Finite Group Databasebeta

← #26115759

Subgroups — #26115759

Order 12032.

406 conjugacy classes of subgroups; only the 127 normal subgroups are shown.

normal subgroups only

This group has 406 conjugacy classes of subgroups — too many to draw. Only its 127 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#20243560C211yesmaximal, characteristic
2#20242073C211yesmaximal, characteristic
3#20242069C211yesmaximal, characteristic
4#20242060C211yesmaximal, characteristic
5#20242060C211yesmaximal, characteristic
6#20241680C211yesmaximal, characteristic
7C2×C47×#487C211yesmaximal, characteristic
8#15689176C2211yescharacteristic
9#15689176C2211yescharacteristic
10C2×#13093960—22no—
11#15689147C2211yescharacteristic
12#15689147C2211yescharacteristic
13#15688872—22no—
14#15688869—22no—
15#15688869—22no—
16#15688869—22no—
17#15688845—22no—
18C2×C4⋊Q8×C47C2211yescharacteristic
19C2×C4⋊Q8×C47C2211yescharacteristic
20C47×#487—22no—
21C47×#487C414yes—
22C2×#103×C47—22no—
23C2×C4×C8×C47C2211yescharacteristic
24C2×#10625329—21no—
25C2×#10625329—21no—
26#13093960—44no—
27C4⋊(C47⋊C8)—21no—
28C4⋊(C47⋊C8)—21no—
29C4⋊(C47⋊C8)—21no—
30C4⋊(C47⋊C8)—21no—
31C4⋊(C47⋊C8)D412yes—
32C4⋊(C47⋊C8)D412yes—
33C22⋊(C47⋊C8)—21no—
34C22⋊(C47⋊C8)—21no—
35C4×C47⋊C8—21no—
36C4×C47⋊C8—21no—
37C22×Q8×C47—21no—
38C22×Q8×C47—21no—
39C22×C8×C47D412yes—
40C4⋊Q8×C47—21no—
41C4⋊Q8×C47—21no—
42C4⋊Q8×C47—21no—
43C4⋊Q8×C47—21no—
44C4⋊Q8×C47—21no—
45C4⋊Q8×C47—21no—
46C4⋊Q8×C47C2×C412yes—
47C4⋊Q8×C47C2×C412yes—
48C2×C4⋊C4×C47—21no—
49C2×C4⋊C4×C47—21no—
50C2×C4⋊C4×C47—21no—
51C2×C4⋊C4×C47—21no—
52C2×C42×C47C2311yescharacteristic
53#103×C47—28no—
54C4×C8×C47C2×C412yes—
55C4×C8×C47D412yes—
56C2×Q8×C47—22no—
57C2×Q8×C47—22no—
58C2×Q8×C47—41no—
59C2×Q8×C47—41no—
60C2×Q8×C47—42no—
61C2×Q8×C47—42no—
62C2×Q8×C47—82no—
63C22×C4×C47—41no—
64C22×C4×C47—41no—
65C22×C4×C47C2×D411yescharacteristic
66C22×C4×C47#4111yescharacteristic
67C22×C4×C47#4111yescharacteristic
68C2×C8×C47—22no—
69C2×C8×C47—22no—
70C2×C8×C47C22⋊C414yes—
71C4⋊C4×C47—22no—
72C4⋊C4×C47—22no—
73C4⋊C4×C47—22no—
74C4⋊C4×C47—22no—
75C4⋊C4×C47—41no—
76C4⋊C4×C47—41no—
77C4⋊C4×C47—41no—
78C4⋊C4×C47—41no—
79C42×C47C22×C411yescharacteristic
80C42×C47C2×D411yescharacteristic
81C42×C47C2×D411yescharacteristic
82C42×C47C2×D411yescharacteristic
83#10625329—42no—
84#10625329—42no—
85C2×C47⋊C8—22no—
86C2×C47⋊C8—22no—
87C2×C47⋊C8—41no—
88C2×C47⋊C8—41no—
89C23×C47#12411yescharacteristic
90Q8×C47—44no—
91Q8×C47—82no—
92Q8×C47—82no—
93Q8×C47—81no—
94Q8×C47—81no—
95C2×C4×C47—22no—
96C2×C4×C47—22no—
97C2×C4×C47—42no—
98C2×C4×C47—42no—
99C2×C4×C47—82no—
100C2×C4×C47—82no—
101C2×C4×C47C2×C22⋊C411yescharacteristic
102C2×C4×C47C4×D411yescharacteristic
103C2×C4×C47C4×D411yescharacteristic
104C2×C4×C47#12111yescharacteristic
105C2×C4×C47#12111yescharacteristic
106C2×C4×C47#12711yescharacteristic
107C2×C4×C47AGL(1,ℤ/8)12yes—
108C2×C4×C47#13712yes—
109C8×C47—24no—
110C47⋊C8—42no—
111C47⋊C8—42no—
112C47⋊C8—81no—
113C47⋊C8—81no—
114#9775—471nomaximal, Sylow
115C22×C47—21no—
116C22×C47—21no—
117C22×C47#39011yescharacteristic
118C22×C47#48912yes—
119C4×C47—21no—
120C4×C47—21no—
121C4×C47—82no—
122C4×C47—82no—
123C4×C47#41712yes—
124C4×C47#47112yes—
125C4×C47#47312yes—
126C4×C47#49611yescharacteristic
127C4×C47#49711yescharacteristic
