Finite Group Databasebeta

← #24988640

Subgroups — #24988640

Order 11008.

760 conjugacy classes of subgroups.

The subgroup lattice has 584 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19134615C211yesmaximal, characteristic
2C4×#13063249C211yesmaximal, characteristic, complemented
3#19133094C211yesmaximal, characteristic, complemented
4#19133050C211yesmaximal, characteristic, complemented
5#19133024C211yesmaximal, characteristic, complemented
6#19132977C211yesmaximal, characteristic
7Q8×#41×C43C211yesmaximal, characteristic
8#14582952C2211yescharacteristic
9#14582923C2211yescharacteristic
10C2×#13063252—21no—
11C2×#13063249—21no—
12C2×C4×C43⋊C8C2211yescharacteristic
13C4×C4⋊Dic43C2211yescharacteristic
14#14582661—21no—
15#14582658—21no—
16#14582636—22no—
17Q8⋊(C43⋊C8)—21no—
18Q8⋊(C43⋊C8)—21no—
19Q8⋊(C43⋊C8)—21no—
20Q8⋊(C43⋊C8)—22no—
21D4⋊(C43⋊C8)—21no—
22Q82×C43C411yescharacteristic, complemented
23C43×#557—21no—
24C43×#557C411yescharacteristic, complemented
25C43×#554—22no—
26C43×#554—21no—
27C43×#554—21no—
28C43×#554C411yescharacteristic, complemented
29D4×Q8×C43—21no—
30D4×Q8×C43C411yescharacteristic, complemented
31C43×#533—22no—
32C43×#533—21no—
33C43×#533—21no—
34C43×#533C2211yescharacteristic
35C4×#41×C43—21no—
36C4×#41×C43C2211yescharacteristic
37C2×C4×Q8×C43—21no—
38C2×C4×Q8×C43C2211yescharacteristic
39C2×#10621877—21no—
40C22×C43⋊C8—21no—
41C2×C4⋊Dic43—21no—
42C2×C4×Dic43—21no—
43C4⋊(C43⋊C8)—21no—
44C4⋊(C43⋊C8)—21no—
45C4⋊(C43⋊C8)—21no—
46#13063252—42no—
47#13063249—24no—
48C22⋊(C43⋊C8)—21no—
49C4×C43⋊C8—21no—
50C4×C43⋊C8—21no—
51C4×C43⋊C8—21no—
52C43⋊#95—21no—
53C2×#41×C43D411yescharacteristic
54C22×Q8×C43—21no—
55C22×Q8×C43D411yescharacteristic
56C4⋊Q8×C43—22no—
57C4⋊Q8×C43—21no—
58C4⋊Q8×C43—22no—
59C4⋊Q8×C43—21no—
60C4⋊Q8×C43—21no—
61C4⋊Q8×C43—21no—
62C4⋊Q8×C43C2×C411yescharacteristic
63C4⋊Q8×C43C2×C411yescharacteristic
64#125×C43—22no—
65#125×C43—22no—
66#125×C43—22no—
67#125×C43—21no—
68#125×C43—21no—
69#125×C43—21no—
70C22⋊Q8×C43—22no—
71C22⋊Q8×C43—22no—
72C22⋊Q8×C43—22no—
73C22⋊Q8×C43—22no—
74C22⋊Q8×C43—22no—
75C22⋊Q8×C43—21no—
76C22⋊Q8×C43—22no—
77C22⋊Q8×C43—21no—
78C22⋊Q8×C43—21no—
79C22⋊Q8×C43—22no—
80C22⋊Q8×C43D412yes—
81C4×Q8×C43—22no—
82C4×Q8×C43—22no—
83C4×Q8×C43—22no—
84C4×Q8×C43—21no—
85C4×Q8×C43—21no—
86C4×Q8×C43—21no—
87C4×Q8×C43—21no—
88C4×Q8×C43—21no—
89C4×Q8×C43—21no—
90C4×Q8×C43—21no—
91C4×Q8×C43C2×C411yescharacteristic
92C4×Q8×C43C2×C411yescharacteristic
93C4×Q8×C43C2×C411yescharacteristic
94C4×Q8×C43D411yescharacteristic
95C4×Q8×C43D411yescharacteristic
96C4×Q8×C43D411yescharacteristic
97C4×Q8×C43D412yes—
98C4×D4×C43—22no—
99C4×D4×C43—22no—
100C4×D4×C43—21no—
101C4×D4×C43—21no—
102C4×D4×C43—21no—
103C4×D4×C43—21no—
104C4×D4×C43C2×C411yescharacteristic
105C4×D4×C43D411yescharacteristic
