Finite Group Databasebeta

← #25064111

Subgroups — #25064111

Order 11008.

994 conjugacy classes of subgroups.

The subgroup lattice has 658 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583451C211yesmaximal, characteristic
2C2×#14582953C211yesmaximal, characteristic
3#19136990C211yesmaximal, characteristic
4#19133168C211yesmaximal, characteristic
5#19133167C211yesmaximal, characteristic
6#19133166C211yesmaximal, characteristic
7#19133144C214yesmaximal, complemented
8#19133105C214yesmaximal, complemented
9C43×#1520C211yesmaximal, characteristic
10#14583451—21no—
11#14583451—21no—
12#14583451—21no—
13#14583451—21no—
14#14583451C412yescomplemented
15#14583451C412yescomplemented
16#14583451C2212yes—
17#14583451C2212yes—
18C2×#13063324C411yescharacteristic, complemented
19C2×#13063323C411yescharacteristic, complemented
20C2×#13063315—21no—
21C2×#13063304C2211yescharacteristic
22C2×#13063302—21no—
23C2×Q8×Dic43C411yescharacteristic, complemented
24C2×#13063290—21no—
25C2×#13063290C411yescharacteristic, complemented
26C2×#13063281—21no—
27C22×C4×Dic43C2211yescharacteristic
28#14582953—21no—
29#14582953—21no—
30#14582953C2212yes—
31#14582953C2212yes—
32C2×Dic43⋊C8—21no—
33C2×C22⋊(C43⋊C8)C2211yescharacteristic
34C2×#13063235—21no—
35#14582766C2212yes—
36#14582764—21no—
37#14582760—21no—
38#14582759C2211yescharacteristic
39C4⋊C4×Dic43—21no—
40C22⋊C4×Dic43—21no—
41#14582744C2212yes—
42#14582637C2214yes—
43#14582636C2214yes—
44#14582635C2214yes—
45C2×C22⋊Q8×C43C2211yescharacteristic
46C2×C22⋊C8×C43C2211yescharacteristic
47C43×#380C2211yescharacteristic
48C43×#328C2214yes—
49C22×Dic86—21no—
50C22×Dic86C2×C411yescharacteristic
51C23×Dic43D411yescharacteristic
52C23×Dic43D411yescharacteristic
53C22×C43⋊C8—21no—
54#13063324—21no—
55#13063324—21no—
56#13063324C2×C412yes—
57#13063324C2×C412yes—
58#13063323—21no—
59#13063323—21no—
60#13063323C2×C412yes—
61#13063323C2×C412yes—
62#13063315—22no—
63#13063315—22no—
64#13063315—22no—
65#13063315—22no—
66#13063304—21no—
67#13063304—21no—
68#13063304C2×C412yes—
69#13063304C2312yes—
70#13063302—22no—
71#13063302—22no—
72#13063302—22no—
73#13063302—22no—
74Q8×Dic43—21no—
75Q8×Dic43—21no—
76Q8×Dic43C2×C412yes—
77Q8×Dic43C2×C412yes—
78#13063290—22no—
79#13063290—22no—
80#13063290—21no—
81#13063290—21no—
82#13063290—22no—
83#13063290—22no—
84#13063290C2×C412yes—
85#13063290C2×C412yes—
86#13063281—22no—
87#13063281—22no—
88#13063281—22no—
89#13063281—22no—
