Finite Group Databasebeta

← #29584153

Subgroups — #29584153

Order 15616.

370 conjugacy classes of subgroups; only the 77 normal subgroups are shown.

normal subgroups only

This group has 370 conjugacy classes of subgroups — too many to draw. Only its 77 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#21445959C211yesmaximal, characteristic, complemented
2#21444541C212yesmaximal, complemented
3#21444430C212yesmaximal, complemented
4#21443730C211yesmaximal, characteristic, complemented
5C61×#3253C211yesmaximal, characteristic
6#16839819C2212yes—
7#16839786C2211yescharacteristic
8C2×#14519688C2211yescharacteristic
9#16839526—22no—
10#16839508—22no—
11#16839506—22no—
12#16839502—24no—
13C61×#532C2212yes—
14C61×#476—22no—
15C61×#469—22no—
16C61×#459—22no—
17C61×#423C2211yescharacteristic
18C2×#11758194—21no—
19C22×#92418—21no—
20C4⋊#92418—22no—
21C4⋊#92418—22no—
22C22⋊#92418—22no—
23#14519688—21no—
24#14519688—22no—
25#14519688D412yes—
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—84no—
41C2×Q8×C61—22no—
42C2×D4×C61—22no—
43C2×D4×C61—22no—
44C2×D4×C61—22no—
45C2×D4×C61—42no—
46C22×C4×C61—42no—
47C22×C4×C61C2×D411yescharacteristic
48C22×C4×C61#4112yes—
49D8×C61—82no—
50M16×C61—42no—
51C2×C8×C61—22no—
52C4⋊C4×C61—22no—
53C4⋊C4×C61—22no—
54C22⋊C4×C61—42no—
55C22⋊C4×C61—42no—
56C42×C61C2×D412yes—
57C42×C61C2×D411yescharacteristic
58C42×C61#4111yescharacteristic
59#11758194—42no—
60C2×#92418—22no—
61C2×#92418—41no—
62C2×#92418—41no—
63C2×#92418—41no—
64C2×#92418—42no—
65C23×C61—42no—
66C23×C61#12411yescharacteristic
67Q8×C61—82no—
68D4×C61—42no—
69D4×C61—42no—
70D4×C61—82no—
71D4×C61—82no—
72D4×C61—84no—
73C2×C4×C61—21no—
74C2×C4×C61—21no—
75C2×C4×C61—42no—
76C2×C4×C61—42no—
77C2×C4×C61—84no—
78C2×C4×C61#12011yescharacteristic
79C2×C4×C61#12111yescharacteristic
80C2×C4×C61#12112yes—
81C2×C4×C61#12312yes—
82C8×C61—42no—
83#92418—42no—
84#92418—82no—
85#92418—81no—
86#10525—611nomaximal, Sylow
87C22×C61—22no—
88C22×C61—21no—
89C22×C61—82no—
90C22×C61—82no—
91C22×C61—82no—
92C22×C61#39411yescharacteristic
93C4×C61—22no—
94C4×C61—22no—
95C4×C61—21no—
96C4×C61—82no—
97C4×C61#45411yescharacteristic
98C4×C61#45511yescharacteristic
99#3253D6111yescharacteristic
100#1838—611no—
101#1557—612no—
102#1530—612no—
103#1307—611no—
104C2×C61—41no—
105C2×C61—162no—
106C2×C61#204011yescharacteristic
107C2×C61#204812yes—
108#532C2×D6112yes—
109#476—22no—
110#469—22no—
111#459—22no—
112#432—612no—
113#423—611no—
114#423C2×D6111yescharacteristic
115C2×#97—611no—
116#341—1222no—
117#332—1222no—
118#331—1222no—
119#329—1224no—
120C61#1052511yescharacteristic, complemented, Sylow
121C2×#41—22no—
122C2×D8—22no—
123C2×M16—1221no—
124C2×M16C22⋊D6112yes—
125C22×C8—1221no—
126C4⋊Q8C22⋊D6112yes—
127#127C22⋊D6112yes—
128#124—22no—
129#121—22no—
130#121—22no—
131C4×D4—22no—
132C4×D4—22no—
133C2×C42C22×D6111yescharacteristic
134#106—22no—
135C4⋊C8—22no—
136C4⋊C8—1222no—
137C4⋊C8—1222no—
138#102—24no—
139C22⋊C8—1222no—
140#97—612no—
141#97—1222no—
142#97—1221no—
143#41—84no—
144C2×Q8—22no—
145C2×D4—22no—
146C2×D4—22no—
147C2×D4—22no—
148C2×D4—42no—
149C22×C4—42no—
150C22×C4#1175822412yes—
151C22×C4C2×C22⋊D6111yescharacteristic
152D8—82no—
153M16—42no—
154M16—2442no—
155C2×C8—22no—
156C2×C8—1222no—
157C2×C8—2441no—
158C2×C8—2442no—
159C2×C8—2441no—
160C2×C8—2441no—
161C4⋊C4—22no—
162C4⋊C4—22no—
163C22⋊C4—42no—
164C22⋊C4—42no—
165C42D4×D6111yescharacteristic
166C42#1175822411yescharacteristic
167C42C2×C22⋊D6112yes—
168C23—42no—
169C23#1451976411yescharacteristic
170Q8—82no—
171D4—42no—
172D4—42no—
173D4—82no—
174D4—82no—
175D4—84no—
176C2×C4—21no—
177C2×C4—21no—
178C2×C4—42no—
179C2×C4—42no—
180C2×C4—84no—
181C2×C4#1451974611yescharacteristic
182C2×C4#1451974811yescharacteristic
183C2×C4#1451974912yes—
184C2×C4#1451975812yes—
185C8—42no—
186C8—4882no—
187C8—4881no—
188C8—2442no—
189C22—21no—
190C22—22no—
191C22—82no—
192C22—82no—
193C22—82no—
194C22#1683967611yescharacteristic
195C4—21no—
196C4—22no—
197C4—22no—
198C4—82no—
199C4#1683993511yescharacteristic
200C4#1683994011yescharacteristic
201C2—41no—
202C2—162no—
203C2#2144704511yescharacteristic
204C2#2144708912yes—
subgroupG/H
centerC22#16839676
commutator, cosocleC2×C42×C61C23
FrattiniC2×C42C22×D61
Fitting, prime radicalC61×#3253C2
socleC22×C61#394
hypercenter#3253D61
hypocenterC61#10525
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. #21445959C2semidirect
2. #21444541C2semidirect
3. #21444430C2semidirect
4. #21443730C2semidirect
120. C61#10525semidirect

Maximal subgroups

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

subgroupindex
#214459592
#214445412
#214444302
#214437302
C61×#32532
#1052561