Finite Group Databasebeta

← #11865058

Subgroups — #11865058

Order 1152.

1691 conjugacy classes of subgroups.

The subgroup lattice has 594 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#1004C211yesmaximal, characteristic, complemented
2#10596276C211yesmaximal, characteristic, complemented
3#10594795C212yesmaximal, complemented
4C2×C3×#833C211yesmaximal, characteristic, complemented
5#10591513C214yesmaximal, complemented
6#10591510C214yesmaximal, complemented
7#10591110C212yesmaximal, complemented
8#84104—31nomaximal
9#78700—31nomaximal
10C22×C32×D4C2211yescharacteristic
11C2×#3828C2211yescharacteristic, complemented
12C22×C3×#67—22no—
13C3×#1004—22no—
14C3×#1004—24no—
15C3×#1004C2214yes—
16C2×C3×#237—22no—
17C2×C3×D3×D4—22no—
18C2×C3×#235C2212yes—
19#64162—22no—
20#64149C2212yescomplemented
21#64147—22no—
22#64145C2212yescomplemented
23#64135C2211yescharacteristic, complemented
24C2×C3×#208C2212yescomplemented
25#63833—22no—
26#63831C2214yescomplemented
27#63830—22no—
28#63829—24no—
29#63825C2214yescomplemented
30C3×#833C2214yescomplemented
31#63568C2218yescomplemented
32C2×C3×H(5,𝔽2)—31no—
33C2×#1004D311yescharacteristic, complemented
34#5822—32no—
35#5805—31no—
36#5805—31no—
37#5805—61no—
38#5748—32no—
39C2×C3×#100—31no—
40#5242—34no—
41#5241—34no—
42#5236—32no—
43C2×#833D311yescharacteristic, complemented
44#5139—32no—
45#4747—34no—
46#4746—34no—
47C24×C32D412yes—
48C23×C3×D3—22no—
49C2×C32×D4—22no—
50C2×C32×D4—22no—
51C2×C32×D4D412yes—
52C2×C32×D4C2312yes—
53C22×C32×C4C2311yescharacteristic
54C2×#638—21no—
55C2×#638—24no—
56#3828—22no—
57#3828—22no—
58C2×C4⋊(C3⋊D3)C2311yescharacteristic, complemented
59C2×C4×C3⋊D3—21no—
60C2×#634C2311yescharacteristic, complemented
61C2×C3×#67—24no—
62C2×C3×#67—28no—
63C2×C3×#67—22no—
64C2×C3×#67—28no—
65C22×C3×Dic3—22no—
66C3×#237—28no—
67C3×#237—28no—
68C3×D3×D4—28no—
69C3×D3×D4—28no—
70C3×#235—22no—
71C3×#235—22no—
72C3×#235D414yescomplemented
73C3×#235C2314yes—
74C2×C3×D12D412yescomplemented
75C2×C3×C4×D3—22no—
76C2×C3×Dic6D412yescomplemented
77#3757—21no—
78#3757—24no—
79C4⋊(C3⋊Dic3)—21no—
80C4×C3⋊Dic3C2312yescomplemented
81C3×#208—22no—
82C3×#208C2314yescomplemented
83C2×C3×C3⋊C8—22no—
84#3719—24no—
85#3717—24no—
86#3716—24no—
87#3714—24no—
88#3019—91noSylow
89C3×H(5,𝔽2)—34no—
90C3×H(5,𝔽2)—64no—
91C3×H(5,𝔽2)—62no—
92C2×C3×#41—32no—
93C2×C3×#41—62no—
94C22×C3×D4—21no—
95C22×C3×D4—62no—
96C22×C3×D4—62no—
97C22×C3×D4C2×D311yescharacteristic
98C22×C3×D4C2×D311yescharacteristic