90C2×C4⋊Dic43—21no—
91C2×C4⋊Dic43—21no—
92C2×C4⋊Dic43C2×C411yescharacteristic
93C2×Dic43⋊C4—21no—
94C2×Dic43⋊C4—21no—
95C2×Dic43⋊C4—21no—
96C2×Dic43⋊C4—21no—
97C2×Dic43⋊C4—21no—
98C2×C22⋊Dic43—21no—
99C2×C22⋊Dic43—21no—
100C2×C4×Dic43—21no—
101C2×C4×Dic43—21no—
102C2×C4×Dic43—22no—
103C2×C4×Dic43C2×C411yescharacteristic
104C2×C4×Dic43C2×C411yescharacteristic
105C2×C4×Dic43C2×C411yescharacteristic
106C2×C4×Dic43C2×C411yescharacteristic
107C2×C4×Dic43D411yescharacteristic
108C2×C4×Dic43D411yescharacteristic
109C2×C4×Dic43D411yescharacteristic
110C2×C4×Dic43D411yescharacteristic
111C2×C4×Dic43D411yescharacteristic
112C2×C4×Dic43D411yescharacteristic
113C2×C4×Dic43C2311yescharacteristic
114C2×C4×Dic43C2311yescharacteristic
115Dic43⋊C8—22no—
116Dic43⋊C8—22no—
117C22⋊(C43⋊C8)—21no—
118C22⋊(C43⋊C8)C2312yes—
119#13063235—22no—
120#13063235—22no—
121C43⋊#95—22no—
122C43⋊#95—22no—
123C43⋊#95—22no—
124C43⋊#95C2312yes—
125C22×Q8×C43C2×C411yescharacteristic
126C23×C4×C43C2311yescharacteristic
127C22×C8×C43—21no—
128C22⋊Q8×C43—21no—
129C22⋊Q8×C43—21no—
130C22⋊Q8×C43C2×C412yes—
131C22⋊Q8×C43C2312yes—
132C2×C4⋊C4×C43—21no—
133C2×C4⋊C4×C43—21no—
134C2×C4⋊C4×C43C2×C411yescharacteristic
135C2×C22⋊C4×C43—21no—
136C2×C22⋊C4×C43—21no—
137C22⋊C8×C43—21no—
138C22⋊C8×C43C2312yes—
139#95×C43C2312yes—
140C24×C43C2×D411yescharacteristic
141C2×Q8×C43—21no—
142C2×Q8×C43—42no—
143C2×Q8×C43C22×C412yes—
144C22×C4×C43—21no—
145C22×C4×C43—21no—
146C22×C4×C43—22no—
147C22×C4×C43—42no—
148C22×C4×C43C22×C411yescharacteristic
149C22×C4×C43C22×C411yescharacteristic
150C22×C4×C43C2×D411yescharacteristic
151C22×C4×C43C2×D411yescharacteristic
152C22×C4×C43C2×D411yescharacteristic
153C22×C4×C43C2411yescharacteristic
154C22×Dic43—21no—
155C22×Dic43—21no—
156C22×Dic43—22no—
157C22×Dic43—22no—
158C22×Dic43—22no—
159C22×Dic43—42no—
160C22×Dic43C22⋊C411yescharacteristic
161C22×Dic43C22⋊C411yescharacteristic
162C22×Dic43C22⋊C411yescharacteristic
163C22×Dic43C22⋊C411yescharacteristic
164C22×Dic43C22⋊C411yescharacteristic
165C22×Dic43C22⋊C411yescharacteristic
166C22×Dic43C22⋊C411yescharacteristic
167C22×Dic43C22⋊C411yescharacteristic
168C22×Dic43C2×D411yescharacteristic
169C22×Dic43C2×D411yescharacteristic
170C22×Dic43C2×D411yescharacteristic
171C22×Dic43C2×D411yescharacteristic
172C2×Dic86—21no—
173C2×Dic86—22no—
174C2×Dic86—22no—
175C2×Dic86—44no—
176C2×Dic86—42no—
177C2×Dic86C22×C412yes—
178C2×C8×C43—22no—
179C2×C8×C43—42no—
180C4⋊C4×C43—22no—
