Finite Group Databasebeta

← #11860942

Subgroups — #11860942

Order 1152.

1022 conjugacy classes of subgroups.

The subgroup lattice has 491 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#919C211yesmaximal, characteristic
2#10595394C212yesmaximal, complemented
3#10592883C211yesmaximal, characteristic, complemented
4C3×#5184C211yesmaximal, characteristic, complemented
5#10591571C212yesmaximal, complemented
6Dic3×#215C212yesmaximal, complemented
7#10591550C212yesmaximal, complemented
8#10590781C211yesmaximal, characteristic, complemented
9#10590771C211yesmaximal, characteristic, complemented
10#10590693C211yesmaximal, characteristic, complemented
11D3×#817C211yesmaximal, characteristic, complemented
12#83899—31nomaximal
13#79832—31nomaximal
14C2×C3×#239C2212yes—
15C2×C32×Q16C2211yescharacteristic
16Q8×C3⋊Dic3C2212yes—
17C3×Q8×Dic3C2212yes—
18C2×C3×#215C2212yes—
19C3×#919C418yescomplemented
20C2×C3×D24C2211yescharacteristic
21C2×C3×D3×C8C2211yescharacteristic
22#63898—22no—
23#63898C2212yes—
24Dic3×D12—22no—
25Dic3×D12C2212yes—
26D3×C4⋊Dic3—22no—
27D3×C4⋊Dic3C2212yes—
28#63855—22no—
29#63855C2211yescharacteristic
30C2×#3711C2211yescharacteristic
31#63662C2212yes—
32#63644C2211yescharacteristic
33#63642C2211yescharacteristic
34C3×#835C2212yes—
35C3×#817C2211yescharacteristic
36C3×#815C2211yescharacteristic
37#63573C2212yes—
38#63563C2212yes—
39#63562C2212yes—
40#63553C2211yescharacteristic
41Dic3×C3⋊C8C2211yescharacteristic
42C2×C3×#135—31no—
43#5827—32no—
44C2×#919D311yescharacteristic
45#5574—32no—
46C3×#441—31no—
47#5232—32no—
48#5184—31no—
49#5184—31no—
50#5184—61no—
51#5184D311yescharacteristic, complemented
52Dic3×SD16—32no—
53Dic3×SD16—32no—
54#5152—31no—
55#5152—31no—
56C2×#817—31no—
57#5101—31no—
58C4×#215—32no—
59#4869—31no—
60D3×#106—31no—
61#4803—32no—
62#4788—32no—
63#4711—31no—
64#4708—31no—
65C2×C32×Q8C2312yes—
66C3×#239—24no—
67C3×#239C2×C418yescomplemented
68C2×C3×D12—22no—
69C2×C3×D12C2312yes—
70C2×C3×C4×D3—22no—
71C2×C3×C4×D3C2311yescharacteristic
72C2×D3×Dic3—22no—
73C2×D3×Dic3—22no—
74C2×D3×Dic3—22no—
75C32×Q16C2×C414yescomplemented
76C2×C32×C8C2311yescharacteristic
77C4⋊(C3⋊Dic3)—22no—
78C4⋊(C3⋊Dic3)C2312yes—
79C4×C3⋊Dic3—22no—
80C4×C3⋊Dic3C2311yescharacteristic
81C2×C3⋊(C3⋊C8)C2311yescharacteristic
82C3×#215C2×C418yescomplemented
83C3×C4⋊Dic3—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⋊Dic3—22no—
92Dic3⋊Dic3D412yes—
93(C2×D3)⋊Dic3—22no—
94(C2×D3)⋊Dic3—22no—
95(C2×D3)⋊Dic3D412yes—
96#3711—22no—
97#2952—91noSylow
98C2×C3×#41—32no—
99C2×#239C2×D312yes—
100C3×#135—38no—
101C2×C3×Q16—21no—
102C2×C3×Q16C2×D311yescharacteristic
103C2×C3×Q16C2×D311yescharacteristic
104C2×C3×SD16—32no—
105C2×C3×D8—31no—
106C22×C3×C8—31no—
107C3×C4×Q8—32no—
108Q8×Dic3—32no—
109Q8×Dic3—32no—
110Q8×Dic3—62no—
111Q8×Dic3C2×D312yes—
