Finite Group Databasebeta

← #11887154

Subgroups — #11887154

Order 1152.

991 conjugacy classes of subgroups.

The subgroup lattice has 588 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10594004C211yesmaximal, characteristic
2#10593958C211yesmaximal, characteristic, complemented
3#10592533C211yesmaximal, characteristic, complemented
4C3×#4848C211yesmaximal, characteristic, complemented
5C3×#4842C211yesmaximal, characteristic, complemented
6#10590943C212yesmaximal, complemented
7#10590940C212yesmaximal, complemented
8#10590843C212yesmaximal, complemented
9#10590649C212yesmaximal, complemented
10C4×#3715C211yesmaximal, characteristic, complemented
11#10590277C211yesmaximal, characteristic, complemented
12#81075—31nomaximal
13#80395—31nomaximal
14C2×#3802C2212yes—
15C2×D3×D12—21no—
16C2×C8×C3⋊D3C2212yescomplemented
17C4×C4⋊(C3⋊D3)C2211yescharacteristic
18C2×C3×#204C2212yescomplemented
19C3×#874C2211yescharacteristic
20C3×C4×D12C2211yescharacteristic
21C3×#869C2211yescharacteristic, complemented
22C3×C4×Dic6C2211yescharacteristic, complemented
23#63922—22no—
24#63916C2212yes—
25#63908—21no—
26#63900C2212yescomplemented
27#63894—21no—
28#63888—22no—
29#63871C2212yescomplemented
30#63869—21no—
31C2×#3715C2211yescharacteristic
32C32×C4⋊C8C2211yescharacteristic, complemented
33#63647C2212yescomplemented
34C4×C3⋊(C3⋊C8)C2211yescharacteristic, complemented
35C3×#821C2212yes—
36C3×#821C2212yescomplemented
37C3×#817C2212yescomplemented
38#63574C2211yescharacteristic, complemented
39#63565C2211yescharacteristic, complemented
40#63562C2211yescharacteristic
41#63562C2212yescomplemented
42#63562C2212yescomplemented
43#5730—31no—
44#5717—31no—
45#5579—31no—
46D4×D12—31no—
47C3×#476—31no—
48C3×#460—31no—
49#5171—32no—
50#5169—32no—
51#5088—31no—
52#5070—31no—
53C4×#215—31no—
54C4×#214—31no—
55#4864—32no—
56#4863—32no—
57#4848D311yescharacteristic, complemented
58#4842D311yescharacteristic, complemented
59#4834—31no—
60#4834—31no—
61#4834—61no—
62#4777—32no—
63#4776—32no—
64D3×#102—32no—
65D3×#102—32no—
66C22×D32—22no—
67C2×C4⋊(C3⋊D3)D411yescharacteristic
68C2×C4×C3⋊D3C2312yes—
69C2×C3×D12—21no—
70C2×C3×D12—21no—
71C2×C3×D12C2312yes—
72C2×C3×D12C2311yescharacteristic
73C2×C3×C4×D3—21no—
74C2×C3×Dic6—21no—
75C2×C3×Dic6C2311yescharacteristic
76C2×#626—22no—
77C2×#625—22no—
78C2×#624—22no—
79#3802—24no—
80#3802—42no—
81D3×D12—44no—
82C2×C32×C8C2312yes—
83C32×C42C2311yescharacteristic
84#3752D412yes—
85C4⋊(C3⋊Dic3)D411yescharacteristic
86C2×C3⋊(C3⋊C8)C2311yescharacteristic
87C2×C3⋊(C3⋊C8)C2311yescharacteristic
88C8×C3⋊D3—42no—
89C3×(C2×D3)⋊C4—21no—
90C3×C4⋊Dic3—21no—
91C3×C4⋊Dic3C2311yescharacteristic
92C3×C4⋊Dic3C2312yes—
93C3×C4⋊Dic3C2311yescharacteristic
94C3×Dic3⋊C4—21no—
95C3×C4×Dic3—21no—
96C3×#204—42no—
97#3724—22no—
98Dic3⋊Dic3—22no—
99#3722—22no—
100(C2×D3)⋊Dic3—22no—
101#3715—22no—
102#3295—91noSylow
103C2×D3×D4—32no—
104C2×D3×D4—32no—
105C2×D3×D4—61no—
106C22×D12—61no—
107C2×C3×SD16—32no—
108C3×C4⋊Q8—31no—
109C3×#127—31no—
110C3×C4×Q8—31no—
