Finite Group Databasebeta

← #25125324

Subgroups — #25125324

Order 11008.

960 conjugacy classes of subgroups; only the 247 normal subgroups are shown.

normal subgroups only

This group has 960 conjugacy classes of subgroups — too many to draw. Only its 247 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×#14582947C213yesmaximal, complemented
2C2×#14582881C213yesmaximal
3#19135997C214yesmaximal, complemented
4#19135994C214yesmaximal, complemented
5C2×C43×#338C211yesmaximal, characteristic, complemented
6C22×#10621898C2211yescharacteristic
7C22×#10621877C2213yes—
8#14582947—26no—
9#14582947C22112yes—
10C2×#13063260—26no—
11#14582881—26no—
12#14582881—26no—
13C2×#13063243C2216yes—
14C2×#13063241C2216yes—
15C22×M16×C43C2213yes—
16C43×#338C2214yes—
17C2×#10621898—23no—
18C2×#10621898—23no—
19C2×#10621898—23no—
20C2×#10621898—23no—
21C22×Dic86C2311yescharacteristic
22C22×D172C2311yescharacteristic
23C22×C22⋊D43Q812yes—
24C22×C4×D43Q812yes—
25C2×#10621877—23no—
26C2×#10621877—23no—
27C2×#10621877—23no—
28C2×#10621877D416yes—
29C2×#10621877D416yes—
30C2×#10621877C2316yes—
31C22×C43⋊C8—23no—
32#13063260—224no—
33#13063243—212no—
34#13063241—212no—
35C23×C4×C43C2311yescharacteristic
36C2×M16×C43—23no—
37C2×M16×C43—23no—
38C2×M16×C43—23no—
39C2×M16×C43—23no—
40C2×M16×C43—23no—
41C2×M16×C43C2316yes—
42C22×C8×C43—23no—
43C24×C43C2×Q811yescharacteristic
44C23×D43C2×Q812yes—
45C22×C4×C43C2×D413yes—
46C22×C4×C43C2×D413yes—
47C22×C4×C43C2×Q811yescharacteristic
48C22×C4×C43#4113yes—
49C22×C4×C43#4113yes—
50C22×C4×C43C2411yescharacteristic
51C2×C22⋊D43—26no—
52C2×C22⋊D43—26no—
53C22×Dic43C2×Q812yes—
54#10621898—43no—
55#10621898—43no—
56#10621898—43no—
57#10621898—43no—
58#10621898—43no—
59#10621898—41no—
60C2×D172—23no—
61C2×D172—23no—
62C2×C4×D43—26no—
63C2×C4×D43—26no—
64C2×Dic86—23no—
65C2×Dic86—23no—
66M16×C43—26no—
67M16×C43—26no—
68M16×C43—43no—
69M16×C43—43no—
70C2×C8×C43—26no—
71C2×C8×C43—43no—
72C2×C8×C43—43no—
73#10621877—26no—
74#10621877—26no—
75#10621877—26no—
76#10621877C2×D4112yes—
77C2×C43⋊C8—26no—
78C2×C43⋊C8—26no—
79C2×C43⋊C8—26no—
80C23×C43—81no—
81C23×C43C22⋊Q813yes—
82C23×C43C22⋊Q813yes—
83C23×C43C22×Q811yescharacteristic
84C22×D43—26no—
85C22×D43—82no—
86C2×C4×C43#12113yes—
87C2×C4×C43#12113yes—
88C2×C4×C43#12113yes—
89C2×C4×C43#12113yes—
90C2×C4×C43C22⋊Q813yes—
91C2×C4×C43C22⋊Q813yes—
92C2×C4×C43#12613yes—
93C2×C4×C43#12611yescharacteristic
94C2×C4×C43C22×D413yes—
95C2×C4×C43C2×#4113yes—
96C22⋊D43—46no—
97C22⋊D43—42no—
98C2×Dic43—26no—
99D172—43no—
100D172—41no—
101C4×D43—46no—
102C4×D43—42no—
103Dic86—43no—
104Dic86—41no—
105C8×C43—46no—
106C43⋊C8—212no—
107#23622—431nomaximal, Sylow
108C22×C43—41no—
109C22×C43—43no—
110C22×C43—43no—
111C22×C43#39613yes—
112C22×C43#39611yescharacteristic
113C22×C43C2×C22⋊Q813yes—
114C2×D43—42no—
115C2×D43—86no—
116C4×C43#39613yes—
117C4×C43#39611yescharacteristic
118C4×C43C2×#12113yes—
119C4×C43C2×#12611yescharacteristic
120Dic43—42no—
121C2×#430—433no—
122C2×#413—433no—
123#2070—434no—
124#2069—434no—
125C2×#338D4311yescharacteristic, complemented
