Finite Group Databasebeta

← #25151829

Subgroups — #25151829

Order 11008.

1534 conjugacy classes of subgroups.

The subgroup lattice has 660 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583294C211yesmaximal, characteristic, complemented
2C2×#14583109C211yesmaximal, characteristic, complemented
3C2×#14583061C212yesmaximal, complemented
4C2×#14583055C212yesmaximal, complemented
5#19139548C211yesmaximal, characteristic, complemented
6#19135603C212yesmaximal, complemented
7#19135598C212yesmaximal, complemented
8#19135528C211yesmaximal, characteristic, complemented
9#19135394C211yesmaximal, characteristic, complemented
10#19134425C211yesmaximal, characteristic, complemented
11C2×C43×#548C211yesmaximal, characteristic
12C22×#10621885C2212yes—
13C22×#10621885C2212yes—
14C22×#10621883C2212yes—
15C2×#13063325C2211yescharacteristic
16C2×#13063304C2212yes—
17C2×#13063304C2212yes—
18#14583294—24no—
19#14583109—24no—
20#14583061—28no—
21#14583055—28no—
22C2×C4⋊(C43⋊C8)C2211yescharacteristic
23C2×#13063249C2212yes—
24C2×#13063249C2212yes—
25C2×#13063248C2212yes—
26C2×#13063246C2212yes—
27C2×C22⋊(C43⋊C8)C2212yes—
28C2×C22⋊(C43⋊C8)C2212yes—
29C2×#13063236C2211yescharacteristic
30#14582835—21no—
31#14582835—21no—
32#14582802—21no—
33#14582768—21no—
34C4×C4⋊Dic43C2211yescharacteristic
35#14582661C2212yes—
36C22×#41×C43C2211yescharacteristic
37C23×Q8×C43C2211yescharacteristic
38C43×#548—24no—
39C43×#548—24no—
40C2×#124×C43—21no—
41C2×#124×C43C2211yescharacteristic
42C2×C22⋊Q8×C43—21no—
43C2×C22⋊Q8×C43C2211yescharacteristic
44C2×#121×C43—21no—
45C2×#121×C43C2211yescharacteristic
46C2×C4×Q8×C43C2211yescharacteristic
47C2×C4×D4×C43—21no—
48C2×C4×D4×C43C2211yescharacteristic
49C22×Dic86C2312yes—
50C2×#10621885—24no—
51C2×#10621885—24no—
52C2×#10621885—24no—
53C2×#10621885—24no—
54C2×#10621885—24no—
55C2×#10621885—42no—
56C2×#10621883—24no—
57C2×#10621883—24no—
58C2×#10621883—42no—
59C22×C43⋊C8C2312yes—
60C22×C43⋊C8C2312yes—
61#13063325—22no—
62#13063325—22no—
63#13063304—24no—
64#13063304—24no—
65#13063304—42no—
66#13063304—42no—
67C2×C4⋊Dic43—21no—
68C2×C4⋊Dic43—21no—
69C2×C4⋊Dic43C2312yes—
70C2×Dic43⋊C4—22no—
71C2×Dic43⋊C4—22no—
72C2×C22⋊Dic43—22no—
73C2×C22⋊Dic43—22no—
74C2×C4×Dic43—21no—
75C4⋊(C43⋊C8)—22no—
76#13063249—24no—
77#13063249D418yescomplemented
78#13063248—24no—
79#13063246—24no—
80C22⋊(C43⋊C8)—24no—
81C22⋊(C43⋊C8)—24no—
82#13063236—22no—
83C43⋊#95—21no—
