Finite Group Databasebeta

← #25016070

Subgroups — #25016070

Order 11008.

444 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 444 conjugacy classes of subgroups — too many to draw. Only its 75 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#19141627C211yesmaximal, characteristic
2C2×#14582697C212yesmaximal
3#19134988C212yesmaximal
4#19132722C211yesmaximal, characteristic
5C43×#1857C211yesmaximal, characteristic
6C2×#13063323C2212yes—
7#14582907—22no—
8C2×#13063244C2212yes—
9#14582829—21no—
10#14582820—22no—
11#14582797—21no—
12#14582784—22no—
13#14582697—24no—
14#14582658—22no—
15C43×#519C2211yescharacteristic
16C43×#428—21no—
17C2×#101×C43C2211yescharacteristic
18C43×#391C2211yescharacteristic
19C43×#339—21no—
20C22×Dic86D412yes—
21C2×#10621877—22no—
22#13063323—22no—
23#13063323—22no—
24#13063323—22no—
25#13063323—22no—
26C2×C4⋊Dic43—21no—
27C2×C4⋊Dic43—21no—
28C2×C4⋊Dic43—21no—
29C2×Dic43⋊C4—22no—
30C2×Dic43⋊C4—22no—
31C2×C4×Dic43D412yes—
32#13063248—42no—
33#13063248—42no—
34#13063244—22no—
35#13063244—22no—
36C43⋊#95—21no—
37C43⋊#95—22no—
38C43⋊#95—22no—
39C22×Q8×C43C2311yescharacteristic
40C2×M16×C43—21no—
41C4×Q8×C43—41no—
42C4×Q8×C43—41no—
43#117×C43—21no—
44#117×C43—22no—
45C2×C4⋊C4×C43D411yescharacteristic
46C2×C42×C43D411yescharacteristic
47#107×C43—41no—
48#106×C43—41no—
49#101×C43—21no—
50#101×C43D412yes—
51#95×C43—22no—
52C2×Q8×C43—41no—
53C2×Q8×C43—41no—
54C2×Q8×C43C2×D411yescharacteristic
55C2×Q8×C43#4111yescharacteristic
56C2×Q8×C43#4112yes—
57C22×C4×C43—21no—
58C22×C4×C43—21no—
59C22×C4×C43C2×D412yes—
60C22×C4×C43C2×D411yescharacteristic
61C22×Dic43—22no—
62C22×Dic43—22no—
63C2×Dic86—22no—
64C2×Dic86—22no—
65C2×Dic86—42no—
66C2×Dic86—42no—
67M16×C43—22no—
68M16×C43—41no—
69C2×C8×C43—41no—
70C4⋊C4×C43—21no—
71C4⋊C4×C43—21no—
72C4⋊C4×C43—22no—
73C4⋊C4×C43—22no—
74C4⋊C4×C43—41no—
75C22⋊C4×C43—41no—
76C42×C43—41no—
77C42×C43—42no—
78C42×C43—41no—
79C4⋊Dic43—24no—
80C4⋊Dic43—81no—
81C4⋊Dic43—81no—
82Dic43⋊C4—42no—
83Dic43⋊C4—42no—
84Dic43⋊C4—42no—
85Dic43⋊C4—42no—
86C4×Dic43—22no—
87C4×Dic43—22no—
88#10621877—42no—
89#10621877—42no—
90C2×C43⋊C8—42no—
91C23×C43#12011yescharacteristic
92Q8×C43—41no—
93Q8×C43—41no—
94Q8×C43—42no—
95C2×C4×C43—22no—
96C2×C4×C43—21no—
97C2×C4×C43—22no—
98C2×C4×C43—21no—
99C2×C4×C43—22no—
100C2×C4×C43—41no—
101C2×C4×C43—41no—
102C2×C4×C43—42no—
103C2×C4×C43—41no—
104C2×C4×C43—41no—
105C2×C4×C43—41no—
106C2×C4×C43#12111yescharacteristic
107C2×C4×C43#12112yes—
108C2×C4×C43#12312yes—
109C2×C4×C43#12411yescharacteristic
110C2×Dic43—24no—
111C2×Dic43—42no—
112C2×Dic43—42no—
113C2×Dic43—42no—
114C2×Dic43—42no—
115C2×Dic43—42no—
116Dic86—44no—
117Dic86—82no—
118C8×C43—42no—
119C43⋊C8—82no—
120#13428—431nomaximal, Sylow
121C22×C43—21no—
122C22×C43—21no—
123C22×C43#39411yescharacteristic
124C22×C43B(4,𝔽2)11yescharacteristic
125C22×C43#45811yescharacteristic
126C4×C43—22no—
127C4×C43—21no—
128C4×C43—22no—
129C4×C43—21no—
130C4×C43—42no—
131C4×C43—81no—
132C4×C43—81no—
133C4×C43—81no—
134Dic43—44no—
135Dic43—82no—
136#2734—431no—
137C2×#356—432no—
138#1886—432no—
139#1857D4311yescharacteristic
140#1394—431no—
141C2×C43—21no—
