Finite Group Databasebeta

← #25112772

Subgroups — #25112772

Order 11008.

1106 conjugacy classes of subgroups.

The subgroup lattice has 596 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583604C211yesmaximal, characteristic
2M16×C22⋊D43C212yesmaximal
3#19135582C212yesmaximal, complemented
4#19135063C212yesmaximal, complemented
5#19135062C212yesmaximal, complemented
6#19134675C211yesmaximal, characteristic, complemented
7#19134674C211yesmaximal, characteristic, complemented
8#19134590C211yesmaximal, characteristic, complemented
9#19134390C211yesmaximal, characteristic, complemented
10#343×D43C211yesmaximal, characteristic, complemented
11C2×C43×#343C211yesmaximal, characteristic, complemented
12C2×M16×D43C2212yes—
13#14583604—22no—
14#14583604—22no—
15#14583604—22no—
16#14583604—22no—
17C2×#13063324C2211yescharacteristic
18C2×#13063315C412yes—
19C2×#13063305C2211yescharacteristic
20C2×#13063304C412yes—
21C2×#13063304C2211yescharacteristic
22C2×#13063303C412yes—
23C2×#13063290C2211yescharacteristic
24C2×C4×C22⋊D43C412yes—
25C2×C4×C22⋊D43C2211yescharacteristic
26C2×C4⋊C4×D43C2211yescharacteristic
27#14582975—22no—
28#14582970—22no—
29#14582968—22no—
30C8×C22⋊D43—22no—
31#14582922C2212yes—
32C2×#13063243C2212yes—
33C2×#13063243C2212yes—
34#14582863C2212yes—
35#14582862C2212yes—
36M16×Dic43C2212yes—
37#14582668C2212yes—
38#14582668C2211yescharacteristic
39#14582668C2211yescharacteristic
40#14582667C2212yes—
41#14582667C2212yes—
42C22×M16×C43C2212yes—
43C22×C4⋊C4×C43C2211yescharacteristic
44C43×#343C2212yes—
45C43×#343C2211yescharacteristic
46C43×#343C2211yescharacteristic
47C22×Dic86C2×C412yes—
48C22×Dic86C2311yescharacteristic
49C22×C22⋊D43C2×C411yescharacteristic
50C22×C4×D43C2×C412yes—
51C22×C4×D43C2311yescharacteristic
52C2×#10621877C2312yes—
53C2×#10621877C2312yes—
54C2×#10621872—22no—
55M16×D43—24no—
56M16×D43—42no—
57C2×C8×D43—22no—
58#13063324—22no—
59#13063324—22no—
60#13063315—24no—
61#13063315—24no—
62#13063305—22no—
63#13063305—22no—
64#13063304—22no—
65#13063304—22no—
66#13063304—24no—
67#13063304—24no—
68#13063303—24no—
69#13063303—24no—
70#13063290—22no—
71#13063290—22no—
72C4×C22⋊D43—22no—
73C4×C22⋊D43—22no—
74C4×C22⋊D43—22no—
75C4×C22⋊D43—22no—
76C4×C22⋊D43D412yes—
77C4×C22⋊D43D412yes—
78C4×C22⋊D43D412yes—
79C4×C22⋊D43D412yes—
80C2×C4⋊Dic43C2×C412yes—
81C2×C4⋊Dic43C2311yescharacteristic
82C2×Dic43⋊C4C2×C412yes—
83C2×Dic43⋊C4C2×C412yes—
84C2×Dic43⋊C4C2×C412yes—
85C2×Dic43⋊C4C2×C412yes—
86C2×Dic43⋊C4C2×C411yescharacteristic
87C4⋊C4×D43—22no—
88C4⋊C4×D43—22no—
89C2×C22⋊Dic43C2×C412yes—
90C2×C22⋊Dic43C2×C411yescharacteristic
91C2×(C2×D43)⋊C4C2×C412yes—
92C2×(C2×D43)⋊C4C2×C411yescharacteristic
