Finite Group Databasebeta

← #11870843

Subgroups — #11870843

Order 1152.

1362 conjugacy classes of subgroups.

The subgroup lattice has 555 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596028C211yesmaximal, characteristic, complemented
2C4×D4×C3⋊D3C211yesmaximal, characteristic, complemented
3C32×C4×D8C211yesmaximal, characteristic, complemented
4#10592855C211yesmaximal, characteristic
5#10592852C211yesmaximal, characteristic, complemented
6C4×#3754C211yesmaximal, characteristic, complemented
7C4×#3753C211yesmaximal, characteristic, complemented
8#10592590C211yesmaximal, characteristic, complemented
9#10592583C211yesmaximal, characteristic, complemented
10#10592486C211yesmaximal, characteristic, complemented
11#10592476C211yesmaximal, characteristic, complemented
12#10592475C211yesmaximal, characteristic, complemented
13#10592462C211yesmaximal, characteristic, complemented
14C4×#3744C211yesmaximal, characteristic, complemented
15#10592384C211yesmaximal, characteristic, complemented
16#79592—34nomaximal
17C2×D4×C3⋊D3C2211yescharacteristic
18C22×C4×C3⋊D3—21no—
19C2×C32×D8C2211yescharacteristic
20C32×C4×D4C2211yescharacteristic
21C32×C4×D4C2211yescharacteristic, complemented
22#64147C2211yescharacteristic
23#64145C2211yescharacteristic, complemented
24D4×C3⋊Dic3C2211yescharacteristic
25C2×#3754C2211yescharacteristic
26C2×#3753C2211yescharacteristic
27C4×#638—21no—
28C4×#638—21no—
29#64135—21no—
30C2×#3744C2211yescharacteristic
31#64106C2211yescharacteristic
32#64102C2211yescharacteristic
33C4⋊C4×C3⋊D3C2211yescharacteristic
34#64099C2211yescharacteristic, complemented
35#64092—21no—
36#64090—21no—
37C22⋊C4×C3⋊D3—21no—
38#64088—21no—
39C4×C4⋊(C3⋊D3)C2211yescharacteristic
40C42×C3⋊D3C2211yescharacteristic
41C4×#634C2211yescharacteristic, complemented
42C32×#107C2211yescharacteristic, complemented
43C32×#102C2211yescharacteristic
44C32×#102C2211yescharacteristic, complemented
45C32×C4×C8C2211yescharacteristic, complemented
46#63659C2211yescharacteristic
47#63659C2211yescharacteristic, complemented
48#63648C2211yescharacteristic
49#63647C2211yescharacteristic
50#63647C2211yescharacteristic
51#63644C2211yescharacteristic, complemented
52#63643C2211yescharacteristic, complemented
53#63641C2211yescharacteristic, complemented
54#63641C2211yescharacteristic, complemented
55#63637C2211yescharacteristic, complemented
56#63636C2211yescharacteristic
57#63635C2211yescharacteristic, complemented
58#63634C2211yescharacteristic, complemented
59C4×C3⋊(C3⋊C8)C2211yescharacteristic, complemented
60#5557—34no—
61C4×D3×D4—34no—
62C3×C4×D8D314yescomplemented
63#5156—34no—
64#5153—34no—
65C4×#214—34no—
66C4×#213—34no—
67#4891—34no—
68#4884—34no—
69#4787—34no—
70#4777—34no—
71#4776—34no—
72#4763—34no—
73C4×#204—34no—
74#4685—34no—
75C23×C3⋊D3—21no—
76C2×C32×D4C2311yescharacteristic
77C2×C32×D4C2311yescharacteristic
78C22×C32×C4—21no—
79C22×C32×C4—21no—
80C2×#638—21no—
81C2×#638—21no—
82C22×C3⋊Dic3—21no—
83D4×C3⋊D3—22no—
84D4×C3⋊D3—22no—
85C2×C4⋊(C3⋊D3)C2311yescharacteristic
86C2×C4×C3⋊D3—21no—
