Finite Group Databasebeta

← #25150806

Subgroups — #25150806

Order 11008.

1092 conjugacy classes of subgroups.

The subgroup lattice has 540 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19144988C211yesmaximal, characteristic, complemented
2#19144410C211yesmaximal, characteristic, complemented
3#19142991C211yesmaximal, characteristic, complemented
4#19135816C214yesmaximal, complemented
5#19135585C211yesmaximal, characteristic, complemented
6#19135424C211yesmaximal, characteristic, complemented
7#19134821C214yesmaximal, complemented
8C4×#13063252C211yesmaximal, characteristic, complemented
9C43×#3511C211yesmaximal, characteristic
10C2×#13063325C2211yescharacteristic
11C2×#13063323—22no—
12#14583258—22no—
13#14583249—21no—
14#14583245—21no—
15#14583194—21no—
16#14583189—21no—
17#14583184—21no—
18#14583179—21no—
19#14582942C2212yes—
20#14582923C2211yescharacteristic
21C2×#13063252C2212yes—
22C2×#13063252C2214yes—
23#14582900C2214yes—
24#14582900C2212yes—
25C4×#10621877C2211yescharacteristic
26#14582768—22no—
27#14582768C2214yes—
28C42×Dic43C2211yescharacteristic
29#14582668C2214yes—
30#14582658C2212yes—
31C43×#556—21no—
32C43×#555—21no—
33C43×#554—21no—
34C43×#553—22no—
35C43×#548—22no—
36C43×#547—21no—
37C43×#542—22no—
38C43×#537C2212yes—
39C43×#533—21no—
40C43×#532—21no—
41C43×#532C2211yescharacteristic
42C2×C4⋊Q8×C43C2211yescharacteristic
43C43×#520C2212yes—
44C4×#41×C43C2211yescharacteristic
45C22×Dic86—21no—
46C2×#10621877C2312yes—
47C2×#10621877C2312yes—
48#13063325—21no—
49#13063325—21no—
50#13063325—21no—
51#13063325—21no—
52#13063323—48no—
53C2×C4⋊Dic43—21no—
54C2×C4⋊Dic43C2312yes—
55C2×Dic43⋊C4—28no—
56C2×C4×Dic43—21no—
57C2×C4×Dic43—21no—
58C2×C4×Dic43C2312yes—
59#13063258—22no—
60#13063256—22no—
61C4⋊(C43⋊C8)—21no—
62C4⋊(C43⋊C8)—21no—
63#13063252—24no—
64#13063252—28no—
65#13063249—22no—
66#13063249—24no—
67#13063246—22no—
68#13063246—24no—
69#13063236—21no—
70C4×C43⋊C8—21no—
71C2×#41×C43—22no—
72C2×#41×C43C2311yescharacteristic
73C2×#41×C43C2312yes—
74C22×Q8×C43D412yes—
75C4⋊Q8×C43—21no—
76C4⋊Q8×C43—21no—
77C4⋊Q8×C43—21no—
78C4⋊Q8×C43—21no—
79C4⋊Q8×C43D411yescharacteristic
80#127×C43D411yescharacteristic
81#126×C43—24no—
82#125×C43—22no—
83#124×C43—22no—
84#124×C43—24no—
85#124×C43D412yes—
86#123×C43—24no—
87C22⋊Q8×C43—22no—
88C22⋊Q8×C43—24no—
89C22⋊Q8×C43—22no—
90C22⋊Q8×C43—22no—
91#121×C43—22no—
92#121×C43—22no—
93#121×C43—22no—
94#121×C43—21no—
95#121×C43—21no—
96#121×C43—24no—
97C4×Q8×C43—22no—
98C4×Q8×C43—22no—
99C4×Q8×C43D411yescharacteristic
100C4×Q8×C43D411yescharacteristic
101C4×D4×C43—22no—
102C4×D4×C43—22no—
103C4×D4×C43—21no—
104C4×D4×C43—21no—
105C4×D4×C43—24no—
106C4×D4×C43—21no—
107C4×D4×C43—21no—
108C4×D4×C43D411yescharacteristic
109C4×D4×C43D411yescharacteristic
110#117×C43—22no—
111#117×C43—22no—
112#117×C43—21no—
113#117×C43C2311yescharacteristic
114C2×C4⋊C4×C43—22no—
115C2×C4⋊C4×C43D412yes—
116C2×C4⋊C4×C43C2312yes—
117C2×C42×C43—21no—
118C2×C42×C43C2311yescharacteristic
