Finite Group Databasebeta

← #25130913

Subgroups — #25130913

Order 11008.

1198 conjugacy classes of subgroups.

The subgroup lattice has 616 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583454C211yesmaximal, characteristic, complemented
2C2×#14583190C211yesmaximal, characteristic, complemented
3C2×#14583101C211yesmaximal, characteristic, complemented
4C4×#13063300C211yesmaximal, characteristic
5#19135790C212yesmaximal, complemented
6#19135597C212yesmaximal
7#19135543C211yesmaximal, characteristic, complemented
8#19134948C212yesmaximal, complemented
9#19134865C212yesmaximal, complemented
10#19134572C211yesmaximal, characteristic, complemented
11C43×#1981C211yesmaximal, characteristic, complemented
12C22×#10621884C2212yes—
13#14583454—24no—
14#14583454—24no—
15C2×#13063325C2211yescharacteristic
16C2×#13063316—21no—
17C2×#13063305—21no—
18C2×#13063301C2212yes—
19C2×#13063300C2211yescharacteristic
20C2×Q8×Dic43C2212yes—
21C2×#13063290—21no—
22C2×C4×D172—21no—
23C2×C4×D172C2211yescharacteristic
24C2×#13063283—21no—
25C2×C42×D43C2211yescharacteristic
26#14583190—24no—
27#14583101—24no—
28C2×#13063257C2212yes—
29C2×C4⋊(C43⋊C8)C2211yescharacteristic
30C2×#13063249C2212yes—
31C2×#13063247C2212yes—
32C2×(C2×D43)⋊C8C2212yes—
33#14582800C2211yescharacteristic
34#14582798C2211yescharacteristic
35#14582791—21no—
36#14582777—21no—
37#14582756C2211yescharacteristic
38C4×(C2×D43)⋊C4—21no—
39#14582661C2212yes—
40#14582661C2212yes—
41#14582653C2212yes—
42C2×C4⋊Q8×C43C2211yescharacteristic
43C2×C4⋊C8×C43C2211yescharacteristic
44C2×#103×C43C2212yes—
45C2×#103×C43C2212yes—
46C4×C4⋊C4×C43C2211yescharacteristic
47C22×Dic86—21no—
48C22×D172—21no—
49C22×D172C2311yescharacteristic
50C22×C4×D43—21no—
51C22×C4×D43D411yescharacteristic
52C22×C4×D43D411yescharacteristic
53C22×C4×D43C2311yescharacteristic
54C2×#10621884—24no—
55C2×#10621884—24no—
56C2×#10621884—42no—
57C22×C43⋊C8C2312yes—
58#13063325—22no—
59#13063325D414yescomplemented
60#13063316—28no—
61#13063305—28no—
62#13063301—24no—
63#13063301—24no—
64#13063300—22no—
65#13063300—22no—
66Q8×Dic43—24no—
67Q8×Dic43—24no—
68#13063290—28no—
69C4×D172—22no—
70C4×D172—22no—
71C4×D172—44no—
72#13063283—28no—
73C2×C4⋊Dic43—21no—
74C2×C4⋊Dic43—22no—
75C2×C4⋊Dic43—21no—
76C2×C4⋊Dic43C2311yescharacteristic
77C2×C4⋊Dic43C2312yes—
78C2×Dic43⋊C4—22no—
79C2×(C2×D43)⋊C4—22no—
80C2×(C2×D43)⋊C4—21no—
81C2×(C2×D43)⋊C4—21no—
82C2×(C2×D43)⋊C4—21no—
83C2×(C2×D43)⋊C4—21no—
84C2×(C2×D43)⋊C4—21no—
85C2×C4×Dic43—22no—
86C2×C4×Dic43D411yescharacteristic
87C2×C4×Dic43D411yescharacteristic
88C2×C4×Dic43C2311yescharacteristic
89C42×D43—22no—
90C42×D43—22no—
91#13063257—24no—
92C4⋊(C43⋊C8)—22no—
93#13063249—24no—
94#13063247—24no—
95(C2×D43)⋊C8—42no—
96C43⋊#95—21no—
97C43⋊#95—21no—
98C22×Q8×C43C2312yes—
99C22×C8×C43C2312yes—
