Finite Group Databasebeta

← #25033308

Subgroups — #25033308

Order 11008.

1934 conjugacy classes of subgroups.

The subgroup lattice has 614 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13063324C211yesmaximal, characteristic
2C2×#14582820C212yesmaximal
3C2×#14582819C212yesmaximal
4C2×#14582796C211yesmaximal, characteristic
5C2×#14582768C212yesmaximal
6#19132860C211yesmaximal, characteristic
7#19132859C211yesmaximal, characteristic
8#19132858C211yesmaximal, characteristic
9Dic43⋊#95C212yesmaximal
10#95×Dic43C211yesmaximal, characteristic
11C43×#1444C211yesmaximal, characteristic
12C23×Dic86C2212yes—
13C2×#13063324—28no—
14C2×#13063324—24no—
15C22×C4⋊Dic43C2211yescharacteristic
16C22×C4⋊Dic43C2211yescharacteristic
17C22×C4⋊Dic43C2212yes—
18C22×Dic43⋊C4C2211yescharacteristic
19C22×Dic43⋊C4C2211yescharacteristic
20C22×Dic43⋊C4C2212yes—
21C22×Dic43⋊C4C2212yes—
22C22×Dic43⋊C4C2212yes—
23C22×Dic43⋊C4C2211yescharacteristic
24C22×C4×Dic43C2211yescharacteristic
25C22×C4×Dic43C2212yes—
26#14582820—28no—
27#14582819—28no—
28#14582796—24no—
29#14582768—28no—
30C2×C43⋊#95C2212yes—
31C2×C43⋊#95C2212yes—
32C2×C43⋊#95C2212yes—
33C2×C43⋊#95C2211yescharacteristic
34C2×C43⋊#95C2212yes—
35C2×C43⋊#95C2211yescharacteristic
36C22×C4⋊C4×C43C2211yescharacteristic
37C22×C4⋊C4×C43C2212yes—
38C2×#95×C43C2212yes—
39C2×#95×C43C2211yescharacteristic
40C2×#95×C43C2211yescharacteristic
41C22×Dic86—24no—
42C22×Dic86—24no—
43C22×Dic86—24no—
44C22×Dic86—24no—
45C22×Dic86—24no—
46C22×Dic86—42no—
47C22×Dic86—42no—
48C23×Dic43C2311yescharacteristic
49C23×Dic43C2312yes—
50C23×Dic43C2311yescharacteristic
51C23×Dic43C2311yescharacteristic
52C23×Dic43C2312yes—
53C23×Dic43C2311yescharacteristic
54#13063324—232no—
55C2×C4⋊Dic43—22no—
56C2×C4⋊Dic43—24no—
57C2×C4⋊Dic43—24no—
58C2×C4⋊Dic43—22no—
59C2×C4⋊Dic43—24no—
60C2×C4⋊Dic43—24no—
61C2×C4⋊Dic43—42no—
62C2×Dic43⋊C4—22no—
63C2×Dic43⋊C4—24no—
64C2×Dic43⋊C4—24no—
65C2×Dic43⋊C4—22no—
66C2×Dic43⋊C4—24no—
67C2×Dic43⋊C4—22no—
68C2×Dic43⋊C4—22no—
69C2×Dic43⋊C4—24no—
70C2×Dic43⋊C4—24no—
71C2×Dic43⋊C4—24no—
72C2×Dic43⋊C4—24no—
73C2×Dic43⋊C4—24no—
74C2×Dic43⋊C4—42no—
75C2×Dic43⋊C4—42no—
76C2×Dic43⋊C4D418yes—
77C2×Dic43⋊C4Q814yescomplemented
78C2×C4×Dic43—24no—
79C2×C4×Dic43—24no—
80C2×C4×Dic43—24no—
81C2×C4×Dic43D414yes—
82C2×C4×Dic43Q818yescomplemented
83C43⋊#95—22no—
84C43⋊#95—24no—
