Finite Group Databasebeta

← #11887688

Subgroups — #11887688

Order 1152.

1158 conjugacy classes of subgroups.

The subgroup lattice has 537 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596302C211yesmaximal, characteristic
2#10596110C211yesmaximal, characteristic, complemented
3C32×#452C211yesmaximal, characteristic, complemented
4#10592932C211yesmaximal, characteristic, complemented
5#10592885C211yesmaximal, characteristic, complemented
6Q16×C3⋊Dic3C211yesmaximal, characteristic, complemented
7#10592870C211yesmaximal, characteristic, complemented
8#10592865C211yesmaximal, characteristic, complemented
9#10592750C211yesmaximal, characteristic, complemented
10C3⋊D3×#103C211yesmaximal, characteristic, complemented
11#10592498C211yesmaximal, characteristic, complemented
12#10592473C211yesmaximal, characteristic, complemented
13#10592467C211yesmaximal, characteristic, complemented
14#10592424C211yesmaximal, characteristic, complemented
15#10592422C211yesmaximal, characteristic, complemented
16#80247—34nomaximal
17C2×C32×#41C2211yescharacteristic
18C2×Q8×C3⋊D3C2211yescharacteristic
19C2×C32×Q16C2211yescharacteristic
20C2×C32×SD16C2211yescharacteristic
21C32×C22⋊Q8C2211yescharacteristic
22#64155C2211yescharacteristic
23Q8×C3⋊Dic3C2211yescharacteristic
24Q8×C3⋊Dic3C2211yescharacteristic
25C2×#3756C2211yescharacteristic
26#64147—21no—
27#64147C2211yescharacteristic
28#64145—21no—
29#64145C2211yescharacteristic
30C4×#638—21no—
31C4×#638C2211yescharacteristic
32#64135C2211yescharacteristic
33#64133—21no—
34#64133C2211yescharacteristic
35C22×C3⋊(C3⋊C8)C2211yescharacteristic
36C2×C8×C3⋊D3C2211yescharacteristic
37#64101—21no—
38C4⋊C4×C3⋊D3C2211yescharacteristic
39#64099C2211yescharacteristic
40#64098—21no—
41#64092—21no—
42#64088—21no—
43C32×#103C2211yescharacteristic
44C32×#102C2211yescharacteristic
45C32×C22⋊C8C2211yescharacteristic
46#63662C2211yescharacteristic
47#63662C2211yescharacteristic
48#63662C2211yescharacteristic
49#63659C2211yescharacteristic
50#63659C2211yescharacteristic
51#63647C2211yescharacteristic
52#63645C2211yescharacteristic
53#63644C2211yescharacteristic
54#63643C2211yescharacteristic
55#63643C2211yescharacteristic
56#63641C2211yescharacteristic
57C8×C3⋊Dic3C2211yescharacteristic
58#63637C2211yescharacteristic
59#63634C2211yescharacteristic
60#5831—34no—
61#5639—34no—
62C3×#452D314yescomplemented
63#5233—34no—
64#5186—34no—
65Dic3×Q16—34no—
66#5171—34no—
67#5166—34no—
68#5051—34no—
69D3×#103—34no—
70#4799—34no—
71#4774—34no—
72#4768—34no—
73#67⋊C8—34no—
74#4723—34no—
75C32×#41—22no—
76C32×#41—41no—
77C2×C32×Q8C2311yescharacteristic
78C2×C32×Q8C2311yescharacteristic
79C2×C32×D4—21no—
80C2×C32×D4C2311yescharacteristic
81C22×C32×C4—21no—
82C22×C32×C4C2311yescharacteristic
83C2×#638—21no—
84C2×#638D411yescharacteristic
85Q8×C3⋊D3—22no—
86Q8×C3⋊D3—41no—
87C2×C4×C3⋊D3—21no—
88C2×C4×C3⋊D3—21no—
89C2×C4×C3⋊D3C2311yescharacteristic
90C2×#634—21no—
91C2×#634C2311yescharacteristic
92C32×Q16—22no—
93C32×SD16—41no—
