Finite Group Databasebeta

← #25008921

Subgroups — #25008921

Order 11008.

478 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 478 conjugacy classes of subgroups — too many to draw. Only its 59 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#19135819C211yesmaximal, characteristic, complemented
2#19133563C211yesmaximal, characteristic, complemented
3#19133529C211yesmaximal, characteristic
4#19132625C211yesmaximal, characteristic, complemented
5#19132598C211yesmaximal, characteristic, complemented
6#19132541C211yesmaximal, characteristic, complemented
7C43×#2680C211yesmaximal, characteristic, complemented
8#14583480C2211yescharacteristic
9#14583038—21no—
10#14583033—21no—
11C2×#13063253—21no—
12#14582898—21no—
13#14582668C2211yescharacteristic
14#14582632—21no—
15#14582632—21no—
16#14582625C2211yescharacteristic
17#14582625C2211yescharacteristic
18C2×#123×C43—21no—
19C2×C22⋊Q8×C43—21no—
20C43×#398—21no—
21C43×#397—21no—
22C43×#395C2211yescharacteristic
23C43×#394C2211yescharacteristic
24C43×#388—21no—
25C43×#385—21no—
26C43×#384C2211yescharacteristic
27C2×#10621898—21no—
28C2×#10621884—41no—
29C2×#10621882—41no—
30C2×#10621877—21no—
31#13063305—41no—
32#13063300—41no—
33#13063299—21no—
34#13063299—21no—
35#13063253—42no—
36#13063249—41no—
37#13063248—41no—
38#13063246—41no—
39#13063245—41no—
40C22⋊(C43⋊C8)—21no—
41C22⋊(C43⋊C8)—21no—
42C22×Q8×C43D411yescharacteristic
43C22×D4×C43D411yescharacteristic
44C23×C4×C43—21no—
45#123×C43—44no—
46C22⋊Q8×C43—44no—
47C2×C4⋊C4×C43—21no—
48C2×C4⋊C4×C43—21no—
49C2×C4⋊C4×C43—21no—
50C2×C4⋊C4×C43—21no—
51C2×C4⋊C4×C43—21no—
52C2×C4⋊C4×C43D411yescharacteristic
53C2×C4⋊C4×C43C2311yescharacteristic
54C2×C22⋊C4×C43—21no—
55C2×C22⋊C4×C43—21no—
56C2×C22⋊C4×C43—21no—
57C2×C22⋊C4×C43—21no—
58C2×C22⋊C4×C43—21no—
59C2×C42×C43D411yescharacteristic
60#95×C43—21no—
61#95×C43—21no—
62#95×C43—21no—
63#95×C43D411yescharacteristic
64#95×C43D411yescharacteristic
65C24×C43—21no—
66C2×Q8×C43—42no—
67C2×Q8×C43—41no—
68C2×D4×C43—42no—
69C2×D4×C43—41no—
70C22×C4×C43—21no—
71C22×C4×C43—21no—
72C22×C4×C43—21no—
73C22×C4×C43—21no—
74C22×C4×C43—21no—
75C22×C4×C43—42no—
76C22×C4×C43—42no—
77C22×C4×C43—81no—
78C22×C4×C43C2×D411yescharacteristic
79C22×C4×C43C2×D411yescharacteristic
80C22×C4×C43C2×D411yescharacteristic
81C2×C22⋊D43—41no—
82#10621898—41no—
83#10621898—41no—
84#10621898—41no—
85#10621898—41no—
86C2×D172—21no—
87C2×D172—21no—
88C2×D172—21no—
89C2×C4×D43—41no—
90C2×Dic86—21no—
91C4⋊C4×C43—41no—
92C4⋊C4×C43—41no—
93C4⋊C4×C43—42no—
94C4⋊C4×C43—42no—
95C4⋊C4×C43—42no—
96C4⋊C4×C43—42no—
97C4⋊C4×C43—42no—
98C22⋊C4×C43—24no—
99C22⋊C4×C43—42no—
100C22⋊C4×C43—42no—
101C22⋊C4×C43—42no—
102C22⋊C4×C43—41no—
103C22⋊C4×C43—41no—
104C42×C43—21no—
105C42×C43—21no—
106#10621884—82no—
107#10621882—82no—
108(C2×D43)⋊C4—41no—
109(C2×D43)⋊C4—41no—
110C4⋊Dic43—21no—
111C4⋊Dic43—21no—
112#10621877—41no—
113#10621877—41no—
114C2×C43⋊C8—41no—
115C2×C43⋊C8—41no—
116C2×C43⋊C8—41no—