112C2×#215C2×D312yes—
113D4×Dic3—32no—
114D4×Dic3—32no—
115D4×Dic3—62no—
116D4×Dic3—62no—
117#926—31no—
118#926—62no—
119C2×C4⋊Dic3—32no—
120C2×C4⋊Dic3—62no—
121C2×#208—31no—
122#919Dic318yescomplemented
123C2×D24C2×D311yescharacteristic
124C2×ΓL(1,𝔽25)—31no—
125C2×D3×C8C2×D311yescharacteristic
126#893—32no—
127#893—62no—
128D3×C4⋊C4—32no—
129D3×C4⋊C4—62no—
130C4×D12—32no—
131C4×D12—62no—
132#872—31no—
133#872—62no—
134C3×#106—31no—
135C3×#103—32no—
136C3×#97—31no—
137#835—32no—
138#835—32no—
139#835—62no—
140#835C2×D312yes—
141#832—32no—
142#832—32no—
143#821—32no—
144#817—31no—
145#817—31no—
146#817—32no—
147#817—61no—
148#817C2×D311yescharacteristic
149#815—31no—
150#815—31no—
151#815—61no—
152#815C2×D311yescharacteristic
153C8×Dic3—31no—
154C8×Dic3—31no—
155C8×Dic3—31no—
156#809—32no—
157#808—32no—
158C4×C3⋊C8—31no—
159C22×C3×D3—22no—
160C22×C3×D3C2×D411yescharacteristic
161C32×Q8—22no—
162C32×Q8C22×C414yes—
163C2×C32×C4—22no—
164C2×C32×C4C2411yescharacteristic
165C2×C3⋊Dic3—22no—
166C2×C3⋊Dic3C2×D412yes—
167C2×C3×Dic3—22no—
168C2×C3×Dic3C2×D412yes—
169C2×C3×Dic3C2×D411yescharacteristic
170C3×D12—28no—
171C3×D12—22no—
172C3×D12C22×C414yes—
173C3×C4×D3—28no—
174C3×C4×D3C22×C412yes—
175C3×C4×D3#4112yes—
176D3×Dic3—82no—
177D3×Dic3—82no—
178D3×Dic3—82no—
179C32×C8C22×C412yes—
180C3⋊(C3⋊C8)—21no—
181C3×C3⋊C8—21no—
182C3×C3⋊C8C22×C412yes—
183C2×#135—31no—
184#520—92no—
185#442—91no—
186#442—91no—
187#441—31no—
188#441—91no—
189C4×SD16—92no—
190C4×SD16—92no—
191C2×#106—91no—
192#417—92no—
193#405—91no—
194C3×#41—38no—
195C3×#41—64no—
196C2×C3×Q8—22no—
197C2×C3×Q8C22×D312yes—
198C2×C3×Q8C22×D312yes—
199C2×C3×D4—32no—
200C2×C3×D4—62no—
201C22×C3×C4—31no—
202C22×C3×C4—62no—
203C22×Dic3—62no—
204C22×Dic3—62no—
205C22×Dic3—62no—
206#239—24no—
207#239C2×Dic318yescomplemented
208C2×D12—22no—
209C2×D12C22×D312yes—
210C2×C4×D3—22no—
211C2×C4×D3—62no—
212C2×C4×D3—62no—
213C2×C4×D3—62no—
214C2×C4×D3C22×D311yescharacteristic
215C3×Q16—24no—
216C3×Q16C4×D314yescomplemented
217C3×Q16C2×Dic314yescomplemented
218C3×SD16—38no—
219C3×D8—34no—
220C2×C3×C8—21no—
221C2×C3×C8—31no—
222C2×C3×C8—34no—
223C2×C3×C8—31no—
224C2×C3×C8C22×D311yescharacteristic
225C2×C3×C8C22×D311yescharacteristic
226C3×C4⋊C4—32no—
227C3×C4⋊C4—62no—
228C3×C42—31no—
229C3×C42—62no—
230#217—32no—
231#217—62no—
232#217—62no—
233#215C2×Dic318yescomplemented
234(C2×D3)⋊C4—32no—
235(C2×D3)⋊C4—62no—
236(C2×D3)⋊C4—62no—
237C4⋊Dic3—22no—
238C4⋊Dic3—32no—
239C4⋊Dic3—32no—
240C4⋊Dic3—32no—
241C4⋊Dic3—62no—
242C4⋊Dic3—62no—
243C4⋊Dic3—62no—
244C4⋊Dic3—62no—
245C4⋊Dic3—122no—
246C4⋊Dic3C22×D312yes—
247Dic3⋊C4—32no—
248Dic3⋊C4—62no—
249C4×Dic3—22no—
250C4×Dic3—31no—
251C4×Dic3—31no—
252C4×Dic3—61no—
253C4×Dic3—62no—
254C4×Dic3—62no—
255C4×Dic3—122no—
256C4×Dic3C22×D311yescharacteristic
