Finite Group Databasebeta

← #11866283

Subgroups — #11866283

Order 1152.

1137 conjugacy classes of subgroups.

The subgroup lattice has 529 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64158C211yesmaximal, characteristic
2C3×#5825C211yesmaximal, characteristic, complemented
3#10594996C211yesmaximal, characteristic, complemented
4C22×#3717C211yesmaximal, characteristic, complemented
5C3×#5233C211yesmaximal, characteristic, complemented
6#10591565C214yesmaximal, complemented
7#10591432C214yesmaximal, complemented
8#10591116C211yesmaximal, characteristic, complemented
9#10591099C211yesmaximal, characteristic, complemented
10#83405—31nomaximal
11#78863—31nomaximal
12C2×C32×#41C2211yescharacteristic
13C22×C4⋊(C3⋊D3)C2211yescharacteristic
14C22×C3×Dic6C2211yescharacteristic
15#64158—24no—
16C2×#3755C2212yes—
17C2×#3753C2212yes—
18C2×#3748C2211yescharacteristic
19C3×#944C2212yescomplemented
20C3×#936C2212yescomplemented
21C3×#935—22no—
22C3×#926C2211yescharacteristic
23C3×#926C2211yescharacteristic
24C3×#924—22no—
25C22×C3×C3⋊C8C2211yescharacteristic
26#63974—22no—
27#63894—22no—
28#63894C2214yes—
29C2×#3717—24no—
30C2×#3717C2214yes—
31C3×#835C2212yescomplemented
32C3×#832C2212yescomplemented
33Dic3⋊(C3⋊C8)C2214yescomplemented
34#63565C2214yescomplemented
35C3×#536—31no—
36#5825D311yescharacteristic, complemented
37C2×#949—31no—
38C2×#949—31no—
39C2×#949—61no—
40C22×#215—31no—
41C22×#204—31no—
42#5521—31no—
43#5521—31no—
44C3×#416—31no—
45#5233D311yescharacteristic, complemented
46#5225—31no—
47#5102—31no—
48#5083—34no—
49#5057—34no—
50#5004—31no—
51#4999—31no—
52#4818—34no—
53#4787—34no—
54C23×C3⋊D3—21no—
55C32×#41—22no—
56C32×#41—22no—
57C2×C32×Q8C2311yescharacteristic
58C2×C32×D4—21no—
59C2×C32×D4C2311yescharacteristic
60C22×C32×C4—21no—
61C22×C32×C4C2311yescharacteristic
62C2×C4⋊(C3⋊D3)—21no—
63C2×C4⋊(C3⋊D3)—22no—
64C2×C4⋊(C3⋊D3)D414yes—
65C2×C4⋊(C3⋊D3)C2312yes—
66C22×C3×Dic3—21no—
67C2×C3×Dic6—22no—
68C2×C3×Dic6—22no—
69C2×C3×Dic6—21no—
70C2×C3×Dic6C2312yes—
71C2×#624—24no—
72#3755—24no—
73#3753—24no—
74#3748—22no—
75C2×C3⋊(C3⋊C8)C2312yes—
76C3×#217—21no—
77C3×#217—24no—
78C3×#217D412yes—
79C3×C4⋊Dic3D412yes—
80C3×C4⋊Dic3C2312yes—
81C3×Dic3⋊C4—24no—
82C3×C4×Dic3—21no—
83C3×C4×Dic3C2312yes—
84C2×C3×C3⋊C8—22no—
85C2×C3×C3⋊C8C2312yes—
86#3722—24no—
87#3717—28no—
88#3042—91noSylow
89C2×C3×#41—21no—
90C2×C3×#41C2×D311yescharacteristic
91C2×C3×#41C2×D311yescharacteristic
92C22×C3×Q8—31no—
93C22×D12—31no—
94C22×D12—31no—
95C22×D12—61no—
96C22×Dic6C2×D311yescharacteristic
97C22×C3×C8—31no—
98C3×C4⋊Q8—32no—
99C3×#124—32no—
100C3×#123—62no—
101C3×C22⋊Q8—62no—
102C3×#117—31no—
103C3×#117—31no—
104#949—64no—
105#949—64no—
106#949—68no—
107#944C2×D312yescomplemented
108C2×#215—32no—
109C2×#215—32no—
110C2×#215—34no—
111C2×#215—62no—
112C2×#215—64no—
113#936C2×D312yescomplemented
114#935—22no—
