Finite Group Databasebeta

← #11887842

Subgroups — #11887842

Order 1152.

1194 conjugacy classes of subgroups.

The subgroup lattice has 555 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596302C211yesmaximal, characteristic, complemented
2#10596085C211yesmaximal, characteristic, complemented
3C32×#449C211yesmaximal, characteristic, complemented
4#10592932C211yesmaximal, characteristic, complemented
5#10592869C211yesmaximal, characteristic, complemented
6SD16×C3⋊Dic3C211yesmaximal, characteristic, complemented
7#10592856C211yesmaximal, characteristic, complemented
8#10592852C211yesmaximal, characteristic, complemented
9#10592740C211yesmaximal, characteristic, complemented
10C3⋊D3×#103C211yesmaximal, characteristic, complemented
11#10592495C211yesmaximal, characteristic, complemented
12#10592476C211yesmaximal, characteristic, complemented
13#10592467C211yesmaximal, characteristic, complemented
14#10592424C211yesmaximal, characteristic, complemented
15#10592422C211yesmaximal, characteristic, complemented
16#80103—34nomaximal
17C2×C32×#41C2211yescharacteristic
18C2×Q8×C3⋊D3C2211yescharacteristic
19C2×C32×SD16C2211yescharacteristic
20C2×C32×D8C2211yescharacteristic
21C32×#121C2211yescharacteristic
22Q8×C3⋊Dic3C2211yescharacteristic
23#64147—21no—
24#64147—21no—
25#64147C2211yescharacteristic
26#64147C2211yescharacteristic
27#64145—21no—
28#64145C2211yescharacteristic
29#64144—21no—
30D4×C3⋊Dic3C2211yescharacteristic
31C2×#3754C2211yescharacteristic
32C4×#638—21no—
33C4×#638C2211yescharacteristic
34#64135C2211yescharacteristic
35#64133—21no—
36#64133C2211yescharacteristic
37C22×C3⋊(C3⋊C8)C2211yescharacteristic
38C2×C8×C3⋊D3C2211yescharacteristic
39C4⋊C4×C3⋊D3C2211yescharacteristic
40#64099C2211yescharacteristic
41#64090—21no—
42#64088—21no—
43C32×#103C2211yescharacteristic
44C32×#102C2211yescharacteristic
45C32×C22⋊C8C2211yescharacteristic
46#63662C2211yescharacteristic
47#63662C2211yescharacteristic
48#63659C2211yescharacteristic
49#63659C2211yescharacteristic
50#63659C2211yescharacteristic
51#63647C2211yescharacteristic
52#63645C2211yescharacteristic
53#63644C2211yescharacteristic
54#63643C2211yescharacteristic
55#63643C2211yescharacteristic
56#63641C2211yescharacteristic
57C8×C3⋊Dic3C2211yescharacteristic
58#63637C2211yescharacteristic
59#63635C2211yescharacteristic
60#5831—34no—
61#5614—34no—
62C3×#449D314yescomplemented
63#5233—34no—
64#5170—34no—
65Dic3×SD16—34no—
66#5157—34no—
67#5153—34no—
68#5041—34no—
69D3×#103—34no—
70#4796—34no—
