Finite Group Databasebeta

← #25005811

Subgroups — #25005811

Order 11008.

306 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 306 conjugacy classes of subgroups — too many to draw. Only its 85 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#19143238C211yesmaximal, characteristic
2#19136395C212yesmaximal, complemented
3#19132537C211yesmaximal, characteristic, complemented
4#19132520C212yesmaximal
5C43×#1323C211yesmaximal, characteristic, complemented
6#14583367C411yescharacteristic
7#14582959—22no—
8#14582951—22no—
9#14582926C411yescharacteristic
10#14582867C411yescharacteristic
11#14582865C2211yescharacteristic
12M16×Dic43C411yescharacteristic
13C2×C8×Dic43C2211yescharacteristic
14Dic43⋊C16—22no—
15C22⋊(C43⋊C16)C2212yes—
16#14582674—22no—
17C43×#424C2211yescharacteristic
18C43×C22⋊C16C2212yes—
19C2×#10621898C2×C411yescharacteristic
20C2×#10621877C2×C411yescharacteristic
21C22×C43⋊C8C2×C411yescharacteristic
22#13063290C812yes—
23#13063287C812yes—
24(C22⋊D43)⋊C4—22no—
25#13063282—21no—
26C2×C4×Dic43C2×C411yescharacteristic
27C42×D43—21no—
28C2×C43⋊C16—22no—
29C4⋊(C43⋊C8)—22no—
30(C2×D43)⋊C8—22no—
31(C2×D43)⋊C8—22no—
32#13063235—21no—
33C8×Dic43—21no—
34C8×Dic43D412yes—
35C8×Dic43D412yes—
36C2×M16×C43C2×C411yescharacteristic
37C22×C8×C43C2311yescharacteristic
38#117×C43C2×C411yescharacteristic
39C2×C16×C43—22no—
40C4⋊C8×C43—22no—
41C22×C4×C43C22×C411yescharacteristic
42C2×C22⋊D43—21no—
43C22×Dic43M1612yes—
44#10621898—41no—
45#10621898—41no—
46C2×D172C2×C811yescharacteristic
47C2×C4×D43—21no—
48C2×C4×D43—22no—
49C2×Dic86C2×C811yescharacteristic
50M16×C43—41no—
51C2×C8×C43—21no—
52C2×C8×C43—41no—
53C2×C8×C43C2×D412yes—
54C4⋊C4×C43C2×C812yes—
55C22⋊C4×C43—21no—
56C42×C43—21no—
57(C2×D43)⋊C4—22no—
58Dic43⋊C4—22no—
59C4×Dic43—22no—
60C4×Dic43C22⋊C411yescharacteristic
61C4×Dic43C22⋊C411yescharacteristic
62C4×Dic43C2×C812yes—
63#10621877—41no—
64C2×C43⋊C8—21no—
65C2×C43⋊C8—41no—
66C2×C43⋊C8C22⋊C412yes—
67C16×C43—42no—
68C43⋊C16—42no—
69C23×C43C2×M1611yescharacteristic
70C22×D43—21no—
71C2×C4×C43—21no—
72C2×C4×C43—21no—
73C2×C4×C43—22no—
74C2×C4×C43C2×C22⋊C411yescharacteristic
75C2×C4×C43C22×C811yescharacteristic
76C22⋊D43—42no—
77C2×Dic43—21no—
78C2×Dic43—42no—
79C2×Dic43C22⋊C812yes—
80C2×Dic43C22⋊C812yes—
81D172—41no—
82C4×D43—44no—
83C4×D43—41no—
84C4×D43—41no—
85Dic86—41no—
86C8×C43—22no—
87C8×C43—41no—
88C43⋊C8—22no—
89C43⋊C8—41no—
90#11463—431nomaximal, Sylow
91C22×C43—22no—
92C22×C43—21no—
93C22×C43C2×C22⋊C811yescharacteristic
94C2×D43—42no—
95C2×D43—41no—
96C4×C43—21no—
97C4×C43—42no—
98C4×C43#41011yescharacteristic
99C4×C43#41311yescharacteristic
100Dic43—22no—
101Dic43—22no—
102Dic43—41no—
103#2922—431no—