119#41×C43—24no—
120#41×C43—22no—
121#41×C43—24no—
122#41×C43—22no—
123#41×C43—84no—
124C2×Q8×C43—22no—
125C2×Q8×C43—22no—
126C2×Q8×C43—44no—
127C2×Q8×C43C2×D412yes—
128C2×Q8×C43C2×D411yescharacteristic
129C2×D4×C43—24no—
130C2×D4×C43—21no—
131C2×D4×C43—21no—
132C2×D4×C43—21no—
133C2×D4×C43—22no—
134C2×D4×C43C2×D412yes—
135C2×D4×C43C2×D411yescharacteristic
136C22×C4×C43—24no—
137C22×C4×C43—21no—
138C22×C4×C43—21no—
139C22×C4×C43—21no—
140C22×C4×C43—22no—
141C22×C4×C43C2×D411yescharacteristic
142C22×C4×C43C2×D411yescharacteristic
143C22×C4×C43C2×D414yes—
144C22×C4×C43C2411yescharacteristic
145C22×Dic43—22no—
146C22×Dic43—22no—
147C2×Dic86—44no—
148C2×Dic86—41no—
149C2×Dic86—41no—
150C4⋊C4×C43—24no—
151C4⋊C4×C43—24no—
152C4⋊C4×C43—22no—
153C4⋊C4×C43—22no—
154C4⋊C4×C43—21no—
155C4⋊C4×C43—21no—
156C4⋊C4×C43—21no—
157C4⋊C4×C43—21no—
158C4⋊C4×C43—22no—
159C4⋊C4×C43—22no—
160C4⋊C4×C43C2×D411yescharacteristic
161C4⋊C4×C43C2×D411yescharacteristic
162C22⋊C4×C43—24no—
163C22⋊C4×C43—24no—
164C22⋊C4×C43—24no—
165C22⋊C4×C43—21no—
166C22⋊C4×C43—21no—
167C22⋊C4×C43—22no—
168C22⋊C4×C43—22no—
169C22⋊C4×C43—21no—
170C42×C43—24no—
171C42×C43—21no—
172C42×C43—21no—
173C42×C43—21no—
174C42×C43C2×D411yescharacteristic
175C42×C43C2×D411yescharacteristic
176C42×C43C2×D411yescharacteristic
177C42×C43C2×D411yescharacteristic
178C4⋊Dic43—22no—
179C4⋊Dic43—22no—
180C4⋊Dic43—41no—
181C4⋊Dic43—41no—
182Dic43⋊C4—416no—
183C4×Dic43—24no—
184C4×Dic43—24no—
185C4×Dic43—22no—
186C4×Dic43#4114yescomplemented
187#10621877—24no—
188#10621877—22no—
189#10621877—22no—
190C2×C43⋊C8—22no—
191C2×C43⋊C8—22no—
192C23×C43—21no—
193C23×C43—22no—
194C23×C43C22×D411yescharacteristic
195Q8×C43—21no—
196Q8×C43—21no—
197Q8×C43—24no—
198Q8×C43—44no—
199Q8×C43—82no—
200D4×C43—21no—
201D4×C43—21no—
202D4×C43—24no—
203D4×C43—44no—
204D4×C43—42no—
205D4×C43—42no—
206D4×C43—42no—
207D4×C43—84no—
208C2×C4×C43—22no—
209C2×C4×C43—22no—
210C2×C4×C43—21no—
211C2×C4×C43—22no—
212C2×C4×C43—21no—
213C2×C4×C43—21no—
214C2×C4×C43—24no—
215C2×C4×C43—42no—
216C2×C4×C43—42no—
217C2×C4×C43—42no—
218C2×C4×C43—42no—
219C2×C4×C43—42no—
220C2×C4×C43—44no—
221C2×C4×C43—84no—
222C2×C4×C43#12011yescharacteristic
223C2×C4×C43#12011yescharacteristic
224C2×C4×C43#12011yescharacteristic
225C2×C4×C43#12011yescharacteristic
226C2×C4×C43C22×D411yescharacteristic
227C2×C4×C43C22×D411yescharacteristic
228C2×C4×C43C2×#4112yes—
229C2×C4×C432−1+412yes—
230C2×Dic43—24no—
231C2×Dic43—24no—
232C2×Dic43—24no—
233C2×Dic43—44no—
234C2×Dic43—42no—
235Dic86—82no—
236Dic86—82no—
237C43⋊C8—42no—
238C43⋊C8—42no—
239#25666—431nomaximal, Sylow
240C22×C43—21no—
241C22×C43—21no—
242C22×C43—42no—
243C22×C43—41no—
244C22×C43—41no—
245C22×C43—42no—
246C22×C43—41no—
247C22×C43—42no—
248C22×C43C2×#12011yescharacteristic
249C22×C43#54812yes—
250C4×C43—21no—
251C4×C43—21no—
252C4×C43—42no—
253C4×C43—41no—
254C4×C43—41no—
255C4×C43—44no—
256C4×C43—41no—
257C4×C43#45312yes—
258C4×C43#45612yes—
259C4×C43#53211yescharacteristic
