Finite Group Databasebeta

← #25019081

Subgroups — #25019081

Order 11008.

1370 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×#14582798C211yesmaximal, characteristic
2C2×C4⋊C4×Dic43C211yesmaximal, characteristic
3#19132854C212yesmaximal
4#19132851C212yesmaximal
5#19132825C211yesmaximal, characteristic
6#19132824C211yesmaximal, characteristic
7#19132824C211yesmaximal, characteristic
8#19132824C212yesmaximal
9#19132821C212yesmaximal
10C4×C43⋊#95C211yesmaximal, characteristic
11C2×C43×#389C211yesmaximal, characteristic
12C22×C4⋊Dic43C2211yescharacteristic
13C22×C4⋊Dic43C2212yes—
14C22×C4⋊Dic43C2211yescharacteristic
15C22×C4×Dic43C2211yescharacteristic
16C22×C4×Dic43C2211yescharacteristic
17C22×C4×Dic43C2212yes—
18#14582798—24no—
19C4⋊C4×Dic43C418yescomplemented
20C2×C43⋊#95C2212yes—
21C2×C43⋊#95C2211yescharacteristic
22C2×C43⋊#95C2211yescharacteristic
23C2×C43⋊#95C2211yescharacteristic
24C2×C43⋊#95C2212yes—
25C2×C43⋊#95C2212yes—
26C2×C43⋊#95C2212yes—
27C2×C43⋊#95C2212yes—
28C2×C43⋊#95C2212yes—
29C2×C43⋊#95C2212yes—
30C2×C43⋊#95C2212yes—
31C2×C43⋊#95C2211yescharacteristic
32C22×C4⋊C4×C43C2211yescharacteristic
33C22×C4⋊C4×C43C2212yes—
34C22×C4⋊C4×C43C2211yescharacteristic
35C22×C42×C43C2211yescharacteristic
36C43×#389—24no—
37C2×#95×C43C2212yes—
38C23×Dic43C2312yes—
39C23×Dic43C2312yes—
40C23×Dic43C2311yescharacteristic
41C23×Dic43C2311yescharacteristic
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—22no—
50C2×C4⋊Dic43—24no—
51C2×C4⋊Dic43—42no—
52C2×C4⋊Dic43C2×C414yes—
53C2×C4×Dic43—22no—
54C2×C4×Dic43—22no—
55C2×C4×Dic43—22no—
56C2×C4×Dic43—22no—
57C2×C4×Dic43—22no—
58C2×C4×Dic43—42no—
59C2×C4×Dic43—42no—
60C2×C4×Dic43C2×C414yes—
61C2×C4×Dic43C2×C418yes—
62C43⋊#95—24no—
63C43⋊#95—22no—
64C43⋊#95—22no—
65C43⋊#95—22no—
66C43⋊#95—24no—
67C43⋊#95—42no—
68C43⋊#95—42no—
69C43⋊#95—42no—
70C43⋊#95—42no—
71C43⋊#95—42no—
72C43⋊#95C2×C418yes—
73C43⋊#95Q814yes—
74C23×C4×C43C2312yes—
75C23×C4×C43C2311yescharacteristic
76C23×C4×C43C2311yescharacteristic
77C23×C4×C43C2312yes—
78C23×C4×C43C2311yescharacteristic
79C2×C4⋊C4×C43—24no—
80C2×C4⋊C4×C43—22no—
81C2×C4⋊C4×C43—24no—
82C2×C4⋊C4×C43—22no—
83C2×C4⋊C4×C43—22no—
84C2×C4⋊C4×C43—42no—
85C2×C4⋊C4×C43C2×C414yes—
86C2×C4⋊C4×C43D414yes—
87C2×C4⋊C4×C43Q814yes—
88C2×C42×C43—22no—
89C2×C42×C43—22no—
90C2×C42×C43—22no—
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—21no—
101C22×C4×C43—21no—
102C22×C4×C43—21no—
103C22×C4×C43—21no—
104C22×C4×C43—22no—
105C22×C4×C43—22no—
106C22×C4×C43—22no—
107C22×C4×C43—22no—
108C22×C4×C43—22no—
109C22×C4×C43—22no—
110C22×C4×C43—21no—
111C22×C4×C43—21no—
112C22×C4×C43—21no—
113C22×C4×C43—22no—
114C22×C4×C43—22no—
115C22×C4×C43—21no—
116C22×C4×C43C22×C414yes—
117C22×C4×C43C22×C412yes—
118C22×C4×C43C2×D414yes—
119C22×C4×C43C2×D412yes—
120C22×C4×C43C2×Q814yes—
121C22×C4×C43C2×Q812yes—
122C22×C4×C43C2×Q812yes—
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—21no—
