Finite Group Databasebeta

← #24988294

Subgroups — #24988294

Order 11008.

780 conjugacy classes of subgroups.

The subgroup lattice has 560 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583584C211yesmaximal, characteristic
2#19134681C211yesmaximal, characteristic, complemented
3#19134580C211yesmaximal, characteristic
4#19133168C211yesmaximal, characteristic, complemented
5#19133166C211yesmaximal, characteristic, complemented
6#19132911C211yesmaximal, characteristic
7C43×#1823C211yesmaximal, characteristic, complemented
8#14583584—22no—
9#14583584—22no—
10#14583584—22no—
11#14583584—22no—
12C2×#13063320—21no—
13C2×#13063316C411yescharacteristic, complemented
14C2×#13063315—21no—
15C2×#13063308—21no—
16C2×#13063305C411yescharacteristic, complemented
17C2×#13063304C2211yescharacteristic
18C2×#13063290C411yescharacteristic, complemented
19C2×C4×C22⋊D43C2211yescharacteristic
20C2×#13063284—21no—
21C2×#13063283C411yescharacteristic, complemented
22C2×#13063239—21no—
23C2×C22⋊(C43⋊C8)C2211yescharacteristic
24#14582759C2211yescharacteristic
25#14582665—21no—
26#14582661—22no—
27#14582637—22no—
28#14582635—22no—
29#14582624—21no—
30#14582622—21no—
31C22×C4⋊C4×C43C2211yescharacteristic
32C2×C22⋊C8×C43C2211yescharacteristic
33C43×#380C2211yescharacteristic
34C43×#340—22no—
35C22×Dic86C2×C411yescharacteristic
36C22×C22⋊D43D411yescharacteristic
37C22×C4×D43C2×C411yescharacteristic
38C22×C43⋊C8—21no—
39#13063320—24no—
40#13063320—24no—
41#13063316—22no—
42#13063316—22no—
43#13063315—24no—
44#13063315—24no—
45#13063308—24no—
46#13063308—24no—
47#13063305—22no—
48#13063305—22no—
49#13063304—21no—
50#13063304—21no—
51#13063304D412yes—
52#13063304D412yes—
53#13063290—22no—
54#13063290—22no—
55C4×C22⋊D43—21no—
56C4×C22⋊D43—21no—
57C4×C22⋊D43—21no—
58C4×C22⋊D43—21no—
59#13063284—24no—
60#13063284—24no—
61#13063283—22no—
62#13063283—22no—
63C2×C4⋊Dic43—21no—
64C2×C4⋊Dic43—21no—
65C2×C4⋊Dic43—21no—
66C2×C4⋊Dic43C2×C411yescharacteristic
67C2×Dic43⋊C4—21no—
68C2×Dic43⋊C4—21no—
69C2×Dic43⋊C4—21no—
70C2×Dic43⋊C4D411yescharacteristic
71C2×C22⋊Dic43—21no—
72C2×C22⋊Dic43—21no—
73C2×C22⋊Dic43D411yescharacteristic
74C2×(C2×D43)⋊C4—21no—
75C2×(C2×D43)⋊C4—21no—
76C2×(C2×D43)⋊C4D411yescharacteristic
77C2×C4×Dic43—21no—
78C2×C4×Dic43—21no—
79C2×C4×Dic43C2×C411yescharacteristic
80#13063239—42no—
81C22⋊(C43⋊C8)—21no—
82C22⋊(C43⋊C8)—21no—
83C43⋊#95—21no—
84C23×C4×C43—21no—
85C23×C4×C43C2311yescharacteristic
86C22×C8×C43—21no—
87C2×C4⋊C4×C43—21no—
88C2×C4⋊C4×C43—21no—
89C2×C4⋊C4×C43—21no—
