Finite Group Databasebeta

← #24996807

Subgroups — #24996807

Order 11008.

968 conjugacy classes of subgroups.

The subgroup lattice has 572 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583038C211yesmaximal, characteristic, complemented
2#19140329C211yesmaximal, characteristic
3#19134530C211yesmaximal, characteristic, complemented
4C2×#14582632C211yesmaximal, characteristic, complemented
5C2×#14582623C211yesmaximal, characteristic, complemented
6#19132474C211yesmaximal, characteristic, complemented
7C2×C43×#393C211yesmaximal, characteristic, complemented
8C22×#10621884—21no—
9C2×#13063299C2211yescharacteristic
10C2×#13063294—21no—
11#14583038—22no—
12#14583038—22no—
13C2×#13063249—21no—
14C2×#13063249—22no—
15C2×C22⋊(C43⋊C8)C2211yescharacteristic
16C2×C22⋊(C43⋊C8)C2211yescharacteristic
17#14582824—21no—
18#14582815—22no—
19#14582808—21no—
20#14582778—21no—
21#14582759C2211yescharacteristic
22#14582632—22no—
23#14582623—22no—
24C23×Q8×C43C2211yescharacteristic
25C22×C22⋊C4×C43—21no—
26C22×C22⋊C4×C43C2211yescharacteristic
27C43×#393—22no—
28C43×#393—22no—
29C2×#95×C43—21no—
30C2×#95×C43C2211yescharacteristic
31C22×D172D411yescharacteristic
32C22×C22⋊D43—21no—
33C22×C22⋊D43—22no—
34C2×#10621884—24no—
35C2×#10621884—44no—
36C22×C43⋊C8—21no—
37C22×C43⋊C8—21no—
38#13063299—21no—
39#13063299—21no—
40#13063299—21no—
41#13063299—21no—
42#13063294—42no—
43#13063294—42no—
44C2×C4⋊Dic43D411yescharacteristic
45C2×C4⋊Dic43D412yes—
46C2×C22⋊Dic43—22no—
47C2×C22⋊Dic43—21no—
48C2×(C2×D43)⋊C4—21no—
49C2×(C2×D43)⋊C4—22no—
50#13063249—24no—
51#13063249—44no—
52C22⋊(C43⋊C8)—21no—
53C22⋊(C43⋊C8)—21no—
54C22⋊(C43⋊C8)—21no—
55C22⋊(C43⋊C8)D412yescomplemented
56C43⋊#95—22no—
57C43⋊#95—21no—
58C25×C43D411yescharacteristic
59C22×Q8×C43—21no—
60C22×Q8×C43—21no—
61C22×Q8×C43—21no—
62C22×Q8×C43—21no—
63C22×Q8×C43—21no—
64C22×Q8×C43—44no—
65C22×Q8×C43D412yescomplemented
66C23×C4×C43—21no—
67C23×C4×C43—21no—
68C23×C4×C43D411yescharacteristic
69C23×C4×C43C2311yescharacteristic
70C2×C22⋊C4×C43—24no—
71C2×C22⋊C4×C43—21no—
72C2×C22⋊C4×C43—21no—
73C2×C22⋊C4×C43—21no—
74C2×C22⋊C4×C43—21no—
75C2×C22⋊C4×C43—21no—
76C2×C22⋊C4×C43—21no—
77C2×C22⋊C4×C43—44no—
78#95×C43—24no—
79#95×C43—21no—
80#95×C43D412yescomplemented
81C24×C43—21no—
82C24×C43—21no—
83C24×C43—21no—
84C24×C43—21no—
85C24×C43—21no—
86C24×C43—21no—
87C24×C43—42no—
88C24×C43—42no—
89C24×C43SD1612yescomplemented
90C24×C43C2×D411yescharacteristic
91C23×D43—21no—
92C2×Q8×C43—24no—
93C2×Q8×C43—24no—
94C2×Q8×C43—22no—
95C2×Q8×C43—22no—