130C22×Dic43—22no—
131C22×Dic43—21no—
132C22×Dic43—21no—
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—22no—
144C22×Dic43—22no—
145C22×Dic43—22no—
146C22×Dic43—22no—
147C22×Dic43—22no—
148C22×Dic43—22no—
149C22×Dic43—21no—
150C22×Dic43—21no—
151C22×Dic43—21no—
152C22×Dic43—22no—
153C22×Dic43—21no—
154C22×Dic43—21no—
155C22×Dic43—22no—
156C22×Dic43—22no—
157C22×Dic43—21no—
158C22×Dic43—22no—
159C22×Dic43—22no—
160C22×Dic43—22no—
161C22×Dic43—21no—
162C22×Dic43—21no—
163C22×Dic43C22×C412yes—
164C22×Dic43C22×C414yes—
165C22×Dic43C22×C412yes—
166C22×Dic43C2×Q812yes—
167C22×Dic43C2×Q812yes—
168C22×Dic43#4112yes—
169C22×Dic43#4112yes—
170C4⋊C4×C43—48no—
171C4⋊C4×C43—44no—
172C4⋊C4×C43C4⋊C4116yes—
173C42×C43—44no—
174C4⋊Dic43—28no—
175C4⋊Dic43—48no—
176C4⋊Dic43—44no—
177C4×Dic43—28no—
178C4×Dic43—48no—
179C4×Dic43—44no—
180C23×C43C23×C411yescharacteristic
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×C43H(5,𝔽2)11yescharacteristic
194C23×C432−1+411yescharacteristic
195C2×C4×C43—24no—
196C2×C4×C43—24no—
197C2×C4×C43—24no—
198C2×C4×C43—24no—
199C2×C4×C43—24no—
200C2×C4×C43—24no—
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—41no—
208C2×C4×C43—41no—
209C2×C4×C43—41no—
210C2×C4×C43—41no—
211C2×C4×C43—41no—
212C2×C4×C43—41no—
213C2×C4×C43—41no—
214C2×C4×C43—41no—
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×C43—42no—
222C2×C4×C43C2×C4⋊C418yes—
223C2×C4×C43C2×C4⋊C414yes—
224C2×C4×C43#11714yes—
225C2×C4×C43#11714yes—
226C2×C4×C43#12414yes—
227C2×C4×C43#12414yes—
228C2×C4×C43#12514yes—
229C2×C4×C43#12514yes—
230C2×Dic43—22no—
231C2×Dic43—22no—
232C2×Dic43—22no—
233C2×Dic43—22no—
234C2×Dic43—22no—
235C2×Dic43—22no—
236C2×Dic43—22no—
237C2×Dic43—24no—
238C2×Dic43—22no—
239C2×Dic43—24no—
240C2×Dic43—24no—
241C2×Dic43—22no—
242C2×Dic43—22no—
243C2×Dic43—22no—
244C2×Dic43—22no—
245C2×Dic43—22no—
246C2×Dic43—22no—
247C2×Dic43—22no—
248C2×Dic43—41no—
249C2×Dic43—41no—
250C2×Dic43—42no—
251C2×Dic43—42no—
252C2×Dic43—41no—
253C2×Dic43—42no—
254C2×Dic43—42no—
255C2×Dic43—41no—
256C2×Dic43—41no—
257C2×Dic43—41no—
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×Dic43C4×Q814yes—
272#13933—431nomaximal, Sylow
273C22×C43C22×C4⋊C411yescharacteristic
274C22×C43C2×#11711yescharacteristic
275C22×C43C2×#11711yescharacteristic
276C22×C43C2×C4×Q811yescharacteristic
277C22×C43C4×#4111yescharacteristic
278C22×C43#51811yescharacteristic
279C22×C43#52011yescharacteristic
280C22×C43C2×#12411yescharacteristic
281C22×C43C2×#12411yescharacteristic
282C22×C43C2×#12511yescharacteristic
283C22×C43C2×#12511yescharacteristic
284C22×C43#52911yescharacteristic
285C22×C43#52911yescharacteristic
286C22×C43#53311yescharacteristic
287C22×C43#53311yescharacteristic
288C22×C43#54011yescharacteristic
289C22×C43#54011yescharacteristic
290C22×C43#54211yescharacteristic
291C22×C43#54211yescharacteristic
292C22×C43#54611yescharacteristic
