Finite Group Databasebeta

← #11866213

Subgroups — #11866213

Order 1152.

1147 conjugacy classes of subgroups.

The subgroup lattice has 532 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5521C211yesmaximal, characteristic, complemented
2#10595045C211yesmaximal, characteristic, complemented
3C22×#3714C211yesmaximal, characteristic, complemented
4C2×#63823C211yesmaximal, characteristic, complemented
5#10592700C211yesmaximal, characteristic, complemented
6C3×#5002C211yesmaximal, characteristic, complemented
7#10591116C211yesmaximal, characteristic, complemented
8#10590547C214yesmaximal, complemented
9#10590534C214yesmaximal, complemented
10#82540—31nomaximal
11#78862—31nomaximal
12C22×C4⋊(C3⋊D3)C2211yescharacteristic
13C2×C3×#235C2211yescharacteristic
14C22×C3×D12C2211yescharacteristic
15C32×#117C2211yescharacteristic
16C2×#3748C2211yescharacteristic
17C3×#926C2211yescharacteristic
18C22×C3×C3⋊C8C2211yescharacteristic
19C3×#893C2214yescomplemented
20C3×D3×C22⋊C4—22no—
21C3×C4×D12—22no—
22#63981—22no—
23#63911C2212yescomplemented
24#63909—22no—
25#63864C2212yescomplemented
26C2×#3715C2212yescomplemented
27C2×#3714—24no—
28C2×#3714C2214yes—
29#63823—24no—
30C2×#3713C2212yescomplemented
31#63636C2214yescomplemented
32C3×#810C2212yescomplemented
33C3×#809C2212yescomplemented
34Dic3⋊(C3⋊C8)C2214yescomplemented
35C3×#518—31no—
36#5830—31no—
37C2×#949—31no—
38C2×#932—31no—
39C22×#213—31no—
40C22×D24—31no—
41#5525—31no—
42#5521D311yescharacteristic, complemented
43C3×#416—31no—
44#5102—31no—
45#5016—34no—
46#5015—34no—
47#5002D311yescharacteristic, complemented
48#5001—31no—
49#5001—31no—
50#5001—61no—
51#4999—31no—
52#4819—34no—
53#4786—34no—
54C23×C3⋊D3—21no—
55C23×C3×D3—21no—
56C22×C32×C4C2311yescharacteristic
57C2×C4⋊(C3⋊D3)—22no—
58C2×C4⋊(C3⋊D3)—22no—
59C2×C4⋊(C3⋊D3)—21no—
60C2×C4⋊(C3⋊D3)C2312yes—
61C2×C3×#67—21no—
62C3×#235—22no—
63C3×#235—22no—
64C2×C3×D12—21no—
65C2×C3×D12—22no—
66C2×C3×D12D414yescomplemented
67C2×C3×D12C2311yescharacteristic
68C2×C3×D12C2312yes—
69C2×C3×C4×D3—21no—
70C2×C3×C4×D3—24no—
71C2×C3×Dic6C2311yescharacteristic
72C2×#626—24no—
73C32×C4⋊C4C2312yes—
74C32×C22⋊C4—21no—
75C32×C42—21no—
76#3748—22no—
77C2×C3⋊(C3⋊C8)C2312yes—
78C3×#217D412yes—
79C3×(C2×D3)⋊C4—24no—
80C3×C4⋊Dic3D412yes—
81C3×C4×Dic3C2312yes—
82C2×C3×C3⋊C8—22no—
83C2×C3×C3⋊C8C2312yes—
84#3722—24no—
85#3715—24no—
86#3714—28no—
87#3713—24no—
88#3041—91noSylow
89C2×C3×#41—31no—
90C22×C3×D4—31no—
91C2×#235C2×D311yescharacteristic
92C22×D12—31no—
93C22×D12—31no—
94C22×D12—61no—
95C22×D12C2×D311yescharacteristic
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#947—32no—
106C2×#215—32no—
107#940—32no—
108#937—62no—
109C2×#214—32no—
110#932—64no—
111C2×#213—32no—
112C2×#213—32no—
113C2×#213—34no—
114C2×#213—64no—
115#930—62no—
