Finite Group Databasebeta

← #11866239

Subgroups — #11866239

Order 1152.

1482 conjugacy classes of subgroups.

The subgroup lattice has 597 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×SD16×C3⋊D3C211yesmaximal, characteristic, complemented
2C2×#64120C211yesmaximal, characteristic
3#10596146C211yesmaximal, characteristic, complemented
4#10596016C211yesmaximal, characteristic, complemented
5C32×#463C211yesmaximal, characteristic, complemented
6#10592861C211yesmaximal, characteristic, complemented
7#10592852C211yesmaximal, characteristic, complemented
8#10592756C211yesmaximal, characteristic, complemented
9#10592718C211yesmaximal, characteristic, complemented
10#10592540C211yesmaximal, characteristic, complemented
11#10592538C211yesmaximal, characteristic, complemented
12#10592517C211yesmaximal, characteristic, complemented
13#10592501C211yesmaximal, characteristic, complemented
14#10592486C211yesmaximal, characteristic, complemented
15#10592471C211yesmaximal, characteristic, complemented
16#80537—34nomaximal
17C2×Q8×C3⋊D3C2211yescharacteristic
18C2×#3830C2211yescharacteristic
19C2×D4×C3⋊D3C2211yescharacteristic
20C2×C32×SD16C2211yescharacteristic
21C2×C32×D8C2211yescharacteristic
22C32×#124C2211yescharacteristic, complemented
23C32×C4×D4C2211yescharacteristic
24#64153C2211yescharacteristic, complemented
25C2×#3755C2211yescharacteristic
26#64145C2211yescharacteristic, complemented
27D4×C3⋊Dic3C2211yescharacteristic
28C2×#3754C2211yescharacteristic
29C2×#3754C2211yescharacteristic
30C2×#3753C2211yescharacteristic
31C4×#638—21no—
32C2×#3752—21no—
33SD16×C3⋊D3—24no—
34#64120—24no—
35C2×#3744C2211yescharacteristic
36C2×#3744C2211yescharacteristic
37C2×#3743C2211yescharacteristic
38C2×C8×C3⋊D3C2211yescharacteristic
39#64102C2211yescharacteristic
40#64101C2211yescharacteristic
41#64092—21no—
42#64092—21no—
43#64090—21no—
44C22⋊C4×C3⋊D3—21no—
45#64087—21no—
46#64087—21no—
47C4×C4⋊(C3⋊D3)C2211yescharacteristic
48#64081C2211yescharacteristic
49#64078C2211yescharacteristic, complemented
50C32×C4⋊C8C2211yescharacteristic, complemented
51C32×#103C2211yescharacteristic, complemented
52C32×#102C2211yescharacteristic, complemented
53#63662C2211yescharacteristic, complemented
54#63659C2211yescharacteristic, complemented
55#63643C2211yescharacteristic, complemented
56#63643C2211yescharacteristic, complemented
57#63641C2211yescharacteristic, complemented
58#63641C2211yescharacteristic, complemented
59#63637C2211yescharacteristic, complemented
60#63637C2211yescharacteristic, complemented
61C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic, complemented
62C2×D3×SD16—34no—
63C2×#911—34no—
64#5675—34no—
65#5545—34no—
66C3×#463D314yescomplemented
67#5162—34no—
68#5153—34no—
69#5057—34no—
70#5019—34no—
71#4841—34no—
72#4839—34no—
73#4818—34no—
74#4802—34no—
75#4787—34no—
76#4772—34no—
77C23×C3⋊D3—21no—
78C2×C32×Q8C2311yescharacteristic
79C2×C32×D4C2311yescharacteristic
80C2×C32×D4C2311yescharacteristic
81C22×C32×C4—21no—
82C2×#638—21no—
83C2×#638—21no—
84C22×C3⋊Dic3—21no—
85C22×C3⋊Dic3—21no—
86Q8×C3⋊D3—22no—
87Q8×C3⋊D3—22no—
88#3830—22no—
89#3830—22no—
90D4×C3⋊D3—22no—
91D4×C3⋊D3D414yes—
92C2×C4⋊(C3⋊D3)C2311yescharacteristic
93C2×C4×C3⋊D3—21no—
