Finite Group Databasebeta

← #30616104

Subgroups — #30616104

Order 15616.

764 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
1#21462507C211yesmaximal, characteristic, complemented
2#21462391C211yesmaximal, characteristic, complemented
3#21461903C212yesmaximal, complemented
4#21461884C212yesmaximal, complemented
5#21461809C212yesmaximal
6#21461787C212yesmaximal, complemented
7C4×#14519848C211yesmaximal, characteristic, complemented
8#21461583C211yesmaximal, characteristic, complemented
9#21461583C211yesmaximal, characteristic, complemented
10#21461537C211yesmaximal, characteristic, complemented
11C4×#14519800C211yesmaximal, characteristic
12C2×#14519865C2212yes—
13#16840787—22no—
14#16840785—21no—
15#16840784—21no—
16C2×#14519848C2212yes—
17#16840769C2212yes—
18C2×#14519842C2212yes—
19C2×#14519842C2212yes—
20#16840737C2212yes—
21#16840727—22no—
22#16840727C2212yes—
23C4×#11758213—21no—
24C4×#11758213C2211yescharacteristic
25C4×#11758213C2211yescharacteristic
26#16840721—21no—
27#16840721C2211yescharacteristic
28#16840698C2211yescharacteristic
29#16840638C2212yes—
30#16840632C2212yes—
31#16840632C2212yes—
32(C2×#6923)⋊C8C2212yes—
33(C2×#6923)⋊C8C2212yes—
34C2×#14519800C2211yescharacteristic
35C4×#11758226C2211yescharacteristic
36C4×#11758226C2211yescharacteristic
37Q16×Dic61C411yescharacteristic, complemented
38C4×#11758201C411yescharacteristic, complemented
39C4×#11758201C411yescharacteristic, complemented
40#16839847C411yescharacteristic, complemented
41#16839847C411yescharacteristic, complemented
42C4×D488C411yescharacteristic, complemented
43#16839844C411yescharacteristic, complemented
44#16839799C2211yescharacteristic
45#16839757C2211yescharacteristic
46#16839757C2211yescharacteristic
47C4×C8×D61C2211yescharacteristic
48C4×Q16×C61C411yescharacteristic, complemented
49#14519865—24no—
50#14519865—24no—
51C2×#11758213—22no—
52C2×#11758213C2312yes—
53C2×#11758213C2312yes—
54C2×D61⋊C8—22no—
55C2×D61⋊C8C2312yes—
56C2×C4×#6923C2312yes—
57#14519848—24no—
58#14519844—22no—
59C4⋊#92420—22no—
60#14519842—24no—
61#14519842—24no—
62#14519834—22no—
63#14519834—22no—
64#14519832—22no—
65#14519832—21no—
66#14519832—21no—
67#14519832D411yescharacteristic
68#14519832D411yescharacteristic
69#14519832D412yes—
70C4×#92420—22no—
71C4×#92420—21no—
72C4×#92420—21no—
73(C2×#6923)⋊C4—21no—
74(C2×#6923)⋊C4—21no—
75C2×#11758226C2311yescharacteristic
76C2×#11758226C2311yescharacteristic
77#14519800—24no—
78C2×#11758201C2×C411yescharacteristic
79C2×#11758201C2×C411yescharacteristic
80C2×D488C2×C411yescharacteristic
81C2×C8×D61C2311yescharacteristic
82C2×C8×D61C2311yescharacteristic
83Q8×Dic61C2×C411yescharacteristic
84Q8×Dic61C2×C411yescharacteristic
85C4×D244—21no—
86C4×D244—21no—
87C4×D244C2×C411yescharacteristic
88C4×D244C2×C411yescharacteristic
89#14519739—21no—
90#14519739—21no—
91#14519739C2×C411yescharacteristic
92#14519739C2×C411yescharacteristic
93#14519735—21no—
94#14519735—21no—
95#14519735C2311yescharacteristic
96#14519735C2311yescharacteristic
97C42×D61—21no—
98C42×D61—21no—
99C42×D61C2311yescharacteristic
100#14519711C2×C411yescharacteristic
101#14519708C2×C411yescharacteristic
102#14519708C2×C411yescharacteristic
