Finite Group Databasebeta

← #11904433

Subgroups — #11904433

Order 1152.

3289 conjugacy classes of subgroups.

The subgroup lattice has 568 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#1004C211yesmaximal, characteristic, complemented
2C22×C3×#237C211yesmaximal, characteristic, complemented
3#10596269C211yesmaximal, characteristic, complemented
4#10595518C214yesmaximal, complemented
5C2×#63961C214yesmaximal, complemented
6#10595252C218yesmaximal, complemented
7#10595244C218yesmaximal, complemented
8#10595022C212yesmaximal, complemented
9#10594855C212yesmaximal, complemented
10#87280—31nomaximal
11#87273—31nomaximal
12C22×C32×D4C2211yescharacteristic
13C22×C3×#67C2214yes—
14C22×C3×#67C2212yescomplemented
15C23×C3×Dic3C2212yescomplemented
16C3×#1004—28no—
17C2×C3×#237—28no—
18C2×C3×#237C2218yescomplemented
19C2×C3×#237C2214yescomplemented
20C2×C3×D3×D4C2214yescomplemented
21C2×C3×#235C2212yes—
22C22×C3×C4×D3C2211yescharacteristic, complemented
23C22×C3×Dic6C2211yescharacteristic, complemented
24C2×#3757C2214yescomplemented
25D4×C3⋊Dic3C2218yescomplemented
26#64135C2212yescomplemented
27#63980C22116yescomplemented
28#63976C2218yescomplemented
29#63976C2214yescomplemented
30C2×#3724C2218yescomplemented
31#63961C2218yescomplemented
32#63961C2214yescomplemented
33#63961C22116yescomplemented
34#63961C2218yescomplemented
35C2×(C2×D3)⋊Dic3C2218yescomplemented
36#63908C2214yescomplemented
37C4×#625C2218yescomplemented
38#63873C2214yescomplemented
39#63863C2214yescomplemented
40#63856C2218yescomplemented
41#63856C2214yescomplemented
42C2×C3×H(5,𝔽2)—31no—
43C22×C3×#41—31no—
44C2×#1004D311yescharacteristic, complemented
45C22×#237D311yescharacteristic, complemented
46#5829—38no—
47#5828—32no—
48#5825—32no—
49#5824—38no—
50#5824—38no—
51#5816—32no—
52#5806—38no—
53#5804—34no—
54#5804—34no—
55#5798—31no—
56#5798—31no—
57#5798—61no—
58C2×#935—34no—
59#5791—32no—
60C2×#929—34no—
61C24×C32C2312yes—
62C23×C3×D3C2311yescharacteristic
63C23×C3×D3C2314yes—
64C2×C32×D4D418yescomplemented
65C2×C32×D4C2314yes—
66C22×C32×C4C2311yescharacteristic
67C22×C3⋊Dic3C2318yes—
68C2×C3×#67—28no—
69C2×C3×#67—216no—
70C2×C3×#67C2314yes—
71C2×C3×#67C2318yes—
72C2×C3×#67C2318yes—
73C22×C3×Dic3—28no—
74C22×C3×Dic3C2312yes—
75C22×C3×Dic3C2311yescharacteristic
76C22×C3×Dic3C2318yes—
77C22×C3×Dic3C2314yes—
78C3×#237—232no—
79C3×#237—216no—
80C3×D3×D4—216no—
81C3×#235—28no—
82C2×C3×D12C2312yes—
83C2×C3×C4×D3—24no—
84C2×C3×C4×D3C2314yes—
85C2×C3×C4×D3C2314yes—
86C2×C3×Dic6—24no—
87C2×C3×Dic6C2314yes—
88C2×C3×Dic6C2312yes—
89C2×#625C2318yes—
90#3757C2314yes—
91#3757C2318yes—
