Finite Group Databasebeta

← #30624309

Subgroups — #30624309

Order 15616.

642 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#21462599C211yesmaximal, characteristic, complemented
2#21462596C211yesmaximal, characteristic, complemented
3#21462222C212yesmaximal, complemented
4#21462221C212yesmaximal, complemented
5#21462220C212yesmaximal, complemented
6#21462219C212yesmaximal, complemented
7#21462175C211yesmaximal, characteristic, complemented
8C2×#16840677C211yesmaximal, characteristic, complemented
9D61⋊#359C211yesmaximal, characteristic, complemented
10#21462031C211yesmaximal, characteristic, complemented
11#21458954C211yesmaximal, characteristic
12#16840842—21no—
13#16840841—21no—
14C2×D61⋊C16C2211yescharacteristic
15#16840808—22no—
16#16840807—22no—
17#16840806C2212yescomplemented
18#16840806C2212yescomplemented
19#16840806C2212yescomplemented
20#16840804C2212yescomplemented
21C2×#14519848C2211yescharacteristic
22D61⋊#108C2211yescharacteristic
23#16840761—21no—
24#16840759—21no—
25#16840725C2211yescharacteristic
26#16840691C2212yescomplemented
27#16840690C2212yescomplemented
28#16840677C2211yescharacteristic, complemented
29#16840677C2211yescharacteristic, complemented
30#16840677C2212yescomplemented
31#16840677C2212yescomplemented
32#16840676C2211yescharacteristic, complemented
33#16840676C2211yescharacteristic, complemented
34#16840649C2212yescomplemented
35C16×#6923C2212yescomplemented
36C2×#14519800C2211yescharacteristic
37#135×D61C2211yescharacteristic
38#16840204C412yescomplemented
39#16840203C411yescharacteristic, complemented
40#16840200C411yescharacteristic, complemented
41#16840199C412yescomplemented
42#16840197C411yescharacteristic, complemented
43#16840195C2212yes—
44#16840193C2212yes—
45M32×D61C2211yescharacteristic
46C61×#510C411yescharacteristic, complemented
47#14519865—22no—
48#14519865—22no—
49#14519865—22no—
50#14519865—41no—
51#14519865—41no—
52#14519864—22no—
53#14519864—42no—
54C2×#11758213—21no—
55C2×#11758213—41no—
56D61⋊M16—21no—
57D61⋊M16—42no—
58D61⋊M16—41no—
59D61⋊M16D411yescharacteristic
60#14519856D411yescharacteristic
61D61⋊C16—21no—
62D61⋊C16C2311yescharacteristic
63D61⋊C16C2311yescharacteristic
64C2×#11758187—21no—
65#14519848—21no—
66#14519848C2311yescharacteristic
67#14519848C2311yescharacteristic
68#14519848C2312yes—
69#14519847—21no—
70#14519842—22no—
71#14519842—22no—
72#14519842—22no—
73#14519841—22no—
74#14519831D412yes—
75C8×#6923C2312yes—
76C2×#11758226—21no—
77#41×D61—21no—
78#14519800—21no—
79#14519800—21no—
80#14519800C2×C412yes—
81#14519800C2312yes—
82#14519800C2311yescharacteristic
83#14519799C2×C411yescharacteristic
84#14519798—21no—
85#14519797—21no—
86#14519796C2311yescharacteristic
87Q16×D61C2×C411yescharacteristic
88C2×#11758201—21no—
89SD16×D61—21no—
90C2×D488C2×C411yescharacteristic
91D8×D61C2×C411yescharacteristic
92C2×C8×D61C2311yescharacteristic
93#14519723C2×C412yes—
94#14519722C2×C412yes—
95#14519720C2×C412yes—
96#14519720C2×C412yes—
97D976C2×C412yes—
98#14519718C2×C412yes—
99#14519717C2×C411yescharacteristic
100#14519716C2×C412yes—
101C16×D61C2312yes—
102#135×C61C2×C411yescharacteristic
103C2×Q16×C61C2×C411yescharacteristic
104Q32×C61C2×C412yes—
105SD32×C61C2×C412yes—
106M32×C61C2×C411yescharacteristic
107#41×C61—21no—
108C2×Q8×C61—21no—
109#11758226—22no—
110#11758226—21no—
111#11758226—22no—
112#11758226—41no—
113#11758226—41no—
114Q8×D61—21no—
115#11758224—21no—
116#11758224—41no—
117D4×D61—21no—
118D4×D61—41no—
119#11758222—21no—
120#11758222—41no—
