Finite Group Databasebeta

← #26130430

Subgroups — #26130430

Order 12032.

218 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 218 conjugacy classes of subgroups — too many to draw. Only its 71 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#20245439C211yesmaximal, characteristic
3#20242985C211yesmaximal, characteristic
4C8×Dic188C211yesmaximal, characteristic
5#20241445C211yesmaximal, characteristic
6#20241438C211yesmaximal, characteristic
7C47×#1367C211yesmaximal, characteristic
8C2×Dic376—21no—
9#15689528C2211yescharacteristic
10#15689521—21no—
11#15689503C2211yescharacteristic
12#15689474—21no—
13C8×Dic94—21no—
14C4×Dic188C2211yescharacteristic
15#15688949—21no—
16#15688928—21no—
17#15688928—21no—
18#15688876C2211yescharacteristic
19#15688855—21no—
20C47×C4⋊C16C2211yescharacteristic
21C47×C4⋊C16C2211yescharacteristic
22C82×C47C2211yescharacteristic
23C2×Dic188—21no—
24C2×Dic188—21no—
25C2×Dic188D411yescharacteristic
26#13094024—21no—
27#13094024—21no—
28C4×Dic94—21no—
29Dic376—42no—
30#13093958—21no—
31#13093958—21no—
32#13093958D411yescharacteristic
33#13093956—41no—
34#13093956—41no—
35C4⋊(C47⋊C8)—21no—
36Dic47⋊C8—41no—
37#13093949—21no—
38#13093949—42no—
39C8×Dic47—41no—
40C2×C16×C47—21no—
41C2×C16×C47—21no—
42C4×C8×C47D411yescharacteristic
43C4×C8×C47D411yescharacteristic
44C4×C8×C47C2311yescharacteristic
45C2×Dic94—21no—
46C2×Dic94—41no—
47C2×Dic94—41no—
48C2×C8×C47—21no—
49C2×C8×C47D811yescharacteristic
50C2×C8×C47D811yescharacteristic
51C2×C8×C47C2×D411yescharacteristic
52C2×C8×C47#4111yescharacteristic
53C42×C47C2×D411yescharacteristic
54C4⋊Dic47—21no—
55C4⋊Dic47—41no—
56C4⋊Dic47—41no—
57C4⋊Dic47—41no—
58C4⋊Dic47—41no—
59Dic47⋊C4—41no—
60C4×Dic47—41no—
61C2×C47⋊C8—41no—
62Dic188—21no—
63Dic188—41no—
64Dic188—41no—
65Dic188—81no—
66Dic188SD1612yes—
67C16×C47—41no—
68C16×C47—41no—
69C2×C4×C47#12111yescharacteristic
70C2×C4×C47C2×D811yescharacteristic
71C2×C4×C47AGL(1,ℤ/8)11yescharacteristic
72C2×Dic47—41no—
73C2×Dic47—41no—
74C2×Dic47—81no—
75C2×Dic47—81no—
76Dic94—22no—
77Dic94—41no—
78Dic94—82no—
79Dic94—81no—
80Dic94—81no—
81C8×C47—21no—
82C8×C47—21no—
83C8×C47—41no—
84C8×C47Q3212yescomplemented
85C8×C47C2×SD1611yescharacteristic
86C8×C47#13511yescharacteristic
87C47⋊C8—81no—
88#12421—471nomaximal, Sylow
89C22×C47#45911yescharacteristic
90C4×C47—21no—
91C4×C47#46511yescharacteristic
92C4×C47#47111yescharacteristic
93C4×C47C2×Q3211yescharacteristic
94C4×C47#51011yescharacteristic
95Dic47—42no—
96Dic47—81no—
97Dic47—161no—
98Dic47—161no—
99#2227—471no—
100#2209—471no—
101#1707—471no—
102C8×Q16—471no—
103#1367D4711yescharacteristic
104#1365—471no—
105#1362—471no—
106C2×C47#166511yescharacteristic
107C2×C47#220911yescharacteristic
108C2×C47#221211yescharacteristic
109C2×Q32—941no—
110#500—471no—
111#498—941no—
112#494—471no—
113#487—941no—
114C8×Q8—941no—
115C4×Q16—471no—
116#366—941no—
117C4⋊C16C2×D4711yescharacteristic
118C4⋊C16C2×D4711yescharacteristic
119#358—941no—
120#358—941no—
121#335—471no—
122Q8⋊C8—941no—
123C82C2×D4711yescharacteristic
124C47#1242111yescharacteristic, complemented, Sylow
125C2×Q16—471no—
126C2×Q16—941no—
127C2×Q16—941no—
128C4⋊Q8—941no—
129C4⋊Q8—941no—
130C4×Q8—941no—
131Q32—1882no—
132C2×C16—21no—
133C2×C16—21no—
134#107—471no—
135#107—941no—
136#107—941no—
137#106—1881no—
138#106—1881no—
139C4⋊C8—941no—
140C4⋊C8—1881no—
141#103—941no—
142#103—1882no—
143C4×C8—1881no—
144C4×C8D18811yescharacteristic
145C4×C8D18811yescharacteristic
146C4×C8C22×D4711yescharacteristic
147C2×Q8—941no—
148C2×Q8—1881no—
149C2×Q8—1881no—
150Q16—472no—
151Q16—941no—
152Q16—3761no—
153Q16—1881no—
154Q16—1881no—
155C2×C8—21no—
156C2×C8—1881no—
157C2×C8D37611yescharacteristic
158C2×C8D37611yescharacteristic
159C2×C8D4×D4711yescharacteristic
160C2×C8#1062535411yescharacteristic
161C4⋊C4—941no—
162C4⋊C4—1881no—
163C4⋊C4—1881no—
164C4⋊C4—1881no—
165C4⋊C4—1881no—
166C4⋊C4—1881no—
167C42—1881no—
168C42C2×D18811yescharacteristic
169C16—41no—
170C16—41no—
171Q8—942no—
172Q8—3762no—
173Q8—3761no—
174Q8—3761no—
175Q8—1881no—
176C2×C4—3761no—
177C2×C4—3761no—
178C2×C4—1881no—
179C2×C4—1881no—
180C2×C4#1309399911yescharacteristic
181C2×C4C2×D37611yescharacteristic
182C2×C4#1309405211yescharacteristic
183C8—21no—
184C8—21no—
185C8—41no—
186C8—3761no—
187C8Dic37612yescomplemented
188C8SD16×D4711yescharacteristic
189C8#1309404511yescharacteristic
190C22#1568931911yescharacteristic
191C4—21no—
192C4—3761no—
193C4—1882no—
194C4—7521no—
195C4—7521no—
196C4#1568935311yescharacteristic
197C4#1568938711yescharacteristic
198C4C2×Dic37611yescharacteristic
199C4#1568956611yescharacteristic
200C2#2024273011yescharacteristic
201C2#2024543911yescharacteristic
202C2#2024545811yescharacteristic
subgroupG/H
centerC22#15689319
commutator, cosocleC4×C8×C47C23
FrattiniC4×C8C22×D47
FittingC47×#1367C2
socle, prime radicalC22×C47#459
hypercenter#1367D47
hypocenterC47#12421
LCSG ▷ C4×C8×C47 ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C42 ◁ C82 ◁ #1367

Complements

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

NH ≅ G/Ntype
84. C8×C47Q32semidirect
124. C47#12421semidirect
187. C8Dic376semidirect

Maximal subgroups

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

subgroupindex
#202455412
#202454392
#202429852
C8×Dic1882
#202414452
#202414382
C47×#13672
#1242147