Finite Group Databasebeta

← #29834416

Subgroups — #29834416

Order 15616.

706 conjugacy classes of subgroups.

The subgroup lattice has 454 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840197C211yesmaximal, characteristic, complemented
2#21456306C211yesmaximal, characteristic, complemented
3#21454736C211yesmaximal, characteristic, complemented
4#21447893C214yesmaximal, complemented
5#21447890C214yesmaximal, complemented
6#21447584C211yesmaximal, characteristic, complemented
7#21447568C211yesmaximal, characteristic, complemented
8C2×#16839576C211yesmaximal, characteristic, complemented
9C61×#3414C211yesmaximal, characteristic, complemented
10C2×#14519802—21no—
11C22×D488C2211yescharacteristic
12#16840529—21no—
13#16840326—21no—
14#16840197—22no—
15#16840197C2214yes—
16C2×#14519720—21no—
17C2×#14519718—21no—
18C2×#14519717C2211yescharacteristic
19#16840148—22no—
20#16840147C2212yescomplemented
21#16840137C2212yescomplemented
22#16839884—22no—
23#16839879C2214yescomplemented
24C2×#14519713C2211yescharacteristic
25#16839779—21no—
26#16839717C2211yescharacteristic
27#16839582C2214yescomplemented
28#16839578C2212yescomplemented
29#16839576C2214yescomplemented
30#16839575C2212yescomplemented
31C2×#135×C61C2211yescharacteristic
32C2×#135×C61C2211yescharacteristic
33C61×#510—21no—
34C61×#510C2212yescomplemented
35C61×#509—21no—
36C61×#509C2212yescomplemented
37C61×#508—22no—
38C2×M32×C61C2211yescharacteristic
39C22×D244—21no—
40#14519802—42no—
41#14519802—42no—
42C2×#11758201—22no—
43C2×D488—21no—
44C2×D488—21no—
45C2×D488—21no—
46C2×D488—21no—
47C2×D488—21no—
48C2×D488C2312yes—
49C2×#11758199—22no—
50#14519784—24no—
51#14519784—42no—
52C2×#11758194—21no—
53C2×#11758194—42no—
54C2×#11758194D411yescharacteristic
55#14519773—22no—
56#14519766—22no—
57#14519751—42no—
58#14519745—42no—
59#14519736D411yescharacteristic
60#14519720—24no—
61#14519718—24no—
62#14519717—21no—
63#14519717C2312yes—
64C2×#11758185—21no—
65#14519713—21no—
66#14519713C2312yes—
67#14519704—24no—
68#14519687D412yes—
69C8×Dic61C2312yes—
70C2×#41×C61—21no—
71C2×#41×C61—21no—
72#135×C61—21no—
73#135×C61—21no—
74#135×C61—21no—
75#135×C61—21no—
76#135×C61—21no—
77#135×C61—21no—
78#135×C61D412yescomplemented
79#135×C61C2312yes—
80C2×Q16×C61D411yescharacteristic, complemented
81C2×Q16×C61C2311yescharacteristic
82C2×SD16×C61—21no—
83C2×SD16×C61—21no—
84C2×D8×C61D411yescharacteristic, complemented
85C2×D8×C61C2311yescharacteristic
86C22×C8×C61C2311yescharacteristic
87Q32×C61—22no—
88SD32×C61—22no—
89SD32×C61—22no—
90D16×C61—22no—
91M32×C61—21no—
92M32×C61C2312yes—
93C2×C16×C61—21no—
94C23×D61—41no—
95#41×C61—22no—
96#41×C61—22no—
97#41×C61—41no—
98#41×C61—41no—
99#41×C61—41no—
100#41×C61—41no—
101#41×C61—41no—
102#41×C61—41no—
