊C8)—42no—
107C22×#41C3⋊D311yescharacteristic, complemented
108C2×AGL(1,ℤ/8)—91no—
109C2×AGL(1,ℤ/8)—91no—
110C2×#121—91no—
111#449—92no—
112#449—92no—
113#448—92no—
114#447—92no—
115#417—91no—
116#417—91no—
117#407—91no—
118C24×C3—21no—
119C24×C3#6711yescharacteristic
120C23×D3—61no—
121C22×A4—23no—
122C22×A4#6713yes—
123C2×S4—66no—
124C2×S4—126no—
125C3×#41—32no—
126C3×#41—32no—
127C3×#41—31no—
128C3×#41—31no—
129C3×#41—31no—
130C3×#41—43no—
131C3×#41—61no—
132C3×#41—61no—
133C3×#41—61no—
134C3×#41—62no—
135C3×#41—62no—
136C3×#41S411yescharacteristic, complemented
137C2×C3×Q8—31no—
138C2×C3×Q8—31no—
139C2×C3×Q8—61no—
140C2×C3×D4—31no—
141C2×C3×D4—31no—
142C2×C3×D4—61no—
143C2×C3×D4—61no—
144C2×C3×D4—61no—
145C2×C3×D4—61no—
146C2×C3×D4—61no—
147C22×C3×C4—21no—
148C22×C3×C4—31no—
149C22×C3×C4—31no—
150C22×C3×C4—31no—
151C22×C3×C4—31no—
152C22×C3×C4—61no—
153C22×C3×C4—61no—
154C22×C3×C4—61no—
155C22×C3×C4—61no—
156C22×C3×C4#6711yescharacteristic
157C22×C3×C4C22×D311yescharacteristic
158C2×#67—62no—
159C2×#67—62no—
160C2×#67—122no—
161C2×#67—122no—
162C22×Dic3—61no—
163C2×D12—32no—
164C2×D12—61no—
165C2×D12—61no—
166C2×D12—61no—
167C2×D12—61no—
168C2×D12—61no—
169C2×D12—123no—
170C4×A4—23no—
171C4×A4#6713yes—
172C4×A4C22×D313yes—
173#215—64no—
174#215—62no—
175#215—62no—
176#215—126no—
177#213—64no—
178#213—62no—
179#213—62no—
180#213—126no—
181(C2×D3)⋊C4—62no—
182(C2×D3)⋊C4—62no—
183C4⋊Dic3—32no—
184C4⋊Dic3—61no—
185#208—61no—
186#208—61no—
187#208—61no—
188#208—61no—
189#208—123no—
190C2×C3⋊C8—32no—
191C2×C3⋊C8—32no—
192C22×C32—41no—
193C22×C32—81no—
194C2×C3⋊D3—82no—
195C2×C3⋊D3—162no—
196C3×A4AGL(1,ℤ/8)11yescharacteristic, complemented
197C32×C4—41no—
198C32×C4—41no—
199C32×C4—81no—
200C2×#41—31no—
201C2×#41—31no—
202C2×#41—31no—
203C2×#41—31no—
204C2×#41—61no—
205C2×#41—61no—
206C22×Q8C2×C3⋊D311yescharacteristic, complemented
207C22×D4—21no—
208C22×D4—91no—
209C22×D4—181no—
210C22×D4C2×C3⋊D311yescharacteristic, complemented
211C23×C4—21no—
212C23×C4C2×C3⋊D311yescharacteristic
213AGL(1,ℤ/8)—182no—
214AGL(1,ℤ/8)—182no—
215AGL(1,ℤ/8)—181no—
216AGL(1,ℤ/8)—181no—
217AGL(1,ℤ/8)—181no—
218AGL(1,ℤ/8)—181no—
219C2×SD16—92no—
220C2×SD16—92no—
221C2×D8—92no—
222C2×D8—92no—
223C2×M16—91no—
224C2×M16—91no—
225#121—92no—
226#121—92no—
227#121—181no—
228#121—181no—
229C2×C4⋊C4—91no—
230C2×C22⋊C4—181no—
231#103—92no—
232#103—92no—
233#102—92no—
234#102—92no—
235C22⋊C8—92no—
236C22⋊C8—92no—
237C23×C3—21no—
238C23×C3—31no—
239C23×C3—31no—
240C23×C3—41no—
241C23×C3—61no—
242C23×C3—61no—
243C23×C3—61no—
244C23×C3—121no—
245C23×C3C2×#6711yescharacteristic
246C22×D3—62no—
247C22×D3—121no—
248C22×D3—122no—
249C22×D3—122no—
250C22×D3—121no—
251C22×D3—243no—
252C2×A4—23no—
253C2×A4—43no—
254C2×A4C2×#6713yes—
255S4—126no—
256C3×Q8—32no—
257C3×Q8—31no—
258C3×Q8—43no—
259C3×Q8—61no—
260C3×Q8C2×S411yescharacteristic, complemented
261C3×D4—21no—
262C3×D4—32no—
263C3×D4—31no—
264C3×D4—43no—
265C3×D4—61no—
266C3×D4—61no—
267C3×D4—61no—
268C3×D4—62no—
269C3×D4—61no—
270C3×D4—83no—
271C3×D4C2×S411yescharacteristic, complemented
272C2×C3×C4—21no—
273C2×C3×C4—31no—
274C2×C3×C4—31no—
275C2×C3×C4—31no—
276C2×C3×C4—31no—
277C2×C3×C4—31no—
278C2×C3×C4—31no—
279C2×C3×C4—31no—
280C2×C3×C4—43no—
281C2×C3×C4—61no—
282C2×C3×C4—61no—
283C2×C3×C4—61no—
284C2×C3×C4—61no—
285C2×C3×C4—62no—
286C2×C3×C4—61no—
287C2×C3×C4—61no—
288C2×C3×C4—83no—
289C2×C3×C4C2×S411yescharacteristic
290#67—122no—
291#67—124no—
292#67—122no—
293C2×Dic3—62no—
294C2×Dic3—122no—
295D12—62no—
296D12—62no—
297D12—126no—
298D12—121no—
299D12—121no—
300D12—243no—
301C3⋊C8—62no—
302C3⋊C8—62no—
303C3⋊C8—126no—
304C2×C32—41no—
