Finite Group Databasebeta

← #11866198

Subgroups — #11866198

Order 1152.

1219 conjugacy classes of subgroups.

The subgroup lattice has 553 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596276C211yesmaximal, characteristic, complemented
2C22×C3×#213C211yesmaximal, characteristic, complemented
3#10594982C211yesmaximal, characteristic, complemented
4C2×#63830C211yesmaximal, characteristic, complemented
5C3×#5215C211yesmaximal, characteristic, complemented
6#10591434C214yesmaximal, complemented
7#10591433C214yesmaximal, complemented
8#10591119C211yesmaximal, characteristic, complemented
9#10591105C211yesmaximal, characteristic, complemented
10#83826—31nomaximal
11#78944—31nomaximal
12C22×C32×D4C2211yescharacteristic
13C2×#3828C2211yescharacteristic
14C22×C3×D12C2211yescharacteristic
15#64162—22no—
16#64149C2212yescomplemented
17#64147—22no—
18#64145C2212yescomplemented
19#64135C2211yescharacteristic
20C2×C3×#213—24no—
21C2×C3×#213C2214yes—
22C3×#926C2211yescharacteristic
23C2×C3×#208C2211yescharacteristic
24C22×C3×C3⋊C8C2211yescharacteristic
25D3×#217—22no—
26#63898C2214yescomplemented
27Dic3×D12—22no—
28#63830—24no—
29C2×#3716C2212yescomplemented
30C2×#3714C2212yescomplemented
31C3×#832C2214yescomplemented
32#63572C2214yescomplemented
33#63567C2212yescomplemented
34#63564C2212yescomplemented
35C22×C3×D8—31no—
36#5805—31no—
37#5805—31no—
38#5805—61no—
39#5798—31no—
40C2×#932—31no—
41C22×#213D311yescharacteristic, complemented
42C2×#908—31no—
43#5521—31no—
44C3×#418—31no—
45#5215D311yescharacteristic, complemented
46#5153—34no—
47#5150—34no—
48#5119—31no—
49#5113—31no—
50#5102—31no—
51#5002—31no—
52#4787—34no—
53#4786—34no—
54C24×C32—21no—
55C23×C3×D3—21no—
56C2×C32×D4—22no—
57C2×C32×D4—21no—
58C2×C32×D4—22no—
59C2×C32×D4C2312yes—
60C22×C32×C4C2311yescharacteristic
61C2×#638—21no—
62C2×#638—24no—
63#3828—22no—
64#3828—22no—
65C2×C4⋊(C3⋊D3)C2311yescharacteristic
66C2×C4×C3⋊D3—21no—
67C2×#634C2311yescharacteristic
68C2×C3×D12—21no—
69C2×C3×D12—22no—
70C2×C3×D12D414yescomplemented
71C2×C3×D12C2312yes—
72C2×D3×Dic3—24no—
73#3757—24no—
74#3757D412yes—
75C4⋊(C3⋊Dic3)D412yes—
76C4×C3⋊Dic3C2312yes—
77C3×#217—21no—
78C3×#213—28no—
79C3×C4⋊Dic3C2312yes—
80C3×C4×Dic3—21no—
81C3×#208—22no—
82C2×C3×C3⋊C8—22no—
83C2×C3×C3⋊C8C2312yes—
84C2×C3×C3⋊C8C2312yes—
85(C2×D3)⋊Dic3—24no—
86#3716—24no—
87#3714—24no—
88#3041—91noSylow
89C22×C3×D4—21no—
90C22×C3×D4—31no—
91C22×C3×D4C2×D311yescharacteristic
92C22×C3×D4C2×D311yescharacteristic
93C2×#235—31no—
94C2×#235—31no—
95C2×#235—61no—
96C22×D12C2×D311yescharacteristic
97C2×C3×D8—34no—
98C2×C3×D8—64no—
99C2×C3×M16—31no—
100C22×C3×C8—31no—
101C3×#117—31no—
102#953—62no—
103#953—62no—
104#953—64no—
105C2×#217—62no—
106#940—32no—
107#940—32no—
108#940—62no—
109#938—62no—
110#938—62no—
111#938—64no—
112#936—32no—
113#936—32no—
114#936—62no—
115D4×Dic3—34no—
116D4×Dic3—62no—
117C2×#214—32no—
118#932—64no—
119C2×#213—24no—
120C2×#213—32no—
