Finite Group Databasebeta

← #11803876

Subgroups — #11803876

Order 1152.

1729 conjugacy classes of subgroups.

The subgroup lattice has 561 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64149C211yesmaximal, characteristic
2C2×C3×D4×Dic3C211yesmaximal, characteristic, complemented
3C2×#63894C211yesmaximal, characteristic, complemented
4C3×#5221C211yesmaximal, characteristic, complemented
5#10591722C214yesmaximal, complemented
6#10591711C214yesmaximal, complemented
7#10591320C211yesmaximal, characteristic, complemented
8#10591230C211yesmaximal, characteristic, complemented
9#10591222C211yesmaximal, characteristic, complemented
10#82329—31nomaximal
11#76298—31nomaximal
12C22×C32×D4C2211yescharacteristic
13C22×#638C2214yes—
14C22×C4⋊(C3⋊D3)C2211yescharacteristic
15C23×C3×Dic3C2212yes—
16C22×#624C2212yes—
17#64149C418yescomplemented
18C2×C4×C3⋊Dic3C2211yescharacteristic
19C2×C3×#217C2212yes—
20C2×C3×#217C2214yes—
21C3×D4×Dic3—24no—
22C2×C3×C4⋊Dic3C2211yescharacteristic
23C2×C3×C4⋊Dic3C2211yescharacteristic
24C2×C3×C4×Dic3C2211yescharacteristic
25C2×C3×C4×Dic3C2211yescharacteristic
26C2×#3722C2212yes—
27C2×#3722C2214yes—
28#63894—24no—
29#63579C2212yes—
30#63579C2214yes—
31#63579C2212yes—
32C2×C3×C4×D4—31no—
33C2×#940—31no—
34C2×#940—31no—
35C2×#940—61no—
36C2×D4×Dic3D311yescharacteristic, complemented
37C2×#893—31no—
38C2×C4×D12—31no—
39C3×#390—31no—
40#5221D311yescharacteristic, complemented
41#5213—34no—
42#4988—31no—
43#4977—31no—
44#4977—31no—
45#4958—34no—
46#4956—34no—
47#4956—34no—
48#4939—31no—
49#4932—31no—
50#4932—31no—
51C24×C32C2312yes—
52C23×C3⋊D3C2312yes—
53C2×C32×D4—22no—
54C2×C32×D4—22no—
55C2×C32×D4C2×C414yescomplemented
56C22×C32×C4C2311yescharacteristic
57C2×#638—44no—
58C2×#638—44no—
59C2×#638C2×C4116yescomplemented
60C22×C3⋊Dic3C2312yes—
61C2×C4⋊(C3⋊D3)—22no—
62C2×C4⋊(C3⋊D3)—22no—
63C2×C4⋊(C3⋊D3)C2×C414yescomplemented
64C22×C3×Dic3—24no—
65C22×C3×Dic3—44no—
66C22×C3×Dic3C2312yes—
67C22×C3×Dic3C2312yes—
68C22×C3×Dic3C2312yes—
69C22×C3×Dic3C2311yescharacteristic
70C22×C3×Dic3C2311yescharacteristic
71C2×#624—24no—
72C2×#624—44no—
73C4×C3⋊Dic3C2×C414yescomplemented
74C3×#217—24no—
75C3×#217—44no—
76C3×C4⋊Dic3—22no—
77C3×C4⋊Dic3—22no—
78C3×C4×Dic3—22no—
79C3×C4×Dic3D414yescomplemented
80#3722—24no—
81#3722—44no—
82#2328—91noSylow
83C22×C3×D4—21no—
84C22×C3×D4C2×D311yescharacteristic
85C22×C3×D4C2×D311yescharacteristic
86C23×C3×C4—32no—
87C22×#67—34no—
88C22×#67—34no—
89C22×#67—64no—
90C23×Dic3C2×D312yes—
