Finite Group Databasebeta

← #29834288

Subgroups — #29834288

Order 15616.

770 conjugacy classes of subgroups.

The subgroup lattice has 488 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840200C211yesmaximal, characteristic, complemented
2C2×#16840197C211yesmaximal, characteristic, complemented
3#21456243C211yesmaximal, characteristic, complemented
4C2×#16839844C211yesmaximal, characteristic, complemented
5#21447877C212yesmaximal, complemented
6#21447873C212yesmaximal, complemented
7#21447863C212yesmaximal, complemented
8#21447853C212yesmaximal, complemented
9#21447574C211yesmaximal, characteristic, complemented
10#21447529C211yesmaximal, characteristic, complemented
11C61×#2139C211yesmaximal, characteristic, complemented
12C2×#14519799C2211yescharacteristic
13C2×#14519797—21no—
14C22×D488C2211yescharacteristic
15#16840308—21no—
16C2×#14519739—21no—
17#16840200—24no—
18#16840197—24no—
19C2×#14519722C2212yes—
20C2×#14519720C2212yes—
21C2×D976C2212yes—
22C2×#14519718C2212yes—
23C2×#14519717C2211yescharacteristic
24#16840147C2211yescharacteristic, complemented
25#16840145C2211yescharacteristic, complemented
26#16840143—21no—
27#16840140C2211yescharacteristic, complemented
28#16840137C2211yescharacteristic, complemented
29#16840133—21no—
30#16839844—21no—
31#16839844—21no—
32#16839844C2212yes—
33#16839844C2212yes—
34C2×#14519697—21no—
35C2×C8×Dic61C2211yescharacteristic
36#16839580C2212yescomplemented
37#16839580C2212yescomplemented
38#16839565C2212yescomplemented
39#16839562C2212yescomplemented
40C2×#135×C61C2211yescharacteristic
41C2×M32×C61C2211yescharacteristic
42C2×#107×C61C2211yescharacteristic
43C61×#358C2212yescomplemented
44C61×#357C2212yescomplemented
45C2×#11758222—21no—
46C22×D244—21no—
47C22×C4×D61—41no—
48#14519799—22no—
49#14519799—22no—
50#14519797—44no—
51C2×Dic244C2311yescharacteristic
52C2×#11758202—21no—
53C2×#11758190—21no—
54C2×#11758200—21no—
55C2×#11758201—21no—
56C2×D488—21no—
57C2×D488—22no—
58C2×D488D414yescomplemented
59C2×D488C2311yescharacteristic
60C2×D488C2312yes—
61C2×#11758199—21no—
62C22×#92418D411yescharacteristic
63#14519775—21no—
64#14519773—21no—
65#14519766—21no—
66#14519764—21no—
67#14519749—41no—
68#14519749—41no—
69#14519739—22no—
70#14519739—22no—
71#14519739—41no—
72#14519739—41no—
73C4×C22⋊D61—41no—
74C4×C22⋊D61—41no—
75C2×#11758198—41no—
76C2×C4×Dic61D411yescharacteristic
77#14519722—24no—
78#14519720—24no—
79D976—24no—
80#14519718—24no—
81#14519717—22no—
82C2×#11758185C2312yes—
83#14519697—22no—
84#14519697—22no—
85C8×Dic61D411yescharacteristic
86C8×Dic61D411yescharacteristic
87C8×Dic61C2311yescharacteristic
88C8×Dic61C2311yescharacteristic
89C2×#41×C61—21no—
90#135×C61—22no—
91#135×C61—22no—
92C2×Q16×C61C2311yescharacteristic
93C2×SD16×C61—21no—
94C2×D8×C61C2311yescharacteristic
95C22×C8×C61C2311yescharacteristic
96C2×C4⋊C4×C61—21no—
97M32×C61—22no—
98C2×C16×C61C2312yes—