92C4⋊(C3⋊Dic3)C2314yes—
93C4×C3⋊Dic3C2314yes—
94#3724C23116yes—
95#3724C2318yes—
96(C2×D3)⋊Dic3C23116yes—
97(C2×D3)⋊Dic3C2318yes—
98(C2×D3)⋊Dic3C2318yes—
99#3485—91noSylow
100C3×H(5,𝔽2)—68no—
101C2×C3×#41—38no—
102C2×C3×#41—34no—
103C2×C3×#41—32no—
104C2×C3×#41—68no—
105C22×C3×Q8—31no—
106C22×C3×D4—21no—
107C22×C3×D4—32no—
108C22×C3×D4—34no—
109C22×C3×D4—34no—
110C22×C3×D4C2×D311yescharacteristic
111C22×C3×D4C2×D311yescharacteristic
112C23×C3×C4—32no—
113C23×C3×C4—31no—
114C22×#67C2×D314yes—
115C22×#67C2×D312yescomplemented
116C23×Dic3C2×D312yescomplemented
117#1004—28no—
118C2×#237—28no—
119C2×#237C2×D318yescomplemented
120C2×#237C2×D314yescomplemented
121C2×D3×D4C2×D314yescomplemented
122C2×#235C2×D312yes—
123C22×C4×D3C2×D311yescharacteristic, complemented
124C22×Dic6C2×D311yescharacteristic, complemented
125#953—34no—
126#953—38no—
127C2×#217—34no—
128C2×#217—34no—
129C2×#217—38no—
130C2×#217—64no—
131#947—34no—
132#946—38no—
133#946—34no—
134#944—34no—
135#944—34no—
136#939—316no—
137#939—316no—
138#938—34no—
139#937—34no—
140#937—38no—
141#936—34no—
142#935—34no—
143#935—38no—
144#935—316no—
145#935—38no—
146D4×Dic3—38no—
147D4×Dic3—38no—
148D4×Dic3—68no—
149#930—34no—
150#929—34no—
151#929—38no—
152#929—316no—
153#929—38no—
154C4×#67—38no—
155C4×#67—38no—
156C2×(C2×D3)⋊C4—38no—
157#926—32no—
158#926—32no—
159#926—62no—
160#924—34no—
161#924—38no—
162C2×Dic3⋊C4—38no—
163C2×Dic3⋊C4—38no—
164C23×C32—44no—
165C23×C32C2×D418yes—
166C23×C32C2411yescharacteristic
167C23×C32C2414yes—
168C22×C3×D3—22no—
169C22×C3×D3—28no—
170C22×C3×D3—42no—
171C22×C3×D3—48no—
172C22×C3×D3C2414yes—
173C22×C3×D3C2412yes—
174C32×D4C2×D4116yes—
175C2×C32×C4C2×D414yes—
176C2×C32×C4C2412yes—
177C2×C3⋊Dic3—48no—
178C2×C3⋊Dic3C2418yes—
179C3×#67—28no—
180C3×#67—216no—
181C3×#67—216no—
182C2×C3×Dic3—24no—
183C2×C3×Dic3—22no—
184C2×C3×Dic3—216no—
185C2×C3×Dic3—28no—
186C2×C3×Dic3C2414yes—
187C2×C3×Dic3C2412yes—
188C2×C3×Dic3C2414yes—
189C3×D12—24no—
190C3×C4×D3—28no—
191C3×C4×D3—28no—
192C3×Dic6—28no—
193C3×Dic6—24no—
194#625—48no—
195C2×H(5,𝔽2)—31no—
196C22×#41—31no—
197#547—98no—
198#546—98no—
199#536—92no—
200#534—94no—
201#525—92no—
202C2×#123—94no—
203#518—91no—
204C24×C3—22no—
205C24×C3—34no—
206C24×C3—31no—
207C24×C3C22×D312yes—
208C24×C3C22×D312yes—
209C23×D3C22×D314yes—
210C23×D3C22×D311yescharacteristic
211C3×#41—632no—
212C3×#41—616no—
213C3×#41—68no—
214C2×C3×Q8—32no—
215C2×C3×Q8—34no—
216C2×C3×Q8—64no—
217C2×C3×D4—28no—
218C2×C3×D4—24no—
219C2×C3×D4—34no—
220C2×C3×D4—38no—
221C2×C3×D4—38no—
222C2×C3×D4—32no—
223C2×C3×D4—68no—
224C2×C3×D4—616no—
225C2×C3×D4—616no—