121C2×#213C2×D314yes—
122#926—31no—
123#926—31no—
124#926—61no—
125#926C2×D311yescharacteristic
126C2×#208C2×D311yescharacteristic
127C22×C3⋊C8C2×D311yescharacteristic
128#908—64no—
129C2×D24—32no—
130C2×#204—32no—
131#893—34no—
132D3×C22⋊C4—62no—
133C4×D12—62no—
134C3×#102—34no—
135#832C2×D314yescomplemented
136#821—32no—
137#816—32no—
138Dic3⋊C8—34no—
139Dic3⋊C8—34no—
140#810—32no—
141#809—32no—
142C23×C32—22no—
143C23×C32—42no—
144C23×C32—82no—
145C23×C32C2×D411yescharacteristic
146C22×C3⋊D3—21no—
147C22×C3×D3—22no—
148C22×C3×D3—24no—
149C22×C3×D3—82no—
150C32×D4—22no—
151C32×D4—22no—
152C32×D4—42no—
153C2×C32×C4C2×D411yescharacteristic
154C2×C32×C4C2×D412yes—
155C2×C32×C4#4112yes—
156C2×C32×C4C2411yescharacteristic
157#638—42no—
158#638—84no—
159C2×C3⋊Dic3—21no—
160C2×C3⋊Dic3C2×D414yes—
161C4⋊(C3⋊D3)—21no—
162C4⋊(C3⋊D3)—21no—
163C4×C3⋊D3—42no—
164#634—21no—
165#634—21no—
166C2×C3×Dic3—22no—
167C3×D12—24no—
168C3×D12—22no—
169C3×D12C2×D414yes—
170D3×Dic3—84no—
171C3×C3⋊C8—22no—
172C3×C3⋊C8—22no—
173C2×AGL(1,ℤ/8)—91no—
174C22×D8—31no—
175#535—91no—
176#518—91no—
177#463—94no—
178#459—94no—
179#424—91no—
180#418—31no—
181#416—91no—
182C24×C3—22no—
183C24×C3—21no—
184C24×C3—21no—
185C24×C3—61no—
186C23×D3—21no—
187C2×C3×D4—22no—
188C2×C3×D4—22no—
189C2×C3×D4—22no—
190C2×C3×D4—21no—
191C2×C3×D4—21no—
192C2×C3×D4—22no—
193C2×C3×D4—22no—
194C2×C3×D4—22no—
195C2×C3×D4—34no—
196C2×C3×D4—32no—
197C2×C3×D4—42no—
198C2×C3×D4—42no—
199C2×C3×D4—62no—
200C2×C3×D4—61no—
201C2×C3×D4C22×D312yes—
202C2×C3×D4C22×D312yes—
203C22×C3×C4—21no—
204C22×C3×C4C22×D311yescharacteristic
205C22×C3×C4C22×D311yescharacteristic
206C2×#67—64no—
207C2×#67—64no—
208C2×#67—62no—
209C2×#67—61no—
210C2×#67—61no—
211C2×#67—68no—
212C22×Dic3—64no—
213#235—62no—
214#235—62no—
215#235—62no—
216#235—62no—
217#235—122no—
218#235—122no—
219C2×D12—21no—
220C2×D12—22no—
221C2×D12—31no—
222C2×D12—31no—
223C2×D12—61no—
224C2×D12#6714yescomplemented
225C2×D12C22×D312yes—
226C2×C4×D3—62no—
227C2×C4×D3—61no—
228C2×C4×D3—61no—
229C2×C4×D3—64no—
230C2×Dic6—31no—
231C2×Dic6—31no—
232C2×Dic6—61no—
233C3×D8—68no—
234C3×M16—62no—
235C2×C3×C8—32no—
236C2×C3×C8—32no—
237C2×C3×C8—62no—
238C3×C4⋊C4—32no—
239C3×C22⋊C4—61no—
240C3×C42—61no—
241#217—21no—
242#217—32no—
243#217—32no—
244#217—62no—
245#217—64no—
246#217—64no—
247#217—64no—
248#217—68no—
249#214—64no—
250#213—28no—
251#213—64no—
252(C2×D3)⋊C4—64no—
253C4⋊Dic3—32no—
254C4⋊Dic3—32no—
255C4⋊Dic3—62no—
256C4⋊Dic3C22×D312yes—
257C4×Dic3—21no—
258C4×Dic3—32no—
259C4×Dic3—32no—
260C4×Dic3—62no—
261#208—22no—
262C2×C3⋊C8—22no—
263C2×C3⋊C8C22×D312yes—
264C2×C3⋊C8C22×D312yes—
265D24—64no—
266#204—64no—
267C22×C32—22no—
268C22×C32—42no—
269C22×C32—44no—
270C22×C32—84no—
271C22×C32#12112yes—
272C22×C32C22×D411yescharacteristic
273C2×C3⋊D3—41no—
274C2×C3⋊D3—42no—
275C2×C3×D3—24no—
276C2×C3×D3—44no—
277C2×C3×D3—84no—
278C32×C4#12112yes—
279C32×C4C22×D411yescharacteristic
