Finite Group Databasebeta

← #29575240

Subgroups — #29575240

Order 15616.

470 conjugacy classes of subgroups.

The subgroup lattice has 394 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21456378C211yesmaximal, characteristic
2#21454762C211yesmaximal, characteristic, complemented
3#21446737C211yesmaximal, characteristic
4#21444317C211yesmaximal, characteristic, complemented
5#21444217C211yesmaximal, characteristic
6#21443656C211yesmaximal, characteristic, complemented
7C61×#1279C211yesmaximal, characteristic, complemented
8#16840319C2211yescharacteristic
9#16840312C2211yescharacteristic
10#16840160C411yescharacteristic, complemented
11#16840135C411yescharacteristic, complemented
12#16840113C411yescharacteristic, complemented
13#16840109C411yescharacteristic, complemented
14#16839991—22no—
15#16839891—22no—
16#16839889—21no—
17#16839886—21no—
18C4×#11758190—22no—
19#16839815C2211yescharacteristic
20#16839788—21no—
21C2×#14519705—21no—
22C2×#14519705—21no—
23#16839717—21no—
24C4×#11758194C2211yescharacteristic
25#16839498—22no—
26#16839489—21no—
27#16839489—21no—
28C2×C4⋊C8×C61C2211yescharacteristic
29C2×C4×C8×C61C2211yescharacteristic
30C4×C4⋊C4×C61C2211yescharacteristic
31C2×#11758222—21no—
32C2×#11758190—22no—
33C2×#11758194D411yescharacteristic
34C2×#11758194D411yescharacteristic
35#14519777C2×C411yescharacteristic
36#14519777C2×C411yescharacteristic
37#14519777C2×C411yescharacteristic
38#14519774C2×C411yescharacteristic
39#14519769—21no—
40#14519765—21no—
41#14519756—21no—
42#14519756D412yes—
43#14519751—21no—
44#14519751—21no—
45C4×Dic122—21no—
46C4×Dic122D412yes—
47C4×D244—21no—
48C4×D244—21no—
49#14519736—21no—
50#14519709—22no—
51C4⋊#92418—21no—
52#14519706—22no—
53#14519706—22no—
54#14519705—42no—
55#14519705—42no—
56#14519702—22no—
57#14519699—22no—
58C22⋊#92418—21no—
59#14519688—21no—
60#14519687—22no—
61C4×#92418—21no—
62C4×#92418—21no—
63C8×Dic61—22no—
64C22×C8×C61—21no—
65C22×C8×C61—21no—
66C2×C4⋊C4×C61—21no—
67C2×C42×C61—21no—
68C2×C42×C61C2311yescharacteristic
69C4⋊C8×C61—21no—
70C4⋊C8×C61D411yescharacteristic
71C4⋊C8×C61D411yescharacteristic
72C4×C8×C61—21no—
73C4×C8×C61C2×C411yescharacteristic
74C4×C8×C61C2×C411yescharacteristic
75#95×C61—21no—
76C22×C4×C61—41no—
77C22×C4×C61C2×D411yescharacteristic
78C22×C4×C61C2×D411yescharacteristic
79C22×C4×C61#4111yescharacteristic
80C2×C22⋊D61—41no—
81#11758222—41no—
82#11758222—41no—
83#11758222—41no—
84#11758222—41no—
85C2×D244—21no—
86C2×D244—21no—
87C2×D244—21no—
88C2×C4×D61—41no—
89C2×Dic122—21no—
90C2×Dic122—21no—
91C2×Dic122C22⋊C412yes—
92C2×C8×C61—21no—
93C2×C8×C61—21no—
94C2×C8×C61—21no—
95C2×C8×C61—21no—
96C2×C8×C61—42no—
97C2×C8×C61—41no—
98C2×C8×C61—41no—
99C4⋊C4×C61—22no—
100C4⋊C4×C61—41no—
101C42×C61—41no—
102C42×C61—41no—
103C42×C61C22×C411yescharacteristic
104C42×C61C2×D411yescharacteristic
105C42×C61C2×D411yescharacteristic
106C42×C61#4111yescharacteristic
107C22⋊Dic61—22no—
108#11758198—41no—
109#11758198—41no—
110C4⋊Dic61—21no—
111C4⋊Dic61—21no—
112C4⋊Dic61—21no—
113C4⋊Dic61—21no—
114C4⋊Dic61—21no—
115C4⋊Dic61C22⋊C412yes—
116#11758196—22no—
117#11758196—22no—
118C4×Dic61—22no—
119#11758194—21no—
120#11758194—21no—
121#11758194—21no—