111C3×C4×D4—31no—
112#946—32no—
113#946—62no—
114C2×#215—31no—
115#938—32no—
116#938—61no—
117#937—62no—
118C2×#214—31no—
119#930—61no—
120C2×#204C2×D312yescomplemented
121C2×D3×C8—32no—
122C2×D3×C8—32no—
123C2×D3×C8—62no—
124#897—32no—
125#896—62no—
126#895—32no—
127#893—61no—
128D3×C4⋊C4—32no—
129D3×C4⋊C4—32no—
130#890—61no—
131#882—62no—
132#874C2×D311yescharacteristic
133C4×D12—31no—
134C4×D12—31no—
135C4×D12—61no—
136C4×D12—61no—
137C4×D12C2×D311yescharacteristic
138#870—61no—
139#869C2×D311yescharacteristic, complemented
140C4×Dic6C2×D311yescharacteristic, complemented
141C3×#106—32no—
142C3×C4⋊C8—21no—
143C3×C4⋊C8C2×D311yescharacteristic, complemented
144C3×C4⋊C8C2×D311yescharacteristic, complemented
145C3×#102—32no—
146C3×#102—32no—
147#835—31no—
148#832—32no—
149#832—32no—
150#832—31no—
151#821C2×D312yes—
152#821C2×D312yescomplemented
153(C2×D3)⋊C8—32no—
154(C2×D3)⋊C8—32no—
155(C2×D3)⋊C8—62no—
156#817C2×D312yescomplemented
157#810—31no—
158#809—32no—
159#809—31no—
160#809—32no—
161#808—31no—
162#808—31no—
163C4×C3⋊C8—31no—
164C4×C3⋊C8—31no—
165C4×C3⋊C8—61no—
166C22×C3⋊D3C2×D412yes—
167C22×C3×D3—21no—
168C22×C3×D3—22no—
169C2×D32—44no—
170C2×D32—44no—
171C2×D32—82no—
172C2×C32×C4C2×D411yescharacteristic
173C2×C32×C4C2×D411yescharacteristic
174C2×C32×C4C2411yescharacteristic
175C2×C3⋊Dic3C2×D412yes—
176C4⋊(C3⋊D3)SD1614yescomplemented
177C4×C3⋊D3—22no—
178C4×C3⋊D3—22no—
179C2×C3×Dic3—21no—
180C2×C3×Dic3—21no—
181C2×C3×Dic3—22no—
182C2×C3×Dic3—21no—
183C3×D12—22no—
184C3×D12—21no—
185C3×D12—22no—
186C3×D12—42no—
187C3×D12—81no—
188C3×D12#4112yes—
189C3×C4×D3—42no—
190C3×Dic6—21no—
191C3×Dic6—21no—
192C3×Dic6—81no—
193#626—44no—
194#625—44no—
195#624—82no—
196C32×C8—22no—
197C3⋊(C3⋊C8)—21no—
198C3⋊(C3⋊C8)—21no—
199#554—91no—
200D42—91no—
201#486—91no—
202#481—92no—
203#476—31no—
204#465—92no—
205#460—31no—
206#450—92no—
207C4×SD16—91no—
208C8×D4—91no—
209C2×#102—92no—
210C23×D3—62no—
211C23×D3—62no—
212C2×C3×Q8—31no—
213C2×C3×Q8—61no—
214C2×C3×D4—31no—
215C2×C3×D4—32no—
216C2×C3×D4—61no—
217C2×C3×D4—61no—
218C22×C3×C4—61no—
219C2×#67—62no—
220C2×#67—62no—
221C2×#67—62no—
222D3×D4—64no—
223D3×D4—64no—
224D3×D4—124no—
225D3×D4—122no—
226D3×D4—122no—
227C2×D12—21no—
228C2×D12—21no—
229C2×D12—31no—
230C2×D12—31no—
231C2×D12—61no—
232C2×D12—62no—
233C2×D12—124no—
234C2×D12C22×D312yes—
235C2×D12C22×D311yescharacteristic
236C2×C4×D3—21no—
237C2×C4×D3—32no—
238C2×C4×D3—32no—
239C2×C4×D3—62no—
240C2×C4×D3—62no—
241C2×C4×D3—62no—
242C2×Dic6—21no—
243C2×Dic6C22×D311yescharacteristic
244C3×SD16—122no—
245C2×C3×C8—22no—
246C2×C3×C8C22×D312yes—
247C2×C3×C8C22×D312yes—
248C3×C4⋊C4—31no—
249C3×C4⋊C4—31no—
250C3×C4⋊C4—32no—
251C3×C4⋊C4—61no—
252C3×C4⋊C4—61no—
253C3×C22⋊C4—61no—
254C3×C42—21no—
255C3×C42—61no—
256C3×C42C22×D311yescharacteristic
257C3×C42C22×D311yescharacteristic
258#217—62no—
259#215—62no—
260#214—62no—
261(C2×D3)⋊C4—21no—
262(C2×D3)⋊C4—32no—
263(C2×D3)⋊C4—32no—
264(C2×D3)⋊C4—62no—
265(C2×D3)⋊C4—62no—
266(C2×D3)⋊C4—62no—
