Finite Group Databasebeta

← #29598777

Subgroups — #29598777

Order 15616.

516 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 516 conjugacy classes of subgroups — too many to draw. Only its 99 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
1C22×Dic488C211yesmaximal, characteristic, complemented
2C2×#16840037C212yesmaximal
3C2×#16839579C212yesmaximal, complemented
4#21443913C211yesmaximal, characteristic, complemented
5C61×#2113C211yesmaximal, characteristic
6C2×#14519807—22no—
7C22×Dic244C2212yes—
8C2×Dic488—24no—
9C2×Dic488—22no—
10#16840037—24no—
11#16840037—24no—
12C2×#14519713C2212yes—
13C2×#14519695—22no—
14#16839579—24no—
15C2×#131×C61C2211yescharacteristic
16C2×M32×C61C2211yescharacteristic
17C22×C16×C61C2211yescharacteristic
18C61×C22⋊C16—22no—
19C22×Dic122—22no—
20#14519807—28no—
21#14519807—44no—
22C2×Dic244—22no—
23C2×Dic244—22no—
24C2×Dic244—22no—
25C2×Dic244—22no—
26C2×Dic244—22no—
27C2×Dic244D414yes—
28C2×#11758202—42no—
29C2×#11758200—42no—
30C2×#11758194—22no—
31Dic488—28no—
32#14519713—22no—
33#14519713D414yes—
34#14519695—28no—
35C2×#41×C61D411yescharacteristic
36#131×C61—22no—
37#131×C61—22no—
38C2×M16×C61—21no—
39C2×M16×C61D411yescharacteristic
40C22×C8×C61—21no—
41C22×C8×C61C2311yescharacteristic
42M32×C61—22no—
43C2×C16×C61—22no—
44C2×C16×C61—21no—
45C2×C16×C61D412yes—
46#41×C61—22no—
47#41×C61—22no—
48C2×Q8×C61D811yescharacteristic
49C2×D4×C61—21no—
50C2×D4×C61D811yescharacteristic
51C22×C4×C61—21no—
52C22×C4×C61C2×D411yescharacteristic
53C22×Dic61—42no—
54C2×Dic122—24no—
55C2×Dic122—42no—
56C2×Dic122—42no—
57C2×Dic122—42no—
58C2×Dic122—42no—
59C2×Dic122—42no—
60M16×C61—22no—
61M16×C61—42no—
62C2×C8×C61—21no—
63C2×C8×C61—41no—
64C2×C8×C61—41no—
65C2×C8×C61C2×D412yes—
66C2×C8×C61C2×D411yescharacteristic
67C2×C8×C61C2×D412yes—
68C2×C8×C61#4111yescharacteristic
69#11758202—48no—
70#11758200—48no—
71#11758194—24no—
72#11758194—42no—
73C2×#92418—42no—
74Dic244—24no—
75Dic244—24no—
76Dic244—42no—
77Dic244—42no—
78C16×C61—22no—
79C16×C61—41no—
80C23×C61—21no—
81C23×C61#13511yescharacteristic
82Q8×C61—22no—
83D4×C61—22no—
84D4×C61—42no—
85C2×C4×C61—21no—
86C2×C4×C61—41no—
87C2×C4×C61—41no—
88C2×C4×C61#12012yes—
89C2×C4×C61#12111yescharacteristic
90C2×C4×C61C2×D811yescharacteristic
91C2×C4×C61AGL(1,ℤ/8)12yes—
92C2×Dic61—44no—
93C2×Dic61—82no—
94C2×Dic61—82no—
95Dic122—44no—
96Dic122—44no—
97Dic122—82no—
98Dic122—82no—
99C8×C61—41no—
100C8×C61#12011yescharacteristic
101C8×C61#12112yes—
102C8×C61#12711yescharacteristic
103#92418—44no—
104#13315—611nomaximal, Sylow
105C22×C61—22no—
106C22×C61—42no—
107C22×C61—41no—
108C22×C61#44912yes—
109C22×C61#46611yescharacteristic
110C4×C61—41no—
111C4×C61#39211yescharacteristic
112C4×C61#44712yes—
113C4×C61#46911yescharacteristic
114Dic61—84no—
115C22×Q32—611no—
116C2×#473—612no—
117C2×#362—612no—
118#2113D6111yescharacteristic
119#1381—611no—
120C2×C61—22no—
121C2×C61—81no—
