Finite Group Databasebeta

← #11783286

Subgroups — #11783286

Order 1152.

953 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
1C22×C3×ΓL(1,𝔽25)C211yesmaximal, characteristic
2C2×D3×C4⋊Dic3C211yesmaximal, characteristic
3C2×#63841C211yesmaximal, characteristic
4#10589417C211yesmaximal, characteristic, complemented
5C3×#4551C211yesmaximal, characteristic, complemented
6#10589164C211yesmaximal, characteristic, complemented
7#10589164C211yesmaximal, characteristic, complemented
8#71985—31nomaximal
9#68867—31nomaximal
10C22×C3×C4×D3C2211yescharacteristic
11C22×D3×Dic3—21no—
12C22×C32×C8C2211yescharacteristic
13C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
14C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
15C2×C3×C4⋊Dic3C2211yescharacteristic
16C2×C3×C4⋊Dic3C2211yescharacteristic
17C22×C3×C3⋊C8C2211yescharacteristic
18C2×C3×ΓL(1,𝔽25)—22no—
19C2×C3×ΓL(1,𝔽25)—22no—
20C2×C3×ΓL(1,𝔽25)C414yescomplemented
21C2×Dic3⋊Dic3—21no—
22C2×(C2×D3)⋊Dic3—21no—
23C2×Dic32—21no—
24D3×C4⋊Dic3—22no—
25D3×C4⋊Dic3C414yescomplemented
26#63841—22no—
27#63841C414yescomplemented
28C22×C3×M16—31no—
29C2×#926—31no—
30C22×C4⋊Dic3—31no—
31C22×ΓL(1,𝔽25)D311yescharacteristic
32C2×#892—31no—
33C2×D3×C4⋊C4—31no—
34C3×#340—31no—
35#4551—31no—
36#4551—31no—
37#4551—31no—
38#4551—31no—
39#4551—61no—
40#4551D311yescharacteristic, complemented
41#4529—31no—
42#4529—31no—
43C23×C3×D3D411yescharacteristic
44C22×C32×C4C2311yescharacteristic
45C22×C3⋊Dic3—21no—
46C22×C3⋊Dic3—21no—
47C22×C3×Dic3—21no—
48C22×C3×Dic3—21no—
49C22×C3×Dic3D411yescharacteristic
50C2×C3×C4×D3C2×C412yes—
51C2×C3×C4×D3C2×C412yes—
52C2×C3×C4×D3C2×C412yes—
53C2×C3×C4×D3D412yes—
54C2×C3×C4×D3D412yes—
55C2×C3×C4×D3Q812yes—
56C2×D3×Dic3—24no—
57C2×D3×Dic3—42no—
58C2×D3×Dic3—42no—
59C2×C32×C8—21no—
60C2×C32×C8—21no—
61C2×C32×C8C2×C412yescomplemented
62C4⋊(C3⋊Dic3)—21no—
63C4⋊(C3⋊Dic3)—21no—
64C4⋊(C3⋊Dic3)C2×C412yes—
65C4⋊(C3⋊Dic3)C2×C412yescomplemented
66C3×C4⋊Dic3—21no—
67C3×C4⋊Dic3—21no—
68C3×C4⋊Dic3C2×C412yes—
69C3×C4⋊Dic3C2×C412yescomplemented
70C2×C3×C3⋊C8—21no—
71C2×C3×C3⋊C8—21no—
72C2×C3×C3⋊C8C2×C412yescomplemented
73C3×ΓL(1,𝔽25)—28no—
74Dic3⋊Dic3—24no—
75(C2×D3)⋊Dic3—24no—
76Dic32—24no—
77#1736—91noSylow
78C23×C3×C4—31no—
79C23×Dic3—61no—
80C22×C4×D3—61no—
81C22×C4×D3C2×D311yescharacteristic
82C2×C3×M16—34no—