100C4⋊Q8×C43—22no—
101C4⋊Q8×C43D414yescomplemented
102C2×C4⋊C4×C43—21no—
103C2×C4⋊C4×C43—21no—
104C2×C4⋊C4×C43C2311yescharacteristic
105C2×C4⋊C4×C43C2311yescharacteristic
106C2×C42×C43—21no—
107C2×C42×C43C2311yescharacteristic
108C4⋊C8×C43—22no—
109#103×C43—24no—
110#103×C43—42no—
111#95×C43—21no—
112C23×D43—21no—
113C23×D43C2×D411yescharacteristic
114C2×Q8×C43—22no—
115C2×Q8×C43—22no—
116C2×Q8×C43—22no—
117C2×Q8×C43—22no—
118C2×Q8×C43—22no—
119C2×Q8×C43C2×D414yes—
120C22×C4×C43—21no—
121C22×C4×C43—22no—
122C22×C4×C43—21no—
123C22×C4×C43C2×D411yescharacteristic
124C22×C4×C43C2×D411yescharacteristic
125C22×C4×C43C2411yescharacteristic
126C22×Dic43—22no—
127C22×Dic43—21no—
128C22×Dic43C2×D411yescharacteristic
129C22×Dic43C2×D411yescharacteristic
130C22×Dic43C2×D411yescharacteristic
131C2×D172—24no—
132C2×D172—21no—
133C2×D172—21no—
134C2×D172—21no—
135C2×D172—21no—
136C2×D172—21no—
137C2×D172—42no—
138C2×D172—42no—
139C2×D172#4112yes—
140C2×C4×D43—22no—
141C2×C4×D43—22no—
142C2×C4×D43—22no—
143C2×C4×D43—21no—
144C2×C4×D43—21no—
145C2×C4×D43—21no—
146C2×C4×D43—21no—
147C2×C4×D43—21no—
148C2×C4×D43—21no—
149C2×C4×D43—41no—
150C2×C4×D43—41no—
151C2×C4×D43—42no—
152C2×C4×D43—42no—
153C2×C4×D43—42no—
154C2×C4×D43SD1614yescomplemented
155C2×Dic86—24no—
156C2×Dic86—42no—
157C2×Dic86—42no—
158C2×C8×C43—22no—
159C2×C8×C43—22no—
160C2×C8×C43—22no—
161C4⋊C4×C43—24no—
162C4⋊C4×C43—24no—
163C4⋊C4×C43—21no—
164C4⋊C4×C43—21no—
165C4⋊C4×C43—21no—
166C4⋊C4×C43#4112yes—
167C42×C43—42no—
168C42×C43C2×D412yes—
169C42×C43C2×D412yes—
170#10621884—48no—
171(C2×D43)⋊C4—28no—
172(C2×D43)⋊C4—24no—
173(C2×D43)⋊C4—42no—
174(C2×D43)⋊C4—42no—
175(C2×D43)⋊C4—42no—
176(C2×D43)⋊C4—42no—
177C4⋊Dic43—28no—
178C4⋊Dic43—24no—
179C4⋊Dic43—22no—
180C4⋊Dic43—21no—
181C4⋊Dic43—21no—
182C4⋊Dic43—42no—
183C4⋊Dic43C2×D414yes—
184Dic43⋊C4—28no—
185C4×Dic43—28no—
186C4×Dic43—22no—
187C4×Dic43—22no—
188C4×Dic43—21no—
189C4×Dic43—21no—
190C2×C43⋊C8—22no—
191C2×C43⋊C8—22no—
192C2×C43⋊C8—22no—
193C23×C43C22×D411yescharacteristic
194C22×D43—21no—
195C22×D43—21no—
196C22×D43—21no—
197C22×D43—21no—
198C22×D43—21no—
199C22×D43—21no—
200C22×D43—22no—
201C22×D43—41no—
202C22×D43—41no—
203C22×D43—41no—
204C22×D43—41no—
205C22×D43—41no—
206C22×D43—41no—
207C22×D43C2×SD1612yes—
208Q8×C43—24no—
209Q8×C43—24no—
210Q8×C43—42no—
211Q8×C43—42no—
212C2×C4×C43—21no—
213C2×C4×C43—21no—
214C2×C4×C43—24no—
215C2×C4×C43—22no—
216C2×C4×C43—42no—
217C2×C4×C43—42no—
218C2×C4×C43—41no—
219C2×C4×C43—41no—
220C2×C4×C43—41no—
221C2×C4×C43—41no—
222C2×C4×C43—41no—
223C2×C4×C43#12012yes—
224C2×C4×C43#12012yes—
225C2×C4×C43C2×SD1612yes—
226C2×C4×C43#13712yes—
227C2×C4×C43C22×D411yescharacteristic
228C2×C4×C43C22×D411yescharacteristic
229C2×C4×C43C2×#4111yescharacteristic
230C2×C4×C43C2×#4111yescharacteristic
