Finite Group Databasebeta

← #11866363

Subgroups — #11866363

Order 1152.

1075 conjugacy classes of subgroups.

The subgroup lattice has 512 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5516C211yesmaximal, characteristic, complemented
2#10595045C211yesmaximal, characteristic
3C22×#3717C211yesmaximal, characteristic, complemented
4C2×#63827C211yesmaximal, characteristic, complemented
5#10592700C211yesmaximal, characteristic, complemented
6C3×#5002C211yesmaximal, characteristic, complemented
7#10591116C211yesmaximal, characteristic, complemented
8#10590549C214yesmaximal, complemented
9#10590536C214yesmaximal, complemented
10#82551—31nomaximal
11#78864—31nomaximal
12C22×C4⋊(C3⋊D3)C2211yescharacteristic
13C2×C3×#235C2211yescharacteristic
14C22×C3×Dic6C2211yescharacteristic
15C32×#117C2211yescharacteristic
16C2×#3748C2211yescharacteristic
17C3×#926C2211yescharacteristic
18C22×C3×C3⋊C8C2211yescharacteristic
19C3×#887C2214yescomplemented
20C3×#877—22no—
21C3×C4×Dic6—22no—
22#63981—22no—
23#63911C2212yes—
24#63909—22no—
25#63864C2212yes—
26C2×#3718C2212yescomplemented
27C2×#3717—24no—
28C2×#3717C2214yes—
29#63827—24no—
30C2×#3715C2212yescomplemented
31#63636C2214yes—
32C3×#810C2212yescomplemented
33C3×#809C2212yescomplemented
34Dic3⋊(C3⋊C8)C2214yescomplemented
35C3×#519—31no—
36#5830—31no—
37C2×#951—31no—
38C2×#942—31no—
39C22×#215—31no—
40C22×#204—31no—
41#5525—31no—
42#5516D311yescharacteristic, complemented
43C3×#416—31no—
44#5102—31no—
45#5028—34no—
46#5027—34no—
47#5002D311yescharacteristic, complemented
48#5001—31no—
49#5001—31no—
50#5001—61no—
51#4999—31no—
52#4798—34no—
53#4762—34no—
54C23×C3⋊D3—21no—
55C22×C32×C4C2311yescharacteristic
56C2×C4⋊(C3⋊D3)—22no—
57C2×C4⋊(C3⋊D3)—22no—
58C2×C4⋊(C3⋊D3)—21no—
59C2×C4⋊(C3⋊D3)C2312yes—
60C2×C3×#67—21no—
61C22×C3×Dic3—21no—
62C3×#235—22no—
63C3×#235—22no—
64C2×C3×D12C2311yescharacteristic
65C2×C3×C4×D3—21no—
66C2×C3×Dic6—21no—
67C2×C3×Dic6—22no—
68C2×C3×Dic6D414yescomplemented
69C2×C3×Dic6C2311yescharacteristic
70C2×C3×Dic6C2312yes—
71C2×#626—24no—
72C32×C4⋊C4C2312yes—
73C32×C22⋊C4—21no—
74C32×C42—21no—
75#3748—22no—
76C2×C3⋊(C3⋊C8)C2312yes—
77C3×#217D412yes—
78C3×C4⋊Dic3D412yes—
79C3×Dic3⋊C4—24no—
80C3×C4×Dic3—24no—
81C3×C4×Dic3C2312yes—
82C2×C3×C3⋊C8—22no—
83C2×C3×C3⋊C8C2312yes—
84#3722—24no—
85#3718—24no—
86#3717—28no—
87#3715—24no—
88#3043—91noSylow
89C2×C3×#41—31no—
90C22×C3×Q8—31no—
91C2×#235C2×D311yescharacteristic
92C22×D12—31no—
93C22×D12—31no—
94C22×D12—61no—
95C22×Dic6C2×D311yescharacteristic
96C22×C3×C8—31no—
97C3×C4×Q8—34no—
98C3×C4×Q8—62no—
99C3×#117—21no—
100C3×#117—31no—
101C3×#117—62no—
102C3×#117C2×D311yescharacteristic
103C3×#117C2×D311yescharacteristic
104#951—64no—
105#947—32no—
106C2×#216—32no—
