Finite Group Databasebeta

← #30613417

Subgroups — #30613417

Order 15616.

656 conjugacy classes of subgroups.

The subgroup lattice has 498 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21462660C211yesmaximal, characteristic, complemented
2#21462656C211yesmaximal, characteristic, complemented
3#21461457C212yesmaximal, complemented
4#21461425C212yesmaximal, complemented
5#21461422C212yesmaximal, complemented
6#21461399C212yesmaximal, complemented
7#21461379C211yesmaximal, characteristic, complemented
8#21461152C211yesmaximal, characteristic, complemented
9#21461150C211yesmaximal, characteristic, complemented
10C8×#11758217C211yesmaximal, characteristic, complemented
11#21454587C211yesmaximal, characteristic
12#16840813C2212yes—
13#16840812C2212yes—
14#16840794—22no—
15#16840793—22no—
16#16840790C2212yes—
17D4×#92420C2212yes—
18#16840784—21no—
19#16840783C2211yescharacteristic
20#16840783C2211yescharacteristic
21#16840782—21no—
22#16840779C2211yescharacteristic
23C4×#11758217C2211yescharacteristic
24#16840721—21no—
25C2×#14519832—21no—
26#16840626C2212yes—
27#16840623C2212yes—
28#16840612C2212yes—
29Q8⋊#92420C2212yes—
30#16840610C2212yes—
31D4⋊#92420C2212yes—
32#92420⋊C8C2212yes—
33C8×#92420C2212yes—
34C2×#14519797C411yescharacteristic
35#41×Dic61C2211yescharacteristic
36#16840230C2211yescharacteristic
37#16839854C411yescharacteristic
38#16839854C2211yescharacteristic
39#16839853C411yescharacteristic
40#16839853C2211yescharacteristic
41#16839847C411yescharacteristic
42#16839847C2211yescharacteristic
43#16839842C411yescharacteristic
44#16839842C2211yescharacteristic
45#16839798C411yescharacteristic
46#16839759C411yescharacteristic
47C2×C8×Dic61C2211yescharacteristic
48C61×#416C411yescharacteristic
49C2×#11758217D412yes—
50C2×D61⋊C8—22no—
51C22×#92420—22no—
52#14519844—22no—
53#14519844—21no—
54C4⋊#92420—22no—
55C4⋊#92420C2312yes—
56C4⋊#92420C2312yes—
57#14519834—22no—
58C22⋊#92420—21no—
59C22⋊#92420—21no—
60C22⋊#92420—21no—
61C22⋊#92420—22no—
62#14519832—22no—
63#14519832—22no—
64#14519832—21no—
65#14519832—21no—
66#14519832D411yescharacteristic
67#14519832D411yescharacteristic
68C4×#92420C2312yes—
69C4×#92420C2312yes—
70C2×#11758222C2×C411yescharacteristic
71#14519797—24no—
72C2×#11758202C2×C411yescharacteristic
73C2×#11758200C2×C411yescharacteristic
74C2×#11758201C2×C411yescharacteristic
75C2×#11758199C2×C411yescharacteristic
76C22×#92418C2×C411yescharacteristic
77Q8×Dic61C2×C411yescharacteristic
78Q8×Dic61C2311yescharacteristic
79#14519742C2×C411yescharacteristic
80#14519742C2311yescharacteristic
81D4×Dic61—21no—
82D4×Dic61—21no—
83D4×Dic61C2×C411yescharacteristic
84D4×Dic61C2311yescharacteristic
85#14519739C2×C411yescharacteristic
86#14519739C2311yescharacteristic
87#14519737—21no—
88#14519737—21no—
89#14519736—21no—
90#14519736C2×C411yescharacteristic
91#14519734—21no—
92C2×C4×Dic61—21no—
93C2×C4×Dic61C2311yescharacteristic
94C42×D61—21no—
95#14519710C2×C411yescharacteristic
96#14519710C2×C411yescharacteristic
