Finite Group Databasebeta

← #26132288

Subgroups — #26132288

Order 12032.

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

normal subgroups only

This group has 432 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#20246106C211yesmaximal, characteristic
2C2×#15688921C212yesmaximal
3#20243382C212yesmaximal
4#20241515C211yesmaximal, characteristic
5C47×#1394C211yesmaximal, characteristic
6C2×#13094022C2211yescharacteristic
7C2×Q8×Dic47C2211yescharacteristic
8C2×#13093989C411yescharacteristic
9#15689146—22no—
10C2×#13093943C2212yes—
11#15689029C411yescharacteristic
12#15689010—22no—
13#15689005—22no—
14#15688988C411yescharacteristic
15#15688969C411yescharacteristic
16#15688921—24no—
17#15688891—22no—
18C2×#101×C47C2212yes—
19C47×#391C2211yescharacteristic
20C22×Dic94C2×C411yescharacteristic
21C2×#10625329—22no—
22#13094022—22no—
23#13094022D412yes—
24#13094022Q812yes—
25Q8×Dic47—42no—
26#13093989—42no—
27C2×C4⋊Dic47C2×C411yescharacteristic
28C2×C4⋊Dic47D412yes—
29C2×Dic47⋊C4—22no—
30C2×Dic47⋊C4—21no—
31C2×C4×Dic47—21no—
32C2×C4×Dic47C2×C411yescharacteristic
33C2×C4×Dic47C2×C411yescharacteristic
34C2×C4×Dic47D412yes—
35Dic47⋊C8—44no—
36#13093943—22no—
37#13093943—22no—
38C47⋊#95—21no—
39C47⋊#95—21no—
40C47⋊#95—22no—
41C47⋊#95—22no—
42C22×Q8×C47C2311yescharacteristic
43C2×M16×C47—22no—
44C2×C4⋊C4×C47C2×C411yescharacteristic
45C2×C42×C47C2×C411yescharacteristic
46#101×C47—22no—
47#101×C47—22no—
48#95×C47—22no—
49C2×Q8×C47—41no—
50C2×Q8×C47—41no—
51C2×Q8×C47C2×D411yescharacteristic
52C2×Q8×C47C2×Q811yescharacteristic
53C2×Q8×C47#4112yes—
54C22×C4×C47—21no—
55C22×C4×C47—21no—
56C22×C4×C47C22×C411yescharacteristic
57C22×C4×C47C2×D412yes—
58C22×Dic47—21no—
59C22×Dic47—21no—
60C22×Dic47C22⋊C412yes—
61C22×Dic47C22⋊C411yescharacteristic
62C22×Dic47C22⋊C411yescharacteristic
63C2×Dic94—21no—
64C2×Dic94—41no—
65C2×Dic94—41no—
66C2×Dic94C4⋊C412yes—
67M16×C47—42no—
68M16×C47—42no—
69C2×C8×C47—42no—
70C4⋊C4×C47—41no—
71C42×C47—41no—
72C4⋊Dic47—41no—
73C4⋊Dic47—42no—
74Dic47⋊C4—24no—
75Dic47⋊C4—24no—
76Dic47⋊C4—42no—
77C4×Dic47—21no—
78C4×Dic47—24no—
79C4×Dic47—22no—
80C4×Dic47—42no—
81C4×Dic47C4⋊C412yes—
82#10625329—42no—
83#10625329—42no—
84C2×C47⋊C8—42no—
85C23×C47C2×C22⋊C411yescharacteristic
86Q8×C47—41no—
87Q8×C47—41no—
88Q8×C47—42no—
89C2×C4×C47—22no—
90C2×C4×C47—21no—
91C2×C4×C47—22no—
92C2×C4×C47—21no—
93C2×C4×C47—41no—
94C2×C4×C47—41no—
95C2×C4×C47—42no—
96C2×C4×C47—41no—
97C2×C4×C47—41no—
98C2×C4×C47C2×C4⋊C411yescharacteristic
99C2×C4×C47#11711yescharacteristic
100C2×C4×C47#12112yes—
101C2×C4×C47C22⋊Q812yes—
102C2×Dic47—22no—
103C2×Dic47—22no—
104C2×Dic47—21no—
105C2×Dic47—22no—
106C2×Dic47—41no—
107C2×Dic47—41no—
108C2×Dic47—41no—
109C2×Dic47—41no—
110C2×Dic47—41no—
111C2×Dic47—42no—
112C2×Dic47—41no—
113C2×Dic47#9912yes—
114Dic94—42no—
115Dic94—42no—
116C8×C47—82no—
117C47⋊C8—82no—
118#12804—471nomaximal, Sylow
119C22×C47—21no—
120C22×C47—21no—
121C22×C47#38011yescharacteristic
122C22×C47C2×#9911yescharacteristic
123C22×C47#41011yescharacteristic
124C4×C47—22no—
125C4×C47—21no—
126C4×C47—21no—
127C4×C47—22no—
128C4×C47—81no—
129C4×C47—81no—
130Dic47—22no—
131Dic47—42no—
132Dic47—42no—
133Dic47—41no—
134Dic47—42no—
135#2327—471no—
136C2×#356—472no—
