Finite Group Databasebeta

← #11860692

Subgroups — #11860692

Order 1152.

1122 conjugacy classes of subgroups.

The subgroup lattice has 523 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D3×D24C211yesmaximal, characteristic
2#10593994C212yesmaximal, complemented
3#10592410C211yesmaximal, characteristic, complemented
4C3×#4711C211yesmaximal, characteristic, complemented
5C3×#4708C211yesmaximal, characteristic, complemented
6#10590939C212yesmaximal, complemented
7#10590771C211yesmaximal, characteristic, complemented
8#10590768C211yesmaximal, characteristic, complemented
9#10590745C212yesmaximal, complemented
10#10590706C211yesmaximal, characteristic, complemented
11C4×#3714C212yesmaximal, complemented
12#79867—31nomaximal
13#78561—31nomaximal
14C2×D3×D12C2212yes—
15C2×#3745C2211yescharacteristic
16C4×C4⋊(C3⋊D3)C2212yescomplemented
17C2×C3×D24C2211yescharacteristic
18C2×C3×ΓL(1,𝔽25)C2211yescharacteristic
19C2×C3×D3×C8C2211yescharacteristic
20C3×C4×D12C2212yescomplemented
21C3×#872C2211yescharacteristic
22#63921—22no—
23D3×(C2×D3)⋊C4—22no—
24#63904—22no—
25#63894C2212yescomplemented
26Dic3×D12C2212yescomplemented
27#63881—22no—
28#63841C2212yes—
29C2×#3714C2212yes—
30D3×D24C418yescomplemented
31C32×#97C2211yescharacteristic, complemented
32#63648C2212yescomplemented
33#63644C2211yescharacteristic, complemented
34C3×#821C2212yescomplemented
35C3×#817C2211yescharacteristic, complemented
36C3×#815C2211yescharacteristic, complemented
37C3×C8×Dic3C2211yescharacteristic, complemented
38C3×C4×C3⋊C8C2211yescharacteristic, complemented
39#63575C2212yescomplemented
40#63564C2212yescomplemented
41#63563C2212yescomplemented
42C2×D3×D8—31no—
43C22×D24—31no—
44#5545—32no—
45#5521—32no—
46C3×#442—31no—
47C3×#405—31no—
48#5152—31no—
49#5131—32no—
50#5106—31no—
51C4×#213—32no—
52#4869—31no—
53#4860—31no—
54#4770—32no—
55#4756—32no—
56#4711—31no—
57#4711—31no—
58#4711—31no—
59#4711—31no—
60#4711—61no—
61#4711D311yescharacteristic, complemented
62#4708D311yescharacteristic, complemented
63C4×D24—32no—
64C4×D24—32no—
65C22×D32—22no—
66C2×C4⋊(C3⋊D3)C2312yes—
67C2×C4×C3⋊D3—22no—
68C2×C3×D12C2312yes—
69C2×C3×C4×D3—22no—
70C2×C3×C4×D3C2311yescharacteristic
71C2×#626—22no—
72C2×#624—22no—
73C2×D3×Dic3—22no—
74D3×D12—24no—
75D3×D12C2×C418yescomplemented
76C2×C32×C8C2311yescharacteristic
77C2×C32×C8C2311yescharacteristic
78C32×C42C2311yescharacteristic
79#3752—22no—
80C4⋊(C3⋊Dic3)C2312yes—
81#3745C2×C414yescomplemented
82C3×(C2×D3)⋊C4—22no—
83C3×(C2×D3)⋊C4D412yes—
84C3×C4⋊Dic3C2312yes—
85C3×Dic3⋊C4D412yes—
86C3×C4×Dic3C2311yescharacteristic
87C2×C3×C3⋊C8C2311yescharacteristic
88C2×C3×C3⋊C8C2311yescharacteristic
89C3×D24C2×C414yescomplemented
90C3×ΓL(1,𝔽25)—22no—
91C3×D3×C8C2×C414yescomplemented
92#3722—22no—
93(C2×D3)⋊Dic3—22no—
94(C2×D3)⋊Dic3—22no—
