Finite Group Databasebeta

← #25033334

Subgroups — #25033334

Order 11008.

1294 conjugacy classes of subgroups.

The subgroup lattice has 668 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14582841C212yesmaximal
2C2×#14582795C211yesmaximal, characteristic
3C2×#14582769C211yesmaximal, characteristic
4#19132852C212yesmaximal
5#19132851C212yesmaximal
6#19132847C212yesmaximal
7#19132824C211yesmaximal, characteristic
8#19132824C211yesmaximal, characteristic
9#19132824C211yesmaximal, characteristic
10C4×C43⋊#95C211yesmaximal, characteristic
11C43×C4⋊#95C211yesmaximal, characteristic
12C22×C4⋊Dic43C2211yescharacteristic
13C22×C4⋊Dic43C2212yes—
14C22×C4⋊Dic43C2212yes—
15C22×C4⋊Dic43C2211yescharacteristic
16C22×Dic43⋊C4C2212yes—
17C22×C4×Dic43C2211yescharacteristic
18C22×C4×Dic43C2211yescharacteristic
19#14582841—28no—
20#14582795—24no—
21#14582769—24no—
22C2×C43⋊#95C2212yes—
23C2×C43⋊#95C2212yes—
24C2×C43⋊#95C2212yes—
25C2×C43⋊#95C2212yes—
26C2×C43⋊#95C2211yescharacteristic
27C2×C43⋊#95C2211yescharacteristic
28C2×C43⋊#95C2212yes—
29C2×C43⋊#95C2212yes—
30C2×C43⋊#95C2212yes—
31C2×C43⋊#95C2211yescharacteristic
32C2×C43⋊#95C2211yescharacteristic
33C22×C4⋊C4×C43C2211yescharacteristic
34C22×C4⋊C4×C43C2211yescharacteristic
35C22×C42×C43C2211yescharacteristic
36C2×#95×C43C2212yes—
37C2×#95×C43C2212yes—
38C23×Dic43C2312yes—
39C23×Dic43C2311yescharacteristic
40C23×Dic43C2311yescharacteristic
41C23×Dic43C2312yes—
42C23×Dic43C2311yescharacteristic
43C23×Dic43C2311yescharacteristic
44C2×C4⋊Dic43—22no—
45C2×C4⋊Dic43—22no—
46C2×C4⋊Dic43—24no—
47C2×C4⋊Dic43—22no—
48C2×C4⋊Dic43—22no—
49C2×C4⋊Dic43—24no—
50C2×C4⋊Dic43—22no—
51C2×C4⋊Dic43—24no—
52C2×C4⋊Dic43—24no—
53C2×C4⋊Dic43—42no—
54C2×C4⋊Dic43—42no—
55C2×C4⋊Dic43D414yes—
56C2×Dic43⋊C4—24no—
57C2×Dic43⋊C4—24no—
58C2×Dic43⋊C4—42no—
59C2×C4×Dic43—22no—
60C2×C4×Dic43—22no—
61C2×C4×Dic43—22no—
62C2×C4×Dic43—22no—
63C2×C4×Dic43—22no—
64C2×C4×Dic43—22no—
65C43⋊#95—22no—
66C43⋊#95—22no—
67C43⋊#95—24no—
68C43⋊#95—24no—
69C43⋊#95—24no—
70C43⋊#95—24no—
71C43⋊#95—42no—
72C43⋊#95—42no—
73C43⋊#95—42no—
74C43⋊#95D414yes—
75C43⋊#95Q814yes—
76C23×C4×C43C2312yes—
77C23×C4×C43C2312yes—
78C23×C4×C43C2311yescharacteristic
79C23×C4×C43C2311yescharacteristic
80C23×C4×C43C2311yescharacteristic
81C2×C4⋊C4×C43—22no—
82C2×C4⋊C4×C43—22no—
83C2×C4⋊C4×C43—22no—
84C2×C4⋊C4×C43—22no—
85C2×C4⋊C4×C43—22no—
86C2×C4⋊C4×C43—22no—
87C2×C42×C43—22no—
88C2×C42×C43—22no—
89C2×C42×C43Q814yes—
90#95×C43—24no—
91#95×C43—24no—
92C24×C43C2411yescharacteristic
93C22×C4×C43—21no—
94C22×C4×C43—21no—
95C22×C4×C43—22no—
96C22×C4×C43—22no—
97C22×C4×C43—22no—
98C22×C4×C43—21no—
99C22×C4×C43—21no—
100C22×C4×C43—22no—