94C2×C4×C3⋊D3—21no—
95C2×C4×C3⋊D3—21no—
96C2×C4×C3⋊D3C2311yescharacteristic
97C2×#634—21no—
98C2×#634C2311yescharacteristic
99C2×#634C2311yescharacteristic
100C32×SD16—22no—
101C32×D8—22no—
102C2×C32×C8C2311yescharacteristic
103C2×C32×C8C2311yescharacteristic
104C32×C4⋊C4C2311yescharacteristic
105C32×C22⋊C4—21no—
106C32×C22⋊C4—21no—
107C32×C22⋊C4—21no—
108C32×C42C2311yescharacteristic
109#3757—21no—
110#3757—21no—
111#3757—21no—
112#3755—22no—
113#3754—22no—
114#3754—22no—
115#3753—22no—
116#3752—21no—
117#3752—21no—
118#3752—21no—
119#3752D411yescharacteristic
120#3752D411yescharacteristic
121C4⋊(C3⋊Dic3)—21no—
122C4⋊(C3⋊Dic3)—21no—
123C4⋊(C3⋊Dic3)C2311yescharacteristic
124#3750—21no—
125#3750—21no—
126#3750D411yescharacteristic
127#3750D411yescharacteristic
128C4×C3⋊Dic3—21no—
129C4×C3⋊Dic3C2311yescharacteristic
130C2×C3⋊(C3⋊C8)C2311yescharacteristic
131C2×C3⋊(C3⋊C8)C2311yescharacteristic
132#3744—22no—
133#3744—22no—
134#3743—22no—
135C8×C3⋊D3—22no—
136#3042—91noSylow
137C2×D3×Q8—34no—
138C2×#237—34no—
139C2×D3×D4—34no—
140C2×C3×SD16C2×D314yes—
141C2×C3×D8C2×D314yes—
142C3×#124C2×D314yescomplemented
143C3×C4×D4C2×D314yes—
144#944—34no—
145C2×#215—34no—
146#936—34no—
147D4×Dic3—34no—
148C2×#214—34no—
149C2×#214—34no—
150C2×#213—34no—
151C4×#67—64no—
152C2×(C2×D3)⋊C4—64no—
153D3×SD16—616no—
154#911—616no—
155C2×#204—34no—
156C2×#204—34no—
157C2×ΓL(1,𝔽25)—34no—
158C2×D3×C8—34no—
159#893—34no—
160#892—34no—
161#883—64no—
162#883—64no—
163#67⋊C4—64no—
164D3×C22⋊C4—64no—
165#878—64no—
166#878—64no—
167C4×D12—34no—
168#872—34no—
169#869—34no—
170C3×C4⋊C8C2×D314yescomplemented
171C3×#103C2×D314yescomplemented
172C3×#102C2×D314yescomplemented
173#835—34no—
174#832—34no—
175#816—34no—
176#816—34no—
177Dic3⋊C8—34no—
178Dic3⋊C8—34no—
179#810—34no—
180#810—34no—
181C4⋊(C3⋊C8)—34no—
182C23×C32—21no—
183C23×C32—21no—
184C22×C3⋊D3—21no—
185C22×C3⋊D3—24no—
186C22×C3⋊D3—81no—
187C22×C3⋊D3—81no—
188C22×C3⋊D3C2×D411yescharacteristic
189C32×Q8—21no—
190C32×Q8—21no—
191C32×D4—21no—
192C32×D4—21no—
193C32×D4—21no—
194C32×D4C2×D412yes—
195C2×C32×C4—21no—
196C2×C32×C4—21no—
197C2×C32×C4—81no—
198C2×C32×C4C2×D411yescharacteristic
199C2×C32×C4C2×D411yescharacteristic
200C2×C32×C4C2411yescharacteristic
201#638—24no—
202#638—42no—
203C2×C3⋊Dic3—21no—
204C2×C3⋊Dic3—21no—
205C2×C3⋊Dic3—21no—
206C2×C3⋊Dic3—42no—
207C2×C3⋊Dic3—81no—
208C2×C3⋊Dic3C2×D411yescharacteristic
209C2×C3⋊Dic3C2×D411yescharacteristic
210C2×C3⋊Dic3C2×D411yescharacteristic
211C4⋊(C3⋊D3)—21no—
212C4⋊(C3⋊D3)C2×D412yes—
213C4×C3⋊D3—42no—
214C4×C3⋊D3—81no—
215C4×C3⋊D3—81no—
216C4×C3⋊D3C2×D412yes—
217C4×C3⋊D3#4112yes—
218#634—21no—
219#634—21no—
220#634—21no—
221#634—21no—
222#634—42no—
223C32×C8—21no—
224C32×C8—21no—
225C3⋊(C3⋊C8)—21no—
226C3⋊(C3⋊C8)—21no—
227C2×AGL(1,ℤ/8)—91no—
228C22×SD16—91no—
229#536—91no—
230#518—91no—
231#463—91no—
232#463—91no—
233#463—91no—
234#463C3⋊D311yescharacteristic, complemented
235#461—91no—
236#461—91no—
237#461—91no—
238#461—91no—
239#424—91no—
240#419—91no—
241#416—91no—
242C23×D3—64no—
243C2×C3×Q8C22×D314yes—
244C2×C3×D4C22×D314yes—
245C2×C3×D4C22×D314yes—
246C22×C3×C4—24no—
247C2×#67—64no—
248C2×#67—64no—
249C22×Dic3—64no—
250C22×Dic3—64no—
251D3×Q8—68no—
