Finite Group Databasebeta

← #25151100

Subgroups — #25151100

Order 11008.

1094 conjugacy classes of subgroups.

The subgroup lattice has 526 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19145142C211yesmaximal, characteristic, complemented
2#19144988C211yesmaximal, characteristic, complemented
3#19139548C211yesmaximal, characteristic, complemented
4#19135802C214yesmaximal, complemented
5#19135540C211yesmaximal, characteristic, complemented
6#19135515C211yesmaximal, characteristic, complemented
7#19134821C214yesmaximal, complemented
8C4×#13063242C211yesmaximal, characteristic, complemented
9C43×#3506C211yesmaximal, characteristic
10C2×#13063325C2211yescharacteristic
11C2×#13063304—22no—
12#14583309—22no—
13#14583302—21no—
14#14583295—21no—
15#14583258—22no—
16#14583249—21no—
17#14583245—21no—
18#14582942C2214yes—
19C2×#13063252C2214yes—
20#14582900C2214yes—
21C2×#13063242C2212yes—
22C4×#10621877C2211yescharacteristic
23C4×#10621877C2211yescharacteristic
24#14582835—22no—
25#14582802C2212yes—
26#14582768C2212yes—
27C4×C4⋊Dic43C2211yescharacteristic
28#14582668C2212yes—
29#14582658C2214yes—
30C43×#559—22no—
31C43×#556—21no—
32C43×#555—21no—
33C43×#553—22no—
34C43×#550—21no—
35C43×#547—21no—
36C43×#538—22no—
37C43×#535C2212yes—
38C43×#533C2211yescharacteristic
39C43×#532C2211yescharacteristic
40C43×#525—22no—
41C43×#520C2212yes—
42C2×C4×D4×C43C2211yescharacteristic
43C22×Dic86—21no—
44C2×#10621877C2312yes—
45C2×#10621877C2312yes—
46#13063325—21no—
47#13063325—21no—
48#13063325—21no—
49#13063325—21no—
50#13063304—48no—
51C2×C4⋊Dic43—21no—
52C2×C4⋊Dic43—21no—
53C2×C4⋊Dic43C2312yes—
54C2×Dic43⋊C4—24no—
55C2×C22⋊Dic43—24no—
56C2×C4×Dic43C2312yes—
57#13063258—24no—
58#13063256—24no—
59#13063252—28no—
60#13063249—24no—
61#13063246—24no—
62#13063242—24no—
63#13063236—21no—
64#13063236—21no—
65C4×C43⋊C8—21no—
66C4×C43⋊C8—21no—
67C43⋊#95—21no—
68C2×#41×C43—22no—
69C2×#41×C43C2312yes—
70C22×D4×C43C2311yescharacteristic
71C23×C4×C43D412yes—
72C4⋊Q8×C43D411yescharacteristic
73C4⋊Q8×C43D411yescharacteristic
74C4⋊Q8×C43D411yescharacteristic
75#127×C43—22no—
76#127×C43D411yescharacteristic
77#126×C43—24no—
78#125×C43D412yes—
79#124×C43—24no—
80#124×C43—22no—
81#124×C43D412yes—
82#123×C43—24no—
83#123×C43—24no—
84C22⋊Q8×C43—22no—
85C22⋊Q8×C43—21no—
86C22⋊Q8×C43—21no—
87#121×C43—22no—
88#121×C43—24no—
89#121×C43—21no—
90#121×C43—21no—
91#121×C43—22no—
92#121×C43—22no—
93#120×C43—24no—
94C4×Q8×C43—22no—
95C4×Q8×C43—21no—
96C4×Q8×C43—21no—
97C4×D4×C43—24no—
98C4×D4×C43—22no—
99C4×D4×C43—24no—
100C4×D4×C43—21no—
101C4×D4×C43—21no—
102C4×D4×C43—21no—
103C4×D4×C43—21no—
104C4×D4×C43—21no—
105C4×D4×C43—21no—
106#117×C43—22no—
107#117×C43—22no—
108#117×C43C2312yes—
109C2×C4⋊C4×C43—22no—
110C2×C4⋊C4×C43C2311yescharacteristic
111C2×C22⋊C4×C43D412yes—
112C2×C42×C43C2311yescharacteristic
113C24×C43C2×D412yes—
114#41×C43—24no—