94C2×C32×C8C2311yescharacteristic
95C2×C32×C8C2311yescharacteristic
96C32×C4⋊C4—21no—
97C32×C4⋊C4C2311yescharacteristic
98C32×C22⋊C4—21no—
99#3757—21no—
100#3757—21no—
101#3757—21no—
102#3757—21no—
103#3757—21no—
104#3757D411yescharacteristic
105#3756—41no—
106#3752—21no—
107#3752D411yescharacteristic
108C4⋊(C3⋊Dic3)—21no—
109C4⋊(C3⋊Dic3)—21no—
110C4⋊(C3⋊Dic3)—21no—
111C4⋊(C3⋊Dic3)C2311yescharacteristic
112C4⋊(C3⋊Dic3)C2311yescharacteristic
113C4⋊(C3⋊Dic3)C2311yescharacteristic
114#3750—21no—
115#3750—21no—
116#3750—21no—
117#3750—21no—
118#3750D411yescharacteristic
119C4×C3⋊Dic3—21no—
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#3300—91noSylow
128C2×C3×#41C2×D314yes—
129C2×D3×Q8—34no—
130C2×C3×Q16C2×D314yes—
131C2×C3×SD16C2×D314yes—
132C3×C22⋊Q8C2×D314yes—
133#946—34no—
134Q8×Dic3—34no—
135Q8×Dic3—34no—
136C2×#216—34no—
137#938—34no—
138#938—64no—
139#936—34no—
140#936—64no—
141C4×#67—34no—
142C4×#67—64no—
143#926—34no—
144#924—34no—
145#924—64no—
146C22×C3⋊C8—34no—
147C2×D3×C8—34no—
148#892—64no—
149D3×C4⋊C4—34no—
150#890—34no—
151#889—64no—
152#883—64no—
153#879—64no—
154C3×#103C2×D314yes—
155C3×#102C2×D314yes—
156C3×C22⋊C8C2×D314yes—
157#835—34no—
158#835—34no—
159#835—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#807—34no—
171C23×C32—21no—
172C23×C32C2×D411yescharacteristic
173C22×C3⋊D3C2×D411yescharacteristic
174C32×Q8—21no—
175C32×Q8—21no—
176C32×Q8—21no—
177C32×Q8#4112yes—
178C32×D4—21no—
179C32×D4—21no—
180C32×D4—42no—
181C2×C32×C4—21no—
182C2×C32×C4—21no—
183C2×C32×C4—21no—
184C2×C32×C4—21no—
185C2×C32×C4—21no—
186C2×C32×C4—42no—
187C2×C32×C4C2×D411yescharacteristic
188C2×C32×C4C2411yescharacteristic
189#638—22no—
190#638—42no—
191C2×C3⋊Dic3—21no—
192C2×C3⋊Dic3—21no—
193C2×C3⋊Dic3—21no—
194C2×C3⋊Dic3—21no—
195C2×C3⋊Dic3C2×D411yescharacteristic
196C2×C3⋊Dic3C2×D411yescharacteristic
197C2×C3⋊Dic3C2×D411yescharacteristic
198C4×C3⋊D3—21no—
199C4×C3⋊D3—21no—
200C4×C3⋊D3—42no—
201C4×C3⋊D3—42no—
202#634—21no—
203#634—21no—
204#634—42no—
205C32×C8—21no—
206C32×C8—21no—
207C3⋊(C3⋊C8)—21no—
208C3⋊(C3⋊C8)—21no—
209#552—91no—
210#548—91no—
211#488—91no—
212#485—91no—
213#480—91no—
214#479—91no—
215#467—91no—
216#465—91no—
217#464—91no—
218#452C3⋊D311yescharacteristic, complemented
219#451—91no—
220C4×Q16—91no—
221C8×D4—91no—
222#416—91no—
223C2×#103—91no—
224C3×#41—28no—
225C3×#41—44no—
226C2×C3×Q8C22×D314yes—
227C2×C3×Q8C22×D314yes—
228C2×C3×D4—24no—
229C2×C3×D4C22×D314yes—
230C22×C3×C4—24no—
231C22×C3×C4C22×D314yes—
232C2×#67—34no—
233C2×#67—64no—
234D3×Q8—68no—
235D3×Q8—124no—
236C2×C4×D3—34no—
237C2×C4×D3—64no—
238C2×C4×D3—64no—
239C2×Dic6—34no—
240C2×Dic6—64no—
241C3×Q16—28no—
242C3×SD16—44no—
243C2×C3×C8C22×D314yes—
244C2×C3×C8C22×D314yes—
245C3×C4⋊C4—24no—
246C3×C4⋊C4C22×D314yes—
247C3×C22⋊C4—24no—
248#217—34no—
249#217—64no—
250#217—64no—
251#217—64no—
252#217—64no—
253#217—64no—
254#216—124no—
255(C2×D3)⋊C4—34no—
256(C2×D3)⋊C4—64no—
257C4⋊Dic3—34no—
258C4⋊Dic3—34no—
259C4⋊Dic3—34no—
260C4⋊Dic3—64no—
