Finite Group Databasebeta

← #11887715

Subgroups — #11887715

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#10596023C211yesmaximal, characteristic
2#10596012C211yesmaximal, characteristic, complemented
3C32×C8×D4C211yesmaximal, characteristic, complemented
4#10592815C211yesmaximal, characteristic, complemented
5#10592813C211yesmaximal, characteristic, complemented
6#10592812C211yesmaximal, characteristic, complemented
7C2×#63643C211yesmaximal, characteristic, complemented
8#10592544C211yesmaximal, characteristic, complemented
9#10592528C211yesmaximal, characteristic, complemented
10#10592438C211yesmaximal, characteristic, complemented
11#10592435C211yesmaximal, characteristic, complemented
12#10592432C211yesmaximal, characteristic, complemented
13#10592422C211yesmaximal, characteristic, complemented
14C4×#3746C211yesmaximal, characteristic, complemented
15#10592396C211yesmaximal, characteristic, complemented
16#79449—34nomaximal
17C2×#3828C2211yescharacteristic
18C22×#634C2211yescharacteristic
19C22×C32×C8C2211yescharacteristic
20C22×C32×C8C2211yescharacteristic
21C32×C4×D4C2211yescharacteristic
22#64148—21no—
23#64144—21no—
24#64139C2211yescharacteristic
25#64135C2211yescharacteristic
26C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
27#64133C2211yescharacteristic
28#64133C2211yescharacteristic
29#64133C2211yescharacteristic
30C2×#3746C2211yescharacteristic
31C2×#3746C2211yescharacteristic
32C2×#3744C2211yescharacteristic
33#64105—21no—
34#64098—21no—
35#64094—21no—
36#64090—21no—
37#64088—21no—
38#64086—21no—
39#64084C2211yescharacteristic
40#64079C2211yescharacteristic
41C4×#634C2211yescharacteristic
42C4×#634C2211yescharacteristic
43C32×C4⋊C8C2211yescharacteristic
44C32×C22⋊C8C2211yescharacteristic
45C32×C22⋊C8C2211yescharacteristic
46C32×C4×C8C2211yescharacteristic
47#63648C2211yescharacteristic
48#63648C2211yescharacteristic
49#63648C2211yescharacteristic
50#63645C2211yescharacteristic
51#63645C2211yescharacteristic
52#63644C2211yescharacteristic
53#63643C2211yescharacteristic
54#63643C2211yescharacteristic
55#63643C2211yescharacteristic
56#63643C2211yescharacteristic
57#63643C2211yescharacteristic
58#63643C2211yescharacteristic
59#63643C2211yescharacteristic
60#5552—34no—
61#5541—34no—
62C3×C8×D4D314yescomplemented
63#5116—34no—
64#5114—34no—
65#5113—34no—
66C2×#816—34no—
67#4845—34no—
68#4829—34no—
69#4739—34no—
70#4736—34no—
71#4733—34no—
72#4723—34no—
73C4×Dic12—34no—
74#4697—34no—
75C2×C32×D4D411yescharacteristic
76C22×C32×C4C2311yescharacteristic
77C22×C32×C4C2311yescharacteristic
78C2×#638—21no—
79C2×#638—21no—
80C22×C3⋊Dic3—21no—
81C22×C3⋊Dic3—21no—
82#3828—22no—
83#3828—41no—
84C2×C4⋊(C3⋊D3)C2311yescharacteristic
85C2×C4×C3⋊D3—21no—
86C2×#634—22no—
87C2×#634—21no—
88C2×#634—41no—
89C2×#634C2311yescharacteristic
90C2×#634C2311yescharacteristic
91C2×#634C2311yescharacteristic
92C2×C32×C8—41no—
93C2×C32×C8—41no—
94C2×C32×C8C2311yescharacteristic
95C2×C32×C8C2311yescharacteristic
96C2×C32×C8C2311yescharacteristic
