Finite Group Databasebeta

← #25070498

Subgroups — #25070498

Order 11008.

1282 conjugacy classes of subgroups; only the 187 normal subgroups are shown.

normal subgroups only

This group has 1282 conjugacy classes of subgroups — too many to draw. Only its 187 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#19145343C212yesmaximal, complemented
3#19133597C214yesmaximal, complemented
4#19133529C214yesmaximal, complemented
5#19133162C212yesmaximal, complemented
6C2×#14582625C211yesmaximal, characteristic, complemented
7C43×#2618C211yesmaximal, 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#14583212C2214yescomplemented
17#14583210—22no—
18#14583133—24no—
19#14583033C2214yescomplemented
20#14583032—22no—
21C2×C22⋊(C43⋊C8)C2212yes—
22#14582632C2218yescomplemented
23#14582625C2214yescomplemented
24C2×#123×C43—21no—
25C2×#121×C43C2211yescharacteristic
26C22×C4⋊C4×C43C2211yescharacteristic
27C43×#398C2212yescomplemented
28C43×#396—22no—
29C43×#394C2212yescomplemented
30C43×#386—21no—
31C43×#380C2211yescharacteristic
32C2×#10621898—24no—
33C2×#10621898—24no—
34C2×#10621898—44no—
35C2×#10621898—44no—
36C22×Dic86—21no—
37C22×D172—21no—
38C22×D172—21no—
39C22×D172D412yes—
40C22×C22⋊D43—22no—
41C22×C4×D43—22no—
42C2×#10621882—24no—
43C22×C43⋊C8—22no—
44#13063305—28no—
45#13063305—28no—
46#13063300—28no—
47#13063300—28no—
48#13063299—24no—
49#13063299—24no—
50#13063299—22no—
51#13063299—22no—
52#13063299D414yes—
53#13063299C2314yes—
54C2×C4⋊Dic43—21no—
55C2×C4⋊Dic43D412yes—
56C2×(C2×D43)⋊C4—22no—
57C2×(C2×D43)⋊C4—22no—
58#13063258—24no—
59#13063246—24no—
60#13063245—24no—
61C22⋊(C43⋊C8)—22no—
62C22⋊(C43⋊C8)C2314yes—
63C22×D4×C43—21no—
64C22×D4×C43C2311yescharacteristic
65C23×C4×C43D411yescharacteristic
66C23×C4×C43D411yescharacteristic
67C23×C4×C43C2311yescharacteristic
68#123×C43—44no—
69#121×C43—22no—
70#121×C43—22no—
71C2×C4⋊C4×C43—22no—
72C2×C4⋊C4×C43—22no—
73C2×C4⋊C4×C43—22no—
74C2×C4⋊C4×C43—21no—
75C2×C4⋊C4×C43D412yes—
76C2×C4⋊C4×C43C2311yescharacteristic
77C2×C4⋊C4×C43C2312yes—
78C2×C22⋊C4×C43—21no—
79C2×C22⋊C4×C43—21no—
80C2×C22⋊C4×C43—22no—
81C2×C22⋊C4×C43—22no—
82#95×C43—22no—
83#95×C43C2312yes—
84C24×C43—21no—
85C24×C43C2×D411yescharacteristic
86C23×D43—22no—
87C2×D4×C43—22no—
88C2×D4×C43—41no—
89C2×D4×C43—41no—
90C2×D4×C43—42no—
91C2×D4×C43—42no—
92C2×D4×C43—81no—
93C22×C4×C43—21no—
94C22×C4×C43—21no—
95C22×C4×C43—21no—
96C22×C4×C43—21no—
97C22×C4×C43—22no—
98C22×C4×C43—21no—
99C22×C4×C43—22no—
100C22×C4×C43—81no—
101C22×C4×C43—81no—
102C22×C4×C43D814yescomplemented
103C22×C4×C43C2×D412yes—
104C22×C4×C43C2×D412yes—
105C22×C4×C43C2×D412yes—
106C22×C4×C43C2×D412yes—
