Finite Group Databasebeta

← #25165241

Subgroups — #25165241

Order 11008.

732 conjugacy classes of subgroups.

The subgroup lattice has 608 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19139111C211yesmaximal, characteristic, complemented
2#19137664C211yesmaximal, characteristic
3#19136000C211yesmaximal, characteristic
4#19135968C211yesmaximal, characteristic
5#19135837C211yesmaximal, characteristic
6#19135837C211yesmaximal, characteristic
7#19135271C211yesmaximal, characteristic, complemented
8#19135230C211yesmaximal, characteristic, complemented
9#19135188C211yesmaximal, characteristic, complemented
10#19135181C211yesmaximal, characteristic, complemented
11#19134852C211yesmaximal, characteristic, complemented
12#19134845C211yesmaximal, characteristic
13#19134601C211yesmaximal, characteristic, complemented
14C4×#13063247C211yesmaximal, characteristic
15C43×#1916C211yesmaximal, characteristic, complemented
16C2×#13063315—21no—
17C2×#13063313C2211yescharacteristic
18C2×C4×Dic86C2211yescharacteristic
19C2×C4×D172C2211yescharacteristic
20C2×#13063259C2211yescharacteristic
21C2×#13063257C2211yescharacteristic
22C2×#13063250C2211yescharacteristic
23C2×#13063250C2211yescharacteristic
24C2×#13063250C2211yescharacteristic
25C2×#13063250C2211yescharacteristic
26C2×#13063247C2211yescharacteristic
27C2×#13063247C2211yescharacteristic
28C2×#13063247C2211yescharacteristic
29C2×#13063247C2211yescharacteristic
30#14582839—21no—
31#14582829—21no—
32#14582805C2211yescharacteristic
33#14582801C2211yescharacteristic
34#14582797C2211yescharacteristic
35#14582797C2211yescharacteristic
36#14582797C2211yescharacteristic
37#14582797C2211yescharacteristic
38#14582789—21no—
39#14582788—21no—
40#14582784—21no—
41#14582770—21no—
42#14582769C2211yescharacteristic
43C4×C4⋊Dic43C2211yescharacteristic
44C4×C4⋊Dic43C2211yescharacteristic
45#14582746—21no—
46#14582662C2211yescharacteristic
47#14582662C2211yescharacteristic
48#14582662C2211yescharacteristic
49#14582662C2211yescharacteristic
50#14582662C2211yescharacteristic
51#14582662C2211yescharacteristic
52C2×C4⋊C8×C43C2211yescharacteristic
53C2×C4×C8×C43C2211yescharacteristic
54C4×C4⋊C4×C43C2211yescharacteristic
55C43×#336C2211yescharacteristic
56C43×#336C2211yescharacteristic
57C43×#336C2211yescharacteristic
58C43×#336C2211yescharacteristic
59C22×Dic86C2311yescharacteristic
60C22×D172C2311yescharacteristic
61C22×C4×D43—21no—
62#13063315—44no—
63#13063313—22no—
64#13063313—22no—
65C4×Dic86—22no—
66C4×Dic86—41no—
67C4×D172—22no—
68C4×D172—41no—
69C2×C4⋊Dic43—21no—
70C2×C4⋊Dic43—21no—
71C2×C4⋊Dic43C2311yescharacteristic
72C2×C4⋊Dic43C2311yescharacteristic
73C2×C4⋊Dic43C2311yescharacteristic
74C2×C4⋊Dic43C2311yescharacteristic
75C2×C4⋊Dic43C2311yescharacteristic
76C2×C4⋊Dic43C2311yescharacteristic
77C2×Dic43⋊C4—21no—
78C2×Dic43⋊C4—21no—
79C2×Dic43⋊C4—21no—
