Finite Group Databasebeta

← #25069266

Subgroups — #25069266

Order 11008.

1218 conjugacy classes of subgroups.

The subgroup lattice has 582 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19148398C211yesmaximal, characteristic, complemented
2#19143855C212yesmaximal, complemented
3#19133568C212yesmaximal, complemented
4#19133551C212yesmaximal, complemented
5#19133534C212yesmaximal, complemented
6#19133517C212yesmaximal, complemented
7#19133114C212yesmaximal, complemented
8#19132933C211yesmaximal, characteristic, complemented
9C43×#2388C211yesmaximal, characteristic
10C2×#13063355—22no—
11#14583608—24no—
12#14583606—22no—
13D4×Dic86—22no—
14#14583530C2212yes—
15#14583525—21no—
16#14583525C2212yes—
17#14583456—21no—
18C2×#13063304—21no—
19C2×#13063304C2212yes—
20#14583374—21no—
21#14583061—24no—
22#14583055C2214yes—
23#14583050C2214yes—
24#14582900—22no—
25#14582863C2212yes—
26#14582635C2214yes—
27#14582635C2214yes—
28#14582625C2212yes—
29#14582623C2212yes—
30C22×#41×C43C2211yescharacteristic
31C2×C4×D4×C43—21no—
32C2×C4×D4×C43C2211yescharacteristic
33C43×#395C2211yescharacteristic
34C43×#394—21no—
35C43×#394C2211yescharacteristic
36C43×#393C2211yescharacteristic
37C43×#392—21no—
38C43×#392C2211yescharacteristic
39C4×C22⋊C4×C43—21no—
40C4×C22⋊C4×C43C2211yescharacteristic
41C22×Dic86—21no—
42C22×Dic86D412yescomplemented
43#13063355—48no—
44C2×#10621885—24no—
45C2×#10621883—24no—
46C2×#10621877—22no—
47#13063325—21no—
48#13063325—21no—
49#13063324—24no—
50#13063317—22no—
51#13063316—24no—
52#13063304—22no—
53#13063304—22no—
54#13063304—22no—
55#13063304—22no—
56#13063304—22no—
57#13063304—22no—
58#13063304D414yescomplemented
59#13063304C2314yes—
60#13063302—24no—
61#13063302—24no—
62#13063302—24no—
63#13063302—24no—
64C4×Dic86—22no—
65C4×Dic86—22no—
66D4×Dic43—24no—
67D4×Dic43—24no—
68#13063284—22no—
69C2×C4⋊Dic43—21no—
70C2×C4⋊Dic43D412yescomplemented
71C2×Dic43⋊C4—22no—
72C2×Dic43⋊C4—22no—
73C2×C22⋊Dic43—22no—
74C2×C22⋊Dic43—22no—
75#13063249—24no—
76#13063246—24no—
77C22⋊(C43⋊C8)—22no—
78C22⋊(C43⋊C8)C2314yes—
79C2×#41×C43—22no—
80C2×#41×C43—22no—
81C2×#41×C43—44no—
82C22×Q8×C43C2311yescharacteristic
83C22×D4×C43—21no—
84C22×D4×C43—21no—
85C22×D4×C43D411yescharacteristic
86C22×D4×C43C2311yescharacteristic
87C23×C4×C43—21no—
88C23×C4×C43D411yescharacteristic
89C23×C4×C43C2311yescharacteristic
90C4×D4×C43—22no—
91C4×D4×C43—22no—
92C4×D4×C43—44no—
93C2×C4⋊C4×C43—21no—
94C2×C4⋊C4×C43C2311yescharacteristic
95C2×C22⋊C4×C43—21no—
96C2×C22⋊C4×C43—21no—
97C2×C22⋊C4×C43—21no—
98C2×C22⋊C4×C43—21no—
