Finite Group Databasebeta

← #24997933

Subgroups — #24997933

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×#14583309C212yesmaximal
2#19135414C211yesmaximal, characteristic
3C2×#14582641C212yesmaximal
4#19132476C211yesmaximal, characteristic
5C43×#2822C211yesmaximal, characteristic
6C2×#13063325C2211yescharacteristic
7#14583309—24no—
8#14583309—24no—
9C2×#13063258—22no—
10C2×#13063256—22no—
11C2×#13063248—22no—
12C2×#13063236C2211yescharacteristic
13C2×#13063236C2212yes—
14#14582641—24no—
15C2×#125×C43C2212yes—
16C43×#400—22no—
17C43×#398—22no—
18C43×#398—22no—
19C43×#382C2211yescharacteristic
20C22×Dic86—21no—
21C22×C43⋊C8—22no—
22C22×C43⋊C8—21no—
23#13063325—22no—
24#13063325—21no—
25#13063325D412yes—
26C2×C4⋊Dic43—22no—
27#13063258—28no—
28#13063256—28no—
29#13063248—44no—
30#13063236—22no—
31#13063236—22no—
32#13063236D414yes—
33#125×C43—22no—
34#125×C43—22no—
35#125×C43—22no—
36#125×C43—22no—
37C2×C4⋊C4×C43—22no—
38C2×C4⋊C4×C43—22no—
39C2×C4⋊C4×C43—22no—
40C2×C4⋊C4×C43D412yes—
41C2×C4⋊C4×C43D412yes—
42C2×C4⋊C4×C43D412yes—
43C2×C42×C43C2311yescharacteristic
44#95×C43—24no—
45#95×C43—22no—
46#95×C43—22no—
47C22×C4×C43—22no—
48C22×C4×C43—22no—
49C22×C4×C43—22no—
50C22×C4×C43C2×D412yes—
51C22×C4×C43C2×D411yescharacteristic
52C22×Dic43—41no—
53C2×Dic86—22no—
54C2×Dic86—42no—
55C2×Dic86—42no—
56C2×Dic86—41no—
57C4⋊C4×C43—22no—
58C4⋊C4×C43—22no—
59C4⋊C4×C43—22no—
60C4⋊C4×C43—22no—
61C4⋊C4×C43—42no—
62C4⋊C4×C43—42no—
63C4⋊C4×C43—42no—
64C4⋊C4×C43—42no—
65C4⋊C4×C43—42no—
66C4⋊C4×C43—82no—
67C42×C43C2×D411yescharacteristic
68C42×C43C2×D412yes—
69C42×C43#4111yescharacteristic
70C4⋊Dic43—24no—
71C4⋊Dic43—42no—
72C2×C43⋊C8—28no—
73C2×C43⋊C8—24no—
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—42no—
83C2×C4×C43—42no—
84C2×C4×C43—42no—
85C2×C4×C43—42no—
86C2×C4×C43—44no—
87C2×C4×C43—44no—
88C2×C4×C43#12012yes—
89C2×C4×C43#12111yescharacteristic
90C2×C4×C43#12112yes—
91C2×C4×C43#12711yescharacteristic
92C2×Dic43—42no—
93C2×Dic43—81no—
94C2×Dic43—81no—
95Dic86—44no—
96Dic86—82no—
97C43⋊C8—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—
109C4×C43—82no—
110C4×C43—82no—
111Dic43—82no—
112C2×#501—432no—
113#2822D4311yescharacteristic
114#1960—431no—
115C2×#330—432no—
116#1295—431no—
117C2×C43#166012yes—
118C2×C43#166312yes—
119C2×C43#200512yes—
120C2×C43#200611yescharacteristic
121C2×C4⋊Q8—431no—
122C2×#125C2×D4312yes—
123#501—864no—
124#501—864no—
125C2×#107—862no—
126C2×#106—862no—
127C2×#103—862no—
128C2×#97—432no—
129C2×#97—431no—
130#400—22no—
131#398—22no—
132#398—22no—
133#382C2×D4311yescharacteristic
134#330—864no—
135C43#1008711yescharacteristic, complemented, Sylow
136C22×Q8—861no—
137C22×C8—862no—
138C22×C8—861no—
139C4⋊Q8—432no—
140C4⋊Q8—862no—
141C4⋊Q8—861no—
142#125—22no—
143#125—22no—
144#125—22no—
145#125—22no—
146C2×C4⋊C4—22no—
147C2×C4⋊C4—22no—
148C2×C4⋊C4—22no—
149C2×C4⋊C4—862no—
150C2×C4⋊C4C22⋊D4312yes—
151C2×C4⋊C4C22⋊D4312yes—
152C2×C4⋊C4C22⋊D4312yes—
153C2×C42C22×D4311yescharacteristic
154#107—868no—
155#106—868no—
156#103—1724no—
157#97—434no—
158#97—862no—
159#97—862no—
160#95—24no—
161#95—22no—
162#95—22no—
163C2×Q8—862no—
164C2×Q8—1722no—
165C2×Q8—1722no—
166C2×Q8—1721no—
167C22×C4—22no—
168C22×C4—22no—
169C22×C4—22no—
170C22×C4—1721no—
171C22×C4C2×C22⋊D4312yes—
172C22×C4C2×C22⋊D4311yescharacteristic
173C2×C8—868no—
174C2×C8—864no—
175C2×C8—862no—
176C2×C8—1721no—
177C2×C8—1721no—
178C4⋊C4—22no—
179C4⋊C4—22no—
180C4⋊C4—22no—
181C4⋊C4—22no—
182C4⋊C4—42no—
183C4⋊C4—42no—
184C4⋊C4—42no—
185C4⋊C4—42no—
186C4⋊C4—42no—
187C4⋊C4—82no—
188C4⋊C4—864no—
189C4⋊C4—1722no—
190C42D4×D4311yescharacteristic
191C42D4×D4312yes—
192C42#1062190011yescharacteristic
193C23#1306329411yescharacteristic
194Q8—3442no—
195Q8—1724no—
196C2×C4—21no—
197C2×C4—21no—
198C2×C4—24no—
199C2×C4—42no—
200C2×C4—42no—
201C2×C4—42no—
202C2×C4—42no—
203C2×C4—42no—
204C2×C4—44no—
205C2×C4—44no—
206C2×C4—3441no—
207C2×C4—3441no—
208C2×C4—1722no—
209C2×C4#1306329312yes—
210C2×C4#1306329611yescharacteristic
211C2×C4#1306329712yes—
212C2×C4#1306332111yescharacteristic
213C8—868no—
214C8—1722no—
215C22#1458280711yescharacteristic
216C22#1458306711yescharacteristic
217C22#1458307211yescharacteristic
218C22#1458308214yes—
219C4—22no—
220C4—22no—
221C4—21no—
222C4—21no—
223C4—82no—
224C4—82no—
225C4—82no—
226C4—3442no—
227C2#1913390612yes—
228C2#1913392312yes—
229C2#1913562912yes—
230C2#1913563711yescharacteristic
subgroupG/H
centerC23#13063294
commutator, cosocleC2×C42×C43C23
FrattiniC2×C42C22×D43
FittingC43×#2822C2
socle, prime radicalC23×C43#120
hypercenter#2822D43
hypocenterC43#10087
LCSG ▷ C2×C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2822

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×#145833092
#191354142
C2×#145826412
#191324762
C43×#28222
#1008743