Finite Group Databasebeta

← #11860632

Subgroups — #11860632

Order 1152.

1069 conjugacy classes of subgroups.

The subgroup lattice has 584 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64160C211yesmaximal, characteristic
2C3×#5827C211yesmaximal, characteristic
3#10594828C211yesmaximal, characteristic, complemented
4C3×#5233C211yesmaximal, characteristic
5#10591541C212yesmaximal, complemented
6#10591537C212yesmaximal, complemented
7#10591405C212yesmaximal, complemented
8#10591401C212yesmaximal, complemented
9#10591139C211yesmaximal, characteristic, complemented
10C2×#63567C211yesmaximal, characteristic, complemented
11#10591055C211yesmaximal, characteristic, complemented
12#82571—31nomaximal
13#78821—31nomaximal
14C2×C32×#41C2211yescharacteristic
15C22×#634C2211yescharacteristic
16#64160C418yescomplemented
17C2×#3756C2212yes—
18C2×#3754C2212yes—
19C2×#3748C2211yescharacteristic
20C3×Q8×Dic3C2212yes—
21C3×D4×Dic3—22no—
22C3×D4×Dic3C2212yes—
23C3×#926—21no—
24C3×#926C2211yescharacteristic
25C3×#926C2211yescharacteristic
26C2×C3×C4⋊Dic3—21no—
27C2×C3×C4⋊Dic3C2211yescharacteristic
28C22×C3×C3⋊C8C2211yescharacteristic
29#63957—22no—
30#63844—21no—
31#63844—21no—
32#63844C2212yes—
33#63844C2212yes—
34C3×#835C2211yescharacteristic
35C3×#835C2211yescharacteristic
36C3×#832C2211yescharacteristic
37C3×#832C2211yescharacteristic
38#63576C2212yes—
39#63574C2212yes—
40#63567C2212yes—
41#63567C2212yes—
42#63554C2212yes—
43Dic3×C3⋊C8C2212yes—
44C3×#520—31no—
45#5827D311yescharacteristic
46C2×#951—31no—
47C2×#951—31no—
48C2×#951—61no—
49#5516—31no—
50#5516—31no—
51C3×#416—31no—
52#5233D311yescharacteristic
53C2×#816—31no—
54#5101—31no—
55#5030—32no—
56C4×#216—32no—
57#5018—32no—
58C4×#214—32no—
59#4997—31no—
60#4995—31no—
61C2×#810—31no—
62#4964—31no—
63#4790—32no—
64#4789—32no—
65#4758—32no—
66#4757—32no—
67C32×#41—22no—
68C32×#41C2×C414yes—
69C2×C32×Q8C2311yescharacteristic
70C2×C32×D4—21no—
71C2×C32×D4C2311yescharacteristic
72C22×C32×C4—21no—
73C22×C32×C4C2311yescharacteristic
74C22×C3⋊Dic3—21no—
75C2×#634—21no—
76C2×#634—22no—
77C2×#634C2×C414yescomplemented
78C2×#634C2312yes—
79C22×C3×Dic3—21no—
80C22×C3×Dic3—22no—
81#3756C2×C418yescomplemented
82#3754C2×C418yescomplemented
83#3748C2×C414yescomplemented
84C2×C3⋊(C3⋊C8)C2312yes—
85C3×#217—21no—
86C3×#217—22no—
87C3×#217D412yes—
88C3×C4⋊Dic3—21no—
89C3×C4⋊Dic3—22no—
90C3×C4⋊Dic3D411yescharacteristic
91C3×C4⋊Dic3D411yescharacteristic
92C3×C4⋊Dic3C2312yes—
93C3×C4⋊Dic3C2311yescharacteristic
94C3×C4⋊Dic3C2311yescharacteristic
95C3×C4×Dic3—21no—