96C2×Q8×C43—44no—
97C2×Q8×C43—42no—
98C2×Q8×C43—42no—
99C2×Q8×C43—44no—
100C2×Q8×C43—44no—
101C2×Q8×C43—44no—
102C2×Q8×C43—41no—
103C2×Q8×C43—41no—
104C22×C4×C43—24no—
105C22×C4×C43—22no—
106C22×C4×C43—21no—
107C22×C4×C43—22no—
108C22×C4×C43—21no—
109C22×C4×C43—21no—
110C22×C4×C43—42no—
111C22×C4×C43—42no—
112C22×C4×C43—42no—
113C22×C4×C43—42no—
114C22×C4×C43—42no—
115C22×C4×C43—41no—
116C22×C4×C43—41no—
117C22×C4×C43—41no—
118C22×C4×C43—41no—
119C22×C4×C43C2×D411yescharacteristic
120C22×C4×C43C2×D411yescharacteristic
121C22×C4×C43C2×D411yescharacteristic
122C22×C4×C43C2×D411yescharacteristic
123C22×C4×C43C2×D411yescharacteristic
124C22×C4×C43#4111yescharacteristic
125C2×C22⋊D43—44no—
126C2×C22⋊D43—41no—
127C2×C22⋊D43—41no—
128C2×C22⋊D43—41no—
129C2×C22⋊D43—41no—
130C2×C22⋊D43—41no—
131C2×C22⋊D43—41no—
132C2×C22⋊D43—82no—
133C2×C22⋊D43—82no—
134C22×Dic43—21no—
135C22×Dic43—22no—
136C2×D172—21no—
137C2×D172—21no—
138C2×D172—42no—
139C22⋊C4×C43—48no—
140C22⋊C4×C43—41no—
141C22⋊C4×C43—41no—
142C22⋊C4×C43—41no—
143C22⋊C4×C43—41no—
144C22⋊Dic43—44no—
145C22⋊Dic43—41no—
146C22⋊Dic43—41no—
147#10621884—48no—
148(C2×D43)⋊C4—41no—
149(C2×D43)⋊C4—41no—
150(C2×D43)⋊C4—82no—
151C4⋊Dic43—21no—
152C4⋊Dic43—21no—
153C4⋊Dic43—42no—
154C2×C43⋊C8—22no—
155C2×C43⋊C8—42no—
156C2×C43⋊C8—42no—
157C2×C43⋊C8—41no—
158C23×C43—22no—
159C23×C43—22no—
160C23×C43—22no—
161C23×C43—22no—
162C23×C43—22no—
163C23×C43—44no—
164C23×C43—42no—
165C23×C43—44no—
166C23×C43—42no—
167C23×C43—41no—
168C23×C43—41no—
169C23×C43—41no—
170C23×C43—42no—
171C23×C43—42no—
172C23×C43—41no—
173C23×C43—82no—
174C23×C43—82no—
175C23×C43—81no—
176C23×C43—81no—
177C23×C43#12011yescharacteristic
178C23×C43#12011yescharacteristic
179C23×C43#12111yescharacteristic
180C23×C43C2×SD1611yescharacteristic
181C23×C43#13511yescharacteristic
182C23×C43AGL(1,ℤ/8)11yescharacteristic
183C23×C43#13711yescharacteristic
184C22×D43—41no—
185C22×D43—41no—
186C22×D43—41no—
187C22×D43—42no—
188C22×D43—42no—
189Q8×C43—24no—
190Q8×C43—24no—
191Q8×C43—42no—
192Q8×C43—44no—
193Q8×C43—44no—
194Q8×C43—42no—
195C2×C4×C43—22no—
196C2×C4×C43—22no—
197C2×C4×C43—24no—
198C2×C4×C43—41no—
199C2×C4×C43—41no—
200C2×C4×C43—41no—
201C2×C4×C43—41no—
202C2×C4×C43—42no—
203C2×C4×C43—44no—
204C2×C4×C43—42no—
205C2×C4×C43—44no—
206C2×C4×C43—42no—
207C2×C4×C43—42no—
208C2×C4×C43—42no—
209C2×C4×C43—41no—
210C2×C4×C43—42no—
211C2×C4×C43—42no—
212C2×C4×C43—82no—
213C2×C4×C43—82no—
214C2×C4×C43—81no—
215C2×C4×C43#12011yescharacteristic
216C2×C4×C43#12111yescharacteristic
