Finite Group Databasebeta

← #11790845

Subgroups — #11790845

Order 1152.

1029 conjugacy classes of subgroups.

The subgroup lattice has 554 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64139C211yesmaximal, characteristic
2C3×#5212C211yesmaximal, characteristic, complemented
3C3×C4×#217C211yesmaximal, characteristic, complemented
4C2×#63581C214yesmaximal, complemented
5#69528—31nomaximal
6#69456—31nomaximal
7C23×C32×C4C2211yescharacteristic
8C22×#638C2212yes—
9C22×C4⋊(C3⋊D3)C411yescharacteristic, complemented
10#64139—21no—
11#64139—21no—
12#64139—21no—
13#64139—21no—
14C2×#3752C412yescomplemented
15C2×C4⋊(C3⋊Dic3)C411yescharacteristic, complemented
16C2×C3×#217C2212yes—
17C2×C3×#217C2212yes—
18C2×C3×C4⋊Dic3—21no—
19C2×C3×C4×Dic3—21no—
20C3×C3⋊#95—21no—
21C3×C3⋊#95—21no—
22#63581—28no—
23C2×#930—31no—
24C2×#930—31no—
25C2×#930—61no—
26C3×#380—31no—
27C3×C4×C22⋊C4—31no—
28#5212D311yescharacteristic, complemented
29C4×#217D311yescharacteristic, complemented
30C2×#806—34no—
31C2×#806—34no—
32C24×C32C2311yescharacteristic
33C23×C3⋊D3C2×C412yes—
34C22×C32×C4—42no—
35C22×C32×C4C2×C411yescharacteristic
36C22×C32×C4C2×C411yescharacteristic
37C22×C32×C4D411yescharacteristic
38C22×C32×C4D411yescharacteristic
39C22×C32×C4D411yescharacteristic
40C22×C32×C4D411yescharacteristic
41C2×#638—22no—
42C2×#638—22no—
43C2×#638—24no—
44C2×#638—24no—
45C22×C3⋊Dic3C2×C412yes—
46C2×C4⋊(C3⋊D3)—21no—
47C2×C4⋊(C3⋊D3)—21no—
48C2×C4⋊(C3⋊D3)—42no—
49C22×C3×Dic3—22no—
50C22×C3×Dic3—22no—
51#3752—22no—
52#3752—22no—
53C4⋊(C3⋊Dic3)—21no—
54C4⋊(C3⋊Dic3)—21no—
55C3×#217—22no—
56C3×#217—24no—
57C3×#217D414yescomplemented
58C3×C4⋊Dic3—42no—
59C3×C4×Dic3—42no—
60#1964—91noSylow
61C23×C3×C4—21no—
62C23×C3×C4C2×D311yescharacteristic
63C23×C3×C4C2×D311yescharacteristic
64C22×#67—32no—
65C22×#67—32no—
66C22×#67—62no—
67C22×D12—31no—
68C22×D12—31no—
69C22×D12—61no—
70C2×C3×C4⋊C4—61no—
71C2×C3×C22⋊C4—32no—
72C2×C3×C22⋊C4—32no—
73C2×C3×C42—61no—
74C2×#217C2×D312yes—
75C2×#217C2×D312yes—
76#930—62no—
77#930—62no—
78#930—62no—
79#930—62no—
80#930—61no—
81#930—61no—
82#930—61no—
83#930—61no—
84#930—61no—
85#930—61no—
86#930—61no—
87#930—61no—
88C2×(C2×D3)⋊C4—32no—
89C2×(C2×D3)⋊C4—32no—
90C2×(C2×D3)⋊C4—62no—
91C2×C4⋊Dic3—21no—
92C2×C4⋊Dic3—31no—
93C2×C4⋊Dic3—31no—
94C2×C4⋊Dic3—61no—
95C2×C4×Dic3—21no—
96C3×#95—61no—
97C3×#95—61no—
98C3⋊#95—21no—
99C3⋊#95—21no—
100#806—68no—
101#806—68no—
102C23×C32—41no—
103C23×C32—41no—
