Finite Group Databasebeta

← #24985408

Subgroups — #24985408

Order 11008.

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

normal subgroups only

This group has 536 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
1#19135928C212yesmaximal, complemented
2#19135677C211yesmaximal, characteristic
3#19132418C212yesmaximal, complemented
4#19132416C211yesmaximal, characteristic
5C43×#2683C211yesmaximal, characteristic
6C22×#10621883—21no—
7C2×#13063325C2211yescharacteristic
8C2×#13063256—22no—
9C2×#13063248—21no—
10#14582661—22no—
11#14582654C2212yes—
12#14582654C2211yescharacteristic
13C2×C22⋊Q8×C43—22no—
14C43×#396—22no—
15C43×#395—21no—
16C43×#390C2211yescharacteristic
17C43×#389C2212yes—
18C43×#386—21no—
19C22×Dic86—21no—
20C2×#10621883—42no—
21C2×#10621883—42no—
22C2×#10621883—42no—
23C22×C43⋊C8—21no—
24C22×C43⋊C8—22no—
25#13063325—42no—
26C2×C4⋊Dic43—22no—
27#13063256—44no—
28#13063248—42no—
29C22×Q8×C43—21no—
30C22×D4×C43D411yescharacteristic
31C23×C4×C43—21no—
32C22⋊Q8×C43—44no—
33C22⋊Q8×C43—44no—
34C2×C4⋊C4×C43—22no—
35C2×C4⋊C4×C43—22no—
36C2×C4⋊C4×C43D412yes—
37C2×C4⋊C4×C43D411yescharacteristic
38C2×C4⋊C4×C43D412yes—
39C2×C22⋊C4×C43—22no—
40C2×C22⋊C4×C43—22no—
41C2×C22⋊C4×C43—21no—
42C2×C42×C43C2311yescharacteristic
43#95×C43—21no—
44#95×C43—22no—
45C24×C43—21no—
46C2×Q8×C43—44no—
47C2×Q8×C43—81no—
48C2×D4×C43—21no—
49C2×D4×C43—41no—
50C2×D4×C43—41no—
51C2×D4×C43SD1612yes—
52C22×C4×C43—22no—
53C22×C4×C43—22no—
54C22×C4×C43—21no—
55C22×C4×C43—44no—
56C22×C4×C43—81no—
57C22×C4×C43C2×D412yes—
58C22×C4×C43C2×D411yescharacteristic
59C22×Dic43—41no—
60C2×Dic86—22no—
61C2×Dic86—41no—
62C2×Dic86—41no—
63C2×Dic86—41no—
64C2×Dic86—41no—
65C2×Dic86—41no—
66C4⋊C4×C43—22no—
67C4⋊C4×C43—41no—
68C4⋊C4×C43—42no—
69C4⋊C4×C43—44no—
70C4⋊C4×C43—42no—
71C4⋊C4×C43—42no—
72C4⋊C4×C43SD1614yescomplemented
73C22⋊C4×C43—44no—
74C22⋊C4×C43—42no—
75C22⋊C4×C43—42no—
76C22⋊C4×C43—81no—
77C42×C43—41no—
78#10621883—48no—
79C4⋊Dic43—24no—
80C4⋊Dic43—42no—
81C2×C43⋊C8—22no—
82C2×C43⋊C8—24no—
83C2×C43⋊C8—42no—
84C2×C43⋊C8—41no—
85C2×C43⋊C8—41no—
86C2×C43⋊C8—42no—
87C23×C43—22no—
88C23×C43—42no—
89C23×C43—41no—
90C23×C43—42no—
91C23×C43—41no—
92C23×C43#12011yescharacteristic
93Q8×C43—84no—
94D4×C43—42no—
95D4×C43—81no—
96C2×C4×C43—21no—
97C2×C4×C43—22no—
98C2×C4×C43—22no—
99C2×C4×C43—21no—
100C2×C4×C43—24no—
101C2×C4×C43—42no—
102C2×C4×C43—42no—
103C2×C4×C43—42no—
104C2×C4×C43—42no—
105C2×C4×C43—41no—
106C2×C4×C43—42no—
107C2×C4×C43—42no—
108C2×C4×C43—84no—
109C2×C4×C43C2×SD1611yescharacteristic
110C2×C4×C43C2×SD1612yes—
111C2×C4×C43AGL(1,ℤ/8)12yes—
112C2×C4×C43#13711yescharacteristic
113C2×Dic43—42no—
114C2×Dic43—81no—
115C2×Dic43—81no—
116Dic86—42no—
117Dic86—42no—
118Dic86—81no—
119Dic86—81no—
120C43⋊C8—44no—
121C43⋊C8—42no—
122#7754—431nomaximal, Sylow
123C22×C43—42no—
124C22×C43—44no—
125C22×C43—82no—
126C22×C43—81no—
127C22×C43—81no—
128C22×C43#44811yescharacteristic
129C22×C43#45012yes—
130C22×C43#45311yescharacteristic
131C22×C43#45612yes—
132C22×C43B(4,𝔽2)11yescharacteristic
133C4×C43—21no—
134C4×C43—21no—
135C4×C43—22no—
136C4×C43—22no—
137C4×C43—44no—
138C4×C43—82no—
139C4×C43—81no—
140Dic43—82no—
141#2683D4311yescharacteristic
142#2058—432no—
143#2013—431no—
144#1271—432no—
145#1270—431no—
146C2×C43—82no—
147C2×C43#159611yescharacteristic
148C2×C43#160412yes—
