Finite Group Databasebeta

← #11900764

Subgroups — #11900764

Order 1152.

3601 conjugacy classes of subgroups.

The subgroup lattice has 553 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64319C212yesmaximal, complemented
2C3⋊D3×C4⋊Q8C211yesmaximal, characteristic, complemented
3C3×#5725C212yesmaximal, complemented
4#10595432C212yesmaximal, complemented
5#10595359C214yesmaximal, complemented
6#10594612C214yesmaximal, complemented
7#10594605C214yesmaximal, complemented
8#10594367C218yesmaximal, complemented
9#10594008C211yesmaximal, characteristic, complemented
10C42×D32C211yesmaximal, characteristic, complemented
11#10593897C212yesmaximal, complemented
12D3×#532—32nomaximal
13C2×Q8×C3⋊D3C2212yes—
14C2×C3×#239C2214yescomplemented
15#64319—216no—
16C2×#3802C2214yes—
17C2×#3802C2214yes—
18C2×#3802C2212yes—
19C2×C4×D32C2214yes—
20C2×C4×D32C2212yes—
21C2×C4×D32C2211yescharacteristic
22C2×#3795C2214yescomplemented
23C2×#3795C2218yescomplemented
24C32×C4⋊Q8C2211yescharacteristic, complemented
25#64153C2212yescomplemented
26C4⋊C4×C3⋊D3C2214yes—
27#64097C2214yescomplemented
28C42×C3⋊D3C2211yescharacteristic
29#64078C2211yescharacteristic, complemented
30C3×#947C2214yescomplemented
31C3×#895C2218yescomplemented
32C3×#893C2218yescomplemented
33C3×#874C2212yescomplemented
34C3×C42×D3C2212yescomplemented
35#63921C2218yes—
36#63914C2212yescomplemented
37#63914C2214yescomplemented
38#63913C2218yescomplemented
39#63908C2218yescomplemented
40Dic3×D12C2218yescomplemented
41#63885C22116yescomplemented
42C4×#624C2212yes—
43C4×#624C2211yescharacteristic
44#63879C22116yescomplemented
45C4×D3×Dic3C2212yescomplemented
46C4×D3×Dic3C2214yescomplemented
47#63860C2214yescomplemented
48C2×D3×#41—34no—
49C3×#532—32no—
50#5832—34no—
51#5725D312yescomplemented
52D3×C4⋊Q8—32no—
53D3×C4⋊Q8—61no—
54#5716—32no—
55D3×#127—32no—
56D3×#124—34no—
57#5668—34no—
58D3×#121—38no—
59#5596—38no—
60#5548—38no—
61C4×D3×D4—38no—
62#5477—32no—
63C2×C42×D3—32no—
64C22×D32C2314yes—
65C22×D32C2311yescharacteristic
66C2×C32×Q8C2312yes—
67Q8×C3⋊D3—28no—
68C2×C4×C3⋊D3C2314yes—
69C2×C4×C3⋊D3C2311yescharacteristic
70C2×C4×C3⋊D3C2312yes—
71C2×#634C2312yes—
72C2×#634C2314yes—
73C3×#239—216no—
74C2×C3×D12C2318yes—
75C2×C3×D12C2318yes—
76C2×C3×D12C2314yes—
77C2×C3×C4×D3C2318yes—
78C2×C3×C4×D3C2314yes—
79C2×C3×C4×D3C2312yes—
80C2×#625C2318yes—
81C2×#625C2314yes—
82C2×#625C2318yes—
83C2×#624C2312yes—
84C2×#624C2311yescharacteristic
85C2×D3×Dic3C2318yes—
86C2×D3×Dic3C2314yes—
87C2×D3×Dic3C2312yes—
88#3802—216no—
89#3802—28no—
90#3802—216no—
91C4×D32—28no—
92C4×D32—216no—
93C4×D32D418yescomplemented
94#3795—216no—
95#3795—232no—
96C32×C4⋊C4C2314yes—
97C32×C42C2311yescharacteristic
98C4⋊(C3⋊Dic3)C2314yes—
99#3750C2318yes—
100C4×C3⋊Dic3C2312yes—