85C43⋊#95—24no—
86C43⋊#95—24no—
87C43⋊#95D418yes—
88C43⋊#95Q814yescomplemented
89C23×C4×C43C2311yescharacteristic
90C23×C4×C43C2312yes—
91C23×C4×C43C2311yescharacteristic
92C23×C4×C43C2311yescharacteristic
93C23×C4×C43C2312yes—
94C2×C4⋊C4×C43—24no—
95C2×C4⋊C4×C43—22no—
96C2×C4⋊C4×C43—24no—
97C2×C4⋊C4×C43—24no—
98C2×C4⋊C4×C43—42no—
99#95×C43—22no—
100#95×C43—24no—
101#95×C43Q814yescomplemented
102C24×C43C2411yescharacteristic
103C22×C4×C43—22no—
104C22×C4×C43—22no—
105C22×C4×C43—22no—
106C22×C4×C43—21no—
107C22×C4×C43—22no—
108C22×C4×C43—22no—
109C22×C4×C43—22no—
110C22×C4×C43—22no—
111C22×C4×C43—21no—
112C22×C4×C43—22no—
113C22×C4×C43—22no—
114C22×C4×C43—22no—
115C22×C4×C43—21no—
116C22×C4×C43—22no—
117C22×C4×C43—22no—
118C22×C4×C43—22no—
119C22×C4×C43—21no—
120C22×C4×C43—21no—
121C22×C4×C43—22no—
122C22×C4×C43—22no—
123C22×C4×C43—22no—
124C22×C4×C43C2×D414yes—
125C22×C4×C43C2×D412yes—
126C22×C4×C43C2×D414yes—
127C22×C4×C43C2×Q812yes—
128C22×C4×C43C2×Q814yes—
129C22×C4×C43C2×Q812yes—
130C22×C4×C43C2×Q812yes—
131C22×C4×C43C2×Q814yes—
132C22×Dic43—22no—
133C22×Dic43—22no—
134C22×Dic43—22no—
135C22×Dic43—21no—
136C22×Dic43—22no—
137C22×Dic43—22no—
138C22×Dic43—22no—
139C22×Dic43—22no—
140C22×Dic43—21no—
141C22×Dic43—22no—
142C22×Dic43—22no—
143C22×Dic43—22no—
144C22×Dic43—21no—
145C22×Dic43—22no—
146C22×Dic43—21no—
147C22×Dic43—21no—
148C22×Dic43—22no—
149C22×Dic43—22no—
150C22×Dic43—21no—
151C22×Dic43—21no—
152C22×Dic43—22no—
153C22×Dic43—22no—
154C22×Dic43C2×D414yes—
155C22×Dic43C2×D414yes—
156C22×Dic43C2×D412yes—
157C22×Dic43C2×D414yes—
158C22×Dic43C2×D414yes—
159C22×Dic43C2×D412yes—
160C22×Dic43C2×Q812yes—
161C22×Dic43C2×Q814yes—
162C22×Dic43C2×Q814yes—
163C22×Dic43C2×Q814yes—
164C22×Dic43C2×Q812yes—
165C22×Dic43#4112yes—
166C2×Dic86—216no—
167C2×Dic86—48no—
168C2×Dic86—48no—
169C2×Dic86—48no—
170C2×Dic86—48no—
171C2×Dic86—48no—
172C2×Dic86—48no—
173C4⋊C4×C43—28no—
174C4⋊C4×C43—48no—
175C4⋊Dic43—28no—
176C4⋊Dic43—48no—
177C4⋊Dic43—44no—
178Dic43⋊C4—216no—
179Dic43⋊C4—28no—
180Dic43⋊C4—48no—
181Dic43⋊C4—48no—
182Dic43⋊C4—44no—
183Dic43⋊C4—44no—
184C4×Dic43—28no—
185C4×Dic43—216no—
186C23×C43C22×D411yescharacteristic
187C23×C43C22×D412yes—
188C23×C43C22×D412yes—
189C23×C43C22×Q812yes—
190C23×C43C22×Q811yescharacteristic
191C23×C43C22×Q811yescharacteristic
192C23×C43C22×Q811yescharacteristic
