Finite Group Databasebeta

← #25010015

Subgroups — #25010015

Order 11008.

362 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 362 conjugacy classes of subgroups — too many to draw. Only its 67 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#19136676C212yesmaximal, complemented
2#19134264C211yesmaximal, characteristic, complemented
3#19132636C211yesmaximal, characteristic, complemented
4#19132571C212yesmaximal, complemented
5C43×#3291C211yesmaximal, characteristic
6#14583339—22no—
7#14583302—21no—
8#14583279C2211yescharacteristic, complemented
9#14583245—21no—
10#14582720C2212yescomplemented
11#14582714—22no—
12#14582620C2211yescharacteristic, complemented
13C43×#577—22no—
14C43×#492C2211yescharacteristic
15C43×#471—22no—
16C43×#456—21no—
17C43×#453—21no—
18C43×#443C2212yes—
19C2×Dic172—22no—
20#13063325—21no—
21#13063271—42no—
22#13063269—42no—
23#13063265—22no—
24#13063258—42no—
25#13063246—42no—
26C4×C43⋊C8—21no—
272−1+4×C43—21no—
28H(5,𝔽2)×C43—21no—
29#137×C43—22no—
30#137×C43—42no—
31AGL(1,ℤ/8)×C43—22no—
32AGL(1,ℤ/8)×C43—42no—
33#135×C43—42no—
34#135×C43D412yes—
35C2×SD16×C43—22no—
36C2×SD16×C43—42no—
37#131×C43—22no—
38C4⋊Q8×C43D411yescharacteristic
39#127×C43D411yescharacteristic
40#108×C43D412yes—
41#104×C43—22no—
42#101×C43—21no—
43#100×C43—21no—
44C4×C8×C43C2311yescharacteristic
45#41×C43—22no—
46#41×C43—42no—
47#41×C43—42no—
48#41×C43—81no—
49C2×Q8×C43—21no—
50C2×Q8×C43—42no—
51C2×D4×C43—21no—
52C2×D4×C43—41no—
53C2×D4×C43—42no—
54C2×D4×C43—81no—
55C2×Dic86—41no—
56Q16×C43—42no—
57Q16×C43D812yes—
58SD16×C43—22no—
59SD16×C43—42no—
60SD16×C43—42no—
61SD16×C43—42no—
62SD16×C43—42no—
63D8×C43—42no—
64D8×C43D812yes—
65M16×C43—22no—
66M16×C43—42no—
67C2×C8×C43—42no—
68C2×C8×C43C2×D412yes—
69C4⋊C4×C43—41no—
70C42×C43C2×D411yescharacteristic
71C4⋊Dic43—41no—
72C4⋊Dic43—41no—
73C2×C43⋊C8—22no—
74Dic172—42no—
75Dic172—42no—
76C43⋊C16—42no—
77C23×C43—41no—
78C23×C43—81no—
79Q8×C43—22no—
80Q8×C43—42no—
81Q8×C43—81no—
82D4×C43—22no—
83D4×C43—42no—
84D4×C43—42no—
85D4×C43—82no—
86D4×C43—82no—
87D4×C43—81no—
88C2×C4×C43—21no—
89C2×C4×C43—42no—
90C2×C4×C43—41no—
91C2×C4×C43—81no—
92C2×C4×C43—82no—
93C2×C4×C43#12011yescharacteristic
94C2×Dic43—81no—
95Dic86—82no—
96C8×C43—42no—
97C8×C43C2×D812yes—
98C8×C43AGL(1,ℤ/8)12yes—
99C43⋊C8—42no—
100#12315—431nomaximal, Sylow
101C22×C43—42no—
102C22×C43—81no—
103C22×C43—161no—
104C22×C43—321no—
105C22×C43#45311yescharacteristic
106C4×C43—22no—
107C4×C43—42no—
108C4×C43—81no—
109C4×C43#44712yes—
110Dic43—161no—
111#3291D4311yescharacteristic
112#2214—432no—
113#1722—431no—
114#1359—431no—
115#1336—432no—
116C2×C43—21no—
