Finite Group Databasebeta

← #25001095

Subgroups — #25001095

Order 11008.

406 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 406 conjugacy classes of subgroups — too many to draw. Only its 97 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#19142867C211yesmaximal, characteristic
2#19134764C211yesmaximal, characteristic
3#19134763C212yesmaximal
4#19132477C212yesmaximal
5C43×#1295C211yesmaximal, characteristic
6C2×#13063259—22no—
7C2×#13063258—21no—
8C2×#13063257—22no—
9C2×#13063256—21no—
10C2×#13063236C2211yescharacteristic
11#14582841—22no—
12#14582838—21no—
13#14582820—22no—
14#14582819—21no—
15#14582769C2211yescharacteristic
16#14582765C2212yes—
17C2×#97×C43C2212yes—
18C43×#382C2211yescharacteristic
19C22×Dic86—21no—
20C22×C43⋊C8—21no—
21C2×C4⋊Dic43—21no—
22C2×C4⋊Dic43—22no—
23C2×C4⋊Dic43—21no—
24C2×C4⋊Dic43D412yes—
25C2×C4⋊Dic43D412yes—
26C2×Dic43⋊C4—22no—
27#13063259—44no—
28#13063258—42no—
29#13063257—44no—
30#13063256—42no—
31#13063236—21no—
32#13063236Q812yescomplemented
33C43⋊#95—21no—
34C43⋊#95—22no—
35C43⋊#95—21no—
36C43⋊#95—22no—
37C43⋊#95—22no—
38C22×C8×C43—22no—
39C2×C4⋊C4×C43D411yescharacteristic
40C2×C4⋊C4×C43D411yescharacteristic
41C2×C42×C43C2311yescharacteristic
42#97×C43—22no—
43#97×C43Q814yescomplemented
44#95×C43—22no—
45C22×C4×C43—21no—
46C22×C4×C43—21no—
47C22×C4×C43C2×D411yescharacteristic
48C22×C4×C43C2×D412yes—
49C22×Dic43—22no—
50C22×Dic43—22no—
51C22×Dic43—41no—
52C2×Dic86—82no—
53C2×Dic86—81no—
54C2×C8×C43—24no—
55C2×C8×C43—24no—
56C2×C8×C43—24no—
57C4⋊C4×C43—41no—
58C4⋊C4×C43—41no—
59C42×C43C2×Q812yes—
60C42×C43C2×Q811yescharacteristic
61C42×C43#4111yescharacteristic
62C4⋊Dic43—42no—
63C4⋊Dic43—42no—
64C4⋊Dic43—41no—
65C4⋊Dic43—42no—
66C4⋊Dic43—41no—
67C4⋊Dic43—42no—
68C4⋊Dic43—81no—
69Dic43⋊C4—82no—
70C2×C43⋊C8—22no—
71C2×C43⋊C8—22no—
72C2×C43⋊C8—22no—
73C23×C43#12011yescharacteristic
74C2×C4×C43—21no—
75C2×C4×C43—22no—
76C2×C4×C43—21no—
77C2×C4×C43—22no—
78C2×C4×C43—42no—
79C2×C4×C43—41no—
80C2×C4×C43—41no—
81C2×C4×C43—42no—
82C2×C4×C43C22⋊Q812yes—
83C2×C4×C43C22⋊Q811yescharacteristic
84C2×C4×C43C4⋊Q812yes—
85C2×C4×C43C4⋊Q811yescharacteristic
86C2×Dic43—42no—
87C2×Dic43—42no—
88C2×Dic43—42no—
89C2×Dic43—42no—
90C2×Dic43—42no—
91C2×Dic43—42no—
92C2×Dic43—82no—
93C2×Dic43—81no—
94Dic86—84no—
95C8×C43—28no—
96C43⋊C8—24no—
97#10583—431nomaximal, Sylow
98C22×C43#39511yescharacteristic
99C22×C43#45312yes—
100C22×C43#45311yescharacteristic
101C22×C43#45612yes—
102C22×C43#45611yescharacteristic
103C4×C43—21no—
104C4×C43—22no—
105C4×C43—22no—
106C4×C43—21no—
107C4×C43—81no—
108C4×C43—81no—
109Dic43—82no—
110Dic43—82no—
111Dic43—161no—
112#2844—431no—
113#1847—432no—
114#1847—431no—
115#1295—432no—
116#1295D4311yescharacteristic
117C2×C43#165511yescharacteristic
118C2×C43#166011yescharacteristic
119C2×C43#166012yes—
