Finite Group Databasebeta

← #25062826

Subgroups — #25062826

Order 11008.

944 conjugacy classes of subgroups.

The subgroup lattice has 652 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583584C211yesmaximal, characteristic
2#19143249C212yesmaximal, complemented
3#19132963C212yesmaximal, complemented
4#19132949C212yesmaximal, complemented
5#19132941C212yesmaximal
6#19132937C211yesmaximal, characteristic, complemented
7#19132928C211yesmaximal, characteristic, complemented
8#19132925C211yesmaximal, characteristic, complemented
9#19132917C211yesmaximal, characteristic, complemented
10#19132908C211yesmaximal, characteristic, complemented
11C2×C43×#324C211yesmaximal, characteristic, complemented
12#14583584—22no—
13#14583584—22no—
14#14583584—22no—
15#14583584—22no—
16C2×#13063320C411yescharacteristic
17C2×#13063320C2211yescharacteristic
18C2×#13063316C411yescharacteristic
19C2×#13063315C411yescharacteristic
20C2×#13063315C2211yescharacteristic
21C2×#13063308C411yescharacteristic
22C2×#13063308C2211yescharacteristic
23C2×#13063305C411yescharacteristic
24C2×#13063304C411yescharacteristic
25C2×#13063290C2211yescharacteristic
26C2×C4×C22⋊D43C411yescharacteristic
27C2×#13063284C411yescharacteristic
28C2×#13063284C2211yescharacteristic
29C2×#13063283C2211yescharacteristic
30#14582957—22no—
31#14582957—22no—
32#14582953C2212yes—
33#14582953C2212yes—
34#14582949C2212yes—
35#14582949C2212yes—
36#14582925—22no—
37#14582863C2212yes—
38#14582854—22no—
39#14582625C2211yescharacteristic
40#14582625C2211yescharacteristic
41#14582625C2212yes—
42#14582624C2212yes—
43#14582624C2212yes—
44#14582622C2212yes—
45#14582622C2212yes—
46C22×C4⋊C4×C43C2211yescharacteristic
47C2×C22⋊C8×C43C2212yes—
48C43×#324C2211yescharacteristic
49C43×#324C2212yes—
50C43×#324C2211yescharacteristic
51C22×Dic86C2×C411yescharacteristic
52C22×C22⋊D43C2×C411yescharacteristic
53C22×C4×D43C2×C411yescharacteristic
54C2×#10621877—22no—
55#13063320—22no—
56#13063320—22no—
57#13063320—22no—
58#13063320—22no—
59#13063316—22no—
60#13063316—22no—
61#13063315—22no—
62#13063315—22no—
63#13063315—22no—
64#13063315—22no—
65#13063308—22no—
66#13063308—22no—
67#13063308—22no—
68#13063308—22no—
69#13063305—22no—
70#13063305—22no—
71#13063304—22no—
72#13063304—22no—
73#13063290—22no—
74#13063290—22no—
75C4×C22⋊D43—21no—
76C4×C22⋊D43—21no—
77C4×C22⋊D43—21no—
78C4×C22⋊D43—21no—
79#13063284—21no—
80#13063284—21no—
81#13063284—21no—
82#13063284—21no—
83#13063284D412yes—
84#13063284D412yes—
85#13063284D412yes—
