Finite Group Databasebeta

← #25063042

Subgroups — #25063042

Order 11008.

1214 conjugacy classes of subgroups.

The subgroup lattice has 654 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×Q8×D43C211yesmaximal, characteristic
2#19143226C211yesmaximal, characteristic
3#19143225C211yesmaximal, characteristic
4#19133043C211yesmaximal, characteristic, complemented
5#19133042C211yesmaximal, characteristic, complemented
6#19133041C211yesmaximal, characteristic, complemented
7#19133022C214yesmaximal, complemented
8#19132988C214yesmaximal, complemented
9C43×#1491C211yesmaximal, characteristic, complemented
10C22×Q8×D43C411yescharacteristic
11C2×Q8×Dic43C411yescharacteristic
12C2×C4×Dic86—21no—
13C2×C4×Dic86C2211yescharacteristic
14C2×#13063290—21no—
15C2×#13063290C411yescharacteristic
16C4×Q8×D43—21no—
17C4×Q8×D43—21no—
18C4×Q8×D43—21no—
19C4×Q8×D43—21no—
20C4×Q8×D43C412yes—
21C4×Q8×D43C412yes—
22C4×Q8×D43C2212yes—
23C4×Q8×D43C2212yes—
24C2×C4⋊C4×D43—21no—
25C2×C4⋊C4×D43C411yescharacteristic
26C2×C42×D43—21no—
27C2×C42×D43C2211yescharacteristic
28#14582956C2211yescharacteristic
29#14582954—21no—
30#14582954—21no—
31#14582954—21no—
32#14582951C2212yes—
33#14582950C2212yes—
34#14582950C2212yes—
35#14582949—21no—
36#14582922—21no—
37#14582921C2212yes—
38#14582862—21no—
39#14582861—21no—
40C4×#10621877C2211yescharacteristic
41#14582851—21no—
42#14582631C2214yescomplemented
43Q8⋊(C43⋊C8)C2214yescomplemented
44#14582629C2214yescomplemented
45C2×C4×Q8×C43C2211yescharacteristic
46C43×#432C2211yescharacteristic
47C4×M16×C43C2211yescharacteristic
48C43×Q8⋊C8C2214yescomplemented
49C22×Dic86—21no—
50C22×Dic86C2×C411yescharacteristic
51C2×Q8×D43—28no—
52C2×Q8×D43—21no—
53C2×Q8×D43—21no—
54C2×Q8×D43C2×C412yes—
55C2×Q8×D43C2×C412yes—
56C22×C4×D43—21no—
57C22×C4×D43—21no—
58C22×C4×D43C2×C411yescharacteristic
59C22×C4×D43D411yescharacteristic
60C22×C4×D43D411yescharacteristic
61C2×#10621877—21no—
62C2×#10621872—22no—
63Q8×Dic43—21no—
64Q8×Dic43—21no—
65Q8×Dic43C2×C412yes—
66Q8×Dic43C2×C412yes—
67C4×Dic86—21no—
68C4×Dic86—21no—
69C4×Dic86—22no—
70C4×Dic86—22no—
71C4×Dic86—22no—
72C4×Dic86—22no—
73C4×Dic86C2×C412yes—
74C4×Dic86C2312yes—
75#13063290—21no—
76#13063290—21no—
77#13063290—22no—
78#13063290—22no—
79#13063290—22no—
80#13063290—22no—
81#13063290C2×C412yes—
82#13063290C2×C412yes—
83C2×C4⋊Dic43—21no—
84C2×C4⋊Dic43C2×C411yescharacteristic
85C2×Dic43⋊C4—21no—
86C2×Dic43⋊C4—21no—
87C2×Dic43⋊C4—21no—
88C4⋊C4×D43—22no—
89C4⋊C4×D43—22no—
