Finite Group Databasebeta

← #24990019

Subgroups — #24990019

Order 11008.

630 conjugacy classes of subgroups; only the 155 normal subgroups are shown.

normal subgroups only

This group has 630 conjugacy classes of subgroups — too many to draw. Only its 155 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#384×D43C211yesmaximal, characteristic
2#19134572C212yesmaximal
3#19132479C212yesmaximal, complemented
4#19132478C211yesmaximal, characteristic, complemented
5C43×#1296C211yesmaximal, characteristic, complemented
6C2×C4⋊C4×D43—22no—
7C2×C4⋊C4×D43C412yes—
8C2×C42×D43C2211yescharacteristic
9C2×C4⋊(C43⋊C8)C2212yes—
10C2×(C2×D43)⋊C8—22no—
11#14582769C2211yescharacteristic
12#14582768—22no—
13#14582768C412yes—
14#14582653—22no—
15C2×C4⋊C8×C43C2212yes—
16C43×#384C2211yescharacteristic
17C22×C4×D43—22no—
18C22×C4×D43C2×C411yescharacteristic
19C22×C4×D43D412yes—
20C22×C43⋊C8—22no—
21C2×C4⋊Dic43—22no—
22C2×C4⋊Dic43C2×C412yes—
23C2×Dic43⋊C4—24no—
24C2×Dic43⋊C4—22no—
25C4⋊C4×D43—44no—
26C4⋊C4×D43—44no—
27C4⋊C4×D43—44no—
28C2×C4×Dic43C2×C411yescharacteristic
29C2×C4×Dic43D412yes—
30C42×D43—22no—
31C42×D43—21no—
32C42×D43—21no—
33C4⋊(C43⋊C8)—22no—
34C4⋊(C43⋊C8)—22no—
35(C2×D43)⋊C8—44no—
36C22×C8×C43—22no—
37C2×C4⋊C4×C43—22no—
38C2×C4⋊C4×C43C2×C412yes—
39C2×C42×C43C2311yescharacteristic
40C4⋊C8×C43—22no—
41C4⋊C8×C43—22no—
42C23×D43C22⋊C411yescharacteristic
43C22×C4×C43—22no—
44C22×C4×C43C22×C411yescharacteristic
45C22×C4×C43C2×D412yes—
46C22×Dic43—22no—
47C22×Dic43C22⋊C411yescharacteristic
48C22×Dic43C22⋊C412yes—
49C2×C4×D43—21no—
50C2×C4×D43—21no—
51C2×C4×D43—22no—
52C2×C4×D43—22no—
53C2×C4×D43—22no—
54C2×C4×D43—22no—
55C2×C4×D43—22no—
56C2×C4×D43—22no—
57C2×C4×D43—48no—
58C2×C4×D43—44no—
59C2×C4×D43SD1614yes—
60C2×C4×D43Q1614yes—
61C2×C8×C43—42no—
62C2×C8×C43—42no—
63C2×C8×C43—42no—
64C4⋊C4×C43—42no—
65C4⋊C4×C43—42no—
66C4⋊C4×C43—42no—
67C42×C43#4112yes—
68C42×C43#4111yescharacteristic
69C42×C43#4111yescharacteristic
70C4⋊Dic43—42no—
71C4⋊Dic43—42no—
72C4⋊Dic43—42no—
73Dic43⋊C4—44no—
74Dic43⋊C4—48no—
75C4×Dic43—21no—
76C4×Dic43—21no—
77C4×Dic43—22no—
78C4×Dic43—22no—
79C2×C43⋊C8—42no—
80C2×C43⋊C8—42no—
81C2×C43⋊C8—42no—
82C23×C43C2×C22⋊C411yescharacteristic
83C22×D43—21no—
84C22×D43—21no—
85C22×D43—22no—
86C22×D43#10012yes—
87C22×D43#10314yes—
88C2×C4×C43—21no—
89C2×C4×C43—21no—
90C2×C4×C43—42no—
91C2×C4×C43—44no—
92C2×C4×C43#11711yescharacteristic
93C2×C4×C43#11711yescharacteristic
94C2×C4×C43#12312yes—
95C2×C4×C43#12312yes—
96C2×C4×C43C2×SD1612yes—
97C2×C4×C43C2×Q1612yes—
98C2×C4×C43AGL(1,ℤ/8)12yes—
99C2×C4×C43AGL(1,ℤ/8)12yes—
100C2×Dic43—21no—
101C2×Dic43—22no—
102C2×Dic43—21no—
103C2×Dic43—22no—
104C2×Dic43—42no—
105C2×Dic43—44no—
106C2×Dic43#10112yes—
107C2×Dic43#10314yes—
108C4×D43—24no—
109C4×D43—24no—
110C4×D43—24no—
111C4×D43—24no—
112C4×D43—24no—
113C4×D43—24no—
114C4×D43—88no—
115C8×C43—82no—
116C43⋊C8—82no—
117#8725—431nomaximal, Sylow
118C22×C43#38111yescharacteristic
119C22×C43C2×#10011yescharacteristic
120C22×C43C2×#10111yescharacteristic
121C22×C43C2×#10312yes—
122C22×C43#41812yes—
123C2×D43—24no—
124C2×D43—22no—
125C2×D43—22no—
126C2×D43—24no—
127C2×D43#33314yes—
128C4×C43—21no—
129C4×C43—21no—
130C4×C43—82no—
131C4×C43#48112yes—
132C4×C43#48112yes—
133C4×C43#48412yes—
134C4×C43#48412yes—
135Dic43—22no—
136Dic43—24no—
137Dic43—82no—
138C2×#384—431no—
139#1797—432no—
140#1296—432no—
141#1296—431no—
142#1296D4311yescharacteristic, complemented
