Finite Group Databasebeta

← #29580230

Subgroups — #29580230

Order 15616.

872 conjugacy classes of subgroups.

The subgroup lattice has 524 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839901C211yesmaximal, characteristic
2#21451561C211yesmaximal, characteristic
3#21445754C211yesmaximal, characteristic, complemented
4C2×#16839495C211yesmaximal, characteristic
5C2×#16839488C211yesmaximal, characteristic, complemented
6#21443698C211yesmaximal, characteristic, complemented
7C2×C61×#395C211yesmaximal, characteristic, complemented
8C22×#11758201—21no—
9C2×#14519760—21no—
10C2×#14519751C2211yescharacteristic
11#16839901—22no—
12#16839901—22no—
13C2×#14519701—21no—
14C2×#14519701—22no—
15C2×C22⋊#92418C2211yescharacteristic
16C2×C22⋊#92418C2211yescharacteristic
17#16839692—21no—
18#16839684—22no—
19#16839679—21no—
20#16839641—21no—
21#16839622C2211yescharacteristic
22#16839495—22no—
23#16839488—22no—
24C23×Q8×C61C2211yescharacteristic
25C22×C4⋊C4×C61—21no—
26C22×C4⋊C4×C61C2211yescharacteristic
27C61×#395—22no—
28C61×#395—22no—
29C2×#95×C61—21no—
30C2×#95×C61C2211yescharacteristic
31C22×D244D411yescharacteristic
32C22×C22⋊D61—21no—
33C2×#11758201—24no—
34C2×#11758201—44no—
35C22×#92418—21no—
36C22×#92418—21no—
37#14519760—42no—
38#14519760—42no—
39#14519751—21no—
40#14519751—21no—
41#14519751—21no—
42#14519751—21no—
43C2×C4⋊Dic61D411yescharacteristic
44C2×C4⋊Dic61D412yes—
45C2×#11758196—22no—
46C2×C22⋊Dic61—21no—
47C2×#11758198—22no—
48C2×#11758198—21no—
49C2×#11758198—22no—
50#14519701—24no—
51#14519701—44no—
52C22⋊#92418—21no—
53C22⋊#92418—21no—
54C22⋊#92418—21no—
55C22⋊#92418D412yes—
56#14519684—22no—
57#14519684—21no—
58C22×Q8×C61—21no—
59C22×Q8×C61—21no—
60C22×Q8×C61—21no—
61C22×Q8×C61—21no—
62C22×Q8×C61—21no—
63C22×Q8×C61—44no—
64C22×Q8×C61D412yes—
65C23×C4×C61—21no—
66C23×C4×C61—21no—
67C23×C4×C61D411yescharacteristic
68C23×C4×C61D411yescharacteristic
69C23×C4×C61C2311yescharacteristic
70C2×C4⋊C4×C61—24no—
71C2×C4⋊C4×C61—21no—
72C2×C4⋊C4×C61—21no—
73C2×C4⋊C4×C61—21no—
74C2×C4⋊C4×C61—21no—
75C2×C4⋊C4×C61—21no—
76C2×C4⋊C4×C61—21no—
77C2×C4⋊C4×C61—44no—
78#95×C61—24no—
79#95×C61—21no—
80#95×C61D412yes—
81C24×C61C2×D411yescharacteristic
82C23×D61—21no—
83C2×Q8×C61—24no—
84C2×Q8×C61—24no—
85C2×Q8×C61—22no—
86C2×Q8×C61—22no—
87C2×Q8×C61—44no—
88C2×Q8×C61—42no—
89C2×Q8×C61—42no—
90C2×Q8×C61—44no—
91C2×Q8×C61—44no—
92C2×Q8×C61—44no—
93C2×Q8×C61—41no—
94C2×Q8×C61—41no—
95C22×C4×C61—24no—
96C22×C4×C61—24no—
97C22×C4×C61—21no—
98C22×C4×C61—22no—
99C22×C4×C61—22no—
100C22×C4×C61—21no—
101C22×C4×C61—21no—
102C22×C4×C61—21no—
103C22×C4×C61—21no—
104C22×C4×C61—21no—
105C22×C4×C61—21no—
106C22×C4×C61—21no—
107C22×C4×C61—21no—
108C22×C4×C61—42no—
109C22×C4×C61—42no—
110C22×C4×C61—42no—
111C22×C4×C61—41no—
112C22×C4×C61—41no—
113C22×C4×C61—41no—
114C22×C4×C61—41no—
115C22×C4×C61—42no—
116C22×C4×C61SD1612yescomplemented
117C22×C4×C61C2×D411yescharacteristic
