Finite Group Databasebeta

← #25016282

Subgroups — #25016282

Order 11008.

416 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 416 conjugacy classes of subgroups — too many to draw. Only its 79 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#19142588C211yesmaximal, characteristic
2#19134810C212yesmaximal
3#19132722C211yesmaximal, characteristic
4#19132721C212yesmaximal
5C43×#1857C211yesmaximal, characteristic
6#14582942—22no—
7C2×#13063244C2212yes—
8#14582820—22no—
9#14582819—21no—
10#14582806C2212yes—
11#14582805—21no—
12#14582803—22no—
13#14582658—22no—
14C43×#519C2211yescharacteristic
15C43×#428—21no—
16C2×#101×C43C2211yescharacteristic
17C43×#391C2211yescharacteristic
18C43×#339—21no—
19C22×Dic86—21no—
20C22×Dic86—21no—
21C2×#10621877—22no—
22C2×C4⋊Dic43—21no—
23C2×C4⋊Dic43D412yes—
24C2×Dic43⋊C4—22no—
25C2×C4×Dic43D412yes—
26#13063258—42no—
27#13063256—42no—
28#13063244—22no—
29#13063244Q814yescomplemented
30C43⋊#95—21no—
31C43⋊#95—22no—
32C43⋊#95—22no—
33C43⋊#95—22no—
34C22×Q8×C43C2311yescharacteristic
35C2×M16×C43—21no—
36C4×Q8×C43—41no—
37C4×Q8×C43—41no—
38#117×C43—21no—
39#117×C43—22no—
40C2×C4⋊C4×C43D411yescharacteristic
41C2×C42×C43D411yescharacteristic
42#107×C43—41no—
43#106×C43—41no—
44#101×C43—21no—
45#101×C43Q812yescomplemented
46#95×C43—22no—
47C2×Q8×C43—41no—
48C2×Q8×C43—41no—
49C2×Q8×C43C2×Q811yescharacteristic
50C2×Q8×C43C2×Q812yes—
51C2×Q8×C43#4111yescharacteristic
52C22×C4×C43—21no—
53C22×C4×C43—21no—
54C22×C4×C43C2×D412yes—
55C22×C4×C43C2×D411yescharacteristic
56C22×Dic43—22no—
57C22×Dic43—22no—
58C2×Dic86—24no—
59C2×Dic86—81no—
60C2×Dic86—81no—
61C2×Dic86—82no—
62C2×Dic86—81no—
63M16×C43—22no—
64M16×C43—41no—
65C2×C8×C43—41no—
66C4⋊C4×C43—21no—
67C4⋊C4×C43—21no—
68C4⋊C4×C43—22no—
69C4⋊C4×C43—22no—
70C4⋊C4×C43—41no—
71C22⋊C4×C43—41no—
72C42×C43—41no—
73C42×C43—42no—
74C42×C43—41no—
75C4⋊Dic43—42no—
76C4⋊Dic43—81no—
77Dic43⋊C4—82no—
78C4×Dic43—42no—
79#10621877—24no—
80#10621877—42no—
81C2×C43⋊C8—42no—
82C23×C43#12011yescharacteristic
83Q8×C43—41no—
84Q8×C43—42no—
85Q8×C43—41no—
86C2×C4×C43—22no—
87C2×C4×C43—21no—
88C2×C4×C43—22no—
89C2×C4×C43—21no—
90C2×C4×C43—22no—
91C2×C4×C43—41no—
92C2×C4×C43—41no—
93C2×C4×C43—42no—
94C2×C4×C43—41no—
95C2×C4×C43—41no—
96C2×C4×C43—41no—
97C2×C4×C43C22⋊Q812yes—
98C2×C4×C43C22⋊Q811yescharacteristic
99C2×C4×C43C4⋊Q811yescharacteristic
100C2×C4×C43C4⋊Q812yes—
101C2×Dic43—24no—
102C2×Dic43—42no—
103C2×Dic43—42no—
104C2×Dic43—42no—
105C2×Dic43—42no—
106C2×Dic43—42no—
107Dic86—84no—
108Dic86—84no—
109C8×C43—42no—
110C43⋊C8—44no—
111#13464—431nomaximal, Sylow
112C22×C43—21no—
113C22×C43—21no—
114C22×C43#39511yescharacteristic
115C22×C43B(4,𝔽2)11yescharacteristic
116C22×C43#45811yescharacteristic
117C4×C43—22no—
118C4×C43—21no—
119C4×C43—21no—
120C4×C43—22no—
121C4×C43—42no—
122C4×C43—81no—
123C4×C43—81no—
124C4×C43—81no—
125Dic43—44no—
126Dic43—82no—
127#2811—431no—
128#1857—432no—
129#1857D4311yescharacteristic
130#1394—432no—
131#1394—431no—
132C2×C43—21no—
133C2×C43—21no—
134C2×C43#206211yescharacteristic