107C22×C4×C43C2×D411yescharacteristic
108C22×C4×C43C2411yescharacteristic
109C2×C22⋊D43—24no—
110C2×C22⋊D43—24no—
111C2×C22⋊D43—44no—
112C2×C22⋊D43—44no—
113C22×Dic43—22no—
114#10621898—48no—
115#10621898—416no—
116#10621898—48no—
117C2×D172—24no—
118C2×D172—24no—
119C2×D172—22no—
120C2×D172—44no—
121C2×D172—82no—
122C2×D172—82no—
123C2×D172C2×D414yes—
124C2×C4×D43—28no—
125C2×C4×D43—48no—
126C2×Dic86—24no—
127C2×Dic86—44no—
128C4⋊C4×C43—24no—
129C4⋊C4×C43—24no—
130C4⋊C4×C43—22no—
131C4⋊C4×C43—44no—
132C4⋊C4×C43—81no—
133C22⋊C4×C43—42no—
134C22⋊C4×C43—44no—
135C22⋊C4×C43—42no—
136C22⋊C4×C43—82no—
137#10621882—84no—
138(C2×D43)⋊C4—28no—
139(C2×D43)⋊C4—24no—
140(C2×D43)⋊C4—24no—
141C4⋊Dic43—24no—
142C4⋊Dic43—22no—
143C4⋊Dic43C2×D414yes—
144C2×C43⋊C8—24no—
145C2×C43⋊C8—82no—
146C23×C43—41no—
147C23×C43—41no—
148C23×C43—42no—
149C23×C43—42no—
150C23×C43—41no—
151C23×C43—41no—
152C23×C43—41no—
153C23×C43#12011yescharacteristic
154C23×C43#12011yescharacteristic
155C23×C43C2×D812yes—
156C23×C43AGL(1,ℤ/8)12yes—
157C23×C43C22×D411yescharacteristic
158C22×D43—24no—
159C22×D43—44no—
160C22×D43—44no—
161C22×D43—44no—
162D4×C43—44no—
163D4×C43—82no—
164D4×C43—82no—
165C2×C4×C43—22no—
166C2×C4×C43—22no—
167C2×C4×C43—24no—
168C2×C4×C43—24no—
169C2×C4×C43—22no—
170C2×C4×C43—42no—
171C2×C4×C43—41no—
172C2×C4×C43—42no—
173C2×C4×C43—41no—
174C2×C4×C43—42no—
175C2×C4×C43—42no—
176C2×C4×C43—42no—
177C2×C4×C43—42no—
178C2×C4×C43—41no—
179C2×C4×C43—42no—
180C2×C4×C43—41no—
181C2×C4×C43—41no—
182C2×C4×C43—81no—
183C2×C4×C43#12012yes—
184C2×C4×C43C2×D814yes—
185C2×C4×C43C22×D412yes—
186C22⋊D43—44no—
187C22⋊D43—44no—
188C22⋊D43—48no—
189C2×Dic43—24no—
190C2×Dic43—44no—
191D172—44no—
192D172—48no—
193D172—82no—
194D172—84no—
195C4×D43—416no—
196Dic86—48no—
197C43⋊C8—44no—
198#18292—431nomaximal, Sylow
199C22×C43—21no—
200C22×C43—21no—
201C22×C43—21no—
202C22×C43—21no—
203C22×C43—21no—
204C22×C43—21no—
205C22×C43—42no—
206C22×C43—42no—
207C22×C43—82no—
208C22×C43—82no—
209C22×C43—81no—
210C22×C43—81no—
211C22×C43—81no—
212C22×C43#44712yes—
213C22×C43#44712yes—
214C22×C43C2×#12011yescharacteristic
215C22×C43C22×D811yescharacteristic
216C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
217C2×D43—44no—
218C2×D43—44no—
219C2×D43—44no—
220C2×D43—88no—
221C4×C43—24no—
222C4×C43—22no—
223C4×C43—22no—
224C4×C43—42no—
225C4×C43—82no—
226C4×C43—81no—
227Dic43—44no—
228C2×#537—431no—
229#3186—432no—
230#2618D4311yescharacteristic, complemented
231#1610—434no—
232#1598—434no—
233#1519—432no—
234C2×#324—431no—
235C2×C43—21no—
236C2×C43—22no—
237C2×C43—21no—
238C2×C43—22no—
239C2×C43—161no—
