Finite Group Databasebeta

← #11774003

Subgroups — #11774003

Order 1152.

731 conjugacy classes of subgroups.

The subgroup lattice has 543 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64138C211yesmaximal, characteristic
2C3×#5207C211yesmaximal, characteristic, complemented
3C2×C3×#830C211yesmaximal, characteristic, complemented
4#10589148C212yesmaximal, complemented
5#10589146C212yesmaximal, complemented
6#69969—31nomaximal
7#69920—31nomaximal
8C23×C32×C4C2211yescharacteristic
9C22×#638C411yescharacteristic
10C2×#3757C411yescharacteristic
11#64138—21no—
12#64138—21no—
13#64138—21no—
14#64138—21no—
15C2×#3752C411yescharacteristic
16C2×#3752C2211yescharacteristic
17C2×#3750C411yescharacteristic
18C2×#3750C2211yescharacteristic
19C2×C3×#208—21no—
20C22×C3×C3⋊C8—21no—
21C3×#830—21no—
22C3×#830—21no—
23C3×#830C2212yes—
24C3×#830C2212yes—
25C2×#929—31no—
26C2×#929—31no—
27C2×#929—61no—
28C3×#407—31no—
29C2×C3×C22⋊C8—31no—
30#5207D311yescharacteristic, complemented
31C2×#830D311yescharacteristic, complemented
32#4469—32no—
33#4469—32no—
34#4468—32no—
35#4468—32no—
36C24×C32C2×C411yescharacteristic
37C23×C3⋊D3C2×C411yescharacteristic
38C22×C32×C4—42no—
39C22×C32×C4C2×C411yescharacteristic
40C22×C32×C4D411yescharacteristic
41C22×C32×C4D411yescharacteristic
42C22×C32×C4D411yescharacteristic
43C22×C32×C4D411yescharacteristic
44C22×C32×C4C2311yescharacteristic
45C2×#638—21no—
46C2×#638—21no—
47C2×#638—42no—
48C22×C3⋊Dic3C2×C411yescharacteristic
49C22×C3⋊Dic3C2×C411yescharacteristic
50C22×C3⋊Dic3C2×C411yescharacteristic
51#3757—21no—
52#3757—21no—
53#3752—21no—
54#3752—21no—
55#3752—21no—
56#3752—21no—
57#3750—21no—
58#3750—21no—
59#3750—21no—
60#3750—21no—
61C3×#208—42no—
62C2×C3×C3⋊C8—22no—
63C2×C3×C3⋊C8—22no—
64C2×C3×C3⋊C8—42no—
65#1468—91noSylow
66C23×C3×C4—21no—
67C23×C3×C4C2×D311yescharacteristic
68C23×C3×C4C2×D311yescharacteristic
69C22×#67—31no—
70C22×#67—31no—
71C22×#67—61no—
72C2×C3×M16—61no—
73C22×C3×C8—61no—
74C2×#217—31no—
75C2×#217—31no—
76C2×#217—61no—
77#929—62no—
78#929—62no—
79#929—62no—
80#929—62no—
81#929—61no—
82#929—61no—
83#929—61no—
84#929—61no—
85#929—61no—
86#929—61no—
87#929—61no—
88#929—61no—
89C2×(C2×D3)⋊C4—31no—
90C2×(C2×D3)⋊C4—31no—
91C2×(C2×D3)⋊C4—31no—
92C2×(C2×D3)⋊C4—31no—
93C2×(C2×D3)⋊C4—61no—
94C2×(C2×D3)⋊C4—61no—
95C2×Dic3⋊C4—31no—
96C2×Dic3⋊C4—31no—
97C2×Dic3⋊C4—31no—
98C2×Dic3⋊C4—31no—
99C2×Dic3⋊C4—61no—
100C2×Dic3⋊C4—61no—
101C2×#208—21no—
102C22×C3⋊C8—21no—
103C3×C22⋊C8—32no—
104C3×C22⋊C8—32no—
105C3×C22⋊C8—61no—
106C3×C22⋊C8—61no—
107#830—21no—
108#830—21no—
109#830C2×D312yes—
110#830C2×D312yes—
111C23×C32—22no—
112C23×C32—22no—
113C23×C32—41no—
114C23×C32C22⋊C411yescharacteristic
115C23×C32C22⋊C411yescharacteristic
116C23×C32C22×C411yescharacteristic
117C22×C3⋊D3—21no—
118C22×C3⋊D3—22no—
119C22×C3⋊D3—41no—
120C22×C3⋊D3—41no—
121C2×C32×C4—22no—
122C2×C32×C4—22no—