143C2×C43C2×#33311yescharacteristic
144C2×C43#154912yes—
145C2×C43#155511yescharacteristic
146C2×C43#182111yescharacteristic
147C2×C43#182412yes—
148D43—24no—
149C22×C4⋊C4—432no—
150C22×C4⋊C4—862no—
151C22×C42—431no—
152C2×C4⋊C8—432no—
153C2×C4⋊C8C2×D4312yes—
154C2×C22⋊C8—862no—
155#384—432no—
156#384—431no—
157#384—862no—
158#384C2×D4311yescharacteristic
159#336—862no—
160C43#872511yescharacteristic, complemented, Sylow
161C23×C4—432no—
162C23×C4—431no—
163C23×C4—862no—
164C22×C8—22no—
165C22×C8—862no—
166C2×C4⋊C4—22no—
167C2×C4⋊C4—432no—
168C2×C4⋊C4—862no—
169C2×C4⋊C4—864no—
170C2×C4⋊C4—862no—
171C2×C4⋊C4—1724no—
172C2×C4⋊C4—1724no—
173C2×C4⋊C4—1724no—
174C2×C4⋊C4C4×D4312yes—
175C2×C42—431no—
176C2×C42—432no—
177C2×C42—862no—
178C2×C42—861no—
179C2×C42—861no—
180C2×C42C22×D4311yescharacteristic
181C4⋊C8—22no—
182C4⋊C8—22no—
183C4⋊C8—862no—
184C4⋊C8—862no—
185C22⋊C8—1724no—
186C24—431no—
187C22×C4—22no—
188C22×C4—431no—
189C22×C4—432no—
190C22×C4—434no—
191C22×C4—434no—
192C22×C4—862no—
193C22×C4—862no—
194C22×C4—861no—
195C22×C4—861no—
196C22×C4—862no—
197C22×C4—862no—
198C22×C4—862no—
199C22×C4—862no—
200C22×C4—862no—
201C22×C4—1724no—
202C22×C4—1728no—
203C22×C4C2×C4×D4311yescharacteristic
204C22×C4D4×D4312yes—
205C2×C8—42no—
206C2×C8—42no—
207C2×C8—42no—
208C2×C8—1722no—
209C2×C8—1722no—
210C2×C8—1722no—
211C4⋊C4—42no—
212C4⋊C4—42no—
213C4⋊C4—42no—
214C4⋊C4—1722no—
215C4⋊C4—1724no—
216C4⋊C4—1728no—
217C4⋊C4—1722no—
218C4⋊C4—1722no—
219C42—861no—
220C42—861no—
221C42—862no—
222C42—862no—
223C42#1062189812yes—
224C42#1062190011yescharacteristic
225C42#1062190211yescharacteristic
226C23—432no—
227C23—434no—
228C23—861no—
229C23—862no—
230C23—861no—
231C23C22⋊C4×D4311yescharacteristic
232C2×C4—21no—
233C2×C4—21no—
234C2×C4—42no—
235C2×C4—44no—
236C2×C4—432no—
237C2×C4—434no—
238C2×C4—864no—
239C2×C4—864no—
240C2×C4—861no—
241C2×C4—862no—
242C2×C4—861no—
243C2×C4—862no—
244C2×C4—864no—
245C2×C4—864no—
246C2×C4—864no—
247C2×C4—864no—
248C2×C4—3448no—
249C2×C4—1722no—
250C2×C4—1724no—
251C2×C4#1306328211yescharacteristic
252C2×C4#1306328311yescharacteristic
253C2×C4#1306330712yes—
254C2×C4#1306331012yes—
255C2×C4SD16×D4312yes—
256C2×C4Q16×D4312yes—
257C2×C4#1306334912yes—
258C2×C4#1306335212yes—
259C8—82no—
260C8—3442no—
261C22—434no—
262C22—864no—
263C22—862no—
264C22—862no—
265C22—864no—
266C22#1458276111yescharacteristic
267C22#100×D4311yescharacteristic
268C22#101×D4311yescharacteristic
269C22#103×D4312yes—
270C22#1458290212yes—
271C4—21no—
272C4—21no—
273C4—82no—
274C4—862no—
275C4—864no—
276C4—3442no—
277C4#1458321612yes—
278C4#1458321912yes—
279C4#1458323312yes—
280C4#1458323612yes—
281C2—864no—
282C2#333×D4311yescharacteristic
283C2#1913327812yes—
284C2#1913330711yescharacteristic
285C2#1913467411yescharacteristic
286C2#1913468412yes—
subgroupG/H
centerC23C22⋊C4×D43
commutatorC22×C4×C43C22×C4
FrattiniC2×C42C22×D43
FittingC43×#1296C2
socleC23×C43C2×C22⋊C4
prime radicalC23×D43C22⋊C4
cosocleC2×C42×C43C23
hypercenter#1296D43
hypocenterC43#8725
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1296

Complements

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

NH ≅ G/Ntype
3. #19132479C2semidirect
4. #19132478C2semidirect
5. C43×#1296C2semidirect
142. #1296D43semidirect
160. C43#8725semidirect

Maximal subgroups

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

subgroupindex
#384×D432
#191345722
#191324792
#191324782
C43×#12962
#872543