90C2×C4⋊C4×C43—21no—
91C2×C4⋊C4×C43C2×C411yescharacteristic
92C2×C4⋊C4×C43C2×C411yescharacteristic
93C2×C4⋊C4×C43D412yes—
94C2×C4⋊C4×C43D412yes—
95C2×C22⋊C4×C43—21no—
96C22⋊C8×C43—21no—
97C22⋊C8×C43—21no—
98#95×C43—21no—
99C24×C43C2×D411yescharacteristic
100C23×D43C22⋊C411yescharacteristic
101C22×C4×C43—21no—
102C22×C4×C43—21no—
103C22×C4×C43—22no—
104C22×C4×C43—22no—
105C22×C4×C43—42no—
106C22×C4×C43—41no—
107C22×C4×C43—41no—
108C22×C4×C43—41no—
109C22×C4×C43—41no—
110C22×C4×C43—41no—
111C22×C4×C43C22×C411yescharacteristic
112C22×C4×C43C2×D411yescharacteristic
113C22×C4×C43C2×D411yescharacteristic
114C22×C4×C43C2×D411yescharacteristic
115C22×C4×C43C2×D411yescharacteristic
116C22×C4×C43C2×D411yescharacteristic
117C2×C22⋊D43—21no—
118C2×C22⋊D43—21no—
119C2×C22⋊D43—21no—
120C2×C22⋊D43—21no—
121C2×C22⋊D43—21no—
122C2×C22⋊D43—21no—
123C22×Dic43—21no—
124C22×Dic43—21no—
125C22×Dic43—41no—
126C22×Dic43C22⋊C411yescharacteristic
127C22×Dic43C22⋊C411yescharacteristic
128C22×Dic43C22⋊C411yescharacteristic
129C2×C4×D43—21no—
130C2×C4×D43—21no—
131C2×C4×D43—42no—
132C2×Dic86—21no—
133C2×Dic86—42no—
134C2×Dic86C22⋊C412yes—
135C2×C8×C43—42no—
136C2×C8×C43—41no—
137C4⋊C4×C43—21no—
138C4⋊C4×C43—21no—
139C4⋊C4×C43—22no—
140C4⋊C4×C43—22no—
141C4⋊C4×C43—42no—
142C4⋊C4×C43C22⋊C412yes—
143C4⋊C4×C43C22⋊C412yes—
144C22⋊C4×C43—41no—
145C22⋊C4×C43—41no—
146C22⋊Dic43—22no—
147C22⋊Dic43—22no—
148C22⋊Dic43—21no—
149C22⋊Dic43—21no—
150C22⋊Dic43—41no—
151C22⋊Dic43—41no—
152(C2×D43)⋊C4—24no—
153(C2×D43)⋊C4—24no—
154(C2×D43)⋊C4—21no—
155(C2×D43)⋊C4—21no—
156C4⋊Dic43—24no—
157C4⋊Dic43—24no—
158C4⋊Dic43—21no—
159C4⋊Dic43—42no—
160C4⋊Dic43C22⋊C412yes—
161Dic43⋊C4—24no—
162Dic43⋊C4—24no—
163Dic43⋊C4—22no—
164Dic43⋊C4—22no—
165Dic43⋊C4—21no—
166Dic43⋊C4—21no—
167C4×Dic43—24no—
168C4×Dic43—24no—
169C4×Dic43—21no—
170C4×Dic43—21no—
171C2×C43⋊C8—42no—
172C2×C43⋊C8—41no—
173C23×C43—41no—
174C23×C43—41no—
175C23×C43C2×C22⋊C411yescharacteristic
176C23×C43#12011yescharacteristic
177C23×C43#12011yescharacteristic
178C23×C43#13511yescharacteristic
179C23×C43#13511yescharacteristic
180C23×C43AGL(1,ℤ/8)11yescharacteristic
181C23×C43#13711yescharacteristic
182C22×D43—21no—
183C22×D43—21no—
184C22×D43—21no—
185C22×D43—41no—
186C22×D43—41no—
187C2×C4×C43—22no—
188C2×C4×C43—22no—
189C2×C4×C43—22no—
190C2×C4×C43—22no—
191C2×C4×C43—22no—
192C2×C4×C43—41no—
193C2×C4×C43—41no—
194C2×C4×C43—41no—
195C2×C4×C43—41no—
196C2×C4×C43—41no—
197C2×C4×C43—41no—
198C2×C4×C43—41no—
199C2×C4×C43—42no—
200C2×C4×C43—42no—
201C2×C4×C43—42no—
