Finite Group Databasebeta

← #11885762

Subgroups — #11885762

Order 1152.

1321 conjugacy classes of subgroups; only the 174 normal subgroups are shown.

normal subgroups only

This group has 1321 conjugacy classes of subgroups — too many to draw. Only its 174 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
1#10595288C212yesmaximal, complemented
2C2×D3×#213C212yesmaximal, complemented
3#10592850C211yesmaximal, characteristic, complemented
4C3×#5156C212yesmaximal, complemented
5#10591449C212yesmaximal, complemented
6#10591433C212yesmaximal, complemented
7#10590947C212yesmaximal, complemented
8#10590740C211yesmaximal, characteristic, complemented
9#10590718C211yesmaximal, characteristic, complemented
10#80024—32nomaximal
11C2×C3×D3×D4C2212yescomplemented
12C2×D3×#67—22no—
13C2×D3×D12C2212yescomplemented
14C2×C32×D8C2211yescharacteristic, complemented
15#64149C2212yescomplemented
16C2×#3753C2212yescomplemented
17C2×#3745C2211yescharacteristic, complemented
18C3×#938C2212yescomplemented
19C2×C3×#213C2212yescomplemented
20#63983—22no—
21#63977—22no—
22#63971—22no—
23D3×#213—28no—
24#63909C2212yescomplemented
25C4×#625C2211yescharacteristic
26#63898C2212yescomplemented
27C2×#3714C2212yescomplemented
28C2×#3713C2211yescharacteristic
29C2×D3×C3⋊C8C2212yescomplemented
30C8×C3⋊Dic3C2211yescharacteristic, complemented
31C3×#832C2212yescomplemented
32C3×#821C2212yescomplemented
33C3×(C2×D3)⋊C8C2212yescomplemented
34#63576C2211yescharacteristic, complemented
35#63572C2211yescharacteristic, complemented
36#63564C2212yescomplemented
37D4×#67—32no—
38C22×#213—32no—
39C2×D3×D8—32no—
40#5609—32no—
41C3×#447—32no—
42#5156D312yescomplemented
43#5151—32no—
44#5151—61no—
45#5150—32no—
46#5038—32no—
47#4786—32no—
48#4775—32no—
49#4773—32no—
50#4756—32no—
51#4732—32no—
52#67⋊C8—32no—
53C23×C3×D3—22no—
54C22×D32—22no—
55C2×C32×D4C2312yes—
56C2×#638—22no—
57C2×#638—22no—
58C2×C4⋊(C3⋊D3)C2312yes—
59C2×C3×#67—22no—
60C2×C3×#67—22no—
61C3×D3×D4—24no—
62C3×D3×D4—42no—
63C2×C3×D12C2312yes—
64C2×C3×C4×D3C2312yes—
65D3×#67—48no—
66C2×#626—22no—
67C2×#626—22no—
68C2×#625D411yescharacteristic
69C2×D3×Dic3—22no—
70D3×D12—24no—
71D3×D12—42no—
72C32×D8—41no—
73C2×C32×C8C2311yescharacteristic
74#3753—24no—
75C4×C3⋊Dic3C2311yescharacteristic
76C2×C3⋊(C3⋊C8)C2311yescharacteristic
77#3745—41no—
78C3×#217—22no—
79C3×#213—24no—
80C3×C4⋊Dic3C2312yes—
81C2×C3×C3⋊C8C2312yes—
82#3724D411yescharacteristic
83#3722—22no—
84(C2×D3)⋊Dic3—22no—
85(C2×D3)⋊Dic3D412yes—
86#3714—24no—
87#3713D414yescomplemented
88D3×C3⋊C8—24no—
89D4×D8—91noSylow
90C22×C3×D4—32no—
91C22×#67—62no—
92C2×D3×D4—32no—
93C2×D3×D4—62no—
94C2×D3×D4C2×D312yescomplemented
95C22×D12—32no—
96C2×C3×D8—21no—
97C2×C3×D8—32no—
98C2×C3×D8C2×D312yescomplemented
99C3×#121—32no—
100#953—62no—
101#940—32no—
102#940—32no—
103#940—62no—
104#939—62no—
105#938C2×D312yescomplemented
106#937—62no—
107#937—62no—
108D4×Dic3—32no—
109C2×#213—32no—
110C2×#213—32no—
111C2×#213—32no—
112C2×#213—32no—
113C2×#213—62no—
114C2×#213—68no—
115C2×#213C2×D312yescomplemented
116#930—32no—
117C4×#67—32no—
118C22×C3⋊C8—32no—
119D3×D8—68no—
120C2×D24—32no—
121C2×D24—32no—
122C2×D24—61no—
123C2×D3×C8—32no—
124#895—32no—
125#893—32no—
126#884—62no—
127#882—62no—
128C3×#102—32no—
129C3×#102—32no—
130C3×C22⋊C8—32no—
131#832C2×D312yescomplemented
132#821—32no—
133#821C2×D312yescomplemented
134(C2×D3)⋊C8C2×D312yescomplemented
135Dic3⋊C8—32no—
136C8×Dic3—32no—
137C8×Dic3—61no—
138#809—32no—
139#807—32no—
140C23×C32—22no—
141C22×C3⋊D3—22no—
142C22×C3×D3—22no—
143C22×C3×D3—44no—
