Finite Group Databasebeta

← #11860553

Subgroups — #11860553

Order 1152.

822 conjugacy classes of subgroups.

The subgroup lattice has 620 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64236C211yesmaximal, characteristic
2#10594181C211yesmaximal, characteristic, complemented
3#10594051C211yesmaximal, characteristic, complemented
4#10593738C211yesmaximal, characteristic, complemented
5#10593507C211yesmaximal, characteristic, complemented
6#10593498C211yesmaximal, characteristic, complemented
7C2×#63739C211yesmaximal, characteristic, complemented
8#10593433C211yesmaximal, characteristic, complemented
9#10593432C211yesmaximal, characteristic, complemented
10#10593431C211yesmaximal, characteristic, complemented
11C4×#3775C211yesmaximal, characteristic, complemented
12#10593420C211yesmaximal, characteristic, complemented
13#10593419C211yesmaximal, characteristic, complemented
14#10593419C211yesmaximal, characteristic, complemented
15C4×#3774C211yesmaximal, characteristic, complemented
16C22×#625C2211yescharacteristic
17C2×#3805C2211yescharacteristic
18C2×#3792C2211yescharacteristic
19C22×#622C2211yescharacteristic
20C2×#3775C2211yescharacteristic
21C2×#3775C2211yescharacteristic
22#64236C418yescomplemented
23C2×#3774C2211yescharacteristic
24C2×#3774C2211yescharacteristic
25#64086C2211yescharacteristic
26C3×#67⋊C4—21no—
27C3×D3×C22⋊C4—21no—
28Dic3×#67—21no—
29D3×#217—21no—
30C2×#3724C2211yescharacteristic
31#63957C2211yescharacteristic
32C4×#627C2211yescharacteristic, complemented
33#63902C2211yescharacteristic
34#63902C2211yescharacteristic
35#63902C2211yescharacteristic, complemented
36C4×#625C2211yescharacteristic
37C4×#625C2211yescharacteristic
38C4×#625C2211yescharacteristic, complemented
39#63879—21no—
40#63879—21no—
41#63877—21no—
42D3×Dic3⋊C4—21no—
43#63838C2211yescharacteristic, complemented
44#63777C2211yescharacteristic, complemented
45#63777C2211yescharacteristic, complemented
46C4×#622C2211yescharacteristic, complemented
47C4×#622C2211yescharacteristic, complemented
48#63743C2211yescharacteristic, complemented
49#63743C2211yescharacteristic, complemented
50#63742C2211yescharacteristic, complemented
51#63742C2211yescharacteristic, complemented
52#63740C2211yescharacteristic, complemented
53#63740C2211yescharacteristic, complemented
54#63739C2211yescharacteristic
55#63739C2211yescharacteristic
56#63739C2211yescharacteristic
57#63739C2211yescharacteristic
58#63739C2211yescharacteristic, complemented
59#63739C2211yescharacteristic, complemented
60#5546—61no—
61#5486—61no—
62C23×C3×D3—21no—
63C22×C3⋊Dic3C2311yescharacteristic
64C2×C3×#67—21no—
65C22×C3×Dic3—21no—
66C2×C3×C4×D3—21no—
67C2×C3×C4×D3—21no—
68C2×C3×C4×D3—21no—
69C2×#627C2311yescharacteristic
70C2×#625—21no—
71C2×#625—22no—
72C2×#625C2×C414yescomplemented
73C2×#625C2311yescharacteristic
74C2×#625C2311yescharacteristic
75C2×#625C2311yescharacteristic
76#3805—22no—
77#3805C2×C414yescomplemented
78C2×D3×Dic3—21no—
79C2×D3×Dic3—21no—
80C2×D3×Dic3—21no—
81C2×D3×Dic3—21no—
82#3792C2×C414yescomplemented
83C2×#622—22no—
84C2×#622C2311yescharacteristic
85C2×#622C2311yescharacteristic
86C2×#622C2311yescharacteristic
87C2×#622C2311yescharacteristic