101C4×C3⋊Dic3C2311yescharacteristic
102C3×(C2×D3)⋊C4C23116yes—
103C3×C4×Dic3C2314yes—
104C3×C4×Dic3C2312yes—
105(C2×D3)⋊Dic3C23116yes—
106Dic32C2314yes—
107Dic32C2312yes—
108C2×#532—91noSylow
109C2×C3×#41—34no—
110D3×#41—632no—
111C2×#239C2×D314yescomplemented
112C2×D3×Q8—34no—
113C2×D3×Q8—62no—
114C2×#237—34no—
115C2×#237—38no—
116C2×D3×D4—34no—
117C2×D3×D4—38no—
118C2×D3×D4—38no—
119C2×#235—34no—
120C2×#235—38no—
121C22×C4×D3—32no—
122C22×C4×D3—38no—
123C22×C4×D3—34no—
124C3×C4⋊Q8—21no—
125C3×C4⋊Q8C2×D312yescomplemented
126C3×#127—32no—
127C3×#124—34no—
128C3×#121—38no—
129C3×C4×D4—38no—
130C2×C3×C42—32no—
131#947C2×D314yescomplemented
132#944—34no—
133#944—62no—
134#940—34no—
135#940—38no—
136#939—316no—
137#938—38no—
138#936—34no—
139D4×Dic3—38no—
140#930—38no—
141C4×#67—316no—
142C2×C4×Dic3—32no—
143C2×C4×Dic3—34no—
144#895C2×D318yescomplemented
145#893C2×D318yescomplemented
146D3×C4⋊C4—38no—
147D3×C4⋊C4—64no—
148#888—38no—
149#888—64no—
150#885—316no—
151#884—316no—
152#67⋊C4—316no—
153D3×C22⋊C4—316no—
154#875—34no—
155#874C2×D312yescomplemented
156C4×D12—38no—
157C42×D3—32no—
158C42×D3—34no—
159C42×D3—32no—
160C42×D3—32no—
161C42×D3—34no—
162C42×D3—61no—
163C42×D3C2×D312yescomplemented
164#869—32no—
165#869—61no—
166C22×C3⋊D3C2411yescharacteristic
167C22×C3×D3C2418yes—
168C22×C3×D3C2412yes—
169C2×D32—24no—
170C2×D32—28no—
171C2×D32—216no—
172C2×D32C2×D414yes—
173C32×Q8—24no—
174C2×C32×C4C2414yes—
175C2×C32×C4C2411yescharacteristic
176C2×C32×C4C2412yes—
177C2×C3⋊Dic3C2414yes—
178C2×C3⋊Dic3C2411yescharacteristic
179C2×C3⋊Dic3C2412yes—
180C4×C3⋊D3—28no—
181C4×C3⋊D3C2×D414yes—
182C4×C3⋊D3#4118yescomplemented
183#634—24no—
184#634—28no—
185C2×C3×Dic3C2414yes—
186C2×C3×Dic3C2412yes—
187C3×D12—216no—
188C3×D12—28no—
189C3×D12—216no—
190C3×C4×D3—28no—
191C3×C4×D3—216no—
192C3×C4×D3C2×D418yescomplemented
193#625—216no—
194#625—28no—
195#625—216no—
196#624—24no—
197#624C2×D414yes—
198D3×Dic3—28no—
199D3×Dic3—216no—
200D3×Dic3C2×D418yescomplemented
201C22×#41—92no—
202#532—32no—
203#532—92no—
204#532—98no—
205#532—94no—
206C2×C4⋊Q8—91no—
207C2×#127—91no—
208C2×#124—92no—
209C2×#121—94no—
210C2×C4×D4—94no—
211C22×C42—91no—
212C23×D3—32no—
213C23×D3—38no—
214C3×#41—616no—
215C2×C3×Q8—22no—
216C2×C3×Q8C22×D314yes—
217C2×C3×D4—38no—
218C2×C3×D4—34no—
219C2×C3×D4—38no—
220C22×C3×C4—32no—
221C22×C3×C4—34no—
222C22×C3×C4—38no—
223C2×#67—316no—
224C2×#67—38no—
225C2×#67—38no—
226C2×#67—38no—
227C22×Dic3—32no—
228C22×Dic3—38no—
229C22×Dic3—34no—
230#239—216no—
231D3×Q8—616no—
232D3×Q8—128no—
233#237—632no—
234#237—616no—
235D3×D4—632no—
236D3×D4—616no—
237D3×D4—632no—
238#235—632no—
239#235—616no—
240C2×D12C22×D318yes—
241C2×D12C22×D314yes—
242C2×D12C22×D318yes—
243C2×C4×D3—32no—
244C2×C4×D3—34no—