240C2×C43C2×#44711yescharacteristic
241C2×C43#302011yescharacteristic
242C2×C43#302611yescharacteristic
243D43—84no—
244C22×#41—861no—
245#537—434no—
246#537—864no—
247#537—862no—
248C2×#123—21no—
249C2×C22⋊Q8—862no—
250C2×#121—432no—
251C2×#121—862no—
252C2×#121—861no—
253C2×#121C2×D4311yescharacteristic
254C22×C4⋊C4C2×D4311yescharacteristic
255#480—434no—
256#480—862no—
257#466—864no—
258#447—434no—
259#447—862no—
260C2×C22⋊C8—432no—
261#398C2×D4312yescomplemented
262#396—22no—
263#394C2×D4312yescomplemented
264#386—21no—
265#380C2×D4311yescharacteristic
266#327—438no—
267#324—434no—
268C43#1829211yescharacteristic, complemented, Sylow
269C2×#41—864no—
270C2×#41—864no—
271C2×#41—1724no—
272C2×#41—1724no—
273C22×Q8—861no—
274C22×D4—21no—
275C22×D4—432no—
276C22×D4—861no—
277C22×D4—861no—
278C22×D4—862no—
279C22×D4C22×D4311yescharacteristic
280C23×C4—862no—
281C23×C4C22⋊D4311yescharacteristic
282C23×C4C22⋊D4311yescharacteristic
283C23×C4C22×D4311yescharacteristic
284C2×D8—864no—
285C22×C8—862no—
286#123—44no—
287C22⋊Q8—868no—
288C22⋊Q8—868no—
289#121—22no—
290#121—22no—
291#121—434no—
292#121—434no—
293#121—868no—
294#121—868no—
295#121—864no—
296#121—862no—
297#121—862no—
298#121—864no—
299C2×C4⋊C4—22no—
300C2×C4⋊C4—22no—
301C2×C4⋊C4—22no—
302C2×C4⋊C4—21no—
303C2×C4⋊C4—432no—
304C2×C4⋊C4—861no—
305C2×C4⋊C4C22⋊D4312yes—
306C2×C4⋊C4C22×D4311yescharacteristic
307C2×C4⋊C4C22×D4312yes—
308C2×C22⋊C4—21no—
309C2×C22⋊C4—21no—
310C2×C22⋊C4—22no—
311C2×C22⋊C4—22no—
312C2×C22⋊C4—862no—
313C2×C22⋊C4—862no—
314#107—864no—
315#102—864no—
316#102—864no—
317C22⋊C8—434no—
318C22⋊C8—862no—
319#95—22no—
320#95C22×D4312yes—
321C24—21no—
322C24—862no—
323C24C2×C22⋊D4311yescharacteristic
324#41—1728no—
325#41—17216no—
326#41—1728no—
327C2×Q8—864no—
328C2×Q8—1724no—
329C2×D4—22no—
330C2×D4—41no—
331C2×D4—41no—
332C2×D4—42no—
333C2×D4—42no—
334C2×D4—81no—
335C2×D4—434no—
336C2×D4—864no—
337C2×D4—864no—
338C2×D4—864no—
339C2×D4—864no—
340C2×D4—862no—
341C2×D4—3442no—
342C2×D4—3442no—
343C2×D4—1724no—
344C2×D4—1724no—
345C2×D4—1724no—
346C22×C4—21no—
347C22×C4—21no—
348C22×C4—22no—
349C22×C4—21no—
350C22×C4—21no—
351C22×C4—21no—
352C22×C4—22no—
353C22×C4—81no—
354C22×C4—81no—
355C22×C4—868no—
356C22×C4—862no—
357C22×C4—1728no—
358C22×C4#1062188214yescomplemented
359C22×C4D4×D4312yes—
360C22×C4D4×D4312yes—
361C22×C4C2×C22⋊D4312yes—
362C22×C4C2×C22⋊D4312yes—
363C22×C4C2×C22⋊D4311yescharacteristic
364C22×C4C23×D4311yescharacteristic
365D8—3444no—
366C2×C8—864no—
367C2×C8—3442no—
368C4⋊C4—24no—
369C4⋊C4—24no—
370C4⋊C4—22no—
371C4⋊C4—44no—
372C4⋊C4—81no—
373C4⋊C4—434no—
374C4⋊C4—864no—
375C4⋊C4—862no—
