Finite Group Databasebeta

← #25009391

Subgroups — #25009391

Order 11008.

400 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 400 conjugacy classes of subgroups — too many to draw. Only its 59 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#19140260C211yesmaximal, characteristic
2#19135762C211yesmaximal, characteristic
3#19133554C212yesmaximal
4#19132617C212yesmaximal
5C43×#1317C211yesmaximal, characteristic
6#14583525C2211yescharacteristic
7#14583057—22no—
8#14582835—21no—
9#14582811C2212yes—
10#14582803—22no—
11#14582786—22no—
12#14582762—21no—
13C4×C22⋊Dic43—21no—
14#14582666C2211yescharacteristic
15#14582665—21no—
16#14582637—22no—
17C43×#381C2211yescharacteristic
18C43×#323C2212yes—
19C22×Dic86D412yes—
20C2×Dic172—42no—
21#13063304—22no—
22#13063302—42no—
23C2×C4⋊Dic43—21no—
24C2×Dic43⋊C4—22no—
25C2×C22⋊Dic43—22no—
26C2×C22⋊Dic43—21no—
27C2×C22⋊Dic43—21no—
28C2×C4×Dic43—21no—
29C2×C4×Dic43—21no—
30#13063250—42no—
31C43⋊#95—22no—
32C43⋊#95—21no—
33C43⋊#95—22no—
34C43⋊#95—42no—
35C43⋊#95D412yes—
36C23×C4×C43D411yescharacteristic
37C2×C22⋊C4×C43D411yescharacteristic
38C2×C22⋊C4×C43C2311yescharacteristic
39C22⋊C8×C43—22no—
40#95×C43—22no—
41C24×C43C2×D411yescharacteristic
42C22×C4×C43—21no—
43C22×C4×C43—21no—
44C22×C4×C43—21no—
45C22×C4×C43—41no—
46C22×C4×C43—41no—
47C22×C4×C43Q1612yescomplemented
48C22×C4×C43C2×D412yes—
49C22×Dic43—22no—
50C22×Dic43—22no—
51C22×Dic43—22no—
52C22×Dic43—41no—
53C2×Dic86—22no—
54C2×Dic86—42no—
55C2×Dic86—44no—
56C2×C8×C43—42no—
57C22⋊C4×C43—41no—
58C22⋊C4×C43—41no—
59C22⋊Dic43—41no—
60C22⋊Dic43—41no—
61C22⋊Dic43—44no—
62C22⋊Dic43—41no—
63C22⋊Dic43—41no—
64C4⋊Dic43—22no—
65C4⋊Dic43—81no—
66Dic43⋊C4—44no—
67Dic43⋊C4—42no—
68C4×Dic43—81no—
69C4×Dic43—81no—
70Dic172—84no—
71C23×C43—21no—
72C23×C43—21no—
73C23×C43—42no—
74C23×C43#12011yescharacteristic
75C23×C43C2×Q1611yescharacteristic
76C23×C43#13711yescharacteristic
77C2×C4×C43—22no—
78C2×C4×C43—22no—
79C2×C4×C43—41no—
80C2×C4×C43—41no—
81C2×C4×C43—42no—
82C2×C4×C43—42no—
83C2×C4×C43—42no—
84C2×C4×C43—41no—
85C2×C4×C43—81no—
86C2×Dic43—24no—
87C2×Dic43—42no—
88C2×Dic43—42no—
89C2×Dic43—42no—
90C2×Dic43—42no—
91C2×Dic43—42no—
92C2×Dic43—42no—
93C2×Dic43—82no—
94C2×Dic43—81no—
95C2×Dic43—82no—
96Dic86—44no—
97Dic86—82no—
98Dic86—82no—
99C8×C43—82no—
100#12215—431nomaximal, Sylow
101C22×C43—22no—
102C22×C43—21no—
103C22×C43—21no—
104C22×C43—41no—
105C22×C43—41no—
106C22×C43—42no—
107C22×C43—81no—
108C22×C43#45111yescharacteristic
109C22×C43#45511yescharacteristic
110C22×C43B(4,𝔽2)11yescharacteristic
111C4×C43—42no—
112C4×C43—42no—
113C4×C43—81no—
114Dic43—44no—
115Dic43—82no—
116Dic43—82no—
117Dic43—161no—
118#2607—431no—
119#2030—431no—
120#1602—432no—
121#1351—432no—
122#1317D4311yescharacteristic
123C2×C43—21no—
124C2×C43—21no—
125C2×C43—41no—
126C2×C43—41no—