280C32×C4C2×#4111yescharacteristic
281C3⋊Dic3—24no—
282C3⋊Dic3—41no—
283C3×Dic3—42no—
284C2×#41—91no—
285C22×D4—31no—
286C22×D4D3211yescharacteristic
287AGL(1,ℤ/8)—184no—
288C2×SD16—92no—
289C2×D8—34no—
290C2×D8—64no—
291C2×D8—92no—
292C2×M16—31no—
293C22×C8—31no—
294#127—92no—
295#124—92no—
296#121—182no—
297#120—182no—
298C4×D4—94no—
299C4×D4—182no—
300#117—31no—
301#117—91no—
302C2×C22⋊C4—182no—
303C4⋊C8—94no—
304#103—92no—
305#102—34no—
306#102—92no—
307C23×C3—24no—
308C23×C3—22no—
309C23×C3—22no—
310C23×C3—21no—
311C23×C3—44no—
312C23×C3—42no—
313C23×C3—42no—
314C23×C3—62no—
315C23×C3—64no—
316C23×C3—82no—
317C23×C3—82no—
318C23×C3—84no—
319C23×C3—242no—
320C23×C3D3×D411yescharacteristic
321C23×C3D3×D411yescharacteristic
322C22×D3—22no—
323C22×D3—24no—
324C22×D3—62no—
325C22×D3—61no—
326C22×D3—61no—
327C22×D3—82no—
328C3×D4—22no—
329C3×D4—22no—
330C3×D4—22no—
331C3×D4—22no—
332C3×D4—34no—
333C3×D4—42no—
334C3×D4—42no—
335C3×D4—44no—
336C3×D4—42no—
337C3×D4—42no—
338C3×D4—64no—
339C3×D4—62no—
340C2×C3×C4—21no—
341C2×C3×C4—22no—
342C2×C3×C4—22no—
343C2×C3×C4—21no—
344C2×C3×C4—62no—
345C2×C3×C4#23512yes—
346C2×C3×C4D3×D412yes—
347C2×C3×C4D3×D411yescharacteristic
348C2×C3×C4D3×D411yescharacteristic
349C2×C3×C4#23712yes—
350C2×C3×C4C2×#6712yes—
351C2×C3×C4C23×D311yescharacteristic
352C2×C3×C4C23×D311yescharacteristic
353#67—124no—
354#67—122no—
355#67—122no—
356#67—244no—
357#67—244no—
358#67—248no—
359C2×Dic3—22no—
360C2×Dic3—34no—
361C2×Dic3—34no—
362C2×Dic3—64no—
363C2×Dic3—62no—
364C2×Dic3—61no—
365C2×Dic3—61no—
366C2×Dic3—244no—
367D12—24no—
368D12—22no—
369D12—61no—
370D12—61no—
371D12—61no—
372D12—61no—
373D12—121no—
374D12—121no—
375D12C2×#6714yes—
376C4×D3—124no—
377C4×D3—122no—
378C4×D3—122no—
379C4×D3—244no—
380Dic6—61no—
381Dic6—61no—
382Dic6—61no—
383Dic6—61no—
384Dic6—121no—
385Dic6—121no—
386C3×C8—62no—
387C3×C8—62no—
388C3⋊C8—22no—
389C3⋊C8—22no—
390C2×C32—22no—
391C2×C32—82no—
392C2×C32C2×#12111yescharacteristic
393C2×C32#57612yes—
394C3⋊D3—81no—
395C3×D3—44no—
396C24—21no—
397C24—61no—
398#41—182no—
399#41—182no—
400C2×Q8—91no—
401C2×D4—22no—
402C2×D4—22no—
403C2×D4—21no—
404C2×D4—32no—
405C2×D4—34no—
406C2×D4—62no—
407C2×D4—61no—
408C2×D4—91no—
409C2×D4—184no—
410C2×D4—181no—
411C2×D4C2×D3212yes—
412C22×C4—184no—
413C22×C4—181no—
414C22×C4C2×D3211yescharacteristic
415SD16—184no—
416D8—68no—
417D8—184no—
418M16—62no—
419C2×C8—32no—
420C2×C8—32no—
421C2×C8—62no—
422C4⋊C4—32no—
423C4⋊C4—92no—
424C22⋊C4—61no—
425C22⋊C4—92no—
426C22⋊C4—184no—
427C22⋊C4—184no—
428C42—61no—
429C42—92no—
430C22×C3—22no—
431C22×C3—22no—
432C22×C3—21no—
433C22×C3—22no—
434C22×C3—42no—
435C22×C3—48no—
436C22×C3—44no—
437C22×C3—42no—
438C22×C3—44no—
439C22×C3—44no—
440C22×C3—42no—
441C22×C3—64no—
442C22×C3—84no—
443C22×C3—84no—
444C22×C3—88no—
445C22×C3—124no—
446C22×C3—244no—
447C22×C3#88412yes—
448C22×C3#93912yes—
449C22×C3C2×D3×D411yescharacteristic