376C22⋊C4—42no—
377C22⋊C4—42no—
378C22⋊C4—44no—
379C22⋊C4—82no—
380C22⋊C4—868no—
381C22⋊C4—864no—
382C22⋊C4—864no—
383C23—41no—
384C23—41no—
385C23—42no—
386C23—42no—
387C23—41no—
388C23—41no—
389C23—41no—
390C23—864no—
391C23—1724no—
392C23—1724no—
393C23—1724no—
394C23#1306329311yescharacteristic
395C23#1306329311yescharacteristic
396C23C2×#1062188212yes—
397C23#1306335012yes—
398C23C22×C22⋊D4311yescharacteristic
399Q8—1728no—
400D4—44no—
401D4—82no—
402D4—82no—
403D4—3442no—
404D4—3444no—
405D4—1724no—
406D4—1728no—
407D4—1724no—
408D4—1724no—
409D4—1728no—
410C2×C4—22no—
411C2×C4—22no—
412C2×C4—24no—
413C2×C4—24no—
414C2×C4—22no—
415C2×C4—41no—
416C2×C4—42no—
417C2×C4—42no—
418C2×C4—41no—
419C2×C4—42no—
420C2×C4—42no—
421C2×C4—42no—
422C2×C4—42no—
423C2×C4—41no—
424C2×C4—42no—
425C2×C4—41no—
426C2×C4—41no—
427C2×C4—81no—
428C2×C4—864no—
429C2×C4—17216no—
430C2×C4—1724no—
431C2×C4#1306329312yes—
432C2×C4C2×#1062188214yes—
433C2×C4C2×D4×D4312yes—
434C8—1724no—
435C22—21no—
436C22—21no—
437C22—21no—
438C22—21no—
439C22—21no—
440C22—21no—
441C22—42no—
442C22—42no—
443C22—82no—
444C22—82no—
445C22—81no—
446C22—81no—
447C22—81no—
448C22—3448no—
449C22—1724no—
450C22—1724no—
451C22—1724no—
452C22#1458303212yes—
453C22#1458303212yes—
454C22C2×#1306329311yescharacteristic
455C22C22×#1062188211yescharacteristic
456C22C2×#1306335011yescharacteristic
457C4—22no—
458C4—22no—
459C4—24no—
460C4—42no—
461C4—82no—
462C4—81no—
463C4—1724no—
464C2—21no—
465C2—21no—
466C2—22no—
467C2—22no—
468C2—161no—
469C2—3444no—
470C2C2×#1458303211yescharacteristic
471C2#1914395811yescharacteristic
472C2#1914399111yescharacteristic
subgroupG/H
centerC22C2×#13063293
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#2618C2
socleC22×C43C2×#120
hypercenter#2618D43
hypocenterC43#18292
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ #2618

Complements

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

NH ≅ G/Ntype
1. C2×#14583480C2semidirect
2. #19145343C2semidirect
3. #19133597C2semidirect
4. #19133529C2semidirect
5. #19133162C2semidirect
6. C2×#14582625C2semidirect
7. C43×#2618C2semidirect
16. #14583212C22semidirect
19. #14583033C22semidirect
22. #14582632C22semidirect
23. #14582625C22semidirect
27. C43×#398C22semidirect
29. C43×#394C22semidirect
102. C22×C4×C43D8semidirect
230. #2618D43semidirect
261. #398C2×D43semidirect
263. #394C2×D43semidirect
268. C43#18292semidirect
358. C22×C4#10621882semidirect

Maximal subgroups

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

subgroupindex
C2×#145834802
#191453432
#191335972
#191335292
#191331622
C2×#145826252
C43×#26182
#1829243