95Dic32—22no—
96#3714C2×C418yescomplemented
97#2948—91noSylow
98C2×D3×D4—32no—
99C22×D12—32no—
100C2×C3×D8—31no—
101C2×C3×M16—31no—
102C22×C3×C8—31no—
103C3×C4×D4—32no—
104C3×#117—31no—
105D4×Dic3—32no—
106C2×#213—32no—
107C4×#67—62no—
108C2×(C2×D3)⋊C4—62no—
109#926—32no—
110D3×D8—38no—
111C2×D24—32no—
112C2×D24—31no—
113C2×D24—31no—
114C2×D24—38no—
115C2×D24—61no—
116C2×D24C2×D311yescharacteristic
117C2×ΓL(1,𝔽25)C2×D311yescharacteristic
118C2×D3×C8C2×D311yescharacteristic
119#893—32no—
120#893—62no—
121#893—62no—
122#892—32no—
123#67⋊C4—62no—
124D3×C22⋊C4—62no—
125D3×C22⋊C4—62no—
126D3×C22⋊C4—62no—
127C4×D12—32no—
128C4×D12—32no—
129C4×D12—32no—
130C4×D12—32no—
131C4×D12—62no—
132C4×D12C2×D312yescomplemented
133#872C2×D311yescharacteristic
134C3×#106—31no—
135C3×#102—32no—
136C3×#97—21no—
137C3×#97—31no—
138C3×#97C2×D311yescharacteristic, complemented
139C3×#97C2×D311yescharacteristic, complemented
140C3×C4×C8—31no—
141C3×C4×C8—31no—
142#832—32no—
143#821—32no—
144#821—32no—
145#821—32no—
146#821—32no—
147#821—62no—
148#821C2×D312yescomplemented
149#818—32no—
150#817—31no—
151#817—31no—
152#817—61no—
153#817C2×D311yescharacteristic, complemented
154#815C2×D311yescharacteristic, complemented
155C8×Dic3C2×D311yescharacteristic, complemented
156#809—32no—
157#807—32no—
158C4×C3⋊C8C2×D311yescharacteristic, complemented
159C22×C3⋊D3—22no—
160C22×C3×D3—22no—
161C22×C3×D3C2×D411yescharacteristic
162C2×D32—28no—
163C2×D32—82no—
164C2×D32—82no—
165C2×C32×C4C2×D412yes—
166C2×C32×C4C2411yescharacteristic
167C2×C3⋊Dic3—22no—
168C4⋊(C3⋊D3)—22no—
169C4⋊(C3⋊D3)C22×C414yes—
170C4×C3⋊D3—82no—
171C2×C3×Dic3—22no—
172C2×C3×Dic3C2×D412yes—
173C2×C3×Dic3C2×D411yescharacteristic
174C3×D12—22no—
175C3×D12C22×C414yes—
176C3×C4×D3—82no—
177C3×C4×D3C22×C412yes—
178C3×C4×D3#4112yes—
179#626—28no—
180#624—82no—
181D3×Dic3—82no—
182C32×C8—21no—
183C32×C8C22×C412yes—
184C3×C3⋊C8—21no—
185C3×C3⋊C8C22×C412yes—
186C22×D8—91no—
187#518—92no—
188#442—31no—
189#442—91no—
190#442—91no—
191#442—91no—
192C4×D8—92no—
193C4×D8—92no—
194#427—91no—
195#418—92no—
196#405—31no—
197C23×D3—62no—
198C23×D3—62no—
199C2×C3×D4—32no—
200C22×C3×C4—31no—
201C22×C3×C4—62no—
202C2×#67—62no—
203C22×Dic3—62no—
204D3×D4—38no—
205D3×D4—64no—
206C2×D12—32no—
207C2×D12—32no—
208C2×D12—38no—
209C2×D12—62no—
210C2×D12—64no—
211C2×D12—62no—
212C2×D12C22×D312yes—
213C2×C4×D3—22no—
214C2×C4×D3—62no—
215C2×C4×D3—62no—
216C2×C4×D3—62no—
217C2×C4×D3—62no—
218C2×C4×D3—62no—
219C2×C4×D3—122no—
220C2×C4×D3C22×D311yescharacteristic
221C3×D8—34no—
222C3×M16—62no—
223C2×C3×C8—21no—
224C2×C3×C8—21no—
225C2×C3×C8—31no—
226C2×C3×C8—34no—
227C2×C3×C8—31no—
228C2×C3×C8C22×D311yescharacteristic
229C2×C3×C8C22×D311yescharacteristic
230C2×C3×C8C22×D311yescharacteristic
231C2×C3×C8C22×D311yescharacteristic
232C3×C4⋊C4—32no—