202C2×C4×C43—42no—
203C2×C4×C43—81no—
204C2×C4×C43—81no—
205C2×C4×C43—81no—
206C2×C4×C43C2×C22⋊C411yescharacteristic
207C2×C4×C43C2×C22⋊C411yescharacteristic
208C2×C4×C43#12011yescharacteristic
209C2×C4×C43#12011yescharacteristic
210C22⋊D43—41no—
211C22⋊D43—41no—
212C22⋊D43—41no—
213C22⋊D43—41no—
214C2×Dic43—21no—
215C2×Dic43—21no—
216C2×Dic43—21no—
217C2×Dic43—22no—
218C2×Dic43—22no—
219C2×Dic43—21no—
220C2×Dic43—21no—
221C2×Dic43—42no—
222C2×Dic43—42no—
223C2×Dic43—41no—
224C2×Dic43—41no—
225C2×Dic43—81no—
226C2×Dic43—81no—
227C2×Dic43—81no—
228C4×D43—42no—
229C4×D43—42no—
230Dic86—42no—
231Dic86—42no—
232C8×C43—81no—
233C43⋊C8—81no—
234#8382—431nomaximal, Sylow
235C22×C43—21no—
236C22×C43—21no—
237C22×C43—21no—
238C22×C43—21no—
239C22×C43—21no—
240C22×C43—21no—
241C22×C43—41no—
242C22×C43—41no—
243C22×C43—41no—
244C22×C43—41no—
245C22×C43#37911yescharacteristic
246C22×C43#41611yescharacteristic
247C22×C43#41711yescharacteristic
248C22×C43#44911yescharacteristic
249C22×C43#44911yescharacteristic
250C22×C43#45211yescharacteristic
251C22×C43#45211yescharacteristic
252C2×D43—41no—
253C2×D43—41no—
254C2×D43—41no—
255C2×D43—81no—
256C2×D43—81no—
257C4×C43—21no—
258C4×C43—21no—
259C4×C43—21no—
260C4×C43—42no—
261C4×C43—42no—
262C4×C43—161no—
263C4×C43#41012yes—
264Dic43—41no—
265Dic43—42no—
266Dic43—42no—
267Dic43—41no—
268Dic43—41no—
269Dic43—161no—
270C2×#552—431no—
271#1823—431no—
272#1823D4311yescharacteristic, complemented
273#1799—431no—
274#1520—431no—
275#1520—431no—
276#1459—431no—
277C2×C43—21no—
278C2×C43—21no—
279C2×C43—21no—
280C2×C43—21no—
281C2×C43—21no—
282C2×C43—21no—
283C2×C43#178211yescharacteristic
284C2×C43#178811yescharacteristic
285C2×C43#179611yescharacteristic
286D43—81no—
287#552—862no—
288#552—862no—
289#552—862no—
290#552—862no—
291C2×#126—861no—
292C2×#125—431no—
293C2×#125—861no—
294C2×#123—861no—
295C2×C22⋊Q8—431no—
296C2×C22⋊Q8—431no—
297C2×C4×Q8—431no—
298C2×C4×D4—431no—
299C2×#117—431no—
300C2×#117—861no—
301C22×C4⋊C4C2×D4311yescharacteristic
302C2×#99—861no—
303C2×C22⋊C8—431no—
304C2×C22⋊C8C2×D4311yescharacteristic
305#380—431no—
306#380C2×D4311yescharacteristic
307#342—861no—
308#340—22no—
309#340—862no—
310#328—862no—
311#328—862no—
312#324—861no—
313#323—861no—
314C43#838211yescharacteristic, complemented, Sylow
315C22×Q8—431no—
316C22×D4—431no—
317C23×C4—21no—
318C23×C4—431no—
319C23×C4C22×D4311yescharacteristic
320C22×C8—21no—
321C22×C8—861no—
322#126—864no—
323#126—864no—
324#125—862no—
325#125—864no—
326#125—864no—
327#125—862no—
328#123—864no—