137#1801—472no—
138#1394—471no—
139#1394D4711yescharacteristic
140C2×C47—21no—
141C2×C47—21no—
142C2×C47#179911yescharacteristic
143C2×C47#213311yescharacteristic
144C2×C47#213511yescharacteristic
145C2×C4⋊Q8—471no—
146C2×C4×Q8—471no—
147C2×C4×Q8—471no—
148#423—942no—
149C2×#101—472no—
150C2×#101C2×D4712yes—
151#391—471no—
152#391C2×D4711yescharacteristic
153#387—942no—
154#387—942no—
155#382—471no—
156#376—471no—
157#356—944no—
158#343—942no—
159C47#1280411yescharacteristic, complemented, Sylow
160C22×Q8—471no—
161C22×Q8C22×D4711yescharacteristic
162C2×M16—22no—
163C2×M16—942no—
164C4⋊Q8—472no—
165C4⋊Q8—472no—
166C4⋊Q8—942no—
167C4×Q8—1882no—
168C4×Q8—1882no—
169C2×C4⋊C4—471no—
170C2×C4⋊C4—472no—
171C2×C4⋊C4—942no—
172C2×C4⋊C4—941no—
173C2×C4⋊C4C4×D4711yescharacteristic
174C2×C42—471no—
175C2×C42—471no—
176C2×C42—472no—
177C2×C42—941no—
178C2×C42C4×D4711yescharacteristic
179C4⋊C8—1884no—
180#101—22no—
181#101—22no—
182#101—942no—
183#101—942no—
184#95—22no—
185#95—941no—
186#95—941no—
187#95—942no—
188#95—942no—
189C2×Q8—41no—
190C2×Q8—41no—
191C2×Q8—472no—
192C2×Q8—941no—
193C2×Q8—1881no—
194C2×Q8—1881no—
195C2×Q8#1062535012yes—
196C2×Q8D4×D4711yescharacteristic
197C2×Q8Q8×D4711yescharacteristic
198C22×C4—21no—
199C22×C4—21no—
200C22×C4—471no—
201C22×C4—472no—
202C22×C4—471no—
203C22×C4—941no—
204C22×C4—941no—
205C22×C4C2×C4×D4711yescharacteristic
206C22×C4D4×D4712yes—
207M16—42no—
208M16—42no—
209M16—1882no—
210M16—1882no—
211C2×C8—42no—
212C2×C8—1882no—
213C4⋊C4—41no—
214C4⋊C4—944no—
215C4⋊C4—944no—
216C4⋊C4—1881no—
217C4⋊C4—1882no—
218C4⋊C4—1882no—
219C42—41no—
220C42—472no—
221C42—944no—
222C42—942no—
223C42—941no—
224C42—1882no—
225C23C22⋊C4×D4711yescharacteristic
226Q8—42no—
227Q8—41no—
228Q8—41no—
229Q8—1882no—
230Q8—1882no—
231C2×C4—21no—
232C2×C4—22no—
233C2×C4—21no—
234C2×C4—22no—
235C2×C4—41no—
236C2×C4—41no—
237C2×C4—42no—
238C2×C4—41no—
239C2×C4—41no—
240C2×C4—472no—
241C2×C4—942no—
242C2×C4—942no—
243C2×C4—941no—
244C2×C4—942no—
245C2×C4—1881no—
246C2×C4—1881no—
247C2×C4—1881no—
248C2×C4—1881no—
249C2×C4—1881no—
250C2×C4—1882no—
251C2×C4—1881no—
252C2×C4C4⋊C4×D4711yescharacteristic
253C2×C4#1309398111yescharacteristic
254C2×C4#1309399712yes—
255C2×C4#1309400212yes—
256C8—82no—
257C8—3762no—
258C22—21no—
259C22—21no—
260C22#1568898211yescharacteristic
261C22#99×D4711yescharacteristic
262C22#1568909511yescharacteristic
263C4—22no—
264C4—21no—
265C4—21no—
266C4—22no—
267C4—81no—
268C4—81no—
269C4—942no—
270C4—1882no—
271C4—1881no—
272C4—1882no—
273C4—1882no—
274C2—21no—
275C2—21no—
276C2#2024337511yescharacteristic
277C2#2024507411yescharacteristic
278C2#2024508111yescharacteristic
subgroupG/H
centerC22#99×D47
commutatorC22×C4×C47C22×C4
FrattiniC22×Q8C22×D47
FittingC47×#1394C2
socleC22×C47C2×#99
prime radicalC23×C47C2×C22⋊C4
cosocleC22×Q8×C47C23
hypercenter#1394D47
hypocenterC47#12804
LCSG ▷ C22×C4×C47 ▷ C22×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C23 ◁ C22×Q8 ◁ #1394

Complements

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

NH ≅ G/Ntype
159. C47#12804semidirect

Maximal subgroups

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

subgroupindex
#202461062
C2×#156889212
#202433822
#202415152
C47×#13942
#1280447