90C4⋊C4×D43—21no—
91C4⋊C4×D43—21no—
92C4⋊C4×D43—22no—
93C4⋊C4×D43—22no—
94C4⋊C4×D43C2×C412yes—
95C4⋊C4×D43C2×C412yes—
96C2×C4×Dic43—21no—
97C2×C4×Dic43—21no—
98C2×C4×Dic43—21no—
99C2×C4×Dic43C2×C411yescharacteristic
100C2×C4×Dic43D411yescharacteristic
101C2×C4×Dic43D411yescharacteristic
102C42×D43—22no—
103C42×D43—22no—
104C42×D43—22no—
105C42×D43—22no—
106C42×D43C2×C411yescharacteristic
107C42×D43C2×C411yescharacteristic
108C42×D43D411yescharacteristic
109C42×D43D411yescharacteristic
110C42×D43D411yescharacteristic
111C42×D43D411yescharacteristic
112C42×D43C2311yescharacteristic
113C42×D43C2311yescharacteristic
114C4⋊(C43⋊C8)C2312yes—
115Dic43⋊C8—22no—
116Dic43⋊C8—22no—
117Dic43⋊C8—22no—
118C22⋊(C43⋊C8)—21no—
119(C2×D43)⋊C8—22no—
120(C2×D43)⋊C8—22no—
121(C2×D43)⋊C8—22no—
122#13063236—21no—
123#13063236—21no—
124C4×C43⋊C8C2312yes—
125C8×Dic43—22no—
126C22×Q8×C43C2×C411yescharacteristic
127C2×M16×C43—21no—
128C4×Q8×C43—21no—
129C4×Q8×C43—21no—
130C4×Q8×C43C2×C412yes—
131C4×Q8×C43C2312yes—
132C2×C4⋊C4×C43—21no—
133C2×C4⋊C4×C43C2×C411yescharacteristic
134C2×C42×C43—21no—
135C2×C42×C43C2311yescharacteristic
136C4⋊C8×C43C2312yes—
137C22⋊C8×C43—21no—
138#97×C43—21no—
139#97×C43—21no—
140C4×C8×C43C2312yes—
141C23×D43C22⋊C411yescharacteristic
142C2×Q8×C43—24no—
143C2×Q8×C43—21no—
144C2×Q8×C43C22×C412yes—
145C22×C4×C43—21no—
146C22×C4×C43—21no—
147C22×C4×C43C22×C411yescharacteristic
148C22×C4×C43C2×D411yescharacteristic
149C22×C4×C43C2×D411yescharacteristic
150C22×Dic43—21no—
151C22×Dic43—21no—
152C22×Dic43C22⋊C411yescharacteristic
153C22×Dic43C22⋊C411yescharacteristic
154C22×Dic43C22⋊C411yescharacteristic
155Q8×D43—28no—
156Q8×D43—28no—
157Q8×D43—24no—
158Q8×D43—24no—
159Q8×D43—24no—
160Q8×D43M1618yescomplemented
161C2×C4×D43—28no—
162C2×C4×D43—24no—
163C2×C4×D43—24no—
164C2×C4×D43—22no—
165C2×C4×D43—22no—
166C2×C4×D43—22no—
167C2×C4×D43—22no—
168C2×C4×D43—42no—
169C2×C4×D43—44no—
170C2×C4×D43C22⋊C411yescharacteristic
171C2×C4×D43C22⋊C411yescharacteristic
172C2×C4×D43C22⋊C411yescharacteristic
173C2×C4×D43C22⋊C411yescharacteristic
174C2×C4×D43C22⋊C411yescharacteristic
175C2×C4×D43C22⋊C411yescharacteristic
176C2×C4×D43C22×C411yescharacteristic
177C2×C4×D43C22×C411yescharacteristic
178C2×C4×D43C2×D411yescharacteristic
179C2×C4×D43C2×D411yescharacteristic
180C2×C4×D43C2×D411yescharacteristic
181C2×C4×D43C2×D411yescharacteristic
182C2×Dic86—28no—
183C2×Dic86—21no—
184C2×Dic86—22no—
185C2×Dic86—22no—
186C2×Dic86—24no—
