Finite Group Databasebeta

← #24997935

Subgroups — #24997935

Order 11008.

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

normal subgroups only

This group has 500 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
1C2×#14583308C212yesmaximal
2#19142663C211yesmaximal, characteristic
3#19135414C211yesmaximal, characteristic
4C2×#14582640C212yesmaximal
5C43×#1295C211yesmaximal, characteristic
6C2×#13063325C2211yescharacteristic
7C2×#13063317C2212yes—
8#14583308—24no—
9#14583308—24no—
10C2×#13063259—22no—
11C2×#13063257—22no—
12C2×#13063248—22no—
13C2×#13063236C2211yescharacteristic
14#14582839—22no—
15#14582831—22no—
16#14582829—22no—
17#14582640—24no—
18C2×#97×C43C2212yes—
19C43×#382C2211yescharacteristic
20C22×Dic86—21no—
21C22×C43⋊C8—21no—
22#13063325—22no—
23#13063325—21no—
24#13063325D412yes—
25#13063317—22no—
26#13063317—22no—
27#13063317—22no—
28#13063317—22no—
29C2×C4⋊Dic43—22no—
30C2×C4⋊Dic43—22no—
31C2×C4⋊Dic43D412yes—
32C2×C4⋊Dic43D412yes—
33C2×Dic43⋊C4—22no—
34C2×Dic43⋊C4—22no—
35#13063259—28no—
36#13063257—28no—
37#13063248—44no—
38#13063236—22no—
39C43⋊#95—24no—
40C43⋊#95—22no—
41C22×C8×C43—22no—
42C2×C4⋊C4×C43D412yes—
43C2×C42×C43C2311yescharacteristic
44#97×C43—22no—
45#97×C43D414yes—
46#95×C43—22no—
47C22×C4×C43—22no—
48C22×C4×C43C2×D411yescharacteristic
49C22×C4×C43C2×D412yes—
50C22×Dic43—22no—
51C22×Dic43—22no—
52C22×Dic43—41no—
53C2×Dic86—22no—
54C2×Dic86—42no—
55C2×Dic86—42no—
56C2×Dic86—41no—
57C2×C8×C43—28no—
58C2×C8×C43—24no—
59C4⋊C4×C43—42no—
60C42×C43C2×D412yes—
61C42×C43C2×D411yescharacteristic
62C42×C43#4111yescharacteristic
63C4⋊Dic43—22no—
64C4⋊Dic43—24no—
65C4⋊Dic43—22no—
66C4⋊Dic43—22no—
67C4⋊Dic43—22no—
68C4⋊Dic43—42no—
69C4⋊Dic43—82no—
70Dic43⋊C4—42no—
71Dic43⋊C4—42no—
72Dic43⋊C4—42no—
73Dic43⋊C4—42no—
74C2×C43⋊C8—22no—
75C2×C43⋊C8—41no—
76C2×C43⋊C8—41no—
77C23×C43#12011yescharacteristic
78C2×C4×C43—21no—
79C2×C4×C43—21no—
80C2×C4×C43—24no—
81C2×C4×C43—42no—
82C2×C4×C43—44no—
83C2×C4×C43#12012yes—
84C2×C4×C43#12111yescharacteristic
85C2×C4×C43#12112yes—
86C2×C4×C43#12711yescharacteristic
87C2×Dic43—42no—
88C2×Dic43—42no—
89C2×Dic43—42no—
90C2×Dic43—42no—
91C2×Dic43—42no—
92C2×Dic43—44no—
93C2×Dic43—81no—
94C2×Dic43—81no—
95Dic86—44no—
96Dic86—82no—
97C8×C43—28no—
98C43⋊C8—42no—
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—
109Dic43—82no—
110Dic43—82no—
111Dic43—82no—
112C2×#501—432no—
113#2822—431no—
114#1960—431no—
115C2×#330—432no—
116#1295D4311yescharacteristic
117C2×C43#166012yes—
118C2×C43#166312yes—
119C2×C43#200512yes—
