Finite Group Databasebeta

← #25199685

Subgroups — #25199685

Order 11008.

746 conjugacy classes of subgroups.

The subgroup lattice has 606 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19142977C211yesmaximal, characteristic, complemented
2#19137059C211yesmaximal, characteristic
3#19136093C211yesmaximal, characteristic, complemented
4#19135989C211yesmaximal, characteristic, complemented
5#19135982C211yesmaximal, characteristic
6#19135913C211yesmaximal, characteristic
7#19135449C211yesmaximal, characteristic
8#19135328C211yesmaximal, characteristic, complemented
9#19135278C211yesmaximal, characteristic
10#19135271C211yesmaximal, characteristic, complemented
11#19135237C211yesmaximal, characteristic, complemented
12#19135174C211yesmaximal, characteristic, complemented
13#19134928C211yesmaximal, characteristic
14#19134845C211yesmaximal, characteristic
15C4×C4⋊C8×C43C211yesmaximal, characteristic, complemented
16C22×#10621873C2211yescharacteristic
17C2×C4×D172C2211yescharacteristic
18C2×#13063282—21no—
19C2×#13063259C2211yescharacteristic
20C2×#13063259C2211yescharacteristic
21C2×#13063257C2211yescharacteristic
22C2×#13063250C2211yescharacteristic
23C2×#13063250C2211yescharacteristic
24C2×#13063250C2211yescharacteristic
25C2×#13063247C2211yescharacteristic
26C2×#13063247C2211yescharacteristic
27C2×#13063247C2211yescharacteristic
28#14582805C2211yescharacteristic
29#14582805C2211yescharacteristic
30#14582805C2211yescharacteristic
31#14582801C2211yescharacteristic
32#14582801C2211yescharacteristic
33#14582797C2211yescharacteristic
34#14582797C2211yescharacteristic
35#14582797C2211yescharacteristic
36#14582797C2211yescharacteristic
37#14582797C2211yescharacteristic
38#14582790—21no—
39#14582790—21no—
40#14582783—21no—
41#14582783—21no—
42#14582783—21no—
43#14582767—21no—
44C4×C4⋊Dic43C2211yescharacteristic
45C4×(C2×D43)⋊C4—21no—
46#14582662C2211yescharacteristic
47#14582662C2211yescharacteristic
48#14582662C2211yescharacteristic
49#14582662C2211yescharacteristic
50#14582662C2211yescharacteristic
51#14582662C2211yescharacteristic
52C2×C4⋊C8×C43C2211yescharacteristic
53C2×C4⋊C8×C43C2211yescharacteristic
54C2×C4×C8×C43C2211yescharacteristic
55C2×C4×C8×C43C2211yescharacteristic
56C43×C43C2211yescharacteristic
57C43×#336C2211yescharacteristic
58C43×#336C2211yescharacteristic
59C22×Dic86C2311yescharacteristic
60C22×D172C2311yescharacteristic
61C22×C4×D43—21no—
62C2×#10621873—22no—
63C2×#10621873—22no—
64C2×#10621873—41no—
65C4×D172—22no—
66C4×D172—22no—
67#13063282—44no—
68C2×C4⋊Dic43C2311yescharacteristic
69C2×C4⋊Dic43C2311yescharacteristic
70C2×C4⋊Dic43C2311yescharacteristic
71C2×C4⋊Dic43C2311yescharacteristic
72C2×C4⋊Dic43C2311yescharacteristic
73C2×C4⋊Dic43C2311yescharacteristic
74C2×Dic43⋊C4—21no—
75C2×Dic43⋊C4—21no—
76C2×Dic43⋊C4—21no—
77C2×Dic43⋊C4—21no—
78C2×Dic43⋊C4—21no—
79C2×(C2×D43)⋊C4—21no—
80C2×(C2×D43)⋊C4—21no—
81C2×(C2×D43)⋊C4—21no—
82C2×(C2×D43)⋊C4—21no—
83C2×(C2×D43)⋊C4—21no—
84C2×C4×Dic43—21no—
85#13063259—22no—
86#13063259—41no—
87#13063257—22no—
88#13063250—22no—
89#13063250—22no—
90#13063250—41no—
91#13063247—22no—
92#13063247—22no—
93#13063247—41no—
94C43⋊#95—21no—
95C43⋊#95—21no—
