Finite Group Databasebeta

← #25033244

Subgroups — #25033244

Order 11008.

1814 conjugacy classes of subgroups.

The subgroup lattice has 676 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14582835C212yesmaximal
2C2×#14582796C212yesmaximal, complemented
3C2×#14582768C211yesmaximal, characteristic, complemented
4C2×#14582757C212yesmaximal
5C2×C22⋊C4×Dic43C211yesmaximal, characteristic
6#19132861C212yesmaximal, complemented
7#19132860C211yesmaximal, characteristic, complemented
8#19132858C211yesmaximal, characteristic, complemented
9#19132840C211yesmaximal, characteristic
10Dic43⋊#95C211yesmaximal, characteristic, complemented
11C43×#1439C211yesmaximal, characteristic
12C24×Dic43C2211yescharacteristic
13C22×C4⋊Dic43C2212yes—
14C22×C4⋊Dic43C2211yescharacteristic
15C22×Dic43⋊C4C2212yes—
16C22×Dic43⋊C4C2212yes—
17C22×Dic43⋊C4C2212yes—
18C22×Dic43⋊C4C2212yes—
19C22×C22⋊Dic43C2212yes—
20C22×C22⋊Dic43C2211yescharacteristic
21C22×C4×Dic43C2211yescharacteristic
22C22×C4×Dic43C2211yescharacteristic
23#14582835—28no—
24#14582796—28no—
25#14582768—24no—
26#14582757—28no—
27C22⋊C4×Dic43—24no—
28C2×C43⋊#95C2212yes—
29C2×C43⋊#95C2212yes—
30C2×C43⋊#95C2211yescharacteristic
31C2×C43⋊#95C2211yescharacteristic
32C2×C43⋊#95C2211yescharacteristic
33C2×C43⋊#95C2212yes—
34C2×C43⋊#95C2212yes—
35C22×C4⋊C4×C43C2211yescharacteristic
36C22×C22⋊C4×C43C2212yes—
37C22×C22⋊C4×C43C2211yescharacteristic
38C2×#95×C43C2212yes—
39C2×#95×C43C2211yescharacteristic
40C23×Dic43—22no—
41C23×Dic43—24no—
42C23×Dic43—24no—
43C23×Dic43—22no—
44C23×Dic43Q814yes—
45C23×Dic43C2312yes—
46C23×Dic43C2311yescharacteristic
47C23×Dic43C2312yes—
48C23×Dic43C2311yescharacteristic
49C23×Dic43C2311yescharacteristic
50C23×Dic43C2311yescharacteristic
51C2×C4⋊Dic43—24no—
52C2×C4⋊Dic43—22no—
53C2×C4⋊Dic43—24no—
54C2×C4⋊Dic43—42no—
55C2×C4⋊Dic43—42no—
56C2×Dic43⋊C4—24no—
57C2×Dic43⋊C4—24no—
58C2×Dic43⋊C4—24no—
59C2×Dic43⋊C4—24no—
60C2×Dic43⋊C4—24no—
61C2×Dic43⋊C4—24no—
62C2×Dic43⋊C4—24no—
63C2×Dic43⋊C4—24no—
64C2×Dic43⋊C4—24no—
65C2×Dic43⋊C4—24no—
66C2×Dic43⋊C4—42no—
67C2×Dic43⋊C4D418yes—
68C2×C22⋊Dic43—22no—
69C2×C22⋊Dic43—22no—
70C2×C22⋊Dic43—24no—
71C2×C22⋊Dic43—24no—
72C2×C22⋊Dic43—42no—
73C2×C22⋊Dic43D414yes—
74C2×C4×Dic43—24no—
75C2×C4×Dic43—24no—
76C2×C4×Dic43—22no—
77C2×C4×Dic43D414yes—
78C43⋊#95—22no—
79C43⋊#95—24no—
80C43⋊#95—22no—
81C43⋊#95—24no—
82C43⋊#95—24no—
83C43⋊#95—22no—
84C43⋊#95—24no—
85C25×C43C2311yescharacteristic
86C23×C4×C43C2312yes—
87C23×C4×C43C2312yes—