83C2×C3×M16—62no—
84C2×C3×M16—62no—
85C22×C3×C8—21no—
86C22×C3×C8—31no—
87C22×C3×C8C2×D311yescharacteristic
88C22×C3×C8C2×D311yescharacteristic
89C2×C3×C4⋊C4—31no—
90C2×C3×C4⋊C4—31no—
91C2×#217—61no—
92C2×(C2×D3)⋊C4—61no—
93#926—34no—
94#926—62no—
95C2×C4⋊Dic3—31no—
96C2×C4⋊Dic3—31no—
97C2×C4⋊Dic3—31no—
98C2×C4⋊Dic3—31no—
99C2×C4⋊Dic3—34no—
100C2×C4⋊Dic3—61no—
101C2×C4⋊Dic3—61no—
102C2×C4⋊Dic3—62no—
103C2×C4⋊Dic3—61no—
104C2×C4⋊Dic3C2×D311yescharacteristic
105C2×C4⋊Dic3C2×D311yescharacteristic
106C2×Dic3⋊C4—61no—
107C2×C4×Dic3—61no—
108C2×C4×Dic3—61no—
109C22×C3⋊C8C2×D311yescharacteristic
110C2×ΓL(1,𝔽25)—22no—
111C2×ΓL(1,𝔽25)—22no—
112C2×ΓL(1,𝔽25)Dic314yescomplemented
113#892—34no—
114#892—62no—
115D3×C4⋊C4—34no—
116D3×C4⋊C4—62no—
117C23×C32C2×D411yescharacteristic
118C22×C3×D3—21no—
119C22×C3×D3—21no—
120C22×C3×D3—21no—
121C22×C3×D3—21no—
122C22×C3×D3C22⋊C412yes—
123C22×C3×D3C22⋊C412yes—
124C22×C3×D3C4⋊C412yes—
125C2×C32×C4C22×C411yescharacteristic
126C2×C32×C4C22×C411yescharacteristic
127C2×C32×C4C22×C411yescharacteristic
128C2×C32×C4C2×D411yescharacteristic
129C2×C32×C4C2×D411yescharacteristic
130C2×C32×C4C2×Q811yescharacteristic
131C2×C3⋊Dic3—22no—
132C2×C3⋊Dic3—22no—
133C2×C3⋊Dic3—41no—
134C2×C3⋊Dic3—41no—
135C2×C3⋊Dic3—41no—
136C2×C3⋊Dic3—41no—
137C2×C3×Dic3—22no—
138C2×C3×Dic3—22no—
139C2×C3×Dic3—41no—
140C2×C3×Dic3—41no—
141C2×C3×Dic3—41no—
142C2×C3×Dic3—41no—
143C2×C3×Dic3C22⋊C412yes—
144C2×C3×Dic3C22⋊C412yes—
145C2×C3×Dic3C4⋊C412yes—
146C3×C4×D3C4214yes—
147C3×C4×D3C22⋊C414yes—
148C3×C4×D3C4⋊C414yes—
149C3×C4×D3C4⋊C414yes—
150D3×Dic3—48no—
151C32×C8—22no—
152C3×C3⋊C8—22no—
153C22×M16—31no—
154C2×#117—91no—
155C22×C4⋊C4—91no—
156#340—31no—
157#340—91no—
158#340—91no—
159#340—91no—
160C24×C3—31no—
161C23×D3D1211yescharacteristic
162C22×C3×C4—21no—
163C22×C3×C4—31no—
164C22×C3×C4—32no—
165C22×C3×C4—32no—
166C22×C3×C4—32no—
167C22×C3×C4—32no—
168C22×C3×C4—32no—
169C22×C3×C4—32no—
170C22×C3×C4—61no—
171C22×C3×C4—61no—
172C22×C3×C4C22×D311yescharacteristic
173C22×C3×C4C22×D311yescharacteristic
174C22×Dic3—21no—
175C22×Dic3—21no—
176C22×Dic3—64no—
177C22×Dic3—61no—
178C22×Dic3—61no—
179C22×Dic3—61no—
180C22×Dic3—61no—
181C22×Dic3—121no—
182C22×Dic3—121no—
183C22×Dic3—122no—
184C22×Dic3—122no—
185C22×Dic3D1211yescharacteristic
186C2×C4×D3—64no—
187C2×C4×D3—122no—
188C2×C4×D3—122no—