99C22×#67—22no—
100#1004—22no—
101#1004—24no—
102#1004C2×D314yes—
103C2×#237—22no—
104C2×D3×D4—22no—
105C2×#235—31no—
106C2×#235—31no—
107C2×#235—61no—
108C2×#235C2×D312yes—
109C2×C3×M16—32no—
110#953—64no—
111#953—62no—
112#953—62no—
113#951—34no—
114#950—64no—
115#949—34no—
116#942—62no—
117#940—32no—
118#940—32no—
119#940—62no—
120#938—64no—
121#938—62no—
122#938—62no—
123#936—32no—
124#936—32no—
125#936—62no—
126#932—62no—
127#926—31no—
128#926—31no—
129#926—61no—
130C2×#208C2×D312yescomplemented
131#909—34no—
132#909—62no—
133#908—34no—
134#908—62no—
135#904—64no—
136C3×#100—34no—
137#837—38no—
138#833C2×D314yescomplemented
139#825—38no—
140C23×C32—22no—
141C23×C32—22no—
142C23×C32—82no—
143C23×C32C2×D414yes—
144C23×C32C2×D411yescharacteristic
145C22×C3⋊D3—21no—
146C22×C3×D3—22no—
147C22×C3×D3—28no—
148C22×C3×D3—84no—
149C32×D4—24no—
150C32×D4—24no—
151C2×C32×C4C2×D411yescharacteristic
152C2×C32×C4C2×D412yes—
153C2×C32×C4C2×D412yes—
154C2×C32×C4C2411yescharacteristic
155#638—41no—
156#638—41no—
157#638—84no—
158C2×C3⋊Dic3—22no—
159C2×C3⋊Dic3—21no—
160C4⋊(C3⋊D3)—22no—
161C4×C3⋊D3—42no—
162#634—22no—
163C3×#67—216no—
164C3×#67—24no—
165C3×#67—24no—
166C2×C3×Dic3—28no—
167C2×C3×Dic3—22no—
168C3×D12—22no—
169C3×D12C2×D414yes—
170C3×C4×D3—24no—
171C3×C4×D3—24no—
172C3×Dic6—22no—
173C3×Dic6C2×D414yes—
174C3×C3⋊C8—24no—
175C2×H(5,𝔽2)—31no—
176#575—92no—
177#535—91no—
178#455—94no—
179#453—94no—
180#421—92no—
181C2×#100—31no—
182C24×C3—22no—
183C24×C3—62no—
184C24×C3D1212yes—
185C24×C3#6712yes—
186C23×D3—22no—
187C3×#41—34no—
188C3×#41—34no—
189C3×#41—68no—
190C3×#41—68no—
191C3×#41—62no—
192C3×#41—62no—
193C2×C3×Q8—32no—
194C2×C3×D4—22no—
195C2×C3×D4—22no—
196C2×C3×D4—22no—
197C2×C3×D4—22no—
198C2×C3×D4—22no—
199C2×C3×D4—22no—
200C2×C3×D4—32no—
201C2×C3×D4—42no—
202C2×C3×D4—42no—
203C2×C3×D4—68no—
204C2×C3×D4—68no—
205C2×C3×D4—64no—
206C2×C3×D4—68no—
207C2×C3×D4—62no—
208C2×C3×D4—68no—
209C2×C3×D4D1212yes—
210C2×C3×D4#6712yes—
211C2×C3×D4C22×D312yes—
212C2×C3×D4C22×D312yes—
213C22×C3×C4—21no—
214C22×C3×C4—62no—
215C22×C3×C4—62no—
216C22×C3×C4C22×D311yescharacteristic
217C22×C3×C4C22×D311yescharacteristic
218C2×#67—24no—
219C2×#67—28no—
220C2×#67—22no—
221C2×#67—28no—
222C2×#67—62no—
223C2×#67—61no—
224C2×#67—61no—
225C2×#67—68no—
226C2×#67—64no—
227C2×#67—64no—
228C22×Dic3—22no—
229#237—28no—
230#237—28no—
231D3×D4—28no—
232D3×D4—28no—
233#235—22no—
234#235—22no—
235#235—62no—
236#235—62no—
237#235—62no—
238#235—62no—
239#235—122no—
