Finite Group Databasebeta

← #29665483

Subgroups — #29665483

Order 15616.

662 conjugacy classes of subgroups.

The subgroup lattice has 490 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21456947C211yesmaximal, characteristic, complemented
2#21455274C211yesmaximal, characteristic
3#21454930C211yesmaximal, characteristic, complemented
4#21445237C212yesmaximal, complemented
5#21445230C212yesmaximal, complemented
6#21445203C212yesmaximal, complemented
7#21445196C212yesmaximal, complemented
8#21444591C211yesmaximal, characteristic, complemented
9#21444497C211yesmaximal, characteristic, complemented
10C2×#16839511C211yesmaximal, characteristic, complemented
11C61×#3079C211yesmaximal, characteristic, complemented
12C2×#14519797—21no—
13#16840312C2211yescharacteristic
14#16840158C2212yes—
15#16840110C2212yes—
16#16840080—22no—
17#16840049—21no—
18#16840049—21no—
19#16839984—21no—
20#16839977—21no—
21#16839972C2211yescharacteristic
22#16839967C2211yescharacteristic
23#16839962C2211yescharacteristic
24#16839957C2211yescharacteristic
25Q8×#92418C2212yes—
26D4×#92418—22no—
27D4×#92418C2212yes—
28#16839815—21no—
29#16839815C2211yescharacteristic
30C2×C4⋊#92418—21no—
31C2×C4⋊#92418C2211yescharacteristic
32C2×C4⋊#92418C2211yescharacteristic
33#16839756—21no—
34#16839512C2212yes—
35#16839512C2212yes—
36#16839511C2212yes—
37#16839511C2212yes—
38#16839509C2212yes—
39#16839505C2212yes—
40C2×C4⋊Q8×C61C2211yescharacteristic
41C4×#41×C61C2211yescharacteristic
42C61×#477C2212yes—
43C61×#476C2212yes—
44C61×#475—21no—
45C61×#474—21no—
46C61×#428—21no—
47C61×#423C2211yescharacteristic
48C61×#417—21no—
49C2×#11758222—21no—
50#14519797—44no—
51C2×#11758202—21no—
52C2×#11758200—21no—
53C2×#11758201—21no—
54C2×#11758199—21no—
55C22×#92418—21no—
56C22×#92418—21no—
57C22×#92418—22no—
58#14519777C2311yescharacteristic
59#14519774C2311yescharacteristic
60#14519765—21no—
61#14519751—21no—
62#14519751—21no—
63C4×D244—21no—
64C4×D244—21no—
65#14519708—22no—
66#14519708—22no—
67C4⋊#92418—21no—
68C4⋊#92418—21no—
69C4⋊#92418—22no—
70C4⋊#92418D411yescharacteristic
71C4⋊#92418D411yescharacteristic
72C4⋊#92418C2311yescharacteristic
73C4⋊#92418C2311yescharacteristic
74C4⋊#92418C2312yes—
75#14519700—21no—
76#14519700—21no—
77#14519697—21no—
78#14519697—21no—
79#14519697—22no—
80#14519697—22no—
81C22⋊#92418—22no—
82C22⋊#92418D412yes—
83C4×#92418—22no—
84C4×#92418C2312yes—
85C2×#41×C61D411yescharacteristic
86C22×Q8×C61—21no—
87C2×M16×C61—21no—
88C4⋊Q8×C61—21no—
89C4⋊Q8×C61—21no—
90C4⋊Q8×C61—21no—
91C4⋊Q8×C61C2312yes—
92C4×Q8×C61D411yescharacteristic
93C4×Q8×C61C2311yescharacteristic
94C4×D4×C61—21no—
95C4×D4×C61—21no—
96C4×D4×C61D411yescharacteristic
97C4×D4×C61C2311yescharacteristic
98#117×C61—21no—
99#117×C61D411yescharacteristic
100C2×C4⋊C4×C61—21no—
101C2×C4⋊C4×C61—21no—
102C2×C42×C61—21no—
103C2×C42×C61C2311yescharacteristic