71#4777—34no—
72#4768—34no—
73#67⋊C8—34no—
74#4723—34no—
75C32×#41—22no—
76C32×#41—41no—
77C2×C32×Q8C2311yescharacteristic
78C2×C32×D4—21no—
79C2×C32×D4—21no—
80C2×C32×D4C2311yescharacteristic
81C2×C32×D4C2311yescharacteristic
82C22×C32×C4—21no—
83C22×C32×C4C2311yescharacteristic
84C2×#638—21no—
85C2×#638—21no—
86C2×#638D411yescharacteristic
87C22×C3⋊Dic3—21no—
88Q8×C3⋊D3—22no—
89Q8×C3⋊D3—41no—
90C2×C4×C3⋊D3—21no—
91C2×C4×C3⋊D3—21no—
92C2×C4×C3⋊D3C2311yescharacteristic
93C2×#634—21no—
94C2×#634C2311yescharacteristic
95C32×SD16—22no—
96C32×D8—41no—
97C2×C32×C8C2311yescharacteristic
98C2×C32×C8C2311yescharacteristic
99C32×C4⋊C4C2311yescharacteristic
100C32×C22⋊C4—21no—
101#3757—21no—
102#3757—21no—
103#3757—21no—
104#3757—21no—
105#3757—21no—
106#3757—21no—
107#3757—21no—
108#3757D411yescharacteristic
109#3754—41no—
110#3752D411yescharacteristic
111C4⋊(C3⋊Dic3)—21no—
112C4⋊(C3⋊Dic3)—21no—
113C4⋊(C3⋊Dic3)C2311yescharacteristic
114C4⋊(C3⋊Dic3)C2311yescharacteristic
115C4⋊(C3⋊Dic3)C2311yescharacteristic
116#3750—21no—
117#3750—21no—
118#3750—21no—
119#3750D411yescharacteristic
120C4×C3⋊Dic3—21no—
121C4×C3⋊Dic3—21no—
122C4×C3⋊Dic3C2311yescharacteristic
123C2×C3⋊(C3⋊C8)—41no—
124C2×C3⋊(C3⋊C8)C2311yescharacteristic
125C2×C3⋊(C3⋊C8)C2311yescharacteristic
126C8×C3⋊D3—41no—
127#3301—91noSylow
128C2×C3×#41C2×D314yes—
129C2×D3×Q8—34no—
130C2×C3×SD16C2×D314yes—
131C2×C3×D8C2×D314yes—
132C3×#121C2×D314yes—
133Q8×Dic3—34no—
134#938—34no—
135#938—34no—
136#938—64no—
137#938—64no—
138#936—34no—
139#936—64no—
140#935—64no—
141D4×Dic3—34no—
142C2×#214—34no—
143C4×#67—34no—
144C4×#67—64no—
145#926—34no—
146#924—34no—
147#924—64no—
148C22×C3⋊C8—34no—
149C2×D3×C8—34no—
150D3×C4⋊C4—34no—
151#890—34no—
152#67⋊C4—64no—
153#879—64no—
154C3×#103C2×D314yes—
155C3×#102C2×D314yes—
156C3×C22⋊C8C2×D314yes—
157#835—34no—
158#835—34no—
159#832—34no—
160#832—34no—
161#832—34no—
162(C2×D3)⋊C8—34no—
163#818—34no—
164#817—34no—
165#816—34no—
166#816—34no—
167Dic3⋊C8—34no—
168C8×Dic3—34no—
169#810—34no—
170#808—34no—
171C23×C32—21no—
172C23×C32—21no—
173C23×C32C2×D411yescharacteristic
174C22×C3⋊D3C2×D411yescharacteristic
175C32×Q8—21no—
176C32×Q8#4112yes—
177C32×D4—21no—
178C32×D4—21no—
179C32×D4—21no—
180C32×D4—21no—
181C32×D4—42no—
182C32×D4—81no—
183C2×C32×C4—21no—
184C2×C32×C4—21no—
185C2×C32×C4—21no—
186C2×C32×C4—21no—
187C2×C32×C4—42no—
188C2×C32×C4C2×D411yescharacteristic
189C2×C32×C4C2411yescharacteristic
190#638—22no—
191#638—42no—
192#638—42no—
193C2×C3⋊Dic3—21no—
