Finite Group Databasebeta

← #24997529

Subgroups — #24997529

Order 11008.

564 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 564 conjugacy classes of subgroups — too many to draw. Only its 83 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#19145905C211yesmaximal, characteristic, complemented
2#19144686C212yesmaximal, complemented
3#19133205C212yesmaximal, complemented
4#19132465C211yesmaximal, characteristic, complemented
5C43×#1955C211yesmaximal, characteristic, complemented
6#14583449C2212yes—
7#14583217—22no—
8#14583189—22no—
9#14583180—22no—
10#14583135—22no—
11#14583095—22no—
12#14583094—22no—
13#14583033—22no—
14#14583009—24no—
15#14582956C2212yes—
16#14582638—24no—
17C2×C4×D4×C43C2211yescharacteristic
18C2×C4⋊C8×C43C2211yescharacteristic
19C2×C22⋊C8×C43—22no—
20C2×#97×C43C2211yescharacteristic
21C2×#10621898—22no—
22C2×D344—22no—
23C2×#10621882—24no—
24#13063325D412yes—
25#13063322D412yes—
26#13063313—22no—
27#13063299—22no—
28#13063299—22no—
29C4×D172—22no—
30C4×D172—22no—
31#13063259—22no—
32#13063256—24no—
33C4⋊(C43⋊C8)—22no—
34#13063247—24no—
35#13063246—24no—
36#13063245—24no—
37C22⋊(C43⋊C8)—22no—
38#13063236D414yes—
39C22×D4×C43D411yescharacteristic
40C23×C4×C43—21no—
41C22×C8×C43—21no—
42C22×C8×C43D412yes—
43C4×D4×C43—22no—
44C4×D4×C43—22no—
45C2×C4⋊C4×C43D411yescharacteristic
46C2×C22⋊C4×C43—21no—
47C2×C42×C43C2311yescharacteristic
48C4⋊C8×C43—22no—
49C22⋊C8×C43—44no—
50#97×C43—22no—
51C24×C43—21no—
52C2×D4×C43—22no—
53C2×D4×C43—42no—
54C22×C4×C43—21no—
55C22×C4×C43—42no—
56C22×C4×C43—42no—
57C22×C4×C43—41no—
58C22×C4×C43—41no—
59C22×C4×C43C2×D411yescharacteristic
60C22×C4×C43C2×D411yescharacteristic
61C22×C4×C43#4111yescharacteristic
62C2×C22⋊D43—42no—
63#10621898—84no—
64C2×D172—22no—
65C2×D172—22no—
66C2×D172—22no—
67C2×C4×D43—42no—
68C2×Dic86—22no—
69C2×C8×C43—22no—
70C2×C8×C43—22no—
71C2×C8×C43—41no—
72C2×C8×C43—41no—
73C2×C8×C43—42no—
74C4⋊C4×C43—22no—
75C22⋊C4×C43—42no—
76C42×C43C2×D412yes—
77C42×C43C2×D412yes—
78#10621882—48no—
79(C2×D43)⋊C4—42no—
80(C2×D43)⋊C4—42no—
81C4⋊Dic43—22no—
82C4⋊Dic43—22no—
83C2×C43⋊C8—24no—
84D344—82no—
85C23×C43—22no—
86C23×C43—42no—
87C23×C43—41no—
88C23×C43—41no—
89C23×C43—42no—
90C23×C43#12111yescharacteristic
91C22×D43—42no—
92D4×C43—24no—
93D4×C43—42no—
94C2×C4×C43—22no—
95C2×C4×C43—21no—
96C2×C4×C43—21no—
97C2×C4×C43—41no—
98C2×C4×C43—42no—
99C2×C4×C43—41no—
100C2×C4×C43—82no—
101C2×C4×C43—81no—
102C2×C4×C43—81no—
103C2×C4×C43#12011yescharacteristic
104C2×C4×C43#12012yes—
105C2×C4×C43#12112yes—
106C2×C4×C43#12711yescharacteristic
107C22⋊D43—84no—
108C2×Dic43—42no—
109D172—44no—
110D172—42no—
111D172—42no—
112D172—82no—
113C4×D43—84no—
114Dic86—82no—
115C8×C43—42no—
116C8×C43—42no—
117C43⋊C8—44no—
118#10026—431nomaximal, Sylow
119C22×C43—21no—
120C22×C43—21no—
121C22×C43—44no—
122C22×C43—42no—
123C22×C43—82no—
124C22×C43—81no—
125C22×C43—81no—
126C22×C43#39211yescharacteristic
127C22×C43#47212yes—
128C2×D43—82no—
129C2×D43—82no—
130C2×D43—82no—
131C4×C43—21no—
132C4×C43—22no—
133C4×C43—22no—
134C4×C43—81no—
135C4×C43#45311yescharacteristic
136C4×C43#45411yescharacteristic
137Dic43—82no—
138#3245—431no—
139#3109—432no—
140#1955D4311yescharacteristic, complemented
141#1530—432no—
142#1290—431no—
143C2×C43—22no—
144C2×C43—82no—
