Finite Group Databasebeta

← #24988284

Subgroups — #24988284

Order 11008.

818 conjugacy classes of subgroups.

The subgroup lattice has 554 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583604C211yesmaximal, characteristic
2#19134685C211yesmaximal, characteristic, complemented
3#19134580C211yesmaximal, characteristic
4#19133168C211yesmaximal, characteristic, complemented
5#19133166C211yesmaximal, characteristic, complemented
6#19132911C211yesmaximal, characteristic
7C43×#1824C211yesmaximal, characteristic, complemented
8#14583604—22no—
9#14583604—22no—
10#14583604—22no—
11#14583604—22no—
12C2×#13063324C411yescharacteristic, complemented
13C2×#13063315—21no—
14C2×#13063305C411yescharacteristic, complemented
15C2×#13063304—21no—
16C2×#13063304C2211yescharacteristic
17C2×#13063303—21no—
18C2×#13063290C411yescharacteristic, complemented
19C2×C4×C22⋊D43—21no—
20C2×C4×C22⋊D43C2211yescharacteristic
21C2×C4⋊C4×D43C411yescharacteristic, 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×Dic86—21no—
36C22×Dic86C2×C411yescharacteristic
37C22×C22⋊D43D411yescharacteristic
38C22×C4×D43—21no—
39C22×C4×D43C2×C411yescharacteristic
40C22×C43⋊C8—21no—
41#13063324—22no—
42#13063324—22no—
43#13063315—24no—
44#13063315—24no—
45#13063305—22no—
46#13063305—22no—
47#13063304—24no—
48#13063304—24no—
49#13063304—21no—
50#13063304—21no—
51#13063304D412yes—
52#13063304D412yes—
53#13063303—24no—
54#13063303—24no—
55#13063290—22no—
56#13063290—22no—
57C4×C22⋊D43—24no—
58C4×C22⋊D43—24no—
59C4×C22⋊D43—21no—
60C4×C22⋊D43—21no—
61C4×C22⋊D43—21no—
62C4×C22⋊D43—21no—
63C2×C4⋊Dic43—21no—
64C2×C4⋊Dic43—21no—
65C2×C4⋊Dic43C2×C411yescharacteristic
66C2×Dic43⋊C4—21no—
67C2×Dic43⋊C4—21no—
68C2×Dic43⋊C4—21no—
69C2×Dic43⋊C4—21no—
70C2×Dic43⋊C4D411yescharacteristic
71C4⋊C4×D43—22no—
72C4⋊C4×D43—22no—
73C2×C22⋊Dic43—21no—
74C2×C22⋊Dic43—21no—
75C2×C22⋊Dic43D411yescharacteristic
76C2×(C2×D43)⋊C4—21no—
77C2×(C2×D43)⋊C4D411yescharacteristic
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—82no—
108C22×C4×C43C22×C411yescharacteristic
109C22×C4×C43C2×D411yescharacteristic
110C22×C4×C43C2×D411yescharacteristic
111C22×C4×C43C2×D411yescharacteristic
112C22×C4×C43C2×D411yescharacteristic
113C22×C4×C43C2×D411yescharacteristic
114C2×C22⋊D43—21no—
115C2×C22⋊D43—21no—
116C2×C22⋊D43—21no—
117C2×C22⋊D43—21no—
118C2×C22⋊D43SD1612yes—
119C2×C22⋊D43Q1612yes—
120C22×Dic43—21no—
121C22×Dic43—21no—
122C22×Dic43—41no—
123C22×Dic43C22⋊C411yescharacteristic
124C22×Dic43C22⋊C411yescharacteristic
125C22×Dic43C22⋊C411yescharacteristic
126C2×C4×D43—21no—
127C2×C4×D43—21no—
128C2×C4×D43—24no—
129C2×C4×D43—42no—
130C2×C4×D43—82no—
131C2×Dic86—21no—
132C2×Dic86—24no—
133C2×Dic86—42no—
134C2×Dic86—82no—
135C2×Dic86C22⋊C412yes—
136C2×C8×C43—42no—
137C2×C8×C43—41no—
138C4⋊C4×C43—21no—
139C4⋊C4×C43—21no—
140C4⋊C4×C43—22no—
141C4⋊C4×C43—22no—
142C4⋊C4×C43—42no—
143C4⋊C4×C43C22⋊C412yes—
144C4⋊C4×C43C22⋊C412yes—