231C2×C4×C43H(5,𝔽2)11yescharacteristic
232C2×C4×C432−1+411yescharacteristic
233C2×Dic43—21no—
234C2×Dic43—21no—
235C2×Dic43—21no—
236C2×Dic43—21no—
237C2×Dic43—24no—
238C2×Dic43—21no—
239C2×Dic43—21no—
240C2×Dic43—21no—
241C2×Dic43—21no—
242C2×Dic43—42no—
243C2×Dic43—42no—
244C2×Dic43—41no—
245C2×Dic43—41no—
246C2×Dic43—41no—
247C2×Dic43C2×SD1612yes—
248D172—22no—
249D172—22no—
250D172—48no—
251D172—41no—
252D172—41no—
253C4×D43—28no—
254C4×D43—44no—
255C4×D43—41no—
256C4×D43—41no—
257C4×D43—41no—
258C4×D43—41no—
259C4×D43—84no—
260Dic86—48no—
261C8×C43—42no—
262C43⋊C8—42no—
263#24151—431nomaximal, Sylow
264C22×C43C2×#12011yescharacteristic
265C22×C43#52511yescharacteristic
266C22×C43#53711yescharacteristic
267C22×C43C22×SD1611yescharacteristic
268C22×C43C2×#13711yescharacteristic
269C22×C43#57511yescharacteristic
270C22×C43#57511yescharacteristic
271C2×D43—22no—
272C2×D43—22no—
273C2×D43—22no—
274C2×D43—41no—
275C2×D43—41no—
276C2×D43—41no—
277C2×D43—41no—
278C2×D43—42no—
279C2×D43—42no—
280C2×D43—42no—
281C2×D43—81no—
282C2×D43—81no—
283C2×D43—81no—
284C2×D43—81no—
285C4×C43—22no—
286C4×C43—42no—
287C4×C43—44no—
288C4×C43—81no—
289C4×C43#44814yes—
290C4×C43#54611yescharacteristic
291C4×C43#54711yescharacteristic
292C4×C43#54811yescharacteristic
293C4×C43#55011yescharacteristic
294Dic43—22no—
295Dic43—41no—
296Dic43—44no—
297Dic43—41no—
298Dic43—81no—
299C2×#533—431no—
300C2×#476—431no—
301C2×#461—431no—
302C4×#121—431no—
303#2035—432no—
304#2000—432no—
305#1987—431no—
306#1981D4311yescharacteristic, complemented
307#1880—432no—
308#1865—432no—
309#1797—431no—
310C2×C43#240711yescharacteristic
311C2×C43C2×#44811yescharacteristic
312C2×C43#300511yescharacteristic
313C2×C43#310111yescharacteristic
314C2×C43#311611yescharacteristic
315C2×C43#324611yescharacteristic
316C2×C43#325211yescharacteristic
317D43—42no—
318D43—82no—
319C22×SD16—432no—
320#533—864no—
321#533—864no—
322C2×C4⋊Q8—431no—
323C2×C4⋊Q8C2×D4311yescharacteristic
324C2×#125—861no—
325C2×C22⋊Q8—432no—
326C2×C22⋊Q8—861no—
327C2×#121—431no—
328C2×C4×Q8—432no—
329C2×C4×Q8—861no—
330C2×C4×D4—431no—
331C2×C4×D4—861no—
332C2×#117—861no—
333C22×C42—431no—
334#476—864no—
335#461—864no—
336C2×#106—432no—
337C2×C4⋊C8—431no—
338C2×C4⋊C8C2×D4311yescharacteristic
339C2×#103—432no—
340C2×#103C2×D4312yes—
341C2×#103C2×D4312yes—
342C2×#102—432no—
343C2×C22⋊C8—432no—
344#390—431no—
345#389—431no—
346#388—861no—
347#386—861no—
348#380—431no—
349C4×C4⋊C4C2×D4311yescharacteristic
350C4×C22⋊C4—861no—
351#340—432no—
352#340—432no—
353#336—432no—
354C43#2415111yescharacteristic, complemented, Sylow
355C22×Q8—861no—
356C22×Q8C22×D4312yes—
357C22×D4—431no—
358C22×D4—861no—
359C23×C4—431no—
360C23×C4—431no—
361C23×C4—431no—
362C23×C4—861no—
363C2×SD16—864no—
364C2×SD16—864no—