80C2×Dic43⋊C4—21no—
81C2×Dic43⋊C4—21no—
82C2×(C2×D43)⋊C4—21no—
83C2×(C2×D43)⋊C4—21no—
84C2×(C2×D43)⋊C4—21no—
85C2×(C2×D43)⋊C4—21no—
86C2×(C2×D43)⋊C4—21no—
87C2×C4×Dic43—21no—
88C2×C4×Dic43—21no—
89C2×C4×Dic43—21no—
90#13063259—22no—
91#13063257—22no—
92#13063250—22no—
93#13063250—22no—
94#13063250—22no—
95#13063250—41no—
96#13063247—22no—
97#13063247—22no—
98#13063247—22no—
99#13063247—41no—
100C43⋊#95—21no—
101C43⋊#95—21no—
102C43⋊#95—21no—
103C43⋊#95—21no—
104C43⋊#95—21no—
105C43⋊#95—21no—
106C43⋊#95—21no—
107C43⋊#95—21no—
108C22×C8×C43C2311yescharacteristic
109C22×C8×C43C2311yescharacteristic
110C22×C8×C43C2311yescharacteristic
111C22×C8×C43C2311yescharacteristic
112C2×C4⋊C4×C43D411yescharacteristic
113C2×C4⋊C4×C43D411yescharacteristic
114C2×C42×C43C2311yescharacteristic
115C2×C42×C43C2311yescharacteristic
116C2×C42×C43C2311yescharacteristic
117C4⋊C8×C43—41no—
118C4×C8×C43—41no—
119#95×C43D411yescharacteristic
120#95×C43D411yescharacteristic
121C23×D43—21no—
122C22×C4×C43C2×D411yescharacteristic
123C22×C4×C43C2×D411yescharacteristic
124C22×C4×C43C2×D411yescharacteristic
125C22×C4×C43C2×D411yescharacteristic
126C22×C4×C43C2×D411yescharacteristic
127C22×C4×C43C2×D411yescharacteristic
128C22×C4×C43C2411yescharacteristic
129C22×Dic43—21no—
130C22×Dic43—21no—
131C22×Dic43—21no—
132C22×Dic43—21no—
133C22×Dic43—21no—
134C22×Dic43—21no—
135C22×Dic43—21no—
136C2×D172—21no—
137C2×D172—21no—
138C2×D172—21no—
139C2×D172—21no—
140C2×D172—21no—
141C2×D172#4112yes—
142C2×C4×D43—42no—
143C2×C4×D43—42no—
144C2×C4×D43—81no—
145C2×Dic86—21no—
146C2×Dic86—21no—
147C2×Dic86—21no—
148C2×Dic86—21no—
149C2×Dic86—21no—
150C2×Dic86#4112yes—
151C2×C8×C43—21no—
152C2×C8×C43—21no—
153C2×C8×C43—21no—
154C2×C8×C43—21no—
155C2×C8×C43—21no—
156C2×C8×C43—21no—
157C2×C8×C43—21no—
158C2×C8×C43—21no—
159C2×C8×C43—21no—
160C2×C8×C43—21no—
161C2×C8×C43—21no—
162C2×C8×C43—21no—
163C4⋊C4×C43—22no—
164C4⋊C4×C43—22no—
165C42×C43—21no—
166C42×C43—21no—
167C42×C43—21no—
168C42×C43—21no—
169C42×C43—21no—
170C42×C43—21no—
171(C2×D43)⋊C4—24no—
172(C2×D43)⋊C4—24no—
173(C2×D43)⋊C4—42no—
174(C2×D43)⋊C4—42no—
175(C2×D43)⋊C4—81no—
176C4⋊Dic43—21no—
177C4⋊Dic43—21no—
178C4⋊Dic43—21no—
179C4⋊Dic43—21no—
180C4⋊Dic43—21no—
181C4⋊Dic43—21no—
182C4⋊Dic43—21no—
183C4⋊Dic43—21no—
184C4⋊Dic43—21no—
185C4⋊Dic43—21no—
186C4⋊Dic43—42no—
187C4⋊Dic43—42no—
188C4⋊Dic43#4112yes—
189C4⋊Dic43#4112yes—
190Dic43⋊C4—42no—
191Dic43⋊C4—42no—
192Dic43⋊C4—42no—
193Dic43⋊C4—42no—
194Dic43⋊C4—42no—
195C4×Dic43—42no—
196C4×Dic43—42no—
197C4×Dic43—81no—
198C23×C43C22×D411yescharacteristic
199C22×D43—22no—
200C22×D43—41no—
201C22×D43—41no—
202C22×D43—41no—
203C22×D43—41no—
204C22×D43—41no—
205C22×D43—41no—
206C2×C4×C43—21no—
207C2×C4×C43—21no—
208C2×C4×C43—21no—
209C2×C4×C43—21no—
210C2×C4×C43—21no—
211C2×C4×C43—21no—
212C2×C4×C43—21no—
213C2×C4×C43—21no—