88C23×C4×C43C2311yescharacteristic
89C23×C4×C43C2311yescharacteristic
90C2×C4⋊C4×C43—22no—
91C2×C4⋊C4×C43—42no—
92C2×C22⋊C4×C43—22no—
93C2×C22⋊C4×C43—22no—
94C2×C22⋊C4×C43—24no—
95C2×C22⋊C4×C43—24no—
96C2×C22⋊C4×C43—42no—
97C2×C22⋊C4×C43Q814yes—
98#95×C43—24no—
99#95×C43—22no—
100C24×C43—21no—
101C24×C43—22no—
102C24×C43—21no—
103C24×C43—21no—
104C24×C43—21no—
105C24×C43—22no—
106C24×C43—22no—
107C24×C43—22no—
108C24×C43C2×D412yes—
109C24×C43C2×Q812yes—
110C24×C43C2×Q812yes—
111C24×C43C2411yescharacteristic
112C22×C4×C43—22no—
113C22×C4×C43—21no—
114C22×C4×C43—22no—
115C22×C4×C43—22no—
116C22×C4×C43—22no—
117C22×C4×C43—22no—
118C22×C4×C43—22no—
119C22×C4×C43—22no—
120C22×C4×C43—22no—
121C22×C4×C43—21no—
122C22×C4×C43—22no—
123C22×C4×C43—22no—
124C22×C4×C43—22no—
125C22×C4×C43—22no—
126C22×C4×C43—22no—
127C22×C4×C43—22no—
128C22×C4×C43—22no—
129C22×C4×C43—22no—
130C22×C4×C43—22no—
131C22×C4×C43C2×D414yes—
132C22×C4×C43C2×D412yes—
133C22×C4×C43C2×Q812yes—
134C22×C4×C43C2×Q812yes—
135C22×C4×C43#4112yes—
136C22×Dic43—28no—
137C22×Dic43—216no—
138C22×Dic43—21no—
139C22×Dic43—22no—
140C22×Dic43—21no—
141C22×Dic43—22no—
142C22×Dic43—22no—
143C22×Dic43—22no—
144C22×Dic43—22no—
145C22×Dic43—22no—
146C22×Dic43—22no—
147C22×Dic43—22no—
148C22×Dic43—22no—
149C22×Dic43—21no—
150C22×Dic43—22no—
151C22×Dic43—22no—
152C22×Dic43—21no—
153C22×Dic43—22no—
154C22×Dic43—22no—
155C22×Dic43—22no—
156C22×Dic43—22no—
157C22×Dic43—22no—
158C22×Dic43—22no—
159C22×Dic43—22no—
160C22×Dic43—22no—
161C22×Dic43—44no—
162C22×Dic43—48no—
163C22×Dic43—44no—
164C22×Dic43C2×D414yes—
165C22×Dic43C2×D412yes—
166C22×Dic43C2×D412yes—
167C22×Dic43C2×D412yes—
168C22×Dic43C2×D412yes—
169C22×Dic43C2×D414yes—
170C22×Dic43C2×Q812yes—
171C22×Dic43C2×Q812yes—
172C22×Dic43#4112yes—
173C22×Dic43#4114yes—
174C22×Dic43#4112yes—
175C4⋊C4×C43—44no—
176C22⋊C4×C43—28no—
177C22⋊C4×C43—48no—
178C22⋊Dic43—28no—
179C22⋊Dic43—48no—
180C4⋊Dic43—48no—
181C4⋊Dic43—44no—
182Dic43⋊C4—216no—
183Dic43⋊C4—48no—
184Dic43⋊C4—48no—
185Dic43⋊C4—48no—
186C4×Dic43—28no—
187C4×Dic43—44no—
188C23×C43—22no—
189C23×C43—22no—
190C23×C43—22no—
191C23×C43—24no—
192C23×C43—22no—
193C23×C43—22no—
194C23×C43—22no—
195C23×C43—24no—
196C23×C43—24no—
197C23×C43—24no—
198C23×C43—24no—
199C23×C43—24no—
200C23×C43—42no—
201C23×C43—41no—
202C23×C43—41no—
203C23×C43—41no—
204C23×C43—41no—
205C23×C43—42no—
206C23×C43—42no—
207C23×C43—42no—
208C23×C43—42no—
209C23×C43—42no—
210C23×C43C4⋊Q814yes—
211C23×C43C22×D411yescharacteristic
