Finite Group Databasebeta

← #11866284

Subgroups — #11866284

Order 1152.

1067 conjugacy classes of subgroups.

The subgroup lattice has 516 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5825C211yesmaximal, characteristic, complemented
2C2×C3×#949C211yesmaximal, characteristic
3#10594982C211yesmaximal, characteristic, complemented
4C22×#3715C211yesmaximal, characteristic, complemented
5#10592932C211yesmaximal, characteristic, complemented
6#10591564C214yesmaximal, complemented
7#10591431C214yesmaximal, complemented
8#10591117C211yesmaximal, characteristic, complemented
9#10591100C211yesmaximal, characteristic, complemented
10#83935—31nomaximal
11#83405—31nomaximal
12C2×C32×#41C2211yescharacteristic
13C22×C3×D12C2211yescharacteristic
14C22×C3×Dic6C2211yescharacteristic
15#64135C2211yescharacteristic
16C22×C3⋊(C3⋊C8)C2211yescharacteristic
17C3×#949—24no—
18C3×#944C2212yescomplemented
19C2×C3×#215C2212yes—
20C3×#936C2212yescomplemented
21C3×#935—22no—
22C2×C3×#213C2212yes—
23C3×#926C2211yescharacteristic
24C3×#924—22no—
25C2×C3×#208C2211yescharacteristic
26D3×#217—22no—
27#63898—22no—
28Dic3×D12C2214yes—
29C2×#3715—24no—
30C2×#3715C2214yes—
31#63662C2212yescomplemented
32#63659C2212yescomplemented
33Dic3⋊(C3⋊C8)C2214yescomplemented
34#63566C2214yescomplemented
35C2×C3×AGL(1,ℤ/8)—31no—
36C3×#536—31no—
37#5825D311yescharacteristic, complemented
38C2×#949D311yescharacteristic
39C22×#215—31no—
40#5798—31no—
41C22×#214—31no—
42#5521—31no—
43#5233—31no—
44#5233—31no—
45#5233—61no—
46#5225—31no—
47#5162—34no—
48#5153—34no—
49#5120—31no—
50#5119—31no—
51#5083—34no—
52#5057—34no—
53#4999—31no—
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
62C22×C3×Dic3—21no—
63C2×C3×D12—21no—
64C2×C3×D12—22no—
65C2×C3×D12D414yes—
66C2×C3×D12C2312yes—
67C2×C3×Dic6—22no—
68C2×C3×Dic6—22no—
69C2×C3×Dic6—21no—
70C2×C3×Dic6C2312yes—
71C2×D3×Dic3—24no—
72#3757—21no—
73C4⋊(C3⋊Dic3)C2312yes—
74C4×C3⋊Dic3—21no—
75C2×C3⋊(C3⋊C8)—22no—
76C2×C3⋊(C3⋊C8)C2312yes—
77C3×#217—24no—
78C3×#217D412yes—
79C3×#215—24no—
80C3×#213—24no—
81C3×C4⋊Dic3D412yes—
82C3×Dic3⋊C4—24no—
83C3×C4×Dic3C2312yes—
84C3×#208—22no—
85C2×C3×C3⋊C8C2312yes—
86(C2×D3)⋊Dic3—24no—
87#3715—28no—
88#3042—91noSylow
89C2×C3×#41—21no—
90C2×C3×#41C2×D311yescharacteristic
91C2×C3×#41C2×D311yescharacteristic
92C22×C3×Q8—31no—
93C22×C3×D4—31no—
94C22×D12C2×D311yescharacteristic
95C22×Dic6C2×D311yescharacteristic
96C3×AGL(1,ℤ/8)—64no—
97C2×C3×SD16—32no—
98C2×C3×D8—32no—
99C2×C3×M16—31no—
100C3×C4⋊Q8—32no—
101C3×#124—32no—
102C3×#123—62no—
103C3×C22⋊Q8—62no—
104C3×#117—31no—
105C2×#217—62no—
106#949—24no—
107#944C2×D312yescomplemented
108C2×#215—34no—
109C2×#215—64no—
110C2×#215C2×D312yes—
111#936C2×D312yescomplemented
112#935—22no—
113D4×Dic3—34no—
