Finite Group Databasebeta

← #30616087

Subgroups — #30616087

Order 15616.

800 conjugacy classes of subgroups.

The subgroup lattice has 532 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21462503C211yesmaximal, characteristic, complemented
2C4×#14519864C211yesmaximal, characteristic, complemented
3#21461901C212yesmaximal, complemented
4#21461887C212yesmaximal, complemented
5#21461810C212yesmaximal
6#21461788C212yesmaximal, complemented
7C4×#14519847C211yesmaximal, characteristic, complemented
8C4×#14519841C211yesmaximal, characteristic, complemented
9C4×#14519841C211yesmaximal, characteristic, complemented
10#21461532C211yesmaximal, characteristic, complemented
11C4×#14519796C211yesmaximal, characteristic
12C2×#14519864C2212yes—
13#16840786—22no—
14#16840779—21no—
15#16840778—21no—
16C2×#14519847C2212yes—
17#16840769C2212yes—
18C2×#14519841C2212yes—
19C2×#14519841C2212yes—
20#16840736C2212yes—
21#16840727C2212yes—
22#16840726—22no—
23C4×#11758213C2211yescharacteristic
24C4×#11758213C2211yescharacteristic
25C4×#11758217—21no—
26C4×D61⋊C8C2211yescharacteristic
27C2×C4×#92420—21no—
28C42×#6923C2211yescharacteristic
29#16840638C2212yes—
30#16840632C2212yes—
31#16840632C2212yes—
32(C2×#6923)⋊C8C2212yes—
33(C2×#6923)⋊C8C2212yes—
34C2×#14519796C2211yescharacteristic
35C4×#11758224C2211yescharacteristic
36C4×#11758224C2211yescharacteristic
37C4×Dic244C411yescharacteristic, complemented
38#16839856C411yescharacteristic, complemented
39#16839853C411yescharacteristic, complemented
40#16839853C411yescharacteristic, complemented
41C4×#11758200C411yescharacteristic, complemented
42C4×#11758200C411yescharacteristic, complemented
43D8×Dic61C411yescharacteristic, complemented
44#16839799C2211yescharacteristic
45#16839755C2211yescharacteristic
46#16839755C2211yescharacteristic
47C4×C8×D61C2211yescharacteristic
48C4×D8×C61C411yescharacteristic, complemented
49#14519864—24no—
50#14519864—24no—
51C2×#11758213C2312yes—
52C2×#11758213C2312yes—
53C2×#11758217—22no—
54C2×D61⋊C8C2312yes—
55C22×#92420—22no—
56C2×C4×#6923—21no—
57C2×C4×#6923—21no—
58C2×C4×#6923C2312yes—
59#14519847—24no—
60#14519844—22no—
61C4⋊#92420—22no—
62#14519841—24no—
63#14519841—24no—
64C22⋊#92420—22no—
65C22⋊#92420—22no—
66#14519832—22no—
67#14519832—21no—
68#14519832—21no—
69C4×#92420—22no—
70C4×#92420—21no—
71C4×#92420—21no—
72C4×#92420D411yescharacteristic
73C4×#92420D411yescharacteristic
74C4×#92420D412yes—
75C2×#11758224C2311yescharacteristic
76C2×#11758224C2311yescharacteristic
77#14519796—24no—
78C2×Dic244C2×C411yescharacteristic
79C2×#11758200C2×C411yescharacteristic
80C2×#11758200C2×C411yescharacteristic
81C2×C8×D61C2311yescharacteristic
82C2×C8×D61C2311yescharacteristic
83C4×Dic122C2×C411yescharacteristic
84C4×Dic122C2×C411yescharacteristic
85#14519742C2×C411yescharacteristic
86#14519742C2×C411yescharacteristic
87D4×Dic61C2×C411yescharacteristic
88D4×Dic61C2×C411yescharacteristic
89C4×C22⋊D61—21no—
90C4×C22⋊D61—21no—
91#14519737—21no—
92#14519737—21no—
93#14519735C2311yescharacteristic
94#14519735C2311yescharacteristic
95#14519733—21no—
96#14519733—21no—
97C2×C4×Dic61—21no—
98C2×C4×Dic61—21no—
99C42×D61C2311yescharacteristic
100#14519711C2×C411yescharacteristic
101#14519708C2×C411yescharacteristic
