Finite Group Databasebeta

← #11866288

Subgroups — #11866288

Order 1152.

1063 conjugacy classes of subgroups.

The subgroup lattice has 508 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5521C211yesmaximal, characteristic, complemented
2#10594856C211yesmaximal, characteristic, complemented
3C22×#3716C211yesmaximal, characteristic, complemented
4C2×#63823C211yesmaximal, characteristic
5#10592703C211yesmaximal, characteristic, complemented
6C3×#5002C211yesmaximal, characteristic, complemented
7#10591116C211yesmaximal, characteristic, complemented
8#10590559C214yesmaximal, complemented
9#10590530C214yesmaximal, complemented
10#82544—31nomaximal
11#78863—31nomaximal
12C22×#634C2211yescharacteristic
13C2×C3×#235C2211yescharacteristic
14C22×C3×D12C2211yescharacteristic
15C32×#117C2211yescharacteristic
16C2×#3748C2211yescharacteristic
17C3×#926C2211yescharacteristic
18C22×C3×C3⋊C8C2211yescharacteristic
19C3×#893C2214yes—
20C3×D3×C22⋊C4—22no—
21C3×C4×D12—22no—
22#63962—22no—
23#63866C2212yescomplemented
24#63860C2212yescomplemented
25#63857—22no—
26C2×#3716—24no—
27C2×#3716C2214yes—
28C2×#3715C2212yes—
29#63823—24no—
30C2×#3713C2212yes—
31#63637C2214yescomplemented
32C3×#810C2212yescomplemented
33C3×#809C2212yescomplemented
34Dic3⋊(C3⋊C8)C2214yescomplemented
35C3×#518—31no—
36#5825—31no—
37C2×#949—31no—
38C22×#214—31no—
39C2×#932—31no—
40C22×#204—31no—
41#5526—31no—
42#5521D311yescharacteristic, complemented
43C3×#416—31no—
44#5102—31no—
45#5019—34no—
46#5016—34no—
47#5004—31no—
48#5004—31no—
49#5004—61no—
50#5002D311yescharacteristic, complemented
51#4999—31no—
52#4818—34no—
53#4787—34no—
54C23×C3×D3—21no—
55C22×C32×C4C2311yescharacteristic
56C22×C3⋊Dic3—21no—
57C2×#634—22no—
58C2×#634—22no—
59C2×#634—21no—
60C2×#634C2312yes—
61C2×C3×#67—21no—
62C3×#235—22no—
63C3×#235—22no—
64C2×C3×D12—21no—
65C2×C3×D12—22no—
66C2×C3×D12D414yes—
67C2×C3×D12C2311yescharacteristic
68C2×C3×D12C2312yes—
69C2×C3×C4×D3—21no—
70C2×C3×C4×D3—24no—
71C2×C3×Dic6C2311yescharacteristic
72C32×C4⋊C4C2312yes—
73C32×C22⋊C4—21no—
74C32×C42—21no—
75#3748—22no—
76C2×C3⋊(C3⋊C8)C2312yes—
77C3×#217D412yes—
78C3×(C2×D3)⋊C4—24no—
79C3×C4⋊Dic3D412yes—
80C3×C4×Dic3C2312yes—
81C2×C3×C3⋊C8—22no—
82C2×C3×C3⋊C8C2312yes—
83Dic3⋊Dic3—24no—
84(C2×D3)⋊Dic3—24no—
85#3716—28no—
86#3715—24no—
87#3713—24no—
88#3042—91noSylow
89C2×C3×#41—31no—
90C22×C3×D4—31no—
91C2×#235C2×D311yescharacteristic
92C22×D12C2×D311yescharacteristic
93C22×Dic6—31no—
94C22×Dic6—31no—
95C22×Dic6—61no—
96C22×C3×C8—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#949—64no—
105#944—32no—
106C2×#215—32no—
107#936—32no—
108#935—62no—
109C2×#214—32no—
110C2×#214—34no—
111C2×#214—64no—
