Finite Group Databasebeta

← #11887067

Subgroups — #11887067

Order 1152.

1055 conjugacy classes of subgroups.

The subgroup lattice has 545 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10594618C211yesmaximal, characteristic, complemented
2#10594512C211yesmaximal, characteristic, complemented
3#10592571C211yesmaximal, characteristic, complemented
4C3×#4882C212yesmaximal, complemented
5#10590947C212yesmaximal, complemented
6#10590885C211yesmaximal, characteristic, complemented
7#10590718C211yesmaximal, characteristic, complemented
8D3×#809C212yesmaximal, complemented
9#10590576C212yesmaximal, complemented
10#10590551C211yesmaximal, characteristic, complemented
11#10590430C211yesmaximal, characteristic, complemented
12#81302—32nomaximal
13C2×#3802—21no—
14C2×D3×D12C2212yes—
15C2×#3798—21no—
16C2×#3745C2211yescharacteristic
17#64102C2211yescharacteristic
18#64102C2211yescharacteristic, complemented
19C3×#895C2212yes—
20C3×D3×C4⋊C4C2212yescomplemented
21#63922—22no—
22#63919C2211yescharacteristic, complemented
23#63914C2211yescharacteristic
24#63912—21no—
25#63909C2212yescomplemented
26C4×#625C2211yescharacteristic
27#63865—21no—
28#63850—22no—
29C2×#3714C2212yescomplemented
30C2×D3×C3⋊C8C2212yescomplemented
31C32×#107C2211yescharacteristic, complemented
32C8×C3⋊Dic3C2211yescharacteristic, complemented
33#63636C2211yescharacteristic
34#63636C2211yescharacteristic, complemented
35C3×#821C2212yescomplemented
36C3×(C2×D3)⋊C8C2212yescomplemented
37C3×#809C2212yescomplemented
38C3×#807C2212yescomplemented
39#63572C2211yescharacteristic, complemented
40#63564C2212yes—
41#63562C2212yescomplemented
42#5609—32no—
43#5507—32no—
44C3×#480—32no—
45#5038—32no—
46C2×#809—32no—
47#4890—32no—
48#4883—32no—
49#4882D312yescomplemented
50#4872—32no—
51#4872—61no—
52#4786—32no—
53#4773—32no—
54D3×#102—32no—
55#4760—32no—
56#4732—32no—
57#67⋊C8—32no—
58C22×D32—22no—
59C2×C4⋊(C3⋊D3)C2311yescharacteristic
60C2×C4⋊(C3⋊D3)C2311yescharacteristic
61C2×C4×C3⋊D3—21no—
62C2×C4×C3⋊D3—21no—
63C2×C3×D12—22no—
64C2×C3×D12C2312yes—
65C2×C3×C4×D3—22no—
66C2×C3×C4×D3C2312yes—
67C2×#627—21no—
68C2×#626—22no—
69C2×#626—22no—
70C2×#625—21no—
71C2×#625—21no—
72C2×#625D411yescharacteristic
73#3802—44no—
74D3×D12—24no—
75D3×D12—42no—
76#3798—44no—
77C2×C32×C8C2311yescharacteristic
78C32×C4⋊C4C2311yescharacteristic
79C32×C4⋊C4C2311yescharacteristic
80#3752—21no—
81#3752—21no—
82C4×C3⋊Dic3C2311yescharacteristic
83C2×C3⋊(C3⋊C8)C2311yescharacteristic
84#3745—22no—
85C3×(C2×D3)⋊C4—22no—
86C3×C4⋊Dic3C2312yes—
87C3×Dic3⋊C4—22no—
88C2×C3×C3⋊C8C2312yes—
89#3724—21no—
90#3724D411yescharacteristic
91#3722—22no—
92(C2×D3)⋊Dic3D412yes—
93#3714—42no—
94D3×C3⋊C8—42no—
95#3294—91noSylow
96C2×D3×D4—32no—
97C2×D3×D4—62no—
98C2×#235—62no—
99C22×D12—32no—
100C3×#121—32no—
101C2×C3×C4⋊C4—32no—
102#940—32no—
103#937—62no—
104C2×#213—32no—
105#930—32no—
106#929—62no—
107C4×#67—32no—
108C22×C3⋊C8—32no—
109C2×D24—32no—
110C2×D24—32no—
111C2×D24—61no—
112C2×D3×C8—32no—
113#896—62no—
114#895—32no—
115#895C2×D312yes—
116#894—62no—
117#893—32no—
118#893—32no—
119#893—61no—
120#893—61no—
121D3×C4⋊C4C2×D312yescomplemented
122#888—32no—
123#884—62no—
124#882—62no—
125C3×#107—21no—
126C3×#107—32no—
127C3×#107C2×D312yescomplemented
128C3×#102—32no—
129C3×#102—32no—
130C3×C22⋊C8—32no—
131#832—32no—
132#821—32no—
133#821C2×D312yescomplemented
134(C2×D3)⋊C8C2×D312yescomplemented
135Dic3⋊C8—32no—
136C8×Dic3—32no—
137C8×Dic3—61no—
138#809—32no—
139#809—32no—
140#809—32no—
141#809—32no—
142#809—61no—
143#809—61no—