135C2×C43#220211yescharacteristic
136C2×C43#220511yescharacteristic
137#519C2×D4311yescharacteristic
138#428—21no—
139#428—862no—
140C2×#101—432no—
141C2×#101C2×D4311yescharacteristic
142#395—862no—
143#395—861no—
144#391—432no—
145#391—862no—
146#391—861no—
147#391C2×D4311yescharacteristic
148#339—21no—
149#339—862no—
150C43#1346411yescharacteristic, complemented, Sylow
151C22×Q8—861no—
152C22×Q8—861no—
153C22×Q8C22×D4311yescharacteristic
154C2×M16—21no—
155C2×M16—862no—
156C4×Q8—41no—
157C4×Q8—41no—
158#117—22no—
159#117—21no—
160C2×C4⋊C4—432no—
161C2×C4⋊C4—862no—
162C2×C4⋊C4—861no—
163C2×C4⋊C4C22⋊D4311yescharacteristic
164C2×C42—432no—
165C2×C42C22⋊D4311yescharacteristic
166#107—41no—
167#107—1722no—
168#106—41no—
169#106—1722no—
170#101—21no—
171#101—434no—
172#101—862no—
173#101Dic8612yescomplemented
174#95—22no—
175#95—862no—
176#95—861no—
177#95—862no—
178#95—862no—
179C2×Q8—41no—
180C2×Q8—41no—
181C2×Q8—864no—
182C2×Q8—3441no—
183C2×Q8—3441no—
184C2×Q8—3442no—
185C2×Q8—3441no—
186C2×Q8C2×Dic8611yescharacteristic
187C2×Q8#1062189811yescharacteristic
188C2×Q8Q8×D4312yes—
189C22×C4—21no—
190C22×C4—21no—
191C22×C4—862no—
192C22×C4—862no—
193C22×C4D4×D4312yes—
194C22×C4C2×C22⋊D4311yescharacteristic
195M16—22no—
196M16—41no—
197M16—864no—
198M16—1722no—
199C2×C8—41no—
200C2×C8—1722no—
201C4⋊C4—21no—
202C4⋊C4—22no—
203C4⋊C4—21no—
204C4⋊C4—22no—
205C4⋊C4—41no—
206C4⋊C4—3442no—
207C4⋊C4—3441no—
208C4⋊C4—1722no—
209C22⋊C4—41no—
210C42—41no—
211C42—41no—
212C42—42no—
213C42—1722no—
214C23#1306329311yescharacteristic
215Q8—41no—
216Q8—41no—
217Q8—42no—
218Q8—3444no—
219Q8—3444no—
220C2×C4—21no—
221C2×C4—22no—
222C2×C4—21no—
223C2×C4—22no—
224C2×C4—22no—
225C2×C4—41no—
226C2×C4—41no—
227C2×C4—42no—
228C2×C4—41no—
229C2×C4—41no—
230C2×C4—41no—
231C2×C4—864no—
232C2×C4—1722no—
233C2×C4—1722no—
234C2×C4—1722no—
235C2×C4—1722no—
236C2×C4—1722no—
237C2×C4#1306330312yes—
238C2×C4#1306330411yescharacteristic
239C2×C4#1306332311yescharacteristic
240C2×C4#1306332412yes—
241C8—42no—
242C8—1724no—
243C22—21no—
244C22—21no—
245C22#1458281911yescharacteristic
246C22#1458308511yescharacteristic
247C22#1458308811yescharacteristic
248C4—21no—
249C4—22no—
250C4—21no—
251C4—22no—
252C4—42no—
253C4—81no—
254C4—81no—
255C4—81no—
256C4—3442no—
257C4—1724no—
258C2—21no—
259C2—21no—
260C2#1913594811yescharacteristic
261C2#1913661111yescharacteristic
262C2#1913662411yescharacteristic
subgroupG/H
centerC22#14583085
commutator, cosocleC22×Q8×C43C23
FrattiniC22×Q8C22×D43
FittingC43×#1857C2
socleC22×C43B(4,𝔽2)
prime radicalC23×C43#120
hypercenter#1857D43
hypocenterC43#13464
LCSG ▷ C22×Q8×C43 ▷ C22×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23 ◁ C22×Q8 ◁ #1857

Complements

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

NH ≅ G/Ntype
29. #13063244Q8semidirect
45. #101×C43Q8semidirect
150. C43#13464semidirect
173. #101Dic86semidirect

Maximal subgroups

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

subgroupindex
#191425882
#191348102
#191327222
#191327212
C43×#18572
#1346443