Finite Group Databasebeta

← #24984147

Subgroups — #24984147

Order 11008.

224 conjugacy classes of subgroups; only the 41 normal subgroups are shown.

normal subgroups only

This group has 224 conjugacy classes of subgroups — too many to draw. Only its 41 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#19135824C211yesmaximal, characteristic
2#19132476C211yesmaximal, characteristic, complemented
3C43×#1324C211yesmaximal, characteristic, complemented
4#14583480C411yescharacteristic
5C2×#13063253—21no—
6#14582898—21no—
7C2×#13063236—21no—
8#14582668C411yescharacteristic
9C43×#382C2211yescharacteristic
10C43×#324—21no—
11C2×#10621898—21no—
12C2×#10621877—21no—
13C22×C43⋊C8—41no—
14#13063305—41no—
15#13063300—41no—
16#13063299—41no—
17#13063253—41no—
18#13063253—41no—
19#13063248—41no—
20#13063245—41no—
21#13063236—22no—
22#13063236—41no—
23C2×C4⋊C4×C43C2×C411yescharacteristic
24C2×C4⋊C4×C43D411yescharacteristic
25C2×C42×C43D411yescharacteristic
26C22⋊C8×C43—41no—
27#95×C43—41no—
28C22×C4×C43—21no—
29C22×C4×C43—21no—
30C22×C4×C43—21no—
31C22×C4×C43C22⋊C411yescharacteristic
32C2×C22⋊D43—41no—
33#10621898—41no—
34#10621898—41no—
35#10621898—41no—
36#10621898—41no—
37C2×D172—21no—
38C2×D172—41no—
39C2×C4×D43—41no—
40C2×Dic86—21no—
41C2×C8×C43—81no—
42C4⋊C4×C43—41no—
43C4⋊C4×C43—41no—
44C42×C43—21no—
45C42×C43D811yescharacteristic
46C42×C43SD1611yescharacteristic
47(C2×D43)⋊C4—42no—
48C4⋊Dic43—41no—
49#10621877—41no—
50#10621877—41no—
51C2×C43⋊C8—42no—
52C2×C43⋊C8—42no—
53C2×C43⋊C8—42no—
54C2×C43⋊C8—41no—
55C23×C43#9911yescharacteristic
56C22×D43—41no—
57C2×C4×C43—21no—
58C2×C4×C43—21no—
59C2×C4×C43—21no—
60C2×C4×C43—21no—
61C2×C4×C43—41no—
62C2×C4×C43—41no—
63C2×C4×C43—41no—
64C2×C4×C43—41no—
65C2×C4×C43—81no—
66C2×C4×C43—81no—
67C2×C4×C43#10211yescharacteristic
68C2×C4×C43#10411yescharacteristic
69C22⋊D43—81no—
70C22⋊D43—81no—
71C2×Dic43—41no—
72D172—41no—
73D172—41no—
74D172—161no—
75C4×D43—81no—
76C4×D43—81no—
77Dic86—41no—
78Dic86—41no—
79C8×C43—161no—
80C43⋊C8—44no—
81C43⋊C8—81no—
82#7416—431nomaximal, Sylow
83C22×C43—21no—
84C22×C43—21no—
85C22×C43#32711yescharacteristic
86C22×C43AΣL(1,𝔽16)11yescharacteristic
87C22×C43#35511yescharacteristic
88C2×D43—81no—
89C2×D43—81no—
90C2×D43—81no—
91C4×C43—21no—
92C4×C43—21no—
93C4×C43—41no—
94C4×C43—41no—
95C4×C43—81no—
96C4×C43—81no—
97Dic43—81no—
98#2040—431no—
99#1324D4311yescharacteristic, complemented
100#1295—431no—
101C2×C43—21no—
102C2×C43—21no—
103C2×C43#134511yescharacteristic
104C2×C43#140311yescharacteristic
105C2×C43#140411yescharacteristic
106D43—161no—
107#537—431no—
108C2×#104—861no—
109#417—861no—
110C2×#97—861no—
111#382C2×D4311yescharacteristic
112#343—431no—
113#324—21no—
114C43#741611yescharacteristic, complemented, Sylow
115C2×#41—861no—
116C2×M16—861no—
117C22×C8—1721no—
118C22⋊Q8—1721no—
119#121—1721no—
120#121—1721no—
121C2×C4⋊C4C4×D4311yescharacteristic
122C2×C4⋊C4C22⋊D4311yescharacteristic
123C2×C42D17211yescharacteristic
124#104—1721no—
125#104—1721no—
126#103—1721no—
127#102—1721no—
128C22⋊C8—41no—
129#97—862no—
130#97—1721no—
131#95—41no—
132#41—1721no—
133#41—1721no—
134#41—1721no—
135#41—1721no—
136C2×Q8—861no—
137C2×D4—861no—
138C2×D4—1721no—
139C2×D4—1721no—
140C22×C4—21no—
141C22×C4—21no—
142C22×C4—21no—
143C22×C4—1721no—
144C22×C4(C2×D43)⋊C411yescharacteristic
145M16—1721no—
146M16—1721no—
147C2×C8—81no—
148C2×C8—1721no—
149C2×C8—1722no—
150C2×C8—1722no—
151C2×C8—1722no—
152C4⋊C4—41no—
153C4⋊C4—41no—
154C4⋊C4—1721no—
155C22⋊C4—1722no—
156C42—21no—
157C42#1062187311yescharacteristic
158C42D34411yescharacteristic
159C23—1721no—
160C23#1306323911yescharacteristic
161Q8—1721no—
162Q8—1721no—
163D4—3441no—
164D4—3441no—
165D4—1721no—
166D4—1721no—
167D4—6881no—
168C2×C4—21no—
169C2×C4—21no—
170C2×C4—21no—
171C2×C4—21no—
172C2×C4—41no—
173C2×C4—41no—
174C2×C4—41no—
175C2×C4—41no—
176C2×C4—81no—
177C2×C4—81no—
178C2×C4—3441no—
179C2×C4—3441no—
180C2×C4—1721no—
181C2×C4#1306324711yescharacteristic
182C2×C4#1306325111yescharacteristic
183C8—161no—
184C8—3441no—
185C8—1724no—
186C22—21no—
187C22—21no—
188C22—3441no—
189C22—3441no—
190C22—3441no—
191C22#1458263411yescharacteristic
192C22#1458268511yescharacteristic
193C22#1458269511yescharacteristic
194C4—21no—
195C4—21no—
196C4—41no—
197C4—41no—
198C4—81no—
199C4—81no—
200C4—3441no—
201C2—21no—
202C2—21no—
203C2—6881no—
204C2#1913259911yescharacteristic
205C2#1913274211yescharacteristic
206C2#1913274511yescharacteristic
subgroupG/H
centerC22#14582685
commutatorC2×C4⋊C4×C43C2×C4
Frattini#382C2×D43
FittingC43×#1324C2
socleC22×C43AΣL(1,𝔽16)
prime radical#14583480C4
cosocleC43×#382C22
hypercenter#1324D43
hypocenterC43#7416
LCSG ▷ C2×C4⋊C4×C43 ▷ C22×C4×C43 ▷ C22×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23 ◁ C22×C4 ◁ #382 ◁ #1324

Complements

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

NH ≅ G/Ntype
2. #19132476C2semidirect
3. C43×#1324C2semidirect
99. #1324D43semidirect
114. C43#7416semidirect

Maximal subgroups

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

subgroupindex
#191358242
#191324762
C43×#13242
#741643