Finite Group Databasebeta

← #29837755

Subgroups — #29837755

Order 15616.

518 conjugacy classes of subgroups.

The subgroup lattice has 482 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21458793C211yesmaximal, characteristic
2#21458707C211yesmaximal, characteristic, complemented
3#21448062C211yesmaximal, characteristic, complemented
4#21448059C211yesmaximal, characteristic, complemented
5#21448041C211yesmaximal, characteristic, complemented
6#21447975C211yesmaximal, characteristic, complemented
7#21447955C211yesmaximal, characteristic, complemented
8#21447860C211yesmaximal, characteristic, complemented
9#21447858C211yesmaximal, characteristic, complemented
10#21447858C211yesmaximal, characteristic, complemented
11#21447726C211yesmaximal, characteristic, complemented
12#21447683C211yesmaximal, characteristic, complemented
13#21447682C211yesmaximal, characteristic, complemented
14#21447670C211yesmaximal, characteristic, complemented
15C61×#2228C211yesmaximal, characteristic, complemented
16#16840489—21no—
17#16840433—21no—
18C2×#14519722C2211yescharacteristic
19C2×#14519722C2211yescharacteristic
20C2×#14519721C2211yescharacteristic
21#16840166C2211yescharacteristic
22#16840163C2211yescharacteristic
23#16840139C2211yescharacteristic
24#16840137C2211yescharacteristic
25#16840137C2211yescharacteristic
26#16840072—21no—
27#16840066—21no—
28#16840046—21no—
29#16839957—21no—
30#16839956—21no—
31#16839956—21no—
32C8×Dic122C2211yescharacteristic
33C4×Dic244C2211yescharacteristic
34#16839856C2211yescharacteristic
35#16839856C2211yescharacteristic
36#16839844C2211yescharacteristic
37#16839844C2211yescharacteristic
38#16839587C2211yescharacteristic
39#16839580C2211yescharacteristic
40#16839580C2211yescharacteristic
41#16839565C2211yescharacteristic
42#16839564C2211yescharacteristic
43#16839564C2211yescharacteristic
44#16839563C2211yescharacteristic
45#16839562C2211yescharacteristic
46#16839562C2211yescharacteristic
47#16839562C2211yescharacteristic
48#16839562C2211yescharacteristic
49#16839538C2211yescharacteristic
50#16839537C2211yescharacteristic
51C16×Dic61C2211yescharacteristic
52C61×#499C2211yescharacteristic
53C4×D8×C61C2211yescharacteristic
54C61×#367C2211yescharacteristic
55C61×#366C2211yescharacteristic
56C61×C4⋊C16C2211yescharacteristic
57C61×#357C2211yescharacteristic
58C61×#357C2211yescharacteristic
59C2×#11758222—41no—
60C2×Dic244C2311yescharacteristic
61C2×D488—21no—
62C2×D488C2311yescharacteristic
63C2×D488C2311yescharacteristic
64C2×#11758199—21no—
65C2×#11758199—21no—
66#14519776—21no—
67#14519776—41no—
68#14519774—21no—
69#14519773—21no—
70#14519773—21no—
71#14519768—21no—
72#14519767—41no—
73#14519767—41no—
74#14519751—41no—
75#14519750—41no—
76#14519750—41no—
77C4×Dic122—21no—
78C4×Dic122D411yescharacteristic
79#14519742—21no—
80#14519742—21no—
81#14519742—41no—
82#14519739—21no—
83#14519739—21no—
84#14519722—22no—
85#14519722—22no—