103C2×Q8×C61—21no—
104C2×Q8×C61—21no—
105C2×D4×C61—21no—
106C2×D4×C61—21no—
107C2×D4×C61—41no—
108C2×D4×C61—41no—
109C22×C4×C61—41no—
110C22×C4×C61—41no—
111C22×C4×C61C2×D411yescharacteristic
112C2×C22⋊D61—44no—
113C2×D244—22no—
114C2×D244—41no—
115C2×D244—41no—
116C2×D244—41no—
117C2×D244—41no—
118C2×D244—41no—
119Q16×C61—21no—
120Q16×C61—21no—
121Q16×C61—21no—
122Q16×C61C2×D412yes—
123SD16×C61—22no—
124SD16×C61—22no—
125SD16×C61—41no—
126SD16×C61—41no—
127D8×C61—21no—
128D8×C61—21no—
129D8×C61—21no—
130D8×C61C2×D412yes—
131C2×C8×C61C2×D411yescharacteristic
132C2×C8×C61C2×D411yescharacteristic
133C2×C8×C61C2×D411yescharacteristic
134C2×C8×C61#4111yescharacteristic
135C2×C8×C61#4111yescharacteristic
136C2×C8×C61C2411yescharacteristic
137C22⋊Dic61—21no—
138#11758201—44no—
139#11758199—44no—
140#11758198—44no—
141C4⋊Dic61—21no—
142C4×Dic61C2×D412yes—
143#11758194—22no—
144#11758194—41no—
145#11758194—44no—
146#11758194D812yes—
147#11758194D812yes—
148C2×#92418—41no—
149C2×#92418—44no—
150C2×#92418C2×D412yes—
151D488—22no—
152D488—22no—
153D488—41no—
154D488—41no—
155C16×C61—22no—
156#11758185—22no—
157C23×C61—41no—
158C23×C61—41no—
159C23×C61AGL(1,ℤ/8)11yescharacteristic
160C22×D61—42no—
161C22×D61—81no—
162C22×D61—81no—
163C22×D61—162no—
164Q8×C61—22no—
165Q8×C61—41no—
166Q8×C61—41no—
167Q8×C61—41no—
168D4×C61—22no—
169D4×C61—42no—
170D4×C61—42no—
171D4×C61—41no—
172D4×C61—41no—
173D4×C61—41no—
174D4×C61—81no—
175D4×C61—81no—
176C2×C4×C61—41no—
177C2×C4×C61—42no—
178C2×C4×C61—42no—
179C2×C4×C61—41no—
180C2×C4×C61—81no—
181C2×C4×C61—81no—
182C2×C4×C61#12111yescharacteristic
183C2×C4×C61#12111yescharacteristic
184C2×C4×C61C2×D811yescharacteristic
185C2×C4×C61C2×D811yescharacteristic
186C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
187C2×C4×C61C22×D411yescharacteristic
188C22⋊D61—164no—
189C2×Dic61—22no—
190D244—42no—
191D244—42no—
192D244—81no—
193D244—81no—
194C8×C61#12111yescharacteristic
195C8×C61#12111yescharacteristic
196C8×C61C22×D411yescharacteristic
197C8×C61C2×#4111yescharacteristic
198#92418—42no—
199#92418C2×D814yes—
200#33595—611nomaximal, Sylow
201C22×C61—41no—
202C22×C61—42no—
203C22×C61—82no—
204C22×C61—81no—
205C22×C61—161no—
206C22×C61#45911yescharacteristic
207C22×C61#45911yescharacteristic
208C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
209C2×D61—84no—
210C2×D61—82no—
211C2×D61—162no—
212C2×D61—162no—
213C4×C61—42no—
214C4×C61—81no—
215C4×C61#45911yescharacteristic
216C4×C61#45911yescharacteristic
217C4×C61C2×#12111yescharacteristic
218C4×C61C22×D811yescharacteristic
219Dic61—42no—
220#3414D6111yescharacteristic, complemented
221C2×#509—611no—
222#3155—611no—
223#2957—611no—
224#2213—614no—
225#2212—614no—
226#2153—611no—
227#2148—611no—
228C2×#361—611no—