212C23×C43C22×D411yescharacteristic
213C23×C43C22×D412yes—
214C23×C43C22×Q811yescharacteristic
215C23×C43C22×Q811yescharacteristic
216C23×C43C2×#4111yescharacteristic
217C23×C43C2×#4111yescharacteristic
218C23×C43C2×#4112yes—
219C23×C43C2×#4111yescharacteristic
220C23×C43H(5,𝔽2)12yes—
221C23×C432−1+412yes—
222C2×C4×C43—22no—
223C2×C4×C43—22no—
224C2×C4×C43—24no—
225C2×C4×C43—24no—
226C2×C4×C43—22no—
227C2×C4×C43—24no—
228C2×C4×C43—24no—
229C2×C4×C43—24no—
230C2×C4×C43—24no—
231C2×C4×C43—41no—
232C2×C4×C43—42no—
233C2×C4×C43—41no—
234C2×C4×C43—42no—
235C2×C4×C43—42no—
236C2×C4×C43—42no—
237C2×C4×C43—42no—
238C2×C4×C43—42no—
239C2×C4×C43—42no—
240C2×C4×C43—42no—
241C2×C4×C43—42no—
242C2×C4×C43—42no—
243C2×C4×C43—42no—
244C2×C4×C43—42no—
245C2×C4×C43C22⋊Q814yes—
246C2×Dic43—22no—
247C2×Dic43—22no—
248C2×Dic43—24no—
249C2×Dic43—24no—
250C2×Dic43—22no—
251C2×Dic43—22no—
252C2×Dic43—24no—
253C2×Dic43—24no—
254C2×Dic43—24no—
255C2×Dic43—24no—
256C2×Dic43—24no—
257C2×Dic43—42no—
258C2×Dic43—41no—
259C2×Dic43—41no—
260C2×Dic43—41no—
261C2×Dic43—42no—
262C2×Dic43—41no—
263C2×Dic43—42no—
264C2×Dic43—42no—
265C2×Dic43—42no—
266C2×Dic43—42no—
267C2×Dic43—416no—
268C2×Dic43—42no—
269C2×Dic43—42no—
270C2×Dic43—42no—
271C2×Dic43—42no—
272C2×Dic43—42no—
273C2×Dic43—42no—
274C2×Dic43—42no—
275C2×Dic43#12114yes—
276C2×Dic43C22⋊Q814yes—
277C2×Dic43C22⋊Q818yes—
278C2×Dic43#12314yes—
279C2×Dic43#12318yes—
280C2×Dic43#12714yes—
281#15135—431nomaximal, Sylow
282C22×C43—24no—
283C22×C43—28no—
284C22×C43—42no—
285C22×C43—42no—
286C22×C43—44no—
287C22×C43—44no—
288C22×C43—44no—
289C22×C43—42no—
290C22×C43—42no—
291C22×C43—42no—
292C22×C43—42no—
293C22×C43C2×#12111yescharacteristic
294C22×C43C2×C22⋊Q811yescharacteristic
295C22×C43C2×C22⋊Q812yes—
296C22×C43C2×C22⋊Q811yescharacteristic
297C22×C43C2×#12312yes—
298C22×C43C2×#12311yescharacteristic
299C22×C43C2×#12711yescharacteristic
300C22×C43C2×C4⋊Q811yescharacteristic
301C22×C43#53211yescharacteristic
302C22×C43#53311yescharacteristic
303C22×C43#53311yescharacteristic
304C22×C43#53511yescharacteristic
305C22×C43#53611yescharacteristic
306C22×C43#54212yes—
307C22×C43#54412yes—
308C22×C43D4212yes—
309C22×C43#54712yes—
310C22×C43#54712yes—
311C22×C43D4×Q812yes—
312C22×C43#55012yes—
313C22×C43#55212yes—
314C22×C43#55312yes—
315C22×C43#55412yes—
316C4×C43—24no—
317C4×C43—44no—
318C4×C43—42no—
319C4×C43—82no—
320Dic43—24no—
321Dic43—42no—
322Dic43—44no—
323Dic43—42no—
324Dic43—82no—