101C22×C4×C43—22no—
102C22×C4×C43—22no—
103C22×C4×C43—22no—
104C22×C4×C43—22no—
105C22×C4×C43—22no—
106C22×C4×C43—22no—
107C22×C4×C43—21no—
108C22×C4×C43—21no—
109C22×C4×C43—22no—
110C22×C4×C43—22no—
111C22×C4×C43—21no—
112C22×C4×C43—21no—
113C22×C4×C43—22no—
114C22×C4×C43—22no—
115C22×C4×C43C2×D412yes—
116C22×C4×C43C2×D412yes—
117C22×C4×C43C2×Q812yes—
118C22×C4×C43C2×Q812yes—
119C22×C4×C43C2×Q812yes—
120C22×C4×C43C2×Q812yes—
121C22×C4×C43#4112yes—
122C22×C4×C43#4112yes—
123C22×C4×C43#4112yes—
124C22×C4×C43#4112yes—
125C22×C4×C43#4112yes—
126C22×C4×C43#4112yes—
127C22×C4×C43#4112yes—
128C22×Dic43—21no—
129C22×Dic43—22no—
130C22×Dic43—21no—
131C22×Dic43—22no—
132C22×Dic43—22no—
133C22×Dic43—21no—
134C22×Dic43—21no—
135C22×Dic43—21no—
136C22×Dic43—21no—
137C22×Dic43—21no—
138C22×Dic43—21no—
139C22×Dic43—21no—
140C22×Dic43—21no—
141C22×Dic43—21no—
142C22×Dic43—21no—
143C22×Dic43—21no—
144C22×Dic43—21no—
145C22×Dic43—21no—
146C22×Dic43—21no—
147C22×Dic43—22no—
148C22×Dic43—22no—
149C22×Dic43—22no—
150C22×Dic43—22no—
151C22×Dic43—22no—
152C22×Dic43—22no—
153C22×Dic43—21no—
154C22×Dic43—21no—
155C22×Dic43—21no—
156C22×Dic43—22no—
157C22×Dic43—21no—
158C22×Dic43—22no—
159C22×Dic43—22no—
160C22×Dic43—22no—
161C22×Dic43—21no—
162C22×Dic43—21no—
163C22×Dic43—21no—
164C22×Dic43—21no—
165C22×Dic43C2×D412yes—
166C22×Dic43C2×D412yes—
167C22×Dic43C2×D414yes—
168C22×Dic43C2×Q812yes—
169C22×Dic43C2×Q812yes—
170C4⋊C4×C43—44no—
171C4⋊C4×C43—44no—
172C42×C43—28no—
173C4⋊Dic43—28no—
174C4⋊Dic43—48no—
175C4⋊Dic43—48no—
176C4⋊Dic43—44no—
177Dic43⋊C4—48no—
178C4×Dic43—44no—
179C4×Dic43—44no—
180C23×C43C22×D411yescharacteristic
181C23×C43C22×D411yescharacteristic
182C23×C43C22×Q811yescharacteristic
183C23×C43C22×Q811yescharacteristic
184C23×C43C2×#4111yescharacteristic
185C23×C43C2×#4111yescharacteristic
186C23×C43C2×#4111yescharacteristic
187C23×C43C2×#4111yescharacteristic
188C23×C43C2×#4111yescharacteristic
189C23×C43C2×#4111yescharacteristic
190C23×C43C2×#4111yescharacteristic
191C23×C43H(5,𝔽2)11yescharacteristic
192C23×C43H(5,𝔽2)11yescharacteristic
193C23×C432−1+411yescharacteristic
194C23×C432−1+411yescharacteristic
195C2×C4×C43—22no—
196C2×C4×C43—22no—
197C2×C4×C43—22no—
198C2×C4×C43—22no—
199C2×C4×C43—22no—
200C2×C4×C43—22no—
201C2×C4×C43—22no—
202C2×C4×C43—22no—
203C2×C4×C43—22no—
204C2×C4×C43—22no—
205C2×C4×C43—22no—
206C2×C4×C43—22no—
207C2×C4×C43—42no—
208C2×C4×C43—42no—
209C2×C4×C43—42no—
210C2×C4×C43—42no—
211C2×C4×C43—42no—
212C2×C4×C43—42no—
213C2×C4×C43—42no—
214C2×C4×C43—42no—
215C2×C4×C43—42no—
216C2×C4×C43—42no—
217C2×C4×C43—42no—
218C2×C4×C43—42no—
219C2×C4×C43—42no—
220C2×C4×C43—42no—
221C2×C4×C43C22⋊Q814yes—