87C2×C4×C3⋊D3—21no—
88C2×C4×C3⋊D3—21no—
89C2×C4×C3⋊D3—44no—
90C2×C4×C3⋊D3D411yescharacteristic
91C2×C4×C3⋊D3D411yescharacteristic
92C2×C4×C3⋊D3C2311yescharacteristic
93C2×#634C2311yescharacteristic
94C32×D8—22no—
95C2×C32×C8C2311yescharacteristic
96C2×C32×C8C2311yescharacteristic
97C32×C4⋊C4C2311yescharacteristic
98C32×C4⋊C4C2311yescharacteristic
99C32×C22⋊C4—21no—
100C32×C22⋊C4—21no—
101C32×C42C2311yescharacteristic
102#3757—21no—
103#3757—21no—
104#3757—21no—
105#3757—21no—
106#3754—22no—
107#3753—22no—
108#3752—21no—
109#3752—21no—
110#3752—21no—
111C4⋊(C3⋊Dic3)—21no—
112C4⋊(C3⋊Dic3)—21no—
113C4⋊(C3⋊Dic3)C2311yescharacteristic
114C4⋊(C3⋊Dic3)C2311yescharacteristic
115#3750—21no—
116#3750—21no—
117#3750—21no—
118C4×C3⋊Dic3—21no—
119C4×C3⋊Dic3D411yescharacteristic
120C4×C3⋊Dic3D411yescharacteristic
121C4×C3⋊Dic3C2311yescharacteristic
122C2×C3⋊(C3⋊C8)C2311yescharacteristic
123C2×C3⋊(C3⋊C8)C2311yescharacteristic
124#3744—22no—
125#3105—91noSylow
126C2×D3×D4—34no—
127C22×C4×D3—64no—
128C2×C3×D8C2×D314yes—
129C3×C4×D4C2×D314yes—
130C3×C4×D4C2×D314yescomplemented
131#938—34no—
132#936—34no—
133D4×Dic3—34no—
134C2×#214—34no—
135C2×#213—34no—
136C4×#67—64no—
137C4×#67—64no—
138#926—64no—
139C2×#204—34no—
140#897—34no—
141#893—34no—
142D3×C4⋊C4—34no—
143#890—34no—
144#883—64no—
145#67⋊C4—64no—
146D3×C22⋊C4—64no—
147#879—64no—
148C4×D12—34no—
149C42×D3—34no—
150C4×Dic6—34no—
151C3×#107C2×D314yescomplemented
152C3×#102C2×D314yes—
153C3×#102C2×D314yescomplemented
154C3×C4×C8C2×D314yescomplemented
155#832—34no—
156#832—34no—
157#821—34no—
158(C2×D3)⋊C8—34no—
159(C2×D3)⋊C8—34no—
160#817—34no—
161#816—34no—
162Dic3⋊C8—34no—
163Dic3⋊C8—34no—
164#810—34no—
165#809—34no—
166#808—34no—
167#807—34no—
168C4×C3⋊C8—34no—
169C23×C32—21no—
170C23×C32—21no—
171C22×C3⋊D3—24no—
172C22×C3⋊D3—21no—
173C22×C3⋊D3—42no—
174C22×C3⋊D3—42no—
175C22×C3⋊D3C2×D411yescharacteristic
176C32×D4—21no—
177C32×D4—21no—
178C32×D4—21no—
179C32×D4#4112yes—
180C2×C32×C4—21no—
181C2×C32×C4—21no—
182C2×C32×C4—42no—
183C2×C32×C4—42no—
184C2×C32×C4C2×D411yescharacteristic
185C2×C32×C4C2×D411yescharacteristic
186C2×C32×C4C2411yescharacteristic
187#638—24no—
188#638—42no—
189C2×C3⋊Dic3—21no—
190C2×C3⋊Dic3—21no—
191C2×C3⋊Dic3—21no—
192C2×C3⋊Dic3—42no—
193C2×C3⋊Dic3C2×D411yescharacteristic
194C2×C3⋊Dic3C2×D411yescharacteristic
195C2×C3⋊Dic3C2×D411yescharacteristic
196C4⋊(C3⋊D3)—21no—
197C4⋊(C3⋊D3)#4112yes—
198C4×C3⋊D3—22no—
199C4×C3⋊D3—22no—
200C4×C3⋊D3—21no—
201C4×C3⋊D3—21no—
202C4×C3⋊D3—42no—
203C4×C3⋊D3—42no—
204C4×C3⋊D3—42no—
205#634—21no—
206#634—21no—
207C32×C8—21no—
208C32×C8—21no—
209C3⋊(C3⋊C8)—21no—
210C3⋊(C3⋊C8)—21no—
211#529—91no—
212C2×C4×D4—91no—
213#484—91no—
214#481—91no—
215#478—91no—
216#478—91no—
217#463—91no—
218#463—91no—
219#450—91no—
220#447—91no—
221C4×SD16—91no—
222C4×SD16—91no—
223C4×D8—91no—
224C4×D8C3⋊D311yescharacteristic, complemented
225#431—91no—
226C23×D3—64no—
227C2×C3×D4C22×D314yes—
228C2×C3×D4C22×D314yes—
229C22×C3×C4—24no—
230C22×C3×C4—24no—
231C2×#67—64no—
232C2×#67—64no—
