Finite Group Databasebeta

← #11878841

Subgroups — #11878841

Order 1152.

1035 conjugacy classes of subgroups.

The subgroup lattice has 542 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10594008C211yesmaximal, characteristic
2#10593866C211yesmaximal, characteristic, complemented
3#10592384C211yesmaximal, characteristic, complemented
4C3×#4694C211yesmaximal, characteristic, complemented
5C3×#4693C211yesmaximal, characteristic, complemented
6#10590943C214yesmaximal, complemented
7#10590876C214yesmaximal, complemented
8#10590375C211yesmaximal, characteristic, complemented
9#10590277C211yesmaximal, characteristic, complemented
10#81766—31nomaximal
11#81568—31nomaximal
12C2×#3802—21no—
13C2×#3802—21no—
14C2×#3802C2212yes—
15C42×C3⋊D3C2211yescharacteristic
16C2×C3×#204C2214yescomplemented
17C3×#874C2211yescharacteristic
18C3×#874C2211yescharacteristic
19C3×#869C2211yescharacteristic, complemented
20C3×#869C2211yescharacteristic, complemented
21#63914—21no—
22#63914—21no—
23#63914C2212yes—
24#63872—21no—
25#63871—21no—
26#63871C2212yes—
27#63849—21no—
28#63843—21no—
29#63843C2212yescomplemented
30C2×#3715C2214yescomplemented
31C32×C4×C8C2211yescharacteristic, complemented
32#63647C2212yes—
33#63641C2212yescomplemented
34C4×C3⋊(C3⋊C8)C2211yescharacteristic, complemented
35C3×#821C2214yescomplemented
36#63562C2214yescomplemented
37#5728—31no—
38#5728—31no—
39D3×#127—31no—
40D3×#127—31no—
41C3×#492—31no—
42C3×#486—31no—
43#5169—34no—
44#5163—34no—
45#5088—31no—
46#5085—31no—
47#5076—31no—
48#5070—31no—
49#4776—34no—
50#4762—34no—
51#4694D311yescharacteristic, complemented
52#4693D311yescharacteristic, complemented
53#4685—31no—
54#4685—31no—
55#4685—61no—
56C22×D32—22no—
57C2×C4×C3⋊D3D411yescharacteristic
58C2×C4×C3⋊D3D411yescharacteristic
59C2×C4×C3⋊D3C2311yescharacteristic
60C2×C3×D12—21no—
61C2×C3×D12—21no—
62C2×C3×D12—21no—
63C2×C3×D12—21no—
64C2×C3×D12C2312yes—
65C2×C3×D12C2312yes—
66C2×C3×Dic6—21no—
67C2×C3×Dic6C2312yes—
68C2×#625—22no—
69C2×#625—22no—
70C2×#625—22no—
71#3802—44no—
72#3802—44no—
73#3802—44no—
74C2×C32×C8C2312yes—
75C32×C42C2311yescharacteristic
76C4×C3⋊Dic3D411yescharacteristic
77C4×C3⋊Dic3D411yescharacteristic
78C4×C3⋊Dic3C2311yescharacteristic
79C2×C3⋊(C3⋊C8)C2312yes—
80C3×C4⋊Dic3—21no—
81C3×C4⋊Dic3—21no—
82C3×C4⋊Dic3—21no—
83C3×C4⋊Dic3C2312yes—
84C3×#204—44no—
85Dic3⋊Dic3—22no—
86Dic3⋊Dic3—22no—
87#3722—22no—
88Dic32—22no—
89#3715—44no—
90#3208—91noSylow
91C2×D3×D4—32no—
92C2×D3×D4—32no—
93C2×D3×D4—61no—
94C2×D3×D4—61no—
95C2×D3×D4—61no—
96C2×D3×D4—61no—
97C2×C3×SD16—34no—
98C3×C4⋊Q8—31no—
99C3×C4⋊Q8—31no—
100C3×#127—31no—
101C3×#127—31no—
102#946—32no—
103#946—61no—
104Q8×Dic3—32no—
105Q8×Dic3—61no—
106C2×#215—34no—
107#940—32no—
108#940—32no—
109#940—61no—
110#940—61no—
111#940—61no—
112#940—61no—
113C2×#214—34no—
114C2×#204C2×D314yescomplemented
115#897—32no—
116#897—61no—
117#892—61no—
118#892—61no—
119#890—61no—
120#890—61no—
121#887—32no—
122#887—61no—
123#874C2×D311yescharacteristic
124#874C2×D311yescharacteristic
125C42×D3—31no—
126C42×D3—31no—
127C42×D3—61no—
128#869C2×D311yescharacteristic, complemented
129#869C2×D311yescharacteristic, complemented
130C3×#102—34no—
131C3×C4×C8—21no—
132C3×C4×C8C2×D311yescharacteristic, complemented
133C3×C4×C8C2×D311yescharacteristic, complemented
134#832—34no—
135#821C2×D314yescomplemented
136(C2×D3)⋊C8—32no—
137(C2×D3)⋊C8—32no—
138(C2×D3)⋊C8—62no—
139Dic3⋊C8—32no—
140Dic3⋊C8—32no—
141Dic3⋊C8—62no—
142#809—34no—
143C4×C3⋊C8—31no—
144C4×C3⋊C8—31no—
145C4×C3⋊C8—61no—
146C22×C3⋊D3C2×D411yescharacteristic
147C22×C3×D3—22no—
148C22×C3×D3—22no—
149C2×D32—44no—
150C2×D32—44no—
151C2×D32—44no—