104C23×C32C22×C411yescharacteristic
105C23×C32C2×D412yes—
106C23×C32C2×D411yescharacteristic
107C23×C32C2×D411yescharacteristic
108C23×C32#4112yes—
109C22×C3⋊D3—22no—
110C22×C3⋊D3—24no—
111C22×C3⋊D3—42no—
112C22×C3⋊D3—42no—
113C2×C32×C4—22no—
114C2×C32×C4—22no—
115C2×C32×C4—22no—
116C2×C32×C4—41no—
117C2×C32×C4—41no—
118C2×C32×C4—41no—
119C2×C32×C4C22⋊C411yescharacteristic
120C2×C32×C4C22⋊C411yescharacteristic
121C2×C32×C4C22⋊C411yescharacteristic
122C2×C32×C4C22⋊C411yescharacteristic
123#638—44no—
124#638—42no—
125#638—42no—
126C2×C3⋊Dic3—22no—
127C2×C3⋊Dic3—24no—
128C4⋊(C3⋊D3)—42no—
129C4⋊(C3⋊D3)—42no—
130C2×C3×Dic3—24no—
131C2×C3×Dic3—42no—
132C2×C3×Dic3—42no—
133C2×C3×Dic3—42no—
134C2×C3×Dic3—42no—
135C2×C3×Dic3—42no—
136C2×#121—91no—
137C2×#99—94no—
138#380—31no—
139C4×C22⋊C4—31no—
140C24×C3—21no—
141C24×C3C22×D311yescharacteristic
142C24×C3C22×D311yescharacteristic
143C23×D3—32no—
144C23×D3—32no—
145C23×D3—62no—
146C22×C3×C4—21no—
147C22×C3×C4—21no—
148C22×C3×C4—21no—
149C22×C3×C4—21no—
150C22×C3×C4—21no—
151C22×C3×C4—21no—
152C22×C3×C4—42no—
153C22×C3×C4—42no—
154C22×C3×C4—44no—
155C22×C3×C4—62no—
156C22×C3×C4—62no—
157C22×C3×C4C4×D311yescharacteristic
158C22×C3×C4C4×D311yescharacteristic
159C22×C3×C4C4×D311yescharacteristic
160C22×C3×C4C4×D311yescharacteristic
161C22×C3×C4D1211yescharacteristic
162C22×C3×C4D1211yescharacteristic
163C22×C3×C4D1211yescharacteristic
164C22×C3×C4D1211yescharacteristic
165C22×C3×C4#6711yescharacteristic
166C22×C3×C4#6711yescharacteristic
167C22×C3×C4#6711yescharacteristic
168C22×C3×C4#6711yescharacteristic
169C2×#67—64no—
170C2×#67—64no—
171C2×#67—64no—
172C2×#67—62no—
173C2×#67—62no—
174C2×#67—64no—
175C2×#67—64no—
176C2×#67—64no—
177C2×#67—62no—
178C2×#67—62no—
179C2×#67—124no—
180C2×#67—124no—
181C22×Dic3—22no—
182C22×Dic3—22no—
183C22×Dic3—32no—
184C22×Dic3—32no—
185C22×Dic3—62no—
186C2×D12—62no—
187C2×D12—62no—
188C2×D12—61no—
189C2×D12—61no—
190C2×D12—61no—
191C2×D12—61no—
192C2×D12—124no—
193C2×D12—122no—
194C2×D12—122no—
195C3×C4⋊C4—122no—
196C3×C22⋊C4—34no—
197C3×C22⋊C4—62no—
198C3×C22⋊C4—64no—
199C3×C42—122no—
200#217—22no—
201#217—24no—
202#217D1214yescomplemented
203(C2×D3)⋊C4—64no—
204(C2×D3)⋊C4—64no—
205(C2×D3)⋊C4—62no—
206(C2×D3)⋊C4—62no—
207(C2×D3)⋊C4—62no—
208(C2×D3)⋊C4—62no—
209C4⋊Dic3—42no—
210C4⋊Dic3—62no—
211C4⋊Dic3—62no—
212C4⋊Dic3—61no—
213C4⋊Dic3—61no—
214C4⋊Dic3—61no—
215C4⋊Dic3—61no—
216C4×Dic3—42no—
217C22×C32—21no—
218C22×C32—21no—
