Finite Group Databasebeta

← #29697155

Subgroups — #29697155

Order 15616.

1218 conjugacy classes of subgroups.

The subgroup lattice has 520 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14519697C211yesmaximal, characteristic
2C22⋊C4×D244C211yesmaximal, characteristic
3#21446501C212yesmaximal, complemented
4#21446439C212yesmaximal, complemented
5#21446065C212yesmaximal, complemented
6#21445905C211yesmaximal, characteristic, complemented
7#21445846C211yesmaximal, characteristic, complemented
8#21445749C211yesmaximal, characteristic
9C4×#14519697C212yesmaximal, complemented
10C22⋊C4×#92418C211yesmaximal, characteristic, complemented
11C61×#2344C211yesmaximal, characteristic, complemented
12C23×D244C2211yescharacteristic
13C23×#92418C2211yescharacteristic
14C2×C4×D244C2212yes—
15C2×C22⋊C4×D61—21no—
16C2×#14519710C2212yescomplemented
17C2×#14519697C418yescomplemented
18C2×#14519697C2212yes—
19C2×#14519697C2212yes—
20C2×#14519697C2211yescharacteristic
21C2×#14519697C2211yescharacteristic
22C2×#14519697C2211yescharacteristic
23C2×#14519697C2211yescharacteristic
24C2×C22⋊#92418C2211yescharacteristic
25C2×C4×#92418C2212yescomplemented
26#16839664C2212yes—
27#16839640—22no—
28#16839622C2211yescharacteristic
29#16839617—21no—
30#16839524C2212yescomplemented
31#16839524C2212yescomplemented
32#16839524C2212yescomplemented
33#16839517C2212yescomplemented
34C2×#117×C61—21no—
35C22×C4⋊C4×C61C2211yescharacteristic
36C61×#389C2212yescomplemented
37C61×#387—22no—
38C61×#381—21no—
39C61×#380C2211yescharacteristic
40C4×C4⋊C4×C61C2212yescomplemented
41C4×C22⋊C4×C61C2211yescharacteristic
42C24×D61—21no—
43C22×D244—24no—
44C22×D244—21no—
45C22×D244—22no—
46C22×D244—42no—
47C22×D244C2×C414yes—
48C22×D244C2311yescharacteristic
49C22×D244C2311yescharacteristic
50C22×C4×D61—22no—
51C22×#92418—42no—
52C22×#92418C2×C414yescomplemented
53C22×#92418C2312yes—
54C22×#92418C2311yescharacteristic
55C22×#92418C2311yescharacteristic
56C4×D244—24no—
57C4×D244—42no—
58C2×C4⋊Dic61C2312yes—
59C2×C22⋊Dic61—21no—
60C2×#11758198—22no—
61C2×#11758198—22no—
62C2×#11758198—22no—
63C22⋊C4×D61—44no—
64#14519710—42no—
65#14519697—24no—
66#14519697—42no—
67#14519697C2×C414yes—
68#14519697C2×C414yes—
69#14519697C2×C414yescomplemented
70#14519697C2×C414yescomplemented
71C22⋊#92418—22no—
72C4×#92418—42no—
73#14519684—21no—
74C23×C4×C61—21no—
75C23×C4×C61C2311yescharacteristic
76#117×C61—44no—
77C2×C4⋊C4×C61—21no—
78C2×C4⋊C4×C61—22no—
79C2×C4⋊C4×C61—22no—
80C2×C4⋊C4×C61C2×C414yescomplemented
81C2×C4⋊C4×C61C2312yes—
82C2×C4⋊C4×C61C2311yescharacteristic
83C2×C4⋊C4×C61C2311yescharacteristic
84C2×C22⋊C4×C61—21no—
85C2×C22⋊C4×C61D411yescharacteristic
86C2×C22⋊C4×C61D411yescharacteristic
87C2×C42×C61—22no—
88C2×C42×C61C2312yes—
89#95×C61—22no—
90#95×C61—21no—
91#95×C61—22no—
92#95×C61D412yes—
93C24×C61C2×D411yescharacteristic
94C23×D61—21no—
95C23×D61—21no—
96C23×D61—24no—
97C23×D61—44no—
98C23×D61—42no—
99C23×D61—42no—
100C23×D61—82no—
101C22×C4×C61—22no—
102C22×C4×C61—22no—
103C22×C4×C61—24no—
104C22×C4×C61—21no—
105C22×C4×C61—21no—
106C22×C4×C61—22no—
107C22×C4×C61—42no—
108C22×C4×C61—42no—
109C22×C4×C61C22×C412yes—
110C22×C4×C61C2×D412yes—
111C22×C4×C61C2×D411yescharacteristic
112C22×C4×C61C2×D412yes—
113C22×C4×C61#4112yes—
114C22×C4×C61C2411yescharacteristic
115C22×Dic61—22no—
116C2×D244—21no—
117C2×D244—22no—
118C2×D244—22no—
119C2×D244—22no—
120C2×D244—28no—
121C2×D244—24no—
122C2×D244—21no—
123C2×D244—44no—
124C2×D244—48no—
125C2×D244—44no—
126C2×D244C22×C412yes—
127C2×D244C22×C412yes—
128C2×D244#4114yes—
129C2×C4×D61—44no—
130C2×C4×D61—44no—
131C2×C4×D61—82no—
132C4⋊C4×C61—24no—
133C4⋊C4×C61—21no—
134C4⋊C4×C61—21no—
135C4⋊C4×C61—22no—
136C4⋊C4×C61—22no—
137C4⋊C4×C61—44no—
138C4⋊C4×C61C22×C412yes—
139C4⋊C4×C61C22×C412yes—