144#809C2×D312yescomplemented
145#807C2×D312yescomplemented
146C22×C3⋊D3—21no—
147C22×C3⋊D3—21no—
148C22×C3×D3—22no—
149C22×C3×D3C2×D412yes—
150C2×D32—44no—
151C2×D32—44no—
152C2×D32—82no—
153C2×C32×C4—21no—
154C2×C32×C4—21no—
155C2×C32×C4C2411yescharacteristic
156C2×C3⋊Dic3C2×D411yescharacteristic
157C2×C3⋊Dic3C2×D411yescharacteristic
158C4⋊(C3⋊D3)—21no—
159C4⋊(C3⋊D3)—21no—
160C4⋊(C3⋊D3)—21no—
161C4⋊(C3⋊D3)#4112yescomplemented
162C4×C3⋊D3—42no—
163C4×C3⋊D3—42no—
164C2×C3×Dic3—22no—
165C2×C3×Dic3C2×D412yes—
166C3×D12—22no—
167C3×D12—22no—
168C3×D12—44no—
169C3×C4×D3—22no—
170C3×C4×D3—22no—
171C3×C4×D3—44no—
172#627—42no—
173#626—44no—
174#626—44no—
175#625—42no—
176#625—81no—
177#625D814yescomplemented
178C32×C8—21no—
179C3⋊(C3⋊C8)—21no—
180C3×C3⋊C8—22no—
181#547—91no—
182D42—91no—
183#486—91no—
184#480—32no—
185#474—91no—
186#466—92no—
187#459—91no—
188#447—92no—
189C4×D8—91no—
190C8×D4—91no—
191C2×#102—92no—
192C23×D3—62no—
193C23×D3—62no—
194C2×C3×D4—32no—
195C2×C3×D4—62no—
196C22×C3×C4—32no—
197C22×C3×C4—62no—
198C2×#67—32no—
199C2×#67—62no—
200C2×#67—62no—
201C2×#67—62no—
202C2×#67—62no—
203D3×D4—64no—
204D3×D4—122no—
205D3×D4—128no—
206#235—128no—
207C2×D12—22no—
208C2×D12—32no—
209C2×D12—32no—
210C2×D12—61no—
211C2×D12—61no—
212C2×D12—64no—
213C2×D12—62no—
214C2×D12—62no—
215C2×D12—122no—
216C2×D12C22×D312yes—
217C2×C4×D3—22no—
218C2×C4×D3—62no—
219C2×C4×D3—62no—
220C2×C4×D3—121no—
221C2×C4×D3—121no—
222C2×C4×D3C22×D312yes—
223C2×Dic6—62no—
224C2×C3×C8—21no—
225C2×C3×C8—32no—
226C2×C3×C8C22×D312yes—
227C3×C4⋊C4—21no—
228C3×C4⋊C4—21no—
229C3×C4⋊C4—32no—
230C3×C4⋊C4—62no—
231C3×C4⋊C4C22×D312yes—
232C3×C4⋊C4C22×D312yes—
233C3×C22⋊C4—62no—
234#217—32no—
235#213—122no—
236(C2×D3)⋊C4—22no—
237(C2×D3)⋊C4—32no—
238(C2×D3)⋊C4—62no—
239(C2×D3)⋊C4—62no—
240(C2×D3)⋊C4—62no—
241(C2×D3)⋊C4—62no—
242(C2×D3)⋊C4—121no—
243(C2×D3)⋊C4—121no—
244C4⋊Dic3C22×D312yes—
245Dic3⋊C4—22no—
246Dic3⋊C4—32no—
247Dic3⋊C4—62no—
248C4×Dic3—32no—
249C4×Dic3—61no—
250C2×C3⋊C8—32no—
251C2×C3⋊C8—61no—
252C2×C3⋊C8—122no—
253C2×C3⋊C8C22×D312yes—
254D24—64no—
255D24—64no—
256D24—122no—
257D3×C8—122no—
258C22×C32C22×D411yescharacteristic
259C2×C3⋊D3—22no—
260C2×C3⋊D3—41no—
261C2×C3⋊D3—41no—
262C2×C3⋊D3—41no—
263C2×C3⋊D3—41no—
264C2×C3⋊D3—41no—
265C2×C3×D3—22no—
266C2×C3×D3—22no—
267C2×C3×D3—42no—
268C2×C3×D3—42no—
269C2×C3×D3—42no—
270C2×C3×D3C2×D814yes—
271D32—88no—
272C32×C4—41no—
273C32×C4—41no—
274C32×C4C2×#4111yescharacteristic
275C32×C4H(5,𝔽2)11yescharacteristic
276C3⋊Dic3—21no—
277C3⋊Dic3C2×D812yes—
278C3×Dic3—22no—
279C3×Dic3—42no—
280C2×#41—181no—
281C22×D4—92no—
282C22×D4—181no—
283C2×D8—92no—
284C2×D8—91no—
285C22×C8—92no—
286C4⋊Q8—91no—
287#127—91no—
288#123—182no—
289C22⋊Q8—181no—
290#121—32no—
291#121—92no—
292#121—181no—
293#120—182no—
294C4×D4—91no—
295C4×D4—91no—
296C4×D4—91no—
297C2×C4⋊C4—32no—
298#107—32no—
299#107D3211yescharacteristic, complemented
300C4⋊C8—91no—
301#102—32no—
302#102—32no—
303#102—92no—
304#102—92no—
305#102—91no—
306#102—91no—
307C22⋊C8—32no—
308C4×C8—91no—
309C23×C3—32no—
310C23×C3—62no—
311C22×D3—22no—
312C22×D3—62no—
313C22×D3—62no—
314C22×D3—121no—
315C22×D3—121no—
316C22×D3—124no—
317C22×D3—124no—
318C22×D3—124no—
319C22×D3—124no—
320C22×D3—242no—
321C22×D3—242no—
322C22×D3D3×D412yes—
323C3×D4—62no—
324C3×D4—62no—
325C3×D4—124no—
326C2×C3×C4—22no—
327C2×C3×C4—22no—
328C2×C3×C4—21no—
329C2×C3×C4—32no—
330C2×C3×C4—41no—
331C2×C3×C4—41no—
332C2×C3×C4—62no—
333C2×C3×C4—62no—
334C2×C3×C4—62no—
335C2×C3×C4—124no—
336C2×C3×C4C23×D312yes—
337#67—38no—