187C2×Dic86C22×C412yes—
188M16×C43—42no—
189C2×C8×C43—22no—
190C2×C8×C43—22no—
191C4⋊C4×C43—22no—
192C4⋊C4×C43—21no—
193C4⋊C4×C43—22no—
194C4⋊C4×C43C22×C412yes—
195C42×C43—22no—
196C42×C43—22no—
197C42×C43C22×C411yescharacteristic
198C42×C43C2×D411yescharacteristic
199C42×C43C2×D411yescharacteristic
200C42×C43C2411yescharacteristic
201C4⋊Dic43—21no—
202C4⋊Dic43—22no—
203C4⋊Dic43—22no—
204C4⋊Dic43C22×C412yes—
205Dic43⋊C4—22no—
206Dic43⋊C4—22no—
207Dic43⋊C4—22no—
208Dic43⋊C4—22no—
209Dic43⋊C4—22no—
210Dic43⋊C4—22no—
211C4×Dic43—22no—
212C4×Dic43—22no—
213C4×Dic43—22no—
214C4×Dic43—22no—
215C4×Dic43—22no—
216C4×Dic43—22no—
217C4×Dic43C22⋊C411yescharacteristic
218C4×Dic43C22⋊C411yescharacteristic
219C4×Dic43C22⋊C411yescharacteristic
220C4×Dic43C22⋊C411yescharacteristic
221C4×Dic43C22⋊C411yescharacteristic
222C4×Dic43C22⋊C411yescharacteristic
223C4×Dic43C22×C411yescharacteristic
224C4×Dic43C22×C411yescharacteristic
225C4×Dic43C2×D411yescharacteristic
226C4×Dic43C2×D411yescharacteristic
227C4×Dic43C2×D411yescharacteristic
228C4×Dic43C2×D411yescharacteristic
229#10621877—42no—
230C2×C43⋊C8—22no—
231C2×C43⋊C8—22no—
232#10621872—44no—
233C23×C43C2×C22⋊C411yescharacteristic
234C22×D43—22no—
235C22×D43—22no—
236C22×D43—22no—
237C22×D43C2×C22⋊C411yescharacteristic
238C22×D43C2×C22⋊C411yescharacteristic
239Q8×C43—24no—
240Q8×C43—22no—
241Q8×C43C2×M1614yes—
242C2×C4×C43—24no—
243C2×C4×C43—22no—
244C2×C4×C43—22no—
245C2×C4×C43—22no—
246C2×C4×C43—22no—
247C2×C4×C43—22no—
248C2×C4×C43—42no—
249C2×C4×C43C2×C22⋊C411yescharacteristic
250C2×C4×C43C2×C22⋊C411yescharacteristic
251C2×C4×C43C2×C22⋊C411yescharacteristic
252C2×C4×C43C23×C411yescharacteristic
253C2×C4×C43C22×D411yescharacteristic
254C2×C4×C43C22×D411yescharacteristic
255C2×Dic43—24no—
256C2×Dic43—22no—
257C2×Dic43—22no—
258C2×Dic43—22no—
259C2×Dic43—22no—
260C2×Dic43—22no—
261C2×Dic43—42no—
262C2×Dic43C2×C22⋊C411yescharacteristic
263C2×Dic43C2×C22⋊C411yescharacteristic
264C2×Dic43C2×C22⋊C411yescharacteristic
265C2×Dic43C2×C22⋊C411yescharacteristic
266C2×Dic43C2×C22⋊C411yescharacteristic
267C2×Dic43C2×C22⋊C411yescharacteristic
268C4×D43—28no—
269C4×D43—28no—
270C4×D43—22no—
271C4×D43—22no—
272C4×D43—22no—
273C4×D43—22no—
274C4×D43—22no—
275C4×D43—22no—
276C4×D43—41no—
277C4×D43—41no—
278C4×D43—41no—
279C4×D43—41no—
280C4×D43—44no—
281C4×D43—44no—
282C4×D43C2×M1614yes—
283C4×D43#13714yes—
284Dic86—28no—
285Dic86—24no—
286Dic86—22no—
287Dic86—28no—
288Dic86C2×M1614yes—
289C8×C43—42no—
