Finite Group Databasebeta

← #29584187

Subgroups — #29584187

Order 15616.

386 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 386 conjugacy classes of subgroups — too many to draw. Only its 85 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#21445956C211yesmaximal, characteristic, complemented
2#21444554C212yesmaximal, complemented
3#21444270C212yesmaximal, complemented
4#21443732C211yesmaximal, characteristic, complemented
5C61×#3253C211yesmaximal, characteristic
6#16839786C2211yescharacteristic
7#16839786C2212yes—
8C2×C4×#92418C2211yescharacteristic
9#16839526—22no—
10#16839511—22no—
11#16839506—22no—
12D4⋊#92418—24no—
13C61×#532C2212yes—
14C61×#476—22no—
15C61×#469—22no—
16C61×#459—22no—
17C61×#423C2211yescharacteristic
18C2×#11758194—21no—
19C2×#11758194—22no—
20C22×#92418—21no—
21C4⋊#92418—22no—
22C4⋊#92418—22no—
23C4⋊#92418—22no—
24C4×#92418—21no—
25C4×#92418D412yes—
26C2×#41×C61—22no—
27C2×D8×C61—22no—
28C2×M16×C61D412yes—
29C4⋊Q8×C61D412yes—
30#127×C61D412yes—
31#124×C61—22no—
32#121×C61—22no—
33#121×C61—22no—
34C4×D4×C61—22no—
35C4×D4×C61—22no—
36C2×C42×C61C2311yescharacteristic
37#106×C61—22no—
38C4⋊C8×C61—22no—
39#102×C61—24no—
40#41×C61—82no—
41#41×C61—82no—
42C2×Q8×C61—22no—
43C2×D4×C61—22no—
44C2×D4×C61—22no—
45C2×D4×C61—22no—
46C2×D4×C61—42no—
47C22×C4×C61—42no—
48C22×C4×C61C2×D411yescharacteristic
49C22×C4×C61#4112yes—
50D8×C61—82no—
51M16×C61—42no—
52C2×C8×C61—22no—
53C4⋊C4×C61—22no—
54C4⋊C4×C61—22no—
55C22⋊C4×C61—42no—
56C22⋊C4×C61—42no—
57C42×C61C2×D412yes—
58C42×C61C2×D411yescharacteristic
59C42×C61#4111yescharacteristic
60#11758194—42no—
61#11758194—82no—
62C2×#92418—22no—
63C2×#92418—41no—
64C2×#92418—41no—
65C2×#92418—41no—
66C2×#92418—42no—
67C23×C61—42no—
68C23×C61#12411yescharacteristic
69Q8×C61—82no—
70D4×C61—42no—
71D4×C61—42no—
72D4×C61—42no—
73D4×C61—42no—
74D4×C61—82no—
75D4×C61—84no—
76C2×C4×C61—21no—
77C2×C4×C61—21no—
78C2×C4×C61—22no—
79C2×C4×C61—22no—
80C2×C4×C61—42no—
81C2×C4×C61—82no—
82C2×C4×C61—82no—
83C2×C4×C61#12011yescharacteristic
84C2×C4×C61#12111yescharacteristic
85C2×C4×C61#12112yes—
86C2×C4×C61#12312yes—
87C8×C61—42no—
88#92418—42no—
89#92418—81no—
90#92418—82no—
91#10531—611nomaximal, Sylow
92C22×C61—22no—
93C22×C61—21no—
94C22×C61—82no—
95C22×C61—82no—
96C22×C61—82no—
97C22×C61#39411yescharacteristic
98C4×C61—22no—
99C4×C61—21no—
100C4×C61—82no—
101C4×C61#45411yescharacteristic
102C4×C61#45511yescharacteristic
103C4×C61#47112yes—
104C4×C61#47212yes—
105#3253D6111yescharacteristic
106#1837—611no—
107#1560—612no—
108#1492—612no—
109#1309—611no—
110C2×C61—41no—
111C2×C61—162no—
112C2×C61#204011yescharacteristic
113C2×C61#205112yes—
114#532C2×D6112yes—
115#476—22no—
116#469—22no—
117#459—22no—
118#423—611no—
119#423—612no—
120#423C2×D6111yescharacteristic
121C2×C4×C8—611no—
122#341—1222no—
123#333—1222no—
124#331—1222no—
125D4⋊C8—1224no—
126C61#1053111yescharacteristic, complemented, Sylow
127C2×#41—22no—
128C2×D8—22no—
129C2×M16—1222no—
130C2×M16—1221no—
131C2×M16C22⋊D6112yes—
132C22×C8—1221no—
133C4⋊Q8C22⋊D6112yes—
134#127C22⋊D6112yes—
135#124—22no—
136#121—22no—
137#121—22no—
138C4×D4—22no—
139C4×D4—22no—
140C2×C42C22×D6111yescharacteristic
141#106—22no—
142C4⋊C8—22no—
143C4⋊C8—1222no—
144C4⋊C8—1222no—
145C4⋊C8—1222no—
146#102—24no—
147C4×C8—612no—
148C4×C8—1221no—
149#41—82no—
150#41—82no—
151C2×Q8—22no—
152C2×D4—22no—
153C2×D4—22no—
154C2×D4—22no—
155C2×D4—42no—
156C22×C4—42no—
157C22×C4#1175822412yes—
158C22×C4C2×C22⋊D6111yescharacteristic
159D8—82no—
160M16—42no—
161M16—4882no—
162M16—2442no—
163C2×C8—22no—
164C2×C8—1222no—
165C2×C8—2441no—
166C2×C8—2442no—
167C2×C8—2441no—
168C2×C8—2441no—
169C4⋊C4—22no—
170C4⋊C4—22no—
171C22⋊C4—42no—
172C22⋊C4—42no—
173C42D4×D6111yescharacteristic
174C42#1175822411yescharacteristic
175C42C2×C22⋊D6112yes—
176C23—42no—
177C23#1451976411yescharacteristic
178Q8—82no—
179D4—42no—
180D4—42no—
181D4—42no—
182D4—42no—
183D4—82no—
184D4—84no—
185C2×C4—21no—
186C2×C4—22no—
187C2×C4—22no—
188C2×C4—21no—
189C2×C4—42no—
190C2×C4—82no—
191C2×C4—82no—
192C2×C4#1451974611yescharacteristic
193C2×C4#1451974811yescharacteristic
194C2×C4#1451974912yes—
195C2×C4#1451975812yes—
196C8—42no—
197C8—4882no—
198C8—4881no—
199C8—2442no—
200C22—21no—
201C22—22no—
202C22—82no—
203C22—82no—
204C22—82no—
205C22#1683967611yescharacteristic
206C4—21no—
207C4—22no—
208C4—82no—
209C4#1683993511yescharacteristic
210C4#1683994011yescharacteristic
211C4#1684002312yes—
212C4#1684003012yes—
213C2—41no—
214C2—162no—
215C2#2144704511yescharacteristic
216C2#2144710812yes—
subgroupG/H
centerC22#16839676
commutator, cosocleC2×C42×C61C23
FrattiniC2×C42C22×D61
Fitting, prime radicalC61×#3253C2
socleC22×C61#394
hypercenter#3253D61
hypocenterC61#10531
LCSG ▷ C2×C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3253

Complements

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

NH ≅ G/Ntype
1. #21445956C2semidirect
2. #21444554C2semidirect
3. #21444270C2semidirect
4. #21443732C2semidirect
126. C61#10531semidirect

Maximal subgroups

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

subgroupindex
#214459562
#214445542
#214442702
#214437322
C61×#32532
#1053161