114D4×Dic3—62no—
115C2×#214—34no—
116C2×#214—64no—
117C2×#213C2×D312yes—
118#926—31no—
119#926—31no—
120#926—61no—
121#926C2×D311yescharacteristic
122#924—22no—
123C2×#208C2×D311yescharacteristic
124C22×C3⋊C8—31no—
125C22×C3⋊C8—31no—
126C22×C3⋊C8—61no—
127#893—62no—
128D3×C22⋊C4—62no—
129C4×D12—34no—
130#835—32no—
131#835—32no—
132#835—34no—
133#835—62no—
134#832—32no—
135#832—32no—
136#832—62no—
137#816—34no—
138Dic3⋊C8—34no—
139C4⋊(C3⋊C8)—34no—
140C23×C32—21no—
141C23×C32C2×D411yescharacteristic
142C22×C3×D3—22no—
143C22×C3×D3—24no—
144C22×C3×D3—82no—
145C32×Q8—21no—
146C32×Q8—21no—
147C32×D4—21no—
148C32×D4—21no—
149C32×D4—42no—
150C2×C32×C4—21no—
151C2×C32×C4—42no—
152C2×C32×C4C2×D411yescharacteristic
153C2×C32×C4C2×D412yes—
154C2×C32×C4#4112yes—
155C2×C32×C4C2411yescharacteristic
156C2×C3⋊Dic3—22no—
157C2×C3×Dic3—22no—
158C2×C3×Dic3—42no—
159C2×C3×Dic3C2×D414yes—
160C3×D12—24no—
161C3×D12—22no—
162C3×D12C2×D414yes—
163C3×Dic6—22no—
164C3×Dic6—22no—
165C3×Dic6—42no—
166D3×Dic3—84no—
167C3⋊(C3⋊C8)—22no—
168C3×C3⋊C8—22no—
169C2×AGL(1,ℤ/8)—31no—
170C22×SD16—91no—
171#536—31no—
172#518—91no—
173#463—94no—
174#461—94no—
175#424—91no—
176#419—91no—
177#416—91no—
178C24×C3—61no—
179C23×D3—21no—
180C3×#41—24no—
181C3×#41—22no—
182C3×#41—22no—
183C3×#41—22no—
184C3×#41—22no—
185C3×#41—42no—
186C2×C3×Q8—21no—
187C2×C3×Q8—32no—
188C2×C3×Q8—61no—
189C2×C3×Q8—62no—
190C2×C3×Q8—62no—
191C2×C3×Q8C22×D311yescharacteristic
192C2×C3×Q8C22×D311yescharacteristic
193C2×C3×D4—21no—
194C2×C3×D4—21no—
195C2×C3×D4—21no—
196C2×C3×D4—34no—
197C2×C3×D4—32no—
198C2×C3×D4—41no—
199C2×C3×D4—62no—
200C2×C3×D4—61no—
201C2×C3×D4C22×D311yescharacteristic
202C2×C3×D4C22×D311yescharacteristic
203C22×C3×C4—21no—
204C22×C3×C4—21no—
205C22×C3×C4—21no—
206C22×C3×C4—41no—
207C22×C3×C4—61no—
208C22×C3×C4C22×D311yescharacteristic
209C22×C3×C4C22×D311yescharacteristic
210C22×Dic3—21no—
211C22×Dic3—64no—
212C2×D12—21no—
213C2×D12—22no—
214C2×D12#6714yes—
215C2×D12C22×D312yes—
216C2×C4×D3—64no—
217C2×Dic6—22no—
218C2×Dic6—22no—
219C2×Dic6—21no—
220C2×Dic6C22×D312yes—
221C3×SD16—64no—
222C3×D8—64no—
223C3×M16—62no—
224C2×C3×C8—32no—
225C3×C4⋊C4—32no—
226C3×C4⋊C4—64no—
227C3×C22⋊C4—32no—
228C3×C22⋊C4—64no—
229C3×C42—32no—
230#217—24no—
231#217—61no—
232#217—61no—
233#217—64no—
234#217—121no—
235#217#6712yes—
236#215—24no—
237#215—68no—
238#214—68no—
239#213—24no—
240(C2×D3)⋊C4—64no—
241C4⋊Dic3—32no—
242C4⋊Dic3—32no—
243C4⋊Dic3—62no—
244C4⋊Dic3#6712yes—
245Dic3⋊C4—24no—
246C4×Dic3—61no—
247C4×Dic3—61no—
248C4×Dic3—121no—
249C4×Dic3C22×D312yes—
250#208—22no—
251C2×C3⋊C8—32no—
252C2×C3⋊C8—32no—
253C2×C3⋊C8—62no—
254C2×C3⋊C8—62no—
255C2×C3⋊C8—62no—
256C2×C3⋊C8—122no—
257C2×C3⋊C8C22×D312yes—
258C22×C32—22no—
259C22×C32—41no—
260C22×C32—42no—
