Finite Group Databasebeta

← #25148479

Subgroups — #25148479

Order 11008.

774 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
1C2×#14583200C211yesmaximal, characteristic
2#19139983C211yesmaximal, characteristic, complemented
3#19139953C211yesmaximal, characteristic
4#19136093C211yesmaximal, characteristic, complemented
5#19136088C211yesmaximal, characteristic, complemented
6#19135982C211yesmaximal, characteristic
7#19135968C211yesmaximal, characteristic
8#19135560C211yesmaximal, characteristic, complemented
9#19135365C211yesmaximal, characteristic, complemented
10#19135328C211yesmaximal, characteristic, complemented
11#19135323C211yesmaximal, characteristic, complemented
12#19135278C211yesmaximal, characteristic
13#19135278C211yesmaximal, characteristic
14C4×#13063247C211yesmaximal, characteristic
15C2×C8×Q8×C43C211yesmaximal, characteristic, complemented
16C2×#13063317C2211yescharacteristic
17C2×C4×D172C2211yescharacteristic
18#14583200—24no—
19C2×#13063259C2211yescharacteristic
20C2×#13063259C2211yescharacteristic
21C2×#13063257C2211yescharacteristic
22C2×#13063257C2211yescharacteristic
23C2×#13063247C2211yescharacteristic
24C2×#13063247C2211yescharacteristic
25C2×#13063247C2211yescharacteristic
26C2×#13063247C2211yescharacteristic
27#14582834—21no—
28#14582830—21no—
29#14582818—21no—
30#14582810—21no—
31#14582801C2211yescharacteristic
32#14582801C2211yescharacteristic
33#14582797C2211yescharacteristic
34#14582797C2211yescharacteristic
35#14582797C2211yescharacteristic
36#14582797C2211yescharacteristic
37#14582797C2211yescharacteristic
38#14582797C2211yescharacteristic
39#14582794—21no—
40#14582794—21no—
41#14582770—21no—
42#14582770—21no—
43#14582765C2211yescharacteristic
44C4×C4⋊Dic43C2211yescharacteristic
45#14582662C2211yescharacteristic
46#14582662C2211yescharacteristic
47#14582662C2211yescharacteristic
48#14582662C2211yescharacteristic
49#14582662C2211yescharacteristic
50#14582662C2211yescharacteristic
51#14582662C2211yescharacteristic
52#14582662C2211yescharacteristic
53C2×C4×Q8×C43C2211yescharacteristic
54C8×Q8×C43—24no—
55C2×C4⋊C8×C43C2211yescharacteristic
56C2×C4⋊C8×C43C2211yescharacteristic
57C2×C4⋊C8×C43C2211yescharacteristic
58C2×C4×C8×C43C2211yescharacteristic
59C2×C4×C8×C43C2211yescharacteristic
60C2×C4×C8×C43C2211yescharacteristic
61C22×D172C2311yescharacteristic
62C22×C4×D43—21no—
63#13063317—22no—
64#13063317—22no—
65C4×D172—22no—
66C4×D172—22no—
67C2×C4⋊Dic43C2311yescharacteristic
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×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—
88#13063259—22no—
89#13063259—22no—
90#13063257—22no—
91#13063257—22no—
92#13063247—22no—
93#13063247—22no—
94#13063247—22no—
95#13063247Q814yescomplemented
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—
105C22×Q8×C43D411yescharacteristic
106C22×C8×C43C2311yescharacteristic
107C22×C8×C43C2311yescharacteristic
108C22×C8×C43C2311yescharacteristic
109C22×C8×C43C2311yescharacteristic
110C4×Q8×C43—22no—
111C4×Q8×C43—22no—
112C2×C4⋊C4×C43D411yescharacteristic
