Finite Group Databasebeta

← #25009734

Subgroups — #25009734

Order 11008.

372 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 372 conjugacy classes of subgroups — too many to draw. Only its 55 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#19142018C211yesmaximal, characteristic
2#19133586C211yesmaximal, characteristic
3#19133552C211yesmaximal, characteristic
4#19132615C211yesmaximal, characteristic
5#19132594C211yesmaximal, characteristic
6#19132525C211yesmaximal, characteristic
7C43×#2030C211yesmaximal, characteristic
8#14583227—21no—
9#14583054—21no—
10#14582840—21no—
11#14582833—21no—
12#14582824C2211yescharacteristic
13#14582811C2211yescharacteristic
14#14582803—21no—
15#14582793—21no—
16#14582772—21no—
17#14582766—21no—
18#14582636—21no—
19#14582636—21no—
20#14582623C2211yescharacteristic
21#14582623C2211yescharacteristic
22C43×#543C2211yescharacteristic
23C43×#381—21no—
24C43×#381C2211yescharacteristic
25C43×#342—21no—
26C43×#342C2211yescharacteristic
27C22×Dic86D411yescharacteristic
28C2×#10621885—41no—
29C2×C4⋊Dic43D411yescharacteristic
30C2×Dic43⋊C4—21no—
31C2×Dic43⋊C4—21no—
32C2×Dic43⋊C4—21no—
33C2×C22⋊Dic43—21no—
34C2×C22⋊Dic43—21no—
35C2×C4×Dic43—21no—
36#13063256—41no—
37#13063249—41no—
38#13063248—41no—
39C22⋊(C43⋊C8)—21no—
40C22⋊(C43⋊C8)—21no—
41C43⋊#95—21no—
42C43⋊#95—21no—
43C43⋊#95—21no—
44C43⋊#95—21no—
45C43⋊#95—21no—
46C43⋊#95—21no—
47C43⋊#95D411yescharacteristic
48C43⋊#95D411yescharacteristic
49C23×C4×C43D411yescharacteristic
50C22⋊Q8×C43—21no—
51C22⋊Q8×C43—21no—
52C22⋊Q8×C43—41no—
53C22⋊Q8×C43—41no—
54C2×C22⋊C4×C43—21no—
55C2×C22⋊C4×C43—21no—
56C2×C22⋊C4×C43D411yescharacteristic
57C2×C22⋊C4×C43C2311yescharacteristic
58#95×C43—21no—
59#95×C43—21no—
60#95×C43—41no—
61#95×C43—41no—
62C24×C43C2×D411yescharacteristic
63C2×Q8×C43—21no—
64C2×Q8×C43—21no—
65C22×C4×C43—21no—
66C22×C4×C43—21no—
67C22×C4×C43—21no—
68C22×C4×C43—21no—
69C22×C4×C43—21no—
70C22×C4×C43—21no—
71C22×C4×C43—41no—
72C22×C4×C43—41no—
73C22×C4×C43—41no—
74C22×C4×C43C2×D411yescharacteristic
75C22×C4×C43C2×D411yescharacteristic
76C22×Dic43—21no—
77C22×Dic43—21no—
78C22×Dic43—21no—
79C22×Dic43—21no—
80C2×Dic86—41no—
81C2×Dic86—42no—
82C4⋊C4×C43—21no—
83C4⋊C4×C43—21no—
84C4⋊C4×C43—41no—
85C4⋊C4×C43—41no—
86C22⋊C4×C43—41no—
87C22⋊C4×C43—41no—
88C22⋊C4×C43—41no—
89C22⋊C4×C43—41no—
90C22⋊C4×C43—41no—
91C22⋊C4×C43—41no—
92C22⋊Dic43—42no—
93C22⋊Dic43—41no—
94C22⋊Dic43—41no—
95#10621885—82no—
96C4⋊Dic43—41no—
97Dic43⋊C4—81no—
98Dic43⋊C4—81no—
99Dic43⋊C4—81no—
100C4×Dic43—42no—
101C2×C43⋊C8—41no—
102C2×C43⋊C8—41no—
103C23×C43—21no—