123C2×C32×C4—41no—
124C2×C32×C4—41no—
125C2×C32×C4—41no—
126C2×C32×C4—41no—
127C2×C32×C4C22⋊C411yescharacteristic
128C2×C32×C4C22⋊C411yescharacteristic
129C2×C32×C4C2×D411yescharacteristic
130C2×C32×C4C2×D411yescharacteristic
131#638—42no—
132#638—42no—
133C2×C3⋊Dic3—21no—
134C2×C3⋊Dic3—21no—
135C2×C3⋊Dic3—21no—
136C2×C3⋊Dic3—22no—
137C2×C3⋊Dic3—41no—
138C2×C3⋊Dic3—41no—
139C3×C3⋊C8—42no—
140C3×C3⋊C8—42no—
141C2×#123—91no—
142#407—31no—
143C2×C22⋊C8—31no—
144#324—92no—
145#323—92no—
146C24×C3—21no—
147C24×C3C4×D311yescharacteristic
148C24×C3C4×D311yescharacteristic
149C23×D3—31no—
150C23×D3—31no—
151C23×D3—61no—
152C22×C3×C4—21no—
153C22×C3×C4—21no—
154C22×C3×C4—21no—
155C22×C3×C4—21no—
156C22×C3×C4—21no—
157C22×C3×C4—21no—
158C22×C3×C4—42no—
159C22×C3×C4—42no—
160C22×C3×C4—44no—
161C22×C3×C4C4×D311yescharacteristic
162C22×C3×C4C4×D311yescharacteristic
163C22×C3×C4D1211yescharacteristic
164C22×C3×C4D1211yescharacteristic
165C22×C3×C4D1211yescharacteristic
166C22×C3×C4D1211yescharacteristic
167C22×C3×C4#6711yescharacteristic
168C22×C3×C4#6711yescharacteristic
169C22×C3×C4#6711yescharacteristic
170C22×C3×C4#6711yescharacteristic
171C22×C3×C4C22×D311yescharacteristic
172C22×C3×C4C22×D311yescharacteristic
173C2×#67—62no—
174C2×#67—62no—
175C2×#67—61no—
176C2×#67—61no—
177C2×#67—61no—
178C2×#67—61no—
179C2×#67—124no—
180C2×#67—122no—
181C2×#67—122no—
182C22×Dic3—31no—
183C22×Dic3—31no—
184C22×Dic3—31no—
185C22×Dic3—31no—
186C22×Dic3—31no—
187C22×Dic3—31no—
188C22×Dic3—61no—
189C22×Dic3—61no—
190C22×Dic3—61no—
191C3×M16—122no—
192C2×C3×C8—62no—
193C2×C3×C8—62no—
194C2×C3×C8—122no—
195#217—62no—
196#217—62no—
197#217—61no—
198#217—61no—
199#217—61no—
200#217—61no—
201(C2×D3)⋊C4—62no—
202(C2×D3)⋊C4—62no—
203(C2×D3)⋊C4—62no—
204(C2×D3)⋊C4—62no—
205(C2×D3)⋊C4—61no—
206(C2×D3)⋊C4—61no—
207(C2×D3)⋊C4—61no—
208(C2×D3)⋊C4—61no—
209(C2×D3)⋊C4—61no—
210(C2×D3)⋊C4—61no—
211(C2×D3)⋊C4—61no—
212(C2×D3)⋊C4—61no—
213Dic3⋊C4—62no—
214Dic3⋊C4—62no—
215Dic3⋊C4—62no—
216Dic3⋊C4—62no—
217Dic3⋊C4—61no—
218Dic3⋊C4—61no—
219Dic3⋊C4—61no—
220Dic3⋊C4—61no—
221Dic3⋊C4—61no—
222Dic3⋊C4—61no—
223Dic3⋊C4—61no—
224Dic3⋊C4—61no—
225#208—42no—
226C2×C3⋊C8—22no—
227C2×C3⋊C8—22no—
228C2×C3⋊C8—42no—
229C22×C32—21no—
230C22×C32—21no—
231C22×C32—21no—
232C22×C32—21no—
233C22×C32—21no—
234C22×C32—21no—
235C22×C32—21no—
236C22×C32—44no—
237C22×C32#9912yes—
238C22×C32C2×C22⋊C411yescharacteristic
239C22×C32#13112yes—
240C2×C3⋊D3—41no—
241C2×C3⋊D3—41no—
242C2×C3⋊D3—41no—
243C2×C3⋊D3—82no—
244C32×C4—21no—
245C32×C4—21no—
246C32×C4—21no—
247C32×C4—21no—
248C3⋊Dic3—41no—
249C3⋊Dic3—41no—
250C3⋊Dic3—41no—
251C22×D4—91no—
252C23×C4D3211yescharacteristic
253C2×M16—61no—
254C22×C8—61no—
255#123—181no—
256#123—181no—
257#123—181no—
258#123—181no—
259C2×C4⋊C4—91no—
260C2×C4⋊C4—91no—
261C2×C22⋊C4—91no—
262C2×C22⋊C4—91no—
263C2×C22⋊C4—91no—
264C22⋊C8—32no—
