Finite Group Databasebeta

← #24997437

Subgroups — #24997437

Order 11008.

734 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 734 conjugacy classes of subgroups — too many to draw. Only its 103 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#19144591C212yesmaximal, complemented
2#19137876C211yesmaximal, characteristic, complemented
3#19133019C212yesmaximal, complemented
4#19132424C211yesmaximal, characteristic, complemented
5C43×#1963C211yesmaximal, characteristic, complemented
6C2×C4×D172—22no—
7C2×C4×D172C2212yes—
8#14583210—22no—
9#14583176—22no—
10#14583091—22no—
11#14583032—22no—
12C4×#10621882—24no—
13#14582952C2212yes—
14#14582836—22no—
15#14582809—22no—
16#14582626—24no—
17C43×#532C2211yescharacteristic
18C43×#423C2211yescharacteristic
19C2×#104×C43—22no—
20C43×#376C2211yescharacteristic
21C22×D172—22no—
22C22×D172D412yes—
23C22×C4×D43—22no—
24C2×#10621882—24no—
25C4×D172—22no—
26C4×D172—22no—
27C4×D172—22no—
28C4×D172—22no—
29C4×D172—44no—
30C4×D172—44no—
31C2×C4⋊Dic43—22no—
32C2×C4⋊Dic43D412yes—
33C2×(C2×D43)⋊C4—24no—
34C2×(C2×D43)⋊C4—22no—
35#13063258—24no—
36C4⋊(C43⋊C8)—22no—
37#13063246—24no—
38#13063245—24no—
39C22⋊(C43⋊C8)—22no—
40C4×C43⋊C8D414yescomplemented
41C2×#41×C43—21no—
42C2×M16×C43—21no—
43C4⋊Q8×C43D411yescharacteristic, complemented
44#127×C43D411yescharacteristic, complemented
45#124×C43—21no—
46#121×C43—22no—
47C4×D4×C43—22no—
48C2×C42×C43D412yes—
49C2×C42×C43C2311yescharacteristic
50C4⋊C8×C43—22no—
51#104×C43—44no—
52#95×C43—22no—
53C23×D43—22no—
54#41×C43—42no—
55#41×C43—42no—
56C2×Q8×C43—21no—
57C2×D4×C43—22no—
58C2×D4×C43—21no—
59C2×D4×C43—41no—
60C22×C4×C43—22no—
61C22×C4×C43—41no—
62C22×C4×C43C2×D412yes—
63C22×C4×C43C2×D411yescharacteristic
64C22×Dic43—22no—
65C2×D172—22no—
66C2×D172—22no—
67C2×D172—44no—
68C2×D172—48no—
69C2×D172—44no—
70C2×C4×D43—42no—
71C2×C4×D43—42no—
72C2×C4×D43—44no—
73C2×C4×D43—44no—
74M16×C43—42no—
75C2×C8×C43—41no—
76C4⋊C4×C43—22no—
77C22⋊C4×C43—42no—
78C42×C43—22no—
79C42×C43D814yescomplemented
80C42×C43C2×D411yescharacteristic
81C42×C43C2×D412yes—
82C42×C43#4111yescharacteristic
83#10621882—48no—
84(C2×D43)⋊C4—48no—
85(C2×D43)⋊C4—42no—
86(C2×D43)⋊C4—42no—
87C4⋊Dic43—22no—
88C4⋊Dic43—22no—
89C4⋊Dic43—44no—
90C2×C43⋊C8—24no—
91C23×C43—41no—
92C23×C43#12011yescharacteristic
93C22×D43—24no—
94C22×D43—44no—
95C22×D43—42no—
96C22×D43—42no—
97C22×D43—44no—
98Q8×C43—42no—
99D4×C43—44no—
100D4×C43—42no—
101D4×C43—82no—
102C2×C4×C43—24no—
103C2×C4×C43—42no—
104C2×C4×C43—44no—
105C2×C4×C43—41no—
106C2×C4×C43—81no—
107C2×C4×C43—81no—
108C2×C4×C43#12012yes—
109C2×C4×C43#12112yes—
110C2×C4×C43#12111yescharacteristic
111C2×C4×C43#12711yescharacteristic
112C2×C4×C43C2×D812yes—
113C2×C4×C43AGL(1,ℤ/8)12yes—
114C2×Dic43—42no—
115C2×Dic43—44no—
116D172—24no—
117D172—24no—
118D172—42no—
119D172—42no—
120D172—416no—
121C4×D43—84no—
122C4×D43—82no—
123C4×D43—82no—
124C8×C43—81no—
125C43⋊C8—44no—
126#10012—431nomaximal, Sylow
127C22×C43—22no—
128C22×C43—82no—
129C22×C43—81no—
130C22×C43#39211yescharacteristic
131C22×C43#44712yes—
132C2×D43—48no—
133C2×D43—44no—
134C2×D43—84no—
135C2×D43—82no—
136C2×D43—82no—
137C4×C43—22no—
138C4×C43—22no—
139C4×C43—44no—
140C4×C43—81no—
141C4×C43#45912yes—
142C4×C43#49311yescharacteristic
143C4×C43#49611yescharacteristic
144Dic43—82no—
145#3100—432no—
146#2397—431no—
147#1963D4311yescharacteristic, complemented
148#1486—432no—
149#1274—431no—
150C2×C43—22no—
151C2×C43—161no—
152C2×C43#201012yes—
153C2×C43#201111yescharacteristic
154D43—84no—