115#41×C43—24no—
116#41×C43—84no—
117C2×Q8×C43—21no—
118C2×Q8×C43—21no—
119C2×Q8×C43C2×D412yes—
120C2×D4×C43—24no—
121C2×D4×C43—24no—
122C2×D4×C43—21no—
123C2×D4×C43—21no—
124C2×D4×C43—21no—
125C2×D4×C43—21no—
126C2×D4×C43—22no—
127C2×D4×C43—22no—
128C2×D4×C43—22no—
129C2×D4×C43C2×D412yes—
130C22×C4×C43—24no—
131C22×C4×C43—22no—
132C22×C4×C43—22no—
133C22×C4×C43—22no—
134C22×C4×C43—44no—
135C22×C4×C43C2×D411yescharacteristic
136C22×C4×C43C2×D412yes—
137C22×C4×C43C2×D411yescharacteristic
138C22×C4×C43C2411yescharacteristic
139C22×Dic43—22no—
140C22×Dic43—22no—
141C2×Dic86—44no—
142C2×Dic86—41no—
143C2×Dic86—41no—
144C4⋊C4×C43—24no—
145C4⋊C4×C43—21no—
146C4⋊C4×C43—21no—
147C4⋊C4×C43—22no—
148C4⋊C4×C43—21no—
149C4⋊C4×C43—22no—
150C4⋊C4×C43—21no—
151C4⋊C4×C43—21no—
152C4⋊C4×C43—21no—
153C4⋊C4×C43C2×D412yes—
154C4⋊C4×C43C2×D412yes—
155C22⋊C4×C43—24no—
156C22⋊C4×C43—24no—
157C22⋊C4×C43—24no—
158C22⋊C4×C43—22no—
159C22⋊C4×C43—22no—
160C22⋊C4×C43—22no—
161C22⋊C4×C43—22no—
162C22⋊C4×C43—22no—
163C42×C43—24no—
164C42×C43—22no—
165C42×C43C2×D411yescharacteristic
166C42×C43C2×D411yescharacteristic
167C42×C43C2×D411yescharacteristic
168C42×C43C2×D411yescharacteristic
169C22⋊Dic43—48no—
170C4⋊Dic43—24no—
171C4⋊Dic43—22no—
172C4⋊Dic43—22no—
173C4⋊Dic43—41no—
174C4⋊Dic43—41no—
175Dic43⋊C4—48no—
176C4×Dic43—24no—
177#10621877—22no—
178#10621877—22no—
179#10621877—22no—
180#10621877#4114yescomplemented
181C2×C43⋊C8—22no—
182C2×C43⋊C8—22no—
183C23×C43—22no—
184C23×C43—22no—
185C23×C43—22no—
186C23×C43—22no—
187C23×C43—42no—
188C23×C43—42no—
189C23×C43C22×D411yescharacteristic
190Q8×C43—24no—
191Q8×C43—42no—
192Q8×C43—81no—
193D4×C43—24no—
194D4×C43—42no—
195D4×C43—42no—
196D4×C43—42no—
197D4×C43—42no—
198D4×C43—42no—
199D4×C43—81no—
200D4×C43—84no—
201D4×C43—84no—
202C2×C4×C43—22no—
203C2×C4×C43—22no—
204C2×C4×C43—22no—
205C2×C4×C43—22no—
206C2×C4×C43—22no—
207C2×C4×C43—41no—
208C2×C4×C43—44no—
209C2×C4×C43—44no—
210C2×C4×C43—42no—
211C2×C4×C43—82no—
212C2×C4×C43—84no—
213C2×C4×C43#12011yescharacteristic
214C2×C4×C43#12011yescharacteristic
215C2×C4×C43#12011yescharacteristic
216C2×C4×C43#12011yescharacteristic
217C2×C4×C43C22×D411yescharacteristic
218C2×C4×C43C22×D411yescharacteristic
219C2×C4×C43C2×#4112yes—
220C2×C4×C432−1+412yes—
221C2×Dic43—24no—
222C2×Dic43—42no—
223C2×Dic43—42no—
224C2×Dic43—44no—
225C2×Dic43—42no—
226Dic86—82no—
227Dic86—82no—
228C43⋊C8—24no—
229C43⋊C8—42no—
230#25694—431nomaximal, Sylow
231C22×C43—21no—
232C22×C43—21no—
233C22×C43—44no—
234C22×C43—42no—
235C22×C43—42no—
236C22×C43—42no—
237C22×C43—42no—
238C22×C43—42no—
239C22×C43—42no—
240C22×C43—82no—
241C22×C43C2×#12011yescharacteristic
242C22×C43#53211yescharacteristic
243C22×C43#53611yescharacteristic
244C4×C43—21no—
245C4×C43—21no—
246C4×C43—21no—
247C4×C43—42no—
248C4×C43—42no—
249C4×C43—42no—
250C4×C43—42no—
251C4×C43#45312yes—
252C4×C43#54712yes—