338#67—124no—
339#67—124no—
340#67—124no—
341#67—242no—
342C2×Dic3—22no—
343C2×Dic3—32no—
344C2×Dic3—32no—
345C2×Dic3—61no—
346C2×Dic3—61no—
347C2×Dic3D3×D412yes—
348D12—22no—
349D12—22no—
350D12—34no—
351D12—44no—
352D12—62no—
353D12—62no—
354D12—62no—
355D12—62no—
356D12—62no—
357D12—121no—
358D12—121no—
359D12—124no—
360D12—124no—
361C4×D3—22no—
362C4×D3—22no—
363C4×D3—44no—
364C4×D3—124no—
365C4×D3—124no—
366C4×D3—242no—
367C4×D3—242no—
368Dic6—124no—
369C3×C8—22no—
370C3×C8—22no—
371C3×C8—62no—
372C3⋊C8—22no—
373C3⋊C8—62no—
374C3⋊C8—121no—
375C2×C32#54611yescharacteristic
376C2×C32C22×D811yescharacteristic
377C2×C32#57711yescharacteristic
378C3⋊D3—42no—
379C3⋊D3—81no—
380C3×D3—24no—
381C3×D3—82no—
382C24—182no—
383#41—364no—
384C2×Q8—181no—
385C2×D4—32no—
386C2×D4—62no—
387C2×D4—91no—
388C2×D4—91no—
389C2×D4—91no—
390C2×D4—182no—
391C2×D4—184no—
392C2×D4—182no—
393C2×D4—181no—
394C2×D4—181no—
395C2×D4—362no—
396C2×D4—364no—
397C22×C4—32no—
398C22×C4—62no—
399C22×C4—181no—
400C22×C4—181no—
401D8—182no—
402D8—362no—
403C2×C8—32no—
404C2×C8—91no—
405C2×C8—362no—
406C2×C8C2×D3211yescharacteristic
407C4⋊C4—32no—
408C4⋊C4—62no—
409C4⋊C4—91no—
410C4⋊C4—181no—
411C4⋊C4C2×D3211yescharacteristic
412C4⋊C4C2×D3211yescharacteristic
413C22⋊C4—62no—
414C22⋊C4—92no—
415C22⋊C4—181no—
416C22⋊C4—181no—
417C22⋊C4—182no—
418C42—91no—
419C22×C3—21no—
420C22×C3—34no—
421C22×C3—62no—
422C22×C3—62no—
423C22×C3—122no—
424C22×C3—122no—
425C22×C3—122no—
426C22×C3C2×D3×D412yes—
427C2×D3—22no—
428C2×D3—22no—
429C2×D3—42no—
430C2×D3—42no—
431C2×D3—42no—
432C2×D3—64no—
433C2×D3—122no—
434C2×D3—122no—
435C2×D3—122no—
436C2×D3—122no—
437C2×D3—122no—
438C2×D3—122no—
439C2×D3—122no—
440C2×D3—241no—
441C2×D3—241no—
442C2×D3—241no—
443C2×D3—241no—
444C2×D3—248no—
445C2×D3—248no—
446C2×D3D3×D814yes—
447C3×C4—21no—
448C3×C4—21no—
449C3×C4—42no—
450C3×C4—42no—
451C3×C4—62no—
452C3×C4—81no—
453C3×C4—81no—
454C3×C4—122no—
455C3×C4D3×#4112yes—
456C3×C4#100912yes—
457Dic3—22no—
458Dic3—34no—
459Dic3—42no—
460Dic3—62no—
461Dic3—62no—
462Dic3—121no—
463C32#329411yescharacteristic, complemented, Sylow
464C23—32no—
465C23—62no—
466C23—181no—
467C23—181no—
468C23—364no—
469C23—364no—
470C23—722no—
471Q8—362no—
472D4—62no—
473D4—62no—
474D4—94no—
475D4—92no—
476D4—124no—
477D4—181no—
478D4—181no—
479D4—181no—
480D4—364no—
481D4—362no—
482D4—364no—
483D4—721no—
484C2×C4—21no—
485C2×C4—21no—
486C2×C4—32no—
487C2×C4—62no—
488C2×C4—62no—
489C2×C4—62no—
490C2×C4—91no—
491C2×C4—91no—
492C2×C4—124no—
493C2×C4—362no—
494C2×C4—362no—
495C2×C4C22×D3211yescharacteristic
496C8—21no—
497C8—62no—
498C8—181no—
499C2×C3—21no—
500C2×C3—21no—
501C2×C3—21no—
502C2×C3—64no—
503C2×C3—242no—
504C2×C3#565412yes—
505C2×C3C2×D3×D812yes—
506C2×C3#577812yes—
507D3—24no—
508D3—82no—
509D3—124no—
510D3—242no—
511D3—242no—
512D3—242no—
513C22—34no—
514C22—62no—
515C22—62no—
516C22—122no—
517C22—122no—
518C22—122no—
519C22—182no—
520C22—361no—
521C22—361no—
522C22—361no—
523C22—361no—
524C22—361no—
525C22—728no—
526C22D32×D411yescharacteristic
527C4—41no—
528C4—41no—
529C4—62no—
530C4—92no—
531C4—122no—
532C4—181no—
533C4#6430611yescharacteristic
534C4#6432011yescharacteristic
535C3—21no—
536C3#8130212yescomplemented
537C2—64no—
538C2—242no—
539C2—362no—
540C2—721no—
541C2#1059461611yescharacteristic
542C2D32×D811yescharacteristic
543C2#1059476711yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#107C22
socleC22×C32C22×D4
hypercenter#107D32
hypocenterC32#3294
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ #107