290C8×C43—42no—
291C43⋊C8—42no—
292C43⋊C8—42no—
293#17449—431nomaximal, Sylow
294C22×C43—21no—
295C22×C43—21no—
296C22×C43#42112yes—
297C22×C43C22×C22⋊C411yescharacteristic
298C2×D43—28no—
299C2×D43—21no—
300C2×D43—21no—
301C2×D43—21no—
302C2×D43—21no—
303C2×D43#40712yes—
304C2×D43#41912yes—
305C4×C43—24no—
306C4×C43—21no—
307C4×C43—21no—
308C4×C43—21no—
309C4×C43—21no—
310C4×C43—42no—
311C4×C43C22×M1612yes—
312C4×C43C2×#13712yes—
313Dic43—21no—
314Dic43—24no—
315Dic43—21no—
316Dic43—21no—
317Dic43—21no—
318Dic43—42no—
319Dic43#40712yes—
320Dic43#41912yes—
321C22×C4×Q8—431no—
322#2920—431no—
323#2920—431no—
324#1491—431no—
325#1491—431no—
326#1491—431no—
327#1491D4311yescharacteristic, complemented
328#1487—434no—
329#1479—434no—
330C2×C43—22no—
331C2×C43C2×#40711yescharacteristic
332C2×C43C2×#41911yescharacteristic
333C2×C43C2×#42111yescharacteristic
334D43—22no—
335D43—22no—
336C23×Q8—431no—
337C2×C4×Q8—431no—
338C2×C4×Q8—432no—
339C2×C4×Q8—432no—
340C2×C4×Q8—432no—
341C2×C4×Q8—432no—
342C2×C4×Q8—431no—
343C2×C4×Q8—431no—
344C2×C4×Q8—861no—
345C2×C4×Q8—861no—
346C2×C4×Q8—861no—
347C2×C4×Q8—861no—
348C2×C4×Q8—861no—
349C2×C4×Q8—861no—
350C2×C4×Q8C2×D4311yescharacteristic
351C22×C4⋊C4—431no—
352C22×C4⋊C4—861no—
353C22×C42—431no—
354C22×C42—861no—
355#432—431no—
356#432—861no—
357#432—861no—
358#432—861no—
359#432C2×D4311yescharacteristic
360#431—432no—
361#431—432no—
362#431—432no—
363#431—861no—
364#423—432no—
365#423—861no—
366#407—861no—
367#407—861no—
368C4×M16—431no—
369C4×M16—861no—
370C4×M16C2×D4311yescharacteristic
371Q8⋊C8—434no—
372Q8⋊C8—434no—
373Q8⋊C8—434no—
374Q8⋊C8C2×D4314yescomplemented
375C43#1744911yescharacteristic, complemented, Sylow
376C22×Q8—432no—
377C22×Q8—432no—
378C22×Q8—431no—
379C22×Q8—861no—
380C22×Q8—861no—
381C22×Q8—861no—
382C22×Q8—868no—
383C22×Q8C4×D4311yescharacteristic
384C23×C4—431no—
385C23×C4—431no—
386C23×C4—431no—
387C23×C4—861no—
388C23×C4—861no—
389C2×M16—21no—
390C2×M16—862no—
391C2×M16—861no—
392C4×Q8—21no—
393C4×Q8—21no—
394C4×Q8—432no—
395C4×Q8—432no—
396C4×Q8—432no—
397C4×Q8—432no—
398C4×Q8—432no—
399C4×Q8—432no—
400C4×Q8—862no—
401C4×Q8—862no—
402C4×Q8—862no—
403C4×Q8—862no—
404C4×Q8—862no—
405C4×Q8—862no—
406C4×Q8—861no—
407C4×Q8—861no—
408C4×Q8—862no—
409C4×Q8—862no—
410C4×Q8—861no—
411C4×Q8—861no—
412C4×Q8—861no—
413C4×Q8—861no—
414C4×Q8C4×D4312yes—
415C4×Q8C22×D4312yes—
416C2×C4⋊C4—21no—
417C2×C4⋊C4—431no—
418C2×C4⋊C4—432no—
419C2×C4⋊C4—432no—
420C2×C4⋊C4—861no—