104#2163—432no—
105#1323—431no—
106#1323D4311yescharacteristic, complemented
107#1315—432no—
108C2×C43—41no—
109C2×C43#145811yescharacteristic
110C2×C43#211712yes—
111D43—81no—
112C4×#41—431no—
113#433—862no—
114#431—862no—
115#424—431no—
116#424C2×D4311yescharacteristic
117#408—431no—
118#408—431no—
119C4×M16—431no—
120C2×C4×C8—431no—
121C4⋊C16—862no—
122C22⋊C16—432no—
123C22⋊C16C2×D4312yes—
124#346—862no—
125C43#1146311yescharacteristic, complemented, Sylow
126C2×#41—431no—
127C2×M16—431no—
128C2×M16C4×D4311yescharacteristic
129C22×C8—431no—
130C22×C8C22×D4311yescharacteristic
131C4×Q8—432no—
132C4×D4—432no—
133C4×D4—862no—
134#117—861no—
135#117C4×D4311yescharacteristic
136C2×C42—431no—
137C2×C42—861no—
138C2×C16—22no—
139C2×C16—862no—
140C4⋊C8—22no—
141C4⋊C8—862no—
142C22⋊C8—862no—
143C22⋊C8—862no—
144#97—861no—
145C4×C8—432no—
146C4×C8—432no—
147C4×C8—861no—
148#41—1721no—
149#41—1721no—
150C2×Q8—431no—
151C2×D4—431no—
152C2×D4—861no—
153C22×C4—432no—
154C22×C4—862no—
155C22×C4—861no—
156C22×C4C2×C4×D4311yescharacteristic
157M16—41no—
158M16—1721no—
159C2×C8—21no—
160C2×C8—41no—
161C2×C8—432no—
162C2×C8—861no—
163C2×C8—1721no—
164C2×C8D4×D4312yes—
165C4⋊C4—862no—
166C4⋊C4C8×D4312yes—
167C22⋊C4—21no—
168C22⋊C4—862no—
169C42—21no—
170C42—431no—
171C42—431no—
172C42—432no—
173C42—862no—
174C16—42no—
175C16—1722no—
176C23—861no—
177C23M16×D4311yescharacteristic
178Q8—1721no—
179D4—1721no—
180D4—1722no—
181C2×C4—21no—
182C2×C4—21no—
183C2×C4—22no—
184C2×C4—432no—
185C2×C4—432no—
186C2×C4—861no—
187C2×C4—1724no—
188C2×C4—1722no—
189C2×C4—1721no—
190C2×C4—1721no—
191C2×C4C22⋊C4×D4311yescharacteristic
192C2×C4C2×C8×D4311yescharacteristic
193C8—22no—
194C8—41no—
195C8—862no—
196C8—1721no—
197C22—22no—
198C22—21no—
199C22—1722no—
200C22—1721no—
201C22C22⋊C8×D4311yescharacteristic
202C4—21no—
203C4—42no—
204C4—862no—
205C4—862no—
206C4—1721no—
207C4#1458287111yescharacteristic
208C4#1458288211yescharacteristic
209C2—41no—
210C2—3441no—
211C2#1913290811yescharacteristic
212C2#1913622112yes—
subgroupG/H
centerC2×C4C22⋊C4×D43
commutatorC2×C4×C43C22×C8
FrattiniC22×C8C22×D43
FittingC43×#1323C2
socleC22×C43C2×C22⋊C8
prime radicalC2×#10621898C2×C4
cosocleC22×C8×C43C23
hypercenter#1323D43
hypocenterC43#11463
LCSG ▷ C2×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C22×C8 ◁ #1323

Complements

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

NH ≅ G/Ntype
2. #19136395C2semidirect
3. #19132537C2semidirect
5. C43×#1323C2semidirect
106. #1323D43semidirect
125. C43#11463semidirect

Maximal subgroups

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

subgroupindex
#191432382
#191363952
#191325372
#191325202
C43×#13232
#1146343