117C23×C43—22no—
118C23×C43—41no—
119C23×C43—41no—
120C23×C43—41no—
121C23×C43—41no—
122C23×C43—41no—
123C23×C43—41no—
124C23×C43#12011yescharacteristic
125C22×D43—41no—
126Q8×C43—42no—
127Q8×C43—81no—
128D4×C43—42no—
129D4×C43—81no—
130C2×C4×C43—21no—
131C2×C4×C43—21no—
132C2×C4×C43—22no—
133C2×C4×C43—22no—
134C2×C4×C43—21no—
135C2×C4×C43—21no—
136C2×C4×C43—41no—
137C2×C4×C43—41no—
138C2×C4×C43—41no—
139C2×C4×C43—41no—
140C2×C4×C43—41no—
141C2×C4×C43—41no—
142C2×C4×C43—41no—
143C2×C4×C43—41no—
144C2×C4×C43—41no—
145C2×C4×C43—41no—
146C2×C4×C43—41no—
147C2×C4×C43—41no—
148C2×C4×C43—41no—
149C2×C4×C43—41no—
150C2×C4×C43—41no—
151C2×C4×C43—84no—
152C2×C4×C43#13511yescharacteristic
153C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
154C22⋊D43—81no—
155C22⋊D43—81no—
156C2×Dic43—41no—
157D172—41no—
158D172—41no—
159D172—81no—
160D172—81no—
161C4×D43—81no—
162C4×D43—81no—
163Dic86—41no—
164Dic86—41no—
165C43⋊C8—81no—
166C43⋊C8—81no—
167C43⋊C8—81no—
168#12140—431nomaximal, Sylow
169C22×C43—21no—
170C22×C43—21no—
171C22×C43—42no—
172C22×C43—42no—
173C22×C43—42no—
174C22×C43—81no—
175C22×C43—81no—
176C22×C43—81no—
177C22×C43—81no—
178C22×C43#44911yescharacteristic
179C22×C43#45411yescharacteristic
180C22×C43B(4,𝔽2)11yescharacteristic
181C2×D43—81no—
182C2×D43—81no—
183C2×D43—81no—
184C4×C43—21no—
185C4×C43—21no—
186C4×C43—42no—
187C4×C43—41no—
188C4×C43—41no—
189C4×C43—42no—
190C4×C43—81no—
191C4×C43—81no—
192C4×C43—81no—
193Dic43—81no—
194#2680D4311yescharacteristic, complemented
195#2039—431no—
196#1604—431no—
197#1598—431no—
198#1354—431no—
199#1345—431no—
200#1325—431no—
201C2×C43—21no—
202C2×C43—21no—
203C2×C43—82no—
204C2×C43#159711yescharacteristic
205C2×C43#219611yescharacteristic
206C2×C43#220311yescharacteristic
207D43—161no—
208#537—431no—
209C2×#123—21no—
210C2×C22⋊Q8—21no—
211#448—861no—
212#447—861no—
213C2×#104—861no—
214#417—861no—
215#398—21no—
216#397—21no—
217#395C2×D4311yescharacteristic
218#394C2×D4311yescharacteristic
219#388—21no—
220#385—21no—
221#384C2×D4311yescharacteristic
222#343—431no—
223#327—861no—
224#327—861no—
225#324—431no—
226#324—431no—
227C43#1214011yescharacteristic, complemented, Sylow
228C2×#41—861no—
229C22×Q8C22⋊D4311yescharacteristic
230C22×D4C22⋊D4311yescharacteristic
231C23×C4—21no—
232C2×SD16—1721no—
233C2×D8—1721no—
234C2×M16—861no—
235#123—44no—
236C22⋊Q8—44no—
237C22⋊Q8—1721no—
238#121—861no—
239#121—861no—
240#121—1721no—
241C2×C4⋊C4—21no—
242C2×C4⋊C4—21no—
243C2×C4⋊C4—21no—
244C2×C4⋊C4—21no—
245C2×C4⋊C4—21no—
246C2×C4⋊C4C22⋊D4311yescharacteristic
247C2×C4⋊C4C22×D4311yescharacteristic
248C2×C22⋊C4—21no—
249C2×C22⋊C4—21no—
250C2×C22⋊C4—21no—
251C2×C22⋊C4—21no—
252C2×C22⋊C4—21no—
253C2×C42C22⋊D4311yescharacteristic
254#104—1722no—
255#103—1721no—
256#103—1721no—
257#102—1721no—
258#102—1721no—
259C22⋊C8—861no—
260C22⋊C8—861no—
261#95—21no—
262#95—21no—
263#95—21no—
264#95C22⋊D4311yescharacteristic
265#95C22⋊D4311yescharacteristic
266C24—21no—
