Finite Group Databasebeta

← #25069083

Subgroups — #25069083

Order 11008.

1210 conjugacy classes of subgroups; only the 167 normal subgroups are shown.

normal subgroups only

This group has 1210 conjugacy classes of subgroups — too many to draw. Only its 167 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
1C2×#14583480C211yesmaximal, characteristic
2#19144535C212yesmaximal, complemented
3#19133631C214yesmaximal, complemented
4#19133597C214yesmaximal, complemented
5#19133123C212yesmaximal, complemented
6#19132925C211yesmaximal, characteristic, complemented
7C43×#2484C211yesmaximal, characteristic, complemented
8C22×#10621898—21no—
9#14583480—24no—
10#14583480—22no—
11#14583480C2214yes—
12C2×#13063305—22no—
13C2×#13063300—22no—
14C2×#13063299—21no—
15C2×#13063299C2212yes—
16#14583223—24no—
17#14583217C2214yescomplemented
18#14583212C2214yescomplemented
19#14582942—22no—
20#14582903—22no—
21#14582863C2212yes—
22#14582632C2218yescomplemented
23#14582625C2214yescomplemented
24C2×#117×C43C2211yescharacteristic
25C22×C4⋊C4×C43C2211yescharacteristic
26C43×#400C2212yescomplemented
27C43×#398C2212yescomplemented
28C43×#387—22no—
29C43×#385—21no—
30C43×#381—21no—
31C43×#381C2211yescharacteristic
32C2×#10621898—24no—
33C2×#10621898—24no—
34C2×#10621898—48no—
35C22×Dic86—21no—
36C22×D172—21no—
37C22×D172—21no—
38C22×D172D412yes—
39C22×C22⋊D43—22no—
40C22×C4×D43—22no—
41C2×#10621877—22no—
42#13063305—28no—
43#13063305—28no—
44#13063300—28no—
45#13063300—28no—
46#13063299—24no—
47#13063299—24no—
48#13063299—22no—
49#13063299—22no—
50#13063299D414yes—
51#13063299C2314yes—
52C2×C4⋊Dic43—21no—
53C2×C4⋊Dic43D412yes—
54C2×(C2×D43)⋊C4—22no—
55C2×(C2×D43)⋊C4—22no—
56#13063258—24no—
57#13063256—24no—
58#13063245—24no—
59#13063245—24no—
60C22⋊(C43⋊C8)—22no—
61C22⋊(C43⋊C8)C2314yes—
62C23×C4×C43D411yescharacteristic
63C23×C4×C43D411yescharacteristic
64C23×C4×C43C2311yescharacteristic
65#117×C43—22no—
66#117×C43—22no—
67C2×C4⋊C4×C43—22no—
68C2×C4⋊C4×C43—22no—
69C2×C4⋊C4×C43—22no—
70C2×C4⋊C4×C43D412yes—
71C2×C4⋊C4×C43C2311yescharacteristic
72C2×C4⋊C4×C43C2311yescharacteristic
73C2×C4⋊C4×C43C2312yes—
74C2×C22⋊C4×C43—21no—
75C2×C22⋊C4×C43—21no—
76C2×C42×C43—21no—
77#95×C43—22no—
78#95×C43—22no—
79#95×C43—21no—
80#95×C43—22no—
81#95×C43C2312yes—
82C24×C43C2×D411yescharacteristic
83C23×D43—22no—
84C22×C4×C43—24no—
85C22×C4×C43—21no—
86C22×C4×C43—21no—
87C22×C4×C43—21no—
88C22×C4×C43—21no—
89C22×C4×C43—22no—
90C22×C4×C43—21no—
91C22×C4×C43—21no—
92C22×C4×C43—42no—
93C22×C4×C43—42no—
94C22×C4×C43C2×D412yes—
95C22×C4×C43C2×D412yes—
96C22×C4×C43C2×D412yes—
97C22×C4×C43C2×D412yes—
98C22×C4×C43C2×D411yescharacteristic
99C22×C4×C43C2411yescharacteristic
100C2×C22⋊D43—24no—
101C2×C22⋊D43—24no—
102C2×C22⋊D43—48no—
103C22×Dic43—22no—
104#10621898—416no—
105#10621898—48no—
106#10621898—48no—
107C2×D172—24no—
108C2×D172—24no—
109C2×D172—22no—
110C2×D172—44no—
111C2×D172—44no—
112C2×D172—82no—
113C2×D172C2×D414yes—
114C2×C4×D43—28no—
115C2×C4×D43—48no—
116C2×Dic86—24no—
117C2×Dic86—44no—
118C4⋊C4×C43—24no—
119C4⋊C4×C43—24no—
120C4⋊C4×C43—22no—
121C4⋊C4×C43—22no—
122C4⋊C4×C43—44no—
123C22⋊C4×C43—42no—
124C22⋊C4×C43—41no—
125C22⋊C4×C43—41no—
