Finite Group Databasebeta

← #25070777

Subgroups — #25070777

Order 11008.

1230 conjugacy classes of subgroups; only the 167 normal subgroups are shown.

normal subgroups only

This group has 1230 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#19145397C212yesmaximal, complemented
3#19133597C214yesmaximal, complemented
4#19133563C214yesmaximal, complemented
5#19133110C212yesmaximal, complemented
6#19132925C211yesmaximal, characteristic, complemented
7C43×#2583C211yesmaximal, 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#14583232—22no—
17#14583212C2214yescomplemented
18#14583147—24no—
19#14583049—22no—
20#14583038C2214yescomplemented
21#14582863C2212yes—
22#14582632C2218yescomplemented
23#14582625C2214yescomplemented
24C2×C22⋊Q8×C43C2211yescharacteristic
25C22×C4⋊C4×C43C2211yescharacteristic
26C43×#398C2212yescomplemented
27C43×#395C2212yescomplemented
28C43×#389—22no—
29C43×#385—21no—
30C43×#385—21no—
31C4×C22⋊C4×C43C2211yescharacteristic
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×#10621884—24no—
42C2×#10621877—22no—
43#13063305—28no—
44#13063305—28no—
45#13063300—28no—
46#13063300—28no—
47#13063299—24no—
48#13063299—24no—
49#13063299—22no—
50#13063299—22no—
51#13063299D414yes—
52#13063299C2314yes—
53C2×C4⋊Dic43—21no—
54C2×C4⋊Dic43D412yes—
55C2×(C2×D43)⋊C4—22no—
56C2×(C2×D43)⋊C4—22no—
57#13063258—24no—
58#13063249—24no—
59#13063245—24no—
60C22⋊(C43⋊C8)—22no—
61C22⋊(C43⋊C8)C2314yes—
62C22×Q8×C43C2311yescharacteristic
63C23×C4×C43D411yescharacteristic
64C23×C4×C43D411yescharacteristic
65C23×C4×C43C2311yescharacteristic
66C22⋊Q8×C43—22no—
67C22⋊Q8×C43—22no—
68C2×C4⋊C4×C43—22no—
69C2×C4⋊C4×C43—22no—
70C2×C4⋊C4×C43—21no—
71C2×C4⋊C4×C43—22no—
72C2×C4⋊C4×C43—22no—
73C2×C4⋊C4×C43D412yes—
74C2×C4⋊C4×C43C2311yescharacteristic
75C2×C4⋊C4×C43C2312yes—
76C2×C22⋊C4×C43—21no—
77C2×C22⋊C4×C43—21no—
78C2×C42×C43—21no—
79#95×C43—22no—
80#95×C43—22no—
81#95×C43C2312yes—
82C24×C43C2×D411yescharacteristic
83C23×D43—22no—
84C2×Q8×C43—22no—
85C2×Q8×C43—81no—
86C22×C4×C43—24no—
87C22×C4×C43—21no—
88C22×C4×C43—21no—
89C22×C4×C43—21no—
90C22×C4×C43—21no—
91C22×C4×C43—22no—
92C22×C4×C43—21no—
93C22×C4×C43—21no—
94C22×C4×C43—81no—
95C22×C4×C43—81no—
96C22×C4×C43C2×D412yes—
97C22×C4×C43C2×D412yes—
98C22×C4×C43C2×D412yes—
99C22×C4×C43C2×D412yes—
100C22×C4×C43C2×D411yescharacteristic
101C22×C4×C43C2411yescharacteristic
102C2×C22⋊D43—24no—
103C2×C22⋊D43—24no—
104C2×C22⋊D43—48no—
105C22×Dic43—22no—
106#10621898—416no—
107#10621898—48no—
108#10621898—48no—
109C2×D172—24no—
110C2×D172—24no—
111C2×D172—22no—
112C2×D172—44no—
113C2×D172—82no—
114C2×D172—82no—
115C2×D172C2×D414yes—
116C2×C4×D43—28no—
117C2×C4×D43—48no—
118C2×Dic86—24no—
119C2×Dic86—44no—
120C4⋊C4×C43—24no—
121C4⋊C4×C43—24no—
122C4⋊C4×C43—22no—
123C4⋊C4×C43—42no—
124C4⋊C4×C43—44no—
125C4⋊C4×C43—82no—
126C22⋊C4×C43—24no—
127C22⋊C4×C43—41no—
128C22⋊C4×C43—41no—
129C42×C43—81no—
130#10621884—84no—
131(C2×D43)⋊C4—28no—
132(C2×D43)⋊C4—24no—
133(C2×D43)⋊C4—24no—
134C4⋊Dic43—24no—
135C4⋊Dic43—22no—
136C4⋊Dic43C2×D414yes—
137#10621877—82no—
138C2×C43⋊C8—24no—
139C23×C43—22no—
140C23×C43—22no—