325Dic43#39918yescomplemented
326C2×#399—432no—
327C2×#389—432no—
328C2×#384—431no—
329C2×#380—432no—
330C2×C4×C22⋊C4—431no—
331#1445—432no—
332#1444—431no—
333#1444—431no—
334#1439—431no—
335#1439D4311yescharacteristic
336C4⋊#95—431no—
337C2×C43—44no—
338C2×C43C2×#39911yescharacteristic
339C2×C43#242212yes—
340C2×C43#242312yes—
341C2×C43#244012yes—
342C2×C43#244112yes—
343C2×C43#248611yescharacteristic
344C2×C43#248711yescharacteristic
345C2×C43#254111yescharacteristic
346C2×C43#254211yescharacteristic
347C2×C43#262811yescharacteristic
348C2×C43#285711yescharacteristic
349C24×C4—431no—
350C22×C4⋊C4—432no—
351C22×C4⋊C4—432no—
352C22×C4⋊C4—432no—
353C22×C4⋊C4—432no—
354C22×C4⋊C4—432no—
355C22×C4⋊C4—431no—
356C22×C4⋊C4C2×D4311yescharacteristic
357C22×C22⋊C4—431no—
358C22×C22⋊C4—432no—
359C22×C22⋊C4C2×D4312yes—
360C22×C22⋊C4C2×D4311yescharacteristic
361C22×C42—431no—
362C22×C42—431no—
363#399—868no—
364#389—868no—
365#384—864no—
366#380—868no—
367C4×C22⋊C4—864no—
368C2×#95—432no—
369C2×#95—431no—
370C2×#95—432no—
371C2×#95—431no—
372C2×#95—432no—
373C2×#95—432no—
374C2×#95—431no—
375C2×#95C2×D4311yescharacteristic
376C2×#95C2×D4312yes—
377C43#1513511yescharacteristic, complemented, Sylow
378C25C22×D4311yescharacteristic
379C23×C4—431no—
380C23×C4—431no—
381C23×C4—434no—
382C23×C4—431no—
383C23×C4—432no—
384C23×C4—431no—
385C23×C4—432no—
386C23×C4—862no—
387C23×C4—864no—
388C23×C4—864no—
389C23×C4—862no—
390C23×C4C22×D4312yes—
391C23×C4C22×D4311yescharacteristic
392C23×C4C22×D4312yes—
393C23×C4C22×D4311yescharacteristic
394C2×C4⋊C4—22no—
395C2×C4⋊C4—42no—
396C2×C4⋊C4—438no—
397C2×C4⋊C4—864no—
398C2×C4⋊C4—864no—
399C2×C4⋊C4—864no—
400C2×C4⋊C4—864no—
401C2×C4⋊C4—864no—
402C2×C4⋊C4—864no—
403C2×C4⋊C4—864no—
404C2×C4⋊C4—864no—
405C2×C4⋊C4—864no—
406C2×C4⋊C4—864no—
407C2×C4⋊C4—864no—
408C2×C4⋊C4—862no—
409C2×C4⋊C4—864no—
410C2×C4⋊C4—1722no—
411C2×C4⋊C4—1722no—
412C2×C4⋊C4—1722no—
413C2×C22⋊C4—22no—
414C2×C22⋊C4—22no—
415C2×C22⋊C4—24no—
416C2×C22⋊C4—24no—
417C2×C22⋊C4—42no—
418C2×C22⋊C4—434no—
419C2×C22⋊C4—862no—
420C2×C22⋊C4—862no—
421C2×C22⋊C4—864no—
422C2×C22⋊C4—864no—
423C2×C22⋊C4—1722no—
424C2×C22⋊C4Dic8614yes—
425C2×C42—434no—
426C2×C42—864no—
427C2×C42—862no—
428C2×C42—864no—
429#95—24no—
430#95—22no—
431#95—862no—
432#95—864no—
433#95—864no—
434#95—864no—
435#95—862no—
436#95—864no—
437#95—862no—
438C24—22no—
439C24—21no—
440C24—21no—
441C24—22no—
442C24—21no—
443C24—21no—
444C24—22no—
445C24—22no—
446C24C2×Dic8612yes—
447C24D4×D4312yes—