113C2×C4⋊C4×C43D411yescharacteristic
114C2×C4⋊C4×C43D411yescharacteristic
115C2×C42×C43C2311yescharacteristic
116C2×C42×C43C2311yescharacteristic
117C2×C42×C43C2311yescharacteristic
118C4⋊C8×C43—22no—
119C4⋊C8×C43—22no—
120C4⋊C8×C43D414yes—
121C4×C8×C43—22no—
122C4×C8×C43—22no—
123C4×C8×C43—22no—
124C23×D43—21no—
125C2×Q8×C43—22no—
126C2×Q8×C43—22no—
127C2×Q8×C43—22no—
128C22×C4×C43C2×D411yescharacteristic
129C22×C4×C43C2×D411yescharacteristic
130C22×C4×C43C2×D411yescharacteristic
131C22×C4×C43C2×D411yescharacteristic
132C22×C4×C43C2×D411yescharacteristic
133C22×C4×C43C2×D411yescharacteristic
134C22×C4×C43C2411yescharacteristic
135C22×Dic43—21no—
136C22×Dic43—21no—
137C22×Dic43—21no—
138C22×Dic43—21no—
139C22×Dic43—21no—
140C22×Dic43—21no—
141C22×Dic43—21no—
142C2×D172—21no—
143C2×D172—21no—
144C2×D172—21no—
145C2×D172—21no—
146C2×D172—21no—
147C2×D172C2×Q812yes—
148C2×C4×D43—42no—
149C2×C4×D43—81no—
150C2×C4×D43—81no—
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×C43C2×D412yes—
161C2×C8×C43C2×D412yes—
162C2×C8×C43C2×Q812yes—
163C4⋊C4×C43—22no—
164C4⋊C4×C43—22no—
165C4⋊C4×C43—22no—
166C42×C43—21no—
167C42×C43—21no—
168C42×C43—21no—
169C42×C43—21no—
170C42×C43C2×D412yes—
171C42×C43#4112yes—
172(C2×D43)⋊C4—42no—
173(C2×D43)⋊C4—42no—
174(C2×D43)⋊C4—42no—
175(C2×D43)⋊C4—81no—
176(C2×D43)⋊C4—81no—
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—21no—
187C4⋊Dic43—21no—
188C4⋊Dic43—21no—
189C4⋊Dic43C2×Q812yes—
190C4⋊Dic43#4112yes—
191Dic43⋊C4—42no—
192Dic43⋊C4—42no—
193Dic43⋊C4—42no—
194Dic43⋊C4—42no—
195Dic43⋊C4—81no—
196Dic43⋊C4—81no—
197Dic43⋊C4—81no—
198Dic43⋊C4—81no—
199C4×Dic43—81no—
200C23×C43C22×D411yescharacteristic
201C22×D43—22no—
202C22×D43—41no—
203C22×D43—41no—
204C22×D43—41no—
205C22×D43—41no—
206C22×D43—41no—
207C22×D43—41no—
208Q8×C43—28no—
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—21no—
223C2×C4×C43#12112yes—
224C2×C4×C43#12112yes—
225C2×C4×C43#13512yes—
226C2×C4×C43#13512yes—
227C2×C4×C43C22×D411yescharacteristic
228C2×C4×C43C22×Q811yescharacteristic
229C2×C4×C43C2×#4111yescharacteristic
230C2×C4×C43C2×#4111yescharacteristic
231C2×C4×C432−1+411yescharacteristic
232C2×C4×C432−1+411yescharacteristic
233C2×Dic43—22no—
234C2×Dic43—22no—
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—
251C2×Dic43—41no—
252C2×Dic43—41no—
253C2×Dic43—41no—
254D172—22no—
255D172—22no—
256D172—41no—
257D172—41no—
258C4×D43—84no—
259C8×C43—22no—
260C8×C43—22no—
261C8×C43—22no—
262C8×C43—41no—
263#25473—431nomaximal, Sylow
264C22×C43C2×#12111yescharacteristic
265C22×C43#54811yescharacteristic
266C22×C43D4×Q811yescharacteristic
267C22×C43C2×#13511yescharacteristic
268C22×C43C2×#13511yescharacteristic
269C22×C43#57611yescharacteristic
270C22×C43#57711yescharacteristic
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#53311yescharacteristic
285C4×C43#54111yescharacteristic
286C4×C43#54711yescharacteristic
287C4×C43D4×Q811yescharacteristic
288Dic43—42no—
289Dic43—42no—
290Dic43—81no—
291Dic43—81no—
292Dic43—81no—
293Dic43—81no—
294Dic43—81no—
295C2×#478—431no—
296C2×C8×Q8D4311yescharacteristic, complemented