214C2×C4×C43—21no—
215C2×C4×C43—21no—
216C2×C4×C43—21no—
217C2×C4×C43—21no—
218C2×C4×C43—21no—
219C2×C4×C43—21no—
220C2×C4×C43—21no—
221C2×C4×C43—21no—
222C2×C4×C43#13512yes—
223C2×C4×C43AGL(1,ℤ/8)12yes—
224C2×C4×C43C2×#4111yescharacteristic
225C2×C4×C43C2×#4111yescharacteristic
226C2×C4×C43C2×#4111yescharacteristic
227C2×C4×C43C2×#4111yescharacteristic
228C2×C4×C43H(5,𝔽2)11yescharacteristic
229C2×C4×C432−1+411yescharacteristic
230C2×Dic43—22no—
231C2×Dic43—22no—
232C2×Dic43—22no—
233C2×Dic43—41no—
234C2×Dic43—41no—
235C2×Dic43—41no—
236C2×Dic43—41no—
237C2×Dic43—41no—
238C2×Dic43—41no—
239C2×Dic43—41no—
240C2×Dic43—41no—
241C2×Dic43—41no—
242C2×Dic43—41no—
243C2×Dic43—41no—
244C2×Dic43—41no—
245C2×Dic43—41no—
246C2×Dic43—41no—
247C2×Dic43—41no—
248C2×Dic43—41no—
249C2×Dic43—41no—
250C2×Dic43—41no—
251D172—22no—
252D172—22no—
253D172—41no—
254D172—41no—
255C4×D43—84no—
256Dic86—22no—
257Dic86—22no—
258Dic86—41no—
259Dic86—41no—
260C8×C43—41no—
261C8×C43—41no—
262C8×C43—41no—
263C8×C43—41no—
264#26761—431nomaximal, Sylow
265C22×C43#52511yescharacteristic
266C22×C43#54611yescharacteristic
267C22×C43#54811yescharacteristic
268C22×C43C2×#13511yescharacteristic
269C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
270C22×C43#57711yescharacteristic
271C22×C43#57811yescharacteristic
272C2×D43—42no—
273C2×D43—42no—
274C2×D43—42no—
275C2×D43—81no—
276C2×D43—81no—
277C2×D43—81no—
278C2×D43—81no—
279C4×C43—22no—
280C4×C43—22no—
281C4×C43—41no—
282C4×C43—41no—
283C4×C43—41no—
284C4×C43—41no—
285C4×C43#52911yescharacteristic
286C4×C43#53911yescharacteristic
287C4×C43#55211yescharacteristic
288C4×C43#55311yescharacteristic
289Dic43—42no—
290Dic43—42no—
291Dic43—42no—
292Dic43—81no—
293Dic43—81no—
294Dic43—81no—
295Dic43—81no—
296#2506—431no—
297#2367—431no—
298#2071—431no—
299#2065—431no—
300#2042—431no—
301#2042—431no—
302#1933—431no—
303#1927—431no—
304#1921—431no—
305#1920—431no—
306#1916D4311yescharacteristic, complemented
307#1863—431no—
308#1862—431no—
309#1803—431no—
310C4×#102—431no—
311C2×C43#246011yescharacteristic
312C2×C43#310611yescharacteristic
313C2×C43#312011yescharacteristic
314C2×C43#330011yescharacteristic
315C2×C43#330611yescharacteristic
316C2×C43#336511yescharacteristic
317C2×C43#336711yescharacteristic
318D43—82no—
319C2×#125—861no—
320C2×#124—431no—
321C2×C4×Q8—431no—
322C2×C4×D4—431no—
323C2×#107—431no—
324C2×#106—431no—
325C2×C4⋊C8C2×D4311yescharacteristic
326C2×#103—431no—
327C2×#103—431no—
328C2×#103—431no—
329C2×#103—431no—
330C2×#102—431no—
331C2×#102—431no—
332C2×#102—431no—
333C2×#102—431no—
334C2×C4×C8C2×D4311yescharacteristic
335#400—861no—
336#398—861no—
337#391—431no—
338#390—431no—
339#389—431no—
340#389—431no—
341#389—431no—
342#389—431no—
343#388—861no—
344#388—861no—
345#387—861no—
346#385—861no—
347#384—431no—
348C4×C4⋊C4—431no—
349C4×C4⋊C4—431no—
