Finite Group Databasebeta

← #25165224

Subgroups — #25165224

Order 11008.

704 conjugacy classes of subgroups.

The subgroup lattice has 602 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19137664C211yesmaximal, characteristic
2#19136009C211yesmaximal, characteristic
3#19135966C211yesmaximal, characteristic
4#19135836C211yesmaximal, characteristic
5#19135836C211yesmaximal, characteristic
6#19135270C211yesmaximal, characteristic, complemented
7#19135229C211yesmaximal, characteristic, complemented
8#19135177C211yesmaximal, characteristic, complemented
9#19135170C211yesmaximal, characteristic, complemented
10#19135154C211yesmaximal, characteristic, complemented
11#19134862C211yesmaximal, characteristic, complemented
12#19134855C211yesmaximal, characteristic
13#19134607C211yesmaximal, characteristic, complemented
14C4×#13063245C211yesmaximal, characteristic
15C43×#2508C211yesmaximal, characteristic, complemented
16C2×#13063313C2211yescharacteristic
17C2×C4×Dic86C2211yescharacteristic
18C2×C4×D172C2211yescharacteristic
19C2×#13063256C2211yescharacteristic
20C2×#13063256C2211yescharacteristic
21C2×C4⋊(C43⋊C8)C2211yescharacteristic
22C2×#13063248C2211yescharacteristic
23C2×#13063248C2211yescharacteristic
24C2×#13063248C2211yescharacteristic
25C2×#13063248C2211yescharacteristic
26C2×#13063245C2211yescharacteristic
27C2×#13063245C2211yescharacteristic
28C2×#13063245C2211yescharacteristic
29C2×#13063245C2211yescharacteristic
30C2×C4×C43⋊C8C2211yescharacteristic
31#14582805C2211yescharacteristic
32#14582801C2211yescharacteristic
33#14582789—21no—
34#14582788—21no—
35#14582770—21no—
36C4×C4⋊Dic43C2211yescharacteristic
37#14582746—21no—
38#14582661C2211yescharacteristic
39#14582661C2211yescharacteristic
40#14582661C2211yescharacteristic
41#14582661C2211yescharacteristic
42#14582661C2211yescharacteristic
43#14582661C2211yescharacteristic
44#14582654C2211yescharacteristic
45#14582654C2211yescharacteristic
46#14582654C2211yescharacteristic
47#14582654C2211yescharacteristic
48C43×#400—21no—
49C43×#398—21no—
50C43×#389C2211yescharacteristic
51C43×#389C2211yescharacteristic
52C43×#389C2211yescharacteristic
53C43×#389C2211yescharacteristic
54C43×#387—21no—
55C43×#382—21no—
56C43×#382C2211yescharacteristic
57C4×C4⋊C4×C43C2211yescharacteristic
58C4×C4⋊C4×C43C2211yescharacteristic
59C22×Dic86C2311yescharacteristic
60C22×D172C2311yescharacteristic
61C22×C4×D43—21no—
62C22×C43⋊C8C2311yescharacteristic
63C22×C43⋊C8C2311yescharacteristic
64C22×C43⋊C8C2311yescharacteristic
65C22×C43⋊C8C2311yescharacteristic
66#13063313—22no—
67#13063313—22no—
68C4×Dic86—22no—
69C4×Dic86—41no—
70C4×D172—22no—
71C4×D172—41no—
72C2×C4⋊Dic43C2311yescharacteristic
73C2×C4⋊Dic43C2311yescharacteristic
74C2×Dic43⋊C4—21no—
75C2×(C2×D43)⋊C4—21no—
76C2×(C2×D43)⋊C4—21no—
