Finite Group Databasebeta

← #11865788

Subgroups — #11865788

Order 1152.

1147 conjugacy classes of subgroups.

The subgroup lattice has 583 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#41×C3⋊Dic3C211yesmaximal, characteristic, complemented
2C2×C3×#950C212yesmaximal, complemented
3#10595032C211yesmaximal, characteristic, complemented
4#10591633C211yesmaximal, characteristic, complemented
5#10591622C211yesmaximal, characteristic, complemented
6#10591612C212yesmaximal, complemented
7#10591497C211yesmaximal, characteristic, complemented
8#10591486C211yesmaximal, characteristic, complemented
9#10591476C212yesmaximal, complemented
10C2×#63572C211yesmaximal, characteristic, complemented
11#10591084C212yesmaximal, complemented
12#83900—32nomaximal
13C2×C32×#41C2211yescharacteristic
14C2×C3×#235C2212yes—
15Q8×C3⋊Dic3C2211yescharacteristic
16Q8×C3⋊Dic3C2211yescharacteristic
17D4×C3⋊Dic3—21no—
18D4×C3⋊Dic3—21no—
19D4×C3⋊Dic3C2211yescharacteristic
20D4×C3⋊Dic3C2211yescharacteristic
21#64135—21no—
22#64135C2211yescharacteristic
23C2×C4×C3⋊Dic3—21no—
24C2×C4×C3⋊Dic3C2211yescharacteristic
25C3×#950—28no—
26C2×C3×#216C2212yes—
27C2×C3×#215C2212yes—
28C2×C3×#214C2212yes—
29C2×C3×#213C2212yes—
30C22×C3×C3⋊C8C2212yes—
31#63980—21no—
32#63980—21no—
33#63914C2211yescharacteristic
34C4×#625—21no—
35C4×#625—21no—
36#63873C2211yescharacteristic
37#63863C2212yes—
38#63572C2211yescharacteristic
39#63572C2212yes—
40#63572C2211yescharacteristic
41#63566C2212yes—
42#63566C2212yes—
43#63563C2212yes—
44#63563C2212yes—
45C2×C3×#135—32no—
46#5832—32no—
47Dic3×#41—32no—
48Dic3×#41—61no—
49C2×#950D312yescomplemented
50#5233—32no—
51#5185—32no—
52#5182—32no—
53#5166—32no—
54#5165—32no—
55#5163—32no—
56#5162—32no—
57#5153—32no—
58#5150—32no—
59#5113—32no—
60C2×Dic3⋊C8—32no—
61C32×#41—22no—
62C32×#41D414yescomplemented
63C2×C32×Q8C2311yescharacteristic
64C2×C32×D4—21no—
65C2×C32×D4C2311yescharacteristic
66C22×C32×C4—21no—
67C22×C32×C4C2311yescharacteristic
68C22×C3⋊Dic3—21no—
69C22×C3⋊Dic3—21no—
70C22×C3⋊Dic3D411yescharacteristic
71C22×C3⋊Dic3D411yescharacteristic
72C2×C3×#67—22no—
73C3×#235—24no—
74C3×#235—24no—
75C2×C3×D12C2312yes—
76C2×C3×C4×D3—22no—
77C2×C3×Dic6C2312yes—
78C2×#625—21no—
79C2×#625—21no—
80#3757—21no—
81#3757—21no—
82#3757—21no—
83C4⋊(C3⋊Dic3)—21no—
84C4⋊(C3⋊Dic3)—21no—
85C4⋊(C3⋊Dic3)C2311yescharacteristic
86C4⋊(C3⋊Dic3)C2311yescharacteristic
87C4×C3⋊Dic3—21no—