121C2×D244—21no—
122C2×D244—41no—
123C2×C4×D61—41no—
124C2×C4×D61—41no—
125C2×C4×D61C2×D411yescharacteristic
126C22⋊#6923—21no—
127#11758217—41no—
128#11758217—42no—
129#11758217D812yes—
130C2×#92420—41no—
131C2×#92420—42no—
132C4⋊#6923—21no—
133C4×#6923C2×D412yes—
134#11758213—22no—
135#11758213—21no—
136#11758213—21no—
137#11758213—41no—
138#11758213—42no—
139#11758213—42no—
140#11758213—42no—
141#11758213D811yescharacteristic
142#11758213D811yescharacteristic
143D61⋊C8—41no—
144D61⋊C8—42no—
145D61⋊C8—42no—
146D61⋊C8—42no—
147D61⋊C8C2×D412yes—
148Q16×C61—21no—
149Q16×C61C22×C412yes—
150Q16×C61C22×C411yescharacteristic
151SD16×C61—21no—
152D8×C61C22×C411yescharacteristic
153C2×C8×C61C22×C411yescharacteristic
154#11758202—21no—
155#11758201—22no—
156#11758201—21no—
157#11758201—22no—
158#11758200—21no—
159#11758199—21no—
160C2×#92418#4111yescharacteristic
161Dic244C22×C411yescharacteristic
162D488—21no—
163D488C22×C412yes—
164D488C22×C411yescharacteristic
165#11758190—21no—
166C8×D61C22×C411yescharacteristic
167C8×D61C2×D411yescharacteristic
168C8×D61#4111yescharacteristic
169C8×D61C2411yescharacteristic
170#11758187—21no—
171#11758187—21no—
172C16×C61C22×C412yes—
173#11758185C22×C412yes—
174C22×D61—41no—
175C22×D61—41no—
176C22×D61#13511yescharacteristic
177C2×#6923—22no—
178Q8×C61—22no—
179Q8×C61—21no—
180Q8×C61—41no—
181D4×C61—21no—
182D4×C61—41no—
183C2×C4×C61—41no—
184C2×C4×C61—41no—
185C2×C4×C61C4×D411yescharacteristic
186C22⋊D61—41no—
187C22⋊D61—41no—
188C22⋊D61—41no—
189C2×Dic61—41no—
190C2×Dic61C2×D811yescharacteristic
191D244—21no—
192D244—22no—
193D244—42no—
194D244—41no—
195D244—42no—
196D244—41no—
197C4×D61—41no—
198C4×D61—41no—
199C4×D61—41no—
200C4×D61—42no—
201C4×D61—42no—
202C4×D61C4×D411yescharacteristic
203C4×D61C2×D811yescharacteristic
204C4×D61#13511yescharacteristic
205C4×D61C22×D411yescharacteristic
206Dic122—21no—
207Dic122—41no—
208#92420—41no—
209#92420—41no—
210#92420—42no—
211#92420C2×D812yes—
212#92420C2×D812yes—
213C8×C61C4×D411yescharacteristic
214C8×C61C23×C411yescharacteristic
215#92418C4×D411yescharacteristic
216#92418C2×#4111yescharacteristic
217#33464—611nomaximal, Sylow
218C22×C61—41no—
219C22×C61C4×D811yescharacteristic
220C2×D61—41no—
221C2×D61—42no—
222C2×D61—41no—
223C2×D61—161no—
224C2×D61—161no—
225C2×D61C4×D811yescharacteristic
226C2×D61C2×#13511yescharacteristic
227#6923—42no—
228C4×C61—41no—
229C4×C61—42no—
230C4×C61C4×D811yescharacteristic
231C4×C61C2×C4×D411yescharacteristic
232Dic61—41no—
233Dic61C4×D811yescharacteristic
234Dic61C22×D811yescharacteristic
235#3414—611no—
236#2957—611no—
237#2957—611no—
238#2179—612no—
239#2179—612no—
240#2178—612no—
241#2178—612no—
242#2161—611no—
243C2×#359—611no—
244C2×#359—611no—
245#2108—611no—
246C2×C61—21no—
247C2×C61—81no—
248C2×C61C2×C4×D811yescharacteristic
249D61—21no—
250D61—21no—
251D61—82no—
252D61—81no—
253C2×#135—611no—
254C2×#135—611no—
255#568—1221no—
256#568—1221no—
257#510—611no—
258#510—612no—
259#510#692311yescharacteristic, complemented
260#509—611no—
261#509—612no—
262#509—611no—
263#508—612no—
264#508—612no—
265C2×M32—611no—
266C22×C16—611no—
267#444—1222no—
268#444—1222no—
269#443—612no—
270#443—612no—
271#443—612no—
272#443—612no—
273C2×#108—611no—
274C2×#108—611no—
275#421—1221no—
276#421—1221no—
277#405—611no—
278#368—612no—
279#368—612no—
280#359—611no—
281#359—611no—
282#359—612no—
283#359—611no—
284#359—611no—
285#359—612no—
286#346—612no—
287C4×C16—612no—
288C61#3346411yescharacteristic, complemented, Sylow
289C2×#41—1221no—
