Finite Group Databasebeta

← #24997212

Subgroups — #24997212

Order 11008.

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

normal subgroups only

This group has 544 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#19144531C212yesmaximal, complemented
2#19134664C211yesmaximal, characteristic, complemented
3#19132955C212yesmaximal, complemented
4#19132472C211yesmaximal, characteristic, complemented
5C43×#3186C211yesmaximal, characteristic
6C2×#13063284C2211yescharacteristic
7#14583220—24no—
8#14583215—22no—
9#14583210—22no—
10#14582939—22no—
11#14582904—22no—
12#14582863C2212yes—
13C2×C22⋊(C43⋊C8)C2211yescharacteristic
14#14582653—22no—
15#14582623—24no—
16C2×#121×C43C2212yes—
17C43×#480—22no—
18C43×#466—22no—
19C43×#447—22no—
20C2×C22⋊C8×C43C2211yescharacteristic
21C2×#10621877—22no—
22C22×C43⋊C8—21no—
23#13063284—22no—
24#13063284—22no—
25C2×C4⋊Dic43D411yescharacteristic
26C2×C4⋊Dic43D411yescharacteristic
27C2×C22⋊Dic43—21no—
28C2×C4×Dic43—21no—
29#13063258—24no—
30#13063256—24no—
31#13063246—24no—
32#13063246—24no—
33C22⋊(C43⋊C8)—22no—
34C22⋊(C43⋊C8)—22no—
35C22⋊(C43⋊C8)D414yes—
36C22×D4×C43—22no—
37C22×D4×C43D412yes—
38C23×C4×C43C2311yescharacteristic
39C2×D8×C43—22no—
40C22×C8×C43D412yes—
41#121×C43—22no—
42#121×C43—22no—
43#121×C43—22no—
44#121×C43—22no—
45C2×C4⋊C4×C43D412yes—
46C2×C22⋊C4×C43—22no—
47#107×C43—22no—
48#102×C43—24no—
49C22⋊C8×C43—22no—
50C24×C43—22no—
51C24×C43#4111yescharacteristic
52C2×D4×C43—22no—
53C2×D4×C43—22no—
54C2×D4×C43—42no—
55C2×D4×C43—42no—
56C2×D4×C43—44no—
57C2×D4×C43—84no—
58C22×C4×C43—22no—
59C22×C4×C43—42no—
60C22×C4×C43C2×D411yescharacteristic
61C22×C4×C43C2×D412yes—
62C22×C4×C43C2×D412yes—
63C22×C4×C43C2×D411yescharacteristic
64C22×Dic43—21no—
65C22×Dic43—21no—
66D8×C43—82no—
67C2×C8×C43—22no—
68C2×C8×C43—42no—
69C4⋊C4×C43—22no—
70C4⋊C4×C43—22no—
71C22⋊C4×C43—42no—
72C22⋊C4×C43—42no—
73C22⋊Dic43—42no—
74C4⋊Dic43—22no—
75C4⋊Dic43—22no—
76C4×Dic43—41no—
77C4×Dic43—41no—
78#10621877—44no—
79C2×C43⋊C8—24no—
80C2×C43⋊C8—42no—
81C2×C43⋊C8—41no—
82C23×C43—22no—
83C23×C43—41no—
84C23×C43—41no—
85C23×C43—44no—
86C23×C43—42no—
87C23×C43—82no—
88C23×C43—82no—
89C23×C43#12111yescharacteristic
90C23×C43#12112yes—
91D4×C43—44no—
92D4×C43—44no—
93D4×C43—84no—
94D4×C43—84no—
95C2×C4×C43—22no—
96C2×C4×C43—24no—
97C2×C4×C43—41no—
98C2×C4×C43—42no—
99C2×C4×C43—42no—
100C2×C4×C43—82no—
101C2×C4×C43#12012yes—
102C2×C4×C43#12011yescharacteristic
103C2×C4×C43#12711yescharacteristic
104C2×Dic43—42no—
105C2×Dic43—41no—
106C2×Dic43—41no—
107C2×Dic43—42no—
108C8×C43—42no—
109C43⋊C8—44no—
110C43⋊C8—81no—
111#9977—431nomaximal, Sylow
112C22×C43—21no—
113C22×C43—21no—
114C22×C43—22no—
115C22×C43—22no—
116C22×C43—22no—
117C22×C43—82no—
118C22×C43—82no—
119C22×C43—82no—
120C22×C43—82no—
121C22×C43—164no—
122C22×C43#39211yescharacteristic
123C22×C43#47212yes—
124C4×C43—22no—
125C4×C43—21no—
126C4×C43—82no—
127C4×C43#45812yes—
128Dic43—81no—
129Dic43—81no—
130#3186D4311yescharacteristic
131#3094—432no—
132#1818—431no—
133#1471—432no—
134#1293—431no—
135C2×C43—22no—
