Finite Group Databasebeta

← #29575715

Subgroups — #29575715

Order 15616.

752 conjugacy classes of subgroups.

The subgroup lattice has 528 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839784C211yesmaximal, characteristic, complemented
2#21454161C211yesmaximal, characteristic
3#21445796C211yesmaximal, characteristic, complemented
4C2×#16839506C211yesmaximal, characteristic, complemented
5#21443703C211yesmaximal, characteristic, complemented
6#21443703C211yesmaximal, characteristic, complemented
7C2×C61×#331C211yesmaximal, characteristic, complemented
8C22×#11758189—21no—
9C2×#14519748—21no—
10C2×#14519748—21no—
11C2×#14519748C412yes—
12C2×C42×D61C2211yescharacteristic
13#16839784—22no—
14#16839784—22no—
15C2×C4⋊#92418C2211yescharacteristic
16C2×C4⋊#92418C2211yescharacteristic
17C2×#14519706—21no—
18C2×#14519689—21no—
19#16839665—21no—
20#16839665—21no—
21#16839665C412yes—
22#16839632C2211yescharacteristic
23#16839516—21no—
24#16839506—22no—
25C2×#127×C61C2211yescharacteristic
26C2×C4⋊C8×C61C2211yescharacteristic
27C2×C4⋊C8×C61C2211yescharacteristic
28C61×#331—22no—
29C22×C22⋊D61—22no—
30C22×C4×D61C2×C411yescharacteristic
31C22×C4×D61D411yescharacteristic
32C22×C4×D61D411yescharacteristic
33C2×#11758189—24no—
34C2×#11758189—42no—
35C2×#11758189—42no—
36C22×#92418—21no—
37C22×#92418—21no—
38#14519748—42no—
39#14519748—42no—
40#14519748—42no—
41#14519748—42no—
42#14519748—44no—
43C2×C4⋊Dic61—21no—
44C2×C4⋊Dic61—21no—
45C2×C4⋊Dic61C2×C412yes—
46C2×C22⋊Dic61—22no—
47C2×C22⋊Dic61—22no—
48C2×C22⋊Dic61—22no—
49C2×C4×Dic61C2×C411yescharacteristic
50C2×C4×Dic61D411yescharacteristic
51C2×C4×Dic61D411yescharacteristic
52C42×D61—21no—
53C42×D61—21no—
54C42×D61—21no—
55C42×D61—21no—
56C4⋊#92418—21no—
57C4⋊#92418—21no—
58C4⋊#92418—21no—
59C4⋊#92418D412yescomplemented
60#14519706—24no—
61#14519689—42no—
62C22×D4×C61—21no—
63C22×D4×C61—21no—
64C22×D4×C61C2×C412yes—
65C22×C8×C61—21no—
66C22×C8×C61—21no—
67#127×C61—21no—
68#127×C61—21no—
69#127×C61—21no—
70#127×C61—21no—
71C2×C42×C61C2311yescharacteristic
72C4⋊C8×C61—21no—
73C4⋊C8×C61—21no—
74C4⋊C8×C61—21no—
75C4⋊C8×C61D412yescomplemented
76C24×C61—22no—
77C23×D61C22⋊C411yescharacteristic
78C2×D4×C61—22no—
79C2×D4×C61—22no—
80C2×D4×C61—42no—
81C2×D4×C61—42no—
82C2×D4×C61—41no—
83C2×D4×C61—41no—
84C2×D4×C61—41no—
85C2×D4×C61—41no—
86C2×D4×C61—41no—
87C2×D4×C61—41no—
88C2×D4×C61—41no—
89C2×D4×C61—41no—
90C2×D4×C61—41no—
91C2×D4×C61—41no—
92C2×D4×C61—41no—
93C2×D4×C61—41no—
94C22×C4×C61C22×C411yescharacteristic
95C22×C4×C61C2×D411yescharacteristic
96C22×C4×C61C2×D411yescharacteristic
97C2×C22⋊D61—44no—
98C2×C22⋊D61—44no—
99C2×C22⋊D61—44no—
100C22×Dic61—22no—
101C22×Dic61C22⋊C411yescharacteristic
102C22×Dic61C22⋊C411yescharacteristic
103C22×Dic61C22⋊C411yescharacteristic
104C2×C4×D61—21no—
105C2×C4×D61—21no—
106C2×C4×D61—21no—
107C2×C4×D61—21no—
108C2×C4×D61—21no—
109C2×C4×D61—21no—
110C2×C4×D61—21no—
111C2×C4×D61—21no—
112C2×C4×D61—21no—
113C2×C4×D61—21no—
114C2×C4×D61—21no—
115C2×C4×D61—21no—
116C2×C4×D61—22no—
117C2×C4×D61—41no—
118C2×C4×D61D812yes—
119C2×C4×D61SD1612yes—
120C2×C8×C61—22no—
121C2×C8×C61—41no—
