Finite Group Databasebeta

← #29709153

Subgroups — #29709153

Order 15616.

1092 conjugacy classes of subgroups.

The subgroup lattice has 540 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×D488C212yesmaximal, complemented
2C4×#14519774C211yesmaximal, characteristic, complemented
3#21448283C211yesmaximal, characteristic, complemented
4#21447292C211yesmaximal, characteristic, complemented
5#21447224C211yesmaximal, characteristic, complemented
6#21447206C212yesmaximal, complemented
7#21447130C212yesmaximal, complemented
8#21447054C211yesmaximal, characteristic, complemented
9#21446892C211yesmaximal, characteristic
10C4×#14519699C212yesmaximal, complemented
11C4×C4⋊C8×C61C211yesmaximal, characteristic, complemented
12C22×D488C2212yes—
13C2×#14519774C2211yescharacteristic
14C2×C4×D244—21no—
15C2×C4×D244—21no—
16C2×C4×D244C2212yes—
17C2×C4×D244C2211yescharacteristic
18C2×#14519734—21no—
19C4×D488—28no—
20C2×#14519711C2212yes—
21C2×#14519699C2212yes—
22C2×#14519699C2212yes—
23C2×#14519699C2212yes—
24C2×#14519699C2212yes—
25#16839664—21no—
26#16839664—21no—
27#16839664C2212yes—
28#16839664C2211yescharacteristic
29#16839664C2211yescharacteristic
30#16839660C2211yescharacteristic
31#16839660C2211yescharacteristic
32#16839653—21no—
33#16839653—21no—
34#16839632C2211yescharacteristic
35C4×C4⋊Dic61C2211yescharacteristic
36C4×#11758198—21no—
37#16839525C2212yes—
38#16839525C2212yes—
39C2×C4⋊C8×C61C2212yes—
40C2×C4×C8×C61C2212yes—
41C43×C61C2211yescharacteristic
42C61×#336C2211yescharacteristic
43C61×#336C2211yescharacteristic
44C22×D244—21no—
45C22×D244—21no—
46C22×D244C2311yescharacteristic
47C22×D244C2312yes—
48C22×C4×D61—21no—
49C22×C4×D61—22no—
50C2×D488—24no—
51C2×D488—24no—
52C2×D488—24no—
53#14519774—24no—
54C4×D244—22no—
55C4×D244—24no—
56C4×D244—24no—
57C4×D244—44no—
58C4×D244—44no—
59C4×D244D414yescomplemented
60#14519734—44no—
61C2×C4⋊Dic61—21no—
62C2×C4⋊Dic61—21no—
63C2×C4⋊Dic61C2312yes—
64C2×C4⋊Dic61C2311yescharacteristic
65C2×C4⋊Dic61C2311yescharacteristic
66C2×C4⋊Dic61C2311yescharacteristic
67C2×#11758196—21no—
68C2×#11758196—21no—
69C2×#11758198—21no—
70C2×#11758198—21no—
71C2×#11758198—21no—
72C2×#11758198—22no—
73C2×#11758198—22no—
74C2×#11758198—22no—
75C2×#11758198—21no—
76C2×#11758198—21no—
77C2×C4×Dic61—21no—
78#14519711—24no—
79#14519699—24no—
80#14519699—24no—
81#14519699—24no—
82#14519699—24no—
83#14519684—21no—
84#14519684—21no—
85#14519684—21no—
86C22×C8×C61C2312yes—
87C22×C8×C61C2312yes—
88C2×C42×C61D411yescharacteristic
89C2×C42×C61D411yescharacteristic
90C2×C42×C61D411yescharacteristic
91C2×C42×C61D411yescharacteristic
92C2×C42×C61C2311yescharacteristic
93C2×C42×C61C2311yescharacteristic
94C2×C42×C61C2311yescharacteristic
95C4⋊C8×C61—24no—
96C4×C8×C61—24no—
97C23×D61—22no—
98C23×D61—21no—
99C22×C4×C61C2×D411yescharacteristic
100C22×C4×C61C2×D411yescharacteristic
101C22×C4×C61C2×D411yescharacteristic
102C22×C4×C61C2×D411yescharacteristic
103C22×C4×C61C2×D411yescharacteristic
104C22×C4×C61C2×D411yescharacteristic
105C22×C4×C61C2411yescharacteristic
106C22×Dic61—21no—
107C22×Dic61—22no—
108C22×Dic61—21no—
109C22×Dic61—21no—
110C2×D244—22no—