107C2×#216—32no—
108#942—64no—
109C2×#215—32no—
110C2×#215—34no—
111C2×#215—64no—
112#940—32no—
113#937—62no—
114C2×#214—32no—
115#930—62no—
116#926C2×D311yescharacteristic
117C2×#208—31no—
118C2×#208—31no—
119C2×#208—61no—
120C22×C3⋊C8C2×D311yescharacteristic
121C2×#204—34no—
122C2×#204—64no—
123#895—62no—
124#887C2×D314yescomplemented
125#882—62no—
126#877—22no—
127#875—32no—
128#874—32no—
129C4×Dic6—22no—
130C3×#103—32no—
131C3×#102—32no—
132Dic3⋊C8—34no—
133#810C2×D312yescomplemented
134#809—34no—
135#809—34no—
136#809—64no—
137#809C2×D312yescomplemented
138C4⋊(C3⋊C8)—34no—
139C23×C32C2×D411yescharacteristic
140C22×C3⋊D3—22no—
141C22×C3⋊D3—42no—
142C22×C3⋊D3—82no—
143C22×C3×D3—21no—
144C2×C32×C4—22no—
145C2×C32×C4C2×D412yes—
146C2×C32×C4C2×D411yescharacteristic
147C2×C32×C4#4112yes—
148C2×C32×C4C2411yescharacteristic
149C4⋊(C3⋊D3)—22no—
150C4⋊(C3⋊D3)—22no—
151C4⋊(C3⋊D3)—42no—
152C3×#67—42no—
153C2×C3×Dic3—24no—
154C2×C3×Dic3—22no—
155C2×C3×Dic3—21no—
156C2×C3×Dic3C2×D414yes—
157C3×D12—21no—
158C3×D12—21no—
159C3×C4×D3—42no—
160C3×Dic6—24no—
161C3×Dic6—22no—
162C3×Dic6—21no—
163C3×Dic6—21no—
164C3×Dic6C2×D414yes—
165#626—84no—
166C3⋊(C3⋊C8)—22no—
167C3×C3⋊C8—22no—
168C2×#137—91no—
169C22×SD16—91no—
170#535—91no—
171#519—31no—
172#464—94no—
173#460—94no—
174#424—91no—
175#418—91no—
176#416—31no—
177C23×D3—61no—
178C23×D3—61no—
179C23×D3—121no—
180C3×#41—62no—
181C3×#41—62no—
182C2×C3×Q8—34no—
183C2×C3×Q8—32no—
184C2×C3×Q8—31no—
185C2×C3×Q8—62no—
186C2×C3×Q8—61no—
187C2×C3×D4—31no—
188C2×C3×D4—61no—
189C22×C3×C4—21no—
190C22×C3×C4—61no—
191C22×C3×C4—61no—
192C22×C3×C4C22×D311yescharacteristic
193C22×C3×C4C22×D311yescharacteristic
194C2×#67—21no—
195C2×#67—64no—
196C22×Dic3—21no—
197#235—22no—
198#235—22no—
199C2×D12—32no—
200C2×D12—32no—
201C2×D12—62no—
202C2×D12—64no—
203C2×D12—62no—
204C2×D12—62no—
205C2×D12—62no—
206C2×D12—62no—
207C2×D12—61no—
208C2×D12—61no—
209C2×D12—64no—
210C2×D12—122no—
211C2×D12—121no—
212C2×D12C22×D311yescharacteristic
213C2×C4×D3—21no—
214C2×Dic6—22no—
215C2×Dic6—21no—
216C2×Dic6D1214yescomplemented
217C2×Dic6C22×D311yescharacteristic
218C2×Dic6C22×D312yes—
219C2×C3×C8—32no—
220C2×C3×C8—62no—
221C3×C4⋊C4—22no—
222C3×C4⋊C4—32no—
223C3×C4⋊C4—64no—
224C3×C4⋊C4C22×D312yes—
225C3×C4⋊C4C22×D312yes—
226C3×C22⋊C4—21no—
227C3×C22⋊C4—21no—
228C3×C22⋊C4—32no—
229C3×C22⋊C4—41no—
230C3×C42—21no—
231C3×C42—21no—
232C3×C42—32no—
233C3×C42—41no—
234C3×C42—64no—
235#217#6712yes—
236#216—64no—
237#216—64no—
238#215—68no—
239#215—64no—
240#214—64no—
241(C2×D3)⋊C4—64no—
242(C2×D3)⋊C4—64no—
243C4⋊Dic3#6712yes—
244Dic3⋊C4—24no—
245C4×Dic3—24no—
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—42no—
260C2×C3⋊D3—44no—
261C2×C3⋊D3—84no—
262C2×C3×D3—41no—
