Finite Group Databasebeta

← #26130428

Subgroups — #26130428

Order 12032.

218 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 218 conjugacy classes of subgroups — too many to draw. Only its 65 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#20245541C211yesmaximal, characteristic
2#20245435C211yesmaximal, characteristic
3#20242982C211yesmaximal, characteristic
4#20242194C211yesmaximal, characteristic
5#20241451C211yesmaximal, characteristic
6#20241447C211yesmaximal, characteristic
7C47×#1362C211yesmaximal, characteristic
8C2×#13093970—21no—
9#15689528C2211yescharacteristic
10#15689519—21no—
11#15689475—21no—
12#15689247—21no—
13C4×Dic188C2211yescharacteristic
14#15688949—21no—
15C4⋊(C47⋊C16)C2211yescharacteristic
16#15688928—21no—
17#15688927—21no—
18#15688853—21no—
19C8×C47⋊C8C2211yescharacteristic
20C47×#494C2211yescharacteristic
21C47×C4⋊C16C2211yescharacteristic
22C47×#335C2211yescharacteristic
23C2×Dic188D411yescharacteristic
24#13094024—21no—
25C4×Dic94—21no—
26#13093970—42no—
27C2×C47⋊C16—21no—
28#13093958—21no—
29#13093958—21no—
30#13093958D411yescharacteristic
31#13093955—41no—
32#13093955—41no—
33Dic47⋊C8—41no—
34#13093949—21no—
35#13093947—42no—
36C4×C47⋊C8D411yescharacteristic
37C4×C47⋊C8D411yescharacteristic
38C8×Dic47—41no—
39C2×Q16×C47—21no—
40C2×Q16×C47—21no—
41C4⋊Q8×C47—21no—
42C2×C16×C47—21no—
43C4⋊C8×C47—21no—
44C4×C8×C47C2311yescharacteristic
45C2×Q8×C47—41no—
46C2×Dic94—21no—
47C2×Dic94—41no—
48Q16×C47—41no—
49Q16×C47—41no—
50Q16×C47—81no—
51C2×C8×C47—41no—
52C2×C8×C47C2×D411yescharacteristic
53C2×C8×C47#4111yescharacteristic
54C4⋊C4×C47—41no—
55C4⋊C4×C47—41no—
56C42×C47C2×D411yescharacteristic
57C4⋊Dic47—21no—
58C4⋊Dic47—41no—
59C4⋊Dic47—41no—
60Dic47⋊C4—41no—
61C4×Dic47—41no—
62C2×C47⋊C8—21no—
63C2×C47⋊C8D811yescharacteristic
64C2×C47⋊C8D811yescharacteristic
65Dic188—21no—
66Dic188SD1612yes—
67C16×C47—41no—
68C47⋊C16—41no—
69Q8×C47—81no—
70Q8×C47—81no—
71C2×C4×C47—81no—
72C2×C4×C47#12111yescharacteristic
73C2×C4×C47C2×D811yescharacteristic
74C2×C4×C47AGL(1,ℤ/8)11yescharacteristic
75C2×Dic47—41no—
76C2×Dic47—41no—
77C2×Dic47—81no—
78Dic94—22no—
79Dic94—41no—
80Dic94—82no—
81C8×C47—21no—
82C8×C47—81no—
83C8×C47C2×SD1611yescharacteristic
84C8×C47#13511yescharacteristic
85C47⋊C8—21no—
86C47⋊C8—41no—
87C47⋊C8Q3212yescomplemented
88#12421—471nomaximal, Sylow
89C22×C47#45911yescharacteristic
90C4×C47—21no—
91C4×C47—161no—
92C4×C47#46511yescharacteristic
93C4×C47#47111yescharacteristic
94C4×C47C2×Q3211yescharacteristic
95C4×C47#51011yescharacteristic
96Dic47—42no—
97Dic47—81no—
98Dic47—161no—
99#2227—471no—
100#2209—471no—
101#1707—471no—
102C8×Q16—471no—
103#1367—471no—
104#1365—471no—
105#1362D4711yescharacteristic
106C2×C47#166511yescharacteristic
107C2×C47#220911yescharacteristic
108C2×C47#221211yescharacteristic
109C2×Q32—941no—
110#500—471no—
111#498—941no—
112#494C2×D4711yescharacteristic
113#487—941no—
114C8×Q8—941no—
115C4×Q16—471no—
116#366—941no—
117C4⋊C16—471no—
118C4⋊C16C2×D4711yescharacteristic
119#358—941no—
120#358—941no—
121#335C2×D4711yescharacteristic
122Q8⋊C8—941no—
123C82—471no—
124C47#1242111yescharacteristic, complemented, Sylow
125C2×Q16—21no—
126C2×Q16—21no—
127C2×Q16—471no—
128C4⋊Q8—21no—
129C4⋊Q8—941no—
130C4×Q8—941no—
131Q32—1882no—
132C2×C16—21no—
133C2×C16—941no—
134#107—471no—
135#107—941no—
136#107—941no—
137#106—1881no—
138#106—1881no—
139C4⋊C8—21no—
140C4⋊C8—1881no—
141#103—941no—
142#103—1882no—
143C4×C8—471no—
144C4×C8—471no—
145C4×C8—1881no—
146C4×C8C22×D4711yescharacteristic
147C2×Q8—41no—
148C2×Q8—941no—
149C2×Q8—1881no—
150Q16—41no—
151Q16—41no—
152Q16—81no—
153Q16—472no—
154Q16—941no—
155C2×C8—41no—
156C2×C8—471no—
157C2×C8—471no—
158C2×C8—941no—
159C2×C8#1062535011yescharacteristic
160C2×C8D4×D4711yescharacteristic
161C4⋊C4—41no—
162C4⋊C4—41no—
163C4⋊C4—941no—
164C4⋊C4—1881no—
165C4⋊C4—1881no—
166C4⋊C4—1881no—
167C42—1881no—
168C42D4×D4711yescharacteristic
169C16—41no—
170C16—1881no—
171Q8—81no—
172Q8—81no—
173Q8—942no—
174Q8—3762no—
175Q8—1881no—
176C2×C4—81no—
177C2×C4—3761no—
178C2×C4—1881no—
179C2×C4—1881no—
180C2×C4#1309399711yescharacteristic
181C2×C4D8×D4711yescharacteristic
182C2×C4#1309405111yescharacteristic
183C8—21no—
184C8—81no—
185C8—472no—
186C8—941no—
187C8—1881no—
188C8SD16×D4711yescharacteristic
189C8#1309404311yescharacteristic
190C22#1568931711yescharacteristic
191C4—21no—
192C4—161no—
193C4—3761no—
194C4—1882no—
195C4—7521no—
196C4#1568935111yescharacteristic
197C4#1568938511yescharacteristic
198C4Q32×D4711yescharacteristic
199C4#1568956211yescharacteristic
200C2#2024272811yescharacteristic
201C2#2024543711yescharacteristic
202C2#2024546011yescharacteristic
subgroupG/H
centerC22#15689317
commutator, cosocleC4×C8×C47C23
FrattiniC4×C8C22×D47
FittingC47×#1362C2
socle, prime radicalC22×C47#459
hypercenter#1362D47
hypocenterC47#12421
LCSG ▷ C4×C8×C47 ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #1362

Complements

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

NH ≅ G/Ntype
87. C47⋊C8Q32semidirect
124. C47#12421semidirect

Maximal subgroups

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

subgroupindex
#202455412
#202454352
#202429822
#202421942
#202414512
#202414472
C47×#13622
#1242147