Finite Group Databasebeta

← #25010807

Subgroups — #25010807

Order 11008.

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

normal subgroups only

This group has 236 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#19136847C211yesmaximal, characteristic, complemented
2#19136414C211yesmaximal, characteristic
3#19133961C211yesmaximal, characteristic
4#19133957C211yesmaximal, characteristic
5#19132666C211yesmaximal, characteristic, complemented
6#19132645C211yesmaximal, characteristic, complemented
7C43×#1362C211yesmaximal, characteristic, complemented
8C2×#13063271—21no—
9C2×#13063271—21no—
10C2×C16×D43—21no—
11#14583279C2211yescharacteristic
12#14583180—21no—
13#14583176—21no—
14C8×D172C2211yescharacteristic
15(C2×D43)⋊C16—21no—
16C4×C43⋊C16C2211yescharacteristic
17#14582652C2211yescharacteristic
18#14582645—21no—
19#14582644—21no—
20C43×#494C2211yescharacteristic
21C43×C4⋊C16C2211yescharacteristic
22C43×#335C2211yescharacteristic
23C2×Dic172—21no—
24C2×Dic172—21no—
25C2×C8×D43—21no—
26#13063325—21no—
27C4×D172D411yescharacteristic
28#13063271—42no—
29#13063271—42no—
30C2×C43⋊C16D411yescharacteristic
31C2×C43⋊C16D411yescharacteristic
32C16×D43—42no—
33#13063259—41no—
34#13063258—41no—
35C4⋊(C43⋊C8)—21no—
36C4⋊(C43⋊C8)D411yescharacteristic
37#13063247—41no—
38#13063245—41no—
39(C2×D43)⋊C8—21no—
40C2×Q16×C43—21no—
41C2×Q16×C43—21no—
42C4⋊Q8×C43—21no—
43C2×C16×C43—21no—
44C4⋊C8×C43—21no—
45C4×C8×C43C2311yescharacteristic
46C2×Q8×C43—41no—
47C2×D172D811yescharacteristic
48C2×C4×D43—21no—
49C2×Dic86—41no—
50Q16×C43—41no—
51Q16×C43—41no—
52Q16×C43—81no—
53C2×C8×C43—41no—
54C2×C8×C43C2×D411yescharacteristic
55C2×C8×C43#4111yescharacteristic
56C4⋊C4×C43—41no—
57C4⋊C4×C43—41no—
58C42×C43C2×D411yescharacteristic
59(C2×D43)⋊C4—21no—
60C4⋊Dic43—41no—
61C4⋊Dic43—41no—
62C4⋊Dic43D811yescharacteristic
63C2×C43⋊C8—21no—
64C2×C43⋊C8—41no—
65Dic172—41no—
66Dic172—41no—
67Dic172—81no—
68C8×D43—41no—
69C8×D43—41no—
70C16×C43—41no—
71C43⋊C16—21no—
72C43⋊C16D812yes—
73C22×D43—21no—
74Q8×C43—81no—
75Q8×C43—81no—
76C2×C4×C43—81no—
77C2×C4×C43#12111yescharacteristic
78C2×C4×C43C2×D811yescharacteristic
79C2×C4×C43#13511yescharacteristic
80C2×Dic43—21no—
81C2×Dic43—81no—
82D172—21no—
83D172Q3212yescomplemented
84C4×D43—41no—
85C4×D43—41no—
86Dic86—81no—
87Dic86—81no—
88C8×C43—21no—
89C8×C43—81no—
90C8×C43C2×D811yescharacteristic
91C8×C43AGL(1,ℤ/8)11yescharacteristic
92C43⋊C8—41no—
93C43⋊C8—81no—
94#12431—431nomaximal, Sylow
95C22×C43#46611yescharacteristic
96C2×D43—22no—
97C2×D43—41no—
98C2×D43—41no—
99C4×C43—21no—
100C4×C43—161no—
101C4×C43#45911yescharacteristic
102C4×C43#47211yescharacteristic
103C4×C43C2×Q3211yescharacteristic
104C4×C43#50811yescharacteristic
105Dic43—41no—
106Dic43—161no—
107#2247—431no—
108D4×C16—431no—
109#1669—431no—
