Finite Group Databasebeta

← #26117614

Subgroups — #26117614

Order 12032.

500 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 500 conjugacy classes of subgroups — too many to draw. Only its 97 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×#15689533C212yesmaximal
2#20244207C211yesmaximal, characteristic
3C2×#15688865C212yesmaximal
4#20241269C211yesmaximal, characteristic
5C47×#2822C211yesmaximal, characteristic
6C2×#13094024C2211yescharacteristic
7#15689533—24no—
8#15689533—24no—
9C2×#13093957—22no—
10C2×#13093955—22no—
11C2×#13093947—22no—
12C2×#13093935C2211yescharacteristic
13C2×#13093935C2212yes—
14#15688865—24no—
15C2×#125×C47C2212yes—
16C47×#400—22no—
17C47×#398—22no—
18C47×#398—22no—
19C47×#382C2211yescharacteristic
20C22×Dic94—21no—
21C22×C47⋊C8—22no—
22C22×C47⋊C8—21no—
23#13094024—22no—
24#13094024—21no—
25#13094024D412yes—
26C2×C4⋊Dic47—22no—
27#13093957—28no—
28#13093955—28no—
29#13093947—44no—
30#13093935—22no—
31#13093935—22no—
32#13093935D414yes—
33#125×C47—22no—
34#125×C47—22no—
35#125×C47—22no—
36#125×C47—22no—
37C2×C4⋊C4×C47—22no—
38C2×C4⋊C4×C47—22no—
39C2×C4⋊C4×C47—22no—
40C2×C4⋊C4×C47D412yes—
41C2×C4⋊C4×C47D412yes—
42C2×C4⋊C4×C47D412yes—
43C2×C42×C47C2311yescharacteristic
44#95×C47—24no—
45#95×C47—22no—
46#95×C47—22no—
47C22×C4×C47—22no—
48C22×C4×C47—22no—
49C22×C4×C47—22no—
50C22×C4×C47C2×D412yes—
51C22×C4×C47C2×D411yescharacteristic
52C22×Dic47—41no—
53C2×Dic94—22no—
54C2×Dic94—42no—
55C2×Dic94—42no—
56C2×Dic94—41no—
57C4⋊C4×C47—22no—
58C4⋊C4×C47—22no—
59C4⋊C4×C47—22no—
60C4⋊C4×C47—22no—
61C4⋊C4×C47—42no—
62C4⋊C4×C47—42no—
63C4⋊C4×C47—42no—
64C4⋊C4×C47—42no—
65C4⋊C4×C47—42no—
66C4⋊C4×C47—82no—
67C42×C47C2×D411yescharacteristic
68C42×C47C2×D412yes—
69C42×C47#4111yescharacteristic
70C4⋊Dic47—24no—
71C4⋊Dic47—42no—
72C2×C47⋊C8—28no—
73C2×C47⋊C8—24no—
74C2×C47⋊C8—22no—
75C2×C47⋊C8—41no—
76C2×C47⋊C8—41no—
77C23×C47#12011yescharacteristic
78C2×C4×C47—21no—
79C2×C4×C47—21no—
80C2×C4×C47—24no—
81C2×C4×C47—42no—
82C2×C4×C47—42no—
83C2×C4×C47—42no—
84C2×C4×C47—42no—
85C2×C4×C47—42no—
86C2×C4×C47—44no—
87C2×C4×C47—44no—
88C2×C4×C47#12012yes—
89C2×C4×C47#12111yescharacteristic
90C2×C4×C47#12112yes—
91C2×C4×C47#12711yescharacteristic
92C2×Dic47—42no—
93C2×Dic47—81no—
94C2×Dic47—81no—
95Dic94—44no—
96Dic94—82no—
97C47⋊C8—28no—
98C47⋊C8—42no—
99#10087—471nomaximal, Sylow
100C22×C47#39211yescharacteristic
101C22×C47#45311yescharacteristic
102C22×C47#45411yescharacteristic
103C22×C47#45614yes—
104C4×C47—22no—
105C4×C47—22no—
106C4×C47—21no—
107C4×C47—21no—
108C4×C47—82no—
109C4×C47—82no—
110C4×C47—82no—
111Dic47—82no—
112C2×#501—472no—
113#2822D4711yescharacteristic
114#1960—471no—
115C2×#330—472no—
