Finite Group Databasebeta

← #26127012

Subgroups — #26127012

Order 12032.

434 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 434 conjugacy classes of subgroups — too many to draw. Only its 95 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#20243468C211yesmaximal, characteristic
2#20241718C211yesmaximal, characteristic
3#20241415C214yesmaximal, complemented
4C2×C47×#400C211yesmaximal, characteristic
5#15689087—21no—
6#15689087—21no—
7#15688892—21no—
8#15688892C2212yes—
9#15688849—21no—
10#15688849C2212yes—
11C22×C4⋊C4×C47C411yescharacteristic
12C22×C4⋊C4×C47C2211yescharacteristic
13C47×#400—21no—
14C47×#400—21no—
15C47×#400C412yes—
16C47×#400C2212yes—
17C2×#95×C47—21no—
18C2×#95×C47—21no—
19C2×#95×C47C411yescharacteristic
20C2×#10625329—22no—
21C2×#10625329—41no—
22C22⋊(C47⋊C8)—22no—
23C22⋊(C47⋊C8)—41no—
24C22⋊(C47⋊C8)—41no—
25C22⋊(C47⋊C8)—41no—
26C23×C4×C47—21no—
27C23×C4×C47—21no—
28C23×C4×C47C2×C411yescharacteristic
29C23×C4×C47D411yescharacteristic
30C23×C4×C47D411yescharacteristic
31C2×C4⋊C4×C47—21no—
32C2×C4⋊C4×C47—41no—
33C2×C4⋊C4×C47—41no—
34C2×C4⋊C4×C47—41no—
35C2×C4⋊C4×C47—41no—
36C2×C4⋊C4×C47C2×C412yes—
37C2×C4⋊C4×C47C2×C411yescharacteristic
38C2×C4⋊C4×C47D411yescharacteristic
39C2×C4⋊C4×C47D411yescharacteristic
40C2×C4⋊C4×C47C2311yescharacteristic
41#95×C47—22no—
42#95×C47—22no—
43#95×C47—21no—
44#95×C47—22no—
45#95×C47—22no—
46#95×C47C2×C412yes—
47C24×C47C22⋊C411yescharacteristic
48C22×C4×C47—21no—
49C22×C4×C47—21no—
50C22×C4×C47—21no—
51C22×C4×C47—21no—
52C22×C4×C47—21no—
53C22×C4×C47—21no—
54C22×C4×C47—22no—
55C22×C4×C47—22no—
56C22×C4×C47—22no—
57C22×C4×C47—41no—
58C22×C4×C47—42no—
59C22×C4×C47—42no—
60C22×C4×C47—42no—
61C22×C4×C47—42no—
62C22×C4×C47—44no—
63C22×C4×C47—42no—
64C22×C4×C47—41no—
65C22×C4×C47—41no—
66C22×C4×C47C22⋊C411yescharacteristic
67C22×C4×C47C22⋊C411yescharacteristic
68C22×C4×C47C22⋊C411yescharacteristic
69C22×C4×C47C22×C411yescharacteristic
70C22×C4×C47C2×D411yescharacteristic
71C22×C4×C47C2×D411yescharacteristic
72C4⋊C4×C47—41no—
73C4⋊C4×C47—41no—
74C4⋊C4×C47—41no—
75C4⋊C4×C47—41no—
76C4⋊C4×C47—42no—
77C4⋊C4×C47—42no—
78#10625329—42no—
79#10625329—42no—
80#10625329—82no—
81C2×C47⋊C8—42no—
82C2×C47⋊C8—42no—
83C23×C47—22no—
84C23×C47—22no—
85C23×C47—21no—
86C23×C47—21no—
87C23×C47#9911yescharacteristic
88C23×C47#9911yescharacteristic
89C23×C47C2×C22⋊C411yescharacteristic
90C2×C4×C47—21no—
91C2×C4×C47—21no—
92C2×C4×C47—21no—
93C2×C4×C47—21no—
94C2×C4×C47—21no—
95C2×C4×C47—21no—
96C2×C4×C47—21no—
97C2×C4×C47—21no—
98C2×C4×C47—21no—
99C2×C4×C47—42no—
100C2×C4×C47—42no—
101C2×C4×C47—42no—
102C2×C4×C47—42no—
103C2×C4×C47—42no—
104C2×C4×C47—41no—
105C2×C4×C47—41no—
106C2×C4×C47—41no—
107C2×C4×C47—41no—
108C2×C4×C47—42no—
109C2×C4×C47—42no—
110C2×C4×C47—44no—
111C2×C4×C47—42no—
112C2×C4×C47—42no—
113C2×C4×C47—81no—
114C2×C4×C47—84no—
115C2×C4×C47—82no—
116C2×C4×C47—82no—
117C2×C4×C47#13712yes—
118C47⋊C8—82no—
119C47⋊C8—82no—
120#11814—471nomaximal, Sylow
121C22×C47—24no—
122C22×C47—24no—
123C22×C47—21no—
124C22×C47—21no—
125C22×C47—21no—
126C22×C47—21no—
127C22×C47—21no—
128C22×C47—21no—
129C22×C47#35212yes—
130C22×C47#35512yes—
131C22×C47C2×#9911yescharacteristic
132C22×C47#41911yescharacteristic
133C22×C47#42111yescharacteristic
134C4×C47—22no—
135C4×C47—41no—
136C4×C47—41no—
137C4×C47—41no—
138C4×C47—41no—
139C4×C47—41no—
140C4×C47—82no—
141C4×C47—82no—
142C2×#400D4711yescharacteristic
143#1821—471no—
144#1463—471no—
145#1353—474no—
146C2×C47—21no—
147C2×C47—22no—
148C2×C47—22no—
149C2×C47—21no—
