Finite Group Databasebeta

← #30603299

Subgroups — #30603299

Order 15616.

1054 conjugacy classes of subgroups.

The subgroup lattice has 526 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21462472C211yesmaximal, characteristic, complemented
2#21462263C212yesmaximal
3#21461501C212yesmaximal, complemented
4#21461491C211yesmaximal, characteristic, complemented
5#407×D61C211yesmaximal, characteristic
6C2×#14519856C2212yes—
7C2×#14519856C2212yes—
8#16840773—24no—
9#16840772—22no—
10#16840705—22no—
11#16840704—24no—
12#16840703—22no—
13C4×C22⋊#6923—24no—
14#16840634—24no—
15#16840630—22no—
16C23×C4×D61C2211yescharacteristic
17C2×M16×D61C2211yescharacteristic
18C2×M16×D61C2211yescharacteristic
19#16839726C411yescharacteristic, complemented
20#16839725C411yescharacteristic, complemented
21#16839725C411yescharacteristic, complemented
22#16839724—22no—
23C22⋊C8×D61—22no—
24C61×#407C411yescharacteristic, complemented
25#14519856—22no—
26#14519856—22no—
27#14519856—22no—
28#14519856—22no—
29#14519856—22no—
30#14519856—22no—
31#14519856—22no—
32#14519856—22no—
33C2×C4⋊#6923—22no—
34C2×C4⋊#6923D414yes—
35C2×C22⋊#6923—28no—
36C2×C22⋊#6923—22no—
37C2×C22⋊#6923—22no—
38C2×C4×#6923—22no—
39C2×C4×#6923D414yes—
40#14519846—24no—
41#14519845—24no—
42(C2×#6923)⋊C4—28no—
43C24×D61D411yescharacteristic
44C23×Dic61Q811yescharacteristic
45C22×C4×D61—22no—
46C22×C4×D61—21no—
47C22×C4×D61—21no—
48C22×C4×D61—22no—
49C22×C4×D61—21no—
50C22×C4×D61—21no—
51C22×C4×D61—22no—
52C22×C4×D61—22no—
53C22×C4×D61C2×C411yescharacteristic
54C22×C4×D61D411yescharacteristic
55C22×C4×D61Q811yescharacteristic
56C22×C4×D61C2311yescharacteristic
57C2×#11758194C2×C411yescharacteristic
58C2×#11758194C2×C411yescharacteristic
59C2×#11758189—21no—
60C2×#11758189D412yes—
61M16×D61—22no—
62M16×D61—22no—
63M16×D61—22no—
64M16×D61—22no—
65C2×C8×D61—21no—
66C2×C8×D61D412yes—
67C22⋊#92418—22no—
68#14519689—22no—
69#14519689—22no—
70C23×C4×C61C2×C411yescharacteristic
71C2×M16×C61C2×C411yescharacteristic
72C2×M16×C61C2×C411yescharacteristic
73C22⋊C8×C61—22no—
74C24×C61C4⋊C411yescharacteristic
75C23×D61—22no—
76C23×D61—21no—
77C23×D61—21no—
78C23×D61—22no—
79C23×D61—44no—
80C23×D61C4⋊C411yescharacteristic
81C23×D61C2×D411yescharacteristic
82C22×#6923—24no—
83C22×#6923—24no—
84C22×C4×C61—21no—
85C22×C4×C61—21no—
86C22×C4×C61—22no—
87C22×C4×C61—22no—
88C22×C4×C61C4⋊C411yescharacteristic
89C22×C4×C61C22×C411yescharacteristic
90C22×Dic61—21no—
91C22×Dic61—21no—
92C22×Dic61—22no—
93C22×Dic61—22no—
94C22×Dic61C4⋊C411yescharacteristic
95C22×Dic61C2×Q811yescharacteristic
96C2×C4×D61—22no—
97C2×C4×D61—21no—
98C2×C4×D61—21no—
99C2×C4×D61—22no—
100C2×C4×D61—21no—
101C2×C4×D61—21no—
102C2×C4×D61—22no—
103C2×C4×D61—22no—
104C2×C4×D61—22no—
105C2×C4×D61—21no—
106C2×C4×D61—21no—
107C2×C4×D61—22no—
108C2×C4×D61—41no—
109C2×C4×D61—42no—
110C2×C4×D61—42no—
111C2×C4×D61—42no—