193C23×C43C2×#4111yescharacteristic
194C23×C43H(5,𝔽2)11yescharacteristic
195C23×C43H(5,𝔽2)11yescharacteristic
196C23×C432−1+412yes—
197C2×C4×C43—22no—
198C2×C4×C43—24no—
199C2×C4×C43—22no—
200C2×C4×C43—24no—
201C2×C4×C43—24no—
202C2×C4×C43—24no—
203C2×C4×C43—24no—
204C2×C4×C43—24no—
205C2×C4×C43—24no—
206C2×C4×C43—24no—
207C2×C4×C43—24no—
208C2×C4×C43—22no—
209C2×C4×C43—24no—
210C2×C4×C43—24no—
211C2×C4×C43—24no—
212C2×C4×C43—41no—
213C2×C4×C43—42no—
214C2×C4×C43—42no—
215C2×C4×C43—41no—
216C2×C4×C43—42no—
217C2×C4×C43—42no—
218C2×C4×C43—42no—
219C2×C4×C43—41no—
220C2×C4×C43—41no—
221C2×C4×C43—41no—
222C2×C4×C43—42no—
223C2×C4×C43—42no—
224C2×C4×C43C4⋊Q814yes—
225C2×C4×C43C4⋊Q818yescomplemented
226C2×Dic43—22no—
227C2×Dic43—24no—
228C2×Dic43—22no—
229C2×Dic43—24no—
230C2×Dic43—24no—
231C2×Dic43—24no—
232C2×Dic43—24no—
233C2×Dic43—24no—
234C2×Dic43—24no—
235C2×Dic43—24no—
236C2×Dic43—24no—
237C2×Dic43—22no—
238C2×Dic43—24no—
239C2×Dic43—24no—
240C2×Dic43—24no—
241C2×Dic43—41no—
242C2×Dic43—42no—
243C2×Dic43—42no—
244C2×Dic43—41no—
245C2×Dic43—42no—
246C2×Dic43—42no—
247C2×Dic43—42no—
248C2×Dic43—41no—
249C2×Dic43—41no—
250C2×Dic43—41no—
251C2×Dic43—42no—
252C2×Dic43—42no—
253C2×Dic43#12014yes—
254C2×Dic43C22⋊Q818yes—
255C2×Dic43C22⋊Q814yes—
256C2×Dic43#12714yes—
257C2×Dic43C4⋊Q814yes—
258C2×Dic43C4⋊Q818yes—
259C2×Dic43C4⋊Q818yescomplemented
260Dic86—432no—
261#15143—431nomaximal, Sylow
262C22×C43C2×#12011yescharacteristic
263C22×C43C2×C22⋊Q811yescharacteristic
264C22×C43C2×C22⋊Q812yes—
265C22×C43C2×#12711yescharacteristic
266C22×C43C2×C4⋊Q811yescharacteristic
267C22×C43C2×C4⋊Q812yes—
268C22×C43C2×C4⋊Q812yes—
269C22×C43C2×C4⋊Q811yescharacteristic
270C22×C43C2×C4⋊Q812yes—
271C22×C43#53511yescharacteristic
272C22×C43#53611yescharacteristic
273C22×C43#54412yes—
274C22×C43#54412yes—
275C22×C43D4212yes—
276C22×C43D4212yes—
277C22×C43#54712yes—
278C22×C43D4×Q812yes—
279C22×C43D4×Q812yes—
280C22×C43D4×Q812yes—
281C22×C43#55411yescharacteristic
282C22×C43#55411yescharacteristic
283C22×C43Q8211yescharacteristic
284C22×C43Q8211yescharacteristic
285C4×C43—24no—
286C4×C43—28no—
287C4×C43—44no—
288C4×C43—42no—
289C4×C43—81no—
290Dic43—24no—
291Dic43—28no—
292Dic43—44no—
293Dic43—42no—
294Dic43—81no—
295Dic43#39518yescomplemented
296C22×C4⋊Q8—431no—
297C2×#395—432no—
298C2×#395—432no—
