Finite Group Databasebeta

← #11887712

Subgroups — #11887712

Order 1152.

1158 conjugacy classes of subgroups.

The subgroup lattice has 537 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596302C211yesmaximal, characteristic
2#10596000C211yesmaximal, characteristic, complemented
3C32×#416C211yesmaximal, characteristic, complemented
4#10592938C211yesmaximal, characteristic, complemented
5#10592815C211yesmaximal, characteristic, complemented
6C8×#638C211yesmaximal, characteristic, complemented
7#10592695C211yesmaximal, characteristic, complemented
8#10592508C211yesmaximal, characteristic, complemented
9C3⋊D3×#103C211yesmaximal, characteristic, complemented
10#10592495C211yesmaximal, characteristic, complemented
11#10592489C211yesmaximal, characteristic, complemented
12#10592477C211yesmaximal, characteristic, complemented
13#10592473C211yesmaximal, characteristic, complemented
14#10592467C211yesmaximal, characteristic, complemented
15#10592466C211yesmaximal, characteristic, complemented
16#78847—34nomaximal
17C2×C32×#41C2211yescharacteristic
18C2×Q8×C3⋊D3C2211yescharacteristic
19C22×C32×C8C2211yescharacteristic
20C32×#117C2211yescharacteristic
21Q8×C3⋊Dic3C2211yescharacteristic
22C2×#3756C2211yescharacteristic
23#64147—21no—
24#64147C2211yescharacteristic
25#64145—21no—
26#64145C2211yescharacteristic
27C2×#3754C2211yescharacteristic
28C4×#638—21no—
29C4×#638C2211yescharacteristic
30#64133—21no—
31#64133C2211yescharacteristic
32#64133C2211yescharacteristic
33C2×#3746C2211yescharacteristic
34C2×C8×C3⋊D3C2211yescharacteristic
35#64106C2211yescharacteristic
36C4⋊C4×C3⋊D3C2211yescharacteristic
37#64099C2211yescharacteristic
38#64096C2211yescharacteristic
39#64092—21no—
40#64088—21no—
41#64081—21no—
42#64079—21no—
43C32×#103C2211yescharacteristic
44C32×#103C2211yescharacteristic
45C32×#102C2211yescharacteristic
46C32×#102C2211yescharacteristic
47#63662C2211yescharacteristic
48#63659C2211yescharacteristic
49#63657C2211yescharacteristic
50#63647C2211yescharacteristic
51#63645C2211yescharacteristic
52#63643C2211yescharacteristic
53#63643C2211yescharacteristic
54#63641C2211yescharacteristic
55C8×C3⋊Dic3C2211yescharacteristic
56#63637C2211yescharacteristic
57#63637C2211yescharacteristic
58#63635C2211yescharacteristic
59#63634C2211yescharacteristic
60#5831—34no—
61#5529—34no—
62C3×#416D314yescomplemented
63#5239—34no—
64#5116—34no—
65C8×#67—34no—
66#4996—34no—
67#4809—34no—
68D3×#103—34no—
69#4796—34no—
70#4790—34no—
71#4778—34no—
72#4774—34no—
73#4768—34no—
74#4767—34no—
75C32×#41—22no—
76C32×#41—41no—
77C2×C32×Q8C2311yescharacteristic
78C2×C32×D4—21no—
79C2×C32×D4C2311yescharacteristic
80C22×C32×C4—21no—
81C22×C32×C4C2311yescharacteristic
82C2×#638—21no—
83C2×#638D411yescharacteristic
84Q8×C3⋊D3—22no—
85Q8×C3⋊D3—41no—
86C2×C4×C3⋊D3—21no—
87C2×C4×C3⋊D3—21no—
88C2×C4×C3⋊D3C2311yescharacteristic
89C2×#634—21no—
90C2×#634C2311yescharacteristic
91C2×#634C2311yescharacteristic
92C2×C32×C8—41no—
93C2×C32×C8C2311yescharacteristic
94C2×C32×C8C2311yescharacteristic