421C2×C4⋊C4—861no—
422C2×C4⋊C4—862no—
423C2×C4⋊C4—862no—
424C2×C4⋊C4—862no—
425C2×C4⋊C4—862no—
426C2×C4⋊C4—861no—
427C2×C4⋊C4—861no—
428C2×C4⋊C4—861no—
429C2×C4⋊C4—861no—
430C2×C4⋊C4C4×D4311yescharacteristic
431C2×C42—21no—
432C2×C42—431no—
433C2×C42—431no—
434C2×C42—431no—
435C2×C42—431no—
436C2×C42—431no—
437C2×C42—431no—
438C2×C42—431no—
439C2×C42—431no—
440C2×C42—431no—
441C2×C42—431no—
442C2×C42—431no—
443C2×C42—862no—
444C2×C42—862no—
445C2×C42—862no—
446C2×C42—862no—
447C2×C42—861no—
448C2×C42—861no—
449C2×C42—861no—
450C2×C42C22×D4311yescharacteristic
451C4⋊C8—432no—
452C4⋊C8—862no—
453C4⋊C8—862no—
454C4⋊C8—862no—
455C4⋊C8C22×D4312yes—
456C22⋊C8—21no—
457C22⋊C8—862no—
458C22⋊C8—862no—
459C22⋊C8—862no—
460C22⋊C8—861no—
461#97—21no—
462#97—21no—
463#97—861no—
464#97—861no—
465C4×C8—432no—
466C4×C8—862no—
467C4×C8C22×D4312yes—
468C24—431no—
469C2×Q8—24no—
470C2×Q8—21no—
471C2×Q8—438no—
472C2×Q8—432no—
473C2×Q8—862no—
474C2×Q8—862no—
475C2×Q8—864no—
476C2×Q8—868no—
477C2×Q8—864no—
478C2×Q8—864no—
479C2×Q8—868no—
480C2×Q8—868no—
481C2×Q8—864no—
482C2×Q8—861no—
483C2×Q8C2×C4×D4312yes—
484C22×C4—21no—
485C22×C4—21no—
486C22×C4—431no—
487C22×C4—431no—
488C22×C4—431no—
489C22×C4—431no—
490C22×C4—431no—
491C22×C4—431no—
492C22×C4—431no—
493C22×C4—431no—
494C22×C4—431no—
495C22×C4—431no—
496C22×C4—431no—
497C22×C4—431no—
498C22×C4—431no—
499C22×C4—431no—
500C22×C4—431no—
501C22×C4—864no—
502C22×C4—864no—
503C22×C4—862no—
504C22×C4—862no—
505C22×C4—868no—
506C22×C4—862no—
507C22×C4—862no—
508C22×C4—861no—
509C22×C4—861no—
510C22×C4—1722no—
511C22×C4—1724no—
512C22×C4C2×C4×D4311yescharacteristic
513C22×C4D4×D4311yescharacteristic
514C22×C4D4×D4311yescharacteristic
515M16—42no—
516M16—1724no—
517M16—1722no—
518C2×C8—22no—
519C2×C8—22no—
520C2×C8—862no—
521C2×C8—862no—
522C4⋊C4—22no—
523C4⋊C4—21no—
524C4⋊C4—22no—
525C4⋊C4—432no—
526C4⋊C4—862no—
527C4⋊C4—862no—
528C4⋊C4—862no—
529C4⋊C4—862no—
530C4⋊C4—862no—
531C4⋊C4—862no—
532C4⋊C4—861no—
533C4⋊C4—862no—
534C4⋊C4—862no—
535C4⋊C4C2×C4×D4312yes—
536C42—22no—
537C42—22no—
538C42—431no—
539C42—431no—
540C42—431no—
541C42—431no—
542C42—431no—
543C42—431no—
544C42—431no—
545C42—431no—
546C42—431no—
547C42—431no—
548C42—431no—
549C42—431no—
550C42—862no—
551C42—862no—
552C42—862no—
553C42—862no—
554C42—862no—
555C42—862no—
556C42C2×C4×D4311yescharacteristic
557C42D4×D4311yescharacteristic
558C42D4×D4311yescharacteristic
559C42C23×D4311yescharacteristic
560C23—431no—
561C23—431no—