448C24Q8×D4312yes—
449C24C23×D4311yescharacteristic
450C22×C4—22no—
451C22×C4—22no—
452C22×C4—22no—
453C22×C4—21no—
454C22×C4—22no—
455C22×C4—22no—
456C22×C4—22no—
457C22×C4—22no—
458C22×C4—21no—
459C22×C4—22no—
460C22×C4—22no—
461C22×C4—22no—
462C22×C4—22no—
463C22×C4—22no—
464C22×C4—22no—
465C22×C4—22no—
466C22×C4—22no—
467C22×C4—22no—
468C22×C4—22no—
469C22×C4—432no—
470C22×C4—434no—
471C22×C4—432no—
472C22×C4—434no—
473C22×C4—432no—
474C22×C4—432no—
475C22×C4—432no—
476C22×C4—432no—
477C22×C4—434no—
478C22×C4—432no—
479C22×C4—432no—
480C22×C4—868no—
481C22×C4—8616no—
482C22×C4—862no—
483C22×C4—862no—
484C22×C4—862no—
485C22×C4—861no—
486C22×C4—861no—
487C22×C4—862no—
488C22×C4—862no—
489C22×C4—861no—
490C22×C4—862no—
491C22×C4—862no—
492C22×C4—862no—
493C22×C4—861no—
494C22×C4—862no—
495C22×C4—862no—
496C22×C4—862no—
497C22×C4—862no—
498C22×C4—862no—
499C22×C4—862no—
500C22×C4—862no—
501C22×C4—862no—
502C22×C4—862no—
503C22×C4—862no—
504C22×C4—862no—
505C22×C4—1724no—
506C22×C4—1728no—
507C22×C4—1724no—
508C22×C4C2×Dic8612yes—
509C22×C4C2×Dic8612yes—
510C22×C4D4×D4314yes—
511C22×C4D4×D4312yes—
512C22×C4#1062190012yes—
513C4⋊C4—44no—
514C4⋊C4—8616no—
515C4⋊C4—1728no—
516C4⋊C4—1724no—
517C4⋊C4—1728no—
518C4⋊C4—1728no—
519C4⋊C4—1728no—
520C22⋊C4—28no—
521C22⋊C4—48no—
522C22⋊C4—868no—
523C22⋊C4—1728no—
524C42—868no—
525C42—1724no—
526C23—24no—
527C23—24no—
528C23—22no—
529C23—22no—
530C23—24no—
531C23—22no—
532C23—22no—
533C23—22no—
534C23—22no—
535C23—24no—
536C23—24no—
537C23—24no—
538C23—42no—
539C23—42no—
540C23—42no—
541C23—42no—
542C23—41no—
543C23—41no—
544C23—41no—
545C23—41no—
546C23—42no—
547C23—42no—
548C23#1306332414yes—
549C23C2×D4×D4312yes—
550C23C2×D4×D4311yescharacteristic
551C23C2×D4×D4311yescharacteristic
552C23C2×Q8×D4311yescharacteristic
553C23C22×Dic8611yescharacteristic
554C23#41×D4311yescharacteristic
555C23#41×D4312yes—
556C23#41×D4311yescharacteristic
557C23C2×#1062190011yescharacteristic
558C23#1306337012yes—
559C23#1306337212yes—
560C2×C4—24no—
561C2×C4—24no—
562C2×C4—22no—
563C2×C4—22no—
564C2×C4—24no—
565C2×C4—22no—
566C2×C4—24no—
567C2×C4—24no—
568C2×C4—24no—
569C2×C4—42no—
570C2×C4—41no—
571C2×C4—42no—
572C2×C4—41no—
573C2×C4—42no—
574C2×C4—42no—
575C2×C4—42no—
576C2×C4—42no—
577C2×C4—42no—
578C2×C4—42no—
579C2×C4—42no—
580C2×C4—42no—
581C2×C4—42no—
582C2×C4—42no—
583C2×C4—434no—
584C2×C4—438no—
585C2×C4—434no—
586C2×C4—438no—
587C2×C4—434no—
588C2×C4—434no—
589C2×C4—864no—
590C2×C4—862no—