84C2×#41×C43—22no—
85C2×#41×C43—22no—
86C2×#41×C43—24no—
87C2×#41×C43—42no—
88C22×Q8×C43—22no—
89C22×Q8×C43—22no—
90C22×Q8×C43—21no—
91C22×Q8×C43—24no—
92C22×Q8×C43—42no—
93C22×Q8×C43C2311yescharacteristic
94C22×Q8×C43C2311yescharacteristic
95C22×D4×C43—21no—
96C22×D4×C43—21no—
97C22×D4×C43D411yescharacteristic
98C22×D4×C43C2311yescharacteristic
99C23×C4×C43—21no—
100C23×C4×C43—21no—
101C23×C4×C43C2311yescharacteristic
102C23×C4×C43C2311yescharacteristic
103#124×C43—28no—
104#124×C43—22no—
105#124×C43D414yes—
106C22⋊Q8×C43—28no—
107C22⋊Q8×C43—22no—
108C22⋊Q8×C43—22no—
109#121×C43—28no—
110#121×C43—22no—
111#121×C43—22no—
112C4×Q8×C43—22no—
113C4×Q8×C43D414yes—
114C4×D4×C43—28no—
115C4×D4×C43—22no—
116C4×D4×C43—22no—
117C2×C4⋊C4×C43—21no—
118C2×C4⋊C4×C43—21no—
119C2×C4⋊C4×C43D411yescharacteristic
120C2×C4⋊C4×C43C2311yescharacteristic
121C2×C22⋊C4×C43—21no—
122C2×C22⋊C4×C43—21no—
123C2×C22⋊C4×C43—21no—
124C2×C22⋊C4×C43—21no—
125C2×C22⋊C4×C43D411yescharacteristic
126C2×C22⋊C4×C43D411yescharacteristic
127C2×C42×C43—21no—
128C2×C42×C43C2311yescharacteristic
129C24×C43—21no—
130C24×C43C2×D411yescharacteristic
131C24×C43C2×D411yescharacteristic
132#41×C43—48no—
133#41×C43—44no—
134#41×C43—44no—
135C2×Q8×C43—24no—
136C2×Q8×C43—21no—
137C2×Q8×C43—21no—
138C2×Q8×C43—22no—
139C2×Q8×C43—22no—
140C2×Q8×C43—22no—
141C2×Q8×C43—44no—
142C2×Q8×C43—48no—
143C2×Q8×C43—44no—
144C2×Q8×C43—44no—
145C2×Q8×C43C2×D414yes—
146C2×Q8×C43C2×D412yes—
147C2×Q8×C43C2×D412yes—
148C2×D4×C43—24no—
149C2×D4×C43—24no—
150C2×D4×C43—22no—
151C2×D4×C43—21no—
152C2×D4×C43—22no—
153C2×D4×C43—22no—
154C2×D4×C43—22no—
155C2×D4×C43—41no—
156C2×D4×C43—44no—
157C2×D4×C43—42no—
158C2×D4×C43—42no—
159C2×D4×C43C2×D412yes—
160C22×C4×C43—24no—
161C22×C4×C43—24no—
162C22×C4×C43—21no—
163C22×C4×C43—21no—
164C22×C4×C43—21no—
165C22×C4×C43—21no—
166C22×C4×C43—22no—
167C22×C4×C43—22no—
168C22×C4×C43—22no—
169C22×C4×C43—22no—
170C22×C4×C43—21no—
171C22×C4×C43—21no—
172C22×C4×C43—21no—
173C22×C4×C43—44no—
174C22×C4×C43—44no—
175C22×C4×C43C2×D411yescharacteristic
176C22×C4×C43C2×D411yescharacteristic
177C22×C4×C43C2×D411yescharacteristic
178C22×C4×C43C2×D411yescharacteristic
179C22×C4×C43C2411yescharacteristic
180C22×Dic43—22no—
181C22×Dic43—22no—
182C2×Dic86—22no—
183C2×Dic86—22no—
184C2×Dic86—22no—
185C2×Dic86—22no—
186C2×Dic86—22no—
187C2×Dic86—22no—
188C4⋊C4×C43—24no—
189C4⋊C4×C43—24no—
190C4⋊C4×C43—22no—
191C4⋊C4×C43—21no—