260C4×C43#53611yescharacteristic
261C4×C43#54712yes—
262Dic43—28no—
263Dic43—82no—
264#3511D4311yescharacteristic
265#3141—431no—
266#3079—431no—
267#2868—431no—
268#2039—434no—
269#1997—431no—
270#1962—431no—
271#1859—434no—
272C4×#104—431no—
273C2×C43—22no—
274C2×C43—81no—
275C2×C43—82no—
276C2×C43#243211yescharacteristic
277C2×C43C2×#45311yescharacteristic
278C2×C43C2×#45611yescharacteristic
279#556—21no—
280#555—21no—
281#554—21no—
282#553—22no—
283#548—22no—
284#547—21no—
285#542—22no—
286#537C2×D4312yes—
287#533—21no—
288#532—21no—
289#532C2×D4311yescharacteristic
290C2×C4⋊Q8—431no—
291C2×C4⋊Q8—862no—
292C2×C4⋊Q8C2×D4311yescharacteristic
293#520C2×D4312yes—
294C4×#41C2×D4311yescharacteristic
295#489—862no—
296#487—861no—
297#486—861no—
298#477—861no—
299#476—861no—
300#475—861no—
301#474—861no—
302#428—432no—
303#423—431no—
304C2×#104—434no—
305C2×#104—432no—
306#417—432no—
307#417—434no—
308C4×M16—431no—
309#384—434no—
310#384—862no—
311C43—431no—
312#343—434no—
313#339—432no—
314C43#2566611yescharacteristic, complemented, Sylow
315C2×#41—22no—
316C2×#41C22×D4311yescharacteristic
317C2×#41C22×D4312yes—
318C22×Q8—861no—
319C22×Q8C22⋊D4312yes—
320C2×M16—432no—
321C2×M16—432no—
322C4⋊Q8—21no—
323C4⋊Q8—21no—
324C4⋊Q8—21no—
325C4⋊Q8—21no—
326C4⋊Q8—861no—
327C4⋊Q8—861no—
328C4⋊Q8—861no—
329C4⋊Q8—861no—
330C4⋊Q8—1728no—
331C4⋊Q8C22⋊D4311yescharacteristic
332#127C22⋊D4311yescharacteristic
333#126—24no—
334#125—22no—
335#124—22no—
336#124—24no—
337#124C22⋊D4312yes—
338#123—24no—
339C22⋊Q8—22no—
340C22⋊Q8—24no—
341C22⋊Q8—22no—
342C22⋊Q8—22no—
343#121—22no—
344#121—22no—
345#121—22no—
346#121—21no—
347#121—21no—
348#121—24no—
349C4×Q8—22no—
350C4×Q8—22no—
351C4×Q8C22⋊D4311yescharacteristic
352C4×Q8C22⋊D4311yescharacteristic
353C4×D4—22no—
354C4×D4—22no—
355C4×D4—21no—
356C4×D4—21no—
357C4×D4—24no—
358C4×D4—21no—
359C4×D4—21no—
360C4×D4C22⋊D4311yescharacteristic
361C4×D4C22⋊D4311yescharacteristic
362#117—22no—
363#117—22no—
364#117—21no—
365#117C22×D4311yescharacteristic
366C2×C4⋊C4—22no—
367C2×C4⋊C4—432no—
368C2×C4⋊C4—861no—
369C2×C4⋊C4—868no—
370C2×C4⋊C4C22⋊D4312yes—
371C2×C4⋊C4C22×D4312yes—
372C2×C42—21no—
373C2×C42—432no—
374C2×C42—861no—
375C2×C42—861no—
376C2×C42C22×D4311yescharacteristic
377#107—862no—
378#106—862no—
379C4⋊C8—861no—
380C4⋊C8—861no—
381#104—868no—
382#104—864no—
383#103—862no—
384#103—864no—
385#102—862no—
386#102—864no—
387#97—861no—
388C4×C8—861no—
389#41—24no—
390#41—22no—
391#41—24no—
392#41—22no—
393#41—84no—
394C2×Q8—22no—
395C2×Q8—22no—
396C2×Q8—44no—
397C2×Q8—1724no—
398C2×Q8—1721no—
399C2×Q8—1721no—
400C2×Q8C2×C22⋊D4312yes—
401C2×Q8C2×C22⋊D4311yescharacteristic
402C2×D4—21no—
403C2×D4—22no—
404C2×D4—24no—
405C2×D4—21no—
406C2×D4—21no—
407C2×D4C2×C22⋊D4312yes—
408C2×D4C2×C22⋊D4311yescharacteristic
409C22×C4—24no—
410C22×C4—21no—
411C22×C4—21no—
412C22×C4—21no—
413C22×C4—22no—
414C22×C4—862no—
415C22×C4—862no—
416C22×C4C2×C22⋊D4311yescharacteristic
417C22×C4C2×C22⋊D4311yescharacteristic
418C22×C4C2×C22⋊D4314yes—