97C2×C32×C8C2311yescharacteristic
98C32×C4⋊C4D411yescharacteristic
99C32×C22⋊C4D411yescharacteristic
100C32×C22⋊C4D411yescharacteristic
101C32×C42C2311yescharacteristic
102#3757—21no—
103#3757—21no—
104#3757—21no—
105#3757—21no—
106#3752—21no—
107#3752—21no—
108#3752—21no—
109C4⋊(C3⋊Dic3)—21no—
110C4⋊(C3⋊Dic3)C2311yescharacteristic
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#3750—21no—
119#3750—21no—
120#3750—21no—
121C4×C3⋊Dic3—21no—
122C4×C3⋊Dic3—21no—
123C4×C3⋊Dic3—21no—
124#3746—22no—
125#3746—41no—
126#3744—41no—
127#3300—91noSylow
128C2×#235—34no—
129C22×Dic6—34no—
130C22×C3×C8C2×D314yes—
131C22×C3×C8C2×D314yes—
132C3×C4×D4C2×D314yes—
133#939—64no—
134#935—64no—
135#930—34no—
136#926—34no—
137C2×C4⋊Dic3—34no—
138#924—34no—
139#924—34no—
140#924—34no—
141C2×Dic12—34no—
142C2×Dic12—34no—
143C2×#204—34no—
144#896—64no—
145#889—64no—
146#885—64no—
147#67⋊C4—64no—
148#879—64no—
149#877—64no—
150#875—34no—
151#870—34no—
152C4×Dic6—34no—
153C4×Dic6—34no—
154C3×C4⋊C8C2×D314yes—
155C3×C22⋊C8C2×D314yes—
156C3×C22⋊C8C2×D314yes—
157C3×C4×C8C2×D314yes—
158#821—34no—
159#821—34no—
160#821—34no—
161#818—34no—
162#818—34no—
163#817—34no—
164#816—34no—
165#816—34no—
166#816—34no—
167#816—34no—
168#816—34no—
169#816—34no—
170#816—34no—
171C23×C32C2×D411yescharacteristic
172C23×C32C2×D411yescharacteristic
173C22×C3⋊D3—21no—
174C32×D4—22no—
175C2×C32×C4—21no—
176C2×C32×C4—21no—
177C2×C32×C4—21no—
178C2×C32×C4—21no—
179C2×C32×C4C2×D411yescharacteristic
180C2×C32×C4C2×D411yescharacteristic
181C2×C32×C4C2×D411yescharacteristic
182C2×C32×C4C2×D411yescharacteristic
183C2×C32×C4C2411yescharacteristic
184#638—42no—
185#638—42no—
186C2×C3⋊Dic3—21no—
187C2×C3⋊Dic3—21no—
188C2×C3⋊Dic3—21no—
189C2×C3⋊Dic3—21no—
190C2×C3⋊Dic3—21no—
191C2×C3⋊Dic3—21no—
192C2×C3⋊Dic3—21no—
193C2×C3⋊Dic3—42no—
194C2×C3⋊Dic3—42no—
195C4⋊(C3⋊D3)—21no—
196C4⋊(C3⋊D3)—21no—
197C4×C3⋊D3—42no—
198#634—21no—
199#634—21no—
200#634—21no—
201#634—21no—
202#634—21no—
203#634—42no—
204#634#4112yes—
205C32×C8—21no—
206C32×C8—21no—
207C32×C8—21no—
208C32×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#452—91no—
219#451—91no—
220C4×Q16—91no—
221C8×D4C3⋊D311yescharacteristic, complemented
222#416—91no—
223C2×#103—91no—
224C2×C3×D4D1214yes—
225C22×C3×C4C22×D314yes—
226C22×C3×C4C22×D314yes—
227C2×#67—64no—
228C2×#67—64no—
229C22×Dic3—64no—
230C22×Dic3—64no—
231#235—68no—
232#235—124no—
233C2×D12—34no—
234C2×C4×D3—64no—
235C2×Dic6—34no—
236C2×Dic6—34no—
237C2×Dic6—34no—
238C2×Dic6—68no—
239C2×Dic6—64no—
240C2×Dic6—124no—
241C2×C3×C8—44no—
242C2×C3×C8—44no—
243C2×C3×C8C22×D314yes—
244C2×C3×C8C22×D314yes—
245C2×C3×C8C22×D314yes—
246C2×C3×C8C22×D314yes—
247C3×C4⋊C4D1214yes—
248C3×C22⋊C4D1214yes—
249C3×C22⋊C4D1214yes—
250C3×C42C22×D314yes—
251#217—64no—
252#217—64no—
253#217—64no—
254#217—64no—
255(C2×D3)⋊C4—64no—
256(C2×D3)⋊C4—64no—
257(C2×D3)⋊C4—64no—
258C4⋊Dic3—34no—
259C4⋊Dic3—34no—
260C4⋊Dic3—34no—
261C4⋊Dic3—34no—
262C4⋊Dic3—64no—
263Dic3⋊C4—64no—
264Dic3⋊C4—64no—
265Dic3⋊C4—64no—
266Dic3⋊C4—64no—
267Dic3⋊C4—64no—