350C4×C4⋊C4C2×D4311yescharacteristic
351C4×C22⋊C4—861no—
352#340—431no—
353#340—431no—
354#340—431no—
355#340—431no—
356#340—431no—
357#340—431no—
358#336C2×D4311yescharacteristic
359#336C2×D4311yescharacteristic
360#336C2×D4311yescharacteristic
361#336C2×D4311yescharacteristic
362C43#2676111yescharacteristic, complemented, Sylow
363C22×Q8—431no—
364C22×D4—431no—
365C23×C4—861no—
366C22×C8C22×D4311yescharacteristic
367C22×C8C22×D4311yescharacteristic
368C22×C8C22×D4311yescharacteristic
369C22×C8C22×D4311yescharacteristic
370#125—1724no—
371#124—862no—
372#124—862no—
373C4×Q8—862no—
374C4×Q8—1721no—
375C4×D4—862no—
376C4×D4—1721no—
377C2×C4⋊C4—431no—
378C2×C4⋊C4—431no—
379C2×C4⋊C4—431no—
380C2×C4⋊C4—431no—
381C2×C4⋊C4—431no—
382C2×C4⋊C4—431no—
383C2×C4⋊C4—861no—
384C2×C4⋊C4—861no—
385C2×C4⋊C4—861no—
386C2×C4⋊C4—861no—
387C2×C4⋊C4—861no—
388C2×C4⋊C4—861no—
389C2×C4⋊C4—861no—
390C2×C4⋊C4D17211yescharacteristic
391C2×C4⋊C4D17211yescharacteristic
392C2×C22⋊C4—861no—
393C2×C22⋊C4—861no—
394C2×C22⋊C4—861no—
395C2×C22⋊C4—861no—
396C2×C22⋊C4—861no—
397C2×C42—861no—
398C2×C42—861no—
399C2×C42—861no—
400C2×C42C22×D4311yescharacteristic
401C2×C42C22×D4311yescharacteristic
402C2×C42C22×D4311yescharacteristic
403#107—862no—
404#106—862no—
405C4⋊C8—41no—
406#103—862no—
407#103—862no—
408#103—862no—
409#103—1721no—
410#102—862no—
411#102—862no—
412#102—862no—
413#102—1721no—
414C4×C8—41no—
415#95—861no—
416#95—861no—
417#95—861no—
418#95—861no—
419#95—861no—
420#95—861no—
421#95—861no—
422#95—861no—
423#95D17211yescharacteristic
424#95D17211yescharacteristic
425C24—861no—
426C2×Q8—432no—
427C2×Q8—861no—
428C2×Q8—861no—
429C2×Q8—861no—
430C2×Q8—861no—
431C2×Q8—861no—
432C2×D4—432no—
433C2×D4—861no—
434C2×D4—861no—
435C2×D4—861no—
436C2×D4—861no—
437C2×D4—861no—
438C22×C4—861no—
439C22×C4—861no—
440C22×C4—861no—
441C22×C4—861no—
442C22×C4—861no—
443C22×C4—861no—
444C22×C4—861no—
445C22×C4—3441no—
446C22×C4—1722no—
447C22×C4—1722no—
448C22×C4C2×D17211yescharacteristic
449C22×C4C2×D17211yescharacteristic
450C22×C4C2×D17211yescharacteristic
451C22×C4C2×D17211yescharacteristic
452C22×C4C2×D17211yescharacteristic
453C22×C4C2×D17211yescharacteristic
454C22×C4C23×D4311yescharacteristic
455C2×C8—21no—
456C2×C8—21no—
457C2×C8—21no—
458C2×C8—21no—
459C2×C8—21no—
460C2×C8—21no—
461C2×C8—21no—
462C2×C8—21no—
463C2×C8—21no—
464C2×C8—21no—
465C2×C8—21no—
466C2×C8—21no—
467C4⋊C4—22no—
468C4⋊C4—22no—
469C4⋊C4—432no—
470C4⋊C4—432no—
471C4⋊C4—861no—
472C4⋊C4—861no—
473C4⋊C4—861no—
474C4⋊C4—861no—
475C4⋊C4—861no—
476C4⋊C4—861no—
477C4⋊C4—861no—
478C4⋊C4—861no—
479C4⋊C4—861no—
480C4⋊C4—861no—
481C4⋊C4—1722no—
482C4⋊C4—1722no—
483C4⋊C4—1722no—
484C4⋊C4—1722no—
485C4⋊C4—1722no—
486C4⋊C4—1722no—
487C4⋊C4—1722no—
488C22⋊C4—864no—
489C22⋊C4—864no—
490C22⋊C4—3441no—
491C22⋊C4—1722no—
492C22⋊C4—1722no—
493C42—21no—