95C32×C4⋊C4C2311yescharacteristic
96C32×C4⋊C4C2311yescharacteristic
97C32×C22⋊C4—21no—
98C32×C42—21no—
99#3757—21no—
100#3757—21no—
101#3757—21no—
102#3757—21no—
103#3757—21no—
104#3757D411yescharacteristic
105#3756—22no—
106#3754—41no—
107#3752—21no—
108#3752D411yescharacteristic
109C4⋊(C3⋊Dic3)—21no—
110C4⋊(C3⋊Dic3)—21no—
111C4⋊(C3⋊Dic3)—21no—
112C4⋊(C3⋊Dic3)C2311yescharacteristic
113C4⋊(C3⋊Dic3)C2311yescharacteristic
114#3750—21no—
115#3750—21no—
116#3750—21no—
117#3750—21no—
118#3750—21no—
119#3750D411yescharacteristic
120C4×C3⋊Dic3—21no—
121C4×C3⋊Dic3—21no—
122C4×C3⋊Dic3C2311yescharacteristic
123C2×C3⋊(C3⋊C8)C2311yescharacteristic
124C2×C3⋊(C3⋊C8)C2311yescharacteristic
125#3746—41no—
126C8×C3⋊D3—41no—
127#3300—91noSylow
128C2×C3×#41C2×D314yes—
129C2×D3×Q8—34no—
130C22×C3×C8C2×D314yes—
131C3×#117C2×D314yes—
132Q8×Dic3—34no—
133C2×#216—34no—
134#938—34no—
135#938—64no—
136#936—34no—
137#936—64no—
138C2×#214—34no—
139C4×#67—34no—
140C4×#67—64no—
141#924—34no—
142#924—34no—
143#924—64no—
144C2×Dic12—34no—
145C2×D3×C8—34no—
146#897—34no—
147D3×C4⋊C4—34no—
148#890—34no—
149#887—34no—
150#883—64no—
151#879—64no—
152#872—64no—
153#870—64no—
154C3×#103C2×D314yes—
155C3×#103C2×D314yes—
156C3×#102C2×D314yes—
157C3×#102C2×D314yes—
158#835—34no—
159#832—34no—
160#830—34no—
161(C2×D3)⋊C8—34no—
162#818—34no—
163#816—34no—
164#816—34no—
165Dic3⋊C8—34no—
166C8×Dic3—34no—
167#810—34no—
168#810—34no—
169#808—34no—
170#807—34no—
171C23×C32—21no—
172C23×C32C2×D411yescharacteristic
173C22×C3⋊D3C2×D411yescharacteristic
174C32×Q8—21no—
175C32×Q8#4112yes—
176C32×D4—21no—
177C32×D4—21no—
178C32×D4—42no—
179C2×C32×C4—21no—
180C2×C32×C4—21no—
181C2×C32×C4—21no—
182C2×C32×C4—21no—
183C2×C32×C4—21no—
184C2×C32×C4—42no—
185C2×C32×C4C2×D411yescharacteristic
186C2×C32×C4C2411yescharacteristic
187#638—22no—
188#638—42no—
189C2×C3⋊Dic3—21no—
190C2×C3⋊Dic3—21no—
191C2×C3⋊Dic3—21no—
192C2×C3⋊Dic3—21no—
193C2×C3⋊Dic3C2×D411yescharacteristic
194C2×C3⋊Dic3C2×D411yescharacteristic
195C2×C3⋊Dic3C2×D411yescharacteristic
196C4×C3⋊D3—21no—
197C4×C3⋊D3—21no—
198C4×C3⋊D3—42no—
199C4×C3⋊D3—42no—
200#634—21no—
201#634—21no—
202#634—21no—
203#634—21no—
204#634—42no—
205C32×C8—21no—
206C32×C8—21no—
207C3⋊(C3⋊C8)—21no—
208C3⋊(C3⋊C8)—21no—
209#552—91no—
210#548—91no—
211#488—91no—
212#485—91no—
213#480—91no—
214#479—91no—
215#467—91no—
216#465—91no—
217#464—91no—
218#452—91no—
219#451—91no—
220C4×Q16—91no—
221C8×D4—91no—
222#416C3⋊D311yescharacteristic, complemented
223C2×#103—91no—
224C3×#41—28no—
225C3×#41—44no—
226C2×C3×Q8C22×D314yes—
227C2×C3×D4—24no—
228C2×C3×D4C22×D314yes—
229C22×C3×C4—24no—
230C22×C3×C4C22×D314yes—
231C2×#67—34no—
232C2×#67—64no—
233D3×Q8—68no—
234D3×Q8—124no—
235C2×C4×D3—34no—
236C2×C4×D3—64no—
237C2×C4×D3—64no—
238C2×Dic6—34no—
239C2×Dic6—34no—
240C2×Dic6—64no—
241C2×C3×C8—44no—
242C2×C3×C8C22×D314yes—
243C2×C3×C8C22×D314yes—
244C3×C4⋊C4C22×D314yes—
245C3×C4⋊C4C22×D314yes—
246C3×C22⋊C4—24no—
247C3×C42—24no—
248#217—34no—
249#217—64no—
250#217—64no—
251#217—64no—
252#217—64no—
253#217—64no—
254#216—68no—