267(C2×D3)⋊C4—62no—
268C4⋊Dic3—21no—
269C4⋊Dic3—31no—
270C4⋊Dic3—31no—
271C4⋊Dic3—61no—
272C4⋊Dic3—62no—
273C4⋊Dic3C22×D311yescharacteristic
274C4⋊Dic3C22×D311yescharacteristic
275C4⋊Dic3C22×D312yes—
276Dic3⋊C4—21no—
277Dic3⋊C4—62no—
278Dic3⋊C4—62no—
279Dic3⋊C4—62no—
280C4×Dic3—21no—
281C2×C3⋊C8—31no—
282C2×C3⋊C8—31no—
283C2×C3⋊C8—31no—
284C2×C3⋊C8—31no—
285C2×C3⋊C8—61no—
286C2×C3⋊C8—61no—
287#204—42no—
288D3×C8—122no—
289D3×C8—122no—
290D3×C8—124no—
291C22×C32C22×D411yescharacteristic
292C2×C3⋊D3—22no—
293C2×C3⋊D3—22no—
294C2×C3⋊D3C2×SD1614yes—
295C2×C3×D3—22no—
296C2×C3×D3—41no—
297C2×C3×D3—41no—
298C2×C3×D3—42no—
299C2×C3×D3—42no—
300C2×C3×D3—42no—
301D32—88no—
302C32×C4—21no—
303C32×C4C2×SD1612yes—
304C32×C4C2×#4111yescharacteristic
305C32×C4H(5,𝔽2)11yescharacteristic
306C3⋊Dic3—22no—
307C3×Dic3—41no—
308C3×Dic3—41no—
309C3×Dic3—41no—
310C3×Dic3—42no—
311C22×D4—92no—
312C22×D4—181no—
313C2×SD16—32no—
314C2×SD16—91no—
315C22×C8—92no—
316C4⋊Q8—31no—
317#127—31no—
318#125—181no—
319C22⋊Q8—92no—
320C22⋊Q8—182no—
321#121—92no—
322#121—181no—
323#120—182no—
324C4×Q8—31no—
325C4×D4—31no—
326C4×D4—91no—
327C4×D4—181no—
328C2×C4⋊C4—92no—
329#106—32no—
330#106—91no—
331C4⋊C8D3211yescharacteristic, complemented
332#103—91no—
333#102—32no—
334#102—32no—
335#102—91no—
336#102—92no—
337#102—92no—
338C22⋊C8—92no—
339C4×C8—91no—
340C23×C3—61no—
341C23×C3—62no—
342C22×D3—21no—
343C22×D3—22no—
344C22×D3—32no—
345C22×D3—32no—
346C22×D3—62no—
347C22×D3—124no—
348C22×D3—124no—
349C22×D3—124no—
350C22×D3—124no—
351C22×D3—242no—
352C22×D3—242no—
353C3×Q8—61no—
354C3×Q8—61no—
355C3×Q8—241no—
356C3×D4—32no—
357C3×D4—61no—
358C3×D4—62no—
359C3×D4—62no—
360C3×D4—122no—
361C3×D4—241no—
362C2×C3×C4—21no—
363C2×C3×C4—21no—
364C2×C3×C4—21no—
365C2×C3×C4—61no—
366C2×C3×C4—61no—
367C2×C3×C4—62no—
368C2×C3×C4—61no—
369C2×C3×C4—122no—
370C2×C3×C4D3×D411yescharacteristic
371C2×C3×C4D3×D411yescharacteristic
372C2×C3×C4D3×D411yescharacteristic
373C2×C3×C4D3×D411yescharacteristic
374C2×C3×C4C23×D311yescharacteristic
375C2×C3×C4C23×D311yescharacteristic
376#67—124no—
377#67—124no—
378#67—124no—
379C2×Dic3—21no—
380C2×Dic3—21no—
381C2×Dic3—22no—
382C2×Dic3—21no—
383C2×Dic3—32no—
384C2×Dic3—32no—
385C2×Dic3—62no—
386D12—22no—
387D12—22no—
388D12—21no—
389D12—34no—
390D12—34no—
391D12—42no—
392D12—64no—
393D12—81no—
394D12—124no—
395D12#23912yes—
396C4×D3—42no—
397C4×D3—62no—
398C4×D3—62no—
399C4×D3—62no—
400C4×D3—62no—
401C4×D3—122no—
402C4×D3—122no—
403C4×D3—242no—
404C4×D3—242no—
405Dic6—21no—
406Dic6—21no—
407Dic6—81no—
408C3×C8—22no—
409C3×C8—22no—
410C3×C8—42no—
411C3⋊C8—62no—
412C3⋊C8—61no—
413C3⋊C8—61no—
414C3⋊C8—61no—
415C3⋊C8—61no—
416C3⋊C8—121no—
417C2×C32#54611yescharacteristic
418C2×C32C22×SD1611yescharacteristic
419C2×C32#57611yescharacteristic
420C3⋊D3—24no—
421C3×D3—42no—
422C3×D3—82no—
423C24—182no—
424C2×Q8—31no—
425C2×Q8—61no—
426C2×D4—31no—
427C2×D4—32no—
428C2×D4—61no—
429C2×D4—61no—
430C2×D4—91no—
431C2×D4—182no—
432C2×D4—182no—
433C2×D4—184no—
434C2×D4—364no—