194C2×C3⋊Dic3—21no—
195C2×C3⋊Dic3—21no—
196C2×C3⋊Dic3—21no—
197C2×C3⋊Dic3—81no—
198C2×C3⋊Dic3C2×D411yescharacteristic
199C2×C3⋊Dic3C2×D411yescharacteristic
200C2×C3⋊Dic3C2×D411yescharacteristic
201C4×C3⋊D3—21no—
202C4×C3⋊D3—21no—
203C4×C3⋊D3—42no—
204C4×C3⋊D3—81no—
205#634—21no—
206#634—21no—
207#634—42no—
208C32×C8—21no—
209C32×C8—21no—
210C3⋊(C3⋊C8)—21no—
211C3⋊(C3⋊C8)—21no—
212#553—91no—
213#548—91no—
214#488—91no—
215#485—91no—
216#481—91no—
217#479—91no—
218#466—91no—
219#465—91no—
220#463—91no—
221#449C3⋊D311yescharacteristic, complemented
222#448—91no—
223C4×SD16—91no—
224C8×D4—91no—
225#416—91no—
226C2×#103—91no—
227C3×#41—28no—
228C3×#41—44no—
229C2×C3×Q8C22×D314yes—
230C2×C3×D4—24no—
231C2×C3×D4—24no—
232C2×C3×D4C22×D314yes—
233C2×C3×D4C22×D314yes—
234C22×C3×C4—24no—
235C22×C3×C4C22×D314yes—
236C2×#67—34no—
237C2×#67—64no—
238C2×#67—64no—
239C22×Dic3—64no—
240D3×Q8—68no—
241D3×Q8—124no—
242C2×C4×D3—34no—
243C2×C4×D3—64no—
244C2×C4×D3—64no—
245C2×Dic6—34no—
246C2×Dic6—64no—
247C3×SD16—28no—
248C3×D8—44no—
249C2×C3×C8C22×D314yes—
250C2×C3×C8C22×D314yes—
251C3×C4⋊C4C22×D314yes—
252C3×C22⋊C4—24no—
253#217—34no—
254#217—64no—
255#217—64no—
256#217—64no—
257#217—64no—
258#217—64no—
259#217—64no—
260#217—64no—
261#214—124no—
262(C2×D3)⋊C4—34no—
263C4⋊Dic3—34no—
264C4⋊Dic3—34no—
265C4⋊Dic3—34no—
266C4⋊Dic3—64no—
267C4⋊Dic3—64no—
268Dic3⋊C4—34no—
269Dic3⋊C4—64no—
270Dic3⋊C4—64no—
271Dic3⋊C4—64no—
272C4×Dic3—34no—
273C4×Dic3—64no—
274C4×Dic3—64no—
275C2×C3⋊C8—34no—
276C2×C3⋊C8—34no—
277C2×C3⋊C8—124no—
278D3×C8—124no—
279C22×C32—21no—
280C22×C32—21no—
281C22×C32—21no—
282C22×C32—41no—
283C22×C32—41no—
284C22×C32—41no—
285C22×C32—41no—
286C22×C32—41no—
287C22×C32—41no—
288C22×C32C22×D411yescharacteristic
289C2×C3⋊D3—21no—
290C2×C3⋊D3—21no—
291C2×C3⋊D3#13512yes—
292C32×C4—22no—
293C32×C4—21no—
294C32×C4—41no—
295C32×C4C2×#4111yescharacteristic
296C32×C4H(5,𝔽2)11yescharacteristic
297C3⋊Dic3—21no—
298C3⋊Dic3—21no—
299C3⋊Dic3—21no—
300C3⋊Dic3—41no—
301C3⋊Dic3—41no—
302C3⋊Dic3—41no—
303C3⋊Dic3—41no—
304C2×#41C2×C3⋊D311yescharacteristic
305C22×Q8—91no—
306C2×SD16—91no—
307C2×SD16C2×C3⋊D311yescharacteristic
308C2×D8C2×C3⋊D311yescharacteristic
309C22×C8—91no—
310C22×C8—91no—
311#126—181no—
312#125—91no—
313#124—91no—
314#124—181no—
315#123—181no—
316C22⋊Q8—91no—
317C22⋊Q8—181no—
318#121—91no—
319#121—91no—
320#121—181no—
321#121—181no—
322#121C2×C3⋊D311yescharacteristic
323C4×Q8—91no—
324C4×D4—91no—
325C4×D4—91no—
326C4×D4—181no—
327C4×D4—181no—
