Finite Group Databasebeta

← #25013438

Subgroups — #25013438

Order 11008.

460 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 460 conjugacy classes of subgroups — too many to draw. Only its 103 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#19137685C211yesmaximal, characteristic
2#19134989C211yesmaximal, characteristic
3#19134812C212yesmaximal
4#19132721C212yesmaximal
5C2×C43×#356C211yesmaximal, characteristic
6#14583377C2211yescharacteristic
7#14582941—22no—
8#14582908—21no—
9C2×#13063244C2211yescharacteristic
10#14582806—21no—
11#14582806C2212yes—
12#14582798—22no—
13C4⋊C4×Dic43—22no—
14C4×C4⋊Dic43—21no—
15#14582660—22no—
16#14582659—21no—
17C2×C4⋊Q8×C43C2211yescharacteristic
18C2×#101×C43C2212yes—
19C43×#356C414yescomplemented
20C2×#10621877—21no—
21Q8×Dic43—41no—
22Q8×Dic43—41no—
23#13063284—21no—
24#13063284—22no—
25C2×C4⋊Dic43—21no—
26C2×C4⋊Dic43—21no—
27C2×C4⋊Dic43—21no—
28C2×C4⋊Dic43D412yes—
29C2×C4×Dic43—22no—
30C2×C4×Dic43—21no—
31C2×C4×Dic43D412yes—
32#13063259—42no—
33#13063257—42no—
34#13063249—41no—
35#13063249—41no—
36#13063244—22no—
37C43⋊#95—22no—
38C43⋊#95—22no—
39C43⋊#95—22no—
40C22×Q8×C43D411yescharacteristic
41C22×Q8×C43C2311yescharacteristic
42C2×M16×C43—22no—
43C4⋊Q8×C43—22no—
44C4⋊Q8×C43C2×C412yes—
45C4⋊Q8×C43Q812yes—
46C2×C4⋊C4×C43—22no—
47C2×C42×C43D411yescharacteristic
48#101×C43—22no—
49#101×C43C2×C414yes—
50C2×Q8×C43—21no—
51C2×Q8×C43—41no—
52C2×Q8×C43—41no—
53C2×Q8×C43—41no—
54C2×Q8×C43—41no—
55C2×Q8×C43C4⋊C412yes—
56C2×Q8×C43C22×C411yescharacteristic
57C2×Q8×C43C2×Q811yescharacteristic
58C2×Q8×C43#4112yes—
59C22×C4×C43—21no—
60C22×C4×C43—21no—
61C22×C4×C43C2×D411yescharacteristic
62C22×C4×C43C2×D412yes—
63C22×Dic43—22no—
64C22×Dic43—22no—
65M16×C43—24no—
66M16×C43—42no—
67C2×C8×C43—42no—
68C4⋊C4×C43—24no—
69C4⋊C4×C43—24no—
70C42×C43—21no—
71C42×C43C4⋊C412yes—
72C22⋊Dic43—41no—
73C4⋊Dic43—24no—
74C4⋊Dic43—21no—
75C4⋊Dic43—21no—
76C4⋊Dic43—22no—
77C4⋊Dic43—22no—
78C4⋊Dic43—42no—
79C4⋊Dic43—42no—
80C4⋊Dic43—81no—
81C4×Dic43—44no—
82C4×Dic43—41no—
83C4×Dic43—42no—
84C4×Dic43—42no—
85C4×Dic43—81no—
86#10621877—41no—
87#10621877—41no—
88C2×C43⋊C8—41no—
89C23×C43#12011yescharacteristic
90Q8×C43—41no—
91Q8×C43—41no—
92Q8×C43—42no—
93Q8×C43—42no—
94Q8×C43—81no—
95C2×C4×C43—22no—
96C2×C4×C43—22no—
97C2×C4×C43—22no—
98C2×C4×C43—21no—
99C2×C4×C43—22no—
100C2×C4×C43—21no—
101C2×C4×C43—22no—
102C2×C4×C43—22no—
103C2×C4×C43—41no—
104C2×C4×C43—41no—
105C2×C4×C43C2×C4⋊C411yescharacteristic
106C2×C4×C43C4×D412yes—
107C2×C4×C43C22⋊Q812yes—
108C2×C4×C43#12311yescharacteristic
109C2×Dic43—24no—
110C2×Dic43—42no—
111C2×Dic43—42no—
112C2×Dic43—42no—
113C2×Dic43—42no—
114C2×Dic43—41no—
115C2×Dic43—41no—
116C2×Dic43—42no—
117C8×C43—44no—
118C43⋊C8—81no—
119#12973—431nomaximal, Sylow
120C22×C43—21no—
121C22×C43—21no—
122C22×C43#38511yescharacteristic
123C22×C43B(4,𝔽2)11yescharacteristic
124C22×C43#45811yescharacteristic
125C4×C43—24no—
126C4×C43—21no—
127C4×C43—22no—
128C4×C43—21no—
129C4×C43—22no—
130C4×C43—42no—
131Dic43—44no—
132Dic43—81no—
133Dic43—82no—
134Dic43—81no—
135#2369—431no—
136C2×#356D4311yescharacteristic
137#1886—431no—
138#1857—432no—
139#1394—432no—
140C2×C43—21no—
141C2×C43—21no—
