Finite Group Databasebeta

← #29597402

Subgroups — #29597402

Order 15616.

510 conjugacy classes of subgroups.

The subgroup lattice has 466 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×M32×D61C211yesmaximal, characteristic, complemented
2#21455396C211yesmaximal, characteristic
3C2×#16839572C211yesmaximal, characteristic, complemented
4#21445841C211yesmaximal, characteristic, complemented
5#21443926C211yesmaximal, characteristic, complemented
6#21443925C211yesmaximal, characteristic, complemented
7C2×C61×#360C211yesmaximal, characteristic, complemented
8C22×C8×D61C2211yescharacteristic
9#16840269—21no—
10C2×#14519717C2211yescharacteristic
11C2×#14519716—21no—
12M32×D61—22no—
13M32×D61—22no—
14C2×C16×D61—21no—
15#16840000C411yescharacteristic, complemented
16#16840000C411yescharacteristic, complemented
17#16839995C411yescharacteristic, complemented
18#16839995C411yescharacteristic, complemented
19#16839988—21no—
20#16839988—21no—
21#16839800C2211yescharacteristic
22C2×#14519709C2211yescharacteristic
23#16839758—21no—
24#16839619—21no—
25#16839572—22no—
26#16839524—21no—
27C2×#135×C61C2211yescharacteristic
28C2×M32×C61C2211yescharacteristic
29C2×#106×C61C2211yescharacteristic
30C61×#360—22no—
31C22×C4×D61D411yescharacteristic
32C22×#92418D411yescharacteristic
33C2×C8×D61—21no—
34C2×C8×D61—21no—
35C2×C8×D61—21no—
36C2×C8×D61—21no—
37C2×C8×D61C2×C411yescharacteristic
38C2×C8×D61C2×C411yescharacteristic
39C2×C8×D61D411yescharacteristic
40C2×C8×D61D411yescharacteristic
41#14519758—41no—
42#14519753—21no—
43#14519753—21no—
44#14519748—21no—
45#14519748—21no—
46#14519745—41no—
47C4×C22⋊D61—41no—
48C4×C22⋊D61—41no—
49#14519736—21no—
50C2×C4⋊Dic61—21no—
51C2×#11758198—41no—
52#14519717—21no—
53#14519717D412yescomplemented
54#14519716—24no—
55C2×#11758185—21no—
56C16×D61—24no—
57#14519711C2×C411yescharacteristic
58#14519711C2×C411yescharacteristic
59#14519709—21no—
60#14519709—21no—
61#14519709—21no—
62#14519701—21no—
63#14519701—21no—
64#14519698—21no—
65#14519698—21no—
66#14519684—41no—
67C2×#41×C61—21no—
68#135×C61—21no—
69#135×C61—21no—
70#135×C61—21no—
71#135×C61—21no—
72C2×Q16×C61C2×C411yescharacteristic
73C2×SD16×C61—21no—
74C2×D8×C61C2×C411yescharacteristic
75C22×C8×C61C2311yescharacteristic
76C2×C4⋊C4×C61—21no—
77M32×C61—21no—
78M32×C61D412yescomplemented
79C2×C16×C61—21no—
80#106×C61—21no—
81#106×C61—21no—
82C23×D61D811yescharacteristic
83#41×C61—41no—
84#41×C61—41no—
85#41×C61—41no—
86#41×C61—41no—
87C2×Q8×C61—21no—
88C2×D4×C61—21no—
89C2×D4×C61—41no—
90C22×C4×C61—41no—
91C22×C4×C61—41no—
92C22×C4×C61C2×D411yescharacteristic
93C2×C22⋊D61—41no—
94C2×C22⋊D61—41no—
95C22×Dic61—41no—
96C22×Dic61D811yescharacteristic
97C2×C4×D61—21no—
98C2×C4×D61—21no—
99C2×C4×D61—21no—
100C2×C4×D61—21no—
