Finite Group Databasebeta

← #25016132

Subgroups — #25016132

Order 11008.

406 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 406 conjugacy classes of subgroups — too many to draw. Only its 71 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#19145490C211yesmaximal, characteristic
2#19136250C212yesmaximal
3#19135117C212yesmaximal
4#19132716C211yesmaximal, characteristic
5C43×#1858C211yesmaximal, characteristic
6#14583470C2212yes—
7#14583241—22no—
8#14583157—21no—
9#14583140—21no—
10#14583057—22no—
11#14582909—22no—
12#14582873C2212yes—
13#14582690—24no—
14#14582656—22no—
15C43×#568C2211yescharacteristic
16C43×#430—21no—
17C43×#413C2211yescharacteristic
18C43×#408C2211yescharacteristic
19C43×#341—21no—
20C22×Dic86D412yes—
21C2×Dic172—21no—
22C2×Dic172—21no—
23#13063323—22no—
24#13063312—22no—
25#13063306—22no—
26#13063306—22no—
27#13063304—22no—
28#13063304—22no—
29#13063284—22no—
30#13063284D412yes—
31#13063259—21no—
32#13063257—21no—
33#13063250—22no—
34#13063250—22no—
35#13063250—44no—
36#13063240—22no—
37#13063240—22no—
38C2×#41×C43C2311yescharacteristic
39#131×C43—42no—
40C2×M16×C43—22no—
41C2×M16×C43—21no—
42C2×M16×C43—21no—
43C2×M16×C43D411yescharacteristic
44C22×C8×C43D411yescharacteristic
45#108×C43—42no—
46#101×C43—21no—
47#100×C43D412yes—
48C22⋊C8×C43—22no—
49#41×C43—41no—
50#41×C43—41no—
51C2×Q8×C43#4111yescharacteristic
52C2×D4×C43C2×D411yescharacteristic
53C2×D4×C43#4112yes—
54C22×C4×C43C2×D412yes—
55C22×C4×C43C2×D411yescharacteristic
56C22×Dic43—22no—
57C2×Dic86—22no—
58C2×Dic86—22no—
59C2×Dic86—42no—
60C2×Dic86—42no—
61M16×C43—22no—
62M16×C43—22no—
63M16×C43—41no—
64M16×C43—42no—
65M16×C43—41no—
66M16×C43—41no—
67C2×C8×C43—24no—
68C2×C8×C43—21no—
69C2×C8×C43—21no—
70C2×C8×C43—41no—
71C2×C8×C43—41no—
72C2×C8×C43—41no—
73C22⋊Dic43—22no—
74C22⋊Dic43—42no—
75C22⋊Dic43—42no—
76C22⋊Dic43—42no—
77C4⋊Dic43—22no—
78C4⋊Dic43—42no—
79Dic43⋊C4—42no—
80Dic43⋊C4—42no—
81C4×Dic43—22no—
82C4×Dic43—42no—
83Dic172—81no—
84Dic172—81no—
85C23×C43#12112yes—
86C23×C43#12411yescharacteristic
87Q8×C43—41no—
88D4×C43—41no—
89D4×C43—42no—
90C2×C4×C43—22no—
91C2×C4×C43—21no—
92C2×C4×C43—22no—
93C2×C4×C43—21no—
94C2×C4×C43#12011yescharacteristic
95C2×C4×C43#12111yescharacteristic
96C2×C4×C43#12312yes—
97C2×Dic43—42no—
98C2×Dic43—42no—
99C2×Dic43—82no—
100C2×Dic43—82no—
101Dic86—44no—
102Dic86—42no—
103Dic86—42no—
104C8×C43—42no—
105C8×C43—41no—
106C8×C43—42no—
107C8×C43—41no—
108#13438—431nomaximal, Sylow
109C22×C43—22no—
110C22×C43—21no—
111C22×C43—42no—
112C22×C43—41no—
113C22×C43#39411yescharacteristic
114C4×C43—21no—
115C4×C43—22no—
116C4×C43B(4,𝔽2)11yescharacteristic
117C4×C43#45811yescharacteristic
118Dic43—82no—
119Dic43—82no—
120Dic43—162no—
121#3202—431no—
122#2123—432no—
123#1909—432no—
124#1858D4311yescharacteristic