104#107×C61—22no—
105#106×C61—22no—
106C4⋊C8×C61—21no—
107C4⋊C8×C61C2312yes—
108#103×C61—22no—
109#102×C61—22no—
110#41×C61—22no—
111#41×C61SD1614yes—
112C2×Q8×C61—22no—
113C2×Q8×C61—41no—
114C2×Q8×C61—82no—
115C2×Q8×C61C2×D411yescharacteristic
116C2×D4×C61—21no—
117C2×D4×C61C2×D411yescharacteristic
118C22×C4×C61—21no—
119C22×C4×C61—21no—
120C22×C4×C61—21no—
121C22×C4×C61—41no—
122C22×C4×C61C2×D411yescharacteristic
123C22×C4×C61C2×D411yescharacteristic
124C22×C4×C61#4111yescharacteristic
125C2×C22⋊D61—41no—
126#11758222—42no—
127#11758222—42no—
128C2×D244—21no—
129C2×D244—21no—
130C2×D244—21no—
131C2×C4×D61—41no—
132C2×Dic122—21no—
133M16×C61—42no—
134C2×C8×C61—22no—
135C4⋊C4×C61—21no—
136C4⋊C4×C61—21no—
137C4⋊C4×C61—22no—
138C4⋊C4×C61—22no—
139C4⋊C4×C61—41no—
140C4⋊C4×C61—41no—
141C4⋊C4×C61C2×D411yescharacteristic
142C4⋊C4×C61C2×D411yescharacteristic
143C22⋊C4×C61—21no—
144C22⋊C4×C61—21no—
145C22⋊C4×C61—21no—
146C42×C61—21no—
147C42×C61—21no—
148C42×C61—21no—
149C42×C61C2×D411yescharacteristic
150C42×C61C2×D411yescharacteristic
151C42×C61#4111yescharacteristic
152C42×C61C2411yescharacteristic
153#11758202—42no—
154#11758201—42no—
155#11758200—42no—
156#11758199—42no—
157#11758198—41no—
158#11758198—41no—
159C4⋊Dic61—21no—
160C4⋊Dic61—21no—
161C2×#92418—22no—
162C2×#92418—21no—
163C2×#92418—21no—
164C2×#92418—42no—
165C2×#92418—82no—
166C2×#92418—81no—
167C2×#92418C2×D412yes—
168C2×#92418C2×D412yes—
169C23×C61—21no—
170C23×C61#12111yescharacteristic
171C22×D61—41no—
172Q8×C61—21no—
173Q8×C61—82no—
174Q8×C61—82no—
175Q8×C61C2×SD1612yes—
176D4×C61—24no—
177D4×C61—21no—
178D4×C61C2×SD1612yes—
179C2×C4×C61—21no—
180C2×C4×C61—21no—
181C2×C4×C61—21no—
182C2×C4×C61—24no—
183C2×C4×C61—21no—
184C2×C4×C61—21no—
185C2×C4×C61—41no—
186C2×C4×C61—41no—
187C2×C4×C61—41no—
188C2×C4×C61—42no—
189C2×C4×C61—81no—
190C2×C4×C61—82no—
191C2×C4×C61#12111yescharacteristic
192C2×C4×C61#12111yescharacteristic
193C2×C4×C61#12111yescharacteristic
194C2×C4×C61C2×SD1612yes—
195C2×C4×C61#13512yes—
196C2×C4×C61C22×D411yescharacteristic
197C2×C4×C61C22×D411yescharacteristic
198C2×C4×C61C2×#4111yescharacteristic
199C22⋊D61—82no—
200C2×Dic61—41no—
201D244—41no—
202D244—41no—
203D244—41no—
204D244—41no—
205D244—81no—
206C4×D61—82no—
207Dic122—41no—
208Dic122—41no—
209C8×C61—42no—
210#92418—22no—
211#92418—22no—
212#92418—41no—
213#92418—41no—
214#92418—42no—
215#19414—611nomaximal, Sylow
216C22×C61—21no—
217C22×C61—21no—
218C22×C61—22no—
219C22×C61—41no—
220C22×C61—41no—
221C22×C61#46512yes—
222C22×C61C2×#12111yescharacteristic
223C2×D61—81no—
224C2×D61—81no—
225C2×D61—81no—
226C4×C61—21no—
227C4×C61—22no—
228C4×C61—21no—
229C4×C61—21no—
230C4×C61—41no—
231C4×C61—41no—
232C4×C61—82no—
233C4×C61#46512yes—
234C4×C61C22×SD1611yescharacteristic
235C4×C61C2×#13511yescharacteristic
236C4×C61#57711yescharacteristic