86#14519721—22no—
87C2×#11758185C2311yescharacteristic
88C2×#11758185C2311yescharacteristic
89#14519711C2311yescharacteristic
90#14519710—21no—
91#14519708—21no—
92C4⋊#92418D411yescharacteristic
93#14519706D411yescharacteristic
94#14519706D411yescharacteristic
95#14519702—21no—
96#14519700—21no—
97#14519700—21no—
98#14519697—21no—
99#14519697—21no—
100C8×Dic61C2311yescharacteristic
101C8×Dic61C2311yescharacteristic
102C2×D8×C61C2311yescharacteristic
103#125×C61—21no—
104C4×D4×C61—21no—
105C2×C16×C61C2311yescharacteristic
106C2×C16×C61C2311yescharacteristic
107#107×C61C2311yescharacteristic
108#107×C61C2311yescharacteristic
109#107×C61C2311yescharacteristic
110#106×C61—21no—
111#102×C61—21no—
112C4×C8×C61C2311yescharacteristic
113C2×D4×C61—21no—
114C22×C4×C61—41no—
115C2×C22⋊D61—41no—
116C2×C22⋊D61—41no—
117C2×C22⋊D61—41no—
118C2×C22⋊D61—41no—
119#11758222—84no—
120C2×D244—21no—
121C2×D244—21no—
122C2×D244—41no—
123C2×D244—41no—
124C2×C4×D61—41no—
125C2×C4×D61—41no—
126C2×Dic122—21no—
127C2×Dic122—41no—
128C2×Dic122D811yescharacteristic
129D8×C61—21no—
130D8×C61—21no—
131C2×C8×C61C2×D411yescharacteristic
132C2×C8×C61C2411yescharacteristic
133C4⋊C4×C61—21no—
134C4⋊C4×C61—21no—
135C4⋊C4×C61—21no—
136C4⋊C4×C61—41no—
137C4⋊C4×C61—41no—
138C22⋊C4×C61—41no—
139C42×C61C2×D411yescharacteristic
140#11758199—81no—
141#11758199—81no—
142#11758198—41no—
143#11758198—41no—
144C4⋊Dic61—21no—
145C4⋊Dic61—41no—
146C4⋊Dic61D811yescharacteristic
147#11758196—41no—
148#11758196—41no—
149#11758196—41no—
150#11758196—41no—
151#11758196—41no—
152#11758196D811yescharacteristic
153#11758196D811yescharacteristic
154C4×Dic61—41no—
155C4×Dic61—41no—
156C4×Dic61—41no—
157C4×Dic61C2×D411yescharacteristic
158C4×Dic61C2×D411yescharacteristic
159C2×#92418C2×D411yescharacteristic
160C2×#92418C2×D411yescharacteristic
161Dic244—21no—
162Dic244#4112yescomplemented
163D488—21no—
164D488—21no—
165D488—21no—
166D488—21no—
167D488—81no—
168C16×C61—21no—
169C16×C61—21no—
170#11758185—21no—
171#11758185—21no—
172C23×C61—41no—
173C22×D61—41no—
174C22×D61—41no—
175D4×C61—41no—
176D4×C61—41no—
177C2×C4×C61—41no—
178C2×C4×C61—41no—
179C2×C4×C61—41no—
180C2×C4×C61—82no—
181C2×C4×C61C2×D811yescharacteristic
182C2×C4×C61C2×D811yescharacteristic
183C2×C4×C61C22×D411yescharacteristic
184C22⋊D61—82no—
185C22⋊D61—82no—
186C22⋊D61—161no—
187C22⋊D61—161no—
188C2×Dic61—41no—
189C2×Dic61—41no—
190C2×Dic61C2×D811yescharacteristic
191C2×Dic61C2×D811yescharacteristic
192C2×Dic61C2×D811yescharacteristic
193C2×Dic61C2×D811yescharacteristic
194D244—41no—
195D244—41no—
196D244—41no—
197D244—41no—
198D244—82no—
199D244—161no—
200C4×D61—82no—
201C4×D61—82no—
202Dic122—22no—
203Dic122—22no—
204Dic122—41no—
205Dic122—82no—
206C8×C61—21no—
207C8×C61C2×#4111yescharacteristic
208C8×C612−1+411yescharacteristic
209#92418—21no—
210#92418—21no—
211#33935—611nomaximal, Sylow
212C22×C61—81no—
213C22×C61—81no—
214C22×C61—81no—