122C2×C8×C61—41no—
123C2×C8×C61—41no—
124C2×C8×C61—41no—
125C2×C8×C61—41no—
126C42×C61C2×D411yescharacteristic
127C42×C61C2×D411yescharacteristic
128C42×C61#4111yescharacteristic
129C42×C61#4111yescharacteristic
130C22⋊Dic61—44no—
131C22⋊Dic61—44no—
132C22⋊Dic61—44no—
133C4⋊Dic61—41no—
134C4⋊Dic61—41no—
135C4⋊Dic61—41no—
136C4⋊Dic61—41no—
137C4⋊Dic61—42no—
138C4×Dic61—21no—
139C4×Dic61—21no—
140C4×Dic61—21no—
141C4×Dic61—21no—
142C4×Dic61—21no—
143C4×Dic61—21no—
144C2×#92418—22no—
145C2×#92418—41no—
146C2×#92418—41no—
147C2×#92418—41no—
148C2×#92418—41no—
149C2×#92418—41no—
150#11758189—48no—
151C23×C61—42no—
152C23×C61—42no—
153C23×C61—42no—
154C23×C61—42no—
155C23×C61—42no—
156C23×C61—42no—
157C23×C61—42no—
158C23×C61C2×C22⋊C411yescharacteristic
159C22×D61—21no—
160C22×D61—21no—
161C22×D61—21no—
162C22×D61—21no—
163C22×D61—21no—
164C22×D61—21no—
165C22×D61#10212yes—
166D4×C61—82no—
167D4×C61—82no—
168D4×C61—81no—
169D4×C61—81no—
170D4×C61—81no—
171D4×C61—81no—
172D4×C61—81no—
173D4×C61—81no—
174D4×C61—81no—
175D4×C61—81no—
176C2×C4×C61—21no—
177C2×C4×C61—21no—
178C2×C4×C61C4×D411yescharacteristic
179C2×C4×C61C4×D411yescharacteristic
180C2×C4×C61#12011yescharacteristic
181C2×C4×C61#12111yescharacteristic
182C2×C4×C61#12111yescharacteristic
183C2×C4×C61#12311yescharacteristic
184C2×C4×C61C2×D811yescharacteristic
185C2×C4×C61C2×SD1611yescharacteristic
186C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
187C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
188C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
189C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
190C2×C4×C61#13711yescharacteristic
191C2×C4×C61#13711yescharacteristic
192C22⋊D61—88no—
193C2×Dic61—21no—
194C2×Dic61—21no—
195C2×Dic61—21no—
196C2×Dic61—21no—
197C2×Dic61—21no—
198C2×Dic61—21no—
199C2×Dic61—21no—
200C2×Dic61—42no—
201C2×Dic61—42no—
202C2×Dic61—42no—
203C2×Dic61#10012yes—
204C2×Dic61#10212yes—
205C4×D61—22no—
206C4×D61—22no—
207C4×D61—22no—
208C4×D61—22no—
209C4×D61—42no—
210C4×D61—42no—
211C4×D61—41no—
212C4×D61—41no—
213C4×D61—41no—
214C4×D61—41no—
215C8×C61—42no—
216C8×C61—81no—
217#92418—42no—
218#92418—81no—
219#9141—611nomaximal, Sylow
220C22×C61—82no—
221C22×C61—82no—
222C22×C61—82no—
223C22×C61—82no—
224C22×C61—82no—
225C22×C61—82no—
226C22×C61—82no—
227C22×C61#38611yescharacteristic
228C22×C61C2×#10011yescharacteristic
229C22×C61#41311yescharacteristic
230C22×C61C2×#10211yescharacteristic
231C22×C61#41711yescharacteristic
232C22×C61#41711yescharacteristic
233C22×C61#41811yescharacteristic
234C2×D61—22no—
235C2×D61—22no—
236C2×D61—22no—
237C2×D61—41no—
238C2×D61—41no—
239C2×D61—41no—
240C2×D61—41no—
241C4×C61—21no—
242C4×C61—21no—
243C4×C61#44711yescharacteristic
244C4×C61#44811yescharacteristic
245C4×C61#46811yescharacteristic
246C4×C61#46811yescharacteristic
247C4×C61#46911yescharacteristic
248C4×C61#46911yescharacteristic
249C4×C61#48011yescharacteristic
250C4×C61#48111yescharacteristic
251Dic61—22no—
252Dic61—22no—
253Dic61—41no—
254Dic61—82no—
255C2×#423—611no—
256#2856—611no—
257#1797—611no—
258C2×#331—611no—