237C4×C61#57811yescharacteristic
238Dic61—81no—
239#3227—611no—
240#3079D6111yescharacteristic, complemented
241#3035—611no—
242#2988—611no—
243#1678—612no—
244#1677—612no—
245#1672—612no—
246#1671—612no—
247#1570—611no—
248#1547—611no—
249C2×#333—611no—
250C2×C61—22no—
251C2×C61—42no—
252C2×C61#304611yescharacteristic
253C2×C61C2×#46511yescharacteristic
254C2×C61#306811yescharacteristic
255D61—161no—
256C2×#135—1221no—
257#532—611no—
258C2×C4⋊Q8C2×D6111yescharacteristic
259C4×#41C2×D6111yescharacteristic
260#498—612no—
261#486—612no—
262#481—1222no—
263#477C2×D6112yes—
264#476—1221no—
265#476—1221no—
266#476C2×D6112yes—
267#475—21no—
268#474—21no—
269#464—1221no—
270#463—1221no—
271#462—611no—
272#461—611no—
273#460—611no—
274#459—611no—
275C8×Q8—612no—
276C8×D4—612no—
277C8×D4—1222no—
278#431—611no—
279#431—1221no—
280#428—21no—
281#423C2×D6111yescharacteristic
282C2×C4⋊C8—611no—
283C2×C4⋊C8—611no—
284C2×C4⋊C8—1221no—
285#417—21no—
286#416—1221no—
287#334—612no—
288#334—612no—
289#333—612no—
290#333—612no—
291#332—612no—
292#331—612no—
293C61#1941411yescharacteristic, complemented, Sylow
294C2×#41—1221no—
295C2×#41C22⋊D6111yescharacteristic
296C22×Q8—21no—
297#135—2444no—
298C2×Q16—1221no—
299C2×SD16—1221no—
300C2×SD16—1221no—
301C2×D8—1221no—
302C2×M16—21no—
303C22×C8—1222no—
304C22×C8—1221no—
305C22×C8—1221no—
306C4⋊Q8—21no—
307C4⋊Q8—21no—
308C4⋊Q8—21no—
309C4⋊Q8—611no—
310C4⋊Q8C22×D6112yes—
311#127—611no—
312#124—1221no—
313#121—1221no—
314#121—1221no—
315C4×Q8C22⋊D6111yescharacteristic
316C4×Q8C22×D6111yescharacteristic
317C4×D4—21no—
318C4×D4—21no—
319C4×D4—1221no—
320C4×D4—1221no—
321C4×D4C22⋊D6111yescharacteristic
322C4×D4C22×D6111yescharacteristic
323#117—21no—
324#117C22⋊D6111yescharacteristic
325C2×C4⋊C4—21no—
326C2×C4⋊C4—21no—
327C2×C42—21no—
328C2×C42C22×D6111yescharacteristic
329#107—22no—
330#106—22no—
331#106—1222no—
332#106—1222no—
333C4⋊C8—21no—
334C4⋊C8—611no—
335C4⋊C8—611no—
336C4⋊C8—612no—
337C4⋊C8—611no—
338C4⋊C8—611no—
339C4⋊C8—1222no—
340C4⋊C8—1221no—
341C4⋊C8—1221no—
342C4⋊C8C22×D6112yes—
343#103—22no—
344#103—1221no—
345#103—1221no—
346#102—22no—
347#102—1222no—
348#102—1222no—
349#102—1221no—
350#102—1221no—
351C22⋊C8—612no—
352C22⋊C8—1222no—
353C4×C8—612no—
354C4×C8—1222no—
355#41—22no—
356#41—2442no—
357#41—2442no—
358#41#1175820114yes—
359C2×Q8—22no—
360C2×Q8—41no—
361C2×Q8—82no—
362C2×Q8—1221no—
363C2×Q8C2×C22⋊D6111yescharacteristic
364C2×D4—21no—
365C2×D4—1221no—
366C2×D4—1221no—
367C2×D4—1221no—
368C2×D4—2441no—
369C2×D4C2×C22⋊D6111yescharacteristic
370C22×C4—21no—
371C22×C4—21no—
372C22×C4—21no—
373C22×C4—41no—
374C22×C4—2441no—
375C22×C4D4×D6111yescharacteristic
376C22×C4#1175822411yescharacteristic
377C22×C4C2×C22⋊D6111yescharacteristic
378Q16—2442no—
379SD16—2442no—
380SD16—2442no—
381D8—2442no—
382M16—42no—
383C2×C8—22no—
384C2×C8—612no—
385C2×C8—612no—
