Finite Group Databasebeta

← #25010293

Subgroups — #25010293

Order 11008.

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

normal subgroups only

This group has 312 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#19147460C211yesmaximal, characteristic, complemented
2#19136818C211yesmaximal, characteristic, complemented
3#19133952C211yesmaximal, characteristic, complemented
4#19132652C211yesmaximal, characteristic, complemented
5#19132573C211yesmaximal, characteristic, complemented
6#19132556C211yesmaximal, characteristic, complemented
7C43×#2206C211yesmaximal, characteristic
8#14583606—21no—
9#14583304C2211yescharacteristic
10#14583300—21no—
11#14583197—22no—
12#14583189—21no—
13#14583096—21no—
14C8×Dic86C2211yescharacteristic
15D8×Dic43—21no—
16#14582700—22no—
17C4×C43⋊C16C2211yescharacteristic
18#14582652C2211yescharacteristic
19#14582643—21no—
20C2×D16×C43—21no—
21C43×#493C2211yescharacteristic
22C4×D8×C43C2211yescharacteristic
23C43×C4⋊C16C2211yescharacteristic
24C43×#357—21no—
25C2×#10621883—41no—
26#13063325—21no—
27#13063316—22no—
28#13063304—41no—
29#13063302—42no—
30C4×Dic86D411yescharacteristic
31D4×Dic43—22no—
32C2×C4⋊Dic43—41no—
33C2×C43⋊C16—21no—
34#13063259—21no—
35#13063259D412yes—
36#13063256—22no—
37C4⋊(C43⋊C8)—21no—
38C4⋊(C43⋊C8)D411yescharacteristic
39Dic43⋊C8—21no—
40#13063246—22no—
41#13063246—41no—
42C8×Dic43—21no—
43C2×D8×C43—21no—
44C2×D8×C43—21no—
45C2×D8×C43D411yescharacteristic
46#127×C43—21no—
47C4×D4×C43—21no—
48D16×C43—42no—
49C2×C16×C43—21no—
50#107×C43D411yescharacteristic
51#102×C43—21no—
52C4×C8×C43C2311yescharacteristic
53C2×D4×C43—21no—
54C2×D4×C43—41no—
55C2×D4×C43—41no—
56C2×D4×C43—41no—
57C22×C4×C43—41no—
58C22×Dic43—42no—
59C2×Dic86—41no—
60C2×Dic86D811yescharacteristic
61D8×C43—21no—
62D8×C43—42no—
63D8×C43—41no—
64D8×C43—41no—
65D8×C43SD1612yescomplemented
66C2×C8×C43C2×D411yescharacteristic
67C2×C8×C43C2×D411yescharacteristic
68C4⋊C4×C43—21no—
69C22⋊C4×C43—41no—
70C42×C43C2×D411yescharacteristic
71C22⋊Dic43—42no—
72#10621883—82no—
73C4⋊Dic43—22no—
74C4⋊Dic43—42no—
75C4⋊Dic43—41no—
76C4⋊Dic43D811yescharacteristic
77Dic43⋊C4—21no—
78Dic43⋊C4—42no—
79C4×Dic43—21no—
80C2×C43⋊C8—21no—
81C2×C43⋊C8—41no—
82C16×C43—41no—
83C43⋊C16—41no—
84C23×C43—41no—
85C23×C43—81no—
86D4×C43—22no—
87D4×C43—41no—
88D4×C43—81no—
89D4×C43—81no—
90D4×C43—81no—
91D4×C43—81no—
92D4×C43—161no—
93C2×C4×C43—41no—
94C2×C4×C43—81no—
95C2×C4×C43—81no—
96C2×C4×C43#12011yescharacteristic
97C2×C4×C43C2×D811yescharacteristic
98C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
99C2×Dic43—21no—
100C2×Dic43—21no—
101C2×Dic43—42no—
102C2×Dic43—162no—
103Dic86—21no—
104Dic86—21no—
105Dic86—161no—
106C8×C43—21no—
107C8×C43C2×SD1611yescharacteristic
108C8×C43#13711yescharacteristic
109C43⋊C8—41no—
110C43⋊C8—81no—
111#12355—431nomaximal, Sylow
112C22×C43—42no—
113C22×C43—81no—
114C22×C43—81no—
115C22×C43—161no—
116C22×C43—161no—
117C22×C43—161no—
118C22×C43#44711yescharacteristic
119C4×C43—21no—
120C4×C43—81no—
121C4×C43#44811yescharacteristic
122C4×C43#45411yescharacteristic
123C4×C43#50811yescharacteristic
124C4×C43#50911yescharacteristic
125Dic43—41no—
126Dic43—41no—
127Dic43—82no—
128#3380—431no—
129#2240—431no—
130#2206D4311yescharacteristic
131#1668—431no—
132#1365—431no—
