Finite Group Databasebeta

← #25009805

Subgroups — #25009805

Order 11008.

344 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 344 conjugacy classes of subgroups — too many to draw. Only its 67 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#19145370C211yesmaximal, characteristic
2#19136793C212yesmaximal, complemented
3#19136018C211yesmaximal, characteristic
4#19132608C212yesmaximal, complemented
5C43×#1314C211yesmaximal, characteristic
6C2×#13063304—21no—
7#14583235—22no—
8#14583140—21no—
9#14583140C2212yes—
10#14583057—22no—
11C2×#13063259C2211yescharacteristic
12#14582759—21no—
13#14582727—22no—
14#14582704—22no—
15#14582662—21no—
16#14582662C2211yescharacteristic
17C2×C22⋊C8×C43C2211yescharacteristic
18C43×C22⋊C16C2212yes—
19C22×Dic86—21no—
20C2×Dic172—21no—
21C2×Dic172D412yes—
22#13063304—22no—
23#13063304—22no—
24#13063304—41no—
25#13063304—41no—
26C2×C4⋊Dic43—21no—
27C2×C4⋊Dic43—21no—
28C2×C4⋊Dic43—21no—
29C2×Dic43⋊C4—41no—
30C2×C22⋊Dic43—41no—
31C2×C22⋊Dic43—41no—
32#13063259—21no—
33#13063259—22no—
34#13063259D412yes—
35#13063250—22no—
36#13063250—22no—
37C43⋊#95—41no—
38C23×C4×C43D411yescharacteristic
39C22×C8×C43D411yescharacteristic
40C22×C8×C43C2311yescharacteristic
41C2×C16×C43—22no—
42C22⋊C8×C43—22no—
43C24×C43D811yescharacteristic
44C22×C4×C43—21no—
45C22×C4×C43—21no—
46C22×C4×C43—41no—
47C22×C4×C43—41no—
48C22×C4×C43D811yescharacteristic
49C22×C4×C43C2×D411yescharacteristic
50C22×Dic43—41no—
51C22×Dic43—41no—
52C22×Dic43—41no—
53C22×Dic43—41no—
54C2×Dic86—22no—
55C2×Dic86—41no—
56C2×Dic86—81no—
57C2×Dic86—81no—
58C2×C8×C43—21no—
59C2×C8×C43—41no—
60C2×C8×C43—41no—
61C2×C8×C43C2×D412yes—
62C22⋊Dic43—42no—
63C22⋊Dic43—42no—
64C22⋊Dic43—82no—
65C4⋊Dic43—22no—
66C4⋊Dic43—41no—
67C4⋊Dic43—41no—
68C4⋊Dic43—41no—
69C4⋊Dic43—41no—
70C4⋊Dic43—41no—
71Dic43⋊C4—42no—
72Dic43⋊C4—42no—
73Dic172—42no—
74Dic172—81no—
75C16×C43—42no—
76C23×C43—21no—
77C23×C43—21no—
78C23×C43—41no—
79C23×C43—41no—
80C23×C43SD3212yes—
81C23×C43C2×D811yescharacteristic
82C2×C4×C43—21no—
83C2×C4×C43—21no—
84C2×C4×C43—21no—
85C2×C4×C43—41no—
86C2×C4×C43—41no—
87C2×C4×C43—41no—
88C2×C4×C43—81no—
89C2×C4×C43#12011yescharacteristic
90C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
91C2×Dic43—42no—
92C2×Dic43—42no—
93C2×Dic43—82no—
94C2×Dic43—82no—
95C2×Dic43—81no—
96C2×Dic43—81no—
97C2×Dic43—81no—
98C2×Dic43—81no—
99C2×Dic43—81no—
100C2×Dic43—81no—
101Dic86—42no—
102Dic86—42no—
103Dic86—82no—
104C8×C43—22no—
105C8×C43—41no—
106#12279—431nomaximal, Sylow
107C22×C43—21no—
108C22×C43—21no—
109C22×C43—22no—
110C22×C43—42no—
111C22×C43—41no—
112C22×C43—41no—
113C22×C43—81no—
114C22×C43#44711yescharacteristic
115C22×C43C2×SD3211yescharacteristic
116C22×C43#51011yescharacteristic
117C4×C43—21no—
118C4×C43—41no—
119C4×C43#45511yescharacteristic
120C4×C43#45811yescharacteristic
121Dic43—82no—
122Dic43—82no—
123Dic43—161no—
124Dic43—161no—
125#3189—431no—
126#2235—432no—
127#2075—431no—
128#1348—432no—
129#1314D4311yescharacteristic
130C2×C43—21no—
131C2×C43—21no—
132C2×C43—42no—