386C2×C8—1222no—
387C2×C8—1221no—
388C2×C8—1221no—
389C2×C8—4882no—
390C2×C8—4881no—
391C2×C8—2442no—
392C4⋊C4—21no—
393C4⋊C4—21no—
394C4⋊C4—22no—
395C4⋊C4—22no—
396C4⋊C4—41no—
397C4⋊C4—41no—
398C4⋊C4—1221no—
399C4⋊C4—1221no—
400C4⋊C4C2×C22⋊D6111yescharacteristic
401C4⋊C4C2×C22⋊D6111yescharacteristic
402C22⋊C4—21no—
403C22⋊C4—21no—
404C22⋊C4—21no—
405C22⋊C4—2441no—
406C22⋊C4—2441no—
407C42—21no—
408C42—21no—
409C42—21no—
410C42D4×D6111yescharacteristic
411C42#1175822411yescharacteristic
412C42C2×C22⋊D6111yescharacteristic
413C42C23×D6111yescharacteristic
414C23—21no—
415C23—2441no—
416C23#1451974911yescharacteristic
417Q8—21no—
418Q8—82no—
419Q8—82no—
420Q8—2441no—
421Q8—2441no—
422Q8C2×#1175820112yes—
423D4—24no—
424D4—21no—
425D4—4881no—
426D4—4882no—
427D4—2441no—
428D4—2441no—
429D4—2441no—
430D4—2441no—
431D4C2×#1175820112yes—
432C2×C4—21no—
433C2×C4—24no—
434C2×C4—21no—
435C2×C4—21no—
436C2×C4—21no—
437C2×C4—21no—
438C2×C4—41no—
439C2×C4—41no—
440C2×C4—41no—
441C2×C4—42no—
442C2×C4—81no—
443C2×C4—82no—
444C2×C4—4882no—
445C2×C4—2441no—
446C2×C4#1451974911yescharacteristic
447C2×C4#1451974911yescharacteristic
448C2×C4#1451974911yescharacteristic
449C2×C4C2×#1175820112yes—
450C2×C4#1451979712yes—
451C2×C4C2×D4×D6111yescharacteristic
452C2×C4C22×C22⋊D6111yescharacteristic
453C2×C4C2×#1175822411yescharacteristic
454C8—42no—
455C8—1222no—
456C8—1222no—
457C8—2441no—
458C8—2441no—
459C8—2442no—
460C22—21no—
461C22—21no—
462C22—22no—
463C22—41no—
464C22—41no—
465C22—4881no—
466C22—4881no—
467C22—4881no—
468C22#1683999312yes—
469C22C2×#1451974911yescharacteristic
470C4—21no—
471C4—22no—
472C4—21no—
473C4—21no—
474C4—41no—
475C4—41no—
476C4—82no—
477C4—4881no—
478C4#1683999312yes—
479C4C22×#1175820111yescharacteristic
480C4C2×#1451979711yescharacteristic
481C4#1684057111yescharacteristic
482C4#1684057811yescharacteristic
483C2—22no—
484C2—42no—
485C2—9761no—
486C2#2145537311yescharacteristic
487C2C2×#1683999311yescharacteristic
488C2#2145554411yescharacteristic
subgroupG/H
centerC22C2×#14519749
commutator, cosocleC42×C61C24
FrattiniC42C23×D61
FittingC61×#3079C2
socleC22×C61C2×#121
prime radical#21455274C2
hypercenter#3079D61
hypocenterC61#19414
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3079

Complements

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

NH ≅ G/Ntype
1. #21456947C2semidirect
3. #21454930C2semidirect
4. #21445237C2semidirect
5. #21445230C2semidirect
6. #21445203C2semidirect
7. #21445196C2semidirect
8. #21444591C2semidirect
9. #21444497C2semidirect
10. C2×#16839511C2semidirect
11. C61×#3079C2semidirect
240. #3079D61semidirect
293. C61#19414semidirect

Maximal subgroups

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

subgroupindex
#214569472
#214552742
#214549302
#214452372
#214452302
#214452032
#214451962
#214445912
#214444972
C2×#168395112
C61×#30792
#1941461