Finite Group Databasebeta

← #11866205

Subgroups — #11866205

Order 1152.

1221 conjugacy classes of subgroups.

The subgroup lattice has 539 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596269C211yesmaximal, characteristic, complemented
2C2×C3×#932C211yesmaximal, characteristic, complemented
3C22×C3×#213C211yesmaximal, characteristic, complemented
4#10595040C211yesmaximal, characteristic, complemented
5#10591486C214yesmaximal, complemented
6#10591476C214yesmaximal, complemented
7#10591119C211yesmaximal, characteristic, complemented
8#10591086C211yesmaximal, characteristic, complemented
9#10591084C211yesmaximal, characteristic, complemented
10#83934—31nomaximal
11#83826—31nomaximal
12C22×C32×D4C2211yescharacteristic
13C2×C3×#235C2211yescharacteristic
14C22×C3×D12C2211yescharacteristic
15C2×#3757—22no—
16D4×C3⋊Dic3—22no—
17D4×C3⋊Dic3C2214yescomplemented
18#64135C2211yescharacteristic
19#64135C2211yescharacteristic
20C2×C3×#214C2212yescomplemented
21C3×#932—24no—
22C2×C3×#213—24no—
23C2×C3×#213C2214yes—
24C2×C3×#213C2212yescomplemented
25C2×C3×#208C2211yescharacteristic
26C22×C3×C3⋊C8C2211yescharacteristic
27#63976—22no—
28#63914C2212yescomplemented
29#63908—22no—
30#63863C2212yescomplemented
31#63572C2214yescomplemented
32#63566C2212yescomplemented
33#63563C2212yescomplemented
34#63563C2214yescomplemented
35C2×C3×AGL(1,ℤ/8)—31no—
36C22×C3×D8—31no—
37#5830—31no—
38#5805—31no—
39#5798—31no—
40#5798—31no—
41#5798—61no—
42C2×#932D311yescharacteristic, complemented
43C22×#213D311yescharacteristic, complemented
44#5233—31no—
45#5215—31no—
46#5165—34no—
47#5153—34no—
48#5150—34no—
49#5150—34no—
50#5131—31no—
51#5119—31no—
52#5113—31no—
53#5102—31no—
54C24×C32—21no—
55C23×C3×D3—21no—
56C2×C32×D4—21no—
57C2×C32×D4—22no—
58C2×C32×D4D414yescomplemented
59C2×C32×D4C2312yes—
60C22×C32×C4C2311yescharacteristic
61C22×C3⋊Dic3—24no—
62C2×C3×#67—21no—
63C3×#235—22no—
64C3×#235—22no—
65C2×C3×D12—22no—
66C2×C3×D12—22no—
67C2×C3×D12—21no—
68C2×C3×D12C2312yes—
69C2×C3×D12C2311yescharacteristic
70C2×C3×C4×D3—21no—
71C2×C3×Dic6C2311yescharacteristic
72C2×#625—24no—
73#3757—21no—
74#3757—24no—
75#3757D412yes—
76C4⋊(C3⋊Dic3)D412yes—
77C4⋊(C3⋊Dic3)C2312yes—
78C4×C3⋊Dic3—21no—
79C4×C3⋊Dic3C2312yes—
80C3×#214—24no—
81C3×#213—28no—
82C3×#213—24no—
83C3×#208—22no—
84C2×C3×C3⋊C8—22no—
85C2×C3×C3⋊C8C2312yes—
86C2×C3×C3⋊C8C2312yes—
87(C2×D3)⋊Dic3—24no—
88#3041—91noSylow
89C2×C3×#41—31no—
90C22×C3×D4—21no—
91C22×C3×D4—31no—
92C22×C3×D4C2×D311yescharacteristic
93C22×C3×D4C2×D311yescharacteristic
94C2×#235C2×D311yescharacteristic
95C22×D12C2×D311yescharacteristic
96C3×AGL(1,ℤ/8)—64no—
97C2×C3×SD16—32no—
98C2×C3×D8—34no—
99C2×C3×D8—32no—
100C2×C3×D8—64no—
101C2×C3×M16—31no—
102C22×C3×C8—31no—
103#953—62no—
104C2×#217—62no—
105C2×#217—62no—
106C2×#217—64no—
107#947—32no—
108#940—32no—
109#940—32no—
110#938—62no—
111#937—62no—
112#936—32no—
113D4×Dic3—34no—