252D3×Q8—68no—
253#237—68no—
254#237—68no—
255D3×D4—316no—
256D3×D4—68no—
257C2×D12—34no—
258C2×C4×D3—34no—
259C2×C4×D3—64no—
260C2×C4×D3—64no—
261C2×C4×D3—64no—
262C2×Dic6—34no—
263C2×Dic6—34no—
264C2×Dic6—64no—
265C3×SD16—28no—
266C3×D8—28no—
267C2×C3×C8C22×D314yes—
268C2×C3×C8C22×D314yes—
269C3×C4⋊C4C22×D314yes—
270C3×C22⋊C4—24no—
271C3×C22⋊C4—24no—
272C3×C22⋊C4—24no—
273C3×C42C22×D314yes—
274#217—64no—
275#217—64no—
276#217—64no—
277#215—68no—
278#214—68no—
279#214—68no—
280#213—68no—
281(C2×D3)⋊C4—34no—
282(C2×D3)⋊C4—34no—
283(C2×D3)⋊C4—64no—
284(C2×D3)⋊C4—64no—
285(C2×D3)⋊C4—64no—
286C4⋊Dic3—34no—
287C4⋊Dic3—64no—
288C4⋊Dic3—64no—
289Dic3⋊C4—34no—
290Dic3⋊C4—34no—
291Dic3⋊C4—64no—
292Dic3⋊C4—64no—
293C4×Dic3—34no—
294C4×Dic3—64no—
295C2×C3⋊C8—34no—
296C2×C3⋊C8—34no—
297#204—68no—
298#204—68no—
299ΓL(1,𝔽25)—68no—
300D3×C8—68no—
301C22×C32—22no—
302C22×C32—41no—
303C22×C32—41no—
304C22×C32—41no—
305C22×C32—41no—
306C22×C32—41no—
307C22×C32C22×D411yescharacteristic
308C2×C3⋊D3—21no—
309C2×C3⋊D3—21no—
310C2×C3⋊D3—22no—
311C2×C3⋊D3—41no—
312C2×C3⋊D3—41no—
313C2×C3⋊D3—84no—
314C2×C3⋊D3#12112yes—
315C32×C4—21no—
316C32×C4—21no—
317C32×C4—41no—
318C32×C4—41no—
319C32×C4C22×D411yescharacteristic
320C32×C4C2×#4111yescharacteristic
321C3⋊Dic3—21no—
322C3⋊Dic3—21no—
323C3⋊Dic3—41no—
324C3⋊Dic3—41no—
325C3⋊Dic3—41no—
326C3⋊Dic3#12112yes—
327C2×#41—91no—
328C22×Q8—91no—
329C22×D4—91no—
330AGL(1,ℤ/8)—184no—
331C2×SD16—91no—
332C2×SD16—91no—
333C2×SD16—91no—
334C2×SD16—91no—
335C2×SD16—91no—
336C2×SD16—184no—
337C2×SD16C2×C3⋊D311yescharacteristic
338C2×D8—91no—
339C2×D8C2×C3⋊D311yescharacteristic
340C2×M16—91no—
341C22×C8—91no—
342C4⋊Q8—91no—
343C4⋊Q8—91no—
344#124—91no—
345#124C2×C3⋊D311yescharacteristic, complemented
346#123—181no—
347#123—181no—
348C22⋊Q8—181no—
349C22⋊Q8—181no—
350C4×D4—91no—
351C4×D4—91no—
352C4×D4—91no—
353C4×D4—181no—
354C4×D4—181no—
355C4×D4C2×C3⋊D311yescharacteristic
356#117—91no—
357#117—91no—
358C2×C22⋊C4—181no—
359C2×C22⋊C4—181no—
360C4⋊C8—91no—
361C4⋊C8—91no—
362C4⋊C8—91no—
363C4⋊C8C2×C3⋊D311yescharacteristic, complemented
364#103—91no—
365#103—91no—
366#103—91no—
367#103—91no—
368#103—91no—
369#103C2×C3⋊D311yescharacteristic, complemented
370#102—91no—
371#102C2×C3⋊D311yescharacteristic, complemented
372C23×C3—24no—
373C23×C3—24no—
374C22×D3—34no—
375C22×D3—616no—
376C22×D3—64no—
377C22×D3—244no—
378C22×D3—244no—
379C3×Q8—24no—
380C3×Q8—24no—
381C3×D4—24no—
382C3×D4—24no—
383C3×D4—24no—
384C3×D4D3×D418yes—
385C2×C3×C4—24no—
386C2×C3×C4—24no—
387C2×C3×C4—84no—
388C2×C3×C4D3×D414yes—
389C2×C3×C4D3×D414yes—
390C2×C3×C4C23×D314yes—
391#67—616no—
392#67—128no—
393C2×Dic3—34no—
394C2×Dic3—34no—
395C2×Dic3—34no—
396C2×Dic3—64no—
397C2×Dic3—64no—
398C2×Dic3—64no—
399C2×Dic3—128no—
400C2×Dic3—244no—
401D12—38no—
402D12—64no—
403C4×D3—38no—
404C4×D3—38no—
405C4×D3—128no—
406C4×D3—244no—
407C4×D3—244no—
408Dic6—64no—
409Dic6—64no—
410Dic6—64no—
411Dic6—64no—
412Dic6—128no—
413C3×C8—24no—
414C3×C8—24no—
415C3⋊C8—64no—
416C3⋊C8—64no—
417C2×C32—42no—
418C2×C32—81no—
419C2×C32C2×#12111yescharacteristic
420C2×C32#57711yescharacteristic
421C2×C32#57711yescharacteristic
422C3⋊D3—22no—
423C3⋊D3—42no—
424C24—181no—
425#41—182no—