328#117—91no—
329C2×C4⋊C4—91no—
330#107—91no—
331#106—91no—
332#106—91no—
333C4⋊C8—91no—
334#103—91no—
335#103—91no—
336#103—91no—
337#103—91no—
338#103—91no—
339#103C2×C3⋊D311yescharacteristic
340#102—91no—
341#102—91no—
342#102—91no—
343#102C2×C3⋊D311yescharacteristic
344C22⋊C8—91no—
345C22⋊C8C2×C3⋊D311yescharacteristic
346C4×C8—91no—
347C23×C3—24no—
348C23×C3—24no—
349C23×C3D3×D414yes—
350C22×D3—34no—
351C3×Q8—24no—
352C3×Q8#23718yes—
353C3×D4—24no—
354C3×D4—24no—
355C3×D4—24no—
356C3×D4—24no—
357C3×D4—48no—
358C3×D4—84no—
359C2×C3×C4—24no—
360C2×C3×C4—24no—
361C2×C3×C4—24no—
362C2×C3×C4—24no—
363C2×C3×C4—48no—
364C2×C3×C4D3×D414yes—
365C2×C3×C4C23×D314yes—
366#67—68no—
367#67—128no—
368#67—128no—
369C2×Dic3—34no—
370C2×Dic3—34no—
371C2×Dic3—34no—
372C2×Dic3—64no—
373C2×Dic3—64no—
374C2×Dic3—64no—
375C2×Dic3—64no—
376C2×Dic3—244no—
377C4×D3—64no—
378C4×D3—64no—
379C4×D3—128no—
380C4×D3—244no—
381Dic6—64no—
382Dic6—64no—
383Dic6—128no—
384C3×C8—24no—
385C3×C8—24no—
386C3⋊C8—64no—
387C3⋊C8—64no—
388C2×C32—41no—
389C2×C32—81no—
390C2×C32—81no—
391C2×C32#54611yescharacteristic
392C2×C32C2×#13511yescharacteristic
393C2×C32#57711yescharacteristic
394C3⋊D3—22no—
395#41—22no—
396#41—41no—
397C2×Q8—91no—
398C2×Q8—181no—
399C2×Q8—182no—
400C2×Q8—361no—
401C2×Q8C22×C3⋊D311yescharacteristic
402C2×D4—21no—
403C2×D4—21no—
404C2×D4—91no—
405C2×D4—181no—
406C2×D4—181no—
407C2×D4C22×C3⋊D311yescharacteristic
408C2×D4C22×C3⋊D311yescharacteristic
409C22×C4—21no—
410C22×C4—91no—
411C22×C4—181no—
412C22×C4—181no—
413C22×C4—181no—
414C22×C4C22×C3⋊D311yescharacteristic
415SD16—22no—
416SD16—361no—
417D8—41no—
418C2×C8—91no—
419C2×C8—91no—
420C2×C8—361no—
421C2×C8—361no—
422C2×C8C22×C3⋊D311yescharacteristic
423C2×C8C22×C3⋊D311yescharacteristic
424C4⋊C4—91no—
425C4⋊C4—91no—
426C4⋊C4—91no—
427C4⋊C4—91no—
428C4⋊C4—181no—
429C4⋊C4—181no—
430C4⋊C4—181no—
431C4⋊C4—181no—
432C4⋊C4—181no—
433C4⋊C4C22×C3⋊D311yescharacteristic
434C22⋊C4—21no—
435C22⋊C4—91no—
436C22⋊C4—91no—
437C22⋊C4—181no—
438C22⋊C4—181no—
439C22⋊C4—181no—
440C22⋊C4—181no—
441C22⋊C4—181no—
442C22⋊C4—181no—
443C22⋊C4—181no—
444C42—91no—
445C42—181no—
446C42—181no—
447C22×C3—24no—
448C22×C3—24no—
449C22×C3—24no—
450C22×C3—44no—
451C22×C3—44no—
452C22×C3—44no—
453C22×C3—44no—
454C22×C3—44no—
455C22×C3—44no—
456C22×C3C2×D3×D414yes—
457C2×D3—38no—
458C2×D3—64no—
459C2×D3—64no—
460C3×C4—28no—
461C3×C4—24no—
462C3×C4—44no—
463C3×C4C2×#23714yes—
464C3×C4#100414yes—
465Dic3—64no—
466Dic3—64no—
467Dic3—64no—
468Dic3—124no—