192C4⋊C4×C43C2×D412yes—
193C22⋊C4×C43—24no—
194C22⋊C4×C43—24no—
195C22⋊C4×C43—24no—
196C22⋊C4×C43—24no—
197C22⋊C4×C43—22no—
198C22⋊C4×C43—22no—
199C42×C43—24no—
200C42×C43C2×D412yes—
201C42×C43C2×D412yes—
202C22⋊Dic43—44no—
203C22⋊Dic43—44no—
204#10621885—48no—
205#10621885—48no—
206#10621883—48no—
207C4⋊Dic43—22no—
208C4⋊Dic43—42no—
209C4⋊Dic43—42no—
210C4⋊Dic43C2×D414yes—
211Dic43⋊C4—44no—
212Dic43⋊C4—44no—
213C4×Dic43—42no—
214C2×C43⋊C8—22no—
215C2×C43⋊C8—22no—
216C2×C43⋊C8—22no—
217C2×C43⋊C8—22no—
218C2×C43⋊C8—22no—
219C2×C43⋊C8C2×D414yes—
220C23×C43—21no—
221C23×C43—22no—
222C23×C43—21no—
223C23×C43—22no—
224C23×C43—21no—
225C23×C43—22no—
226C23×C43—22no—
227C23×C43—21no—
228C23×C43—21no—
229C23×C43—22no—
230C23×C43—42no—
231C23×C43—41no—
232C23×C43—41no—
233C23×C43—42no—
234C23×C43#13712yes—
235C23×C43C22×D411yescharacteristic
236Q8×C43—22no—
237Q8×C43—24no—
238Q8×C43—24no—
239Q8×C43—48no—
240Q8×C43—41no—
241Q8×C43—41no—
242Q8×C43#12714yes—
243D4×C43—24no—
244D4×C43—44no—
245D4×C43—48no—
246D4×C43—48no—
247D4×C43—41no—
248D4×C43—41no—
249C2×C4×C43—22no—
250C2×C4×C43—24no—
251C2×C4×C43—21no—
252C2×C4×C43—21no—
253C2×C4×C43—22no—
254C2×C4×C43—22no—
255C2×C4×C43—22no—
256C2×C4×C43—21no—
257C2×C4×C43—21no—
258C2×C4×C43—22no—
259C2×C4×C43—22no—
260C2×C4×C43—48no—
261C2×C4×C43—48no—
262C2×C4×C43—42no—
263C2×C4×C43—41no—
264C2×C4×C43—41no—
265C2×C4×C43—41no—
266C2×C4×C43—41no—
267C2×C4×C43—41no—
268C2×C4×C43—41no—
269C2×C4×C43—42no—
270C2×C4×C43—42no—
271C2×C4×C43#12012yes—
272C2×C4×C43#12012yes—
273C2×C4×C43C22×D412yes—
274C2×C4×C43C22×D411yescharacteristic
275C2×C4×C43C22×D411yescharacteristic
276C2×C4×C43H(5,𝔽2)12yes—
277C2×Dic43—24no—
278C2×Dic43—42no—
279C2×Dic43—42no—
280C2×Dic43—42no—
281C2×Dic43—42no—
282C2×Dic43—42no—
283Dic86—42no—
284Dic86—42no—
285Dic86—42no—
286Dic86—42no—
287C43⋊C8—24no—
288C43⋊C8—42no—
289#25767—431nomaximal, Sylow
290C22×C43—22no—
291C22×C43—24no—
292C22×C43—41no—
293C22×C43—41no—
294C22×C43—42no—
295C22×C43—41no—
296C22×C43—42no—
297C22×C43—41no—
298C22×C43—42no—
299C22×C43—41no—
300C22×C43—42no—
301C22×C43—42no—
302C22×C43—42no—
303C22×C43—82no—
304C22×C43—82no—
305C22×C43C2×#12011yescharacteristic
306C22×C43D4212yes—
307C22×C43C2×#13711yescharacteristic
308C22×C43#57511yescharacteristic
309C22×C43#57812yes—
310C4×C43—24no—
311C4×C43—22no—
312C4×C43—22no—
313C4×C43—41no—
314C4×C43—41no—
315C4×C43—42no—
316C4×C43—42no—