118C22×C4×C61C2×D411yescharacteristic
119C22×C4×C61C2×D411yescharacteristic
120C22×C4×C61C2×D411yescharacteristic
121C22×C4×C61C2×D411yescharacteristic
122C22×C4×C61#4111yescharacteristic
123C2×C22⋊D61—41no—
124C2×C22⋊D61—41no—
125C2×C22⋊D61—41no—
126C2×C22⋊D61—41no—
127C2×C22⋊D61—41no—
128C2×C22⋊D61—41no—
129C22×Dic61—21no—
130C22×Dic61—22no—
131C2×D244—21no—
132C2×D244—21no—
133C2×D244—42no—
134C4⋊C4×C61—48no—
135C4⋊C4×C61—41no—
136C4⋊C4×C61—41no—
137C4⋊C4×C61—41no—
138C4⋊C4×C61—41no—
139C22⋊Dic61—41no—
140C22⋊Dic61—41no—
141#11758201—48no—
142#11758198—44no—
143#11758198—41no—
144#11758198—41no—
145#11758198—82no—
146C4⋊Dic61—21no—
147C4⋊Dic61—21no—
148C4⋊Dic61—42no—
149#11758196—44no—
150C2×#92418—22no—
151C2×#92418—42no—
152C2×#92418—42no—
153C2×#92418—41no—
154C23×C61—22no—
155C23×C61—22no—
156C23×C61#12011yescharacteristic
157C23×C61#12011yescharacteristic
158C23×C61#12111yescharacteristic
159C23×C61C2×SD1611yescharacteristic
160C23×C61#13511yescharacteristic
161C23×C61AGL(1,ℤ/8)11yescharacteristic
162C23×C61#13711yescharacteristic
163C22×D61—41no—
164C22×D61—41no—
165C22×D61—41no—
166C22×D61—42no—
167C22×D61—42no—
168Q8×C61—24no—
169Q8×C61—24no—
170Q8×C61—42no—
171Q8×C61—44no—
172Q8×C61—44no—
173Q8×C61—42no—
174C2×C4×C61—22no—
175C2×C4×C61—22no—
176C2×C4×C61—24no—
177C2×C4×C61—24no—
178C2×C4×C61—22no—
179C2×C4×C61—22no—
180C2×C4×C61—22no—
181C2×C4×C61—41no—
182C2×C4×C61—41no—
183C2×C4×C61—41no—
184C2×C4×C61—41no—
185C2×C4×C61—42no—
186C2×C4×C61—44no—
187C2×C4×C61—44no—
188C2×C4×C61—42no—
189C2×C4×C61—44no—
190C2×C4×C61—41no—
191C2×C4×C61—42no—
192C2×C4×C61—41no—
193C2×C4×C61—42no—
194C2×C4×C61—41no—
195C2×C4×C61—44no—
196C2×C4×C61—41no—
197C2×C4×C61—42no—
198C2×C4×C61—41no—
199C2×C4×C61—42no—
200C2×C4×C61—81no—
201C2×C4×C61#12011yescharacteristic
202C2×C4×C61#12111yescharacteristic
203C2×C4×C61#12111yescharacteristic
204C2×C4×C61#12711yescharacteristic
205C22⋊D61—81no—
206C22⋊D61—81no—
207C22⋊D61—81no—
208C22⋊D61—81no—
209C2×Dic61—41no—
210C2×Dic61—41no—
211C2×Dic61—42no—
212C2×Dic61—41no—
213C2×Dic61—42no—
214C2×Dic61—42no—
215D244—42no—
216D244—81no—
217#92418—42no—
218#92418—81no—
219#9917—611nomaximal, Sylow
220C22×C61—22no—
221C22×C61—22no—
222C22×C61—22no—
223C22×C61—22no—
224C22×C61—21no—
225C22×C61—21no—
226C22×C61—21no—
227C22×C61—21no—
228C22×C61#39211yescharacteristic
229C22×C61#44811yescharacteristic
230C22×C61#44911yescharacteristic
231C22×C61#45011yescharacteristic
232C22×C61#45211yescharacteristic
233C22×C61#45612yes—
234C22×C61B(4,𝔽2)12yes—
235C22×C61#46511yescharacteristic
236C22×C61#46811yescharacteristic
237C2×D61—82no—
238C2×D61—82no—
239C2×D61—81no—
240C2×D61—81no—
241C2×D61—81no—
242C4×C61—21no—
243C4×C61—21no—
244C4×C61—21no—
245C4×C61—21no—
246C4×C61—44no—
247C4×C61—42no—
248C4×C61—44no—
249C4×C61—81no—
250Dic61—82no—
251Dic61—81no—
252C2×#448—611no—
253#2618—611no—
254C2×#395D6111yescharacteristic, complemented