144C22×C3×D3—44no—
145C22×C3×D3—82no—
146C22×C3×D3C2×D412yes—
147C2×D32—44no—
148C2×D32—44no—
149C2×D32—82no—
150C32×D4—22no—
151C32×D4—22no—
152C2×C32×C4C2411yescharacteristic
153#638—44no—
154#638—82no—
155C2×C3⋊Dic3C2×D411yescharacteristic
156C2×C3⋊Dic3C2×D411yescharacteristic
157C4⋊(C3⋊D3)—22no—
158C4⋊(C3⋊D3)—22no—
159C3×#67—44no—
160C3×#67—44no—
161C2×C3×Dic3—22no—
162C2×C3×Dic3C2×D412yes—
163C3×D12—22no—
164C3×D12C2×D414yescomplemented
165C3×C4×D3—22no—
166C3×C4×D3—22no—
167#626—44no—
168#626—44no—
169#625D814yescomplemented
170D3×Dic3—44no—
171C32×C8—21no—
172C3⋊(C3⋊C8)C2×D412yescomplemented
173C3×C3⋊C8—22no—
174C22×D8—92no—
175D42—92no—
176#493—91no—
177#466—92no—
178#459—92no—
179#447—32no—
180#447—92no—
181C4×D8—91no—
182C8×D4—91no—
183C24×C3—62no—
184C23×D3—22no—
185C23×D3—62no—
186C23×D3—62no—
187C2×C3×D4—22no—
188C2×C3×D4—32no—
189C2×C3×D4—62no—
190C2×C3×D4—64no—
191C2×C3×D4—62no—
192C2×C3×D4—122no—
193C2×C3×D4C22×D312yes—
194C2×C3×D4C22×D312yes—
195C22×C3×C4—32no—
196C2×#67—22no—
197C2×#67—22no—
198C2×#67—32no—
199C2×#67—62no—
200C2×#67—62no—
201C2×#67—62no—
202C2×#67—62no—
203C2×#67—62no—
204C2×#67—62no—
205C2×#67—122no—
206C2×#67—122no—
207C2×#67—128no—
208C22×Dic3—62no—
209D3×D4—24no—
210D3×D4—42no—
211D3×D4—64no—
212D3×D4—122no—
213D3×D4—128no—
214C2×D12—32no—
215C2×D12—32no—
216C2×D12—62no—
217C2×D12—64no—
218C2×D12—62no—
219C2×D12—62no—
220C2×D12—122no—
221C2×D12C22×D312yes—
222C2×C4×D3—62no—
223C2×C4×D3C22×D312yes—
224C3×D8—42no—
225C3×D8—42no—
226C3×D8—64no—
227C2×C3×C8—21no—
228C2×C3×C8—32no—
229C2×C3×C8C22×D312yes—
230C3×C4⋊C4—32no—
231C3×C22⋊C4—62no—
232#217—22no—
233#217—32no—
234#217—62no—
235#213—24no—
236#213—38no—
237#213—64no—
238#213—64no—
239#213—64no—
240#213—124no—
241(C2×D3)⋊C4—32no—
242(C2×D3)⋊C4—62no—
243(C2×D3)⋊C4—62no—
244(C2×D3)⋊C4—62no—
245C4⋊Dic3C22×D312yes—
246Dic3⋊C4—32no—
247C4×Dic3—32no—
248C4×Dic3—61no—
249C2×C3⋊C8—32no—
250C2×C3⋊C8—61no—
251C2×C3⋊C8—64no—
252C2×C3⋊C8C22×D312yes—
253D24—64no—
254D24—122no—
255D24—122no—
256D3×C8—64no—
257C22×C32—42no—
258C22×C32—42no—
259C22×C32—42no—
260C22×C32C22×D411yescharacteristic
261C2×C3⋊D3—42no—
262C2×C3⋊D3—42no—
263C2×C3⋊D3—42no—
264C2×C3×D3—22no—
265C2×C3×D3—22no—
266C2×C3×D3—24no—
267C2×C3×D3—42no—
268C2×C3×D3—42no—
269C2×C3×D3—88no—
270C2×C3×D3C2×D814yescomplemented
271D32—88no—
272C32×C4C22×D411yescharacteristic
273C32×C4H(5,𝔽2)11yescharacteristic
274C3⋊Dic3—21no—
275C3⋊Dic3C2×D812yescomplemented
276C3×Dic3—22no—
277C3×Dic3—42no—
278C22×D4—32no—
279C22×D4—92no—
280C22×D4—182no—
281C2×D8—32no—
282C2×D8—92no—
283C2×D8—91no—
284C2×D8—92no—
285C2×D8—91no—
286C2×D8—188no—
287C2×D8D3211yescharacteristic, complemented
288C22×C8—92no—
289#127—92no—
290#121—32no—
291#121—92no—
292#121—182no—
293#120—182no—
294#120—182no—
295C4×D4—91no—
296C4×D4—92no—
297#107—91no—
298C4⋊C8—91no—
299#102—32no—
300#102—32no—
301#102—92no—
302C22⋊C8—32no—
303C4×C8—91no—
304C23×C3—22no—
305C23×C3—22no—
306C23×C3—32no—
307C23×C3—42no—
308C23×C3—62no—
309C23×C3—124no—
310C23×C3—124no—
311C23×C3—242no—
312C22×D3—22no—
313C22×D3—44no—
314C22×D3—44no—
315C22×D3—62no—
316C22×D3—62no—
317C22×D3—82no—
318C22×D3—122no—
319C22×D3—124no—
320C22×D3—124no—
321C22×D3—124no—
322C22×D3—124no—
323C22×D3—242no—
324C22×D3—242no—
325C22×D3D3×D412yes—
326C3×D4—22no—
327C3×D4—22no—
328C3×D4—22no—
329C3×D4—22no—
330C3×D4—34no—
331C3×D4—42no—
332C3×D4—42no—
333C3×D4—62no—
334C3×D4—124no—
335C3×D4—124no—
336C2×C3×C4—21no—
337C2×C3×C4—32no—
338C2×C3×C4—62no—
339C2×C3×C4—62no—
340C2×C3×C4—62no—
341C2×C3×C4C23×D312yes—