96C3×C4×Dic3—22no—
97C3×C4×Dic3C2312yes—
98C2×C3×C3⋊C8—22no—
99C2×C3×C3⋊C8C2311yescharacteristic
100C2×C3×C3⋊C8C2311yescharacteristic
101#3724—22no—
102#3724—22no—
103Dic32—22no—
104Dic32—22no—
105#2947—91noSylow
106C2×C3×#41—21no—
107C2×C3×#41C2×D311yescharacteristic
108C2×C3×#41C2×D311yescharacteristic
109C22×Dic6—31no—
110C22×Dic6—31no—
111C22×Dic6—61no—
112C22×C3×C8—31no—
113C3×C4×Q8—32no—
114C3×C4×D4—32no—
115C3×C4×D4—62no—
116C3×#117—31no—
117C3×#117—31no—
118C3×#117—61no—
119C2×C3×C4⋊C4—31no—
120C2×C3×C4⋊C4—61no—
121#951—38no—
122#951—38no—
123#951—68no—
124Q8×Dic3C2×D312yes—
125C2×#216—32no—
126C2×#216—32no—
127C2×#216—62no—
128D4×Dic3—22no—
129D4×Dic3C2×D312yes—
130C2×#214—32no—
131C2×#214—32no—
132C2×#214—62no—
133#926—21no—
134#926C2×D311yescharacteristic
135#926C2×D311yescharacteristic
136C2×C4⋊Dic3—21no—
137C2×C4⋊Dic3C2×D311yescharacteristic
138C2×#208—31no—
139C2×#208—31no—
140C2×#208—61no—
141C22×C3⋊C8C2×D311yescharacteristic
142#887—32no—
143#887—32no—
144#887—61no—
145#887—61no—
146#877—62no—
147#877—62no—
148C4×Dic6—32no—
149C4×Dic6—32no—
150C4×Dic6—61no—
151C4×Dic6—61no—
152C3×#103—31no—
153C3×#103—31no—
154C3×#102—31no—
155C3×#102—31no—
156#835C2×D311yescharacteristic
157#835C2×D311yescharacteristic
158#832C2×D311yescharacteristic
159#832C2×D311yescharacteristic
160#816—32no—
161#816—32no—
162#815—32no—
163C8×Dic3—32no—
164#810—32no—
165#810—32no—
166#808—32no—
167#808—32no—
168#807—32no—
169#807—32no—
170#803—32no—
171C4×C3⋊C8—32no—
172C23×C32—21no—
173C23×C32C2×D411yescharacteristic
174C32×Q8—21no—
175C32×Q8C22×C412yes—
176C32×D4—24no—
177C32×D4—21no—
178C32×D4C22×C412yes—
179C2×C32×C4—21no—
180C2×C32×C4—24no—
181C2×C32×C4C22×C412yes—
182C2×C32×C4C2×D411yescharacteristic
183C2×C32×C4#4112yes—
184C2×C32×C4C2411yescharacteristic
185C2×C3⋊Dic3—24no—
186C2×C3⋊Dic3—22no—
187#634—24no—
188#634—22no—
189#634C22×C414yes—
190C2×C3×Dic3—21no—
191C2×C3×Dic3—21no—
192C2×C3×Dic3—22no—
193C2×C3×Dic3—82no—
194C2×C3×Dic3—81no—
195C2×C3×Dic3C2×D412yes—
196C2×C3×Dic3C2×D412yes—
197C3⋊(C3⋊C8)C22×C414yes—
198C3×C3⋊C8—21no—
199C3×C3⋊C8—21no—
200C2×#137—91no—
201#520—31no—
202#519—91no—
203#441—92no—
204#440—92no—
205C4×Q16—92no—
206C4×SD16—92no—
207#428—91no—
208#416—31no—
209C2×#103—91no—
210#405—91no—
211C3×#41—22no—
212C3×#41—22no—
213C3×#41—24no—
214C3×#41—42no—
215C3×#41C4×D314yes—
216C3×#41C4×D314yes—
217C2×C3×Q8—21no—
218C2×C3×Q8C22×D311yescharacteristic
219C2×C3×Q8C22×D311yescharacteristic
220C2×C3×D4—21no—
221C2×C3×D4—21no—
222C2×C3×D4—21no—
223C2×C3×D4—41no—