450C22×C3C2×D3×D411yescharacteristic
451C2×D3—24no—
452C2×D3—44no—
453C2×D3—84no—
454C2×D3—122no—
455C2×D3—124no—
456C2×D3—121no—
457C2×D3—122no—
458C2×D3—122no—
459C2×D3—121no—
460C3×C4—21no—
461C3×C4—21no—
462C3×C4—22no—
463C3×C4—122no—
464C3×C4#88412yes—
465C3×C4#93912yes—
466C3×C4C2×#23511yescharacteristic
467C3×C4C2×D3×D411yescharacteristic
468C3×C4C2×#23711yescharacteristic
469C3×C4C22×#6711yescharacteristic
470Dic3—42no—
471Dic3—64no—
472Dic3—64no—
473Dic3—124no—
474Dic3—122no—
475Dic3—121no—
476Dic3—121no—
477C32#304111yescharacteristic, complemented, Sylow
478C23—22no—
479C23—42no—
480C23—62no—
481C23—64no—
482C23—82no—
483C23—181no—
484C23—242no—
485C23#381111yescharacteristic
486Q8—181no—
487Q8—181no—
488D4—22no—
489D4—22no—
490D4—34no—
491D4—42no—
492D4—62no—
493D4—64no—
494D4—181no—
495D4—181no—
496D4—362no—
497D4—724no—
498C2×C4—62no—
499C2×C4—94no—
500C2×C4—181no—
501C2×C4—362no—
502C2×C4—724no—
503C2×C4#380412yes—
504C2×C4D3×#6712yes—
505C2×C4#381111yescharacteristic
506C2×C4C22×D3211yescharacteristic
507C8—62no—
508C8—62no—
509C2×C3—22no—
510C2×C3—22no—
511C2×C3—22no—
512C2×C3—21no—
513C2×C3—42no—
514C2×C3—84no—
515C2×C3—82no—
516C2×C3—82no—
517C2×C3—124no—
518C2×C3C2×#88411yescharacteristic
519C2×C3#575712yes—
520C2×C3#577412yes—
521C2×C3C2×#93911yescharacteristic
522D3—44no—
523D3—242no—
524D3—241no—
525D3—241no—
526C22—22no—
527C22—44no—
528C22—42no—
529C22—64no—
530C22—84no—
531C22—124no—
532C22—244no—
533C22—362no—
534C22—361no—
535C22#6397112yes—
536C22C2×#381111yescharacteristic
537C4—122no—
538C4—184no—
539C4—361no—
540C4#6397112yes—
541C4C2×#380411yescharacteristic
542C4C2×D3×#6711yescharacteristic
543C3—21no—
544C3#7894411yescharacteristic, complemented
545C3#8382611yescharacteristic, complemented
546C2—22no—
547C2—82no—
548C2—124no—
549C2—721no—
550C2#1059510212yes—
551C2C2×#6397111yescharacteristic
subgroupG/H
centerC22C2×#3811
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC22×C32×D4C22
socleC22×C32C22×D4
hypercenterC22×D4D32
hypocenterC32#3041
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
1. #10596276C2semidirect
2. C22×C3×#213C2semidirect
3. #10594982C2semidirect
4. C2×#63830C2semidirect
5. C3×#5215C2semidirect
6. #10591434C2semidirect
7. #10591433C2semidirect
8. #10591119C2semidirect
9. #10591105C2semidirect
16. #64149C22semidirect
18. #64145C22semidirect
26. #63898C22semidirect
29. C2×#3716C22semidirect
30. C2×#3714C22semidirect
31. C3×#832C22semidirect
32. #63572C22semidirect
33. #63567C22semidirect
34. #63564C22semidirect
41. C22×#213D3semidirect
45. #5215D3semidirect
70. C2×C3×D12D4semidirect
135. #832C2×D3semidirect
224. C2×D12#67semidirect
477. C32#3041semidirect
544. C3#78944semidirect
545. C3#83826semidirect

Maximal subgroups

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

subgroupindex
#105962762
C22×C3×#2132
#105949822
C2×#638302
C3×#52152
#105914342
#105914332
#105911192
#105911052
#838263
#789443