181C4⋊C4×C43—21no—
182C4⋊C4×C43—22no—
183C4⋊C4×C43—42no—
184C4⋊C4×C43C22×C412yes—
185C22⋊C4×C43—22no—
186C22⋊C4×C43—22no—
187C22⋊C4×C43—42no—
188C22⋊Dic43—22no—
189C22⋊Dic43—22no—
190C22⋊Dic43—42no—
191C4⋊Dic43—21no—
192C4⋊Dic43—22no—
193C4⋊Dic43—22no—
194C4⋊Dic43—42no—
195C4⋊Dic43C22×C412yes—
196Dic43⋊C4—22no—
197Dic43⋊C4—22no—
198Dic43⋊C4—22no—
199Dic43⋊C4—22no—
200Dic43⋊C4—22no—
201Dic43⋊C4—22no—
202Dic43⋊C4—22no—
203Dic43⋊C4—22no—
204Dic43⋊C4—22no—
205Dic43⋊C4—22no—
206C4×Dic43—22no—
207C4×Dic43—22no—
208C4×Dic43—22no—
209C4×Dic43—22no—
210C4×Dic43—44no—
211C4×Dic43C22⋊C411yescharacteristic
212C4×Dic43C22⋊C411yescharacteristic
213C4×Dic43C22⋊C411yescharacteristic
214C4×Dic43C22⋊C411yescharacteristic
215C4×Dic43C22⋊C411yescharacteristic
216C4×Dic43C22⋊C411yescharacteristic
217C4×Dic43C22⋊C411yescharacteristic
218C4×Dic43C22⋊C411yescharacteristic
219C4×Dic43C22×C411yescharacteristic
220C4×Dic43C22×C411yescharacteristic
221C4×Dic43C22×C411yescharacteristic
222C4×Dic43C22×C411yescharacteristic
223C4×Dic43C2×D411yescharacteristic
224C4×Dic43C2×D411yescharacteristic
225C4×Dic43C2×D411yescharacteristic
226C4×Dic43C2×D411yescharacteristic
227C2×C43⋊C8—22no—
228C2×C43⋊C8—42no—
229C23×C43—41no—
230C23×C43—41no—
231C23×C43C2×C22⋊C411yescharacteristic
232C23×C43C2×C22⋊C411yescharacteristic
233C23×C43#13712yes—
234C23×C43#13712yes—
235C23×C43C22×D411yescharacteristic
236Q8×C43—42no—
237Q8×C43—42no—
238C2×C4×C43—22no—
239C2×C4×C43—22no—
240C2×C4×C43—22no—
241C2×C4×C43—22no—
242C2×C4×C43—22no—
243C2×C4×C43—41no—
244C2×C4×C43—41no—
245C2×C4×C43—41no—
246C2×C4×C43—42no—
247C2×C4×C43—42no—
248C2×C4×C43—42no—
249C2×C4×C43—42no—
250C2×C4×C43—42no—
251C2×C4×C43C2×C22⋊C411yescharacteristic
252C2×C4×C43C2×C22⋊C411yescharacteristic
253C2×C4×C43C23×C411yescharacteristic
254C2×C4×C43C22×D411yescharacteristic
255C2×Dic43—21no—
256C2×Dic43—21no—
257C2×Dic43—21no—
258C2×Dic43—21no—
259C2×Dic43—22no—
260C2×Dic43—22no—
261C2×Dic43—22no—
262C2×Dic43—22no—
263C2×Dic43—22no—
264C2×Dic43—22no—
265C2×Dic43—22no—
266C2×Dic43—22no—
267C2×Dic43—22no—
268C2×Dic43—41no—
269C2×Dic43—41no—
270C2×Dic43—41no—
271C2×Dic43—42no—
272C2×Dic43—42no—
273C2×Dic43—42no—
274C2×Dic43—42no—
275C2×Dic43—42no—
276C2×Dic43C2×C22⋊C411yescharacteristic
277C2×Dic43C2×C22⋊C411yescharacteristic
278C2×Dic43C2×C22⋊C411yescharacteristic
279C2×Dic43C2×C22⋊C411yescharacteristic
280C2×Dic43C2×C22⋊C411yescharacteristic
281C2×Dic43C2×C22⋊C411yescharacteristic