435C2×D4—362no—
436C22×C4—61no—
437C22×C4—92no—
438C22×C4—182no—
439SD16—122no—
440SD16—182no—
441C2×C8—91no—
442C2×C8—91no—
443C2×C8—362no—
444C2×C8C2×D3212yes—
445C4⋊C4—31no—
446C4⋊C4—32no—
447C4⋊C4—31no—
448C4⋊C4—61no—
449C4⋊C4—61no—
450C4⋊C4—91no—
451C4⋊C4—182no—
452C4⋊C4—182no—
453C22⋊C4—61no—
454C22⋊C4—92no—
455C22⋊C4—182no—
456C22⋊C4—182no—
457C42—61no—
458C42C2×D3211yescharacteristic
459C22×C3—21no—
460C22×C3—62no—
461C22×C3—121no—
462C22×C3—121no—
463C22×C3—122no—
464C22×C3—122no—
465C22×C3—122no—
466C22×C3C2×D3×D411yescharacteristic
467C22×C3C2×D3×D411yescharacteristic
468C2×D3—22no—
469C2×D3—34no—
470C2×D3—34no—
471C2×D3—41no—
472C2×D3—41no—
473C2×D3—42no—
474C2×D3—42no—
475C2×D3—42no—
476C2×D3—64no—
477C2×D3—62no—
478C2×D3—62no—
479C2×D3—62no—
480C2×D3—62no—
481C2×D3—122no—
482C2×D3—122no—
483C2×D3—248no—
484C2×D3—248no—
485C3×C4—21no—
486C3×C4—21no—
487C3×C4—22no—
488C3×C4—21no—
489C3×C4—21no—
490C3×C4—41no—
491C3×C4—121no—
492C3×C4—121no—
493C3×C4—122no—
494C3×C4—121no—
495C3×C4D3×SD1612yes—
496C3×C4D3×SD1612yes—
497C3×C4#100411yescharacteristic
498C3×C4C2×#23911yescharacteristic
499C3×C4D3×#4111yescharacteristic
500C3×C4#100911yescharacteristic
501Dic3—41no—
502Dic3—42no—
503Dic3—41no—
504Dic3—41no—
505Dic3—62no—
506Dic3—62no—
507Dic3—122no—
508C32#329511yescharacteristic, complemented, Sylow
509C23—61no—
510C23—62no—
511C23—92no—
512C23—364no—
513C23—364no—
514C23—722no—
515Q8—61no—
516Q8—61no—
517Q8—241no—
518D4—32no—
519D4—61no—
520D4—62no—
521D4—62no—
522D4—94no—
523D4—122no—
524D4—241no—
525D4—364no—
526D4—364no—
527C2×C4—61no—
528C2×C4—61no—
529C2×C4—61no—
530C2×C4—62no—
531C2×C4—92no—
532C2×C4—122no—
533C2×C4—182no—
534C2×C4—182no—
535C2×C4—722no—
536C2×C4#380211yescharacteristic
537C2×C4#380211yescharacteristic
538C2×C4C22×D3211yescharacteristic
539C8—22no—
540C8—181no—
541C8—181no—
542C2×C3—21no—
543C2×C3—21no—
544C2×C3—21no—
545C2×C3—122no—
546C2×C3—242no—
547C2×C3#561211yescharacteristic
548C2×C3#563011yescharacteristic
549C2×C3C2×D3×SD1611yescharacteristic
550C2×C3C2×D3×SD1611yescharacteristic
551C2×C3#577411yescharacteristic
552C2×C3#577411yescharacteristic
553D3—42no—
554D3—64no—
555D3—64no—
556D3—82no—
557D3—124no—
558C22—62no—
559C22—94no—
560C22—121no—
561C22—121no—
562C22—122no—
563C22—122no—
564C22—122no—
565C22—182no—
566C22—182no—
567C22—728no—
568C22C2×#380211yescharacteristic
569C4—21no—
570C4—121no—
571C4—121no—
572C4—121no—
573C4—122no—
574C4—182no—
575C4#6379612yes—
576C4#6431411yescharacteristic
577C4D3×#23911yescharacteristic
578C3—21no—
579C3#8039511yescharacteristic, complemented
580C3#8107511yescharacteristic, complemented
581C2—122no—
582C2—184no—
583C2—242no—
584C2#1059463311yescharacteristic
585C2C2×#6379611yescharacteristic
586C2#1059472011yescharacteristic
subgroupG/H
centerC22C2×#3802
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4⋊C8C22
socleC22×C32C22×D4
prime radical#10594004C2
hypercenterC4⋊C8D32
hypocenterC32#3295
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊C8

