Finite Group Databasebeta

← #11866290

Subgroups — #11866290

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×#5521C211yesmaximal, characteristic, complemented
2#10594866C211yesmaximal, characteristic, complemented
3C2×#63830C211yesmaximal, characteristic
4C22×#3715C211yesmaximal, characteristic, complemented
5#10592701C211yesmaximal, characteristic, complemented
6C3×#5004C211yesmaximal, characteristic, complemented
7#10591117C211yesmaximal, characteristic, complemented
8#10590559C214yesmaximal, complemented
9#10590534C214yesmaximal, complemented
10#82544—31nomaximal
11#78976—31nomaximal
12C2×#3828C2211yescharacteristic
13C22×C3×D12C2211yescharacteristic
14C22×C3×Dic6C2211yescharacteristic
15C32×#117C2211yescharacteristic
16C22×C3⋊(C3⋊C8)C2211yescharacteristic
17C3×#926C2211yescharacteristic
18C2×C3×#208C2211yescharacteristic
19C3×#893C2214yes—
20C3×D3×C22⋊C4—22no—
21C3×C4×D12—22no—
22#63966—22no—
23#63871—22no—
24#63866C2212yescomplemented
25#63864C2212yescomplemented
26#63830—24no—
27C2×#3716C2212yes—
28C2×#3715—24no—
29C2×#3715C2214yes—
30C2×#3714C2212yes—
31#63637C2212yescomplemented
32#63636C2212yescomplemented
33C3×#810C2214yescomplemented
34Dic3⋊(C3⋊C8)C2214yescomplemented
35C3×#518—31no—
36#5816—31no—
37C22×#215—31no—
38C22×#214—31no—
39C2×#932—31no—
40C2×#908—31no—
41#5526—31no—
42#5521D311yescharacteristic, complemented
43C3×#419—31no—
44#5119—31no—
45#5019—34no—
46#5016—34no—
47#5004D311yescharacteristic, complemented
48#5002—31no—
49#5002—31no—
50#5002—61no—
51#4999—31no—
52#4819—34no—
53#4818—34no—
54C23×C3×D3—21no—
55C22×C32×C4C2311yescharacteristic
56C2×#638—21no—
57#3828—22no—
58#3828—22no—
59C2×C4⋊(C3⋊D3)C2311yescharacteristic
60C2×C4×C3⋊D3—21no—
61C2×#634C2311yescharacteristic
62C22×C3×Dic3—21no—
63C2×C3×D12—21no—
64C2×C3×D12—22no—
65C2×C3×D12D414yes—
66C2×C3×D12C2312yes—
67C2×C3×C4×D3—24no—
68C2×C3×Dic6—22no—
69C2×C3×Dic6—22no—
70C2×C3×Dic6—21no—
71C2×C3×Dic6C2312yes—
72C32×C4⋊C4C2312yes—
73C32×C22⋊C4—21no—
74C32×C42—21no—
75C2×C3⋊(C3⋊C8)—22no—
76C2×C3⋊(C3⋊C8)C2312yes—
77C3×#217D412yes—
78C3×(C2×D3)⋊C4—24no—
79C3×C4⋊Dic3D412yes—
80C3×C4×Dic3C2312yes—
81C3×#208—22no—
82C2×C3×C3⋊C8C2312yes—
83Dic3⋊Dic3—24no—
84#3722—24no—
85#3716—24no—
86#3715—28no—
87#3714—24no—
88#3042—91noSylow
89C22×C3×Q8—31no—
90C22×C3×D4—31no—
91C2×#235—31no—
92C2×#235—31no—
93C2×#235—61no—
94C22×D12C2×D311yescharacteristic
95C22×Dic6C2×D311yescharacteristic
96C2×C3×M16—31no—
97C3×C4×D4—34no—
98C3×C4×D4—62no—
99C3×#117—21no—
100C3×#117—31no—
101C3×#117C2×D311yescharacteristic
102C3×#117C2×D311yescharacteristic
103C2×C3×C22⋊C4—62no—
104#947—32no—
105#946—62no—
106#944—32no—
107C2×#215—34no—
108C2×#215—64no—
109C2×#214—34no—
110C2×#214—32no—
111C2×#214—64no—
112#932—64no—
