Finite Group Databasebeta

← #11858675

Subgroups — #11858675

Order 1152.

1009 conjugacy classes of subgroups.

The subgroup lattice has 492 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596216C211yesmaximal, characteristic
2#10594780C211yesmaximal, characteristic
3C2×#63817C211yesmaximal, characteristic
4C3×#5124C211yesmaximal, characteristic, complemented
5C2×C3×#822C211yesmaximal, characteristic, complemented
6#10591141C211yesmaximal, characteristic, complemented
7C2×#63577C211yesmaximal, characteristic, complemented
8#10590974C214yesmaximal, complemented
9#10590972C214yesmaximal, complemented
10#79260—31nomaximal
11#79252—31nomaximal
12C2×#3828C2211yescharacteristic
13C2×C32×M16C2211yescharacteristic
14C2×#3748C2211yescharacteristic
15#64116—22no—
16M16×C3⋊D3C2214yes—
17#64110—22no—
18C2×C3×#208C2211yescharacteristic
19C2×C3×#208C2211yescharacteristic
20C2×C3×#208C2211yescharacteristic
21C22×C3×C3⋊C8C2211yescharacteristic
22C2×#3712C2212yes—
23#63818C2214yes—
24#63817—22no—
25#63817—22no—
26#63817C414yes—
27#63817C414yes—
28C2×#3710C2212yes—
29C3×#822C2212yes—
30C3×#822C2212yes—
31C3×#822C2214yes—
32#63577C2212yes—
33#63577C2212yes—
34#63577C2214yes—
35#5745—31no—
36#5745—31no—
37#5745—31no—
38#5745—31no—
39#5745—61no—
40C2×#907—31no—
41C2×#901—31no—
42C3×#430—31no—
43C2×C3×#108—31no—
44#5125—31no—
45#5124—31no—
46#5124D311yescharacteristic, complemented
47C2×#822—31no—
48C2×#822D311yescharacteristic, complemented
49C2×#819—31no—
50#4893—34no—
51#4893—34no—
52D3×#108—34no—
53D3×#108—34no—
54C22×C32×C4C2311yescharacteristic
55C2×#638Q812yes—
56#3828C2×C412yes—
57#3828C2×C412yes—
58#3828D412yes—
59#3828D412yes—
60C2×C4⋊(C3⋊D3)Q811yescharacteristic
61C2×C4×C3⋊D3C2312yes—
62C2×#634Q811yescharacteristic
63C32×M16—21no—
64C32×M16C2312yes—
65C2×C32×C8—21no—
66#3748—21no—
67#3748C2312yes—
68C2×C3⋊(C3⋊C8)—21no—
69#3743—24no—
70C8×C3⋊D3—24no—
71C3×#208—21no—
72C3×#208—21no—
73C3×#208C2×C412yes—
74C3×#208C2×C412yes—
75C3×#208C2312yes—
76C3×#208C2312yes—
77C2×C3×C3⋊C8—21no—
78C2×C3×C3⋊C8—21no—
79C2×C3×C3⋊C8C2×C412yes—
80C2×C3×C3⋊C8C2×C412yes—
81C2×C3×C3⋊C8C2311yescharacteristic
82C2×C3×C3⋊C8C2311yescharacteristic
83C2×C3×C3⋊C8C2312yes—
84#3712—24no—
85#3712C2×C418yes—
86#3710—24no—
87#3710C2×C418yes—
88#2916—91noSylow
89C2×#235—31no—
90C2×#235—31no—
91C2×#235—61no—
92C2×C3×M16—21no—
93C2×C3×M16—31no—
94C2×C3×M16—31no—
95C2×C3×M16—31no—
96C2×C3×M16C2×D311yescharacteristic
97C2×C3×M16C2×D311yescharacteristic
98C22×C3×C8—31no—
99C2×#208—31no—
100C2×#208—31no—
101C2×#208—61no—
102C2×#208C2×D311yescharacteristic
103C2×#208C2×D311yescharacteristic
104C2×#208C2×D311yescharacteristic
105C22×C3⋊C8C2×D311yescharacteristic
106#907—34no—
107#907—34no—
108#907—62no—
109#907—62no—
110#907—62no—
