Finite Group Databasebeta

← #25010789

Subgroups — #25010789

Order 11008.

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

normal subgroups only

This group has 256 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
1#19136640C211yesmaximal, characteristic, complemented
2#19136630C211yesmaximal, characteristic
3#19134201C211yesmaximal, characteristic, complemented
4#19132665C211yesmaximal, characteristic, complemented
5#19132643C211yesmaximal, characteristic, complemented
6#19132640C211yesmaximal, characteristic, complemented
7C8×D8×C43C211yesmaximal, characteristic, complemented
8C2×#13063269—21no—
9C2×#13063266—21no—
10#14583279C2211yescharacteristic
11#14583276C2211yescharacteristic
12#14583246—21no—
13#14583246—21no—
14C4⋊(C43⋊C16)C2211yescharacteristic
15C4⋊(C43⋊C16)C2211yescharacteristic
16#14582702—21no—
17#14582699—21no—
18C4×D8×C43C2211yescharacteristic
19C8×D4×C43—21no—
20C43×#335C2211yescharacteristic
21C43×D4⋊C8—21no—
22C82×C43C2211yescharacteristic
23C2×Dic172—21no—
24C2×Dic172—21no—
25C2×D344—21no—
26C2×D344—21no—
27#13063325—21no—
28#13063322—21no—
29#13063269—42no—
30#13063266—42no—
31C2×C43⋊C16—21no—
32C2×C43⋊C16—21no—
33#13063247—42no—
34#13063247—41no—
35#13063247—41no—
36C2×D8×C43D411yescharacteristic
37C22×C8×C43—41no—
38C4×D4×C43—21no—
39#107×C43D411yescharacteristic
40C4⋊C8×C43—21no—
41#102×C43—21no—
42C22⋊C8×C43—41no—
43C4×C8×C43D411yescharacteristic
44C4×C8×C43D411yescharacteristic
45C4×C8×C43C2311yescharacteristic
46C2×D4×C43—21no—
47C22×C4×C43—41no—
48C2×D172—41no—
49C2×D172—41no—
50C2×D172—41no—
51C2×Dic86—41no—
52D8×C43—21no—
53D8×C43D812yes—
54C2×C8×C43—21no—
55C2×C8×C43—41no—
56C2×C8×C43—82no—
57C2×C8×C43D811yescharacteristic
58C2×C8×C43D811yescharacteristic
59C2×C8×C43C2×D411yescharacteristic
60C2×C8×C43#4111yescharacteristic
61C4⋊C4×C43—21no—
62C22⋊C4×C43—41no—
63C42×C43C2×D411yescharacteristic
64C4⋊Dic43—41no—
65C4⋊Dic43—41no—
66Dic172—41no—
67Dic172—41no—
68Dic172—81no—
69D344—41no—
70D344—41no—
71D344—81no—
72C43⋊C16—41no—
73C43⋊C16—41no—
74C23×C43—41no—
75C22×D43—81no—
76D4×C43—22no—
77D4×C43—41no—
78C2×C4×C43—41no—
79C2×C4×C43—81no—
80C2×C4×C43—81no—
81C2×C4×C43#12111yescharacteristic
82C2×C4×C43C2×D811yescharacteristic
83C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
84C2×Dic43—81no—
85D172—82no—
86D172—81no—
87D172—81no—
88D172—81no—
89D172—81no—
90Dic86—81no—
91Dic86—81no—
92C8×C43—21no—
93C8×C43—21no—
94C8×C43—21no—
95C8×C43—41no—
96C8×C43—81no—
97C8×C43C2×D811yescharacteristic
98C8×C43#13511yescharacteristic
99#12428—431nomaximal, Sylow
100C22×C43—42no—
101C22×C43—81no—
102C22×C43—81no—
103C22×C43#45911yescharacteristic
104C2×D43—161no—
105C2×D43—161no—
106C2×D43—161no—
107C4×C43—21no—
108C4×C43—81no—
109C4×C43#46611yescharacteristic
110C4×C43#47211yescharacteristic
111C4×C43#50811yescharacteristic
112C4×C43#50911yescharacteristic
113Dic43—161no—
114#2208—431no—
115#2206—431no—
116#1709—431no—
117C8×D8D4311yescharacteristic, complemented
118#1370—431no—
119#1362—431no—
120#1361—431no—
121C2×C43—82no—