253C4×C43#54812yes—
254Dic43—44no—
255Dic43—82no—
256#3506D4311yescharacteristic
257#3165—431no—
258#3141—431no—
259#2542—431no—
260#2037—434no—
261#1986—431no—
262#1980—431no—
263#1859—434no—
264C4×#100—431no—
265C2×C43—21no—
266C2×C43—21no—
267C2×C43—82no—
268C2×C43—82no—
269C2×C43#243211yescharacteristic
270C2×C43C2×#45311yescharacteristic
271C2×C43#302211yescharacteristic
272#559—22no—
273#556—21no—
274#555—21no—
275#553—22no—
276#550—21no—
277#547—21no—
278#538—22no—
279#535C2×D4312yes—
280#533C2×D4311yescharacteristic
281#532C2×D4311yescharacteristic
282C2×C4⋊Q8—431no—
283#525—22no—
284C2×C22⋊Q8—862no—
285#520C2×D4312yes—
286C2×C4×D4C2×D4311yescharacteristic
287#501—862no—
288#500—861no—
289#498—861no—
290#489—862no—
291#487—861no—
292#486—861no—
293#428—434no—
294C2×#104—434no—
295#417—434no—
296C2×#100—432no—
297C4×M16—431no—
298C4×M16—431no—
299#399—862no—
300#390—432no—
301#384—432no—
302C4×C4⋊C4—431no—
303#343—432no—
304#339—434no—
305C43#2569411yescharacteristic, complemented, Sylow
306C2×#41—22no—
307C2×#41C22×D4312yes—
308C22×Q8—861no—
309C22×D4C22×D4311yescharacteristic
310C23×C4C22⋊D4312yes—
311C2×M16—432no—
312C2×M16—432no—
313C4⋊Q8—861no—
314C4⋊Q8—861no—
315C4⋊Q8—861no—
316C4⋊Q8—861no—
317C4⋊Q8C22⋊D4311yescharacteristic
318C4⋊Q8C22⋊D4311yescharacteristic
319C4⋊Q8C22⋊D4311yescharacteristic
320#127—22no—
321#127C22⋊D4311yescharacteristic
322#126—24no—
323#125C22⋊D4312yes—
324#124—24no—
325#124—22no—
326#124C22⋊D4312yes—
327#123—24no—
328#123—24no—
329C22⋊Q8—22no—
330C22⋊Q8—21no—
331C22⋊Q8—21no—
332C22⋊Q8—1728no—
333#121—22no—
334#121—24no—
335#121—21no—
336#121—21no—
337#121—22no—
338#121—22no—
339#120—24no—
340C4×Q8—22no—
341C4×Q8—21no—
342C4×Q8—21no—
343C4×D4—24no—
344C4×D4—22no—
345C4×D4—24no—
346C4×D4—21no—
347C4×D4—21no—
348C4×D4—21no—
349C4×D4—21no—
350C4×D4—21no—
351C4×D4—21no—
352#117—22no—
353#117—22no—
354#117C22×D4312yes—
355C2×C4⋊C4—22no—
356C2×C4⋊C4—432no—
357C2×C4⋊C4—861no—
358C2×C4⋊C4—864no—
359C2×C4⋊C4—861no—
360C2×C4⋊C4C22×D4311yescharacteristic
361C2×C22⋊C4—864no—
362C2×C22⋊C4C22⋊D4312yes—
363C2×C42—432no—
364C2×C42C22×D4311yescharacteristic
365#107—864no—
366#106—864no—
367#104—868no—
368#103—864no—
369#102—864no—
370#100—864no—
371#97—861no—
372#97—861no—
373C4×C8—861no—
374C4×C8—861no—
375#95—861no—
376C24C2×C22⋊D4312yes—
377#41—24no—
378#41—24no—
379#41—84no—
380C2×Q8—21no—
381C2×Q8—21no—
382C2×Q8—1724no—
383C2×Q8—1721no—
384C2×Q8—1721no—
385C2×Q8C2×C22⋊D4312yes—
386C2×D4—22no—
387C2×D4—24no—
388C2×D4—24no—
389C2×D4—21no—
390C2×D4—21no—
391C2×D4—21no—
392C2×D4—21no—
393C2×D4—22no—
394C2×D4—22no—
395C2×D4C2×C22⋊D4312yes—
396C22×C4—24no—
397C22×C4—22no—
398C22×C4—22no—
399C22×C4—22no—
400C22×C4—44no—
401C22×C4—862no—
402C22×C4—862no—
403C22×C4C2×C22⋊D4311yescharacteristic
404C22×C4C2×C22⋊D4312yes—
405C22×C4C2×C22⋊D4311yescharacteristic
406C22×C4C23×D4311yescharacteristic
407M16—434no—