88C4×C3⋊Dic3—21no—
89C4×C3⋊Dic3—21no—
90C4×C3⋊Dic3D411yescharacteristic
91C4×C3⋊Dic3D411yescharacteristic
92C4×C3⋊Dic3C2311yescharacteristic
93C4×C3⋊Dic3C2311yescharacteristic
94C3×#216—24no—
95C3×#215—24no—
96C3×#214—24no—
97C3×#213—24no—
98C2×C3×C3⋊C8—24no—
99C2×C3×C3⋊C8C2312yes—
100C2×C3×C3⋊C8C2312yes—
101#3724—21no—
102#3724—21no—
103(C2×D3)⋊Dic3—22no—
104(C2×D3)⋊Dic3—22no—
105#3035—91noSylow
106C2×C3×#41—21no—
107C2×C3×#41—32no—
108C2×C3×#41C2×D312yes—
109C2×#235C2×D312yes—
110C3×#135—68no—
111C2×C3×Q16—32no—
112C2×C3×SD16—32no—
113C2×C3×SD16—32no—
114C2×C3×D8—32no—
115C22×C3×C8—32no—
116#950—28no—
117#947—32no—
118Q8×Dic3—32no—
119Q8×Dic3—32no—
120Q8×Dic3—61no—
121Q8×Dic3—61no—
122#944—32no—
123C2×#216C2×D312yes—
124C2×#215C2×D312yes—
125#940—32no—
126#939—62no—
127#939—62no—
128#936—32no—
129D4×Dic3—32no—
130D4×Dic3—32no—
131D4×Dic3—61no—
132D4×Dic3—61no—
133D4×Dic3—62no—
134D4×Dic3—62no—
135D4×Dic3—62no—
136D4×Dic3—62no—
137C2×#214C2×D312yes—
138C2×#213C2×D312yes—
139C4×#67—62no—
140C4×#67—62no—
141#926—32no—
142#926—61no—
143#926—62no—
144#926—62no—
145C2×C4×Dic3—32no—
146C2×C4×Dic3—61no—
147C2×C4×Dic3—62no—
148C2×C4×Dic3—62no—
149C22×C3⋊C8C2×D312yes—
150#835—32no—
151#835—32no—
152#832—32no—
153#832—32no—
154#821—32no—
155#821—32no—
156#816—32no—
157#816—32no—
158Dic3⋊C8—32no—
159Dic3⋊C8—32no—
160Dic3⋊C8—32no—
161Dic3⋊C8—32no—
162C23×C32—21no—
163C23×C32C2×D411yescharacteristic
164C22×C3×D3—22no—
165C32×Q8—21no—
166C32×Q8C2×D412yes—
167C32×D4—24no—
168C32×D4—21no—
169C32×D4C2×D412yes—
170C2×C32×C4—21no—
171C2×C32×C4—24no—
172C2×C32×C4C2×D411yescharacteristic
173C2×C32×C4C2×D412yes—
174C2×C32×C4#4112yes—
175C2×C32×C4C2411yescharacteristic
176C2×C3⋊Dic3—21no—
177C2×C3⋊Dic3—21no—
178C2×C3⋊Dic3—22no—
179C2×C3⋊Dic3—41no—
180C2×C3⋊Dic3—42no—
181C2×C3⋊Dic3—42no—
182C2×C3⋊Dic3C2×D411yescharacteristic
183C2×C3⋊Dic3C2×D411yescharacteristic
184C2×C3⋊Dic3C2×D411yescharacteristic
185C2×C3⋊Dic3C2×D411yescharacteristic
186C3×#67—44no—
187C2×C3×Dic3—22no—
188C3×D12—22no—
189C3×D12—22no—
190C3×C4×D3—44no—
191C3×Dic6—22no—
192C3×Dic6—22no—
193#625—42no—
194#625—42no—
195C3×C3⋊C8—22no—
196C3×C3⋊C8—22no—
197C2×#135—32no—
198#532—91no—
199C4×#41—91no—
200#464—92no—
201#463—92no—
202#462—91no—
203#461—91no—
204#460—91no—
205#459—91no—
206C2×C4⋊C8—91no—
207#416—92no—
208C3×#41—24no—
209C3×#41—24no—
210C3×#41—24no—
211C3×#41—64no—
212C3×#41—64no—
213C3×#41#6718yescomplemented