142C2×C43#186711yescharacteristic
143C2×C43#220411yescharacteristic
144C2×C43#220511yescharacteristic
145C2×C4⋊Q8C2×D4311yescharacteristic
146#519—431no—
147#428—862no—
148#419—861no—
149C2×#101—431no—
150C2×#101C2×D4312yes—
151#391—432no—
152#391—861no—
153#389—862no—
154C4×C4⋊C4—862no—
155C4×C4⋊C4—861no—
156#356Dic4314yescomplemented
157#339—862no—
158#339—861no—
159C43#1297311yescharacteristic, complemented, Sylow
160C22×Q8D17211yescharacteristic
161C22×Q8C22×D4311yescharacteristic
162C2×M16—22no—
163C2×M16—861no—
164C4⋊Q8—22no—
165C4⋊Q8Dic8612yes—
166C4⋊Q8C2×Dic4312yes—
167C4×Q8—1721no—
168C4×Q8—1721no—
169#117—861no—
170#117—862no—
171C2×C4⋊C4—22no—
172C2×C4⋊C4—432no—
173C2×C4⋊C4—861no—
174C2×C4⋊C4—861no—
175C2×C4⋊C4—861no—
176C2×C42—432no—
177C2×C42—861no—
178C2×C42—862no—
179C2×C42D17211yescharacteristic
180#107—1722no—
181#106—1722no—
182#103—1721no—
183#103—1721no—
184#101—22no—
185#101—862no—
186#101C2×Dic4314yes—
187#95—862no—
188#95—862no—
189#95—862no—
190C2×Q8—21no—
191C2×Q8—41no—
192C2×Q8—41no—
193C2×Q8—41no—
194C2×Q8—41no—
195C2×Q8C4⋊Dic4312yes—
196C2×Q8C2×Dic8611yescharacteristic
197C2×Q8#1062190012yes—
198C2×Q8C22×Dic4311yescharacteristic
199C22×C4—21no—
200C22×C4—21no—
201C22×C4—862no—
202C22×C4—862no—
203C22×C4C2×D17211yescharacteristic
204C22×C4D4×D4312yes—
205M16—24no—
206M16—42no—
207M16—1721no—
208M16—1721no—
209C2×C8—42no—
210C2×C8—1721no—
211C4⋊C4—24no—
212C4⋊C4—24no—
213C4⋊C4—864no—
214C4⋊C4—861no—
215C4⋊C4—861no—
216C4⋊C4—862no—
217C4⋊C4—862no—
218C4⋊C4—3441no—
219C4⋊C4—1722no—
220C4⋊C4—1722no—
221C22⋊C4—1721no—
222C42—21no—
223C42—3441no—
224C42—1722no—
225C42—1724no—
226C42—1722no—
227C42—1721no—
228C42C4⋊Dic4312yes—
229C23#1306329511yescharacteristic
230Q8—41no—
231Q8—42no—
232Q8—41no—
233Q8—42no—
234Q8—81no—
235C2×C4—22no—
236C2×C4—22no—
237C2×C4—22no—
238C2×C4—21no—
239C2×C4—22no—
240C2×C4—21no—
241C2×C4—22no—
242C2×C4—22no—
243C2×C4—41no—
244C2×C4—41no—
245C2×C4—864no—
246C2×C4—1722no—
247C2×C4—1722no—
248C2×C4—1721no—
249C2×C4—1721no—
250C2×C4—1722no—
251C2×C4—1722no—
252C2×C4—1722no—
253C2×C4C2×C4⋊Dic4311yescharacteristic
254C2×C4D4×Dic4312yes—
255C2×C4#1306330212yes—
256C2×C4#1306330911yescharacteristic
257C8—44no—
258C8—3441no—
259C22—21no—
260C22—21no—
261C22#1458277411yescharacteristic
262C22#1458308711yescharacteristic
263C22#1458309011yescharacteristic
264C4—24no—
265C4—22no—
266C4—21no—
267C4—21no—
268C4—22no—
269C4—42no—
270C4—3442no—
271C4—3441no—
272C4—3441no—
273C4—1724no—
274C2—21no—
275C2—21no—
276C2#1913487811yescharacteristic
277C2#1913662311yescharacteristic
278C2#1913662611yescharacteristic
subgroupG/H
centerC22#14583087
commutatorC2×Q8×C43C22×C4
FrattiniC22×Q8C22×D43
FittingC2×C43×#356C2
socleC22×C43B(4,𝔽2)
prime radicalC23×C43#120
cosocleC22×Q8×C43C23
hypercenterC2×#356D43
hypocenterC43#12973
LCSG ▷ C2×Q8×C43 ▷ C22×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23 ◁ C22×Q8 ◁ C2×#356

Complements

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

NH ≅ G/Ntype
19. C43×#356C4semidirect
156. #356Dic43semidirect
159. C43#12973semidirect

Maximal subgroups

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

subgroupindex
#191376852
#191349892
#191348122
#191327212
C2×C43×#3562
#1297343