145C22⋊C4×C43—41no—
146C22⋊C4×C43—41no—
147C22⋊Dic43—22no—
148C22⋊Dic43—22no—
149C22⋊Dic43—21no—
150C22⋊Dic43—21no—
151C22⋊Dic43—41no—
152C22⋊Dic43—41no—
153(C2×D43)⋊C4—24no—
154(C2×D43)⋊C4—21no—
155(C2×D43)⋊C4—21no—
156C4⋊Dic43—24no—
157C4⋊Dic43—21no—
158C4⋊Dic43—42no—
159C4⋊Dic43C22⋊C412yes—
160Dic43⋊C4—24no—
161Dic43⋊C4—24no—
162Dic43⋊C4—24no—
163Dic43⋊C4—22no—
164Dic43⋊C4—22no—
165Dic43⋊C4—21no—
166Dic43⋊C4—21no—
167C4×Dic43—24no—
168C4×Dic43—21no—
169C4×Dic43—21no—
170C2×C43⋊C8—42no—
171C2×C43⋊C8—41no—
172C23×C43—41no—
173C23×C43—41no—
174C23×C43C2×C22⋊C411yescharacteristic
175C23×C43#12011yescharacteristic
176C23×C43#12011yescharacteristic
177C23×C43C2×SD1611yescharacteristic
178C23×C43C2×Q1611yescharacteristic
179C23×C43#13711yescharacteristic
180C23×C43#13711yescharacteristic
181C22×D43—21no—
182C22×D43—21no—
183C22×D43—41no—
184C22×D43—41no—
185C22×D43#10312yes—
186C2×C4×C43—22no—
187C2×C4×C43—22no—
188C2×C4×C43—22no—
189C2×C4×C43—22no—
190C2×C4×C43—22no—
191C2×C4×C43—41no—
192C2×C4×C43—41no—
193C2×C4×C43—41no—
194C2×C4×C43—42no—
195C2×C4×C43—42no—
196C2×C4×C43—82no—
197C2×C4×C43—82no—
198C2×C4×C43—81no—
199C2×C4×C43—81no—
200C2×C4×C43—81no—
201C2×C4×C43C2×C22⋊C411yescharacteristic
202C2×C4×C43C2×C22⋊C411yescharacteristic
203C2×C4×C43#12011yescharacteristic
204C2×C4×C43#12011yescharacteristic
205C22⋊D43—22no—
206C22⋊D43—22no—
207C22⋊D43—22no—
208C22⋊D43—22no—
209C2×Dic43—21no—
210C2×Dic43—21no—
211C2×Dic43—22no—
212C2×Dic43—21no—
213C2×Dic43—21no—
214C2×Dic43—22no—
215C2×Dic43—42no—
216C2×Dic43—42no—
217C2×Dic43—41no—
218C2×Dic43—41no—
219C2×Dic43—81no—
220C2×Dic43—81no—
221C2×Dic43—81no—
222C2×Dic43#10312yes—
223C4×D43—42no—
224C4×D43—42no—
225C4×D43—84no—
226Dic86—42no—
227Dic86—42no—
228Dic86—84no—
229C8×C43—81no—
230C43⋊C8—81no—
231#8380—431nomaximal, Sylow
232C22×C43—21no—
233C22×C43—21no—
234C22×C43—21no—
235C22×C43—21no—
236C22×C43—21no—
237C22×C43—21no—
238C22×C43—41no—
239C22×C43—41no—
240C22×C43—41no—
241C22×C43—41no—
242C22×C43#37911yescharacteristic
243C22×C43C2×#10311yescharacteristic
244C22×C43#41911yescharacteristic
245C22×C43#44811yescharacteristic
246C22×C43#44811yescharacteristic
247C22×C43#45111yescharacteristic
248C22×C43#45111yescharacteristic
249C2×D43—22no—
250C2×D43—42no—
251C2×D43—41no—
252C2×D43—41no—
253C2×D43—42no—
254C4×C43—21no—
255C4×C43—21no—
256C4×C43—21no—
257C4×C43—42no—
258C4×C43—42no—
259C4×C43—161no—
260C4×C43#41012yes—
261Dic43—22no—
262Dic43—41no—
263Dic43—42no—
264Dic43—42no—
265Dic43—41no—
266Dic43—161no—
267C2×#554—431no—
268#1824—431no—
269#1824D4311yescharacteristic, complemented
270#1799—431no—
271#1520—431no—
272#1520—431no—
273#1459—431no—
274C2×C43—21no—
275C2×C43—21no—
276C2×C43—21no—
277C2×C43—21no—
278C2×C43—21no—
279C2×C43—21no—
280C2×C43#178211yescharacteristic
281C2×C43#178711yescharacteristic
282C2×C43#179511yescharacteristic
283D43—42no—
284#554—862no—
285#554—862no—