268Dic3⋊C4—64no—
269Dic3⋊C4—64no—
270C4×Dic3—64no—
271C4×Dic3—64no—
272C4×Dic3—64no—
273Dic12—68no—
274Dic12—124no—
275#204—124no—
276C22×C32—21no—
277C22×C32—21no—
278C22×C32—21no—
279C22×C32—21no—
280C22×C32—21no—
281C22×C32#13512yes—
282C22×C32C22×D411yescharacteristic
283C2×C3⋊D3—41no—
284C2×C3⋊D3—41no—
285C2×C3⋊D3—41no—
286C32×C4—21no—
287C32×C4—21no—
288C32×C4—21no—
289C32×C4—21no—
290C32×C4C2×#4111yescharacteristic
291C32×C4H(5,𝔽2)11yescharacteristic
292C3⋊Dic3—22no—
293C3⋊Dic3—41no—
294C3⋊Dic3—41no—
295C3⋊Dic3—41no—
296C3⋊Dic3—41no—
297C3⋊Dic3—41no—
298C3⋊Dic3—41no—
299C2×#41—91no—
300C22×Q8—91no—
301C2×Q16—91no—
302C2×Q16—91no—
303C2×SD16—91no—
304C22×C8C2×C3⋊D311yescharacteristic
305C22×C8C2×C3⋊D311yescharacteristic
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—91no—
315C22⋊Q8—181no—
316#121—91no—
317#121—181no—
318C4×Q8—91no—
319C4×Q8—91no—
320C4×D4—181no—
321C4×D4C2×C3⋊D311yescharacteristic
322#117—91no—
323#117—181no—
324C2×C4⋊C4—91no—
325#107—91no—
326#107—91no—
327#106—91no—
328C4⋊C8C2×C3⋊D311yescharacteristic
329#103—91no—
330#103—91no—
331#103—91no—
332#103—91no—
333#103—91no—
334#103—91no—
335#103—91no—
336#102—91no—
337#102—91no—
338#102—91no—
339C22⋊C8C2×C3⋊D311yescharacteristic
340C22⋊C8C2×C3⋊D311yescharacteristic
341C4×C8C2×C3⋊D311yescharacteristic
342C23×C3C2×D1214yes—
343C23×C3C2×D1214yes—
344C22×D3—64no—
345C3×D4—28no—
346C2×C3×C4—24no—
347C2×C3×C4—24no—
348C2×C3×C4—24no—
349C2×C3×C4—24no—
350C2×C3×C4C2×D1214yes—
351C2×C3×C4C2×D1214yes—
352C2×C3×C4C2×D1214yes—
353C2×C3×C4C2×D1214yes—
354C2×C3×C4C23×D314yes—
355#67—128no—
356#67—128no—
357C2×Dic3—64no—
358C2×Dic3—64no—
359C2×Dic3—64no—
360C2×Dic3—64no—
361C2×Dic3—64no—
362C2×Dic3—64no—
363C2×Dic3—64no—
364C2×Dic3—128no—
365C2×Dic3—128no—
366D12—64no—
367D12—64no—
368C4×D3—128no—
369Dic6—38no—
370Dic6—64no—
371Dic6—64no—
372Dic6—64no—
373Dic6—64no—
374Dic6—64no—
375Dic6—128no—
376C3×C8—24no—
377C3×C8—24no—
378C3×C8—24no—
379C3×C8—24no—
380C2×C32—22no—
381C2×C32—41no—
382C2×C32#54611yescharacteristic
383C2×C32C2×#13511yescharacteristic
384C2×C32#57811yescharacteristic
385C3⋊D3—81no—
386#41—182no—
387#41—361no—
388C2×Q8—91no—
389C2×Q8—91no—
390C2×Q8—91no—
391C2×Q8—182no—
392C2×Q8—181no—
393C2×Q8—361no—
394C2×D4—91no—
395C2×D4—181no—
396C2×D4—181no—
397C2×D4C4⋊(C3⋊D3)11yescharacteristic
398C22×C4—181no—
399C22×C4—181no—
400C22×C4—181no—
401C22×C4C22×C3⋊D311yescharacteristic
402C22×C4C22×C3⋊D311yescharacteristic
403Q16—182no—
404Q16—361no—
405SD16—361no—
406C2×C8—41no—
407C2×C8—41no—
408C2×C8C22×C3⋊D311yescharacteristic
409C2×C8C22×C3⋊D311yescharacteristic
410C2×C8C22×C3⋊D311yescharacteristic
411C2×C8C22×C3⋊D311yescharacteristic
412C4⋊C4—91no—
413C4⋊C4—91no—
414C4⋊C4—91no—
415C4⋊C4—91no—
416C4⋊C4—181no—
417C4⋊C4—181no—
418C4⋊C4—181no—
419C4⋊C4—181no—
420C4⋊C4—181no—
421C4⋊C4—181no—
422C4⋊C4—181no—
423C4⋊C4—181no—
424C4⋊C4C4⋊(C3⋊D3)11yescharacteristic
425C22⋊C4—181no—
426C22⋊C4—181no—
427C22⋊C4—181no—
428C22⋊C4—181no—
429C22⋊C4—181no—
430C22⋊C4—181no—
431C22⋊C4—181no—
