Finite Group Databasebeta

← #24999589

Subgroups — #24999589

Order 11008.

640 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 640 conjugacy classes of subgroups — too many to draw. Only its 109 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#19134529C212yesmaximal
2#19132865C211yesmaximal, characteristic
3#19132473C212yesmaximal
4#19132438C211yesmaximal, characteristic
5C43×#2646C211yesmaximal, characteristic
6C23×Dic86C2211yescharacteristic
7C2×#13063248—22no—
8C2×#13063248—22no—
9C2×C22⋊(C43⋊C8)C2212yes—
10C2×C43⋊#95—22no—
11C2×C43⋊#95C2211yescharacteristic
12C43×#400—22no—
13C43×#398—22no—
14C43×#385—22no—
15C43×#380C2212yes—
16C2×#95×C43C2211yescharacteristic
17C22×Dic86—22no—
18C22×Dic86—22no—
19C22×Dic86—21no—
20C22×Dic86—44no—
21C22×Dic86Q812yes—
22C23×Dic43—21no—
23C23×Dic43—21no—
24C22×C43⋊C8—22no—
25#13063248—44no—
26#13063248—44no—
27C22⋊(C43⋊C8)—22no—
28C22⋊(C43⋊C8)—22no—
29C43⋊#95—22no—
30C43⋊#95—44no—
31C23×C4×C43D412yes—
32C23×C4×C43C2311yescharacteristic
33C2×C4⋊C4×C43—22no—
34C2×C4⋊C4×C43—22no—
35C2×C4⋊C4×C43D412yes—
36C2×C4⋊C4×C43D412yes—
37C2×C22⋊C4×C43—22no—
38#95×C43—22no—
39#95×C43—22no—
40#95×C43—22no—
41#95×C43—22no—
42C24×C43C2×D411yescharacteristic
43C22×C4×C43—22no—
44C22×C4×C43—22no—
45C22×C4×C43—22no—
46C22×C4×C43—22no—
47C22×C4×C43—22no—
48C22×C4×C43—42no—
49C22×C4×C43—42no—
50C22×C4×C43—42no—
51C22×C4×C43C2×D412yes—
52C22×C4×C43C2×Q811yescharacteristic
53C22×C4×C43#4111yescharacteristic
54C22×C4×C43#4112yes—
55C22×Dic43—24no—
56C22×Dic43—22no—
57C22×Dic43—22no—
58C22×Dic43—42no—
59C22×Dic43—42no—
60C22×Dic43—41no—
61C22×Dic43—41no—
62C22×Dic43—41no—
63C22×Dic43—41no—
64C22×Dic43—42no—
65C2×Dic86—24no—
66C2×Dic86—24no—
67C2×Dic86—24no—
68C2×Dic86—44no—
69C2×Dic86—48no—
70C2×Dic86—44no—
71C2×Dic86—42no—
72C2×Dic86—42no—
73C2×Dic86—42no—
74C4⋊C4×C43—42no—
75C4⋊C4×C43—42no—
76C4⋊C4×C43—82no—
77C4⋊C4×C43—82no—
78C22⋊C4×C43—42no—
79C22⋊C4×C43—42no—
80C2×C43⋊C8—42no—
81C2×C43⋊C8—42no—
82C2×C43⋊C8—42no—
83C23×C43—21no—
84C23×C43—21no—
85C23×C43—22no—
86C23×C43#12011yescharacteristic
87C23×C43C22⋊Q811yescharacteristic
88C23×C43#12411yescharacteristic
89C23×C43#13512yes—
90C23×C43#13712yes—
91C2×C4×C43—22no—
92C2×C4×C43—22no—
93C2×C4×C43—41no—
94C2×C4×C43—41no—
95C2×C4×C43—42no—
96C2×C4×C43—44no—
97C2×C4×C43—42no—
98C2×C4×C43—42no—
99C2×C4×C43—42no—
100C2×C4×C43—42no—
101C2×C4×C43—42no—
102C2×C4×C43—42no—
103C2×C4×C43—42no—
104C2×C4×C43—42no—
105C2×C4×C43—42no—
106C2×C4×C43—82no—
107C2×C4×C43C22⋊Q812yes—
108C2×C4×C43#12412yes—
109C2×Dic43—24no—
110C2×Dic43—42no—
111C2×Dic43—44no—
112C2×Dic43—42no—
113C2×Dic43—44no—
114C2×Dic43—44no—
115C2×Dic43—42no—
116C2×Dic43—82no—
117C2×Dic43—81no—
118C2×Dic43—81no—
119Dic86—28no—
120Dic86—44no—
121Dic86—44no—
122Dic86—44no—
123C43⋊C8—82no—
124#10345—431nomaximal, Sylow
125C22×C43—22no—
126C22×C43—22no—
127C22×C43—22no—
128C22×C43—22no—
129C22×C43—21no—
130C22×C43—21no—
131C22×C43—21no—
132C22×C43—21no—
133C22×C43#39311yescharacteristic
134C22×C43#45212yes—
135C22×C43#45511yescharacteristic
136C22×C43#45611yescharacteristic
137C22×C43B(4,𝔽2)12yes—
138C22×C43#47912yes—
139C22×C43#48811yescharacteristic
140C22×C43#49111yescharacteristic
141C4×C43—22no—
142C4×C43—22no—
143C4×C43—82no—
144C4×C43—82no—
145C4×C43—82no—
146Dic43—44no—
147Dic43—82no—
148#2646D4311yescharacteristic
149#1787—432no—
150#1446—431no—
151#1294—432no—
152#1280—431no—
153C2×C43—21no—
154C2×C43—22no—
155C2×C43—21no—
156C2×C43#160312yes—