116#926C2×D311yescharacteristic
117C2×#208—31no—
118C2×#208—31no—
119C2×#208—61no—
120C22×C3⋊C8C2×D311yescharacteristic
121C2×D24—34no—
122C2×D24—64no—
123#895—62no—
124#893C2×D314yescomplemented
125#882—62no—
126D3×C22⋊C4—22no—
127#875—32no—
128#874—32no—
129C4×D12—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—22no—
144C22×C3×D3—24no—
145C22×C3×D3—21no—
146C22×C3×D3—82no—
147C2×C32×C4—22no—
148C2×C32×C4C2×D412yes—
149C2×C32×C4C2×D411yescharacteristic
150C2×C32×C4#4112yes—
151C2×C32×C4C2411yescharacteristic
152C4⋊(C3⋊D3)—22no—
153C4⋊(C3⋊D3)—22no—
154C4⋊(C3⋊D3)—42no—
155C3×#67—42no—
156C2×C3×Dic3—21no—
157C2×C3×Dic3C2×D414yes—
158C3×D12—24no—
159C3×D12—21no—
160C3×D12—22no—
161C3×D12—21no—
162C3×D12C2×D414yes—
163C3×C4×D3—42no—
164C3×C4×D3—84no—
165C3×Dic6—21no—
166C3×Dic6—21no—
167#626—84no—
168C3⋊(C3⋊C8)—22no—
169C3×C3⋊C8—22no—
170C2×AGL(1,ℤ/8)—91no—
171C22×D8—91no—
172#535—91no—
173#518—31no—
174#463—94no—
175#459—94no—
176#424—91no—
177#418—91no—
178#416—31no—
179C24×C3—61no—
180C23×D3—21no—
181C23×D3—61no—
182C23×D3—61no—
183C23×D3—121no—
184C3×#41—62no—
185C3×#41—62no—
186C2×C3×Q8—31no—
187C2×C3×D4—34no—
188C2×C3×D4—32no—
189C2×C3×D4—31no—
190C2×C3×D4—61no—
191C2×C3×D4—62no—
192C2×C3×D4—61no—
193C22×C3×C4—21no—
194C22×C3×C4—64no—
195C22×C3×C4—61no—
196C22×C3×C4C22×D311yescharacteristic
197C22×C3×C4C22×D311yescharacteristic
198C2×#67—21no—
199C2×#67—64no—
200#235—22no—
201#235—22no—
202C2×D12—22no—
203C2×D12—21no—
204C2×D12—32no—
205C2×D12—32no—
206C2×D12—62no—
207C2×D12—64no—
208C2×D12—62no—
209C2×D12—62no—
210C2×D12—62no—
211C2×D12—62no—
212C2×D12—61no—
213C2×D12—61no—
214C2×D12—64no—
215C2×D12—122no—
216C2×D12—121no—
217C2×D12D1214yescomplemented
218C2×D12C22×D311yescharacteristic
219C2×D12C22×D312yes—
220C2×C4×D3—21no—
221C2×C4×D3—24no—
222C2×Dic6C22×D311yescharacteristic
223C2×C3×C8—32no—
224C2×C3×C8—62no—
225C3×C4⋊C4—22no—
226C3×C4⋊C4—32no—
227C3×C4⋊C4C22×D312yes—
228C3×C4⋊C4C22×D312yes—
229C3×C22⋊C4—21no—
230C3×C22⋊C4—21no—
231C3×C22⋊C4—32no—
232C3×C22⋊C4—41no—
233C3×C22⋊C4—64no—
234C3×C42—21no—
235C3×C42—21no—
236C3×C42—32no—
237C3×C42—41no—
238#217#6712yes—
239#215—64no—
240#214—64no—
241#213—68no—
242#213—64no—
243#213—64no—
244(C2×D3)⋊C4—24no—
245(C2×D3)⋊C4—64no—
246(C2×D3)⋊C4—64no—
247C4⋊Dic3#6712yes—
248C4×Dic3C22×D312yes—
249#208—62no—
250#208—62no—
251#208—122no—
252C2×C3⋊C8—22no—
253C2×C3⋊C8—32no—
254C2×C3⋊C8—32no—
255C2×C3⋊C8—62no—
256C2×C3⋊C8C22×D312yes—
257D24—68no—
258C22×C32—22no—
259C22×C32#12112yes—
260C22×C32C22×D411yescharacteristic
261C2×C3⋊D3—42no—
262C2×C3⋊D3—44no—
263C2×C3⋊D3—84no—
264C2×C3×D3—24no—
265C2×C3×D3—44no—
266C2×C3×D3—41no—
267C2×C3×D3—42no—
268C2×C3×D3—84no—
269C32×C4—42no—
270C32×C4#12112yes—
271C32×C4C22×D411yescharacteristic
272C32×C4C2×#4111yescharacteristic
273C3×Dic3—24no—