233C3×C4⋊C4—32no—
234C3×C22⋊C4—32no—
235C3×C22⋊C4—62no—
236C3×C42—21no—
237C3×C42—31no—
238C3×C42C22×D311yescharacteristic
239C3×C42C22×D311yescharacteristic
240#217—62no—
241#217—62no—
242#213—38no—
243(C2×D3)⋊C4—22no—
244(C2×D3)⋊C4—62no—
245(C2×D3)⋊C4—62no—
246(C2×D3)⋊C4—62no—
247(C2×D3)⋊C4—62no—
248(C2×D3)⋊C4—62no—
249(C2×D3)⋊C4—62no—
250(C2×D3)⋊C4—122no—
251(C2×D3)⋊C4D1212yes—
252C4⋊Dic3—32no—
253C4⋊Dic3—32no—
254C4⋊Dic3—62no—
255C4⋊Dic3C22×D312yes—
256Dic3⋊C4D1212yes—
257C4×Dic3—62no—
258C4×Dic3—62no—
259C4×Dic3C22×D311yescharacteristic
260C2×C3⋊C8C22×D311yescharacteristic
261C2×C3⋊C8C22×D311yescharacteristic
262D24—38no—
263D24—34no—
264D24—34no—
265D24—64no—
266D24C4×D314yescomplemented
267ΓL(1,𝔽25)—22no—
268D3×C8C4×D314yescomplemented
269C22×C32C22×D411yescharacteristic
270C2×C3⋊D3—24no—
271C2×C3⋊D3—42no—
272C2×C3⋊D3—42no—
273C2×C3×D3—22no—
274C2×C3×D3—24no—
275C2×C3×D3—42no—
276C2×C3×D3—42no—
277C2×C3×D3C4×D412yes—
278D32—88no—
279C32×C4—22no—
280C32×C4C23×C411yescharacteristic
281C32×C4C2×#4111yescharacteristic
282C3⋊Dic3—42no—
283C3×Dic3—22no—
284C3×Dic3—42no—
285C3×Dic3C4×D412yes—
286C22×D4—92no—
287C2×D8—31no—
288C2×D8—98no—
289C2×D8—92no—
290C2×D8—91no—
291C2×M16—31no—
292C22×C8—31no—
293C4×D4—32no—
294C4×D4—92no—
295C4×D4—92no—
296C4×D4—92no—
297C4×D4—182no—
298C4×D4—182no—
299#117—31no—
300#117—92no—
301C2×C22⋊C4—182no—
302C2×C22⋊C4—182no—
303#107—92no—
304#106—31no—
305#106—91no—
306#102—32no—
307#102—92no—
308#102—92no—
309#102—92no—
310#97—31no—
311#97D3211yescharacteristic, complemented
312C4×C8—31no—
313C4×C8—31no—
314C23×C3—31no—
315C23×C3—62no—
316C22×D3—22no—
317C22×D3—68no—
318C22×D3—62no—
319C22×D3—62no—
320C22×D3—68no—
321C22×D3—122no—
322C22×D3—242no—
323C22×D3—242no—
324C22×D3—242no—
325C22×D3—242no—
326C22×D3C2×D1211yescharacteristic
327C3×D4—34no—
328C3×D4—62no—
329C2×C3×C4—21no—
330C2×C3×C4—22no—
331C2×C3×C4—31no—
332C2×C3×C4—32no—
333C2×C3×C4—32no—
334C2×C3×C4—32no—
335C2×C3×C4—62no—
336C2×C3×C4—242no—
337C2×C3×C4C2×D1212yes—
338C2×C3×C4D3×D412yes—
339C2×C3×C4C23×D311yescharacteristic
340C2×C3×C4C23×D311yescharacteristic
341#67—68no—
342C2×Dic3—22no—
343C2×Dic3—62no—
344C2×Dic3—62no—
345C2×Dic3—122no—
346C2×Dic3—242no—
347C2×Dic3C2×D1212yes—
348C2×Dic3C2×D1211yescharacteristic
349D12—22no—
350D12—34no—
351D12—34no—
352D12—64no—
353D12—68no—
354D12—62no—
355D12—62no—
356D12—122no—
357D12C2×C4×D314yes—
358C4×D3—82no—
359C4×D3—242no—
360C4×D3—242no—
361C4×D3—242no—
362C4×D3—242no—
363C4×D3—242no—
364C4×D3—244no—
365C4×D3C2×C4×D312yes—
366C4×D3#23512yes—
367C3×C8—21no—
368C3×C8—21no—
369C3×C8—22no—
370C3×C8—32no—
371C3×C8—41no—
372C3×C8—61no—
373C3×C8C2×C4×D312yes—
374C3×C8C2×C4×D312yes—
375C3⋊C8—21no—
376C3⋊C8C2×C4×D312yes—
377C2×C32C2×C4×D411yescharacteristic
378C2×C32#57612yes—
379C3⋊D3—44no—