111#907—62no—
112#907—64no—
113D3×M16—34no—
114D3×M16—34no—
115D3×M16—34no—
116D3×M16—34no—
117D3×M16—64no—
118#901—34no—
119#901—34no—
120#901—62no—
121#901—62no—
122#901—62no—
123#901—62no—
124#901—64no—
125C2×ΓL(1,𝔽25)—32no—
126C2×ΓL(1,𝔽25)—32no—
127C2×D3×C8—32no—
128C2×D3×C8—32no—
129C3×#108—32no—
130C3×#108—34no—
131C3×#108—32no—
132#822—32no—
133#822—32no—
134#822—34no—
135#822C2×D312yes—
136#822C2×D312yes—
137#822C2×D314yes—
138#819—34no—
139#819—32no—
140#819—32no—
141C23×C32C2×Q811yescharacteristic
142C22×C3⋊D3C2×Q812yes—
143C2×C32×C4C22×C411yescharacteristic
144C2×C32×C4C22×C411yescharacteristic
145C2×C32×C4C2×D411yescharacteristic
146C2×C32×C4C2×D411yescharacteristic
147C2×C32×C4C2×Q811yescharacteristic
148C2×C32×C4C2411yescharacteristic
149#638C4⋊C414yes—
150#638C4⋊C414yes—
151C2×C3⋊Dic3C2×Q812yes—
152C4⋊(C3⋊D3)C4⋊C412yes—
153C4⋊(C3⋊D3)C4⋊C412yes—
154C4×C3⋊D3C22×C414yes—
155C4×C3⋊D3C2×D414yes—
156#634C4⋊C412yes—
157#634C4⋊C412yes—
158C32×C8—22no—
159C3⋊(C3⋊C8)—22no—
160C3×C3⋊C8—22no—
161C3×C3⋊C8—22no—
162C3×C3⋊C8C22×C412yes—
163C3×C3⋊C8C22×C414yes—
164C3×C3⋊C8C22×C412yes—
165#568—91no—
166#568—91no—
167C2×#131—91no—
168#430—31no—
169#430—94no—
170#430—91no—
171C2×#108—31no—
172C2×#108—94no—
173C2×#108—91no—
174C22×C3×C4—21no—
175C22×C3×C4C22×D311yescharacteristic
176C22×C3×C4C22×D311yescharacteristic
177C2×#67—32no—
178C2×#67—32no—
179C2×#67—62no—
180#235—32no—
181#235—32no—
182#235—32no—
183#235—32no—
184#235—32no—
185#235—32no—
186#235—32no—
187#235—32no—
188#235—62no—
189#235—62no—
190#235—62no—
191#235—62no—
192C2×D12—31no—
193C2×D12—31no—
194C2×D12—61no—
195C2×C4×D3—32no—
196C2×C4×D3—32no—
197C2×C4×D3—62no—
198C2×Dic6—31no—
199C2×Dic6—31no—
200C2×Dic6—61no—
201C3×M16—22no—
202C3×M16—21no—
203C3×M16—21no—
204C3×M16—22no—
205C3×M16—32no—
206C3×M16—32no—
207C3×M16—32no—
208C3×M16—32no—
209C3×M16—61no—
210C3×M16—61no—
211C3×M16C22×D312yes—
212C3×M16C22×D312yes—
213C2×C3×C8—22no—
214C2×C3×C8—21no—
215C2×C3×C8—21no—
216C2×C3×C8—32no—
217C2×C3×C8—32no—
218C2×C3×C8—31no—
219C2×C3×C8—32no—
220C2×C3×C8—31no—
221C2×C3×C8—61no—
222C2×C3×C8—61no—
223#208—21no—
224#208—21no—
225#208—32no—
226#208—32no—
227#208—62no—
228#208—62no—
229#208—61no—
230#208—61no—
231#208C4×D312yes—
232#208C4×D312yes—
233#208C22×D312yes—
234#208C22×D312yes—
235C2×C3⋊C8—21no—
236C2×C3⋊C8—21no—
237C2×C3⋊C8—62no—
238C2×C3⋊C8—61no—
239C2×C3⋊C8—61no—
240C2×C3⋊C8C4×D312yes—
241C2×C3⋊C8C4×D312yes—
242C2×C3⋊C8C22×D311yescharacteristic
243C2×C3⋊C8C22×D312yes—
244C2×C3⋊C8C22×D311yescharacteristic
245ΓL(1,𝔽25)—38no—
246ΓL(1,𝔽25)—38no—
247ΓL(1,𝔽25)—64no—
248ΓL(1,𝔽25)—64no—
249ΓL(1,𝔽25)—64no—
250ΓL(1,𝔽25)—64no—
251ΓL(1,𝔽25)—68no—
252D3×C8—38no—
253D3×C8—38no—
254D3×C8—64no—
255D3×C8—64no—
256D3×C8—64no—
257D3×C8—64no—
258D3×C8—68no—