342#67—38no—
343#67—44no—
344#67—44no—
345#67—124no—
346#67—124no—
347#67—124no—
348#67—124no—
349#67—244no—
350#67—242no—
351#67—242no—
352#67—244no—
353C2×Dic3—22no—
354C2×Dic3—32no—
355C2×Dic3—32no—
356C2×Dic3—61no—
357C2×Dic3—61no—
358C2×Dic3—124no—
359C2×Dic3D3×D412yes—
360D12—22no—
361D12—62no—
362D12—62no—
363D12—62no—
364D12—62no—
365D12—122no—
366D12—122no—
367D12—124no—
368D12—124no—
369D12D3×D414yescomplemented
370C4×D3—22no—
371C4×D3—22no—
372C4×D3—124no—
373C3×C8—22no—
374C3×C8—22no—
375C3×C8—62no—
376C3⋊C8—22no—
377C3⋊C8—34no—
378C3⋊C8—62no—
379C2×C32—82no—
380C2×C32D4211yescharacteristic
381C2×C32C22×D811yescharacteristic
382C2×C32#57611yescharacteristic
383C3⋊D3—82no—
384C3×D3—24no—
385C3×D3—44no—
386C24—62no—
387C24—182no—
388C2×D4—32no—
389C2×D4—62no—
390C2×D4—64no—
391C2×D4—62no—
392C2×D4—91no—
393C2×D4—92no—
394C2×D4—122no—
395C2×D4—182no—
396C2×D4—184no—
397C2×D4—182no—
398C2×D4—182no—
399C2×D4—182no—
400C2×D4—362no—
401C2×D4—368no—
402C2×D4C2×D3212yes—
403C22×C4—32no—
404C22×C4—182no—
405D8—41no—
406D8—64no—
407D8—94no—
408D8—184no—
409D8—184no—
410D8—361no—
411C2×C8—32no—
412C2×C8—91no—
413C2×C8—184no—
414C2×C8C2×D3211yescharacteristic
415C4⋊C4—32no—
416C4⋊C4—91no—
417C22⋊C4—62no—
418C22⋊C4—92no—
419C22⋊C4—182no—
420C22⋊C4—182no—
421C42—91no—
422C22×C3—21no—
423C22×C3—34no—
424C22×C3—42no—
425C22×C3—42no—
426C22×C3—42no—
427C22×C3—42no—
428C22×C3—42no—
429C22×C3—42no—
430C22×C3—62no—
431C22×C3—62no—
432C22×C3—64no—
433C22×C3—82no—
434C22×C3—82no—
435C22×C3—82no—
436C22×C3—122no—
437C22×C3—122no—
438C22×C3—248no—
439C22×C3C2×D3×D412yes—
440C2×D3—22no—
441C2×D3—22no—
442C2×D3—24no—
443C2×D3—42no—
444C2×D3—42no—
445C2×D3—88no—
446C2×D3—122no—
447C2×D3—122no—
448C2×D3—122no—
449C2×D3—122no—
450C2×D3—122no—
451C2×D3—122no—
452C2×D3—242no—
453C2×D3—242no—
454C2×D3—242no—
455C2×D3—248no—
456C2×D3—248no—
457C2×D3D3×D814yescomplemented
458C3×C4—21no—
459C3×C4—21no—
460C3×C4—62no—
461C3×C4—122no—
462C3×C4C2×D3×D412yes—
463C3×C4#100412yes—
464Dic3—22no—
465Dic3—34no—
466Dic3—42no—
467Dic3—62no—
468Dic3—62no—
469Dic3—62no—
470C32D4×D811yescharacteristic, complemented, Sylow
471C23—22no—
472C23—32no—
473C23—62no—
474C23—124no—
475C23—124no—
476C23—182no—
477C23—242no—
478C23—364no—
479C23—364no—
480C23—722no—
481D4—22no—
482D4—22no—
483D4—34no—
484D4—62no—
485D4—94no—
486D4—124no—
487D4—124no—
488D4—182no—
489D4—182no—
490D4—364no—
491D4—364no—
492D4—364no—
493D4—722no—
494C2×C4—32no—
495C2×C4—62no—
496C2×C4—62no—
497C2×C4—62no—
498C2×C4—91no—
499C2×C4—91no—
500C2×C4—364no—
501C2×C4C22×D3211yescharacteristic
502C8—21no—
503C8—62no—
504C8—92no—
505C2×C3—21no—
506C2×C3—21no—
507C2×C3—21no—
508C2×C3—64no—
509C2×C3—82no—
510C2×C3—82no—
511C2×C3—124no—
512C2×C3—162no—
513C2×C3#559012yes—
514C2×C3C2×D3×D812yes—
515C2×C3#577412yes—
516D3—24no—
517D3—44no—
518D3—242no—
519D3—242no—
520D3—482no—
521C22—34no—
522C22—42no—
523C22—42no—
524C22—42no—
525C22—62no—
526C22—62no—
527C22—64no—
528C22—122no—
529C22—122no—
530C22—248no—
531C22—362no—
532C22—362no—
533C22—362no—
534C22—728no—
535C22D32×D411yescharacteristic
536C4—62no—
537C4—92no—
538C4—122no—
539C4—181no—
540C4D32×D411yescharacteristic
541C4#6433011yescharacteristic
542C3—21no—
543C3#8002412yescomplemented
544C2—64no—
545C2—82no—
546C2—124no—
547C2—722no—
548C2D32×D811yescharacteristic
549C2#1059473511yescharacteristic
550C2#1059528911yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×D8C22
socleC22×C32C22×D4
hypercenterC2×D8D32
hypocenterC32D4×D8
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×D8