257#208—62no—
258C2×C3⋊C8—31no—
259C2×C3⋊C8—31no—
260C2×C3⋊C8—61no—
261C2×C3⋊C8C22×D311yescharacteristic
262C2×C3⋊C8C22×D311yescharacteristic
263D24C2×Dic314yescomplemented
264ΓL(1,𝔽25)—62no—
265D3×C8C2×Dic314yescomplemented
266C22×C32C22×D411yescharacteristic
267C2×C3×D3—22no—
268C2×C3×D3—24no—
269C2×C3×D3—42no—
270C2×C3×D3—42no—
271C2×C3×D3C4×D412yes—
272C32×C4—24no—
273C32×C4C23×C411yescharacteristic
274C32×C4C2×#4111yescharacteristic
275C3⋊Dic3—22no—
276C3⋊Dic3—42no—
277C3×Dic3—22no—
278C3×Dic3—42no—
279C3×Dic3C4×D412yes—
280C2×#41—32no—
281#135—38no—
282C2×Q16D3211yescharacteristic
283C2×SD16—32no—
284C2×D8—31no—
285C2×M16—91no—
286C22×C8—31no—
287C4×Q8—32no—
288C4×Q8—92no—
289C4×D4—92no—
290C4×D4—92no—
291C4×D4—182no—
292C4×D4—182no—
293#117—91no—
294#117—182no—
295C2×C4⋊C4—92no—
296C2×C4⋊C4—182no—
297#106—31no—
298#106—92no—
299#106—91no—
300#103—32no—
301#103—92no—
302#102—92no—
303#102—92no—
304#97—31no—
305#97—91no—
306C4×C8—91no—
307C4×C8—91no—
308C23×C3—31no—
309C23×C3—62no—
310C22×D3—22no—
311C22×D3D3×D411yescharacteristic
312C3×Q8—22no—
313C3×Q8—22no—
314C3×Q8—24no—
315C3×Q8—42no—
316C3×Q8C2×C4×D314yes—
317C3×Q8C22×Dic314yes—
318C3×D4—34no—
319C3×D4—68no—
320C3×D4—62no—
321C2×C3×C4—22no—
322C2×C3×C4—22no—
323C2×C3×C4—21no—
324C2×C3×C4—31no—
325C2×C3×C4—32no—
326C2×C3×C4—32no—
327C2×C3×C4—32no—
328C2×C3×C4—42no—
329C2×C3×C4—68no—
330C2×C3×C4—62no—
331C2×C3×C4C23×D311yescharacteristic
332C2×C3×C4C23×D311yescharacteristic
333C2×Dic3—22no—
334C2×Dic3—32no—
335C2×Dic3—32no—
336C2×Dic3—62no—
337C2×Dic3—62no—
338C2×Dic3—62no—
339C2×Dic3—122no—
340C2×Dic3—242no—
341C2×Dic3—242no—
342C2×Dic3—242no—
343C2×Dic3D3×D412yes—
344C2×Dic3D3×D411yescharacteristic
345D12—28no—
346D12—22no—
347D12C22×Dic314yes—
348C4×D3—28no—
349C4×D3—242no—
350C4×D3—242no—
351C4×D3—242no—
352C4×D3#23712yes—
353C4×D3C22×Dic312yes—
354C3×C8—22no—
355C3×C8—32no—
356C3×C8—61no—
357C3×C8C2×C4×D312yes—
358C3×C8C22×Dic312yes—
359C3⋊C8—21no—
360C3⋊C8—61no—
361C3⋊C8—61no—
362C3⋊C8—121no—
363C3⋊C8C22×Dic312yes—
364C2×C32C2×C4×D411yescharacteristic
365C2×C32#57712yes—
366C3×D3—22no—
367C3×D3—44no—
368#41—38no—
369#41—64no—
370C2×Q8C2×D3212yes—
371C2×D4—32no—
372C2×D4—62no—
373C22×C4—31no—
374C22×C4—62no—
375C22×C4—182no—
376C22×C4—182no—
377C22×C4—182no—
378Q16D3×Dic314yescomplemented
379SD16—38no—
380D8—34no—
381M16—182no—
382C2×C8—31no—
383C2×C8—34no—
384C2×C8—31no—
385C2×C8—91no—
386C2×C8C2×D3211yescharacteristic
387C4⋊C4—32no—
388C4⋊C4—62no—
389C4⋊C4—92no—
390C4⋊C4—92no—
391C4⋊C4—182no—
392C4⋊C4—182no—
393C22⋊C4—92no—
394C22⋊C4—182no—
395C22⋊C4—182no—
396C42—31no—
397C42—62no—
398C42—91no—
399C42—182no—
400C22×C3—21no—
401C22×C3—32no—
402C22×C3—62no—
403C22×C3—64no—
404C22×C3—122no—
405C22×C3—122no—
406C22×C3C2×D3×D411yescharacteristic