226C2×C3×D4#6718yescomplemented
227C2×C3×D4#6718yescomplemented
228C2×C3×D4C22×D314yes—
229C2×C3×D4C22×D314yes—
230C22×C3×C4—21no—
231C22×C3×C4—34no—
232C22×C3×C4—38no—
233C22×C3×C4—31no—
234C22×C3×C4—32no—
235C22×C3×C4—34no—
236C22×C3×C4—34no—
237C22×C3×C4—68no—
238C22×C3×C4—64no—
239C22×C3×C4C22×D311yescharacteristic
240C22×C3×C4C22×D311yescharacteristic
241C2×#67—28no—
242C2×#67—216no—
243C2×#67—38no—
244C2×#67—38no—
245C2×#67C22×D314yes—
246C2×#67C22×D318yes—
247C2×#67C22×D318yes—
248C22×Dic3—28no—
249C22×Dic3—38no—
250C22×Dic3—38no—
251C22×Dic3—68no—
252C22×Dic3C22×D314yes—
253C22×Dic3C22×D318yes—
254C22×Dic3C22×D312yes—
255C22×Dic3C22×D311yescharacteristic
256#237—232no—
257#237—216no—
258D3×D4—216no—
259#235—28no—
260C2×D12C22×D312yes—
261C2×C4×D3—24no—
262C2×C4×D3C22×D314yes—
263C2×C4×D3C22×D314yes—
264C2×Dic6—24no—
265C2×Dic6C22×D314yes—
266C2×Dic6C22×D312yes—
267#217—34no—
268#217—34no—
269#217—38no—
270#217—38no—
271#217—38no—
272#217—316no—
273#217—38no—
274#217—64no—
275#217—68no—
276(C2×D3)⋊C4—38no—
277(C2×D3)⋊C4—316no—
278(C2×D3)⋊C4—38no—
279C4⋊Dic3—34no—
280C4⋊Dic3—34no—
281C4⋊Dic3—64no—
282Dic3⋊C4—38no—
283Dic3⋊C4—38no—
284Dic3⋊C4—316no—
285Dic3⋊C4—316no—
286C4×Dic3—34no—
287C4×Dic3—34no—
288C4×Dic3—64no—
289C22×C32—28no—
290C22×C32—22no—
291C22×C32—48no—
292C22×C32C22×D412yes—
293C22×C32C22×D418yes—
294C22×C32C2511yescharacteristic
295C2×C3×D3—22no—
296C2×C3×D3—24no—
297C2×C3×D3—24no—
298C2×C3×D3—28no—
299C2×C3×D3—44no—
300C2×C3×D3—88no—
301C32×C4C22×D414yes—
302C3⋊Dic3—28no—
303C3×Dic3—24no—
304C3×Dic3—24no—
305C3×Dic3—22no—
306H(5,𝔽2)—68no—
307C2×#41—38no—
308C2×#41—34no—
309C2×#41—32no—
310C2×#41—68no—
311C22×Q8—31no—
312C22×D4—34no—
313C22×D4—32no—
314C22×D4—34no—
315C22×D4D3211yescharacteristic
316C23×C4—32no—
317C23×C4—31no—
318C4⋊Q8—94no—
319#124—94no—
320#123—94no—
321#123—98no—
322#123—916no—
323#123—98no—
324C22⋊Q8—94no—
325C22⋊Q8—98no—
326#121—94no—
327#121—916no—
328#120—94no—
329#120—98no—
330C4×D4—98no—
331C4×D4—98no—
332#117—92no—
333C2×C4⋊C4—98no—
334C2×C22⋊C4—98no—
335C2×C22⋊C4—94no—
336C23×C3—21no—
337C23×C3—24no—
338C23×C3—28no—
339C23×C3—34no—
340C23×C3—32no—
341C23×C3—44no—
342C23×C3—44no—
343C23×C3—62no—
344C23×C3—68no—
345C23×C3—84no—
346C23×C3—122no—
347C23×C3—128no—
348C23×C3C2×#6718yes—
349C23×C3C2×#6718yes—
350C23×C3C23×D311yescharacteristic
351C23×C3C23×D311yescharacteristic
352C23×C3C23×D314yes—
353C23×C3C23×D314yes—
354C22×D3—22no—
355C22×D3—28no—
356C22×D3—42no—
357C22×D3—48no—
358C22×D3C23×D314yes—
359C22×D3C23×D312yes—
360C3×Q8—68no—
361C3×Q8—64no—
362C3×D4—216no—
363C3×D4—68no—
364C3×D4—616no—
