Finite Group Databasebeta

← #29834406

Subgroups — #29834406

Order 15616.

696 conjugacy classes of subgroups.

The subgroup lattice has 428 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21458953C212yesmaximal, complemented
2#21456247C211yesmaximal, characteristic, complemented
3#21447900C212yesmaximal, complemented
4#21447895C212yesmaximal, complemented
5#21447888C214yesmaximal, complemented
6C2×#16839583C211yesmaximal, characteristic, complemented
7#21447566C212yesmaximal, complemented
8C2×C61×#443C211yesmaximal, characteristic, complemented
9C2×#14519799—21no—
10C2×#14519799C2212yes—
11#16840312—21no—
12#16840203—22no—
13#16840202C2214yes—
14#16840198—22no—
15#16840197C2214yes—
16#16840192—24no—
17C2×#14519717C2212yes—
18#16840146—21no—
19#16840146C2212yescomplemented
20#16840142C2211yescharacteristic, complemented
21#16840139C2211yescharacteristic, complemented
22#16840135—21no—
23#16839583C2212yescomplemented
24#16839583C2212yescomplemented
25#16839577C2214yescomplemented
26#16839574C2214yescomplemented
27C2×#135×C61C2211yescharacteristic
28C2×#131×C61—21no—
29C61×#443—21no—
30C61×#443—21no—
31C61×#443C2212yes—
32C61×#443C2212yes—
33C2×#108×C61C2211yescharacteristic
34C2×#104×C61—21no—
35C2×C4×C8×C61C2211yescharacteristic
36C2×#11758222—22no—
37#14519799—22no—
38#14519799—22no—
39#14519799—22no—
40#14519799—22no—
41#14519799—41no—
42#14519799—41no—
43#14519799—41no—
44#14519799—41no—
45C2×Dic244—21no—
46C2×Dic244C2312yes—
47C2×#11758190—22no—
48C2×#11758190—22no—
49C2×D488—21no—
50C2×D488C2312yes—
51#14519777—21no—
52#14519774—21no—
53#14519765—22no—
54#14519751—42no—
55C4×D244—42no—
56#14519723—24no—
57#14519721—24no—
58#14519720—24no—
59#14519718—24no—
60#14519717—22no—
61#14519717C2314yes—
62C2×#11758185—22no—
63C2×#41×C61—21no—
64#135×C61—21no—
65#135×C61—21no—
66#135×C61D412yescomplemented
67#135×C61C2312yes—
68C2×Q16×C61D411yescharacteristic, complemented
69C2×SD16×C61—21no—
70C2×D8×C61D411yescharacteristic, complemented
71#131×C61—22no—
72#131×C61—22no—
73#131×C61—41no—
74#131×C61—41no—
75C2×M16×C61—21no—
76C2×M16×C61—41no—
77C22×C8×C61—41no—
78C22×C8×C61D411yescharacteristic
79C22×C8×C61C2311yescharacteristic
80C2×C42×C61D411yescharacteristic
81#108×C61—21no—
82#108×C61C2312yes—
83#104×C61—22no—
84#104×C61—22no—
85C4×C8×C61D411yescharacteristic
86C4×C8×C61D411yescharacteristic
87C4×C8×C61C2311yescharacteristic
88C4×C8×C61C2311yescharacteristic
89#41×C61—22no—
90#41×C61—22no—
91#41×C61—41no—
92#41×C61—41no—
93C2×Q8×C61—21no—
94C2×D4×C61—21no—
95C2×D4×C61—41no—
96C22×C4×C61—21no—
97C22×C4×C61—41no—
98C22×C4×C61C2×D411yescharacteristic
99C2×C22⋊D61—42no—
100#11758222—42no—
101#11758222—42no—
102#11758222—42no—
103#11758222—42no—
104C2×D244—22no—
