Finite Group Databasebeta

← #11860709

Subgroups — #11860709

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#10594604C212yesmaximal, complemented
3#10592568C211yesmaximal, characteristic, complemented
4C3×#4869C211yesmaximal, characteristic, complemented
5C3×#4860C211yesmaximal, characteristic, complemented
6#10590781C211yesmaximal, characteristic, complemented
7#10590768C211yesmaximal, characteristic, complemented
8#10590693C211yesmaximal, characteristic, complemented
9#10590592C212yesmaximal, complemented
10#10590459C212yesmaximal, complemented
11#10590456C212yesmaximal, complemented
12#79867—31nomaximal
13#79167—31nomaximal
14C2×D3×D12C2212yes—
15C2×#3745C2211yescharacteristic
16#64102C2212yescomplemented
17C2×C3×D24C2211yescharacteristic
18C2×C3×D3×C8C2211yescharacteristic
19C3×#893C2212yescomplemented
20C3×#892C2212yes—
21#63921—22no—
22D3×(C2×D3)⋊C4—22no—
23C4×#626—22no—
24#63898C2212yescomplemented
25#63894C2212yescomplemented
26#63880—22no—
27#63855C2211yescharacteristic
28C2×#3714C2212yes—
29C2×#3711C2211yescharacteristic
30D3×D24C418yescomplemented
31C32×#106C2211yescharacteristic, complemented
32#63642C2211yescharacteristic, complemented
33#63636C2212yescomplemented
34C3×#817C2211yescharacteristic, complemented
35C3×#815C2211yescharacteristic, complemented
36C3×#809C2212yescomplemented
37C3×#807C2212yescomplemented
38#63564C2212yescomplemented
39#63562C2212yescomplemented
40#63553C2211yescharacteristic, complemented
41Dic3×C3⋊C8C2211yescharacteristic, complemented
42C2×D3×D8—31no—
43C22×D24—31no—
44#5545—32no—
45#5521—32no—
46C3×#442—31no—
47C3×#427—31no—
48#5152—31no—
49#5101—31no—
50C4×#213—32no—
51#5001—32no—
52#4872—32no—
53#4872—32no—
54#4869—31no—
55#4869—31no—
56#4869—31no—
57#4869—31no—
58#4869—61no—
59#4869D311yescharacteristic, complemented
60#4860D311yescharacteristic, complemented
61#4770—32no—
62#4756—32no—
63#4711—31no—
64#4708—31no—
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
77C32×C4⋊C4C2312yes—
78#3752—22no—
79C4×C3⋊Dic3C2311yescharacteristic
80C2×C3⋊(C3⋊C8)C2311yescharacteristic
81#3745C2×C414yescomplemented
82C3×(C2×D3)⋊C4—22no—
83C3×(C2×D3)⋊C4—22no—
84C3×C4⋊Dic3C2312yes—
85C3×C4×Dic3—22no—
86C3×C4×Dic3C2311yescharacteristic
87C2×C3×C3⋊C8C2311yescharacteristic
88C2×C3×C3⋊C8C2311yescharacteristic
89C3×D24C2×C414yescomplemented
90C3×D3×C8C2×C414yescomplemented
91Dic3⋊Dic3D412yes—
92#3722—22no—
93(C2×D3)⋊Dic3—22no—
94(C2×D3)⋊Dic3D412yes—
95#3714C2×C418yescomplemented
96#3711—22no—
97#2948—91noSylow
98C2×D3×D4—32no—
99C22×D12—32no—
100C2×C3×D8—31no—
101C22×C3×C8—31no—
102C3×C4×D4—32no—
103C3×#117—32no—
104D4×Dic3—32no—
105C2×#213—32no—
106C4×#67—62no—
107C2×(C2×D3)⋊C4—62no—
108#926—31no—
109C2×#208—31no—
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)—31no—
118C2×D3×C8C2×D311yescharacteristic
119#893—32no—
120#893—32no—
121#893—32no—
122#893—32no—
123#893—62no—
124#893C2×D312yescomplemented
125#892C2×D312yes—
126#67⋊C4—62no—
127D3×C22⋊C4—62no—
128D3×C22⋊C4—62no—
129D3×C22⋊C4—62no—
130C4×D12—32no—
131C4×D12—62no—
132C4×D12—62no—
133#872—31no—
134C3×#107—32no—
135C3×#106—21no—
136C3×#106—31no—
137C3×#106C2×D311yescharacteristic, complemented
138C3×#106C2×D311yescharacteristic, complemented
139C3×#102—32no—
140C3×#97—31no—
141#832—32no—
142#821—32no—
143#817C2×D311yescharacteristic, complemented
144#815—31no—
145#815—31no—
146#815—61no—
147#815C2×D311yescharacteristic, complemented
148C8×Dic3—31no—
149C8×Dic3—31no—
150C8×Dic3—31no—
151#809—32no—
152#809—32no—
153#809—32no—
154#809—32no—
155#809—62no—
156#809C2×D312yescomplemented
157#807C2×D312yescomplemented
158C4×C3⋊C8—31no—
159C22×C3⋊D3—22no—
160C22×C3×D3—22no—
161C22×C3×D3C2×D411yescharacteristic
162C2×D32—28no—
163C2×D32—82no—
164C2×D32—82no—
165C2×C32×C4—22no—
166C2×C32×C4C2411yescharacteristic
167C2×C3⋊Dic3C2×D412yes—
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×C8C22×C412yes—
183C3⋊(C3⋊C8)—21no—
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—31no—
195#418—92no—
196#405—91no—
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—
222C2×C3×C8—21no—
223C2×C3×C8—31no—
224C2×C3×C8—34no—
225C2×C3×C8—31no—
226C2×C3×C8C22×D311yescharacteristic