214C2×C3×Q8—21no—
215C2×C3×Q8—32no—
216C2×C3×Q8C22×D312yes—
217C2×C3×D4—22no—
218C2×C3×D4—22no—
219C2×C3×D4—21no—
220C2×C3×D4—32no—
221C2×C3×D4—62no—
222C2×C3×D4C22×D312yes—
223C22×C3×C4—22no—
224C22×C3×C4—22no—
225C22×C3×C4—21no—
226C22×C3×C4—62no—
227C22×C3×C4C22×D312yes—
228C2×#67—22no—
229C2×#67—62no—
230C2×#67—62no—
231C22×Dic3—32no—
232C22×Dic3—32no—
233C22×Dic3—61no—
234C22×Dic3—61no—
235C22×Dic3—62no—
236C22×Dic3—62no—
237C22×Dic3—62no—
238C22×Dic3—62no—
239#235—24no—
240#235—24no—
241C2×D12C22×D312yes—
242C2×C4×D3—22no—
243C2×Dic6C22×D312yes—
244C3×Q16—64no—
245C3×SD16—64no—
246C3×SD16—64no—
247C3×D8—64no—
248C2×C3×C8—32no—
249C2×C3×C8—32no—
250C2×C3×C8—64no—
251#217—62no—
252#217—62no—
253#217—62no—
254#217—62no—
255#217—62no—
256#217—62no—
257#217—62no—
258#217—62no—
259#216—24no—
260#215—24no—
261#214—24no—
262#213—24no—
263(C2×D3)⋊C4—62no—
264(C2×D3)⋊C4—62no—
265C4⋊Dic3—32no—
266C4⋊Dic3—32no—
267C4⋊Dic3—61no—
268C4⋊Dic3—61no—
269C4⋊Dic3—62no—
270C4⋊Dic3—62no—
271C4⋊Dic3—62no—
272C4⋊Dic3—62no—
273Dic3⋊C4—62no—
274Dic3⋊C4—62no—
275C4×Dic3—32no—
276C4×Dic3—32no—
277C4×Dic3—32no—
278C4×Dic3—32no—
279C4×Dic3—61no—
280C4×Dic3—61no—
281C4×Dic3—61no—
282C4×Dic3—61no—
283C4×Dic3—62no—
284C4×Dic3—62no—
285C4×Dic3—62no—
286C4×Dic3—62no—
287C4×Dic3—62no—
288C4×Dic3—62no—
289C2×C3⋊C8—24no—
290C2×C3⋊C8C22×D312yes—
291C2×C3⋊C8C22×D312yes—
292C22×C32—22no—
293C22×C32—21no—
294C22×C32—21no—
295C22×C32—41no—
296C22×C32—41no—
297C22×C32#12112yes—
298C22×C32C22×D411yescharacteristic
299C2×C3×D3—42no—
300C2×C3×D3—42no—
301C2×C3×D3—42no—
302C32×C4—22no—
303C32×C4#12112yes—
304C32×C4C22×D411yescharacteristic
305C32×C4C2×#4111yescharacteristic
306C3⋊Dic3—21no—
307C3⋊Dic3—21no—
308C3⋊Dic3—21no—
309C3⋊Dic3—41no—
310C3⋊Dic3—41no—
311C3⋊Dic3#13512yescomplemented
312C3×Dic3—42no—
313C2×#41—32no—
314C2×#41D3211yescharacteristic
315#135—68no—
316C2×Q16—32no—
317C2×SD16—32no—
318C2×SD16—32no—
319C2×D8—32no—
320C22×C8—32no—
321C4⋊Q8—91no—
322#127—91no—
323#124—92no—
324#121—181no—
325#121—181no—
326C4×Q8—91no—
327C4×Q8—91no—
328C4×D4—91no—
329C4×D4—91no—
330C4×D4—181no—
331C4×D4—181no—
332C4×D4—181no—
333C4×D4—181no—
334#117—91no—
335#117—181no—
336C2×C42—91no—
337C2×C42—181no—
338C4⋊C8—91no—
339C4⋊C8—91no—
340C4⋊C8—92no—
341#103—92no—
342#103—92no—
343#102—92no—
344#102—92no—
345C23×C3—22no—
346C23×C3—22no—
347C23×C3—21no—
348C23×C3—62no—
349C23×C3D3×D412yes—
350C22×D3—22no—
351C3×Q8—22no—
