Finite Group Databasebeta

← #26110686

Subgroups — #26110686

Order 12032.

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

normal subgroups only

This group has 336 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
1#20244370C211yesmaximal, characteristic
2#20242156C212yesmaximal
3#20241983C211yesmaximal, characteristic
4#20241280C212yesmaximal
5C47×#2987C211yesmaximal, characteristic
6#15689147C2211yescharacteristic
7C4×#10625329C2212yes—
8#15688969C2211yescharacteristic
9#15688882—22no—
10#15688875—22no—
11#15688873—22no—
12#15688865C411yescharacteristic, complemented
13#15688865C412yescomplemented
14#15688865C411yescharacteristic, complemented
15C47×#533C2211yescharacteristic
16C47×#446—22no—
17C47×#446—22no—
18C47×#433—22no—
19C47×#432C2212yes—
20C2×#10625329—22no—
21C2×#10625329—21no—
22C2×C4×Dic47—21no—
23C4⋊(C47⋊C8)—22no—
24#13093935C2×C412yes—
25#13093935C2×C412yes—
26C4×C47⋊C8—22no—
27C47⋊#95—22no—
28C4⋊Q8×C47Q812yes—
29#125×C47C2×C411yescharacteristic
30#125×C47C2×C411yescharacteristic
31C22⋊Q8×C47—22no—
32C4×Q8×C47—22no—
33#117×C47D412yes—
34C2×C42×C47C2311yescharacteristic
35C4⋊C8×C47—22no—
36C4⋊C8×C47—22no—
37C4⋊C8×C47D412yes—
38C4⋊C8×C47D412yes—
39C22⋊C8×C47—22no—
40#97×C47—22no—
41#97×C47—22no—
42C4×C8×C47—22no—
43C2×Q8×C47—22no—
44C22×C4×C47C2×D411yescharacteristic
45C22×C4×C47#4112yes—
46C22×Dic47—41no—
47C2×C8×C47—22no—
48C2×C8×C47—22no—
49C4⋊C4×C47—22no—
50C4⋊C4×C47—22no—
51C4⋊C4×C47—22no—
52C4⋊C4×C47C4⋊C412yes—
53C4⋊C4×C47C4⋊C412yes—
54C22⋊C4×C47—22no—
55C42×C47—22no—
56C42×C47C22×C411yescharacteristic
57C42×C47C2×D412yes—
58C42×C47C2×Q811yescharacteristic
59C4×Dic47—22no—
60C4×Dic47—41no—
61#10625329—44no—
62#10625329—42no—
63C2×C47⋊C8—22no—
64C2×C47⋊C8—22no—
65C2×C47⋊C8—41no—
66C23×C47#12311yescharacteristic
67Q8×C47—82no—
68C2×C4×C47—21no—
69C2×C4×C47—21no—
70C2×C4×C47—22no—
71C2×C4×C47—22no—
72C2×C4×C47—42no—
73C2×C4×C47C2×C4⋊C411yescharacteristic
74C2×C4×C47C4×D412yes—
75C2×C4×C47#12011yescharacteristic
76C2×C4×C47C22⋊Q812yes—
77C2×Dic47—42no—
78C2×Dic47—82no—
79C8×C47—42no—
80C8×C47—42no—
81C47⋊C8—24no—
82C47⋊C8—42no—
83C47⋊C8—81no—
84#8919—471nomaximal, Sylow
85C22×C47—21no—
86C22×C47—22no—
87C22×C47#38511yescharacteristic
88C4×C47—21no—
89C4×C47—22no—
90C4×C47—22no—
91C4×C47—42no—
92C4×C47—42no—
93C4×C47#45411yescharacteristic
94C4×C47#45611yescharacteristic
95Dic47—82no—
96#2987D4711yescharacteristic
97#1995—471no—
98#1569—472no—
99#1526—471no—
100#1300—472no—
101C2×C47—41no—
102C2×C47#185711yescharacteristic
103C2×C47#186112yes—
104#533C2×D4711yescharacteristic
105#446—22no—
106#446—22no—
107#433—22no—
108#432C2×D4712yes—
109#423—471no—
110C4×M16—472no—
111#376—471no—
112#339—942no—
113#335—942no—
114#334—942no—
115#330—471no—
116#330—472no—
117#330—471no—
118C47#891911yescharacteristic, complemented, Sylow
119C2×M16—942no—
120C2×M16—941no—
121C4⋊Q8Dic9412yes—
122#125C4×D4711yescharacteristic
123#125C4×D4711yescharacteristic
124C22⋊Q8—22no—
125C4×Q8—22no—
126#117C22⋊D4712yes—
127C2×C42—941no—
128C2×C42C22×D4711yescharacteristic
129C4⋊C8—22no—
130C4⋊C8—22no—
131C4⋊C8—942no—
132C4⋊C8C22⋊D4712yes—
133C4⋊C8C22⋊D4712yes—
134C22⋊C8—22no—
135#97—22no—
136#97—22no—
137#97—472no—
138#97—472no—
139C4×C8—22no—
140C4×C8—942no—
141#95—942no—
142C2×Q8—22no—
143C22×C4—1881no—
144C22×C4#1062535012yes—
145C22×C4C2×C22⋊D4711yescharacteristic
146M16—1884no—
147M16—1882no—
148C2×C8—22no—
149C2×C8—22no—
150C2×C8—942no—
151C2×C8—942no—
152C2×C8—1881no—
153C4⋊C4—22no—
154C4⋊C4—22no—
155C4⋊C4—22no—
156C4⋊C4Dic47⋊C412yes—
157C4⋊C4Dic47⋊C412yes—
158C22⋊C4—22no—
159C42—22no—
160C42—942no—
161C42—1881no—
162C42C2×Dic9411yescharacteristic
163C42C2×C4×D4711yescharacteristic
164C42C2×C22⋊D4712yes—
165C23#1309400711yescharacteristic
166Q8—82no—
167C2×C4—21no—
168C2×C4—21no—
169C2×C4—22no—
170C2×C4—22no—
171C2×C4—42no—
172C2×C4—3762no—
173C2×C4—1882no—
174C2×C4C2×Dic47⋊C411yescharacteristic
175C2×C4C4×C22⋊D4712yes—
176C2×C4#1309399311yescharacteristic
177C2×C4#1309400312yes—
178C8—42no—
179C8—42no—
180C8—944no—
181C8—3761no—
182C8—1882no—
183C22—21no—
184C22—22no—
185C22#1568899611yescharacteristic
186C4—21no—
187C4—22no—
188C4—22no—
189C4—42no—
190C4—42no—
191C4—3762no—
192C4#1568929611yescharacteristic
193C4#1568930611yescharacteristic
194C2—41no—
195C2#2024360311yescharacteristic
196C2#2024362812yes—
subgroupG/H
centerC2×C4#13093993
commutatorC42×C47C22×C4
FrattiniC2×C42C22×D47
FittingC47×#2987C2
socleC22×C47#385
prime radicalC23×C47#123
cosocleC2×C42×C47C23
hypercenter#2987D47
hypocenterC47#8919
LCSG ▷ C42×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #2987

Complements

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

NH ≅ G/Ntype
12. #15688865C4semidirect
13. #15688865C4semidirect
14. #15688865C4semidirect
118. C47#8919semidirect

Maximal subgroups

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

subgroupindex
#202443702
#202421562
#202419832
#202412802
C47×#29872
#891947