Finite Group Databasebeta

← #11901809

Subgroups — #11901809

Order 1152.

2235 conjugacy classes of subgroups.

The subgroup lattice has 598 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595948C211yesmaximal, characteristic, complemented
2C2×C3×#872C211yesmaximal, characteristic, complemented
3C3×#5470C211yesmaximal, characteristic, complemented
4#10595038C214yesmaximal, complemented
5#10595023C212yesmaximal, complemented
6#10594980C214yesmaximal, complemented
7#10594954C212yesmaximal, complemented
8#10593989C212yesmaximal, complemented
9#10593934C218yesmaximal, complemented
10#10593881C212yesmaximal, complemented
11#10593877C214yesmaximal, complemented
12#86273—31nomaximal
13#85738—31nomaximal
14C2×#3828C2212yes—
15C22×C3×C4×D3C2211yescharacteristic
16C2×C32×C42C2211yescharacteristic
17#64139C2214yes—
18#64084C2212yescomplemented
19#64083C2211yescharacteristic, complemented
20C4×C4⋊(C3⋊D3)C2214yescomplemented
21#64078C2211yescharacteristic, complemented
22C2×C3×(C2×D3)⋊C4C2212yes—
23C3×#926C2212yes—
24C3×#924C2214yes—
25C2×C3×Dic3⋊C4C2212yes—
26C2×C3×C4×Dic3C2211yescharacteristic
27C3×#872C2212yes—
28C3×#872C2212yes—
29C3×#872C2214yes—
30C3×#870C2212yescomplemented
31C3×#869C2212yescomplemented
32C3×C4×Dic6C2214yescomplemented
33#63977C2214yes—
34#63966C2214yes—
35#63952C2218yes—
36#63910C2218yes—
37#63909C2214yes—
38#63907C2218yes—
39C4×#626C2218yes—
40#63897C2218yescomplemented
41#63894C2214yescomplemented
42#63888C2218yescomplemented
43C4×#624C2214yescomplemented
44#63874C2214yescomplemented
45#63861C2218yes—
46#63857C2214yes—
47#63854C2218yes—
48#63848C2218yescomplemented
49#63845C2218yescomplemented
50#63844C2214yescomplemented
51C3×#533—31no—
52C2×C3×#117—31no—
53#5791—32no—
54#5733—34no—
55#5698—32no—
56#5697—32no—
57#5645—34no—
58#5644—34no—
59#5580—38no—
60#5535—32no—
61#5534—34no—
62#5528—38no—
63#5524—32no—
64#5522—32no—
65#5518—32no—
66#5515—34no—
67#5494—34no—
68#5477—31no—
69#5477—31no—
70#5477—61no—
71C4×#235—32no—
72C2×#872D311yescharacteristic, complemented
73#5470D311yescharacteristic, complemented
74C23×C3×D3C2311yescharacteristic
75C22×C32×C4C2312yes—
76C22×C32×C4C2311yescharacteristic
77C2×#638C2314yes—
78#3828—28no—
79C2×C4⋊(C3⋊D3)C2312yes—
80C2×C4⋊(C3⋊D3)C2314yes—
81C2×C4×C3⋊D3C2314yes—
82C2×#634C2312yes—
83C22×C3×Dic3C2311yescharacteristic
84C22×C3×Dic3C2312yes—
85C2×C3×C4×D3—24no—
86C2×C3×C4×D3C2312yes—
87C2×C3×C4×D3C2312yes—
88C2×C3×Dic6C2314yes—
89C2×#626C2318yes—
90C2×#624C2318yes—
91C32×C42C2311yescharacteristic
92C32×C42C2312yes—
93C32×C42C2311yescharacteristic
94#3752C2318yes—
95C4⋊(C3⋊Dic3)C2314yes—
96C3×#217C2314yes—
97C3×(C2×D3)⋊C4C2314yes—
