Finite Group Databasebeta

← #24998900

Subgroups — #24998900

Order 11008.

744 conjugacy classes of subgroups.

The subgroup lattice has 542 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583099C211yesmaximal, characteristic, complemented
2C2×#14583094C211yesmaximal, characteristic
3#19135400C211yesmaximal, characteristic, complemented
4C2×Q8⋊(C43⋊C8)C211yesmaximal, characteristic, complemented
5C2×D4⋊(C43⋊C8)C211yesmaximal, characteristic, complemented
6#19132478C211yesmaximal, characteristic, complemented
7C43×#2538C211yesmaximal, characteristic, complemented
8C22×#10621884—21no—
9C22×#10621882—21no—
10C2×#13063322C2211yescharacteristic
11#14583099—22no—
12#14583099—22no—
13#14583094—22no—
14#14583094—22no—
15C2×C4⋊(C43⋊C8)C2211yescharacteristic
16C2×C4⋊(C43⋊C8)C2211yescharacteristic
17C2×#13063245—21no—
18C2×#13063245—21no—
19C2×#13063245—22no—
20C2×C4×C43⋊C8C2211yescharacteristic
21Q8⋊(C43⋊C8)—22no—
22D4⋊(C43⋊C8)—22no—
23C2×C22⋊Q8×C43—21no—
24C2×C4×Q8×C43C2211yescharacteristic
25C2×C4×D4×C43C2211yescharacteristic
26C43×#396—22no—
27C43×#390—21no—
28C43×#389—21no—
29C43×#384C2211yescharacteristic
30C43×#380—21no—
31C22×D172—21no—
32C22×D172—21no—
33C22×D172—21no—
34C2×#10621884—24no—
35C2×#10621884—42no—
36C2×#10621884—42no—
37C2×#10621882—24no—
38C2×#10621882—42no—
39C2×#10621882—42no—
40C22×C43⋊C8—21no—
41C22×C43⋊C8—21no—
42C22×C43⋊C8—21no—
43#13063322—21no—
44#13063322—21no—
45#13063322—21no—
46#13063322D412yes—
47C4⋊(C43⋊C8)—21no—
48C4⋊(C43⋊C8)—21no—
49C4⋊(C43⋊C8)D412yes—
50C4⋊(C43⋊C8)D412yes—
51#13063245—24no—
52#13063245—24no—
53#13063245—44no—
54C4×C43⋊C8—21no—
55C4×C43⋊C8—21no—
56C22×Q8×C43D411yescharacteristic
57C22×D4×C43D411yescharacteristic
58C23×C4×C43—21no—
59C22⋊Q8×C43—42no—
60C22⋊Q8×C43—42no—
61C4×Q8×C43—21no—
62C4×Q8×C43—21no—
63C4×Q8×C43—21no—
64C4×Q8×C43—21no—
65C4×D4×C43—21no—
66C4×D4×C43—21no—
67C4×D4×C43—21no—
68C4×D4×C43—21no—
69C2×C4⋊C4×C43—22no—
70C2×C4⋊C4×C43—21no—
71C2×C4⋊C4×C43—21no—
72C2×C4⋊C4×C43—21no—
73C2×C4⋊C4×C43D411yescharacteristic
74C2×C4⋊C4×C43D411yescharacteristic
75C2×C4⋊C4×C43D412yes—
76C2×C22⋊C4×C43—22no—
77C2×C22⋊C4×C43—21no—
78C2×C22⋊C4×C43—22no—
79C2×C42×C43—21no—
80C2×C42×C43C2311yescharacteristic
81#95×C43—22no—
82C24×C43—21no—
83C23×D43—41no—
84C2×Q8×C43—21no—
85C2×Q8×C43—21no—
86C2×Q8×C43—21no—
87C2×Q8×C43—21no—
88C2×Q8×C43—21no—
89C2×Q8×C43D812yescomplemented
90C2×D4×C43—21no—
91C2×D4×C43—21no—
92C2×D4×C43—21no—
93C2×D4×C43—21no—
94C2×D4×C43—21no—
95C2×D4×C43SD1612yescomplemented
96C22×C4×C43—21no—