101C2×C4×D61C22⋊C411yescharacteristic
102C2×C4×D61C22⋊C411yescharacteristic
103C2×C4×D61SD1611yescharacteristic
104C2×C4×D61SD1611yescharacteristic
105Q16×C61—21no—
106Q16×C61—21no—
107SD16×C61—41no—
108SD16×C61—41no—
109D8×C61—21no—
110D8×C61—21no—
111C2×C8×C61C22×C411yescharacteristic
112C2×C8×C61C2×D411yescharacteristic
113C2×C8×C61C2×D411yescharacteristic
114C2×C8×C61C2×D411yescharacteristic
115C2×C8×C61#4111yescharacteristic
116C2×C8×C61#4111yescharacteristic
117C4⋊C4×C61—41no—
118C4⋊C4×C61—41no—
119C22⋊Dic61—41no—
120C22⋊Dic61—41no—
121C22⋊Dic61—41no—
122#11758198—41no—
123#11758198—41no—
124#11758198—82no—
125C4⋊Dic61—21no—
126C4⋊Dic61—21no—
127C4⋊Dic61—41no—
128C4⋊Dic61—41no—
129#11758196—41no—
130#11758196—41no—
131C4×Dic61—41no—
132C2×#92418—21no—
133C2×#92418—21no—
134C2×#92418C22⋊C411yescharacteristic
135C2×#92418C22⋊C411yescharacteristic
136C8×D61—21no—
137C8×D61—21no—
138C8×D61—21no—
139C8×D61—21no—
140C8×D61—21no—
141C8×D61—21no—
142C8×D61—21no—
143C8×D61—21no—
144C16×C61—22no—
145#11758185—22no—
146C23×C61—41no—
147C23×C61C2×D811yescharacteristic
148C22×D61—21no—
149C22×D61—21no—
150C22×D61—22no—
151C22×D61—41no—
152C22×D61#10211yescharacteristic
153C22×D61#10211yescharacteristic
154Q8×C61—41no—
155Q8×C61—41no—
156D4×C61—41no—
157D4×C61—41no—
158D4×C61—81no—
159D4×C61—81no—
160C2×C4×C61—41no—
161C2×C4×C61—81no—
162C2×C4×C61—81no—
163C2×C4×C61—81no—
164C2×C4×C61—81no—
165C2×C4×C61—81no—
166C2×C4×C61C2×C22⋊C411yescharacteristic
167C2×C4×C61#12111yescharacteristic
168C2×C4×C61#12111yescharacteristic
169C2×C4×C61C2×SD1611yescharacteristic
170C2×C4×C61#13511yescharacteristic
171C2×C4×C61#13511yescharacteristic
172C22⋊D61—82no—
173C22⋊D61—82no—
174C2×Dic61—21no—
175C2×Dic61—21no—
176C2×Dic61—41no—
177C2×Dic61—41no—
178C2×Dic61—81no—
179C2×Dic61—81no—
180C2×Dic61—81no—
181C2×Dic61#10211yescharacteristic
182C2×Dic61#10211yescharacteristic
183C4×D61—21no—
184C4×D61—21no—
185C4×D61—21no—
186C4×D61—21no—
187C4×D61—21no—
188C4×D61—21no—
189C4×D61—21no—
190C4×D61—21no—
191C8×C61C4×D411yescharacteristic
192C8×C61C4×D411yescharacteristic
193C8×C61#12011yescharacteristic
194C8×C61#12311yescharacteristic
195#92418—21no—
196#92418—21no—
197#13065—611nomaximal, Sylow
198C22×C61—21no—
199C22×C61—21no—
200C22×C61—81no—
201C22×C61—81no—
202C22×C61—81no—
203C22×C61C2×#10211yescharacteristic
204C22×C61#46611yescharacteristic
205C22×C61#46611yescharacteristic
206C2×D61—21no—
207C2×D61—21no—
208C2×D61—21no—
209C2×D61—21no—
210C2×D61—21no—
211C2×D61—42no—
212C2×D61—42no—
213C2×D61#36012yescomplemented
214C4×C61—81no—
215C4×C61—161no—
216C4×C61#38611yescharacteristic
217C4×C61#41611yescharacteristic
218C4×C61#46511yescharacteristic
219C4×C61#46511yescharacteristic
220Dic61—21no—
221Dic61—21no—
222Dic61—81no—
223Dic61—81no—
224Dic61—161no—