282C2×Dic43C2×C22⋊C411yescharacteristic
283C2×Dic43C2×C22⋊C411yescharacteristic
284Dic86—44no—
285Dic86—42no—
286Dic86—44no—
287Dic86—42no—
288C8×C43—42no—
289C43⋊C8—42no—
290#17596—431nomaximal, Sylow
291C22×C43—21no—
292C22×C43—21no—
293C22×C43—21no—
294C22×C43—21no—
295C22×C43—21no—
296C22×C43—21no—
297C22×C43—42no—
298C22×C43—42no—
299C22×C43#41912yes—
300C22×C43#41912yes—
301C22×C43C22×C22⋊C411yescharacteristic
302C22×C43C2×#13711yescharacteristic
303C22×C43C2×#13711yescharacteristic
304C4×C43—21no—
305C4×C43—21no—
306C4×C43—21no—
307C4×C43—42no—
308C4×C43—42no—
309C4×C43—82no—
310C4×C43#41012yes—
311Dic43—21no—
312Dic43—21no—
313Dic43—21no—
314Dic43—21no—
315Dic43—21no—
316Dic43—21no—
317Dic43—21no—
318Dic43—42no—
319Dic43—42no—
320Dic43—82no—
321Dic43#42112yes—
322C2×#533—431no—
323C2×#432—431no—
324#2283—431no—
325#1520—431no—
326#1520—431no—
327#1520—431no—
328#1520D4311yescharacteristic
329#1515—434no—
330#1506—434no—
331C2×C43—21no—
332C2×C43—21no—
333C2×C43—22no—
334C2×C43—22no—
335C2×C43C2×#41011yescharacteristic
336C2×C43C2×#41911yescharacteristic
337C2×C43C2×#42111yescharacteristic
338#533—432no—
339#533—432no—
340#533—432no—
341#533—432no—
342#533—861no—
343#533—861no—
344#533—861no—
345#533—861no—
346C2×C4⋊Q8—431no—
347C2×C4⋊Q8—431no—
348C2×#125—861no—
349C2×C22⋊Q8—431no—
350C2×C22⋊Q8—861no—
351C2×C22⋊Q8C2×D4311yescharacteristic
352C2×C4×Q8—431no—
353C2×C4×Q8—431no—
354C2×C4×Q8—861no—
355C2×#117—861no—
356C22×C42—431no—
357#432—432no—
358#432—432no—
359#432—861no—
360#432—861no—
361C2×C4⋊C8—861no—
362C2×C22⋊C8—431no—
363C2×C22⋊C8C2×D4311yescharacteristic
364C2×#97—861no—
365#383—432no—
366#382—861no—
367#381—861no—
368#380—431no—
369#380C2×D4311yescharacteristic
370C4×C4⋊C4—861no—
371C4×C22⋊C4—861no—
372#376—432no—
373#328—434no—
374#328—434no—
375#328—434no—
376#328C2×D4314yes—
377C43#1759611yescharacteristic, complemented, Sylow
378C22×Q8—431no—
379C22×Q8—861no—
380C22×Q8C4×D4311yescharacteristic
381C23×C4—431no—
382C23×C4—431no—
383C23×C4C22×D4311yescharacteristic
384C22×C8—21no—
385C22×C8—861no—
386C4⋊Q8—432no—
387C4⋊Q8—432no—
388C4⋊Q8—432no—
389C4⋊Q8—432no—
390C4⋊Q8—861no—
391C4⋊Q8—861no—
392C4⋊Q8—861no—
393C4⋊Q8—861no—
394#125—862no—
395#125—862no—
396#125—862no—
397#125—862no—
398C22⋊Q8—21no—
399C22⋊Q8—21no—
400C22⋊Q8—432no—
401C22⋊Q8—432no—
402C22⋊Q8—862no—
403C22⋊Q8—862no—
404C22⋊Q8—862no—
405C22⋊Q8—862no—
406C22⋊Q8—861no—
407C22⋊Q8—861no—
408C22⋊Q8C4×D4312yes—