140C22⋊C4×C61—22no—
141C22⋊C4×C61—42no—
142C22⋊C4×C61D814yes—
143C42×C61—22no—
144C42×C61—22no—
145C42×C61—44no—
146C22⋊Dic61—42no—
147#11758198—44no—
148#11758198—44no—
149#11758198—82no—
150C4⋊Dic61—22no—
151C4⋊Dic61—22no—
152C2×#92418—22no—
153C2×#92418—22no—
154C2×#92418—22no—
155C2×#92418—22no—
156C2×#92418—22no—
157C2×#92418—44no—
158C2×#92418C22×C412yes—
159C2×#92418C22×C412yes—
160C23×C61—22no—
161C23×C61—22no—
162C23×C61C4×D412yes—
163C23×C61C2×D812yes—
164C23×C61#13512yes—
165C23×C61C22×D411yescharacteristic
166C22×D61—22no—
167C22×D61—24no—
168C22×D61—22no—
169C22×D61—48no—
170C22×D61—41no—
171C22×D61—41no—
172C22×D61—42no—
173C22×D61—42no—
174C22×D61—41no—
175C22×D61—41no—
176C22×D61—42no—
177C22×D61—48no—
178C22×D61—84no—
179C22×D61—88no—
180C22×D61—88no—
181C2×C4×C61—22no—
182C2×C4×C61—22no—
183C2×C4×C61—22no—
184C2×C4×C61—22no—
185C2×C4×C61—22no—
186C2×C4×C61—24no—
187C2×C4×C61—22no—
188C2×C4×C61—22no—
189C2×C4×C61—22no—
190C2×C4×C61—22no—
191C2×C4×C61—22no—
192C2×C4×C61—41no—
193C2×C4×C61—41no—
194C2×C4×C61—41no—
195C2×C4×C61—41no—
196C2×C4×C61—48no—
197C2×C4×C61—42no—
198C2×C4×C61—42no—
199C2×C4×C61—42no—
200C2×C4×C61C4×D412yes—
201C2×C4×C61C2×D814yes—
202C2×C4×C61C23×C411yescharacteristic
203C2×C4×C61C2×#4112yes—
204C2×C4×C61C2×#4111yescharacteristic
205C2×C4×C61H(5,𝔽2)12yes—
206C2×Dic61—42no—
207C2×Dic61—42no—
208C2×Dic61—42no—
209D244—22no—
210D244—22no—
211D244—22no—
212D244—24no—
213D244—48no—
214D244—42no—
215D244#11714yescomplemented
216C4×D61—88no—
217#92418—22no—
218#92418—22no—
219#92418—42no—
220#22570—611nomaximal, Sylow
221C22×C61—22no—
222C22×C61—22no—
223C22×C61—24no—
224C22×C61—24no—
225C22×C61C4×D814yes—
226C22×C61C2×C4×D411yescharacteristic
227C22×C61#54612yes—
228C22×C61C22×D811yescharacteristic
229C22×C61C2×#13511yescharacteristic
230C22×C61#57712yes—
231C2×D61—24no—
232C2×D61—42no—
233C2×D61—42no—
234C2×D61—44no—
235C2×D61—44no—
236C2×D61—42no—
237C2×D61—42no—
238C2×D61—42no—
239C2×D61—816no—
240C2×D61—82no—
241C2×D61—82no—
242C4×C61—22no—
243C4×C61—24no—
244C4×C61—42no—
245C4×C61—42no—
246C4×C61—42no—
247C4×C61—82no—
248C4×C61C2×#11711yescharacteristic
249C4×C61#51811yescharacteristic
250C4×C61#55112yes—
251Dic61—82no—
252C22×#102—611no—
253#2344D6111yescharacteristic, complemented
254D4×C22⋊C4—611no—
255#1934—612no—
256#1925—612no—
257#1862—612no—
258#1823—611no—
259#1808—611no—
260#1786—611no—
261C4×#102—612no—
262C8×C22⋊C4—611no—
263C2×C61—24no—
264C2×C61#234211yescharacteristic
265C2×C61C2×C4×D811yescharacteristic
266C2×C61#294911yescharacteristic
267C2×C61#329412yes—
268C2×C61#329612yes—
269D61—44no—
270D61—82no—
271C23×D4—611no—
272C23×C8—611no—
273C2×C4×D4—612no—
274C2×#117—21no—
275C22×C4⋊C4C2×D6111yescharacteristic
276C22×C22⋊C4—1221no—
277C2×#107—612no—
278C2×#102—618no—
279C2×#102—611no—
280C2×#102—611no—
281C2×#102—611no—
282C2×#102—611no—
283C2×#102—612no—
284C2×#102—612no—
285C2×C22⋊C8—611no—
286C2×C4×C8—612no—
287#390—612no—
288#389C2×D6112yescomplemented
289#387—22no—
290#386—1222no—
291#381—21no—
292#380—611no—
293#380C2×D6111yescharacteristic
294#379—1221no—
295C4×C4⋊C4C2×D6112yescomplemented
296C4×C22⋊C4C2×D6111yescharacteristic
297#340—612no—
298#340—612no—
299#340—612no—
300#336—612no—
301C61#2257011yescharacteristic, complemented, Sylow
302C25—1221no—
303C22×D4—614no—
304C22×D4—611no—
305C22×D4—611no—
306C22×D4—1224no—
307C22×D4—1222no—
308C22×D4—1221no—
309C22×D4—2442no—
310C23×C4—21no—
311C23×C4—1222no—
312C23×C4C22×D6111yescharacteristic
313C22×C8—611no—
314C22×C8—611no—
315C22×C8—614no—
316C22×C8—612no—
317C22×C8—2442no—
318C4×D4—1224no—
319C4×D4—2442no—
320#117—44no—
321C2×C4⋊C4—22no—
322C2×C4⋊C4—21no—
323C2×C4⋊C4—22no—
324C2×C4⋊C4—612no—
325C2×C4⋊C4C4×D6114yescomplemented
326C2×C4⋊C4C22×D6112yes—
327C2×C4⋊C4C22×D6111yescharacteristic