Complements

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

NH ≅ G/Ntype
1. #10595288C2semidirect
2. C2×D3×#213C2semidirect
3. #10592850C2semidirect
4. C3×#5156C2semidirect
5. #10591449C2semidirect
6. #10591433C2semidirect
7. #10590947C2semidirect
8. #10590740C2semidirect
9. #10590718C2semidirect
11. C2×C3×D3×D4C22semidirect
13. C2×D3×D12C22semidirect
14. C2×C32×D8C22semidirect
15. #64149C22semidirect
16. C2×#3753C22semidirect
17. C2×#3745C22semidirect
18. C3×#938C22semidirect
19. C2×C3×#213C22semidirect
24. #63909C22semidirect
26. #63898C22semidirect
27. C2×#3714C22semidirect
29. C2×D3×C3⋊C8C22semidirect
30. C8×C3⋊Dic3C22semidirect
31. C3×#832C22semidirect
32. C3×#821C22semidirect
33. C3×(C2×D3)⋊C8C22semidirect
34. #63576C22semidirect
35. #63572C22semidirect
36. #63564C22semidirect
42. #5156D3semidirect
87. #3713D4semidirect
94. C2×D3×D4C2×D3semidirect
98. C2×C3×D8C2×D3semidirect
105. #938C2×D3semidirect
115. C2×#213C2×D3semidirect
131. #832C2×D3semidirect
133. #821C2×D3semidirect
134. (C2×D3)⋊C8C2×D3semidirect
164. C3×D12C2×D4semidirect
169. #625D8semidirect
172. C3⋊(C3⋊C8)C2×D4semidirect
270. C2×C3×D3C2×D8semidirect
275. C3⋊Dic3C2×D8semidirect
287. C2×D8D32semidirect
369. D12D3×D4semidirect
457. C2×D3D3×D8semidirect
470. C32D4×D8semidirect
543. C3#80024semidirect

Maximal subgroups

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

subgroupindex
#105952882
C2×D3×#2132
#105928502
C3×#51562
#105914492
#105914332
#105909472
#105907402
#105907182
#800243