122#11758194SD1612yescomplemented
123C2×#92418—21no—
124C2×#92418—21no—
125C2×#92418—41no—
126#11758190—44no—
127C23×C61#12111yescharacteristic
128C22×D61—41no—
129C2×C4×C61—21no—
130C2×C4×C61—21no—
131C2×C4×C61—41no—
132C2×C4×C61—42no—
133C2×C4×C61—81no—
134C2×C4×C61—81no—
135C2×C4×C61C2×C22⋊C411yescharacteristic
136C2×C4×C61C4×D411yescharacteristic
137C2×C4×C61C4×D411yescharacteristic
138C2×C4×C61#12011yescharacteristic
139C2×C4×C61#12111yescharacteristic
140C2×C4×C61#12311yescharacteristic
141C2×C4×C61C2×SD1611yescharacteristic
142C2×C4×C61#13511yescharacteristic
143C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
144C2×C4×C61#13711yescharacteristic
145C22⋊D61—81no—
146C22⋊D61—81no—
147C2×Dic61—22no—
148C2×Dic61—22no—
149C2×Dic61—41no—
150D244—42no—
151D244—41no—
152D244—41no—
153D244—41no—
154D244—41no—
155C4×D61—81no—
156C4×D61—81no—
157Dic122—41no—
158Dic122—41no—
159Dic122—42no—
160Dic122—41no—
161Dic122—41no—
162C8×C61—22no—
163C8×C61—41no—
164C8×C61—41no—
165C8×C61—41no—
166#92418—22no—
167#92418—41no—
168#92418—81no—
169#9054—611nomaximal, Sylow
170C22×C61—21no—
171C22×C61—21no—
172C22×C61#38611yescharacteristic
173C22×C61#46011yescharacteristic
174C22×C61#46411yescharacteristic
175C2×D61—81no—
176C2×D61—81no—
177C2×D61—81no—
178C4×C61—21no—
179C4×C61—21no—
180C4×C61—21no—
181C4×C61—82no—
182C4×C61C4×SD1611yescharacteristic
183C4×C61#44011yescharacteristic
184C4×C61#44311yescharacteristic
185C4×C61#44411yescharacteristic
186C4×C61#44811yescharacteristic
187C4×C61#44911yescharacteristic
188Dic61—42no—
189Dic61—42no—
190Dic61—81no—
191#3167—611no—
192#2962—611no—
193#1980—611no—
194#1503—611no—
195#1480—611no—
196#1279D6111yescharacteristic, complemented
197#1278—611no—
198C2×C61—21no—
199C2×C61—21no—
200C2×C61#187611yescharacteristic
201C2×C61#188011yescharacteristic
202C2×C61#188411yescharacteristic
203D61—161no—
204#533—611no—
205#532—611no—
206#498—611no—
207#492—611no—
208#487—611no—
209#486—611no—
210#465—1222no—
211#446—1222no—
212#446—1221no—
213C8×Q8—1221no—
214C4×SD16—1222no—
215#431—611no—
216#424—1221no—
217C2×C4⋊C8C2×D6111yescharacteristic
218C2×#104—1221no—
219C2×#104—1221no—
220#405—1221no—
221C4×M16—611no—
222C2×C4×C8C2×D6111yescharacteristic
223C4×C4⋊C4C2×D6111yescharacteristic
224#328—1222no—
225D4⋊C8—1221no—
226D4⋊C8—1221no—
227C61#905411yescharacteristic, complemented, Sylow
228C2×#41—1221no—
229C2×SD16—1222no—
230C2×M16—611no—
231C2×M16—611no—
232C22×C8—21no—
233C22×C8—21no—
234C4⋊Q8—611no—
235C4⋊Q8—611no—
236C4⋊Q8—611no—
237#127—611no—
238#125—1221no—
239#124—1221no—
240C22⋊Q8—612no—
241C22⋊Q8—1221no—
242#121—1221no—
243#121—1221no—
244C4×Q8—612no—
245C4×Q8—1221no—
246C4×D4—1221no—
247C4×D4—1221no—
248#117—1221no—
249C2×C4⋊C4—21no—
250C2×C42—21no—
251C2×C42C22×D6111yescharacteristic
252#106—1222no—
253C4⋊C8—21no—
254C4⋊C8—1222no—
255C4⋊C8—1222no—
256C4⋊C8—1221no—
257C4⋊C8D24411yescharacteristic
258C4⋊C8D24411yescharacteristic
259#104—2442no—
260#104—2442no—
261#103—1222no—
262#102—1222no—
263C22⋊C8—1221no—
264#97—1222no—
265#97—1221no—
266C4×C8—21no—
267C4×C8—1222no—
268C4×C8—1221no—
269C4×C8—1221no—
270C4×C8C4×D6111yescharacteristic
271C4×C8C4×D6111yescharacteristic
272#95—21no—
273#41—2441no—
274#41—2441no—
