Finite Group Databasebeta

← #24999346

Subgroups — #24999346

Order 11008.

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

normal subgroups only

This group has 576 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#19145741C211yesmaximal, characteristic
2#19145739C211yesmaximal, characteristic
3#19142991C211yesmaximal, characteristic
4#19135571C211yesmaximal, characteristic
5#19133268C211yesmaximal, characteristic
6#19132427C211yesmaximal, characteristic
7C43×#1546C211yesmaximal, characteristic
8#14583456C2211yescharacteristic
9C2×#13063325C2211yescharacteristic
10C2×#13063323—22no—
11#14583297—21no—
12#14583295—21no—
13#14583251—21no—
14#14583250—21no—
15#14583230—22no—
16#14583229—22no—
17#14583185—22no—
18#14583181—22no—
19#14582952C2211yescharacteristic
20#14582768—22no—
21#14582768—22no—
22C42×Dic43C2211yescharacteristic
23#14582660—22no—
24#14582646—22no—
25C2×C4⋊Q8×C43C2211yescharacteristic
26C43×#431C2211yescharacteristic
27C43×#423C2211yescharacteristic
28C43×#332—22no—
29C22×Dic86—21no—
30#13063325—21no—
31#13063325—21no—
32#13063325—21no—
33#13063325—21no—
34#13063325D411yescharacteristic
35#13063325D411yescharacteristic
36#13063323—44no—
37#13063323—44no—
38#13063317—21no—
39#13063304—21no—
40#13063304—21no—
41C4×Dic86—21no—
42C4×Dic86—21no—
43#13063284—21no—
44C2×C4⋊Dic43—21no—
45C2×C4⋊Dic43D412yes—
46C2×Dic43⋊C4—28no—
47C2×C4×Dic43—21no—
48C2×C4×Dic43—21no—
49C2×C4×Dic43D412yes—
50#13063257—24no—
51#13063256—24no—
52C4⋊(C43⋊C8)D412yes—
53#13063250—24no—
54#13063248—24no—
55C22⋊(C43⋊C8)—21no—
56C4×C43⋊C8—21no—
57C22×Q8×C43—21no—
58C2×M16×C43—21no—
59C4⋊Q8×C43—21no—
60C4⋊Q8×C43—21no—
61C4⋊Q8×C43—21no—
62C4⋊Q8×C43—21no—
63C2×C4⋊C4×C43—21no—
64C2×C4⋊C4×C43D412yes—
65C2×C42×C43C2311yescharacteristic
66C4⋊C8×C43—21no—
67C4⋊C8×C43—21no—
68C4⋊C8×C43D412yes—
69C22⋊C8×C43—21no—
70C4×C8×C43—21no—
71C2×Q8×C43—41no—
72C2×Q8×C43—41no—
73C2×Q8×C43—42no—
74C2×Q8×C43—42no—
75C22×C4×C43—22no—
76C22×C4×C43C2×D411yescharacteristic
77C22×C4×C43C2×D411yescharacteristic
78C22×C4×C43C2×D411yescharacteristic
79C22×Dic43—22no—
80C22×Dic43—22no—
81C2×Dic86—21no—
82C2×Dic86—21no—
83C2×Dic86—41no—
84C2×Dic86—41no—
85C2×Dic86—42no—
86C2×Dic86—42no—
87M16×C43—42no—
88C2×C8×C43—22no—
89C2×C8×C43—41no—
90C4⋊C4×C43—22no—
91C4⋊C4×C43—22no—
92C4⋊C4×C43—41no—
93C4⋊C4×C43—41no—
94C42×C43C2×D411yescharacteristic
95C42×C43C2×D411yescharacteristic
96C42×C43C2×D411yescharacteristic
97C42×C43#4111yescharacteristic
98C22⋊Dic43—41no—
99C4⋊Dic43—22no—
100C4⋊Dic43—21no—
101C4⋊Dic43—21no—
102C4⋊Dic43—22no—
