Finite Group Databasebeta

← #25010032

Subgroups — #25010032

Order 11008.

384 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 384 conjugacy classes of subgroups — too many to draw. Only its 69 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#19146345C211yesmaximal, characteristic, complemented
2#19136632C211yesmaximal, characteristic, complemented
3#19133947C211yesmaximal, characteristic
4#19132644C211yesmaximal, characteristic, complemented
5#19132560C211yesmaximal, characteristic, complemented
6#19132551C211yesmaximal, characteristic, complemented
7C43×#2248C211yesmaximal, characteristic, complemented
8C2×Q16×D43—21no—
9#14583564—21no—
10C2×#13063269—21no—
11#14583137—21no—
12#14583106—21no—
13#14583091—21no—
14#14583053—22no—
15C4×Dic172C2211yescharacteristic
16C8×D172C2211yescharacteristic
17C4⋊(C43⋊C16)C2211yescharacteristic
18#14582700—21no—
19#14582652C2211yescharacteristic
20#14582643—21no—
21C2×SD32×C43—22no—
22C43×#494C2211yescharacteristic
23C43×#493C2211yescharacteristic
24C4×C16×C43C2211yescharacteristic
25C2×Q8×D43—22no—
26C2×Dic172D411yescharacteristic
27C2×#10621885—22no—
28Q16×D43—42no—
29Q16×D43—42no—
30C2×#10621882—41no—
31C2×C8×D43—21no—
32#13063324—41no—
33#13063303—42no—
34#13063301—22no—
35C4×Dic86—21no—
36C4×D172D411yescharacteristic
37#13063287—41no—
38#13063269—42no—
39C2×C43⋊C16—21no—
40#13063259D411yescharacteristic
41C4⋊(C43⋊C8)—21no—
42C4⋊(C43⋊C8)D411yescharacteristic
43#13063250—21no—
44#13063249—22no—
45#13063246—41no—
46(C2×D43)⋊C8—21no—
47C2×Q16×C43—21no—
48C2×Q16×C43D412yes—
49C2×D8×C43—21no—
50C2×D8×C43—21no—
51C4⋊Q8×C43—21no—
52#127×C43—21no—
53SD32×C43—44no—
54C2×C16×C43—21no—
55C4×C8×C43C2311yescharacteristic
56C2×Q8×C43—22no—
57C2×D4×C43—41no—
58C2×D4×C43—41no—
59C2×D4×C43—41no—
60Q8×D43—44no—
61Q8×D43—82no—
62C2×D172D811yescharacteristic
63C2×C4×D43—21no—
64C2×C4×D43—42no—
65C2×Dic86—21no—
66C2×Dic86—42no—
67Q16×C43—42no—
68Q16×C43—41no—
69Q16×C43—41no—
70D8×C43—42no—
71D8×C43—41no—
72D8×C43—41no—
73C2×C8×C43C2×D411yescharacteristic
74C2×C8×C43C2×D411yescharacteristic
75C4⋊C4×C43—41no—
76C4⋊C4×C43—41no—
77C42×C43C2×D411yescharacteristic
78#10621885—44no—
79#10621882—82no—
80(C2×D43)⋊C4—21no—
81(C2×D43)⋊C4—42no—
82C4⋊Dic43—21no—
83C4⋊Dic43D811yescharacteristic
84Dic43⋊C4—42no—
85Dic43⋊C4—41no—
86C4×Dic43—41no—
87C2×C43⋊C8—21no—
88C2×C43⋊C8—41no—
89Dic172—21no—
90Dic172D812yescomplemented
91C8×D43—41no—
92C8×D43—41no—
93C16×C43—22no—
94C43⋊C16—41no—
95C23×C43—81no—
96C22×D43—21no—
97Q8×C43—42no—
98Q8×C43—42no—
99D4×C43—81no—
100D4×C43—81no—
101D4×C43—81no—
102D4×C43—81no—
103D4×C43—161no—
104C2×C4×C43—42no—
105C2×C4×C43#12011yescharacteristic
106C2×C4×C43C2×D811yescharacteristic
107C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
108C2×Dic43—21no—
109C2×Dic43—41no—
110C2×Dic43—41no—
111D172—21no—
112D172SD3212yescomplemented
113C4×D43—41no—
114C4×D43—41no—
115C4×D43—84no—
116Dic86—22no—
117Dic86—41no—
118Dic86—84no—
119C8×C43—21no—
120C8×C43C2×D811yescharacteristic
121C8×C43AGL(1,ℤ/8)11yescharacteristic
122C43⋊C8—41no—
123C43⋊C8—81no—
124#12318—431nomaximal, Sylow
125C22×C43—161no—
126C22×C43—161no—
127C22×C43—161no—
128C22×C43#44711yescharacteristic
129C2×D43—22no—
130C2×D43—41no—
131C2×D43—41no—
132C4×C43—21no—
133C4×C43—82no—
134C4×C43#44711yescharacteristic
135C4×C43#45311yescharacteristic
136C4×C43C2×SD3211yescharacteristic
137C4×C43#51011yescharacteristic
138Dic43—42no—
139Dic43—41no—
140Dic43—81no—
141D4×Q16—431no—
142#2248D4311yescharacteristic, complemented