102#14519708C2×C411yescharacteristic
103#14519702C2×C411yescharacteristic
104#14519702C2×C411yescharacteristic
105#14519700C2×C411yescharacteristic
106#14519700C2×C411yescharacteristic
107#14519698C2×C411yescharacteristic
108#14519698C2×C411yescharacteristic
109C4×#92418C2×C411yescharacteristic
110C8×Dic61C2×C411yescharacteristic
111C8×Dic61C2×C411yescharacteristic
112C2×D8×C61C2×C411yescharacteristic
113C4×D4×C61C2×C411yescharacteristic
114C4×D4×C61C2×C411yescharacteristic
115#107×C61C2×C411yescharacteristic
116#102×C61C2×C411yescharacteristic
117#102×C61C2×C411yescharacteristic
118C4×C8×C61C2×C411yescharacteristic
119C22×#6923—22no—
120C2×D4×C61C22×C411yescharacteristic
121C2×D4×C61C22×C411yescharacteristic
122C22×C4×C61—21no—
123C22×C4×C61—21no—
124C2×C22⋊D61—21no—
125C2×C22⋊D61—21no—
126C22×Dic61—21no—
127C22×Dic61—21no—
128C22×Dic61—21no—
129C22×Dic61—21no—
130#11758224—22no—
131#11758224—22no—
132#11758224—22no—
133#11758224#4114yes—
134C2×C4×D61#4111yescharacteristic
135C2×C4×D61#4111yescharacteristic
136C2×C4×D61C2411yescharacteristic
137C2×Dic122C22×C411yescharacteristic
138C2×Dic122C22×C411yescharacteristic
139#11758217—28no—
140C2×#92420—28no—
141C2×#92420—22no—
142C2×#92420—22no—
143C2×#92420C2×D412yes—
144C2×#92420C2×D412yes—
145C4×#6923—24no—
146C4×#6923—22no—
147C4×#6923—22no—
148C4×#6923—42no—
149#11758213—22no—
150#11758213—22no—
151#11758213—22no—
152#11758213#4114yes—
153D61⋊C8—22no—
154D61⋊C8—22no—
155D8×C61—22no—
156C2×C8×C61C22×C411yescharacteristic
157C2×C8×C61C22×C411yescharacteristic
158C4⋊C4×C61C22×C411yescharacteristic
159C4⋊C4×C61C22×C411yescharacteristic
160C22⋊C4×C61—21no—
161C22⋊C4×C61—21no—
162C42×C61C22×C411yescharacteristic
163C22⋊Dic61—21no—
164C22⋊Dic61—21no—
165#11758200—22no—
166#11758200—22no—
167#11758198—21no—
168#11758198—21no—
169C4⋊Dic61C22×C411yescharacteristic
170C4⋊Dic61C22×C411yescharacteristic
171#11758196—21no—
172#11758196—21no—
173#11758196—21no—
174#11758196—21no—
175C4×Dic61—21no—
176C4×Dic61—21no—
177C4×Dic61—21no—
178C4×Dic61—21no—
179C4×Dic61—21no—
180C4×Dic61—21no—
181C4×Dic61C22×C411yescharacteristic
182C4×Dic61C2×D411yescharacteristic
183C4×Dic61C2×D411yescharacteristic
184C2×#92418C22×C411yescharacteristic
185C2×#92418C22×C411yescharacteristic
186Dic244—22no—
187C8×D61—22no—
188C8×D61—22no—
189C23×C61—21no—
190C23×C61—21no—
191C22×D61C2×#4111yescharacteristic
192C2×#6923—24no—
193C2×#6923—42no—
194C2×#6923—42no—
195D4×C61—21no—
196D4×C61—21no—
197D4×C61—21no—
198D4×C61#11712yes—
199C2×C4×C61—21no—
200C2×C4×C61—21no—
201C2×C4×C61—42no—
202C2×C4×C61—42no—
203C2×C4×C61C4×D411yescharacteristic
204C2×C4×C61C4×D411yescharacteristic
205C2×C4×C61C23×C411yescharacteristic
206C22⋊D61—24no—
207C22⋊D61—42no—
208C2×Dic61—21no—
209C2×Dic61—24no—
210C2×Dic61—21no—
211C2×Dic61—21no—
212C2×Dic61—21no—
213C2×Dic61—42no—
214C2×Dic61—42no—
215C2×Dic61—42no—
216C2×Dic61C4×D411yescharacteristic
217C2×Dic61C4×D411yescharacteristic
218C2×Dic61C22×D411yescharacteristic
219C4×D61—22no—
220C4×D61—22no—
221C4×D61C2×#4112yes—
222C4×D61C2×#4112yes—
223Dic122—21no—
224Dic122—21no—
225Dic122—21no—
226Dic122#11712yes—
227#92420—22no—
228#92420—22no—
229#92420—24no—
230#92420—42no—
231C8×C61—21no—
232C8×C61—21no—
233#92418—21no—
234#92418—21no—