299C2×#389—431no—
300C2×#384—432no—
301#1444—431no—
302#1444—431no—
303#1444—431no—
304#1444D4311yescharacteristic
305C4⋊#95—432no—
306C4×#95—431no—
307C2×C43C2×#39511yescharacteristic
308C2×C43#243311yescharacteristic
309C2×C43#243411yescharacteristic
310C2×C43#244012yes—
311C2×C43#244012yes—
312C2×C43#254211yescharacteristic
313C2×C43#255112yes—
314C2×C43#255112yes—
315C2×C43#256711yescharacteristic
316C2×C43#266011yescharacteristic
317C2×C43#286811yescharacteristic
318C23×Q8—432no—
319C2×C4⋊Q8—864no—
320C2×C4⋊Q8—868no—
321C22×C4⋊C4—432no—
322C22×C4⋊C4—431no—
323C22×C4⋊C4—431no—
324C22×C4⋊C4—431no—
325C22×C4⋊C4—431no—
326C22×C4⋊C4—431no—
327C22×C4⋊C4—432no—
328C22×C4⋊C4—432no—
329C22×C4⋊C4—432no—
330C22×C4⋊C4C2×D4311yescharacteristic
331C22×C4⋊C4C2×D4312yes—
332C22×C42—431no—
333C22×C42—432no—
334#395—868no—
335#395—868no—
336#389—864no—
337#384—868no—
338C2×#95—432no—
339C2×#95—431no—
340C2×#95—432no—
341C2×#95—432no—
342C2×#95—432no—
343C2×#95—431no—
344C2×#95C2×D4312yes—
345C2×#95C2×D4311yescharacteristic
346C2×#95C2×D4311yescharacteristic
347C43#1514311yescharacteristic, complemented, Sylow
348C22×Q8—864no—
349C22×Q8—864no—
350C22×Q8—864no—
351C22×Q8—864no—
352C22×Q8—864no—
353C22×Q8—1722no—
354C22×Q8—1722no—
355C23×C4—431no—
356C23×C4—431no—
357C23×C4—432no—
358C23×C4—432no—
359C23×C4—431no—
360C23×C4—431no—
361C23×C4C22×D4311yescharacteristic
362C23×C4C22×D4312yes—
363C23×C4C22×D4311yescharacteristic
364C23×C4C22×D4311yescharacteristic
365C23×C4C22×D4312yes—
366C4⋊Q8—8632no—
367C2×C4⋊C4—24no—
368C2×C4⋊C4—22no—
369C2×C4⋊C4—24no—
370C2×C4⋊C4—24no—
371C2×C4⋊C4—42no—
372C2×C4⋊C4—438no—
373C2×C4⋊C4—434no—
374C2×C4⋊C4—864no—
375C2×C4⋊C4—864no—
376C2×C4⋊C4—864no—
377C2×C4⋊C4—862no—
378C2×C4⋊C4—862no—
379C2×C4⋊C4—862no—
380C2×C4⋊C4—864no—
381C2×C4⋊C4—864no—
382C2×C4⋊C4—862no—
383C2×C4⋊C4—862no—
384C2×C4⋊C4—864no—
385C2×C4⋊C4—864no—
386C2×C4⋊C4—864no—
387C2×C4⋊C4—864no—
388C2×C4⋊C4—862no—
389C2×C4⋊C4—864no—
390C2×C4⋊C4—864no—
391C2×C4⋊C4—864no—
392C2×C4⋊C4—1722no—
393C2×C4⋊C4—1722no—
394C2×C4⋊C4—1722no—
395C2×C42—434no—
396C2×C42—438no—
397C2×C42—864no—
398C2×C42—864no—
399C2×C42—864no—
400#95—22no—
401#95—24no—
402#95—438no—
403#95—434no—
404#95—864no—
405#95—864no—
406#95—862no—
407#95—864no—
408#95Dic8614yescomplemented
409C24C23×D4311yescharacteristic
410C2×Q8—8616no—
411C2×Q8—1728no—