97C22×C4×C43—21no—
98C22×C4×C43—21no—
99C22×C4×C43—22no—
100C22×C4×C43—41no—
101C22×C4×C43—41no—
102C22×C4×C43—41no—
103C22×C4×C43—41no—
104C22×C4×C43—41no—
105C22×C4×C43—41no—
106C22×C4×C43C2×D411yescharacteristic
107C22×C4×C43C2×D411yescharacteristic
108C22×C4×C43C2×D411yescharacteristic
109C2×D172—22no—
110C2×D172—22no—
111C2×D172—22no—
112C2×D172—41no—
113C2×D172—41no—
114C2×D172—41no—
115C2×D172—42no—
116C2×D172—42no—
117C2×D172—41no—
118C2×D172—41no—
119C2×D172—41no—
120C2×D172—41no—
121C2×D172—41no—
122C2×D172—41no—
123C2×D172—41no—
124C2×D172—41no—
125C4⋊C4×C43—21no—
126C4⋊C4×C43—21no—
127C4⋊C4×C43—21no—
128C4⋊C4×C43—21no—
129C4⋊C4×C43—42no—
130C4⋊C4×C43—44no—
131C4⋊C4×C43—41no—
132C4⋊C4×C43—41no—
133C4⋊C4×C43—41no—
134C4⋊C4×C43—41no—
135C4⋊C4×C43—41no—
136C4⋊C4×C43—41no—
137C22⋊C4×C43—44no—
138C22⋊C4×C43—41no—
139C22⋊C4×C43—41no—
140C22⋊C4×C43—82no—
141C42×C43—41no—
142C42×C43—41no—
143C42×C43C2×D411yescharacteristic
144C42×C43C2×D411yescharacteristic
145C42×C43C2×D411yescharacteristic
146C42×C43#4111yescharacteristic
147#10621884—48no—
148#10621882—48no—
149C2×C43⋊C8—22no—
150C2×C43⋊C8—22no—
151C2×C43⋊C8—22no—
152C2×C43⋊C8—41no—
153C2×C43⋊C8—41no—
154C2×C43⋊C8—41no—
155C2×C43⋊C8—41no—
156C2×C43⋊C8—41no—
157C2×C43⋊C8—41no—
158C23×C43—22no—
159C23×C43—41no—
160C23×C43—41no—
161C23×C43—41no—
162C23×C43—41no—
163C23×C43—41no—
164C23×C43—41no—
165C23×C43#12011yescharacteristic
166C22×D43—42no—
167C22×D43—81no—
168C22×D43—81no—
169C22×D43—81no—
170C22×D43—81no—
171C22×D43—81no—
172C22×D43—81no—
173Q8×C43—22no—
174Q8×C43—22no—
175Q8×C43—41no—
176Q8×C43—41no—
177D4×C43—22no—
178D4×C43—22no—
179D4×C43—41no—
180D4×C43—41no—
181C2×C4×C43—21no—
182C2×C4×C43—21no—
183C2×C4×C43—22no—
184C2×C4×C43—41no—
185C2×C4×C43—41no—
186C2×C4×C43—41no—
187C2×C4×C43—41no—
188C2×C4×C43—42no—
189C2×C4×C43—41no—
190C2×C4×C43—42no—
191C2×C4×C43—41no—
192C2×C4×C43—41no—
193C2×C4×C43—42no—
194C2×C4×C43—41no—
195C2×C4×C43—81no—
196C2×C4×C43—81no—
197C2×C4×C43—81no—
198C2×C4×C43—81no—
199C2×C4×C43#12011yescharacteristic
200C2×C4×C43#12011yescharacteristic
201C2×C4×C43#12111yescharacteristic
202C2×C4×C43#12111yescharacteristic
203C2×C4×C43#12111yescharacteristic
204C2×C4×C43#12711yescharacteristic
205C2×C4×C43C2×D811yescharacteristic
206C2×C4×C43C2×SD1611yescharacteristic
207C2×C4×C43#13511yescharacteristic
208C2×C4×C43#13511yescharacteristic
209C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
210C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
211C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