233C22×Dic3—64no—
234D3×D4—68no—
235D3×D4—68no—
236C2×D12—34no—
237C2×C4×D3—34no—
238C2×C4×D3—34no—
239C2×C4×D3—34no—
240C2×C4×D3—64no—
241C2×C4×D3—64no—
242C2×C4×D3—64no—
243C2×C4×D3—1216no—
244C2×Dic6—34no—
245C3×D8—28no—
246C2×C3×C8C22×D314yes—
247C2×C3×C8C22×D314yes—
248C3×C4⋊C4C22×D314yes—
249C3×C4⋊C4C22×D314yes—
250C3×C22⋊C4—24no—
251C3×C22⋊C4—24no—
252C3×C42C22×D314yes—
253#217—64no—
254#217—64no—
255#217—64no—
256#217—64no—
257#214—68no—
258#213—68no—
259(C2×D3)⋊C4—64no—
260(C2×D3)⋊C4—64no—
261(C2×D3)⋊C4—64no—
262C4⋊Dic3—34no—
263C4⋊Dic3—34no—
264C4⋊Dic3—64no—
265C4⋊Dic3—64no—
266Dic3⋊C4—64no—
267Dic3⋊C4—64no—
268Dic3⋊C4—64no—
269C4×Dic3—34no—
270C4×Dic3—34no—
271C4×Dic3—34no—
272C4×Dic3—64no—
273C2×C3⋊C8—34no—
274C2×C3⋊C8—34no—
275#204—68no—
276C22×C32—22no—
277C22×C32—41no—
278C22×C32—41no—
279C22×C32—41no—
280C22×C32—41no—
281C22×C32—41no—
282C22×C32C22×D411yescharacteristic
283C2×C3⋊D3—21no—
284C2×C3⋊D3—21no—
285C2×C3⋊D3—22no—
286C2×C3⋊D3—48no—
287C2×C3⋊D3—41no—
288C2×C3⋊D3—41no—
289C2×C3⋊D3#13512yes—
290C32×C4—21no—
291C32×C4—41no—
292C32×C4—41no—
293C32×C4AGL(1,ℤ/8)12yes—
294C32×C4C2×#4111yescharacteristic
295C32×C4C2×#4111yescharacteristic
296C3⋊Dic3—21no—
297C3⋊Dic3—21no—
298C3⋊Dic3—21no—
299C3⋊Dic3—41no—
300C3⋊Dic3—41no—
301C3⋊Dic3—41no—
302C22×D4—91no—
303C23×C4—181no—
304C2×SD16—91no—
305C2×SD16—91no—
306C2×D8—91no—
307C2×D8C2×C3⋊D311yescharacteristic
308#126—181no—
309#125—91no—
310#124—91no—
311#123—181no—
312C22⋊Q8—91no—
313#121—91no—
314C4×Q8—91no—
315C4×D4—91no—
316C4×D4—91no—
317C4×D4—91no—
318C4×D4—181no—
319C4×D4—181no—
320C4×D4—181no—
321C4×D4C2×C3⋊D311yescharacteristic
322C4×D4C2×C3⋊D311yescharacteristic, complemented
323#117—181no—
324C2×C4⋊C4—91no—
325C2×C22⋊C4—181no—
326C2×C42—91no—
327#107—91no—
328#107C2×C3⋊D311yescharacteristic, complemented
329#106—91no—
330#106—91no—
331C4⋊C8—91no—
332C4⋊C8—91no—
333#103—91no—
334#103—91no—
335#102—91no—
336#102—91no—
337#102—91no—
338#102—91no—
339#102C2×C3⋊D311yescharacteristic
340#102C2×C3⋊D311yescharacteristic, complemented
341C22⋊C8—91no—
342C22⋊C8—91no—
343C4×C8—91no—
344C4×C8C2×C3⋊D311yescharacteristic, complemented
345C23×C3—24no—
346C23×C3—24no—
347C22×D3—34no—
348C22×D3—616no—
349C22×D3—64no—
350C22×D3—128no—
351C22×D3—128no—
352C3×D4—24no—
353C3×D4—24no—
354C3×D4—24no—
355C3×D4#23518yes—
356C2×C3×C4—24no—
357C2×C3×C4—24no—
358C2×C3×C4—48no—
359C2×C3×C4—48no—
360C2×C3×C4D3×D414yes—
361C2×C3×C4D3×D414yes—
362C2×C3×C4C23×D314yes—
363#67—616no—
364#67—128no—
365C2×Dic3—34no—
366C2×Dic3—34no—
367C2×Dic3—34no—
368C2×Dic3—64no—
369C2×Dic3—64no—
370C2×Dic3—64no—
371C2×Dic3—128no—
372D12—38no—
373D12—64no—
374C4×D3—68no—
375C4×D3—68no—
376C4×D3—64no—
377C4×D3—64no—
378C4×D3—128no—
379C4×D3—128no—
380C4×D3—128no—
381Dic6—64no—
382Dic6—64no—
383C3×C8—24no—
384C3×C8—24no—
385C3⋊C8—64no—
386C3⋊C8—64no—
387C2×C32—42no—
388C2×C32—81no—
389C2×C32#52511yescharacteristic
390C2×C32C2×#13511yescharacteristic
391C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
392C3⋊D3—22no—
393C3⋊D3—42no—
394C24—181no—
395C2×Q8—91no—
