Finite Group Databasebeta

← #24989196

Subgroups — #24989196

Order 11008.

718 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 718 conjugacy classes of subgroups — too many to draw. Only its 107 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#19148293C211yesmaximal, characteristic
2#19134678C211yesmaximal, characteristic, complemented
3#19132941C214yesmaximal, complemented
4C43×#1818C211yesmaximal, characteristic, complemented
5#14583582—24no—
6#14583573—24no—
7#14583525C411yescharacteristic
8#14583496—22no—
9#14583461C411yescharacteristic
10#14583433—22no—
11C2×#13063308C2212yes—
12#14583372C412yes—
13#14582863C2212yes—
14#14582668—22no—
15#14582624—24no—
16#14582622—24no—
17C2×#117×C43C2211yescharacteristic
18C2×C22⋊C8×C43C2212yes—
19C43×#336—22no—
20C22×C22⋊D43C2×C412yes—
21C2×#10621877—22no—
22#13063320—24no—
23#13063319—24no—
24#13063317—22no—
25#13063315—24no—
26#13063313—22no—
27#13063310—24no—
28#13063309—22no—
29#13063308—24no—
30#13063308—22no—
31#13063308—22no—
32#13063304—22no—
33#13063303—24no—
34#13063302—24no—
35#13063299—22no—
36#13063295—22no—
37C4×Dic86—22no—
38C4×D172—22no—
39C4×C22⋊D43—24no—
40(C22⋊D43)⋊C4—24no—
41#13063282—24no—
42#13063281—22no—
43C2×Dic43⋊C4D414yes—
44C2×C22⋊Dic43C2×C412yes—
45C2×(C2×D43)⋊C4D414yes—
46C22⋊C4×D43—22no—
47C22⋊(C43⋊C8)—24no—
48C23×C4×C43C2311yescharacteristic
49C22×C8×C43—22no—
50#117×C43—24no—
51C2×C4⋊C4×C43D412yes—
52C2×C22⋊C4×C43C2×C411yescharacteristic
53C2×C22⋊C4×C43C2×C411yescharacteristic
54C2×C42×C43D412yes—
55C22⋊C8×C43—24no—
56C24×C43C22×C411yescharacteristic
57C23×D43C22⋊C412yes—
58C22×C4×C43—42no—
59C22×C4×C43C22⋊C412yes—
60C22×C4×C43C22⋊C412yes—
61C22×C4×C43C2×D411yescharacteristic
62C22×C4×C43C2×D414yes—
63C22×C4×C43C2×D411yescharacteristic
64C2×C22⋊D43—22no—
65C2×C22⋊D43—22no—
66C2×C22⋊D43—44no—
67C22×Dic43C22⋊C414yes—
68C22×Dic43C22⋊C412yes—
69C2×D172—22no—
70C2×C4×D43—24no—
71C2×Dic86—22no—
72C2×C8×C43—44no—
73C2×C8×C43—42no—
74C4⋊C4×C43—24no—
75C22⋊C4×C43—22no—
76C22⋊C4×C43—22no—
77C42×C43—22no—
78C42×C43—22no—
79C22⋊Dic43—22no—
80C22⋊Dic43—22no—
81(C2×D43)⋊C4—24no—
82(C2×D43)⋊C4—24no—
83(C2×D43)⋊C4—24no—
84(C2×D43)⋊C4—24no—
85C4⋊Dic43—22no—
86C4⋊Dic43—22no—
87Dic43⋊C4—24no—
88Dic43⋊C4—24no—
89Dic43⋊C4—24no—
90Dic43⋊C4—24no—
91C4×Dic43—24no—
92#10621877—44no—
93C2×C43⋊C8—42no—
94C23×C43—22no—
95C23×C43—42no—
96C23×C43C2×C22⋊C412yes—
97C23×C43C2×C22⋊C411yescharacteristic
98C22×D43—22no—
99C22×D43—42no—
100C22×D43—44no—
101C2×C4×C43—22no—
102C2×C4×C43—22no—
103C2×C4×C43—22no—
104C2×C4×C43—22no—
105C2×C4×C43—44no—
106C2×C4×C43—42no—
107C2×C4×C43—42no—
108C2×C4×C43#12012yes—
109C2×C4×C43#12012yes—
110C22⋊D43—44no—
111C22⋊D43—44no—
112C2×Dic43—22no—
113C2×Dic43—24no—
114C2×Dic43—44no—
115C2×Dic43—42no—
116D172—82no—
117C4×D43—84no—
118Dic86—82no—
119C8×C43—82no—
120C43⋊C8—82no—
121#8540—431nomaximal, Sylow
122C22×C43—22no—
123C22×C43—22no—
124C22×C43—24no—
125C22×C43—82no—
126C22×C43#37911yescharacteristic
127C22×C43#41012yes—
128C2×D43—42no—
129C2×D43—44no—
130C2×D43—162no—
131C4×C43—22no—
132C4×C43—22no—
133C4×C43—42no—
134C4×C43—42no—
135Dic43—42no—
136Dic43—44no—
137#3491—431no—
138#1822—431no—
139#1818D4311yescharacteristic, complemented