93C2×C4×Dic43C2×C412yes—
94C2×C4×Dic43C2311yescharacteristic
95Dic43⋊C8—22no—
96Dic43⋊C8—22no—
97#13063243—24no—
98#13063243—42no—
99C22⋊(C43⋊C8)—22no—
100C22⋊(C43⋊C8)—22no—
101(C2×D43)⋊C8—22no—
102(C2×D43)⋊C8—22no—
103#13063235—22no—
104C8×Dic43—22no—
105C23×C4×C43C2×C412yes—
106C23×C4×C43C2311yescharacteristic
107C2×M16×C43—22no—
108C2×M16×C43—24no—
109C2×M16×C43—42no—
110C2×M16×C43C2312yes—
111C2×M16×C43C2312yes—
112C22×C8×C43—22no—
113C2×C4⋊C4×C43—22no—
114C2×C4⋊C4×C43—22no—
115C2×C4⋊C4×C43C2×C412yes—
116C2×C4⋊C4×C43C2311yescharacteristic
117C2×C4⋊C4×C43C2311yescharacteristic
118C24×C43C22×C411yescharacteristic
119C23×D43C22×C411yescharacteristic
120C22×C4×C43—22no—
121C22×C4×C43—21no—
122C22×C4×C43—21no—
123C22×C4×C43—22no—
124C22×C4×C43—22no—
125C22×C4×C43—82no—
126C22×C4×C43C22×C411yescharacteristic
127C22×C4×C43C22×C412yes—
128C22×C4×C43C22×C412yes—
129C22×C4×C43C2×D412yes—
130C22×C4×C43C2×D412yes—
131C22×C4×C43C2411yescharacteristic
132C2×C22⋊D43—24no—
133C2×C22⋊D43C22⋊C411yescharacteristic
134C2×C22⋊D43C22⋊C411yescharacteristic
135C2×C22⋊D43C22⋊C411yescharacteristic
136C2×C22⋊D43C22⋊C411yescharacteristic
137C22×Dic43C22×C412yes—
138C22×Dic43C22×C411yescharacteristic
139C22×Dic43C22×C411yescharacteristic
140C22×Dic43C22×C412yes—
141C22×Dic43C22×C411yescharacteristic
142C2×C4×D43—22no—
143C2×C4×D43—21no—
144C2×C4×D43—21no—
145C2×C4×D43—22no—
146C2×C4×D43—22no—
147C2×C4×D43—82no—
148C2×C4×D43C2×D412yes—
149C2×C4×D43C2×D412yes—
150C2×Dic86—22no—
151C2×Dic86—22no—
152C2×Dic86—21no—
153C2×Dic86—21no—
154C2×Dic86—24no—
155C2×Dic86—82no—
156M16×C43—22no—
157M16×C43—22no—
158M16×C43—22no—
159M16×C43—44no—
160M16×C43#4114yes—
161C2×C8×C43—22no—
162C2×C8×C43—22no—
163C2×C8×C43—44no—
164C4⋊C4×C43—24no—
165C4⋊C4×C43—22no—
166C4⋊C4×C43—22no—
167C22⋊Dic43—22no—
168C22⋊Dic43—22no—
169C22⋊Dic43C22⋊C412yes—
170C22⋊Dic43C22⋊C412yes—
171(C2×D43)⋊C4—22no—
172(C2×D43)⋊C4—22no—
173(C2×D43)⋊C4C22⋊C412yes—
174(C2×D43)⋊C4C22⋊C412yes—
175C4⋊Dic43—22no—
176C4⋊Dic43—24no—
177Dic43⋊C4—24no—
178Dic43⋊C4—24no—
179Dic43⋊C4—22no—
180Dic43⋊C4—22no—
181Dic43⋊C4—24no—
182Dic43⋊C4C22⋊C412yes—
183Dic43⋊C4C22⋊C412yes—
184C4×Dic43—22no—
185C4×Dic43—22no—
186C4×Dic43C2×D412yes—
187C4×Dic43C2×D412yes—
188#10621877—22no—
189#10621877—22no—
190#10621877—22no—
191#10621877—22no—
192C2×C43⋊C8—22no—
193C2×C43⋊C8—22no—
194#10621872—44no—
195C8×D43—44no—
196C23×C43—21no—
197C23×C43—21no—
198C23×C43—22no—
199C23×C43—41no—
200C23×C43C2×C22⋊C411yescharacteristic
201C23×C43C2×C22⋊C411yescharacteristic
202C23×C43C23×C411yescharacteristic
203C22×D43—21no—
204C22×D43—21no—
205C22×D43—22no—
206C22×D43—41no—
207C22×D43C2×C22⋊C411yescharacteristic
208C22×D43C2×C22⋊C411yescharacteristic