98C3×(C2×D3)⋊C4C2314yes—
99C3×C4⋊Dic3C2314yes—
100C3×C4⋊Dic3C2314yes—
101C3×Dic3⋊C4C2314yes—
102C3×Dic3⋊C4C2314yes—
103C3×Dic3⋊C4C2318yes—
104C3×C4×Dic3C2312yes—
105C3×C4×Dic3C2312yes—
106C3×C4×Dic3C2314yes—
107#3724C2318yes—
108Dic3⋊Dic3C2318yes—
109#3722C2318yes—
110#3722C2318yes—
111(C2×D3)⋊Dic3C2318yes—
112Dic32C2318yes—
113#3455—91noSylow
114C23×C3×C4—31no—
115C2×#235—32no—
116C2×#235—32no—
117C2×#235—62no—
118C22×C4×D3C2×D311yescharacteristic
119C3×C4⋊Q8—32no—
120C3×#125—32no—
121C3×C22⋊Q8—34no—
122C3×C4×Q8—34no—
123C3×#117—32no—
124C3×#117—32no—
125C3×#117—34no—
126C3×#117—32no—
127C2×C3×C4⋊C4—32no—
128C2×C3×C22⋊C4—32no—
129C2×C3×C42—21no—
130C2×C3×C42—31no—
131C2×C3×C42C2×D311yescharacteristic
132C2×C3×C42C2×D311yescharacteristic
133#953—34no—
134#947—38no—
135#946—38no—
136#930—34no—
137#930—34no—
138#930—34no—
139#930—64no—
140#929—34no—
141C4×#67—38no—
142C4×#67—38no—
143C2×(C2×D3)⋊C4C2×D312yes—
144#926C2×D312yes—
145#924—34no—
146#924C2×D314yes—
147C2×Dic3⋊C4C2×D312yes—
148C2×C4×Dic3C2×D311yescharacteristic
149#898—38no—
150#898—38no—
151#898—38no—
152#897—34no—
153#896—38no—
154#895—34no—
155#895—38no—
156#894—38no—
157#894—38no—
158#894—38no—
159#893—34no—
160#890—38no—
161#889—38no—
162#887—34no—
163#886—34no—
164#885—38no—
165#884—38no—
166#883—38no—
167#882—34no—
168#67⋊C4—38no—
169#879—38no—
170#875—32no—
171#875—32no—
172#875—62no—
173#874—31no—
174#874—31no—
175#874—61no—
176C4×D12—38no—
177C4×D12—34no—
178C4×D12—34no—
179C4×D12—34no—
180C4×D12—64no—
181#872—34no—
182#872—34no—
183#872C2×D312yes—
184#872C2×D312yes—
185#872C2×D314yes—
186C42×D3—34no—
187C42×D3—34no—
188#870C2×D312yescomplemented
189#869—31no—
190#869—31no—
191#869—61no—
192#869C2×D312yescomplemented
193C4×Dic6—34no—
194C4×Dic6C2×D314yescomplemented
195C23×C32C2411yescharacteristic
196C22×C3⋊D3C2414yes—
197C22×C3×D3—22no—
198C22×C3×D3—42no—
199C22×C3×D3C2412yes—
200C2×C32×C4—42no—
201C2×C32×C4#4114yes—
202C2×C32×C4C2412yes—
203C2×C32×C4C2412yes—
204C2×C32×C4C2411yescharacteristic
205C2×C32×C4C2411yescharacteristic
206#638—28no—
207C2×C3⋊Dic3C2414yes—
208C4⋊(C3⋊D3)—24no—
209C4⋊(C3⋊D3)—44no—
210C4×C3⋊D3—28no—
211#634—24no—
212C2×C3×Dic3—22no—
213C2×C3×Dic3—42no—
214C2×C3×Dic3C2414yes—
215C2×C3×Dic3C2418yes—
216C2×C3×Dic3C2412yes—
217C3×C4×D3—24no—
218C3×C4×D3—24no—
219C3×Dic6—44no—
220#626—48no—
221#624—48no—
222#542—94no—
223#541—92no—
224#540—92no—
225#539—94no—
226#538—94no—
227#533—31no—
228#532—91no—
229#529—98no—
230#525—92no—
231C4×#41—92no—
232C2×#117—31no—
233C24×C3—31no—
234C23×D3C22×D311yescharacteristic
235C2×C3×Q8—34no—
236C22×C3×C4—21no—
237C22×C3×C4—22no—
