Finite Group Databasebeta

← #25070770

Subgroups — #25070770

Order 11008.

1256 conjugacy classes of subgroups; only the 167 normal subgroups are shown.

normal subgroups only

This group has 1256 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, complemented
2#19145392C212yesmaximal, complemented
3#19133631C214yesmaximal, complemented
4#19133529C214yesmaximal, complemented
5#19133110C212yesmaximal, complemented
6#19132925C211yesmaximal, characteristic, complemented
7C43×#2591C211yesmaximal, 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#14583217C2214yescomplemented
17#14583215—22no—
18#14583150—24no—
19#14583033C2214yescomplemented
20#14583032—22no—
21#14582863C2212yes—
22#14582632C2218yescomplemented
23#14582625C2214yescomplemented
24C2×#121×C43C2211yescharacteristic
25C22×C4⋊C4×C43C2211yescharacteristic
26C43×#400C2212yescomplemented
27C43×#394C2212yescomplemented
28C43×#388—22no—
29C43×#386—21no—
30C43×#386—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×#10621882—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#13063256—24no—
58#13063246—24no—
59#13063245—24no—
60C22⋊(C43⋊C8)—22no—
61C22⋊(C43⋊C8)C2314yes—
62C22×D4×C43—21no—
63C22×D4×C43C2311yescharacteristic
64C23×C4×C43D411yescharacteristic
65C23×C4×C43D411yescharacteristic
66C23×C4×C43C2311yescharacteristic
67#121×C43—22no—
68#121×C43—22no—
69C2×C4⋊C4×C43—22no—
70C2×C4⋊C4×C43—22no—
71C2×C4⋊C4×C43D412yes—
72C2×C4⋊C4×C43C2311yescharacteristic
73C2×C4⋊C4×C43C2312yes—
74C2×C22⋊C4×C43—21no—
75C2×C22⋊C4×C43—21no—
76C2×C22⋊C4×C43—22no—
77C2×C22⋊C4×C43—22no—
78C2×C42×C43—21no—
79#95×C43—22no—
80#95×C43—22no—
81#95×C43C2312yes—
82C24×C43—21no—
83C24×C43C2×D411yescharacteristic
84C23×D43—22no—
85C2×D4×C43—22no—
86C2×D4×C43—44no—
87C2×D4×C43—41no—
88C2×D4×C43—41no—
89C2×D4×C43—81no—
90C22×C4×C43—24no—
91C22×C4×C43—21no—
92C22×C4×C43—21no—
93C22×C4×C43—21no—
94C22×C4×C43—21no—
95C22×C4×C43—21no—
96C22×C4×C43—22no—
97C22×C4×C43—81no—
98C22×C4×C43—81no—
99C22×C4×C43C2×D412yes—
100C22×C4×C43C2×D412yes—
101C22×C4×C43C2×D412yes—
102C22×C4×C43C2×D412yes—
103C22×C4×C43C2×D411yescharacteristic
104C22×C4×C43C2411yescharacteristic
105C2×C22⋊D43—24no—
106C2×C22⋊D43—24no—
107C2×C22⋊D43—48no—
108C22×Dic43—22no—
109#10621898—416no—
110#10621898—48no—
111#10621898—48no—
112C2×D172—24no—
113C2×D172—24no—
114C2×D172—22no—
115C2×D172—44no—
116C2×D172—82no—
117C2×D172—82no—
118C2×D172C2×D414yes—
119C2×C4×D43—28no—
120C2×C4×D43—48no—
121C2×Dic86—24no—
122C2×Dic86—44no—
123C4⋊C4×C43—24no—
124C4⋊C4×C43—24no—
125C4⋊C4×C43—22no—
126C22⋊C4×C43—42no—
127C22⋊C4×C43—42no—
128C22⋊C4×C43—44no—
129C22⋊C4×C43—82no—
130C42×C43—81no—
131#10621882—84no—
132(C2×D43)⋊C4—28no—
133(C2×D43)⋊C4—24no—
134(C2×D43)⋊C4—24no—
135C4⋊Dic43—24no—
136C4⋊Dic43—22no—
137C4⋊Dic43C2×D414yes—
138#10621877—82no—
139C2×C43⋊C8—24no—
140C23×C43—22no—
141C23×C43—22no—
142C23×C43—41no—
143C23×C43—42no—
144C23×C43—42no—
145C23×C43—41no—
146C23×C43—42no—
147C23×C43#12011yescharacteristic
148C23×C43#12011yescharacteristic
149C23×C43C22×D411yescharacteristic
150C22×D43—24no—
151C22×D43—44no—
152C22×D43—44no—
153C22×D43—44no—