97#14519708C2×C411yescharacteristic
98#14519708C2×C411yescharacteristic
99#14519702C2×C411yescharacteristic
100#14519702C2×C411yescharacteristic
101#14519699C2×C411yescharacteristic
102#14519699C2×C411yescharacteristic
103C8×Dic61C2×C411yescharacteristic
104C8×Dic61C2×C411yescharacteristic
105C8×Dic61C2311yescharacteristic
106C8×Dic61C2311yescharacteristic
107C2×#41×C61C2×C411yescharacteristic
108C22×C8×C61C2×C411yescharacteristic
109#117×C61C2×C411yescharacteristic
110#103×C61C2×C411yescharacteristic
111#103×C61C2×C411yescharacteristic
112#102×C61C2×C411yescharacteristic
113#102×C61C2×C411yescharacteristic
114#41×C61—22no—
115#41×C61—41no—
116C2×Q8×C61C22×C411yescharacteristic
117C2×D4×C61—21no—
118C2×D4×C61C22×C411yescharacteristic
119C22×C4×C61—21no—
120C22×C4×C61C22×C411yescharacteristic
121C2×C22⋊D61—21no—
122C22×Dic61—21no—
123C22×Dic61—21no—
124C22×Dic61C2×D411yescharacteristic
125C22×Dic61#4111yescharacteristic
126#11758222—22no—
127#11758222—41no—
128C2×D244C22×C411yescharacteristic
129C2×C4×D61—21no—
130C2×C4×D61—21no—
131C2×C4×D61—21no—
132C2×Dic122C22×C411yescharacteristic
133#11758217—24no—
134C2×#92420—22no—
135C2×#92420—22no—
136C2×#92420—22no—
137C2×#92420—44no—
138C2×#92420C2×D412yes—
139C2×#92420C2×D412yes—
140D61⋊C8—44no—
141C2×C8×C61—41no—
142C2×C8×C61C22×C411yescharacteristic
143C2×C8×C61C22×C411yescharacteristic
144C4⋊C4×C61C22×C411yescharacteristic
145C4⋊C4×C61C22×C411yescharacteristic
146C22⋊C4×C61—21no—
147C42×C61—21no—
148C22⋊Dic61—21no—
149C22⋊Dic61—21no—
150C22⋊Dic61—21no—
151#11758202—22no—
152#11758201—22no—
153#11758200—22no—
154#11758199M1614yescomplemented
155#11758198—21no—
156#11758198—21no—
157C4⋊Dic61—21no—
158C4⋊Dic61—21no—
159C4⋊Dic61C22×C411yescharacteristic
160C4⋊Dic61C22×C411yescharacteristic
161#11758196—21no—
162#11758196—21no—
163C4×Dic61—21no—
164C4×Dic61—21no—
165C4×Dic61—21no—
166C4×Dic61—21no—
167C4×Dic61—21no—
168C4×Dic61C22×C411yescharacteristic
169C4×Dic61C2×D411yescharacteristic
170C4×Dic61#4111yescharacteristic
171C4×Dic61C2411yescharacteristic
172C2×#92418—22no—
173C2×#92418C22×C411yescharacteristic
174C2×#92418C22×C411yescharacteristic
175C23×C61—21no—
176C23×C61C4×D411yescharacteristic
177C22×D61—21no—
178Q8×C61—21no—
179Q8×C61—21no—
180D4×C61—21no—
181D4×C61—42no—
182D4×C61C2×M1612yes—
183C2×C4×C61—21no—
184C2×C4×C61—21no—
185C2×C4×C61—21no—
186C2×C4×C61—21no—
187C2×C4×C61—21no—
188C2×C4×C61—42no—
189C2×C4×C61C4×D411yescharacteristic
190C2×C4×C61C23×C411yescharacteristic
191C22⋊D61—42no—
192C2×Dic61—22no—
193C2×Dic61—21no—
194C2×Dic61—21no—
195C2×Dic61—21no—
196C2×Dic61—41no—
197C2×Dic61—42no—
198C2×Dic61—81no—
199C2×Dic61C4×D411yescharacteristic
200C2×Dic61C4×D411yescharacteristic
201C2×Dic61C22×D411yescharacteristic
202C2×Dic61C2×#4111yescharacteristic
203D244—21no—
204D244C2×M1612yes—
205C4×D61—42no—
206C4×D61—42no—
207C4×D61—81no—
208Dic122—21no—
209Dic122—21no—
210#92420—22no—
211#92420—42no—
212#92420—42no—
213#92420—42no—
214#92420#13514yescomplemented
215C8×C61—21no—