104C23×C43—21no—
105C23×C43—41no—
106C23×C43—41no—
107C23×C43#12011yescharacteristic
108C23×C43#13511yescharacteristic
109C23×C43#13711yescharacteristic
110Q8×C43—81no—
111Q8×C43—81no—
112C2×C4×C43—21no—
113C2×C4×C43—21no—
114C2×C4×C43—41no—
115C2×C4×C43—41no—
116C2×C4×C43—41no—
117C2×C4×C43—41no—
118C2×C4×C43—42no—
119C2×C4×C43—41no—
120C2×C4×C43—41no—
121C2×C4×C43—41no—
122C2×C4×C43—41no—
123C2×C4×C43—41no—
124C2×C4×C43—41no—
125C2×C4×C43—81no—
126C2×C4×C43—81no—
127C2×C4×C43—81no—
128C2×C4×C43—81no—
129C2×C4×C43—81no—
130C2×C4×C43—81no—
131C2×Dic43—22no—
132C2×Dic43—41no—
133C2×Dic43—41no—
134C2×Dic43—41no—
135C2×Dic43—41no—
136C2×Dic43—41no—
137C2×Dic43—41no—
138C2×Dic43—41no—
139C2×Dic43—41no—
140C2×Dic43—41no—
141C2×Dic43—41no—
142C2×Dic43—41no—
143Dic86—42no—
144Dic86—81no—
145C43⋊C8—81no—
146C43⋊C8—81no—
147#12269—431nomaximal, Sylow
148C22×C43—21no—
149C22×C43—21no—
150C22×C43—21no—
151C22×C43—21no—
152C22×C43—41no—
153C22×C43—41no—
154C22×C43—41no—
155C22×C43—41no—
156C22×C43—81no—
157C22×C43#45211yescharacteristic
158C22×C43#45511yescharacteristic
159C22×C43B(4,𝔽2)11yescharacteristic
160C4×C43—41no—
161C4×C43—41no—
162C4×C43—81no—
163C4×C43—81no—
164C4×C43—81no—
165C4×C43—81no—
166C4×C43—161no—
167Dic43—42no—
168Dic43—81no—
169Dic43—81no—
170Dic43—81no—
171#2764—431no—
172#2030D4311yescharacteristic
173#1608—431no—
174#1602—431no—
175#1351—431no—
176#1344—431no—
177#1317—431no—
178C2×C43—21no—
179C2×C43—21no—
180C2×C43—41no—
181C2×C43—41no—
182C2×C43#160611yescharacteristic
183C2×C43#219711yescharacteristic
184C2×C43#220111yescharacteristic
185#543C2×D4311yescharacteristic
186#483—861no—
187#451—861no—
188#400—861no—
189#398—861no—
190#397—431no—
191#393—431no—
192#391—861no—
193#388—861no—
194#385—861no—
195#383—861no—
196#381—21no—
197#381C2×D4311yescharacteristic
198#342—21no—
199#342C2×D4311yescharacteristic
200#328—861no—
201#328—861no—
202#323—431no—
203#323—431no—
204C43#1226911yescharacteristic, complemented, Sylow
205C22×Q8—431no—
206C23×C4C22⋊D4311yescharacteristic
207C2×Q16—1721no—
208C22⋊Q8—21no—
209C22⋊Q8—21no—
210C22⋊Q8—41no—
211C22⋊Q8—41no—
212C2×C4⋊C4—431no—
213C2×C4⋊C4—861no—
214C2×C4⋊C4—861no—
215C2×C4⋊C4—861no—
216C2×C22⋊C4—21no—
217C2×C22⋊C4—21no—
218C2×C22⋊C4—861no—
219C2×C22⋊C4—861no—
220C2×C22⋊C4C22⋊D4311yescharacteristic
221C2×C22⋊C4C22×D4311yescharacteristic
222C2×C42—861no—
223#106—1721no—
224#103—1721no—
225#103—1721no—
226C22⋊C8—861no—
227C22⋊C8—861no—
228#95—21no—
229#95—21no—
230#95—41no—
231#95—41no—
232#95—431no—
233#95—431no—
234#95—861no—
235#95—861no—
236#95—861no—
237#95—861no—