209C2×C4×C43—21no—
210C2×C4×C43—21no—
211C2×C4×C43—22no—
212C2×C4×C43—22no—
213C2×C4×C43—22no—
214C2×C4×C43—22no—
215C2×C4×C43—22no—
216C2×C4×C43—22no—
217C2×C4×C43—42no—
218C2×C4×C43—42no—
219C2×C4×C43—82no—
220C2×C4×C43—82no—
221C2×C4×C43C2×C22⋊C412yes—
222C2×C4×C43C22×D412yes—
223C2×C4×C43C2×#4112yes—
224C2×C4×C43H(5,𝔽2)11yescharacteristic
225C2×C4×C432−1+411yescharacteristic
226C22⋊D43—22no—
227C22⋊D43—22no—
228C22⋊D43—22no—
229C22⋊D43#10114yescomplemented
230C2×Dic43—21no—
231C2×Dic43—21no—
232C2×Dic43—22no—
233C2×Dic43—22no—
234C2×Dic43—22no—
235C2×Dic43—22no—
236C2×Dic43—22no—
237C2×Dic43—41no—
238C2×Dic43—42no—
239C2×Dic43C2×C22⋊C411yescharacteristic
240C2×Dic43C2×C22⋊C412yes—
241C2×Dic43C2×C22⋊C412yes—
242C2×Dic43C2×C22⋊C411yescharacteristic
243C4×D43—22no—
244C4×D43—22no—
245C4×D43—22no—
246C4×D43—22no—
247C4×D43—82no—
248C4×D43—82no—
249Dic86—42no—
250Dic86—42no—
251Dic86—84no—
252C8×C43—24no—
253C8×C43—42no—
254C43⋊C8—42no—
255C43⋊C8—42no—
256#22481—431nomaximal, Sylow
257C22×C43—21no—
258C22×C43—21no—
259C22×C43—21no—
260C22×C43—21no—
261C22×C43—21no—
262C22×C43—21no—
263C22×C43—21no—
264C22×C43—42no—
265C22×C43—42no—
266C22×C43C2×#10112yes—
267C22×C43C22×C22⋊C411yescharacteristic
268C22×C43C4×#4111yescharacteristic
269C22×C43#52011yescharacteristic
270C2×D43—21no—
271C2×D43—21no—
272C2×D43—21no—
273C2×D43—21no—
274C2×D43—21no—
275C2×D43—42no—
276C2×D43—42no—
277C2×D43C2×#10112yes—
278C4×C43—22no—
279C4×C43—42no—
280C4×C43—42no—
281C4×C43#54612yes—
282C4×C43#54712yes—
283Dic43—22no—
284Dic43—21no—
285Dic43—22no—
286Dic43—42no—
287Dic43—42no—
288Dic43C2×#10112yes—
289C2×#554—431no—
290D4×M16—432no—
291#1997—432no—
292#1901—432no—
293#1901—432no—
294#1821—431no—
295#1821—431no—
296#1801—431no—
297C4×#101—431no—
298C2×#343—431no—
299C2×#343D4311yescharacteristic, complemented
300C2×C43—21no—
301C2×C43—21no—
302C2×C43—22no—
303C2×C43—41no—
304C2×C43#233911yescharacteristic
305C2×C43C22×#10111yescharacteristic
306C2×C43#288811yescharacteristic
307D43—22no—
308D43—41no—
309C22×M16—432no—
310C22×M16C2×D4312yes—
311#554—862no—
312#554—862no—
313#554—862no—
314#554—862no—
315C2×C4⋊Q8—431no—
316C2×#125—432no—
317C2×C22⋊Q8—431no—
318C2×C22⋊Q8—432no—
319C2×C22⋊Q8—431no—
320C2×C22⋊Q8—432no—
321C2×C4×Q8—431no—
322C2×C4×D4—431no—
323C2×C4×D4—432no—
324C22×C4⋊C4—431no—
325C22×C4⋊C4C2×D4311yescharacteristic
326#436—862no—
327#435—862no—
328#435—862no—
329C8×D4—862no—
330#423—432no—
331C2×#101—432no—
332C2×#101—432no—
333#407—432no—
334#407—432no—
335C4×M16—432no—
336#343—432no—
337#343—432no—
338#343—431no—
339#343—431no—
340#343—432no—
341#343C2×D4311yescharacteristic
342#343C2×D4312yes—
343#343C2×D4311yescharacteristic