215C22×C61C22×D811yescharacteristic
216C2×D61—81no—
217C2×D61—81no—
218C2×D61—81no—
219C2×D61—81no—
220C2×D61—81no—
221C2×D61—81no—
222C4×C61—21no—
223C4×C61—21no—
224C4×C61—81no—
225C4×C61—81no—
226C4×C61—81no—
227C4×C61#54811yescharacteristic
228C4×C61#57711yescharacteristic
229Dic61—21no—
230Dic61—21no—
231Dic61—21no—
232Dic61—42no—
233Dic61—81no—
234Dic61#50912yes—
235#3391—611no—
236#3383—611no—
237#2244—611no—
238#2244—611no—
239#2240—611no—
240#2228—611no—
241#2228D6111yescharacteristic, complemented
242#2224—611no—
243#2207—611no—
244#2207—611no—
245#2207—611no—
246#2183—611no—
247#2175—611no—
248#2175—611no—
249C4×SD32—611no—
250C2×C61—161no—
251C2×C61#335811yescharacteristic
252C2×C61C2×#50911yescharacteristic
253C2×C61#341611yescharacteristic
254D61—161no—
255D61—161no—
256#557—1221no—
257#550—1221no—
258C2×SD32—611no—
259C2×SD32—611no—
260C2×SD32—611no—
261#500—611no—
262#499—611no—
263#499C2×D6111yescharacteristic
264#493—611no—
265#493—611no—
266#493—611no—
267#479—1221no—
268#479—1221no—
269#475—1221no—
270#459—1221no—
271#459—1221no—
272#459—1221no—
273C8×Q8—611no—
274C4×Q16—611no—
275C4×Q16—611no—
276C4×Q16—611no—
277C4×D8—611no—
278C4×D8—611no—
279C4×D8C2×D6111yescharacteristic
280#367C2×D6111yescharacteristic
281#366—611no—
282#366C2×D6111yescharacteristic
283C4⋊C16—611no—
284C4⋊C16—611no—
285C4⋊C16C2×D6111yescharacteristic
286#358—611no—
287#357—611no—
288#357—611no—
289#357—611no—
290#357—611no—
291#357—611no—
292#357—611no—
293#357—611no—
294#357C2×D6111yescharacteristic
295#357C2×D6111yescharacteristic
296#346—611no—
297#346—611no—
298C4×C16—611no—
299C61#3393511yescharacteristic, complemented, Sylow
300C2×#41—2441no—
301C2×Q16—611no—
302C2×D8—611no—
303C2×D8—611no—
304C2×D8—1221no—
305C2×D8—1221no—
306C2×D8—1221no—
307C2×D8C22×D6111yescharacteristic
308C4⋊Q8—1221no—
309C4⋊Q8—2441no—
310#127—1221no—
311#127—1221no—
312#127—1221no—
313#125—21no—
314#125—1221no—
315#125—2441no—
316#125—2441no—
317#121—2441no—
318#121—2441no—
319#121—2441no—
320C4×Q8—611no—
321C4×Q8—1221no—
322C4×Q8—1221no—
323C4×Q8—1221no—
324C4×Q8—2441no—
325C4×D4—21no—
326C4×D4—1221no—
327C4×D4—1221no—
328SD32—1222no—
329SD32—1222no—
330SD32—1222no—
331C2×C16—611no—
332C2×C16—611no—
333C2×C16C22×D6111yescharacteristic
334C2×C16C22×D6111yescharacteristic
335#107—611no—
336#107—1221no—
337#107C22×D6111yescharacteristic
338#107C22×D6111yescharacteristic
339#107C22×D6111yescharacteristic
340#106—21no—
341#106—1221no—
342C4⋊C8—611no—
343C4⋊C8—611no—
344C4⋊C8—611no—
345#103—1221no—
346#103—1221no—
347#103—1221no—
348#102—21no—
349#102—1221no—
350#102—1221no—
351C4×C8—611no—
352C4×C8—611no—
353C4×C8C22×D6111yescharacteristic
354#41—4884no—
355C2×Q8—611no—
356C2×Q8—1221no—
357C2×Q8—2441no—
358C2×D4—21no—
359C2×D4—1221no—
360C2×D4—1221no—
361C2×D4—2441no—
362C2×D4—2441no—
363C2×D4—2441no—
364C2×D4—2441no—
365C2×D4—2441no—
366C2×D4—2441no—
367C22×C4—41no—
368C22×C4—2441no—
369C22×C4—2441no—