494C42—21no—
495C42—21no—
496C42—21no—
497C42—21no—
498C42—21no—
499C42—3441no—
500C42—1722no—
501C42—1722no—
502C23—862no—
503C23—1721no—
504C23—1721no—
505C23—1721no—
506C23—1721no—
507C23—1721no—
508C23—1721no—
509C23C22×D17211yescharacteristic
510Q8—862no—
511Q8—862no—
512Q8—1721no—
513Q8—1721no—
514D4—862no—
515D4—862no—
516D4—1721no—
517D4—1721no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—862no—
535C2×C4—862no—
536C2×C4—862no—
537C2×C4—3444no—
538C2×C4—1721no—
539C2×C4—1721no—
540C2×C4—1721no—
541C2×C4—1721no—
542C2×C4—1721no—
543C2×C4—1721no—
544C2×C4—1721no—
545C2×C4—1721no—
546C2×C4—1721no—
547C2×C4—1721no—
548C2×C4—1721no—
549C2×C4—1721no—
550C2×C4—1721no—
551C2×C4—1721no—
552C2×C4—1721no—
553C2×C4—1721no—
554C2×C4—1721no—
555C2×C4—1721no—
556C2×C4#1306334712yes—
557C2×C4#1306335312yes—
558C2×C4#41×D4311yescharacteristic
559C2×C4#41×D4311yescharacteristic
560C2×C4#41×D4311yescharacteristic
561C2×C4#41×D4311yescharacteristic
562C2×C4#1306337011yescharacteristic
563C2×C4#1306337311yescharacteristic
564C8—41no—
565C8—41no—
566C8—41no—
567C8—41no—
568C22—3441no—
569C22—3441no—
570C22—3441no—
571C22—3441no—
572C22—1722no—
573C22—1722no—
574C22—1722no—
575C22#1458341111yescharacteristic
576C22#1458354411yescharacteristic
577C22#1458356111yescharacteristic
578C22C2×#1306334711yescharacteristic
579C22C2×#1306335311yescharacteristic
580C22#1458371111yescharacteristic
581C22#1458371611yescharacteristic
582C4—22no—
583C4—22no—
584C4—41no—
585C4—41no—
586C4—41no—
587C4—41no—
588C4—3441no—
589C4—3441no—
590C4—3441no—
591C4—3441no—
592C4—1722no—
593C4—1722no—
594C4—1722no—
595C4#1458343211yescharacteristic
596C4#1458349511yescharacteristic
597C4#1458358111yescharacteristic
598C4#1458359411yescharacteristic
599C2—3442no—
600C2#1913854511yescharacteristic
601C2#1914465611yescharacteristic
602C2#1914481111yescharacteristic
603C2#1914648411yescharacteristic
604C2#1914655811yescharacteristic
605C2#1914729311yescharacteristic
606C2#1914731511yescharacteristic
subgroupG/H
centerC23C22×D172
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#1916C2
socleC23×C43C22×D4
prime radicalC22×D172C23
hypercenter#1916D43
hypocenterC43#26761
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C4×C4⋊C4 ◁ #1916

Complements

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

NH ≅ G/Ntype
1. #19139111C2semidirect
7. #19135271C2semidirect
8. #19135230C2semidirect
9. #19135188C2semidirect
10. #19135181C2semidirect
11. #19134852C2semidirect
13. #19134601C2semidirect
15. C43×#1916C2semidirect
306. #1916D43semidirect
362. C43#26761semidirect

Maximal subgroups

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

subgroupindex
#191391112
#191376642
#191360002
#191359682
#191358372
#191352712
#191352302
#191351882
#191351812
#191348522
#191348452
#191346012
C4×#130632472
C43×#19162
#2676143