128C2×#487D4711yescharacteristic
129#1848—471no—
130#1549—471no—
131#1548—471no—
132#1546—471no—
133#1546—471no—
134#1452—471no—
135C2×C47—22no—
136C2×C47#195911yescharacteristic
137C2×C47#197711yescharacteristic
138C2×C47#197911yescharacteristic
139C2×C4⋊Q8C2×D4711yescharacteristic
140C2×C4⋊Q8C2×D4711yescharacteristic
141#487—22no—
142#487Dic4714yes—
143#431—471no—
144#431—471no—
145C2×#108—942no—
146#423—471no—
147#423—471no—
148C2×#103—22no—
149C2×C4×C8C2×D4711yescharacteristic
150#333—942no—
151#332—942no—
152#332—942no—
153#332—942no—
154#322—942no—
155C47#977511yescharacteristic, complemented, Sylow
156C22×Q8—21no—
157C22×Q8—21no—
158C2×M16—941no—
159C2×M16—941no—
160C22×C8C22⋊D4712yes—
161C4⋊Q8—21no—
162C4⋊Q8—21no—
163C4⋊Q8—21no—
164C4⋊Q8—21no—
165C4⋊Q8—21no—
166C4⋊Q8—21no—
167C4⋊Q8C2×Dic4712yes—
168C4⋊Q8C2×Dic4712yes—
169C2×C4⋊C4—21no—
170C2×C4⋊C4—21no—
171C2×C4⋊C4—21no—
172C2×C4⋊C4—21no—
173C2×C42C22×D4711yescharacteristic
174#108—1884no—
175C4⋊C8—472no—
176C4⋊C8—472no—
177C4⋊C8—941no—
178C4⋊C8—941no—
179C4⋊C8—941no—
180C4⋊C8—941no—
181#103—28no—
182C22⋊C8—941no—
183C22⋊C8—941no—
184C4×C8—941no—
185C4×C8—941no—
186C4×C8C2×Dic4712yes—
187C4×C8C22⋊D4712yes—
188C2×Q8—22no—
189C2×Q8—22no—
190C2×Q8—41no—
191C2×Q8—41no—
192C2×Q8—42no—
193C2×Q8—42no—
194C2×Q8—82no—
195C22×C4—41no—
196C22×C4—41no—
197C22×C4#1062535211yescharacteristic
198C22×C4#1062535211yescharacteristic
199C22×C4C2×C22⋊D4711yescharacteristic
200M16—1882no—
201M16—1882no—
202C2×C8—22no—
203C2×C8—22no—
204C2×C8—942no—
205C2×C8—942no—
206C2×C8—1881no—
207C2×C8—1881no—
208C2×C8C22⋊Dic4714yes—
209C4⋊C4—22no—
210C4⋊C4—22no—
211C4⋊C4—22no—
212C4⋊C4—22no—
213C4⋊C4—41no—
214C4⋊C4—41no—
215C4⋊C4—41no—
216C4⋊C4—41no—
217C42D4×D4711yescharacteristic
218C42D4×D4711yescharacteristic
219C42C22×Dic4711yescharacteristic
220C42C2×C22⋊D4711yescharacteristic
221C23#1309401111yescharacteristic
222Q8—44no—
223Q8—82no—
224Q8—81no—
225Q8—81no—
226Q8—82no—
227C2×C4—22no—
228C2×C4—22no—
229C2×C4—42no—
230C2×C4—42no—
231C2×C4—82no—
232C2×C4—82no—
233C2×C4C2×C22⋊Dic4711yescharacteristic
234C2×C4D4×Dic4711yescharacteristic
235C2×C4D4×Dic4711yescharacteristic
236C2×C4#1309399511yescharacteristic
237C2×C4#1309399511yescharacteristic
238C2×C4#1309402011yescharacteristic
239C2×C4#1309404912yes—
240C2×C4#1309405412yes—
241C8—24no—
242C8—3761no—
243C8—3761no—
244C8—1882no—
245C8—1882no—
246C22—21no—
247C22—21no—
248C22#1568902611yescharacteristic
249C22#1568948212yes—
250C4—21no—
251C4—21no—
252C4—82no—
253C4—82no—
254C4#1568912412yes—
255C4#1568938312yes—
256C4#1568939512yes—
257C4#1568951311yescharacteristic
258C4#1568951811yescharacteristic
259C2—22no—
260C2#2024420511yescharacteristic
261C2#2024429311yescharacteristic
262C2#2024430411yescharacteristic
subgroupG/H
centerC22#15689026
commutatorC42×C47C22×C4
FrattiniC2×C42C22×D47
FittingC2×C47×#487C2
socleC22×C47#390
prime radicalC23×C47#124
cosocleC2×C42×C47C23
hypercenterC2×#487D47
hypocenterC47#9775
LCSG ▷ C42×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×#487

Complements

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

NH ≅ G/Ntype
155. C47#9775semidirect

Maximal subgroups

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

subgroupindex
#202435602
#202420732
#202420692
#202420602
#202416802
C2×C47×#4872
#977547