Finite Group Databasebeta

← #25000732

Subgroups — #25000732

Order 11008.

386 conjugacy classes of subgroups; only the 77 normal subgroups are shown.

normal subgroups only

This group has 386 conjugacy classes of subgroups — too many to draw. Only its 77 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#19134769C211yesmaximal, characteristic, complemented
2#19133317C212yesmaximal, complemented
3#19133206C212yesmaximal, complemented
4#19132506C211yesmaximal, characteristic, complemented
5C43×#3253C211yesmaximal, characteristic
6#14582956C2212yes—
7C2×#13063260—22no—
8#14582923C2211yescharacteristic
9C2×#13063236C2211yescharacteristic
10#14582645—22no—
11#14582643—22no—
12#14582639—24no—
13C43×#532C2212yes—
14C43×#476—22no—
15C43×#469—22no—
16C43×#459—22no—
17C43×#423C2211yescharacteristic
18C2×#10621877—21no—
19C22×C43⋊C8—21no—
20#13063260—44no—
21C4⋊(C43⋊C8)—22no—
22C4⋊(C43⋊C8)—22no—
23C22⋊(C43⋊C8)—22no—
24#13063236—21no—
25#13063236—22no—
26#13063236D412yes—
27C2×#41×C43—22no—
28C2×D8×C43—22no—
29C2×M16×C43D412yes—
30C4⋊Q8×C43D412yes—
31#127×C43D412yes—
32#124×C43—22no—
33#121×C43—22no—
34#121×C43—22no—
35C4×D4×C43—22no—
36C4×D4×C43—22no—
37C2×C42×C43C2311yescharacteristic
38#106×C43—22no—
39C4⋊C8×C43—22no—
40#102×C43—24no—
41#41×C43—84no—
42C2×Q8×C43—22no—
43C2×D4×C43—22no—
44C2×D4×C43—22no—
45C2×D4×C43—22no—
46C2×D4×C43—42no—
47C22×C4×C43—42no—
48C22×C4×C43C2×D411yescharacteristic
49C22×C4×C43#4112yes—
50D8×C43—82no—
51M16×C43—42no—
52C2×C8×C43—22no—
53C4⋊C4×C43—22no—
54C4⋊C4×C43—22no—
55C22⋊C4×C43—42no—
56C22⋊C4×C43—42no—
57C42×C43C2×D411yescharacteristic
58C42×C43C2×D412yes—
59C42×C43#4111yescharacteristic
60#10621877—42no—
61C2×C43⋊C8—22no—
62C2×C43⋊C8—22no—
63C2×C43⋊C8—22no—
64C2×C43⋊C8—41no—
65C2×C43⋊C8—42no—
66C23×C43—42no—
67C23×C43#12411yescharacteristic
68Q8×C43—82no—
69D4×C43—42no—
70D4×C43—42no—
71D4×C43—82no—
72D4×C43—82no—
73D4×C43—84no—
74C2×C4×C43—21no—
75C2×C4×C43—21no—
76C2×C4×C43—42no—
77C2×C4×C43—42no—
78C2×C4×C43—84no—
79C2×C4×C43#12011yescharacteristic
80C2×C4×C43#12111yescharacteristic
81C2×C4×C43#12112yes—
82C2×C4×C43#12312yes—
83C8×C43—42no—
84C43⋊C8—24no—
85C43⋊C8—82no—
86C43⋊C8—81no—
87#10524—431nomaximal, Sylow
88C22×C43—22no—
89C22×C43—21no—
90C22×C43—82no—
91C22×C43—82no—
92C22×C43—82no—
93C22×C43#39411yescharacteristic
94C4×C43—22no—
95C4×C43—22no—
96C4×C43—21no—
97C4×C43—82no—
98C4×C43#45311yescharacteristic
99C4×C43#45611yescharacteristic
100#3253D4311yescharacteristic
101#1849—431no—
102#1557—432no—
103#1530—432no—
104#1307—431no—
105C2×C43—41no—
106C2×C43—162no—
107C2×C43#203911yescharacteristic
108C2×C43#204812yes—
109#532C2×D4312yes—
110#476—22no—
111#469—22no—
112#459—22no—
113#432—432no—
114C2×#108—862no—
115#423—431no—
116#423C2×D4311yescharacteristic
117C2×#97—431no—
118#332—862no—
119#331—862no—
120#329—864no—
121C43#1052411yescharacteristic, complemented, Sylow
122C2×#41—22no—
123C2×D8—22no—
124C2×M16—861no—
125C2×M16C22⋊D4312yes—
126C22×C8—861no—
127C4⋊Q8C22⋊D4312yes—
128#127C22⋊D4312yes—
129#124—22no—
130#121—22no—
131#121—22no—
132C4×D4—22no—
133C4×D4—22no—
134C2×C42C22×D4311yescharacteristic
135#108—1724no—
136#106—22no—
137C4⋊C8—22no—
138C4⋊C8—862no—
139C4⋊C8—862no—
140#102—24no—
141C22⋊C8—862no—
142#97—432no—
143#97—862no—
144#97—861no—
145#41—84no—
146C2×Q8—22no—
147C2×D4—22no—
148C2×D4—22no—
149C2×D4—22no—
150C2×D4—42no—
151C22×C4—42no—
152C22×C4#1062190012yes—
153C22×C4C2×C22⋊D4311yescharacteristic
154D8—82no—
155M16—42no—
156M16—1722no—
157C2×C8—22no—
158C2×C8—862no—
159C2×C8—862no—
160C2×C8—862no—
161C2×C8—1721no—
162C2×C8—1722no—
163C4⋊C4—22no—
164C4⋊C4—22no—
165C22⋊C4—42no—
166C22⋊C4—42no—
167C42D4×D4311yescharacteristic
168C42#1062190011yescharacteristic
169C42C2×C22⋊D4312yes—
170C23—42no—
171C23#1306331211yescharacteristic
172Q8—82no—
173D4—42no—
174D4—42no—
175D4—82no—
176D4—82no—
177D4—84no—
178C2×C4—21no—
179C2×C4—21no—
180C2×C4—42no—
181C2×C4—42no—
182C2×C4—84no—
183C2×C4#1306329411yescharacteristic
184C2×C4#1306329611yescharacteristic
185C2×C4#1306329712yes—
186C2×C4#1306330612yes—
187C8—42no—
188C8—864no—
189C8—3442no—
190C8—3441no—
191C22—21no—
192C22—22no—
193C22—82no—
194C22—82no—
195C22—82no—
196C22#1458281311yescharacteristic
197C4—21no—
198C4—22no—
199C4—22no—
200C4—82no—
201C4#1458306711yescharacteristic
202C4#1458308211yescharacteristic
203C2—41no—
204C2—162no—
205C2#1913581611yescharacteristic
206C2#1913586512yes—
subgroupG/H
centerC22#14582813
commutator, cosocleC2×C42×C43C23
FrattiniC2×C42C22×D43
Fitting, prime radicalC43×#3253C2
socleC22×C43#394
hypercenter#3253D43
hypocenterC43#10524
LCSG ▷ C2×C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3253

Complements

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

NH ≅ G/Ntype
1. #19134769C2semidirect
2. #19133317C2semidirect
3. #19133206C2semidirect
4. #19132506C2semidirect
121. C43#10524semidirect

Maximal subgroups

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

subgroupindex
#191347692
#191333172
#191332062
#191325062
C43×#32532
#1052443