Finite Group Databasebeta

← #30616088

Subgroups — #30616088

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#21462504C211yesmaximal, characteristic, complemented
2C4×#14519865C211yesmaximal, characteristic, complemented
3#21461903C212yesmaximal, complemented
4#21461887C212yesmaximal, complemented
5#21461809C212yesmaximal
6#21461787C212yesmaximal, complemented
7C4×#14519848C211yesmaximal, characteristic, complemented
8C4×#14519842C211yesmaximal, characteristic, complemented
9C4×#14519842C211yesmaximal, characteristic, complemented
10#21461532C211yesmaximal, characteristic, complemented
11C4×#14519800C211yesmaximal, characteristic
12C2×#14519865C2212yes—
13#16840787—22no—
14#16840781—21no—
15#16840780—21no—
16C2×#14519848C2212yes—
17#16840769C2212yes—
18C2×#14519842C2212yes—
19C2×#14519842C2212yes—
20#16840737C2212yes—
21#16840727—22no—
22#16840727C2212yes—
23C4×#11758213—21no—
24C4×#11758213C2211yescharacteristic
25C4×#11758213C2211yescharacteristic
26C4×D61⋊C8—21no—
27C4×D61⋊C8C2211yescharacteristic
28C42×#6923C2211yescharacteristic
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×#6923—21no—
57C2×C4×#6923—21no—
58C2×C4×#6923C2312yes—
59#14519848—24no—
60#14519844—22no—
61C4⋊#92420—22no—
62#14519842—24no—
63#14519842—24no—
64#14519834—22no—
65#14519834—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×#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—24no—
144C4×#6923—22no—
145C4×#6923—22no—
146C4×#6923—42no—
147#11758213—28no—
148#11758213—22no—
149#11758213—22no—
150#11758213—22no—
151#11758213#4114yes—
152D61⋊C8—28no—
153D61⋊C8—22no—
154D61⋊C8—22no—
155Q16×C61—22no—
156C2×C8×C61C22×C411yescharacteristic
157C2×C8×C61C22×C411yescharacteristic
158C4⋊C4×C61—21no—
159C4⋊C4×C61—21no—
160C4⋊C4×C61C22×C411yescharacteristic
161C4⋊C4×C61C22×C411yescharacteristic
162C42×C61—21no—
163C42×C61—21no—
164C42×C61C22×C411yescharacteristic
165#11758201—22no—
166#11758201—22no—
167#11758198—21no—
168#11758198—21no—
169#11758198—21no—
170#11758198—21no—
171#11758198—21no—
172#11758198—21no—
173C4⋊Dic61—21no—
174C4⋊Dic61—21no—
175C4⋊Dic61C22×C411yescharacteristic
176C4⋊Dic61C22×C411yescharacteristic
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
186D488—22no—
187C8×D61—22no—
188C8×D61—22no—
189C22×D61—21no—
190C22×D61—21no—
191C22×D61C2×#4111yescharacteristic
192C2×#6923—24no—
193C2×#6923—42no—
194C2×#6923—42no—
195Q8×C61—21no—
196Q8×C61—21no—
197Q8×C61—21no—
198Q8×C61#11712yes—
199C2×C4×C61—21no—
200C2×C4×C61—21no—
201C2×C4×C61—21no—
202C2×C4×C61—21no—
203C2×C4×C61C4×D411yescharacteristic
204C2×C4×C61C4×D411yescharacteristic
205C2×C4×C61C23×C411yescharacteristic
206C2×Dic61—21no—
207C2×Dic61—21no—
208C2×Dic61C4×D411yescharacteristic
209C2×Dic61C4×D411yescharacteristic
210C2×Dic61C22×D411yescharacteristic
211D244—24no—
212D244—21no—
213D244—21no—
214D244—21no—
215D244—42no—
216D244#11712yes—
217C4×D61—22no—
218C4×D61—24no—
219C4×D61—22no—
220C4×D61—42no—
221C4×D61—42no—
222C4×D61—42no—
223C4×D61—42no—
224C4×D61—42no—
225C4×D61C2×#4112yes—
226C4×D61C2×#4112yes—
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×C61C2×C4×D411yescharacteristic
237C2×D61—21no—
238C2×D61—21no—
239C2×D61—22no—
240C2×D61—41no—
241C2×D61—41no—
242C2×D61—41no—
243C2×D61—41no—
244C2×D61—41no—
245C2×D61#52912yes—
246#6923—44no—
247C4×C61—21no—
248C4×C61—22no—
249C4×C61—41no—
250C4×C61—41no—
251C4×C61—41no—
252C4×C61#44312yes—
253C4×C61C2×#11711yescharacteristic
254C4×C61C4×#4111yescharacteristic
255Dic61—21no—
256Dic61—41no—
257Dic61—41no—
258Dic61#44412yes—
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#229011yescharacteristic
272C2×C61C2×#44311yescharacteristic
273C2×C61C2×#44411yescharacteristic
274D61—22no—
275D61—42no—
276D61—81no—
277C2×#135—611no—
278C2×#131—612no—
279C4×#41—611no—