111C2×D244—22no—
112C2×D244—22no—
113C2×D244—22no—
114C2×D244—22no—
115C2×D244—22no—
116C2×D244—24no—
117C2×D244—24no—
118C2×D244—21no—
119C2×D244—22no—
120C2×D244—42no—
121C2×D244—42no—
122C2×D244—42no—
123C2×D244—42no—
124C2×D244C2×D412yes—
125C2×D244#4114yes—
126C2×C4×D61—24no—
127C2×C4×D61—42no—
128C2×C4×D61—42no—
129C2×C4×D61—44no—
130C2×C4×D61—44no—
131C2×C4×D61—44no—
132C2×C8×C61—22no—
133C2×C8×C61—22no—
134C2×C8×C61—22no—
135C2×C8×C61—22no—
136C2×C8×C61—22no—
137C2×C8×C61#4114yes—
138C42×C61—22no—
139C42×C61—22no—
140C42×C61—22no—
141C42×C61—22no—
142C42×C61—41no—
143C42×C61D814yescomplemented
144C42×C61C2×D412yes—
145C42×C61#4112yes—
146#11758198—24no—
147#11758198—42no—
148#11758198—44no—
149#11758198—44no—
150#11758198—42no—
151#11758198—42no—
152#11758198—44no—
153#11758198—42no—
154C4⋊Dic61—21no—
155C4⋊Dic61—22no—
156C4⋊Dic61—22no—
157C4⋊Dic61—22no—
158C4⋊Dic61—22no—
159C4⋊Dic61—42no—
160C4⋊Dic61—42no—
161C4⋊Dic61C2×D412yes—
162#11758196—42no—
163#11758196—42no—
164C4×Dic61—42no—
165D488—216no—
166C23×C61C22×D411yescharacteristic
167C22×D61—22no—
168C22×D61—24no—
169C22×D61—42no—
170C22×D61—41no—
171C22×D61—42no—
172C22×D61—41no—
173C22×D61—41no—
174C22×D61—42no—
175C22×D61—41no—
176C22×D61—42no—
177C22×D61—42no—
178C22×D61—41no—
179C22×D61—41no—
180C22×D61—42no—
181C2×C4×C61—21no—
182C2×C4×C61—21no—
183C2×C4×C61—21no—
184C2×C4×C61—21no—
185C2×C4×C61—21no—
186C2×C4×C61—21no—
187C2×C4×C61—21no—
188C2×C4×C61—21no—
189C2×C4×C61—21no—
190C2×C4×C61—21no—
191C2×C4×C61—21no—
192C2×C4×C61#12112yes—
193C2×C4×C61#12112yes—
194C2×C4×C61C2×D812yes—
195C2×C4×C61C2×D812yes—
196C2×C4×C61C2×D812yes—
197C2×C4×C61#13512yes—
198C2×C4×C61AGL(1,ℤ/8)12yes—
199C2×C4×C61C22×D411yescharacteristic
200C2×C4×C61C2×#4112yes—
201C2×C4×C61C2×#4112yes—
202C2×C4×C61C2×#4111yescharacteristic
203C2×Dic61—22no—
204C2×Dic61—41no—
205C2×Dic61—41no—
206C2×Dic61—42no—
207C2×Dic61—41no—
208C2×Dic61—41no—
209C2×Dic61—41no—
210C2×Dic61—41no—
211C2×Dic61—42no—
212C2×Dic61—41no—
213C2×Dic61—42no—
214C2×Dic61—41no—
215D244—24no—
216D244—24no—
217D244—24no—
218D244—48no—
219D244—48no—
220D244—42no—
221D244—42no—
222D244—42no—
223C4×D61—48no—
224C4×D61—88no—
225C8×C61—24no—
226C8×C61—42no—
227#23676—611nomaximal, Sylow
228C22×C61C2×#12111yescharacteristic
229C22×C61#52511yescharacteristic
230C22×C61#53211yescharacteristic
231C22×C61C22×D811yescharacteristic
232C22×C61C2×#13511yescharacteristic
233C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
234C22×C61#57511yescharacteristic
235C2×D61—44no—
236C2×D61—44no—
237C2×D61—42no—
238C2×D61—44no—
239C2×D61—42no—
240C2×D61—42no—
241C2×D61—81no—
242C2×D61—81no—
243C2×D61—81no—
244C2×D61—82no—
245C2×D61—82no—
246C2×D61—81no—
247C2×D61—82no—
248C2×D61—82no—
249C4×C61—22no—
250C4×C61—22no—
251C4×C61—22no—
252C4×C61—22no—
253C4×C61—41no—
254C4×C61#45914yes—
255C4×C61#52512yes—
256C4×C61#52912yes—
257Dic61—42no—
258Dic61—81no—
259Dic61—81no—
260Dic61—82no—
261C2×C4×D8—612no—
262C4×#127—611no—
263#2293—611no—
264#2083—611no—
265#2071—611no—
266#2067—612no—
267#2054—612no—
268#2041—611no—
269#2011—611no—
270C4×C4⋊C8D6111yescharacteristic, complemented
271C4×#102—612no—