189C2×C4×D3Dic612yes—
190C2×C4×D3C4×D312yes—
191C2×C4×D3C4×D312yes—
192C2×C4×D3C2×Dic312yes—
193C2×C4×D3#6712yes—
194C2×C4×D3#6712yes—
195C3×M16—68no—
196C2×C3×C8—21no—
197C2×C3×C8—21no—
198C2×C3×C8—21no—
199C2×C3×C8—21no—
200C2×C3×C8—22no—
201C2×C3×C8—32no—
202C2×C3×C8—41no—
203C2×C3×C8—41no—
204C2×C3×C8—61no—
205C2×C3×C8—61no—
206C2×C3×C8C4×D312yescomplemented
207C2×C3×C8C2×Dic312yescomplemented
208C3×C4⋊C4—32no—
209C3×C4⋊C4—32no—
210C3×C4⋊C4—61no—
211C3×C4⋊C4—61no—
212#217—64no—
213(C2×D3)⋊C4—64no—
214C4⋊Dic3—21no—
215C4⋊Dic3—21no—
216C4⋊Dic3—32no—
217C4⋊Dic3—32no—
218C4⋊Dic3—32no—
219C4⋊Dic3—32no—
220C4⋊Dic3—62no—
221C4⋊Dic3—62no—
222C4⋊Dic3—64no—
223C4⋊Dic3—61no—
224C4⋊Dic3—61no—
225C4⋊Dic3—61no—
226C4⋊Dic3—61no—
227C4⋊Dic3—121no—
228C4⋊Dic3—121no—
229C4⋊Dic3C4×D312yes—
230C4⋊Dic3C4×D312yescomplemented
231Dic3⋊C4—64no—
232C4×Dic3—64no—
233C4×Dic3—64no—
234C2×C3⋊C8—21no—
235C2×C3⋊C8—21no—
236C2×C3⋊C8C2×Dic312yescomplemented
237ΓL(1,𝔽25)—28no—
238C22×C32C2×C22⋊C411yescharacteristic
239C22×C32C2×C22⋊C411yescharacteristic
240C22×C32C2×C4⋊C411yescharacteristic
241C22×C32AGL(1,ℤ/8)11yescharacteristic
242C22×C32AGL(1,ℤ/8)11yescharacteristic
243C22×C32#13711yescharacteristic
244C22×C32#13711yescharacteristic
245C2×C3×D3—22no—
246C2×C3×D3—22no—
247C2×C3×D3—22no—
248C2×C3×D3—22no—
249C2×C3×D3—22no—
250C2×C3×D3—22no—
251C2×C3×D3#9514yes—
252C32×C4C2×C4211yescharacteristic
253C32×C4C2×C22⋊C411yescharacteristic
254C32×C4C2×C4⋊C411yescharacteristic
255C32×C4C2×C4⋊C411yescharacteristic
256C3⋊Dic3—42no—
257C3⋊Dic3—42no—
258C3×Dic3—42no—
259C3×Dic3—42no—
260C3×Dic3#9514yes—
261C23×C4—31no—
262C23×C4—181no—
263C2×M16—34no—
264C2×M16—62no—
265C2×M16—62no—
266C22×C8—31no—
267C22×C8D3211yescharacteristic
268#117—94no—
269#117—182no—
270C2×C4⋊C4—31no—
271C2×C4⋊C4—31no—
272C2×C4⋊C4—94no—
273C2×C4⋊C4—91no—
274C2×C4⋊C4—91no—
275C2×C4⋊C4—182no—
276C2×C4⋊C4—181no—
277C2×C22⋊C4—181no—
278C2×C42—181no—
279C23×C3—21no—
280C23×C3—32no—
281C23×C3—32no—
282C23×C3—32no—
283C23×C3—61no—
284C23×C3—61no—
285C23×C3—61no—
286C23×C3—61no—
287C23×C3C2×D1211yescharacteristic
288C23×C3D3×D411yescharacteristic
289C22×D3—21no—
290C22×D3—21no—
291C22×D3—21no—
292C22×D3—21no—
293C22×D3C4⋊Dic312yes—
294C22×D3(C2×D3)⋊C412yes—
295C22×D3(C2×D3)⋊C412yes—
296C2×C3×C4—21no—
297C2×C3×C4—21no—
298C2×C3×C4—21no—