86#13063284D412yes—
87#13063283—22no—
88#13063283—22no—
89C2×C4⋊Dic43C2×C411yescharacteristic
90C2×C4⋊Dic43C2×C411yescharacteristic
91C2×C4⋊Dic43C2×C411yescharacteristic
92C2×C4⋊Dic43C2×C411yescharacteristic
93C2×C4⋊Dic43C2×C411yescharacteristic
94C2×Dic43⋊C4C2×C411yescharacteristic
95C2×Dic43⋊C4C2×C411yescharacteristic
96C2×Dic43⋊C4C2×C411yescharacteristic
97C2×Dic43⋊C4C2×C411yescharacteristic
98C2×Dic43⋊C4C2×C411yescharacteristic
99C2×Dic43⋊C4C2×C411yescharacteristic
100C2×Dic43⋊C4C2311yescharacteristic
101C2×C22⋊Dic43C2×C411yescharacteristic
102C2×C22⋊Dic43C2×C411yescharacteristic
103C2×C22⋊Dic43C2×C411yescharacteristic
104C2×(C2×D43)⋊C4C2×C411yescharacteristic
105C2×(C2×D43)⋊C4C2×C411yescharacteristic
106C2×(C2×D43)⋊C4C2×C411yescharacteristic
107C2×(C2×D43)⋊C4C2×C411yescharacteristic
108C2×(C2×D43)⋊C4C2311yescharacteristic
109C2×C4×Dic43C2×C411yescharacteristic
110C2×C4×Dic43C2×C411yescharacteristic
111C2×C4×Dic43C2×C411yescharacteristic
112C2×C4×Dic43C2311yescharacteristic
113C2×C4×Dic43C2311yescharacteristic
114Dic43⋊C8—22no—
115Dic43⋊C8—22no—
116Dic43⋊C8—22no—
117Dic43⋊C8—22no—
118C22⋊(C43⋊C8)—22no—
119C22⋊(C43⋊C8)C2312yes—
120C22⋊(C43⋊C8)C2312yes—
121#13063235—22no—
122#13063235—22no—
123C8×Dic43—22no—
124C8×Dic43—22no—
125C23×C4×C43C2×C411yescharacteristic
126C23×C4×C43C2×C411yescharacteristic
127C23×C4×C43C2311yescharacteristic
128C22×C8×C43—22no—
129C2×C4⋊C4×C43—22no—
130C2×C4⋊C4×C43—22no—
131C2×C4⋊C4×C43C2×C411yescharacteristic
132C2×C4⋊C4×C43C2×C411yescharacteristic
133C2×C4⋊C4×C43C2311yescharacteristic
134C2×C4⋊C4×C43C2311yescharacteristic
135C22⋊C8×C43—22no—
136C22⋊C8×C43C2312yes—
137C22⋊C8×C43C2312yes—
138C24×C43C22×C411yescharacteristic
139C23×D43C22×C411yescharacteristic
140C22×C4×C43—22no—
141C22×C4×C43—21no—
142C22×C4×C43—21no—
143C22×C4×C43—21no—
144C22×C4×C43—21no—
145C22×C4×C43—41no—
146C22×C4×C43—42no—
147C22×C4×C43—42no—
148C22×C4×C43C22×C411yescharacteristic
149C22×C4×C43C22×C411yescharacteristic
150C22×C4×C43C22×C411yescharacteristic
151C22×C4×C43C22×C411yescharacteristic
152C22×C4×C43C22×C411yescharacteristic
153C22×C4×C43C2×D412yes—
154C22×C4×C43C2×D412yes—
155C22×C4×C43C2411yescharacteristic
156C2×C22⋊D43—21no—
157C2×C22⋊D43—21no—
158C2×C22⋊D43—42no—
159C22×Dic43C22×C411yescharacteristic
160C22×Dic43C22×C411yescharacteristic
161C22×Dic43C22×C411yescharacteristic
162C22×Dic43C22×C411yescharacteristic
163C22×Dic43C22×C411yescharacteristic
164C22×Dic43C22×C411yescharacteristic
165C22×Dic43C22×C411yescharacteristic
