Finite Group Databasebeta

← #30613607

Subgroups — #30613607

Order 15616.

650 conjugacy classes of subgroups.

The subgroup lattice has 510 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21462752C211yesmaximal, characteristic, complemented
2#21462746C211yesmaximal, characteristic, complemented
3#21461461C212yesmaximal, complemented
4#21461431C212yesmaximal, complemented
5#21461419C212yesmaximal, complemented
6#21461411C212yesmaximal, complemented
7#21461376C211yesmaximal, characteristic, complemented
8#21461156C211yesmaximal, characteristic, complemented
9#21461156C211yesmaximal, characteristic, complemented
10#21461028C211yesmaximal, characteristic, complemented
11#21454590C211yesmaximal, characteristic
12#16840812C2212yes—
13#16840811C2212yes—
14#16840796C2212yes—
15#16840795—22no—
16#16840794—22no—
17#16840790C2212yes—
18#16840785—21no—
19#16840780—21no—
20#16840779C2211yescharacteristic
21#16840767—21no—
22#16840765C2211yescharacteristic
23#16840765C2211yescharacteristic
24D61⋊(C4⋊C8)—21no—
25C4×#11758217C2211yescharacteristic
26#16840626C2212yes—
27#16840625C2212yes—
28#16840612C2212yes—
29#16840612C2212yes—
30#16840610C2212yes—
31#16840610C2212yes—
32#92420⋊C8C2212yes—
33#16840603C2212yes—
34C2×#14519799C411yescharacteristic
35#16840230C2211yescharacteristic
36#16840230C2211yescharacteristic
37#16839856C411yescharacteristic
38#16839856C2211yescharacteristic
39#16839849C411yescharacteristic
40#16839849C411yescharacteristic
41#16839849C2211yescharacteristic
42#16839849C2211yescharacteristic
43#16839844C411yescharacteristic
44#16839844C2211yescharacteristic
45#16839756C411yescharacteristic
46#16839756C411yescharacteristic
47C2×C8×Dic61C2211yescharacteristic
48C61×#427C411yescharacteristic
49C2×#11758213—22no—
50C2×#11758217—21no—
51C2×#11758217—21no—
52C2×#11758217—21no—
53C2×D61⋊C8—22no—
54#14519844—22no—
55#14519844—21no—
56#14519844—21no—
57#14519844D411yescharacteristic
58#14519844D411yescharacteristic
59C4⋊#92420—22no—
60C4⋊#92420C2312yes—
61C4⋊#92420C2312yes—
62#14519834—22no—
63#14519834—22no—
64C22⋊#92420D412yes—
65#14519832—22no—
66#14519832—21no—
67C4×#92420—22no—
68C4×#92420C2312yes—
69C4×#92420C2312yes—
70C2×#11758222C2×C411yescharacteristic
71C2×#11758222C2×C411yescharacteristic
72#14519799—24no—
73C2×Dic244C2×C411yescharacteristic
74C2×#11758190C2×C411yescharacteristic
75C2×#11758190C2×C411yescharacteristic
76C2×D488C2×C411yescharacteristic
77C22×#92418C2×C411yescharacteristic
78#14519742C2×C411yescharacteristic
79#14519742C2×C411yescharacteristic
80#14519742C2311yescharacteristic
81#14519742C2311yescharacteristic
82#14519739C2×C411yescharacteristic
83#14519739C2×C411yescharacteristic
84#14519739C2311yescharacteristic
85#14519739C2311yescharacteristic
86#14519737—21no—
87#14519737—21no—
88#14519737—21no—
89#14519737—21no—
90#14519734—21no—
91#14519734—21no—
92C2×C4×Dic61C2311yescharacteristic
93C42×D61—21no—
94C42×D61—21no—
95#14519700C2×C411yescharacteristic
96#14519700C2×C411yescharacteristic
97#14519700C2×C411yescharacteristic