88#3775C2×C414yescomplemented
89#3775C2×C414yescomplemented
90#3774C2×C414yescomplemented
91#3774C2×C414yescomplemented
92C32×C22⋊C4D411yescharacteristic
93#3757D411yescharacteristic
94#3750D411yescharacteristic
95#3750D411yescharacteristic
96C4×C3⋊Dic3C2311yescharacteristic
97C4×C3⋊Dic3C2311yescharacteristic
98C3×#217—21no—
99C3×(C2×D3)⋊C4—21no—
100C3×(C2×D3)⋊C4—21no—
101C3×(C2×D3)⋊C4—21no—
102C3×Dic3⋊C4—21no—
103C3×C4×Dic3—21no—
104#3724—21no—
105#3724C2311yescharacteristic
106#3724C2311yescharacteristic
107#3724C2311yescharacteristic
108#3724C2311yescharacteristic
109Dic3⋊Dic3—21no—
110(C2×D3)⋊Dic3—21no—
111(C2×D3)⋊Dic3—21no—
112(C2×D3)⋊Dic3—21no—
113Dic32—21no—
114Dic32—21no—
115#2946—91nomaximal, Sylow
116C22×#67—61no—
117C2×#237—61no—
118C3×C4×D4—61no—
119C2×C3×C22⋊C4—61no—
120C2×#217—61no—
121D4×Dic3—61no—
122C4×#67—61no—
123C4×#67—61no—
124C4×#67—61no—
125C4×#67—61no—
126C4×#67—61no—
127C4×#67—61no—
128C2×Dic3⋊C4—61no—
129C2×Dic3⋊C4—61no—
130D3×C4⋊C4—61no—
131#887—61no—
132#67⋊C4—21no—
133#67⋊C4—61no—
134#67⋊C4—61no—
135#67⋊C4—61no—
136#67⋊C4—61no—
137#67⋊C4—61no—
138D3×C22⋊C4—21no—
139D3×C22⋊C4—61no—
140#877—61no—
141#877—61no—
142#877—61no—
143#877—61no—
144#872—61no—
145C4×Dic6—61no—
146C23×C32C2×D411yescharacteristic
147C22×C3×D3—21no—
148C22×C3×D3—21no—
149C22×C3×D3—21no—
150C22×C3×D3—24no—
151C22×C3×D3—81no—
152C22×C3×D3—81no—
153C2×C32×C4C2×D411yescharacteristic
154C2×C32×C4C2×D411yescharacteristic
155C2×C3⋊Dic3C22×C412yes—
156C2×C3⋊Dic3C2×D411yescharacteristic
157C2×C3⋊Dic3C2×D411yescharacteristic
158C2×C3⋊Dic3C2×D411yescharacteristic
159C2×C3⋊Dic3#4112yes—
160C2×C3⋊Dic3C2411yescharacteristic
161C3×#67—24no—
162C2×C3×Dic3—21no—
163C2×C3×Dic3—21no—
164C2×C3×Dic3—21no—
165C2×C3×Dic3—21no—
166C2×C3×Dic3—21no—
167C2×C3×Dic3—81no—
168C3×C4×D3—81no—
169C3×C4×D3—81no—
170C3×C4×D3—81no—
171#627—21no—
172#627C22×C412yes—
173#625—24no—
174#625—21no—
175#625—21no—
176#625—21no—
177#625C22×C412yes—
178#625C22×C412yes—
179#625C22×C412yes—
180D3×Dic3—24no—
181D3×Dic3—81no—
182D3×Dic3—81no—
183D3×Dic3—81no—
184#622—21no—
185#622—21no—
186#622C22×C412yes—
187#622C22×C412yes—
188C2×AGL(1,ℤ/8)—91no—
189#520—91no—
190#518—91no—
191#442—91no—
192#442—91no—
193#440—91no—
194#440—91no—
195C4×SD16—91no—
196C4×SD16—91no—
197C4×D8—91no—
198C4×D8—91no—
199#428—91no—
200#416—91no—
201C2×#102—91no—
202#405—91no—
203C24×C3—61no—
204C23×D3—21no—
205C2×C3×D4—61no—
206C22×C3×C4—61no—
207C22×C3×C4—61no—
208C22×C3×C4—61no—
209C22×C3×C4—61no—
210C2×#67—21no—
211C2×#67—61no—
212C2×#67—61no—
213C2×#67—61no—
214C2×#67—64no—
215C2×#67—61no—
216C2×#67—61no—
217C2×#67—64no—
218C22×Dic3—21no—
219C22×Dic3—61no—
220C22×Dic3—61no—
221C22×Dic3—61no—
222C22×Dic3—61no—
223C22×Dic3—61no—
224C22×Dic3—61no—
225#237—64no—
226#237—64no—
227C2×C4×D3—21no—
228C2×C4×D3—21no—
229C2×C4×D3—21no—
230C2×C4×D3—61no—
231C2×C4×D3—61no—
232C2×C4×D3—61no—
233C2×C4×D3—61no—
234C2×Dic6—61no—
235C3×C4⋊C4—61no—
236C3×C22⋊C4—21no—
237C3×C22⋊C4—21no—
238C3×C22⋊C4—61no—
239C3×C22⋊C4—61no—
240C3×C22⋊C4—61no—
241C3×C22⋊C4—61no—
242C3×C42—61no—
243#217—21no—
244#217—61no—
245#217—61no—
246#217—61no—
247#217—61no—
248#217—61no—
249(C2×D3)⋊C4—21no—