141C23×C43—41no—
142C23×C43#12011yescharacteristic
143C23×C43#12011yescharacteristic
144C23×C43C22×D411yescharacteristic
145C22×D43—24no—
146C22×D43—44no—
147C22×D43—44no—
148C22×D43—44no—
149Q8×C43—44no—
150C2×C4×C43—24no—
151C2×C4×C43—24no—
152C2×C4×C43—22no—
153C2×C4×C43—22no—
154C2×C4×C43—24no—
155C2×C4×C43—22no—
156C2×C4×C43—42no—
157C2×C4×C43—41no—
158C2×C4×C43—42no—
159C2×C4×C43—41no—
160C2×C4×C43—42no—
161C2×C4×C43—42no—
162C2×C4×C43—42no—
163C2×C4×C43—42no—
164C2×C4×C43—42no—
165C2×C4×C43—41no—
166C2×C4×C43—41no—
167C2×C4×C43—42no—
168C2×C4×C43—81no—
169C2×C4×C43#12012yes—
170C2×C4×C43AGL(1,ℤ/8)14yes—
171C2×C4×C43C22×D412yes—
172C22⋊D43—48no—
173C22⋊D43—48no—
174C2×Dic43—24no—
175C2×Dic43—44no—
176D172—44no—
177D172—48no—
178D172—82no—
179D172—84no—
180C4×D43—416no—
181Dic86—48no—
182C43⋊C8—44no—
183#18325—431nomaximal, Sylow
184C22×C43—21no—
185C22×C43—21no—
186C22×C43—21no—
187C22×C43—21no—
188C22×C43—21no—
189C22×C43—21no—
190C22×C43—21no—
191C22×C43—44no—
192C22×C43#45612yes—
193C22×C43C2×#12011yescharacteristic
194C22×C43C2×AGL(1,ℤ/8)12yes—
195C2×D43—44no—
196C2×D43—44no—
197C2×D43—44no—
198C2×D43—88no—
199C4×C43—24no—
200C4×C43—22no—
201C4×C43—22no—
202C4×C43—44no—
203C4×C43—42no—
204C4×C43—81no—
205C4×C43—81no—
206Dic43—44no—
207C2×#537—431no—
208#3193—432no—
209#2583D4311yescharacteristic, complemented
210#1610—434no—
211#1604—434no—
212#1507—432no—
213#1463—431no—
214C2×C43—22no—
215C2×C43—22no—
216C2×C43—41no—
217C2×C43#300311yescharacteristic
218C2×C43C2×#45611yescharacteristic
219C2×C43#302611yescharacteristic
220D43—84no—
221C22×#41—861no—
222#537—434no—
223#537—864no—
224#537—862no—
225C2×C22⋊Q8—862no—
226C2×C22⋊Q8C2×D4311yescharacteristic
227C2×#121—432no—
228C2×#121—862no—
229C2×#121—861no—
230C22×C4⋊C4C2×D4311yescharacteristic
231#484—862no—
232#480—434no—
233#468—864no—
234#450—862no—
235#448—434no—
236#407—432no—
237#398C2×D4312yescomplemented
238#395C2×D4312yescomplemented
239#389—22no—
240#385—21no—
241#385—21no—
242C4×C22⋊C4C2×D4311yescharacteristic
243#327—438no—
244#324—434no—
245C43#1832511yescharacteristic, complemented, Sylow
246C2×#41—864no—
247C2×#41—864no—
248C2×#41—1728no—
249C22×Q8—861no—
250C22×Q8C22×D4311yescharacteristic
251C22×D4—432no—
252C22×D4—861no—
253C22×D4—861no—
254C22×D4—862no—
255C23×C4—862no—
256C23×C4C22⋊D4311yescharacteristic
257C23×C4C22⋊D4311yescharacteristic
258C23×C4C22×D4311yescharacteristic
259C2×SD16—864no—
260C2×M16—862no—
261C22⋊Q8—22no—
262C22⋊Q8—22no—
263C22⋊Q8—868no—
264C22⋊Q8—868no—
265#121—434no—
266#121—434no—
267#121—868no—
268#121—868no—
269#121—864no—
270#121—862no—
271#121—862no—
272#121—864no—
273C2×C4⋊C4—22no—
274C2×C4⋊C4—22no—
275C2×C4⋊C4—21no—
276C2×C4⋊C4—22no—
277C2×C4⋊C4—22no—
278C2×C4⋊C4—432no—
279C2×C4⋊C4—861no—
280C2×C4⋊C4C22⋊D4312yes—
281C2×C4⋊C4C22×D4311yescharacteristic
282C2×C4⋊C4C22×D4312yes—
283C2×C22⋊C4—21no—
284C2×C22⋊C4—21no—
285C2×C22⋊C4—862no—
286C2×C22⋊C4—862no—
287C2×C42—21no—
288#107—864no—
289#103—864no—
290#102—864no—
291C22⋊C8—434no—
292C22⋊C8—862no—
293#95—22no—
294#95—22no—
295#95C22×D4312yes—
296C24—862no—
297C24C2×C22⋊D4311yescharacteristic
