Finite Group Databasebeta

← #11865875

Subgroups — #11865875

Order 1152.

1159 conjugacy classes of subgroups.

The subgroup lattice has 562 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5477C211yesmaximal, characteristic, complemented
2C2×C3×C4×D12C211yesmaximal, characteristic, complemented
3C2×#63823C212yesmaximal, complemented
4#10592623C211yesmaximal, characteristic, complemented
5#10591087C212yesmaximal, complemented
6#10590363C212yesmaximal, complemented
7#10590348C214yesmaximal, complemented
8#10590347C212yesmaximal, complemented
9#83297—31nomaximal
10#82307—31nomaximal
11C2×C3×#235C2212yes—
12C22×C3×D12C2211yescharacteristic
13C22×C3×C4×D3—21no—
14C2×C32×C42C2211yescharacteristic
15C2×#3748C2212yes—
16C3×#930—21no—
17C3×#930—21no—
18C2×C3×(C2×D3)⋊C4—21no—
19C2×C3×C4⋊Dic3C2211yescharacteristic
20C3×#875C2212yescomplemented
21C3×#874C2211yescharacteristic, complemented
22C3×C4×D12—21no—
23C3×C4×D12—21no—
24C3×C4×D12—21no—
25C3×C4×D12—21no—
26C3×C4×D12C2212yes—
27C3×C4×D12C2212yes—
28C3×#869C2211yescharacteristic, complemented
29C2×#3715C2214yes—
30#63823—28no—
31C2×#3713C2214yes—
32C4⋊(C3⋊(C3⋊C8))C2212yescomplemented
33C4⋊(C3⋊(C3⋊C8))C2212yescomplemented
34#63565C2214yescomplemented
35#63562C2214yescomplemented
36C3×#532—31no—
37C2×C3×C4×D4—31no—
38C2×#949—32no—
39C2×#932—32no—
40#5477D311yescharacteristic, complemented
41C2×C4×D12D311yescharacteristic, complemented
42#5232—32no—
43#5083—32no—
44#5072—32no—
45#5057—34no—
46#5019—32no—
47#5016—34no—
48#5015—32no—
49#4966—32no—
50#4924—31no—
51#4924—31no—
52#4924—61no—
53C23×C3×D3—21no—
54C22×C32×C4D411yescharacteristic
55C22×C32×C4D411yescharacteristic
56C22×C32×C4C2311yescharacteristic
57C2×C3×#67—22no—
58C22×C3×Dic3—21no—
59C3×#235—24no—
60C3×#235—24no—
61C2×C3×D12—21no—
62C2×C3×D12—22no—
63C2×C3×D12—21no—
64C2×C3×D12—21no—
65C2×C3×D12D414yescomplemented
66C2×C3×D12C2312yes—
67C2×C3×D12C2312yes—
68C2×C3×C4×D3—22no—
69C2×C3×C4×D3—22no—
70C2×C3×C4×D3—22no—
71C2×C3×C4×D3—44no—
72C2×C3×Dic6C2312yes—
73C32×C42D411yescharacteristic
74C32×C42D411yescharacteristic
75C32×C42C2311yescharacteristic
76C32×C42C2311yescharacteristic
77#3748—24no—
78C2×C3⋊(C3⋊C8)C2314yes—
79C3×(C2×D3)⋊C4—22no—
80C3×(C2×D3)⋊C4—22no—
81C3×(C2×D3)⋊C4—22no—
82C3×(C2×D3)⋊C4—22no—
83C3×C4⋊Dic3—21no—
84C3×C4⋊Dic3—21no—
85C3×C4⋊Dic3—21no—
86C3×C4⋊Dic3C2312yes—
87#3715—28no—
88#3713—28no—
89#3036—91noSylow
90C2×C3×#41—32no—
91C22×C3×D4—31no—
92C23×C3×C4—61no—
93C2×#235C2×D312yes—
94C22×D12C2×D311yescharacteristic
95C22×C4×D3—21no—
96C3×C4⋊Q8—31no—
97C3×#127—31no—
98C3×#124—32no—
99C3×#121—61no—
100C3×#121—61no—