77C2×(C2×D43)⋊C4—21no—
78C2×(C2×D43)⋊C4—21no—
79C2×(C2×D43)⋊C4—21no—
80C2×C4×Dic43—21no—
81C2×C4×Dic43—21no—
82#13063256—22no—
83#13063256—22no—
84C4⋊(C43⋊C8)—41no—
85#13063248—22no—
86#13063248—22no—
87#13063248—22no—
88#13063248—41no—
89#13063245—22no—
90#13063245—22no—
91#13063245—22no—
92#13063245—41no—
93C4×C43⋊C8—41no—
94C43⋊#95—21no—
95C43⋊#95—21no—
96C43⋊#95—21no—
97C2×C4⋊C4×C43—21no—
98C2×C4⋊C4×C43—21no—
99C2×C4⋊C4×C43—21no—
100C2×C4⋊C4×C43—21no—
101C2×C4⋊C4×C43D411yescharacteristic
102C2×C4⋊C4×C43D411yescharacteristic
103C2×C4⋊C4×C43C2311yescharacteristic
104C2×C4⋊C4×C43C2311yescharacteristic
105C2×C4⋊C4×C43C2311yescharacteristic
106C2×C4⋊C4×C43C2311yescharacteristic
107C2×C42×C43—21no—
108C2×C42×C43C2311yescharacteristic
109C2×C42×C43C2311yescharacteristic
110C2×C42×C43C2311yescharacteristic
111#95×C43—21no—
112#95×C43—21no—
113#95×C43—21no—
114#95×C43—21no—
115#95×C43—21no—
116#95×C43—21no—
117#95×C43—21no—
118#95×C43D411yescharacteristic
119#95×C43D411yescharacteristic
120C23×D43—21no—
121C22×C4×C43—21no—
122C22×C4×C43—21no—
123C22×C4×C43—21no—
124C22×C4×C43—21no—
125C22×C4×C43C2×D411yescharacteristic
126C22×C4×C43C2×D411yescharacteristic
127C22×C4×C43C2×D411yescharacteristic
128C22×C4×C43C2×D411yescharacteristic
129C22×C4×C43C2×D411yescharacteristic
130C22×C4×C43C2×D411yescharacteristic
131C22×C4×C43C2411yescharacteristic
132C22×Dic43—21no—
133C22×Dic43—21no—
134C22×Dic43—21no—
135C2×D172—21no—
136C2×D172—21no—
137C2×D172—21no—
138C2×D172—21no—
139C2×D172—21no—
140C2×D172#4112yes—
141C2×C4×D43—42no—
142C2×C4×D43—42no—
143C2×C4×D43—81no—
144C2×Dic86—21no—
145C2×Dic86—21no—
146C2×Dic86—21no—
147C2×Dic86—21no—
148C2×Dic86—21no—
149C2×Dic86#4112yes—
150C4⋊C4×C43—22no—
151C4⋊C4×C43—21no—
152C4⋊C4×C43—21no—
153C4⋊C4×C43—21no—
154C4⋊C4×C43—21no—
155C4⋊C4×C43—21no—
156C4⋊C4×C43—21no—
157C4⋊C4×C43—21no—
158C4⋊C4×C43—41no—
159C4⋊C4×C43—42no—
160C4⋊C4×C43—81no—
161C4⋊C4×C43—81no—
162C4⋊C4×C43—81no—
163C4⋊C4×C43#4112yes—
164C42×C43—21no—
165C42×C43—21no—
166C42×C43—21no—
167C42×C43—21no—
168C42×C43—21no—
169C42×C43—21no—
170C42×C43—42no—
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#4112yes—
180Dic43⋊C4—42no—
181C4×Dic43—42no—
182C4×Dic43—81no—
183C2×C43⋊C8—21no—
184C2×C43⋊C8—21no—
185C2×C43⋊C8—21no—
186C2×C43⋊C8—21no—
187C2×C43⋊C8—21no—
188C2×C43⋊C8—21no—
189C2×C43⋊C8—21no—
190C2×C43⋊C8—21no—
191C2×C43⋊C8—21no—
192C2×C43⋊C8—21no—
193C2×C43⋊C8—21no—
194C2×C43⋊C8—21no—
195C23×C43C22×D411yescharacteristic
196C22×D43—22no—
197C22×D43—41no—
198C22×D43—41no—
199C22×D43—41no—
200C22×D43—41no—
201C22×D43—41no—
202C22×D43—41no—
203C2×C4×C43—21no—
204C2×C4×C43—21no—
205C2×C4×C43—21no—
206C2×C4×C43—21no—
207C2×C4×C43—21no—
208C2×C4×C43—21no—
209C2×C4×C43—21no—
210C2×C4×C43—22no—