293C22×C43#54611yescharacteristic
294C22×C43D4×Q811yescharacteristic
295C22×C43#55011yescharacteristic
296C22×C43#55311yescharacteristic
297C22×C43#55311yescharacteristic
298C22×C43#55311yescharacteristic
299C22×C43#55311yescharacteristic
300C22×C43#55411yescharacteristic
301C22×C43#55411yescharacteristic
302C22×C43#55411yescharacteristic
303C22×C43#55411yescharacteristic
304C22×C43#55611yescharacteristic
305C22×C43#55611yescharacteristic
306C22×C43#55711yescharacteristic
307C22×C43Q8211yescharacteristic
308C4×C43—28no—
309C4×C43—42no—
310C4×C43—42no—
311C4×C43—82no—
312C4×C43#38218yes—
313Dic43—24no—
314Dic43—44no—
315Dic43—42no—
316Dic43—42no—
317Dic43—42no—
318Dic43—82no—
319C2×#389—431no—
320C2×#389D4311yescharacteristic
321C2×C4×C4⋊C4—431no—
322#1442—432no—
323#1442—432no—
324C4⋊#95—431no—
325C4⋊#95—431no—
326C4⋊#95—431no—
327C4⋊#95—432no—
328#1434—432no—
329C4×#95—431no—
330C2×C43C2×#38211yescharacteristic
331C2×C43#229511yescharacteristic
332C2×C43#231911yescharacteristic
333C2×C43#234511yescharacteristic
334C2×C43#234711yescharacteristic
335C2×C43#234911yescharacteristic
336C2×C43Q8×C4⋊C411yescharacteristic
337C2×C43#249011yescharacteristic
338C2×C43#249011yescharacteristic
339C2×C43#249211yescharacteristic
340C2×C43#249211yescharacteristic
341C2×C43#250711yescharacteristic
342C2×C43#250711yescharacteristic
343C2×C43#250911yescharacteristic
344C2×C43#250911yescharacteristic
345C22×C4⋊C4—431no—
346C22×C4⋊C4—431no—
347C22×C4⋊C4—432no—
348C22×C4⋊C4C2×D4311yescharacteristic
349C22×C4⋊C4C2×D4312yes—
350C22×C4⋊C4C2×D4311yescharacteristic
351C22×C42—431no—
352C22×C42—432no—
353C22×C42—431no—
354C22×C42C2×D4311yescharacteristic
355#389—24no—
356#389—864no—
357C4×C4⋊C4—438no—
358C2×#95—431no—
359C2×#95—432no—
360C2×#95—431no—
361C2×#95—431no—
362C2×#95—431no—
363C2×#95—432no—
364C2×#95—432no—
365C2×#95—432no—
366C2×#95—432no—
367C2×#95—432no—
368C2×#95—432no—
369C2×#95—432no—
370C2×#95C2×D4312yes—
371C43#1393311yescharacteristic, complemented, Sylow
372C23×C4—431no—
373C23×C4—431no—
374C23×C4—432no—
375C23×C4—431no—
376C23×C4—431no—
377C23×C4—432no—
378C23×C4C22×D4312yes—
379C23×C4C22×D4311yescharacteristic
380C23×C4C22×D4311yescharacteristic
381C23×C4C22×D4312yes—
382C23×C4C22×D4311yescharacteristic
383C2×C4⋊C4—24no—
384C2×C4⋊C4—22no—
385C2×C4⋊C4—22no—
386C2×C4⋊C4—24no—
387C2×C4⋊C4—22no—
388C2×C4⋊C4—42no—
389C2×C4⋊C4—434no—
390C2×C4⋊C4—862no—
391C2×C4⋊C4—862no—
392C2×C4⋊C4—864no—
393C2×C4⋊C4—862no—
394C2×C4⋊C4—862no—
395C2×C4⋊C4—864no—
396C2×C4⋊C4—862no—
397C2×C4⋊C4—1722no—
398C2×C4⋊C4Dic8614yes—
399C2×C4⋊C4C4×D4314yes—
400C2×C4⋊C4C22⋊D4314yes—
401C2×C42—22no—
402C2×C42—22no—
403C2×C42—22no—
404C2×C42—434no—
405C2×C42—438no—
406C2×C42—862no—
407C2×C42—862no—
408C2×C42—862no—
409C2×C42—862no—
410C2×C42—862no—
411C2×C42—1722no—
412C2×C42—1722no—
413#95—24no—
414#95—438no—
415#95—434no—
416#95—862no—
417#95—862no—
418#95—864no—