412C2×Q8—1728no—
413C2×Q8—1728no—
414C2×Q8—1728no—
415C2×Q8—1728no—
416C2×Q8—1728no—
417C22×C4—22no—
418C22×C4—22no—
419C22×C4—22no—
420C22×C4—22no—
421C22×C4—22no—
422C22×C4—22no—
423C22×C4—22no—
424C22×C4—21no—
425C22×C4—22no—
426C22×C4—22no—
427C22×C4—22no—
428C22×C4—22no—
429C22×C4—21no—
430C22×C4—22no—
431C22×C4—22no—
432C22×C4—22no—
433C22×C4—21no—
434C22×C4—22no—
435C22×C4—22no—
436C22×C4—21no—
437C22×C4—21no—
438C22×C4—432no—
439C22×C4—434no—
440C22×C4—434no—
441C22×C4—432no—
442C22×C4—432no—
443C22×C4—434no—
444C22×C4—434no—
445C22×C4—432no—
446C22×C4—434no—
447C22×C4—434no—
448C22×C4—434no—
449C22×C4—432no—
450C22×C4—862no—
451C22×C4—862no—
452C22×C4—862no—
453C22×C4—861no—
454C22×C4—862no—
455C22×C4—861no—
456C22×C4—862no—
457C22×C4—862no—
458C22×C4—861no—
459C22×C4—862no—
460C22×C4—862no—
461C22×C4—862no—
462C22×C4—862no—
463C22×C4—861no—
464C22×C4—862no—
465C22×C4—862no—
466C22×C4—862no—
467C22×C4—861no—
468C22×C4—862no—
469C22×C4—862no—
470C22×C4—861no—
471C22×C4—861no—
472C22×C4C2×Dic8612yes—
473C22×C4C2×Dic8614yes—
474C22×C4D4×D4314yes—
475C22×C4D4×D4312yes—
476C22×C4D4×D4314yes—
477C22×C4Q8×D4312yes—
478C22×C4Q8×D4312yes—
479C22×C4Q8×D4314yes—
480C4⋊C4—28no—
481C4⋊C4—48no—
482C4⋊C4—8616no—
483C4⋊C4—868no—
484C4⋊C4—868no—
485C4⋊C4—1728no—
486C4⋊C4—1728no—
487C4⋊C4—1724no—
488C4⋊C4—1724no—
489C4⋊C4—1724no—
490C4⋊C4—1728no—
491C42—868no—
492C42—8616no—
493C23C2×D4×D4312yes—
494C23C2×D4×D4312yes—
495C23C2×D4×D4311yescharacteristic
496C23C2×Q8×D4311yescharacteristic
497C23C2×Q8×D4311yescharacteristic
498C23C2×Q8×D4312yes—
499C23C22×Dic8611yescharacteristic
500C23#41×D4311yescharacteristic
501C23#1306337011yescharacteristic
502C23#1306337111yescharacteristic
503C23#1306337212yes—
504Q8—17232no—
505C2×C4—24no—
506C2×C4—24no—
507C2×C4—24no—
508C2×C4—24no—
509C2×C4—22no—
510C2×C4—24no—
511C2×C4—22no—
512C2×C4—24no—
513C2×C4—24no—
514C2×C4—24no—
515C2×C4—24no—
516C2×C4—24no—
517C2×C4—22no—
518C2×C4—24no—
519C2×C4—24no—
520C2×C4—41no—
521C2×C4—42no—
522C2×C4—42no—
523C2×C4—41no—
524C2×C4—42no—
525C2×C4—42no—
526C2×C4—42no—
527C2×C4—41no—
528C2×C4—41no—
529C2×C4—41no—
530C2×C4—42no—
531C2×C4—42no—
532C2×C4—434no—
533C2×C4—438no—
534C2×C4—434no—
535C2×C4—438no—
536C2×C4—434no—
537C2×C4—434no—
538C2×C4—438no—
539C2×C4—864no—
540C2×C4—864no—
541C2×C4—862no—
542C2×C4—864no—