426#41—182no—
427C2×Q8—91no—
428C2×Q8—91no—
429C2×Q8—181no—
430C2×Q8—182no—
431C2×Q8—182no—
432C2×Q8C22×C3⋊D311yescharacteristic
433C2×D4—94no—
434C2×D4—91no—
435C2×D4—182no—
436C2×D4—181no—
437C2×D4—181no—
438C2×D4C22×C3⋊D311yescharacteristic
439C2×D4C22×C3⋊D311yescharacteristic
440C22×C4—21no—
441C22×C4—91no—
442C22×C4—181no—
443C22×C4—181no—
444C22×C4—181no—
445C22×C4—181no—
446C22×C4—181no—
447SD16—22no—
448SD16—182no—
449SD16—182no—
450SD16—182no—
451SD16—182no—
452SD16—182no—
453D8—22no—
454D8—182no—
455M16—182no—
456C2×C8—91no—
457C2×C8—91no—
458C2×C8—182no—
459C2×C8C22×C3⋊D311yescharacteristic
460C2×C8C22×C3⋊D311yescharacteristic
461C4⋊C4—91no—
462C4⋊C4—91no—
463C4⋊C4—91no—
464C4⋊C4—181no—
465C4⋊C4—181no—
466C4⋊C4—181no—
467C4⋊C4—181no—
468C4⋊C4C22×C3⋊D311yescharacteristic
469C22⋊C4—21no—
470C22⋊C4—21no—
471C22⋊C4—21no—
472C22⋊C4—91no—
473C22⋊C4—91no—
474C22⋊C4—181no—
475C22⋊C4—181no—
476C22⋊C4—181no—
477C22⋊C4—181no—
478C22⋊C4—181no—
479C22⋊C4—181no—
480C42—91no—
481C42—181no—
482C42C22×C3⋊D311yescharacteristic
483C22×C3—28no—
484C22×C3—44no—
485C22×C3—44no—
486C22×C3—44no—
487C22×C3—44no—
488C22×C3—44no—
489C22×C3C2×D3×D414yes—
490C2×D3—38no—
491C2×D3—64no—
492C2×D3—64no—
493C2×D3—68no—
494C2×D3—124no—
495C2×D3—124no—
496C2×D3—2416no—
497C3×C4—24no—
498C3×C4—24no—
499C3×C4—44no—
500C3×C4—44no—
501C3×C4C2×D3×D414yes—
502C3×C4D3×#4114yes—
503Dic3—38no—
504Dic3—64no—
505Dic3—64no—
506Dic3—124no—
507Dic3—124no—
508Dic3—124no—
509C32#304211yescharacteristic, complemented, Sylow
510C23—21no—
511C23—21no—
512C23—91no—
513C23—184no—
514C23—181no—
515C23—721no—
516C23—721no—
517Q8—21no—
518Q8—21no—
519Q8—181no—
520Q8—181no—
521Q8—181no—
522Q8—181no—
523Q8—362no—
524D4—21no—
525D4—21no—
526D4—21no—
527D4—92no—
528D4—184no—
529D4—181no—
530D4—362no—
531D4D4×C3⋊D312yes—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—81no—
535C2×C4—91no—
536C2×C4—92no—
537C2×C4—92no—
538C2×C4—91no—
539C2×C4—91no—
540C2×C4—181no—
541C2×C4—181no—
542C2×C4—181no—
543C2×C4—362no—
544C2×C4—362no—
545C2×C4—721no—
546C2×C4—721no—
547C2×C4—721no—
548C2×C4D4×C3⋊D311yescharacteristic
549C2×C4D4×C3⋊D311yescharacteristic
550C2×C4C23×C3⋊D311yescharacteristic
551C8—21no—
552C8—21no—
553C8—181no—
554C8—181no—
555C2×C3—48no—
556C2×C3—84no—
557C2×C3D3×#12114yes—
558C2×C3#577014yes—
559C2×C3#577514yes—
560D3—68no—
561D3—128no—
562C22—22no—
563C22—41no—
564C22—41no—
565C22—41no—
566C22—41no—
567C22—41no—
568C22—92no—
569C22—181no—
570C22—181no—
571C22—182no—
572C22—361no—
573C22—361no—
574C22—724no—
575C22C2×D4×C3⋊D311yescharacteristic
576C4—21no—
577C4—21no—
578C4—41no—
579C4—41no—
580C4—92no—
581C4—181no—
582C4—181no—
583C4—361no—
584C4—361no—
585C4—361no—
586C4C2×D4×C3⋊D311yescharacteristic
587C4#41×C3⋊D311yescharacteristic
588C3#8053714yescomplemented
589C2—42no—
590C2—81no—
591C2—182no—
592C2—362no—
593C2C3⋊D3×#12111yescharacteristic
594C2#1059624111yescharacteristic
595C2#1059624611yescharacteristic
subgroupG/H
centerC22C2×D4×C3⋊D3
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C23×C3⋊D3
FittingC32×#463C2
socleC22×C32C22×D4
prime radicalC2×#64120C2
hypercenter#463C3⋊D3
hypocenterC32#3042
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ #463

