Finite Group Databasebeta

← #30616411

Subgroups — #30616411

Order 15616.

722 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
1#21462507C211yesmaximal, characteristic, complemented
2#21462506C211yesmaximal, characteristic, complemented
3#21461971C212yesmaximal
4#21461926C212yesmaximal, complemented
5#21461915C212yesmaximal, complemented
6#21461914C212yesmaximal, complemented
7C4×#14519847C211yesmaximal, characteristic, complemented
8#21461583C211yesmaximal, characteristic, complemented
9#21461582C211yesmaximal, characteristic, complemented
10#21461475C211yesmaximal, characteristic, complemented
11C4×#14519798C211yesmaximal, characteristic
12#16840787—22no—
13#16840786—22no—
14#16840785—21no—
15#16840784—21no—
16#16840783—21no—
17#16840782—21no—
18C2×#14519847C2212yes—
19#16840769C2212yes—
20#16840769C2212yes—
21C2×#14519842C2212yes—
22C2×#14519841C2212yes—
23#16840737C2212yes—
24#16840736C2212yes—
25C4×#11758213C2211yescharacteristic
26C4×#11758213C2211yescharacteristic
27#16840721C2211yescharacteristic
28C2×#14519831C2212yes—
29C2×C8×#6923C2212yes—
30#16840698C2211yescharacteristic
31#16840638C2212yes—
32#16840632C2212yes—
33#16840632C2212yes—
34C2×#14519798C2211yescharacteristic
35C4×#11758226C2211yescharacteristic
36C4×#11758224C2211yescharacteristic
37C4×#11758202C411yescharacteristic, complemented
38#16839854C411yescharacteristic, complemented
39C4×#11758190C411yescharacteristic, complemented
40SD16×Dic61C411yescharacteristic, complemented
41#16839849C411yescharacteristic, complemented
42C4×#11758199C411yescharacteristic, complemented
43#16839842C411yescharacteristic, complemented
44#16839797C2211yescharacteristic
45#16839757C2211yescharacteristic
46#16839755C2211yescharacteristic
47C4×C8×D61C2211yescharacteristic
48C4×SD16×C61C411yescharacteristic, complemented
49C2×#11758213C2312yes—
50C2×#11758213C2312yes—
51C2×D61⋊C8C2312yes—
52C2×C4×#6923C2312yes—
53#14519847—24no—
54#14519844—22no—
55#14519844—22no—
56C4⋊#92420—22no—
57C4⋊#92420—22no—
58#14519842—24no—
59#14519841—24no—
60#14519834—22no—
61#14519834—22no—
62C22⋊#92420—22no—
63C22⋊#92420—22no—
64#14519832—21no—
65#14519832—21no—
66#14519832D411yescharacteristic
67#14519832D411yescharacteristic
68#14519832D412yes—
69#14519831—24no—
70C4×#92420—21no—
71C4×#92420—21no—
72C8×#6923—24no—
73(C2×#6923)⋊C4—21no—
74(C2×#6923)⋊C4—21no—
75C2×#11758226C2311yescharacteristic
76C2×#11758224C2311yescharacteristic
77#14519798—24no—
78C2×#11758202C2×C411yescharacteristic
79C2×#11758190C2×C411yescharacteristic
80C2×#11758199C2×C411yescharacteristic
81C2×C8×D61C2311yescharacteristic
82C2×C8×D61C2311yescharacteristic
83Q8×Dic61C2×C411yescharacteristic
84C4×Dic122C2×C411yescharacteristic
85#14519742C2×C411yescharacteristic
86C4×D244—21no—
87C4×D244C2×C411yescharacteristic
88D4×Dic61C2×C411yescharacteristic
89#14519739—21no—
90#14519739C2×C411yescharacteristic
91C4×C22⋊D61—21no—
92#14519737—21no—
93#14519735—21no—
94#14519735C2311yescharacteristic
95#14519735C2311yescharacteristic
96#14519733—21no—
97C2×C4×Dic61—21no—
98C42×D61—21no—
99C42×D61C2311yescharacteristic
100#14519710C2×C411yescharacteristic
101#14519710C2×C411yescharacteristic
