Finite Group Databasebeta

← #24997527

Subgroups — #24997527

Order 11008.

564 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 564 conjugacy classes of subgroups — too many to draw. Only its 85 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#19144682C212yesmaximal, complemented
2#19135392C211yesmaximal, characteristic, complemented
3#19133206C212yesmaximal, complemented
4#19132465C211yesmaximal, characteristic, complemented
5C43×#3245C211yesmaximal, characteristic, complemented
6C2×C4×D172C2211yescharacteristic
7#14583215—22no—
8#14583186—22no—
9#14583091—22no—
10#14583032—22no—
11#14583009—24no—
12#14582956C2212yes—
13C2×(C2×D43)⋊C8—22no—
14C2×#13063236C2211yescharacteristic
15#14582639—24no—
16C43×#532C2212yes—
17C43×#474—22no—
18C43×#466—22no—
19C43×#459—22no—
20C2×C4⋊C8×C43C2211yescharacteristic
21C22×D172D411yescharacteristic
22C22×C4×D43—21no—
23C2×#10621882—24no—
24C22×C43⋊C8—21no—
25C4×D172—22no—
26C4×D172—22no—
27C2×C4⋊Dic43D411yescharacteristic
28C2×(C2×D43)⋊C4—21no—
29#13063256—24no—
30C4⋊(C43⋊C8)—22no—
31#13063246—24no—
32#13063245—24no—
33C22⋊(C43⋊C8)—22no—
34(C2×D43)⋊C8—44no—
35#13063236—22no—
36#13063236D414yes—
37C2×#41×C43—22no—
38C2×D8×C43—22no—
39C22×C8×C43D412yes—
40C4⋊Q8×C43D412yes—
41#127×C43D412yes—
42#124×C43—22no—
43#121×C43—22no—
44#121×C43—22no—
45C4×D4×C43—22no—
46C4×D4×C43—22no—
47C2×C42×C43C2311yescharacteristic
48#107×C43—22no—
49C4⋊C8×C43—22no—
50#102×C43—24no—
51C23×D43—21no—
52#41×C43—84no—
53C2×Q8×C43—22no—
54C2×D4×C43—22no—
55C2×D4×C43—22no—
56C2×D4×C43—22no—
57C2×D4×C43—42no—
58C22×C4×C43—42no—
59C22×C4×C43C2×D411yescharacteristic
60C22×C4×C43C2×D411yescharacteristic
61C22×C4×C43#4111yescharacteristic
62C22×Dic43—21no—
63C2×D172—22no—
64C2×D172—42no—
65C2×C4×D43—42no—
66C2×C4×D43—42no—
67C2×C4×D43—41no—
68C2×C4×D43—41no—
69D8×C43—82no—
70C2×C8×C43—22no—
71C2×C8×C43—42no—
72C4⋊C4×C43—22no—
73C4⋊C4×C43—22no—
74C22⋊C4×C43—42no—
75C22⋊C4×C43—42no—
76C42×C43C2×D412yes—
77C42×C43C2×D412yes—
78#10621882—48no—
79(C2×D43)⋊C4—42no—
80C4⋊Dic43—22no—
81C2×C43⋊C8—22no—
82C2×C43⋊C8—24no—
83C2×C43⋊C8—41no—
84C2×C43⋊C8—41no—
85C23×C43—42no—
86C23×C43#12111yescharacteristic
87C22×D43—22no—
88C22×D43—42no—
89C22×D43—41no—
90C22×D43—41no—
91C22×D43—42no—
92Q8×C43—82no—
93D4×C43—44no—
94D4×C43—42no—
95D4×C43—42no—
96D4×C43—82no—
97D4×C43—84no—
98C2×C4×C43—22no—
99C2×C4×C43—21no—
100C2×C4×C43—21no—
101C2×C4×C43—41no—
102C2×C4×C43—42no—
103C2×C4×C43—84no—
104C2×C4×C43#12012yes—
105C2×C4×C43#12011yescharacteristic
106C2×C4×C43#12112yes—
107C2×C4×C43#12711yescharacteristic
108C2×Dic43—42no—
109C2×Dic43—41no—
110D172—24no—
111D172—42no—
112C4×D43—82no—
113C4×D43—81no—
114C4×D43—81no—
115C8×C43—42no—
116C43⋊C8—42no—
117C43⋊C8—44no—
118#10026—431nomaximal, Sylow
119C22×C43—21no—
120C22×C43—21no—
121C22×C43—82no—
122C22×C43—82no—
123C22×C43—82no—
124C22×C43#39211yescharacteristic
125C22×C43#47212yes—
126C2×D43—44no—
127C2×D43—42no—
128C2×D43—82no—
129C2×D43—81no—
130C2×D43—81no—
131C4×C43—21no—
132C4×C43—22no—
133C4×C43—22no—
134C4×C43—82no—
135C4×C43#45311yescharacteristic
136C4×C43#45411yescharacteristic
137Dic43—81no—
138#3245D4311yescharacteristic, complemented
139#3109—432no—
140#1955—431no—
141#1530—432no—
142#1290—431no—
143C2×C43—22no—