240#235—122no—
241#235#6714yescomplemented
242#235C22×D314yes—
243C2×D12—31no—
244C2×D12—31no—
245C2×D12—61no—
246C2×D12#6712yescomplemented
247C2×C4×D3—22no—
248C2×C4×D3—62no—
249C2×C4×D3—61no—
250C2×C4×D3—61no—
251C2×Dic6—31no—
252C2×Dic6—31no—
253C2×Dic6—61no—
254C2×Dic6#6712yescomplemented
255C3×M16—34no—
256C3×M16—62no—
257C2×C3×C8—62no—
258#217—62no—
259#217—68no—
260#217—61no—
261#217—64no—
262#217—61no—
263#217—64no—
264#216—64no—
265#215—64no—
266#214—64no—
267#213—64no—
268C4⋊Dic3—62no—
269C4⋊Dic3—61no—
270C4⋊Dic3—61no—
271C4×Dic3—32no—
272C4×Dic3—32no—
273C4×Dic3—62no—
274#208—22no—
275#208C22×D314yescomplemented
276C2×C3⋊C8—22no—
277Dic12—64no—
278D24—64no—
279#204—64no—
280#204—64no—
281C22×C32—24no—
282C22×C32—41no—
283C22×C32—44no—
284C22×C32—44no—
285C22×C32—82no—
286C22×C32#12011yescharacteristic
287C22×C32#12011yescharacteristic
288C22×C32C22×D411yescharacteristic
289C2×C3⋊D3—42no—
290C2×C3⋊D3—41no—
291C2×C3×D3—24no—
292C2×C3×D3—44no—
293C2×C3×D3—88no—
294C32×C4#12012yes—
295C32×C4C22×D412yes—
296C3⋊Dic3—42no—
297C3⋊Dic3—41no—
298C3×Dic3—24no—
299H(5,𝔽2)—34no—
300H(5,𝔽2)—64no—
301H(5,𝔽2)—62no—
302C2×#41—32no—
303C2×#41—62no—
304C2×#41—91no—
305C22×D4—62no—
306C22×D4—62no—
307C22×D4D3211yescharacteristic
308#137—94no—
309#137—182no—
310AGL(1,ℤ/8)—94no—
311AGL(1,ℤ/8)—182no—
312#135—184no—
313C2×M16—32no—
314#127—92no—
315#124—92no—
316#121—182no—
317#120—182no—
318#117—91no—
319#104—98no—
320#100—34no—
321C23×C3—22no—
322C23×C3—22no—
323C23×C3—22no—
324C23×C3—22no—
325C23×C3—21no—
326C23×C3—24no—
327C23×C3—42no—
328C23×C3—42no—
329C23×C3—68no—
330C23×C3—62no—
331C23×C3—82no—
332C23×C3—82no—
333C23×C3—84no—
334C23×C3—244no—
335C23×C3C2×D1214yes—
336C23×C3C2×D1211yescharacteristic
337C23×C3C2×#6714yes—
338C23×C3C2×#6711yescharacteristic
339C22×D3—22no—
340C22×D3—28no—
341C22×D3—62no—
342C22×D3—61no—
343C22×D3—61no—
344C22×D3—84no—
345C3×Q8—34no—
346C3×Q8—62no—
347C3×D4—24no—
348C3×D4—24no—
349C3×D4—24no—
350C3×D4—24no—
351C3×D4—34no—
352C3×D4—44no—
353C3×D4—44no—
354C3×D4—616no—
355C3×D4—64no—
356C3×D4—64no—
357C3×D4—62no—
358C2×C3×C4—21no—
359C2×C3×C4—21no—
360C2×C3×C4—22no—
361C2×C3×C4—22no—
362C2×C3×C4—68no—
363C2×C3×C4—62no—
364C2×C3×C4—64no—
365C2×C3×C4—64no—
366C2×C3×C4C2×D1211yescharacteristic
367C2×C3×C4D3×D412yes—
368C2×C3×C4D3×D412yes—
369C2×C3×C4C2×#6711yescharacteristic
370C2×C3×C4C2×#6712yes—
371C2×C3×C4C2×#6712yes—
372C2×C3×C4C23×D311yescharacteristic
373C2×C3×C4C23×D311yescharacteristic
374#67—216no—