102#14519709C2×C411yescharacteristic
103#14519702C2×C411yescharacteristic
104#14519701C2×C411yescharacteristic
105#14519700C2×C411yescharacteristic
106#14519699C2×C411yescharacteristic
107#14519698C2×C411yescharacteristic
108#14519697C2×C411yescharacteristic
109C4×#92418C2×C411yescharacteristic
110C8×Dic61C2×C411yescharacteristic
111C8×Dic61C2×C411yescharacteristic
112C2×SD16×C61C2×C411yescharacteristic
113C4×Q8×C61C2×C411yescharacteristic
114C4×D4×C61C2×C411yescharacteristic
115#106×C61C2×C411yescharacteristic
116#103×C61C2×C411yescharacteristic
117#102×C61C2×C411yescharacteristic
118C4×C8×C61C2×C411yescharacteristic
119C22×#6923—22no—
120C2×Q8×C61C22×C411yescharacteristic
121C2×D4×C61C22×C411yescharacteristic
122C22×C4×C61—21no—
123C2×C22⋊D61—21no—
124C22×Dic61—21no—
125C22×Dic61—21no—
126#11758226—22no—
127#11758226—22no—
128#11758224—22no—
129#11758224—22no—
130C2×D244—21no—
131C2×D244C22×C411yescharacteristic
132C2×C4×D61—21no—
133C2×C4×D61—21no—
134C2×C4×D61—21no—
135C2×C4×D61#4111yescharacteristic
136C2×C4×D61#4111yescharacteristic
137C2×C4×D61C2411yescharacteristic
138C2×Dic122C22×C411yescharacteristic
139C2×#92420—22no—
140C2×#92420—22no—
141C2×#92420C2×D412yes—
142C2×#92420C2×D412yes—
143C4×#6923—22no—
144C4×#6923#4114yes—
145#11758213—22no—
146#11758213—22no—
147#11758213—22no—
148#11758213—22no—
149D61⋊C8—22no—
150D61⋊C8—22no—
151SD16×C61—22no—
152C2×C8×C61C22×C411yescharacteristic
153C2×C8×C61C22×C411yescharacteristic
154C4⋊C4×C61—21no—
155C4⋊C4×C61C22×C411yescharacteristic
156C4⋊C4×C61C22×C411yescharacteristic
157C22⋊C4×C61—21no—
158C42×C61—21no—
159C42×C61C22×C411yescharacteristic
160C22⋊Dic61—21no—
161#11758202—22no—
162#11758199—22no—
163#11758198—21no—
164#11758198—21no—
165#11758198—21no—
166#11758198—21no—
167C4⋊Dic61—21no—
168C4⋊Dic61C22×C411yescharacteristic
169C4⋊Dic61C22×C411yescharacteristic
170#11758196—21no—
171#11758196—21no—
172C4×Dic61—21no—
173C4×Dic61—21no—
174C4×Dic61—21no—
175C4×Dic61—21no—
176C4×Dic61—21no—
177C4×Dic61C22×C411yescharacteristic
178C4×Dic61C2×D411yescharacteristic
179C4×Dic61C2×D411yescharacteristic
180C2×#92418C22×C411yescharacteristic
181C2×#92418C22×C411yescharacteristic
182#11758190—22no—
183C8×D61—22no—
184C8×D61#4114yes—
185C23×C61—21no—
186C22×D61—21no—
187C22×D61C2×#4111yescharacteristic
188C2×#6923—24no—
189C2×#6923—42no—
190C2×#6923—42no—
191Q8×C61—21no—
192Q8×C61—21no—
193D4×C61—21no—
194D4×C61—21no—
195C2×C4×C61—21no—
196C2×C4×C61—21no—
197C2×C4×C61—21no—
198C2×C4×C61—81no—
199C2×C4×C61C4×D411yescharacteristic
200C2×C4×C61C4×D411yescharacteristic
201C2×C4×C61C23×C411yescharacteristic
202C22⋊D61—42no—
203C2×Dic61—21no—
204C2×Dic61—21no—
205C2×Dic61—21no—
206C2×Dic61—42no—
207C2×Dic61—81no—
208C2×Dic61C4×D411yescharacteristic
209C2×Dic61C4×D411yescharacteristic
210C2×Dic61C22×D411yescharacteristic
211D244—21no—
212D244—21no—
213D244—42no—
214C4×D61—41no—
215C4×D61—41no—
216C4×D61—42no—
217C4×D61—81no—
218C4×D61—81no—
219C4×D61C2×#4112yes—
220C4×D61C2×#4112yes—
221Dic122—21no—
222Dic122—21no—
223#92420—22no—
224#92420—22no—
225#92420—42no—
226#92420—42no—
227C8×C61—21no—
228C8×C61#11712yes—
229#92418—21no—
230#92418#11712yes—
231#21294—611nomaximal, Sylow