98#14519700C2×C411yescharacteristic
99#14519697C2×C411yescharacteristic
100#14519697C2×C411yescharacteristic
101#14519697C2×C411yescharacteristic
102#14519697C2×C411yescharacteristic
103C8×Dic61C2×C411yescharacteristic
104C8×Dic61C2×C411yescharacteristic
105C8×Dic61C2311yescharacteristic
106C8×Dic61C2311yescharacteristic
107C22×C8×C61C2×C411yescharacteristic
108#117×C61C2×C411yescharacteristic
109#117×C61C2×C411yescharacteristic
110#107×C61C2×C411yescharacteristic
111#107×C61C2×C411yescharacteristic
112#106×C61C2×C411yescharacteristic
113#106×C61C2×C411yescharacteristic
114C22×C4×C61C22×C411yescharacteristic
115C2×C22⋊D61—21no—
116C2×C22⋊D61—21no—
117C22×Dic61C2×D411yescharacteristic
118C22×Dic61#4111yescharacteristic
119#11758222—22no—
120#11758222—22no—
121#11758222—41no—
122#11758222—41no—
123C2×D244C22×C411yescharacteristic
124C2×D244C22×C411yescharacteristic
125C2×C4×D61—21no—
126C2×C4×D61—21no—
127C2×C4×D61—21no—
128C2×C4×D61—21no—
129C2×C4×D61—21no—
130C2×C4×D61—21no—
131C2×Dic122C22×C411yescharacteristic
132C2×Dic122C22×C411yescharacteristic
133#11758217—42no—
134#11758217—81no—
135#11758217—81no—
136C2×#92420—22no—
137C2×#92420—22no—
138C2×#92420—22no—
139C2×#92420C2×D412yes—
140C2×#92420C2×D412yes—
141#11758213—82no—
142D61⋊C8—82no—
143C2×C8×C61—22no—
144C2×C8×C61C22×C411yescharacteristic
145C2×C8×C61C22×C411yescharacteristic
146C4⋊C4×C61C22×C411yescharacteristic
147C4⋊C4×C61C22×C411yescharacteristic
148C4⋊C4×C61C22×C411yescharacteristic
149C4⋊C4×C61C22×C411yescharacteristic
150C22⋊C4×C61—21no—
151C22⋊C4×C61—21no—
152C42×C61—21no—
153C42×C61—21no—
154#11758198—21no—
155#11758198—21no—
156#11758198—21no—
157#11758198—21no—
158#11758196—21no—
159#11758196—21no—
160#11758196—21no—
161#11758196—21no—
162C4×Dic61—21no—
163C4×Dic61—21no—
164C4×Dic61—21no—
165C4×Dic61—21no—
166C4×Dic61C22×C411yescharacteristic
167C4×Dic61C2×D411yescharacteristic
168C4×Dic61#4111yescharacteristic
169C4×Dic61C2411yescharacteristic
170C2×#92418—41no—
171C2×#92418C22×C411yescharacteristic
172C2×#92418C22×C411yescharacteristic
173Dic244—22no—
174D488—22no—
175#11758190—22no—
176#11758190M1614yescomplemented
177C23×C61C4×D411yescharacteristic
178C22×D61—21no—
179C22×D61—21no—
180C2×C4×C61—21no—
181C2×C4×C61—21no—
182C2×C4×C61—21no—
183C2×C4×C61—21no—
184C2×C4×C61—21no—
185C2×C4×C61—21no—
186C2×C4×C61C4×D411yescharacteristic
187C2×C4×C61C23×C411yescharacteristic
188C22⋊D61—42no—
189C22⋊D61—42no—
190C2×Dic61—21no—
191C2×Dic61—21no—
192C2×Dic61—21no—
193C2×Dic61—22no—
194C2×Dic61—21no—
195C2×Dic61C4×D411yescharacteristic
196C2×Dic61C4×D411yescharacteristic
197C2×Dic61C22×D411yescharacteristic
198C2×Dic61C2×#4111yescharacteristic
199D244—21no—
200D244—21no—
201D244—21no—
202D244C2×M1612yes—
203C4×D61—42no—
204C4×D61—42no—
205C4×D61—41no—
206C4×D61—41no—
207C4×D61—41no—
208C4×D61—41no—
209C4×D61—42no—
210C4×D61—42no—
211Dic122—21no—
212Dic122—21no—
213Dic122—21no—
214Dic122C2×M1612yes—
215#92420—22no—
216#92420—22no—
217#92420—42no—
218#92420—42no—
219#92420—42no—
220C8×C61—21no—
221C8×C61C2×M1612yes—
222#92418—21no—