216C8×C61—21no—
217#92418—21no—
218#92418C2×M1612yes—
219#18035—611nomaximal, Sylow
220C22×C61—21no—
221C22×C61—22no—
222C22×C61—21no—
223C22×C61—21no—
224C22×C61—41no—
225C22×C61—41no—
226C22×C61C2×C4×D411yescharacteristic
227C2×D61—22no—
228C2×D61—41no—
229C2×D61—41no—
230C4×C61—21no—
231C4×C61—41no—
232C4×C61—41no—
233C4×C61—41no—
234C4×C61C22×M1611yescharacteristic
235C4×C61#56811yescharacteristic
236Dic61—21no—
237Dic61—21no—
238Dic61—21no—
239Dic61—41no—
240Dic61—41no—
241Dic61—41no—
242Dic61C2×#13512yes—
243#2970—611no—
244#2970—611no—
245C4×#135—611no—
246#1591—612no—
247#1582—612no—
248#1582—612no—
249C8×D8—612no—
250#1568—611no—
251#1488—611no—
252#1488—611no—
253C8×M16—611no—
254C2×C61—41no—
255C2×C61—42no—
256C2×C61D4×M1611yescharacteristic
257C2×C61C4×#13511yescharacteristic
258C2×C61#295711yescharacteristic
259D61—42no—
260C2×#135—611no—
261C4×#41—611no—
262C4×#41—611no—
263#446—612no—
264#446—612no—
265C4×Q16—611no—
266C4×Q16—611no—
267C4×SD16—611no—
268C4×SD16—611no—
269C4×SD16—611no—
270C4×SD16—611no—
271C4×D8—611no—
272C4×D8—611no—
273#435—1222no—
274#435—1222no—
275C8×D4—612no—
276C8×D4—612no—
277#432—611no—
278#432—611no—
279#432—1221no—
280#432—1221no—
281#431—611no—
282#427—611no—
283#416—611no—
284#416#692311yescharacteristic
285C4×M16—611no—
286C2×#97—1221no—
287C2×#97—1221no—
288C2×C4×C8—611no—
289#335—612no—
290#334—612no—
291Q8⋊C8—612no—
292Q8⋊C8—612no—
293D4⋊C8—612no—
294D4⋊C8—612no—
295#322—612no—
296C82—612no—
297C61#1803511yescharacteristic, complemented, Sylow
298C2×#41—611no—
299C2×#41C2×#692311yescharacteristic
300#135—1224no—
301C2×Q16—611no—
302C2×SD16—611no—
303C2×SD16—611no—
304C2×D8—611no—
305C2×M16—612no—
306C22×C8—611no—
307C22×C8—1222no—
308C22×C8—1222no—
309C22×C8C2×#692311yescharacteristic
310C4×Q8—611no—
311C4×Q8—611no—
312C4×Q8—611no—
313C4×Q8—611no—
314C4×D4—611no—
315C4×D4—611no—
316C4×D4—611no—
317C4×D4—611no—
318C4×D4—1221no—
319C4×D4—1221no—
320C4×D4—1221no—
321C4×D4—1221no—
322#117—611no—
323#117—1221no—
324#117—1221no—
325#117C2×#692311yescharacteristic
326C2×C42—611no—
327C2×C42—1221no—
328C2×C42—1221no—
329#107—611no—
330#107—611no—
331#106—611no—
332#106—611no—
333C4⋊C8—612no—
334C4⋊C8—612no—
335C4⋊C8—1221no—
336C4⋊C8—1222no—
337C4⋊C8—1222no—
338#103—611no—
339#103—611no—
340#103C2×#692311yescharacteristic
341#103C2×#692311yescharacteristic
342#102—611no—
343#102—611no—
344#102C2×#692311yescharacteristic
345#102C2×#692311yescharacteristic
346C22⋊C8—1222no—
347C22⋊C8—1222no—
348C22⋊C8—1221no—
349C22⋊C8—1221no—
350C22⋊C8—1221no—
351#97—611no—
352#97—611no—
353#97—1221no—
354#97—1221no—
355#97—1222no—
356#97—1222no—
357C4×C8—612no—
358C4×C8—611no—
359C4×C8—611no—
360C4×C8—611no—
361C4×C8—611no—
362C4×C8—612no—
363#41—22no—
364#41—41no—
365#41—1222no—
366#41—2441no—
367C2×Q8—611no—
368C2×Q8C22×#692311yescharacteristic
369C2×D4—21no—
370C2×D4—611no—
371C2×D4—1221no—
372C2×D4C22×#692311yescharacteristic
373C22×C4—21no—
374C22×C4—611no—
375C22×C4—611no—
376C22×C4—1221no—
