Finite Group Databasebeta

← #24994196

Subgroups — #24994196

Order 11008.

504 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 504 conjugacy classes of subgroups — too many to draw. Only its 107 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#19145055C211yesmaximal, characteristic
2#19133330C211yesmaximal, characteristic
3#19133279C212yesmaximal, complemented
4#19132486C212yesmaximal, complemented
5C43×#2979C211yesmaximal, characteristic
6C2×#13063355—22no—
7C2×#13063325C2211yescharacteristic
8#14583294C414yes—
9#14583278—21no—
10#14583271—21no—
11#14582923C2212yes—
12C4×#10621877C2211yescharacteristic
13#14582648—21no—
14#14582646—22no—
15#14582646—22no—
16#14582643—21no—
17C43×#532C2211yescharacteristic
18C43×#436—22no—
19C8×D4×C43—22no—
20C43×#431C2212yes—
21C43×#408—22no—
22C22×Dic86—21no—
23#13063355—44no—
24#13063355—44no—
25C2×#10621885—24no—
26C2×#10621883—24no—
27C2×#10621877—21no—
28C2×#10621877—22no—
29#13063325—22no—
30#13063325—21no—
31#13063325C2×C412yes—
32C2×C4⋊Dic43—22no—
33C4⋊(C43⋊C8)—22no—
34C4⋊(C43⋊C8)—22no—
35#13063236C2×C412yes—
36C4×C43⋊C8—21no—
37C2×#41×C43D412yes—
38C2×M16×C43—22no—
39C22×C8×C43—22no—
40C4⋊Q8×C43D411yescharacteristic
41#127×C43D411yescharacteristic
42#124×C43C2×C412yes—
43#121×C43—22no—
44C4×D4×C43—22no—
45C2×C42×C43C2311yescharacteristic
46C4⋊C8×C43D412yes—
47C4⋊C8×C43D412yes—
48C22⋊C8×C43—24no—
49C22⋊C8×C43—22no—
50C4×C8×C43—22no—
51#41×C43—42no—
52#41×C43—42no—
53C2×Q8×C43C22⋊C412yes—
54C2×D4×C43—22no—
55C2×D4×C43—22no—
56C2×D4×C43C22⋊C412yes—
57C22×C4×C43—22no—
58C22×C4×C43C2×D411yescharacteristic
59C22×C4×C43#4112yes—
60C22×Dic43—41no—
61C2×Dic86—22no—
62C2×Dic86—42no—
63C2×Dic86—42no—
64C2×Dic86—41no—
65M16×C43—82no—
66C2×C8×C43—22no—
67C2×C8×C43—22no—
68C2×C8×C43—82no—
69C4⋊C4×C43—22no—
70C22⋊C4×C43—24no—
71C42×C43C22×C411yescharacteristic
72C42×C43C2×D411yescharacteristic
73C42×C43C2×D412yes—
74#10621885—48no—
75#10621883—48no—
76C4⋊Dic43—24no—
77C4⋊Dic43—42no—
78#10621877—22no—
79#10621877—22no—
80#10621877—82no—
81C2×C43⋊C8—22no—
82C2×C43⋊C8—42no—
83C23×C43—22no—
84C23×C43#12311yescharacteristic
85Q8×C43—42no—
86D4×C43—42no—
87D4×C43—42no—
88D4×C43—42no—
89D4×C43—82no—
90C2×C4×C43—21no—
91C2×C4×C43—21no—
92C2×C4×C43—22no—
93C2×C4×C43—22no—
94C2×C4×C43—22no—
95C2×C4×C43—42no—
96C2×C4×C43—42no—
97C2×C4×C43C2×C22⋊C411yescharacteristic
98C2×C4×C43C4×D412yes—
99C2×C4×C43#12011yescharacteristic
100C2×C4×C43#12112yes—
101C2×Dic43—42no—
102C2×Dic43—82no—
103Dic86—44no—
104Dic86—81no—
105Dic86—81no—
106C8×C43—42no—
107C8×C43—42no—
108C43⋊C8—24no—
109C43⋊C8—82no—
110#9435—431nomaximal, Sylow
111C22×C43—21no—
112C22×C43—22no—
113C22×C43—42no—
114C22×C43—44no—
115C22×C43#38611yescharacteristic
116C4×C43—21no—
117C4×C43—22no—
118C4×C43—42no—
119C4×C43#45311yescharacteristic
120C4×C43#45311yescharacteristic
121C4×C43#47112yes—
122C4×C43#47312yes—
123Dic43—82no—
124#3152—431no—
125#2979D4311yescharacteristic
126#1560—431no—