299C2×C3×C4—21no—
300C2×C3×C4—21no—
301C2×C3×C4—21no—
302C2×C3×C4—32no—
303C2×C3×C4—32no—
304C2×C3×C4—32no—
305C2×C3×C4—34no—
306C2×C3×C4—34no—
307C2×C3×C4—34no—
308C2×C3×C4—34no—
309C2×C3×C4—62no—
310C2×C3×C4—62no—
311C2×C3×C4—121no—
312C2×C3×C4—121no—
313C2×C3×C4—121no—
314C2×C3×C4—121no—
315C2×C3×C4C2×Dic611yescharacteristic
316C2×C3×C4C2×C4×D311yescharacteristic
317C2×C3×C4C2×C4×D311yescharacteristic
318C2×C3×C4C2×C4×D311yescharacteristic
319C2×C3×C4C2×C4×D311yescharacteristic
320C2×C3×C4C2×C4×D311yescharacteristic
321C2×C3×C4D3×D411yescharacteristic
322C2×C3×C4D3×D411yescharacteristic
323C2×C3×C4D3×Q811yescharacteristic
324C2×C3×C4C22×Dic311yescharacteristic
325C2×C3×C4C2×#6711yescharacteristic
326C2×C3×C4C2×#6711yescharacteristic
327C2×Dic3—22no—
328C2×Dic3—22no—
329C2×Dic3—41no—
330C2×Dic3—41no—
331C2×Dic3—41no—
332C2×Dic3—41no—
333C2×Dic3—62no—
334C2×Dic3—62no—
335C2×Dic3—62no—
336C2×Dic3—62no—
337C2×Dic3—122no—
338C2×Dic3—122no—
339C2×Dic3—128no—
340C2×Dic3—121no—
341C2×Dic3—121no—
342C2×Dic3—121no—
343C2×Dic3—121no—
344C2×Dic3—121no—
345C2×Dic3—121no—
346C2×Dic3—121no—
347C2×Dic3—121no—
348C2×Dic3—241no—
349C2×Dic3—241no—
350C2×Dic3—241no—
351C2×Dic3—241no—
352C2×Dic3C4⋊Dic312yes—
353C2×Dic3(C2×D3)⋊C412yes—
354C2×Dic3(C2×D3)⋊C412yes—
355C4×D3—128no—
356C4×D3C4×Dic314yes—
357C4×D3Dic3⋊C414yes—
358C4×D3Dic3⋊C414yes—
359C4×D3#21714yes—
360C3×C8—22no—
361C3×C8—22no—
362C3×C8—42no—
363C3×C8—62no—
364C3⋊C8—22no—
365C2×C32C2×#9511yescharacteristic
366C2×C32#41711yescharacteristic
367C2×C32#41711yescharacteristic
368C2×C32#41811yescharacteristic
369C2×C32#41911yescharacteristic
370C2×C32#42811yescharacteristic
371C2×C32#42811yescharacteristic
372C3×D3—24no—
373C24—31no—
374C22×C4—31no—
375C22×C4—32no—
376C22×C4—32no—
377C22×C4—32no—
378C22×C4—32no—
379C22×C4—32no—
380C22×C4—32no—
381C22×C4—61no—
382C22×C4—61no—
383C22×C4—184no—
384C22×C4—181no—
385C22×C4—181no—
386C22×C4—362no—
387C22×C4—362no—
388C22×C4C2×D3211yescharacteristic
389M16—68no—
390C2×C8—21no—
391C2×C8—21no—
392C2×C8—32no—
393C2×C8—61no—
394C2×C8—61no—
395C2×C8D3×Dic312yescomplemented
396C4⋊C4—32no—
397C4⋊C4—32no—
398C4⋊C4—61no—
399C4⋊C4—61no—
400C4⋊C4—92no—
401C4⋊C4—92no—
402C4⋊C4—184no—
403C4⋊C4—181no—
404C4⋊C4—181no—
405C22⋊C4—184no—
406C42—184no—
407C22×C3—21no—
408C22×C3—21no—
409C22×C3—21no—