91C22×D12—31no—
92C22×D12—31no—
93C22×D12—61no—
94C22×C4×D3—32no—
95C22×C4×D3—32no—
96C3×C4×D4—64no—
97C2×C3×C4⋊C4—31no—
98C2×C3×C4⋊C4—31no—
99C2×C3×C22⋊C4—32no—
100C2×C3×C22⋊C4—34no—
101C2×C3×C42—31no—
102C2×C3×C42—31no—
103C2×#217C2×D312yes—
104C2×#217C2×D314yes—
105#940—38no—
106#940—38no—
107#940—68no—
108D4×Dic3—24no—
109C2×(C2×D3)⋊C4—32no—
110C2×(C2×D3)⋊C4—32no—
111C2×(C2×D3)⋊C4—34no—
112C2×(C2×D3)⋊C4—34no—
113C2×C4⋊Dic3C2×D311yescharacteristic
114C2×C4⋊Dic3C2×D311yescharacteristic
115C2×C4×Dic3—31no—
116C2×C4×Dic3—31no—
117C2×C4×Dic3—61no—
118C2×C4×Dic3C2×D311yescharacteristic
119C2×C4×Dic3C2×D311yescharacteristic
120#893—64no—
121C4×D12—64no—
122C3⋊#95—32no—
123C3⋊#95—32no—
124C3⋊#95—32no—
125C3⋊#95—32no—
126C3⋊#95—34no—
127C3⋊#95—34no—
128C23×C32—22no—
129C23×C32—22no—
130C23×C32—24no—
131C23×C32—24no—
132C23×C32C22×C414yes—
133C23×C32C2411yescharacteristic
134C22×C3⋊D3—22no—
135C22×C3⋊D3—22no—
136C22×C3⋊D3—24no—
137C22×C3⋊D3—24no—
138C22×C3⋊D3C22×C414yes—
139C32×D4—28no—
140C2×C32×C4C22×C412yes—
141C2×C32×C4C2×D412yes—
142C2×C32×C4#4112yes—
143#638—416no—
144C2×C3⋊Dic3—22no—
145C2×C3⋊Dic3—22no—
146C2×C3⋊Dic3C22×C414yes—
147C4⋊(C3⋊D3)—28no—
148C2×C3×Dic3—22no—
149C2×C3×Dic3—22no—
150C2×C3×Dic3—22no—
151C2×C3×Dic3—22no—
152C2×C3×Dic3—22no—
153C2×C3×Dic3—22no—
154C2×C3×Dic3—24no—
155C2×C3×Dic3—22no—
156C2×C3×Dic3—24no—
157C2×C3×Dic3—48no—
158C2×C3×Dic3C2×D412yes—
159C2×C3×Dic3C2×D412yes—
160#624—48no—
161C2×#127—91no—
162C2×C4×D4—31no—
163C2×C4×D4—91no—
164#390—31no—
165#390—91no—
166#386—94no—
167#386—94no—
168#382—91no—
169#376—91no—
170C24×C3—22no—
171C24×C3C22×D312yes—
172C24×C3C22×D312yes—
173C23×D3—32no—
174C23×D3—32no—
175C23×D3—62no—
176C2×C3×D4—22no—
177C2×C3×D4—22no—
178C2×C3×D4—22no—
179C2×C3×D4—22no—
180C2×C3×D4—24no—
181C2×C3×D4—42no—
182C2×C3×D4—42no—
183C2×C3×D4C4×D314yescomplemented
184C2×C3×D4C4×D314yescomplemented
185C22×C3×C4—21no—
186C22×C3×C4—31no—
187C22×C3×C4—31no—
188C22×C3×C4—32no—
189C22×C3×C4—32no—
190C22×C3×C4—32no—
191C22×C3×C4—64no—
192C22×C3×C4—124no—
193C22×C3×C4C22×D311yescharacteristic
194C22×C3×C4C22×D311yescharacteristic
195C2×#67—316no—
196C2×#67—316no—
197C2×#67—616no—
198C2×#67—124no—
199C2×#67—124no—
200C2×#67—124no—
201C2×#67—124no—
202C2×#67—128no—
203C2×#67—128no—
204C22×Dic3—24no—
205C22×Dic3—32no—
206C22×Dic3—32no—
207C22×Dic3—44no—
208C22×Dic3—62no—
209C22×Dic3C22×D312yes—
210C22×Dic3C22×D312yes—
211C22×Dic3C22×D312yes—
212C22×Dic3C22×D311yescharacteristic
