Finite Group Databasebeta

← #29593525

Subgroups — #29593525

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#21447856C211yesmaximal, characteristic, complemented
3#21445176C211yesmaximal, characteristic, complemented
4#21443865C211yesmaximal, characteristic, complemented
5#21443799C211yesmaximal, characteristic, complemented
6#21443784C211yesmaximal, characteristic, complemented
7C61×#2246C211yesmaximal, characteristic
8#16840498—21no—
9C2×#14519721—21no—
10#16840145—21no—
11#16839975—22no—
12#16839959—21no—
13#16839959—21no—
14C8×Dic122C2211yescharacteristic
15C4×Dic244C2211yescharacteristic
16D8×Dic61—21no—
17C4⋊#11758185C2211yescharacteristic
18#16839563—21no—
19#16839515C2211yescharacteristic
20#16839506—21no—
21C2×D16×C61—22no—
22C61×#493C2211yescharacteristic
23C61×#493C2211yescharacteristic
24C4×C16×C61C2211yescharacteristic
25C2×Dic244D411yescharacteristic
26C2×#11758200—22no—
27C2×#11758200—41no—
28#14519764—22no—
29#14519764—41no—
30#14519758—42no—
31C4×Dic122—21no—
32C4×Dic122D411yescharacteristic
33D4×Dic61—22no—
34D4×Dic61—41no—
35#14519721—42no—
36C2×#11758185—21no—
37#14519711D411yescharacteristic
38C4⋊#92418—21no—
39C4⋊#92418D411yescharacteristic
40#14519706—21no—
41#14519702—21no—
42#14519698—22no—
43#14519698—41no—
44C8×Dic61—21no—
45C2×D8×C61—21no—
46C2×D8×C61—21no—
47C2×D8×C61—21no—
48C2×D8×C61D412yes—
49#127×C61—21no—
50#127×C61—21no—
51D16×C61—44no—
52C2×C16×C61—21no—
53C4×C8×C61C2311yescharacteristic
54C2×D4×C61—22no—
55C2×D4×C61—41no—
56C2×D4×C61—41no—
57C2×D4×C61—41no—
58C2×D4×C61—41no—
59C2×D4×C61—41no—
60C22×Dic61—42no—
61C2×Dic122—21no—
62C2×Dic122D811yescharacteristic
63D8×C61—42no—
64D8×C61—42no—
65D8×C61—41no—
66D8×C61—41no—
67D8×C61—41no—
68D8×C61—41no—
69C2×C8×C61C2×D411yescharacteristic
70C2×C8×C61C2×D411yescharacteristic
71C42×C61C2×D411yescharacteristic
72C22⋊Dic61—42no—
73C22⋊Dic61—42no—
74C22⋊Dic61—42no—
75#11758200—82no—
76#11758200—82no—
77C4⋊Dic61—21no—
78C4⋊Dic61D811yescharacteristic
79#11758196—21no—
80#11758196—41no—
81C4×Dic61—21no—
82C4×Dic61—41no—
83C2×#92418—21no—
84C2×#92418—41no—
85Dic244—21no—
86Dic244—21no—
87C16×C61—22no—
88#11758185—41no—
89C23×C61—42no—
90C23×C61—81no—
91D4×C61—42no—
92D4×C61—42no—
93D4×C61—81no—
94D4×C61—81no—
95D4×C61—81no—
96D4×C61—81no—
97D4×C61—81no—
98D4×C61—81no—
99D4×C61—161no—
100D4×C61—161no—
101C2×C4×C61#12011yescharacteristic
102C2×C4×C61C2×D811yescharacteristic
103C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
104C2×Dic61—21no—
105C2×Dic61—21no—
106C2×Dic61—41no—
107C2×Dic61—41no—
108C2×Dic61—162no—
109Dic122—21no—
110Dic122—21no—
111Dic122—41no—
112Dic122—41no—
113C8×C61—21no—
114C8×C61#13511yescharacteristic
115C8×C61AGL(1,ℤ/8)11yescharacteristic
116#92418—41no—
117#92418—81no—
118#12329—611nomaximal, Sylow
119C22×C61—82no—
120C22×C61—82no—
121C22×C61—82no—
122C22×C61—161no—
123C22×C61—161no—
124C22×C61—161no—
125C22×C61#44711yescharacteristic
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#2246D6111yescharacteristic
137#2207—611no—