223#92418—21no—
224#18061—611nomaximal, Sylow
225C22×C61—21no—
226C22×C61—21no—
227C22×C61—21no—
228C22×C61C2×C4×D411yescharacteristic
229C2×D61—22no—
230C2×D61—41no—
231C2×D61—41no—
232C2×D61—41no—
233C2×D61—41no—
234C2×D61—41no—
235C4×C61—21no—
236C4×C61—41no—
237C4×C61—41no—
238C4×C61—41no—
239C4×C61—41no—
240C4×C61C22×M1611yescharacteristic
241C4×C61#56811yescharacteristic
242Dic61—22no—
243Dic61—21no—
244Dic61—21no—
245Dic61—41no—
246Dic61#44412yes—
247Dic61#57611yescharacteristic
248Dic61#57811yescharacteristic
249#2991—611no—
250#2990—611no—
251C4×#135—611no—
252#1592—612no—
253#1584—612no—
254#1581—612no—
255SD16⋊C8—612no—
256#1567—611no—
257#1489—611no—
258#1489—611no—
259#1451—611no—
260C2×C61—41no—
261C2×C61D4×M1611yescharacteristic
262C2×C61#295111yescharacteristic
263C2×C61C2×#44411yescharacteristic
264D61—42no—
265D61—81no—
266C2×#135—611no—
267C4×#41—611no—
268C4×#41—611no—
269#446—612no—
270C8×Q8—612no—
271C4×Q16—611no—
272C4×Q16—611no—
273C4×SD16—611no—
274C4×SD16—611no—
275C4×SD16—611no—
276C4×SD16—611no—
277C4×D8—611no—
278C4×D8—611no—
279#436—612no—
280#436—1222no—
281#435—1222no—
282C8×D4—612no—
283#432—1221no—
284#431—611no—
285#431—1221no—
286#427#692311yescharacteristic
287#423—611no—
288#423—611no—
289#423—1221no—
290C2×C4⋊C8—1221no—
291#416—611no—
292#416—611no—
293C4×M16—611no—
294C2×C4×C8—611no—
295#335—612no—
296#335—612no—
297Q8⋊C8—612no—
298Q8⋊C8—612no—
299D4⋊C8—612no—
300D4⋊C8—612no—
301#322—612no—
302#322—612no—
303C61#1806111yescharacteristic, complemented, Sylow
304C2×#41—611no—
305C2×#41—611no—
306#135—1224no—
307C2×Q16—611no—
308C2×SD16—611no—
309C2×SD16—611no—
310C2×D8—611no—
311C2×M16—1222no—
312C2×M16—1221no—
313C2×M16—1221no—
314C2×M16—1221no—
315C22×C8—611no—
316C22×C8—1222no—
317C22×C8C2×#692311yescharacteristic
318C4×Q8—611no—
319C4×Q8—611no—
320C4×Q8—611no—
321C4×Q8—611no—
322C4×D4—611no—
323C4×D4—611no—
324C4×D4—611no—
325C4×D4—611no—
326C4×D4—1221no—
327C4×D4—1221no—
328C4×D4—1221no—
329C4×D4—1221no—
330#117—1221no—
331#117—1221no—
332#117C2×#692311yescharacteristic
333#117C2×#692311yescharacteristic
334C2×C42—611no—
335C2×C42—1221no—
336C2×C42—1221no—
337#107C2×#692311yescharacteristic
338#107C2×#692311yescharacteristic
339#106C2×#692311yescharacteristic
340#106C2×#692311yescharacteristic
341C4⋊C8—611no—
342C4⋊C8—611no—
343C4⋊C8—612no—
344C4⋊C8—612no—
345C4⋊C8—1221no—
346C4⋊C8—1221no—
347C4⋊C8—1222no—
348C4⋊C8—1222no—
349#103—611no—
350#103—611no—
351#103—611no—
352#103—611no—
353#102—611no—
354#102—611no—
355#102—611no—
356#102—611no—
357C22⋊C8—612no—
358C22⋊C8—1222no—
359C22⋊C8—1222no—
360#97—1221no—
361#97—1222no—
362C4×C8—612no—
363C4×C8—611no—
364C4×C8—611no—
365C4×C8—611no—
366C4×C8—611no—
367C4×C8—612no—
368C4×C8—1222no—
369#41—1222no—
370#41—1222no—
371#41—2441no—
372#41—2441no—
373C2×Q8—611no—
374C2×Q8—611no—
375C2×D4—611no—
376C2×D4—611no—
377C2×D4—1221no—
378C2×D4—1221no—
379C22×C4—611no—
380C22×C4—611no—
381C22×C4—1221no—
382C22×C4—1221no—
383C22×C4—1221no—
384C22×C4—1221no—
385C22×C4—1221no—
386C22×C4—1221no—
