Finite Group Databasebeta

← #25010155

Subgroups — #25010155

Order 11008.

312 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 312 conjugacy classes of subgroups — too many to draw. Only its 65 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#19147585C211yesmaximal, characteristic
2#19136847C211yesmaximal, characteristic, complemented
3#19136641C211yesmaximal, characteristic
4#19133966C211yesmaximal, characteristic, complemented
5#19132573C211yesmaximal, characteristic, complemented
6#19132555C211yesmaximal, characteristic
7C43×#1362C211yesmaximal, characteristic, complemented
8#14583623—21no—
9C2×#13063271—22no—
10C2×#13063270—21no—
11#14583284—21no—
12#14583279C2211yescharacteristic
13#14583185—21no—
14#14583123—22no—
15#14583101—21no—
16C8×Dic86C2211yescharacteristic
17Q16×Dic43—21no—
18C4×D344C2211yescharacteristic
19#14582704—21no—
20C4×C43⋊C16C2211yescharacteristic
21#14582644—21no—
22C43×#494C2211yescharacteristic
23C43×C4⋊C16C2211yescharacteristic
24C43×#335C2211yescharacteristic
25C2×Dic172—21no—
26C2×Dic172—21no—
27C2×#10621884—22no—
28C2×D344D411yescharacteristic
29#13063325—21no—
30#13063320—42no—
31#13063314—22no—
32#13063305—41no—
33Q8×Dic43—22no—
34C4×Dic86D411yescharacteristic
35C4×D172—21no—
36#13063283—41no—
37#13063271—44no—
38#13063270—42no—
39C2×C43⋊C16—21no—
40#13063259D411yescharacteristic
41#13063257—41no—
42C4⋊(C43⋊C8)D411yescharacteristic
43Dic43⋊C8—21no—
44#13063250—41no—
45#13063249—22no—
46#13063247—21no—
47C8×Dic43—21no—
48C2×Q16×C43—21no—
49C2×Q16×C43D412yes—
50C4⋊Q8×C43—21no—
51C2×C16×C43—21no—
52C4⋊C8×C43—21no—
53C4×C8×C43C2311yescharacteristic
54C2×Q8×C43—22no—
55C2×D172—21no—
56C2×C4×D43—41no—
57C2×Dic86—41no—
58C2×Dic86D811yescharacteristic
59Q16×C43—42no—
60Q16×C43—41no—
61Q16×C43—41no—
62C2×C8×C43—41no—
63C2×C8×C43C2×D411yescharacteristic
64C2×C8×C43C2×D411yescharacteristic
65C4⋊C4×C43—41no—
66C4⋊C4×C43—41no—
67C42×C43C2×D411yescharacteristic
68#10621884—82no—
69(C2×D43)⋊C4—42no—
70(C2×D43)⋊C4—42no—
71(C2×D43)⋊C4—41no—
72C4⋊Dic43—21no—
73C4⋊Dic43—42no—
74C4⋊Dic43—41no—
75C4⋊Dic43—41no—
76C4⋊Dic43D811yescharacteristic
77Dic43⋊C4—21no—
78C4×Dic43—21no—
79C4×Dic43—42no—
80C2×C43⋊C8—21no—
81Dic172—42no—
82Dic172—41no—
83Dic172—41no—
84D344—21no—
85D344—21no—
86C16×C43—41no—
87C43⋊C16—22no—
88C22×D43—41no—
89Q8×C43—42no—
90Q8×C43—42no—
91C2×C4×C43—42no—
92C2×C4×C43#12011yescharacteristic
93C2×C4×C43C2×D811yescharacteristic
94C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
95C2×Dic43—21no—
96C2×Dic43—21no—
97C2×Dic43—41no—
98C2×Dic43—81no—
99D172—41no—
100D172—41no—
101C4×D43—81no—
102C4×D43—81no—
103Dic86—21no—
104Dic86—21no—
105Dic86—81no—
106Dic86—81no—
107C8×C43—21no—
108C8×C43—81no—
109C8×C43#13511yescharacteristic
110C8×C43AGL(1,ℤ/8)11yescharacteristic
111C43⋊C8—41no—
112#12335—431nomaximal, Sylow
113C22×C43#44711yescharacteristic
114C2×D43—81no—
115C2×D43—81no—
116C2×D43—81no—
117C4×C43—21no—
118C4×C43—82no—
119C4×C43#44911yescharacteristic
120C4×C43#45311yescharacteristic
121C4×C43#50811yescharacteristic
122C4×C43#51011yescharacteristic
123Dic43—41no—
124Dic43—41no—
125Dic43—81no—
126Dic43—161no—
127#3393—431no—
128#2247—431no—
129#2208—431no—
130#1670—431no—