591C2×C4—862no—
592C2×C4—864no—
593C2×C4—862no—
594C2×C4—862no—
595C2×C4—864no—
596C2×C4—864no—
597C2×C4—864no—
598C2×C4—864no—
599C2×C4—864no—
600C2×C4—17216no—
601C2×C4—1722no—
602C2×C4—1722no—
603C2×C4—1722no—
604C2×C4—1722no—
605C2×C4—1722no—
606C2×C4—1722no—
607C2×C4—1722no—
608C2×C4—1722no—
609C2×C4—1722no—
610C2×C4—1722no—
611C2×C4—1721no—
612C2×C4—1721no—
613C2×C4—1721no—
614C2×C4—1722no—
615C2×C4—1721no—
616C2×C4—1722no—
617C2×C4—1722no—
618C2×C4#1306330214yes—
619C22—24no—
620C22—28no—
621C22—42no—
622C22—44no—
623C22—42no—
624C22—44no—
625C22—42no—
626C22—42no—
627C22—42no—
628C22—42no—
629C22—44no—
630C22#121×D4311yescharacteristic
631C22C22⋊Q8×D4311yescharacteristic
632C22C22⋊Q8×D4312yes—
633C22C2×#1306330211yescharacteristic
634C22#123×D4312yes—
635C22#123×D4311yescharacteristic
636C22#127×D4311yescharacteristic
637C22C2×#1306332411yescharacteristic
638C22#1458344411yescharacteristic
639C22#1458345111yescharacteristic
640C22#1458345211yescharacteristic
641C22#1458346411yescharacteristic
642C22#1458346911yescharacteristic
643C22#1458351312yes—
644C22#1458352812yes—
645C22#1458353112yes—
646C22#1458354712yes—
647C22#1458354912yes—
648C22D4×Dic8612yes—
649C22#1458356712yes—
650C22#1458358512yes—
651C22#1458359212yes—
652C22#1458360812yes—
653C4—24no—
654C4—44no—
655C4—42no—
656C4—82no—
657C4—438no—
658C4—864no—
659C4—3442no—
660C4—1722no—
661C4—1724no—
662C4—1722no—
663C2—44no—
664C2#399×D4311yescharacteristic
665C2#1913810212yes—
666C2#1913811712yes—
667C2#1913829612yes—
668C2#1913830312yes—
669C2#1913889611yescharacteristic
670C2#1913890911yescharacteristic
671C2#1913953611yescharacteristic
672C2#1913954611yescharacteristic
673C2#1914041511yescharacteristic
674C2#1914294511yescharacteristic
subgroupG/H
center, FrattiniC24C23×D43
commutator, socle, cosocleC24×C43C24
FittingC43×#1439C2
prime radicalC25×C43C23
hypercenter#1439D43
hypocenterC43#15135
LCSG ▷ C24×C43 ▷ C43
UCSC1 ◁ C24 ◁ #1439

Complements

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

NH ≅ G/Ntype
2. C2×#14582796C2semidirect
3. C2×#14582768C2semidirect
6. #19132861C2semidirect
7. #19132860C2semidirect
8. #19132858C2semidirect
10. Dic43⋊#95C2semidirect
325. Dic43#399semidirect
377. C43#15135semidirect

Maximal subgroups

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

subgroupindex
C2×#145828352
C2×#145827962
C2×#145827682
C2×#145827572
C2×C22⋊C4×Dic432
#191328612
#191328602
#191328582
#191328402
Dic43⋊#952
C43×#14392
#1513543