Finite Group Databasebeta

← #26137135

Subgroups — #26137135

Order 12032.

200 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 200 conjugacy classes of subgroups — too many to draw. Only its 55 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
1C2×#15688961C211yesmaximal, characteristic, complemented
2C2×#15688956C211yesmaximal, characteristic, complemented
3#20245480C211yesmaximal, characteristic, complemented
4#20245471C211yesmaximal, characteristic
5#20241587C211yesmaximal, characteristic, complemented
6#20241570C211yesmaximal, characteristic, complemented
7C47×#1415C211yesmaximal, characteristic, complemented
8C2×Dic376C2211yescharacteristic
9C2×C16×D47C2211yescharacteristic
10#15689365—21no—
11#15689356—21no—
12#15688961—22no—
13#15688956—22no—
14C2×C47⋊C32C2211yescharacteristic
15#15688949C2211yescharacteristic
16#15688926—21no—
17#15688924—21no—
18C2×D16×C47C2211yescharacteristic
19C2×C32×C47C2211yescharacteristic
20C47×#366C2211yescharacteristic
21C2×Dic188—21no—
22C2×C8×D47D411yescharacteristic
23#13094004—41no—
24#13093995—41no—
25Dic376—21no—
26Dic376—21no—
27C2×C47⋊C16D411yescharacteristic
28C16×D47—21no—
29C16×D47—21no—
30#13093958—21no—
31#13093947—41no—
32#13093945—41no—
33C47⋊C32D412yescomplemented
34C2×D8×C47—21no—
35D16×C47—21no—
36D16×C47—21no—
37C2×C16×C47C2311yescharacteristic
38#107×C47—21no—
39C32×C47—21no—
40C2×D4×C47—41no—
41C2×C22⋊D47—81no—
42C2×C4×D47D811yescharacteristic
43C2×Dic94—41no—
44D8×C47—41no—
45D8×C47—41no—
46C2×C8×C47C2×D411yescharacteristic
47C4⋊C4×C47—41no—
48C22⋊Dic47—81no—
49(C2×D47)⋊C4—81no—
50C4⋊Dic47—41no—
51C4⋊Dic47—81no—
52C2×C47⋊C8D811yescharacteristic
53Dic188—41no—
54Dic188—41no—
55C8×D47—21no—
56C8×D47—21no—
57C16×C47C2×D411yescharacteristic
58C16×C47#4111yescharacteristic
59C47⋊C16—21no—
60C23×C47—81no—
61C22×D47D1611yescharacteristic
62D4×C47—81no—
63D4×C47—81no—
64C2×C4×C47—81no—
65C2×C4×C47C2×D811yescharacteristic
66C22⋊D47—162no—
67C2×Dic47—81no—
68C2×Dic47—81no—
69C2×Dic47D1611yescharacteristic
70C4×D47—21no—
71C4×D47—21no—
72Dic94—81no—
73Dic94—81no—
74C8×C47#12111yescharacteristic
75C8×C47#13511yescharacteristic
76C47⋊C8—21no—
77#13699—471nomaximal, Sylow
78C22×C47—161no—
79C22×C47—161no—
80C22×C47—161no—
81C22×C47C2×D1611yescharacteristic
82C2×D47—21no—
83C2×D47—21no—
84C2×D47—21no—
85C4×C47—161no—
86C4×C47#46611yescharacteristic
87C4×C47#50811yescharacteristic
88Dic47—21no—
89Dic47—161no—
90Dic47—161no—
91C2×SD64—471no—
92C2×M64—471no—
93#2216—471no—
94#2215—471no—
95#1423—471no—
96#1416—471no—
97#1415D4711yescharacteristic, complemented
98C2×C47—321no—
99C2×C47#221511yescharacteristic
100C2×C47#226311yescharacteristic
101C2×C47#226411yescharacteristic
102D47—41no—
103C2×Q32—471no—
104C2×D16C2×D4711yescharacteristic
105C22×C16—471no—
106#467—941no—
107#466—941no—
108SD64—942no—
109M64—942no—
110C2×C32—471no—
111C2×C32C2×D4711yescharacteristic
112#366—471no—
113#366C2×D4711yescharacteristic
114#358—941no—
115#357—941no—
116C47#1369911yescharacteristic, complemented, Sylow
117C2×Q16—941no—
118C2×D8—21no—
119C22×C8—471no—
120C22⋊Q8—1881no—
121#121—1881no—
122Q32—941no—
123Q32—941no—
124D16—21no—
125D16—21no—
126C2×C16—471no—
127C2×C16—941no—
128C2×C16—941no—
129C2×C16C22×D4711yescharacteristic
130#107—21no—
131#107—941no—
132#103—1881no—
133#102—1881no—
134C32—21no—
135C32—472no—
136C2×Q8—1881no—
137C2×D4—41no—
138C2×D4—3761no—
139C22×C4—471no—
140Q16—1881no—
141Q16—1881no—
142D8—41no—
143D8—41no—
144C2×C8—471no—
145C2×C8—941no—
146C2×C8—941no—
147C2×C8D4×D4711yescharacteristic
148C4⋊C4—41no—
149C4⋊C4—3761no—
150C4⋊C4—1881no—
151C22⋊C4—3761no—
152C22⋊C4—3761no—
153C16—941no—
154C16#1062535011yescharacteristic
155C16D4×D4711yescharacteristic
156C23—81no—
157C23—471no—
158Q8—3761no—
159Q8—3761no—
160D4—81no—
161D4—81no—
162D4—7522no—
163C2×C4—81no—
164C2×C4—471no—
165C2×C4—941no—
166C2×C4—941no—
167C2×C4—3761no—
168C2×C4—3761no—
169C2×C4D8×D4711yescharacteristic
170C8—941no—
171C8#1309399711yescharacteristic
172C8#1309404511yescharacteristic
173C22—161no—
174C22—161no—
175C22—161no—
176C22—941no—
177C22—941no—
178C22—941no—
179C22D16×D4711yescharacteristic
180C4—161no—
181C4—941no—
182C4—7521no—
183C4—7521no—
184C4#1568935811yescharacteristic
185C4#1568955411yescharacteristic
186C2—321no—
187C2—1881no—
188C2#2024547311yescharacteristic
189C2#2024569911yescharacteristic
190C2#2024570411yescharacteristic
subgroupG/H
centerC22D16×D47
commutator, cosocleC2×C16×C47C23
FrattiniC2×C16C22×D47
FittingC47×#1415C2
socleC22×C47C2×D16
prime radical#20245471C2
hypercenter#1415D47
hypocenterC47#13699
LCSG ▷ C2×C16×C47 ▷ C8×C47 ▷ C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ C2×C16 ◁ #1415

Complements

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

NH ≅ G/Ntype
1. C2×#15688961C2semidirect
2. C2×#15688956C2semidirect
3. #20245480C2semidirect
5. #20241587C2semidirect
6. #20241570C2semidirect
7. C47×#1415C2semidirect
33. C47⋊C32D4semidirect
97. #1415D47semidirect
116. C47#13699semidirect

Maximal subgroups

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

subgroupindex
C2×#156889612
C2×#156889562
#202454802
#202454712
#202415872
#202415702
C47×#14152
#1369947