365C3×D4—616no—
366C3×D4—64no—
367C3×D4C2×#67116yes—
368C3×D4C2×#67116yes—
369C2×C3×C4—22no—
370C2×C3×C4—24no—
371C2×C3×C4—34no—
372C2×C3×C4—32no—
373C2×C3×C4—34no—
374C2×C3×C4—62no—
375C2×C3×C4—64no—
376C2×C3×C4—616no—
377C2×C3×C4—68no—
378C2×C3×C4—68no—
379C2×C3×C4—68no—
380C2×C3×C4C2×#6714yes—
381C2×C3×C4C2×#6714yes—
382C2×C3×C4C23×D312yes—
383C2×C3×C4C23×D312yes—
384#67—28no—
385#67—216no—
386#67—216no—
387#67—128no—
388#67—128no—
389C2×Dic3—24no—
390C2×Dic3—22no—
391C2×Dic3—216no—
392C2×Dic3—28no—
393C2×Dic3—38no—
394C2×Dic3—38no—
395C2×Dic3—68no—
396C2×Dic3—128no—
397C2×Dic3—128no—
398C2×Dic3—248no—
399C2×Dic3C23×D314yes—
400C2×Dic3C23×D314yes—
401C2×Dic3C23×D312yes—
402D12—24no—
403C4×D3—28no—
404C4×D3—28no—
405Dic6—28no—
406Dic6—24no—
407C2×C32—22no—
408C2×C32—28no—
409C2×C32C23×D411yescharacteristic
410C2×C32#58512yes—
411C3×D3—42no—
412C3×D3—44no—
413C24—34no—
414C24—31no—
415C24C2×D3212yes—
416#41—632no—
417#41—616no—
418#41—68no—
419C2×Q8—34no—
420C2×Q8—32no—
421C2×Q8—64no—
422C2×D4—38no—
423C2×D4—34no—
424C2×D4—38no—
425C2×D4—32no—
426C2×D4—68no—
427C2×D4—616no—
428C2×D4—616no—
429C2×D4—98no—
430C2×D4#62518yescomplemented
431C2×D4C2×D3214yes—
432C22×C4—38no—
433C22×C4—34no—
434C22×C4—31no—
435C22×C4—32no—
436C22×C4—34no—
437C22×C4—34no—
438C22×C4—68no—
439C22×C4—64no—
440C22×C4—98no—
441C22×C4C2×D3211yescharacteristic
442C4⋊C4—98no—
443C4⋊C4—916no—
444C4⋊C4—94no—
445C22⋊C4—98no—
446C22⋊C4—916no—
447C22⋊C4—98no—
448C22⋊C4—94no—
449C22⋊C4—98no—
450C42—94no—
451C22×C3—28no—
452C22×C3—22no—
453C22×C3—28no—
454C22×C3—22no—
455C22×C3—22no—
456C22×C3—28no—
457C22×C3—21no—
458C22×C3—48no—
459C22×C3—42no—
460C22×C3—48no—
461C22×C3—48no—
462C22×C3—68no—
463C22×C3—64no—
464C22×C3—62no—
465C22×C3—64no—
466C22×C3—88no—
467C22×C3—124no—
468C22×C3—248no—
469C22×C3C22×#6712yes—
470C22×C3C22×#6718yes—
471C22×C3C22×#6718yes—
472C22×C3C22×#6712yes—
473C22×C3C24×D311yescharacteristic
474C22×C3C24×D311yescharacteristic
475C2×D3—24no—
476C2×D3—28no—
477C2×D3—22no—
478C2×D3—24no—
479C2×D3—44no—
480C2×D3—88no—
481C3×C4—24no—
482C3×C4—62no—
483C3×C4—64no—
484C3×C4—64no—
485C3×C4C22×#6714yes—
486C3×C4C22×#6714yes—
487Dic3—24no—
488Dic3—24no—
489Dic3—22no—
490Dic3—68no—
491Dic3—68no—
492Dic3—128no—
493C32#348511yescharacteristic, complemented, Sylow
494C23—34no—
495C23—32no—
496C23—44no—
497C23—62no—
498C23—68no—
499C23—122no—
500C23—128no—
501C23C2×#62518yes—
502C23C22×D3211yescharacteristic
503C23C22×D3214yes—
504Q8—68no—
505Q8—64no—
506D4—68no—
507D4—616no—
508D4—616no—
509D4—64no—
510D4—368no—
511D4C2×#625116yes—
512C2×C4—32no—
513C2×C4—34no—