126C2×C43—23no—
127C2×C43—23no—
128C2×C43—21no—
129C2×C43C2×#39611yescharacteristic
130D43—82no—
131C22×#41—431no—
132C22×M16—433no—
133C22×M16C2×D4313yes—
134#430—4312no—
135#430—866no—
136C2×#108—866no—
137#413—866no—
138#413—866no—
139C2×#101—436no—
140C2×#100—436no—
141#338C2×D4314yes—
142C43#2362211yescharacteristic, complemented, Sylow
143C2×#41—863no—
144C2×#41—863no—
145C2×#41—863no—
146C2×#41—863no—
147C22×Q8—431no—
148C22×D4—432no—
149C22×D4—431no—
150C23×C4—432no—
151C23×C4C22×D4311yescharacteristic
152C2×M16—23no—
153C2×M16—23no—
154C2×M16—23no—
155C2×M16—23no—
156C2×M16—23no—
157C2×M16—436no—
158C2×M16—436no—
159C2×M16—436no—
160C2×M16—863no—
161C2×M16—863no—
162C2×M16—863no—
163C2×M16C22×D4316yes—
164C22×C8—23no—
165C22×C8—863no—
166#108—8624no—
167#101—8612no—
168#100—8612no—
169C24—432no—
170C24Q8×D4311yescharacteristic
171#41—1723no—
172#41—1723no—
173#41—1723no—
174#41—1723no—
175#41—1723no—
176#41—1721no—
177C2×Q8—863no—
178C2×Q8—863no—
179C2×D4—866no—
180C2×D4—866no—
181C2×D4—863no—
182C2×D4—863no—
183C22×C4—432no—
184C22×C4—866no—
185C22×C4—866no—
186C22×C4#1062189813yes—
187C22×C4#1062189813yes—
188C22×C4D4×D4313yes—
189C22×C4D4×D4313yes—
190C22×C4Q8×D4311yescharacteristic
191C22×C4C23×D4311yescharacteristic
192M16—26no—
193M16—26no—
194M16—43no—
195M16—43no—
196M16—4312no—
197M16—866no—
198M16—866no—
199M16—866no—
200C2×C8—26no—
201C2×C8—43no—
202C2×C8—43no—
203C2×C8—866no—
204C2×C8—866no—
205C2×C8—866no—
206C23—81no—
207C23—866no—
208C23—3442no—
209C23#1306330313yes—
210C23#1306330313yes—
211C23C2×Q8×D4311yescharacteristic
212Q8—1723no—
213Q8—1721no—
214D4—1722no—
215D4—1726no—
216D4—1723no—
217D4—1721no—
218C2×C4—866no—
219C2×C4—1726no—
220C2×C4—1722no—
221C2×C4#1306329813yes—
222C2×C4#1306329813yes—
223C2×C4#1306329813yes—
224C2×C4#1306329813yes—
225C2×C4#1306330313yes—
226C2×C4#1306330313yes—
227C2×C4#1306331913yes—
228C2×C4#1306331911yescharacteristic
229C2×C4C2×D4×D4313yes—
230C2×C4C2×#1062189813yes—
231C8—46no—
232C8—8612no—
233C22—41no—
234C22—43no—
235C22—43no—
236C22—3446no—
237C22—1722no—
238C22#1458282311yescharacteristic
239C22#1458282313yes—
240C22C2×#1306330313yes—
241C4—1722no—
242C4#1458282313yes—
243C4#1458282311yescharacteristic
244C4C2×#1306329813yes—
245C4C2×#1306331911yescharacteristic
246C2—23no—
247C2—21no—
248C2—23no—
249C2—3442no—
250C2C2×#1458282311yescharacteristic
subgroupG/H
centerC4#14582823
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC2×C43×#338C2
socleC2×C43C2×#396
prime radicalC22×#10621898C22
hypercenterC2×#338D43
hypocenterC43#23622
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C4 ◁ C23×C4 ◁ C2×#338

Complements

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

NH ≅ G/Ntype
1. C2×#14582947C2semidirect
3. #19135997C2semidirect
4. #19135994C2semidirect
5. C2×C43×#338C2semidirect
125. C2×#338D43semidirect
142. C43#23622semidirect

Maximal subgroups

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

subgroupindex
C2×#145829472
C2×#145828812
#191359972
#191359942
C2×C43×#3382
#2362243