96C43⋊#95—21no—
97C43⋊#95—21no—
98C43⋊#95—21no—
99C43⋊#95—21no—
100C43⋊#95—21no—
101C43⋊#95—21no—
102C43⋊#95—21no—
103C43⋊#95—21no—
104C43⋊#95—21no—
105C43⋊#95—21no—
106C22×C8×C43C2311yescharacteristic
107C22×C8×C43C2311yescharacteristic
108C22×C8×C43C2311yescharacteristic
109C22×C8×C43C2311yescharacteristic
110C2×C42×C43D411yescharacteristic
111C2×C42×C43D411yescharacteristic
112C2×C42×C43D411yescharacteristic
113C2×C42×C43D411yescharacteristic
114C2×C42×C43C2311yescharacteristic
115C2×C42×C43C2311yescharacteristic
116C2×C42×C43C2311yescharacteristic
117C4⋊C8×C43—22no—
118C4⋊C8×C43—22no—
119C4×C8×C43—41no—
120C4×C8×C43—41no—
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—24no—
143C2×C4×D43—42no—
144C2×C4×D43—42no—
145C2×Dic86—21no—
146C2×Dic86—21no—
147C2×Dic86—21no—
148C2×Dic86—21no—
149C2×Dic86—21no—
150C2×Dic86—21no—
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#4112yes—
162C2×C8×C43#4112yes—
163C42×C43—22no—
164C42×C43—22no—
165C42×C43—22no—
166C42×C43—22no—
167C42×C43—21no—
168C42×C43—21no—
169C42×C43—21no—
170C42×C43—21no—
171C42×C43—21no—
172C42×C43—21no—
173(C2×D43)⋊C4—24no—
174(C2×D43)⋊C4—42no—
175(C2×D43)⋊C4—42no—
176(C2×D43)⋊C4—42no—
177(C2×D43)⋊C4—42no—
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—21no—
187C4⋊Dic43—21no—
188C4⋊Dic43—21no—
189C4⋊Dic43#4112yes—
190Dic43⋊C4—42no—
191Dic43⋊C4—42no—
192Dic43⋊C4—42no—
193Dic43⋊C4—42no—
194Dic43⋊C4—42no—
195C4×Dic43—42no—
196#10621873—44no—
197C23×C43C22×D411yescharacteristic
198C22×D43—22no—
199C22×D43—41no—
200C22×D43—41no—
201C22×D43—41no—
202C22×D43—41no—
203C22×D43—41no—
204C22×D43—41no—
205C2×C4×C43—21no—
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#13512yes—
220C2×C4×C43#13512yes—
221C2×C4×C43AGL(1,ℤ/8)12yes—
222C2×C4×C43#13712yes—
223C2×C4×C43C2×#4111yescharacteristic
224C2×C4×C43C2×#4111yescharacteristic
225C2×C4×C43C2×#4111yescharacteristic
226C2×C4×C43C2×#4111yescharacteristic
227C2×C4×C43H(5,𝔽2)11yescharacteristic
228C2×C4×C432−1+411yescharacteristic
229C2×Dic43—22no—
230C2×Dic43—41no—
231C2×Dic43—41no—
232C2×Dic43—41no—
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—
250D172—22no—
251D172—22no—
252D172—41no—
253D172—41no—
254C4×D43—48no—
255Dic86—41no—
256Dic86—41no—
257Dic86—41no—
258Dic86—41no—
259C8×C43—22no—
260C8×C43—22no—
261C8×C43—41no—
262C8×C43—41no—
263#29433—431nomaximal, Sylow
264C22×C43#52511yescharacteristic
265C22×C43#53211yescharacteristic
266C22×C43#53711yescharacteristic
267C22×C43C2×#13511yescharacteristic
268C22×C43C2×#13511yescharacteristic
269C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
270C22×C43C2×#13711yescharacteristic
271C2×D43—42no—
272C2×D43—42no—
273C2×D43—42no—
274C2×D43—81no—
275C2×D43—81no—
276C2×D43—81no—
277C2×D43—81no—
278C4×C43—22no—
279C4×C43—22no—
280C4×C43—22no—
281C4×C43—22no—
282C4×C43—41no—
283C4×C43—41no—
284C4×C43#55111yescharacteristic
285C4×C43#55211yescharacteristic
286C4×C43#55311yescharacteristic
287C4×C43#55611yescharacteristic
288Dic43—42no—
289Dic43—81no—
290Dic43—81no—
291Dic43—81no—
292Dic43—81no—
293Dic43—81no—
294Dic43—81no—
295#2863—431no—
296#2293—431no—
297#2088—431no—
298#2068—431no—
299#2067—431no—
300#2055—431no—
