Finite Group Databasebeta

← #29591529

Subgroups — #29591529

Order 15616.

292 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 292 conjugacy classes of subgroups — too many to draw. Only its 69 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#21456470C211yesmaximal, characteristic
2#21447634C211yesmaximal, characteristic, complemented
3#21447583C211yesmaximal, characteristic, complemented
4#21443880C211yesmaximal, characteristic, complemented
5#21443855C211yesmaximal, characteristic, complemented
6#21443855C211yesmaximal, characteristic, complemented
7C61×#1366C211yesmaximal, characteristic, complemented
8#16840368C412yes—
9M32×D61—21no—
10#16840139C2211yescharacteristic
11#16840128C412yes—
12#16840016—21no—
13#16839999—21no—
14#16839873—21no—
15#16839844—21no—
16#16839716C2211yescharacteristic
17#16839583C2211yescharacteristic
18#16839583C2211yescharacteristic
19#16839582—21no—
20#16839543—21no—
21#16839539—21no—
22C61×#499C2211yescharacteristic
23C61×#364C2211yescharacteristic
24C61×#364C2211yescharacteristic
25C2×D488—21no—
26C2×D488—21no—
27C2×#11758189D411yescharacteristic
28C2×C8×D61D411yescharacteristic
29#14519774C2×C412yes—
30#14519762—42no—
31#14519752—22no—
32#14519752—42no—
33#14519739—22no—
34#14519734C2×C411yescharacteristic
35#14519717—21no—
36#14519717—21no—
37#14519716—41no—
38C16×D61—41no—
39#14519697—22no—
40#14519697—22no—
41#14519688C2×C411yescharacteristic
42#14519687D411yescharacteristic
43C8×Dic61D411yescharacteristic
44#125×C61C2×C412yes—
45M32×C61—21no—
46M32×C61—21no—
47#107×C61—21no—
48#106×C61—21no—
49C4×C8×C61C2311yescharacteristic
50C2×D244—22no—
51C2×D244—42no—
52C2×D244—42no—
53C2×C4×D61—42no—
54C2×C4×D61C22⋊C411yescharacteristic
55C2×C8×C61C2×D411yescharacteristic
56C2×C8×C61C2×D411yescharacteristic
57C4⋊C4×C61—22no—
58C4⋊C4×C61—42no—
59C42×C61C22×C411yescharacteristic
60#11758198—21no—
61#11758198—42no—
62#11758198—42no—
63#11758196—21no—
64C4×Dic61C22⋊C411yescharacteristic
65C2×#92418C22⋊C411yescharacteristic
66C2×#92418C22⋊C411yescharacteristic
67D488—41no—
68D488—41no—
69D488—41no—
70D488—41no—
71#11758189—21no—
72#11758189—21no—
73C8×D61—21no—
74C8×D61—21no—
75C16×C61—41no—
76C16×C61—41no—
77#11758185—41no—
78#11758185—41no—
79C22×D61—42no—
80C22×D61#10011yescharacteristic
81C2×C4×C61—21no—
82C2×C4×C61—42no—
83C2×C4×C61C2×C22⋊C411yescharacteristic
84C2×Dic61—21no—
85C2×Dic61#10011yescharacteristic
86D244—42no—
87D244—42no—
88D244—162no—
89D244—162no—
90C4×D61—21no—
91C4×D61—21no—
92C4×D61—162no—
93C8×C61#13511yescharacteristic
94C8×C61#13511yescharacteristic
95C8×C61AGL(1,ℤ/8)11yescharacteristic
96C8×C61#13711yescharacteristic
97#92418—21no—
98#92418—21no—
99#11989—611nomaximal, Sylow
100C22×C61C2×#10011yescharacteristic
101C2×D61—21no—
102C2×D61—41no—
103C2×D61—82no—
104C2×D61—82no—
105C2×D61—82no—
106C4×C61—41no—
107C4×C61—82no—
108C4×C61#41611yescharacteristic
109C4×C61#41711yescharacteristic
110Dic61—21no—
111Dic61—41no—
112#3176—611no—