114D4×Dic3—34no—
115D4×Dic3—64no—
116D4×Dic3—62no—
117D4×Dic3—62no—
118D4×Dic3—64no—
119C2×#214C2×D312yescomplemented
120#932—24no—
121C2×#213—24no—
122C2×#213C2×D314yes—
123C2×#213C2×D312yescomplemented
124#930—62no—
125#926—31no—
126#926—31no—
127#926—31no—
128#926—31no—
129#926—61no—
130#926—61no—
131C2×#208C2×D311yescharacteristic
132C22×C3⋊C8C2×D311yescharacteristic
133#835—32no—
134#832—32no—
135#832—34no—
136#821—34no—
137#821—32no—
138#816—32no—
139Dic3⋊C8—34no—
140Dic3⋊C8—34no—
141C23×C32—22no—
142C23×C32—24no—
143C23×C32—82no—
144C23×C32C2×D411yescharacteristic
145C22×C3×D3—22no—
146C22×C3×D3—21no—
147C22×C3×D3—42no—
148C22×C3×D3—82no—
149C32×D4—24no—
150C32×D4—22no—
151C32×D4C2×D414yes—
152C2×C32×C4C2×D411yescharacteristic
153C2×C32×C4C2×D412yes—
154C2×C32×C4#4112yes—
155C2×C32×C4C2411yescharacteristic
156C2×C3⋊Dic3—22no—
157C2×C3⋊Dic3—84no—
158C2×C3⋊Dic3C2×D414yes—
159C3×#67—42no—
160C2×C3×Dic3—21no—
161C3×D12—22no—
162C3×D12—21no—
163C3×D12—22no—
164C3×D12—21no—
165C3×D12—42no—
166C3×C4×D3—42no—
167C3×Dic6—21no—
168C3×Dic6—21no—
169#625—84no—
170C3×C3⋊C8—22no—
171C3×C3⋊C8—22no—
172C2×AGL(1,ℤ/8)—31no—
173C22×D8—31no—
174#535—91no—
175#518—91no—
176#463—94no—
177#459—94no—
178#424—91no—
179#418—91no—
180#416—91no—
181C24×C3—22no—
182C24×C3—21no—
183C24×C3—21no—
184C24×C3—61no—
185C23×D3—21no—
186C3×#41—62no—
187C3×#41—62no—
188C2×C3×Q8—31no—
189C2×C3×D4—22no—
190C2×C3×D4—24no—
191C2×C3×D4—21no—
192C2×C3×D4—21no—
193C2×C3×D4—22no—
194C2×C3×D4—22no—
195C2×C3×D4—24no—
196C2×C3×D4—22no—
197C2×C3×D4—32no—
198C2×C3×D4—31no—
199C2×C3×D4—61no—
200C2×C3×D4—61no—
201C2×C3×D4—62no—
202C2×C3×D4—62no—
203C2×C3×D4#6714yescomplemented
204C2×C3×D4#6714yescomplemented
205C2×C3×D4C22×D312yes—
206C2×C3×D4C22×D312yes—
207C22×C3×C4—21no—
208C22×C3×C4—61no—
209C22×C3×C4C22×D311yescharacteristic
210C22×C3×C4C22×D311yescharacteristic
211C2×#67—21no—
212C2×#67—64no—
213C2×#67—64no—
214C22×Dic3—64no—
215C22×Dic3—64no—
216C22×Dic3—68no—
217#235—22no—
218#235—22no—
219C2×D12—22no—
220C2×D12—22no—
221C2×D12—21no—
222C2×D12C22×D312yes—
223C2×D12C22×D311yescharacteristic
224C2×C4×D3—21no—
225C2×Dic6C22×D311yescharacteristic
226C3×SD16—64no—
227C3×D8—68no—
228C3×D8—64no—
229C3×M16—62no—
230C2×C3×C8—32no—
231C2×C3×C8—32no—
232C2×C3×C8—62no—
233#217—32no—
234#217—32no—
235#217—62no—
236#217—64no—
237#217—64no—
238#217—64no—
239#217—62no—
240#217—68no—
241#217—61no—
242#217—61no—
243#214—24no—
244#213—28no—
245#213—24no—
246(C2×D3)⋊C4—64no—
247C4⋊Dic3—32no—
248C4⋊Dic3—32no—
249C4⋊Dic3—32no—
250C4⋊Dic3—32no—
251C4⋊Dic3—62no—
252C4⋊Dic3—62no—
253C4×Dic3—32no—
254C4×Dic3—32no—
255C4×Dic3—62no—
256C4×Dic3—62no—
257C4×Dic3—61no—
258C4×Dic3—61no—
259#208—22no—
260C2×C3⋊C8—22no—
261C2×C3⋊C8C22×D312yes—
262C2×C3⋊C8C22×D312yes—
263C22×C32—24no—
264C22×C32—22no—
265C22×C32—44no—
266C22×C32—84no—
267C22×C32#12112yes—
268C22×C32C22×D411yescharacteristic
269C2×C3×D3—41no—