259C2×#331D6111yescharacteristic, complemented
260#1296—611no—
261#1296—611no—
262C2×C61—162no—
263C2×C61#154511yescharacteristic
264C2×C61#154711yescharacteristic
265C2×C61#155711yescharacteristic
266C2×C61#156011yescharacteristic
267C2×C61#187411yescharacteristic
268C2×C61#189511yescharacteristic
269C2×C61#190011yescharacteristic
270D61—42no—
271C22×M16—1221no—
272C2×#127C2×D6111yescharacteristic
273C2×#121—612no—
274C2×#121—1221no—
275C2×#121—1221no—
276C22×C42—611no—
277#423—1222no—
278#423—1222no—
279C2×C4⋊C8—611no—
280C2×C4⋊C8—611no—
281C2×C4⋊C8—1221no—
282C2×C4⋊C8C2×D6111yescharacteristic
283C2×C4⋊C8C2×D6111yescharacteristic
284C2×C22⋊C8—1221no—
285#390—612no—
286#390—1221no—
287#390—1221no—
288#384—611no—
289#336—1221no—
290#331—22no—
291#331—1222no—
292C61#914111yescharacteristic, complemented, Sylow
293C22×D4—21no—
294C22×D4—21no—
295C22×D4—1222no—
296C22×D4C4×D6112yes—
297C23×C4—611no—
298C23×C4—611no—
299C23×C4—611no—
300C2×M16—1224no—
301C2×M16—2442no—
302C2×M16—2442no—
303C22×C8—21no—
304C22×C8—21no—
305C22×C8—1221no—
306C22×C8—1221no—
307#127—21no—
308#127—21no—
309#127—21no—
310#127—21no—
311#121—2442no—
312#121—2442no—
313#121—2442no—
314#121—2442no—
315#121—2444no—
316C2×C4⋊C4—612no—
317C2×C4⋊C4—1221no—
318C2×C4⋊C4—1221no—
319C2×C22⋊C4—1222no—
320C2×C22⋊C4—1222no—
321C2×C22⋊C4—1222no—
322C2×C42—611no—
323C2×C42—611no—
324C2×C42—611no—
325C2×C42—1221no—
326C2×C42—1221no—
327C2×C42—1221no—
328C2×C42—1221no—
329C2×C42C22×D6111yescharacteristic
330C4⋊C8—21no—
331C4⋊C8—21no—
332C4⋊C8—21no—
333C4⋊C8—612no—
334C4⋊C8—1224no—
335C4⋊C8—1221no—
336C4⋊C8—1221no—
337C4⋊C8—1221no—
338C4⋊C8C22⋊D6112yescomplemented
339C22⋊C8—2442no—
340C24—22no—
341C24—611no—
342C2×D4—22no—
343C2×D4—22no—
344C2×D4—42no—
345C2×D4—42no—
346C2×D4—41no—
347C2×D4—41no—
348C2×D4—41no—
349C2×D4—41no—
350C2×D4—41no—
351C2×D4—41no—
352C2×D4—41no—
353C2×D4—41no—
354C2×D4—41no—
355C2×D4—41no—
356C2×D4—41no—
357C2×D4—41no—
358C2×D4—2444no—
359C2×D4—2444no—
360C2×D4—2444no—
361C22×C4—611no—
362C22×C4—611no—
363C22×C4—612no—
364C22×C4—612no—
365C22×C4—611no—
366C22×C4—1222no—
367C22×C4—1221no—
368C22×C4—1221no—
369C22×C4—1221no—
370C22×C4—1221no—
371C22×C4—1221no—
372C22×C4—1221no—
373C22×C4—1221no—
374C22×C4—1221no—
375C22×C4—1221no—
376C22×C4—1221no—
377C22×C4—1221no—
378C22×C4—1221no—
379C22×C4—1222no—
380C22×C4—2441no—
381C22×C4C2×C4×D6111yescharacteristic
382C22×C4D4×D6111yescharacteristic
383C22×C4D4×D6111yescharacteristic
384M16—2448no—
385C2×C8—22no—
386C2×C8—41no—
387C2×C8—41no—
388C2×C8—41no—
389C2×C8—41no—
390C2×C8—41no—
391C2×C8—1222no—
392C2×C8—2441no—
393C2×C8—2441no—
394C2×C8—2441no—
395C2×C8—2441no—
396C2×C8—2441no—
397C4⋊C4—2442no—
398C4⋊C4—2441no—
399C4⋊C4—2441no—
400C4⋊C4—2441no—
401C4⋊C4—2441no—
402C22⋊C4—2444no—
403C22⋊C4—2444no—
404C22⋊C4—2444no—
405C42—1221no—
406C42—1221no—
407C42—1221no—
408C42—1221no—
409C42—1221no—
410C42—1221no—
411C42#1175822211yescharacteristic
412C42D4×D6111yescharacteristic
413C42#1175822411yescharacteristic
414C42C2×C22⋊D6111yescharacteristic
415C23—42no—
416C23—42no—
417C23—42no—
418C23—42no—
419C23—42no—
420C23—42no—
421C23—42no—
422C23—612no—