Complements

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

NH ≅ G/Ntype
1. C2×SD16×C3⋊D3C2semidirect
3. #10596146C2semidirect
4. #10596016C2semidirect
5. C32×#463C2semidirect
6. #10592861C2semidirect
7. #10592852C2semidirect
8. #10592756C2semidirect
9. #10592718C2semidirect
10. #10592540C2semidirect
11. #10592538C2semidirect
12. #10592517C2semidirect
13. #10592501C2semidirect
14. #10592486C2semidirect
15. #10592471C2semidirect
22. C32×#124C22semidirect
24. #64153C22semidirect
26. #64145C22semidirect
49. #64078C22semidirect
50. C32×C4⋊C8C22semidirect
51. C32×#103C22semidirect
52. C32×#102C22semidirect
53. #63662C22semidirect
54. #63659C22semidirect
55. #63643C22semidirect
56. #63643C22semidirect
57. #63641C22semidirect
58. #63641C22semidirect
59. #63637C22semidirect
60. #63637C22semidirect
61. C4⋊(C3⋊(C3⋊C8))C22semidirect
66. C3×#463D3semidirect
142. C3×#124C2×D3semidirect
170. C3×C4⋊C8C2×D3semidirect
171. C3×#103C2×D3semidirect
172. C3×#102C2×D3semidirect
234. #463C3⋊D3semidirect
345. #124C2×C3⋊D3semidirect
363. C4⋊C8C2×C3⋊D3semidirect
369. #103C2×C3⋊D3semidirect
371. #102C2×C3⋊D3semidirect
509. C32#3042semidirect
588. C3#80537semidirect

Maximal subgroups

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

subgroupindex
C2×SD16×C3⋊D32
C2×#641202
#105961462
#105960162
C32×#4632
#105928612
#105928522
#105927562
#105927182
#105925402
#105925382
#105925172
#105925012
#105924862
#105924712
#805373