238C22×C3×C4—31no—
239C22×C3×C4—32no—
240C22×C3×C4—32no—
241C22×C3×C4—32no—
242C22×C3×C4—64no—
243C22×C3×C4C22×D312yes—
244C22×C3×C4C22×D312yes—
245C22×C3×C4C22×D311yescharacteristic
246C22×C3×C4C22×D311yescharacteristic
247C2×#67—34no—
248C2×#67—34no—
249C2×#67—38no—
250C2×#67—64no—
251C22×Dic3C22×D311yescharacteristic
252C22×Dic3C22×D312yes—
253#235—68no—
254#235—68no—
255#235—128no—
256C2×D12—32no—
257C2×D12—32no—
258C2×D12—38no—
259C2×D12—34no—
260C2×D12—34no—
261C2×D12—64no—
262C2×D12—62no—
263C2×C4×D3—24no—
264C2×C4×D3—34no—
265C2×C4×D3—34no—
266C2×C4×D3—38no—
267C2×C4×D3—38no—
268C2×C4×D3—64no—
269C2×C4×D3C22×D312yes—
270C2×C4×D3C22×D312yes—
271C2×Dic6—32no—
272C2×Dic6—32no—
273C2×Dic6—62no—
274C2×Dic6C22×D314yes—
275C3×C4⋊C4—34no—
276C3×C4⋊C4—34no—
277C3×C4⋊C4—38no—
278C3×C4⋊C4—34no—
279C3×C4⋊C4—34no—
280C3×C22⋊C4—34no—
281C3×C22⋊C4—34no—
282C3×C22⋊C4—34no—
283C3×C42—21no—
284C3×C42—22no—
285C3×C42—21no—
286C3×C42—32no—
287C3×C42—32no—
288C3×C42—34no—
289C3×C42C22×D312yes—
290C3×C42C22×D311yescharacteristic
291C3×C42C22×D311yescharacteristic
292C3×C42C22×D311yescharacteristic
293C3×C42C22×D312yes—
294C3×C42C22×D311yescharacteristic
295#217—38no—
296#217C22×D314yes—
297(C2×D3)⋊C4—38no—
298(C2×D3)⋊C4—38no—
299(C2×D3)⋊C4—38no—
300(C2×D3)⋊C4—38no—
301(C2×D3)⋊C4—38no—
302(C2×D3)⋊C4—38no—
303(C2×D3)⋊C4—38no—
304(C2×D3)⋊C4—68no—
305(C2×D3)⋊C4C22×D314yes—
306(C2×D3)⋊C4C22×D314yes—
307C4⋊Dic3—34no—
308C4⋊Dic3—34no—
309C4⋊Dic3—38no—
310C4⋊Dic3—64no—
311C4⋊Dic3C22×D314yes—
312C4⋊Dic3C22×D314yes—
313Dic3⋊C4—38no—
314Dic3⋊C4—38no—
315Dic3⋊C4—38no—
316Dic3⋊C4C22×D318yes—
317Dic3⋊C4C22×D314yes—
318Dic3⋊C4C22×D314yes—
319C4×Dic3—38no—
320C4×Dic3—38no—
321C4×Dic3C22×D314yes—
322C4×Dic3C22×D312yes—
323C4×Dic3C22×D312yes—
324C22×C32—22no—
325C22×C32C2×#4112yes—
326C22×C32C2511yescharacteristic
327C2×C3⋊D3—24no—
328C2×C3⋊D3—28no—
329C2×C3×D3—22no—
330C2×C3×D3—24no—
331C2×C3×D3—44no—
332C32×C4—22no—
333C32×C4—22no—
334C32×C4C2×#4112yes—
335C32×C4C2×#4112yes—
336C3⋊Dic3—24no—
337C3×Dic3—22no—
338C3×Dic3—24no—
339C3×Dic3—28no—
340C2×#41—92no—
341C23×C4—31no—
342C4⋊Q8—32no—
343C4⋊Q8—91no—
344#127—91no—
345#126—98no—
346#126—98no—
347#125—32no—
348#125—98no—
349#124—98no—
350#124—92no—
351#123—98no—
352#123—94no—
353#123—98no—
354C22⋊Q8—34no—
355C22⋊Q8—94no—
356C22⋊Q8—98no—
357#121—98no—
358#121—94no—
359#121—94no—
360#120—94no—
361C4×Q8—34no—
362C4×Q8—94no—
363C4×D4—94no—
364C4×D4—98no—
365C4×D4—98no—
366C4×D4—94no—
367#117—32no—
368#117—34no—
369#117—32no—
370#117—32no—
371#117—94no—
372C2×C4⋊C4—32no—
373C2×C22⋊C4—32no—
374C2×C42—31no—
375C2×C42—94no—
376C2×C42D3211yescharacteristic
377C23×C3—21no—