166C2×C4×D43—22no—
167C2×C4×D43—21no—
168C2×C4×D43—21no—
169C2×C4×D43—41no—
170C2×Dic86—22no—
171C2×Dic86—22no—
172C2×Dic86—41no—
173C2×C8×C43—22no—
174C2×C8×C43—22no—
175C2×C8×C43—44no—
176C4⋊C4×C43—22no—
177C4⋊C4×C43—22no—
178C4⋊C4×C43—22no—
179C4⋊C4×C43—22no—
180C22⋊Dic43—21no—
181C22⋊Dic43—21no—
182C22⋊Dic43C22⋊C411yescharacteristic
183C22⋊Dic43C22⋊C411yescharacteristic
184C22⋊Dic43C22⋊C411yescharacteristic
185C22⋊Dic43C22⋊C411yescharacteristic
186C22⋊Dic43C22⋊C412yes—
187C22⋊Dic43C22⋊C412yes—
188(C2×D43)⋊C4—22no—
189(C2×D43)⋊C4—22no—
190(C2×D43)⋊C4—22no—
191(C2×D43)⋊C4—21no—
192(C2×D43)⋊C4—21no—
193(C2×D43)⋊C4—22no—
194C4⋊Dic43—22no—
195C4⋊Dic43—21no—
196C4⋊Dic43—21no—
197C4⋊Dic43—21no—
198C4⋊Dic43—21no—
199C4⋊Dic43C22⋊C412yes—
200C4⋊Dic43C22⋊C412yes—
201C4⋊Dic43C22⋊C412yes—
202C4⋊Dic43C22⋊C412yes—
203Dic43⋊C4—22no—
204Dic43⋊C4—22no—
205Dic43⋊C4—21no—
206Dic43⋊C4—21no—
207Dic43⋊C4—22no—
208Dic43⋊C4—22no—
209Dic43⋊C4—22no—
210Dic43⋊C4—22no—
211C4×Dic43—21no—
212C4×Dic43—21no—
213C4×Dic43—21no—
214C4×Dic43—21no—
215C4×Dic43—21no—
216C4×Dic43—21no—
217C4×Dic43C2×D412yes—
218C4×Dic43C2×D412yes—
219C4×Dic43C2×D412yes—
220C4×Dic43C2×D412yes—
221#10621877—44no—
222C2×C43⋊C8—22no—
223C2×C43⋊C8—22no—
224C23×C43—21no—
225C23×C43—21no—
226C23×C43—22no—
227C23×C43—41no—
228C23×C43C2×C22⋊C411yescharacteristic
229C23×C43C2×C22⋊C411yescharacteristic
230C23×C43C23×C411yescharacteristic
231C22×D43—21no—
232C22×D43—21no—
233C22×D43—21no—
234C22×D43—41no—
235C22×D43—41no—
236C2×C4×C43—21no—
237C2×C4×C43—21no—
238C2×C4×C43—24no—
239C2×C4×C43—21no—
240C2×C4×C43—21no—
241C2×C4×C43—21no—
242C2×C4×C43—21no—
243C2×C4×C43—21no—
244C2×C4×C43—41no—
245C2×C4×C43—42no—
246C2×C4×C43—41no—
247C2×C4×C43—42no—
248C2×C4×C43—42no—
249C2×C4×C43—42no—
250C2×C4×C43—42no—
251C2×C4×C43—41no—
252C2×C4×C43—41no—
253C2×C4×C43C2×C22⋊C412yes—
254C2×C4×C43#13112yes—
255C2×C4×C43C22×D412yes—
256C22⋊D43—42no—
257C22⋊D43—42no—
258C2×Dic43—21no—
259C2×Dic43—21no—
260C2×Dic43—21no—
261C2×Dic43—21no—
262C2×Dic43—21no—
263C2×Dic43—21no—
264C2×Dic43—21no—
265C2×Dic43—21no—
266C2×Dic43—21no—
267C2×Dic43—41no—
268C2×Dic43—41no—
269C2×Dic43—41no—
270C2×Dic43—41no—
271C2×Dic43C2×C22⋊C411yescharacteristic
272C2×Dic43C2×C22⋊C411yescharacteristic
273C2×Dic43C2×C22⋊C411yescharacteristic
274C2×Dic43C2×C22⋊C411yescharacteristic
275C2×Dic43C2×C22⋊C412yes—
276C2×Dic43C2×C22⋊C412yes—
277C4×D43—42no—
278C4×D43—42no—
279Dic86—44no—
280C8×C43—42no—
281C8×C43—42no—
282C43⋊C8—42no—
283C43⋊C8—42no—