133Q8⋊C16—431no—
134#1331—431no—
135C2×C43—82no—
136C2×C43—321no—
137C2×C43#162711yescharacteristic
138C2×C43#218611yescharacteristic
139C2×C43#219211yescharacteristic
140#554—861no—
141C2×D16—21no—
142#500—431no—
143#499—861no—
144#493C2×D4311yescharacteristic
145#478—862no—
146#476—861no—
147#460—861no—
148C8×Q8—431no—
149C4×D8—861no—
150C4×D8C2×D4311yescharacteristic
151C4⋊C16C2×D4311yescharacteristic
152#357—21no—
153#357—862no—
154C4×C16—431no—
155#335—431no—
156#331—861no—
157C43#1235511yescharacteristic, complemented, Sylow
158C2×SD16—1721no—
159C2×D8—21no—
160C2×D8—21no—
161C2×D8C22⋊D4311yescharacteristic
162C4⋊Q8—861no—
163#127—21no—
164#125—862no—
165C22⋊Q8—1722no—
166C22⋊Q8—1721no—
167C4×Q8—431no—
168C4×D4—21no—
169C4×D4—862no—
170C2×C4⋊C4—1721no—
171D16—42no—
172C2×C16—21no—
173C2×C16—861no—
174#107—432no—
175#107—861no—
176#107C22⋊D4311yescharacteristic
177#106—862no—
178C4⋊C8—431no—
179C4⋊C8—861no—
180C4⋊C8—861no—
181#102—21no—
182#102—862no—
183#102—1721no—
184C4×C8—861no—
185C4×C8C22×D4311yescharacteristic
186C2×Q8—431no—
187C2×Q8—1721no—
188C2×D4—21no—
189C2×D4—41no—
190C2×D4—41no—
191C2×D4—41no—
192C22×C4—41no—
193C22×C4—1722no—
194SD16—3442no—
195D8—21no—
196D8—42no—
197D8—41no—
198D8—41no—
199D8#1062188312yescomplemented
200C2×C8—861no—
201C2×C8—1721no—
202C2×C8D4×D4311yescharacteristic
203C2×C8C2×C22⋊D4311yescharacteristic
204C4⋊C4—21no—
205C4⋊C4—431no—
206C4⋊C4—861no—
207C4⋊C4—862no—
208C4⋊C4—1722no—
209C4⋊C4—1722no—
210C4⋊C4—1721no—
211C22⋊C4—41no—
212C22⋊C4—1722no—
213C42—861no—
214C42D4×D4311yescharacteristic
215C16—41no—
216C16—1721no—
217C23—41no—
218C23—81no—
219Q8—861no—
220Q8—861no—
221Q8—6881no—
222D4—22no—
223D4—41no—
224D4—81no—
225D4—81no—
226D4—81no—
227D4—81no—
228D4—161no—
229C2×C4—41no—
230C2×C4—81no—
231C2×C4—81no—
232C2×C4—861no—
233C2×C4—861no—
234C2×C4—1722no—
235C2×C4—6882no—
236C2×C4#1306329311yescharacteristic
237C2×C4D8×D4311yescharacteristic
238C2×C4#1306334911yescharacteristic
239C8—21no—
240C8—3441no—
241C8—1721no—
242C8C2×#1062188311yescharacteristic
243C8#1306335511yescharacteristic
244C22—42no—
245C22—81no—
246C22—81no—
247C22—161no—
248C22—161no—
249C22—161no—
250C22#1458303111yescharacteristic
251C4—21no—
252C4—81no—
253C4—3442no—
254C4—1721no—
255C4—1721no—
256C4#1458303711yescharacteristic
257C4#1458307011yescharacteristic
258C4#1458332811yescharacteristic
259C4#1458333311yescharacteristic
260C2—82no—
261C2—321no—
262C2#1913369711yescharacteristic
263C2#1913651511yescharacteristic
264C2#1913654911yescharacteristic
subgroupG/H
centerC22#14583031
commutator, cosocleC4×C8×C43C23
FrattiniC4×C8C22×D43
Fitting, prime radicalC43×#2206C2
socleC22×C43#447
hypercenter#2206D43
hypocenterC43#12355
LCSG ▷ C4×C8×C43 ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #2206

Complements

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

NH ≅ G/Ntype
1. #19147460C2semidirect
2. #19136818C2semidirect
3. #19133952C2semidirect
4. #19132652C2semidirect
5. #19132573C2semidirect
6. #19132556C2semidirect
65. D8×C43SD16semidirect
157. C43#12355semidirect
199. D8#10621883semidirect

Maximal subgroups

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

subgroupindex
#191474602
#191368182
#191339522
#191326522
#191325732
#191325562
C43×#22062
#1235543