106#117×C43—22no—
107#117×C43—21no—
108#117×C43—21no—
109#117×C43D411yescharacteristic
110C2×C4⋊C4×C43—22no—
111C2×C4⋊C4×C43—21no—
112C2×C4⋊C4×C43—21no—
113C2×C4⋊C4×C43D411yescharacteristic
114C2×C42×C43—22no—
115C2×C42×C43—21no—
116C2×C42×C43—21no—
117C2×C42×C43C2311yescharacteristic
118#41×C43—21no—
119#41×C43—21no—
120#41×C43SD1612yes—
121#41×C43Q1612yes—
122C2×Q8×C43—22no—
123C2×Q8×C43—22no—
124C2×Q8×C43—21no—
125C2×Q8×C43—21no—
126C2×Q8×C43—22no—
127C2×Q8×C43—41no—
128C2×Q8×C43—42no—
129C2×Q8×C43—42no—
130C2×Q8×C43C22⋊C411yescharacteristic
131C2×Q8×C43C22⋊C411yescharacteristic
132C2×Q8×C43C22⋊C411yescharacteristic
133C2×Q8×C43C22⋊C412yes—
134C2×D4×C43—21no—
135C2×D4×C43C22⋊C411yescharacteristic
136C22×C4×C43—21no—
137C22×C4×C43—22no—
138C22×C4×C43—22no—
139C22×C4×C43—21no—
140C22×C4×C43—21no—
141C22×C4×C43—21no—
142C22×C4×C43—21no—
143C22×C4×C43C2×D411yescharacteristic
144C22×C4×C43C2×D411yescharacteristic
145C22×C4×C43C2×D411yescharacteristic
146C22×Dic43—41no—
147C4⋊C4×C43—22no—
148C4⋊C4×C43—22no—
149C4⋊C4×C43—22no—
150C4⋊C4×C43—22no—
151C4⋊C4×C43—22no—
152C4⋊C4×C43—22no—
153C4⋊C4×C43—22no—
154C4⋊C4×C43—22no—
155C4⋊C4×C43—21no—
156C4⋊C4×C43—21no—
157C4⋊C4×C43—21no—
158C4⋊C4×C43—21no—
159C4⋊C4×C43—21no—
160C4⋊C4×C43—21no—
161C4⋊C4×C43—21no—
162C4⋊C4×C43—22no—
163C4⋊C4×C43—21no—
164C4⋊C4×C43—21no—
165C4⋊C4×C43—21no—
166C4⋊C4×C43—22no—
167C4⋊C4×C43C22⋊C411yescharacteristic
168C4⋊C4×C43C22⋊C411yescharacteristic
169C4⋊C4×C43C22⋊C411yescharacteristic
170C4⋊C4×C43C22⋊C411yescharacteristic
171C4⋊C4×C43C22⋊C412yes—
172C22⋊C4×C43—22no—
173C22⋊C4×C43—22no—
174C22⋊C4×C43—21no—
175C22⋊C4×C43—21no—
176C22⋊C4×C43—22no—
177C22⋊C4×C43—21no—
178C42×C43—22no—
179C42×C43—22no—
180C42×C43—21no—
181C42×C43—21no—
182C42×C43—21no—
183C42×C43—21no—
184C42×C43—22no—
185C42×C43—21no—
186C42×C43—21no—
187C42×C43—21no—
188C42×C43C22×C411yescharacteristic
189C42×C43C2×D411yescharacteristic
190C42×C43C2×D411yescharacteristic
191C42×C43C2×D411yescharacteristic
192C4⋊Dic43—22no—
193C4⋊Dic43—41no—
194C4×Dic43—41no—
195C4×Dic43—41no—
196#10621877—41no—
197#10621877—41no—
198C2×C43⋊C8—22no—
199C2×C43⋊C8—41no—
200C2×C43⋊C8—41no—
201C2×C43⋊C8—41no—
202C2×C43⋊C8—41no—
203C23×C43—21no—
204C23×C43#12011yescharacteristic
205Q8×C43—21no—
206Q8×C43—21no—
207Q8×C43—21no—
208Q8×C43—21no—
209Q8×C43—42no—
210Q8×C43—42no—
211Q8×C43—44no—
212Q8×C43—41no—
213Q8×C43—41no—
214Q8×C43—82no—
215Q8×C43#10312yescomplemented
216Q8×C43#10412yescomplemented
217D4×C43—22no—
218D4×C43—22no—
219D4×C43—21no—
220D4×C43#10312yescomplemented
221C2×C4×C43—21no—
222C2×C4×C43—21no—
223C2×C4×C43—21no—
224C2×C4×C43—21no—
225C2×C4×C43—22no—
226C2×C4×C43—22no—
227C2×C4×C43—21no—
228C2×C4×C43—22no—
229C2×C4×C43—21no—
230C2×C4×C43—21no—
231C2×C4×C43—21no—
232C2×C4×C43—22no—