213C22×Dic3C22×D311yescharacteristic
214C2×D12—34no—
215C2×D12—34no—
216C2×D12—64no—
217C2×D12—62no—
218C2×D12—62no—
219C2×D12—62no—
220C2×D12—62no—
221C2×D12—122no—
222C2×D12—122no—
223C2×C4×D3—64no—
224C2×C4×D3—64no—
225C2×C4×D3—124no—
226C2×C4×D3—124no—
227C3×C4⋊C4—62no—
228C3×C4⋊C4—62no—
229C3×C22⋊C4—64no—
230C3×C22⋊C4—124no—
231C3×C42—34no—
232C3×C42—62no—
233#217—24no—
234#217—44no—
235(C2×D3)⋊C4—64no—
236(C2×D3)⋊C4—64no—
237(C2×D3)⋊C4—124no—
238(C2×D3)⋊C4—124no—
239C4⋊Dic3—22no—
240C4⋊Dic3—22no—
241C4×Dic3—22no—
242C4×Dic3—34no—
243C4×Dic3—34no—
244C4×Dic3—64no—
245C4×Dic3#6714yescomplemented
246C22×C32—24no—
247C22×C32—28no—
248C22×C32—42no—
249C22×C32—42no—
250C22×C32—44no—
251C22×C32C23×C411yescharacteristic
252C22×C32C22×D411yescharacteristic
253C22×C32C2×#4111yescharacteristic
254C22×C32H(5,𝔽2)12yes—
255C22×C32H(5,𝔽2)12yes—
256C2×C3⋊D3—24no—
257C2×C3⋊D3—28no—
258C2×C3⋊D3—42no—
259C2×C3⋊D3—42no—
260C2×C3⋊D3—44no—
261C32×C4C4×D414yes—
262C3⋊Dic3—24no—
263C3×Dic3—22no—
264C3×Dic3—22no—
265C3×Dic3—42no—
266C3×Dic3—42no—
267C3×Dic3—42no—
268C22×D4—94no—
269C22×D4—91no—
270C22×D4D3211yescharacteristic
271C23×C4—32no—
272C23×C4—92no—
273#127—98no—
274C4×D4—64no—
275C4×D4—184no—
276C2×C4⋊C4—31no—
277C2×C4⋊C4—31no—
278C2×C22⋊C4—32no—
279C2×C22⋊C4—34no—
280C2×C22⋊C4—92no—
281C2×C22⋊C4—94no—
282C2×C42—31no—
283C2×C42—31no—
284C2×C42—91no—
285#95—92no—
286#95—92no—
287#95—94no—
288C23×C3—22no—
289C23×C3—22no—
290C23×C3—22no—
291C23×C3—24no—
292C23×C3—24no—
293C23×C3—24no—
294C23×C3—24no—
295C23×C3—22no—
296C23×C3—21no—
297C23×C3—24no—
298C23×C3—44no—
299C23×C3—44no—
300C23×C3—42no—
301C23×C3—42no—
302C23×C3C2×C4×D314yes—
303C23×C3C2×C4×D314yes—
304C23×C3C23×D311yescharacteristic
305C23×C3C23×D311yescharacteristic
306C22×D3—34no—
307C22×D3—34no—
308C22×D3—64no—
309C22×D3—62no—
310C22×D3—62no—
311C22×D3—62no—
312C22×D3—64no—
313C22×D3—64no—
314C22×D3—64no—
315C22×D3—64no—
316C22×D3—62no—
317C22×D3—122no—
318C22×D3—122no—
319C22×D3—124no—
320C22×D3—124no—
321C3×D4—28no—
322C3×D4—28no—
323C3×D4—48no—
324C2×C3×C4—22no—
325C2×C3×C4—22no—
326C2×C3×C4—22no—
327C2×C3×C4—32no—
328C2×C3×C4—32no—
329C2×C3×C4—62no—
330C2×C3×C4—62no—
331C2×C3×C4—62no—
332C2×C3×C4—62no—
333C2×C3×C4—62no—
334C2×C3×C4—64no—
335C2×C3×C4—62no—
336C2×C3×C4—64no—
337C2×C3×C4—62no—
338C2×C3×C4—128no—
339C2×C3×C4C2×C4×D312yes—
340C2×C3×C4C2×C4×D312yes—
341C2×C3×C4#23512yes—
342C2×C3×C4D3×D412yes—
343C2×C3×C4#23712yes—
344C2×C3×C4C2×#6712yes—
345#67—1216no—
346#67—1216no—