225C22×M32—611no—
226#3050—611no—
227C2×#360—611no—
228C2×#360D6111yescharacteristic, complemented
229#1807—611no—
230#1386—611no—
231#1386—611no—
232C2×C61—21no—
233C2×C61—21no—
234C2×C61—161no—
235C2×C61#189311yescharacteristic
236C2×C61C2×#36011yescharacteristic
237C2×C61#214511yescharacteristic
238D61—22no—
239D61—41no—
240C2×#135C2×D6111yescharacteristic
241C23×C8—611no—
242#525—1221no—
243C2×M32—611no—
244C2×M32—1221no—
245C2×M32—1222no—
246C2×M32—1222no—
247C2×M32C2×D6111yescharacteristic
248C22×C16—1221no—
249#467—611no—
250#467—611no—
251#466—611no—
252#466—611no—
253#465—1221no—
254#465—1221no—
255#427—611no—
256C2×#106—611no—
257C2×#106C2×D6111yescharacteristic
258#416—1221no—
259#380—1221no—
260#360—22no—
261#360—1222no—
262#340—1221no—
263C61#1306511yescharacteristic, complemented, Sylow
264C2×#41—21no—
265C23×C4—611no—
266#135—21no—
267#135—21no—
268#135—21no—
269#135—21no—
270C2×Q16C4×D6111yescharacteristic
271C2×SD16—21no—
272C2×D8C4×D6111yescharacteristic
273C22×C8—611no—
274C22×C8—611no—
275C22×C8—611no—
276C22×C8—611no—
277C22×C8—611no—
278C22×C8—1221no—
279C22×C8—1221no—
280C22×C8—1221no—
281C22×C8—1221no—
282C22×C8C22×D6111yescharacteristic
283#123—2441no—
284C22⋊Q8—1221no—
285C22⋊Q8—1221no—
286#121—1221no—
287#121—1221no—
288#120—2441no—
289C4×D4—2441no—
290C4×D4—2441no—
291#117—1221no—
292C2×C4⋊C4—21no—
293C2×C4⋊C4—1221no—
294C2×C22⋊C4—2441no—
295M32—21no—
296M32—612no—
297M32—1224no—
298M32—1221no—
299M32C22⋊D6112yescomplemented
300C2×C16—21no—
301C2×C16—1224no—
302C2×C16—1221no—
303#107—611no—
304#107—611no—
305#106—21no—
306#106—21no—
307#106—1221no—
308#106—1221no—
309#106—1221no—
310#103—1221no—
311#103—1221no—
312#102—1221no—
313#102—1221no—
314#95—2441no—
315C24—611no—
316#41—41no—
317#41—41no—
318#41—41no—
319#41—41no—
320C2×Q8—21no—
321C2×D4—21no—
322C2×D4—41no—
323C2×D4—2441no—
324C2×D4—2441no—
325C22×C4—41no—
326C22×C4—41no—
327C22×C4—611no—
328C22×C4—611no—
329C22×C4—611no—
330C22×C4—611no—
331C22×C4—611no—
332C22×C4—1221no—
333C22×C4—1221no—
334C22×C4—1221no—
335C22×C4—1221no—
336C22×C4—2441no—
337C22×C4D4×D6111yescharacteristic
338Q16—21no—
339Q16—21no—
340SD16—41no—
341SD16—41no—
342D8—21no—
343D8—21no—
344C2×C8—611no—
345C2×C8—611no—
346C2×C8—1221no—
347C2×C8—1221no—
348C2×C8—1221no—
349C2×C8—1221no—
350C2×C8—1221no—
351C2×C8—1221no—
352C2×C8—1221no—
353C2×C8—1221no—
354C2×C8—1221no—
355C2×C8—1221no—
356C2×C8C2×C4×D6111yescharacteristic
357C2×C8#1175822211yescharacteristic
358C2×C8D4×D6111yescharacteristic
359C2×C8D4×D6111yescharacteristic
360C2×C8#1175822411yescharacteristic
361C2×C8C2×C22⋊D6111yescharacteristic
362C4⋊C4—41no—
363C4⋊C4—41no—
364C4⋊C4—1221no—
365C4⋊C4—1221no—
366C4⋊C4—2441no—
367C4⋊C4—2441no—
368C4⋊C4—2441no—
369C4⋊C4—2441no—
370C22⋊C4—4882no—
371C22⋊C4—2441no—