99C2×C22⋊C4×C43—21no—
100C2×C22⋊C4×C43D411yescharacteristic
101C2×C22⋊C4×C43C2311yescharacteristic
102C2×C42×C43—21no—
103C2×C42×C43D411yescharacteristic
104#95×C43—21no—
105#95×C43—21no—
106#95×C43C2311yescharacteristic
107#95×C43C2311yescharacteristic
108C24×C43—21no—
109C24×C43C2×D411yescharacteristic
110C24×C43C2×D411yescharacteristic
111#41×C43—28no—
112#41×C43—44no—
113#41×C43—44no—
114#41×C43—44no—
115C2×Q8×C43—22no—
116C2×Q8×C43—42no—
117C2×D4×C43—22no—
118C2×D4×C43—22no—
119C2×D4×C43—22no—
120C2×D4×C43—22no—
121C2×D4×C43—42no—
122C2×D4×C43—42no—
123C2×D4×C43—42no—
124C2×D4×C43—42no—
125C2×D4×C43—42no—
126C2×D4×C43—42no—
127C2×D4×C43—42no—
128C22×C4×C43—24no—
129C22×C4×C43—21no—
130C22×C4×C43—21no—
131C22×C4×C43—21no—
132C22×C4×C43—21no—
133C22×C4×C43—21no—
134C22×C4×C43—42no—
135C22×C4×C43—42no—
136C22×C4×C43—42no—
137C22×C4×C43—41no—
138C22×C4×C43—41no—
139C22×C4×C43C2×D412yes—
140C22×C4×C43C2×D412yes—
141C22×C4×C43C2×D411yescharacteristic
142C22×C4×C43C2×D411yescharacteristic
143C22×C4×C43C2×D411yescharacteristic
144C22×C4×C43C2×D411yescharacteristic
145C22×C4×C43C2411yescharacteristic
146C22×Dic43—22no—
147C22×Dic43—22no—
148C22×Dic43—22no—
149C22×Dic43—22no—
150C2×Dic86—22no—
151C2×Dic86—22no—
152C2×Dic86—22no—
153C2×Dic86—44no—
154C2×Dic86—82no—
155C2×Dic86C2×D414yes—
156C4⋊C4×C43—22no—
157C4⋊C4×C43—42no—
158C22⋊C4×C43—22no—
159C22⋊C4×C43—22no—
160C22⋊C4×C43—42no—
161C22⋊C4×C43—42no—
162C22⋊C4×C43—42no—
163C22⋊C4×C43—42no—
164C22⋊C4×C43—42no—
165C42×C43—21no—
166C42×C43—21no—
167C42×C43—42no—
168C22⋊Dic43—24no—
169C22⋊Dic43—24no—
170C22⋊Dic43—24no—
171#10621885—48no—
172#10621883—48no—
173C4⋊Dic43—22no—
174C4⋊Dic43—22no—
175C4⋊Dic43—22no—
176C4⋊Dic43—22no—
177C4⋊Dic43—22no—
178C4⋊Dic43C2×D414yes—
179Dic43⋊C4—24no—
180Dic43⋊C4—24no—
181Dic43⋊C4—24no—
182Dic43⋊C4—24no—
183C4×Dic43—24no—
184#10621877—44no—
185C2×C43⋊C8—24no—
186C23×C43—21no—
187C23×C43—21no—
188C23×C43—21no—
189C23×C43—21no—
190C23×C43—22no—
191C23×C43—41no—
192C23×C43—41no—
193C23×C43—41no—
194C23×C43—41no—
195C23×C43—41no—
196C23×C43—41no—
197C23×C43—41no—
198C23×C43—41no—
199C23×C43—41no—
200C23×C43—41no—
201C23×C43#12012yes—
202C23×C43#13712yescomplemented
203C23×C43C22×D411yescharacteristic
204Q8×C43—24no—
205Q8×C43—42no—
206D4×C43—28no—
207D4×C43—24no—
208D4×C43—42no—
209D4×C43—48no—
210D4×C43—48no—
211C2×C4×C43—21no—
212C2×C4×C43—21no—
213C2×C4×C43—24no—
214C2×C4×C43—22no—
215C2×C4×C43—22no—
216C2×C4×C43—22no—
217C2×C4×C43—21no—
218C2×C4×C43—21no—
219C2×C4×C43—42no—
220C2×C4×C43—41no—
221C2×C4×C43—44no—