103#14519701C2×C411yescharacteristic
104#14519701C2×C411yescharacteristic
105#14519699C2×C411yescharacteristic
106#14519699C2×C411yescharacteristic
107#14519697C2×C411yescharacteristic
108#14519697C2×C411yescharacteristic
109C4×#92418C2×C411yescharacteristic
110C8×Dic61C2×C411yescharacteristic
111C8×Dic61C2×C411yescharacteristic
112C2×Q16×C61C2×C411yescharacteristic
113C4×Q8×C61C2×C411yescharacteristic
114C4×Q8×C61C2×C411yescharacteristic
115#107×C61C2×C411yescharacteristic
116#103×C61C2×C411yescharacteristic
117#103×C61C2×C411yescharacteristic
118C4×C8×C61C2×C411yescharacteristic
119C22×#6923—22no—
120C2×Q8×C61C22×C411yescharacteristic
121C2×Q8×C61C22×C411yescharacteristic
122#11758226—22no—
123#11758226—22no—
124#11758226—22no—
125#11758226#4114yes—
126C2×D244—21no—
127C2×D244—21no—
128C2×D244C22×C411yescharacteristic
129C2×D244C22×C411yescharacteristic
130C2×C4×D61—21no—
131C2×C4×D61—21no—
132C2×C4×D61—21no—
133C2×C4×D61—21no—
134C2×C4×D61—21no—
135C2×C4×D61—21no—
136C2×C4×D61#4111yescharacteristic
137C2×C4×D61#4111yescharacteristic
138C2×C4×D61C2411yescharacteristic
139C2×#92420—22no—
140C2×#92420—22no—
141C2×#92420C2×D412yes—
142C2×#92420C2×D412yes—
143C4×#6923—22no—
144C4×#6923—22no—
145#11758213—28no—
146#11758213—22no—
147#11758213—22no—
148#11758213—22no—
149#11758213#4114yes—
150D61⋊C8—28no—
151D61⋊C8—22no—
152D61⋊C8—22no—
153Q16×C61—22no—
154C2×C8×C61C22×C411yescharacteristic
155C2×C8×C61C22×C411yescharacteristic
156C4⋊C4×C61—21no—
157C4⋊C4×C61—21no—
158C4⋊C4×C61C22×C411yescharacteristic
159C4⋊C4×C61C22×C411yescharacteristic
160C42×C61—21no—
161C42×C61—21no—
162C42×C61C22×C411yescharacteristic
163#11758201—22no—
164#11758201—22no—
165#11758198—21no—
166#11758198—21no—
167#11758198—21no—
168#11758198—21no—
169#11758198—21no—
170#11758198—21no—
171C4⋊Dic61—21no—
172C4⋊Dic61—21no—
173C4⋊Dic61C22×C411yescharacteristic
174C4⋊Dic61C22×C411yescharacteristic
175C4×Dic61—21no—
176C4×Dic61—21no—
177C4×Dic61—21no—
178C4×Dic61—21no—
179C4×Dic61C22×C411yescharacteristic
180C4×Dic61C2×D411yescharacteristic
181C4×Dic61C2×D411yescharacteristic
182C2×#92418C22×C411yescharacteristic
183C2×#92418C22×C411yescharacteristic
184D488—22no—
185C8×D61—22no—
186C8×D61—22no—
187C22×D61—21no—
188C22×D61—21no—
189C22×D61C2×#4111yescharacteristic
190C2×#6923—42no—
191C2×#6923—42no—
192C2×#6923—42no—
193Q8×C61—21no—
194Q8×C61—21no—
195Q8×C61—21no—
196Q8×C61#11712yes—
197C2×C4×C61—21no—
198C2×C4×C61—21no—
199C2×C4×C61—21no—
200C2×C4×C61—21no—
201C2×C4×C61C4×D411yescharacteristic
202C2×C4×C61C4×D411yescharacteristic
203C2×C4×C61C23×C411yescharacteristic
204C2×Dic61—21no—
205C2×Dic61—21no—
206C2×Dic61C4×D411yescharacteristic
207C2×Dic61C4×D411yescharacteristic
208C2×Dic61C22×D411yescharacteristic
209D244—24no—
210D244—21no—
211D244—21no—
212D244—21no—
213D244—42no—
214D244#11712yes—
215C4×D61—24no—
216C4×D61—41no—
217C4×D61—41no—
218C4×D61—42no—
219C4×D61—81no—
220C4×D61—81no—
221C4×D61—81no—
222C4×D61—81no—
223C4×D61C2×#4112yes—
224C4×D61C2×#4112yes—
225#92420—22no—
226#92420—22no—
227#92420—24no—
228#92420—42no—
229C8×C61—21no—
230C8×C61—21no—
231#92418—21no—
232#92418—21no—
233#21140—611nomaximal, Sylow