105C2×D244—42no—
106C2×C4×D61—42no—
107C2×Dic122—22no—
108Q16×C61—21no—
109Q16×C61C2×D412yes—
110SD16×C61—22no—
111SD16×C61—22no—
112D8×C61—21no—
113D8×C61C2×D412yes—
114M16×C61—22no—
115M16×C61—41no—
116M16×C61—42no—
117M16×C61—42no—
118C2×C8×C61—41no—
119C2×C8×C61—42no—
120C2×C8×C61—42no—
121C2×C8×C61D811yescharacteristic
122C2×C8×C61D811yescharacteristic
123C2×C8×C61D811yescharacteristic
124C2×C8×C61D811yescharacteristic
125C2×C8×C61C2×D411yescharacteristic
126C2×C8×C61C2×D411yescharacteristic
127C2×C8×C61C2×D411yescharacteristic
128C2×C8×C61C2×D411yescharacteristic
129C2×C8×C61C2×D411yescharacteristic
130C2×C8×C61#4111yescharacteristic
131C2×C8×C61#4111yescharacteristic
132C2×C8×C61C2411yescharacteristic
133C42×C61—21no—
134C42×C61C2×D411yescharacteristic
135C42×C61C2×D411yescharacteristic
136#11758198—44no—
137C4⋊Dic61—42no—
138Dic244—22no—
139Dic244—22no—
140Dic244—41no—
141Dic244—41no—
142D488—22no—
143D488—22no—
144D488—41no—
145D488—41no—
146#11758190—42no—
147#11758190—42no—
148#11758190—42no—
149#11758190—42no—
150#11758185—24no—
151C23×C61—41no—
152C23×C61AGL(1,ℤ/8)11yescharacteristic
153C22×D61—42no—
154Q8×C61—22no—
155Q8×C61—41no—
156D4×C61—22no—
157D4×C61—42no—
158D4×C61—42no—
159D4×C61—41no—
160C2×C4×C61—21no—
161C2×C4×C61—21no—
162C2×C4×C61—42no—
163C2×C4×C61—41no—
164C2×C4×C61—42no—
165C2×C4×C61—42no—
166C2×C4×C61#12111yescharacteristic
167C2×C4×C61#12111yescharacteristic
168C2×C4×C61C2×D811yescharacteristic
169C2×C4×C61C2×D811yescharacteristic
170C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
171C2×C4×C61C22×D411yescharacteristic
172C22⋊D61—82no—
173C22⋊D61—82no—
174C2×Dic61—42no—
175D244—42no—
176D244—42no—
177D244—84no—
178C4×D61—82no—
179C4×D61—82no—
180Dic122—42no—
181Dic122—42no—
182C8×C61—42no—
183C8×C61#12111yescharacteristic
184C8×C61#12111yescharacteristic
185C8×C61C2×D811yescharacteristic
186C8×C61C2×D811yescharacteristic
187C8×C61C2×D811yescharacteristic
188C8×C61C2×D811yescharacteristic
189C8×C61C22×D411yescharacteristic
190C8×C61C2×#4111yescharacteristic
191#33594—611nomaximal, Sylow
192C22×C61—41no—
193C22×C61—42no—
194C22×C61—82no—
195C22×C61#45911yescharacteristic
196C22×C61#45911yescharacteristic
197C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
198C2×D61—84no—
199C2×D61—82no—
200C4×C61—22no—
201C4×C61—41no—
202C4×C61—42no—
203C4×C61#45911yescharacteristic
204C4×C61#45911yescharacteristic
205C4×C61C2×#12111yescharacteristic
206C4×C61C22×D811yescharacteristic
207Dic61—82no—
208#3414—612no—
209#3147—611no—
210C2×#443D6111yescharacteristic, complemented
211#2214—612no—
212#2213—612no—
213#2212—614no—
214C2×#364—611no—
215#2148—612no—
216C2×C61—21no—
217C2×C61—21no—
218C2×C61—21no—
219C2×C61—82no—