301#1968—431no—
302#1942—431no—
303#1934—431no—
304#1933—431no—
305#1928—431no—
306#1919—431no—
307#1877—431no—
308#1862—431no—
309C4×C4⋊C8D4311yescharacteristic, complemented
310C2×C43#260111yescharacteristic
311C2×C43#310511yescharacteristic
312C2×C43#310711yescharacteristic
313C2×C43#316811yescharacteristic
314C2×C43#318211yescharacteristic
315C2×C43#324711yescharacteristic
316C2×C43#324811yescharacteristic
317D43—82no—
318C22×SD16—431no—
319C2×C4×D4—431no—
320C2×#117—861no—
321C2×#107—431no—
322C2×#107—431no—
323C2×#106—431no—
324C2×C4⋊C8C2×D4311yescharacteristic
325C2×C4⋊C8C2×D4311yescharacteristic
326C2×#103—431no—
327C2×#103—431no—
328C2×#103—431no—
329C2×#102—431no—
330C2×#102—431no—
331C2×#102—431no—
332C2×C4×C8C2×D4311yescharacteristic
333C2×C4×C8C2×D4311yescharacteristic
334#391—431no—
335#391—431no—
336#391—431no—
337#390—431no—
338#390—431no—
339#389—431no—
340#389—431no—
341#389—431no—
342#389—431no—
343#389—431no—
344#388—861no—
345#388—861no—
346#387—861no—
347#387—861no—
348#387—861no—
349#383—861no—
350C4×C4⋊C4—431no—
351C4×C22⋊C4—861no—
352C43C2×D4311yescharacteristic
353#340—431no—
354#340—431no—
355#340—431no—
356#340—431no—
357#340—431no—
358#340—431no—
359#336C2×D4311yescharacteristic
360#336C2×D4311yescharacteristic
361C43#2943311yescharacteristic, complemented, Sylow
362C22×Q8—431no—
363C22×D4—431no—
364C23×C4—861no—
365C2×SD16—862no—
366C2×SD16—862no—
367C2×SD16—1721no—
368C22×C8C22×D4311yescharacteristic
369C22×C8C22×D4311yescharacteristic
370C22×C8C22×D4311yescharacteristic
371C22×C8C22×D4311yescharacteristic
372C4×D4—862no—
373C4×D4—862no—
374#117—1724no—
375C2×C4⋊C4—431no—
376C2×C4⋊C4—431no—
377C2×C4⋊C4—431no—
378C2×C4⋊C4—431no—
379C2×C4⋊C4—431no—
380C2×C4⋊C4—431no—
381C2×C4⋊C4—861no—
382C2×C4⋊C4—861no—
383C2×C4⋊C4—861no—
384C2×C4⋊C4—861no—
385C2×C4⋊C4—861no—
386C2×C22⋊C4—861no—
387C2×C22⋊C4—861no—
388C2×C22⋊C4—861no—
389C2×C22⋊C4—861no—
390C2×C22⋊C4—861no—
391C2×C42—861no—
392C2×C42D17211yescharacteristic
393C2×C42D17211yescharacteristic
394C2×C42D17211yescharacteristic
395C2×C42D17211yescharacteristic
396C2×C42C22×D4311yescharacteristic
397C2×C42C22×D4311yescharacteristic
398C2×C42C22×D4311yescharacteristic
399#107—862no—
400#107—1721no—
401#106—862no—
402C4⋊C8—22no—
403C4⋊C8—22no—
404#103—862no—
405#103—862no—
406#103—1721no—
407#102—862no—
408#102—862no—
409#102—1721no—
410C4×C8—41no—
411C4×C8—41no—
412#95—861no—
413#95—861no—
414#95—861no—
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#95—861no—
424C24—861no—
425C2×Q8—861no—
426C2×Q8—861no—
427C2×Q8—861no—
428C2×Q8—861no—
429C2×Q8—861no—
430C2×Q8—861no—
431C2×D4—432no—
432C2×D4—861no—
433C2×D4—861no—
434C2×D4—861no—
435C2×D4—861no—
436C2×D4—861no—
437C22×C4—864no—
438C22×C4—861no—
439C22×C4—861no—
440C22×C4—861no—
441C22×C4—861no—
442C22×C4—861no—
443C22×C4—861no—
444C22×C4—861no—
445C22×C4—1722no—
446C22×C4—1722no—
447C22×C4C2×D17211yescharacteristic
448C22×C4C2×D17211yescharacteristic
449C22×C4C2×D17211yescharacteristic
450C22×C4C2×D17211yescharacteristic
451C22×C4C2×D17211yescharacteristic
452C22×C4C2×D17211yescharacteristic
453C22×C4C23×D4311yescharacteristic
454SD16—1724no—