142C2×C43—21no—
143C2×C43#204411yescharacteristic
144C2×C43#220311yescharacteristic
145C2×C43#220511yescharacteristic
146C2×C4⋊Q8—432no—
147#519C2×D4311yescharacteristic
148#428—21no—
149#419—862no—
150C2×#101—432no—
151C2×#101C2×D4311yescharacteristic
152#398—861no—
153#395—862no—
154#391C2×D4311yescharacteristic
155#389—861no—
156#387—862no—
157#356—864no—
158#339—21no—
159#339—862no—
160C43#1342811yescharacteristic, complemented, Sylow
161C22×Q8—432no—
162C22×Q8C22×D4311yescharacteristic
163C2×M16—21no—
164C2×M16—862no—
165C4⋊Q8—862no—
166C4⋊Q8—862no—
167C4⋊Q8—862no—
168C4⋊Q8—862no—
169C4×Q8—41no—
170C4×Q8—41no—
171#117—22no—
172#117—21no—
173C2×C4⋊C4—861no—
174C2×C4⋊C4—861no—
175C2×C4⋊C4—861no—
176C2×C4⋊C4—862no—
177C2×C4⋊C4—862no—
178C2×C4⋊C4C22⋊D4311yescharacteristic
179C2×C42—432no—
180C2×C42C22⋊D4311yescharacteristic
181#107—41no—
182#106—41no—
183#103—1722no—
184#103—1722no—
185#101—21no—
186#101—862no—
187#101—862no—
188#101D17212yes—
189#95—22no—
190#95—861no—
191#95—862no—
192#95—862no—
193C2×Q8—41no—
194C2×Q8—41no—
195C2×Q8—862no—
196C2×Q8—862no—
197C2×Q8—1722no—
198C2×Q8—1722no—
199C2×Q8C2×D17211yescharacteristic
200C2×Q8#1062189811yescharacteristic
201C2×Q8#1062190212yes—
202C22×C4—21no—
203C22×C4—21no—
204C22×C4—862no—
205C22×C4—862no—
206C22×C4D4×D4312yes—
207C22×C4C2×C22⋊D4311yescharacteristic
208M16—22no—
209M16—41no—
210M16—1722no—
211M16—1722no—
212C2×C8—41no—
213C2×C8—1722no—
214C4⋊C4—22no—
215C4⋊C4—22no—
216C4⋊C4—21no—
217C4⋊C4—21no—
218C4⋊C4—41no—
219C4⋊C4—864no—
220C4⋊C4—3441no—
221C4⋊C4—3441no—
222C4⋊C4—1722no—
223C4⋊C4—1722no—
224C4⋊C4—1722no—
225C4⋊C4—1722no—
226C22⋊C4—41no—
227C42—41no—
228C42—41no—
229C42—42no—
230C42—862no—
231C42—862no—
232C23#1306329311yescharacteristic
233Q8—41no—
234Q8—41no—
235Q8—42no—
236Q8—3442no—
237Q8—1724no—
238C2×C4—21no—
239C2×C4—22no—
240C2×C4—21no—
241C2×C4—22no—
242C2×C4—22no—
243C2×C4—41no—
244C2×C4—41no—
245C2×C4—42no—
246C2×C4—41no—
247C2×C4—41no—
248C2×C4—41no—
249C2×C4—864no—
250C2×C4—1722no—
251C2×C4—1722no—
252C2×C4—1722no—
253C2×C4—1722no—
254C2×C4—1722no—
255C2×C4#1306329911yescharacteristic
256C2×C4#1306330012yes—
257C2×C4#1306331012yes—
258C2×C4#1306331411yescharacteristic
259C8—42no—
260C8—3442no—
261C22—21no—
262C22—21no—
263C22#1458281611yescharacteristic
264C22#1458308511yescharacteristic
265C22#1458308811yescharacteristic
266C4—21no—
267C4—22no—
268C4—22no—
269C4—21no—
270C4—42no—
271C4—81no—
272C4—81no—
273C4—81no—
274C4—3442no—
275C4—1724no—
276C2—21no—
277C2—21no—
278C2#1913584611yescharacteristic
279C2#1913661511yescharacteristic
280C2#1913662411yescharacteristic
subgroupG/H
centerC22#14583085
commutator, cosocleC22×Q8×C43C23
FrattiniC22×Q8C22×D43
FittingC43×#1857C2
socleC22×C43B(4,𝔽2)
prime radicalC23×C43#120
hypercenter#1857D43
hypocenterC43#13428
LCSG ▷ C22×Q8×C43 ▷ C22×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23 ◁ C22×Q8 ◁ #1857

Complements

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

NH ≅ G/Ntype
160. C43#13428semidirect

Maximal subgroups

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

subgroupindex
#191416272
C2×#145826972
#191349882
#191327222
C43×#18572
#1342843