432C22⋊C4C4⋊(C3⋊D3)11yescharacteristic
433C22⋊C4C4⋊(C3⋊D3)11yescharacteristic
434C42—181no—
435C42—181no—
436C42—181no—
437C42C22×C3⋊D311yescharacteristic
438C22×C3—24no—
439C22×C3—24no—
440C22×C3—24no—
441C22×C3—24no—
442C22×C3—24no—
443C22×C3#90418yes—
444C22×C3C22×D1214yes—
445C2×D3—124no—
446C2×D3—124no—
447C2×D3—124no—
448C3×C4—24no—
449C3×C4—24no—
450C3×C4—24no—
451C3×C4—24no—
452C3×C4#100414yes—
453C3×C4D3×#4114yes—
454Dic3—68no—
455Dic3—124no—
456Dic3—124no—
457Dic3—124no—
458Dic3—124no—
459Dic3—124no—
460Dic3—124no—
461C32#330011yescharacteristic, complemented, Sylow
462C23—181no—
463C23C2×C4⋊(C3⋊D3)11yescharacteristic
464C23C2×C4⋊(C3⋊D3)11yescharacteristic
465Q8—92no—
466Q8—181no—
467Q8—181no—
468Q8—181no—
469Q8—181no—
470Q8—181no—
471Q8—362no—
472D4—22no—
473D4—181no—
474D4—181no—
475D4—362no—
476D4—362no—
477C2×C4—21no—
478C2×C4—21no—
479C2×C4—21no—
480C2×C4—21no—
481C2×C4—181no—
482C2×C4—181no—
483C2×C4—181no—
484C2×C4—181no—
485C2×C4—181no—
486C2×C4—181no—
487C2×C4—181no—
488C2×C4—362no—
489C2×C4—362no—
490C2×C4—362no—
491C2×C4C2×C4⋊(C3⋊D3)11yescharacteristic
492C2×C4C2×C4⋊(C3⋊D3)11yescharacteristic
493C2×C4C2×C4⋊(C3⋊D3)11yescharacteristic
494C2×C4C2×C4⋊(C3⋊D3)11yescharacteristic
495C2×C4C23×C3⋊D311yescharacteristic
496C8—21no—
497C8—21no—
498C8—21no—
499C8—21no—
500C2×C3—28no—
501C2×C3—44no—
502C2×C3#555414yes—
503C2×C3C2×#90414yes—
504C2×C3#575314yes—
505D3—244no—
506C22—21no—
507C22—21no—
508C22—21no—
509C22—21no—
510C22—21no—
511C22—361no—
512C22—361no—
513C22—361no—
514C22#6411312yes—
515C22C22×C4⋊(C3⋊D3)11yescharacteristic
516C4—21no—
517C4—21no—
518C4—21no—
519C4—21no—
520C4—182no—
521C4—361no—
522C4—361no—
523C4—361no—
524C4—361no—
525C4—361no—
526C4—361no—
527C4#6436111yescharacteristic
528C4#41×C3⋊D311yescharacteristic
529C3#7944914yescomplemented
530C2—22no—
531C2—41no—
532C2—721no—
533C2#1059602511yescharacteristic
534C2C2×#6411311yescharacteristic
535C2#1059622411yescharacteristic
subgroupG/H
centerC22C22×C4⋊(C3⋊D3)
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C23×C3⋊D3
FittingC32×C8×D4C2
socleC22×C32C22×D4
prime radical#10596023C2
hypercenterC8×D4C3⋊D3
hypocenterC32#3300
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C4×D4 ◁ C8×D4

Complements

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

NH ≅ G/Ntype
2. #10596012C2semidirect
3. C32×C8×D4C2semidirect
4. #10592815C2semidirect
5. #10592813C2semidirect
6. #10592812C2semidirect
7. C2×#63643C2semidirect
8. #10592544C2semidirect
9. #10592528C2semidirect
10. #10592438C2semidirect
11. #10592435C2semidirect
12. #10592432C2semidirect
13. #10592422C2semidirect
14. C4×#3746C2semidirect
15. #10592396C2semidirect
62. C3×C8×D4D3semidirect
221. C8×D4C3⋊D3semidirect
461. C32#3300semidirect
529. C3#79449semidirect

Maximal subgroups

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

subgroupindex
#105960232
#105960122
C32×C8×D42
#105928152
#105928132
#105928122
C2×#636432
#105925442
#105925282
#105924382
#105924352
#105924322
#105924222
C4×#37462
#105923962
#794493