255#214—124no—
256(C2×D3)⋊C4—34no—
257(C2×D3)⋊C4—64no—
258C4⋊Dic3—34no—
259C4⋊Dic3—34no—
260C4⋊Dic3—64no—
261C4⋊Dic3—64no—
262C4⋊Dic3—64no—
263Dic3⋊C4—34no—
264Dic3⋊C4—64no—
265Dic3⋊C4—64no—
266Dic3⋊C4—64no—
267Dic3⋊C4—64no—
268Dic3⋊C4—64no—
269C4×Dic3—34no—
270C4×Dic3—64no—
271C4×Dic3—64no—
272C2×C3⋊C8—34no—
273C2×C3⋊C8—34no—
274Dic12—124no—
275D3×C8—124no—
276C22×C32—21no—
277C22×C32—21no—
278C22×C32—21no—
279C22×C32—41no—
280C22×C32—41no—
281C22×C32—41no—
282C22×C32C22×D411yescharacteristic
283C2×C3⋊D3—21no—
284C2×C3⋊D3—21no—
285C2×C3⋊D3#13512yes—
286C32×C4—22no—
287C32×C4—21no—
288C32×C4—41no—
289C32×C4—41no—
290C32×C4C2×#4111yescharacteristic
291C32×C4H(5,𝔽2)11yescharacteristic
292C3⋊Dic3—21no—
293C3⋊Dic3—21no—
294C3⋊Dic3—21no—
295C3⋊Dic3—41no—
296C3⋊Dic3—41no—
297C3⋊Dic3—41no—
298C3⋊Dic3—41no—
299C2×#41C2×C3⋊D311yescharacteristic
300C22×Q8—91no—
301C2×Q16—91no—
302C2×Q16—91no—
303C2×SD16—91no—
304C22×C8—91no—
305C22×C8C2×C3⋊D311yescharacteristic
306#126—181no—
307#125—91no—
308#125—181no—
309#124—91no—
310#124—181no—
311#123—181no—
312C22⋊Q8—91no—
313C22⋊Q8—91no—
314C22⋊Q8—91no—
315C22⋊Q8—181no—
316#121—91no—
317#121—181no—
318C4×Q8—91no—
319C4×Q8—91no—
320C4×D4—91no—
321C4×D4—181no—
322#117—181no—
323#117C2×C3⋊D311yescharacteristic
324C2×C4⋊C4—91no—
325#107—91no—
326#107—91no—
327#106—91no—
328C4⋊C8—91no—
329#103—91no—
330#103—91no—
331#103—91no—
332#103—91no—
333#103—91no—
334#103C2×C3⋊D311yescharacteristic
335#103C2×C3⋊D311yescharacteristic
336#102—91no—
337#102C2×C3⋊D311yescharacteristic
338#102C2×C3⋊D311yescharacteristic
339C22⋊C8—91no—
340C22⋊C8—91no—
341C4×C8—91no—
342C23×C3—24no—
343C23×C3D3×D414yes—
344C22×D3—34no—
345C3×Q8—24no—
346C3×Q8#23518yes—
347C3×D4—24no—
348C3×D4—24no—
349C3×D4—48no—
350C2×C3×C4—24no—
351C2×C3×C4—24no—
352C2×C3×C4—24no—
353C2×C3×C4—24no—
354C2×C3×C4—24no—
355C2×C3×C4—48no—
356C2×C3×C4D3×D414yes—
357C2×C3×C4C23×D314yes—
358#67—68no—
359#67—128no—
360C2×Dic3—34no—
361C2×Dic3—34no—
362C2×Dic3—34no—
363C2×Dic3—64no—
364C2×Dic3—64no—
365C2×Dic3—64no—
366C2×Dic3—64no—
367C4×D3—64no—
368C4×D3—64no—
369C4×D3—128no—
370C4×D3—128no—
371Dic6—64no—
372Dic6—64no—
373Dic6—64no—
374Dic6—64no—
375Dic6—128no—
376C3×C8—24no—
377C3×C8—24no—
378C3⋊C8—64no—
379C3⋊C8—64no—
380C2×C32—41no—
381C2×C32—81no—
382C2×C32#54611yescharacteristic
383C2×C32C2×#13511yescharacteristic
384C2×C32#57811yescharacteristic
385C3⋊D3—22no—
386#41—22no—
387#41—41no—
388C2×Q8—91no—
389C2×Q8—91no—
390C2×Q8—181no—
391C2×Q8—182no—
392C2×Q8—361no—
393C2×Q8C22×C3⋊D311yescharacteristic
394C2×D4—21no—
395C2×D4—91no—
396C2×D4—181no—
397C2×D4C22×C3⋊D311yescharacteristic
398C22×C4—21no—
399C22×C4—91no—
400C22×C4—181no—
401C22×C4—181no—
402C22×C4C22×C3⋊D311yescharacteristic
403Q16—182no—
404Q16—361no—
405SD16—361no—
406C2×C8—41no—
407C2×C8—91no—
408C2×C8—91no—
409C2×C8—361no—
410C2×C8C22×C3⋊D311yescharacteristic
411C2×C8C22×C3⋊D311yescharacteristic
412C4⋊C4—91no—
413C4⋊C4—91no—
414C4⋊C4—91no—
415C4⋊C4—181no—
416C4⋊C4—181no—
417C4⋊C4—181no—
418C4⋊C4—181no—
419C4⋊C4—181no—
420C4⋊C4—181no—