245C2×C4×D3—32no—
246C2×C4×D3—32no—
247C2×C4×D3—316no—
248C2×C4×D3—34no—
249C2×C4×D3—38no—
250C2×C4×D3—38no—
251C2×C4×D3—34no—
252C2×C4×D3—62no—
253C2×C4×D3—61no—
254C2×C4×D3—64no—
255C2×C4×D3—616no—
256C2×C4×D3—632no—
257C2×C4×D3C22×D314yes—
258C2×C4×D3C22×D318yes—
259C2×C4×D3C22×D312yes—
260C2×Dic6—34no—
261C2×Dic6—38no—
262C2×Dic6—62no—
263C2×Dic6—64no—
264C3×C4⋊C4—24no—
265C3×C4⋊C4C22×D318yes—
266C3×C22⋊C4—316no—
267C3×C42—21no—
268C3×C42—34no—
269C3×C42—32no—
270C3×C42C22×D312yes—
271#217—316no—
272(C2×D3)⋊C4—316no—
273(C2×D3)⋊C4C22×D3116yes—
274C4⋊Dic3—38no—
275C4⋊Dic3—64no—
276Dic3⋊C4—316no—
277Dic3⋊C4—68no—
278C4×Dic3—34no—
279C4×Dic3—32no—
280C4×Dic3—34no—
281C4×Dic3—34no—
282C4×Dic3—34no—
283C4×Dic3—62no—
284C4×Dic3—61no—
285C4×Dic3C22×D314yes—
286C4×Dic3C22×D312yes—
287C22×C32C2511yescharacteristic
288C2×C3⋊D3C22×D412yes—
289C2×C3⋊D3C2×#4114yes—
290C2×C3×D3—24no—
291C2×C3×D3—28no—
292C2×C3×D3—216no—
293C2×C3×D3C22×D414yes—
294D32—28no—
295D32—416no—
296C32×C4—24no—
297C32×C4C22×D412yes—
298C32×C4C2×#4114yescomplemented
299C3⋊Dic3—24no—
300C3⋊Dic3C22×D412yes—
301C3⋊Dic3C2×#4114yescomplemented
302C3×Dic3—24no—
303C3×Dic3C22×D414yes—
304C2×#41—34no—
305C2×#41—94no—
306C2×#41—98no—
307C2×#41—1816no—
308C22×Q8—92no—
309C22×D4—94no—
310C22×D4—94no—
311C22×D4—92no—
312C23×C4—91no—
313C23×C4—94no—
314C23×C4—92no—
315C4⋊Q8—92no—
316C4⋊Q8—94no—
317C4⋊Q8—91no—
318C4⋊Q8D3211yescharacteristic, complemented
319#127—32no—
320#127—94no—
321#127—92no—
322#124—34no—
323#124—94no—
324#124—98no—
325#121—38no—
326#121—916no—
327#121—98no—
328C4×D4—38no—
329C4×D4—98no—
330C4×D4—916no—
331C2×C4⋊C4—94no—
332C2×C22⋊C4—98no—
333C2×C42—32no—
334C2×C42—92no—
335C2×C42—91no—
336C2×C42—94no—
337C2×C42—92no—
338C2×C42—91no—
339C23×C3—32no—
340C23×C3—38no—
341C22×D3—32no—
342C22×D3—38no—
343C22×D3—61no—
344C22×D3—68no—
345C22×D3—616no—
346C22×D3—632no—
347C22×D3C23×D318yes—
348C22×D3C23×D312yes—
349C3×Q8—28no—
350C3×Q8—44no—
351C3×D4—616no—
352C3×D4—68no—
353C3×D4—616no—
354C2×C3×C4—22no—
355C2×C3×C4—21no—
356C2×C3×C4—24no—
357C2×C3×C4—32no—
358C2×C3×C4—38no—
359C2×C3×C4—34no—
360C2×C3×C4—616no—
361C2×C3×C4—68no—
362C2×C3×C4C23×D318yes—
363C2×C3×C4C23×D312yes—
364C2×C3×C4C23×D314yes—
365#67—616no—
366#67—632no—
367#67—616no—
368#67—616no—
369C2×Dic3—34no—
370C2×Dic3—32no—
371C2×Dic3—38no—
372C2×Dic3—38no—
373C2×Dic3—62no—
374C2×Dic3—61no—
375C2×Dic3—64no—
376C2×Dic3—68no—
377C2×Dic3—616no—
378C2×Dic3C23×D314yes—
379C2×Dic3C23×D312yes—
380D12—216no—
381D12—28no—
382D12—216no—
383C4×D3—28no—
384C4×D3—216no—
385C4×D3—38no—
386C4×D3—38no—
387C4×D3—316no—
388C4×D3—38no—
389C4×D3—64no—
390C4×D3—68no—
391C4×D3—68no—
392C4×D3—68no—
393C4×D3—616no—
394C4×D3—616no—
395C4×D3—128no—
396C4×D3D3×D418yescomplemented
397Dic6—616no—