290C2×#41—1221no—
291#135—611no—
292#135—612no—
293#135—612no—
294#135—611no—
295#135—611no—
296#135—1221no—
297#135—1221no—
298#135—1221no—
299#135—1221no—
300#135C2×#692311yescharacteristic
301C2×Q16—611no—
302C2×Q16C2×#692311yescharacteristic
303C2×SD16—1221no—
304C2×SD16—1221no—
305C2×D8—611no—
306C2×D8—611no—
307#131—1222no—
308#131—1222no—
309#131—1222no—
310#131—1222no—
311#131—2442no—
312#131—2441no—
313#131—2441no—
314C2×M16—611no—
315C2×M16—1221no—
316C2×M16—1221no—
317C2×M16—2441no—
318C2×M16—2442no—
319C2×M16—2441no—
320C22×C8—611no—
321#117—611no—
322Q32—612no—
323Q32C2×#692312yes—
324SD32—612no—
325SD32—612no—
326SD32—612no—
327SD32C2×#692312yes—
328D16—612no—
329D16—612no—
330M32—611no—
331M32—612no—
332M32C2×#692311yescharacteristic
333C2×C16—612no—
334C2×C16—611no—
335C2×C16—611no—
336C2×C16—1221no—
337C2×C16—1221no—
338#108—611no—
339#108—611no—
340#108—612no—
341#108—1221no—
342#108—1221no—
343#104—1222no—
344#104—1222no—
345#104—1222no—
346#104—1222no—
347#97—612no—
348C4×C8—612no—
349#41—21no—
350#41—1221no—
351#41—1221no—
352#41—1222no—
353#41—1222no—
354#41—1221no—
355#41—2441no—
356#41—2441no—
357#41—2441no—
358#41—2441no—
359C2×Q8—21no—
360C2×Q8—1221no—
361C2×D4—1221no—
362C2×D4—1221no—
363C2×D4—2441no—
364C2×D4—2441no—
365C22×C4—611no—
366C22×C4—2441no—
367C22×C4—2441no—
368Q16—21no—
369Q16—611no—
370Q16—1221no—
371Q16C22×#692311yescharacteristic
372Q16C22×#692312yes—
373SD16—21no—
374SD16—1221no—
375SD16—1222no—
376SD16—1221no—
377SD16—1222no—
378SD16—1221no—
379D8—612no—
380D8—611no—
381D8—1221no—
382D8—1221no—
383D8C22×#692311yescharacteristic
384M16—611no—
385M16—611no—
386M16—612no—
387M16—1222no—
388M16—1221no—
389M16—1221no—
390M16—2442no—
391M16—2442no—
392M16—2442no—
393M16—2442no—
394M16—2441no—
395M16—2441no—
396C2×C8—612no—
397C2×C8—611no—
398C2×C8—611no—
399C2×C8—611no—
400C2×C8—611no—
401C2×C8—611no—
402C2×C8—2442no—
403C2×C8—2442no—
404C2×C8—2442no—
405C2×C8—2442no—
406C2×C8—2441no—
407C2×C8—2441no—
408C2×C8C22×#692311yescharacteristic
409C4⋊C4—1221no—
410C22⋊C4—1221no—
411C42—612no—
412C16—612no—
413C16—1221no—
414C16—1221no—
415C16C22×#692312yes—
416C23—611no—
417C23—2441no—
418C23—2441no—
419Q8—21no—
420Q8—22no—
421Q8—41no—
422Q8—1221no—
423Q8—2441no—
424D4—21no—
425D4—41no—
426D4—1221no—
427D4—1222no—
428D4—2441no—
429D4—2442no—
430D4—2442no—
431D4—2441no—
432D4—2441no—
433D4—2441no—
434D4—2441no—
435C2×C4—41no—
436C2×C4—41no—
437C2×C4—611no—
438C2×C4—611no—
439C2×C4—611no—
440C2×C4—611no—
441C2×C4—611no—
442C2×C4—1222no—
443C2×C4—2441no—
444C2×C4—2442no—
445C2×C4—2442no—
446C2×C4—2441no—
447C2×C4—2441no—
448C2×C4—2441no—
449C2×C4D4×#692311yescharacteristic
450C8—612no—
451C8—612no—
452C8—611no—
453C8—611no—
454C8—2441no—
455C8—2441no—
456C8—2442no—
457C8D4×#692311yescharacteristic
458C8C23×#692311yescharacteristic
459C22—41no—
460C22—611no—
461C22—611no—
462C22—9761no—
463C22—9761no—
464C22—2441no—
465C22—2442no—
466C22—2441no—
467C22D8×#692311yescharacteristic
468C4—41no—
469C4—42no—
470C4—611no—
471C4—611no—
472C4—2442no—
473C4—2441no—
474C4D8×#692311yescharacteristic
475C4C2×D4×#692311yescharacteristic
476C2—21no—
477C2—81no—
478C2—1221no—
479C2—1221no—
480C2—4882no—
481C2—4881no—
482C2C2×D8×#692311yescharacteristic
subgroupG/H
centerC2C2×D8×#6923
commutatorC8×C61C23×C4
FrattiniC8C23×#6923
FittingC61×#510C4
socleC2×C61C2×C4×D8
prime radical#21458954C2
cosocleC8×D61C24
hypercenter#510#6923
hypocenterC61#33464
LCSG ▷ C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ #510

