Finite Group Databasebeta

← #29593529

Subgroups — #29593529

Order 15616.

340 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 340 conjugacy classes of subgroups — too many to draw. Only its 65 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21458833C211yesmaximal, characteristic, complemented
2#21448068C211yesmaximal, characteristic
3#21447860C211yesmaximal, characteristic, complemented
4#21445180C211yesmaximal, characteristic, complemented
5#21443797C211yesmaximal, characteristic, complemented
6#21443782C211yesmaximal, characteristic, complemented
7C61×#1361C211yesmaximal, characteristic, complemented
8#16840498—21no—
9C2×#14519722—21no—
10C2×#14519718—22no—
11#16840145—21no—
12#16840139C2211yescharacteristic
13#16839975—22no—
14#16839963—21no—
15#16839959—21no—
16C8×Dic122C2211yescharacteristic
17C4×Dic244C2211yescharacteristic
18D8×Dic61—21no—
19#16839564—21no—
20C4×#11758185C2211yescharacteristic
21#16839505—21no—
22C61×#493C2211yescharacteristic
23C61×C4⋊C16C2211yescharacteristic
24C61×#335C2211yescharacteristic
25C2×Dic244D411yescharacteristic
26C2×#11758190—41no—
27C2×#11758200—22no—
28C2×D488—21no—
29C2×D488—21no—
30#14519774—21no—
31#14519764—22no—
32#14519764—41no—
33#14519758—42no—
34C4×Dic122—21no—
35C4×Dic122D411yescharacteristic
36D4×Dic61—22no—
37D4×Dic61—41no—
38#14519722—42no—
39#14519718—44no—
40C2×#11758185—21no—
41#14519711D411yescharacteristic
42C4⋊#92418D411yescharacteristic
43#14519706—21no—
44#14519702—21no—
45#14519699—41no—
46#14519698—22no—
47C8×Dic61—21no—
48C2×D8×C61—21no—
49C2×D8×C61D412yes—
50#127×C61—21no—
51C2×C16×C61—21no—
52C4⋊C8×C61—21no—
53C4×C8×C61C2311yescharacteristic
54C2×D4×C61—22no—
55C2×D4×C61—41no—
56C2×D4×C61—41no—
57C22×Dic61—42no—
58C2×D244—41no—
59C2×D244—41no—
60C2×D244—41no—
61C2×Dic122—21no—
62C2×Dic122D811yescharacteristic
63D8×C61—42no—
64D8×C61—41no—
65D8×C61—41no—
66C2×C8×C61—41no—
67C2×C8×C61C2×D411yescharacteristic
68C2×C8×C61C2×D411yescharacteristic
69C42×C61C2×D411yescharacteristic
70C22⋊Dic61—42no—
71C22⋊Dic61—42no—
72C22⋊Dic61—42no—
73#11758200—82no—
74C4⋊Dic61—21no—
75C4⋊Dic61D811yescharacteristic
76#11758196—21no—
77#11758196—41no—
78C4×Dic61—21no—
79C4×Dic61—41no—
80C2×#92418—21no—
81Dic244—21no—
82Dic244—21no—
83D488—42no—
84D488—41no—
85D488—41no—
86#11758190—82no—
87C16×C61—41no—
88#11758185—22no—
89C23×C61—42no—
90C22×D61—81no—
91D4×C61—42no—
92D4×C61—42no—
93D4×C61—81no—
94D4×C61—81no—
95D4×C61—161no—
96C2×C4×C61#12011yescharacteristic
97C2×C4×C61C2×D811yescharacteristic
98C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
99C2×Dic61—21no—
100C2×Dic61—21no—
101C2×Dic61—41no—
102C2×Dic61—41no—
103C2×Dic61—162no—
104D244—81no—
105D244—81no—
106D244—81no—
107D244—81no—
108D244—161no—
109Dic122—21no—
110Dic122—21no—
111Dic122—41no—
112Dic122—41no—
113C8×C61—21no—
114C8×C61—81no—
115C8×C61#13511yescharacteristic
116C8×C61AGL(1,ℤ/8)11yescharacteristic
117#92418—41no—
118#12329—611nomaximal, Sylow
119C22×C61—82no—
120C22×C61—82no—
121C22×C61—82no—
122C22×C61#44711yescharacteristic
123C2×D61—161no—
124C2×D61—161no—
125C2×D61—161no—
126C4×C61—21no—
127C4×C61#44911yescharacteristic
128C4×C61#45311yescharacteristic
129C4×C61#50811yescharacteristic
130C4×C61#50911yescharacteristic
131Dic61—41no—
132Dic61—41no—
133Dic61—81no—
134Dic61—81no—
135#3396—611no—
136#2246—611no—
137#2207—611no—
138#1668—611no—