144C2×C43—162no—
145C2×C43#200611yescharacteristic
146C2×C43#201011yescharacteristic
147C2×C43#201811yescharacteristic
148D43—82no—
149#532C2×D4312yes—
150C2×C4×D4—431no—
151#481—862no—
152#476—862no—
153#474—22no—
154#466—22no—
155#459—22no—
156#459—862no—
157#447—862no—
158#442—864no—
159#432—432no—
160C2×C4⋊C8C2×D4311yescharacteristic
161C2×C22⋊C8—862no—
162C2×#97—431no—
163#329—864no—
164C43#1002611yescharacteristic, complemented, Sylow
165C2×#41—22no—
166C22×D4—431no—
167C23×C4—861no—
168C2×D8—22no—
169C2×D8—864no—
170C22×C8—861no—
171C22×C8C22⋊D4312yes—
172C4⋊Q8C22⋊D4312yes—
173#127C22⋊D4312yes—
174#124—22no—
175#121—22no—
176#121—22no—
177C4×D4—22no—
178C4×D4—22no—
179C4×D4—862no—
180C4×D4—862no—
181C2×C4⋊C4—431no—
182C2×C22⋊C4—861no—
183C2×C42C22×D4311yescharacteristic
184#107—22no—
185#106—864no—
186C4⋊C8—22no—
187C4⋊C8—862no—
188#102—24no—
189#102—864no—
190#102—864no—
191C22⋊C8—862no—
192C22⋊C8—1724no—
193#97—434no—
194#97—862no—
195C24—861no—
196#41—84no—
197C2×Q8—22no—
198C2×D4—22no—
199C2×D4—22no—
200C2×D4—22no—
201C2×D4—42no—
202C2×D4—862no—
203C2×D4—1722no—
204C22×C4—42no—
205C22×C4—861no—
206C22×C4—1722no—
207C22×C4—1722no—
208C22×C4—1721no—
209C22×C4—1721no—
210C22×C4D4×D4311yescharacteristic
211C22×C4#1062190011yescharacteristic
212C22×C4C2×C22⋊D4311yescharacteristic
213D8—82no—
214D8—1728no—
215C2×C8—22no—
216C2×C8—42no—
217C2×C8—862no—
218C2×C8—864no—
219C2×C8—1721no—
220C2×C8—1721no—
221C4⋊C4—22no—
222C4⋊C4—22no—
223C4⋊C4—862no—
224C22⋊C4—42no—
225C22⋊C4—42no—
226C22⋊C4—1722no—
227C42D4×D4312yes—
228C42C2×C22⋊D4312yes—
229C23—42no—
230C23—862no—
231C23—1722no—
232C23—1721no—
233C23—1721no—
234C23—1722no—
235C23#1306329611yescharacteristic
236Q8—82no—
237D4—44no—
238D4—42no—
239D4—42no—
240D4—82no—
241D4—84no—
242D4—864no—
243D4—1722no—
244C2×C4—22no—
245C2×C4—21no—
246C2×C4—21no—
247C2×C4—41no—
248C2×C4—42no—
249C2×C4—84no—
250C2×C4—3442no—
251C2×C4—3441no—
252C2×C4—3441no—
253C2×C4—1722no—
254C2×C4—1721no—
255C2×C4#1306329312yes—
256C2×C4#1306329411yescharacteristic
257C2×C4#1306329712yes—
258C2×C4#1306332111yescharacteristic
259C8—42no—
260C8—1722no—
261C8—1724no—
262C22—21no—
263C22—21no—
264C22—82no—
265C22—82no—
266C22—82no—
267C22—3442no—
268C22—3441no—
269C22—3441no—
270C22—1724no—
271C22—1722no—
272C22#1458280711yescharacteristic
273C22#1458316612yes—
274C4—21no—
275C4—22no—
276C4—22no—
277C4—82no—
278C4—3441no—
279C4#1458306711yescharacteristic
280C4#1458307211yescharacteristic
281C2—22no—
282C2—162no—
283C2—3442no—
284C2#1913563711yescharacteristic
285C2#1913565911yescharacteristic
286C2#1913570211yescharacteristic
subgroupG/H
centerC22#14582807
commutator, cosocleC2×C42×C43C23
FrattiniC2×C42C22×D43
FittingC43×#3245C2
socleC22×C43#392
hypercenter#3245D43
hypocenterC43#10026
LCSG ▷ C2×C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3245

Complements

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

NH ≅ G/Ntype
1. #19144682C2semidirect
2. #19135392C2semidirect
3. #19133206C2semidirect
4. #19132465C2semidirect
5. C43×#3245C2semidirect
138. #3245D43semidirect
164. C43#10026semidirect

Maximal subgroups

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

subgroupindex
#191446822
#191353922
#191332062
#191324652
C43×#32452
#1002643