377C22×C4—1221no—
378C22×C4—1221no—
379C22×C4—1221no—
380C22×C4—1221no—
381C22×C4C22×#692311yescharacteristic
382Q16—1222no—
383SD16—1222no—
384SD16—1222no—
385D8—614no—
386M16—1224no—
387C2×C8—41no—
388C2×C8—612no—
389C2×C8—611no—
390C2×C8—612no—
391C2×C8—611no—
392C2×C8—1222no—
393C2×C8—1222no—
394C2×C8—1222no—
395C2×C8—1222no—
396C2×C8—2444no—
397C2×C8—2444no—
398C2×C8C22×#692311yescharacteristic
399C2×C8C22×#692311yescharacteristic
400C4⋊C4—611no—
401C4⋊C4—611no—
402C4⋊C4—1221no—
403C4⋊C4—1221no—
404C4⋊C4—1221no—
405C4⋊C4—1221no—
406C4⋊C4C22×#692311yescharacteristic
407C4⋊C4C22×#692311yescharacteristic
408C22⋊C4—21no—
409C22⋊C4—1221no—
410C22⋊C4—1221no—
411C22⋊C4—1221no—
412C22⋊C4—1221no—
413C22⋊C4—1221no—
414C42—21no—
415C42—611no—
416C42—611no—
417C42—611no—
418C42—611no—
419C42—1221no—
420C42—1221no—
421C42—1221no—
422C42—1221no—
423C42—1221no—
424C23—21no—
425C23—1221no—
426C23D4×#692311yescharacteristic
427Q8—21no—
428Q8—21no—
429Q8—1221no—
430Q8—1221no—
431D4—21no—
432D4—42no—
433D4—612no—
434D4—1221no—
435D4—2442no—
436D4D61⋊M1612yes—
437C2×C4—21no—
438C2×C4—21no—
439C2×C4—21no—
440C2×C4—21no—
441C2×C4—21no—
442C2×C4—42no—
443C2×C4—611no—
444C2×C4—611no—
445C2×C4—611no—
446C2×C4—611no—
447C2×C4—1222no—
448C2×C4—1221no—
449C2×C4—1221no—
450C2×C4—1221no—
451C2×C4—4881no—
452C2×C4—4881no—
453C2×C4—2442no—
454C2×C4—2442no—
455C2×C4—2442no—
456C2×C4—2441no—
457C2×C4D4×#692311yescharacteristic
458C2×C4C23×#692311yescharacteristic
459C8—21no—
460C8—21no—
461C8—614no—
462C8—612no—
463C8—1222no—
464C8—1221no—
465C8—2442no—
466C8—2442no—
467C8—2442no—
468C22—21no—
469C22—22no—
470C22—21no—
471C22—21no—
472C22—41no—
473C22—41no—
474C22—1222no—
475C22—2441no—
476C22—2441no—
477C22C2×D4×#692311yescharacteristic
478C4—21no—
479C4—41no—
480C4—41no—
481C4—41no—
482C4—612no—
483C4—1221no—
484C4—1221no—
485C4—1221no—
486C4—2441no—
487C4—2441no—
488C4—2441no—
489C4C2×D61⋊M1611yescharacteristic
490C4#1684084011yescharacteristic
491C2—41no—
492C2—42no—
493C2—2442no—
494C2#2146255711yescharacteristic
495C2#135×#692311yescharacteristic
496C2#2146259811yescharacteristic
subgroupG/H
centerC22C2×D4×#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC61×#416C4
socleC22×C61C2×C4×D4
prime radicalC2×#14519797C4
cosocleC4×Dic61C24
hypercenter#416#6923
hypocenterC61#18035
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #416

Complements

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

NH ≅ G/Ntype
1. #21462660C2semidirect
2. #21462656C2semidirect
3. #21461457C2semidirect
4. #21461425C2semidirect
5. #21461422C2semidirect
6. #21461399C2semidirect
7. #21461379C2semidirect
8. #21461152C2semidirect
9. #21461150C2semidirect
10. C8×#11758217C2semidirect
154. #11758199M16semidirect
214. #92420#135semidirect
297. C61#18035semidirect

Maximal subgroups

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

subgroupindex
#214626602
#214626562
#214614572
#214614252
#214614222
#214613992
#214613792
#214611522
#214611502
C8×#117582172
#214545872
#1803561