407C22×C3C2×D3×D411yescharacteristic
408C2×D3—22no—
409C2×D3—24no—
410C2×D3—42no—
411C2×D3—42no—
412C2×D3D4×Dic312yes—
413C3×C4—24no—
414C3×C4—24no—
415C3×C4—21no—
416C3×C4—21no—
417C3×C4—32no—
418C3×C4—44no—
419C3×C4—62no—
420C3×C4—122no—
421C3×C4C22×C4×D311yescharacteristic
422C3×C4C2×#23711yescharacteristic
423C3×C4D3×#4111yescharacteristic
424C3×C4C23×Dic311yescharacteristic
425Dic3—22no—
426Dic3—42no—
427Dic3—62no—
428Dic3—62no—
429Dic3—122no—
430Dic3—122no—
431Dic3—122no—
432Dic3—242no—
433Dic3D4×Dic312yes—
434C32#295211yescharacteristic, complemented, Sylow
435C23—31no—
436C23—62no—
437Q8—22no—
438Q8C2×D3×Dic314yes—
439D4—34no—
440D4—68no—
441D4—62no—
442C2×C4—22no—
443C2×C4—31no—
444C2×C4—32no—
445C2×C4—32no—
446C2×C4—32no—
447C2×C4—68no—
448C2×C4—62no—
449C2×C4—92no—
450C2×C4—182no—
451C2×C4—722no—
452C2×C4—722no—
453C2×C4—722no—
454C2×C4C22×D3211yescharacteristic
455C8—32no—
456C8—61no—
457C8—181no—
458C8C2×D3×Dic312yes—
459C2×C3—21no—
460C2×C3—22no—
461C2×C3—62no—
462C2×C3—124no—
463C2×C3C4×D3×D411yescharacteristic
464C2×C3#577012yes—
465C2×C3#577812yes—
466C2×C3C2×D4×Dic311yescharacteristic
467D3—22no—
468D3—44no—
469C22—32no—
470C22—62no—
471C22—64no—
472C22—122no—
473C22—122no—
474C22D32×D411yescharacteristic
475C4—24no—
476C4—32no—
477C4—62no—
478C4—122no—
479C4—182no—
480C4—362no—
481C4D3×#23711yescharacteristic
482C4C22×D3×Dic311yescharacteristic
483C3—21no—
484C3#7983211yescharacteristic, complemented
485C3#8389911yescharacteristic, complemented
486C2—62no—
487C2—124no—
488C2#1059477012yes—
489C2D3×D4×Dic311yescharacteristic
subgroupG/H
centerC22D32×D4
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC2×C32×Q16C22
socleC22×C32C22×D4
prime radicalC2×C3×#919C2
cosocleC2×C32×C4C24
hypercenterC2×Q16D32
hypocenterC32#2952
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×Q16

Complements

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

NH ≅ G/Ntype
2. #10595394C2semidirect
3. #10592883C2semidirect
4. C3×#5184C2semidirect
5. #10591571C2semidirect
6. Dic3×#215C2semidirect
7. #10591550C2semidirect
8. #10590781C2semidirect
9. #10590771C2semidirect
10. #10590693C2semidirect
11. D3×#817C2semidirect
19. C3×#919C4semidirect
51. #5184D3semidirect
67. C3×#239C2×C4semidirect
75. C32×Q16C2×C4semidirect
82. C3×#215C2×C4semidirect
89. C3×D24C2×C4semidirect
90. C3×D3×C8C2×C4semidirect
122. #919Dic3semidirect
207. #239C2×Dic3semidirect
216. C3×Q16C4×D3semidirect
217. C3×Q16C2×Dic3semidirect
233. #215C2×Dic3semidirect
263. D24C2×Dic3semidirect
265. D3×C8C2×Dic3semidirect
378. Q16D3×Dic3semidirect
434. C32#2952semidirect
484. C3#79832semidirect
485. C3#83899semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#9192
#105953942
#105928832
C3×#51842
#105915712
Dic3×#2152
#105915502
#105907812
#105907712
#105906932
D3×#8172
#838993
#798323