234C22×C61C2×C4×D411yescharacteristic
235C2×D61—21no—
236C2×D61—21no—
237C2×D61—22no—
238C2×D61—41no—
239C2×D61—41no—
240C2×D61—41no—
241C2×D61—41no—
242C2×D61—41no—
243C2×D61#52912yes—
244#6923—82no—
245C4×C61—21no—
246C4×C61—21no—
247C4×C61—22no—
248C4×C61—41no—
249C4×C61—41no—
250C4×C61—41no—
251C4×C61C2×#11711yescharacteristic
252C4×C61C4×#4111yescharacteristic
253Dic61—21no—
254Dic61—21no—
255Dic61—41no—
256Dic61—41no—
257Dic61#52512yes—
258C4×#135—611no—
259#2923—611no—
260#2875—611no—
261#1929—612no—
262#1922—612no—
263#1876—612no—
264#1866—612no—
265C4×#108—611no—
266#1759—611no—
267#1759—611no—
268#1746—611no—
269C2×C61#229011yescharacteristic
270C2×C61#295711yescharacteristic
271C2×C61#295711yescharacteristic
272D61—22no—
273D61—42no—
274D61—81no—
275C2×#135—611no—
276C2×#131—612no—
277C4×#41—611no—
278C4×#41—611no—
279C4×Q16—611no—
280C4×Q16#692311yescharacteristic, complemented
281C4×SD16—611no—
282C4×SD16—611no—
283C4×SD16—611no—
284C4×SD16—611no—
285C4×D8—611no—
286C4×D8—611no—
287#433—1222no—
288#432—1221no—
289#432—1221no—
290C2×#108—612no—
291#427—611no—
292#424—612no—
293C2×#104—612no—
294C2×#104—612no—
295#416—611no—
296#416—611no—
297#408—612no—
298#405—612no—
299#405—1222no—
300C4×M16—611no—
301C4×M16—611no—
302C4×M16—1221no—
303C2×#97—611no—
304C2×#97—1221no—
305C2×C4×C8—611no—
306#376—611no—
307#341—612no—
308#339—612no—
309#339—612no—
310#336—612no—
311#336—612no—
312C61#2114011yescharacteristic, complemented, Sylow
313C2×#41—611no—
314C2×#41—611no—
315#135—1224no—
316C2×Q16C2×#692311yescharacteristic
317C2×SD16—611no—
318C2×SD16—611no—
319C2×D8—611no—
320#131—1224no—
321#131—1224no—
322C2×M16—612no—
323C2×M16—612no—
324C2×M16—1222no—
325C22×C8—612no—
326C22×C8—611no—
327C22×C8—611no—
328C22×C8—1222no—
329C4×Q8—611no—
330C4×Q8—611no—
331C4×Q8C2×#692311yescharacteristic
332C4×Q8C2×#692311yescharacteristic
333C4×D4—611no—
334C4×D4—611no—
335C4×D4—611no—
336C4×D4—611no—
337C4×D4—1221no—
338C4×D4—1221no—
339C4×D4—1221no—
340C4×D4—1221no—
341#117—611no—
342#117—611no—
343#117—1221no—
344#117—1221no—
345C2×C42—611no—
346C2×C42—612no—
347C2×C42—1221no—
348C2×C42—1221no—
349#108—1224no—
350#107—611no—
351#107C2×#692311yescharacteristic
352#106—611no—
353#106—611no—
354C4⋊C8—1222no—
355C4⋊C8—1222no—
356#104—1224no—
357#104—1224no—
358#103—611no—
359#103—611no—
360#103C2×#692311yescharacteristic
361#103C2×#692311yescharacteristic
362#102—611no—
363#102—611no—
364#102—611no—
365#102—611no—
366C22⋊C8—1222no—
367C22⋊C8—1222no—
368#97—611no—
369#97—611no—
370#97—612no—
371#97—1221no—
372#97—1221no—
373#97—1222no—
374C4×C8—611no—
375C4×C8—611no—
376C4×C8—611no—
377C4×C8—1221no—
378C4×C8—1221no—
379C4×C8—1222no—
380C4×C8C2×#692311yescharacteristic
381#95—1221no—
382#95—1221no—
383#41—614no—
384#41—1222no—
385#41—1222no—
386#41—1222no—
387C2×Q8C22×#692311yescharacteristic
388C2×Q8C22×#692311yescharacteristic
389C2×D4—611no—
390C2×D4—611no—
391C2×D4—1221no—
392C2×D4—1221no—
393C22×C4—611no—
394C22×C4—611no—
395C22×C4—611no—
396C22×C4—1221no—
397C22×C4—1221no—
398C22×C4—1221no—
399C22×C4—1221no—
400C22×C4—1221no—
401C22×C4—1221no—
402C22×C4—1222no—
403Q16—22no—
404SD16—1222no—
405SD16—1222no—
406D8—1222no—