370Q16—612no—
371Q16—1221no—
372D8—21no—
373D8—21no—
374D8—1221no—
375D8—1221no—
376D8—1221no—
377D8—1221no—
378D8—4881no—
379D8—4881no—
380D8—4881no—
381C2×C8—611no—
382C2×C8—611no—
383C2×C8D4×D6111yescharacteristic
384C2×C8C23×D6111yescharacteristic
385C4⋊C4—21no—
386C4⋊C4—21no—
387C4⋊C4—21no—
388C4⋊C4—41no—
389C4⋊C4—41no—
390C4⋊C4—611no—
391C4⋊C4—611no—
392C4⋊C4—611no—
393C4⋊C4—1221no—
394C4⋊C4—2441no—
395C4⋊C4—2441no—
396C4⋊C4—2441no—
397C4⋊C4—2441no—
398C4⋊C4—2441no—
399C4⋊C4—2441no—
400C22⋊C4—41no—
401C22⋊C4—2441no—
402C22⋊C4—2441no—
403C42—611no—
404C42—611no—
405C42—2441no—
406C42—2441no—
407C42—2441no—
408C42D4×D6111yescharacteristic
409C16—21no—
410C16—21no—
411C16—1221no—
412C16—1221no—
413C23—41no—
414C23—2441no—
415C23—2441no—
416Q8—1222no—
417Q8—1222no—
418Q8—4882no—
419Q8—2441no—
420D4—41no—
421D4—41no—
422D4—9761no—
423D4—9761no—
424D4—9761no—
425D4—4882no—
426D4—4882no—
427D4—4882no—
428D4—2441no—
429D4—2441no—
430D4—2441no—
431D4—2441no—
432C2×C4—41no—
433C2×C4—41no—
434C2×C4—41no—
435C2×C4—82no—
436C2×C4—611no—
437C2×C4—611no—
438C2×C4—611no—
439C2×C4—611no—
440C2×C4—4882no—
441C2×C4—4882no—
442C2×C4—2441no—
443C2×C4—2441no—
444C2×C4D8×D6111yescharacteristic
445C2×C4D8×D6111yescharacteristic
446C2×C4C2×D4×D6111yescharacteristic
447C8—21no—
448C8—1221no—
449C8—1221no—
450C8#41×D6111yescharacteristic
451C8#1451982511yescharacteristic
452C22—81no—
453C22—81no—
454C22—81no—
455C22—4881no—
456C22—4881no—
457C22—4881no—
458C22—4881no—
459C22—4881no—
460C22—4881no—
461C22C2×D8×D6111yescharacteristic
462C4—21no—
463C4—21no—
464C4—81no—
465C4—81no—
466C4—81no—
467C4—612no—
468C4—1221no—
469C4—1221no—
470C4—1221no—
471C4—4881no—
472C4—2442no—
473C4#1684042211yescharacteristic
474C4#1684057111yescharacteristic
475C2—161no—
476C2—9761no—
477C2—9761no—
478C2#2145845311yescharacteristic
479C2#509×D6111yescharacteristic
480C2#2145896211yescharacteristic
subgroupG/H
centerC22C2×D8×D61
commutator, cosocleC2×C8×C61C24
FrattiniC2×C8C23×D61
FittingC61×#2228C2
socleC22×C61C22×D8
prime radical#21458793C2
hypercenter#2228D61
hypocenterC61#33935
LCSG ▷ C2×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #2228

Complements

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

NH ≅ G/Ntype
2. #21458707C2semidirect
3. #21448062C2semidirect
4. #21448059C2semidirect
5. #21448041C2semidirect
6. #21447975C2semidirect
7. #21447955C2semidirect
8. #21447860C2semidirect
9. #21447858C2semidirect
10. #21447858C2semidirect
11. #21447726C2semidirect
12. #21447683C2semidirect
13. #21447682C2semidirect
14. #21447670C2semidirect
15. C61×#2228C2semidirect
162. Dic244#41semidirect
241. #2228D61semidirect
299. C61#33935semidirect

Maximal subgroups

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

subgroupindex
#214587932
#214587072
#214480622
#214480592
#214480412
#214479752
#214479552
#214478602
#214478582
#214477262
#214476832
#214476822
#214476702
C61×#22282
#3393561