115C2×#213—32no—
116C2×#213—32no—
117C2×#213—62no—
118#926C2×D311yescharacteristic
119#926C2×D311yescharacteristic
120#924—22no—
121C2×#208—31no—
122C2×#208—31no—
123C2×#208—61no—
124C22×C3⋊C8C2×D311yescharacteristic
125C2×#204—34no—
126C2×#204—64no—
127#893—34no—
128#893—62no—
129D3×C22⋊C4—62no—
130D3×C22⋊C4—62no—
131C4×D12—34no—
132C4×D12—62no—
133C3×#103—32no—
134C3×#102—32no—
135#835—34no—
136#835C2×D312yescomplemented
137#832C2×D312yescomplemented
138Dic3⋊C8—34no—
139#810—34no—
140C4⋊(C3⋊C8)—34no—
141C23×C32—21no—
142C23×C32C2×D411yescharacteristic
143C22×C3⋊D3—22no—
144C22×C3⋊D3—24no—
145C22×C3⋊D3—82no—
146C32×Q8—21no—
147C32×Q8—21no—
148C32×D4—21no—
149C32×D4—21no—
150C32×D4—42no—
151C2×C32×C4—21no—
152C2×C32×C4—42no—
153C2×C32×C4C2×D412yes—
154C2×C32×C4C2×D411yescharacteristic
155C2×C32×C4#4112yes—
156C2×C32×C4C2411yescharacteristic
157C4⋊(C3⋊D3)—24no—
158C4⋊(C3⋊D3)—22no—
159C4⋊(C3⋊D3)C2×D414yes—
160C2×C3×Dic3—22no—
161C2×C3×Dic3—22no—
162C2×C3×Dic3—42no—
163C2×C3×Dic3C2×D414yes—
164C3×Dic6—22no—
165C3×Dic6—22no—
166C3×Dic6—42no—
167#624—84no—
168C3⋊(C3⋊C8)—22no—
169C3×C3⋊C8—22no—
170C2×AGL(1,ℤ/8)—91no—
171C22×SD16—91no—
172#536—31no—
173#518—91no—
174#463—94no—
175#461—94no—
176#424—91no—
177#419—91no—
178#416—31no—
179C23×D3—61no—
180C23×D3—61no—
181C23×D3—121no—
182C3×#41—24no—
183C3×#41—22no—
184C3×#41—22no—
185C3×#41—22no—
186C3×#41—22no—
187C3×#41—42no—
188C2×C3×Q8—21no—
189C2×C3×Q8—32no—
190C2×C3×Q8—61no—
191C2×C3×Q8—62no—
192C2×C3×Q8—62no—
193C2×C3×Q8C22×D311yescharacteristic
194C2×C3×Q8C22×D311yescharacteristic
195C2×C3×D4—21no—
196C2×C3×D4—21no—
197C2×C3×D4—21no—
198C2×C3×D4—41no—
199C2×C3×D4C22×D311yescharacteristic
200C2×C3×D4C22×D311yescharacteristic
201C22×C3×C4—21no—
202C22×C3×C4—21no—
203C22×C3×C4—21no—
204C22×C3×C4—41no—
205C22×C3×C4—61no—
206C22×C3×C4C22×D311yescharacteristic
207C22×C3×C4C22×D311yescharacteristic
208C22×Dic3—21no—
209C2×D12—34no—
210C2×D12—34no—
211C2×D12—32no—
212C2×D12—32no—
213C2×D12—62no—
214C2×D12—64no—
215C2×D12—62no—
216C2×D12—61no—
217C2×D12—62no—
218C2×D12—61no—
219C2×D12—122no—
220C2×D12—121no—
221C2×C4×D3—64no—
222C2×C4×D3—64no—
223C2×Dic6—22no—
224C2×Dic6—22no—
225C2×Dic6—21no—
226C2×Dic6C22×D312yes—
227C2×C3×C8—32no—
228C2×C3×C8—62no—
229C3×C4⋊C4—32no—
230C3×C4⋊C4—32no—
231C3×C4⋊C4—64no—
232C3×C22⋊C4—32no—
233C3×C22⋊C4—64no—
234C3×C22⋊C4—61no—
235C3×C42—32no—
236C3×C42—61no—
237#217—21no—
238#217—24no—
239#217#6712yes—
240#215—68no—
241#215—64no—
242#215—64no—
243#215—68no—
244#213—64no—
245#213—64no—
246#213—68no—
247(C2×D3)⋊C4—64no—
248(C2×D3)⋊C4—64no—
249C4⋊Dic3#6712yes—
250C4⋊Dic3C22×D312yes—
251Dic3⋊C4—24no—
252C4×Dic3—21no—
253C4×Dic3C22×D312yes—
254#208—64no—
255#208—62no—
256#208—62no—
257C2×C3⋊C8—22no—
258C2×C3⋊C8—32no—
259C2×C3⋊C8—32no—
260C2×C3⋊C8—62no—
261C2×C3⋊C8C22×D312yes—
262#204—68no—
263C22×C32—22no—
264C22×C32—41no—
265C22×C32—42no—
