Finite Group Databasebeta

← #11878843

Subgroups — #11878843

Order 1152.

1035 conjugacy classes of subgroups.

The subgroup lattice has 536 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5728C211yesmaximal, characteristic, complemented
2D3×#874C211yesmaximal, characteristic
3#10592787C211yesmaximal, characteristic, complemented
4C3×#5088C211yesmaximal, characteristic, complemented
5#10590596C214yesmaximal, complemented
6#10590549C214yesmaximal, complemented
7#10590375C211yesmaximal, characteristic, complemented
8#10590373C211yesmaximal, characteristic, complemented
9#10590261C211yesmaximal, characteristic, complemented
10#83355—31nomaximal
11#81568—31nomaximal
12C2×D3×D12—21no—
13C2×D3×D12—21no—
14C2×D3×D12C2212yes—
15C32×C4⋊Q8C2211yescharacteristic, complemented
16#64083C2211yescharacteristic
17C3×#946—21no—
18C3×Q8×Dic3—21no—
19C3×#897C2212yes—
20C3×#892—21no—
21C3×#890—21no—
22C3×#887C2212yescomplemented
23C3×#874C2211yescharacteristic
24C3×C42×D3C2211yescharacteristic
25C3×#869C2211yescharacteristic, complemented
26#63911—21no—
27#63911—21no—
28#63911C2212yes—
29C2×#3717C2214yescomplemented
30C2×#3715C2214yescomplemented
31#63636C2214yescomplemented
32C4×C3⋊(C3⋊C8)C2211yescharacteristic, complemented
33C3×#809C2214yescomplemented
34C3×C4×C3⋊C8C2211yescharacteristic, complemented
35Dic3⋊(C3⋊C8)C2212yescomplemented
36(C2×D3)⋊(C3⋊C8)C2212yes—
37C3×#533—31no—
38#5728D311yescharacteristic, complemented
39D3×#127—31no—
40C2×#874—31no—
41C3×#486—31no—
42#5088—31no—
43#5088—31no—
44#5088—61no—
45#5088D311yescharacteristic, complemented
46#5085—31no—
47#5085—31no—
48#5076—31no—
49#5046—34no—
50#5027—34no—
51#4925—31no—
52#4776—34no—
53#4762—34no—
54#4693—31no—
55#4685—31no—
56C22×D32—22no—
57C2×C32×Q8—21no—
58C2×C4⋊(C3⋊D3)—21no—
59C2×C4⋊(C3⋊D3)—21no—
60C2×C4⋊(C3⋊D3)C2312yes—
61C2×C3×D12—21no—
62C2×C3×D12—21no—
63C2×C3×D12C2312yes—
64C2×C3×C4×D3D411yescharacteristic
65C2×C3×C4×D3D411yescharacteristic
66C2×C3×C4×D3C2311yescharacteristic
67C2×C3×Dic6C2312yes—
68C2×#626—22no—
69C2×#626—22no—
70C2×#626—22no—
71D3×D12—44no—
72D3×D12—44no—
73D3×D12—44no—
74C32×C4⋊C4—21no—
75C32×C4⋊C4C2312yes—
76C32×C42C2311yescharacteristic
77C2×C3⋊(C3⋊C8)C2312yes—
78C3×(C2×D3)⋊C4—22no—
79C3×C4⋊Dic3—21no—
80C3×C4⋊Dic3—21no—
81C3×C4⋊Dic3—22no—
82C3×Dic3⋊C4—22no—
83C3×C4×Dic3—22no—
84C3×C4×Dic3D411yescharacteristic
85C3×C4×Dic3D411yescharacteristic
86C3×C4×Dic3C2311yescharacteristic
87C2×C3×C3⋊C8C2312yes—
88#3717—44no—
89#3715—44no—
90#3208—91noSylow
91C2×D3×D4—32no—
92C2×D3×D4—61no—
93C2×D3×D4—61no—
94C22×D12—32no—
95C22×D12—61no—
96C22×D12—61no—
97C3×C4⋊Q8—21no—
98C3×C4⋊Q8—31no—
99C3×C4⋊Q8C2×D311yescharacteristic, complemented
100C3×C4⋊Q8C2×D311yescharacteristic, complemented
101C3×#127—31no—
102C3×#125—61no—
103C3×C22⋊Q8—32no—