238#95—861no—
239#95—861no—
240C24C2×C22⋊D4311yescharacteristic
241C2×Q8—21no—
242C2×Q8—21no—
243C2×Q8—1721no—
244C2×Q8—1722no—
245C22×C4—21no—
246C22×C4—21no—
247C22×C4—21no—
248C22×C4—21no—
249C22×C4—21no—
250C22×C4—21no—
251C22×C4—41no—
252C22×C4—41no—
253C22×C4—41no—
254C22×C4—861no—
255C22×C4—861no—
256C22×C4—861no—
257C22×C4—861no—
258C22×C4D4×D4311yescharacteristic
259C22×C4D4×D4311yescharacteristic
260Q16—3442no—
261C2×C8—1721no—
262C2×C8—1721no—
263C4⋊C4—21no—
264C4⋊C4—21no—
265C4⋊C4—41no—
266C4⋊C4—41no—
267C4⋊C4—3441no—
268C4⋊C4—3441no—
269C4⋊C4—3441no—
270C4⋊C4—1721no—
271C22⋊C4—41no—
272C22⋊C4—41no—
273C22⋊C4—41no—
274C22⋊C4—41no—
275C22⋊C4—41no—
276C22⋊C4—41no—
277C22⋊C4—1722no—
278C22⋊C4—1721no—
279C22⋊C4—1721no—
280C42—1722no—
281C23—21no—
282C23—21no—
283C23—41no—
284C23—41no—
285C23#1306329311yescharacteristic
286C23#1306334511yescharacteristic
287C23#1306335611yescharacteristic
288Q8—81no—
289Q8—81no—
290Q8—3441no—
291Q8—1722no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—41no—
295C2×C4—41no—
296C2×C4—41no—
297C2×C4—42no—
298C2×C4—41no—
299C2×C4—41no—
300C2×C4—41no—
301C2×C4—41no—
302C2×C4—41no—
303C2×C4—41no—
304C2×C4—41no—
305C2×C4—81no—
306C2×C4—81no—
307C2×C4—81no—
308C2×C4—81no—
309C2×C4—81no—
310C2×C4—81no—
311C2×C4—862no—
312C2×C4—1721no—
313C2×C4—1721no—
314C2×C4—1721no—
315C2×C4—1721no—
316C2×C4—1721no—
317C2×C4—1721no—
318C2×C4—1721no—
319C2×C4—1721no—
320C2×C4—1721no—
321C2×C4—1721no—
322C2×C4—1721no—
323C8—3441no—
324C8—3441no—
325C22—21no—
326C22—21no—
327C22—21no—
328C22—21no—
329C22—41no—
330C22—41no—
331C22—41no—
332C22—41no—
333C22—81no—
334C22#1458305911yescharacteristic
335C22#1458307611yescharacteristic
336C22#1458308511yescharacteristic
337C4—41no—
338C4—41no—
339C4—81no—
340C4—81no—
341C4—81no—
342C4—81no—
343C4—161no—
344C4—3441no—
345C4—3441no—
346C4—3441no—
347C4—1722no—
348C2—21no—
349C2—21no—
350C2—41no—
351C2—41no—
352C2#1913357311yescharacteristic
353C2#1913658211yescharacteristic
354C2#1913660611yescharacteristic
subgroupG/H
centerC22#14583085
commutator, cosocleC2×C22⋊C4×C43C23
FrattiniC2×C22⋊C4C22×D43
FittingC43×#2030C2
socleC22×C43B(4,𝔽2)
prime radicalC24×C43C2×D4
hypercenter#2030D43
hypocenterC43#12269
LCSG ▷ C2×C22⋊C4×C43 ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23 ◁ C2×C22⋊C4 ◁ #2030

Complements

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

NH ≅ G/Ntype
204. C43#12269semidirect

Maximal subgroups

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

subgroupindex
#191420182
#191335862
#191335522
#191326152
#191325942
#191325252
C43×#20302
#1226943