224C2×C3×D4C22×D311yescharacteristic
225C2×C3×D4C22×D311yescharacteristic
226C22×C3×C4—21no—
227C22×C3×C4—21no—
228C22×C3×C4—21no—
229C22×C3×C4—41no—
230C22×C3×C4—62no—
231C22×C3×C4—61no—
232C22×C3×C4C22×D311yescharacteristic
233C22×C3×C4C22×D311yescharacteristic
234C22×Dic3—21no—
235C22×Dic3—22no—
236C22×Dic3—61no—
237C22×Dic3—61no—
238C22×Dic3—121no—
239C2×Dic6—34no—
240C2×Dic6—34no—
241C2×Dic6—32no—
242C2×Dic6—32no—
243C2×Dic6—62no—
244C2×Dic6—64no—
245C2×Dic6—62no—
246C2×Dic6—61no—
247C2×Dic6—62no—
248C2×Dic6—61no—
249C2×Dic6—122no—
250C2×Dic6—121no—
251C2×C3×C8—31no—
252C2×C3×C8—31no—
253C2×C3×C8—62no—
254C3×C4⋊C4—31no—
255C3×C4⋊C4—31no—
256C3×C4⋊C4—31no—
257C3×C4⋊C4—32no—
258C3×C4⋊C4—31no—
259C3×C4⋊C4—62no—
260C3×C4⋊C4—61no—
261C3×C22⋊C4—32no—
262C3×C22⋊C4—62no—
263C3×C22⋊C4—61no—
264C3×C42—32no—
265C3×C42—62no—
266C3×C42—61no—
267#217—21no—
268#217—22no—
269#217#6712yes—
270#216—38no—
271#216—38no—
272#216—68no—
273#214—38no—
274#214—38no—
275#214—68no—
276C4⋊Dic3—21no—
277C4⋊Dic3—22no—
278C4⋊Dic3#6711yescharacteristic
279C4⋊Dic3#6711yescharacteristic
280C4⋊Dic3C22×D311yescharacteristic
281C4⋊Dic3C22×D312yes—
282C4⋊Dic3C22×D311yescharacteristic
283Dic3⋊C4—62no—
284Dic3⋊C4—62no—
285Dic3⋊C4—62no—
286Dic3⋊C4—62no—
287C4×Dic3—21no—
288C4×Dic3—22no—
289C4×Dic3—62no—
290C4×Dic3—62no—
291C4×Dic3—62no—
292C4×Dic3—62no—
293C4×Dic3C22×D312yes—
294#208—34no—
295#208—34no—
296#208—64no—
297C2×C3⋊C8—22no—
298C2×C3⋊C8—32no—
299C2×C3⋊C8—32no—
300C2×C3⋊C8—62no—
301C2×C3⋊C8C22×D311yescharacteristic
302C2×C3⋊C8C22×D311yescharacteristic
303C22×C32—21no—
304C22×C32—21no—
305C22×C32—22no—
306C22×C32—41no—
307C22×C32—41no—
308C22×C32C4×D412yes—
309C22×C32C22×D411yescharacteristic
310C32×C4—22no—
311C32×C4C4×D412yes—
312C32×C4C23×C411yescharacteristic
313C32×C4C2×#4111yescharacteristic
314C3⋊Dic3—24no—
315C3×Dic3—22no—
316C3×Dic3—22no—
317C3×Dic3—41no—
318C3×Dic3—42no—
319C3×Dic3—41no—
320C2×#41D3211yescharacteristic
321C22×Q8—91no—
322#137—98no—
323C2×Q16—92no—
324C2×SD16—92no—
325C2×M16—91no—
326C22×C8—31no—
327C4×Q8—32no—
328C4×Q8—92no—
329C4×Q8—92no—
330C4×Q8—181no—
331C4×Q8—181no—
332C4×D4—32no—
333C4×D4—62no—
334#117—31no—
335#117—31no—
336#117—61no—
337#117—182no—
338C2×C4⋊C4—31no—
339C2×C4⋊C4—61no—
340#107—92no—
341#106—92no—
342#103—31no—
343#103—31no—
344#103—92no—
345#103—92no—
346#102—31no—
347#102—31no—
348#97—92no—
349C4×C8—92no—
350C23×C3—21no—
351C23×C3—21no—
352C23×C3—21no—
353C23×C3—41no—
354C23×C3D3×D411yescharacteristic
355C23×C3C2×#6711yescharacteristic
356C3×Q8—21no—
357C3×Q8—21no—
358C3×Q8—22no—
