Finite Group Databasebeta

← #24989132

Subgroups — #24989132

Order 11008.

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

normal subgroups only

This group has 784 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
1C2×#14583505C211yesmaximal, characteristic
2#19133308C212yesmaximal, complemented
3#19133222C211yesmaximal, characteristic, complemented
4#19132927C212yesmaximal, complemented
5C43×#1534C211yesmaximal, characteristic, complemented
6#14583505—24no—
7#14583505—22no—
8#14583505—22no—
9C2×#13063322C2211yescharacteristic
10C2×#13063310—22no—
11C2×#13063300—22no—
12C2×#13063300C412yes—
13C2×#13063287C412yes—
14C2×#13063282C2211yescharacteristic
15#14582956C2212yes—
16#14582642—24no—
17#14582641—22no—
18#14582624—22no—
19#14582622—22no—
20C2×#125×C43C2211yescharacteristic
21C43×#432C2212yes—
22C43×#330—22no—
23C22×D172—22no—
24C22×D172—22no—
25C22×D172C2×C412yes—
26C22×C4×D43—22no—
27C22×C4×D43C2×C411yescharacteristic
28#13063322—21no—
29#13063322—21no—
30#13063322D414yes—
31#13063310—28no—
32#13063310—28no—
33#13063300—28no—
34#13063300—28no—
35#13063300—24no—
36#13063300—24no—
37#13063287—24no—
38#13063287—24no—
39#13063282—21no—
40#13063282—22no—
41#13063282—21no—
42C2×Dic43⋊C4D412yes—
43C2×(C2×D43)⋊C4—22no—
44C2×(C2×D43)⋊C4—22no—
45C2×(C2×D43)⋊C4D412yes—
46C2×C4×Dic43C2×C411yescharacteristic
47C4⋊(C43⋊C8)—22no—
48C22⋊(C43⋊C8)—22no—
49#13063236—22no—
50#125×C43—22no—
51#125×C43D412yes—
52#125×C43D412yes—
53C2×C4⋊C4×C43—22no—
54C2×C4⋊C4×C43C2×C412yes—
55C2×C42×C43C2311yescharacteristic
56C4⋊C8×C43—22no—
57C22⋊C8×C43—22no—
58#97×C43—22no—
59C23×D43—22no—
60C23×D43C22⋊C411yescharacteristic
61C22×C4×C43—22no—
62C22×C4×C43C22×C411yescharacteristic
63C22×C4×C43C2×D412yes—
64C22×Dic43C22⋊C411yescharacteristic
65C22×Dic43C22⋊C412yes—
66C2×D172—22no—
67C2×D172—28no—
68C2×D172—24no—
69C2×D172—24no—
70C2×D172—44no—
71C2×D172—84no—
72C2×D172—84no—
73C2×D172C22⋊C414yes—
74C2×C4×D43—21no—
75C2×C4×D43—21no—
76C2×C4×D43—28no—
77C2×C4×D43—42no—
78C2×C4×D43—84no—
79C2×C8×C43—42no—
80C4⋊C4×C43—22no—
81C4⋊C4×C43—24no—
82C4⋊C4×C43—24no—
83C4⋊C4×C43C22⋊C414yes—
84C42×C43C2×D411yescharacteristic
85C42×C43C2×D412yes—
86C42×C43C2×D411yescharacteristic
87(C2×D43)⋊C4—28no—
88(C2×D43)⋊C4—28no—
89(C2×D43)⋊C4—22no—
90(C2×D43)⋊C4—22no—
91Dic43⋊C4—22no—
92Dic43⋊C4—22no—
93C4×Dic43—21no—
94C4×Dic43—21no—
95C2×C43⋊C8—42no—
96C23×C43C2×C22⋊C411yescharacteristic
97C22×D43—21no—
98C22×D43—24no—
99C22×D43—22no—
100C22×D43—44no—
101C22×D43—44no—
102C22×D43—44no—
103C22×D43—42no—
104C2×C4×C43—22no—
105C2×C4×C43—24no—
106C2×C4×C43—42no—
107C2×C4×C43—44no—
108C2×C4×C43C2×C22⋊C411yescharacteristic
109C2×C4×C43C2×C22⋊C411yescharacteristic
110C2×C4×C43#12012yes—
111C2×C4×C43#12012yes—
112C2×Dic43—22no—
113C2×Dic43—21no—
114C2×Dic43—22no—
115C2×Dic43—42no—
116D172—44no—
117D172—44no—
118D172—84no—
119D172—84no—
120D172—88no—
121C4×D43—42no—
122C4×D43—42no—
123C4×D43—88no—
124C8×C43—82no—
125C43⋊C8—82no—
126#8526—431nomaximal, Sylow
127C22×C43—22no—
128C22×C43#37911yescharacteristic
129C22×C43#41312yes—
130C2×D43—44no—
131C2×D43—44no—
132C2×D43—42no—
133C2×D43—41no—
134C2×D43—44no—
135C2×D43—88no—
136C2×D43—82no—
137C4×C43—22no—
138C4×C43—22no—
139C4×C43—21no—
140C4×C43—21no—
141C4×C43—44no—
142Dic43—42no—
143Dic43—41no—
144C2×#540—431no—
145#1555—432no—
146#1534—431no—