469Dic3—124no—
470Dic3—124no—
471Dic3—124no—
472C32#330111yescharacteristic, complemented, Sylow
473C23—21no—
474C23—21no—
475C23—91no—
476C23D4×C3⋊D311yescharacteristic
477Q8—21no—
478Q8—181no—
479Q8—181no—
480Q8—362no—
481Q8#383012yes—
482D4—21no—
483D4—21no—
484D4—21no—
485D4—21no—
486D4—42no—
487D4—81no—
488D4—182no—
489D4—362no—
490D4—362no—
491C2×C4—21no—
492C2×C4—21no—
493C2×C4—21no—
494C2×C4—21no—
495C2×C4—42no—
496C2×C4—91no—
497C2×C4—91no—
498C2×C4—91no—
499C2×C4—181no—
500C2×C4—181no—
501C2×C4—181no—
502C2×C4—181no—
503C2×C4—181no—
504C2×C4—181no—
505C2×C4—362no—
506C2×C4—721no—
507C2×C4—721no—
508C2×C4D4×C3⋊D311yescharacteristic
509C2×C4C23×C3⋊D311yescharacteristic
510C8—21no—
511C8—21no—
512C8—181no—
513C8—181no—
514C2×C3—44no—
515C2×C3—84no—
516C2×C3—84no—
517C2×C3#559114yes—
518C2×C3D3×#13514yes—
519C2×C3#577514yes—
520D3—68no—
521C22—21no—
522C22—21no—
523C22—21no—
524C22—41no—
525C22—41no—
526C22—41no—
527C22—41no—
528C22—41no—
529C22—41no—
530C22—92no—
531C22—181no—
532C22—181no—
533C22C2×D4×C3⋊D311yescharacteristic
534C4—21no—
535C4—22no—
536C4—41no—
537C4—181no—
538C4—181no—
539C4—181no—
540C4—361no—
541C4—361no—
542C4—361no—
543C4—361no—
544C4C2×#383011yescharacteristic
545C4#6436111yescharacteristic
546C3#8010314yescomplemented
547C2—41no—
548C2—81no—
549C2—81no—
550C2—182no—
551C2#1059606211yescharacteristic
552C2C3⋊D3×#13511yescharacteristic
553C2#1059624611yescharacteristic
subgroupG/H
centerC22C2×D4×C3⋊D3
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C23×C3⋊D3
FittingC32×#449C2
socleC22×C32C22×D4
hypercenter#449C3⋊D3
hypocenterC32#3301
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ #449

Complements

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

NH ≅ G/Ntype
1. #10596302C2semidirect
2. #10596085C2semidirect
3. C32×#449C2semidirect
4. #10592932C2semidirect
5. #10592869C2semidirect
6. SD16×C3⋊Dic3C2semidirect
7. #10592856C2semidirect
8. #10592852C2semidirect
9. #10592740C2semidirect
10. C3⋊D3×#103C2semidirect
11. #10592495C2semidirect
12. #10592476C2semidirect
13. #10592467C2semidirect
14. #10592424C2semidirect
15. #10592422C2semidirect
62. C3×#449D3semidirect
221. #449C3⋊D3semidirect
472. C32#3301semidirect
546. C3#80103semidirect

Maximal subgroups

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

subgroupindex
#105963022
#105960852
C32×#4492
#105929322
#105928692
SD16×C3⋊Dic32
#105928562
#105928522
#105927402
C3⋊D3×#1032
#105924952
#105924762
#105924672
#105924242
#105924222
#801033