126C42×C43—42no—
127(C2×D43)⋊C4—28no—
128(C2×D43)⋊C4—24no—
129(C2×D43)⋊C4—24no—
130C4⋊Dic43—24no—
131C4⋊Dic43—22no—
132C4⋊Dic43C2×D414yes—
133#10621877—44no—
134C2×C43⋊C8—24no—
135C23×C43—22no—
136C23×C43—22no—
137C23×C43—41no—
138C23×C43#12011yescharacteristic
139C23×C43#12011yescharacteristic
140C23×C43C22×D411yescharacteristic
141C22×D43—24no—
142C22×D43—44no—
143C22×D43—44no—
144C22×D43—44no—
145C2×C4×C43—24no—
146C2×C4×C43—24no—
147C2×C4×C43—22no—
148C2×C4×C43—22no—
149C2×C4×C43—24no—
150C2×C4×C43—22no—
151C2×C4×C43—42no—
152C2×C4×C43—41no—
153C2×C4×C43—41no—
154C2×C4×C43—42no—
155C2×C4×C43—42no—
156C2×C4×C43—42no—
157C2×C4×C43—42no—
158C2×C4×C43—42no—
159C2×C4×C43—41no—
160C2×C4×C43—41no—
161C2×C4×C43—42no—
162C2×C4×C43—42no—
163C2×C4×C43—81no—
164C2×C4×C43#12012yes—
165C2×C4×C43AGL(1,ℤ/8)14yes—
166C2×C4×C43C22×D412yes—
167C22⋊D43—48no—
168C22⋊D43—48no—
169C2×Dic43—24no—
170C2×Dic43—44no—
171D172—44no—
172D172—48no—
173D172—82no—
174D172—84no—
175C4×D43—416no—
176Dic86—48no—
177C43⋊C8—44no—
178#18147—431nomaximal, Sylow
179C22×C43—21no—
180C22×C43—21no—
181C22×C43—21no—
182C22×C43—21no—
183C22×C43—21no—
184C22×C43—21no—
185C22×C43—21no—
186C22×C43—44no—
187C22×C43#45812yes—
188C22×C43C2×#12011yescharacteristic
189C22×C43C2×AGL(1,ℤ/8)12yes—
190C2×D43—44no—
191C2×D43—44no—
192C2×D43—44no—
193C2×D43—88no—
194C4×C43—24no—
195C4×C43—22no—
196C4×C43—22no—
197C4×C43—42no—
198C4×C43—82no—
199C4×C43—81no—
200C4×C43—81no—
201Dic43—44no—
202C2×#537—431no—
203#3094—432no—
204#2484D4311yescharacteristic, complemented
205#1616—434no—
206#1610—434no—
207#1510—432no—
208#1463—431no—
209C2×C43—22no—
210C2×C43—22no—
211C2×C43—41no—
212C2×C43#300311yescharacteristic
213C2×C43#302011yescharacteristic
214C2×C43C2×#45811yescharacteristic
215D43—84no—
216C22×#41—861no—
217#537—434no—
218#537—864no—
219#537—862no—
220C2×C22⋊Q8—862no—
221C2×#121—432no—
222C2×#121—862no—
223C2×#121—861no—
224C2×#117C2×D4311yescharacteristic
225C22×C4⋊C4C2×D4311yescharacteristic
226#482—864no—
227#481—434no—
228#480—434no—
229#428—862no—
230#418—862no—
231#407—432no—
232#400C2×D4312yescomplemented
233#398C2×D4312yescomplemented
234#387—22no—
235#385—21no—
236#381—21no—
237#381C2×D4311yescharacteristic
238#327—438no—
239#324—434no—
240C43#1814711yescharacteristic, complemented, Sylow
241C2×#41—864no—
242C2×#41—864no—
243C2×#41—1728no—
244C22×Q8—861no—
245C22×D4—432no—
246C22×D4—861no—
247C22×D4—861no—
248C22×D4—862no—
249C23×C4—862no—
250C23×C4C22⋊D4311yescharacteristic
251C23×C4C22⋊D4311yescharacteristic
252C23×C4C22×D4311yescharacteristic
253C2×M16—862no—
254C22⋊Q8—868no—
255C22⋊Q8—868no—
256#121—434no—
257#121—434no—
258#121—868no—
259#121—868no—
260#121—864no—
261#121—862no—
262#121—862no—
263#121—864no—
264#117—22no—
265#117—22no—
266C2×C4⋊C4—22no—
267C2×C4⋊C4—22no—
268C2×C4⋊C4—22no—
269C2×C4⋊C4—432no—
270C2×C4⋊C4—861no—
271C2×C4⋊C4C22⋊D4312yes—
272C2×C4⋊C4C22×D4311yescharacteristic
273C2×C4⋊C4C22×D4311yescharacteristic
274C2×C4⋊C4C22×D4312yes—
275C2×C22⋊C4—21no—
276C2×C22⋊C4—21no—
277C2×C22⋊C4—862no—
278C2×C22⋊C4—862no—
279C2×C42—21no—
280#107—864no—
281#106—864no—
282#102—864no—
283#102—864no—
284C22⋊C8—434no—
285C22⋊C8—862no—