297#2584—431no—
298#2580—431no—
299#2088—431no—
300#2087—431no—
301#2067—431no—
302#2065—431no—
303#1991—431no—
304#1949—431no—
305#1942—431no—
306#1941—431no—
307#1934—431no—
308#1934—431no—
309C4×#102—431no—
310C2×C43#242911yescharacteristic
311C2×C43#305011yescharacteristic
312C2×C43#306211yescharacteristic
313C2×C43#336111yescharacteristic
314C2×C43#336511yescharacteristic
315C2×C43#338011yescharacteristic
316C2×C43#338111yescharacteristic
317D43—82no—
318C2×#125—431no—
319C2×C4×Q8C2×D4311yescharacteristic
320C2×C4×D4—431no—
321#478—864no—
322C8×Q8—24no—
323C2×#107—431no—
324C2×#107—431no—
325C2×#106—431no—
326C2×#106—431no—
327C2×C4⋊C8C2×D4311yescharacteristic
328C2×C4⋊C8C2×D4311yescharacteristic
329C2×C4⋊C8C2×D4311yescharacteristic
330C2×#102—431no—
331C2×#102—431no—
332C2×#102—431no—
333C2×#102—431no—
334C2×C4×C8C2×D4311yescharacteristic
335C2×C4×C8C2×D4311yescharacteristic
336C2×C4×C8C2×D4311yescharacteristic
337#399—861no—
338#398—861no—
339#395—861no—
340#393—861no—
341#390—431no—
342#390—431no—
343#389—431no—
344#389—431no—
345#389—431no—
346#389—431no—
347#389—431no—
348#389—431no—
349#389—861no—
350#389—861no—
351#385—861no—
352#385—861no—
353#382—431no—
354C4×C4⋊C4—431no—
355#340—431no—
356#340—431no—
357#340—431no—
358#340—431no—
359#340—431no—
360#340—431no—
361#340—431no—
362#340—431no—
363C43#2547311yescharacteristic, complemented, Sylow
364C22×Q8D17211yescharacteristic
365C22×D4—431no—
366C23×C4—861no—
367C22×C8C22×D4311yescharacteristic
368C22×C8C22×D4311yescharacteristic
369C22×C8C22×D4311yescharacteristic
370C22×C8C22×D4311yescharacteristic
371#125—862no—
372#125—862no—
373C4×Q8—22no—
374C4×Q8—22no—
375C4×D4—862no—
376C4×D4—862no—
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—431no—
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⋊C4—861no—
391C2×C4⋊C4—861no—
392C2×C4⋊C4D17211yescharacteristic
393C2×C4⋊C4D17211yescharacteristic
394C2×C4⋊C4D17211yescharacteristic
395C2×C22⋊C4—861no—
396C2×C22⋊C4—861no—
397C2×C22⋊C4—861no—
398C2×C22⋊C4—861no—
399C2×C22⋊C4—861no—
400C2×C42—861no—
401C2×C42C22×D4311yescharacteristic
402C2×C42C22×D4311yescharacteristic
403C2×C42C22×D4311yescharacteristic
404#107—862no—
405#107—862no—
406#106—862no—
407#106—862no—
408C4⋊C8—22no—
409C4⋊C8—22no—
410C4⋊C8C22⋊D4314yes—
411#102—434no—
412#102—862no—
413#102—862no—
414#102—862no—
415C4×C8—22no—
416C4×C8—22no—
417C4×C8—22no—
418#95—861no—
419#95—861no—
420#95—861no—
421#95—861no—
422#95—861no—
423#95—861no—
424#95—861no—
425#95—861no—
426#95—861no—
427C24—861no—
428C2×Q8—22no—
429C2×Q8—22no—
430C2×Q8—22no—
431C2×D4—432no—
432C2×D4—861no—
433C2×D4—861no—
434C2×D4—861no—
435C2×D4—861no—
436C2×D4—861no—
437C22×C4—861no—
438C22×C4—861no—
439C22×C4—861no—
440C22×C4—861no—
441C22×C4—861no—
442C22×C4—861no—
443C22×C4—861no—
444C22×C4—3441no—
445C22×C4—3441no—
446C22×C4—1722no—
447C22×C4C2×D17211yescharacteristic
448C22×C4C2×D17211yescharacteristic
449C22×C4C2×D17211yescharacteristic
450C22×C4C2×D17211yescharacteristic
451C22×C4C2×D17211yescharacteristic
452C22×C4C2×D17211yescharacteristic