298#41—17216no—
299#41—1728no—
300#41—1728no—
301C2×Q8—22no—
302C2×Q8—81no—
303C2×Q8—864no—
304C2×Q8—1724no—
305C2×D4—434no—
306C2×D4—864no—
307C2×D4—864no—
308C2×D4—864no—
309C2×D4—864no—
310C2×D4—862no—
311C2×D4—3442no—
312C2×D4—3442no—
313C2×D4—1724no—
314C2×D4—1728no—
315C22×C4—21no—
316C22×C4—21no—
317C22×C4—24no—
318C22×C4—21no—
319C22×C4—22no—
320C22×C4—21no—
321C22×C4—21no—
322C22×C4—21no—
323C22×C4—81no—
324C22×C4—81no—
325C22×C4—868no—
326C22×C4—862no—
327C22×C4—1728no—
328C22×C4D4×D4312yes—
329C22×C4D4×D4312yes—
330C22×C4C2×C22⋊D4312yes—
331C22×C4C2×C22⋊D4312yes—
332C22×C4C2×C22⋊D4311yescharacteristic
333C22×C4C23×D4311yescharacteristic
334SD16—3444no—
335M16—3442no—
336C2×C8—864no—
337C4⋊C4—24no—
338C4⋊C4—24no—
339C4⋊C4—22no—
340C4⋊C4—42no—
341C4⋊C4—44no—
342C4⋊C4—82no—
343C4⋊C4—434no—
344C4⋊C4—864no—
345C4⋊C4—862no—
346C22⋊C4—24no—
347C22⋊C4—41no—
348C22⋊C4—41no—
349C22⋊C4—868no—
350C22⋊C4—864no—
351C22⋊C4—864no—
352C42—81no—
353C23—22no—
354C23—22no—
355C23—41no—
356C23—864no—
357C23—1724no—
358C23—1724no—
359C23—1724no—
360C23#1306329311yescharacteristic
361C23#1306329311yescharacteristic
362C23C22×C22⋊D4311yescharacteristic
363Q8—44no—
364Q8—1728no—
365D4—3442no—
366D4—3444no—
367D4—1724no—
368D4—1728no—
369D4—1728no—
370D4—1728no—
371C2×C4—24no—
372C2×C4—24no—
373C2×C4—22no—
374C2×C4—22no—
375C2×C4—24no—
376C2×C4—22no—
377C2×C4—41no—
378C2×C4—42no—
379C2×C4—42no—
380C2×C4—41no—
381C2×C4—42no—
382C2×C4—42no—
383C2×C4—42no—
384C2×C4—42no—
385C2×C4—42no—
386C2×C4—41no—
387C2×C4—41no—
388C2×C4—42no—
389C2×C4—81no—
390C2×C4—864no—
391C2×C4—17216no—
392C2×C4—1724no—
393C2×C4#1306329312yes—
394C2×C4#1306335014yes—
395C2×C4C2×D4×D4312yes—
396C8—1724no—
397C22—21no—
398C22—21no—
399C22—21no—
400C22—21no—
401C22—21no—
402C22—21no—
403C22—21no—
404C22—44no—
405C22—3448no—
406C22—1724no—
407C22—1724no—
408C22—1724no—
409C22#1458308112yes—
410C22C2×#1306329311yescharacteristic
411C22C2×#1306335012yes—
412C4—22no—
413C4—22no—
414C4—24no—
415C4—44no—
416C4—42no—
417C4—81no—
418C4—81no—
419C4—1724no—
420C2—22no—
421C2—22no—
422C2—41no—
423C2—3444no—
424C2#1914382111yescharacteristic
425C2C2×#1458308111yescharacteristic
426C2#1914399111yescharacteristic
subgroupG/H
centerC22C2×#13063293
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#2583C2
socleC22×C43C2×#120
prime radicalC2×#14583480C2
hypercenter#2583D43
hypocenterC43#18325
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ #2583

Complements

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

NH ≅ G/Ntype
2. #19145397C2semidirect
3. #19133597C2semidirect
4. #19133563C2semidirect
5. #19133110C2semidirect
6. #19132925C2semidirect
7. C43×#2583C2semidirect
17. #14583212C22semidirect
20. #14583038C22semidirect
22. #14582632C22semidirect
23. #14582625C22semidirect
26. C43×#398C22semidirect
27. C43×#395C22semidirect
209. #2583D43semidirect
237. #398C2×D43semidirect
238. #395C2×D43semidirect
245. C43#18325semidirect

Maximal subgroups

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

subgroupindex
C2×#145834802
#191453972
#191335972
#191335632
#191331102
#191329252
C43×#25832
#1832543