250(C2×D3)⋊C4—21no—
251(C2×D3)⋊C4—21no—
252(C2×D3)⋊C4—61no—
253(C2×D3)⋊C4—61no—
254(C2×D3)⋊C4—61no—
255C4⋊Dic3—61no—
256Dic3⋊C4—21no—
257Dic3⋊C4—61no—
258Dic3⋊C4—61no—
259Dic3⋊C4—61no—
260Dic3⋊C4—61no—
261Dic3⋊C4—61no—
262Dic3⋊C4—61no—
263Dic3⋊C4—61no—
264Dic3⋊C4—61no—
265Dic3⋊C4—61no—
266Dic3⋊C4—61no—
267Dic3⋊C4—61no—
268C4×Dic3—21no—
269C4×Dic3—61no—
270C4×Dic3—61no—
271C4×Dic3—61no—
272C4×Dic3—61no—
273C4×Dic3—61no—
274C4×Dic3—61no—
275C4×Dic3—61no—
276C4×Dic3—61no—
277C22×C32—21no—
278C22×C32—21no—
279C22×C32C4×D412yes—
280C22×C32C22×D411yescharacteristic
281C2×C3×D3—22no—
282C2×C3×D3—22no—
283C2×C3×D3—22no—
284C2×C3×D3—41no—
285C2×C3×D3—41no—
286C2×C3×D3—41no—
287C2×C3×D3—41no—
288C2×C3×D3—41no—
289C2×C3×D3—41no—
290C2×C3×D3—84no—
291C32×C4—21no—
292C32×C4—21no—
293C3⋊Dic3—21no—
294C3⋊Dic3—21no—
295C3⋊Dic3C4×D412yes—
296C3⋊Dic3C23×C411yescharacteristic
297C3⋊Dic3C2×#4111yescharacteristic
298C3×Dic3—22no—
299C3×Dic3—41no—
300C3×Dic3—41no—
301C3×Dic3—41no—
302C3×Dic3—41no—
303C2×#41—91no—
304C22×D4—91no—
305AGL(1,ℤ/8)—98no—
306C2×SD16—91no—
307C2×SD16—91no—
308C2×D8—91no—
309C2×D8—91no—
310C2×M16—91no—
311C22×C8—91no—
312C4×Q8—91no—
313C4×Q8—91no—
314C4×D4—61no—
315C4×D4—91no—
316C4×D4—91no—
317C4×D4—91no—
318C4×D4—91no—
319C4×D4—91no—
320C4×D4—91no—
321C4×D4—181no—
322C4×D4—181no—
323C4×D4—181no—
324#117—91no—
325#117—91no—
326#117—181no—
327C2×C4⋊C4—91no—
328C2×C4⋊C4—181no—
329C2×C22⋊C4—61no—
330C2×C22⋊C4—181no—
331#107—91no—
332#107—91no—
333#106—91no—
334#106—91no—
335#103—91no—
336#103—91no—
337#102—91no—
338#102—91no—
339#102—91no—
340#102—91no—
341#102—91no—
342#102—91no—
343#97—91no—
344#97—91no—
345C4×C8—91no—
346C4×C8—91no—
347C23×C3—21no—
348C23×C3—21no—
349C23×C3—61no—
350C23×C3—61no—
351C23×C3—61no—
352C23×C3—64no—
353C23×C3—241no—
354C23×C3—241no—
355C22×D3—21no—
356C22×D3—21no—
357C22×D3—21no—
358C22×D3—24no—
359C22×D3—81no—
360C22×D3—81no—
361C3×D4—64no—
362C2×C3×C4—21no—
363C2×C3×C4—21no—
364C2×C3×C4—21no—
365C2×C3×C4—21no—
366C2×C3×C4—61no—
367C2×C3×C4—61no—
368C2×C3×C4—61no—
369C2×C3×C4—61no—
370C2×C3×C4—61no—
371C2×C3×C4—241no—
372C2×C3×C4—241no—
373C2×C3×C4—241no—
374C2×C3×C4—241no—
375#67—24no—
376#67—62no—
377#67—62no—
378#67—62no—
379#67—62no—
380#67—64no—
381#67—64no—
382#67—62no—
383#67—62no—
384C2×Dic3—21no—
385C2×Dic3—21no—
386C2×Dic3—21no—
387C2×Dic3—21no—
388C2×Dic3—21no—
389C2×Dic3—62no—
390C2×Dic3—62no—
391C2×Dic3—61no—
392C2×Dic3—61no—
393C2×Dic3—62no—
394C2×Dic3—62no—
395C2×Dic3—61no—
396C2×Dic3—61no—
397C2×Dic3—61no—
398C2×Dic3—61no—
399C2×Dic3—61no—
400C2×Dic3—61no—
401C2×Dic3—64no—
402C2×Dic3—81no—
403C2×Dic3—241no—
404C2×Dic3—241no—
405C2×Dic3—241no—
406C4×D3—64no—
407C4×D3—81no—
408C4×D3—81no—
409C4×D3—81no—
410C4×D3—241no—
411C4×D3—241no—
412C4×D3—241no—
413Dic6—62no—
414Dic6—62no—
415C2×C32—22no—
416C2×C32C2×C4×D411yescharacteristic
417C2×C32#57611yescharacteristic
418C2×C32#57711yescharacteristic
419C3×D3—42no—
420C3×D3—42no—
421C3×D3—42no—
422C24—61no—
423#41—94no—
424#41—182no—
425C2×Q8—91no—
426C2×D4—61no—
427C2×D4—91no—
428C2×D4—91no—
429C2×D4—91no—
430C2×D4—94no—
431C2×D4—181no—
432C2×D4—182no—
433C22×C4—61no—
434C22×C4—61no—
435C22×C4—61no—
436C22×C4—61no—
