Finite Group Databasebeta

← #29584148

Subgroups — #29584148

Order 15616.

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

normal subgroups only

This group has 386 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#21445993C211yesmaximal, characteristic, complemented
2#21444541C212yesmaximal, complemented
3#21444430C212yesmaximal, complemented
4#21443730C211yesmaximal, characteristic, complemented
5C61×#3253C211yesmaximal, characteristic
6#16839819C2212yes—
7C2×#14519712—22no—
8#16839786C2211yescharacteristic
9C2×#14519688C2211yescharacteristic
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—
20#14519712—44no—
21C4⋊#92418—22no—
22C4⋊#92418—22no—
23C22⋊#92418—22no—
24#14519688—21no—
25#14519688—22no—
26#14519688D412yes—
27C2×#41×C61—22no—
28C2×D8×C61—22no—
29C2×M16×C61D412yes—
30C4⋊Q8×C61D412yes—
31#127×C61D412yes—
32#124×C61—22no—
33#121×C61—22no—
34#121×C61—22no—
35C4×D4×C61—22no—
36C4×D4×C61—22no—
37C2×C42×C61C2311yescharacteristic
38#106×C61—22no—
39C4⋊C8×C61—22no—
40#102×C61—24no—
41#41×C61—84no—
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—
61C2×#92418—22no—
62C2×#92418—22no—
63C2×#92418—22no—
64C2×#92418—41no—
65C2×#92418—42no—
66C23×C61—42no—
67C23×C61#12411yescharacteristic
68Q8×C61—82no—
69D4×C61—42no—
70D4×C61—42no—
71D4×C61—82no—
72D4×C61—82no—
73D4×C61—84no—
74C2×C4×C61—21no—
75C2×C4×C61—21no—
76C2×C4×C61—42no—
77C2×C4×C61—42no—
78C2×C4×C61—84no—
79C2×C4×C61#12011yescharacteristic
80C2×C4×C61#12111yescharacteristic
81C2×C4×C61#12112yes—
82C2×C4×C61#12312yes—
83C8×C61—42no—
84#92418—24no—
85#92418—82no—
86#92418—81no—
87#10524—611nomaximal, Sylow
88C22×C61—22no—
89C22×C61—21no—
90C22×C61—82no—
91C22×C61—82no—
92C22×C61—82no—
93C22×C61#39411yescharacteristic
94C4×C61—22no—
95C4×C61—22no—
96C4×C61—21no—
97C4×C61—82no—
98C4×C61#45311yescharacteristic
99C4×C61#45611yescharacteristic
100#3253D6111yescharacteristic
101#1849—611no—
102#1557—612no—
103#1530—612no—
104#1307—611no—
105C2×C61—41no—
106C2×C61—162no—
107C2×C61#203911yescharacteristic
108C2×C61#204812yes—
109#532C2×D6112yes—
110#476—22no—
111#469—22no—
112#459—22no—
113#432—612no—
114C2×#108—1222no—
115#423—611no—
116#423C2×D6111yescharacteristic
117C2×#97—611no—
118#332—1222no—
119#331—1222no—
120#329—1224no—
121C61#1052411yescharacteristic, complemented, Sylow
122C2×#41—22no—
123C2×D8—22no—
124C2×M16—1221no—
125C2×M16C22⋊D6112yes—
126C22×C8—1221no—
127C4⋊Q8C22⋊D6112yes—
128#127C22⋊D6112yes—
129#124—22no—
130#121—22no—
131#121—22no—
132C4×D4—22no—
133C4×D4—22no—
134C2×C42C22×D6111yescharacteristic
135#108—2444no—
136#106—22no—
137C4⋊C8—22no—
138C4⋊C8—1222no—
139C4⋊C8—1222no—
140#102—24no—
141C22⋊C8—1222no—
142#97—612no—
143#97—1222no—
144#97—1221no—
145#41—84no—
146C2×Q8—22no—
147C2×D4—22no—
148C2×D4—22no—
149C2×D4—22no—
150C2×D4—42no—
151C22×C4—42no—
152C22×C4#1175822412yes—
153C22×C4C2×C22⋊D6111yescharacteristic
154D8—82no—
155M16—42no—
156M16—2442no—
157C2×C8—22no—
158C2×C8—1222no—
159C2×C8—1222no—
160C2×C8—1222no—
161C2×C8—2441no—
162C2×C8—2442no—
163C4⋊C4—22no—
164C4⋊C4—22no—
165C22⋊C4—42no—
166C22⋊C4—42no—
167C42D4×D6111yescharacteristic
168C42#1175822411yescharacteristic
169C42C2×C22⋊D6112yes—
170C23—42no—
171C23#1451976411yescharacteristic
172Q8—82no—
173D4—42no—
174D4—42no—
175D4—82no—
176D4—82no—
177D4—84no—
178C2×C4—21no—
179C2×C4—21no—
180C2×C4—42no—
181C2×C4—42no—
182C2×C4—84no—
183C2×C4#1451974611yescharacteristic
184C2×C4#1451974811yescharacteristic
185C2×C4#1451974912yes—
186C2×C4#1451975812yes—
187C8—42no—
188C8—1224no—
189C8—4882no—
190C8—4881no—
191C22—21no—
192C22—22no—
193C22—82no—
194C22—82no—
195C22—82no—
196C22#1683967611yescharacteristic
197C4—21no—
198C4—22no—
199C4—22no—
200C4—82no—
201C4#1683993011yescharacteristic
202C4#1683994511yescharacteristic
203C2—41no—
204C2—162no—
205C2#2144704011yescharacteristic
206C2#2144708912yes—
subgroupG/H
centerC22#16839676
commutator, cosocleC2×C42×C61C23
FrattiniC2×C42C22×D61
Fitting, prime radicalC61×#3253C2
socleC22×C61#394
hypercenter#3253D61
hypocenterC61#10524
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. #21445993C2semidirect
2. #21444541C2semidirect
3. #21444430C2semidirect
4. #21443730C2semidirect
121. C61#10524semidirect

Maximal subgroups

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

subgroupindex
#214459932
#214445412
#214444302
#214437302
C61×#32532
#1052461