212C2×C4×C43#13711yescharacteristic
213D172—44no—
214D172—42no—
215D172—42no—
216D172—42no—
217D172—42no—
218D172—82no—
219D172—81no—
220D172—81no—
221D172—81no—
222D172—81no—
223C43⋊C8—42no—
224C43⋊C8—42no—
225C43⋊C8—42no—
226#10229—431nomaximal, Sylow
227C22×C43—42no—
228C22×C43—42no—
229C22×C43—42no—
230C22×C43—81no—
231C22×C43—81no—
232C22×C43—81no—
233C22×C43—81no—
234C22×C43#39211yescharacteristic
235C22×C43#44711yescharacteristic
236C22×C43#44811yescharacteristic
237C22×C43#44911yescharacteristic
238C22×C43#44911yescharacteristic
239C22×C43#45311yescharacteristic
240C22×C43#45411yescharacteristic
241C2×D43—82no—
242C2×D43—82no—
243C2×D43—82no—
244C2×D43—161no—
245C2×D43—161no—
246C2×D43—161no—
247C2×D43—161no—
248C4×C43—21no—
249C4×C43—21no—
250C4×C43—42no—
251C4×C43—82no—
252C4×C43—81no—
253C4×C43—81no—
254C4×C43#44711yescharacteristic
255C4×C43#44911yescharacteristic
256C4×C43#45011yescharacteristic
257C4×C43#45211yescharacteristic
258C4×C43#46511yescharacteristic
259C4×C43#46611yescharacteristic
260C4×C43#46811yescharacteristic
261C4×C43#46911yescharacteristic
262C2×#460—431no—
263C2×#459—431no—
264#2538D4311yescharacteristic, complemented
265#1957—431no—
266C2×Q8⋊C8—431no—
267C2×D4⋊C8—431no—
268#1296—431no—
269C2×C43—82no—
270C2×C43#162111yescharacteristic
271C2×C43#162211yescharacteristic
272C2×C43#162711yescharacteristic
273C2×C43#162811yescharacteristic
274C2×C43#199911yescharacteristic
275C2×C43#200011yescharacteristic
276C2×C43#200611yescharacteristic
277D43—162no—
278C22×SD16—861no—
279C22×D8—861no—
280C2×#127—431no—
281C2×C22⋊Q8—21no—
282C2×C4×Q8C2×D4311yescharacteristic
283C2×C4×D4C2×D4311yescharacteristic
284#460—862no—
285#460—862no—
286#459—862no—
287#459—862no—
288C2×C4⋊C8—431no—
289C2×C4⋊C8—431no—
290C2×#102—861no—
291C2×#102—861no—
292C2×#102—862no—
293C2×C4×C8—431no—
294#396—22no—
295#390—21no—
296#389—21no—
297#384C2×D4311yescharacteristic
298#380—21no—
299Q8⋊C8—862no—
300D4⋊C8—862no—
301C43#1022911yescharacteristic, complemented, Sylow
302C22×Q8C22⋊D4311yescharacteristic
303C22×D4—861no—
304C22×D4—861no—
305C22×D4—861no—
306C22×D4C22⋊D4311yescharacteristic
307C23×C4—21no—
308C2×SD16—864no—
309C2×SD16—1722no—
310C2×SD16—1722no—
311C2×D8—864no—
312C2×D8—1722no—
313C2×D8—1722no—
314C22×C8—861no—
315C22×C8—861no—
316C22×C8—861no—
317#127—432no—
318#127—861no—
319#127—861no—
320#127—861no—
321C22⋊Q8—42no—
322C22⋊Q8—42no—
323C4×Q8—21no—
324C4×Q8—21no—
325C4×Q8—21no—
326C4×Q8—21no—
327C4×D4—21no—
328C4×D4—21no—
329C4×D4—21no—
330C4×D4—21no—