274C3×Dic3—41no—
275C2×#41—31no—
276C22×D4—31no—
277C22×D4—91no—
278AGL(1,ℤ/8)—184no—
279C2×SD16—92no—
280C2×D8—94no—
281C2×D8—92no—
282C2×D8—184no—
283C2×M16—91no—
284C22×C8—31no—
285#127—92no—
286#124—92no—
287#121—182no—
288#120—182no—
289C4×D4—34no—
290C4×D4—62no—
291#117—31no—
292#117D3211yescharacteristic
293C2×C22⋊C4—62no—
294C4⋊C8—94no—
295#103—32no—
296#102—32no—
297#102—94no—
298C23×C3—21no—
299C23×C3—62no—
300C23×C3—64no—
301C23×C3—61no—
302C23×C3—242no—
303C23×C3D3×D411yescharacteristic
304C23×C3C2×#6711yescharacteristic
305C22×D3—22no—
306C22×D3—24no—
307C22×D3—21no—
308C22×D3—62no—
309C22×D3—62no—
310C22×D3—82no—
311C22×D3—122no—
312C22×D3—124no—
313C22×D3—122no—
314C22×D3—122no—
315C22×D3—242no—
316C22×D3—242no—
317C22×D3—244no—
318C3×Q8—61no—
319C3×Q8—61no—
320C3×D4—34no—
321C3×D4—64no—
322C3×D4—61no—
323C3×D4—62no—
324C3×D4—61no—
325C3×D4—122no—
326C2×C3×C4—22no—
327C2×C3×C4—22no—
328C2×C3×C4—21no—
329C2×C3×C4—22no—
330C2×C3×C4—22no—
331C2×C3×C4—21no—
332C2×C3×C4—34no—
333C2×C3×C4—42no—
334C2×C3×C4—61no—
335C2×C3×C4—122no—
336C2×C3×C4—244no—
337C2×C3×C4C2×D1212yes—
338C2×C3×C4#23512yes—
339C2×C3×C4#23512yes—
340C2×C3×C4D3×D412yes—
341C2×C3×C4D3×D411yescharacteristic
342C2×C3×C4C2×#6711yescharacteristic
343C2×C3×C4C23×D311yescharacteristic
344C2×C3×C4C23×D311yescharacteristic
345#67—42no—
346#67—244no—
347C2×Dic3—21no—
348C2×Dic3C2×#6714yes—
349D12—24no—
350D12—22no—
351D12—21no—
352D12—21no—
353D12—64no—
354D12—62no—
355D12—62no—
356D12—62no—
357D12—62no—
358D12—122no—
359D12—124no—
360D12—122no—
361D12—122no—
362D12—244no—
363D12C2×D1214yes—
364C4×D3—42no—
365C4×D3—84no—
366Dic6—21no—
367Dic6—21no—
368C3×C8—62no—
369C3⋊C8—22no—
370C3⋊C8—62no—
371C3⋊C8—62no—
372C3⋊C8—122no—
373C2×C32—22no—
374C2×C32C2×#12111yescharacteristic
375C2×C32#57612yes—
376C3⋊D3—82no—
377C3×D3—44no—
378C3×D3—81no—
379C24—61no—
380C24—181no—
381#41—62no—
382#41—62no—
383C2×Q8—31no—
384C2×D4—32no—
385C2×D4—31no—
386C2×D4—34no—
387C2×D4—61no—
388C2×D4—62no—
389C2×D4—61no—
390C2×D4—92no—
391C2×D4—184no—
392C2×D4—182no—
393C2×D4—182no—
394C2×D4—181no—
395C22×C4—64no—
396C22×C4—61no—
397C22×C4C2×D3211yescharacteristic
398SD16—184no—
399D8—188no—
400D8—184no—
401M16—182no—
402C2×C8—32no—
403C2×C8—62no—
404C2×C8—92no—
405C4⋊C4—32no—
406C4⋊C4C2×D3212yes—
407C22⋊C4—21no—
408C22⋊C4—32no—
409C22⋊C4—64no—
410C22⋊C4—184no—
411C42—21no—
412C42—32no—
413C22×C3—22no—
414C22×C3—22no—
415C22×C3—21no—
416C22×C3—22no—
417C22×C3—42no—
418C22×C3—64no—
419C22×C3—124no—
420C22×C3—121no—
421C22×C3—122no—
422C22×C3—244no—
423C22×C3#88412yes—
424C22×C3#93012yes—
425C22×C3C2×D3×D411yescharacteristic
426C22×C3C22×#6711yescharacteristic
427C2×D3—24no—
428C2×D3—44no—
429C2×D3—41no—
430C2×D3—42no—
431C2×D3—84no—
432C2×D3—124no—
433C2×D3—122no—
434C2×D3—124no—
435C2×D3—122no—