154D4×C43—44no—
155D4×C43—82no—
156D4×C43—82no—
157C2×C4×C43—24no—
158C2×C4×C43—24no—
159C2×C4×C43—22no—
160C2×C4×C43—22no—
161C2×C4×C43—22no—
162C2×C4×C43—42no—
163C2×C4×C43—41no—
164C2×C4×C43—42no—
165C2×C4×C43—41no—
166C2×C4×C43—42no—
167C2×C4×C43—42no—
168C2×C4×C43—42no—
169C2×C4×C43—42no—
170C2×C4×C43—42no—
171C2×C4×C43—41no—
172C2×C4×C43—42no—
173C2×C4×C43—81no—
174C2×C4×C43#12012yes—
175C2×C4×C43AGL(1,ℤ/8)14yes—
176C2×C4×C43C22×D412yes—
177C22⋊D43—48no—
178C22⋊D43—48no—
179C2×Dic43—24no—
180C2×Dic43—44no—
181D172—44no—
182D172—48no—
183D172—82no—
184D172—84no—
185C4×D43—416no—
186Dic86—48no—
187C43⋊C8—44no—
188#18324—431nomaximal, Sylow
189C22×C43—21no—
190C22×C43—21no—
191C22×C43—21no—
192C22×C43—21no—
193C22×C43—21no—
194C22×C43—21no—
195C22×C43—21no—
196C22×C43—44no—
197C22×C43—84no—
198C22×C43—81no—
199C22×C43—81no—
200C22×C43—81no—
201C22×C43#45412yes—
202C22×C43C2×#12011yescharacteristic
203C22×C43C2×AGL(1,ℤ/8)12yes—
204C2×D43—44no—
205C2×D43—44no—
206C2×D43—44no—
207C2×D43—88no—
208C4×C43—24no—
209C4×C43—22no—
210C4×C43—22no—
211C4×C43—42no—
212C4×C43—82no—
213C4×C43—81no—
214Dic43—44no—
215C2×#537—431no—
216#3192—432no—
217#2591D4311yescharacteristic, complemented
218#1616—434no—
219#1598—434no—
220#1507—432no—
221#1463—431no—
222C2×C43—22no—
223C2×C43—22no—
224C2×C43—41no—
225C2×C43—161no—
226C2×C43#300311yescharacteristic
227C2×C43C2×#45411yescharacteristic
228C2×C43#302611yescharacteristic
229D43—84no—
230C22×#41—861no—
231#537—434no—
232#537—864no—
233#537—862no—
234C2×C22⋊Q8—862no—
235C2×#121—432no—
236C2×#121—862no—
237C2×#121—861no—
238C2×#121C2×D4311yescharacteristic
239C22×C4⋊C4C2×D4311yescharacteristic
240#481—434no—
241#481—862no—
242#469—864no—
243#447—434no—
244#447—862no—
245#407—432no—
246#400C2×D4312yescomplemented
247#394C2×D4312yescomplemented
248#388—22no—
249#386—21no—
250#386—21no—
251C4×C22⋊C4C2×D4311yescharacteristic
252#327—438no—
253#324—434no—
254C43#1832411yescharacteristic, complemented, Sylow
255C2×#41—864no—
256C2×#41—864no—
257C2×#41—1728no—
258C22×Q8—861no—
259C22×D4—21no—
260C22×D4—432no—
261C22×D4—861no—
262C22×D4—861no—
263C22×D4—862no—
264C22×D4C22×D4311yescharacteristic
265C23×C4—862no—
266C23×C4C22⋊D4311yescharacteristic
267C23×C4C22⋊D4311yescharacteristic
268C23×C4C22×D4311yescharacteristic
269C2×D8—864no—
270C2×M16—862no—
271C22⋊Q8—868no—
272C22⋊Q8—868no—
273#121—22no—
274#121—22no—
275#121—434no—
276#121—434no—
277#121—868no—
278#121—868no—
279#121—864no—
280#121—862no—
281#121—862no—
282#121—864no—
283C2×C4⋊C4—22no—
284C2×C4⋊C4—22no—
285C2×C4⋊C4—432no—
286C2×C4⋊C4—861no—
287C2×C4⋊C4C22⋊D4312yes—
288C2×C4⋊C4C22×D4311yescharacteristic
289C2×C4⋊C4C22×D4312yes—
290C2×C22⋊C4—21no—
291C2×C22⋊C4—21no—
292C2×C22⋊C4—22no—
293C2×C22⋊C4—22no—
294C2×C22⋊C4—862no—
295C2×C22⋊C4—862no—
296C2×C42—21no—
297#106—864no—
298#102—864no—
299#102—864no—
300C22⋊C8—434no—
301C22⋊C8—862no—
302#95—22no—
303#95—22no—
304#95C22×D4312yes—
305C24—21no—
306C24—862no—
307C24C2×C22⋊D4311yescharacteristic
308#41—17216no—
309#41—1728no—
310#41—1728no—
311C2×Q8—864no—
312C2×Q8—1724no—
313C2×D4—22no—
314C2×D4—44no—