375#67—24no—
376#67—24no—
377#67—122no—
378#67—122no—
379#67—121no—
380#67—121no—
381#67—121no—
382#67—121no—
383#67—244no—
384#67—244no—
385#67—248no—
386C2×Dic3—28no—
387C2×Dic3—22no—
388C2×Dic3—64no—
389C2×Dic3—62no—
390C2×Dic3—62no—
391C2×Dic3—61no—
392C2×Dic3—62no—
393C2×Dic3—61no—
394D12—22no—
395D12—62no—
396D12—62no—
397D12—122no—
398D12C2×#6714yes—
399C4×D3—24no—
400C4×D3—24no—
401C4×D3—124no—
402C4×D3—122no—
403C4×D3—122no—
404Dic6—22no—
405Dic6—62no—
406Dic6—62no—
407Dic6—122no—
408Dic6C2×#6714yes—
409C3×C8—64no—
410C3⋊C8—24no—
411C2×C32—21no—
412C2×C32—21no—
413C2×C32—21no—
414C2×C32—44no—
415C2×C32C2×#12011yescharacteristic
416C3⋊D3—81no—
417C3×D3—44no—
418C24—62no—
419C24#62612yes—
420#41—34no—
421#41—34no—
422#41—68no—
423#41—68no—
424#41—62no—
425#41—62no—
426#41—182no—
427#41—182no—
428C2×Q8—32no—
429C2×Q8—91no—
430C2×D4—22no—
431C2×D4—22no—
432C2×D4—32no—
433C2×D4—68no—
434C2×D4—68no—
435C2×D4—64no—
436C2×D4—68no—
437C2×D4—62no—
438C2×D4—68no—
439C2×D4—91no—
440C2×D4—181no—
441C2×D4—184no—
442C2×D4#62612yes—
443C2×D4C2×D3212yes—
444C22×C4—62no—
445C22×C4—62no—
446C22×C4—181no—
447C22×C4C2×D3211yescharacteristic
448Q16—184no—
449SD16—184no—
450SD16—184no—
451D8—184no—
452M16—34no—
453M16—62no—
454C2×C8—62no—
455C4⋊C4—181no—
456C22⋊C4—181no—
457C22⋊C4—184no—
458C42—92no—
459C22×C3—24no—
460C22×C3—24no—
461C22×C3—21no—
462C22×C3—21no—
463C22×C3—21no—
464C22×C3—44no—
465C22×C3—41no—
466C22×C3—41no—
467C22×C3—44no—
468C22×C3—44no—
469C22×C3—44no—
470C22×C3—42no—
471C22×C3—44no—
472C22×C3—48no—
473C22×C3—64no—
474C22×C3—84no—
475C22×C3—82no—
476C22×C3—82no—
477C22×C3—84no—
478C22×C3—124no—
479C22×C3—248no—
480C22×C3#88211yescharacteristic
481C22×C3#88211yescharacteristic
482C22×C3#95311yescharacteristic
483C22×C3#95311yescharacteristic
484C22×C3C22×D1211yescharacteristic
485C22×C3C22×#6711yescharacteristic
486C2×D3—24no—
487C2×D3—44no—
488C2×D3—88no—
489C2×D3—122no—
490C2×D3—124no—
491C2×D3—122no—
492C2×D3—122no—
493C2×D3—121no—
494C2×D3—121no—
495C3×C4—22no—
496C3×C4—22no—
497C3×C4—64no—
498C3×C4#88212yes—
499C3×C4#95312yes—
500C3×C4C2×D3×D412yes—
501C3×C4C22×#6712yes—
502Dic3—24no—
503Dic3—122no—
504Dic3—124no—
505Dic3—122no—
506Dic3—122no—
507Dic3—121no—
508Dic3—121no—
509C32#301911yescharacteristic, complemented, Sylow
510C23—22no—
511C23—22no—
512C23—68no—
513C23—62no—
514C23—82no—
515C23—181no—
516C23—244no—
517C23C2×#62614yes—
518C23C2×#62611yescharacteristic
519Q8—34no—
520Q8—62no—
521Q8—182no—
522D4—24no—