266C22×C32#12112yes—
267C22×C32C22×D411yescharacteristic
268C2×C3⋊D3—24no—
269C2×C3⋊D3—44no—
270C2×C3⋊D3—84no—
271C32×C4—41no—
272C32×C4#12112yes—
273C32×C4C22×D411yescharacteristic
274C32×C4C2×#4111yescharacteristic
275C3×Dic3—24no—
276C3×Dic3—42no—
277C3×Dic3—42no—
278C2×#41D3211yescharacteristic
279C22×Q8—31no—
280C22×D4—91no—
281AGL(1,ℤ/8)—184no—
282C2×SD16—94no—
283C2×SD16—92no—
284C2×SD16—184no—
285C2×D8—92no—
286C2×M16—91no—
287C22×C8—31no—
288C4⋊Q8—32no—
289#124—32no—
290#123—62no—
291C22⋊Q8—62no—
292C4×D4—94no—
293C4×D4—182no—
294#117—31no—
295#117—31no—
296C2×C22⋊C4—182no—
297C4⋊C8—94no—
298#103—32no—
299#103—94no—
300#102—32no—
301C23×C3—21no—
302C23×C3—21no—
303C23×C3—21no—
304C23×C3—41no—
305C23×C3D3×D411yescharacteristic
306C23×C3C2×#6711yescharacteristic
307C22×D3—62no—
308C22×D3—62no—
309C22×D3—64no—
310C22×D3—64no—
311C22×D3—122no—
312C22×D3—124no—
313C22×D3—242no—
314C22×D3—242no—
315C22×D3—244no—
316C3×Q8—22no—
317C3×Q8—21no—
318C3×Q8—21no—
319C3×Q8—21no—
320C3×Q8—21no—
321C3×Q8—41no—
322C3×Q8—62no—
323C3×Q8—62no—
324C3×Q8—122no—
325C3×D4—22no—
326C3×D4—21no—
327C3×D4—21no—
328C3×D4—21no—
329C3×D4—21no—
330C3×D4—41no—
331C3×D4—44no—
332C3×D4—42no—
333C3×D4—42no—
334C2×C3×C4—21no—
335C2×C3×C4—21no—
336C2×C3×C4—21no—
337C2×C3×C4—22no—
338C2×C3×C4—21no—
339C2×C3×C4—22no—
340C2×C3×C4—34no—
341C2×C3×C4—41no—
342C2×C3×C4—44no—
343C2×C3×C4—42no—
344C2×C3×C4—42no—
345C2×C3×C4—62no—
346C2×C3×C4—62no—
347C2×C3×C4—122no—
348C2×C3×C4#23512yes—
349C2×C3×C4D3×D411yescharacteristic
350C2×C3×C4D3×D412yes—
351C2×C3×C4D3×D412yes—
352C2×C3×C4#23712yes—
353C2×C3×C4C2×#6711yescharacteristic
354C2×C3×C4C23×D311yescharacteristic
355C2×C3×C4C23×D311yescharacteristic
356C2×Dic3—22no—
357C2×Dic3—22no—
358C2×Dic3—42no—
359C2×Dic3C2×#6714yes—
360D12—34no—
361D12—34no—
362D12—64no—
363D12—64no—
364D12—64no—
365D12—62no—
366D12—62no—
367D12—122no—
368D12—124no—
369C4×D3—244no—
370C4×D3—244no—
371Dic6—22no—
372Dic6—22no—
373Dic6—42no—
374C3×C8—62no—
375C3⋊C8—22no—
376C3⋊C8—64no—
377C3⋊C8—62no—
378C3⋊C8—62no—
379C2×C32—22no—
380C2×C32—81no—
381C2×C32C2×#12111yescharacteristic
382C2×C32#57712yes—
383C3⋊D3—44no—
384C24—181no—
385#41—22no—
386#41—22no—
387C2×Q8—32no—
388C2×Q8—61no—
389C2×Q8—62no—
390C2×Q8—62no—
391C2×Q8C2×D3211yescharacteristic
392C2×D4—21no—
393C2×D4—92no—
394C2×D4—94no—
395C2×D4—182no—
396C2×D4—181no—
397C2×D4C2×D3211yescharacteristic
398C22×C4—21no—
399C22×C4—61no—
400C22×C4—184no—
401C22×C4C2×D3211yescharacteristic
402SD16—188no—
403SD16—184no—
404D8—184no—
405M16—182no—
406C2×C8—32no—
407C2×C8—62no—
408C2×C8—92no—
409C4⋊C4—32no—
410C4⋊C4—32no—
411C4⋊C4—64no—
412C22⋊C4—32no—
413C22⋊C4—64no—
414C22⋊C4—61no—
415C22⋊C4—184no—
416C42—32no—
417C42—61no—
418C22×C3—22no—
419C22×C3—22no—
420C22×C3—21no—
421C22×C3—22no—
422C22×C3—42no—
423C22×C3—42no—
424C22×C3—41no—
425C22×C3—42no—
426C22×C3—41no—