372C22⋊C4—2441no—
373C22⋊C4—2441no—
374C22⋊C4—2441no—
375C22⋊C4—2441no—
376C42—2441no—
377C16—22no—
378C16—1222no—
379C23—41no—
380C23—611no—
381C23—611no—
382C23—1222no—
383C23—1221no—
384C23—1221no—
385C23—2441no—
386C23D8×D6111yescharacteristic
387Q8—41no—
388Q8—41no—
389D4—41no—
390D4—41no—
391D4—81no—
392D4—81no—
393D4—4882no—
394D4—4882no—
395C2×C4—41no—
396C2×C4—81no—
397C2×C4—81no—
398C2×C4—81no—
399C2×C4—81no—
400C2×C4—81no—
401C2×C4—611no—
402C2×C4—611no—
403C2×C4—1221no—
404C2×C4—1221no—
405C2×C4—1221no—
406C2×C4—1221no—
407C2×C4—1221no—
408C2×C4—1221no—
409C2×C4—1221no—
410C2×C4—1221no—
411C2×C4—1221no—
412C2×C4—1221no—
413C2×C4—4881no—
414C2×C4—4881no—
415C2×C4—4881no—
416C2×C4—2441no—
417C2×C4—2441no—
418C2×C4C22⋊C4×D6111yescharacteristic
419C2×C4#1451974811yescharacteristic
420C2×C4#1451975011yescharacteristic
421C2×C4SD16×D6111yescharacteristic
422C2×C4#1451979611yescharacteristic
423C2×C4#1451979811yescharacteristic
424C8—1221no—
425C8—1221no—
426C8#1451973711yescharacteristic
427C8C4×C22⋊D6111yescharacteristic
428C8#1451974511yescharacteristic
429C8#1451975911yescharacteristic
430C22—21no—
431C22—21no—
432C22—81no—
433C22—81no—
434C22—81no—
435C22—612no—
436C22—1221no—
437C22—1221no—
438C22—1221no—
439C22—1221no—
440C22—1221no—
441C22—2442no—
442C22—2442no—
443C22#102×D6111yescharacteristic
444C22#1683999511yescharacteristic
445C22#1683999711yescharacteristic
446C4—81no—
447C4—161no—
448C4—1221no—
449C4—1221no—
450C4—9761no—
451C4—4881no—
452C4—4881no—
453C4#1683963811yescharacteristic
454C4#1683975511yescharacteristic
455C4#1683998811yescharacteristic
456C4#1683999011yescharacteristic
457C2—21no—
458C2—21no—
459C2—161no—
460C2—1222no—
461C2—2441no—
462C2#2144624411yescharacteristic
463C2#360×D6111yescharacteristic
464C2#2144755311yescharacteristic
subgroupG/H
centerC22#102×D61
commutatorC2×C8×C61C22×C4
FrattiniC22×C8C22×D61
FittingC2×C61×#360C2
socleC22×C61C2×#102
prime radical#21455396C2
cosocleC22×C8×C61C23
hypercenterC2×#360D61
hypocenterC61#13065
LCSG ▷ C2×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ C2×#360

Complements

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

NH ≅ G/Ntype
1. C2×M32×D61C2semidirect
3. C2×#16839572C2semidirect
4. #21445841C2semidirect
5. #21443926C2semidirect
6. #21443925C2semidirect
7. C2×C61×#360C2semidirect
15. #16840000C4semidirect
16. #16840000C4semidirect
17. #16839995C4semidirect
18. #16839995C4semidirect
53. #14519717D4semidirect
78. M32×C61D4semidirect
213. C2×D61#360semidirect
228. C2×#360D61semidirect
263. C61#13065semidirect
299. M32C22⋊D61semidirect

Maximal subgroups

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

subgroupindex
C2×M32×D612
#214553962
C2×#168395722
#214458412
#214439262
#214439252
C2×C61×#3602
#1306561