Finite Group Databasebeta

← #29583151

Subgroups — #29583151

Order 15616.

402 conjugacy classes of subgroups; only the 91 normal subgroups are shown.

normal subgroups only

This group has 402 conjugacy classes of subgroups — too many to draw. Only its 91 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#21449124C211yesmaximal, characteristic, complemented
2#21444314C212yesmaximal
3#21443720C212yesmaximal, complemented
4#21443648C211yesmaximal, characteristic, complemented
5C61×#1963C211yesmaximal, characteristic
6#16839815C2212yes—
7#16839704—22no—
8#16839696—22no—
9C4×#11758196—22no—
10C4×C4⋊Dic61C2212yes—
11#16839496—22no—
12#16839496—22no—
13C61×#532C2211yescharacteristic
14C61×#423C2211yescharacteristic
15C2×#104×C61—22no—
16C61×#376C2211yescharacteristic
17C2×C4⋊Dic61—22no—
18C2×#11758196—22no—
19C2×#11758196—22no—
20C2×C4×Dic61—22no—
21C4⋊#92418—22no—
22C22⋊#92418—22no—
23C4×#92418—22no—
24#14519684—22no—
25#14519684—22no—
26#14519684D412yes—
27#14519684D412yes—
28C2×#41×C61—21no—
29C2×M16×C61—21no—
30C4⋊Q8×C61Q811yescharacteristic
31#127×C61Q811yescharacteristic
32#124×C61—21no—
33#121×C61—22no—
34C4×D4×C61—22no—
35C2×C42×C61D412yes—
36C2×C42×C61C2311yescharacteristic
37C4⋊C8×C61—22no—
38#104×C61—44no—
39#95×C61—22no—
40#41×C61—42no—
41#41×C61—42no—
42C2×Q8×C61—21no—
43C2×D4×C61—21no—
44C2×D4×C61—22no—
45C2×D4×C61—41no—
46C22×C4×C61—22no—
47C22×C4×C61—41no—
48C22×C4×C61C2×D412yes—
49C22×C4×C61C2×D411yescharacteristic
50C22×Dic61—22no—
51C22×Dic61—22no—
52M16×C61—42no—
53C2×C8×C61—41no—
54C4⋊C4×C61—22no—
55C22⋊C4×C61—42no—
56C42×C61—22no—
57C42×C61—22no—
58C42×C61C2×Q811yescharacteristic
59C42×C61#4111yescharacteristic
60C42×C61#4112yes—
61C4⋊Dic61—44no—
62#11758196—44no—
63#11758196—44no—
64C4×Dic61—42no—
65C4×Dic61—42no—
66C2×#92418—42no—
67C23×C61—41no—
68C23×C61#12011yescharacteristic
69Q8×C61—42no—
70D4×C61—42no—
71D4×C61—82no—
72D4×C61—82no—
73C2×C4×C61—42no—
74C2×C4×C61—42no—
75C2×C4×C61—42no—
76C2×C4×C61—41no—
77C2×C4×C61—42no—
78C2×C4×C61—81no—
79C2×C4×C61—81no—
80C2×C4×C61C22⋊Q812yes—
81C2×C4×C61C22⋊Q811yescharacteristic
82C2×C4×C61#12412yes—
83C2×C4×C61#12411yescharacteristic
84C2×C4×C61#13512yes—
85C2×C4×C61AGL(1,ℤ/8)12yes—
86C2×Dic61—24no—
87C2×Dic61—42no—
88C2×Dic61—42no—
89C2×Dic61—42no—
90C2×Dic61—42no—
91C2×Dic61—42no—
92C8×C61—81no—
93#92418—82no—
94#10372—611nomaximal, Sylow
95C22×C61—22no—
96C22×C61—81no—
97C22×C61—82no—
98C22×C61#39311yescharacteristic
99C22×C61#44912yes—
100C4×C61—22no—
101C4×C61—22no—
102C4×C61—82no—
103C4×C61—81no—
104C4×C61#47812yes—
105C4×C61#48811yescharacteristic
106C4×C61#49011yescharacteristic
107Dic61—44no—
108Dic61—82no—
109#2402—611no—
110#1963D6111yescharacteristic
111#1502—612no—
112#1303—612no—
113#1274—611no—