437C22×C4—91no—
438C22×C4—181no—
439C22×C4—181no—
440C22×C4—181no—
441C22×C4—181no—
442SD16—94no—
443SD16—94no—
444D8—94no—
445D8—94no—
446M16—94no—
447C2×C8—91no—
448C2×C8—91no—
449C2×C8—91no—
450C2×C8—91no—
451C2×C8—182no—
452C4⋊C4—61no—
453C4⋊C4—91no—
454C4⋊C4—91no—
455C4⋊C4—91no—
456C4⋊C4—91no—
457C4⋊C4—91no—
458C4⋊C4—91no—
459C4⋊C4—181no—
460C4⋊C4—181no—
461C22⋊C4—61no—
462C22⋊C4—61no—
463C22⋊C4—61no—
464C22⋊C4—61no—
465C22⋊C4—91no—
466C22⋊C4—181no—
467C22⋊C4—181no—
468C22⋊C4—181no—
469C22⋊C4GO+(4,𝔽2)11yescharacteristic
470C42—61no—
471C42—91no—
472C42—91no—
473C42—181no—
474C42—181no—
475C22×C3—21no—
476C22×C3—21no—
477C22×C3—22no—
478C22×C3—22no—
479C22×C3—41no—
480C22×C3—41no—
481C22×C3—41no—
482C22×C3—41no—
483C22×C3—62no—
484C22×C3—62no—
485C22×C3—62no—
486C22×C3—121no—
487C22×C3—121no—
488C22×C3—121no—
489C22×C3—121no—
490C22×C3—121no—
491C22×C3—121no—
492C22×C3—244no—
493C2×D3—22no—
494C2×D3—22no—
495C2×D3—22no—
496C2×D3—41no—
497C2×D3—41no—
498C2×D3—41no—
499C2×D3—41no—
500C2×D3—41no—
501C2×D3—41no—
502C2×D3—84no—
503C3×C4—41no—
504C3×C4—41no—
505C3×C4—41no—
506C3×C4—41no—
507C3×C4—62no—
508C3×C4—121no—
509C3×C4—121no—
510C3×C4—121no—
511C3×C4—121no—
512Dic3—22no—
513Dic3—41no—
514Dic3—41no—
515Dic3—41no—
516Dic3—41no—
517Dic3—61no—
518Dic3—61no—
519Dic3—62no—
520Dic3—62no—
521Dic3—61no—
522Dic3—61no—
523Dic3—121no—
524Dic3—121no—
525Dic3—121no—
526Dic3—121no—
527C32#294611yescharacteristic, complemented, Sylow
528C23—61no—
529C23—61no—
530C23—61no—
531C23—64no—
532C23—241no—
533C23—241no—
534C23C2×GO+(4,𝔽2)11yescharacteristic
535Q8—92no—
536Q8—181no—
537D4—64no—
538D4—92no—
539D4—92no—
540D4—92no—
541D4—181no—
542D4—181no—
543D4—184no—
544D4—181no—
545C2×C4—61no—
546C2×C4—61no—
547C2×C4—61no—
548C2×C4—61no—
549C2×C4—61no—
550C2×C4—91no—
551C2×C4—91no—
552C2×C4—92no—
553C2×C4—92no—
554C2×C4—91no—
555C2×C4—91no—
556C2×C4—184no—
557C2×C4—241no—
558C2×C4—241no—
559C2×C4—241no—
560C2×C4—241no—
561C2×C4—721no—
562C2×C4—721no—
563C2×C4—721no—
564C2×C4C2×GO+(4,𝔽2)11yescharacteristic
565C2×C4C2×GO+(4,𝔽2)11yescharacteristic
566C8—92no—
567C8—92no—
568C8—181no—
569C8—181no—
570C2×C3—21no—
571C2×C3—21no—
572C2×C3—21no—
573C2×C3—21no—
574C2×C3—21no—
575C2×C3—21no—
576C2×C3—42no—
577C2×C3—42no—
578C2×C3—122no—
579C2×C3—122no—
580C2×C3—122no—
581D3—42no—
582D3—42no—
583D3—42no—
584C22—21no—
585C22—21no—
586C22—62no—
587C22—62no—
588C22—62no—
589C22—121no—
590C22—121no—
591C22—121no—
592C22—121no—
593C22—121no—
594C22—121no—
595C22—244no—
596C22C4×GO+(4,𝔽2)12yes—
597C22C22×GO+(4,𝔽2)11yescharacteristic
598C4—21no—
599C4—21no—
600C4—62no—
601C4—91no—
602C4—91no—
603C4—92no—
604C4—121no—
605C4—121no—
606C4—121no—
607C4—121no—
608C4—181no—
609C4—181no—
610C3—21no—
611C3—21no—
612C2—22no—
613C2—122no—
614C2—122no—
615C2—122no—
616C2C2×C4×GO+(4,𝔽2)11yescharacteristic
617C2#1059651411yescharacteristic
618C2#1059651511yescharacteristic
subgroupG/H
center, FrattiniC22C22×GO+(4,𝔽2)
commutatorC3⋊Dic3C23×C4
FittingC32×C22⋊C4D4
socleC22×C32C22×D4
prime radicalC2×#64236C2
cosocleC2×C3⋊Dic3C24
hypercenterC22⋊C4GO+(4,𝔽2)
hypocenterC32#2946
LCSG ▷ C3⋊Dic3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22⋊C4