152C2×C32×C4C2×D411yescharacteristic
153C2×C32×C4C2×D411yescharacteristic
154C2×C32×C4C2411yescharacteristic
155C2×C3⋊Dic3C2×D411yescharacteristic
156C2×C3⋊Dic3C2×D411yescharacteristic
157C2×C3⋊Dic3C2×D411yescharacteristic
158C4×C3⋊D3—22no—
159C4×C3⋊D3—22no—
160C4×C3⋊D3SD1614yescomplemented
161C2×C3×Dic3—22no—
162C2×C3×Dic3—22no—
163C3×D12—24no—
164C3×D12—24no—
165C3×D12—42no—
166C3×D12—42no—
167C3×D12—42no—
168C3×D12—42no—
169C3×Dic6—24no—
170C3×Dic6—42no—
171#625—44no—
172#625—44no—
173#625—44no—
174C32×C8—22no—
175C3⋊(C3⋊C8)—22no—
176#533—91no—
177C2×#127—91no—
178#492—31no—
179#492—91no—
180#486—31no—
181#486—91no—
182#460—94no—
183#450—94no—
184#431—91no—
185C23×D3—62no—
186C23×D3—62no—
187C2×C3×Q8—32no—
188C2×C3×Q8—61no—
189C2×C3×D4—32no—
190C2×C3×D4—32no—
191C2×C3×D4—61no—
192C2×C3×D4—61no—
193C2×C3×D4—61no—
194C2×C3×D4—61no—
195C2×#67—62no—
196C2×#67—62no—
197C2×#67—62no—
198C2×#67—62no—
199C2×#67—62no—
200C2×#67—62no—
201D3×D4—124no—
202D3×D4—124no—
203D3×D4—124no—
204D3×D4—124no—
205D3×D4—124no—
206D3×D4—124no—
207C2×D12—21no—
208C2×D12—21no—
209C2×D12—21no—
210C2×D12—21no—
211C2×D12C22×D312yes—
212C2×D12C22×D312yes—
213C2×C4×D3—31no—
214C2×C4×D3—31no—
215C2×C4×D3—31no—
216C2×C4×D3—31no—
217C2×C4×D3—31no—
218C2×C4×D3—31no—
219C2×C4×D3—61no—
220C2×C4×D3—61no—
221C2×C4×D3—61no—
222C2×Dic6—21no—
223C2×Dic6C22×D312yes—
224C3×SD16—124no—
225C2×C3×C8—22no—
226C2×C3×C8C22×D312yes—
227C2×C3×C8C22×D312yes—
228C3×C4⋊C4—32no—
229C3×C4⋊C4—61no—
230C3×C4⋊C4—61no—
231C3×C4⋊C4—61no—
232C3×C42—21no—
233C3×C42C22×D311yescharacteristic
234C3×C42C22×D311yescharacteristic
235#215—124no—
236#214—124no—
237(C2×D3)⋊C4—62no—
238(C2×D3)⋊C4—62no—
239C4⋊Dic3—21no—
240C4⋊Dic3—21no—
241C4⋊Dic3—21no—
242C4⋊Dic3—62no—
243C4⋊Dic3—62no—
244C4⋊Dic3C22×D312yes—
245Dic3⋊C4—62no—
246Dic3⋊C4—62no—
247C4×Dic3—31no—
248C4×Dic3—31no—
249C4×Dic3—31no—
250C4×Dic3—31no—
251C4×Dic3—31no—
252C4×Dic3—31no—
253C4×Dic3—61no—
254C4×Dic3—61no—
255C4×Dic3—61no—
256C4×Dic3—62no—
257C4×Dic3—62no—
258C2×C3⋊C8—32no—
259C2×C3⋊C8—32no—
260C2×C3⋊C8—62no—
261#204—44no—
262C22×C32C22×D411yescharacteristic
263C2×C3⋊D3—21no—
264C2×C3⋊D3—21no—
265C2×C3⋊D3C2×SD1612yes—
266C2×C3×D3—42no—
267C2×C3×D3—42no—
268C2×C3×D3—42no—
269C2×C3×D3—42no—
270C2×C3×D3—42no—
271C2×C3×D3—42no—
272D32—88no—
273C32×C4C2×SD1612yes—
274C32×C4AGL(1,ℤ/8)12yes—
275C32×C4H(5,𝔽2)12yes—
276C3⋊Dic3—21no—
277C3⋊Dic3—21no—
278C3⋊Dic3C2×SD1612yes—
279C3×Dic3—42no—
280C3×Dic3—42no—
281C22×D4—92no—
282C22×D4—181no—
283C22×D4—181no—
284C2×SD16—34no—
285C2×SD16—94no—
286C4⋊Q8—31no—
287C4⋊Q8—31no—
288#127—31no—
289#127—31no—
290#127—92no—
291#127—181no—
292#127—181no—
293#125—181no—
294C22⋊Q8—92no—
295C22⋊Q8—181no—
296C4×Q8—92no—
297C4×Q8—181no—
298#117—181no—
299C2×C42—91no—
300C4⋊C8—92no—
301#102—34no—
302#102—94no—
303C22⋊C8—92no—
304C4×C8—91no—
305C4×C8D3211yescharacteristic, complemented
306C23×C3—62no—
307C23×C3—62no—
308C22×D3—22no—
309C22×D3—22no—
310C22×D3—31no—
311C22×D3—31no—
312C22×D3—61no—
313C22×D3—124no—
314C22×D3—124no—
315C22×D3—124no—
316C22×D3—124no—
317C22×D3—124no—
318C22×D3—124no—
319C3×Q8—64no—
320C3×Q8—122no—
321C3×D4—64no—
322C3×D4—64no—
323C3×D4—122no—
324C3×D4—122no—
325C3×D4—122no—
326C3×D4—122no—
327C2×C3×C4—21no—
328C2×C3×C4—21no—
329C2×C3×C4—21no—
330C2×C3×C4—62no—
331C2×C3×C4—62no—
332C2×C3×C4D3×D411yescharacteristic
333C2×C3×C4D3×D411yescharacteristic
334C2×C3×C4D3×D411yescharacteristic
335C2×C3×C4D3×D411yescharacteristic
336C2×C3×C4C23×D311yescharacteristic
337C2×C3×C4C23×D311yescharacteristic
338#67—124no—
339#67—124no—
340#67—124no—
341#67—124no—
342#67—124no—
343#67—124no—
344C2×Dic3—22no—
345C2×Dic3—22no—
346C2×Dic3—31no—