229C2×C61—21no—
230C2×C61—21no—
231C2×C61—21no—
232C2×C61—82no—
233C2×C61—161no—
234C2×C61C2×#45911yescharacteristic
235D61—162no—
236C2×AGL(1,ℤ/8)—1221no—
237C2×#135C2×D6111yescharacteristic
238C2×#135C2×D6111yescharacteristic
239C22×D8—611no—
240#568—1221no—
241#535—1221no—
242#510—21no—
243#510C2×D6112yescomplemented
244#509—21no—
245#509—614no—
246#509—1222no—
247#509C2×D6112yescomplemented
248#508—22no—
249C2×SD32—1221no—
250C2×D16—1221no—
251C2×M32—611no—
252C2×M32C2×D6111yescharacteristic
253#496—1222no—
254#495—612no—
255#493—612no—
256#444—1222no—
257#443—614no—
258C2×#108—611no—
259#421—1221no—
260#405—611no—
261#364—614no—
262#362—612no—
263#361—612no—
264#361—614no—
265C61#3359511yescharacteristic, complemented, Sylow
266C2×#41—21no—
267C2×#41—21no—
268C22×D4—1221no—
269AGL(1,ℤ/8)—2442no—
270AGL(1,ℤ/8)—2442no—
271#135—21no—
272#135—21no—
273#135—21no—
274#135—21no—
275#135—21no—
276#135—21no—
277#135C22⋊D6112yescomplemented
278#135C22×D6112yes—
279C2×Q16C22⋊D6111yescharacteristic, complemented
280C2×Q16C22×D6111yescharacteristic
281C2×SD16—21no—
282C2×SD16—21no—
283C2×SD16—1222no—
284C2×D8—612no—
285C2×D8—1222no—
286C2×D8—1221no—
287C2×D8—1221no—
288C2×D8—1221no—
289C2×D8—1221no—
290C2×D8—1221no—
291C2×D8C22⋊D6111yescharacteristic, complemented
292C2×D8C22×D6111yescharacteristic
293#131—1224no—
294#131—2442no—
295C2×M16—611no—
296C2×M16—1221no—
297C2×M16—2442no—
298C22×C8C22×D6111yescharacteristic
299#127—1222no—
300#124—1222no—
301#121—2442no—
302#120—2442no—
303#117—611no—
304Q32—22no—
305SD32—22no—
306SD32—22no—
307SD32—1224no—
308D16—22no—
309D16—1224no—
310M32—21no—
311M32—612no—
312M32—1221no—
313M32C22×D6112yes—
314C2×C16—21no—
315C2×C16—1221no—
316#108—612no—
317#108—1221no—
318#104—1224no—
319#97—612no—
320C4×C8—612no—
321C24—2441no—
322#41—22no—
323#41—22no—
324#41—41no—
325#41—41no—
326#41—41no—
327#41—41no—
328#41—41no—
329#41—41no—
330C2×Q8—21no—
331C2×Q8—21no—
332C2×D4—21no—
333C2×D4—21no—
334C2×D4—41no—
335C2×D4—41no—
336C2×D4—1222no—
337C2×D4—2444no—
338C2×D4—2441no—
339C2×D4—2441no—
340C2×D4—2441no—
341C2×D4—2441no—
342C2×D4—2441no—
343C22×C4—41no—
344C22×C4—41no—
345C22×C4D4×D6111yescharacteristic
346Q16—21no—
347Q16—21no—
348Q16—21no—
349Q16C2×C22⋊D6112yes—
350SD16—22no—
351SD16—22no—
352SD16—41no—
353SD16—41no—
354SD16—2444no—
355D8—21no—
356D8—21no—
357D8—21no—
358D8—1222no—
359D8—1222no—
360D8—2444no—
361D8—2441no—
362D8—2441no—
363D8C2×C22⋊D6112yes—
364M16—612no—
365M16—612no—
366M16—1222no—
367M16—2444no—
368M16—2441no—
369C2×C8—612no—
370C2×C8—2444no—
371C2×C8—2441no—
372C2×C8D4×D6111yescharacteristic
373C2×C8#1175822411yescharacteristic
374C2×C8#1175822411yescharacteristic
375C2×C8C2×C22⋊D6111yescharacteristic
376C2×C8C2×C22⋊D6111yescharacteristic