387C22×C4C22×#692311yescharacteristic
388Q16—1222no—
389SD16—614no—
390SD16—1222no—
391D8—1222no—
392M16—4882no—
393M16—4881no—
394M16—4881no—
395M16—2442no—
396C2×C8—22no—
397C2×C8—612no—
398C2×C8—612no—
399C2×C8—611no—
400C2×C8—611no—
401C2×C8—1222no—
402C2×C8—1222no—
403C2×C8—1222no—
404C2×C8—4882no—
405C2×C8—2441no—
406C2×C8C22×#692311yescharacteristic
407C2×C8C22×#692311yescharacteristic
408C4⋊C4—1221no—
409C4⋊C4—1221no—
410C4⋊C4—1221no—
411C4⋊C4—1221no—
412C4⋊C4C22×#692311yescharacteristic
413C4⋊C4C22×#692311yescharacteristic
414C4⋊C4C22×#692311yescharacteristic
415C4⋊C4C22×#692311yescharacteristic
416C22⋊C4—21no—
417C22⋊C4—21no—
418C22⋊C4—1221no—
419C22⋊C4—1221no—
420C22⋊C4—1221no—
421C22⋊C4—1221no—
422C42—21no—
423C42—21no—
424C42—611no—
425C42—611no—
426C42—611no—
427C42—611no—
428C42—1221no—
429C42—1221no—
430C42—1221no—
431C42—1221no—
432C23—1221no—
433C23—1221no—
434C23D4×#692311yescharacteristic
435Q8—612no—
436Q8—1221no—
437Q8—1221no—
438Q8—1221no—
439D4—612no—
440D4—1221no—
441D4—1221no—
442D4—1221no—
443D4—2442no—
444D4—2442no—
445C2×C4—21no—
446C2×C4—21no—
447C2×C4—21no—
448C2×C4—21no—
449C2×C4—21no—
450C2×C4—21no—
451C2×C4—611no—
452C2×C4—611no—
453C2×C4—611no—
454C2×C4—611no—
455C2×C4—1221no—
456C2×C4—1222no—
457C2×C4—1221no—
458C2×C4—1221no—
459C2×C4—1221no—
460C2×C4—2442no—
461C2×C4—2442no—
462C2×C4—2441no—
463C2×C4—2441no—
464C2×C4—2441no—
465C2×C4—2441no—
466C2×C4—2442no—
467C2×C4—2442no—
468C2×C4D4×#692311yescharacteristic
469C2×C4C23×#692311yescharacteristic
470C8—21no—
471C8—1222no—
472C8—1222no—
473C8—1221no—
474C8—1221no—
475C8—2442no—
476C8—2442no—
477C8—2442no—
478C8D61⋊M1612yes—
479C22—21no—
480C22—21no—
481C22—21no—
482C22—1222no—
483C22—2441no—
484C22—2441no—
485C22—2441no—
486C22—2441no—
487C22—2441no—
488C22C2×D4×#692311yescharacteristic
489C4—21no—
490C4—41no—
491C4—41no—
492C4—41no—
493C4—41no—
494C4—611no—
495C4—611no—
496C4—612no—
497C4—1222no—
498C4—1221no—
499C4—1221no—
500C4—2441no—
501C4C2×D61⋊M1611yescharacteristic
502C4#1684084211yescharacteristic
503C2—41no—
504C2—4881no—
505C2—2442no—
506C2#2146255911yescharacteristic
507C2#2146258111yescharacteristic
508C2D61⋊#44411yescharacteristic
subgroupG/H
centerC22C2×D4×#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC61×#427C4
socleC22×C61C2×C4×D4
prime radicalC2×#14519799C4
cosocleC4×Dic61C24
hypercenter#427#6923
hypocenterC61#18061
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #427

Complements

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

NH ≅ G/Ntype
1. #21462752C2semidirect
2. #21462746C2semidirect
3. #21461461C2semidirect
4. #21461431C2semidirect
5. #21461419C2semidirect
6. #21461411C2semidirect
7. #21461376C2semidirect
8. #21461156C2semidirect
9. #21461156C2semidirect
10. #21461028C2semidirect
176. #11758190M16semidirect
303. C61#18061semidirect

Maximal subgroups

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

subgroupindex
#214627522
#214627462
#214614612
#214614312
#214614192
#214614112
#214613762
#214611562
#214610282
#214545902
#1806161