Finite Group Databasebeta

← #26134822

Subgroups — #26134822

Order 12032.

308 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 308 conjugacy classes of subgroups — too many to draw. Only its 115 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#20252326C211yesmaximal, characteristic
2#20245154C211yesmaximal, characteristic
3#20241473C212yesmaximal
4#20241467C212yesmaximal
5C47×#2110C211yesmaximal, characteristic
6#15689676C411yescharacteristic
7C2×#13093964C2212yes—
8#15689253—22no—
9#15689251—22no—
10#15689151C411yescharacteristic
11#15689150C411yescharacteristic
12#15689146C411yescharacteristic
13#15689078C2211yescharacteristic
14C2×#13093934C2211yescharacteristic
15#15688944—22no—
16C2×M32×C47C2212yes—
17C47×#405C2211yescharacteristic
18C47×#347—22no—
19C2×#10625329C2×C411yescharacteristic
20C22×C47⋊C8C2×C411yescharacteristic
21#13094023—21no—
22#13094015—21no—
23#13094001—22no—
24C4×Dic94—22no—
25#13093983C2×C411yescharacteristic
26C2×C4×Dic47C2×C411yescharacteristic
27#13093964—22no—
28#13093964—22no—
29C2×C47⋊C16—22no—
30C4⋊(C47⋊C8)—22no—
31Dic47⋊C8—22no—
32Dic47⋊C8—22no—
33#13093934—21no—
34#13093934—21no—
35#13093934—21no—
36C8×Dic47—21no—
37C2×M16×C47C2×C411yescharacteristic
38C22×C8×C47C2311yescharacteristic
39#117×C47C2×C411yescharacteristic
40M32×C47—22no—
41M32×C47—22no—
42C2×C16×C47Q814yescomplemented
43#97×C47D412yes—
44C4×C8×C47D412yes—
45C22×C4×C47C22×C411yescharacteristic
46C22×Dic47—21no—
47C2×Dic94—22no—
48M16×C47—22no—
49C2×C8×C47C22⋊C412yes—
50C2×C8×C47C2×D411yescharacteristic
51C2×C8×C47C2×D411yescharacteristic
52C2×C8×C47C2×Q812yes—
53C2×C8×C47#4112yes—
54C4⋊C4×C47—21no—
55C22⋊C4×C47—21no—
56C42×C47C22⋊C412yes—
57C22⋊Dic47M1612yes—
58C4⋊Dic47—22no—
59C4⋊Dic47—21no—
60Dic47⋊C4—22no—
61Dic47⋊C4—22no—
62C4×Dic47—21no—
63C4×Dic47—21no—
64C4×Dic47M1611yescharacteristic
65C4×Dic47M1611yescharacteristic
66#10625329—22no—
67C2×C47⋊C8—21no—
68C2×C47⋊C8—21no—
69C2×C47⋊C8—22no—
70C16×C47—24no—
71C47⋊C16—42no—
72C23×C47C2×M1611yescharacteristic
73C2×C4×C47—22no—
74C2×C4×C47C2×C22⋊C411yescharacteristic
75C2×C4×C47C4×Q812yes—
76C2×C4×C47C2×M1611yescharacteristic
77C2×C4×C47#13112yes—
78C2×Dic47—21no—
79C2×Dic47—21no—
80C2×Dic47—22no—
81C2×Dic47—81no—
82Dic94—82no—
83C8×C47—22no—
84C8×C47C22⋊Q812yes—
85C8×C47#12411yescharacteristic
86C8×C47C4⋊Q811yescharacteristic
87C47⋊C8—41no—
88C47⋊C8—41no—
89#13269—471nomaximal, Sylow
90C22×C47—41no—
91C22×C47#40711yescharacteristic
92C22×C47#44612yes—
93C4×C47—42no—
94C4×C47#39111yescharacteristic
95C4×C47#40811yescharacteristic
96C4×C47#44612yes—
97Dic47—41no—
98Dic47—42no—
99Dic47—41no—
100#2961—471no—
101#2153—471no—