347#67—1232no—
348C2×Dic3—22no—
349C2×Dic3—22no—
350C2×Dic3—22no—
351C2×Dic3—22no—
352C2×Dic3—24no—
353C2×Dic3—22no—
354C2×Dic3—24no—
355C2×Dic3—22no—
356C2×Dic3—22no—
357C2×Dic3—34no—
358C2×Dic3—34no—
359C2×Dic3—48no—
360C2×Dic3—64no—
361C2×Dic3—64no—
362C2×Dic3—64no—
363C2×Dic3—62no—
364C2×Dic3—62no—
365C2×Dic3—62no—
366C2×Dic3—62no—
367C2×Dic3C2×#6712yes—
368C2×Dic3C2×#6712yes—
369D12—68no—
370D12—68no—
371D12—128no—
372C4×D3—128no—
373C4×D3—128no—
374C2×C32—44no—
375C2×C32C2×C4×D411yescharacteristic
376C2×C32#51812yes—
377C2×C32#53511yescharacteristic
378C2×C32#53511yescharacteristic
379C2×C32#54012yes—
380C3⋊D3—44no—
381C24—92no—
382C24C2×D3212yes—
383C2×D4—22no—
384C2×D4—22no—
385C2×D4—916no—
386C2×D4—94no—
387C2×D4—182no—
388C2×D4—182no—
389C2×D4—364no—
390C2×D4—364no—
391C2×D4#62414yescomplemented
392C22×C4—31no—
393C22×C4—31no—
394C22×C4—32no—
395C22×C4—32no—
396C22×C4—32no—
397C22×C4—64no—
398C22×C4—92no—
399C22×C4—124no—
400C22×C4—184no—
401C22×C4—364no—
402C22×C4C2×D3211yescharacteristic
403C4⋊C4—62no—
404C4⋊C4—62no—
405C22⋊C4—64no—
406C22⋊C4—124no—
407C22⋊C4—184no—
408C22⋊C4—364no—
409C42—34no—
410C42—62no—
411C42—94no—
412C22×C3—24no—
413C22×C3—24no—
414C22×C3—28no—
415C22×C3—28no—
416C22×C3—22no—
417C22×C3—22no—
418C22×C3—21no—
419C22×C3—21no—
420C22×C3—21no—
421C22×C3—48no—
422C22×C3—44no—
423C22×C3—42no—
424C22×C3—42no—
425C22×C3—42no—
426C22×C3—44no—
427C22×C3—42no—
428C22×C3—44no—
429C22×C3—84no—
430C22×C3—82no—
431C22×C3—82no—
432C22×C3C22×C4×D311yescharacteristic
433C22×C3C22×C4×D311yescharacteristic
434C22×C3C2×#23511yescharacteristic
435C22×C3C2×D3×D411yescharacteristic
436C22×C3C2×#23711yescharacteristic
437C22×C3#100412yes—
438C22×C3#100412yes—
439C22×C3#100912yes—
440C22×C3#100912yes—
441C22×C3C22×#6711yescharacteristic
442C2×D3—64no—
443C2×D3—64no—
444C2×D3—68no—
445C2×D3—68no—
446C2×D3—124no—
447C2×D3—128no—
448C2×D3—122no—
449C2×D3—122no—
450C2×D3—122no—
451C2×D3—124no—
452C2×D3—122no—
453C2×D3—124no—
454C2×D3—244no—
455C2×D3—242no—
456C2×D3—242no—
457C3×C4—24no—
458C3×C4—62no—
459C3×C4—62no—
460C3×C4—122no—
461C3×C4—122no—
462C3×C4—122no—
463C3×C4#67⋊C414yes—
464C3×C4C4×#6714yes—
465Dic3—22no—
466Dic3—22no—
467Dic3—42no—
468Dic3—42no—
469Dic3—42no—
470Dic3—68no—
471Dic3—64no—
472Dic3—64no—
473C32#232811yescharacteristic, complemented, Sylow
474C23—24no—
475C23—24no—
476C23—22no—
477C23—22no—
478C23—94no—
479C23—184no—
480C23—184no—
481C23—182no—
482C23—182no—
483C23C2×#62414yes—