398Dic6—68no—
399Dic6—128no—
400Dic6—124no—
401C2×C32C23×D411yescharacteristic
402C2×C32C22×#4112yes—
403C3⋊D3#53214yescomplemented
404C3×D3—24no—
405C3×D3—48no—
406C24—91no—
407C24—94no—
408#41—616no—
409#41—1816no—
410#41—1832no—
411C2×Q8—94no—
412C2×Q8—92no—
413C2×Q8—188no—
414C2×Q8C2×D3212yes—
415C2×D4—38no—
416C2×D4—38no—
417C2×D4—34no—
418C2×D4—98no—
419C2×D4—98no—
420C2×D4—94no—
421C2×D4—188no—
422C2×D4—1816no—
423C2×D4—1816no—
424C22×C4—32no—
425C22×C4—34no—
426C22×C4—38no—
427C22×C4—91no—
428C22×C4—98no—
429C22×C4—92no—
430C22×C4—92no—
431C22×C4—94no—
432C22×C4—98no—
433C22×C4—92no—
434C22×C4—91no—
435C22×C4—94no—
436C22×C4—1816no—
437C22×C4—188no—
438C4⋊C4—98no—
439C4⋊C4—94no—
440C4⋊C4C2×D3214yes—
441C22⋊C4—316no—
442C22⋊C4—916no—
443C42—34no—
444C42—32no—
445C42—94no—
446C42—92no—
447C42—91no—
448C42—92no—
449C42C2×D3211yescharacteristic
450C22×C3—21no—
451C22×C3—34no—
452C22×C3—64no—
453C22×C3—68no—
454C22×C3—616no—
455C22×C3C24×D312yes—
456C2×D3—24no—
457C2×D3—28no—
458C2×D3—216no—
459C2×D3—34no—
460C2×D3—38no—
461C2×D3—62no—
462C2×D3—64no—
463C2×D3—616no—
464C2×D3—1232no—
465C2×D3C2×D3×D414yes—
466C3×C4—28no—
467C3×C4—22no—
468C3×C4—24no—
469C3×C4—34no—
470C3×C4—44no—
471C3×C4—64no—
472C3×C4C2×D3×D414yes—
473C3×C4D3×#4118yescomplemented
474Dic3—24no—
475Dic3—34no—
476Dic3—38no—
477Dic3—62no—
478Dic3—64no—
479Dic3—68no—
480Dic3—124no—
481Dic3C2×D3×D414yes—
482C32C2×#53211yescharacteristic, complemented, Sylow
483C23—32no—
484C23—38no—
485C23—94no—
486C23—91no—
487C23—184no—
488C23—188no—
489C23—1816no—
490Q8—24no—
491Q8—188no—
492Q8—184no—
493D4—616no—
494D4—68no—
495D4—616no—
496D4—188no—
497D4—1816no—
498D4—1816no—
499C2×C4—32no—
500C2×C4—38no—
501C2×C4—34no—
502C2×C4—616no—
503C2×C4—68no—
504C2×C4—94no—
505C2×C4—98no—
506C2×C4—92no—
507C2×C4—91no—
508C2×C4—94no—
509C2×C4—98no—
510C2×C4—94no—
511C2×C4—188no—
512C2×C4—1816no—
513C2×C4—184no—
514C2×C4—188no—
515C2×C4C22×D3214yes—
516C2×C4C22×D3211yescharacteristic
517C2×C4C22×D3212yes—
518C2×C3—21no—
519C2×C3—22no—
520C2×C3—64no—
521C2×C3—128no—
522C2×C3C22×D3×D412yes—
523C2×C3C2×D3×#4114yes—
524D3—24no—
525D3—38no—
526D3—48no—
527D3—64no—
528C22—34no—
529C22—64no—
530C22—68no—
531C22—616no—
532C22—92no—
533C22—94no—
534C22—188no—
535C22—3616no—
536C22C23×D3211yescharacteristic
537C4—24no—
538C4—34no—
539C4—64no—
540C4—92no—
541C4—94no—
542C4—184no—
543C4D32×D412yes—
544C4#6431914yescomplemented
545C3—21no—
546C3D3×#53212yescomplemented
547C2—64no—
548C2—94no—
549C2—128no—
550C2C2×D32×D411yescharacteristic
551C2C2×#6431912yes—
subgroupG/H
center, FrattiniC22C23×D32
commutator, socle, cosocleC22×C32C25
FittingC32×C4⋊Q8C22
hypercenterC4⋊Q8D32
hypocenterC32C2×#532
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C4⋊Q8