328C2×C4⋊C4C22×D6111yescharacteristic
329C2×C22⋊C4—21no—
330C2×C22⋊C4—1222no—
331C2×C22⋊C4—1221no—
332C2×C22⋊C4—1222no—
333C2×C22⋊C4—1222no—
334C2×C22⋊C4—2444no—
335C2×C22⋊C4C22⋊D6111yescharacteristic
336C2×C22⋊C4C22⋊D6111yescharacteristic
337C2×C42—22no—
338C2×C42C22×D6112yes—
339#107—2442no—
340#102—614no—
341#102—614no—
342#102—614no—
343#102—614no—
344#102—1224no—
345#102—2442no—
346C22⋊C8—1222no—
347C4×C8—2442no—
348#95—22no—
349#95—21no—
350#95—22no—
351#95—1221no—
352#95C22⋊D6112yes—
353C24—1221no—
354C24—1224no—
355C24—1221no—
356C24—4882no—
357C24—2444no—
358C24—2442no—
359C24—2442no—
360C24C2×C22⋊D6111yescharacteristic
361C2×D4—612no—
362C2×D4—612no—
363C2×D4—614no—
364C2×D4—1228no—
365C2×D4—1222no—
366C2×D4—1221no—
367C2×D4—1221no—
368C2×D4—1222no—
369C2×D4—1222no—
370C2×D4—1224no—
371C2×D4—2444no—
372C2×D4—2448no—
373C2×D4—2444no—
374C22×C4—22no—
375C22×C4—22no—
376C22×C4—21no—
377C22×C4—21no—
378C22×C4—24no—
379C22×C4—22no—
380C22×C4—42no—
381C22×C4—42no—
382C22×C4—1222no—
383C22×C4—4882no—
384C22×C4—2444no—
385C22×C4—2444no—
386C22×C4C2×C4×D6112yes—
387C22×C4#1175822212yes—
388C22×C4C2×C22⋊D6112yes—
389C22×C4C2×C22⋊D6111yescharacteristic
390C22×C4C2×C22⋊D6112yes—
391C22×C4C23×D6111yescharacteristic
392C2×C8—612no—
393C2×C8—612no—
394C2×C8—1222no—
395C2×C8—1222no—
396C2×C8—1222no—
397C2×C8—1222no—
398C2×C8—1222no—
399C2×C8—2444no—
400C4⋊C4—21no—
401C4⋊C4—21no—
402C4⋊C4—24no—
403C4⋊C4—22no—
404C4⋊C4—22no—
405C4⋊C4—44no—
406C4⋊C4—1222no—
407C4⋊C4—1222no—
408C4⋊C4C2×C4×D6112yes—
409C4⋊C4C2×C4×D6112yes—
410C22⋊C4—22no—
411C22⋊C4—42no—
412C22⋊C4—4882no—
413C22⋊C4—2444no—
414C22⋊C4—2442no—
415C22⋊C4—2444no—
416C22⋊C4#1175819914yes—
417C42—22no—
418C42—22no—
419C42—44no—
420C23—22no—
421C23—22no—
422C23—1222no—
423C23—1224no—
424C23—1222no—
425C23—4888no—
426C23—4888no—
427C23—4884no—
428C23—2448no—
429C23—2441no—
430C23—2441no—
431C23—2442no—
432C23—2448no—
433C23—2442no—
434C23—2441no—
435C23—2441no—
436C23—2442no—
437C23C4×C22⋊D6112yes—
438C23C2×#1175819912yes—
439C23#1451979712yes—
440C23C22×C22⋊D6111yescharacteristic
441D4—614no—
442D4—1222no—
443D4—1222no—
444D4—1222no—
445D4—1224no—
446D4—2448no—
447D4—2442no—
448C2×C4—22no—
449C2×C4—22no—
450C2×C4—22no—
451C2×C4—22no—
452C2×C4—22no—
453C2×C4—24no—
454C2×C4—22no—
455C2×C4—22no—
456C2×C4—22no—
457C2×C4—22no—
458C2×C4—22no—
459C2×C4—41no—
460C2×C4—41no—
461C2×C4—41no—
462C2×C4—41no—
463C2×C4—48no—
464C2×C4—42no—
465C2×C4—42no—
466C2×C4—42no—
467C2×C4—4888no—
468C2×C4—2442no—
469C2×C4—2442no—
470C2×C4—2442no—
471C2×C4C4×C22⋊D6112yes—
472C2×C4C2×#1175819914yes—
473C2×C4C22×C4×D6111yescharacteristic
474C2×C4#41×D6112yes—
475C2×C4C2×#1175822211yescharacteristic
476C2×C4#1451982312yes—
477C8—1222no—
478C8—1222no—
479C8—2442no—
480C22—22no—
481C22—24no—
482C22—22no—
483C22—24no—
484C22—1224no—
485C22—48816no—
486C22—4882no—
487C22—4882no—
488C22—2442no—
489C22—2442no—
490C22—2442no—
491C22—2442no—
492C22—2444no—
493C22—2442no—
494C22—2444no—
495C22C4×#1175819914yes—
496C22C2×C4×C22⋊D6111yescharacteristic
497C22#1684040012yes—
498C22C22×#1175819911yescharacteristic
499C22C2×#1451979711yescharacteristic
500C22#1684057012yes—
501C4—24no—
502C4—22no—
503C4—42no—
504C4—42no—
505C4—42no—
506C4—82no—
507C4—4882no—
508C4#117×D6111yescharacteristic
509C4#1684023611yescharacteristic
510C4#1684043612yes—
511C2—24no—
512C2—4882no—
513C2—2444no—
514C2#2144866911yescharacteristic
515C2C2×C4×#1175819911yescharacteristic
516C2#2145467811yescharacteristic
517C2#2145762612yes—
518C2#2145764812yes—
subgroupG/H
centerC23C22×C22⋊D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#2344C2
socleC23×C61C22×D4
prime radicalC23×D244C22
cosocleC22×C4×C61C24
hypercenter#2344D61
hypocenterC61#22570
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #2344