104C3×C22⋊Q8—61no—
105C3×C4×Q8—32no—
106C3×C4×Q8—61no—
107C3×#117—61no—
108C2×C3×C42—31no—
109#946—21no—
110Q8×Dic3—21no—
111C2×#215—34no—
112C2×#215—34no—
113#940—32no—
114#940—61no—
115#940—61no—
116C2×#214—34no—
117C2×#204—34no—
118#897C2×D312yes—
119#892—21no—
120#890—21no—
121#887C2×D312yescomplemented
122#874—32no—
123#874—31no—
124#874—31no—
125#874—61no—
126#874—61no—
127#874—61no—
128#874C2×D311yescharacteristic
129C42×D3C2×D311yescharacteristic
130#869C2×D311yescharacteristic, complemented
131C3×#102—34no—
132C3×C4×C8—31no—
133#830—32no—
134(C2×D3)⋊C8—32no—
135Dic3⋊C8—32no—
136#809—34no—
137#809—34no—
138#809—64no—
139#809C2×D314yescomplemented
140C4⋊(C3⋊C8)—32no—
141C4×C3⋊C8—31no—
142C4×C3⋊C8—31no—
143C4×C3⋊C8—61no—
144C4×C3⋊C8C2×D311yescharacteristic, complemented
145C22×C3⋊D3—22no—
146C22×C3×D3—22no—
147C22×C3×D3C2×D411yescharacteristic
148C2×D32—44no—
149C2×D32—44no—
150C2×D32—44no—
151C32×Q8—42no—
152C2×C32×C4—22no—
153C2×C32×C4C2×D411yescharacteristic
154C2×C32×C4C2×D411yescharacteristic
155C2×C32×C4C2411yescharacteristic
156C4⋊(C3⋊D3)—24no—
157C4⋊(C3⋊D3)—42no—
158C4⋊(C3⋊D3)—42no—
159C2×C3×Dic3—22no—
160C2×C3×Dic3C2×D411yescharacteristic
161C2×C3×Dic3C2×D411yescharacteristic
162C2×C3×Dic3C2×D411yescharacteristic
163C3×D12—24no—
164C3×D12—42no—
165C3×D12—42no—
166C3×C4×D3—22no—
167C3×C4×D3—22no—
168C3×C4×D3SD1614yescomplemented
169C3×Dic6—24no—
170#626—44no—
171#626—44no—
172#626—44no—
173C3⋊(C3⋊C8)—22no—
174C3×C3⋊C8—22no—
175#533—31no—
176C2×#127—91no—
177#492—91no—
178#492—91no—
179#486—31no—
180#486—91no—
181#460—94no—
182#450—94no—
183#431—91no—
184C23×D3—62no—
185C23×D3—62no—
186C2×C3×Q8—21no—
187C2×C3×Q8—21no—
188C2×C3×Q8—32no—
189C2×C3×Q8—41no—
190C2×C3×D4—32no—
191C2×C3×D4—61no—
192C2×C3×D4—61no—
193C22×C3×C4—31no—
194C22×C3×C4—31no—
195C22×C3×C4—31no—
196C2×#67—62no—
197C2×#67—62no—
198C2×#67—62no—
199D3×D4—124no—
200D3×D4—124no—
201D3×D4—124no—
202C2×D12—21no—
203C2×D12—21no—
204C2×D12—32no—
205C2×D12—32no—
206C2×D12—62no—
207C2×D12—62no—
208C2×D12—62no—
209C2×D12—62no—
210C2×D12—61no—
211C2×D12—61no—
212C2×D12—61no—
213C2×D12—61no—
214C2×D12—121no—
215C2×D12—121no—
216C2×D12—124no—
217C2×D12—124no—
218C2×D12—124no—
219C2×D12C22×D312yes—
220C2×C4×D3#6711yescharacteristic
221C2×C4×D3#6711yescharacteristic
222C2×C4×D3C22×D311yescharacteristic
223C2×Dic6C22×D312yes—
224C2×C3×C8—32no—
225C3×C4⋊C4—21no—
226C3×C4⋊C4—21no—
227C3×C4⋊C4—22no—
228C3×C4⋊C4—41no—
229C3×C4⋊C4—62no—
230C3×C4⋊C4—62no—
231C3×C4⋊C4—61no—
232C3×C4⋊C4—61no—
233C3×C4⋊C4C22×D312yes—
234C3×C4⋊C4C22×D312yes—
235C3×C22⋊C4—62no—
236C3×C42—21no—
237C3×C42—31no—
238C3×C42—31no—
239C3×C42—31no—
240C3×C42—62no—
241C3×C42C22×D311yescharacteristic
242C3×C42C22×D311yescharacteristic
243#215—124no—
244#215—124no—
245#214—124no—