219C22×C32—21no—
220C22×C32—21no—
221C22×C32—21no—
222C22×C32—21no—
223C22×C32—42no—
224C22×C32—42no—
225C22×C32C2×C22⋊C411yescharacteristic
226C22×C32C4×D412yes—
227C22×C32#12112yes—
228C22×C32#12411yescharacteristic
229C22×C32#12711yescharacteristic
230C2×C3⋊D3—42no—
231C2×C3⋊D3—42no—
232C2×C3⋊D3—42no—
233C2×C3⋊D3—84no—
234C32×C4—21no—
235C32×C4—21no—
236C32×C4—21no—
237C32×C4#9912yescomplemented
238C3⋊Dic3—42no—
239C3×Dic3—44no—
240C3×Dic3—82no—
241C22×D4—92no—
242C22×D4—91no—
243C23×C4D3211yescharacteristic
244#121—181no—
245#121—181no—
246#121—181no—
247#121—181no—
248C2×C4⋊C4—61no—
249C2×C4⋊C4—91no—
250C2×C22⋊C4—32no—
251C2×C22⋊C4—32no—
252C2×C22⋊C4—92no—
253C2×C42—61no—
254#99—188no—
255#95—61no—
256#95—61no—
257C23×C3—22no—
258C23×C3—22no—
259C23×C3—21no—
260C23×C3—21no—
261C23×C3—21no—
262C23×C3—41no—
263C23×C3—41no—
264C23×C3—41no—
265C23×C3—41no—
266C23×C3—42no—
267C23×C3—42no—
268C23×C3C2×C4×D311yescharacteristic
269C23×C3C2×C4×D311yescharacteristic
270C23×C3C2×D1212yes—
271C23×C3C2×D1211yescharacteristic
272C23×C3C2×D1211yescharacteristic
273C23×C3#23512yes—
274C23×C3D3×D412yes—
275C23×C3#23912yes—
276C23×C3C2×#6711yescharacteristic
277C23×C3C2×#6711yescharacteristic
278C22×D3—64no—
279C22×D3—62no—
280C22×D3—62no—
281C22×D3—64no—
282C22×D3—64no—
283C22×D3—124no—
284C22×D3—124no—
285C22×D3—124no—
286C22×D3—122no—
287C22×D3—122no—
288C22×D3—122no—
289C22×D3—122no—
290C2×C3×C4—24no—
291C2×C3×C4—22no—
292C2×C3×C4—22no—
293C2×C3×C4—22no—
294C2×C3×C4—22no—
295C2×C3×C4—22no—
296C2×C3×C4—22no—
297C2×C3×C4—21no—
298C2×C3×C4—21no—
299C2×C3×C4—21no—
300C2×C3×C4—21no—
301C2×C3×C4—42no—
302C2×C3×C4—42no—
303C2×C3×C4—41no—
304C2×C3×C4—41no—
305C2×C3×C4—41no—
306C2×C3×C4—41no—
307C2×C3×C4—41no—
308C2×C3×C4—41no—
309C2×C3×C4—42no—
310C2×C3×C4—42no—
311C2×C3×C4—42no—
312C2×C3×C4—64no—
313C2×C3×C4—122no—
314C2×C3×C4—122no—
315C2×C3×C4—122no—
316C2×C3×C4—122no—
317C2×C3×C4—122no—
318C2×C3×C4(C2×D3)⋊C411yescharacteristic
319C2×C3×C4(C2×D3)⋊C411yescharacteristic
320C2×C3×C4(C2×D3)⋊C411yescharacteristic
321C2×C3×C4(C2×D3)⋊C411yescharacteristic
322C2×C3×C4(C2×D3)⋊C411yescharacteristic
323C2×C3×C4(C2×D3)⋊C411yescharacteristic
324C2×C3×C4(C2×D3)⋊C411yescharacteristic
325C2×C3×C4(C2×D3)⋊C411yescharacteristic
326#67—124no—
327#67—128no—
328#67—124no—
329#67—122no—
330#67—122no—
331#67—124no—
332#67—124no—
333#67—122no—
334#67—122no—
335C2×Dic3—24no—
336C2×Dic3—42no—
337C2×Dic3—42no—
338C2×Dic3—42no—
339C2×Dic3—42no—