101C3×C4×D4—32no—
102C3×C4×D4—32no—
103C3×C4×D4—61no—
104C3×C4×D4—61no—
105C3×C4×D4—61no—
106C3×C4×D4—61no—
107C2×C3×C4⋊C4—31no—
108C2×C3×C22⋊C4—61no—
109C2×C3×C42—21no—
110C2×C3×C42C2×D311yescharacteristic
111C2×C3×C42C2×D311yescharacteristic
112#949—68no—
113C2×#215—34no—
114C2×#214—34no—
115#932—68no—
116C2×#213—34no—
117C2×#213—34no—
118#930—21no—
119#930—21no—
120C2×(C2×D3)⋊C4—21no—
121C2×C4⋊Dic3C2×D311yescharacteristic
122C2×#208—32no—
123C2×#208—32no—
124C2×#208—62no—
125#875C2×D312yescomplemented
126#874C2×D311yescharacteristic, complemented
127C4×D12—21no—
128C4×D12—21no—
129C4×D12—21no—
130C4×D12—21no—
131C4×D12C2×D312yes—
132C4×D12C2×D312yes—
133#869C2×D311yescharacteristic, complemented
134#835—34no—
135#832—34no—
136#810—34no—
137#809—34no—
138C4⋊(C3⋊C8)—32no—
139C4⋊(C3⋊C8)—32no—
140C4⋊(C3⋊C8)—32no—
141C4⋊(C3⋊C8)—32no—
142C4⋊(C3⋊C8)—62no—
143C4⋊(C3⋊C8)—62no—
144C23×C32C2×D411yescharacteristic
145C22×C3×D3—24no—
146C22×C3×D3—22no—
147C22×C3×D3—22no—
148C22×C3×D3—42no—
149C22×C3×D3—42no—
150C2×C32×C4—22no—
151C2×C32×C4—41no—
152C2×C32×C4C2×D412yes—
153C2×C32×C4C2×D411yescharacteristic
154C2×C32×C4C2×D411yescharacteristic
155C2×C32×C4C2×D411yescharacteristic
156C2×C32×C4C2×D411yescharacteristic
157C2×C32×C4C2×D411yescharacteristic
158C2×C32×C4#4112yes—
159C2×C32×C4C2411yescharacteristic
160C3×#67—44no—
161C2×C3×Dic3—22no—
162C2×C3×Dic3—22no—
163C2×C3×Dic3—42no—
164C3×D12—24no—
165C3×D12—22no—
166C3×D12—22no—
167C3×D12—22no—
168C3×D12—42no—
169C3×D12—42no—
170C3×D12C2×D414yes—
171C3×C4×D3—44no—
172C3×C4×D3—44no—
173C3×C4×D3—44no—
174C3×Dic6—22no—
175C3×Dic6—22no—
176C3⋊(C3⋊C8)—24no—
177C2×AGL(1,ℤ/8)—92no—
178#532—31no—
179C2×C4×D4—31no—
180#463—94no—
181#461—92no—
182#459—92no—
183#423—91no—
184#417—92no—
185C24×C3—61no—
186C23×D3—21no—
187C3×#41—64no—
188C3×#41—64no—
189C2×C3×Q8—32no—
190C2×C3×D4—34no—
191C2×C3×D4—32no—
192C2×C3×D4—32no—
193C2×C3×D4—62no—
194C2×C3×D4—62no—
195C2×C3×D4—61no—
196C2×C3×D4—61no—
197C2×C3×D4—61no—
198C22×C3×C4—21no—
199C22×C3×C4—21no—
200C22×C3×C4—21no—
201C22×C3×C4—61no—
202C22×C3×C4—62no—
203C22×C3×C4—62no—
204C22×C3×C4—62no—
205C22×C3×C4—124no—
206C22×C3×C4#6711yescharacteristic
207C22×C3×C4#6711yescharacteristic
208C22×C3×C4#6711yescharacteristic
209C22×C3×C4#6711yescharacteristic
210C22×C3×C4C22×D311yescharacteristic
211C22×C3×C4C22×D311yescharacteristic
212C2×#67—22no—
213C22×Dic3—21no—
214#235—24no—
215#235—24no—
216C2×D12—22no—
217C2×D12—21no—
218C2×D12—21no—
219C2×D12—21no—
220C2×D12D1214yescomplemented
221C2×D12C22×D312yes—
222C2×D12C22×D312yes—
223C2×C4×D3—22no—
224C2×C4×D3—22no—
225C2×C4×D3—22no—