331C2×C4⋊C4—22no—
332C2×C4⋊C4—21no—
333C2×C4⋊C4—21no—
334C2×C4⋊C4—21no—
335C2×C4⋊C4C22⋊D4311yescharacteristic
336C2×C4⋊C4C22⋊D4311yescharacteristic
337C2×C4⋊C4C22⋊D4312yes—
338C2×C22⋊C4—22no—
339C2×C22⋊C4—21no—
340C2×C22⋊C4—22no—
341C2×C42—21no—
342C2×C42C22×D4311yescharacteristic
343C4⋊C8—432no—
344C4⋊C8—432no—
345C4⋊C8—861no—
346C4⋊C8—861no—
347#102—864no—
348#102—864no—
349#102—1724no—
350C4×C8—861no—
351C4×C8—861no—
352#95—22no—
353C24—21no—
354C24—1721no—
355C2×Q8—21no—
356C2×Q8—21no—
357C2×Q8—21no—
358C2×Q8—21no—
359C2×Q8—21no—
360C2×Q8#1062188212yescomplemented
361C2×D4—21no—
362C2×D4—21no—
363C2×D4—21no—
364C2×D4—21no—
365C2×D4—21no—
366C2×D4—862no—
367C2×D4—862no—
368C2×D4—862no—
369C2×D4—1722no—
370C2×D4—1722no—
371C2×D4—1721no—
372C2×D4—1721no—
373C2×D4—1721no—
374C2×D4—1721no—
375C2×D4—1721no—
376C2×D4—1721no—
377C2×D4—1721no—
378C2×D4—1721no—
379C2×D4—1721no—
380C2×D4—1721no—
381C2×D4—1721no—
382C2×D4#1062188412yescomplemented
383C22×C4—21no—
384C22×C4—21no—
385C22×C4—21no—
386C22×C4—22no—
387C22×C4—41no—
388C22×C4—41no—
389C22×C4—41no—
390C22×C4—41no—
391C22×C4—41no—
392C22×C4—41no—
393C22×C4C2×C22⋊D4311yescharacteristic
394C22×C4C2×C22⋊D4311yescharacteristic
395C22×C4C2×C22⋊D4311yescharacteristic
396SD16—1728no—
397D8—1728no—
398C2×C8—862no—
399C2×C8—862no—
400C2×C8—862no—
401C2×C8—1721no—
402C2×C8—1721no—
403C2×C8—1721no—
404C2×C8—1721no—
405C2×C8—1721no—
406C2×C8—1721no—
407C4⋊C4—21no—
408C4⋊C4—21no—
409C4⋊C4—21no—
410C4⋊C4—21no—
411C4⋊C4—42no—
412C4⋊C4—44no—
413C4⋊C4—41no—
414C4⋊C4—41no—
415C4⋊C4—41no—
416C4⋊C4—41no—
417C4⋊C4—41no—
418C4⋊C4—41no—
419C22⋊C4—44no—
420C22⋊C4—41no—
421C22⋊C4—41no—
422C22⋊C4—82no—
423C42—41no—
424C42—41no—
425C42D4×D4311yescharacteristic
426C42D4×D4311yescharacteristic
427C42D4×D4311yescharacteristic
428C42#1062190011yescharacteristic
429C23—22no—
430C23—41no—
431C23—41no—
432C23—41no—
433C23—41no—
434C23—41no—
435C23—41no—
436C23—3441no—
437C23—3441no—
438C23—3441no—
439C23—3441no—
440C23—3441no—
441C23—3441no—
442C23—1722no—
443C23#1306329411yescharacteristic
444Q8—22no—
445Q8—22no—
446Q8—41no—
447Q8—41no—
448D4—22no—
449D4—22no—
450D4—41no—
451D4—41no—
452D4—3442no—
453D4—3441no—
454D4—3441no—
455D4—3441no—
456D4—3441no—
457D4—1724no—
458D4—1722no—
459D4—1722no—
460D4—1722no—
461D4—1722no—
462C2×C4—21no—
463C2×C4—21no—
464C2×C4—22no—
465C2×C4—41no—
466C2×C4—41no—
467C2×C4—42no—
468C2×C4—41no—
469C2×C4—41no—
470C2×C4—41no—
471C2×C4—41no—
472C2×C4—42no—
473C2×C4—41no—
474C2×C4—42no—
475C2×C4—41no—
476C2×C4—81no—