235#21137—611nomaximal, Sylow
236C22×C61—22no—
237C22×C61—41no—
238C22×C61—41no—
239C22×C61—41no—
240C22×C61—41no—
241C22×C61—41no—
242C22×C61C2×C4×D411yescharacteristic
243C2×D61—21no—
244C2×D61—21no—
245C2×D61#52912yes—
246#6923—44no—
247C4×C61—21no—
248C4×C61—41no—
249C4×C61—41no—
250C4×C61#44412yes—
251C4×C61C2×#11711yescharacteristic
252C4×C61C4×#4111yescharacteristic
253Dic61—21no—
254Dic61—22no—
255Dic61—41no—
256Dic61—41no—
257Dic61—41no—
258Dic61#44312yes—
259Dic61#52512yes—
260C4×#135—611no—
261#2922—611no—
262C4×#131—611no—
263#1929—612no—
264#1922—612no—
265#1876—612no—
266#1866—612no—
267C4×#108—611no—
268C4×#104—611no—
269C4×#104—611no—
270#1744—611no—
271C2×C61—42no—
272C2×C61—81no—
273C2×C61#229011yescharacteristic
274C2×C61C2×#44311yescharacteristic
275C2×C61C2×#44411yescharacteristic
276D61—22no—
277C2×#135—611no—
278C2×#131—612no—
279C4×#41—611no—
280C4×#41—611no—
281C4×Q16—611no—
282C4×Q16—611no—
283C4×SD16—611no—
284C4×SD16—611no—
285C4×SD16—611no—
286C4×SD16—611no—
287C4×D8—611no—
288C4×D8#692311yescharacteristic, complemented
289#433—1222no—
290#431—1221no—
291#431—1221no—
292C2×#108—612no—
293#427—611no—
294#424—612no—
295C2×#104—612no—
296C2×#104—612no—
297#416—611no—
298#416—611no—
299#408—612no—
300#405—612no—
301#405—1222no—
302C4×M16—611no—
303C4×M16—611no—
304C4×M16—1221no—
305C2×C4×C8—611no—
306C2×C4×C8—611no—
307C2×C4×C8—1221no—
308C43—611no—
309#341—612no—
310#339—612no—
311#339—612no—
312#336—612no—
313#336—612no—
314C61#2113711yescharacteristic, complemented, Sylow
315C2×#41—611no—
316C2×#41—611no—
317#135—1224no—
318C2×Q16—611no—
319C2×SD16—611no—
320C2×SD16—611no—
321C2×D8C2×#692311yescharacteristic
322#131—1224no—
323#131—1224no—
324C2×M16—612no—
325C2×M16—612no—
326C2×M16—1222no—
327C22×C8—612no—
328C22×C8—611no—
329C22×C8—611no—
330C22×C8—1222no—
331C4×Q8—611no—
332C4×Q8—611no—
333C4×Q8—611no—
334C4×Q8—611no—
335C4×D4—611no—
336C4×D4—611no—
337C4×D4—1221no—
338C4×D4—1221no—
339C4×D4—1221no—
340C4×D4—1221no—
341C4×D4C2×#692311yescharacteristic
342C4×D4C2×#692311yescharacteristic
343#117—611no—
344#117—611no—
345#117—1221no—
346#117—1221no—
347C2×C42—611no—
348C2×C42—612no—
349C2×C42—1221no—
350C2×C42—1221no—
351C2×C42—1221no—
352C2×C42—1221no—
353#108—1224no—
354#107—611no—
355#107C2×#692311yescharacteristic
356#106—611no—
357#106—611no—
358C4⋊C8—1222no—
359C4⋊C8—1222no—
360#104—1224no—
361#104—1224no—
362#103—611no—
363#103—611no—
364#103—611no—
365#103—611no—
366#102—611no—
367#102—611no—
368#102C2×#692311yescharacteristic
369#102C2×#692311yescharacteristic
370C22⋊C8—1222no—
371C22⋊C8—1222no—
372#97—1221no—
373#97—1221no—
374#97—1222no—
375C4×C8—611no—
376C4×C8—611no—
377C4×C8—612no—
378C4×C8—611no—
379C4×C8—611no—
380C4×C8—611no—
381C4×C8—1221no—
382C4×C8—1221no—
383C4×C8—1222no—
384C4×C8C2×#692311yescharacteristic
385#41—614no—
386#41—1222no—
387#41—1222no—
388#41—1222no—
389C2×Q8—611no—
390C2×Q8—611no—
391C2×D4—1221no—
392C2×D4—1221no—
393C2×D4C22×#692311yescharacteristic
394C2×D4C22×#692311yescharacteristic
395C22×C4—21no—
396C22×C4—21no—
397C22×C4—611no—
398C22×C4—611no—
399C22×C4—611no—
400C22×C4—1221no—
401C22×C4—1221no—
402C22×C4—1221no—
403C22×C4—1221no—
404C22×C4—1222no—
405Q16—1222no—
406SD16—1222no—
407SD16—1222no—