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#1062189812yes—
466C2×C8#1062189812yes—
467C4⋊C4—432no—
468C4⋊C4—861no—
469C4⋊C4—861no—
470C4⋊C4—861no—
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—1722no—
480C4⋊C4—1722no—
481C4⋊C4—1722no—
482C4⋊C4—1722no—
483C4⋊C4—1722no—
484C22⋊C4—864no—
485C22⋊C4—1722no—
486C22⋊C4—1722no—
487C22⋊C4—1722no—
488C22⋊C4—1722no—
489C42—22no—
490C42—22no—
491C42—22no—
492C42—22no—
493C42—21no—
494C42—21no—
495C42—21no—
496C42—21no—
497C42—21no—
498C42—21no—
499C42—1722no—
500C23—862no—
501C23—1721no—
502C23—1721no—
503C23—1721no—
504C23—1721no—
505C23—1721no—
506C23—1721no—
507C23C22×D17211yescharacteristic
508Q8—1721no—
509Q8—1721no—
510Q8—1721no—
511Q8—1721no—
512D4—862no—
513D4—862no—
514D4—1721no—
515D4—1721no—
516C2×C4—21no—
517C2×C4—21no—
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—862no—
531C2×C4—1728no—
532C2×C4—1721no—
533C2×C4—1721no—
534C2×C4—1721no—
535C2×C4—1721no—
536C2×C4—1721no—
537C2×C4—1721no—
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#1306334712yes—
553C2×C4#1306334712yes—
554C2×C4#1306335312yes—
555C2×C4#1306335812yes—
556C2×C4#41×D4311yescharacteristic
557C2×C4#41×D4311yescharacteristic
558C2×C4C2×#1062189811yescharacteristic
559C2×C4C2×#1062189811yescharacteristic
560C2×C4#1306337011yescharacteristic
561C2×C4#1306337311yescharacteristic
562C8—22no—
563C8—22no—
564C8—41no—
565C8—41no—
566C22—3441no—
567C22—3441no—
568C22—3441no—
569C22—3441no—
570C22—1722no—
571C22—1722no—
572C22—1722no—
573C22#1458341111yescharacteristic
574C22#1458344911yescharacteristic
575C22#1458348011yescharacteristic
576C22C2×#1306334711yescharacteristic
577C22C2×#1306334711yescharacteristic
578C22C2×#1306335311yescharacteristic
579C22C2×#1306335811yescharacteristic
580C4—22no—
581C4—22no—
582C4—22no—
583C4—22no—
584C4—41no—
585C4—41no—
586C4—3441no—
587C4—3441no—
588C4—3441no—
589C4—3441no—
590C4—3441no—
591C4—3441no—
592C4—1722no—
593C4#1458357811yescharacteristic
594C4#1458359011yescharacteristic
595C4#1458359811yescharacteristic
596C4#1458362111yescharacteristic
597C2—3442no—
598C2#1914018611yescharacteristic
599C2#1914464411yescharacteristic
600C2#1914466711yescharacteristic
601C2#1914516511yescharacteristic
602C2#1914531311yescharacteristic
603C2#1914592211yescharacteristic
604C2#1914593311yescharacteristic
subgroupG/H
centerC23C22×D172
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC4×C4⋊C8×C43C2
socleC23×C43C22×D4
prime radicalC22×D172C23
hypercenterC4×C4⋊C8D43
hypocenterC43#29433
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C43 ◁ C4×C4⋊C8

Complements

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

NH ≅ G/Ntype
1. #19142977C2semidirect
3. #19136093C2semidirect
4. #19135989C2semidirect
8. #19135328C2semidirect
10. #19135271C2semidirect
11. #19135237C2semidirect
12. #19135174C2semidirect
15. C4×C4⋊C8×C43C2semidirect
309. C4×C4⋊C8D43semidirect
361. C43#29433semidirect

Maximal subgroups

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

subgroupindex
#191429772
#191370592
#191360932
#191359892
#191359822
#191359132
#191354492
#191353282
#191352782
#191352712
#191352372
#191351742
#191349282
#191348452
C4×C4⋊C8×C432
#2943343