344C43#2248111yescharacteristic, complemented, Sylow
345C22×Q8—432no—
346C22×Q8—431no—
347C22×D4—431no—
348C23×C4—431no—
349C23×C4—432no—
350C23×C4C4×D4312yes—
351C23×C4C22×D4311yescharacteristic
352C2×M16—22no—
353C2×M16—24no—
354C2×M16—42no—
355C2×M16—432no—
356C2×M16—432no—
357C2×M16—862no—
358C2×M16—864no—
359C2×M16—1722no—
360C2×M16C22×D4312yes—
361C2×M16C22×D4312yes—
362C22×C8—22no—
363C22×C8—862no—
364C4⋊Q8—862no—
365C4⋊Q8—862no—
366#125—864no—
367#125—864no—
368C22⋊Q8—864no—
369C22⋊Q8—864no—
370C22⋊Q8—864no—
371C22⋊Q8—864no—
372C22⋊Q8—862no—
373C22⋊Q8—862no—
374C22⋊Q8—862no—
375C22⋊Q8—862no—
376C4×Q8—862no—
377C4×Q8—862no—
378C4×D4—432no—
379C4×D4—432no—
380C4×D4—432no—
381C4×D4—432no—
382C4×D4—862no—
383C4×D4—862no—
384C4×D4—862no—
385C4×D4—862no—
386C2×C4⋊C4—22no—
387C2×C4⋊C4—22no—
388C2×C4⋊C4—431no—
389C2×C4⋊C4—432no—
390C2×C4⋊C4—432no—
391C2×C4⋊C4—432no—
392C2×C4⋊C4—432no—
393C2×C4⋊C4—432no—
394C2×C4⋊C4—431no—
395C2×C4⋊C4—862no—
396C2×C4⋊C4—862no—
397C2×C4⋊C4C4×D4312yes—
398C2×C4⋊C4C22×D4311yescharacteristic
399C2×C4⋊C4C22×D4311yescharacteristic
400C2×C22⋊C4—431no—
401C2×C22⋊C4—431no—
402C2×C22⋊C4—432no—
403C2×C22⋊C4—432no—
404C2×C42—431no—
405C2×C42—432no—
406C4⋊C8—862no—
407C4⋊C8—862no—
408#101—864no—
409#101—1722no—
410C22⋊C8—862no—
411C22⋊C8—862no—
412C22⋊C8—862no—
413C22⋊C8—862no—
414#97—862no—
415C4×C8—862no—
416C24—431no—
417C24C2×C4×D4311yescharacteristic
418C2×Q8—864no—
419C2×Q8—862no—
420C2×Q8—862no—
421C2×Q8—861no—
422C2×Q8—861no—
423C2×Q8—3442no—
424C2×D4—431no—
425C2×D4—431no—
426C2×D4—431no—
427C2×D4—431no—
428C2×D4—864no—
429C22×C4—22no—
430C22×C4—21no—
431C22×C4—21no—
432C22×C4—22no—
433C22×C4—22no—
434C22×C4—82no—
435C22×C4—431no—
436C22×C4—431no—
437C22×C4—431no—
438C22×C4—432no—
439C22×C4—432no—
440C22×C4—432no—
441C22×C4—432no—
442C22×C4—862no—
443C22×C4—862no—
444C22×C4—862no—
445C22×C4—861no—
446C22×C4—861no—
447C22×C4—3442no—
448C22×C4C2×C4×D4311yescharacteristic
449C22×C4C2×C4×D4312yes—
450C22×C4C2×C4×D4312yes—
451C22×C4D4×D4312yes—
452C22×C4D4×D4312yes—
453C22×C4C23×D4311yescharacteristic
454M16—22no—
455M16—22no—
456M16—22no—
457M16—44no—
458M16—862no—
459M16—862no—
460M16—862no—
461M16—862no—
462M16—1724no—
463M16#1062189814yes—
464C2×C8—22no—
465C2×C8—22no—
466C2×C8—44no—
467C2×C8—862no—
468C2×C8—862no—
469C2×C8—1724no—
470C4⋊C4—24no—
471C4⋊C4—22no—
472C4⋊C4—22no—
473C4⋊C4—432no—
474C4⋊C4—432no—
475C4⋊C4—864no—
476C4⋊C4—862no—
477C4⋊C4—862no—
478C4⋊C4—864no—
479C4⋊C4—864no—
480C4⋊C4—864no—
481C4⋊C4—862no—
482C22⋊C4—432no—
483C22⋊C4—432no—
484C22⋊C4—432no—
485C22⋊C4—432no—
486C22⋊C4—862no—
487C22⋊C4—862no—
488C22⋊C4—862no—
489C22⋊C4—862no—
490C42—432no—
491C42—432no—