305C2×C32—81no—
306C2×C32—161no—
307C3⋊D3—162no—
308C24—21no—
309C24—181no—
310C24#63811yescharacteristic
311#41—32no—
312#41—32no—
313#41—31no—
314#41—31no—
315#41—31no—
316#41—61no—
317#41—61no—
318#41—61no—
319#41—62no—
320#41—62no—
321#41C3⋊S411yescharacteristic, complemented
322C2×Q8—31no—
323C2×Q8—31no—
324C2×Q8—61no—
325C2×D4—31no—
326C2×D4—31no—
327C2×D4—61no—
328C2×D4—61no—
329C2×D4—61no—
330C2×D4—61no—
331C2×D4—61no—
332C2×D4—92no—
333C2×D4—181no—
334C2×D4—181no—
335C2×D4—181no—
336C2×D4—181no—
337C2×D4—182no—
338C2×D4—182no—
339C2×D4—181no—
340C2×D4—362no—
341C2×D4—362no—
342C22×C4—21no—
343C22×C4—31no—
344C22×C4—31no—
345C22×C4—31no—
346C22×C4—31no—
347C22×C4—61no—
348C22×C4—61no—
349C22×C4—61no—
350C22×C4—61no—
351C22×C4—181no—
352C22×C4#63811yescharacteristic
353C22×C4C22×C3⋊D311yescharacteristic
354SD16—184no—
355SD16—182no—
356SD16—182no—
357D8—184no—
358D8—182no—
359D8—182no—
360M16—181no—
361M16—181no—
362M16—181no—
363M16—181no—
364C2×C8—92no—
365C2×C8—92no—
366C4⋊C4—92no—
367C4⋊C4—181no—
368C22⋊C4—182no—
369C22⋊C4—182no—
370C22×C3—21no—
371C22×C3—31no—
372C22×C3—31no—
373C22×C3—31no—
374C22×C3—43no—
375C22×C3—61no—
376C22×C3—61no—
377C22×C3—61no—
378C22×C3—61no—
379C22×C3—61no—
380C22×C3—83no—
381C22×C3—121no—
382C22×C3—121no—
383C22×C3—121no—
384C22×C3—121no—
385C22×C3#94911yescharacteristic, complemented
386C22×C3GL(2,ℤ/4)11yescharacteristic
387C2×D3—122no—
388C2×D3—122no—
389C2×D3—122no—
390C2×D3—246no—
391C2×D3—242no—
392C2×D3—242no—
393C2×D3—486no—
394A4#94913yescomplemented
395C3×C4—21no—
396C3×C4—31no—
397C3×C4—31no—
398C3×C4—43no—
399C3×C4—43no—
400C3×C4—61no—
401C3×C4—83no—
402C3×C4GL(2,ℤ/4)11yescharacteristic
403C3×C4C22×S411yescharacteristic
404Dic3—122no—
405C32—41noSylow
406C23—21no—
407C23—31no—
408C23—31no—
409C23—41no—
410C23—61no—
411C23—61no—
412C23—61no—
413C23—121no—
414C23—182no—
415C23—361no—
416C23—362no—
417C23—362no—
418C23—361no—
419C23C2×#63811yescharacteristic
420Q8—32no—
421Q8—31no—
422Q8—61no—
423Q8C2×C3⋊S411yescharacteristic, complemented
424D4—21no—
425D4—32no—
426D4—31no—
427D4—61no—
428D4—61no—
429D4—61no—
430D4—62no—
431D4—61no—
432D4—182no—
433D4—182no—
434D4—361no—
435D4—362no—
436D4—364no—
437D4—362no—
438D4—361no—
439D4C2×C3⋊S411yescharacteristic, complemented
440C2×C4—21no—
441C2×C4—31no—
442C2×C4—31no—
443C2×C4—31no—
444C2×C4—31no—
445C2×C4—31no—
446C2×C4—31no—
447C2×C4—31no—
448C2×C4—61no—
449C2×C4—61no—
450C2×C4—61no—
451C2×C4—61no—
452C2×C4—62no—
453C2×C4—61no—
454C2×C4—61no—
455C2×C4—182no—
456C2×C4—362no—
457C2×C4C2×C3⋊S411yescharacteristic
458C8—182no—
459C8—182no—
460C2×C3—21no—
461C2×C3—31no—
462C2×C3—31no—
463C2×C3—41no—
464C2×C3—43no—
465C2×C3—61no—
466C2×C3—83no—
467C2×C3—121no—
468C2×C3—163no—
469C2×C3C2×GL(2,ℤ/4)11yescharacteristic
470D3—242no—
471D3—486no—
472C22—21no—
473C22—31no—
474C22—31no—
475C22—31no—
476C22—61no—
477C22—61no—
478C22—61no—
479C22—61no—
480C22—61no—
481C22—121no—
482C22—121no—
483C22—121no—
484C22—121no—
485C22—362no—
486C22—362no—
487C22—362no—
488C22—722no—
489C22—722no—
490C22#6415811yescharacteristic, complemented
491C22#6426911yescharacteristic
492C4—21no—
493C4—31no—
494C4—31no—
495C4—61no—
496C4—362no—
497C4#6426911yescharacteristic
498C4C22×C3⋊S411yescharacteristic
499C3—43no—
500C3#8551311yescharacteristic, complemented
501C2—21no—
502C2—31no—
503C2—31no—
504C2—41no—
505C2—61no—
506C2—121no—
507C2—722no—
508C2C2×#6426911yescharacteristic
subgroupG/H
centerC2C2×#64269
commutator, cosocleC3×C4×A4C23
FrattiniC4C22×C3⋊S4
FittingC22×C3×#41D3
socleC23×C3C2×#67
hypercenter#41C3⋊S4
hypocenterC3×A4AGL(1,ℤ/8)
LCSG ▷ C3×C4×A4 ▷ C2×C3×A4 ▷ C3×A4
UCSC1 ◁ C2 ◁ C2×C4 ◁ #41