220C2×C61C2×#45911yescharacteristic
221D61—162no—
222C2×#135—612no—
223C2×#135—1221no—
224C2×#135C2×D6111yescharacteristic
225C2×#131—21no—
226#532—1221no—
227#510—614no—
228#510—1222no—
229#509—614no—
230#509—1222no—
231#508—1224no—
232C2×M32—612no—
233#495—612no—
234#495—1221no—
235#494—611no—
236#493—611no—
237#492—1221no—
238#443—21no—
239#443—21no—
240#443C2×D6112yes—
241#443C2×D6112yes—
242C2×#108C2×D6111yescharacteristic
243C2×#104—21no—
244C2×C4×C8C2×D6111yescharacteristic
245#364—612no—
246#364—612no—
247#362—614no—
248#361—614no—
249C61#3359411yescharacteristic, complemented, Sylow
250C2×#41—21no—
251C2×#41—1222no—
252#135—21no—
253#135—21no—
254#135—1222no—
255#135—1222no—
256#135—1222no—
257#135—1222no—
258#135—2441no—
259#135—2441no—
260#135—2441no—
261#135—2441no—
262#135D24412yescomplemented
263#135C22×D6112yes—
264C2×Q16—612no—
265C2×Q16—1221no—
266C2×Q16D24411yescharacteristic, complemented
267C2×SD16—21no—
268C2×SD16—1222no—
269C2×SD16—1222no—
270C2×D8—612no—
271C2×D8—1221no—
272C2×D8D24411yescharacteristic, complemented
273#131—22no—
274#131—22no—
275#131—41no—
276#131—41no—
277C2×M16—21no—
278C2×M16—41no—
279C22×C8—41no—
280C22×C8C22⋊D6111yescharacteristic
281C22×C8C22×D6111yescharacteristic
282C4⋊Q8—1221no—
283#127—1221no—
284#124—1222no—
285#121—2442no—
286C4×D4—2442no—
287C2×C42C22⋊D6111yescharacteristic
288Q32—1224no—
289SD32—1224no—
290SD32—1224no—
291D16—1224no—
292M32—614no—
293M32—1222no—
294C2×C16—1222no—
295#108—21no—
296#108C22×D6112yes—
297#104—22no—
298#104—22no—
299C4×C8C22⋊D6111yescharacteristic
300C4×C8C22⋊D6111yescharacteristic
301C4×C8C22×D6111yescharacteristic
302C4×C8C22×D6111yescharacteristic
303#41—22no—
304#41—22no—
305#41—41no—
306#41—41no—
307#41—2442no—
308#41—2442no—
309#41—2442no—
310#41—2442no—
311C2×Q8—21no—
312C2×Q8—1222no—
313C2×D4—21no—
314C2×D4—41no—
315C2×D4—1222no—
316C2×D4—2442no—
317C2×D4—2442no—
318C22×C4—21no—
319C22×C4—41no—
320C22×C4—2442no—
321C22×C4C2×C22⋊D6111yescharacteristic
322Q16—21no—
323Q16—1222no—
324Q16—1222no—
325Q16—2441no—
326Q16—2441no—
327Q16C2×D24412yes—
328SD16—22no—
329SD16—22no—
330SD16—2442no—
331SD16—2442no—
332SD16—2442no—
333SD16—2442no—
334D8—21no—
335D8—1222no—
336D8—1222no—
337D8—2441no—
338D8—2441no—
339D8C2×D24412yes—
340M16—22no—
341M16—41no—
342M16—42no—
343M16—42no—
344C2×C8—41no—
345C2×C8—42no—
346C2×C8—42no—
347C2×C8#1175819911yescharacteristic
348C2×C8#1175819911yescharacteristic
349C2×C8#1175819911yescharacteristic
350C2×C8#1175819911yescharacteristic
351C2×C8C2×D24411yescharacteristic
352C2×C8C2×D24411yescharacteristic
353C2×C8#1175822211yescharacteristic
354C2×C8#1175822211yescharacteristic
355C2×C8C2×C22⋊D6111yescharacteristic
356C2×C8C2×C22⋊D6111yescharacteristic