103C4⋊Dic43—21no—
104C4⋊Dic43—21no—
105C4⋊Dic43—41no—
106C4⋊Dic43—41no—
107Dic43⋊C4—416no—
108Dic43⋊C4—41no—
109Dic43⋊C4—41no—
110C4×Dic43—24no—
111C4×Dic43—24no—
112C4×Dic43—22no—
113C4×Dic43—41no—
114C4×Dic43SD1614yes—
115C2×C43⋊C8—22no—
116C23×C43#12011yescharacteristic
117Q8×C43—82no—
118Q8×C43—81no—
119Q8×C43—81no—
120C2×C4×C43—22no—
121C2×C4×C43—22no—
122C2×C4×C43—42no—
123C2×C4×C43—44no—
124C2×C4×C43#12011yescharacteristic
125C2×C4×C43#12011yescharacteristic
126C2×C4×C43#12111yescharacteristic
127C2×C4×C43#12111yescharacteristic
128C2×C4×C43#12111yescharacteristic
129C2×C4×C43#12711yescharacteristic
130C2×C4×C43C2×SD1612yes—
131C2×C4×C43AGL(1,ℤ/8)12yes—
132C2×Dic43—24no—
133C2×Dic43—24no—
134C2×Dic43—24no—
135C2×Dic43—41no—
136C2×Dic43—41no—
137C2×Dic43—42no—
138C2×Dic43—44no—
139Dic86—42no—
140Dic86—42no—
141Dic86—82no—
142Dic86—81no—
143Dic86—81no—
144C8×C43—42no—
145C8×C43—81no—
146C43⋊C8—42no—
147#10299—431nomaximal, Sylow
148C22×C43—21no—
149C22×C43—21no—
150C22×C43#39211yescharacteristic
151C22×C43#45012yes—
152C4×C43—21no—
153C4×C43—21no—
154C4×C43—82no—
155C4×C43#45612yes—
156C4×C43#45612yes—
157C4×C43#46012yes—
158C4×C43#49211yescharacteristic
159C4×C43#49611yescharacteristic
160Dic43—28no—
161Dic43—81no—
162Dic43—81no—
163Dic43—82no—
164#3229—431no—
165#3229—431no—
166#2868—431no—
167#1994—431no—
168#1546—431no—
169#1546D4311yescharacteristic
170#1276—431no—
171C2×C43—22no—
172C2×C43#200511yescharacteristic
173C2×C43#200511yescharacteristic
174C2×C43#201411yescharacteristic
175#533—431no—
176C2×C4⋊Q8—431no—
177C2×C4⋊Q8—862no—
178C2×C4⋊Q8C2×D4311yescharacteristic
179#498—861no—
180#498—861no—
181#487—861no—
182#487—861no—
183#483—862no—
184#483—862no—
185#475—862no—
186#475—862no—
187#431—431no—
188#431C2×D4311yescharacteristic
189#423C2×D4311yescharacteristic
190#384—862no—
191#384—862no—
192C43—431no—
193#339—862no—
194#332—22no—
195#332—862no—
196C43#1029911yescharacteristic, complemented, Sylow
197C22×Q8—21no—
198C22×Q8—861no—
199C2×M16—21no—
200C4⋊Q8—21no—
201C4⋊Q8—21no—
202C4⋊Q8—21no—
203C4⋊Q8—21no—
204C4⋊Q8—431no—
205C4⋊Q8—431no—
206C4⋊Q8—861no—
207C4⋊Q8—861no—
208C4⋊Q8—861no—
209C4⋊Q8—861no—
210C4⋊Q8—1724no—
211C4⋊Q8—1724no—
212#125—861no—
213C22⋊Q8—861no—
214C22⋊Q8—861no—
215C4×Q8—861no—
216C4×Q8—861no—
217#117—861no—
218C2×C4⋊C4—21no—
219C2×C4⋊C4—432no—
220C2×C4⋊C4—868no—
221C2×C4⋊C4—861no—
222C2×C4⋊C4D17212yes—
223C2×C42—432no—
224C2×C42—861no—
225C2×C42—861no—
226C2×C42C22×D4311yescharacteristic
227#106—864no—
228#106—864no—
229C4⋊C8—21no—
230C4⋊C8—21no—
231C4⋊C8—432no—
