Finite Group Databasebeta

← #29593541

Subgroups — #29593541

Order 15616.

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

normal subgroups only

This group has 328 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#21458805C211yesmaximal, characteristic, complemented
2#21448074C211yesmaximal, characteristic, complemented
3#21445176C211yesmaximal, characteristic, complemented
4#21443869C211yesmaximal, characteristic, complemented
5#21443797C211yesmaximal, characteristic, complemented
6#21443780C211yesmaximal, characteristic, complemented
7C61×#2206C211yesmaximal, characteristic
8#16840482—21no—
9C2×#14519721—22no—
10#16840145—21no—
11#16840142C2211yescharacteristic
12#16839983—22no—
13#16839967—21no—
14#16839959—21no—
15C8×Dic122C2211yescharacteristic
16#16839856—21no—
17C4×#11758185C2211yescharacteristic
18#16839515C2211yescharacteristic
19#16839506—21no—
20C2×D16×C61—21no—
21C61×#493C2211yescharacteristic
22C4×D8×C61C2211yescharacteristic
23C61×C4⋊C16C2211yescharacteristic
24C61×#357—21no—
25C2×Dic244—21no—
26C2×Dic244D412yes—
27C2×#11758200—22no—
28C2×#11758200—41no—
29#14519777—21no—
30#14519770—42no—
31#14519764—22no—
32#14519756—41no—
33C4×Dic122D411yescharacteristic
34#14519742—22no—
35#14519736—41no—
36#14519721—44no—
37C2×#11758185—21no—
38C4⋊#92418—21no—
39C4⋊#92418D411yescharacteristic
40#14519706—21no—
41#14519700—22no—
42#14519698—41no—
43C8×Dic61—21no—
44C2×D8×C61—21no—
45C2×D8×C61—21no—
46C2×D8×C61D411yescharacteristic
47#127×C61—21no—
48C4×D4×C61—21no—
49D16×C61—42no—
50C2×C16×C61—21no—
51#107×C61D411yescharacteristic
52#102×C61—21no—
53C4×C8×C61C2311yescharacteristic
54C2×D4×C61—21no—
55C2×D4×C61—41no—
56C2×D4×C61—41no—
57C2×D4×C61—41no—
58C22×C4×C61—41no—
59C2×Dic122—22no—
60C2×Dic122D811yescharacteristic
61D8×C61—21no—
62D8×C61—21no—
63D8×C61—42no—
64D8×C61—41no—
65D8×C61—41no—
66C2×C8×C61C2×D411yescharacteristic
67C2×C8×C61C2×D411yescharacteristic
68C4⋊C4×C61—21no—
69C22⋊C4×C61—41no—
70C42×C61C2×D411yescharacteristic
71C22⋊Dic61—42no—
72C22⋊Dic61—42no—
73#11758200—82no—
74#11758200—82no—
75C4⋊Dic61—41no—
76C4⋊Dic61—41no—
77C4⋊Dic61D811yescharacteristic
78#11758196—21no—
79#11758196—42no—
80C4×Dic61—21no—
81C4×Dic61—42no—
82C2×#92418—21no—
83C2×#92418—41no—
84Dic244—42no—
85Dic244—41no—
86Dic244—41no—
87C16×C61—41no—
88#11758185—22no—
89C23×C61—41no—
90C23×C61—81no—
91D4×C61—41no—
92D4×C61—41no—
93D4×C61—81no—
94D4×C61—81no—
95D4×C61—81no—
96D4×C61—81no—
97D4×C61—161no—
98C2×C4×C61—41no—
99C2×C4×C61—81no—
100C2×C4×C61—81no—
101C2×C4×C61#12011yescharacteristic
102C2×C4×C61C2×D811yescharacteristic
103C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
104C2×Dic61—21no—
105C2×Dic61—21no—
106C2×Dic61—42no—
107Dic122—21no—
108Dic122—21no—
109Dic122—42no—
110Dic122—42no—
111C8×C61—21no—
112C8×C61#13511yescharacteristic
113C8×C61AGL(1,ℤ/8)11yescharacteristic
114#92418—41no—
115#92418—81no—
116#12331—611nomaximal, Sylow
117C22×C61—81no—
118C22×C61—81no—
119C22×C61—81no—
120C22×C61—161no—
121C22×C61—161no—
122C22×C61—161no—
123C22×C61#44711yescharacteristic
124C4×C61—21no—
125C4×C61—81no—
126C4×C61#44911yescharacteristic
127C4×C61#45311yescharacteristic
128C4×C61#50811yescharacteristic
129C4×C61#50911yescharacteristic
130Dic61—41no—
131Dic61—41no—
132Dic61—82no—
133#3393—611no—
134#2248—611no—
135#2206D6111yescharacteristic
