Finite Group Databasebeta

← #26129540

Subgroups — #26129540

Order 12032.

354 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 354 conjugacy classes of subgroups — too many to draw. Only its 67 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#20254698C211yesmaximal, characteristic
2#20245568C212yesmaximal, complemented
3#20241396C212yesmaximal, complemented
4#20241328C211yesmaximal, characteristic, complemented
5C47×#2086C211yesmaximal, characteristic, complemented
6#15689673—21no—
7#15689404—22no—
8#15689359—21no—
9#15689359C2212yes—
10#15689319—22no—
11#15688948—22no—
12#15688923—22no—
13C22⋊(C47⋊C16)C2212yes—
14C2×#107×C47C2211yescharacteristic
15C2×C4⋊C8×C47C2211yescharacteristic
16C47×#389—21no—
17C47×#340—21no—
18C47×#340C2211yescharacteristic
19C2×#10625350—41no—
20C2×D376—21no—
21C2×D376D412yes—
22#13094024—21no—
23#13094021—21no—
24#13094012—41no—
25#13093998—22no—
26#13093998—41no—
27C4×D188—22no—
28C4×D188—41no—
29C2×C47⋊C16—22no—
30#13093958—21no—
31#13093958D412yes—
32#13093946—22no—
33#13093946—22no—
34C22×C8×C47D411yescharacteristic
35C22×C8×C47C2311yescharacteristic
36C2×C4⋊C4×C47—21no—
37C2×C4⋊C4×C47—21no—
38C2×C4⋊C4×C47—41no—
39C2×C42×C47D411yescharacteristic
40#107×C47—22no—
41C4⋊C8×C47—22no—
42#95×C47—41no—
43C22×C4×C47—41no—
44C22×C4×C47—41no—
45C22×C4×C47D811yescharacteristic
46C22×C4×C47D811yescharacteristic
47C22×C4×C47C2×D411yescharacteristic
48C2×C22⋊D47—42no—
49#10625350—82no—
50#10625350—82no—
51C2×D188—22no—
52C2×D188—41no—
53C2×D188—41no—
54C2×C4×D47—42no—
55C2×Dic94—41no—
56C2×C8×C47—21no—
57C2×C8×C47—41no—
58C2×C8×C47—41no—
59C2×C8×C47C2×D412yes—
60C4⋊C4×C47—22no—
61C4⋊C4×C47—41no—
62C4⋊C4×C47—41no—
63C4⋊C4×C47—41no—
64C4⋊C4×C47—82no—
65C42×C47—21no—
66C42×C47—21no—
67(C2×D47)⋊C4—42no—
68(C2×D47)⋊C4—42no—
69C4⋊Dic47—22no—
70C4⋊Dic47—41no—
71D376—42no—
72D376—81no—
73C47⋊C16—42no—
74C23×C47C2×D811yescharacteristic
75C22×D47—42no—
76C2×C4×C47—21no—
77C2×C4×C47—21no—
78C2×C4×C47—21no—
79C2×C4×C47—21no—
80C2×C4×C47—21no—
81C2×C4×C47—41no—
82C2×C4×C47—42no—
83C2×C4×C47—81no—
84C2×C4×C47—81no—
85C2×C4×C47—81no—
86C2×C4×C47—81no—
87C2×C4×C47—81no—
88C2×C4×C47D1612yes—
89C2×C4×C47#12011yescharacteristic
90C2×C4×C47AGL(1,ℤ/8)11yescharacteristic
91C22⋊D47—82no—
92C22⋊D47—82no—
93C2×Dic47—42no—
94D188—42no—
95D188—42no—
96D188—82no—
97D188—82no—
98C4×D47—84no—
99Dic94—82no—
100C8×C47—22no—
101C8×C47—41no—
102#12288—471nomaximal, Sylow
103C22×C47—21no—
104C22×C47—21no—
105C22×C47#44711yescharacteristic
106C22×C47C2×D1611yescharacteristic
107C22×C47#50911yescharacteristic
108C2×D47—82no—
109C2×D47—82no—
110C2×D47—82no—
111C4×C47—21no—
112C4×C47—22no—
113C4×C47—41no—
114C4×C47—82no—
115C4×C47—161no—
116C4×C47#45611yescharacteristic
117C4×C47#45811yescharacteristic
118Dic47—82no—
119#3245—471no—
120#2232—472no—
121#2086D4711yescharacteristic, complemented
122#1347—472no—
123#1322—471no—
124C2×C47—21no—
125C2×C47—21no—
126C2×C47#161011yescharacteristic
127C2×C47#218411yescharacteristic