419#95—862no—
420#95—864no—
421#95—1722no—
422#95—1722no—
423#95—1722no—
424#95—1722no—
425#95—1722no—
426C24C23×D4311yescharacteristic
427C22×C4—22no—
428C22×C4—22no—
429C22×C4—22no—
430C22×C4—22no—
431C22×C4—21no—
432C22×C4—21no—
433C22×C4—21no—
434C22×C4—21no—
435C22×C4—21no—
436C22×C4—21no—
437C22×C4—21no—
438C22×C4—21no—
439C22×C4—21no—
440C22×C4—21no—
441C22×C4—21no—
442C22×C4—21no—
443C22×C4—22no—
444C22×C4—22no—
445C22×C4—22no—
446C22×C4—22no—
447C22×C4—22no—
448C22×C4—22no—
449C22×C4—22no—
450C22×C4—432no—
451C22×C4—432no—
452C22×C4—432no—
453C22×C4—432no—
454C22×C4—434no—
455C22×C4—432no—
456C22×C4—432no—
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—861no—
468C22×C4—862no—
469C22×C4—861no—
470C22×C4—861no—
471C22×C4—861no—
472C22×C4—861no—
473C22×C4—861no—
474C22×C4—862no—
475C22×C4—861no—
476C22×C4—862no—
477C22×C4—861no—
478C22×C4—861no—
479C22×C4—862no—
480C22×C4—862no—
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×C4—862no—
492C22×C4C2×Dic8614yes—
493C22×C4C2×Dic8612yes—
494C22×C4C2×C4×D4314yes—
495C22×C4C2×C4×D4312yes—
496C22×C4#1062190012yes—
497C22×C4#1062190012yes—
498C22×C4#1062190012yes—
499C22×C4Q8×D4312yes—
500C22×C4#1062190212yes—
501C22×C4#1062190212yes—
502C22×C4C2×C22⋊D4314yes—
503C22×C4C2×C22⋊D4312yes—
504C4⋊C4—48no—
505C4⋊C4—44no—
506C4⋊C4—868no—
507C4⋊C4—1728no—
508C4⋊C4—1724no—
509C4⋊C4Dic43⋊C4116yes—
510C42—44no—
511C42—868no—
512C42—1728no—
513C42—1724no—
514C23C22×C4×D4311yescharacteristic
515C23C22×C22⋊D4311yescharacteristic
516C23C2×Q8×D4311yescharacteristic
517C23C22×Dic8611yescharacteristic
518C23#41×D4311yescharacteristic
519C23#41×D4311yescharacteristic
520C23C2×#1062190011yescharacteristic
521C23C2×#1062190011yescharacteristic
522C23C2×#1062190011yescharacteristic
523C23C2×#1062190211yescharacteristic
524C23C2×#1062190211yescharacteristic
525C23#1306337011yescharacteristic
526C23#1306337111yescharacteristic
527C23#1306337111yescharacteristic
528C23#1306337311yescharacteristic
529C2×C4—24no—
530C2×C4—24no—
531C2×C4—24no—
532C2×C4—24no—
533C2×C4—24no—
534C2×C4—24no—
535C2×C4—22no—
536C2×C4—22no—
537C2×C4—22no—
538C2×C4—22no—
539C2×C4—22no—
540C2×C4—22no—
541C2×C4—41no—
542C2×C4—41no—
543C2×C4—41no—
544C2×C4—41no—
545C2×C4—41no—
546C2×C4—41no—
547C2×C4—41no—
548C2×C4—41no—
549C2×C4—42no—
550C2×C4—42no—
551C2×C4—42no—
552C2×C4—42no—
553C2×C4—42no—
554C2×C4—42no—
555C2×C4—42no—
556C2×C4—434no—
557C2×C4—862no—
558C2×C4—862no—
559C2×C4—862no—
560C2×C4—862no—
561C2×C4—862no—
562C2×C4—862no—
563C2×C4—862no—
564C2×C4—862no—
565C2×C4—862no—
566C2×C4—864no—
567C2×C4—862no—
568C2×C4—862no—
569C2×C4—864no—
570C2×C4—862no—
571C2×C4—864no—
572C2×C4—862no—
573C2×C4—862no—
574C2×C4—862no—
575C2×C4—1722no—
576C2×C4—1722no—
577C2×C4—1722no—
578C2×C4—1722no—
579C2×C4—1722no—
580C2×C4—1722no—
581C2×C4—1722no—
582C2×C4—1721no—
583C2×C4—1721no—
584C2×C4—1721no—
585C2×C4—1721no—
586C2×C4—1721no—