263C2×C3×D3—42no—
264C32×C4—42no—
265C32×C4#12112yes—
266C32×C4C22×D411yescharacteristic
267C32×C4C2×#4111yescharacteristic
268C3×Dic3—24no—
269C3×Dic3—24no—
270C3×Dic3—41no—
271C2×#41—31no—
272C22×Q8—31no—
273C22×D4—91no—
274#137—184no—
275C2×Q16—92no—
276C2×SD16—94no—
277C2×SD16—92no—
278C2×SD16—184no—
279C2×M16—91no—
280C22×C8—31no—
281#127—92no—
282#124—92no—
283#121—182no—
284#120—182no—
285C4×Q8—34no—
286C4×Q8—62no—
287#117—31no—
288#117—62no—
289#117D3211yescharacteristic
290C4⋊C8—94no—
291#103—32no—
292#102—32no—
293#102—94no—
294C23×C3—21no—
295C23×C3—61no—
296C23×C3D3×D411yescharacteristic
297C23×C3C2×#6711yescharacteristic
298C22×D3—21no—
299C22×D3—62no—
300C22×D3—62no—
301C22×D3—122no—
302C22×D3—124no—
303C22×D3—122no—
304C22×D3—122no—
305C22×D3—242no—
306C22×D3—242no—
307C22×D3—244no—
308C3×Q8—34no—
309C3×Q8—64no—
310C3×Q8—62no—
311C3×Q8—61no—
312C3×Q8—61no—
313C3×D4—61no—
314C3×D4—61no—
315C3×D4—122no—
316C2×C3×C4—22no—
317C2×C3×C4—22no—
318C2×C3×C4—21no—
319C2×C3×C4—22no—
320C2×C3×C4—22no—
321C2×C3×C4—21no—
322C2×C3×C4—34no—
323C2×C3×C4—42no—
324C2×C3×C4—64no—
325C2×C3×C4—62no—
326C2×C3×C4—61no—
327C2×C3×C4—122no—
328C2×C3×C4C2×D1212yes—
329C2×C3×C4#23512yes—
330C2×C3×C4#23512yes—
331C2×C3×C4D3×D412yes—
332C2×C3×C4D3×D411yescharacteristic
333C2×C3×C4C2×#6711yescharacteristic
334C2×C3×C4C23×D311yescharacteristic
335C2×C3×C4C23×D311yescharacteristic
336#67—42no—
337#67—244no—
338C2×Dic3—24no—
339C2×Dic3—22no—
340C2×Dic3—21no—
341C2×Dic3C2×#6714yes—
342D12—21no—
343D12—21no—
344D12—64no—
345D12—62no—
346D12—62no—
347D12—62no—
348D12—62no—
349D12—122no—
350D12—124no—
351D12—122no—
352D12—122no—
353D12—244no—
354C4×D3—42no—
355Dic6—24no—
356Dic6—22no—
357Dic6—21no—
358Dic6—21no—
359Dic6C2×D1214yes—
360C3×C8—62no—
361C3⋊C8—22no—
362C3⋊C8—62no—
363C3⋊C8—62no—
364C3⋊C8—122no—
365C2×C32—22no—
366C2×C32C2×#12111yescharacteristic
367C2×C32#57712yes—
368C3⋊D3—82no—
369C3×D3—81no—
370C24—181no—
371#41—62no—
372#41—62no—
373C2×Q8—32no—
374C2×Q8—31no—
375C2×Q8—34no—
376C2×Q8—62no—
377C2×Q8—61no—
378C2×D4—31no—
379C2×D4—61no—
380C2×D4—92no—
381C2×D4—184no—
382C2×D4—182no—
383C2×D4—182no—
384C2×D4—181no—
385C22×C4—61no—
386C22×C4—61no—
387C22×C4C2×D3211yescharacteristic
388Q16—184no—
389SD16—188no—
390SD16—184no—
391M16—182no—
392C2×C8—32no—
393C2×C8—62no—
394C2×C8—92no—
395C4⋊C4—32no—
396C4⋊C4—64no—
397C4⋊C4C2×D3212yes—
398C22⋊C4—21no—
399C22⋊C4—32no—
400C22⋊C4—184no—
401C42—21no—
402C42—32no—
403C42—64no—
404C22×C3—22no—
405C22×C3—22no—
406C22×C3—21no—
407C22×C3—22no—
408C22×C3—42no—
409C22×C3—121no—
410C22×C3—122no—
411C22×C3#88412yes—
412C22×C3#93012yes—
413C22×C3C2×D3×D411yescharacteristic
414C22×C3C22×#6711yescharacteristic
415C2×D3—41no—
416C2×D3—42no—
417C2×D3—124no—