380C3×D3—22no—
381C3×D3—44no—
382C24—182no—
383C2×D4—32no—
384C2×D4—98no—
385C2×D4—92no—
386C2×D4—184no—
387C2×D4—182no—
388C22×C4—31no—
389C22×C4—62no—
390C22×C4—182no—
391C22×C4—182no—
392C22×C4—182no—
393D8—34no—
394D8—98no—
395D8—94no—
396M16—62no—
397C2×C8—31no—
398C2×C8—34no—
399C2×C8—31no—
400C2×C8C2×D3211yescharacteristic
401C2×C8C2×D3211yescharacteristic
402C4⋊C4—32no—
403C4⋊C4—32no—
404C4⋊C4—92no—
405C22⋊C4—32no—
406C22⋊C4—62no—
407C22⋊C4—182no—
408C22⋊C4—182no—
409C22⋊C4—182no—
410C22⋊C4—182no—
411C42—31no—
412C42—182no—
413C42C2×D3211yescharacteristic
414C22×C3—21no—
415C22×C3—32no—
416C22×C3—62no—
417C22×C3—64no—
418C22×C3—122no—
419C22×C3—122no—
420C22×C3C22×D1211yescharacteristic
421C22×C3C2×D3×D411yescharacteristic
422C2×D3—22no—
423C2×D3—24no—
424C2×D3—42no—
425C2×D3—42no—
426C2×D3—64no—
427C2×D3—64no—
428C2×D3—124no—
429C2×D3—122no—
430C2×D3—122no—
431C2×D3—122no—
432C2×D3—122no—
433C2×D3—242no—
434C2×D3—242no—
435C2×D3—248no—
436C2×D3—248no—
437C2×D3C4×D1212yes—
438C3×C4—22no—
439C3×C4—22no—
440C3×C4—21no—
441C3×C4—21no—
442C3×C4—32no—
443C3×C4—42no—
444C3×C4—62no—
445C3×C4—122no—
446C3×C4C22×C4×D311yescharacteristic
447C3×C4C22×C4×D311yescharacteristic
448C3×C4C2×#23511yescharacteristic
449C3×C4D3×#4111yescharacteristic
450Dic3—22no—
451Dic3—42no—
452Dic3—122no—
453Dic3—122no—
454Dic3—242no—
455Dic3C4×D1212yes—
456C32#294811yescharacteristic, complemented, Sylow
457C23—31no—
458C23—62no—
459C23—188no—
460C23—182no—
461C23—722no—
462C23—722no—
463D4—34no—
464D4—62no—
465D4—94no—
466D4—188no—
467D4—182no—
468C2×C4—31no—
469C2×C4—32no—
470C2×C4—32no—
471C2×C4—32no—
472C2×C4—62no—
473C2×C4—182no—
474C2×C4—242no—
475C2×C4—722no—
476C2×C4—722no—
477C2×C4—722no—
478C2×C4D3×D1212yes—
479C2×C4C22×D3211yescharacteristic
480C8—21no—
481C8—32no—
482C8—61no—
483C8C4×D3212yes—
484C2×C3—22no—
485C2×C3—21no—
486C2×C3—62no—
487C2×C3—124no—
488C2×C3C2×C4×D1211yescharacteristic
489C2×C3C4×D3×D411yescharacteristic
490C2×C3#575212yes—
491C2×C3#577412yes—
492D3—22no—
493D3—44no—
494D3—124no—
495D3—124no—
496D3—244no—
497C22—32no—
498C22—62no—
499C22—64no—
500C22—122no—
501C22—122no—
502C22—184no—
503C22—362no—
504C22—362no—
505C22—728no—
506C22C2×D3×D1211yescharacteristic
507C4—22no—
508C4—32no—
509C4—62no—
510C4—122no—
511C4—362no—
512C4C2×C4×D3211yescharacteristic
513C4D3×#23511yescharacteristic
514C3—21no—
515C3#7856111yescharacteristic, complemented
516C3#7986711yescharacteristic, complemented
517C2—62no—
518C2—124no—
519C2—364no—
520C2C4×D3×D1211yescharacteristic
521C2#1059471412yes—
subgroupG/H
centerC22C2×D3×D12
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC32×#97C22
socleC22×C32C22×D4
prime radicalC2×D3×D24C2
cosocleC2×C32×C4C24
hypercenter#97D32
hypocenterC32#2948
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ #97