421C4⋊C4—181no—
422C4⋊C4—181no—
423C4⋊C4C22×C3⋊D311yescharacteristic
424C4⋊C4C22×C3⋊D311yescharacteristic
425C22⋊C4—21no—
426C22⋊C4—91no—
427C22⋊C4—91no—
428C22⋊C4—181no—
429C22⋊C4—181no—
430C22⋊C4—181no—
431C22⋊C4—181no—
432C22⋊C4—181no—
433C22⋊C4—181no—
434C42—21no—
435C42—91no—
436C42—181no—
437C42—181no—
438C22×C3—24no—
439C22×C3—24no—
440C22×C3—24no—
441C22×C3—44no—
442C22×C3—44no—
443C22×C3—44no—
444C22×C3C2×D3×D414yes—
445C2×D3—38no—
446C2×D3—64no—
447C2×D3—64no—
448C3×C4—28no—
449C3×C4—24no—
450C3×C4—44no—
451C3×C4—44no—
452C3×C4C2×#23514yes—
453C3×C4#100414yes—
454Dic3—64no—
455Dic3—64no—
456Dic3—64no—
457Dic3—124no—
458Dic3—124no—
459Dic3—124no—
460Dic3—124no—
461C32#330011yescharacteristic, complemented, Sylow
462C23—21no—
463C23—91no—
464C23D4×C3⋊D311yescharacteristic
465Q8—21no—
466Q8—181no—
467Q8—181no—
468Q8—181no—
469Q8—181no—
470Q8—362no—
471Q8#382812yes—
472D4—21no—
473D4—21no—
474D4—42no—
475D4—182no—
476D4—362no—
477C2×C4—21no—
478C2×C4—21no—
479C2×C4—21no—
480C2×C4—21no—
481C2×C4—21no—
482C2×C4—42no—
483C2×C4—91no—
484C2×C4—91no—
485C2×C4—91no—
486C2×C4—181no—
487C2×C4—181no—
488C2×C4—181no—
489C2×C4—181no—
490C2×C4—181no—
491C2×C4—181no—
492C2×C4—362no—
493C2×C4—362no—
494C2×C4D4×C3⋊D311yescharacteristic
495C2×C4C23×C3⋊D311yescharacteristic
496C8—21no—
497C8—21no—
498C8—181no—
499C8—181no—
500C2×C3—44no—
501C2×C3—84no—
502C2×C3#549014yes—
503C2×C3D3×#13514yes—
504C2×C3#577114yes—
505D3—68no—
506C22—21no—
507C22—21no—
508C22—21no—
509C22—41no—
510C22—41no—
511C22—41no—
512C22—92no—
513C22—181no—
514C22—181no—
515C22C2×D4×C3⋊D311yescharacteristic
516C4—21no—
517C4—22no—
518C4—41no—
519C4—41no—
520C4—181no—
521C4—181no—
522C4—181no—
523C4—361no—
524C4—361no—
525C4—361no—
526C4—361no—
527C4C2×#382811yescharacteristic
528C4#6436111yescharacteristic
529C3#7884714yescomplemented
530C2—41no—
531C2—81no—
532C2—182no—
533C2#1059596111yescharacteristic
534C2C3⋊D3×#13511yescharacteristic
535C2#1059624211yescharacteristic
subgroupG/H
centerC22C2×D4×C3⋊D3
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C23×C3⋊D3
FittingC32×#416C2
socleC22×C32C22×D4
prime radical#10596302C2
hypercenter#416C3⋊D3
hypocenterC32#3300
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ #416

Complements

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

NH ≅ G/Ntype
2. #10596000C2semidirect
3. C32×#416C2semidirect
4. #10592938C2semidirect
5. #10592815C2semidirect
6. C8×#638C2semidirect
7. #10592695C2semidirect
8. #10592508C2semidirect
9. C3⋊D3×#103C2semidirect
10. #10592495C2semidirect
11. #10592489C2semidirect
12. #10592477C2semidirect
13. #10592473C2semidirect
14. #10592467C2semidirect
15. #10592466C2semidirect
62. C3×#416D3semidirect
222. #416C3⋊D3semidirect
461. C32#3300semidirect
529. C3#78847semidirect

Maximal subgroups

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

subgroupindex
#105963022
#105960002
C32×#4162
#105929382
#105928152
C8×#6382
#105926952
#105925082
C3⋊D3×#1032
#105924952
#105924892
#105924772
#105924732
#105924672
#105924662
#788473