265C22⋊C8—32no—
266C22⋊C8—61no—
267C22⋊C8—61no—
268C23×C3—24no—
269C23×C3—22no—
270C23×C3—22no—
271C23×C3—22no—
272C23×C3—22no—
273C23×C3—21no—
274C23×C3—21no—
275C23×C3—21no—
276C23×C3—42no—
277C23×C3—41no—
278C23×C3—41no—
279C23×C3—42no—
280C23×C3(C2×D3)⋊C411yescharacteristic
281C23×C3(C2×D3)⋊C411yescharacteristic
282C23×C3(C2×D3)⋊C411yescharacteristic
283C23×C3(C2×D3)⋊C411yescharacteristic
284C23×C3C2×C4×D311yescharacteristic
285C23×C3C2×C4×D311yescharacteristic
286C22×D3—62no—
287C22×D3—61no—
288C22×D3—61no—
289C22×D3—62no—
290C22×D3—62no—
291C22×D3—122no—
292C22×D3—122no—
293C22×D3—122no—
294C22×D3—121no—
295C22×D3—121no—
296C22×D3—121no—
297C22×D3—121no—
298C2×C3×C4—22no—
299C2×C3×C4—22no—
300C2×C3×C4—22no—
301C2×C3×C4—22no—
302C2×C3×C4—21no—
303C2×C3×C4—21no—
304C2×C3×C4—21no—
305C2×C3×C4—21no—
306C2×C3×C4—42no—
307C2×C3×C4—42no—
308C2×C3×C4—41no—
309C2×C3×C4—41no—
310C2×C3×C4—41no—
311C2×C3×C4—41no—
312C2×C3×C4—41no—
313C2×C3×C4—41no—
314C2×C3×C4—41no—
315C2×C3×C4—41no—
316C2×C3×C4—42no—
317C2×C3×C4—42no—
318C2×C3×C4—42no—
319C2×C3×C4—42no—
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×C4C2×D1211yescharacteristic
325C2×C3×C4C2×D1211yescharacteristic
326C2×C3×C4C2×#6711yescharacteristic
327C2×C3×C4C2×#6711yescharacteristic
328#67—124no—
329#67—122no—
330#67—122no—
331#67—124no—
332#67—122no—
333#67—122no—
334C2×Dic3—62no—
335C2×Dic3—62no—
336C2×Dic3—62no—
337C2×Dic3—62no—
338C2×Dic3—62no—
339C2×Dic3—61no—
340C2×Dic3—61no—
341C2×Dic3—61no—
342C2×Dic3—61no—
343C2×Dic3—61no—
344C2×Dic3—61no—
345C2×Dic3—122no—
346C2×Dic3—122no—
347C2×Dic3—122no—
348C2×Dic3—121no—
349C2×Dic3—121no—
350C2×Dic3—121no—
351C2×Dic3—121no—
352C3×C8—122no—
353C3×C8—122no—
354C3⋊C8—42no—
355C3⋊C8—42no—
356C2×C32—22no—
357C2×C32—22no—
358C2×C32—41no—
359C2×C32#40811yescharacteristic
360C2×C32C2×#9911yescharacteristic
361C2×C32#41311yescharacteristic
362C3⋊D3—81no—
363C24—91no—
364C24#62411yescharacteristic
365C2×D4—181no—
366C2×D4—181no—
367C2×D4—362no—
368C22×C4—42no—
369C22×C4—91no—
370C22×C4—91no—
371C22×C4—91no—
372C22×C4#62411yescharacteristic
373C22×C4#62611yescharacteristic
374C22×C4#62611yescharacteristic
375C22×C4#62611yescharacteristic
376C22×C4#62611yescharacteristic
377C22×C4C2×D3211yescharacteristic
378M16—122no—
379C2×C8—62no—
380C2×C8—62no—
381C2×C8—122no—
382C4⋊C4—181no—
383C4⋊C4—181no—
384C4⋊C4—181no—
385C4⋊C4—181no—
386C22⋊C4—181no—
387C22⋊C4—181no—
388C22⋊C4—181no—
389C22⋊C4—181no—
390C22⋊C4—181no—
391C22⋊C4—181no—
392C22×C3—22no—
393C22×C3—22no—
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—22no—
403C22×C3—21no—
404C22×C3—21no—
405C22×C3—21no—
406C22×C3—21no—
407C22×C3—21no—
408C22×C3—21no—
409C22×C3—22no—
410C22×C3—22no—
411C22×C3—21no—
412C22×C3—41no—
413C22×C3—41no—
414C22×C3—41no—
415C22×C3—41no—
416C22×C3—44no—
417C22×C3—44no—
418C22×C3—48no—
419C22×C3#80612yes—
420C22×C3#80612yes—
421C22×C3#90112yes—