217C2×C4×C43#12111yescharacteristic
218C2×C4×C43#12711yescharacteristic
219C22⋊D43—88no—
220C22⋊D43—81no—
221C22⋊D43—81no—
222C22⋊D43—81no—
223C22⋊D43—81no—
224C2×Dic43—41no—
225C2×Dic43—42no—
226C2×Dic43—41no—
227C2×Dic43—41no—
228C2×Dic43—42no—
229C2×Dic43—42no—
230D172—42no—
231D172—81no—
232C43⋊C8—42no—
233C43⋊C8—81no—
234#9916—431nomaximal, Sylow
235C22×C43—22no—
236C22×C43—22no—
237C22×C43—22no—
238C22×C43—22no—
239C22×C43—21no—
240C22×C43—21no—
241C22×C43—21no—
242C22×C43—21no—
243C22×C43—44no—
244C22×C43—44no—
245C22×C43—42no—
246C22×C43—82no—
247C22×C43—82no—
248C22×C43—82no—
249C22×C43—82no—
250C22×C43—81no—
251C22×C43—81no—
252C22×C43#39211yescharacteristic
253C22×C43#44811yescharacteristic
254C22×C43#44911yescharacteristic
255C22×C43#45011yescharacteristic
256C22×C43#45211yescharacteristic
257C22×C43#45512yes—
258C22×C43B(4,𝔽2)12yes—
259C22×C43#46511yescharacteristic
260C22×C43#46811yescharacteristic
261C2×D43—82no—
262C2×D43—82no—
263C2×D43—81no—
264C2×D43—81no—
265C2×D43—81no—
266C4×C43—21no—
267C4×C43—21no—
268C4×C43—21no—
269C4×C43—21no—
270C4×C43—44no—
271C4×C43—82no—
272C4×C43—81no—
273Dic43—82no—
274Dic43—81no—
275C2×#448—431no—
276#2617—431no—
277C2×#393D4311yescharacteristic, complemented
278#1787—431no—
279C2×#327—431no—
280C2×#323—431no—
281#1294—431no—
282C2×C43—21no—
283C2×C43—21no—
284C2×C43—21no—
285C2×C43—21no—
286C2×C43—82no—
287C2×C43#160112yes—
288C2×C43#160612yes—
289C2×C43#200011yescharacteristic
290C2×C43#200411yescharacteristic
291C2×C43#202111yescharacteristic
292D43—161no—
293C23×Q8C2×D4311yescharacteristic
294C22×SD16—861no—
295C2×#121—431no—
296C2×#120—861no—
297C22×C22⋊C4—21no—
298C22×C22⋊C4C2×D4311yescharacteristic
299#448—862no—
300#448—862no—
301C2×#103—861no—
302C2×#103—862no—
303C2×C22⋊C8—431no—
304C2×C22⋊C8—431no—
305#397—861no—
306#394—862no—
307#393—22no—
308#393—22no—
309#392—861no—
310#386—861no—
311#380—431no—
312C2×#95—21no—
313C2×#95C2×D4311yescharacteristic
314#327—862no—
315#323—862no—
316C43#991611yescharacteristic, complemented, Sylow
317C25C22⋊D4311yescharacteristic
318C22×Q8—21no—
319C22×Q8—21no—
320C22×Q8—21no—
321C22×Q8—21no—
322C22×Q8—21no—
323C22×Q8—44no—
324C22×Q8C22⋊D4312yescomplemented
325C22×D4—431no—
326C22×D4—862no—
327C22×D4—861no—
328C23×C4—21no—
329C23×C4—21no—
330C23×C4C22⋊D4311yescharacteristic
331C23×C4C22×D4311yescharacteristic
332C2×SD16—864no—
333C2×SD16—1724no—
334C22×C8—861no—
335C22×C8—861no—
336#121—861no—
337#121—861no—
338#121—861no—
339#121—861no—
340#120—1722no—