112#932—64no—
113C2×#213—32no—
114C2×#213—32no—
115#926C2×D311yescharacteristic
116#924—62no—
117C2×#208—31no—
118C2×#208—31no—
119C2×#208—61no—
120C22×C3⋊C8C2×D311yescharacteristic
121C2×#204—34no—
122C2×#204—64no—
123#897—62no—
124#893C2×D314yes—
125#886—62no—
126D3×C22⋊C4—22no—
127#875—32no—
128C4×D12—22no—
129#869—32no—
130C3×#103—32no—
131C3×#102—32no—
132Dic3⋊C8—34no—
133#810—34no—
134#810—34no—
135#810—64no—
136#810C2×D312yescomplemented
137#809C2×D312yescomplemented
138C4⋊(C3⋊C8)—34no—
139C23×C32C2×D411yescharacteristic
140C22×C3×D3—22no—
141C22×C3×D3—24no—
142C22×C3×D3—21no—
143C22×C3×D3—82no—
144C2×C32×C4—22no—
145C2×C32×C4C2×D412yes—
146C2×C32×C4C2×D411yescharacteristic
147C2×C32×C4#4112yes—
148C2×C32×C4C2411yescharacteristic
149C2×C3⋊Dic3—22no—
150C2×C3⋊Dic3—42no—
151#634—22no—
152#634—22no—
153#634—42no—
154C3×#67—42no—
155C2×C3×Dic3—21no—
156C2×C3×Dic3C2×D414yes—
157C3×D12—24no—
158C3×D12—21no—
159C3×D12—22no—
160C3×D12—21no—
161C3×D12C2×D414yes—
162C3×C4×D3—42no—
163C3×C4×D3—84no—
164C3×Dic6—21no—
165C3×Dic6—21no—
166C3⋊(C3⋊C8)—22no—
167C3×C3⋊C8—22no—
168C2×AGL(1,ℤ/8)—91no—
169C22×SD16—91no—
170#536—91no—
171#518—31no—
172#463—94no—
173#461—94no—
174#424—91no—
175#419—91no—
176#416—31no—
177C24×C3—61no—
178C23×D3—21no—
179C3×#41—62no—
180C3×#41—62no—
181C2×C3×Q8—31no—
182C2×C3×D4—34no—
183C2×C3×D4—32no—
184C2×C3×D4—31no—
185C2×C3×D4—61no—
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—21no—
194C22×Dic3—61no—
195C22×Dic3—61no—
196C22×Dic3—121no—
197#235—22no—
198#235—22no—
199C2×D12—22no—
200C2×D12—21no—
201C2×D12D1214yes—
202C2×D12C22×D311yescharacteristic
203C2×D12C22×D312yes—
204C2×C4×D3—21no—
205C2×C4×D3—24no—
206C2×Dic6—32no—
207C2×Dic6—32no—
208C2×Dic6—62no—
209C2×Dic6—64no—
210C2×Dic6—62no—
211C2×Dic6—62no—
212C2×Dic6—62no—
213C2×Dic6—62no—
214C2×Dic6—61no—
215C2×Dic6—61no—
216C2×Dic6—121no—
217C2×Dic6—122no—
218C2×Dic6C22×D311yescharacteristic
219C2×C3×C8—32no—
220C2×C3×C8—62no—
221C3×C4⋊C4—22no—
222C3×C4⋊C4—32no—
223C3×C4⋊C4C22×D312yes—
224C3×C4⋊C4C22×D312yes—
225C3×C22⋊C4—21no—
226C3×C22⋊C4—21no—
227C3×C22⋊C4—32no—
228C3×C22⋊C4—41no—
229C3×C22⋊C4—64no—
230C3×C42—21no—
231C3×C42—21no—
232C3×C42—32no—
233C3×C42—41no—
234#217—64no—
235#217#6712yes—
236#215—64no—
237#214—68no—
238#214—64no—
239#213—64no—
240#213—64no—
241(C2×D3)⋊C4—24no—
242(C2×D3)⋊C4—64no—
243C4⋊Dic3—64no—
244C4⋊Dic3#6712yes—
245Dic3⋊C4—64no—
246C4×Dic3C22×D312yes—
247#208—62no—
248#208—62no—
249#208—122no—
250C2×C3⋊C8—22no—
251C2×C3⋊C8—32no—
252C2×C3⋊C8—32no—
253C2×C3⋊C8—62no—
254C2×C3⋊C8C22×D312yes—
255#204—68no—
256C22×C32—22no—
257C22×C32#12112yes—
258C22×C32C22×D411yescharacteristic
259C2×C3×D3—24no—