396C2×D4—91no—
397C2×D4—181no—
398C2×D4—182no—
399C2×D4—182no—
400C2×D4—181no—
401C2×D4C22×C3⋊D311yescharacteristic
402C2×D4C22×C3⋊D311yescharacteristic
403C22×C4—21no—
404C22×C4—21no—
405C22×C4—91no—
406C22×C4—91no—
407C22×C4—91no—
408C22×C4—181no—
409C22×C4—181no—
410C22×C4—181no—
411C22×C4—181no—
412C22×C4—364no—
413SD16—182no—
414SD16—182no—
415D8—22no—
416D8—182no—
417C2×C8—91no—
418C2×C8—91no—
419C2×C8C22×C3⋊D311yescharacteristic
420C2×C8C22×C3⋊D311yescharacteristic
421C4⋊C4—91no—
422C4⋊C4—91no—
423C4⋊C4—181no—
424C4⋊C4—181no—
425C4⋊C4—181no—
426C4⋊C4—181no—
427C4⋊C4—181no—
428C4⋊C4C22×C3⋊D311yescharacteristic
429C4⋊C4C22×C3⋊D311yescharacteristic
430C22⋊C4—21no—
431C22⋊C4—21no—
432C22⋊C4—181no—
433C22⋊C4—181no—
434C22⋊C4—181no—
435C22⋊C4—181no—
436C22⋊C4—181no—
437C22⋊C4—181no—
438C22⋊C4—181no—
439C42—91no—
440C42—91no—
441C42—91no—
442C42—181no—
443C42C22×C3⋊D311yescharacteristic
444C22×C3—28no—
445C22×C3—44no—
446C22×C3—44no—
447C22×C3—44no—
448C22×C3—44no—
449C22×C3—44no—
450C22×C3C2×D3×D414yes—
451C2×D3—38no—
452C2×D3—64no—
453C2×D3—64no—
454C2×D3—68no—
455C2×D3—1232no—
456C2×D3—124no—
457C2×D3—124no—
458C3×C4—24no—
459C3×C4—44no—
460C3×C4—44no—
461C3×C4#91118yes—
462C3×C4C2×#23514yes—
463C3×C4D3×#4114yes—
464Dic3—64no—
465Dic3—64no—
466Dic3—64no—
467Dic3—124no—
468Dic3—124no—
469Dic3—124no—
470C32#310511yescharacteristic, complemented, Sylow
471C23—21no—
472C23—21no—
473C23—91no—
474C23—184no—
475C23—181no—
476C23—362no—
477C23—362no—
478Q8—181no—
479Q8—181no—
480D4—21no—
481D4—21no—
482D4—21no—
483D4—92no—
484D4—184no—
485D4—181no—
486D4—362no—
487D4#382812yes—
488C2×C4—21no—
489C2×C4—21no—
490C2×C4—42no—
491C2×C4—42no—
492C2×C4—91no—
493C2×C4—91no—
494C2×C4—91no—
495C2×C4—182no—
496C2×C4—181no—
497C2×C4—181no—
498C2×C4—182no—
499C2×C4—181no—
500C2×C4—181no—
501C2×C4—181no—
502C2×C4—362no—
503C2×C4—362no—
504C2×C4—362no—
505C2×C4—362no—
506C2×C4D4×C3⋊D311yescharacteristic
507C2×C4D4×C3⋊D311yescharacteristic
508C2×C4C23×C3⋊D311yescharacteristic
509C8—21no—
510C8—21no—
511C8—181no—
512C8—181no—
513C2×C3—48no—
514C2×C3—84no—
515C2×C3#554714yes—
516C2×C3C2×#91114yes—
517C2×C3D3×#13514yes—
518D3—68no—
519D3—128no—
520C22—22no—
521C22—41no—
522C22—41no—
523C22—41no—
524C22—41no—
525C22—41no—
526C22—92no—
527C22—181no—
528C22—181no—
529C22—182no—
530C22—368no—
531C22—361no—
532C22—361no—
533C22C2×D4×C3⋊D311yescharacteristic
534C4—21no—
535C4—41no—
536C4—41no—
537C4—181no—
538C4—181no—
539C4—181no—
540C4—361no—
541C4—361no—
542C4—361no—
543C4#6412012yes—
544C4C2×#382811yescharacteristic
545C4#41×C3⋊D311yescharacteristic
546C3#7959214yescomplemented
547C2—42no—
548C2—81no—
549C2—182no—
550C2—362no—
551C2#1059601811yescharacteristic
552C2C2×#6412011yescharacteristic
553C2C3⋊D3×#13511yescharacteristic
subgroupG/H
centerC2×C4D4×C3⋊D3
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C23×C3⋊D3
FittingC32×C4×D8C2
socleC22×C32C22×D4
prime radical#10592855C2
hypercenterC4×D8C3⋊D3
hypocenterC32#3105
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C42 ◁ C4×D8