523D4—24no—
524D4—34no—
525D4—616no—
526D4—64no—
527D4—64no—
528D4—62no—
529D4—182no—
530D4—361no—
531D4—361no—
532D4—724no—
533C2×C4—68no—
534C2×C4—62no—
535C2×C4—64no—
536C2×C4—64no—
537C2×C4—182no—
538C2×C4—181no—
539C2×C4—362no—
540C2×C4C2×#62611yescharacteristic
541C2×C4D3×#6712yes—
542C2×C4D3×#6712yes—
543C2×C4C22×D3211yescharacteristic
544C8—64no—
545C2×C3—22no—
546C2×C3—21no—
547C2×C3—21no—
548C2×C3—21no—
549C2×C3—21no—
550C2×C3—21no—
551C2×C3—21no—
552C2×C3—21no—
553C2×C3—41no—
554C2×C3—41no—
555C2×C3—44no—
556C2×C3—44no—
557C2×C3—84no—
558C2×C3—124no—
559C2×C3C2×#88211yescharacteristic
560C2×C3C2×#95311yescharacteristic
561D3—44no—
562D3—242no—
563D3—241no—
564D3—241no—
565C22—24no—
566C22—41no—
567C22—44no—
568C22—44no—
569C22—64no—
570C22—82no—
571C22—124no—
572C22—248no—
573C22—362no—
574C22—361no—
575C22#6397711yescharacteristic
576C22#6397711yescharacteristic
577C22C22×#62611yescharacteristic
578C4—64no—
579C4—362no—
580C4—361no—
581C4#6397712yes—
582C4C2×D3×#6712yes—
583C3—21no—
584C3#7870011yescharacteristic, complemented
585C3#8410411yescharacteristic, complemented
586C2—21no—
587C2—21no—
588C2—21no—
589C2—44no—
590C2—124no—
591C2—721no—
592C2C2×#6397711yescharacteristic
subgroupG/H
centerC2C2×#63977
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC22×C32×D4C22
socleC2×C32C2×#120
hypercenterC22×D4D32
hypocenterC32#3019
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C22×C4 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
1. C2×C3×#1004C2semidirect
2. #10596276C2semidirect
3. #10594795C2semidirect
4. C2×C3×#833C2semidirect
5. #10591513C2semidirect
6. #10591510C2semidirect
7. #10591110C2semidirect
11. C2×#3828C22semidirect
20. #64149C22semidirect
22. #64145C22semidirect
23. #64135C22semidirect
24. C2×C3×#208C22semidirect
26. #63831C22semidirect
29. #63825C22semidirect
30. C3×#833C22semidirect
31. #63568C22semidirect
33. C2×#1004D3semidirect
43. C2×#833D3semidirect
58. C2×C4⋊(C3⋊D3)C23semidirect
60. C2×#634C23semidirect
72. C3×#235D4semidirect
74. C2×C3×D12D4semidirect
76. C2×C3×Dic6D4semidirect
80. C4×C3⋊Dic3C23semidirect
82. C3×#208C23semidirect
130. C2×#208C2×D3semidirect
138. #833C2×D3semidirect
241. #235#67semidirect
246. C2×D12#67semidirect
254. C2×Dic6#67semidirect
275. #208C22×D3semidirect
509. C32#3019semidirect
584. C3#78700semidirect
585. C3#84104semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#10042
#105962762
#105947952
C2×C3×#8332
#105915132
#105915102
#105911102
#841043
#787003