418C2×D3—122no—
419C2×D3—124no—
420C2×D3—122no—
421C2×D3—124no—
422C2×D3—244no—
423C2×D3—244no—
424C2×D3—244no—
425C2×D3—248no—
426C3×C4—21no—
427C3×C4—21no—
428C3×C4—22no—
429C3×C4—42no—
430C3×C4—42no—
431C3×C4—64no—
432C3×C4—64no—
433C3×C4—82no—
434C3×C4—121no—
435C3×C4#88412yes—
436C3×C4#93012yes—
437C3×C4C22×D1211yescharacteristic
438C3×C4C2×#23511yescharacteristic
439C3×C4C2×#23511yescharacteristic
440C3×C4C2×D3×D411yescharacteristic
441Dic3—24no—
442Dic3—24no—
443Dic3—41no—
444C32#304311yescharacteristic, complemented, Sylow
445C23—61no—
446C23—182no—
447C23—362no—
448C23—722no—
449C23D3×#6711yescharacteristic
450Q8—34no—
451Q8—62no—
452Q8—64no—
453Q8—61no—
454Q8—61no—
455D4—61no—
456D4—61no—
457D4—122no—
458D4—182no—
459D4—182no—
460D4—362no—
461D4—724no—
462C2×C4—22no—
463C2×C4—34no—
464C2×C4—62no—
465C2×C4—64no—
466C2×C4—61no—
467C2×C4—122no—
468C2×C4#379812yes—
469C2×C4D3×D1212yes—
470C2×C4D3×#6711yescharacteristic
471C2×C4C22×D3211yescharacteristic
472C8—62no—
473C8—182no—
474C2×C3—22no—
475C2×C3—22no—
476C2×C3—22no—
477C2×C3—21no—
478C2×C3—42no—
479C2×C3—241no—
480C2×C3C2×#88411yescharacteristic
481C2×C3#577012yes—
482C2×C3C2×#93011yescharacteristic
483C2×C3#583712yes—
484D3—81no—
485D3—244no—
486D3—242no—
487D3—242no—
488C22—22no—
489C22—122no—
490C22—121no—
491C22—364no—
492C22—362no—
493C22—724no—
494C22#6390612yes—
495C22C2×D3×#6711yescharacteristic
496C4—42no—
497C4—64no—
498C4—64no—
499C4—121no—
500C4#6390612yes—
501C4C2×#379811yescharacteristic
502C4C2×D3×D1211yescharacteristic
503C3—21no—
504C3#7886411yescharacteristic, complemented
505C3#8255111yescharacteristic, complemented
506C2—22no—
507C2—241no—
508C2—722no—
509C2C2×#6390611yescharacteristic
510C2#1059545712yes—
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#117C22
socleC22×C32C22×D4
prime radical#10595045C2
hypercenter#117D32
hypocenterC32#3043
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×#5516C2semidirect
3. C22×#3717C2semidirect
4. C2×#63827C2semidirect
5. #10592700C2semidirect
6. C3×#5002C2semidirect
7. #10591116C2semidirect
8. #10590549C2semidirect
9. #10590536C2semidirect
19. C3×#887C22semidirect
26. C2×#3718C22semidirect
30. C2×#3715C22semidirect
32. C3×#810C22semidirect
33. C3×#809C22semidirect
34. Dic3⋊(C3⋊C8)C22semidirect
42. #5516D3semidirect
47. #5002D3semidirect
68. C2×C3×Dic6D4semidirect
124. #887C2×D3semidirect
133. #810C2×D3semidirect
137. #809C2×D3semidirect
216. C2×Dic6D12semidirect
444. C32#3043semidirect
504. C3#78864semidirect
505. C3#82551semidirect

Maximal subgroups

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

subgroupindex
C3×#55162
#105950452
C22×#37172
C2×#638272
#105927002
C3×#50022
#105911162
#105905492
#105905362
#825513
#788643