226C2×C4×D3—44no—
227C2×Dic6C22×D312yes—
228C3×C4⋊C4—32no—
229C3×C4⋊C4—61no—
230C3×C4⋊C4—61no—
231C3×C4⋊C4—61no—
232C3×C22⋊C4—62no—
233C3×C22⋊C4—62no—
234C3×C22⋊C4—62no—
235C3×C22⋊C4—62no—
236C3×C42—21no—
237C3×C42—21no—
238C3×C42—21no—
239C3×C42—21no—
240C3×C42#6711yescharacteristic
241C3×C42#6711yescharacteristic
242C3×C42#6711yescharacteristic
243C3×C42#6711yescharacteristic
244C3×C42C22×D311yescharacteristic
245C3×C42C22×D311yescharacteristic
246C3×C42C22×D311yescharacteristic
247C3×C42C22×D311yescharacteristic
248#215—68no—
249#214—68no—
250#213—68no—
251#213—68no—
252(C2×D3)⋊C4—22no—
253(C2×D3)⋊C4—22no—
254(C2×D3)⋊C4—22no—
255(C2×D3)⋊C4—22no—
256C4⋊Dic3—21no—
257C4⋊Dic3—21no—
258C4⋊Dic3—21no—
259C4⋊Dic3C22×D312yes—
260#208—64no—
261#208—64no—
262#208—124no—
263C2×C3⋊C8—34no—
264C2×C3⋊C8—34no—
265C2×C3⋊C8—64no—
266C22×C32—21no—
267C22×C32—21no—
268C22×C32#12112yes—
269C22×C32C22×D411yescharacteristic
270C2×C3×D3—24no—
271C2×C3×D3—48no—
272C2×C3×D3—42no—
273C2×C3×D3—42no—
274C2×C3×D3—42no—
275C2×C3×D3—42no—
276C2×C3×D3—42no—
277C32×C4—21no—
278C32×C4—21no—
279C32×C4—21no—
280C32×C4#12112yes—
281C32×C4AGL(1,ℤ/8)12yescomplemented
282C32×C4C22×D411yescharacteristic
283C32×C4C2×#4111yescharacteristic
284C3×Dic3—42no—
285C3×Dic3—42no—
286C2×#41—32no—
287C22×D4—31no—
288C23×C4—61no—
289AGL(1,ℤ/8)—188no—
290C2×SD16—94no—
291C2×D8—94no—
292C2×M16—92no—
293C4⋊Q8—31no—
294#127—31no—
295#124—32no—
296#121—61no—
297#121—61no—
298C4×D4—32no—
299C4×D4—32no—
300C4×D4—61no—
301C4×D4—61no—
302C4×D4—61no—
303C4×D4—61no—
304C2×C4⋊C4—31no—
305C2×C22⋊C4—61no—
306C2×C42D3211yescharacteristic
307C4⋊C8—92no—
308C4⋊C8—92no—
309#103—94no—
310#102—94no—
311C23×C3—21no—
312C23×C3—64no—
313C23×C3—62no—
314C23×C3—62no—
315C23×C3—122no—
316C23×C3—122no—
317C23×C3C2×#6711yescharacteristic
318C23×C3C2×#6711yescharacteristic
319C22×D3—24no—
320C22×D3—22no—
321C22×D3—22no—
322C22×D3—42no—
323C22×D3—42no—
324C3×Q8—62no—
325C3×Q8—62no—
326C3×D4—34no—
327C3×D4—64no—
328C3×D4—62no—
329C3×D4—62no—
330C3×D4—62no—
331C3×D4—122no—
332C3×D4—124no—
333C3×D4—122no—
334C2×C3×C4—22no—
335C2×C3×C4—22no—
336C2×C3×C4—21no—
337C2×C3×C4—22no—
338C2×C3×C4—22no—
339C2×C3×C4—21no—
340C2×C3×C4—21no—
341C2×C3×C4—21no—
342C2×C3×C4—21no—
343C2×C3×C4—21no—
344C2×C3×C4—42no—
345C2×C3×C4—41no—
346C2×C3×C4—41no—
347C2×C3×C4—42no—
348C2×C3×C4—62no—
349C2×C3×C4—62no—
350C2×C3×C4—124no—
351C2×C3×C4—122no—
352C2×C3×C4—124no—
353C2×C3×C4—124no—
354C2×C3×C4C2×D1212yes—
355C2×C3×C4#23512yes—
356C2×C3×C4D3×D412yes—
357C2×C3×C4#23712yes—
358C2×C3×C4C2×#6711yescharacteristic
359C2×C3×C4C2×#6711yescharacteristic