232C4⋊C8C22⋊D4312yes—
233#103—864no—
234#103—864no—
235C22⋊C8—21no—
236C22⋊C8—861no—
237C4×C8—21no—
238C4×C8—861no—
239C2×Q8—41no—
240C2×Q8—41no—
241C2×Q8—42no—
242C2×Q8—42no—
243C2×Q8—861no—
244C2×Q8—861no—
245C2×Q8—1721no—
246C2×Q8—1721no—
247C2×Q8—1722no—
248C2×Q8—1722no—
249C22×C4—22no—
250C22×C4—862no—
251C22×C4—862no—
252C22×C4C2×D17211yescharacteristic
253C22×C4D4×D4311yescharacteristic
254C22×C4D4×D4311yescharacteristic
255M16—42no—
256C2×C8—22no—
257C2×C8—41no—
258C2×C8—862no—
259C4⋊C4—22no—
260C4⋊C4—22no—
261C4⋊C4—41no—
262C4⋊C4—41no—
263C4⋊C4—862no—
264C4⋊C4—861no—
265C4⋊C4—861no—
266C4⋊C4—862no—
267C4⋊C4—861no—
268C4⋊C4—861no—
269C4⋊C4—17216no—
270C4⋊C4—1721no—
271C4⋊C4—1721no—
272C4⋊C4—1721no—
273C4⋊C4—1721no—
274C22⋊C4—1721no—
275C42—434no—
276C42—864no—
277C42—864no—
278C42—862no—
279C42—1721no—
280C42#1062189811yescharacteristic
281C42D4×D4311yescharacteristic
282C42D4×D4311yescharacteristic
283C42C2×C22⋊D4311yescharacteristic
284C23#1306329511yescharacteristic
285Q8—82no—
286Q8—81no—
287Q8—81no—
288Q8—3442no—
289Q8—3441no—
290Q8—3441no—
291Q8—1722no—
292Q8—1722no—
293C2×C4—22no—
294C2×C4—22no—
295C2×C4—44no—
296C2×C4—42no—
297C2×C4—864no—
298C2×C4—864no—
299C2×C4—864no—
300C2×C4—1724no—
301C2×C4—1721no—
302C2×C4—1721no—
303C2×C4—1722no—
304C2×C4#1306329311yescharacteristic
305C2×C4#1306329511yescharacteristic
306C2×C4#1306329811yescharacteristic
307C2×C4#1306329811yescharacteristic
308C2×C4#1306329911yescharacteristic
309C2×C4#1306332111yescharacteristic
310C2×C4SD16×D4312yes—
311C2×C4#1306334912yes—
312C8—42no—
313C8—81no—
314C8—1722no—
315C22—21no—
316C22—21no—
317C22#1458280811yescharacteristic
318C22#1458305112yes—
319C4—21no—
320C4—21no—
321C4—82no—
322C4—868no—
323C4—3441no—
324C4—3441no—
325C4—3442no—
326C4#1458308012yes—
327C4#1458308412yes—
328C4#1458309812yes—
329C4#1458327011yescharacteristic
330C4#1458328711yescharacteristic
331C2—22no—
332C2#1913563211yescharacteristic
333C2#1913563311yescharacteristic
334C2#1913568411yescharacteristic
subgroupG/H
centerC22#14582808
commutator, cosocleC2×C42×C43C23
FrattiniC2×C42C22×D43
FittingC43×#1546C2
socleC22×C43#392
prime radicalC23×C43#120
hypercenter#1546D43
hypocenterC43#10299
LCSG ▷ C2×C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1546

Complements

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

NH ≅ G/Ntype
196. C43#10299semidirect

Maximal subgroups

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

subgroupindex
#191457412
#191457392
#191429912
#191355712
#191332682
#191324272
C43×#15462
#1029943