514C2×C4—34no—
515C2×C4—62no—
516C2×C4—64no—
517C2×C4—616no—
518C2×C4—68no—
519C2×C4—68no—
520C2×C4—68no—
521C2×C4—98no—
522C2×C4—368no—
523C2×C4C2×#62514yes—
524C2×C4C22×D3212yes—
525C2×C3—22no—
526C2×C3—28no—
527C2×C3—28no—
528C2×C3—22no—
529C2×C3—22no—
530C2×C3—21no—
531C2×C3—42no—
532C2×C3—48no—
533C2×C3—124no—
534C2×C3—122no—
535C2×C3#596412yes—
536C2×C3#596612yes—
537C2×C3C23×#6711yescharacteristic
538C2×C3C23×#6711yescharacteristic
539D3—42no—
540D3—44no—
541C22—28no—
542C22—22no—
543C22—48no—
544C22—64no—
545C22—68no—
546C22—62no—
547C22—64no—
548C22—124no—
549C22—248no—
550C22C22×#62512yes—
551C22C22×#62518yes—
552C22C23×D3211yescharacteristic
553C4—62no—
554C4—64no—
555C4—64no—
556C4—188no—
557C4C22×#62514yes—
558C3—21no—
559C3#8727311yescharacteristic, complemented
560C3#8728011yescharacteristic, complemented
561C2—22no—
562C2—28no—
563C2—122no—
564C2—124no—
565C2#1059667812yes—
566C2C23×#62511yescharacteristic
subgroupG/H
center, FrattiniC22C23×D32
commutator, socle, cosocleC22×C32C25
FittingC22×C32×D4C22
hypercenterC22×D4D32
hypocenterC32#3485
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
1. C2×C3×#1004C2semidirect
2. C22×C3×#237C2semidirect
3. #10596269C2semidirect
4. #10595518C2semidirect
5. C2×#63961C2semidirect
6. #10595252C2semidirect
7. #10595244C2semidirect
8. #10595022C2semidirect
9. #10594855C2semidirect
14. C22×C3×#67C22semidirect
15. C23×C3×Dic3C22semidirect
18. C2×C3×#237C22semidirect
19. C2×C3×#237C22semidirect
20. C2×C3×D3×D4C22semidirect
22. C22×C3×C4×D3C22semidirect
23. C22×C3×Dic6C22semidirect
24. C2×#3757C22semidirect
25. D4×C3⋊Dic3C22semidirect
26. #64135C22semidirect
27. #63980C22semidirect
28. #63976C22semidirect
29. #63976C22semidirect
30. C2×#3724C22semidirect
31. #63961C22semidirect
32. #63961C22semidirect
33. #63961C22semidirect
34. #63961C22semidirect
35. C2×(C2×D3)⋊Dic3C22semidirect
36. #63908C22semidirect
37. C4×#625C22semidirect
38. #63873C22semidirect
39. #63863C22semidirect
40. #63856C22semidirect
41. #63856C22semidirect
44. C2×#1004D3semidirect
45. C22×#237D3semidirect
64. C2×C32×D4D4semidirect
115. C22×#67C2×D3semidirect
116. C23×Dic3C2×D3semidirect
119. C2×#237C2×D3semidirect
120. C2×#237C2×D3semidirect
121. C2×D3×D4C2×D3semidirect
123. C22×C4×D3C2×D3semidirect
124. C22×Dic6C2×D3semidirect
226. C2×C3×D4#67semidirect
227. C2×C3×D4#67semidirect
430. C2×D4#625semidirect
493. C32#3485semidirect
559. C3#87273semidirect
560. C3#87280semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#10042
C22×C3×#2372
#105962692
#105955182
C2×#639612
#105952522
#105952442
#105950222
#105948552
#872803
#872733