365C2×SD16—1722no—
366C22×C8—432no—
367C22×C8C22×D4312yes—
368C4⋊Q8—22no—
369C4⋊Q8—434no—
370C4⋊Q8—862no—
371C4⋊Q8D17214yescomplemented
372#125—868no—
373C22⋊Q8—868no—
374C22⋊Q8—864no—
375C22⋊Q8—864no—
376#121—862no—
377#121—862no—
378C4×Q8—868no—
379C4×Q8—864no—
380C4×Q8—864no—
381C4×D4—862no—
382C4×D4—862no—
383C4×D4—1724no—
384#117—868no—
385C2×C4⋊C4—21no—
386C2×C4⋊C4—21no—
387C2×C4⋊C4—432no—
388C2×C4⋊C4—431no—
389C2×C4⋊C4—862no—
390C2×C4⋊C4—862no—
391C2×C4⋊C4—861no—
392C2×C4⋊C4—861no—
393C2×C4⋊C4C22×D4311yescharacteristic
394C2×C4⋊C4C22×D4311yescharacteristic
395C2×C22⋊C4—861no—
396C2×C22⋊C4—862no—
397C2×C22⋊C4—861no—
398C2×C22⋊C4—861no—
399C2×C22⋊C4—861no—
400C2×C22⋊C4—861no—
401C2×C42—21no—
402C2×C42—431no—
403C2×C42—431no—
404C2×C42—431no—
405C2×C42—862no—
406C2×C42—862no—
407C2×C42—862no—
408C2×C42C22×D4311yescharacteristic
409#106—864no—
410C4⋊C8—22no—
411C4⋊C8—862no—
412#103—24no—
413#103—42no—
414#103—864no—
415#102—864no—
416C22⋊C8—1722no—
417#95—21no—
418#95—861no—
419#95—861no—
420C24—431no—
421C24—861no—
422C2×Q8—22no—
423C2×Q8—22no—
424C2×Q8—22no—
425C2×Q8—22no—
426C2×Q8—22no—
427C2×Q8—864no—
428C2×Q8—1722no—
429C2×Q8—1722no—
430C2×Q8C2×D17214yes—
431C2×D4—432no—
432C2×D4—864no—
433C2×D4—861no—
434C2×D4—861no—
435C2×D4—861no—
436C2×D4—861no—
437C2×D4—861no—
438C2×D4—1722no—
439C2×D4—1722no—
440C22×C4—21no—
441C22×C4—22no—
442C22×C4—21no—
443C22×C4—431no—
444C22×C4—434no—
445C22×C4—431no—
446C22×C4—431no—
447C22×C4—862no—
448C22×C4—862no—
449C22×C4—862no—
450C22×C4—862no—
451C22×C4—861no—
452C22×C4—861no—
453C22×C4—861no—
454C22×C4—861no—
455C22×C4—861no—
456C22×C4—861no—
457C22×C4—861no—
458C22×C4—1721no—
459C22×C4—1721no—
460C22×C4—1722no—
461C22×C4—1722no—
462C22×C4—1722no—
463C22×C4D4×D4311yescharacteristic
464C22×C4D4×D4311yescharacteristic
465C22×C4C23×D4311yescharacteristic
466SD16—1728no—
467C2×C8—22no—
468C2×C8—22no—
469C2×C8—22no—
470C2×C8—862no—
471C2×C8—862no—
472C2×C8—862no—
473C4⋊C4—24no—
474C4⋊C4—24no—
475C4⋊C4—21no—
476C4⋊C4—21no—
477C4⋊C4—21no—
478C4⋊C4—434no—
479C4⋊C4—868no—
480C4⋊C4—868no—
481C4⋊C4—864no—
482C4⋊C4—862no—
483C4⋊C4—861no—
484C4⋊C4—861no—
485C4⋊C4—1722no—
486C4⋊C4#1062190012yes—
487C22⋊C4—868no—
488C22⋊C4—864no—
489C22⋊C4—1722no—
490C22⋊C4—1722no—
491C22⋊C4—1722no—
492C22⋊C4—1722no—
493C42—42no—
494C42—868no—
495C42—862no—
496C42—862no—
497C42—861no—
498C42—861no—
499C42C2×D17212yes—
500C42D4×D4312yes—
501C23—432no—
502C23—861no—
503C23—861no—
504C23—861no—
505C23—861no—
506C23—861no—
507C23—861no—
508C23—862no—
509C23—1721no—
510C23—1721no—
511C23—1721no—
512C23—1721no—
513C23—1721no—
514C23—1721no—
515C23C2×D4×D4311yescharacteristic
516Q8—24no—
517Q8—24no—
518Q8—42no—
519Q8—42no—
520Q8—1728no—
521D4—862no—
522D4—862no—
523D4—1728no—
524D4—1721no—