423C23—1221no—
424C23—1221no—
425C23—1221no—
426C23—1221no—
427C23—1221no—
428C23—1221no—
429C23C22⋊C4×D6111yescharacteristic
430D4—82no—
431D4—82no—
432D4—81no—
433D4—81no—
434D4—81no—
435D4—81no—
436D4—81no—
437D4—81no—
438D4—81no—
439D4—81no—
440D4—4888no—
441C2×C4—21no—
442C2×C4—21no—
443C2×C4—612no—
444C2×C4—612no—
445C2×C4—1221no—
446C2×C4—1221no—
447C2×C4—1221no—
448C2×C4—1221no—
449C2×C4—1222no—
450C2×C4—1222no—
451C2×C4—1222no—
452C2×C4—1222no—
453C2×C4—1221no—
454C2×C4—1221no—
455C2×C4—1221no—
456C2×C4—2442no—
457C2×C4—2442no—
458C2×C4—2442no—
459C2×C4—2442no—
460C2×C4—2442no—
461C2×C4—2441no—
462C2×C4—2441no—
463C2×C4—2441no—
464C2×C4—2441no—
465C2×C4#1451973711yescharacteristic
466C2×C4C4×C22⋊D6111yescharacteristic
467C2×C4#1451974511yescharacteristic
468C2×C4#1451974811yescharacteristic
469C2×C4#1451975011yescharacteristic
470C2×C4#1451975911yescharacteristic
471C2×C4D8×D6111yescharacteristic
472C2×C4SD16×D6111yescharacteristic
473C2×C4#1451980111yescharacteristic
474C2×C4#1451980111yescharacteristic
475C2×C4#1451980111yescharacteristic
476C2×C4#1451980411yescharacteristic
477C2×C4#1451980611yescharacteristic
478C2×C4#1451980611yescharacteristic
479C8—42no—
480C8—81no—
481C8—4881no—
482C8—2442no—
483C22—82no—
484C22—82no—
485C22—82no—
486C22—82no—
487C22—82no—
488C22—82no—
489C22—82no—
490C22—1222no—
491C22—1222no—
492C22—1222no—
493C22—2441no—
494C22—2441no—
495C22—2441no—
496C22—2441no—
497C22#1683963811yescharacteristic
498C22#100×D6111yescharacteristic
499C22#1683974311yescharacteristic
500C22#102×D6111yescharacteristic
501C22#1683976011yescharacteristic
502C22#1683976011yescharacteristic
503C22#1683976511yescharacteristic
504C4—21no—
505C4—21no—
506C4—1222no—
507C4—1222no—
508C4—4882no—
509C4—2441no—
510C4#1683989411yescharacteristic
511C4#1683989911yescharacteristic
512C4#1684000511yescharacteristic
513C4#1684000711yescharacteristic
514C4#1684001211yescharacteristic
515C4#1684001411yescharacteristic
516C4#1684007411yescharacteristic
517C4#1684007911yescharacteristic
518C2—162no—
519C2—2442no—
520C2#2144448511yescharacteristic
521C2#2144449311yescharacteristic
522C2#2144453811yescharacteristic
523C2#2144455111yescharacteristic
524C2#2144613311yescharacteristic
525C2#2144625411yescharacteristic
526C2#2144627911yescharacteristic
subgroupG/H
centerC23C22⋊C4×D61
commutatorC22×C4×C61C22×C4
FrattiniC2×C42C22×D61
FittingC2×C61×#331C2
socleC23×C61C2×C22⋊C4
prime radical#21454161C2
cosocleC2×C42×C61C23
hypercenterC2×#331D61
hypocenterC61#9141
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#331

Complements

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

NH ≅ G/Ntype
1. C2×#16839784C2semidirect
3. #21445796C2semidirect
4. C2×#16839506C2semidirect
5. #21443703C2semidirect
6. #21443703C2semidirect
7. C2×C61×#331C2semidirect
59. C4⋊#92418D4semidirect
75. C4⋊C8×C61D4semidirect
259. C2×#331D61semidirect
292. C61#9141semidirect
338. C4⋊C8C22⋊D61semidirect

Maximal subgroups

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

subgroupindex
C2×#168397842
#214541612
#214457962
C2×#168395062
#214437032
C2×C61×#3312
#914161