Complements

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

NH ≅ G/Ntype
2. #10594181C2semidirect
3. #10594051C2semidirect
4. #10593738C2semidirect
5. #10593507C2semidirect
6. #10593498C2semidirect
7. C2×#63739C2semidirect
8. #10593433C2semidirect
9. #10593432C2semidirect
10. #10593431C2semidirect
11. C4×#3775C2semidirect
12. #10593420C2semidirect
13. #10593419C2semidirect
14. #10593419C2semidirect
15. C4×#3774C2semidirect
22. #64236C4semidirect
32. C4×#627C22semidirect
35. #63902C22semidirect
38. C4×#625C22semidirect
43. #63838C22semidirect
44. #63777C22semidirect
45. #63777C22semidirect
46. C4×#622C22semidirect
47. C4×#622C22semidirect
48. #63743C22semidirect
49. #63743C22semidirect
50. #63742C22semidirect
51. #63742C22semidirect
52. #63740C22semidirect
53. #63740C22semidirect
58. #63739C22semidirect
59. #63739C22semidirect
72. C2×#625C2×C4semidirect
77. #3805C2×C4semidirect
82. #3792C2×C4semidirect
88. #3775C2×C4semidirect
89. #3775C2×C4semidirect
90. #3774C2×C4semidirect
91. #3774C2×C4semidirect
527. C32#2946semidirect

Maximal subgroups

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

subgroupindex
C2×#642362
#105941812
#105940512
#105937382
#105935072
#105934982
C2×#637392
#105934332
#105934322
#105934312
C4×#37752
#105934202
#105934192
C4×#37742
#29469