Finite Group Databasebeta

← #24991005

Subgroups — #24991005

Order 11008.

336 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 336 conjugacy classes of subgroups — too many to draw. Only its 99 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#19135577C211yesmaximal, characteristic
2#19133363C212yesmaximal
3#19133190C211yesmaximal, characteristic
4#19132487C212yesmaximal
5C43×#2987C211yesmaximal, characteristic
6#14582923C2211yescharacteristic
7C4×#10621877C2212yes—
8#14582745C2211yescharacteristic
9#14582658—22no—
10#14582651—22no—
11#14582649—22no—
12#14582641C411yescharacteristic, complemented
13#14582641C412yescomplemented
14#14582641C411yescharacteristic, complemented
15C43×#533C2211yescharacteristic
16C43×#446—22no—
17C43×#446—22no—
18C43×#433—22no—
19C43×#432C2212yes—
20C2×#10621877—22no—
21C2×#10621877—21no—
22C2×C4×Dic43—21no—
23C4⋊(C43⋊C8)—22no—
24#13063236C2×C412yes—
25#13063236C2×C412yes—
26C4×C43⋊C8—22no—
27C43⋊#95—22no—
28C4⋊Q8×C43Q812yes—
29#125×C43C2×C411yescharacteristic
30#125×C43C2×C411yescharacteristic
31C22⋊Q8×C43—22no—
32C4×Q8×C43—22no—
33#117×C43D412yes—
34C2×C42×C43C2311yescharacteristic
35C4⋊C8×C43—22no—
36C4⋊C8×C43—22no—
37C4⋊C8×C43D412yes—
38C4⋊C8×C43D412yes—
39C22⋊C8×C43—22no—
40#97×C43—22no—
41#97×C43—22no—
42C4×C8×C43—22no—
43C2×Q8×C43—22no—
44C22×C4×C43C2×D411yescharacteristic
45C22×C4×C43#4112yes—
46C22×Dic43—41no—
47C2×C8×C43—22no—
48C2×C8×C43—22no—
49C4⋊C4×C43—22no—
50C4⋊C4×C43—22no—
51C4⋊C4×C43—22no—
52C4⋊C4×C43C4⋊C412yes—
53C4⋊C4×C43C4⋊C412yes—
54C22⋊C4×C43—22no—
55C42×C43—22no—
56C42×C43C22×C411yescharacteristic
57C42×C43C2×D412yes—
58C42×C43C2×Q811yescharacteristic
59C4×Dic43—22no—
60C4×Dic43—41no—
61#10621877—44no—
62#10621877—42no—
63C2×C43⋊C8—22no—
64C2×C43⋊C8—22no—
65C2×C43⋊C8—41no—
66C23×C43#12311yescharacteristic
67Q8×C43—82no—
68C2×C4×C43—21no—
69C2×C4×C43—21no—
70C2×C4×C43—22no—
71C2×C4×C43—22no—
72C2×C4×C43—42no—
73C2×C4×C43C2×C4⋊C411yescharacteristic
74C2×C4×C43C4×D412yes—
75C2×C4×C43#12011yescharacteristic
76C2×C4×C43C22⋊Q812yes—
77C2×Dic43—42no—
78C2×Dic43—82no—
79C8×C43—42no—
80C8×C43—42no—
81C43⋊C8—24no—
82C43⋊C8—42no—
83C43⋊C8—81no—
84#8919—431nomaximal, Sylow
85C22×C43—21no—
86C22×C43—22no—
87C22×C43#38511yescharacteristic
88C4×C43—21no—
89C4×C43—22no—
90C4×C43—22no—
91C4×C43—42no—
92C4×C43—42no—
93C4×C43#45411yescharacteristic
94C4×C43#45611yescharacteristic
95Dic43—82no—
96#2987D4311yescharacteristic
97#1995—431no—
98#1569—432no—
99#1526—431no—
100#1300—432no—
101C2×C43—41no—
102C2×C43#185711yescharacteristic
103C2×C43#186112yes—
104#533C2×D4311yescharacteristic
105#446—22no—
106#446—22no—
107#433—22no—
108#432C2×D4312yes—
109#423—431no—
110C4×M16—432no—
111#376—431no—
112#339—862no—
113#335—862no—
114#334—862no—
115#330—431no—
116#330—432no—
117#330—431no—
118C43#891911yescharacteristic, complemented, Sylow
119C2×M16—862no—
120C2×M16—861no—
121C4⋊Q8Dic8612yes—
122#125C4×D4311yescharacteristic
123#125C4×D4311yescharacteristic
124C22⋊Q8—22no—
125C4×Q8—22no—
126#117C22⋊D4312yes—
127C2×C42—861no—
128C2×C42C22×D4311yescharacteristic
129C4⋊C8—22no—
130C4⋊C8—22no—
131C4⋊C8—862no—
132C4⋊C8C22⋊D4312yes—
133C4⋊C8C22⋊D4312yes—
134C22⋊C8—22no—
135#97—22no—
136#97—22no—
137#97—432no—
138#97—432no—
139C4×C8—22no—
140C4×C8—862no—
141#95—862no—
142C2×Q8—22no—
143C22×C4—1721no—
144C22×C4#1062189812yes—
145C22×C4C2×C22⋊D4311yescharacteristic
146M16—1724no—
147M16—1722no—
148C2×C8—22no—
149C2×C8—22no—
150C2×C8—862no—
151C2×C8—862no—
152C2×C8—1721no—
153C4⋊C4—22no—
154C4⋊C4—22no—
155C4⋊C4—22no—
156C4⋊C4Dic43⋊C412yes—
157C4⋊C4Dic43⋊C412yes—
158C22⋊C4—22no—
159C42—22no—
160C42—862no—
161C42—1721no—
162C42C2×Dic8611yescharacteristic
163C42C2×C4×D4311yescharacteristic
164C42C2×C22⋊D4312yes—
165C23#1306330811yescharacteristic
166Q8—82no—
167C2×C4—21no—
168C2×C4—21no—
169C2×C4—22no—
170C2×C4—22no—
171C2×C4—42no—
172C2×C4—3442no—
173C2×C4—1722no—
174C2×C4C2×Dic43⋊C411yescharacteristic
175C2×C4C4×C22⋊D4312yes—
176C2×C4#1306329411yescharacteristic
177C2×C4#1306330412yes—
178C8—42no—
179C8—42no—
180C8—864no—
181C8—3441no—
182C8—1722no—
183C22—21no—
184C22—22no—
185C22#1458277211yescharacteristic
186C4—21no—
187C4—22no—
188C4—22no—
189C4—42no—
190C4—42no—
191C4—3442no—
192C4#1458307211yescharacteristic
193C4#1458308211yescharacteristic
194C2—41no—
195C2#1913481011yescharacteristic
196C2#1913483512yes—
subgroupG/H
centerC2×C4#13063294
commutatorC42×C43C22×C4
FrattiniC2×C42C22×D43
FittingC43×#2987C2
socleC22×C43#385
prime radicalC23×C43#123
cosocleC2×C42×C43C23
hypercenter#2987D43
hypocenterC43#8919
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #2987

Complements

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

NH ≅ G/Ntype
12. #14582641C4semidirect
13. #14582641C4semidirect
14. #14582641C4semidirect
118. C43#8919semidirect

Maximal subgroups

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

subgroupindex
#191355772
#191333632
#191331902
#191324872
C43×#29872
#891943