261C4⋊Dic3—64no—
262C4⋊Dic3—64no—
263Dic3⋊C4—34no—
264Dic3⋊C4—64no—
265Dic3⋊C4—64no—
266Dic3⋊C4—64no—
267Dic3⋊C4—64no—
268C4×Dic3—34no—
269C4×Dic3—64no—
270C4×Dic3—64no—
271C4×Dic3—64no—
272C2×C3⋊C8—34no—
273C2×C3⋊C8—34no—
274C2×C3⋊C8—124no—
275D3×C8—124no—
276C22×C32—21no—
277C22×C32—21no—
278C22×C32—21no—
279C22×C32—41no—
280C22×C32—41no—
281C22×C32—41no—
282C22×C32C22×D411yescharacteristic
283C2×C3⋊D3—21no—
284C2×C3⋊D3—21no—
285C2×C3⋊D3#13512yes—
286C32×C4—22no—
287C32×C4—21no—
288C32×C4—41no—
289C32×C4—41no—
290C32×C4C2×#4111yescharacteristic
291C32×C4H(5,𝔽2)11yescharacteristic
292C3⋊Dic3—21no—
293C3⋊Dic3—21no—
294C3⋊Dic3—21no—
295C3⋊Dic3—41no—
296C3⋊Dic3—41no—
297C3⋊Dic3—41no—
298C3⋊Dic3—41no—
299C2×#41C2×C3⋊D311yescharacteristic
300C22×Q8—91no—
301C2×Q16—91no—
302C2×Q16C2×C3⋊D311yescharacteristic
303C2×SD16C2×C3⋊D311yescharacteristic
304C22×C8—91no—
305C22×C8—91no—
306#126—181no—
307#125—91no—
308#125—181no—
309#124—91no—
310#124—181no—
311#123—181no—
312C22⋊Q8—91no—
313C22⋊Q8—91no—
314C22⋊Q8—181no—
315C22⋊Q8C2×C3⋊D311yescharacteristic
316#121—91no—
317#121—181no—
318C4×Q8—91no—
319C4×Q8—91no—
320C4×D4—91no—
321C4×D4—181no—
322#117—91no—
323#117—181no—
324C2×C4⋊C4—91no—
325#107—91no—
326#107—91no—
327#106—91no—
328C4⋊C8—91no—
329#103—91no—
330#103—91no—
331#103—91no—
332#103—91no—
333#103—91no—
334#103—91no—
335#103C2×C3⋊D311yescharacteristic
336#102—91no—
337#102—91no—
338#102C2×C3⋊D311yescharacteristic
339C22⋊C8—91no—
340C22⋊C8C2×C3⋊D311yescharacteristic
341C4×C8—91no—
342C23×C3—24no—
343C23×C3D3×D414yes—
344C22×D3—34no—
345C3×Q8—24no—
346C3×Q8—24no—
347C3×Q8—24no—
348C3×Q8#23718yes—
349C3×D4—24no—
350C3×D4—24no—
351C3×D4—48no—
352C2×C3×C4—24no—
353C2×C3×C4—24no—
354C2×C3×C4—24no—
355C2×C3×C4—24no—
356C2×C3×C4—24no—
357C2×C3×C4—48no—
358C2×C3×C4D3×D414yes—
359C2×C3×C4C23×D314yes—
360#67—68no—
361#67—128no—
362C2×Dic3—34no—
363C2×Dic3—34no—
364C2×Dic3—34no—
365C2×Dic3—64no—
366C2×Dic3—64no—
367C2×Dic3—64no—
368C2×Dic3—64no—
369C4×D3—64no—
370C4×D3—64no—
371C4×D3—128no—
372C4×D3—128no—
373Dic6—64no—
374Dic6—64no—
375Dic6—128no—
376C3×C8—24no—
377C3×C8—24no—
378C3⋊C8—64no—
379C3⋊C8—64no—
380C2×C32—41no—
381C2×C32—81no—
382C2×C32#54611yescharacteristic
383C2×C32C2×#13511yescharacteristic
384C2×C32#57811yescharacteristic
385C3⋊D3—22no—
386#41—22no—
387#41—41no—
388C2×Q8—91no—
389C2×Q8—181no—
390C2×Q8—182no—
391C2×Q8—361no—
392C2×Q8C22×C3⋊D311yescharacteristic
393C2×Q8C22×C3⋊D311yescharacteristic
394C2×D4—21no—
395C2×D4—91no—
396C2×D4—181no—
397C2×D4C22×C3⋊D311yescharacteristic
398C22×C4—21no—
399C22×C4—91no—
400C22×C4—181no—
401C22×C4—181no—
402C22×C4C22×C3⋊D311yescharacteristic
403Q16—22no—
404Q16—361no—
405SD16—41no—
406C2×C8—91no—
407C2×C8—91no—
408C2×C8—361no—
409C2×C8—361no—
410C2×C8C22×C3⋊D311yescharacteristic
411C2×C8C22×C3⋊D311yescharacteristic
412C4⋊C4—21no—
413C4⋊C4—91no—
414C4⋊C4—91no—
415C4⋊C4—91no—
416C4⋊C4—91no—
417C4⋊C4—181no—
418C4⋊C4—181no—
419C4⋊C4—181no—
420C4⋊C4—181no—
421C4⋊C4—181no—
422C4⋊C4—181no—