116#1295—471no—
117C2×C47#166012yes—
118C2×C47#166312yes—
119C2×C47#200512yes—
120C2×C47#200611yescharacteristic
121C2×C4⋊Q8—471no—
122C2×#125C2×D4712yes—
123#501—944no—
124#501—944no—
125C2×#107—942no—
126C2×#106—942no—
127C2×#103—942no—
128C2×#97—472no—
129C2×#97—471no—
130#400—22no—
131#398—22no—
132#398—22no—
133#382C2×D4711yescharacteristic
134#330—944no—
135C47#1008711yescharacteristic, complemented, Sylow
136C22×Q8—941no—
137C22×C8—942no—
138C22×C8—941no—
139C4⋊Q8—472no—
140C4⋊Q8—942no—
141C4⋊Q8—941no—
142#125—22no—
143#125—22no—
144#125—22no—
145#125—22no—
146C2×C4⋊C4—22no—
147C2×C4⋊C4—22no—
148C2×C4⋊C4—22no—
149C2×C4⋊C4—942no—
150C2×C4⋊C4C22⋊D4712yes—
151C2×C4⋊C4C22⋊D4712yes—
152C2×C4⋊C4C22⋊D4712yes—
153C2×C42C22×D4711yescharacteristic
154#107—948no—
155#106—948no—
156#103—1884no—
157#97—474no—
158#97—942no—
159#97—942no—
160#95—24no—
161#95—22no—
162#95—22no—
163C2×Q8—942no—
164C2×Q8—1882no—
165C2×Q8—1882no—
166C2×Q8—1881no—
167C22×C4—22no—
168C22×C4—22no—
169C22×C4—22no—
170C22×C4—1881no—
171C22×C4C2×C22⋊D4712yes—
172C22×C4C2×C22⋊D4711yescharacteristic
173C2×C8—948no—
174C2×C8—944no—
175C2×C8—942no—
176C2×C8—1881no—
177C2×C8—1881no—
178C4⋊C4—22no—
179C4⋊C4—22no—
180C4⋊C4—22no—
181C4⋊C4—22no—
182C4⋊C4—42no—
183C4⋊C4—42no—
184C4⋊C4—42no—
185C4⋊C4—42no—
186C4⋊C4—42no—
187C4⋊C4—82no—
188C4⋊C4—944no—
189C4⋊C4—1882no—
190C42D4×D4711yescharacteristic
191C42D4×D4712yes—
192C42#1062535211yescharacteristic
193C23#1309399311yescharacteristic
194Q8—3762no—
195Q8—1884no—
196C2×C4—21no—
197C2×C4—21no—
198C2×C4—24no—
199C2×C4—42no—
200C2×C4—42no—
201C2×C4—42no—
202C2×C4—42no—
203C2×C4—42no—
204C2×C4—44no—
205C2×C4—44no—
206C2×C4—3761no—
207C2×C4—3761no—
208C2×C4—1882no—
209C2×C4#1309399212yes—
210C2×C4#1309399511yescharacteristic
211C2×C4#1309399612yes—
212C2×C4#1309402011yescharacteristic
213C8—948no—
214C8—1882no—
215C22#1568903111yescharacteristic
216C22#1568929111yescharacteristic
217C22#1568929611yescharacteristic
218C22#1568930614yes—
219C4—22no—
220C4—22no—
221C4—21no—
222C4—21no—
223C4—82no—
224C4—82no—
225C4—82no—
226C4—3762no—
227C2#2024269912yes—
228C2#2024271612yes—
229C2#2024442212yes—
230C2#2024443011yescharacteristic
subgroupG/H
centerC23#13093993
commutator, cosocleC2×C42×C47C23
FrattiniC2×C42C22×D47
FittingC47×#2822C2
socle, prime radicalC23×C47#120
hypercenter#2822D47
hypocenterC47#10087
LCSG ▷ C2×C42×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2822

Complements

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

NH ≅ G/Ntype
135. C47#10087semidirect

Maximal subgroups

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

subgroupindex
C2×#156895332
#202442072
C2×#156888652
#202412692
C47×#28222
#1008747