Complements

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

NH ≅ G/Ntype
1. C3×A4×#41C2semidirect
2. C2×C4⋊(C3⋊S4)C2semidirect
3. #10593651C2semidirect
4. #10593649C2semidirect
5. #10593643C2semidirect
9. C3×Q8×A4C22semidirect
11. C3×D4×A4C22semidirect
17. C3⋊(A4⋊C8)C22semidirect
18. C22×C3×#41D3semidirect
19. A4×#41D3semidirect
54. C22×C3×Q8C2×D3semidirect
56. C22×C3×D4C2×D3semidirect
61. Q8×A4C2×D3semidirect
63. D4×A4C2×D3semidirect
107. C22×#41C3⋊D3semidirect
136. C3×#41S4semidirect
196. C3×A4AGL(1,ℤ/8)semidirect
206. C22×Q8C2×C3⋊D3semidirect
210. C22×D4C2×C3⋊D3semidirect
260. C3×Q8C2×S4semidirect
271. C3×D4C2×S4semidirect
321. #41C3⋊S4semidirect
385. C22×C3#949semidirect
394. A4#949semidirect
423. Q8C2×C3⋊S4semidirect
439. D4C2×C3⋊S4semidirect
490. C22#64158semidirect
500. C3#85513semidirect

Maximal subgroups

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

subgroupindex
C3×A4×#412
C2×C4⋊(C3⋊S4)2
#105936512
#105936492
#105936432
#855133
#840823
#641584