587C2×C4—1721no—
588C2×C4—1721no—
589C2×C4—1721no—
590C2×C4—1721no—
591C2×C4—1722no—
592C2×C4—1721no—
593C2×C4—1722no—
594C2×C4—1722no—
595C2×C4—1721no—
596C2×C4—1722no—
597C2×C4—1721no—
598C2×C4C2×Dic43⋊C418yes—
599C2×C4C2×Dic43⋊C414yes—
600C2×C4#1306328314yes—
601C2×C4#1306328314yes—
602C2×C4#1306331214yes—
603C2×C4#1306331414yes—
604C2×C4#1306331614yes—
605C2×C4#1306331614yes—
606C22C22×Dic43⋊C411yescharacteristic
607C22C2×#1306328311yescharacteristic
608C22C2×#1306328311yescharacteristic
609C22C4×Q8×D4311yescharacteristic
610C22C4×#1062190011yescharacteristic
611C22#1458337111yescharacteristic
612C22#1458338111yescharacteristic
613C22C2×#1306331211yescharacteristic
614C22C2×#1306331411yescharacteristic
615C22C2×#1306331611yescharacteristic
616C22C2×#1306331611yescharacteristic
617C22#1458343011yescharacteristic
618C22#1458343411yescharacteristic
619C22#1458345111yescharacteristic
620C22#1458345411yescharacteristic
621C22#1458350211yescharacteristic
622C22#1458350511yescharacteristic
623C22#1458352211yescharacteristic
624C22#1458352311yescharacteristic
625C22#1458353711yescharacteristic
626C22#1458354311yescharacteristic
627C22Q8×C22⋊D4311yescharacteristic
628C22#1458356811yescharacteristic
629C22#1458359611yescharacteristic
630C22#1458360111yescharacteristic
631C22#1458360211yescharacteristic
632C22#1458360211yescharacteristic
633C22#1458360611yescharacteristic
634C22#1458360711yescharacteristic
635C22#1458360811yescharacteristic
636C22#1458361011yescharacteristic
637C22#1458362011yescharacteristic
638C22#1458362311yescharacteristic
639C22#1458362511yescharacteristic
640C22Q8×Dic8611yescharacteristic
641C4—28no—
642C4—42no—
643C4—42no—
644C4—82no—
645C4—864no—
646C4—3442no—
647C4—1722no—
648C4—1722no—
649C4—1722no—
650C4—1724no—
651C4#1458276418yes—
652C2C2×#1458276411yescharacteristic
653C2#1913706611yescharacteristic
654C2#1913723411yescharacteristic
655C2#1913747111yescharacteristic
656C2#1913748711yescharacteristic
657C2#1913750011yescharacteristic
658C2Q8×Dic43⋊C411yescharacteristic
659C2#1913894911yescharacteristic
660C2#1913895011yescharacteristic
661C2#1913897111yescharacteristic
662C2#1913897211yescharacteristic
663C2#1913912411yescharacteristic
664C2#1913912511yescharacteristic
665C2#1913914611yescharacteristic
666C2#1913914711yescharacteristic
subgroupG/H
center, FrattiniC24C23×D43
commutatorC23×C43C23×C4
FittingC2×C43×#389C2
socle, prime radical, cosocleC24×C43C24
hypercenterC2×#389D43
hypocenterC43#13933
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C24 ◁ C2×#389

Complements

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

NH ≅ G/Ntype
19. C4⋊C4×Dic43C4semidirect
371. C43#13933semidirect

Maximal subgroups

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

subgroupindex
C2×#145827982
C2×C4⋊C4×Dic432
#191328542
#191328512
#191328252
#191328242
#191328212
C4×C43⋊#952
C2×C43×#3892
#1393343