315C2×D4—41no—
316C2×D4—41no—
317C2×D4—81no—
318C2×D4—434no—
319C2×D4—864no—
320C2×D4—864no—
321C2×D4—864no—
322C2×D4—864no—
323C2×D4—862no—
324C2×D4—3442no—
325C2×D4—3442no—
326C2×D4—1724no—
327C2×D4—1728no—
328C22×C4—21no—
329C22×C4—21no—
330C22×C4—24no—
331C22×C4—21no—
332C22×C4—21no—
333C22×C4—21no—
334C22×C4—22no—
335C22×C4—81no—
336C22×C4—81no—
337C22×C4—868no—
338C22×C4—862no—
339C22×C4—1728no—
340C22×C4D4×D4312yes—
341C22×C4D4×D4312yes—
342C22×C4C2×C22⋊D4312yes—
343C22×C4C2×C22⋊D4312yes—
344C22×C4C2×C22⋊D4311yescharacteristic
345C22×C4C23×D4311yescharacteristic
346D8—3444no—
347M16—3442no—
348C2×C8—864no—
349C4⋊C4—24no—
350C4⋊C4—24no—
351C4⋊C4—22no—
352C4⋊C4—434no—
353C4⋊C4—864no—
354C4⋊C4—862no—
355C22⋊C4—42no—
356C22⋊C4—42no—
357C22⋊C4—44no—
358C22⋊C4—82no—
359C22⋊C4—868no—
360C22⋊C4—864no—
361C22⋊C4—864no—
362C42—81no—
363C23—22no—
364C23—22no—
365C23—41no—
366C23—42no—
367C23—42no—
368C23—41no—
369C23—42no—
370C23—864no—
371C23—1724no—
372C23—1724no—
373C23—1724no—
374C23#1306329311yescharacteristic
375C23#1306329311yescharacteristic
376C23C22×C22⋊D4311yescharacteristic
377Q8—1728no—
378D4—44no—
379D4—82no—
380D4—82no—
381D4—3442no—
382D4—3444no—
383D4—1724no—
384D4—1728no—
385D4—1728no—
386D4—1728no—
387C2×C4—24no—
388C2×C4—24no—
389C2×C4—22no—
390C2×C4—22no—
391C2×C4—22no—
392C2×C4—41no—
393C2×C4—42no—
394C2×C4—42no—
395C2×C4—41no—
396C2×C4—42no—
397C2×C4—42no—
398C2×C4—42no—
399C2×C4—42no—
400C2×C4—42no—
401C2×C4—41no—
402C2×C4—42no—
403C2×C4—81no—
404C2×C4—864no—
405C2×C4—17216no—
406C2×C4—1724no—
407C2×C4#1306329312yes—
408C2×C4#1306335014yes—
409C2×C4C2×D4×D4312yes—
410C8—1724no—
411C22—21no—
412C22—21no—
413C22—21no—
414C22—21no—
415C22—21no—
416C22—21no—
417C22—21no—
418C22—44no—
419C22—84no—
420C22—81no—
421C22—81no—
422C22—81no—
423C22—3448no—
424C22—1724no—
425C22—1724no—
426C22—1724no—
427C22#1458307112yes—
428C22C2×#1306329311yescharacteristic
429C22C2×#1306335012yes—
430C4—22no—
431C4—22no—
432C4—24no—
433C4—42no—
434C4—82no—
435C4—81no—
436C4—1724no—
437C2—22no—
438C2—22no—
439C2—41no—
440C2—161no—
441C2—3444no—
442C2#1914382111yescharacteristic
443C2C2×#1458307111yescharacteristic
444C2#1914399111yescharacteristic
subgroupG/H
centerC22C2×#13063293
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#2591C2
socleC22×C43C2×#120
hypercenter#2591D43
hypocenterC43#18324
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ #2591

Complements

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

NH ≅ G/Ntype
1. C2×#14583480C2semidirect
2. #19145392C2semidirect
3. #19133631C2semidirect
4. #19133529C2semidirect
5. #19133110C2semidirect
6. #19132925C2semidirect
7. C43×#2591C2semidirect
16. #14583217C22semidirect
19. #14583033C22semidirect
22. #14582632C22semidirect
23. #14582625C22semidirect
26. C43×#400C22semidirect
27. C43×#394C22semidirect
217. #2591D43semidirect
246. #400C2×D43semidirect
247. #394C2×D43semidirect
254. C43#18324semidirect

Maximal subgroups

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

subgroupindex
C2×#145834802
#191453922
#191336312
#191335292
#191331102
#191329252
C43×#25912
#1832443