155#532C2×D4311yescharacteristic
156C2×C4×D4—432no—
157C2×C4×D4—862no—
158#480—862no—
159#474—862no—
160#459—862no—
161#447—862no—
162C4×D8—864no—
163#431—432no—
164#423C2×D4311yescharacteristic
165C2×#104—22no—
166#399—862no—
167#392—862no—
168#376C2×D4311yescharacteristic
169D4⋊C8—864no—
170C43#1001211yescharacteristic, complemented, Sylow
171C2×#41—21no—
172C22×D4—432no—
173C22×D4—862no—
174C23×C4—862no—
175C2×D8—864no—
176C2×M16—21no—
177C4⋊Q8D17211yescharacteristic, complemented
178#127D17211yescharacteristic, complemented
179#124—21no—
180#121—22no—
181C4×D4—22no—
182C4×D4—862no—
183C4×D4—862no—
184C4×D4—862no—
185C4×D4—862no—
186C4×D4—1724no—
187C4×D4—1724no—
188C2×C4⋊C4—432no—
189C2×C4⋊C4—862no—
190C2×C22⋊C4—864no—
191C2×C22⋊C4—862no—
192C2×C42C22⋊D4312yes—
193C2×C42C22×D4311yescharacteristic
194#107—864no—
195C4⋊C8—22no—
196C4⋊C8—862no—
197#104—44no—
198#102—864no—
199#102—864no—
200C22⋊C8—862no—
201C4×C8—434no—
202#95—22no—
203C24—862no—
204#41—42no—
205#41—42no—
206C2×Q8—21no—
207C2×D4—22no—
208C2×D4—21no—
209C2×D4—41no—
210C2×D4—862no—
211C2×D4—862no—
212C2×D4—1724no—
213C2×D4—1724no—
214C2×D4—1728no—
215C22×C4—22no—
216C22×C4—41no—
217C22×C4—862no—
218C22×C4—1722no—
219C22×C4—1722no—
220C22×C4—1724no—
221C22×C4—1724no—
222C22×C4D4×D4312yes—
223C22×C4C2×C22⋊D4311yescharacteristic
224D8—1728no—
225M16—42no—
226C2×C8—41no—
227C2×C8—864no—
228C4⋊C4—22no—
229C4⋊C4—862no—
230C4⋊C4—862no—
231C4⋊C4—1724no—
232C22⋊C4—42no—
233C22⋊C4—1728no—
234C22⋊C4—1722no—
235C22⋊C4—1722no—
236C42—22no—
237C42#1062188214yescomplemented
238C42C2×D17211yescharacteristic
239C42#1062189811yescharacteristic
240C42D4×D4312yes—
241C23—41no—
242C23—864no—
243C23—1722no—
244C23—1724no—
245C23—1722no—
246C23—1724no—
247C23#1306329311yescharacteristic
248Q8—42no—
249D4—44no—
250D4—42no—
251D4—82no—
252D4—864no—
253D4—864no—
254D4—1722no—
255D4—1722no—
256D4—17216no—
257C2×C4—24no—
258C2×C4—42no—
259C2×C4—44no—
260C2×C4—41no—
261C2×C4—81no—
262C2×C4—81no—
263C2×C4—3444no—
264C2×C4—3442no—
265C2×C4—3442no—
266C2×C4—1722no—
267C2×C4—1724no—
268C2×C4#1306329512yes—
269C2×C4#1306329812yes—
270C2×C4#1306329911yescharacteristic
271C2×C4#1306332111yescharacteristic
272C2×C4C2×#1062188212yes—
273C2×C4#1306335012yes—
274C8—81no—
275C8—1724no—
276C22—22no—
277C22—82no—
278C22—81no—
279C22—3444no—
280C22—3442no—
281C22—3442no—
282C22—1728no—
283C22—1724no—
284C22#1458280811yescharacteristic
285C22#1458303212yes—
286C4—22no—
287C4—22no—
288C4—44no—
289C4—81no—
290C4—3442no—
291C4#1458309412yes—
292C4#1458327511yescharacteristic
293C4#1458328911yescharacteristic
294C2—22no—
295C2—161no—
296C2—3444no—
297C2#1913566112yes—
298C2#1913566511yescharacteristic
subgroupG/H
centerC2×C4#13063321
commutator, cosocleC2×C42×C43C23
FrattiniC2×C42C22×D43
FittingC43×#1963C2
socleC22×C43#392
hypercenter#1963D43
hypocenterC43#10012
LCSG ▷ C2×C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1963

Complements

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

NH ≅ G/Ntype
1. #19144591C2semidirect
2. #19137876C2semidirect
3. #19133019C2semidirect
4. #19132424C2semidirect
5. C43×#1963C2semidirect
40. C4×C43⋊C8D4semidirect
43. C4⋊Q8×C43D4semidirect
44. #127×C43D4semidirect
79. C42×C43D8semidirect
147. #1963D43semidirect
170. C43#10012semidirect
177. C4⋊Q8D172semidirect
178. #127D172semidirect
237. C42#10621882semidirect

Maximal subgroups

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

subgroupindex
#191445912
#191378762
#191330192
#191324242
C43×#19632
#1001243