347C2×Dic3—31no—
348C2×Dic3—31no—
349C2×Dic3—31no—
350C2×Dic3—31no—
351C2×Dic3—31no—
352C2×Dic3—61no—
353C2×Dic3—61no—
354C2×Dic3—61no—
355D12—24no—
356D12—24no—
357D12—42no—
358D12—42no—
359D12—42no—
360D12—42no—
361C4×D3—34no—
362C4×D3—34no—
363C4×D3—64no—
364C4×D3—62no—
365C4×D3—62no—
366C4×D3—62no—
367C4×D3—62no—
368C4×D3—122no—
369C4×D3—122no—
370Dic6—24no—
371Dic6—42no—
372C3×C8—22no—
373C3×C8—22no—
374C3×C8—42no—
375C3⋊C8—62no—
376C3⋊C8—62no—
377C3⋊C8—122no—
378C2×C32#53511yescharacteristic
379C2×C32C22×SD1611yescharacteristic
380C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
381C3⋊D3—22no—
382C3×D3—82no—
383C3×D3—82no—
384C24—182no—
385C2×Q8—32no—
386C2×Q8—61no—
387C2×D4—32no—
388C2×D4—32no—
389C2×D4—61no—
390C2×D4—61no—
391C2×D4—61no—
392C2×D4—61no—
393C2×D4—182no—
394C2×D4—182no—
395C2×D4—182no—
396C2×D4—364no—
397C2×D4—364no—
398C2×D4—364no—
399C22×C4—91no—
400C22×C4—91no—
401C22×C4—91no—
402SD16—124no—
403SD16—364no—
404C2×C8—92no—
405C2×C8C2×D3212yes—
406C4⋊C4—32no—
407C4⋊C4—61no—
408C4⋊C4—61no—
409C4⋊C4—61no—
410C4⋊C4—182no—
411C4⋊C4—182no—
412C22⋊C4—182no—
413C42—91no—
414C42—91no—
415C42—91no—
416C42—182no—
417C42C2×D3211yescharacteristic
418C22×C3—21no—
419C22×C3—122no—
420C22×C3—122no—
421C22×C3—122no—
422C22×C3—122no—
423C22×C3—122no—
424C22×C3—122no—
425C22×C3C2×D3×D411yescharacteristic
426C22×C3C2×D3×D411yescharacteristic
427C2×D3—32no—
428C2×D3—32no—
429C2×D3—42no—
430C2×D3—42no—
431C2×D3—42no—
432C2×D3—42no—
433C2×D3—42no—
434C2×D3—42no—
435C2×D3—62no—
436C2×D3—61no—
437C2×D3—61no—
438C2×D3—61no—
439C2×D3—61no—
440C2×D3—121no—
441C2×D3—121no—
442C2×D3—248no—
443C2×D3—248no—
444C3×C4—22no—
445C3×C4—22no—
446C3×C4—22no—
447C3×C4—122no—
448C3×C4—122no—
449C3×C4#91112yes—
450C3×C4D3×SD1612yes—
451C3×C4D3×SD1612yes—
452C3×C4#91412yes—
453C3×C4#100412yes—
454C3×C4#100912yes—
455Dic3—32no—
456Dic3—32no—
457Dic3—42no—
458Dic3—42no—
459Dic3—62no—
460Dic3—61no—
461Dic3—61no—
462Dic3—61no—
463Dic3—61no—
464Dic3—121no—
465Dic3—121no—
466C32#320811yescharacteristic, complemented, Sylow
467C23—62no—
468C23—62no—
469C23—91no—
470C23—364no—
471C23—364no—
472C23—364no—
473Q8—64no—
474Q8—122no—
475D4—64no—
476D4—64no—
477D4—122no—
478D4—122no—
479D4—122no—
480D4—122no—
481D4—364no—
482D4—364no—
483D4—364no—
484C2×C4—62no—
485C2×C4—62no—
486C2×C4—91no—
487C2×C4—94no—
488C2×C4—91no—
489C2×C4—91no—
490C2×C4—182no—
491C2×C4—182no—
492C2×C4#380211yescharacteristic
493C2×C4#380211yescharacteristic
494C2×C4C22×D3211yescharacteristic
495C8—22no—
496C8—182no—
497C2×C3—21no—
498C2×C3—21no—
499C2×C3—21no—
500C2×C3—242no—
501C2×C3—242no—
502C2×C3#567411yescharacteristic
503C2×C3#571511yescharacteristic
504C2×C3C2×#91111yescharacteristic
505C2×C3C2×D3×SD1611yescharacteristic
506C2×C3C2×D3×SD1611yescharacteristic
507C2×C3C2×#91411yescharacteristic
508D3—62no—
509D3—62no—
510D3—82no—
511D3—82no—
512D3—122no—
513C22—92no—
514C22—122no—
515C22—122no—
516C22—122no—
517C22—122no—
518C22—122no—
519C22—122no—
520C22—181no—
521C22—181no—
522C22—728no—
523C22C2×#380211yescharacteristic
524C4—92no—
525C4—122no—
526C4—122no—
527C4—181no—
528C4—181no—
529C4#6379612yes—
530C4#6379812yes—
531C4#6430712yes—
532C3—21no—
533C3#8156811yescharacteristic, complemented
534C3#8176611yescharacteristic, complemented
535C2—182no—
536C2—242no—
537C2—242no—
538C2#1059401011yescharacteristic
539C2C2×#6379611yescharacteristic
540C2C2×#6379811yescharacteristic
subgroupG/H
centerC22C2×#3802
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4×C8C22
socleC22×C32C22×D4
prime radical#10594008C2
hypercenterC4×C8D32
hypocenterC32#3208
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8