409C22⋊Q8C22×D4312yes—
410C4×Q8—432no—
411C4×Q8—432no—
412C4×Q8—432no—
413C4×Q8—432no—
414C4×Q8—861no—
415C4×Q8—861no—
416C4×Q8—862no—
417C4×Q8—862no—
418C4×Q8—862no—
419C4×Q8—862no—
420C4×Q8—861no—
421C4×Q8—861no—
422#117—862no—
423#117—862no—
424#117—862no—
425#117—862no—
426C2×C4⋊C4—21no—
427C2×C4⋊C4—21no—
428C2×C4⋊C4—431no—
429C2×C4⋊C4—861no—
430C2×C4⋊C4—861no—
431C2×C4⋊C4—861no—
432C2×C4⋊C4—861no—
433C2×C4⋊C4—861no—
434C2×C4⋊C4—861no—
435C2×C4⋊C4—861no—
436C2×C4⋊C4C4×D4311yescharacteristic
437C2×C22⋊C4—21no—
438C2×C22⋊C4—21no—
439C2×C22⋊C4—861no—
440C2×C22⋊C4—861no—
441C2×C42—431no—
442C2×C42—431no—
443C2×C42—431no—
444C2×C42—431no—
445C2×C42—431no—
446C2×C42—431no—
447C2×C42—431no—
448C2×C42—431no—
449C2×C42—431no—
450C2×C42—431no—
451C2×C42—431no—
452C2×C42—431no—
453C2×C42—861no—
454C2×C42—861no—
455C2×C42—862no—
456C4⋊C8—862no—
457C4⋊C8—862no—
458C22⋊C8—21no—
459C22⋊C8—432no—
460C22⋊C8—861no—
461C22⋊C8C22×D4312yes—
462#97—862no—
463#97—862no—
464#95—432no—
465#95—862no—
466#95—862no—
467#95—862no—
468#95C22×D4312yes—
469C24D4×D4311yescharacteristic
470C2×Q8—21no—
471C2×Q8—42no—
472C2×Q8—432no—
473C2×Q8—862no—
474C2×Q8—862no—
475C2×Q8—861no—
476C2×Q8—1722no—
477C2×Q8—1724no—
478C2×Q8C2×C4×D4312yes—
479C22×C4—21no—
480C22×C4—21no—
481C22×C4—22no—
482C22×C4—42no—
483C22×C4—431no—
484C22×C4—431no—
485C22×C4—431no—
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—862no—
496C22×C4—862no—
497C22×C4—861no—
498C22×C4—861no—
499C22×C4—862no—
500C22×C4—1722no—
501C22×C4C2×C4×D4311yescharacteristic
502C22×C4C2×C4×D4311yescharacteristic
503C22×C4D4×D4311yescharacteristic
504C22×C4D4×D4311yescharacteristic
505C22×C4D4×D4311yescharacteristic
506C22×C4C23×D4311yescharacteristic
507C2×C8—22no—
508C2×C8—42no—
509C2×C8—862no—
510C2×C8—1722no—
511C4⋊C4—22no—
512C4⋊C4—21no—
513C4⋊C4—22no—
514C4⋊C4—42no—
515C4⋊C4—432no—
516C4⋊C4—862no—
517C4⋊C4—862no—
518C4⋊C4—862no—
519C4⋊C4—862no—
520C4⋊C4—862no—
521C4⋊C4—862no—
522C4⋊C4—862no—
523C4⋊C4—862no—
524C4⋊C4—862no—
525C4⋊C4—862no—
526C4⋊C4—861no—
527C4⋊C4—862no—
528C4⋊C4—862no—
529C4⋊C4—1722no—
530C4⋊C4C2×C4×D4312yes—
531C22⋊C4—22no—
532C22⋊C4—22no—
533C22⋊C4—42no—
534C22⋊C4—862no—
535C22⋊C4—862no—
536C22⋊C4—1722no—
537C42—431no—
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—431no—
551C42—431no—
552C42—431no—
553C42—862no—
554C42—862no—
555C42—862no—
556C42—862no—
557C42—1724no—
558C23—41no—
559C23—41no—
560C23C22⋊C4×D4311yescharacteristic