357C2×C8C2×C22⋊D6111yescharacteristic
358C2×C8C23×D6111yescharacteristic
359C4⋊C4—2442no—
360C22⋊C4—2444no—
361C42—21no—
362C42C2×C22⋊D6111yescharacteristic
363C42C2×C22⋊D6111yescharacteristic
364C16—1224no—
365C23—41no—
366C23—2442no—
367C23#1451980211yescharacteristic
368Q8—22no—
369Q8—41no—
370Q8—2442no—
371Q8—2442no—
372D4—22no—
373D4—42no—
374D4—42no—
375D4—41no—
376D4—4884no—
377D4—4882no—
378D4—4882no—
379D4—2442no—
380D4—2442no—
381C2×C4—21no—
382C2×C4—21no—
383C2×C4—42no—
384C2×C4—41no—
385C2×C4—42no—
386C2×C4—42no—
387C2×C4—4882no—
388C2×C4—4882no—
389C2×C4—2442no—
390C2×C4#1451975111yescharacteristic
391C2×C4#1451975111yescharacteristic
392C2×C4C2×#1175819911yescharacteristic
393C2×C4C2×#1175819911yescharacteristic
394C2×C4#1451980211yescharacteristic
395C2×C4C22×C22⋊D6111yescharacteristic
396C8—42no—
397C8#1451975111yescharacteristic
398C8#1451975111yescharacteristic
399C8C2×#1175819911yescharacteristic
400C8C2×#1175819911yescharacteristic
401C8C2×#1175819911yescharacteristic
402C8C2×#1175819911yescharacteristic
403C8C22×D24411yescharacteristic
404C8C2×#1175822211yescharacteristic
405C22—41no—
406C22—42no—
407C22—82no—
408C22—4884no—
409C22—4882no—
410C22#1683995711yescharacteristic
411C22#1683995711yescharacteristic
412C22C2×#1451980211yescharacteristic
413C4—22no—
414C4—41no—
415C4—42no—
416C4—4882no—
417C4#1683995711yescharacteristic
418C4#1683995711yescharacteristic
419C4C2×#1451975111yescharacteristic
420C4C22×#1175819911yescharacteristic
421C2—21no—
422C2—21no—
423C2—21no—
424C2—82no—
425C2—9762no—
426C2C2×#1683995711yescharacteristic
subgroupG/H
centerC4#16839957
commutator, cosocleC2×C8×C61C24
FrattiniC2×C8C23×D61
FittingC2×C61×#443C2
socleC2×C61C2×#459
hypercenterC2×#443D61
hypocenterC61#33594
LCSG ▷ C2×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C4 ◁ C22×C4 ◁ C2×C4×C8 ◁ C2×#443

Complements

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

NH ≅ G/Ntype
1. #21458953C2semidirect
2. #21456247C2semidirect
3. #21447900C2semidirect
4. #21447895C2semidirect
5. #21447888C2semidirect
6. C2×#16839583C2semidirect
7. #21447566C2semidirect
8. C2×C61×#443C2semidirect
19. #16840146C22semidirect
20. #16840142C22semidirect
21. #16840139C22semidirect
23. #16839583C22semidirect
24. #16839583C22semidirect
25. #16839577C22semidirect
26. #16839574C22semidirect
66. #135×C61D4semidirect
68. C2×Q16×C61D4semidirect
70. C2×D8×C61D4semidirect
210. C2×#443D61semidirect
249. C61#33594semidirect
262. #135D244semidirect
266. C2×Q16D244semidirect
272. C2×D8D244semidirect

Maximal subgroups

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

subgroupindex
#214589532
#214562472
#214479002
#214478952
#214478882
C2×#168395832
#214475662
C2×C61×#4432
#3359461