150C2×C47#151111yescharacteristic
151C2×C47C2×#35211yescharacteristic
152C2×C47C2×#35511yescharacteristic
153C22×C4⋊C4Dic4711yescharacteristic
154C22×C4⋊C4C2×D4711yescharacteristic
155#407—941no—
156#407—941no—
157#400—21no—
158#400—21no—
159#400Dic4712yes—
160#400C2×D4712yes—
161C2×#95—21no—
162C2×#95—21no—
163C2×#95Dic4711yescharacteristic
164#343—472no—
165#343—941no—
166#324—472no—
167#324—941no—
168C47#1181411yescharacteristic, complemented, Sylow
169C23×C4—21no—
170C23×C4—21no—
171C23×C4C2×Dic4711yescharacteristic
172C23×C4C22⋊D4711yescharacteristic
173C23×C4C22⋊D4711yescharacteristic
174C2×M16—942no—
175C2×M16—1881no—
176C2×C4⋊C4—21no—
177C2×C4⋊C4—41no—
178C2×C4⋊C4—41no—
179C2×C4⋊C4—41no—
180C2×C4⋊C4—41no—
181C2×C4⋊C4C2×Dic4712yes—
182C2×C4⋊C4C2×Dic4711yescharacteristic
183C2×C4⋊C4C22⋊D4711yescharacteristic
184C2×C4⋊C4C22⋊D4711yescharacteristic
185C2×C4⋊C4C22×D4711yescharacteristic
186C22⋊C8—942no—
187C22⋊C8—1881no—
188C22⋊C8—1881no—
189C22⋊C8—1881no—
190#95—22no—
191#95—22no—
192#95—21no—
193#95—22no—
194#95—22no—
195#95C2×Dic4712yes—
196C24C22⋊Dic4711yescharacteristic
197C22×C4—21no—
198C22×C4—21no—
199C22×C4—21no—
200C22×C4—21no—
201C22×C4—21no—
202C22×C4—21no—
203C22×C4—22no—
204C22×C4—22no—
205C22×C4—22no—
206C22×C4—41no—
207C22×C4—42no—
208C22×C4—42no—
209C22×C4—42no—
210C22×C4—42no—
211C22×C4—44no—
212C22×C4—42no—
213C22×C4—41no—
214C22×C4—41no—
215C22×C4C22⋊Dic4711yescharacteristic
216C22×C4C22⋊Dic4711yescharacteristic
217C22×C4C22⋊Dic4711yescharacteristic
218C22×C4C22×Dic4711yescharacteristic
219C22×C4C2×C22⋊D4711yescharacteristic
220C22×C4C2×C22⋊D4711yescharacteristic
221M16—3762no—
222M16—1882no—
223M16—1882no—
224C2×C8—1882no—
225C2×C8—1882no—
226C4⋊C4—41no—
227C4⋊C4—41no—
228C4⋊C4—41no—
229C4⋊C4—41no—
230C4⋊C4—42no—
231C4⋊C4—42no—
232C23—21no—
233C23—21no—
234C23—22no—
235C23—22no—
236C23#1309393911yescharacteristic
237C23#1309393911yescharacteristic
238C23C2×C22⋊Dic4711yescharacteristic
239C2×C4—21no—
240C2×C4—21no—
241C2×C4—21no—
242C2×C4—21no—
243C2×C4—21no—
244C2×C4—21no—
245C2×C4—21no—
246C2×C4—21no—
247C2×C4—21no—
248C2×C4—42no—
249C2×C4—42no—
250C2×C4—42no—
251C2×C4—42no—
252C2×C4—42no—
253C2×C4—41no—
254C2×C4—41no—
255C2×C4—41no—
256C2×C4—41no—
257C2×C4—42no—
258C2×C4—42no—
259C2×C4—44no—
260C2×C4—42no—
261C2×C4—42no—
262C2×C4—81no—
263C2×C4—84no—
264C2×C4—82no—
265C2×C4—82no—
266C2×C4#1309405512yes—
267C8—3762no—
268C8—3762no—
269C22—24no—
270C22—24no—
271C22—21no—
272C22—21no—
273C22—21no—
274C22—21no—
275C22—21no—
276C22—21no—
277C22#1568891312yes—
278C22#1568892012yes—
279C22C2×#1309393911yescharacteristic
280C22#1568913211yescharacteristic
281C22#1568914011yescharacteristic
282C4—22no—
283C4—41no—
284C4—41no—
285C4—41no—
286C4—41no—
287C4—41no—
288C4—82no—
289C4—82no—
290C2—21no—
291C2—21no—
292C2—22no—
293C2—22no—
294C2#2024192111yescharacteristic
295C2C2×#1568891311yescharacteristic
296C2C2×#1568892011yescharacteristic
subgroupG/H
centerC22C2×#13093939
commutatorC22×C4×C47C22×C4
FrattiniC2×C4⋊C4C22×D47
FittingC2×C47×#400C2
socleC22×C47C2×#99
prime radicalC24×C47C22⋊C4
cosocleC2×C4⋊C4×C47C23
hypercenterC2×#400D47
hypocenterC47#11814
LCSG ▷ C22×C4×C47 ▷ C23×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C24 ◁ C22×C4⋊C4 ◁ C2×#400

Complements

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

NH ≅ G/Ntype
3. #20241415C2semidirect
168. C47#11814semidirect

Maximal subgroups

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

subgroupindex
#202434682
#202417182
#202414152
C2×C47×#4002
#1181447