255#1787—611no—
256C2×#327—611no—
257C2×#324—611no—
258#1294—611no—
259C2×C61—21no—
260C2×C61—21no—
261C2×C61—21no—
262C2×C61—21no—
263C2×C61#160312yes—
264C2×C61#160412yes—
265C2×C61#200011yescharacteristic
266C2×C61#200511yescharacteristic
267C2×C61#202111yescharacteristic
268D61—161no—
269C23×Q8C2×D6111yescharacteristic
270C22×SD16—1221no—
271C2×#123—1221no—
272C2×#121—611no—
273C22×C4⋊C4—21no—
274C22×C4⋊C4C2×D6111yescharacteristic
275#448—1222no—
276#448—1222no—
277C2×#103—1221no—
278C2×#103—1222no—
279C2×C22⋊C8—611no—
280C2×C22⋊C8—611no—
281#398—1221no—
282#396—1222no—
283#395—22no—
284#395—22no—
285#394—1221no—
286#386—1221no—
287#380—611no—
288C2×#95—21no—
289C2×#95C2×D6111yescharacteristic
290#327—1222no—
291#324—1222no—
292C61#991711yescharacteristic, complemented, Sylow
293C22×Q8—21no—
294C22×Q8—21no—
295C22×Q8—21no—
296C22×Q8—21no—
297C22×Q8—21no—
298C22×Q8—44no—
299C22×Q8C22⋊D6112yes—
300C22×D4—611no—
301C22×D4—1221no—
302C23×C4—21no—
303C23×C4—21no—
304C23×C4C22⋊D6111yescharacteristic
305C23×C4C22⋊D6111yescharacteristic
306C23×C4C22×D6111yescharacteristic
307C2×SD16—1224no—
308C2×SD16—2444no—
309C22×C8—1221no—
310C22×C8—1221no—
311#123—2442no—
312#123—2442no—
313#121—1221no—
314#121—1221no—
315#121—1221no—
316#121—1221no—
317C2×C4⋊C4—24no—
318C2×C4⋊C4—21no—
319C2×C4⋊C4—21no—
320C2×C4⋊C4—21no—
321C2×C4⋊C4—21no—
322C2×C4⋊C4—21no—
323C2×C4⋊C4—21no—
324C2×C4⋊C4—44no—
325C2×C4⋊C4—611no—
326C2×C4⋊C4—612no—
327C2×C4⋊C4—1222no—
328C2×C22⋊C4—1222no—
329C2×C22⋊C4—1222no—
330C2×C22⋊C4—1221no—
331C2×C22⋊C4—1221no—
332#103—1224no—
333#103—2444no—
334C22⋊C8—612no—
335C22⋊C8—1221no—
336C22⋊C8—1221no—
337C22⋊C8—1221no—
338#95—24no—
339#95—21no—
340#95—1222no—
341#95—1221no—
342#95C22⋊D6112yes—
343C24—1221no—
344C24C2×C22⋊D6111yescharacteristic
345C2×Q8—24no—
346C2×Q8—24no—
347C2×Q8—22no—
348C2×Q8—22no—
349C2×Q8—44no—
350C2×Q8—42no—
351C2×Q8—42no—
352C2×Q8—44no—
353C2×Q8—44no—
354C2×Q8—44no—
355C2×Q8—41no—
356C2×Q8—41no—
357C2×D4—1221no—
358C2×D4—1221no—
359C2×D4—2442no—
360C2×D4—2441no—
361C2×D4—2441no—
362C2×D4—2441no—
363C2×D4—2441no—
364C2×D4—2441no—
365C2×D4—2441no—
366C22×C4—24no—
367C22×C4—24no—
368C22×C4—21no—
369C22×C4—21no—
370C22×C4—21no—
371C22×C4—22no—
372C22×C4—22no—
373C22×C4—21no—
374C22×C4—21no—
375C22×C4—21no—
376C22×C4—21no—
377C22×C4—21no—
378C22×C4—21no—
379C22×C4—42no—
380C22×C4—42no—
381C22×C4—42no—
382C22×C4—41no—
383C22×C4—41no—
384C22×C4—41no—
385C22×C4—41no—
386C22×C4—42no—
387C22×C4—1222no—
388C22×C4—1221no—
389C22×C4#1175820112yescomplemented
390C22×C4D4×D6111yescharacteristic
391C22×C4D4×D6111yescharacteristic
392C22×C4D4×D6111yescharacteristic
393C22×C4#1175822411yescharacteristic
394C22×C4C2×C22⋊D6111yescharacteristic
395C22×C4C2×C22⋊D6111yescharacteristic
396SD16—2448no—
397C2×C8—1222no—
398C2×C8—2442no—
399C2×C8—2441no—
400C2×C8—2442no—
401C4⋊C4—48no—
402C4⋊C4—41no—
403C4⋊C4—41no—
404C4⋊C4—41no—
405C4⋊C4—41no—