233C2×C4×C43—21no—
234C2×C4×C43—41no—
235C2×C4×C43—42no—
236C2×C4×C43—44no—
237C2×C4×C43—41no—
238C2×C4×C43—41no—
239C2×C4×C43—81no—
240C2×C4×C43—81no—
241C2×C4×C43—82no—
242C2×C4×C43C2×C22⋊C411yescharacteristic
243C2×C4×C43C2×C22⋊C411yescharacteristic
244C2×C4×C43C2×C22⋊C411yescharacteristic
245C2×C4×C43#12011yescharacteristic
246C2×C4×C43#12011yescharacteristic
247C2×C4×C43#12011yescharacteristic
248C2×C4×C43C2×SD1611yescharacteristic
249C2×C4×C43C2×Q1611yescharacteristic
250C2×C4×C43#13711yescharacteristic
251C2×C4×C43#13711yescharacteristic
252C2×Dic43—42no—
253C2×Dic43—81no—
254C2×Dic43—81no—
255C43⋊C8—42no—
256C43⋊C8—81no—
257C43⋊C8—81no—
258#8439—431nomaximal, Sylow
259C22×C43—21no—
260C22×C43—21no—
261C22×C43—22no—
262C22×C43—41no—
263C22×C43—41no—
264C22×C43#37911yescharacteristic
265C22×C43#44811yescharacteristic
266C22×C43#45111yescharacteristic
267C4×C43—21no—
268C4×C43—21no—
269C4×C43—22no—
270C4×C43—21no—
271C4×C43—22no—
272C4×C43—41no—
273C4×C43—42no—
274C4×C43—41no—
275C4×C43—41no—
276C4×C43—41no—
277C4×C43—42no—
278C4×C43—41no—
279C4×C43C2×#10311yescharacteristic
280C4×C43#41911yescharacteristic
281C4×C43C2×#10411yescharacteristic
282C4×C43#42111yescharacteristic
283C4×C43#44811yescharacteristic
284C4×C43#45111yescharacteristic
285Dic43—82no—
286Q8×#41D4311yescharacteristic
287#1806—431no—
288C4×#103—431no—
289#1503—431no—
290#1493—431no—
291#1487—431no—
292#1476—431no—
293C2×C43—21no—
294C2×C43—21no—
295C2×C43—42no—
296C2×C43#178711yescharacteristic
297C2×C43#178911yescharacteristic
298C2×C43#179411yescharacteristic
299Q82Dic4311yescharacteristic, complemented
300#557—21no—
301#557Dic4311yescharacteristic, complemented
302#554—22no—
303#554—21no—
304#554—21no—
305#554Dic4311yescharacteristic, complemented
306D4×Q8—21no—
307D4×Q8Dic4311yescharacteristic, complemented
308#533—22no—
309#533—21no—
310#533—21no—
311#533C2×D4311yescharacteristic
312C4×#41—21no—
313C4×#41C2×D4311yescharacteristic
314C2×C4×Q8—21no—
315C2×C4×Q8C2×D4311yescharacteristic
316#431—431no—
317#423—431no—
318C2×#104—861no—
319C2×#103—861no—
320C2×C4×C8—431no—
321C4×C4⋊C4—431no—
322#340—861no—
323#339—861no—
324#328—862no—
325Q8⋊C8—861no—
326Q8⋊C8—861no—
327Q8⋊C8—861no—
328Q8⋊C8—862no—
329D4⋊C8—861no—
330C43#843911yescharacteristic, complemented, Sylow
331C2×#41C22⋊D4311yescharacteristic
332C22×Q8—21no—
333C22×Q8C22⋊D4311yescharacteristic
334C2×M16—861no—
335C22×C8—861no—
336C4⋊Q8—22no—
337C4⋊Q8—21no—
338C4⋊Q8—22no—
339C4⋊Q8—21no—
340C4⋊Q8—21no—
341C4⋊Q8—21no—
342C4⋊Q8C2×Dic4311yescharacteristic
343C4⋊Q8C2×Dic4311yescharacteristic
344#125—22no—
345#125—22no—
346#125—22no—
347#125—21no—
348#125—21no—
349#125—21no—
350C22⋊Q8—22no—
351C22⋊Q8—22no—
352C22⋊Q8—22no—
353C22⋊Q8—22no—
354C22⋊Q8—22no—
355C22⋊Q8—21no—
356C22⋊Q8—22no—