112C2×C4×D61—42no—
113C2×C4×D61—41no—
114C2×C4×D61—42no—
115C2×C4×D61—41no—
116C2×C4×D61—42no—
117C2×C4×D61—41no—
118C2×C4×D61C2×D412yes—
119C2×C4×D61C2×D411yescharacteristic
120C2×C4×D61C2×D411yescharacteristic
121C2×C4×D61C2×D412yes—
122C2×C4×D61#4111yescharacteristic
123C2×C4×D61#4112yes—
124C2×C4×D61#4112yes—
125C2×C4×D61#4111yescharacteristic
126C22⋊#6923—416no—
127C22⋊#6923—42no—
128C22⋊#6923—42no—
129C22⋊#6923—42no—
130C22⋊#6923—42no—
131C4⋊#6923—24no—
132C4⋊#6923—24no—
133C4⋊#6923—42no—
134C4⋊#6923—42no—
135C4×#6923—24no—
136C4×#6923—24no—
137C4×#6923—42no—
138C4×#6923—42no—
139M16×C61—22no—
140M16×C61—22no—
141C2×C8×C61—21no—
142C2×C8×C61C22⋊C412yescomplemented
143#11758194—22no—
144#11758194—22no—
145C2×#92418—21no—
146C2×#92418C22⋊C412yescomplemented
147#11758189—24no—
148#11758189—42no—
149C8×D61—22no—
150C8×D61—22no—
151C8×D61—41no—
152C8×D61—41no—
153C23×C61—21no—
154C23×C61—22no—
155C23×C61—42no—
156C23×C61C2×C4⋊C411yescharacteristic
157C22×D61—28no—
158C22×D61—24no—
159C22×D61—21no—
160C22×D61—22no—
161C22×D61—42no—
162C22×D61—42no—
163C22×D61—44no—
164C22×D61—42no—
165C22×D61—42no—
166C22×D61—44no—
167C22×D61—42no—
168C22×D61—44no—
169C22×D61—41no—
170C22×D61—42no—
171C22×D61—41no—
172C22×D61#12012yes—
173C22×D61#12111yescharacteristic
174C22×D61#12111yescharacteristic
175C22×D61#12312yes—
176C2×#6923—48no—
177C2×#6923—48no—
178C2×#6923—44no—
179C2×#6923—44no—
180C2×C4×C61—21no—
181C2×C4×C61—22no—
182C2×C4×C61—41no—
183C2×C4×C61—42no—
184C2×C4×C61—41no—
185C2×C4×C61C2×C22⋊C411yescharacteristic
186C2×C4×C61#11711yescharacteristic
187C2×C4×C61C4×D412yes—
188C2×C4×C61C4×D412yes—
189C2×Dic61—21no—
190C2×Dic61—22no—
191C2×Dic61—41no—
192C2×Dic61—42no—
193C2×Dic61—41no—
194C2×Dic61C22⋊Q812yes—
195C2×Dic61C22⋊Q811yescharacteristic
196C2×Dic61C22⋊Q811yescharacteristic
197C2×Dic61C22⋊Q812yes—
198C4×D61—41no—
199C4×D61—42no—
200C4×D61—41no—
201C4×D61—41no—
202C4×D61—42no—
203C4×D61—41no—
204C4×D61—41no—
205C4×D61—42no—
206C4×D61—41no—
207C4×D61#12011yescharacteristic
208C4×D61#12112yes—
209C4×D61#12112yes—
210C4×D61#12112yes—
211C4×D61#12311yescharacteristic
212C4×D61#12312yes—
213C4×D61#12412yes—
214C4×D61#12411yescharacteristic
215C4×D61#12612yes—
216C4×D61#12711yescharacteristic
217C8×C61—22no—
218C8×C61—41no—
219#92418—22no—
220#92418—41no—
221#11100—611nomaximal, Sylow
222C22×C61—22no—
223C22×C61—24no—
224C22×C61—41no—
225C22×C61—41no—
226C22×C61—42no—
227C22×C61—41no—
228C22×C61#38011yescharacteristic
229C22×C61#38512yes—
230C2×D61—24no—
231C2×D61—22no—
232C2×D61—22no—
233C2×D61—24no—
234C2×D61—41no—
235C2×D61—42no—
236C2×D61—48no—
237C2×D61—44no—
238C2×D61—41no—
239C2×D61—42no—
240C2×D61—41no—
241C2×D61—44no—
242C2×D61#39211yescharacteristic
243C2×D61#39412yes—
244C2×D61#39711yescharacteristic
245#6923—84no—
246#6923—84no—
247C4×C61—41no—
248C4×C61#38611yescharacteristic
249C4×C61#38812yes—