378C23×C3—32no—
379C23×C3—62no—
380C23×C3—122no—
381C23×C3C23×D311yescharacteristic
382C23×C3C23×D311yescharacteristic
383C22×D3—22no—
384C22×D3—34no—
385C22×D3—34no—
386C22×D3—42no—
387C22×D3—64no—
388C22×D3C23×D312yes—
389C3×Q8—124no—
390C2×C3×C4—22no—
391C2×C3×C4—21no—
392C2×C3×C4—22no—
393C2×C3×C4—21no—
394C2×C3×C4—24no—
395C2×C3×C4—34no—
396C2×C3×C4—38no—
397C2×C3×C4—32no—
398C2×C3×C4—42no—
399C2×C3×C4—42no—
400C2×C3×C4—44no—
401C2×C3×C4—62no—
402C2×C3×C4—64no—
403C2×C3×C4—64no—
404C2×C3×C4—122no—
405C2×C3×C4#23514yes—
406C2×C3×C4#23914yes—
407C2×C3×C4C23×D312yes—
408C2×C3×C4C23×D312yes—
409C2×C3×C4C23×D312yes—
410C2×C3×C4C23×D312yes—
411C2×C3×C4C23×D311yescharacteristic
412C2×C3×C4C23×D311yescharacteristic
413C2×C3×C4C23×D311yescharacteristic
414C2×C3×C4C23×D311yescharacteristic
415#67—68no—
416#67—68no—
417#67—128no—
418#67—128no—
419C2×Dic3—22no—
420C2×Dic3—34no—
421C2×Dic3—34no—
422C2×Dic3—42no—
423C2×Dic3—64no—
424C2×Dic3C23×D314yes—
425C2×Dic3C23×D318yes—
426C2×Dic3C23×D312yes—
427D12—64no—
428D12—64no—
429D12—124no—
430D12—124no—
431D12—124no—
432D12—128no—
433D12—128no—
434C4×D3—24no—
435C4×D3—24no—
436C4×D3—68no—
437C4×D3—68no—
438C4×D3—128no—
439C4×D3—128no—
440C4×D3—128no—
441Dic6—44no—
442Dic6—64no—
443Dic6—64no—
444Dic6—124no—
445C2×C32—22no—
446C2×C32C22×#4111yescharacteristic
447C2×C32#58512yes—
448C3⋊D3—44no—
449C3×D3—42no—
450C24—31no—
451#41—188no—
452C2×Q8—34no—
453C2×Q8—92no—
454C2×D4—98no—
455C2×D4—94no—
456C2×D4—92no—
457C2×D4—94no—
458C22×C4—31no—
459C22×C4—32no—
460C22×C4—32no—
461C22×C4—32no—
462C22×C4—64no—
463C22×C4—98no—
464C22×C4—94no—
465C22×C4C2×D3212yes—
466C22×C4C2×D3211yescharacteristic
467C4⋊C4—34no—
468C4⋊C4—34no—
469C4⋊C4—34no—
470C4⋊C4—38no—
471C4⋊C4—34no—
472C4⋊C4—98no—
473C4⋊C4—98no—
474C4⋊C4—94no—
475C22⋊C4—34no—
476C22⋊C4—34no—
477C22⋊C4—34no—
478C22⋊C4—98no—
479C22⋊C4—98no—
480C22⋊C4—98no—
481C22⋊C4—98no—
482C42—32no—
483C42—32no—
484C42—34no—
485C42—98no—
486C42C2×D3211yescharacteristic
487C42C2×D3211yescharacteristic
488C42C2×D3212yes—
489C22×C3—22no—
490C22×C3—22no—
491C22×C3—22no—
492C22×C3—21no—
493C22×C3—42no—
494C22×C3—62no—
495C22×C3—64no—
496C22×C3—124no—
497C22×C3C2×#23512yes—
498C22×C3C2×#23912yes—
499C22×C3C24×D311yescharacteristic
500C22×C3C24×D311yescharacteristic
501C2×D3—22no—
502C2×D3—24no—
503C2×D3—44no—
504C2×D3—64no—
505C2×D3—64no—
506C2×D3—68no—
507C2×D3—68no—
508C2×D3—124no—
509C2×D3—128no—
510C3×C4—24no—
511C3×C4—22no—
512C3×C4—22no—
513C3×C4—22no—
514C3×C4—22no—
515C3×C4—22no—
516C3×C4—22no—
517C3×C4—42no—
518C3×C4—62no—
519C3×C4—64no—
520C3×C4—68no—
521C3×C4C2×#23512yes—
522C3×C4C2×#23512yes—
