Finite Group Databasebeta

← #24997551

Subgroups — #24997551

Order 11008.

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

normal subgroups only

This group has 520 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#19144690C212yesmaximal
2#19135392C211yesmaximal, characteristic
3#19133210C212yesmaximal, complemented
4#19132465C211yesmaximal, characteristic, complemented
5C43×#3249C211yesmaximal, characteristic, complemented
6C2×C4×D172C2211yescharacteristic
7#14583232—22no—
8#14583176—22no—
9#14583101—22no—
10#14583049—22no—
11#14582997—24no—
12#14582956C2212yes—
13C2×(C2×D43)⋊C8—22no—
14C2×#13063236C2211yescharacteristic
15#14582641—24no—
16C43×#533C2212yes—
17C43×#477—22no—
18C43×#467—22no—
19C43×#462—22no—
20C2×C4⋊C8×C43C2211yescharacteristic
21C22×D172D411yescharacteristic
22C22×C4×D43—21no—
23C2×#10621884—24no—
24C22×C43⋊C8—21no—
25C4×D172—22no—
26C4×D172—22no—
27C2×C4⋊Dic43D411yescharacteristic
28C2×(C2×D43)⋊C4—21no—
29#13063258—24no—
30C4⋊(C43⋊C8)—22no—
31#13063249—24no—
32#13063245—24no—
33C22⋊(C43⋊C8)—22no—
34(C2×D43)⋊C8—44no—
35#13063236—22no—
36#13063236D414yes—
37C2×Q16×C43—22no—
38C22×C8×C43D412yes—
39C4⋊Q8×C43D412yes—
40C4⋊Q8×C43D412yes—
41#125×C43—22no—
42C22⋊Q8×C43—22no—
43C22⋊Q8×C43—22no—
44C4×Q8×C43—22no—
45C4×Q8×C43—22no—
46#117×C43—22no—
47C2×C42×C43C2311yescharacteristic
48#107×C43—22no—
49C4⋊C8×C43—22no—
50#103×C43—24no—
51C23×D43—21no—
52C2×Q8×C43—22no—
53C2×Q8×C43—22no—
54C22×C4×C43C2×D411yescharacteristic
55C22×C4×C43C2×D411yescharacteristic
56C22×C4×C43#4111yescharacteristic
57C22×Dic43—21no—
58C2×D172—22no—
59C2×D172—42no—
60C2×C4×D43—42no—
61C2×C4×D43—42no—
62C2×C4×D43—41no—
63C2×C4×D43—41no—
64Q16×C43—82no—
65C2×C8×C43—22no—
66C2×C8×C43—42no—
67C4⋊C4×C43—22no—
68C4⋊C4×C43—22no—
69C4⋊C4×C43—22no—
70C4⋊C4×C43—22no—
71C4⋊C4×C43—42no—
72C4⋊C4×C43—42no—
73C22⋊C4×C43—42no—
74C42×C43—42no—
75C42×C43C2×D412yes—
76C42×C43C2×D412yes—
77#10621884—48no—
78(C2×D43)⋊C4—42no—
79C4⋊Dic43—22no—
80C2×C43⋊C8—22no—
81C2×C43⋊C8—24no—
82C2×C43⋊C8—41no—
83C2×C43⋊C8—41no—
84C23×C43#12111yescharacteristic
85C22×D43—22no—
86C22×D43—42no—
87C22×D43—41no—
88C22×D43—41no—
89C22×D43—42no—
90Q8×C43—44no—
91Q8×C43—42no—
92Q8×C43—42no—
93C2×C4×C43—22no—
94C2×C4×C43—21no—
95C2×C4×C43—21no—
96C2×C4×C43—41no—
97C2×C4×C43—42no—
98C2×C4×C43—42no—
99C2×C4×C43#12012yes—
100C2×C4×C43#12011yescharacteristic
101C2×C4×C43#12112yes—
102C2×C4×C43#12711yescharacteristic
103C2×Dic43—42no—
104C2×Dic43—41no—
105D172—24no—
106D172—42no—
107C4×D43—82no—
108C4×D43—81no—
109C4×D43—81no—
110C8×C43—42no—
111C43⋊C8—42no—
112C43⋊C8—44no—
113#10030—431nomaximal, Sylow
114C22×C43—21no—
115C22×C43—21no—
116C22×C43#39211yescharacteristic
117C22×C43#47312yes—
118C2×D43—44no—
119C2×D43—42no—
120C2×D43—82no—
121C2×D43—81no—
122C2×D43—81no—
123C4×C43—21no—
124C4×C43—22no—
125C4×C43—22no—
126C4×C43—82no—
127C4×C43—82no—
128C4×C43#45311yescharacteristic
129C4×C43#45411yescharacteristic
130Dic43—81no—
131#3249D4311yescharacteristic, complemented
132#3110—432no—
133#1955—431no—
134#1531—432no—
135#1290—431no—
136C2×C43—22no—
137C2×C43#200611yescharacteristic