259C22×C32—41no—
260C22×C32C2×C4⋊C411yescharacteristic
261C22×C32C2×C4⋊C411yescharacteristic
262C22×C32C22×Q811yescharacteristic
263C2×C3⋊D3—42no—
264C2×C3⋊D3C2×C4⋊C414yes—
265C32×C4C2×C4⋊C411yescharacteristic
266C32×C4C2×C4⋊C411yescharacteristic
267C32×C4C23×C411yescharacteristic
268C32×C4C22×D411yescharacteristic
269C3⋊Dic3C2×C4⋊C414yes—
270C2×#41—91no—
271#131—94no—
272#131—94no—
273#131—182no—
274#131—182no—
275#131—182no—
276#131—182no—
277C2×M16—31no—
278C2×M16—31no—
279C2×M16—31no—
280C2×M16—92no—
281C2×M16—94no—
282C2×M16—91no—
283C2×M16—94no—
284C2×M16D3211yescharacteristic
285C22×C8—31no—
286C22×C8—92no—
287#108—32no—
288#108—32no—
289#108—34no—
290#108—92no—
291#108—92no—
292#108—94no—
293C23×C3—21no—
294C23×C3D3×Q811yescharacteristic
295C23×C3D3×Q811yescharacteristic
296C22×D3—32no—
297C22×D3—32no—
298C22×D3—62no—
299C2×C3×C4—21no—
300C2×C3×C4—21no—
301C2×C3×C4—21no—
302C2×C3×C4—21no—
303C2×C3×C4—21no—
304C2×C3×C4—21no—
305C2×C3×C4C2×C4×D311yescharacteristic
306C2×C3×C4C2×C4×D311yescharacteristic
307C2×C3×C4C2×C4×D311yescharacteristic
308C2×C3×C4C2×C4×D311yescharacteristic
309C2×C3×C4D3×D411yescharacteristic
310C2×C3×C4D3×D411yescharacteristic
311C2×C3×C4D3×D411yescharacteristic
312C2×C3×C4D3×D411yescharacteristic
313C2×C3×C4D3×Q811yescharacteristic
314C2×C3×C4D3×Q811yescharacteristic
315C2×C3×C4C23×D311yescharacteristic
316C2×C3×C4C23×D311yescharacteristic
317#67—34no—
318#67—34no—
319#67—34no—
320#67—34no—
321#67—64no—
322#67—64no—
323C2×Dic3—32no—
324C2×Dic3—32no—
325C2×Dic3—62no—
326D12—32no—
327D12—32no—
328D12—32no—
329D12—32no—
330D12—62no—
331D12—62no—
332C4×D3—34no—
333C4×D3—34no—
334C4×D3—34no—
335C4×D3—34no—
336C4×D3—64no—
337C4×D3—64no—
338Dic6—32no—
339Dic6—32no—
340Dic6—32no—
341Dic6—32no—
342Dic6—62no—
343Dic6—62no—
344C3×C8—24no—
345C3×C8—22no—
346C3×C8—22no—
347C3×C8—32no—
348C3×C8—34no—
349C3×C8—32no—
350C3×C8—62no—
351C3×C8—62no—
352C3⋊C8—22no—
353C3⋊C8—22no—
354C3⋊C8—64no—
355C3⋊C8—62no—
356C3⋊C8—62no—
357C3⋊C8C2×C4×D312yes—
358C3⋊C8C2×C4×D314yes—
359C3⋊C8C2×C4×D312yes—
360C2×C32—21no—
361C2×C32—21no—
362C2×C32—21no—
363C2×C32C22×C4⋊C411yescharacteristic
364C3⋊D3—24no—
365#41—92no—
366#41—92no—
367#41—92no—
368#41—92no—
369C2×Q8—91no—
370C2×D4—92no—
371C2×D4—91no—
372C22×C4—92no—
373C22×C4C2×D3211yescharacteristic
374M16—21no—
375M16—32no—
376M16—32no—
377M16—32no—
378M16—32no—
379M16—61no—
380M16—61no—
381M16—98no—
382M16—92no—
383M16—184no—
384M16—184no—
385M16—181no—
386M16C2×D3212yes—
387C2×C8—21no—
388C2×C8—31no—
389C2×C8—31no—
390C2×C8—32no—
391C2×C8—32no—
392C2×C8—32no—
393C2×C8—61no—
394C2×C8—61no—
395C2×C8—98no—
396C2×C8—184no—
397C2×C8—184no—
398C2×C8—181no—
399C22×C3—21no—
400C22×C3—21no—
401C22×C3—21no—
402C22×C3—41no—
403C22×C3—41no—