272C2×C61#239211yescharacteristic
273C2×C61C2×#45911yescharacteristic
274C2×C61#303511yescharacteristic
275C2×C61#310011yescharacteristic
276C2×C61#310511yescharacteristic
277C2×C61#316911yescharacteristic
278C2×C61#317111yescharacteristic
279D61—84no—
280D61—82no—
281C22×D8—612no—
282C2×#127—611no—
283C2×C4×D4—611no—
284C2×C4×D4—612no—
285C2×C4×D4—1221no—
286C2×C4×D4—1221no—
287C2×#117—1221no—
288C4×D8—1228no—
289C2×#107—612no—
290C2×C4⋊C8C2×D6112yes—
291C2×#102—612no—
292C2×#102—612no—
293C2×#102—612no—
294C2×#102—612no—
295C2×C4×C8C2×D6112yes—
296#390—612no—
297#390—611no—
298#390—611no—
299#390—1221no—
300#390—1221no—
301#389—611no—
302#389—611no—
303#388—1221no—
304#388—1221no—
305#384—611no—
306C4×C4⋊C4—611no—
307C4×C22⋊C4—1221no—
308C43C2×D6111yescharacteristic
309#340—612no—
310#340—612no—
311#336C2×D6111yescharacteristic
312#336C2×D6111yescharacteristic
313C61#2367611yescharacteristic, complemented, Sylow
314C22×D4—612no—
315C22×D4—611no—
316C22×D4—1221no—
317C22×D4—1221no—
318C23×C4—1221no—
319C23×C4—1222no—
320C2×D8—1224no—
321C2×D8—1224no—
322C2×D8—1224no—
323C22×C8C22×D6112yes—
324C22×C8C22×D6112yes—
325#127—1224no—
326C4×D4—614no—
327C4×D4—1224no—
328C4×D4—1222no—
329C4×D4—1224no—
330C4×D4—2444no—
331C4×D4—2444no—
332#117—2444no—
333C2×C4⋊C4—611no—
334C2×C4⋊C4—612no—
335C2×C4⋊C4—611no—
336C2×C4⋊C4—611no—
337C2×C4⋊C4—1221no—
338C2×C4⋊C4—1221no—
339C2×C4⋊C4—1221no—
340C2×C4⋊C4—1221no—
341C2×C22⋊C4—1221no—
342C2×C22⋊C4—1221no—
343C2×C22⋊C4—1221no—
344C2×C22⋊C4—1222no—
345C2×C22⋊C4—1222no—
346C2×C22⋊C4—1222no—
347C2×C22⋊C4—1221no—
348C2×C22⋊C4—1221no—
349C2×C42—1221no—
350C2×C42D24411yescharacteristic
351C2×C42D24411yescharacteristic
352C2×C42D24411yescharacteristic
353C2×C42D24411yescharacteristic
354C2×C42C22×D6111yescharacteristic
355C2×C42C22×D6111yescharacteristic
356C2×C42C22×D6111yescharacteristic
357#107—1224no—
358C4⋊C8—24no—
359#102—1224no—
360#102—1224no—
361#102—1224no—
362#102—1224no—
363C4×C8—24no—
364#95—1221no—
365#95—1221no—
366#95—1221no—
367C24—1221no—
368C24—1222no—
369C2×D4—612no—
370C2×D4—614no—
371C2×D4—1224no—
372C2×D4—1224no—
373C2×D4—1222no—
374C2×D4—1222no—
375C2×D4—1222no—
376C2×D4—1222no—
377C2×D4—1222no—
378C2×D4—1222no—
379C2×D4—1222no—
380C2×D4—1221no—
381C2×D4—2442no—
382C2×D4—2442no—
383C2×D4—2442no—
384C2×D4—2442no—
385C22×C4—1221no—
386C22×C4—1224no—
387C22×C4—1221no—
388C22×C4—1221no—
389C22×C4—1222no—
390C22×C4—2444no—
391C22×C4—2444no—
392C22×C4—2444no—
393C22×C4—2442no—
394C22×C4—2442no—
395C22×C4C2×D24411yescharacteristic
396C22×C4C2×D24411yescharacteristic
397C22×C4C2×D24411yescharacteristic
398C22×C4C2×D24411yescharacteristic
399C22×C4C2×D24411yescharacteristic
400C22×C4C2×D24411yescharacteristic
401C22×C4C23×D6111yescharacteristic
402D8—12216no—
403C2×C8—22no—
404C2×C8—22no—
405C2×C8—22no—
406C2×C8—22no—
407C2×C8—22no—
408C2×C8#1175822214yes—
409C4⋊C4—612no—
410C4⋊C4—1221no—
411C4⋊C4—1222no—
412C4⋊C4—1222no—
413C4⋊C4—1222no—
414C4⋊C4—1222no—
415C4⋊C4—2442no—
416C4⋊C4—2442no—
417C4⋊C4—2442no—
418C4⋊C4—2442no—
419C22⋊C4—1224no—
420C22⋊C4—2444no—
421C22⋊C4—2442no—
422C22⋊C4—2444no—
423C22⋊C4—2442no—
424C22⋊C4—2442no—