317C4×C43C2×#12711yescharacteristic
318C4×C43#53511yescharacteristic
319C4×C43D4212yes—
320Dic43—44no—
321Dic43—82no—
322C2×#548D4311yescharacteristic
323C2×#497—431no—
324C2×#462—431no—
325C2×#452—432no—
326C2×#451—432no—
327#2542—431no—
328#2001—432no—
329#2000—432no—
330#1983—431no—
331#1955—431no—
332#1763—431no—
333C2×C43—42no—
334C2×C43—81no—
335C2×C43—82no—
336C2×C43#243311yescharacteristic
337C2×C43#300711yescharacteristic
338C2×C43#301111yescharacteristic
339C2×C43#326912yes—
340C2×C43#327012yes—
341C22×#41C2×D4311yescharacteristic
342C23×Q8C2×D4311yescharacteristic
343C22×Q16—432no—
344C22×Q16—432no—
345C22×SD16—432no—
346#548—24no—
347#548—24no—
348C2×C4⋊Q8—431no—
349C2×#124—21no—
350C2×#124C2×D4311yescharacteristic
351C2×C22⋊Q8—21no—
352C2×C22⋊Q8—432no—
353C2×C22⋊Q8—432no—
354C2×C22⋊Q8C2×D4311yescharacteristic
355C2×#121—21no—
356C2×#121C2×D4311yescharacteristic
357C2×C4×Q8C2×D4311yescharacteristic
358C2×C4×D4—21no—
359C2×C4×D4C2×D4311yescharacteristic
360#497—864no—
361#462—864no—
362#452—868no—
363#451—868no—
364C2×C4⋊C8—431no—
365C2×#103—432no—
366C2×#103—432no—
367C2×#103—432no—
368C2×#102—432no—
369C2×C22⋊C8—432no—
370C2×C22⋊C8—432no—
371C2×#97—431no—
372#399—861no—
373#399—861no—
374#390—861no—
375#384—861no—
376C4×C4⋊C4—431no—
377#340—432no—
378C43#2576711yescharacteristic, complemented, Sylow
379C2×#41—22no—
380C2×#41—22no—
381C2×#41—24no—
382C2×#41—42no—
383C22×Q8—22no—
384C22×Q8—22no—
385C22×Q8—21no—
386C22×Q8—24no—
387C22×Q8—42no—
388C22×Q8—432no—
389C22×Q8C22×D4311yescharacteristic
390C22×Q8C22×D4311yescharacteristic
391C22×D4—21no—
392C22×D4—21no—
393C22×D4C22⋊D4311yescharacteristic
394C22×D4C22×D4311yescharacteristic
395C23×C4—21no—
396C23×C4—21no—
397C23×C4C22×D4311yescharacteristic
398C23×C4C22×D4311yescharacteristic
399C2×Q16—864no—
400C2×Q16—864no—
401C2×Q16—864no—
402C2×Q16—864no—
403C2×Q16—864no—
404C2×Q16—1722no—
405C2×SD16—864no—
406C2×SD16—864no—
407C2×SD16—1722no—
408C22×C8—432no—
409C22×C8—432no—
410C4⋊Q8—862no—
411C4⋊Q8—862no—
412#124—28no—
413#124—22no—
414#124C22⋊D4314yes—
415C22⋊Q8—28no—
416C22⋊Q8—22no—
417C22⋊Q8—22no—
418C22⋊Q8—864no—
419C22⋊Q8—864no—
420C22⋊Q8—1722no—
421C22⋊Q8—1722no—
422#121—28no—
423#121—22no—
424#121—22no—
425C4×Q8—22no—
426C4×Q8C22⋊D4314yes—
427C4×D4—28no—
428C4×D4—22no—
429C4×D4—22no—
430C2×C4⋊C4—21no—
431C2×C4⋊C4—21no—
432C2×C4⋊C4—432no—
433C2×C4⋊C4—862no—
434C2×C4⋊C4—862no—
435C2×C4⋊C4—861no—
436C2×C4⋊C4—861no—