286#554—862no—
287#554—862no—
288C2×C4⋊Q8—431no—
289C2×#125—861no—
290C2×C22⋊Q8—431no—
291C2×C22⋊Q8—431no—
292C2×C22⋊Q8—861no—
293C2×C22⋊Q8—861no—
294C2×C4×Q8—431no—
295C2×C4×D4—431no—
296C2×C4×D4—861no—
297C22×C4⋊C4—431no—
298C22×C4⋊C4C2×D4311yescharacteristic
299C2×#99—861no—
300C2×C22⋊C8—431no—
301C2×C22⋊C8C2×D4311yescharacteristic
302#380—431no—
303#380C2×D4311yescharacteristic
304#342—861no—
305#340—22no—
306#340—862no—
307#328—862no—
308#328—862no—
309#324—861no—
310#323—861no—
311C43#838011yescharacteristic, complemented, Sylow
312C22×Q8—431no—
313C22×Q8—861no—
314C22×D4—431no—
315C23×C4—21no—
316C23×C4—431no—
317C23×C4—861no—
318C23×C4C22×D4311yescharacteristic
319C22×C8—21no—
320C22×C8—861no—
321C4⋊Q8—862no—
322C4⋊Q8—862no—
323#125—864no—
324#125—864no—
325C22⋊Q8—432no—
326C22⋊Q8—432no—
327C22⋊Q8—862no—
328C22⋊Q8—864no—
329C22⋊Q8—864no—
330C22⋊Q8—864no—
331C22⋊Q8—864no—
332C22⋊Q8—861no—
333C22⋊Q8—861no—
334C22⋊Q8—862no—
335C4×Q8—862no—
336C4×Q8—862no—
337C4×D4—864no—
338C4×D4—864no—
339C4×D4—861no—
340C4×D4—861no—
341C4×D4—861no—
342C4×D4—861no—
343C2×C4⋊C4—21no—
344C2×C4⋊C4—21no—
345C2×C4⋊C4—21no—
346C2×C4⋊C4—21no—
347C2×C4⋊C4—431no—
348C2×C4⋊C4—431no—
349C2×C4⋊C4—862no—
350C2×C4⋊C4—861no—
351C2×C4⋊C4—861no—
352C2×C4⋊C4—861no—
353C2×C4⋊C4—861no—
354C2×C4⋊C4—861no—
355C2×C4⋊C4—862no—
356C2×C4⋊C4—861no—
357C2×C4⋊C4C4×D4311yescharacteristic
358C2×C4⋊C4C4×D4311yescharacteristic
359C2×C4⋊C4D17212yes—
360C2×C4⋊C4C22⋊D4312yes—
361C2×C22⋊C4—21no—
362C2×C22⋊C4—431no—
363C2×C22⋊C4—431no—
364C2×C22⋊C4—861no—
365C2×C22⋊C4—861no—
366C2×C22⋊C4—861no—
367C2×C42—431no—
368C2×C42—861no—
369#99—1722no—
370C22⋊C8—21no—
371C22⋊C8—21no—
372C22⋊C8—861no—
373C22⋊C8—861no—
374#95—21no—
375#95—861no—
376C24—431no—
377C24D4×D4311yescharacteristic
378C2×Q8—432no—
379C2×Q8—864no—
380C2×Q8—861no—
381C2×Q8—3442no—
382C2×Q8—1722no—
383C2×D4—432no—
384C2×D4—432no—
385C2×D4—861no—
386C2×D4—861no—
387C2×D4—861no—
388C2×D4—861no—
389C22×C4—21no—
390C22×C4—21no—
391C22×C4—22no—
392C22×C4—22no—
393C22×C4—42no—
394C22×C4—41no—
395C22×C4—82no—
396C22×C4—431no—
397C22×C4—431no—
398C22×C4—431no—
399C22×C4—864no—
400C22×C4—861no—
401C22×C4—861no—
402C22×C4—861no—
403C22×C4—861no—
404C22×C4—3442no—
405C22×C4—1722no—
406C22×C4—1721no—
407C22×C4C2×C4×D4311yescharacteristic
408C22×C4C2×D17211yescharacteristic
409C22×C4D4×D4311yescharacteristic
410C22×C4D4×D4311yescharacteristic
411C22×C4D4×D4311yescharacteristic
412C22×C4C2×C22⋊D4311yescharacteristic
413C2×C8—42no—
414C2×C8—41no—
415C2×C8—1722no—
416C2×C8—1721no—
417C4⋊C4—21no—
418C4⋊C4—21no—
419C4⋊C4—22no—
420C4⋊C4—22no—
421C4⋊C4—42no—
422C4⋊C4—432no—
423C4⋊C4—864no—
424C4⋊C4—864no—
425C4⋊C4—864no—
426C4⋊C4—864no—
427C4⋊C4—861no—
428C4⋊C4—861no—
429C4⋊C4—862no—
430C4⋊C4—861no—
431C4⋊C4—862no—
432C4⋊C4—1722no—
433C4⋊C4(C2×D43)⋊C412yes—
434C4⋊C4(C2×D43)⋊C412yes—
435C22⋊C4—41no—
436C22⋊C4—41no—
437C22⋊C4—864no—
438C22⋊C4—861no—