99#107×C61—21no—
100#107×C61C2312yes—
101C23×D61—41no—
102#41×C61—42no—
103#41×C61—42no—
104C2×Q8×C61—21no—
105C2×D4×C61—21no—
106C2×D4×C61—41no—
107C22×C4×C61—41no—
108C22×C4×C61—41no—
109C22×C4×C61C2×D411yescharacteristic
110C2×C22⋊D61—41no—
111C2×C22⋊D61—41no—
112C2×C22⋊D61—41no—
113C22×Dic61D811yescharacteristic
114C22×Dic61D811yescharacteristic
115#11758222—42no—
116#11758222—42no—
117C2×D244—24no—
118C2×D244—22no—
119C2×D244—21no—
120C2×D244—41no—
121C2×D244—42no—
122C2×C4×D61—41no—
123C2×C4×D61—42no—
124C2×C4×D61—42no—
125C2×C4×D61—84no—
126C2×Dic122—21no—
127Q16×C61—21no—
128Q16×C61—21no—
129SD16×C61—42no—
130D8×C61—21no—
131D8×C61—21no—
132C2×C8×C61C2×D411yescharacteristic
133C2×C8×C61C2×D412yes—
134C2×C8×C61#4112yes—
135C2×C8×C61C2411yescharacteristic
136C4⋊C4×C61—22no—
137C4⋊C4×C61—41no—
138C22⋊Dic61—41no—
139C22⋊Dic61—41no—
140#11758202—42no—
141#11758201—42no—
142#11758200—42no—
143#11758199—42no—
144#11758198—42no—
145#11758198—42no—
146#11758198—41no—
147#11758198—41no—
148#11758196—41no—
149#11758196—41no—
150C4×Dic61D811yescharacteristic
151C4×Dic61D811yescharacteristic
152C4×Dic61C2×D411yescharacteristic
153C4×Dic61C2×D411yescharacteristic
154C2×#92418—22no—
155C2×#92418C2×D411yescharacteristic
156C2×#92418C2×D411yescharacteristic
157Dic244—21no—
158Dic244—21no—
159D488—24no—
160D488—21no—
161D488—22no—
162D488—21no—
163D488C2×D414yes—
164#11758190—42no—
165C16×C61—22no—
166#11758185—22no—
167C23×C61—41no—
168C23×C61C2×D811yescharacteristic
169C22×D61—42no—
170C22×D61—44no—
171C22×D61—41no—
172C22×D61—82no—
173C22×D61—82no—
174Q8×C61—41no—
175Q8×C61—41no—
176D4×C61—41no—
177D4×C61—41no—
178D4×C61—82no—
179C2×C4×C61—41no—
180C2×C4×C61—42no—
181C2×C4×C61—82no—
182C2×C4×C61—82no—
183C2×C4×C61#12112yes—
184C2×C4×C61C2×D811yescharacteristic
185C2×C4×C61AGL(1,ℤ/8)12yes—
186C2×C4×C61C22×D411yescharacteristic
187C22⋊D61—82no—
188C22⋊D61—82no—
189C22⋊D61—82no—
190C2×Dic61—22no—
191C2×Dic61—41no—
192C2×Dic61—41no—
193C2×Dic61C2×D811yescharacteristic
194C2×Dic61C2×D811yescharacteristic
195C2×Dic61C2×D811yescharacteristic
196C2×Dic61C2×D811yescharacteristic
197D244—24no—
198D244—41no—
199D244—42no—
200D244—41no—
201D244—44no—
202C4×D61—84no—
203C4×D61—82no—
204C4×D61—84no—
205Dic122—41no—
206Dic122—41no—
207C8×C61#12112yes—
208C8×C61C22×D411yescharacteristic
209C8×C61C2×#4111yescharacteristic
210#92418—21no—
211#92418—21no—
212#33580—611nomaximal, Sylow
213C22×C61—21no—
214C22×C61—21no—
215C22×C61—81no—
216C22×C61—81no—
217C22×C61—81no—
218C22×C61#45912yes—
219C22×C61C22×D811yescharacteristic
220C2×D61—44no—
221C2×D61—88no—
222C2×D61—82no—
223C2×D61—82no—
224C2×D61—81no—
225C2×D61—81no—
226C2×D61—81no—
227C4×C61—82no—
228C4×C61—81no—
229C4×C61#45912yes—
230C4×C61C2×#12111yescharacteristic
231C4×C61C2×AGL(1,ℤ/8)11yescharacteristic
232Dic61—21no—
233Dic61—21no—
234Dic61—21no—
235Dic61—81no—
236Dic61#50912yescomplemented