359C3×Q8—41no—
360C3×Q8C2×C4×D312yes—
361C3×Q8C2×C4×D312yes—
362C3×D4—24no—
363C3×D4—24no—
364C3×D4—21no—
365C3×D4—21no—
366C3×D4—22no—
367C3×D4—41no—
368C3×D4—44no—
369C3×D4C2×C4×D312yes—
370C3×D4C2×C4×D312yes—
371C2×C3×C4—21no—
372C2×C3×C4—21no—
373C2×C3×C4—24no—
374C2×C3×C4—24no—
375C2×C3×C4—21no—
376C2×C3×C4—22no—
377C2×C3×C4—22no—
378C2×C3×C4—21no—
379C2×C3×C4—32no—
380C2×C3×C4—32no—
381C2×C3×C4—44no—
382C2×C3×C4—41no—
383C2×C3×C4—62no—
384C2×C3×C4—61no—
385C2×C3×C4—61no—
386C2×C3×C4—242no—
387C2×C3×C4—241no—
388C2×C3×C4C2×C4×D312yes—
389C2×C3×C4C2×C4×D312yes—
390C2×C3×C4#23512yes—
391C2×C3×C4D3×D411yescharacteristic
392C2×C3×C4#23712yes—
393C2×C3×C4C2×#6711yescharacteristic
394C2×C3×C4C23×D311yescharacteristic
395C2×C3×C4C23×D311yescharacteristic
396C2×Dic3—21no—
397C2×Dic3—21no—
398C2×Dic3—22no—
399C2×Dic3—64no—
400C2×Dic3—64no—
401C2×Dic3—62no—
402C2×Dic3—62no—
403C2×Dic3—82no—
404C2×Dic3—81no—
405C2×Dic3—122no—
406C2×Dic3—124no—
407C2×Dic3C2×#6712yes—
408C2×Dic3C2×#6712yes—
409Dic6—34no—
410Dic6—34no—
411Dic6—64no—
412Dic6—64no—
413Dic6—64no—
414Dic6—62no—
415Dic6—62no—
416Dic6—122no—
417Dic6—124no—
418C3×C8—61no—
419C3×C8—61no—
420C3⋊C8—21no—
421C3⋊C8—21no—
422C3⋊C8—34no—
423C3⋊C8—34no—
424C3⋊C8—64no—
425C2×C32—22no—
426C2×C32—42no—
427C2×C32C2×C4×D411yescharacteristic
428C2×C32#57711yescharacteristic
429C2×C32#57811yescharacteristic
430#41—22no—
431#41#62414yes—
432C2×Q8—92no—
433C2×Q8—94no—
434C2×Q8—182no—
435C2×Q8—181no—
436C2×Q8C2×D3211yescharacteristic
437C2×D4—21no—
438C2×D4C2×D3211yescharacteristic
439C22×C4—21no—
440C22×C4—62no—
441C22×C4—61no—
442C22×C4—181no—
443C22×C4C2×D3211yescharacteristic
444Q16—98no—
445SD16—98no—
446M16—94no—
447C2×C8—31no—
448C2×C8—31no—
449C2×C8—62no—
450C2×C8—92no—
451C4⋊C4—31no—
452C4⋊C4—31no—
453C4⋊C4—31no—
454C4⋊C4—31no—
455C4⋊C4—32no—
456C4⋊C4—62no—
457C4⋊C4—61no—
458C4⋊C4—182no—
459C4⋊C4—182no—
460C22⋊C4—32no—
461C22⋊C4—62no—
462C22⋊C4—61no—
463C42—32no—
464C42—62no—
465C42—61no—
466C42—182no—
467C42—182no—
468C22×C3—21no—
469C22×C3—21no—
470C22×C3—21no—
471C22×C3—21no—
472C22×C3—22no—
473C22×C3—22no—
474C22×C3—21no—
475C22×C3—22no—
476C22×C3—41no—
477C22×C3—41no—
478C22×C3—42no—
479C22×C3—41no—
480C22×C3—41no—
481C22×C3—41no—
482C22×C3—41no—
483C22×C3—81no—
484C22×C3—81no—
485C22×C3#67⋊C412yes—
486C22×C3C4×#6712yes—
487C22×C3C2×D3×D411yescharacteristic
488C22×C3C22×#6711yescharacteristic
489C3×C4—22no—
490C3×C4—22no—
491C3×C4—21no—
492C3×C4—21no—
493C3×C4—22no—
494C3×C4—42no—
495C3×C4—62no—
496C3×C4—62no—
497C3×C4—122no—
498C3×C4—121no—