222C2×C4×C43#12314yes—
223C2×C4×C43#12414yes—
224C2×C4×C43#12514yes—
225C2×C4×C43#12514yes—
226C2×C4×C43#12514yes—
227C2×C4×C43#12614yes—
228C2×C4×C43#12614yes—
229C2×C4×C43C4⋊Q814yes—
230C2×Dic43—24no—
231C2×Dic43—22no—
232C2×Dic43—22no—
233C2×Dic43—22no—
234C2×Dic43—22no—
235C2×Dic43—22no—
236C2×Dic43—24no—
237C2×Dic43—24no—
238C2×Dic43—22no—
239C2×Dic43—22no—
240C2×Dic43—22no—
241C2×Dic43—22no—
242C2×Dic43—22no—
243C2×Dic43—22no—
244C2×Dic43—22no—
245C2×Dic43—41no—
246C2×Dic43—41no—
247C2×Dic43—41no—
248C2×Dic43—41no—
249C2×Dic43—42no—
250C2×Dic43—42no—
251C2×Dic43—41no—
252C2×Dic43—41no—
253C2×Dic43—41no—
254C2×Dic43—41no—
255C2×Dic43—41no—
256C2×Dic43—41no—
257C2×Dic43—42no—
258C2×Dic43—41no—
259C2×Dic43—41no—
260C2×Dic43—41no—
261C2×Dic43—41no—
262C2×Dic43—41no—
263C2×Dic43—41no—
264C2×Dic43—42no—
265C2×Dic43—42no—
266C2×Dic43—42no—
267C2×Dic43—42no—
268C2×Dic43—42no—
269C2×Dic43—42no—
270C2×Dic43—42no—
271C2×Dic43—42no—
272#15146—431nomaximal, Sylow
273C22×C43C2×C22⋊Q811yescharacteristic
274C22×C43C2×#12311yescharacteristic
275C22×C43C2×#12411yescharacteristic
276C22×C43C2×#12511yescharacteristic
277C22×C43C2×#12511yescharacteristic
278C22×C43C2×#12511yescharacteristic
279C22×C43C2×#12611yescharacteristic
280C22×C43C2×#12611yescharacteristic
281C22×C43C2×C4⋊Q811yescharacteristic
282C22×C43#53211yescharacteristic
283C22×C43#53211yescharacteristic
284C22×C43#53311yescharacteristic
285C22×C43#53311yescharacteristic
286C22×C43#54011yescharacteristic
287C22×C43#54111yescharacteristic
288C22×C43#54211yescharacteristic
289C22×C43#54211yescharacteristic
290C22×C43#54411yescharacteristic
291C22×C43#54411yescharacteristic
292C22×C43D4211yescharacteristic
293C22×C43#54611yescharacteristic
294C22×C43#54711yescharacteristic
295C22×C43#54711yescharacteristic
296C22×C43#54811yescharacteristic
297C22×C43D4×Q811yescharacteristic
298C22×C43#55011yescharacteristic
299C22×C43#55211yescharacteristic
300C22×C43#55311yescharacteristic
301C22×C43#55411yescharacteristic
302C22×C43#55411yescharacteristic
303C22×C43#55511yescharacteristic
304C22×C43#55611yescharacteristic
305C22×C43#55611yescharacteristic
306C22×C43#55711yescharacteristic
307C22×C43#55911yescharacteristic
308C4×C43—24no—
309C4×C43—24no—
310C4×C43—82no—
311C4×C43—82no—
312C4×C43#40018yescomplemented
313Dic43—44no—
314Dic43—42no—
315Dic43—42no—
316Dic43—42no—
317Dic43—42no—
318Dic43—82no—
319C2×#400—432no—
320C2×#389—431no—
321C2×#384—431no—
322#1442—432no—
323#1442—432no—
324#1441—432no—
325C4⋊#95—431no—
326C4⋊#95—431no—
327C4⋊#95—431no—
328C4⋊#95D4311yescharacteristic
329C4×#95—431no—
330C2×C43C2×#40011yescharacteristic
331C2×C43#244011yescharacteristic