377C2×C8C23×D6111yescharacteristic
378C4⋊C4—1221no—
379C22⋊C4—1221no—
380C22⋊C4—2444no—
381C42—612no—
382C16—22no—
383C16—1222no—
384C23—41no—
385C23—41no—
386C23—9762no—
387C23—4881no—
388C23—4881no—
389C23—2442no—
390C23#1451980111yescharacteristic
391Q8—22no—
392Q8—41no—
393Q8—41no—
394Q8—41no—
395D4—22no—
396D4—42no—
397D4—42no—
398D4—41no—
399D4—41no—
400D4—41no—
401D4—81no—
402D4—81no—
403D4—9764no—
404D4—4881no—
405D4—4881no—
406D4—2442no—
407D4—2442no—
408C2×C4—41no—
409C2×C4—42no—
410C2×C4—42no—
411C2×C4—41no—
412C2×C4—81no—
413C2×C4—81no—
414C2×C4—1222no—
415C2×C4#1451974911yescharacteristic
416C2×C4#1451974911yescharacteristic
417C2×C4D8×D6111yescharacteristic
418C2×C4D8×D6111yescharacteristic
419C2×C4#1451980111yescharacteristic
420C2×C4C2×D4×D6111yescharacteristic
421C8—614no—
422C8—2442no—
423C8#1451974911yescharacteristic
424C8#1451974911yescharacteristic
425C8C22×C22⋊D6111yescharacteristic
426C8C2×#1175822411yescharacteristic
427C22—41no—
428C22—42no—
429C22—82no—
430C22—81no—
431C22—161no—
432C22—9762no—
433C22—9762no—
434C22—4884no—
435C22—4882no—
436C22#1683995511yescharacteristic
437C22#1683995511yescharacteristic
438C22C2×#1451980111yescharacteristic
439C4—42no—
440C4—81no—
441C4—2442no—
442C4#1683995511yescharacteristic
443C4#1683995511yescharacteristic
444C4C2×#1451974911yescharacteristic
445C4C2×D8×D6111yescharacteristic
446C2—21no—
447C2—21no—
448C2—21no—
449C2—82no—
450C2—161no—
451C2—9762no—
452C2C2×#1683995511yescharacteristic
subgroupG/H
centerC2C2×#16839955
commutator, cosocleC2×C8×C61C24
FrattiniC2×C8C23×D61
FittingC61×#3414C2
socleC2×C61C2×#459
hypercenter#3414D61
hypocenterC61#33595
LCSG ▷ C2×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C22×C4 ◁ C22×C8 ◁ #3414

Complements

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

NH ≅ G/Ntype
1. C2×#16840197C2semidirect
2. #21456306C2semidirect
3. #21454736C2semidirect
4. #21447893C2semidirect
5. #21447890C2semidirect
6. #21447584C2semidirect
7. #21447568C2semidirect
8. C2×#16839576C2semidirect
9. C61×#3414C2semidirect
20. #16840147C22semidirect
21. #16840137C22semidirect
23. #16839879C22semidirect
27. #16839582C22semidirect
28. #16839578C22semidirect
29. #16839576C22semidirect
30. #16839575C22semidirect
34. C61×#510C22semidirect
36. C61×#509C22semidirect
78. #135×C61D4semidirect
80. C2×Q16×C61D4semidirect
84. C2×D8×C61D4semidirect
220. #3414D61semidirect
243. #510C2×D61semidirect
247. #509C2×D61semidirect
265. C61#33595semidirect
277. #135C22⋊D61semidirect
279. C2×Q16C22⋊D61semidirect
291. C2×D8C22⋊D61semidirect

Maximal subgroups

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

subgroupindex
C2×#168401972
#214563062
#214547362
#214478932
#214478902
#214475842
#214475682
C2×#168395762
C61×#34142
#3359561