357C22⋊Q8—21no—
358C22⋊Q8—21no—
359C22⋊Q8—22no—
360C22⋊Q8C22⋊D4312yes—
361C4×Q8—22no—
362C4×Q8—22no—
363C4×Q8—22no—
364C4×Q8—21no—
365C4×Q8—21no—
366C4×Q8—21no—
367C4×Q8—21no—
368C4×Q8—21no—
369C4×Q8—21no—
370C4×Q8—21no—
371C4×Q8C2×Dic4311yescharacteristic
372C4×Q8C2×Dic4311yescharacteristic
373C4×Q8C2×Dic4311yescharacteristic
374C4×Q8C22⋊D4311yescharacteristic
375C4×Q8C22⋊D4311yescharacteristic
376C4×Q8C22⋊D4311yescharacteristic
377C4×Q8C22⋊D4312yes—
378C4×D4—22no—
379C4×D4—22no—
380C4×D4—21no—
381C4×D4—21no—
382C4×D4—21no—
383C4×D4—21no—
384C4×D4C2×Dic4311yescharacteristic
385C4×D4C22⋊D4311yescharacteristic
386#117—22no—
387#117—21no—
388#117—21no—
389#117C22⋊D4311yescharacteristic
390C2×C4⋊C4—22no—
391C2×C4⋊C4—21no—
392C2×C4⋊C4—21no—
393C2×C4⋊C4—861no—
394C2×C4⋊C4C22⋊D4311yescharacteristic
395C2×C42—22no—
396C2×C42—21no—
397C2×C42—21no—
398C2×C42—861no—
399C2×C42C22×D4311yescharacteristic
400C4⋊C8—861no—
401C4⋊C8—861no—
402C4⋊C8—861no—
403#104—1722no—
404#103—864no—
405C22⋊C8—861no—
406C4×C8—861no—
407C4×C8—861no—
408C4×C8—861no—
409#95—861no—
410#41—21no—
411#41—21no—
412#41#1062188412yes—
413#41#1062188512yes—
414C2×Q8—22no—
415C2×Q8—22no—
416C2×Q8—21no—
417C2×Q8—21no—
418C2×Q8—22no—
419C2×Q8—41no—
420C2×Q8—42no—
421C2×Q8—42no—
422C2×Q8C22⋊Dic4311yescharacteristic
423C2×Q8C22⋊Dic4311yescharacteristic
424C2×Q8C22⋊Dic4311yescharacteristic
425C2×Q8C22⋊Dic4312yes—
426C2×D4—21no—
427C2×D4C22⋊Dic4311yescharacteristic
428C22×C4—21no—
429C22×C4—22no—
430C22×C4—21no—
431C22×C4—22no—
432C22×C4—21no—
433C22×C4—21no—
434C22×C4—21no—
435C22×C4—1721no—
436C22×C4C2×C22⋊D4311yescharacteristic
437C22×C4C2×C22⋊D4311yescharacteristic
438C22×C4C2×C22⋊D4311yescharacteristic
439M16—1721no—
440M16—1721no—
441C2×C8—862no—
442C2×C8—1721no—
443C2×C8—1721no—
444C2×C8—1721no—
445C2×C8—1721no—
446C4⋊C4—22no—
447C4⋊C4—22no—
448C4⋊C4—22no—
449C4⋊C4—22no—
450C4⋊C4—22no—
451C4⋊C4—22no—
452C4⋊C4—22no—
453C4⋊C4—22no—
454C4⋊C4—21no—
455C4⋊C4—21no—
456C4⋊C4—21no—
457C4⋊C4—21no—
458C4⋊C4—21no—
459C4⋊C4—21no—
460C4⋊C4—21no—
461C4⋊C4—22no—
462C4⋊C4—21no—
463C4⋊C4—21no—
464C4⋊C4—21no—
465C4⋊C4—22no—
466C4⋊C4—862no—
467C4⋊C4—1721no—
468C4⋊C4C22⋊Dic4311yescharacteristic
469C4⋊C4C22⋊Dic4311yescharacteristic
470C4⋊C4C22⋊Dic4311yescharacteristic
471C4⋊C4C22⋊Dic4311yescharacteristic
472C4⋊C4C22⋊Dic4312yes—
473C22⋊C4—22no—
474C22⋊C4—22no—
475C22⋊C4—22no—
476C22⋊C4—21no—
477C22⋊C4—21no—
478C22⋊C4—21no—
479C42—22no—
480C42—22no—
481C42—21no—
482C42—21no—
483C42—21no—
484C42—21no—
485C42—21no—
486C42—22no—
487C42—21no—
488C42—21no—
489C42—1721no—
490C42—1721no—
491C42C22×Dic4311yescharacteristic
492C42C2×C22⋊D4311yescharacteristic
493C42C2×C22⋊D4311yescharacteristic
494C42C2×C22⋊D4311yescharacteristic
495C23—21no—
496C23#1306329411yescharacteristic
497Q8—21no—