260C2×C3×D3—44no—
261C2×C3×D3—41no—
262C2×C3×D3—42no—
263C2×C3×D3—84no—
264C32×C4—42no—
265C32×C4#12112yes—
266C32×C4C22×D411yescharacteristic
267C32×C4C2×#4111yescharacteristic
268C3⋊Dic3—42no—
269C3×Dic3—24no—
270C3×Dic3—41no—
271C2×#41—31no—
272C22×Q8—91no—
273C22×D4—31no—
274AGL(1,ℤ/8)—184no—
275C2×SD16—94no—
276C2×SD16—92no—
277C2×SD16—184no—
278C2×D8—92no—
279C2×M16—91no—
280C22×C8—31no—
281C4⋊Q8—92no—
282#124—92no—
283#123—182no—
284C22⋊Q8—182no—
285C4×D4—34no—
286C4×D4—62no—
287#117—31no—
288#117D3211yescharacteristic
289C2×C22⋊C4—62no—
290C4⋊C8—94no—
291#103—32no—
292#103—94no—
293#102—32no—
294C23×C3—21no—
295C23×C3—62no—
296C23×C3—64no—
297C23×C3—61no—
298C23×C3—242no—
299C23×C3D3×D411yescharacteristic
300C23×C3C2×#6711yescharacteristic
301C22×D3—22no—
302C22×D3—24no—
303C22×D3—21no—
304C22×D3—82no—
305C3×Q8—61no—
306C3×Q8—61no—
307C3×D4—34no—
308C3×D4—64no—
309C3×D4—61no—
310C3×D4—62no—
311C3×D4—61no—
312C3×D4—122no—
313C2×C3×C4—22no—
314C2×C3×C4—22no—
315C2×C3×C4—21no—
316C2×C3×C4—22no—
317C2×C3×C4—22no—
318C2×C3×C4—21no—
319C2×C3×C4—34no—
320C2×C3×C4—42no—
321C2×C3×C4—61no—
322C2×C3×C4—122no—
323C2×C3×C4—244no—
324C2×C3×C4C2×D1212yes—
325C2×C3×C4#23512yes—
326C2×C3×C4#23512yes—
327C2×C3×C4D3×D412yes—
328C2×C3×C4D3×D411yescharacteristic
329C2×C3×C4C2×#6711yescharacteristic
330C2×C3×C4C23×D311yescharacteristic
331C2×C3×C4C23×D311yescharacteristic
332#67—42no—
333C2×Dic3—21no—
334C2×Dic3—62no—
335C2×Dic3—62no—
336C2×Dic3—122no—
337C2×Dic3—124no—
338C2×Dic3—122no—
339C2×Dic3—122no—
340C2×Dic3C2×#6714yes—
341D12—24no—
342D12—22no—
343D12—21no—
344D12—21no—
345D12C2×D1214yes—
346C4×D3—42no—
347C4×D3—84no—
348Dic6—21no—
349Dic6—21no—
350Dic6—64no—
351Dic6—62no—
352Dic6—62no—
353Dic6—62no—
354Dic6—62no—
355Dic6—122no—
356Dic6—124no—
357Dic6—122no—
358Dic6—122no—
359C3×C8—62no—
360C3⋊C8—22no—
361C3⋊C8—62no—
362C3⋊C8—62no—
363C3⋊C8—122no—
364C2×C32—22no—
365C2×C32C2×#12111yescharacteristic
366C2×C32#57712yes—
367C3×D3—44no—
368C3×D3—81no—
369C24—61no—
370#41—62no—
371#41—62no—
372C2×Q8—31no—
373C2×Q8—92no—
374C2×Q8—181no—
375C2×Q8—182no—
376C2×Q8—182no—
377C2×D4—32no—
378C2×D4—31no—
379C2×D4—34no—
380C2×D4—61no—
381C2×D4—62no—
382C2×D4—61no—
383C22×C4—64no—
384C22×C4—61no—
385C22×C4—181no—
386C22×C4C2×D3211yescharacteristic
387SD16—188no—
388SD16—184no—
389D8—184no—
390M16—182no—
391C2×C8—32no—
392C2×C8—62no—
393C2×C8—92no—
394C4⋊C4—32no—
395C4⋊C4—184no—
396C4⋊C4C2×D3212yes—
397C22⋊C4—21no—
398C22⋊C4—32no—
399C22⋊C4—64no—
400C22⋊C4—184no—
401C42—21no—
402C42—32no—
403C22×C3—22no—
404C22×C3—22no—
405C22×C3—21no—
406C22×C3—22no—
407C22×C3—42no—
408C22×C3—64no—
409C22×C3—124no—
410C22×C3—121no—
411C22×C3—122no—