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—41no—
222C2×C4×C43—41no—
223C2×C4×C43—41no—
224C2×C4×C43—41no—
225C2×C4×C43—41no—
226C2×C4×C43—41no—
227C2×C4×C43—41no—
228C2×C4×C43—41no—
229C2×C4×C43—41no—
230C2×C4×C43—41no—
231C2×C4×C43—41no—
232C2×C4×C43#13512yes—
233C2×C4×C43C2×#4111yescharacteristic
234C2×C4×C43C2×#4111yescharacteristic
235C2×C4×C43C2×#4111yescharacteristic
236C2×C4×C43C2×#4111yescharacteristic
237C2×C4×C43H(5,𝔽2)11yescharacteristic
238C2×C4×C432−1+411yescharacteristic
239C2×Dic43—22no—
240C2×Dic43—22no—
241C2×Dic43—41no—
242C2×Dic43—41no—
243C2×Dic43—41no—
244C2×Dic43—41no—
245C2×Dic43—41no—
246C2×Dic43—41no—
247C2×Dic43—41no—
248D172—22no—
249D172—22no—
250D172—41no—
251D172—41no—
252C4×D43—84no—
253Dic86—22no—
254Dic86—22no—
255Dic86—41no—
256Dic86—41no—
257C43⋊C8—41no—
258C43⋊C8—41no—
259C43⋊C8—41no—
260C43⋊C8—41no—
261#26760—431nomaximal, Sylow
262C22×C43#52511yescharacteristic
263C22×C43#54611yescharacteristic
264C22×C43#54811yescharacteristic
265C22×C43C2×#13511yescharacteristic
266C22×C43#57511yescharacteristic
267C22×C43#57711yescharacteristic
268C22×C43#57711yescharacteristic
269C2×D43—42no—
270C2×D43—42no—
271C2×D43—42no—
272C2×D43—81no—
273C2×D43—81no—
274C2×D43—81no—
275C2×D43—81no—
276C4×C43—22no—
277C4×C43—41no—
278C4×C43—42no—
279C4×C43—41no—
280C4×C43—41no—
281C4×C43—41no—
282C4×C43—41no—
283C4×C43—81no—
284C4×C43—81no—
285C4×C43—81no—
286C4×C43#52911yescharacteristic
287C4×C43#53911yescharacteristic
288C4×C43#55211yescharacteristic
289C4×C43#55311yescharacteristic
290Dic43—42no—
291Dic43—42no—
292Dic43—81no—
293#2508D4311yescharacteristic, complemented
294#2367—431no—
295#2073—431no—
296#2065—431no—
297#2042—431no—
298#2042—431no—
299#1933—431no—
300#1927—431no—
301#1920—431no—
302#1919—431no—
303#1916—431no—
304#1865—431no—
305#1864—431no—
306#1805—431no—
307C4×#102—431no—
308C2×C43#246011yescharacteristic
309C2×C43#310211yescharacteristic
310C2×C43#312511yescharacteristic
311C2×C43#329611yescharacteristic
312C2×C43#332111yescharacteristic
313C2×C43#336011yescharacteristic
314C2×C43#337111yescharacteristic
315D43—82no—
316C2×#124—431no—
317C2×C4×Q8—431no—
318C2×C4×D4—431no—
319C2×#106—431no—
320C2×#106—431no—
321C2×C4⋊C8—431no—
322C2×#103—431no—
323C2×#103—431no—
324C2×#103—431no—
325C2×#103—431no—
326C2×#102—431no—
327C2×#102—431no—
328C2×#102—431no—
329C2×#102—431no—
330C2×C4×C8—431no—
331#400—21no—
332#398—21no—
333#391—431no—
334#390—431no—
335#389C2×D4311yescharacteristic
336#389C2×D4311yescharacteristic
337#389C2×D4311yescharacteristic
338#389C2×D4311yescharacteristic
339#388—861no—
340#388—861no—
341#387—21no—
342#385—861no—
343#382—21no—
344#382C2×D4311yescharacteristic
345C4×C4⋊C4—431no—
346C4×C4⋊C4C2×D4311yescharacteristic
347C4×C4⋊C4C2×D4311yescharacteristic
348C4×C22⋊C4—861no—