113C2×#213—32no—
114#929—62no—
115#926C2×D311yescharacteristic
116C2×#208C2×D311yescharacteristic
117C22×C3⋊C8—31no—
118C22×C3⋊C8—31no—
119C22×C3⋊C8—61no—
120#908—64no—
121C2×D24—32no—
122C2×#204—32no—
123#897—62no—
124#893C2×D314yes—
125#886—62no—
126D3×C22⋊C4—22no—
127#875—32no—
128C4×D12—22no—
129#869—32no—
130C3×#103—34no—
131Dic3⋊C8—34no—
132#810—32no—
133#810—32no—
134#810—62no—
135#810C2×D314yescomplemented
136#809—32no—
137#809—32no—
138#809—62no—
139C4⋊(C3⋊C8)—34no—
140C23×C32C2×D411yescharacteristic
141C22×C3⋊D3—21no—
142C22×C3×D3—22no—
143C22×C3×D3—24no—
144C22×C3×D3—82no—
145C2×C32×C4—22no—
146C2×C32×C4C2×D412yes—
147C2×C32×C4C2×D411yescharacteristic
148C2×C32×C4#4112yes—
149C2×C32×C4C2411yescharacteristic
150#638—42no—
151C2×C3⋊Dic3—21no—
152C4⋊(C3⋊D3)—21no—
153C4⋊(C3⋊D3)—21no—
154C4×C3⋊D3—42no—
155#634—21no—
156#634—21no—
157C2×C3×Dic3—22no—
158C2×C3×Dic3—42no—
159C2×C3×Dic3C2×D414yes—
160C3×D12—24no—
161C3×D12—22no—
162C3×D12C2×D414yes—
163C3×C4×D3—84no—
164C3×Dic6—22no—
165C3×Dic6—22no—
166C3×Dic6—42no—
167C3⋊(C3⋊C8)—22no—
168C3×C3⋊C8—22no—
169C2×AGL(1,ℤ/8)—91no—
170C22×SD16—91no—
171#536—91no—
172#518—31no—
173#463—94no—
174#461—94no—
175#424—91no—
176#419—31no—
177#416—91no—
178C24×C3—61no—
179C23×D3—21no—
180C2×C3×Q8—32no—
181C2×C3×Q8—61no—
182C2×C3×Q8—62no—
183C2×C3×Q8—62no—
184C2×C3×D4—34no—
185C2×C3×D4—32no—
186C2×C3×D4—62no—
187C2×C3×D4—61no—
188C22×C3×C4—21no—
189C22×C3×C4—64no—
190C22×C3×C4—61no—
191C22×C3×C4C22×D311yescharacteristic
192C22×C3×C4C22×D311yescharacteristic
193C2×#67—61no—
194C2×#67—61no—
195C2×#67—121no—
196C22×Dic3—21no—
197#235—64no—
198#235—62no—
199#235—62no—
200#235—62no—
201#235—62no—
202#235—122no—
203C2×D12—22no—
204C2×D12—21no—
205C2×D12—31no—
206C2×D12—31no—
207C2×D12—61no—
208C2×D12D1214yes—
209C2×D12C22×D312yes—
210C2×C4×D3—24no—
211C2×C4×D3—61no—
212C2×C4×D3—61no—
213C2×C4×D3—121no—
214C2×Dic6—22no—
215C2×Dic6—22no—
216C2×Dic6—21no—
217C2×Dic6—31no—
218C2×Dic6—31no—
219C2×Dic6—61no—
220C2×Dic6C22×D312yes—
221C3×M16—62no—
222C2×C3×C8—32no—
223C3×C4⋊C4—22no—
224C3×C4⋊C4—32no—
225C3×C4⋊C4C22×D312yes—
226C3×C4⋊C4C22×D312yes—
227C3×C22⋊C4—21no—
228C3×C22⋊C4—21no—
229C3×C22⋊C4—32no—
230C3×C22⋊C4—41no—
231C3×C22⋊C4—64no—
232C3×C42—21no—
233C3×C42—21no—
234C3×C42—32no—
235C3×C42—41no—
236#217#6712yes—
237#215—68no—
238#214—64no—
239#214—68no—
240#213—64no—
241(C2×D3)⋊C4—24no—
242(C2×D3)⋊C4—64no—
243(C2×D3)⋊C4—64no—
244C4⋊Dic3—64no—
245C4⋊Dic3#6712yes—
246Dic3⋊C4—64no—
247C4×Dic3C22×D312yes—
248#208—22no—
249C2×C3⋊C8—32no—
250C2×C3⋊C8—32no—
251C2×C3⋊C8—62no—
252C2×C3⋊C8—62no—
253C2×C3⋊C8—62no—
254C2×C3⋊C8—122no—
255C2×C3⋊C8C22×D312yes—
256D24—64no—
257#204—64no—
258C22×C32—22no—
259C22×C32#12112yes—
260C22×C32C22×D411yescharacteristic