340C2×Dic3—42no—
341C2×Dic3—64no—
342C2×Dic3—64no—
343C2×Dic3—64no—
344C2×Dic3—62no—
345C2×Dic3—62no—
346C2×Dic3—124no—
347D12—124no—
348D12—122no—
349D12—122no—
350D12—124no—
351D12—122no—
352D12—122no—
353C2×C32—22no—
354C2×C32—22no—
355C2×C32—21no—
356C2×C32—21no—
357C2×C32#39011yescharacteristic
358C2×C32C2×#9911yescharacteristic
359C2×C32#41011yescharacteristic
360C3⋊D3—82no—
361C24—92no—
362C24C2×D3211yescharacteristic
363C2×D4—184no—
364C2×D4—184no—
365C2×D4—182no—
366C2×D4—182no—
367C2×D4—181no—
368C2×D4—181no—
369C2×D4—362no—
370C22×C4—42no—
371C22×C4—62no—
372C22×C4—62no—
373C22×C4—92no—
374C22×C4#62411yescharacteristic
375C22×C4#62411yescharacteristic
376C22×C4#62611yescharacteristic
377C22×C4#62611yescharacteristic
378C22×C4#62611yescharacteristic
379C22×C4#62611yescharacteristic
380C4⋊C4—122no—
381C4⋊C4—181no—
382C4⋊C4—181no—
383C22⋊C4—34no—
384C22⋊C4—62no—
385C22⋊C4—64no—
386C22⋊C4—182no—
387C22⋊C4—182no—
388C42—122no—
389C22×C3—22no—
390C22×C3—22no—
391C22×C3—21no—
392C22×C3—21no—
393C22×C3—21no—
394C22×C3—21no—
395C22×C3—21no—
396C22×C3—21no—
397C22×C3—21no—
398C22×C3—21no—
399C22×C3—21no—
400C22×C3—21no—
401C22×C3—21no—
402C22×C3—21no—
403C22×C3—21no—
404C22×C3—22no—
405C22×C3—22no—
406C22×C3—21no—
407C22×C3—21no—
408C22×C3—41no—
409C22×C3—41no—
410C22×C3—41no—
411C22×C3—41no—
412C22×C3—42no—
413C22×C3—42no—
414C22×C3—42no—
415C22×C3—42no—
416C22×C3—44no—
417C22×C3—44no—
418C22×C3C4×D1212yes—
419C22×C3#87411yescharacteristic
420C22×C3#87511yescharacteristic
421C22×C3#89312yes—
422C22×C3#89512yes—
423C22×C3C2×(C2×D3)⋊C411yescharacteristic
424C22×C3C2×(C2×D3)⋊C411yescharacteristic
425C22×C3#93012yes—
426C22×C3#94011yescharacteristic
427C22×C3#94711yescharacteristic
428C2×D3—124no—
429C2×D3—124no—
430C2×D3—124no—
431C2×D3—122no—
432C2×D3—122no—
433C2×D3—122no—
434C2×D3—122no—
435C2×D3—122no—
436C2×D3—122no—
437C2×D3—248no—
438C2×D3—244no—
439C2×D3—244no—
440C3×C4—22no—
441C3×C4—21no—
442C3×C4—21no—
443C3×C4—21no—
444C3×C4—21no—
445C3×C4—21no—
446C3×C4—21no—
447C3×C4—22no—
448C3×C4—41no—
449C3×C4—41no—
450C3×C4—124no—
451C3×C4—242no—
452C3×C4#80612yescomplemented
453C3×C4#80612yescomplemented
454Dic3—44no—
455Dic3—82no—
456Dic3—124no—
457Dic3—122no—
458Dic3—122no—
459C32#196411yescharacteristic, complemented, Sylow
460C23—41no—
461C23—41no—
462C23—182no—
463C23—184no—
464C23—362no—
465C23—362no—
466C23#379912yes—
467C23D3×D1212yes—
468C23C2×#62411yescharacteristic