543C2×C4—862no—
544C2×C4—864no—
545C2×C4—864no—
546C2×C4—864no—
547C2×C4—864no—
548C2×C4—864no—
549C2×C4—864no—
550C2×C4—864no—
551C2×C4—862no—
552C2×C4—864no—
553C2×C4—864no—
554C2×C4—1721no—
555C2×C4—1721no—
556C2×C4—1721no—
557C2×C4—1722no—
558C2×C4—1722no—
559C2×C4—1721no—
560C2×C4—1722no—
561C2×C4—1722no—
562C2×C4—1721no—
563C2×C4—1722no—
564C2×C4—1722no—
565C2×C4—1722no—
566C2×C4#1306332414yes—
567C2×C4#1306332418yescomplemented
568C22#120×D4311yescharacteristic
569C22C22⋊Q8×D4311yescharacteristic
570C22C22⋊Q8×D4312yes—
571C22#127×D4311yescharacteristic
572C22C4⋊Q8×D4312yes—
573C22C4⋊Q8×D4311yescharacteristic
574C22C4⋊Q8×D4312yes—
575C22C2×#1306332412yes—
576C22C2×#1306332411yescharacteristic
577C22#1458346511yescharacteristic
578C22#1458347111yescharacteristic
579C22#1458352812yes—
580C22#1458352912yes—
581C22#1458353112yes—
582C22#1458353312yes—
583C22#1458354712yes—
584C22#1458356212yes—
585C22#1458356212yes—
586C22D4×Dic8612yes—
587C22#1458360511yescharacteristic
588C22#1458360811yescharacteristic
589C22#1458362911yescharacteristic
590C22Q8×Dic8611yescharacteristic
591C4—24no—
592C4—28no—
593C4—44no—
594C4—42no—
595C4—81no—
596C4—438no—
597C4—864no—
598C4—868no—
599C4—3441no—
600C4—1724no—
601C4—1722no—
602C2#395×D4311yescharacteristic
603C2#1913822711yescharacteristic
604C2#1913823711yescharacteristic
605C2#1913829212yes—
606C2#1913829612yes—
607C2#1913954311yescharacteristic
608C2#1913962012yes—
609C2#1913962312yes—
610C2#1913980211yescharacteristic
611C2#1914071811yescharacteristic
612C2#1914299211yescharacteristic
subgroupG/H
center, FrattiniC24C23×D43
commutator, socle, prime radical, cosocleC24×C43C24
FittingC43×#1444C2
hypercenter#1444D43
hypocenterC43#15143
LCSG ▷ C24×C43 ▷ C43
UCSC1 ◁ C24 ◁ #1444

Complements

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

NH ≅ G/Ntype
77. C2×Dic43⋊C4Q8semidirect
82. C2×C4×Dic43Q8semidirect
88. C43⋊#95Q8semidirect
101. #95×C43Q8semidirect
225. C2×C4×C43C4⋊Q8semidirect
259. C2×Dic43C4⋊Q8semidirect
295. Dic43#395semidirect
347. C43#15143semidirect
408. #95Dic86semidirect
567. C2×C4#13063324semidirect

Maximal subgroups

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

subgroupindex
C22×#130633242
C2×#145828202
C2×#145828192
C2×#145827962
C2×#145827682
#191328602
#191328592
#191328582
Dic43⋊#952
#95×Dic432
C43×#14442
#1514343