406C4⋊C4—1221no—
407C4⋊C4—1221no—
408C4⋊C4—2442no—
409C4⋊C4—2444no—
410C22⋊C4—4882no—
411C22⋊C4—2444no—
412C22⋊C4—2441no—
413C22⋊C4—2441no—
414C22⋊C4—2441no—
415C22⋊C4—2441no—
416C23—22no—
417C23—22no—
418C23—2442no—
419C23—2442no—
420C23—2441no—
421C23—2441no—
422C23—2441no—
423C23#1451974511yescharacteristic
424C23#1451974611yescharacteristic
425C23#1451974911yescharacteristic
426C23C2×#1175820111yescharacteristic
427C23#1451979711yescharacteristic
428C23#1451980211yescharacteristic
429C23#1451980811yescharacteristic
430Q8—24no—
431Q8—24no—
432Q8—44no—
433Q8—42no—
434Q8—44no—
435Q8—42no—
436D4—4881no—
437D4—4881no—
438D4—4881no—
439D4—4881no—
440D4—4881no—
441D4—2442no—
442C2×C4—22no—
443C2×C4—22no—
444C2×C4—24no—
445C2×C4—24no—
446C2×C4—22no—
447C2×C4—22no—
448C2×C4—22no—
449C2×C4—41no—
450C2×C4—41no—
451C2×C4—41no—
452C2×C4—41no—
453C2×C4—42no—
454C2×C4—44no—
455C2×C4—44no—
456C2×C4—42no—
457C2×C4—44no—
458C2×C4—44no—
459C2×C4—41no—
460C2×C4—41no—
461C2×C4—42no—
462C2×C4—41no—
463C2×C4—41no—
464C2×C4—42no—
465C2×C4—42no—
466C2×C4—42no—
467C2×C4—41no—
468C2×C4—81no—
469C2×C4—2442no—
470C2×C4—2442no—
471C2×C4—2442no—
472C2×C4—2441no—
473C2×C4—2441no—
474C2×C4—2441no—
475C2×C4#1451974511yescharacteristic
476C2×C4#1451974811yescharacteristic
477C2×C4#1451974911yescharacteristic
478C2×C4#1451977311yescharacteristic
479C8—4881no—
480C8—2442no—
481C22—21no—
482C22—21no—
483C22—22no—
484C22—22no—
485C22—22no—
486C22—22no—
487C22—21no—
488C22—21no—
489C22—4881no—
490C22—4881no—
491C22—4882no—
492C22—4882no—
493C22—4881no—
494C22#1683967011yescharacteristic
495C22#1683990111yescharacteristic
496C22#1683990711yescharacteristic
497C22#1683991211yescharacteristic
498C22#1683992211yescharacteristic
499C22#1683994412yes—
500C22#1683994812yes—
501C22#1683999311yescharacteristic
502C22#1684001011yescharacteristic
503C4—21no—
504C4—21no—
505C4—21no—
506C4—21no—
507C4—44no—
508C4—44no—
509C4—42no—
510C4—81no—
511C4—4881no—
512C4—4882no—
513C2—21no—
514C2—21no—
515C2—21no—
516C2—21no—
517C2—9761no—
518C2#2144478012yes—
519C2#2144478712yes—
520C2#2144682011yescharacteristic
521C2#2144685511yescharacteristic
522C2#2144694211yescharacteristic
subgroupG/H
centerC23#14519745
commutator, cosocleC23×C4×C61C23
FrattiniC23×C4C22×D61
FittingC2×C61×#395C2
socleC23×C61#120
prime radicalC2×#14519751C22
hypercenterC2×#395D61
hypocenterC61#9917
LCSG ▷ C23×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#395

Complements

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

NH ≅ G/Ntype
3. #21445754C2semidirect
5. C2×#16839488C2semidirect
6. #21443698C2semidirect
7. C2×C61×#395C2semidirect
116. C22×C4×C61SD16semidirect
254. C2×#395D61semidirect
292. C61#9917semidirect
389. C22×C4#11758201semidirect

Maximal subgroups

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

subgroupindex
C2×#168399012
#214515612
#214457542
C2×#168394952
C2×#168394882
#214436982
C2×C61×#3952
#991761