410C22×C3—21no—
411C22×C3—21no—
412C22×C3—21no—
413C22×C3—21no—
414C22×C3—34no—
415C22×C3—62no—
416C22×C3—62no—
417C22×C3—62no—
418C22×C3—62no—
419C22×C3—62no—
420C22×C3—62no—
421C22×C3D3×C22⋊C411yescharacteristic
422C22×C3D3×C22⋊C411yescharacteristic
423C22×C3D3×C4⋊C411yescharacteristic
424C22×C3#90811yescharacteristic
425C22×C3#90811yescharacteristic
426C22×C3#90911yescharacteristic
427C22×C3#90911yescharacteristic
428C22×C3#91111yescharacteristic
429C22×C3#91411yescharacteristic
430C22×C3#91511yescharacteristic
431C22×C3#91811yescharacteristic
432C22×C3C2×C4⋊Dic311yescharacteristic
433C22×C3C2×(C2×D3)⋊C411yescharacteristic
434C22×C3C2×(C2×D3)⋊C411yescharacteristic
435C2×D3—22no—
436C2×D3—22no—
437C2×D3—22no—
438C2×D3—22no—
439C2×D3—22no—
440C2×D3—22no—
441C2×D3C3⋊#9514yes—
442C3×C4—21no—
443C3×C4—21no—
444C3×C4—21no—
445C3×C4—21no—
446C3×C4—34no—
447C3×C4—122no—
448C3×C4—122no—
449C3×C4C42×D311yescharacteristic
450C3×C4D3×C22⋊C411yescharacteristic
451C3×C4D3×C4⋊C411yescharacteristic
452C3×C4D3×C4⋊C411yescharacteristic
453C3×C4C2×C4×Dic311yescharacteristic
454C3×C4C2×Dic3⋊C411yescharacteristic
455C3×C4C2×Dic3⋊C411yescharacteristic
456C3×C4C2×#21711yescharacteristic
457Dic3—42no—
458Dic3—42no—
459Dic3—122no—
460Dic3—122no—
461Dic3—122no—
462Dic3—122no—
463Dic3—242no—
464Dic3—242no—
465Dic3C3⋊#9514yes—
466C32#173611yescharacteristic, complemented, Sylow
467C23—32no—
468C23—32no—
469C23—32no—
470C23—61no—
471C23—61no—
472C23—61no—
473C23—61no—
474C23D3×D1211yescharacteristic
475C2×C4—32no—
476C2×C4—32no—
477C2×C4—32no—
478C2×C4—34no—
479C2×C4—34no—
480C2×C4—34no—
481C2×C4—34no—
482C2×C4—62no—
483C2×C4—62no—
484C2×C4—121no—
485C2×C4—121no—
486C2×C4—121no—
487C2×C4—121no—
488C2×C4—182no—
489C2×C4—182no—
490C2×C4—368no—
491C2×C4—361no—
492C2×C4—361no—
493C2×C4—361no—
494C2×C4—361no—
495C2×C4D3×Dic611yescharacteristic
496C2×C4C4×D3211yescharacteristic
497C2×C4C4×D3211yescharacteristic
498C2×C4C2×D3×Dic311yescharacteristic
499C2×C4D3×#6711yescharacteristic
500C2×C4D3×#6711yescharacteristic
501C8—22no—
502C8—62no—
503C2×C3—21no—
504C2×C3—21no—
505C2×C3—21no—
506C2×C3—21no—
507C2×C3—21no—
508C2×C3—21no—
509C2×C3—21no—
510C2×C3—64no—
511C2×C3D3×#9511yescharacteristic
512C2×C3#477011yescharacteristic
513C2×C3#477111yescharacteristic
514C2×C3#480211yescharacteristic
