Finite Group Databasebeta

← #25016087

Subgroups — #25016087

Order 11008.

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

normal subgroups only

This group has 402 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#19136289C212yesmaximal
3#19135147C212yesmaximal
4#19132718C211yesmaximal, characteristic
5C43×#1858C211yesmaximal, characteristic
6#14583470C2212yes—
7#14583241—22no—
8#14583157—21no—
9#14583140—21no—
10#14583057—22no—
11#14582883C2212yes—
12C2×#13063243—22no—
13#14582697—24no—
14#14582671—22no—
15C43×#568C2211yescharacteristic
16C43×#430—21no—
17C43×#413C2211yescharacteristic
18C43×#408C2211yescharacteristic
19C43×#341—21no—
20C22×Dic86D412yes—
21C2×Dic172—21no—
22C2×Dic172—21no—
23C2×#10621877—22no—
24#13063323—22no—
25#13063312—22no—
26#13063306—22no—
27#13063306—22no—
28#13063304—22no—
29#13063304—22no—
30#13063284D412yes—
31#13063259—21no—
32#13063257—21no—
33#13063250—22no—
34#13063250—22no—
35#13063244—22no—
36#13063243—44no—
37#13063242—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×C43D412yes—
47#100×C43—21no—
48C22⋊C8×C43—22no—
49#41×C43—41no—
50#41×C43—41no—
51C2×Q8×C43C2×D411yescharacteristic
52C2×D4×C43#4111yescharacteristic
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—24no—
63M16×C43—22no—
64M16×C43—41no—
65M16×C43—41no—
66M16×C43—41no—
67C2×C8×C43—21no—
68C2×C8×C43—21no—
69C2×C8×C43—41no—
70C2×C8×C43—42no—
71C2×C8×C43—41no—
72C2×C8×C43—41no—
73C22⋊Dic43—22no—
74C22⋊Dic43—42no—
75C22⋊Dic43—42no—
76C4⋊Dic43—22no—
77Dic43⋊C4—42no—
78Dic43⋊C4—42no—
79C4×Dic43—22no—
80#10621877—42no—
81#10621877—42no—
82C2×C43⋊C8—42no—
83Dic172—81no—
84Dic172—81no—
85C23×C43#12312yes—
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#12112yes—
97C2×Dic43—44no—
98C2×Dic43—42no—
99C2×Dic43—42no—
100Dic86—42no—
101Dic86—42no—
102Dic86—82no—
103C8×C43—42no—
104C8×C43—41no—
105C8×C43—42no—
106C8×C43—41no—
107C43⋊C8—82no—
108#13431—431nomaximal, Sylow
109C22×C43—22no—
110C22×C43—21no—
111C22×C43—42no—
112C22×C43—41no—
113C22×C43#39411yescharacteristic
114C4×C43—22no—
115C4×C43—21no—
116C4×C43B(4,𝔽2)11yescharacteristic
117C4×C43#45811yescharacteristic
118Dic43—82no—
119Dic43—82no—
120#3202—431no—
121#2135—432no—
122#1915—432no—
123#1858D4311yescharacteristic
124#1392—431no—
125C2×C43—21no—
126C2×C43—42no—
127C2×C43—41no—
128C2×C43#204411yescharacteristic
129#568C2×D4311yescharacteristic
130#536—432no—
131#485—862no—
132#470—861no—
133#467—861no—
134#451—862no—
135#430—21no—
136#413—432no—
137#413C2×D4311yescharacteristic
138C2×#101—862no—
139#408C2×D4311yescharacteristic
140#356—864no—
141#344—862no—
142#341—21no—
143C43#1343111yescharacteristic, complemented, Sylow
144C2×#41C22×D4311yescharacteristic
145C22×Q8—432no—
146C2×Q16—861no—
147C2×Q16—861no—
148#131—42no—
149C2×M16—22no—
150C2×M16—21no—
151C2×M16—21no—
152C2×M16—862no—
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#108—42no—
163#107—861no—
164#106—861no—
165#103—862no—
166#103—862no—
167#101—862no—
168#101—1724no—
169#101D17212yes—
170#100—21no—
171#100—862no—
172C22⋊C8—22no—
173#41—41no—
174#41—41no—
175C2×Q8—862no—
176C2×Q8—862no—
177C2×Q8—1722no—
178C2×Q8—1722no—
179C2×Q8C2×D17211yescharacteristic
180C2×D4#1062189811yescharacteristic
181C2×D4#1062190212yes—
182C22×C4—862no—
183C22×C4D4×D4312yes—
184C22×C4C2×C22⋊D4311yescharacteristic
185Q16—3441no—
186Q16—3441no—
187M16—24no—
188M16—22no—
189M16—22no—
190M16—41no—
191M16—41no—
192M16—41no—
193M16—1722no—
194M16—1722no—
195C2×C8—21no—
196C2×C8—21no—
197C2×C8—41no—
198C2×C8—41no—
199C2×C8—42no—
200C2×C8—41no—
201C2×C8—1722no—
202C4⋊C4—862no—
203C4⋊C4—1722no—
204C4⋊C4—1722no—
205C22⋊C4—862no—
206C22⋊C4—1722no—
207C22⋊C4—1722no—
208C42—862no—
209C23#1306331012yes—
210C23#1306331411yescharacteristic
211Q8—41no—
212Q8—3442no—
213Q8—1722no—
214Q8—1722no—
215D4—41no—
216D4—42no—
217C2×C4—21no—
218C2×C4—22no—
219C2×C4—21no—
220C2×C4—22no—
221C2×C4—1724no—
222C2×C4—1722no—
223C2×C4—1722no—
224C2×C4#1306329311yescharacteristic
225C2×C4#1306329911yescharacteristic
226C2×C4#1306330012yes—
227C8—42no—
228C8—41no—
229C8—42no—
230C8—41no—
231C8—3442no—
232C22—22no—
233C22—21no—
234C22—42no—
235C22—41no—
236C22#1458281611yescharacteristic
237C4—21no—
238C4—22no—
239C4—3442no—
240C4—3442no—
241C4#1458308511yescharacteristic
242C4#1458308811yescharacteristic
243C2—21no—
244C2—42no—
245C2—41no—
246C2#1913584611yescharacteristic
subgroupG/H
centerC2#19135846
commutator, prime radical, cosocleC2×#41×C43C23
FrattiniC2×#41C22×D43
FittingC43×#1858C2
socleC2×C43#2044
hypercenter#1858D43
hypocenterC43#13431
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
143. C43#13431semidirect

Maximal subgroups

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

subgroupindex
#191454902
#191362892
#191351472
#191327182
C43×#18582
#1343143