122C2×C61#199911yescharacteristic
123C2×C61#222212yes—
124C2×#137—1222no—
125C22×Q16—612no—
126C2×#131C2×D6111yescharacteristic
127C2×Q32—1224no—
128C2×Q32—1222no—
129C2×M32C2×D6111yescharacteristic
130C22×C16C2×D6111yescharacteristic
131#473—1224no—
132#473—1224no—
133C2×#108—612no—
134C2×#101—1222no—
135#362—1224no—
136C22⋊C16—22no—
137C61#1331511yescharacteristic, complemented, Sylow
138C2×#41D24411yescharacteristic
139C22×Q8—1222no—
140#137—1228no—
141#137—2444no—
142C2×Q16—614no—
143C2×Q16—1222no—
144C2×Q16—1222no—
145C2×Q16—1222no—
146C2×Q16—1222no—
147C2×Q16—1222no—
148C2×Q16—2442no—
149C2×SD16—2442no—
150#131—22no—
151#131—22no—
152C2×M16—21no—
153C2×M16—1222no—
154C2×M16D24411yescharacteristic
155C22×C8—21no—
156C22×C8C22×D6111yescharacteristic
157Q32—1228no—
158M32—22no—
159C2×C16—22no—
160C2×C16—21no—
161C2×C16C22⋊D6112yes—
162#108—614no—
163#108—1222no—
164#101—1228no—
165#41—22no—
166#41—22no—
167C2×Q8—1224no—
168C2×Q8—2442no—
169C2×Q8—2442no—
170C2×Q8—2442no—
171C2×Q8—2442no—
172C2×Q8—2442no—
173C2×Q8D48811yescharacteristic
174C2×D4—21no—
175C2×D4D48811yescharacteristic
176C22×C4—21no—
177C22×C4—2442no—
178C22×C4C2×D24411yescharacteristic
179Q16—1224no—
180Q16—1224no—
181Q16—2448no—
182Q16—2442no—
183Q16—2442no—
184SD16—2448no—
185M16—22no—
186M16—42no—
187M16—1224no—
188M16—2442no—
189C2×C8—21no—
190C2×C8—41no—
191C2×C8—41no—
192C2×C8—2442no—
193C2×C8#1175822211yescharacteristic
194C2×C8D4×D6112yes—
195C2×C8D4×D6112yes—
196C2×C8C2×C22⋊D6111yescharacteristic
197C16—22no—
198C16—41no—
199C23—21no—
200C23#1451979911yescharacteristic
201Q8—22no—
202Q8—4882no—
203Q8—4882no—
204Q8—2444no—
205Q8—2444no—
206D4—22no—
207D4—42no—
208C2×C4—21no—
209C2×C4—41no—
210C2×C4—41no—
211C2×C4—4882no—
212C2×C4—4882no—
213C2×C4—2444no—
214C2×C4#1451974712yes—
215C2×C4#1451975111yescharacteristic
216C2×C4C2×D48811yescharacteristic
217C2×C4#1451980512yes—
218C8—41no—
219C8—2444no—
220C8#1451974511yescharacteristic
221C8#1451975012yes—
222C8#1451977311yescharacteristic
223C22—22no—
224C22—42no—
225C22—41no—
226C22#1683990912yes—
227C22#1683999811yescharacteristic
228C4—41no—
229C4—4884no—
230C4#1683967111yescharacteristic
231C4#1683989812yes—
232C4#1684001511yescharacteristic
233C2—22no—
234C2—81no—
235C2#2144681711yescharacteristic
236C2#2144794412yes—
subgroupG/H
centerC22#16839998
commutator, cosocleC22×C8×C61C23
FrattiniC22×C8C22×D61
FittingC61×#2113C2
socleC22×C61#466
prime radicalC2×#41×C61D4
hypercenter#2113D61
hypocenterC61#13315
LCSG ▷ C22×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#131 ◁ #2113

Complements

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

NH ≅ G/Ntype
1. C22×Dic488C2semidirect
3. C2×#16839579C2semidirect
4. #21443913C2semidirect
137. C61#13315semidirect

Maximal subgroups

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

subgroupindex
C22×Dic4882
C2×#168400372
C2×#168395792
#214439132
C61×#21132
#1331561