498Q8—21no—
499Q8—21no—
500Q8—21no—
501Q8—42no—
502Q8—42no—
503Q8—44no—
504Q8—41no—
505Q8—41no—
506Q8—82no—
507Q8#1306324912yescomplemented
508Q8#1306325212yescomplemented
509D4—22no—
510D4—22no—
511D4—21no—
512D4#1306324912yescomplemented
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—22no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—22no—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—22no—
522C2×C4—22no—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—41no—
527C2×C4—42no—
528C2×C4—44no—
529C2×C4—41no—
530C2×C4—41no—
531C2×C4—81no—
532C2×C4—81no—
533C2×C4—82no—
534C2×C4—3441no—
535C2×C4—3441no—
536C2×C4—1722no—
537C2×C4C2×C22⋊Dic4311yescharacteristic
538C2×C4C2×C22⋊Dic4311yescharacteristic
539C2×C4C2×C22⋊Dic4311yescharacteristic
540C2×C4#1306329411yescharacteristic
541C2×C4#1306329411yescharacteristic
542C2×C4#1306329411yescharacteristic
543C2×C4C2×#1062188411yescharacteristic
544C2×C4C2×#1062188511yescharacteristic
545C2×C4#1306335611yescharacteristic
546C2×C4#1306335611yescharacteristic
547C8—3441no—
548C8—3441no—
549C8—1722no—
550C22—21no—
551C22—21no—
552C22—22no—
553C22—41no—
554C22—41no—
555C22#1458275511yescharacteristic
556C22#1458303811yescharacteristic
557C22#1458305511yescharacteristic
558C4—22no—
559C4—21no—
560C4—22no—
561C4—21no—
562C4—21no—
563C4—41no—
564C4—42no—
565C4—41no—
566C4—41no—
567C4—42no—
568C4—41no—
569C4—41no—
570C4—3442no—
571C4C2×#1306324911yescharacteristic
572C4#1458290811yescharacteristic
573C4C2×#1306325211yescharacteristic
574C4#1458291611yescharacteristic
575C4#1458303811yescharacteristic
576C4#1458305511yescharacteristic
577C2—21no—
578C2—21no—
579C2—42no—
580C2#1913453011yescharacteristic
581C2#1913453911yescharacteristic
582C2#1913455911yescharacteristic
subgroupG/H
centerC2×C4#13063294
commutatorC42×C43C22×C4
FrattiniC2×C42C22×D43
FittingQ8×#41×C43C2
socleC22×C43#379
prime radicalC2×#41×C43D4
cosocleC2×C42×C43C23
hypercenterQ8×#41D43
hypocenterC43#8439
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ Q8×#41

Complements

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

NH ≅ G/Ntype
2. C4×#13063249C2semidirect
3. #19133094C2semidirect
4. #19133050C2semidirect
5. #19133024C2semidirect
22. Q82×C43C4semidirect
24. C43×#557C4semidirect
28. C43×#554C4semidirect
30. D4×Q8×C43C4semidirect
215. Q8×C43#103semidirect
216. Q8×C43#104semidirect
220. D4×C43#103semidirect
299. Q82Dic43semidirect
301. #557Dic43semidirect
305. #554Dic43semidirect
307. D4×Q8Dic43semidirect
330. C43#8439semidirect
507. Q8#13063249semidirect
508. Q8#13063252semidirect
512. D4#13063249semidirect

Maximal subgroups

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

subgroupindex
#191346152
C4×#130632492
#191330942
#191330502
#191330242
#191329772
Q8×#41×C432
#843943