360C2×C3×C4C2×#6711yescharacteristic
361C2×C3×C4C2×#6711yescharacteristic
362C2×C3×C4C2×#6711yescharacteristic
363C2×C3×C4C2×#6711yescharacteristic
364C2×C3×C4C2×#6711yescharacteristic
365C2×C3×C4C2×#6711yescharacteristic
366C2×C3×C4C2×#6711yescharacteristic
367C2×C3×C4C2×#6711yescharacteristic
368C2×C3×C4C23×D311yescharacteristic
369C2×C3×C4C23×D311yescharacteristic
370#67—44no—
371C2×Dic3—22no—
372C2×Dic3—22no—
373C2×Dic3—42no—
374D12—24no—
375D12—22no—
376D12—22no—
377D12—22no—
378D12—42no—
379D12—42no—
380D12C2×D1214yes—
381C4×D3—44no—
382C4×D3—44no—
383C4×D3—44no—
384Dic6—22no—
385Dic6—22no—
386C3⋊C8—64no—
387C3⋊C8—64no—
388C3⋊C8—124no—
389C2×C32—22no—
390C2×C32C2×#12111yescharacteristic
391C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
392C2×C32#57511yescharacteristic
393C3×D3—44no—
394C3×D3—82no—
395C24—61no—
396#41—64no—
397#41—64no—
398C2×Q8—32no—
399C2×D4—32no—
400C2×D4—32no—
401C2×D4—34no—
402C2×D4—62no—
403C2×D4—62no—
404C2×D4—61no—
405C2×D4—61no—
406C2×D4—61no—
407C22×C4—61no—
408C22×C4—62no—
409C22×C4—62no—
410C22×C4—62no—
411C22×C4—124no—
412C22×C4#62511yescharacteristic
413C22×C4#62511yescharacteristic
414C22×C4C2×D3211yescharacteristic
415SD16—188no—
416D8—188no—
417M16—184no—
418C2×C8—94no—
419C4⋊C4—32no—
420C4⋊C4—61no—
421C4⋊C4—61no—
422C4⋊C4—61no—
423C22⋊C4—62no—
424C22⋊C4—62no—
425C22⋊C4—62no—
426C22⋊C4—62no—
427C42#62511yescharacteristic
428C42#62511yescharacteristic
429C42C2×D3211yescharacteristic
430C42C2×D3211yescharacteristic
431C22×C3—21no—
432C22×C3—21no—
433C22×C3—21no—
434C22×C3—21no—
435C22×C3—21no—
436C22×C3—22no—
437C22×C3—41no—
438C22×C3—41no—
439C22×C3—64no—
440C22×C3—128no—
441C22×C3—122no—
442C22×C3—122no—
443C22×C3—122no—
444C22×C3—122no—
445C22×C3—122no—
446C22×C3#93012yes—
447C22×C3#93812yes—
448C22×C3C22×#6711yescharacteristic
449C22×C3C22×#6711yescharacteristic
450C2×D3—24no—
451C2×D3—48no—
452C2×D3—42no—
453C2×D3—42no—
454C2×D3—42no—
455C2×D3—42no—
456C2×D3—42no—
457C3×C4—22no—
458C3×C4—21no—
459C3×C4—21no—
460C3×C4—21no—
461C3×C4—21no—
462C3×C4—21no—
463C3×C4—21no—
464C3×C4—21no—
465C3×C4—21no—
466C3×C4—22no—
467C3×C4—22no—
468C3×C4—41no—
469C3×C4—41no—
470C3×C4—122no—
471C3×C4—122no—
472C3×C4#93012yes—
473C3×C4#93212yescomplemented
474C3×C4#93812yes—
475C3×C4#94912yescomplemented
476C3×C4C22×D1211yescharacteristic
477C3×C4C2×#23511yescharacteristic
478C3×C4C2×D3×D411yescharacteristic
479C3×C4C2×#23711yescharacteristic
480Dic3—42no—
481Dic3—42no—
482C32#303611yescharacteristic, complemented, Sylow
483C23—62no—
484C23—64no—
485C23—62no—
486C23—122no—
487C23—122no—
488C23C2×#62511yescharacteristic
489Q8—62no—
