Finite Group Databasebeta

← #26121263

Subgroups — #26121263

Order 12032.

320 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 320 conjugacy classes of subgroups — too many to draw. Only its 93 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#20244327C211yesmaximal, characteristic
2#20243562C211yesmaximal, characteristic
3#20242162C211yesmaximal, characteristic
4#20241818C211yesmaximal, characteristic
5#20241816C211yesmaximal, characteristic
6#20241218C211yesmaximal, characteristic
7C47×#1571C211yesmaximal, characteristic
8C2×C4×Dic94C2211yescharacteristic
9#15689176C2211yescharacteristic
10C2×#13093959—22no—
11#15689147C2211yescharacteristic
12C2×#13093935C2211yescharacteristic
13#15688877—22no—
14#15688875—22no—
15#15688855—22no—
16#15688853—22no—
17C47×#431C2211yescharacteristic
18C47×#423C2211yescharacteristic
19C2×C4⋊C8×C47C2211yescharacteristic
20C47×#335—22no—
21C22×Dic94Q811yescharacteristic
22C2×#10625329—21no—
23C22×C47⋊C8D412yes—
24C4×Dic94—21no—
25C4×Dic94—21no—
26C4×Dic94—21no—
27C4×Dic94—21no—
28C2×C4⋊Dic47Q811yescharacteristic
29C2×Dic47⋊C4—21no—
30C2×C4×Dic47—21no—
31#13093959—44no—
32C4⋊(C47⋊C8)—21no—
33C4⋊(C47⋊C8)—21no—
34C4⋊(C47⋊C8)—21no—
35C22⋊(C47⋊C8)—21no—
36#13093935—21no—
37#13093935—21no—
38C4×C47⋊C8D412yes—
39C2×M16×C47—21no—
40C22×C8×C47—21no—
41C2×C42×C47C2311yescharacteristic
42C4⋊C8×C47—21no—
43C4⋊C8×C47—21no—
44C4⋊C8×C47—21no—
45C4⋊C8×C47—21no—
46C4⋊C8×C47—21no—
47C22⋊C8×C47—21no—
48C4×C8×C47D412yes—
49C22×C4×C47C2×D411yescharacteristic
50C22×C4×C47C2×Q811yescharacteristic
51C22×C4×C47#4111yescharacteristic
52C22×Dic47—21no—
53C22×Dic47—21no—
54C2×Dic94—21no—
55C2×Dic94—21no—
56C2×Dic94—42no—
57M16×C47—42no—
58C2×C8×C47—22no—
59C2×C8×C47—41no—
60C2×C8×C47—41no—
61C2×C8×C47—42no—
62C42×C47C2×D411yescharacteristic
63C42×C47C2×D411yescharacteristic
64C42×C47#4111yescharacteristic
65C42×C47#4111yescharacteristic
66C4⋊Dic47—21no—
67C4⋊Dic47—21no—
68Dic47⋊C4—41no—
69Dic47⋊C4—41no—
70C4×Dic47—41no—
71C4×Dic47—41no—
72#10625329—42no—
73C2×C47⋊C8—22no—
74C2×C47⋊C8—22no—
75C2×C47⋊C8—22no—
76C2×C47⋊C8—41no—
77C2×C47⋊C8Q1614yes—
78C23×C47C22⋊Q811yescharacteristic
79C2×C4×C47—41no—
80C2×C4×C47—41no—
81C2×C4×C47C22⋊Q811yescharacteristic
82C2×C4×C47C22⋊Q811yescharacteristic
83C2×C4×C47#12311yescharacteristic
84C2×C4×C47#12311yescharacteristic
85C2×C4×C47#12311yescharacteristic
86C2×C4×C47#12711yescharacteristic
87C2×C4×C47C2×Q1612yes—
88C2×C4×C47AGL(1,ℤ/8)12yes—
89C2×Dic47—22no—
90C2×Dic47—41no—
91C2×Dic47—41no—
92C2×Dic47—42no—
93C2×Dic47—41no—
94Dic94—22no—
95Dic94—22no—
96Dic94—41no—
97Dic94—41no—
98C8×C47—42no—
99C8×C47—81no—
100C8×C47—81no—
101C47⋊C8—24no—
102C47⋊C8—42no—
103C47⋊C8—81no—
104#10662—471nomaximal, Sylow
105C22×C47—21no—
106C22×C47—21no—
107C22×C47#39911yescharacteristic
108C22×C47#47712yes—
109C4×C47—21no—
110C4×C47—21no—
111C4×C47—21no—
112C4×C47—21no—
113C4×C47#48412yes—
114C4×C47#49411yescharacteristic
115C4×C47#49611yescharacteristic
116Dic47—42no—
117Dic47—81no—
118#1985—471no—
119#1849—471no—
120#1571—471no—