439C22⋊C4—862no—
440C22⋊C4—861no—
441C22⋊C4—862no—
442C22⋊C4—861no—
443C22⋊C4—861no—
444C22⋊C4—1721no—
445C22⋊C4—1721no—
446C42—864no—
447C42—861no—
448C42—861no—
449C23—41no—
450C23—41no—
451C23—432no—
452C23—861no—
453C23—861no—
454C23—1721no—
455C23—1721no—
456C23C22⋊C4×D4311yescharacteristic
457C23#1306329311yescharacteristic
458C23#1306329511yescharacteristic
459C23SD16×D4311yescharacteristic
460C23Q16×D4311yescharacteristic
461C23#1306335411yescharacteristic
462C23#1306335711yescharacteristic
463Q8—3444no—
464Q8—1722no—
465Q8—1722no—
466D4—862no—
467D4—862no—
468D4—862no—
469D4—862no—
470C2×C4—22no—
471C2×C4—22no—
472C2×C4—22no—
473C2×C4—22no—
474C2×C4—22no—
475C2×C4—41no—
476C2×C4—41no—
477C2×C4—41no—
478C2×C4—42no—
479C2×C4—42no—
480C2×C4—82no—
481C2×C4—82no—
482C2×C4—81no—
483C2×C4—81no—
484C2×C4—81no—
485C2×C4—432no—
486C2×C4—861no—
487C2×C4—861no—
488C2×C4—862no—
489C2×C4—861no—
490C2×C4—862no—
491C2×C4—861no—
492C2×C4—3444no—
493C2×C4—3441no—
494C2×C4—3441no—
495C2×C4—3441no—
496C2×C4—1722no—
497C2×C4—1722no—
498C2×C4—1722no—
499C2×C4—1722no—
500C2×C4—1721no—
501C2×C4—1721no—
502C2×C4C22⋊C4×D4311yescharacteristic
503C2×C4C2×(C2×D43)⋊C411yescharacteristic
504C2×C4#1306329311yescharacteristic
505C2×C4#1306329511yescharacteristic
506C8—81no—
507C8—3441no—
508C22—21no—
509C22—21no—
510C22—21no—
511C22—21no—
512C22—21no—
513C22—21no—
514C22—41no—
515C22—41no—
516C22—41no—
517C22—41no—
518C22—862no—
519C22—1722no—
520C22—1722no—
521C22—1721no—
522C22—1721no—
523C22#1458275411yescharacteristic
524C22#103×D4311yescharacteristic
525C22#1458290611yescharacteristic
526C22#1458303611yescharacteristic
527C22#1458303911yescharacteristic
528C22#1458305311yescharacteristic
529C22#1458305611yescharacteristic
530C4—21no—
531C4—21no—
532C4—21no—
533C4—42no—
534C4—42no—
535C4—161no—
536C4—862no—
537C4—1721no—
538C4—1722no—
539C4—1722no—
540C4—1721no—
541C4—6881no—
542C4#1458287212yes—
543C2—21no—
544C2—21no—
545C2—21no—
546C2—21no—
547C2—21no—
548C2—21no—
549C2—1722no—
550C2#1913451211yescharacteristic
551C2#1913452811yescharacteristic
552C2#1913456211yescharacteristic
subgroupG/H
centerC22#14582754
commutatorC22×C4×C43C22×C4
FrattiniC23×C4C22×D43
FittingC43×#1824C2
socleC22×C43#379
prime radicalC22×C22⋊D43D4
cosocleC23×C4×C43C23
hypercenter#1824D43
hypocenterC43#8380
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1824

Complements

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

NH ≅ G/Ntype
2. #19134685C2semidirect
4. #19133168C2semidirect
5. #19133166C2semidirect
7. C43×#1824C2semidirect
12. C2×#13063324C4semidirect
14. C2×#13063305C4semidirect
18. C2×#13063290C4semidirect
21. C2×C4⋊C4×D43C4semidirect
269. #1824D43semidirect
311. C43#8380semidirect

Maximal subgroups

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

subgroupindex
C2×#145836042
#191346852
#191345802
#191331682
#191331662
#191329112
C43×#18242
#838043