329#123—864no—
330C22⋊Q8—432no—
331C22⋊Q8—432no—
332C22⋊Q8—862no—
333C22⋊Q8—861no—
334C22⋊Q8—861no—
335C22⋊Q8—862no—
336C4×Q8—862no—
337C4×Q8—862no—
338C4×D4—861no—
339C4×D4—861no—
340C4×D4—861no—
341C4×D4—861no—
342#117—862no—
343#117—864no—
344#117—864no—
345#117—862no—
346C2×C4⋊C4—21no—
347C2×C4⋊C4—21no—
348C2×C4⋊C4—21no—
349C2×C4⋊C4—21no—
350C2×C4⋊C4—431no—
351C2×C4⋊C4—431no—
352C2×C4⋊C4—861no—
353C2×C4⋊C4—861no—
354C2×C4⋊C4—861no—
355C2×C4⋊C4—861no—
356C2×C4⋊C4—861no—
357C2×C4⋊C4—861no—
358C2×C4⋊C4C4×D4311yescharacteristic
359C2×C4⋊C4C4×D4311yescharacteristic
360C2×C4⋊C4D17212yes—
361C2×C4⋊C4C22⋊D4312yes—
362C2×C22⋊C4—21no—
363C2×C22⋊C4—431no—
364C2×C22⋊C4—431no—
365C2×C22⋊C4—861no—
366C2×C22⋊C4—861no—
367C2×C22⋊C4—861no—
368C2×C22⋊C4—861no—
369C2×C42—431no—
370C2×C42—861no—
371C2×C42—861no—
372#99—1722no—
373C22⋊C8—21no—
374C22⋊C8—21no—
375C22⋊C8—861no—
376C22⋊C8—861no—
377#95—21no—
378#95—861no—
379C24—431no—
380C24D4×D4311yescharacteristic
381C2×Q8—432no—
382C2×Q8—861no—
383C2×Q8—1722no—
384C2×D4—861no—
385C2×D4—861no—
386C2×D4—861no—
387C2×D4—861no—
388C2×D4—861no—
389C2×D4—861no—
390C22×C4—21no—
391C22×C4—21no—
392C22×C4—22no—
393C22×C4—22no—
394C22×C4—42no—
395C22×C4—41no—
396C22×C4—41no—
397C22×C4—41no—
398C22×C4—41no—
399C22×C4—41no—
400C22×C4—431no—
401C22×C4—431no—
402C22×C4—431no—
403C22×C4—861no—
404C22×C4—861no—
405C22×C4—861no—
406C22×C4—861no—
407C22×C4—1722no—
408C22×C4—1721no—
409C22×C4C2×C4×D4311yescharacteristic
410C22×C4C2×D17211yescharacteristic
411C22×C4D4×D4311yescharacteristic
412C22×C4D4×D4311yescharacteristic
413C22×C4D4×D4311yescharacteristic
414C22×C4C2×C22⋊D4311yescharacteristic
415C2×C8—42no—
416C2×C8—41no—
417C2×C8—1722no—
418C2×C8—1721no—
419C4⋊C4—21no—
420C4⋊C4—21no—
421C4⋊C4—22no—
422C4⋊C4—22no—
423C4⋊C4—42no—
424C4⋊C4—432no—
425C4⋊C4—864no—
426C4⋊C4—864no—
427C4⋊C4—864no—
428C4⋊C4—864no—
429C4⋊C4—861no—
430C4⋊C4—861no—
431C4⋊C4—862no—
432C4⋊C4—861no—
433C4⋊C4—862no—
434C4⋊C4—1722no—
435C4⋊C4(C2×D43)⋊C412yes—
436C4⋊C4(C2×D43)⋊C412yes—
437C22⋊C4—41no—
438C22⋊C4—41no—
439C22⋊C4—864no—
440C22⋊C4—864no—
441C22⋊C4—861no—
442C22⋊C4—862no—
443C22⋊C4—861no—
444C22⋊C4—862no—
445C22⋊C4—861no—
446C22⋊C4—861no—
447C22⋊C4—1721no—
448C22⋊C4—1721no—
449C42—864no—
450C42—864no—
451C42—861no—
452C42—861no—
453C23—41no—
454C23—41no—
455C23—861no—
456C23—861no—
457C23—861no—
458C23—1721no—
459C23—1721no—
460C23C22⋊C4×D4311yescharacteristic
461C23#1306329311yescharacteristic
462C23#1306329511yescharacteristic
463C23#1306334411yescharacteristic
