Finite Group Databasebeta

← #24997932

Subgroups — #24997932

Order 11008.

500 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 500 conjugacy classes of subgroups — too many to draw. Only its 95 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
1C2×#14583305C212yesmaximal
2#19142663C211yesmaximal, characteristic
3C2×#14582640C212yesmaximal
4#19132476C211yesmaximal, characteristic
5C43×#1960C211yesmaximal, characteristic
6C2×#13063317C2212yes—
7#14583305—24no—
8#14583305—24no—
9C2×#13063258—22no—
10C2×#13063256—22no—
11C2×#13063236C2212yes—
12#14582839—22no—
13#14582831—22no—
14#14582829—22no—
15#14582640—24no—
16C2×C4⋊Q8×C43C2211yescharacteristic
17C2×#103×C43—22no—
18C2×#97×C43C2211yescharacteristic
19C43×#382C2211yescharacteristic
20C22×C43⋊C8—22no—
21#13063317—22no—
22#13063317—22no—
23#13063317—22no—
24#13063317—22no—
25C2×C4⋊Dic43—22no—
26C2×C4⋊Dic43D412yes—
27C2×C4⋊Dic43D412yes—
28C2×Dic43⋊C4—22no—
29C2×Dic43⋊C4—22no—
30#13063258—28no—
31#13063256—28no—
32#13063236—22no—
33#13063236D414yes—
34C43⋊#95—24no—
35C43⋊#95—22no—
36C22×Q8×C43—21no—
37C22×C8×C43—21no—
38C4⋊Q8×C43—22no—
39C4⋊Q8×C43—21no—
40C4⋊Q8×C43D412yes—
41C2×C4⋊C4×C43—22no—
42C2×C4⋊C4×C43D412yes—
43C2×C42×C43C2311yescharacteristic
44#103×C43—44no—
45#97×C43—22no—
46#95×C43—22no—
47C2×Q8×C43—22no—
48C2×Q8×C43—42no—
49C2×Q8×C43—42no—
50C2×Q8×C43—41no—
51C22×C4×C43—22no—
52C22×C4×C43—41no—
53C22×C4×C43C2×D412yes—
54C22×C4×C43C2×D411yescharacteristic
55C22×Dic43—22no—
56C22×Dic43—22no—
57C2×C8×C43—22no—
58C2×C8×C43—41no—
59C2×C8×C43—41no—
60C4⋊C4×C43—24no—
61C4⋊C4×C43—42no—
62C4⋊C4×C43—42no—
63C42×C43C2×D411yescharacteristic
64C42×C43C2×D412yes—
65C42×C43#4111yescharacteristic
66C4⋊Dic43—22no—
67C4⋊Dic43—22no—
68C4⋊Dic43—22no—
69C4⋊Dic43—22no—
70C4⋊Dic43—82no—
71Dic43⋊C4—42no—
72Dic43⋊C4—42no—
73Dic43⋊C4—42no—
74Dic43⋊C4—42no—
75C2×C43⋊C8—28no—
76C2×C43⋊C8—24no—
77C23×C43#12011yescharacteristic
78Q8×C43—44no—
79Q8×C43—82no—
80C2×C4×C43—21no—
81C2×C4×C43—21no—
82C2×C4×C43—24no—
83C2×C4×C43—42no—
84C2×C4×C43—42no—
85C2×C4×C43—44no—
86C2×C4×C43—81no—
87C2×C4×C43—81no—
88C2×C4×C43#12012yes—
89C2×C4×C43#12112yes—
90C2×C4×C43#12111yescharacteristic
91C2×C4×C43#12711yescharacteristic
92C2×Dic43—42no—
93C2×Dic43—42no—
94C2×Dic43—42no—
95C2×Dic43—42no—
96C2×Dic43—44no—
97C8×C43—42no—
98C43⋊C8—28no—
99#10087—431nomaximal, Sylow
100C22×C43#39211yescharacteristic
101C22×C43#45311yescharacteristic
102C22×C43#45411yescharacteristic
103C22×C43#45614yes—
104C4×C43—22no—
105C4×C43—22no—
106C4×C43—21no—
107C4×C43—21no—
108C4×C43—82no—
109C4×C43—82no—
110Dic43—82no—
111Dic43—82no—
112C2×#501—432no—
113#2822—431no—
114#1960D4311yescharacteristic
115C2×#330—432no—
116#1295—431no—