136#1668—611no—
137#1362—611no—
138Q8⋊C16—611no—
139#1331—611no—
140C2×C61—161no—
141C2×C61—321no—
142C2×C61#162111yescharacteristic
143C2×C61#218611yescharacteristic
144C2×C61#219311yescharacteristic
145#556—1221no—
146C2×SD32—1222no—
147C2×D16—21no—
148#495—1221no—
149#494—611no—
150#493C2×D6111yescharacteristic
151#464—1222no—
152#461—1221no—
153#460—1221no—
154C8×Q8—611no—
155C4×Q16—1221no—
156C4×D8C2×D6111yescharacteristic
157C4⋊C16C2×D6111yescharacteristic
158#357—21no—
159C4×C16—611no—
160#335—611no—
161#331—1221no—
162C61#1233111yescharacteristic, complemented, Sylow
163C2×Q16—612no—
164C2×Q16—1221no—
165C2×SD16—1222no—
166C2×SD16—2441no—
167C2×D8—21no—
168C2×D8—21no—
169C2×D8C22⋊D6111yescharacteristic
170C4⋊Q8—1221no—
171#127—21no—
172#126—2442no—
173#124—1222no—
174C22⋊Q8—2441no—
175C4×Q8—611no—
176C4×Q8—1222no—
177C4×D4—21no—
178#117—2441no—
179SD32—2444no—
180D16—42no—
181C2×C16—21no—
182C2×C16—1221no—
183#107C22⋊D6111yescharacteristic
184C4⋊C8—611no—
185C4⋊C8—1221no—
186C4⋊C8—1221no—
187#103—1222no—
188#102—21no—
189#102—2441no—
190C4×C8—1221no—
191C4×C8C22×D6111yescharacteristic
192C2×Q8—611no—
193C2×Q8—1222no—
194C2×D4—21no—
195C2×D4—41no—
196C2×D4—41no—
197C2×D4—41no—
198C22×C4—41no—
199Q16—2442no—
200Q16—2441no—
201Q16—2441no—
202SD16—4882no—
203SD16—4882no—
204D8—21no—
205D8—21no—
206D8—42no—
207D8—41no—
208D8—41no—
209C2×C8—1221no—
210C2×C8—2441no—
211C2×C8D4×D6111yescharacteristic
212C2×C8C2×C22⋊D6111yescharacteristic
213C4⋊C4—21no—
214C4⋊C4—611no—
215C4⋊C4—1221no—
216C4⋊C4—2442no—
217C4⋊C4—2441no—
218C4⋊C4—2441no—
219C22⋊C4—41no—
220C22⋊C4—2442no—
221C22⋊C4—2442no—
222C42—1221no—
223C42—2442no—
224C42D4×D6111yescharacteristic
225C16—41no—
226C16—1222no—
227C23—41no—
228C23—81no—
229Q8—1221no—
230Q8—1221no—
231Q8—2442no—
232Q8—2442no—
233D4—41no—
234D4—41no—
235D4—81no—
236D4—81no—
237D4—81no—
238D4—81no—
239D4—161no—
240C2×C4—41no—
241C2×C4—81no—
242C2×C4—81no—
243C2×C4—1221no—
244C2×C4—1221no—
245C2×C4—2442no—
246C2×C4#1451974511yescharacteristic
247C2×C4D8×D6111yescharacteristic
248C2×C4#1451980111yescharacteristic
249C8—21no—
250C8—4881no—
251C8—2441no—
252C8#1451979711yescharacteristic
253C8#1451980311yescharacteristic
254C22—81no—
255C22—81no—
256C22—81no—
257C22—161no—
258C22—161no—
259C22—161no—
260C22#1683989411yescharacteristic
261C4—21no—
262C4—81no—
263C4—4882no—
264C4—2441no—
265C4—2441no—
266C4#1683990511yescharacteristic
267C4#1683992811yescharacteristic
268C4#1684019111yescharacteristic
269C4#1684019611yescharacteristic
270C2—161no—
271C2—321no—
272C2#2144488311yescharacteristic
273C2#2144773911yescharacteristic
274C2#2144778011yescharacteristic
subgroupG/H
centerC22#16839894
commutator, cosocleC4×C8×C61C23
FrattiniC4×C8C22×D61
Fitting, prime radicalC61×#2206C2
socleC22×C61#447
hypercenter#2206D61
hypocenterC61#12331
LCSG ▷ C4×C8×C61 ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #2206

Complements

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

NH ≅ G/Ntype
1. #21458805C2semidirect
2. #21448074C2semidirect
3. #21445176C2semidirect
4. #21443869C2semidirect
5. #21443797C2semidirect
6. #21443780C2semidirect
162. C61#12331semidirect

Maximal subgroups

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

subgroupindex
#214588052
#214480742
#214451762
#214438692
#214437972
#214437802
C61×#22062
#1233161