Complements

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

NH ≅ G/Ntype
2. #10593994C2semidirect
3. #10592410C2semidirect
4. C3×#4711C2semidirect
5. C3×#4708C2semidirect
6. #10590939C2semidirect
7. #10590771C2semidirect
8. #10590768C2semidirect
9. #10590745C2semidirect
10. #10590706C2semidirect
11. C4×#3714C2semidirect
16. C4×C4⋊(C3⋊D3)C22semidirect
20. C3×C4×D12C22semidirect
25. #63894C22semidirect
26. Dic3×D12C22semidirect
30. D3×D24C4semidirect
31. C32×#97C22semidirect
32. #63648C22semidirect
33. #63644C22semidirect
34. C3×#821C22semidirect
35. C3×#817C22semidirect
36. C3×#815C22semidirect
37. C3×C8×Dic3C22semidirect
38. C3×C4×C3⋊C8C22semidirect
39. #63575C22semidirect
40. #63564C22semidirect
41. #63563C22semidirect
61. #4711D3semidirect
62. #4708D3semidirect
75. D3×D12C2×C4semidirect
81. #3745C2×C4semidirect
89. C3×D24C2×C4semidirect
91. C3×D3×C8C2×C4semidirect
96. #3714C2×C4semidirect
132. C4×D12C2×D3semidirect
138. C3×#97C2×D3semidirect
139. C3×#97C2×D3semidirect
148. #821C2×D3semidirect
153. #817C2×D3semidirect
154. #815C2×D3semidirect
155. C8×Dic3C2×D3semidirect
158. C4×C3⋊C8C2×D3semidirect
266. D24C4×D3semidirect
268. D3×C8C4×D3semidirect
311. #97D32semidirect
456. C32#2948semidirect
515. C3#78561semidirect
516. C3#79867semidirect

Maximal subgroups

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

subgroupindex
C2×D3×D242
#105939942
#105924102
C3×#47112
C3×#47082
#105909392
#105907712
#105907682
#105907452
#105907062
C4×#37142
#798673
#785613