Finite Group Databasebeta

← #29835560

Subgroups — #29835560

Order 15616.

526 conjugacy classes of subgroups.

The subgroup lattice has 484 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21456389C211yesmaximal, characteristic, complemented
2#21448095C211yesmaximal, characteristic, complemented
3#21448078C211yesmaximal, characteristic, complemented
4#21448053C211yesmaximal, characteristic, complemented
5#21448050C211yesmaximal, characteristic, complemented
6#21447917C211yesmaximal, characteristic, complemented
7#21447913C211yesmaximal, characteristic, complemented
8#21447908C211yesmaximal, characteristic, complemented
9#21447903C211yesmaximal, characteristic
10C4×#14519723C211yesmaximal, characteristic, complemented
11C4×#14519720C211yesmaximal, characteristic, complemented
12C4×#14519721C211yesmaximal, characteristic, complemented
13C4×#14519718C211yesmaximal, characteristic, complemented
14C2×C4×#11758185C211yesmaximal, characteristic, complemented
15C61×#3168C211yesmaximal, characteristic, complemented
16#16840296—21no—
17C2×#14519723C2211yescharacteristic
18C2×#14519721C2211yescharacteristic
19C2×#14519720C2211yescharacteristic
20C2×#14519718C2211yescharacteristic
21C22×#11758185C2211yescharacteristic
22C22×#11758185C2211yescharacteristic
23#16840164C2211yescharacteristic
24#16840146C2211yescharacteristic
25#16840117—21no—
26#16840003C2211yescharacteristic
27#16839998C2211yescharacteristic
28#16839991—21no—
29C4×Dic244C2211yescharacteristic
30C4×#11758190—21no—
31C4×D488C2211yescharacteristic
32#16839589C2211yescharacteristic
33#16839589C2211yescharacteristic
34#16839587C2211yescharacteristic
35#16839587C2211yescharacteristic
36#16839566C2211yescharacteristic
37#16839566C2211yescharacteristic
38#16839565C2211yescharacteristic
39#16839565C2211yescharacteristic
40#16839563C2211yescharacteristic
41#16839563C2211yescharacteristic
42#16839562C2211yescharacteristic
43#16839562C2211yescharacteristic
44C4×#11758185C2211yescharacteristic
45C4×#11758185C2211yescharacteristic
46C4×#11758185C2211yescharacteristic
47C4×#11758185C2211yescharacteristic
48C61×#529—21no—
49C61×#499C2211yescharacteristic
50C61×#495C2211yescharacteristic
51C61×#488—21no—
52C61×#467C2211yescharacteristic
53C61×#466C2211yescharacteristic
54C61×#465—21no—
55C4×Q16×C61C2211yescharacteristic
56C4×SD16×C61—21no—
57C4×D8×C61C2211yescharacteristic
58C2×C4×C8×C61C2211yescharacteristic
59C2×Dic244C2311yescharacteristic
60C2×#11758190—21no—
61C2×D488C2311yescharacteristic
62#14519771—41no—
63#14519769—21no—
64#14519765—21no—
65#14519760—41no—
66#14519756—21no—
67#14519751—21no—
68C4×Dic122—21no—
69C4×D244—21no—
70C4×C22⋊D61—41no—
71#14519734—41no—
72#14519723—22no—
73#14519721—22no—
74#14519720—22no—
75#14519718—22no—
76C2×#11758185—22no—
77C2×#11758185—22no—
78C2×#11758185C2311yescharacteristic
79C2×#11758185C2311yescharacteristic
80C2×#11758185C2311yescharacteristic
81C2×#11758185C2311yescharacteristic
82#14519711C2311yescharacteristic
83#14519711C2311yescharacteristic
84#14519709—21no—
85#14519702—21no—
86#14519702—21no—