145C2×C43#200611yescharacteristic
146C2×C43#201011yescharacteristic
147C2×C43#201811yescharacteristic
148D43—162no—
149#532—432no—
150C2×C4×D4C2×D4311yescharacteristic
151#481—862no—
152#476—862no—
153#474—862no—
154#466—862no—
155#459—862no—
156#459—862no—
157#447—862no—
158#442—864no—
159#432—432no—
160C2×C4⋊C8C2×D4311yescharacteristic
161C2×C22⋊C8—22no—
162C2×#97C2×D4311yescharacteristic
163#329—864no—
164C43#1002611yescharacteristic, complemented, Sylow
165C2×#41—862no—
166C22×D4D17211yescharacteristic
167C23×C4—21no—
168C2×D8—862no—
169C2×D8—864no—
170C22×C8—21no—
171C22×C8C22⋊D4312yes—
172C4⋊Q8—432no—
173#127—432no—
174#124—862no—
175#121—862no—
176#121—862no—
177C4×D4—22no—
178C4×D4—22no—
179C4×D4—862no—
180C4×D4—862no—
181C2×C4⋊C4D17211yescharacteristic
182C2×C22⋊C4—21no—
183C2×C42C22×D4311yescharacteristic
184#107—862no—
185#106—864no—
186C4⋊C8—22no—
187C4⋊C8—862no—
188#102—864no—
189#102—864no—
190#102—864no—
191C22⋊C8—44no—
192C22⋊C8—862no—
193#97—22no—
194#97—434no—
195C24—21no—
196#41—3444no—
197C2×Q8—862no—
198C2×D4—22no—
199C2×D4—42no—
200C2×D4—862no—
201C2×D4—862no—
202C2×D4—862no—
203C2×D4—1722no—
204C22×C4—21no—
205C22×C4—42no—
206C22×C4—42no—
207C22×C4—41no—
208C22×C4—41no—
209C22×C4—1722no—
210C22×C4C2×D17211yescharacteristic
211C22×C4#1062189811yescharacteristic
212C22×C4C2×C22⋊D4311yescharacteristic
213D8—3442no—
214D8—1728no—
215C2×C8—22no—
216C2×C8—22no—
217C2×C8—41no—
218C2×C8—41no—
219C2×C8—42no—
220C2×C8—864no—
221C4⋊C4—22no—
222C4⋊C4—862no—
223C4⋊C4—862no—
224C22⋊C4—42no—
225C22⋊C4—1722no—
226C22⋊C4—1722no—
227C42D4×D4312yes—
228C42D4×D4312yes—
229C23—22no—
230C23—42no—
231C23—41no—
232C23—41no—
233C23—42no—
234C23—1722no—
235C23#1306329911yescharacteristic
236Q8—3442no—
237D4—24no—
238D4—42no—
239D4—3442no—
240D4—3444no—
241D4—1724no—
242D4—1722no—
243D4—1722no—
244C2×C4—22no—
245C2×C4—21no—
246C2×C4—21no—
247C2×C4—41no—
248C2×C4—42no—
249C2×C4—41no—
250C2×C4—82no—
251C2×C4—81no—
252C2×C4—81no—
253C2×C4—3444no—
254C2×C4—1722no—
255C2×C4#1306329311yescharacteristic
256C2×C4#1306329512yes—
257C2×C4#1306329812yes—
258C2×C4#1306332111yescharacteristic
259C8—42no—
260C8—42no—
261C8—1724no—
262C22—21no—
263C22—21no—
264C22—44no—
265C22—42no—
266C22—82no—
267C22—81no—
268C22—81no—
269C22—3442no—
270C22—3442no—
271C22—3442no—
272C22#1458280811yescharacteristic
273C22#1458316912yes—
274C4—21no—
275C4—22no—
276C4—22no—
277C4—81no—
278C4—3442no—
279C4#1458306611yescharacteristic
280C4#1458307111yescharacteristic
281C2—22no—
282C2—82no—
283C2—6882no—
284C2#1913563611yescharacteristic
285C2#1913566211yescharacteristic
286C2#1913570411yescharacteristic
subgroupG/H
centerC22#14582808
commutator, cosocleC2×C42×C43C23
FrattiniC2×C42C22×D43
FittingC43×#1955C2
socleC22×C43#392
hypercenter#1955D43
hypocenterC43#10026
LCSG ▷ C2×C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1955

Complements

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

NH ≅ G/Ntype
1. #19145905C2semidirect
2. #19144686C2semidirect
3. #19133205C2semidirect
4. #19132465C2semidirect
5. C43×#1955C2semidirect
140. #1955D43semidirect
164. C43#10026semidirect

Maximal subgroups

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

subgroupindex
#191459052
#191446862
#191332052
#191324652
C43×#19552
#1002643