117C2×C43—82no—
118C2×C43—161no—
119C2×C43#161911yescharacteristic
120#577—22no—
121#510—862no—
122#500—861no—
123#494—431no—
124#492C2×D4311yescharacteristic
125#486—861no—
126#471—22no—
127#456—21no—
128#453—21no—
129#443C2×D4312yes—
130#364—432no—
131#362—862no—
132#322—431no—
133C43#1231511yescharacteristic, complemented, Sylow
1342−1+4—21no—
135H(5,𝔽2)—21no—
136#137—22no—
137#137—42no—
138AGL(1,ℤ/8)—22no—
139AGL(1,ℤ/8)—42no—
140#135—42no—
141#135C22⋊D4312yes—
142C2×Q16—862no—
143C2×SD16—22no—
144C2×SD16—42no—
145#131—22no—
146C4⋊Q8—861no—
147C4⋊Q8C22⋊D4311yescharacteristic
148#127C22⋊D4311yescharacteristic
149Q32—1722no—
150SD32—1722no—
151M32—862no—
152#108C22⋊D4312yes—
153#107—1722no—
154#104—22no—
155#102—1722no—
156#101—21no—
157#100—21no—
158C4×C8—861no—
159C4×C8C22×D4311yescharacteristic
160#41—22no—
161#41—42no—
162#41—42no—
163#41—81no—
164C2×Q8—21no—
165C2×Q8—42no—
166C2×Q8—1721no—
167C2×D4—21no—
168C2×D4—41no—
169C2×D4—42no—
170C2×D4—81no—
171Q16—42no—
172Q16—1722no—
173Q16—1722no—
174Q16#1062188212yes—
175SD16—22no—
176SD16—42no—
177SD16—42no—
178SD16—42no—
179SD16—42no—
180D8—42no—
181D8#1062188212yes—
182M16—22no—
183M16—42no—
184C2×C8—42no—
185C2×C8—862no—
186C2×C8C2×C22⋊D4312yes—
187C4⋊C4—41no—
188C4⋊C4—1721no—
189C4⋊C4—1721no—
190C42C2×C22⋊D4311yescharacteristic
191C16—1722no—
192C23—41no—
193C23—81no—
194Q8—22no—
195Q8—42no—
196Q8—81no—
197Q8—3442no—
198D4—22no—
199D4—42no—
200D4—42no—
201D4—82no—
202D4—82no—
203D4—81no—
204C2×C4—21no—
205C2×C4—42no—
206C2×C4—41no—
207C2×C4—81no—
208C2×C4—82no—
209C2×C4—3441no—
210C2×C4#1306329411yescharacteristic
211C8—42no—
212C8—1722no—
213C8C2×#1062188212yes—
214C8#1306335112yes—
215C22—42no—
216C22—81no—
217C22—161no—
218C22—321no—
219C22#1458306711yescharacteristic
220C4—22no—
221C4—42no—
222C4—81no—
223C4—6881no—
224C4#1458303312yes—
225C2—21no—
226C2—82no—
227C2—161no—
228C2#1913364911yescharacteristic
subgroupG/H
centerC2#19133649
commutator, cosocleC4×C8×C43C23
FrattiniC4×C8C22×D43
Fitting, prime radicalC43×#3291C2
socleC2×C43#1619
hypercenter#3291D43
hypocenterC43#12315
LCSG ▷ C4×C8×C43 ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2 ◁ C2×C4 ◁ C4×C8 ◁ #3291

Complements

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

NH ≅ G/Ntype
1. #19136676C2semidirect
2. #19134264C2semidirect
3. #19132636C2semidirect
4. #19132571C2semidirect
8. #14583279C22semidirect
10. #14582720C22semidirect
12. #14582620C22semidirect
133. C43#12315semidirect

Maximal subgroups

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

subgroupindex
#191366762
#191342642
#191326362
#191325712
C43×#32912
#1231543