128C2×C47#219111yescharacteristic
129D47—162no—
130#532—941no—
131#474—942no—
132#466—472no—
133#466—941no—
134#459—942no—
135C2×#107C2×D4711yescharacteristic
136C2×C4⋊C8C2×D4711yescharacteristic
137#389—21no—
138#366—942no—
139#357—942no—
140C22⋊C16—472no—
141#340—21no—
142#340C2×D4711yescharacteristic
143C47#1228811yescharacteristic, complemented, Sylow
144C2×#41—1881no—
145C2×D8—472no—
146C2×D8—941no—
147C22×C8C22⋊D4711yescharacteristic
148C22×C8C22×D4711yescharacteristic
149C4⋊Q8—941no—
150#127—941no—
151#124—1881no—
152#121—942no—
153#121—1881no—
154C4×D4—942no—
155C4×D4—1881no—
156C2×C4⋊C4—21no—
157C2×C4⋊C4—21no—
158C2×C4⋊C4—41no—
159C2×C42C22⋊D4711yescharacteristic
160C2×C16—942no—
161#107—22no—
162#107—472no—
163#107—941no—
164C4⋊C8—22no—
165#102—942no—
166#102—942no—
167#95—41no—
168#41—3762no—
169#41—3762no—
170C2×Q8—1881no—
171C2×D4—942no—
172C2×D4—1881no—
173C2×D4—1881no—
174C2×D4—1882no—
175C22×C4—41no—
176C22×C4—41no—
177C22×C4—1882no—
178C22×C4#1062533411yescharacteristic
179C22×C4#1062533411yescharacteristic
180C22×C4C2×C22⋊D4711yescharacteristic
181D8—3761no—
182D8—1882no—
183C2×C8—21no—
184C2×C8—41no—
185C2×C8—41no—
186C2×C8D4×D4712yes—
187C4⋊C4—22no—
188C4⋊C4—41no—
189C4⋊C4—41no—
190C4⋊C4—41no—
191C4⋊C4—82no—
192C4⋊C4—942no—
193C4⋊C4—1881no—
194C22⋊C4—1882no—
195C22⋊C4—1882no—
196C42—21no—
197C42—21no—
198C16—1882no—
199C23—1882no—
200C23C2×#1062533411yescharacteristic
201Q8—3762no—
202D4—3762no—
203D4—3762no—
204D4—3762no—
205D4—3762no—
206D4—1882no—
207D4—1882no—
208C2×C4—21no—
209C2×C4—21no—
210C2×C4—21no—
211C2×C4—21no—
212C2×C4—21no—
213C2×C4—41no—
214C2×C4—42no—
215C2×C4—81no—
216C2×C4—81no—
217C2×C4—81no—
218C2×C4—81no—
219C2×C4—81no—
220C2×C4—3764no—
221C2×C4—1882no—
222C2×C4#1309396512yes—
223C2×C4#1309399211yescharacteristic
224C2×C4#1309404911yescharacteristic
225C8—22no—
226C8—41no—
227C22—21no—
228C22—21no—
229C22—3762no—
230C22—3762no—
231C22—3762no—
232C22#1568925611yescharacteristic
233C22C2×#1309396511yescharacteristic
234C22#1568955811yescharacteristic
235C4—22no—
236C4—21no—
237C4—41no—
238C4—82no—
239C4—161no—
240C4—3762no—
241C4#1568930511yescharacteristic
242C4#1568931211yescharacteristic
243C2—21no—
244C2—21no—
245C2—7522no—
246C2#2024239011yescharacteristic
247C2#2024529911yescharacteristic
248C2#2024533811yescharacteristic
subgroupG/H
centerC22#15689256
commutator, cosocleC22×C8×C47C23
FrattiniC22×C8C22×D47
FittingC47×#2086C2
socleC22×C47#447
prime radical#20254698C2
hypercenter#2086D47
hypocenterC47#12288
LCSG ▷ C22×C8×C47 ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊C8 ◁ #2086

Complements

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

NH ≅ G/Ntype
2. #20245568C2semidirect
3. #20241396C2semidirect
4. #20241328C2semidirect
5. C47×#2086C2semidirect
121. #2086D47semidirect
143. C47#12288semidirect

Maximal subgroups

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

subgroupindex
#202546982
#202455682
#202413962
#202413282
C47×#20862
#1228847