237C2×#509—611no—
238C2×#509—611no—
239#3147—611no—
240C2×C4×D8—611no—
241#2210—612no—
242#2210—612no—
243#2208—612no—
244#2206—612no—
245#2150—611no—
246#2139—611no—
247#2139D6111yescharacteristic, complemented
248C2×C61—22no—
249C2×C61—161no—
250C2×C61C2×#45911yescharacteristic
251C2×C61C2×#50911yescharacteristic
252C2×C61#341411yescharacteristic
253D61—84no—
254D61—161no—
255C2×#135—611no—
256C2×#135—1221no—
257C2×#135C2×D6111yescharacteristic
258C22×D8—611no—
259#532—1221no—
260C2×C4×D4—1221no—
261#509—1224no—
262#509—1224no—
263C2×SD32—612no—
264C2×SD32—612no—
265C2×D16—612no—
266C2×D16—612no—
267C2×M32—611no—
268C2×M32C2×D6111yescharacteristic
269#495—611no—
270#495—611no—
271#495—1221no—
272#494—611no—
273#493—611no—
274#492—1221no—
275C4×D8—612no—
276C4×D8—612no—
277C4×D8—1221no—
278C4×D8—1221no—
279C2×#107C2×D6111yescharacteristic
280C2×#102—1221no—
281C2×C4×C8—611no—
282C4⋊C16—612no—
283C4⋊C16—612no—
284#358—612no—
285#358C2×D6112yescomplemented
286#357—612no—
287#357C2×D6112yescomplemented
288C61#3358011yescharacteristic, complemented, Sylow
289C2×#41—21no—
290C2×#41—1221no—
291C22×D4—1221no—
292C23×C4—2441no—
293#135—22no—
294#135—22no—
295#135—1222no—
296#135—1222no—
297#135—2444no—
298C2×Q16—611no—
299C2×Q16—1221no—
300C2×Q16C22×D6111yescharacteristic
301C2×SD16—21no—
302C2×SD16—1221no—
303C2×SD16—1221no—
304C2×SD16—1221no—
305C2×D8—614no—
306C2×D8—612no—
307C2×D8—611no—
308C2×D8—1221no—
309C2×D8—1222no—
310C2×D8—1221no—
311C2×D8C22×D6111yescharacteristic
312C22×C8—611no—
313C22×C8C22×D6111yescharacteristic
314C4⋊Q8—1221no—
315#127—1221no—
316#124—1221no—
317#124—1221no—
318#121—2441no—
319#121—2441no—
320C4×D4—1222no—
321C4×D4—1222no—
322C4×D4—2441no—
323C4×D4—2441no—
324C4×D4—2441no—
325C4×D4—2441no—
326C2×C4⋊C4—21no—
327C2×C22⋊C4—2441no—
328C2×C42—611no—
329SD32—1224no—
330SD32—1224no—
331D16—1224no—
332D16—1224no—
333M32—22no—
334M32—1222no—
335C2×C16—612no—
336C2×C16C22×D6112yes—
337#107—21no—
338#107C22×D6112yes—
339#102—1222no—
340#102—1222no—
341C4×C8—611no—
342C4×C8—611no—
343C4×C8—611no—
344C4×C8—611no—
345C24—2441no—
346#41—42no—
347#41—42no—
348#41—2442no—
349#41—2442no—
350C2×Q8—21no—
351C2×Q8—1221no—
352C2×D4—21no—
353C2×D4—41no—
354C2×D4—1222no—
355C2×D4—1221no—
356C2×D4—1224no—
357C2×D4—2441no—
358C2×D4—2441no—
359C2×D4—2441no—
360C2×D4—2441no—
361C2×D4—2442no—
362C22×C4—41no—
363C22×C4—41no—
364C22×C4—611no—
365C22×C4—611no—
366C22×C4—4884no—
367C22×C4—2442no—
368C22×C4—2442no—
369C22×C4—2441no—
370C22×C4D4×D6111yescharacteristic
371Q16—21no—
372Q16—21no—
373Q16—1221no—
374Q16—1221no—
375Q16—2442no—
376SD16—42no—
377SD16—2442no—
378SD16—2442no—
379SD16—2442no—
380D8—21no—
381D8—21no—
382D8—614no—
383D8—1221no—
384D8—1222no—
385D8—1221no—
386D8—1224no—
387D8—2442no—
388C2×C8—611no—
389C2×C8—611no—
390C2×C8—1222no—
391C2×C8#1175822212yes—
392C2×C8D4×D6112yes—
393C2×C8D4×D6111yescharacteristic