87#14519699—21no—
88#14519699—21no—
89C2×Q16×C61C2311yescharacteristic
90C2×SD16×C61—21no—
91C2×D8×C61C2311yescharacteristic
92C22×C8×C61D411yescharacteristic
93C22×C8×C61C2311yescharacteristic
94#126×C61—41no—
95#125×C61—21no—
96#124×C61—21no—
97#123×C61—41no—
98C22⋊Q8×C61—21no—
99#121×C61—21no—
100C4×Q8×C61—21no—
101C4×D4×C61—21no—
102C4×D4×C61—41no—
103#117×C61—41no—
104C2×C42×C61D411yescharacteristic
105#107×C61C2311yescharacteristic
106#107×C61C2311yescharacteristic
107#106×C61—21no—
108#103×C61—21no—
109#103×C61—21no—
110#102×C61—21no—
111#102×C61—21no—
112C4×C8×C61D411yescharacteristic
113C4×C8×C61D411yescharacteristic
114C4×C8×C61C2311yescharacteristic
115C4×C8×C61C2311yescharacteristic
116C2×Q8×C61—21no—
117C2×D4×C61—21no—
118C2×D4×C61—41no—
119C22×C4×C61—41no—
120C22×C4×C61D811yescharacteristic
121C22×C4×C61D811yescharacteristic
122C22×C4×C61C2×D411yescharacteristic
123C2×C22⋊D61—41no—
124C2×D244—21no—
125C2×C4×D61—41no—
126C2×Dic122—21no—
127Q16×C61—21no—
128Q16×C61—21no—
129SD16×C61—42no—
130D8×C61—21no—
131D8×C61—21no—
132C2×C8×C61—22no—
133C2×C8×C61—21no—
134C2×C8×C61—21no—
135C2×C8×C61C2×D411yescharacteristic
136C2×C8×C61C2×D411yescharacteristic
137C2×C8×C61C2×D411yescharacteristic
138C2×C8×C61C2411yescharacteristic
139C4⋊C4×C61—21no—
140C4⋊C4×C61—21no—
141C4⋊C4×C61—41no—
142C4⋊C4×C61—41no—
143C4⋊C4×C61—41no—
144C4⋊C4×C61—41no—
145C22⋊C4×C61—41no—
146C22⋊C4×C61—41no—
147C22⋊C4×C61—41no—
148C22⋊C4×C61—41no—
149C22⋊C4×C61—41no—
150C42×C61—41no—
151C42×C61D811yescharacteristic
152C42×C61D811yescharacteristic
153C42×C61C2×D411yescharacteristic
154C42×C61C2×D411yescharacteristic
155C22⋊Dic61—41no—
156#11758198—41no—
157#11758198—41no—
158#11758198—41no—
159#11758198—41no—
160C4⋊Dic61—21no—
161C4⋊Dic61—21no—
162#11758196—41no—
163#11758196—41no—
164#11758196—41no—
165#11758196—41no—
166C4×Dic61—41no—
167Dic244—21no—
168Dic244—21no—
169D488—21no—
170D488—21no—
171#11758190—42no—
172#11758185—21no—
173#11758185—21no—
174#11758185#4112yes—
175#11758185#4112yes—
176C23×C61—41no—
177C23×C61C2×D811yescharacteristic
178C22×D61—41no—
179Q8×C61—41no—
180Q8×C61—41no—
181D4×C61—41no—
182D4×C61—41no—
183D4×C61—82no—
184C2×C4×C61—22no—
185C2×C4×C61—21no—
186C2×C4×C61—21no—
187C2×C4×C61—22no—
188C2×C4×C61—41no—
189C2×C4×C61—41no—
190C2×C4×C61—41no—
191C2×C4×C61—82no—
192C2×C4×C61C2×D811yescharacteristic
193C2×C4×C61C2×D811yescharacteristic
194C2×C4×C61C2×D811yescharacteristic
195C2×C4×C61C2×D811yescharacteristic
196C2×C4×C61C2×D811yescharacteristic
197C2×C4×C61C22×D411yescharacteristic
198C22⋊D61—82no—
199C2×Dic61—41no—
200C2×Dic61—41no—
201C2×Dic61—41no—
202D244—41no—
203D244—41no—
204C4×D61—82no—
205Dic122—41no—
206Dic122—41no—
207C8×C61—21no—
208C8×C61—21no—
209C8×C61#13512yes—
210C8×C61C2×#4111yescharacteristic
211C8×C61C2×#4111yescharacteristic
212#33735—611nomaximal, Sylow
213C22×C61—21no—
214C22×C61—21no—
215C22×C61—81no—
216C22×C61—81no—
217C22×C61—81no—
218C22×C61#50812yes—
219C22×C61C22×D811yescharacteristic
220C2×D61—81no—
221C2×D61—81no—
222C2×D61—81no—
223C4×C61—21no—
224C4×C61—21no—
225C4×C61—21no—