408M16—862no—
409M16—862no—
410M16—862no—
411C2×C8—862no—
412C2×C8—862no—
413C4⋊C4—24no—
414C4⋊C4—21no—
415C4⋊C4—21no—
416C4⋊C4—22no—
417C4⋊C4—21no—
418C4⋊C4—22no—
419C4⋊C4—21no—
420C4⋊C4—21no—
421C4⋊C4—21no—
422C4⋊C4—864no—
423C4⋊C4—862no—
424C4⋊C4—862no—
425C4⋊C4—1728no—
426C4⋊C4—1721no—
427C4⋊C4—1721no—
428C4⋊C4C2×C22⋊D4312yes—
429C4⋊C4C2×C22⋊D4312yes—
430C22⋊C4—24no—
431C22⋊C4—24no—
432C22⋊C4—24no—
433C22⋊C4—22no—
434C22⋊C4—22no—
435C22⋊C4—22no—
436C22⋊C4—22no—
437C22⋊C4—22no—
438C22⋊C4—1728no—
439C42—24no—
440C42—22no—
441C42—864no—
442C42C2×C22⋊D4311yescharacteristic
443C42C2×C22⋊D4311yescharacteristic
444C42C2×C22⋊D4311yescharacteristic
445C42C2×C22⋊D4311yescharacteristic
446C23—22no—
447C23—22no—
448C23—22no—
449C23—22no—
450C23—42no—
451C23—42no—
452C23C22×C22⋊D4311yescharacteristic
453Q8—24no—
454Q8—42no—
455Q8—81no—
456Q8—3442no—
457Q8—3442no—
458D4—24no—
459D4—42no—
460D4—42no—
461D4—42no—
462D4—42no—
463D4—42no—
464D4—81no—
465D4—84no—
466D4—84no—
467C2×C4—22no—
468C2×C4—22no—
469C2×C4—22no—
470C2×C4—22no—
471C2×C4—22no—
472C2×C4—41no—
473C2×C4—44no—
474C2×C4—44no—
475C2×C4—42no—
476C2×C4—82no—
477C2×C4—84no—
478C2×C4—864no—
479C2×C4—1724no—
480C2×C4—1722no—
481C2×C4—1722no—
482C2×C4—1722no—
483C2×C4#1306329411yescharacteristic
484C2×C4#1306329411yescharacteristic
485C2×C4#1306329411yescharacteristic
486C2×C4#1306329411yescharacteristic
487C2×C4C22×C22⋊D4311yescharacteristic
488C2×C4C22×C22⋊D4311yescharacteristic
489C2×C4#41×D4312yes—
490C2×C4#1306337212yes—
491C8—864no—
492C8—1722no—
493C22—21no—
494C22—21no—
495C22—44no—
496C22—42no—
497C22—42no—
498C22—42no—
499C22—42no—
500C22—42no—
501C22—42no—
502C22—82no—
503C22C2×#1306329411yescharacteristic
504C22#1458344511yescharacteristic
505C22#1458347011yescharacteristic
506C4—21no—
507C4—21no—
508C4—21no—
509C4—42no—
510C4—42no—
511C4—42no—
512C4—42no—
513C4—3442no—
514C4—1724no—
515C4#1458306712yes—
516C4#1458354812yes—
517C4#1458355612yes—
518C2—21no—
519C2—21no—
520C2—82no—
521C2—82no—
522C2#1913821911yescharacteristic
523C2C2×#1458306711yescharacteristic
524C2#1914397411yescharacteristic
subgroupG/H
centerC22C2×#13063294
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
Fitting, prime radicalC43×#3506C2
socleC22×C43C2×#120
hypercenter#3506D43
hypocenterC43#25694
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3506

Complements

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

NH ≅ G/Ntype
1. #19145142C2semidirect
2. #19144988C2semidirect
3. #19139548C2semidirect
4. #19135802C2semidirect
5. #19135540C2semidirect
6. #19135515C2semidirect
7. #19134821C2semidirect
8. C4×#13063242C2semidirect
180. #10621877#41semidirect
305. C43#25694semidirect

Maximal subgroups

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

subgroupindex
#191451422
#191449882
#191395482
#191358022
#191355402
#191355152
#191348212
C4×#130632422
C43×#35062
#2569443