394C2×C8C23×D6111yescharacteristic
395C4⋊C4—22no—
396C4⋊C4—41no—
397C4⋊C4—2441no—
398C4⋊C4—2441no—
399C22⋊C4—2442no—
400C22⋊C4—2442no—
401C22⋊C4—2441no—
402C22⋊C4—2441no—
403C22⋊C4—2441no—
404C22⋊C4—2441no—
405C42—611no—
406C42—611no—
407C42—611no—
408C42—611no—
409C16—22no—
410C16—1222no—
411C23—41no—
412C23—4882no—
413C23—4882no—
414C23—2441no—
415C23—2444no—
416C23—2442no—
417C23D8×D6111yescharacteristic
418Q8—41no—
419Q8—41no—
420Q8—2441no—
421Q8—2441no—
422D4—41no—
423D4—41no—
424D4—82no—
425D4—1224no—
426D4—4882no—
427D4—4882no—
428D4—4882no—
429D4—2444no—
430D4—2441no—
431D4—2441no—
432D4—2442no—
433C2×C4—42no—
434C2×C4—41no—
435C2×C4—82no—
436C2×C4—82no—
437C2×C4—611no—
438C2×C4—611no—
439C2×C4—611no—
440C2×C4—611no—
441C2×C4—1222no—
442C2×C4—4884no—
443C2×C4—4884no—
444C2×C4—4882no—
445C2×C4—2441no—
446C2×C4—2441no—
447C2×C4#1451975012yes—
448C2×C4D8×D6111yescharacteristic
449C2×C4#1451980412yes—
450C2×C4C2×D4×D6111yescharacteristic
451C8—1221no—
452C8—1221no—
453C8#1451975012yes—
454C8C2×D4×D6111yescharacteristic
455C8C2×#1175822211yescharacteristic
456C22—21no—
457C22—21no—
458C22—81no—
459C22—81no—
460C22—81no—
461C22—4888no—
462C22—4881no—
463C22—4881no—
464C22—4881no—
465C22—4882no—
466C22—4882no—
467C22—2444no—
468C22#1683995612yes—
469C22C2×D8×D6111yescharacteristic
470C4—81no—
471C4—82no—
472C4—612no—
473C4—1221no—
474C4—1221no—
475C4—1221no—
476C4—4881no—
477C4#1683995612yes—
478C4C2×#1451975011yescharacteristic
479C4C2×#1451980411yescharacteristic
480C2—22no—
481C2—161no—
482C2—9761no—
483C2—4884no—
484C2C2×#1683995611yescharacteristic
485C2#509×D6111yescharacteristic
486C2#2145895411yescharacteristic
subgroupG/H
centerC22C2×D8×D61
commutator, cosocleC2×C8×C61C24
FrattiniC2×C8C23×D61
FittingC61×#2139C2
socleC22×C61C22×D8
hypercenter#2139D61
hypocenterC61#33580
LCSG ▷ C2×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #2139

Complements

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

NH ≅ G/Ntype
1. C2×#16840200C2semidirect
2. C2×#16840197C2semidirect
3. #21456243C2semidirect
4. C2×#16839844C2semidirect
5. #21447877C2semidirect
6. #21447873C2semidirect
7. #21447863C2semidirect
8. #21447853C2semidirect
9. #21447574C2semidirect
10. #21447529C2semidirect
11. C61×#2139C2semidirect
24. #16840147C22semidirect
25. #16840145C22semidirect
27. #16840140C22semidirect
28. #16840137C22semidirect
36. #16839580C22semidirect
37. #16839580C22semidirect
38. #16839565C22semidirect
39. #16839562C22semidirect
43. C61×#358C22semidirect
44. C61×#357C22semidirect
58. C2×D488D4semidirect
236. Dic61#509semidirect
247. #2139D61semidirect
285. #358C2×D61semidirect
287. #357C2×D61semidirect
288. C61#33580semidirect

Maximal subgroups

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

subgroupindex
C2×#168402002
C2×#168401972
#214562432
C2×#168398442
#214478772
#214478732
#214478632
#214478532
#214475742
#214475292
C61×#21392
#3358061