407M16—614no—
408M16—1222no—
409M16—1228no—
410M16—1222no—
411M16—1222no—
412C2×C8—612no—
413C2×C8—612no—
414C2×C8—611no—
415C2×C8—611no—
416C2×C8—1222no—
417C2×C8—1222no—
418C2×C8—1222no—
419C2×C8—1222no—
420C2×C8—1222no—
421C2×C8—1228no—
422C2×C8—1222no—
423C2×C8C22×#692311yescharacteristic
424C2×C8C22×#692311yescharacteristic
425C4⋊C4—21no—
426C4⋊C4—21no—
427C4⋊C4—611no—
428C4⋊C4—611no—
429C4⋊C4—1221no—
430C4⋊C4—1221no—
431C4⋊C4C22×#692311yescharacteristic
432C4⋊C4C22×#692311yescharacteristic
433C22⋊C4—1221no—
434C22⋊C4—1221no—
435C22⋊C4—1221no—
436C22⋊C4—1221no—
437C22⋊C4—1221no—
438C22⋊C4—1221no—
439C42—21no—
440C42—21no—
441C42—611no—
442C42—611no—
443C42—611no—
444C42—1221no—
445C42—1221no—
446C42—1221no—
447C42—1221no—
448C42—1222no—
449C42—1222no—
450C42C22×#692311yescharacteristic
451C23—611no—
452C23—1221no—
453C23—1221no—
454Q8—21no—
455Q8—21no—
456Q8—21no—
457Q8#1451985612yes—
458D4—612no—
459D4—1224no—
460D4—1221no—
461D4—1221no—
462D4—1221no—
463D4—2442no—
464C2×C4—21no—
465C2×C4—21no—
466C2×C4—21no—
467C2×C4—21no—
468C2×C4—611no—
469C2×C4—612no—
470C2×C4—612no—
471C2×C4—611no—
472C2×C4—611no—
473C2×C4—1224no—
474C2×C4—1221no—
475C2×C4—1221no—
476C2×C4—4881no—
477C2×C4—4881no—
478C2×C4—4881no—
479C2×C4—4881no—
480C2×C4—2441no—
481C2×C4—2441no—
482C2×C4—2442no—
483C2×C4—2442no—
484C2×C4—2442no—
485C2×C4—2442no—
486C2×C4D4×#692311yescharacteristic
487C2×C4D4×#692311yescharacteristic
488C2×C4C23×#692311yescharacteristic
489C8—21no—
490C8—21no—
491C8—1222no—
492C8—1222no—
493C8—1224no—
494C8—1221no—
495C8—1221no—
496C8—2442no—
497C22—612no—
498C22—1221no—
499C22—1221no—
500C22—1222no—
501C22—2441no—
502C22—2441no—
503C22—2441no—
504C22—2441no—
505C22—2441no—
506C22C2×D4×#692311yescharacteristic
507C4—22no—
508C4—21no—
509C4—21no—
510C4—41no—
511C4—41no—
512C4—41no—
513C4—612no—
514C4—1221no—
515C4—1221no—
516C4—4882no—
517C4—2441no—
518C4—2441no—
519C4C2×#1451985611yescharacteristic
520C4#41×#692311yescharacteristic
521C2—1222no—
522C2—4881no—
523C2—2442no—
524C2#2146227311yescharacteristic
525C2#2146259611yescharacteristic
526C2#2146259911yescharacteristic
subgroupG/H
centerC22C2×D4×#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC4×Q16×C61C4
socleC22×C61C2×C4×D4
prime radicalC2×#14519800C22
cosocleC2×C4×D61C24
hypercenterC4×Q16#6923
hypocenterC61#21140
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ C4×Q16

Complements

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

NH ≅ G/Ntype
1. #21462507C2semidirect
2. #21462391C2semidirect
3. #21461903C2semidirect
4. #21461884C2semidirect
6. #21461787C2semidirect
7. C4×#14519848C2semidirect
8. #21461583C2semidirect
9. #21461583C2semidirect
10. #21461537C2semidirect
37. Q16×Dic61C4semidirect
38. C4×#11758201C4semidirect
39. C4×#11758201C4semidirect
40. #16839847C4semidirect
41. #16839847C4semidirect
42. C4×D488C4semidirect
43. #16839844C4semidirect
48. C4×Q16×C61C4semidirect
280. C4×Q16#6923semidirect
312. C61#21140semidirect

Maximal subgroups

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

subgroupindex
#214625072
#214623912
#214619032
#214618842
#214618092
#214617872
C4×#145198482
#214615832
#214615372
C4×#145198002
#2114061