222C2×C4×C43—41no—
223C2×C4×C43—41no—
224C2×C4×C43—41no—
225C2×C4×C43—41no—
226C2×C4×C43—42no—
227C2×C4×C43—44no—
228C2×C4×C43—41no—
229C2×C4×C43—41no—
230C2×C4×C43—41no—
231C2×C4×C43—41no—
232C2×C4×C43—41no—
233C2×C4×C43—81no—
234C2×C4×C43#12011yescharacteristic
235C2×C4×C43#12011yescharacteristic
236C2×C4×C43#13712yescomplemented
237C2×C4×C43C22×D412yes—
238C2×Dic43—24no—
239C2×Dic43—24no—
240C2×Dic43—82no—
241C2×Dic43—82no—
242C2×Dic43—82no—
243C2×Dic43—82no—
244Dic86—44no—
245Dic86—44no—
246Dic86—82no—
247Dic86—82no—
248C43⋊C8—44no—
249#18167—431nomaximal, Sylow
250C22×C43—21no—
251C22×C43—21no—
252C22×C43—22no—
253C22×C43—22no—
254C22×C43—22no—
255C22×C43—22no—
256C22×C43—42no—
257C22×C43—42no—
258C22×C43—42no—
259C22×C43—41no—
260C22×C43—41no—
261C22×C43—42no—
262C22×C43—81no—
263C22×C43—81no—
264C22×C43—81no—
265C22×C43—81no—
266C22×C43—81no—
267C22×C43—81no—
268C22×C43—81no—
269C22×C43C2×#12011yescharacteristic
270C22×C43C2×#13711yescharacteristic
271C22×C43C2×#13711yescharacteristic
272C4×C43—22no—
273C4×C43—22no—
274C4×C43—21no—
275C4×C43—42no—
276C4×C43—41no—
277C4×C43—41no—
278C4×C43—42no—
279C4×C43—81no—
280C4×C43B(4,𝔽2)12yes—
281Dic43—44no—
282Dic43—44no—
283#3501—431no—
284#3007—432no—
285#2388D4311yescharacteristic
286#1605—432no—
287#1602—432no—
288#1599—432no—
289#1596—432no—
290#1508—432no—
291#1465—431no—
292C2×C43—21no—
293C2×C43—21no—
294C2×C43—42no—
295C2×C43—42no—
296C2×C43—82no—
297C2×C43#300411yescharacteristic
298C2×C43#301811yescharacteristic
299C2×C43C2×B(4,𝔽2)11yescharacteristic
300C22×#41C2×D4311yescharacteristic
301C2×#137—862no—
302#554—862no—
303#554—864no—
304D4×Q8—862no—
305#544—432no—
306#543—432no—
307#543—861no—
308#533—861no—
309C2×C22⋊Q8—432no—
310C2×C22⋊Q8—861no—
311#518—861no—
312C2×C4×D4—21no—
313C2×C4×D4C2×D4311yescharacteristic
314#452—864no—
315#451—434no—
316#450—434no—
317#417—862no—
318#407—432no—
319#395C2×D4311yescharacteristic
320#394—21no—
321#394C2×D4311yescharacteristic
322#393C2×D4311yescharacteristic
323#392—21no—
324#392C2×D4311yescharacteristic
325C4×C22⋊C4—21no—
326C4×C22⋊C4C2×D4311yescharacteristic
327#328—434no—
328#328—434no—
329#324—432no—
330#323—432no—
331C43#1816711yescharacteristic, complemented, Sylow
332C2×#41—22no—
333C2×#41—22no—
334C2×#41—44no—
335C22×Q8—432no—
336C22×Q8—861no—
337C22×Q8C22×D4311yescharacteristic
338C22×D4—21no—
339C22×D4—21no—
340C22×D4C22⋊D4311yescharacteristic
341C22×D4C22×D4311yescharacteristic
342C23×C4—21no—
343C23×C4C22⋊D4311yescharacteristic
344C23×C4C22×D4311yescharacteristic
345#137—1728no—