404C22×C3—81no—
405C22×C3D3×C4⋊C411yescharacteristic
406C22×C3D3×C4⋊C411yescharacteristic
407C22×C3D3×C4⋊C411yescharacteristic
408C22×C3D3×C4⋊C411yescharacteristic
409C22×C3C2×D3×Q811yescharacteristic
410C22×C3C2×D3×Q811yescharacteristic
411C2×D3—34no—
412C2×D3—34no—
413C2×D3—64no—
414C2×D3—122no—
415C2×D3—122no—
416C2×D3—242no—
417C3×C4—21no—
418C3×C4—21no—
419C3×C4—21no—
420C3×C4—21no—
421C3×C4D3×C4⋊C411yescharacteristic
422C3×C4D3×C4⋊C411yescharacteristic
423C3×C4D3×C4⋊C411yescharacteristic
424C3×C4D3×C4⋊C411yescharacteristic
425C3×C4C22×C4×D311yescharacteristic
426C3×C4C22×C4×D311yescharacteristic
427C3×C4C2×D3×D411yescharacteristic
428C3×C4C2×D3×D411yescharacteristic
429Dic3—34no—
430Dic3—34no—
431Dic3—64no—
432C32#291611yescharacteristic, complemented, Sylow
433C23—92no—
434C23#379711yescharacteristic
435Q8—92no—
436Q8—92no—
437D4—94no—
438D4—94no—
439D4—92no—
440D4—92no—
441C2×C4—92no—
442C2×C4—94no—
443C2×C4—94no—
444C2×C4#379711yescharacteristic
445C2×C4C4×D3211yescharacteristic
446C2×C4C4×D3211yescharacteristic
447C2×C4#381111yescharacteristic
448C2×C4#381111yescharacteristic
449C2×C4C22×D3211yescharacteristic
450C8—22no—
451C8—32no—
452C8—32no—
453C8—34no—
454C8—62no—
455C8—62no—
456C8—182no—
457C2×C3—21no—
458C2×C3—21no—
459C2×C3—21no—
460C2×C3—21no—
461C2×C3—21no—
462C2×C3—21no—
463C2×C3—21no—
464C2×C3—41no—
465C2×C3—41no—
466C2×C3—41no—
467C2×C3C2×D3×C4⋊C411yescharacteristic
468C2×C3C2×D3×C4⋊C411yescharacteristic
469D3—64no—
470D3—64no—
471D3—124no—
472C22—41no—
473C22—94no—
474C22—362no—
475C22#6388311yescharacteristic
476C22#6388311yescharacteristic
477C22C2×#379711yescharacteristic
478C4—94no—
479C4#6388311yescharacteristic
480C4#6388311yescharacteristic
481C4C2×C4×D3211yescharacteristic
482C4C2×#381111yescharacteristic
483C3—21no—
484C3#7925211yescharacteristic, complemented
485C3#7926011yescharacteristic, complemented
486C2—21no—
487C2—21no—
488C2—21no—
489C2—184no—
490C2C2×#6388311yescharacteristic
subgroupG/H
centerC4C2×#3811
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC2×C32×M16C22
socleC2×C32C22×C4⋊C4
prime radicalC2×#3828C22
cosocleC2×C32×C4C24
hypercenterC2×M16D32
hypocenterC32#2916
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C4 ◁ C22×C4 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
4. C3×#5124C2semidirect
5. C2×C3×#822C2semidirect
6. #10591141C2semidirect
7. C2×#63577C2semidirect
8. #10590974C2semidirect
9. #10590972C2semidirect
46. #5124D3semidirect
48. C2×#822D3semidirect
432. C32#2916semidirect
484. C3#79252semidirect
485. C3#79260semidirect

Maximal subgroups

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

subgroupindex
#105962162
#105947802
C2×#638172
C3×#51242
C2×C3×#8222
#105911412
C2×#635772
#105909742
#105909722
#792603
#792523