136C2×C43—42no—
137C2×C43—162no—
138C2×C43#201711yescharacteristic
139C2×C43#201811yescharacteristic
140C2×C43#202211yescharacteristic
141C2×#121C2×D4312yes—
142C2×#117—431no—
143#482—864no—
144#481—862no—
145#480—22no—
146#480—862no—
147#466—22no—
148#447—22no—
149#428—862no—
150#418—862no—
151#407—432no—
152C2×C22⋊C8—431no—
153C2×C22⋊C8C2×D4311yescharacteristic
154#336—862no—
155#323—864no—
156C43#997711yescharacteristic, complemented, Sylow
157C22×D4—22no—
158C22×D4C22⋊D4312yes—
159C23×C4C22×D4311yescharacteristic
160C2×D8—22no—
161C2×M16—862no—
162C22×C8—861no—
163C22×C8C22⋊D4312yes—
164#121—22no—
165#121—22no—
166#121—22no—
167#121—22no—
168#117—862no—
169#117—862no—
170C2×C4⋊C4—431no—
171C2×C4⋊C4—431no—
172C2×C4⋊C4C22⋊D4312yes—
173C2×C22⋊C4—22no—
174C2×C22⋊C4—861no—
175C2×C42—861no—
176#107—22no—
177#107—864no—
178#106—864no—
179#102—24no—
180#102—864no—
181#102—864no—
182C22⋊C8—22no—
183C22⋊C8—434no—
184C22⋊C8—862no—
185C22⋊C8—862no—
186C24—22no—
187C24#1062190011yescharacteristic
188C2×D4—22no—
189C2×D4—22no—
190C2×D4—44no—
191C2×D4—42no—
192C2×D4—42no—
193C2×D4—84no—
194C22×C4—22no—
195C22×C4—42no—
196C22×C4—861no—
197C22×C4—861no—
198C22×C4D4×D4311yescharacteristic
199C22×C4D4×D4312yes—
200C22×C4C2×C22⋊D4312yes—
201C22×C4C2×C22⋊D4311yescharacteristic
202D8—82no—
203M16—1724no—
204C2×C8—22no—
205C2×C8—42no—
206C2×C8—864no—
207C2×C8—1722no—
208C2×C8—1721no—
209C4⋊C4—22no—
210C4⋊C4—22no—
211C4⋊C4—862no—
212C4⋊C4—862no—
213C22⋊C4—42no—
214C22⋊C4—42no—
215C22⋊C4—1722no—
216C42—1721no—
217C42—1721no—
218C23—22no—
219C23—41no—
220C23—41no—
221C23—44no—
222C23—42no—
223C23—82no—
224C23—82no—
225C23#1306329611yescharacteristic
226C23#1306329712yes—
227D4—44no—
228D4—44no—
229D4—84no—
230D4—84no—
231C2×C4—22no—
232C2×C4—24no—
233C2×C4—42no—
234C2×C4—41no—
235C2×C4—42no—
236C2×C4—82no—
237C2×C4—1722no—
238C2×C4—1721no—
239C2×C4—1721no—
240C2×C4—1722no—
241C2×C4#1306329312yes—
242C2×C4#1306329411yescharacteristic
243C2×C4#1306332111yescharacteristic
244C8—42no—
245C8—3441no—
246C8—1724no—
247C22—21no—
248C22—21no—
249C22—22no—
250C22—22no—
251C22—22no—
252C22—82no—
253C22—82no—
254C22—82no—
255C22—82no—
256C22—164no—
257C22#1458280711yescharacteristic
258C22#1458316612yes—
259C4—21no—
260C4—22no—
261C4—82no—
262C4—3441no—
263C4—3441no—
264C4#1458308912yes—
265C2—22no—
266C2—42no—
267C2—162no—
268C2#1913569811yescharacteristic
269C2#1913570211yescharacteristic
270C2#1913572411yescharacteristic
subgroupG/H
centerC22#14582807
commutator, cosocleC23×C4×C43C23
FrattiniC23×C4C22×D43
Fitting, prime radicalC43×#3186C2
socleC22×C43#392
hypercenter#3186D43
hypocenterC43#9977
LCSG ▷ C23×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ #3186

Complements

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

NH ≅ G/Ntype
1. #19144531C2semidirect
2. #19134664C2semidirect
3. #19132955C2semidirect
4. #19132472C2semidirect
156. C43#9977semidirect

Maximal subgroups

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

subgroupindex
#191445312
#191346642
#191329552
#191324722
C43×#31862
#997743