523C3×C4C2×#23912yes—
524C3×C4C2×#23912yes—
525Dic3—22no—
526Dic3—28no—
527Dic3—24no—
528Dic3—64no—
529Dic3—64no—
530Dic3—124no—
531C32#345511yescharacteristic, complemented, Sylow
532C23—32no—
533C23—62no—
534C23—94no—
535C23—122no—
536C23C22×D3211yescharacteristic
537Q8—124no—
538Q8—184no—
539D4—188no—
540D4—184no—
541D4—364no—
542D4—368no—
543C2×C4—34no—
544C2×C4—38no—
545C2×C4—32no—
546C2×C4—42no—
547C2×C4—62no—
548C2×C4—64no—
549C2×C4—64no—
550C2×C4—94no—
551C2×C4—122no—
552C2×C4—188no—
553C2×C4—368no—
554C2×C4#379914yes—
555C2×C4C22×D3212yes—
556C2×C4C22×D3212yes—
557C2×C4C22×D3211yescharacteristic
558C2×C4C22×D3211yescharacteristic
559C2×C3—22no—
560C2×C3—22no—
561C2×C3—21no—
562C2×C3—22no—
563C2×C3—42no—
564C2×C3—122no—
565C2×C3C22×#23511yescharacteristic
566C2×C3C22×#23911yescharacteristic
567C2×C3#596412yes—
568C2×C3#596412yes—
569D3—42no—
570D3—124no—
571D3—124no—
572D3—244no—
573C22—22no—
574C22—62no—
575C22—64no—
576C22—124no—
577C22—184no—
578C22—188no—
579C22C2×#379912yes—
580C22C23×D3211yescharacteristic
581C4—22no—
582C4—22no—
583C4—62no—
584C4—64no—
585C4—68no—
586C4—184no—
587C4C2×#379912yes—
588C4C2×#379912yes—
589C3—21no—
590C3#8573811yescharacteristic, complemented
591C3#8627311yescharacteristic, complemented
592C2—22no—
593C2—122no—
594C2—364no—
595C2C22×#379911yescharacteristic
596C2#1059666912yes—
subgroupG/H
centerC2×C4C22×D32
commutator, socle, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC2×C32×C42C22
hypercenterC2×C42D32
hypocenterC32#3455
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
1. #10595948C2semidirect
2. C2×C3×#872C2semidirect
3. C3×#5470C2semidirect
4. #10595038C2semidirect
5. #10595023C2semidirect
6. #10594980C2semidirect
7. #10594954C2semidirect
8. #10593989C2semidirect
9. #10593934C2semidirect
10. #10593881C2semidirect
11. #10593877C2semidirect
18. #64084C22semidirect
19. #64083C22semidirect
20. C4×C4⋊(C3⋊D3)C22semidirect
21. #64078C22semidirect
30. C3×#870C22semidirect
31. C3×#869C22semidirect
32. C3×C4×Dic6C22semidirect
40. #63897C22semidirect
41. #63894C22semidirect
42. #63888C22semidirect
43. C4×#624C22semidirect
44. #63874C22semidirect
48. #63848C22semidirect
49. #63845C22semidirect
50. #63844C22semidirect
72. C2×#872D3semidirect
73. #5470D3semidirect
188. #870C2×D3semidirect
192. #869C2×D3semidirect
194. C4×Dic6C2×D3semidirect
531. C32#3455semidirect
590. C3#85738semidirect
591. C3#86273semidirect

Maximal subgroups

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

subgroupindex
#105959482
C2×C3×#8722
C3×#54702
#105950382
#105950232
#105949802
#105949542
#105939892
#105939342
#105938812
#105938772
#862733
#857383