122C2×C43#166711yescharacteristic
123C2×C43#221011yescharacteristic
124C2×C43#221211yescharacteristic
125D43—321no—
126C2×SD32—861no—
127C2×D16—861no—
128#494—431no—
129#493—431no—
130#486—861no—
131#486—861no—
132C4×D8C2×D4311yescharacteristic
133C8×D4—21no—
134C4⋊C16—431no—
135C4⋊C16—431no—
136#358—861no—
137#357—861no—
138#335C2×D4311yescharacteristic
139D4⋊C8—21no—
140C82C2×D4311yescharacteristic
141C43#1242811yescharacteristic, complemented, Sylow
142C2×Q16—861no—
143C2×Q16—861no—
144C2×D8—861no—
145C2×D8—861no—
146C2×D8D17211yescharacteristic
147C22×C8—41no—
148C4⋊Q8—861no—
149#127—861no—
150C4×D4—21no—
151SD32—1722no—
152D16—1722no—
153C2×C16—861no—
154C2×C16—861no—
155#107D17211yescharacteristic
156C4⋊C8—21no—
157#102—21no—
158#102—1722no—
159#102—1721no—
160#102—1721no—
161C22⋊C8—41no—
162C4×C8C22⋊D4311yescharacteristic
163C4×C8C22⋊D4311yescharacteristic
164C4×C8C22×D4311yescharacteristic
165C2×Q8—1721no—
166C2×D4—21no—
167C2×D4—1721no—
168C2×D4—1721no—
169C2×D4—1721no—
170C22×C4—41no—
171Q16—3441no—
172Q16—1721no—
173Q16—1721no—
174D8—21no—
175D8—3441no—
176D8—1721no—
177D8—1721no—
178D8D34412yes—
179C2×C8—21no—
180C2×C8—41no—
181C2×C8—82no—
182C2×C8#1062188211yescharacteristic
183C2×C8#1062188211yescharacteristic
184C2×C8C2×D17211yescharacteristic
185C2×C8#1062189811yescharacteristic
186C4⋊C4—21no—
187C4⋊C4—1721no—
188C4⋊C4—1721no—
189C22⋊C4—41no—
190C42C2×C22⋊D4311yescharacteristic
191C16—1721no—
192C16—1721no—
193C23—41no—
194C23—3441no—
195Q8—3441no—
196Q8—3441no—
197D4—22no—
198D4—41no—
199D4—3442no—
200D4—3441no—
201D4—3441no—
202D4—3441no—
203D4—3441no—
204C2×C4—41no—
205C2×C4—81no—
206C2×C4—81no—
207C2×C4—3441no—
208C2×C4#1306329911yescharacteristic
209C2×C4C2×#1062188211yescharacteristic
210C2×C4#1306335011yescharacteristic
211C8—21no—
212C8—21no—
213C8—21no—
214C8—41no—
215C8—81no—
216C8C2×D34411yescharacteristic
217C8#1306334711yescharacteristic
218C22—42no—
219C22—81no—
220C22—81no—
221C22—6881no—
222C22—6881no—
223C22—6881no—
224C22#1458309411yescharacteristic
225C4—21no—
226C4—81no—
227C4—6881no—
228C4#1458313511yescharacteristic
229C4#1458316911yescharacteristic
230C4#1458332911yescharacteristic
231C4#1458333511yescharacteristic
232C2—82no—
233C2—13761no—
234C2#1913395011yescharacteristic
235C2#1913665011yescharacteristic
236C2#1913666411yescharacteristic
subgroupG/H
centerC22#14583094
commutator, cosocleC4×C8×C43C23
FrattiniC4×C8C22×D43
FittingC8×D8×C43C2
socleC22×C43#459
prime radical#19136630C2
hypercenterC8×D8D43
hypocenterC43#12428
LCSG ▷ C4×C8×C43 ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ C82 ◁ C8×D8

Complements

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

NH ≅ G/Ntype
1. #19136640C2semidirect
3. #19134201C2semidirect
4. #19132665C2semidirect
5. #19132643C2semidirect
6. #19132640C2semidirect
7. C8×D8×C43C2semidirect
117. C8×D8D43semidirect
141. C43#12428semidirect

Maximal subgroups

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

subgroupindex
#191366402
#191366302
#191342012
#191326652
#191326432
#191326402
C8×D8×C432
#1242843