Finite Group Databasebeta

← #25010034

Subgroups — #25010034

Order 11008.

384 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 384 conjugacy classes of subgroups — too many to draw. Only its 71 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
1Q16×D172C211yesmaximal, characteristic, complemented
2#19136850C211yesmaximal, characteristic, complemented
3#19133947C211yesmaximal, characteristic
4#19132645C211yesmaximal, characteristic, complemented
5#19132559C211yesmaximal, characteristic, complemented
6#19132549C211yesmaximal, characteristic, complemented
7C43×#2207C211yesmaximal, characteristic, complemented
8C2×Q16×D43—21no—
9Q8×D172—21no—
10C2×#13063269—22no—
11#14583279C2211yescharacteristic
12#14583141—21no—
13#14583109—21no—
14#14583091—21no—
15#14583056—22no—
16C8×D172C2211yescharacteristic
17C4×C43⋊C16C2211yescharacteristic
18#14582652C2211yescharacteristic
19#14582643—21no—
20C2×SD32×C43—21no—
21C43×#493C2211yescharacteristic
22C4×Q16×C43C2211yescharacteristic
23C43×C4⋊C16C2211yescharacteristic
24C43×#357—21no—
25C2×Q8×D43—22no—
26C2×Dic172—21no—
27C2×Dic172D412yes—
28C2×#10621885—22no—
29Q16×D43—42no—
30Q16×D43—42no—
31C2×#10621882—41no—
32C2×C8×D43—21no—
33#13063325—21no—
34#13063325—41no—
35#13063305—22no—
36#13063305—42no—
37C4×D172—41no—
38C4×D172D411yescharacteristic
39#13063269—44no—
40C2×C43⋊C16—21no—
41C4⋊(C43⋊C8)—21no—
42C4⋊(C43⋊C8)D411yescharacteristic
43#13063248—22no—
44#13063246—41no—
45(C2×D43)⋊C8—21no—
46C2×Q16×C43D411yescharacteristic
47C2×D8×C43—21no—
48C2×D8×C43—21no—
49#127×C43—21no—
50C4×Q8×C43—21no—
51SD32×C43—42no—
52C2×C16×C43—21no—
53#107×C43D411yescharacteristic
54#103×C43—21no—
55C4×C8×C43C2311yescharacteristic
56C2×Q8×C43—21no—
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—22no—
66C2×Dic86—42no—
67Q16×C43—21no—
68Q16×C43D812yescomplemented
69D8×C43—42no—
70D8×C43—41no—
71D8×C43—41no—
72C2×C8×C43C2×D411yescharacteristic
73C2×C8×C43C2×D411yescharacteristic
74C4⋊C4×C43—21no—
75C4⋊C4×C43—41no—
76C42×C43—41no—
77C42×C43C2×D411yescharacteristic
78#10621885—44no—
79#10621882—82no—
80(C2×D43)⋊C4—21no—
81(C2×D43)⋊C4—42no—
82C4⋊Dic43—42no—
83C4⋊Dic43—41no—
84C4⋊Dic43—41no—
85C4⋊Dic43D811yescharacteristic
86C2×C43⋊C8—21no—
87C2×C43⋊C8—41no—
88Dic172—42no—
89Dic172—41no—
90Dic172—41no—
91C8×D43—41no—
92C8×D43—41no—
93C16×C43—41no—
94C43⋊C16—22no—
95C23×C43—81no—
96C22×D43—21no—
97Q8×C43—22no—
98Q8×C43—41no—
99D4×C43—81no—
100D4×C43—81no—
101D4×C43—81no—
102D4×C43—81no—
103D4×C43—161no—
104C2×C4×C43—41no—
105C2×C4×C43—41no—
106C2×C4×C43#12011yescharacteristic
107C2×C4×C43C2×D811yescharacteristic
108C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
109C2×Dic43—21no—
110C2×Dic43—42no—
111D172—21no—
112D172SD3212yescomplemented
113C4×D43—41no—
114C4×D43—41no—
115C4×D43—84no—
116Dic86—42no—
117Dic86—42no—
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—42no—
134C4×C43—81no—
135C4×C43#44711yescharacteristic
136C4×C43#45311yescharacteristic
137C4×C43C2×SD3211yescharacteristic
138C4×C43#51011yescharacteristic
139Dic43—41no—
140Dic43—82no—
141D4×Q16—431no—
142#2248—431no—
143#2207D4311yescharacteristic, complemented