561C23C22⋊C4×D4311yescharacteristic
562C23#1306335412yes—
563C23#1306335712yes—
564C23C2×D4×D4311yescharacteristic
565Q8—42no—
566Q8—42no—
567Q8—1722no—
568Q8—1724no—
569Q8—1724no—
570Q8—1722no—
571C2×C4—22no—
572C2×C4—22no—
573C2×C4—22no—
574C2×C4—22no—
575C2×C4—22no—
576C2×C4—41no—
577C2×C4—41no—
578C2×C4—41no—
579C2×C4—42no—
580C2×C4—42no—
581C2×C4—42no—
582C2×C4—42no—
583C2×C4—42no—
584C2×C4—431no—
585C2×C4—431no—
586C2×C4—431no—
587C2×C4—431no—
588C2×C4—431no—
589C2×C4—431no—
590C2×C4—431no—
591C2×C4—431no—
592C2×C4—862no—
593C2×C4—862no—
594C2×C4—862no—
595C2×C4—862no—
596C2×C4—862no—
597C2×C4—862no—
598C2×C4—862no—
599C2×C4—861no—
600C2×C4—861no—
601C2×C4—861no—
602C2×C4—861no—
603C2×C4—862no—
604C2×C4—862no—
605C2×C4—1721no—
606C2×C4—1721no—
607C2×C4—1721no—
608C2×C4—1722no—
609C2×C4—1722no—
610C2×C4—1722no—
611C2×C4—1722no—
612C2×C4—1722no—
613C2×C4C22⋊C4×D4311yescharacteristic
614C2×C4C22⋊C4×D4311yescharacteristic
615C2×C4C22×C4×D4311yescharacteristic
616C2×C4C2×D4×D4311yescharacteristic
617C8—42no—
618C8—1722no—
619C22—21no—
620C22—21no—
621C22—21no—
622C22—21no—
623C22—21no—
624C22—21no—
625C22—42no—
626C22—42no—
627C22#1458290612yes—
628C22#1458290612yes—
629C22C2×C22⋊C4×D4311yescharacteristic
630C22C2×#1306335411yescharacteristic
631C22C2×#1306335711yescharacteristic
632C4—21no—
633C4—21no—
634C4—21no—
635C4—42no—
636C4—42no—
637C4—82no—
638C4—432no—
639C4—861no—
640C4—861no—
641C4—861no—
642C4—861no—
643C4—861no—
644C4—861no—
645C4—861no—
646C4—3442no—
647C4—1722no—
648C4—1722no—
649C4#1458287112yes—
650C2—21no—
651C2—21no—
652C2—22no—
653C2—22no—
654C2C2×#1458287111yescharacteristic
655C2C2×#1458290611yescharacteristic
656C2#421×D4311yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1520C2
socleC22×C43C22×C22⋊C4
prime radicalC24×C43C2×D4
cosocleC22×C4×C43C24
hypercenter#1520D43
hypocenterC43#17596
LCSG ▷ C2×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1520

Complements

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

NH ≅ G/Ntype
7. #19133144C2semidirect
8. #19133105C2semidirect
14. #14583451C4semidirect
15. #14583451C4semidirect
18. C2×#13063324C4semidirect
19. C2×#13063323C4semidirect
23. C2×Q8×Dic43C4semidirect
25. C2×#13063290C4semidirect
377. C43#17596semidirect

Maximal subgroups

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

subgroupindex
C2×#145834512
C2×#145829532
#191369902
#191331682
#191331672
#191331662
#191331442
#191331052
C43×#15202
#1759643