Complements

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

NH ≅ G/Ntype
1. #10594618C2semidirect
2. #10594512C2semidirect
3. #10592571C2semidirect
4. C3×#4882C2semidirect
5. #10590947C2semidirect
6. #10590885C2semidirect
7. #10590718C2semidirect
8. D3×#809C2semidirect
9. #10590576C2semidirect
10. #10590551C2semidirect
11. #10590430C2semidirect
18. #64102C22semidirect
20. C3×D3×C4⋊C4C22semidirect
22. #63919C22semidirect
25. #63909C22semidirect
29. C2×#3714C22semidirect
30. C2×D3×C3⋊C8C22semidirect
31. C32×#107C22semidirect
32. C8×C3⋊Dic3C22semidirect
34. #63636C22semidirect
35. C3×#821C22semidirect
36. C3×(C2×D3)⋊C8C22semidirect
37. C3×#809C22semidirect
38. C3×#807C22semidirect
39. #63572C22semidirect
41. #63562C22semidirect
49. #4882D3semidirect
121. D3×C4⋊C4C2×D3semidirect
127. C3×#107C2×D3semidirect
133. #821C2×D3semidirect
134. (C2×D3)⋊C8C2×D3semidirect
144. #809C2×D3semidirect
145. #807C2×D3semidirect
161. C4⋊(C3⋊D3)#41semidirect
177. #625D8semidirect
299. #107D32semidirect
463. C32#3294semidirect
536. C3#81302semidirect

Maximal subgroups

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

subgroupindex
#105946182
#105945122
#105925712
C3×#48822
#105909472
#105908852
#105907182
D3×#8092
#105905762
#105905512
#105904302
#813023