Complements

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

NH ≅ G/Ntype
2. #10593958C2semidirect
3. #10592533C2semidirect
4. C3×#4848C2semidirect
5. C3×#4842C2semidirect
6. #10590943C2semidirect
7. #10590940C2semidirect
8. #10590843C2semidirect
9. #10590649C2semidirect
10. C4×#3715C2semidirect
11. #10590277C2semidirect
16. C2×C8×C3⋊D3C22semidirect
18. C2×C3×#204C22semidirect
21. C3×#869C22semidirect
22. C3×C4×Dic6C22semidirect
26. #63900C22semidirect
29. #63871C22semidirect
32. C32×C4⋊C8C22semidirect
33. #63647C22semidirect
34. C4×C3⋊(C3⋊C8)C22semidirect
36. C3×#821C22semidirect
37. C3×#817C22semidirect
38. #63574C22semidirect
39. #63565C22semidirect
41. #63562C22semidirect
42. #63562C22semidirect
57. #4848D3semidirect
58. #4842D3semidirect
120. C2×#204C2×D3semidirect
139. #869C2×D3semidirect
140. C4×Dic6C2×D3semidirect
143. C3×C4⋊C8C2×D3semidirect
144. C3×C4⋊C8C2×D3semidirect
152. #821C2×D3semidirect
156. #817C2×D3semidirect
176. C4⋊(C3⋊D3)SD16semidirect
331. C4⋊C8D32semidirect
508. C32#3295semidirect
579. C3#80395semidirect
580. C3#81075semidirect

Maximal subgroups

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

subgroupindex
#105940042
#105939582
#105925332
C3×#48482
C3×#48422
#105909432
#105909402
#105908432
#105906492
C4×#37152
#105902772
#810753
#803953