525D4—1721no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—24no—
529C2×C4—22no—
530C2×C4—42no—
531C2×C4—41no—
532C2×C4—41no—
533C2×C4—42no—
534C2×C4—41no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—432no—
538C2×C4—861no—
539C2×C4—861no—
540C2×C4—868no—
541C2×C4—861no—
542C2×C4—861no—
543C2×C4—864no—
544C2×C4—861no—
545C2×C4—861no—
546C2×C4—861no—
547C2×C4—861no—
548C2×C4—3444no—
549C2×C4—1724no—
550C2×C4—1721no—
551C2×C4—1721no—
552C2×C4—1721no—
553C2×C4—1722no—
554C2×C4—1722no—
555C2×C4—1721no—
556C2×C4—1721no—
557C2×C4—1721no—
558C2×C4—1721no—
559C2×C4#1306329512yes—
560C2×C4#1306329512yes—
561C2×C4SD16×D4312yes—
562C2×C4#1306335712yes—
563C2×C4C2×D4×D4311yescharacteristic
564C2×C4C22×D17211yescharacteristic
565C2×C4#41×D4311yescharacteristic
566C2×C4C2×#1062190011yescharacteristic
567C2×C4#1306337011yescharacteristic
568C2×C4#1306337211yescharacteristic
569C8—42no—
570C8—1722no—
571C22—862no—
572C22—862no—
573C22—862no—
574C22—3441no—
575C22—3441no—
576C22—3441no—
577C22—3441no—
578C22—1722no—
579C22—1722no—
580C22—1722no—
581C22—1721no—
582C22—1721no—
583C22—1721no—
584C22—1721no—
585C22C2×#1306329511yescharacteristic
586C22#1458340911yescharacteristic
587C22#1458347811yescharacteristic
588C22C2×SD16×D4311yescharacteristic
589C22C2×#1306335711yescharacteristic
590C22#1458369811yescharacteristic
591C22#1458369811yescharacteristic
592C4—22no—
593C4—44no—
594C4—42no—
595C4—81no—
596C4—862no—
597C4—3441no—
598C4—1721no—
599C4—1721no—
600C4—1724no—
601C4#1458303914yes—
602C4#1458354411yescharacteristic
603C4#1458355311yescharacteristic
604C4#1458355711yescharacteristic
605C4#1458356911yescharacteristic
606C2—3442no—
607C2—1722no—
608C2#1913793811yescharacteristic
609C2C2×#1458303911yescharacteristic
610C2#1914384111yescharacteristic
611C2#1914460211yescharacteristic
612C2#1914475611yescharacteristic
613C2#1914590811yescharacteristic
614C2#1914596611yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#1981C2
socleC23×C43C22×D4
prime radicalC2×#13063300C22
hypercenter#1981D43
hypocenterC43#24151
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1981

Complements

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

NH ≅ G/Ntype
1. C2×#14583454C2semidirect
2. C2×#14583190C2semidirect
3. C2×#14583101C2semidirect
5. #19135790C2semidirect
7. #19135543C2semidirect
8. #19134948C2semidirect
9. #19134865C2semidirect
10. #19134572C2semidirect
11. C43×#1981C2semidirect
59. #13063325D4semidirect
101. C4⋊Q8×C43D4semidirect
154. C2×C4×D43SD16semidirect
306. #1981D43semidirect
354. C43#24151semidirect
371. C4⋊Q8D172semidirect

Maximal subgroups

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

subgroupindex
C2×#145834542
C2×#145831902
C2×#145831012
C4×#130633002
#191357902
#191355972
#191355432
#191349482
#191348652
#191345722
C43×#19812
#2415143