102#2110D4711yescharacteristic
103#1378—472no—
104#1375—472no—
105C2×C47—21no—
106C2×C47—22no—
107C2×C47#198511yescharacteristic
108#533—471no—
109C2×M32—472no—
110C2×M32C2×D4712yes—
111#446—942no—
112#446—942no—
113#424—471no—
114#424—471no—
115#423—471no—
116#405—471no—
117#405C2×D4711yescharacteristic
118C2×#97—471no—
119#364—942no—
120#347—22no—
121C47#1326911yescharacteristic, complemented, Sylow
122C2×M16—471no—
123C2×M16C4×D4711yescharacteristic
124C22×C8—471no—
125C22×C8C22×D4711yescharacteristic
126C4⋊Q8—941no—
127#125—941no—
128C22⋊Q8—942no—
129C4×Q8—942no—
130#117—471no—
131#117C4×D4711yescharacteristic
132C2×C42—471no—
133M32—22no—
134M32—22no—
135M32—942no—
136M32—942no—
137C2×C16—942no—
138C2×C16Dic9414yescomplemented
139C4⋊C8—942no—
140C4⋊C8—942no—
141C4⋊C8—942no—
142#97—941no—
143#97—941no—
144#97—941no—
145#97C22⋊D4712yes—
146C4×C8—941no—
147C4×C8D18812yes—
148C2×Q8—942no—
149C22×C4—941no—
150C22×C4C2×C4×D4711yescharacteristic
151M16—22no—
152M16—942no—
153C2×C8—941no—
154C2×C8—941no—
155C2×C8—942no—
156C2×C8(C2×D47)⋊C412yes—
157C2×C8C2×Dic9412yes—
158C2×C8C2×D18811yescharacteristic
159C2×C8#1062535012yes—
160C2×C8C2×C22⋊D4711yescharacteristic
161C4⋊C4—21no—
162C4⋊C4—942no—
163C4⋊C4—942no—
164C4⋊C4—942no—
165C4⋊C4—941no—
166C22⋊C4—21no—
167C22⋊C4—472no—
168C42—471no—
169C42—471no—
170C42—941no—
171C42—941no—
172C42(C2×D47)⋊C412yes—
173C16—24no—
174C16—1882no—
175C23M16×D4711yescharacteristic
176Q8—3762no—
177C2×C4—22no—
178C2×C4—941no—
179C2×C4—941no—
180C2×C4—942no—
181C2×C4—3761no—
182C2×C4C2×(C2×D47)⋊C411yescharacteristic
183C2×C4C4×Dic9412yes—
184C2×C4M16×D4711yescharacteristic
185C2×C4#1309403212yes—
186C8—22no—
187C8—1881no—
188C8—1881no—
189C8#1309400312yes—
190C8#1309401211yescharacteristic
191C8#1309402411yescharacteristic
192C22—41no—
193C22#1568908611yescharacteristic
194C22#1568925112yes—
195C4—42no—
196C4—1881no—
197C4—1881no—
198C4—1882no—
199C4#1568902911yescharacteristic
200C4#1568909111yescharacteristic
201C4#1568925112yes—
202C2—21no—
203C2—22no—
204C2#2024432811yescharacteristic
subgroupG/H
centerC4#15689029
commutatorC22×C4×C47C22×C4
FrattiniC22×C8C22×D47
FittingC47×#2110C2
socleC2×C47#1985
prime radicalC23×C47C2×M16
cosocleC22×C8×C47C23
hypercenter#2110D47
hypocenterC47#13269
LCSG ▷ C22×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C4 ◁ C22×C8 ◁ #2110

Complements

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

NH ≅ G/Ntype
42. C2×C16×C47Q8semidirect
121. C47#13269semidirect
138. C2×C16Dic94semidirect

Maximal subgroups

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

subgroupindex
#202523262
#202451542
#202414732
#202414672
C47×#21102
#1326947