436C2×D3—124no—
437C2×D3—244no—
438C2×D3—244no—
439C2×D3—244no—
440C2×D3—248no—
441C3×C4—21no—
442C3×C4—21no—
443C3×C4—22no—
444C3×C4—42no—
445C3×C4—42no—
446C3×C4—64no—
447C3×C4—82no—
448C3×C4—121no—
449C3×C4#88412yes—
450C3×C4#93012yes—
451C3×C4C22×D1211yescharacteristic
452C3×C4C2×#23511yescharacteristic
453C3×C4C2×#23511yescharacteristic
454C3×C4C2×D3×D411yescharacteristic
455Dic3—24no—
456Dic3—41no—
457C32#304111yescharacteristic, complemented, Sylow
458C23—62no—
459C23—64no—
460C23—61no—
461C23—182no—
462C23—242no—
463C23—362no—
464C23—722no—
465C23D3×#6711yescharacteristic
466Q8—61no—
467Q8—61no—
468D4—34no—
469D4—62no—
470D4—61no—
471D4—61no—
472D4—64no—
473D4—122no—
474D4—182no—
475D4—182no—
476D4—362no—
477D4—724no—
478C2×C4—22no—
479C2×C4—34no—
480C2×C4—61no—
481C2×C4—122no—
482C2×C4—244no—
483C2×C4#379812yes—
484C2×C4D3×D1212yes—
485C2×C4D3×#6711yescharacteristic
486C2×C4C22×D3211yescharacteristic
487C8—62no—
488C8—182no—
489C2×C3—22no—
490C2×C3—22no—
491C2×C3—22no—
492C2×C3—21no—
493C2×C3—42no—
494C2×C3—124no—
495C2×C3—241no—
496C2×C3C2×#88411yescharacteristic
497C2×C3#576912yes—
498C2×C3C2×#93011yescharacteristic
499C2×C3#583512yes—
500D3—44no—
501D3—81no—
502D3—244no—
503D3—242no—
504D3—242no—
505C22—22no—
506C22—64no—
507C22—124no—
508C22—122no—
509C22—121no—
510C22—244no—
511C22—364no—
512C22—362no—
513C22—724no—
514C22#6390612yes—
515C22C2×D3×#6711yescharacteristic
516C4—42no—
517C4—64no—
518C4—121no—
519C4#6390612yes—
520C4C2×#379811yescharacteristic
521C4C2×D3×D1211yescharacteristic
522C3—21no—
523C3#7886211yescharacteristic, complemented
524C3#8254011yescharacteristic, complemented
525C2—22no—
526C2—124no—
527C2—241no—
528C2—722no—
529C2C2×#6390611yescharacteristic
530C2#1059545612yes—
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#117C22
socleC22×C32C22×D4
hypercenter#117D32
hypocenterC32#3041
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. #10595045C2semidirect
3. C22×#3714C2semidirect
4. C2×#63823C2semidirect
5. #10592700C2semidirect
6. C3×#5002C2semidirect
7. #10591116C2semidirect
8. #10590547C2semidirect
9. #10590534C2semidirect
19. C3×#893C22semidirect
23. #63911C22semidirect
25. #63864C22semidirect
26. C2×#3715C22semidirect
30. C2×#3713C22semidirect
31. #63636C22semidirect
32. C3×#810C22semidirect
33. C3×#809C22semidirect
34. Dic3⋊(C3⋊C8)C22semidirect
42. #5521D3semidirect
47. #5002D3semidirect
66. C2×C3×D12D4semidirect
124. #893C2×D3semidirect
133. #810C2×D3semidirect
137. #809C2×D3semidirect
217. C2×D12D12semidirect
457. C32#3041semidirect
523. C3#78862semidirect
524. C3#82540semidirect

Maximal subgroups

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

subgroupindex
C3×#55212
#105950452
C22×#37142
C2×#638232
#105927002
C3×#50022
#105911162
#105905472
#105905342
#825403
#788623