250C4×C61#39011yescharacteristic
251Dic61—41no—
252Dic61#39311yescharacteristic
253Dic61#39612yes—
254Dic61#39911yescharacteristic
255#2911—611no—
256C2×#407—611no—
257#2280—612no—
258#1733—612no—
259C2×H(3,ℤ/4)—611no—
260C2×C61—21no—
261C2×C61—22no—
262C2×C61—42no—
263C2×C61#143911yescharacteristic
264D61—22no—
265D61—21no—
266D61—42no—
267D61#201012yes—
268C24×C4—611no—
269C22×M16—611no—
270C22×M16—611no—
271C2×#117—612no—
272C2×#117—612no—
273#428—1224no—
274#427—1222no—
275#407—611no—
276#407—611no—
277#407—611no—
278#407—1222no—
279#407#692311yescharacteristic, complemented
280C2×C22⋊C8—1222no—
281#381—1222no—
282#380—1224no—
283#379—1222no—
284C4×C22⋊C4—1224no—
285#339—1224no—
286H(3,ℤ/4)—1222no—
287C61#1110011yescharacteristic, complemented, Sylow
288C25—611no—
289C23×C4—611no—
290C23×C4—611no—
291C23×C4—611no—
292C23×C4—611no—
293C23×C4—611no—
294C23×C4—1221no—
295C23×C4—1221no—
296C23×C4—1222no—
297C23×C4—1222no—
298C23×C4—1222no—
299C23×C4—1222no—
300C23×C4—1221no—
301C23×C4—1221no—
302C23×C4C2×#692311yescharacteristic
303C2×M16—611no—
304C2×M16—612no—
305C2×M16—611no—
306C2×M16—1221no—
307C2×M16—1222no—
308C2×M16—1222no—
309C2×M16—1222no—
310C2×M16—1222no—
311C2×M16C2×#692311yescharacteristic
312C2×M16C2×#692311yescharacteristic
313C22×C8—612no—
314C22×C8—1221no—
315#117—1222no—
316#117—1222no—
317#117—1222no—
318#117—1222no—
319#117—1222no—
320#117—1222no—
321#117—1222no—
322#117—1222no—
323C2×C4⋊C4—614no—
324C2×C4⋊C4—1222no—
325C2×C22⋊C4—1222no—
326C2×C22⋊C4—1222no—
327C2×C22⋊C4—1228no—
328C2×C42—614no—
329C2×C42—1222no—
330#107—1224no—
331#106—1224no—
332C22⋊C8—22no—
333C22⋊C8—1222no—
334C22⋊C8—1222no—
335C22⋊C8—1222no—
336#95—1228no—
337C24—611no—
338C24—611no—
339C24—1222no—
340C24—1221no—
341C24—1221no—
342C24—1222no—
343C24—2444no—
344C24C4⋊#692311yescharacteristic
345C22×C4—21no—
346C22×C4—21no—
347C22×C4—22no—
348C22×C4—22no—
349C22×C4—611no—
350C22×C4—611no—
351C22×C4—611no—
352C22×C4—611no—
353C22×C4—611no—
354C22×C4—612no—
355C22×C4—612no—
356C22×C4—612no—
357C22×C4—612no—
358C22×C4—611no—
359C22×C4—1221no—
360C22×C4—1221no—
361C22×C4—1222no—
362C22×C4—1222no—
363C22×C4—1222no—
364C22×C4—1221no—
365C22×C4—1221no—
366C22×C4—1222no—
367C22×C4—1221no—
368C22×C4—1221no—
369C22×C4—1222no—
370C22×C4—1222no—
371C22×C4—1221no—
372C22×C4—1221no—
373C22×C4—1222no—
374C22×C4—1222no—
375C22×C4—1224no—
376C22×C4—1224no—
377C22×C4—2441no—
378C22×C4—2442no—
379C22×C4—2441no—
380C22×C4—2442no—
381C22×C4—2442no—
382C22×C4—2442no—
383C22×C4—2442no—
384C22×C4—2442no—
385C22×C4—2441no—
386C22×C4—2441no—
387C22×C4C4⋊#692311yescharacteristic
388C22×C4C22×#692311yescharacteristic
389M16—22no—
390M16—22no—
391M16—1224no—
392M16—1222no—
393M16—1222no—
394M16—2442no—
395C2×C8—21no—
396C2×C8—612no—
397C2×C8—1222no—
398C2×C8—1222no—
399C2×C8—1221no—
400C2×C8—2441no—
401C2×C8—2441no—
402C2×C8C22⋊#692312yescomplemented