408D8—22no—
409M16—614no—
410M16—1222no—
411M16—1228no—
412M16—1222no—
413M16—1222no—
414C2×C8—612no—
415C2×C8—612no—
416C2×C8—611no—
417C2×C8—611no—
418C2×C8—1222no—
419C2×C8—1222no—
420C2×C8—1222no—
421C2×C8—1222no—
422C2×C8—1222no—
423C2×C8—1228no—
424C2×C8—1222no—
425C2×C8C22×#692311yescharacteristic
426C2×C8C22×#692311yescharacteristic
427C4⋊C4—611no—
428C4⋊C4—611no—
429C4⋊C4—1221no—
430C4⋊C4—1221no—
431C4⋊C4—1221no—
432C4⋊C4—1221no—
433C4⋊C4C22×#692311yescharacteristic
434C4⋊C4C22×#692311yescharacteristic
435C22⋊C4—21no—
436C22⋊C4—21no—
437C22⋊C4—1221no—
438C22⋊C4—1221no—
439C22⋊C4—1221no—
440C22⋊C4—1221no—
441C42—611no—
442C42—611no—
443C42—611no—
444C42—1221no—
445C42—1221no—
446C42—1221no—
447C42—1221no—
448C42—1222no—
449C42—1222no—
450C42—1224no—
451C42—1221no—
452C42—1221no—
453C42—2442no—
454C42C22×#692311yescharacteristic
455C23—21no—
456C23—21no—
457C23—611no—
458Q8—612no—
459Q8—1221no—
460Q8—1221no—
461Q8—1221no—
462D4—21no—
463D4—21no—
464D4—21no—
465D4—1224no—
466D4—2442no—
467D4#1451985612yes—
468C2×C4—21no—
469C2×C4—21no—
470C2×C4—42no—
471C2×C4—42no—
472C2×C4—611no—
473C2×C4—611no—
474C2×C4—612no—
475C2×C4—612no—
476C2×C4—611no—
477C2×C4—1222no—
478C2×C4—1224no—
479C2×C4—1221no—
480C2×C4—1222no—
481C2×C4—1224no—
482C2×C4—1221no—
483C2×C4—1221no—
484C2×C4—1221no—
485C2×C4—2442no—
486C2×C4—2442no—
487C2×C4—2442no—
488C2×C4—2442no—
489C2×C4—2442no—
490C2×C4D4×#692311yescharacteristic
491C2×C4D4×#692311yescharacteristic
492C2×C4C23×#692311yescharacteristic
493C8—21no—
494C8—21no—
495C8—1222no—
496C8—1222no—
497C8—1224no—
498C8—1221no—
499C8—1221no—
500C8—2442no—
501C22—22no—
502C22—41no—
503C22—41no—
504C22—41no—
505C22—41no—
506C22—41no—
507C22—612no—
508C22—1221no—
509C22—1221no—
510C22C2×D4×#692311yescharacteristic
511C4—21no—
512C4—41no—
513C4—41no—
514C4—612no—
515C4—612no—
516C4—1222no—
517C4—1221no—
518C4—2444no—
519C4—2441no—
520C4—2441no—
521C4—2441no—
522C4#1684080912yes—
523C4C2×#1451985611yescharacteristic
524C4#41×#692311yescharacteristic
525C2—42no—
526C2—81no—
527C2—1222no—
528C2#2146227311yescharacteristic
529C2D61⋊#44311yescharacteristic
530C2C2×#1684080911yescharacteristic
subgroupG/H
centerC2×C4D4×#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC4×D8×C61C4
socleC22×C61C2×C4×D4
prime radicalC2×#14519796C22
cosocleC2×C4×D61C24
hypercenterC4×D8#6923
hypocenterC61#21137
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C42 ◁ C4×D8

Complements

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

NH ≅ G/Ntype
1. #21462503C2semidirect
2. C4×#14519864C2semidirect
3. #21461901C2semidirect
4. #21461887C2semidirect
6. #21461788C2semidirect
7. C4×#14519847C2semidirect
8. C4×#14519841C2semidirect
9. C4×#14519841C2semidirect
10. #21461532C2semidirect
37. C4×Dic244C4semidirect
38. #16839856C4semidirect
39. #16839853C4semidirect
40. #16839853C4semidirect
41. C4×#11758200C4semidirect
42. C4×#11758200C4semidirect
43. D8×Dic61C4semidirect
48. C4×D8×C61C4semidirect
288. C4×D8#6923semidirect
314. C61#21137semidirect

Maximal subgroups

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

subgroupindex
#214625032
C4×#145198642
#214619012
#214618872
#214618102
#214617882
C4×#145198472
C4×#145198412
#214615322
C4×#145197962
#2113761