246(C2×D3)⋊C4—22no—
247C4⋊Dic3—21no—
248C4⋊Dic3—21no—
249C4⋊Dic3—22no—
250Dic3⋊C4—22no—
251C4×Dic3—22no—
252C4×Dic3#6711yescharacteristic
253C4×Dic3#6711yescharacteristic
254C4×Dic3C22×D311yescharacteristic
255C2×C3⋊C8—32no—
256C2×C3⋊C8—32no—
257C2×C3⋊C8—62no—
258C2×C3⋊C8C22×D312yes—
259#204—124no—
260C22×C32C22×D411yescharacteristic
261C2×C3⋊D3—42no—
262C2×C3⋊D3—42no—
263C2×C3⋊D3—42no—
264C2×C3×D3—21no—
265C2×C3×D3—21no—
266C2×C3×D3—42no—
267C2×C3×D3—42no—
268C2×C3×D3—42no—
269C2×C3×D3C2×SD1612yes—
270D32—88no—
271C32×C4—42no—
272C32×C4C2×SD1612yes—
273C32×C4AGL(1,ℤ/8)12yes—
274C32×C4H(5,𝔽2)12yes—
275C3×Dic3—21no—
276C3×Dic3—21no—
277C3×Dic3—42no—
278C3×Dic3C2×SD1612yes—
279C22×D4—92no—
280C22×D4—181no—
281C22×D4—181no—
282C2×SD16—94no—
283C2×SD16—94no—
284C4⋊Q8—31no—
285C4⋊Q8D3211yescharacteristic, complemented
286#127—31no—
287#127—92no—
288#127—91no—
289#127—181no—
290#127—181no—
291#125—61no—
292C22⋊Q8—32no—
293C22⋊Q8—61no—
294C4×Q8—32no—
295C4×Q8—61no—
296#117—61no—
297C2×C42—31no—
298C4⋊C8—92no—
299#102—34no—
300#102—94no—
301C22⋊C8—92no—
302C4×C8—31no—
303C4×C8—91no—
304C23×C3—31no—
305C23×C3—62no—
306C22×D3—22no—
307C22×D3—62no—
308C22×D3—62no—
309C22×D3—122no—
310C22×D3—124no—
311C22×D3—124no—
312C22×D3—124no—
313C22×D3—124no—
314C22×D3—124no—
315C22×D3—124no—
316C22×D3C2×#6711yescharacteristic
317C3×Q8—42no—
318C3×Q8—42no—
319C3×Q8—64no—
320C3×Q8—82no—
321C3×D4—64no—
322C3×D4—122no—
323C3×D4—122no—
324C2×C3×C4—22no—
325C2×C3×C4—22no—
326C2×C3×C4—21no—
327C2×C3×C4—21no—
328C2×C3×C4—21no—
329C2×C3×C4—31no—
330C2×C3×C4—34no—
331C2×C3×C4—31no—
332C2×C3×C4—31no—
333C2×C3×C4—42no—
334C2×C3×C4—62no—
335C2×C3×C4—62no—
336C2×C3×C4—62no—
337C2×C3×C4D3×D411yescharacteristic
338C2×C3×C4D3×D411yescharacteristic
339C2×C3×C4C2×#6711yescharacteristic
340C2×C3×C4C2×#6711yescharacteristic
341C2×C3×C4C23×D311yescharacteristic
342C2×C3×C4C23×D311yescharacteristic
343#67—124no—
344#67—124no—
345#67—124no—
346C2×Dic3—22no—
347C2×Dic3C2×#6711yescharacteristic
348C2×Dic3C2×#6711yescharacteristic
349C2×Dic3C2×#6711yescharacteristic
350D12—24no—
351D12—42no—
352D12—42no—
353D12—64no—
354D12—64no—
355D12—124no—
356D12—124no—
357D12—124no—
358D12—124no—
359D12—122no—
360D12—122no—
361D12—122no—
362D12—122no—
363D12—242no—
364D12—242no—
365C4×D3—22no—
366C4×D3—22no—
367C4×D3#21514yescomplemented
368Dic6—24no—
369C3×C8—62no—
370C3⋊C8—22no—
371C3⋊C8—62no—
372C3⋊C8—62no—
373C3⋊C8—122no—
374C2×C32#53511yescharacteristic
375C2×C32C22×SD1611yescharacteristic
376C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
377C3⋊D3—82no—
378C3×D3—22no—
379C3×D3—82no—
380C24—182no—
381C2×Q8—21no—
382C2×Q8—32no—
383C2×D4—32no—
384C2×D4—61no—
385C2×D4—61no—
386C2×D4—92no—
387C2×D4—182no—
388C2×D4—182no—
389C2×D4—182no—
390C2×D4—181no—