332C2×C43#244211yescharacteristic
333C2×C43#244511yescharacteristic
334C2×C43#244611yescharacteristic
335C2×C43#249111yescharacteristic
336C2×C43#249211yescharacteristic
337C2×C43#249611yescharacteristic
338C2×C43#249711yescharacteristic
339C2×C43#251111yescharacteristic
340C2×C43#251211yescharacteristic
341C2×C43#255211yescharacteristic
342C2×C43#257111yescharacteristic
343C2×C43#264711yescharacteristic
344C2×C43#285911yescharacteristic
345C22×C4⋊C4—431no—
346C22×C4⋊C4—431no—
347C22×C4⋊C4—432no—
348C22×C4⋊C4—432no—
349C22×C4⋊C4—432no—
350C22×C4⋊C4C2×D4311yescharacteristic
351C22×C4⋊C4C2×D4311yescharacteristic
352C22×C42—431no—
353C22×C42—431no—
354C22×C42C2×D4311yescharacteristic
355#400—868no—
356#389—864no—
357#384—864no—
358C2×#95—431no—
359C2×#95—431no—
360C2×#95—432no—
361C2×#95—432no—
362C2×#95—432no—
363C2×#95—431no—
364C2×#95—431no—
365C2×#95—432no—
366C2×#95—432no—
367C2×#95—432no—
368C2×#95—432no—
369C2×#95C2×D4312yes—
370C2×#95C2×D4312yes—
371C43#1514611yescharacteristic, complemented, Sylow
372C23×C4—432no—
373C23×C4—431no—
374C23×C4—431no—
375C23×C4—431no—
376C23×C4—431no—
377C23×C4—432no—
378C23×C4C22×D4312yes—
379C23×C4C22×D4312yes—
380C23×C4C22×D4311yescharacteristic
381C23×C4C22×D4311yescharacteristic
382C23×C4C22×D4311yescharacteristic
383C2×C4⋊C4—22no—
384C2×C4⋊C4—22no—
385C2×C4⋊C4—22no—
386C2×C4⋊C4—22no—
387C2×C4⋊C4—22no—
388C2×C4⋊C4—22no—
389C2×C4⋊C4—434no—
390C2×C4⋊C4—862no—
391C2×C4⋊C4—862no—
392C2×C4⋊C4—864no—
393C2×C4⋊C4—864no—
394C2×C4⋊C4—864no—
395C2×C4⋊C4—864no—
396C2×C4⋊C4—862no—
397C2×C4⋊C4—862no—
398C2×C4⋊C4—864no—
399C2×C4⋊C4—864no—
400C2×C4⋊C4—862no—
401C2×C4⋊C4—1722no—
402C2×C4⋊C4—1722no—
403C2×C4⋊C4—1722no—
404C2×C42—22no—
405C2×C42—22no—
406C2×C42—862no—
407C2×C42—862no—
408C2×C42—862no—
409C2×C42—862no—
410C2×C42—862no—
411C2×C42—862no—
412C2×C42Dic8614yes—
413#95—24no—
414#95—24no—
415#95—434no—
416#95—434no—
417#95—864no—
418#95—864no—
419#95—864no—
420#95—864no—
421#95—862no—
422#95—862no—
423#95—1722no—
424#95—1722no—
425#95—1722no—
426C24C23×D4311yescharacteristic
427C22×C4—21no—
428C22×C4—21no—
429C22×C4—21no—
430C22×C4—21no—
431C22×C4—21no—
432C22×C4—21no—
433C22×C4—21no—
434C22×C4—21no—
435C22×C4—22no—
436C22×C4—22no—
437C22×C4—22no—
438C22×C4—22no—
439C22×C4—22no—
440C22×C4—22no—
441C22×C4—22no—
442C22×C4—22no—
443C22×C4—22no—
444C22×C4—22no—
445C22×C4—22no—
446C22×C4—22no—
447C22×C4—22no—
448C22×C4—22no—
449C22×C4—432no—
450C22×C4—432no—
451C22×C4—434no—
452C22×C4—432no—
453C22×C4—432no—
454C22×C4—861no—
455C22×C4—862no—
456C22×C4—861no—
457C22×C4—861no—
458C22×C4—861no—
459C22×C4—861no—
460C22×C4—861no—
461C22×C4—861no—
462C22×C4—861no—