226C4×C61—21no—
227C4×C61—81no—
228C4×C61—81no—
229C4×C61—81no—
230C4×C61#50812yes—
231C4×C61#53211yescharacteristic
232C4×C61C2×#13511yescharacteristic
233Dic61—81no—
234Dic61—81no—
235Dic61—81no—
236#3168—611no—
237#3168D6111yescharacteristic, complemented
238#2253—611no—
239#2249—611no—
240#2242—611no—
241#2242—611no—
242#2217—611no—
243#2217—611no—
244#2216—611no—
245#2215—611no—
246C4×Q32—611no—
247C4×SD32—611no—
248C4×SD32—611no—
249C4×D16—611no—
250C2×C4×C16—611no—
251C2×C61—22no—
252C2×C61—161no—
253C2×C61#316911yescharacteristic
254C2×C61C2×#50811yescharacteristic
255C2×C61C2×#50811yescharacteristic
256D61—161no—
257#529—21no—
258#529—1221no—
259C2×Q32—611no—
260C2×SD32—611no—
261C2×SD32—611no—
262C2×D16—611no—
263C22×C16—611no—
264C22×C16—611no—
265#499—611no—
266#499C2×D6111yescharacteristic
267#495—611no—
268#495C2×D6111yescharacteristic
269#488—21no—
270#488—1221no—
271#467—611no—
272#467C2×D6111yescharacteristic
273#466—611no—
274#466C2×D6111yescharacteristic
275#465—21no—
276#465—1221no—
277C4×Q16—611no—
278C4×Q16C2×D6111yescharacteristic
279C4×SD16—21no—
280C4×SD16—1221no—
281C4×D8—611no—
282C4×D8C2×D6111yescharacteristic
283C2×C4×C8C2×D6111yescharacteristic
284#367—611no—
285#367—611no—
286#366—611no—
287#366—611no—
288#358—611no—
289#358—611no—
290#358—611no—
291#358—611no—
292#357—611no—
293#357—611no—
294#357—611no—
295#357—611no—
296C4×C16—611no—
297C4×C16—611no—
298C4×C16—611no—
299C4×C16—611no—
300C61#3373511yescharacteristic, complemented, Sylow
301C2×Q16—611no—
302C2×Q16C22×D6111yescharacteristic
303C2×SD16—21no—
304C2×SD16—1221no—
305C2×D8—611no—
306C2×D8C22×D6111yescharacteristic
307C22×C8C22⋊D6111yescharacteristic
308C22×C8C22×D6111yescharacteristic
309#126—41no—
310#126—2441no—
311#125—21no—
312#125—1221no—
313#124—21no—
314#124—1221no—
315#123—41no—
316#123—2441no—
317C22⋊Q8—21no—
318C22⋊Q8—1221no—
319#121—21no—
320#121—1221no—
321C4×Q8—21no—
322C4×Q8—1221no—
323C4×D4—21no—
324C4×D4—41no—
325C4×D4—1221no—
326C4×D4—2441no—
327#117—41no—
328#117—2441no—
329C2×C42C22⋊D6111yescharacteristic
330Q32—1222no—
331SD32—1222no—
332SD32—1222no—
333D16—1222no—
334C2×C16—611no—
335C2×C16—611no—
336C2×C16—611no—
337C2×C16—611no—
338C2×C16—1222no—
339C2×C16—1222no—
340#107—611no—
341#107—611no—
342#107C22×D6111yescharacteristic
343#107C22×D6111yescharacteristic
344#106—21no—
345#106—1221no—
346#103—21no—
347#103—21no—
348#103—1221no—
349#103—1221no—
350#102—21no—
351#102—21no—
352#102—1221no—
353#102—1221no—
354C4×C8C22⋊D6111yescharacteristic
355C4×C8C22⋊D6111yescharacteristic
356C4×C8C22×D6111yescharacteristic
357C4×C8C22×D6111yescharacteristic
358C2×Q8—21no—
359C2×Q8—1221no—
360C2×D4—21no—
361C2×D4—41no—
362C2×D4—1221no—
363C2×D4—2441no—
364C22×C4—41no—
365C22×C4—2441no—
366C22×C4#1175819911yescharacteristic
367C22×C4#1175819911yescharacteristic
368C22×C4C2×C22⋊D6111yescharacteristic
369Q16—21no—
370Q16—21no—
371Q16—1221no—
372Q16—1221no—
373SD16—42no—
374SD16—2442no—
375D8—21no—
376D8—21no—
377D8—1221no—
378D8—1221no—
379C2×C8—21no—
380C2×C8—21no—
381C2×C8—22no—