562C23—862no—
563C23—862no—
564C23—862no—
565C23C22⋊C4×D4311yescharacteristic
566Q8—24no—
567Q8—22no—
568Q8—434no—
569Q8—868no—
570Q8—868no—
571Q8—864no—
572Q8—862no—
573Q8M16×D4314yes—
574C2×C4—24no—
575C2×C4—22no—
576C2×C4—22no—
577C2×C4—22no—
578C2×C4—22no—
579C2×C4—22no—
580C2×C4—42no—
581C2×C4—431no—
582C2×C4—431no—
583C2×C4—434no—
584C2×C4—434no—
585C2×C4—431no—
586C2×C4—431no—
587C2×C4—431no—
588C2×C4—431no—
589C2×C4—862no—
590C2×C4—862no—
591C2×C4—862no—
592C2×C4—862no—
593C2×C4—868no—
594C2×C4—868no—
595C2×C4—862no—
596C2×C4—862no—
597C2×C4—864no—
598C2×C4—862no—
599C2×C4—862no—
600C2×C4—862no—
601C2×C4—862no—
602C2×C4—862no—
603C2×C4—1721no—
604C2×C4—1721no—
605C2×C4—1721no—
606C2×C4—1721no—
607C2×C4—1724no—
608C2×C4—1724no—
609C2×C4—1722no—
610C2×C4C22⋊C4×D4311yescharacteristic
611C2×C4C22⋊C4×D4311yescharacteristic
612C2×C4C22⋊C4×D4311yescharacteristic
613C2×C4C22×C4×D4311yescharacteristic
614C2×C4C2×D4×D4311yescharacteristic
615C2×C4C2×D4×D4311yescharacteristic
616C8—42no—
617C8—42no—
618C8—1722no—
619C8—1722no—
620C22—21no—
621C22—21no—
622C22—432no—
623C22—432no—
624C22—868no—
625C22—861no—
626C22—861no—
627C22—861no—
628C22—861no—
629C22#1458291412yes—
630C22C2×C22⋊C4×D4311yescharacteristic
631C4—24no—
632C4—21no—
633C4—21no—
634C4—21no—
635C4—21no—
636C4—42no—
637C4—432no—
638C4—432no—
639C4—861no—
640C4—864no—
641C4—861no—
642C4—861no—
643C4—861no—
644C4—1722no—
645C4C2×M16×D4312yes—
646C4#137×D4312yes—
647C2—22no—
648C2—862no—
649C2—862no—
650C2#407×D4311yescharacteristic
651C2#419×D4311yescharacteristic
652C2C2×#1458291411yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC42C23×D43
FittingC43×#1491C2
socleC22×C43C22×C22⋊C4
prime radicalC23×D43C22⋊C4
cosocleC42×C43C24
hypercenter#1491D43
hypocenterC43#17449
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1491

Complements

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

NH ≅ G/Ntype
4. #19133043C2semidirect
5. #19133042C2semidirect
6. #19133041C2semidirect
7. #19133022C2semidirect
8. #19132988C2semidirect
9. C43×#1491C2semidirect
42. #14582631C22semidirect
43. Q8⋊(C43⋊C8)C22semidirect
44. #14582629C22semidirect
48. C43×Q8⋊C8C22semidirect
160. Q8×D43M16semidirect
327. #1491D43semidirect
374. Q8⋊C8C2×D43semidirect
375. C43#17449semidirect

Maximal subgroups

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

subgroupindex
C2×C4×Q8×D432
#191432262
#191432252
#191330432
#191330422
#191330412
#191330222
#191329882
C43×#14912
#1744943