275#41—2441no—
276#41—2441no—
277C2×Q8—612no—
278C2×Q8—1221no—
279C2×Q8—1221no—
280C2×D4—1221no—
281C2×D4—1221no—
282C2×D4—1221no—
283C2×D4—2441no—
284C22×C4—41no—
285C22×C4—2441no—
286C22×C4#1175822211yescharacteristic
287C22×C4D4×D6111yescharacteristic
288C22×C4D4×D6111yescharacteristic
289SD16—2444no—
290M16—612no—
291M16—1221no—
292M16—1221no—
293M16—1221no—
294C2×C8—21no—
295C2×C8—21no—
296C2×C8—21no—
297C2×C8—21no—
298C2×C8—42no—
299C2×C8—41no—
300C2×C8—41no—
301C2×C8—1221no—
302C2×C8—1221no—
303C2×C8—2441no—
304C4⋊C4—22no—
305C4⋊C4—41no—
306C4⋊C4—612no—
307C4⋊C4—1221no—
308C4⋊C4—1221no—
309C4⋊C4—1221no—
310C4⋊C4—1222no—
311C4⋊C4—1222no—
312C4⋊C4—1221no—
313C4⋊C4—1221no—
314C22⋊C4—1222no—
315C22⋊C4—2441no—
316C22⋊C4—2441no—
317C42—41no—
318C42—41no—
319C42—1222no—
320C42C2×C4×D6111yescharacteristic
321C42C2×D24411yescharacteristic
322C42D4×D6111yescharacteristic
323C42#1175822611yescharacteristic
324C23—2441no—
325C23#1451975011yescharacteristic
326Q8—2442no—
327Q8—2441no—
328Q8—2441no—
329Q8—2441no—
330Q8—2441no—
331D4—4881no—
332D4—4881no—
333D4—2442no—
334D4—2441no—
335D4—2441no—
336D4—2441no—
337D4—2441no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—41no—
341C2×C4—42no—
342C2×C4—81no—
343C2×C4—81no—
344C2×C4—1222no—
345C2×C4—1222no—
346C2×C4—4881no—
347C2×C4—4881no—
348C2×C4—2441no—
349C2×C4C22⋊C4×D6111yescharacteristic
350C2×C4#1451973911yescharacteristic
351C2×C4C4×D24411yescharacteristic
352C2×C4#1451974711yescharacteristic
353C2×C4#1451975211yescharacteristic
354C2×C4#1451976211yescharacteristic
355C2×C4SD16×D6111yescharacteristic
356C2×C4#1451979811yescharacteristic
357C2×C4#1451980111yescharacteristic
358C2×C4#1451980911yescharacteristic
359C8—22no—
360C8—41no—
361C8—41no—
362C8—41no—
363C8—1222no—
364C8—4881no—
365C8—2441no—
366C22—21no—
367C22—21no—
368C22—4881no—
369C22—4881no—
370C22—4881no—
371C22#1683964011yescharacteristic
372C22#1683996111yescharacteristic
373C22#1683998711yescharacteristic
374C4—21no—
375C4—21no—
376C4—21no—
377C4—82no—
378C4—4881no—
379C4—2442no—
380C4—2442no—
381C4#1683984911yescharacteristic
382C4#1683986111yescharacteristic
383C4#1683988011yescharacteristic
384C4#1683988511yescharacteristic
385C4#1683990211yescharacteristic
386C4#1683990811yescharacteristic
387C2—21no—
388C2—21no—
389C2—9761no—
390C2#2144614511yescharacteristic
391C2#2144617511yescharacteristic
392C2#2144620111yescharacteristic
subgroupG/H
centerC2×C4#14519747
commutatorC42×C61C22×C4
FrattiniC2×C42C22×D61
FittingC61×#1279C2
socleC22×C61#386
prime radical#16840312C22
cosocleC2×C42×C61C23
hypercenter#1279D61
hypocenterC61#9054
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1279

Complements

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

NH ≅ G/Ntype
2. #21454762C2semidirect
4. #21444317C2semidirect
6. #21443656C2semidirect
7. C61×#1279C2semidirect
10. #16840160C4semidirect
11. #16840135C4semidirect
12. #16840113C4semidirect
13. #16840109C4semidirect
122. #11758194SD16semidirect
196. #1279D61semidirect
227. C61#9054semidirect

Maximal subgroups

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

subgroupindex
#214563782
#214547622
#214467372
#214443172
#214442172
#214436562
C61×#12792
#905461