Finite Group Databasebeta

← #29657811

Subgroups — #29657811

Order 15616.

1134 conjugacy classes of subgroups.

The subgroup lattice has 444 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21456834C212yesmaximal, complemented
2C2×#16840138C211yesmaximal, characteristic, complemented
3#21444884C214yesmaximal, complemented
4#21444878C212yesmaximal, complemented
5#21444873C212yesmaximal, complemented
6#21444533C211yesmaximal, characteristic, complemented
7#21444279C212yesmaximal, complemented
8C61×#3543C211yesmaximal, characteristic, complemented
9C22×#11758199—22no—
10C2×#14519774C2211yescharacteristic, complemented
11#16840152—22no—
12#16840138—22no—
13#16840138C2212yes—
14#16840138C2212yescomplemented
15#16840128—22no—
16#16839962C2214yescomplemented
17#16839957C2214yescomplemented
18#16839912—22no—
19#16839895—22no—
20#16839819C2212yescomplemented
21C2×C4×#92418C2211yescharacteristic, complemented
22#16839506C2212yescomplemented
23#16839506C2212yescomplemented
24Q8⋊#92418C2214yescomplemented
25D4⋊#92418C2214yescomplemented
26C61×#560—22no—
27C61×#559C2211yescharacteristic, complemented
28C61×#550C2212yescomplemented
29C61×#546—22no—
30D42×C61—22no—
31D42×C61C2211yescharacteristic, complemented
32C61×#540—22no—
33C61×#535—22no—
34C61×#534—22no—
35C2×#127×C61C2211yescharacteristic
36C61×#529C2212yes—
37C22×D244—21no—
38C22×D244—22no—
39C2×#11758201—24no—
40C2×#11758199—24no—
41C2×#11758199—24no—
42C2×#11758199—24no—
43C2×#11758199—48no—
44C22×#92418—21no—
45#14519774—22no—
46#14519774—21no—
47#14519774C2312yes—
48C4⋊#92418C2314yes—
49#14519697—24no—
50#14519697—24no—
51C22⋊#92418—22no—
52#14519688—22no—
53C4×#92418—21no—
54C4×#92418C2312yes—
55C2×#41×C61—22no—
56C22×D4×C61—22no—
57C22×D4×C61—22no—
58C22×D4×C61—22no—
59C22×D4×C61D412yes—
60#127×C61—22no—
61#127×C61—22no—
62#127×C61D412yes—
63#127×C61C2311yescharacteristic
64#127×C61C2311yescharacteristic
65#126×C61—22no—
66#125×C61D412yes—
67#124×C61—22no—
68#124×C61D412yes—
69#123×C61—22no—
70#123×C61—24no—
71#123×C61—22no—
72#123×C61—22no—
73C22⋊Q8×C61D412yes—
74#121×C61—24no—
75#121×C61—24no—
76#121×C61—24no—
77#121×C61—24no—
78#121×C61—22no—
79#121×C61—22no—
80#121×C61D412yes—
81#120×C61—22no—
82#120×C61—24no—
83#120×C61—24no—
84#120×C61—22no—
85C4×Q8×C61C2312yes—
86C4×D4×C61—22no—
87C4×D4×C61—22no—
88C4×D4×C61—22no—
89C4×D4×C61C2312yes—
90#117×C61—22no—
91C2×C22⋊C4×C61—22no—
92C2×C42×C61C2311yescharacteristic
93C24×C61—22no—
94C24×C61—22no—
95C23×D61—41no—
96#41×C61—84no—
97C2×Q8×C61C2×D412yes—
98C2×D4×C61—22no—
99C2×D4×C61—24no—
100C2×D4×C61—24no—
101C2×D4×C61—24no—
102C2×D4×C61—22no—
103C2×D4×C61—24no—
104C2×D4×C61—22no—
105C2×D4×C61—22no—
106C2×D4×C61—44no—
107C2×D4×C61—84no—
108C2×D4×C61—84no—
109C2×D4×C61—84no—
110C2×D4×C61C2×D412yes—
111C2×D4×C61C2×D412yes—
112C2×D4×C61C2×D412yes—
113C22×C4×C61—24no—
114C22×C4×C61—22no—
115C22×C4×C61—22no—
116C22×C4×C61C2×D412yes—
117C22×C4×C61C2×D411yescharacteristic
118C2×D244—24no—
119C2×D244—22no—
120C2×D244—44no—
121C2×D244—41no—
122C2×D244—42no—
123C2×D244—84no—
124C4⋊C4×C61—22no—
125C4⋊C4×C61—22no—
126C4⋊C4×C61—22no—
127C4⋊C4×C61—22no—
128C4⋊C4×C61C2×D412yes—
129C4⋊C4×C61C2×D412yes—
130C22⋊C4×C61—22no—
131C22⋊C4×C61—22no—
132C22⋊C4×C61—24no—
133C22⋊C4×C61—24no—
134C22⋊C4×C61—22no—
135C22⋊C4×C61—22no—
136C22⋊C4×C61—22no—
137C22⋊C4×C61—22no—