232C22×C61—41no—
233C22×C61—41no—
234C22×C61—41no—
235C22×C61C2×C4×D411yescharacteristic
236C2×D61—21no—
237C2×D61—21no—
238C2×D61—41no—
239C2×D61—41no—
240C2×D61—41no—
241C2×D61#52912yes—
242#6923—44no—
243C4×C61—21no—
244C4×C61—21no—
245C4×C61—41no—
246C4×C61—41no—
247C4×C61—41no—
248C4×C61C2×#11711yescharacteristic
249C4×C61C4×#4111yescharacteristic
250Dic61—21no—
251Dic61—21no—
252Dic61—41no—
253Dic61—41no—
254Dic61—41no—
255Dic61#53212yes—
256C4×#135—611no—
257#2923—611no—
258#2923—611no—
259#1974—612no—
260#1945—612no—
261#1938—612no—
262#1938—612no—
263C4×#108—611no—
264#1759—611no—
265#1759—611no—
266#1726—611no—
267C2×C61—81no—
268C2×C61#229311yescharacteristic
269C2×C61#295711yescharacteristic
270C2×C61#295711yescharacteristic
271D61—22no—
272D61—81no—
273C2×#135—611no—
274C4×#41—611no—
275C4×#41—611no—
276C4×Q16—611no—
277C4×Q16—611no—
278C4×SD16—611no—
279C4×SD16—611no—
280C4×SD16—611no—
281C4×SD16#692311yescharacteristic, complemented
282C4×D8—611no—
283C4×D8—611no—
284#433—1222no—
285#433—1222no—
286#432—1221no—
287#432—1221no—
288#432—1221no—
289#432—1221no—
290C2×#108—612no—
291#427—611no—
292#424—612no—
293#424—612no—
294C2×#104—612no—
295C2×#104—612no—
296#416—611no—
297#416—611no—
298#408—612no—
299#408—612no—
300C4×M16—611no—
301C4×M16—611no—
302C2×#97—611no—
303C2×#97—612no—
304C2×C4×C8—611no—
305C2×C4×C8—612no—
306#376—611no—
307#341—612no—
308#339—612no—
309#339—612no—
310C61#2129411yescharacteristic, complemented, Sylow
311C2×#41—611no—
312C2×#41—611no—
313#135—1224no—
314C2×Q16—611no—
315C2×SD16—611no—
316C2×SD16C2×#692311yescharacteristic
317C2×D8—611no—
318C2×M16—612no—
319C2×M16—612no—
320C22×C8—611no—
321C22×C8—612no—
322C22×C8—611no—
323C4×Q8—611no—
324C4×Q8—611no—
325C4×Q8—611no—
326C4×Q8C2×#692311yescharacteristic
327C4×D4—611no—
328C4×D4—611no—
329C4×D4—611no—
330C4×D4—1221no—
331C4×D4—1221no—
332C4×D4—1221no—
333C4×D4—1221no—
334C4×D4C2×#692311yescharacteristic
335#117—611no—
336#117—611no—
337#117—1221no—
338#117—1221no—
339C2×C42—611no—
340C2×C42—612no—
341C2×C42—1221no—
342C2×C42—1221no—
343#108—1224no—
344#107—611no—
345#107—611no—
346#106—611no—
347#106C2×#692311yescharacteristic
348C4⋊C8—1222no—
349C4⋊C8—1222no—
350C4⋊C8—1222no—
351C4⋊C8—1222no—
352#104—1224no—
353#104—1224no—
354#103—611no—
355#103—611no—
356#103—611no—
357#103C2×#692311yescharacteristic
358#102—611no—
359#102—611no—
360#102—611no—
361#102C2×#692311yescharacteristic
362C22⋊C8—1222no—
363C22⋊C8—1222no—
364C22⋊C8—1222no—
365C22⋊C8—1222no—
366#97—611no—
367#97—611no—
368#97—612no—
369#97—1224no—
370#97—1221no—
371#97—1221no—
372C4×C8—611no—
373C4×C8—611no—
374C4×C8—611no—
375C4×C8—1221no—
376C4×C8—1221no—
377C4×C8—1224no—
378C4×C8C2×#692311yescharacteristic
379#95—1221no—
380#95—1221no—
381#41—1222no—
382#41—1222no—
383#41—1222no—
384#41—1222no—
385C2×Q8—611no—
386C2×Q8C22×#692311yescharacteristic
387C2×D4—611no—
388C2×D4—1221no—
389C2×D4—1221no—
390C2×D4C22×#692311yescharacteristic
391C22×C4—21no—
392C22×C4—611no—
393C22×C4—611no—
394C22×C4—611no—
395C22×C4—1221no—
396C22×C4—1221no—
397C22×C4—1221no—
398C22×C4—1221no—
399C22×C4—1222no—
400C22×C4—1221no—
401Q16—1222no—
402SD16—22no—
403SD16—1222no—