127#1549—432no—
128#1299—432no—
129C2×C43—41no—
130C2×C43—82no—
131C2×C43#188711yescharacteristic
132C2×C43#190812yes—
133C2×#137—862no—
134#532C2×D4311yescharacteristic
135C2×C4⋊Q8—431no—
136#497—434no—
137#494—861no—
138#492—861no—
139#436—22no—
140C8×D4—22no—
141#431C2×D4312yes—
142#423—432no—
143#408—22no—
144C4×M16—431no—
145#333—861no—
146#332—862no—
147#332—862no—
148#331—861no—
149C43#943511yescharacteristic, complemented, Sylow
150C2×#41C22⋊D4312yes—
151C22×Q8—861no—
152#137—1724no—
153#137—1724no—
154C2×Q16—864no—
155C2×SD16—864no—
156C2×M16—22no—
157C2×M16—861no—
158C2×M16—862no—
159C22×C8—22no—
160C4⋊Q8—432no—
161C4⋊Q8—861no—
162C4⋊Q8—862no—
163C4⋊Q8D17211yescharacteristic
164#127D17211yescharacteristic
165#124C4×D4312yes—
166#121—22no—
167C4×D4—22no—
168C2×C4⋊C4—862no—
169C2×C42C22×D4311yescharacteristic
170C4⋊C8—862no—
171C4⋊C8—862no—
172C4⋊C8C22⋊D4312yes—
173C4⋊C8C22⋊D4312yes—
174C22⋊C8—24no—
175C22⋊C8—22no—
176#97—432no—
177C4×C8—22no—
178C4×C8—861no—
179#41—42no—
180#41—42no—
181C2×Q8—862no—
182C2×Q8—1722no—
183C2×Q8—1722no—
184C2×Q8—1721no—
185C2×Q8(C2×D43)⋊C412yes—
186C2×D4—22no—
187C2×D4—22no—
188C2×D4(C2×D43)⋊C412yes—
189C22×C4—22no—
190C22×C4—1721no—
191C22×C4#1062189812yes—
192C22×C4C2×C22⋊D4311yescharacteristic
193Q16—1728no—
194SD16—1728no—
195M16—82no—
196M16—862no—
197M16—862no—
198M16—3442no—
199C2×C8—22no—
200C2×C8—22no—
201C2×C8—82no—
202C2×C8—862no—
203C2×C8—1722no—
204C4⋊C4—22no—
205C4⋊C4—864no—
206C4⋊C4—1722no—
207C22⋊C4—24no—
208C42C2×C4×D4311yescharacteristic
209C42C2×D17211yescharacteristic
210C42C2×C22⋊D4312yes—
211C23—22no—
212C23#1306330811yescharacteristic
213Q8—42no—
214Q8—3441no—
215Q8—3441no—
216Q8—1724no—
217D4—42no—
218D4—42no—
219D4—42no—
220D4—82no—
221C2×C4—21no—
222C2×C4—21no—
223C2×C4—22no—
224C2×C4—22no—
225C2×C4—22no—
226C2×C4—42no—
227C2×C4—42no—
228C2×C4—3442no—
229C2×C4—1722no—
230C2×C4C2×(C2×D43)⋊C411yescharacteristic
231C2×C4C4×C22⋊D4312yes—
232C2×C4#1306329411yescharacteristic
233C2×C4#1306329912yes—
234C8—42no—
235C8—42no—
236C8—864no—
237C8—3442no—
238C22—21no—
239C22—22no—
240C22—42no—
241C22—44no—
242C22#1458277811yescharacteristic
243C4—21no—
244C4—22no—
245C4—42no—
246C4—3442no—
247C4#1458306711yescharacteristic
248C4#1458306711yescharacteristic
249C4#1458316212yes—
250C4#1458317412yes—
251C2—41no—
252C2—82no—
253C2#1913499311yescharacteristic
254C2#1913511012yes—
subgroupG/H
centerC22#14582778
commutatorC42×C43C22×C4
FrattiniC2×C42C22×D43
FittingC43×#2979C2
socleC22×C43#386
prime radicalC43×#532C22
cosocleC2×C42×C43C23
hypercenter#2979D43
hypocenterC43#9435
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2979

Complements

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

NH ≅ G/Ntype
3. #19133279C2semidirect
4. #19132486C2semidirect
149. C43#9435semidirect

Maximal subgroups

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

subgroupindex
#191450552
#191333302
#191332792
#191324862
C43×#29792
#943543