352C3×Q8—22no—
353C3×Q8—22no—
354C3×Q8—62no—
355C3×Q8—62no—
356C3×Q8C2×#6714yes—
357C3×D4—28no—
358C3×D4—22no—
359C3×D4—28no—
360C3×D4—22no—
361C3×D4—22no—
362C3×D4—62no—
363C3×D4—62no—
364C3×D4—124no—
365C3×D4C2×#6714yes—
366C2×C3×C4—22no—
367C2×C3×C4—28no—
368C2×C3×C4—22no—
369C2×C3×C4—28no—
370C2×C3×C4—21no—
371C2×C3×C4—22no—
372C2×C3×C4—22no—
373C2×C3×C4—21no—
374C2×C3×C4—62no—
375C2×C3×C4—124no—
376C2×C3×C4D3×D412yes—
377C2×C3×C4#23714yes—
378C2×C3×C4C2×#6714yes—
379C2×C3×C4C23×D312yes—
380#67—44no—
381#67—124no—
382#67—124no—
383C2×Dic3—22no—
384C2×Dic3—32no—
385C2×Dic3—32no—
386C2×Dic3—32no—
387C2×Dic3—32no—
388C2×Dic3—61no—
389C2×Dic3—61no—
390C2×Dic3—61no—
391C2×Dic3—61no—
392C2×Dic3—64no—
393C2×Dic3—62no—
394C2×Dic3—62no—
395C2×Dic3—62no—
396C2×Dic3—62no—
397C2×Dic3—122no—
398C2×Dic3—124no—
399C2×Dic3—122no—
400C2×Dic3—124no—
401C2×Dic3—122no—
402C2×Dic3—124no—
403C2×Dic3—124no—
404D12—22no—
405D12—22no—
406C4×D3—44no—
407Dic6—22no—
408Dic6—22no—
409C3×C8—62no—
410C3×C8—62no—
411C3⋊C8—22no—
412C3⋊C8—22no—
413C2×C32—22no—
414C2×C32—42no—
415C2×C32C2×#12111yescharacteristic
416C2×C32C2×#13511yescharacteristic
417C2×C32#57511yescharacteristic
418C3×D3—82no—
419#41—22no—
420#41—64no—
421#41—64no—
422#41#62514yescomplemented
423C2×Q8—32no—
424C2×Q8C2×D3211yescharacteristic
425C2×D4—21no—
426C2×D4—32no—
427C2×D4—62no—
428C2×D4—181no—
429C2×D4—181no—
430C2×D4C2×D3211yescharacteristic
431C22×C4—21no—
432C22×C4—62no—
433C22×C4—91no—
434C22×C4—91no—
435C22×C4—181no—
436C22×C4—181no—
437C22×C4C2×D3211yescharacteristic
438Q16—64no—
439SD16—64no—
440SD16—64no—
441D8—64no—
442C2×C8—32no—
443C2×C8—32no—
444C2×C8—64no—
445C4⋊C4—91no—
446C4⋊C4—91no—
447C4⋊C4—181no—
448C4⋊C4—181no—
449C4⋊C4—181no—
450C4⋊C4—181no—
451C22⋊C4—182no—
452C22⋊C4—182no—
453C22⋊C4—181no—
454C22⋊C4—181no—
455C22⋊C4—181no—
456C42—91no—
457C42—91no—
458C42—91no—
459C42—91no—
460C42—181no—
461C42—181no—
462C42—181no—
463C22×C3—22no—
464C22×C3—22no—
465C22×C3—24no—
466C22×C3—24no—
467C22×C3—21no—
468C22×C3—22no—
469C22×C3—41no—
470C22×C3—41no—
471C22×C3—42no—
472C22×C3—42no—
473C22×C3—42no—
474C22×C3—42no—
475C22×C3—122no—
476C22×C3—122no—
477C22×C3—122no—
478C22×C3#93914yes—
479C22×C3C2×D3×D412yes—
480C2×D3—42no—
481C2×D3—42no—
482C2×D3—42no—
483C3×C4—24no—
484C3×C4—24no—
485C3×C4—21no—
486C3×C4—21no—
487C3×C4—22no—
488C3×C4—122no—
489C3×C4#93914yes—
490C3×C4C2×#23712yes—
491C3×C4C22×#6712yes—