120C2×C43#200611yescharacteristic
121C2×C4⋊Q8—431no—
122C2×#125—432no—
123#501—864no—
124#501—864no—
125C2×#107—862no—
126C2×#106—862no—
127C2×#103—862no—
128C2×#97—431no—
129C2×#97C2×D4312yes—
130#400—862no—
131#398—862no—
132#398—862no—
133#382C2×D4311yescharacteristic
134#330—864no—
135C43#1008711yescharacteristic, complemented, Sylow
136C22×Q8—861no—
137C22×C8—22no—
138C22×C8—861no—
139C4⋊Q8—432no—
140C4⋊Q8—862no—
141C4⋊Q8—861no—
142#125—862no—
143#125—862no—
144#125—862no—
145#125—862no—
146C2×C4⋊C4—432no—
147C2×C4⋊C4—432no—
148C2×C4⋊C4—862no—
149C2×C4⋊C4—862no—
150C2×C4⋊C4—862no—
151C2×C4⋊C4—862no—
152C2×C4⋊C4D17212yes—
153C2×C42C22×D4311yescharacteristic
154#107—868no—
155#106—868no—
156#103—1724no—
157#97—22no—
158#97—862no—
159#97D17214yes—
160#95—22no—
161#95—864no—
162#95—862no—
163C2×Q8—862no—
164C2×Q8—1722no—
165C2×Q8—1722no—
166C2×Q8—1721no—
167C22×C4—22no—
168C22×C4—862no—
169C22×C4—862no—
170C22×C4—1721no—
171C22×C4C2×D17211yescharacteristic
172C22×C4D4×D4312yes—
173C2×C8—28no—
174C2×C8—24no—
175C2×C8—862no—
176C2×C8—1721no—
177C2×C8—1721no—
178C4⋊C4—42no—
179C4⋊C4—862no—
180C4⋊C4—864no—
181C4⋊C4—862no—
182C4⋊C4—862no—
183C4⋊C4—862no—
184C4⋊C4—3442no—
185C4⋊C4—1722no—
186C4⋊C4—1722no—
187C4⋊C4—1722no—
188C4⋊C4—1722no—
189C4⋊C4—1722no—
190C42C2×D17212yes—
191C42D4×D4311yescharacteristic
192C42#1062190211yescharacteristic
193C23#1306329511yescharacteristic
194Q8—3442no—
195Q8—1724no—
196C2×C4—21no—
197C2×C4—21no—
198C2×C4—24no—
199C2×C4—42no—
200C2×C4—44no—
201C2×C4—3441no—
202C2×C4—3441no—
203C2×C4—1722no—
204C2×C4—1722no—
205C2×C4—1722no—
206C2×C4—1722no—
207C2×C4—1722no—
208C2×C4—1724no—
209C2×C4#1306329512yes—
210C2×C4#1306330012yes—
211C2×C4#1306330011yescharacteristic
212C2×C4#1306332211yescharacteristic
213C8—28no—
214C8—1722no—
215C22#1458280911yescharacteristic
216C22#1458306911yescharacteristic
217C22#1458307411yescharacteristic
218C22#1458308314yes—
219C4—22no—
220C4—22no—
221C4—21no—
222C4—21no—
223C4—82no—
224C4—3442no—
225C4—3442no—
226C4—3442no—
227C2#1913390712yes—
228C2#1913392412yes—
229C2#1913563412yes—
230C2#1913563911yescharacteristic
subgroupG/H
centerC23#13063295
commutator, cosocleC2×C42×C43C23
FrattiniC2×C42C22×D43
FittingC43×#1295C2
socle, prime radicalC23×C43#120
hypercenter#1295D43
hypocenterC43#10087
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
135. C43#10087semidirect

Maximal subgroups

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

subgroupindex
C2×#145833082
#191426632
#191354142
C2×#145826402
C43×#12952
#1008743