382C2×C8C2×C22⋊D6111yescharacteristic
383C2×C8C2×C22⋊D6111yescharacteristic
384C2×C8C2×C22⋊D6111yescharacteristic
385C2×C8C23×D6111yescharacteristic
386C4⋊C4—21no—
387C4⋊C4—21no—
388C4⋊C4—41no—
389C4⋊C4—41no—
390C4⋊C4—41no—
391C4⋊C4—41no—
392C4⋊C4—1221no—
393C4⋊C4—1221no—
394C4⋊C4—2441no—
395C4⋊C4—2441no—
396C4⋊C4—2441no—
397C4⋊C4—2441no—
398C22⋊C4—41no—
399C22⋊C4—41no—
400C22⋊C4—41no—
401C22⋊C4—41no—
402C22⋊C4—41no—
403C22⋊C4—2441no—
404C22⋊C4—2441no—
405C22⋊C4—2441no—
406C22⋊C4—2441no—
407C22⋊C4—2441no—
408C42—41no—
409C42—2441no—
410C42#1175819911yescharacteristic
411C42#1175819911yescharacteristic
412C42C2×C22⋊D6111yescharacteristic
413C42C2×C22⋊D6111yescharacteristic
414C16—612no—
415C16—612no—
416C16—1221no—
417C16—1221no—
418C23—41no—
419C23—2441no—
420C23C2×#1175819911yescharacteristic
421Q8—41no—
422Q8—41no—
423Q8—2441no—
424Q8—2441no—
425D4—41no—
426D4—41no—
427D4—82no—
428D4—4882no—
429D4—2441no—
430D4—2441no—
431C2×C4—22no—
432C2×C4—22no—
433C2×C4—21no—
434C2×C4—21no—
435C2×C4—41no—
436C2×C4—41no—
437C2×C4—41no—
438C2×C4—82no—
439C2×C4—4882no—
440C2×C4—2441no—
441C2×C4—2441no—
442C2×C4—2441no—
443C2×C4C2×#1175819911yescharacteristic
444C2×C4C2×#1175819911yescharacteristic
445C2×C4C2×#1175819911yescharacteristic
446C2×C4C2×#1175819911yescharacteristic
447C2×C4C2×#1175819911yescharacteristic
448C2×C4C22×C22⋊D6111yescharacteristic
449C8—21no—
450C8—21no—
451C8#1451979712yes—
452C8#41×D6111yescharacteristic
453C8#41×D6111yescharacteristic
454C22—21no—
455C22—21no—
456C22—81no—
457C22—81no—
458C22—81no—
459C22—4881no—
460C22—4881no—
461C22—4881no—
462C22#1684019212yes—
463C22C22×#1175819911yescharacteristic
464C4—21no—
465C4—21no—
466C4—21no—
467C4—21no—
468C4—81no—
469C4—81no—
470C4—81no—
471C4—4881no—
472C4—4881no—
473C4—4881no—
474C4#1684019212yes—
475C4#1684030811yescharacteristic
476C4C2×#1451979711yescharacteristic
477C2—22no—
478C2—161no—
479C2—9761no—
480C2#2145639411yescharacteristic
481C2C2×#1684019211yescharacteristic
482C2C2×#1684019211yescharacteristic
subgroupG/H
centerC2×C4C2×#11758199
commutator, cosocleC2×C8×C61C24
FrattiniC2×C8C23×D61
FittingC61×#3168C2
socleC22×C61C22×D8
prime radical#21447903C2
hypercenter#3168D61
hypocenterC61#33735
LCSG ▷ C2×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C2×C4×C8 ◁ #3168

Complements

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

NH ≅ G/Ntype
1. #21456389C2semidirect
2. #21448095C2semidirect
3. #21448078C2semidirect
4. #21448053C2semidirect
5. #21448050C2semidirect
6. #21447917C2semidirect
7. #21447913C2semidirect
8. #21447908C2semidirect
10. C4×#14519723C2semidirect
11. C4×#14519720C2semidirect
12. C4×#14519721C2semidirect
13. C4×#14519718C2semidirect
14. C2×C4×#11758185C2semidirect
15. C61×#3168C2semidirect
237. #3168D61semidirect
300. C61#33735semidirect

Maximal subgroups

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

subgroupindex
#214563892
#214480952
#214480782
#214480532
#214480502
#214479172
#214479132
#214479082
#214479032
C4×#145197232
C4×#145197202
C4×#145197212
C4×#145197182
C2×C4×#117581852
C61×#31682
#3373561