425C22⋊C4—2444no—
426C22⋊C4—2442no—
427C42—22no—
428C42—22no—
429C42—22no—
430C42—22no—
431C42—41no—
432C42—2442no—
433C42D48814yescomplemented
434C42D4×D6112yes—
435C42#1175822612yes—
436C23—1222no—
437C23—1224no—
438C23—2442no—
439C23—2441no—
440C23—2441no—
441C23—2442no—
442C23—2441no—
443C23—2442no—
444C23—2442no—
445C23—2441no—
446C23—2441no—
447C23—2442no—
448C23—2442no—
449C23—2441no—
450C23C22×D24411yescharacteristic
451D4—1224no—
452D4—1224no—
453D4—1224no—
454D4—2448no—
455D4—2448no—
456D4—2442no—
457D4—2442no—
458D4—2442no—
459C2×C4—21no—
460C2×C4—21no—
461C2×C4—21no—
462C2×C4—21no—
463C2×C4—21no—
464C2×C4—21no—
465C2×C4—21no—
466C2×C4—21no—
467C2×C4—21no—
468C2×C4—21no—
469C2×C4—21no—
470C2×C4—1222no—
471C2×C4—4888no—
472C2×C4—2442no—
473C2×C4—2441no—
474C2×C4—2441no—
475C2×C4—2441no—
476C2×C4—2442no—
477C2×C4—2441no—
478C2×C4—2442no—
479C2×C4—2441no—
480C2×C4—2441no—
481C2×C4—2441no—
482C2×C4—2441no—
483C2×C4—2448no—
484C2×C4#1451975212yes—
485C2×C4#1451975212yes—
486C2×C4C2×D48812yes—
487C2×C4C2×D48812yes—
488C2×C4C2×D48812yes—
489C2×C4#1451979912yes—
490C2×C4#1451980512yes—
491C2×C4C2×D4×D6111yescharacteristic
492C2×C4#41×D6112yes—
493C2×C4C2×#1175822212yes—
494C2×C4C2×#1175822611yescharacteristic
495C8—24no—
496C8—42no—
497C22—4881no—
498C22—4882no—
499C22—4882no—
500C22—4881no—
501C22—4882no—
502C22—4882no—
503C22—4881no—
504C22—4881no—
505C22—2442no—
506C22—2444no—
507C22—2442no—
508C22—2442no—
509C22—2444no—
510C22—2444no—
511C22C2×#1451975211yescharacteristic
512C22#1684027411yescharacteristic
513C22#1684031211yescharacteristic
514C22C22×D48811yescharacteristic
515C22C2×#1451979911yescharacteristic
516C22C2×#1451980511yescharacteristic
517C22#1684056211yescharacteristic
518C4—22no—
519C4—22no—
520C4—22no—
521C4—22no—
522C4—41no—
523C4—4881no—
524C4—4882no—
525C4—4881no—
526C4—2442no—
527C4#1683995814yes—
528C4#1684027112yes—
529C4#1684029912yes—
530C2—4884no—
531C2—4882no—
532C2#2144905911yescharacteristic
533C2C2×#1683995811yescharacteristic
534C2#2145527611yescharacteristic
535C2#2145582011yescharacteristic
536C2#2145586811yescharacteristic
537C2#2145639811yescharacteristic
538C2#2145641411yescharacteristic
subgroupG/H
centerC22×C4C2×D244
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC4×C4⋊C8×C61C2
socleC23×C61C22×D4
prime radical#21446892C2
hypercenterC4×C4⋊C8D61
hypocenterC61#23676
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22×C4 ◁ C43 ◁ C4×C4⋊C8

Complements

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

NH ≅ G/Ntype
1. C2×C4×D488C2semidirect
2. C4×#14519774C2semidirect
3. #21448283C2semidirect
4. #21447292C2semidirect
5. #21447224C2semidirect
6. #21447206C2semidirect
7. #21447130C2semidirect
8. #21447054C2semidirect
10. C4×#14519699C2semidirect
11. C4×C4⋊C8×C61C2semidirect
59. C4×D244D4semidirect
143. C42×C61D8semidirect
270. C4×C4⋊C8D61semidirect
313. C61#23676semidirect
433. C42D488semidirect

Maximal subgroups

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

subgroupindex
C2×C4×D4882
C4×#145197742
#214482832
#214472922
#214472242
#214472062
#214471302
#214470542
#214468922
C4×#145196992
C4×C4⋊C8×C612
#2367661