404D8—1222no—
405M16—1222no—
406M16—1222no—
407M16—1222no—
408M16—1222no—
409C2×C8—611no—
410C2×C8—614no—
411C2×C8—612no—
412C2×C8—612no—
413C2×C8—611no—
414C2×C8—1222no—
415C2×C8—1222no—
416C2×C8—1222no—
417C2×C8—1222no—
418C2×C8—1222no—
419C2×C8C22×#692311yescharacteristic
420C2×C8C22×#692311yescharacteristic
421C4⋊C4—21no—
422C4⋊C4—611no—
423C4⋊C4—611no—
424C4⋊C4—1221no—
425C4⋊C4—1221no—
426C4⋊C4—1221no—
427C4⋊C4C22×#692311yescharacteristic
428C4⋊C4C22×#692311yescharacteristic
429C22⋊C4—21no—
430C22⋊C4—1221no—
431C22⋊C4—1221no—
432C22⋊C4—1221no—
433C22⋊C4—1221no—
434C22⋊C4—1221no—
435C42—21no—
436C42—611no—
437C42—611no—
438C42—611no—
439C42—614no—
440C42—1221no—
441C42—1221no—
442C42—1221no—
443C42—1221no—
444C42—1222no—
445C42—1221no—
446C42C22×#692311yescharacteristic
447C23—21no—
448C23—611no—
449C23—1221no—
450Q8—21no—
451Q8—21no—
452Q8—1221no—
453Q8—1221no—
454D4—21no—
455D4—21no—
456D4—1221no—
457D4—1221no—
458D4—2442no—
459D4—2442no—
460C2×C4—21no—
461C2×C4—21no—
462C2×C4—21no—
463C2×C4—81no—
464C2×C4—611no—
465C2×C4—612no—
466C2×C4—612no—
467C2×C4—611no—
468C2×C4—611no—
469C2×C4—1224no—
470C2×C4—1221no—
471C2×C4—1221no—
472C2×C4—1221no—
473C2×C4—4881no—
474C2×C4—4881no—
475C2×C4—4881no—
476C2×C4—2441no—
477C2×C4—2441no—
478C2×C4—2442no—
479C2×C4—2442no—
480C2×C4—2442no—
481C2×C4—2442no—
482C2×C4D4×#692311yescharacteristic
483C2×C4D4×#692311yescharacteristic
484C2×C4C23×#692311yescharacteristic
485C8—21no—
486C8—612no—
487C8—1222no—
488C8—1222no—
489C8—1221no—
490C8—2442no—
491C8—2442no—
492C8#1451985612yes—
493C22—41no—
494C22—41no—
495C22—41no—
496C22—612no—
497C22—1221no—
498C22—1221no—
499C22—2441no—
500C22—2441no—
501C22—2441no—
502C22C2×D4×#692311yescharacteristic
503C4—21no—
504C4—21no—
505C4—41no—
506C4—41no—
507C4—41no—
508C4—612no—
509C4—1221no—
510C4—1221no—
511C4—2444no—
512C4—2441no—
513C4—2441no—
514C4—2441no—
515C4C2×#1451985611yescharacteristic
516C4#41×#692311yescharacteristic
517C2—81no—
518C2—1222no—
519C2—4881no—
520C2#2146227611yescharacteristic
521C2#2146259711yescharacteristic
522C2#2146259811yescharacteristic
subgroupG/H
centerC22C2×D4×#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC4×SD16×C61C4
socleC22×C61C2×C4×D4
prime radicalC2×#14519798C22
cosocleC2×C4×D61C24
hypercenterC4×SD16#6923
hypocenterC61#21294
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ C4×SD16

Complements

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

NH ≅ G/Ntype
1. #21462507C2semidirect
2. #21462506C2semidirect
4. #21461926C2semidirect
5. #21461915C2semidirect
6. #21461914C2semidirect
7. C4×#14519847C2semidirect
8. #21461583C2semidirect
9. #21461582C2semidirect
10. #21461475C2semidirect
37. C4×#11758202C4semidirect
38. #16839854C4semidirect
39. C4×#11758190C4semidirect
40. SD16×Dic61C4semidirect
41. #16839849C4semidirect
42. C4×#11758199C4semidirect
43. #16839842C4semidirect
48. C4×SD16×C61C4semidirect
281. C4×SD16#6923semidirect
310. C61#21294semidirect

Maximal subgroups

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

subgroupindex
#214625072
#214625062
#214619712
#214619262
#214619152
#214619142
C4×#145198472
#214615832
#214615822
#214614752
C4×#145197982
#2129461