270C2×C3×D3—42no—
271C2×C3×D3—42no—
272C2×C3×D3—44no—
273C2×C3×D3—84no—
274C32×C4#12112yes—
275C32×C4C22×D411yescharacteristic
276C32×C4C2×#4111yescharacteristic
277C3⋊Dic3—24no—
278C3⋊Dic3—42no—
279C3×Dic3—41no—
280C2×#41—31no—
281C22×D4—31no—
282C22×D4D3211yescharacteristic
283AGL(1,ℤ/8)—64no—
284C2×SD16—32no—
285C2×D8—34no—
286C2×D8—32no—
287C2×D8—64no—
288C2×M16—31no—
289C22×C8—31no—
290#127—92no—
291#124—92no—
292#121—182no—
293#120—182no—
294C4×D4—94no—
295C4×D4—182no—
296#117—91no—
297#117—91no—
298C2×C22⋊C4—182no—
299C4⋊C8—94no—
300#103—92no—
301#102—92no—
302#102—94no—
303C23×C3—24no—
304C23×C3—28no—
305C23×C3—22no—
306C23×C3—22no—
307C23×C3—24no—
308C23×C3—24no—
309C23×C3—21no—
310C23×C3—62no—
311C23×C3—61no—
312C23×C3—82no—
313C23×C3—82no—
314C23×C3—84no—
315C23×C3—122no—
316C23×C3—242no—
317C23×C3D3×D411yescharacteristic
318C23×C3D3×D411yescharacteristic
319C22×D3—22no—
320C22×D3—21no—
321C22×D3—42no—
322C22×D3—82no—
323C3×Q8—61no—
324C3×Q8—61no—
325C3×D4—24no—
326C3×D4—28no—
327C3×D4—24no—
328C3×D4—24no—
329C3×D4—22no—
330C3×D4—22no—
331C3×D4—24no—
332C3×D4—62no—
333C3×D4—61no—
334C3×D4—62no—
335C3×D4—61no—
336C3×D4—122no—
337C3×D4—122no—
338C3×D4C2×#6714yes—
339C3×D4C2×#6714yes—
340C2×C3×C4—21no—
341C2×C3×C4—22no—
342C2×C3×C4—22no—
343C2×C3×C4—21no—
344C2×C3×C4—61no—
345C2×C3×C4—122no—
346C2×C3×C4D3×D411yescharacteristic
347C2×C3×C4D3×D411yescharacteristic
348C2×C3×C4#23712yes—
349C2×C3×C4#23712yes—
350C2×C3×C4C2×#6712yes—
351C2×C3×C4C2×#6712yes—
352C2×C3×C4C23×D311yescharacteristic
353C2×C3×C4C23×D311yescharacteristic
354#67—42no—
355#67—244no—
356#67—244no—
357C2×Dic3—21no—
358C2×Dic3—34no—
359C2×Dic3—34no—
360C2×Dic3—64no—
361C2×Dic3—64no—
362C2×Dic3—62no—
363C2×Dic3—62no—
364C2×Dic3—244no—
365C2×Dic3—244no—
366C2×Dic3—248no—
367D12—22no—
368D12—21no—
369D12—22no—
370D12—21no—
371D12—42no—
372C4×D3—42no—
373Dic6—21no—
374Dic6—21no—
375C3×C8—62no—
376C3×C8—62no—
377C3⋊C8—22no—
378C3⋊C8—22no—
379C2×C32—22no—
380C2×C32—44no—
381C2×C32C2×#12111yescharacteristic
382C2×C32#57612yes—
383C3×D3—81no—
384C3×D3—82no—
385C24—21no—
386C24—61no—
387#41—62no—
388#41—62no—
389C2×Q8—31no—
390C2×D4—22no—
391C2×D4—21no—
392C2×D4—32no—
393C2×D4—31no—
394C2×D4—61no—
395C2×D4—62no—
396C2×D4—62no—
397C2×D4—61no—
398C2×D4—184no—
399C2×D4#62514yescomplemented
400C2×D4C2×D3212yes—
401C22×C4—61no—
402C22×C4—184no—
403C22×C4C2×D3211yescharacteristic
404SD16—64no—
405D8—68no—
406D8—64no—
407M16—62no—
408C2×C8—32no—
409C2×C8—32no—
410C2×C8—62no—
411C4⋊C4—92no—
412C4⋊C4—92no—
413C22⋊C4—92no—
414C22⋊C4—184no—
415C22⋊C4—184no—
416C22⋊C4—181no—
417C42—92no—
418C42—181no—
419C22×C3—22no—
420C22×C3—22no—
421C22×C3—28no—
422C22×C3—24no—
423C22×C3—24no—
424C22×C3—21no—
425C22×C3—22no—
426C22×C3—42no—
427C22×C3—48no—
428C22×C3—44no—
429C22×C3—44no—
430C22×C3—84no—
431C22×C3—84no—
432C22×C3—88no—
433C22×C3—122no—
434C22×C3—124no—
435C22×C3—121no—
436C22×C3—122no—