140#1468—434no—
141C2×C43—22no—
142C2×C43—42no—
143C2×C43#178211yescharacteristic
144C2×C43#179112yes—
145D43—82no—
146#552—864no—
147#551—864no—
148#543—431no—
149#539—862no—
150#534—431no—
151#529—862no—
152C2×#123—432no—
153#518—432no—
154C2×#117C2×D4311yescharacteristic
155#407—432no—
156C2×C22⋊C8C2×D4312yes—
157#343—862no—
158#336—22no—
159#324—864no—
160#323—864no—
161C43#854011yescharacteristic, complemented, Sylow
162C22×D4—432no—
163C23×C4C22×D4311yescharacteristic
164C2×M16—862no—
165C22×C8—22no—
166#126—864no—
167#126—864no—
168#125—862no—
169#125—864no—
170#124—862no—
171#123—862no—
172#123—864no—
173#123—862no—
174#123—864no—
175#123—862no—
176C22⋊Q8—864no—
177C22⋊Q8—864no—
178C22⋊Q8—862no—
179#121—862no—
180#120—862no—
181C4×Q8—862no—
182C4×D4—862no—
183C4×D4—864no—
184C4×D4—864no—
185#117—24no—
186#117—864no—
187#117—862no—
188C2×C4⋊C4—434no—
189C2×C4⋊C4D17212yes—
190C2×C22⋊C4—432no—
191C2×C22⋊C4—434no—
192C2×C22⋊C4—862no—
193C2×C22⋊C4C4×D4311yescharacteristic
194C2×C22⋊C4C4×D4311yescharacteristic
195C2×C42C22⋊D4312yes—
196C22⋊C8—24no—
197C22⋊C8—864no—
198C24—432no—
199C24C2×C4×D4311yescharacteristic
200C2×Q8—862no—
201C2×D4—862no—
202C2×D4—862no—
203C2×D4—862no—
204C2×D4—1724no—
205C22×C4—42no—
206C22×C4—434no—
207C22×C4—432no—
208C22×C4—864no—
209C22×C4(C2×D43)⋊C412yes—
210C22×C4(C2×D43)⋊C412yes—
211C22×C4C2×D17211yescharacteristic
212C22×C4D4×D4314yes—
213C22×C4C2×C22⋊D4311yescharacteristic
214M16—1724no—
215C2×C8—44no—
216C2×C8—42no—
217C2×C8—1722no—
218C4⋊C4—24no—
219C4⋊C4—864no—
220C4⋊C4—864no—
221C4⋊C4—862no—
222C4⋊C4—862no—
223C4⋊C4—864no—
224C4⋊C4—864no—
225C22⋊C4—22no—
226C22⋊C4—22no—
227C22⋊C4—864no—
228C22⋊C4—864no—
229C22⋊C4—862no—
230C22⋊C4—862no—
231C22⋊C4—864no—
232C22⋊C4—864no—
233C42—22no—
234C42—22no—
235C42—864no—
236C23—22no—
237C23—42no—
238C23—862no—
239C23—1722no—
240C23—1724no—
241C23C22⋊C4×D4312yes—
242C23C2×(C2×D43)⋊C411yescharacteristic
243Q8—3442no—
244D4—3442no—
245D4—1724no—
246D4—1724no—
247C2×C4—22no—
248C2×C4—22no—
249C2×C4—22no—
250C2×C4—22no—
251C2×C4—44no—
252C2×C4—42no—
253C2×C4—42no—
254C2×C4—862no—
255C2×C4—864no—
256C2×C4—3444no—
257C2×C4—1722no—
258C2×C4—1724no—
259C2×C4#1306329312yes—
260C2×C4#1306329512yes—
261C8—82no—
262C8—3442no—
263C22—22no—
264C22—22no—
265C22—24no—
266C22—82no—
267C22—1722no—
268C22—1724no—
269C22—6882no—
270C22#1458275411yescharacteristic
271C22#1458287212yes—
272C4—22no—
273C4—22no—
274C4—42no—
275C4—42no—
276C4—1722no—
277C4—1724no—
278C2—22no—
279C2—42no—
280C2—3442no—
281C2#1913451211yescharacteristic
282C2#1913454512yes—
subgroupG/H
centerC22#14582754
commutatorC24×C43C22×C4
FrattiniC23×C4C22×D43
FittingC43×#1818C2
socleC22×C43#379
prime radical#14583461C4
cosocleC23×C4×C43C23
hypercenter#1818D43
hypocenterC43#8540
LCSG ▷ C24×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1818

Complements

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

NH ≅ G/Ntype
2. #19134678C2semidirect
3. #19132941C2semidirect
4. C43×#1818C2semidirect
139. #1818D43semidirect
161. C43#8540semidirect

Maximal subgroups

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

subgroupindex
#191482932
#191346782
#191329412
C43×#18182
#854043