157C2×C43#160612yes—
158C2×C43#202611yescharacteristic
159C2×C43#202811yescharacteristic
160C2×C43#202911yescharacteristic
161C23×Q8—431no—
162C2×#103—862no—
163C2×#103—862no—
164C2×C22⋊C8—432no—
165#400—22no—
166#398—22no—
167#385—22no—
168#380C2×D4312yes—
169C2×#95—431no—
170C2×#95—862no—
171C2×#95C2×D4311yescharacteristic
172C43#1034511yescharacteristic, complemented, Sylow
173C22×Q8—432no—
174C22×Q8—861no—
175C22×Q8—862no—
176C22×Q8—862no—
177C22×Q8—1724no—
178C23×C4—861no—
179C23×C4—861no—
180C23×C4C22⋊D4312yes—
181C23×C4C22×D4311yescharacteristic
182C22×C8—862no—
183C2×C4⋊C4—22no—
184C2×C4⋊C4—22no—
185C2×C4⋊C4C22⋊D4312yes—
186C2×C4⋊C4C22⋊D4312yes—
187C2×C22⋊C4—22no—
188#103—1724no—
189#103—1724no—
190C22⋊C8—862no—
191C22⋊C8—862no—
192#95—22no—
193#95—22no—
194#95—22no—
195#95—22no—
196#95—862no—
197#95—1724no—
198C24C2×C22⋊D4311yescharacteristic
199C2×Q8—864no—
200C2×Q8—864no—
201C2×Q8—864no—
202C2×Q8—1722no—
203C2×Q8—1722no—
204C2×Q8—1724no—
205C2×Q8—1724no—
206C2×Q8—1728no—
207C2×Q8—1722no—
208C22×C4—22no—
209C22×C4—22no—
210C22×C4—22no—
211C22×C4—22no—
212C22×C4—22no—
213C22×C4—42no—
214C22×C4—42no—
215C22×C4—42no—
216C22×C4—864no—
217C22×C4—862no—
218C22×C4—862no—
219C22×C4—1722no—
220C22×C4—1721no—
221C22×C4—1721no—
222C22×C4—1722no—
223C22×C4—1722no—
224C22×C4—1721no—
225C22×C4—1721no—
226C22×C4Q8×D4311yescharacteristic
227C22×C4#1062190212yes—
228C22×C4#1062190211yescharacteristic
229C22×C4C2×C22⋊D4312yes—
230C2×C8—1722no—
231C2×C8—1722no—
232C2×C8—1722no—
233C4⋊C4—42no—
234C4⋊C4—42no—
235C4⋊C4—82no—
236C4⋊C4—82no—
237C22⋊C4—42no—
238C22⋊C4—42no—
239C23—21no—
240C23—21no—
241C23—22no—
242C23#1306329411yescharacteristic
243C23#1306330111yescharacteristic
244C23#1306331411yescharacteristic
245C23#1306334512yes—
246C23#1306335512yes—
247Q8—868no—
248Q8—1724no—
249Q8—1724no—
250Q8—1724no—
251C2×C4—22no—
252C2×C4—22no—
253C2×C4—41no—
254C2×C4—41no—
255C2×C4—42no—
256C2×C4—44no—
257C2×C4—42no—
258C2×C4—42no—
259C2×C4—42no—
260C2×C4—42no—
261C2×C4—42no—
262C2×C4—42no—
263C2×C4—42no—
264C2×C4—42no—
265C2×C4—42no—
266C2×C4—82no—
267C2×C4—864no—
268C2×C4—3441no—
269C2×C4—3442no—
270C2×C4—3441no—
271C2×C4—1722no—
272C2×C4—1724no—
273C2×C4—1722no—
274C2×C4—1724no—
275C2×C4—1722no—
276C2×C4—1724no—
277C2×C4#1306330112yes—
278C2×C4#1306331412yes—
279C8—3442no—
280C22—21no—
281C22—21no—
282C22—21no—
283C22—21no—
284C22—22no—
285C22—22no—
286C22—22no—
287C22—22no—
288C22#1458281011yescharacteristic
289C22#1458306112yes—
290C22#1458307711yescharacteristic
291C22#1458308211yescharacteristic
292C22#1458308612yes—
293C22#1458320312yes—
294C22#1458325611yescharacteristic
295C22#1458326911yescharacteristic
296C4—22no—
297C4—22no—
298C4—82no—
299C4—82no—
300C4—82no—
301C4—3442no—
302C4—1724no—
303C2—21no—
304C2—22no—
305C2—21no—
306C2#1913355812yes—
307C2#1913357512yes—
308C2#1913574311yescharacteristic
309C2#1913575311yescharacteristic
310C2#1913575811yescharacteristic
subgroupG/H
centerC23#13063294
commutator, cosocleC23×C4×C43C23
FrattiniC23×C4C22×D43
FittingC43×#2646C2
socleC23×C43#120
prime radicalC24×C43C2×D4
hypercenter#2646D43
hypocenterC43#10345
LCSG ▷ C23×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ #2646

Complements

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

NH ≅ G/Ntype
172. C43#10345semidirect

Maximal subgroups

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

subgroupindex
#191345292
#191328652
#191324732
#191324382
C43×#26462
#1034543