515C2×C3#480311yescharacteristic
516C2×C3#486111yescharacteristic
517C2×C3#488111yescharacteristic
518C2×C3#512011yescharacteristic
519C2×C3#512111yescharacteristic
520C2×C3#512111yescharacteristic
521C2×C3#513111yescharacteristic
522C2×C3#513311yescharacteristic
523C2×C3#513311yescharacteristic
524C2×C3C2×C3⋊#9511yescharacteristic
525D3—24no—
526C22—34no—
527C22—62no—
528C22—62no—
529C22—62no—
530C22—62no—
531C22—62no—
532C22—62no—
533C22#6379411yescharacteristic
534C22#6379511yescharacteristic
535C22#6380011yescharacteristic
536C22#6380111yescharacteristic
537C22D3×C4⋊Dic311yescharacteristic
538C22D3×(C2×D3)⋊C411yescharacteristic
539C22D3×(C2×D3)⋊C411yescharacteristic
540C4—34no—
541C4—122no—
542C4—122no—
543C4—362no—
544C4—362no—
545C4C4×D3×Dic311yescharacteristic
546C4D3×Dic3⋊C411yescharacteristic
547C4D3×Dic3⋊C411yescharacteristic
548C4D3×#21711yescharacteristic
549C3—21no—
550C3#6886711yescharacteristic, complemented
551C3#7198511yescharacteristic, complemented
552C2—64no—
553C2#1059067011yescharacteristic
554C2#1059067111yescharacteristic
555C2#1059068111yescharacteristic
556C2#1059068311yescharacteristic
557C2#1059093911yescharacteristic
558C2#1059094811yescharacteristic
559C2D3×C3⋊#9511yescharacteristic
subgroupG/H
centerC23D3×D12
commutatorC32×C4C2×C42
FrattiniC22×C4C2×D32
FittingC22×C32×C8C22
socleC23×C32C2×D4
prime radicalC23×C3×D3D4
cosocleC22×C32×C4C23
hypercenterC22×C8D32
hypocenterC32#1736
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×C8

Complements

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

NH ≅ G/Ntype
4. #10589417C2semidirect
5. C3×#4551C2semidirect
6. #10589164C2semidirect
7. #10589164C2semidirect
20. C2×C3×ΓL(1,𝔽25)C4semidirect
25. D3×C4⋊Dic3C4semidirect
27. #63841C4semidirect
40. #4551D3semidirect
61. C2×C32×C8C2×C4semidirect
65. C4⋊(C3⋊Dic3)C2×C4semidirect
69. C3×C4⋊Dic3C2×C4semidirect
72. C2×C3×C3⋊C8C2×C4semidirect
112. C2×ΓL(1,𝔽25)Dic3semidirect
206. C2×C3×C8C4×D3semidirect
207. C2×C3×C8C2×Dic3semidirect
230. C4⋊Dic3C4×D3semidirect
236. C2×C3⋊C8C2×Dic3semidirect
395. C2×C8D3×Dic3semidirect
466. C32#1736semidirect
550. C3#68867semidirect
551. C3#71985semidirect

Maximal subgroups

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

subgroupindex
C22×C3×ΓL(1,𝔽25)2
C2×D3×C4⋊Dic32
C2×#638412
#105894172
C3×#45512
#105891642
#719853
#688673