149C2×C43#162911yescharacteristic
150C2×C43#165112yes—
151C2×C43#166011yescharacteristic
152C22×SD16—861no—
153C2×C4⋊Q8—431no—
154C2×C22⋊Q8—22no—
155C2×#106—862no—
156C2×#103—861no—
157#396—22no—
158#395—21no—
159#390C2×D4311yescharacteristic
160#389C2×D4312yes—
161#386—21no—
162#340—862no—
163#336—432no—
164#336—431no—
165C43#775411yescharacteristic, complemented, Sylow
166C22×Q8—21no—
167C22×Q8—861no—
168C22×D4C22⋊D4311yescharacteristic
169C23×C4—21no—
170C2×SD16—1722no—
171C2×SD16—1722no—
172C2×SD16—1722no—
173C22×C8—861no—
174C22×C8—862no—
175C4⋊Q8—1722no—
176C22⋊Q8—44no—
177C22⋊Q8—44no—
178C2×C4⋊C4—22no—
179C2×C4⋊C4—22no—
180C2×C4⋊C4—862no—
181C2×C4⋊C4C22⋊D4312yes—
182C2×C4⋊C4C22⋊D4312yes—
183C2×C4⋊C4C22⋊D4311yescharacteristic
184C2×C22⋊C4—22no—
185C2×C22⋊C4—22no—
186C2×C22⋊C4—21no—
187C2×C42C22×D4311yescharacteristic
188#106—1724no—
189#103—1722no—
190#95—21no—
191#95—22no—
192C24—21no—
193C2×Q8—44no—
194C2×Q8—81no—
195C2×Q8—862no—
196C2×Q8—1721no—
197C2×Q8—1721no—
198C2×Q8—1721no—
199C2×Q8—1721no—
200C2×Q8—1721no—
201C2×D4—21no—
202C2×D4—41no—
203C2×D4—41no—
204C2×D4#1062188412yes—
205C22×C4—22no—
206C22×C4—22no—
207C22×C4—21no—
208C22×C4—44no—
209C22×C4—81no—
210C22×C4—1721no—
211C22×C4C2×C22⋊D4311yescharacteristic
212C22×C4C2×C22⋊D4312yes—
213SD16—1728no—
214C2×C8—862no—
215C2×C8—864no—
216C2×C8—1722no—
217C2×C8—1721no—
218C2×C8—1721no—
219C2×C8—1722no—
220C4⋊C4—22no—
221C4⋊C4—41no—
222C4⋊C4—42no—
223C4⋊C4—44no—
224C4⋊C4—42no—
225C4⋊C4—42no—
226C4⋊C4—864no—
227C4⋊C4—1722no—
228C4⋊C4#1062188314yescomplemented
229C22⋊C4—44no—
230C22⋊C4—42no—
231C22⋊C4—42no—
232C22⋊C4—81no—
233C42—41no—
234C23—22no—
235C23—42no—
236C23—41no—
237C23—42no—
238C23—41no—
239C23#1306329411yescharacteristic
240Q8—84no—
241Q8—3441no—
242Q8—3441no—
243Q8—1722no—
244Q8—1722no—
245D4—42no—
246D4—81no—
247C2×C4—21no—
248C2×C4—22no—
249C2×C4—22no—
250C2×C4—21no—
251C2×C4—24no—
252C2×C4—42no—
253C2×C4—42no—
254C2×C4—42no—
255C2×C4—42no—
256C2×C4—41no—
257C2×C4—42no—
258C2×C4—42no—
259C2×C4—84no—
260C2×C4—3441no—
261C2×C4—3441no—
262C2×C4—1722no—
263C2×C4C2×#1062188411yescharacteristic
264C2×C4C2×#1062188312yes—
265C2×C4#1306335112yes—
266C2×C4#1306335611yescharacteristic
267C8—1722no—
268C8—1724no—
269C22—42no—
270C22—44no—
271C22—81no—
272C22—82no—
273C22—81no—
274C22#1458303811yescharacteristic
275C22#1458305012yes—
276C22#1458306711yescharacteristic
277C22#1458308212yes—
278C22#1458308611yescharacteristic
279C4—21no—
280C4—21no—
281C4—22no—
282C4—22no—
283C4—44no—
284C4—81no—
285C4—82no—
286C4—3442no—
287C2—82no—
288C2#1913351811yescharacteristic
289C2#1913356412yes—
290C2#1913371111yescharacteristic
291C2#1913385812yes—
292C2#1913390611yescharacteristic
subgroupG/H
centerC23#13063294
commutator, cosocleC2×C42×C43C23
FrattiniC2×C42C22×D43
FittingC43×#2683C2
socleC23×C43#120
prime radicalC22×D4×C43D4
hypercenter#2683D43
hypocenterC43#7754
LCSG ▷ C2×C42×C43 ▷ C23×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2683

Complements

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

NH ≅ G/Ntype
1. #19135928C2semidirect
3. #19132418C2semidirect
72. C4⋊C4×C43SD16semidirect
165. C43#7754semidirect
228. C4⋊C4#10621883semidirect

Maximal subgroups

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

subgroupindex
#191359282
#191356772
#191324182
#191324162
C43×#26832
#775443