133C2×C43#160711yescharacteristic
134C2×C43#218511yescharacteristic
135C2×C43#219111yescharacteristic
136C2×C22⋊Q8—861no—
137#484—862no—
138#467—432no—
139#467—861no—
140#451—862no—
141C2×#107—431no—
142C2×C22⋊C8C2×D4311yescharacteristic
143#380—861no—
144#367—862no—
145#358—862no—
146C22⋊C16C2×D4312yes—
147#340—431no—
148#340—861no—
149C43#1227911yescharacteristic, complemented, Sylow
150C22×Q8—861no—
151C23×C4D17211yescharacteristic
152C2×Q16—432no—
153C2×Q16—861no—
154C22×C8D17211yescharacteristic
155C22×C8C22×D4311yescharacteristic
156C22⋊Q8—862no—
157C22⋊Q8—862no—
158C22⋊Q8—1721no—
159C22⋊Q8—1721no—
160C2×C4⋊C4—861no—
161C2×C4⋊C4—861no—
162C2×C4⋊C4—861no—
163C2×C4⋊C4—1721no—
164C2×C22⋊C4—1721no—
165C2×C22⋊C4—1721no—
166C2×C16—22no—
167#107—432no—
168#107—861no—
169#107—862no—
170#103—862no—
171#103—862no—
172C22⋊C8—22no—
173#95—1721no—
174C24D34411yescharacteristic
175C2×Q8—862no—
176C2×Q8—3441no—
177C2×Q8—3441no—
178C2×Q8—1721no—
179C22×C4—21no—
180C22×C4—21no—
181C22×C4—41no—
182C22×C4—41no—
183C22×C4—1721no—
184C22×C4—1721no—
185C22×C4—1721no—
186C22×C4—1721no—
187C22×C4D34411yescharacteristic
188C22×C4C2×D17211yescharacteristic
189Q16—3441no—
190Q16—1722no—
191C2×C8—21no—
192C2×C8—41no—
193C2×C8—41no—
194C2×C8D4×D4312yes—
195C4⋊C4—862no—
196C4⋊C4—1721no—
197C4⋊C4—1721no—
198C4⋊C4—1721no—
199C4⋊C4—1722no—
200C4⋊C4—1721no—
201C4⋊C4—1721no—
202C4⋊C4—1722no—
203C22⋊C4—3442no—
204C22⋊C4—1722no—
205C22⋊C4—1722no—
206C16—42no—
207C23—21no—
208C23—21no—
209C23—41no—
210C23—41no—
211C23#1306327012yes—
212C23C2×D34411yescharacteristic
213Q8—3442no—
214Q8—1722no—
215Q8—1722no—
216C2×C4—21no—
217C2×C4—21no—
218C2×C4—21no—
219C2×C4—41no—
220C2×C4—41no—
221C2×C4—41no—
222C2×C4—81no—
223C2×C4—3442no—
224C2×C4—3442no—
225C2×C4—3441no—
226C2×C4—3441no—
227C2×C4—3441no—
228C2×C4—3441no—
229C2×C4—3441no—
230C2×C4—3441no—
231C2×C4—1722no—
232C2×C4—1722no—
233C2×C4#1306329511yescharacteristic
234C2×C4#1306335311yescharacteristic
235C8—22no—
236C8—41no—
237C22—21no—
238C22—21no—
239C22—22no—
240C22—42no—
241C22—41no—
242C22—41no—
243C22—81no—
244C22#1458303511yescharacteristic
245C22C2×#1306327011yescharacteristic
246C22#1458334211yescharacteristic
247C4—21no—
248C4—41no—
249C4—3442no—
250C4—3442no—
251C4—6881no—
252C4—6881no—
253C4#1458307911yescharacteristic
254C4#1458309011yescharacteristic
255C2—21no—
256C2—21no—
257C2—42no—
258C2#1913358311yescharacteristic
259C2#1913651411yescharacteristic
260C2#1913654811yescharacteristic
subgroupG/H
centerC22#14583035
commutator, cosocleC22×C8×C43C23
FrattiniC22×C8C22×D43
FittingC43×#1314C2
socleC22×C43#447
prime radicalC24×C43D8
hypercenter#1314D43
hypocenterC43#12279
LCSG ▷ C22×C8×C43 ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C22⋊C8 ◁ #1314

Complements

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

NH ≅ G/Ntype
2. #19136793C2semidirect
4. #19132608C2semidirect
149. C43#12279semidirect

Maximal subgroups

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

subgroupindex
#191453702
#191367932
#191360182
#191326082
C43×#13142
#1227943