127C2×C43#160211yescharacteristic
128C2×C43#219712yes—
129#543—431no—
130#451—862no—
131#399—861no—
132#393—432no—
133#391—862no—
134#387—862no—
135#381—861no—
136#381C2×D4311yescharacteristic
137C4×C22⋊C4—861no—
138#342—431no—
139#342—861no—
140#328—862no—
141#323C2×D4312yes—
142C43#1221511yescharacteristic, complemented, Sylow
143C22×Q8—432no—
144C23×C4D17211yescharacteristic
145C2×Q16—1722no—
146C22⋊Q8—862no—
147C22⋊Q8—1722no—
148C2×C4⋊C4—861no—
149C2×C4⋊C4—862no—
150C2×C22⋊C4—861no—
151C2×C22⋊C4—862no—
152C2×C22⋊C4—861no—
153C2×C22⋊C4D17211yescharacteristic
154C2×C22⋊C4C22×D4311yescharacteristic
155C2×C42—861no—
156C2×C42—861no—
157#103—1722no—
158C22⋊C8—22no—
159#95—22no—
160#95—432no—
161#95—862no—
162#95—861no—
163#95—862no—
164#95—1722no—
165C24C2×D17211yescharacteristic
166C2×Q8—862no—
167C2×Q8—1722no—
168C2×Q8—1724no—
169C22×C4—21no—
170C22×C4—21no—
171C22×C4—21no—
172C22×C4—41no—
173C22×C4—41no—
174C22×C4—862no—
175C22×C4—862no—
176C22×C4—862no—
177C22×C4—1721no—
178C22×C4Dic17212yescomplemented
179C22×C4D4×D4312yes—
180Q16—3444no—
181C2×C8—42no—
182C4⋊C4—862no—
183C4⋊C4—3441no—
184C4⋊C4—1722no—
185C4⋊C4—1724no—
186C22⋊C4—41no—
187C22⋊C4—41no—
188C22⋊C4—1724no—
189C22⋊C4—1721no—
190C22⋊C4—1721no—
191C22⋊C4—1721no—
192C22⋊C4—1721no—
193C42—3441no—
194C42—3441no—
195C23—21no—
196C23—21no—
197C23—42no—
198C23#1306329511yescharacteristic
199C23C2×Dic17211yescharacteristic
200C23#1306335811yescharacteristic
201Q8—3442no—
202Q8—3442no—
203Q8—1724no—
204C2×C4—22no—
205C2×C4—22no—
206C2×C4—41no—
207C2×C4—41no—
208C2×C4—42no—
209C2×C4—42no—
210C2×C4—42no—
211C2×C4—41no—
212C2×C4—81no—
213C2×C4—864no—
214C2×C4—3442no—
215C2×C4—3441no—
216C2×C4—3442no—
217C2×C4—1722no—
218C2×C4—1722no—
219C2×C4—1722no—
220C2×C4—1722no—
221C2×C4—1722no—
222C2×C4—1722no—
223C8—82no—
224C22—22no—
225C22—21no—
226C22—21no—
227C22—41no—
228C22—41no—
229C22—42no—
230C22—81no—
231C22#1458305711yescharacteristic
232C22#1458307911yescharacteristic
233C22#1458308711yescharacteristic
234C4—42no—
235C4—42no—
236C4—81no—
237C4—3442no—
238C4—3442no—
239C4—1724no—
240C4—6881no—
241C2—21no—
242C2—21no—
243C2—41no—
244C2—41no—
245C2#1913355411yescharacteristic
246C2#1913658612yes—
subgroupG/H
centerC22#14583087
commutator, cosocleC2×C22⋊C4×C43C23
FrattiniC2×C22⋊C4C22×D43
FittingC43×#1317C2
socleC22×C43B(4,𝔽2)
prime radicalC24×C43C2×D4
hypercenter#1317D43
hypocenterC43#12215
LCSG ▷ C2×C22⋊C4×C43 ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23 ◁ C2×C22⋊C4 ◁ #1317

Complements

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

NH ≅ G/Ntype
47. C22×C4×C43Q16semidirect
142. C43#12215semidirect
178. C22×C4Dic172semidirect

Maximal subgroups

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

subgroupindex
#191402602
#191357622
#191335542
#191326172
C43×#13172
#1221543