484C23C22×D3211yescharacteristic
485D4—28no—
486D4—188no—
487D4—3616no—
488C2×C4—32no—
489C2×C4—32no—
490C2×C4—62no—
491C2×C4—62no—
492C2×C4—62no—
493C2×C4—64no—
494C2×C4—62no—
495C2×C4—64no—
496C2×C4—62no—
497C2×C4—62no—
498C2×C4—62no—
499C2×C4—94no—
500C2×C4—128no—
501C2×C4—182no—
502C2×C4—182no—
503C2×C4—368no—
504C2×C4#380412yes—
505C2×C4C2×#62412yes—
506C2×C4D3×#6712yes—
507C2×C3—22no—
508C2×C3—21no—
509C2×C3—22no—
510C2×C3—21no—
511C2×C3—21no—
512C2×C3—44no—
513C2×C3—44no—
514C2×C3—84no—
515C2×C3C2×#67⋊C411yescharacteristic
516C2×C3#554512yes—
517C2×C3#554512yes—
518C2×C3#556212yes—
519C2×C3#561912yes—
520C2×C3#567411yescharacteristic
521C2×C3#571511yescharacteristic
522C2×C3C2×C4×#6711yescharacteristic
523C2×C3#580511yescharacteristic
524C2×C3#583011yescharacteristic
525D3—124no—
526D3—124no—
527D3—244no—
528C22—24no—
529C22—28no—
530C22—44no—
531C22—42no—
532C22—42no—
533C22—184no—
534C22—188no—
535C22—364no—
536C22—362no—
537C22—362no—
538C22#6431412yes—
539C22#6431412yes—
540C22C2×#380411yescharacteristic
541C22C22×#62411yescharacteristic
542C22C2×D3×#6711yescharacteristic
543C4—62no—
544C4—62no—
545C4—122no—
546C4—122no—
547C4—122no—
548C4—184no—
549C4#6395214yes—
550C3—21no—
551C3#7629811yescharacteristic, complemented
552C3#8232911yescharacteristic, complemented
553C2—44no—
554C2—364no—
555C2#1059512512yes—
556C2#1059522312yes—
557C2#1059523511yescharacteristic
558C2#1059530311yescharacteristic
559C2C2×#6395211yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC22×C32×D4C22
socle, cosocleC23×C32C24
prime radicalC2×#64149C2
hypercenterC22×D4D32
hypocenterC32#2328
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
2. C2×C3×D4×Dic3C2semidirect
3. C2×#63894C2semidirect
4. C3×#5221C2semidirect
5. #10591722C2semidirect
6. #10591711C2semidirect
7. #10591320C2semidirect
8. #10591230C2semidirect
9. #10591222C2semidirect
17. #64149C4semidirect
36. C2×D4×Dic3D3semidirect
40. #5221D3semidirect
55. C2×C32×D4C2×C4semidirect
59. C2×#638C2×C4semidirect
63. C2×C4⋊(C3⋊D3)C2×C4semidirect
73. C4×C3⋊Dic3C2×C4semidirect
79. C3×C4×Dic3D4semidirect
183. C2×C3×D4C4×D3semidirect
184. C2×C3×D4C4×D3semidirect
245. C4×Dic3#67semidirect
391. C2×D4#624semidirect
473. C32#2328semidirect
551. C3#76298semidirect
552. C3#82329semidirect

Maximal subgroups

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

subgroupindex
C2×#641492
C2×C3×D4×Dic32
C2×#638942
C3×#52212
#105917222
#105917112
#105913202
#105912302
#105912222
#823293
#762983