284#17417—431nomaximal, Sylow
285C22×C43—21no—
286C22×C43—21no—
287C22×C43—21no—
288C22×C43—21no—
289C22×C43—21no—
290C22×C43—21no—
291C22×C43—21no—
292C22×C43—42no—
293C22×C43—42no—
294C22×C43#41012yes—
295C22×C43C22×C22⋊C411yescharacteristic
296C22×C43C2×#13111yescharacteristic
297C22×C43#56811yescharacteristic
298C2×D43—41no—
299C2×D43—41no—
300C2×D43—41no—
301C2×D43—81no—
302C2×D43—81no—
303C4×C43—22no—
304C4×C43—22no—
305C4×C43—22no—
306C4×C43—41no—
307C4×C43—41no—
308C4×C43—41no—
309Dic43—22no—
310Dic43—21no—
311Dic43—21no—
312Dic43—21no—
313Dic43—21no—
314Dic43—22no—
315Dic43—41no—
316Dic43—41no—
317Dic43—41no—
318C2×#552—431no—
319#2924—432no—
320#1473—432no—
321#1470—432no—
322#1468—432no—
323#1467—431no—
324#1464—431no—
325#1463—431no—
326#1461—431no—
327#1458—431no—
328C2×#324D4311yescharacteristic, complemented
329C2×C43—21no—
330C2×C43—21no—
331C2×C43—22no—
332C2×C43—41no—
333C2×C43#288011yescharacteristic
334C2×C43C2×#41011yescharacteristic
335C2×C43#288911yescharacteristic
336D43—81no—
337#552—862no—
338#552—862no—
339#552—862no—
340#552—862no—
341C2×#126—431no—
342C2×#126—431no—
343C2×#125—431no—
344C2×#125—431no—
345C2×#125—431no—
346C2×#123—431no—
347C2×#123—431no—
348C2×C22⋊Q8—431no—
349C2×C22⋊Q8—431no—
350C2×C4×Q8—431no—
351C2×C4×D4—431no—
352C2×#117—431no—
353C2×#117—431no—
354C2×#117—431no—
355C22×C4⋊C4C2×D4311yescharacteristic
356#433—862no—
357#433—862no—
358#432—432no—
359#432—432no—
360#431—432no—
361#431—432no—
362#424—862no—
363#407—432no—
364C2×C22⋊C8C2×D4312yes—
365#405—862no—
366#324—431no—
367#324—431no—
368#324—432no—
369#324—432no—
370#324—432no—
371#324C2×D4311yescharacteristic
372#324C2×D4311yescharacteristic
373#324C2×D4312yes—
374#323—432no—
375#323—432no—
376C43#1741711yescharacteristic, complemented, Sylow
377C22×Q8—431no—
378C22×D4—431no—
379C23×C4—431no—
380C23×C4C4×D4311yescharacteristic
381C23×C4C4×D4311yescharacteristic
382C23×C4C22×D4311yescharacteristic
383C2×M16—862no—
384C22×C8—22no—
385#126—862no—
386#126—862no—
387#126—862no—
388#126—862no—
389#125—862no—
390#125—862no—
391#125—862no—
392#125—862no—
393#125—862no—
394#125—862no—
395#123—862no—
396#123—862no—
397#123—862no—
398#123—862no—
399C22⋊Q8—862no—
400C22⋊Q8—862no—
401C22⋊Q8—862no—
402C22⋊Q8—862no—
403C4×Q8—862no—
404C4×Q8—862no—
405C4×D4—861no—
406C4×D4—861no—
407C4×D4—861no—
408C4×D4—861no—
409#117—432no—
410#117—432no—
411#117—432no—
412#117—432no—
413#117—862no—
414#117—862no—
415#117—861no—
416#117—861no—
417#117—861no—
418#117—861no—