437C2×C4⋊C4C22⋊D4311yescharacteristic
438C2×C4⋊C4C22×D4311yescharacteristic
439C2×C22⋊C4—21no—
440C2×C22⋊C4—21no—
441C2×C22⋊C4—21no—
442C2×C22⋊C4—21no—
443C2×C22⋊C4—862no—
444C2×C22⋊C4—862no—
445C2×C22⋊C4C22⋊D4311yescharacteristic
446C2×C22⋊C4C22⋊D4311yescharacteristic
447C2×C42—21no—
448C2×C42—861no—
449C2×C42C22×D4311yescharacteristic
450C4⋊C8—862no—
451#103—438no—
452#103—864no—
453#103—864no—
454#102—864no—
455C22⋊C8—864no—
456C22⋊C8—864no—
457#97—862no—
458#95—861no—
459C24—21no—
460C24C2×C22⋊D4311yescharacteristic
461C24C2×C22⋊D4311yescharacteristic
462#41—48no—
463#41—44no—
464#41—44no—
465C2×Q8—24no—
466C2×Q8—21no—
467C2×Q8—21no—
468C2×Q8—22no—
469C2×Q8—22no—
470C2×Q8—22no—
471C2×Q8—44no—
472C2×Q8—48no—
473C2×Q8—44no—
474C2×Q8—44no—
475C2×Q8—862no—
476C2×Q8—862no—
477C2×Q8—862no—
478C2×Q8—862no—
479C2×Q8—862no—
480C2×Q8—862no—
481C2×Q8D4×D4314yes—
482C2×Q8C2×C22⋊D4312yes—
483C2×Q8C2×C22⋊D4312yes—
484C2×D4—24no—
485C2×D4—24no—
486C2×D4—22no—
487C2×D4—22no—
488C2×D4—22no—
489C2×D4—21no—
490C2×D4—22no—
491C2×D4—41no—
492C2×D4—44no—
493C2×D4—42no—
494C2×D4—42no—
495C2×D4C2×C22⋊D4312yes—
496C22×C4—21no—
497C22×C4—24no—
498C22×C4—24no—
499C22×C4—21no—
500C22×C4—21no—
501C22×C4—22no—
502C22×C4—22no—
503C22×C4—21no—
504C22×C4—21no—
505C22×C4—21no—
506C22×C4—21no—
507C22×C4—22no—
508C22×C4—22no—
509C22×C4—44no—
510C22×C4—44no—
511C22×C4—862no—
512C22×C4—862no—
513C22×C4C2×C22⋊D4311yescharacteristic
514C22×C4C2×C22⋊D4311yescharacteristic
515C22×C4C2×C22⋊D4311yescharacteristic
516C22×C4C2×C22⋊D4311yescharacteristic
517C22×C4C23×D4311yescharacteristic
518Q16—1728no—
519Q16—1728no—
520SD16—1728no—
521C2×C8—434no—
522C2×C8—862no—
523C2×C8—862no—
524C2×C8—862no—
525C2×C8—862no—
526C2×C8—862no—
527C4⋊C4—24no—
528C4⋊C4—24no—
529C4⋊C4—22no—
530C4⋊C4—21no—
531C4⋊C4—434no—
532C4⋊C4—862no—
533C4⋊C4—1724no—
534C4⋊C4—1724no—
535C4⋊C4—1722no—
536C4⋊C4—1722no—
537C4⋊C4C2×C22⋊D4312yes—
538C22⋊C4—24no—
539C22⋊C4—24no—
540C22⋊C4—24no—
541C22⋊C4—24no—
542C22⋊C4—22no—
543C22⋊C4—22no—
544C22⋊C4—1724no—
545C22⋊C4—1724no—
546C42—24no—
547C42—1722no—
548C42C2×C22⋊D4312yes—
549C42C2×C22⋊D4312yes—
550C23—21no—
551C23—21no—
552C23—22no—
553C23—22no—
554C23—21no—
555C23—22no—
556C23—21no—
557C23—21no—
558C23—22no—
559C23—22no—
560C23—41no—
561C23—41no—
562C23—42no—
563C23—42no—
564C23#1306335512yes—
565C23C22×C22⋊D4311yescharacteristic
566Q8—22no—
567Q8—24no—
568Q8—24no—
569Q8—48no—