131#1362D4311yescharacteristic, complemented
132Q8⋊C16—431no—
133#1331—431no—
134C2×C43#162111yescharacteristic
135C2×C43#218911yescharacteristic
136C2×C43#219511yescharacteristic
137D43—161no—
138#556—861no—
139C2×Q32—862no—
140C2×SD32—861no—
141#495—861no—
142#494—431no—
143#494C2×D4311yescharacteristic
144#475—861no—
145#464—862no—
146#461—861no—
147C8×Q8—431no—
148C4×Q16—861no—
149C4×D8—431no—
150C4⋊C16C2×D4311yescharacteristic
151#358—861no—
152C4×C16—431no—
153#335C2×D4311yescharacteristic
154#332—861no—
155C43#1233511yescharacteristic, complemented, Sylow
156C2×Q16—21no—
157C2×Q16—861no—
158C2×Q16—861no—
159C2×Q16D17212yes—
160C2×SD16—862no—
161C2×D8—431no—
162C4⋊Q8—21no—
163C4⋊Q8—861no—
164#126—1722no—
165#124—862no—
166C22⋊Q8—1721no—
167C4×Q8—431no—
168C4×Q8—862no—
169C4×D4—861no—
170#117—1721no—
171Q32—1724no—
172SD32—1722no—
173C2×C16—21no—
174C2×C16—861no—
175#107—431no—
176#106—1721no—
177C4⋊C8—21no—
178C4⋊C8—431no—
179C4⋊C8—861no—
180#103—862no—
181#103—1721no—
182#102—861no—
183C4×C8—861no—
184C4×C8C22×D4311yescharacteristic
185C2×Q8—22no—
186C2×Q8—431no—
187C2×Q8—1721no—
188C2×D4—861no—
189C22×C4—1721no—
190Q16—42no—
191Q16—41no—
192Q16—41no—
193Q16—1722no—
194Q16—1721no—
195Q16—1721no—
196SD16—3442no—
197D8—861no—
198D8—861no—
199C2×C8—41no—
200C2×C8—861no—
201C2×C8C2×D17211yescharacteristic
202C2×C8D4×D4311yescharacteristic
203C4⋊C4—41no—
204C4⋊C4—41no—
205C4⋊C4—431no—
206C4⋊C4—861no—
207C4⋊C4—861no—
208C4⋊C4—1722no—
209C4⋊C4—1721no—
210C4⋊C4—1721no—
211C22⋊C4—1722no—
212C22⋊C4—1722no—
213C22⋊C4—1721no—
214C42—861no—
215C42—1722no—
216C42D4×D4311yescharacteristic
217C16—41no—
218C16—862no—
219C23—1721no—
220Q8—42no—
221Q8—42no—
222Q8—861no—
223Q8—861no—
224Q8—3441no—
225Q8—3441no—
226D4—1721no—
227D4—1721no—
228C2×C4—42no—
229C2×C4—861no—
230C2×C4—861no—
231C2×C4—3441no—
232C2×C4—3441no—
233C2×C4—3441no—
234C2×C4—1721no—
235C2×C4#1306329511yescharacteristic
236C2×C4D8×D4311yescharacteristic
237C2×C4#1306335211yescharacteristic
238C8—21no—
239C8—81no—
240C8—1721no—
241C8#1306334611yescharacteristic
242C8#1306334911yescharacteristic
243C22—3441no—
244C22—3441no—
245C22—3441no—
246C22#1458303411yescharacteristic
247C4—21no—
248C4—82no—
249C4—3441no—
250C4—1721no—
251C4—1721no—
252C4—6881no—
253C4#1458304511yescharacteristic
254C4#1458306911yescharacteristic
255C4#1458333011yescharacteristic
256C4#1458334111yescharacteristic
257C2—6881no—
258C2#1913366111yescharacteristic
259C2#1913653811yescharacteristic
260C2#1913657611yescharacteristic
subgroupG/H
centerC22#14583034
commutator, cosocleC4×C8×C43C23
FrattiniC4×C8C22×D43
FittingC43×#1362C2
socleC22×C43#447
prime radicalC2×D344D4
hypercenter#1362D43
hypocenterC43#12335
LCSG ▷ C4×C8×C43 ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #1362

Complements

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

NH ≅ G/Ntype
2. #19136847C2semidirect
4. #19133966C2semidirect
5. #19132573C2semidirect
7. C43×#1362C2semidirect
131. #1362D43semidirect
155. C43#12335semidirect

Maximal subgroups

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

subgroupindex
#191475852
#191368472
#191366412
#191339662
#191325732
#191325552
C43×#13622
#1233543