412C22×C3—244no—
413C22×C3#88412yes—
414C22×C3#93012yes—
415C22×C3C2×D3×D411yescharacteristic
416C22×C3C22×#6711yescharacteristic
417C2×D3—24no—
418C2×D3—44no—
419C2×D3—41no—
420C2×D3—42no—
421C2×D3—84no—
422C3×C4—21no—
423C3×C4—21no—
424C3×C4—22no—
425C3×C4—42no—
426C3×C4—42no—
427C3×C4—64no—
428C3×C4—82no—
429C3×C4—121no—
430C3×C4#88412yes—
431C3×C4#93012yes—
432C3×C4C22×D1211yescharacteristic
433C3×C4C2×#23511yescharacteristic
434C3×C4C2×#23511yescharacteristic
435C3×C4C2×D3×D411yescharacteristic
436Dic3—24no—
437Dic3—41no—
438Dic3—124no—
439Dic3—122no—
440Dic3—122no—
441C32#304211yescharacteristic, complemented, Sylow
442C23—62no—
443C23—64no—
444C23—61no—
445C23—242no—
446C23D3×#6711yescharacteristic
447Q8—61no—
448Q8—61no—
449Q8—182no—
450Q8—182no—
451Q8—362no—
452D4—34no—
453D4—62no—
454D4—61no—
455D4—61no—
456D4—64no—
457D4—122no—
458C2×C4—22no—
459C2×C4—34no—
460C2×C4—61no—
461C2×C4—122no—
462C2×C4—182no—
463C2×C4—244no—
464C2×C4—362no—
465C2×C4#379812yes—
466C2×C4D3×D1212yes—
467C2×C4D3×#6711yescharacteristic
468C2×C4C22×D3211yescharacteristic
469C8—62no—
470C8—182no—
471C2×C3—22no—
472C2×C3—22no—
473C2×C3—22no—
474C2×C3—21no—
475C2×C3—42no—
476C2×C3—124no—
477C2×C3—241no—
478C2×C3C2×#88411yescharacteristic
479C2×C3#577012yes—
480C2×C3C2×#93011yescharacteristic
481C2×C3#583612yes—
482D3—44no—
483D3—81no—
484C22—22no—
485C22—64no—
486C22—124no—
487C22—122no—
488C22—121no—
489C22—244no—
490C22#6390612yes—
491C22C2×D3×#6711yescharacteristic
492C4—42no—
493C4—64no—
494C4—121no—
495C4—362no—
496C4#6390612yes—
497C4C2×#379811yescharacteristic
498C4C2×D3×D1211yescharacteristic
499C3—21no—
500C3#7886311yescharacteristic, complemented
501C3#8254411yescharacteristic, complemented
502C2—22no—
503C2—124no—
504C2—241no—
505C2C2×#6390611yescharacteristic
506C2#1059546612yes—
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#117C22
socleC22×C32C22×D4
prime radicalC2×#63823C2
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. #10594856C2semidirect
3. C22×#3716C2semidirect
5. #10592703C2semidirect
6. C3×#5002C2semidirect
7. #10591116C2semidirect
8. #10590559C2semidirect
9. #10590530C2semidirect
23. #63866C22semidirect
24. #63860C22semidirect
31. #63637C22semidirect
32. C3×#810C22semidirect
33. C3×#809C22semidirect
34. Dic3⋊(C3⋊C8)C22semidirect
42. #5521D3semidirect
50. #5002D3semidirect
136. #810C2×D3semidirect
137. #809C2×D3semidirect
441. C32#3042semidirect
500. C3#78863semidirect
501. C3#82544semidirect

Maximal subgroups

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

subgroupindex
C3×#55212
#105948562
C22×#37162
C2×#638232
#105927032
C3×#50022
#105911162
#105905592
#105905302
#825443
#788633