349#340—431no—
350#340—431no—
351#340—431no—
352#340—431no—
353#340—431no—
354#340—431no—
355#336—431no—
356#336—431no—
357#336—431no—
358#336—431no—
359C43#2676011yescharacteristic, complemented, Sylow
360C22×Q8—431no—
361C22×D4—431no—
362C23×C4—861no—
363C22×C8—431no—
364C22×C8—431no—
365C22×C8—431no—
366C22×C8—431no—
367#124—862no—
368#124—862no—
369C4×Q8—862no—
370C4×Q8—1721no—
371C4×D4—862no—
372C4×D4—1721no—
373C2×C4⋊C4—21no—
374C2×C4⋊C4—21no—
375C2×C4⋊C4—21no—
376C2×C4⋊C4—21no—
377C2×C4⋊C4—431no—
378C2×C4⋊C4—431no—
379C2×C4⋊C4—861no—
380C2×C4⋊C4C22⋊D4311yescharacteristic
381C2×C4⋊C4C22⋊D4311yescharacteristic
382C2×C4⋊C4C22×D4311yescharacteristic
383C2×C4⋊C4C22×D4311yescharacteristic
384C2×C4⋊C4C22×D4311yescharacteristic
385C2×C4⋊C4C22×D4311yescharacteristic
386C2×C22⋊C4—861no—
387C2×C22⋊C4—861no—
388C2×C22⋊C4—861no—
389C2×C22⋊C4—861no—
390C2×C22⋊C4—861no—
391C2×C42—21no—
392C2×C42—861no—
393C2×C42—861no—
394C2×C42C22×D4311yescharacteristic
395C2×C42C22×D4311yescharacteristic
396C2×C42C22×D4311yescharacteristic
397#106—862no—
398#106—862no—
399C4⋊C8—1721no—
400#103—862no—
401#103—862no—
402#103—862no—
403#103—1721no—
404#102—862no—
405#102—862no—
406#102—862no—
407#102—1721no—
408C4×C8—1721no—
409#95—21no—
410#95—21no—
411#95—21no—
412#95—21no—
413#95—21no—
414#95—21no—
415#95—21no—
416#95—861no—
417#95—861no—
418#95—861no—
419#95C22⋊D4311yescharacteristic
420#95C22⋊D4311yescharacteristic
421C24—861no—
422C2×Q8—432no—
423C2×Q8—861no—
424C2×Q8—861no—
425C2×Q8—861no—
426C2×Q8—861no—
427C2×Q8—861no—
428C2×D4—432no—
429C2×D4—861no—
430C2×D4—861no—
431C2×D4—861no—
432C2×D4—861no—
433C2×D4—861no—
434C22×C4—21no—
435C22×C4—21no—
436C22×C4—21no—
437C22×C4—21no—
438C22×C4—861no—
439C22×C4—861no—
440C22×C4—861no—
441C22×C4—3441no—
442C22×C4—1722no—
443C22×C4—1722no—
444C22×C4C2×C22⋊D4311yescharacteristic
445C22×C4C2×C22⋊D4311yescharacteristic
446C22×C4C2×C22⋊D4311yescharacteristic
447C22×C4C2×C22⋊D4311yescharacteristic
448C22×C4C2×C22⋊D4311yescharacteristic
449C22×C4C2×C22⋊D4311yescharacteristic
450C22×C4C23×D4311yescharacteristic
451C2×C8—861no—
452C2×C8—861no—
453C2×C8—861no—
454C2×C8—861no—
455C2×C8—861no—
456C2×C8—861no—
457C2×C8—861no—
458C2×C8—861no—
459C2×C8—861no—
460C2×C8—861no—
461C2×C8—861no—
462C2×C8—861no—
463C4⋊C4—22no—
464C4⋊C4—21no—
465C4⋊C4—21no—
466C4⋊C4—21no—
467C4⋊C4—21no—
468C4⋊C4—21no—
469C4⋊C4—21no—
470C4⋊C4—21no—
471C4⋊C4—41no—
472C4⋊C4—42no—
473C4⋊C4—81no—
474C4⋊C4—81no—
475C4⋊C4—81no—
476C4⋊C4—432no—
477C4⋊C4—861no—
478C4⋊C4—861no—
479C4⋊C4—861no—
480C4⋊C4—1722no—
481C4⋊C4#1062190212yes—
482C22⋊C4—864no—
483C22⋊C4—864no—
484C22⋊C4—3441no—
485C22⋊C4—1722no—
486C22⋊C4—1722no—
487C42—21no—
488C42—21no—
489C42—21no—
490C42—21no—
491C42—21no—
492C42—21no—
493C42—42no—
494C42—3441no—
495C42—1722no—