492Dic3—34no—
493Dic3—42no—
494Dic3—62no—
495Dic3—62no—
496Dic3—62no—
497Dic3—62no—
498Dic3—62no—
499Dic3—121no—
500Dic3—121no—
501Dic3—122no—
502Dic3—122no—
503Dic3—122no—
504Dic3—122no—
505C32#303511yescharacteristic, complemented, Sylow
506C23—21no—
507C23—62no—
508C23#381111yescharacteristic
509Q8—21no—
510Q8—62no—
511Q8—62no—
512Q8C2×#62512yes—
513D4—24no—
514D4—21no—
515D4—62no—
516D4—62no—
517D4—124no—
518D4—362no—
519D4—362no—
520D4C2×#62512yes—
521C2×C4—21no—
522C2×C4—24no—
523C2×C4—62no—
524C2×C4—91no—
525C2×C4—91no—
526C2×C4—91no—
527C2×C4—91no—
528C2×C4—124no—
529C2×C4—182no—
530C2×C4—181no—
531C2×C4—181no—
532C2×C4—362no—
533C2×C4—361no—
534C2×C4—362no—
535C2×C4#380512yes—
536C2×C4C2×#62512yes—
537C2×C4#381111yescharacteristic
538C2×C4C22×D3211yescharacteristic
539C8—62no—
540C8—62no—
541C2×C3—24no—
542C2×C3—21no—
543C2×C3—21no—
544C2×C3—21no—
545C2×C3—42no—
546C2×C3—44no—
547C2×C3—44no—
548C2×C3—242no—
549C2×C3D3×#13512yes—
550C2×C3#576812yes—
551C2×C3C2×#93912yes—
552D3—82no—
553C22—21no—
554C22—21no—
555C22—22no—
556C22—41no—
557C22—41no—
558C22—122no—
559C22—122no—
560C22—122no—
561C22#6398012yes—
562C22C2×#381111yescharacteristic
563C4—22no—
564C4—92no—
565C4—122no—
566C4—181no—
567C4—181no—
568C4—181no—
569C4—361no—
570C4—361no—
571C4#6398012yes—
572C4C2×#380511yescharacteristic
573C4C22×#62511yescharacteristic
574C3—21no—
575C3#8390012yescomplemented
576C2—22no—
577C2—42no—
578C2—242no—
579C2#1059545911yescharacteristic
580C2#1059546011yescharacteristic
581C2C2×#6398011yescharacteristic
subgroupG/H
centerC2×C4#3811
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×#41C22
socleC22×C32C22×D4
hypercenterC2×#41D32
hypocenterC32#3035
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
1. #41×C3⋊Dic3C2semidirect
2. C2×C3×#950C2semidirect
3. #10595032C2semidirect
4. #10591633C2semidirect
5. #10591622C2semidirect
6. #10591612C2semidirect
7. #10591497C2semidirect
8. #10591486C2semidirect
9. #10591476C2semidirect
10. C2×#63572C2semidirect
11. #10591084C2semidirect
49. C2×#950D3semidirect
62. C32×#41D4semidirect
213. C3×#41#67semidirect
311. C3⋊Dic3#135semidirect
422. #41#625semidirect
505. C32#3035semidirect
575. C3#83900semidirect

Maximal subgroups

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

subgroupindex
#41×C3⋊Dic32
C2×C3×#9502
#105950322
#105916332
#105916222
#105916122
#105914972
#105914862
#105914762
C2×#635722
#105910842
#839003