Complements

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

NH ≅ G/Ntype
3. #21446501C2semidirect
4. #21446439C2semidirect
5. #21446065C2semidirect
6. #21445905C2semidirect
7. #21445846C2semidirect
9. C4×#14519697C2semidirect
10. C22⋊C4×#92418C2semidirect
11. C61×#2344C2semidirect
16. C2×#14519710C22semidirect
17. C2×#14519697C4semidirect
25. C2×C4×#92418C22semidirect
30. #16839524C22semidirect
31. #16839524C22semidirect
32. #16839524C22semidirect
33. #16839517C22semidirect
36. C61×#389C22semidirect
40. C4×C4⋊C4×C61C22semidirect
52. C22×#92418C2×C4semidirect
69. #14519697C2×C4semidirect
70. #14519697C2×C4semidirect
80. C2×C4⋊C4×C61C2×C4semidirect
215. D244#117semidirect
253. #2344D61semidirect
288. #389C2×D61semidirect
295. C4×C4⋊C4C2×D61semidirect
301. C61#22570semidirect
325. C2×C4⋊C4C4×D61semidirect

Maximal subgroups

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

subgroupindex
C22×#145196972
C22⋊C4×D2442
#214465012
#214464392
#214460652
#214459052
#214458462
#214457492
C4×#145196972
C22⋊C4×#924182
C61×#23442
#2257061