Complements

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

NH ≅ G/Ntype
1. #21462599C2semidirect
2. #21462596C2semidirect
3. #21462222C2semidirect
4. #21462221C2semidirect
5. #21462220C2semidirect
6. #21462219C2semidirect
7. #21462175C2semidirect
8. C2×#16840677C2semidirect
9. D61⋊#359C2semidirect
10. #21462031C2semidirect
17. #16840806C22semidirect
18. #16840806C22semidirect
19. #16840806C22semidirect
20. #16840804C22semidirect
26. #16840691C22semidirect
27. #16840690C22semidirect
28. #16840677C22semidirect
29. #16840677C22semidirect
30. #16840677C22semidirect
31. #16840677C22semidirect
32. #16840676C22semidirect
33. #16840676C22semidirect
34. #16840649C22semidirect
35. C16×#6923C22semidirect
38. #16840204C4semidirect
39. #16840203C4semidirect
40. #16840200C4semidirect
41. #16840199C4semidirect
42. #16840197C4semidirect
46. C61×#510C4semidirect
259. #510#6923semidirect
288. C61#33464semidirect

Maximal subgroups

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

subgroupindex
#214625992
#214625962
#214622222
#214622212
#214622202
#214622192
#214621752
C2×#168406772
D61⋊#3592
#214620312
#214589542
#3346461