499C3×C4—121no—
500C3×C4#67⋊C412yes—
501C3×C4C4×#6712yes—
502C3×C4C22×C4×D311yescharacteristic
503C3×C4C22×C4×D311yescharacteristic
504C3×C4C2×#23511yescharacteristic
505C3×C4C2×#23711yescharacteristic
506Dic3—22no—
507Dic3—22no—
508Dic3—41no—
509Dic3—41no—
510Dic3—42no—
511Dic3—64no—
512Dic3—64no—
513Dic3—124no—
514C32#294711yescharacteristic, complemented, Sylow
515C23—21no—
516C23D3×#6711yescharacteristic
517Q8—21no—
518Q8—94no—
519Q8—182no—
520Q8—184no—
521Q8C2×#62412yes—
522D4—24no—
523D4—21no—
524D4C2×#62412yes—
525C2×C4—21no—
526C2×C4—24no—
527C2×C4—32no—
528C2×C4—32no—
529C2×C4—61no—
530C2×C4—61no—
531C2×C4—62no—
532C2×C4—182no—
533C2×C4—184no—
534C2×C4—242no—
535C2×C4—241no—
536C2×C4#380412yes—
537C2×C4C2×#62412yes—
538C2×C4D3×#6711yescharacteristic
539C2×C4C22×D3211yescharacteristic
540C8—61no—
541C8—61no—
542C8—94no—
543C2×C3—22no—
544C2×C3—22no—
545C2×C3—21no—
546C2×C3—21no—
547C2×C3—21no—
548C2×C3—42no—
549C2×C3—42no—
550C2×C3—42no—
551C2×C3—82no—
552C2×C3C2×#67⋊C411yescharacteristic
553C2×C3#577011yescharacteristic
554C2×C3#577111yescharacteristic
555C2×C3C2×C4×#6711yescharacteristic
556C2×C3#583611yescharacteristic
557C2×C3#583811yescharacteristic
558C22—21no—
559C22—21no—
560C22—22no—
561C22—41no—
562C22—41no—
563C22#6395212yes—
564C22C2×D3×#6711yescharacteristic
565C4—22no—
566C4—62no—
567C4—62no—
568C4—122no—
569C4—121no—
570C4—121no—
571C4—184no—
572C4#6395212yes—
573C4C2×#380411yescharacteristic
574C4C22×#62411yescharacteristic
575C3—21no—
576C3#7882111yescharacteristic, complemented
577C3#8257111yescharacteristic, complemented
578C2—22no—
579C2—42no—
580C2#1059546611yescharacteristic
581C2#1059546711yescharacteristic
582C2C2×#6395211yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
Fitting, prime radicalC2×C32×#41C22
socleC22×C32C22×D4
cosocleC2×C32×C4C24
hypercenterC2×#41D32
hypocenterC32#2947
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
3. #10594828C2semidirect
5. #10591541C2semidirect
6. #10591537C2semidirect
7. #10591405C2semidirect
8. #10591401C2semidirect
9. #10591139C2semidirect
10. C2×#63567C2semidirect
11. #10591055C2semidirect
16. #64160C4semidirect
77. C2×#634C2×C4semidirect
81. #3756C2×C4semidirect
82. #3754C2×C4semidirect
83. #3748C2×C4semidirect
514. C32#2947semidirect
576. C3#78821semidirect
577. C3#82571semidirect

Maximal subgroups

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

subgroupindex
C2×#641602
C3×#58272
#105948282
C3×#52332
#105915412
#105915372
#105914052
#105914012
#105911392
C2×#635672
#105910552
#825713
#788213