110#1669—431no—
111#1371—431no—
112#1362—431no—
113#1362D4311yescharacteristic, complemented
114C2×C43#166711yescharacteristic
115C2×C43#221611yescharacteristic
116C2×C43#222211yescharacteristic
117D43—42no—
118C2×Q32—861no—
119C2×Q32—861no—
120C22×C16—861no—
121#494—431no—
122#494C2×D4311yescharacteristic
123#474—861no—
124#474—861no—
125C8×D4—431no—
126C4⋊C16C2×D4311yescharacteristic
127C22⋊C16—861no—
128C4×C16—431no—
129#335—431no—
130#335C2×D4311yescharacteristic
131#332—861no—
132#332—861no—
133C43#1243111yescharacteristic, complemented, Sylow
134C2×Q16—21no—
135C2×Q16—21no—
136C2×Q16—861no—
137C2×Q16—861no—
138C22×C8—861no—
139C4⋊Q8—21no—
140C4⋊Q8—861no—
141C4×D4—431no—
142Q32—1722no—
143Q32—1722no—
144C2×C16—21no—
145C2×C16—431no—
146C2×C16—431no—
147C2×C16—1722no—
148#107—1721no—
149#107—1721no—
150C4⋊C8—21no—
151C4⋊C8—431no—
152C4⋊C8—861no—
153#102—1721no—
154#102—1721no—
155C22⋊C8—861no—
156C4×C8C22×D4311yescharacteristic
157C2×Q8—41no—
158C2×Q8—1721no—
159C2×D4—431no—
160C22×C4—861no—
161Q16—41no—
162Q16—41no—
163Q16—81no—
164Q16—3441no—
165Q16—1721no—
166Q16—1721no—
167C2×C8—41no—
168C2×C8—861no—
169C2×C8—1721no—
170C2×C8—1721no—
171C2×C8—1721no—
172C2×C8#1062189811yescharacteristic
173C2×C8D4×D4311yescharacteristic
174C4⋊C4—41no—
175C4⋊C4—41no—
176C4⋊C4—431no—
177C4⋊C4—1721no—
178C4⋊C4—1721no—
179C22⋊C4—861no—
180C42D4×D4311yescharacteristic
181C16—41no—
182C16—432no—
183C16—861no—
184C23—861no—
185Q8—81no—
186Q8—81no—
187Q8—3441no—
188Q8—3441no—
189D4—432no—
190D4—861no—
191C2×C4—81no—
192C2×C4—861no—
193C2×C4—3441no—
194C2×C4—1721no—
195C2×C4—1721no—
196C2×C4#1306329811yescharacteristic
197C2×C4D8×D4311yescharacteristic
198C2×C4#1306334611yescharacteristic
199C8—21no—
200C8—81no—
201C8—3441no—
202C8—1721no—
203C8D8×D4311yescharacteristic
204C8#1306335211yescharacteristic
205C22—862no—
206C22—1721no—
207C22—1721no—
208C22#1458313411yescharacteristic
209C4—21no—
210C4—161no—
211C4—1721no—
212C4—6881no—
213C4#1458309311yescharacteristic
214C4#1458316811yescharacteristic
215C4Q32×D4311yescharacteristic
216C4#1458333011yescharacteristic
217C2—1722no—
218C2#1913394911yescharacteristic
219C2#1913668511yescharacteristic
220C2#1913671911yescharacteristic
subgroupG/H
centerC22#14583134
commutator, cosocleC4×C8×C43C23
FrattiniC4×C8C22×D43
FittingC43×#1362C2
socleC22×C43#466
prime radicalC2×D172D8
hypercenter#1362D43
hypocenterC43#12431
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
1. #19136847C2semidirect
5. #19132666C2semidirect
6. #19132645C2semidirect
7. C43×#1362C2semidirect
83. D172Q32semidirect
113. #1362D43semidirect
133. C43#12431semidirect

Maximal subgroups

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

subgroupindex
#191368472
#191364142
#191339612
#191339572
#191326662
#191326452
C43×#13622
#1243143