492C42—862no—
493C42—862no—
494C23—21no—
495C23—21no—
496C23—22no—
497C23—41no—
498C23—431no—
499C23—431no—
500C23—862no—
501C23—861no—
502C23—861no—
503C23—1721no—
504C23C22⋊C4×D4311yescharacteristic
505C23C22⋊C4×D4311yescharacteristic
506C23C22×C4×D4311yescharacteristic
507Q8—3444no—
508Q8—1722no—
509Q8—1722no—
510D4—434no—
511D4—862no—
512D4—862no—
513D4—862no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—22no—
517C2×C4—22no—
518C2×C4—22no—
519C2×C4—22no—
520C2×C4—22no—
521C2×C4—22no—
522C2×C4—42no—
523C2×C4—42no—
524C2×C4—82no—
525C2×C4—82no—
526C2×C4—431no—
527C2×C4—431no—
528C2×C4—432no—
529C2×C4—432no—
530C2×C4—862no—
531C2×C4—861no—
532C2×C4—861no—
533C2×C4—862no—
534C2×C4—862no—
535C2×C4—862no—
536C2×C4—862no—
537C2×C4—862no—
538C2×C4—862no—
539C2×C4—862no—
540C2×C4—862no—
541C2×C4—3442no—
542C2×C4—3442no—
543C2×C4—1721no—
544C2×C4—1722no—
545C2×C4C22⋊C4×D4312yes—
546C2×C4C2×D4×D4312yes—
547C2×C4C2×#1062189812yes—
548C2×C4#1306337011yescharacteristic
549C2×C4#1306337311yescharacteristic
550C8—24no—
551C8—42no—
552C8—1722no—
553C8—1722no—
554C22—21no—
555C22—21no—
556C22—21no—
557C22—21no—
558C22—21no—
559C22—21no—
560C22—21no—
561C22—42no—
562C22—42no—
563C22—432no—
564C22—861no—
565C22—861no—
566C22—861no—
567C22—861no—
568C22—861no—
569C22—1722no—
570C22—1722no—
571C22#101×D4312yes—
572C22C2×C22⋊C4×D4311yescharacteristic
573C22C4×#1062189811yescharacteristic
574C22#1458338011yescharacteristic
575C4—22no—
576C4—42no—
577C4—42no—
578C4—432no—
579C4—862no—
580C4—861no—
581C4—862no—
582C4—1722no—
583C4—1722no—
584C4#1458353912yes—
585C4#1458355012yes—
586C2—21no—
587C2—21no—
588C2—22no—
589C2—41no—
590C2—862no—
591C2—1721no—
592C2#1913742211yescharacteristic
593C2C2×#101×D4311yescharacteristic
594C2#1914307111yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D43
commutatorC23×C43C23×C4
FrattiniC22×C4C23×D43
FittingC2×C43×#343C2
socleC22×C43C22×C22⋊C4
prime radicalC22×C22⋊D43C2×C4
cosocleC22×C4×C43C24
hypercenterC2×#343D43
hypocenterC43#22481
LCSG ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#343

Complements

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

NH ≅ G/Ntype
3. #19135582C2semidirect
4. #19135063C2semidirect
5. #19135062C2semidirect
6. #19134675C2semidirect
7. #19134674C2semidirect
8. #19134590C2semidirect
9. #19134390C2semidirect
10. #343×D43C2semidirect
11. C2×C43×#343C2semidirect
229. C22⋊D43#101semidirect
299. C2×#343D43semidirect
344. C43#22481semidirect

Maximal subgroups

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

subgroupindex
C2×#145836042
M16×C22⋊D432
#191355822
#191350632
#191350622
#191346752
#191346742
#191345902
#191343902
#343×D432
C2×C43×#3432
#2248143