341#120—1722no—
342C2×C4⋊C4—431no—
343C2×C4⋊C4—432no—
344C2×C22⋊C4—24no—
345C2×C22⋊C4—21no—
346C2×C22⋊C4—21no—
347C2×C22⋊C4—21no—
348C2×C22⋊C4—21no—
349C2×C22⋊C4—21no—
350C2×C22⋊C4—21no—
351C2×C22⋊C4—44no—
352C2×C22⋊C4—862no—
353C2×C22⋊C4—862no—
354C2×C22⋊C4—861no—
355C2×C22⋊C4—861no—
356#103—864no—
357#103—1724no—
358C22⋊C8—432no—
359C22⋊C8—861no—
360C22⋊C8—861no—
361C22⋊C8—861no—
362#95—24no—
363#95—21no—
364#95—862no—
365#95—861no—
366#95C22⋊D4312yescomplemented
367C24—21no—
368C24—21no—
369C24—21no—
370C24—21no—
371C24—21no—
372C24—21no—
373C24—42no—
374C24—42no—
375C24—861no—
376C24#1062188412yescomplemented
377C24C2×C22⋊D4311yescharacteristic
378C2×Q8—24no—
379C2×Q8—24no—
380C2×Q8—22no—
381C2×Q8—22no—
382C2×Q8—44no—
383C2×Q8—42no—
384C2×Q8—42no—
385C2×Q8—44no—
386C2×Q8—44no—
387C2×Q8—44no—
388C2×Q8—41no—
389C2×Q8—41no—
390C2×D4—861no—
391C2×D4—861no—
392C2×D4—3442no—
393C2×D4—3442no—
394C2×D4—1722no—
395C2×D4—1724no—
396C2×D4—1721no—
397C2×D4—1721no—
398C2×D4—1721no—
399C2×D4—1721no—
400C2×D4—1721no—
401C2×D4—1721no—
402C22×C4—24no—
403C22×C4—22no—
404C22×C4—21no—
405C22×C4—21no—
406C22×C4—22no—
407C22×C4—21no—
408C22×C4—42no—
409C22×C4—42no—
410C22×C4—41no—
411C22×C4—41no—
412C22×C4—42no—
413C22×C4—42no—
414C22×C4—42no—
415C22×C4—41no—
416C22×C4—41no—
417C22×C4—861no—
418C22×C4—862no—
419C22×C4D4×D4311yescharacteristic
420C22×C4D4×D4311yescharacteristic
421C22×C4D4×D4311yescharacteristic
422C22×C4#1062190011yescharacteristic
423C22×C4C2×C22⋊D4311yescharacteristic
424C22×C4C2×C22⋊D4311yescharacteristic
425SD16—1728no—
426C2×C8—862no—
427C2×C8—1722no—
428C2×C8—1721no—
429C2×C8—1722no—
430C4⋊C4—861no—
431C4⋊C4—861no—
432C4⋊C4—1722no—
433C22⋊C4—48no—
434C22⋊C4—41no—
435C22⋊C4—41no—
436C22⋊C4—41no—
437C22⋊C4—41no—
438C22⋊C4—3442no—
439C22⋊C4—1724no—
440C22⋊C4—1721no—
441C22⋊C4—1721no—
442C22⋊C4—1721no—
443C22⋊C4—1721no—
444C23—22no—
445C23—22no—
446C23—22no—
447C23—22no—
448C23—22no—
449C23—44no—
450C23—42no—
451C23—44no—
452C23—42no—
453C23—41no—
454C23—41no—
455C23—41no—
456C23—42no—
457C23—42no—
458C23—41no—
459C23—82no—
460C23—82no—
461C23—81no—
462C23—81no—
463C23—1721no—
464C23—1721no—
465C23—1721no—
466C23—1722no—
467C23—1722no—
468C23#1306329311yescharacteristic
469C23#1306329411yescharacteristic
470C23#1306329711yescharacteristic
471C23C2×#1062188411yescharacteristic
472C23#1306334511yescharacteristic
473C23#1306335011yescharacteristic
474C23#1306335611yescharacteristic
475Q8—24no—
476Q8—24no—
477Q8—44no—
478Q8—42no—
479Q8—44no—
480Q8—42no—
481D4—3441no—