261C22×C32#12112yes—
262C22×C32C22×D411yescharacteristic
263C2×C3×D3—24no—
264C2×C3×D3—44no—
265C2×C3×D3—84no—
266C32×C4—41no—
267C32×C4#12112yes—
268C32×C4C22×D411yescharacteristic
269C32×C4C2×#4111yescharacteristic
270C3⋊Dic3—42no—
271C3×Dic3—24no—
272C3×Dic3—42no—
273C2×#41D3211yescharacteristic
274C22×Q8—31no—
275C22×D4—31no—
276AGL(1,ℤ/8)—64no—
277C2×SD16—32no—
278C2×SD16—94no—
279C2×SD16—184no—
280C2×D8—32no—
281C2×M16—31no—
282C22×C8—91no—
283C4⋊Q8—32no—
284#124—32no—
285#123—62no—
286C22⋊Q8—62no—
287C4×D4—94no—
288C4×D4—182no—
289#117—31no—
290#117—91no—
291C2×C22⋊C4—182no—
292C4⋊C8—94no—
293#103—94no—
294#103—92no—
295#102—92no—
296C23×C3—21no—
297C23×C3—21no—
298C23×C3—21no—
299C23×C3—41no—
300C23×C3—62no—
301C23×C3—64no—
302C23×C3—242no—
303C23×C3D3×D411yescharacteristic
304C23×C3C2×#6711yescharacteristic
305C22×D3—22no—
306C22×D3—24no—
307C22×D3—82no—
308C3×Q8—22no—
309C3×Q8—21no—
310C3×Q8—21no—
311C3×Q8—21no—
312C3×Q8—21no—
313C3×Q8—41no—
314C3×Q8—62no—
315C3×Q8—62no—
316C3×Q8—122no—
317C3×D4—22no—
318C3×D4—21no—
319C3×D4—21no—
320C3×D4—21no—
321C3×D4—21no—
322C3×D4—34no—
323C3×D4—41no—
324C3×D4—44no—
325C3×D4—42no—
326C3×D4—42no—
327C3×D4—64no—
328C3×D4—62no—
329C2×C3×C4—21no—
330C2×C3×C4—21no—
331C2×C3×C4—21no—
332C2×C3×C4—22no—
333C2×C3×C4—22no—
334C2×C3×C4—21no—
335C2×C3×C4—34no—
336C2×C3×C4—41no—
337C2×C3×C4—44no—
338C2×C3×C4—42no—
339C2×C3×C4—42no—
340C2×C3×C4—62no—
341C2×C3×C4—122no—
342C2×C3×C4D3×D412yes—
343C2×C3×C4D3×D411yescharacteristic
344C2×C3×C4#23712yes—
345C2×C3×C4#23712yes—
346C2×C3×C4C2×#6711yescharacteristic
347C2×C3×C4C2×#6712yes—
348C2×C3×C4C23×D311yescharacteristic
349C2×C3×C4C23×D311yescharacteristic
350C2×Dic3—22no—
351C2×Dic3—42no—
352C2×Dic3—62no—
353C2×Dic3—62no—
354C2×Dic3—122no—
355C2×Dic3—244no—
356C2×Dic3C2×#6714yes—
357D12—24no—
358D12—22no—
359D12C2×#6714yes—
360C4×D3—244no—
361Dic6—22no—
362Dic6—22no—
363Dic6—42no—
364C3×C8—62no—
365C3⋊C8—22no—
366C3⋊C8—62no—
367C3⋊C8—62no—
368C3⋊C8—122no—
369C2×C32—22no—
370C2×C32—81no—
371C2×C32C2×#12111yescharacteristic
372C2×C32#57712yes—
373C3×D3—44no—
374C24—61no—
375#41—22no—
376#41—22no—
377C2×Q8—32no—
378C2×Q8—61no—
379C2×Q8—62no—
380C2×Q8—62no—
381C2×Q8C2×D3211yescharacteristic
382C2×D4—21no—
383C2×D4—32no—
384C2×D4—34no—
385C2×D4—62no—
386C2×D4—61no—
387C2×D4C2×D3211yescharacteristic
388C22×C4—21no—
389C22×C4—61no—
390C22×C4—184no—
391C22×C4C2×D3211yescharacteristic
392SD16—64no—
393SD16—188no—
394D8—64no—
395M16—62no—
396C2×C8—32no—
397C2×C8—92no—
398C2×C8—182no—
399C4⋊C4—32no—
400C4⋊C4—64no—
401C4⋊C4—92no—
402C22⋊C4—32no—
403C22⋊C4—64no—
404C22⋊C4—184no—
405C22⋊C4—181no—
406C42—32no—
407C42—181no—
408C22×C3—22no—
409C22×C3—22no—
410C22×C3—21no—
411C22×C3—22no—
412C22×C3—42no—
413C22×C3—42no—