121#1571D4711yescharacteristic
122#1487—471no—
123#1487—471no—
124#1275—471no—
125C2×C47—22no—
126C2×C47#209111yescharacteristic
127C2×C47#209511yescharacteristic
128C2×C47#209811yescharacteristic
129C2×C4×Q8—471no—
130#431—471no—
131#431C2×D4711yescharacteristic
132C2×#108—942no—
133#423—471no—
134#423C2×D4711yescharacteristic
135C2×C4⋊C8C2×D4711yescharacteristic
136C2×#97—471no—
137#336—942no—
138#335—22no—
139#335—942no—
140Q8⋊C8—942no—
141Q8⋊C8—942no—
142C47#1066211yescharacteristic, complemented, Sylow
143C22×Q8—471no—
144C2×M16—21no—
145C2×M16—941no—
146C22×C8—21no—
147C22×C8—472no—
148C4×Q8—941no—
149C4×Q8—941no—
150C4×Q8—941no—
151C4×Q8—941no—
152C2×C4⋊C4—471no—
153C2×C4⋊C4—941no—
154C2×C42—941no—
155C2×C42C22×D4711yescharacteristic
156#108—1884no—
157C4⋊C8—21no—
158C4⋊C8—21no—
159C4⋊C8—21no—
160C4⋊C8—21no—
161C4⋊C8—21no—
162C4⋊C8—941no—
163C4⋊C8—941no—
164C4⋊C8—941no—
165C22⋊C8—21no—
166C22⋊C8—941no—
167#97—941no—
168#97—941no—
169C4×C8—472no—
170C4×C8C22⋊D4712yes—
171C2×Q8—941no—
172C2×Q8—941no—
173C2×Q8—1882no—
174C22×C4—941no—
175C22×C4—941no—
176C22×C4#1062535011yescharacteristic
177C22×C4D4×D4711yescharacteristic
178C22×C4Q8×D4711yescharacteristic
179M16—42no—
180M16—1882no—
181C2×C8—22no—
182C2×C8—41no—
183C2×C8—41no—
184C2×C8—42no—
185C2×C8—474no—
186C2×C8—942no—
187C2×C8—942no—
188C2×C8—942no—
189C2×C8—1881no—
190C4⋊C4—941no—
191C4⋊C4—941no—
192C4⋊C4—1881no—
193C4⋊C4—1881no—
194C42—1881no—
195C42—1881no—
196C42#1062535011yescharacteristic
197C42D4×D4711yescharacteristic
198C42#1062535411yescharacteristic
199C42C2×C22⋊D4711yescharacteristic
200C23#1309400211yescharacteristic
201Q8—942no—
202Q8—942no—
203Q8—1881no—
204Q8—1881no—
205C2×C4—41no—
206C2×C4—41no—
207C2×C4—942no—
208C2×C4—1882no—
209C2×C4—1881no—
210C2×C4—1881no—
211C2×C4—1881no—
212C2×C4#1309400011yescharacteristic
213C2×C4#1309400211yescharacteristic
214C2×C4#1309400711yescharacteristic
215C2×C4#1309400911yescharacteristic
216C2×C4#1309400911yescharacteristic
217C2×C4#1309402011yescharacteristic
218C2×C4Q16×D4712yes—
219C2×C4#1309404812yes—
220C8—42no—
221C8—81no—
222C8—81no—
223C8—944no—
224C8—3761no—
225C8—1882no—
226C22—21no—
227C22—21no—
228C22#1568905811yescharacteristic
229C22#1568941712yes—
230C4—21no—
231C4—21no—
232C4—21no—
233C4—21no—
234C4—3761no—
235C4—1882no—
236C4#1568946012yes—
237C4#1568950111yescharacteristic
238C4#1568951111yescharacteristic
239C2—22no—
240C2#2024490311yescharacteristic
241C2#2024492311yescharacteristic
242C2#2024494411yescharacteristic
subgroupG/H
centerC2×C4#13094020
commutator, cosocleC2×C42×C47C23
FrattiniC2×C42C22×D47
FittingC47×#1571C2
socleC22×C47#399
prime radicalC23×C47C22⋊Q8
hypercenter#1571D47
hypocenterC47#10662
LCSG ▷ C2×C42×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1571

Complements

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

NH ≅ G/Ntype
142. C47#10662semidirect

Maximal subgroups

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

subgroupindex
#202443272
#202435622
#202421622
#202418182
#202418162
#202412182
C47×#15712
#1066247