346C2×Q16—864no—
347C2×SD16—864no—
348C2×M16—862no—
349C4⋊Q8—861no—
350C4⋊Q8—861no—
351C4⋊Q8—864no—
352#125—862no—
353#125—864no—
354C22⋊Q8—434no—
355C22⋊Q8—434no—
356C22⋊Q8—864no—
357C22⋊Q8—864no—
358C22⋊Q8—864no—
359C22⋊Q8—864no—
360C22⋊Q8—862no—
361C22⋊Q8—862no—
362C22⋊Q8—862no—
363C22⋊Q8—862no—
364C22⋊Q8—862no—
365C22⋊Q8—862no—
366C4×Q8—862no—
367C4×Q8—862no—
368C4×D4—22no—
369C4×D4—22no—
370C4×D4—44no—
371C4×D4—864no—
372C4×D4—864no—
373#117—862no—
374C2×C4⋊C4—21no—
375C2×C4⋊C4—432no—
376C2×C4⋊C4—862no—
377C2×C4⋊C4—861no—
378C2×C4⋊C4—862no—
379C2×C4⋊C4C22×D4311yescharacteristic
380C2×C22⋊C4—21no—
381C2×C22⋊C4—21no—
382C2×C22⋊C4—21no—
383C2×C22⋊C4—21no—
384C2×C22⋊C4—21no—
385C2×C22⋊C4—862no—
386C2×C22⋊C4—862no—
387C2×C22⋊C4C22⋊D4311yescharacteristic
388C2×C22⋊C4C22×D4311yescharacteristic
389C2×C42—21no—
390C2×C42C22⋊D4311yescharacteristic
391#103—864no—
392#102—864no—
393C22⋊C8—434no—
394C22⋊C8—862no—
395#95—21no—
396#95—21no—
397#95C22×D4311yescharacteristic
398#95C22×D4311yescharacteristic
399C24—21no—
400C24C2×C22⋊D4311yescharacteristic
401C24C2×C22⋊D4311yescharacteristic
402#41—28no—
403#41—44no—
404#41—44no—
405#41—44no—
406C2×Q8—22no—
407C2×Q8—42no—
408C2×Q8—434no—
409C2×Q8—862no—
410C2×Q8—862no—
411C2×Q8—862no—
412C2×Q8—3442no—
413C2×Q8—1724no—
414C2×D4—22no—
415C2×D4—22no—
416C2×D4—22no—
417C2×D4—22no—
418C2×D4—42no—
419C2×D4—42no—
420C2×D4—42no—
421C2×D4—42no—
422C2×D4—42no—
423C2×D4—42no—
424C2×D4—42no—
425C22×C4—24no—
426C22×C4—21no—
427C22×C4—21no—
428C22×C4—21no—
429C22×C4—21no—
430C22×C4—21no—
431C22×C4—42no—
432C22×C4—42no—
433C22×C4—42no—
434C22×C4—41no—
435C22×C4—41no—
436C22×C4—862no—
437C22×C4—862no—
438C22×C4—862no—
439C22×C4—862no—
440C22×C4D4×D4312yes—
441C22×C4D4×D4312yes—
442C22×C4C2×C22⋊D4311yescharacteristic
443C22×C4C2×C22⋊D4311yescharacteristic
444C22×C4C2×C22⋊D4311yescharacteristic
445C22×C4C2×C22⋊D4311yescharacteristic
446C22×C4C23×D4311yescharacteristic
447Q16—1728no—
448SD16—1728no—
449M16—1724no—
450C2×C8—864no—
451C4⋊C4—22no—
452C4⋊C4—42no—
453C4⋊C4—434no—
454C4⋊C4—862no—
455C4⋊C4—864no—
456C4⋊C4—862no—
457C4⋊C4—862no—
458C4⋊C4—864no—
459C4⋊C4—862no—
460C4⋊C4—862no—
461C4⋊C4—864no—
462C4⋊C4—864no—
463C22⋊C4—22no—
464C22⋊C4—22no—
465C22⋊C4—42no—
466C22⋊C4—42no—
467C22⋊C4—42no—
468C22⋊C4—42no—
469C22⋊C4—42no—
470C22⋊C4—864no—
471C22⋊C4—864no—
472C22⋊C4—864no—
473C42—21no—
474C42—21no—
475C42—42no—
476C42—864no—
477C23—21no—
478C23—21no—
479C23—21no—
480C23—21no—
481C23—22no—
482C23—41no—
483C23—41no—
484C23—41no—
485C23—41no—
486C23—41no—
487C23—41no—
488C23—41no—