138C2×C43#201011yescharacteristic
139C2×C43#202011yescharacteristic
140D43—82no—
141#533C2×D4312yes—
142C2×C4×D4—431no—
143#484—862no—
144#477—22no—
145#474—862no—
146#467—22no—
147#462—22no—
148#461—862no—
149#450—862no—
150#440—864no—
151#432—432no—
152C2×C4⋊C8C2×D4311yescharacteristic
153C2×C22⋊C8—862no—
154C2×#97—431no—
155#330—864no—
156C43#1003011yescharacteristic, complemented, Sylow
157C22×D4—431no—
158C23×C4—861no—
159C2×Q16—22no—
160C2×SD16—864no—
161C22×C8—861no—
162C22×C8C22⋊D4312yes—
163C4⋊Q8C22⋊D4312yes—
164C4⋊Q8C22⋊D4312yes—
165#125—22no—
166C22⋊Q8—22no—
167C22⋊Q8—22no—
168C4×Q8—22no—
169C4×Q8—22no—
170C4×D4—862no—
171C4×D4—862no—
172#117—22no—
173C2×C4⋊C4—431no—
174C2×C22⋊C4—861no—
175C2×C42C22×D4311yescharacteristic
176#107—22no—
177#107—864no—
178C4⋊C8—22no—
179C4⋊C8—862no—
180#103—24no—
181#103—864no—
182#102—864no—
183C22⋊C8—862no—
184C22⋊C8—1724no—
185#97—434no—
186#97—862no—
187C24—861no—
188C2×Q8—22no—
189C2×Q8—22no—
190C2×D4—862no—
191C2×D4—1722no—
192C22×C4—861no—
193C22×C4—1722no—
194C22×C4—1722no—
195C22×C4—1721no—
196C22×C4—1721no—
197C22×C4D4×D4311yescharacteristic
198C22×C4#1062190011yescharacteristic
199C22×C4C2×C22⋊D4311yescharacteristic
200Q16—82no—
201SD16—1728no—
202C2×C8—22no—
203C2×C8—42no—
204C2×C8—862no—
205C2×C8—864no—
206C2×C8—1721no—
207C2×C8—1721no—
208C4⋊C4—22no—
209C4⋊C4—22no—
210C4⋊C4—22no—
211C4⋊C4—22no—
212C4⋊C4—42no—
213C4⋊C4—42no—
214C4⋊C4—862no—
215C22⋊C4—42no—
216C22⋊C4—1722no—
217C42—42no—
218C42D4×D4312yes—
219C42C2×C22⋊D4312yes—
220C23—862no—
221C23—1722no—
222C23—1721no—
223C23—1721no—
224C23—1722no—
225C23#1306329611yescharacteristic
226Q8—44no—
227Q8—42no—
228Q8—42no—
229D4—864no—
230D4—1722no—
231C2×C4—22no—
232C2×C4—21no—
233C2×C4—21no—
234C2×C4—41no—
235C2×C4—42no—
236C2×C4—42no—
237C2×C4—3442no—
238C2×C4—3441no—
239C2×C4—3441no—
240C2×C4—1722no—
241C2×C4—1721no—
242C2×C4#1306329312yes—
243C2×C4#1306329411yescharacteristic
244C2×C4#1306329712yes—
245C2×C4#1306332111yescharacteristic
246C8—42no—
247C8—1722no—
248C8—1724no—
249C22—21no—
250C22—21no—
251C22—3442no—
252C22—3441no—
253C22—3441no—
254C22—1724no—
255C22—1722no—
256C22#1458280711yescharacteristic
257C22#1458317112yes—
258C4—21no—
259C4—22no—
260C4—22no—
261C4—82no—
262C4—82no—
263C4—3441no—
264C4#1458306711yescharacteristic
265C4#1458307211yescharacteristic
266C2—22no—
267C2—3442no—
268C2#1913563711yescharacteristic
269C2#1913565911yescharacteristic
270C2#1913571411yescharacteristic
subgroupG/H
centerC22#14582807
commutator, cosocleC2×C42×C43C23
FrattiniC2×C42C22×D43
FittingC43×#3249C2
socleC22×C43#392
prime radicalC22×D172D4
hypercenter#3249D43
hypocenterC43#10030
LCSG ▷ C2×C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3249

Complements

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

NH ≅ G/Ntype
3. #19133210C2semidirect
4. #19132465C2semidirect
5. C43×#3249C2semidirect
131. #3249D43semidirect
156. C43#10030semidirect

Maximal subgroups

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

subgroupindex
#191446902
#191353922
#191332102
#191324652
C43×#32492
#1003043