286#95—22no—
287#95—22no—
288#95—21no—
289#95—22no—
290#95C22×D4312yes—
291C24—862no—
292C24C2×C22⋊D4311yescharacteristic
293#41—17216no—
294#41—1728no—
295#41—1728no—
296C2×Q8—864no—
297C2×Q8—1724no—
298C2×D4—434no—
299C2×D4—864no—
300C2×D4—864no—
301C2×D4—864no—
302C2×D4—864no—
303C2×D4—862no—
304C2×D4—3442no—
305C2×D4—1724no—
306C2×D4—1724no—
307C2×D4—1728no—
308C22×C4—21no—
309C22×C4—21no—
310C22×C4—24no—
311C22×C4—21no—
312C22×C4—21no—
313C22×C4—22no—
314C22×C4—21no—
315C22×C4—21no—
316C22×C4—42no—
317C22×C4—42no—
318C22×C4—868no—
319C22×C4—862no—
320C22×C4—1728no—
321C22×C4D4×D4312yes—
322C22×C4D4×D4312yes—
323C22×C4C2×C22⋊D4312yes—
324C22×C4C2×C22⋊D4312yes—
325C22×C4C2×C22⋊D4311yescharacteristic
326C22×C4C23×D4311yescharacteristic
327M16—1724no—
328C2×C8—864no—
329C4⋊C4—24no—
330C4⋊C4—24no—
331C4⋊C4—22no—
332C4⋊C4—22no—
333C4⋊C4—44no—
334C4⋊C4—434no—
335C4⋊C4—864no—
336C4⋊C4—862no—
337C22⋊C4—42no—
338C22⋊C4—41no—
339C22⋊C4—41no—
340C22⋊C4—868no—
341C22⋊C4—864no—
342C22⋊C4—864no—
343C42—42no—
344C23—22no—
345C23—22no—
346C23—41no—
347C23—864no—
348C23—1724no—
349C23—1724no—
350C23—1724no—
351C23#1306329311yescharacteristic
352C23#1306329311yescharacteristic
353C23C22×C22⋊D4311yescharacteristic
354Q8—1728no—
355D4—3442no—
356D4—3444no—
357D4—1724no—
358D4—1728no—
359D4—1728no—
360D4—1728no—
361C2×C4—24no—
362C2×C4—24no—
363C2×C4—24no—
364C2×C4—22no—
365C2×C4—22no—
366C2×C4—22no—
367C2×C4—42no—
368C2×C4—41no—
369C2×C4—41no—
370C2×C4—42no—
371C2×C4—42no—
372C2×C4—42no—
373C2×C4—42no—
374C2×C4—42no—
375C2×C4—41no—
376C2×C4—41no—
377C2×C4—42no—
378C2×C4—42no—
379C2×C4—81no—
380C2×C4—864no—
381C2×C4—17216no—
382C2×C4—1724no—
383C2×C4#1306329312yes—
384C2×C4#1306335014yes—
385C2×C4C2×D4×D4312yes—
386C8—1724no—
387C22—21no—
388C22—21no—
389C22—21no—
390C22—21no—
391C22—21no—
392C22—21no—
393C22—21no—
394C22—44no—
395C22—3448no—
396C22—1724no—
397C22—1724no—
398C22—1724no—
399C22#1458308812yes—
400C22C2×#1306329311yescharacteristic
401C22C2×#1306335012yes—
402C4—22no—
403C4—22no—
404C4—24no—
405C4—42no—
406C4—82no—
407C4—81no—
408C4—81no—
409C4—1724no—
410C2—22no—
411C2—22no—
412C2—41no—
413C2—3444no—
414C2#1914382111yescharacteristic
415C2#1914395811yescharacteristic
416C2C2×#1458308811yescharacteristic
subgroupG/H
centerC22C2×#13063293
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#2484C2
socleC22×C43C2×#120
prime radicalC2×#14583480C2
hypercenter#2484D43
hypocenterC43#18147
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ #2484

Complements

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

NH ≅ G/Ntype
2. #19144535C2semidirect
3. #19133631C2semidirect
4. #19133597C2semidirect
5. #19133123C2semidirect
6. #19132925C2semidirect
7. C43×#2484C2semidirect
17. #14583217C22semidirect
18. #14583212C22semidirect
22. #14582632C22semidirect
23. #14582625C22semidirect
26. C43×#400C22semidirect
27. C43×#398C22semidirect
204. #2484D43semidirect
232. #400C2×D43semidirect
233. #398C2×D43semidirect
240. C43#18147semidirect

Maximal subgroups

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

subgroupindex
C2×#145834802
#191445352
#191336312
#191335972
#191331232
#191329252
C43×#24842
#1814743