469C23C2×#62611yescharacteristic
470C23C2×#62611yescharacteristic
471D4—362no—
472D4—362no—
473D4—364no—
474D4—362no—
475D4—362no—
476C2×C4—22no—
477C2×C4—22no—
478C2×C4—22no—
479C2×C4—41no—
480C2×C4—41no—
481C2×C4—41no—
482C2×C4—64no—
483C2×C4—122no—
484C2×C4—122no—
485C2×C4—122no—
486C2×C4—122no—
487C2×C4—122no—
488C2×C4—184no—
489C2×C4—182no—
490C2×C4#372211yescharacteristic
491C2×C4#372211yescharacteristic
492C2×C4#372211yescharacteristic
493C2×C4#372211yescharacteristic
494C2×C3—24no—
495C2×C3—22no—
496C2×C3—21no—
497C2×C3—22no—
498C2×C3—21no—
499C2×C3—21no—
500C2×C3—22no—
501C2×C3—22no—
502C2×C3—21no—
503C2×C3—21no—
504C2×C3—21no—
505C2×C3—21no—
506C2×C3—42no—
507C2×C3—41no—
508C2×C3—41no—
509C2×C3#493911yescharacteristic
510C2×C3C2×#80611yescharacteristic
511C2×C3C2×#80611yescharacteristic
512C2×C3#498811yescharacteristic
513C2×C3#500611yescharacteristic
514C2×C3#500611yescharacteristic
515D3—244no—
516D3—242no—
517D3—242no—
518C22—21no—
519C22—21no—
520C22—21no—
521C22—21no—
522C22—21no—
523C22—21no—
524C22—42no—
525C22—42no—
526C22—362no—
527C22—362no—
528C22—362no—
529C22—724no—
530C22#6386411yescharacteristic
531C22#6389412yes—
532C22#6390912yes—
533C22#6391111yescharacteristic
534C22C2×#372211yescharacteristic
535C4—21no—
536C4—21no—
537C4—21no—
538C4—124no—
539C4—242no—
540C4—362no—
541C4#6358112yescomplemented
542C3—21no—
543C3#6945611yescharacteristic, complemented
544C3#6952811yescharacteristic, complemented
545C2—22no—
546C2—21no—
547C2—22no—
548C2—21no—
549C2—722no—
550C2#1059123211yescharacteristic
551C2#1059132011yescharacteristic
552C2C2×#6358111yescharacteristic
subgroupG/H
centerC22C2×#3722
commutatorC23×C32C22×C4
FrattiniC24C2×D32
FittingC23×C32×C4C22
socleC22×C32C2×C22⋊C4
prime radicalC2×#64139C2
cosocleC24×C32C23
hypercenterC23×C4D32
hypocenterC32#1964
LCSG ▷ C23×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
2. C3×#5212C2semidirect
3. C3×C4×#217C2semidirect
4. C2×#63581C2semidirect
9. C22×C4⋊(C3⋊D3)C4semidirect
14. C2×#3752C4semidirect
15. C2×C4⋊(C3⋊Dic3)C4semidirect
28. #5212D3semidirect
29. C4×#217D3semidirect
57. C3×#217D4semidirect
202. #217D12semidirect
237. C32×C4#99semidirect
452. C3×C4#806semidirect
453. C3×C4#806semidirect
459. C32#1964semidirect
541. C4#63581semidirect
543. C3#69456semidirect
544. C3#69528semidirect

Maximal subgroups

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

subgroupindex
C2×#641392
C3×#52122
C3×C4×#2172
C2×#635812
#695283
#694563