419C2×C4⋊C4—22no—
420C2×C4⋊C4—22no—
421C2×C4⋊C4—431no—
422C2×C4⋊C4—431no—
423C2×C4⋊C4—431no—
424C2×C4⋊C4—431no—
425C2×C4⋊C4—431no—
426C2×C4⋊C4—431no—
427C2×C4⋊C4—431no—
428C2×C4⋊C4—431no—
429C2×C4⋊C4—431no—
430C2×C4⋊C4—431no—
431C2×C4⋊C4—431no—
432C2×C4⋊C4—431no—
433C2×C4⋊C4C4×D4311yescharacteristic
434C2×C4⋊C4C4×D4311yescharacteristic
435C2×C4⋊C4C22×D4311yescharacteristic
436C2×C4⋊C4C22×D4311yescharacteristic
437C2×C22⋊C4—431no—
438C2×C22⋊C4—431no—
439C2×C22⋊C4—431no—
440C2×C22⋊C4—431no—
441C2×C22⋊C4—431no—
442C2×C22⋊C4—431no—
443C2×C22⋊C4—431no—
444C2×C22⋊C4—431no—
445C2×C42—431no—
446C2×C42—431no—
447C2×C42—431no—
448C2×C42—431no—
449C2×C42—431no—
450C4⋊C8—862no—
451C4⋊C8—862no—
452C4⋊C8—862no—
453C4⋊C8—862no—
454C22⋊C8—22no—
455C22⋊C8—432no—
456C22⋊C8—432no—
457C22⋊C8—862no—
458C22⋊C8C22×D4312yes—
459C22⋊C8C22×D4312yes—
460#97—862no—
461#97—862no—
462C4×C8—862no—
463C4×C8—862no—
464C24—431no—
465C24C2×C4×D4311yescharacteristic
466C2×Q8—862no—
467C2×Q8—862no—
468C2×Q8—1721no—
469C2×D4—861no—
470C2×D4—861no—
471C2×D4—1722no—
472C22×C4—21no—
473C22×C4—21no—
474C22×C4—21no—
475C22×C4—21no—
476C22×C4—22no—
477C22×C4—42no—
478C22×C4—41no—
479C22×C4—42no—
480C22×C4—431no—
481C22×C4—431no—
482C22×C4—431no—
483C22×C4—431no—
484C22×C4—431no—
485C22×C4—431no—
486C22×C4—431no—
487C22×C4—861no—
488C22×C4—861no—
489C22×C4—862no—
490C22×C4—1721no—
491C22×C4C2×C4×D4311yescharacteristic
492C22×C4C2×C4×D4311yescharacteristic
493C22×C4C2×C4×D4311yescharacteristic
494C22×C4C2×C4×D4311yescharacteristic
495C22×C4C2×C4×D4311yescharacteristic
496C22×C4D4×D4312yes—
497C22×C4D4×D4312yes—
498C22×C4C23×D4311yescharacteristic
499M16—1724no—
500C2×C8—22no—
501C2×C8—22no—
502C2×C8—44no—
503C2×C8—862no—
504C2×C8—862no—
505C4⋊C4—22no—
506C4⋊C4—22no—
507C4⋊C4—22no—
508C4⋊C4—22no—
509C4⋊C4—432no—
510C4⋊C4—432no—
511C4⋊C4—432no—
512C4⋊C4—432no—
513C4⋊C4—862no—
514C4⋊C4—861no—
515C4⋊C4—861no—
516C4⋊C4—861no—
517C4⋊C4—861no—
518C4⋊C4—861no—
519C4⋊C4—861no—
520C4⋊C4—862no—
521C4⋊C4—862no—
522C4⋊C4—862no—
523C4⋊C4—862no—
524C4⋊C4—862no—
525C4⋊C4—862no—
526C22⋊C4—431no—
527C22⋊C4—431no—
528C22⋊C4—431no—
529C22⋊C4—431no—
530C22⋊C4—432no—
531C22⋊C4—432no—
532C22⋊C4—862no—
533C22⋊C4—861no—
534C22⋊C4—861no—
535C22⋊C4—862no—
536C22⋊C4—861no—
537C22⋊C4—861no—
538C22⋊C4—862no—
539C22⋊C4—862no—
540C42—432no—
541C42—432no—
542C42—432no—
543C42—432no—
544C42—861no—
545C42—861no—
546C42—861no—
547C42—861no—
548C42—861no—
549C42—861no—
550C23—22no—
551C23—21no—
552C23—21no—
553C23—41no—
554C23—861no—