453C22×C4C23×D4311yescharacteristic
454C2×C8—21no—
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×C8Q8×D4312yes—
464C2×C8C2×C22⋊D4312yes—
465C2×C8C2×C22⋊D4312yes—
466C4⋊C4—22no—
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—861no—
482C4⋊C4—861no—
483C4⋊C4—3441no—
484C4⋊C4—3441no—
485C4⋊C4—3441no—
486C4⋊C4—3441no—
487C4⋊C4—1722no—
488C4⋊C4—1722no—
489C4⋊C4—1722no—
490C4⋊C4—1722no—
491C22⋊C4—3441no—
492C22⋊C4—3441no—
493C22⋊C4—1722no—
494C22⋊C4—1722no—
495C22⋊C4—1722no—
496C42—21no—
497C42—21no—
498C42—21no—
499C42—21no—
500C42—3441no—
501C42#1062189812yes—
502C42C2×C22⋊D4312yes—
503C23—862no—
504C23—1721no—
505C23—1721no—
506C23—1721no—
507C23—1721no—
508C23—1721no—
509C23—1721no—
510C23C22×D17211yescharacteristic
511Q8—28no—
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—862no—
532C2×C4—3444no—
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#1306329912yes—
553C2×C4#1306329912yes—
554C2×C4#1306334712yes—
555C2×C4#1306334712yes—
556C2×C4C22×C22⋊D4311yescharacteristic
557C2×C4C2×Q8×D4311yescharacteristic
558C2×C4#41×D4311yescharacteristic
559C2×C4C2×#1062189811yescharacteristic
560C2×C4#1306337211yescharacteristic
561C2×C4#1306337311yescharacteristic
562C8—22no—
563C8—22no—
564C8—22no—
565C8—41no—
566C22—3441no—
567C22—3441no—
568C22—3441no—
569C22—3441no—
570C22—1722no—
571C22—1722no—
572C22—1722no—
573C22C2×#1306329911yescharacteristic
574C22#1458356111yescharacteristic
575C22Q8×D17211yescharacteristic
576C22C2×#1306334711yescharacteristic
577C22C2×#1306334711yescharacteristic
578C22#1458370411yescharacteristic
579C22#1458371111yescharacteristic
580C4—22no—
581C4—22no—
582C4—22no—
583C4—22no—
584C4—41no—
585C4—41no—
586C4—3441no—
587C4—3441no—
588C4—3441no—
589C4—3441no—
590C4—3441no—
591C4—1722no—
592C4—1722no—
593C4#1458345311yescharacteristic
594C4#1458350711yescharacteristic
595C4#1458354811yescharacteristic
596C4Q8×C22⋊D4311yescharacteristic
597C2—3442no—
598C2#1913818811yescharacteristic
599C2#1914417611yescharacteristic
600C2#1914427511yescharacteristic
601C2#1914725711yescharacteristic
602C2#1914729311yescharacteristic
603C2#1914746311yescharacteristic
604C2#1914747211yescharacteristic
subgroupG/H
centerC23C22×D172
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC2×C8×Q8×C43C2
socleC23×C43C22×D4
prime radicalC22×D172C23
hypercenterC2×C8×Q8D43
hypocenterC43#25473
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C4×Q8 ◁ C2×C8×Q8

Complements

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

NH ≅ G/Ntype
2. #19139983C2semidirect
4. #19136093C2semidirect
5. #19136088C2semidirect
8. #19135560C2semidirect
9. #19135365C2semidirect
10. #19135328C2semidirect
11. #19135323C2semidirect
15. C2×C8×Q8×C43C2semidirect
95. #13063247Q8semidirect
296. C2×C8×Q8D43semidirect
363. C43#25473semidirect

Maximal subgroups

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

subgroupindex
C2×#145832002
#191399832
#191399532
#191360932
#191360882
#191359822
#191359682
#191355602
#191353652
#191353282
#191353232
#191352782
C4×#130632472
C2×C8×Q8×C432
#2547343