138C22⋊C4×C61—22no—
139C42×C61—22no—
140C42×C61C2×D412yes—
141C42×C61C2×D411yescharacteristic
142C42×C61C2411yescharacteristic
143#11758201—84no—
144#11758199—48no—
145#11758199—48no—
146#11758199—84no—
147C2×#92418—24no—
148C2×#92418—22no—
149C2×#92418—24no—
150C23×C61—22no—
151C23×C61—22no—
152C23×C61—22no—
153C23×C61—44no—
154C23×C61—84no—
155C23×C61—84no—
156C23×C61—82no—
157C23×C61#12011yescharacteristic
158C22×D61—42no—
159C22×D61—84no—
160C22×D61—82no—
161Q8×C61—24no—
162D4×C61—24no—
163D4×C61—42no—
164D4×C61—42no—
165D4×C61—44no—
166D4×C61—44no—
167D4×C61—44no—
168D4×C61—82no—
169D4×C61—84no—
170D4×C61—84no—
171D4×C61—84no—
172D4×C61—84no—
173C2×C4×C61—22no—
174C2×C4×C61—24no—
175C2×C4×C61—22no—
176C2×C4×C61—22no—
177C2×C4×C61—22no—
178C2×C4×C61—44no—
179C2×C4×C61—82no—
180C2×C4×C61—84no—
181C2×C4×C61#12012yes—
182C2×C4×C61#12011yescharacteristic
183C2×C4×C61C22×D411yescharacteristic
184C2×C4×C61C22×D412yes—
185D244—44no—
186D244—44no—
187D244—44no—
188D244—82no—
189D244—84no—
190#92418—24no—
191#92418—44no—
192#18682—611nomaximal, Sylow
193C22×C61—22no—
194C22×C61—42no—
195C22×C61—44no—
196C22×C61—42no—
197C22×C61—44no—
198C22×C61—42no—
199C22×C61—42no—
200C22×C61—42no—
201C22×C61—164no—
202C22×C61—164no—
203C22×C61#45312yes—
204C22×C61C2×#12011yescharacteristic
205C2×D61—84no—
206C2×D61—82no—
207C2×D61—164no—
208C4×C61—22no—
209C4×C61—21no—
210C4×C61—21no—
211C4×C61—42no—
212C4×C61—42no—
213C4×C61—42no—
214C4×C61#57614yes—
215#3543D6111yescharacteristic, complemented
216#3217—612no—
217C2×#493—611no—
218#1621—614no—
219#1620—612no—
220#1619—612no—
221#1555—611no—
222#1494—612no—
223C2×C61—22no—
224C2×C61—82no—
225C2×C61—82no—
226C2×C61—82no—
227C2×C61#300812yes—
228C2×C61C2×#45311yescharacteristic
229D61—162no—
230C22×D8—1222no—
231#560—22no—
232#559C2×D6111yescharacteristic, complemented
233#550C2×D6112yescomplemented
234#546—22no—
235D42—22no—
236D42C2×D6111yescharacteristic, complemented
237#540—22no—
238#535—22no—
239#534—22no—
240C2×#127—611no—
241C2×#127C2×D6111yescharacteristic
242#529C2×D6112yes—
243#496—1222no—
244#493—612no—
245#493—612no—
246#493—1222no—
247#490—1222no—
248#460—614no—
249#459—614no—
250#450—1222no—
251#447—1222no—
252#432—612no—
253C2×C4×C8—611no—
254#331—612no—
255#331—612no—
256Q8⋊C8—614no—
257D4⋊C8—614no—
258C61#1868211yescharacteristic, complemented, Sylow
259C2×#41—22no—
260C22×D4—22no—
261C22×D4—22no—
262C22×D4—22no—
263C22×D4—1222no—
264C22×D4—1221no—
265C22×D4C22⋊D6112yes—
266C2×SD16—1224no—
267C2×D8—1224no—
268C2×D8—1224no—
269C2×D8—1224no—
270C2×D8—2448no—
271C22×C8—1221no—
272#127—22no—
273#127—22no—
274#127—612no—
275#127—1222no—
276#127—1221no—
277#127C22⋊D6112yes—
278#127C22×D6111yescharacteristic
279#127C22×D6111yescharacteristic
280#126—22no—
281#125C22⋊D6112yes—
282#124—22no—
283#124C22⋊D6112yes—
284#123—22no—
285#123—24no—
286#123—22no—
287#123—22no—
288C22⋊Q8C22⋊D6112yes—
289#121—24no—
290#121—24no—
291#121—24no—
292#121—24no—
293#121—22no—
294#121—22no—
295#121C22⋊D6112yes—
296#120—22no—
297#120—24no—
298#120—24no—
299#120—22no—
300C4×Q8C22×D6112yes—
301C4×D4—22no—
302C4×D4—22no—
303C4×D4—22no—
304C4×D4C22×D6112yes—
305#117—22no—
306C2×C22⋊C4—22no—
307C2×C42C22×D6111yescharacteristic
308C4⋊C8—614no—
309#102—1224no—
310#102—1224no—
311C22⋊C8—1222no—
312#97—1222no—
313C4×C8—612no—
314C4×C8—1221no—