113#2166—611no—
114#2153—611no—
115#1366—611no—
116#1366D6111yescharacteristic, complemented
117#1357—611no—
118#1357—611no—
119C2×C61—21no—
120C2×C61#155111yescharacteristic
121D61—41no—
122D61—162no—
123#540—612no—
124C2×M32—1221no—
125#499C2×D6111yescharacteristic
126#493—611no—
127#490—612no—
128#469—1221no—
129#466—1221no—
130#442—1221no—
131C4×D8—1221no—
132#405—611no—
133#364—611no—
134#364—611no—
135#364—1221no—
136#364C2×D6111yescharacteristic
137#364C2×D6111yescharacteristic
138#349—1221no—
139#347—1221no—
140C61#1198911yescharacteristic, complemented, Sylow
141C2×D8—1221no—
142C2×D8—1221no—
143C2×M16—611no—
144C22×C8—611no—
145#127—612no—
146#125C4×D6112yes—
147#123—2442no—
148#121—1222no—
149#121—2442no—
150C4×D4—1222no—
151#117—611no—
152M32—21no—
153M32—21no—
154M32—1221no—
155M32—1221no—
156M32—2441no—
157C2×C16—2441no—
158#107—21no—
159#106—21no—
160#102—1222no—
161#102—1222no—
162#97—611no—
163#97—611no—
164C4×C8—611no—
165C4×C8C22×D6111yescharacteristic
166C2×D4—1222no—
167C2×D4—2442no—
168C2×D4—2442no—
169C22×C4—611no—
170C22×C4—2442no—
171D8—2441no—
172D8—2441no—
173D8—2441no—
174D8—2441no—
175M16—1221no—
176M16—1221no—
177C2×C8—611no—
178C2×C8—611no—
179C2×C8—1221no—
180C2×C8—1221no—
181C2×C8D4×D6111yescharacteristic
182C2×C8D4×D6111yescharacteristic
183C4⋊C4—22no—
184C4⋊C4—42no—
185C4⋊C4—1221no—
186C22⋊C4—1221no—
187C22⋊C4—2442no—
188C22⋊C4—2442no—
189C42—611no—
190C42C2×C4×D6111yescharacteristic
191C16—41no—
192C16—41no—
193C16—2441no—
194C16—2441no—
195C23—611no—
196C23—2442no—
197D4—9762no—
198D4—9762no—
199D4—2442no—
200D4—2442no—
201C2×C4—21no—
202C2×C4—42no—
203C2×C4—611no—
204C2×C4—1221no—
205C2×C4—1221no—
206C2×C4—1221no—
207C2×C4—9762no—
208C2×C4C22⋊C4×D6111yescharacteristic
209C8—1221no—
210C8—1221no—
211C8#1451979811yescharacteristic
212C8#1451980011yescharacteristic
213C8#1451980411yescharacteristic
214C8#1451980911yescharacteristic
215C22—1221no—
216C22—4882no—
217C22—4882no—
218C22—4882no—
219C22—2441no—
220C22#100×D6111yescharacteristic
221C4—41no—
222C4—82no—
223C4—1221no—
224C4—2441no—
225C4#1683975711yescharacteristic
226C4#1683976211yescharacteristic
227C2—21no—
228C2—9762no—
229C2—2441no—
230C2#2144451311yescharacteristic
subgroupG/H
centerC2#21444513
commutatorC42×C61C22×C4
FrattiniC4×C8C22×D61
FittingC61×#1366C2
socleC2×C61#1551
prime radical#21456470C2
cosocleC4×C8×C61C23
hypercenter#1366D61
hypocenterC61#11989
LCSG ▷ C42×C61 ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C2×C4 ◁ C4×C8 ◁ #1366

Complements

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

NH ≅ G/Ntype
2. #21447634C2semidirect
3. #21447583C2semidirect
4. #21443880C2semidirect
5. #21443855C2semidirect
6. #21443855C2semidirect
7. C61×#1366C2semidirect
116. #1366D61semidirect
140. C61#11989semidirect

Maximal subgroups

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

subgroupindex
#214564702
#214476342
#214475832
#214438802
#214438552
C61×#13662
#1198961