138#1668—611no—
139#1361—611no—
140Q8⋊C16—611no—
141#1332—611no—
142C2×C61—162no—
143C2×C61—321no—
144C2×C61#162111yescharacteristic
145C2×C61#218611yescharacteristic
146C2×C61#219211yescharacteristic
147#559—1221no—
148C2×SD32—1221no—
149C2×D16—22no—
150#495—1221no—
151#493C2×D6111yescharacteristic
152#493C2×D6111yescharacteristic
153#463—1222no—
154#460—1221no—
155#460—1221no—
156C8×Q8—611no—
157C4×Q16—611no—
158C4×D8—1221no—
159C4⋊C16—611no—
160#357—1221no—
161C4×C16C2×D6111yescharacteristic
162#335—611no—
163#331—1221no—
164C61#1232911yescharacteristic, complemented, Sylow
165C2×Q16—611no—
166C2×SD16—1222no—
167C2×SD16—2441no—
168C2×D8—21no—
169C2×D8—21no—
170C2×D8—21no—
171C2×D8C22⋊D6112yes—
172#127—21no—
173#127—21no—
174#124—1222no—
175#124—2441no—
176#123—2442no—
177C4×Q8—611no—
178C4×Q8—1221no—
179C4×D4—1222no—
180C4×D4—2441no—
181SD32—2442no—
182D16—44no—
183C2×C16—21no—
184C2×C16—1221no—
185#107—611no—
186C4⋊C8—611no—
187C4⋊C8—1221no—
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—41no—
200C2×D4—41no—
201C2×D4—41no—
202C22×C4—2442no—
203Q16—1221no—
204Q16—1221no—
205SD16—4882no—
206SD16—4882no—
207D8—42no—
208D8—42no—
209D8—41no—
210D8—41no—
211D8—41no—
212D8—41no—
213C2×C8—1221no—
214C2×C8—2441no—
215C2×C8D4×D6111yescharacteristic
216C2×C8C2×C22⋊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—22no—
228C16—2441no—
229C23—42no—
230C23—81no—
231Q8—1221no—
232Q8—1221no—
233Q8—2441no—
234Q8—2441no—
235D4—42no—
236D4—42no—
237D4—81no—
238D4—81no—
239D4—81no—
240D4—81no—
241D4—81no—
242D4—81no—
243D4—161no—
244D4—161no—
245C2×C4—1221no—
246C2×C4—1221no—
247C2×C4—9762no—
248C2×C4—2441no—
249C2×C4—2441no—
250C2×C4#1451974511yescharacteristic
251C2×C4D8×D6111yescharacteristic
252C2×C4#1451980111yescharacteristic
253C8—21no—
254C8—4881no—
255C8—2441no—
256C8#1451979611yescharacteristic
257C8#1451980111yescharacteristic
258C22—82no—
259C22—82no—
260C22—82no—
261C22—161no—
262C22—161no—
263C22—161no—
264C22#1683989411yescharacteristic
265C4—21no—
266C4—4881no—
267C4—4881no—
268C4—2441no—
269C4—2441no—
270C4#1683990411yescharacteristic
271C4#1683992911yescharacteristic
272C4#1684019111yescharacteristic
273C4#1684019611yescharacteristic
274C2—162no—
275C2—321no—
276C2#2144488111yescharacteristic
277C2#2144773911yescharacteristic
278C2#2144777511yescharacteristic
subgroupG/H
centerC22#16839894
commutator, cosocleC4×C8×C61C23
FrattiniC4×C8C22×D61
Fitting, prime radicalC61×#2246C2
socleC22×C61#447
hypercenter#2246D61
hypocenterC61#12329
LCSG ▷ C4×C8×C61 ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #2246

Complements

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

NH ≅ G/Ntype
1. #21458833C2semidirect
2. #21447856C2semidirect
3. #21445176C2semidirect
4. #21443865C2semidirect
5. #21443799C2semidirect
6. #21443784C2semidirect
164. C61#12329semidirect

Maximal subgroups

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

subgroupindex
#214588332
#214478562
#214451762
#214438652
#214437992
#214437842
C61×#22462
#1232961