437C22×C3—244no—
438C22×C3#93912yes—
439C22×C3#93912yes—
440C22×C3C2×D3×D411yescharacteristic
441C22×C3C2×D3×D411yescharacteristic
442C2×D3—44no—
443C2×D3—42no—
444C2×D3—41no—
445C2×D3—42no—
446C2×D3—84no—
447C3×C4—21no—
448C3×C4—21no—
449C3×C4—22no—
450C3×C4—121no—
451C3×C4#93912yes—
452C3×C4#93912yes—
453C3×C4C2×#23711yescharacteristic
454C3×C4C2×#23711yescharacteristic
455C3×C4C22×#6711yescharacteristic
456C3×C4C22×#6711yescharacteristic
457Dic3—41no—
458Dic3—64no—
459Dic3—64no—
460Dic3—124no—
461Dic3—124no—
462Dic3—122no—
463Dic3—122no—
464C32#304111yescharacteristic, complemented, Sylow
465C23—22no—
466C23—24no—
467C23—62no—
468C23—61no—
469C23—82no—
470C23—122no—
471C23—242no—
472C23#381111yescharacteristic
473Q8—61no—
474Q8—61no—
475D4—22no—
476D4—24no—
477D4—62no—
478D4—61no—
479D4—62no—
480D4—61no—
481D4—122no—
482D4—122no—
483D4—724no—
484D4C2×#62514yes—
485C2×C4—61no—
486C2×C4—94no—
487C2×C4—122no—
488C2×C4—182no—
489C2×C4—724no—
490C2×C4#380512yes—
491C2×C4C2×#62512yes—
492C2×C4#381111yescharacteristic
493C2×C4C22×D3211yescharacteristic
494C8—62no—
495C8—62no—
496C2×C3—22no—
497C2×C3—22no—
498C2×C3—22no—
499C2×C3—21no—
500C2×C3—42no—
501C2×C3—48no—
502C2×C3—44no—
503C2×C3—44no—
504C2×C3—241no—
505C2×C3—242no—
506C2×C3#575712yes—
507C2×C3#577412yes—
508C2×C3C2×#93911yescharacteristic
509C2×C3C2×#93911yescharacteristic
510D3—82no—
511D3—81no—
512C22—22no—
513C22—24no—
514C22—44no—
515C22—84no—
516C22—122no—
517C22—124no—
518C22—121no—
519C22—122no—
520C22—244no—
521C22#6398012yes—
522C22C2×#381111yescharacteristic
523C4—121no—
524C4—184no—
525C4—362no—
526C4#6398012yes—
527C4C2×#380511yescharacteristic
528C4C22×#62511yescharacteristic
529C3—21no—
530C3#8382611yescharacteristic, complemented
531C3#8393411yescharacteristic, complemented
532C2—22no—
533C2—44no—
534C2—242no—
535C2—241no—
536C2#1059510212yes—
537C2C2×#6398011yescharacteristic
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. #10596269C2semidirect
2. C2×C3×#932C2semidirect
3. C22×C3×#213C2semidirect
4. #10595040C2semidirect
5. #10591486C2semidirect
6. #10591476C2semidirect
7. #10591119C2semidirect
8. #10591086C2semidirect
9. #10591084C2semidirect
17. D4×C3⋊Dic3C22semidirect
20. C2×C3×#214C22semidirect
24. C2×C3×#213C22semidirect
28. #63914C22semidirect
30. #63863C22semidirect
31. #63572C22semidirect
32. #63566C22semidirect
33. #63563C22semidirect
34. #63563C22semidirect
42. C2×#932D3semidirect
43. C22×#213D3semidirect
58. C2×C32×D4D4semidirect
119. C2×#214C2×D3semidirect
123. C2×#213C2×D3semidirect
203. C2×C3×D4#67semidirect
204. C2×C3×D4#67semidirect
399. C2×D4#625semidirect
464. C32#3041semidirect
530. C3#83826semidirect
531. C3#83934semidirect

Maximal subgroups

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

subgroupindex
#105962692
C2×C3×#9322
C22×C3×#2132
#105950402
#105914862
#105914762
#105911192
#105910862
#105910842
#839343
#838263