419C22×C4C23×D4311yescharacteristic
420M16—864no—
421M16—862no—
422M16—862no—
423C2×C8—862no—
424C2×C8—862no—
425C4⋊C4—24no—
426C4⋊C4—24no—
427C4⋊C4—22no—
428C4⋊C4—22no—
429C4⋊C4—21no—
430C4⋊C4—21no—
431C4⋊C4—21no—
432C4⋊C4—21no—
433C4⋊C4—22no—
434C4⋊C4—22no—
435C4⋊C4—862no—
436C4⋊C4—862no—
437C4⋊C4—17216no—
438C4⋊C4—1721no—
439C4⋊C4—1721no—
440C4⋊C4C2×C22⋊D4311yescharacteristic
441C4⋊C4C2×C22⋊D4311yescharacteristic
442C22⋊C4—24no—
443C22⋊C4—24no—
444C22⋊C4—24no—
445C22⋊C4—21no—
446C22⋊C4—21no—
447C22⋊C4—21no—
448C22⋊C4—22no—
449C22⋊C4—22no—
450C42—24no—
451C42—21no—
452C42—21no—
453C42—21no—
454C42—434no—
455C42—864no—
456C42—864no—
457C42—862no—
458C42C2×C22⋊D4311yescharacteristic
459C42C2×C22⋊D4311yescharacteristic
460C42C2×C22⋊D4311yescharacteristic
461C42C2×C22⋊D4311yescharacteristic
462C23—21no—
463C23—22no—
464C23C22×C22⋊D4311yescharacteristic
465Q8—21no—
466Q8—21no—
467Q8—24no—
468Q8—44no—
469Q8—82no—
470Q8—3442no—
471Q8—3442no—
472D4—21no—
473D4—21no—
474D4—24no—
475D4—44no—
476D4—42no—
477D4—42no—
478D4—42no—
479D4—84no—
480C2×C4—22no—
481C2×C4—22no—
482C2×C4—21no—
483C2×C4—22no—
484C2×C4—21no—
485C2×C4—21no—
486C2×C4—24no—
487C2×C4—42no—
488C2×C4—42no—
489C2×C4—42no—
490C2×C4—42no—
491C2×C4—42no—
492C2×C4—44no—
493C2×C4—84no—
494C2×C4—864no—
495C2×C4—864no—
496C2×C4—864no—
497C2×C4—1724no—
498C2×C4—1722no—
499C2×C4#1306329411yescharacteristic
500C2×C4#1306329411yescharacteristic
501C2×C4#1306329411yescharacteristic
502C2×C4#1306329411yescharacteristic
503C2×C4C22×C22⋊D4311yescharacteristic
504C2×C4C22×C22⋊D4311yescharacteristic
505C2×C4#41×D4312yes—
506C2×C4#1306337212yes—
507C8—1722no—
508C8—1722no—
509C22—21no—
510C22—21no—
511C22—41no—
512C22—42no—
513C22—42no—
514C22—41no—
515C22—41no—
516C22—42no—
517C22C2×#1306329411yescharacteristic
518C22#1458355612yes—
519C4—21no—
520C4—21no—
521C4—41no—
522C4—42no—
523C4—41no—
524C4—41no—
525C4—44no—
526C4—868no—
527C4—3442no—
528C4#1458306712yes—
529C4#1458308212yes—
530C4#1458344511yescharacteristic
531C4#1458347011yescharacteristic
532C4#1458354812yes—
533C2—22no—
534C2—81no—
535C2—82no—
536C2#1913821911yescharacteristic
537C2C2×#1458306711yescharacteristic
538C2C2×#1458308211yescharacteristic
subgroupG/H
centerC22C2×#13063294
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
Fitting, prime radicalC43×#3511C2
socleC22×C43C2×#120
hypercenter#3511D43
hypocenterC43#25666
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3511

Complements

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

NH ≅ G/Ntype
1. #19144988C2semidirect
2. #19144410C2semidirect
3. #19142991C2semidirect
4. #19135816C2semidirect
5. #19135585C2semidirect
6. #19135424C2semidirect
7. #19134821C2semidirect
8. C4×#13063252C2semidirect
186. C4×Dic43#41semidirect
314. C43#25666semidirect

Maximal subgroups

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

subgroupindex
#191449882
#191444102
#191429912
#191358162
#191355852
#191354242
#191348212
C4×#130632522
C43×#35112
#2566643