125#1391—431no—
126C2×C43—21no—
127C2×C43—42no—
128C2×C43—41no—
129C2×C43#204411yescharacteristic
130#568C2×D4311yescharacteristic
131#536—432no—
132#485—862no—
133#470—861no—
134#467—861no—
135#451—862no—
136#430—21no—
137#419—862no—
138#413C2×D4311yescharacteristic
139#410—432no—
140#408C2×D4311yescharacteristic
141#352—864no—
142#341—21no—
143H(3,ℤ/4)—862no—
144C43#1343811yescharacteristic, complemented, Sylow
145C2×#41C22×D4311yescharacteristic
146C22×Q8—432no—
147C2×Q16—861no—
148C2×Q16—861no—
149#131—42no—
150C2×M16—22no—
151C2×M16—21no—
152C2×M16—21no—
153C2×M16C22⋊D4311yescharacteristic
154C22×C8C22⋊D4311yescharacteristic
155C4⋊Q8—862no—
156#124—862no—
157#123—862no—
158#123—862no—
159C22⋊Q8—862no—
160C22⋊Q8—862no—
161#117—432no—
162#117—862no—
163#108—42no—
164#107—861no—
165#106—861no—
166#103—862no—
167#103—862no—
168#103—1724no—
169#101—21no—
170#100D17212yes—
171#99—862no—
172#99—862no—
173C22⋊C8—22no—
174#41—41no—
175#41—41no—
176C2×Q8—862no—
177C2×Q8—862no—
178C2×Q8—1722no—
179C2×Q8—1722no—
180C2×Q8#1062189811yescharacteristic
181C2×D4C2×D17211yescharacteristic
182C2×D4#1062190212yes—
183C22×C4—862no—
184C22×C4D4×D4312yes—
185C22×C4C2×C22⋊D4311yescharacteristic
186Q16—3441no—
187Q16—3441no—
188M16—22no—
189M16—22no—
190M16—42no—
191M16—41no—
192M16—41no—
193M16—41no—
194C2×C8—24no—
195C2×C8—21no—
196C2×C8—21no—
197C2×C8—41no—
198C2×C8—41no—
199C2×C8—41no—
200C4⋊C4—862no—
201C4⋊C4—1722no—
202C4⋊C4—1722no—
203C4⋊C4—1722no—
204C22⋊C4—862no—
205C22⋊C4—1722no—
206C22⋊C4—1722no—
207C22⋊C4—1722no—
208C42—862no—
209C42—1722no—
210C23#1306330012yes—
211C23#1306331411yescharacteristic
212Q8—41no—
213Q8—1724no—
214Q8—1722no—
215Q8—1722no—
216D4—41no—
217D4—42no—
218C2×C4—22no—
219C2×C4—21no—
220C2×C4—22no—
221C2×C4—21no—
222C2×C4—3442no—
223C2×C4—3442no—
224C2×C4—1722no—
225C2×C4—1722no—
226C2×C4#1306329311yescharacteristic
227C2×C4#1306329911yescharacteristic
228C2×C4#1306331012yes—
229C8—42no—
230C8—42no—
231C8—41no—
232C8—41no—
233C22—22no—
234C22—21no—
235C22—42no—
236C22—41no—
237C22#1458281611yescharacteristic
238C4—21no—
239C4—22no—
240C4—3442no—
241C4—3442no—
242C4—6882no—
243C4#1458308511yescharacteristic
244C4#1458308811yescharacteristic
245C2—21no—
246C2—42no—
247C2—41no—
248C2#1913584611yescharacteristic
subgroupG/H
centerC2#19135846
commutator, prime radical, cosocleC2×#41×C43C23
FrattiniC2×#41C22×D43
FittingC43×#1858C2
socleC2×C43#2044
hypercenter#1858D43
hypocenterC43#13438
LCSG ▷ C2×#41×C43 ▷ C22×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×#41 ◁ #1858

Complements

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

NH ≅ G/Ntype
144. C43#13438semidirect

Maximal subgroups

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

subgroupindex
#191454902
#191362502
#191351172
#191327162
C43×#18582
#1343843