423C4⋊C4—181no—
424C4⋊C4C22×C3⋊D311yescharacteristic
425C22⋊C4—21no—
426C22⋊C4—91no—
427C22⋊C4—91no—
428C22⋊C4—181no—
429C22⋊C4—181no—
430C22⋊C4—181no—
431C22⋊C4—181no—
432C22⋊C4—181no—
433C22⋊C4—181no—
434C42—91no—
435C42—181no—
436C42—181no—
437C42—181no—
438C22×C3—24no—
439C22×C3—24no—
440C22×C3—24no—
441C22×C3—44no—
442C22×C3—44no—
443C22×C3—44no—
444C22×C3C2×D3×D414yes—
445C2×D3—38no—
446C2×D3—64no—
447C2×D3—64no—
448C3×C4—28no—
449C3×C4—24no—
450C3×C4—44no—
451C3×C4—44no—
452C3×C4C2×#23714yes—
453C3×C4#100414yes—
454Dic3—64no—
455Dic3—64no—
456Dic3—64no—
457Dic3—124no—
458Dic3—124no—
459Dic3—124no—
460Dic3—124no—
461C32#330011yescharacteristic, complemented, Sylow
462C23—21no—
463C23—91no—
464C23D4×C3⋊D311yescharacteristic
465Q8—21no—
466Q8—21no—
467Q8—21no—
468Q8—181no—
469Q8—181no—
470Q8—362no—
471Q8#383012yes—
472D4—21no—
473D4—21no—
474D4—42no—
475D4—182no—
476D4—362no—
477C2×C4—21no—
478C2×C4—21no—
479C2×C4—21no—
480C2×C4—21no—
481C2×C4—21no—
482C2×C4—42no—
483C2×C4—91no—
484C2×C4—91no—
485C2×C4—91no—
486C2×C4—181no—
487C2×C4—181no—
488C2×C4—181no—
489C2×C4—181no—
490C2×C4—181no—
491C2×C4—181no—
492C2×C4—362no—
493C2×C4—362no—
494C2×C4D4×C3⋊D311yescharacteristic
495C2×C4C23×C3⋊D311yescharacteristic
496C8—21no—
497C8—21no—
498C8—181no—
499C8—181no—
500C2×C3—44no—
501C2×C3—84no—
502C2×C3#559114yes—
503C2×C3D3×#13514yes—
504C2×C3#577914yes—
505D3—68no—
506C22—21no—
507C22—21no—
508C22—21no—
509C22—41no—
510C22—41no—
511C22—41no—
512C22—92no—
513C22—181no—
514C22—181no—
515C22C2×D4×C3⋊D311yescharacteristic
516C4—21no—
517C4—22no—
518C4—41no—
519C4—41no—
520C4—181no—
521C4—181no—
522C4—181no—
523C4—361no—
524C4—361no—
525C4—361no—
526C4—361no—
527C4C2×#383011yescharacteristic
528C4#6436111yescharacteristic
529C3#8024714yescomplemented
530C2—41no—
531C2—81no—
532C2—182no—
533C2#1059606211yescharacteristic
534C2C3⋊D3×#13511yescharacteristic
535C2#1059625011yescharacteristic
subgroupG/H
centerC22C2×D4×C3⋊D3
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C23×C3⋊D3
FittingC32×#452C2
socleC22×C32C22×D4
prime radical#10596302C2
hypercenter#452C3⋊D3
hypocenterC32#3300
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ #452

Complements

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

NH ≅ G/Ntype
2. #10596110C2semidirect
3. C32×#452C2semidirect
4. #10592932C2semidirect
5. #10592885C2semidirect
6. Q16×C3⋊Dic3C2semidirect
7. #10592870C2semidirect
8. #10592865C2semidirect
9. #10592750C2semidirect
10. C3⋊D3×#103C2semidirect
11. #10592498C2semidirect
12. #10592473C2semidirect
13. #10592467C2semidirect
14. #10592424C2semidirect
15. #10592422C2semidirect
62. C3×#452D3semidirect
218. #452C3⋊D3semidirect
461. C32#3300semidirect
529. C3#80247semidirect

Maximal subgroups

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

subgroupindex
#105963022
#105961102
C32×#4522
#105929322
#105928852
Q16×C3⋊Dic32
#105928702
#105928652
#105927502
C3⋊D3×#1032
#105924982
#105924732
#105924672
#105924242
#105924222
#802473