Complements

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

NH ≅ G/Ntype
1. #10596028C2semidirect
2. C4×D4×C3⋊D3C2semidirect
3. C32×C4×D8C2semidirect
5. #10592852C2semidirect
6. C4×#3754C2semidirect
7. C4×#3753C2semidirect
8. #10592590C2semidirect
9. #10592583C2semidirect
10. #10592486C2semidirect
11. #10592476C2semidirect
12. #10592475C2semidirect
13. #10592462C2semidirect
14. C4×#3744C2semidirect
15. #10592384C2semidirect
21. C32×C4×D4C22semidirect
23. #64145C22semidirect
34. #64099C22semidirect
41. C4×#634C22semidirect
42. C32×#107C22semidirect
44. C32×#102C22semidirect
45. C32×C4×C8C22semidirect
47. #63659C22semidirect
51. #63644C22semidirect
52. #63643C22semidirect
53. #63641C22semidirect
54. #63641C22semidirect
55. #63637C22semidirect
57. #63635C22semidirect
58. #63634C22semidirect
59. C4×C3⋊(C3⋊C8)C22semidirect
62. C3×C4×D8D3semidirect
130. C3×C4×D4C2×D3semidirect
151. C3×#107C2×D3semidirect
153. C3×#102C2×D3semidirect
154. C3×C4×C8C2×D3semidirect
224. C4×D8C3⋊D3semidirect
322. C4×D4C2×C3⋊D3semidirect
328. #107C2×C3⋊D3semidirect
340. #102C2×C3⋊D3semidirect
344. C4×C8C2×C3⋊D3semidirect
470. C32#3105semidirect
546. C3#79592semidirect

Maximal subgroups

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

subgroupindex
#105960282
C4×D4×C3⋊D32
C32×C4×D82
#105928552
#105928522
C4×#37542
C4×#37532
#105925902
#105925832
#105924862
#105924762
#105924752
#105924622
C4×#37442
#105923842
#795923