490Q8—62no—
491D4—34no—
492D4—62no—
493D4—62no—
494D4—62no—
495D4—64no—
496D4—122no—
497D4—124no—
498D4—122no—
499C2×C4—22no—
500C2×C4—41no—
501C2×C4—62no—
502C2×C4—62no—
503C2×C4—124no—
504C2×C4—122no—
505C2×C4—124no—
506C2×C4—124no—
507C2×C4#379512yes—
508C2×C4D3×D1212yes—
509C2×C4C2×#62511yescharacteristic
510C2×C4C2×#62511yescharacteristic
511C2×C4C2×#62511yescharacteristic
512C2×C4C2×#62511yescharacteristic
513C2×C4C2×#62511yescharacteristic
514C2×C4C22×D3211yescharacteristic
515C8—184no—
516C2×C3—22no—
517C2×C3—22no—
518C2×C3—21no—
519C2×C3—21no—
520C2×C3—21no—
521C2×C3—42no—
522C2×C3—124no—
523C2×C3—242no—
524C2×C3C2×#93011yescharacteristic
525C2×C3C2×#93211yescharacteristic
526C2×C3C2×#93811yescharacteristic
527C2×C3C2×#94911yescharacteristic
528C2×C3#582211yescharacteristic
529C2×C3#582211yescharacteristic
530D3—44no—
531D3—82no—
532C22—21no—
533C22—21no—
534C22—64no—
535C22—128no—
536C22—122no—
537C22—122no—
538C22—122no—
539C22—122no—
540C22—122no—
541C22#6390812yes—
542C22C22×#62511yescharacteristic
543C4—21no—
544C4—21no—
545C4—21no—
546C4—122no—
547C4—122no—
548C4#6382312yescomplemented
549C4#6390812yes—
550C4C2×#379511yescharacteristic
551C4C2×D3×D1211yescharacteristic
552C3—21no—
553C3#8230711yescharacteristic, complemented
554C3#8329711yescharacteristic, complemented
555C2—22no—
556C2—124no—
557C2—242no—
558C2C2×#6382311yescharacteristic
559C2#1059478611yescharacteristic
560C2C2×#6390811yescharacteristic
subgroupG/H
centerC22C22×#625
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×C42C22
socleC22×C32C22×D4
hypercenterC2×C42D32
hypocenterC32#3036
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
1. C3×#5477C2semidirect
2. C2×C3×C4×D12C2semidirect
3. C2×#63823C2semidirect
4. #10592623C2semidirect
5. #10591087C2semidirect
6. #10590363C2semidirect
7. #10590348C2semidirect
8. #10590347C2semidirect
20. C3×#875C22semidirect
21. C3×#874C22semidirect
28. C3×#869C22semidirect
32. C4⋊(C3⋊(C3⋊C8))C22semidirect
33. C4⋊(C3⋊(C3⋊C8))C22semidirect
34. #63565C22semidirect
35. #63562C22semidirect
40. #5477D3semidirect
41. C2×C4×D12D3semidirect
65. C2×C3×D12D4semidirect
125. #875C2×D3semidirect
126. #874C2×D3semidirect
133. #869C2×D3semidirect
220. C2×D12D12semidirect
281. C32×C4AGL(1,ℤ/8)semidirect
473. C3×C4#932semidirect
475. C3×C4#949semidirect
482. C32#3036semidirect
548. C4#63823semidirect
553. C3#82307semidirect
554. C3#83297semidirect

Maximal subgroups

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

subgroupindex
C3×#54772
C2×C3×C4×D122
C2×#638232
#105926232
#105910872
#105903632
#105903482
#105903472
#832973
#823073