463C22×C4—861no—
464C22×C4—861no—
465C22×C4—861no—
466C22×C4—861no—
467C22×C4—862no—
468C22×C4—861no—
469C22×C4—861no—
470C22×C4—861no—
471C22×C4—861no—
472C22×C4—862no—
473C22×C4—862no—
474C22×C4—861no—
475C22×C4—861no—
476C22×C4—861no—
477C22×C4—862no—
478C22×C4—861no—
479C22×C4—862no—
480C22×C4—861no—
481C22×C4—861no—
482C22×C4—861no—
483C22×C4—861no—
484C22×C4—862no—
485C22×C4—862no—
486C22×C4—862no—
487C22×C4—862no—
488C22×C4—862no—
489C22×C4—862no—
490C22×C4—862no—
491C22×C4C2×Dic8612yes—
492C22×C4C2×Dic8612yes—
493C22×C4C2×Dic8612yes—
494C22×C4#1062189812yes—
495C22×C4#1062189812yes—
496C22×C4D4×D4312yes—
497C22×C4D4×D4312yes—
498C22×C4#1062190012yes—
499C22×C4#1062190012yes—
500C22×C4#1062190012yes—
501C22×C4Q8×D4312yes—
502C22×C4#1062190212yes—
503C22×C4#1062190212yes—
504C4⋊C4—44no—
505C4⋊C4—44no—
506C4⋊C4—868no—
507C4⋊C4—1728no—
508C4⋊C4—1728no—
509C4⋊C4—1728no—
510C4⋊C4—1724no—
511C42—28no—
512C42—1724no—
513C42—1724no—
514C23C2×D4×D4311yescharacteristic
515C23C2×D4×D4311yescharacteristic
516C23C2×Q8×D4311yescharacteristic
517C23C22×Dic8611yescharacteristic
518C23C2×#1062190011yescharacteristic
519C23C2×#1062190011yescharacteristic
520C23C2×#1062190011yescharacteristic
521C23C2×#1062189811yescharacteristic
522C23C2×#1062189811yescharacteristic
523C23C2×#1062190211yescharacteristic
524C23C2×#1062190211yescharacteristic
525C23#1306337111yescharacteristic
526C23#1306337111yescharacteristic
527C23#1306337211yescharacteristic
528C23#1306337211yescharacteristic
529C2×C4—22no—
530C2×C4—22no—
531C2×C4—22no—
532C2×C4—22no—
533C2×C4—22no—
534C2×C4—22no—
535C2×C4—22no—
536C2×C4—22no—
537C2×C4—22no—
538C2×C4—22no—
539C2×C4—22no—
540C2×C4—22no—
541C2×C4—42no—
542C2×C4—42no—
543C2×C4—42no—
544C2×C4—42no—
545C2×C4—42no—
546C2×C4—42no—
547C2×C4—42no—
548C2×C4—42no—
549C2×C4—42no—
550C2×C4—42no—
551C2×C4—42no—
552C2×C4—42no—
553C2×C4—42no—
554C2×C4—42no—
555C2×C4—862no—
556C2×C4—862no—
557C2×C4—862no—
558C2×C4—862no—
559C2×C4—862no—
560C2×C4—862no—
561C2×C4—864no—
562C2×C4—862no—
563C2×C4—862no—
564C2×C4—862no—
565C2×C4—862no—
566C2×C4—864no—
567C2×C4—862no—
568C2×C4—864no—
569C2×C4—862no—
570C2×C4—1722no—
571C2×C4—1722no—
572C2×C4—1722no—
573C2×C4—1722no—
574C2×C4—1722no—
575C2×C4—1722no—
576C2×C4—1722no—
577C2×C4—1721no—
578C2×C4—1722no—
579C2×C4—1721no—
580C2×C4—1721no—
581C2×C4—1721no—
582C2×C4—1721no—
583C2×C4—1721no—
584C2×C4—1721no—
585C2×C4—1722no—
586C2×C4—1721no—
587C2×C4—1721no—
588C2×C4—1721no—
589C2×C4—1721no—
590C2×C4—1722no—
591C2×C4—1722no—
592C2×C4—1721no—
593C2×C4—1721no—
594C2×C4—1721no—
595C2×C4—1721no—
596C2×C4—1721no—
597C2×C4#1306330214yes—
598C2×C4#1306331014yes—
599C2×C4#1306331114yes—