489C23—41no—
490C23—41no—
491C23—41no—
492C23#1306329312yes—
493C23#1306335512yescomplemented
494C23C22×C22⋊D4311yescharacteristic
495Q8—24no—
496Q8—42no—
497Q8—3442no—
498Q8—3442no—
499Q8—1724no—
500Q8—1724no—
501D4—28no—
502D4—24no—
503D4—42no—
504D4—48no—
505D4—48no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—22no—
509C2×C4—24no—
510C2×C4—22no—
511C2×C4—22no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—42no—
515C2×C4—41no—
516C2×C4—44no—
517C2×C4—41no—
518C2×C4—41no—
519C2×C4—41no—
520C2×C4—41no—
521C2×C4—44no—
522C2×C4—42no—
523C2×C4—41no—
524C2×C4—41no—
525C2×C4—41no—
526C2×C4—41no—
527C2×C4—41no—
528C2×C4—81no—
529C2×C4—864no—
530C2×C4—864no—
531C2×C4—3442no—
532C2×C4—3442no—
533C2×C4—3442no—
534C2×C4—3442no—
535C2×C4#1306329311yescharacteristic
536C2×C4#1306329311yescharacteristic
537C2×C4#1306335512yescomplemented
538C2×C4C2×D4×D4312yes—
539C8—1724no—
540C22—21no—
541C22—21no—
542C22—22no—
543C22—22no—
544C22—22no—
545C22—22no—
546C22—42no—
547C22—42no—
548C22—42no—
549C22—41no—
550C22—41no—
551C22—42no—
552C22—81no—
553C22—81no—
554C22—81no—
555C22—81no—
556C22—81no—
557C22—81no—
558C22—81no—
559C22C2×#1306329311yescharacteristic
560C22C2×#1306335511yescharacteristic
561C22C2×#1306335511yescharacteristic
562C4—22no—
563C4—21no—
564C4—22no—
565C4—42no—
566C4—41no—
567C4—42no—
568C4—41no—
569C4—81no—
570C4—1724no—
571C4—1724no—
572C4#1458308512yes—
573C2—21no—
574C2—21no—
575C2—42no—
576C2—42no—
577C2—82no—
578C2#1914382811yescharacteristic
579C2#1914394311yescharacteristic
580C2C2×#1458308511yescharacteristic
subgroupG/H
centerC22C2×#13063293
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
Fitting, prime radicalC43×#2388C2
socleC22×C43C2×#120
hypercenter#2388D43
hypocenterC43#18167
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ #2388

Complements

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

NH ≅ G/Ntype
1. #19148398C2semidirect
2. #19143855C2semidirect
3. #19133568C2semidirect
4. #19133551C2semidirect
5. #19133534C2semidirect
6. #19133517C2semidirect
7. #19133114C2semidirect
8. #19132933C2semidirect
42. C22×Dic86D4semidirect
58. #13063304D4semidirect
70. C2×C4⋊Dic43D4semidirect
202. C23×C43#137semidirect
236. C2×C4×C43#137semidirect
331. C43#18167semidirect
493. C23#13063355semidirect
537. C2×C4#13063355semidirect

Maximal subgroups

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

subgroupindex
#191483982
#191438552
#191335682
#191335512
#191335342
#191335172
#191331142
#191329332
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