267#41—1721no—
268#41—1721no—
269#41—1721no—
270#41—1721no—
271C2×Q8—42no—
272C2×Q8—41no—
273C2×Q8—861no—
274C2×D4—41no—
275C2×D4—42no—
276C2×D4—861no—
277C2×D4—861no—
278C2×D4—861no—
279C2×D4—1721no—
280C22×C4—21no—
281C22×C4—21no—
282C22×C4—21no—
283C22×C4—21no—
284C22×C4—21no—
285C22×C4—42no—
286C22×C4—42no—
287C22×C4—81no—
288C22×C4—1721no—
289C22×C4C2×C22⋊D4311yescharacteristic
290C22×C4C2×C22⋊D4311yescharacteristic
291C22×C4C2×C22⋊D4311yescharacteristic
292SD16—3442no—
293D8—3442no—
294M16—1721no—
295M16—1721no—
296C2×C8—1721no—
297C2×C8—1721no—
298C2×C8—1721no—
299C4⋊C4—41no—
300C4⋊C4—41no—
301C4⋊C4—42no—
302C4⋊C4—42no—
303C4⋊C4—42no—
304C4⋊C4—42no—
305C4⋊C4—42no—
306C4⋊C4—861no—
307C4⋊C4—861no—
308C22⋊C4—24no—
309C22⋊C4—42no—
310C22⋊C4—42no—
311C22⋊C4—42no—
312C22⋊C4—41no—
313C22⋊C4—41no—
314C22⋊C4—1721no—
315C22⋊C4—1721no—
316C42—21no—
317C42—21no—
318C23—22no—
319C23—41no—
320C23—41no—
321C23—41no—
322C23—41no—
323C23—41no—
324C23—41no—
325C23—1721no—
326C23#1306329411yescharacteristic
327Q8—42no—
328Q8—81no—
329Q8—1721no—
330Q8—1721no—
331D4—42no—
332D4—81no—
333D4—3441no—
334D4—3441no—
335D4—3441no—
336D4—3441no—
337D4—1721no—
338D4—1721no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—22no—
342C2×C4—22no—
343C2×C4—21no—
344C2×C4—21no—
345C2×C4—41no—
346C2×C4—41no—
347C2×C4—41no—
348C2×C4—41no—
349C2×C4—41no—
350C2×C4—41no—
351C2×C4—41no—
352C2×C4—41no—
353C2×C4—41no—
354C2×C4—41no—
355C2×C4—41no—
356C2×C4—41no—
357C2×C4—41no—
358C2×C4—41no—
359C2×C4—41no—
360C2×C4—84no—
361C2×C4—3441no—
362C2×C4—3441no—
363C2×C4—1721no—
364C2×C4#1306334511yescharacteristic
365C2×C4#1306335011yescharacteristic
366C8—3441no—
367C8—3441no—
368C8—3441no—
369C22—21no—
370C22—21no—
371C22—42no—
372C22—42no—
373C22—42no—
374C22—81no—
375C22—81no—
376C22—81no—
377C22—81no—
378C22—3441no—
379C22—3441no—
380C22—3441no—
381C22#1458304411yescharacteristic
382C22#1458307211yescharacteristic
383C22#1458308611yescharacteristic
384C4—21no—
385C4—21no—
386C4—42no—
387C4—41no—
388C4—41no—
389C4—42no—
390C4—81no—
391C4—81no—
392C4—81no—
393C4—3441no—
394C2—21no—
395C2—21no—
396C2—82no—
397C2—6881no—
398C2#1913352411yescharacteristic
399C2#1913657911yescharacteristic
400C2#1913661611yescharacteristic
subgroupG/H
centerC22#14583086
commutator, cosocleC2×C4⋊C4×C43C23
FrattiniC2×C4⋊C4C22×D43
FittingC43×#2680C2
socleC22×C43B(4,𝔽2)
prime radical#19133529C2
hypercenter#2680D43
hypocenterC43#12140
LCSG ▷ C2×C4⋊C4×C43 ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #2680

Complements

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

NH ≅ G/Ntype
1. #19135819C2semidirect
2. #19133563C2semidirect
4. #19132625C2semidirect
5. #19132598C2semidirect
6. #19132541C2semidirect
7. C43×#2680C2semidirect
194. #2680D43semidirect
227. C43#12140semidirect

Maximal subgroups

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

subgroupindex
#191358192
#191335632
#191335292
#191326252
#191325982
#191325412
C43×#26802
#1214043