114C2×C61—22no—
115C2×C61—161no—
116C2×C61#202511yescharacteristic
117C2×C61#203112yes—
118#532C2×D6111yescharacteristic
119#431—612no—
120#423C2×D6111yescharacteristic
121C2×#104—22no—
122#400—1222no—
123#398—1222no—
124C4×C4⋊C4—612no—
125C4×C4⋊C4—1222no—
126#376C2×D6111yescharacteristic
127#327—1222no—
128#327—1222no—
129C61#1037211yescharacteristic, complemented, Sylow
130C2×#41—21no—
131C2×M16—21no—
132C4⋊Q8Dic12211yescharacteristic
133#127Dic12211yescharacteristic
134#124—21no—
135#121—22no—
136C4×D4—22no—
137C2×C4⋊C4—1222no—
138C2×C4⋊C4—1222no—
139C2×C4⋊C4—1222no—
140C2×C42—1222no—
141C2×C42C22⋊D6112yes—
142C2×C42C22×D6111yescharacteristic
143C4⋊C8—22no—
144C4⋊C8—1222no—
145#104—44no—
146C22⋊C8—1222no—
147C4×C8—1222no—
148#95—22no—
149#95—612no—
150#95—612no—
151#95—1222no—
152#95—1222no—
153#41—42no—
154#41—42no—
155C2×Q8—21no—
156C2×D4—22no—
157C2×D4—21no—
158C2×D4—41no—
159C22×C4—22no—
160C22×C4—41no—
161C22×C4—1222no—
162C22×C4—1222no—
163C22×C4D4×D6112yes—
164C22×C4C2×C22⋊D6111yescharacteristic
165M16—42no—
166C2×C8—41no—
167C2×C8—2442no—
168C4⋊C4—22no—
169C4⋊C4—2444no—
170C4⋊C4—2444no—
171C4⋊C4—2444no—
172C22⋊C4—42no—
173C42—22no—
174C42—22no—
175C42—2442no—
176C42—2442no—
177C42C2×Dic12211yescharacteristic
178C42#1175822211yescharacteristic
179C42#1175822412yes—
180C23—41no—
181C23#1451974511yescharacteristic
182Q8—42no—
183D4—42no—
184D4—82no—
185D4—82no—
186C2×C4—42no—
187C2×C4—42no—
188C2×C4—42no—
189C2×C4—42no—
190C2×C4—41no—
191C2×C4—81no—
192C2×C4—81no—
193C2×C4—1224no—
194C2×C4—2442no—
195C2×C4—2442no—
196C2×C4—2442no—
197C2×C4—2442no—
198C2×C4—2442no—
199C2×C4#1451975412yes—
200C2×C4#1451975611yescharacteristic
201C2×C4#1451976312yes—
202C2×C4#1451976411yescharacteristic
203C2×C4#1451979712yes—
204C2×C4#1451980312yes—
205C8—81no—
206C8—4882no—
207C22—22no—
208C22—81no—
209C22—82no—
210C22#1683967411yescharacteristic
211C22#1683990512yes—
212C4—22no—
213C4—22no—
214C4—82no—
215C4—81no—
216C4—4882no—
217C4—2444no—
218C4#1684006212yes—
219C4#1684011611yescharacteristic
220C4#1684012611yescharacteristic
221C2—22no—
222C2—161no—
223C2#2144696511yescharacteristic
224C2#2144698912yes—
subgroupG/H
centerC2×C4#14519764
commutator, cosocleC2×C42×C61C23
FrattiniC2×C42C22×D61
FittingC61×#1963C2
socleC22×C61#393
prime radicalC61×#532C22
hypercenter#1963D61
hypocenterC61#10372
LCSG ▷ C2×C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1963

Complements

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

NH ≅ G/Ntype
1. #21449124C2semidirect
3. #21443720C2semidirect
4. #21443648C2semidirect
129. C61#10372semidirect

Maximal subgroups

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

subgroupindex
#214491242
#214443142
#214437202
#214436482
C61×#19632
#1037261