391C2×D4—181no—
392C2×D4—364no—
393C2×D4—364no—
394C2×D4—364no—
395C22×C4—31no—
396C22×C4—31no—
397C22×C4—31no—
398SD16—364no—
399SD16—364no—
400C2×C8—32no—
401C2×C8—92no—
402C4⋊C4—21no—
403C4⋊C4—62no—
404C4⋊C4—62no—
405C4⋊C4—61no—
406C4⋊C4—61no—
407C4⋊C4C2×D3212yes—
408C22⋊C4—62no—
409C42—31no—
410C42—31no—
411C42—31no—
412C42—62no—
413C42C2×D3211yescharacteristic
414C22×C3—21no—
415C22×C3—32no—
416C22×C3—61no—
417C22×C3—61no—
418C22×C3—122no—
419C22×C3—122no—
420C22×C3—122no—
421C22×C3C2×D3×D411yescharacteristic
422C22×C3C22×#6711yescharacteristic
423C2×D3—21no—
424C2×D3—21no—
425C2×D3—42no—
426C2×D3—42no—
427C2×D3—42no—
428C2×D3—122no—
429C2×D3—122no—
430C2×D3—122no—
431C2×D3—122no—
432C2×D3—122no—
433C2×D3—122no—
434C2×D3—242no—
435C2×D3—242no—
436C2×D3—242no—
437C2×D3—248no—
438C2×D3—248no—
439C2×D3C2×#21512yes—
440C3×C4—22no—
441C3×C4—22no—
442C3×C4—22no—
443C3×C4—32no—
444C3×C4—42no—
445C3×C4—42no—
446C3×C4—61no—
447C3×C4—61no—
448C3×C4—82no—
449C3×C4—122no—
450C3×C4#91112yes—
451C3×C4D3×SD1612yes—
452C3×C4C2×#21512yes—
453C3×C4#94912yes—
454C3×C4#100912yes—
455C3×C4#100912yes—
456Dic3—21no—
457Dic3—21no—
458Dic3—42no—
459Dic3C2×#21512yes—
460C32#320811yescharacteristic, complemented, Sylow
461C23—31no—
462C23—62no—
463C23—182no—
464C23—364no—
465C23—364no—
466C23—364no—
467Q8—42no—
468Q8—64no—
469D4—64no—
470D4—122no—
471D4—122no—
472D4—184no—
473D4—364no—
474D4—364no—
475D4—364no—
476D4—362no—
477D4—362no—
478C2×C4—22no—
479C2×C4—31no—
480C2×C4—34no—
481C2×C4—31no—
482C2×C4—31no—
483C2×C4—62no—
484C2×C4—62no—
485C2×C4—62no—
486C2×C4D3×#6711yescharacteristic
487C2×C4D3×#6711yescharacteristic
488C2×C4C22×D3211yescharacteristic
489C8—62no—
490C8—182no—
491C2×C3—21no—
492C2×C3—21no—
493C2×C3—21no—
494C2×C3—62no—
495C2×C3—242no—
496C2×C3#567411yescharacteristic
497C2×C3C2×#91111yescharacteristic
498C2×C3C2×D3×SD1611yescharacteristic
499C2×C3C22×#21511yescharacteristic
500C2×C3C2×#94911yescharacteristic
501C2×C3#583011yescharacteristic
502D3—22no—
503D3—82no—
504D3—242no—
505D3—242no—
506D3—482no—
507C22—32no—
508C22—61no—
509C22—61no—
510C22—122no—
511C22—122no—
512C22—122no—
513C22—362no—
514C22—362no—
515C22—362no—
516C22—728no—
517C22C2×D3×#6711yescharacteristic
518C4—32no—
519C4—42no—
520C4—61no—
521C4—61no—
522C4—122no—
523C4#6392512yes—
524C4D3×#21512yes—
525C4#6432012yes—
526C3—21no—
527C3#8156811yescharacteristic, complemented
528C3#8335511yescharacteristic, complemented
529C2—62no—
530C2—242no—
531C2—722no—
532C2C2×#6392511yescharacteristic
533C2C2×D3×#21511yescharacteristic
534C2#1059542611yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4⋊Q8C22
socleC22×C32C22×D4
prime radicalD3×#874C2
hypercenterC4⋊Q8D32
hypocenterC32#3208
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊Q8