570Q8—41no—
571Q8—41no—
572Q8—1722no—
573Q8—1722no—
574Q8—1722no—
575Q8—1722no—
576Q8#1306332114yes—
577D4—24no—
578D4—44no—
579D4—48no—
580D4—48no—
581D4—41no—
582D4—41no—
583C2×C4—22no—
584C2×C4—21no—
585C2×C4—21no—
586C2×C4—22no—
587C2×C4—24no—
588C2×C4—22no—
589C2×C4—22no—
590C2×C4—21no—
591C2×C4—21no—
592C2×C4—22no—
593C2×C4—22no—
594C2×C4—48no—
595C2×C4—48no—
596C2×C4—41no—
597C2×C4—41no—
598C2×C4—42no—
599C2×C4—41no—
600C2×C4—41no—
601C2×C4—41no—
602C2×C4—41no—
603C2×C4—42no—
604C2×C4—42no—
605C2×C4—864no—
606C2×C4—1722no—
607C2×C4—1722no—
608C2×C4—1722no—
609C2×C4—1722no—
610C2×C4—1722no—
611C2×C4#1306329412yes—
612C2×C4#1306329412yes—
613C2×C4C2×D4×D4312yes—
614C2×C4C22×C22⋊D4311yescharacteristic
615C2×C4C22×C22⋊D4311yescharacteristic
616C2×C4#1306337012yes—
617C8—864no—
618C8—1722no—
619C22—22no—
620C22—24no—
621C22—42no—
622C22—41no—
623C22—41no—
624C22—42no—
625C22—41no—
626C22—42no—
627C22—42no—
628C22—42no—
629C22—41no—
630C22—41no—
631C22—42no—
632C22—82no—
633C22—82no—
634C22C2×#1306329411yescharacteristic
635C22D4×C22⋊D4312yes—
636C22C2×#1306335511yescharacteristic
637C22#1458369711yescharacteristic
638C22#1458371412yes—
639C4—22no—
640C4—24no—
641C4—22no—
642C4—42no—
643C4—41no—
644C4—41no—
645C4—42no—
646C4—3442no—
647C4—1724no—
648C4C2×#1306332111yescharacteristic
649C4#1458346611yescharacteristic
650C4D4×C22⋊D4312yes—
651C2—42no—
652C2—81no—
653C2—82no—
654C2#1913822811yescharacteristic
655C2#1914385511yescharacteristic
656C2#1914389011yescharacteristic
657C2#1914615112yes—
658C2#1914616112yes—
subgroupG/H
centerC23C22×C22⋊D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
Fitting, prime radicalC2×C43×#548C2
socleC23×C43C22×D4
hypercenterC2×#548D43
hypocenterC43#25767
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#548

Complements

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

NH ≅ G/Ntype
1. C2×#14583294C2semidirect
2. C2×#14583109C2semidirect
3. C2×#14583061C2semidirect
4. C2×#14583055C2semidirect
5. #19139548C2semidirect
6. #19135603C2semidirect
7. #19135598C2semidirect
8. #19135528C2semidirect
9. #19135394C2semidirect
10. #19134425C2semidirect
77. #13063249D4semidirect
378. C43#25767semidirect

Maximal subgroups

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

subgroupindex
C2×#145832942
C2×#145831092
C2×#145830612
C2×#145830552
#191395482
#191356032
#191355982
#191355282
#191353942
#191344252
C2×C43×#5482
#2576743