496C23—862no—
497C23—1721no—
498C23—1721no—
499C23—1721no—
500C23—1721no—
501C23—1721no—
502C23—1721no—
503C23C22×C22⋊D4311yescharacteristic
504Q8—862no—
505Q8—862no—
506Q8—1721no—
507Q8—1721no—
508D4—862no—
509D4—862no—
510D4—1721no—
511D4—1721no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—22no—
515C2×C4—21no—
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—41no—
531C2×C4—41no—
532C2×C4—41no—
533C2×C4—41no—
534C2×C4—41no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—41no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—41no—
541C2×C4—862no—
542C2×C4—862no—
543C2×C4—3444no—
544C2×C4—1721no—
545C2×C4—1721no—
546C2×C4—1721no—
547C2×C4—1721no—
548C2×C4—1721no—
549C2×C4—1721no—
550C2×C4—1721no—
551C2×C4#1306334512yes—
552C2×C4#41×D4311yescharacteristic
553C2×C4#41×D4311yescharacteristic
554C2×C4#41×D4311yescharacteristic
555C2×C4C2×#1062190211yescharacteristic
556C2×C4#1306337111yescharacteristic
557C2×C4#1306337311yescharacteristic
558C8—1721no—
559C8—1721no—
560C8—1721no—
561C8—1721no—
562C22—3441no—
563C22—3441no—
564C22—3441no—
565C22—3441no—
566C22—1722no—
567C22—1722no—
568C22—1722no—
569C22#1458340611yescharacteristic
570C22#1458353711yescharacteristic
571C22#1458356011yescharacteristic
572C22C2×#1306334511yescharacteristic
573C22#1458369711yescharacteristic
574C22#1458370711yescharacteristic
575C22#1458371011yescharacteristic
576C4—22no—
577C4—41no—
578C4—41no—
579C4—41no—
580C4—41no—
581C4—41no—
582C4—42no—
583C4—81no—
584C4—81no—
585C4—81no—
586C4—3441no—
587C4—1722no—
588C4—1722no—
589C4#1458343411yescharacteristic
590C4#1458349711yescharacteristic
591C4#1458358111yescharacteristic
592C4#1458360211yescharacteristic
593C2—3442no—
594C2#1913854311yescharacteristic
595C2#1914460711yescharacteristic
596C2#1914486611yescharacteristic
597C2#1914642411yescharacteristic
598C2#1914677511yescharacteristic
599C2#1914724411yescharacteristic
600C2#1914736311yescharacteristic
subgroupG/H
centerC23C22×C22⋊D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#2508C2
socleC23×C43C22×D4
prime radicalC22×D172C23
hypercenter#2508D43
hypocenterC43#26760
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C4×C4⋊C4 ◁ #2508

Complements

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

NH ≅ G/Ntype
6. #19135270C2semidirect
7. #19135229C2semidirect
8. #19135177C2semidirect
9. #19135170C2semidirect
10. #19135154C2semidirect
11. #19134862C2semidirect
13. #19134607C2semidirect
15. C43×#2508C2semidirect
293. #2508D43semidirect
359. C43#26760semidirect

Maximal subgroups

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

subgroupindex
#191376642
#191360092
#191359662
#191358362
#191352702
#191352292
#191351772
#191351702
#191351542
#191348622
#191348552
#191346072
C4×#130632452
C43×#25082
#2676043