280C4×#41—611no—
281C4×Q16—611no—
282C4×Q16#692311yescharacteristic, complemented
283C4×SD16—611no—
284C4×SD16—611no—
285C4×SD16—611no—
286C4×SD16—611no—
287C4×D8—611no—
288C4×D8—611no—
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×Q16C2×#692311yescharacteristic
319C2×SD16—611no—
320C2×SD16—611no—
321C2×D8—611no—
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×Q8C2×#692311yescharacteristic
334C4×Q8C2×#692311yescharacteristic
335C4×D4—611no—
336C4×D4—611no—
337C4×D4—611no—
338C4×D4—611no—
339C4×D4—1221no—
340C4×D4—1221no—
341C4×D4—1221no—
342C4×D4—1221no—
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#103C2×#692311yescharacteristic
365#103C2×#692311yescharacteristic
366#102—611no—
367#102—611no—
368#102—611no—
369#102—611no—
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×Q8C22×#692311yescharacteristic
390C2×Q8C22×#692311yescharacteristic
391C2×D4—611no—
392C2×D4—611no—
393C2×D4—1221no—
394C2×D4—1221no—
395C22×C4—611no—
396C22×C4—611no—
397C22×C4—611no—
398C22×C4—1221no—
399C22×C4—1221no—
400C22×C4—1221no—
401C22×C4—1221no—
402C22×C4—1222no—
403C22×C4—1221no—
404C22×C4—1221no—
405Q16—22no—
406SD16—1222no—
407SD16—1222no—
408D8—1222no—
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—21no—
428C4⋊C4—21no—
429C4⋊C4—611no—
430C4⋊C4—611no—
431C4⋊C4—1221no—
432C4⋊C4—1221no—
433C4⋊C4C22×#692311yescharacteristic
434C4⋊C4C22×#692311yescharacteristic
435C22⋊C4—1221no—
436C22⋊C4—1221no—
437C22⋊C4—1221no—
438C22⋊C4—1221no—
439C22⋊C4—1221no—
440C22⋊C4—1221no—
441C42—21no—
442C42—21no—
443C42—611no—
444C42—611no—
445C42—611no—
446C42—1221no—
447C42—1221no—
448C42—1221no—
449C42—1221no—
450C42—1222no—
451C42—1222no—
452C42—1224no—
453C42—2442no—
454C42C22×#692311yescharacteristic
455C23—611no—
456C23—1221no—
457C23—1221no—
458Q8—21no—
459Q8—21no—
460Q8—21no—
461Q8#1451985612yes—
462D4—612no—
463D4—1224no—
464D4—1221no—
465D4—1221no—
466D4—1221no—
467D4—2442no—
468C2×C4—21no—
469C2×C4—21no—
470C2×C4—21no—
471C2×C4—21no—
472C2×C4—611no—
473C2×C4—611no—
474C2×C4—612no—
475C2×C4—612no—
476C2×C4—611no—
477C2×C4—1222no—
478C2×C4—1224no—
479C2×C4—1222no—
480C2×C4—1224no—
481C2×C4—1221no—
482C2×C4—1221no—
483C2×C4—2442no—
484C2×C4—2442no—
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—612no—
502C22—1221no—
503C22—1221no—
504C22—1222no—
505C22—2441no—
506C22—2441no—
507C22—2441no—
508C22—2441no—
509C22—2441no—
510C22C2×D4×#692311yescharacteristic
511C4—22no—
512C4—21no—
513C4—41no—
514C4—41no—
515C4—41no—
516C4—612no—
517C4—612no—
518C4—1221no—
519C4—2444no—
520C4—2441no—
521C4—2441no—
522C4#1684080612yes—
523C4C2×#1451985611yescharacteristic
524C4#41×#692311yescharacteristic
525C2—1222no—
526C2—4881no—
527C2—2442no—
528C2#2146227311yescharacteristic
529C2C2×#1684080611yescharacteristic
530C2D61⋊#44411yescharacteristic
subgroupG/H
centerC2×C4D4×#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#21137
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C42 ◁ C4×Q16

Complements

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

NH ≅ G/Ntype
1. #21462504C2semidirect
2. C4×#14519865C2semidirect
3. #21461903C2semidirect
4. #21461887C2semidirect
6. #21461787C2semidirect
7. C4×#14519848C2semidirect
8. C4×#14519842C2semidirect
9. C4×#14519842C2semidirect
10. #21461532C2semidirect
37. Q16×Dic61C4semidirect
38. C4×#11758201C4semidirect
39. C4×#11758201C4semidirect
40. #16839847C4semidirect
41. #16839847C4semidirect
42. C4×D488C4semidirect
43. #16839844C4semidirect
48. C4×Q16×C61C4semidirect
282. C4×Q16#6923semidirect
314. C61#21137semidirect

Maximal subgroups

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

subgroupindex
#214625042
C4×#145198652
#214619032
#214618872
#214618092
#214617872
C4×#145198482
C4×#145198422
#214615322
C4×#145198002
#2113761