414C22×C3—42no—
415C22×C3—41no—
416C22×C3—41no—
417C22×C3—42no—
418C22×C3—64no—
419C22×C3—82no—
420C22×C3—124no—
421C22×C3—244no—
422C22×C3#93812yes—
423C22×C3#93912yes—
424C22×C3C2×D3×D411yescharacteristic
425C22×C3C22×#6711yescharacteristic
426C2×D3—24no—
427C2×D3—44no—
428C2×D3—84no—
429C3×C4—21no—
430C3×C4—21no—
431C3×C4—22no—
432C3×C4—42no—
433C3×C4—41no—
434C3×C4—41no—
435C3×C4—64no—
436C3×C4—122no—
437C3×C4#93812yes—
438C3×C4#93912yes—
439C3×C4C2×D3×D411yescharacteristic
440C3×C4C2×#23711yescharacteristic
441C3×C4C2×#23711yescharacteristic
442C3×C4C22×#6711yescharacteristic
443Dic3—24no—
444Dic3—42no—
445Dic3—122no—
446Dic3—122no—
447Dic3—242no—
448C32#304211yescharacteristic, complemented, Sylow
449C23—21no—
450C23—62no—
451C23—64no—
452C23—242no—
453C23D3×#6711yescharacteristic
454Q8—21no—
455Q8—21no—
456Q8—62no—
457Q8—62no—
458Q8—122no—
459D4—21no—
460D4—21no—
461D4—34no—
462D4—42no—
463D4—62no—
464D4—64no—
465C2×C4—21no—
466C2×C4—34no—
467C2×C4—42no—
468C2×C4—62no—
469C2×C4—122no—
470C2×C4—182no—
471C2×C4—724no—
472C2×C4#380512yes—
473C2×C4D3×#6712yes—
474C2×C4D3×#6711yescharacteristic
475C2×C4C22×D3211yescharacteristic
476C8—62no—
477C8—182no—
478C2×C3—22no—
479C2×C3—22no—
480C2×C3—22no—
481C2×C3—21no—
482C2×C3—42no—
483C2×C3—82no—
484C2×C3—81no—
485C2×C3—81no—
486C2×C3—124no—
487C2×C3#577512yes—
488C2×C3C2×#93811yescharacteristic
489C2×C3C2×#93911yescharacteristic
490C2×C3#583712yes—
491D3—44no—
492C22—22no—
493C22—42no—
494C22—41no—
495C22—64no—
496C22—124no—
497C22—244no—
498C22#6397012yes—
499C22C2×D3×#6711yescharacteristic
500C4—41no—
501C4—64no—
502C4—122no—
503C4—362no—
504C4#6397012yes—
505C4C2×#380511yescharacteristic
506C4C2×D3×#6711yescharacteristic
507C3—21no—
508C3#8340511yescharacteristic, complemented
509C3#8393511yescharacteristic, complemented
510C2—22no—
511C2—81no—
512C2—124no—
513C2#1059545512yes—
514C2C2×#6397011yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×#41C22
socleC22×C32C22×D4
prime radicalC2×C3×#949C2
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
1. C3×#5825C2semidirect
3. #10594982C2semidirect
4. C22×#3715C2semidirect
5. #10592932C2semidirect
6. #10591564C2semidirect
7. #10591431C2semidirect
8. #10591117C2semidirect
9. #10591100C2semidirect
18. C3×#944C22semidirect
20. C3×#936C22semidirect
31. #63662C22semidirect
32. #63659C22semidirect
33. Dic3⋊(C3⋊C8)C22semidirect
34. #63566C22semidirect
37. #5825D3semidirect
107. #944C2×D3semidirect
111. #936C2×D3semidirect
448. C32#3042semidirect
508. C3#83405semidirect
509. C3#83935semidirect

Maximal subgroups

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

subgroupindex
C3×#58252
C2×C3×#9492
#105949822
C22×#37152
#105929322
#105915642
#105914312
#105911172
#105911002
#839353
#834053