261C2×C3⋊D3—41no—
262C2×C3⋊D3—42no—
263C2×C3×D3—24no—
264C2×C3×D3—44no—
265C2×C3×D3—84no—
266C32×C4—42no—
267C32×C4#12112yes—
268C32×C4C22×D411yescharacteristic
269C32×C4C2×#4111yescharacteristic
270C3⋊Dic3—41no—
271C3×Dic3—24no—
272C3×Dic3—42no—
273C2×#41—91no—
274C22×Q8—31no—
275C22×D4—31no—
276AGL(1,ℤ/8)—184no—
277C2×SD16—92no—
278C2×SD16—94no—
279C2×SD16—184no—
280C2×D8—92no—
281C2×M16—31no—
282C22×C8—91no—
283C4⋊Q8—92no—
284#124—92no—
285#123—182no—
286C22⋊Q8—182no—
287C4×D4—34no—
288C4×D4—62no—
289#117—31no—
290#117D3211yescharacteristic
291C2×C22⋊C4—62no—
292C4⋊C8—94no—
293#103—34no—
294#103—92no—
295#102—92no—
296C23×C3—21no—
297C23×C3—62no—
298C23×C3—64no—
299C23×C3—242no—
300C23×C3D3×D411yescharacteristic
301C23×C3C2×#6711yescharacteristic
302C22×D3—22no—
303C22×D3—24no—
304C22×D3—61no—
305C22×D3—61no—
306C22×D3—82no—
307C22×D3—121no—
308C3×Q8—62no—
309C3×Q8—62no—
310C3×Q8—122no—
311C3×D4—34no—
312C3×D4—64no—
313C3×D4—62no—
314C2×C3×C4—22no—
315C2×C3×C4—22no—
316C2×C3×C4—21no—
317C2×C3×C4—22no—
318C2×C3×C4—22no—
319C2×C3×C4—21no—
320C2×C3×C4—34no—
321C2×C3×C4—42no—
322C2×C3×C4—62no—
323C2×C3×C4—122no—
324C2×C3×C4—244no—
325C2×C3×C4C2×D1212yes—
326C2×C3×C4#23512yes—
327C2×C3×C4#23512yes—
328C2×C3×C4D3×D412yes—
329C2×C3×C4D3×D411yescharacteristic
330C2×C3×C4C2×#6711yescharacteristic
331C2×C3×C4C23×D311yescharacteristic
332C2×C3×C4C23×D311yescharacteristic
333#67—124no—
334#67—122no—
335#67—122no—
336C2×Dic3—22no—
337C2×Dic3—42no—
338C2×Dic3—61no—
339C2×Dic3—61no—
340C2×Dic3—121no—
341C2×Dic3C2×#6714yes—
342D12—24no—
343D12—22no—
344D12—62no—
345D12—61no—
346D12—61no—
347D12—61no—
348D12—61no—
349D12—121no—
350D12C2×D1214yes—
351C4×D3—84no—
352C4×D3—124no—
353C4×D3—122no—
354C4×D3—122no—
355Dic6—22no—
356Dic6—22no—
357Dic6—42no—
358Dic6—62no—
359Dic6—61no—
360Dic6—61no—
361Dic6—61no—
362Dic6—61no—
363Dic6—121no—
364C3×C8—62no—
365C3⋊C8—22no—
366C3⋊C8—62no—
367C3⋊C8—62no—
368C3⋊C8—122no—
369C2×C32—22no—
370C2×C32C2×#12111yescharacteristic
371C2×C32#57712yes—
372C3⋊D3—81no—
373C3×D3—44no—
374C24—61no—
375#41—182no—
376#41—182no—
377C2×Q8—32no—
378C2×Q8—61no—
379C2×Q8—62no—
380C2×Q8—62no—
381C2×Q8—91no—
382C2×D4—32no—
383C2×D4—34no—
384C2×D4—62no—
385C2×D4—61no—
386C2×D4—91no—
387C2×D4—181no—
388C22×C4—64no—
389C22×C4—61no—
390C22×C4—181no—
391C22×C4C2×D3211yescharacteristic
392SD16—184no—
393SD16—188no—
394D8—184no—
395M16—62no—
396C2×C8—32no—
397C2×C8—92no—
398C2×C8—182no—
399C4⋊C4—32no—
400C4⋊C4—184no—
401C4⋊C4C2×D3212yes—
402C22⋊C4—21no—
403C22⋊C4—32no—
404C22⋊C4—64no—
405C22⋊C4—184no—
406C42—21no—
407C42—32no—
408C22×C3—22no—
409C22×C3—22no—
410C22×C3—21no—
411C22×C3—22no—
412C22×C3—42no—
413C22×C3—64no—
414C22×C3—124no—
415C22×C3—244no—