427C22×C3—42no—
428C22×C3—82no—
429C22×C3#88412yes—
430C22×C3#93812yes—
431C22×C3C2×D3×D411yescharacteristic
432C22×C3C22×#6711yescharacteristic
433C2×D3—64no—
434C2×D3—64no—
435C2×D3—124no—
436C2×D3—124no—
437C2×D3—124no—
438C2×D3—244no—
439C2×D3—244no—
440C2×D3—244no—
441C2×D3—248no—
442C3×C4—21no—
443C3×C4—21no—
444C3×C4—22no—
445C3×C4—42no—
446C3×C4—41no—
447C3×C4—41no—
448C3×C4—64no—
449C3×C4—122no—
450C3×C4—122no—
451C3×C4#88412yes—
452C3×C4#93812yes—
453C3×C4C2×#23511yescharacteristic
454C3×C4C2×D3×D411yescharacteristic
455C3×C4C2×D3×D411yescharacteristic
456C3×C4C2×#23711yescharacteristic
457Dic3—24no—
458Dic3—42no—
459Dic3—42no—
460C32#304211yescharacteristic, complemented, Sylow
461C23—21no—
462C23—182no—
463C23—184no—
464C23—722no—
465C23D3×#6711yescharacteristic
466Q8—21no—
467Q8—21no—
468Q8—62no—
469Q8—62no—
470Q8—122no—
471D4—21no—
472D4—21no—
473D4—42no—
474D4—94no—
475D4—182no—
476D4—184no—
477C2×C4—21no—
478C2×C4—34no—
479C2×C4—42no—
480C2×C4—62no—
481C2×C4—62no—
482C2×C4—122no—
483C2×C4—724no—
484C2×C4#380412yes—
485C2×C4D3×#6711yescharacteristic
486C2×C4#381112yes—
487C2×C4C22×D3211yescharacteristic
488C8—62no—
489C8—182no—
490C2×C3—22no—
491C2×C3—22no—
492C2×C3—22no—
493C2×C3—21no—
494C2×C3—42no—
495C2×C3—82no—
496C2×C3—81no—
497C2×C3—81no—
498C2×C3C2×#88411yescharacteristic
499C2×C3#577012yes—
500C2×C3C2×#93811yescharacteristic
501C2×C3#583712yes—
502D3—124no—
503D3—124no—
504D3—244no—
505C22—22no—
506C22—42no—
507C22—41no—
508C22—184no—
509C22—364no—
510C22—724no—
511C22#6395812yes—
512C22C2×D3×#6711yescharacteristic
513C4—41no—
514C4—64no—
515C4—122no—
516C4—122no—
517C4#6395812yes—
518C4C2×#380411yescharacteristic
519C4C2×#381111yescharacteristic
520C3—21no—
521C3#7886311yescharacteristic, complemented
522C3#8340511yescharacteristic, complemented
523C2—22no—
524C2—81no—
525C2—364no—
526C2#1059545712yes—
527C2C2×#6395811yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×#41C22
socleC22×C32C22×D4
prime radicalC2×#64158C2
hypercenterC2×#41D32
hypocenterC32#3042
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
2. C3×#5825C2semidirect
3. #10594996C2semidirect
4. C22×#3717C2semidirect
5. C3×#5233C2semidirect
6. #10591565C2semidirect
7. #10591432C2semidirect
8. #10591116C2semidirect
9. #10591099C2semidirect
19. C3×#944C22semidirect
20. C3×#936C22semidirect
31. C3×#835C22semidirect
32. C3×#832C22semidirect
33. Dic3⋊(C3⋊C8)C22semidirect
34. #63565C22semidirect
36. #5825D3semidirect
45. #5233D3semidirect
107. #944C2×D3semidirect
113. #936C2×D3semidirect
136. #835C2×D3semidirect
137. #832C2×D3semidirect
460. C32#3042semidirect
521. C3#78863semidirect
522. C3#83405semidirect

Maximal subgroups

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

subgroupindex
C2×#641582
C3×#58252
#105949962
C22×#37172
C3×#52332
#105915652
#105914322
#105911162
#105910992
#834053
#788633