143#2207—431no—
144#1667—431no—
145#1362—431no—
146#1332—431no—
147D4⋊C16—431no—
148C2×C43—321no—
149C2×C43#161911yescharacteristic
150C2×C43#218511yescharacteristic
151C2×C43#219311yescharacteristic
152D43—42no—
153C22×Q16—861no—
154D4×Q8—861no—
155C2×SD32—22no—
156C2×SD32—861no—
157#494C2×D4311yescharacteristic
158#493C2×D4311yescharacteristic
159#467—861no—
160#462—861no—
161#459—861no—
162#451—862no—
163C4×Q16—431no—
164C8×D4—431no—
165C4⋊C16—431no—
166#357—861no—
167C4×C16C2×D4311yescharacteristic
168#335—431no—
169#331—861no—
170C43#1231811yescharacteristic, complemented, Sylow
171C22×Q8—862no—
172C2×Q16—21no—
173C2×Q16—431no—
174C2×Q16—862no—
175C2×Q16—1722no—
176C2×Q16—1722no—
177C2×Q16C22⋊D4312yes—
178C2×D8—21no—
179C2×D8—21no—
180C2×D8—1721no—
181C22×C8—861no—
182C4⋊Q8—21no—
183C4⋊Q8—1721no—
184#127—21no—
185C22⋊Q8—862no—
186C22⋊Q8—1722no—
187C4×Q8—861no—
188C4×D4—431no—
189C4×D4—1721no—
190SD32—44no—
191SD32—1722no—
192C2×C16—21no—
193C2×C16—861no—
194#107—431no—
195C4⋊C8—431no—
196C4⋊C8—861no—
197#103—862no—
198#103—861no—
199#102—1721no—
200C22⋊C8—861no—
201C4×C8C22×D4311yescharacteristic
202C2×Q8—22no—
203C2×Q8—861no—
204C2×Q8—3442no—
205C2×Q8—1722no—
206C2×Q8—1724no—
207C2×D4—41no—
208C2×D4—41no—
209C2×D4—41no—
210C2×D4—431no—
211C22×C4—861no—
212C22×C4—1722no—
213Q16—42no—
214Q16—41no—
215Q16—41no—
216Q16—432no—
217Q16—861no—
218Q16—1724no—
219D8—42no—
220D8—41no—
221D8—41no—
222D8—3442no—
223C2×C8—861no—
224C2×C8—1721no—
225C2×C8—1721no—
226C2×C8—1721no—
227C2×C8D4×D4311yescharacteristic
228C2×C8C2×C22⋊D4311yescharacteristic
229C4⋊C4—41no—
230C4⋊C4—41no—
231C4⋊C4—431no—
232C4⋊C4—861no—
233C4⋊C4—1722no—
234C4⋊C4—1721no—
235C22⋊C4—861no—
236C22⋊C4—1722no—
237C42—1721no—
238C42D4×D4311yescharacteristic
239C16—22no—
240C16—1721no—
241C23—81no—
242C23—861no—
243Q8—42no—
244Q8—42no—
245Q8—862no—
246Q8—3444no—
247Q8—1721no—
248D4—81no—
249D4—81no—
250D4—81no—
251D4—81no—
252D4—161no—
253D4—432no—
254D4—861no—
255C2×C4—42no—
256C2×C4—861no—
257C2×C4—3444no—
258C2×C4—1721no—
259C2×C4—1721no—
260C2×C4—1721no—
261C2×C4—1721no—
262C2×C4#1306329311yescharacteristic
263C2×C4D8×D4311yescharacteristic
264C2×C4#1306334911yescharacteristic
265C8—21no—
266C8—3441no—
267C8—1721no—
268C8D8×D4311yescharacteristic
269C8#1306334911yescharacteristic
270C22—161no—
271C22—161no—
272C22—161no—
273C22—862no—
274C22—1721no—
275C22—1721no—
276C22#1458303111yescharacteristic
277C4—21no—
278C4—82no—
279C4—3441no—
280C4—1721no—
281C4—1722no—
282C4#1458303111yescharacteristic
283C4#1458306611yescharacteristic
284C4SD32×D4311yescharacteristic
285C4#1458333811yescharacteristic
286C2—321no—
287C2—1722no—
288C2#1913364711yescharacteristic
289C2#1913651011yescharacteristic
290C2#1913655811yescharacteristic
subgroupG/H
centerC22#14583031
commutator, cosocleC4×C8×C43C23
FrattiniC4×C8C22×D43
FittingC43×#2248C2
socleC22×C43#447
prime radical#19133947C2
hypercenter#2248D43
hypocenterC43#12318
LCSG ▷ C4×C8×C43 ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #2248

Complements

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

NH ≅ G/Ntype
1. #19146345C2semidirect
2. #19136632C2semidirect
4. #19132644C2semidirect
5. #19132560C2semidirect
6. #19132551C2semidirect
7. C43×#2248C2semidirect
90. Dic172D8semidirect
112. D172SD32semidirect
142. #2248D43semidirect
170. C43#12318semidirect

Maximal subgroups

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

subgroupindex
#191463452
#191366322
#191339472
#191326442
#191325602
#191325512
C43×#22482
#1231843