600C2×C4#1306331614yes—
601C2×C4#1306331614yes—
602C2×C4#1306331714yes—
603C2×C4#1306331814yes—
604C2×C4#1306332014yes—
605C2×C4#1306332414yes—
606C22C2×#1306330211yescharacteristic
607C22C2×#1306331011yescharacteristic
608C22C2×#1306331111yescharacteristic
609C22C2×#1306331611yescharacteristic
610C22C2×#1306331611yescharacteristic
611C22C2×#1306331711yescharacteristic
612C22C2×#1306331811yescharacteristic
613C22C2×#1306332011yescharacteristic
614C22C2×#1306332411yescharacteristic
615C22#1458344711yescharacteristic
616C22#1458345011yescharacteristic
617C22#1458345411yescharacteristic
618C22#1458345411yescharacteristic
619C22#1458350511yescharacteristic
620C22#1458351211yescharacteristic
621C22#1458351811yescharacteristic
622C22#1458351811yescharacteristic
623C22#1458352711yescharacteristic
624C22#1458352711yescharacteristic
625C22#1458353311yescharacteristic
626C22#1458354011yescharacteristic
627C22#1458354911yescharacteristic
628C22#1458355411yescharacteristic
629C22#1458355511yescharacteristic
630C22#1458356211yescharacteristic
631C22#1458357011yescharacteristic
632C22#1458359111yescharacteristic
633C22#1458360111yescharacteristic
634C22#1458360711yescharacteristic
635C22#1458360911yescharacteristic
636C22#1458361411yescharacteristic
637C22#1458361911yescharacteristic
638C22#1458362211yescharacteristic
639C22#1458362711yescharacteristic
640C22#1458363411yescharacteristic
641C4—24no—
642C4—24no—
643C4—82no—
644C4—82no—
645C4—3442no—
646C4—1724no—
647C4—1722no—
648C4—1722no—
649C4—1722no—
650C4—1722no—
651C4#1458284118yescomplemented
652C2C2×#1458284111yescharacteristic
653C2#1913829811yescharacteristic
654C2#1913832011yescharacteristic
655C2#1913836211yescharacteristic
656C2#1913837311yescharacteristic
657C2#1913895611yescharacteristic
658C2#1913896711yescharacteristic
659C2#1913901511yescharacteristic
660C2#1913902611yescharacteristic
661C2#1913917211yescharacteristic
662C2#1913918311yescharacteristic
663C2#1913963011yescharacteristic
664C2#1913983411yescharacteristic
665C2#1914057411yescharacteristic
666C2#1914295611yescharacteristic
subgroupG/H
center, FrattiniC24C23×D43
commutator, socle, prime radical, cosocleC24×C43C24
FittingC43×C4⋊#95C2
hypercenterC4⋊#95D43
hypocenterC43#15146
LCSG ▷ C24×C43 ▷ C43
UCSC1 ◁ C24 ◁ C4⋊#95

Complements

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

NH ≅ G/Ntype
312. C4×C43#400semidirect
371. C43#15146semidirect
651. C4#14582841semidirect

Maximal subgroups

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

subgroupindex
C2×#145828412
C2×#145827952
C2×#145827692
#191328522
#191328512
#191328472
#191328242
C4×C43⋊#952
C43×C4⋊#952
#1514643