422C22×C3#90712yes—
423C22×C3C2×(C2×D3)⋊C411yescharacteristic
424C22×C3C2×(C2×D3)⋊C411yescharacteristic
425C2×D3—122no—
426C2×D3—122no—
427C2×D3—122no—
428C2×D3—121no—
429C2×D3—121no—
430C2×D3—121no—
431C2×D3—121no—
432C2×D3—121no—
433C2×D3—121no—
434C2×D3—244no—
435C2×D3—242no—
436C2×D3—242no—
437C3×C4—21no—
438C3×C4—21no—
439C3×C4—21no—
440C3×C4—21no—
441C3×C4—21no—
442C3×C4—21no—
443C3×C4—21no—
444C3×C4—21no—
445C3×C4—41no—
446C3×C4—41no—
447C3×C4—41no—
448C3×C4—41no—
449Dic3—122no—
450Dic3—122no—
451Dic3—122no—
452Dic3—121no—
453Dic3—121no—
454Dic3—121no—
455Dic3—121no—
456Dic3—121no—
457Dic3—121no—
458C32#146811yescharacteristic, complemented, Sylow
459C23—22no—
460C23—22no—
461C23—41no—
462C23—181no—
463C23—182no—
464C23—361no—
465C23—361no—
466C23#372211yescharacteristic
467C23#372211yescharacteristic
468C23C2×#62411yescharacteristic
469D4—362no—
470D4—362no—
471C2×C4—22no—
472C2×C4—22no—
473C2×C4—41no—
474C2×C4—41no—
475C2×C4—41no—
476C2×C4—41no—
477C2×C4—182no—
478C2×C4—181no—
479C2×C4—181no—
480C2×C4—181no—
481C2×C4—361no—
482C2×C4—361no—
483C2×C4#372211yescharacteristic
484C2×C4#372211yescharacteristic
485C2×C4C2×#62611yescharacteristic
486C2×C4C2×#62611yescharacteristic
487C8—122no—
488C8—122no—
489C2×C3—24no—
490C2×C3—22no—
491C2×C3—22no—
492C2×C3—22no—
493C2×C3—22no—
494C2×C3—21no—
495C2×C3—21no—
496C2×C3—21no—
497C2×C3—42no—
498C2×C3—42no—
499C2×C3—41no—
500C2×C3—41no—
501C2×C3C2×#80611yescharacteristic
502C2×C3C2×#80611yescharacteristic
503C2×C3#511011yescharacteristic
504C2×C3#512911yescharacteristic
505C2×C3#513211yescharacteristic
506C2×C3#513211yescharacteristic
507D3—242no—
508D3—241no—
509D3—241no—
510C22—21no—
511C22—21no—
512C22—21no—
513C22—21no—
514C22—21no—
515C22—21no—
516C22—21no—
517C22—44no—
518C22—361no—
519C22—361no—
520C22—361no—
521C22—722no—
522C22#6358112yes—
523C22#6381712yes—
524C22C2×#372211yescharacteristic
525C4—21no—
526C4—21no—
527C4—21no—
528C4—21no—
529C4—361no—
530C4—361no—
531C4—361no—
532C3—21no—
533C3#6992011yescharacteristic, complemented
534C3#6996911yescharacteristic, complemented
535C2—22no—
536C2—22no—
537C2—41no—
538C2—721no—
539C2#1059107311yescharacteristic
540C2#1059107811yescharacteristic
541C2C2×#6358111yescharacteristic
subgroupG/H
centerC22C2×#3722
commutatorC23×C32C22×C4
FrattiniC22×C4C2×D32
FittingC23×C32×C4C22
socleC22×C32C2×C22⋊C4
prime radicalC22×#638C4
cosocleC22×C32×C4C23
hypercenterC23×C4D32
hypocenterC32#1468
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×#5207C2semidirect
3. C2×C3×#830C2semidirect
4. #10589148C2semidirect
5. #10589146C2semidirect
30. #5207D3semidirect
31. C2×#830D3semidirect
458. C32#1468semidirect
533. C3#69920semidirect
534. C3#69969semidirect

Maximal subgroups

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

subgroupindex
C2×#641382
C3×#52072
C2×C3×#8302
#105891482
#105891462
#699693
#699203