464C23#1306334611yescharacteristic
465C23#1306334911yescharacteristic
466C23#1306335411yescharacteristic
467Q8—1722no—
468Q8—1722no—
469D4—1721no—
470D4—1721no—
471D4—1721no—
472D4—1721no—
473C2×C4—22no—
474C2×C4—22no—
475C2×C4—22no—
476C2×C4—22no—
477C2×C4—22no—
478C2×C4—41no—
479C2×C4—41no—
480C2×C4—41no—
481C2×C4—42no—
482C2×C4—42no—
483C2×C4—42no—
484C2×C4—42no—
485C2×C4—41no—
486C2×C4—41no—
487C2×C4—41no—
488C2×C4—41no—
489C2×C4—81no—
490C2×C4—81no—
491C2×C4—81no—
492C2×C4—861no—
493C2×C4—861no—
494C2×C4—861no—
495C2×C4—861no—
496C2×C4—862no—
497C2×C4—862no—
498C2×C4—861no—
499C2×C4—3441no—
500C2×C4—3441no—
501C2×C4—3441no—
502C2×C4—1722no—
503C2×C4—1722no—
504C2×C4—1722no—
505C2×C4—1722no—
506C2×C4—1721no—
507C2×C4—1721no—
508C2×C4C22⋊C4×D4311yescharacteristic
509C2×C4C2×(C2×D43)⋊C411yescharacteristic
510C2×C4#1306329311yescharacteristic
511C2×C4#1306329511yescharacteristic
512C8—81no—
513C8—3441no—
514C22—21no—
515C22—21no—
516C22—21no—
517C22—21no—
518C22—21no—
519C22—21no—
520C22—41no—
521C22—41no—
522C22—41no—
523C22—41no—
524C22—3441no—
525C22—3441no—
526C22—1721no—
527C22—1721no—
528C22—1721no—
529C22#1458275411yescharacteristic
530C22#1458289211yescharacteristic
531C22#1458289711yescharacteristic
532C22#1458304111yescharacteristic
533C22#1458304511yescharacteristic
534C22#1458305811yescharacteristic
535C22#1458306211yescharacteristic
536C4—21no—
537C4—21no—
538C4—21no—
539C4—42no—
540C4—42no—
541C4—161no—
542C4—1721no—
543C4—1722no—
544C4—1721no—
545C4—1722no—
546C4—1721no—
547C4—6881no—
548C4#1458287212yes—
549C2—21no—
550C2—21no—
551C2—21no—
552C2—21no—
553C2—21no—
554C2—21no—
555C2—3441no—
556C2#1913451211yescharacteristic
557C2#1913453211yescharacteristic
558C2#1913456711yescharacteristic
subgroupG/H
centerC22#14582754
commutatorC22×C4×C43C22×C4
FrattiniC23×C4C22×D43
FittingC43×#1823C2
socleC22×C43#379
prime radicalC22×C22⋊D43D4
cosocleC23×C4×C43C23
hypercenter#1823D43
hypocenterC43#8382
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1823

Complements

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

NH ≅ G/Ntype
2. #19134681C2semidirect
4. #19133168C2semidirect
5. #19133166C2semidirect
7. C43×#1823C2semidirect
13. C2×#13063316C4semidirect
16. C2×#13063305C4semidirect
18. C2×#13063290C4semidirect
21. C2×#13063283C4semidirect
272. #1823D43semidirect
314. C43#8382semidirect

Maximal subgroups

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

subgroupindex
C2×#145835842
#191346812
#191345802
#191331682
#191331662
#191329112
C43×#18232
#838243