403C4⋊C4—1224no—
404C4⋊C4—1224no—
405C4⋊C4—2442no—
406C4⋊C4—2442no—
407C22⋊C4—2442no—
408C22⋊C4—2442no—
409C22⋊C4—2442no—
410C22⋊C4—2442no—
411C22⋊C4—24416no—
412C42—1224no—
413C42—1224no—
414C42—2442no—
415C42—2442no—
416C23—21no—
417C23—22no—
418C23—42no—
419C23—611no—
420C23—612no—
421C23—611no—
422C23—612no—
423C23—1228no—
424C23—1224no—
425C23—1221no—
426C23—1222no—
427C23—2442no—
428C23—2444no—
429C23—2441no—
430C23—2442no—
431C23—2441no—
432C23—2442no—
433C23—2442no—
434C23—2444no—
435C23—2442no—
436C23—2442no—
437C23—2444no—
438C23C2×C4⋊#692311yescharacteristic
439C2×C4—21no—
440C2×C4—22no—
441C2×C4—41no—
442C2×C4—42no—
443C2×C4—41no—
444C2×C4—611no—
445C2×C4—611no—
446C2×C4—612no—
447C2×C4—612no—
448C2×C4—611no—
449C2×C4—612no—
450C2×C4—611no—
451C2×C4—612no—
452C2×C4—612no—
453C2×C4—612no—
454C2×C4—612no—
455C2×C4—612no—
456C2×C4—611no—
457C2×C4—611no—
458C2×C4—1221no—
459C2×C4—1222no—
460C2×C4—2441no—
461C2×C4—2442no—
462C2×C4—2441no—
463C2×C4—2441no—
464C2×C4—2442no—
465C2×C4—2441no—
466C2×C4—2441no—
467C2×C4—2442no—
468C2×C4—2441no—
469C2×C4—2444no—
470C2×C4—2444no—
471C2×C4—2448no—
472C2×C4—2448no—
473C2×C4—2441no—
474C2×C4—2442no—
475C2×C4—2441no—
476C2×C4C2×C22⋊#692311yescharacteristic
477C2×C4#1451985611yescharacteristic
478C2×C4D4×#692312yes—
479C2×C4D4×#692312yes—
480C8—22no—
481C8—41no—
482C8—1222no—
483C8—2441no—
484C22—22no—
485C22—24no—
486C22—41no—
487C22—41no—
488C22—42no—
489C22—41no—
490C22—611no—
491C22—612no—
492C22—611no—
493C22—1224no—
494C22—1222no—
495C22—1222no—
496C22—1224no—
497C22—2441no—
498C22—2442no—
499C22—2441no—
500C22—2442no—
501C22—2444no—
502C22—2448no—
503C22—2444no—
504C22—2441no—
505C22#1684070411yescharacteristic
506C22#1684070912yes—
507C4—41no—
508C4—611no—
509C4—612no—
510C4—611no—
511C4—4884no—
512C4—4884no—
513C4—2441no—
514C4#1684071011yescharacteristic
515C4#1684071212yes—
516C4#1684071411yescharacteristic
517C2—21no—
518C2—22no—
519C2—42no—
520C2—612no—
521C2—1222no—
522C2—1221no—
523C2—2442no—
524C2#2146100211yescharacteristic
subgroupG/H
centerC4#16840714
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC61×#407C4
socleC2×C61#1439
prime radicalC24×D61D4
cosocleC22×C4×D61C23
hypercenter#407#6923
hypocenterC61#11100
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C4 ◁ C22×C4 ◁ #407

Complements

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

NH ≅ G/Ntype
1. #21462472C2semidirect
3. #21461501C2semidirect
4. #21461491C2semidirect
19. #16839726C4semidirect
20. #16839725C4semidirect
21. #16839725C4semidirect
24. C61×#407C4semidirect
142. C2×C8×C61C22⋊C4semidirect
146. C2×#92418C22⋊C4semidirect
279. #407#6923semidirect
287. C61#11100semidirect
402. C2×C8C22⋊#6923semidirect

Maximal subgroups

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

subgroupindex
#214624722
#214622632
#214615012
#214614912
#407×D612
#1110061