139#1361D6111yescharacteristic, complemented
140Q8⋊C16—611no—
141#1332—611no—
142C2×C61—162no—
143C2×C61#162111yescharacteristic
144C2×C61#218611yescharacteristic
145C2×C61#219211yescharacteristic
146D61—321no—
147#559—1221no—
148C2×SD32—1221no—
149C2×D16—1222no—
150#495—1221no—
151#493—611no—
152#493C2×D6111yescharacteristic
153#463—1222no—
154#460—1221no—
155#460—1221no—
156C8×Q8—611no—
157C4×Q16—611no—
158C4×D8—1221no—
159C4⋊C16C2×D6111yescharacteristic
160#357—1221no—
161C4×C16—611no—
162#335C2×D6111yescharacteristic
163#331—1221no—
164C61#1232911yescharacteristic, complemented, Sylow
165C2×Q16—611no—
166C2×SD16—1222no—
167C2×SD16—2441no—
168C2×D8—21no—
169C2×D8—1221no—
170C2×D8—1221no—
171C2×D8D24412yes—
172#127—21no—
173#127—1221no—
174#124—1222no—
175#124—2441no—
176#123—2442no—
177C4×Q8—611no—
178C4×Q8—1221no—
179C4×D4—1222no—
180C4×D4—2441no—
181SD32—2442no—
182D16—2444no—
183C2×C16—21no—
184C2×C16—1221no—
185#107—611no—
186C4⋊C8—21no—
187C4⋊C8—611no—
188C4⋊C8—1221no—
189#103—1221no—
190#102—1222no—
191#102—2441no—
192C4×C8—1221no—
193C4×C8C22×D6111yescharacteristic
194C2×Q8—611no—
195C2×Q8—1221no—
196C2×D4—22no—
197C2×D4—41no—
198C2×D4—41no—
199C2×D4—2441no—
200C2×D4—2441no—
201C2×D4—2441no—
202C22×C4—2442no—
203Q16—1221no—
204Q16—1221no—
205SD16—4882no—
206SD16—4882no—
207D8—42no—
208D8—41no—
209D8—41no—
210D8—2442no—
211D8—2441no—
212D8—2441no—
213C2×C8—41no—
214C2×C8—1221no—
215C2×C8C2×D24411yescharacteristic
216C2×C8D4×D6111yescharacteristic
217C4⋊C4—611no—
218C4⋊C4—1221no—
219C4⋊C4—1221no—
220C4⋊C4—2441no—
221C22⋊C4—2442no—
222C22⋊C4—2442no—
223C22⋊C4—2442no—
224C42—1221no—
225C42—2441no—
226C42D4×D6111yescharacteristic
227C16—41no—
228C16—1222no—
229C23—42no—
230C23—4881no—
231Q8—1221no—
232Q8—1221no—
233Q8—2441no—
234Q8—2441no—
235D4—42no—
236D4—42no—
237D4—81no—
238D4—81no—
239D4—161no—
240D4—9761no—
241D4—4881no—
242D4—4881no—
243D4—4881no—
244D4—4881no—
245C2×C4—1221no—
246C2×C4—1221no—
247C2×C4—9762no—
248C2×C4—2441no—
249C2×C4—2441no—
250C2×C4#1451974711yescharacteristic
251C2×C4D8×D6111yescharacteristic
252C2×C4#1451980411yescharacteristic
253C8—21no—
254C8—81no—
255C8—2441no—
256C8#1451979811yescharacteristic
257C8#1451980111yescharacteristic
258C22—82no—
259C22—82no—
260C22—82no—
261C22—9761no—
262C22—9761no—
263C22—9761no—
264C22#1683989711yescharacteristic
265C4—21no—
266C4—4881no—
267C4—4881no—
268C4—2441no—
269C4—2441no—
270C4#1683990811yescharacteristic
271C4#1683993211yescharacteristic
272C4#1684019311yescharacteristic
273C4#1684019611yescharacteristic
274C2—162no—
275C2—19521no—
276C2#2144488511yescharacteristic
277C2#2144774311yescharacteristic
278C2#2144777911yescharacteristic
subgroupG/H
centerC22#16839897
commutator, cosocleC4×C8×C61C23
FrattiniC4×C8C22×D61
FittingC61×#1361C2
socleC22×C61#447
prime radical#21448068C2
hypercenter#1361D61
hypocenterC61#12329
LCSG ▷ C4×C8×C61 ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #1361

Complements

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

NH ≅ G/Ntype
1. #21458833C2semidirect
3. #21447860C2semidirect
4. #21445180C2semidirect
5. #21443797C2semidirect
6. #21443782C2semidirect
7. C61×#1361C2semidirect
139. #1361D61semidirect
164. C61#12329semidirect

Maximal subgroups

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

subgroupindex
#214588332
#214480682
#214478602
#214451802
#214437972
#214437822
C61×#13612
#1232961