555C23—861no—
556C23—861no—
557C23—1721no—
558C23—1721no—
559C23C22⋊C4×D4311yescharacteristic
560C23C22⋊C4×D4311yescharacteristic
561C23C22×C4×D4311yescharacteristic
562Q8—1724no—
563D4—1722no—
564D4—1722no—
565C2×C4—21no—
566C2×C4—24no—
567C2×C4—21no—
568C2×C4—21no—
569C2×C4—21no—
570C2×C4—21no—
571C2×C4—21no—
572C2×C4—21no—
573C2×C4—41no—
574C2×C4—42no—
575C2×C4—41no—
576C2×C4—42no—
577C2×C4—42no—
578C2×C4—42no—
579C2×C4—42no—
580C2×C4—41no—
581C2×C4—41no—
582C2×C4—431no—
583C2×C4—431no—
584C2×C4—431no—
585C2×C4—431no—
586C2×C4—432no—
587C2×C4—432no—
588C2×C4—861no—
589C2×C4—861no—
590C2×C4—861no—
591C2×C4—861no—
592C2×C4—861no—
593C2×C4—861no—
594C2×C4—861no—
595C2×C4—861no—
596C2×C4—861no—
597C2×C4—1722no—
598C2×C4—1722no—
599C2×C4—1721no—
600C2×C4—1721no—
601C2×C4—1721no—
602C2×C4—1721no—
603C2×C4C22⋊C4×D4312yes—
604C2×C4#1306333112yes—
605C2×C4C2×D4×D4312yes—
606C8—42no—
607C8—42no—
608C8—1722no—
609C8—1722no—
610C22—21no—
611C22—21no—
612C22—21no—
613C22—21no—
614C22—21no—
615C22—21no—
616C22—21no—
617C22—42no—
618C22—42no—
619C22—3441no—
620C22—3441no—
621C22—1721no—
622C22—1721no—
623C22—1721no—
624C22#1458287112yes—
625C22C2×C22⋊C4×D4311yescharacteristic
626C22C2×#1306333111yescharacteristic
627C22#1458366511yescharacteristic
628C4—22no—
629C4—22no—
630C4—22no—
631C4—41no—
632C4—41no—
633C4—41no—
634C4—861no—
635C4—861no—
636C4—862no—
637C4—861no—
638C4—861no—
639C4—862no—
640C4—1721no—
641C4—1721no—
642C4—1721no—
643C2—21no—
644C2—21no—
645C2—22no—
646C2—41no—
647C2—3441no—
648C2#1914304111yescharacteristic
649C2C2×#1458287111yescharacteristic
650C2#1914307511yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D43
commutatorC23×C43C23×C4
FrattiniC22×C4C23×D43
FittingC2×C43×#324C2
socleC22×C43C22×C22⋊C4
prime radicalC22×C22⋊D43C2×C4
cosocleC22×C4×C43C24
hypercenterC2×#324D43
hypocenterC43#17417
LCSG ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#324

Complements

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

NH ≅ G/Ntype
2. #19143249C2semidirect
3. #19132963C2semidirect
4. #19132949C2semidirect
6. #19132937C2semidirect
7. #19132928C2semidirect
8. #19132925C2semidirect
9. #19132917C2semidirect
10. #19132908C2semidirect
11. C2×C43×#324C2semidirect
328. C2×#324D43semidirect
376. C43#17417semidirect

Maximal subgroups

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

subgroupindex
C2×#145835842
#191432492
#191329632
#191329492
#191329412
#191329372
#191329282
#191329252
#191329172
#191329082
C2×C43×#3242
#1741743