482D4—3448no—
483D4—3441no—
484D4—3441no—
485D4—3441no—
486D4—3441no—
487D4—1722no—
488C2×C4—22no—
489C2×C4—22no—
490C2×C4—24no—
491C2×C4—41no—
492C2×C4—41no—
493C2×C4—41no—
494C2×C4—41no—
495C2×C4—42no—
496C2×C4—44no—
497C2×C4—42no—
498C2×C4—44no—
499C2×C4—42no—
500C2×C4—42no—
501C2×C4—42no—
502C2×C4—42no—
503C2×C4—41no—
504C2×C4—42no—
505C2×C4—82no—
506C2×C4—82no—
507C2×C4—81no—
508C2×C4—1722no—
509C2×C4—1721no—
510C2×C4—1721no—
511C2×C4—1721no—
512C2×C4—1722no—
513C2×C4—1722no—
514C2×C4#1306329311yescharacteristic
515C2×C4#1306329611yescharacteristic
516C2×C4#1306329711yescharacteristic
517C2×C4#1306332111yescharacteristic
518C8—3441no—
519C8—1722no—
520C22—22no—
521C22—22no—
522C22—22no—
523C22—22no—
524C22—21no—
525C22—21no—
526C22—21no—
527C22—21no—
528C22—44no—
529C22—44no—
530C22—42no—
531C22—82no—
532C22—82no—
533C22—82no—
534C22—82no—
535C22—81no—
536C22—81no—
537C22—3442no—
538C22—3441no—
539C22—3442no—
540C22—3441no—
541C22—3441no—
542C22#1458280711yescharacteristic
543C22#1458303811yescharacteristic
544C22#1458304411yescharacteristic
545C22#1458304911yescharacteristic
546C22#1458305911yescharacteristic
547C22#1458307612yes—
548C22#1458308512yes—
549C22#1458313011yescharacteristic
550C22#1458314711yescharacteristic
551C4—21no—
552C4—21no—
553C4—21no—
554C4—21no—
555C4—44no—
556C4—82no—
557C4—81no—
558C4—3442no—
559C4—3441no—
560C2—21no—
561C2—21no—
562C2—21no—
563C2—21no—
564C2—82no—
565C2—6881no—
566C2#1913354612yes—
567C2#1913357312yes—
568C2#1913559611yescharacteristic
569C2#1913562411yescharacteristic
570C2#1913571811yescharacteristic
subgroupG/H
centerC23#13063293
commutator, cosocleC23×C4×C43C23
FrattiniC23×C4C22×D43
FittingC2×C43×#393C2
socleC23×C43#120
prime radical#19140329C2
hypercenterC2×#393D43
hypocenterC43#9916
LCSG ▷ C23×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#393

Complements

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

NH ≅ G/Ntype
1. C2×#14583038C2semidirect
3. #19134530C2semidirect
4. C2×#14582632C2semidirect
5. C2×#14582623C2semidirect
6. #19132474C2semidirect
7. C2×C43×#393C2semidirect
55. C22⋊(C43⋊C8)D4semidirect
65. C22×Q8×C43D4semidirect
80. #95×C43D4semidirect
89. C24×C43SD16semidirect
277. C2×#393D43semidirect
316. C43#9916semidirect
324. C22×Q8C22⋊D43semidirect
366. #95C22⋊D43semidirect
376. C24#10621884semidirect

Maximal subgroups

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

subgroupindex
C2×#145830382
#191403292
#191345302
C2×#145826322
C2×#145826232
#191324742
C2×C43×#3932
#991643