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—21no—
156C2×SD32—862no—
157#494—431no—
158#493C2×D4311yescharacteristic
159#467—861no—
160#462—861no—
161#459—861no—
162#451—862no—
163C4×Q16C2×D4311yescharacteristic
164C8×D4—431no—
165C4⋊C16C2×D4311yescharacteristic
166#357—21no—
167C4×C16—431no—
168#335—431no—
169#331—861no—
170C43#1231811yescharacteristic, complemented, Sylow
171C22×Q8—862no—
172C2×Q16—432no—
173C2×Q16—862no—
174C2×Q16—861no—
175C2×Q16—1722no—
176C2×Q16—1722no—
177C2×Q16C22⋊D4311yescharacteristic
178C2×D8—21no—
179C2×D8—21no—
180C2×D8—1721no—
181C22×C8—861no—
182C4⋊Q8—861no—
183C4⋊Q8—1721no—
184#127—21no—
185C22⋊Q8—862no—
186C22⋊Q8—1722no—
187C4×Q8—21no—
188C4×D4—431no—
189C4×D4—1721no—
190SD32—42no—
191SD32—1724no—
192C2×C16—21no—
193C2×C16—861no—
194#107C22⋊D4311yescharacteristic
195C4⋊C8—431no—
196C4⋊C8—861no—
197#103—21no—
198#103—862no—
199#102—1721no—
200C22⋊C8—861no—
201C4×C8C22×D4311yescharacteristic
202C2×Q8—21no—
203C2×Q8—862no—
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—21no—
214Q16—1722no—
215Q16—1724no—
216Q16—1721no—
217Q16—1721no—
218Q16#1062188212yescomplemented
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—21no—
230C4⋊C4—41no—
231C4⋊C4—431no—
232C4⋊C4—1722no—
233C4⋊C4—1721no—
234C4⋊C4—1721no—
235C22⋊C4—861no—
236C22⋊C4—1722no—
237C42—41no—
238C42D4×D4311yescharacteristic
239C16—41no—
240C16—862no—
241C23—81no—
242C23—861no—
243Q8—22no—
244Q8—41no—
245Q8—3444no—
246Q8—1722no—
247Q8—1722no—
248D4—81no—
249D4—81no—
250D4—81no—
251D4—81no—
252D4—161no—
253D4—432no—
254D4—861no—
255C2×C4—41no—
256C2×C4—41no—
257C2×C4—861no—
258C2×C4—3444no—
259C2×C4—1722no—
260C2×C4—1721no—
261C2×C4—1721no—
262C2×C4#1306329311yescharacteristic
263C2×C4D8×D4311yescharacteristic
264C2×C4#1306334911yescharacteristic
265C8—21no—
266C8—3441no—
267C8—1721no—
268C8C2×#1062188211yescharacteristic
269C8#1306335011yescharacteristic
270C22—161no—
271C22—161no—
272C22—161no—
273C22—862no—
274C22—1721no—
275C22—1721no—
276C22#1458303111yescharacteristic
277C4—21no—
278C4—42no—
279C4—81no—
280C4—3442no—
281C4—1721no—
282C4#1458303211yescharacteristic
283C4#1458306511yescharacteristic
284C4SD32×D4311yescharacteristic
285C4#1458333811yescharacteristic
286C2—321no—
287C2—1722no—
288C2#1913364811yescharacteristic
289C2#1913651011yescharacteristic
290C2#1913655611yescharacteristic
subgroupG/H
centerC22#14583031
commutator, cosocleC4×C8×C43C23
FrattiniC4×C8C22×D43
FittingC43×#2207C2
socleC22×C43#447
prime radical#19133947C2
hypercenter#2207D43
hypocenterC43#12318
LCSG ▷ C4×C8×C43 ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #2207

Complements

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

NH ≅ G/Ntype
1. Q16×D172C2semidirect
2. #19136850C2semidirect
4. #19132645C2semidirect
5. #19132559C2semidirect
6. #19132549C2semidirect
7. C43×#2207C2semidirect
68. Q16×C43D8semidirect
112. D172SD32semidirect
143. #2207D43semidirect
170. C43#12318semidirect
218. Q16#10621882semidirect

Maximal subgroups

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

subgroupindex
Q16×D1722
#191368502
#191339472
#191326452
#191325592
#191325492
C43×#22072
#1231843