147#1534D4311yescharacteristic, complemented
148#1464—432no—
149C2×C43—22no—
150C2×C43#178511yescharacteristic
151C2×C43#179512yes—
152D43—81no—
153D43—84no—
154#540—864no—
155#540—862no—
156#540—862no—
157C2×#127—431no—
158C2×#125C2×D4311yescharacteristic
159C2×#123—862no—
160C2×#121—432no—
161C2×#121—862no—
162C2×C4×D4—432no—
163C2×#117—431no—
164#432—432no—
165#432C2×D4312yes—
166#331—864no—
167#330—22no—
168#330—862no—
169#324—862no—
170#323—862no—
171C43#852611yescharacteristic, complemented, Sylow
172C22×D4—432no—
173C22×D4—862no—
174C22×D4—862no—
175C23×C4—431no—
176C23×C4—862no—
177#127—434no—
178#127—861no—
179#127—861no—
180#125—22no—
181#125D17212yes—
182#125C22⋊D4312yes—
183#123—868no—
184#123—868no—
185#121—864no—
186#121—868no—
187#121—868no—
188#121—864no—
189C4×D4—864no—
190C4×D4—864no—
191#117—861no—
192#117—862no—
193#117—861no—
194C2×C4⋊C4—22no—
195C2×C4⋊C4—432no—
196C2×C4⋊C4C4×D4312yes—
197C2×C22⋊C4—432no—
198C2×C22⋊C4—862no—
199C2×C22⋊C4—862no—
200C2×C42—431no—
201C2×C42C22×D4311yescharacteristic
202C4⋊C8—22no—
203C4⋊C8—862no—
204C22⋊C8—22no—
205C22⋊C8—862no—
206#97—22no—
207#97—862no—
208C24—431no—
209C24—862no—
210C2×D4—434no—
211C2×D4—868no—
212C2×D4—862no—
213C2×D4—864no—
214C2×D4—864no—
215C2×D4—3444no—
216C2×D4—3444no—
217C2×D4—1724no—
218C22×C4—22no—
219C22×C4—431no—
220C22×C4—432no—
221C22×C4—868no—
222C22×C4—861no—
223C22×C4—861no—
224C22×C4—3444no—
225C22×C4—1722no—
226C22×C4C2×C4×D4311yescharacteristic
227C22×C4D4×D4312yes—
228C2×C8—42no—
229C2×C8—1722no—
230C4⋊C4—22no—
231C4⋊C4—24no—
232C4⋊C4—24no—
233C4⋊C4—862no—
234C4⋊C4—862no—
235C4⋊C4(C2×D43)⋊C414yes—
236C22⋊C4—868no—
237C22⋊C4—868no—
238C22⋊C4—862no—
239C22⋊C4—862no—
240C42—861no—
241C42—861no—
242C42C2×D17211yescharacteristic
243C42D4×D4312yes—
244C42C2×C22⋊D4311yescharacteristic
245C23—862no—
246C23—864no—
247C23—861no—
248C23—1722no—
249C23—1724no—
250C23—1724no—
251C23—1724no—
252C23C22⋊C4×D4311yescharacteristic
253D4—3444no—
254D4—3444no—
255D4—3448no—
256D4—1724no—
257D4—1724no—
258C2×C4—22no—
259C2×C4—24no—
260C2×C4—42no—
261C2×C4—44no—
262C2×C4—862no—
263C2×C4—862no—
264C2×C4—861no—
265C2×C4—3448no—
266C2×C4—1722no—
267C2×C4—1722no—
268C2×C4—1722no—
269C2×C4C22⋊C4×D4311yescharacteristic
270C2×C4C2×(C2×D43)⋊C411yescharacteristic
271C2×C4#1306329312yes—
272C2×C4#1306329512yes—
273C8—82no—
274C8—3442no—
275C22—22no—
276C22—3442no—
277C22—3448no—
278C22—1721no—
279C22—1724no—
280C22—1724no—
281C22—1724no—
282C22—1722no—
283C22#1458275411yescharacteristic
284C22#1458288212yes—
285C4—21no—
286C4—21no—
287C4—22no—
288C4—22no—
289C4—44no—
290C4—1721no—
291C4—1722no—
292C2—22no—
293C2—3444no—
294C2—3441no—
295C2#1913452211yescharacteristic
296C2#1913456412yes—
subgroupG/H
centerC22#14582754
commutatorC22×C4×C43C22×C4
FrattiniC2×C42C22×D43
FittingC43×#1534C2
socleC22×C43#379
prime radicalC2×#14583505C2
cosocleC2×C42×C43C23
hypercenter#1534D43
hypocenterC43#8526
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1534

Complements

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

NH ≅ G/Ntype
2. #19133308C2semidirect
3. #19133222C2semidirect
4. #19132927C2semidirect
5. C43×#1534C2semidirect
147. #1534D43semidirect
171. C43#8526semidirect

Maximal subgroups

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

subgroupindex
C2×#145835052
#191333082
#191332222
#191329272
C43×#15342
#852643