Complements

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

NH ≅ G/Ntype
1. C2×#64319C2semidirect
2. C3⋊D3×C4⋊Q8C2semidirect
3. C3×#5725C2semidirect
4. #10595432C2semidirect
5. #10595359C2semidirect
6. #10594612C2semidirect
7. #10594605C2semidirect
8. #10594367C2semidirect
9. #10594008C2semidirect
10. C42×D32C2semidirect
11. #10593897C2semidirect
14. C2×C3×#239C22semidirect
22. C2×#3795C22semidirect
23. C2×#3795C22semidirect
24. C32×C4⋊Q8C22semidirect
25. #64153C22semidirect
27. #64097C22semidirect
29. #64078C22semidirect
30. C3×#947C22semidirect
31. C3×#895C22semidirect
32. C3×#893C22semidirect
33. C3×#874C22semidirect
34. C3×C42×D3C22semidirect
36. #63914C22semidirect
37. #63914C22semidirect
38. #63913C22semidirect
39. #63908C22semidirect
40. Dic3×D12C22semidirect
41. #63885C22semidirect
44. #63879C22semidirect
45. C4×D3×Dic3C22semidirect
46. C4×D3×Dic3C22semidirect
47. #63860C22semidirect
51. #5725D3semidirect
93. C4×D32D4semidirect
111. C2×#239C2×D3semidirect
125. C3×C4⋊Q8C2×D3semidirect
131. #947C2×D3semidirect
144. #895C2×D3semidirect
145. #893C2×D3semidirect
155. #874C2×D3semidirect
163. C42×D3C2×D3semidirect
182. C4×C3⋊D3#41semidirect
192. C3×C4×D3C2×D4semidirect
200. D3×Dic3C2×D4semidirect
298. C32×C4C2×#41semidirect
301. C3⋊Dic3C2×#41semidirect
318. C4⋊Q8D32semidirect
396. C4×D3D3×D4semidirect
403. C3⋊D3#532semidirect
473. C3×C4D3×#41semidirect
482. C32C2×#532semidirect
544. C4#64319semidirect
546. C3D3×#532semidirect

Maximal subgroups

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

subgroupindex
C2×#643192
C3⋊D3×C4⋊Q82
C3×#57252
#105954322
#105953592
#105946122
#105946052
#105943672
#105940082
C42×D322
#105938972
D3×#5323