Complements

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

NH ≅ G/Ntype
1. C3×#5728C2semidirect
3. #10592787C2semidirect
4. C3×#5088C2semidirect
5. #10590596C2semidirect
6. #10590549C2semidirect
7. #10590375C2semidirect
8. #10590373C2semidirect
9. #10590261C2semidirect
15. C32×C4⋊Q8C22semidirect
22. C3×#887C22semidirect
25. C3×#869C22semidirect
29. C2×#3717C22semidirect
30. C2×#3715C22semidirect
31. #63636C22semidirect
32. C4×C3⋊(C3⋊C8)C22semidirect
33. C3×#809C22semidirect
34. C3×C4×C3⋊C8C22semidirect
35. Dic3⋊(C3⋊C8)C22semidirect
38. #5728D3semidirect
45. #5088D3semidirect
99. C3×C4⋊Q8C2×D3semidirect
100. C3×C4⋊Q8C2×D3semidirect
121. #887C2×D3semidirect
130. #869C2×D3semidirect
139. #809C2×D3semidirect
144. C4×C3⋊C8C2×D3semidirect
168. C3×C4×D3SD16semidirect
285. C4⋊Q8D32semidirect
367. C4×D3#215semidirect
460. C32#3208semidirect
527. C3#81568semidirect
528. C3#83355semidirect

Maximal subgroups

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

subgroupindex
C3×#57282
D3×#8742
#105927872
C3×#50882
#105905962
#105905492
#105903752
#105903732
#105902612
#833553
#815683