477C2×C4—81no—
478C2×C4—81no—
479C2×C4—81no—
480C2×C4#1306329311yescharacteristic
481C2×C4#1306329311yescharacteristic
482C2×C4#1306329611yescharacteristic
483C2×C4#1306329711yescharacteristic
484C2×C4#1306329711yescharacteristic
485C2×C4#1306332111yescharacteristic
486C2×C4C2×#1062188211yescharacteristic
487C2×C4C2×#1062188411yescharacteristic
488C2×C4#1306334511yescharacteristic
489C2×C4#1306334511yescharacteristic
490C2×C4#1306335011yescharacteristic
491C2×C4#1306335011yescharacteristic
492C2×C4#1306335111yescharacteristic
493C2×C4#1306335611yescharacteristic
494C8—1722no—
495C8—1722no—
496C8—1722no—
497C22—42no—
498C22—42no—
499C22—42no—
500C22—81no—
501C22—81no—
502C22—81no—
503C22—81no—
504C22—3442no—
505C22—3442no—
506C22—3442no—
507C22—6881no—
508C22—6881no—
509C22—6881no—
510C22—6881no—
511C22#1458280711yescharacteristic
512C22#1458303311yescharacteristic
513C22#1458303811yescharacteristic
514C22#1458304411yescharacteristic
515C22#1458304411yescharacteristic
516C22#1458306711yescharacteristic
517C22#1458307211yescharacteristic
518C4—21no—
519C4—21no—
520C4—42no—
521C4—81no—
522C4—81no—
523C4—82no—
524C4#1458303211yescharacteristic
525C4#1458304211yescharacteristic
526C4#1458304911yescharacteristic
527C4#1458305911yescharacteristic
528C4#1458313011yescharacteristic
529C4#1458313311yescharacteristic
530C4#1458314711yescharacteristic
531C4#1458315011yescharacteristic
532C2—82no—
533C2—6882no—
534C2#1913366011yescharacteristic
535C2#1913366711yescharacteristic
536C2#1913369811yescharacteristic
537C2#1913370511yescharacteristic
538C2#1913559111yescharacteristic
539C2#1913559611yescharacteristic
540C2#1913563711yescharacteristic
subgroupG/H
centerC23#13063294
commutator, cosocleC2×C42×C43C23
FrattiniC2×C42C22×D43
FittingC43×#2538C2
socleC23×C43#120
prime radicalC2×#14583094C2
hypercenter#2538D43
hypocenterC43#10229
LCSG ▷ C2×C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2538

Complements

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

NH ≅ G/Ntype
1. C2×#14583099C2semidirect
3. #19135400C2semidirect
4. C2×Q8⋊(C43⋊C8)C2semidirect
5. C2×D4⋊(C43⋊C8)C2semidirect
6. #19132478C2semidirect
7. C43×#2538C2semidirect
89. C2×Q8×C43D8semidirect
95. C2×D4×C43SD16semidirect
264. #2538D43semidirect
301. C43#10229semidirect
360. C2×Q8#10621882semidirect
382. C2×D4#10621884semidirect

Maximal subgroups

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

subgroupindex
C2×#145830992
C2×#145830942
#191354002
C2×Q8⋊(C43⋊C8)2
C2×D4⋊(C43⋊C8)2
#191324782
C43×#25382
#1022943