416C22×C3#88412yes—
417C22×C3#93012yes—
418C22×C3C2×D3×D411yescharacteristic
419C22×C3C22×#6711yescharacteristic
420C2×D3—24no—
421C2×D3—44no—
422C2×D3—84no—
423C2×D3—122no—
424C2×D3—121no—
425C2×D3—122no—
426C2×D3—121no—
427C2×D3—122no—
428C2×D3—242no—
429C3×C4—21no—
430C3×C4—21no—
431C3×C4—22no—
432C3×C4—42no—
433C3×C4—42no—
434C3×C4—64no—
435C3×C4—82no—
436C3×C4—122no—
437C3×C4#88412yes—
438C3×C4#93012yes—
439C3×C4C22×D1211yescharacteristic
440C3×C4C2×#23511yescharacteristic
441C3×C4C2×#23511yescharacteristic
442C3×C4C2×D3×D411yescharacteristic
443Dic3—24no—
444Dic3—42no—
445Dic3—122no—
446Dic3—121no—
447Dic3—121no—
448C32#304211yescharacteristic, complemented, Sylow
449C23—62no—
450C23—64no—
451C23—181no—
452C23—242no—
453C23D3×#6711yescharacteristic
454Q8—62no—
455Q8—62no—
456Q8—122no—
457Q8—181no—
458Q8—181no—
459D4—34no—
460D4—62no—
461D4—64no—
462D4—181no—
463D4—181no—
464D4—362no—
465C2×C4—22no—
466C2×C4—34no—
467C2×C4—62no—
468C2×C4—122no—
469C2×C4—181no—
470C2×C4—244no—
471C2×C4—362no—
472C2×C4#379812yes—
473C2×C4D3×D1212yes—
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—124no—
484C2×C3C2×#88411yescharacteristic
485C2×C3#577812yes—
486C2×C3C2×#93011yescharacteristic
487C2×C3#583612yes—
488D3—44no—
489D3—242no—
490D3—241no—
491D3—241no—
492C22—22no—
493C22—64no—
494C22—124no—
495C22—244no—
496C22—362no—
497C22—361no—
498C22#6390612yes—
499C22C2×D3×#6711yescharacteristic
500C4—42no—
501C4—64no—
502C4—122no—
503C4—361no—
504C4#6390612yes—
505C4C2×#379811yescharacteristic
506C4C2×D3×D1211yescharacteristic
507C3—21no—
508C3#7897611yescharacteristic, complemented
509C3#8254411yescharacteristic, complemented
510C2—22no—
511C2—124no—
512C2—721no—
513C2C2×#6390611yescharacteristic
514C2#1059546412yes—
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#117C22
socleC22×C32C22×D4
prime radicalC2×#63830C2
hypercenter#117D32
hypocenterC32#3042
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ #117

Complements

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

NH ≅ G/Ntype
1. C3×#5521C2semidirect
2. #10594866C2semidirect
4. C22×#3715C2semidirect
5. #10592701C2semidirect
6. C3×#5004C2semidirect
7. #10591117C2semidirect
8. #10590559C2semidirect
9. #10590534C2semidirect
24. #63866C22semidirect
25. #63864C22semidirect
31. #63637C22semidirect
32. #63636C22semidirect
33. C3×#810C22semidirect
34. Dic3⋊(C3⋊C8)C22semidirect
42. #5521D3semidirect
47. #5004D3semidirect
135. #810C2×D3semidirect
448. C32#3042semidirect
508. C3#78976semidirect
509. C3#82544semidirect

Maximal subgroups

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

subgroupindex
C3×#55212
#105948662
C2×#638302
C22×#37152
#105927012
C3×#50042
#105911172
#105905592
#105905342
#825443
#789763