120C2×C43#206012yes—
121C2×C43#206011yescharacteristic
122C2×#107—862no—
123C2×#107—861no—
124C2×#106—862no—
125C2×#106—861no—
126C2×#97—431no—
127C2×#97C2×D4312yes—
128#400—862no—
129#400—861no—
130#395—862no—
131#395—861no—
132#384—431no—
133#382—432no—
134#382C2×D4311yescharacteristic
135C43#1058311yescharacteristic, complemented, Sylow
136C22×Q8—861no—
137C22×C8—22no—
138C22×C8—861no—
139C2×C4⋊C4—432no—
140C2×C4⋊C4—432no—
141C2×C4⋊C4—862no—
142C2×C4⋊C4—861no—
143C2×C4⋊C4—861no—
144C2×C4⋊C4—862no—
145C2×C4⋊C4D17211yescharacteristic
146C2×C4⋊C4D17211yescharacteristic
147C2×C42C22×D4311yescharacteristic
148#107—1722no—
149#107—1724no—
150#106—1722no—
151#106—1724no—
152#97—22no—
153#97—432no—
154#97—861no—
155#97Dic8614yescomplemented
156#95—22no—
157#95—862no—
158#95—861no—
159#95—861no—
160#95—862no—
161#95—862no—
162C2×Q8—3442no—
163C2×Q8—3441no—
164C22×C4—21no—
165C22×C4—21no—
166C22×C4—862no—
167C22×C4—862no—
168C22×C4—1721no—
169C22×C4C2×D17211yescharacteristic
170C22×C4D4×D4312yes—
171C2×C8—24no—
172C2×C8—24no—
173C2×C8—24no—
174C2×C8—862no—
175C2×C8—862no—
176C2×C8—862no—
177C4⋊C4—41no—
178C4⋊C4—41no—
179C4⋊C4—3442no—
180C4⋊C4—3441no—
181C4⋊C4—1722no—
182C4⋊C4—1721no—
183C4⋊C4—1722no—
184C4⋊C4—1721no—
185C4⋊C4—1722no—
186C4⋊C4—1722no—
187C42C2×Dic8612yes—
188C42#1062190011yescharacteristic
189C42Q8×D4311yescharacteristic
190C23#1306329511yescharacteristic
191Q8—3444no—
192C2×C4—22no—
193C2×C4—21no—
194C2×C4—22no—
195C2×C4—21no—
196C2×C4—42no—
197C2×C4—41no—
198C2×C4—41no—
199C2×C4—42no—
200C2×C4—3442no—
201C2×C4—3441no—
202C2×C4—1722no—
203C2×C4—1722no—
204C2×C4—1722no—
205C2×C4—1722no—
206C2×C4—1722no—
207C2×C4—1722no—
208C2×C4#1306330212yes—
209C2×C4#1306330511yescharacteristic
210C2×C4#1306332412yes—
211C2×C4#1306332511yescharacteristic
212C8—28no—
213C8—864no—
214C22#1458282011yescharacteristic
215C22#1458306812yes—
216C22#1458306911yescharacteristic
217C22#1458308312yes—
218C22#1458308411yescharacteristic
219C4—22no—
220C4—22no—
221C4—21no—
222C4—21no—
223C4—81no—
224C4—81no—
225C4—3442no—
226C4—3442no—
227C4—6881no—
228C2#1913388511yescharacteristic
229C2#1913390711yescharacteristic
230C2#1913390812yes—
231C2#1913593912yes—
232C2#1913594111yescharacteristic
subgroupG/H
centerC23#13063295
commutator, cosocleC2×C42×C43C23
FrattiniC2×C42C22×D43
FittingC43×#1295C2
socle, prime radicalC23×C43#120
hypercenter#1295D43
hypocenterC43#10583
LCSG ▷ C2×C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1295

Complements

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

NH ≅ G/Ntype
32. #13063236Q8semidirect
43. #97×C43Q8semidirect
135. C43#10583semidirect
155. #97Dic86semidirect

Maximal subgroups

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

subgroupindex
#191428672
#191347642
#191347632
#191324772
C43×#12952
#1058343