227C2×C3×C8C22×D311yescharacteristic
228C3×C4⋊C4—22no—
229C3×C4⋊C4—32no—
230C3×C4⋊C4C22×D312yes—
231C3×C4⋊C4C22×D312yes—
232C3×C22⋊C4—62no—
233C3×C22⋊C4—62no—
234C3×C42—31no—
235C3×C42—62no—
236#217—32no—
237#217—62no—
238#213—38no—
239(C2×D3)⋊C4—22no—
240(C2×D3)⋊C4—22no—
241(C2×D3)⋊C4—32no—
242(C2×D3)⋊C4—62no—
243(C2×D3)⋊C4—62no—
244(C2×D3)⋊C4—62no—
245(C2×D3)⋊C4—62no—
246(C2×D3)⋊C4—62no—
247(C2×D3)⋊C4—122no—
248C4⋊Dic3—32no—
249C4⋊Dic3C22×D312yes—
250Dic3⋊C4—32no—
251C4×Dic3—22no—
252C4×Dic3—31no—
253C4×Dic3—31no—
254C4×Dic3—61no—
255C4×Dic3C22×D311yescharacteristic
256#208—62no—
257C2×C3⋊C8—31no—
258C2×C3⋊C8—31no—
259C2×C3⋊C8—61no—
260C2×C3⋊C8C22×D311yescharacteristic
261C2×C3⋊C8C22×D311yescharacteristic
262D24—38no—
263D24—34no—
264D24—34no—
265D24—64no—
266D24C4×D314yescomplemented
267ΓL(1,𝔽25)—62no—
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—42no—
280C32×C4C23×C411yescharacteristic
281C32×C4C2×#4111yescharacteristic
282C3⋊Dic3—22no—
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—91no—
292C22×C8—31no—
293C4×D4—32no—
294C4×D4—92no—
295C4×D4—92no—
296C4×D4—92no—
297C4×D4—182no—
298C4×D4—182no—
299#117—32no—
300#117—91no—
301C2×C22⋊C4—182no—
302C2×C22⋊C4—182no—
303#107—32no—
304#106—31no—
305#106D3211yescharacteristic, complemented
306#102—32no—
307#102—92no—
308#102—92no—
309#102—92no—
310#97—31no—
311#97—91no—
312C4×C8—91no—
313C4×C8—91no—
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×D3D3×D411yescharacteristic
327C3×D4—34no—
328C3×D4—62no—
329C2×C3×C4—22no—
330C2×C3×C4—22no—
331C2×C3×C4—21no—
332C2×C3×C4—31no—
333C2×C3×C4—32no—
334C2×C3×C4—32no—
335C2×C3×C4—32no—
336C2×C3×C4—42no—
337C2×C3×C4—62no—
338C2×C3×C4—242no—
339C2×C3×C4C23×D311yescharacteristic
340C2×C3×C4C23×D311yescharacteristic
341#67—68no—
342C2×Dic3—22no—
343C2×Dic3—32no—
344C2×Dic3—32no—
345C2×Dic3—62no—
346C2×Dic3—242no—
347C2×Dic3D3×D412yes—
348C2×Dic3D3×D411yescharacteristic
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#23912yes—
367C3×C8—22no—
368C3×C8—32no—
369C3×C8—61no—
370C3×C8C2×C4×D312yes—
371C3×C8C2×C4×D312yes—
372C3⋊C8—21no—
373C3⋊C8—61no—
374C3⋊C8—61no—
375C3⋊C8—121no—
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—182no—
397C2×C8—31no—
398C2×C8—34no—
399C2×C8—31no—
400C2×C8—91no—
401C2×C8C2×D3211yescharacteristic
402C4⋊C4—32no—
403C4⋊C4—92no—
404C4⋊C4C2×D3212yes—
405C22⋊C4—62no—
406C22⋊C4—62no—
407C22⋊C4—92no—
408C22⋊C4—182no—
409C22⋊C4—182no—
410C22⋊C4—182no—
411C42—31no—
412C42—62no—
413C42—91no—
414C22×C3—21no—
415C22×C3—32no—
416C22×C3—62no—
417C22×C3—64no—
418C22×C3—122no—
419C22×C3—122no—
420C22×C3C2×D3×D411yescharacteristic
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×D3#89312yes—
438C3×C4—21no—
439C3×C4—21no—
440C3×C4—32no—
441C3×C4—42no—
442C3×C4—42no—
443C3×C4—62no—
444C3×C4—82no—
445C3×C4—122no—
446C3×C4C22×C4×D311yescharacteristic
447C3×C4C22×C4×D311yescharacteristic
448C3×C4C2×#23911yescharacteristic
449C3×C4D3×#4111yescharacteristic
450Dic3—22no—
451Dic3—42no—
452Dic3—62no—
453Dic3—62no—
454Dic3—122no—
455Dic3#89312yes—
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—22no—
469C2×C4—31no—
470C2×C4—32no—
471C2×C4—32no—
472C2×C4—32no—
473C2×C4—62no—
474C2×C4—92no—
475C2×C4—242no—
476C2×C4—722no—
477C2×C4—722no—
478C2×C4—722no—
479C2×C4C22×D3211yescharacteristic
480C8—32no—
481C8—61no—
482C8—181no—
483C8C4×D3212yes—
484C2×C3—21no—
485C2×C3—22no—
486C2×C3—62no—
487C2×C3—124no—
488C2×C3C2×#89311yescharacteristic
489C2×C3C4×D3×D411yescharacteristic
490C2×C3#576912yes—
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—
506C22D32×D411yescharacteristic
507C4—32no—
508C4—42no—
509C4—62no—
510C4—122no—
511C4—182no—
512C4C2×C4×D3211yescharacteristic
513C4D3×#23911yescharacteristic
514C3—21no—
515C3#7916711yescharacteristic, complemented
516C3#7986711yescharacteristic, complemented
517C2—62no—
518C2—124no—
519C2—364no—
520C2D3×#89311yescharacteristic
521C2#1059475512yes—
subgroupG/H
centerC22D32×D4
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC32×#106C22
socleC22×C32C22×D4
prime radicalC2×D3×D24C2
cosocleC2×C32×C4C24
hypercenter#106D32
hypocenterC32#2948
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ #106