117C2×C43#166012yes—
118C2×C43#166312yes—
119C2×C43#200512yes—
120C2×C43#200611yescharacteristic
121C2×C4⋊Q8C2×D4311yescharacteristic
122C2×#125—432no—
123#501—864no—
124#501—864no—
125C2×#107—862no—
126C2×#106—862no—
127C2×#103—22no—
128C2×#97—432no—
129C2×#97C2×D4311yescharacteristic
130#400—862no—
131#398—862no—
132#398—862no—
133#382C2×D4311yescharacteristic
134#330—864no—
135C43#1008711yescharacteristic, complemented, Sylow
136C22×Q8—21no—
137C22×C8—21no—
138C22×C8—862no—
139C4⋊Q8—21no—
140C4⋊Q8—22no—
141C4⋊Q8D17212yes—
142#125—862no—
143#125—862no—
144#125—862no—
145#125—862no—
146C2×C4⋊C4—22no—
147C2×C4⋊C4—432no—
148C2×C4⋊C4—432no—
149C2×C4⋊C4—862no—
150C2×C4⋊C4—862no—
151C2×C4⋊C4—862no—
152C2×C4⋊C4C22⋊D4312yes—
153C2×C42C22×D4311yescharacteristic
154#107—868no—
155#106—868no—
156#103—44no—
157#97—22no—
158#97—434no—
159#97—862no—
160#95—22no—
161#95—864no—
162#95—862no—
163C2×Q8—22no—
164C2×Q8—42no—
165C2×Q8—42no—
166C2×Q8—41no—
167C22×C4—22no—
168C22×C4—41no—
169C22×C4—862no—
170C22×C4—862no—
171C22×C4D4×D4312yes—
172C22×C4C2×C22⋊D4311yescharacteristic
173C2×C8—22no—
174C2×C8—41no—
175C2×C8—41no—
176C2×C8—868no—
177C2×C8—864no—
178C4⋊C4—24no—
179C4⋊C4—42no—
180C4⋊C4—42no—
181C4⋊C4—862no—
182C4⋊C4—862no—
183C4⋊C4—862no—
184C4⋊C4—862no—
185C4⋊C4—3442no—
186C4⋊C4—1722no—
187C4⋊C4—1722no—
188C4⋊C4—1722no—
189C4⋊C4—1722no—
190C42C2×D17211yescharacteristic
191C42#1062189811yescharacteristic
192C42D4×D4312yes—
193C23#1306329311yescharacteristic
194Q8—44no—
195Q8—82no—
196C2×C4—21no—
197C2×C4—21no—
198C2×C4—24no—
199C2×C4—42no—
200C2×C4—42no—
201C2×C4—44no—
202C2×C4—81no—
203C2×C4—81no—
204C2×C4—1722no—
205C2×C4—1722no—
206C2×C4—1722no—
207C2×C4—1722no—
208C2×C4—1724no—
209C2×C4#1306329512yes—
210C2×C4#1306329812yes—
211C2×C4#1306329911yescharacteristic
212C2×C4#1306332111yescharacteristic
213C8—42no—
214C8—868no—
215C22#1458280811yescharacteristic
216C22#1458306611yescharacteristic
217C22#1458307111yescharacteristic
218C22#1458308014yes—
219C4—22no—
220C4—22no—
221C4—21no—
222C4—21no—
223C4—82no—
224C4—82no—
225C4—3442no—
226C4—3442no—
227C2#1913390412yes—
228C2#1913392112yes—
229C2#1913563212yes—
230C2#1913563611yescharacteristic
subgroupG/H
centerC23#13063293
commutator, cosocleC2×C42×C43C23
FrattiniC2×C42C22×D43
FittingC43×#1960C2
socle, prime radicalC23×C43#120
hypercenter#1960D43
hypocenterC43#10087
LCSG ▷ C2×C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1960

Complements

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

NH ≅ G/Ntype
135. C43#10087semidirect

Maximal subgroups

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

subgroupindex
C2×#145833052
#191426632
C2×#145826402
#191324762
C43×#19602
#1008743