Complements

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

NH ≅ G/Ntype
2. #10593866C2semidirect
3. #10592384C2semidirect
4. C3×#4694C2semidirect
5. C3×#4693C2semidirect
6. #10590943C2semidirect
7. #10590876C2semidirect
8. #10590375C2semidirect
9. #10590277C2semidirect
16. C2×C3×#204C22semidirect
19. C3×#869C22semidirect
20. C3×#869C22semidirect
29. #63843C22semidirect
30. C2×#3715C22semidirect
31. C32×C4×C8C22semidirect
33. #63641C22semidirect
34. C4×C3⋊(C3⋊C8)C22semidirect
35. C3×#821C22semidirect
36. #63562C22semidirect
51. #4694D3semidirect
52. #4693D3semidirect
114. C2×#204C2×D3semidirect
128. #869C2×D3semidirect
129. #869C2×D3semidirect
132. C3×C4×C8C2×D3semidirect
133. C3×C4×C8C2×D3semidirect
135. #821C2×D3semidirect
160. C4×C3⋊D3SD16semidirect
305. C4×C8D32semidirect
466. C32#3208semidirect
533. C3#81568semidirect
534. C3#81766semidirect

Maximal subgroups

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

subgroupindex
#105940082
#105938662
#105923842
C3×#46942
C3×#46932
#105909432
#105908762
#105903752
#105902772
#817663
#815683