Complements

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

NH ≅ G/Ntype
2. #10594604C2semidirect
3. #10592568C2semidirect
4. C3×#4869C2semidirect
5. C3×#4860C2semidirect
6. #10590781C2semidirect
7. #10590768C2semidirect
8. #10590693C2semidirect
9. #10590592C2semidirect
10. #10590459C2semidirect
11. #10590456C2semidirect
16. #64102C22semidirect
19. C3×#893C22semidirect
24. #63898C22semidirect
25. #63894C22semidirect
30. D3×D24C4semidirect
31. C32×#106C22semidirect
32. #63642C22semidirect
33. #63636C22semidirect
34. C3×#817C22semidirect
35. C3×#815C22semidirect
36. C3×#809C22semidirect
37. C3×#807C22semidirect
38. #63564C22semidirect
39. #63562C22semidirect
40. #63553C22semidirect
41. Dic3×C3⋊C8C22semidirect
59. #4869D3semidirect
60. #4860D3semidirect
75. D3×D12C2×C4semidirect
81. #3745C2×C4semidirect
89. C3×D24C2×C4semidirect
90. C3×D3×C8C2×C4semidirect
95. #3714C2×C4semidirect
124. #893C2×D3semidirect
137. C3×#106C2×D3semidirect
138. C3×#106C2×D3semidirect
143. #817C2×D3semidirect
147. #815C2×D3semidirect
156. #809C2×D3semidirect
157. #807C2×D3semidirect
266. D24C4×D3semidirect
268. D3×C8C4×D3semidirect
305. #106D32semidirect
456. C32#2948semidirect
515. C3#79167semidirect
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
#105946042
#105925682
C3×#48692
C3×#48602
#105907812
#105907682
#105906932
#105905922
#105904592
#105904562
#798673
#791673