315C24—22no—
316C24—22no—
317C24—2441no—
318#41—84no—
319C2×Q8C2×C22⋊D6112yes—
320C2×D4—22no—
321C2×D4—24no—
322C2×D4—24no—
323C2×D4—24no—
324C2×D4—22no—
325C2×D4—22no—
326C2×D4—22no—
327C2×D4—24no—
328C2×D4—44no—
329C2×D4—84no—
330C2×D4—84no—
331C2×D4—84no—
332C2×D4—1224no—
333C2×D4—1222no—
334C2×D4—4884no—
335C2×D4—2444no—
336C2×D4—2442no—
337C2×D4—2441no—
338C2×D4C2×C22⋊D6112yes—
339C2×D4C2×C22⋊D6112yes—
340C2×D4C2×C22⋊D6112yes—
341C22×C4—24no—
342C22×C4—22no—
343C22×C4—22no—
344C22×C4C2×C22⋊D6112yes—
345C22×C4C2×C22⋊D6111yescharacteristic
346SD16—4884no—
347D8—4884no—
348D8—2448no—
349D8—2448no—
350C2×C8—1224no—
351C2×C8—1222no—
352C2×C8—1224no—
353C4⋊C4—22no—
354C4⋊C4—22no—
355C4⋊C4—22no—
356C4⋊C4—22no—
357C4⋊C4C2×C22⋊D6112yes—
358C4⋊C4C2×C22⋊D6112yes—
359C22⋊C4—22no—
360C22⋊C4—22no—
361C22⋊C4—24no—
362C22⋊C4—24no—
363C22⋊C4—22no—
364C22⋊C4—22no—
365C22⋊C4—22no—
366C22⋊C4—22no—
367C22⋊C4—22no—
368C42—22no—
369C42C2×C22⋊D6111yescharacteristic
370C42C2×C22⋊D6112yes—
371C42C23×D6111yescharacteristic
372C23—22no—
373C23—22no—
374C23—22no—
375C23—44no—
376C23—84no—
377C23—82no—
378C23—84no—
379C23—4884no—
380C23—4882no—
381C23—2442no—
382C23#1451974611yescharacteristic
383Q8—24no—
384D4—24no—
385D4—42no—
386D4—42no—
387D4—44no—
388D4—44no—
389D4—44no—
390D4—82no—
391D4—84no—
392D4—84no—
393D4—84no—
394D4—84no—
395D4—4884no—
396D4—4882no—
397D4—2444no—
398D4—2444no—
399D4—2444no—
400C2×C4—22no—
401C2×C4—24no—
402C2×C4—22no—
403C2×C4—22no—
404C2×C4—22no—
405C2×C4—44no—
406C2×C4—82no—
407C2×C4—84no—
408C2×C4#1451974611yescharacteristic
409C2×C4#1451974612yes—
410C2×C4C22×C22⋊D6111yescharacteristic
411C2×C4C22×C22⋊D6112yes—
412C8—1224no—
413C8—2444no—
414C22—22no—
415C22—42no—
416C22—42no—
417C22—42no—
418C22—42no—
419C22—44no—
420C22—42no—
421C22—44no—
422C22—164no—
423C22—164no—
424C22—9764no—
425C22—4882no—
426C22—4884no—
427C22#1683993012yes—
428C22C2×#1451974611yescharacteristic
429C4—21no—
430C4—21no—
431C4—22no—
432C4—42no—
433C4—42no—
434C4—42no—
435C4#1684056514yes—
436C2—22no—
437C2—82no—
438C2—82no—
439C2—82no—
440C2—9762no—
441C2#2145508712yes—
442C2C2×#1683993011yescharacteristic
subgroupG/H
centerC22C2×#14519746
commutator, cosocleC42×C61C24
FrattiniC42C23×D61
FittingC61×#3543C2
socleC22×C61C2×#120
hypercenter#3543D61
hypocenterC61#18682
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3543

Complements

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

NH ≅ G/Ntype
1. #21456834C2semidirect
2. C2×#16840138C2semidirect
3. #21444884C2semidirect
4. #21444878C2semidirect
5. #21444873C2semidirect
6. #21444533C2semidirect
7. #21444279C2semidirect
8. C61×#3543C2semidirect
10. C2×#14519774C22semidirect
14. #16840138C22semidirect
16. #16839962C22semidirect
17. #16839957C22semidirect
20. #16839819C22semidirect
21. C2×C4×#92418C22semidirect
22. #16839506C22semidirect
23. #16839506C22semidirect
24. Q8⋊#92418C22semidirect
25. D4⋊#92418C22semidirect
27. C61×#559C22semidirect
28. C61×#550C22semidirect
31. D42×C61C22semidirect
215. #3543D61semidirect
232. #559C2×D61semidirect
233. #550C2×D61semidirect
236. D42C2×D61semidirect
258. C61#18682semidirect

Maximal subgroups

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

subgroupindex
#214568342
C2×#168401382
#214448842
#214448782
#214448732
#214445332
#214442792
C61×#35432
#1868261